LMFDB - Embedded newform 525.2.z.a.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.8
Character	$\chi$	$=$	525.64
Dual form			525.2.z.a.484.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.341242 + 0.469679i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.513881 - 1.58156i) q^{4} +(2.23604 + 0.0116437i) q^{5} +(0.179402 + 0.552141i) q^{6} +1.00000i q^{7} +(2.02247 - 0.657140i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.341242 + 0.469679i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.513881 - 1.58156i) q^{4} +(2.23604 + 0.0116437i) q^{5} +(0.179402 + 0.552141i) q^{6} +1.00000i q^{7} +(2.02247 - 0.657140i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.757561 + 1.05419i) q^{10} +(0.946657 - 0.687786i) q^{11} +(0.977461 - 1.34536i) q^{12} +(-1.54516 + 2.12672i) q^{13} +(-0.469679 + 0.341242i) q^{14} +(2.12300 + 0.702047i) q^{15} +(-1.69192 - 1.22925i) q^{16} +(-3.33914 + 1.08495i) q^{17} +0.580555i q^{18} +(-1.05143 - 3.23598i) q^{19} +(1.16747 - 3.53045i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.646078 + 0.209923i) q^{22} +(-0.121638 - 0.167420i) q^{23} +2.12655 q^{24} +(4.99973 + 0.0520717i) q^{25} -1.52615 q^{26} +(0.587785 + 0.809017i) q^{27} +(1.58156 + 0.513881i) q^{28} +(1.14792 - 3.53292i) q^{29} +(0.394720 + 1.23670i) q^{30} +(1.39556 + 4.29510i) q^{31} -5.46723i q^{32} +(1.11286 - 0.361591i) q^{33} +(-1.64903 - 1.19809i) q^{34} +(-0.0116437 + 2.23604i) q^{35} +(1.34536 - 0.977461i) q^{36} +(-1.46992 + 2.02317i) q^{37} +(1.16108 - 1.59809i) q^{38} +(-2.12672 + 1.54516i) q^{39} +(4.52997 - 1.44584i) q^{40} +(-2.40888 - 1.75015i) q^{41} +(-0.552141 + 0.179402i) q^{42} +9.46600i q^{43} +(-0.601309 - 1.85064i) q^{44} +(1.80215 + 1.32373i) q^{45} +(0.0371259 - 0.114262i) q^{46} +(-8.75783 - 2.84559i) q^{47} +(-1.22925 - 1.69192i) q^{48} -1.00000 q^{49} +(1.68166 + 2.36604i) q^{50} -3.51098 q^{51} +(2.56952 + 3.53665i) q^{52} +(2.25751 + 0.733509i) q^{53} +(-0.179402 + 0.552141i) q^{54} +(2.12477 - 1.52689i) q^{55} +(0.657140 + 2.02247i) q^{56} -3.40251i q^{57} +(2.05106 - 0.666429i) q^{58} +(-2.23899 - 1.62672i) q^{59} +(2.20130 - 2.99689i) q^{60} +(0.435372 - 0.316316i) q^{61} +(-1.54110 + 2.12114i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(-0.816000 + 0.592859i) q^{64} +(-3.47979 + 4.73744i) q^{65} +(0.549587 + 0.399298i) q^{66} +(2.75254 - 0.894355i) q^{67} +5.83860i q^{68} +(-0.0639489 - 0.196815i) q^{69} +(-1.05419 + 0.757561i) q^{70} +(-0.0641303 + 0.197373i) q^{71} +(2.02247 + 0.657140i) q^{72} +(5.74597 + 7.90864i) q^{73} -1.45184 q^{74} +(4.73893 + 1.59452i) q^{75} -5.65822 q^{76} +(0.687786 + 0.946657i) q^{77} +(-1.45145 - 0.471606i) q^{78} +(1.78427 - 5.49141i) q^{79} +(-3.76889 - 2.76836i) q^{80} +(0.309017 + 0.951057i) q^{81} -1.72862i q^{82} +(-12.4019 + 4.02962i) q^{83} +(1.34536 + 0.977461i) q^{84} +(-7.47907 + 2.38711i) q^{85} +(-4.44598 + 3.23020i) q^{86} +(2.18347 - 3.00528i) q^{87} +(1.46261 - 2.01311i) q^{88} +(-4.55869 + 3.31208i) q^{89} +(-0.00675984 + 1.29814i) q^{90} +(-2.12672 - 1.54516i) q^{91} +(-0.327294 + 0.106344i) q^{92} +4.51614i q^{93} +(-1.65202 - 5.08441i) q^{94} +(-2.31336 - 7.24801i) q^{95} +(1.68947 - 5.19965i) q^{96} +(15.1939 + 4.93679i) q^{97} +(-0.341242 - 0.469679i) q^{98} +1.17013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	0.341242	+	0.469679i	0.241294	+	0.332113i	0.912439	−	0.409213i	$-0.134197\pi$
$2$	0.341242	+	0.469679i	0.241294	+	0.332113i	−0.671144	+	0.741327i	$0.734197\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.513881	−	1.58156i	0.256941	−	0.790782i
$5$	2.23604	+	0.0116437i	0.999986	+	0.00520724i
$5$	2.23604	+	0.0116437i	0.999986	+	0.00520724i
$6$	0.179402	+	0.552141i	0.0732404	+	0.225411i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.02247	−	0.657140i	0.715050	−	0.232334i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.757561	+	1.05419i	0.239562	+	0.333365i
$11$	0.946657	−	0.687786i	0.285428	−	0.207375i	−0.435854	−	0.900018i	$-0.643553\pi$
$11$	0.946657	−	0.687786i	0.285428	−	0.207375i	0.721281	+	0.692642i	$0.243553\pi$
$12$	0.977461	−	1.34536i	0.282169	−	0.388372i
$13$	−1.54516	+	2.12672i	−0.428549	+	0.589847i	−0.967619	−	0.252414i	$-0.918776\pi$
$13$	−1.54516	+	2.12672i	−0.428549	+	0.589847i	0.539070	+	0.842261i	$0.318776\pi$
$14$	−0.469679	+	0.341242i	−0.125527	+	0.0912007i
$15$	2.12300	+	0.702047i	0.548156	+	0.181268i
$16$	−1.69192	−	1.22925i	−0.422981	−	0.307313i
$17$	−3.33914	+	1.08495i	−0.809859	+	0.263139i	−0.684538	−	0.728977i	$-0.739996\pi$
$17$	−3.33914	+	1.08495i	−0.809859	+	0.263139i	−0.125321	+	0.992116i	$0.539996\pi$
$18$			0.580555i			0.136838i
$19$	−1.05143	−	3.23598i	−0.241215	−	0.742384i	−0.996236	−	0.0866830i	$-0.972373\pi$
$19$	−1.05143	−	3.23598i	−0.241215	−	0.742384i	0.755021	−	0.655701i	$-0.227627\pi$
$20$	1.16747	−	3.53045i	0.261055	−	0.789434i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	0.646078	+	0.209923i	0.137744	+	0.0447558i
$23$	−0.121638	−	0.167420i	−0.0253633	−	0.0349096i	0.796147	−	0.605103i	$-0.206868\pi$
$23$	−0.121638	−	0.167420i	−0.0253633	−	0.0349096i	−0.821510	+	0.570194i	$0.806868\pi$
$24$	2.12655			0.434080
$25$	4.99973	+	0.0520717i	0.999946	+	0.0104143i
$26$	−1.52615			−0.299303
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	1.58156	+	0.513881i	0.298888	+	0.0971145i
$29$	1.14792	−	3.53292i	0.213163	−	0.656047i	−0.786116	−	0.618079i	$-0.787911\pi$
$29$	1.14792	−	3.53292i	0.213163	−	0.656047i	0.999279	−	0.0379686i	$-0.0120887\pi$
$30$	0.394720	+	1.23670i	0.0720656	+	0.225789i
$31$	1.39556	+	4.29510i	0.250651	+	0.771423i	0.994656	+	0.103249i	$0.0329239\pi$
$31$	1.39556	+	4.29510i	0.250651	+	0.771423i	−0.744005	+	0.668174i	$0.767076\pi$
$32$		−	5.46723i		−	0.966479i
$33$	1.11286	−	0.361591i	0.193724	−	0.0629449i
$34$	−1.64903	−	1.19809i	−0.282807	−	0.205471i
$35$	−0.0116437	+	2.23604i	−0.00196815	+	0.377959i
$36$	1.34536	−	0.977461i	0.224227	−	0.162910i
$37$	−1.46992	+	2.02317i	−0.241654	+	0.332608i	−0.912566	−	0.408929i	$-0.865903\pi$
$37$	−1.46992	+	2.02317i	−0.241654	+	0.332608i	0.670913	+	0.741536i	$0.265903\pi$
$38$	1.16108	−	1.59809i	0.188352	−	0.259244i
$39$	−2.12672	+	1.54516i	−0.340548	+	0.247423i
$40$	4.52997	−	1.44584i	0.716251	−	0.228607i
$41$	−2.40888	−	1.75015i	−0.376203	−	0.273328i	0.383575	−	0.923510i	$-0.374693\pi$
$41$	−2.40888	−	1.75015i	−0.376203	−	0.273328i	−0.759779	+	0.650182i	$0.774693\pi$
$42$	−0.552141	+	0.179402i	−0.0851972	+	0.0276823i
$43$			9.46600i			1.44355i	0.692127	+	0.721776i	$0.256674\pi$
$43$			9.46600i			1.44355i	−0.692127	+	0.721776i	$0.743326\pi$
$44$	−0.601309	−	1.85064i	−0.0906508	−	0.278994i
$45$	1.80215	+	1.32373i	0.268648	+	0.197330i
$46$	0.0371259	−	0.114262i	0.00547392	−	0.0168470i
$47$	−8.75783	−	2.84559i	−1.27746	−	0.415072i	−0.409776	−	0.912186i	$-0.634393\pi$
$47$	−8.75783	−	2.84559i	−1.27746	−	0.415072i	−0.867685	+	0.497114i	$0.834393\pi$
$48$	−1.22925	−	1.69192i	−0.177427	−	0.244208i
$49$	−1.00000			−0.142857
$50$	1.68166	+	2.36604i	0.237823	+	0.334608i
$51$	−3.51098			−0.491635
$52$	2.56952	+	3.53665i	0.356329	+	0.490445i
$53$	2.25751	+	0.733509i	0.310093	+	0.100755i	0.459929	−	0.887956i	$-0.347875\pi$
$53$	2.25751	+	0.733509i	0.310093	+	0.100755i	−0.149837	+	0.988711i	$0.547875\pi$
$54$	−0.179402	+	0.552141i	−0.0244135	+	0.0751369i
$55$	2.12477	−	1.52689i	0.286504	−	0.205886i
$56$	0.657140	+	2.02247i	0.0878140	+	0.270264i
$57$		−	3.40251i		−	0.450673i
$58$	2.05106	−	0.666429i	0.269317	−	0.0875064i
$59$	−2.23899	−	1.62672i	−0.291492	−	0.211781i	0.432422	−	0.901671i	$-0.357659\pi$
$59$	−2.23899	−	1.62672i	−0.291492	−	0.211781i	−0.723914	+	0.689890i	$0.757659\pi$
$60$	2.20130	−	2.99689i	0.284187	−	0.386897i
$61$	0.435372	−	0.316316i	0.0557437	−	0.0405001i	−0.559564	−	0.828787i	$-0.689032\pi$
$61$	0.435372	−	0.316316i	0.0557437	−	0.0405001i	0.615308	+	0.788287i	$0.289032\pi$
$62$	−1.54110	+	2.12114i	−0.195719	+	0.269385i
$63$	−0.587785	+	0.809017i	−0.0740540	+	0.101927i
$64$	−0.816000	+	0.592859i	−0.102000	+	0.0741073i
$65$	−3.47979	+	4.73744i	−0.431615	+	0.587608i
$66$	0.549587	+	0.399298i	0.0676494	+	0.0491502i
$67$	2.75254	−	0.894355i	0.336276	−	0.109263i	−0.136011	−	0.990707i	$-0.543428\pi$
$67$	2.75254	−	0.894355i	0.336276	−	0.109263i	0.472288	+	0.881444i	$0.343428\pi$
$68$			5.83860i			0.708034i
$69$	−0.0639489	−	0.196815i	−0.00769855	−	0.0236937i
$70$	−1.05419	+	0.757561i	−0.126000	+	0.0905459i
$71$	−0.0641303	+	0.197373i	−0.00761087	+	0.0234238i	−0.954790	−	0.297282i	$-0.903920\pi$
$71$	−0.0641303	+	0.197373i	−0.00761087	+	0.0234238i	0.947179	+	0.320705i	$0.103920\pi$
$72$	2.02247	+	0.657140i	0.238350	+	0.0774447i
$73$	5.74597	+	7.90864i	0.672514	+	0.925637i	0.999814	−	0.0192840i	$-0.00613865\pi$
$73$	5.74597	+	7.90864i	0.672514	+	0.925637i	−0.327300	+	0.944921i	$0.606139\pi$
$74$	−1.45184			−0.168773
$75$	4.73893	+	1.59452i	0.547205	+	0.184120i
$76$	−5.65822			−0.649042
$77$	0.687786	+	0.946657i	0.0783805	+	0.107882i
