LMFDB - Embedded newform 250.2.e.c.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(49,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.e (of order $10$, degree $4$, not 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			99.3
Root			$0.0566033 + 1.17421i$ of defining polynomial
Character	$\chi$	$=$	250.99
Dual form			250.2.e.c.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 - 0.309017i) q^{2} +(-1.74363 - 2.39991i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.39991 - 1.74363i) q^{6} -1.83337i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.79224 + 5.51595i) q^{9} +(-0.566541 - 1.74363i) q^{11} +(-2.82126 - 0.916683i) q^{12} +(-2.29951 - 0.747156i) q^{13} +(-0.566541 - 1.74363i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-1.63679 + 2.25284i) q^{17} +5.79981i q^{18} +(-1.35294 - 0.982966i) q^{19} +(-4.39991 + 3.19672i) q^{21} +(-1.07763 - 1.48322i) q^{22} +(7.38615 - 2.39991i) q^{23} -2.96645 q^{24} -2.41785 q^{26} +(7.89900 - 2.56654i) q^{27} +(-1.07763 - 1.48322i) q^{28} +(6.13597 - 4.45805i) q^{29} +(4.28304 + 3.11181i) q^{31} -1.00000i q^{32} +(-3.19672 + 4.39991i) q^{33} +(-0.860510 + 2.64838i) q^{34} +(1.79224 + 5.51595i) q^{36} +(1.25051 + 0.406315i) q^{37} +(-1.59047 - 0.516776i) q^{38} +(2.21640 + 6.82138i) q^{39} +(1.08621 - 3.34301i) q^{41} +(-3.19672 + 4.39991i) q^{42} -4.30550i q^{43} +(-1.48322 - 1.07763i) q^{44} +(6.28304 - 4.56489i) q^{46} +(1.07763 + 1.48322i) q^{47} +(-2.82126 + 0.916683i) q^{48} +3.63877 q^{49} +8.26057 q^{51} +(-2.29951 + 0.747156i) q^{52} +(3.83082 + 5.27267i) q^{53} +(6.71929 - 4.88185i) q^{54} +(-1.48322 - 1.07763i) q^{56} +4.96086i q^{57} +(4.45805 - 6.13597i) q^{58} +(2.79981 - 8.61694i) q^{59} +(0.799717 + 2.46127i) q^{61} +(5.03501 + 1.63597i) q^{62} +(10.1128 + 3.28583i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.68061 + 5.17240i) q^{66} +(-5.58402 + 7.68574i) q^{67} +2.78467i q^{68} +(-18.6383 - 13.5415i) q^{69} +(-0.247156 + 0.179569i) q^{71} +(3.40904 + 4.69215i) q^{72} +(-14.2164 + 4.61920i) q^{73} +1.31486 q^{74} -1.67232 q^{76} +(-3.19672 + 1.03868i) q^{77} +(4.21584 + 5.80261i) q^{78} +(-2.79981 + 2.03418i) q^{79} +(-5.85599 - 4.25462i) q^{81} -3.51505i q^{82} +(-3.74572 + 5.15555i) q^{83} +(-1.68061 + 5.17240i) q^{84} +(-1.33047 - 4.09478i) q^{86} +(-21.3978 - 6.95256i) q^{87} +(-1.74363 - 0.566541i) q^{88} +(1.02608 + 3.15794i) q^{89} +(-1.36981 + 4.21584i) q^{91} +(4.56489 - 6.28304i) q^{92} -15.7047i q^{93} +(1.48322 + 1.07763i) q^{94} +(-2.39991 + 1.74363i) q^{96} +(6.51864 + 8.97214i) q^{97} +(3.46068 - 1.12444i) q^{98} +10.6332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46}+ \cdots + 84 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	−1.74363	−	2.39991i	−1.00669	−	1.38559i	−0.921131	−	0.389254i	$-0.872733\pi$
$3$	−1.74363	−	2.39991i	−1.00669	−	1.38559i	−0.0855571	−	0.996333i	$-0.527267\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	−2.39991	−	1.74363i	−0.979758	−	0.711836i
$7$		−	1.83337i		−	0.692947i	−0.938060	−	0.346474i	$-0.887379\pi$
$7$		−	1.83337i		−	0.692947i	0.938060	−	0.346474i	$-0.112621\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.79224	+	5.51595i	−0.597414	+	1.83865i
$10$		0			0
$11$	−0.566541	−	1.74363i	−0.170819	−	0.525726i	0.828599	−	0.559842i	$-0.189138\pi$
$11$	−0.566541	−	1.74363i	−0.170819	−	0.525726i	−0.999418	+	0.0341166i	$0.989138\pi$
$12$	−2.82126	−	0.916683i	−0.814428	−	0.264624i
$13$	−2.29951	−	0.747156i	−0.637769	−	0.207224i	−0.0277557	−	0.999615i	$-0.508836\pi$
$13$	−2.29951	−	0.747156i	−0.637769	−	0.207224i	−0.610014	+	0.792391i	$0.708836\pi$
$14$	−0.566541	−	1.74363i	−0.151414	−	0.466006i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.63679	+	2.25284i	−0.396979	+	0.546395i	−0.959983	−	0.280060i	$-0.909646\pi$
$17$	−1.63679	+	2.25284i	−0.396979	+	0.546395i	0.563003	+	0.826455i	$0.309646\pi$
$18$			5.79981i			1.36703i
$19$	−1.35294	−	0.982966i	−0.310385	−	0.225508i	0.421677	−	0.906746i	$-0.361442\pi$
$19$	−1.35294	−	0.982966i	−0.310385	−	0.225508i	−0.732062	+	0.681238i	$0.761442\pi$
$20$		0			0
$21$	−4.39991	+	3.19672i	−0.960138	+	0.697581i
$22$	−1.07763	−	1.48322i	−0.229750	−	0.316224i
$23$	7.38615	−	2.39991i	1.54012	−	0.500415i	0.588710	−	0.808344i	$-0.299636\pi$
$23$	7.38615	−	2.39991i	1.54012	−	0.500415i	0.951409	+	0.307929i	$0.0996359\pi$
$24$	−2.96645			−0.605524
$25$		0			0
$26$	−2.41785			−0.474179
$27$	7.89900	−	2.56654i	1.52016	−	0.493931i
$28$	−1.07763	−	1.48322i	−0.203652	−	0.280303i
$29$	6.13597	−	4.45805i	1.13942	−	0.827838i	0.152383	−	0.988321i	$-0.451305\pi$
$29$	6.13597	−	4.45805i	1.13942	−	0.827838i	0.987039	+	0.160483i	$0.0513052\pi$
$30$		0			0
$31$	4.28304	+	3.11181i	0.769256	+	0.558897i	0.901735	−	0.432288i	$-0.142294\pi$
$31$	4.28304	+	3.11181i	0.769256	+	0.558897i	−0.132479	+	0.991186i	$0.542294\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.19672	+	4.39991i	−0.556477	+	0.765925i
$34$	−0.860510	+	2.64838i	−0.147576	+	0.454193i
$35$		0			0
$36$	1.79224	+	5.51595i	0.298707	+	0.919325i
$37$	1.25051	+	0.406315i	0.205582	+	0.0667977i	0.409998	−	0.912086i	$-0.365529\pi$
$37$	1.25051	+	0.406315i	0.205582	+	0.0667977i	−0.204416	+	0.978884i	$0.565529\pi$
$38$	−1.59047	−	0.516776i	−0.258009	−	0.0838321i
$39$	2.21640	+	6.82138i	0.354908	+	1.09229i
$40$		0			0
$41$	1.08621	−	3.34301i	0.169637	−	0.522090i	−0.829711	−	0.558194i	$-0.811495\pi$
$41$	1.08621	−	3.34301i	0.169637	−	0.522090i	0.999348	+	0.0361034i	$0.0114946\pi$
$42$	−3.19672	+	4.39991i	−0.493265	+	0.678920i
$43$		−	4.30550i		−	0.656583i	−0.944576	−	0.328291i	$-0.893527\pi$
$43$		−	4.30550i		−	0.656583i	0.944576	−	0.328291i	$-0.106473\pi$
$44$	−1.48322	−	1.07763i	−0.223604	−	0.162458i
$45$		0			0
$46$	6.28304	−	4.56489i	0.926383	−	0.673057i
$47$	1.07763	+	1.48322i	0.157188	+	0.216350i	0.880346	−	0.474332i	$-0.157310\pi$
$47$	1.07763	+	1.48322i	0.157188	+	0.216350i	−0.723158	+	0.690682i	$0.757310\pi$
$48$	−2.82126	+	0.916683i	−0.407214	+	0.132312i
$49$	3.63877			0.519824
$50$		0			0
$51$	8.26057			1.15671
$52$	−2.29951	+	0.747156i	−0.318885	+	0.103612i
$53$	3.83082	+	5.27267i	0.526203	+	0.724257i	0.986546	−	0.163485i	$-0.0522734\pi$
