LMFDB - Embedded newform 430.2.l.a.7.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (of order $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.19
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.118826 - 0.443464i) q^{3} -1.00000i q^{4} +(-0.834055 - 2.07469i) q^{5} +(-0.229554 - 0.397599i) q^{6} +(-0.174257 - 0.650336i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.41554 + 1.39461i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.118826 - 0.443464i) q^{3} -1.00000i q^{4} +(-0.834055 - 2.07469i) q^{5} +(-0.229554 - 0.397599i) q^{6} +(-0.174257 - 0.650336i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.41554 + 1.39461i) q^{9} +(-2.05680 - 0.877264i) q^{10} +2.80750 q^{11} +(-0.443464 - 0.118826i) q^{12} +(-0.896566 - 3.34603i) q^{13} +(-0.583075 - 0.336639i) q^{14} +(-1.01916 + 0.123346i) q^{15} -1.00000 q^{16} +(-4.78417 + 1.28191i) q^{17} +(2.69418 - 0.721903i) q^{18} +(-2.97899 - 5.15976i) q^{19} +(-2.07469 + 0.834055i) q^{20} -0.309107 q^{21} +(1.98520 - 1.98520i) q^{22} +(-3.36822 - 0.902511i) q^{23} +(-0.397599 + 0.229554i) q^{24} +(-3.60871 + 3.46082i) q^{25} +(-2.99997 - 1.73203i) q^{26} +(1.87940 - 1.87940i) q^{27} +(-0.650336 + 0.174257i) q^{28} +(2.79661 - 4.84387i) q^{29} +(-0.633436 + 0.807874i) q^{30} +(4.15390 + 7.19476i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.333604 - 1.24503i) q^{33} +(-2.47647 + 4.28937i) q^{34} +(-1.20391 + 0.903945i) q^{35} +(1.39461 - 2.41554i) q^{36} +(8.70451 + 2.33237i) q^{37} +(-5.75496 - 1.54204i) q^{38} -1.59038 q^{39} +(-0.877264 + 2.05680i) q^{40} +6.87802 q^{41} +(-0.218572 + 0.218572i) q^{42} +(-6.22006 + 2.07626i) q^{43} -2.80750i q^{44} +(0.878699 - 6.17468i) q^{45} +(-3.01986 + 1.74352i) q^{46} +(7.75894 + 7.75894i) q^{47} +(-0.118826 + 0.443464i) q^{48} +(5.66961 - 3.27335i) q^{49} +(-0.104573 + 4.99891i) q^{50} +2.27393i q^{51} +(-3.34603 + 0.896566i) q^{52} +(13.7979 + 3.69713i) q^{53} -2.65788i q^{54} +(-2.34161 - 5.82470i) q^{55} +(-0.336639 + 0.583075i) q^{56} +(-2.64215 + 0.707962i) q^{57} +(-1.44763 - 5.40264i) q^{58} +9.10162i q^{59} +(0.123346 + 1.01916i) q^{60} +(-11.3415 - 6.54803i) q^{61} +(8.02471 + 2.15021i) q^{62} +(0.486041 - 1.81393i) q^{63} +1.00000i q^{64} +(-6.19420 + 4.65087i) q^{65} +(-0.644473 - 1.11626i) q^{66} +(1.78565 - 6.66414i) q^{67} +(1.28191 + 4.78417i) q^{68} +(-0.800464 + 1.38644i) q^{69} +(-0.212105 + 1.49048i) q^{70} +(6.46834 + 3.73450i) q^{71} +(-0.721903 - 2.69418i) q^{72} +(-13.4368 + 3.60039i) q^{73} +(7.80425 - 4.50579i) q^{74} +(1.10594 + 2.01157i) q^{75} +(-5.15976 + 2.97899i) q^{76} +(-0.489226 - 1.82582i) q^{77} +(-1.12457 + 1.12457i) q^{78} +(9.11916 + 5.26495i) q^{79} +(0.834055 + 2.07469i) q^{80} +(3.57370 + 6.18983i) q^{81} +(4.86349 - 4.86349i) q^{82} +(-8.04016 - 2.15435i) q^{83} +0.309107i q^{84} +(6.64984 + 8.85649i) q^{85} +(-2.93011 + 5.86638i) q^{86} +(-1.81578 - 1.81578i) q^{87} +(-1.98520 - 1.98520i) q^{88} +(-1.25426 - 2.17245i) q^{89} +(-3.74482 - 4.98749i) q^{90} +(-2.01981 + 1.16614i) q^{91} +(-0.902511 + 3.36822i) q^{92} +(3.68421 - 0.987181i) q^{93} +10.9728 q^{94} +(-8.22028 + 10.4840i) q^{95} +(0.229554 + 0.397599i) q^{96} +(-6.07571 - 6.07571i) q^{97} +(1.69441 - 6.32362i) q^{98} +(6.78161 + 3.91537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.118826	−	0.443464i	0.0686042	−	0.256034i	−0.923103	−	0.384553i	$-0.874356\pi$
$3$	0.118826	−	0.443464i	0.0686042	−	0.256034i	0.991707	+	0.128519i	$0.0410222\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−0.834055	−	2.07469i	−0.373001	−	0.927831i
$5$	−0.834055	−	2.07469i	−0.373001	−	0.927831i
$6$	−0.229554	−	0.397599i	−0.0937151	−	0.162319i
$7$	−0.174257	−	0.650336i	−0.0658629	−	0.245804i	0.925144	−	0.379617i	$-0.123944\pi$
$7$	−0.174257	−	0.650336i	−0.0658629	−	0.245804i	−0.991007	+	0.133814i	$0.957278\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.41554	+	1.39461i	0.805178	+	0.464870i
$10$	−2.05680	−	0.877264i	−0.650416	−	0.277415i
$11$	2.80750			0.846493			0.423246	−	0.906015i	$-0.360890\pi$
$11$	2.80750			0.846493			0.423246	+	0.906015i	$0.360890\pi$
$12$	−0.443464	−	0.118826i	−0.128017	−	0.0343021i
$13$	−0.896566	−	3.34603i	−0.248663	−	0.928021i	−0.971507	−	0.237011i	$-0.923832\pi$
$13$	−0.896566	−	3.34603i	−0.248663	−	0.928021i	0.722844	−	0.691011i	$-0.242834\pi$
$14$	−0.583075	−	0.336639i	−0.155833	−	0.0899704i
$15$	−1.01916	+	0.123346i	−0.263146	+	0.0318479i
$16$	−1.00000			−0.250000
$17$	−4.78417	+	1.28191i	−1.16033	+	0.310910i	−0.787098	−	0.616828i	$-0.788417\pi$
$17$	−4.78417	+	1.28191i	−1.16033	+	0.310910i	−0.373233	+	0.927738i	$0.621751\pi$
$18$	2.69418	−	0.721903i	0.635024	−	0.170154i
$19$	−2.97899	−	5.15976i	−0.683427	−	1.18373i	−0.973929	−	0.226855i	$-0.927156\pi$
$19$	−2.97899	−	5.15976i	−0.683427	−	1.18373i	0.290502	−	0.956874i	$-0.406178\pi$
$20$	−2.07469	+	0.834055i	−0.463916	+	0.186500i
$21$	−0.309107			−0.0674527
$22$	1.98520	−	1.98520i	0.423246	−	0.423246i
$23$	−3.36822	−	0.902511i	−0.702322	−	0.188187i	−0.110052	−	0.993926i	$-0.535102\pi$
$23$	−3.36822	−	0.902511i	−0.702322	−	0.188187i	−0.592270	+	0.805739i	$0.701768\pi$
$24$	−0.397599	+	0.229554i	−0.0811596	+	0.0468575i
$25$	−3.60871	+	3.46082i	−0.721741	+	0.692163i
$26$	−2.99997	−	1.73203i	−0.588342	−	0.339679i
$27$	1.87940	−	1.87940i	0.361691	−	0.361691i
$28$	−0.650336	+	0.174257i	−0.122902	+	0.0329315i
$29$	2.79661	−	4.84387i	0.519318	−	0.899485i	−0.480430	−	0.877033i	$-0.659519\pi$
$29$	2.79661	−	4.84387i	0.519318	−	0.899485i	0.999748	−	0.0224517i	$-0.00714721\pi$
$30$	−0.633436	+	0.807874i	−0.115649	+	0.147497i
$31$	4.15390	+	7.19476i	0.746062	+	1.29222i	0.949697	+	0.313170i	$0.101391\pi$
$31$	4.15390	+	7.19476i	0.746062	+	1.29222i	−0.203635	+	0.979047i	$0.565276\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.333604	−	1.24503i	0.0580730	−	0.216731i
$34$	−2.47647	+	4.28937i	−0.424711	+	0.735620i
$35$	−1.20391	+	0.903945i	−0.203497	+	0.152795i
$36$	1.39461	−	2.41554i	0.232435	−	0.402589i
$37$	8.70451	+	2.33237i	1.43101	+	0.383439i	0.889377	−	0.457174i	$-0.151138\pi$
$37$	8.70451	+	2.33237i	1.43101	+	0.383439i	0.541636	+	0.840613i	$0.317805\pi$
$38$	−5.75496	−	1.54204i	−0.933578	−	0.250151i
$39$	−1.59038			−0.254665
$40$	−0.877264	+	2.05680i	−0.138708	+	0.325208i
$41$	6.87802			1.07417			0.537083	−	0.843529i	$-0.319526\pi$
$41$	6.87802			1.07417			0.537083	+	0.843529i	$0.319526\pi$
$42$	−0.218572	+	0.218572i	−0.0337263	+	0.0337263i
$43$	−6.22006	+	2.07626i	−0.948550	+	0.316627i
$43$	−6.22006	+	2.07626i	−0.948550	+	0.316627i
$44$		−	2.80750i		−	0.423246i
$45$	0.878699	−	6.17468i	0.130989	−	0.920466i
$46$	−3.01986	+	1.74352i	−0.445254	+	0.257068i
$47$	7.75894	+	7.75894i	1.13176	+	1.13176i	0.989885	+	0.141873i	$0.0453123\pi$
$47$	7.75894	+	7.75894i	1.13176	+	1.13176i	0.141873	+	0.989885i	$0.454688\pi$
$48$	−0.118826	+	0.443464i	−0.0171510	+	0.0640086i
$49$	5.66961	−	3.27335i	0.809944	−	0.467621i
$50$	−0.104573	+	4.99891i	−0.0147889	+	0.706952i
$51$			2.27393i			0.318414i
$52$	−3.34603	+	0.896566i	−0.464011	+	0.124331i
$53$	13.7979	+	3.69713i	1.89528	+	0.507839i	0.997762	+	0.0668651i	$0.0212997\pi$
$53$	13.7979	+	3.69713i	1.89528	+	0.507839i	0.897520	+	0.440974i	$0.145367\pi$
$54$		−	2.65788i		−	0.361691i
$55$	−2.34161	−	5.82470i	−0.315742	−	0.785402i
$56$	−0.336639	+	0.583075i	−0.0449852	+	0.0779167i
$57$	−2.64215	+	0.707962i	−0.349961	+	0.0937719i
$58$	−1.44763	−	5.40264i	−0.190083	−	0.709401i
$59$			9.10162i			1.18493i	0.805596	+	0.592465i	$0.201845\pi$
$59$			9.10162i			1.18493i	−0.805596	+	0.592465i	$0.798155\pi$
$60$	0.123346	+	1.01916i	0.0159239	+	0.131573i
$61$	−11.3415	−	6.54803i	−1.45213	−	0.838390i	−0.453531	−	0.891240i	$-0.649836\pi$
$61$	−11.3415	−	6.54803i	−1.45213	−	0.838390i	−0.998602	+	0.0528508i	$0.983169\pi$
$62$	8.02471	+	2.15021i	1.01914	+	0.273078i
$63$	0.486041	−	1.81393i	0.0612354	−	0.228534i
$64$			1.00000i			0.125000i
$65$	−6.19420	+	4.65087i	−0.768296	+	0.576869i
$66$	−0.644473	−	1.11626i	−0.0793291	−	0.137402i
$67$	1.78565	−	6.66414i	0.218152	−	0.814155i	−0.766881	−	0.641789i	$-0.778192\pi$
$67$	1.78565	−	6.66414i	0.218152	−	0.814155i	0.985033	−	0.172365i	$-0.0551409\pi$
$68$	1.28191	+	4.78417i	0.155455	+	0.580166i
$69$	−0.800464	+	1.38644i	−0.0963645	+	0.166908i
$70$	−0.212105	+	1.49048i	−0.0253514	+	0.178146i
$71$	6.46834	+	3.73450i	0.767651	+	0.443204i	0.832036	−	0.554722i	$-0.187175\pi$
$71$	6.46834	+	3.73450i	0.767651	+	0.443204i	−0.0643849	+	0.997925i	$0.520509\pi$
$72$	−0.721903	−	2.69418i	−0.0850771	−	0.317512i
$73$	−13.4368	+	3.60039i	−1.57266	+	0.421394i	−0.936645	−	0.350280i	$-0.886086\pi$
$73$	−13.4368	+	3.60039i	−1.57266	+	0.421394i	−0.636018	+	0.771674i	$0.719420\pi$
$74$	7.80425	−	4.50579i	0.907226	−	0.523787i
$75$	1.10594	+	2.01157i	0.127703	+	0.232276i
$76$	−5.15976	+	2.97899i	−0.591865	+	0.341713i
$77$	−0.489226	−	1.82582i	−0.0557525	−	0.208071i
$78$	−1.12457	+	1.12457i	−0.127332	+	0.127332i
$79$	9.11916	+	5.26495i	1.02599	+	0.592353i	0.915832	−	0.401562i	$-0.131532\pi$
