LMFDB - Embedded newform 390.2.t.a.343.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(307,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("390.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 $ x^12 + 6x^10 - 24x^9 + 18x^8 + 40x^7 - 82x^6 + 12x^5 + 228x^4 - 284x^3 + 124x^2 - 16x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.4
Root			$-1.46953 + 0.608701i$ of defining polynomial
Character	$\chi$	$=$	390.343
Dual form			390.2.t.a.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.23563 + 0.0440169i) q^{5} +(-0.707107 + 0.707107i) q^{6} -4.35328 q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.23563 + 0.0440169i) q^{5} +(-0.707107 + 0.707107i) q^{6} -4.35328 q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.0440169 - 2.23563i) q^{10} +(-0.747451 - 0.747451i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.32711 - 1.38936i) q^{13} -4.35328i q^{14} +(-1.61196 - 1.54971i) q^{15} +1.00000 q^{16} +(-4.23990 - 4.23990i) q^{17} -1.00000 q^{18} +(-2.33730 - 2.33730i) q^{19} +(2.23563 - 0.0440169i) q^{20} +(-3.07824 - 3.07824i) q^{21} +(0.747451 - 0.747451i) q^{22} +(-5.77210 + 5.77210i) q^{23} +(0.707107 - 0.707107i) q^{24} +(4.99613 - 0.196811i) q^{25} +(1.38936 + 3.32711i) q^{26} +(-0.707107 + 0.707107i) q^{27} +4.35328 q^{28} +8.52201i q^{29} +(1.54971 - 1.61196i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} -1.05706i q^{33} +(4.23990 - 4.23990i) q^{34} +(9.73235 - 0.191618i) q^{35} -1.00000i q^{36} -7.52501 q^{37} +(2.33730 - 2.33730i) q^{38} +(3.33505 + 1.37020i) q^{39} +(0.0440169 + 2.23563i) q^{40} +(-5.52833 + 5.52833i) q^{41} +(3.07824 - 3.07824i) q^{42} +(-2.48784 + 2.48784i) q^{43} +(0.747451 + 0.747451i) q^{44} +(-0.0440169 - 2.23563i) q^{45} +(-5.77210 - 5.77210i) q^{46} -2.03197 q^{47} +(0.707107 + 0.707107i) q^{48} +11.9511 q^{49} +(0.196811 + 4.99613i) q^{50} -5.99613i q^{51} +(-3.32711 + 1.38936i) q^{52} +(-1.80319 - 1.80319i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(1.70393 + 1.63813i) q^{55} +4.35328i q^{56} -3.30544i q^{57} -8.52201 q^{58} +(2.51231 - 2.51231i) q^{59} +(1.61196 + 1.54971i) q^{60} +15.0391 q^{61} +(1.00000 + 1.00000i) q^{62} -4.35328i q^{63} -1.00000 q^{64} +(-7.37705 + 3.25255i) q^{65} +1.05706 q^{66} -4.15834i q^{67} +(4.23990 + 4.23990i) q^{68} -8.16298 q^{69} +(0.191618 + 9.73235i) q^{70} +(-8.14309 + 8.14309i) q^{71} +1.00000 q^{72} -0.693572i q^{73} -7.52501i q^{74} +(3.67196 + 3.39363i) q^{75} +(2.33730 + 2.33730i) q^{76} +(3.25387 + 3.25387i) q^{77} +(-1.37020 + 3.33505i) q^{78} -6.33756i q^{79} +(-2.23563 + 0.0440169i) q^{80} -1.00000 q^{81} +(-5.52833 - 5.52833i) q^{82} +0.717629 q^{83} +(3.07824 + 3.07824i) q^{84} +(9.66550 + 9.29224i) q^{85} +(-2.48784 - 2.48784i) q^{86} +(-6.02597 + 6.02597i) q^{87} +(-0.747451 + 0.747451i) q^{88} +(10.7389 - 10.7389i) q^{89} +(2.23563 - 0.0440169i) q^{90} +(-14.4839 + 6.04828i) q^{91} +(5.77210 - 5.77210i) q^{92} +1.41421 q^{93} -2.03197i q^{94} +(5.32822 + 5.12246i) q^{95} +(-0.707107 + 0.707107i) q^{96} +11.0892i q^{97} +11.9511i q^{98} +(0.747451 - 0.747451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 4 * q^5	$ 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.23563	+	0.0440169i	−0.999806	+	0.0196849i
$5$	−2.23563	+	0.0440169i	−0.999806	+	0.0196849i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−4.35328			−1.64539			−0.822693	−	0.568486i	$-0.807529\pi$
$7$	−4.35328			−1.64539			−0.822693	+	0.568486i	$0.807529\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	−0.0440169	−	2.23563i	−0.0139194	−	0.706970i
$11$	−0.747451	−	0.747451i	−0.225365	−	0.225365i	0.585388	−	0.810753i	$-0.300942\pi$
$11$	−0.747451	−	0.747451i	−0.225365	−	0.225365i	−0.810753	+	0.585388i	$0.800942\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	3.32711	−	1.38936i	0.922775	−	0.385340i
$13$	3.32711	−	1.38936i	0.922775	−	0.385340i
$14$		−	4.35328i		−	1.16346i
$15$	−1.61196	−	1.54971i	−0.416206	−	0.400133i
$16$	1.00000			0.250000
$17$	−4.23990	−	4.23990i	−1.02833	−	1.02833i	−0.999587	−	0.0287400i	$-0.990851\pi$
$17$	−4.23990	−	4.23990i	−1.02833	−	1.02833i	−0.0287400	−	0.999587i	$-0.509149\pi$
$18$	−1.00000			−0.235702
$19$	−2.33730	−	2.33730i	−0.536213	−	0.536213i	0.386202	−	0.922414i	$-0.373787\pi$
$19$	−2.33730	−	2.33730i	−0.536213	−	0.536213i	−0.922414	+	0.386202i	$0.873787\pi$
$20$	2.23563	−	0.0440169i	0.499903	−	0.00984247i
$21$	−3.07824	−	3.07824i	−0.671726	−	0.671726i
$22$	0.747451	−	0.747451i	0.159357	−	0.159357i
$23$	−5.77210	+	5.77210i	−1.20357	+	1.20357i	−0.230492	+	0.973074i	$0.574034\pi$
$23$	−5.77210	+	5.77210i	−1.20357	+	1.20357i	−0.973074	+	0.230492i	$0.925966\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	4.99613	−	0.196811i	0.999225	−	0.0393622i
$26$	1.38936	+	3.32711i	0.272476	+	0.652500i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.35328			0.822693
$29$			8.52201i			1.58250i	0.611495	+	0.791248i	$0.290568\pi$
$29$			8.52201i			1.58250i	−0.611495	+	0.791248i	$0.709432\pi$
$30$	1.54971	−	1.61196i	0.282937	−	0.294302i
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	−0.611578	−	0.791184i	$-0.709465\pi$
$31$	1.00000	−	1.00000i	0.179605	−	0.179605i	0.791184	+	0.611578i	$0.209465\pi$
$32$			1.00000i			0.176777i
$33$		−	1.05706i		−	0.184010i
$34$	4.23990	−	4.23990i	0.727137	−	0.727137i
$35$	9.73235	−	0.191618i	1.64507	−	0.0323893i
$36$		−	1.00000i		−	0.166667i
$37$	−7.52501			−1.23710			−0.618552	−	0.785744i	$-0.712280\pi$
$37$	−7.52501			−1.23710			−0.618552	+	0.785744i	$0.712280\pi$
$38$	2.33730	−	2.33730i	0.379160	−	0.379160i
$39$	3.33505	+	1.37020i	0.534035	+	0.219407i
$40$	0.0440169	+	2.23563i	0.00695968	+	0.353485i
$41$	−5.52833	+	5.52833i	−0.863379	+	0.863379i	−0.991729	−	0.128350i	$-0.959032\pi$
$41$	−5.52833	+	5.52833i	−0.863379	+	0.863379i	0.128350	+	0.991729i	$0.459032\pi$
$42$	3.07824	−	3.07824i	0.474982	−	0.474982i
$43$	−2.48784	+	2.48784i	−0.379393	+	0.379393i	−0.870883	−	0.491490i	$-0.836452\pi$
$43$	−2.48784	+	2.48784i	−0.379393	+	0.379393i	0.491490	+	0.870883i	$0.336452\pi$
$44$	0.747451	+	0.747451i	0.112683	+	0.112683i
$45$	−0.0440169	−	2.23563i	−0.00656165	−	0.333269i
$46$	−5.77210	−	5.77210i	−0.851050	−	0.851050i
$47$	−2.03197			−0.296394			−0.148197	−	0.988958i	$-0.547347\pi$
$47$	−2.03197			−0.296394			−0.148197	+	0.988958i	$0.547347\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	11.9511			1.70730
$50$	0.196811	+	4.99613i	0.0278333	+	0.706559i
$51$		−	5.99613i		−	0.839625i
$52$	−3.32711	+	1.38936i	−0.461387	+	0.192670i
$53$	−1.80319	−	1.80319i	−0.247687	−	0.247687i	0.572334	−	0.820021i	$-0.306038\pi$
$53$	−1.80319	−	1.80319i	−0.247687	−	0.247687i	−0.820021	+	0.572334i	$0.806038\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	1.70393	+	1.63813i	0.229758	+	0.220885i
$56$			4.35328i			0.581732i
$57$		−	3.30544i		−	0.437816i
$58$	−8.52201			−1.11899
$59$	2.51231	−	2.51231i	0.327075	−	0.327075i	−0.524398	−	0.851473i	$-0.675710\pi$
$59$	2.51231	−	2.51231i	0.327075	−	0.327075i	0.851473	+	0.524398i	$0.175710\pi$
$60$	1.61196	+	1.54971i	0.208103	+	0.200066i
$61$	15.0391			1.92556			0.962780	−	0.270286i	$-0.0871183\pi$
$61$	15.0391			1.92556			0.962780	+	0.270286i	$0.0871183\pi$
$62$	1.00000	+	1.00000i	0.127000	+	0.127000i
$63$		−	4.35328i		−	0.548462i
$64$	−1.00000			−0.125000
$65$	−7.37705	+	3.25255i	−0.915011	+	0.403430i
$66$	1.05706			0.130115
$67$		−	4.15834i		−	0.508022i	−0.967201	−	0.254011i	$-0.918250\pi$
$67$		−	4.15834i		−	0.508022i	0.967201	−	0.254011i	$-0.0817499\pi$
$68$	4.23990	+	4.23990i	0.514163	+	0.514163i
$69$	−8.16298			−0.982708
$70$	0.191618	+	9.73235i	0.0229027	+	1.16324i
$71$	−8.14309	+	8.14309i	−0.966407	+	0.966407i	−0.999454	−	0.0330464i	$-0.989479\pi$
$71$	−8.14309	+	8.14309i	−0.966407	+	0.966407i	0.0330464	+	0.999454i	$0.489479\pi$
$72$	1.00000			0.117851
$73$		−	0.693572i		−	0.0811764i	−0.999176	−	0.0405882i	$-0.987077\pi$
$73$		−	0.693572i		−	0.0811764i	0.999176	−	0.0405882i	$-0.0129232\pi$
$74$		−	7.52501i		−	0.874765i
$75$	3.67196	+	3.39363i	0.424001	+	0.391862i
$76$	2.33730	+	2.33730i	0.268106	+	0.268106i
$77$	3.25387	+	3.25387i	0.370813	+	0.370813i
$78$	−1.37020	+	3.33505i	−0.155144	+	0.377620i
$79$		−	6.33756i		−	0.713031i	−0.934289	−	0.356516i	$-0.883965\pi$
