LMFDB - Embedded newform 77.2.l.b.62.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(6,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("77.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.l (of order $10$, degree $4$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 $ x^16 + 20x^14 + 260x^12 + 2030x^10 + 11605x^8 + 42100x^6 + 106925x^4 + 113575*x^2 + 87025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			62.4
Root			$-0.551501 + 0.955228i$ of defining polynomial
Character	$\chi$	$=$	77.62
Dual form			77.2.l.b.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395472 + 0.544320i) q^{2} +(2.52275 + 0.819690i) q^{3} +(0.478148 + 1.47159i) q^{4} +(-2.08654 - 2.87188i) q^{5} +(-1.44385 + 1.04902i) q^{6} +(-2.62801 - 0.305873i) q^{7} +(-2.26988 - 0.737529i) q^{8} +(3.26531 + 2.37239i) q^{9} +O(q^{10})$	\(q+(-0.395472 + 0.544320i) q^{2} +(2.52275 + 0.819690i) q^{3} +(0.478148 + 1.47159i) q^{4} +(-2.08654 - 2.87188i) q^{5} +(-1.44385 + 1.04902i) q^{6} +(-2.62801 - 0.305873i) q^{7} +(-2.26988 - 0.737529i) q^{8} +(3.26531 + 2.37239i) q^{9} +2.38839 q^{10} +(2.70528 - 1.91872i) q^{11} +4.10438i q^{12} +(0.892348 + 0.648328i) q^{13} +(1.20580 - 1.30951i) q^{14} +(-2.90977 - 8.95534i) q^{15} +(-1.20449 + 0.875112i) q^{16} +(-3.37610 + 2.45288i) q^{17} +(-2.58268 + 0.839162i) q^{18} +(0.384885 - 1.18455i) q^{19} +(3.22854 - 4.44371i) q^{20} +(-6.37909 - 2.92579i) q^{21} +(-0.0254657 + 2.23133i) q^{22} +2.85410 q^{23} +(-5.12179 - 3.72120i) q^{24} +(-2.34894 + 7.22930i) q^{25} +(-0.705796 + 0.229327i) q^{26} +(1.61550 + 2.22355i) q^{27} +(-0.806459 - 4.01360i) q^{28} +(1.94279 - 0.631251i) q^{29} +(6.02530 + 1.95774i) q^{30} +(-1.76059 + 2.42325i) q^{31} -5.77510i q^{32} +(8.39749 - 2.62294i) q^{33} -2.80772i q^{34} +(4.60503 + 8.18554i) q^{35} +(-1.92987 + 5.93954i) q^{36} +(0.853512 + 2.62684i) q^{37} +(0.492566 + 0.677958i) q^{38} +(1.71974 + 2.36702i) q^{39} +(2.61811 + 8.05771i) q^{40} +(-1.69854 + 5.22758i) q^{41} +(4.11532 - 2.31520i) q^{42} +1.73205i q^{43} +(4.11708 + 3.06362i) q^{44} -14.3277i q^{45} +(-1.12872 + 1.55354i) q^{46} +(-6.49438 - 2.11015i) q^{47} +(-3.75594 + 1.22038i) q^{48} +(6.81288 + 1.60767i) q^{49} +(-3.00611 - 4.13756i) q^{50} +(-10.5276 + 3.42064i) q^{51} +(-0.527398 + 1.62316i) q^{52} +(-0.873619 - 0.634721i) q^{53} -1.84921 q^{54} +(-11.1550 - 3.76575i) q^{55} +(5.73968 + 2.63253i) q^{56} +(1.94194 - 2.67285i) q^{57} +(-0.424716 + 1.30714i) q^{58} +(2.17773 - 0.707589i) q^{59} +(11.7873 - 8.56395i) q^{60} +(10.8018 - 7.84799i) q^{61} +(-0.622757 - 1.91665i) q^{62} +(-7.85563 - 7.23343i) q^{63} +(0.734523 + 0.533662i) q^{64} -3.91548i q^{65} +(-1.89325 + 5.60822i) q^{66} +0.489806 q^{67} +(-5.22389 - 3.79538i) q^{68} +(7.20018 + 2.33948i) q^{69} +(-6.27671 - 0.730543i) q^{70} +(-8.25697 + 5.99904i) q^{71} +(-5.66216 - 7.79330i) q^{72} +(3.87124 + 11.9144i) q^{73} +(-1.76738 - 0.574257i) q^{74} +(-11.8516 + 16.3123i) q^{75} +1.92721 q^{76} +(-7.69638 + 4.21493i) q^{77} -1.96852 q^{78} +(7.30806 - 10.0587i) q^{79} +(5.02643 + 1.63319i) q^{80} +(-1.48883 - 4.58215i) q^{81} +(-2.17375 - 2.99191i) q^{82} +(-1.30949 + 0.951400i) q^{83} +(1.25542 - 10.7863i) q^{84} +(14.0887 + 4.57770i) q^{85} +(-0.942790 - 0.684977i) q^{86} +5.41860 q^{87} +(-7.55577 + 2.36003i) q^{88} +2.30985i q^{89} +(7.79883 + 5.66618i) q^{90} +(-2.14679 - 1.97676i) q^{91} +(1.36468 + 4.20006i) q^{92} +(-6.42784 + 4.67010i) q^{93} +(3.71694 - 2.70052i) q^{94} +(-4.20498 + 1.36628i) q^{95} +(4.73379 - 14.5691i) q^{96} +(7.44620 - 10.2488i) q^{97} +(-3.56939 + 3.07260i) q^{98} +(13.3855 + 0.152766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{2} - 10 q^{4} - 10 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 + 10 * q^8 + 8 * q^9	$ 16 q - 10 q^{2} - 10 q^{4} - 10 q^{7} + 10 q^{8} + 8 q^{9} + 2 q^{11} + 8 q^{14} - 14 q^{16} - 20 q^{18} + 42 q^{22} - 8 q^{23} - 30 q^{25} - 10 q^{28} + 10 q^{29} - 40 q^{30} + 40 q^{35} + 20 q^{36} + 4 q^{37} + 30 q^{39} + 50 q^{42} - 10 q^{44} - 10 q^{46} + 8 q^{49} - 60 q^{50} - 10 q^{51} - 4 q^{56} - 90 q^{57} - 2 q^{58} + 120 q^{60} - 20 q^{63} - 38 q^{64} - 4 q^{67} - 56 q^{71} + 30 q^{72} + 90 q^{74} + 2 q^{77} - 20 q^{78} + 50 q^{79} - 16 q^{81} - 70 q^{84} + 80 q^{85} + 6 q^{86} - 86 q^{88} - 30 q^{91} + 20 q^{92} - 40 q^{93} - 60 q^{95} + 36 q^{99}+O(q^{100}) $ 16 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 + 10 * q^8 + 8 * q^9 + 2 * q^11 + 8 * q^14 - 14 * q^16 - 20 * q^18 + 42 * q^22 - 8 * q^23 - 30 * q^25 - 10 * q^28 + 10 * q^29 - 40 * q^30 + 40 * q^35 + 20 * q^36 + 4 * q^37 + 30 * q^39 + 50 * q^42 - 10 * q^44 - 10 * q^46 + 8 * q^49 - 60 * q^50 - 10 * q^51 - 4 * q^56 - 90 * q^57 - 2 * q^58 + 120 * q^60 - 20 * q^63 - 38 * q^64 - 4 * q^67 - 56 * q^71 + 30 * q^72 + 90 * q^74 + 2 * q^77 - 20 * q^78 + 50 * q^79 - 16 * q^81 - 70 * q^84 + 80 * q^85 + 6 * q^86 - 86 * q^88 - 30 * q^91 + 20 * q^92 - 40 * q^93 - 60 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.395472	+	0.544320i	−0.279641	+	0.384892i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−0.395472	+	0.544320i	−0.279641	+	0.384892i	0.645974	+	0.763359i	$0.276451\pi$
$3$	2.52275	+	0.819690i	1.45651	+	0.473248i	0.927002	−	0.375057i	$-0.122377\pi$
$3$	2.52275	+	0.819690i	1.45651	+	0.473248i	0.529507	+	0.848305i	$0.322377\pi$
$4$	0.478148	+	1.47159i	0.239074	+	0.735793i
$5$	−2.08654	−	2.87188i	−0.933130	−	1.28434i	−0.958626	−	0.284668i	$-0.908117\pi$
$5$	−2.08654	−	2.87188i	−0.933130	−	1.28434i	0.0254964	−	0.999675i	$-0.491883\pi$
$6$	−1.44385	+	1.04902i	−0.589449	+	0.428260i
$7$	−2.62801	−	0.305873i	−0.993295	−	0.115609i
$7$	−2.62801	−	0.305873i	−0.993295	−	0.115609i
$8$	−2.26988	−	0.737529i	−0.802524	−	0.260756i
$9$	3.26531	+	2.37239i	1.08844	+	0.790796i
$10$	2.38839			0.755275
$11$	2.70528	−	1.91872i	0.815672	−	0.578514i
$11$	2.70528	−	1.91872i	0.815672	−	0.578514i
$12$			4.10438i			1.18483i
$13$	0.892348	+	0.648328i	0.247493	+	0.179814i	0.704615	−	0.709590i	$-0.251120\pi$
$13$	0.892348	+	0.648328i	0.247493	+	0.179814i	−0.457122	+	0.889404i	$0.651120\pi$
$14$	1.20580	−	1.30951i	0.322263	−	0.349983i
$15$	−2.90977	−	8.95534i	−0.751299	−	2.31226i
$16$	−1.20449	+	0.875112i	−0.301122	+	0.218778i
$17$	−3.37610	+	2.45288i	−0.818823	+	0.594910i	−0.916375	−	0.400320i	$-0.868899\pi$
$17$	−3.37610	+	2.45288i	−0.818823	+	0.594910i	0.0975518	+	0.995230i	$0.468899\pi$
$18$	−2.58268	+	0.839162i	−0.608743	+	0.197792i
$19$	0.384885	−	1.18455i	0.0882987	−	0.271756i	−0.897151	−	0.441725i	$-0.854367\pi$
$19$	0.384885	−	1.18455i	0.0882987	−	0.271756i	0.985449	+	0.169969i	$0.0543668\pi$
$20$	3.22854	−	4.44371i	0.721924	−	0.993644i
$21$	−6.37909	−	2.92579i	−1.39203	−	0.638461i
$22$	−0.0254657	+	2.23133i	−0.00542931	+	0.475722i
$23$	2.85410			0.595121			0.297561	−	0.954703i	$-0.403827\pi$
$23$	2.85410			0.595121			0.297561	+	0.954703i	$0.403827\pi$
$24$	−5.12179	−	3.72120i	−1.04548	−	0.759586i
$25$	−2.34894	+	7.22930i	−0.469789	+	1.44586i
$26$	−0.705796	+	0.229327i	−0.138418	+	0.0449747i
$27$	1.61550	+	2.22355i	0.310904	+	0.427922i
$28$	−0.806459	−	4.01360i	−0.152406	−	0.758499i
$29$	1.94279	−	0.631251i	0.360767	−	0.117220i	−0.123024	−	0.992404i	$-0.539259\pi$
$29$	1.94279	−	0.631251i	0.360767	−	0.117220i	0.483791	+	0.875183i	$0.339259\pi$
$30$	6.02530	+	1.95774i	1.10006	+	0.357433i
$31$	−1.76059	+	2.42325i	−0.316212	+	0.435228i	−0.937306	−	0.348508i	$-0.886688\pi$
$31$	−1.76059	+	2.42325i	−0.316212	+	0.435228i	0.621094	+	0.783736i	$0.286688\pi$
$32$		−	5.77510i		−	1.02090i
$33$	8.39749	−	2.62294i	1.46181	−	0.456596i
$34$		−	2.80772i		−	0.481520i
$35$	4.60503	+	8.18554i	0.778391	+	1.38361i
$36$	−1.92987	+	5.93954i	−0.321646	+	0.989924i
$37$	0.853512	+	2.62684i	0.140316	+	0.431850i	0.996379	−	0.0850225i	$-0.0270962\pi$
$37$	0.853512	+	2.62684i	0.140316	+	0.431850i	−0.856063	+	0.516872i	$0.827096\pi$
$38$	0.492566	+	0.677958i	0.0799047	+	0.109979i
$39$	1.71974	+	2.36702i	0.275379	+	0.379026i
$40$	2.61811	+	8.05771i	0.413959	+	1.27404i
$41$	−1.69854	+	5.22758i	−0.265268	+	0.816410i	0.726364	+	0.687310i	$0.241209\pi$
$41$	−1.69854	+	5.22758i	−0.265268	+	0.816410i	−0.991632	+	0.129100i	$0.958791\pi$
$42$	4.11532	−	2.31520i	0.635007	−	0.357242i
$43$			1.73205i			0.264135i	0.991241	+	0.132068i	$0.0421616\pi$
$43$			1.73205i			0.264135i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	4.11708	+	3.06362i	0.620673	+	0.461859i
$45$		−	14.3277i		−	2.13584i
$46$	−1.12872	+	1.55354i	−0.166420	+	0.229058i
$47$	−6.49438	−	2.11015i	−0.947303	−	0.307797i	−0.205684	−	0.978618i	$-0.565942\pi$
$47$	−6.49438	−	2.11015i	−0.947303	−	0.307797i	−0.741619	+	0.670821i	$0.765942\pi$
$48$	−3.75594	+	1.22038i	−0.542123	+	0.176147i
$49$	6.81288	+	1.60767i	0.973269	+	0.229668i
$50$	−3.00611	−	4.13756i	−0.425129	−	0.585139i
$51$	−10.5276	+	3.42064i	−1.47416	+	0.478985i
$52$	−0.527398	+	1.62316i	−0.0731369	+	0.225092i
$53$	−0.873619	−	0.634721i	−0.120001	−	0.0871857i	0.526166	−	0.850382i	$-0.323629\pi$
$53$	−0.873619	−	0.634721i	−0.120001	−	0.0871857i	−0.646167	+	0.763196i	$0.723629\pi$
$54$	−1.84921			−0.251645
$55$	−11.1550	−	3.76575i	−1.50414	−	0.507774i
$56$	5.73968	+	2.63253i	0.766997	+	0.351786i
$57$	1.94194	−	2.67285i	0.257216	−	0.354027i
$58$	−0.424716	+	1.30714i	−0.0557679	+	0.171636i
$59$	2.17773	−	0.707589i	0.283517	−	0.0921202i	−0.163807	−	0.986492i	$-0.552377\pi$
$59$	2.17773	−	0.707589i	0.283517	−	0.0921202i	0.447323	+	0.894372i	$0.352377\pi$
$60$	11.7873	−	8.56395i	1.52173	−	1.10560i
