LMFDB - Embedded newform 366.3.s.a.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [366,3,Mod(37,366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(366, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("366.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 366 = 2 \cdot 3 \cdot 61 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	366.s (of order $20$, degree $8$, 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:	$9.97277767559$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	366.37
Dual form			366.3.s.a.277.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642040 + 1.26007i) q^{2} +(1.64728 - 0.535233i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-1.15144 - 1.58482i) q^{5} +(-0.383185 + 2.41933i) q^{6} +(-6.58739 + 3.35644i) q^{7} +(2.79360 - 0.442463i) q^{8} +(2.42705 - 1.76336i) q^{9} +(2.73627 - 0.433382i) q^{10} +(4.59003 - 4.59003i) q^{11} +(-2.80252 - 2.03615i) q^{12} +14.4301 q^{13} -10.4556i q^{14} +(-2.74500 - 1.99436i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-2.16400 + 13.6629i) q^{17} +(0.663695 + 4.19041i) q^{18} +(20.4774 - 6.65353i) q^{19} +(-1.21070 + 3.72615i) q^{20} +(-9.05478 + 9.05478i) q^{21} +(2.83680 + 8.73076i) q^{22} +(38.9787 + 6.17361i) q^{23} +(4.36502 - 2.22409i) q^{24} +(6.53958 - 20.1267i) q^{25} +(-9.26472 + 18.1830i) q^{26} +(3.05422 - 4.20378i) q^{27} +(13.1748 + 6.71288i) q^{28} +(23.9329 - 23.9329i) q^{29} +(4.27543 - 2.17844i) q^{30} +(-12.1460 - 23.8378i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(5.10432 - 10.0178i) q^{33} +(-15.8269 - 11.4989i) q^{34} +(12.9044 + 6.57510i) q^{35} +(-5.70634 - 1.85410i) q^{36} +(-8.49106 - 16.6646i) q^{37} +(-4.76340 + 30.0749i) q^{38} +(23.7704 - 7.72349i) q^{39} +(-3.91790 - 3.91790i) q^{40} +(3.25815 + 1.05864i) q^{41} +(-5.59616 - 17.2232i) q^{42} +(-34.3497 + 5.44045i) q^{43} +(-12.8227 - 2.03092i) q^{44} +(-5.58922 - 1.81605i) q^{45} +(-32.8050 + 45.1523i) q^{46} +81.9708 q^{47} +6.92820i q^{48} +(3.32649 - 4.57852i) q^{49} +(21.1625 + 21.1625i) q^{50} +(3.74815 + 23.6649i) q^{51} +(-16.9636 - 23.3484i) q^{52} +(4.55868 + 28.7823i) q^{53} +(3.33614 + 6.54753i) q^{54} +(-12.5596 - 1.98924i) q^{55} +(-16.9175 + 12.2912i) q^{56} +(30.1709 - 21.9204i) q^{57} +(14.7914 + 45.5231i) q^{58} +(60.8792 + 31.0195i) q^{59} +6.78600i q^{60} +(-59.2986 + 14.3066i) q^{61} +37.8356 q^{62} +(-10.0693 + 19.7622i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-16.6155 - 22.8692i) q^{65} +(9.34599 + 12.8636i) q^{66} +(-10.8712 + 68.6381i) q^{67} +(24.6510 - 12.5603i) q^{68} +(67.5130 - 10.6930i) q^{69} +(-16.5702 + 12.0390i) q^{70} +(-83.2417 + 13.1842i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-2.53143 - 1.83919i) q^{73} +26.4503 q^{74} -36.6545i q^{75} +(-34.8383 - 25.3115i) q^{76} +(-14.8301 + 45.6425i) q^{77} +(-5.52941 + 34.9113i) q^{78} +(-8.87355 - 56.0254i) q^{79} +(7.45229 - 2.42140i) q^{80} +(2.78115 - 8.55951i) q^{81} +(-3.42582 + 3.42582i) q^{82} +(22.8010 + 70.1743i) q^{83} +(25.2955 + 4.00641i) q^{84} +(24.1451 - 12.3025i) q^{85} +(15.1985 - 46.7761i) q^{86} +(26.6145 - 52.2339i) q^{87} +(10.7918 - 14.8537i) q^{88} +(-60.5462 - 30.8498i) q^{89} +(5.87685 - 5.87685i) q^{90} +(-95.0569 + 48.4339i) q^{91} +(-35.8330 - 70.3263i) q^{92} +(-32.7666 - 32.7666i) q^{93} +(-52.6285 + 103.289i) q^{94} +(-34.1233 - 24.7920i) q^{95} +(-8.73005 - 4.44818i) q^{96} +(99.5654 + 32.3508i) q^{97} +(3.63354 + 7.13122i) q^{98} +(3.04638 - 19.2341i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 20 q^{2} - 40 q^{5} + 20 q^{7} + 40 q^{8} + 60 q^{9} + 60 q^{10} + 20 q^{11} - 32 q^{13} + 80 q^{16} + 80 q^{17} + 60 q^{18} - 100 q^{19} - 40 q^{20} + 12 q^{21} - 60 q^{22} + 56 q^{23} + 144 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) $ 80 * q - 20 * q^2 - 40 * q^5 + 20 * q^7 + 40 * q^8 + 60 * q^9 + 60 * q^10 + 20 * q^11 - 32 * q^13 + 80 * q^16 + 80 * q^17 + 60 * q^18 - 100 * q^19 - 40 * q^20 + 12 * q^21 - 60 * q^22 + 56 * q^23 + 144 * q^25 + 48 * q^26 - 40 * q^28 - 4 * q^29 - 68 * q^31 - 320 * q^32 + 12 * q^33 + 20 * q^34 + 12 * q^35 + 100 * q^37 + 148 * q^38 + 120 * q^39 + 280 * q^41 - 36 * q^42 - 260 * q^43 + 40 * q^44 - 40 * q^46 + 392 * q^47 + 20 * q^49 - 416 * q^50 + 96 * q^51 + 40 * q^52 - 504 * q^53 + 188 * q^55 + 72 * q^57 + 92 * q^58 + 108 * q^59 + 236 * q^61 - 136 * q^62 - 60 * q^63 + 120 * q^65 - 180 * q^66 - 600 * q^67 - 280 * q^68 - 360 * q^69 - 96 * q^70 + 424 * q^71 + 480 * q^72 - 324 * q^73 - 560 * q^74 + 136 * q^76 - 548 * q^77 + 48 * q^78 - 252 * q^79 - 180 * q^81 + 136 * q^82 - 312 * q^83 + 24 * q^84 + 992 * q^85 - 340 * q^86 - 108 * q^87 + 1128 * q^89 - 416 * q^91 + 48 * q^92 + 36 * q^93 - 88 * q^94 - 132 * q^95 - 260 * q^97 - 4 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/366\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.642040	+	1.26007i	−0.321020	+	0.630037i
$2$	−0.642040	+	1.26007i	−0.321020	+	0.630037i
$3$	1.64728	−	0.535233i	0.549093	−	0.178411i
$3$	1.64728	−	0.535233i	0.549093	−	0.178411i
$4$	−1.17557	−	1.61803i	−0.293893	−	0.404508i
$5$	−1.15144	−	1.58482i	−0.230288	−	0.316965i	0.678198	−	0.734879i	$-0.262761\pi$
$5$	−1.15144	−	1.58482i	−0.230288	−	0.316965i	−0.908486	+	0.417914i	$0.862761\pi$
$6$	−0.383185	+	2.41933i	−0.0638641	+	0.403222i
$7$	−6.58739	+	3.35644i	−0.941055	+	0.479492i	−0.856052	−	0.516889i	$-0.827090\pi$
$7$	−6.58739	+	3.35644i	−0.941055	+	0.479492i	−0.0850029	+	0.996381i	$0.527090\pi$
$8$	2.79360	−	0.442463i	0.349201	−	0.0553079i
$9$	2.42705	−	1.76336i	0.269672	−	0.195928i
$10$	2.73627	−	0.433382i	0.273627	−	0.0433382i
$11$	4.59003	−	4.59003i	0.417276	−	0.417276i	−0.466988	−	0.884264i	$-0.654661\pi$
$11$	4.59003	−	4.59003i	0.417276	−	0.417276i	0.884264	+	0.466988i	$0.154661\pi$
$12$	−2.80252	−	2.03615i	−0.233543	−	0.169679i
$13$	14.4301			1.11001			0.555005	−	0.831847i	$-0.312716\pi$
$13$	14.4301			1.11001			0.555005	+	0.831847i	$0.312716\pi$
$14$		−	10.4556i		−	0.746826i
$15$	−2.74500	−	1.99436i	−0.183000	−	0.132957i
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	−2.16400	+	13.6629i	−0.127294	+	0.803703i	0.838597	+	0.544753i	$0.183376\pi$
$17$	−2.16400	+	13.6629i	−0.127294	+	0.803703i	−0.965891	+	0.258950i	$0.916624\pi$
$18$	0.663695	+	4.19041i	0.0368720	+	0.232800i
$19$	20.4774	−	6.65353i	1.07776	−	0.350186i	0.284255	−	0.958749i	$-0.408254\pi$
$19$	20.4774	−	6.65353i	1.07776	−	0.350186i	0.793505	+	0.608563i	$0.208254\pi$
$20$	−1.21070	+	3.72615i	−0.0605349	+	0.186307i
$21$	−9.05478	+	9.05478i	−0.431180	+	0.431180i
$22$	2.83680	+	8.73076i	0.128945	+	0.396853i
$23$	38.9787	+	6.17361i	1.69472	+	0.268418i	0.927734	−	0.373241i	$-0.121754\pi$
$23$	38.9787	+	6.17361i	1.69472	+	0.268418i	0.766990	+	0.641659i	$0.221754\pi$
$24$	4.36502	−	2.22409i	0.181876	−	0.0926704i
$25$	6.53958	−	20.1267i	0.261583	−	0.805070i
$26$	−9.26472	+	18.1830i	−0.356335	+	0.699347i
$27$	3.05422	−	4.20378i	0.113119	−	0.155695i
$28$	13.1748	+	6.71288i	0.470528	+	0.239746i
$29$	23.9329	−	23.9329i	0.825274	−	0.825274i	−0.161585	−	0.986859i	$-0.551661\pi$
$29$	23.9329	−	23.9329i	0.825274	−	0.825274i	0.986859	+	0.161585i	$0.0516606\pi$
$30$	4.27543	−	2.17844i	0.142514	−	0.0726147i
$31$	−12.1460	−	23.8378i	−0.391805	−	0.768961i	0.607880	−	0.794029i	$-0.292020\pi$
$31$	−12.1460	−	23.8378i	−0.391805	−	0.768961i	−0.999686	+	0.0250674i	$0.992020\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	5.10432	−	10.0178i	0.154676	−	0.303570i
$34$	−15.8269	−	11.4989i	−0.465498	−	0.338204i
$35$	12.9044	+	6.57510i	0.368696	+	0.187860i
$36$	−5.70634	−	1.85410i	−0.158509	−	0.0515028i
$37$	−8.49106	−	16.6646i	−0.229488	−	0.450396i	0.747334	−	0.664449i	$-0.231334\pi$
$37$	−8.49106	−	16.6646i	−0.229488	−	0.450396i	−0.976822	+	0.214053i	$0.931334\pi$
$38$	−4.76340	+	30.0749i	−0.125353	+	0.791445i
$39$	23.7704	−	7.72349i	0.609499	−	0.198038i
$40$	−3.91790	−	3.91790i	−0.0979475	−	0.0979475i
$41$	3.25815	+	1.05864i	0.0794670	+	0.0258204i	0.348481	−	0.937316i	$-0.386698\pi$
$41$	3.25815	+	1.05864i	0.0794670	+	0.0258204i	−0.269014	+	0.963136i	$0.586698\pi$
$42$	−5.59616	−	17.2232i	−0.133242	−	0.410077i
$43$	−34.3497	+	5.44045i	−0.798829	+	0.126522i	−0.542487	−	0.840064i	$-0.682517\pi$
$43$	−34.3497	+	5.44045i	−0.798829	+	0.126522i	−0.256342	+	0.966586i	$0.582517\pi$
$44$	−12.8227	−	2.03092i	−0.291426	−	0.0461573i
$45$	−5.58922	−	1.81605i	−0.124205	−	0.0403566i
$46$	−32.8050	+	45.1523i	−0.713153	+	0.981571i
$47$	81.9708			1.74406			0.872030	−	0.489452i	$-0.162803\pi$
$47$	81.9708			1.74406			0.872030	+	0.489452i	$0.162803\pi$
$48$			6.92820i			0.144338i
$49$	3.32649	−	4.57852i	0.0678876	−	0.0934393i
$50$	21.1625	+	21.1625i	0.423250	+	0.423250i
$51$	3.74815	+	23.6649i	0.0734932	+	0.464018i
$52$	−16.9636	−	23.3484i	−0.326224	−	0.449009i
$53$	4.55868	+	28.7823i	0.0860127	+	0.543063i	0.992637	+	0.121125i	$0.0386501\pi$
$53$	4.55868	+	28.7823i	0.0860127	+	0.543063i	−0.906625	+	0.421938i	$0.861350\pi$
$54$	3.33614	+	6.54753i	0.0617803	+	0.121251i
$55$	−12.5596	−	1.98924i	−0.228355	−	0.0361680i
$56$	−16.9175	+	12.2912i	−0.302097	+	0.219487i
$57$	30.1709	−	21.9204i	0.529313	−	0.384569i
$58$	14.7914	+	45.5231i	0.255024	+	0.784882i
$59$	60.8792	+	31.0195i	1.03185	+	0.525755i	0.886065	−	0.463561i	$-0.153429\pi$
$59$	60.8792	+	31.0195i	1.03185	+	0.525755i	0.145787	+	0.989316i	$0.453429\pi$
$60$			6.78600i			0.113100i
$61$	−59.2986	+	14.3066i	−0.972108	+	0.234535i