$79$		−	6.33756i		−	0.713031i	0.934289	−	0.356516i	$-0.116035\pi$
$80$	−2.23563	+	0.0440169i	−0.249952	+	0.00492123i
$81$	−1.00000			−0.111111
$82$	−5.52833	−	5.52833i	−0.610501	−	0.610501i
$83$	0.717629			0.0787701			0.0393850	−	0.999224i	$-0.487460\pi$
$83$	0.717629			0.0787701			0.0393850	+	0.999224i	$0.487460\pi$
$84$	3.07824	+	3.07824i	0.335863	+	0.335863i
$85$	9.66550	+	9.29224i	1.04837	+	1.00789i
$86$	−2.48784	−	2.48784i	−0.268271	−	0.268271i
$87$	−6.02597	+	6.02597i	−0.646052	+	0.646052i
$88$	−0.747451	+	0.747451i	−0.0796786	+	0.0796786i
$89$	10.7389	−	10.7389i	1.13832	−	1.13832i	0.149565	−	0.988752i	$-0.452213\pi$
$89$	10.7389	−	10.7389i	1.13832	−	1.13832i	0.988752	−	0.149565i	$-0.0477874\pi$
$90$	2.23563	−	0.0440169i	0.235657	−	0.00463978i
$91$	−14.4839	+	6.04828i	−1.51832	+	0.634032i
$92$	5.77210	−	5.77210i	0.601783	−	0.601783i
$93$	1.41421			0.146647
$94$		−	2.03197i		−	0.209582i
$95$	5.32822	+	5.12246i	0.546664	+	0.525553i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			11.0892i			1.12594i	0.826479	+	0.562968i	$0.190341\pi$
$97$			11.0892i			1.12594i	−0.826479	+	0.562968i	$0.809659\pi$
$98$			11.9511i			1.20724i
$99$	0.747451	−	0.747451i	0.0751217	−	0.0751217i
$100$	−4.99613	+	0.196811i	−0.499613	+	0.0196811i
$101$			6.14711i			0.611660i	0.952086	+	0.305830i	$0.0989339\pi$
$101$			6.14711i			0.611660i	−0.952086	+	0.305830i	$0.901066\pi$
$102$	5.99613			0.593705
$103$	−9.15260	+	9.15260i	−0.901832	+	0.901832i	−0.995595	−	0.0937625i	$-0.970111\pi$
$103$	−9.15260	+	9.15260i	−0.901832	+	0.901832i	0.0937625	+	0.995595i	$0.470111\pi$
$104$	−1.38936	−	3.32711i	−0.136238	−	0.326250i
$105$	7.01730	+	6.74632i	0.684819	+	0.658373i
$106$	1.80319	−	1.80319i	0.175141	−	0.175141i
$107$	−0.249153	+	0.249153i	−0.0240865	+	0.0240865i	−0.719047	−	0.694961i	$-0.755422\pi$
$107$	−0.249153	+	0.249153i	−0.0240865	+	0.0240865i	0.694961	+	0.719047i	$0.255422\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−5.43020	−	5.43020i	−0.520119	−	0.520119i	0.397488	−	0.917607i	$-0.369882\pi$
$109$	−5.43020	−	5.43020i	−0.520119	−	0.520119i	−0.917607	+	0.397488i	$0.869882\pi$
$110$	−1.63813	+	1.70393i	−0.156189	+	0.162463i
$111$	−5.32099	−	5.32099i	−0.505046	−	0.505046i
$112$	−4.35328			−0.411347
$113$	−3.20629	−	3.20629i	−0.301622	−	0.301622i	0.540026	−	0.841648i	$-0.318414\pi$
$113$	−3.20629	−	3.20629i	−0.301622	−	0.301622i	−0.841648	+	0.540026i	$0.818414\pi$
$114$	3.30544			0.309582
$115$	12.6502	−	13.1584i	1.17964	−	1.22703i
$116$		−	8.52201i		−	0.791248i
$117$	1.38936	+	3.32711i	0.128447	+	0.307592i
$118$	2.51231	+	2.51231i	0.231277	+	0.231277i
$119$	18.4575	+	18.4575i	1.69200	+	1.69200i
$120$	−1.54971	+	1.61196i	−0.141468	+	0.147151i
$121$		−	9.88263i		−	0.898421i
$122$			15.0391i			1.36158i
$123$	−7.81823			−0.704946
$124$	−1.00000	+	1.00000i	−0.0898027	+	0.0898027i
$125$	−11.1608	+	0.659912i	−0.998257	+	0.0590243i
$126$	4.35328			0.387821
$127$	1.80235	+	1.80235i	0.159933	+	0.159933i	0.782537	−	0.622604i	$-0.213925\pi$
$127$	1.80235	+	1.80235i	0.159933	+	0.159933i	−0.622604	+	0.782537i	$0.713925\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−3.51834			−0.309773
$130$	−3.25255	−	7.37705i	−0.285268	−	0.647010i
$131$	1.86044			0.162547			0.0812736	−	0.996692i	$-0.474101\pi$
$131$	1.86044			0.162547			0.0812736	+	0.996692i	$0.474101\pi$
$132$			1.05706i			0.0920049i
$133$	10.1749	+	10.1749i	0.882277	+	0.882277i
$134$	4.15834			0.359226
$135$	1.54971	−	1.61196i	0.133378	−	0.138735i
$136$	−4.23990	+	4.23990i	−0.363568	+	0.363568i
$137$	9.79864			0.837154			0.418577	−	0.908181i	$-0.362529\pi$
$137$	9.79864			0.837154			0.418577	+	0.908181i	$0.362529\pi$
$138$		−	8.16298i		−	0.694879i
$139$		−	8.75345i		−	0.742458i	−0.928541	−	0.371229i	$-0.878937\pi$
$139$		−	8.75345i		−	0.742458i	0.928541	−	0.371229i	$-0.121063\pi$
$140$	−9.73235	+	0.191618i	−0.822534	+	0.0161947i
$141$	−1.43682	−	1.43682i	−0.121002	−	0.121002i
$142$	−8.14309	−	8.14309i	−0.683353	−	0.683353i
$143$	−3.52533	−	1.44837i	−0.294803	−	0.121119i
$144$			1.00000i			0.0833333i
$145$	−0.375112	−	19.0521i	−0.0311514	−	1.58219i
$146$	0.693572			0.0574004
$147$	8.45068	+	8.45068i	0.697001	+	0.697001i
$148$	7.52501			0.618552
$149$	−9.87070	−	9.87070i	−0.808640	−	0.808640i	0.175788	−	0.984428i	$-0.443753\pi$
$149$	−9.87070	−	9.87070i	−0.808640	−	0.808640i	−0.984428	+	0.175788i	$0.943753\pi$
$150$	−3.39363	+	3.67196i	−0.277089	+	0.299814i
$151$	1.91281	+	1.91281i	0.155662	+	0.155662i	0.780641	−	0.624979i	$-0.214893\pi$
$151$	1.91281	+	1.91281i	0.155662	+	0.155662i	−0.624979	+	0.780641i	$0.714893\pi$
$152$	−2.33730	+	2.33730i	−0.189580	+	0.189580i
$153$	4.23990	−	4.23990i	0.342776	−	0.342776i
$154$	−3.25387	+	3.25387i	−0.262204	+	0.262204i
$155$	−2.19162	+	2.27965i	−0.176035	+	0.183106i
$156$	−3.33505	−	1.37020i	−0.267018	−	0.109704i
$157$	−3.24188	+	3.24188i	−0.258730	+	0.258730i	−0.824537	−	0.565808i	$-0.808565\pi$
$157$	−3.24188	+	3.24188i	−0.258730	+	0.258730i	0.565808	+	0.824537i	$0.308565\pi$
$158$	6.33756			0.504189
$159$		−	2.55009i		−	0.202236i
$160$	−0.0440169	−	2.23563i	−0.00347984	−	0.176742i
$161$	25.1276	−	25.1276i	1.98033	−	1.98033i
$162$		−	1.00000i		−	0.0785674i
$163$			22.9433i			1.79706i	0.438913	+	0.898529i	$0.355364\pi$
$163$			22.9433i			1.79706i	−0.438913	+	0.898529i	$0.644636\pi$
$164$	5.52833	−	5.52833i	0.431690	−	0.431690i
$165$	0.0465283	+	2.36319i	0.00362222	+	0.183974i
$166$			0.717629i			0.0556989i
$167$	−18.7357			−1.44981			−0.724905	−	0.688849i	$-0.758116\pi$
$167$	−18.7357			−1.44981			−0.724905	+	0.688849i	$0.758116\pi$
$168$	−3.07824	+	3.07824i	−0.237491	+	0.237491i
$169$	9.13935	−	9.24512i	0.703027	−	0.711163i
$170$	−9.29224	+	9.66550i	−0.712682	+	0.741310i
$171$	2.33730	−	2.33730i	0.178738	−	0.178738i
$172$	2.48784	−	2.48784i	0.189696	−	0.189696i
$173$	3.19031	−	3.19031i	0.242554	−	0.242554i	−0.575352	−	0.817906i	$-0.695135\pi$
$173$	3.19031	−	3.19031i	0.242554	−	0.242554i	0.817906	+	0.575352i	$0.195135\pi$
$174$	−6.02597	−	6.02597i	−0.456827	−	0.456827i
$175$	−21.7495	+	0.856775i	−1.64411	+	0.0647661i
$176$	−0.747451	−	0.747451i	−0.0563413	−	0.0563413i
$177$	3.55294			0.267056
$178$	10.7389	+	10.7389i	0.804912	+	0.804912i
$179$	−22.8203			−1.70567			−0.852835	−	0.522181i	$-0.825119\pi$
$179$	−22.8203			−1.70567			−0.852835	+	0.522181i	$0.825119\pi$
$180$	0.0440169	+	2.23563i	0.00328082	+	0.166634i
$181$		−	2.78317i		−	0.206871i	−0.994636	−	0.103436i	$-0.967016\pi$
$181$		−	2.78317i		−	0.206871i	0.994636	−	0.103436i	$-0.0329836\pi$
$182$	−6.04828	−	14.4839i	−0.448329	−	1.07362i
$183$	10.6343	+	10.6343i	0.786107	+	0.786107i
$184$	5.77210	+	5.77210i	0.425525	+	0.425525i
$185$	16.8232	−	0.331227i	1.23686	−	0.0243523i
$186$			1.41421i			0.103695i
$187$			6.33824i			0.463498i
$188$	2.03197			0.148197
$189$	3.07824	−	3.07824i	0.223909	−	0.223909i
$190$	−5.12246	+	5.32822i	−0.371622	+	0.386550i
$191$	9.57472			0.692802			0.346401	−	0.938087i	$-0.387404\pi$
$191$	9.57472			0.692802			0.346401	+	0.938087i	$0.387404\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$		−	25.8907i		−	1.86365i	−0.362904	−	0.931826i	$-0.618215\pi$
$193$		−	25.8907i		−	1.86365i	0.362904	−	0.931826i	$-0.381785\pi$
$194$	−11.0892			−0.796157
$195$	−7.51627	−	2.91646i	−0.538251	−	0.208852i
$196$	−11.9511			−0.853648
$197$		−	8.26912i		−	0.589151i	−0.955628	−	0.294575i	$-0.904822\pi$
$197$		−	8.26912i		−	0.589151i	0.955628	−	0.294575i	$-0.0951782\pi$
$198$	0.747451	+	0.747451i	0.0531191	+	0.0531191i
$199$	−6.35598			−0.450563			−0.225282	−	0.974294i	$-0.572330\pi$
$199$	−6.35598			−0.450563			−0.225282	+	0.974294i	$0.572330\pi$
$200$	−0.196811	−	4.99613i	−0.0139167	−	0.353279i
$201$	2.94039	−	2.94039i	0.207399	−	0.207399i
$202$	−6.14711			−0.432509
$203$		−	37.0987i		−	2.60382i
$204$			5.99613i			0.419813i
$205$	12.1160	−	12.6027i	0.846216	−	0.880208i
$206$	−9.15260	−	9.15260i	−0.637692	−	0.637692i
$207$	−5.77210	−	5.77210i	−0.401189	−	0.401189i
$208$	3.32711	−	1.38936i	0.230694	−	0.0963349i
$209$			3.49403i			0.241687i
$210$	−6.74632	+	7.01730i	−0.465540	+	0.484240i
$211$	−14.4467			−0.994548			−0.497274	−	0.867593i	$-0.665666\pi$
$211$	−14.4467			−0.994548			−0.497274	+	0.867593i	$0.665666\pi$
$212$	1.80319	+	1.80319i	0.123844	+	0.123844i
$213$	−11.5161			−0.789068
