LMFDB - Embedded newform 63.3.k.a.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(31,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.k (of order $6$, degree $2$, 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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	63.61
Dual form			63.3.k.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32841 - 2.30087i) q^{2} +(0.187748 + 2.99412i) q^{3} +(-1.52933 + 2.64888i) q^{4} +9.20400i q^{5} +(6.63967 - 4.40939i) q^{6} +(6.96620 - 0.687028i) q^{7} -2.50096 q^{8} +(-8.92950 + 1.12428i) q^{9} +O(q^{10})$	\(q+(-1.32841 - 2.30087i) q^{2} +(0.187748 + 2.99412i) q^{3} +(-1.52933 + 2.64888i) q^{4} +9.20400i q^{5} +(6.63967 - 4.40939i) q^{6} +(6.96620 - 0.687028i) q^{7} -2.50096 q^{8} +(-8.92950 + 1.12428i) q^{9} +(21.1772 - 12.2267i) q^{10} +7.05467 q^{11} +(-8.21819 - 4.08168i) q^{12} +(4.15930 - 2.40137i) q^{13} +(-10.8347 - 15.1157i) q^{14} +(-27.5579 + 1.72803i) q^{15} +(9.43962 + 16.3499i) q^{16} +(-2.74329 + 1.58384i) q^{17} +(14.4488 + 19.0521i) q^{18} +(1.70864 + 0.986484i) q^{19} +(-24.3803 - 14.0760i) q^{20} +(3.36493 + 20.7287i) q^{21} +(-9.37147 - 16.2319i) q^{22} -5.02797 q^{23} +(-0.469549 - 7.48818i) q^{24} -59.7137 q^{25} +(-11.0505 - 6.38000i) q^{26} +(-5.04271 - 26.5249i) q^{27} +(-8.83378 + 19.5033i) q^{28} +(22.9425 - 39.7376i) q^{29} +(40.5841 + 61.1116i) q^{30} +(13.2265 + 7.63630i) q^{31} +(20.0774 - 34.7751i) q^{32} +(1.32450 + 21.1225i) q^{33} +(7.28840 + 4.20796i) q^{34} +(6.32341 + 64.1170i) q^{35} +(10.6781 - 25.3726i) q^{36} +(17.6998 - 30.6570i) q^{37} -5.24181i q^{38} +(7.97089 + 12.0026i) q^{39} -23.0189i q^{40} +(48.4509 - 27.9732i) q^{41} +(43.2239 - 35.2784i) q^{42} +(-3.45068 + 5.97676i) q^{43} +(-10.7889 + 18.6870i) q^{44} +(-10.3479 - 82.1872i) q^{45} +(6.67920 + 11.5687i) q^{46} +(-44.4658 + 25.6723i) q^{47} +(-47.1813 + 31.3330i) q^{48} +(48.0560 - 9.57195i) q^{49} +(79.3241 + 137.393i) q^{50} +(-5.25724 - 7.91637i) q^{51} +14.6900i q^{52} +(-10.3556 - 17.9365i) q^{53} +(-54.3316 + 46.8385i) q^{54} +64.9312i q^{55} +(-17.4222 + 1.71823i) q^{56} +(-2.63286 + 5.30108i) q^{57} -121.908 q^{58} +(-42.7391 - 24.6754i) q^{59} +(37.5678 - 75.6402i) q^{60} +(1.99551 - 1.15211i) q^{61} -40.5764i q^{62} +(-61.4323 + 13.9668i) q^{63} -31.1668 q^{64} +(22.1022 + 38.2822i) q^{65} +(46.8406 - 31.1068i) q^{66} +(-15.4139 + 26.6977i) q^{67} -9.68884i q^{68} +(-0.943990 - 15.0544i) q^{69} +(139.125 - 99.7228i) q^{70} +81.2604 q^{71} +(22.3323 - 2.81177i) q^{72} +(-61.7481 + 35.6503i) q^{73} -94.0503 q^{74} +(-11.2111 - 178.790i) q^{75} +(-5.22615 + 3.01732i) q^{76} +(49.1442 - 4.84675i) q^{77} +(17.0278 - 34.2843i) q^{78} +(14.5179 + 25.1458i) q^{79} +(-150.485 + 86.8823i) q^{80} +(78.4720 - 20.0785i) q^{81} +(-128.725 - 74.3195i) q^{82} +(55.9283 + 32.2902i) q^{83} +(-60.0538 - 22.7877i) q^{84} +(-14.5776 - 25.2492i) q^{85} +18.3357 q^{86} +(123.287 + 61.2320i) q^{87} -17.6434 q^{88} +(89.0979 + 51.4407i) q^{89} +(-175.356 + 132.987i) q^{90} +(27.3247 - 19.5860i) q^{91} +(7.68944 - 13.3185i) q^{92} +(-20.3808 + 41.0353i) q^{93} +(118.137 + 68.2067i) q^{94} +(-9.07960 + 15.7263i) q^{95} +(107.890 + 53.5852i) q^{96} +(-48.7891 - 28.1684i) q^{97} +(-85.8617 - 97.8551i) q^{98} +(-62.9946 + 7.93140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9}+O(q^{10}) $ 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} - 6 q^{10} - 14 q^{11} - 3 q^{12} + 15 q^{13} - 11 q^{14} - 18 q^{15} - 27 q^{16} - 33 q^{17} + 33 q^{18} - 6 q^{19} + 108 q^{20} + 12 q^{21} - 10 q^{22} - 68 q^{23} + 42 q^{24} - 62 q^{25} + 54 q^{26} - 81 q^{27} - 16 q^{28} + 70 q^{29} - 6 q^{30} + 45 q^{31} + 153 q^{32} - 114 q^{33} + 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} - 120 q^{39} - 234 q^{41} - 51 q^{42} + 30 q^{43} + 51 q^{44} + 276 q^{45} - 22 q^{46} - 111 q^{47} + 147 q^{48} + 34 q^{49} + 241 q^{50} - 6 q^{51} + 148 q^{53} + 378 q^{54} - 412 q^{56} + 189 q^{57} - 34 q^{58} + 42 q^{59} + 456 q^{60} + 120 q^{61} - 222 q^{63} - 48 q^{64} + 114 q^{65} - 447 q^{66} - 34 q^{67} + 78 q^{69} + 264 q^{70} - 350 q^{71} - 339 q^{72} - 6 q^{73} - 718 q^{74} - 123 q^{75} + 72 q^{76} - 32 q^{77} - 375 q^{78} - 82 q^{79} - 609 q^{80} - 3 q^{81} - 18 q^{82} + 738 q^{83} + 609 q^{84} + 3 q^{85} - 34 q^{86} + 3 q^{87} - 50 q^{88} + 21 q^{89} - 543 q^{90} + 39 q^{91} + 288 q^{92} + 252 q^{93} - 3 q^{94} + 507 q^{95} - 582 q^{96} - 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * q^96 - 57 * q^97 + 811 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.32841	−	2.30087i	−0.664204	−	1.15043i	−0.979501	−	0.201441i	$-0.935437\pi$
$2$	−1.32841	−	2.30087i	−0.664204	−	1.15043i	0.315297	−	0.948993i	$-0.397896\pi$
$3$	0.187748	+	2.99412i	0.0625825	+	0.998040i
$3$	0.187748	+	2.99412i	0.0625825	+	0.998040i
$4$	−1.52933	+	2.64888i	−0.382333	+	0.662220i
$5$			9.20400i			1.84080i	0.390977	+	0.920400i	$0.372137\pi$
$5$			9.20400i			1.84080i	−0.390977	+	0.920400i	$0.627863\pi$
$6$	6.63967	−	4.40939i	1.10661	−	0.734899i
$7$	6.96620	−	0.687028i	0.995172	−	0.0981468i
$7$	6.96620	−	0.687028i	0.995172	−	0.0981468i
$8$	−2.50096			−0.312620
$9$	−8.92950	+	1.12428i	−0.992167	+	0.124920i
$10$	21.1772	−	12.2267i	2.11772	−	1.22267i
$11$	7.05467			0.641333			0.320667	−	0.947192i	$-0.396093\pi$
$11$	7.05467			0.641333			0.320667	+	0.947192i	$0.396093\pi$
$12$	−8.21819	−	4.08168i	−0.684849	−	0.340140i
$13$	4.15930	−	2.40137i	0.319946	−	0.184721i	−0.331423	−	0.943482i	$-0.607529\pi$
$13$	4.15930	−	2.40137i	0.319946	−	0.184721i	0.651368	+	0.758762i	$0.274195\pi$
$14$	−10.8347	−	15.1157i	−0.773908	−	1.07969i
$15$	−27.5579	+	1.72803i	−1.83719	+	0.115202i
$16$	9.43962	+	16.3499i	0.589976	+	1.02187i
$17$	−2.74329	+	1.58384i	−0.161370	+	0.0931669i	−0.578510	−	0.815675i	$-0.696366\pi$
$17$	−2.74329	+	1.58384i	−0.161370	+	0.0931669i	0.417140	+	0.908842i	$0.363032\pi$
$18$	14.4488	+	19.0521i	0.802713	+	1.05845i
$19$	1.70864	+	0.986484i	0.0899284	+	0.0519202i	0.544290	−	0.838897i	$-0.316799\pi$
$19$	1.70864	+	0.986484i	0.0899284	+	0.0519202i	−0.454361	+	0.890817i	$0.650133\pi$
$20$	−24.3803	−	14.0760i	−1.21901	−	0.703798i
$21$	3.36493	+	20.7287i	0.160235	+	0.987079i
$22$	−9.37147	−	16.2319i	−0.425976	−	0.737812i
$23$	−5.02797			−0.218608			−0.109304	−	0.994008i	$-0.534862\pi$
$23$	−5.02797			−0.218608			−0.109304	+	0.994008i	$0.534862\pi$
$24$	−0.469549	−	7.48818i	−0.0195646	−	0.312007i
$25$	−59.7137			−2.38855
$26$	−11.0505	−	6.38000i	−0.425018	−	0.245384i
$27$	−5.04271	−	26.5249i	−0.186767	−	0.982404i
$28$	−8.83378	+	19.5033i	−0.315492	+	0.696547i
$29$	22.9425	−	39.7376i	0.791121	−	1.37026i	−0.134152	−	0.990961i	$-0.542831\pi$
$29$	22.9425	−	39.7376i	0.791121	−	1.37026i	0.925273	−	0.379301i	$-0.123836\pi$
$30$	40.5841	+	61.1116i	1.35280	+	2.03705i
$31$	13.2265	+	7.63630i	0.426660	+	0.246332i	0.697923	−	0.716173i	$-0.254108\pi$
$31$	13.2265	+	7.63630i	0.426660	+	0.246332i	−0.271263	+	0.962505i	$0.587441\pi$
$32$	20.0774	−	34.7751i	0.627418	−	1.08672i
$33$	1.32450	+	21.1225i	0.0401362	+	0.640076i
$34$	7.28840	+	4.20796i	0.214365	+	0.123764i
$35$	6.32341	+	64.1170i	0.180669	+	1.83191i
$36$	10.6781	−	25.3726i	0.296614	−	0.704793i
$37$	17.6998	−	30.6570i	0.478373	−	0.828567i	−0.521319	−	0.853362i	$-0.674560\pi$
$37$	17.6998	−	30.6570i	0.478373	−	0.828567i	0.999693	+	0.0247946i	$0.00789319\pi$
$38$		−	5.24181i		−	0.137942i
$39$	7.97089	+	12.0026i	0.204382	+	0.307758i
$40$		−	23.0189i		−	0.575471i
$41$	48.4509	−	27.9732i	1.18173	−	0.682272i	0.225316	−	0.974286i	$-0.427659\pi$
$41$	48.4509	−	27.9732i	1.18173	−	0.682272i	0.956414	+	0.292014i	$0.0943253\pi$
$42$	43.2239	−	35.2784i	1.02914	−	0.839961i
$43$	−3.45068	+	5.97676i	−0.0802485	+	0.138994i	−0.903357	−	0.428890i	$-0.858905\pi$
$43$	−3.45068	+	5.97676i	−0.0802485	+	0.138994i	0.823108	+	0.567885i	$0.192238\pi$
$44$	−10.7889	+	18.6870i	−0.245203	+	0.424703i
$45$	−10.3479	−	82.1872i	−0.229952	−	1.82638i
$46$	6.67920	+	11.5687i	0.145200	+	0.251494i
$47$	−44.4658	+	25.6723i	−0.946081	+	0.546220i	−0.891861	−	0.452309i	$-0.850600\pi$
$47$	−44.4658	+	25.6723i	−0.946081	+	0.546220i	−0.0542197	+	0.998529i	$0.517267\pi$
$48$	−47.1813	+	31.3330i	−0.982943	+	0.652771i
$49$	48.0560	−	9.57195i	0.980734	−	0.195346i
$50$	79.3241	+	137.393i	1.58648	+	2.74787i
$51$	−5.25724	−	7.91637i	−0.103083	−	0.155223i
$52$			14.6900i			0.282499i
$53$	−10.3556	−	17.9365i	−0.195390	−	0.338425i	0.751639	−	0.659575i	$-0.229264\pi$
$53$	−10.3556	−	17.9365i	−0.195390	−	0.338425i	−0.947028	+	0.321151i	$0.895930\pi$
$54$	−54.3316	+	46.8385i	−1.00614	+	0.867380i
$55$			64.9312i			1.18057i
$56$	−17.4222	+	1.71823i	−0.311111	+	0.0306827i
$57$	−2.63286	+	5.30108i	−0.0461905	+	0.0930014i
$58$	−121.908			−2.10186
$59$	−42.7391	−	24.6754i	−0.724391	−	0.418227i	0.0919759	−	0.995761i	$-0.470682\pi$
$59$	−42.7391	−	24.6754i	−0.724391	−	0.418227i	−0.816367	+	0.577534i	$0.804015\pi$
$60$	37.5678	−	75.6402i	0.626130	−	1.26067i
$61$	1.99551	−	1.15211i	0.0327133	−	0.0188871i	−0.483554	−	0.875314i	$-0.660654\pi$
$61$	1.99551	−	1.15211i	0.0327133	−	0.0188871i	0.516267	+	0.856427i	$0.327321\pi$
$62$		−	40.5764i		−	0.654459i
