LMFDB - Embedded newform 54.8.e.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(7,54)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.8687913761$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	54.7
Dual form			54.8.e.a.31.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.51754 + 2.73616i) q^{2} +(44.9983 - 12.7340i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-22.9934 - 130.402i) q^{5} +(-303.434 + 218.851i) q^{6} +(812.804 + 682.023i) q^{7} +(-256.000 + 443.405i) q^{8} +(1862.69 - 1146.01i) q^{9} +(529.655 + 917.389i) q^{10} +(91.2393 - 517.444i) q^{11} +(1682.27 - 2475.46i) q^{12} +(891.055 + 324.317i) q^{13} +(-7976.41 - 2903.18i) q^{14} +(-2695.20 - 5575.07i) q^{15} +(711.263 - 4033.77i) q^{16} +(-4235.68 - 7336.41i) q^{17} +(-10867.2 + 13711.8i) q^{18} +(-6165.88 + 10679.6i) q^{19} +(-6491.83 - 5447.29i) q^{20} +(45259.6 + 20339.7i) q^{21} +(729.914 + 4139.55i) q^{22} +(42964.5 - 36051.5i) q^{23} +(-5873.25 + 23212.4i) q^{24} +(56937.5 - 20723.6i) q^{25} -7585.93 q^{26} +(69224.6 - 75288.1i) q^{27} +67906.5 q^{28} +(216787. - 78904.0i) q^{29} +(35515.6 + 34536.3i) q^{30} +(17533.3 - 14712.2i) q^{31} +(5690.10 + 32270.2i) q^{32} +(-2483.50 - 24445.9i) q^{33} +(51915.5 + 43562.3i) q^{34} +(70248.1 - 121673. i) q^{35} +(44176.7 - 132814. i) q^{36} +(280620. + 486049. i) q^{37} +(17131.1 - 97155.3i) q^{38} +(44225.8 + 3247.06i) q^{39} +(63707.2 + 23187.5i) q^{40} +(-150203. - 54669.3i) q^{41} +(-395894. - 29066.5i) q^{42} +(33219.0 - 188394. i) q^{43} +(-16813.6 - 29122.1i) q^{44} +(-192272. - 216548. i) q^{45} +(-224344. + 388576. i) q^{46} +(-460784. - 386644. i) q^{47} +(-19360.3 - 190570. i) q^{48} +(52487.3 + 297670. i) q^{49} +(-371327. + 311580. i) q^{50} +(-284020. - 276189. i) q^{51} +(57027.5 - 20756.3i) q^{52} -811351. q^{53} +(-314398. + 755391. i) q^{54} -69573.6 q^{55} +(-510490. + 185803. i) q^{56} +(-141460. + 559081. i) q^{57} +(-1.41381e6 + 1.18633e6i) q^{58} +(-278261. - 1.57809e6i) q^{59} +(-361487. - 162452. i) q^{60} +(-424841. - 356484. i) q^{61} +(-91552.3 + 158573. i) q^{62} +(2.29561e6 + 338915. i) q^{63} +(-131072. - 227023. i) q^{64} +(21803.3 - 123653. i) q^{65} +(85557.8 + 176978. i) q^{66} +(3.31315e6 + 1.20589e6i) q^{67} +(-509470. - 185432. i) q^{68} +(1.47425e6 - 2.16936e6i) q^{69} +(-195175. + 1.10689e6i) q^{70} +(199089. + 344832. i) q^{71} +(31299.3 + 1.11931e6i) q^{72} +(-2.22890e6 + 3.86056e6i) q^{73} +(-3.43948e6 - 2.88607e6i) q^{74} +(2.29820e6 - 1.65756e6i) q^{75} +(137049. + 777243. i) q^{76} +(427068. - 358353. i) q^{77} +(-341354. + 96599.0i) q^{78} +(-3.77861e6 + 1.37530e6i) q^{79} -542367. q^{80} +(2.15627e6 - 4.26934e6i) q^{81} +1.27874e6 q^{82} +(-8.65002e6 + 3.14835e6i) q^{83} +(3.05568e6 - 864720. i) q^{84} +(-859291. + 721030. i) q^{85} +(265752. + 1.50716e6i) q^{86} +(8.75028e6 - 6.31110e6i) q^{87} +(206080. + 172922. i) q^{88} +(-138467. + 239832. i) q^{89} +(2.03792e6 + 1.10182e6i) q^{90} +(503061. + 871326. i) q^{91} +(623312. - 3.53498e6i) q^{92} +(601623. - 885291. i) q^{93} +(4.52188e6 + 1.64583e6i) q^{94} +(1.53442e6 + 558483. i) q^{95} +(666973. + 1.37965e6i) q^{96} +(-1.12746e6 + 6.39414e6i) q^{97} +(-1.20905e6 - 2.09413e6i) q^{98} +(-423047. - 1.06840e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 213 q^{5} - 72 q^{6} + 1677 q^{7} - 15360 q^{8} - 3024 q^{9} + 3000 q^{10} - 15744 q^{11} + 2880 q^{12} + 9924 q^{13} + 13416 q^{14} + 2322 q^{15} + 29478 q^{17} + 49680 q^{18} + 61731 q^{19} - 27264 q^{20}+ \cdots + 36391797 q^{99}+O(q^{100}) $ 60 * q + 213 * q^5 - 72 * q^6 + 1677 * q^7 - 15360 * q^8 - 3024 * q^9 + 3000 * q^10 - 15744 * q^11 + 2880 * q^12 + 9924 * q^13 + 13416 * q^14 + 2322 * q^15 + 29478 * q^17 + 49680 * q^18 + 61731 * q^19 - 27264 * q^20 + 160884 * q^21 - 125952 * q^22 + 29478 * q^23 - 343017 * q^25 - 316368 * q^26 - 524124 * q^27 - 263424 * q^28 + 132153 * q^29 + 292824 * q^30 - 1372860 * q^31 - 1065834 * q^33 - 121656 * q^34 - 321081 * q^35 - 369216 * q^36 + 759795 * q^37 + 224760 * q^38 - 2283894 * q^39 + 109056 * q^40 + 704616 * q^41 + 527400 * q^42 + 2124585 * q^43 + 255552 * q^44 + 3259908 * q^45 + 524472 * q^46 + 3452931 * q^47 + 552960 * q^48 - 1987017 * q^49 + 190152 * q^50 + 5107401 * q^51 + 635136 * q^52 - 2951976 * q^53 + 1065312 * q^54 - 2539854 * q^55 + 858624 * q^56 + 5722920 * q^57 + 47496 * q^58 + 3732204 * q^59 + 2512512 * q^60 - 5504796 * q^61 + 2859936 * q^62 + 1888047 * q^63 - 7864320 * q^64 - 803499 * q^65 - 9421632 * q^66 - 7979400 * q^67 - 5893440 * q^68 - 629100 * q^69 + 1111128 * q^70 + 3531612 * q^71 + 3096576 * q^72 - 875661 * q^73 + 15158904 * q^74 + 26002422 * q^75 + 1798080 * q^76 + 5672523 * q^77 - 13012848 * q^78 - 10290369 * q^79 - 3072000 * q^80 - 42838956 * q^81 - 3798096 * q^82 - 16555878 * q^83 + 2005056 * q^84 + 30956175 * q^85 + 16996680 * q^86 + 22863879 * q^87 + 2509824 * q^88 + 32327814 * q^89 + 34182072 * q^90 + 1976658 * q^91 - 1108608 * q^92 - 17967789 * q^93 - 24396768 * q^94 - 35592135 * q^95 - 2949120 * q^96 - 25380039 * q^97 - 15123648 * q^98 + 36391797 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.51754	+	2.73616i	−0.664463	+	0.241845i
$2$	−7.51754	+	2.73616i	−0.664463	+	0.241845i
$3$	44.9983	−	12.7340i	0.962214	−	0.272295i
$3$	44.9983	−	12.7340i	0.962214	−	0.272295i
$4$	49.0268	−	41.1384i	0.383022	−	0.321394i
$5$	−22.9934	−	130.402i	−0.0822637	−	0.466541i	−0.997914	−	0.0645638i	$-0.979434\pi$
$5$	−22.9934	−	130.402i	−0.0822637	−	0.466541i	0.915650	−	0.401977i	$-0.131677\pi$
$6$	−303.434	+	218.851i	−0.573502	+	0.413636i
$7$	812.804	+	682.023i	0.895659	+	0.751547i	0.969337	−	0.245735i	$-0.0790294\pi$
$7$	812.804	+	682.023i	0.895659	+	0.751547i	−0.0736784	+	0.997282i	$0.523474\pi$
$8$	−256.000	+	443.405i	−0.176777	+	0.306186i
$9$	1862.69	−	1146.01i	0.851711	−	0.524012i
$10$	529.655	+	917.389i	0.167492	+	0.290104i
$11$	91.2393	−	517.444i	0.0206684	−	0.117216i	−0.972728	−	0.231949i	$-0.925490\pi$
$11$	91.2393	−	517.444i	0.0206684	−	0.117216i	0.993396	+	0.114732i	$0.0366010\pi$
$12$	1682.27	−	2475.46i	0.281035	−	0.413545i
$13$	891.055	+	324.317i	0.112487	+	0.0409420i	0.397651	−	0.917537i	$-0.369826\pi$
$13$	891.055	+	324.317i	0.112487	+	0.0409420i	−0.285163	+	0.958479i	$0.592048\pi$
$14$	−7976.41	−	2903.18i	−0.776890	−	0.282765i
$15$	−2695.20	−	5575.07i	−0.206192	−	0.426512i
$16$	711.263	−	4033.77i	0.0434120	−	0.246202i
$17$	−4235.68	−	7336.41i	−0.209099	−	0.362170i	0.742332	−	0.670032i	$-0.233720\pi$
$17$	−4235.68	−	7336.41i	−0.209099	−	0.362170i	−0.951431	+	0.307862i	$0.900386\pi$
$18$	−10867.2	+	13711.8i	−0.439201	+	0.554168i
$19$	−6165.88	+	10679.6i	−0.206233	+	0.357206i	−0.950525	−	0.310649i	$-0.899454\pi$
$19$	−6165.88	+	10679.6i	−0.206233	+	0.357206i	0.744292	+	0.667854i	$0.232787\pi$
$20$	−6491.83	−	5447.29i	−0.181452	−	0.152256i
$21$	45259.6	+	20339.7i	1.06646	+	0.479265i
$22$	729.914	+	4139.55i	0.0146148	+	0.0828846i
$23$	42964.5	−	36051.5i	0.736312	−	0.617839i	−0.195532	−	0.980697i	$-0.562643\pi$
$23$	42964.5	−	36051.5i	0.736312	−	0.617839i	0.931844	+	0.362858i	$0.118199\pi$
$24$	−5873.25	+	23212.4i	−0.0867240	+	0.342752i
$25$	56937.5	−	20723.6i	0.728800	−	0.265261i
$26$	−7585.93			−0.0846451
$27$	69224.6	−	75288.1i	0.676842	−	0.736128i
$28$	67906.5			0.584600
$29$	216787.	−	78904.0i	1.65059	−	0.600767i	0.661750	−	0.749725i	$-0.269814\pi$
$29$	216787.	−	78904.0i	1.65059	−	0.600767i	0.988844	+	0.148958i	$0.0475919\pi$
$30$	35515.6	+	34536.3i	0.240157	+	0.233535i
$31$	17533.3	−	14712.2i	0.105705	−	0.0886974i	−0.588403	−	0.808568i	$-0.700243\pi$
$31$	17533.3	−	14712.2i	0.105705	−	0.0886974i	0.694109	+	0.719870i	$0.255799\pi$
$32$	5690.10	+	32270.2i	0.0306970	+	0.174091i
$33$	−2483.50	−	24445.9i	−0.0120300	−	0.118415i
$34$	51915.5	+	43562.3i	0.226527	+	0.190079i
$35$	70248.1	−	121673.i	0.276947	−	0.479686i
$36$	44176.7	−	132814.i	0.157810	−	0.474443i
$37$	280620.	+	486049.i	0.910779	+	1.57752i	0.812966	+	0.582311i	$0.197851\pi$
$37$	280620.	+	486049.i	0.910779	+	1.57752i	0.0978133	+	0.995205i	$0.468815\pi$
$38$	17131.1	−	97155.3i	0.0506457	−	0.287226i
$39$	44225.8	+	3247.06i	0.119385	+	0.00876525i
$40$	63707.2	+	23187.5i	0.157391	+	0.0572855i
$41$	−150203.	−	54669.3i	−0.340356	−	0.123880i	0.166186	−	0.986094i	$-0.446855\pi$
$41$	−150203.	−	54669.3i	−0.340356	−	0.123880i	−0.506543	+	0.862215i	$0.669077\pi$
$42$	−395894.	−	29066.5i	−0.824529	−	0.0605370i
$43$	33219.0	−	188394.i	0.0637158	−	0.361350i	−0.936234	−	0.351376i	$-0.885714\pi$
$43$	33219.0	−	188394.i	0.0637158	−	0.361350i	0.999950	−	0.00997435i	$-0.00317499\pi$
$44$	−16813.6	−	29122.1i	−0.0297562	−	0.0515392i
$45$	−192272.	−	216548.i	−0.314538	−	0.354251i
$46$	−224344.	+	388576.i	−0.339831	+	0.588604i
$47$	−460784.	−	386644.i	−0.647374	−	0.543211i	0.258899	−	0.965904i	$-0.416640\pi$
$47$	−460784.	−	386644.i	−0.647374	−	0.543211i	−0.906273	+	0.422693i	$0.861085\pi$
$48$	−19360.3	−	190570.i	−0.0252679	−	0.248720i
$49$	52487.3	+	297670.i	0.0637335	+	0.361451i
$50$	−371327.	+	311580.i	−0.420108	+	0.352513i
$51$	−284020.	−	276189.i	−0.299815	−	0.291548i
$52$	57027.5	−	20756.3i	0.0562435	−	0.0204710i
$53$	−811351.			−0.748588			−0.374294	−	0.927310i	$-0.622115\pi$
$53$	−811351.			−0.748588			−0.374294	+	0.927310i	$0.622115\pi$
$54$	−314398.	+	755391.i	−0.271708	+	0.652821i
$55$	−69573.6			−0.0563865
$56$	−510490.	+	185803.i	−0.388445	+	0.141382i
$57$	−141460.	+	559081.i	−0.101175	+	0.399864i
$58$	−1.41381e6	+	1.18633e6i	−0.951466	+	0.798375i
$59$	−278261.	−	1.57809e6i	−0.176388	−	1.00035i	−0.936529	−	0.350590i	$-0.885981\pi$
$59$	−278261.	−	1.57809e6i	−0.176388	−	1.00035i	0.760141	−	0.649758i	$-0.225130\pi$
$60$	−361487.	−	162452.i	−0.216054	−	0.0970947i
$61$	−424841.	−	356484.i	−0.239647	−	0.201088i	0.515052	−	0.857159i	$-0.327773\pi$
$61$	−424841.	−	356484.i	−0.239647	−	0.201088i	−0.754699	+	0.656071i	$0.772217\pi$
$62$	−91552.3	+	158573.i	−0.0487863	+	0.0845004i
$63$	2.29561e6	+	338915.i	1.15666	+	0.170765i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	21803.3	−	123653.i	0.00984748	−	0.0558478i
$66$	85557.8	+	176978.i	0.0366316	+	0.0757731i
