LMFDB - Embedded newform 400.2.s.d.243.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.3
Root			$-0.635486 - 1.26339i$ of defining polynomial
Character	$\chi$	$=$	400.243
Dual form			400.2.s.d.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.828280 - 1.14628i) q^{2} -0.692712 q^{3} +(-0.627905 + 1.89888i) q^{4} +(0.573759 + 0.794040i) q^{6} +(0.343872 - 0.343872i) q^{7} +(2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +O(q^{10})$	\(q+(-0.828280 - 1.14628i) q^{2} -0.692712 q^{3} +(-0.627905 + 1.89888i) q^{4} +(0.573759 + 0.794040i) q^{6} +(0.343872 - 0.343872i) q^{7} +(2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +(0.843672 + 0.843672i) q^{11} +(0.434957 - 1.31538i) q^{12} +3.68390i q^{13} +(-0.678995 - 0.109350i) q^{14} +(-3.21147 - 2.38463i) q^{16} +(-0.412137 + 0.412137i) q^{17} +(2.08739 + 2.88879i) q^{18} +(5.37721 + 5.37721i) q^{19} +(-0.238204 + 0.238204i) q^{21} +(0.268286 - 1.66588i) q^{22} +(3.08788 + 3.08788i) q^{23} +(-1.86805 + 0.590917i) q^{24} +(4.22278 - 3.05130i) q^{26} +3.82387 q^{27} +(0.437052 + 0.868890i) q^{28} +(4.22969 - 4.22969i) q^{29} +8.75966i q^{31} +(-0.0734474 + 5.65638i) q^{32} +(-0.584422 - 0.584422i) q^{33} +(0.813788 + 0.131059i) q^{34} +(1.58241 - 4.78546i) q^{36} -5.41752i q^{37} +(1.70994 - 10.6176i) q^{38} -2.55188i q^{39} +2.54777i q^{41} +(0.470348 + 0.0757484i) q^{42} -4.30732i q^{43} +(-2.13178 + 1.07228i) q^{44} +(0.981939 - 6.09720i) q^{46} +(4.56972 + 4.56972i) q^{47} +(2.22462 + 1.65186i) q^{48} +6.76350i q^{49} +(0.285492 - 0.285492i) q^{51} +(-6.99528 - 2.31314i) q^{52} -6.07536 q^{53} +(-3.16724 - 4.38322i) q^{54} +(0.633987 - 1.22067i) q^{56} +(-3.72486 - 3.72486i) q^{57} +(-8.35177 - 1.34503i) q^{58} +(7.33694 - 7.33694i) q^{59} +(-4.81576 - 4.81576i) q^{61} +(10.0410 - 7.25545i) q^{62} +(-0.866609 + 0.866609i) q^{63} +(6.54461 - 4.60087i) q^{64} +(-0.185845 + 1.15397i) q^{66} +14.3626i q^{67} +(-0.523815 - 1.04138i) q^{68} +(-2.13901 - 2.13901i) q^{69} -2.97605 q^{71} +(-6.79614 + 2.14981i) q^{72} +(-6.87152 + 6.87152i) q^{73} +(-6.20998 + 4.48722i) q^{74} +(-13.5870 + 6.83429i) q^{76} +0.580231 q^{77} +(-2.92517 + 2.11367i) q^{78} -10.1654 q^{79} +4.91161 q^{81} +(2.92046 - 2.11027i) q^{82} +7.15276 q^{83} +(-0.302751 - 0.601890i) q^{84} +(-4.93739 + 3.56767i) q^{86} +(-2.92996 + 2.92996i) q^{87} +(2.99484 + 1.55545i) q^{88} -1.10953 q^{89} +(1.26679 + 1.26679i) q^{91} +(-7.80240 + 3.92461i) q^{92} -6.06792i q^{93} +(1.45316 - 9.02318i) q^{94} +(0.0508779 - 3.91824i) q^{96} +(-7.15920 + 7.15920i) q^{97} +(7.75285 - 5.60207i) q^{98} +(-2.12618 - 2.12618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} + 6 q^{17} + 24 q^{18} - 2 q^{19} - 16 q^{21} - 12 q^{22} + 2 q^{23} - 4 q^{24} - 16 q^{26} + 24 q^{27} - 40 q^{28} + 14 q^{29} - 20 q^{32} + 8 q^{33} + 28 q^{34} - 4 q^{36} - 24 q^{38} - 8 q^{42} - 44 q^{44} + 12 q^{46} - 38 q^{47} - 4 q^{48} + 8 q^{51} - 8 q^{52} - 12 q^{53} + 4 q^{54} + 20 q^{56} + 24 q^{57} - 20 q^{58} + 10 q^{59} + 14 q^{61} + 40 q^{62} + 6 q^{63} + 16 q^{64} + 4 q^{66} + 60 q^{68} - 32 q^{69} + 24 q^{71} + 68 q^{72} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 44 q^{77} + 36 q^{78} - 16 q^{79} + 2 q^{81} - 48 q^{82} - 40 q^{83} + 24 q^{84} - 36 q^{86} - 24 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{92} - 28 q^{94} - 40 q^{96} - 18 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 + 6 * q^17 + 24 * q^18 - 2 * q^19 - 16 * q^21 - 12 * q^22 + 2 * q^23 - 4 * q^24 - 16 * q^26 + 24 * q^27 - 40 * q^28 + 14 * q^29 - 20 * q^32 + 8 * q^33 + 28 * q^34 - 4 * q^36 - 24 * q^38 - 8 * q^42 - 44 * q^44 + 12 * q^46 - 38 * q^47 - 4 * q^48 + 8 * q^51 - 8 * q^52 - 12 * q^53 + 4 * q^54 + 20 * q^56 + 24 * q^57 - 20 * q^58 + 10 * q^59 + 14 * q^61 + 40 * q^62 + 6 * q^63 + 16 * q^64 + 4 * q^66 + 60 * q^68 - 32 * q^69 + 24 * q^71 + 68 * q^72 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 44 * q^77 + 36 * q^78 - 16 * q^79 + 2 * q^81 - 48 * q^82 - 40 * q^83 + 24 * q^84 - 36 * q^86 - 24 * q^87 + 8 * q^88 + 12 * q^89 + 8 * q^92 - 28 * q^94 - 40 * q^96 - 18 * q^97 + 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.828280	−	1.14628i	−0.585682	−	0.810541i
$2$	−0.828280	−	1.14628i	−0.585682	−	0.810541i
$3$	−0.692712			−0.399937			−0.199969	−	0.979802i	$-0.564084\pi$
$3$	−0.692712			−0.399937			−0.199969	+	0.979802i	$0.564084\pi$
$4$	−0.627905	+	1.89888i	−0.313952	+	0.949439i
$5$		0			0
$5$		0			0
$6$	0.573759	+	0.794040i	0.234236	+	0.324166i
$7$	0.343872	−	0.343872i	0.129971	−	0.129971i	−0.639129	−	0.769100i	$-0.720705\pi$
$7$	0.343872	−	0.343872i	0.129971	−	0.129971i	0.769100	+	0.639129i	$0.220705\pi$
$8$	2.69672	−	0.853049i	0.953435	−	0.301598i
$9$	−2.52015			−0.840050
$10$		0			0
$11$	0.843672	+	0.843672i	0.254377	+	0.254377i	0.822762	−	0.568386i	$-0.192432\pi$
$11$	0.843672	+	0.843672i	0.254377	+	0.254377i	−0.568386	+	0.822762i	$0.692432\pi$
$12$	0.434957	−	1.31538i	0.125561	−	0.379716i
$13$			3.68390i			1.02173i	0.859661	+	0.510865i	$0.170675\pi$
$13$			3.68390i			1.02173i	−0.859661	+	0.510865i	$0.829325\pi$
$14$	−0.678995	−	0.109350i	−0.181469	−	0.0292251i
$15$		0			0
$16$	−3.21147	−	2.38463i	−0.802868	−	0.596157i
$17$	−0.412137	+	0.412137i	−0.0999579	+	0.0999579i	−0.755317	−	0.655359i	$-0.772517\pi$
$17$	−0.412137	+	0.412137i	−0.0999579	+	0.0999579i	0.655359	+	0.755317i	$0.272517\pi$
$18$	2.08739	+	2.88879i	0.492003	+	0.680895i
$19$	5.37721	+	5.37721i	1.23362	+	1.23362i	0.962565	+	0.271052i	$0.0873714\pi$
$19$	5.37721	+	5.37721i	1.23362	+	1.23362i	0.271052	+	0.962565i	$0.412629\pi$
$20$		0			0
$21$	−0.238204	+	0.238204i	−0.0519804	+	0.0519804i
$22$	0.268286	−	1.66588i	0.0571987	−	0.355167i
$23$	3.08788	+	3.08788i	0.643868	+	0.643868i	0.951504	−	0.307636i	$-0.0995380\pi$
$23$	3.08788	+	3.08788i	0.643868	+	0.643868i	−0.307636	+	0.951504i	$0.599538\pi$
$24$	−1.86805	+	0.590917i	−0.381314	+	0.120621i
$25$		0			0
$26$	4.22278	−	3.05130i	0.828154	−	0.598410i
$27$	3.82387			0.735905
$28$	0.437052	+	0.868890i	0.0825951	+	0.164205i
$29$	4.22969	−	4.22969i	0.785434	−	0.785434i	−0.195308	−	0.980742i	$-0.562571\pi$
$29$	4.22969	−	4.22969i	0.785434	−	0.785434i	0.980742	+	0.195308i	$0.0625707\pi$
$30$		0			0
$31$			8.75966i			1.57328i	0.617411	+	0.786641i	$0.288182\pi$
$31$			8.75966i			1.57328i	−0.617411	+	0.786641i	$0.711818\pi$
$32$	−0.0734474	+	5.65638i	−0.0129838	+	0.999916i
$33$	−0.584422	−	0.584422i	−0.101735	−	0.101735i
$34$	0.813788	+	0.131059i	0.139564	+	0.0224764i
$35$		0			0
$36$	1.58241	−	4.78546i	0.263736	−	0.797576i
$37$		−	5.41752i		−	0.890634i	−0.895373	−	0.445317i	$-0.853091\pi$
$37$		−	5.41752i		−	0.890634i	0.895373	−	0.445317i	$-0.146909\pi$
$38$	1.70994	−	10.6176i	0.277389	−	1.72240i
$39$		−	2.55188i		−	0.408628i
$40$		0			0
$41$			2.54777i			0.397895i	0.980010	+	0.198948i	$0.0637524\pi$
$41$			2.54777i			0.397895i	−0.980010	+	0.198948i	$0.936248\pi$
$42$	0.470348	+	0.0757484i	0.0725763	+	0.0116882i
$43$		−	4.30732i		−	0.656861i	−0.944528	−	0.328430i	$-0.893480\pi$
$43$		−	4.30732i		−	0.656861i	0.944528	−	0.328430i	$-0.106520\pi$
$44$	−2.13178	+	1.07228i	−0.321377	+	0.161653i
$45$		0			0
$46$	0.981939	−	6.09720i	0.144779	−	0.898983i
$47$	4.56972	+	4.56972i	0.666562	+	0.666562i	0.956919	−	0.290356i	$-0.0937738\pi$
$47$	4.56972	+	4.56972i	0.666562	+	0.666562i	−0.290356	+	0.956919i	$0.593774\pi$
$48$	2.22462	+	1.65186i	0.321097	+	0.238425i
$49$			6.76350i			0.966215i
$50$		0			0
$51$	0.285492	−	0.285492i	0.0399769	−	0.0399769i
$52$	−6.99528	−	2.31314i	−0.970071	−	0.320775i
$53$	−6.07536			−0.834515			−0.417257	−	0.908788i	$-0.637009\pi$
$53$	−6.07536			−0.834515			−0.417257	+	0.908788i	$0.637009\pi$
$54$	−3.16724	−	4.38322i	−0.431007	−	0.596481i
$55$		0			0
$56$	0.633987	−	1.22067i	0.0847201	−	0.163118i
$57$	−3.72486	−	3.72486i	−0.493369	−	0.493369i
$58$	−8.35177	−	1.34503i	−1.09664	−	0.176611i
$59$	7.33694	−	7.33694i	0.955189	−	0.955189i	−0.0438495	−	0.999038i	$-0.513962\pi$
$59$	7.33694	−	7.33694i	0.955189	−	0.955189i	0.999038	+	0.0438495i	$0.0139622\pi$
$60$		0			0
$61$	−4.81576	−	4.81576i	−0.616595	−	0.616595i	0.328062	−	0.944656i	$-0.393605\pi$
$61$	−4.81576	−	4.81576i	−0.616595	−	0.616595i	−0.944656	+	0.328062i	$0.893605\pi$
$62$	10.0410	−	7.25545i	1.27521	−	0.921444i