$61$	10.8018	−	7.84799i	1.38303	−	1.00483i	0.386442	−	0.922314i	$-0.373704\pi$
$61$	10.8018	−	7.84799i	1.38303	−	1.00483i	0.996590	−	0.0825181i	$-0.0262962\pi$
$62$	−0.622757	−	1.91665i	−0.0790903	−	0.243415i
$63$	−7.85563	−	7.23343i	−0.989716	−	0.911327i
$64$	0.734523	+	0.533662i	0.0918153	+	0.0667077i
$65$		−	3.91548i		−	0.485655i
$66$	−1.89325	+	5.60822i	−0.233043	+	0.690324i
$67$	0.489806			0.0598393			0.0299197	−	0.999552i	$-0.490475\pi$
$67$	0.489806			0.0598393			0.0299197	+	0.999552i	$0.490475\pi$
$68$	−5.22389	−	3.79538i	−0.633490	−	0.460258i
$69$	7.20018	+	2.33948i	0.866800	+	0.281640i
$70$	−6.27671	−	0.730543i	−0.750210	−	0.0873165i
$71$	−8.25697	+	5.99904i	−0.979921	+	0.711955i	−0.957691	−	0.287798i	$-0.907077\pi$
$71$	−8.25697	+	5.99904i	−0.979921	+	0.711955i	−0.0222304	+	0.999753i	$0.507077\pi$
$72$	−5.66216	−	7.79330i	−0.667292	−	0.918449i
$73$	3.87124	+	11.9144i	0.453094	+	1.39448i	0.873358	+	0.487078i	$0.161937\pi$
$73$	3.87124	+	11.9144i	0.453094	+	1.39448i	−0.420264	+	0.907402i	$0.638063\pi$
$74$	−1.76738	−	0.574257i	−0.205454	−	0.0667560i
$75$	−11.8516	+	16.3123i	−1.36850	+	1.88358i
$76$	1.92721			0.221066
$77$	−7.69638	+	4.21493i	−0.877084	+	0.480336i
$78$	−1.96852			−0.222891
$79$	7.30806	−	10.0587i	0.822221	−	1.13169i	−0.167100	−	0.985940i	$-0.553440\pi$
$79$	7.30806	−	10.0587i	0.822221	−	1.13169i	0.989321	−	0.145750i	$-0.0465597\pi$
$80$	5.02643	+	1.63319i	0.561972	+	0.182596i
$81$	−1.48883	−	4.58215i	−0.165426	−	0.509127i
$82$	−2.17375	−	2.99191i	−0.240050	−	0.330401i
$83$	−1.30949	+	0.951400i	−0.143735	+	0.104430i	−0.657329	−	0.753604i	$-0.728314\pi$
$83$	−1.30949	+	0.951400i	−0.143735	+	0.104430i	0.513594	+	0.858033i	$0.328314\pi$
$84$	1.25542	−	10.7863i	0.136977	−	1.17689i
$85$	14.0887	+	4.57770i	1.52814	+	0.496522i
$86$	−0.942790	−	0.684977i	−0.101664	−	0.0738629i
$87$	5.41860			0.580935
$88$	−7.55577	+	2.36003i	−0.805447	+	0.251580i
$89$			2.30985i			0.244844i	0.992478	+	0.122422i	$0.0390661\pi$
$89$			2.30985i			0.244844i	−0.992478	+	0.122422i	$0.960934\pi$
$90$	7.79883	+	5.66618i	0.822069	+	0.597268i
$91$	−2.14679	−	1.97676i	−0.225045	−	0.207221i
$92$	1.36468	+	4.20006i	0.142278	+	0.437886i
$93$	−6.42784	+	4.67010i	−0.666536	+	0.484267i
$94$	3.71694	−	2.70052i	0.383373	−	0.278537i
$95$	−4.20498	+	1.36628i	−0.431422	+	0.140177i
$96$	4.73379	−	14.5691i	0.483141	−	1.48695i
$97$	7.44620	−	10.2488i	0.756047	−	1.04061i	−0.241485	−	0.970405i	$-0.577634\pi$
$97$	7.44620	−	10.2488i	0.756047	−	1.04061i	0.997533	−	0.0702056i	$-0.0223655\pi$
$98$	−3.56939	+	3.07260i	−0.360563	+	0.310379i
$99$	13.3855	+	0.152766i	1.34530	+	0.0153536i
$100$	−11.7617			−1.17617
$101$	−2.56175	−	1.86122i	−0.254903	−	0.185198i	0.452994	−	0.891514i	$-0.350356\pi$
$101$	−2.56175	−	1.86122i	−0.254903	−	0.185198i	−0.707897	+	0.706316i	$0.750356\pi$
$102$	2.30146	−	7.08317i	0.227879	−	0.701338i
$103$	−9.25587	+	3.00742i	−0.912008	+	0.296329i	−0.727184	−	0.686442i	$-0.759171\pi$
$103$	−9.25587	+	3.00742i	−0.912008	+	0.296329i	−0.184824	+	0.982772i	$0.559171\pi$
$104$	−1.54736	−	2.12976i	−0.151731	−	0.208840i
$105$	4.90771	+	24.4248i	0.478943	+	2.38361i
$106$	0.690983	−	0.224514i	0.0671142	−	0.0218067i
$107$	−10.0400	−	3.26220i	−0.970606	−	0.315369i	−0.219546	−	0.975602i	$-0.570457\pi$
$107$	−10.0400	−	3.26220i	−0.970606	−	0.315369i	−0.751061	+	0.660233i	$0.770457\pi$
$108$	−2.49970	+	3.44054i	−0.240534	+	0.331066i
$109$			3.04683i			0.291833i	0.989297	+	0.145917i	$0.0466131\pi$
$109$			3.04683i			0.291833i	−0.989297	+	0.145917i	$0.953387\pi$
$110$	6.46126	−	4.58264i	0.616057	−	0.436937i
$111$			7.32647i			0.695397i
$112$	3.43308	−	1.93138i	0.324396	−	0.182499i
$113$	2.24257	−	6.90191i	0.210963	−	0.649277i	−0.788453	−	0.615096i	$-0.789117\pi$
$113$	2.24257	−	6.90191i	0.210963	−	0.649277i	0.999416	−	0.0341819i	$-0.0108826\pi$
$114$	0.686903	+	2.11407i	0.0643343	+	0.198001i
$115$	−5.95520	−	8.19663i	−0.555326	−	0.764340i
$116$	1.85788	+	2.55715i	0.172500	+	0.237426i
$117$	1.37571	+	4.23399i	0.127184	+	0.391432i
$118$	−0.476077	+	1.46521i	−0.0438265	+	0.134884i
$119$	9.62268	−	5.41353i	0.882110	−	0.496258i
$120$			22.4736i			2.05155i
$121$	3.63706	−	10.3813i	0.330642	−	0.943756i
$122$			8.98330i			0.813310i
$123$	−8.56999	+	11.7956i	−0.772730	+	1.06357i
$124$	−4.40784	−	1.43219i	−0.395836	−	0.128615i
$125$	8.78237	−	2.85357i	0.785519	−	0.255231i
$126$	7.04398	−	1.41536i	0.627527	−	0.126090i
$127$	−3.60298	−	4.95908i	−0.319713	−	0.440047i	0.618666	−	0.785654i	$-0.287673\pi$
$127$	−3.60298	−	4.95908i	−0.319713	−	0.440047i	−0.938380	+	0.345606i	$0.887673\pi$
$128$	10.4039	−	3.38044i	0.919585	−	0.298791i
$129$	−1.41975	+	4.36953i	−0.125002	+	0.384715i
$130$	2.13127	+	1.54846i	0.186925	+	0.135809i
$131$	18.8287			1.64507			0.822534	−	0.568715i	$-0.192559\pi$
$131$	18.8287			1.64507			0.822534	+	0.568715i	$0.192559\pi$
$132$	7.87513	+	11.1035i	0.685442	+	0.966434i
$133$	−1.37381	+	2.99530i	−0.119124	+	0.259725i
$134$	−0.193704	+	0.266611i	−0.0167335	+	0.0230317i
$135$	3.01495	−	9.27906i	0.259485	−	0.798614i
$136$	9.47240	−	3.07777i	0.812252	−	0.263917i
$137$	2.39419	−	1.73948i	0.204550	−	0.148614i	−0.480795	−	0.876833i	$-0.659652\pi$
$137$	2.39419	−	1.73948i	0.204550	−	0.148614i	0.685344	+	0.728219i	$0.259652\pi$
$138$	−4.12089	+	2.99400i	−0.350794	+	0.254866i
$139$	−4.56525	−	14.0504i	−0.387219	−	1.19174i	−0.934857	−	0.355024i	$-0.884473\pi$
$139$	−4.56525	−	14.0504i	−0.387219	−	1.19174i	0.547638	−	0.836715i	$-0.315527\pi$
$140$	−9.84386	+	10.6906i	−0.831958	+	0.903520i
$141$	−14.6540	−	10.6468i	−1.23409	−	0.896619i
$142$		−	6.86688i		−	0.576256i
$143$	3.65801	+	0.0417480i	0.305898	+	0.00349115i
$144$	−6.00914			−0.500761
$145$	−5.86659	−	4.26232i	−0.487193	−	0.353967i
$146$	−8.01623	−	2.60463i	−0.663428	−	0.215561i
$147$	15.8694	+	9.64021i	1.30889	+	0.795111i
$148$	−3.45752	+	2.51203i	−0.284206	+	0.206488i
$149$	4.41558	+	6.07752i	0.361738	+	0.497890i	0.950632	−	0.310320i	$-0.100436\pi$
$149$	4.41558	+	6.07752i	0.361738	+	0.497890i	−0.588894	+	0.808210i	$0.700436\pi$
$150$	−4.19215	−	12.9021i	−0.342287	−	1.05345i
$151$	12.1054	+	3.93330i	0.985127	+	0.320087i	0.756907	−	0.653523i	$-0.226710\pi$
$151$	12.1054	+	3.93330i	0.985127	+	0.320087i	0.228220	+	0.973610i	$0.426710\pi$
$152$	−1.74729	+	2.40493i	−0.141724	+	0.195066i
$153$	−16.8432			−1.36169
$154$	0.749428	−	5.85618i	0.0603906	−	0.471905i
$155$	10.6328			0.854048
$156$	−2.66098	+	3.66253i	−0.213049	+	0.293237i
$157$	−14.5146	−	4.71608i	−1.15839	−	0.376384i	−0.334093	−	0.942540i	$-0.608430\pi$
$157$	−14.5146	−	4.71608i	−1.15839	−	0.376384i	−0.824298	+	0.566156i	$0.808430\pi$
$158$	2.58501	+	7.95585i	0.205652	+	0.632933i
$159$	−1.68365	−	2.31734i	−0.133522	−	0.183777i
$160$	−16.5854	+	12.0500i	−1.31119	+	0.952634i
$161$	−7.50061	−	0.872992i	−0.591131	−	0.0688014i
$162$	3.08294	+	1.00171i	0.242219	+	0.0787017i
$163$	−17.0168	−	12.3634i	−1.33286	−	0.968378i	−0.999674	−	0.0255158i	$-0.991877\pi$
$163$	−17.0168	−	12.3634i	−1.33286	−	0.968378i	−0.333183	−	0.942862i	$-0.608123\pi$
$164$	−8.50499			−0.664128
$165$	−25.0545	−	18.6437i	−1.95049	−	1.45141i
$166$		−	1.08903i		−	0.0845253i
$167$	−6.74802	−	4.90273i	−0.522178	−	0.379384i	0.295246	−	0.955421i	$-0.404598\pi$
$167$	−6.74802	−	4.90273i	−0.522178	−	0.379384i	−0.817424	+	0.576037i	$0.804598\pi$
$168$	12.3219	+	11.3460i	0.950656	+	0.875360i
$169$	−3.64127	−	11.2067i	−0.280097	−	0.862051i
$170$	−8.06343	+	5.85842i	−0.618437	+	0.449320i
$171$	4.06699	−	2.95484i	0.311011	−	0.225963i
$172$	−2.54886	+	0.828176i	−0.194349	+	0.0631478i
$173$	−4.96246	+	15.2729i	−0.377289	+	1.16117i	0.564633	+	0.825342i	$0.309018\pi$
$173$	−4.96246	+	15.2729i	−0.377289	+	1.16117i	−0.941922	+	0.335833i	$0.890982\pi$
$174$	−2.14290	+	2.94945i	−0.162453	+	0.223597i
$175$	8.38430	−	18.2802i	0.633793	−	1.38185i
$176$	−1.57939	+	4.67849i	−0.119051	+	0.352655i
$177$	6.07388			0.456540
$178$	−1.25730	−	0.913480i	−0.0942384	−	0.0684682i
$179$	2.27689	−	7.00754i	0.170182	−	0.523768i	−0.829198	−	0.558955i	$-0.811203\pi$
$179$	2.27689	−	7.00754i	0.170182	−	0.523768i	0.999381	+	0.0351868i	$0.0112026\pi$
$180$	21.0844	−	6.85074i	1.57154	−	0.510624i
$181$	8.51032	+	11.7134i	0.632567	+	0.870654i	0.998192	−	0.0601085i	$-0.0191447\pi$
$181$	8.51032	+	11.7134i	0.632567	+	0.870654i	−0.365625	+	0.930762i	$0.619145\pi$
$182$	1.92498	−	0.386790i	0.142689	−	0.0286708i
$183$	33.6832	−	10.9443i	2.48993	−	0.809028i
$184$	−6.47847	−	2.10498i	−0.477599	−	0.155181i
$185$	5.76307	−	7.93219i	0.423710	−	0.583186i
$186$		−	5.34569i		−	0.391965i
$187$	−4.42691	+	13.1135i	−0.323727	+	0.958953i
$188$		−	10.5660i		−	0.770606i
$189$	−3.56544	−	6.33765i	−0.259347	−	0.460996i
$190$	0.919255	−	2.82918i	0.0666898	−	0.205250i
$191$	0.491165	+	1.51165i	0.0355394	+	0.109379i	0.967253	−	0.253816i	$-0.0816858\pi$
$191$	0.491165	+	1.51165i	0.0355394	+	0.109379i	−0.931713	+	0.363195i	$0.881686\pi$
$192$	1.41558	+	1.94838i	0.102161	+	0.140612i
$193$	6.58503	+	9.06352i	0.474001	+	0.652406i	0.977338	−	0.211684i	$-0.0678946\pi$
$193$	6.58503	+	9.06352i	0.474001	+	0.652406i	−0.503337	+	0.864090i	$0.667895\pi$
$194$	2.63388	+	8.10623i	0.189101	+	0.581994i
$195$	3.20948	−	9.87776i	0.229836	−	0.707361i
$196$	0.891733	+	10.7945i	0.0636952	+	0.771033i
$197$			15.0339i			1.07112i	0.844496	+	0.535561i	$0.179900\pi$
$197$			15.0339i			1.07112i	−0.844496	+	0.535561i	$0.820100\pi$
$198$	−5.37674	+	7.22559i	−0.382109	+	0.513500i
$199$			21.9453i			1.55566i	0.628476	+	0.777829i	$0.283679\pi$