$78$	−1.45145	−	0.471606i	−0.164345	−	0.0533989i
$79$	1.78427	−	5.49141i	0.200746	−	0.617831i	−0.799116	−	0.601177i	$-0.794699\pi$
$79$	1.78427	−	5.49141i	0.200746	−	0.617831i	0.999861	−	0.0166542i	$-0.00530145\pi$
$80$	−3.76889	−	2.76836i	−0.421375	−	0.309512i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	1.72862i		−	0.190895i
$83$	−12.4019	+	4.02962i	−1.36129	+	0.442308i	−0.896472	−	0.443100i	$-0.853879\pi$
$83$	−12.4019	+	4.02962i	−1.36129	+	0.442308i	−0.464813	+	0.885409i	$0.653879\pi$
$84$	1.34536	+	0.977461i	0.146791	+	0.106650i
$85$	−7.47907	+	2.38711i	−0.811219	+	0.258919i
$86$	−4.44598	+	3.23020i	−0.479423	+	0.348321i
$87$	2.18347	−	3.00528i	0.234092	−	0.322200i
$88$	1.46261	−	2.01311i	0.155915	−	0.214598i
$89$	−4.55869	+	3.31208i	−0.483220	+	0.351080i	−0.802571	−	0.596557i	$-0.796535\pi$
$89$	−4.55869	+	3.31208i	−0.483220	+	0.351080i	0.319351	+	0.947637i	$0.396535\pi$
$90$	−0.00675984	+	1.29814i	−0.000712549	+	0.136836i
$91$	−2.12672	−	1.54516i	−0.222941	−	0.161976i
$92$	−0.327294	+	0.106344i	−0.0341227	+	0.0110872i
$93$			4.51614i			0.468302i
$94$	−1.65202	−	5.08441i	−0.170393	−	0.524416i
$95$	−2.31336	−	7.24801i	−0.237346	−	0.743630i
$96$	1.68947	−	5.19965i	0.172431	−	0.530687i
$97$	15.1939	+	4.93679i	1.54270	+	0.501255i	0.952121	−	0.305722i	$-0.0988978\pi$
$97$	15.1939	+	4.93679i	1.54270	+	0.501255i	0.590583	+	0.806977i	$0.298898\pi$
$98$	−0.341242	−	0.469679i	−0.0344706	−	0.0474448i
$99$	1.17013			0.117603
$100$	2.65162	−	7.88064i	0.265162	−	0.788064i
$101$	−4.31902			−0.429758			−0.214879	−	0.976641i	$-0.568936\pi$
$101$	−4.31902			−0.429758			−0.214879	+	0.976641i	$0.568936\pi$
$102$	−1.19809	−	1.64903i	−0.118629	−	0.163279i
$103$	−4.27201	−	1.38806i	−0.420934	−	0.136770i	0.0908885	−	0.995861i	$-0.471029\pi$
$103$	−4.27201	−	1.38806i	−0.420934	−	0.136770i	−0.511822	+	0.859091i	$0.671029\pi$
$104$	−1.72747	+	5.31661i	−0.169393	+	0.521337i
$105$	−0.702047	+	2.12300i	−0.0685128	+	0.207184i
$106$	0.425843	+	1.31061i	0.0413615	+	0.127298i
$107$		−	20.4588i		−	1.97783i	−0.148495	−	0.988913i	$-0.547443\pi$
$107$		−	20.4588i		−	1.97783i	0.148495	−	0.988913i	$-0.452557\pi$
$108$	1.58156	−	0.513881i	0.152186	−	0.0494483i
$109$	−16.0207	−	11.6397i	−1.53450	−	1.11488i	−0.953670	−	0.300855i	$-0.902728\pi$
$109$	−16.0207	−	11.6397i	−1.53450	−	1.11488i	−0.580830	−	0.814025i	$-0.697272\pi$
$110$	1.44221	+	0.476920i	0.137509	+	0.0454725i
$111$	−2.02317	+	1.46992i	−0.192031	+	0.139519i
$112$	1.22925	−	1.69192i	0.116154	−	0.159872i
$113$	−7.41388	+	10.2043i	−0.697439	+	0.959943i	0.302538	+	0.953137i	$0.402166\pi$
$113$	−7.41388	+	10.2043i	−0.697439	+	0.959943i	−0.999977	+	0.00680513i	$0.997834\pi$
$114$	1.59809	−	1.16108i	0.149675	−	0.108745i
$115$	−0.270038	−	0.375775i	−0.0251812	−	0.0350412i
$116$	−4.99765	−	3.63101i	−0.464020	−	0.337131i
$117$	−2.50011	+	0.812336i	−0.231136	+	0.0751005i
$118$		−	1.60672i		−	0.147910i
$119$	−1.08495	−	3.33914i	−0.0994573	−	0.306098i
$120$	4.75504	+	0.0247610i	0.434074	+	0.00226036i
$121$	−2.97608	+	9.15943i	−0.270553	+	0.832675i
$122$	0.297134	+	0.0965448i	0.0269013	+	0.00874076i
$123$	−1.75015	−	2.40888i	−0.157806	−	0.217201i
$124$	7.51014			0.674430
$125$	11.1790	+	0.174650i	0.999878	+	0.0156211i
$126$	−0.580555			−0.0517200
$127$	−6.60937	−	9.09702i	−0.586487	−	0.807230i	0.407901	−	0.913026i	$-0.366261\pi$
$127$	−6.60937	−	9.09702i	−0.586487	−	0.807230i	−0.994388	+	0.105796i	$0.966261\pi$
$128$	−10.9562	−	3.55988i	−0.968400	−	0.314652i
$129$	−2.92516	+	9.00270i	−0.257546	+	0.792644i
$130$	−3.41253	−	0.0177701i	−0.299299	−	0.00155854i
$131$	−0.676022	−	2.08058i	−0.0590643	−	0.181781i	0.917171	−	0.398493i	$-0.130467\pi$
$131$	−0.676022	−	2.08058i	−0.0590643	−	0.181781i	−0.976236	+	0.216712i	$0.930467\pi$
$132$		−	1.94588i		−	0.169367i
$133$	3.23598	−	1.05143i	0.280595	−	0.0911707i
$134$	1.35934	+	0.987620i	0.117429	+	0.0853174i
$135$	1.30489	+	1.81584i	0.112307	+	0.156282i
$136$	−6.04033	+	4.38856i	−0.517954	+	0.376316i
$137$	9.38883	−	12.9226i	0.802142	−	1.10405i	−0.190347	−	0.981717i	$-0.560961\pi$
$137$	9.38883	−	12.9226i	0.802142	−	1.10405i	0.992489	−	0.122337i	$-0.0390388\pi$
$138$	0.0706177	−	0.0971969i	0.00601138	−	0.00827395i
$139$	−7.50832	+	5.45512i	−0.636848	+	0.462697i	−0.858766	−	0.512368i	$-0.828768\pi$
$139$	−7.50832	+	5.45512i	−0.636848	+	0.462697i	0.221918	+	0.975065i	$0.428768\pi$
$140$	3.53045	+	1.16747i	0.298378	+	0.0986695i
$141$	−7.44985	−	5.41264i	−0.627391	−	0.455826i
$142$	−0.114586	+	0.0372312i	−0.00961583	+	0.00312437i
$143$			3.07601i			0.257229i
$144$	−0.646257	−	1.98897i	−0.0538547	−	0.165748i
$145$	2.60792	−	7.88638i	0.216576	−	0.654928i
$146$	−1.75376	+	5.39752i	−0.145142	+	0.446702i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	2.44441	+	3.36445i	0.200930	+	0.276556i
$149$	−0.441738			−0.0361886			−0.0180943	−	0.999836i	$-0.505760\pi$
$149$	−0.441738			−0.0361886			−0.0180943	+	0.999836i	$0.505760\pi$
$150$	0.868208	+	2.76990i	0.0708889	+	0.226161i
$151$	−6.10182			−0.496559			−0.248280	−	0.968688i	$-0.579865\pi$
$151$	−6.10182			−0.496559			−0.248280	+	0.968688i	$0.579865\pi$
$152$	−4.25298	−	5.85372i	−0.344962	−	0.474799i
$153$	−3.33914	−	1.08495i	−0.269953	−	0.0877131i
$154$	−0.209923	+	0.646078i	−0.0169161	+	0.0520624i
$155$	3.07052	+	9.62026i	0.246630	+	0.772718i
$156$	1.35088	+	4.15758i	0.108157	+	0.332873i
$157$			10.3495i			0.825981i	0.910735	+	0.412991i	$0.135516\pi$
$157$			10.3495i			0.825981i	−0.910735	+	0.412991i	$0.864484\pi$
$158$	3.18807	−	1.03587i	0.253629	−	0.0824090i
$159$	1.92035	+	1.39522i	0.152294	+	0.110648i
$160$	0.0636590	−	12.2249i	0.00503269	−	0.966466i
$161$	0.167420	−	0.121638i	0.0131946	−	0.00958643i
$162$	−0.341242	+	0.469679i	−0.0268105	+	0.0369015i
$163$	9.57441	−	13.1781i	0.749926	−	1.03218i	−0.248060	−	0.968745i	$-0.579793\pi$
$163$	9.57441	−	13.1781i	0.749926	−	1.03218i	0.997986	−	0.0634398i	$-0.0202071\pi$
$164$	−4.00585	+	2.91042i	−0.312805	+	0.227266i
$165$	2.49261	−	0.795573i	0.194049	−	0.0619352i
$166$	−6.12468	−	4.44984i	−0.475367	−	0.345375i
$167$	−1.21292	+	0.394103i	−0.0938589	+	0.0304966i	−0.355570	−	0.934650i	$-0.615713\pi$
$167$	−1.21292	+	0.394103i	−0.0938589	+	0.0304966i	0.261711	+	0.965146i	$0.415713\pi$
$168$			2.12655i			0.164067i
$169$	1.88177	+	5.79150i	0.144752	+	0.445500i
$170$	−3.67335	−	2.69818i	−0.281733	−	0.206941i
$171$	1.05143	−	3.23598i	0.0804050	−	0.247461i
$172$	14.9711	+	4.86440i	1.14154	+	0.370907i
$173$	6.35497	+	8.74687i	0.483159	+	0.665012i	0.979108	−	0.203340i	$-0.0651796\pi$
$173$	6.35497	+	8.74687i	0.483159	+	0.665012i	−0.495949	+	0.868352i	$0.665180\pi$
$174$	2.15661			0.163492
$175$	−0.0520717	+	4.99973i	−0.00393625	+	0.377944i
$176$	−2.44713			−0.184460
$177$	−1.62672	−	2.23899i	−0.122272	−	0.168293i
$178$	−3.11123	−	1.01090i	−0.233197	−	0.0757702i
$179$	7.09273	−	21.8292i	0.530136	−	1.63159i	−0.223796	−	0.974636i	$-0.571845\pi$
$179$	7.09273	−	21.8292i	0.530136	−	1.63159i	0.753931	−	0.656953i	$-0.228155\pi$
$180$	3.01966	−	2.16997i	0.225072	−	0.161740i
$181$	5.22444	+	16.0792i	0.388329	+	1.19515i	0.934036	+	0.357178i	$0.116261\pi$
$181$	5.22444	+	16.0792i	0.388329	+	1.19515i	−0.545707	+	0.837976i	$0.683739\pi$
$182$		−	1.52615i		−	0.113126i
$183$	0.511810	−	0.166297i	0.0378341	−	0.0122931i
$184$	−0.356028	−	0.258669i	−0.0262467	−	0.0190694i
$185$	−3.31036	+	4.50678i	−0.243382	+	0.331345i
$186$	−2.12114	+	1.54110i	−0.155529	+	0.112999i
$187$	−2.41480	+	3.32369i	−0.176588	+	0.243052i
$188$	−9.00097	+	12.3888i	−0.656463	+	0.903544i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	2.61482	−	3.55986i	0.189699	−	0.258260i
$191$	0.473934	+	0.344333i	0.0342927	+	0.0249151i	0.604800	−	0.796378i	$-0.293253\pi$
$191$	0.473934	+	0.344333i	0.0342927	+	0.0249151i	−0.570507	+	0.821293i	$0.693253\pi$
$192$	−0.959265	+	0.311684i	−0.0692290	+	0.0224939i
$193$			6.33866i			0.456267i	0.973630	+	0.228133i	$0.0732622\pi$
$193$			6.33866i			0.456267i	−0.973630	+	0.228133i	$0.926738\pi$
$194$	2.86608	+	8.82089i	0.205773	+	0.633303i
$195$	−4.77343	+	3.43026i	−0.341832	+	0.245646i
$196$	−0.513881	+	1.58156i	−0.0367058	+	0.112969i
$197$	3.22909	+	1.04920i	0.230063	+	0.0747521i	0.421780	−	0.906698i	$-0.361405\pi$
$197$	3.22909	+	1.04920i	0.230063	+	0.0747521i	−0.191717	+	0.981450i	$0.561405\pi$
$198$	0.399298	+	0.549587i	0.0283769	+	0.0390574i
$199$	−2.03409			−0.144193			−0.0720965	−	0.997398i	$-0.522969\pi$
$199$	−2.03409			−0.144193			−0.0720965	+	0.997398i	$0.522969\pi$
$200$	10.1460	−	3.18021i	0.717431	−	0.224875i
$201$	2.89419			0.204141
$202$	−1.47383	−	2.02855i	−0.103698	−	0.142728i
$203$	3.53292	+	1.14792i	0.247963	+	0.0805679i
$204$	−1.80423	+	5.55283i	−0.126321	+	0.388776i
$205$	−5.36596	−	3.94145i	−0.374775	−	0.275283i
$206$	−0.805846	−	2.48014i	−0.0561459	−	0.172799i
$207$		−	0.206943i		−	0.0143835i
$208$	5.22857	−	1.69886i	0.362536	−	0.117795i
$209$	−3.22101	−	2.34020i	−0.222802	−	0.161875i
$210$	−1.23670	+	0.394720i	−0.0853402	+	0.0272382i