$67$	3.31315e6	+	1.20589e6i	1.34580	+	0.489830i	0.911633	−	0.411004i	$-0.134822\pi$
$67$	3.31315e6	+	1.20589e6i	1.34580	+	0.489830i	0.434163	+	0.900834i	$0.357044\pi$
$68$	−509470.	−	185432.i	−0.196489	−	0.0715161i
$69$	1.47425e6	−	2.16936e6i	0.540255	−	0.794987i
$70$	−195175.	+	1.10689e6i	−0.0680114	+	0.385712i
$71$	199089.	+	344832.i	0.0660150	+	0.114341i	0.897144	−	0.441739i	$-0.145638\pi$
$71$	199089.	+	344832.i	0.0660150	+	0.114341i	−0.831129	+	0.556080i	$0.812305\pi$
$72$	31299.3	+	1.11931e6i	0.00988259	+	0.353415i
$73$	−2.22890e6	+	3.86056e6i	−0.670594	+	1.16150i	0.307141	+	0.951664i	$0.400628\pi$
$73$	−2.22890e6	+	3.86056e6i	−0.670594	+	1.16150i	−0.977736	+	0.209840i	$0.932706\pi$
$74$	−3.43948e6	−	2.88607e6i	−0.986693	−	0.827934i
$75$	2.29820e6	−	1.65756e6i	0.629032	−	0.453687i
$76$	137049.	+	777243.i	0.0358119	+	0.203100i
$77$	427068.	−	358353.i	0.106606	−	0.0894526i
$78$	−341354.	+	96599.0i	−0.0814467	+	0.0230484i
$79$	−3.77861e6	+	1.37530e6i	−0.862258	+	0.313836i	−0.735028	−	0.678037i	$-0.762831\pi$
$79$	−3.77861e6	+	1.37530e6i	−0.862258	+	0.313836i	−0.127230	+	0.991873i	$0.540609\pi$
$80$	−542367.			−0.118434
$81$	2.15627e6	−	4.26934e6i	0.450823	−	0.892613i
$82$	1.27874e6			0.256114
$83$	−8.65002e6	+	3.14835e6i	−1.66052	+	0.604379i	−0.990444	−	0.137915i	$-0.955960\pi$
$83$	−8.65002e6	+	3.14835e6i	−1.66052	+	0.604379i	−0.670074	+	0.742294i	$0.733738\pi$
$84$	3.05568e6	−	864720.i	0.562510	−	0.159184i
$85$	−859291.	+	721030.i	−0.151766	+	0.127347i
$86$	265752.	+	1.50716e6i	0.0450539	+	0.255513i
$87$	8.75028e6	−	6.31110e6i	1.42464	−	1.02751i
$88$	206080.	+	172922.i	0.0322364	+	0.0270495i
$89$	−138467.	+	239832.i	−0.0208200	+	0.0360614i	−0.876248	−	0.481861i	$-0.839961\pi$
$89$	−138467.	+	239832.i	−0.0208200	+	0.0360614i	0.855428	+	0.517922i	$0.173294\pi$
$90$	2.03792e6	+	1.10182e6i	0.294672	+	0.159317i
$91$	503061.	+	871326.i	0.0699802	+	0.121209i
$92$	623312.	−	3.53498e6i	0.0834542	−	0.473292i
$93$	601623.	−	885291.i	0.0775594	−	0.114129i
$94$	4.52188e6	+	1.64583e6i	0.561529	+	0.204380i
$95$	1.53442e6	+	558483.i	0.183616	+	0.0668309i
$96$	666973.	+	1.37965e6i	0.0769411	+	0.159154i
$97$	−1.12746e6	+	6.39414e6i	−0.125430	+	0.711346i	0.855622	+	0.517601i	$0.173175\pi$
$97$	−1.12746e6	+	6.39414e6i	−0.125430	+	0.711346i	−0.981052	+	0.193745i	$0.937936\pi$
$98$	−1.20905e6	−	2.09413e6i	−0.129764	−	0.224757i
$99$	−423047.	−	1.06840e6i	−0.0438193	−	0.110665i
$100$	1.93893e6	−	3.35833e6i	0.193893	−	0.335833i
$101$	−1.31024e6	−	1.09942e6i	−0.126539	−	0.106179i	0.577322	−	0.816517i	$-0.304098\pi$
$101$	−1.31024e6	−	1.09942e6i	−0.126539	−	0.106179i	−0.703861	+	0.710338i	$0.748542\pi$
$102$	2.89083e6	+	1.29914e6i	0.269725	+	0.121214i
$103$	−1.19050e6	−	6.75165e6i	−0.107349	−	0.608807i	−0.990256	−	0.139259i	$-0.955528\pi$
$103$	−1.19050e6	−	6.75165e6i	−0.107349	−	0.608807i	0.882907	−	0.469548i	$-0.155583\pi$
$104$	−371914.	+	312073.i	−0.0324210	+	0.0272044i
$105$	1.61166e6	−	6.36963e6i	0.135866	−	0.536972i
$106$	6.09936e6	−	2.21999e6i	0.497409	−	0.181042i
$107$	−1.43280e6			−0.113068			−0.0565342	−	0.998401i	$-0.518005\pi$
$107$	−1.43280e6			−0.113068			−0.0565342	+	0.998401i	$0.518005\pi$
$108$	296631.	−	6.53893e6i	0.0226586	−	0.499486i
$109$	−8.09937e6			−0.599044			−0.299522	−	0.954089i	$-0.596827\pi$
$109$	−8.09937e6			−0.599044			−0.299522	+	0.954089i	$0.596827\pi$
$110$	523022.	−	190365.i	0.0374667	−	0.0136368i
$111$	1.88168e7	+	1.82979e7i	1.30591	+	1.26991i
$112$	3.32924e6	−	2.79357e6i	0.223915	−	0.187887i
$113$	2.92591e6	+	1.65937e7i	0.190760	+	1.08185i	0.918329	+	0.395818i	$0.129539\pi$
$113$	2.92591e6	+	1.65937e7i	0.190760	+	1.08185i	−0.727569	+	0.686034i	$0.759350\pi$
$114$	−466303.	−	4.58997e6i	−0.0294782	−	0.290164i
$115$	−5.68908e6	−	4.77371e6i	−0.348819	−	0.292694i
$116$	7.38239e6	−	1.27867e7i	0.439131	−	0.760598i
$117$	2.03143e6	−	417058.i	0.117261	−	0.0240739i
$118$	6.40976e6	+	1.11020e7i	0.359132	+	0.622036i
$119$	1.56083e6	−	8.85189e6i	0.0849064	−	0.481528i
$120$	3.16199e6	+	232153.i	0.167042	+	0.0122642i
$121$	1.80525e7	+	6.57058e6i	0.926380	+	0.337175i
$122$	4.16916e6	+	1.51745e6i	0.207869	+	0.0756580i
$123$	−7.45502e6	−	547348.i	−0.361228	−	0.0265213i
$124$	254366.	−	1.44258e6i	0.0119807	−	0.0679461i
$125$	−9.18399e6	−	1.59071e7i	−0.420578	−	0.728462i
$126$	−1.81847e7	+	3.73336e6i	−0.809857	+	0.166266i
$127$	−1.12801e7	+	1.95377e7i	−0.488651	+	0.846369i	−0.999915	−	0.0130550i	$-0.995844\pi$
$127$	−1.12801e7	+	1.95377e7i	−0.488651	+	0.846369i	0.511263	+	0.859424i	$0.329178\pi$
$128$	1.60651e6	+	1.34802e6i	0.0677094	+	0.0568149i
$129$	−904211.	−	8.90044e6i	−0.0370856	−	0.365046i
$130$	174426.	+	989220.i	0.00696322	+	0.0394904i
$131$	−2.47405e7	+	2.07597e7i	−0.961521	+	0.806812i	−0.981200	−	0.192995i	$-0.938180\pi$
$131$	−2.47405e7	+	2.07597e7i	−0.961521	+	0.806812i	0.0196790	+	0.999806i	$0.493736\pi$
$132$	−1.12742e6	−	1.09634e6i	−0.0426657	−	0.0414893i
$133$	−1.22954e7	+	4.47516e6i	−0.453171	+	0.164941i
$134$	−2.82063e7			−1.01269
$135$	−1.14094e7	−	7.29590e6i	−0.399113	−	0.255218i
$136$	4.33734e6			0.147855
$137$	−9.03433e6	+	3.28823e6i	−0.300175	+	0.109255i	−0.487717	−	0.873002i	$-0.662170\pi$
$137$	−9.03433e6	+	3.28823e6i	−0.300175	+	0.109255i	0.187542	+	0.982257i	$0.439948\pi$
$138$	−5.14700e6	+	2.03420e7i	−0.166716	+	0.658898i
$139$	−1.05412e7	+	8.84512e6i	−0.332919	+	0.279352i	−0.793888	−	0.608064i	$-0.791946\pi$
$139$	−1.05412e7	+	8.84512e6i	−0.332919	+	0.279352i	0.460969	+	0.887416i	$0.347502\pi$
$140$	−1.56140e6	−	8.85515e6i	−0.0480913	−	0.272739i
$141$	−2.56580e7	−	1.15307e7i	−0.770826	−	0.346409i
$142$	−2.44018e6	−	2.04755e6i	−0.0715174	−	0.0600102i
$143$	249115.	−	431480.i	0.00712400	−	0.0123391i
$144$	−3.29790e6	−	8.32879e6i	−0.0920382	−	0.232441i
$145$	−1.52739e7	−	2.64552e7i	−0.416066	−	0.720647i
$146$	6.19270e6	−	3.51206e7i	0.164682	−	0.933956i
$147$	6.15236e6	+	1.27263e7i	0.159747	+	0.330439i
$148$	3.37532e7	+	1.22852e7i	0.855853	+	0.311505i
$149$	5.23606e7	+	1.90577e7i	1.29674	+	0.471975i	0.895934	−	0.444188i	$-0.146508\pi$
$149$	5.23606e7	+	1.90577e7i	1.29674	+	0.471975i	0.400807	+	0.916163i	$0.368730\pi$
$150$	−1.27414e7	+	1.87490e7i	−0.308247	+	0.453586i
$151$	−6.68548e6	+	3.79152e7i	−0.158020	+	0.896178i	0.797952	+	0.602721i	$0.205917\pi$
$151$	−6.68548e6	+	3.79152e7i	−0.158020	+	0.896178i	−0.955972	+	0.293457i	$0.905194\pi$
$152$	−3.15693e6	−	5.46797e6i	−0.0729143	−	0.126291i
$153$	−1.62974e7	−	8.81133e6i	−0.367873	−	0.198894i
$154$	−2.22999e6	+	3.86246e6i	−0.0492018	+	0.0852200i
$155$	−2.32165e6	−	1.94809e6i	−0.0500766	−	0.0420193i
$156$	2.30183e6	−	1.66019e6i	0.0485442	−	0.0350123i
$157$	−7.61460e6	−	4.31846e7i	−0.157036	−	0.890594i	−0.956901	−	0.290414i	$-0.906207\pi$
$157$	−7.61460e6	−	4.31846e7i	−0.157036	−	0.890594i	0.799865	−	0.600180i	$-0.204904\pi$
$158$	2.46428e7	−	2.06778e7i	0.497039	−	0.417065i
$159$	−3.65094e7	+	1.03317e7i	−0.720302	+	0.203837i
$160$	4.07726e6	−	1.48400e6i	0.0786953	−	0.0286427i
$161$	5.95096e7			1.12382
$162$	−4.52826e6	+	3.79949e7i	−0.0836813	+	0.702138i
$163$	−8.13942e7			−1.47210			−0.736049	−	0.676928i	$-0.763311\pi$
$163$	−8.13942e7			−1.47210			−0.736049	+	0.676928i	$0.763311\pi$
$164$	−9.61297e6	+	3.49883e6i	−0.170178	+	0.0619398i
$165$	−3.13069e6	+	885949.i	−0.0542559	+	0.0153538i
$166$	5.64125e7	−	4.73357e7i	0.957187	−	0.803175i
$167$	1.61108e7	+	9.13692e7i	0.267677	+	1.51807i	0.761303	+	0.648396i	$0.224560\pi$
$167$	1.61108e7	+	9.13692e7i	0.267677	+	1.51807i	−0.493626	+	0.869674i	$0.664329\pi$
$168$	−2.06052e7	+	1.48614e7i	−0.335269	+	0.241812i
$169$	−4.73794e7	−	3.97560e7i	−0.755067	−	0.633577i
$170$	4.48690e6	−	7.77153e6i	0.0700446	−	0.121321i
$171$	753858.	+	2.69590e7i	0.0115293	+	0.412304i
$172$	−6.12162e6	−	1.06030e7i	−0.0917312	−	0.158883i
$173$	8.12390e6	−	4.60729e7i	0.119290	−	0.676526i	−0.865247	−	0.501346i	$-0.832838\pi$
$173$	8.12390e6	−	4.60729e7i	0.119290	−	0.676526i	0.984536	−	0.175180i	$-0.0560507\pi$
$174$	−4.85124e7	+	7.13862e7i	−0.698120	+	1.02729i
$175$	6.04129e7	+	2.19885e7i	0.852112	+	0.310143i
$176$	−2.02235e6	−	736077.i	−0.0279617	−	0.0101772i
$177$	−3.26167e7	−	6.74682e7i	−0.442113	−	0.914519i
$178$	384713.	−	2.18181e6i	0.00511289	−	0.0289967i
$179$	4.58288e7	+	7.93778e7i	0.597246	+	1.03446i	0.993226	+	0.116201i	$0.0370716\pi$
$179$	4.58288e7	+	7.93778e7i	0.597246	+	1.03446i	−0.395980	+	0.918259i	$0.629595\pi$
$180$	−1.83349e7	−	2.70690e6i	−0.234329	−	0.0345954i
$181$	7.14924e7	−	1.23829e8i	0.896159	−	1.55219i	0.0637951	−	0.997963i	$-0.479680\pi$
$181$	7.14924e7	−	1.23829e8i	0.896159	−	1.55219i	0.832364	−	0.554230i	$-0.186987\pi$
$182$	−6.16587e6	−	5.17378e6i	−0.0758131	−	0.0636148i
$183$	−2.36566e7	−	1.06312e7i	−0.285347	−	0.128235i
$184$	4.98650e6	+	2.82798e7i	0.0590110	+	0.334668i
$185$	5.69293e7	−	4.77694e7i	0.661051	−	0.554688i
$186$	−2.10043e6	+	8.30135e6i	−0.0239339	+	0.0945918i
$187$	−4.18264e6	+	1.52236e6i	−0.0467740	+	0.0170244i
$188$	−3.84967e7			−0.422543
$189$	1.07614e8	−	1.39817e7i	1.15945	−	0.150641i
$190$	−1.30632e7			−0.138169
$191$	6.39933e7	−	2.32917e7i	0.664535	−	0.241871i	0.0123417	−	0.999924i	$-0.496071\pi$
$191$	6.39933e7	−	2.32917e7i	0.664535	−	0.241871i	0.652193	+	0.758053i	$0.273849\pi$
$192$	−8.78893e6	−	8.54660e6i	−0.0896152	−	0.0871443i
$193$	1.33738e8	−	1.12219e8i	1.33907	−	1.12361i	0.357208	−	0.934025i	$-0.383729\pi$
$193$	1.33738e8	−	1.12219e8i	1.33907	−	1.12361i	0.981863	−	0.189590i	$-0.0607157\pi$
$194$	−9.01967e6	−	5.11531e7i	−0.0886921	−	0.502998i
$195$	−593478.	−	5.84179e6i	−0.00573170	−	0.0564190i
$196$	1.48190e7	+	1.24346e7i	0.140579	+	0.117960i
$197$	−9.81286e7	+	1.69964e8i	−0.914458	+	1.58389i	−0.106765	+	0.994284i	$0.534049\pi$
$197$	−9.81286e7	+	1.69964e8i	−0.914458	+	1.58389i	−0.807693	+	0.589603i	$0.799284\pi$
$198$	6.10359e6	+	6.87421e6i	0.0558801	+	0.0629354i
$199$	−6.35627e7	−	1.10094e8i	−0.571764	−	0.990324i	−0.996385	−	0.0849529i	$-0.972926\pi$
$199$	−6.35627e7	−	1.10094e8i	−0.571764	−	0.990324i	0.424621	−	0.905371i	$-0.360407\pi$
$200$	−5.38707e6	+	3.05516e7i	−0.0476154	+	0.270041i
$201$	1.64442e8	+	1.20733e7i	1.42832	+	0.104867i