$63$	−0.866609	+	0.866609i	−0.109183	+	0.109183i
$64$	6.54461	−	4.60087i	0.818077	−	0.575109i
$65$		0			0
$66$	−0.185845	+	1.15397i	−0.0228759	+	0.142044i
$67$			14.3626i			1.75467i	0.479880	+	0.877334i	$0.340680\pi$
$67$			14.3626i			1.75467i	−0.479880	+	0.877334i	$0.659320\pi$
$68$	−0.523815	−	1.04138i	−0.0635219	−	0.126286i
$69$	−2.13901	−	2.13901i	−0.257507	−	0.257507i
$70$		0			0
$71$	−2.97605			−0.353193			−0.176596	−	0.984283i	$-0.556509\pi$
$71$	−2.97605			−0.353193			−0.176596	+	0.984283i	$0.556509\pi$
$72$	−6.79614	+	2.14981i	−0.800933	+	0.253358i
$73$	−6.87152	+	6.87152i	−0.804250	+	0.804250i	−0.983757	−	0.179507i	$-0.942550\pi$
$73$	−6.87152	+	6.87152i	−0.804250	+	0.804250i	0.179507	+	0.983757i	$0.442550\pi$
$74$	−6.20998	+	4.48722i	−0.721895	+	0.521629i
$75$		0			0
$76$	−13.5870	+	6.83429i	−1.55854	+	0.783947i
$77$	0.580231			0.0661234
$78$	−2.92517	+	2.11367i	−0.331210	+	0.239326i
$79$	−10.1654			−1.14369			−0.571847	−	0.820360i	$-0.693773\pi$
$79$	−10.1654			−1.14369			−0.571847	+	0.820360i	$0.693773\pi$
$80$		0			0
$81$	4.91161			0.545734
$82$	2.92046	−	2.11027i	0.322510	−	0.233040i
$83$	7.15276			0.785118			0.392559	−	0.919727i	$-0.371590\pi$
$83$	7.15276			0.785118			0.392559	+	0.919727i	$0.371590\pi$
$84$	−0.302751	−	0.601890i	−0.0330329	−	0.0656716i
$85$		0			0
$86$	−4.93739	+	3.56767i	−0.532412	+	0.384712i
$87$	−2.92996	+	2.92996i	−0.314124	+	0.314124i
$88$	2.99484	+	1.55545i	0.319251	+	0.165812i
$89$	−1.10953			−0.117610			−0.0588050	−	0.998269i	$-0.518729\pi$
$89$	−1.10953			−0.117610			−0.0588050	+	0.998269i	$0.518729\pi$
$90$		0			0
$91$	1.26679	+	1.26679i	0.132796	+	0.132796i
$92$	−7.80240	+	3.92461i	−0.813457	+	0.409169i
$93$		−	6.06792i		−	0.629214i
$94$	1.45316	−	9.02318i	0.149882	−	0.930670i
$95$		0			0
$96$	0.0508779	−	3.91824i	0.00519270	−	0.399904i
$97$	−7.15920	+	7.15920i	−0.726906	+	0.726906i	−0.970002	−	0.243096i	$-0.921837\pi$
$97$	−7.15920	+	7.15920i	−0.726906	+	0.726906i	0.243096	+	0.970002i	$0.421837\pi$
$98$	7.75285	−	5.60207i	0.783156	−	0.565895i
$99$	−2.12618	−	2.12618i	−0.213689	−	0.213689i
$100$		0			0
$101$	0.953394	−	0.953394i	0.0948663	−	0.0948663i	−0.658081	−	0.752947i	$-0.728632\pi$
$101$	0.953394	−	0.953394i	0.0948663	−	0.0948663i	0.752947	+	0.658081i	$0.228632\pi$
$102$	−0.563721	−	0.0907858i	−0.0558167	−	0.00898914i
$103$	−9.59425	−	9.59425i	−0.945350	−	0.945350i	0.0532322	−	0.998582i	$-0.483048\pi$
$103$	−9.59425	−	9.59425i	−0.945350	−	0.945350i	−0.998582	+	0.0532322i	$0.983048\pi$
$104$	3.14255	+	9.93446i	0.308152	+	0.974154i
$105$		0			0
$106$	5.03210	+	6.96405i	0.488761	+	0.676408i
$107$	5.28201			0.510631			0.255316	−	0.966858i	$-0.417821\pi$
$107$	5.28201			0.510631			0.255316	+	0.966858i	$0.417821\pi$
$108$	−2.40103	+	7.26107i	−0.231039	+	0.698697i
$109$	−1.53980	+	1.53980i	−0.147486	+	0.147486i	−0.776994	−	0.629508i	$-0.783256\pi$
$109$	−1.53980	+	1.53980i	−0.147486	+	0.147486i	0.629508	+	0.776994i	$0.283256\pi$
$110$		0			0
$111$			3.75278i			0.356198i
$112$	−1.92434	+	0.284329i	−0.181833	+	0.0268665i
$113$	2.99656	+	2.99656i	0.281893	+	0.281893i	0.833863	−	0.551971i	$-0.186124\pi$
$113$	2.99656	+	2.99656i	0.281893	+	0.281893i	−0.551971	+	0.833863i	$0.686124\pi$
$114$	−1.18450	+	7.35494i	−0.110938	+	0.688854i
$115$		0			0
$116$	5.37582	+	10.6875i	0.499133	+	0.992310i
$117$		−	9.28399i		−	0.858305i
$118$	−14.4872	−	2.33313i	−1.33366	−	0.214782i
$119$			0.283445i			0.0259833i
$120$		0			0
$121$		−	9.57643i		−	0.870585i
$122$	−1.53140	+	9.50899i	−0.138646	+	0.860904i
$123$		−	1.76487i		−	0.159133i
$124$	−16.6335	−	5.50023i	−1.49373	−	0.493935i
$125$		0			0
$126$	1.71117	+	0.275580i	0.152443	+	0.0245506i
$127$	−10.5522	−	10.5522i	−0.936360	−	0.936360i	0.0617330	−	0.998093i	$-0.480337\pi$
$127$	−10.5522	−	10.5522i	−0.936360	−	0.936360i	−0.998093	+	0.0617330i	$0.980337\pi$
$128$	−10.6947	−	3.69113i	−0.945282	−	0.326253i
$129$			2.98373i			0.262703i
$130$		0			0
$131$	−0.850513	+	0.850513i	−0.0743096	+	0.0743096i	−0.743285	−	0.668975i	$-0.766733\pi$
$131$	−0.850513	+	0.850513i	−0.0743096	+	0.0743096i	0.668975	+	0.743285i	$0.266733\pi$
$132$	1.47671	−	0.742784i	0.128531	−	0.0646511i
$133$	3.69814			0.320670
$134$	16.4635	−	11.8962i	1.42223	−	1.02768i
$135$		0			0
$136$	−0.759845	+	1.46299i	−0.0651562	+	0.125451i
$137$	−5.50145	−	5.50145i	−0.470021	−	0.470021i	0.431901	−	0.901921i	$-0.357843\pi$
$137$	−5.50145	−	5.50145i	−0.470021	−	0.470021i	−0.901921	+	0.431901i	$0.857843\pi$
$138$	−0.680201	+	4.22360i	−0.0579025	+	0.359537i
$139$	−3.03517	+	3.03517i	−0.257440	+	0.257440i	−0.824012	−	0.566572i	$-0.808269\pi$
$139$	−3.03517	+	3.03517i	−0.257440	+	0.257440i	0.566572	+	0.824012i	$0.308269\pi$
$140$		0			0
$141$	−3.16550	−	3.16550i	−0.266583	−	0.266583i
$142$	2.46501	+	3.41138i	0.206859	+	0.286277i
$143$	−3.10801	+	3.10801i	−0.259905	+	0.259905i
$144$	8.09339	+	6.00962i	0.674449	+	0.500802i
$145$		0			0
$146$	13.5682	+	2.18513i	1.12291	+	0.180842i
$147$		−	4.68516i		−	0.386425i
$148$	10.2872	+	3.40168i	0.845603	+	0.279617i
$149$	−11.1571	−	11.1571i	−0.914023	−	0.914023i	0.0825625	−	0.996586i	$-0.473690\pi$
$149$	−11.1571	−	11.1571i	−0.914023	−	0.914023i	−0.996586	+	0.0825625i	$0.973690\pi$
$150$		0			0
$151$	3.18265			0.259000			0.129500	−	0.991579i	$-0.458663\pi$
$151$	3.18265			0.259000			0.129500	+	0.991579i	$0.458663\pi$
$152$	19.0879	+	9.91381i	1.54823	+	0.804116i
$153$	1.03865	−	1.03865i	0.0839696	−	0.0839696i
$154$	−0.480593	−	0.665105i	−0.0387273	−	0.0535957i
$155$		0			0
$156$	4.84571	+	1.60234i	0.387968	+	0.128290i
$157$	7.05454			0.563014			0.281507	−	0.959559i	$-0.409166\pi$
$157$	7.05454			0.563014			0.281507	+	0.959559i	$0.409166\pi$
$158$	8.41978	+	11.6523i	0.669842	+	0.927011i
$159$	4.20847			0.333754
$160$		0			0
$161$	2.12367			0.167369
$162$	−4.06819	−	5.63007i	−0.319627	−	0.442340i
$163$	16.0208			1.25484			0.627422	−	0.778680i	$-0.284110\pi$
$163$	16.0208			1.25484			0.627422	+	0.778680i	$0.284110\pi$
$164$	−4.83791	−	1.59976i	−0.377777	−	0.124920i
$165$		0			0
$166$	−5.92449	−	8.19905i	−0.459830	−	0.636370i
$167$	16.6023	−	16.6023i	1.28473	−	1.28473i	0.346780	−	0.937946i	$-0.387275\pi$
$167$	16.6023	−	16.6023i	1.28473	−	1.28473i	0.937946	−	0.346780i	$-0.112725\pi$
$168$	−0.439171	+	0.845571i	−0.0338827	+	0.0652372i
$169$	−0.571141			−0.0439339
$170$		0			0
$171$	−13.5514	−	13.5514i	−1.03630	−	1.03630i
$172$	8.17908	+	2.70459i	0.623649	+	0.206223i
$173$		−	14.9958i		−	1.14011i	−0.821607	−	0.570054i	$-0.806922\pi$
$173$		−	14.9958i		−	1.14011i	0.821607	−	0.570054i	$-0.193078\pi$
$174$	5.78537	+	0.931719i	0.438588	+	0.0706335i
$175$		0			0
$176$	−0.697585	−	4.72127i	−0.0525825	−	0.355879i
$177$	−5.08239	+	5.08239i	−0.382016	+	0.382016i
$178$	0.919002	+	1.27183i	0.0688821	+	0.0953277i
$179$	9.91310	+	9.91310i	0.740940	+	0.740940i	0.972759	−	0.231819i	$-0.0744678\pi$
$179$	9.91310	+	9.91310i	0.740940	+	0.740940i	−0.231819	+	0.972759i	$0.574468\pi$
$180$		0			0
$181$	1.04015	−	1.04015i	0.0773139	−	0.0773139i	−0.667392	−	0.744706i	$-0.732590\pi$
$181$	1.04015	−	1.04015i	0.0773139	−	0.0773139i	0.744706	+	0.667392i	$0.232590\pi$
$182$	0.402837	−	2.50135i	0.0298602	−	0.185413i
$183$	3.33593	+	3.33593i	0.246599	+	0.246599i
$184$	10.9613	+	5.69304i	0.808075	+	0.419696i
$185$		0			0
$186$	−6.95552	+	5.02594i	−0.510004	+	0.368520i
$187$	−0.695417			−0.0508539
$188$	−11.5467	+	5.80799i	−0.842129	+	0.423591i
$189$	1.31492	−	1.31492i	0.0956466	−	0.0956466i
$190$		0			0
$191$		−	3.08419i		−	0.223164i	−0.993755	−	0.111582i	$-0.964408\pi$
$191$		−	3.08419i		−	0.223164i	0.993755	−	0.111582i	$-0.0355918\pi$
$192$	−4.53353	+	3.18708i	−0.327179	+	0.230008i
$193$	12.0915	+	12.0915i	0.870368	+	0.870368i	0.992512	−	0.122144i	$-0.0389770\pi$
$193$	12.0915	+	12.0915i	0.870368	+	0.870368i	−0.122144	+	0.992512i	$0.538977\pi$
$194$	14.1362	+	2.27661i	1.01492	+	0.163451i
$195$		0			0
$196$	−12.8431	−	4.24683i	−0.917362	−	0.303345i
$197$			13.0186i			0.927540i	0.885956	+	0.463770i	$0.153504\pi$
$197$			13.0186i			0.927540i	−0.885956	+	0.463770i	$0.846496\pi$
$198$	−0.676120	+	4.19827i	−0.0480498	+	0.298358i
$199$			10.6279i			0.753395i	0.926336	+	0.376697i	$0.122940\pi$
$199$			10.6279i			0.753395i	−0.926336	+	0.376697i	$0.877060\pi$