$211$	−19.2484	+	13.9848i	−1.32511	+	0.962752i	−0.325261	+	0.945624i	$0.605452\pi$
$211$	−19.2484	+	13.9848i	−1.32511	+	0.962752i	−0.999853	+	0.0171273i	$0.994548\pi$
$212$	2.32018	−	3.19346i	0.159351	−	0.219328i
$213$	−0.121983	+	0.167895i	−0.00835814	+	0.0115040i
$214$	9.60907	−	6.98140i	0.656863	−	0.477239i
$215$	−0.110220	+	21.1663i	−0.00751692	+	1.44353i
$216$	1.72041	+	1.24995i	0.117059	+	0.0850486i
$217$	−4.29510	+	1.39556i	−0.291571	+	0.0947370i
$218$		−	11.4965i		−	0.778642i
$219$	3.02083	+	9.29717i	0.204129	+	0.628244i
$220$	−1.32300	−	4.14510i	−0.0891967	−	0.279463i
$221$	2.85209	−	8.77784i	0.191853	−	0.590461i
$222$	−1.38078	−	0.448644i	−0.0926721	−	0.0301110i
$223$	10.1659	+	13.9922i	0.680760	+	0.936986i	0.999943	−	0.0107071i	$-0.00340824\pi$
$223$	10.1659	+	13.9922i	0.680760	+	0.936986i	−0.319182	+	0.947693i	$0.603408\pi$
$224$	5.46723			0.365295
$225$	4.01426	+	2.98089i	0.267617	+	0.198726i
$226$	−7.32269			−0.487098
$227$	0.994533	+	1.36886i	0.0660095	+	0.0908542i	0.840745	−	0.541431i	$-0.182117\pi$
$227$	0.994533	+	1.36886i	0.0660095	+	0.0908542i	−0.774736	+	0.632285i	$0.782117\pi$
$228$	−5.38128	−	1.74848i	−0.356384	−	0.115796i
$229$	4.99515	−	15.3735i	0.330089	−	1.01591i	−0.639002	−	0.769205i	$-0.720653\pi$
$229$	4.99515	−	15.3735i	0.330089	−	1.01591i	0.969091	−	0.246704i	$-0.0793474\pi$
$230$	0.0843454	−	0.255061i	0.00556157	−	0.0168182i
$231$	0.361591	+	1.11286i	0.0237909	+	0.0732209i
$232$		−	7.89956i		−	0.518632i
$233$	23.4015	−	7.60362i	1.53309	−	0.498130i	0.583627	−	0.812022i	$-0.301633\pi$
$233$	23.4015	−	7.60362i	1.53309	−	0.498130i	0.949459	+	0.313892i	$0.101633\pi$
$234$	−1.23468	−	0.897048i	−0.0807136	−	0.0586419i
$235$	−19.5497	−	6.46482i	−1.27528	−	0.421719i
$236$	−3.72335	+	2.70517i	−0.242369	+	0.176092i
$237$	3.39388	−	4.67127i	0.220456	−	0.303432i
$238$	1.19809	−	1.64903i	0.0776608	−	0.106891i
$239$	−14.9530	+	10.8640i	−0.967232	+	0.702735i	−0.954819	−	0.297188i	$-0.903951\pi$
$239$	−14.9530	+	10.8640i	−0.967232	+	0.702735i	−0.0124130	+	0.999923i	$0.503951\pi$
$240$	−2.72896	−	3.79752i	−0.176153	−	0.245129i
$241$	16.2979	+	11.8411i	1.04984	+	0.762752i	0.972182	−	0.234228i	$-0.0752562\pi$
$241$	16.2979	+	11.8411i	1.04984	+	0.762752i	0.0776567	+	0.996980i	$0.475256\pi$
$242$	−5.31756	+	1.72778i	−0.341825	+	0.111066i
$243$			1.00000i			0.0641500i
$244$	−0.276545	−	0.851118i	−0.0177040	−	0.0544872i
$245$	−2.23604	−	0.0116437i	−0.142855	−	0.000743891i
$246$	0.534174	−	1.64402i	0.0340577	−	0.104819i
$247$	8.50665	+	2.76398i	0.541265	+	0.175868i
$248$	5.64497	+	7.76963i	0.358456	+	0.493372i
$249$	−13.0401			−0.826385
$250$	3.73271	+	5.31013i	0.236077	+	0.335842i
$251$	23.2213			1.46572			0.732859	−	0.680381i	$-0.238186\pi$
$251$	23.2213			1.46572			0.732859	+	0.680381i	$0.238186\pi$
$252$	0.977461	+	1.34536i	0.0615742	+	0.0847497i
$253$	−0.230299	−	0.0748287i	−0.0144788	−	0.00470444i
$254$	2.01729	−	6.20857i	0.126576	−	0.389560i
$255$	−7.85067	−	0.0408809i	−0.491628	−	0.00256006i
$256$	−1.44334	−	4.44215i	−0.0902089	−	0.277634i
$257$		−	7.75507i		−	0.483748i	−0.970308	−	0.241874i	$-0.922238\pi$
$257$		−	7.75507i		−	0.483748i	0.970308	−	0.241874i	$-0.0777620\pi$
$258$	−5.22657	+	1.69822i	−0.325392	+	0.105726i
$259$	−2.02317	−	1.46992i	−0.125714	−	0.0913365i
$260$	5.70437	+	7.93799i	0.353770	+	0.492294i
$261$	3.00528	−	2.18347i	0.186022	−	0.135153i
$262$	0.746519	−	1.02750i	0.0461201	−	0.0634789i
$263$	9.84102	−	13.5450i	0.606823	−	0.835220i	−0.389488	−	0.921031i	$-0.627348\pi$
$263$	9.84102	−	13.5450i	0.606823	−	0.835220i	0.996311	+	0.0858111i	$0.0273481\pi$
$264$	2.01311	−	1.46261i	0.123898	−	0.0900175i
$265$	5.03934	+	1.66644i	0.309564	+	0.102369i
$266$	1.59809	+	1.16108i	0.0979850	+	0.0711902i
$267$	−5.35906	+	1.74126i	−0.327969	+	0.106564i
$268$		−	4.81291i		−	0.293996i
$269$	−1.21665	−	3.74447i	−0.0741805	−	0.228304i	0.907091	−	0.420935i	$-0.138298\pi$
$269$	−1.21665	−	3.74447i	−0.0741805	−	0.228304i	−0.981271	+	0.192631i	$0.938298\pi$
$270$	−0.407578	+	1.23252i	−0.0248044	+	0.0750087i
$271$	8.70797	−	26.8004i	0.528972	−	1.62801i	−0.227354	−	0.973812i	$-0.573007\pi$
$271$	8.70797	−	26.8004i	0.528972	−	1.62801i	0.756326	−	0.654195i	$-0.226993\pi$
$272$	6.98324	+	2.26899i	0.423421	+	0.137578i
$273$	−1.54516	−	2.12672i	−0.0935171	−	0.128715i
$274$	9.27335			0.560224
$275$	4.76884	−	3.38945i	0.287572	−	0.204392i
$276$	−0.344137			−0.0207146
$277$	12.5777	+	17.3118i	0.755722	+	1.04016i	0.997558	+	0.0698454i	$0.0222506\pi$
$277$	12.5777	+	17.3118i	0.755722	+	1.04016i	−0.241835	+	0.970317i	$0.577749\pi$
$278$	−5.12431	−	1.66499i	−0.307336	−	0.0998594i
$279$	−1.39556	+	4.29510i	−0.0835502	+	0.257141i
$280$	1.44584	+	4.52997i	0.0864055	+	0.270717i
$281$	−0.243662	−	0.749915i	−0.0145357	−	0.0447362i	0.943526	−	0.331300i	$-0.107487\pi$
$281$	−0.243662	−	0.749915i	−0.0145357	−	0.0447362i	−0.958061	+	0.286563i	$0.907487\pi$
$282$		−	5.34606i		−	0.318353i
$283$	4.35001	−	1.41340i	0.258581	−	0.0840181i	−0.176858	−	0.984236i	$-0.556593\pi$
$283$	4.35001	−	1.41340i	0.258581	−	0.0840181i	0.435439	+	0.900218i	$0.356593\pi$
$284$	0.279202	+	0.202852i	0.0165676	+	0.0120371i
$285$	0.0396179	−	7.60813i	0.00234676	−	0.450667i
$286$	−1.44474	+	1.04967i	−0.0854293	+	0.0620680i
$287$	1.75015	−	2.40888i	0.103308	−	0.142192i
$288$	3.21356	−	4.42308i	0.189361	−	0.260633i
$289$	−3.78058	+	2.74675i	−0.222387	+	0.161574i
$290$	4.59400	−	1.46628i	0.269769	−	0.0861028i
$291$	12.9247	+	9.39033i	0.757658	+	0.550471i
$292$	15.4608	−	5.02351i	0.904773	−	0.293979i
$293$			27.1954i			1.58877i	0.607411	+	0.794387i	$0.292208\pi$
$293$			27.1954i			1.58877i	−0.607411	+	0.794387i	$0.707792\pi$
$294$	−0.179402	−	0.552141i	−0.0104629	−	0.0322015i
$295$	−4.98753	−	3.66349i	−0.290385	−	0.213296i
$296$	−1.64336	+	5.05775i	−0.0955185	+	0.293976i
$297$	1.11286	+	0.361591i	0.0645748	+	0.0209816i
$298$	−0.150740	−	0.207475i	−0.00873211	−	0.0120187i
$299$	0.544007			0.0314607
$300$	4.95709	−	6.67553i	0.286198	−	0.385412i
$301$	−9.46600			−0.545611
$302$	−2.08220	−	2.86590i	−0.119817	−	0.164914i
$303$	−4.10763	−	1.33465i	−0.235977	−	0.0766736i
$304$	−2.19889	+	6.76750i	−0.126115	+	0.388143i
$305$	0.977191	−	0.702226i	0.0559538	−	0.0402093i
$306$	−0.629874	−	1.93855i	−0.0360075	−	0.110820i
$307$			23.7130i			1.35337i	0.736271	+	0.676687i	$0.236585\pi$
$307$			23.7130i			1.35337i	−0.736271	+	0.676687i	$0.763415\pi$
$308$	1.85064	−	0.601309i	0.105450	−	0.0342628i
$309$	−3.63399	−	2.64025i	−0.206730	−	0.150198i
$310$	−3.47065	+	4.72500i	−0.197119	+	0.268362i
$311$	26.3825	−	19.1680i	1.49601	−	1.08692i	0.524076	−	0.851672i	$-0.324411\pi$
$311$	26.3825	−	19.1680i	1.49601	−	1.08692i	0.971936	−	0.235245i	$-0.0755891\pi$
$312$	−3.28585	+	4.52258i	−0.186025	+	0.256041i
$313$	11.7447	−	16.1651i	0.663847	−	0.913707i	−0.335754	−	0.941950i	$-0.608991\pi$
$313$	11.7447	−	16.1651i	0.663847	−	0.913707i	0.999601	+	0.0282428i	$0.00899115\pi$
$314$	−4.86095	+	3.53169i	−0.274319	+	0.199305i
$315$	−1.32373	+	1.80215i	−0.0745837	+	0.101540i
$316$	−7.76811	−	5.64386i	−0.436990	−	0.317492i
$317$	17.4712	−	5.67673i	0.981279	−	0.318837i	0.225919	−	0.974146i	$-0.427462\pi$
$317$	17.4712	−	5.67673i	0.981279	−	0.318837i	0.755361	+	0.655309i	$0.227462\pi$
$318$			1.37806i			0.0772776i
$319$	−1.34321	−	4.13399i	−0.0752055	−	0.231459i
$320$	−1.83151	+	1.31615i	−0.102385	+	0.0735752i
$321$	6.32211	−	19.4575i	0.352866	−	1.08601i
$322$	0.114262	+	0.0371259i	0.00636756	+	0.00206895i
$323$	7.02175	+	9.66461i	0.390701	+	0.537753i
$324$	1.66296			0.0923864
$325$	−7.83610	+	10.5526i	−0.434669	+	0.585352i
$326$	9.45665			0.523755
$327$	−11.6397	−	16.0207i	−0.643676	−	0.885944i
$328$	−6.02197	−	1.95666i	−0.332508	−	0.108038i
$329$	2.84559	−	8.75783i	0.156883	−	0.482835i
$330$	1.22425	+	0.899245i	0.0673926	+	0.0495018i
$331$	3.14207	+	9.67029i	0.172704	+	0.531527i	0.999521	−	0.0309432i	$-0.00985110\pi$
$331$	3.14207	+	9.67029i	0.172704	+	0.531527i	−0.826818	+	0.562470i	$0.809851\pi$
$332$			21.6852i			1.19013i
$333$	−2.37838	+	0.772784i	−0.130335	+	0.0423483i
$334$	−0.599002	−	0.435201i	−0.0327760	−	0.0238131i
$335$	6.16520	−	1.96776i	0.336841	−	0.107510i
$336$	1.69192	−	1.22925i	0.0923019	−	0.0670613i
$337$	12.1056	−	16.6620i	0.659437	−	0.907637i	−0.340026	−	0.940416i	$-0.610436\pi$
$337$	12.1056	−	16.6620i	0.659437	−	0.907637i	0.999463	+	0.0327793i	$0.0104358\pi$
$338$	−2.07801	+	2.86013i	−0.113029	+	0.155571i
$339$	−10.2043	+	7.41388i	−0.554223	+	0.402667i
$340$	−0.0679831	+	13.0553i	−0.00368690	+	0.708024i
$341$	4.27523	+	3.10614i	0.231517	+	0.168207i
$342$	1.87866	−	0.610415i	0.101586	−	0.0330074i
$343$		−	1.00000i		−	0.0539949i
$344$	6.22049	+	19.1447i	0.335386	+	1.03221i
$345$	−0.140701	−	0.440829i	−0.00757506	−	0.0237335i
$346$	−1.93964	+	5.96959i	−0.104276	+	0.320927i
$347$	−7.70788	−	2.50444i	−0.413781	−	0.134445i	0.0947263	−	0.995503i	$-0.469802\pi$
$347$	−7.70788	−	2.50444i	−0.413781	−	0.134445i	−0.508507	+	0.861058i	$0.669802\pi$