$199$			21.9453i			1.55566i	−0.628476	+	0.777829i	$0.716321\pi$
$200$	10.6636	−	14.6772i	0.754033	−	1.03784i
$201$	1.23566	+	0.401489i	0.0871565	+	0.0283189i
$202$	2.02620	−	0.658351i	0.142563	−	0.0463214i
$203$	−5.29875	+	1.06469i	−0.371900	+	0.0747264i
$204$	−10.0675	−	13.8568i	−0.704868	−	0.970167i
$205$	18.5570	−	6.02955i	1.29608	−	0.421122i
$206$	2.02344	−	6.22750i	0.140980	−	0.433891i
$207$	9.31953	+	6.77104i	0.647752	+	0.470620i
$208$	−1.64218			−0.113865
$209$	−1.23160	−	3.94304i	−0.0851917	−	0.272746i
$210$	−15.2357	−	6.98793i	−1.05137	−	0.482213i
$211$	−8.44647	+	11.6256i	−0.581479	+	0.800337i	−0.993857	−	0.110676i	$-0.964698\pi$
$211$	−8.44647	+	11.6256i	−0.581479	+	0.800337i	0.412378	+	0.911013i	$0.364698\pi$
$212$	0.516329	−	1.58910i	0.0354616	−	0.109140i
$213$	−25.7476	+	8.36590i	−1.76420	+	0.573222i
$214$	5.74623	−	4.17488i	0.392804	−	0.285389i
$215$	4.97424	−	3.61400i	0.339240	−	0.246472i
$216$	−2.02707	−	6.23867i	−0.137924	−	0.424488i
$217$	5.36806	−	5.82980i	0.364408	−	0.395753i
$218$	−1.65845	−	1.20493i	−0.112324	−	0.0816084i
$219$			33.2303i			2.24550i
$220$	0.207897	−	18.2161i	0.0140164	−	1.22813i
$221$	−4.60292			−0.309626
$222$	−3.98794	−	2.89741i	−0.267653	−	0.194461i
$223$	16.8550	+	5.47651i	1.12869	+	0.366734i	0.813079	−	0.582154i	$-0.197790\pi$
$223$	16.8550	+	5.47651i	1.12869	+	0.366734i	0.315613	+	0.948888i	$0.397790\pi$
$224$	−1.76644	+	15.1770i	−0.118025	+	1.01406i
$225$	−24.8207	+	18.0333i	−1.65472	+	1.20222i
$226$	2.86998	+	3.95018i	0.190908	+	0.262762i
$227$	−1.26738	−	3.90058i	−0.0841186	−	0.258891i	0.900147	−	0.435587i	$-0.143459\pi$
$227$	−1.26738	−	3.90058i	−0.0841186	−	0.258891i	−0.984265	+	0.176696i	$0.943459\pi$
$228$	4.86186	+	1.57971i	0.321984	+	0.104619i
$229$	5.76104	−	7.92939i	0.380700	−	0.523989i	−0.575070	−	0.818104i	$-0.695025\pi$
$229$	5.76104	−	7.92939i	0.380700	−	0.523989i	0.955770	+	0.294116i	$0.0950251\pi$
$230$	6.81670			0.449480
$231$	−22.8710	+	4.32456i	−1.50480	+	0.284535i
$232$	−4.87547			−0.320090
$233$	−0.0599317	+	0.0824889i	−0.00392626	+	0.00540403i	−0.810976	−	0.585080i	$-0.801063\pi$
$233$	−0.0599317	+	0.0824889i	−0.00392626	+	0.00540403i	0.807049	+	0.590484i	$0.201063\pi$
$234$	−2.84870	−	0.925598i	−0.186225	−	0.0605082i
$235$	7.49070	+	23.0540i	0.488639	+	1.50388i
$236$	2.08256	+	2.86639i	0.135563	+	0.186586i
$237$	26.6814	−	19.3852i	1.73314	−	1.25920i
$238$	−0.858804	+	7.37872i	−0.0556680	+	0.478291i
$239$	−5.83544	−	1.89605i	−0.377463	−	0.122645i	0.114140	−	0.993465i	$-0.463589\pi$
$239$	−5.83544	−	1.89605i	−0.377463	−	0.122645i	−0.491603	+	0.870820i	$0.663589\pi$
$240$	11.3417	+	8.24023i	0.732104	+	0.531905i
$241$	4.31560			0.277992			0.138996	−	0.990293i	$-0.455612\pi$
$241$	4.31560			0.277992			0.138996	+	0.990293i	$0.455612\pi$
$242$	4.21240	+	6.08524i	0.270784	+	0.391174i
$243$		−	21.0254i		−	1.34878i
$244$	16.7139	+	12.1433i	1.07000	+	0.777397i
$245$	−9.59832	−	22.9202i	−0.613214	−	1.46432i
$246$	−3.03138	−	9.32963i	−0.193274	−	0.594835i
$247$	1.11143	−	0.807503i	0.0707187	−	0.0513802i
$248$	5.78355	−	4.20199i	0.367256	−	0.266827i
$249$	−4.08336	+	1.32677i	−0.258773	+	0.0840803i
$250$	−1.91993	+	5.90892i	−0.121427	+	0.373713i
$251$	−18.0415	+	24.8321i	−1.13877	+	1.56739i	−0.368552	+	0.929607i	$0.620146\pi$
$251$	−18.0415	+	24.8321i	−1.13877	+	1.56739i	−0.770220	+	0.637778i	$0.779854\pi$
$252$	6.88847	−	15.0189i	0.433933	−	0.946101i
$253$	7.72114	−	5.47621i	0.485424	−	0.344286i
$254$	4.12420			0.258776
$255$	31.7900	+	23.0968i	1.99077	+	1.44638i
$256$	−2.83554	+	8.72689i	−0.177221	+	0.545431i
$257$	−6.40319	+	2.08052i	−0.399420	+	0.129779i	−0.501837	−	0.864962i	$-0.667342\pi$
$257$	−6.40319	+	2.08052i	−0.399420	+	0.129779i	0.102417	+	0.994742i	$0.467342\pi$
$258$	−1.81695	−	2.50082i	−0.113118	−	0.155694i
$259$	−1.43956	−	7.16443i	−0.0894499	−	0.445176i
$260$	5.76197	−	1.87218i	0.357342	−	0.116107i
$261$	7.84139	+	2.54782i	0.485370	+	0.157706i
$262$	−7.44620	+	10.2488i	−0.460028	+	0.633174i
$263$		−	24.4460i		−	1.50741i	−0.657215	−	0.753703i	$-0.728266\pi$
$263$		−	24.4460i		−	1.50741i	0.657215	−	0.753703i	$-0.271734\pi$
$264$	−20.9958	−	0.239620i	−1.29220	−	0.0147476i
$265$			3.83330i			0.235478i
$266$	−1.08710	−	1.93234i	−0.0666543	−	0.118480i
$267$	−1.89336	+	5.82717i	−0.115872	+	0.356617i
$268$	0.234200	+	0.720792i	0.0143060	+	0.0440294i
$269$	14.8827	+	20.4842i	0.907412	+	1.24895i	0.968043	+	0.250785i	$0.0806888\pi$
$269$	14.8827	+	20.4842i	0.907412	+	1.24895i	−0.0606307	+	0.998160i	$0.519311\pi$
$270$	3.85845	+	5.31070i	0.234818	+	0.323199i
$271$	−8.44881	−	26.0028i	−0.513229	−	1.57956i	−0.786482	−	0.617613i	$-0.788100\pi$
$271$	−8.44881	−	26.0028i	−0.513229	−	1.57956i	0.273254	−	0.961942i	$-0.411900\pi$
$272$	1.91993	−	5.90892i	0.116413	−	0.358281i
$273$	−3.79549	−	6.74657i	−0.229713	−	0.408321i
$274$			1.99112i			0.120288i
$275$	7.51643	+	24.0642i	0.453258	+	1.45113i
$276$			11.7143i			0.705118i
$277$	−13.1776	+	18.1373i	−0.791762	+	1.08977i	0.202124	+	0.979360i	$0.435216\pi$
$277$	−13.1776	+	18.1373i	−0.791762	+	1.08977i	−0.993886	+	0.110407i	$0.964784\pi$
$278$	9.45334	+	3.07158i	0.566973	+	0.184221i
$279$	−11.4978	+	3.73585i	−0.688353	+	0.223659i
$280$	−4.41578	−	21.9765i	−0.263894	−	1.31335i
$281$	−12.6475	−	17.4078i	−0.754487	−	1.03846i	−0.997653	−	0.0684773i	$-0.978186\pi$
$281$	−12.6475	−	17.4078i	−0.754487	−	1.03846i	0.243166	−	0.969985i	$-0.421814\pi$
$282$	11.5905	−	3.76598i	0.690204	−	0.224261i
$283$	9.56200	−	29.4288i	0.568402	−	1.74936i	−0.0892187	−	0.996012i	$-0.528437\pi$
$283$	9.56200	−	29.4288i	0.568402	−	1.74936i	0.657621	−	0.753349i	$-0.271563\pi$
$284$	−12.7762	−	9.28242i	−0.758125	−	0.550810i
$285$	−11.7280			−0.694708
$286$	−1.46936	+	1.97462i	−0.0868852	+	0.116761i
$287$	6.06276	−	13.2186i	0.357873	−	0.780269i
$288$	13.7008	−	18.8575i	0.807326	−	1.11119i
$289$	0.128126	−	0.394331i	0.00753681	−	0.0231959i
$290$	4.64014	−	1.50767i	0.272478	−	0.0885335i
$291$	27.1858	−	19.7516i	1.59366	−	1.15786i
$292$	−15.6821	+	11.3937i	−0.917726	+	0.666767i
$293$	7.67937	+	23.6347i	0.448634	+	1.38075i	0.878449	+	0.477836i	$0.158579\pi$
$293$	7.67937	+	23.6347i	0.448634	+	1.38075i	−0.429816	+	0.902917i	$0.641421\pi$
$294$	−11.5233	+	4.82560i	−0.672050	+	0.281435i
$295$	−6.57604	−	4.77777i	−0.382872	−	0.278173i
$296$		−	6.59210i		−	0.383158i
$297$	8.63675	+	2.91563i	0.501155	+	0.169182i
$298$	−5.05435			−0.292791
$299$	2.54685	+	1.85040i	0.147288	+	0.107011i
$300$	−29.6718	−	9.64095i	−1.71310	−	0.556620i
$301$	0.529787	−	4.55185i	0.0305364	−	0.262364i
$302$	−6.92833	+	5.03373i	−0.398681	+	0.289658i
$303$	−4.93702	−	6.79522i	−0.283624	−	0.390375i
$304$	0.573029	+	1.76360i	0.0328654	+	0.101149i
$305$	−45.0769	−	14.6464i	−2.58110	−	0.838649i
$306$	6.66100	−	9.16808i	0.380784	−	0.524104i
$307$	−10.0029			−0.570896			−0.285448	−	0.958394i	$-0.592142\pi$
$307$	−10.0029			−0.570896			−0.285448	+	0.958394i	$0.592142\pi$
$308$	−9.88265	−	9.31054i	−0.563116	−	0.530517i
$309$	−25.8154			−1.46859
$310$	−4.20498	+	5.78765i	−0.238827	+	0.328717i
$311$	−17.8028	−	5.78448i	−1.00950	−	0.328008i	−0.242847	−	0.970065i	$-0.578081\pi$
$311$	−17.8028	−	5.78448i	−1.00950	−	0.328008i	−0.766657	+	0.642057i	$0.778081\pi$
$312$	−2.15786	−	6.64120i	−0.122165	−	0.375984i
$313$	3.10702	+	4.27645i	0.175619	+	0.241719i	0.887748	−	0.460330i	$-0.152269\pi$
$313$	3.10702	+	4.27645i	0.175619	+	0.241719i	−0.712129	+	0.702049i	$0.752269\pi$
$314$	8.30717	−	6.03551i	0.468801	−	0.340604i
$315$	−4.38244	+	37.6533i	−0.246923	+	2.12152i
$316$	18.2966	+	5.94491i	1.02926	+	0.334427i
$317$	23.2626	+	16.9013i	1.30656	+	0.949269i	0.999997	−	0.00258214i	$-0.000821923\pi$
$317$	23.2626	+	16.9013i	1.30656	+	0.949269i	0.306560	+	0.951851i	$0.400822\pi$
$318$	1.92721			0.108072
$319$	4.04460	−	5.43537i	0.226454	−	0.304322i
$320$		−	3.22297i		−	0.180169i
$321$	−22.6545	−	16.4594i	−1.26445	−	0.918676i
$322$	3.44147	−	3.73749i	0.191785	−	0.208282i
$323$	1.60616	+	4.94325i	0.0893690	+	0.275050i
$324$	6.03115	−	4.38188i	0.335064	−	0.243438i
$325$	−6.78304	+	4.92817i	−0.376255	+	0.273365i
$326$	13.4593	−	4.37320i	0.745442	−	0.242209i
$327$	−2.49745	+	7.68638i	−0.138110	+	0.425058i
$328$	7.71098	−	10.6132i	0.425767	−	0.586019i
$329$	16.4219	+	7.53196i	0.905367	+	0.415250i
$330$	20.0565	−	6.26461i	1.10407	−	0.344855i
$331$	12.2266			0.672035			0.336017	−	0.941856i	$-0.390920\pi$
$331$	12.2266			0.672035			0.336017	+	0.941856i	$0.390920\pi$
$332$	−2.02620	−	1.47212i	−0.111202	−	0.0807930i
$333$	−3.44490	+	10.6023i	−0.188779	+	0.581003i
$334$	5.33730	−	1.73419i	0.292044	−	0.0948909i
$335$	−1.02200	−	1.40666i	−0.0558379	−	0.0768542i
$336$	10.2439	−	2.05833i	0.558853	−	0.112291i
$337$	−34.3180	+	11.1506i	−1.86942	+	0.607412i	−0.877665	+	0.479274i	$0.840900\pi$
$337$	−34.3180	+	11.1506i	−1.86942	+	0.607412i	−0.991756	+	0.128138i	$0.959100\pi$
$338$	7.54003	+	2.44990i	0.410123	+	0.133257i
$339$	11.3149	−	15.5736i	0.614539	−	0.845841i
$340$			22.9216i			1.24310i
$341$	−0.113370	+	9.93363i	−0.00613935	+	0.537936i
$342$			3.38230i			0.182894i
$343$	−17.4126	−	6.30886i	−0.940192	−	0.340646i
$344$	1.27744	−	3.93155i	0.0688748	−	0.211975i
$345$	−8.30477	−	25.5595i	−0.447114	−	1.37608i
$346$	−6.35082	−	8.74115i	−0.341422	−	0.469927i
$347$	16.1695	+	22.2554i	0.868022	+	1.19473i	0.979597	+	0.200974i	$0.0644108\pi$
$347$	16.1695	+	22.2554i	0.868022	+	1.19473i	−0.111574	+	0.993756i	$0.535589\pi$
$348$	2.59089	+	7.97394i	0.138886	+	0.427448i
$349$	−4.36532	+	13.4351i	−0.233670	+	0.719164i	0.763625	+	0.645661i	$0.223418\pi$