$63$	−61.4323	+	13.9668i	−0.975116	+	0.221695i
$64$	−31.1668			−0.486982
$65$	22.1022	+	38.2822i	0.340034	+	0.588957i
$66$	46.8406	−	31.1068i	0.709707	−	0.471315i
$67$	−15.4139	+	26.6977i	−0.230059	+	0.398473i	−0.957825	−	0.287352i	$-0.907225\pi$
$67$	−15.4139	+	26.6977i	−0.230059	+	0.398473i	0.727766	+	0.685825i	$0.240558\pi$
$68$		−	9.68884i		−	0.142483i
$69$	−0.943990	−	15.0544i	−0.0136810	−	0.218179i
$70$	139.125	−	99.7228i	1.98750	−	1.42461i
$71$	81.2604			1.14451			0.572256	−	0.820075i	$-0.306068\pi$
$71$	81.2604			1.14451			0.572256	+	0.820075i	$0.306068\pi$
$72$	22.3323	−	2.81177i	0.310171	−	0.0390524i
$73$	−61.7481	+	35.6503i	−0.845864	+	0.488360i	−0.859253	−	0.511551i	$-0.829071\pi$
$73$	−61.7481	+	35.6503i	−0.845864	+	0.488360i	0.0133893	+	0.999910i	$0.495738\pi$
$74$	−94.0503			−1.27095
$75$	−11.2111	−	178.790i	−0.149481	−	2.38387i
$76$	−5.22615	+	3.01732i	−0.0687651	+	0.0397016i
$77$	49.1442	−	4.84675i	0.638237	−	0.0629448i
$78$	17.0278	−	34.2843i	0.218305	−	0.439542i
$79$	14.5179	+	25.1458i	0.183771	+	0.318301i	0.943162	−	0.332334i	$-0.107836\pi$
$79$	14.5179	+	25.1458i	0.183771	+	0.318301i	−0.759391	+	0.650635i	$0.774503\pi$
$80$	−150.485	+	86.8823i	−1.88106	+	1.08603i
$81$	78.4720	−	20.0785i	0.968790	−	0.247882i
$82$	−128.725	−	74.3195i	−1.56982	−	0.906335i
$83$	55.9283	+	32.2902i	0.673835	+	0.389039i	0.797528	−	0.603282i	$-0.206140\pi$
$83$	55.9283	+	32.2902i	0.673835	+	0.389039i	−0.123693	+	0.992321i	$0.539474\pi$
$84$	−60.0538	−	22.7877i	−0.714926	−	0.271282i
$85$	−14.5776	−	25.2492i	−0.171502	−	0.297050i
$86$	18.3357			0.213205
$87$	123.287	+	61.2320i	1.41709	+	0.703816i
$88$	−17.6434			−0.200494
$89$	89.0979	+	51.4407i	1.00110	+	0.577985i	0.908574	−	0.417725i	$-0.137172\pi$
$89$	89.0979	+	51.4407i	1.00110	+	0.577985i	0.0925265	+	0.995710i	$0.470506\pi$
$90$	−175.356	+	132.987i	−1.94840	+	1.47763i
$91$	27.3247	−	19.5860i	0.300271	−	0.215231i
$92$	7.68944	−	13.3185i	0.0835808	−	0.144766i
$93$	−20.3808	+	41.0353i	−0.219148	+	0.441240i
$94$	118.137	+	68.2067i	1.25678	+	0.725603i
$95$	−9.07960	+	15.7263i	−0.0955747	+	0.165540i
$96$	107.890	+	53.5852i	1.12386	+	0.558179i
$97$	−48.7891	−	28.1684i	−0.502981	−	0.290396i	0.226963	−	0.973903i	$-0.427120\pi$
$97$	−48.7891	−	28.1684i	−0.502981	−	0.290396i	−0.729944	+	0.683507i	$0.760454\pi$
$98$	−85.8617	−	97.8551i	−0.876140	−	0.998521i
$99$	−62.9946	+	7.93140i	−0.636310	+	0.0801151i
$100$	91.3220	−	158.174i	0.913220	−	1.58174i
$101$		−	111.997i		−	1.10888i	−0.832223	−	0.554442i	$-0.812932\pi$
$101$		−	111.997i		−	1.10888i	0.832223	−	0.554442i	$-0.187068\pi$
$102$	−11.2308	+	22.6124i	−0.110105	+	0.221690i
$103$			86.5479i			0.840271i	0.907461	+	0.420136i	$0.138018\pi$
$103$			86.5479i			0.840271i	−0.907461	+	0.420136i	$0.861982\pi$
$104$	−10.4022	+	6.00573i	−0.100022	+	0.0577474i
$105$	−190.787	+	30.9708i	−1.81702	+	0.294960i
$106$	−27.5130	+	47.6540i	−0.259557	+	0.449566i
$107$	−25.4526	+	44.0852i	−0.237875	+	0.412012i	−0.960104	−	0.279642i	$-0.909784\pi$
$107$	−25.4526	+	44.0852i	−0.237875	+	0.412012i	0.722229	+	0.691654i	$0.243118\pi$
$108$	77.9733	+	27.2078i	0.721975	+	0.251924i
$109$	21.9214	+	37.9690i	0.201114	+	0.348340i	0.948888	−	0.315614i	$-0.102211\pi$
$109$	21.9214	+	37.9690i	0.201114	+	0.348340i	−0.747774	+	0.663954i	$0.768877\pi$
$110$	149.398	−	86.2550i	1.35816	−	0.784137i
$111$	95.1138	+	47.2396i	0.856881	+	0.425582i
$112$	76.9911	+	107.411i	0.687421	+	0.959031i
$113$	−53.2988	−	92.3163i	−0.471671	−	0.816959i	0.527803	−	0.849367i	$-0.323016\pi$
$113$	−53.2988	−	92.3163i	−0.471671	−	0.816959i	−0.999475	+	0.0324080i	$0.989682\pi$
$114$	15.6946	−	0.984136i	0.137672	−	0.00863278i
$115$		−	46.2775i		−	0.402413i
$116$	70.1734	+	121.544i	0.604943	+	1.04779i
$117$	−34.4406	+	26.1192i	−0.294364	+	0.223241i
$118$			131.116i			1.11115i
$119$	−18.0222	+	12.9180i	−0.151447	+	0.108555i
$120$	68.9212	−	4.32173i	0.574343	−	0.0360144i
$121$	−71.2317			−0.588692
$122$	−5.30171	−	3.06094i	−0.0434566	−	0.0250897i
$123$	92.8515	+	139.816i	0.754890	+	1.13672i
$124$	−40.4553	+	23.3568i	−0.326252	+	0.188362i
$125$		−	319.505i		−	2.55604i
$126$	113.743	+	122.794i	0.902721	+	0.974557i
$127$	−184.052			−1.44923			−0.724614	−	0.689155i	$-0.757982\pi$
$127$	−184.052			−1.44923			−0.724614	+	0.689155i	$0.757982\pi$
$128$	−38.9073	−	67.3894i	−0.303963	−	0.526480i
$129$	−18.5430	−	9.20964i	−0.143744	−	0.0713925i
$130$	58.7215	−	101.709i	0.451704	−	0.782374i
$131$		−	7.27407i		−	0.0555272i	−0.999615	−	0.0277636i	$-0.991161\pi$
$131$		−	7.27407i		−	0.0555272i	0.999615	−	0.0277636i	$-0.00883857\pi$
$132$	−57.9766	−	28.7949i	−0.439216	−	0.218143i
$133$	12.5805	+	5.69816i	0.0945900	+	0.0428433i
$134$	81.9039			0.611223
$135$	244.135	−	46.4131i	1.80841	−	0.343801i
$136$	6.86085	−	3.96111i	0.0504474	−	0.0291258i
$137$	−47.2720			−0.345051			−0.172526	−	0.985005i	$-0.555193\pi$
$137$	−47.2720			−0.345051			−0.172526	+	0.985005i	$0.555193\pi$
$138$	−33.3841	+	22.1703i	−0.241914	+	0.160654i
$139$	219.353	−	126.643i	1.57808	−	0.911103i	0.582948	−	0.812509i	$-0.301899\pi$
$139$	219.353	−	126.643i	1.57808	−	0.911103i	0.995128	−	0.0985934i	$-0.0314343\pi$
$140$	−179.509	−	81.3061i	−1.28220	−	0.580758i
$141$	−85.2144	−	128.316i	−0.604358	−	0.910043i
$142$	−107.947	−	186.970i	−0.760190	−	1.31669i
$143$	29.3424	−	16.9409i	0.205192	−	0.118468i
$144$	−102.673	−	135.384i	−0.713006	−	0.940165i
$145$	365.745	+	211.163i	2.52238	+	1.45630i
$146$	164.053	+	94.7161i	1.12365	+	0.648741i
$147$	37.6819	+	142.088i	0.256340	+	0.966587i
$148$	54.1378	+	93.7693i	0.365796	+	0.633577i
$149$	−256.844			−1.72378			−0.861892	−	0.507092i	$-0.830720\pi$
$149$	−256.844			−1.72378			−0.861892	+	0.507092i	$0.830720\pi$
$150$	−396.479	+	263.301i	−2.64320	+	1.75534i
$151$	−118.386			−0.784016			−0.392008	−	0.919962i	$-0.628220\pi$
$151$	−118.386			−0.784016			−0.392008	+	0.919962i	$0.628220\pi$
$152$	−4.27324	−	2.46716i	−0.0281134	−	0.0162313i
$153$	22.7155	−	17.2271i	0.148467	−	0.112595i
$154$	−76.4353	−	106.636i	−0.496333	−	0.692441i
$155$	−70.2845	+	121.736i	−0.453448	+	0.785396i
$156$	−43.9835	+	2.75800i	−0.281945	+	0.0176795i
$157$	−44.1884	−	25.5122i	−0.281455	−	0.162498i	0.352627	−	0.935764i	$-0.385288\pi$
$157$	−44.1884	−	25.5122i	−0.281455	−	0.162498i	−0.634082	+	0.773266i	$0.718622\pi$
$158$	38.5714	−	66.8077i	0.244123	−	0.422833i
$159$	51.7598	−	34.3736i	0.325533	−	0.216186i
$160$	320.070	+	184.792i	2.00044	+	1.15495i
$161$	−35.0259	+	3.45436i	−0.217552	+	0.0214556i
$162$	−150.441	−	153.881i	−0.928646	−	0.949885i
$163$	143.157	−	247.955i	0.878263	−	1.52120i	0.0250163	−	0.999687i	$-0.492036\pi$
$163$	143.157	−	247.955i	0.878263	−	1.52120i	0.853246	−	0.521508i	$-0.174630\pi$
$164$			171.121i			1.04342i
$165$	−194.412	+	12.1907i	−1.17825	+	0.0738828i
$166$		−	171.578i		−	1.03360i
$167$	−162.132	+	93.6068i	−0.970848	+	0.560519i	−0.899495	−	0.436932i	$-0.856065\pi$
$167$	−162.132	+	93.6068i	−0.970848	+	0.560519i	−0.0713535	+	0.997451i	$0.522732\pi$
$168$	−8.41556	−	51.8416i	−0.0500926	−	0.308581i
$169$	−72.9668	+	126.382i	−0.431756	+	0.747824i
$170$	−38.7301	+	67.0825i	−0.227824	+	0.394603i
$171$	−16.3664	−	6.88782i	−0.0957098	−	0.0402797i
$172$	−10.5545	−	18.2809i	−0.0613632	−	0.106284i
$173$	−128.939	+	74.4430i	−0.745313	+	0.430306i	−0.823998	−	0.566593i	$-0.808261\pi$
$173$	−128.939	+	74.4430i	−0.745313	+	0.430306i	0.0786851	+	0.996900i	$0.474928\pi$
$174$	−22.8879	−	365.007i	−0.131540	−	2.09774i
$175$	−415.978	+	41.0250i	−2.37702	+	0.234428i
$176$	66.5933	+	115.343i	0.378371	+	0.655358i
$177$	65.8570	−	132.599i	0.372073	−	0.749144i
$178$		−	273.337i		−	1.53560i
$179$	98.1713	+	170.038i	0.548443	+	0.949931i	0.998381	+	0.0568718i	$0.0181126\pi$
$179$	98.1713	+	170.038i	0.548443	+	0.949931i	−0.449938	+	0.893060i	$0.648554\pi$
$180$	233.529	+	98.2812i	1.29738	+	0.546007i
$181$			80.6783i			0.445736i	0.974849	+	0.222868i	$0.0715419\pi$
$181$			80.6783i			0.445736i	−0.974849	+	0.222868i	$0.928458\pi$
$182$	−81.3631	−	36.8524i	−0.447050	−	0.202486i
$183$	3.82421	+	5.75850i	0.0208973	+	0.0314672i
$184$	12.5748			0.0683411
$185$	282.167	+	162.909i	1.52523	+	0.880590i
$186$	121.491	−	7.61813i	0.653176	−	0.0409577i
$187$	−19.3530	+	11.1734i	−0.103492	+	0.0597510i
$188$		−	157.046i		−	0.835351i
$189$	−53.3519	−	181.313i	−0.282285	−	0.959331i
$190$	48.2456			0.253924
$191$	−13.7811	−	23.8695i	−0.0721521	−	0.124971i	0.827692	−	0.561182i	$-0.189653\pi$
$191$	−13.7811	−	23.8695i	−0.0721521	−	0.124971i	−0.899844	+	0.436211i	$0.856320\pi$
$192$	−5.85150	−	93.3172i	−0.0304765	−	0.486027i
$193$	62.2668	−	107.849i	0.322626	−	0.558804i	−0.658403	−	0.752665i	$-0.728768\pi$
$193$	62.2668	−	107.849i	0.322626	−	0.558804i	0.981029	+	0.193861i	$0.0621012\pi$
$194$			149.676i			0.771528i
$195$	−110.472	+	73.3641i	−0.566522	+	0.376226i
$196$	−48.1386	+	141.933i	−0.245605	+	0.724149i
$197$	−115.102			−0.584274			−0.292137	−	0.956376i	$-0.594366\pi$
$197$	−115.102			−0.584274			−0.292137	+	0.956376i	$0.594366\pi$
$198$	101.932	+	134.406i	0.514806	+	0.678820i
$199$	−104.660	+	60.4253i	−0.525928	+	0.303645i	−0.739357	−	0.673314i	$-0.764870\pi$