$348$	−3.63101	−	4.99765i	−0.194642	−	0.267902i
$349$	−6.77216			−0.362505			−0.181253	−	0.983437i	$-0.558015\pi$
$349$	−6.77216			−0.362505			−0.181253	+	0.983437i	$0.558015\pi$
$350$	−2.36604	+	1.68166i	−0.126470	+	0.0898885i
$351$	−2.62878			−0.140314
$352$	−3.76029	−	5.17559i	−0.200424	−	0.275860i
$353$	−22.8895	−	7.43725i	−1.21829	−	0.395845i	−0.371828	−	0.928302i	$-0.621269\pi$
$353$	−22.8895	−	7.43725i	−1.21829	−	0.395845i	−0.846457	+	0.532456i	$0.821269\pi$
$354$	0.496502	−	1.52808i	0.0263888	−	0.0812164i
$355$	−0.145696	+	0.440586i	−0.00773274	+	0.0233839i
$356$	2.89564	+	8.91188i	0.153469	+	0.472329i
$357$		−	3.51098i		−	0.185821i
$358$	12.6730	−	4.11772i	0.669791	−	0.217628i
$359$	25.3705	+	18.4328i	1.33900	+	0.972844i	0.999480	+	0.0322468i	$0.0102663\pi$
$359$	25.3705	+	18.4328i	1.33900	+	0.972844i	0.339525	+	0.940597i	$0.389734\pi$
$360$	4.51466	+	1.49294i	0.237944	+	0.0786848i
$361$	6.00529	−	4.36310i	0.316068	−	0.229637i
$362$	−5.76925	+	7.94069i	−0.303225	+	0.417354i
$363$	−5.66084	+	7.79147i	−0.297117	+	0.408946i
$364$	−3.53665	+	2.56952i	−0.185371	+	0.134680i
$365$	12.7561	+	17.7509i	0.667685	+	0.929126i
$366$	0.252758	+	0.183639i	0.0132119	+	0.00959897i
$367$	−18.8360	+	6.12018i	−0.983230	+	0.319471i	−0.756145	−	0.654404i	$-0.772920\pi$
$367$	−18.8360	+	6.12018i	−0.983230	+	0.319471i	−0.227085	+	0.973875i	$0.572920\pi$
$368$			0.432787i			0.0225606i
$369$	−0.920109	−	2.83180i	−0.0478990	−	0.147418i
$370$	−3.24637	−	0.0169049i	−0.168771	−	0.000878842i
$371$	−0.733509	+	2.25751i	−0.0380819	+	0.117204i
$372$	7.14257	+	2.32076i	0.370325	+	0.120326i
$373$	−1.12219	−	1.54456i	−0.0581047	−	0.0799742i	0.778976	−	0.627054i	$-0.215739\pi$
$373$	−1.12219	−	1.54456i	−0.0581047	−	0.0799742i	−0.837080	+	0.547080i	$0.815739\pi$
$374$	−2.38510			−0.123331
$375$	10.5779	+	3.62060i	0.546239	+	0.186967i
$376$	−19.5824			−1.00988
$377$	5.73984	+	7.90021i	0.295617	+	0.406882i
$378$	−0.552141	−	0.179402i	−0.0283991	−	0.00922742i
$379$	11.0119	−	33.8910i	0.565642	−	1.74087i	−0.100396	−	0.994948i	$-0.532011\pi$
$379$	11.0119	−	33.8910i	0.565642	−	1.74087i	0.666037	−	0.745918i	$-0.267989\pi$
$380$	−12.6520	−	0.0658828i	−0.649033	−	0.00337972i
$381$	−3.47475	−	10.6942i	−0.178017	−	0.547880i
$382$			0.340098i			0.0174009i
$383$	4.97223	−	1.61558i	0.254069	−	0.0825521i	−0.179213	−	0.983810i	$-0.557355\pi$
$383$	4.97223	−	1.61558i	0.254069	−	0.0825521i	0.433283	+	0.901258i	$0.357355\pi$
$384$	−9.31990	−	6.77130i	−0.475604	−	0.345547i
$385$	1.52689	+	2.12477i	0.0778177	+	0.108288i
$386$	−2.97714	+	2.16302i	−0.151532	+	0.110095i
$387$	−5.56398	+	7.65816i	−0.282833	+	0.389286i
$388$	15.6157	−	21.4932i	0.792767	−	1.09115i
$389$	−15.0238	+	10.9154i	−0.761737	+	0.553434i	−0.899443	−	0.437039i	$-0.856027\pi$
$389$	−15.0238	+	10.9154i	−0.761737	+	0.553434i	0.137706	+	0.990473i	$0.456027\pi$
$390$	−3.24002	−	1.07143i	−0.164065	−	0.0542540i
$391$	0.587809	+	0.427068i	0.0297268	+	0.0215978i
$392$	−2.02247	+	0.657140i	−0.102150	+	0.0331906i
$393$		−	2.18765i		−	0.110353i
$394$	0.609117	+	1.87467i	0.0306869	+	0.0944444i
$395$	4.05363	−	12.2582i	0.203960	−	0.616778i
$396$	0.601309	−	1.85064i	0.0302169	−	0.0929981i
$397$	−27.2471	−	8.85311i	−1.36749	−	0.444325i	−0.468955	−	0.883222i	$-0.655369\pi$
$397$	−27.2471	−	8.85311i	−1.36749	−	0.444325i	−0.898537	+	0.438897i	$0.855369\pi$
$398$	−0.694117	−	0.955371i	−0.0347930	−	0.0478884i
$399$	3.40251			0.170338
$400$	−8.39514	−	6.23404i	−0.419757	−	0.311702i
$401$	19.6113			0.979344			0.489672	−	0.871907i	$-0.337117\pi$
$401$	19.6113			0.979344			0.489672	+	0.871907i	$0.337117\pi$
$402$	0.987620	+	1.35934i	0.0492580	+	0.0677978i
$403$	−11.2909	−	3.66862i	−0.562438	−	0.182747i
$404$	−2.21946	+	6.83080i	−0.110422	+	0.339845i
$405$	0.679900	+	2.13020i	0.0337845	+	0.105850i
$406$	0.666429	+	2.05106i	0.0330743	+	0.101792i
$407$			2.92624i			0.145049i
$408$	−7.10084	+	2.30720i	−0.351544	+	0.114223i
$409$	−17.3735	−	12.6226i	−0.859065	−	0.624147i	0.0685654	−	0.997647i	$-0.478158\pi$
$409$	−17.3735	−	12.6226i	−0.859065	−	0.624147i	−0.927630	+	0.373499i	$0.878158\pi$
$410$	0.0201277	−	3.86527i	0.000994034	−	0.190892i
$411$	12.9226	−	9.38883i	0.637426	−	0.463117i
$412$	−4.39061	+	6.04316i	−0.216310	+	0.297725i
$413$	1.62672	−	2.23899i	0.0800459	−	0.110174i
$414$	0.0971969	−	0.0706177i	0.00477697	−	0.00347067i
$415$	−27.7780	+	8.86598i	−1.36357	+	0.435214i
$416$	11.6273	+	8.44772i	0.570075	+	0.414184i
$417$	−8.82656	+	2.86792i	−0.432239	+	0.140443i
$418$		−	2.31141i		−	0.113055i
$419$	−9.88400	−	30.4198i	−0.482865	−	1.48611i	−0.835049	−	0.550175i	$-0.814561\pi$
$419$	−9.88400	−	30.4198i	−0.482865	−	1.48611i	0.352184	−	0.935931i	$-0.385439\pi$
$420$	2.99689	+	2.20130i	0.146233	+	0.107413i
$421$	−1.65891	+	5.10559i	−0.0808502	+	0.248831i	−0.983309	−	0.181946i	$-0.941760\pi$
$421$	−1.65891	+	5.10559i	−0.0808502	+	0.248831i	0.902458	+	0.430777i	$0.141760\pi$
$422$	−13.1367	−	4.26838i	−0.639485	−	0.207781i
$423$	−5.41264	−	7.44985i	−0.263171	−	0.362224i
$424$	5.04776			0.245141
$425$	−16.7513	+	5.25059i	−0.812556	+	0.254691i
$426$	−0.120483			−0.00583741
$427$	0.316316	+	0.435372i	0.0153076	+	0.0210691i
$428$	−32.3569	−	10.5134i	−1.56403	−	0.508184i
$429$	−0.950541	+	2.92546i	−0.0458925	+	0.141243i
$430$	−9.97900	+	7.17107i	−0.481230	+	0.345820i
$431$	−2.94457	−	9.06244i	−0.141835	−	0.436522i	0.854756	−	0.519031i	$-0.173707\pi$
$431$	−2.94457	−	9.06244i	−0.141835	−	0.436522i	−0.996590	+	0.0825082i	$0.973707\pi$
$432$		−	2.09133i		−	0.100619i
$433$	16.1752	−	5.25565i	0.777332	−	0.252570i	0.106631	−	0.994299i	$-0.465994\pi$
$433$	16.1752	−	5.25565i	0.777332	−	0.252570i	0.670700	+	0.741728i	$0.265994\pi$
$434$	−2.12114	−	1.54110i	−0.101818	−	0.0739750i
$435$	4.91731	−	6.69450i	0.235767	−	0.320977i
$436$	−26.6416	+	19.3563i	−1.27590	+	0.926998i
$437$	−0.413874	+	0.569649i	−0.0197983	+	0.0272500i
$438$	−3.33585	+	4.59141i	−0.159393	+	0.219386i
$439$	−4.80306	+	3.48963i	−0.229238	+	0.166551i	−0.696475	−	0.717581i	$-0.745249\pi$
$439$	−4.80306	+	3.48963i	−0.229238	+	0.166551i	0.467237	+	0.884132i	$0.345249\pi$
$440$	3.29389	−	4.48436i	0.157030	−	0.213784i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	5.09602	−	1.65580i	0.242393	−	0.0787583i
$443$		−	15.1501i		−	0.719805i	−0.932990	−	0.359902i	$-0.882810\pi$
$443$		−	15.1501i		−	0.719805i	0.932990	−	0.359902i	$-0.117190\pi$
$444$	1.28510	+	3.95515i	0.0609884	+	0.187703i
$445$	−10.2320	+	7.35286i	−0.485042	+	0.348559i
$446$	−3.10280	+	9.54944i	−0.146922	+	0.452179i
$447$	−0.420118	−	0.136505i	−0.0198709	−	0.00645645i
$448$	−0.592859	−	0.816000i	−0.0280099	−	0.0385524i
$449$	30.1718			1.42389			0.711947	−	0.702233i	$-0.247814\pi$
$449$	30.1718			1.42389			0.711947	+	0.702233i	$0.247814\pi$
$450$	−0.0302305	+	2.90262i	−0.00142508	+	0.136831i
$451$	−3.48411			−0.164060
$452$	12.3289	+	16.9693i	0.579905	+	0.798171i
$453$	−5.80318	−	1.88557i	−0.272657	−	0.0885916i
$454$	−0.303547	+	0.934223i	−0.0142462	+	0.0438453i
$455$	−4.73744	−	3.47979i	−0.222095	−	0.163135i
$456$	−2.23592	−	6.88146i	−0.104707	−	0.322254i
$457$			28.0291i			1.31115i	0.755131	+	0.655574i	$0.227573\pi$
$457$			28.0291i			1.31115i	−0.755131	+	0.655574i	$0.772427\pi$
$458$	8.92516	−	2.89996i	0.417045	−	0.135506i
$459$	−2.84044	−	2.06370i	−0.132580	−	0.0963253i
$460$	−0.733080	+	0.233979i	−0.0341800	+	0.0109093i
$461$	26.0471	−	18.9243i	1.21313	−	0.881393i	0.217622	−	0.976033i	$-0.430170\pi$
$461$	26.0471	−	18.9243i	1.21313	−	0.881393i	0.995512	+	0.0946396i	$0.0301699\pi$
$462$	−0.399298	+	0.549587i	−0.0185770	+	0.0255691i
$463$	16.5164	−	22.7328i	0.767580	−	1.05648i	−0.228965	−	0.973435i	$-0.573534\pi$
$463$	16.5164	−	22.7328i	0.767580	−	1.05648i	0.996545	−	0.0830491i	$-0.0264658\pi$
$464$	−6.28504	+	4.56635i	−0.291776	+	0.211988i
$465$	−0.0525847	+	10.0983i	−0.00243856	+	0.468295i
$466$	11.5568	+	8.39654i	0.535361	+	0.388962i
$467$	−26.0424	+	8.46170i	−1.20510	+	0.391561i	−0.841635	−	0.540047i	$-0.818406\pi$
$467$	−26.0424	+	8.46170i	−1.20510	+	0.391561i	−0.363465	+	0.931608i	$0.618406\pi$
$468$			4.37154i			0.202074i
$469$	0.894355	+	2.75254i	0.0412975	+	0.127101i
$470$	−3.63479	−	11.3882i	−0.167660	−	0.525297i
$471$	−3.19818	+	9.84297i	−0.147364	+	0.453540i
$472$	−5.59728	−	1.81867i	−0.257636	−	0.0837109i
$473$	6.51059	+	8.96105i	0.299357	+	0.412030i
$474$	3.35213			0.153968
$475$	−5.08837	−	16.2338i	−0.233471	−	0.744856i
$476$	−5.83860			−0.267612
$477$	1.39522	+	1.92035i	0.0638826	+	0.0879269i
$478$	−10.2052	−	3.31587i	−0.466776	−	0.151665i
$479$	3.74270	−	11.5188i	0.171008	−	0.526309i	−0.828420	−	0.560107i	$-0.810760\pi$
$479$	3.74270	−	11.5188i	0.171008	−	0.526309i	0.999429	+	0.0337975i	$0.0107601\pi$
$480$	3.83826	−	11.6069i	0.175192	−	0.529782i
$481$	−2.03147	−	6.25224i	−0.0926273	−	0.285077i
$482$			11.6955i			0.532713i
$483$	0.196815	−	0.0639489i	0.00895537	−	0.00290978i
$484$	12.9569	+	9.41372i	0.588949	+	0.427896i
$485$	33.9166	+	11.2158i	1.54007	+	0.509281i