$61$	−59.2986	+	14.3066i	−0.972108	+	0.234535i
$62$	37.8356			0.610251
$63$	−10.0693	+	19.7622i	−0.159831	+	0.313685i
$64$	7.60845	−	2.47214i	0.118882	−	0.0386271i
$65$	−16.6155	−	22.8692i	−0.255623	−	0.351834i
$66$	9.34599	+	12.8636i	0.141606	+	0.194904i
$67$	−10.8712	+	68.6381i	−0.162257	+	1.02445i	0.763356	+	0.645978i	$0.223550\pi$
$67$	−10.8712	+	68.6381i	−0.162257	+	1.02445i	−0.925613	+	0.378471i	$0.876450\pi$
$68$	24.6510	−	12.5603i	0.362515	−	0.184711i
$69$	67.5130	−	10.6930i	0.978449	−	0.154971i
$70$	−16.5702	+	12.0390i	−0.236717	+	0.171985i
$71$	−83.2417	+	13.1842i	−1.17242	+	0.185693i	−0.712111	−	0.702067i	$-0.752261\pi$
$71$	−83.2417	+	13.1842i	−1.17242	+	0.185693i	−0.460308	+	0.887759i	$0.652261\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−2.53143	−	1.83919i	−0.0346771	−	0.0251944i	0.570312	−	0.821428i	$-0.306822\pi$
$73$	−2.53143	−	1.83919i	−0.0346771	−	0.0251944i	−0.604989	+	0.796234i	$0.706822\pi$
$74$	26.4503			0.357436
$75$		−	36.6545i		−	0.488727i
$76$	−34.8383	−	25.3115i	−0.458399	−	0.333046i
$77$	−14.8301	+	45.6425i	−0.192599	+	0.592760i
$78$	−5.52941	+	34.9113i	−0.0708898	+	0.447581i
$79$	−8.87355	−	56.0254i	−0.112323	−	0.709182i	−0.978004	−	0.208586i	$-0.933114\pi$
$79$	−8.87355	−	56.0254i	−0.112323	−	0.709182i	0.865681	−	0.500597i	$-0.166886\pi$
$80$	7.45229	−	2.42140i	0.0931536	−	0.0302674i
$81$	2.78115	−	8.55951i	0.0343352	−	0.105673i
$82$	−3.42582	+	3.42582i	−0.0417783	+	0.0417783i
$83$	22.8010	+	70.1743i	0.274711	+	0.845474i	0.989296	+	0.145925i	$0.0466158\pi$
$83$	22.8010	+	70.1743i	0.274711	+	0.845474i	−0.714585	+	0.699549i	$0.753384\pi$
$84$	25.2955	+	4.00641i	0.301137	+	0.0476954i
$85$	24.1451	−	12.3025i	0.284060	−	0.144736i
$86$	15.1985	−	46.7761i	0.176726	−	0.543908i
$87$	26.6145	−	52.2339i	0.305914	−	0.600390i
$88$	10.7918	−	14.8537i	0.122634	−	0.168792i
$89$	−60.5462	−	30.8498i	−0.680294	−	0.346627i	0.0794597	−	0.996838i	$-0.474680\pi$
$89$	−60.5462	−	30.8498i	−0.680294	−	0.346627i	−0.759754	+	0.650211i	$0.774680\pi$
$90$	5.87685	−	5.87685i	0.0652983	−	0.0652983i
$91$	−95.0569	+	48.4339i	−1.04458	+	0.532241i
$92$	−35.8330	−	70.3263i	−0.389490	−	0.764416i
$93$	−32.7666	−	32.7666i	−0.352329	−	0.352329i
$94$	−52.6285	+	103.289i	−0.559878	+	1.09882i
$95$	−34.1233	−	24.7920i	−0.359192	−	0.260968i
$96$	−8.73005	−	4.44818i	−0.0909380	−	0.0463352i
$97$	99.5654	+	32.3508i	1.02645	+	0.333513i	0.773385	−	0.633937i	$-0.218562\pi$
$97$	99.5654	+	32.3508i	1.02645	+	0.333513i	0.253063	+	0.967450i	$0.418562\pi$
$98$	3.63354	+	7.13122i	0.0370769	+	0.0727675i
$99$	3.04638	−	19.2341i	0.0307715	−	0.194284i
$100$	−40.2535	+	13.0792i	−0.402535	+	0.130792i
$101$	47.5552	+	47.5552i	0.470844	+	0.470844i	0.902188	−	0.431344i	$-0.141960\pi$
$101$	47.5552	+	47.5552i	0.470844	+	0.470844i	−0.431344	+	0.902188i	$0.641960\pi$
$102$	−32.2260	−	10.4709i	−0.315941	−	0.102655i
$103$	−55.1027	−	169.589i	−0.534978	−	1.64649i	−0.743696	−	0.668518i	$-0.766929\pi$
$103$	−55.1027	−	169.589i	−0.534978	−	1.64649i	0.208718	−	0.977976i	$-0.433071\pi$
$104$	40.3121	−	6.38481i	0.387616	−	0.0613924i
$105$	24.7763	+	3.92418i	0.235965	+	0.0373731i
$106$	−39.1947	−	12.7351i	−0.369761	−	0.120143i
$107$	−15.5805	+	21.4447i	−0.145612	+	0.200418i	−0.875593	−	0.483050i	$-0.839529\pi$
$107$	−15.5805	+	21.4447i	−0.145612	+	0.200418i	0.729981	+	0.683468i	$0.239529\pi$
$108$	−10.3923			−0.0962250
$109$		−	116.798i		−	1.07154i	−0.844363	−	0.535771i	$-0.820021\pi$
$109$		−	116.798i		−	1.07154i	0.844363	−	0.535771i	$-0.179979\pi$
$110$	10.5703	−	14.5488i	0.0960938	−	0.132262i
$111$	−22.9066	−	22.9066i	−0.206366	−	0.206366i
$112$	−4.62620	−	29.2087i	−0.0413054	−	0.260792i
$113$	−9.03896	−	12.4411i	−0.0799908	−	0.110098i	0.767147	−	0.641472i	$-0.221676\pi$
$113$	−9.03896	−	12.4411i	−0.0799908	−	0.110098i	−0.847137	+	0.531374i	$0.821676\pi$
$114$	8.25045	+	52.0913i	0.0723724	+	0.456941i
$115$	−35.0976	−	68.8829i	−0.305196	−	0.598981i
$116$	−66.8592	−	10.5894i	−0.576372	−	0.0912884i
$117$	35.0227	−	25.4455i	0.299339	−	0.217483i
$118$	−78.1738	+	56.7966i	−0.662489	+	0.481327i
$119$	−31.6038	−	97.2664i	−0.265578	−	0.817365i
$120$	−8.55086	−	4.35688i	−0.0712572	−	0.0363074i
$121$			78.8632i			0.651762i
$122$	20.0446	−	83.9060i	0.164300	−	0.687754i
$123$	5.93369			0.0482414
$124$	−24.2919	+	47.6756i	−0.195903	+	0.384481i
$125$	−86.0041	+	27.9444i	−0.688033	+	0.223555i
$126$	−18.4369	−	25.3762i	−0.146324	−	0.201398i
$127$	−53.1403	−	73.1414i	−0.418428	−	0.575917i	0.546821	−	0.837250i	$-0.315838\pi$
$127$	−53.1403	−	73.1414i	−0.418428	−	0.575917i	−0.965249	+	0.261333i	$0.915838\pi$
$128$	−1.76985	+	11.1744i	−0.0138270	+	0.0873001i
$129$	−53.6715	+	27.3470i	−0.416058	+	0.211992i
$130$	39.4847	−	6.25376i	0.303728	−	0.0481058i
$131$	131.963	−	95.8770i	1.00735	−	0.731885i	0.0437015	−	0.999045i	$-0.486085\pi$
$131$	131.963	−	95.8770i	1.00735	−	0.731885i	0.963652	+	0.267159i	$0.0860850\pi$
$132$	−22.2096	+	3.51766i	−0.168255	+	0.0266489i
$133$	−112.561	+	112.561i	−0.846321	+	0.846321i
$134$	−79.5093	−	57.7669i	−0.593353	−	0.431096i
$135$	−10.1790			−0.0754000
$136$			39.1264i			0.287694i
$137$	−85.8307	−	62.3597i	−0.626502	−	0.455180i	0.228685	−	0.973501i	$-0.426557\pi$
$137$	−85.8307	−	62.3597i	−0.626502	−	0.455180i	−0.855186	+	0.518320i	$0.826557\pi$
$138$	−29.8720	+	91.9367i	−0.216464	+	0.666208i
$139$	−39.4302	+	248.953i	−0.283671	+	1.79103i	0.274800	+	0.961501i	$0.411388\pi$
$139$	−39.4302	+	248.953i	−0.283671	+	1.79103i	−0.558471	+	0.829524i	$0.688612\pi$
$140$	−4.53125	−	28.6092i	−0.0323661	−	0.204351i
$141$	135.029	−	43.8735i	0.957651	−	0.311160i
$142$	36.8314	−	113.355i	0.259376	−	0.798278i
$143$	66.2348	−	66.2348i	0.463180	−	0.463180i
$144$	3.70820	+	11.4127i	0.0257514	+	0.0792547i
$145$	−65.4869	−	10.3721i	−0.451634	−	0.0715318i
$146$	3.94279	−	2.00895i	0.0270054	−	0.0137599i
$147$	3.02908	−	9.32255i	0.0206060	−	0.0634187i
$148$	−16.9821	+	33.3293i	−0.114744	+	0.225198i
$149$	−75.1163	+	103.389i	−0.504136	+	0.693884i	−0.982917	−	0.184050i	$-0.941079\pi$
$149$	−75.1163	+	103.389i	−0.504136	+	0.693884i	0.478780	+	0.877935i	$0.341079\pi$
$150$	46.1874	+	23.5337i	0.307916	+	0.156891i
$151$	97.5440	−	97.5440i	0.645987	−	0.645987i	−0.306034	−	0.952021i	$-0.599002\pi$
$151$	97.5440	−	97.5440i	0.645987	−	0.645987i	0.952021	+	0.306034i	$0.0990021\pi$
$152$	54.2619	−	27.6478i	0.356987	−	0.181894i
$153$	18.8405	+	36.9766i	0.123141	+	0.241677i
$154$	−47.9914	−	47.9914i	−0.311632	−	0.311632i
$155$	−23.7933	+	46.6971i	−0.153505	+	0.301271i
$156$	−40.4407	−	29.3819i	−0.259235	−	0.188345i
$157$	−223.990	−	114.129i	−1.42669	−	0.726934i	−0.441316	−	0.897352i	$-0.645488\pi$
$157$	−223.990	−	114.129i	−1.42669	−	0.726934i	−0.985372	+	0.170417i	$0.945488\pi$
$158$	76.2933	+	24.7892i	0.482869	+	0.156894i
$159$	22.9147	+	44.9726i	0.144117	+	0.282846i
$160$	−1.73353	+	10.9451i	−0.0108346	+	0.0684067i
$161$	−277.489	+	90.1616i	−1.72353	+	0.560010i
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−65.0527	−	21.1369i	−0.399096	−	0.129674i	0.102590	−	0.994724i	$-0.467287\pi$
$163$	−65.0527	−	21.1369i	−0.399096	−	0.129674i	−0.501687	+	0.865050i	$0.667287\pi$
$164$	−2.11727	−	6.51630i	−0.0129102	−	0.0397335i
$165$	−21.7538	+	3.44546i	−0.131841	+	0.0208816i
$166$	−103.064	−	16.3237i	−0.620867	−	0.0983357i
$167$	124.612	+	40.4890i	0.746182	+	0.242449i	0.657338	−	0.753596i	$-0.271683\pi$
$167$	124.612	+	40.4890i	0.746182	+	0.242449i	0.0888445	+	0.996046i	$0.471683\pi$
$168$	−21.2891	+	29.3019i	−0.126721	+	0.174416i
$169$	39.2287			0.232123
$170$			38.3233i			0.225431i
$171$	37.9673	−	52.2575i	0.222031	−	0.305599i
$172$	49.1833	+	49.1833i	0.285949	+	0.285949i
$173$	−28.7178	−	181.317i	−0.165999	−	1.04808i	−0.920205	−	0.391438i	$-0.871978\pi$
$173$	−28.7178	−	181.317i	−0.165999	−	1.04808i	0.754206	−	0.656638i	$-0.228022\pi$
$174$	48.7310	+	67.0725i	0.280063	+	0.385474i
$175$	24.4755	+	154.532i	0.139860	+	0.883042i
$176$	11.7879	+	23.1351i	0.0669769	+	0.131450i
$177$	116.888	+	18.5132i	0.660383	+	0.104594i
$178$	77.7461	−	56.4858i	0.436776	−	0.317336i
$179$	211.268	−	153.495i	1.18027	−	0.857516i	0.188068	−	0.982156i	$-0.439778\pi$
$179$	211.268	−	153.495i	1.18027	−	0.857516i	0.992202	+	0.124640i	$0.0397775\pi$
$180$	3.63209	+	11.1784i	0.0201783	+	0.0621024i
$181$	−194.005	−	98.8506i	−1.07185	−	0.546136i	−0.173240	−	0.984880i	$-0.555424\pi$
$181$	−194.005	−	98.8506i	−1.07185	−	0.546136i	−0.898612	+	0.438744i	$0.855424\pi$
$182$		−	150.875i		−	0.828984i
$183$	−90.0239	+	55.3055i	−0.491934	+	0.302216i
$184$	111.623			0.606644
$185$	−16.6336	+	32.6452i	−0.0899111	+	0.176461i
$186$	62.3257	−	20.2508i	0.335084	−	0.108876i
$187$	52.7805	+	72.6462i	0.282249	+	0.388482i
$188$	−96.3625	−	132.632i	−0.512566	−	0.705487i
$189$	−6.00961	+	37.9432i	−0.0317969	+	0.200758i
$190$	53.1482	−	27.0804i	0.279728	−	0.142528i
$191$	−140.098	+	22.1893i	−0.733497	+	0.116175i	−0.511999	−	0.858986i	$-0.671095\pi$
$191$	−140.098	+	22.1893i	−0.733497	+	0.116175i	−0.221498	+	0.975161i	$0.571095\pi$
$192$	11.2101	−	8.14459i	0.0583858	−	0.0424197i
$193$	17.4860	−	2.76951i	0.0906009	−	0.0143498i	−0.110969	−	0.993824i	$-0.535396\pi$
$193$	17.4860	−	2.76951i	0.0906009	−	0.0143498i	0.201570	+	0.979474i	$0.435396\pi$
$194$	−104.689	+	104.689i	−0.539635	+	0.539635i
$195$	−39.6107	−	28.7788i	−0.203132	−	0.147584i
$196$	−11.3187			−0.0577487
$197$			125.585i			0.637486i	0.947841	+	0.318743i	$0.103261\pi$