$79$	9.11916	+	5.26495i	1.02599	+	0.592353i	0.110153	+	0.993915i	$0.464866\pi$
$80$	0.834055	+	2.07469i	0.0932502	+	0.231958i
$81$	3.57370	+	6.18983i	0.397078	+	0.687759i
$82$	4.86349	−	4.86349i	0.537083	−	0.537083i
$83$	−8.04016	−	2.15435i	−0.882522	−	0.236471i	−0.211027	−	0.977480i	$-0.567681\pi$
$83$	−8.04016	−	2.15435i	−0.882522	−	0.236471i	−0.671495	+	0.741009i	$0.734348\pi$
$84$			0.309107i			0.0337263i
$85$	6.64984	+	8.85649i	0.721276	+	0.960622i
$86$	−2.93011	+	5.86638i	−0.315962	+	0.632588i
$87$	−1.81578	−	1.81578i	−0.194672	−	0.194672i
$88$	−1.98520	−	1.98520i	−0.211623	−	0.211623i
$89$	−1.25426	−	2.17245i	−0.132952	−	0.230279i	0.791861	−	0.610701i	$-0.209112\pi$
$89$	−1.25426	−	2.17245i	−0.132952	−	0.230279i	−0.924813	+	0.380422i	$0.875779\pi$
$90$	−3.74482	−	4.98749i	−0.394739	−	0.525728i
$91$	−2.01981	+	1.16614i	−0.211734	+	0.122244i
$92$	−0.902511	+	3.36822i	−0.0940933	+	0.351161i
$93$	3.68421	−	0.987181i	0.382035	−	0.102366i
$94$	10.9728			1.13176
$95$	−8.22028	+	10.4840i	−0.843383	+	1.07564i
$96$	0.229554	+	0.397599i	0.0234288	+	0.0405798i
$97$	−6.07571	−	6.07571i	−0.616894	−	0.616894i	0.327839	−	0.944734i	$-0.393680\pi$
$97$	−6.07571	−	6.07571i	−0.616894	−	0.616894i	−0.944734	+	0.327839i	$0.893680\pi$
$98$	1.69441	−	6.32362i	0.171161	−	0.638783i
$99$	6.78161	+	3.91537i	0.681578	+	0.393509i
$100$	3.46082	+	3.60871i	0.346082	+	0.360871i
$101$	1.38599	−	2.40060i	0.137911	−	0.238869i	−0.788795	−	0.614657i	$-0.789295\pi$
$101$	1.38599	−	2.40060i	0.137911	−	0.238869i	0.926706	+	0.375788i	$0.122628\pi$
$102$	1.60791	+	1.60791i	0.159207	+	0.159207i
$103$	0.157173	+	0.586578i	0.0154867	+	0.0577973i	0.973237	−	0.229805i	$-0.0738087\pi$
$103$	0.157173	+	0.586578i	0.0154867	+	0.0577973i	−0.957750	+	0.287602i	$0.907142\pi$
$104$	−1.73203	+	2.99997i	−0.169840	+	0.294171i
$105$	0.257812	+	0.641302i	0.0251599	+	0.0625847i
$106$	12.3708	−	7.14230i	1.20156	−	0.693721i
$107$	4.22318	+	4.22318i	0.408270	+	0.408270i	0.881135	−	0.472865i	$-0.156780\pi$
$107$	4.22318	+	4.22318i	0.408270	+	0.408270i	−0.472865	+	0.881135i	$0.656780\pi$
$108$	−1.87940	−	1.87940i	−0.180846	−	0.180846i
$109$	10.2617	−	5.92459i	0.982892	−	0.567473i	0.0797502	−	0.996815i	$-0.474588\pi$
$109$	10.2617	−	5.92459i	0.982892	−	0.567473i	0.903142	+	0.429342i	$0.141254\pi$
$110$	−5.77445	−	2.46292i	−0.550572	−	0.234830i
$111$	2.06864	−	3.58300i	0.196347	−	0.340083i
$112$	0.174257	+	0.650336i	0.0164657	+	0.0614510i
$113$	−7.29733	−	7.29733i	−0.686475	−	0.686475i	0.274976	−	0.961451i	$-0.411330\pi$
$113$	−7.29733	−	7.29733i	−0.686475	−	0.686475i	−0.961451	+	0.274976i	$0.911330\pi$
$114$	−1.36768	+	2.36889i	−0.128095	+	0.221867i
$115$	0.936844	+	7.74076i	0.0873612	+	0.721830i
$116$	−4.84387	−	2.79661i	−0.449742	−	0.259659i
$117$	2.50072	−	9.33281i	0.231192	−	0.862819i
$118$	6.43582	+	6.43582i	0.592465	+	0.592465i
$119$	1.66735	+	2.88793i	0.152846	+	0.264736i
$120$	0.807874	+	0.633436i	0.0737485	+	0.0578245i
$121$	−3.11795			−0.283450
$122$	−12.6498	+	3.38951i	−1.14526	+	0.306872i
$123$	0.817287	−	3.05016i	0.0736923	−	0.275023i
$124$	7.19476	−	4.15390i	0.646108	−	0.373031i
$125$	10.1900	+	4.60045i	0.911420	+	0.411476i
$126$	−0.938959	−	1.62632i	−0.0836491	−	0.144884i
$127$	−1.89725	−	1.89725i	−0.168354	−	0.168354i	0.617902	−	0.786255i	$-0.287983\pi$
$127$	−1.89725	−	1.89725i	−0.168354	−	0.168354i	−0.786255	+	0.617902i	$0.787983\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.181643	+	3.00509i	0.0159928	+	0.264583i
$130$	−1.09130	+	7.66862i	−0.0957132	+	0.672583i
$131$			21.0066i			1.83536i	0.397321	+	0.917680i	$0.369940\pi$
$131$			21.0066i			1.83536i	−0.397321	+	0.917680i	$0.630060\pi$
$132$	−1.24503	−	0.333604i	−0.108366	−	0.0290365i
$133$	−2.83647	+	2.83647i	−0.245953	+	0.245953i
$134$	−3.44961	−	5.97491i	−0.298001	−	0.516153i
$135$	−5.46671	−	2.33166i	−0.470500	−	0.200677i
$136$	4.28937	+	2.47647i	0.367810	+	0.212355i
$137$	11.5605	−	11.5605i	0.987680	−	0.987680i	−0.0122446	−	0.999925i	$-0.503898\pi$
$137$	11.5605	−	11.5605i	0.987680	−	0.987680i	0.999925	+	0.0122446i	$0.00389769\pi$
$138$	0.414350	+	1.54638i	0.0352718	+	0.131636i
$139$	−11.2744	+	6.50925i	−0.956278	+	0.552107i	−0.895025	−	0.446015i	$-0.852843\pi$
$139$	−11.2744	+	6.50925i	−0.956278	+	0.552107i	−0.0612524	+	0.998122i	$0.519509\pi$
$140$	0.903945	+	1.20391i	0.0763973	+	0.101749i
$141$	4.36278	−	2.51885i	0.367412	−	0.212125i
$142$	7.21450	−	1.93312i	0.605427	−	0.162224i
$143$	−2.51711	−	9.39397i	−0.210491	−	0.785564i
$144$	−2.41554	−	1.39461i	−0.201295	−	0.116217i
$145$	−12.3821	−	1.76206i	−1.02828	−	0.146331i
$146$	−6.95542	+	12.0471i	−0.575635	+	0.997028i
$147$	−0.777918	−	2.90323i	−0.0641616	−	0.239454i
$148$	2.33237	−	8.70451i	0.191719	−	0.715507i
$149$	5.28844	+	9.15986i	0.433246	+	0.750405i	0.997151	−	0.0754355i	$-0.0240347\pi$
$149$	5.28844	+	9.15986i	0.433246	+	0.750405i	−0.563904	+	0.825840i	$0.690701\pi$
$150$	2.20441	+	0.640374i	0.179989	+	0.0522863i
$151$		−	11.6227i		−	0.945845i	−0.881104	−	0.472923i	$-0.843199\pi$
$151$		−	11.6227i		−	0.945845i	0.881104	−	0.472923i	$-0.156801\pi$
$152$	−1.54204	+	5.75496i	−0.125076	+	0.466789i
$153$	−13.3441	−	3.57554i	−1.07881	−	0.289065i
$154$	−1.63698	−	0.945113i	−0.131912	−	0.0761593i
$155$	11.4623	−	14.6189i	0.920677	−	1.17422i
$156$			1.59038i			0.127332i
$157$	−0.156270	−	0.583207i	−0.0124717	−	0.0465450i	0.959410	−	0.282016i	$-0.0910033\pi$
$157$	−0.156270	−	0.583207i	−0.0124717	−	0.0465450i	−0.971881	+	0.235471i	$0.924337\pi$
$158$	10.1711	−	2.72534i	0.809169	−	0.216816i
$159$	3.27909	−	5.67955i	0.260049	−	0.450417i
$160$	2.05680	+	0.877264i	0.162604	+	0.0693538i
$161$			2.34774i			0.185028i
$162$	6.90386	+	1.84988i	0.542419	+	0.145341i
$163$	−2.11175	+	0.565842i	−0.165405	+	0.0443202i	−0.340571	−	0.940219i	$-0.610620\pi$
$163$	−2.11175	+	0.565842i	−0.165405	+	0.0443202i	0.175166	+	0.984539i	$0.443954\pi$
$164$		−	6.87802i		−	0.537083i
$165$	−2.86129	+	0.346295i	−0.222751	+	0.0269590i
$166$	−7.20861	+	4.16189i	−0.559497	+	0.323026i
$167$	−2.47488	+	9.23638i	−0.191512	+	0.714733i	0.801630	+	0.597820i	$0.203966\pi$
$167$	−2.47488	+	9.23638i	−0.191512	+	0.714733i	−0.993142	+	0.116912i	$0.962700\pi$
$168$	0.218572	+	0.218572i	0.0168632	+	0.0168632i
$169$	0.866252	−	0.500131i	0.0666348	−	0.0384716i
$170$	10.9646	+	1.56034i	0.840949	+	0.119673i
$171$		−	16.6181i		−	1.27082i
$172$	2.07626	+	6.22006i	0.158313	+	0.474275i
$173$	3.23920	−	3.23920i	0.246271	−	0.246271i	−0.573167	−	0.819439i	$-0.694285\pi$
$173$	3.23920	−	3.23920i	0.246271	−	0.246271i	0.819439	+	0.573167i	$0.194285\pi$
$174$	−2.56789			−0.194672
$175$	2.87953	+	1.74380i	0.217672	+	0.131819i
$176$	−2.80750			−0.211623
$177$	4.03624	+	1.08151i	0.303383	+	0.0812911i
$178$	−2.42305	−	0.649255i	−0.181615	−	0.0486637i
$179$	−10.4076	+	18.0265i	−0.777901	+	1.34736i	0.155248	+	0.987875i	$0.450382\pi$
$179$	−10.4076	+	18.0265i	−0.777901	+	1.34736i	−0.933149	+	0.359489i	$0.882951\pi$
$180$	−6.17468	−	0.878699i	−0.460233	−	0.0654944i
$181$	4.08674	−	7.07844i	0.303765	−	0.526136i	−0.673221	−	0.739442i	$-0.735090\pi$
$181$	4.08674	−	7.07844i	0.303765	−	0.526136i	0.976986	+	0.213305i	$0.0684229\pi$
$182$	−0.603637	+	2.25280i	−0.0447446	+	0.166989i
$183$	−4.25149	+	4.25149i	−0.314279	+	0.314279i
$184$	1.74352	+	3.01986i	0.128534	+	0.222627i
$185$	−2.42109	−	20.0045i	−0.178002	−	1.47076i
$186$	1.90709	−	3.30317i	0.139834	−	0.242200i
$187$	−13.4315	+	3.59897i	−0.982212	+	0.263183i
$188$	7.75894	−	7.75894i	0.565879	−	0.565879i
$189$	−1.54974	−	0.894744i	−0.112727	−	0.0650831i
$190$	1.60070	+	13.2259i	0.116127	+	0.959509i
$191$	−18.1845	+	10.4988i	−1.31578	+	0.759666i	−0.983047	−	0.183354i	$-0.941304\pi$
$191$	−18.1845	+	10.4988i	−1.31578	+	0.759666i	−0.332734	+	0.943021i	$0.607971\pi$
$192$	0.443464	+	0.118826i	0.0320043	+	0.00857552i
$193$	−3.58390	+	3.58390i	−0.257975	+	0.257975i	−0.824230	−	0.566255i	$-0.808392\pi$
$193$	−3.58390	+	3.58390i	−0.257975	+	0.257975i	0.566255	+	0.824230i	$0.308392\pi$
$194$	−8.59235			−0.616894
$195$	1.32646	+	3.29955i	0.0949901	+	0.236286i
$196$	−3.27335	−	5.66961i	−0.233811	−	0.404972i
$197$	−16.1146	+	4.31791i	−1.14812	+	0.307638i	−0.782212	−	0.623013i	$-0.785909\pi$
$197$	−16.1146	+	4.31791i	−1.14812	+	0.307638i	−0.365909	+	0.930651i	$0.619242\pi$
$198$	7.56391	−	2.02674i	0.537543	−	0.144034i
$199$	0.0629382			0.00446157			0.00223078	−	0.999998i	$-0.499290\pi$
$199$	0.0629382			0.00446157			0.00223078	+	0.999998i	$0.499290\pi$
$200$	4.99891	+	0.104573i	0.353476	+	0.00739445i
$201$	−2.74313	−	1.58375i	−0.193485	−	0.111709i
$202$	−0.717440	−	2.67752i	−0.0504789	−	0.188390i
$203$	−3.63747	−	0.974658i	−0.255301	−	0.0684076i
$204$	2.27393			0.159207
$205$	−5.73664	−	14.2698i	−0.400665	−	0.996644i
$206$	0.525912	+	0.303635i	0.0366420	+	0.0211553i
$207$	−6.87740	−	6.87740i	−0.478012	−	0.478012i
$208$	0.896566	+	3.34603i	0.0621656	+	0.232005i
$209$	−8.36351	−	14.4860i	−0.578516	−	1.00202i
$210$	0.635770	+	0.271168i	0.0438723	+	0.0187124i
$211$			3.02238i			0.208069i	0.994574	+	0.104035i	$0.0331753\pi$