$214$	−0.249153	−	0.249153i	−0.0170317	−	0.0170317i
$215$	5.45240	−	5.67142i	0.371851	−	0.386788i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−4.35328	+	4.35328i	−0.295520	+	0.295520i
$218$	5.43020	−	5.43020i	0.367780	−	0.367780i
$219$	0.490429	−	0.490429i	0.0331401	−	0.0331401i
$220$	−1.70393	−	1.63813i	−0.114879	−	0.110443i
$221$	−19.9974	−	8.21587i	−1.34517	−	0.552659i
$222$	5.32099	−	5.32099i	0.357121	−	0.357121i
$223$	−4.67193			−0.312855			−0.156428	−	0.987689i	$-0.549998\pi$
$223$	−4.67193			−0.312855			−0.156428	+	0.987689i	$0.549998\pi$
$224$		−	4.35328i		−	0.290866i
$225$	0.196811	+	4.99613i	0.0131207	+	0.333075i
$226$	3.20629	−	3.20629i	0.213279	−	0.213279i
$227$		−	4.32302i		−	0.286929i	−0.989655	−	0.143464i	$-0.954176\pi$
$227$		−	4.32302i		−	0.286929i	0.989655	−	0.143464i	$-0.0458243\pi$
$228$			3.30544i			0.218908i
$229$	−14.1938	+	14.1938i	−0.937954	+	0.937954i	−0.998184	−	0.0602308i	$-0.980816\pi$
$229$	−14.1938	+	14.1938i	−0.937954	+	0.937954i	0.0602308	+	0.998184i	$0.480816\pi$
$230$	13.1584	+	12.6502i	0.867638	+	0.834132i
$231$			4.60166i			0.302767i
$232$	8.52201			0.559497
$233$	18.2904	−	18.2904i	1.19824	−	1.19824i	0.223551	−	0.974692i	$-0.428235\pi$
$233$	18.2904	−	18.2904i	1.19824	−	1.19824i	0.974692	−	0.223551i	$-0.0717649\pi$
$234$	−3.32711	+	1.38936i	−0.217500	+	0.0908254i
$235$	4.54275	−	0.0894411i	0.296336	−	0.00583449i
$236$	−2.51231	+	2.51231i	−0.163538	+	0.163538i
$237$	4.48133	−	4.48133i	0.291094	−	0.291094i
$238$	−18.4575	+	18.4575i	−1.19642	+	1.19642i
$239$	10.6351	+	10.6351i	0.687926	+	0.687926i	0.961773	−	0.273847i	$-0.0882961\pi$
$239$	10.6351	+	10.6351i	0.687926	+	0.687926i	−0.273847	+	0.961773i	$0.588296\pi$
$240$	−1.61196	−	1.54971i	−0.104051	−	0.100033i
$241$	17.8276	+	17.8276i	1.14838	+	1.14838i	0.986872	+	0.161505i	$0.0516348\pi$
$241$	17.8276	+	17.8276i	1.14838	+	1.14838i	0.161505	+	0.986872i	$0.448365\pi$
$242$	9.88263			0.635280
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−15.0391			−0.962780
$245$	−26.7182	+	0.526049i	−1.70697	+	0.0336080i
$246$		−	7.81823i		−	0.498472i
$247$	−11.0238	−	4.52910i	−0.701427	−	0.288180i
$248$	−1.00000	−	1.00000i	−0.0635001	−	0.0635001i
$249$	0.507441	+	0.507441i	0.0321577	+	0.0321577i
$250$	−0.659912	−	11.1608i	−0.0417365	−	0.705874i
$251$		−	5.40683i		−	0.341276i	−0.985334	−	0.170638i	$-0.945417\pi$
$251$		−	5.40683i		−	0.341276i	0.985334	−	0.170638i	$-0.0545829\pi$
$252$			4.35328i			0.274231i
$253$	8.62873			0.542484
$254$	−1.80235	+	1.80235i	−0.113089	+	0.113089i
$255$	0.263931	+	13.4051i	0.0165280	+	0.839463i
$256$	1.00000			0.0625000
$257$	9.31786	+	9.31786i	0.581232	+	0.581232i	0.935242	−	0.354010i	$-0.115182\pi$
$257$	9.31786	+	9.31786i	0.581232	+	0.581232i	−0.354010	+	0.935242i	$0.615182\pi$
$258$		−	3.51834i		−	0.219043i
$259$	32.7585			2.03551
$260$	7.37705	−	3.25255i	0.457505	−	0.201715i
$261$	−8.52201			−0.527499
$262$			1.86044i			0.114938i
$263$	−19.7684	−	19.7684i	−1.21897	−	1.21897i	−0.967993	−	0.250978i	$-0.919248\pi$
$263$	−19.7684	−	19.7684i	−1.21897	−	1.21897i	−0.250978	−	0.967993i	$-0.580752\pi$
$264$	−1.05706			−0.0650573
$265$	4.11064	+	3.95190i	0.252515	+	0.242763i
$266$	−10.1749	+	10.1749i	−0.623864	+	0.623864i
$267$	15.1870			0.929432
$268$			4.15834i			0.254011i
$269$			8.27192i			0.504348i	0.967682	+	0.252174i	$0.0811455\pi$
$269$			8.27192i			0.504348i	−0.967682	+	0.252174i	$0.918855\pi$
$270$	1.61196	+	1.54971i	0.0981006	+	0.0943122i
$271$	18.0549	+	18.0549i	1.09676	+	1.09676i	0.994787	+	0.101972i	$0.0325153\pi$
$271$	18.0549	+	18.0549i	1.09676	+	1.09676i	0.101972	+	0.994787i	$0.467485\pi$
$272$	−4.23990	−	4.23990i	−0.257082	−	0.257082i
$273$	−14.5184	−	5.96485i	−0.878695	−	0.361009i
$274$			9.79864i			0.591957i
$275$	−3.88147	−	3.58725i	−0.234061	−	0.216320i
$276$	8.16298			0.491354
$277$	3.55032	+	3.55032i	0.213318	+	0.213318i	0.805675	−	0.592357i	$-0.201803\pi$
$277$	3.55032	+	3.55032i	0.213318	+	0.213318i	−0.592357	+	0.805675i	$0.701803\pi$
$278$	8.75345			0.524997
$279$	1.00000	+	1.00000i	0.0598684	+	0.0598684i
$280$	−0.191618	−	9.73235i	−0.0114514	−	0.581619i
$281$	0.810247	+	0.810247i	0.0483353	+	0.0483353i	0.730861	−	0.682526i	$-0.239119\pi$
$281$	0.810247	+	0.810247i	0.0483353	+	0.0483353i	−0.682526	+	0.730861i	$0.739119\pi$
$282$	1.43682	−	1.43682i	0.0855615	−	0.0855615i
$283$	−8.92833	+	8.92833i	−0.530734	+	0.530734i	−0.920791	−	0.390057i	$-0.872455\pi$
$283$	−8.92833	+	8.92833i	−0.530734	+	0.530734i	0.390057	+	0.920791i	$0.372455\pi$
$284$	8.14309	−	8.14309i	0.483204	−	0.483204i
$285$	0.145495	+	7.38975i	0.00861838	+	0.437731i
$286$	1.44837	−	3.52533i	0.0856442	−	0.208457i
$287$	24.0664	−	24.0664i	1.42059	−	1.42059i
$288$	−1.00000			−0.0589256
$289$			18.9535i			1.11491i
$290$	19.0521	−	0.375112i	1.11878	−	0.0220273i
$291$	−7.84124	+	7.84124i	−0.459661	+	0.459661i
$292$			0.693572i			0.0405882i
$293$			7.40280i			0.432476i	0.976341	+	0.216238i	$0.0693788\pi$
$293$			7.40280i			0.432476i	−0.976341	+	0.216238i	$0.930621\pi$
$294$	−8.45068	+	8.45068i	−0.492854	+	0.492854i
$295$	−5.50603	+	5.72719i	−0.320573	+	0.333450i
$296$			7.52501i			0.437382i
$297$	1.05706			0.0613366
$298$	9.87070	−	9.87070i	0.571795	−	0.571795i
$299$	−11.1849	+	27.2240i	−0.646839	+	1.57440i
$300$	−3.67196	−	3.39363i	−0.212001	−	0.195931i
$301$	10.8303	−	10.8303i	0.624248	−	0.624248i
$302$	−1.91281	+	1.91281i	−0.110070	+	0.110070i
$303$	−4.34666	+	4.34666i	−0.249709	+	0.249709i
$304$	−2.33730	−	2.33730i	−0.134053	−	0.134053i
$305$	−33.6219	+	0.661974i	−1.92519	+	0.0379045i
$306$	4.23990	+	4.23990i	0.242379	+	0.242379i
$307$	−0.825032			−0.0470870			−0.0235435	−	0.999723i	$-0.507495\pi$
$307$	−0.825032			−0.0470870			−0.0235435	+	0.999723i	$0.507495\pi$
$308$	−3.25387	−	3.25387i	−0.185406	−	0.185406i
$309$	−12.9437			−0.736343
$310$	−2.27965	−	2.19162i	−0.129476	−	0.124476i
$311$		−	11.9446i		−	0.677317i	−0.940909	−	0.338659i	$-0.890027\pi$
$311$		−	11.9446i		−	0.677317i	0.940909	−	0.338659i	$-0.109973\pi$
$312$	1.37020	−	3.33505i	0.0775721	−	0.188810i
$313$	−10.4828	−	10.4828i	−0.592523	−	0.592523i	0.345789	−	0.938312i	$-0.387611\pi$
$313$	−10.4828	−	10.4828i	−0.592523	−	0.592523i	−0.938312	+	0.345789i	$0.887611\pi$
$314$	−3.24188	−	3.24188i	−0.182950	−	0.182950i
$315$	0.191618	+	9.73235i	0.0107964	+	0.548356i
$316$			6.33756i			0.356516i
$317$		−	4.72102i		−	0.265159i	−0.991172	−	0.132579i	$-0.957674\pi$
$317$		−	4.72102i		−	0.265159i	0.991172	−	0.132579i	$-0.0423259\pi$
$318$	2.55009			0.143002
$319$	6.36978	−	6.36978i	0.356639	−	0.356639i
$320$	2.23563	−	0.0440169i	0.124976	−	0.00246062i
$321$	−0.352355			−0.0196665
$322$	25.1276	+	25.1276i	1.40031	+	1.40031i
$323$			19.8198i			1.10280i
$324$	1.00000			0.0555556
$325$	16.3492	−	7.59624i	0.906892	−	0.421363i
$326$	−22.9433			−1.27071
$327$		−	7.67946i		−	0.424675i
$328$	5.52833	+	5.52833i	0.305251	+	0.305251i
$329$	8.84575			0.487682
$330$	−2.36319	+	0.0465283i	−0.130089	+	0.00256130i
$331$	−10.9736	+	10.9736i	−0.603162	+	0.603162i	−0.941150	−	0.337988i	$-0.890254\pi$
$331$	−10.9736	+	10.9736i	−0.603162	+	0.603162i	0.337988	+	0.941150i	$0.390254\pi$
$332$	−0.717629			−0.0393850
$333$		−	7.52501i		−	0.412368i
$334$		−	18.7357i		−	1.02517i
$335$	0.183037	+	9.29652i	0.0100004	+	0.507923i
$336$	−3.07824	−	3.07824i	−0.167932	−	0.167932i
$337$	−4.30540	−	4.30540i	−0.234530	−	0.234530i	0.580051	−	0.814580i	$-0.303033\pi$
$337$	−4.30540	−	4.30540i	−0.234530	−	0.234530i	−0.814580	+	0.580051i	$0.803033\pi$
$338$	9.24512	+	9.13935i	0.502868	+	0.497115i
$339$		−	4.53437i		−	0.246273i
$340$	−9.66550	−	9.29224i	−0.524185	−	0.503943i
$341$	−1.49490			−0.0809535
$342$	2.33730	+	2.33730i	0.126387	+	0.126387i
$343$	−21.5534			−1.16377
$344$	2.48784	+	2.48784i	0.134136	+	0.134136i
$345$	18.2494	−	0.359309i	0.982517	−	0.0193445i
$346$	3.19031	+	3.19031i	0.171512	+	0.171512i
$347$	−12.9246	+	12.9246i	−0.693828	+	0.693828i	−0.963072	−	0.269244i	$-0.913226\pi$
$347$	−12.9246	+	12.9246i	−0.693828	+	0.693828i	0.269244	+	0.963072i	$0.413226\pi$
$348$	6.02597	−	6.02597i	0.323026	−	0.323026i
$349$	−19.6667	+	19.6667i	−1.05273	+	1.05273i	−0.0542035	+	0.998530i	$0.517262\pi$
$349$	−19.6667	+	19.6667i	−1.05273	+	1.05273i	−0.998530	+	0.0542035i	$0.982738\pi$