$202$	1.28580e7	+	4.67991e6i	0.109760	+	0.0399492i
$203$	2.30020e8	+	8.37203e7i	1.92987	+	0.702416i
$204$	−2.52866e7	−	1.85654e6i	−0.208538	−	0.0153108i
$205$	−3.67532e6	+	2.08438e7i	−0.0297959	+	0.168981i
$206$	2.74232e7	+	4.74984e7i	0.218566	+	0.378568i
$207$	3.87141e7	−	1.16391e8i	0.303370	−	0.912057i
$208$	1.94200e6	−	3.36364e6i	0.0149633	−	0.0259172i
$209$	4.96353e6	+	4.16490e6i	0.0376079	+	0.0315567i
$210$	5.31261e6	+	5.22937e7i	0.0395859	+	0.389656i
$211$	5.38519e6	+	3.05409e7i	0.0394650	+	0.223817i	0.998161	−	0.0606148i	$-0.0193061\pi$
$211$	5.38519e6	+	3.05409e7i	0.0394650	+	0.223817i	−0.958696	+	0.284432i	$0.908195\pi$
$212$	−3.97780e7	+	3.33777e7i	−0.286726	+	0.240592i
$213$	1.33497e7	+	1.29817e7i	0.0946552	+	0.0920453i
$214$	1.07711e7	−	3.92036e6i	0.0751298	−	0.0273450i
$215$	−2.53308e7			−0.173826
$216$	1.56616e7	+	4.99683e7i	0.105742	+	0.337370i
$217$	2.42852e7			0.161336
$218$	6.08873e7	−	2.21612e7i	0.398042	−	0.144876i
$219$	−5.11362e7	+	2.02101e8i	−0.328984	+	1.30021i
$220$	−3.41097e6	+	2.86215e6i	−0.0215973	+	0.0181223i
$221$	−1.39490e6	−	7.91085e6i	−0.00869299	−	0.0493004i
$222$	−1.91522e8	−	8.60699e7i	−1.17485	−	0.527978i
$223$	−7.81288e7	−	6.55578e7i	−0.471785	−	0.395874i	0.375660	−	0.926757i	$-0.377416\pi$
$223$	−7.81288e7	−	6.55578e7i	−0.471785	−	0.395874i	−0.847445	+	0.530883i	$0.821860\pi$
$224$	−1.73841e7	+	3.01101e7i	−0.103344	+	0.178996i
$225$	8.23075e7	−	1.03853e8i	0.481727	−	0.607826i
$226$	−6.73986e7	−	1.16738e8i	−0.388393	−	0.672716i
$227$	1.99228e7	−	1.12988e8i	0.113047	−	0.641123i	−0.874651	−	0.484753i	$-0.838910\pi$
$227$	1.99228e7	−	1.12988e8i	0.113047	−	0.641123i	0.987699	−	0.156370i	$-0.0499792\pi$
$228$	1.60643e7	+	3.32294e7i	0.0897617	+	0.185674i
$229$	−2.81005e8	−	1.02278e8i	−1.54629	−	0.562802i	−0.578744	−	0.815509i	$-0.696457\pi$
$229$	−2.81005e8	−	1.02278e8i	−1.54629	−	0.562802i	−0.967543	+	0.252707i	$0.918679\pi$
$230$	5.58295e7	+	2.03203e7i	0.302564	+	0.110124i
$231$	1.46541e7	−	2.15635e7i	0.0782198	−	0.115101i
$232$	−2.05110e7	+	1.16324e8i	−0.107840	+	0.611591i
$233$	−1.04499e8	−	1.80997e8i	−0.541208	−	0.937400i	−0.998835	−	0.0482558i	$-0.984634\pi$
$233$	−1.04499e8	−	1.80997e8i	−0.541208	−	0.937400i	0.457627	−	0.889144i	$-0.348700\pi$
$234$	−1.41302e7	+	8.69358e6i	−0.0720932	+	0.0443551i
$235$	−3.98242e7	+	6.89775e7i	−0.200175	+	0.346713i
$236$	−7.85626e7	−	6.59218e7i	−0.389066	−	0.326465i
$237$	−1.52518e8	+	1.10003e8i	−0.744221	+	0.536766i
$238$	1.24866e7	+	7.08152e7i	0.0600379	+	0.340492i
$239$	−1.48735e8	+	1.24804e8i	−0.704728	+	0.591337i	−0.923114	−	0.384525i	$-0.874365\pi$
$239$	−1.48735e8	+	1.24804e8i	−0.704728	+	0.591337i	0.218386	+	0.975862i	$0.429921\pi$
$240$	−2.44056e7	+	6.90648e6i	−0.113959	+	0.0322491i
$241$	−1.82880e8	+	6.65629e7i	−0.841602	+	0.306318i	−0.726612	−	0.687049i	$-0.758906\pi$
$241$	−1.82880e8	+	6.65629e7i	−0.841602	+	0.306318i	−0.114990	+	0.993367i	$0.536684\pi$
$242$	−1.53689e8			−0.697089
$243$	4.26629e7	−	2.19571e8i	0.190734	−	0.981642i
$244$	−3.54938e7			−0.156418
$245$	3.76100e7	−	1.36889e7i	0.163388	−	0.0594685i
$246$	5.75410e7	−	1.62834e7i	0.246436	−	0.0697385i
$247$	−8.95773e6	+	7.51642e6i	−0.0378232	+	0.0317374i
$248$	2.03493e6	+	1.15407e7i	0.00847166	+	0.0480452i
$249$	−3.49145e8	+	2.51819e8i	−1.43320	+	1.03369i
$250$	1.12566e8	+	9.44537e7i	0.455633	+	0.382322i
$251$	−1.67696e8	+	2.90458e8i	−0.669368	+	1.15938i	0.308713	+	0.951155i	$0.400102\pi$
$251$	−1.67696e8	+	2.90458e8i	−0.669368	+	1.15938i	−0.978081	+	0.208224i	$0.933232\pi$
$252$	1.26489e8	−	7.78219e7i	0.497910	−	0.306337i
$253$	−1.47346e7	−	2.55210e7i	−0.0572025	−	0.0990777i
$254$	3.13402e7	−	1.77739e8i	0.120001	−	0.680559i
$255$	−2.94850e7	+	4.33873e7i	−0.111355	+	0.163860i
$256$	−1.57654e7	−	5.73815e6i	−0.0587308	−	0.0213763i
$257$	1.36910e8	+	4.98313e7i	0.503119	+	0.183120i	0.581096	−	0.813835i	$-0.302624\pi$
$257$	1.36910e8	+	4.98313e7i	0.503119	+	0.183120i	−0.0779776	+	0.996955i	$0.524846\pi$
$258$	3.11505e7	+	6.44353e7i	0.112926	+	0.233590i
$259$	−1.03407e8	+	5.86452e8i	−0.369830	+	2.09741i
$260$	−4.01792e6	−	6.95925e6i	−0.0141773	−	0.0245559i
$261$	3.13382e8	−	3.95415e8i	1.09102	−	1.37661i
$262$	1.29186e8	−	2.23756e8i	0.443772	−	0.768635i
$263$	−1.28474e8	−	1.07803e8i	−0.435483	−	0.365413i	0.398533	−	0.917154i	$-0.369519\pi$
$263$	−1.28474e8	−	1.07803e8i	−0.435483	−	0.365413i	−0.834016	+	0.551741i	$0.813964\pi$
$264$	1.14752e7	+	5.15696e6i	0.0383837	+	0.0172496i
$265$	1.86557e7	+	1.05802e8i	0.0615816	+	0.349247i
$266$	8.01864e7	−	6.72844e7i	0.261225	−	0.219194i
$267$	−3.17677e6	+	1.25553e7i	−0.0102140	+	0.0403679i
$268$	2.12042e8	−	7.71769e7i	0.672898	−	0.244915i
$269$	−5.31439e8			−1.66464			−0.832320	−	0.554295i	$-0.812988\pi$
$269$	−5.31439e8			−1.66464			−0.832320	+	0.554295i	$0.812988\pi$
$270$	1.05734e8	+	2.36292e7i	0.326919	+	0.0730593i
$271$	−1.06197e8			−0.324132			−0.162066	−	0.986780i	$-0.551816\pi$
$271$	−1.06197e8			−0.324132			−0.162066	+	0.986780i	$0.551816\pi$
$272$	−3.26061e7	+	1.18677e7i	−0.0982444	+	0.0357580i
$273$	3.37323e7	+	3.28022e7i	0.100341	+	0.0975740i
$274$	5.89188e7	−	4.94388e7i	0.173032	−	0.145191i
$275$	−5.52833e6	−	3.13527e7i	−0.0160299	−	0.0909099i
$276$	−1.69663e7	−	1.67005e8i	−0.0485743	−	0.478132i
$277$	4.10839e8	+	3.44735e8i	1.16143	+	0.974554i	0.999924	−	0.0123183i	$-0.00392113\pi$
$277$	4.10839e8	+	3.44735e8i	1.16143	+	0.974554i	0.161504	+	0.986872i	$0.448366\pi$
$278$	5.50423e7	−	9.53360e7i	0.153652	−	0.266134i
$279$	1.57987e7	−	4.74976e7i	0.0435520	−	0.130935i
$280$	3.59670e7	+	6.22967e7i	0.0979155	+	0.169595i
$281$	6.36942e7	−	3.61228e8i	0.171249	−	0.971201i	−0.771136	−	0.636671i	$-0.780311\pi$
$281$	6.36942e7	−	3.61228e8i	0.171249	−	0.971201i	0.942385	−	0.334531i	$-0.108578\pi$
$282$	2.24435e8	+	1.64780e7i	0.595962	+	0.0437556i
$283$	5.91489e8	+	2.15284e8i	1.55129	+	0.564625i	0.968721	−	0.248153i	$-0.0798237\pi$
$283$	5.91489e8	+	2.15284e8i	1.55129	+	0.564625i	0.582573	+	0.812778i	$0.302046\pi$
$284$	2.39465e7	+	8.71583e6i	0.0620338	+	0.0225785i
$285$	7.61579e7	+	5.59152e6i	0.194876	+	0.0143078i
$286$	−692134.	+	3.92529e6i	−0.00174948	+	0.00992180i
$287$	−8.47995e7	−	1.46877e8i	−0.211742	−	0.366748i
$288$	4.75810e7	+	5.35885e7i	0.117371	+	0.132190i
$289$	1.69287e8	−	2.93214e8i	0.412555	−	0.714567i
$290$	1.87208e8	+	1.57086e8i	0.450745	+	0.378220i
$291$	3.06891e7	+	3.02082e8i	0.0730059	+	0.718621i
$292$	4.95416e7	+	2.80964e8i	0.116447	+	0.660407i
$293$	1.67702e8	−	1.40718e8i	0.389494	−	0.326824i	−0.426922	−	0.904288i	$-0.640402\pi$
$293$	1.67702e8	−	1.40718e8i	0.389494	−	0.326824i	0.816416	+	0.577464i	$0.195958\pi$
$294$	−8.10718e7	−	7.88365e7i	−0.186061	−	0.180930i
$295$	−1.99389e8	+	7.25715e7i	−0.452193	+	0.164585i
$296$	−2.87355e8			−0.644018
$297$	−3.26414e7	−	4.26891e7i	−0.0722971	−	0.0945517i
$298$	−4.45768e8			−0.975781
$299$	4.99758e7	−	1.81897e7i	0.108121	−	0.0393529i
$300$	4.44837e7	−	1.75809e8i	0.0951211	−	0.375939i
$301$	1.55490e8	−	1.30472e8i	0.328639	−	0.275761i
$302$	−5.34838e7	−	3.03322e8i	−0.111737	−	0.633694i
$303$	−7.29585e7	−	3.27875e7i	−0.150670	−	0.0677110i
$304$	3.86936e7	+	3.24678e7i	0.0789917	+	0.0662819i
$305$	−3.67177e7	+	6.35969e7i	−0.0741013	+	0.128347i
$306$	1.46626e8	+	2.16472e7i	0.292540	+	0.0431894i
$307$	−9.45684e7	−	1.63797e8i	−0.186536	−	0.323089i	0.757557	−	0.652769i	$-0.226393\pi$
$307$	−9.45684e7	−	1.63797e8i	−0.186536	−	0.323089i	−0.944093	+	0.329680i	$0.893059\pi$
$308$	6.19574e6	−	3.51378e7i	0.0120828	−	0.0685247i
$309$	−1.39546e8	−	2.88653e8i	−0.269068	−	0.556572i
$310$	2.27834e7	+	8.29247e6i	0.0434362	+	0.0158095i
$311$	1.55841e8	+	5.67216e7i	0.293779	+	0.106927i	0.484705	−	0.874678i	$-0.338927\pi$
$311$	1.55841e8	+	5.67216e7i	0.293779	+	0.106927i	−0.190926	+	0.981604i	$0.561149\pi$
$312$	−1.27616e7	+	1.87787e7i	−0.0237883	+	0.0350045i
$313$	−1.35712e8	+	7.69660e8i	−0.250157	+	1.41871i	0.558047	+	0.829809i	$0.311551\pi$
$313$	−1.35712e8	+	7.69660e8i	−0.250157	+	1.41871i	−0.808204	+	0.588902i	$0.799560\pi$
$314$	1.75403e8	+	3.03807e8i	0.319730	+	0.553789i
$315$	−8.58873e6	−	3.07145e8i	−0.0154825	−	0.553677i
$316$	−1.28676e8	+	2.22873e8i	−0.229399	+	0.397331i
$317$	−5.51795e8	−	4.63011e8i	−0.972905	−	0.816365i	0.0100985	−	0.999949i	$-0.496785\pi$
$317$	−5.51795e8	−	4.63011e8i	−0.972905	−	0.816365i	−0.983004	+	0.183584i	$0.941230\pi$
$318$	2.46192e8	−	1.77565e8i	0.429317	−	0.309643i
$319$	−2.10489e7	−	1.19374e8i	−0.0363046	−	0.205894i
$320$	−2.65905e7	+	2.23121e7i	−0.0453630	+	0.0380641i
$321$	−6.44734e7	+	1.82452e7i	−0.108796	+	0.0307880i
$322$	−4.47366e8	+	1.62828e8i	−0.746736	+	0.271790i
$323$	1.04467e8			0.172492
$324$	−6.99187e7	−	2.98018e8i	−0.114205	−	0.486782i
$325$	5.74554e7			0.0928409
$326$	6.11884e8	−	2.22708e8i	0.978155	−	0.356019i
$327$	−3.64458e8	+	1.03137e8i	−0.576408	+	0.163117i
$328$	6.26925e7	−	5.26053e7i	0.0980973	−	0.0823134i
$329$	−1.10827e8	−	6.28531e8i	−0.171577	−	0.973063i
$330$	2.11110e7	−	1.52262e7i	0.0323378	−	0.0233235i
$331$	3.67751e8	+	3.08580e8i	0.557386	+	0.467702i	0.877433	−	0.479699i	$-0.159254\pi$
$331$	3.67751e8	+	3.08580e8i	0.557386	+	0.467702i	−0.320047	+	0.947402i	$0.603699\pi$
$332$	−2.94565e8	+	5.10201e8i	−0.441772	+	0.765171i
$333$	1.07973e9	+	5.83764e8i	1.60236	+	0.866328i
$334$	−3.71115e8	−	6.42790e8i	−0.544999	−	0.943966i
$335$	8.10697e7	−	4.59769e8i	0.117815	−	0.668164i
$336$	1.14237e8	−	1.68100e8i	0.164293	−	0.241758i
$337$	7.91922e8	+	2.88236e8i	1.12714	+	0.410245i	0.837253	−	0.546816i	$-0.184160\pi$
$337$	7.91922e8	+	2.88236e8i	1.12714	+	0.410245i	0.289886	+	0.957061i	$0.406383\pi$
$338$	4.64955e8	+	1.69230e8i	0.654942	+	0.238379i
$339$	3.42964e8	+	7.09428e8i	0.478134	+	0.989030i
$340$	−1.24663e7	+	7.06997e7i	−0.0172013	+	0.0975531i
$341$	−6.01299e6	−	1.04148e7i	−0.00821203	−	0.0142237i
$342$	−7.94314e7	−	2.00603e8i	−0.107374	−	0.271173i
$343$	2.76550e8	−	4.78998e8i	0.370036	−	0.640921i
$344$	7.50310e7	+	6.29584e7i	0.0993770	+	0.0833872i
$345$	−3.16787e8	−	1.42364e8i	−0.415337	−	0.186652i
$346$	6.49912e7	+	3.68584e8i	0.0843506	+	0.478376i