$199$	−104.660	+	60.4253i	−0.525928	+	0.303645i	0.213429	+	0.976959i	$0.431537\pi$
$200$	149.342			0.746708
$201$	−82.8301	−	41.1387i	−0.412090	−	0.204670i
$202$	−257.691	+	148.778i	−1.27570	+	0.736524i
$203$	132.521	−	292.582i	0.652815	−	1.44129i
$204$	29.0096	−	1.81906i	0.142204	−	0.00891694i
$205$	257.465	+	445.943i	1.25593	+	2.17533i
$206$	199.135	−	114.971i	0.966677	−	0.558111i
$207$	44.8973	−	5.65284i	0.216895	−	0.0273084i
$208$	78.5243	+	45.3360i	0.377521	+	0.217962i
$209$	12.0539	+	6.95931i	0.0576741	+	0.0332981i
$210$	324.702	+	397.833i	1.54620	+	1.89444i
$211$	60.1908	+	104.254i	0.285264	+	0.494092i	0.972673	−	0.232178i	$-0.0745853\pi$
$211$	60.1908	+	104.254i	0.285264	+	0.494092i	−0.687409	+	0.726271i	$0.741252\pi$
$212$	63.3488			0.298815
$213$	15.2564	+	243.303i	0.0716265	+	1.14227i
$214$	135.246			0.631990
$215$	−55.0101	−	31.7601i	−0.255861	−	0.147721i
$216$	12.6116	+	66.3378i	0.0583872	+	0.307119i
$217$	97.3845	+	44.1091i	0.448777	+	0.203268i
$218$	58.2411	−	100.877i	0.267161	−	0.462737i
$219$	−118.334	−	178.188i	−0.540339	−	0.813643i
$220$	−171.995	−	99.3012i	−0.781795	−	0.451369i
$221$	−7.60676	+	13.1753i	−0.0344197	+	0.0596167i
$222$	−17.6577	−	281.598i	−0.0795392	−	1.26846i
$223$	−203.615	−	117.557i	−0.913072	−	0.527162i	−0.0316538	−	0.999499i	$-0.510077\pi$
$223$	−203.615	−	117.557i	−0.913072	−	0.527162i	−0.881418	+	0.472336i	$0.843411\pi$
$224$	115.972	−	256.044i	0.517731	−	1.14305i
$225$	533.214	−	67.1348i	2.36984	−	0.298377i
$226$	−141.605	+	245.267i	−0.626571	+	1.08525i
$227$			151.239i			0.666249i	0.942883	+	0.333125i	$0.108103\pi$
$227$			151.239i			0.666249i	−0.942883	+	0.333125i	$0.891897\pi$
$228$	−10.0154	−	15.0812i	−0.0439272	−	0.0661457i
$229$		−	413.986i		−	1.80780i	−0.427745	−	0.903899i	$-0.640692\pi$
$229$		−	413.986i		−	1.80780i	0.427745	−	0.903899i	$-0.359308\pi$
$230$	−106.478	+	61.4754i	−0.462950	+	0.267284i
$231$	23.7385	+	146.234i	0.102764	+	0.633046i
$232$	−57.3783	+	99.3822i	−0.247320	+	0.428372i
$233$	166.801	−	288.909i	0.715886	−	1.23995i	−0.246731	−	0.969084i	$-0.579356\pi$
$233$	166.801	−	288.909i	0.715886	−	1.23995i	0.962617	−	0.270867i	$-0.0873103\pi$
$234$	105.848	+	44.5464i	0.452342	+	0.190369i
$235$	−236.288	−	409.264i	−1.00548	−	1.74155i
$236$	130.724	−	75.4737i	0.553917	−	0.319804i
$237$	−72.5637	+	48.1894i	−0.306176	+	0.203331i
$238$	53.6635	+	24.3062i	0.225477	+	0.102127i
$239$	−104.819	−	181.552i	−0.438573	−	0.759631i	0.559007	−	0.829163i	$-0.311183\pi$
$239$	−104.819	−	181.552i	−0.438573	−	0.759631i	−0.997580	+	0.0695323i	$0.977849\pi$
$240$	−288.389	−	434.257i	−1.20162	−	1.80940i
$241$		−	227.745i		−	0.945000i	−0.881331	−	0.472500i	$-0.843352\pi$
$241$		−	227.745i		−	0.945000i	0.881331	−	0.472500i	$-0.156648\pi$
$242$	94.6247	+	163.895i	0.391011	+	0.677251i
$243$	74.8503	+	231.185i	0.308026	+	0.951378i
$244$			7.04783i			0.0288846i
$245$	88.1003	+	442.308i	0.359593	+	1.80534i
$246$	198.354	−	399.372i	0.806315	−	1.62346i
$247$	9.47565			0.0383630
$248$	−33.0788	−	19.0981i	−0.133382	−	0.0770084i
$249$	−86.1804	+	173.519i	−0.346106	+	0.696861i
$250$	−735.139	+	424.433i	−2.94056	+	1.69773i
$251$			422.578i			1.68358i	0.539808	+	0.841788i	$0.318497\pi$
$251$			422.578i			1.68358i	−0.539808	+	0.841788i	$0.681503\pi$
$252$	56.9541	−	184.087i	0.226008	−	0.730502i
$253$	−35.4707			−0.140200
$254$	244.496	+	423.479i	0.962582	+	1.66724i
$255$	72.8623	−	48.3877i	0.285734	−	0.189756i
$256$	−165.703	+	287.006i	−0.647278	+	1.12112i
$257$			87.1564i			0.339130i	0.985519	+	0.169565i	$0.0542363\pi$
$257$			87.1564i			0.339130i	−0.985519	+	0.169565i	$0.945764\pi$
$258$	3.44247	+	54.8991i	0.0133429	+	0.212787i
$259$	102.238	−	225.723i	0.394743	−	0.871518i
$260$	−135.206			−0.520025
$261$	−160.189	+	380.631i	−0.613752	+	1.45836i
$262$	−16.7367	+	9.66292i	−0.0638804	+	0.0368814i
$263$	−44.1876			−0.168014			−0.0840069	−	0.996465i	$-0.526772\pi$
$263$	−44.1876			−0.168014			−0.0840069	+	0.996465i	$0.526772\pi$
$264$	−3.31251	−	52.8266i	−0.0125474	−	0.200101i
$265$	165.088	−	95.3134i	0.622972	−	0.359673i
$266$	−3.60127	−	36.5155i	−0.0135386	−	0.137276i
$267$	−137.292	+	276.428i	−0.514201	+	1.03531i
$268$	−47.1460	−	81.6593i	−0.175918	−	0.304699i
$269$	−169.996	+	98.1474i	−0.631957	+	0.364860i	−0.781509	−	0.623893i	$-0.785550\pi$
$269$	−169.996	+	98.1474i	−0.631957	+	0.364860i	0.149553	+	0.988754i	$0.452217\pi$
$270$	−431.102	−	500.068i	−1.59667	−	1.85210i
$271$	−146.761	−	84.7324i	−0.541553	−	0.312666i	0.204155	−	0.978938i	$-0.434555\pi$
$271$	−146.761	−	84.7324i	−0.541553	−	0.312666i	−0.745708	+	0.666273i	$0.767889\pi$
$272$	−51.7912	−	29.9016i	−0.190409	−	0.109932i
$273$	63.7729	+	78.1362i	0.233600	+	0.286213i
$274$	62.7965	+	108.767i	0.229184	+	0.396959i
$275$	−421.260			−1.53186
$276$	41.3208	+	20.5226i	0.149713	+	0.0743572i
$277$	370.101			1.33610			0.668052	−	0.744114i	$-0.267128\pi$
$277$	370.101			1.33610			0.668052	+	0.744114i	$0.267128\pi$
$278$	−582.779	−	336.468i	−2.09633	−	1.21032i
$279$	−126.691	−	53.3181i	−0.454089	−	0.191104i
$280$	−15.8146	−	160.354i	−0.0564807	−	0.572693i
$281$	61.5023	−	106.525i	0.218869	−	0.379093i	−0.735593	−	0.677424i	$-0.763096\pi$
$281$	61.5023	−	106.525i	0.218869	−	0.379093i	0.954463	+	0.298331i	$0.0964298\pi$
$282$	−182.039	+	366.523i	−0.645528	+	1.29973i
$283$	130.292	+	75.2239i	0.460394	+	0.265809i	0.712210	−	0.701967i	$-0.247694\pi$
$283$	130.292	+	75.2239i	0.460394	+	0.265809i	−0.251816	+	0.967775i	$0.581028\pi$
$284$	−124.274	+	215.249i	−0.437585	+	0.757919i
$285$	−48.7912	−	24.2328i	−0.171197	−	0.0850275i
$286$	−77.9574	−	45.0087i	−0.272578	−	0.157373i
$287$	318.301	−	228.154i	1.10906	−	0.794961i
$288$	−140.184	+	333.096i	−0.486751	+	1.15658i
$289$	−139.483	+	241.592i	−0.482640	+	0.835957i
$290$		−	1122.04i		−	3.86911i
$291$	75.1795	−	151.369i	0.258349	−	0.520168i
$292$		−	218.084i		−	0.746864i
$293$	373.737	−	215.777i	1.27555	−	0.736440i	0.299525	−	0.954088i	$-0.403172\pi$
$293$	373.737	−	215.777i	1.27555	−	0.736440i	0.976027	+	0.217648i	$0.0698385\pi$
$294$	276.869	−	275.452i	0.941733	−	0.936912i
$295$	227.113	−	393.370i	0.769873	−	1.33346i
$296$	−44.2666	+	76.6719i	−0.149549	+	0.259027i
$297$	−35.5746	−	187.124i	−0.119780	−	0.630048i
$298$	341.193	+	590.964i	1.14494	+	1.98310i
$299$	−20.9128	+	12.0740i	−0.0699426	+	0.0403814i
$300$	490.738	+	243.732i	1.63579	+	0.812441i
$301$	−19.9320	+	44.0060i	−0.0662192	+	0.146199i
$302$	157.265	+	272.392i	0.520746	+	0.901959i
$303$	335.333	−	21.0272i	1.10671	−	0.0693967i
$304$			37.2481i			0.122527i
$305$	10.6040	+	18.3667i	0.0347673	+	0.0602187i
$306$	−69.8127	−	29.3808i	−0.228146	−	0.0960157i
$307$		−	157.167i		−	0.511946i	−0.966684	−	0.255973i	$-0.917604\pi$
$307$		−	157.167i		−	0.511946i	0.966684	−	0.255973i	$-0.0823958\pi$
$308$	−62.3193	+	137.589i	−0.202336	+	0.446719i
$309$	−259.135	+	16.2492i	−0.838624	+	0.0525863i
$310$	373.466			1.20473
$311$	287.358	+	165.906i	0.923982	+	0.533461i	0.884903	−	0.465775i	$-0.154224\pi$
$311$	287.358	+	165.906i	0.923982	+	0.533461i	0.0390787	+	0.999236i	$0.487558\pi$
$312$	−19.9349	−	30.0180i	−0.0638938	−	0.0962115i
$313$	353.763	−	204.245i	1.13023	−	0.652541i	0.186241	−	0.982504i	$-0.440370\pi$
$313$	353.763	−	204.245i	1.13023	−	0.652541i	0.943994	+	0.329963i	$0.107036\pi$
$314$			135.562i			0.431727i
$315$	−128.550	−	565.423i	−0.408096	−	1.79499i
$316$	−88.8108			−0.281047
$317$	−19.3727	−	33.5545i	−0.0611126	−	0.105850i	0.833850	−	0.551991i	$-0.186132\pi$
$317$	−19.3727	−	33.5545i	−0.0611126	−	0.105850i	−0.894963	+	0.446140i	$0.852798\pi$
$318$	−147.847	−	73.4304i	−0.464928	−	0.230913i
$319$	161.852	−	280.335i	0.507372	−	0.878795i
$320$		−	286.860i		−	0.896437i
$321$	−136.775	−	67.9313i	−0.426091	−	0.211624i
$322$	54.4767	+	76.0012i	0.169182	+	0.236029i
$323$	−6.24972			−0.0193490
$324$	−66.8242	+	238.569i	−0.206248	+	0.736325i
$325$	−248.367	+	143.395i	−0.764206	+	0.441215i
$326$	−760.682			−2.33338
$327$	−109.568	+	72.7639i	−0.335071	+	0.222520i
$328$	−121.174	+	69.9598i	−0.369433	+	0.213292i
$329$	−292.120	+	209.388i	−0.887904	+	0.636438i
$330$	286.307	+	431.122i	0.867597	+	1.30643i
$331$	−142.523	−	246.857i	−0.430583	−	0.745792i	0.566340	−	0.824172i	$-0.308359\pi$
$331$	−142.523	−	246.857i	−0.430583	−	0.745792i	−0.996924	+	0.0783792i	$0.975026\pi$
$332$	−171.066	+	98.7649i	−0.515259	+	0.297485i
$333$	−123.584	+	293.651i	−0.371122	+	0.881835i
$334$	430.754	+	248.696i	1.28968	+	0.744598i
$335$	−245.726	−	141.870i	−0.733510	−	0.423492i
$336$	−307.148	+	250.687i	−0.914130	+	0.746092i
$337$	298.113	+	516.347i	0.884608	+	1.53219i	0.846163	+	0.532925i	$0.178907\pi$
$337$	298.113	+	516.347i	0.884608	+	1.53219i	0.0384451	+	0.999261i	$0.487760\pi$
$338$	387.719			1.14710
$339$	266.399	−	176.915i	0.785839	−	0.521874i
$340$	89.1762			0.262283
$341$	93.3082	+	53.8715i	0.273631	+	0.157981i
$342$	5.89324	+	46.8067i	0.0172317	+	0.136862i
$343$	328.192	−	99.6959i	0.956827	−	0.290659i
$344$	8.63003	−	14.9476i	0.0250873	−	0.0434525i
$345$	138.560	−	8.68849i	0.401624	−	0.0251840i
$346$	342.567	+	197.781i	0.990079	+	0.571622i