$211$			3.02238i			0.208069i	−0.994574	+	0.104035i	$0.966825\pi$
$212$	3.69713	−	13.7979i	0.253920	−	0.947641i
$213$	2.42473	−	2.42473i	0.166139	−	0.166139i
$214$	5.97248			0.408270
$215$	9.49547	+	11.1730i	0.647586	+	0.761992i
$216$	−2.65788			−0.180846
$217$	3.95516	−	3.95516i	0.268494	−	0.268494i
$218$	3.06680	−	11.4454i	0.207710	−	0.775183i
$219$			6.38658i			0.431565i
$220$	−5.82470	+	2.34161i	−0.392701	+	0.157871i
$221$	8.57864	+	14.8586i	0.577062	+	0.999500i
$222$	−1.07081	−	3.99631i	−0.0718680	−	0.268215i
$223$	3.09763	+	3.09763i	0.207433	+	0.207433i	0.803175	−	0.595743i	$-0.203142\pi$
$223$	3.09763	+	3.09763i	0.207433	+	0.207433i	−0.595743	+	0.803175i	$0.703142\pi$
$224$	0.583075	+	0.336639i	0.0389583	+	0.0224926i
$225$	−13.5434	+	3.32699i	−0.902896	+	0.221799i
$226$	−10.3200			−0.686475
$227$	11.6918	+	3.13281i	0.776013	+	0.207932i	0.625026	−	0.780604i	$-0.285088\pi$
$227$	11.6918	+	3.13281i	0.776013	+	0.207932i	0.150987	+	0.988536i	$0.451755\pi$
$228$	0.707962	+	2.64215i	0.0468859	+	0.174981i
$229$	−4.39828	−	2.53935i	−0.290647	−	0.167805i	0.347587	−	0.937648i	$-0.387001\pi$
$229$	−4.39828	−	2.53935i	−0.290647	−	0.167805i	−0.638233	+	0.769843i	$0.720335\pi$
$230$	6.13600	+	4.81110i	0.404596	+	0.317234i
$231$	−0.867818			−0.0570982
$232$	−5.40264	+	1.44763i	−0.354701	+	0.0950417i
$233$	−8.46067	+	2.26703i	−0.554277	+	0.148518i	−0.525076	−	0.851056i	$-0.675963\pi$
$233$	−8.46067	+	2.26703i	−0.554277	+	0.148518i	−0.0292011	+	0.999574i	$0.509296\pi$
$234$	−4.83102	−	8.36757i	−0.315813	−	0.547005i
$235$	9.62604	−	22.5688i	0.627933	−	1.47223i
$236$	9.10162			0.592465
$237$	3.41841	−	3.41841i	0.222050	−	0.222050i
$238$	3.22107	+	0.863083i	0.208791	+	0.0559454i
$239$	−19.0902	+	11.0217i	−1.23484	+	0.712935i	−0.968035	−	0.250816i	$-0.919301\pi$
$239$	−19.0902	+	11.0217i	−1.23484	+	0.712935i	−0.266805	+	0.963751i	$0.585968\pi$
$240$	1.01916	−	0.123346i	0.0657865	−	0.00796197i
$241$	3.58618	+	2.07048i	0.231006	+	0.133371i	0.611036	−	0.791603i	$-0.290753\pi$
$241$	3.58618	+	2.07048i	0.231006	+	0.133371i	−0.380030	+	0.924974i	$0.624086\pi$
$242$	−2.20472	+	2.20472i	−0.141725	+	0.141725i
$243$	10.8716	−	2.91303i	0.697411	−	0.186871i
$244$	−6.54803	+	11.3415i	−0.419195	+	0.726067i
$245$	−11.5200	−	9.03254i	−0.735983	−	0.577068i
$246$	−1.57888	−	2.73470i	−0.100666	−	0.174358i
$247$	−14.5938	+	14.5938i	−0.928584	+	0.928584i
$248$	2.15021	−	8.02471i	0.136539	−	0.509570i
$249$	−1.91076	+	3.30953i	−0.121089	+	0.209733i
$250$	10.4584	−	3.95240i	0.661448	−	0.249972i
$251$	6.06538	−	10.5055i	0.382843	−	0.663104i	−0.608624	−	0.793459i	$-0.708278\pi$
$251$	6.06538	−	10.5055i	0.382843	−	0.663104i	0.991467	+	0.130355i	$0.0416116\pi$
$252$	−1.81393	−	0.486041i	−0.114267	−	0.0306177i
$253$	−9.45627	−	2.53380i	−0.594511	−	0.159299i
$254$	−2.68312			−0.168354
$255$	4.71771	−	1.89658i	0.295435	−	0.118769i
$256$	1.00000			0.0625000
$257$	9.47911	−	9.47911i	0.591291	−	0.591291i	−0.346689	−	0.937980i	$-0.612694\pi$
$257$	9.47911	−	9.47911i	0.591291	−	0.591291i	0.937980	+	0.346689i	$0.112694\pi$
$258$	2.25336	+	1.99648i	0.140288	+	0.124295i
$259$		−	6.06729i		−	0.377003i
$260$	4.65087	+	6.19420i	0.288435	+	0.384148i
$261$	13.5106	−	7.80036i	0.836287	−	0.482830i
$262$	14.8539	+	14.8539i	0.917680	+	0.917680i
$263$	−0.0218938	+	0.0817086i	−0.00135003	+	0.00503837i	−0.966598	−	0.256299i	$-0.917497\pi$
$263$	−0.0218938	+	0.0817086i	−0.00135003	+	0.00503837i	0.965248	+	0.261337i	$0.0841635\pi$
$264$	−1.11626	+	0.644473i	−0.0687011	+	0.0396646i
$265$	−3.83777	−	31.7099i	−0.235752	−	1.94793i
$266$			4.01137i			0.245953i
$267$	−1.11244	+	0.298078i	−0.0680804	+	0.0182421i
$268$	−6.66414	−	1.78565i	−0.407077	−	0.109076i
$269$		−	8.08657i		−	0.493047i	−0.969137	−	0.246523i	$-0.920712\pi$
$269$		−	8.08657i		−	0.493047i	0.969137	−	0.246523i	$-0.0792882\pi$
$270$	−5.51428	+	2.21682i	−0.335589	+	0.134911i
$271$	4.39622	−	7.61447i	0.267051	−	0.462546i	−0.701048	−	0.713114i	$-0.747284\pi$
$271$	4.39622	−	7.61447i	0.267051	−	0.462546i	0.968099	+	0.250568i	$0.0806174\pi$
$272$	4.78417	−	1.28191i	0.290083	−	0.0777274i
$273$	0.277135	+	1.03428i	0.0167730	+	0.0625975i
$274$		−	16.3490i		−	0.987680i
$275$	−10.1314	+	9.71624i	−0.610949	+	0.585911i
$276$	1.38644	+	0.800464i	0.0834541	+	0.0481822i
$277$	−10.0931	−	2.70443i	−0.606434	−	0.162493i	−0.0574808	−	0.998347i	$-0.518307\pi$
$277$	−10.0931	−	2.70443i	−0.606434	−	0.162493i	−0.548953	+	0.835853i	$0.684973\pi$
$278$	−3.36944	+	12.5749i	−0.202085	+	0.754193i
$279$			23.1723i			1.38729i
$280$	1.49048	+	0.212105i	0.0890730	+	0.0126757i
$281$	2.58127	+	4.47089i	0.153986	+	0.266711i	0.932689	−	0.360681i	$-0.117456\pi$
$281$	2.58127	+	4.47089i	0.153986	+	0.266711i	−0.778704	+	0.627392i	$0.784122\pi$
$282$	1.30385	−	4.86605i	0.0776433	−	0.289769i
$283$	−2.29765	−	8.57494i	−0.136581	−	0.509727i	−0.999986	−	0.00521637i	$-0.998340\pi$
$283$	−2.29765	−	8.57494i	−0.136581	−	0.509727i	0.863405	−	0.504511i	$-0.168327\pi$
$284$	3.73450	−	6.46834i	0.221602	−	0.383826i
$285$	3.67250	+	4.89117i	0.217540	+	0.289728i
$286$	−8.42241	−	4.86268i	−0.498027	−	0.287536i
$287$	−1.19854	−	4.47302i	−0.0707477	−	0.264034i
$288$	−2.69418	+	0.721903i	−0.158756	+	0.0425386i
$289$	6.52253	−	3.76578i	0.383678	−	0.221517i
$290$	−10.0014	+	7.50949i	−0.587303	+	0.440972i
$291$	−3.41631	+	1.97241i	−0.200268	+	0.115625i
$292$	3.60039	+	13.4368i	0.210697	+	0.786331i
$293$	5.04516	−	5.04516i	0.294741	−	0.294741i	−0.544209	−	0.838950i	$-0.683170\pi$
$293$	5.04516	−	5.04516i	0.294741	−	0.294741i	0.838950	+	0.544209i	$0.183170\pi$
$294$	−2.60296	−	1.50282i	−0.151808	−	0.0876463i
$295$	18.8831	−	7.59125i	1.09941	−	0.441980i
$296$	−4.50579	−	7.80425i	−0.261894	−	0.453613i
$297$	5.27643	−	5.27643i	0.306169	−	0.306169i
$298$	10.2165	+	2.73750i	0.591825	+	0.158579i
$299$			12.0793i			0.698565i
$300$	2.01157	−	1.10594i	0.116138	−	0.0638515i
$301$	2.43415	+	3.68332i	0.140302	+	0.212303i
$302$	−8.21852	−	8.21852i	−0.472923	−	0.472923i
$303$	−0.899890	−	0.899890i	−0.0516974	−	0.0516974i
$304$	2.97899	+	5.15976i	0.170857	+	0.295932i
$305$	−4.12571	+	28.9916i	−0.236237	+	1.66005i
$306$	−11.9640	+	6.90741i	−0.683936	+	0.394870i
$307$	2.56424	−	9.56988i	0.146349	−	0.546182i	−0.853343	−	0.521350i	$-0.825428\pi$
$307$	2.56424	−	9.56988i	0.146349	−	0.546182i	0.999692	−	0.0248314i	$-0.00790488\pi$
$308$	−1.82582	+	0.489226i	−0.104036	+	0.0278763i
$309$	0.278803			0.0158605
$310$	−2.23201	−	18.4422i	−0.126770	−	1.04745i
$311$	1.65943	+	2.87421i	0.0940974	+	0.162982i	0.909232	−	0.416291i	$-0.136670\pi$
$311$	1.65943	+	2.87421i	0.0940974	+	0.162982i	−0.815134	+	0.579272i	$0.803337\pi$
$312$	1.12457	+	1.12457i	0.0636662	+	0.0636662i
$313$	−1.41477	+	5.27999i	−0.0799675	+	0.298443i	−0.994314	−	0.106491i	$-0.966039\pi$
$313$	−1.41477	+	5.27999i	−0.0799675	+	0.298443i	0.914346	+	0.404933i	$0.132705\pi$
$314$	−0.522889	−	0.301890i	−0.0295083	−	0.0170366i
$315$	−4.16873	+	0.504531i	−0.234881	+	0.0284271i
$316$	5.26495	−	9.11916i	0.296176	−	0.512993i
$317$	−13.4549	−	13.4549i	−0.755700	−	0.755700i	0.219837	−	0.975537i	$-0.429448\pi$
$317$	−13.4549	−	13.4549i	−0.755700	−	0.755700i	−0.975537	+	0.219837i	$0.929448\pi$
$318$	−1.69738	−	6.33471i	−0.0951844	−	0.355233i
$319$	7.85149	−	13.5992i	0.439599	−	0.761407i
$320$	2.07469	−	0.834055i	0.115979	−	0.0466251i
$321$	2.37465	−	1.37101i	0.132540	−	0.0765221i
$322$	1.66010	+	1.66010i	0.0925140	+	0.0925140i
$323$	20.8663	+	20.8663i	1.16103	+	1.16103i
$324$	6.18983	−	3.57370i	0.343880	−	0.198539i
$325$	14.8154	+	8.97198i	0.821812	+	0.497676i
$326$	−1.09312	+	1.89335i	−0.0605425	+	0.104863i
$327$	−1.40799	−	5.25469i	−0.0778621	−	0.290585i
$328$	−4.86349	−	4.86349i	−0.268541	−	0.268541i
$329$	3.69387	−	6.39796i	0.203649	−	0.352731i
$330$	−1.77837	+	2.26811i	−0.0978961	+	0.124855i
$331$	−29.0975	−	16.7994i	−1.59934	−	0.923380i	−0.991614	−	0.129235i	$-0.958748\pi$
$331$	−29.0975	−	16.7994i	−1.59934	−	0.923380i	−0.607728	−	0.794145i	$-0.707919\pi$
$332$	−2.15435	+	8.04016i	−0.118236	+	0.441261i
$333$	17.7733	+	17.7733i	0.973972	+	0.973972i
$334$	4.78110	+	8.28111i	0.261610	+	0.453122i
$335$	−15.3154	+	1.85358i	−0.836769	+	0.101272i
$336$	0.309107			0.0168632
$337$	15.6311	−	4.18835i	0.851481	−	0.228154i	0.193418	−	0.981116i	$-0.438043\pi$
$337$	15.6311	−	4.18835i	0.851481	−	0.228154i	0.658063	+	0.752963i	$0.271376\pi$
$338$	0.258887	−	0.966178i	0.0140816	−	0.0525532i
$339$	−4.10322	+	2.36900i	−0.222856	+	0.128666i
$340$	8.85649	−	6.64984i	0.480311	−	0.360638i
$341$	11.6621	+	20.1993i	0.631536	+	1.09385i
$342$	−11.7508	−	11.7508i	−0.635409	−	0.635409i
$343$	−6.44930	−	6.44930i	−0.348229	−	0.348229i
$344$	5.86638	+	2.93011i	0.316294	+	0.157981i
$345$	3.54408	+	0.504346i	0.190807	+	0.0271531i
$346$		−	4.58091i		−	0.246271i
$347$	1.48611	+	0.398203i	0.0797788	+	0.0213767i	0.298488	−	0.954413i	$-0.403518\pi$
$347$	1.48611	+	0.398203i	0.0797788	+	0.0213767i	−0.218709	+	0.975790i	$0.570185\pi$
$348$	−1.81578	+	1.81578i	−0.0973358	+	0.0973358i