$347$	−1.07510e9	+	9.02117e8i	−1.38133	+	1.15907i	−0.412607	+	0.910909i	$0.635382\pi$
$347$	−1.07510e9	+	9.02117e8i	−1.38133	+	1.15907i	−0.968719	+	0.248160i	$0.920174\pi$
$348$	1.69370e8	−	6.69386e8i	0.215431	−	0.851431i
$349$	−5.31827e8	+	1.93569e8i	−0.669702	+	0.243752i	−0.654420	−	0.756132i	$-0.727087\pi$
$349$	−5.31827e8	+	1.93569e8i	−0.669702	+	0.243752i	−0.0152825	+	0.999883i	$0.504865\pi$
$350$	−5.14321e8			−0.641204
$351$	8.61002e7	−	4.46351e7i	0.106275	−	0.0550937i
$352$	1.72172e7			0.0210408
$353$	9.77591e7	−	3.55814e7i	0.118289	−	0.0430538i	−0.282197	−	0.959356i	$-0.591063\pi$
$353$	9.77591e7	−	3.55814e7i	0.118289	−	0.0430538i	0.400487	+	0.916303i	$0.368841\pi$
$354$	4.29801e8	+	4.17951e8i	0.514939	+	0.500741i
$355$	4.03891e7	−	3.38905e7i	0.0479143	−	0.0402048i
$356$	3.07770e6	+	1.74545e7i	0.00361536	+	0.0205037i
$357$	−4.24852e7	−	4.18196e8i	−0.0494196	−	0.486453i
$358$	−5.61710e8	−	4.71331e8i	−0.647026	−	0.542920i
$359$	3.30511e8	−	5.72463e8i	0.377013	−	0.653005i	−0.613613	−	0.789607i	$-0.710285\pi$
$359$	3.30511e8	−	5.72463e8i	0.377013	−	0.653005i	0.990626	+	0.136602i	$0.0436180\pi$
$360$	1.45240e8	−	2.98182e7i	0.164070	−	0.0336839i
$361$	3.70900e8	+	6.42417e8i	0.414936	+	0.718690i
$362$	−1.98632e8	+	1.12650e9i	−0.220075	+	1.24811i
$363$	8.96002e8	+	6.57845e7i	0.983187	+	0.0721856i
$364$	6.05085e7	+	2.20233e7i	0.0657599	+	0.0239347i
$365$	5.54675e8	+	2.01885e8i	0.597054	+	0.217310i
$366$	2.06928e8	+	1.51927e7i	0.220615	+	0.0161976i
$367$	6.96415e7	−	3.94957e8i	0.0735423	−	0.417079i	−0.925704	−	0.378250i	$-0.876526\pi$
$367$	6.96415e7	−	3.94957e8i	0.0735423	−	0.417079i	0.999246	−	0.0388292i	$-0.0123628\pi$
$368$	−1.14864e8	−	1.98951e8i	−0.120148	−	0.208103i
$369$	−3.42433e8	+	7.03023e7i	−0.354800	+	0.0728412i
$370$	−2.97264e8	+	5.14876e8i	−0.305096	+	0.528441i
$371$	−6.59469e8	−	5.53360e8i	−0.670479	−	0.562599i
$372$	−6.92376e6	−	6.81528e7i	−0.00697336	−	0.0686410i
$373$	−3.35207e8	−	1.90106e9i	−0.334451	−	1.89677i	−0.432585	−	0.901593i	$-0.642399\pi$
$373$	−3.35207e8	−	1.90106e9i	−0.334451	−	1.89677i	0.0981341	−	0.995173i	$-0.468713\pi$
$374$	2.72778e7	−	2.28888e7i	0.0269624	−	0.0226241i
$375$	−6.15825e8	−	5.98845e8i	−0.603042	−	0.586415i
$376$	2.89401e8	−	1.05333e8i	0.280764	−	0.102190i
$377$	2.18759e8			0.210267
$378$	−7.70739e8	+	3.99558e8i	−0.733983	+	0.380503i
$379$	−9.40469e8			−0.887375			−0.443688	−	0.896181i	$-0.646330\pi$
$379$	−9.40469e8			−0.887375			−0.443688	+	0.896181i	$0.646330\pi$
$380$	9.82028e7	−	3.57429e7i	0.0918082	−	0.0334154i
$381$	−2.58792e8	+	1.02280e9i	−0.239725	+	0.947445i
$382$	−4.17342e8	+	3.50192e8i	−0.383064	+	0.321428i
$383$	1.17956e8	+	6.68963e8i	0.107282	+	0.608424i	0.990284	+	0.139056i	$0.0444069\pi$
$383$	1.17956e8	+	6.68963e8i	0.107282	+	0.608424i	−0.883003	+	0.469367i	$0.844482\pi$
$384$	8.94560e7	+	4.02015e7i	0.0806213	+	0.0362312i
$385$	−5.65497e7	−	4.74508e7i	−0.0505030	−	0.0423771i
$386$	−6.98329e8	+	1.20954e9i	−0.618023	+	1.07045i
$387$	−1.54026e8	−	3.88990e8i	−0.135084	−	0.341154i
$388$	2.07769e8	+	3.59866e8i	0.180580	+	0.312774i
$389$	−8.18679e7	+	4.64296e8i	−0.0705164	+	0.399918i	0.929036	+	0.369990i	$0.120639\pi$
$389$	−8.18679e7	+	4.64296e8i	−0.0705164	+	0.399918i	−0.999552	+	0.0299281i	$0.990472\pi$
$390$	2.04456e7	+	4.22921e7i	0.0174531	+	0.0361021i
$391$	−4.46472e8	−	1.62503e8i	−0.377725	−	0.137481i
$392$	−1.45425e8	−	5.29305e7i	−0.121938	−	0.0443817i
$393$	−8.48926e8	+	1.24920e9i	−0.705498	+	1.03814i
$394$	2.72638e8	−	1.54620e9i	0.224569	−	1.27359i
$395$	2.66225e8	+	4.61116e8i	0.217350	+	0.376461i
$396$	−6.46929e7	−	3.49768e7i	−0.0523508	−	0.0283039i
$397$	6.22634e8	−	1.07843e9i	0.499420	−	0.865022i	−0.500579	−	0.865691i	$-0.666880\pi$
$397$	6.22634e8	−	1.07843e9i	0.499420	−	0.865022i	1.00000		0.000669076i	$0.000212974\pi$
$398$	7.79070e8	+	6.53717e8i	0.619421	+	0.519756i
$399$	−4.96285e8	+	3.57944e8i	−0.391135	+	0.282104i
$400$	−4.30966e7	−	2.44413e8i	−0.0336692	−	0.190947i
$401$	−3.62455e8	+	3.04136e8i	−0.280704	+	0.235538i	−0.772259	−	0.635308i	$-0.780873\pi$
$401$	−3.62455e8	+	3.04136e8i	−0.280704	+	0.235538i	0.491555	+	0.870847i	$0.336429\pi$
$402$	−1.26923e9	+	3.59178e8i	−0.974429	+	0.275752i
$403$	2.03945e7	−	7.42300e6i	0.0155219	−	0.00564952i
$404$	−1.09465e8			−0.0825927
$405$	−6.06311e8	−	1.83016e8i	−0.453527	−	0.136898i
$406$	−1.95825e9			−1.45220
$407$	2.77106e8	−	1.00858e8i	0.203735	−	0.0741536i
$408$	1.95173e8	−	5.52315e7i	0.142268	−	0.0402603i
$409$	−3.55062e8	+	2.97932e8i	−0.256609	+	0.215321i	−0.762012	−	0.647563i	$-0.775788\pi$
$409$	−3.55062e8	+	2.97932e8i	−0.256609	+	0.215321i	0.505403	+	0.862883i	$0.331344\pi$
$410$	−2.94025e7	−	1.66750e8i	−0.0210689	−	0.119488i
$411$	−3.64657e8	+	2.63008e8i	−0.259083	+	0.186862i
$412$	−3.36118e8	−	2.82037e8i	−0.236784	−	0.198685i
$413$	8.50126e8	−	1.47246e9i	0.593825	−	1.02853i
$414$	2.74290e7	+	9.80899e8i	0.0189980	+	0.679396i
$415$	6.09444e8	+	1.05559e9i	0.418568	+	0.724980i
$416$	−5.39559e6	+	3.05999e7i	−0.00367462	+	0.0208398i
$417$	−3.61703e8	+	5.32247e8i	−0.244273	+	0.359449i
$418$	−4.87094e7	−	1.77288e7i	−0.0326209	−	0.0118730i
$419$	1.93606e9	+	7.04668e8i	1.28579	+	0.467989i	0.892342	−	0.451359i	$-0.149061\pi$
$419$	1.93606e9	+	7.04668e8i	1.28579	+	0.467989i	0.393446	+	0.919348i	$0.371283\pi$
$420$	−1.83022e8	−	3.78584e8i	−0.120540	−	0.249339i
$421$	3.89938e8	−	2.21145e9i	0.254688	−	1.44441i	−0.542185	−	0.840259i	$-0.682403\pi$
$421$	3.89938e8	−	2.21145e9i	0.254688	−	1.44441i	0.796873	−	0.604147i	$-0.206486\pi$
$422$	−1.24048e8	−	2.14858e8i	−0.0803521	−	0.139174i
$423$	−1.30140e9	−	1.92133e8i	−0.836025	−	0.123427i
$424$	2.07706e8	−	3.59757e8i	0.132333	−	0.229207i
$425$	−3.93205e8	−	3.29939e8i	−0.248461	−	0.208484i
$426$	−1.35877e8	−	6.10631e7i	−0.0851555	−	0.0382689i
$427$	−1.02182e8	−	5.79503e8i	−0.0635150	−	0.360212i
$428$	−7.02455e7	+	5.89430e7i	−0.0433077	+	0.0363395i
$429$	5.71530e6	−	2.25881e7i	0.00349493	−	0.0138127i
$430$	1.90426e8	−	6.93092e7i	0.115501	−	0.0420389i
$431$	2.35695e9			1.41801			0.709007	−	0.705202i	$-0.249144\pi$
$431$	2.35695e9			1.41801			0.709007	+	0.705202i	$0.249144\pi$
$432$	−2.54458e8	−	3.32786e8i	−0.151853	−	0.198597i
$433$	2.21296e9			1.30998			0.654991	−	0.755637i	$-0.272673\pi$
$433$	2.21296e9			1.30998			0.654991	+	0.755637i	$0.272673\pi$
$434$	−1.82565e8	+	6.64481e7i	−0.107202	+	0.0390183i
$435$	−1.02418e9	−	9.95941e8i	−0.596573	−	0.580124i
$436$	−3.97086e8	+	3.33195e8i	−0.229447	+	0.192529i
$437$	1.20102e8	+	6.81133e8i	0.0688439	+	0.390433i
$438$	−1.68563e8	−	1.65922e9i	−0.0958525	−	0.943507i
$439$	−5.43118e8	−	4.55731e8i	−0.306386	−	0.257088i	0.476610	−	0.879115i	$-0.341865\pi$
$439$	−5.43118e8	−	4.55731e8i	−0.306386	−	0.257088i	−0.782996	+	0.622026i	$0.786310\pi$
$440$	1.78108e7	−	3.08493e7i	0.00996782	−	0.0172648i
$441$	4.38902e8	+	4.94317e8i	0.243687	+	0.274454i
$442$	3.21316e7	+	5.56535e7i	0.0176992	+	0.0306559i
$443$	7.39707e7	−	4.19509e8i	0.0404247	−	0.229260i	−0.957901	−	0.287098i	$-0.907310\pi$
$443$	7.39707e7	−	4.19509e8i	0.0404247	−	0.229260i	0.998326	+	0.0578379i	$0.0184207\pi$
$444$	1.67528e9	+	1.22999e8i	0.908334	+	0.0666900i
$445$	3.44584e7	+	1.25418e7i	0.0185368	+	0.00674685i
$446$	7.66713e8	+	2.79061e8i	0.409224	+	0.148945i
$447$	2.59882e9	+	1.90805e8i	1.37626	+	0.101045i
$448$	4.82994e7	−	2.73920e8i	0.0253787	−	0.143930i
$449$	1.98923e8	+	3.44544e8i	0.103710	+	0.179631i	0.913211	−	0.407488i	$-0.133595\pi$
$449$	1.98923e8	+	3.44544e8i	0.103710	+	0.179631i	−0.809500	+	0.587120i	$0.800262\pi$
$450$	−3.34592e8	+	1.00592e9i	−0.173090	+	0.520381i
$451$	−4.19927e7	+	7.27334e7i	−0.0215554	+	0.0373350i
$452$	8.26085e8	+	6.93168e8i	0.420766	+	0.353064i
$453$	1.81976e8	+	1.79125e9i	0.0919754	+	0.905343i
$454$	1.59382e8	+	9.03903e8i	0.0799365	+	0.453342i
$455$	1.02056e8	−	8.56349e7i	0.0507922	−	0.0426197i
$456$	−2.11685e8	−	2.05849e8i	−0.104548	−	0.101665i
$457$	7.98674e8	−	2.90694e8i	0.391438	−	0.142472i	−0.138800	−	0.990320i	$-0.544325\pi$
$457$	7.98674e8	−	2.90694e8i	0.391438	−	0.142472i	0.530238	+	0.847849i	$0.322102\pi$
$458$	2.39232e9			1.16356
$459$	−8.45558e8	−	1.88964e8i	−0.408131	−	0.0912083i
$460$	−4.75300e8			−0.227675
$461$	−3.90041e9	+	1.41963e9i	−1.85420	+	0.674874i	−0.871297	+	0.490757i	$0.836720\pi$
$461$	−3.90041e9	+	1.41963e9i	−1.85420	+	0.674874i	−0.982904	+	0.184117i	$0.941057\pi$
$462$	−5.11614e7	+	2.02201e8i	−0.0241377	+	0.0953972i
$463$	1.48186e9	−	1.24343e9i	0.693863	−	0.582220i	−0.226158	−	0.974091i	$-0.572616\pi$
$463$	1.48186e9	−	1.24343e9i	0.693863	−	0.582220i	0.920020	+	0.391871i	$0.128172\pi$
$464$	−1.64088e8	−	9.30591e8i	−0.0762543	−	0.432460i
$465$	−1.29277e8	−	5.80971e7i	−0.0596261	−	0.0267959i
$466$	1.28081e9	+	1.07473e9i	0.586318	+	0.491979i
$467$	1.85872e9	−	3.21940e9i	0.844511	−	1.46274i	−0.0415346	−	0.999137i	$-0.513225\pi$
$467$	1.85872e9	−	3.21940e9i	0.844511	−	1.46274i	0.886045	−	0.463599i	$-0.153442\pi$
$468$	8.24376e7	−	1.04017e8i	0.0371762	−	0.0469076i
$469$	1.87050e9	+	3.23980e9i	0.837244	+	1.45015i
$470$	1.10646e8	−	6.27506e8i	0.0491580	−	0.278789i
$471$	−8.92555e8	−	1.84627e9i	−0.393606	−	0.814182i
$472$	7.70970e8	+	2.80610e8i	0.337474	+	0.122831i
$473$	−9.44526e7	−	3.43779e7i	−0.0410393	−	0.0149371i
$474$	8.45574e8	−	1.24427e9i	0.364693	−	0.536647i
$475$	−1.29750e8	+	7.35850e8i	−0.0555495	+	0.315037i
$476$	−2.87630e8	−	4.98190e8i	−0.122239	−	0.211724i
$477$	−1.51130e9	+	9.29819e8i	−0.637581	+	0.392269i
$478$	7.76641e8	−	1.34518e9i	0.325254	−	0.563356i
$479$	1.10114e9	+	9.23968e8i	0.457793	+	0.384134i	0.842318	−	0.538981i	$-0.181190\pi$
$479$	1.10114e9	+	9.23968e8i	0.457793	+	0.384134i	−0.384525	+	0.923114i	$0.625635\pi$
$480$	1.64573e8	−	1.18697e8i	0.0679224	−	0.0489888i
$481$	9.24141e7	+	5.24106e8i	0.0378643	+	0.214739i
$482$	1.19268e9	−	1.00078e9i	0.485132	−	0.407074i
$483$	2.67783e9	−	7.57794e8i	1.08135	−	0.306010i
$484$	1.15536e9	−	4.20517e8i	0.463190	−	0.168587i
$485$	8.59733e8			0.342190
$486$	2.80062e8	+	1.76737e9i	0.110669	+	0.698393i
$487$	3.86607e8			0.151676			0.0758382	−	0.997120i	$-0.475837\pi$
$487$	3.86607e8			0.151676			0.0758382	+	0.997120i	$0.475837\pi$