$486$	−0.469679	+	0.341242i	−0.0213051	+	0.0154790i
$487$	−18.2308	+	25.0925i	−0.826115	+	1.13705i	0.162519	+	0.986705i	$0.448038\pi$
$487$	−18.2308	+	25.0925i	−0.826115	+	1.13705i	−0.988634	+	0.150344i	$0.951962\pi$
$488$	0.672662	−	0.925840i	0.0304500	−	0.0419108i
$489$	13.1781	−	9.57441i	0.595932	−	0.432970i
$490$	−0.757561	−	1.05419i	−0.0342231	−	0.0476236i
$491$	−7.30009	−	5.30382i	−0.329448	−	0.239358i	0.410748	−	0.911749i	$-0.365268\pi$
$491$	−7.30009	−	5.30382i	−0.329448	−	0.239358i	−0.740196	+	0.672391i	$0.765268\pi$
$492$	−4.70916	+	1.53010i	−0.212306	+	0.0689823i
$493$			13.0423i			0.587398i
$494$	1.60464	+	4.93858i	0.0721963	+	0.222197i
$495$	2.61646	+	0.0136247i	0.117601	+	0.000612385i
$496$	2.91859	−	8.98248i	0.131048	−	0.403325i
$497$	−0.197373	−	0.0641303i	−0.00885338	−	0.00287664i
$498$	−4.44984	−	6.12468i	−0.199402	−	0.274453i
$499$	40.8254			1.82759			0.913797	−	0.406171i	$-0.133136\pi$
$499$	40.8254			1.82759			0.913797	+	0.406171i	$0.133136\pi$
$500$	6.02089	−	17.5905i	0.269262	−	0.786672i
$501$	−1.27534			−0.0569781
$502$	7.92409	+	10.9066i	0.353670	+	0.486784i
$503$	−37.3490	−	12.1354i	−1.66531	−	0.541093i	−0.683337	−	0.730104i	$-0.739472\pi$
$503$	−37.3490	−	12.1354i	−1.66531	−	0.541093i	−0.981975	+	0.189011i	$0.939472\pi$
$504$	−0.657140	+	2.02247i	−0.0292713	+	0.0900879i
$505$	−9.65748	−	0.0502895i	−0.429752	−	0.00223785i
$506$	−0.0434422	−	0.133701i	−0.00193124	−	0.00594375i
$507$			6.08954i			0.270446i
$508$	−17.7840	+	5.77836i	−0.789036	+	0.256373i
$509$	28.5049	+	20.7101i	1.26346	+	0.917957i	0.998922	−	0.0464185i	$-0.0147808\pi$
$509$	28.5049	+	20.7101i	1.26346	+	0.917957i	0.264537	+	0.964375i	$0.414781\pi$
$510$	−2.65978	−	3.70125i	−0.117777	−	0.163894i
$511$	−7.90864	+	5.74597i	−0.349858	+	0.254187i
$512$	−11.9487	+	16.4460i	−0.528065	+	0.726819i
$513$	1.99994	−	2.75269i	0.0882996	−	0.121534i
$514$	3.64239	−	2.64635i	0.160659	−	0.116726i
$515$	−9.53621	−	3.15350i	−0.420216	−	0.138960i
$516$	12.7352	+	9.25264i	0.560635	+	0.407325i
$517$	−10.2478	+	3.32972i	−0.450698	+	0.146441i
$518$		−	1.45184i		−	0.0637903i
$519$	3.34101	+	10.2826i	0.146654	+	0.451354i
$520$	−3.92460	+	11.8680i	−0.172105	+	0.520448i
$521$	0.0461803	−	0.142128i	0.00202319	−	0.00622675i	−0.950040	−	0.312129i	$-0.898958\pi$
$521$	0.0461803	−	0.142128i	0.00202319	−	0.00622675i	0.952063	+	0.305902i	$0.0989580\pi$
$522$	2.05106	+	0.666429i	0.0897723	+	0.0291688i
$523$	−20.4895	−	28.2013i	−0.895941	−	1.23316i	−0.971745	−	0.236035i	$-0.924152\pi$
$523$	−20.4895	−	28.2013i	−0.895941	−	1.23316i	0.0758034	−	0.997123i	$-0.475848\pi$
$524$	−3.63797			−0.158925
$525$	−1.59452	+	4.73893i	−0.0695907	+	0.206824i
$526$	9.71997			0.423811
$527$	−9.31995	−	12.8278i	−0.405984	−	0.558789i
$528$	−2.32736	−	0.756206i	−0.101285	−	0.0329096i
$529$	7.09416	−	21.8336i	0.308442	−	0.949286i
$530$	0.936940	+	2.93553i	0.0406981	+	0.127511i
$531$	−0.855219	−	2.63209i	−0.0371134	−	0.114223i
$532$		−	5.65822i		−	0.245315i
$533$	7.44418	−	2.41876i	0.322443	−	0.104768i
$534$	−2.64657	−	1.92285i	−0.114528	−	0.0832097i
$535$	0.238217	−	45.7466i	0.0102990	−	1.97780i
$536$	4.97921	−	3.61761i	0.215069	−	0.156257i
$537$	13.4912	−	18.5690i	0.582187	−	0.801312i
$538$	1.34353	−	1.84921i	0.0579235	−	0.0797249i
$539$	−0.946657	+	0.687786i	−0.0407754	+	0.0296251i
$540$	3.54242	−	1.13064i	0.152442	−	0.0486551i
$541$	−25.1060	−	18.2406i	−1.07939	−	0.784223i	−0.101814	−	0.994803i	$-0.532465\pi$
$541$	−25.1060	−	18.2406i	−1.07939	−	0.784223i	−0.977577	+	0.210580i	$0.932465\pi$
$542$	15.5591	−	5.05546i	0.668321	−	0.217151i
$543$			16.9066i			0.725533i
$544$	5.93168	+	18.2558i	0.254319	+	0.782712i
$545$	−35.6873	−	26.2133i	−1.52867	−	1.12286i
$546$	0.471606	−	1.45145i	0.0201829	−	0.0621165i
$547$	−3.79567	−	1.23329i	−0.162291	−	0.0527315i	0.226745	−	0.973954i	$-0.427192\pi$
$547$	−3.79567	−	1.23329i	−0.162291	−	0.0527315i	−0.389036	+	0.921223i	$0.627192\pi$
$548$	−15.6132	−	21.4897i	−0.666963	−	0.917996i
$549$	0.538149			0.0229677
$550$	3.21928	+	1.08320i	0.137271	+	0.0461879i
$551$	−12.6394			−0.538457
$552$	−0.258669	−	0.356028i	−0.0110097	−	0.0151536i
$553$	5.49141	+	1.78427i	0.233518	+	0.0758747i
$554$	−3.83892	+	11.8150i	−0.163100	+	0.501971i
$555$	−4.54101	+	3.26324i	−0.192755	+	0.138517i
$556$	4.76923	+	14.6782i	0.202260	+	0.622494i
$557$		−	10.4646i		−	0.443399i	−0.975115	−	0.221699i	$-0.928840\pi$
$557$		−	10.4646i		−	0.443399i	0.975115	−	0.221699i	$-0.0711603\pi$
$558$	−2.49355	+	0.810202i	−0.105560	+	0.0342986i
$559$	−20.1316	−	14.6264i	−0.851475	−	0.618633i
$560$	2.76836	−	3.76889i	0.116984	−	0.159265i
$561$	−3.32369	+	2.41480i	−0.140326	+	0.101953i
$562$	0.269072	−	0.370345i	0.0113501	−	0.0156221i
$563$	19.1085	−	26.3006i	0.805327	−	1.10844i	−0.186700	−	0.982417i	$-0.559779\pi$
$563$	19.1085	−	26.3006i	0.805327	−	1.10844i	0.992028	−	0.126021i	$-0.0402206\pi$
$564$	−12.3888	+	9.00097i	−0.521662	+	0.379009i
$565$	−16.6965	+	22.7309i	−0.702428	+	0.956298i
$566$	2.14825	+	1.56080i	0.0902978	+	0.0656052i
$567$	−0.951057	+	0.309017i	−0.0399406	+	0.0129775i
$568$			0.441323i			0.0185175i
$569$	10.2492	+	31.5439i	0.429670	+	1.32239i	0.898451	+	0.439074i	$0.144693\pi$
$569$	10.2492	+	31.5439i	0.429670	+	1.32239i	−0.468781	+	0.883314i	$0.655307\pi$
$570$	3.58690	−	2.57761i	0.150239	−	0.107964i
$571$	1.04347	−	3.21148i	0.0436679	−	0.134396i	−0.926846	−	0.375443i	$-0.877491\pi$
$571$	1.04347	−	3.21148i	0.0436679	−	0.134396i	0.970514	+	0.241047i	$0.0774907\pi$
$572$	4.86492	+	1.58071i	0.203412	+	0.0660927i
$573$	0.344333	+	0.473934i	0.0143847	+	0.0197989i
$574$	1.72862			0.0721514
$575$	−0.599440	−	0.843391i	−0.0249984	−	0.0351718i
$576$	−1.00863			−0.0420263
$577$	−13.8927	−	19.1216i	−0.578360	−	0.796044i	0.415155	−	0.909751i	$-0.363727\pi$
$577$	−13.8927	−	19.1216i	−0.578360	−	0.796044i	−0.993514	+	0.113707i	$0.963727\pi$
$578$	−2.58018	−	0.838352i	−0.107321	−	0.0348709i
$579$	−1.95875	+	6.02842i	−0.0814030	+	0.250533i
$580$	−11.1327	−	8.17726i	−0.462259	−	0.339542i
$581$	−4.02962	−	12.4019i	−0.167177	−	0.514518i
$582$			9.27483i			0.384454i
$583$	2.64158	−	0.858303i	0.109403	−	0.0355473i
$584$	16.8181	+	12.2191i	0.695939	+	0.505629i
$585$	−5.59981	+	1.78730i	−0.231524	+	0.0738959i
$586$	−12.7731	+	9.28023i	−0.527653	+	0.383363i
$587$	−7.43963	+	10.2398i	−0.307066	+	0.422640i	−0.934464	−	0.356059i	$-0.884120\pi$
$587$	−7.43963	+	10.2398i	−0.307066	+	0.422640i	0.627397	+	0.778699i	$0.284120\pi$
$588$	−0.977461	+	1.34536i	−0.0403098	+	0.0554817i
$589$	12.4315	−	9.03202i	0.512231	−	0.372158i
$590$	0.0187082	−	3.59268i	0.000770203	−	0.147908i
$591$	2.74683	+	1.99569i	0.112990	+	0.0820917i
$592$	4.97399	−	1.61615i	0.204430	−	0.0664232i
$593$			25.0856i			1.03014i	0.857148	+	0.515071i	$0.172234\pi$
$593$			25.0856i			1.03014i	−0.857148	+	0.515071i	$0.827766\pi$
$594$	0.209923	+	0.646078i	0.00861326	+	0.0265089i
$595$	−2.38711	−	7.47907i	−0.0978620	−	0.306612i
$596$	−0.227001	+	0.698638i	−0.00929833	+	0.0286173i
$597$	−1.93454	−	0.628569i	−0.0791753	−	0.0257256i
$598$	0.185638	+	0.255509i	0.00759130	+	0.0104485i
$599$	−35.0753			−1.43314			−0.716569	−	0.697516i	$-0.754289\pi$
$599$	−35.0753			−1.43314			−0.716569	+	0.697516i	$0.754289\pi$
$600$	10.6322	+	0.110733i	0.434056	+	0.00452065i
$601$	26.3021			1.07289			0.536443	−	0.843936i	$-0.319768\pi$
$601$	26.3021			1.07289			0.536443	+	0.843936i	$0.319768\pi$
$602$	−3.23020	−	4.44598i	−0.131653	−	0.181205i
$603$	2.75254	+	0.894355i	0.112092	+	0.0364209i
$604$	−3.13561	+	9.65042i	−0.127586	+	0.392670i
$605$	−6.76127	+	20.4462i	−0.274885	+	0.831255i
$606$	−0.774838	−	2.38471i	−0.0314756	−	0.0968720i
$607$			34.1007i			1.38411i	0.721847	+	0.692053i	$0.243294\pi$
$607$			34.1007i			1.38411i	−0.721847	+	0.692053i	$0.756706\pi$
$608$	−17.6918	+	5.74842i	−0.717498	+	0.233129i
$609$	3.00528	+	2.18347i	0.121780	+	0.0884785i
$610$	0.663280	+	0.219338i	0.0268554	+	0.00888072i
$611$	19.5840	−	14.2286i	0.792284	−	0.575628i
$612$	−3.43184	+	4.72352i	−0.138724	+	0.190937i
$613$	−16.0804	+	22.1327i	−0.649479	+	0.893932i	−0.999076	−	0.0429684i	$-0.986319\pi$
$613$	−16.0804	+	22.1327i	−0.649479	+	0.893932i	0.349597	+	0.936900i	$0.386319\pi$
$614$	−11.1375	+	8.09188i	−0.449474	+	0.326562i
$615$	−3.88536	−	5.40672i	−0.156673	−	0.218020i
$616$	2.01311	+	1.46261i	0.0811106	+	0.0589303i
$617$	−7.49090	+	2.43394i	−0.301572	+	0.0979868i	−0.455895	−	0.890034i	$-0.650681\pi$
$617$	−7.49090	+	2.43394i	−0.301572	+	0.0979868i	0.154322	+	0.988021i	$0.450681\pi$
$618$		−	2.60777i		−	0.104900i
$619$	5.06367	+	15.5844i	0.203526	+	0.626389i	0.999771	+	0.0214144i	$0.00681693\pi$
$619$	5.06367	+	15.5844i	0.203526	+	0.626389i	−0.796244	+	0.604975i	$0.793183\pi$
$620$	16.7930	+	0.0874461i	0.674421	+	0.00351192i
$621$	0.0639489	−	0.196815i	0.00256618	−	0.00789790i
$622$	18.0056	+	5.85037i	0.721959	+	0.234579i
$623$	−3.31208	−	4.55869i	−0.132696	−	0.182640i
$624$	5.49764			0.220082
$625$	24.9946	+	0.520688i	0.999783	+	0.0208275i