$347$	145.285	−	251.641i	0.418690	−	0.725192i	−0.577118	−	0.816660i	$-0.695823\pi$
$347$	145.285	−	251.641i	0.418690	−	0.725192i	0.995808	+	0.0914690i	$0.0291562\pi$
$348$	−350.742	+	232.927i	−1.00788	+	0.669331i
$349$	−283.473	−	163.663i	−0.812243	−	0.468949i	0.0354909	−	0.999370i	$-0.488701\pi$
$349$	−283.473	−	163.663i	−0.812243	−	0.468949i	−0.847734	+	0.530421i	$0.822034\pi$
$350$	646.981	+	902.612i	1.84852	+	2.57889i
$351$	−84.6703	−	98.2155i	−0.241226	−	0.279816i
$352$	141.639	−	245.326i	0.402384	−	0.696950i
$353$			84.1348i			0.238342i	0.992874	+	0.119171i	$0.0380237\pi$
$353$			84.1348i			0.238342i	−0.992874	+	0.119171i	$0.961976\pi$
$354$	−392.577	+	24.6167i	−1.10897	+	0.0695387i
$355$			747.921i			2.10682i
$356$	−272.520	+	157.340i	−0.765507	+	0.441965i
$357$	−42.0618	−	51.5351i	−0.117820	−	0.144356i
$358$	260.823	−	451.759i	0.728556	−	1.26190i
$359$	−106.191	+	183.928i	−0.295796	+	0.512334i	−0.975170	−	0.221459i	$-0.928918\pi$
$359$	−106.191	+	183.928i	−0.295796	+	0.512334i	0.679374	+	0.733792i	$0.262252\pi$
$360$	25.8796	+	205.547i	0.0718877	+	0.570964i
$361$	−178.554	−	309.264i	−0.494609	−	0.856687i
$362$	185.630	−	107.174i	0.512790	−	0.296060i
$363$	−13.3736	−	213.276i	−0.0368418	−	0.587538i
$364$	10.0924	+	102.333i	0.0277264	+	0.281135i
$365$	−328.125	−	568.329i	−0.898973	−	1.55707i
$366$	8.16945	−	16.4486i	0.0223209	−	0.0449416i
$367$			419.606i			1.14334i	0.820484	+	0.571670i	$0.193704\pi$
$367$			419.606i			1.14334i	−0.820484	+	0.571670i	$0.806296\pi$
$368$	−47.4622	−	82.2069i	−0.128973	−	0.223388i
$369$	−401.193	+	304.259i	−1.08724	+	0.824549i
$370$		−	865.639i		−	2.33957i
$371$	−84.4624	−	117.835i	−0.227661	−	0.317614i
$372$	−77.5286	−	116.743i	−0.208410	−	0.313824i
$373$	−221.059			−0.592652			−0.296326	−	0.955087i	$-0.595761\pi$
$373$	−221.059			−0.592652			−0.296326	+	0.955087i	$0.595761\pi$
$374$	51.4172	+	29.6858i	0.137479	+	0.0793737i
$375$	956.637	−	59.9863i	2.55103	−	0.159963i
$376$	111.207	−	64.2055i	0.295764	−	0.170759i
$377$		−	220.374i		−	0.584546i
$378$	−346.305	+	363.614i	−0.916152	+	0.961941i
$379$	317.062			0.836575			0.418287	−	0.908315i	$-0.362631\pi$
$379$	317.062			0.836575			0.418287	+	0.908315i	$0.362631\pi$
$380$	−27.7714	−	48.1015i	−0.0730827	−	0.126583i
$381$	−34.5553	−	551.073i	−0.0906963	−	1.44639i
$382$	−36.6137	+	63.4168i	−0.0958474	+	0.166013i
$383$			277.585i			0.724766i	0.932029	+	0.362383i	$0.118037\pi$
$383$			277.585i			0.724766i	−0.932029	+	0.362383i	$0.881963\pi$
$384$	194.467	−	129.145i	0.506425	−	0.336316i
$385$	44.6095	+	452.324i	0.115869	+	1.17487i
$386$	−330.862			−0.857156
$387$	24.0934	−	57.2490i	0.0622567	−	0.147930i
$388$	149.229	−	86.1576i	0.384612	−	0.222056i
$389$	−72.4347			−0.186207			−0.0931037	−	0.995656i	$-0.529679\pi$
$389$	−72.4347			−0.186207			−0.0931037	+	0.995656i	$0.529679\pi$
$390$	315.553	+	156.724i	0.809109	+	0.401856i
$391$	13.7932	−	7.96349i	0.0352767	−	0.0203670i
$392$	−120.186	+	23.9391i	−0.306597	+	0.0610691i
$393$	21.7794	−	1.36569i	0.0554184	−	0.00347503i
$394$	152.902	+	264.834i	0.388077	+	0.672169i
$395$	−231.442	+	133.623i	−0.585929	+	0.338286i
$396$	75.3303	−	178.995i	0.190228	−	0.452007i
$397$	−590.904	−	341.158i	−1.48842	−	0.859341i	−0.488510	−	0.872558i	$-0.662459\pi$
$397$	−590.904	−	341.158i	−1.48842	−	0.859341i	−0.999913	+	0.0132172i	$0.995793\pi$
$398$	278.061	+	160.539i	0.698647	+	0.403364i
$399$	−14.6990	+	38.7373i	−0.0368397	+	0.0970858i
$400$	−563.675	−	976.313i	−1.40919	−	2.44078i
$401$	449.653			1.12133			0.560665	−	0.828043i	$-0.310546\pi$
$401$	449.653			1.12133			0.560665	+	0.828043i	$0.310546\pi$
$402$	15.3773	+	245.230i	0.0382519	+	0.610025i
$403$	73.3503			0.182011
$404$	296.667	+	171.281i	0.734324	+	0.423962i
$405$	184.802	+	722.257i	0.456302	+	1.78335i
$406$	−849.236	+	83.7542i	−2.09171	+	0.206291i
$407$	124.866	−	216.275i	0.306797	−	0.531388i
$408$	13.1482	+	19.7985i	0.0322259	+	0.0485258i
$409$	−128.958	−	74.4542i	−0.315302	−	0.182040i	0.333995	−	0.942575i	$-0.391603\pi$
$409$	−128.958	−	74.4542i	−0.315302	−	0.182040i	−0.649296	+	0.760535i	$0.724937\pi$
$410$	684.037	−	1184.79i	1.66838	−	2.88972i
$411$	−8.87521	−	141.538i	−0.0215942	−	0.344375i
$412$	−229.255	−	132.360i	−0.556444	−	0.321263i
$413$	−314.682	−	142.531i	−0.761941	−	0.345111i
$414$	−72.6483	−	95.7935i	−0.175479	−	0.231385i
$415$	−297.199	+	514.765i	−0.716143	+	1.24040i
$416$		−	192.853i		−	0.463589i
$417$	420.368	+	632.991i	1.00808	+	1.51796i
$418$		−	36.9792i		−	0.0884670i
$419$	−399.171	+	230.461i	−0.952675	+	0.550027i	−0.893911	−	0.448245i	$-0.852049\pi$
$419$	−399.171	+	230.461i	−0.952675	+	0.550027i	−0.0587641	+	0.998272i	$0.518716\pi$
$420$	209.738	−	552.735i	0.499376	−	1.31604i
$421$	−63.9001	+	110.678i	−0.151782	+	0.262894i	−0.931883	−	0.362760i	$-0.881834\pi$
$421$	−63.9001	+	110.678i	−0.151782	+	0.262894i	0.780101	+	0.625654i	$0.215168\pi$
$422$	159.916	−	276.982i	0.378947	−	0.656356i
$423$	368.195	−	279.233i	0.870437	−	0.660126i
$424$	25.8991	+	44.8585i	0.0610827	+	0.105798i
$425$	163.812	−	94.5768i	0.385440	−	0.222534i
$426$	539.542	−	358.309i	1.26653	−	0.841101i
$427$	13.1096	−	9.39681i	0.0307017	−	0.0220066i
$428$	−77.8510	−	134.842i	−0.181895	−	0.315051i
$429$	56.2319	+	84.6742i	0.131077	+	0.197376i
$430$			168.761i			0.392468i
$431$	−104.431	−	180.879i	−0.242298	−	0.419673i	0.719070	−	0.694937i	$-0.244568\pi$
$431$	−104.431	−	180.879i	−0.242298	−	0.419673i	−0.961369	+	0.275264i	$0.911235\pi$
$432$	386.078	−	332.833i	0.893700	−	0.770446i
$433$			492.194i			1.13671i	0.822784	+	0.568354i	$0.192419\pi$
$433$			492.194i			1.13671i	−0.822784	+	0.568354i	$0.807581\pi$
$434$	−27.8771	−	282.664i	−0.0642330	−	0.651299i
$435$	−563.580	+	1134.73i	−1.29559	+	2.60857i
$436$	−134.100			−0.307570
$437$	−8.59100	−	4.96001i	−0.0196590	−	0.0113501i
$438$	−252.791	+	508.977i	−0.577148	+	1.16205i
$439$	−61.0093	+	35.2237i	−0.138973	+	0.0802362i	−0.567875	−	0.823115i	$-0.692234\pi$
$439$	−61.0093	+	35.2237i	−0.138973	+	0.0802362i	0.428901	+	0.903351i	$0.358901\pi$
$440$		−	162.390i		−	0.369069i
$441$	−418.354	+	139.501i	−0.948650	+	0.316329i
$442$	40.4195			0.0914468
$443$	−358.035	−	620.135i	−0.808206	−	1.39985i	−0.914105	−	0.405477i	$-0.867105\pi$
$443$	−358.035	−	620.135i	−0.808206	−	1.39985i	0.105899	−	0.994377i	$-0.466228\pi$
$444$	−270.592	+	179.700i	−0.609442	+	0.404729i
$445$	−473.460	+	820.058i	−1.06396	+	1.84283i
$446$			624.655i			1.40057i
$447$	−48.2218	−	769.021i	−0.107879	−	1.72041i
$448$	−217.115	+	21.4125i	−0.484631	+	0.0477957i
$449$	−130.350			−0.290313			−0.145156	−	0.989409i	$-0.546369\pi$
$449$	−130.350			−0.290313			−0.145156	+	0.989409i	$0.546369\pi$
$450$	−862.793	−	1137.67i	−1.91732	−	2.52816i
$451$	341.805	−	197.341i	0.757883	−	0.437564i
$452$	326.046			0.721341
$453$	−22.2268	−	354.463i	−0.0490657	−	0.782480i
$454$	347.980	−	200.906i	0.766476	−	0.442525i
$455$	180.270	+	251.497i	0.396197	+	0.552740i
$456$	6.58467	−	13.2578i	0.0144401	−	0.0290741i
$457$	105.765	+	183.190i	0.231433	+	0.400854i	0.958230	−	0.285998i	$-0.0923252\pi$
$457$	105.765	+	183.190i	0.231433	+	0.400854i	−0.726797	+	0.686852i	$0.758992\pi$
$458$	−952.527	+	549.942i	−2.07975	+	1.20075i
$459$	55.8447	+	64.7786i	0.121666	+	0.141130i
$460$	122.583	+	70.7736i	0.266486	+	0.153856i
$461$	457.027	+	263.865i	0.991381	+	0.572374i	0.905687	−	0.423947i	$-0.139356\pi$
$461$	457.027	+	263.865i	0.991381	+	0.572374i	0.0856943	+	0.996321i	$0.472689\pi$
$462$	304.930	−	248.877i	0.660022	−	0.538695i
$463$	−367.066	−	635.777i	−0.792800	−	1.37317i	−0.924227	−	0.381843i	$-0.875289\pi$
$463$	−367.066	−	635.777i	−0.792800	−	1.37317i	0.131428	−	0.991326i	$-0.458044\pi$
$464$	866.274			1.86697
$465$	−377.689	−	187.585i	−0.812234	−	0.403408i
$466$	−886.321			−1.90198
$467$	280.938	+	162.200i	0.601581	+	0.347323i	0.769663	−	0.638450i	$-0.220424\pi$
$467$	280.938	+	162.200i	0.601581	+	0.347323i	−0.168082	+	0.985773i	$0.553757\pi$
$468$	−16.5156	−	131.174i	−0.0352897	−	0.280286i
$469$	−89.0345	+	196.571i	−0.189839	+	0.419129i
$470$	−627.774	+	1087.34i	−1.33569	+	2.31348i
$471$	68.0903	−	137.095i	0.144565	−	0.291073i
$472$	106.889	+	61.7122i	0.226459	+	0.130746i
$473$	−24.3434	+	42.1640i	−0.0514660	+	0.0891417i
$474$	207.272	+	102.944i	0.437282	+	0.217182i
$475$	−102.029	−	58.9066i	−0.214798	−	0.124014i
$476$	−6.65650	−	67.4945i	−0.0139843	−	0.141795i
$477$	112.636	+	148.521i	0.236135	+	0.311366i
$478$	−278.485	+	482.349i	−0.582604	+	1.00910i
$479$			420.527i			0.877927i	0.898505	+	0.438964i	$0.144654\pi$
$479$			420.527i			0.877927i	−0.898505	+	0.438964i	$0.855346\pi$
$480$	−493.198	+	993.021i	−1.02750	+	2.06879i
$481$		−	170.015i		−	0.353462i
$482$	−524.011	+	302.538i	−1.08716	+	0.627672i
$483$	−16.9188	−	104.223i	−0.0350285	−	0.215783i
$484$	108.937	−	188.684i	0.225076	−	0.389843i
$485$	259.262	−	449.055i	0.534561	−	0.925887i
$486$	432.494	−	479.328i	0.889906	−	0.986272i
$487$	19.3349	+	33.4890i	0.0397020	+	0.0687658i	0.885194	−	0.465223i	$-0.154026\pi$
$487$	19.3349	+	33.4890i	0.0397020	+	0.0687658i	−0.845492	+	0.533989i	$0.820692\pi$
$488$	−4.99070	+	2.88138i	−0.0102268	+	0.00590447i