$350$	−0.856775	−	21.7495i	−0.0457965	−	1.16256i
$351$	−1.37020	+	3.33505i	−0.0731357	+	0.178012i
$352$	0.747451	−	0.747451i	0.0398393	−	0.0398393i
$353$	7.00486			0.372831			0.186416	−	0.982471i	$-0.440313\pi$
$353$	7.00486			0.372831			0.186416	+	0.982471i	$0.440313\pi$
$354$			3.55294i			0.188837i
$355$	17.8465	−	18.5634i	0.947197	−	0.985244i
$356$	−10.7389	+	10.7389i	−0.569159	+	0.569159i
$357$			26.1028i			1.38151i
$358$		−	22.8203i		−	1.20609i
$359$	0.0274935	−	0.0274935i	0.00145105	−	0.00145105i	−0.706381	−	0.707832i	$-0.749673\pi$
$359$	0.0274935	−	0.0274935i	0.00145105	−	0.00145105i	0.707832	+	0.706381i	$0.249673\pi$
$360$	−2.23563	+	0.0440169i	−0.117828	+	0.00231989i
$361$		−	8.07409i		−	0.424952i
$362$	2.78317			0.146280
$363$	6.98808	−	6.98808i	0.366779	−	0.366779i
$364$	14.4839	−	6.04828i	0.759161	−	0.317016i
$365$	0.0305288	+	1.55057i	0.00159795	+	0.0811607i
$366$	−10.6343	+	10.6343i	−0.555861	+	0.555861i
$367$	−0.657074	+	0.657074i	−0.0342990	+	0.0342990i	−0.724048	−	0.689749i	$-0.757721\pi$
$367$	−0.657074	+	0.657074i	−0.0342990	+	0.0342990i	0.689749	+	0.724048i	$0.257721\pi$
$368$	−5.77210	+	5.77210i	−0.300892	+	0.300892i
$369$	−5.52833	−	5.52833i	−0.287793	−	0.287793i
$370$	0.331227	+	16.8232i	0.0172197	+	0.874595i
$371$	7.84979	+	7.84979i	0.407541	+	0.407541i
$372$	−1.41421			−0.0733236
$373$	17.0729	+	17.0729i	0.884003	+	0.884003i	0.993939	−	0.109936i	$-0.0350645\pi$
$373$	17.0729	+	17.0729i	0.884003	+	0.884003i	−0.109936	+	0.993939i	$0.535065\pi$
$374$	−6.33824			−0.327743
$375$	−8.35854	−	7.42528i	−0.431633	−	0.383440i
$376$			2.03197i			0.104791i
$377$	11.8401	+	28.3537i	0.609799	+	1.46029i
$378$	3.07824	+	3.07824i	0.158327	+	0.158327i
$379$	−10.7212	−	10.7212i	−0.550712	−	0.550712i	0.375934	−	0.926646i	$-0.377322\pi$
$379$	−10.7212	−	10.7212i	−0.550712	−	0.550712i	−0.926646	+	0.375934i	$0.877322\pi$
$380$	−5.32822	−	5.12246i	−0.273332	−	0.262777i
$381$			2.54891i			0.130584i
$382$			9.57472i			0.489885i
$383$	13.1664			0.672774			0.336387	−	0.941724i	$-0.390795\pi$
$383$	13.1664			0.672774			0.336387	+	0.941724i	$0.390795\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−7.41768	−	7.13123i	−0.378040	−	0.363441i
$386$	25.8907			1.31780
$387$	−2.48784	−	2.48784i	−0.126464	−	0.126464i
$388$		−	11.0892i		−	0.562968i
$389$	−6.12633			−0.310617			−0.155309	−	0.987866i	$-0.549637\pi$
$389$	−6.12633			−0.310617			−0.155309	+	0.987866i	$0.549637\pi$
$390$	2.91646	−	7.51627i	0.147681	−	0.380601i
$391$	48.9463			2.47532
$392$		−	11.9511i		−	0.603620i
$393$	1.31553	+	1.31553i	0.0663596	+	0.0663596i
$394$	8.26912			0.416592
$395$	0.278960	+	14.1685i	0.0140360	+	0.712893i
$396$	−0.747451	+	0.747451i	−0.0375608	+	0.0375608i
$397$	−10.5494			−0.529458			−0.264729	−	0.964323i	$-0.585283\pi$
$397$	−10.5494			−0.529458			−0.264729	+	0.964323i	$0.585283\pi$
$398$		−	6.35598i		−	0.318596i
$399$			14.3895i			0.720376i
$400$	4.99613	−	0.196811i	0.249806	−	0.00984056i
$401$	15.8695	+	15.8695i	0.792486	+	0.792486i	0.981898	−	0.189412i	$-0.0606582\pi$
$401$	15.8695	+	15.8695i	0.792486	+	0.792486i	−0.189412	+	0.981898i	$0.560658\pi$
$402$	2.94039	+	2.94039i	0.146653	+	0.146653i
$403$	1.93775	−	4.71647i	0.0965262	−	0.234944i
$404$		−	6.14711i		−	0.305830i
$405$	2.23563	−	0.0440169i	0.111090	−	0.00218722i
$406$	37.0987			1.84118
$407$	5.62458	+	5.62458i	0.278800	+	0.278800i
$408$	−5.99613			−0.296852
$409$	−1.76201	−	1.76201i	−0.0871258	−	0.0871258i	0.662201	−	0.749326i	$-0.269623\pi$
$409$	−1.76201	−	1.76201i	−0.0871258	−	0.0871258i	−0.749326	+	0.662201i	$0.769623\pi$
$410$	12.6027	+	12.1160i	0.622401	+	0.598365i
$411$	6.92868	+	6.92868i	0.341767	+	0.341767i
$412$	9.15260	−	9.15260i	0.450916	−	0.450916i
$413$	−10.9368	+	10.9368i	−0.538165	+	0.538165i
$414$	5.77210	−	5.77210i	0.283683	−	0.283683i
$415$	−1.60436	+	0.0315878i	−0.0787548	+	0.00155058i
$416$	1.38936	+	3.32711i	0.0681190	+	0.163125i
$417$	6.18962	−	6.18962i	0.303107	−	0.303107i
$418$	−3.49403			−0.170899
$419$		−	3.40468i		−	0.166330i	−0.996536	−	0.0831648i	$-0.973497\pi$
$419$		−	3.40468i		−	0.166330i	0.996536	−	0.0831648i	$-0.0265028\pi$
$420$	−7.01730	−	6.74632i	−0.342409	−	0.329187i
$421$	−10.4814	+	10.4814i	−0.510831	+	0.510831i	−0.914781	−	0.403950i	$-0.867637\pi$
$421$	−10.4814	+	10.4814i	−0.510831	+	0.510831i	0.403950	+	0.914781i	$0.367637\pi$
$422$		−	14.4467i		−	0.703252i
$423$		−	2.03197i		−	0.0987979i
$424$	−1.80319	+	1.80319i	−0.0875706	+	0.0875706i
$425$	−22.0175	−	20.3486i	−1.06801	−	0.987053i
$426$		−	11.5161i		−	0.557956i
$427$	−65.4695			−3.16829
$428$	0.249153	−	0.249153i	0.0120432	−	0.0120432i
$429$	−1.46863	−	3.51694i	−0.0709062	−	0.169800i
$430$	5.67142	+	5.45240i	0.273500	+	0.262938i
$431$	13.6277	−	13.6277i	0.656426	−	0.656426i	−0.298107	−	0.954532i	$-0.596355\pi$
$431$	13.6277	−	13.6277i	0.656426	−	0.656426i	0.954532	+	0.298107i	$0.0963552\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−27.3611	+	27.3611i	−1.31489	+	1.31489i	−0.397131	+	0.917762i	$0.629994\pi$
$433$	−27.3611	+	27.3611i	−1.31489	+	1.31489i	−0.917762	+	0.397131i	$0.870006\pi$
$434$	−4.35328	−	4.35328i	−0.208964	−	0.208964i
$435$	13.2066	−	13.7371i	0.633209	−	0.658644i
$436$	5.43020	+	5.43020i	0.260059	+	0.260059i
$437$	26.9822			1.29073
$438$	0.490429	+	0.490429i	0.0234336	+	0.0234336i
$439$	12.8276			0.612229			0.306114	−	0.951995i	$-0.400971\pi$
$439$	12.8276			0.612229			0.306114	+	0.951995i	$0.400971\pi$
$440$	1.63813	−	1.70393i	0.0780947	−	0.0812316i
$441$			11.9511i			0.569099i
$442$	8.21587	−	19.9974i	0.390789	−	0.951178i
$443$	−7.08127	−	7.08127i	−0.336441	−	0.336441i	0.518585	−	0.855026i	$-0.326459\pi$
$443$	−7.08127	−	7.08127i	−0.336441	−	0.336441i	−0.855026	+	0.518585i	$0.826459\pi$
$444$	5.32099	+	5.32099i	0.252523	+	0.252523i
$445$	−23.5355	+	24.4809i	−1.11569	+	1.16050i
$446$		−	4.67193i		−	0.221222i
$447$		−	13.9593i		−	0.660252i
$448$	4.35328			0.205673
$449$	−23.9344	+	23.9344i	−1.12954	+	1.12954i	−0.139283	+	0.990253i	$0.544480\pi$
$449$	−23.9344	+	23.9344i	−1.12954	+	1.12954i	−0.990253	+	0.139283i	$0.955520\pi$
$450$	−4.99613	+	0.196811i	−0.235520	+	0.00927777i
$451$	8.26431			0.389151
$452$	3.20629	+	3.20629i	0.150811	+	0.150811i
$453$			2.70512i			0.127097i
$454$	4.32302			0.202889
$455$	32.1144	−	14.1593i	1.50555	−	0.663798i
$456$	−3.30544			−0.154791
$457$			17.9156i			0.838055i	0.907974	+	0.419027i	$0.137629\pi$
$457$			17.9156i			0.838055i	−0.907974	+	0.419027i	$0.862371\pi$
$458$	−14.1938	−	14.1938i	−0.663233	−	0.663233i
$459$	5.99613			0.279875
$460$	−12.6502	+	13.1584i	−0.589820	+	0.613513i
$461$	4.67932	−	4.67932i	0.217938	−	0.217938i	−0.589691	−	0.807629i	$-0.700750\pi$
$461$	4.67932	−	4.67932i	0.217938	−	0.217938i	0.807629	+	0.589691i	$0.200750\pi$
$462$	−4.60166			−0.214089
$463$		−	15.4120i		−	0.716256i	−0.933673	−	0.358128i	$-0.883415\pi$
$463$		−	15.4120i		−	0.716256i	0.933673	−	0.358128i	$-0.116585\pi$
$464$			8.52201i			0.395624i
$465$	−3.16166	+	0.0622492i	−0.146619	+	0.00288674i
$466$	18.2904	+	18.2904i	0.847286	+	0.847286i
$467$	5.23438	+	5.23438i	0.242218	+	0.242218i	0.817767	−	0.575549i	$-0.195212\pi$
$467$	5.23438	+	5.23438i	0.242218	+	0.242218i	−0.575549	+	0.817767i	$0.695212\pi$
$468$	−1.38936	−	3.32711i	−0.0642233	−	0.153796i
$469$			18.1024i			0.835892i
$470$	0.0894411	+	4.54275i	0.00412561	+	0.209541i
$471$	−4.58470			−0.211252
$472$	−2.51231	−	2.51231i	−0.115638	−	0.115638i
$473$	3.71909			0.171004
$474$	4.48133	+	4.48133i	0.205834	+	0.205834i
$475$	−12.1374	−	11.2174i	−0.556904	−	0.514690i
$476$	−18.4575	−	18.4575i	−0.845998	−	0.845998i
$477$	1.80319	−	1.80319i	0.0825623	−	0.0825623i
$478$	−10.6351	+	10.6351i	−0.486437	+	0.486437i
$479$	−7.84354	+	7.84354i	−0.358380	+	0.358380i	−0.863216	−	0.504835i	$-0.831553\pi$
$479$	−7.84354	+	7.84354i	−0.358380	+	0.358380i	0.504835	+	0.863216i	$0.331553\pi$
$480$	1.54971	−	1.61196i	0.0707342	−	0.0735754i
$481$	−25.0366	+	10.4550i	−1.14157	+	0.476705i
$482$	−17.8276	+	17.8276i	−0.812025	+	0.812025i
$483$	35.5358			1.61693
$484$			9.88263i			0.449211i
$485$	−0.488111	−	24.7914i	−0.0221640	−	1.12572i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$		−	9.52685i		−	0.431703i	−0.976426	−	0.215851i	$-0.930747\pi$
$487$		−	9.52685i		−	0.431703i	0.976426	−	0.215851i	$-0.0692526\pi$