$349$	−4.36532	+	13.4351i	−0.233670	+	0.719164i	−0.997295	+	0.0735032i	$0.976582\pi$
$350$	6.63453	+	11.7930i	0.354631	+	0.630365i
$351$			3.03156i			0.161812i
$352$	−11.0808	−	15.6232i	−0.590607	−	0.832722i
$353$		−	8.23958i		−	0.438549i	−0.975663	−	0.219274i	$-0.929631\pi$
$353$		−	8.23958i		−	0.438549i	0.975663	−	0.219274i	$-0.0703690\pi$
$354$	−2.40204	+	3.30613i	−0.127667	+	0.175719i
$355$	34.4570	+	11.1958i	1.82879	+	0.594209i
$356$	−3.39915	+	1.10445i	−0.180154	+	0.0585357i
$357$	28.7130	−	5.76935i	1.51965	−	0.305347i
$358$	2.91390	+	4.01064i	0.154004	+	0.211969i
$359$	−28.4596	+	9.24708i	−1.50204	+	0.488042i	−0.940612	−	0.339484i	$-0.889748\pi$
$359$	−28.4596	+	9.24708i	−1.50204	+	0.488042i	−0.561427	+	0.827526i	$0.689748\pi$
$360$	−10.5671	+	32.5221i	−0.556933	+	1.71406i
$361$	14.1163	+	10.2561i	0.742963	+	0.539794i
$362$	−9.74145			−0.511999
$363$	17.6849	−	23.2082i	0.928214	−	1.21811i
$364$	1.88249	−	4.10438i	0.0986692	−	0.215128i
$365$	26.1393	−	35.9777i	1.36819	−	1.88316i
$366$	−7.36353	+	22.6626i	−0.384898	+	1.18459i
$367$	4.40784	−	1.43219i	0.230087	−	0.0747599i	−0.191704	−	0.981453i	$-0.561401\pi$
$367$	4.40784	−	1.43219i	0.230087	−	0.0747599i	0.421792	+	0.906693i	$0.361401\pi$
$368$	−3.43773	+	2.49766i	−0.179204	+	0.130199i
$369$	−17.9481	+	13.0401i	−0.934341	+	0.678839i
$370$	2.03852	+	6.27391i	0.105977	+	0.326165i
$371$	2.10174	+	1.93527i	0.109117	+	0.100474i
$372$	−9.94591	−	7.22613i	−0.515672	−	0.374657i
$373$			15.2702i			0.790662i	0.918539	+	0.395331i	$0.129370\pi$
$373$			15.2702i			0.790662i	−0.918539	+	0.395331i	$0.870630\pi$
$374$	−5.38721	−	7.59566i	−0.278566	−	0.392762i
$375$	24.4947			1.26490
$376$	13.1852	+	9.57959i	0.679973	+	0.494030i
$377$	2.14290	+	0.696271i	0.110365	+	0.0358598i
$378$	4.85974	+	0.565622i	0.249958	+	0.0290925i
$379$	−18.4125	+	13.3775i	−0.945788	+	0.687155i	−0.949807	−	0.312837i	$-0.898721\pi$
$379$	−18.4125	+	13.3775i	−0.945788	+	0.687155i	0.00401892	+	0.999992i	$0.498721\pi$
$380$	−4.02120	−	5.53471i	−0.206283	−	0.283924i
$381$	−5.02451	−	15.4638i	−0.257413	−	0.792237i
$382$	−1.01706	−	0.330464i	−0.0520375	−	0.0169080i
$383$	16.9956	−	23.3924i	0.868432	−	1.19529i	−0.111060	−	0.993814i	$-0.535425\pi$
$383$	16.9956	−	23.3924i	0.868432	−	1.19529i	0.979493	−	0.201481i	$-0.0645753\pi$
$384$	29.0174			1.48079
$385$	28.1636	+	13.3084i	1.43535	+	0.678261i
$386$	−7.53765			−0.383656
$387$	−4.10910	+	5.65569i	−0.208877	+	0.287495i
$388$	18.6424	+	6.05729i	0.946425	+	0.307512i
$389$	−6.78802	−	20.8914i	−0.344166	−	1.05923i	−0.962029	−	0.272948i	$-0.912001\pi$
$389$	−6.78802	−	20.8914i	−0.344166	−	1.05923i	0.617863	−	0.786286i	$-0.287999\pi$
$390$	4.10740	+	5.65336i	0.207987	+	0.286269i
$391$	−9.63572	+	7.00076i	−0.487299	+	0.354044i
$392$	−14.2787	−	8.67393i	−0.721185	−	0.438099i
$393$	47.5000	+	15.4337i	2.39606	+	0.778526i
$394$	−8.18326	−	5.94549i	−0.412267	−	0.299529i
$395$	−44.1359			−2.22072
$396$	6.17544	+	19.7710i	0.310328	+	0.993530i
$397$			3.02008i			0.151573i	0.997124	+	0.0757866i	$0.0241468\pi$
$397$			3.02008i			0.151573i	−0.997124	+	0.0757866i	$0.975853\pi$
$398$	−11.9452	−	8.67872i	−0.598761	−	0.435025i
$399$	−5.92098	+	6.43028i	−0.296420	+	0.321917i
$400$	−3.49718	−	10.7632i	−0.174859	−	0.538160i
$401$	−6.37835	+	4.63414i	−0.318519	+	0.231418i	−0.735543	−	0.677478i	$-0.763073\pi$
$401$	−6.37835	+	4.63414i	−0.318519	+	0.231418i	0.417024	+	0.908895i	$0.363073\pi$
$402$	−0.707206	+	0.513815i	−0.0352722	+	0.0256268i
$403$	−3.14212	+	1.02094i	−0.156520	+	0.0508565i
$404$	1.51405	−	4.65977i	0.0753269	−	0.231832i
$405$	−10.0529	+	13.8366i	−0.499531	+	0.687545i
$406$	1.51598	−	3.30527i	0.0752366	−	0.164038i
$407$	7.34914	+	5.46868i	0.364283	+	0.271073i
$408$	26.4193			1.30795
$409$	−21.4766	−	15.6036i	−1.06195	−	0.771551i	−0.0875004	−	0.996164i	$-0.527888\pi$
$409$	−21.4766	−	15.6036i	−1.06195	−	0.771551i	−0.974448	+	0.224614i	$0.927888\pi$
$410$	−4.05678	+	12.4855i	−0.200350	+	0.616614i
$411$	7.46578	−	2.42578i	0.368260	−	0.119655i
$412$	−8.85135	−	12.1828i	−0.436075	−	0.600205i
$413$	−5.93954	+	1.19344i	−0.292266	+	0.0587254i
$414$	−7.37122	+	2.39505i	−0.362276	+	0.117711i
$415$	5.46461	+	1.77556i	0.268247	+	0.0871587i
$416$	3.74416	−	5.15339i	0.183573	−	0.252666i
$417$		−	39.1877i		−	1.91903i
$418$	2.63334	+	0.888973i	0.128801	+	0.0434811i
$419$			7.28466i			0.355879i	0.984041	+	0.177940i	$0.0569431\pi$
$419$			7.28466i			0.355879i	−0.984041	+	0.177940i	$0.943057\pi$
$420$	−33.5965	+	18.9008i	−1.63934	+	0.922262i
$421$	−7.35587	+	22.6390i	−0.358503	+	1.10336i	0.595447	+	0.803394i	$0.296975\pi$
$421$	−7.35587	+	22.6390i	−0.358503	+	1.10336i	−0.953950	+	0.299965i	$0.903025\pi$
$422$	−2.98769	−	9.19516i	−0.145438	−	0.447613i
$423$	−16.2001	−	22.2975i	−0.787675	−	1.08414i
$424$	1.51489	+	2.08506i	0.0735694	+	0.101260i
$425$	−9.80234	−	30.1685i	−0.475483	−	1.46339i
$426$	5.62871	−	17.3234i	0.272712	−	0.839322i
$427$	−30.7878	+	17.3206i	−1.48993	+	0.838203i
$428$		−	16.3346i		−	0.789562i
$429$	9.19401	+	3.10375i	0.443891	+	0.149851i
$430$			4.13681i			0.199495i
$431$	−0.376421	+	0.518099i	−0.0181316	+	0.0249560i	−0.817987	−	0.575237i	$-0.804910\pi$
$431$	−0.376421	+	0.518099i	−0.0181316	+	0.0249560i	0.799855	+	0.600193i	$0.204910\pi$
$432$	−3.89171	−	1.26449i	−0.187240	−	0.0608380i
$433$	16.3786	−	5.32173i	0.787105	−	0.255746i	0.112234	−	0.993682i	$-0.464199\pi$
$433$	16.3786	−	5.32173i	0.787105	−	0.255746i	0.674871	+	0.737936i	$0.264199\pi$
$434$	1.05036	+	5.22746i	0.0504190	+	0.250926i
$435$	−11.3061	−	15.5616i	−0.542087	−	0.746119i
$436$	−4.48367	+	1.45683i	−0.214729	+	0.0697696i
$437$	1.09850	−	3.38084i	0.0525485	−	0.161728i
$438$	−18.0879	−	13.1417i	−0.864275	−	0.627933i
$439$	0.0381286			0.00181978			0.000909889	−	1.00000i	$-0.499710\pi$
$439$	0.0381286			0.00181978			0.000909889		1.00000i	$0.499710\pi$
$440$	22.5432	+	16.7749i	1.07470	+	0.799714i
$441$	18.4322	+	21.4124i	0.877722	+	1.01964i
$442$	1.82032	−	2.50546i	0.0865840	−	0.119173i
$443$	9.46891	−	29.1423i	0.449881	−	1.38459i	−0.427159	−	0.904176i	$-0.640486\pi$
$443$	9.46891	−	29.1423i	0.449881	−	1.38459i	0.877041	−	0.480416i	$-0.159514\pi$
$444$	−10.7815	+	3.50313i	−0.511669	+	0.166251i
$445$	6.63361	−	4.81960i	0.314463	−	0.228471i
$446$	−9.64663	+	7.00869i	−0.456781	+	0.331871i
$447$	6.15770	+	18.9515i	0.291249	+	0.896374i
$448$	−1.76710	−	1.62714i	−0.0834877	−	0.0768751i
$449$	23.8836	+	17.3525i	1.12714	+	0.818913i	0.985276	−	0.170974i	$-0.0546913\pi$
$449$	23.8836	+	17.3525i	1.12714	+	0.818913i	0.141861	+	0.989887i	$0.454691\pi$
$450$		−	20.6421i		−	0.973078i
$451$	5.43520	+	17.4011i	0.255934	+	0.819384i
$452$	11.2290			0.528170
$453$	27.3149	+	19.8454i	1.28337	+	0.932420i
$454$	2.62437	+	0.852711i	0.123168	+	0.0400197i
$455$	−1.19764	+	10.2899i	−0.0561461	+	0.482399i
$456$	−6.37927	+	4.63481i	−0.298737	+	0.217045i
$457$	−2.49683	−	3.43660i	−0.116797	−	0.160757i	0.746616	−	0.665256i	$-0.231677\pi$
$457$	−2.49683	−	3.43660i	−0.116797	−	0.160757i	−0.863413	+	0.504498i	$0.831677\pi$
$458$	2.03780	+	6.27169i	0.0952200	+	0.293057i
$459$	−10.9082	−	3.54428i	−0.509151	−	0.165433i
$460$	9.21459	−	12.6828i	0.429633	−	0.591339i
$461$	11.8930			0.553913			0.276957	−	0.960882i	$-0.410674\pi$
$461$	11.8930			0.553913			0.276957	+	0.960882i	$0.410674\pi$
$462$	6.69087	−	14.1594i	0.311288	−	0.658753i
$463$	29.5007			1.37102			0.685508	−	0.728066i	$-0.259580\pi$
$463$	29.5007			1.37102			0.685508	+	0.728066i	$0.259580\pi$
$464$	−1.78765	+	2.46049i	−0.0829897	+	0.114226i
$465$	26.8239	+	8.71562i	1.24393	+	0.404177i
$466$	−0.0211991	−	0.0652440i	−0.000982028	−	0.00302237i
$467$	6.55321	+	9.01971i	0.303246	+	0.417383i	0.933260	−	0.359201i	$-0.116951\pi$
$467$	6.55321	+	9.01971i	0.303246	+	0.417383i	−0.630014	+	0.776584i	$0.716951\pi$
$468$	−5.57289	+	4.04894i	−0.257607	+	0.187162i
$469$	−1.28722	−	0.149818i	−0.0594381	−	0.00691797i
$470$	−15.5111	−	5.03986i	−0.715474	−	0.232472i
$471$	−32.7509	−	23.7950i	−1.50908	−	1.09641i
$472$	−5.46506			−0.251550
$473$	3.32331	+	4.68568i	0.152806	+	0.215448i
$474$			22.1895i			1.01920i
$475$	7.65943	+	5.56491i	0.351439	+	0.255335i
$476$	12.5675	+	11.5721i	0.576033	+	0.530409i
$477$	−1.34683	−	4.14513i	−0.0616673	−	0.189792i
$478$	3.33981	−	2.42651i	0.152759	−	0.110986i
$479$	−9.16744	+	6.66053i	−0.418871	+	0.304328i	−0.777183	−	0.629274i	$-0.783352\pi$
$479$	−9.16744	+	6.66053i	−0.418871	+	0.304328i	0.358312	+	0.933602i	$0.383352\pi$
$480$	−51.7180	+	16.8042i	−2.36059	+	0.767003i
$481$	−0.941425	+	2.89741i	−0.0429253	+	0.132110i
$482$	−1.70670	+	2.34906i	−0.0777378	+	0.106997i
$483$	−18.2066	−	8.35052i	−0.828427	−	0.379962i
$484$	17.0161	+	0.388452i	0.773458	+	0.0176569i
$485$	−44.9702			−2.04199
$486$	11.4445	+	8.31493i	0.519134	+	0.377173i
$487$	4.79157	−	14.7469i	0.217127	−	0.668247i	−0.781869	−	0.623443i	$-0.785733\pi$
$487$	4.79157	−	14.7469i	0.217127	−	0.668247i	0.998996	−	0.0448045i	$-0.0142665\pi$
$488$	−30.3070	+	9.84733i	−1.37193	+	0.445768i
$489$	−32.7949	−	45.1383i	−1.48304	−	2.04122i
$490$	16.2718	+	3.83975i	0.735086	+	0.173462i
$491$	9.89934	−	3.21649i	0.446751	−	0.145158i	−0.0769971	−	0.997031i	$-0.524533\pi$
$491$	9.89934	−	3.21649i	0.446751	−	0.145158i	0.523748	+	0.851873i	$0.324533\pi$
$492$	−21.4559	−	6.97145i	−0.967308	−	0.314297i
$493$	−5.01066	+	6.89659i	−0.225669	+	0.310607i
$494$			0.924319i			0.0415871i
$495$	−27.4907	−	38.7603i	−1.23562	−	1.74215i
$496$		−	4.45949i		−	0.200237i
$497$	23.5343	−	13.2400i	1.05566	−	0.593893i