$197$			125.585i			0.637486i	−0.947841	+	0.318743i	$0.896739\pi$
$198$	22.2805	+	16.1877i	0.112528	+	0.0817562i
$199$	48.2530	−	148.507i	0.242477	−	0.746268i	−0.753564	−	0.657375i	$-0.771667\pi$
$199$	48.2530	−	148.507i	0.242477	−	0.746268i	0.996041	−	0.0888934i	$-0.0283330\pi$
$200$	9.36364	−	59.1197i	0.0468182	−	0.295598i
$201$	18.8295	+	118.885i	0.0936790	+	0.591466i
$202$	−90.4554	+	29.3907i	−0.447799	+	0.145499i
$203$	−77.3260	+	237.985i	−0.380916	+	1.17234i
$204$	33.8844	−	33.8844i	0.166100	−	0.166100i
$205$	−2.07382	−	6.38255i	−0.0101162	−	0.0311344i
$206$	249.073	+	39.4492i	1.20909	+	0.191501i
$207$	105.489	−	53.7496i	0.509611	−	0.259660i
$208$	−17.8366	+	54.8955i	−0.0857530	+	0.263921i
$209$	63.4523	−	124.532i	0.303599	−	0.595847i
$210$	−20.8521	+	28.7005i	−0.0992958	+	0.136669i
$211$	256.914	+	130.904i	1.21760	+	0.620399i	0.940288	−	0.340380i	$-0.110556\pi$
$211$	256.914	+	130.904i	1.21760	+	0.620399i	0.277314	+	0.960779i	$0.410556\pi$
$212$	41.2118	−	41.2118i	0.194395	−	0.194395i
$213$	−130.066	+	66.2718i	−0.610637	+	0.311135i
$214$	−17.0186	−	33.4009i	−0.0795261	−	0.156079i
$215$	48.1738	+	48.1738i	0.224064	+	0.224064i
$216$	6.67227	−	13.0951i	0.0308901	−	0.0606253i
$217$	160.020	+	116.262i	0.737421	+	0.535768i
$218$	147.174	+	74.9890i	0.675111	+	0.343986i
$219$	−5.15436	−	1.67475i	−0.0235359	−	0.00764727i
$220$	11.5460	+	22.6603i	0.0524818	+	0.103001i
$221$	−31.2268	+	197.158i	−0.141298	+	0.892118i
$222$	43.5709	−	14.1571i	0.196265	−	0.0637705i
$223$	302.807	+	302.807i	1.35788	+	1.35788i	0.876525	+	0.481356i	$0.159856\pi$
$223$	302.807	+	302.807i	1.35788	+	1.35788i	0.481356	+	0.876525i	$0.340144\pi$
$224$	39.7753	+	12.9238i	0.177568	+	0.0576955i
$225$	−19.6187	−	60.3802i	−0.0871943	−	0.268357i
$226$	21.4800	−	3.40210i	0.0950443	−	0.0150535i
$227$	419.863	+	66.4998i	1.84962	+	0.292951i	0.979733	−	0.200306i	$-0.0641936\pi$
$227$	419.863	+	66.4998i	1.84962	+	0.292951i	0.869884	+	0.493257i	$0.164194\pi$
$228$	−70.9360	−	23.0485i	−0.311123	−	0.101090i
$229$	67.3842	−	92.7465i	0.294254	−	0.405006i	−0.636136	−	0.771577i	$-0.719468\pi$
$229$	67.3842	−	92.7465i	0.294254	−	0.405006i	0.930390	+	0.366571i	$0.119468\pi$
$230$	109.332			0.475354
$231$			83.1235i			0.359842i
$232$	56.2697	−	77.4486i	0.242542	−	0.333830i
$233$	220.818	+	220.818i	0.947718	+	0.947718i	0.998700	−	0.0509814i	$-0.0162349\pi$
$233$	220.818	+	220.818i	0.947718	+	0.947718i	−0.0509814	+	0.998700i	$0.516235\pi$
$234$	9.57721	+	60.4681i	0.0409282	+	0.258411i
$235$	−94.3847	−	129.909i	−0.401637	−	0.552806i
$236$	−21.3772	−	134.970i	−0.0905814	−	0.571908i
$237$	−44.6039	−	87.5400i	−0.188202	−	0.369367i
$238$	142.854	+	22.6258i	0.600226	+	0.0950664i
$239$	−100.845	+	73.2681i	−0.421945	+	0.306561i	−0.778420	−	0.627744i	$-0.783979\pi$
$239$	−100.845	+	73.2681i	−0.421945	+	0.306561i	0.356475	+	0.934305i	$0.383979\pi$
$240$	10.9800	−	7.97743i	0.0457499	−	0.0332393i
$241$	−13.5226	−	41.6184i	−0.0561105	−	0.172690i	0.919074	−	0.394086i	$-0.128939\pi$
$241$	−13.5226	−	41.6184i	−0.0561105	−	0.172690i	−0.975184	+	0.221396i	$0.928939\pi$
$242$	−99.3734	−	50.6333i	−0.410634	−	0.209228i
$243$		−	15.5885i		−	0.0641500i
$244$	92.8582	+	79.1287i	0.380567	+	0.324298i
$245$	−11.0864			−0.0452507
$246$	−3.80967	+	7.47689i	−0.0154864	+	0.0303939i
$247$	295.492	−	96.0113i	1.19633	−	0.388710i
$248$	−44.4784	−	61.2192i	−0.179348	−	0.246852i
$249$	75.1193	+	103.393i	0.301684	+	0.415232i
$250$	20.0060	−	126.313i	0.0800240	−	0.505252i
$251$	−415.915	+	211.919i	−1.65703	+	0.844300i	−0.661494	+	0.749951i	$0.730077\pi$
$251$	−415.915	+	211.919i	−1.65703	+	0.844300i	−0.995539	+	0.0943498i	$0.969923\pi$
$252$	43.8130	−	6.93931i	0.173861	−	0.0275369i
$253$	207.250	−	150.576i	0.819171	−	0.595163i
$254$	126.282	−	20.0011i	0.497172	−	0.0787443i
$255$	33.1889	−	33.1889i	0.130153	−	0.130153i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−239.658			−0.932520			−0.466260	−	0.884648i	$-0.654399\pi$
$257$	−239.658			−0.932520			−0.466260	+	0.884648i	$0.654399\pi$
$258$		−	85.1879i		−	0.330186i
$259$	111.868	+	81.2767i	0.431922	+	0.313810i
$260$	−17.4705	+	53.7688i	−0.0671944	+	0.206803i
$261$	15.8842	−	100.289i	0.0608589	−	0.384248i
$262$	36.0864	+	227.840i	0.137734	+	0.869620i
$263$	−41.3259	+	13.4276i	−0.157133	+	0.0510555i	−0.386527	−	0.922278i	$-0.626325\pi$
$263$	−41.3259	+	13.4276i	−0.157133	+	0.0510555i	0.229394	+	0.973334i	$0.426325\pi$
$264$	9.82695	−	30.2442i	0.0372233	−	0.114562i
$265$	40.3659	−	40.3659i	0.152324	−	0.152324i
$266$	−69.5663	−	214.103i	−0.261528	−	0.804899i
$267$	−116.248	−	18.4119i	−0.435387	−	0.0689585i
$268$	123.839	−	63.0989i	0.462084	−	0.235444i
$269$	−22.5317	+	69.3453i	−0.0837608	+	0.257789i	−0.984162	−	0.177271i	$-0.943273\pi$
$269$	−22.5317	+	69.3453i	−0.0837608	+	0.257789i	0.900401	+	0.435060i	$0.143273\pi$
$270$	6.53532	−	12.8263i	0.0242049	−	0.0475048i
$271$	−225.674	+	310.613i	−0.832744	+	1.14617i	0.154663	+	0.987967i	$0.450571\pi$
$271$	−225.674	+	310.613i	−0.832744	+	1.14617i	−0.987406	+	0.158206i	$0.949429\pi$
$272$	−49.3021	−	25.1207i	−0.181258	−	0.0923554i
$273$	−130.662	+	130.662i	−0.478614	+	0.478614i
$274$	133.684	−	68.1156i	0.487900	−	0.248597i
$275$	−62.3656	−	122.399i	−0.226784	−	0.445088i
$276$	−96.6680	−	96.6680i	−0.350246	−	0.350246i
$277$	−191.725	+	376.281i	−0.692148	+	1.35842i	0.230614	+	0.973045i	$0.425927\pi$
$277$	−191.725	+	376.281i	−0.692148	+	1.35842i	−0.922762	+	0.385371i	$0.874073\pi$
$278$	−288.383	−	209.522i	−1.03735	−	0.753677i
$279$	−71.5134	−	36.4379i	−0.256320	−	0.130602i
$280$	38.9589	+	12.6585i	0.139139	+	0.0452090i
$281$	−67.9811	−	133.420i	−0.241926	−	0.474806i	0.737834	−	0.674982i	$-0.235849\pi$
$281$	−67.9811	−	133.420i	−0.241926	−	0.474806i	−0.979760	+	0.200176i	$0.935849\pi$
$282$	−31.4100	+	198.315i	−0.111383	+	0.703244i
$283$	247.215	−	80.3249i	0.873550	−	0.283834i	0.162274	−	0.986746i	$-0.448117\pi$
$283$	247.215	−	80.3249i	0.873550	−	0.283834i	0.711277	+	0.702912i	$0.248117\pi$
$284$	119.189	+	119.189i	0.419680	+	0.419680i
$285$	−69.4800	−	22.5754i	−0.243790	−	0.0792120i
$286$	40.9353	+	125.986i	0.143131	+	0.440511i
$287$	−25.0159	+	3.96214i	−0.0871635	+	0.0138053i
$288$	−16.7616	−	2.65478i	−0.0582001	−	0.00921799i
$289$	92.8622	+	30.1727i	0.321322	+	0.104404i
$290$	55.1148	−	75.8590i	0.190051	−	0.261583i
$291$	181.327			0.623117
$292$			6.25803i			0.0214316i
$293$	−98.0839	+	135.001i	−0.334757	+	0.460754i	−0.942901	−	0.333073i	$-0.891914\pi$
$293$	−98.0839	+	135.001i	−0.334757	+	0.460754i	0.608144	+	0.793827i	$0.291914\pi$
$294$	9.80231	+	9.80231i	0.0333412	+	0.0333412i
$295$	−20.9384	−	132.200i	−0.0709778	−	0.448136i
$296$	−31.0941	−	42.7974i	−0.105048	−	0.144586i
$297$	−5.27649	−	33.3144i	−0.0177660	−	0.112170i
$298$	−82.0498	−	161.032i	−0.275335	−	0.540375i
$299$	562.467	+	89.0860i	1.88116	+	0.297947i
$300$	−59.3083	+	43.0900i	−0.197694	+	0.143633i
$301$	208.014	−	151.131i	0.691076	−	0.502096i
$302$	60.2855	+	185.540i	0.199621	+	0.614370i
$303$	103.790	+	52.8835i	0.342541	+	0.174533i
$304$			86.1251i			0.283306i
$305$	90.9524	+	77.5046i	0.298204	+	0.254113i
$306$	−58.6895			−0.191796
$307$	−42.2994	+	83.0173i	−0.137783	+	0.270415i	−0.949580	−	0.313526i	$-0.898490\pi$
$307$	−42.2994	+	83.0173i	−0.137783	+	0.270415i	0.811797	+	0.583940i	$0.198490\pi$
$308$	91.2850	−	29.6603i	0.296380	−	0.0962997i
$309$	−181.539	−	249.867i	−0.587505	−	0.808632i
$310$	−43.5655	−	59.9627i	−0.140534	−	0.193428i
$311$	62.5978	−	395.227i	0.201279	−	1.27083i	−0.655520	−	0.755178i	$-0.727551\pi$
$311$	62.5978	−	395.227i	0.201279	−	1.27083i	0.856800	−	0.515650i	$-0.172449\pi$
$312$	62.9879	−	32.0939i	0.201884	−	0.102865i
$313$	−398.959	+	63.1888i	−1.27463	+	0.201881i	−0.756824	−	0.653618i	$-0.773250\pi$
$313$	−398.959	+	63.1888i	−1.27463	+	0.201881i	−0.517804	+	0.855500i	$0.673250\pi$
$314$	287.621	−	208.969i	0.915990	−	0.665506i
$315$	42.9138	−	6.79688i	0.136234	−	0.0215774i
$316$	−80.2195	+	80.2195i	−0.253859	+	0.253859i
$317$	−468.005	−	340.025i	−1.47636	−	1.07264i	−0.978708	−	0.205256i	$-0.934197\pi$
$317$	−468.005	−	340.025i	−1.47636	−	1.07264i	−0.497648	−	0.867379i	$-0.665803\pi$
$318$	−71.3809			−0.224468
$319$		−	219.706i		−	0.688733i
$320$	−12.6786	−	9.21154i	−0.0396206	−	0.0287861i
$321$	−14.1875	+	43.6645i	−0.0441977	+	0.136027i
$322$	64.5486	−	407.544i	0.200461	−	1.26566i
$323$	46.5936	+	294.180i	0.144253	+	0.910775i
$324$	−17.1190	+	5.56231i	−0.0528365	+	0.0171676i
$325$	94.3670	−	290.432i	0.290360	−	0.893636i
$326$	68.4004	−	68.4004i	0.209817	−	0.209817i
$327$	−62.5143	−	192.399i	−0.191175	−	0.588376i
$328$	9.57039	+	1.51580i	0.0291780	+	0.00462134i
$329$	−539.974	+	275.130i	−1.64126	+	0.836262i
$330$	9.62525	−	29.6235i	0.0291674	−	0.0897681i
$331$	14.5666	−	28.5885i	0.0440077	−	0.0863700i	−0.867956	−	0.496642i	$-0.834566\pi$
$331$	14.5666	−	28.5885i	0.0440077	−	0.0863700i	0.911963	+	0.410272i	$0.134566\pi$
$332$	86.7403	−	119.388i	0.261266	−	0.359602i
$333$	−49.9939	−	25.4732i	−0.150132	−	0.0764960i
$334$	−131.025	+	131.025i	−0.392291	+	0.392291i
$335$	121.297	−	61.8038i	0.362080	−	0.184489i
$336$	−23.2541	−	45.6388i	−0.0692087	−	0.135830i
$337$	−68.5881	−	68.5881i	−0.203526	−	0.203526i	0.597983	−	0.801509i	$-0.295969\pi$
$337$	−68.5881	−	68.5881i	−0.203526	−	0.203526i	−0.801509	+	0.597983i	$0.795969\pi$
$338$	−25.1864	+	49.4311i	−0.0745160	+	0.146246i
$339$	−21.5485	−	15.6559i	−0.0635650	−	0.0461827i
