LMFDB - Embedded newform 77.2.l.b.62.3

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			62.3
Root			$0.551501 - 0.955228i$ of defining polynomial
Character	$\chi$	$=$	77.62
Dual form			77.2.l.b.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395472 + 0.544320i) q^{2} +(-2.52275 - 0.819690i) q^{3} +(0.478148 + 1.47159i) q^{4} +(2.08654 + 2.87188i) q^{5} +(1.44385 - 1.04902i) q^{6} +(-1.94632 + 1.79216i) q^{7} +(-2.26988 - 0.737529i) q^{8} +(3.26531 + 2.37239i) q^{9} +O(q^{10})$	\(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} +(-1.94632 + 1.79216i) 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} +(-0.205796 - 1.76817i) 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} +(-3.56795 - 2.00726i) 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} +(-9.20795 - 1.85017i) 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} +(-0.930179 + 4.62933i) 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} +(0.576309 - 6.97624i) 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} +(-10.6070 + 1.23455i) 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} +(4.64856 - 4.28038i) 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} +(-1.82668 + 8.58273i) 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} +(7.35571 + 7.98842i) 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} +(2.89870 - 0.337378i) 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	−0.529507	−	0.848305i	$-0.677623\pi$
$3$	−2.52275	−	0.819690i	−1.45651	−	0.473248i	−0.927002	+	0.375057i	$0.877623\pi$
$4$	0.478148	+	1.47159i	0.239074	+	0.735793i
$5$	2.08654	+	2.87188i	0.933130	+	1.28434i	0.958626	+	0.284668i	$0.0918834\pi$
$5$	2.08654	+	2.87188i	0.933130	+	1.28434i	−0.0254964	+	0.999675i	$0.508117\pi$
$6$	1.44385	−	1.04902i	0.589449	−	0.428260i
$7$	−1.94632	+	1.79216i	−0.735639	+	0.677374i
$7$	−1.94632	+	1.79216i	−0.735639	+	0.677374i
$8$	−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	0.457122	−	0.889404i	$-0.348880\pi$
$13$	−0.892348	−	0.648328i	−0.247493	−	0.179814i	−0.704615	+	0.709590i	$0.748880\pi$
$14$	−0.205796	−	1.76817i	−0.0550013	−	0.472563i
$15$	−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	−0.0975518	−	0.995230i	$-0.531101\pi$
$17$	3.37610	−	2.45288i	0.818823	−	0.594910i	0.916375	+	0.400320i	$0.131101\pi$
$18$	−2.58268	+	0.839162i	−0.608743	+	0.197792i
$19$	−0.384885	+	1.18455i	−0.0882987	+	0.271756i	−0.985449	−	0.169969i	$-0.945633\pi$
$19$	−0.384885	+	1.18455i	−0.0882987	+	0.271756i	0.897151	+	0.441725i	$0.145633\pi$
$20$	−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
$28$	−3.56795	−	2.00726i	−0.674279	−	0.379336i
$29$	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	−0.621094	−	0.783736i	$-0.713312\pi$
$31$	1.76059	−	2.42325i	0.316212	−	0.435228i	0.937306	+	0.348508i	$0.113312\pi$
$32$		−	5.77510i		−	1.02090i
$33$	−8.39749	+	2.62294i	−1.46181	+	0.456596i
$34$			2.80772i			0.481520i
$35$	−9.20795	−	1.85017i	−1.55643	−	0.312735i
$36$	−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	$-0.758791\pi$
$41$	1.69854	−	5.22758i	0.265268	−	0.816410i	0.991632	−	0.129100i	$-0.0412087\pi$
$42$	−0.930179	+	4.62933i	−0.143530	+	0.714322i
$43$			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	0.741619	−	0.670821i	$-0.234058\pi$
$47$	6.49438	+	2.11015i	0.947303	+	0.307797i	0.205684	+	0.978618i	$0.434058\pi$
$48$	3.75594	−	1.22038i	0.542123	−	0.176147i
$49$	0.576309	−	6.97624i	0.0823298	−	0.996605i
$50$	−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	−0.447323	−	0.894372i	$-0.647623\pi$
$59$	−2.17773	+	0.707589i	−0.283517	+	0.0921202i	0.163807	+	0.986492i	$0.447623\pi$
$60$	11.7873	−	8.56395i	1.52173	−	1.10560i
$61$	−10.8018	+	7.84799i	−1.38303	+	1.00483i	−0.386442	+	0.922314i	$0.626296\pi$