$53$	3.83082	+	5.27267i	0.526203	+	0.724257i	−0.460342	+	0.887741i	$0.652273\pi$
$54$	6.71929	−	4.88185i	0.914380	−	0.664336i
$55$		0			0
$56$	−1.48322	−	1.07763i	−0.198204	−	0.144004i
$57$			4.96086i			0.657082i
$58$	4.45805	−	6.13597i	0.585370	−	0.805693i
$59$	2.79981	−	8.61694i	0.364505	−	1.12183i	−0.585786	−	0.810466i	$-0.699214\pi$
$59$	2.79981	−	8.61694i	0.364505	−	1.12183i	0.950291	−	0.311364i	$-0.100786\pi$
$60$		0			0
$61$	0.799717	+	2.46127i	0.102393	+	0.315134i	0.989110	−	0.147180i	$-0.0470195\pi$
$61$	0.799717	+	2.46127i	0.102393	+	0.315134i	−0.886717	+	0.462313i	$0.847019\pi$
$62$	5.03501	+	1.63597i	0.639447	+	0.207769i
$63$	10.1128	+	3.28583i	1.27409	+	0.413976i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$		0			0
$66$	−1.68061	+	5.17240i	−0.206869	+	0.636679i
$67$	−5.58402	+	7.68574i	−0.682196	+	0.938963i	−0.999958	−	0.00920814i	$-0.997069\pi$
$67$	−5.58402	+	7.68574i	−0.682196	+	0.938963i	0.317761	+	0.948171i	$0.397069\pi$
$68$			2.78467i			0.337691i
$69$	−18.6383	−	13.5415i	−2.24379	−	1.63021i
$70$		0			0
$71$	−0.247156	+	0.179569i	−0.0293320	+	0.0213110i	−0.602355	−	0.798229i	$-0.705771\pi$
$71$	−0.247156	+	0.179569i	−0.0293320	+	0.0213110i	0.573023	+	0.819540i	$0.305771\pi$
$72$	3.40904	+	4.69215i	0.401760	+	0.552975i
$73$	−14.2164	+	4.61920i	−1.66391	+	0.540636i	−0.981685	−	0.190509i	$-0.938986\pi$
$73$	−14.2164	+	4.61920i	−1.66391	+	0.540636i	−0.682222	+	0.731145i	$0.738986\pi$
$74$	1.31486			0.152850
$75$		0			0
$76$	−1.67232			−0.191829
$77$	−3.19672	+	1.03868i	−0.364300	+	0.118368i
$78$	4.21584	+	5.80261i	0.477350	+	0.657016i
$79$	−2.79981	+	2.03418i	−0.315004	+	0.228864i	−0.734041	−	0.679106i	$-0.762368\pi$
$79$	−2.79981	+	2.03418i	−0.315004	+	0.228864i	0.419037	+	0.907969i	$0.362368\pi$
$80$		0			0
$81$	−5.85599	−	4.25462i	−0.650665	−	0.472736i
$82$		−	3.51505i		−	0.388172i
$83$	−3.74572	+	5.15555i	−0.411147	+	0.565895i	−0.963498	−	0.267717i	$-0.913731\pi$
$83$	−3.74572	+	5.15555i	−0.411147	+	0.565895i	0.552351	+	0.833612i	$0.313731\pi$
$84$	−1.68061	+	5.17240i	−0.183370	+	0.564355i
$85$		0			0
$86$	−1.33047	−	4.09478i	−0.143469	−	0.441551i
$87$	−21.3978	−	6.95256i	−2.29408	−	0.745393i
$88$	−1.74363	−	0.566541i	−0.185872	−	0.0603935i
$89$	1.02608	+	3.15794i	0.108764	+	0.334741i	0.990595	−	0.136824i	$-0.0436894\pi$
$89$	1.02608	+	3.15794i	0.108764	+	0.334741i	−0.881832	+	0.471565i	$0.843689\pi$
$90$		0			0
$91$	−1.36981	+	4.21584i	−0.143595	+	0.441940i
$92$	4.56489	−	6.28304i	0.475923	−	0.655052i
$93$		−	15.7047i		−	1.62851i
$94$	1.48322	+	1.07763i	0.152983	+	0.111149i
$95$		0			0
$96$	−2.39991	+	1.74363i	−0.244939	+	0.177959i
$97$	6.51864	+	8.97214i	0.661867	+	0.910982i	0.999541	−	0.0302807i	$-0.00964013\pi$
$97$	6.51864	+	8.97214i	0.661867	+	0.910982i	−0.337674	+	0.941263i	$0.609640\pi$
$98$	3.46068	−	1.12444i	0.349581	−	0.113586i
$99$	10.6332			1.06867
$100$		0			0
$101$	−13.1807			−1.31152			−0.655762	−	0.754968i	$-0.727653\pi$
$101$	−13.1807			−1.31152			−0.655762	+	0.754968i	$0.727653\pi$
$102$	7.85627	−	2.55266i	0.777887	−	0.252751i
$103$	1.54774	+	2.13029i	0.152504	+	0.209903i	0.878432	−	0.477867i	$-0.158590\pi$
$103$	1.54774	+	2.13029i	0.152504	+	0.209903i	−0.725929	+	0.687770i	$0.758590\pi$
$104$	−1.95608	+	1.42118i	−0.191809	+	0.139358i
$105$		0			0
$106$	5.27267	+	3.83082i	0.512127	+	0.372082i
$107$		−	18.8045i		−	1.81790i	−0.416908	−	0.908949i	$-0.636886\pi$
$107$		−	18.8045i		−	1.81790i	0.416908	−	0.908949i	$-0.363114\pi$
$108$	4.88185	−	6.71929i	0.469756	−	0.646564i
$109$	−3.18574	+	9.80470i	−0.305139	+	0.939120i	0.674487	+	0.738287i	$0.264365\pi$
$109$	−3.18574	+	9.80470i	−0.305139	+	0.939120i	−0.979625	+	0.200833i	$0.935635\pi$
$110$		0			0
$111$	−1.20531	−	3.70957i	−0.114403	−	0.352097i
$112$	−1.74363	−	0.566541i	−0.164758	−	0.0535331i
$113$	5.76019	+	1.87160i	0.541873	+	0.176065i	0.567149	−	0.823615i	$-0.308046\pi$
$113$	5.76019	+	1.87160i	0.541873	+	0.176065i	−0.0252760	+	0.999681i	$0.508046\pi$
$114$	1.53299	+	4.71806i	0.143578	+	0.441886i
$115$		0			0
$116$	2.34373	−	7.21327i	0.217610	−	0.669735i
$117$	8.24255	−	11.3449i	0.762024	−	1.04884i
$118$		−	9.06039i		−	0.834076i
$119$	4.13029	+	3.00083i	0.378623	+	0.275086i
$120$		0			0
$121$	6.17989	−	4.48996i	0.561809	−	0.408178i
$122$	1.52115	+	2.09369i	0.137719	+	0.189553i
$123$	−9.91686	+	3.22218i	−0.894174	+	0.290535i
$124$	5.29413			0.475427
$125$		0			0
$126$	10.6332			0.947279
$127$	0.316957	−	0.102986i	0.0281254	−	0.00913850i	−0.294921	−	0.955522i	$-0.595293\pi$
$127$	0.316957	−	0.102986i	0.0281254	−	0.00913850i	0.323046	+	0.946383i	$0.395293\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−10.3328	+	7.50722i	−0.909753	+	0.660974i
$130$		0			0
$131$	4.18910	+	3.04356i	0.366003	+	0.265917i	0.755552	−	0.655089i	$-0.227369\pi$
$131$	4.18910	+	3.04356i	0.366003	+	0.265917i	−0.389548	+	0.921006i	$0.627369\pi$
$132$			5.43858i			0.473368i
$133$	−1.80214	+	2.48043i	−0.156265	+	0.215080i
$134$	−2.93569	+	9.03513i	−0.253605	+	0.780516i
$135$		0			0
$136$	0.860510	+	2.64838i	0.0737881	+	0.227096i
$137$	18.5676	+	6.03299i	1.58634	+	0.515433i	0.963680	−	0.267060i	$-0.0860521\pi$
$137$	18.5676	+	6.03299i	1.58634	+	0.515433i	0.622660	+	0.782493i	$0.286052\pi$
$138$	−21.9106	−	7.11920i	−1.86516	−	0.606026i
$139$	2.45825	+	7.56572i	0.208506	+	0.641716i	0.999551	+	0.0299582i	$0.00953741\pi$
$139$	2.45825	+	7.56572i	0.208506	+	0.641716i	−0.791045	+	0.611758i	$0.790463\pi$
$140$		0			0
$141$	1.68061	−	5.17240i	0.141533	−	0.435595i
$142$	−0.179569	+	0.247156i	−0.0150691	+	0.0207409i
$143$			4.43280i			0.370689i
$144$	4.69215	+	3.40904i	0.391012	+	0.284087i
$145$		0			0
$146$	−12.0932	+	8.78624i	−1.00084	+	0.727154i
$147$	−6.34468	−	8.73271i	−0.523301	−	0.720262i
$148$	1.25051	−	0.406315i	0.102791	−	0.0333989i
$149$	1.67955			0.137594			0.0687969	−	0.997631i	$-0.478084\pi$
$149$	1.67955			0.137594			0.0687969	+	0.997631i	$0.478084\pi$
$150$		0			0
$151$	−21.2664			−1.73063			−0.865316	−	0.501227i	$-0.832882\pi$
$151$	−21.2664			−1.73063			−0.865316	+	0.501227i	$0.832882\pi$
$152$	−1.59047	+	0.516776i	−0.129004	+	0.0419161i