$498$	0.892669	−	2.74735i	0.0400015	−	0.123112i
$499$	−7.17506	−	22.0826i	−0.321200	−	0.988551i	−0.973127	−	0.230269i	$-0.926039\pi$
$499$	−7.17506	−	22.0826i	−0.321200	−	0.988551i	0.651927	−	0.758282i	$-0.273961\pi$
$500$	8.39854	+	11.5596i	0.375594	+	0.516961i
$501$	−13.0048	−	17.8996i	−0.581013	−	0.799696i
$502$	−6.38166	−	19.6407i	−0.284828	−	0.876609i
$503$	−0.357335	+	1.09976i	−0.0159328	+	0.0490360i	−0.958707	−	0.284396i	$-0.908207\pi$
$503$	−0.357335	+	1.09976i	−0.0159328	+	0.0490360i	0.942774	+	0.333432i	$0.108207\pi$
$504$	12.4965	+	22.2128i	0.556637	+	0.989436i
$505$			11.2405i			0.500197i
$506$	−0.0726818	+	6.36846i	−0.00323110	+	0.283112i
$507$		−	31.2563i		−	1.38814i
$508$	5.57496	−	7.67328i	0.247349	−	0.340447i
$509$	−16.9599	−	5.51060i	−0.751734	−	0.244253i	−0.0920067	−	0.995758i	$-0.529328\pi$
$509$	−16.9599	−	5.51060i	−0.751734	−	0.244253i	−0.659727	+	0.751505i	$0.729328\pi$
$510$	−25.1441	+	8.16981i	−1.11340	+	0.361765i
$511$	−6.52935	−	32.4954i	−0.288841	−	1.43751i
$512$	9.23111	+	12.7055i	0.407961	+	0.561510i
$513$	3.25570	−	1.05784i	0.143743	−	0.0467048i
$514$	1.39981	−	4.30817i	0.0617430	−	0.190025i
$515$	27.9497	+	20.3066i	1.23161	+	0.894818i
$516$	−7.10899			−0.312956
$517$	−21.6179	+	6.75232i	−0.950754	+	0.296967i
$518$	4.46905	+	2.04975i	0.196359	+	0.0900607i
$519$	−25.0381	+	34.4619i	−1.09905	+	1.51271i
$520$	−2.88778	+	8.88767i	−0.126637	+	0.389750i
$521$	34.1579	−	11.0986i	1.49649	−	0.486238i	0.557495	−	0.830180i	$-0.311763\pi$
$521$	34.1579	−	11.0986i	1.49649	−	0.486238i	0.938991	+	0.343943i	$0.111763\pi$
$522$	−4.48787	+	3.26063i	−0.196429	+	0.142714i
$523$	−7.97894	+	5.79704i	−0.348895	+	0.253487i	−0.748405	−	0.663242i	$-0.769180\pi$
$523$	−7.97894	+	5.79704i	−0.348895	+	0.253487i	0.399511	+	0.916729i	$0.369180\pi$
$524$	9.00288	+	27.7080i	0.393293	+	1.21043i
$525$	36.1356	−	39.2438i	1.57709	−	1.71274i
$526$	13.3065	+	9.66770i	0.580189	+	0.421532i
$527$		−	12.4996i		−	0.544492i
$528$	−7.81931	+	10.5080i	−0.340292	+	0.457304i
$529$	−14.8541			−0.645831
$530$	−2.08654	−	1.51596i	−0.0906336	−	0.0658491i
$531$	8.78965	+	2.85593i	0.381439	+	0.123937i
$532$	−5.06472	−	0.589480i	−0.219584	−	0.0255572i
$533$	−4.90488	+	3.56360i	−0.212454	+	0.154357i
$534$	−2.42307	−	3.33507i	−0.104857	−	0.144323i
$535$	11.5803	+	35.6405i	0.500659	+	1.54087i
$536$	−1.11180	−	0.361246i	−0.0480225	−	0.0156035i
$537$	11.4880	−	15.8119i	0.495745	−	0.682334i
$538$	−17.0356			−0.734459
$539$	21.5154	−	8.72278i	0.926735	−	0.375717i
$540$	15.0965			0.649651
$541$	12.1252	−	16.6890i	0.521305	−	0.717515i	−0.464469	−	0.885589i	$-0.653755\pi$
$541$	12.1252	−	16.6890i	0.521305	−	0.717515i	0.985774	+	0.168074i	$0.0537549\pi$
$542$	17.4951	+	5.68450i	0.751478	+	0.244170i
$543$	11.8680	+	36.5259i	0.509304	+	1.56748i
$544$	14.1656	+	19.4973i	0.607345	+	0.835939i
$545$	8.75012	−	6.35733i	0.374814	−	0.272318i
$546$	5.17330	+	0.602117i	0.221397	+	0.0257682i
$547$	−27.4543	−	8.92046i	−1.17386	−	0.381411i	−0.343780	−	0.939050i	$-0.611707\pi$
$547$	−27.4543	−	8.92046i	−1.17386	−	0.381411i	−0.830083	+	0.557639i	$0.811707\pi$
$548$	3.70458	+	2.69153i	0.158252	+	0.114977i
$549$	53.8898			2.29996
$550$	−16.0712	−	5.42538i	−0.685277	−	0.231339i
$551$		−	2.54430i		−	0.108391i
$552$	−14.6181	−	10.6207i	−0.622188	−	0.452046i
$553$	−22.2823	+	24.1990i	−0.947542	+	1.02905i
$554$	−4.66117	−	14.3456i	−0.198034	−	0.609486i
$555$	21.0407	−	15.2870i	0.893129	−	0.648896i
$556$	18.4935	−	13.4363i	0.784300	−	0.569827i
$557$	13.8348	−	4.49519i	0.586198	−	0.190467i	−0.000877247	−	1.00000i	$-0.500279\pi$
$557$	13.8348	−	4.49519i	0.586198	−	0.190467i	0.587075	+	0.809532i	$0.300279\pi$
$558$	2.51354	−	7.73588i	0.106407	−	0.327486i
$559$	−1.12294	+	1.54559i	−0.0474952	+	0.0653715i
$560$	−12.7100	−	5.82948i	−0.537094	−	0.246340i
$561$	−21.9170	+	29.4533i	−0.925335	+	1.24352i
$562$	14.4771			0.610681
$563$	4.88979	+	3.55264i	0.206080	+	0.149726i	0.686038	−	0.727565i	$-0.259348\pi$
$563$	4.88979	+	3.55264i	0.206080	+	0.149726i	−0.479958	+	0.877291i	$0.659348\pi$
$564$	8.66086	−	26.6554i	0.364688	−	1.12239i
$565$	−24.5007	+	7.96075i	−1.03075	+	0.334911i
$566$	12.2372	+	16.8430i	0.514367	+	0.707966i
$567$	2.51111	+	12.4973i	0.105457	+	0.524838i
$568$	23.1668	−	7.52735i	0.972057	−	0.315840i
$569$	12.4651	+	4.05014i	0.522563	+	0.169791i	0.558408	−	0.829566i	$-0.311412\pi$
$569$	12.4651	+	4.05014i	0.522563	+	0.169791i	−0.0358454	+	0.999357i	$0.511412\pi$
$570$	4.63810	−	6.38380i	0.194269	−	0.267388i
$571$		−	14.5264i		−	0.607910i	−0.952686	−	0.303955i	$-0.901693\pi$
$571$		−	14.5264i		−	0.607910i	0.952686	−	0.303955i	$-0.0983073\pi$
$572$	1.68763	+	5.40304i	0.0705634	+	0.225912i
$573$			4.21612i			0.176131i
$574$	4.79749	+	8.52766i	0.200243	+	0.355937i
$575$	−6.70412	+	20.6332i	−0.279581	+	0.860463i
$576$	1.13239	+	3.48515i	0.0471830	+	0.145214i
$577$	16.1519	+	22.2313i	0.672414	+	0.925499i	0.999812	−	0.0193876i	$-0.00617165\pi$
$577$	16.1519	+	22.2313i	0.672414	+	0.925499i	−0.327398	+	0.944887i	$0.606172\pi$
$578$	0.163972	+	0.225688i	0.00682033	+	0.00938738i
$579$	9.18310	+	28.2627i	0.381636	+	1.17456i
$580$	3.46729	−	10.6712i	0.143971	−	0.443098i
$581$	3.73236	−	2.09975i	0.154844	−	0.0871124i
$582$			22.6089i			0.937171i
$583$	−3.58123	−	0.0408718i	−0.148320	−	0.00169274i
$584$		−	29.8995i		−	1.23725i
$585$	9.28903	−	12.7853i	0.384054	−	0.528605i
$586$	−15.9018	−	5.16681i	−0.656897	−	0.213439i
$587$	13.6082	−	4.42157i	0.561670	−	0.182498i	−0.0144024	−	0.999896i	$-0.504585\pi$
$587$	13.6082	−	4.42157i	0.561670	−	0.182498i	0.576072	+	0.817399i	$0.304585\pi$
$588$	−6.59849	+	27.9626i	−0.272117	+	1.15316i
$589$	2.19284	+	3.01819i	0.0903545	+	0.124362i
$590$	5.20127	−	1.69000i	0.214133	−	0.0695760i
$591$	−12.3232	+	37.9268i	−0.506907	+	1.56010i
$592$	−3.32682	−	2.41708i	−0.136732	−	0.0993413i
$593$	−31.8607			−1.30836			−0.654181	−	0.756338i	$-0.726987\pi$
$593$	−31.8607			−1.30836			−0.654181	+	0.756338i	$0.726987\pi$
$594$	−5.00262	+	3.54810i	−0.205260	+	0.145580i
$595$	−35.6251	−	16.3396i	−1.46049	−	0.669859i
$596$	−6.83231	+	9.40386i	−0.279862	+	0.385197i
$597$	−17.9883	+	55.3623i	−0.736213	+	2.26583i
$598$	−2.01441	+	0.654523i	−0.0823755	+	0.0267654i
$599$	−18.2421	+	13.2537i	−0.745353	+	0.541530i	−0.894383	−	0.447302i	$-0.852385\pi$
$599$	−18.2421	+	13.2537i	−0.745353	+	0.541530i	0.149030	+	0.988833i	$0.452385\pi$
$600$	38.9325	−	28.2861i	1.58941	−	1.15478i
$601$	−8.94747	−	27.5375i	−0.364975	−	1.12328i	−0.949997	−	0.312259i	$-0.898914\pi$
$601$	−8.94747	−	27.5375i	−0.364975	−	1.12328i	0.585022	−	0.811017i	$-0.301086\pi$
$602$	2.26815	+	2.08850i	0.0924427	+	0.0851209i
$603$	1.59937	+	1.16201i	0.0651314	+	0.0473207i
$604$			19.6949i			0.801374i
$605$	−37.4028	+	11.2159i	−1.52064	+	0.455989i
$606$	5.65123			0.229565
$607$	22.9777	+	16.6942i	0.932634	+	0.677598i	0.946636	−	0.322304i	$-0.104457\pi$
$607$	22.9777	+	16.6942i	0.932634	+	0.677598i	−0.0140022	+	0.999902i	$0.504457\pi$
$608$	−6.84092	−	2.22275i	−0.277436	−	0.0901444i
$609$	−14.2401	−	1.65740i	−0.577039	−	0.0671613i
$610$	25.7990	−	18.7440i	1.04457	−	0.758924i
$611$	−4.42717	−	6.09348i	−0.179104	−	0.246516i
$612$	−8.05353	−	24.7862i	−0.325545	−	1.00192i
$613$	16.1897	+	5.26034i	0.653895	+	0.212463i	0.617131	−	0.786861i	$-0.288295\pi$
$613$	16.1897	+	5.26034i	0.653895	+	0.212463i	0.0367640	+	0.999324i	$0.488295\pi$
$614$	3.95587	−	5.44478i	0.159646	−	0.219734i
$615$	51.7571			2.08705
$616$	20.5785	−	3.89109i	0.829132	−	0.156777i
$617$	19.0794			0.768109			0.384055	−	0.923310i	$-0.374527\pi$
$617$	19.0794			0.768109			0.384055	+	0.923310i	$0.374527\pi$
$618$	10.2092	−	14.0518i	0.410676	−	0.565247i
$619$	−21.5048	−	6.98735i	−0.864353	−	0.280845i	−0.156907	−	0.987613i	$-0.550152\pi$
$619$	−21.5048	−	6.98735i	−0.864353	−	0.280845i	−0.707445	+	0.706768i	$0.750152\pi$
$620$	5.08406	+	15.6471i	0.204181	+	0.628403i
$621$	4.61081	+	6.34624i	0.185025	+	0.254666i
$622$	10.1891	−	7.40282i	0.408546	−	0.296826i
$623$	0.706520	−	6.07031i	0.0283061	−	0.243202i
$624$	−4.14281	−	1.34608i	−0.165845	−	0.0538864i
$625$	4.22819	+	3.07196i	0.169128	+	0.122878i
$626$	−3.55649			−0.142146
$627$	0.125048	−	10.9568i	0.00499393	−	0.437573i
$628$		−	23.6145i		−	0.942320i
$629$	−9.32485	−	6.77490i	−0.371806	−	0.270133i
$630$	−18.7623	−	17.2762i	−0.747507	−	0.688302i
$631$	−2.03699	−	6.26920i	−0.0810912	−	0.249573i	0.902289	−	0.431132i	$-0.141886\pi$
$631$	−2.03699	−	6.26920i	−0.0810912	−	0.249573i	−0.983380	+	0.181559i	$0.941886\pi$
$632$	−24.0070	+	17.4421i	−0.954947	+	0.693810i
$633$	−30.8377	+	22.4049i	−1.22569	+	0.890514i
$634$	−18.3994	+	5.97832i	−0.730733	+	0.237429i
$635$	−6.72410	+	20.6947i	−0.266838	+	0.821242i
$636$	2.60514	−	3.58566i	0.103300	−	0.142181i
$637$	5.03716	+	5.85159i	0.199580	+	0.231848i
$638$	1.35906	+	4.35109i	0.0538056	+	0.172261i
$639$	−41.1936			−1.62959
$640$	−31.4164	−	22.8254i	−1.24184	−	0.902252i
$641$	3.20002	−	9.84866i	0.126393	−	0.388999i	−0.867759	−	0.496985i	$-0.834440\pi$
$641$	3.20002	−	9.84866i	0.126393	−	0.388999i	0.994152	+	0.107987i	$0.0344404\pi$
$642$	17.9184	−	5.82204i	0.707182	−	0.229777i
$643$	17.1501	+	23.6050i	0.676333	+	0.930892i	0.999883	−	0.0153191i	$-0.00487641\pi$
$643$	17.1501	+	23.6050i	0.676333	+	0.930892i	−0.323550	+	0.946211i	$0.604876\pi$
$644$	−2.30172	−	11.4552i	−0.0907003	−	0.451399i
$645$	15.5111	−	5.03986i	0.610749	−	0.198444i
$646$	−3.32590	−	1.08065i	−0.130856	−	0.0425176i
$647$	0.925990	−	1.27452i	0.0364044	−	0.0501064i	−0.790427	−	0.612557i	$-0.790141\pi$