$340$	−48.2902	−	24.6051i	−0.142030	−	0.0723679i
$341$	−165.167	−	53.6659i	−0.484360	−	0.157378i
$342$	41.4718	+	81.3929i	0.121262	+	0.237991i
$343$	50.1256	−	316.481i	0.146139	−	0.922685i
$344$	−93.5521	+	30.3969i	−0.271954	+	0.0883632i
$345$	−94.6839	−	94.6839i	−0.274446	−	0.274446i
$346$	246.911	+	80.2262i	0.713615	+	0.231868i
$347$	55.2948	+	170.180i	0.159351	+	0.490432i	0.998576	−	0.0533527i	$-0.0169908\pi$
$347$	55.2948	+	170.180i	0.159351	+	0.490432i	−0.839225	+	0.543785i	$0.816991\pi$
$348$	−115.803	+	18.3415i	−0.332769	+	0.0527054i
$349$	−337.001	−	53.3758i	−0.965620	−	0.152939i	−0.346340	−	0.938109i	$-0.612576\pi$
$349$	−337.001	−	53.3758i	−0.965620	−	0.152939i	−0.619280	+	0.785170i	$0.712576\pi$
$350$	−210.436	−	68.3749i	−0.601247	−	0.195357i
$351$	44.0728	−	60.6610i	0.125564	−	0.172823i
$352$	−36.7203			−0.104319
$353$			379.670i			1.07555i	0.843088	+	0.537776i	$0.180735\pi$
$353$			379.670i			1.07555i	−0.843088	+	0.537776i	$0.819265\pi$
$354$	−98.3745	+	135.401i	−0.277894	+	0.382488i
$355$	116.743	+	116.743i	0.328853	+	0.328853i
$356$	21.2602	+	134.232i	0.0597198	+	0.377056i
$357$	−104.120	−	143.309i	−0.291654	−	0.401427i
$358$	57.7729	+	364.764i	0.161377	+	1.01889i
$359$	257.209	+	504.802i	0.716460	+	1.40613i	0.905579	+	0.424178i	$0.139437\pi$
$359$	257.209	+	504.802i	0.716460	+	1.40613i	−0.189118	+	0.981954i	$0.560563\pi$
$360$	−16.4176	−	2.60029i	−0.0456044	−	0.00722303i
$361$	83.0013	−	60.3040i	0.229921	−	0.167047i
$362$	249.118	−	180.995i	0.688172	−	0.499986i
$363$	42.2102	+	129.910i	0.116282	+	0.357878i
$364$	190.114	+	96.8678i	0.522291	+	0.266120i
$365$			6.12958i			0.0167934i
$366$	−11.8902	−	148.945i	−0.0324868	−	0.406954i
$367$	581.597			1.58473			0.792366	−	0.610046i	$-0.208849\pi$
$367$	581.597			1.58473			0.792366	+	0.610046i	$0.208849\pi$
$368$	−71.6661	+	140.653i	−0.194745	+	0.382208i
$369$	9.77445	−	3.17591i	0.0264890	−	0.00860680i
$370$	−30.4559	−	41.9190i	−0.0823134	−	0.113295i
$371$	−126.636	−	174.300i	−0.341337	−	0.469810i
$372$	−14.4980	+	91.5368i	−0.0389731	+	0.246067i
$373$	−12.7775	+	6.51046i	−0.0342560	+	0.0174543i	−0.471035	−	0.882115i	$-0.656119\pi$
$373$	−12.7775	+	6.51046i	−0.0342560	+	0.0174543i	0.436779	+	0.899569i	$0.356119\pi$
$374$	−125.427	+	19.8656i	−0.335366	+	0.0531167i
$375$	−126.716	+	92.0645i	−0.337909	+	0.245505i
$376$	228.994	−	36.2691i	0.609027	−	0.0964604i
$377$	345.355	−	345.355i	0.916062	−	0.916062i
$378$	−43.9528	−	31.9336i	−0.116277	−	0.0844804i
$379$	−196.623			−0.518794			−0.259397	−	0.965771i	$-0.583524\pi$
$379$	−196.623			−0.518794			−0.259397	+	0.965771i	$0.583524\pi$
$380$			84.3574i			0.221993i
$381$	−126.685	−	92.0418i	−0.332506	−	0.241579i
$382$	61.9882	−	190.780i	0.162273	−	0.499425i
$383$	−8.17891	+	51.6396i	−0.0213548	+	0.134829i	−0.996062	−	0.0886550i	$-0.971743\pi$
$383$	−8.17891	+	51.6396i	−0.0213548	+	0.134829i	0.974708	+	0.223484i	$0.0717431\pi$
$384$	3.06548	+	19.3547i	0.00798301	+	0.0504028i
$385$	89.4114	−	29.0515i	0.232237	−	0.0754585i
$386$	−7.73690	+	23.8117i	−0.0200438	+	0.0616885i
$387$	−73.7749	+	73.7749i	−0.190633	+	0.190633i
$388$	−64.7015	−	199.131i	−0.166757	−	0.513224i
$389$	−298.313	−	47.2482i	−0.766872	−	0.121461i	−0.239271	−	0.970953i	$-0.576908\pi$
$389$	−298.313	−	47.2482i	−0.766872	−	0.121461i	−0.527601	+	0.849492i	$0.676908\pi$
$390$	61.6950	−	31.4352i	0.158192	−	0.0806031i
$391$	−168.699	+	519.203i	−0.431456	+	1.32789i
$392$	7.26708	−	14.2624i	0.0185385	−	0.0363838i
$393$	166.064	−	228.567i	0.422554	−	0.581596i
$394$	−158.246	−	80.6304i	−0.401640	−	0.204646i
$395$	−78.5730	+	78.5730i	−0.198919	+	0.198919i
$396$	−34.7027	+	17.6819i	−0.0876330	+	0.0446512i
$397$	−92.9254	−	182.376i	−0.234069	−	0.459386i	0.743857	−	0.668339i	$-0.232994\pi$
$397$	−92.9254	−	182.376i	−0.234069	−	0.459386i	−0.977926	+	0.208953i	$0.932994\pi$
$398$	156.150	+	156.150i	0.392336	+	0.392336i
$399$	−125.173	+	245.665i	−0.313716	+	0.615702i
$400$	68.4833	+	49.7561i	0.171208	+	0.124390i
$401$	−293.977	−	149.789i	−0.733110	−	0.373538i	0.0472382	−	0.998884i	$-0.484958\pi$
$401$	−293.977	−	149.789i	−0.733110	−	0.373538i	−0.780348	+	0.625346i	$0.784958\pi$
$402$	−161.893	−	52.6021i	−0.402718	−	0.130851i
$403$	−175.268	−	343.983i	−0.434908	−	0.853555i
$404$	21.0414	−	132.850i	0.0520828	−	0.328838i
$405$	−16.7677	+	5.44814i	−0.0414016	+	0.0134522i
$406$	−250.232	−	250.232i	−0.616336	−	0.616336i
$407$	−115.465	−	37.5170i	−0.283699	−	0.0921794i
$408$	20.9417	+	64.4520i	0.0513277	+	0.157971i
$409$	105.311	−	16.6796i	0.257484	−	0.0407815i	−0.0263578	−	0.999653i	$-0.508391\pi$
$409$	105.311	−	16.6796i	0.257484	−	0.0407815i	0.283842	+	0.958871i	$0.408391\pi$
$410$	9.37396	+	1.48469i	0.0228633	+	0.00362119i
$411$	−174.764	−	56.7843i	−0.425217	−	0.138161i
$412$	−209.623	+	288.522i	−0.508794	+	0.700295i
$413$	−505.150			−1.22312
$414$			167.434i			0.404429i
$415$	84.9599	−	116.937i	0.204723	−	0.281777i
$416$	−57.7205	−	57.7205i	−0.138751	−	0.138751i
$417$	68.2951	+	431.198i	0.163777	+	1.03405i
$418$	116.181	+	159.909i	0.277944	+	0.382557i
$419$	−52.9858	−	334.539i	−0.126458	−	0.798423i	−0.966644	−	0.256124i	$-0.917554\pi$
$419$	−52.9858	−	334.539i	−0.126458	−	0.798423i	0.840186	−	0.542298i	$-0.182446\pi$
$420$	−22.7768	−	44.7020i	−0.0542305	−	0.106433i
$421$	173.483	+	27.4771i	0.412075	+	0.0652662i	0.359030	−	0.933326i	$-0.383108\pi$
$421$	173.483	+	27.4771i	0.412075	+	0.0652662i	0.0530444	+	0.998592i	$0.483108\pi$
$422$	−329.898	+	239.685i	−0.781748	+	0.567973i
$423$	198.947	−	144.544i	0.470325	−	0.341711i
$424$	25.4703	+	78.3894i	0.0600714	+	0.184881i
$425$	260.839	+	132.904i	0.613739	+	0.312716i
$426$		−	206.441i		−	0.484604i
$427$	342.603	−	293.275i	0.802350	−	0.686828i
$428$	53.0141			0.123865
$429$	73.6561	−	144.558i	0.171692	−	0.336965i
$430$	−91.6320	+	29.7730i	−0.213098	+	0.0692396i
$431$	−10.3962	−	14.3092i	−0.0241212	−	0.0332000i	0.796786	−	0.604261i	$-0.206532\pi$
$431$	−10.3962	−	14.3092i	−0.0241212	−	0.0332000i	−0.820907	+	0.571062i	$0.806532\pi$
$432$	12.2169	+	16.8151i	0.0282798	+	0.0389238i
$433$	−50.7351	+	320.329i	−0.117171	+	0.739789i	0.857224	+	0.514944i	$0.172187\pi$
$433$	−50.7351	+	320.329i	−0.117171	+	0.739789i	−0.974395	+	0.224845i	$0.927813\pi$
$434$	−249.238	+	126.993i	−0.574280	+	0.292610i
$435$	−113.427	+	17.9650i	−0.260751	+	0.0412989i
$436$	−188.983	+	137.304i	−0.433448	+	0.314919i
$437$	839.260	−	132.926i	1.92050	−	0.304178i
$438$	5.41961	−	5.41961i	0.0123735	−	0.0123735i
$439$	−127.258	−	92.4584i	−0.289882	−	0.210611i	0.433334	−	0.901233i	$-0.357337\pi$
$439$	−127.258	−	92.4584i	−0.289882	−	0.210611i	−0.723216	+	0.690622i	$0.757337\pi$
$440$	−35.9666			−0.0817422
$441$		−	16.9781i		−	0.0384991i
$442$	−228.385	−	165.931i	−0.516708	−	0.375410i
$443$	111.656	−	343.642i	0.252045	−	0.775715i	−0.742352	−	0.670010i	$-0.766290\pi$
$443$	111.656	−	343.642i	0.252045	−	0.775715i	0.994397	−	0.105706i	$-0.0337101\pi$
$444$	−10.1353	+	63.9920i	−0.0228273	+	0.144126i
$445$	20.8239	+	131.477i	0.0467952	+	0.295453i
$446$	−575.974	+	187.145i	−1.29142	+	0.419608i
$447$	−68.4004	+	210.515i	−0.153021	+	0.470950i
$448$	−41.8222	+	41.8222i	−0.0933532	+	0.0933532i
$449$	43.9043	+	135.123i	0.0977823	+	0.300943i	0.987969	−	0.154653i	$-0.0494261\pi$
$449$	43.9043	+	135.123i	0.0977823	+	0.300943i	−0.890186	+	0.455596i	$0.849426\pi$
$450$	88.6795	+	14.0455i	0.197066	+	0.0312121i
$451$	19.8142	−	10.0958i	0.0439339	−	0.0223854i
$452$	−9.50412	+	29.2507i	−0.0210268	+	0.0647139i
$453$	108.473	−	212.891i	0.239455	−	0.469958i
$454$	−353.363	+	486.363i	−0.778333	+	1.07128i
$455$	186.212	+	94.8796i	0.409257	+	0.208527i
$456$	74.5865	−	74.5865i	0.163567	−	0.163567i
$457$	21.0821	−	10.7419i	0.0461315	−	0.0235052i	−0.430773	−	0.902461i	$-0.641759\pi$
$457$	21.0821	−	10.7419i	0.0461315	−	0.0235052i	0.476904	+	0.878955i	$0.341759\pi$
$458$	73.6040	+	144.456i	0.160707	+	0.315406i
$459$	50.8266	+	50.8266i	0.110733	+	0.110733i
$460$	−70.1952	+	137.766i	−0.152598	+	0.299491i
$461$	50.9714	+	37.0329i	0.110567	+	0.0803316i	0.641695	−	0.766960i	$-0.278232\pi$
$461$	50.9714	+	37.0329i	0.110567	+	0.0803316i	−0.531128	+	0.847292i	$0.678232\pi$
$462$	−104.742	−	53.3686i	−0.226714	−	0.115516i
$463$	109.942	+	35.7225i	0.237457	+	0.0771543i	0.425328	−	0.905039i	$-0.360159\pi$
$463$	109.942	+	35.7225i	0.237457	+	0.0771543i	−0.187871	+	0.982194i	$0.560159\pi$
$464$	61.4636	+	120.629i	0.132465	+	0.259976i
$465$	−14.2004	+	89.6580i	−0.0305386	+	0.192813i
$466$	−420.021	+	136.473i	−0.901334	+	0.292861i
$467$	−96.7006	−	96.7006i	−0.207068	−	0.207068i	0.595952	−	0.803020i	$-0.296775\pi$
$467$	−96.7006	−	96.7006i	−0.207068	−	0.207068i	−0.803020	+	0.595952i	$0.796775\pi$
$468$	−82.3432	−	26.7549i	−0.175947	−	0.0571687i
$469$	−158.767	−	488.634i	−0.338522	−	1.04186i
$470$	224.294	−	35.5247i	0.477221	−	0.0755844i
$471$	−430.059	−	68.1147i	−0.913077	−	0.144617i
$472$	183.798	+	59.7194i	0.389402	+	0.126524i
$473$	−132.694	+	182.638i	−0.280537	+	0.386127i
$474$	138.944			0.293131
$475$		−	455.656i		−	0.959275i
$476$	−120.228	+	165.480i	−0.252580	+	0.347646i
$477$	61.8176	+	61.8176i	0.129597	+	0.129597i
$478$	−27.5768	−	174.113i	−0.0576921	−	0.364253i
$479$	62.3808	+	85.8598i	0.130231	+	0.179248i	0.869153	−	0.494543i	$-0.164665\pi$
$479$	62.3808	+	85.8598i	0.130231	+	0.179248i	−0.738922	+	0.673791i	$0.764665\pi$
$480$	3.00256	+	18.9574i	0.00625533	+	0.0394946i
$481$	−122.527	−	240.473i	−0.254734	−	0.499944i