$200$		0			0
$201$		−	9.94913i		−	0.701758i
$202$	−1.88253	−	0.303177i	−0.132455	−	0.0213315i
$203$		−	2.90894i		−	0.204168i
$204$	0.362853	+	0.721377i	0.0254048	+	0.0505065i
$205$		0			0
$206$	−3.05095	+	18.9444i	−0.212570	+	1.31992i
$207$	−7.78192	−	7.78192i	−0.540881	−	0.540881i
$208$	8.78474	−	11.8308i	0.609112	−	0.820315i
$209$			9.07320i			0.627607i
$210$		0			0
$211$	11.4801	−	11.4801i	0.790321	−	0.790321i	−0.191225	−	0.981546i	$-0.561246\pi$
$211$	11.4801	−	11.4801i	0.790321	−	0.790321i	0.981546	+	0.191225i	$0.0612460\pi$
$212$	3.81475	−	11.5364i	0.261998	−	0.792321i
$213$	2.06155			0.141255
$214$	−4.37499	−	6.05465i	−0.299068	−	0.413888i
$215$		0			0
$216$	10.3119	−	3.26195i	0.701638	−	0.221948i
$217$	3.01220	+	3.01220i	0.204482	+	0.204482i
$218$	3.04042	+	0.489652i	0.205923	+	0.0331634i
$219$	4.75998	−	4.75998i	0.321650	−	0.321650i
$220$		0			0
$221$	−1.51827	−	1.51827i	−0.102130	−	0.102130i
$222$	4.30173	−	3.10835i	0.288713	−	0.208619i
$223$	2.17863	−	2.17863i	0.145892	−	0.145892i	−0.630388	−	0.776280i	$-0.717104\pi$
$223$	2.17863	−	2.17863i	0.145892	−	0.145892i	0.776280	+	0.630388i	$0.217104\pi$
$224$	1.91981	+	1.97033i	0.128273	+	0.131648i
$225$		0			0
$226$	0.952898	−	5.91688i	0.0633859	−	0.393585i
$227$			9.32318i			0.618801i	0.950932	+	0.309401i	$0.100128\pi$
$227$			9.32318i			0.618801i	−0.950932	+	0.309401i	$0.899872\pi$
$228$	9.41190	−	4.73419i	0.623318	−	0.313530i
$229$	2.72259	+	2.72259i	0.179914	+	0.179914i	0.791318	−	0.611404i	$-0.209395\pi$
$229$	2.72259	+	2.72259i	0.179914	+	0.179914i	−0.611404	+	0.791318i	$0.709395\pi$
$230$		0			0
$231$	−0.401933			−0.0264452
$232$	7.79816	−	15.0144i	0.511974	−	0.985746i
$233$	12.3897	−	12.3897i	0.811679	−	0.811679i	−0.173206	−	0.984886i	$-0.555413\pi$
$233$	12.3897	−	12.3897i	0.811679	−	0.811679i	0.984886	+	0.173206i	$0.0554127\pi$
$234$	−10.6420	+	7.68974i	−0.695691	+	0.502694i
$235$		0			0
$236$	9.32506	+	18.5389i	0.607010	+	1.20678i
$237$	7.04168			0.457406
$238$	0.324906	−	0.234772i	0.0210606	−	0.0152180i
$239$	−25.2180			−1.63122			−0.815609	−	0.578604i	$-0.803598\pi$
$239$	−25.2180			−1.63122			−0.815609	+	0.578604i	$0.803598\pi$
$240$		0			0
$241$	12.0218			0.774391			0.387195	−	0.921998i	$-0.373444\pi$
$241$	12.0218			0.774391			0.387195	+	0.921998i	$0.373444\pi$
$242$	−10.9773	+	7.93197i	−0.705645	+	0.509886i
$243$	−14.8740			−0.954164
$244$	12.1684	−	6.12070i	0.779000	−	0.391838i
$245$		0			0
$246$	−2.02303	+	1.46181i	−0.128984	+	0.0932015i
$247$	−19.8091	+	19.8091i	−1.26042	+	1.26042i
$248$	7.47242	+	23.6224i	0.474499	+	1.50002i
$249$	−4.95480			−0.313998
$250$		0			0
$251$	7.48911	+	7.48911i	0.472709	+	0.472709i	0.902790	−	0.430081i	$-0.141515\pi$
$251$	7.48911	+	7.48911i	0.472709	+	0.472709i	−0.430081	+	0.902790i	$0.641515\pi$
$252$	−1.10144	−	2.18973i	−0.0693840	−	0.137940i
$253$			5.21032i			0.327570i
$254$	−3.35559	+	20.8360i	−0.210548	+	1.30737i
$255$		0			0
$256$	4.62710	+	15.3163i	0.289194	+	0.957271i
$257$	10.0809	−	10.0809i	0.628832	−	0.628832i	−0.318942	−	0.947774i	$-0.603328\pi$
$257$	10.0809	−	10.0809i	0.628832	−	0.628832i	0.947774	+	0.318942i	$0.103328\pi$
$258$	3.42019	−	2.47137i	0.212932	−	0.153861i
$259$	−1.86293	−	1.86293i	−0.115757	−	0.115757i
$260$		0			0
$261$	−10.6595	+	10.6595i	−0.659804	+	0.659804i
$262$	1.67939	+	0.270461i	0.103753	+	0.0167091i
$263$	3.83599	+	3.83599i	0.236537	+	0.236537i	0.815415	−	0.578877i	$-0.196509\pi$
$263$	3.83599	+	3.83599i	0.236537	+	0.236537i	−0.578877	+	0.815415i	$0.696509\pi$
$264$	−2.07456	−	1.07748i	−0.127681	−	0.0663144i
$265$		0			0
$266$	−3.06310	−	4.23910i	−0.187811	−	0.259916i
$267$	0.768585			0.0470367
$268$	−27.2728	−	9.01833i	−1.66595	−	0.550882i
$269$	13.4250	−	13.4250i	0.818539	−	0.818539i	−0.167357	−	0.985896i	$-0.553523\pi$
$269$	13.4250	−	13.4250i	0.818539	−	0.818539i	0.985896	+	0.167357i	$0.0535233\pi$
$270$		0			0
$271$		−	12.3519i		−	0.750326i	−0.926959	−	0.375163i	$-0.877587\pi$
$271$		−	12.3519i		−	0.750326i	0.926959	−	0.375163i	$-0.122413\pi$
$272$	2.30636	−	0.340773i	0.139844	−	0.0206624i
$273$	−0.877522	−	0.877522i	−0.0531100	−	0.0531100i
$274$	−1.74945	+	10.8629i	−0.105688	+	0.656253i
$275$		0			0
$276$	5.40482	−	2.71863i	0.325332	−	0.163642i
$277$		−	6.78804i		−	0.407854i	−0.978986	−	0.203927i	$-0.934630\pi$
$277$		−	6.78804i		−	0.407854i	0.978986	−	0.203927i	$-0.0653705\pi$
$278$	5.99312	+	0.965177i	0.359443	+	0.0578875i
$279$		−	22.0757i		−	1.32164i
$280$		0			0
$281$			21.5509i			1.28562i	0.766026	+	0.642810i	$0.222232\pi$
$281$			21.5509i			1.28562i	−0.766026	+	0.642810i	$0.777768\pi$
$282$	−1.00662	+	6.25046i	−0.0599434	+	0.372210i
$283$			9.86809i			0.586597i	0.956021	+	0.293299i	$0.0947530\pi$
$283$			9.86809i			0.586597i	−0.956021	+	0.293299i	$0.905247\pi$
$284$	1.86868	−	5.65116i	0.110886	−	0.335335i
$285$		0			0
$286$	6.13694	+	0.988339i	0.362885	+	0.0584417i
$287$	0.876108	+	0.876108i	0.0517150	+	0.0517150i
$288$	0.185099	−	14.2549i	0.0109070	−	0.839979i
$289$			16.6603i			0.980017i
$290$		0			0
$291$	4.95926	−	4.95926i	0.290717	−	0.290717i
$292$	−8.73351	−	17.3628i	−0.511090	−	1.01608i
$293$	−14.1972			−0.829410			−0.414705	−	0.909956i	$-0.636115\pi$
$293$	−14.1972			−0.829410			−0.414705	+	0.909956i	$0.636115\pi$
$294$	−5.37049	+	3.88062i	−0.313214	+	0.226323i
$295$		0			0
$296$	−4.62141	−	14.6095i	−0.268614	−	0.849162i
$297$	3.22610	+	3.22610i	0.187197	+	0.187197i
$298$	−3.54792	+	22.0303i	−0.205526	+	1.27618i
$299$	−11.3755	+	11.3755i	−0.657859	+	0.657859i
$300$		0			0
$301$	−1.48117	−	1.48117i	−0.0853731	−	0.0853731i
$302$	−2.63612	−	3.64820i	−0.151692	−	0.209930i
$303$	−0.660428	+	0.660428i	−0.0379406	+	0.0379406i
$304$	−4.44611	−	30.0914i	−0.255002	−	1.72586i
$305$		0			0
$306$	−2.05087	−	0.330287i	−0.117240	−	0.0188813i
$307$		−	20.4161i		−	1.16521i	−0.812756	−	0.582604i	$-0.802034\pi$
$307$		−	20.4161i		−	1.16521i	0.812756	−	0.582604i	$-0.197966\pi$
$308$	−0.364329	+	1.10179i	−0.0207596	+	0.0627801i
$309$	6.64605	+	6.64605i	0.378081	+	0.378081i
$310$		0			0
$311$	−6.81074			−0.386202			−0.193101	−	0.981179i	$-0.561854\pi$
$311$	−6.81074			−0.386202			−0.193101	+	0.981179i	$0.561854\pi$
$312$	−2.17688	−	6.88172i	−0.123242	−	0.389601i
$313$	−1.20933	+	1.20933i	−0.0683555	+	0.0683555i	−0.740458	−	0.672103i	$-0.765391\pi$
$313$	−1.20933	+	1.20933i	−0.0683555	+	0.0683555i	0.672103	+	0.740458i	$0.265391\pi$
$314$	−5.84314	−	8.08646i	−0.329747	−	0.456345i
$315$		0			0
$316$	6.38289	−	19.3028i	0.359065	−	1.08587i
$317$	3.44178			0.193310			0.0966548	−	0.995318i	$-0.469186\pi$
$317$	3.44178			0.193310			0.0966548	+	0.995318i	$0.469186\pi$
$318$	−3.48580	−	4.82408i	−0.195474	−	0.270521i
$319$	7.13694			0.399592
$320$		0			0
$321$	−3.65891			−0.204221
$322$	−1.75899	−	2.43432i	−0.0980249	−	0.135659i
$323$	−4.43229			−0.246619
$324$	−3.08402	+	9.32654i	−0.171334	+	0.518141i
$325$		0			0
$326$	−13.2697	−	18.3643i	−0.734940	−	1.01710i
$327$	1.06664	−	1.06664i	0.0589852	−	0.0589852i
$328$	2.17338	+	6.87063i	0.120005	+	0.379367i
$329$	3.14280			0.173268
$330$		0			0
$331$	−1.48462	−	1.48462i	−0.0816019	−	0.0816019i	0.665128	−	0.746730i	$-0.268377\pi$
$331$	−1.48462	−	1.48462i	−0.0816019	−	0.0816019i	−0.746730	+	0.665128i	$0.768377\pi$
$332$	−4.49125	+	13.5822i	−0.246489	+	0.745421i
$333$			13.6530i			0.748177i
$334$	−32.7822	−	5.27950i	−1.79376	−	0.288881i
$335$		0			0
$336$	1.33301	−	0.196958i	0.0727219	−	0.0107449i
$337$	−6.21211	+	6.21211i	−0.338395	+	0.338395i	−0.855763	−	0.517368i	$-0.826912\pi$
$337$	−6.21211	+	6.21211i	−0.338395	+	0.338395i	0.517368	+	0.855763i	$0.326912\pi$
$338$	0.473065	+	0.654686i	0.0257313	+	0.0356102i
$339$	−2.07575	−	2.07575i	−0.112739	−	0.112739i
$340$		0			0
$341$	−7.39028	+	7.39028i	−0.400206	+	0.400206i
$342$	−4.30930	+	26.7580i	−0.233020	+	1.44691i
$343$	4.73288	+	4.73288i	0.255552	+	0.255552i
$344$	−3.67436	−	11.6156i	−0.198108	−	0.626274i
$345$		0			0
$346$	−17.1893	+	12.4207i	−0.924104	+	0.667741i
$347$	−10.1502			−0.544889			−0.272445	−	0.962171i	$-0.587832\pi$
$347$	−10.1502			−0.544889			−0.272445	+	0.962171i	$0.587832\pi$
$348$	−3.72390	−	7.40336i	−0.199622	−	0.396862i
$349$	3.99595	−	3.99595i	0.213898	−	0.213898i	−0.592023	−	0.805921i	$-0.701671\pi$