$153$	−9.49306	−	13.0661i	−0.767468	−	1.05633i
$154$	−2.71929	+	1.97568i	−0.219127	+	0.159205i
$155$		0			0
$156$	5.80261	+	4.21584i	0.464581	+	0.337538i
$157$		−	10.4514i		−	0.834113i	−0.908881	−	0.417056i	$-0.863062\pi$
$157$		−	10.4514i		−	0.834113i	0.908881	−	0.417056i	$-0.136938\pi$
$158$	−2.03418	+	2.79981i	−0.161831	+	0.222741i
$159$	5.97437	−	18.3872i	0.473798	−	1.45820i
$160$		0			0
$161$	−4.39991	−	13.5415i	−0.346761	−	1.06722i
$162$	−6.88413	−	2.23679i	−0.540868	−	0.175739i
$163$	9.90109	+	3.21706i	0.775513	+	0.251980i	0.669923	−	0.742430i	$-0.266327\pi$
$163$	9.90109	+	3.21706i	0.775513	+	0.251980i	0.105590	+	0.994410i	$0.466327\pi$
$164$	−1.08621	−	3.34301i	−0.0848187	−	0.261045i
$165$		0			0
$166$	−1.96924	+	6.06071i	−0.152843	+	0.470402i
$167$	−1.24711	+	1.71650i	−0.0965041	+	0.132826i	−0.854538	−	0.519388i	$-0.826160\pi$
$167$	−1.24711	+	1.71650i	−0.0965041	+	0.132826i	0.758034	+	0.652215i	$0.226160\pi$
$168$			5.43858i			0.419596i
$169$	−5.78772	−	4.20502i	−0.445209	−	0.323463i
$170$		0			0
$171$	7.84678	−	5.70102i	0.600059	−	0.435968i
$172$	−2.53071	−	3.48322i	−0.192965	−	0.265593i
$173$	17.2281	−	5.59774i	1.30983	−	0.425588i	0.430837	−	0.902430i	$-0.358218\pi$
$173$	17.2281	−	5.59774i	1.30983	−	0.425588i	0.878989	+	0.476841i	$0.158218\pi$
$174$	−22.4990			−1.70564
$175$		0			0
$176$	−1.83337			−0.138195
$177$	−25.5617	+	8.30550i	−1.92134	+	0.624280i
$178$	1.95171	+	2.68630i	0.146287	+	0.201347i
$179$	8.54361	−	6.20730i	0.638579	−	0.463955i	−0.220782	−	0.975323i	$-0.570861\pi$
$179$	8.54361	−	6.20730i	0.638579	−	0.463955i	0.859362	+	0.511368i	$0.170861\pi$
$180$		0			0
$181$	−14.6886	−	10.6719i	−1.09180	−	0.793237i	−0.112096	−	0.993697i	$-0.535756\pi$
$181$	−14.6886	−	10.6719i	−1.09180	−	0.793237i	−0.979702	+	0.200460i	$0.935756\pi$
$182$			4.43280i			0.328581i
$183$	4.51242	−	6.21081i	0.333567	−	0.459116i
$184$	2.39991	−	7.38615i	0.176923	−	0.544514i
$185$		0			0
$186$	−4.85303	−	14.9361i	−0.355842	−	1.09517i
$187$	4.85544	+	1.57763i	0.355065	+	0.115368i
$188$	1.74363	+	0.566541i	0.127168	+	0.0413193i
$189$	−4.70541	−	14.4818i	−0.342268	−	1.05339i
$190$		0			0
$191$	−6.76906	+	20.8330i	−0.489792	+	1.50742i	0.335127	+	0.942173i	$0.391221\pi$
$191$	−6.76906	+	20.8330i	−0.489792	+	1.50742i	−0.824919	+	0.565251i	$0.808779\pi$
$192$	−1.74363	+	2.39991i	−0.125836	+	0.173198i
$193$			27.4248i			1.97408i	0.160465	+	0.987041i	$0.448700\pi$
$193$			27.4248i			1.97408i	−0.160465	+	0.987041i	$0.551300\pi$
$194$	8.97214	+	6.51864i	0.644162	+	0.468011i
$195$		0			0
$196$	2.94383	−	2.13882i	0.210273	−	0.152773i
$197$	−0.660507	−	0.909110i	−0.0470592	−	0.0647714i	0.784839	−	0.619700i	$-0.212746\pi$
$197$	−0.660507	−	0.909110i	−0.0470592	−	0.0647714i	−0.831898	+	0.554928i	$0.812746\pi$
$198$	10.1128	−	3.28583i	0.718682	−	0.233514i
$199$	−25.4992			−1.80759			−0.903794	−	0.427968i	$-0.859230\pi$
$199$	−25.4992			−1.80759			−0.903794	+	0.427968i	$0.859230\pi$
$200$		0			0
$201$	28.1815			1.98777
$202$	−12.5355	+	4.07305i	−0.881998	+	0.286579i
$203$	−8.17323	−	11.2495i	−0.573648	−	0.789559i
$204$	6.68294	−	4.85544i	0.467900	−	0.339949i
$205$		0			0
$206$	2.13029	+	1.54774i	0.148424	+	0.107836i
$207$			45.0429i			3.13070i
$208$	−1.42118	+	1.95608i	−0.0985408	+	0.135630i
$209$	−0.947439	+	2.91592i	−0.0655358	+	0.201698i
$210$		0			0
$211$	6.58341	+	20.2617i	0.453221	+	1.39487i	0.873211	+	0.487342i	$0.162033\pi$
$211$	6.58341	+	20.2617i	0.453221	+	1.39487i	−0.419990	+	0.907529i	$0.637967\pi$
$212$	6.19839	+	2.01398i	0.425708	+	0.138321i
$213$	0.861899	+	0.280048i	0.0590564	+	0.0191886i
$214$	−5.81090	−	17.8841i	−0.397225	−	1.22253i
$215$		0			0
$216$	2.56654	−	7.89900i	0.174631	−	0.537459i
$217$	5.70508	−	7.85237i	0.387286	−	0.533054i
$218$			10.3093i			0.698232i
$219$	35.8739	+	26.0639i	2.42413	+	1.76124i
$220$		0			0
$221$	5.44703	−	3.95750i	0.366407	−	0.266210i
$222$	−2.29264	−	3.15555i	−0.153872	−	0.211786i
$223$	−3.08629	+	1.00280i	−0.206673	+	0.0671522i	−0.410524	−	0.911850i	$-0.634654\pi$
$223$	−3.08629	+	1.00280i	−0.206673	+	0.0671522i	0.203851	+	0.979002i	$0.434654\pi$
$224$	−1.83337			−0.122497
$225$		0			0
$226$	6.05662			0.402880
$227$	15.5757	−	5.06085i	1.03380	−	0.335901i	0.257506	−	0.966277i	$-0.417099\pi$
$227$	15.5757	−	5.06085i	1.03380	−	0.335901i	0.776290	+	0.630376i	$0.217099\pi$
$228$	2.91592	+	4.01342i	0.193111	+	0.265795i
$229$	−4.11788	+	2.99181i	−0.272117	+	0.197705i	−0.715472	−	0.698642i	$-0.753788\pi$
$229$	−4.11788	+	2.99181i	−0.272117	+	0.197705i	0.443355	+	0.896346i	$0.353788\pi$
$230$		0			0
$231$	8.06664	+	5.86076i	0.530746	+	0.385609i
$232$		−	7.58448i		−	0.497946i
$233$	−0.977464	+	1.34536i	−0.0640358	+	0.0881378i	−0.839834	−	0.542844i	$-0.817348\pi$
$233$	−0.977464	+	1.34536i	−0.0640358	+	0.0881378i	0.775798	+	0.630981i	$0.217348\pi$
$234$	4.33337	−	13.3367i	0.283281	−	0.871849i
$235$		0			0
$236$	−2.79981	−	8.61694i	−0.182252	−	0.560915i
$237$	9.76370	+	3.17242i	0.634221	+	0.206071i
$238$	4.85544	+	1.57763i	0.314732	+	0.102263i
$239$	−3.95536	−	12.1733i	−0.255851	−	0.787428i	−0.993661	−	0.112420i	$-0.964140\pi$
$239$	−3.95536	−	12.1733i	−0.255851	−	0.787428i	0.737810	−	0.675009i	$-0.235860\pi$
$240$		0			0
$241$	0.122209	−	0.376121i	0.00787219	−	0.0242281i	−0.947043	−	0.321106i	$-0.895945\pi$
$241$	0.122209	−	0.376121i	0.00787219	−	0.0242281i	0.954915	+	0.296878i	$0.0959454\pi$
$242$	4.48996	−	6.17989i	0.288625	−	0.397259i
$243$		−	3.44417i		−	0.220944i
$244$	2.09369	+	1.52115i	0.134034	+	0.0973817i
$245$		0			0
$246$	−8.43579	+	6.12896i	−0.537846	+	0.390768i
$247$	2.37666	+	3.27120i	0.151223	+	0.208141i
$248$	5.03501	−	1.63597i	0.319724	−	0.103885i
$249$	18.9040			1.19799
$250$		0			0
$251$	9.36589			0.591170			0.295585	−	0.955316i	$-0.404485\pi$
$251$	9.36589			0.591170			0.295585	+	0.955316i	$0.404485\pi$
$252$	10.1128	−	3.28583i	0.637044	−	0.206988i
$253$	−8.36912	−	11.5191i	−0.526162	−	0.724200i
$254$	0.269620	−	0.195890i	0.0169175	−	0.0122913i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			4.97926i			0.310598i	0.987868	+	0.155299i	$0.0496341\pi$