$647$	0.925990	−	1.27452i	0.0364044	−	0.0501064i	0.826831	+	0.562450i	$0.190141\pi$
$648$			11.4990i			0.451723i
$649$	4.53371	−	6.09267i	0.177964	−	0.239158i
$650$		−	5.64109i		−	0.221262i
$651$	18.3209	−	10.3070i	0.718052	−	0.403962i
$652$	10.0573	−	30.9532i	0.393875	−	1.21222i
$653$	4.50211	+	13.8561i	0.176181	+	0.542230i	0.999685	−	0.0250804i	$-0.00798416\pi$
$653$	4.50211	+	13.8561i	0.176181	+	0.542230i	−0.823504	+	0.567310i	$0.807984\pi$
$654$	−3.19617	−	4.39916i	−0.124980	−	0.172021i
$655$	−39.2868	−	54.0737i	−1.53506	−	2.11283i
$656$	−2.52884	−	7.78297i	−0.0987346	−	0.303874i
$657$	−15.6249	+	48.0884i	−0.609585	+	1.87611i
$658$	−10.5942	+	5.96008i	−0.413004	+	0.232348i
$659$			28.4616i			1.10871i	0.832281	+	0.554353i	$0.187034\pi$
$659$			28.4616i			1.10871i	−0.832281	+	0.554353i	$0.812966\pi$
$660$	15.4561	−	45.7843i	0.601626	−	1.78215i
$661$		−	32.7887i		−	1.27533i	−0.770313	−	0.637666i	$-0.779900\pi$
$661$		−	32.7887i		−	1.27533i	0.770313	−	0.637666i	$-0.220100\pi$
$662$	−4.83527	+	6.65518i	−0.187928	+	0.258661i
$663$	−11.6120	−	3.77297i	−0.450973	−	0.146530i
$664$	3.67407	−	1.19378i	0.142582	−	0.0463275i
$665$	11.4686	−	2.30441i	0.444735	−	0.0893612i
$666$	−4.40869	−	6.06804i	−0.170833	−	0.235132i
$667$	5.54492	−	1.80165i	0.214700	−	0.0697603i
$668$	3.98824	−	12.2745i	0.154309	−	0.474916i
$669$	38.0318	+	27.6317i	1.47039	+	1.06830i
$670$	1.16985			0.0451951
$671$	14.1639	−	41.9566i	0.546791	−	1.61972i
$672$	−16.8967	+	36.8398i	−0.651806	+	1.42113i
$673$	−6.03622	+	8.30815i	−0.232679	+	0.320255i	−0.909351	−	0.416029i	$-0.863421\pi$
$673$	−6.03622	+	8.30815i	−0.232679	+	0.320255i	0.676672	+	0.736284i	$0.263421\pi$
$674$	7.50231	−	23.0897i	0.288978	−	0.889383i
$675$	−19.8694	+	6.45597i	−0.764775	+	0.248491i
$676$	14.7505	−	10.7169i	0.567328	−	0.412188i
$677$	28.3236	−	20.5783i	1.08856	−	0.790888i	0.109408	−	0.993997i	$-0.465105\pi$
$677$	28.3236	−	20.5783i	1.08856	−	0.790888i	0.979156	+	0.203109i	$0.0651046\pi$
$678$	4.00230	+	12.3178i	0.153707	+	0.473063i
$679$	−22.7035	+	24.6564i	−0.871282	+	0.946227i
$680$	−28.6035	−	20.7817i	−1.09690	−	0.796941i
$681$		−	10.8790i		−	0.416885i
$682$	−5.36224	−	3.99018i	−0.205331	−	0.152792i
$683$	−18.0603			−0.691059			−0.345529	−	0.938408i	$-0.612301\pi$
$683$	−18.0603			−0.691059			−0.345529	+	0.938408i	$0.612301\pi$
$684$	6.29293	+	4.57208i	0.240616	+	0.174818i
$685$	−9.99117	−	3.24633i	−0.381743	−	0.124036i
$686$	10.3202	−	6.98305i	0.394028	−	0.266614i
$687$	21.0333	−	15.2816i	0.802470	−	0.583028i
$688$	−1.51574	−	2.08624i	−0.0577870	−	0.0795370i
$689$	−0.368064	−	1.13278i	−0.0140221	−	0.0431556i
$690$	17.1968	+	5.58759i	0.654672	+	0.212716i
$691$	−13.8812	+	19.1058i	−0.528065	+	0.726819i	−0.986834	−	0.161736i	$-0.948291\pi$
$691$	−13.8812	+	19.1058i	−0.528065	+	0.726819i	0.458769	+	0.888556i	$0.348291\pi$
$692$	−24.8481			−0.944585
$693$	−35.1306	−	4.49573i	−1.33450	−	0.170779i
$694$	−18.5086			−0.702577
$695$	−30.8254	+	42.4276i	−1.16928	+	1.60937i
$696$	−12.2996	−	3.99637i	−0.466214	−	0.151482i
$697$	−7.08816	−	21.8151i	−0.268483	−	0.826306i
$698$	−5.58662	−	7.68933i	−0.211457	−	0.291045i
$699$	−0.218808	+	0.158973i	−0.00827607	+	0.00601292i
$700$	30.9099	+	3.59758i	1.16828	+	0.135976i
$701$	−34.9303	−	11.3496i	−1.31930	−	0.428667i	−0.437046	−	0.899439i	$-0.643975\pi$
$701$	−34.9303	−	11.3496i	−1.31930	−	0.428667i	−0.882255	+	0.470773i	$0.843975\pi$
$702$	−1.65014	−	1.19889i	−0.0622804	−	0.0452493i
$703$	3.44014			0.129747
$704$	3.01103	+	0.0343643i	0.113483	+	0.00129515i
$705$			64.2995i			2.42166i
$706$	4.48497	+	3.25852i	0.168794	+	0.122636i
$707$	6.16300	+	5.67487i	0.231784	+	0.213425i
$708$	2.90421	+	8.93824i	0.109147	+	0.335919i
$709$	20.5986	−	14.9658i	0.773597	−	0.562051i	−0.129453	−	0.991586i	$-0.541322\pi$
$709$	20.5986	−	14.9658i	0.773597	−	0.562051i	0.903051	+	0.429534i	$0.141322\pi$
$710$	−19.7208	+	14.3280i	−0.740110	+	0.537721i
$711$	47.7262	−	15.5072i	1.78987	−	0.581565i
$712$	1.70358	−	5.24308i	0.0638444	−	0.196493i
$713$	−5.02491	+	6.91619i	−0.188184	+	0.259013i
$714$	−8.21481	+	17.9107i	−0.307431	+	0.670290i
$715$	−7.51269	−	10.5925i	−0.280959	−	0.396135i
$716$	11.4009			0.426071
$717$	−13.1672	−	9.56650i	−0.491737	−	0.357268i
$718$	6.22159	−	19.1481i	0.232188	−	0.714600i
$719$	29.0522	−	9.43965i	1.08347	−	0.352039i	0.287748	−	0.957706i	$-0.407094\pi$
$719$	29.0522	−	9.43965i	1.08347	−	0.352039i	0.795718	+	0.605667i	$0.207094\pi$
$720$	12.5383	+	17.2575i	0.467275	+	0.643149i
$721$	25.2444	−	5.07240i	0.940152	−	0.188906i
$722$	−11.1652	+	3.62779i	−0.415525	+	0.135012i
$723$	10.8872	+	3.53745i	0.404898	+	0.131559i
$724$	−13.1682	+	18.1244i	−0.489391	+	0.673589i
$725$			15.5278i			0.576688i
$726$	5.63882	+	18.8044i	0.209276	+	0.697897i
$727$		−	2.80772i		−	0.104133i	−0.998644	−	0.0520663i	$-0.983419\pi$
$727$		−	2.80772i		−	0.104133i	0.998644	−	0.0520663i	$-0.0165807\pi$
$728$	3.41505	+	6.07033i	0.126570	+	0.224981i
$729$	12.7678	−	39.2952i	0.472881	−	1.45538i
$730$	9.24602	+	28.4563i	0.342210	+	1.05322i
$731$	−4.24851	−	5.84757i	−0.157137	−	0.216280i
$732$	32.2111	+	44.3347i	1.19056	+	1.63866i
$733$	−2.08760	−	6.42496i	−0.0771071	−	0.237311i	0.905072	−	0.425258i	$-0.139817\pi$
$733$	−2.08760	−	6.42496i	−0.0771071	−	0.237311i	−0.982179	+	0.187947i	$0.939817\pi$
$734$	−0.963604	+	2.96567i	−0.0355673	+	0.109465i
$735$	−5.42664	−	65.6897i	−0.200165	−	2.42300i
$736$		−	16.4827i		−	0.607561i
$737$	1.32506	−	0.939798i	0.0488093	−	0.0346179i
$738$		−	14.9265i		−	0.549452i
$739$	7.41106	−	10.2004i	0.272620	−	0.375229i	−0.650652	−	0.759376i	$-0.725504\pi$
$739$	7.41106	−	10.2004i	0.272620	−	0.375229i	0.923272	+	0.384147i	$0.125504\pi$
$740$	14.4285	+	4.68811i	0.530403	+	0.172338i
$741$	3.46576	−	1.12610i	0.127318	−	0.0413681i
$742$	−1.88458	+	0.378672i	−0.0691852	+	0.0139015i
$743$	−4.12272	−	5.67443i	−0.151248	−	0.208175i	0.726669	−	0.686987i	$-0.241067\pi$
$743$	−4.12272	−	5.67443i	−0.151248	−	0.208175i	−0.877917	+	0.478813i	$0.841067\pi$
$744$	18.0348	−	5.85985i	0.661187	−	0.214833i
$745$	8.24062	−	25.3620i	0.301913	−	0.929192i
$746$	−8.31189	−	6.03894i	−0.304320	−	0.221101i
$747$	−6.53298			−0.239029
$748$	−21.4143	−	0.244397i	−0.782986	−	0.00893605i
$749$	25.3875	+	11.6441i	0.927639	+	0.425465i
$750$	−9.68698	+	13.3330i	−0.353718	+	0.486852i
$751$	2.75811	−	8.48858i	0.100645	−	0.309753i	−0.888039	−	0.459768i	$-0.847932\pi$
$751$	2.75811	−	8.48858i	0.100645	−	0.309753i	0.988684	+	0.150016i	$0.0479324\pi$
$752$	9.66903	−	3.14166i	0.352593	−	0.114564i
$753$	−65.8689	+	47.8565i	−2.40039	+	1.74399i
$754$	−1.22645	+	0.891068i	−0.0446647	+	0.0324508i
$755$	−13.9626	−	42.9723i	−0.508150	−	1.56392i
$756$	7.62160	−	8.27718i	0.277195	−	0.301038i
$757$	−22.9141	−	16.6481i	−0.832828	−	0.605085i	0.0875299	−	0.996162i	$-0.472103\pi$
$757$	−22.9141	−	16.6481i	−0.832828	−	0.605085i	−0.920358	+	0.391077i	$0.872103\pi$
$758$		−	15.3127i		−	0.556183i
$759$	23.9673	−	7.48615i	0.869957	−	0.271730i
$760$	10.5525			0.382778
$761$	−5.68004	−	4.12679i	−0.205901	−	0.149596i	0.480056	−	0.877238i	$-0.340616\pi$
$761$	−5.68004	−	4.12679i	−0.205901	−	0.149596i	−0.685957	+	0.727642i	$0.740616\pi$
$762$	10.4043	+	3.38057i	0.376909	+	0.122465i
$763$	0.931941	−	8.00710i	0.0337385	−	0.289876i
$764$	−1.98968	+	1.44558i	−0.0719839	+	0.0522994i
$765$	35.1440	+	48.3716i	1.27063	+	1.74888i
$766$	6.01167	+	18.5020i	0.217211	+	0.668506i
$767$	2.40204	+	0.780472i	0.0867328	+	0.0281812i
$768$	−14.3067	+	19.6915i	−0.516249	+	0.710555i
$769$	−27.4453			−0.989703			−0.494851	−	0.868978i	$-0.664778\pi$
$769$	−27.4453			−0.989703			−0.494851	+	0.868978i	$0.664778\pi$
$770$	−18.3820	+	10.0669i	−0.662440	+	0.362786i
$771$	−17.8590			−0.643177
$772$	−10.1891	+	14.0241i	−0.366715	+	0.504740i
$773$	27.2253	+	8.84603i	0.979226	+	0.318170i	0.754535	−	0.656260i	$-0.227863\pi$
$773$	27.2253	+	8.84603i	0.979226	+	0.318170i	0.224691	+	0.974430i	$0.427863\pi$
$774$	−1.45347	−	4.47333i	−0.0522440	−	0.160790i
$775$	−13.3829	−	18.4199i	−0.480726	−	0.661663i
$776$	−24.4608	+	17.7718i	−0.878091	+	0.637971i
$777$	2.24097	−	19.2540i	0.0803942	−	0.690735i
$778$	14.0561	+	4.56709i	0.503934	+	0.163738i
$779$	5.53861	+	4.02403i	0.198441	+	0.144176i
$780$	16.0706			0.575419
$781$	−10.8269	+	32.0718i	−0.387419	+	1.14762i
$782$		−	8.01352i		−	0.286563i
$783$	4.54220	+	3.30010i	0.162325	+	0.117936i
$784$	−9.61293	+	4.02561i	−0.343319	+	0.143772i
$785$	16.7413	+	51.5245i	0.597523	+	1.83899i
$786$	−27.1858	+	19.7516i	−0.969684	+	0.704516i
$787$	6.16756	−	4.48100i	0.219850	−	0.159730i	−0.472409	−	0.881379i	$-0.656616\pi$
$787$	6.16756	−	4.48100i	0.219850	−	0.159730i	0.692259	+	0.721649i	$0.256616\pi$
$788$	−22.1237	+	7.18843i	−0.788125	+	0.256077i
$789$	20.0382	−	61.6711i	0.713378	−	2.19555i
$790$	17.4545	−	24.0240i	0.621003	−	0.854737i
$791$	−8.00460	+	17.4524i	−0.284611	+	0.620535i
$792$	−30.2709	−	10.2190i	−1.07563	−	0.363115i
$793$	14.7271			0.522973
$794$	−1.64389	−	1.19435i	−0.0583394	−	0.0423860i
$795$	−3.14212	+	9.67045i	−0.111439	+	0.342976i
$796$	−32.2943	+	10.4931i	−1.14464	+	0.371917i
$797$	−20.4217	−	28.1080i	−0.723372	−	0.995637i	−0.999405	−	0.0344885i	$-0.989020\pi$
$797$	−20.4217	−	28.1080i	−0.723372	−	0.995637i	0.276033	−	0.961148i	$-0.410980\pi$
$798$	−1.15855	−	5.76590i	−0.0410123	−	0.204111i
$799$	27.1016	−	8.80584i	0.958786	−	0.311528i
$800$	41.7499	+	13.5654i	1.47608	+	0.479608i
$801$	−5.47986	+	7.54238i	−0.193621	+	0.266497i
$802$		−	5.30453i		−	0.187309i