$349$	3.99595	−	3.99595i	0.213898	−	0.213898i	0.805921	+	0.592023i	$0.201671\pi$
$350$		0			0
$351$			14.0868i			0.751897i
$352$	−4.83409	+	4.71016i	−0.257658	+	0.251053i
$353$	−22.6637	−	22.6637i	−1.20627	−	1.20627i	−0.972226	−	0.234043i	$-0.924804\pi$
$353$	−22.6637	−	22.6637i	−1.20627	−	1.20627i	−0.234043	−	0.972226i	$-0.575196\pi$
$354$	10.0355	+	1.61619i	0.533379	+	0.0858994i
$355$		0			0
$356$	0.696680	−	2.10686i	0.0369239	−	0.111664i
$357$		−	0.196346i		−	0.0103917i
$358$	3.15234	−	19.5740i	0.166606	−	1.03452i
$359$		−	4.31874i		−	0.227934i	−0.993485	−	0.113967i	$-0.963644\pi$
$359$		−	4.31874i		−	0.227934i	0.993485	−	0.113967i	$-0.0363559\pi$
$360$		0			0
$361$			38.8288i			2.04362i
$362$	−2.05384	−	0.330766i	−0.107947	−	0.0173847i
$363$			6.63371i			0.348180i
$364$	−3.20091	+	1.61006i	−0.167773	+	0.0843899i
$365$		0			0
$366$	1.06082	−	6.58699i	0.0554499	−	0.344308i
$367$	−6.46940	−	6.46940i	−0.337700	−	0.337700i	0.517801	−	0.855501i	$-0.326751\pi$
$367$	−6.46940	−	6.46940i	−0.337700	−	0.337700i	−0.855501	+	0.517801i	$0.826751\pi$
$368$	−2.55320	−	17.2801i	−0.133095	−	0.900787i
$369$		−	6.42077i		−	0.334252i
$370$		0			0
$371$	−2.08915	+	2.08915i	−0.108463	+	0.108463i
$372$	11.5222	+	3.81008i	0.597400	+	0.197543i
$373$	16.7831			0.868995			0.434497	−	0.900673i	$-0.356926\pi$
$373$	16.7831			0.868995			0.434497	+	0.900673i	$0.356926\pi$
$374$	0.576000	+	0.797141i	0.0297842	+	0.0412192i
$375$		0			0
$376$	16.2215	+	8.42507i	0.836558	+	0.434490i
$377$	15.5818	+	15.5818i	0.802502	+	0.802502i
$378$	−2.59639	−	0.418142i	−0.133544	−	0.0215069i
$379$	7.31046	−	7.31046i	0.375513	−	0.375513i	−0.493967	−	0.869480i	$-0.664454\pi$
$379$	7.31046	−	7.31046i	0.375513	−	0.375513i	0.869480	+	0.493967i	$0.164454\pi$
$380$		0			0
$381$	7.30966	+	7.30966i	0.374485	+	0.374485i
$382$	−3.53533	+	2.55457i	−0.180883	+	0.130703i
$383$	−5.31492	+	5.31492i	−0.271580	+	0.271580i	−0.829736	−	0.558156i	$-0.811509\pi$
$383$	−5.31492	+	5.31492i	−0.271580	+	0.271580i	0.558156	+	0.829736i	$0.311509\pi$
$384$	7.40831	+	2.55689i	0.378054	+	0.130481i
$385$		0			0
$386$	3.84508	−	23.8754i	0.195710	−	1.21523i
$387$			10.8551i			0.551796i
$388$	−9.09915	−	18.0897i	−0.461939	−	0.918367i
$389$	1.28845	+	1.28845i	0.0653271	+	0.0653271i	0.739016	−	0.673688i	$-0.235291\pi$
$389$	1.28845	+	1.28845i	0.0653271	+	0.0653271i	−0.673688	+	0.739016i	$0.735291\pi$
$390$		0			0
$391$	−2.54526			−0.128719
$392$	5.76960	+	18.2393i	0.291409	+	0.921223i
$393$	0.589160	−	0.589160i	0.0297192	−	0.0297192i
$394$	14.9230	−	10.7831i	0.751809	−	0.543244i
$395$		0			0
$396$	5.37239	−	2.70232i	0.269973	−	0.135797i
$397$	−9.53832			−0.478715			−0.239357	−	0.970932i	$-0.576937\pi$
$397$	−9.53832			−0.478715			−0.239357	+	0.970932i	$0.576937\pi$
$398$	12.1826	−	8.80291i	0.610657	−	0.441250i
$399$	−2.56175			−0.128248
$400$		0			0
$401$	−24.6103			−1.22898			−0.614491	−	0.788924i	$-0.710638\pi$
$401$	−24.6103			−1.22898			−0.614491	+	0.788924i	$0.710638\pi$
$402$	−11.4045	+	8.24067i	−0.568803	+	0.411007i
$403$	−32.2697			−1.60747
$404$	1.21174	+	2.40902i	0.0602862	+	0.119853i
$405$		0			0
$406$	−3.33446	+	2.40942i	−0.165486	+	0.119578i
$407$	4.57061	−	4.57061i	0.226557	−	0.226557i
$408$	0.526354	−	1.01343i	0.0260584	−	0.0501724i
$409$	16.9457			0.837911			0.418955	−	0.908007i	$-0.362396\pi$
$409$	16.9457			0.837911			0.418955	+	0.908007i	$0.362396\pi$
$410$		0			0
$411$	3.81092	+	3.81092i	0.187979	+	0.187979i
$412$	24.2426	−	12.1940i	1.19435	−	0.600757i
$413$		−	5.04594i		−	0.248294i
$414$	−2.47463	+	15.3659i	−0.121622	+	0.755190i
$415$		0			0
$416$	−20.8375	−	0.270573i	−1.02164	−	0.0132659i
$417$	2.10250	−	2.10250i	0.102960	−	0.102960i
$418$	10.4004	−	7.51515i	0.508701	−	0.367578i
$419$	6.56956	+	6.56956i	0.320944	+	0.320944i	0.849129	−	0.528185i	$-0.177127\pi$
$419$	6.56956	+	6.56956i	0.320944	+	0.320944i	−0.528185	+	0.849129i	$0.677127\pi$
$420$		0			0
$421$	13.8805	−	13.8805i	0.676493	−	0.676493i	−0.282712	−	0.959205i	$-0.591234\pi$
$421$	13.8805	−	13.8805i	0.676493	−	0.676493i	0.959205	+	0.282712i	$0.0912341\pi$
$422$	−22.6681	−	3.65064i	−1.10346	−	0.177710i
$423$	−11.5164	−	11.5164i	−0.559946	−	0.559946i
$424$	−16.3836	+	5.18258i	−0.795656	+	0.251688i
$425$		0			0
$426$	−1.70754	−	2.36311i	−0.0827305	−	0.114493i
$427$	−3.31201			−0.160279
$428$	−3.31660	+	10.0299i	−0.160314	+	0.484813i
$429$	2.15295	−	2.15295i	0.103946	−	0.103946i
$430$		0			0
$431$		−	12.3740i		−	0.596035i	−0.954560	−	0.298017i	$-0.903675\pi$
$431$		−	12.3740i		−	0.596035i	0.954560	−	0.298017i	$-0.0963254\pi$
$432$	−12.2803	−	9.11852i	−0.590834	−	0.438715i
$433$	0.145326	+	0.145326i	0.00698392	+	0.00698392i	0.710590	−	0.703606i	$-0.248428\pi$
$433$	0.145326	+	0.145326i	0.00698392	+	0.00698392i	−0.703606	+	0.710590i	$0.748428\pi$
$434$	0.957873	−	5.94777i	0.0459794	−	0.285502i
$435$		0			0
$436$	−1.95704	−	3.89074i	−0.0937253	−	0.186332i
$437$			33.2084i			1.58857i
$438$	−9.39886	−	1.51366i	−0.449095	−	0.0723256i
$439$			3.65842i			0.174607i	0.996182	+	0.0873035i	$0.0278250\pi$
$439$			3.65842i			0.174607i	−0.996182	+	0.0873035i	$0.972175\pi$
$440$		0			0
$441$		−	17.0450i		−	0.811669i
$442$	−0.482807	+	2.99792i	−0.0229648	+	0.142596i
$443$		−	3.94027i		−	0.187208i	−0.995610	−	0.0936039i	$-0.970161\pi$
$443$		−	3.94027i		−	0.187208i	0.995610	−	0.0936039i	$-0.0298387\pi$
$444$	−7.12607	−	2.35639i	−0.338188	−	0.111829i
$445$		0			0
$446$	−4.30184	−	0.692800i	−0.203698	−	0.0328050i
$447$	7.72864	+	7.72864i	0.365552	+	0.365552i
$448$	0.668398	−	3.83262i	0.0315788	−	0.181074i
$449$		−	38.0014i		−	1.79340i	−0.442642	−	0.896698i	$-0.645959\pi$
$449$		−	38.0014i		−	1.79340i	0.442642	−	0.896698i	$-0.354041\pi$
$450$		0			0
$451$	−2.14949	+	2.14949i	−0.101215	+	0.101215i
$452$	−7.57165	+	3.80855i	−0.356140	+	0.179139i
$453$	−2.20466			−0.103584
$454$	10.6870	−	7.72221i	0.501564	−	0.362421i
$455$		0			0
$456$	−13.2224	−	6.86742i	−0.619195	−	0.321596i
$457$	18.1142	+	18.1142i	0.847348	+	0.847348i	0.989801	−	0.142454i	$-0.0454993\pi$
$457$	18.1142	+	18.1142i	0.847348	+	0.847348i	−0.142454	+	0.989801i	$0.545499\pi$
$458$	0.865778	−	5.37592i	0.0404551	−	0.251200i
$459$	−1.57596	+	1.57596i	−0.0735595	+	0.0735595i
$460$		0			0
$461$	12.4144	+	12.4144i	0.578197	+	0.578197i	0.934406	−	0.356209i	$-0.115931\pi$
$461$	12.4144	+	12.4144i	0.578197	+	0.578197i	−0.356209	+	0.934406i	$0.615931\pi$
$462$	0.332913	+	0.460726i	0.0154885	+	0.0214349i
$463$	−8.56578	+	8.56578i	−0.398085	+	0.398085i	−0.877557	−	0.479472i	$-0.840828\pi$
$463$	−8.56578	+	8.56578i	−0.398085	+	0.398085i	0.479472	+	0.877557i	$0.340828\pi$
$464$	−23.6698	+	3.49729i	−1.09884	+	0.162358i
$465$		0			0
$466$	−24.4643	−	3.93991i	−1.13329	−	0.182513i
$467$		−	34.3465i		−	1.58937i	−0.607023	−	0.794684i	$-0.707636\pi$
$467$		−	34.3465i		−	1.58937i	0.607023	−	0.794684i	$-0.292364\pi$
$468$	17.6292	+	5.82946i	0.814908	+	0.269467i
$469$	4.93889	+	4.93889i	0.228057	+	0.228057i
$470$		0			0
$471$	−4.88677			−0.225170
$472$	13.5269	−	26.0445i	0.622627	−	1.19879i
$473$	3.63397	−	3.63397i	0.167090	−	0.167090i
$474$	−5.83248	−	8.07172i	−0.267895	−	0.370746i
$475$		0			0
$476$	−0.538227	−	0.177976i	−0.0246696	−	0.00815753i
$477$	15.3108			0.701034
$478$	20.8876	+	28.9068i	0.955375	+	1.32217i
$479$	23.4504			1.07148			0.535738	−	0.844384i	$-0.320034\pi$
$479$	23.4504			1.07148			0.535738	+	0.844384i	$0.320034\pi$
$480$		0			0
$481$	19.9576			0.909988
$482$	−9.95740	−	13.7803i	−0.453547	−	0.627675i
$483$	−1.47109			−0.0669370
$484$	18.1845	+	6.01309i	0.826567	+	0.273322i
$485$		0			0
$486$	12.3198	+	17.0497i	0.558837	+	0.773389i
$487$	5.31215	−	5.31215i	0.240716	−	0.240716i	−0.576430	−	0.817146i	$-0.695555\pi$
$487$	5.31215	−	5.31215i	0.240716	−	0.240716i	0.817146	+	0.576430i	$0.195555\pi$
$488$	−17.0948	−	8.87868i	−0.773847	−	0.401919i
$489$	−11.0978			−0.501859
$490$		0			0
$491$	−3.71980	−	3.71980i	−0.167872	−	0.167872i	0.618171	−	0.786044i	$-0.287874\pi$
$491$	−3.71980	−	3.71980i	−0.167872	−	0.167872i	−0.786044	+	0.618171i	$0.787874\pi$
$492$	3.35128	+	1.10817i	0.151087	+	0.0499602i
$493$			3.48642i			0.157021i
$494$	39.1142	+	6.29925i	1.75983	+	0.283417i
$495$		0			0
$496$	20.8885	−	28.1314i	0.937923	−	1.26314i