$482$	61.1243	+	9.68114i	0.126814	+	0.0200853i
$483$	−408.844	+	297.042i	−0.846468	+	0.614995i
$484$	127.603	−	92.7093i	0.263643	−	0.191548i
$485$	−63.3735	−	195.044i	−0.130667	−	0.402152i
$486$	19.6426	+	10.0084i	0.0404169	+	0.0205934i
$487$			440.275i			0.904056i	0.892004	+	0.452028i	$0.149299\pi$
$487$			440.275i			0.904056i	−0.892004	+	0.452028i	$0.850701\pi$
$488$	−159.327	+	66.2045i	−0.326489	+	0.135665i
$489$	−118.473			−0.242276
$490$	7.11792	−	13.9697i	0.0145264	−	0.0285096i
$491$	28.0503	−	9.11410i	0.0571289	−	0.0185623i	−0.280313	−	0.959909i	$-0.590438\pi$
$491$	28.0503	−	9.11410i	0.0571289	−	0.0185623i	0.337442	+	0.941346i	$0.390438\pi$
$492$	−6.97548	−	9.60092i	−0.0141778	−	0.0195141i
$493$	275.204	+	378.785i	0.558222	+	0.768327i
$494$	−68.7365	+	433.985i	−0.139143	+	0.878512i
$495$	−33.9904	+	17.3190i	−0.0686675	+	0.0349878i
$496$	105.698	−	16.7409i	0.213100	−	0.0337517i
$497$	504.094	−	366.245i	1.01427	−	0.736912i
$498$	−178.512	+	28.2735i	−0.358458	+	0.0567742i
$499$	−99.1735	+	99.1735i	−0.198745	+	0.198745i	−0.799462	−	0.600717i	$-0.794882\pi$
$499$	−99.1735	+	99.1735i	−0.198745	+	0.198745i	0.600717	+	0.799462i	$0.294882\pi$
$500$	146.319	+	106.307i	0.292638	+	0.212614i
$501$	226.942			0.452979
$502$		−	660.144i		−	1.31503i
$503$	−543.206	−	394.662i	−1.07993	−	0.784617i	−0.102261	−	0.994758i	$-0.532608\pi$
$503$	−543.206	−	394.662i	−1.07993	−	0.784617i	−0.977671	+	0.210141i	$0.932608\pi$
$504$	−19.3857	+	59.6630i	−0.0384636	+	0.118379i
$505$	20.6096	−	130.124i	0.0408110	−	0.257671i
$506$	56.6742	+	357.827i	0.112004	+	0.707167i
$507$	64.6207	−	20.9965i	0.127457	−	0.0414133i
$508$	−55.8751	+	171.966i	−0.109990	+	0.338515i
$509$	−615.575	+	615.575i	−1.20938	+	1.20938i	−0.238155	+	0.971227i	$0.576543\pi$
$509$	−615.575	+	615.575i	−1.20938	+	1.20938i	−0.971227	+	0.238155i	$0.923457\pi$
$510$	20.5119	+	63.1291i	0.0402194	+	0.123783i
$511$	22.8486	+	3.61886i	0.0447135	+	0.00708193i
$512$	20.1612	−	10.2726i	0.0393773	−	0.0200637i
$513$	34.5727	−	106.404i	0.0673932	−	0.207415i
$514$	153.870	−	301.986i	0.299357	−	0.587522i
$515$	−205.321	+	282.600i	−0.398681	+	0.548738i
$516$	107.343	+	54.6940i	0.208029	+	0.105996i
$517$	376.249	−	376.249i	0.727754	−	0.727754i
$518$	−174.238	+	88.7788i	−0.336367	+	0.171388i
$519$	−144.353	−	283.309i	−0.278137	−	0.545875i
$520$	−56.5358	−	56.5358i	−0.108723	−	0.108723i
$521$	−2.70826	+	5.31525i	−0.00519819	+	0.0102020i	−0.893591	−	0.448882i	$-0.851822\pi$
$521$	−2.70826	+	5.31525i	−0.00519819	+	0.0102020i	0.888393	+	0.459084i	$0.151822\pi$
$522$	116.173	+	84.4046i	0.222553	+	0.161695i
$523$	−197.110	−	100.433i	−0.376883	−	0.192032i	0.255279	−	0.966867i	$-0.417833\pi$
$523$	−197.110	−	100.433i	−0.376883	−	0.192032i	−0.632163	+	0.774836i	$0.717833\pi$
$524$	−310.264	−	100.811i	−0.592108	−	0.192387i
$525$	123.029	+	241.458i	0.234341	+	0.459919i
$526$	9.61310	−	60.6947i	0.0182758	−	0.115389i
$527$	351.978	−	114.365i	0.667891	−	0.217011i
$528$	31.8007	+	31.8007i	0.0602286	+	0.0602286i
$529$	978.113	+	317.808i	1.84898	+	0.600772i
$530$	24.9475	+	76.7805i	0.0470708	+	0.144869i
$531$	202.455	−	32.0658i	0.381272	−	0.0603876i
$532$	314.450	+	49.8040i	0.591072	+	0.0936165i
$533$	47.0155	+	15.2763i	0.0882092	+	0.0286609i
$534$	97.8363	−	134.660i	0.183214	−	0.252173i
$535$	51.9260			0.0970580
$536$			196.558i			0.366712i
$537$	265.862	−	365.927i	0.495087	−	0.681429i
$538$	−72.9140	−	72.9140i	−0.135528	−	0.135528i
$539$	−5.74687	−	36.2843i	−0.0106621	−	0.0673178i
$540$	11.9661	+	16.4700i	0.0221595	+	0.0305000i
$541$	139.727	+	882.199i	0.258275	+	1.63068i	0.686584	+	0.727050i	$0.259109\pi$
$541$	139.727	+	882.199i	0.258275	+	1.63068i	−0.428309	+	0.903632i	$0.640891\pi$
$542$	−246.504	−	483.791i	−0.454804	−	0.892603i
$543$	−372.489	−	58.9964i	−0.685983	−	0.108649i
$544$	63.3078	−	45.9958i	0.116375	−	0.0845511i
$545$	−185.105	+	134.486i	−0.339641	+	0.246764i
$546$	−80.7534	−	248.533i	−0.147900	−	0.455189i
$547$	−65.6426	−	33.4466i	−0.120005	−	0.0611455i	0.392958	−	0.919557i	$-0.371452\pi$
$547$	−65.6426	−	33.4466i	−0.120005	−	0.0611455i	−0.512962	+	0.858411i	$0.671452\pi$
$548$			212.185i			0.387199i
$549$	−118.693	+	139.287i	−0.216199	+	0.253711i
$550$	194.273			0.353224
$551$	330.847	−	649.324i	0.600448	−	1.17845i
$552$	183.873	−	59.7441i	0.333104	−	0.108232i
$553$	246.499	+	339.277i	0.445750	+	0.613522i
$554$	−351.047	−	483.175i	−0.633659	−	0.872157i
$555$	−9.92731	+	62.6786i	−0.0178870	+	0.112934i
$556$	449.167	−	228.862i	0.807854	−	0.411622i
$557$	−629.608	+	99.7202i	−1.13036	+	0.179031i	−0.693470	−	0.720486i	$-0.743919\pi$
$557$	−629.608	+	99.7202i	−1.13036	+	0.179031i	−0.436886	+	0.899517i	$0.643919\pi$
$558$	91.8288	−	66.7176i	0.164568	−	0.119566i
$559$	−495.670	+	78.5064i	−0.886709	+	0.140441i
$560$	−40.9638	+	40.9638i	−0.0731497	+	0.0731497i
$561$	125.827	+	91.4186i	0.224290	+	0.162956i
$562$	211.766			0.376808
$563$		−	755.764i		−	1.34239i	−0.741282	−	0.671194i	$-0.765782\pi$
$563$		−	755.764i		−	1.34239i	0.741282	−	0.671194i	$-0.234218\pi$
$564$	−229.725	−	166.905i	−0.407313	−	0.295930i
$565$	−9.30905	+	28.6503i	−0.0164762	+	0.0507085i
$566$	−57.5063	+	363.081i	−0.101601	+	0.641485i
$567$	10.4090	+	65.7196i	0.0183580	+	0.115908i
$568$	−226.711	+	73.6629i	−0.399139	+	0.129688i
$569$	21.7862	−	67.0510i	0.0382886	−	0.117840i	−0.930085	−	0.367343i	$-0.880267\pi$
$569$	21.7862	−	67.0510i	0.0382886	−	0.117840i	0.968374	+	0.249503i	$0.0802674\pi$
$570$	73.0556	−	73.0556i	0.128168	−	0.128168i
$571$	95.3616	+	293.493i	0.167008	+	0.513998i	0.999179	−	0.0405219i	$-0.0129020\pi$
$571$	95.3616	+	293.493i	0.167008	+	0.513998i	−0.832171	+	0.554520i	$0.812902\pi$
$572$	−185.034	−	29.3065i	−0.323486	−	0.0512351i
$573$	−218.904	+	111.537i	−0.382031	+	0.194655i
$574$	11.0686	−	34.0658i	0.0192833	−	0.0593480i
$575$	379.159	−	744.141i	0.659406	−	1.29416i
$576$	14.1068	−	19.4164i	0.0244911	−	0.0337090i
$577$	−26.6296	−	13.5685i	−0.0461519	−	0.0235156i	0.430762	−	0.902465i	$-0.358245\pi$
$577$	−26.6296	−	13.5685i	−0.0461519	−	0.0235156i	−0.476914	+	0.878950i	$0.658245\pi$
$578$	−97.6411	+	97.6411i	−0.168929	+	0.168929i
$579$	27.3219	−	13.9212i	0.0471881	−	0.0240436i
$580$	60.2020	+	118.153i	0.103797	+	0.203712i
$581$	−385.735	−	385.735i	−0.663916	−	0.663916i
$582$	−116.419	+	228.486i	−0.200033	+	0.392587i
$583$	153.036	+	111.187i	0.262498	+	0.190716i
$584$	−7.88557	−	4.01790i	−0.0135027	−	0.00687997i
$585$	−80.6532	−	26.2058i	−0.137869	−	0.0447962i
$586$	−107.137	−	210.269i	−0.182828	−	0.358821i
$587$	−74.3497	+	469.426i	−0.126660	+	0.799703i	0.839802	+	0.542893i	$0.182671\pi$
$587$	−74.3497	+	469.426i	−0.126660	+	0.799703i	−0.966462	+	0.256809i	$0.917329\pi$
$588$	−18.6451	+	6.05816i	−0.0317094	+	0.0103030i
$589$	−407.324	−	407.324i	−0.691551	−	0.691551i
$590$	180.025	+	58.4937i	0.305127	+	0.0991419i
$591$	67.2171	+	206.873i	0.113735	+	0.350039i
$592$	73.8916	−	11.7033i	0.124817	−	0.0197690i
$593$	−557.434	−	88.2889i	−0.940024	−	0.148885i	−0.332425	−	0.943130i	$-0.607867\pi$
$593$	−557.434	−	88.2889i	−0.940024	−	0.148885i	−0.607598	+	0.794244i	$0.707867\pi$
$594$	45.3664	+	14.7404i	0.0763744	+	0.0248155i
$595$	−117.760	+	162.083i	−0.197916	+	0.272409i
$596$	255.591			0.428844
$597$		−	270.459i		−	0.453031i
$598$	−473.381	+	651.553i	−0.791607	+	1.08955i
$599$	−15.8858	−	15.8858i	−0.0265205	−	0.0265205i	0.693722	−	0.720243i	$-0.255970\pi$
$599$	−15.8858	−	15.8858i	−0.0265205	−	0.0265205i	−0.720243	+	0.693722i	$0.755970\pi$
$600$	−16.2183	−	102.398i	−0.0270305	−	0.170664i
$601$	−305.259	−	420.153i	−0.507918	−	0.699090i	0.475648	−	0.879636i	$-0.342214\pi$
$601$	−305.259	−	420.153i	−0.507918	−	0.699090i	−0.983567	+	0.180546i	$0.942214\pi$
$602$	56.8830	+	359.145i	0.0944900	+	0.596586i
$603$	94.6484	+	185.758i	0.156962	+	0.308056i
$604$	−272.499	−	43.1597i	−0.451158	−	0.0714564i
$605$	124.984	−	90.8064i	0.206586	−	0.150093i
$606$	−133.274	+	96.8294i	−0.219925	+	0.159785i
$607$	−322.033	−	991.117i	−0.530533	−	1.63281i	−0.753109	−	0.657896i	$-0.771446\pi$
$607$	−322.033	−	991.117i	−0.530533	−	1.63281i	0.222576	−	0.974915i	$-0.428554\pi$
$608$	−108.524	−	55.2957i	−0.178493	−	0.0909469i
$609$			433.415i			0.711683i
$610$	−156.056	+	64.8457i	−0.255830	+	0.106304i
$611$	1182.85			1.93592
$612$	37.6810	−	73.9531i	0.0615703	−	0.120838i
$613$	439.717	−	142.873i	0.717320	−	0.233071i	0.0724592	−	0.997371i	$-0.476915\pi$
$613$	439.717	−	142.873i	0.717320	−	0.233071i	0.644861	+	0.764300i	$0.276915\pi$
$614$	−77.4500	−	106.601i	−0.126140	−	0.173617i
$615$	−6.83231	−	9.40386i	−0.0111094	−	0.0152908i
$616$	−21.2344	+	134.069i	−0.0344715	+	0.217644i
$617$	693.663	−	353.439i	1.12425	−	0.572834i	0.209886	−	0.977726i	$-0.432691\pi$
$617$	693.663	−	353.439i	1.12425	−	0.572834i	0.914365	+	0.404892i	$0.132691\pi$
$618$	431.406	−	68.3280i	0.698068	−	0.110563i
$619$	−365.043	+	265.220i	−0.589731	+	0.428465i	−0.842219	−	0.539135i	$-0.818751\pi$
$619$	−365.043	+	265.220i	−0.589731	+	0.428465i	0.252488	+	0.967600i	$0.418751\pi$
$620$	103.528	−	16.3973i	0.166981	−	0.0264472i
$621$	145.002	−	145.002i	0.233497	−	0.233497i
$622$	457.825	+	332.629i	0.736053	+	0.534774i
$623$	502.387			0.806399
$624$			99.9749i			0.160216i
$625$	−284.705	−	206.850i	−0.455528	−	0.330961i
$626$	176.525	−	543.287i	0.281988	−	0.867870i
$627$	37.8698	−	239.101i	0.0603985	−	0.381341i
$628$	78.6521	+	496.590i	0.125242	+	0.790748i
$629$	246.063	−	79.9506i	0.391197	−	0.127107i