$349$	−8.32967	−	14.4274i	−0.445877	−	0.772282i	0.552236	−	0.833688i	$-0.313775\pi$
$349$	−8.32967	−	14.4274i	−0.445877	−	0.772282i	−0.998113	+	0.0614063i	$0.980441\pi$
$350$	3.26919	−	0.803086i	0.174746	−	0.0429268i
$351$	−7.97355	−	4.60353i	−0.425597	−	0.245718i
$352$	−1.98520	+	1.98520i	−0.105812	+	0.105812i
$353$	6.88545	+	25.6968i	0.366475	+	1.36770i	0.865410	+	0.501065i	$0.167058\pi$
$353$	6.88545	+	25.6968i	0.366475	+	1.36770i	−0.498934	+	0.866640i	$0.666275\pi$
$354$	3.61880	−	2.08931i	0.192337	−	0.111046i
$355$	2.35299	−	16.5346i	0.124884	−	0.877566i
$356$	−2.17245	+	1.25426i	−0.115140	+	0.0664759i
$357$	1.47882	−	0.396249i	0.0782675	−	0.0209717i
$358$	5.38737	+	20.1060i	0.284732	+	1.06263i
$359$	−22.1121	−	12.7664i	−1.16703	−	0.673787i	−0.214054	−	0.976822i	$-0.568667\pi$
$359$	−22.1121	−	12.7664i	−1.16703	−	0.673787i	−0.952979	+	0.303035i	$0.902000\pi$
$360$	−4.98749	+	3.74482i	−0.262864	+	0.197369i
$361$	−8.24873	+	14.2872i	−0.434144	+	0.751959i
$362$	−2.11545	−	7.89498i	−0.111186	−	0.414951i
$363$	−0.370493	+	1.38270i	−0.0194458	+	0.0725729i
$364$	1.16614	+	2.01981i	0.0611222	+	0.105867i
$365$	18.6768	+	24.8744i	0.977587	+	1.30199i
$366$			6.01251i			0.314279i
$367$	3.53788	−	13.2035i	0.184676	−	0.689220i	−0.810024	−	0.586397i	$-0.800546\pi$
$367$	3.53788	−	13.2035i	0.184676	−	0.689220i	0.994700	−	0.102823i	$-0.0327874\pi$
$368$	3.36822	+	0.902511i	0.175581	+	0.0470467i
$369$	16.6141	+	9.59215i	0.864895	+	0.499347i
$370$	−15.8573	−	12.4334i	−0.824382	−	0.646380i
$371$		−	9.61749i		−	0.499315i
$372$	−0.987181	−	3.68421i	−0.0511830	−	0.191017i
$373$	−2.94347	+	0.788701i	−0.152407	+	0.0408374i	−0.334216	−	0.942497i	$-0.608471\pi$
$373$	−2.94347	+	0.788701i	−0.152407	+	0.0408374i	0.181809	+	0.983334i	$0.441805\pi$
$374$	−6.95268	+	12.0424i	−0.359515	+	0.622698i
$375$	3.25097	−	3.97225i	0.167879	−	0.205126i
$376$		−	10.9728i		−	0.565879i
$377$	−18.7151	−	5.01469i	−0.963876	−	0.258270i
$378$	−1.72851	+	0.463154i	−0.0889051	+	0.0238221i
$379$			28.7958i			1.47914i	0.673079	+	0.739571i	$0.264972\pi$
$379$			28.7958i			1.47914i	−0.673079	+	0.739571i	$0.735028\pi$
$380$	10.4840	+	8.22028i	0.537818	+	0.421691i
$381$	−1.06681	+	0.615921i	−0.0546541	+	0.0315546i
$382$	−5.43458	+	20.2821i	−0.278057	+	1.03772i
$383$	5.88014	+	5.88014i	0.300461	+	0.300461i	0.841194	−	0.540733i	$-0.181853\pi$
$383$	5.88014	+	5.88014i	0.300461	+	0.300461i	−0.540733	+	0.841194i	$0.681853\pi$
$384$	0.397599	−	0.229554i	0.0202899	−	0.0117144i
$385$	−3.37997	+	2.53783i	−0.172259	+	0.129340i
$386$			5.06840i			0.257975i
$387$	−17.9203	−	3.65928i	−0.910942	−	0.186012i
$388$	−6.07571	+	6.07571i	−0.308447	+	0.308447i
$389$	11.8699			0.601826			0.300913	−	0.953652i	$-0.402709\pi$
$389$	11.8699			0.601826			0.300913	+	0.953652i	$0.402709\pi$
$390$	3.27109	+	1.39518i	0.165638	+	0.0706478i
$391$	17.2711			0.873435
$392$	−6.32362	−	1.69441i	−0.319391	−	0.0855806i
$393$	9.31570	+	2.49613i	0.469915	+	0.125913i
$394$	−8.34155	+	14.4480i	−0.420241	+	0.727879i
$395$	3.31728	−	23.3107i	0.166910	−	1.17289i
$396$	3.91537	−	6.78161i	0.196755	−	0.340789i
$397$	−9.55677	+	35.6663i	−0.479640	+	1.79004i	0.123429	+	0.992353i	$0.460611\pi$
$397$	−9.55677	+	35.6663i	−0.479640	+	1.79004i	−0.603070	+	0.797689i	$0.706056\pi$
$398$	0.0445040	−	0.0445040i	0.00223078	−	0.00223078i
$399$	0.920826	+	1.59492i	0.0460990	+	0.0798457i
$400$	3.60871	−	3.46082i	0.180435	−	0.173041i
$401$	3.17539	−	5.49994i	0.158571	−	0.274654i	−0.775782	−	0.631001i	$-0.782644\pi$
$401$	3.17539	−	5.49994i	0.158571	−	0.274654i	0.934354	+	0.356347i	$0.115978\pi$
$402$	−3.05956	+	0.819807i	−0.152597	+	0.0408883i
$403$	20.3496	−	20.3496i	1.01369	−	1.01369i
$404$	−2.40060	−	1.38599i	−0.119434	−	0.0689555i
$405$	9.86134	−	12.5770i	0.490014	−	0.624956i
$406$	−3.26127	+	1.88289i	−0.161854	+	0.0934465i
$407$	24.4379	+	6.54812i	1.21134	+	0.324578i
$408$	1.60791	−	1.60791i	0.0796036	−	0.0796036i
$409$	7.38255			0.365044			0.182522	−	0.983202i	$-0.441574\pi$
$409$	7.38255			0.365044			0.182522	+	0.983202i	$0.441574\pi$
$410$	−14.1467	−	6.03384i	−0.698654	−	0.297990i
$411$	−3.75298	−	6.50036i	−0.185121	−	0.320639i
$412$	0.586578	−	0.157173i	0.0288986	−	0.00774337i
$413$	5.91911	−	1.58602i	0.291260	−	0.0780429i
$414$	−9.72611			−0.478012
$415$	2.23631	+	18.4777i	0.109776	+	0.907035i
$416$	2.99997	+	1.73203i	0.147085	+	0.0849199i
$417$	1.54694	+	5.77324i	0.0757538	+	0.282717i
$418$	−16.1571	−	4.32927i	−0.790267	−	0.211751i
$419$	4.63637			0.226501			0.113251	−	0.993566i	$-0.463874\pi$
$419$	4.63637			0.226501			0.113251	+	0.993566i	$0.463874\pi$
$420$	0.641302	−	0.257812i	0.0312924	−	0.0125799i
$421$	19.5372	+	11.2798i	0.952183	+	0.549743i	0.893758	−	0.448549i	$-0.148059\pi$
$421$	19.5372	+	11.2798i	0.952183	+	0.549743i	0.0584245	+	0.998292i	$0.481392\pi$
$422$	2.13715	+	2.13715i	0.104035	+	0.104035i
$423$	7.92130	+	29.5627i	0.385147	+	1.43739i
$424$	−7.14230	−	12.3708i	−0.346861	−	0.600780i
$425$	12.8282	−	21.1832i	0.622258	−	1.02753i
$426$		−	3.42908i		−	0.166139i
$427$	−2.28208	+	8.51684i	−0.110438	+	0.412159i
$428$	4.22318	−	4.22318i	0.204135	−	0.204135i
$429$	−4.46499			−0.215572
$430$	14.6148	+	1.18619i	0.704789	+	0.0572032i
$431$	0.301113			0.0145041			0.00725205	−	0.999974i	$-0.497692\pi$
$431$	0.301113			0.0145041			0.00725205	+	0.999974i	$0.497692\pi$
$432$	−1.87940	+	1.87940i	−0.0904229	+	0.0904229i
$433$	−1.23799	+	4.62024i	−0.0594940	+	0.222035i	−0.989272	−	0.146087i	$-0.953332\pi$
$433$	−1.23799	+	4.62024i	−0.0594940	+	0.222035i	0.929778	+	0.368121i	$0.119999\pi$
$434$		−	5.59345i		−	0.268494i
$435$	−2.25272	+	5.28163i	−0.108010	+	0.253235i
$436$	−5.92459	−	10.2617i	−0.283737	−	0.491446i
$437$	5.37714	+	20.0678i	0.257224	+	0.959971i
$438$	4.51599	+	4.51599i	0.215783	+	0.215783i
$439$	−4.46882	−	2.58007i	−0.213285	−	0.123140i	0.389552	−	0.921004i	$-0.372630\pi$
$439$	−4.46882	−	2.58007i	−0.213285	−	0.123140i	−0.602837	+	0.797864i	$0.705963\pi$
$440$	−2.46292	+	5.77445i	−0.117415	+	0.275286i
$441$	18.2602			0.869532
$442$	16.5727	+	4.44063i	0.788281	+	0.211219i
$443$	8.85838	+	33.0599i	0.420874	+	1.57072i	0.772770	+	0.634686i	$0.218870\pi$
$443$	8.85838	+	33.0599i	0.420874	+	1.57072i	−0.351896	+	0.936039i	$0.614463\pi$
$444$	−3.58300	−	2.06864i	−0.170042	−	0.0981735i
$445$	−3.46104	+	4.41416i	−0.164069	+	0.209251i
$446$	4.38071			0.207433
$447$	4.69047	−	1.25681i	0.221852	−	0.0594450i
$448$	0.650336	−	0.174257i	0.0307255	−	0.00823287i
$449$	0.191563	+	0.331797i	0.00904043	+	0.0156585i	0.870510	−	0.492150i	$-0.163789\pi$
$449$	0.191563	+	0.331797i	0.00904043	+	0.0156585i	−0.861470	+	0.507809i	$0.830456\pi$
$450$	−7.22412	+	11.9292i	−0.340548	+	0.562348i
$451$	19.3100			0.909274
$452$	−7.29733	+	7.29733i	−0.343238	+	0.343238i
$453$	−5.15427	−	1.38108i	−0.242169	−	0.0648890i
$454$	10.4826	−	6.05213i	0.491972	−	0.284040i
$455$	4.10401	+	3.21786i	0.192399	+	0.150856i
$456$	2.36889	+	1.36768i	0.110933	+	0.0640474i
$457$	−18.6917	+	18.6917i	−0.874359	+	0.874359i	−0.992944	−	0.118585i	$-0.962164\pi$
$457$	−18.6917	+	18.6917i	−0.874359	+	0.874359i	0.118585	+	0.992944i	$0.462164\pi$
$458$	−4.90565	+	1.31446i	−0.229226	+	0.0614209i
$459$	−6.58215	+	11.4006i	−0.307228	+	0.532135i
$460$	7.74076	−	0.936844i	0.360915	−	0.0436806i
$461$	−11.6108	−	20.1104i	−0.540767	−	0.936636i	−0.998860	−	0.0477317i	$-0.984801\pi$
$461$	−11.6108	−	20.1104i	−0.540767	−	0.936636i	0.458093	−	0.888904i	$-0.348533\pi$
$462$	−0.613640	+	0.613640i	−0.0285491	+	0.0285491i
$463$	0.235745	−	0.879814i	0.0109560	−	0.0408884i	−0.960231	−	0.279205i	$-0.909929\pi$
$463$	0.235745	−	0.879814i	0.0109560	−	0.0408884i	0.971187	+	0.238317i	$0.0765957\pi$
$464$	−2.79661	+	4.84387i	−0.129829	+	0.224871i
$465$	−5.12093	−	6.82024i	−0.237478	−	0.316281i
$466$	−4.37956	+	7.58563i	−0.202879	+	0.351397i
$467$	−13.3685	−	3.58208i	−0.618621	−	0.165759i	−0.0641202	−	0.997942i	$-0.520424\pi$
$467$	−13.3685	−	3.58208i	−0.618621	−	0.165759i	−0.554501	+	0.832183i	$0.687091\pi$
$468$	−9.33281	−	2.50072i	−0.431409	−	0.115596i
$469$	−4.64509			−0.214490
$470$	−9.15191	−	22.7652i	−0.422146	−	1.05008i
$471$	−0.277200			−0.0127727
$472$	6.43582	−	6.43582i	0.296232	−	0.296232i
$473$	−17.4628	+	5.82910i	−0.802941	+	0.268022i
$474$		−	4.83436i		−	0.222050i
$475$	28.6073	+	8.31032i	1.31259	+	0.381303i
$476$	2.88793	−	1.66735i	0.132368	−	0.0764228i
$477$	28.1732	+	28.1732i	1.28996	+	1.28996i
$478$	−5.70526	+	21.2923i	−0.260952	+	0.973887i
$479$	−16.2904	+	9.40525i	−0.744326	+	0.429737i	−0.823640	−	0.567113i	$-0.808060\pi$
$479$	−16.2904	+	9.40525i	−0.744326	+	0.429737i	0.0793142	+	0.996850i	$0.474727\pi$
$480$	0.633436	−	0.807874i	0.0289123	−	0.0368742i
$481$		−	31.2167i		−	1.42336i
$482$	3.99986	−	1.07176i	0.182189	−	0.0488173i
$483$	1.04114	+	0.278973i	0.0473735	+	0.0126937i
$484$			3.11795i			0.141725i
$485$	−7.53775	+	17.6727i	−0.342272	+	0.802476i
$486$	5.62753	−	9.74717i	0.255270	−	0.442141i
$487$	−40.2822	+	10.7936i	−1.82536	+	0.489104i	−0.997425	−	0.0717205i	$-0.977151\pi$