$488$	2.66826e8	−	9.71167e7i	0.103934	−	0.0378290i
$489$	−3.66260e9	+	1.03647e9i	−1.41647	+	0.400845i
$490$	−2.45279e8	+	2.05814e8i	−0.0941835	+	0.0790293i
$491$	−4.87752e8	−	2.76618e9i	−0.185957	−	1.05462i	−0.924719	−	0.380650i	$-0.875700\pi$
$491$	−4.87752e8	−	2.76618e9i	−0.185957	−	1.05462i	0.738762	−	0.673967i	$-0.235411\pi$
$492$	−3.88013e8	+	2.79853e8i	−0.146882	+	0.105938i
$493$	−1.49711e9	−	1.25623e9i	−0.562717	−	0.472176i
$494$	4.67739e7	−	8.10148e7i	0.0174566	−	0.0302357i
$495$	−1.29594e8	+	7.97323e7i	−0.0480250	+	0.0295472i
$496$	−4.68748e7	−	8.11895e7i	−0.0172486	−	0.0298754i
$497$	−7.33633e7	+	4.16064e8i	−0.0268060	+	0.152024i
$498$	1.93569e9	−	2.84838e9i	0.702318	−	1.03346i
$499$	−3.73288e9	−	1.35866e9i	−1.34491	−	0.489506i	−0.433552	−	0.901129i	$-0.642740\pi$
$499$	−3.73288e9	−	1.35866e9i	−1.34491	−	0.489506i	−0.911354	+	0.411623i	$0.864962\pi$
$500$	−1.10466e9	−	4.02062e8i	−0.395214	−	0.143846i
$501$	1.88845e9	+	3.90630e9i	0.670925	+	1.38782i
$502$	4.65922e8	−	2.64237e9i	0.164380	−	0.932248i
$503$	3.20491e8	+	5.55108e8i	0.112287	+	0.194486i	0.916692	−	0.399595i	$-0.130849\pi$
$503$	3.20491e8	+	5.55108e8i	0.112287	+	0.194486i	−0.804405	+	0.594081i	$0.797516\pi$
$504$	−7.37953e8	+	9.31123e8i	−0.256757	+	0.323967i
$505$	−1.13240e8	+	1.96137e8i	−0.0391273	+	0.0677704i
$506$	1.80597e8	+	1.51539e8i	0.0619704	+	0.0519993i
$507$	−2.63824e9	−	1.18562e9i	−0.899056	−	0.404035i
$508$	2.50722e8	+	1.42191e9i	0.0848534	+	0.481228i
$509$	−3.73965e9	+	3.13794e9i	−1.25695	+	1.05471i	−0.260953	+	0.965352i	$0.584037\pi$
$509$	−3.73965e9	+	3.13794e9i	−1.25695	+	1.05471i	−0.996000	+	0.0893569i	$0.971519\pi$
$510$	1.02940e8	−	4.06842e8i	0.0343629	−	0.135809i
$511$	−4.44465e9	+	1.61772e9i	−1.47355	+	0.536328i
$512$	1.34218e8			0.0441942
$513$	3.77218e8	+	1.20351e9i	0.123362	+	0.393585i
$514$	−1.16558e9			−0.378590
$515$	−8.53055e8	+	3.10487e8i	−0.275202	+	0.100165i
$516$	−4.10480e8	−	3.99163e8i	−0.131528	−	0.127902i
$517$	−2.42108e8	+	2.03153e8i	−0.0770535	+	0.0646556i
$518$	−8.27258e8	−	4.69161e9i	−0.261509	−	1.48309i
$519$	−2.21130e8	−	2.17665e9i	−0.0694323	−	0.683445i
$520$	4.92465e7	+	4.13227e7i	0.0153590	+	0.0128878i
$521$	−7.14920e8	+	1.23828e9i	−0.221475	+	0.383607i	−0.955256	−	0.295780i	$-0.904421\pi$
$521$	−7.14920e8	+	1.23828e9i	−0.221475	+	0.383607i	0.733781	+	0.679386i	$0.237754\pi$
$522$	−1.27394e9	+	3.83001e9i	−0.392016	+	1.17856i
$523$	1.97025e9	+	3.41258e9i	0.602235	+	1.04310i	0.992482	+	0.122391i	$0.0390563\pi$
$523$	1.97025e9	+	3.41258e9i	0.602235	+	1.04310i	−0.390247	+	0.920710i	$0.627610\pi$
$524$	−3.58926e8	+	2.03557e9i	−0.108980	+	0.618054i
$525$	2.99848e9	+	2.20149e8i	0.904365	+	0.0663985i
$526$	1.26078e9	+	4.58885e8i	0.377735	+	0.137484i
$527$	−1.82200e8	−	6.63153e7i	−0.0542264	−	0.0197368i
$528$	−1.00376e8	−	7.36959e6i	−0.0296763	−	0.00217884i
$529$	−4.50050e7	+	2.55236e8i	−0.0132180	+	0.0749631i
$530$	−4.29736e8	−	7.44324e8i	−0.125382	−	0.217168i
$531$	−2.32683e9	−	2.62061e9i	−0.674426	−	0.759578i
$532$	−4.18704e8	+	7.25216e8i	−0.120564	+	0.208822i
$533$	−1.16109e8	−	9.74267e7i	−0.0332138	−	0.0278697i
$534$	−1.04718e7	−	1.03077e8i	−0.00297595	−	0.0292932i
$535$	3.29449e7	+	1.86840e8i	0.00930142	+	0.0527510i
$536$	−1.38286e9	+	1.16036e9i	−0.387885	+	0.325474i
$537$	3.07301e9	+	2.98828e9i	0.856356	+	0.832744i
$538$	3.99512e9	−	1.45410e9i	1.10609	−	0.402585i
$539$	1.58816e8			0.0436853
$540$	−8.59511e8	+	1.11671e8i	−0.234895	+	0.0305184i
$541$	−3.30154e9			−0.896451			−0.448225	−	0.893921i	$-0.647944\pi$
$541$	−3.30154e9			−0.896451			−0.448225	+	0.893921i	$0.647944\pi$
$542$	7.98344e8	−	2.90573e8i	0.215374	−	0.0783896i
$543$	1.64021e9	−	6.48245e9i	0.439642	−	1.73756i
$544$	2.12646e8	−	1.78431e8i	0.0566319	−	0.0475198i
$545$	1.86232e8	+	1.05617e9i	0.0492795	+	0.279478i
$546$	−3.43336e8	−	1.54295e8i	−0.0902704	−	0.0405675i
$547$	−1.31208e9	−	1.10096e9i	−0.342771	−	0.287619i	0.455108	−	0.890436i	$-0.349600\pi$
$547$	−1.31208e9	−	1.10096e9i	−0.342771	−	0.287619i	−0.797880	+	0.602817i	$0.794045\pi$
$548$	−3.07652e8	+	5.32870e8i	−0.0798598	+	0.138321i
$549$	−1.19988e9	−	1.77146e8i	−0.309482	−	0.0456907i
$550$	1.27346e8	+	2.20569e8i	0.0326373	+	0.0565295i
$551$	−4.94018e8	+	2.80171e9i	−0.125809	+	0.713499i
$552$	5.84498e8	+	1.20905e9i	0.147910	+	0.305954i
$553$	−4.00926e9	−	1.45925e9i	−1.00815	−	0.366937i
$554$	−4.03175e9	−	1.46744e9i	−1.00742	−	0.366670i
$555$	1.95343e9	−	2.87448e9i	0.485034	−	0.713729i
$556$	−1.52928e8	+	8.67297e8i	−0.0377333	+	0.213996i
$557$	−9.37835e7	−	1.62438e8i	−0.0229950	−	0.0398285i	0.854299	−	0.519782i	$-0.173987\pi$
$557$	−9.37835e7	−	1.62438e8i	−0.0229950	−	0.0398285i	−0.877294	+	0.479954i	$0.840654\pi$
$558$	1.11934e7	+	4.00293e8i	0.00272737	+	0.0975346i
$559$	9.06996e7	−	1.57096e8i	0.0219616	−	0.0380386i
$560$	−4.40837e8	−	3.69907e8i	−0.106077	−	0.0890090i
$561$	−1.68826e8	+	1.21765e8i	−0.0403710	+	0.0291174i
$562$	5.09554e8	+	2.88982e9i	0.121091	+	0.686743i
$563$	−1.96708e9	+	1.65057e9i	−0.464560	+	0.389813i	−0.844806	−	0.535073i	$-0.820284\pi$
$563$	−1.96708e9	+	1.65057e9i	−0.464560	+	0.389813i	0.380245	+	0.924886i	$0.375840\pi$
$564$	−1.73229e9	+	4.90216e8i	−0.406577	+	0.115056i
$565$	2.09657e9	−	7.63090e8i	0.489035	−	0.177994i
$566$	−5.03559e9			−1.16733
$567$	4.66442e9	−	1.99951e9i	1.07462	−	0.460662i
$568$	−2.03867e8			−0.0466797
$569$	−2.16986e9	+	7.89764e8i	−0.493786	+	0.179723i	−0.576897	−	0.816817i	$-0.695737\pi$
$569$	−2.16986e9	+	7.89764e8i	−0.493786	+	0.179723i	0.0831110	+	0.996540i	$0.473514\pi$
$570$	−5.87820e8	+	1.66346e8i	−0.132948	+	0.0376227i
$571$	−4.68857e9	+	3.93418e9i	−1.05393	+	0.884356i	−0.993502	−	0.113816i	$-0.963693\pi$
$571$	−4.68857e9	+	3.93418e9i	−1.05393	+	0.884356i	−0.0604331	+	0.998172i	$0.519248\pi$
$572$	−5.53708e6	−	3.14023e7i	−0.00123707	−	0.00701577i
$573$	2.58299e9	−	1.86297e9i	0.573564	−	0.413681i
$574$	1.03936e9	+	8.72129e8i	0.229391	+	0.192482i
$575$	1.69917e9	−	2.94306e9i	0.372735	−	0.645596i
$576$	−5.04319e8	−	2.72664e8i	−0.109958	−	0.0594497i
$577$	3.66491e9	+	6.34780e9i	0.794232	+	1.37565i	0.923326	+	0.384018i	$0.125460\pi$
$577$	3.66491e9	+	6.34780e9i	0.794232	+	1.37565i	−0.129093	+	0.991632i	$0.541207\pi$
$578$	−4.70343e8	+	2.66745e9i	−0.101314	+	0.574577i
$579$	4.58898e9	−	6.75269e9i	0.982519	−	1.44578i
$580$	−1.83716e9	−	6.68670e8i	−0.390974	−	0.142303i
$581$	−9.17801e9	−	3.34052e9i	−1.94148	−	0.706640i
$582$	−1.05725e9	−	2.18695e9i	−0.222304	−	0.459841i
$583$	−7.40270e7	+	4.19828e8i	−0.0154721	+	0.0877469i
$584$	−1.14120e9	−	1.97661e9i	−0.237091	−	0.410654i
$585$	−1.01095e8	−	2.55313e8i	−0.0208777	−	0.0527264i
$586$	−8.75676e8	+	1.51672e9i	−0.179764	+	0.311360i
$587$	4.51573e9	+	3.78915e9i	0.921498	+	0.773229i	0.974272	−	0.225377i	$-0.0723615\pi$
$587$	4.51573e9	+	3.78915e9i	0.921498	+	0.773229i	−0.0527730	+	0.998607i	$0.516806\pi$
$588$	8.25170e8	+	3.70831e8i	0.167387	+	0.0752238i
$589$	4.90122e7	+	2.77962e8i	0.00988328	+	0.0560509i
$590$	1.30034e9	−	1.09112e9i	0.260661	−	0.218721i
$591$	−2.25130e9	+	8.89764e9i	−0.448619	+	1.77304i
$592$	2.16020e9	−	7.86250e8i	0.427926	−	0.155752i
$593$	3.12617e9			0.615632			0.307816	−	0.951446i	$-0.400402\pi$
$593$	3.12617e9			0.615632			0.307816	+	0.951446i	$0.400402\pi$
$594$	3.62187e8	+	2.31605e8i	0.0709056	+	0.0453414i
$595$	−1.19019e9			−0.231637
$596$	3.35108e9	−	1.21969e9i	0.648370	−	0.235987i
$597$	−4.26215e9	−	4.14463e9i	−0.819819	−	0.797215i
$598$	−3.25925e8	+	2.73484e8i	−0.0623252	+	0.0522971i
$599$	7.06464e8	+	4.00655e9i	0.134306	+	0.761688i	0.975340	+	0.220706i	$0.0708362\pi$
$599$	7.06464e8	+	4.00655e9i	0.134306	+	0.761688i	−0.841034	+	0.540982i	$0.818053\pi$
$600$	1.46634e8	+	1.44337e9i	0.0277144	+	0.272802i
$601$	1.93751e9	+	1.62576e9i	0.364068	+	0.305489i	0.806410	−	0.591357i	$-0.201408\pi$
$601$	1.93751e9	+	1.62576e9i	0.364068	+	0.305489i	−0.442342	+	0.896847i	$0.645852\pi$
$602$	−8.11911e8	+	1.40627e9i	−0.151677	+	0.262713i
$603$	7.55334e9	−	1.55072e9i	1.40291	−	0.288020i
$604$	1.23200e9	+	2.13389e9i	0.227501	+	0.394043i
$605$	4.41728e8	−	2.50517e9i	0.0810983	−	0.459931i
$606$	6.38180e8	+	4.68552e7i	0.116490	+	0.00855271i
$607$	−7.61868e9	−	2.77297e9i	−1.38267	−	0.503252i	−0.459685	−	0.888082i	$-0.652038\pi$
$607$	−7.61868e9	−	2.77297e9i	−1.38267	−	0.503252i	−0.922987	+	0.384830i	$0.874260\pi$
$608$	−3.79718e8	−	1.38206e8i	−0.0685170	−	0.0249381i
$609$	1.14166e10	+	8.38206e8i	2.04821	+	0.150380i
$610$	1.02015e8	−	5.78558e8i	0.0181975	−	0.103203i
$611$	−2.85189e8	−	4.93961e8i	−0.0505811	−	0.0876090i
$612$	−1.16149e9	+	2.38457e8i	−0.204827	+	0.0420514i
$613$	4.29650e9	−	7.44176e9i	0.753362	−	1.30486i	−0.192823	−	0.981234i	$-0.561764\pi$
$613$	4.29650e9	−	7.44176e9i	0.753362	−	1.30486i	0.946185	−	0.323627i	$-0.104902\pi$
$614$	1.15910e9	+	9.72598e8i	0.202083	+	0.169568i
$615$	1.00041e8	+	9.84735e8i	0.0173426	+	0.170709i
$616$	4.95659e7	+	2.81102e8i	0.00854380	+	0.0484543i
$617$	9.12474e8	−	7.65657e8i	0.156395	−	0.131231i	−0.561232	−	0.827658i	$-0.689673\pi$
$617$	9.12474e8	−	7.65657e8i	0.156395	−	0.131231i	0.717627	+	0.696427i	$0.245228\pi$
$618$	1.83884e9	+	1.78814e9i	0.313389	+	0.304749i
$619$	1.98941e9	−	7.24086e8i	0.337137	−	0.122708i	−0.167903	−	0.985803i	$-0.553700\pi$
$619$	1.98941e9	−	7.24086e8i	0.337137	−	0.122708i	0.505041	+	0.863095i	$0.331477\pi$
$620$	−1.93964e8			−0.0326852
$621$	2.59951e8	−	5.73036e9i	0.0435583	−	0.960200i
$622$	−1.32674e9			−0.221065
$623$	−2.76117e8	+	1.00499e8i	−0.0457494	+	0.0166514i
$624$	4.45541e7	−	1.76087e8i	0.00734076	−	0.0290123i
$625$	1.76309e9	−	1.47941e9i	0.288864	−	0.242386i
$626$	−1.08570e9	−	6.15728e9i	−0.176888	−	1.00318i
$627$	2.76386e8	+	1.24208e8i	0.0447796	+	0.0201239i
$628$	−2.14986e9	−	1.80395e9i	−0.346380	−	0.290647i
$629$	2.37724e9	−	4.11749e9i	0.380886	−	0.659714i
$630$	9.04965e8	+	2.28548e9i	0.144192	+	0.364154i
$631$	3.28799e9	+	5.69496e9i	0.520988	+	0.902377i	0.999702	+	0.0244065i	$0.00776960\pi$
$631$	3.28799e9	+	5.69496e9i	0.520988	+	0.902377i	−0.478714	+	0.877971i	$0.658897\pi$
$632$	3.57509e8	−	2.02753e9i	0.0563348	−	0.319490i
$633$	6.31232e8	+	1.30571e9i	0.0989181	+	0.204614i