$489$	769.284	+	382.076i	1.57318	+	0.781341i
$490$	900.659	−	790.272i	1.83808	−	1.61280i
$491$	435.683	+	754.625i	0.887338	+	1.53691i	0.843011	+	0.537897i	$0.180781\pi$
$491$	435.683	+	754.625i	0.887338	+	1.53691i	0.0443266	+	0.999017i	$0.485886\pi$
$492$	−512.356	+	32.1275i	−1.04137	+	0.0652998i
$493$			145.349i			0.294825i
$494$	−12.5875	−	21.8022i	−0.0254808	−	0.0441341i
$495$	−73.0006	−	579.803i	−0.147476	−	1.17132i
$496$			288.335i			0.581320i
$497$	566.077	−	55.8281i	1.13899	−	0.112330i
$498$	513.726	−	32.2134i	1.03158	−	0.0646856i
$499$	−368.253			−0.737982			−0.368991	−	0.929433i	$-0.620297\pi$
$499$	−368.253			−0.737982			−0.368991	+	0.929433i	$0.620297\pi$
$500$	846.330	+	488.629i	1.69266	+	0.977258i
$501$	−310.710	−	467.867i	−0.620179	−	0.933866i
$502$	972.296	−	561.355i	1.93684	−	1.11824i
$503$			603.853i			1.20050i	0.799811	+	0.600251i	$0.204933\pi$
$503$			603.853i			1.20050i	−0.799811	+	0.600251i	$0.795067\pi$
$504$	153.640	−	34.9303i	0.304841	−	0.0693062i
$505$	1030.82			2.04123
$506$	47.1195	+	81.6134i	0.0931215	+	0.161291i
$507$	−392.103	−	194.743i	−0.773379	−	0.384109i
$508$	281.476	−	487.531i	0.554087	−	0.959707i
$509$		−	228.276i		−	0.448479i	−0.974534	−	0.224240i	$-0.928010\pi$
$509$		−	228.276i		−	0.448479i	0.974534	−	0.224240i	$-0.0719898\pi$
$510$	−208.124	−	103.368i	−0.408087	−	0.202682i
$511$	−405.657	+	290.770i	−0.793849	+	0.569021i
$512$	569.227			1.11177
$513$	17.5502	−	50.2961i	0.0342109	−	0.0980430i
$514$	200.535	−	115.779i	0.390147	−	0.225251i
$515$	−796.588			−1.54677
$516$	52.7536	−	35.0335i	0.102236	−	0.0678945i
$517$	−313.691	+	181.110i	−0.606753	+	0.350309i
$518$	−655.173	+	64.6151i	−1.26481	+	0.124740i
$519$	−247.099	−	372.082i	−0.476106	−	0.716922i
$520$	−55.2768	−	95.7422i	−0.106302	−	0.184120i
$521$	409.376	−	236.354i	0.785751	−	0.453654i	−0.0527134	−	0.998610i	$-0.516787\pi$
$521$	409.376	−	236.354i	0.785751	−	0.453654i	0.838465	+	0.544956i	$0.183454\pi$
$522$	1088.58	−	137.058i	2.08540	−	0.262564i
$523$	242.231	+	139.852i	0.463156	+	0.267403i	0.713370	−	0.700787i	$-0.247168\pi$
$523$	242.231	+	139.852i	0.463156	+	0.267403i	−0.250214	+	0.968190i	$0.580501\pi$
$524$	19.2681	+	11.1245i	0.0367712	+	0.0212299i
$525$	−200.932	−	1237.78i	−0.382728	−	2.35769i
$526$	58.6991	+	101.670i	0.111595	+	0.193289i
$527$	−48.3786			−0.0918000
$528$	−332.848	+	221.044i	−0.630394	+	0.418644i
$529$	−503.719			−0.952211
$530$	−438.607	−	253.230i	−0.827561	−	0.477792i
$531$	409.380	+	172.289i	0.770961	+	0.324460i
$532$	−34.3334	+	24.6098i	−0.0645366	+	0.0462590i
$533$	134.348	−	232.697i	0.252060	−	0.436580i
$534$	818.403	−	51.3183i	1.53259	−	0.0961017i
$535$	−405.761	−	234.266i	−0.758431	−	0.437881i
$536$	38.5496	−	66.7699i	0.0719210	−	0.124571i
$537$	−490.682	+	325.861i	−0.913746	+	0.606817i
$538$	451.649	+	260.759i	0.839496	+	0.484683i
$539$	339.019	−	67.5269i	0.628978	−	0.125282i
$540$	−250.421	+	717.666i	−0.463743	+	1.32901i
$541$	508.919	−	881.473i	0.940700	−	1.62934i	0.176561	−	0.984290i	$-0.443503\pi$
$541$	508.919	−	881.473i	0.940700	−	1.62934i	0.764139	−	0.645051i	$-0.223164\pi$
$542$			450.236i			0.830694i
$543$	−241.560	+	15.1471i	−0.444863	+	0.0278953i
$544$			127.197i			0.233818i
$545$	−349.467	+	201.765i	−0.641224	+	0.370211i
$546$	95.0647	−	250.530i	0.174111	−	0.458846i
$547$	−195.785	+	339.109i	−0.357924	+	0.619943i	−0.987614	−	0.156904i	$-0.949849\pi$
$547$	−195.785	+	339.109i	−0.357924	+	0.619943i	0.629690	+	0.776847i	$0.283182\pi$
$548$	72.2946	−	125.218i	0.131924	−	0.228500i
$549$	−16.5237	+	12.5313i	−0.0300977	+	0.0228256i
$550$	559.605	+	969.264i	1.01746	+	1.76230i
$551$	78.4010	−	45.2648i	0.142289	−	0.0821503i
$552$	2.36088	+	37.6504i	0.00427696	+	0.0682072i
$553$	118.411	+	165.196i	0.214124	+	0.298728i
$554$	−491.645	−	851.554i	−0.887445	−	1.53710i
$555$	−434.793	+	875.428i	−0.783412	+	1.57735i
$556$			774.718i			1.39338i
$557$	249.913	+	432.862i	0.448677	+	0.777131i	0.998300	−	0.0582814i	$-0.0185621\pi$
$557$	249.913	+	432.862i	0.448677	+	0.777131i	−0.549623	+	0.835413i	$0.685229\pi$
$558$	45.6192	+	362.327i	0.0817548	+	0.649332i
$559$			33.1455i			0.0592942i
$560$	−988.615	+	708.627i	−1.76538	+	1.26540i
$561$	−37.0881	−	55.8473i	−0.0661107	−	0.0995496i
$562$	−326.800			−0.581495
$563$	−279.885	−	161.592i	−0.497132	−	0.287019i	0.230397	−	0.973097i	$-0.425998\pi$
$563$	−279.885	−	161.592i	−0.497132	−	0.287019i	−0.727528	+	0.686078i	$0.759331\pi$
$564$	470.215	−	29.4850i	0.833714	−	0.0522784i
$565$	849.680	−	490.563i	1.50386	−	0.868253i
$566$		−	399.712i		−	0.706204i
$567$	532.857	−	193.783i	0.939784	−	0.341769i
$568$	−203.229			−0.357798
$569$	−88.4404	−	153.183i	−0.155431	−	0.269215i	0.777785	−	0.628531i	$-0.216343\pi$
$569$	−88.4404	−	153.183i	−0.155431	−	0.269215i	−0.933216	+	0.359316i	$0.883010\pi$
$570$	9.05800	+	144.453i	0.0158912	+	0.253427i
$571$	278.796	−	482.889i	0.488260	−	0.845691i	−0.511649	−	0.859194i	$-0.670965\pi$
$571$	278.796	−	482.889i	0.488260	−	0.845691i	0.999909	+	0.0135039i	$0.00429856\pi$
$572$			103.633i			0.181176i
$573$	68.8807	−	45.7436i	0.120211	−	0.0798317i
$574$	−947.785	−	429.287i	−1.65119	−	0.747887i
$575$	300.239			0.522155
$576$	278.304	−	35.0402i	0.483167	−	0.0608336i
$577$	−640.283	+	369.668i	−1.10968	+	0.640672i	−0.938745	−	0.344611i	$-0.888011\pi$
$577$	−640.283	+	369.668i	−1.10968	+	0.640672i	−0.170931	+	0.985283i	$0.554677\pi$
$578$	741.160			1.28228
$579$	334.604	+	166.186i	0.577899	+	0.287022i
$580$	−1118.69	+	645.876i	−1.92878	+	1.11358i
$581$	411.792	+	186.516i	0.708765	+	0.321026i
$582$	−448.149	+	28.1014i	−0.770016	+	0.0482842i
$583$	−73.0556	−	126.536i	−0.125310	−	0.217043i
$584$	154.430	−	89.1599i	0.264434	−	0.152671i
$585$	−240.402	−	316.992i	−0.410943	−	0.541866i
$586$	−992.949	−	573.280i	−1.69445	−	0.978293i
$587$	−47.8551	−	27.6292i	−0.0815249	−	0.0470684i	0.458683	−	0.888600i	$-0.348321\pi$
$587$	−47.8551	−	27.6292i	−0.0815249	−	0.0470684i	−0.540208	+	0.841531i	$0.681655\pi$
$588$	−434.003	−	117.485i	−0.738100	−	0.199804i
$589$	15.0662	+	26.0954i	0.0255792	+	0.0443045i
$590$	−1206.79			−2.04541
$591$	−21.6101	−	344.629i	−0.0365653	−	0.583129i
$592$	668.318			1.12892
$593$	−663.928	−	383.319i	−1.11961	−	0.646406i	−0.178307	−	0.983975i	$-0.557062\pi$
$593$	−663.928	−	383.319i	−1.11961	−	0.646406i	−0.941301	+	0.337569i	$0.890395\pi$
$594$	−383.291	+	330.430i	−0.645271	+	0.556279i
$595$	−118.898	−	165.876i	−0.199828	−	0.278783i
$596$	392.799	−	680.348i	0.659059	−	1.14152i
$597$	−200.570	−	302.019i	−0.335963	−	0.505894i
$598$	55.5615	+	32.0785i	0.0929122	+	0.0536429i
$599$	453.133	−	784.849i	0.756482	−	1.31027i	−0.188152	−	0.982140i	$-0.560250\pi$
$599$	453.133	−	784.849i	0.756482	−	1.31027i	0.944634	−	0.328126i	$-0.106417\pi$
$600$	28.0385	+	447.147i	0.0467309	+	0.745245i
$601$	−192.859	−	111.347i	−0.320897	−	0.185270i	0.330895	−	0.943668i	$-0.392649\pi$
$601$	−192.859	−	111.347i	−0.320897	−	0.185270i	−0.651793	+	0.758397i	$0.725983\pi$
$602$	127.730	−	12.5971i	0.212176	−	0.0209254i
$603$	107.623	−	255.727i	0.178479	−	0.424091i
$604$	181.052	−	313.591i	0.299755	−	0.519191i
$605$		−	655.617i		−	1.08366i
$606$	−493.840	−	743.625i	−0.814917	−	1.22710i
$607$			599.115i			0.987010i	0.869743	+	0.493505i	$0.164285\pi$
$607$			599.115i			0.987010i	−0.869743	+	0.493505i	$0.835715\pi$
$608$	68.6100	−	39.6120i	0.112845	−	0.0651514i
$609$	900.907	+	341.853i	1.47932	+	0.561335i
$610$	28.1729	−	48.7970i	0.0461851	−	0.0799950i
$611$	−123.298	+	213.558i	−0.201796	+	0.349522i
$612$	10.8929	+	86.5166i	0.0177989	+	0.141367i
$613$	−270.643	−	468.768i	−0.441506	−	0.764711i	0.556295	−	0.830985i	$-0.312222\pi$
$613$	−270.643	−	468.768i	−0.441506	−	0.764711i	−0.997801	+	0.0662736i	$0.978889\pi$
$614$	−361.622	+	208.782i	−0.588960	+	0.340036i
$615$	−1286.87	+	854.606i	−2.09247	+	1.38960i
$616$	−122.908	+	12.1215i	−0.199526	+	0.0196778i
$617$	331.635	+	574.409i	0.537497	+	0.930972i	0.999038	+	0.0438529i	$0.0139633\pi$
$617$	331.635	+	574.409i	0.537497	+	0.930972i	−0.461541	+	0.887119i	$0.652703\pi$
$618$	381.624	+	574.650i	0.617514	+	0.929854i
$619$			978.753i			1.58118i	0.612343	+	0.790592i	$0.290227\pi$
$619$			978.753i			1.58118i	−0.612343	+	0.790592i	$0.709773\pi$
$620$	−214.977	−	372.350i	−0.346736	−	0.600565i
$621$	25.3546	+	133.367i	0.0408287	+	0.214761i
$622$		−	881.565i		−	1.41731i
$623$	656.015	+	297.134i	1.05299	+	0.476940i
$624$	−120.999	+	243.623i	−0.193908	+	0.390421i
$625$	1447.88			2.31661
$626$	−939.884	−	542.642i	−1.50141	−	0.866840i
$627$	−18.5739	+	37.3973i	−0.0296235	+	0.0596449i
$628$	135.157	−	78.0331i	0.215219	−	0.124257i
$629$			112.135i			0.178274i
$630$	−1130.20	+	1046.89i	−1.79397	+	1.66173i
$631$	256.500			0.406498			0.203249	−	0.979127i	$-0.434850\pi$
$631$	256.500			0.406498			0.203249	+	0.979127i	$0.434850\pi$
$632$	−36.3088	−	62.8886i	−0.0574506	−	0.0995073i
$633$	−300.847	+	199.792i	−0.475271	+	0.315627i
$634$	−51.4697	+	89.1481i	−0.0811824	+	0.140612i
$635$		−	1694.01i		−	2.66774i
$636$	11.8936	+	189.674i	0.0187006	+	0.298229i
$637$	176.893	−	155.213i	0.277697	−	0.243662i
$638$	−860.020			−1.34799
$639$	−725.615	+	91.3592i	−1.13555	+	0.142972i