$488$		−	15.0391i		−	0.680788i
$489$	−16.2234	+	16.2234i	−0.733646	+	0.733646i
$490$	−0.526049	−	26.7182i	−0.0237645	−	1.20701i
$491$			29.7308i			1.34173i	0.741579	+	0.670865i	$0.234077\pi$
$491$			29.7308i			1.34173i	−0.741579	+	0.670865i	$0.765923\pi$
$492$	7.81823			0.352473
$493$	36.1325	−	36.1325i	1.62732	−	1.62732i
$494$	4.52910	−	11.0238i	0.203774	−	0.495984i
$495$	−1.63813	+	1.70393i	−0.0736284	+	0.0765859i
$496$	1.00000	−	1.00000i	0.0449013	−	0.0449013i
$497$	35.4492	−	35.4492i	1.59011	−	1.59011i
$498$	−0.507441	+	0.507441i	−0.0227390	+	0.0227390i
$499$	−15.1666	−	15.1666i	−0.678950	−	0.678950i	0.280813	−	0.959763i	$-0.409396\pi$
$499$	−15.1666	−	15.1666i	−0.678950	−	0.678950i	−0.959763	+	0.280813i	$0.909396\pi$
$500$	11.1608	−	0.659912i	0.499128	−	0.0295122i
$501$	−13.2481	−	13.2481i	−0.591883	−	0.591883i
$502$	5.40683			0.241319
$503$	3.96947	+	3.96947i	0.176990	+	0.176990i	0.790042	−	0.613052i	$-0.210059\pi$
$503$	3.96947	+	3.96947i	0.176990	+	0.176990i	−0.613052	+	0.790042i	$0.710059\pi$
$504$	−4.35328			−0.193911
$505$	−0.270576	−	13.7427i	−0.0120405	−	0.611541i
$506$			8.62873i			0.383594i
$507$	12.9998	−	0.0747921i	0.577341	−	0.00332163i
$508$	−1.80235	−	1.80235i	−0.0799663	−	0.0799663i
$509$	−5.97028	−	5.97028i	−0.264628	−	0.264628i	0.562303	−	0.826931i	$-0.309915\pi$
$509$	−5.97028	−	5.97028i	−0.264628	−	0.264628i	−0.826931	+	0.562303i	$0.809915\pi$
$510$	−13.4051	+	0.263931i	−0.593590	+	0.0116870i
$511$			3.01931i			0.133567i
$512$			1.00000i			0.0441942i
$513$	3.30544			0.145939
$514$	−9.31786	+	9.31786i	−0.410993	+	0.410993i
$515$	20.0590	−	20.8647i	0.883905	−	0.919410i
$516$	3.51834			0.154886
$517$	1.51880	+	1.51880i	0.0667968	+	0.0667968i
$518$			32.7585i			1.43933i
$519$	4.51177			0.198045
$520$	3.25255	+	7.37705i	0.142634	+	0.323505i
$521$	−17.6972			−0.775327			−0.387663	−	0.921801i	$-0.626718\pi$
$521$	−17.6972			−0.775327			−0.387663	+	0.921801i	$0.626718\pi$
$522$		−	8.52201i		−	0.372998i
$523$	−19.1972	−	19.1972i	−0.839436	−	0.839436i	0.149349	−	0.988785i	$-0.452282\pi$
$523$	−19.1972	−	19.1972i	−0.839436	−	0.839436i	−0.988785	+	0.149349i	$0.952282\pi$
$524$	−1.86044			−0.0812736
$525$	−15.9851	−	14.7734i	−0.697646	−	0.644765i
$526$	19.7684	−	19.7684i	0.861942	−	0.861942i
$527$	−8.47980			−0.369386
$528$		−	1.05706i		−	0.0460025i
$529$		−	43.6343i		−	1.89714i
$530$	−3.95190	+	4.11064i	−0.171660	+	0.178555i
$531$	2.51231	+	2.51231i	0.109025	+	0.109025i
$532$	−10.1749	−	10.1749i	−0.441138	−	0.441138i
$533$	−10.7125	+	26.0742i	−0.464011	+	1.12940i
$534$			15.1870i			0.657208i
$535$	0.546047	−	0.567981i	0.0236077	−	0.0245560i
$536$	−4.15834			−0.179613
$537$	−16.1364	−	16.1364i	−0.696337	−	0.696337i
$538$	−8.27192			−0.356628
$539$	−8.93284	−	8.93284i	−0.384765	−	0.384765i
$540$	−1.54971	+	1.61196i	−0.0666888	+	0.0693676i
$541$	−20.1390	−	20.1390i	−0.865843	−	0.865843i	0.126166	−	0.992009i	$-0.459733\pi$
$541$	−20.1390	−	20.1390i	−0.865843	−	0.865843i	−0.992009	+	0.126166i	$0.959733\pi$
$542$	−18.0549	+	18.0549i	−0.775526	+	0.775526i
$543$	1.96800	−	1.96800i	0.0844548	−	0.0844548i
$544$	4.23990	−	4.23990i	0.181784	−	0.181784i
$545$	12.3790	+	11.9009i	0.530257	+	0.509780i
$546$	5.96485	−	14.5184i	0.255272	−	0.621331i
$547$	−4.36351	+	4.36351i	−0.186570	+	0.186570i	−0.794212	−	0.607641i	$-0.792116\pi$
$547$	−4.36351	+	4.36351i	−0.186570	+	0.186570i	0.607641	+	0.794212i	$0.292116\pi$
$548$	−9.79864			−0.418577
$549$			15.0391i			0.641853i
$550$	3.58725	−	3.88147i	0.152961	−	0.165506i
$551$	19.9185	−	19.9185i	0.848555	−	0.848555i
$552$			8.16298i			0.347440i
$553$			27.5892i			1.17321i
$554$	−3.55032	+	3.55032i	−0.150839	+	0.150839i
$555$	12.1300	+	11.6616i	0.514890	+	0.495006i
$556$			8.75345i			0.371229i
$557$	8.54604			0.362107			0.181054	−	0.983473i	$-0.442049\pi$
$557$	8.54604			0.362107			0.181054	+	0.983473i	$0.442049\pi$
$558$	−1.00000	+	1.00000i	−0.0423334	+	0.0423334i
$559$	−4.82082	+	11.7339i	−0.203899	+	0.496289i
$560$	9.73235	−	0.191618i	0.411267	−	0.00809733i
$561$	−4.48181	+	4.48181i	−0.189222	+	0.189222i
$562$	−0.810247	+	0.810247i	−0.0341782	+	0.0341782i
$563$	14.9876	−	14.9876i	0.631654	−	0.631654i	−0.316829	−	0.948483i	$-0.602618\pi$
$563$	14.9876	−	14.9876i	0.631654	−	0.631654i	0.948483	+	0.316829i	$0.102618\pi$
$564$	1.43682	+	1.43682i	0.0605011	+	0.0605011i
$565$	7.30921	+	7.02695i	0.307501	+	0.295626i
$566$	−8.92833	−	8.92833i	−0.375286	−	0.375286i
$567$	4.35328			0.182821
$568$	8.14309	+	8.14309i	0.341677	+	0.341677i
$569$	−20.2802			−0.850189			−0.425094	−	0.905149i	$-0.639759\pi$
$569$	−20.2802			−0.850189			−0.425094	+	0.905149i	$0.639759\pi$
$570$	−7.38975	+	0.145495i	−0.309522	+	0.00609411i
$571$			32.3856i			1.35530i	0.735387	+	0.677648i	$0.237000\pi$
$571$			32.3856i			1.35530i	−0.735387	+	0.677648i	$0.763000\pi$
$572$	3.52533	+	1.44837i	0.147402	+	0.0605596i
$573$	6.77035	+	6.77035i	0.282835	+	0.282835i
$574$	24.0664	+	24.0664i	1.00451	+	1.00451i
$575$	−27.7021	+	29.9742i	−1.15526	+	1.25001i
$576$		−	1.00000i		−	0.0416667i
$577$			14.3112i			0.595784i	0.954600	+	0.297892i	$0.0962836\pi$
$577$			14.3112i			0.595784i	−0.954600	+	0.297892i	$0.903716\pi$
$578$	−18.9535			−0.788362
$579$	18.3075	−	18.3075i	0.760833	−	0.760833i
$580$	0.375112	+	19.0521i	0.0155757	+	0.791095i
$581$	−3.12404			−0.129607
$582$	−7.84124	−	7.84124i	−0.325030	−	0.325030i
$583$			2.69559i			0.111640i
$584$	−0.693572			−0.0287002
$585$	−3.25255	−	7.37705i	−0.134477	−	0.305004i
$586$	−7.40280			−0.305807
$587$		−	15.7965i		−	0.651993i	−0.945371	−	0.325996i	$-0.894300\pi$
$587$		−	15.7965i		−	0.651993i	0.945371	−	0.325996i	$-0.105700\pi$
$588$	−8.45068	−	8.45068i	−0.348500	−	0.348500i
$589$	−4.67459			−0.192613
$590$	−5.72719	−	5.50603i	−0.235785	−	0.226679i
$591$	5.84715	−	5.84715i	0.240520	−	0.240520i
$592$	−7.52501			−0.309276
$593$			8.95630i			0.367791i	0.982946	+	0.183896i	$0.0588708\pi$
$593$			8.95630i			0.367791i	−0.982946	+	0.183896i	$0.941129\pi$
$594$			1.05706i			0.0433715i
$595$	−42.0766	−	40.4518i	−1.72497	−	1.65836i
$596$	9.87070	+	9.87070i	0.404320	+	0.404320i
$597$	−4.49436	−	4.49436i	−0.183942	−	0.183942i
$598$	−27.2240	−	11.1849i	−1.11327	−	0.457384i
$599$		−	18.7161i		−	0.764721i	−0.924013	−	0.382360i	$-0.875111\pi$
$599$		−	18.7161i		−	0.764721i	0.924013	−	0.382360i	$-0.124889\pi$
$600$	3.39363	−	3.67196i	0.138544	−	0.149907i
$601$	−11.4853			−0.468494			−0.234247	−	0.972177i	$-0.575262\pi$
$601$	−11.4853			−0.468494			−0.234247	+	0.972177i	$0.575262\pi$
$602$	10.8303	+	10.8303i	0.441410	+	0.441410i
$603$	4.15834			0.169341
$604$	−1.91281	−	1.91281i	−0.0778310	−	0.0778310i
$605$	0.435002	+	22.0940i	0.0176854	+	0.898247i
$606$	−4.34666	−	4.34666i	−0.176571	−	0.176571i
$607$	19.9293	−	19.9293i	0.808906	−	0.808906i	−0.175563	−	0.984468i	$-0.556174\pi$
$607$	19.9293	−	19.9293i	0.808906	−	0.808906i	0.984468	+	0.175563i	$0.0561744\pi$
$608$	2.33730	−	2.33730i	0.0947899	−	0.0947899i
$609$	26.2327	−	26.2327i	1.06300	−	1.06300i
$610$	−0.661974	−	33.6219i	−0.0268026	−	1.36131i
$611$	−6.76060	+	2.82314i	−0.273505	+	0.114212i
$612$	−4.23990	+	4.23990i	−0.171388	+	0.171388i
$613$	−33.6528			−1.35922			−0.679612	−	0.733572i	$-0.737852\pi$
$613$	−33.6528			−1.35922			−0.679612	+	0.733572i	$0.737852\pi$
$614$		−	0.825032i		−	0.0332956i
$615$	17.4787	−	0.344134i	0.704810	−	0.0138768i
$616$	3.25387	−	3.25387i	0.131102	−	0.131102i
$617$			25.0645i			1.00906i	0.863394	+	0.504530i	$0.168334\pi$
$617$			25.0645i			1.00906i	−0.863394	+	0.504530i	$0.831666\pi$
$618$		−	12.9437i		−	0.520673i
$619$	−26.2122	+	26.2122i	−1.05356	+	1.05356i	−0.0550739	+	0.998482i	$0.517539\pi$
$619$	−26.2122	+	26.2122i	−1.05356	+	1.05356i	−0.998482	+	0.0550739i	$0.982461\pi$
$620$	2.19162	−	2.27965i	0.0880175	−	0.0915530i
$621$		−	8.16298i		−	0.327569i
$622$	11.9446			0.478935
$623$	−46.7493	+	46.7493i	−1.87297	+	1.87297i
$624$	3.33505	+	1.37020i	0.133509	+	0.0548518i
$625$	24.9225	−	1.96659i	0.996901	−	0.0786635i
$626$	10.4828	−	10.4828i	0.418977	−	0.418977i
$627$	−2.47065	+	2.47065i	−0.0986684	+	0.0986684i
$628$	3.24188	−	3.24188i	0.129365	−	0.129365i
$629$	31.9053	+	31.9053i	1.27215	+	1.27215i
$630$	−9.73235	+	0.191618i	−0.387746	+	0.00763424i
$631$	−19.3849	−	19.3849i	−0.771700	−	0.771700i	0.206703	−	0.978404i	$-0.433726\pi$