$487$	−40.2822	+	10.7936i	−1.82536	+	0.489104i	−0.827935	+	0.560824i	$0.810484\pi$
$488$	3.38951	+	12.6498i	0.153436	+	0.572631i
$489$			1.00372i			0.0453900i
$490$	−14.5328	+	1.75887i	−0.656526	+	0.0794576i
$491$	22.8447	+	13.1894i	1.03097	+	0.595229i	0.917262	−	0.398285i	$-0.130395\pi$
$491$	22.8447	+	13.1894i	1.03097	+	0.595229i	0.113706	+	0.993514i	$0.463728\pi$
$492$	−3.05016	−	0.817287i	−0.137512	−	0.0368461i
$493$	−7.17003	+	26.7589i	−0.322922	+	1.20516i
$494$			20.6388i			0.928584i
$495$	2.46695	−	17.3354i	0.110881	−	0.779168i
$496$	−4.15390	−	7.19476i	−0.186515	−	0.323054i
$497$	1.30153	−	4.85736i	0.0583814	−	0.217882i
$498$	0.989082	+	3.69130i	0.0443218	+	0.165411i
$499$	19.3457	−	33.5077i	0.866031	−	1.50001i	1.03421e−5	−	1.00000i	$-0.499997\pi$
$499$	19.3457	−	33.5077i	0.866031	−	1.50001i	0.866020	−	0.500009i	$-0.166670\pi$
$500$	4.60045	−	10.1900i	0.205738	−	0.455710i
$501$	3.80193	+	2.19504i	0.169858	+	0.0980673i
$502$	−3.13967	−	11.7174i	−0.140130	−	0.522973i
$503$	36.7080	−	9.83588i	1.63673	−	0.438560i	0.680874	−	0.732400i	$-0.261600\pi$
$503$	36.7080	−	9.83588i	1.63673	−	0.438560i	0.955855	+	0.293840i	$0.0949333\pi$
$504$	−1.62632	+	0.938959i	−0.0724422	+	0.0418246i
$505$	−6.13650	−	0.873267i	−0.273071	−	0.0388599i
$506$	−8.47826	+	4.89493i	−0.376905	+	0.217606i
$507$	−0.118857	−	0.443580i	−0.00527863	−	0.0197001i
$508$	−1.89725	+	1.89725i	−0.0841769	+	0.0841769i
$509$	−25.8600	−	14.9303i	−1.14622	−	0.661773i	−0.198260	−	0.980149i	$-0.563529\pi$
$509$	−25.8600	−	14.9303i	−1.14622	−	0.661773i	−0.947964	+	0.318376i	$0.896862\pi$
$510$	1.99484	−	4.67702i	0.0883330	−	0.207102i
$511$	4.68292	+	8.11106i	0.207160	+	0.358812i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−15.2960	−	4.09855i	−0.675334	−	0.180955i
$514$		−	13.4055i		−	0.591291i
$515$	1.08588	−	0.815325i	0.0478496	−	0.0359275i
$516$	3.00509	−	0.181643i	0.132292	−	0.00799639i
$517$	21.7832	+	21.7832i	0.958025	+	0.958025i
$518$	−4.29022	−	4.29022i	−0.188501	−	0.188501i
$519$	−1.05157	−	1.82137i	−0.0461587	−	0.0799492i
$520$	7.66862	+	1.09130i	0.336291	+	0.0478566i
$521$	−11.4733	+	6.62408i	−0.502652	+	0.290206i	−0.729808	−	0.683652i	$-0.760391\pi$
$521$	−11.4733	+	6.62408i	−0.502652	+	0.290206i	0.227156	+	0.973858i	$0.427057\pi$
$522$	4.03777	−	15.0691i	0.176728	−	0.659559i
$523$	−37.8104	+	10.1313i	−1.65333	+	0.443010i	−0.960544	−	0.278129i	$-0.910286\pi$
$523$	−37.8104	+	10.1313i	−1.65333	+	0.443010i	−0.692791	+	0.721138i	$0.743619\pi$
$524$	21.0066			0.917680
$525$	1.11548	−	1.06976i	0.0486834	−	0.0466883i
$526$	0.0422955	+	0.0732579i	0.00184417	+	0.00319420i
$527$	−29.0960	−	29.0960i	−1.26744	−	1.26744i
$528$	−0.333604	+	1.24503i	−0.0145182	+	0.0541828i
$529$	−9.38822	−	5.42029i	−0.408183	−	0.235665i
$530$	−25.1360	−	19.7086i	−1.09184	−	0.856087i
$531$	−12.6932	+	21.9853i	−0.550838	+	0.954080i
$532$	2.83647	+	2.83647i	0.122976	+	0.122976i
$533$	−6.16659	−	23.0140i	−0.267105	−	0.996849i
$534$	−0.575843	+	0.997389i	−0.0249192	+	0.0431613i
$535$	5.23944	−	12.2842i	0.226521	−	0.531091i
$536$	−5.97491	+	3.44961i	−0.258077	+	0.149001i
$537$	6.75742	+	6.75742i	0.291604	+	0.291604i
$538$	−5.71807	−	5.71807i	−0.246523	−	0.246523i
$539$	15.9174	−	9.18993i	0.685612	−	0.395838i
$540$	−2.33166	+	5.46671i	−0.100339	+	0.235250i
$541$	4.91921	−	8.52031i	0.211493	−	0.366317i	−0.740689	−	0.671848i	$-0.765501\pi$
$541$	4.91921	−	8.52031i	0.211493	−	0.366317i	0.952182	+	0.305531i	$0.0988341\pi$
$542$	−2.27565	−	8.49284i	−0.0977475	−	0.364799i
$543$	−2.65343	−	2.65343i	−0.113869	−	0.113869i
$544$	2.47647	−	4.28937i	0.106178	−	0.183905i
$545$	−20.8505	−	16.3484i	−0.893139	−	0.700290i
$546$	0.927311	+	0.535383i	0.0396853	+	0.0229123i
$547$	3.99558	−	14.9117i	0.170839	−	0.637579i	−0.826384	−	0.563106i	$-0.809606\pi$
$547$	3.99558	−	14.9117i	0.170839	−	0.637579i	0.997223	−	0.0744722i	$-0.0237272\pi$
$548$	−11.5605	−	11.5605i	−0.493840	−	0.493840i
$549$	−18.2639	−	31.6340i	−0.779484	−	1.35011i
$550$	−0.293590	+	14.0344i	−0.0125187	+	0.598430i
$551$	−33.3243			−1.41966
$552$	1.54638	−	0.414350i	0.0658182	−	0.0176359i
$553$	1.83491	−	6.84797i	0.0780282	−	0.291205i
$554$	−9.04920	+	5.22456i	−0.384464	+	0.221970i
$555$	−9.15898	−	1.30339i	−0.388777	−	0.0553257i
$556$	6.50925	+	11.2744i	0.276054	+	0.478139i
$557$	32.5435	+	32.5435i	1.37891	+	1.37891i	0.846463	+	0.532448i	$0.178728\pi$
$557$	32.5435	+	32.5435i	1.37891	+	1.37891i	0.532448	+	0.846463i	$0.321272\pi$
$558$	16.3853	+	16.3853i	0.693643	+	0.693643i
$559$	12.5239	+	18.9510i	0.529705	+	0.801542i
$560$	1.20391	−	0.903945i	0.0508744	−	0.0381987i
$561$			6.38407i			0.269535i
$562$	4.98663	+	1.33616i	0.210348	+	0.0563626i
$563$	12.4822	−	12.4822i	0.526061	−	0.526061i	−0.393335	−	0.919395i	$-0.628679\pi$
$563$	12.4822	−	12.4822i	0.526061	−	0.526061i	0.919395	+	0.393335i	$0.128679\pi$
$564$	−2.51885	−	4.36278i	−0.106063	−	0.183706i
$565$	−9.05335	+	21.2261i	−0.380877	+	0.892989i
$566$	−7.68808	−	4.43871i	−0.323154	−	0.186573i
$567$	3.40273	−	3.40273i	0.142901	−	0.142901i
$568$	−1.93312	−	7.21450i	−0.0811119	−	0.302714i
$569$	−21.2933	+	12.2937i	−0.892662	+	0.515379i	−0.874812	−	0.484462i	$-0.839015\pi$
$569$	−21.2933	+	12.2937i	−0.892662	+	0.515379i	−0.0178496	+	0.999841i	$0.505682\pi$
$570$	6.05543	+	0.861730i	0.253634	+	0.0360939i
$571$	9.07353	−	5.23861i	0.379716	−	0.219229i	−0.297979	−	0.954572i	$-0.596313\pi$
$571$	9.07353	−	5.23861i	0.379716	−	0.219229i	0.677694	+	0.735344i	$0.262979\pi$
$572$	−9.39397	+	2.51711i	−0.392782	+	0.105246i
$573$	2.49506	+	9.31169i	0.104233	+	0.389001i
$574$	−4.01040	−	2.31541i	−0.167391	−	0.0966432i
$575$	15.2783	−	8.39989i	0.637151	−	0.350299i
$576$	−1.39461	+	2.41554i	−0.0581087	+	0.100647i
$577$	7.40972	+	27.6534i	0.308470	+	1.15123i	0.929917	+	0.367771i	$0.119879\pi$
$577$	7.40972	+	27.6534i	0.308470	+	1.15123i	−0.621446	+	0.783457i	$0.713454\pi$
$578$	1.94931	−	7.27493i	0.0810807	−	0.302597i
$579$	1.16347	+	2.01519i	0.0483522	+	0.0837485i
$580$	−1.76206	+	12.3821i	−0.0731654	+	0.514138i
$581$			5.60421i			0.232502i
$582$	−1.02099	+	3.81040i	−0.0423215	+	0.157946i
$583$	38.7375	+	10.3797i	1.60434	+	0.429882i
$584$	12.0471	+	6.95542i	0.498514	+	0.287817i
$585$	−21.4485	+	2.59585i	−0.886784	+	0.107325i
$586$		−	7.13494i		−	0.294741i
$587$	0.0687605	+	0.256618i	0.00283805	+	0.0105917i	0.967330	−	0.253519i	$-0.0815881\pi$
$587$	0.0687605	+	0.256618i	0.00283805	+	0.0105917i	−0.964492	+	0.264111i	$0.914921\pi$
$588$	−2.90323	+	0.777918i	−0.119727	+	0.0320808i
$589$	24.7488	−	42.8662i	1.01976	−	1.76627i
$590$	7.98452	−	18.7202i	0.328718	−	0.770697i
$591$			7.65935i			0.315064i
$592$	−8.70451	−	2.33237i	−0.357753	−	0.0958597i
$593$	5.83102	−	1.56242i	0.239451	−	0.0641608i	−0.137097	−	0.990558i	$-0.543777\pi$
$593$	5.83102	−	1.56242i	0.239451	−	0.0641608i	0.376549	+	0.926397i	$0.377111\pi$
$594$		−	7.46199i		−	0.306169i
$595$	4.60091	−	5.86793i	0.188619	−	0.240562i
$596$	9.15986	−	5.28844i	0.375202	−	0.216623i
$597$	0.00747869	−	0.0279109i	0.000306082	−	0.00114232i
$598$	8.54137	+	8.54137i	0.349282	+	0.349282i
$599$	15.4768	−	8.93552i	0.632364	−	0.365095i	−0.149303	−	0.988791i	$-0.547703\pi$
$599$	15.4768	−	8.93552i	0.632364	−	0.365095i	0.781667	+	0.623696i	$0.214370\pi$
$600$	0.640374	−	2.20441i	0.0261432	−	0.0899947i
$601$		−	17.9182i		−	0.730897i	−0.930832	−	0.365448i	$-0.880916\pi$
$601$		−	17.9182i		−	0.730897i	0.930832	−	0.365448i	$-0.119084\pi$
$602$	4.32571	+	0.883296i	0.176303	+	0.0360005i
$603$	13.6072	−	13.6072i	0.554127	−	0.554127i
$604$	−11.6227			−0.472923
$605$	2.60054	+	6.46878i	0.105727	+	0.262993i
$606$	−1.27264			−0.0516974
$607$	0.447231	+	0.119835i	0.0181526	+	0.00486396i	0.267884	−	0.963451i	$-0.413676\pi$
$607$	0.447231	+	0.119835i	0.0181526	+	0.00486396i	−0.249731	+	0.968315i	$0.580342\pi$
$608$	5.75496	+	1.54204i	0.233395	+	0.0625379i
$609$	−0.864452	+	1.49728i	−0.0350294	+	0.0606727i
$610$	17.5828	+	23.4175i	0.711909	+	0.948146i
$611$	19.0052	−	32.9180i	0.768869	−	1.33172i
$612$	−3.57554	+	13.3441i	−0.144533	+	0.539403i
$613$	20.2207	−	20.2207i	0.816705	−	0.816705i	−0.168924	−	0.985629i	$-0.554029\pi$
$613$	20.2207	−	20.2207i	0.816705	−	0.816705i	0.985629	+	0.168924i	$0.0540292\pi$
$614$	−4.95373	−	8.58012i	−0.199916	−	0.346265i
$615$	−7.00980	+	0.848378i	−0.282662	+	0.0342099i
$616$	−0.945113	+	1.63698i	−0.0380797	+	0.0659559i
$617$	−3.01564	+	0.808039i	−0.121405	+	0.0325304i	−0.319010	−	0.947751i	$-0.603350\pi$
$617$	−3.01564	+	0.808039i	−0.121405	+	0.0325304i	0.197605	+	0.980282i	$0.436684\pi$
$618$	0.197143	−	0.197143i	0.00793027	−	0.00793027i
$619$	−38.2553	−	22.0867i	−1.53761	−	0.887739i	−0.998978	−	0.0451972i	$-0.985608\pi$
$619$	−38.2553	−	22.0867i	−1.53761	−	0.887739i	−0.538631	−	0.842542i	$-0.681058\pi$
$620$	−14.6189	−	11.4623i	−0.587109	−	0.460339i
$621$	−8.02643	+	4.63406i	−0.322089	+	0.185958i
$622$	3.20577	+	0.858982i	0.128539	+	0.0344421i
$623$	−1.19426	+	1.19426i	−0.0478469	+	0.0478469i
$624$	1.59038			0.0636662
$625$	1.04551	−	24.9781i	0.0418202	−	0.999125i