$61$	−10.8018	+	7.84799i	−1.38303	+	1.00483i	−0.996590	+	0.0825181i	$0.973704\pi$
$62$	0.622757	+	1.91665i	0.0790903	+	0.243415i
$63$	−10.6070	+	1.23455i	−1.33636	+	0.155538i
$64$	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
$70$	4.64856	−	4.28038i	0.555610	−	0.511603i
$71$	−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	$-0.838063\pi$
$73$	−3.87124	−	11.9144i	−0.453094	−	1.39448i	0.420264	−	0.907402i	$-0.361937\pi$
$74$	−1.76738	−	0.574257i	−0.205454	−	0.0667560i
$75$	11.8516	−	16.3123i	1.36850	−	1.88358i
$76$	−1.92721			−0.221066
$77$	−1.82668	+	8.58273i	−0.208170	+	0.978093i
$78$	−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	−0.513594	−	0.858033i	$-0.671686\pi$
$83$	1.30949	−	0.951400i	0.143735	−	0.104430i	0.657329	+	0.753604i	$0.271686\pi$
$84$	7.35571	+	7.98842i	0.802573	+	0.871608i
$85$	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	$-0.960934\pi$
$89$		−	2.30985i		−	0.244844i	0.992478	−	0.122422i	$-0.0390661\pi$
$90$	−7.79883	−	5.66618i	−0.822069	−	0.597268i
$91$	2.89870	−	0.337378i	0.303867	−	0.0353668i
$92$	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	$0.422366\pi$
$97$	−7.44620	+	10.2488i	−0.756047	+	1.04061i	−0.997533	+	0.0702056i	$0.977634\pi$
$98$	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	0.707897	−	0.706316i	$-0.249644\pi$
$101$	2.56175	+	1.86122i	0.254903	+	0.185198i	−0.452994	+	0.891514i	$0.649644\pi$
$102$	2.30146	−	7.08317i	0.227879	−	0.701338i
$103$	9.25587	−	3.00742i	0.912008	−	0.296329i	0.184824	−	0.982772i	$-0.440829\pi$
$103$	9.25587	−	3.00742i	0.912008	−	0.296329i	0.727184	+	0.686442i	$0.240829\pi$
$104$	1.54736	+	2.12976i	0.151731	+	0.208840i
$105$	21.7128	+	12.2152i	2.11895	+	1.19208i
$106$	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
$112$	0.775975	−	3.86189i	0.0733227	−	0.364914i
$113$	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
$119$	−2.17500	+	10.8246i	−0.199382	+	0.992288i
$120$			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
$126$	3.52279	−	6.26185i	0.313835	−	0.557850i
$127$	−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	$-0.807441\pi$
$131$	−18.8287			−1.64507			−0.822534	+	0.568715i	$0.807441\pi$
$132$	−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	$0.115527\pi$
$139$	4.56525	+	14.0504i	0.387219	+	1.19174i	−0.547638	+	0.836715i	$0.684473\pi$
$140$	−1.68007	−	14.4349i	−0.141992	−	1.21998i
$141$	−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
$147$	−7.17224	+	17.1269i	−0.591556	+	1.41260i
$148$	−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
$154$	−3.94935	−	4.38852i	−0.318248	−	0.353637i
$155$	10.6328			0.854048
$156$	−2.66098	+	3.66253i	−0.213049	+	0.293237i
$157$	14.5146	+	4.71608i	1.15839	+	0.376384i	0.824298	−	0.566156i	$-0.191570\pi$
$157$	14.5146	+	4.71608i	1.15839	+	0.376384i	0.334093	+	0.942540i	$0.391570\pi$
$158$	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
$161$	−5.55499	+	5.11501i	−0.437795	+	0.403120i
$162$	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	0.817424	−	0.576037i	$-0.195402\pi$
$167$	6.74802	+	4.90273i	0.522178	+	0.379384i	−0.295246	+	0.955421i	$0.595402\pi$
$168$	−16.6376	+	1.93644i	−1.28362	+	0.149400i
$169$	−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	$-0.690982\pi$
$173$	4.96246	−	15.2729i	0.377289	−	1.16117i	0.941922	−	0.335833i	$-0.109018\pi$
$174$	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	0.365625	−	0.930762i	$-0.380855\pi$
$181$	−8.51032	−	11.7134i	−0.632567	−	0.870654i	−0.998192	+	0.0601085i	$0.980855\pi$
$182$	−0.962712	+	1.71124i	−0.0713610	+	0.126846i
$183$	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
$189$	7.12925	+	1.43249i	0.518576	+	0.104198i
$190$	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