$631$	−19.3849	−	19.3849i	−0.771700	−	0.771700i	−0.978404	+	0.206703i	$0.933726\pi$
$632$	−6.33756			−0.252095
$633$	−10.2153	−	10.2153i	−0.406023	−	0.406023i
$634$	4.72102			0.187496
$635$	−4.10873	−	3.95006i	−0.163050	−	0.156753i
$636$			2.55009i			0.101118i
$637$	39.7626	−	16.6044i	1.57545	−	0.657889i
$638$	6.36978	+	6.36978i	0.252182	+	0.252182i
$639$	−8.14309	−	8.14309i	−0.322136	−	0.322136i
$640$	0.0440169	+	2.23563i	0.00173992	+	0.0883712i
$641$			15.4831i			0.611544i	0.952105	+	0.305772i	$0.0989145\pi$
$641$			15.4831i			0.611544i	−0.952105	+	0.305772i	$0.901085\pi$
$642$		−	0.352355i		−	0.0139063i
$643$	44.2903			1.74664			0.873319	−	0.487149i	$-0.161963\pi$
$643$	44.2903			1.74664			0.873319	+	0.487149i	$0.161963\pi$
$644$	−25.1276	+	25.1276i	−0.990166	+	0.990166i
$645$	7.86573	−	0.154866i	0.309713	−	0.00609786i
$646$	−19.8198			−0.779800
$647$	−7.03072	−	7.03072i	−0.276406	−	0.276406i	0.555267	−	0.831672i	$-0.312616\pi$
$647$	−7.03072	−	7.03072i	−0.276406	−	0.276406i	−0.831672	+	0.555267i	$0.812616\pi$
$648$			1.00000i			0.0392837i
$649$	−3.75566			−0.147423
$650$	7.59624	+	16.3492i	0.297949	+	0.641269i
$651$	−6.15647			−0.241291
$652$		−	22.9433i		−	0.898529i
$653$	−30.6226	−	30.6226i	−1.19836	−	1.19836i	−0.974659	−	0.223697i	$-0.928187\pi$
$653$	−30.6226	−	30.6226i	−1.19836	−	1.19836i	−0.223697	−	0.974659i	$-0.571813\pi$
$654$	7.67946			0.300291
$655$	−4.15926	+	0.0818906i	−0.162516	+	0.00319973i
$656$	−5.52833	+	5.52833i	−0.215845	+	0.215845i
$657$	0.693572			0.0270588
$658$			8.84575i			0.344843i
$659$			28.2203i			1.09931i	0.835393	+	0.549653i	$0.185240\pi$
$659$			28.2203i			1.09931i	−0.835393	+	0.549653i	$0.814760\pi$
$660$	−0.0465283	−	2.36319i	−0.00181111	−	0.0919871i
$661$	−34.2057	−	34.2057i	−1.33045	−	1.33045i	−0.904969	−	0.425478i	$-0.860106\pi$
$661$	−34.2057	−	34.2057i	−1.33045	−	1.33045i	−0.425478	−	0.904969i	$-0.639894\pi$
$662$	−10.9736	−	10.9736i	−0.426500	−	0.426500i
$663$	−8.33078	−	19.9498i	−0.323541	−	0.774785i
$664$		−	0.717629i		−	0.0278494i
$665$	−23.1953	−	22.2995i	−0.899473	−	0.864738i
$666$	7.52501			0.291588
$667$	−49.1899	−	49.1899i	−1.90464	−	1.90464i
$668$	18.7357			0.724905
$669$	−3.30355	−	3.30355i	−0.127723	−	0.127723i
$670$	−9.29652	+	0.183037i	−0.359156	+	0.00707133i
$671$	−11.2410	−	11.2410i	−0.433954	−	0.433954i
$672$	3.07824	−	3.07824i	0.118746	−	0.118746i
$673$	23.9338	−	23.9338i	0.922579	−	0.922579i	−0.0746326	−	0.997211i	$-0.523778\pi$
$673$	23.9338	−	23.9338i	0.922579	−	0.922579i	0.997211	+	0.0746326i	$0.0237784\pi$
$674$	4.30540	−	4.30540i	0.165838	−	0.165838i
$675$	−3.39363	+	3.67196i	−0.130621	+	0.141334i
$676$	−9.13935	+	9.24512i	−0.351513	+	0.355582i
$677$	−0.515714	+	0.515714i	−0.0198205	+	0.0198205i	−0.716948	−	0.697127i	$-0.754461\pi$
$677$	−0.515714	+	0.515714i	−0.0198205	+	0.0198205i	0.697127	+	0.716948i	$0.254461\pi$
$678$	4.53437			0.174142
$679$		−	48.2744i		−	1.85260i
$680$	9.29224	−	9.66550i	0.356341	−	0.370655i
$681$	3.05684	−	3.05684i	0.117138	−	0.117138i
$682$		−	1.49490i		−	0.0572428i
$683$			25.4279i			0.972970i	0.873689	+	0.486485i	$0.161721\pi$
$683$			25.4279i			0.972970i	−0.873689	+	0.486485i	$0.838279\pi$
$684$	−2.33730	+	2.33730i	−0.0893688	+	0.0893688i
$685$	−21.9062	+	0.431305i	−0.836992	+	0.0164793i
$686$		−	21.5534i		−	0.822913i
$687$	−20.0731			−0.765836
$688$	−2.48784	+	2.48784i	−0.0948482	+	0.0948482i
$689$	−8.50469	−	3.49413i	−0.324003	−	0.133116i
$690$	0.359309	+	18.2494i	0.0136787	+	0.694745i
$691$	−22.7521	+	22.7521i	−0.865531	+	0.865531i	−0.991974	−	0.126443i	$-0.959644\pi$
$691$	−22.7521	+	22.7521i	−0.865531	+	0.865531i	0.126443	+	0.991974i	$0.459644\pi$
$692$	−3.19031	+	3.19031i	−0.121277	+	0.121277i
$693$	−3.25387	+	3.25387i	−0.123604	+	0.123604i
$694$	−12.9246	−	12.9246i	−0.490610	−	0.490610i
$695$	0.385299	+	19.5695i	0.0146152	+	0.742314i
$696$	6.02597	+	6.02597i	0.228414	+	0.228414i
$697$	46.8791			1.77567
$698$	−19.6667	−	19.6667i	−0.744395	−	0.744395i
$699$	25.8665			0.978361
$700$	21.7495	−	0.856775i	0.822056	−	0.0323831i
$701$			30.6138i			1.15627i	0.815942	+	0.578134i	$0.196219\pi$
$701$			30.6138i			1.15627i	−0.815942	+	0.578134i	$0.803781\pi$
$702$	−3.33505	−	1.37020i	−0.125873	−	0.0517147i
$703$	17.5882	+	17.5882i	0.663351	+	0.663351i
$704$	0.747451	+	0.747451i	0.0281706	+	0.0281706i
$705$	3.27545	+	3.14896i	0.123361	+	0.118597i
$706$			7.00486i			0.263631i
$707$		−	26.7601i		−	1.00642i
$708$	−3.55294			−0.133528
$709$	18.5237	−	18.5237i	0.695673	−	0.695673i	−0.267801	−	0.963474i	$-0.586297\pi$
$709$	18.5237	−	18.5237i	0.695673	−	0.695673i	0.963474	+	0.267801i	$0.0862970\pi$
$710$	18.5634	+	17.8465i	0.696673	+	0.669769i
$711$	6.33756			0.237677
$712$	−10.7389	−	10.7389i	−0.402456	−	0.402456i
$713$			11.5442i			0.432334i
$714$	−26.1028			−0.976874
$715$	7.94511	+	3.08286i	0.297130	+	0.115293i
$716$	22.8203			0.852835
$717$			15.0403i			0.561690i
$718$	0.0274935	+	0.0274935i	0.00102605	+	0.00102605i
$719$	28.0227			1.04507			0.522535	−	0.852618i	$-0.324986\pi$
$719$	28.0227			1.04507			0.522535	+	0.852618i	$0.324986\pi$
$720$	−0.0440169	−	2.23563i	−0.00164041	−	0.0833172i
$721$	39.8438	−	39.8438i	1.48386	−	1.48386i
$722$	8.07409			0.300487
$723$			25.2120i			0.937646i
$724$			2.78317i			0.103436i
$725$	1.67723	+	42.5770i	0.0622906	+	1.58127i
$726$	6.98808	+	6.98808i	0.259352	+	0.259352i
$727$	−1.57744	−	1.57744i	−0.0585040	−	0.0585040i	0.677249	−	0.735753i	$-0.263172\pi$
$727$	−1.57744	−	1.57744i	−0.0585040	−	0.0585040i	−0.735753	+	0.677249i	$0.763172\pi$
$728$	6.04828	+	14.4839i	0.224164	+	0.536808i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.55057	+	0.0305288i	−0.0573893	+	0.00112992i
$731$	21.0964			0.780280
$732$	−10.6343	−	10.6343i	−0.393053	−	0.393053i
$733$	37.4192			1.38211			0.691055	−	0.722803i	$-0.257146\pi$
$733$	37.4192			1.38211			0.691055	+	0.722803i	$0.257146\pi$
$734$	−0.657074	−	0.657074i	−0.0242531	−	0.0242531i
$735$	−19.2646	−	18.5207i	−0.710586	−	0.683145i
$736$	−5.77210	−	5.77210i	−0.212762	−	0.212762i
$737$	−3.10815	+	3.10815i	−0.114490	+	0.114490i
$738$	5.52833	−	5.52833i	0.203500	−	0.203500i
$739$	11.6276	−	11.6276i	0.427727	−	0.427727i	−0.460126	−	0.887853i	$-0.652196\pi$
$739$	11.6276	−	11.6276i	0.427727	−	0.427727i	0.887853	+	0.460126i	$0.152196\pi$
$740$	−16.8232	+	0.331227i	−0.618432	+	0.0121762i
$741$	−4.59245	−	10.9976i	−0.168708	−	0.404005i
$742$	−7.84979	+	7.84979i	−0.288175	+	0.288175i
$743$	45.9533			1.68586			0.842931	−	0.538021i	$-0.180828\pi$
$743$	45.9533			1.68586			0.842931	+	0.538021i	$0.180828\pi$
$744$		−	1.41421i		−	0.0518476i
$745$	22.5018	+	21.6328i	0.824401	+	0.792565i
$746$	−17.0729	+	17.0729i	−0.625084	+	0.625084i
$747$			0.717629i			0.0262567i
$748$		−	6.33824i		−	0.231749i
$749$	1.08463	−	1.08463i	0.0396316	−	0.0396316i
$750$	7.42528	−	8.35854i	0.271133	−	0.305211i
$751$			24.0277i			0.876784i	0.898784	+	0.438392i	$0.144452\pi$
$751$			24.0277i			0.876784i	−0.898784	+	0.438392i	$0.855548\pi$
$752$	−2.03197			−0.0740984
$753$	3.82321	−	3.82321i	0.139325	−	0.139325i
$754$	−28.3537	+	11.8401i	−1.03258	+	0.431193i
$755$	−4.36053	−	4.19214i	−0.158696	−	0.152568i
$756$	−3.07824	+	3.07824i	−0.111954	+	0.111954i
$757$	−21.3224	+	21.3224i	−0.774976	+	0.774976i	−0.978972	−	0.203995i	$-0.934607\pi$
$757$	−21.3224	+	21.3224i	−0.774976	+	0.774976i	0.203995	+	0.978972i	$0.434607\pi$
$758$	10.7212	−	10.7212i	0.389412	−	0.389412i
$759$	6.10143	+	6.10143i	0.221468	+	0.221468i
$760$	5.12246	−	5.32822i	0.185811	−	0.193275i
$761$	−7.69781	−	7.69781i	−0.279045	−	0.279045i	0.553683	−	0.832728i	$-0.313222\pi$
$761$	−7.69781	−	7.69781i	−0.279045	−	0.279045i	−0.832728	+	0.553683i	$0.813222\pi$
$762$	−2.54891			−0.0923371
$763$	23.6392	+	23.6392i	0.855796	+	0.855796i
$764$	−9.57472			−0.346401
$765$	−9.29224	+	9.66550i	−0.335962	+	0.349457i
$766$			13.1664i			0.475723i
$767$	4.86823	−	11.8492i	0.175782	−	0.427852i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	19.5607	+	19.5607i	0.705376	+	0.705376i	0.965559	−	0.260183i	$-0.0837830\pi$
$769$	19.5607	+	19.5607i	0.705376	+	0.705376i	−0.260183	+	0.965559i	$0.583783\pi$
$770$	7.13123	−	7.41768i	0.256992	−	0.267315i
$771$			13.1774i			0.474574i
$772$			25.8907i			0.931826i