$803$	33.3332	+	24.8041i	1.17630	+	0.875317i
$804$			2.01035i			0.0708995i
$805$	13.1432	+	23.3624i	0.463237	+	0.823416i
$806$	0.686903	−	2.11407i	0.0241951	−	0.0744649i
$807$	20.7545	+	63.8757i	0.730592	+	2.24853i
$808$	4.44216	+	6.11411i	0.156275	+	0.215094i
$809$	13.1809	+	18.1420i	0.463417	+	0.637838i	0.975213	−	0.221269i	$-0.0710197\pi$
$809$	13.1809	+	18.1420i	0.463417	+	0.637838i	−0.511796	+	0.859107i	$0.671020\pi$
$810$	−3.55590	−	10.9439i	−0.124942	−	0.384531i
$811$	6.04102	−	18.5924i	0.212129	−	0.652866i	−0.787216	−	0.616677i	$-0.788478\pi$
$811$	6.04102	−	18.5924i	0.212129	−	0.652866i	0.999345	−	0.0361885i	$-0.0115217\pi$
$812$	−4.10037	−	7.28850i	−0.143895	−	0.255776i
$813$		−	72.5238i		−	2.54352i
$814$	−5.88309	+	1.83758i	−0.206202	+	0.0644070i
$815$			74.6669i			2.61547i
$816$	9.68698	−	13.3330i	0.339112	−	0.466748i
$817$	2.05171	+	0.666641i	0.0717802	+	0.0233228i
$818$	16.9867	−	5.51933i	0.593928	−	0.192979i
$819$	−2.32031	−	11.5478i	−0.0810782	−	0.403511i
$820$	17.7460	+	24.4253i	0.619717	+	0.852968i
$821$	−17.4900	+	5.68285i	−0.610405	+	0.198333i	−0.597876	−	0.801589i	$-0.703988\pi$
$821$	−17.4900	+	5.68285i	−0.610405	+	0.198333i	−0.0125296	+	0.999922i	$0.503988\pi$
$822$	−1.63210	+	5.02310i	−0.0569262	+	0.175201i
$823$	−18.0091	−	13.0844i	−0.627757	−	0.456092i	0.227866	−	0.973693i	$-0.426825\pi$
$823$	−18.0091	−	13.0844i	−0.627757	−	0.456092i	−0.855622	+	0.517601i	$0.826825\pi$
$824$	23.2278			0.809178
$825$	−0.763163	+	66.8691i	−0.0265699	+	2.32808i
$826$	1.69931	−	3.70498i	0.0591264	−	0.128913i
$827$	27.3411	−	37.6318i	0.950744	−	1.30859i	−0.000452329	−	1.00000i	$-0.500144\pi$
$827$	27.3411	−	37.6318i	0.950744	−	1.30859i	0.951196	−	0.308587i	$-0.0998560\pi$
$828$	−5.50806	+	16.9521i	−0.191418	+	0.589125i
$829$	19.7645	−	6.42188i	0.686450	−	0.223041i	0.0550330	−	0.998485i	$-0.482474\pi$
$829$	19.7645	−	6.42188i	0.686450	−	0.223041i	0.631417	+	0.775443i	$0.282474\pi$
$830$	−3.12757	+	2.27231i	−0.108559	+	0.0788731i
$831$	−48.1106	+	34.9544i	−1.66894	+	1.21256i
$832$	0.309461	+	0.952424i	0.0107286	+	0.0330194i
$833$	−26.9444	+	11.2835i	−0.933567	+	0.390950i
$834$	21.3306	+	15.4976i	0.738620	+	0.536639i
$835$			29.6092i			1.02467i
$836$	5.21363	−	3.69776i	0.180317	−	0.127890i
$837$	−8.23245			−0.284555
$838$	−3.96519	−	2.88088i	−0.136975	−	0.0995182i
$839$	−7.17263	−	2.33053i	−0.247627	−	0.0804588i	0.182574	−	0.983192i	$-0.441557\pi$
$839$	−7.17263	−	2.33053i	−0.247627	−	0.0804588i	−0.430200	+	0.902733i	$0.641557\pi$
$840$	6.87406	−	59.0609i	0.237178	−	2.03779i
$841$	−20.0855	+	14.5930i	−0.692605	+	0.503207i
$842$	−9.41384	−	12.9570i	−0.324422	−	0.446529i
$843$	−17.6375	−	54.2825i	−0.607466	−	1.86959i
$844$	−21.1467	−	6.87097i	−0.727899	−	0.236509i
$845$	−24.5865	+	33.8404i	−0.845802	+	1.16415i
$846$	18.5436			0.637544
$847$	−12.7336	+	26.1697i	−0.437532	+	0.899203i
$848$	1.60772			0.0552092
$849$	48.2450	−	66.4036i	1.65577	−	2.27897i
$850$	20.2979	+	6.59517i	0.696211	+	0.226213i
$851$	2.43601	+	7.49727i	0.0835053	+	0.257003i
$852$	−24.6223	−	33.8897i	−0.843546	−	1.16104i
$853$	−1.27999	+	0.929968i	−0.0438260	+	0.0318415i	−0.609483	−	0.792799i	$-0.708623\pi$
$853$	−1.27999	+	0.929968i	−0.0438260	+	0.0318415i	0.565657	+	0.824641i	$0.308623\pi$
$854$	2.74775	−	23.6082i	0.0940259	−	0.807857i
$855$	−16.9719	−	5.51451i	−0.580427	−	0.188592i
$856$	20.3837	+	14.8096i	0.696700	+	0.506182i
$857$	52.3232			1.78733			0.893664	−	0.448737i	$-0.148126\pi$
$857$	52.3232			1.78733			0.893664	+	0.448737i	$0.148126\pi$
$858$	−5.32540	+	3.77703i	−0.181806	+	0.128946i
$859$		−	7.18932i		−	0.245296i	−0.992450	−	0.122648i	$-0.960861\pi$
$859$		−	7.18932i		−	0.245296i	0.992450	−	0.122648i	$-0.0391387\pi$
$860$	7.69673	+	5.59200i	0.262456	+	0.190686i
$861$	26.1300	−	28.3776i	0.890507	−	0.967105i
$862$	−0.133148	−	0.409787i	−0.00453504	−	0.0139574i
$863$	35.4803	−	25.7779i	1.20776	−	0.877490i	0.212736	−	0.977110i	$-0.431762\pi$
$863$	35.4803	−	25.7779i	1.20776	−	0.877490i	0.995026	+	0.0996193i	$0.0317625\pi$
$864$	12.8412	−	9.32969i	0.436867	−	0.317402i
$865$	54.2162	−	17.6159i	1.84341	−	0.598959i
$866$	−3.58055	+	11.0198i	−0.121672	+	0.374468i
$867$	0.646458	−	0.889773i	0.0219549	−	0.0302183i
$868$	11.1458	+	5.11206i	0.378313	+	0.173515i
$869$	0.470591	−	41.2336i	0.0159637	−	1.39876i
$870$	12.9417			0.438765
$871$	0.437077	+	0.317555i	0.0148098	+	0.0107599i
$872$	2.24712	−	6.91593i	0.0760972	−	0.234203i
$873$	48.6284	−	15.8003i	1.64582	−	0.534760i
$874$	1.40583	+	1.93496i	0.0475530	+	0.0654511i
$875$	−23.9530	+	4.81292i	−0.809759	+	0.162706i
$876$	−48.9013	+	15.8890i	−1.65222	+	0.536840i
$877$	13.6738	+	4.44289i	0.461732	+	0.150026i	0.530640	−	0.847597i	$-0.321952\pi$
$877$	13.6738	+	4.44289i	0.461732	+	0.150026i	−0.0689082	+	0.997623i	$0.521952\pi$
$878$	−0.0150788	+	0.0207541i	−0.000508884	+	0.000700419i
$879$			65.9190i			2.22339i
$880$	16.7315	−	5.22607i	0.564019	−	0.176171i
$881$		−	2.45261i		−	0.0826304i	−0.999146	−	0.0413152i	$-0.986845\pi$
$881$		−	2.45261i		−	0.0826304i	0.999146	−	0.0413152i	$-0.0131548\pi$
$882$	−18.9446	+	1.56502i	−0.637897	+	0.0526968i
$883$	1.47928	−	4.55275i	0.0497817	−	0.153212i	−0.923075	−	0.384619i	$-0.874333\pi$
$883$	1.47928	−	4.55275i	0.0497817	−	0.153212i	0.972857	+	0.231407i	$0.0743328\pi$
$884$	−2.20088	−	6.77360i	−0.0740234	−	0.227821i
$885$	−12.6734	−	17.4434i	−0.426011	−	0.586355i
$886$	12.1181	+	16.6791i	0.407114	+	0.560344i
$887$	11.0756	+	34.0871i	0.371882	+	1.14453i	0.945558	+	0.325452i	$0.105517\pi$
$887$	11.0756	+	34.0871i	0.371882	+	1.14453i	−0.573677	+	0.819082i	$0.694483\pi$
$888$	5.40348	−	16.6302i	0.181329	−	0.558073i
$889$	7.95183	+	14.1346i	0.266696	+	0.474058i
$890$			5.51682i			0.184924i
$891$	−12.8195	−	9.53934i	−0.429471	−	0.319580i
$892$			27.4221i			0.918161i
$893$	−4.99918	+	6.88079i	−0.167291	+	0.230257i
$894$	−12.7509	−	4.14300i	−0.426452	−	0.138563i
$895$	−24.8756	+	8.08257i	−0.831500	+	0.270171i
$896$	−28.3756	+	5.70156i	−0.947962	+	0.190476i
$897$	4.90831	+	6.75571i	0.163884	+	0.225567i
$898$	−18.8906	+	6.13792i	−0.630387	+	0.204825i
$899$	−1.89078	+	5.81923i	−0.0630612	+	0.194082i
$900$	−38.4056	−	27.9033i	−1.28019	−	0.930110i
$901$	4.50631			0.150127
$902$	−11.6212	−	3.92314i	−0.386944	−	0.130626i
$903$	5.06763	−	11.0489i	0.168640	−	0.367685i
$904$	−10.1807	+	14.0126i	−0.338606	+	0.466051i
$905$	15.8825	−	48.8812i	0.527951	−	1.62487i
$906$	−21.6045	+	7.01973i	−0.717762	+	0.233215i
$907$	−5.81532	+	4.22508i	−0.193095	+	0.140291i	−0.680132	−	0.733090i	$-0.738078\pi$
$907$	−5.81532	+	4.22508i	−0.193095	+	0.140291i	0.487037	+	0.873381i	$0.338078\pi$
$908$	5.13405	−	3.73011i	0.170379	−	0.123788i
$909$	−3.94937	−	12.1549i	−0.130992	−	0.403153i
$910$	−5.12738	−	4.72127i	−0.169971	−	0.156509i
$911$	−16.1909	−	11.7633i	−0.536427	−	0.389737i	0.286329	−	0.958131i	$-0.407565\pi$
$911$	−16.1909	−	11.7633i	−0.536427	−	0.389737i	−0.822756	+	0.568394i	$0.807565\pi$
$912$			4.91883i			0.162879i
$913$	−1.71707	+	5.08634i	−0.0568267	+	0.168333i
$914$	2.85803			0.0945354
$915$	−101.712	−	73.8982i	−3.36250	−	2.44300i
$916$	14.4234	+	4.68645i	0.476563	+	0.154845i
$917$	−49.4820	−	5.75918i	−1.63404	−	0.190185i
$918$	6.24310	−	4.53588i	0.206053	−	0.149706i
$919$	−2.08305	−	2.86708i	−0.0687136	−	0.0945762i	0.773277	−	0.634068i	$-0.218616\pi$
$919$	−2.08305	−	2.86708i	−0.0687136	−	0.0945762i	−0.841991	+	0.539492i	$0.818616\pi$
$920$	7.47234	+	22.9975i	0.246356	+	0.758206i
$921$	−25.2348	−	8.19929i	−0.831516	−	0.270176i
$922$	−4.70335	+	6.47361i	−0.154897	+	0.213197i
$923$	−11.2574			−0.370543
$924$	−17.2997	−	31.5889i	−0.569117	−	1.03920i
$925$	−20.9951			−0.690314
$926$	−11.6667	+	16.0578i	−0.383391	+	0.527693i
$927$	−37.3581	−	12.1384i	−1.22700	−	0.398677i
$928$	−3.64553	−	11.2198i	−0.119670	−	0.368308i
$929$	−16.0001	−	22.0222i	−0.524946	−	0.722526i	0.461404	−	0.887190i	$-0.347346\pi$
$929$	−16.0001	−	22.0222i	−0.524946	−	0.722526i	−0.986350	+	0.164664i	$0.947346\pi$
$930$	−15.3522	+	11.1540i	−0.503418	+	0.365754i
$931$	4.52656	−	7.45147i	0.148352	−	0.244212i
$932$	−0.150046	−	0.0487528i	−0.00491491	−	0.00159695i
$933$	−40.1705	−	29.1856i	−1.31512	−	0.955493i
$934$	−7.50122			−0.245447
$935$	46.8972	−	14.6483i	1.53370	−	0.479050i
$936$		−	10.6253i		−	0.347298i
$937$	38.8017	+	28.1911i	1.26760	+	0.920964i	0.999104	−	0.0423179i	$-0.0134742\pi$
$937$	38.8017	+	28.1911i	1.26760	+	0.920964i	0.268493	+	0.963282i	$0.413474\pi$
$938$	0.590606	−	0.641408i	0.0192840	−	0.0209427i
$939$	4.33287	+	13.3352i	0.141398	+	0.435177i
$940$	−30.3443	+	22.0464i	−0.989722	+	0.719075i
$941$	8.46335	−	6.14898i	0.275897	−	0.200451i	−0.441229	−	0.897395i	$-0.645457\pi$
$941$	8.46335	−	6.14898i	0.275897	−	0.200451i	0.717126	+	0.696944i	$0.245457\pi$
$942$	25.9041	−	8.41676i	0.844002	−	0.274233i
$943$	−4.84781	+	14.9200i	−0.157866	+	0.485863i
$944$	−2.00384	+	2.75804i	−0.0652193	+	0.0897667i
$945$	−10.7615	+	23.4633i	−0.350073	+	0.763260i
$946$	−3.86478	−	0.0441080i	−0.125655	−	0.00143407i
$947$	−31.5419			−1.02497			−0.512487	−	0.858695i	$-0.671276\pi$
$947$	−31.5419			−1.02497			−0.512487	+	0.858695i	$0.671276\pi$
$948$	41.2846	+	29.9950i	1.34086	+	0.974193i
$949$	−4.26998	+	13.1417i	−0.138610	+	0.426596i
$950$	−6.05818	+	1.96842i	−0.196553	+	0.0638640i
$951$	44.8318	+	61.7057i	1.45377	+	2.00095i
$952$	−25.8350	+	5.19106i	−0.837316	+	0.168243i
$953$	−3.51669	+	1.14264i	−0.113917	+	0.0370138i	−0.365421	−	0.930842i	$-0.619075\pi$
$953$	−3.51669	+	1.14264i	−0.113917	+	0.0370138i	0.251504	+	0.967856i	$0.419075\pi$