$196$	10.5417	−	2.48758i	0.752978	−	0.177684i
$197$			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	$-0.716321\pi$
$199$		−	21.9453i		−	1.55566i	0.628476	−	0.777829i	$-0.283679\pi$
$200$	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
$203$	−2.64998	+	4.71041i	−0.185992	+	0.330606i
$204$	−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
$217$	0.916180	+	7.87168i	0.0621943	+	0.534364i
$218$	−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	−0.315613	−	0.948888i	$-0.602210\pi$
$223$	−16.8550	−	5.47651i	−1.12869	−	0.366734i	−0.813079	+	0.582154i	$0.802210\pi$
$224$	10.3499	+	11.2402i	0.691532	+	0.751016i
$225$	−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	0.984265	−	0.176696i	$-0.0565410\pi$
$227$	1.26738	+	3.90058i	0.0841186	+	0.258891i	−0.900147	+	0.435587i	$0.856541\pi$
$228$	4.86186	+	1.57971i	0.321984	+	0.104619i
$229$	−5.76104	+	7.92939i	−0.380700	+	0.523989i	−0.955770	−	0.294116i	$-0.904975\pi$
$229$	−5.76104	+	7.92939i	−0.380700	+	0.523989i	0.575070	+	0.818104i	$0.304975\pi$
$230$	−6.81670			−0.449480
$231$	11.6434	−	20.1547i	0.766082	−	1.32608i
$232$	−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
$238$	−5.03189	−	5.46471i	−0.326169	−	0.354225i
$239$	−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	$-0.544388\pi$
$241$	−4.31560			−0.277992			−0.138996	+	0.990293i	$0.544388\pi$
$242$	4.21240	+	6.08524i	0.270784	+	0.391174i
$243$			21.0254i			1.34878i
$244$	−16.7139	−	12.1433i	−1.07000	−	0.777397i
$245$	21.2374	−	12.9011i	1.35681	−	0.824222i
$246$	−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	$-0.379854\pi$
$251$	18.0415	−	24.8321i	1.13877	−	1.56739i	0.770220	−	0.637778i	$-0.220146\pi$
$252$	−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	−0.102417	−	0.994742i	$-0.532658\pi$
$257$	6.40319	−	2.08052i	0.399420	−	0.129779i	0.501837	+	0.864962i	$0.332658\pi$
$258$	1.81695	+	2.50082i	0.113118	+	0.155694i
$259$	−6.36893	−	3.58303i	−0.395746	−	0.222639i
$260$	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
$266$	2.17370	+	0.436765i	0.133278	+	0.0267798i
$267$	−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	$-0.919311\pi$
$269$	−14.8827	−	20.4842i	−0.907412	−	1.24895i	0.0606307	−	0.998160i	$-0.480689\pi$
$270$	3.85845	+	5.31070i	0.234818	+	0.323199i
$271$	8.44881	+	26.0028i	0.513229	+	1.57956i	0.786482	+	0.617613i	$0.211900\pi$
$271$	8.44881	+	26.0028i	0.513229	+	1.57956i	−0.273254	+	0.961942i	$0.588100\pi$
$272$	−1.91993	+	5.90892i	−0.116413	+	0.358281i
$273$	−7.58924	−	1.52492i	−0.459322	−	0.0922922i
$274$			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
$280$	19.5364	+	10.9908i	1.16752	+	0.656825i
$281$	−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	$0.471563\pi$
$283$	−9.56200	+	29.4288i	−0.568402	+	1.74936i	−0.657621	+	0.753349i	$0.728437\pi$
$284$	−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	$-0.841421\pi$
$293$	−7.67937	−	23.6347i	−0.448634	−	1.38075i	0.429816	−	0.902917i	$-0.358579\pi$
$294$	−6.48609	−	10.6772i	−0.378276	−	0.622706i
$295$	−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
$301$	−3.10412	−	3.37112i	−0.178918	−	0.194308i
$302$	−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	$-0.407858\pi$
$307$	10.0029			0.570896			0.285448	+	0.958394i	$0.407858\pi$
$308$	−13.5037	+	1.41569i	−0.769442	+	0.0806663i
$309$	−25.8154			−1.46859
$310$	−4.20498	+	5.78765i	−0.238827	+	0.328717i
$311$	17.8028	+	5.78448i	1.00950	+	0.328008i	0.766657	−	0.642057i	$-0.221919\pi$
$311$	17.8028	+	5.78448i	1.00950	+	0.328008i	0.242847	+	0.970065i	$0.421919\pi$
$312$	−2.15786	−	6.64120i	−0.122165	−	0.375984i
$313$	−3.10702	−	4.27645i	−0.175619	−	0.241719i	0.712129	−	0.702049i	$-0.247731\pi$
$313$	−3.10702	−	4.27645i	−0.175619	−	0.241719i	−0.887748	+	0.460330i	$0.847731\pi$