$497$	−1.02338	+	1.02338i	−0.0459050	+	0.0459050i
$498$	4.10396	+	5.67958i	0.183903	+	0.254508i
$499$	−13.6065	−	13.6065i	−0.609111	−	0.609111i	0.333603	−	0.942714i	$-0.391736\pi$
$499$	−13.6065	−	13.6065i	−0.609111	−	0.609111i	−0.942714	+	0.333603i	$0.891736\pi$
$500$		0			0
$501$	−11.5006	+	11.5006i	−0.513810	+	0.513810i
$502$	2.38152	−	14.7877i	0.106292	−	0.660007i
$503$	9.31208	+	9.31208i	0.415205	+	0.415205i	0.883547	−	0.468342i	$-0.155148\pi$
$503$	9.31208	+	9.31208i	0.415205	+	0.415205i	−0.468342	+	0.883547i	$0.655148\pi$
$504$	−1.59774	+	3.07626i	−0.0711691	+	0.137028i
$505$		0			0
$506$	5.97247	−	4.31560i	0.265509	−	0.191852i
$507$	0.395636			0.0175708
$508$	26.6632	−	13.4116i	1.18299	−	0.595044i
$509$	−7.94836	+	7.94836i	−0.352305	+	0.352305i	−0.860966	−	0.508662i	$-0.830140\pi$
$509$	−7.94836	+	7.94836i	−0.352305	+	0.352305i	0.508662	+	0.860966i	$0.330140\pi$
$510$		0			0
$511$			4.72585i			0.209059i
$512$	13.7242	−	17.9902i	0.606531	−	0.795060i
$513$	20.5618	+	20.5618i	0.907824	+	0.907824i
$514$	−19.9054	−	3.20571i	−0.877989	−	0.141398i
$515$		0			0
$516$	−5.66575	−	1.87350i	−0.249421	−	0.0824762i
$517$			7.71069i			0.339116i
$518$	−0.592408	+	3.67847i	−0.0260289	+	0.161623i
$519$			10.3878i			0.455972i
$520$		0			0
$521$		−	29.3979i		−	1.28795i	−0.765048	−	0.643974i	$-0.777285\pi$
$521$		−	29.3979i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$522$	21.0477	+	3.38968i	0.921233	+	0.148362i
$523$			19.5121i			0.853205i	0.904439	+	0.426602i	$0.140290\pi$
$523$			19.5121i			0.853205i	−0.904439	+	0.426602i	$0.859710\pi$
$524$	−1.08098	−	2.14906i	−0.0472228	−	0.0938821i
$525$		0			0
$526$	1.21984	−	7.57438i	0.0531874	−	0.330259i
$527$	−3.61018	−	3.61018i	−0.157262	−	0.157262i
$528$	0.483226	+	3.27048i	0.0210297	+	0.142329i
$529$		−	3.92999i		−	0.170869i
$530$		0			0
$531$	−18.4902	+	18.4902i	−0.802406	+	0.802406i
$532$	−2.32208	+	7.02232i	−0.100675	+	0.304456i
$533$	−9.38575			−0.406542
$534$	−0.636604	−	0.881012i	−0.0275485	−	0.0381251i
$535$		0			0
$536$	12.2520	+	38.7319i	0.529205	+	1.67296i
$537$	−6.86692	−	6.86692i	−0.296329	−	0.296329i
$538$	−26.5085	−	4.26913i	−1.14286	−	0.184055i
$539$	−5.70618	+	5.70618i	−0.245783	+	0.245783i
$540$		0			0
$541$	8.47183	+	8.47183i	0.364232	+	0.364232i	0.865369	−	0.501136i	$-0.167084\pi$
$541$	8.47183	+	8.47183i	0.364232	+	0.364232i	−0.501136	+	0.865369i	$0.667084\pi$
$542$	−14.1587	+	10.2309i	−0.608170	+	0.439453i
$543$	−0.720526	+	0.720526i	−0.0309207	+	0.0309207i
$544$	−2.30093	−	2.36147i	−0.0986516	−	0.101247i
$545$		0			0
$546$	−0.279050	+	1.73272i	−0.0119422	+	0.0741534i
$547$			9.97988i			0.426709i	0.976975	+	0.213355i	$0.0684389\pi$
$547$			9.97988i			0.426709i	−0.976975	+	0.213355i	$0.931561\pi$
$548$	13.9010	−	6.99219i	0.593820	−	0.298692i
$549$	12.1364	+	12.1364i	0.517971	+	0.517971i
$550$		0			0
$551$	45.4879			1.93785
$552$	−7.59300	−	3.94364i	−0.323180	−	0.167852i
$553$	−3.49559	+	3.49559i	−0.148648	+	0.148648i
$554$	−7.78098	+	5.62240i	−0.330582	+	0.238873i
$555$		0			0
$556$	−3.85762	−	7.66922i	−0.163600	−	0.325247i
$557$	−13.4866			−0.571445			−0.285722	−	0.958312i	$-0.592234\pi$
$557$	−13.4866			−0.571445			−0.285722	+	0.958312i	$0.592234\pi$
$558$	−25.3048	+	18.2848i	−1.07124	+	0.774059i
$559$	15.8678			0.671135
$560$		0			0
$561$	0.481724			0.0203384
$562$	24.7033	−	17.8502i	1.04205	−	0.752965i
$563$	20.3451			0.857445			0.428723	−	0.903436i	$-0.358964\pi$
$563$	20.3451			0.857445			0.428723	+	0.903436i	$0.358964\pi$
$564$	7.99853	−	4.02327i	0.336799	−	0.169410i
$565$		0			0
$566$	11.3116	−	8.17354i	0.475461	−	0.343560i
$567$	1.68896	−	1.68896i	0.0709298	−	0.0709298i
$568$	−8.02559	+	2.53872i	−0.336746	+	0.106522i
$569$	17.1460			0.718797			0.359399	−	0.933184i	$-0.382982\pi$
$569$	17.1460			0.718797			0.359399	+	0.933184i	$0.382982\pi$
$570$		0			0
$571$	6.24329	+	6.24329i	0.261274	+	0.261274i	0.825571	−	0.564298i	$-0.190853\pi$
$571$	6.24329	+	6.24329i	0.261274	+	0.261274i	−0.564298	+	0.825571i	$0.690853\pi$
$572$	−3.95019	−	7.85325i	−0.165166	−	0.328361i
$573$			2.13645i			0.0892516i
$574$	0.278600	−	1.72993i	0.0116285	−	0.0722057i
$575$		0			0
$576$	−16.4934	+	11.5949i	−0.687225	+	0.483120i
$577$	10.0373	−	10.0373i	0.417859	−	0.417859i	−0.466606	−	0.884465i	$-0.654523\pi$
$577$	10.0373	−	10.0373i	0.417859	−	0.417859i	0.884465	+	0.466606i	$0.154523\pi$
$578$	19.0973	−	13.7994i	0.794343	−	0.573979i
$579$	−8.37596	−	8.37596i	−0.348093	−	0.348093i
$580$		0			0
$581$	2.45963	−	2.45963i	0.102043	−	0.102043i
$582$	−9.79235	−	1.57703i	−0.405906	−	0.0653701i
$583$	−5.12561	−	5.12561i	−0.212281	−	0.212281i
$584$	−12.6688	+	24.3923i	−0.524240	+	1.00936i
$585$		0			0
$586$	11.7593	+	16.2739i	0.485771	+	0.672270i
$587$	−30.6857			−1.26654			−0.633268	−	0.773933i	$-0.718287\pi$
$587$	−30.6857			−1.26654			−0.633268	+	0.773933i	$0.718287\pi$
$588$	8.89655	+	2.94183i	0.366887	+	0.121319i
$589$	−47.1025	+	47.1025i	−1.94083	+	1.94083i
$590$		0			0
$591$		−	9.01817i		−	0.370958i
$592$	−12.9188	+	17.3982i	−0.530958	+	0.715062i
$593$	2.10671	+	2.10671i	0.0865123	+	0.0865123i	0.749039	−	0.662526i	$-0.230516\pi$
$593$	2.10671	+	2.10671i	0.0865123	+	0.0865123i	−0.662526	+	0.749039i	$0.730516\pi$
$594$	1.02589	−	6.37011i	0.0420928	−	0.261369i
$595$		0			0
$596$	28.1915	−	14.1803i	1.15477	−	0.580850i
$597$		−	7.36210i		−	0.301311i
$598$	22.4615	+	3.61737i	0.918518	+	0.147925i
$599$			32.1322i			1.31289i	0.754375	+	0.656444i	$0.227940\pi$
$599$			32.1322i			1.31289i	−0.754375	+	0.656444i	$0.772060\pi$
$600$		0			0
$601$			14.9811i			0.611091i	0.952177	+	0.305546i	$0.0988388\pi$
$601$			14.9811i			0.611091i	−0.952177	+	0.305546i	$0.901161\pi$
$602$	−0.471008	+	2.92465i	−0.0191968	+	0.119200i
$603$		−	36.1959i		−	1.47401i
$604$	−1.99840	+	6.04345i	−0.0813136	+	0.245905i
$605$		0			0
$606$	1.30405	+	0.210014i	0.0529735	+	0.00853125i
$607$	27.3357	+	27.3357i	1.10952	+	1.10952i	0.993213	+	0.116310i	$0.0371067\pi$
$607$	27.3357	+	27.3357i	1.10952	+	1.10952i	0.116310	+	0.993213i	$0.462893\pi$
$608$	−30.8105	+	30.0206i	−1.24953	+	1.21750i
$609$			2.01506i			0.0816544i
$610$		0			0
$611$	−16.8344	+	16.8344i	−0.681047	+	0.681047i
$612$	1.32009	+	2.62443i	0.0533616	+	0.106086i
$613$	48.3829			1.95417			0.977083	−	0.212859i	$-0.0682775\pi$
$613$	48.3829			1.95417			0.977083	+	0.212859i	$0.0682775\pi$
$614$	−23.4025	+	16.9103i	−0.944449	+	0.682442i
$615$		0			0
$616$	1.56472	−	0.494965i	0.0630444	−	0.0199427i
$617$	−31.1565	−	31.1565i	−1.25432	−	1.25432i	−0.953766	−	0.300549i	$-0.902830\pi$
$617$	−31.1565	−	31.1565i	−1.25432	−	1.25432i	−0.300549	−	0.953766i	$-0.597170\pi$
$618$	2.11343	−	13.1230i	0.0850146	−	0.527885i
$619$	−0.198272	+	0.198272i	−0.00796922	+	0.00796922i	−0.711080	−	0.703111i	$-0.751794\pi$
$619$	−0.198272	+	0.198272i	−0.00796922	+	0.00796922i	0.703111	+	0.711080i	$0.251794\pi$
$620$		0			0
$621$	11.8077	+	11.8077i	0.473825	+	0.473825i
$622$	5.64120	+	7.80700i	0.226191	+	0.313032i
$623$	−0.381537	+	0.381537i	−0.0152859	+	0.0152859i
$624$	−6.08529	+	8.19530i	−0.243607	+	0.328075i
$625$		0			0
$626$	2.38790	+	0.384565i	0.0954395	+	0.0153703i
$627$		−	6.28512i		−	0.251003i
$628$	−4.42958	+	13.3957i	−0.176759	+	0.534547i
$629$	2.23276	+	2.23276i	0.0890259	+	0.0890259i
$630$		0			0
$631$	−32.3314			−1.28709			−0.643547	−	0.765407i	$-0.722538\pi$
$631$	−32.3314			−1.28709			−0.643547	+	0.765407i	$0.722538\pi$
$632$	−27.4132	+	8.67157i	−1.09044	+	0.344936i
$633$	−7.95239	+	7.95239i	−0.316079	+	0.316079i
$634$	−2.85076	−	3.94523i	−0.113218	−	0.156685i
$635$		0			0
$636$	−2.64252	+	7.99138i	−0.104783	+	0.316879i
$637$	−24.9161			−0.987212
$638$	−5.91139	−	8.18092i	−0.234034	−	0.323886i
$639$	7.50010			0.296700
$640$		0			0
$641$	−46.5662			−1.83926			−0.919628	−	0.392790i	$-0.871510\pi$
$641$	−46.5662			−1.83926			−0.919628	+	0.392790i	$0.871510\pi$
$642$	3.03060	+	4.19413i	0.119608	+	0.165529i
$643$	40.2247			1.58631			0.793154	−	0.609021i	$-0.208437\pi$
$643$	40.2247			1.58631			0.793154	+	0.609021i	$0.208437\pi$
$644$	−1.33346	+	4.03259i	−0.0525458	+	0.158906i
$645$		0			0
$646$	3.67118	+	5.08064i	0.144441	+	0.199895i
$647$	10.7938	−	10.7938i	0.424349	−	0.424349i	−0.462349	−	0.886698i	$-0.652993\pi$