$626$	2.73313	+	4.73391i	0.109238	+	0.189205i
$627$	−7.41784	+	1.98760i	−0.296240	+	0.0793772i
$628$	−0.583207	+	0.156270i	−0.0232725	+	0.00623584i
$629$	−44.6338			−1.77966
$630$	−2.59098	+	3.30450i	−0.103227	+	0.131654i
$631$	−17.0964	−	9.87063i	−0.680598	−	0.392944i	0.119482	−	0.992836i	$-0.461877\pi$
$631$	−17.0964	−	9.87063i	−0.680598	−	0.392944i	−0.800080	+	0.599893i	$0.795210\pi$
$632$	−2.72534	−	10.1711i	−0.108408	−	0.404585i
$633$	1.34032	+	0.359137i	0.0532729	+	0.0142744i
$634$	−19.0280			−0.755700
$635$	−2.35380	+	5.51863i	−0.0934078	+	0.219000i
$636$	−5.67955	−	3.27909i	−0.225209	−	0.130024i
$637$	−16.0359	−	16.0359i	−0.635365	−	0.635365i
$638$	−4.06423	−	15.1679i	−0.160904	−	0.600503i
$639$	10.4163	+	18.0416i	0.412064	+	0.713716i
$640$	0.877264	−	2.05680i	0.0346769	−	0.0813020i
$641$		−	21.4986i		−	0.849143i	−0.905394	−	0.424572i	$-0.860425\pi$
$641$		−	21.4986i		−	0.849143i	0.905394	−	0.424572i	$-0.139575\pi$
$642$	0.709685	−	2.64858i	0.0280090	−	0.104531i
$643$	2.48048	−	2.48048i	0.0978205	−	0.0978205i	−0.656503	−	0.754323i	$-0.727965\pi$
$643$	2.48048	−	2.48048i	0.0978205	−	0.0978205i	0.754323	+	0.656503i	$0.227965\pi$
$644$	2.34774			0.0925140
$645$	6.08314	−	2.88326i	0.239523	−	0.113528i
$646$	29.5095			1.16103
$647$	22.4062	−	22.4062i	0.880877	−	0.880877i	−0.112747	−	0.993624i	$-0.535965\pi$
$647$	22.4062	−	22.4062i	0.880877	−	0.880877i	0.993624	+	0.112747i	$0.0359649\pi$
$648$	1.84988	−	6.90386i	0.0726703	−	0.271209i
$649$			25.5528i			1.00303i
$650$	16.8202	−	4.13194i	0.659744	−	0.162068i
$651$	−1.28400	−	2.22395i	−0.0503239	−	0.0871635i
$652$	0.565842	+	2.11175i	0.0221601	+	0.0827026i
$653$	−10.7794	−	10.7794i	−0.421832	−	0.421832i	0.464002	−	0.885834i	$-0.346413\pi$
$653$	−10.7794	−	10.7794i	−0.421832	−	0.421832i	−0.885834	+	0.464002i	$0.846413\pi$
$654$	−4.71123	−	2.72003i	−0.184224	−	0.106362i
$655$	43.5824	−	17.5207i	1.70290	−	0.684590i
$656$	−6.87802			−0.268541
$657$	−37.4783	−	10.0423i	−1.46217	−	0.391787i
$658$	−1.91209	−	7.13600i	−0.0745409	−	0.278190i
$659$	12.5627	+	7.25310i	0.489375	+	0.282541i	0.724315	−	0.689469i	$-0.242156\pi$
$659$	12.5627	+	7.25310i	0.489375	+	0.282541i	−0.234940	+	0.972010i	$0.575489\pi$
$660$	0.346295	+	2.86129i	0.0134795	+	0.111376i
$661$	−4.69247			−0.182516			−0.0912579	−	0.995827i	$-0.529089\pi$
$661$	−4.69247			−0.182516			−0.0912579	+	0.995827i	$0.529089\pi$
$662$	−32.4540	+	8.69603i	−1.26136	+	0.337981i
$663$	7.60865	−	2.03873i	0.295495	−	0.0791777i
$664$	4.16189	+	7.20861i	0.161513	+	0.279748i
$665$	8.25056	+	3.51903i	0.319943	+	0.136462i
$666$	25.1353			0.973972
$667$	−13.7912	+	13.7912i	−0.533999	+	0.533999i
$668$	9.23638	+	2.47488i	0.357366	+	0.0957560i
$669$	1.74177	−	1.00561i	0.0673406	−	0.0388791i
$670$	−9.51893	+	12.1403i	−0.367748	+	0.469020i
$671$	−31.8413	−	18.3836i	−1.22922	−	0.709691i
$672$	0.218572	−	0.218572i	0.00843159	−	0.00843159i
$673$	−31.9588	+	8.56335i	−1.23192	+	0.330093i	−0.815328	−	0.579000i	$-0.803443\pi$
$673$	−31.9588	+	8.56335i	−1.23192	+	0.330093i	−0.416595	+	0.909092i	$0.636777\pi$
$674$	8.09126	−	14.0145i	0.311664	−	0.539817i
$675$	−0.277943	+	13.2865i	−0.0106980	+	0.511397i
$676$	−0.500131	−	0.866252i	−0.0192358	−	0.0333174i
$677$	23.6358	−	23.6358i	0.908398	−	0.908398i	−0.0877446	−	0.996143i	$-0.527966\pi$
$677$	23.6358	−	23.6358i	0.908398	−	0.908398i	0.996143	+	0.0877446i	$0.0279659\pi$
$678$	−1.22628	+	4.57655i	−0.0470951	+	0.175761i
$679$	−2.89251	+	5.00998i	−0.111005	+	0.192265i
$680$	1.56034	−	10.9646i	0.0598364	−	0.420474i
$681$	2.77858	−	4.81264i	0.106475	−	0.184421i
$682$	22.5294	+	6.03673i	0.862694	+	0.231158i
$683$	−27.2742	−	7.30809i	−1.04362	−	0.279636i	−0.304005	−	0.952670i	$-0.598324\pi$
$683$	−27.2742	−	7.30809i	−1.04362	−	0.279636i	−0.739612	+	0.673034i	$0.764991\pi$
$684$	−16.6181			−0.635409
$685$	−33.6266	−	14.3424i	−1.28481	−	0.547995i
$686$	−9.12068			−0.348229
$687$	−1.64874	+	1.64874i	−0.0629034	+	0.0629034i
$688$	6.22006	−	2.07626i	0.237138	−	0.0791567i
$689$		−	49.4828i		−	1.88514i
$690$	2.86267	−	2.14941i	0.108980	−	0.0818268i
$691$	−29.3255	+	16.9311i	−1.11560	+	0.644089i	−0.940273	−	0.340422i	$-0.889430\pi$
$691$	−29.3255	+	16.9311i	−1.11560	+	0.644089i	−0.175323	+	0.984511i	$0.556097\pi$
$692$	−3.23920	−	3.23920i	−0.123136	−	0.123136i
$693$	1.36456	−	5.09261i	0.0518353	−	0.193452i
$694$	1.33241	−	0.769269i	0.0505777	−	0.0292011i
$695$	22.9081	+	17.9617i	0.868955	+	0.681328i
$696$			2.56789i			0.0973358i
$697$	−32.9056	+	8.81703i	−1.24639	+	0.333969i
$698$	−16.0917	−	4.31175i	−0.609079	−	0.163202i
$699$			4.02139i			0.152103i
$700$	1.74380	−	2.87953i	0.0659094	−	0.108836i
$701$	−6.23393	+	10.7975i	−0.235452	+	0.407815i	−0.959404	−	0.282035i	$-0.908990\pi$
$701$	−6.23393	+	10.7975i	−0.235452	+	0.407815i	0.723952	+	0.689851i	$0.242324\pi$
$702$	−8.89334	+	2.38296i	−0.335657	+	0.0899391i
$703$	−13.8962	−	51.8613i	−0.524105	−	1.95599i
$704$			2.80750i			0.105812i
$705$	−8.86464	−	6.95057i	−0.333862	−	0.261773i
$706$	23.0392	+	13.3017i	0.867090	+	0.500615i
$707$	−1.80272	−	0.483036i	−0.0677981	−	0.0181664i
$708$	1.08151	−	4.03624i	0.0406456	−	0.151691i
$709$		−	11.2553i		−	0.422701i	−0.977410	−	0.211350i	$-0.932214\pi$
$709$		−	11.2553i		−	0.422701i	0.977410	−	0.211350i	$-0.0677861\pi$
$710$	−10.0279	−	13.3555i	−0.376341	−	0.501225i
$711$	14.6851	+	25.4353i	0.550734	+	0.953899i
$712$	−0.649255	+	2.42305i	−0.0243319	+	0.0908077i
$713$	−7.49788	−	27.9825i	−0.280798	−	1.04795i
$714$	0.765494	−	1.32587i	0.0286479	−	0.0496196i
$715$	−17.3902	+	13.0573i	−0.650357	+	0.488316i
$716$	18.0265	+	10.4076i	0.673682	+	0.388951i
$717$	2.61933	+	9.77547i	0.0978207	+	0.365072i
$718$	−24.6629	+	6.60839i	−0.920410	+	0.246623i
$719$	37.1823	−	21.4672i	1.38667	−	0.800592i	0.393728	−	0.919227i	$-0.371185\pi$
$719$	37.1823	−	21.4672i	1.38667	−	0.800592i	0.992938	+	0.118635i	$0.0378517\pi$
$720$	−0.878699	+	6.17468i	−0.0327472	+	0.230117i
$721$	0.354084	−	0.204431i	0.0131868	−	0.00761340i
$722$	4.26986	+	15.9353i	0.158908	+	0.593051i
$723$	1.34432	−	1.34432i	0.0499956	−	0.0499956i
$724$	−7.07844	−	4.08674i	−0.263068	−	0.151883i
$725$	6.67161	+	27.1587i	0.247777	+	1.00865i
$726$	0.715738	+	1.23969i	0.0265635	+	0.0460094i
$727$	10.7498	−	10.7498i	0.398690	−	0.398690i	−0.479081	−	0.877771i	$-0.659030\pi$
$727$	10.7498	−	10.7498i	0.398690	−	0.398690i	0.877771	+	0.479081i	$0.159030\pi$
$728$	2.25280	+	0.603637i	0.0834945	+	0.0223723i
$729$			16.2749i			0.602775i
$730$	30.7953	+	4.38239i	1.13979	+	0.162199i
$731$	27.0962	−	17.9068i	1.00219	−	0.662305i
$732$	4.25149	+	4.25149i	0.157140	+	0.157140i
$733$	35.3220	+	35.3220i	1.30465	+	1.30465i	0.925222	+	0.379427i	$0.123879\pi$
$733$	35.3220	+	35.3220i	1.30465	+	1.30465i	0.379427	+	0.925222i	$0.376121\pi$
$734$	−6.83466	−	11.8380i	−0.252272	−	0.436948i
$735$	−5.37448	+	4.03539i	−0.198241	+	0.148848i
$736$	3.01986	−	1.74352i	0.111314	−	0.0642669i
$737$	5.01322	−	18.7096i	0.184664	−	0.689176i
$738$	18.5306	−	4.96526i	0.682121	−	0.182774i
$739$	37.5664			1.38190			0.690952	−	0.722901i	$-0.257192\pi$
$739$	37.5664			1.38190			0.690952	+	0.722901i	$0.257192\pi$
$740$	−20.0045	+	2.42109i	−0.735381	+	0.0890012i
$741$	4.73772	+	8.20598i	0.174045	+	0.301454i
$742$	−6.80059	−	6.80059i	−0.249658	−	0.249658i
$743$	−1.52300	+	5.68392i	−0.0558735	+	0.208523i	−0.988219	−	0.153046i	$-0.951092\pi$
$743$	−1.52300	+	5.68392i	−0.0558735	+	0.208523i	0.932346	+	0.361568i	$0.117759\pi$
$744$	−3.30317	−	1.90709i	−0.121100	−	0.0699172i
$745$	14.5930	−	18.6117i	0.534648	−	0.681881i
$746$	−1.52365	+	2.63904i	−0.0557849	+	0.0966223i
$747$	−16.4168	−	16.4168i	−0.600659	−	0.600659i
$748$	3.59897	+	13.4315i	0.131591	+	0.491106i
$749$	2.01057	−	3.48240i	0.0734645	−	0.127244i
$750$	−0.510019	−	5.10759i	−0.0186233	−	0.186503i
$751$	−2.12909	+	1.22923i	−0.0776916	+	0.0448553i	−0.538343	−	0.842726i	$-0.680949\pi$
$751$	−2.12909	+	1.22923i	−0.0776916	+	0.0448553i	0.460651	+	0.887581i	$0.347616\pi$
$752$	−7.75894	−	7.75894i	−0.282939	−	0.282939i
$753$	−3.93811	−	3.93811i	−0.143513	−	0.143513i
$754$	−16.7795	+	9.68764i	−0.611073	+	0.352803i
$755$	−24.1136	+	9.69400i	−0.877585	+	0.352801i
$756$	−0.894744	+	1.54974i	−0.0325415	+	0.0563636i
$757$	−1.55894	−	5.81803i	−0.0566605	−	0.211460i	0.931792	−	0.362994i	$-0.118245\pi$
$757$	−1.55894	−	5.81803i	−0.0566605	−	0.211460i	−0.988452	+	0.151534i	$0.951579\pi$
$758$	20.3617	+	20.3617i	0.739571	+	0.739571i
$759$	−2.24730	+	3.89244i	−0.0815719	+	0.141287i
$760$	13.2259	−	1.60070i	0.479755	−	0.0580635i
$761$	18.6224	+	10.7517i	0.675063	+	0.389748i	0.797992	−	0.602668i	$-0.205896\pi$
$761$	18.6224	+	10.7517i	0.675063	+	0.389748i	−0.122929	+	0.992415i	$0.539229\pi$
$762$	−0.318824	+	1.18987i	−0.0115498	+	0.0431044i
$763$	−5.64115	−	5.64115i	−0.204223	−	0.204223i
$764$	10.4988	+	18.1845i	0.379833	+	0.657890i
$765$	3.71156	+	30.6671i	0.134192	+	1.10877i
$766$	8.31578			0.300461
$767$	30.4543	−	8.16020i	1.09964	−	0.294648i
$768$	0.118826	−	0.443464i	0.00428776	−	0.0160021i