$954$	2.78891	+	0.906172i	0.0902943	+	0.0293384i
$955$	3.31644	−	4.56469i	0.107317	−	0.147710i
$956$		−	9.49395i		−	0.307056i
$957$	14.6588	−	10.3967i	0.473852	−	0.336079i
$958$		−	7.62407i		−	0.246323i
$959$	−6.82403	+	3.83906i	−0.220359	+	0.123970i
$960$	2.64184	−	8.13073i	0.0852649	−	0.262418i
$961$	6.80709	+	20.9501i	0.219583	+	0.675808i
$962$	−1.20481	−	1.65828i	−0.0388446	−	0.0534651i
$963$	−25.0446	−	34.4710i	−0.807051	−	1.11081i
$964$	2.06349	+	6.35077i	0.0664606	+	0.204545i
$965$	12.2894	−	37.8228i	0.395609	−	1.21756i
$966$	11.7455	−	6.60780i	0.377906	−	0.212603i
$967$		−	22.8572i		−	0.735038i	−0.930016	−	0.367519i	$-0.880207\pi$
$967$		−	22.8572i		−	0.735038i	0.930016	−	0.367519i	$-0.119793\pi$
$968$	−15.9122	+	20.8819i	−0.511438	+	0.671170i
$969$			13.7871i			0.442906i
$970$	17.7844	−	24.4782i	0.571024	−	0.785946i
$971$	−0.977016	−	0.317452i	−0.0313539	−	0.0101875i	0.293298	−	0.956021i	$-0.405247\pi$
$971$	−0.977016	−	0.317452i	−0.0313539	−	0.0101875i	−0.324652	+	0.945834i	$0.605247\pi$
$972$	30.9406	−	10.0532i	0.992421	−	0.322457i
$973$	7.69990	+	38.3210i	0.246847	+	1.22851i
$974$	6.13212	+	8.44014i	0.196486	+	0.270439i
$975$	−21.1515	+	6.87253i	−0.677389	+	0.220097i
$976$	−6.14281	+	18.9056i	−0.196626	+	0.605154i
$977$	−16.4024	−	11.9170i	−0.524759	−	0.381260i	0.293635	−	0.955918i	$-0.405135\pi$
$977$	−16.4024	−	11.9170i	−0.524759	−	0.381260i	−0.818394	+	0.574658i	$0.805135\pi$
$978$	37.5391			1.20037
$979$	4.43194	+	6.24879i	0.141646	+	0.199712i
$980$	29.1397	−	25.0840i	0.930834	−	0.801280i
$981$	−7.22826	+	9.94884i	−0.230780	+	0.317642i
$982$	−2.16411	+	6.66044i	−0.0690595	+	0.212543i
$983$	18.6929	−	6.07370i	0.596212	−	0.193721i	0.00466161	−	0.999989i	$-0.498516\pi$
$983$	18.6929	−	6.07370i	0.596212	−	0.193721i	0.591550	+	0.806268i	$0.298516\pi$
$984$	28.1524	−	20.4539i	0.897466	−	0.652048i
$985$	43.1756	−	31.3689i	1.37569	−	0.999496i
$986$	−1.77237	−	5.45481i	−0.0564439	−	0.173716i
$987$	35.2544	+	32.4621i	1.12216	+	1.03328i
$988$	1.71974	+	1.24946i	0.0547122	+	0.0397507i
$989$			4.94345i			0.157193i
$990$	31.9698	+	0.364865i	1.01607	+	0.0115962i
$991$	12.4581			0.395744			0.197872	−	0.980228i	$-0.436597\pi$
$991$	12.4581			0.395744			0.197872	+	0.980228i	$0.436597\pi$
$992$	13.9945	+	10.1676i	0.444325	+	0.322821i
$993$	30.8446	+	10.0220i	0.978825	+	0.318039i
$994$	−2.10039	+	18.0462i	−0.0666203	+	0.572392i
$995$	63.0241	−	45.7897i	1.99800	−	1.45163i
$996$	−3.90490	−	5.37464i	−0.123732	−	0.170302i
$997$	6.20109	+	19.0850i	0.196391	+	0.604428i	0.999958	+	0.00921365i	$0.00293284\pi$
$997$	6.20109	+	19.0850i	0.196391	+	0.604428i	−0.803567	+	0.595214i	$0.797067\pi$
$998$	14.8575	+	4.82750i	0.470306	+	0.152812i
$999$	−4.46206	+	6.14149i	−0.141173	+	0.194308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.l.b.62.4	yes	16
3.2	odd	2		693.2.bu.d.370.2		16
7.2	even	3		539.2.s.b.227.1		16
7.3	odd	6		539.2.s.c.117.2		16
7.4	even	3		539.2.s.c.117.1		16
7.5	odd	6		539.2.s.b.227.2		16
7.6	odd	2	inner	77.2.l.b.62.3	yes	16
11.2	odd	10		847.2.l.e.699.4		16
11.3	even	5		847.2.l.i.118.1		16
11.4	even	5		847.2.l.e.475.3		16
11.5	even	5		847.2.b.f.846.6		16
11.6	odd	10		847.2.b.f.846.12		16
11.7	odd	10		847.2.l.j.475.1		16
11.8	odd	10	inner	77.2.l.b.41.3	✓	16
11.9	even	5		847.2.l.j.699.2		16
11.10	odd	2		847.2.l.i.524.2		16
21.20	even	2		693.2.bu.d.370.1		16
33.8	even	10		693.2.bu.d.118.1		16
77.6	even	10		847.2.b.f.846.11		16
77.13	even	10		847.2.l.e.699.3		16
77.19	even	30		539.2.s.c.129.1		16
77.20	odd	10		847.2.l.j.699.1		16
77.27	odd	10		847.2.b.f.846.5		16
77.30	odd	30		539.2.s.c.129.2		16
77.41	even	10	inner	77.2.l.b.41.4	yes	16
77.48	odd	10		847.2.l.e.475.4		16
77.52	even	30		539.2.s.b.19.1		16
77.62	even	10		847.2.l.j.475.2		16
77.69	odd	10		847.2.l.i.118.2		16
77.74	odd	30		539.2.s.b.19.2		16
77.76	even	2		847.2.l.i.524.1		16
231.41	odd	10		693.2.bu.d.118.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.l.b.41.3	✓	16	11.8	odd	10	inner
77.2.l.b.41.4	yes	16	77.41	even	10	inner
77.2.l.b.62.3	yes	16	7.6	odd	2	inner
77.2.l.b.62.4	yes	16	1.1	even	1	trivial
539.2.s.b.19.1		16	77.52	even	30
539.2.s.b.19.2		16	77.74	odd	30
539.2.s.b.227.1		16	7.2	even	3
539.2.s.b.227.2		16	7.5	odd	6
539.2.s.c.117.1		16	7.4	even	3
539.2.s.c.117.2		16	7.3	odd	6
539.2.s.c.129.1		16	77.19	even	30
539.2.s.c.129.2		16	77.30	odd	30
693.2.bu.d.118.1		16	33.8	even	10
693.2.bu.d.118.2		16	231.41	odd	10
693.2.bu.d.370.1		16	21.20	even	2
693.2.bu.d.370.2		16	3.2	odd	2
847.2.b.f.846.5		16	77.27	odd	10
847.2.b.f.846.6		16	11.5	even	5
847.2.b.f.846.11		16	77.6	even	10
847.2.b.f.846.12		16	11.6	odd	10
847.2.l.e.475.3		16	11.4	even	5
847.2.l.e.475.4		16	77.48	odd	10
847.2.l.e.699.3		16	77.13	even	10
847.2.l.e.699.4		16	11.2	odd	10
847.2.l.i.118.1		16	11.3	even	5
847.2.l.i.118.2		16	77.69	odd	10
847.2.l.i.524.1		16	77.76	even	2
847.2.l.i.524.2		16	11.10	odd	2
847.2.l.j.475.1		16	11.7	odd	10
847.2.l.j.475.2		16	77.62	even	10
847.2.l.j.699.1		16	77.20	odd	10
847.2.l.j.699.2		16	11.9	even	5

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395472 + 0.544320i) q^{2} +(2.52275 + 0.819690i) q^{3} +(0.478148 + 1.47159i) q^{4} +(-2.08654 - 2.87188i) q^{5} +(-1.44385 + 1.04902i) q^{6} +(-2.62801 - 0.305873i) q^{7} +(-2.26988 - 0.737529i) q^{8} +(3.26531 + 2.37239i) q^{9} +O(q^{10})\)	\(q+(-0.395472 + 0.544320i) q^{2} +(2.52275 + 0.819690i) q^{3} +(0.478148 + 1.47159i) q^{4} +(-2.08654 - 2.87188i) q^{5} +(-1.44385 + 1.04902i) q^{6} +(-2.62801 - 0.305873i) q^{7} +(-2.26988 - 0.737529i) q^{8} +(3.26531 + 2.37239i) q^{9} +2.38839 q^{10} +(2.70528 - 1.91872i) q^{11} +4.10438i q^{12} +(0.892348 + 0.648328i) q^{13} +(1.20580 - 1.30951i) q^{14} +(-2.90977 - 8.95534i) q^{15} +(-1.20449 + 0.875112i) q^{16} +(-3.37610 + 2.45288i) q^{17} +(-2.58268 + 0.839162i) q^{18} +(0.384885 - 1.18455i) q^{19} +(3.22854 - 4.44371i) q^{20} +(-6.37909 - 2.92579i) q^{21} +(-0.0254657 + 2.23133i) q^{22} +2.85410 q^{23} +(-5.12179 - 3.72120i) q^{24} +(-2.34894 + 7.22930i) q^{25} +(-0.705796 + 0.229327i) q^{26} +(1.61550 + 2.22355i) q^{27} +(-0.806459 - 4.01360i) q^{28} +(1.94279 - 0.631251i) q^{29} +(6.02530 + 1.95774i) q^{30} +(-1.76059 + 2.42325i) q^{31} -5.77510i q^{32} +(8.39749 - 2.62294i) q^{33} -2.80772i q^{34} +(4.60503 + 8.18554i) q^{35} +(-1.92987 + 5.93954i) q^{36} +(0.853512 + 2.62684i) q^{37} +(0.492566 + 0.677958i) q^{38} +(1.71974 + 2.36702i) q^{39} +(2.61811 + 8.05771i) q^{40} +(-1.69854 + 5.22758i) q^{41} +(4.11532 - 2.31520i) q^{42} +1.73205i q^{43} +(4.11708 + 3.06362i) q^{44} -14.3277i q^{45} +(-1.12872 + 1.55354i) q^{46} +(-6.49438 - 2.11015i) q^{47} +(-3.75594 + 1.22038i) q^{48} +(6.81288 + 1.60767i) q^{49} +(-3.00611 - 4.13756i) q^{50} +(-10.5276 + 3.42064i) q^{51} +(-0.527398 + 1.62316i) q^{52} +(-0.873619 - 0.634721i) q^{53} -1.84921 q^{54} +(-11.1550 - 3.76575i) q^{55} +(5.73968 + 2.63253i) q^{56} +(1.94194 - 2.67285i) q^{57} +(-0.424716 + 1.30714i) q^{58} +(2.17773 - 0.707589i) q^{59} +(11.7873 - 8.56395i) q^{60} +(10.8018 - 7.84799i) q^{61} +(-0.622757 - 1.91665i) q^{62} +(-7.85563 - 7.23343i) q^{63} +(0.734523 + 0.533662i) q^{64} -3.91548i q^{65} +(-1.89325 + 5.60822i) q^{66} +0.489806 q^{67} +(-5.22389 - 3.79538i) q^{68} +(7.20018 + 2.33948i) q^{69} +(-6.27671 - 0.730543i) q^{70} +(-8.25697 + 5.99904i) q^{71} +(-5.66216 - 7.79330i) q^{72} +(3.87124 + 11.9144i) q^{73} +(-1.76738 - 0.574257i) q^{74} +(-11.8516 + 16.3123i) q^{75} +1.92721 q^{76} +(-7.69638 + 4.21493i) q^{77} -1.96852 q^{78} +(7.30806 - 10.0587i) q^{79} +(5.02643 + 1.63319i) q^{80} +(-1.48883 - 4.58215i) q^{81} +(-2.17375 - 2.99191i) q^{82} +(-1.30949 + 0.951400i) q^{83} +(1.25542 - 10.7863i) q^{84} +(14.0887 + 4.57770i) q^{85} +(-0.942790 - 0.684977i) q^{86} +5.41860 q^{87} +(-7.55577 + 2.36003i) q^{88} +2.30985i q^{89} +(7.79883 + 5.66618i) q^{90} +(-2.14679 - 1.97676i) q^{91} +(1.36468 + 4.20006i) q^{92} +(-6.42784 + 4.67010i) q^{93} +(3.71694 - 2.70052i) q^{94} +(-4.20498 + 1.36628i) q^{95} +(4.73379 - 14.5691i) q^{96} +(7.44620 - 10.2488i) q^{97} +(-3.56939 + 3.07260i) q^{98} +(13.3855 + 0.152766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{2} - 10 q^{4} - 10 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 + 10 * q^8 + 8 * q^9	\( 16 q - 10 q^{2} - 10 q^{4} - 10 q^{7} + 10 q^{8} + 8 q^{9} + 2 q^{11} + 8 q^{14} - 14 q^{16} - 20 q^{18} + 42 q^{22} - 8 q^{23} - 30 q^{25} - 10 q^{28} + 10 q^{29} - 40 q^{30} + 40 q^{35} + 20 q^{36} + 4 q^{37} + 30 q^{39} + 50 q^{42} - 10 q^{44} - 10 q^{46} + 8 q^{49} - 60 q^{50} - 10 q^{51} - 4 q^{56} - 90 q^{57} - 2 q^{58} + 120 q^{60} - 20 q^{63} - 38 q^{64} - 4 q^{67} - 56 q^{71} + 30 q^{72} + 90 q^{74} + 2 q^{77} - 20 q^{78} + 50 q^{79} - 16 q^{81} - 70 q^{84} + 80 q^{85} + 6 q^{86} - 86 q^{88} - 30 q^{91} + 20 q^{92} - 40 q^{93} - 60 q^{95} + 36 q^{99}+O(q^{100}) \) 16 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 + 10 * q^8 + 8 * q^9 + 2 * q^11 + 8 * q^14 - 14 * q^16 - 20 * q^18 + 42 * q^22 - 8 * q^23 - 30 * q^25 - 10 * q^28 + 10 * q^29 - 40 * q^30 + 40 * q^35 + 20 * q^36 + 4 * q^37 + 30 * q^39 + 50 * q^42 - 10 * q^44 - 10 * q^46 + 8 * q^49 - 60 * q^50 - 10 * q^51 - 4 * q^56 - 90 * q^57 - 2 * q^58 + 120 * q^60 - 20 * q^63 - 38 * q^64 - 4 * q^67 - 56 * q^71 + 30 * q^72 + 90 * q^74 + 2 * q^77 - 20 * q^78 + 50 * q^79 - 16 * q^81 - 70 * q^84 + 80 * q^85 + 6 * q^86 - 86 * q^88 - 30 * q^91 + 20 * q^92 - 40 * q^93 - 60 * q^95 + 36 * q^99

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