$634$	5.41502e9	+	1.97091e9i	0.843893	+	0.307152i
$635$	2.80712e9	+	1.02171e9i	0.435064	+	0.158350i
$636$	−1.36491e9	+	2.00847e9i	−0.210380	+	0.309575i
$637$	−4.97706e7	+	2.82263e8i	−0.00762930	+	0.0432679i
$638$	4.84863e8	+	8.39807e8i	0.0739174	+	0.128029i
$639$	7.66024e8	+	4.14157e8i	0.116142	+	0.0627932i
$640$	1.38846e8	−	2.40488e8i	0.0209364	−	0.0362630i
$641$	−4.21867e9	−	3.53988e9i	−0.632662	−	0.530867i	0.269093	−	0.963114i	$-0.413276\pi$
$641$	−4.21867e9	−	3.53988e9i	−0.632662	−	0.530867i	−0.901755	+	0.432248i	$0.857721\pi$
$642$	4.34759e8	−	3.13569e8i	0.0648450	−	0.0467692i
$643$	−5.74671e8	−	3.25912e9i	−0.0852474	−	0.483462i	−0.997303	−	0.0733953i	$-0.976617\pi$
$643$	−5.74671e8	−	3.25912e9i	−0.0852474	−	0.483462i	0.912056	−	0.410067i	$-0.134495\pi$
$644$	2.91757e9	−	2.44813e9i	0.430448	−	0.361188i
$645$	−1.13984e9	+	3.22562e8i	−0.167258	+	0.0473320i
$646$	−7.85333e8	+	2.85838e8i	−0.114615	+	0.0417163i
$647$	5.05239e9			0.733384			0.366692	−	0.930342i	$-0.380490\pi$
$647$	5.05239e9			0.733384			0.366692	+	0.930342i	$0.380490\pi$
$648$	1.34104e9	+	2.04905e9i	0.193611	+	0.295829i
$649$	−8.41963e8			−0.120903
$650$	−4.31924e8	+	1.57207e8i	−0.0616893	+	0.0224531i
$651$	1.09279e9	−	3.09247e8i	0.155240	−	0.0439310i
$652$	−3.99050e9	+	3.34843e9i	−0.563846	+	0.473123i
$653$	−6.11430e8	−	3.46759e9i	−0.0859312	−	0.487340i	−0.997152	−	0.0754213i	$-0.975970\pi$
$653$	−6.11430e8	−	3.46759e9i	−0.0859312	−	0.487340i	0.911221	−	0.411919i	$-0.135141\pi$
$654$	2.45763e9	−	1.77255e9i	0.343553	−	0.247786i
$655$	3.27598e9	+	2.74887e9i	0.455509	+	0.382217i
$656$	−3.27357e8	+	5.66999e8i	−0.0452750	+	0.0784186i
$657$	2.72511e8	+	9.74538e9i	0.0374892	+	1.34066i
$658$	2.55291e9	+	4.42177e9i	0.349337	+	0.605070i
$659$	−7.08052e8	+	4.01556e9i	−0.0963754	+	0.546572i	0.897942	+	0.440114i	$0.145062\pi$
$659$	−7.08052e8	+	4.01556e9i	−0.0963754	+	0.546572i	−0.994317	+	0.106458i	$0.966049\pi$
$660$	−1.17042e8	+	1.72227e8i	−0.0158466	+	0.0233183i
$661$	−9.76813e8	−	3.55531e8i	−0.131555	−	0.0478820i	0.275404	−	0.961329i	$-0.411188\pi$
$661$	−9.76813e8	−	3.55531e8i	−0.131555	−	0.0478820i	−0.406959	+	0.913447i	$0.633411\pi$
$662$	−3.60891e9	−	1.31353e9i	−0.483473	−	0.175970i
$663$	−1.63505e8	−	3.38212e8i	−0.0217888	−	0.0450704i
$664$	8.18411e8	−	4.64144e9i	0.108488	−	0.615268i
$665$	8.66283e8	+	1.50045e9i	0.114231	+	0.197854i
$666$	−9.71417e9	−	1.43416e9i	−1.27422	−	0.188121i
$667$	6.46953e9	−	1.12056e10i	0.844174	−	1.46215i
$668$	4.54865e9	+	3.81677e9i	0.590425	+	0.495425i
$669$	−4.35047e9	−	1.95510e9i	−0.561752	−	0.252451i
$670$	6.48558e8	+	3.67815e9i	0.0833080	+	0.472463i
$671$	−2.23222e8	+	1.87306e8i	−0.0285239	+	0.0239344i
$672$	−3.98832e8	+	1.57627e9i	−0.0506988	+	0.200373i
$673$	5.07788e9	−	1.84820e9i	0.642139	−	0.233720i	−0.000366983	−	1.00000i	$-0.500117\pi$
$673$	5.07788e9	−	1.84820e9i	0.642139	−	0.233720i	0.642506	+	0.766280i	$0.277895\pi$
$674$	−6.74196e9			−0.848158
$675$	2.38124e9	−	5.72130e9i	0.298016	−	0.716030i
$676$	−3.95836e9			−0.492835
$677$	1.13648e9	−	4.13644e8i	0.140767	−	0.0512350i	−0.270676	−	0.962671i	$-0.587247\pi$
$677$	1.13648e9	−	4.13644e8i	0.140767	−	0.0512350i	0.411443	+	0.911436i	$0.365025\pi$
$678$	−4.51936e9	−	4.39475e9i	−0.556894	−	0.541539i
$679$	−5.27735e9	+	4.42823e9i	−0.646952	+	0.542857i
$680$	−9.97301e7	−	5.65598e8i	−0.0121631	−	0.0689805i
$681$	−5.42292e8	−	5.33795e9i	−0.0657989	−	0.647679i
$682$	7.36995e7	+	6.18413e7i	0.00889650	+	0.00746505i
$683$	−2.83577e9	+	4.91170e9i	−0.340564	+	0.589875i	−0.984538	−	0.175173i	$-0.943951\pi$
$683$	−2.83577e9	+	4.91170e9i	−0.340564	+	0.589875i	0.643973	+	0.765048i	$0.277285\pi$
$684$	1.14601e9	+	1.29070e9i	0.136928	+	0.154216i
$685$	6.36522e8	+	1.10249e9i	0.0756652	+	0.131056i
$686$	−7.68358e8	+	4.35757e9i	−0.0908718	+	0.515360i
$687$	−1.39472e10	−	1.02400e9i	−1.64111	−	0.120490i
$688$	−7.36313e8	−	2.67996e8i	−0.0861991	−	0.0313739i
$689$	−7.22958e8	−	2.63135e8i	−0.0842065	−	0.0306487i
$690$	2.77099e9	+	2.03446e8i	0.321117	+	0.0235764i
$691$	−2.14192e9	+	1.21475e10i	−0.246963	+	1.40059i	0.568928	+	0.822387i	$0.307358\pi$
$691$	−2.14192e9	+	1.21475e10i	−0.246963	+	1.40059i	−0.815890	+	0.578207i	$0.803753\pi$
$692$	−1.49708e9	−	2.59302e9i	−0.171741	−	0.297464i
$693$	3.84819e8	−	1.15693e9i	0.0439228	−	0.132050i
$694$	5.61378e9	−	9.72335e9i	0.637525	−	1.10423i
$695$	1.39580e9	+	1.17122e9i	0.157716	+	0.132340i
$696$	5.58303e8	+	5.49556e9i	0.0627680	+	0.617845i
$697$	2.35134e8	+	1.33351e9i	0.0263027	+	0.149170i
$698$	3.46840e9	−	2.91033e9i	0.386042	−	0.323928i
$699$	−7.00706e9	−	6.81386e9i	−0.776007	−	0.754611i
$700$	3.86643e9	−	1.40726e9i	0.426056	−	0.155072i
$701$	2.53668e9			0.278133			0.139067	−	0.990283i	$-0.455590\pi$
$701$	2.53668e9			0.278133			0.139067	+	0.990283i	$0.455590\pi$
$702$	−5.25133e8	+	5.71130e8i	−0.0572914	+	0.0623096i
$703$	−6.92109e9			−0.751330
$704$	−1.29431e8	+	4.71089e7i	−0.0139808	+	0.00508861i
$705$	−9.13662e8	+	3.61099e9i	−0.0982027	+	0.388118i
$706$	−6.37552e8	+	5.34969e8i	−0.0681866	+	0.0572153i
$707$	−3.15136e8	−	1.78723e9i	−0.0335375	−	0.190200i
$708$	−4.37463e9	−	1.96596e9i	−0.463260	−	0.208189i
$709$	−4.49482e9	−	3.77160e9i	−0.473642	−	0.397433i	0.374479	−	0.927235i	$-0.377822\pi$
$709$	−4.49482e9	−	3.77160e9i	−0.473642	−	0.397433i	−0.848121	+	0.529802i	$0.822266\pi$
$710$	−2.10897e8	+	3.65284e8i	−0.0221139	+	0.0383024i
$711$	−5.46227e9	+	6.89210e9i	−0.569941	+	0.719131i
$712$	−7.08951e7	−	1.22794e8i	−0.00736099	−	0.0127496i
$713$	2.22913e8	−	1.26420e9i	0.0230315	−	0.130618i
$714$	1.46364e9	+	3.02756e9i	0.150484	+	0.311278i
$715$	−6.19939e7	−	2.25639e7i	−0.00634275	−	0.00230857i
$716$	5.51232e9	+	2.00632e9i	0.561227	+	0.204270i
$717$	−5.10359e9	+	7.50995e9i	−0.517081	+	0.760887i
$718$	−9.18283e8	+	5.20784e9i	−0.0925851	+	0.525076i
$719$	7.34997e9	+	1.27305e10i	0.737453	+	1.27731i	0.953639	+	0.300954i	$0.0973052\pi$
$719$	7.34997e9	+	1.27305e10i	0.737453	+	1.27731i	−0.216185	+	0.976352i	$0.569361\pi$
$720$	−1.01026e9	+	6.21560e8i	−0.100872	+	0.0620610i
$721$	3.63714e9	−	6.29971e9i	0.361399	−	0.625961i
$722$	−4.54601e9	−	3.81456e9i	−0.449521	−	0.377193i
$723$	−7.38168e9	+	5.32401e9i	−0.726392	+	0.523907i
$724$	−1.58906e9	−	9.01201e9i	−0.155616	−	0.882544i
$725$	1.07081e10	−	8.98519e9i	1.04359	−	0.875678i
$726$	−6.91573e9	+	1.95707e9i	−0.670749	+	0.189814i
$727$	−1.02481e10	+	3.73001e9i	−0.989176	+	0.360031i	−0.785401	−	0.618987i	$-0.787543\pi$
$727$	−1.02481e10	+	3.73001e9i	−0.989176	+	0.360031i	−0.203775	+	0.979018i	$0.565321\pi$
$728$	−5.15134e8			−0.0494835
$729$	−8.76255e8	−	1.04236e10i	−0.0837692	−	0.996485i
$730$	−4.72218e9			−0.449276
$731$	−1.52284e9	+	5.54270e8i	−0.144193	+	0.0524820i
$732$	−1.59716e9	+	4.51977e8i	−0.150508	+	0.0425919i
$733$	8.46555e9	−	7.10344e9i	0.793946	−	0.666200i	−0.152772	−	0.988261i	$-0.548820\pi$
$733$	8.46555e9	−	7.10344e9i	0.793946	−	0.666200i	0.946719	+	0.322061i	$0.104376\pi$
$734$	5.57132e8	+	3.15965e9i	0.0520022	+	0.294919i
$735$	1.51807e9	−	1.09490e9i	0.141022	−	0.101711i
$736$	1.40786e9	+	1.18133e9i	0.130163	+	0.109220i
$737$	9.26269e8	−	1.60434e9i	0.0852316	−	0.147626i
$738$	2.38190e9	−	1.46545e9i	0.218135	−	0.134207i
$739$	2.60041e9	+	4.50405e9i	0.237021	+	0.410532i	0.959858	−	0.280486i	$-0.0904957\pi$
$739$	2.60041e9	+	4.50405e9i	0.237021	+	0.410532i	−0.722837	+	0.691018i	$0.757162\pi$
$740$	8.25909e8	−	4.68396e9i	0.0749241	−	0.424915i
$741$	−3.07368e8	+	4.52294e8i	−0.0277521	+	0.0408373i
$742$	6.47166e9	+	2.35549e9i	0.581570	+	0.211674i
$743$	6.90408e9	+	2.51288e9i	0.617511	+	0.224756i	0.631787	−	0.775142i	$-0.282322\pi$
$743$	6.90408e9	+	2.51288e9i	0.617511	+	0.224756i	−0.0142754	+	0.999898i	$0.504544\pi$
$744$	2.38527e8	+	4.93397e8i	0.0212340	+	0.0439229i
$745$	1.28122e9	−	7.26614e9i	0.113521	−	0.643808i
$746$	7.72153e9	+	1.33741e10i	0.680953	+	1.17945i
$747$	−1.25043e10	+	1.57774e10i	−1.09758	+	1.38489i
$748$	−1.42434e8	+	2.46704e8i	−0.0124440	+	0.0215536i
$749$	−1.16458e9	−	9.77200e8i	−0.101271	−	0.0849762i
$750$	6.26803e9	+	2.81685e9i	0.542521	+	0.243809i
$751$	−2.19938e9	−	1.24733e10i	−0.189479	−	1.07459i	−0.920065	−	0.391767i	$-0.871864\pi$
$751$	−2.19938e9	−	1.24733e10i	−0.189479	−	1.07459i	0.730586	−	0.682821i	$-0.239247\pi$
$752$	−1.88737e9	+	1.58369e9i	−0.161843	+	0.135803i
$753$	−3.84735e9	+	1.52056e10i	−0.328382	+	1.29784i
$754$	−1.64453e9	+	5.98560e8i	−0.139715	+	0.0508520i
$755$	5.09794e9			0.431103
$756$	4.70081e9	−	5.11256e9i	0.395682	−	0.430340i
$757$	−7.37176e9			−0.617640			−0.308820	−	0.951121i	$-0.599934\pi$
$757$	−7.37176e9			−0.617640			−0.308820	+	0.951121i	$0.599934\pi$
$758$	7.07002e9	−	2.57328e9i	0.589628	−	0.214607i
$759$	−9.88013e8	−	9.60772e8i	−0.0820194	−	0.0797579i
$760$	−6.40445e8	+	5.37397e8i	−0.0529218	+	0.0444066i
$761$	3.58398e9	+	2.03257e10i	0.294794	+	1.67186i	0.668038	+	0.744127i	$0.267134\pi$
$761$	3.58398e9	+	2.03257e10i	0.294794	+	1.67186i	−0.373244	+	0.927733i	$0.621755\pi$
$762$	−8.53071e8	−	8.39705e9i	−0.0698462	−	0.687519i
$763$	−6.58320e9	−	5.52396e9i	−0.536538	−	0.450209i
$764$	2.17921e9	−	3.77450e9i	0.176796	−	0.306219i
$765$	−7.74282e8	+	2.32782e9i	−0.0625294	+	0.187990i
$766$	−2.71713e9	−	4.70621e9i	−0.218429	−	0.378330i
$767$	2.63858e8	−	1.49641e9i	0.0211148	−	0.119748i
$768$	−7.82487e8	−	5.74502e7i	−0.0623322	−	0.00457643i
$769$	1.05896e10	+	3.85430e9i	0.839726	+	0.305635i	0.725844	−	0.687859i	$-0.241449\pi$
$769$	1.05896e10	+	3.85430e9i	0.839726	+	0.305635i	0.113882	+	0.993494i	$0.463672\pi$
$770$	5.54948e8	+	2.01984e8i	0.0438061	+	0.0159441i
$771$	6.79528e9	+	4.98910e8i	0.533970	+	0.0392041i
$772$	1.94022e9	−	1.10035e10i	0.151771	−	0.860739i
$773$	−1.02390e10	−	1.77344e10i	−0.797312	−	1.38099i	−0.921360	−	0.388709i	$-0.872921\pi$
$773$	−1.02390e10	−	1.77344e10i	−0.797312	−	1.38099i	0.124048	−	0.992276i	$-0.460412\pi$
$774$	2.22224e9	+	2.50281e9i	0.172265	+	0.194015i
$775$	6.93413e8	−	1.20103e9i	0.0535101	−	0.0926822i
$776$	−2.54656e9	−	2.13682e9i	−0.195631	−	0.164154i
$777$	2.81471e9	+	2.77061e10i	0.215259	+	2.11886i
$778$	−6.54943e8	−	3.71437e9i	−0.0498626	−	0.282785i