$769$	−34.6739	+	20.0190i	−1.25037	+	0.721904i	−0.971184	−	0.238332i	$-0.923399\pi$
$769$	−34.6739	+	20.0190i	−1.25037	+	0.721904i	−0.279190	+	0.960236i	$0.590066\pi$
$770$	−0.595485	+	4.18451i	−0.0214598	+	0.150799i
$771$	−3.07729	−	5.33002i	−0.110826	−	0.191956i
$772$	3.58390	+	3.58390i	0.128987	+	0.128987i
$773$	16.8986	+	16.8986i	0.607802	+	0.607802i	0.942371	−	0.334569i	$-0.108591\pi$
$773$	16.8986	+	16.8986i	0.607802	+	0.607802i	−0.334569	+	0.942371i	$0.608591\pi$
$774$	−15.2591	+	10.0841i	−0.548477	+	0.362465i
$775$	−39.8899	−	11.5879i	−1.43289	−	0.416249i
$776$			8.59235i			0.308447i
$777$	−2.69063	−	0.720951i	−0.0965257	−	0.0258640i
$778$	8.39326	−	8.39326i	0.300913	−	0.300913i
$779$	−20.4895	−	35.4889i	−0.734113	−	1.27152i
$780$	3.29955	−	1.32646i	0.118143	−	0.0474950i
$781$	18.1599	+	10.4846i	0.649811	+	0.375169i
$782$	12.2125	−	12.2125i	0.436718	−	0.436718i
$783$	−3.84763	−	14.3596i	−0.137503	−	0.513169i
$784$	−5.66961	+	3.27335i	−0.202486	+	0.116905i
$785$	−1.07964	+	0.810638i	−0.0385339	+	0.0289329i
$786$	8.35223	−	4.82216i	0.297914	−	0.172001i
$787$	39.0300	−	10.4581i	1.39127	−	0.372789i	0.516067	−	0.856548i	$-0.327395\pi$
$787$	39.0300	−	10.4581i	1.39127	−	0.372789i	0.875201	+	0.483759i	$0.160729\pi$
$788$	4.31791	+	16.1146i	0.153819	+	0.574060i
$789$	0.0336333	+	0.0194182i	0.00119738	+	0.000691306i
$790$	−14.1375	−	18.8288i	−0.502989	−	0.669900i
$791$	−3.47411	+	6.01733i	−0.123525	+	0.213952i
$792$	−2.02674	−	7.56391i	−0.0720172	−	0.268772i
$793$	−11.7415	+	43.8198i	−0.416952	+	1.55609i
$794$	18.4623	+	31.9776i	0.655201	+	1.13484i
$795$	−14.5183	−	2.06605i	−0.514909	−	0.0732752i
$796$		−	0.0629382i		−	0.00223078i
$797$	−0.876043	+	3.26944i	−0.0310310	+	0.115809i	−0.979704	−	0.200449i	$-0.935760\pi$
$797$	−0.876043	+	3.26944i	−0.0310310	+	0.115809i	0.948673	+	0.316258i	$0.102427\pi$
$798$	1.77890	+	0.476655i	0.0629724	+	0.0168734i
$799$	−47.0664	−	27.1738i	−1.66509	−	0.961339i
$800$	0.104573	−	4.99891i	0.00369723	−	0.176738i
$801$		−	6.99684i		−	0.247221i
$802$	−1.64370	−	6.13439i	−0.0580412	−	0.216613i
$803$	−37.7239	+	10.1081i	−1.33125	+	0.356707i
$804$	−1.58375	+	2.74313i	−0.0558544	+	0.0967427i
$805$	4.87084	−	1.95815i	0.171675	−	0.0690156i
$806$		−	28.7787i		−	1.01369i
$807$	−3.58611	−	0.960894i	−0.126237	−	0.0338251i
$808$	−2.67752	+	0.717440i	−0.0941950	+	0.0252395i
$809$			36.6189i			1.28745i	0.765256	+	0.643726i	$0.222612\pi$
$809$			36.6189i			1.28745i	−0.765256	+	0.643726i	$0.777388\pi$
$810$	−1.92026	−	15.8663i	−0.0674710	−	0.557485i
$811$	−37.3883	+	21.5861i	−1.31288	+	0.757992i	−0.982572	−	0.185882i	$-0.940486\pi$
$811$	−37.3883	+	21.5861i	−1.31288	+	0.757992i	−0.330308	+	0.943873i	$0.607153\pi$
$812$	−0.974658	+	3.63747i	−0.0342038	+	0.127650i
$813$	−2.85436	−	2.85436i	−0.100107	−	0.100107i
$814$	21.9104	−	12.6500i	0.767961	−	0.443382i
$815$	2.93527	+	3.90930i	0.102818	+	0.136937i
$816$		−	2.27393i		−	0.0796036i
$817$	29.2425	+	25.9088i	1.02306	+	0.906436i
$818$	5.22025	−	5.22025i	0.182522	−	0.182522i
$819$	−6.50523			−0.227311
$820$	−14.2698	+	5.73664i	−0.498322	+	0.200332i
$821$	−0.304946			−0.0106427			−0.00532135	−	0.999986i	$-0.501694\pi$
$821$	−0.304946			−0.0106427			−0.00532135	+	0.999986i	$0.501694\pi$
$822$	−7.25021	−	1.94269i	−0.252880	−	0.0677590i
$823$	11.5237	+	3.08778i	0.401692	+	0.107633i	0.454008	−	0.890997i	$-0.349994\pi$
$823$	11.5237	+	3.08778i	0.401692	+	0.107633i	−0.0523159	+	0.998631i	$0.516660\pi$
$824$	0.303635	−	0.525912i	0.0105776	−	0.0183210i
$825$	3.10493	+	5.64747i	0.108100	+	0.196620i
$826$	3.06396	−	5.30693i	0.106609	−	0.184652i
$827$	−9.28418	+	34.6490i	−0.322843	+	1.20487i	0.593620	+	0.804745i	$0.297698\pi$
$827$	−9.28418	+	34.6490i	−0.322843	+	1.20487i	−0.916463	+	0.400120i	$0.868969\pi$
$828$	−6.87740	+	6.87740i	−0.239006	+	0.239006i
$829$	22.8679	+	39.6084i	0.794235	+	1.37566i	0.923324	+	0.384022i	$0.125461\pi$
$829$	22.8679	+	39.6084i	0.794235	+	1.37566i	−0.129089	+	0.991633i	$0.541205\pi$
$830$	14.6470	+	11.4844i	0.508406	+	0.398630i
$831$	−2.39864	+	4.15456i	−0.0832078	+	0.144120i
$832$	3.34603	−	0.896566i	0.116003	−	0.0310828i
$833$	−22.9282	+	22.9282i	−0.794415	+	0.794415i
$834$	5.17615	+	2.98845i	0.179235	+	0.103482i
$835$	21.2268	−	2.56903i	0.734585	−	0.0889049i
$836$	−14.4860	+	8.36351i	−0.501009	+	0.289258i
$837$	21.3287	+	5.71501i	0.737228	+	0.197540i
$838$	3.27841	−	3.27841i	0.113251	−	0.113251i
$839$	−30.0300			−1.03675			−0.518375	−	0.855154i	$-0.673463\pi$
$839$	−30.0300			−1.03675			−0.518375	+	0.855154i	$0.673463\pi$
$840$	0.271168	−	0.635770i	0.00935620	−	0.0219361i
$841$	−1.14207	−	1.97813i	−0.0393818	−	0.0682113i
$842$	21.7909	−	5.83885i	0.750963	−	0.201220i
$843$	2.28940	−	0.613443i	0.0788512	−	0.0211281i
$844$	3.02238			0.104035
$845$	−1.76012	−	1.38007i	−0.0605500	−	0.0474759i
$846$	26.5052	+	15.3028i	0.911267	+	0.526120i
$847$	0.543324	+	2.02771i	0.0186688	+	0.0696730i
$848$	−13.7979	−	3.69713i	−0.473820	−	0.126960i
$849$	−4.07570			−0.139878
$850$	−5.90787	−	24.0497i	−0.202638	−	0.824897i
$851$	−27.2137	−	15.7118i	−0.932874	−	0.538595i
$852$	−2.42473	−	2.42473i	−0.0830697	−	0.0830697i
$853$	4.55044	+	16.9825i	0.155804	+	0.581469i	0.999035	+	0.0439177i	$0.0139839\pi$
$853$	4.55044	+	16.9825i	0.155804	+	0.581469i	−0.843231	+	0.537551i	$0.819349\pi$
$854$	4.40864	+	7.63599i	0.150861	+	0.261298i
$855$	−34.4775	+	13.8604i	−1.17910	+	0.474016i
$856$		−	5.97248i		−	0.204135i
$857$	−1.34922	+	5.03536i	−0.0460885	+	0.172004i	−0.985134	−	0.171789i	$-0.945045\pi$
$857$	−1.34922	+	5.03536i	−0.0460885	+	0.172004i	0.939045	+	0.343793i	$0.111712\pi$
$858$	−3.15723	+	3.15723i	−0.107786	+	0.107786i
$859$	34.0029			1.16016			0.580081	−	0.814559i	$-0.303021\pi$
$859$	34.0029			1.16016			0.580081	+	0.814559i	$0.303021\pi$
$860$	11.1730	−	9.49547i	0.380996	−	0.323793i
$861$	−2.12604			−0.0724554
$862$	0.212919	−	0.212919i	0.00725205	−	0.00725205i
$863$	−5.23101	+	19.5224i	−0.178066	+	0.664550i	0.817944	+	0.575298i	$0.195114\pi$
$863$	−5.23101	+	19.5224i	−0.178066	+	0.664550i	−0.996009	+	0.0892513i	$0.971553\pi$
$864$			2.65788i			0.0904229i
$865$	−9.42200	−	4.01867i	−0.320358	−	0.136639i
$866$	2.39161	+	4.14240i	0.0812703	+	0.140764i
$867$	−0.894945	−	3.33998i	−0.0303939	−	0.113432i
$868$	−3.95516	−	3.95516i	−0.134247	−	0.134247i
$869$	25.6020	+	14.7813i	0.868489	+	0.501423i
$870$	2.14176	+	5.32759i	0.0726126	+	0.180622i
$871$	−23.8994			−0.809799
$872$	−11.4454	−	3.06680i	−0.387591	−	0.103855i
$873$	−6.20284	−	23.1493i	−0.209934	−	0.783486i
$874$	17.9923	+	10.3878i	0.608597	+	0.351374i
$875$	1.21616	−	7.42857i	0.0411137	−	0.251132i
$876$	6.38658			0.215783
$877$	−37.9553	+	10.1701i	−1.28166	+	0.343420i	−0.834487	−	0.551027i	$-0.814236\pi$
$877$	−37.9553	+	10.1701i	−1.28166	+	0.343420i	−0.447174	+	0.894447i	$0.647569\pi$
$878$	−4.98432	+	1.33554i	−0.168213	+	0.0450724i
$879$	−1.63785	−	2.83685i	−0.0552434	−	0.0956844i
$880$	2.34161	+	5.82470i	0.0789356	+	0.196351i
$881$	−16.9966			−0.572631			−0.286316	−	0.958135i	$-0.592431\pi$
$881$	−16.9966			−0.572631			−0.286316	+	0.958135i	$0.592431\pi$
$882$	12.9119	−	12.9119i	0.434766	−	0.434766i
$883$	34.5809	+	9.26592i	1.16374	+	0.311823i	0.788459	−	0.615088i	$-0.210879\pi$
$883$	34.5809	+	9.26592i	1.16374	+	0.311823i	0.375281	+	0.926911i	$0.377546\pi$
$884$	14.8586	−	8.57864i	0.499750	−	0.288531i
$885$	−1.12265	−	9.27601i	−0.0377375	−	0.311810i
$886$	29.6407	+	17.1131i	0.995800	+	0.574925i
$887$	16.0220	−	16.0220i	0.537968	−	0.537968i	−0.384964	−	0.922932i	$-0.625786\pi$
$887$	16.0220	−	16.0220i	0.537968	−	0.537968i	0.922932	+	0.384964i	$0.125786\pi$
$888$	−3.99631	+	1.07081i	−0.134108	+	0.0359340i
$889$	−0.903241	+	1.56446i	−0.0302937	+	0.0524703i
$890$	0.673954	+	5.56860i	0.0225910	+	0.186660i
$891$	10.0332	+	17.3780i	0.336124	+	0.582183i
$892$	3.09763	−	3.09763i	0.103716	−	0.103716i
$893$	16.9205	−	63.1480i	0.566222	−	2.11317i
$894$	2.42797	−	4.20536i	0.0812034	−	0.140648i
$895$	46.0800	+	6.55750i	1.54028	+	0.219193i
$896$	0.336639	−	0.583075i	0.0112463	−	0.0194792i
$897$	5.35675	+	1.43534i	0.178857	+	0.0479245i
$898$	0.370072	+	0.0991605i	0.0123495	+	0.00330903i
$899$	46.4673			1.54977
$900$	3.32699	+	13.5434i	0.110900	+	0.451448i
$901$	−70.7507			−2.35705
$902$	13.6543	−	13.6543i	0.454637	−	0.454637i
$903$	1.92266	−	0.641787i	0.0639823	−	0.0213573i
$904$			10.3200i			0.343238i
$905$	−18.0942	−	2.57492i	−0.601470	−	0.0855934i
$906$	−4.62120	+	2.66805i	−0.153529	+	0.0886400i
$907$	21.9257	+	21.9257i	0.728030	+	0.728030i	0.970227	−	0.242197i	$-0.0778680\pi$
$907$	21.9257	+	21.9257i	0.728030	+	0.728030i	−0.242197	+	0.970227i	$0.577868\pi$
$908$	3.13281	−	11.6918i	0.103966	−	0.388006i
$909$	6.69581	−	3.86583i	0.222086	−	0.128221i
$910$	5.17735	−	0.626600i	0.171627	−	0.0207716i
$911$		−	37.2720i		−	1.23488i	−0.786620	−	0.617438i	$-0.788171\pi$
$911$		−	37.2720i		−	1.23488i	0.786620	−	0.617438i	$-0.211829\pi$
$912$	2.64215	−	0.707962i	0.0874903	−	0.0234430i
$913$	−22.5727	−	6.04835i	−0.747049	−	0.200171i