$314$	−8.30717	+	6.03551i	−0.468801	+	0.340604i
$315$	−25.6775	−	27.8862i	−1.44676	−	1.57121i
$316$	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
$322$	−0.587363	−	5.04653i	−0.0327325	−	0.281232i
$323$	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
$336$	−5.12314	+	9.10650i	−0.279490	+	0.496800i
$337$	−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
$343$	11.3809	+	14.6108i	0.614509	+	0.788910i
$344$	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	$-0.776582\pi$
$349$	4.36532	−	13.4351i	0.233670	−	0.719164i	0.997295	−	0.0735032i	$-0.0234179\pi$
$350$	13.2660	+	2.66557i	0.709099	+	0.142480i
$351$			3.03156i			0.161812i
$352$	−11.0808	−	15.6232i	−0.590607	−	0.832722i
$353$			8.23958i			0.438549i	0.975663	+	0.219274i	$0.0703690\pi$
$353$			8.23958i			0.438549i	−0.975663	+	0.219274i	$0.929631\pi$
$354$	−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
$357$	14.3598	−	25.5249i	0.760001	−	1.35092i
$358$	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	−0.421792	−	0.906693i	$-0.638599\pi$
$367$	−4.40784	+	1.43219i	−0.230087	+	0.0747599i	0.191704	+	0.981453i	$0.438599\pi$
$368$	−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
$371$	2.83786	−	0.330297i	0.147335	−	0.0171482i
$372$	−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
$378$	−3.59915	+	3.31408i	−0.185120	+	0.170458i
$379$	−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	$0.464575\pi$
$383$	−16.9956	+	23.3924i	−0.868432	+	1.19529i	−0.979493	+	0.201481i	$0.935425\pi$
$384$	−29.0174			−1.48079
$385$	−28.4600	+	12.6622i	−1.45046	+	0.645326i
$386$	−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
$392$	−6.45333	+	15.4102i	−0.325942	+	0.778332i
$393$	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	$-0.975853\pi$
$397$		−	3.02008i		−	0.151573i	0.997124	−	0.0757866i	$-0.0241468\pi$
$398$	11.9452	+	8.67872i	0.598761	+	0.435025i
$399$	1.01055	+	8.68248i	0.0505907	+	0.434667i
$400$	−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	0.974448	−	0.224614i	$-0.0721121\pi$
$409$	21.4766	+	15.6036i	1.06195	+	0.771551i	0.0875004	+	0.996164i	$0.472112\pi$
$410$	−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
$413$	2.97045	−	5.28004i	0.146166	−	0.259814i
$414$	−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	$-0.943057\pi$
$419$		−	7.28466i		−	0.355879i	0.984041	−	0.177940i	$-0.0569431\pi$
$420$	−7.59378	+	37.7929i	−0.370539	+	1.84410i
$421$	−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
$427$	6.95893	−	34.6333i	0.336766	−	1.67602i
$428$		−	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	−0.674871	−	0.737936i	$-0.735801\pi$
$433$	−16.3786	+	5.32173i	−0.787105	+	0.255746i	−0.112234	+	0.993682i	$0.535801\pi$
$434$	−4.64703	−	2.61433i	−0.223065	−	0.125492i
$435$	−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	$-0.500290\pi$
$439$	−0.0381286			−0.00181978			−0.000909889		1.00000i	$0.500290\pi$
$440$	−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
$448$	−2.38602	+	0.277708i	−0.112729	+	0.0131205i
$449$	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
$455$	7.01717	+	7.62077i	0.328970	+	0.357267i
$456$	−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	$-0.589326\pi$
$461$	−11.8930			−0.553913			−0.276957	+	0.960882i	$0.589326\pi$
$462$	6.36598	+	14.3084i	0.296172	+	0.665686i
$463$	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	0.630014	−	0.776584i	$-0.283049\pi$
$467$	−6.55321	−	9.01971i	−0.303246	−	0.417383i	−0.933260	+	0.359201i	$0.883049\pi$
$468$	5.57289	−	4.04894i	0.257607	−	0.187162i
$469$	−0.953318	+	0.877812i	−0.0440202	+	0.0405336i
$470$	−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
$476$	−16.9693	+	1.97505i	−0.777786	+	0.0905261i