$257$			4.97926i			0.310598i	−0.987868	+	0.155299i	$0.950366\pi$
$258$	−7.50722	+	10.3328i	−0.467379	+	0.643292i
$259$	0.744923	−	2.29264i	0.0462873	−	0.142458i
$260$		0			0
$261$	13.5932	+	41.8356i	0.841399	+	2.58956i
$262$	4.92458	+	1.60009i	0.304242	+	0.0988541i
$263$	−18.8416	−	6.12199i	−1.16182	−	0.377498i	−0.336236	−	0.941778i	$-0.609154\pi$
$263$	−18.8416	−	6.12199i	−1.16182	−	0.377498i	−0.825584	+	0.564279i	$0.809154\pi$
$264$	1.68061	+	5.17240i	0.103435	+	0.318339i
$265$		0			0
$266$	−0.947439	+	2.91592i	−0.0580912	+	0.178786i
$267$	5.78966	−	7.96878i	0.354321	−	0.487681i
$268$			9.50010i			0.580311i
$269$	11.9685	+	8.69564i	0.729734	+	0.530183i	0.889479	−	0.456976i	$-0.151067\pi$
$269$	11.9685	+	8.69564i	0.729734	+	0.530183i	−0.159745	+	0.987158i	$0.551067\pi$
$270$		0			0
$271$	10.1583	−	7.38047i	0.617075	−	0.448331i	−0.234823	−	0.972038i	$-0.575451\pi$
$271$	10.1583	−	7.38047i	0.617075	−	0.448331i	0.851899	+	0.523707i	$0.175451\pi$
$272$	1.63679	+	2.25284i	0.0992448	+	0.136599i
$273$	12.5061	−	4.06347i	0.756902	−	0.245932i
$274$	19.5232			1.17944
$275$		0			0
$276$	−23.0382			−1.38674
$277$	−6.02193	+	1.95664i	−0.361823	+	0.117563i	−0.484286	−	0.874910i	$-0.660921\pi$
$277$	−6.02193	+	1.95664i	−0.361823	+	0.117563i	0.122463	+	0.992473i	$0.460921\pi$
$278$	4.67587	+	6.43579i	0.280440	+	0.385993i
$279$	−24.8408	+	18.0479i	−1.48718	+	1.08050i
$280$		0			0
$281$	16.2525	+	11.8082i	0.969545	+	0.704416i	0.955348	−	0.295484i	$-0.0954808\pi$
$281$	16.2525	+	11.8082i	0.969545	+	0.704416i	0.0141971	+	0.999899i	$0.495481\pi$
$282$		−	5.43858i		−	0.323863i
$283$	1.06788	−	1.46981i	0.0634787	−	0.0873709i	−0.776097	−	0.630613i	$-0.782803\pi$
$283$	1.06788	−	1.46981i	0.0634787	−	0.0873709i	0.839576	+	0.543242i	$0.182803\pi$
$284$	−0.0944052	+	0.290549i	−0.00560192	+	0.0172409i
$285$		0			0
$286$	1.36981	+	4.21584i	0.0809986	+	0.249288i
$287$	−6.12896	−	1.99142i	−0.361781	−	0.117550i
$288$	5.51595	+	1.79224i	0.325031	+	0.105609i
$289$	2.85705	+	8.79311i	0.168062	+	0.517242i
$290$		0			0
$291$	10.1662	−	31.2882i	0.595951	−	1.83415i
$292$	−8.78624	+	12.0932i	−0.514176	+	0.707702i
$293$		−	6.85931i		−	0.400725i	−0.979722	−	0.200363i	$-0.935788\pi$
$293$		−	6.85931i		−	0.400725i	0.979722	−	0.200363i	$-0.0642120\pi$
$294$	−8.73271	−	6.34468i	−0.509302	−	0.370030i
$295$		0			0
$296$	1.06375	−	0.772856i	0.0618290	−	0.0449214i
$297$	−8.95022	−	12.3189i	−0.519344	−	0.714816i
$298$	1.59734	−	0.519009i	0.0925317	−	0.0300654i
$299$	−18.7776			−1.08594
$300$		0			0
$301$	−7.89356			−0.454977
$302$	−20.2255	+	6.57167i	−1.16385	+	0.378157i
$303$	22.9822	+	31.6323i	1.32030	+	1.81723i
$304$	−1.35294	+	0.982966i	−0.0775963	+	0.0563770i
$305$		0			0
$306$	−13.0661	−	9.49306i	−0.746938	−	0.542682i
$307$			2.89526i			0.165241i	0.996581	+	0.0826206i	$0.0263290\pi$
$307$			2.89526i			0.165241i	−0.996581	+	0.0826206i	$0.973671\pi$
$308$	−1.97568	+	2.71929i	−0.112575	+	0.154946i
$309$	2.41379	−	7.42888i	0.137316	−	0.422614i
$310$		0			0
$311$	−6.38090	−	19.6384i	−0.361828	−	1.11359i	−0.951944	−	0.306272i	$-0.900918\pi$
$311$	−6.38090	−	19.6384i	−0.361828	−	1.11359i	0.590116	−	0.807318i	$-0.299082\pi$
$312$	6.82138	+	2.21640i	0.386184	+	0.125479i
$313$	15.6232	+	5.07629i	0.883076	+	0.286929i	0.715234	−	0.698885i	$-0.246320\pi$
$313$	15.6232	+	5.07629i	0.883076	+	0.286929i	0.167842	+	0.985814i	$0.446320\pi$
$314$	−3.22966	−	9.93987i	−0.182260	−	0.560939i
$315$		0			0
$316$	−1.06943	+	3.29138i	−0.0601603	+	0.185154i
$317$	−9.70191	+	13.3535i	−0.544914	+	0.750009i	−0.989311	−	0.145820i	$-0.953418\pi$
$317$	−9.70191	+	13.3535i	−0.544914	+	0.750009i	0.444397	+	0.895830i	$0.353418\pi$
$318$		−	19.3335i		−	1.08417i
$319$	−11.2495	−	8.17323i	−0.629850	−	0.457613i
$320$		0			0
$321$	−45.1290	+	32.7881i	−2.51885	+	1.83005i
$322$	−8.36912	−	11.5191i	−0.466393	−	0.641935i
$323$	4.42894	−	1.43905i	0.246433	−	0.0800709i
$324$	−7.23840			−0.402133
$325$		0			0
$326$	10.4106			0.576591
$327$	29.0851	−	9.45033i	1.60841	−	0.522605i
$328$	−2.06609	−	2.84373i	−0.114081	−	0.157019i
$329$	2.71929	−	1.97568i	0.149919	−	0.108923i
$330$		0			0
$331$	−22.2245	−	16.1471i	−1.22157	−	0.887522i	−0.225340	−	0.974280i	$-0.572349\pi$
$331$	−22.2245	−	16.1471i	−1.22157	−	0.887522i	−0.996229	+	0.0867577i	$0.972349\pi$
$332$			6.37261i			0.349742i
$333$	−4.48242	+	6.16953i	−0.245635	+	0.338088i
$334$	−0.655643	+	2.01786i	−0.0358752	+	0.110413i
$335$		0			0
$336$	1.68061	+	5.17240i	0.0916851	+	0.282178i
$337$	2.61085	+	0.848317i	0.142222	+	0.0462108i	0.379263	−	0.925289i	$-0.376178\pi$
$337$	2.61085	+	0.848317i	0.142222	+	0.0462108i	−0.237041	+	0.971500i	$0.576178\pi$
$338$	−6.80387	−	2.21071i	−0.370082	−	0.120247i
$339$	−5.55200	−	17.0873i	−0.301543	−	0.928054i
$340$		0			0
$341$	2.99934	−	9.23102i	0.162423	−	0.499888i
$342$	5.70102	−	7.84678i	0.308276	−	0.424305i
$343$		−	19.5048i		−	1.05316i
$344$	−3.48322	−	2.53071i	−0.187803	−	0.136447i
$345$		0			0
$346$	14.6551	−	10.6475i	0.787862	−	0.572415i
$347$	−12.5428	−	17.2637i	−0.673332	−	0.926762i	0.326498	−	0.945198i	$-0.394131\pi$
$347$	−12.5428	−	17.2637i	−0.673332	−	0.926762i	−0.999830	+	0.0184361i	$0.994131\pi$
$348$	−21.3978	+	6.95256i	−1.14704	+	0.372697i
$349$	16.7650			0.897411			0.448705	−	0.893680i	$-0.351885\pi$
$349$	16.7650			0.897411			0.448705	+	0.893680i	$0.351885\pi$
$350$		0			0
$351$	−20.0814			−1.07187
$352$	−1.74363	+	0.566541i	−0.0929360	+	0.0301967i
$353$	−1.75667	−	2.41785i	−0.0934981	−	0.128689i	0.759705	−	0.650268i	$-0.225343\pi$
$353$	−1.75667	−	2.41785i	−0.0934981	−	0.128689i	−0.853203	+	0.521579i	$0.825343\pi$
$354$	−21.7441	+	15.7980i	−1.15569	+	0.839654i
$355$		0			0
$356$	2.68630	+	1.95171i	0.142374	+	0.103441i
$357$		−	15.1447i		−	0.801540i
$358$	6.20730	−	8.54361i	0.328066	−	0.451544i
$359$	−2.07194	+	6.37678i	−0.109353	+	0.336554i	−0.990727	−	0.135865i	$-0.956619\pi$
$359$	−2.07194	+	6.37678i	−0.109353	+	0.336554i	0.881375	+	0.472418i	$0.156619\pi$
$360$		0			0
$361$	−5.00711	−	15.4103i	−0.263532	−	0.811068i
$362$	−17.2675	−	5.61056i	−0.907561	−	0.294884i
$363$	−21.5510	−	7.00233i	−1.13113	−	0.367527i
$364$	1.36981	+	4.21584i	0.0717976	+	0.220970i