$626$	11.6002			0.463637
$627$	−2.34020	−	3.22101i	−0.0934585	−	0.128635i
$628$	16.3684	+	5.31842i	0.653171	+	0.212228i
$629$	2.71322	−	8.35045i	0.108183	−	0.332954i
$630$	−1.29814	−	0.00675984i	−0.0517193	−	0.000269318i
$631$	6.07463	+	18.6958i	0.241827	+	0.744267i	0.996142	+	0.0877547i	$0.0279692\pi$
$631$	6.07463	+	18.6958i	0.241827	+	0.744267i	−0.754315	+	0.656513i	$0.772031\pi$
$632$		−	12.2787i		−	0.488421i
$633$	−22.6278	+	7.35223i	−0.899376	+	0.292225i
$634$	8.62814	+	6.26871i	0.342667	+	0.248962i
$635$	−14.6729	−	20.4182i	−0.582276	−	0.810273i
$636$	3.19346	−	2.32018i	0.126629	−	0.0920013i
$637$	1.54516	−	2.12672i	0.0612213	−	0.0842639i
$638$	1.48329	−	2.04157i	0.0587239	−	0.0808265i
$639$	−0.167895	+	0.121983i	−0.00664184	+	0.00482558i
$640$	−24.4570	−	8.08761i	−0.966749	−	0.319691i
$641$	6.33446	+	4.60226i	0.250196	+	0.181778i	0.705814	−	0.708397i	$-0.250582\pi$
$641$	6.33446	+	4.60226i	0.250196	+	0.181778i	−0.455618	+	0.890176i	$0.650582\pi$
$642$	11.2961	−	3.67034i	0.445823	−	0.144857i
$643$			16.6199i			0.655425i	0.944778	+	0.327712i	$0.106278\pi$
$643$			16.6199i			0.655425i	−0.944778	+	0.327712i	$0.893722\pi$
$644$	−0.106344	−	0.327294i	−0.00419055	−	0.0128972i
$645$	−6.64558	+	20.0963i	−0.261670	+	0.791292i
$646$	−2.14315	+	6.59594i	−0.0843212	+	0.259514i
$647$	−32.3212	−	10.5018i	−1.27068	−	0.412868i	−0.405389	−	0.914144i	$-0.632864\pi$
$647$	−32.3212	−	10.5018i	−1.27068	−	0.412868i	−0.865287	+	0.501276i	$0.832864\pi$
$648$	1.24995	+	1.72041i	0.0491028	+	0.0675842i
$649$	−3.23840			−0.127118
$650$	−7.63034	−	0.0794692i	−0.299286	−	0.00311704i
$651$	−4.51614			−0.177001
$652$	−15.9218	−	21.9145i	−0.623547	−	0.858238i
$653$	−9.58183	−	3.11332i	−0.374966	−	0.121834i	0.115470	−	0.993311i	$-0.463162\pi$
$653$	−9.58183	−	3.11332i	−0.374966	−	0.121834i	−0.490436	+	0.871477i	$0.663162\pi$
$654$	3.55262	−	10.9338i	0.138918	−	0.427547i
$655$	−1.48739	−	4.66013i	−0.0581169	−	0.182086i
$656$	1.92425	+	5.92224i	0.0751295	+	0.231225i
$657$			9.77562i			0.381383i
$658$	5.08441	−	1.65202i	0.198211	−	0.0644026i
$659$	−7.83365	−	5.69148i	−0.305156	−	0.221709i	0.424659	−	0.905353i	$-0.360394\pi$
$659$	−7.83365	−	5.69148i	−0.305156	−	0.221709i	−0.729815	+	0.683645i	$0.760394\pi$
$660$	0.0226573	−	4.35106i	0.000881934	−	0.169365i
$661$	35.0297	−	25.4506i	1.36250	−	0.989913i	0.364217	−	0.931314i	$-0.381337\pi$
$661$	35.0297	−	25.4506i	1.36250	−	0.989913i	0.998282	−	0.0585988i	$-0.0186633\pi$
$662$	−3.46973	+	4.77567i	−0.134855	+	0.185612i
$663$	5.42500	−	7.46688i	0.210690	−	0.289989i
$664$	−22.4344	+	16.2996i	−0.870625	+	0.632546i
$665$	7.24801	−	2.31336i	0.281066	−	0.0897084i
$666$	−1.17456	−	0.853371i	−0.0455135	−	0.0330675i
$667$	−0.731114	+	0.237553i	−0.0283088	+	0.00919810i
$668$			2.12084i			0.0820577i
$669$	5.34454	+	16.4488i	0.206632	+	0.635947i
$670$	3.02804	+	2.22418i	0.116983	+	0.0859277i
$671$	0.194590	−	0.598886i	0.00751206	−	0.0231197i
$672$	5.19965	+	1.68947i	0.200581	+	0.0651726i
$673$	10.7656	+	14.8176i	0.414984	+	0.571176i	0.964425	−	0.264356i	$-0.0851594\pi$
$673$	10.7656	+	14.8176i	0.414984	+	0.571176i	−0.549441	+	0.835532i	$0.685159\pi$
$674$	11.9567			0.460557
$675$	2.89664	+	4.07547i	0.111492	+	0.156865i
$676$	10.1266			0.389486
$677$	9.38324	+	12.9149i	0.360627	+	0.496361i	0.950323	−	0.311264i	$-0.100753\pi$
$677$	9.38324	+	12.9149i	0.360627	+	0.496361i	−0.589696	+	0.807625i	$0.700753\pi$
$678$	−6.96429	−	2.26284i	−0.267462	−	0.0869037i
$679$	−4.93679	+	15.1939i	−0.189457	+	0.583087i
$680$	−13.5575	+	9.74265i	−0.519907	+	0.373614i
$681$	0.522857	+	1.60919i	0.0200359	+	0.0616642i
$682$			3.06793i			0.117477i
$683$	−6.58121	+	2.13836i	−0.251823	+	0.0818222i	−0.432208	−	0.901774i	$-0.642265\pi$
$683$	−6.58121	+	2.13836i	−0.251823	+	0.0818222i	0.180385	+	0.983596i	$0.442265\pi$
$684$	−4.57759	−	3.32582i	−0.175029	−	0.127166i
$685$	21.1443	−	28.7861i	0.807880	−	1.09986i
$686$	0.469679	−	0.341242i	0.0179324	−	0.0130287i
$687$	9.50133	−	13.0775i	0.362499	−	0.498936i
$688$	11.6361	−	16.0157i	0.443623	−	0.610594i
$689$	−5.04817	+	3.66771i	−0.192320	+	0.139729i
$690$	0.159036	−	0.216514i	0.00605438	−	0.00824253i
$691$	14.5589	+	10.5777i	0.553847	+	0.402394i	0.829202	−	0.558949i	$-0.188795\pi$
$691$	14.5589	+	10.5777i	0.553847	+	0.402394i	−0.275355	+	0.961343i	$0.588795\pi$
$692$	17.0994	−	5.55594i	0.650023	−	0.211205i
$693$			1.17013i			0.0444496i
$694$	−1.45397	−	4.47485i	−0.0551919	−	0.169863i
$695$	−16.8524	+	12.1104i	−0.639248	+	0.459374i
$696$	2.44110	−	7.51293i	0.0925296	−	0.284777i
$697$	9.94240	+	3.23048i	0.376595	+	0.122363i
$698$	−2.31094	−	3.18074i	−0.0874705	−	0.120393i
$699$	24.6058			0.930678
$700$	7.88064	+	2.65162i	0.297860	+	0.100222i
$701$	−37.4024			−1.41267			−0.706334	−	0.707878i	$-0.749652\pi$
$701$	−37.4024			−1.41267			−0.706334	+	0.707878i	$0.749652\pi$
$702$	−0.897048	−	1.23468i	−0.0338569	−	0.0466000i
$703$	8.09246	+	2.62940i	0.305213	+	0.0991697i
$704$	−0.364712	+	1.12247i	−0.0137456	+	0.0423046i
$705$	−16.5951	−	12.1896i	−0.625009	−	0.459087i
$706$	−4.31774	−	13.2886i	−0.162500	−	0.500124i
$707$		−	4.31902i		−	0.162433i
$708$	−4.37706	+	1.42219i	−0.164500	+	0.0534492i
$709$	19.8836	+	14.4463i	0.746746	+	0.542542i	0.894816	−	0.446434i	$-0.147306\pi$
$709$	19.8836	+	14.4463i	0.746746	+	0.542542i	−0.148071	+	0.988977i	$0.547306\pi$
$710$	−0.256652	+	0.0819162i	−0.00963197	+	0.00307426i
$711$	4.67127	−	3.39388i	0.175186	−	0.127280i
$712$	−7.04330	+	9.69427i	−0.263959	+	0.363308i
$713$	0.549335	−	0.756094i	0.0205727	−	0.0283160i
$714$	1.64903	−	1.19809i	0.0617135	−	0.0448375i
$715$	−0.0358163	+	6.87808i	−0.00133945	+	0.257226i
$716$	−30.8794	−	22.4352i	−1.15402	−	0.838444i
$717$	−17.5784	+	5.71156i	−0.656476	+	0.213302i
$718$			18.2060i			0.679443i
$719$	9.11922	+	28.0661i	0.340089	+	1.04669i	0.964160	+	0.265320i	$0.0854776\pi$
$719$	9.11922	+	28.0661i	0.340089	+	1.04669i	−0.624071	+	0.781368i	$0.714522\pi$
$720$	−1.42190	−	4.45495i	−0.0529909	−	0.166026i
$721$	1.38806	−	4.27201i	0.0516941	−	0.159098i
$722$	4.09852	+	1.33169i	0.152531	+	0.0495603i
$723$	11.8411	+	16.2979i	0.440375	+	0.606124i
$724$	28.1150			1.04488
$725$	5.92323	−	17.6039i	0.219983	−	0.653792i
$726$	−5.59121			−0.207509
$727$	13.3599	+	18.3884i	0.495492	+	0.681987i	0.981389	−	0.192029i	$-0.0615069\pi$
$727$	13.3599	+	18.3884i	0.495492	+	0.681987i	−0.485897	+	0.874016i	$0.661507\pi$
$728$	−5.31661	−	1.72747i	−0.197047	−	0.0640244i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−3.98432	+	12.0486i	−0.147466	+	0.445940i
$731$	−10.2701	−	31.6083i	−0.379855	−	1.16907i
$732$		−	0.894918i		−	0.0330771i
$733$	26.0558	−	8.46606i	0.962395	−	0.312701i	0.214653	−	0.976690i	$-0.431138\pi$
$733$	26.0558	−	8.46606i	0.962395	−	0.312701i	0.747742	+	0.663989i	$0.231138\pi$
$734$	−9.30215	−	6.75841i	−0.343349	−	0.249457i
$735$	−2.12300	−	0.702047i	−0.0783080	−	0.0258954i
$736$	−0.915327	+	0.665024i	−0.0337394	+	0.0245131i
$737$	1.99059	−	2.73981i	0.0733242	−	0.100922i
$738$	1.01606	−	1.39849i	0.0374017	−	0.0514790i
$739$	29.6117	−	21.5142i	1.08928	−	0.791411i	0.110006	−	0.993931i	$-0.464913\pi$
$739$	29.6117	−	21.5142i	1.08928	−	0.791411i	0.979278	+	0.202520i	$0.0649130\pi$
$740$	5.42663	+	7.55149i	0.199487	+	0.277598i
$741$	7.23619	+	5.25740i	0.265828	+	0.193135i
$742$	−1.31061	+	0.425843i	−0.0481140	+	0.0156332i
$743$		−	10.3435i		−	0.379466i	−0.981836	−	0.189733i	$-0.939238\pi$
$743$		−	10.3435i		−	0.379466i	0.981836	−	0.189733i	$-0.0607622\pi$
$744$	2.96773	+	9.13375i	0.108802	+	0.334859i
$745$	−0.987744	−	0.00514349i	−0.0361881	−	0.000188443i
$746$	0.342510	−	1.05414i	0.0125402	−	0.0385947i
$747$	−12.4019	−	4.02962i	−0.453762	−	0.147436i
$748$	4.01571	+	5.52715i	0.146829	+	0.202092i
$749$	20.4588			0.747548
$750$	1.90909	+	6.20370i	0.0697102	+	0.226527i
$751$	11.9203			0.434977			0.217489	−	0.976063i	$-0.430213\pi$
$751$	11.9203			0.434977			0.217489	+	0.976063i	$0.430213\pi$
$752$	11.3196	+	15.5801i	0.412784	+	0.568148i
$753$	22.0848	+	7.17579i	0.804815	+	0.261500i
$754$	−1.75189	+	5.39177i	−0.0638001	+	0.196357i
$755$	−13.6439	−	0.0710480i	−0.496552	−	0.00258570i
$756$	0.513881	+	1.58156i	0.0186897	+	0.0575209i
$757$		−	7.71829i		−	0.280526i	−0.990114	−	0.140263i	$-0.955205\pi$
$757$		−	7.71829i		−	0.280526i	0.990114	−	0.140263i	$-0.0447948\pi$
$758$	19.6756	−	6.39300i	0.714651	−	0.232204i
$759$	−0.195904	−	0.142333i	−0.00711087	−	0.00516635i
$760$	−9.44166	−	13.1387i	−0.342485	−	0.476589i
$761$	−18.4616	+	13.4132i	−0.669233	+	0.486226i	−0.869768	−	0.493460i	$-0.835732\pi$
$761$	−18.4616	+	13.4132i	−0.669233	+	0.486226i	0.200535	+	0.979687i	$0.435732\pi$
$762$	3.83711	−	5.28133i	0.139004	−	0.191322i
$763$	11.6397	−	16.0207i	0.421385	−	0.579987i
$764$	0.788132	−	0.572611i	0.0285136	−	0.0207163i
$765$	−7.45380	−	2.46487i	−0.269493	−	0.0891176i
$766$	2.45554	+	1.78405i	0.0887222	+	0.0644604i
$767$	6.91919	−	2.24818i	0.249837	−	0.0811771i
$768$		−	4.67075i		−	0.168541i