$477$	−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	−0.358312	−	0.933602i	$-0.616648\pi$
$479$	9.16744	−	6.66053i	0.418871	−	0.304328i	0.777183	+	0.629274i	$0.216648\pi$
$480$	−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
$490$	−1.37645	+	16.6620i	−0.0621816	+	0.752711i
$491$	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
$497$	5.31943	−	26.4739i	0.238609	−	1.18751i
$498$	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	−0.942774	−	0.333432i	$-0.891793\pi$
$503$	0.357335	−	1.09976i	0.0159328	−	0.0490360i	0.958707	+	0.284396i	$0.0917931\pi$
$504$	24.9872	+	5.02072i	1.11302	+	0.223641i
$505$			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	0.659727	−	0.751505i	$-0.270672\pi$
$509$	16.9599	+	5.51060i	0.751734	+	0.244253i	0.0920067	+	0.995758i	$0.470672\pi$
$510$	25.1441	−	8.16981i	1.11340	−	0.361765i
$511$	28.8873	+	16.2514i	1.27790	+	0.718920i
$512$	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	−0.938991	−	0.343943i	$-0.888237\pi$
$521$	−34.1579	+	11.0986i	−1.49649	+	0.486238i	−0.557495	+	0.830180i	$0.688237\pi$
$522$	−4.48787	+	3.26063i	−0.196429	+	0.142714i
$523$	7.97894	−	5.79704i	0.348895	−	0.253487i	−0.399511	−	0.916729i	$-0.630820\pi$
$523$	7.97894	−	5.79704i	0.348895	−	0.253487i	0.748405	+	0.663242i	$0.230820\pi$
$524$	−9.00288	−	27.7080i	−0.393293	−	1.21043i
$525$	6.16735	+	52.9889i	0.269165	+	2.31262i
$526$	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
$532$	3.75096	−	3.45387i	0.162625	−	0.149744i
$533$	−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
$539$	−11.8263	−	19.9784i	−0.509396	−	0.860532i
$540$	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
$546$	3.83137	−	3.52791i	0.163968	−	0.150981i
$547$	−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
$553$	3.80298	+	32.6746i	0.161719	+	1.38947i
$554$	−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	0.479958	−	0.877291i	$-0.340652\pi$
$563$	−4.88979	−	3.55264i	−0.206080	−	0.149726i	−0.686038	+	0.727565i	$0.740652\pi$
$564$	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
$567$	11.1097	+	6.25009i	0.466563	+	0.262479i
$568$	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
$574$	−9.59279	−	1.92749i	−0.400395	−	0.0804521i
$575$	−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	0.327398	−	0.944887i	$-0.393828\pi$
$577$	−16.1519	−	22.2313i	−0.672414	−	0.925499i	−0.999812	+	0.0193876i	$0.993828\pi$
$578$	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
$581$	−0.843620	+	4.19854i	−0.0349993	+	0.174185i
$582$			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	−0.576072	−	0.817399i	$-0.695415\pi$
$587$	−13.6082	+	4.42157i	−0.561670	+	0.182498i	0.0144024	+	0.999896i	$0.495415\pi$
$588$	−28.6331	−	2.36539i	−1.18081	−	0.0975469i
$589$	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	$-0.273013\pi$
$593$	31.8607			1.30836			0.654181	+	0.756338i	$0.273013\pi$
$594$	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	$0.101086\pi$
$601$	8.94747	+	27.5375i	0.364975	+	1.12328i	−0.585022	+	0.811017i	$0.698914\pi$
$602$	3.06256	−	0.356449i	0.124821	−	0.0145278i
$603$	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	0.0140022	−	0.999902i	$-0.495543\pi$
$607$	−22.9777	−	16.6942i	−0.932634	−	0.677598i	−0.946636	+	0.322304i	$0.895543\pi$
$608$	6.84092	+	2.22275i	0.277436	+	0.0901444i
$609$	10.5463	−	9.71101i	0.427358	−	0.393510i
$610$	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
$616$	10.4764	−	18.1345i	0.422105	−	0.730661i
$617$	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	0.707445	−	0.706768i	$-0.249848\pi$
$619$	21.5048	+	6.98735i	0.864353	+	0.280845i	0.156907	+	0.987613i	$0.449848\pi$
$620$	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