$647$	10.7938	−	10.7938i	0.424349	−	0.424349i	0.886698	+	0.462349i	$0.152993\pi$
$648$	13.2452	−	4.18984i	0.520322	−	0.164593i
$649$	12.3799			0.485956
$650$		0			0
$651$	−2.08659	−	2.08659i	−0.0817799	−	0.0817799i
$652$	−10.0595	+	30.4215i	−0.393961	+	1.19140i
$653$			3.92443i			0.153575i	0.997047	+	0.0767875i	$0.0244663\pi$
$653$			3.92443i			0.153575i	−0.997047	+	0.0767875i	$0.975534\pi$
$654$	−2.10614	−	0.339188i	−0.0823564	−	0.0132633i
$655$		0			0
$656$	6.07549	−	8.18210i	0.237208	−	0.319457i
$657$	17.3173	−	17.3173i	0.675610	−	0.675610i
$658$	−2.60312	−	3.60252i	−0.101480	−	0.140441i
$659$	−34.6142	−	34.6142i	−1.34838	−	1.34838i	−0.887425	−	0.460952i	$-0.847508\pi$
$659$	−34.6142	−	34.6142i	−1.34838	−	1.34838i	−0.460952	−	0.887425i	$-0.652492\pi$
$660$		0			0
$661$	21.7641	−	21.7641i	0.846525	−	0.846525i	−0.143173	−	0.989698i	$-0.545730\pi$
$661$	21.7641	−	21.7641i	0.846525	−	0.846525i	0.989698	+	0.143173i	$0.0457304\pi$
$662$	−0.472104	+	2.93146i	−0.0183489	+	0.113934i
$663$	1.05173	+	1.05173i	0.0408456	+	0.0408456i
$664$	19.2890	−	6.10166i	0.748559	−	0.236790i
$665$		0			0
$666$	15.6501	−	11.3085i	0.606428	−	0.438194i
$667$	26.1216			1.01143
$668$	21.1011	+	41.9505i	0.816426	+	1.62311i
$669$	−1.50917	+	1.50917i	−0.0583477	+	0.0583477i
$670$		0			0
$671$		−	8.12584i		−	0.313695i
$672$	−1.32988	−	1.36487i	−0.0513012	−	0.0526510i
$673$	−29.4450	−	29.4450i	−1.13502	−	1.13502i	−0.989330	−	0.145691i	$-0.953459\pi$
$673$	−29.4450	−	29.4450i	−1.13502	−	1.13502i	−0.145691	−	0.989330i	$-0.546541\pi$
$674$	12.2662	+	1.97544i	0.472475	+	0.0760910i
$675$		0			0
$676$	0.358622	−	1.08453i	0.0137932	−	0.0417126i
$677$		−	34.7351i		−	1.33498i	−0.744619	−	0.667490i	$-0.767369\pi$
$677$		−	34.7351i		−	1.33498i	0.744619	−	0.667490i	$-0.232631\pi$
$678$	−0.660084	+	4.09869i	−0.0253504	+	0.157409i
$679$			4.92370i			0.188954i
$680$		0			0
$681$		−	6.45828i		−	0.247482i
$682$	14.5925	+	2.35009i	0.558777	+	0.0899897i
$683$			22.2693i			0.852110i	0.904697	+	0.426055i	$0.140097\pi$
$683$			22.2693i			0.852110i	−0.904697	+	0.426055i	$0.859903\pi$
$684$	34.2414	−	17.2234i	1.30925	−	0.658554i
$685$		0			0
$686$	1.50505	−	9.34535i	0.0574629	−	0.356807i
$687$	−1.88597	−	1.88597i	−0.0719543	−	0.0719543i
$688$	−10.2714	+	13.8328i	−0.391592	+	0.527372i
$689$		−	22.3810i		−	0.852650i
$690$		0			0
$691$	15.7043	−	15.7043i	0.597420	−	0.597420i	−0.342205	−	0.939625i	$-0.611174\pi$
$691$	15.7043	−	15.7043i	0.597420	−	0.597420i	0.939625	+	0.342205i	$0.111174\pi$
$692$	28.4751	+	9.41591i	1.08246	+	0.357939i
$693$	−1.46227			−0.0555470
$694$	8.40717	+	11.6349i	0.319132	+	0.441655i
$695$		0			0
$696$	−5.40188	+	10.4007i	−0.204758	+	0.394237i
$697$	−1.05003	−	1.05003i	−0.0397728	−	0.0397728i
$698$	−7.89023	−	1.27070i	−0.298650	−	0.0480968i
$699$	−8.58253	+	8.58253i	−0.324621	+	0.324621i
$700$		0			0
$701$	−21.5588	−	21.5588i	−0.814266	−	0.814266i	0.171004	−	0.985270i	$-0.445299\pi$
$701$	−21.5588	−	21.5588i	−0.814266	−	0.814266i	−0.985270	+	0.171004i	$0.945299\pi$
$702$	16.1474	−	11.6678i	0.609443	−	0.440373i
$703$	29.1311	−	29.1311i	1.09870	−	1.09870i
$704$	9.40314	+	1.63988i	0.354394	+	0.0618053i
$705$		0			0
$706$	−7.20702	+	44.7509i	−0.271240	+	1.68422i
$707$		−	0.655691i		−	0.0246598i
$708$	−6.45958	−	12.8421i	−0.242766	−	0.482635i
$709$	2.96687	+	2.96687i	0.111423	+	0.111423i	0.760620	−	0.649197i	$-0.224895\pi$
$709$	2.96687	+	2.96687i	0.111423	+	0.111423i	−0.649197	+	0.760620i	$0.724895\pi$
$710$		0			0
$711$	25.6183			0.960760
$712$	−2.99210	+	0.946485i	−0.112134	+	0.0354710i
$713$	−27.0488	+	27.0488i	−1.01299	+	1.01299i
$714$	−0.225067	+	0.162629i	−0.00842290	+	0.00608624i
$715$		0			0
$716$	−25.0482	+	12.5993i	−0.936096	+	0.470857i
$717$	17.4688			0.652385
$718$	−4.95047	+	3.57712i	−0.184750	+	0.133497i
$719$	25.8357			0.963509			0.481755	−	0.876306i	$-0.340000\pi$
$719$	25.8357			0.963509			0.481755	+	0.876306i	$0.340000\pi$
$720$		0			0
$721$	−6.59839			−0.245737
$722$	44.5085	−	32.1611i	1.65644	−	1.19691i
$723$	−8.32763			−0.309708
$724$	1.32201	+	2.62824i	0.0491320	+	0.0976777i
$725$		0			0
$726$	7.60407	−	5.49457i	0.282214	−	0.203923i
$727$	−28.9620	+	28.9620i	−1.07414	+	1.07414i	−0.0771198	+	0.997022i	$0.524572\pi$
$727$	−28.9620	+	28.9620i	−1.07414	+	1.07414i	−0.997022	+	0.0771198i	$0.975428\pi$
$728$	4.49682	+	2.33555i	0.166663	+	0.0865612i
$729$	−4.43146			−0.164128
$730$		0			0
$731$	1.77521	+	1.77521i	0.0656584	+	0.0656584i
$732$	−8.42918	+	4.23988i	−0.311551	+	0.156711i
$733$		−	21.1673i		−	0.781832i	−0.920426	−	0.390916i	$-0.872158\pi$
$733$		−	21.1673i		−	0.781832i	0.920426	−	0.390916i	$-0.127842\pi$
$734$	−2.05725	+	12.7742i	−0.0759346	+	0.471504i
$735$		0			0
$736$	−17.6930	+	17.2394i	−0.652173	+	0.635453i
$737$	−12.1173	+	12.1173i	−0.446347	+	0.446347i
$738$	−7.35999	+	5.31820i	−0.270925	+	0.195765i
$739$	−2.23302	−	2.23302i	−0.0821431	−	0.0821431i	0.664841	−	0.746985i	$-0.268499\pi$
$739$	−2.23302	−	2.23302i	−0.0821431	−	0.0821431i	−0.746985	+	0.664841i	$0.768499\pi$
$740$		0			0
$741$	13.7220	−	13.7220i	0.504091	−	0.504091i
$742$	4.12514	+	0.664344i	0.151439	+	0.0243888i
$743$	18.4514	+	18.4514i	0.676915	+	0.676915i	0.959301	−	0.282386i	$-0.0911258\pi$
$743$	18.4514	+	18.4514i	0.676915	+	0.676915i	−0.282386	+	0.959301i	$0.591126\pi$
$744$	−5.17624	−	16.3635i	−0.189770	−	0.599915i
$745$		0			0
$746$	−13.9011	−	19.2381i	−0.508955	−	0.704356i
$747$	−18.0260			−0.659538
$748$	0.436655	−	1.32051i	0.0159657	−	0.0482827i
$749$	1.81634	−	1.81634i	0.0663675	−	0.0663675i
$750$		0			0
$751$		−	42.4243i		−	1.54808i	−0.633134	−	0.774042i	$-0.718232\pi$
$751$		−	42.4243i		−	1.54808i	0.633134	−	0.774042i	$-0.281768\pi$
$752$	−3.77845	−	25.5726i	−0.137786	−	0.932537i
$753$	−5.18780	−	5.18780i	−0.189054	−	0.189054i
$754$	4.95496	−	30.7671i	0.180449	−	1.12047i
$755$		0			0
$756$	1.67123	+	3.32253i	0.0607821	+	0.120839i
$757$		−	19.7595i		−	0.718170i	−0.933305	−	0.359085i	$-0.883089\pi$
$757$		−	19.7595i		−	0.718170i	0.933305	−	0.359085i	$-0.116911\pi$
$758$	−14.4349	−	2.32471i	−0.524300	−	0.0844372i
$759$		−	3.60925i		−	0.131007i
$760$		0			0
$761$		−	48.0351i		−	1.74127i	−0.491928	−	0.870636i	$-0.663708\pi$
$761$		−	48.0351i		−	1.74127i	0.491928	−	0.870636i	$-0.336292\pi$
$762$	2.32445	−	14.4333i	0.0842061	−	0.522865i
$763$			1.05899i			0.0383379i
$764$	5.85649	+	1.93657i	0.211880	+	0.0700628i
$765$		0			0
$766$	10.4946	+	1.69013i	0.379186	+	0.0610669i
$767$	27.0286	+	27.0286i	0.975946	+	0.975946i
$768$	−3.20525	−	10.6098i	−0.115659	−	0.382848i
$769$		−	24.0184i		−	0.866127i	−0.901363	−	0.433064i	$-0.857433\pi$
$769$		−	24.0184i		−	0.866127i	0.901363	−	0.433064i	$-0.142567\pi$
$770$		0			0
$771$	−6.98319	+	6.98319i	−0.251493	+	0.251493i
$772$	−30.5527	+	15.3680i	−1.09962	+	0.553107i
$773$	−22.4630			−0.807937			−0.403969	−	0.914773i	$-0.632370\pi$
$773$	−22.4630			−0.807937			−0.403969	+	0.914773i	$0.632370\pi$
$774$	12.4430	−	8.99106i	0.447253	−	0.323177i
$775$		0			0
$776$	−13.1992	+	25.4135i	−0.473824	+	0.912292i
$777$	1.29048	+	1.29048i	0.0462956	+	0.0462956i
$778$	0.409725	−	2.54412i	0.0146893	−	0.0912113i
$779$	−13.6999	+	13.6999i	−0.490850	+	0.490850i
$780$		0			0
$781$	−2.51081	−	2.51081i	−0.0898440	−	0.0898440i
$782$	2.10819	+	2.91757i	0.0753886	+	0.104332i
$783$	16.1738	−	16.1738i	0.578005	−	0.578005i
$784$	16.1284	−	21.7208i	0.576016	−	0.775743i
$785$		0			0
$786$	−1.16333	−	0.187352i	−0.0414946	−	0.00668261i
$787$			26.1054i			0.930556i	0.885165	+	0.465278i	$0.154046\pi$
$787$			26.1054i			0.930556i	−0.885165	+	0.465278i	$0.845954\pi$
$788$	−24.7208	−	8.17446i	−0.880642	−	0.291203i
$789$	−2.65724	−	2.65724i	−0.0946001	−	0.0946001i
$790$		0			0
$791$	2.06087			0.0732759
$792$	−7.54745	−	3.91998i	−0.268187	−	0.139290i
$793$	17.7408	−	17.7408i	0.629994	−	0.629994i
$794$	7.90040	+	10.9336i	0.280375	+	0.388018i
$795$		0			0
$796$	−20.1812	−	6.67333i	−0.715302	−	0.236530i
$797$	−43.4888			−1.54045			−0.770227	−	0.637770i	$-0.779857\pi$
$797$	−43.4888			−1.54045			−0.770227	+	0.637770i	$0.779857\pi$
$798$	2.12185	+	2.93647i	0.0751125	+	0.103950i
$799$	−3.76670			−0.133256
$800$		0			0
$801$	2.79618			0.0987983
$802$	20.3842	+	28.2103i	0.719793	+	0.996139i
$803$	−11.5946			−0.409165
$804$	18.8922	+	6.24710i	0.666276	+	0.220318i