$630$	−18.9878	+	58.4384i	−0.0301393	+	0.0927594i
$631$	−802.927	+	802.927i	−1.27247	+	1.27247i	−0.327678	+	0.944789i	$0.606266\pi$
$631$	−802.927	+	802.927i	−1.27247	+	1.27247i	−0.944789	+	0.327678i	$0.893734\pi$
$632$	−49.5784	−	152.587i	−0.0784468	−	0.241434i
$633$	493.273	+	78.1268i	0.779262	+	0.123423i
$634$	728.935	−	371.411i	1.14974	−	0.585821i
$635$	−54.7282	+	168.436i	−0.0861862	+	0.265254i
$636$	45.8293	−	89.9451i	0.0720587	−	0.141423i
$637$	48.0017	−	66.0687i	0.0753559	−	0.103719i
$638$	276.846	+	141.060i	0.433927	+	0.221097i
$639$	−178.784	+	178.784i	−0.279786	+	0.279786i
$640$	19.7474	−	10.0618i	0.0308553	−	0.0157215i
$641$	−135.193	−	265.331i	−0.210910	−	0.413933i	0.761181	−	0.648540i	$-0.224620\pi$
$641$	−135.193	−	265.331i	−0.210910	−	0.413933i	−0.972090	+	0.234606i	$0.924620\pi$
$642$	−45.9116	−	45.9116i	−0.0715134	−	0.0715134i
$643$	−43.7832	+	85.9293i	−0.0680920	+	0.133638i	−0.922544	−	0.385893i	$-0.873893\pi$
$643$	−43.7832	+	85.9293i	−0.0680920	+	0.133638i	0.854452	+	0.519531i	$0.173893\pi$
$644$	472.092	+	342.995i	0.733062	+	0.532601i
$645$	105.140	+	53.5714i	0.163008	+	0.0830565i
$646$	−400.604	−	130.164i	−0.620130	−	0.201492i
$647$	177.370	+	348.108i	0.274142	+	0.538034i	0.986496	−	0.163787i	$-0.0523709\pi$
$647$	177.370	+	348.108i	0.274142	+	0.538034i	−0.712354	+	0.701820i	$0.752371\pi$
$648$	3.98217	−	25.1424i	0.00614533	−	0.0388001i
$649$	421.818	−	137.057i	0.649951	−	0.211182i
$650$	305.378	+	305.378i	0.469812	+	0.469812i
$651$	325.825	+	105.867i	0.500499	+	0.162622i
$652$	42.2738	+	130.105i	0.0648371	+	0.199548i
$653$	967.294	−	153.204i	1.48131	−	0.234616i	0.637162	−	0.770730i	$-0.280108\pi$
$653$	967.294	−	153.204i	1.48131	−	0.234616i	0.844146	+	0.536114i	$0.180108\pi$
$654$	282.574	+	44.7553i	0.432070	+	0.0684331i
$655$	−303.896	−	98.7419i	−0.463964	−	0.150751i
$656$	−8.05459	+	11.0862i	−0.0122783	+	0.0168997i
$657$	−9.38704			−0.0142877
$658$		−	857.051i		−	1.30251i
$659$	497.481	−	684.723i	0.754902	−	1.03903i	−0.242719	−	0.970097i	$-0.578039\pi$
$659$	497.481	−	684.723i	0.754902	−	1.03903i	0.997621	−	0.0689370i	$-0.0219607\pi$
$660$	31.1480	+	31.1480i	0.0471939	+	0.0471939i
$661$	−16.8426	−	106.340i	−0.0254805	−	0.160877i	0.971667	−	0.236354i	$-0.0759523\pi$
$661$	−16.8426	−	106.340i	−0.0254805	−	0.160877i	−0.997148	+	0.0754761i	$0.975952\pi$
$662$	26.6713	+	36.7099i	0.0402889	+	0.0554529i
$663$	54.0864	+	341.488i	0.0815782	+	0.515065i
$664$	94.7466	+	185.951i	0.142691	+	0.280046i
$665$	307.996	+	48.7818i	0.463152	+	0.0733561i
$666$	64.1961	−	46.6412i	0.0963906	−	0.0700319i
$667$	1080.63	−	785.121i	1.62013	−	1.17709i
$668$	−80.9781	−	249.225i	−0.121225	−	0.373091i
$669$	660.881	+	336.736i	0.987864	+	0.503342i
$670$			192.523i			0.287348i
$671$	−206.515	+	337.850i	−0.307771	+	0.503503i
$672$	72.4382			0.107795
$673$	−463.647	+	909.959i	−0.688926	+	1.35209i	0.235928	+	0.971770i	$0.424187\pi$
$673$	−463.647	+	909.959i	−0.688926	+	1.35209i	−0.924854	+	0.380322i	$0.875813\pi$
$674$	130.462	−	42.3898i	0.193564	−	0.0628929i
$675$	−64.6350	−	88.9625i	−0.0957556	−	0.131796i
$676$	−46.1162	−	63.4734i	−0.0682192	−	0.0938956i
$677$	31.6672	−	199.939i	0.0467758	−	0.295330i	−0.953200	−	0.302342i	$-0.902232\pi$
$677$	31.6672	−	199.939i	0.0467758	−	0.295330i	0.999975	+	0.00701102i	$0.00223170\pi$
$678$	33.5626	−	17.1010i	0.0495024	−	0.0252227i
$679$	−764.459	+	121.078i	−1.12586	+	0.178319i
$680$	62.0084	−	45.0517i	0.0911888	−	0.0662526i
$681$	727.224	−	115.181i	1.06788	−	0.169135i
$682$	173.666	−	173.666i	0.254643	−	0.254643i
$683$	281.370	+	204.427i	0.411962	+	0.299308i	0.774396	−	0.632702i	$-0.218054\pi$
$683$	281.370	+	204.427i	0.411962	+	0.299308i	−0.362434	+	0.932010i	$0.618054\pi$
$684$	−129.188			−0.188871
$685$			207.830i			0.303402i
$686$	366.607	+	266.355i	0.534412	+	0.388273i
$687$	61.3596	−	188.845i	0.0893153	−	0.274884i
$688$	21.7618	−	137.399i	0.0316305	−	0.199707i
$689$	65.7823	+	415.333i	0.0954750	+	0.602806i
$690$	180.099	−	58.5178i	0.261014	−	0.0848085i
$691$	−374.487	+	1152.55i	−0.541950	+	1.66795i	0.186184	+	0.982515i	$0.440388\pi$
$691$	−374.487	+	1152.55i	−0.541950	+	1.66795i	−0.728134	+	0.685435i	$0.759612\pi$
$692$	−259.617	+	259.617i	−0.375170	+	0.375170i
$693$	44.4904	+	136.927i	0.0641998	+	0.197587i
$694$	−249.941	−	39.5867i	−0.360145	−	0.0570414i
$695$	439.948	−	224.164i	0.633018	−	0.322539i
$696$	51.2388	−	157.697i	0.0736190	−	0.226576i
$697$	−21.5147	+	42.2250i	−0.0308676	+	0.0605811i
$698$	283.626	−	390.377i	0.406340	−	0.559280i
$699$	481.939	+	245.560i	0.689469	+	0.351302i
$700$	221.266	−	221.266i	0.316094	−	0.316094i
$701$	72.3345	−	36.8563i	0.103188	−	0.0525767i	−0.401635	−	0.915800i	$-0.631558\pi$
$701$	72.3345	−	36.8563i	0.103188	−	0.0525767i	0.504823	+	0.863223i	$0.331558\pi$
$702$	48.1409	+	94.4818i	0.0685767	+	0.134589i
$703$	−284.754	−	284.754i	−0.405055	−	0.405055i
$704$	23.5759	−	46.2702i	0.0334884	−	0.0657248i
$705$	−225.010	−	163.479i	−0.319163	−	0.231885i
$706$	−478.412	−	243.763i	−0.677637	−	0.345273i
$707$	−472.881	−	153.648i	−0.668856	−	0.217324i
$708$	−107.455	−	210.892i	−0.151772	−	0.297870i
$709$	−5.84360	+	36.8950i	−0.00824203	+	0.0520381i	−0.991467	−	0.130361i	$-0.958386\pi$
$709$	−5.84360	+	36.8950i	−0.00824203	+	0.0520381i	0.983225	+	0.182399i	$0.0583863\pi$
$710$	−222.058	+	72.1510i	−0.312757	+	0.101621i
$711$	−120.329	−	120.329i	−0.169239	−	0.169239i
$712$	−182.792	−	59.3927i	−0.256730	−	0.0834167i
$713$	−326.268	−	1004.15i	−0.457599	−	1.40834i
$714$	247.430	−	39.1891i	0.346541	−	0.0548866i
$715$	−181.236	−	28.7050i	−0.253477	−	0.0401468i
$716$	−496.722	−	161.395i	−0.693745	−	0.225411i
$717$	−126.904	+	174.669i	−0.176993	+	0.243610i
$718$	−801.226			−1.11591
$719$			777.272i			1.08105i	0.841329	+	0.540523i	$0.181774\pi$
$719$			777.272i			1.08105i	−0.841329	+	0.540523i	$0.818226\pi$
$720$	13.8173	−	19.0179i	0.0191907	−	0.0264137i
$721$	932.198	+	932.198i	1.29292	+	1.29292i
$722$	22.6973	+	143.305i	0.0314368	+	0.198484i
$723$	−44.5511	−	61.3193i	−0.0616198	−	0.0848123i
$724$	68.1232	+	430.113i	0.0940928	+	0.594079i
$725$	−325.181	−	638.203i	−0.448525	−	0.880281i
$726$	−190.796	−	30.2192i	−0.262805	−	0.0416242i
$727$	649.901	−	472.181i	0.893950	−	0.649492i	−0.0429552	−	0.999077i	$-0.513677\pi$
$727$	649.901	−	472.181i	0.893950	−	0.649492i	0.936905	+	0.349585i	$0.113677\pi$
$728$	−244.121	+	177.364i	−0.335331	+	0.243632i
$729$	−8.34346	−	25.6785i	−0.0114451	−	0.0352243i
$730$	−7.72373	−	3.93543i	−0.0105804	−	0.00539101i
$731$		−	481.091i		−	0.658127i
$732$	195.316	+	80.6461i	0.266825	+	0.110172i
$733$	85.2324			0.116279			0.0581394	−	0.998308i	$-0.481483\pi$
$733$	85.2324			0.116279			0.0581394	+	0.998308i	$0.481483\pi$
$734$	−373.408	+	732.854i	−0.508730	+	0.998439i
$735$	−18.2624	+	5.93382i	−0.0248468	+	0.00807322i
$736$	−131.220	−	180.609i	−0.178288	−	0.245393i
$737$	265.152	+	364.950i	0.359772	+	0.495183i
$738$	−2.27370	+	14.3556i	−0.00308089	+	0.0194520i
$739$	−839.806	+	427.903i	−1.13641	+	0.579029i	−0.917902	−	0.396806i	$-0.870118\pi$
$739$	−839.806	+	427.903i	−1.13641	+	0.579029i	−0.218507	+	0.975835i	$0.570118\pi$
$740$	72.3750	−	11.4631i	0.0978040	−	0.0154906i
$741$	435.370	−	316.315i	0.587543	−	0.426875i
$742$	300.936	−	47.6635i	0.405573	−	0.0642365i
$743$	523.261	−	523.261i	0.704254	−	0.704254i	−0.261067	−	0.965321i	$-0.584074\pi$
$743$	523.261	−	523.261i	0.704254	−	0.704254i	0.965321	+	0.261067i	$0.0840743\pi$
$744$	−106.035	−	77.0388i	−0.142520	−	0.103547i
$745$	250.345			0.336034
$746$		−	20.2806i		−	0.0271857i
$747$	179.082	+	130.110i	0.239734	+	0.174177i
$748$	55.4967	−	170.801i	0.0741935	−	0.228344i
$749$	30.6568	−	193.559i	0.0409303	−	0.258424i
$750$	−34.6514	−	218.780i	−0.0462019	−	0.291707i
$751$	−592.885	+	192.640i	−0.789460	+	0.256511i	−0.675874	−	0.737017i	$-0.736234\pi$
$751$	−592.885	+	192.640i	−0.789460	+	0.256511i	−0.113586	+	0.993528i	$0.536234\pi$
$752$	−101.322	+	311.836i	−0.134736	+	0.414675i
$753$	−571.702	+	571.702i	−0.759232	+	0.759232i
$754$	213.441	+	656.905i	0.283079	+	0.871227i
$755$	−266.906	−	42.2738i	−0.353518	−	0.0559918i
$756$	68.4581	−	34.8812i	0.0905531	−	0.0461391i
$757$	57.9383	−	178.316i	0.0765368	−	0.235556i	−0.905467	−	0.424416i	$-0.860479\pi$
$757$	57.9383	−	178.316i	0.0765368	−	0.235556i	0.982004	+	0.188860i	$0.0604793\pi$
$758$	126.240	−	247.759i	0.166543	−	0.326859i
$759$	260.806	−	358.968i	0.343617	−	0.472949i
$760$	−106.296	−	54.1608i	−0.139864	−	0.0712642i
$761$	−522.813	+	522.813i	−0.687008	+	0.687008i	−0.961570	−	0.274561i	$-0.911467\pi$
$761$	−522.813	+	522.813i	−0.687008	+	0.687008i	0.274561	+	0.961570i	$0.411467\pi$
$762$	197.316	−	100.537i	0.258945	−	0.131939i
$763$	392.026	+	769.395i	0.513796	+	1.00838i
$764$	200.598	+	200.598i	0.262563	+	0.262563i
$765$	36.9076	−	72.4353i	0.0482452	−	0.0946866i
$766$	−59.8185	−	43.4607i	−0.0780920	−	0.0567372i
$767$	878.496	+	447.616i	1.14537	+	0.583593i
$768$	−26.3565	−	8.56373i	−0.0343183	−	0.0111507i
$769$	−27.4655	−	53.9041i	−0.0357159	−	0.0700964i	0.872459	−	0.488687i	$-0.162524\pi$
$769$	−27.4655	−	53.9041i	−0.0357159	−	0.0700964i	−0.908175	+	0.418591i	$0.862524\pi$
$770$	−20.7986	+	131.317i	−0.0270112	+	0.170542i
$771$	−394.783	+	128.273i	−0.512040	+	0.166372i
$772$	−25.0371	−	25.0371i	−0.0324315	−	0.0324315i
$773$	−674.458	−	219.145i	−0.872520	−	0.283499i	−0.161672	−	0.986845i	$-0.551689\pi$