$365$		0			0
$366$	2.37232	−	7.30124i	0.124003	−	0.381642i
$367$	−2.36089	+	3.24949i	−0.123237	+	0.169622i	−0.866178	−	0.499736i	$-0.833430\pi$
$367$	−2.36089	+	3.24949i	−0.123237	+	0.169622i	0.742941	+	0.669357i	$0.233430\pi$
$368$		−	7.76626i		−	0.404844i
$369$	16.4931	+	11.9830i	0.858598	+	0.623808i
$370$		0			0
$371$	9.66673	−	7.02329i	0.501872	−	0.364631i
$372$	−9.23102	−	12.7054i	−0.478606	−	0.658745i
$373$	−25.2822	+	8.21467i	−1.30906	+	0.425340i	−0.878725	−	0.477329i	$-0.841605\pi$
$373$	−25.2822	+	8.21467i	−1.30906	+	0.425340i	−0.430336	+	0.902669i	$0.641605\pi$
$374$	5.10532			0.263990
$375$		0			0
$376$	1.83337			0.0945486
$377$	−17.4406	+	5.66679i	−0.898236	+	0.291855i
$378$	−8.95022	−	12.3189i	−0.460350	−	0.633617i
$379$	−12.6431	+	9.18578i	−0.649435	+	0.471842i	−0.863079	−	0.505070i	$-0.831467\pi$
$379$	−12.6431	+	9.18578i	−0.649435	+	0.471842i	0.213644	+	0.976912i	$0.431467\pi$
$380$		0			0
$381$	−0.799814	−	0.581099i	−0.0409757	−	0.0297706i
$382$			21.9051i			1.12076i
$383$	7.90306	−	10.8776i	0.403828	−	0.555821i	−0.557872	−	0.829927i	$-0.688382\pi$
$383$	7.90306	−	10.8776i	0.403828	−	0.555821i	0.961699	+	0.274106i	$0.0883819\pi$
$384$	−0.916683	+	2.82126i	−0.0467793	+	0.143972i
$385$		0			0
$386$	8.47474	+	26.0826i	0.431353	+	1.32757i
$387$	23.7489	+	7.71650i	1.20723	+	0.392252i
$388$	10.5474	+	3.42705i	0.535462	+	0.173982i
$389$	7.75991	+	23.8826i	0.393443	+	1.21089i	0.930167	+	0.367136i	$0.119662\pi$
$389$	7.75991	+	23.8826i	0.393443	+	1.21089i	−0.536724	+	0.843758i	$0.680338\pi$
$390$		0			0
$391$	−6.68294	+	20.5680i	−0.337971	+	1.04017i
$392$	2.13882	−	2.94383i	0.108026	−	0.148686i
$393$		−	15.3603i		−	0.774825i
$394$	−0.909110	−	0.660507i	−0.0458003	−	0.0332759i
$395$		0			0
$396$	8.60242	−	6.25003i	0.432288	−	0.314076i
$397$	2.06794	+	2.84628i	0.103787	+	0.142850i	0.857751	−	0.514065i	$-0.171861\pi$
$397$	2.06794	+	2.84628i	0.103787	+	0.142850i	−0.753964	+	0.656915i	$0.771861\pi$
$398$	−24.2511	+	7.87968i	−1.21560	+	0.394972i
$399$	9.09507			0.455323
$400$		0			0
$401$	29.8696			1.49161			0.745807	−	0.666162i	$-0.232064\pi$
$401$	29.8696			1.49161			0.745807	+	0.666162i	$0.232064\pi$
$402$	26.8022	−	8.70858i	1.33677	−	0.434344i
$403$	−7.52388	−	10.3557i	−0.374791	−	0.515856i
$404$	−10.6634	+	7.74739i	−0.530523	+	0.385447i
$405$		0			0
$406$	−11.2495	−	8.17323i	−0.558303	−	0.405631i
$407$		−	2.41062i		−	0.119490i
$408$	4.85544	−	6.68294i	0.240380	−	0.330855i
$409$	11.9784	−	36.8656i	0.592291	−	1.82289i	0.0245200	−	0.999699i	$-0.492194\pi$
$409$	11.9784	−	36.8656i	0.592291	−	1.82289i	0.567771	−	0.823186i	$-0.307806\pi$
$410$		0			0
$411$	−17.8965	−	55.0799i	−0.882772	−	2.71689i
$412$	2.50430	+	0.813697i	0.123378	+	0.0400880i
$413$	−15.7980	−	5.13308i	−0.777369	−	0.252582i
$414$	13.9190	+	42.8383i	0.684082	+	2.10539i
$415$		0			0
$416$	−0.747156	+	2.29951i	−0.0366323	+	0.112743i
$417$	13.8707	−	19.0914i	0.679253	−	0.934911i
$418$			3.06598i			0.149962i
$419$	−15.2988	−	11.1152i	−0.747395	−	0.543014i	0.147624	−	0.989044i	$-0.452838\pi$
$419$	−15.2988	−	11.1152i	−0.747395	−	0.543014i	−0.895018	+	0.446030i	$0.852838\pi$
$420$		0			0
$421$	17.8414	−	12.9625i	0.869536	−	0.631755i	−0.0609265	−	0.998142i	$-0.519406\pi$
$421$	17.8414	−	12.9625i	0.869536	−	0.631755i	0.930462	+	0.366388i	$0.119406\pi$
$422$	12.5224	+	17.2356i	0.609581	+	0.839016i
$423$	−10.1128	+	3.28583i	−0.491699	+	0.159763i
$424$	6.51738			0.316512
$425$		0			0
$426$	0.906255			0.0439082
$427$	4.51242	−	1.46617i	0.218371	−	0.0709531i
$428$	−11.0530	−	15.2131i	−0.534267	−	0.735355i
$429$	10.6383	−	7.72918i	0.513622	−	0.373168i
$430$		0			0
$431$	7.44763	+	5.41102i	0.358740	+	0.260640i	0.752526	−	0.658562i	$-0.228835\pi$
$431$	7.44763	+	5.41102i	0.358740	+	0.260640i	−0.393787	+	0.919202i	$0.628835\pi$
$432$		−	8.30550i		−	0.399599i
$433$	20.4533	−	28.1516i	0.982923	−	1.35288i	0.0476837	−	0.998862i	$-0.484816\pi$
$433$	20.4533	−	28.1516i	0.982923	−	1.35288i	0.935240	−	0.354015i	$-0.115184\pi$
$434$	2.99934	−	9.23102i	0.143973	−	0.443103i
$435$		0			0
$436$	3.18574	+	9.80470i	0.152569	+	0.469560i
$437$	−12.3520	−	4.01342i	−0.590878	−	0.191988i
$438$	42.1723	+	13.7026i	2.01507	+	0.654736i
$439$	2.58025	+	7.94118i	0.123148	+	0.379012i	0.993559	−	0.113314i	$-0.0361467\pi$
$439$	2.58025	+	7.94118i	0.123148	+	0.379012i	−0.870411	+	0.492326i	$0.836147\pi$
$440$		0			0
$441$	−6.52155	+	20.0713i	−0.310550	+	0.955775i
$442$	3.95750	−	5.44703i	0.188239	−	0.259089i
$443$		−	1.19887i		−	0.0569599i	−0.999594	−	0.0284799i	$-0.990933\pi$
$443$		−	1.19887i		−	0.0569599i	0.999594	−	0.0284799i	$-0.00906667\pi$
$444$	−3.15555	−	2.29264i	−0.149756	−	0.108804i
$445$		0			0
$446$	−2.62535	+	1.90743i	−0.124314	+	0.0903194i
$447$	−2.92852	−	4.03076i	−0.138514	−	0.190648i
$448$	−1.74363	+	0.566541i	−0.0823790	+	0.0267666i
$449$	−32.7953			−1.54771			−0.773853	−	0.633365i	$-0.781673\pi$
$449$	−32.7953			−1.54771			−0.773853	+	0.633365i	$0.781673\pi$
$450$		0			0
$451$	−6.44437			−0.303453
$452$	5.76019	−	1.87160i	0.270936	−	0.0880326i
$453$	37.0808	+	51.0373i	1.74221	+	2.39794i
$454$	13.2495	−	9.62631i	0.621829	−	0.451785i
$455$		0			0
$456$	4.01342	+	2.91592i	0.187946	+	0.136550i
$457$		−	19.7884i		−	0.925664i	−0.886446	−	0.462832i	$-0.846833\pi$
$457$		−	19.7884i		−	0.925664i	0.886446	−	0.462832i	$-0.153167\pi$
$458$	−2.99181	+	4.11788i	−0.139798	+	0.192416i
$459$	−7.14697	+	21.9961i	−0.333592	+	1.02669i
$460$		0			0
$461$	2.90468	+	8.93970i	0.135285	+	0.416363i	0.995634	−	0.0933412i	$-0.0297547\pi$
$461$	2.90468	+	8.93970i	0.135285	+	0.416363i	−0.860350	+	0.509704i	$0.829755\pi$
$462$	9.48290	+	3.08118i	0.441185	+	0.143350i
$463$	16.8650	+	5.47977i	0.783783	+	0.254666i	0.673454	−	0.739229i	$-0.264810\pi$
$463$	16.8650	+	5.47977i	0.783783	+	0.254666i	0.110328	+	0.993895i	$0.464810\pi$
$464$	−2.34373	−	7.21327i	−0.108805	−	0.334868i
$465$		0			0
$466$	−0.513883	+	1.58157i	−0.0238052	+	0.0732649i
$467$	−12.8494	+	17.6857i	−0.594601	+	0.818398i	−0.995201	−	0.0978549i	$-0.968802\pi$
$467$	−12.8494	+	17.6857i	−0.594601	+	0.818398i	0.400599	+	0.916253i	$0.368802\pi$
$468$		−	14.0231i		−	0.648216i