$623$	4.13963	+	4.49570i	0.165851	+	0.180117i
$624$	−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
$630$	25.3337	−	2.94858i	1.00932	−	0.117474i
$631$	−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	0.323550	−	0.946211i	$-0.395124\pi$
$643$	−17.1501	−	23.6050i	−0.676333	−	0.930892i	−0.999883	+	0.0153191i	$0.995124\pi$
$644$	−10.1833	−	5.72892i	−0.401278	−	0.225751i
$645$	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	−0.826831	−	0.562450i	$-0.809859\pi$
$647$	−0.925990	+	1.27452i	−0.0364044	+	0.0501064i	0.790427	+	0.612557i	$0.209859\pi$
$648$			11.4990i			0.451723i
$649$	−4.53371	+	6.09267i	−0.177964	+	0.239158i
$650$			5.64109i			0.221262i
$651$	4.14105	−	20.6092i	0.162300	−	0.807740i
$652$	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
$658$	2.39459	−	11.9174i	0.0933508	−	0.464590i
$659$			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	$0.220100\pi$
$661$			32.7887i			1.27533i	−0.770313	+	0.637666i	$0.779900\pi$
$662$	−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
$665$	5.73563	−	10.1952i	0.222418	−	0.395354i
$666$	−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	−0.979156	−	0.203109i	$-0.934895\pi$
$677$	−28.3236	+	20.5783i	−1.08856	+	0.790888i	−0.109408	+	0.993997i	$0.534895\pi$
$678$	−4.00230	−	12.3178i	−0.153707	−	0.473063i
$679$	−3.87487	−	33.2923i	−0.148704	−	1.27764i
$680$	−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
$686$	−12.4538	+	0.416671i	−0.475487	+	0.0159086i
$687$	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	−0.458769	−	0.888556i	$-0.651709\pi$
$691$	13.8812	−	19.1058i	0.528065	−	0.726819i	0.986834	+	0.161736i	$0.0517094\pi$
$692$	24.8481			0.944585
$693$	−26.3263	+	23.6917i	−1.00005	+	0.899973i
$694$	−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
$700$	22.8920	−	21.0789i	0.865236	−	0.796706i
$701$	−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
$707$	−8.32158	+	0.968544i	−0.312965	+	0.0364258i
$708$	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	−0.795718	−	0.605667i	$-0.792906\pi$
$719$	−29.0522	+	9.43965i	−1.08347	+	0.352039i	−0.287748	+	0.957706i	$0.592906\pi$
$720$	−12.5383	−	17.2575i	−0.467275	−	0.643149i
$721$	−12.6251	+	22.4414i	−0.470183	+	0.835762i
$722$	−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	$0.0165807\pi$
$727$			2.80772i			0.104133i	−0.998644	+	0.0520663i	$0.983419\pi$
$728$	−6.82853	−	1.37207i	−0.253082	−	0.0508522i
$729$	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	0.982179	−	0.187947i	$-0.0601833\pi$
$733$	2.08760	+	6.42496i	0.0771071	+	0.237311i	−0.905072	+	0.425258i	$0.860183\pi$
$734$	0.963604	−	2.96567i	0.0355673	−	0.109465i
$735$	−64.1515	+	15.1382i	−2.36626	+	0.558380i
$736$		−	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
$742$	−0.942507	+	1.67533i	−0.0346005	+	0.0615033i
$743$	−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
$756$	1.30080	+	11.1762i	0.0473095	+	0.406476i
$757$	−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	0.685957	−	0.727642i	$-0.259384\pi$
$761$	5.68004	+	4.12679i	0.205901	+	0.149596i	−0.480056	+	0.877238i	$0.659384\pi$
$762$	−10.4043	−	3.38057i	−0.376909	−	0.122465i
$763$	−5.46041	−	5.93009i	−0.197680	−	0.214684i
$764$	−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	$-0.335222\pi$
$769$	27.4453			0.989703			0.494851	+	0.868978i	$0.335222\pi$
$770$	4.36283	−	20.4989i	0.157225	−	0.738729i
$771$	−17.8590			−0.643177
$772$	−10.1891	+	14.0241i	−0.366715	+	0.504740i
$773$	−27.2253	−	8.84603i	−0.979226	−	0.318170i	−0.224691	−	0.974430i	$-0.572137\pi$
$773$	−27.2253	−	8.84603i	−0.979226	−	0.318170i	−0.754535	+	0.656260i	$0.772137\pi$
$774$	−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
$777$	13.1302	+	14.2596i	0.471044	+	0.511562i