$914$			26.4340i			0.874359i
$915$	12.3665	+	5.27456i	0.408824	+	0.174372i
$916$	−2.53935	+	4.39828i	−0.0839025	+	0.145323i
$917$	13.6614	−	3.66055i	0.451138	−	0.120882i
$918$	3.40717	+	12.7157i	0.112453	+	0.419682i
$919$			51.4033i			1.69564i	0.530285	+	0.847820i	$0.322085\pi$
$919$			51.4033i			1.69564i	−0.530285	+	0.847820i	$0.677915\pi$
$920$	4.81110	−	6.13600i	0.158617	−	0.202298i
$921$	−3.93920	−	2.27430i	−0.129801	−	0.0749407i
$922$	−22.4303	−	6.01017i	−0.738701	−	0.197934i
$923$	6.69645	−	24.9915i	0.220416	−	0.822605i
$924$			0.867818i			0.0285491i
$925$	−39.4839	+	21.7079i	−1.29822	+	0.713751i
$926$	−0.455425	−	0.788820i	−0.0149662	−	0.0259222i
$927$	−0.438391	+	1.63610i	−0.0143986	+	0.0537364i
$928$	1.44763	+	5.40264i	0.0475209	+	0.177350i
$929$	19.2475	−	33.3376i	0.631490	−	1.09377i	−0.355758	−	0.934578i	$-0.615777\pi$
$929$	19.2475	−	33.3376i	0.631490	−	1.09377i	0.987247	−	0.159194i	$-0.0508895\pi$
$930$	−8.44369	−	1.20160i	−0.276879	−	0.0394019i
$931$	−33.7794	−	19.5025i	−1.10707	−	0.639170i
$932$	2.26703	+	8.46067i	0.0742590	+	0.277138i
$933$	1.47179	−	0.394366i	0.0481844	−	0.0129110i
$934$	−11.9859	+	6.92005i	−0.392190	+	0.226431i
$935$	18.6694	+	24.8646i	0.610555	+	0.813159i
$936$	−8.36757	+	4.83102i	−0.273503	+	0.157907i
$937$	9.71490	+	36.2565i	0.317372	+	1.18445i	0.921761	+	0.387759i	$0.126751\pi$
$937$	9.71490	+	36.2565i	0.317372	+	1.18445i	−0.604389	+	0.796690i	$0.706583\pi$
$938$	−3.28458	+	3.28458i	−0.107245	+	0.107245i
$939$	2.17338	+	1.25480i	0.0709255	+	0.0409489i
$940$	−22.5688	−	9.62604i	−0.736113	−	0.313967i
$941$	27.3377	+	47.3502i	0.891182	+	1.54357i	0.838460	+	0.544963i	$0.183456\pi$
$941$	27.3377	+	47.3502i	0.891182	+	1.54357i	0.0527220	+	0.998609i	$0.483210\pi$
$942$	−0.196010	+	0.196010i	−0.00638636	+	0.00638636i
$943$	−23.1667	−	6.20749i	−0.754410	−	0.202144i
$944$		−	9.10162i		−	0.296232i
$945$	−0.563750	+	3.96151i	−0.0183388	+	0.128868i
$946$	−8.22628	+	16.4699i	−0.267459	+	0.535482i
$947$	−27.6417	−	27.6417i	−0.898234	−	0.898234i	0.0970460	−	0.995280i	$-0.469061\pi$
$947$	−27.6417	−	27.6417i	−0.898234	−	0.898234i	−0.995280	+	0.0970460i	$0.969061\pi$
$948$	−3.41841	−	3.41841i	−0.111025	−	0.111025i
$949$	24.0940	+	41.7321i	0.782125	+	1.35468i
$950$	26.1047	−	14.3521i	0.846947	−	0.465644i
$951$	−7.56554	+	4.36797i	−0.245329	+	0.141641i
$952$	0.863083	−	3.22107i	0.0279727	−	0.104395i
$953$	−7.50828	+	2.01184i	−0.243217	+	0.0651698i	−0.378368	−	0.925655i	$-0.623515\pi$
$953$	−7.50828	+	2.01184i	−0.243217	+	0.0651698i	0.135151	+	0.990825i	$0.456848\pi$
$954$	39.8429			1.28996
$955$	36.9486	+	28.9706i	1.19563	+	0.937466i
$956$	11.0217	+	19.0902i	0.356467	+	0.617420i
$957$	−5.09779	−	5.09779i	−0.164788	−	0.164788i
$958$	−4.86851	+	18.1695i	−0.157295	+	0.587031i
$959$	−9.53271	−	5.50371i	−0.307827	−	0.177724i
$960$	−0.123346	−	1.01916i	−0.00398098	−	0.0328933i
$961$	−19.0097	+	32.9258i	−0.613216	+	1.06212i
$962$	−22.0735	−	22.0735i	−0.711679	−	0.711679i
$963$	4.31155	+	16.0909i	0.138938	+	0.518523i
$964$	2.07048	−	3.58618i	0.0666857	−	0.115503i
$965$	10.4247	+	4.44632i	0.335582	+	0.143132i
$966$	0.933461	−	0.538934i	0.0300336	−	0.0173399i
$967$	22.4271	+	22.4271i	0.721207	+	0.721207i	0.968851	−	0.247644i	$-0.0796564\pi$
$967$	22.4271	+	22.4271i	0.721207	+	0.721207i	−0.247644	+	0.968851i	$0.579656\pi$
$968$	2.20472	+	2.20472i	0.0708624	+	0.0708624i
$969$	11.7329	−	6.77402i	0.376916	−	0.217613i
$970$	7.16649	+	17.8265i	0.230102	+	0.572374i
$971$	−19.9453	+	34.5463i	−0.640076	+	1.10864i	0.345339	+	0.938478i	$0.387764\pi$
$971$	−19.9453	+	34.5463i	−0.640076	+	1.10864i	−0.985415	+	0.170166i	$0.945569\pi$
$972$	−2.91303	−	10.8716i	−0.0934353	−	0.348705i
$973$	6.19783	+	6.19783i	0.198693	+	0.198693i
$974$	−20.8516	+	36.1160i	−0.668128	+	1.15723i
$975$	5.73921	−	5.50401i	0.183802	−	0.176269i
$976$	11.3415	+	6.54803i	0.363033	+	0.209597i
$977$	3.68059	−	13.7362i	0.117753	−	0.439459i	−0.881725	−	0.471763i	$-0.843618\pi$
$977$	3.68059	−	13.7362i	0.117753	−	0.439459i	0.999478	+	0.0323041i	$0.0102845\pi$
$978$	0.709740	+	0.709740i	0.0226950	+	0.0226950i
$979$	−3.52135	−	6.09915i	−0.112543	−	0.194930i
$980$	−9.03254	+	11.5200i	−0.288534	+	0.367992i
$981$	33.0500			1.05520
$982$	25.4800	−	6.82733i	0.813098	−	0.217869i
$983$	−3.43065	+	12.8034i	−0.109421	+	0.408364i	−0.998809	−	0.0487887i	$-0.984464\pi$
$983$	−3.43065	+	12.8034i	−0.109421	+	0.408364i	0.889388	+	0.457152i	$0.151131\pi$
$984$	−2.73470	+	1.57888i	−0.0871789	+	0.0503328i
$985$	22.3988	+	29.8316i	0.713686	+	0.950513i
$986$	13.8514	+	23.9914i	0.441120	+	0.764041i
$987$	−2.39834	−	2.39834i	−0.0763401	−	0.0763401i
$988$	14.5938	+	14.5938i	0.464292	+	0.464292i
$989$	22.8244	−	1.37962i	0.725773	−	0.0438695i
$990$	−10.5136	−	14.0024i	−0.334144	−	0.445025i
$991$		−	17.5337i		−	0.556977i	−0.960440	−	0.278488i	$-0.910167\pi$
$991$		−	17.5337i		−	0.556977i	0.960440	−	0.278488i	$-0.0898334\pi$
$992$	−8.02471	−	2.15021i	−0.254785	−	0.0682694i
$993$	−10.9075	+	10.9075i	−0.346139	+	0.346139i
$994$	−2.51435	−	4.35499i	−0.0797504	−	0.138132i
$995$	−0.0524939	−	0.130577i	−0.00166417	−	0.00413958i
$996$	3.30953	+	1.91076i	0.104867	+	0.0605447i
$997$	−13.5418	+	13.5418i	−0.428873	+	0.428873i	−0.888244	−	0.459371i	$-0.848075\pi$
$997$	−13.5418	+	13.5418i	−0.428873	+	0.428873i	0.459371	+	0.888244i	$0.348075\pi$
$998$	−10.0140	−	37.3729i	−0.316989	−	1.18302i
$999$	20.7428	−	11.9758i	0.656272	−	0.378899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.19	✓	88
5.3	odd	4	inner	430.2.l.a.93.8	yes	88
43.37	odd	6	inner	430.2.l.a.37.8	yes	88
215.123	even	12	inner	430.2.l.a.123.19	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.19	✓	88	1.1	even	1	trivial
430.2.l.a.37.8	yes	88	43.37	odd	6	inner
430.2.l.a.93.8	yes	88	5.3	odd	4	inner
430.2.l.a.123.19	yes	88	215.123	even	12	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.118826 - 0.443464i) q^{3} -1.00000i q^{4} +(-0.834055 - 2.07469i) q^{5} +(-0.229554 - 0.397599i) q^{6} +(-0.174257 - 0.650336i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.41554 + 1.39461i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.118826 - 0.443464i) q^{3} -1.00000i q^{4} +(-0.834055 - 2.07469i) q^{5} +(-0.229554 - 0.397599i) q^{6} +(-0.174257 - 0.650336i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.41554 + 1.39461i) q^{9} +(-2.05680 - 0.877264i) q^{10} +2.80750 q^{11} +(-0.443464 - 0.118826i) q^{12} +(-0.896566 - 3.34603i) q^{13} +(-0.583075 - 0.336639i) q^{14} +(-1.01916 + 0.123346i) q^{15} -1.00000 q^{16} +(-4.78417 + 1.28191i) q^{17} +(2.69418 - 0.721903i) q^{18} +(-2.97899 - 5.15976i) q^{19} +(-2.07469 + 0.834055i) q^{20} -0.309107 q^{21} +(1.98520 - 1.98520i) q^{22} +(-3.36822 - 0.902511i) q^{23} +(-0.397599 + 0.229554i) q^{24} +(-3.60871 + 3.46082i) q^{25} +(-2.99997 - 1.73203i) q^{26} +(1.87940 - 1.87940i) q^{27} +(-0.650336 + 0.174257i) q^{28} +(2.79661 - 4.84387i) q^{29} +(-0.633436 + 0.807874i) q^{30} +(4.15390 + 7.19476i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.333604 - 1.24503i) q^{33} +(-2.47647 + 4.28937i) q^{34} +(-1.20391 + 0.903945i) q^{35} +(1.39461 - 2.41554i) q^{36} +(8.70451 + 2.33237i) q^{37} +(-5.75496 - 1.54204i) q^{38} -1.59038 q^{39} +(-0.877264 + 2.05680i) q^{40} +6.87802 q^{41} +(-0.218572 + 0.218572i) q^{42} +(-6.22006 + 2.07626i) q^{43} -2.80750i q^{44} +(0.878699 - 6.17468i) q^{45} +(-3.01986 + 1.74352i) q^{46} +(7.75894 + 7.75894i) q^{47} +(-0.118826 + 0.443464i) q^{48} +(5.66961 - 3.27335i) q^{49} +(-0.104573 + 4.99891i) q^{50} +2.27393i q^{51} +(-3.34603 + 0.896566i) q^{52} +(13.7979 + 3.69713i) q^{53} -2.65788i q^{54} +(-2.34161 - 5.82470i) q^{55} +(-0.336639 + 0.583075i) q^{56} +(-2.64215 + 0.707962i) q^{57} +(-1.44763 - 5.40264i) q^{58} +9.10162i q^{59} +(0.123346 + 1.01916i) q^{60} +(-11.3415 - 6.54803i) q^{61} +(8.02471 + 2.15021i) q^{62} +(0.486041 - 1.81393i) q^{63} +1.00000i q^{64} +(-6.19420 + 4.65087i) q^{65} +(-0.644473 - 1.11626i) q^{66} +(1.78565 - 6.66414i) q^{67} +(1.28191 + 4.78417i) q^{68} +(-0.800464 + 1.38644i) q^{69} +(-0.212105 + 1.49048i) q^{70} +(6.46834 + 3.73450i) q^{71} +(-0.721903 - 2.69418i) q^{72} +(-13.4368 + 3.60039i) q^{73} +(7.80425 - 4.50579i) q^{74} +(1.10594 + 2.01157i) q^{75} +(-5.15976 + 2.97899i) q^{76} +(-0.489226 - 1.82582i) q^{77} +(-1.12457 + 1.12457i) q^{78} +(9.11916 + 5.26495i) q^{79} +(0.834055 + 2.07469i) q^{80} +(3.57370 + 6.18983i) q^{81} +(4.86349 - 4.86349i) q^{82} +(-8.04016 - 2.15435i) q^{83} +0.309107i q^{84} +(6.64984 + 8.85649i) q^{85} +(-2.93011 + 5.86638i) q^{86} +(-1.81578 - 1.81578i) q^{87} +(-1.98520 - 1.98520i) q^{88} +(-1.25426 - 2.17245i) q^{89} +(-3.74482 - 4.98749i) q^{90} +(-2.01981 + 1.16614i) q^{91} +(-0.902511 + 3.36822i) q^{92} +(3.68421 - 0.987181i) q^{93} +10.9728 q^{94} +(-8.22028 + 10.4840i) q^{95} +(0.229554 + 0.397599i) q^{96} +(-6.07571 - 6.07571i) q^{97} +(1.69441 - 6.32362i) q^{98} +(6.78161 + 3.91537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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