$469$	14.0908	+	10.2375i	0.650651	+	0.472726i
$470$		0			0
$471$	−25.0824	+	18.2234i	−1.15574	+	0.839691i
$472$	−5.32556	−	7.33001i	−0.245129	−	0.337391i
$473$	−7.50722	+	2.43924i	−0.345182	+	0.112157i
$474$	10.2662			0.471541
$475$		0			0
$476$	5.10532			0.234002
$477$	−35.9495	+	11.6807i	−1.64602	+	0.534823i
$478$	−7.52354	−	10.3553i	−0.344119	−	0.473639i
$479$	−4.94352	+	3.59168i	−0.225875	+	0.164108i	−0.694967	−	0.719041i	$-0.744581\pi$
$479$	−4.94352	+	3.59168i	−0.225875	+	0.164108i	0.469092	+	0.883149i	$0.344581\pi$
$480$		0			0
$481$	−2.57198	−	1.86865i	−0.117272	−	0.0852031i
$482$		−	0.395477i		−	0.0180135i
$483$	−24.8266	+	34.1708i	−1.12965	+	1.55483i
$484$	2.36051	−	7.26490i	0.107296	−	0.330223i
$485$		0			0
$486$	−1.06431	−	3.27560i	−0.0482780	−	0.148584i
$487$	−4.81415	−	1.56421i	−0.218150	−	0.0708812i	0.197903	−	0.980222i	$-0.436587\pi$
$487$	−4.81415	−	1.56421i	−0.218150	−	0.0708812i	−0.416053	+	0.909340i	$0.636587\pi$
$488$	2.46127	+	0.799717i	0.111417	+	0.0362015i
$489$	−9.54324	−	29.3711i	−0.431560	−	1.32821i
$490$		0			0
$491$	0.736165	−	2.26568i	0.0332227	−	0.102249i	−0.933070	−	0.359695i	$-0.882881\pi$
$491$	0.736165	−	2.26568i	0.0332227	−	0.102249i	0.966293	+	0.257446i	$0.0828809\pi$
$492$	−6.12896	+	8.43579i	−0.276315	+	0.380315i
$493$			21.1203i			0.951209i
$494$	3.27120	+	2.37666i	0.147178	+	0.106931i
$495$		0			0
$496$	4.28304	−	3.11181i	0.192314	−	0.139724i
$497$	0.329216	+	0.453127i	0.0147674	+	0.0203255i
$498$	17.9788	−	5.84166i	0.805648	−	0.261771i
$499$	0.0503313			0.00225314			0.00112657	−	0.999999i	$-0.499641\pi$
$499$	0.0503313			0.00225314			0.00112657	+	0.999999i	$0.499641\pi$
$500$		0			0
$501$	6.29393			0.281192
$502$	8.90749	−	2.89422i	0.397561	−	0.129175i
$503$	3.18040	+	4.37744i	0.141807	+	0.195181i	0.874013	−	0.485903i	$-0.161509\pi$
$503$	3.18040	+	4.37744i	0.141807	+	0.195181i	−0.732206	+	0.681083i	$0.761509\pi$
$504$	8.60242	−	6.25003i	0.383182	−	0.278398i
$505$		0			0
$506$	−11.5191	−	8.36912i	−0.512087	−	0.372053i
$507$			21.2220i			0.942502i
$508$	0.195890	−	0.269620i	0.00869123	−	0.0119625i
$509$	−5.85472	+	18.0190i	−0.259506	+	0.798678i	0.733402	+	0.679795i	$0.237931\pi$
$509$	−5.85472	+	18.0190i	−0.259506	+	0.798678i	−0.992908	+	0.118883i	$0.962069\pi$
$510$		0			0
$511$	8.46868	+	26.0639i	0.374632	+	1.15300i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−13.2097	−	4.29208i	−0.583221	−	0.189500i
$514$	1.53868	+	4.73556i	0.0678681	+	0.208877i
$515$		0			0
$516$	−3.94678	+	12.1469i	−0.173747	+	0.534739i
$517$	1.97568	−	2.71929i	0.0868904	−	0.119594i
$518$		−	2.41062i		−	0.105917i
$519$	−43.4735	−	31.5854i	−1.90828	−	1.38644i
$520$		0			0
$521$	−31.0817	+	22.5822i	−1.36171	+	0.989342i	−0.363379	+	0.931642i	$0.618377\pi$
$521$	−31.0817	+	22.5822i	−1.36171	+	0.989342i	−0.998334	+	0.0577005i	$0.981623\pi$
$522$	25.8558	+	35.5875i	1.13168	+	1.55762i
$523$	11.6662	−	3.79057i	0.510127	−	0.165750i	−0.0426332	−	0.999091i	$-0.513575\pi$
$523$	11.6662	−	3.79057i	0.510127	−	0.165750i	0.552760	+	0.833341i	$0.313575\pi$
$524$	5.17801			0.226202
$525$		0			0
$526$	−19.8112			−0.863809
$527$	−14.0208	+	4.55565i	−0.610757	+	0.198447i
$528$	3.19672	+	4.39991i	0.139119	+	0.191481i
$529$	30.1883	−	21.9331i	1.31254	−	0.953613i
$530$		0			0
$531$	42.5127	+	30.8873i	1.84489	+	1.34039i
$532$			3.06598i			0.132927i
$533$	−4.99550	+	6.87572i	−0.216379	+	0.297820i
$534$	3.04380	−	9.36786i	0.131718	−	0.405387i
$535$		0			0
$536$	2.93569	+	9.03513i	0.126803	+	0.390258i
$537$	−29.7939	−	9.68061i	−1.28570	−	0.417749i
$538$	14.0698	+	4.57157i	0.606594	+	0.197094i
$539$	−2.06151	−	6.34468i	−0.0887957	−	0.273285i
$540$		0			0
$541$	12.9872	−	39.9704i	0.558362	−	1.71846i	−0.128534	−	0.991705i	$-0.541027\pi$
$541$	12.9872	−	39.9704i	0.558362	−	1.71846i	0.686896	−	0.726756i	$-0.258973\pi$
$542$	7.38047	−	10.1583i	0.317018	−	0.436338i
$543$			53.8593i			2.31132i
$544$	2.25284	+	1.63679i	0.0965899	+	0.0701767i
$545$		0			0
$546$	10.6383	−	7.72918i	0.455277	−	0.330778i
$547$	11.3863	+	15.6719i	0.486842	+	0.670080i	0.979802	−	0.199972i	$-0.0640851\pi$
$547$	11.3863	+	15.6719i	0.486842	+	0.670080i	−0.492960	+	0.870052i	$0.664085\pi$
$548$	18.5676	−	6.03299i	0.793170	−	0.257717i
$549$	−15.0096			−0.640592
$550$		0			0
$551$	−12.6837			−0.540344
$552$	−21.9106	+	7.11920i	−0.932579	+	0.303013i
$553$	3.72940	+	5.13308i	0.158590	+	0.218281i
$554$	−5.12256	+	3.72176i	−0.217637	+	0.158122i
$555$		0			0
$556$	6.43579	+	4.67587i	0.272938	+	0.198301i
$557$		−	8.54685i		−	0.362142i	−0.983470	−	0.181071i	$-0.942044\pi$
$557$		−	8.54685i		−	0.362142i	0.983470	−	0.181071i	$-0.0579563\pi$
$558$	−18.0479	+	24.8408i	−0.764029	+	1.05160i
$559$	−3.21688	+	9.90054i	−0.136060	+	0.418748i
$560$		0			0
$561$	−4.67995	−	14.4034i	−0.197588	−	0.608113i
$562$	19.1060	+	6.20792i	0.805938	+	0.261865i
$563$	−22.3116	−	7.24949i	−0.940323	−	0.305529i	−0.201546	−	0.979479i	$-0.564596\pi$
$563$	−22.3116	−	7.24949i	−0.940323	−	0.305529i	−0.738777	+	0.673950i	$0.764596\pi$
$564$	−1.68061	−	5.17240i	−0.0707667	−	0.217797i
$565$		0			0
$566$	0.561416	−	1.72786i	0.0235981	−	0.0726274i
$567$	−7.80028	+	10.7362i	−0.327581	+	0.450877i
$568$			0.305502i			0.0128186i
$569$	−5.74445	−	4.17359i	−0.240820	−	0.174966i	0.460829	−	0.887489i	$-0.347552\pi$
$569$	−5.74445	−	4.17359i	−0.240820	−	0.174966i	−0.701649	+	0.712523i	$0.747552\pi$
$570$		0			0
$571$	9.67745	−	7.03108i	0.404989	−	0.294241i	−0.366581	−	0.930386i	$-0.619472\pi$
$571$	9.67745	−	7.03108i	0.404989	−	0.294241i	0.771570	+	0.636145i	$0.219472\pi$
$572$	2.60553	+	3.58621i	0.108943	+	0.149947i
$573$	61.8001	−	20.0801i	2.58173	−	0.838856i
$574$	−6.44437			−0.268983
$575$		0			0
$576$	5.79981			0.241659
$577$	39.5350	−	12.8457i	1.64587	−	0.534774i	0.668027	−	0.744137i	$-0.267139\pi$
$577$	39.5350	−	12.8457i	1.64587	−	0.534774i	0.977838	+	0.209362i	$0.0671389\pi$
$578$	5.43444	+	7.47987i	0.226043	+	0.311121i
$579$	65.8171	−	47.8189i	2.73526	−	1.98729i
$580$		0			0
$581$	9.45200	+	6.86728i	0.392135	+	0.284903i
$582$		−	32.8984i		−	1.36368i
$583$	7.02329	−	9.66673i	0.290875	−	0.400355i
$584$	−4.61920	+	14.2164i	−0.191144	+	0.588280i