$640$	620.253	−	358.103i	0.969145	−	0.559536i
$641$	−336.160			−0.524431			−0.262215	−	0.965009i	$-0.584453\pi$
$641$	−336.160			−0.524431			−0.262215	+	0.965009i	$0.584453\pi$
$642$	25.3921	+	404.942i	0.0395515	+	0.630751i
$643$	754.603	−	435.671i	1.17357	−	0.677559i	0.219049	−	0.975714i	$-0.429704\pi$
$643$	754.603	−	435.671i	1.17357	−	0.677559i	0.954518	+	0.298155i	$0.0963711\pi$
$644$	44.4160	−	98.0622i	0.0689690	−	0.152270i
$645$	84.7656	−	170.670i	0.131419	−	0.264604i
$646$	8.30217	+	14.3798i	0.0128517	+	0.0222597i
$647$	−707.666	+	408.571i	−1.09376	+	0.631485i	−0.934576	−	0.355763i	$-0.884221\pi$
$647$	−707.666	+	408.571i	−1.09376	+	0.631485i	−0.159189	+	0.987248i	$0.550888\pi$
$648$	−196.255	+	50.2155i	−0.302863	+	0.0774930i
$649$	−301.510	−	174.077i	−0.464576	−	0.268223i
$650$	659.865	+	380.973i	1.01518	+	0.586113i
$651$	−113.784	+	299.862i	−0.174784	+	0.460618i
$652$	437.868	+	758.410i	0.671577	+	1.16321i
$653$	−360.836			−0.552582			−0.276291	−	0.961074i	$-0.589105\pi$
$653$	−360.836			−0.552582			−0.276291	+	0.961074i	$0.589105\pi$
$654$	312.971	+	155.442i	0.478549	+	0.237678i
$655$	66.9506			0.102215
$656$	914.716	+	528.112i	1.39438	+	0.805048i
$657$	511.299	−	387.761i	0.778232	−	0.590199i
$658$	869.829	+	393.978i	1.32193	+	0.598750i
$659$	515.473	−	892.826i	0.782205	−	1.35482i	−0.148449	−	0.988920i	$-0.547428\pi$
$659$	515.473	−	892.826i	0.782205	−	1.35482i	0.930654	−	0.365899i	$-0.119239\pi$
$660$	265.028	−	533.617i	0.401558	−	0.808510i
$661$	−287.835	−	166.182i	−0.435455	−	0.251410i	0.266213	−	0.963914i	$-0.414228\pi$
$661$	−287.835	−	166.182i	−0.435455	−	0.251410i	−0.701668	+	0.712504i	$0.747561\pi$
$662$	−378.657	+	655.854i	−0.571990	+	0.990716i
$663$	−40.8766	−	20.3019i	−0.0616539	−	0.0306213i
$664$	−139.875	−	80.7566i	−0.210654	−	0.121621i
$665$	−52.4459	+	115.791i	−0.0788660	+	0.174121i
$666$	839.822	−	105.739i	1.26099	−	0.158767i
$667$	−115.354	+	199.800i	−0.172945	+	0.299550i
$668$		−	572.623i		−	0.857220i
$669$	313.752	−	631.719i	0.468987	−	0.944273i
$670$			753.844i			1.12514i
$671$	14.0777	−	8.12775i	0.0209801	−	0.0121129i
$672$	788.399	+	299.162i	1.17321	+	0.445181i
$673$	−241.240	+	417.840i	−0.358455	+	0.620862i	−0.987703	−	0.156343i	$-0.950030\pi$
$673$	−241.240	+	417.840i	−0.358455	+	0.620862i	0.629248	+	0.777204i	$0.283363\pi$
$674$	792.030	−	1371.84i	1.17512	−	2.03537i
$675$	301.119	+	1583.90i	0.446102	+	2.34652i
$676$	−223.181	−	386.561i	−0.330149	−	0.571835i
$677$	538.899	−	311.134i	0.796011	−	0.459577i	−0.0460636	−	0.998939i	$-0.514668\pi$
$677$	538.899	−	311.134i	0.796011	−	0.459577i	0.842074	+	0.539362i	$0.181334\pi$
$678$	−760.946	−	377.934i	−1.12234	−	0.557425i
$679$	−359.227	−	162.707i	−0.529054	−	0.239628i
$680$	36.4581	+	63.1473i	0.0536149	+	0.0928637i
$681$	−452.826	+	28.3947i	−0.664943	+	0.0416955i
$682$		−	286.253i		−	0.419726i
$683$	235.625	+	408.115i	0.344986	+	0.597533i	0.985351	−	0.170538i	$-0.0545505\pi$
$683$	235.625	+	408.115i	0.344986	+	0.597533i	−0.640366	+	0.768070i	$0.721217\pi$
$684$	43.2746	−	32.8188i	0.0632670	−	0.0479807i
$685$		−	435.092i		−	0.635171i
$686$	−665.359	−	622.689i	−0.969911	−	0.907710i
$687$	1239.52	−	77.7248i	1.80426	−	0.113137i
$688$	−130.293			−0.189379
$689$	−86.1444	−	49.7355i	−0.125028	−	0.0721850i
$690$	−204.056	−	307.267i	−0.295733	−	0.445315i
$691$	−449.921	+	259.762i	−0.651115	+	0.375921i	−0.788883	−	0.614543i	$-0.789340\pi$
$691$	−449.921	+	259.762i	−0.651115	+	0.375921i	0.137768	+	0.990464i	$0.456007\pi$
$692$		−	455.392i		−	0.658081i
$693$	−433.384	+	98.5308i	−0.625374	+	0.142180i
$694$	−771.992			−1.11238
$695$	1165.63	+	2018.92i	1.67716	+	2.90492i
$696$	−308.335	−	153.139i	−0.443010	−	0.220027i
$697$	−88.6098	+	153.477i	−0.127130	+	0.220196i
$698$			869.645i			1.24591i
$699$	896.343	+	445.182i	1.28232	+	0.636883i
$700$	527.498	−	1164.62i	0.753568	−	1.66374i
$701$	−985.712			−1.40615			−0.703076	−	0.711115i	$-0.748191\pi$
$701$	−985.712			−1.40615			−0.703076	+	0.711115i	$0.748191\pi$
$702$	−113.504	+	325.285i	−0.161687	+	0.463370i
$703$	60.4852	−	34.9212i	0.0860387	−	0.0496745i
$704$	−219.872			−0.312318
$705$	1181.02	−	784.314i	1.67521	−	1.11250i
$706$	193.583	−	111.765i	0.274197	−	0.158308i
$707$	−76.9452	−	780.195i	−0.108833	−	1.10353i
$708$	250.520	+	377.234i	0.353842	+	0.532817i
$709$	−295.114	−	511.152i	−0.416240	−	0.720948i	0.579318	−	0.815102i	$-0.303319\pi$
$709$	−295.114	−	511.152i	−0.416240	−	0.720948i	−0.995558	+	0.0941533i	$0.969986\pi$
$710$	1720.87	−	993.544i	2.42376	−	1.39936i
$711$	−157.909	−	208.217i	−0.222094	−	0.292851i
$712$	−222.830	−	128.651i	−0.312964	−	0.180690i
$713$	−66.5023	−	38.3951i	−0.0932711	−	0.0538501i
$714$	−62.7004	+	165.238i	−0.0878157	+	0.231426i
$715$	155.924	+	270.068i	0.218075	+	0.377717i
$716$	−600.546			−0.838751
$717$	523.908	−	347.926i	0.730695	−	0.485253i
$718$	564.258			0.785875
$719$	320.943	+	185.297i	0.446375	+	0.257715i	0.706298	−	0.707915i	$-0.250364\pi$
$719$	320.943	+	185.297i	0.446375	+	0.257715i	−0.259923	+	0.965629i	$0.583697\pi$
$720$	1246.07	−	945.002i	1.73066	−	1.31250i
$721$	59.4608	+	602.911i	0.0824699	+	0.836214i
$722$	−474.384	+	821.657i	−0.657042	+	1.13803i
$723$	681.896	−	42.7586i	0.943148	−	0.0591405i
$724$	−213.707	−	123.384i	−0.295175	−	0.170420i
$725$	−1369.98	+	2372.88i	−1.88963	+	3.27294i
$726$	−472.955	+	314.088i	−0.651453	+	0.432629i
$727$	98.4688	+	56.8510i	0.135445	+	0.0781995i	0.566192	−	0.824274i	$-0.308416\pi$
$727$	98.4688	+	56.8510i	0.135445	+	0.0781995i	−0.430746	+	0.902473i	$0.641750\pi$
$728$	−68.3380	+	48.9838i	−0.0938709	+	0.0672854i
$729$	−678.142	+	267.515i	−0.930236	+	0.366962i
$730$	−871.768	+	1509.95i	−1.19420	+	2.06842i
$731$		−	21.8613i		−	0.0299060i
$732$	−21.1020	+	1.32321i	−0.0288279	+	0.00180767i
$733$			608.247i			0.829805i	0.909866	+	0.414903i	$0.136184\pi$
$733$			608.247i			0.829805i	−0.909866	+	0.414903i	$0.863816\pi$
$734$	965.458	−	557.407i	1.31534	−	0.759411i
$735$	−1307.78	+	346.825i	−1.77929	+	0.471871i
$736$	−100.949	+	174.848i	−0.137158	+	0.237565i
$737$	−108.740	+	188.343i	−0.147544	+	0.255554i
$738$	1233.01	+	518.913i	1.67074	+	0.703134i
$739$	605.973	+	1049.58i	0.819990	+	1.42026i	0.905689	+	0.423944i	$0.139355\pi$
$739$	605.973	+	1049.58i	0.819990	+	1.42026i	−0.0856983	+	0.996321i	$0.527312\pi$
$740$	−863.054	+	498.284i	−1.16629	+	0.673357i
$741$	1.77903	+	28.3712i	0.00240085	+	0.0382878i
$742$	−158.922	+	350.869i	−0.214180	+	0.472870i
$743$	82.8636	+	143.524i	0.111526	+	0.193168i	0.916386	−	0.400297i	$-0.131093\pi$
$743$	82.8636	+	143.524i	0.111526	+	0.193168i	−0.804860	+	0.593465i	$0.797760\pi$
$744$	50.9715	−	102.628i	0.0685100	−	0.137940i
$745$		−	2363.99i		−	3.17314i
$746$	293.657	+	508.628i	0.393642	+	0.681807i
$747$	−535.715	−	225.457i	−0.717156	−	0.301816i
$748$		−	68.3515i		−	0.0913791i
$749$	−147.020	+	324.593i	−0.196289	+	0.433369i
$750$	−1408.82	−	2121.41i	−1.87843	−	2.82854i
$751$	1353.18			1.80183			0.900916	−	0.433993i	$-0.142896\pi$
$751$	1353.18			1.80183			0.900916	+	0.433993i	$0.142896\pi$
$752$	−839.480	−	484.674i	−1.11633	−	0.644514i
$753$	−1265.25	+	79.3379i	−1.68028	+	0.105362i
$754$	−507.051	+	292.746i	−0.672482	+	0.388258i
$755$		−	1089.63i		−	1.44322i
$756$	561.870	+	135.966i	0.743214	+	0.179849i
$757$	128.108			0.169231			0.0846155	−	0.996414i	$-0.473034\pi$
$757$	128.108			0.169231			0.0846155	+	0.996414i	$0.473034\pi$
$758$	−421.187	−	729.518i	−0.555656	−	0.962424i
$759$	−6.65953	−	106.203i	−0.00877409	−	0.139925i
$760$	22.7077	−	39.3309i	0.0298786	−	0.0517512i
$761$			805.339i			1.05826i	0.848540	+	0.529132i	$0.177482\pi$
$761$			805.339i			1.05826i	−0.848540	+	0.529132i	$0.822518\pi$
$762$	−1222.04	+	811.557i	−1.60373	+	1.06504i
$763$	178.795	+	249.439i	0.234331	+	0.326919i
$764$	84.3032			0.110344
$765$	158.558	+	209.074i	0.207266	+	0.273299i
$766$	638.687	−	368.746i	0.833795	−	0.481392i
$767$	−237.019			−0.309021
$768$	−890.441	−	442.250i	−1.15943	−	0.575847i
$769$	501.209	−	289.373i	0.651767	−	0.376298i	−0.137366	−	0.990520i	$-0.543864\pi$
$769$	501.209	−	289.373i	0.651767	−	0.376298i	0.789133	+	0.614222i	$0.210530\pi$
$770$	981.478	−	703.511i	1.27465	−	0.913650i
$771$	−260.957	+	16.3634i	−0.338465	+	0.0212236i
$772$	190.453	+	329.874i	0.246701	+	0.427298i
$773$	685.032	−	395.504i	0.886200	−	0.511648i	0.0135021	−	0.999909i	$-0.495702\pi$
$773$	685.032	−	395.504i	0.886200	−	0.511648i	0.872698	+	0.488261i	$0.162369\pi$
$774$	−163.728	+	20.6144i	−0.211535	+	0.0266335i
$775$	−789.801	−	455.992i	−1.01910	−	0.588376i
$776$	122.020	+	70.4481i	0.157242	+	0.0907836i
$777$	695.037	+	263.735i	0.894513	+	0.339427i
$778$	96.2228	+	166.663i	0.123680	+	0.214219i
$779$	110.380			0.141695
$780$	−25.3847	−	404.824i	−0.0325445	−	0.519006i
$781$	573.265			0.734014
$782$	−36.6459	−	21.1575i	−0.0468618	−	0.0270557i
$783$	−1169.73	−	408.163i	−1.49391	−	0.521281i
$784$	610.131	+	695.355i	0.778228	+	0.886932i
$785$	234.814	−	406.710i	0.299126	−	0.518102i
$786$	−32.0742	−	48.2974i	−0.0408069	−	0.0614471i
$787$	−856.846	−	494.700i	−1.08875	−	0.628590i	−0.155506	−	0.987835i	$-0.549701\pi$