$773$	−674.458	−	219.145i	−0.872520	−	0.283499i	−0.710848	+	0.703345i	$0.751689\pi$
$774$	−45.5954	−	140.328i	−0.0589088	−	0.181303i
$775$	−559.207	+	88.5696i	−0.721557	+	0.114283i
$776$	292.460	+	46.3212i	0.376882	+	0.0596922i
$777$	227.779	+	74.0100i	0.293152	+	0.0952509i
$778$	251.065	−	345.561i	0.322706	−	0.444166i
$779$	73.7622			0.0946884
$780$			97.9229i			0.125542i
$781$	−321.566	+	442.598i	−0.411737	+	0.566707i
$782$	−545.923	−	545.923i	−0.698111	−	0.698111i
$783$	−27.5122	−	173.705i	−0.0351369	−	0.221846i
$784$	13.3060	+	18.3141i	0.0169719	+	0.0233598i
$785$	77.0378	+	486.397i	0.0981373	+	0.619615i
$786$	181.392	+	356.002i	0.230779	+	0.452929i
$787$	−814.263	−	128.967i	−1.03464	−	0.163871i	−0.384060	−	0.923308i	$-0.625475\pi$
$787$	−814.263	−	128.967i	−1.03464	−	0.163871i	−0.650581	+	0.759437i	$0.725475\pi$
$788$	203.200	−	147.634i	0.257869	−	0.187352i
$789$	−60.8883	+	44.2380i	−0.0771715	+	0.0560684i
$790$	−48.5608	−	149.455i	−0.0614694	−	0.189183i
$791$	101.301	+	51.6153i	0.128067	+	0.0652533i
$792$		−	55.0804i		−	0.0695459i
$793$	−855.686	+	206.446i	−1.07905	+	0.260336i
$794$	289.469			0.364571
$795$	44.8887	−	88.0990i	0.0564638	−	0.110816i
$796$	−297.015	+	96.5059i	−0.373134	+	0.121239i
$797$	−302.581	−	416.468i	−0.379650	−	0.522544i	0.575841	−	0.817561i	$-0.304675\pi$
$797$	−302.581	−	416.468i	−0.379650	−	0.522544i	−0.955492	+	0.295017i	$0.904675\pi$
$798$	−229.190	−	315.453i	−0.287206	−	0.395305i
$799$	−177.385	+	1119.96i	−0.222008	+	1.40171i
$800$	−106.665	+	54.3487i	−0.133332	+	0.0679358i
$801$	−201.348	+	31.8904i	−0.251371	+	0.0398132i
$802$	377.490	−	274.262i	0.470685	−	0.341973i
$803$	−20.0613	+	3.17739i	−0.0249829	+	0.00395690i
$804$	170.224	−	170.224i	0.211721	−	0.211721i
$805$	462.403	+	335.955i	0.574413	+	0.417336i
$806$	545.972			0.677385
$807$			126.291i			0.156494i
$808$	153.892	+	111.809i	0.190460	+	0.138377i
$809$	−264.742	+	814.792i	−0.327246	+	1.00716i	0.643170	+	0.765723i	$0.277619\pi$
$809$	−264.742	+	814.792i	−0.327246	+	1.00716i	−0.970417	+	0.241437i	$0.922381\pi$
$810$	3.90044	−	24.6264i	0.00481536	−	0.0304030i
$811$	−3.46444	−	21.8736i	−0.00427181	−	0.0269712i	0.985460	−	0.169905i	$-0.0543462\pi$
$811$	−3.46444	−	21.8736i	−0.00427181	−	0.0269712i	−0.989732	+	0.142934i	$0.954346\pi$
$812$	475.970	−	154.652i	0.586170	−	0.190458i
$813$	−205.497	+	632.454i	−0.252763	+	0.777926i
$814$	121.408	−	121.408i	0.149149	−	0.149149i
$815$	41.4061	+	127.435i	0.0508051	+	0.156362i
$816$	−94.6597	−	14.9926i	−0.116004	−	0.0183733i
$817$	−667.195	+	339.953i	−0.816640	+	0.416099i
$818$	−46.5963	+	143.409i	−0.0569636	+	0.175316i
$819$	−145.302	+	285.171i	−0.177414	+	0.348194i
$820$	−7.88927	+	10.8586i	−0.00962106	+	0.0132422i
$821$	671.735	+	342.266i	0.818191	+	0.416889i	0.812404	−	0.583094i	$-0.198158\pi$
$821$	671.735	+	342.266i	0.818191	+	0.416889i	0.00578617	+	0.999983i	$0.498158\pi$
$822$	183.758	−	183.758i	0.223550	−	0.223550i
$823$	1280.40	−	652.396i	1.55577	−	0.792705i	0.556499	−	0.830848i	$-0.312144\pi$
$823$	1280.40	−	652.396i	1.55577	−	0.792705i	0.999272	+	0.0381436i	$0.0121444\pi$
$824$	−228.972	−	449.383i	−0.277879	−	0.545368i
$825$	−168.246	−	168.246i	−0.203934	−	0.203934i
$826$	324.326	−	636.527i	0.392647	−	0.770613i
$827$	−1050.61	−	763.313i	−1.27039	−	0.922990i	−0.271169	−	0.962532i	$-0.587410\pi$
$827$	−1050.61	−	763.313i	−1.27039	−	0.922990i	−0.999218	+	0.0395417i	$0.987410\pi$
$828$	−210.979	−	107.499i	−0.254805	−	0.129830i
$829$	−1370.71	−	445.371i	−1.65345	−	0.537239i	−0.673967	−	0.738761i	$-0.735411\pi$
$829$	−1370.71	−	445.371i	−1.65345	−	0.537239i	−0.979484	+	0.201522i	$0.935411\pi$
$830$	92.8020	+	182.134i	0.111810	+	0.219439i
$831$	−114.426	+	722.458i	−0.137697	+	0.869384i
$832$	109.791	−	35.6733i	0.131960	−	0.0428765i
$833$	55.3576	+	55.3576i	0.0664557	+	0.0664557i
$834$	−587.190	−	190.790i	−0.704065	−	0.228764i
$835$	−79.3160	−	244.110i	−0.0949892	−	0.292347i
$836$	−276.090	+	43.7283i	−0.330251	+	0.0523066i
$837$	−137.305	−	21.7470i	−0.164044	−	0.0259821i
$838$	455.563	+	148.021i	0.543631	+	0.176636i
$839$	−351.965	+	484.439i	−0.419506	+	0.577400i	−0.965505	−	0.260386i	$-0.916150\pi$
$839$	−351.965	+	484.439i	−0.419506	+	0.577400i	0.545999	+	0.837786i	$0.316150\pi$
$840$	70.9515			0.0844660
$841$		−	304.571i		−	0.362153i
$842$	−146.006	+	200.961i	−0.173404	+	0.238670i
$843$	−183.395	−	183.395i	−0.217550	−	0.217550i
$844$	−90.2130	−	569.583i	−0.106887	−	0.674861i
$845$	−45.1696	−	62.1707i	−0.0534552	−	0.0735747i
$846$	54.4036	+	343.491i	0.0643069	+	0.406018i
$847$	−264.700	−	519.502i	−0.312514	−	0.613344i
$848$	−115.129	−	18.2347i	−0.135766	−	0.0215032i
$849$	364.239	−	264.635i	0.429021	−	0.311702i
$850$	−334.938	+	243.347i	−0.394045	+	0.286290i
$851$	−228.089	−	701.986i	−0.268025	−	0.824895i
$852$	260.131	+	132.544i	0.305319	+	0.155568i
$853$		−	839.987i		−	0.984744i	−0.870385	−	0.492372i	$-0.836130\pi$
$853$		−	839.987i		−	0.984744i	0.870385	−	0.492372i	$-0.163870\pi$
$854$	149.584	+	620.000i	0.175157	+	0.725995i
$855$	−126.536			−0.147995
$856$	−34.0372	+	66.8017i	−0.0397631	+	0.0780394i
$857$	491.679	−	159.756i	0.573721	−	0.186413i	−0.00776463	−	0.999970i	$-0.502472\pi$
$857$	491.679	−	159.756i	0.573721	−	0.186413i	0.581486	+	0.813557i	$0.302472\pi$
$858$	134.864	+	185.624i	0.157184	+	0.216345i
$859$	−763.309	−	1050.61i	−0.888602	−	1.22306i	−0.973963	−	0.226706i	$-0.927204\pi$
$859$	−763.309	−	1050.61i	−0.888602	−	1.22306i	0.0853611	−	0.996350i	$-0.472796\pi$
$860$	21.3151	−	134.579i	0.0247851	−	0.156487i
$861$	−39.0875	+	19.9161i	−0.0453978	+	0.0231314i
$862$	24.7054	−	3.91296i	0.0286606	−	0.00453939i
$863$	−294.748	+	214.147i	−0.341539	+	0.248143i	−0.745311	−	0.666717i	$-0.767699\pi$
$863$	−294.748	+	214.147i	−0.341539	+	0.248143i	0.403772	+	0.914860i	$0.367699\pi$
$864$	−29.0320	+	4.59822i	−0.0336018	+	0.00532201i
$865$	−254.289	+	254.289i	−0.293976	+	0.293976i
$866$	−371.064	−	269.594i	−0.428480	−	0.311309i
$867$	169.119			0.195063
$868$		−	395.592i		−	0.455751i
$869$	−297.888	−	216.429i	−0.342794	−	0.249055i
$870$	50.1871	−	154.460i	0.0576864	−	0.177540i
$871$	−156.873	+	990.457i	−0.180107	+	1.13715i
$872$	−51.6789	−	326.288i	−0.0592648	−	0.374183i
$873$	298.696	−	97.0523i	0.342149	−	0.111171i
$874$	−371.342	+	1142.87i	−0.424876	+	1.30763i
$875$	472.749	−	472.749i	0.540284	−	0.540284i
$876$	3.34950	+	10.3087i	0.00382363	+	0.0117679i
$877$	1699.44	+	269.165i	1.93779	+	0.306915i	0.999266	−	0.0383109i	$-0.0121977\pi$
$877$	1699.44	+	269.165i	1.93779	+	0.306915i	0.938520	+	0.345226i	$0.112198\pi$
$878$	198.209	−	100.993i	0.225751	−	0.115026i
$879$	−89.3145	+	274.882i	−0.101609	+	0.312721i
$880$	23.0920	−	45.3205i	0.0262409	−	0.0515006i
$881$	−379.809	+	522.762i	−0.431111	+	0.593374i	−0.968208	−	0.250147i	$-0.919521\pi$
$881$	−379.809	+	522.762i	−0.431111	+	0.593374i	0.537097	+	0.843521i	$0.319521\pi$
$882$	21.3937	+	10.9006i	0.0242558	+	0.0123590i
$883$	−1163.55	+	1163.55i	−1.31773	+	1.31773i	−0.402159	+	0.915570i	$0.631740\pi$
$883$	−1163.55	+	1163.55i	−1.31773	+	1.31773i	−0.915570	+	0.402159i	$0.868260\pi$
$884$	355.718	−	181.247i	0.402396	−	0.205031i
$885$	−105.249	−	206.563i	−0.118926	−	0.233405i
$886$	361.326	+	361.326i	0.407818	+	0.407818i
$887$	−450.041	+	883.255i	−0.507374	+	0.995778i	0.485230	+	0.874386i	$0.338736\pi$
$887$	−450.041	+	883.255i	−0.507374	+	0.995778i	−0.992605	+	0.121392i	$0.961264\pi$
$888$	−74.1273	−	53.8566i	−0.0834767	−	0.0606494i
$889$	595.551	+	303.448i	0.669911	+	0.341337i
$890$	−179.040	−	58.1737i	−0.201169	−	0.0653637i
$891$	−26.5228	−	52.0540i	−0.0297675	−	0.0584220i
$892$	133.981	−	845.924i	0.150203	−	0.948346i
$893$	1678.55	−	545.395i	1.87968	−	0.610745i
$894$	−221.348	−	221.348i	−0.247593	−	0.247593i
$895$	−486.526	−	158.082i	−0.543605	−	0.176628i
$896$	−25.8476	−	79.5506i	−0.0288477	−	0.0887842i
$897$	974.222	−	154.302i	1.08609	−	0.172020i
$898$	−198.454	−	31.4320i	−0.220995	−	0.0350022i
$899$	−861.197	−	279.820i	−0.957950	−	0.311257i
$900$	−74.6341	+	102.725i	−0.0829268	+	0.114139i
$901$	−403.117			−0.447410
$902$			31.4493i			0.0348661i
$903$	261.766	−	360.291i	0.289885	−	0.398993i
$904$	−30.7560	−	30.7560i	−0.0340221	−	0.0340221i
$905$	66.7250	+	421.285i	0.0737293	+	0.465508i
$906$	198.614	+	273.369i	0.219221	+	0.301732i
$907$	−218.623	−	1380.33i	−0.241040	−	1.52187i	−0.750209	−	0.661201i	$-0.770047\pi$
$907$	−218.623	−	1380.33i	−0.241040	−	1.52187i	0.509169	−	0.860667i	$-0.329953\pi$
$908$	−385.980	−	757.528i	−0.425088	−	0.834282i
$909$	199.276	+	31.5622i	0.219225	+	0.0347219i
$910$	−239.111	+	173.724i	−0.262759	+	0.190905i
$911$	−525.763	+	381.989i	−0.577127	+	0.419307i	−0.837687	−	0.546150i	$-0.816093\pi$
$911$	−525.763	+	381.989i	−0.577127	+	0.419307i	0.260560	+	0.965458i	$0.416093\pi$
$912$	46.0970	+	141.872i	0.0505449	+	0.155561i
$913$	426.760	+	217.445i	0.467426	+	0.238165i
$914$			33.4617i			0.0366102i
$915$	191.307	+	78.9909i	0.209079	+	0.0863288i
$916$	−229.282			−0.250308
$917$	−547.488	+	1074.51i	−0.597043	+	1.17176i
$918$	−96.6780	+	31.4126i	−0.105314	+	0.0342185i
$919$	−185.488	−	255.302i	−0.201836	−	0.277804i	0.696085	−	0.717959i	$-0.254923\pi$
$919$	−185.488	−	255.302i	−0.201836	−	0.277804i	−0.897922	+	0.440155i	$0.854923\pi$
$920$	−128.527	−	176.902i	−0.139703	−	0.192285i
$921$	−25.2453	+	159.393i	−0.0274108	+	0.173065i
$922$	−79.3898	+	40.4511i	−0.0861061	+	0.0438732i
$923$	−1201.19	+	190.250i	−1.30140	+	0.206121i