$585$		0			0
$586$	−2.11964	−	6.52359i	−0.0875617	−	0.269487i
$587$	−18.1913	−	5.91072i	−0.750836	−	0.243962i	−0.0914953	−	0.995806i	$-0.529165\pi$
$587$	−18.1913	−	5.91072i	−0.750836	−	0.243962i	−0.659341	+	0.751844i	$0.729165\pi$
$588$	−10.2659	−	3.33560i	−0.423359	−	0.137558i
$589$	−2.73588	−	8.42016i	−0.112730	−	0.346947i
$590$		0			0
$591$	−1.03010	+	3.17031i	−0.0423725	+	0.130409i
$592$	0.772856	−	1.06375i	0.0317642	−	0.0437197i
$593$			0.538428i			0.0221106i	0.999939	+	0.0110553i	$0.00351908\pi$
$593$			0.538428i			0.0221106i	−0.999939	+	0.0110553i	$0.996481\pi$
$594$	−12.3189	−	8.95022i	−0.505451	−	0.367232i
$595$		0			0
$596$	1.35878	−	0.987213i	0.0556579	−	0.0404378i
$597$	44.4612	+	61.1956i	1.81968	+	2.50457i
$598$	−17.8586	+	5.80261i	−0.730292	+	0.237286i
$599$	38.4209			1.56983			0.784917	−	0.619601i	$-0.212705\pi$
$599$	38.4209			1.56983			0.784917	+	0.619601i	$0.212705\pi$
$600$		0			0
$601$	19.6034			0.799639			0.399820	−	0.916594i	$-0.369073\pi$
$601$	19.6034			0.799639			0.399820	+	0.916594i	$0.369073\pi$
$602$	−7.50722	+	2.43924i	−0.305971	+	0.0994162i
$603$	−32.3863	−	44.5759i	−1.31887	−	1.81527i
$604$	−17.2048	+	12.5001i	−0.700055	+	0.508620i
$605$		0			0
$606$	31.6323	+	22.9822i	1.28498	+	0.933590i
$607$			32.4415i			1.31676i	0.752685	+	0.658381i	$0.228758\pi$
$607$			32.4415i			1.31676i	−0.752685	+	0.658381i	$0.771242\pi$
$608$	−0.982966	+	1.35294i	−0.0398646	+	0.0548688i
$609$	−12.7466	+	39.2300i	−0.516518	+	1.58968i
$610$		0			0
$611$	−1.36981	−	4.21584i	−0.0554166	−	0.170555i
$612$	−15.3601	−	4.99080i	−0.620895	−	0.201741i
$613$	−22.3216	−	7.25273i	−0.901561	−	0.292935i	−0.178680	−	0.983907i	$-0.557183\pi$
$613$	−22.3216	−	7.25273i	−0.901561	−	0.292935i	−0.722881	+	0.690972i	$0.757183\pi$
$614$	0.894685	+	2.75356i	0.0361065	+	0.111124i
$615$		0			0
$616$	−1.03868	+	3.19672i	−0.0418495	+	0.128799i
$617$	−10.2353	+	14.0876i	−0.412056	+	0.567147i	−0.963718	−	0.266921i	$-0.913994\pi$
$617$	−10.2353	+	14.0876i	−0.412056	+	0.567147i	0.551662	+	0.834068i	$0.313994\pi$
$618$		−	7.81119i		−	0.314212i
$619$	10.1801	+	7.39624i	0.409171	+	0.297280i	0.773266	−	0.634082i	$-0.218622\pi$
$619$	10.1801	+	7.39624i	0.409171	+	0.297280i	−0.364095	+	0.931362i	$0.618622\pi$
$620$		0			0
$621$	52.1838	−	37.9137i	2.09406	−	1.52143i
$622$	−12.1372	−	16.7054i	−0.486657	−	0.669826i
$623$	5.78966	−	1.88117i	0.231958	−	0.0753676i
$624$	7.17242			0.287127
$625$		0			0
$626$	16.4272			0.656563
$627$	8.64992	−	2.81053i	0.345445	−	0.112242i
$628$	−6.14318	−	8.45536i	−0.245140	−	0.337406i
$629$	−2.96218	+	2.15215i	−0.118110	+	0.0858118i
$630$		0			0
$631$	−33.7653	−	24.5319i	−1.34418	−	0.976601i	−0.999279	−	0.0379610i	$-0.987914\pi$
$631$	−33.7653	−	24.5319i	−1.34418	−	0.976601i	−0.344897	−	0.938640i	$-0.612086\pi$
$632$			3.46076i			0.137662i
$633$	37.1470	−	51.1285i	1.47646	−	2.03218i
$634$	−5.10060	+	15.6980i	−0.202571	+	0.623448i
$635$		0			0
$636$	−5.97437	−	18.3872i	−0.236899	−	0.729101i
$637$	−8.36739	−	2.71873i	−0.331528	−	0.107720i
$638$	−13.2246	−	4.29692i	−0.523565	−	0.170117i
$639$	−0.547533	−	1.68513i	−0.0216601	−	0.0666628i
$640$		0			0
$641$	−4.44926	+	13.6934i	−0.175735	+	0.540858i	−0.999666	−	0.0258324i	$-0.991776\pi$
$641$	−4.44926	+	13.6934i	−0.175735	+	0.540858i	0.823931	+	0.566690i	$0.191776\pi$
$642$	−32.7881	+	45.1290i	−1.29404	+	1.78110i
$643$			30.1666i			1.18966i	0.803853	+	0.594828i	$0.202780\pi$
$643$			30.1666i			1.18966i	−0.803853	+	0.594828i	$0.797220\pi$
$644$	−11.5191	−	8.36912i	−0.453916	−	0.329790i
$645$		0			0
$646$	3.76748	−	2.73724i	0.148230	−	0.107695i
$647$	−6.28212	−	8.64660i	−0.246976	−	0.339933i	0.667474	−	0.744633i	$-0.267376\pi$
$647$	−6.28212	−	8.64660i	−0.246976	−	0.339933i	−0.914449	+	0.404701i	$0.867376\pi$
$648$	−6.88413	+	2.23679i	−0.270434	+	0.0878693i
$649$	−16.6110			−0.652039
$650$		0			0
$651$	−28.7925			−1.12847
$652$	9.90109	−	3.21706i	0.387757	−	0.125990i
$653$	−5.97532	−	8.22432i	−0.233832	−	0.321843i	0.675935	−	0.736961i	$-0.263740\pi$
$653$	−5.97532	−	8.22432i	−0.233832	−	0.321843i	−0.909767	+	0.415119i	$0.863740\pi$
$654$	24.7413	−	17.9756i	0.967461	−	0.702902i
$655$		0			0
$656$	−2.84373	−	2.06609i	−0.111029	−	0.0806674i
$657$		−	86.6959i		−	3.38233i
$658$	1.97568	−	2.71929i	0.0770201	−	0.106009i
$659$	−9.61668	+	29.5971i	−0.374613	+	1.15294i	0.569127	+	0.822250i	$0.307281\pi$
$659$	−9.61668	+	29.5971i	−0.374613	+	1.15294i	−0.943740	+	0.330689i	$0.892719\pi$
$660$		0			0
$661$	12.8131	+	39.4347i	0.498372	+	1.53383i	0.811635	+	0.584165i	$0.198578\pi$
$661$	12.8131	+	39.4347i	0.498372	+	1.53383i	−0.313262	+	0.949667i	$0.601422\pi$
$662$	−26.1265	−	8.48901i	−1.01543	−	0.329935i
$663$	−18.9953	−	6.17194i	−0.737715	−	0.239698i
$664$	1.96924	+	6.06071i	0.0764215	+	0.235201i
$665$		0			0
$666$	−2.35655	+	7.25271i	−0.0913144	+	0.281037i
$667$	34.6224	−	47.6536i	1.34058	−	1.84515i
$668$			2.12171i			0.0820913i
$669$	7.78797	+	5.65829i	0.301100	+	0.218762i
$670$		0			0
$671$	3.83849	−	2.78883i	0.148183	−	0.107661i
$672$	3.19672	+	4.39991i	0.123316	+	0.169730i
$673$	−2.03998	+	0.662831i	−0.0786356	+	0.0255503i	−0.348071	−	0.937468i	$-0.613163\pi$
$673$	−2.03998	+	0.662831i	−0.0786356	+	0.0255503i	0.269435	+	0.963019i	$0.413163\pi$
$674$	2.74521			0.105742
$675$		0			0
$676$	−7.15401			−0.275154
$677$	39.5147	−	12.8391i	1.51867	−	0.493446i	0.573274	−	0.819364i	$-0.305673\pi$
$677$	39.5147	−	12.8391i	1.51867	−	0.493446i	0.945398	+	0.325918i	$0.105673\pi$
$678$	−10.5605	−	14.5353i	−0.405575	−	0.558226i
$679$	16.4492	−	11.9510i	0.631263	−	0.458639i
$680$		0			0
$681$	−39.3039	−	28.5560i	−1.50613	−	1.09427i
$682$		−	9.70607i		−	0.371665i
$683$	−16.9464	+	23.3247i	−0.648436	+	0.892495i	−0.999030	−	0.0440323i	$-0.985980\pi$
$683$	−16.9464	+	23.3247i	−0.648436	+	0.892495i	0.350595	+	0.936527i	$0.385980\pi$
$684$	2.99720	−	9.22445i	0.114601	−	0.352706i
$685$		0			0
$686$	−6.02730	−	18.5501i	−0.230123	−	0.708247i
$687$	14.3601	+	4.66589i	0.547874	+	0.178015i
$688$	−4.09478	−	1.33047i	−0.156112	−	0.0507238i
$689$	−4.86950	−	14.9868i	−0.185513	−	0.570951i
$690$		0			0