$787$	−856.846	−	494.700i	−1.08875	−	0.628590i	−0.933243	+	0.359245i	$0.883034\pi$
$788$	176.029	−	304.891i	0.223387	−	0.386918i
$789$	−8.29611	−	132.303i	−0.0105147	−	0.167684i
$790$	614.898	+	355.011i	0.778352	+	0.449382i
$791$	−434.714	−	606.476i	−0.549576	−	0.766721i
$792$	157.547	−	19.8361i	0.198923	−	0.0250456i
$793$	5.53329	−	9.58394i	0.00697766	−	0.0120857i
$794$			1812.79i			2.28311i
$795$	316.375	+	476.397i	0.397955	+	0.599242i
$796$		−	369.641i		−	0.464373i
$797$	−104.384	+	60.2662i	−0.130971	+	0.0756163i	−0.564054	−	0.825738i	$-0.690759\pi$
$797$	−104.384	+	60.2662i	−0.130971	+	0.0756163i	0.433083	+	0.901354i	$0.357426\pi$
$798$	108.656	−	17.6383i	0.136160	−	0.0221032i
$799$	81.3216	−	140.853i	0.101779	−	0.176287i
$800$	−1198.90	+	2076.55i	−1.49862	+	2.59568i
$801$	−853.434	−	359.169i	−1.06546	−	0.448401i
$802$	−597.323	−	1034.59i	−0.744791	−	1.29002i
$803$	−435.612	+	251.501i	−0.542481	+	0.313201i
$804$	235.646	−	156.492i	0.293092	−	0.194642i
$805$	−31.7939	−	322.378i	−0.0394956	−	0.400470i
$806$	−97.4391	−	168.769i	−0.120892	−	0.209391i
$807$	−325.781	−	490.562i	−0.403694	−	0.607884i
$808$			280.101i			0.346659i
$809$	−94.3098	−	163.349i	−0.116576	−	0.201915i	0.801833	−	0.597548i	$-0.203858\pi$
$809$	−94.3098	−	163.349i	−0.116576	−	0.201915i	−0.918409	+	0.395633i	$0.870525\pi$
$810$	1416.33	−	1384.66i	1.74855	−	1.70945i
$811$			1191.68i			1.46940i	0.678394	+	0.734699i	$0.262676\pi$
$811$			1191.68i			1.46940i	−0.678394	+	0.734699i	$0.737324\pi$
$812$	572.346	+	798.488i	0.704860	+	0.983360i
$813$	226.145	−	455.327i	0.278161	−	0.560058i
$814$	−663.493			−0.815102
$815$	2282.18	+	1317.62i	2.80022	+	1.61671i
$816$	79.8054	−	160.683i	0.0978007	−	0.196915i
$817$	−11.7920	+	6.80809i	−0.0144332	+	0.00833303i
$818$			395.622i			0.483645i
$819$	−221.976	+	205.614i	−0.271033	+	0.251055i
$820$	−1575.00			−1.92073
$821$	338.613	+	586.495i	0.412440	+	0.714366i	0.995156	−	0.0983094i	$-0.0313435\pi$
$821$	338.613	+	586.495i	0.412440	+	0.714366i	−0.582716	+	0.812676i	$0.698010\pi$
$822$	−313.871	+	208.441i	−0.381838	+	0.253578i
$823$	805.395	−	1394.98i	0.978608	−	1.69500i	0.311135	−	0.950366i	$-0.399291\pi$
$823$	805.395	−	1394.98i	0.978608	−	1.69500i	0.667473	−	0.744634i	$-0.267376\pi$
$824$		−	216.453i		−	0.262686i
$825$	−79.0906	−	1261.30i	−0.0958674	−	1.52885i
$826$	90.0803	+	913.380i	0.109056	+	1.10579i
$827$	−626.312			−0.757331			−0.378665	−	0.925534i	$-0.623617\pi$
$827$	−626.312			−0.757331			−0.378665	+	0.925534i	$0.623617\pi$
$828$	−53.6892	+	127.573i	−0.0648420	+	0.154073i
$829$	−469.693	+	271.178i	−0.566578	+	0.327114i	−0.755782	−	0.654824i	$-0.772743\pi$
$829$	−469.693	+	271.178i	−0.566578	+	0.327114i	0.189203	+	0.981938i	$0.439409\pi$
$830$	1579.21			1.90266
$831$	69.4855	+	1108.13i	0.0836168	+	1.33349i
$832$	−129.632	+	74.8431i	−0.155808	+	0.0899557i
$833$	−116.671	+	102.371i	−0.140061	+	0.122895i
$834$	898.009	−	1808.08i	1.07675	−	2.16796i
$835$	−861.557	−	1492.26i	−1.03180	−	1.78714i
$836$	−36.8687	+	21.2862i	−0.0441014	+	0.0254619i
$837$	135.855	−	389.338i	0.162312	−	0.465159i
$838$	1060.52	+	612.293i	1.26554	+	0.730660i
$839$	−1281.98	−	740.153i	−1.52799	−	0.882185i	−0.999446	−	0.0332790i	$-0.989405\pi$
$839$	−1281.98	−	740.153i	−1.52799	−	0.882185i	−0.528543	−	0.848906i	$-0.677262\pi$
$840$	477.150	−	77.4568i	0.568036	−	0.0922105i
$841$	−632.218	−	1095.03i	−0.751746	−	1.30206i
$842$	339.541			0.403256
$843$	330.496	+	164.145i	0.392047	+	0.194716i
$844$	−368.207			−0.436264
$845$	−1163.22	−	671.587i	−1.37660	−	0.794778i
$846$	−1131.59	−	476.232i	−1.33758	−	0.562922i
$847$	−496.215	+	48.9381i	−0.585850	+	0.0577782i
$848$	195.507	−	338.627i	0.230550	−	0.399325i
$849$	−200.767	+	404.232i	−0.236475	+	0.476127i
$850$	−435.218	−	251.273i	−0.512021	−	0.295615i
$851$	−88.9942	+	154.143i	−0.104576	+	0.181131i
$852$	−667.813	−	331.679i	−0.783818	−	0.389294i
$853$	744.542	+	429.861i	0.872851	+	0.503941i	0.868294	−	0.496049i	$-0.165216\pi$
$853$	744.542	+	429.861i	0.872851	+	0.503941i	0.00455615	+	0.999990i	$0.498550\pi$
$854$	−39.0357	−	17.6807i	−0.0457093	−	0.0207034i
$855$	63.3955	−	150.636i	0.0741468	−	0.176183i
$856$	63.6560	−	110.255i	0.0743645	−	0.128803i
$857$		−	442.777i		−	0.516659i	−0.966057	−	0.258330i	$-0.916828\pi$
$857$		−	442.777i		−	0.516659i	0.966057	−	0.258330i	$-0.0831720\pi$
$858$	120.125	−	241.864i	0.140006	−	0.281893i
$859$			501.048i			0.583293i	0.956526	+	0.291646i	$0.0942030\pi$
$859$			501.048i			0.583293i	−0.956526	+	0.291646i	$0.905797\pi$
$860$	168.257	−	97.1434i	0.195648	−	0.112957i
$861$	742.880	+	910.195i	0.862811	+	1.05714i
$862$	−277.453	+	480.562i	−0.321871	+	0.557497i
$863$	−182.251	+	315.667i	−0.211183	+	0.365779i	−0.952085	−	0.305834i	$-0.901065\pi$
$863$	−182.251	+	315.667i	−0.211183	+	0.365779i	0.740902	+	0.671613i	$0.234398\pi$
$864$	−1023.65	−	357.190i	−1.18478	−	0.413415i
$865$	−685.174	−	1186.76i	−0.792108	−	1.37197i
$866$	1132.47	−	653.834i	1.30771	−	0.755005i
$867$	−749.541	−	372.270i	−0.864523	−	0.429378i
$868$	−265.773	+	190.502i	−0.306190	+	0.219473i
$869$	102.419	+	177.395i	0.117859	+	0.204137i
$870$	3359.53	−	210.661i	3.86153	−	0.242139i
$871$			148.058i			0.169986i
$872$	−54.8246	−	94.9590i	−0.0628723	−	0.108898i
$873$	467.332	+	196.677i	0.535317	+	0.225289i
$874$			26.3557i			0.0301552i
$875$	−219.509	−	2225.74i	−0.250867	−	2.54370i
$876$	652.970	−	40.9448i	0.745400	−	0.0467406i
$877$	−782.479			−0.892223			−0.446111	−	0.894977i	$-0.647192\pi$
$877$	−782.479			−0.892223			−0.446111	+	0.894977i	$0.647192\pi$
$878$	162.090	+	93.5829i	0.184613	+	0.106586i
$879$	716.230	+	1078.50i	0.814824	+	1.22696i
$880$	−1061.62	+	612.925i	−1.20638	+	0.696506i
$881$			337.263i			0.382818i	0.981510	+	0.191409i	$0.0613058\pi$
$881$			337.263i			0.382818i	−0.981510	+	0.191409i	$0.938694\pi$
$882$	876.718	+	777.265i	0.994012	+	0.881252i
$883$	556.002			0.629674			0.314837	−	0.949146i	$-0.398050\pi$
$883$	556.002			0.629674			0.314837	+	0.949146i	$0.398050\pi$
$884$	−23.2665	−	40.2988i	−0.0263196	−	0.0455868i
$885$	1220.44	+	606.148i	1.37903	+	0.684913i
$886$	−951.233	+	1647.58i	−1.07363	+	1.85958i
$887$		−	722.908i		−	0.815004i	−0.913204	−	0.407502i	$-0.866400\pi$
$887$		−	722.908i		−	0.815004i	0.913204	−	0.407502i	$-0.133600\pi$
$888$	−237.876	−	118.144i	−0.267878	−	0.133045i
$889$	−1282.14	+	126.449i	−1.44223	+	0.142237i
$890$	2515.79			2.82673
$891$	553.594	−	141.647i	0.621317	−	0.158975i
$892$	622.790	−	359.568i	0.698195	−	0.403103i
$893$	−101.301			−0.113439
$894$	−1705.36	+	1132.53i	−1.90756	+	1.26681i
$895$	−1565.03	+	903.569i	−1.74863	+	1.00957i
$896$	−317.335	−	442.718i	−0.354168	−	0.494105i
$897$	−40.0774	−	60.3486i	−0.0446794	−	0.0672783i
$898$	173.158	+	299.919i	0.192827	+	0.333986i
$899$	606.896	−	350.392i	0.675079	−	0.389757i
$900$	−637.628	+	1515.09i	−0.708476	+	1.68343i
$901$	56.8170	+	32.8033i	0.0630599	+	0.0364077i
$902$	−908.113	−	524.299i	−1.00678	−	0.581263i
$903$	−135.502	−	51.4167i	−0.150057	−	0.0569398i
$904$	133.298	+	230.879i	0.147454	+	0.255398i
$905$	−742.563			−0.820512
$906$	−786.047	+	522.012i	−0.867602	+	0.576173i
$907$	1127.74			1.24338			0.621688	−	0.783265i	$-0.286447\pi$
$907$	1127.74			1.24338			0.621688	+	0.783265i	$0.286447\pi$
$908$	−400.613	−	231.294i	−0.441203	−	0.254729i
$909$	125.916	+	1000.08i	0.138521	+	1.10020i
$910$	339.189	−	748.866i	0.372736	−	0.822930i
$911$	−890.109	+	1541.71i	−0.977068	+	1.69233i	−0.304136	+	0.952629i	$0.598368\pi$
$911$	−890.109	+	1541.71i	−0.977068	+	1.69233i	−0.672933	+	0.739703i	$0.734966\pi$
$912$	−111.525	+	6.99324i	−0.122286	+	0.00766803i
$913$	394.556	+	227.797i	0.432153	+	0.249504i
$914$	280.998	−	486.702i	0.307437	−	0.532497i
$915$	−53.0013	+	35.1980i	−0.0579249	+	0.0384678i
$916$	1096.60	+	633.121i	1.19716	+	0.691181i
$917$	−4.99748	−	50.6726i	−0.00544982	−	0.0552591i
$918$	74.8625	−	214.544i	0.0815496	−	0.233708i
$919$	−350.534	+	607.142i	−0.381429	+	0.660655i	−0.991267	−	0.131871i	$-0.957901\pi$
$919$	−350.534	+	607.142i	−0.381429	+	0.660655i	0.609837	+	0.792527i	$0.291235\pi$
$920$			115.738i			0.125802i
$921$	470.578	−	29.5078i	0.510942	−	0.0320389i
$922$		−	1402.08i		−	1.52069i
$923$	337.986	−	195.136i	0.366182	−	0.211415i
$924$	−423.659	−	160.759i	−0.458506	−	0.173982i
$925$	−1056.92	+	1830.64i	−1.14262	+	1.97907i
$926$	−975.227	+	1689.14i	−1.05316	+	1.82413i
$927$	−97.3039	−	772.830i	−0.104966	−	0.833689i
$928$	−921.252	−	1595.65i	−0.992728	−	1.71946i
$929$	−849.720	+	490.586i	−0.914661	+	0.528080i	−0.881928	−	0.471385i	$-0.843754\pi$
$929$	−849.720	+	490.586i	−0.914661	+	0.528080i	−0.0327329	+	0.999464i	$0.510421\pi$
$930$	70.1173	+	1118.20i	0.0753949	+	1.20237i
$931$	91.5529	+	31.0514i	0.0983383	+	0.0333528i
$932$	510.189	+	883.674i	0.547413	+	0.948148i
$933$	−442.793	+	891.534i	−0.474590	+	0.955556i
$934$		−	861.870i		−	0.922773i
$935$	−102.840	−	178.125i	−0.109990	−	0.190508i
$936$	86.1347	−	65.3232i	0.0920242	−	0.0697898i
$937$			949.998i			1.01387i	0.861984	+	0.506936i	$0.169222\pi$
$937$			949.998i			1.01387i	−0.861984	+	0.506936i	$0.830778\pi$
$938$	570.559	−	56.2702i	0.608272	−	0.0599896i