$778$	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
$784$	5.41083	+	8.90713i	0.193244	+	0.318112i
$785$	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	−0.692259	−	0.721649i	$-0.743384\pi$
$787$	−6.16756	+	4.48100i	−0.219850	+	0.159730i	0.472409	+	0.881379i	$0.343384\pi$
$788$	−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	$0.0109802\pi$
$797$	20.4217	+	28.1080i	0.723372	+	0.995637i	−0.276033	+	0.961148i	$0.589020\pi$
$798$	−5.12569	−	2.88361i	−0.181447	−	0.102079i
$799$	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
$805$	−26.2804	−	5.28057i	−0.926263	−	0.186116i
$806$	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	$0.211522\pi$
$811$	−6.04102	+	18.5924i	−0.212129	+	0.652866i	−0.999345	+	0.0361885i	$0.988478\pi$
$812$	−8.19886	−	1.64741i	−0.287724	−	0.0578128i
$813$		−	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
$819$	10.2656	+	5.77520i	0.358708	+	0.201802i
$820$	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	−0.631417	−	0.775443i	$-0.717526\pi$
$829$	−19.7645	+	6.42188i	−0.686450	+	0.223041i	−0.0550330	+	0.998485i	$0.517526\pi$
$830$	−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
$833$	−15.1662	−	24.9661i	−0.525477	−	0.865022i
$834$	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	0.430200	−	0.902733i	$-0.358443\pi$
$839$	7.17263	+	2.33053i	0.247627	+	0.0804588i	−0.182574	+	0.983192i	$0.558443\pi$
$840$	−40.2763	−	43.7408i	−1.38967	−	1.50920i
$841$	−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
$847$	11.5261	+	26.7236i	0.396042	+	0.918232i
$848$	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	−0.565657	−	0.824641i	$-0.691377\pi$
$853$	1.27999	−	0.929968i	0.0438260	−	0.0318415i	0.609483	+	0.792799i	$0.291377\pi$
$854$	16.0995	+	17.4844i	0.550915	+	0.598303i
$855$	−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	$-0.851874\pi$
$857$	−52.3232			−1.78733			−0.893664	+	0.448737i	$0.851874\pi$
$858$	−5.32540	+	3.77703i	−0.181806	+	0.128946i
$859$			7.18932i			0.245296i	0.992450	+	0.122648i	$0.0391387\pi$
$859$			7.18932i			0.245296i	−0.992450	+	0.122648i	$0.960861\pi$
$860$	−7.69673	−	5.59200i	−0.262456	−	0.190686i
$861$	−4.45966	−	38.3167i	−0.151985	−	1.30583i
$862$	−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
$875$	11.9792	−	21.2934i	0.404972	−	0.719848i
$876$	−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	$0.0131548\pi$
$881$			2.45261i			0.0826304i	−0.999146	+	0.0413152i	$0.986845\pi$
$882$	4.36578	+	18.5010i	0.147003	+	0.622960i
$883$	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	$-0.894483\pi$
$887$	−11.0756	−	34.0871i	−0.371882	−	1.14453i	0.573677	−	0.819082i	$-0.305517\pi$
$888$	−5.40348	+	16.6302i	−0.181329	+	0.558073i
$889$	15.9000	+	3.19482i	0.533270	+	0.107151i
$890$			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
$896$	−14.1910	+	25.2249i	−0.474090	+	0.842706i
$897$	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
$910$	−6.92323	+	0.805790i	−0.229503	+	0.0267117i
$911$	−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
$917$	36.6466	−	33.7440i	1.21018	−	1.11433i
$918$	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
$924$	35.2267	+	7.49739i	1.15887	+	0.246646i
$925$	−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	0.986350	−	0.164664i	$-0.0526540\pi$
$929$	16.0001	+	22.0222i	0.524946	+	0.722526i	−0.461404	+	0.887190i	$0.652654\pi$
$930$	15.3522	−	11.1540i	0.503418	−	0.365754i
$931$	8.04192	+	3.36772i	0.263563	+	0.110373i
$932$	−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	−0.268493	−	0.963282i	$-0.586526\pi$
$937$	−38.8017	−	28.1911i	−1.26760	−	0.920964i	−0.999104	+	0.0423179i	$0.986526\pi$
$938$	−0.100800	−	0.866060i	−0.00329124	−	0.0282779i
$939$	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	−0.717126	−	0.696944i	$-0.754543\pi$