$805$		0			0
$806$	26.7284	+	36.9901i	0.941467	+	1.30292i
$807$	−9.29969	+	9.29969i	−0.327364	+	0.327364i
$808$	1.75775	−	3.38433i	0.0618373	−	0.119060i
$809$	−36.6271			−1.28774			−0.643870	−	0.765135i	$-0.722672\pi$
$809$	−36.6271			−1.28774			−0.643870	+	0.765135i	$0.722672\pi$
$810$		0			0
$811$	18.7904	+	18.7904i	0.659821	+	0.659821i	0.955338	−	0.295516i	$-0.0954917\pi$
$811$	18.7904	+	18.7904i	0.659821	+	0.659821i	−0.295516	+	0.955338i	$0.595492\pi$
$812$	5.52373	+	1.82654i	0.193845	+	0.0640990i
$813$			8.55633i			0.300084i
$814$	−9.02493	−	1.45344i	−0.316324	−	0.0509431i
$815$		0			0
$816$	−1.59764	+	0.236058i	−0.0559287	+	0.00826367i
$817$	23.1614	−	23.1614i	0.810314	−	0.810314i
$818$	−14.0358	−	19.4245i	−0.490750	−	0.679161i
$819$	−3.19250	−	3.19250i	−0.111555	−	0.111555i
$820$		0			0
$821$	3.91048	−	3.91048i	0.136477	−	0.136477i	−0.635568	−	0.772045i	$-0.719234\pi$
$821$	3.91048	−	3.91048i	0.136477	−	0.136477i	0.772045	+	0.635568i	$0.219234\pi$
$822$	1.21186	−	7.52488i	0.0422686	−	0.262460i
$823$	−35.4412	−	35.4412i	−1.23540	−	1.23540i	−0.961860	−	0.273542i	$-0.911805\pi$
$823$	−35.4412	−	35.4412i	−1.23540	−	1.23540i	−0.273542	−	0.961860i	$-0.588195\pi$
$824$	−34.0574	−	17.6887i	−1.18645	−	0.616214i
$825$		0			0
$826$	−5.78405	+	4.17945i	−0.201253	+	0.145422i
$827$	44.0700			1.53246			0.766232	−	0.642565i	$-0.222130\pi$
$827$	44.0700			1.53246			0.766232	+	0.642565i	$0.222130\pi$
$828$	19.6632	−	9.89061i	0.683344	−	0.343723i
$829$	−15.1609	+	15.1609i	−0.526561	+	0.526561i	−0.919545	−	0.392984i	$-0.871443\pi$
$829$	−15.1609	+	15.1609i	−0.526561	+	0.526561i	0.392984	+	0.919545i	$0.371443\pi$
$830$		0			0
$831$			4.70216i			0.163116i
$832$	16.9492	+	24.1097i	0.587607	+	0.835854i
$833$	−2.78749	−	2.78749i	−0.0965808	−	0.0965808i
$834$	−4.15151	−	0.668590i	−0.143755	−	0.0231514i
$835$		0			0
$836$	−17.2289	−	5.69711i	−0.595874	−	0.197039i
$837$			33.4958i			1.15779i
$838$	2.08910	−	12.9720i	0.0721669	−	0.448109i
$839$		−	40.3143i		−	1.39180i	−0.718137	−	0.695901i	$-0.755005\pi$
$839$		−	40.3143i		−	1.39180i	0.718137	−	0.695901i	$-0.244995\pi$
$840$		0			0
$841$		−	6.78056i		−	0.233812i
$842$	−27.4078	−	4.41396i	−0.944535	−	0.152115i
$843$		−	14.9286i		−	0.514168i
$844$	14.5909	+	29.0077i	0.502238	+	0.998485i
$845$		0			0
$846$	−3.66218	+	22.7398i	−0.125908	+	0.781809i
$847$	−3.29307	−	3.29307i	−0.113151	−	0.113151i
$848$	19.5108	+	14.4875i	0.670005	+	0.497502i
$849$		−	6.83575i		−	0.234602i
$850$		0			0
$851$	16.7286	−	16.7286i	0.573450	−	0.573450i
$852$	−1.29446	+	3.91463i	−0.0443473	+	0.134113i
$853$	−28.6203			−0.979941			−0.489971	−	0.871739i	$-0.662992\pi$
$853$	−28.6203			−0.979941			−0.489971	+	0.871739i	$0.662992\pi$
$854$	2.74327	+	3.79648i	0.0938728	+	0.129913i
$855$		0			0
$856$	14.2441	−	4.50582i	0.486854	−	0.154006i
$857$	−7.19794	−	7.19794i	−0.245877	−	0.245877i	0.573399	−	0.819276i	$-0.305624\pi$
$857$	−7.19794	−	7.19794i	−0.245877	−	0.245877i	−0.819276	+	0.573399i	$0.805624\pi$
$858$	−4.25113	−	0.684634i	−0.145131	−	0.0233730i
$859$	18.8135	−	18.8135i	0.641910	−	0.641910i	−0.309115	−	0.951025i	$-0.600033\pi$
$859$	18.8135	−	18.8135i	0.641910	−	0.641910i	0.951025	+	0.309115i	$0.100033\pi$
$860$		0			0
$861$	−0.606890	−	0.606890i	−0.0206828	−	0.0206828i
$862$	−14.1840	+	10.2491i	−0.483110	+	0.349087i
$863$	19.2328	−	19.2328i	0.654691	−	0.654691i	−0.299428	−	0.954119i	$-0.596796\pi$
$863$	19.2328	−	19.2328i	0.654691	−	0.654691i	0.954119	+	0.299428i	$0.0967958\pi$
$864$	−0.280854	+	21.6293i	−0.00955484	+	0.735843i
$865$		0			0
$866$	0.0462133	−	0.286955i	0.00157039	−	0.00975112i
$867$		−	11.5408i		−	0.391945i
$868$	−7.61118	+	3.82843i	−0.258340	+	0.129945i
$869$	−8.57624	−	8.57624i	−0.290929	−	0.290929i
$870$		0			0
$871$	−52.9103			−1.79280
$872$	−2.83888	+	5.46593i	−0.0961367	+	0.185100i
$873$	18.0423	−	18.0423i	0.610638	−	0.610638i
$874$	38.0660	−	27.5058i	1.28760	−	0.930398i
$875$		0			0
$876$	6.04981	+	12.0274i	0.204404	+	0.406369i
$877$	−35.4397			−1.19671			−0.598357	−	0.801229i	$-0.704180\pi$
$877$	−35.4397			−1.19671			−0.598357	+	0.801229i	$0.704180\pi$
$878$	4.19357	−	3.03020i	0.141526	−	0.102264i
$879$	9.83458			0.331712
$880$		0			0
$881$	30.2010			1.01750			0.508748	−	0.860915i	$-0.330108\pi$
$881$	30.2010			1.01750			0.508748	+	0.860915i	$0.330108\pi$
$882$	−19.5384	+	14.1181i	−0.657891	+	0.475380i
$883$	−28.9931			−0.975696			−0.487848	−	0.872928i	$-0.662218\pi$
$883$	−28.9931			−0.975696			−0.487848	+	0.872928i	$0.662218\pi$
$884$	3.83634	−	1.92968i	0.129030	−	0.0649023i
$885$		0			0
$886$	−4.51664	+	3.26364i	−0.151740	+	0.109644i
$887$	−5.33418	+	5.33418i	−0.179104	+	0.179104i	−0.790965	−	0.611861i	$-0.790421\pi$
$887$	−5.33418	+	5.33418i	−0.179104	+	0.179104i	0.611861	+	0.790965i	$0.290421\pi$
$888$	3.20131	+	10.1202i	0.107429	+	0.339612i
$889$	−7.25724			−0.243400
$890$		0			0
$891$	4.14379	+	4.14379i	0.138822	+	0.138822i
$892$	2.76898	+	5.50493i	0.0927125	+	0.184319i
$893$			49.1447i			1.64456i
$894$	2.45769	−	15.2606i	0.0821974	−	0.510392i
$895$		0			0
$896$	−4.94687	+	2.40831i	−0.165263	+	0.0804561i
$897$	7.87991	−	7.87991i	0.263103	−	0.263103i
$898$	−43.5602	+	31.4758i	−1.45362	+	1.05036i
$899$	37.0507	+	37.0507i	1.23571	+	1.23571i
$900$		0			0
$901$	2.50388	−	2.50388i	0.0834163	−	0.0834163i
$902$	4.24428	+	0.683531i	0.141319	+	0.0227591i
$903$	1.02602	+	1.02602i	0.0341439	+	0.0341439i
$904$	10.6371	+	5.52467i	0.353785	+	0.183748i
$905$		0			0
$906$	1.82607	+	2.52715i	0.0606672	+	0.0839589i
$907$	−26.2683			−0.872226			−0.436113	−	0.899892i	$-0.643645\pi$
$907$	−26.2683			−0.872226			−0.436113	+	0.899892i	$0.643645\pi$
$908$	−17.7036	−	5.85407i	−0.587514	−	0.194274i
$909$	−2.40270	+	2.40270i	−0.0796924	+	0.0796924i
$910$		0			0
$911$			33.5196i			1.11055i	0.831665	+	0.555277i	$0.187388\pi$
$911$			33.5196i			1.11055i	−0.831665	+	0.555277i	$0.812612\pi$
$912$	3.07988	+	20.8447i	0.101985	+	0.690236i
$913$	6.03459	+	6.03459i	0.199716	+	0.199716i
$914$	5.76028	−	35.7676i	0.190533	−	1.18309i
$915$		0			0
$916$	−6.87940	+	3.46034i	−0.227302	+	0.114333i
$917$			0.584935i			0.0193163i
$918$	3.11182	+	0.501151i	0.102705	+	0.0165405i
$919$			25.7545i			0.849564i	0.905296	+	0.424782i	$0.139649\pi$
$919$			25.7545i			0.849564i	−0.905296	+	0.424782i	$0.860351\pi$
$920$		0			0
$921$			14.1425i			0.466011i
$922$	3.94775	−	24.5130i	0.130012	−	0.807292i
$923$		−	10.9635i		−	0.360868i
$924$	0.252375	−	0.763221i	0.00830254	−	0.0251081i
$925$		0			0
$926$	16.9136	+	2.72390i	0.555816	+	0.0895128i
$927$	24.1790	+	24.1790i	0.794141	+	0.794141i
$928$	23.6141	+	24.2354i	0.775170	+	0.795565i
$929$		−	9.06425i		−	0.297388i	−0.988883	−	0.148694i	$-0.952493\pi$
$929$		−	9.06425i		−	0.297388i	0.988883	−	0.148694i	$-0.0475070\pi$
$930$		0			0
$931$	−36.3688	+	36.3688i	−1.19194	+	1.19194i
$932$	15.7470	+	31.3062i	0.515811	+	1.02547i
$933$	4.71788			0.154456
$934$	−39.3707	+	28.4486i	−1.28825	+	0.930865i
$935$		0			0
$936$	−7.91970	−	25.0363i	−0.258864	−	0.818338i
$937$	−3.38621	−	3.38621i	−0.110623	−	0.110623i	0.649629	−	0.760251i	$-0.274924\pi$
$937$	−3.38621	−	3.38621i	−0.110623	−	0.110623i	−0.760251	+	0.649629i	$0.774924\pi$
$938$	1.57055	−	9.75212i	0.0512804	−	0.318418i
$939$	0.837719	−	0.837719i	0.0273379	−	0.0273379i
$940$		0			0
$941$	−16.9347	−	16.9347i	−0.552054	−	0.552054i	0.374979	−	0.927033i	$-0.377650\pi$
$941$	−16.9347	−	16.9347i	−0.552054	−	0.552054i	−0.927033	+	0.374979i	$0.877650\pi$
$942$	4.04761	+	5.60159i	0.131878	+	0.182510i
$943$	−7.86722	+	7.86722i	−0.256192	+	0.256192i
$944$	−41.0583	+	6.06651i	−1.33633	+	0.197448i
$945$		0			0
$946$	−7.17548	−	1.15559i	−0.233295	−	0.0375716i
$947$		−	1.08633i		−	0.0353011i	−0.999844	−	0.0176505i	$-0.994381\pi$
$947$		−	1.08633i		−	0.0353011i	0.999844	−	0.0176505i	$-0.00561863\pi$
$948$	−4.42150	+	13.3713i	−0.143604	+	0.434279i
$949$	−25.3140	−	25.3140i	−0.821727	−	0.821727i
$950$		0			0
$951$	−2.38416			−0.0773117
$952$	0.241792	+	0.764372i	0.00783654	+	0.0247734i
$953$	10.7914	−	10.7914i	0.349567	−	0.349567i	−0.510381	−	0.859948i	$-0.670496\pi$
$953$	10.7914	−	10.7914i	0.349567	−	0.349567i	0.859948	+	0.510381i	$0.170496\pi$
$954$	−12.6816	−	17.5504i	−0.410583	−	0.568217i
$955$		0			0