$924$	134.497	−	97.7175i	0.145559	−	0.105755i
$925$	−390.933	+	61.9177i	−0.422630	+	0.0669380i
$926$	−115.600	+	115.600i	−0.124838	+	0.124838i
$927$	−432.783	−	314.435i	−0.466864	−	0.339196i
$928$	−191.463			−0.206318
$929$		−	91.8133i		−	0.0988302i	−0.998778	−	0.0494151i	$-0.984264\pi$
$929$		−	91.8133i		−	0.0988302i	0.998778	−	0.0494151i	$-0.0157357\pi$
$930$	−103.858	−	75.4576i	−0.111676	−	0.0811372i
$931$	37.6548	−	115.889i	0.0404455	−	0.124478i
$932$	97.7040	−	616.879i	0.104833	−	0.661887i
$933$	−108.423	−	684.554i	−0.116209	−	0.733712i
$934$	183.935	−	59.7642i	0.196933	−	0.0639874i
$935$	54.3577	−	167.296i	0.0581366	−	0.178926i
$936$	86.5808	−	86.5808i	0.0925009	−	0.0925009i
$937$	65.6949	+	202.188i	0.0701120	+	0.215782i	0.979973	−	0.199131i	$-0.0638119\pi$
$937$	65.6949	+	202.188i	0.0701120	+	0.215782i	−0.909861	+	0.414913i	$0.863812\pi$
$938$	717.650	+	113.665i	0.765085	+	0.121178i
$939$	−623.375	+	317.625i	−0.663871	+	0.338259i
$940$	−99.2419	+	305.435i	−0.105577	+	0.324931i
$941$	585.249	−	1148.62i	0.621944	−	1.22063i	−0.338186	−	0.941079i	$-0.609813\pi$
$941$	585.249	−	1148.62i	0.621944	−	1.22063i	0.960130	−	0.279555i	$-0.0901868\pi$
$942$	361.945	−	498.174i	0.384230	−	0.528847i
$943$	120.463	+	61.3788i	0.127744	+	0.0650888i
$944$	−193.256	+	193.256i	−0.204721	+	0.204721i
$945$	67.0530	−	34.1652i	0.0709556	−	0.0361537i
$946$	−144.942	−	284.465i	−0.153216	−	0.300703i
$947$	434.208	+	434.208i	0.458509	+	0.458509i	0.898166	−	0.439657i	$-0.144900\pi$
$947$	434.208	+	434.208i	0.458509	+	0.458509i	−0.439657	+	0.898166i	$0.644900\pi$
$948$	−89.2077	+	175.080i	−0.0941010	+	0.184684i
$949$	−36.5288	−	26.5397i	−0.0384919	−	0.0279660i
$950$	574.160	+	292.549i	0.604379	+	0.307946i
$951$	−952.927	−	309.625i	−1.00203	−	0.325578i
$952$	−131.325	−	257.740i	−0.137947	−	0.270736i
$953$	−186.575	+	1177.99i	−0.195777	+	1.23608i	0.672535	+	0.740065i	$0.265205\pi$
$953$	−186.575	+	1177.99i	−0.195777	+	1.23608i	−0.868311	+	0.496019i	$0.834795\pi$
$954$	−117.584	+	38.2054i	−0.123254	+	0.0400476i
$955$	196.481	+	196.481i	0.205739	+	0.205739i
$956$	237.101	+	77.0387i	0.248013	+	0.0805844i
$957$	−117.594	−	361.917i	−0.122878	−	0.378178i
$958$	−148.241	+	23.4790i	−0.154740	+	0.0245084i
$959$	774.707	+	122.701i	0.807828	+	0.127947i
$960$	−25.8155	−	8.38796i	−0.0268911	−	0.00873746i
$961$	144.146	−	198.399i	0.149995	−	0.206451i
$962$	381.681			0.396758
$963$			79.5212i			0.0825766i
$964$	−51.4432	+	70.8054i	−0.0533643	+	0.0734496i
$965$	−24.5233	−	24.5233i	−0.0254127	−	0.0254127i
$966$	−111.801	−	705.886i	−0.115736	−	0.730731i
$967$	−948.438	−	1305.41i	−0.980804	−	1.34996i	−0.936395	−	0.350948i	$-0.885860\pi$
$967$	−948.438	−	1305.41i	−0.980804	−	1.34996i	−0.0444089	−	0.999013i	$-0.514140\pi$
$968$	34.8941	+	220.313i	0.0360476	+	0.227596i
$969$	234.208	+	459.659i	0.241700	+	0.474364i
$970$	286.458	+	45.3704i	0.295317	+	0.0467737i
$971$	−657.146	+	477.445i	−0.676773	+	0.491704i	−0.872285	−	0.488997i	$-0.837363\pi$
$971$	−657.146	+	477.445i	−0.676773	+	0.491704i	0.195513	+	0.980701i	$0.437363\pi$
$972$	−25.2227	+	18.3253i	−0.0259492	+	0.0188532i
$973$	−575.853	−	1772.29i	−0.591832	−	1.82147i
$974$	−554.779	−	282.674i	−0.569589	−	0.290220i
$975$		−	528.930i		−	0.542492i
$976$	18.8714	−	243.269i	0.0193355	−	0.249251i
$977$	550.401			0.563359			0.281679	−	0.959509i	$-0.409109\pi$
$977$	550.401			0.563359			0.281679	+	0.959509i	$0.409109\pi$
$978$	76.0643	−	149.285i	0.0777754	−	0.152643i
$979$	−419.511	+	136.307i	−0.428509	+	0.139231i
$980$	13.0329	+	17.9382i	0.0132988	+	0.0183043i
$981$	−205.957	−	283.475i	−0.209946	−	0.288965i
$982$	−6.52497	+	41.1971i	−0.00664458	+	0.0419522i
$983$	1457.15	−	742.457i	1.48235	−	0.755298i	0.489208	−	0.872167i	$-0.337286\pi$
$983$	1457.15	−	742.457i	1.48235	−	0.755298i	0.993147	+	0.116870i	$0.0372860\pi$
$984$	16.5764	−	2.62544i	0.0168459	−	0.00266813i
$985$	199.030	−	144.604i	0.202061	−	0.146806i
$986$	−653.989	+	103.582i	−0.663275	+	0.105052i
$987$	−742.228	+	742.228i	−0.752004	+	0.752004i
$988$	−502.722	−	365.249i	−0.508827	−	0.369685i
$989$	−1372.49			−1.38776
$990$		−	53.9499i		−	0.0544948i
$991$	259.916	+	188.840i	0.262276	+	0.190555i	0.711150	−	0.703040i	$-0.248175\pi$
$991$	259.916	+	188.840i	0.262276	+	0.190555i	−0.448874	+	0.893595i	$0.648175\pi$
$992$	−46.7673	+	143.935i	−0.0471445	+	0.145096i
$993$	8.69367	−	54.8897i	0.00875495	−	0.0552766i
$994$	137.848	+	870.339i	0.138680	+	0.875593i
$995$	−290.918	+	94.5251i	−0.292380	+	0.0950001i
$996$	78.9851	−	243.091i	0.0793023	−	0.244067i
$997$	1149.53	−	1149.53i	1.15299	−	1.15299i	0.167042	−	0.985950i	$-0.446578\pi$
$997$	1149.53	−	1149.53i	1.15299	−	1.15299i	0.985950	−	0.167042i	$-0.0534216\pi$
$998$	−61.2926	−	188.639i	−0.0614155	−	0.189017i
$999$	−95.9880	−	15.2030i	−0.0960840	−	0.0152182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	366.3.s.a.37.8	✓	80
61.33	odd	20	inner	366.3.s.a.277.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.3.s.a.37.8	✓	80	1.1	even	1	trivial
366.3.s.a.277.8	yes	80	61.33	odd	20	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:	\( N \)	\(=\)	\( 366 = 2 \cdot 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	366.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642040 + 1.26007i) q^{2} +(1.64728 - 0.535233i) q^{3} +(-1.17557 - 1.61803i) q^{4} +(-1.15144 - 1.58482i) q^{5} +(-0.383185 + 2.41933i) q^{6} +(-6.58739 + 3.35644i) q^{7} +(2.79360 - 0.442463i) q^{8} +(2.42705 - 1.76336i) q^{9} +(2.73627 - 0.433382i) q^{10} +(4.59003 - 4.59003i) q^{11} +(-2.80252 - 2.03615i) q^{12} +14.4301 q^{13} -10.4556i q^{14} +(-2.74500 - 1.99436i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-2.16400 + 13.6629i) q^{17} +(0.663695 + 4.19041i) q^{18} +(20.4774 - 6.65353i) q^{19} +(-1.21070 + 3.72615i) q^{20} +(-9.05478 + 9.05478i) q^{21} +(2.83680 + 8.73076i) q^{22} +(38.9787 + 6.17361i) q^{23} +(4.36502 - 2.22409i) q^{24} +(6.53958 - 20.1267i) q^{25} +(-9.26472 + 18.1830i) q^{26} +(3.05422 - 4.20378i) q^{27} +(13.1748 + 6.71288i) q^{28} +(23.9329 - 23.9329i) q^{29} +(4.27543 - 2.17844i) q^{30} +(-12.1460 - 23.8378i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(5.10432 - 10.0178i) q^{33} +(-15.8269 - 11.4989i) q^{34} +(12.9044 + 6.57510i) q^{35} +(-5.70634 - 1.85410i) q^{36} +(-8.49106 - 16.6646i) q^{37} +(-4.76340 + 30.0749i) q^{38} +(23.7704 - 7.72349i) q^{39} +(-3.91790 - 3.91790i) q^{40} +(3.25815 + 1.05864i) q^{41} +(-5.59616 - 17.2232i) q^{42} +(-34.3497 + 5.44045i) q^{43} +(-12.8227 - 2.03092i) q^{44} +(-5.58922 - 1.81605i) q^{45} +(-32.8050 + 45.1523i) q^{46} +81.9708 q^{47} +6.92820i q^{48} +(3.32649 - 4.57852i) q^{49} +(21.1625 + 21.1625i) q^{50} +(3.74815 + 23.6649i) q^{51} +(-16.9636 - 23.3484i) q^{52} +(4.55868 + 28.7823i) q^{53} +(3.33614 + 6.54753i) q^{54} +(-12.5596 - 1.98924i) q^{55} +(-16.9175 + 12.2912i) q^{56} +(30.1709 - 21.9204i) q^{57} +(14.7914 + 45.5231i) q^{58} +(60.8792 + 31.0195i) q^{59} +6.78600i q^{60} +(-59.2986 + 14.3066i) q^{61} +37.8356 q^{62} +(-10.0693 + 19.7622i) q^{63} +(7.60845 - 2.47214i) q^{64} +(-16.6155 - 22.8692i) q^{65} +(9.34599 + 12.8636i) q^{66} +(-10.8712 + 68.6381i) q^{67} +(24.6510 - 12.5603i) q^{68} +(67.5130 - 10.6930i) q^{69} +(-16.5702 + 12.0390i) q^{70} +(-83.2417 + 13.1842i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-2.53143 - 1.83919i) q^{73} +26.4503 q^{74} -36.6545i q^{75} +(-34.8383 - 25.3115i) q^{76} +(-14.8301 + 45.6425i) q^{77} +(-5.52941 + 34.9113i) q^{78} +(-8.87355 - 56.0254i) q^{79} +(7.45229 - 2.42140i) q^{80} +(2.78115 - 8.55951i) q^{81} +(-3.42582 + 3.42582i) q^{82} +(22.8010 + 70.1743i) q^{83} +(25.2955 + 4.00641i) q^{84} +(24.1451 - 12.3025i) q^{85} +(15.1985 - 46.7761i) q^{86} +(26.6145 - 52.2339i) q^{87} +(10.7918 - 14.8537i) q^{88} +(-60.5462 - 30.8498i) q^{89} +(5.87685 - 5.87685i) q^{90} +(-95.0569 + 48.4339i) q^{91} +(-35.8330 - 70.3263i) q^{92} +(-32.7666 - 32.7666i) q^{93} +(-52.6285 + 103.289i) q^{94} +(-34.1233 - 24.7920i) q^{95} +(-8.73005 - 4.44818i) q^{96} +(99.5654 + 32.3508i) q^{97} +(3.63354 + 7.13122i) q^{98} +(3.04638 - 19.2341i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 20 q^{2} - 40 q^{5} + 20 q^{7} + 40 q^{8} + 60 q^{9} + 60 q^{10} + 20 q^{11} - 32 q^{13} + 80 q^{16} + 80 q^{17} + 60 q^{18} - 100 q^{19} - 40 q^{20} + 12 q^{21} - 60 q^{22} + 56 q^{23} + 144 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 80 * q - 20 * q^2 - 40 * q^5 + 20 * q^7 + 40 * q^8 + 60 * q^9 + 60 * q^10 + 20 * q^11 - 32 * q^13 + 80 * q^16 + 80 * q^17 + 60 * q^18 - 100 * q^19 - 40 * q^20 + 12 * q^21 - 60 * q^22 + 56 * q^23 + 144 * q^25 + 48 * q^26 - 40 * q^28 - 4 * q^29 - 68 * q^31 - 320 * q^32 + 12 * q^33 + 20 * q^34 + 12 * q^35 + 100 * q^37 + 148 * q^38 + 120 * q^39 + 280 * q^41 - 36 * q^42 - 260 * q^43 + 40 * q^44 - 40 * q^46 + 392 * q^47 + 20 * q^49 - 416 * q^50 + 96 * q^51 + 40 * q^52 - 504 * q^53 + 188 * q^55 + 72 * q^57 + 92 * q^58 + 108 * q^59 + 236 * q^61 - 136 * q^62 - 60 * q^63 + 120 * q^65 - 180 * q^66 - 600 * q^67 - 280 * q^68 - 360 * q^69 - 96 * q^70 + 424 * q^71 + 480 * q^72 - 324 * q^73 - 560 * q^74 + 136 * q^76 - 548 * q^77 + 48 * q^78 - 252 * q^79 - 180 * q^81 + 136 * q^82 - 312 * q^83 + 24 * q^84 + 992 * q^85 - 340 * q^86 - 108 * q^87 + 1128 * q^89 - 416 * q^91 + 48 * q^92 + 36 * q^93 - 88 * q^94 - 132 * q^95 - 260 * q^97 - 4 * q^98 - 60 * q^99

Introduction

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