$779$	1.50998e9	−	1.26702e9i	0.114443	−	0.0960292i
$780$	−2.69418e8	−	2.61990e8i	−0.0203281	−	0.0197676i
$781$	1.96596e8	−	7.15551e7i	0.0147671	−	0.00537479i
$782$	3.80100e9			0.284233
$783$	9.06646e9	−	2.17836e10i	0.674950	−	1.62167i
$784$	1.23807e9			0.0917567
$785$	−5.45627e9	+	1.98592e9i	−0.402580	+	0.146527i
$786$	2.96383e9	−	1.17137e10i	0.217708	−	0.860428i
$787$	−5.81207e9	+	4.87691e9i	−0.425030	+	0.356643i	−0.830073	−	0.557655i	$-0.811701\pi$
$787$	−5.81207e9	+	4.87691e9i	−0.425030	+	0.356643i	0.405043	+	0.914298i	$0.367257\pi$
$788$	2.18110e9	+	1.23696e10i	0.158794	+	0.900565i
$789$	−7.15387e9	−	3.21495e9i	−0.518528	−	0.233026i
$790$	−3.26305e9	−	2.73802e9i	−0.235466	−	0.197579i
$791$	−8.93907e9	+	1.54829e10i	−0.642207	+	1.11233i
$792$	5.82034e8	+	8.59291e7i	0.0416303	+	0.00614613i
$793$	−2.62943e8	−	4.55430e8i	−0.0187243	−	0.0324314i
$794$	−1.72991e9	+	9.81080e9i	−0.122645	+	0.695557i
$795$	2.18675e9	+	4.52334e9i	0.154353	+	0.319282i
$796$	−7.64537e9	−	2.78269e9i	−0.537282	−	0.195555i
$797$	−1.78995e10	−	6.51488e9i	−1.25238	−	0.455829i	−0.371175	−	0.928563i	$-0.621045\pi$
$797$	−1.78995e10	−	6.51488e9i	−1.25238	−	0.455829i	−0.881205	+	0.472734i	$0.843267\pi$
$798$	2.75145e9	−	4.04877e9i	0.191669	−	0.282042i
$799$	−8.84845e8	+	5.01820e9i	−0.0613696	+	0.348044i
$800$	9.92733e8	+	1.71946e9i	0.0685516	+	0.118735i
$801$	1.69294e7	+	6.05418e8i	0.00116393	+	0.0416238i
$802$	1.89260e9	−	3.27809e9i	0.129554	−	0.224393i
$803$	1.79426e9	+	1.50556e9i	0.122287	+	0.102611i
$804$	8.55874e9	−	6.17296e9i	0.580783	−	0.418887i
$805$	−1.36833e9	−	7.76017e9i	−0.0924495	−	0.524307i
$806$	−1.33006e8	+	1.11605e8i	−0.00894745	+	0.00750780i
$807$	−2.39138e10	+	6.76733e9i	−1.60174	+	0.453273i
$808$	8.22909e8	−	2.99515e8i	0.0548798	−	0.0199746i
$809$	−2.31597e10			−1.53785			−0.768923	−	0.639341i	$-0.779207\pi$
$809$	−2.31597e10			−1.53785			−0.768923	+	0.639341i	$0.779207\pi$
$810$	5.05873e9	−	2.83137e8i	0.334460	−	0.0187197i
$811$	−2.72475e10			−1.79372			−0.896859	−	0.442316i	$-0.854157\pi$
$811$	−2.72475e10			−1.79372			−0.896859	+	0.442316i	$0.854157\pi$
$812$	1.47213e10	−	5.35810e9i	0.964936	−	0.351208i
$813$	−4.77870e9	+	1.35232e9i	−0.311884	+	0.0882594i
$814$	−1.80719e9	+	1.51642e9i	−0.117441	+	0.0985446i
$815$	1.87153e9	+	1.06140e10i	0.121100	+	0.686793i
$816$	−1.31610e9	+	9.49229e8i	−0.0847954	+	0.0611583i
$817$	1.80716e9	+	1.51638e9i	0.115936	+	0.0972819i
$818$	1.85400e9	−	3.21122e9i	0.118433	−	0.205132i
$819$	1.93560e9	+	1.04650e9i	0.123118	+	0.0665648i
$820$	6.77290e8	+	1.17310e9i	0.0428969	+	0.0742997i
$821$	3.79153e9	−	2.15028e10i	0.239118	−	1.35611i	−0.594646	−	0.803988i	$-0.702708\pi$
$821$	3.79153e9	−	2.15028e10i	0.239118	−	1.35611i	0.833764	−	0.552121i	$-0.186181\pi$
$822$	2.02170e9	−	2.97493e9i	0.126959	−	0.186821i
$823$	2.09378e10	+	7.62073e9i	1.30928	+	0.476537i	0.900007	−	0.435876i	$-0.143562\pi$
$823$	2.09378e10	+	7.62073e9i	1.30928	+	0.476537i	0.409269	+	0.912414i	$0.365784\pi$
$824$	3.29848e9	+	1.20055e9i	0.205385	+	0.0747540i
$825$	−6.48011e8	−	1.34042e9i	−0.0401785	−	0.0831099i
$826$	−2.36197e9	+	1.33954e10i	−0.145829	+	0.827036i
$827$	−1.04565e10	−	1.81112e10i	−0.642860	−	1.11347i	−0.984791	−	0.173742i	$-0.944414\pi$
$827$	−1.04565e10	−	1.81112e10i	−0.642860	−	1.11347i	0.341931	−	0.939725i	$-0.388919\pi$
$828$	−2.89010e9	−	7.29890e9i	−0.176932	−	0.446839i
$829$	7.56263e9	−	1.30989e10i	0.461033	−	0.798532i	−0.537980	−	0.842958i	$-0.680812\pi$
$829$	7.56263e9	−	1.30989e10i	0.461033	−	0.798532i	0.999013	+	0.0444253i	$0.0141457\pi$
$830$	−7.46978e9	−	6.26789e9i	−0.453455	−	0.380494i
$831$	2.28769e10	+	1.02809e10i	1.38291	+	0.621478i
$832$	−4.31647e7	−	2.44799e8i	−0.00259835	−	0.0147360i
$833$	1.96151e9	−	1.64590e9i	0.117580	−	0.0986614i
$834$	1.26280e9	−	4.99086e9i	0.0753796	−	0.297917i
$835$	1.15443e10	−	4.20178e9i	0.686221	−	0.249764i
$836$	4.14683e8			0.0245468
$837$	1.06083e8	−	2.33849e9i	0.00625326	−	0.137847i
$838$	−1.64825e10			−0.967539
$839$	1.34289e10	−	4.88772e9i	0.785007	−	0.285719i	0.0817479	−	0.996653i	$-0.473950\pi$
$839$	1.34289e10	−	4.88772e9i	0.785007	−	0.285719i	0.703259	+	0.710934i	$0.251728\pi$
$840$	2.41174e9	+	2.34524e9i	0.140395	+	0.136524i
$841$	2.75566e10	−	2.31227e10i	1.59749	−	1.34046i
$842$	3.11950e9	+	1.76916e10i	0.180091	+	1.02135i
$843$	−1.73374e9	−	1.70657e10i	−0.0996751	−	0.981134i
$844$	1.52042e9	+	1.27579e9i	0.0870495	+	0.0730432i
$845$	−4.09485e9	+	7.09249e9i	−0.233475	+	0.404390i
$846$	1.03090e10	−	2.11647e9i	0.585358	−	0.120175i
$847$	1.01919e10	+	1.76528e10i	0.576318	+	0.998211i
$848$	−5.77084e8	+	3.27280e9i	−0.0324977	+	0.184304i
$849$	2.93574e10	+	2.15542e9i	1.64642	+	0.120880i
$850$	3.85870e9	+	1.40445e9i	0.215514	+	0.0784406i
$851$	2.95795e10	+	1.07660e10i	1.64527	+	0.598829i
$852$	1.18854e9	+	8.72627e7i	0.0658378	+	0.00483382i
$853$	2.64067e9	−	1.49760e10i	0.145677	−	0.826178i	−0.821143	−	0.570722i	$-0.806663\pi$
$853$	2.64067e9	−	1.49760e10i	0.145677	−	0.826178i	0.966821	−	0.255456i	$-0.0822255\pi$
$854$	2.35377e9	+	4.07685e9i	0.129319	+	0.223987i
$855$	3.49818e9	−	7.18184e8i	0.191408	−	0.0392966i
$856$	3.66796e8	−	6.35309e8i	0.0199879	−	0.0346200i
$857$	4.30389e9	+	3.61139e9i	0.233576	+	0.195994i	0.752062	−	0.659093i	$-0.229060\pi$
$857$	4.30389e9	+	3.61139e9i	0.233576	+	0.195994i	−0.518486	+	0.855086i	$0.673504\pi$
$858$	1.88397e7	+	1.85445e8i	0.00101828	+	0.0100233i
$859$	4.59916e9	+	2.60831e10i	0.247572	+	1.40405i	0.814442	+	0.580245i	$0.197043\pi$
$859$	4.59916e9	+	2.60831e10i	0.247572	+	1.40405i	−0.566869	+	0.823808i	$0.691846\pi$
$860$	−1.24189e9	+	1.04207e9i	−0.0665792	+	0.0558666i
$861$	−5.68616e9	−	5.52938e9i	−0.303604	−	0.295233i
$862$	−1.77185e10	+	6.44900e9i	−0.942218	+	0.342939i
$863$	1.93119e10			1.02279			0.511396	−	0.859345i	$-0.329128\pi$
$863$	1.93119e10			1.02279			0.511396	+	0.859345i	$0.329128\pi$
$864$	2.82346e9	+	1.80549e9i	0.148930	+	0.0952353i
$865$	−6.19480e9			−0.325440
$866$	−1.66360e10	+	6.05500e9i	−0.870434	+	0.316812i
$867$	3.88386e9	−	1.53498e10i	0.202393	−	0.799903i
$868$	1.19062e9	−	9.99052e8i	0.0617953	−	0.0518524i
$869$	3.66883e8	+	2.08070e9i	0.0189653	+	0.107557i
$870$	1.04244e10	+	4.68470e9i	0.536701	+	0.241193i
$871$	2.56111e9	+	2.14903e9i	0.131330	+	0.110199i
$872$	2.07344e9	−	3.59130e9i	0.105897	−	0.183419i
$873$	5.22766e9	+	1.32024e10i	0.265924	+	0.671588i
$874$	−2.76656e9	−	4.79183e9i	−0.140169	−	0.242779i
$875$	3.38426e9	−	1.91931e10i	0.170779	−	0.968537i
$876$	5.80708e9	+	1.20121e10i	0.291873	+	0.603744i
$877$	2.05562e10	+	7.48183e9i	1.02907	+	0.374549i	0.800725	−	0.599032i	$-0.204448\pi$
$877$	2.05562e10	+	7.48183e9i	1.02907	+	0.374549i	0.228341	+	0.973581i	$0.426670\pi$
$878$	5.32987e9	+	1.93991e9i	0.265758	+	0.0967278i
$879$	5.75438e9	−	8.46760e9i	0.285784	−	0.420532i
$880$	−4.94851e7	+	2.80644e8i	−0.00244785	+	0.0138825i
$881$	2.83694e8	+	4.91372e8i	0.0139777	+	0.0242100i	0.872930	−	0.487846i	$-0.162217\pi$
$881$	2.83694e8	+	4.91372e8i	0.0139777	+	0.0242100i	−0.858952	+	0.512056i	$0.828884\pi$
$882$	−4.65199e9	−	2.51514e9i	−0.228296	−	0.123430i
$883$	2.80652e9	−	4.86103e9i	0.137185	−	0.237611i	−0.789245	−	0.614078i	$-0.789528\pi$
$883$	2.80652e9	−	4.86103e9i	0.137185	−	0.237611i	0.926430	+	0.376467i	$0.122861\pi$
$884$	−3.93827e8	−	3.30460e8i	−0.0191744	−	0.0160893i
$885$	−8.04802e9	+	5.80460e9i	−0.390290	+	0.281495i
$886$	5.91766e8	+	3.35607e9i	0.0285846	+	0.162111i
$887$	−5.48910e8	+	4.60590e8i	−0.0264100	+	0.0221606i	−0.655897	−	0.754850i	$-0.727709\pi$
$887$	−5.48910e8	+	4.60590e8i	−0.0264100	+	0.0221606i	0.629487	+	0.777011i	$0.283265\pi$
$888$	−1.29305e10	+	3.65917e9i	−0.619683	+	0.175363i
$889$	−2.24936e10	+	8.18701e9i	−1.07375	+	0.390813i
$890$	−2.93359e8			−0.0139487
$891$	−2.01241e9	−	1.50528e9i	−0.0953112	−	0.0712928i
$892$	−6.52735e9			−0.307936
$893$	6.97035e9	−	2.53700e9i	0.327548	−	0.119218i
$894$	−2.00588e10	+	5.67640e9i	−0.938910	+	0.265700i
$895$	9.29727e9	−	7.80134e9i	0.433486	−	0.363738i
$896$	3.86395e8	+	2.19136e9i	0.0179454	+	0.101774i
$897$	2.01720e9	−	1.45490e9i	0.0933201	−	0.0673067i
$898$	−2.43814e9	−	2.04584e9i	−0.112355	−	0.0942767i
$899$	2.64014e9	−	4.57285e9i	0.121190	−	0.209908i
$900$	−2.37059e8	−	8.47757e9i	−0.0108395	−	0.387635i
$901$	3.43662e9	+	5.95240e9i	0.156529	+	0.271116i
$902$	1.16671e8	−	6.61675e8i	0.00529347	−	0.0300208i
$903$	5.33536e9	−	7.85100e9i	0.241133	−	0.354828i
$904$	−8.10675e9	−	2.95061e9i	−0.364970	−	0.132838i
$905$	−1.77913e10	−	6.47552e9i	−0.797882	−	0.290405i
$906$	−6.26917e9	−	1.29679e10i	−0.280067	−	0.579323i
$907$	−3.49524e9	+	1.98225e10i	−0.155543	+	0.882130i	0.802744	+	0.596323i	$0.203372\pi$
$907$	−3.49524e9	+	1.98225e10i	−0.155543	+	0.882130i	−0.958287	+	0.285806i	$0.907739\pi$
$908$	−3.67139e9	−	6.35903e9i	−0.162753	−	0.281897i
$909$	−3.70052e9	−	5.46330e8i	−0.163414	−	0.0241258i
$910$	−5.32897e8	+	9.23005e8i	−0.0234422	+	0.0406031i
$911$	−2.53962e10	−	2.13099e10i	−1.11289	−	0.933829i	−0.114670	−	0.993404i	$-0.536581\pi$
$911$	−2.53962e10	−	2.13099e10i	−1.11289	−	0.933829i	−0.998224	+	0.0595751i	$0.981025\pi$
$912$	2.15459e9	+	9.68271e8i	0.0940551	+	0.0422683i
$913$	8.39872e8	+	4.76315e9i	0.0365229	+	0.207132i
$914$	−5.20868e9	+	4.37060e9i	−0.225640	+	0.189334i
$915$	−8.42392e8	+	3.32931e9i	−0.0363530	+	0.143675i
$916$	−1.79843e10	+	6.54576e9i	−0.773144	+	0.281401i
$917$	−3.42678e10			−1.46755
$918$	6.87355e9	−	8.93039e8i	0.293246	−	0.0380997i
$919$	−2.75118e10			−1.16927			−0.584635	−	0.811296i	$-0.698762\pi$
$919$	−2.75118e10			−1.16927			−0.584635	+	0.811296i	$0.698762\pi$
$920$	3.57309e9	−	1.30050e9i	0.151282	−	0.0550621i
$921$	−6.34121e9	−	6.16636e9i	−0.267463	−	0.260088i
$922$	2.54371e10	−	2.13443e10i	1.06883	−	0.896858i
$923$	6.55641e7	+	3.71832e8i	0.00274448	+	0.0155647i
$924$	−1.68646e8	−	1.66004e9i	−0.00703274	−	0.0692255i
$925$	2.60505e10	+	2.18589e10i	1.08223	+	0.908099i
$926$	−7.73772e9	+	1.34021e10i	−0.320239	+	0.554671i
$927$	−9.95501e9	−	1.12119e10i	−0.410452	−	0.462275i
$928$	3.77979e9	+	6.54678e9i	0.155256	+	0.268912i
$929$	−6.03475e8	+	3.42247e9i	−0.0246947	+	0.140051i	−0.994662	−	0.103183i	$-0.967097\pi$