$956$	15.8345	−	47.8859i	0.512124	−	1.54874i
$957$	−4.94385			−0.159812
$958$	−19.4235	−	26.8807i	−0.627544	−	0.868475i
$959$	−3.78359			−0.122178
$960$		0			0
$961$	−45.7317			−1.47522
$962$	−16.5305	−	22.8770i	−0.532964	−	0.737583i
$963$	−13.3115			−0.428956
$964$	−7.54853	+	22.8279i	−0.243122	+	0.735237i
$965$		0			0
$966$	1.21848	+	1.68628i	0.0392038	+	0.0542552i
$967$	31.4724	−	31.4724i	1.01208	−	1.01208i	0.0121587	−	0.999926i	$-0.496130\pi$
$967$	31.4724	−	31.4724i	1.01208	−	1.01208i	0.999926	−	0.0121587i	$-0.00387033\pi$
$968$	−8.16917	−	25.8250i	−0.262567	−	0.830046i
$969$	3.07030			0.0986323
$970$		0			0
$971$	−23.1234	−	23.1234i	−0.742066	−	0.742066i	0.230909	−	0.972975i	$-0.425830\pi$
$971$	−23.1234	−	23.1234i	−0.742066	−	0.742066i	−0.972975	+	0.230909i	$0.925830\pi$
$972$	9.33942	−	28.2438i	0.299562	−	0.905921i
$973$			2.08742i			0.0669196i
$974$	−10.4891	−	1.68925i	−0.336094	−	0.0541271i
$975$		0			0
$976$	3.98188	+	26.9495i	0.127457	+	0.862632i
$977$	−15.3820	+	15.3820i	−0.492114	+	0.492114i	−0.908972	−	0.416858i	$-0.863131\pi$
$977$	−15.3820	+	15.3820i	−0.492114	+	0.492114i	0.416858	+	0.908972i	$0.363131\pi$
$978$	9.19207	+	12.7211i	0.293930	+	0.406777i
$979$	−0.936080	−	0.936080i	−0.0299173	−	0.0299173i
$980$		0			0
$981$	3.88052	−	3.88052i	0.123896	−	0.123896i
$982$	−1.18289	+	7.34496i	−0.0377475	+	0.234387i
$983$	38.5198	+	38.5198i	1.22859	+	1.22859i	0.964497	+	0.264093i	$0.0850726\pi$
$983$	38.5198	+	38.5198i	1.22859	+	1.22859i	0.264093	+	0.964497i	$0.414927\pi$
$984$	−1.50552	−	4.75937i	−0.0479943	−	0.151723i
$985$		0			0
$986$	3.99641	−	2.88773i	0.127272	−	0.0919642i
$987$	−2.17705			−0.0692964
$988$	−25.1769	−	50.0533i	−0.800982	−	1.59241i
$989$	13.3005	−	13.3005i	0.422931	−	0.422931i
$990$		0			0
$991$			22.0556i			0.700619i	0.936634	+	0.350310i	$0.113924\pi$
$991$			22.0556i			0.700619i	−0.936634	+	0.350310i	$0.886076\pi$
$992$	−49.5480	−	0.643375i	−1.57315	−	0.0204272i
$993$	1.02841	+	1.02841i	0.0326356	+	0.0326356i
$994$	2.02073	+	0.325433i	0.0640936	+	0.0103221i
$995$		0			0
$996$	3.11114	−	9.40856i	0.0985804	−	0.298122i
$997$			0.840040i			0.0266043i	0.999912	+	0.0133022i	$0.00423434\pi$
$997$			0.840040i			0.0266043i	−0.999912	+	0.0133022i	$0.995766\pi$
$998$	−4.32684	+	26.8668i	−0.136964	+	0.850455i
$999$		−	20.7159i		−	0.655422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.s.d.243.3		18
4.3	odd	2		1600.2.s.d.943.6		18
5.2	odd	4		400.2.j.d.307.7		18
5.3	odd	4		80.2.j.b.67.3	yes	18
5.4	even	2		80.2.s.b.3.7	yes	18
15.8	even	4		720.2.bd.g.307.7		18
15.14	odd	2		720.2.z.g.163.3		18
16.5	even	4		1600.2.j.d.143.6		18
16.11	odd	4		400.2.j.d.43.7		18
20.3	even	4		320.2.j.b.47.6		18
20.7	even	4		1600.2.j.d.1007.4		18
20.19	odd	2		320.2.s.b.303.4		18
40.3	even	4		640.2.j.c.607.4		18
40.13	odd	4		640.2.j.d.607.6		18
40.19	odd	2		640.2.s.c.223.6		18
40.29	even	2		640.2.s.d.223.4		18
80.3	even	4		640.2.s.d.287.4		18
80.13	odd	4		640.2.s.c.287.6		18
80.19	odd	4		640.2.j.d.543.4		18
80.27	even	4	inner	400.2.s.d.107.3		18
80.29	even	4		640.2.j.c.543.6		18
80.37	odd	4		1600.2.s.d.207.6		18
80.43	even	4		80.2.s.b.27.7	yes	18
80.53	odd	4		320.2.s.b.207.4		18
80.59	odd	4		80.2.j.b.43.3	✓	18
80.69	even	4		320.2.j.b.143.4		18
240.59	even	4		720.2.bd.g.523.7		18
240.203	odd	4		720.2.z.g.667.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.3	✓	18	80.59	odd	4
80.2.j.b.67.3	yes	18	5.3	odd	4
80.2.s.b.3.7	yes	18	5.4	even	2
80.2.s.b.27.7	yes	18	80.43	even	4
320.2.j.b.47.6		18	20.3	even	4
320.2.j.b.143.4		18	80.69	even	4
320.2.s.b.207.4		18	80.53	odd	4
320.2.s.b.303.4		18	20.19	odd	2
400.2.j.d.43.7		18	16.11	odd	4
400.2.j.d.307.7		18	5.2	odd	4
400.2.s.d.107.3		18	80.27	even	4	inner
400.2.s.d.243.3		18	1.1	even	1	trivial
640.2.j.c.543.6		18	80.29	even	4
640.2.j.c.607.4		18	40.3	even	4
640.2.j.d.543.4		18	80.19	odd	4
640.2.j.d.607.6		18	40.13	odd	4
640.2.s.c.223.6		18	40.19	odd	2
640.2.s.c.287.6		18	80.13	odd	4
640.2.s.d.223.4		18	40.29	even	2
640.2.s.d.287.4		18	80.3	even	4
720.2.z.g.163.3		18	15.14	odd	2
720.2.z.g.667.3		18	240.203	odd	4
720.2.bd.g.307.7		18	15.8	even	4
720.2.bd.g.523.7		18	240.59	even	4
1600.2.j.d.143.6		18	16.5	even	4
1600.2.j.d.1007.4		18	20.7	even	4
1600.2.s.d.207.6		18	80.37	odd	4
1600.2.s.d.943.6		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.828280 - 1.14628i) q^{2} -0.692712 q^{3} +(-0.627905 + 1.89888i) q^{4} +(0.573759 + 0.794040i) q^{6} +(0.343872 - 0.343872i) q^{7} +(2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +O(q^{10})\)	\(q+(-0.828280 - 1.14628i) q^{2} -0.692712 q^{3} +(-0.627905 + 1.89888i) q^{4} +(0.573759 + 0.794040i) q^{6} +(0.343872 - 0.343872i) q^{7} +(2.69672 - 0.853049i) q^{8} -2.52015 q^{9} +(0.843672 + 0.843672i) q^{11} +(0.434957 - 1.31538i) q^{12} +3.68390i q^{13} +(-0.678995 - 0.109350i) q^{14} +(-3.21147 - 2.38463i) q^{16} +(-0.412137 + 0.412137i) q^{17} +(2.08739 + 2.88879i) q^{18} +(5.37721 + 5.37721i) q^{19} +(-0.238204 + 0.238204i) q^{21} +(0.268286 - 1.66588i) q^{22} +(3.08788 + 3.08788i) q^{23} +(-1.86805 + 0.590917i) q^{24} +(4.22278 - 3.05130i) q^{26} +3.82387 q^{27} +(0.437052 + 0.868890i) q^{28} +(4.22969 - 4.22969i) q^{29} +8.75966i q^{31} +(-0.0734474 + 5.65638i) q^{32} +(-0.584422 - 0.584422i) q^{33} +(0.813788 + 0.131059i) q^{34} +(1.58241 - 4.78546i) q^{36} -5.41752i q^{37} +(1.70994 - 10.6176i) q^{38} -2.55188i q^{39} +2.54777i q^{41} +(0.470348 + 0.0757484i) q^{42} -4.30732i q^{43} +(-2.13178 + 1.07228i) q^{44} +(0.981939 - 6.09720i) q^{46} +(4.56972 + 4.56972i) q^{47} +(2.22462 + 1.65186i) q^{48} +6.76350i q^{49} +(0.285492 - 0.285492i) q^{51} +(-6.99528 - 2.31314i) q^{52} -6.07536 q^{53} +(-3.16724 - 4.38322i) q^{54} +(0.633987 - 1.22067i) q^{56} +(-3.72486 - 3.72486i) q^{57} +(-8.35177 - 1.34503i) q^{58} +(7.33694 - 7.33694i) q^{59} +(-4.81576 - 4.81576i) q^{61} +(10.0410 - 7.25545i) q^{62} +(-0.866609 + 0.866609i) q^{63} +(6.54461 - 4.60087i) q^{64} +(-0.185845 + 1.15397i) q^{66} +14.3626i q^{67} +(-0.523815 - 1.04138i) q^{68} +(-2.13901 - 2.13901i) q^{69} -2.97605 q^{71} +(-6.79614 + 2.14981i) q^{72} +(-6.87152 + 6.87152i) q^{73} +(-6.20998 + 4.48722i) q^{74} +(-13.5870 + 6.83429i) q^{76} +0.580231 q^{77} +(-2.92517 + 2.11367i) q^{78} -10.1654 q^{79} +4.91161 q^{81} +(2.92046 - 2.11027i) q^{82} +7.15276 q^{83} +(-0.302751 - 0.601890i) q^{84} +(-4.93739 + 3.56767i) q^{86} +(-2.92996 + 2.92996i) q^{87} +(2.99484 + 1.55545i) q^{88} -1.10953 q^{89} +(1.26679 + 1.26679i) q^{91} +(-7.80240 + 3.92461i) q^{92} -6.06792i q^{93} +(1.45316 - 9.02318i) q^{94} +(0.0508779 - 3.91824i) q^{96} +(-7.15920 + 7.15920i) q^{97} +(7.75285 - 5.60207i) q^{98} +(-2.12618 - 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} + 6 q^{17} + 24 q^{18} - 2 q^{19} - 16 q^{21} - 12 q^{22} + 2 q^{23} - 4 q^{24} - 16 q^{26} + 24 q^{27} - 40 q^{28} + 14 q^{29} - 20 q^{32} + 8 q^{33} + 28 q^{34} - 4 q^{36} - 24 q^{38} - 8 q^{42} - 44 q^{44} + 12 q^{46} - 38 q^{47} - 4 q^{48} + 8 q^{51} - 8 q^{52} - 12 q^{53} + 4 q^{54} + 20 q^{56} + 24 q^{57} - 20 q^{58} + 10 q^{59} + 14 q^{61} + 40 q^{62} + 6 q^{63} + 16 q^{64} + 4 q^{66} + 60 q^{68} - 32 q^{69} + 24 q^{71} + 68 q^{72} + 14 q^{73} - 48 q^{74} - 16 q^{76} + 44 q^{77} + 36 q^{78} - 16 q^{79} + 2 q^{81} - 48 q^{82} - 40 q^{83} + 24 q^{84} - 36 q^{86} - 24 q^{87} + 8 q^{88} + 12 q^{89} + 8 q^{92} - 28 q^{94} - 40 q^{96} - 18 q^{97} + 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 + 6 * q^17 + 24 * q^18 - 2 * q^19 - 16 * q^21 - 12 * q^22 + 2 * q^23 - 4 * q^24 - 16 * q^26 + 24 * q^27 - 40 * q^28 + 14 * q^29 - 20 * q^32 + 8 * q^33 + 28 * q^34 - 4 * q^36 - 24 * q^38 - 8 * q^42 - 44 * q^44 + 12 * q^46 - 38 * q^47 - 4 * q^48 + 8 * q^51 - 8 * q^52 - 12 * q^53 + 4 * q^54 + 20 * q^56 + 24 * q^57 - 20 * q^58 + 10 * q^59 + 14 * q^61 + 40 * q^62 + 6 * q^63 + 16 * q^64 + 4 * q^66 + 60 * q^68 - 32 * q^69 + 24 * q^71 + 68 * q^72 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 44 * q^77 + 36 * q^78 - 16 * q^79 + 2 * q^81 - 48 * q^82 - 40 * q^83 + 24 * q^84 - 36 * q^86 - 24 * q^87 + 8 * q^88 + 12 * q^89 + 8 * q^92 - 28 * q^94 - 40 * q^96 - 18 * q^97 + 56 * q^98 + 22 * q^99

Introduction

L-functions

Modular forms

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