$769$	−14.0226	−	43.1572i	−0.505669	−	1.55629i	−0.799644	−	0.600475i	$-0.794978\pi$
$769$	−14.0226	−	43.1572i	−0.505669	−	1.55629i	0.293975	−	0.955813i	$-0.405022\pi$
$770$	−0.476920	+	1.44221i	−0.0171870	+	0.0519737i
$771$	2.39645	−	7.37551i	0.0863060	−	0.265622i
$772$	10.0250	+	3.25732i	0.360807	+	0.117233i
$773$	−9.39431	−	12.9302i	−0.337890	−	0.465066i	0.605934	−	0.795515i	$-0.292800\pi$
$773$	−9.39431	−	12.9302i	−0.337890	−	0.465066i	−0.943824	+	0.330449i	$0.892800\pi$
$774$	−5.49554			−0.197533
$775$	6.75379	+	21.5470i	0.242603	+	0.773992i
$776$	33.9733			1.21957
$777$	−1.46992	−	2.02317i	−0.0527332	−	0.0725810i
$778$	−10.2535	−	3.33156i	−0.367606	−	0.119442i
$779$	−3.13068	+	9.63523i	−0.112168	+	0.345218i
$780$	2.97221	+	9.31223i	0.106422	+	0.333431i
$781$	0.0750409	+	0.230952i	0.00268518	+	0.00826412i
$782$			0.421815i			0.0150841i
$783$	3.53292	−	1.14792i	0.126256	−	0.0410232i
$784$	1.69192	+	1.22925i	0.0604258	+	0.0439019i
$785$	−0.120507	+	23.1419i	−0.00430108	+	0.825970i
$786$	1.02750	−	0.746519i	0.0366495	−	0.0266275i
$787$	13.9317	−	19.1753i	0.496611	−	0.683527i	−0.484979	−	0.874526i	$-0.661173\pi$
$787$	13.9317	−	19.1753i	0.496611	−	0.683527i	0.981590	+	0.190999i	$0.0611727\pi$
$788$	3.31874	−	4.56786i	0.118225	−	0.162723i
$789$	13.5450	−	9.84102i	0.482215	−	0.350349i
$790$	7.14070	−	2.27911i	0.254055	−	0.0810872i
$791$	−10.2043	−	7.41388i	−0.362824	−	0.263607i
$792$	2.36655	−	0.768940i	0.0840919	−	0.0273231i
$793$			1.41467i			0.0502365i
$794$	−5.13972	−	15.8184i	−0.182402	−	0.561376i
$795$	4.27773	+	3.14212i	0.151716	+	0.111439i
$796$	−1.04528	+	3.21705i	−0.0370490	+	0.114025i
$797$	33.6352	+	10.9287i	1.19142	+	0.387116i	0.836598	−	0.547818i	$-0.184541\pi$
$797$	33.6352	+	10.9287i	1.19142	+	0.387116i	0.354823	+	0.934934i	$0.384541\pi$
$798$	1.16108	+	1.59809i	0.0411017	+	0.0565716i
$799$	32.3309			1.14379
$800$	0.284688	−	27.3347i	0.0100652	−	0.966427i
$801$	−5.63485			−0.199098
$802$	6.69221	+	9.21104i	0.236310	+	0.325253i
$803$	10.8789	+	3.53477i	0.383909	+	0.124739i
$804$	1.48727	−	4.57735i	0.0524521	−	0.161431i
$805$	0.375775	−	0.270038i	0.0132443	−	0.00951759i
$806$	−2.12984	−	6.55497i	−0.0750204	−	0.230889i
$807$		−	3.93717i		−	0.138595i
$808$	−8.73507	+	2.83820i	−0.307299	+	0.0998474i
$809$	6.14671	+	4.46584i	0.216107	+	0.157011i	0.690572	−	0.723263i	$-0.257359\pi$
$809$	6.14671	+	4.46584i	0.216107	+	0.157011i	−0.474466	+	0.880274i	$0.657359\pi$
$810$	−0.768499	+	1.04625i	−0.0270023	+	0.0367614i
$811$	31.7361	−	23.0576i	1.11440	−	0.809662i	0.131052	−	0.991375i	$-0.458164\pi$
$811$	31.7361	−	23.0576i	1.11440	−	0.809662i	0.983351	+	0.181714i	$0.0581645\pi$
$812$	3.63101	−	4.99765i	0.127423	−	0.175383i
$813$	16.5635	−	22.7978i	0.580909	−	0.799553i
$814$	−1.37440	+	0.998557i	−0.0481725	+	0.0349994i
$815$	21.5622	−	29.3551i	0.755291	−	1.02827i
$816$	5.94030	+	4.31588i	0.207952	+	0.151086i
$817$	30.6318	−	9.95286i	1.07167	−	0.348206i
$818$		−	12.4673i		−	0.435910i
$819$	−0.812336	−	2.50011i	−0.0283853	−	0.0873611i
$820$	−8.99113	+	6.46117i	−0.313984	+	0.225634i
$821$	−9.96255	+	30.6616i	−0.347695	+	1.07010i	0.612430	+	0.790525i	$0.290192\pi$
$821$	−9.96255	+	30.6616i	−0.347695	+	1.07010i	−0.960125	+	0.279571i	$0.909808\pi$
$822$	8.81948	+	2.86562i	0.307615	+	0.0999501i
$823$	−1.36013	−	1.87206i	−0.0474113	−	0.0652561i	0.784653	−	0.619935i	$-0.212841\pi$
$823$	−1.36013	−	1.87206i	−0.0474113	−	0.0652561i	−0.832064	+	0.554679i	$0.812841\pi$
$824$	−9.55215			−0.332765
$825$	5.58284	−	1.74991i	0.194369	−	0.0609239i
$826$	1.60672			0.0559048
$827$	−4.06701	−	5.59775i	−0.141424	−	0.194653i	0.732430	−	0.680843i	$-0.238386\pi$
$827$	−4.06701	−	5.59775i	−0.141424	−	0.194653i	−0.873853	+	0.486190i	$0.838386\pi$
$828$	−0.327294	−	0.106344i	−0.0113742	−	0.00369572i
$829$	−5.74036	+	17.6670i	−0.199371	+	0.613601i	0.800527	+	0.599297i	$0.204553\pi$
$829$	−5.74036	+	17.6670i	−0.199371	+	0.613601i	−0.999898	+	0.0143036i	$0.995447\pi$
$830$	−13.6432	−	10.0213i	−0.473562	−	0.347845i
$831$	6.61250	+	20.3512i	0.229385	+	0.705975i
$832$		−	2.65147i		−	0.0919230i
$833$	3.33914	−	1.08495i	0.115694	−	0.0375913i
$834$	−4.35900	−	3.16700i	−0.150940	−	0.109664i
$835$	−2.71673	+	0.867106i	−0.0940164	+	0.0300074i
$836$	−5.35639	+	3.89164i	−0.185255	+	0.134595i
$837$	−2.65452	+	3.65363i	−0.0917536	+	0.126288i
$838$	10.9147	−	15.0228i	0.377043	−	0.518955i
$839$	−27.6786	+	20.1097i	−0.955572	+	0.694264i	−0.952118	−	0.305731i	$-0.901099\pi$
$839$	−27.6786	+	20.1097i	−0.955572	+	0.694264i	−0.00345367	+	0.999994i	$0.501099\pi$
$840$	−0.0247610	+	4.75504i	−0.000854335	+	0.164065i
$841$	12.2977	+	8.93478i	0.424057	+	0.308096i
$842$	−2.96408	+	0.963088i	−0.102149	+	0.0331902i
$843$		−	0.788507i		−	0.0271576i
$844$	12.2264	+	37.6291i	0.420851	+	1.29525i
$845$	4.14028	+	12.9719i	0.142430	+	0.446247i
$846$	1.65202	−	5.08441i	0.0567977	−	0.174805i
$847$	−9.15943	−	2.97608i	−0.314722	−	0.102259i
$848$	−2.91786	−	4.01609i	−0.100200	−	0.137913i
$849$	4.57387			0.156975
$850$	−8.18233	−	6.07600i	−0.280652	−	0.208405i
$851$	0.517519			0.0177403
$852$	0.202852	+	0.279202i	0.00694961	+	0.00956532i
$853$	−10.7270	−	3.48542i	−0.367287	−	0.119339i	0.119558	−	0.992827i	$-0.461852\pi$
$853$	−10.7270	−	3.48542i	−0.367287	−	0.119339i	−0.486845	+	0.873489i	$0.661852\pi$
$854$	−0.0965448	+	0.297134i	−0.00330370	+	0.0101677i
$855$	2.38872	−	7.22352i	0.0816925	−	0.247039i
$856$	−13.4443	−	41.3773i	−0.459516	−	1.41425i
$857$			30.8101i			1.05245i	0.850345	+	0.526226i	$0.176394\pi$
$857$			30.8101i			1.05245i	−0.850345	+	0.526226i	$0.823606\pi$
$858$	−1.69839	+	0.551842i	−0.0579822	+	0.0188396i
$859$	−13.8869	−	10.0895i	−0.473816	−	0.344248i	0.325110	−	0.945676i	$-0.394599\pi$
$859$	−13.8869	−	10.0895i	−0.473816	−	0.344248i	−0.798927	+	0.601428i	$0.794599\pi$
$860$	33.4193	+	11.0513i	1.13959	+	0.376846i
$861$	2.40888	−	1.75015i	0.0820943	−	0.0596450i
$862$	3.25163	−	4.47549i	0.110751	−	0.152436i
$863$	6.78609	−	9.34025i	0.231001	−	0.317946i	−0.677743	−	0.735298i	$-0.737042\pi$
$863$	6.78609	−	9.34025i	0.231001	−	0.317946i	0.908745	+	0.417353i	$0.137042\pi$
$864$	4.42308	−	3.21356i	0.150476	−	0.109327i
$865$	14.1081	+	19.6323i	0.479690	+	0.667519i
$866$	7.98813	+	5.80372i	0.271448	+	0.197218i
$867$	−4.44434	+	1.44405i	−0.150938	+	0.0490426i
$868$			7.51014i			0.254911i
$869$	−2.08783	−	6.42567i	−0.0708247	−	0.217976i
$870$	4.82226	+	0.0251110i	0.163490	+	0.000851342i
$871$	−2.35106	+	7.23581i	−0.0796626	+	0.245176i
$872$	−40.0502	−	13.0131i	−1.35627	−	0.440679i
$873$	9.39033	+	12.9247i	0.317815	+	0.437434i
$874$	−0.408784			−0.0138273
$875$	−0.174650	+	11.1790i	−0.00590424	+	0.377918i
$876$	16.2564			0.549254
$877$	−14.3087	−	19.6942i	−0.483169	−	0.665025i	0.495941	−	0.868356i	$-0.334823\pi$
$877$	−14.3087	−	19.6942i	−0.483169	−	0.665025i	−0.979110	+	0.203331i	$0.934823\pi$
$878$	−3.27801	−	1.06509i	−0.110628	−	0.0359451i
$879$	−8.40385	+	25.8644i	−0.283455	+	0.872385i
$880$	−5.47188	−	0.0284938i	−0.184457	−	0.000960525i
$881$	−15.7100	−	48.3503i	−0.529283	−	1.62896i	−0.755688	−	0.654932i	$-0.772697\pi$
$881$	−15.7100	−	48.3503i	−0.529283	−	1.62896i	0.226406	−	0.974033i	$-0.427303\pi$
$882$		−	0.580555i		−	0.0195483i
$883$	−0.918604	+	0.298473i	−0.0309135	+	0.0100444i	−0.324433	−	0.945909i	$-0.605173\pi$
$883$	−0.918604	+	0.298473i	−0.0309135	+	0.0100444i	0.293519	+	0.955953i	$0.405173\pi$
$884$	−12.4171	−	9.02154i	−0.417632	−	0.303427i
$885$	−3.61135	−	5.02542i	−0.121394	−	0.168927i
$886$	7.11571	−	5.16986i	0.239057	−	0.173685i
$887$	−5.92111	+	8.14971i	−0.198811	+	0.273640i	−0.896769	−	0.442498i	$-0.854092\pi$
$887$	−5.92111	+	8.14971i	−0.198811	+	0.273640i	0.697958	+	0.716139i	$0.254092\pi$
$888$	−3.12586	+	4.30238i	−0.104897	+	0.144378i
$889$	9.09702	−	6.60937i	0.305104	−	0.221671i
$890$	−6.94506	−	2.29664i	−0.232799	−	0.0769835i
$891$	0.946657	+	0.687786i	0.0317142	+	0.0230417i
$892$	27.3536	−	8.88773i	0.915867	−	0.297583i
$893$			31.3321i			1.04849i
$894$	−0.0792485	−	0.243902i	−0.00265047	−	0.00815730i
$895$	16.1138	−	48.7283i	0.538624	−	1.62881i
$896$	3.55988	−	10.9562i	0.118927	−	0.366021i
$897$	0.517381	+	0.168107i	0.0172749	+	0.00561294i
$898$	10.2959	+	14.1711i	0.343578	+	0.472894i
$899$	16.7763			0.559520
$900$	6.77733	−	4.81698i	0.225911	−	0.160566i
$901$	−8.33395			−0.277644
$902$	−1.18892	−	1.63641i	−0.0395869	−	0.0544866i
$903$	−9.00270	−	2.92516i	−0.299591	−	0.0973431i
$904$	−8.28866	+	25.5099i	−0.275677	+	0.848446i
$905$	11.4948	+	36.0144i	0.382100	+	1.19716i
$906$	−1.09468	−	3.36907i	−0.0363682	−	0.111930i
$907$			42.4015i			1.40792i	0.710240	+	0.703960i	$0.248587\pi$
$907$			42.4015i			1.40792i	−0.710240	+	0.703960i	$0.751413\pi$
$908$	2.67601	−	0.869488i	0.0888064	−	0.0288550i
$909$	−3.49416	−	2.53865i	−0.115894	−	0.0842018i
$910$	0.0177701	−	3.41253i	0.000589073	−	0.113124i
$911$	−5.14242	+	3.73619i	−0.170376	+	0.123785i	−0.669706	−	0.742627i	$-0.733580\pi$