$929$	−6.03475e8	+	3.42247e9i	−0.0246947	+	0.140051i	0.969968	+	0.243234i	$0.0782083\pi$
$930$	1.13081e9	+	8.30240e7i	0.0460998	+	0.00338465i
$931$	−3.50264e9	−	1.27486e9i	−0.142256	−	0.0517770i
$932$	−1.25691e10	−	4.57480e9i	−0.508569	−	0.185104i
$933$	7.73488e9	+	5.67895e8i	0.311794	+	0.0228919i
$934$	−5.16422e9	+	2.92877e10i	−0.207391	+	1.17617i
$935$	2.94692e8	+	5.10421e8i	0.0117904	+	0.0204215i
$936$	−3.35121e8	+	1.00751e9i	−0.0133578	+	0.0401593i
$937$	8.85315e9	−	1.53341e10i	0.351568	−	0.608933i	−0.634957	−	0.772548i	$-0.718982\pi$
$937$	8.85315e9	−	1.53341e10i	0.351568	−	0.608933i	0.986524	+	0.163615i	$0.0523153\pi$
$938$	−2.29261e10	−	1.92373e10i	−0.907029	−	0.761088i
$939$	3.69403e9	+	3.63616e10i	0.145603	+	1.43322i
$940$	8.85170e8	+	5.02005e9i	0.0347600	+	0.197134i
$941$	3.54542e10	−	2.97496e10i	1.38709	−	1.16390i	0.420584	−	0.907254i	$-0.361825\pi$
$941$	3.54542e10	−	2.97496e10i	1.38709	−	1.16390i	0.966504	−	0.256651i	$-0.0826192\pi$
$942$	1.17615e10	+	1.14372e10i	0.458442	+	0.445802i
$943$	−8.42428e9	+	3.06619e9i	−0.327146	+	0.119071i
$944$	−6.56359e9			−0.253945
$945$	−4.29766e9	−	1.37116e10i	−0.165661	−	0.528540i
$946$	8.04115e8			0.0308816
$947$	−3.88152e10	+	1.41276e10i	−1.48517	+	0.540559i	−0.952174	−	0.305557i	$-0.901157\pi$
$947$	−3.88152e10	+	1.41276e10i	−1.48517	+	0.540559i	−0.532999	+	0.846116i	$0.678935\pi$
$948$	−2.95213e9	+	1.16674e10i	−0.112540	+	0.444781i
$949$	−3.23812e9	+	2.71710e9i	−0.122987	+	0.103199i
$950$	−1.03800e9	−	5.88680e9i	−0.0392794	−	0.222765i
$951$	−3.07258e10	−	1.38082e10i	−1.15844	−	0.520600i
$952$	3.52540e9	+	2.95816e9i	0.132428	+	0.111120i
$953$	−4.94545e9	+	8.56578e9i	−0.185089	+	0.320584i	−0.943607	−	0.331069i	$-0.892591\pi$
$953$	−4.94545e9	+	8.56578e9i	−0.185089	+	0.320584i	0.758517	+	0.651653i	$0.225924\pi$
$954$	8.81709e9	−	1.11251e10i	0.328781	−	0.414844i
$955$	−4.50870e9	−	7.80930e9i	−0.167510	−	0.290135i
$956$	−2.15780e9	+	1.22375e10i	−0.0798745	+	0.452991i
$957$	−2.46727e9	−	5.10360e9i	−0.0909966	−	0.188228i
$958$	−1.08060e10	−	3.93306e9i	−0.397087	−	0.144528i
$959$	−9.58579e9	−	3.48894e9i	−0.350964	−	0.127740i
$960$	−9.12406e8	+	1.34261e9i	−0.0332843	+	0.0489779i
$961$	−4.68655e9	+	2.65787e10i	−0.170342	+	0.966056i
$962$	−2.12877e9	−	3.68713e9i	−0.0770930	−	0.133529i
$963$	−2.66886e9	+	1.64200e9i	−0.0963016	+	0.0592492i
$964$	−6.22774e9	+	1.07868e10i	−0.223904	+	0.387812i
$965$	−1.77087e10	−	1.48594e10i	−0.634369	−	0.532298i
$966$	−1.80572e10	+	1.30237e10i	−0.644513	+	0.464852i
$967$	9.43647e9	+	5.35169e10i	0.335596	+	1.90326i	0.421268	+	0.906936i	$0.361585\pi$
$967$	9.43647e9	+	5.35169e10i	0.335596	+	1.90326i	−0.0856719	+	0.996323i	$0.527304\pi$
$968$	−7.53488e9	+	6.32251e9i	−0.267001	+	0.224040i
$969$	4.70083e9	−	1.33028e9i	0.165974	−	0.0469688i
$970$	−6.46308e9	+	2.35237e9i	−0.227373	+	0.0827569i
$971$	−3.24876e10			−1.13881			−0.569405	−	0.822057i	$-0.692826\pi$
$971$	−3.24876e10			−1.13881			−0.569405	+	0.822057i	$0.692826\pi$
$972$	−6.94118e9	−	1.25200e10i	−0.242438	−	0.437291i
$973$	−1.46005e10			−0.508128
$974$	−2.90633e9	+	1.05782e9i	−0.100783	+	0.0366821i
$975$	2.58540e9	−	7.31636e8i	0.0893328	−	0.0252801i
$976$	−1.74015e9	+	1.46016e9i	−0.0599117	+	0.0502719i
$977$	8.73586e8	+	4.95435e9i	0.0299692	+	0.169964i	0.996119	−	0.0880186i	$-0.0280535\pi$
$977$	8.73586e8	+	4.95435e9i	0.0299692	+	0.169964i	−0.966150	+	0.257982i	$0.916942\pi$
$978$	2.46978e10	−	1.78132e10i	0.844252	−	0.608913i
$979$	1.11466e8	+	9.35310e7i	0.00379667	+	0.00318578i
$980$	1.28076e9	−	2.21834e9i	0.0434686	−	0.0752898i
$981$	−1.50866e10	+	9.28199e9i	−0.510212	+	0.313906i
$982$	1.12354e10	+	1.94603e10i	0.378615	+	0.655781i
$983$	9.77936e9	−	5.54615e10i	0.328377	−	1.86232i	−0.156417	−	0.987691i	$-0.549994\pi$
$983$	9.77936e9	−	5.54615e10i	0.328377	−	1.86232i	0.484794	−	0.874628i	$-0.338895\pi$
$984$	2.15118e9	−	3.16547e9i	0.0719771	−	0.105915i
$985$	2.44199e10	+	8.88812e9i	0.814174	+	0.296335i
$986$	1.46918e10	+	5.34739e9i	0.488098	+	0.177653i
$987$	−1.29907e10	−	2.68716e10i	−0.430054	−	0.889575i
$988$	−1.29955e8	+	7.37013e8i	−0.00428691	+	0.0243123i
$989$	−5.36466e9	−	9.29186e9i	−0.176342	−	0.305433i
$990$	7.56069e8	−	9.53982e8i	0.0247650	−	0.0312476i
$991$	2.59366e9	−	4.49235e9i	0.0846556	−	0.146628i	−0.820589	−	0.571519i	$-0.806354\pi$
$991$	2.59366e9	−	4.49235e9i	0.0846556	−	0.146628i	0.905244	+	0.424891i	$0.139688\pi$
$992$	5.74531e8	+	4.82088e8i	0.0186863	+	0.0156796i
$993$	2.04776e10	+	9.20263e9i	0.663677	+	0.298256i
$994$	−5.86907e8	−	3.32851e9i	−0.0189547	−	0.107497i
$995$	−1.28949e10	+	1.08201e10i	−0.414991	+	0.348219i
$996$	−6.75803e9	+	2.67092e10i	−0.216727	+	0.856550i
$997$	−8.86011e9	+	3.22482e9i	−0.283143	+	0.103056i	−0.479688	−	0.877439i	$-0.659250\pi$
$997$	−8.86011e9	+	3.22482e9i	−0.283143	+	0.103056i	0.196545	+	0.980495i	$0.437028\pi$
$998$	3.17796e10			1.01202
$999$	5.60195e10	+	1.25192e10i	1.77771	+	0.397279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.e.a.7.10	✓	60
27.4	even	9	inner	54.8.e.a.31.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.e.a.7.10	✓	60	1.1	even	1	trivial
54.8.e.a.31.10	yes	60	27.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.51754 + 2.73616i) q^{2} +(44.9983 - 12.7340i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-22.9934 - 130.402i) q^{5} +(-303.434 + 218.851i) q^{6} +(812.804 + 682.023i) q^{7} +(-256.000 + 443.405i) q^{8} +(1862.69 - 1146.01i) q^{9} +(529.655 + 917.389i) q^{10} +(91.2393 - 517.444i) q^{11} +(1682.27 - 2475.46i) q^{12} +(891.055 + 324.317i) q^{13} +(-7976.41 - 2903.18i) q^{14} +(-2695.20 - 5575.07i) q^{15} +(711.263 - 4033.77i) q^{16} +(-4235.68 - 7336.41i) q^{17} +(-10867.2 + 13711.8i) q^{18} +(-6165.88 + 10679.6i) q^{19} +(-6491.83 - 5447.29i) q^{20} +(45259.6 + 20339.7i) q^{21} +(729.914 + 4139.55i) q^{22} +(42964.5 - 36051.5i) q^{23} +(-5873.25 + 23212.4i) q^{24} +(56937.5 - 20723.6i) q^{25} -7585.93 q^{26} +(69224.6 - 75288.1i) q^{27} +67906.5 q^{28} +(216787. - 78904.0i) q^{29} +(35515.6 + 34536.3i) q^{30} +(17533.3 - 14712.2i) q^{31} +(5690.10 + 32270.2i) q^{32} +(-2483.50 - 24445.9i) q^{33} +(51915.5 + 43562.3i) q^{34} +(70248.1 - 121673. i) q^{35} +(44176.7 - 132814. i) q^{36} +(280620. + 486049. i) q^{37} +(17131.1 - 97155.3i) q^{38} +(44225.8 + 3247.06i) q^{39} +(63707.2 + 23187.5i) q^{40} +(-150203. - 54669.3i) q^{41} +(-395894. - 29066.5i) q^{42} +(33219.0 - 188394. i) q^{43} +(-16813.6 - 29122.1i) q^{44} +(-192272. - 216548. i) q^{45} +(-224344. + 388576. i) q^{46} +(-460784. - 386644. i) q^{47} +(-19360.3 - 190570. i) q^{48} +(52487.3 + 297670. i) q^{49} +(-371327. + 311580. i) q^{50} +(-284020. - 276189. i) q^{51} +(57027.5 - 20756.3i) q^{52} -811351. q^{53} +(-314398. + 755391. i) q^{54} -69573.6 q^{55} +(-510490. + 185803. i) q^{56} +(-141460. + 559081. i) q^{57} +(-1.41381e6 + 1.18633e6i) q^{58} +(-278261. - 1.57809e6i) q^{59} +(-361487. - 162452. i) q^{60} +(-424841. - 356484. i) q^{61} +(-91552.3 + 158573. i) q^{62} +(2.29561e6 + 338915. i) q^{63} +(-131072. - 227023. i) q^{64} +(21803.3 - 123653. i) q^{65} +(85557.8 + 176978. i) q^{66} +(3.31315e6 + 1.20589e6i) q^{67} +(-509470. - 185432. i) q^{68} +(1.47425e6 - 2.16936e6i) q^{69} +(-195175. + 1.10689e6i) q^{70} +(199089. + 344832. i) q^{71} +(31299.3 + 1.11931e6i) q^{72} +(-2.22890e6 + 3.86056e6i) q^{73} +(-3.43948e6 - 2.88607e6i) q^{74} +(2.29820e6 - 1.65756e6i) q^{75} +(137049. + 777243. i) q^{76} +(427068. - 358353. i) q^{77} +(-341354. + 96599.0i) q^{78} +(-3.77861e6 + 1.37530e6i) q^{79} -542367. q^{80} +(2.15627e6 - 4.26934e6i) q^{81} +1.27874e6 q^{82} +(-8.65002e6 + 3.14835e6i) q^{83} +(3.05568e6 - 864720. i) q^{84} +(-859291. + 721030. i) q^{85} +(265752. + 1.50716e6i) q^{86} +(8.75028e6 - 6.31110e6i) q^{87} +(206080. + 172922. i) q^{88} +(-138467. + 239832. i) q^{89} +(2.03792e6 + 1.10182e6i) q^{90} +(503061. + 871326. i) q^{91} +(623312. - 3.53498e6i) q^{92} +(601623. - 885291. i) q^{93} +(4.52188e6 + 1.64583e6i) q^{94} +(1.53442e6 + 558483. i) q^{95} +(666973. + 1.37965e6i) q^{96} +(-1.12746e6 + 6.39414e6i) q^{97} +(-1.20905e6 - 2.09413e6i) q^{98} +(-423047. - 1.06840e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 213 q^{5} - 72 q^{6} + 1677 q^{7} - 15360 q^{8} - 3024 q^{9} + 3000 q^{10} - 15744 q^{11} + 2880 q^{12} + 9924 q^{13} + 13416 q^{14} + 2322 q^{15} + 29478 q^{17} + 49680 q^{18} + 61731 q^{19} - 27264 q^{20}+ \cdots + 36391797 q^{99}+O(q^{100}) \) 60 * q + 213 * q^5 - 72 * q^6 + 1677 * q^7 - 15360 * q^8 - 3024 * q^9 + 3000 * q^10 - 15744 * q^11 + 2880 * q^12 + 9924 * q^13 + 13416 * q^14 + 2322 * q^15 + 29478 * q^17 + 49680 * q^18 + 61731 * q^19 - 27264 * q^20 + 160884 * q^21 - 125952 * q^22 + 29478 * q^23 - 343017 * q^25 - 316368 * q^26 - 524124 * q^27 - 263424 * q^28 + 132153 * q^29 + 292824 * q^30 - 1372860 * q^31 - 1065834 * q^33 - 121656 * q^34 - 321081 * q^35 - 369216 * q^36 + 759795 * q^37 + 224760 * q^38 - 2283894 * q^39 + 109056 * q^40 + 704616 * q^41 + 527400 * q^42 + 2124585 * q^43 + 255552 * q^44 + 3259908 * q^45 + 524472 * q^46 + 3452931 * q^47 + 552960 * q^48 - 1987017 * q^49 + 190152 * q^50 + 5107401 * q^51 + 635136 * q^52 - 2951976 * q^53 + 1065312 * q^54 - 2539854 * q^55 + 858624 * q^56 + 5722920 * q^57 + 47496 * q^58 + 3732204 * q^59 + 2512512 * q^60 - 5504796 * q^61 + 2859936 * q^62 + 1888047 * q^63 - 7864320 * q^64 - 803499 * q^65 - 9421632 * q^66 - 7979400 * q^67 - 5893440 * q^68 - 629100 * q^69 + 1111128 * q^70 + 3531612 * q^71 + 3096576 * q^72 - 875661 * q^73 + 15158904 * q^74 + 26002422 * q^75 + 1798080 * q^76 + 5672523 * q^77 - 13012848 * q^78 - 10290369 * q^79 - 3072000 * q^80 - 42838956 * q^81 - 3798096 * q^82 - 16555878 * q^83 + 2005056 * q^84 + 30956175 * q^85 + 16996680 * q^86 + 22863879 * q^87 + 2509824 * q^88 + 32327814 * q^89 + 34182072 * q^90 + 1976658 * q^91 - 1108608 * q^92 - 17967789 * q^93 - 24396768 * q^94 - 35592135 * q^95 - 2949120 * q^96 - 25380039 * q^97 - 15123648 * q^98 + 36391797 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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