$941$	−8.46335	+	6.14898i	−0.275897	+	0.200451i	0.441229	+	0.897395i	$0.354543\pi$
$942$	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
$952$	12.9204	−	22.9664i	0.418754	−	0.744345i
$953$	−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
$959$	−1.54243	+	7.67637i	−0.0498075	+	0.247883i
$960$	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
$966$	−2.65483	+	13.2126i	−0.0854177	+	0.425108i
$967$		−	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	0.324652	−	0.945834i	$-0.394753\pi$
$971$	0.977016	+	0.317452i	0.0313539	+	0.0101875i	−0.293298	+	0.956021i	$0.594753\pi$
$972$	−30.9406	+	10.0532i	−0.992421	+	0.322457i
$973$	−34.0660	−	19.1649i	−1.09211	−	0.614398i
$974$	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	−0.591550	−	0.806268i	$-0.701484\pi$
$983$	−18.6929	+	6.07370i	−0.596212	+	0.193721i	−0.00466161	+	0.999989i	$0.501484\pi$
$984$	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
$987$	47.6021	−	5.54038i	1.51519	−	0.176352i
$988$	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
$994$	12.3066	+	13.3651i	0.390340	+	0.423916i
$995$	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	$-0.997067\pi$
$997$	−6.20109	−	19.0850i	−0.196391	−	0.604428i	0.803567	−	0.595214i	$-0.202933\pi$
$998$	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.62.3	yes	16
3.2	odd	2		693.2.bu.d.370.1		16
7.2	even	3		539.2.s.b.227.2		16
7.3	odd	6		539.2.s.c.117.1		16
7.4	even	3		539.2.s.c.117.2		16
7.5	odd	6		539.2.s.b.227.1		16
7.6	odd	2	inner	77.2.l.b.62.4	yes	16
11.2	odd	10		847.2.l.e.699.3		16
11.3	even	5		847.2.l.i.118.2		16
11.4	even	5		847.2.l.e.475.4		16
11.5	even	5		847.2.b.f.846.5		16
11.6	odd	10		847.2.b.f.846.11		16
11.7	odd	10		847.2.l.j.475.2		16
11.8	odd	10	inner	77.2.l.b.41.4	yes	16
11.9	even	5		847.2.l.j.699.1		16
11.10	odd	2		847.2.l.i.524.1		16
21.20	even	2		693.2.bu.d.370.2		16
33.8	even	10		693.2.bu.d.118.2		16
77.6	even	10		847.2.b.f.846.12		16
77.13	even	10		847.2.l.e.699.4		16
77.19	even	30		539.2.s.c.129.2		16
77.20	odd	10		847.2.l.j.699.2		16
77.27	odd	10		847.2.b.f.846.6		16
77.30	odd	30		539.2.s.c.129.1		16
77.41	even	10	inner	77.2.l.b.41.3	✓	16
77.48	odd	10		847.2.l.e.475.3		16
77.52	even	30		539.2.s.b.19.2		16
77.62	even	10		847.2.l.j.475.1		16
77.69	odd	10		847.2.l.i.118.1		16
77.74	odd	30		539.2.s.b.19.1		16
77.76	even	2		847.2.l.i.524.2		16
231.41	odd	10		693.2.bu.d.118.1		16

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

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)

\(f(q)\)	\(=\)	\(q+(-0.395472 + 0.544320i) q^{2} +(-2.52275 - 0.819690i) q^{3} +(0.478148 + 1.47159i) q^{4} +(2.08654 + 2.87188i) q^{5} +(1.44385 - 1.04902i) q^{6} +(-1.94632 + 1.79216i) q^{7} +(-2.26988 - 0.737529i) q^{8} +(3.26531 + 2.37239i) q^{9} +O(q^{10})\)	\(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} +(-1.94632 + 1.79216i) 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} +(-0.205796 - 1.76817i) 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} +(-3.56795 - 2.00726i) 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} +(-9.20795 - 1.85017i) 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} +(-0.930179 + 4.62933i) 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} +(0.576309 - 6.97624i) 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} +(-10.6070 + 1.23455i) 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} +(4.64856 - 4.28038i) 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} +(-1.82668 + 8.58273i) 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} +(7.35571 + 7.98842i) 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} +(2.89870 - 0.337378i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more