$911$	−5.14242	+	3.73619i	−0.170376	+	0.123785i	0.499330	+	0.866412i	$0.333580\pi$
$912$	−4.18254	+	5.75678i	−0.138498	+	0.190626i
$913$	−8.96882	+	12.3445i	−0.296825	+	0.408544i
$914$	−13.1647	+	9.56471i	−0.435450	+	0.316373i
$915$	1.14636	−	0.365888i	0.0378976	−	0.0120959i
$916$	−21.7472	−	15.8003i	−0.718549	−	0.522056i
$917$	2.08058	−	0.676022i	0.0687069	−	0.0223242i
$918$		−	2.03832i		−	0.0672745i
$919$	1.44094	+	4.43475i	0.0475321	+	0.146289i	0.972006	−	0.234957i	$-0.0754951\pi$
$919$	1.44094	+	4.43475i	0.0475321	+	0.146289i	−0.924474	+	0.381246i	$0.875495\pi$
$920$	−0.793080	−	0.582540i	−0.0261471	−	0.0192058i
$921$	−7.32773	+	22.5524i	−0.241457	+	0.743128i
$922$	17.7767	+	5.77601i	0.585445	+	0.190223i
$923$	−0.320666	−	0.441359i	−0.0105549	−	0.0145275i
$924$	1.94588			0.0640147
$925$	−7.45456	+	10.0388i	−0.245104	+	0.330073i
$926$	16.3132			0.536085
$927$	−2.64025	−	3.63399i	−0.0867171	−	0.119356i
$928$	−19.3153	−	6.27592i	−0.634056	−	0.206017i
$929$	12.7708	−	39.3046i	0.418998	−	1.28954i	−0.489628	−	0.871931i	$-0.662867\pi$
$929$	12.7708	−	39.3046i	0.418998	−	1.28954i	0.908626	−	0.417611i	$-0.137133\pi$
$930$	−4.76089	+	3.42125i	−0.156116	+	0.112187i
$931$	1.05143	+	3.23598i	0.0344593	+	0.106055i
$932$		−	40.9184i		−	1.34033i
$933$	31.0144	−	10.0772i	1.01537	−	0.329913i
$934$	−12.8610	−	9.34410i	−0.420826	−	0.305748i
$935$	−5.43829	+	7.40378i	−0.177851	+	0.242129i
$936$	−4.52258	+	3.28585i	−0.147825	+	0.107401i
$937$	−4.00281	+	5.50939i	−0.130766	+	0.179984i	−0.869379	−	0.494145i	$-0.835481\pi$
$937$	−4.00281	+	5.50939i	−0.130766	+	0.179984i	0.738613	+	0.674129i	$0.235481\pi$
$938$	−0.987620	+	1.35934i	−0.0322469	+	0.0443841i
$939$	16.1651	−	11.7447i	0.527529	−	0.383272i
$940$	−20.2708	+	27.5970i	−0.661159	+	0.900114i
$941$	−1.31621	−	0.956285i	−0.0429073	−	0.0311740i	0.566125	−	0.824319i	$-0.308442\pi$
$941$	−1.31621	−	0.956285i	−0.0429073	−	0.0311740i	−0.609032	+	0.793145i	$0.708442\pi$
$942$	−5.71439	+	1.85672i	−0.186185	+	0.0604952i
$943$			0.616181i			0.0200656i
$944$	1.78855	+	5.50458i	0.0582122	+	0.179159i
$945$	−1.81584	+	1.30489i	−0.0590692	+	0.0424481i
$946$	−1.98714	+	6.11578i	−0.0646074	+	0.198841i
$947$	−47.4573	−	15.4198i	−1.54215	−	0.501076i	−0.590185	−	0.807268i	$-0.700945\pi$
$947$	−47.4573	−	15.4198i	−1.54215	−	0.501076i	−0.951970	+	0.306192i	$0.900945\pi$
$948$	−5.64386	−	7.76811i	−0.183304	−	0.252297i
$949$	−25.6979			−0.834189
$950$	5.88829	−	7.92954i	0.191041	−	0.257268i
$951$	18.3703			0.595697
$952$	−4.38856	−	6.04033i	−0.142234	−	0.195768i
$953$	11.7052	+	3.80325i	0.379168	+	0.123199i	0.492399	−	0.870369i	$-0.336120\pi$
$953$	11.7052	+	3.80325i	0.379168	+	0.123199i	−0.113231	+	0.993569i	$0.536120\pi$
$954$	−0.425843	+	1.31061i	−0.0137872	+	0.0424325i
$955$	1.05573	+	0.775461i	0.0341625	+	0.0250933i
$956$	9.49806	+	29.2320i	0.307189	+	0.945431i
$957$		−	4.34673i		−	0.140510i
$958$	6.68733	−	2.17284i	0.216058	−	0.0702014i
$959$	12.9226	+	9.38883i	0.417293	+	0.303181i
$960$	−2.14858	+	0.685768i	−0.0693452	+	0.0221331i
$961$	8.57921	−	6.23316i	0.276749	−	0.201070i
$962$	2.24332	−	3.08767i	0.0723276	−	0.0995504i
$963$	12.0254	−	16.5515i	0.387512	−	0.533365i
$964$	27.1026	−	19.6912i	0.872917	−	0.634211i
$965$	−0.0738057	+	14.1735i	−0.00237589	+	0.456260i
$966$	0.0971969	+	0.0706177i	0.00312726	+	0.00227209i
$967$	−38.1600	+	12.3989i	−1.22714	+	0.398723i	−0.849678	−	0.527301i	$-0.823204\pi$
$967$	−38.1600	+	12.3989i	−1.22714	+	0.398723i	−0.377464	+	0.926024i	$0.623204\pi$
$968$			20.4803i			0.658263i
$969$	3.69155	+	11.3614i	0.118590	+	0.364982i
$970$	6.30595	+	19.7572i	0.202472	+	0.634366i
$971$	−16.3843	+	50.4256i	−0.525796	+	1.61824i	0.236939	+	0.971525i	$0.423856\pi$
$971$	−16.3843	+	50.4256i	−0.525796	+	1.61824i	−0.762735	+	0.646711i	$0.776144\pi$
$972$	1.58156	+	0.513881i	0.0507287	+	0.0164828i
$973$	−5.45512	−	7.50832i	−0.174883	−	0.240706i
$974$	−18.0065			−0.576966
$975$	−10.7135	+	7.61462i	−0.343107	+	0.243863i
$976$	−1.12545			−0.0360247
$977$	29.3094	+	40.3410i	0.937692	+	1.29062i	0.956783	+	0.290804i	$0.0939229\pi$
$977$	29.3094	+	40.3410i	0.937692	+	1.29062i	−0.0190907	+	0.999818i	$0.506077\pi$
$978$	8.99381	+	2.92226i	0.287590	+	0.0934437i
$979$	−2.03751	+	6.27081i	−0.0651191	+	0.200416i
$980$	−1.16747	+	3.53045i	−0.0372936	+	0.112776i
$981$	−6.11934	−	18.8334i	−0.195376	−	0.601304i
$982$		−	5.23859i		−	0.167170i
$983$	−17.3794	+	5.64692i	−0.554318	+	0.180109i	−0.572763	−	0.819721i	$-0.694128\pi$
$983$	−17.3794	+	5.64692i	−0.554318	+	0.180109i	0.0184450	+	0.999830i	$0.494128\pi$
$984$	−5.12259	−	3.72178i	−0.163302	−	0.118646i
$985$	7.20816	+	2.38364i	0.229671	+	0.0759491i
$986$	−6.12572	+	4.45059i	−0.195083	+	0.141736i
$987$	5.41264	−	7.44985i	0.172286	−	0.237131i
$988$	8.74282	−	12.0335i	0.278146	−	0.382835i
$989$	1.58480	−	1.15143i	0.0503938	−	0.0366132i
$990$	0.886446	+	1.23355i	0.0281731	+	0.0392047i
$991$	−11.1329	−	8.08856i	−0.353650	−	0.256942i	0.396749	−	0.917927i	$-0.370138\pi$
$991$	−11.1329	−	8.08856i	−0.353650	−	0.256942i	−0.750399	+	0.660986i	$0.770138\pi$
$992$	23.4823	−	7.62987i	0.745565	−	0.242249i
$993$			10.1679i			0.322670i
$994$	−0.0372312	−	0.114586i	−0.00118090	−	0.00363444i
$995$	−4.54831	−	0.0236844i	−0.144191	−	0.000750847i
$996$	−6.70108	+	20.6238i	−0.212332	+	0.653490i
$997$	−36.6129	−	11.8963i	−1.15954	−	0.376758i	−0.334813	−	0.942285i	$-0.608673\pi$
$997$	−36.6129	−	11.8963i	−1.15954	−	0.376758i	−0.824730	+	0.565526i	$0.808673\pi$
$998$	13.9313	+	19.1748i	0.440989	+	0.606969i
$999$	−2.50078			−0.0791212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.64.8	✓	56
25.9	even	10	inner	525.2.z.a.484.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.64.8	✓	56	1.1	even	1	trivial
525.2.z.a.484.8	yes	56	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.341242 + 0.469679i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.513881 - 1.58156i) q^{4} +(2.23604 + 0.0116437i) q^{5} +(0.179402 + 0.552141i) q^{6} +1.00000i q^{7} +(2.02247 - 0.657140i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.341242 + 0.469679i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.513881 - 1.58156i) q^{4} +(2.23604 + 0.0116437i) q^{5} +(0.179402 + 0.552141i) q^{6} +1.00000i q^{7} +(2.02247 - 0.657140i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.757561 + 1.05419i) q^{10} +(0.946657 - 0.687786i) q^{11} +(0.977461 - 1.34536i) q^{12} +(-1.54516 + 2.12672i) q^{13} +(-0.469679 + 0.341242i) q^{14} +(2.12300 + 0.702047i) q^{15} +(-1.69192 - 1.22925i) q^{16} +(-3.33914 + 1.08495i) q^{17} +0.580555i q^{18} +(-1.05143 - 3.23598i) q^{19} +(1.16747 - 3.53045i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.646078 + 0.209923i) q^{22} +(-0.121638 - 0.167420i) q^{23} +2.12655 q^{24} +(4.99973 + 0.0520717i) q^{25} -1.52615 q^{26} +(0.587785 + 0.809017i) q^{27} +(1.58156 + 0.513881i) q^{28} +(1.14792 - 3.53292i) q^{29} +(0.394720 + 1.23670i) q^{30} +(1.39556 + 4.29510i) q^{31} -5.46723i q^{32} +(1.11286 - 0.361591i) q^{33} +(-1.64903 - 1.19809i) q^{34} +(-0.0116437 + 2.23604i) q^{35} +(1.34536 - 0.977461i) q^{36} +(-1.46992 + 2.02317i) q^{37} +(1.16108 - 1.59809i) q^{38} +(-2.12672 + 1.54516i) q^{39} +(4.52997 - 1.44584i) q^{40} +(-2.40888 - 1.75015i) q^{41} +(-0.552141 + 0.179402i) q^{42} +9.46600i q^{43} +(-0.601309 - 1.85064i) q^{44} +(1.80215 + 1.32373i) q^{45} +(0.0371259 - 0.114262i) q^{46} +(-8.75783 - 2.84559i) q^{47} +(-1.22925 - 1.69192i) q^{48} -1.00000 q^{49} +(1.68166 + 2.36604i) q^{50} -3.51098 q^{51} +(2.56952 + 3.53665i) q^{52} +(2.25751 + 0.733509i) q^{53} +(-0.179402 + 0.552141i) q^{54} +(2.12477 - 1.52689i) q^{55} +(0.657140 + 2.02247i) q^{56} -3.40251i q^{57} +(2.05106 - 0.666429i) q^{58} +(-2.23899 - 1.62672i) q^{59} +(2.20130 - 2.99689i) q^{60} +(0.435372 - 0.316316i) q^{61} +(-1.54110 + 2.12114i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(-0.816000 + 0.592859i) q^{64} +(-3.47979 + 4.73744i) q^{65} +(0.549587 + 0.399298i) q^{66} +(2.75254 - 0.894355i) q^{67} +5.83860i q^{68} +(-0.0639489 - 0.196815i) q^{69} +(-1.05419 + 0.757561i) q^{70} +(-0.0641303 + 0.197373i) q^{71} +(2.02247 + 0.657140i) q^{72} +(5.74597 + 7.90864i) q^{73} -1.45184 q^{74} +(4.73893 + 1.59452i) q^{75} -5.65822 q^{76} +(0.687786 + 0.946657i) q^{77} +(-1.45145 - 0.471606i) q^{78} +(1.78427 - 5.49141i) q^{79} +(-3.76889 - 2.76836i) q^{80} +(0.309017 + 0.951057i) q^{81} -1.72862i q^{82} +(-12.4019 + 4.02962i) q^{83} +(1.34536 + 0.977461i) q^{84} +(-7.47907 + 2.38711i) q^{85} +(-4.44598 + 3.23020i) q^{86} +(2.18347 - 3.00528i) q^{87} +(1.46261 - 2.01311i) q^{88} +(-4.55869 + 3.31208i) q^{89} +(-0.00675984 + 1.29814i) q^{90} +(-2.12672 - 1.54516i) q^{91} +(-0.327294 + 0.106344i) q^{92} +4.51614i q^{93} +(-1.65202 - 5.08441i) q^{94} +(-2.31336 - 7.24801i) q^{95} +(1.68947 - 5.19965i) q^{96} +(15.1939 + 4.93679i) q^{97} +(-0.341242 - 0.469679i) q^{98} +1.17013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

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