$773$	17.3275			0.623228			0.311614	−	0.950209i	$-0.399130\pi$
$773$	17.3275			0.623228			0.311614	+	0.950209i	$0.399130\pi$
$774$	2.48784	−	2.48784i	0.0894237	−	0.0894237i
$775$	4.79931	−	5.19294i	0.172396	−	0.186536i
$776$	11.0892			0.398079
$777$	23.1638	+	23.1638i	0.830995	+	0.830995i
$778$		−	6.12633i		−	0.219640i
$779$	25.8427			0.925910
$780$	7.51627	+	2.91646i	0.269125	+	0.104426i
$781$	12.1731			0.435589
$782$			48.9463i			1.75031i
$783$	−6.02597	−	6.02597i	−0.215351	−	0.215351i
$784$	11.9511			0.426824
$785$	7.10495	−	7.39035i	0.253587	−	0.263773i
$786$	−1.31553	+	1.31553i	−0.0469233	+	0.0469233i
$787$	29.5923			1.05485			0.527426	−	0.849601i	$-0.323157\pi$
$787$	29.5923			1.05485			0.527426	+	0.849601i	$0.323157\pi$
$788$			8.26912i			0.294575i
$789$		−	27.9567i		−	0.995285i
$790$	−14.1685	+	0.278960i	−0.504092	+	0.00992494i
$791$	13.9579	+	13.9579i	0.496285	+	0.496285i
$792$	−0.747451	−	0.747451i	−0.0265595	−	0.0265595i
$793$	50.0368	−	20.8948i	1.77686	−	0.741994i
$794$		−	10.5494i		−	0.374383i
$795$	0.112247	+	5.70108i	0.00398100	+	0.202196i
$796$	6.35598			0.225282
$797$	−29.3320	−	29.3320i	−1.03899	−	1.03899i	−0.999208	−	0.0397855i	$-0.987333\pi$
$797$	−29.3320	−	29.3320i	−1.03899	−	1.03899i	−0.0397855	−	0.999208i	$-0.512667\pi$
$798$	−14.3895			−0.509383
$799$	8.61536	+	8.61536i	0.304790	+	0.304790i
$800$	0.196811	+	4.99613i	0.00695833	+	0.176640i
$801$	10.7389	+	10.7389i	0.379439	+	0.379439i
$802$	−15.8695	+	15.8695i	−0.560372	+	0.560372i
$803$	−0.518411	+	0.518411i	−0.0182943	+	0.0182943i
$804$	−2.94039	+	2.94039i	−0.103699	+	0.103699i
$805$	−55.0701	+	57.2821i	−1.94096	+	2.01893i
$806$	4.71647	+	1.93775i	0.166131	+	0.0682544i
$807$	−5.84913	+	5.84913i	−0.205899	+	0.205899i
$808$	6.14711			0.216254
$809$		−	38.8185i		−	1.36478i	−0.730986	−	0.682392i	$-0.760940\pi$
$809$		−	38.8185i		−	1.36478i	0.730986	−	0.682392i	$-0.239060\pi$
$810$	0.0440169	+	2.23563i	0.00154659	+	0.0785522i
$811$	1.74363	−	1.74363i	0.0612271	−	0.0612271i	−0.675830	−	0.737057i	$-0.736215\pi$
$811$	1.74363	−	1.74363i	0.0612271	−	0.0612271i	0.737057	+	0.675830i	$0.236215\pi$
$812$			37.0987i			1.30191i
$813$			25.5335i			0.895500i
$814$	−5.62458	+	5.62458i	−0.197141	+	0.197141i
$815$	−1.00989	−	51.2929i	−0.0353750	−	1.79671i
$816$		−	5.99613i		−	0.209906i
$817$	11.6297			0.406870
$818$	1.76201	−	1.76201i	0.0616072	−	0.0616072i
$819$	−6.04828	−	14.4839i	−0.211344	−	0.506107i
$820$	−12.1160	+	12.6027i	−0.423108	+	0.440104i
$821$	−23.4616	+	23.4616i	−0.818816	+	0.818816i	−0.985936	−	0.167121i	$-0.946553\pi$
$821$	−23.4616	+	23.4616i	−0.818816	+	0.818816i	0.167121	+	0.985936i	$0.446553\pi$
$822$	−6.92868	+	6.92868i	−0.241666	+	0.241666i
$823$	−15.3709	+	15.3709i	−0.535797	+	0.535797i	−0.922292	−	0.386495i	$-0.873686\pi$
$823$	−15.3709	+	15.3709i	−0.535797	+	0.535797i	0.386495	+	0.922292i	$0.373686\pi$
$824$	9.15260	+	9.15260i	0.318846	+	0.318846i
$825$	−0.208040	−	5.28118i	−0.00724304	−	0.183867i
$826$	−10.9368	−	10.9368i	−0.380540	−	0.380540i
$827$	56.4519			1.96303			0.981513	−	0.191397i	$-0.0613019\pi$
$827$	56.4519			1.96303			0.981513	+	0.191397i	$0.0613019\pi$
$828$	5.77210	+	5.77210i	0.200594	+	0.200594i
$829$	19.2980			0.670246			0.335123	−	0.942174i	$-0.391222\pi$
$829$	19.2980			0.670246			0.335123	+	0.942174i	$0.391222\pi$
$830$	−0.0315878	−	1.60436i	−0.00109643	−	0.0556881i
$831$			5.02091i			0.174173i
$832$	−3.32711	+	1.38936i	−0.115347	+	0.0481674i
$833$	−50.6714	−	50.6714i	−1.75566	−	1.75566i
$834$	6.18962	+	6.18962i	0.214329	+	0.214329i
$835$	41.8861	−	0.824686i	1.44953	−	0.0285394i
$836$		−	3.49403i		−	0.120844i
$837$			1.41421i			0.0488824i
$838$	3.40468			0.117613
$839$	23.4259	−	23.4259i	0.808753	−	0.808753i	−0.175692	−	0.984445i	$-0.556216\pi$
$839$	23.4259	−	23.4259i	0.808753	−	0.808753i	0.984445	+	0.175692i	$0.0562162\pi$
$840$	6.74632	−	7.01730i	0.232770	−	0.242120i
$841$	−43.6246			−1.50430
$842$	−10.4814	−	10.4814i	−0.361212	−	0.361212i
$843$			1.14586i			0.0394656i
$844$	14.4467			0.497274
$845$	−20.0253	+	21.0710i	−0.688891	+	0.724864i
$846$	2.03197			0.0698607
$847$			43.0219i			1.47825i
$848$	−1.80319	−	1.80319i	−0.0619218	−	0.0619218i
$849$	−12.6266			−0.433343
$850$	20.3486	−	22.0175i	0.697952	−	0.755195i
$851$	43.4351	−	43.4351i	1.48894	−	1.48894i
$852$	11.5161			0.394534
$853$			19.8388i			0.679269i	0.940558	+	0.339634i	$0.110303\pi$
$853$			19.8388i			0.679269i	−0.940558	+	0.339634i	$0.889697\pi$
$854$		−	65.4695i		−	2.24032i
$855$	−5.12246	+	5.32822i	−0.175184	+	0.182221i
$856$	0.249153	+	0.249153i	0.00851586	+	0.00851586i
$857$	4.56177	+	4.56177i	0.155827	+	0.155827i	0.780715	−	0.624888i	$-0.214855\pi$
$857$	4.56177	+	4.56177i	0.155827	+	0.155827i	−0.624888	+	0.780715i	$0.714855\pi$
$858$	3.51694	−	1.46863i	0.120066	−	0.0501383i
$859$		−	2.44142i		−	0.0833002i	−0.999132	−	0.0416501i	$-0.986739\pi$
$859$		−	2.44142i		−	0.0833002i	0.999132	−	0.0416501i	$-0.0132615\pi$
$860$	−5.45240	+	5.67142i	−0.185925	+	0.193394i
$861$	34.0350			1.15991
$862$	13.6277	+	13.6277i	0.464163	+	0.464163i
$863$	−4.64499			−0.158117			−0.0790587	−	0.996870i	$-0.525191\pi$
$863$	−4.64499			−0.158117			−0.0790587	+	0.996870i	$0.525191\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	−6.99193	+	7.27279i	−0.237733	+	0.247282i
$866$	−27.3611	−	27.3611i	−0.929770	−	0.929770i
$867$	−13.4022	+	13.4022i	−0.455161	+	0.455161i
$868$	4.35328	−	4.35328i	0.147760	−	0.147760i
$869$	−4.73702	+	4.73702i	−0.160692	+	0.160692i
$870$	13.7371	+	13.2066i	0.465732	+	0.447746i
$871$	−5.77743	−	13.8353i	−0.195761	−	0.468790i
$872$	−5.43020	+	5.43020i	−0.183890	+	0.183890i
$873$	−11.0892			−0.375312
$874$			26.9822i			0.912687i
$875$	48.5863	−	2.87278i	1.64252	−	0.0971178i
$876$	−0.490429	+	0.490429i	−0.0165701	+	0.0165701i
$877$			26.2839i			0.887543i	0.896140	+	0.443772i	$0.146360\pi$
$877$			26.2839i			0.887543i	−0.896140	+	0.443772i	$0.853640\pi$
$878$			12.8276i			0.432911i
$879$	−5.23457	+	5.23457i	−0.176558	+	0.176558i
$880$	1.70393	+	1.63813i	0.0574394	+	0.0552213i
$881$		−	28.1817i		−	0.949464i	−0.880130	−	0.474732i	$-0.842545\pi$
$881$		−	28.1817i		−	0.949464i	0.880130	−	0.474732i	$-0.157455\pi$
$882$	−11.9511			−0.402413
$883$	−10.2824	+	10.2824i	−0.346030	+	0.346030i	−0.858629	−	0.512598i	$-0.828683\pi$
$883$	−10.2824	+	10.2824i	−0.346030	+	0.346030i	0.512598	+	0.858629i	$0.328683\pi$
$884$	19.9974	+	8.21587i	0.672585	+	0.276330i
$885$	−7.94308	+	0.156389i	−0.267004	+	0.00525697i
$886$	7.08127	−	7.08127i	0.237900	−	0.237900i
$887$	−16.7826	+	16.7826i	−0.563505	+	0.563505i	−0.930301	−	0.366796i	$-0.880455\pi$
$887$	−16.7826	+	16.7826i	−0.563505	+	0.563505i	0.366796	+	0.930301i	$0.380455\pi$
$888$	−5.32099	+	5.32099i	−0.178561	+	0.178561i
$889$	−7.84614	−	7.84614i	−0.263151	−	0.263151i
$890$	−24.4809	−	23.5355i	−0.820600	−	0.788911i
$891$	0.747451	+	0.747451i	0.0250406	+	0.0250406i
$892$	4.67193			0.156428
$893$	4.74932	+	4.74932i	0.158930	+	0.158930i
$894$	13.9593			0.466868
$895$	51.0179	−	1.00448i	1.70534	−	0.0335760i
$896$			4.35328i			0.145433i
$897$	−27.1592	+	11.3413i	−0.906818	+	0.378676i
$898$	−23.9344	−	23.9344i	−0.798703	−	0.798703i
$899$	8.52201	+	8.52201i	0.284225	+	0.284225i
$900$	−0.196811	−	4.99613i	−0.00656037	−	0.166538i
$901$			15.2907i			0.509406i
$902$			8.26431i			0.275171i
$903$	15.3163			0.509696
$904$	−3.20629	+	3.20629i	−0.106639	+	0.106639i
$905$	0.122506	+	6.22215i	0.00407225	+	0.206831i
$906$	−2.70512			−0.0898715
$907$	27.6083	+	27.6083i	0.916719	+	0.916719i	0.996789	−	0.0800702i	$-0.0255144\pi$
$907$	27.6083	+	27.6083i	0.916719	+	0.916719i	−0.0800702	+	0.996789i	$0.525514\pi$
$908$			4.32302i			0.143464i
$909$	−6.14711			−0.203887
$910$	14.1593	+	32.1144i	0.469376	+	1.06458i
$911$	−46.1944			−1.53049			−0.765244	−	0.643740i	$-0.777382\pi$
$911$	−46.1944			−1.53049			−0.765244	+	0.643740i	$0.777382\pi$
$912$		−	3.30544i		−	0.109454i
$913$	−0.536393	−	0.536393i	−0.0177520	−	0.0177520i
$914$	−17.9156			−0.592594
$915$	−24.2424	−	23.3062i	−0.801429	−	0.770480i
$916$	14.1938	−	14.1938i	0.468977	−	0.468977i
$917$	−8.09901			−0.267453
$918$			5.99613i			0.197902i
$919$			37.4976i			1.23693i	0.785812	+	0.618465i	$0.212245\pi$
$919$			37.4976i			1.23693i	−0.785812	+	0.618465i	$0.787755\pi$