$939$	677.953	+	1020.86i	0.721995	+	1.08718i
$940$	1445.45			1.53772
$941$	−329.267	−	190.102i	−0.349912	−	0.202022i	0.314735	−	0.949180i	$-0.398084\pi$
$941$	−329.267	−	190.102i	−0.349912	−	0.202022i	−0.664646	+	0.747158i	$0.731418\pi$
$942$	−405.890	+	25.4515i	−0.430881	+	0.0270186i
$943$	−243.610	+	140.648i	−0.258335	+	0.149150i
$944$		−	931.705i		−	0.986976i
$945$	1668.81	−	491.051i	1.76594	−	0.519631i
$946$	129.352			0.136736
$947$	−163.034	−	282.383i	−0.172159	−	0.298187i	0.767016	−	0.641628i	$-0.221741\pi$
$947$	−163.034	−	282.383i	−0.172159	−	0.298187i	−0.939174	+	0.343441i	$0.888407\pi$
$948$	−16.6740	−	265.910i	−0.0175886	−	0.280496i
$949$	−171.219	+	296.560i	−0.180420	+	0.312497i
$950$			313.008i			0.329482i
$951$	96.8290	−	64.3039i	0.101818	−	0.0676172i
$952$	45.0727	−	32.3075i	0.0473453	−	0.0339365i
$953$	1009.14			1.05891			0.529455	−	0.848338i	$-0.322397\pi$
$953$	1009.14			1.05891			0.529455	+	0.848338i	$0.322397\pi$
$954$	192.101	−	456.458i	0.201364	−	0.478468i
$955$	219.695	−	126.841i	0.230047	−	0.132818i
$956$	641.212			0.670723
$957$	869.745	+	431.971i	0.908825	+	0.451381i
$958$	967.578	−	558.631i	1.01000	−	0.583122i
$959$	−329.307	+	32.4772i	−0.343385	+	0.0338657i
$960$	858.892	−	53.8572i	0.894679	−	0.0561013i
$961$	−363.874	−	630.248i	−0.378641	−	0.655825i
$962$	−391.183	+	225.850i	−0.406635	+	0.234771i
$963$	177.715	−	422.275i	0.184543	−	0.438500i
$964$	603.269	+	348.298i	0.625798	+	0.361304i
$965$	992.644	+	573.103i	1.02865	+	0.593890i
$966$	−217.329	+	177.379i	−0.224978	+	0.183622i
$967$	277.066	+	479.892i	0.286521	+	0.496269i	0.972977	−	0.230902i	$-0.0741678\pi$
$967$	277.066	+	479.892i	0.286521	+	0.496269i	−0.686456	+	0.727172i	$0.740834\pi$
$968$	178.148			0.184037
$969$	−1.17337	−	18.7124i	−0.00121091	−	0.0193110i
$970$	−1377.62			−1.42023
$971$	1334.71	+	770.592i	1.37457	+	0.793607i	0.991499	−	0.130113i	$-0.0415340\pi$
$971$	1334.71	+	770.592i	1.37457	+	0.793607i	0.383069	+	0.923720i	$0.374867\pi$
$972$	−726.851	−	155.289i	−0.747790	−	0.159762i
$973$	1441.05	−	1032.92i	1.48104	−	1.06159i
$974$	51.3691	−	88.9739i	0.0527404	−	0.0913490i
$975$	−475.971	−	716.718i	−0.488176	−	0.735096i
$976$	37.6738	+	21.7510i	0.0386002	+	0.0222858i
$977$	812.692	−	1407.62i	0.831824	−	1.44076i	−0.0647660	−	0.997900i	$-0.520630\pi$
$977$	812.692	−	1407.62i	0.831824	−	1.44076i	0.896590	−	0.442861i	$-0.146037\pi$
$978$	−142.816	−	2277.57i	−0.146029	−	2.32881i
$979$	628.556	+	362.897i	0.642039	+	0.370681i
$980$	−1306.35	−	443.068i	−1.33301	−	0.452110i
$981$	−238.435	−	314.399i	−0.243053	−	0.320488i
$982$	1157.53	−	2004.90i	1.17875	−	2.04165i
$983$		−	35.2712i		−	0.0358812i	−0.999839	−	0.0179406i	$-0.994289\pi$
$983$		−	35.2712i		−	0.0358812i	0.999839	−	0.0179406i	$-0.00571098\pi$
$984$	−232.218	−	349.674i	−0.235994	−	0.355360i
$985$		−	1059.40i		−	1.07553i
$986$	334.429	−	193.082i	0.339177	−	0.195824i
$987$	−681.778	−	835.331i	−0.690757	−	0.846333i
$988$	−14.4914	+	25.0998i	−0.0146674	+	0.0254047i
$989$	17.3499	−	30.0510i	0.0175429	−	0.0303852i
$990$	−1237.08	+	938.179i	−1.24957	+	0.947656i
$991$	567.488	+	982.918i	0.572642	+	0.991845i	0.996293	+	0.0860197i	$0.0274148\pi$
$991$	567.488	+	982.918i	0.572642	+	0.991845i	−0.423652	+	0.905825i	$0.639252\pi$
$992$	531.105	−	306.634i	0.535388	−	0.309107i
$993$	712.362	−	473.078i	0.717384	−	0.476413i
$994$	−880.433	−	1228.31i	−0.885748	−	1.23572i
$995$	−556.155	−	963.288i	−0.558950	−	0.968129i
$996$	−327.831	−	493.649i	−0.329148	−	0.495631i
$997$			51.2724i			0.0514267i	0.999669	+	0.0257133i	$0.00818571\pi$
$997$			51.2724i			0.0514267i	−0.999669	+	0.0257133i	$0.991814\pi$
$998$	489.190	+	847.301i	0.490170	+	0.848999i
$999$	−902.429	−	314.892i	−0.903332	−	0.315207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.k.a.61.3	yes	28
3.2	odd	2		189.3.k.a.19.12		28
7.2	even	3		441.3.l.a.97.3		28
7.3	odd	6		63.3.t.a.52.12	yes	28
7.4	even	3		441.3.t.a.178.12		28
7.5	odd	6		441.3.l.b.97.3		28
7.6	odd	2		441.3.k.b.313.3		28
9.4	even	3		63.3.t.a.40.12	yes	28
9.5	odd	6		189.3.t.a.145.3		28
21.17	even	6		189.3.t.a.73.3		28
63.4	even	3		441.3.k.b.31.3		28
63.13	odd	6		441.3.t.a.166.12		28
63.31	odd	6	inner	63.3.k.a.31.3	✓	28
63.40	odd	6		441.3.l.a.391.3		28
63.58	even	3		441.3.l.b.391.3		28
63.59	even	6		189.3.k.a.10.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.3	✓	28	63.31	odd	6	inner
63.3.k.a.61.3	yes	28	1.1	even	1	trivial
63.3.t.a.40.12	yes	28	9.4	even	3
63.3.t.a.52.12	yes	28	7.3	odd	6
189.3.k.a.10.12		28	63.59	even	6
189.3.k.a.19.12		28	3.2	odd	2
189.3.t.a.73.3		28	21.17	even	6
189.3.t.a.145.3		28	9.5	odd	6
441.3.k.b.31.3		28	63.4	even	3
441.3.k.b.313.3		28	7.6	odd	2
441.3.l.a.97.3		28	7.2	even	3
441.3.l.a.391.3		28	63.40	odd	6
441.3.l.b.97.3		28	7.5	odd	6
441.3.l.b.391.3		28	63.58	even	3
441.3.t.a.166.12		28	63.13	odd	6
441.3.t.a.178.12		28	7.4	even	3

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32841 - 2.30087i) q^{2} +(0.187748 + 2.99412i) q^{3} +(-1.52933 + 2.64888i) q^{4} +9.20400i q^{5} +(6.63967 - 4.40939i) q^{6} +(6.96620 - 0.687028i) q^{7} -2.50096 q^{8} +(-8.92950 + 1.12428i) q^{9} +O(q^{10})\)	\(q+(-1.32841 - 2.30087i) q^{2} +(0.187748 + 2.99412i) q^{3} +(-1.52933 + 2.64888i) q^{4} +9.20400i q^{5} +(6.63967 - 4.40939i) q^{6} +(6.96620 - 0.687028i) q^{7} -2.50096 q^{8} +(-8.92950 + 1.12428i) q^{9} +(21.1772 - 12.2267i) q^{10} +7.05467 q^{11} +(-8.21819 - 4.08168i) q^{12} +(4.15930 - 2.40137i) q^{13} +(-10.8347 - 15.1157i) q^{14} +(-27.5579 + 1.72803i) q^{15} +(9.43962 + 16.3499i) q^{16} +(-2.74329 + 1.58384i) q^{17} +(14.4488 + 19.0521i) q^{18} +(1.70864 + 0.986484i) q^{19} +(-24.3803 - 14.0760i) q^{20} +(3.36493 + 20.7287i) q^{21} +(-9.37147 - 16.2319i) q^{22} -5.02797 q^{23} +(-0.469549 - 7.48818i) q^{24} -59.7137 q^{25} +(-11.0505 - 6.38000i) q^{26} +(-5.04271 - 26.5249i) q^{27} +(-8.83378 + 19.5033i) q^{28} +(22.9425 - 39.7376i) q^{29} +(40.5841 + 61.1116i) q^{30} +(13.2265 + 7.63630i) q^{31} +(20.0774 - 34.7751i) q^{32} +(1.32450 + 21.1225i) q^{33} +(7.28840 + 4.20796i) q^{34} +(6.32341 + 64.1170i) q^{35} +(10.6781 - 25.3726i) q^{36} +(17.6998 - 30.6570i) q^{37} -5.24181i q^{38} +(7.97089 + 12.0026i) q^{39} -23.0189i q^{40} +(48.4509 - 27.9732i) q^{41} +(43.2239 - 35.2784i) q^{42} +(-3.45068 + 5.97676i) q^{43} +(-10.7889 + 18.6870i) q^{44} +(-10.3479 - 82.1872i) q^{45} +(6.67920 + 11.5687i) q^{46} +(-44.4658 + 25.6723i) q^{47} +(-47.1813 + 31.3330i) q^{48} +(48.0560 - 9.57195i) q^{49} +(79.3241 + 137.393i) q^{50} +(-5.25724 - 7.91637i) q^{51} +14.6900i q^{52} +(-10.3556 - 17.9365i) q^{53} +(-54.3316 + 46.8385i) q^{54} +64.9312i q^{55} +(-17.4222 + 1.71823i) q^{56} +(-2.63286 + 5.30108i) q^{57} -121.908 q^{58} +(-42.7391 - 24.6754i) q^{59} +(37.5678 - 75.6402i) q^{60} +(1.99551 - 1.15211i) q^{61} -40.5764i q^{62} +(-61.4323 + 13.9668i) q^{63} -31.1668 q^{64} +(22.1022 + 38.2822i) q^{65} +(46.8406 - 31.1068i) q^{66} +(-15.4139 + 26.6977i) q^{67} -9.68884i q^{68} +(-0.943990 - 15.0544i) q^{69} +(139.125 - 99.7228i) q^{70} +81.2604 q^{71} +(22.3323 - 2.81177i) q^{72} +(-61.7481 + 35.6503i) q^{73} -94.0503 q^{74} +(-11.2111 - 178.790i) q^{75} +(-5.22615 + 3.01732i) q^{76} +(49.1442 - 4.84675i) q^{77} +(17.0278 - 34.2843i) q^{78} +(14.5179 + 25.1458i) q^{79} +(-150.485 + 86.8823i) q^{80} +(78.4720 - 20.0785i) q^{81} +(-128.725 - 74.3195i) q^{82} +(55.9283 + 32.2902i) q^{83} +(-60.0538 - 22.7877i) q^{84} +(-14.5776 - 25.2492i) q^{85} +18.3357 q^{86} +(123.287 + 61.2320i) q^{87} -17.6434 q^{88} +(89.0979 + 51.4407i) q^{89} +(-175.356 + 132.987i) q^{90} +(27.3247 - 19.5860i) q^{91} +(7.68944 - 13.3185i) q^{92} +(-20.3808 + 41.0353i) q^{93} +(118.137 + 68.2067i) q^{94} +(-9.07960 + 15.7263i) q^{95} +(107.890 + 53.5852i) q^{96} +(-48.7891 - 28.1684i) q^{97} +(-85.8617 - 97.8551i) q^{98} +(-62.9946 + 7.93140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9}+O(q^{10}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} - 6 q^{10} - 14 q^{11} - 3 q^{12} + 15 q^{13} - 11 q^{14} - 18 q^{15} - 27 q^{16} - 33 q^{17} + 33 q^{18} - 6 q^{19} + 108 q^{20} + 12 q^{21} - 10 q^{22} - 68 q^{23} + 42 q^{24} - 62 q^{25} + 54 q^{26} - 81 q^{27} - 16 q^{28} + 70 q^{29} - 6 q^{30} + 45 q^{31} + 153 q^{32} - 114 q^{33} + 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} - 120 q^{39} - 234 q^{41} - 51 q^{42} + 30 q^{43} + 51 q^{44} + 276 q^{45} - 22 q^{46} - 111 q^{47} + 147 q^{48} + 34 q^{49} + 241 q^{50} - 6 q^{51} + 148 q^{53} + 378 q^{54} - 412 q^{56} + 189 q^{57} - 34 q^{58} + 42 q^{59} + 456 q^{60} + 120 q^{61} - 222 q^{63} - 48 q^{64} + 114 q^{65} - 447 q^{66} - 34 q^{67} + 78 q^{69} + 264 q^{70} - 350 q^{71} - 339 q^{72} - 6 q^{73} - 718 q^{74} - 123 q^{75} + 72 q^{76} - 32 q^{77} - 375 q^{78} - 82 q^{79} - 609 q^{80} - 3 q^{81} - 18 q^{82} + 738 q^{83} + 609 q^{84} + 3 q^{85} - 34 q^{86} + 3 q^{87} - 50 q^{88} + 21 q^{89} - 543 q^{90} + 39 q^{91} + 288 q^{92} + 252 q^{93} - 3 q^{94} + 507 q^{95} - 582 q^{96} - 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * q^96 - 57 * q^97 + 811 * q^98 - 162 * q^99

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