$920$	−13.1584	−	12.6502i	−0.433819	−	0.417066i
$921$	−0.583385	−	0.583385i	−0.0192232	−	0.0192232i
$922$	4.67932	+	4.67932i	0.154105	+	0.154105i
$923$	−15.7793	+	38.4067i	−0.519382	+	1.26417i
$924$		−	4.60166i		−	0.151384i
$925$	−37.5959	+	1.48101i	−1.23615	+	0.0486952i
$926$	15.4120			0.506469
$927$	−9.15260	−	9.15260i	−0.300611	−	0.300611i
$928$	−8.52201			−0.279749
$929$	−5.41475	−	5.41475i	−0.177652	−	0.177652i	0.612679	−	0.790332i	$-0.290092\pi$
$929$	−5.41475	−	5.41475i	−0.177652	−	0.177652i	−0.790332	+	0.612679i	$0.790092\pi$
$930$	−0.0622492	−	3.16166i	−0.00204123	−	0.103675i
$931$	−27.9332	−	27.9332i	−0.915473	−	0.915473i
$932$	−18.2904	+	18.2904i	−0.599122	+	0.599122i
$933$	8.44612	−	8.44612i	0.276514	−	0.276514i
$934$	−5.23438	+	5.23438i	−0.171274	+	0.171274i
$935$	−0.278989	−	14.1700i	−0.00912393	−	0.463408i
$936$	3.32711	−	1.38936i	0.108750	−	0.0454127i
$937$	24.7191	−	24.7191i	0.807539	−	0.807539i	−0.176722	−	0.984261i	$-0.556549\pi$
$937$	24.7191	−	24.7191i	0.807539	−	0.807539i	0.984261	+	0.176722i	$0.0565492\pi$
$938$	−18.1024			−0.591065
$939$		−	14.8249i		−	0.483793i
$940$	−4.54275	+	0.0894411i	−0.148168	+	0.00291725i
$941$	4.21662	−	4.21662i	0.137458	−	0.137458i	−0.635030	−	0.772488i	$-0.719012\pi$
$941$	4.21662	−	4.21662i	0.137458	−	0.137458i	0.772488	+	0.635030i	$0.219012\pi$
$942$		−	4.58470i		−	0.149378i
$943$		−	63.8201i		−	2.07827i
$944$	2.51231	−	2.51231i	0.0817688	−	0.0817688i
$945$	−6.74632	+	7.01730i	−0.219458	+	0.228273i
$946$			3.71909i			0.120918i
$947$	8.20882			0.266751			0.133375	−	0.991066i	$-0.457418\pi$
$947$	8.20882			0.266751			0.133375	+	0.991066i	$0.457418\pi$
$948$	−4.48133	+	4.48133i	−0.145547	+	0.145547i
$949$	−0.963622	−	2.30759i	−0.0312805	−	0.0749076i
$950$	11.2174	−	12.1374i	0.363941	−	0.393790i
$951$	3.33826	−	3.33826i	0.108251	−	0.108251i
$952$	18.4575	−	18.4575i	0.598211	−	0.598211i
$953$	−2.65431	+	2.65431i	−0.0859814	+	0.0859814i	−0.748789	−	0.662808i	$-0.769365\pi$
$953$	−2.65431	+	2.65431i	−0.0859814	+	0.0859814i	0.662808	+	0.748789i	$0.269365\pi$
$954$	1.80319	+	1.80319i	0.0583804	+	0.0583804i
$955$	−21.4056	+	0.421449i	−0.692668	+	0.0136378i
$956$	−10.6351	−	10.6351i	−0.343963	−	0.343963i
$957$	9.00824			0.291195
$958$	−7.84354	−	7.84354i	−0.253413	−	0.253413i
$959$	−42.6562			−1.37744
$960$	1.61196	+	1.54971i	0.0520257	+	0.0500166i
$961$			29.0000i			0.935484i
$962$	−10.4550	−	25.0366i	−0.337081	−	0.807211i
$963$	−0.249153	−	0.249153i	−0.00802883	−	0.00802883i
$964$	−17.8276	−	17.8276i	−0.574188	−	0.574188i
$965$	1.13963	+	57.8821i	0.0366859	+	1.86329i
$966$			35.5358i			1.14334i
$967$		−	59.5170i		−	1.91394i	−0.290191	−	0.956969i	$-0.593719\pi$
$967$		−	59.5170i		−	1.91394i	0.290191	−	0.956969i	$-0.406281\pi$
$968$	−9.88263			−0.317640
$969$	−14.0147	+	14.0147i	−0.450218	+	0.450218i
$970$	24.7914	−	0.488111i	0.796003	−	0.0156723i
$971$	−19.6398			−0.630270			−0.315135	−	0.949047i	$-0.602050\pi$
$971$	−19.6398			−0.630270			−0.315135	+	0.949047i	$0.602050\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$			38.1062i			1.22163i
$974$	9.52685			0.305260
$975$	16.9320	+	6.18930i	0.542258	+	0.198216i
$976$	15.0391			0.481390
$977$			26.0216i			0.832505i	0.909249	+	0.416253i	$0.136657\pi$
$977$			26.0216i			0.832505i	−0.909249	+	0.416253i	$0.863343\pi$
$978$	−16.2234	−	16.2234i	−0.518766	−	0.518766i
$979$	−16.0536			−0.513074
$980$	26.7182	−	0.526049i	0.853483	−	0.0168040i
$981$	5.43020	−	5.43020i	0.173373	−	0.173373i
$982$	−29.7308			−0.948746
$983$			27.9041i			0.890004i	0.895530	+	0.445002i	$0.146797\pi$
$983$			27.9041i			0.890004i	−0.895530	+	0.445002i	$0.853203\pi$
$984$			7.81823i			0.249236i
$985$	0.363981	+	18.4867i	0.0115974	+	0.589037i
$986$	36.1325	+	36.1325i	1.15069	+	1.15069i
$987$	6.25489	+	6.25489i	0.199095	+	0.199095i
$988$	11.0238	+	4.52910i	0.350714	+	0.144090i
$989$		−	28.7202i		−	0.913249i
$990$	−1.70393	−	1.63813i	−0.0541544	−	0.0520631i
$991$	−46.3709			−1.47302			−0.736509	−	0.676427i	$-0.763527\pi$
$991$	−46.3709			−1.47302			−0.736509	+	0.676427i	$0.763527\pi$
$992$	1.00000	+	1.00000i	0.0317500	+	0.0317500i
$993$	−15.5190			−0.492480
$994$	35.4492	+	35.4492i	1.12438	+	1.12438i
$995$	14.2096	−	0.279770i	0.450476	−	0.00886931i
$996$	−0.507441	−	0.507441i	−0.0160789	−	0.0160789i
$997$	−23.2377	+	23.2377i	−0.735946	+	0.735946i	−0.971791	−	0.235845i	$-0.924214\pi$
$997$	−23.2377	+	23.2377i	−0.735946	+	0.735946i	0.235845	+	0.971791i	$0.424214\pi$
$998$	15.1666	−	15.1666i	0.480090	−	0.480090i
$999$	5.32099	−	5.32099i	0.168349	−	0.168349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.t.a.343.4	yes	12
3.2	odd	2		1170.2.w.f.343.6		12
5.2	odd	4		390.2.j.a.187.5	yes	12
5.3	odd	4		1950.2.j.c.1357.3		12
5.4	even	2		1950.2.t.b.343.3		12
13.8	odd	4		390.2.j.a.73.5	✓	12
15.2	even	4		1170.2.m.f.577.4		12
39.8	even	4		1170.2.m.f.73.4		12
65.8	even	4		1950.2.t.b.307.3		12
65.34	odd	4		1950.2.j.c.1243.1		12
65.47	even	4	inner	390.2.t.a.307.4	yes	12
195.47	odd	4		1170.2.w.f.307.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.a.73.5	✓	12	13.8	odd	4
390.2.j.a.187.5	yes	12	5.2	odd	4
390.2.t.a.307.4	yes	12	65.47	even	4	inner
390.2.t.a.343.4	yes	12	1.1	even	1	trivial
1170.2.m.f.73.4		12	39.8	even	4
1170.2.m.f.577.4		12	15.2	even	4
1170.2.w.f.307.6		12	195.47	odd	4
1170.2.w.f.343.6		12	3.2	odd	2
1950.2.j.c.1243.1		12	65.34	odd	4
1950.2.j.c.1357.3		12	5.3	odd	4
1950.2.t.b.307.3		12	65.8	even	4
1950.2.t.b.343.3		12	5.4	even	2

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.23563 + 0.0440169i) q^{5} +(-0.707107 + 0.707107i) q^{6} -4.35328 q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.23563 + 0.0440169i) q^{5} +(-0.707107 + 0.707107i) q^{6} -4.35328 q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.0440169 - 2.23563i) q^{10} +(-0.747451 - 0.747451i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.32711 - 1.38936i) q^{13} -4.35328i q^{14} +(-1.61196 - 1.54971i) q^{15} +1.00000 q^{16} +(-4.23990 - 4.23990i) q^{17} -1.00000 q^{18} +(-2.33730 - 2.33730i) q^{19} +(2.23563 - 0.0440169i) q^{20} +(-3.07824 - 3.07824i) q^{21} +(0.747451 - 0.747451i) q^{22} +(-5.77210 + 5.77210i) q^{23} +(0.707107 - 0.707107i) q^{24} +(4.99613 - 0.196811i) q^{25} +(1.38936 + 3.32711i) q^{26} +(-0.707107 + 0.707107i) q^{27} +4.35328 q^{28} +8.52201i q^{29} +(1.54971 - 1.61196i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} -1.05706i q^{33} +(4.23990 - 4.23990i) q^{34} +(9.73235 - 0.191618i) q^{35} -1.00000i q^{36} -7.52501 q^{37} +(2.33730 - 2.33730i) q^{38} +(3.33505 + 1.37020i) q^{39} +(0.0440169 + 2.23563i) q^{40} +(-5.52833 + 5.52833i) q^{41} +(3.07824 - 3.07824i) q^{42} +(-2.48784 + 2.48784i) q^{43} +(0.747451 + 0.747451i) q^{44} +(-0.0440169 - 2.23563i) q^{45} +(-5.77210 - 5.77210i) q^{46} -2.03197 q^{47} +(0.707107 + 0.707107i) q^{48} +11.9511 q^{49} +(0.196811 + 4.99613i) q^{50} -5.99613i q^{51} +(-3.32711 + 1.38936i) q^{52} +(-1.80319 - 1.80319i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(1.70393 + 1.63813i) q^{55} +4.35328i q^{56} -3.30544i q^{57} -8.52201 q^{58} +(2.51231 - 2.51231i) q^{59} +(1.61196 + 1.54971i) q^{60} +15.0391 q^{61} +(1.00000 + 1.00000i) q^{62} -4.35328i q^{63} -1.00000 q^{64} +(-7.37705 + 3.25255i) q^{65} +1.05706 q^{66} -4.15834i q^{67} +(4.23990 + 4.23990i) q^{68} -8.16298 q^{69} +(0.191618 + 9.73235i) q^{70} +(-8.14309 + 8.14309i) q^{71} +1.00000 q^{72} -0.693572i q^{73} -7.52501i q^{74} +(3.67196 + 3.39363i) q^{75} +(2.33730 + 2.33730i) q^{76} +(3.25387 + 3.25387i) q^{77} +(-1.37020 + 3.33505i) q^{78} -6.33756i q^{79} +(-2.23563 + 0.0440169i) q^{80} -1.00000 q^{81} +(-5.52833 - 5.52833i) q^{82} +0.717629 q^{83} +(3.07824 + 3.07824i) q^{84} +(9.66550 + 9.29224i) q^{85} +(-2.48784 - 2.48784i) q^{86} +(-6.02597 + 6.02597i) q^{87} +(-0.747451 + 0.747451i) q^{88} +(10.7389 - 10.7389i) q^{89} +(2.23563 - 0.0440169i) q^{90} +(-14.4839 + 6.04828i) q^{91} +(5.77210 - 5.77210i) q^{92} +1.41421 q^{93} -2.03197i q^{94} +(5.32822 + 5.12246i) q^{95} +(-0.707107 + 0.707107i) q^{96} +11.0892i q^{97} +11.9511i q^{98} +(0.747451 - 0.747451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 4 * q^5	\( 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

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