$691$	−15.2050	+	46.7963i	−0.578426	+	1.78021i	0.0457774	+	0.998952i	$0.485424\pi$
$691$	−15.2050	+	46.7963i	−0.578426	+	1.78021i	−0.624204	+	0.781262i	$0.714576\pi$
$692$	10.6475	−	14.6551i	0.404759	−	0.557103i
$693$		−	19.4945i		−	0.740535i
$694$	−17.2637	−	12.5428i	−0.655319	−	0.476117i
$695$		0			0
$696$	−18.2021	+	13.2246i	−0.689947	+	0.501276i
$697$	5.75339	+	7.91886i	0.217925	+	0.299948i
$698$	15.9445	−	5.18067i	0.603507	−	0.196091i
$699$	4.93309			0.186587
$700$		0			0
$701$	−24.9783			−0.943419			−0.471709	−	0.881754i	$-0.656363\pi$
$701$	−24.9783			−0.943419			−0.471709	+	0.881754i	$0.656363\pi$
$702$	−19.0986	+	6.20551i	−0.720830	+	0.234212i
$703$	−1.29247	−	1.77893i	−0.0487462	−	0.0670935i
$704$	−1.48322	+	1.07763i	−0.0559011	+	0.0406145i
$705$		0			0
$706$	−2.41785	−	1.75667i	−0.0909969	−	0.0661131i
$707$			24.1650i			0.908817i
$708$	−15.7980	+	21.7441i	−0.593725	+	0.817193i
$709$	−3.02602	+	9.31312i	−0.113644	+	0.349762i	−0.991662	−	0.128867i	$-0.958866\pi$
$709$	−3.02602	+	9.31312i	−0.113644	+	0.349762i	0.878017	+	0.478629i	$0.158866\pi$
$710$		0			0
$711$	−6.20252	−	19.0894i	−0.232613	−	0.715908i
$712$	3.15794	+	1.02608i	0.118349	+	0.0384538i
$713$	39.1032	+	12.7054i	1.46443	+	0.475821i
$714$	−4.67995	−	14.4034i	−0.175143	−	0.539034i
$715$		0			0
$716$	3.26337	−	10.0436i	0.121958	−	0.375348i
$717$	−22.3182	+	30.7184i	−0.833488	+	1.14720i
$718$			6.70494i			0.250226i
$719$	−6.94474	−	5.04565i	−0.258995	−	0.188171i	0.450709	−	0.892671i	$-0.351171\pi$
$719$	−6.94474	−	5.04565i	−0.258995	−	0.188171i	−0.709704	+	0.704500i	$0.751171\pi$
$720$		0			0
$721$	3.90559	−	2.83758i	0.145452	−	0.105677i
$722$	−9.52408	−	13.1088i	−0.354450	−	0.487858i
$723$	−1.11574	+	0.362527i	−0.0414950	+	0.0134825i
$724$	−18.1561			−0.674768
$725$		0			0
$726$	−22.6600			−0.840992
$727$	−22.8408	+	7.42142i	−0.847118	+	0.275245i	−0.700238	−	0.713909i	$-0.746923\pi$
$727$	−22.8408	+	7.42142i	−0.847118	+	0.275245i	−0.146880	+	0.989154i	$0.546923\pi$
$728$	2.60553	+	3.58621i	0.0965675	+	0.132914i
$729$	−25.8337	+	18.7693i	−0.956802	+	0.695157i
$730$		0			0
$731$	9.69962	+	7.04719i	0.358754	+	0.260650i
$732$		−	7.67698i		−	0.283749i
$733$	−11.1733	+	15.3787i	−0.412695	+	0.568025i	−0.963873	−	0.266362i	$-0.914178\pi$
$733$	−11.1733	+	15.3787i	−0.412695	+	0.568025i	0.551178	+	0.834387i	$0.314178\pi$
$734$	−1.24119	+	3.82000i	−0.0458133	+	0.140999i
$735$		0			0
$736$	−2.39991	−	7.38615i	−0.0884617	−	0.272257i
$737$	16.5647	+	5.38220i	0.610168	+	0.198256i
$738$	19.3888	+	6.29981i	0.713713	+	0.231899i
$739$	6.42507	+	19.7743i	0.236350	+	0.727411i	0.996939	+	0.0781776i	$0.0249101\pi$
$739$	6.42507	+	19.7743i	0.236350	+	0.727411i	−0.760589	+	0.649233i	$0.775090\pi$
$740$		0			0
$741$	3.70653	−	11.4075i	0.136163	−	0.419066i
$742$	7.02329	−	9.66673i	0.257833	−	0.354877i
$743$			6.53365i			0.239696i	0.992792	+	0.119848i	$0.0382408\pi$
$743$			6.53365i			0.239696i	−0.992792	+	0.119848i	$0.961759\pi$
$744$	−12.7054	−	9.23102i	−0.465803	−	0.338426i
$745$		0			0
$746$	−21.5063	+	15.6252i	−0.787401	+	0.572080i
$747$	−21.7245	−	29.9012i	−0.794858	−	1.09403i
$748$	4.85544	−	1.57763i	0.177533	−	0.0576838i
$749$	−34.4755			−1.25971
$750$		0			0
$751$	27.9879			1.02129			0.510646	−	0.859791i	$-0.329406\pi$
$751$	27.9879			1.02129			0.510646	+	0.859791i	$0.329406\pi$
$752$	1.74363	−	0.566541i	0.0635838	−	0.0206596i
$753$	−16.3307	−	22.4773i	−0.595123	−	0.819117i
$754$	−14.8359	+	10.7789i	−0.540290	+	0.392544i
$755$		0			0
$756$	−12.3189	−	8.95022i	−0.448035	−	0.325516i
$757$		−	4.48558i		−	0.163031i	−0.996672	−	0.0815156i	$-0.974024\pi$
$757$		−	4.48558i		−	0.163031i	0.996672	−	0.0815156i	$-0.0259760\pi$
$758$	−9.18578	+	12.6431i	−0.333643	+	0.459220i
$759$	−13.0521	+	40.1702i	−0.473761	+	1.45809i
$760$		0			0
$761$	0.138770	+	0.427091i	0.00503042	+	0.0154820i	0.953540	−	0.301266i	$-0.0974091\pi$
$761$	0.138770	+	0.427091i	0.00503042	+	0.0154820i	−0.948510	+	0.316748i	$0.897409\pi$
$762$	−0.940237	−	0.305502i	−0.0340612	−	0.0110672i
$763$	17.9756	+	5.84063i	0.650760	+	0.211445i
$764$	6.76906	+	20.8330i	0.244896	+	0.753712i
$765$		0			0
$766$	4.15489	−	12.7874i	0.150122	−	0.462028i
$767$	−12.8764	+	17.7228i	−0.464940	+	0.639935i
$768$			2.96645i			0.107042i
$769$	16.9783	+	12.3355i	0.612254	+	0.444829i	0.850207	−	0.526448i	$-0.176476\pi$
$769$	16.9783	+	12.3355i	0.612254	+	0.444829i	−0.237953	+	0.971277i	$0.576476\pi$
$770$		0			0
$771$	11.9498	−	8.68202i	0.430360	−	0.312675i
$772$	16.1199	+	22.1872i	0.580168	+	0.798533i
$773$	−33.3262	+	10.8283i	−1.19866	+	0.389468i	−0.839268	−	0.543718i	$-0.817016\pi$
$773$	−33.3262	+	10.8283i	−1.19866	+	0.389468i	−0.359392	+	0.933187i	$0.617016\pi$
$774$	24.9711			0.897568
$775$		0			0
$776$	11.0902			0.398114
$777$	−6.80099	+	2.20978i	−0.243984	+	0.0792753i
$778$	14.7602	+	20.3157i	0.529180	+	0.728354i
$779$	−4.75564	+	3.45517i	−0.170388	+	0.123794i
$780$		0			0
$781$	0.453127	+	0.329216i	0.0162142	+	0.0117803i
$782$			21.6265i			0.773361i
$783$	37.0263	−	50.9623i	1.32321	−	1.82125i
$784$	1.12444	−	3.46068i	0.0401586	−	0.123596i
$785$		0			0
$786$	−4.74659	−	14.6085i	−0.169305	−	0.521068i
$787$	−37.2807	−	12.1132i	−1.32891	−	0.431790i	−0.443367	−	0.896340i	$-0.646216\pi$
$787$	−37.2807	−	12.1132i	−1.32891	−	0.431790i	−0.885547	+	0.464550i	$0.846216\pi$
$788$	−1.06872	−	0.347249i	−0.0380717	−	0.0123702i
$789$	18.1606	+	55.8925i	0.646534	+	1.98983i
$790$		0			0
$791$	3.43132	−	10.5605i	0.122004	−	0.375489i
$792$	6.25003	−	8.60242i	0.222085	−	0.305674i
$793$		−	6.25724i		−	0.222201i
$794$	2.84628	+	2.06794i	0.101011	+	0.0733884i
$795$		0			0
$796$	−20.6293	+	14.9880i	−0.731185	+	0.531237i
$797$	−5.07475	−	6.98479i	−0.179757	−	0.247414i	0.709625	−	0.704580i	$-0.248865\pi$
$797$	−5.07475	−	6.98479i	−0.179757	−	0.247414i	−0.889381	+	0.457166i	$0.848865\pi$
$798$	8.64992	−	2.81053i	0.306204	−	0.0994917i
$799$	−5.10532			−0.180613
$800$		0			0
$801$	−19.2580			−0.680448
$802$	28.4076	−	9.23020i	1.00311	−	0.325930i
$803$	16.1084	+	22.1713i	0.568453	+	0.782408i
$804$	22.7993	−	16.5647i	0.804071	−	0.584192i
$805$		0			0
$806$	−10.3557	−	7.52388i	−0.364765	−	0.265017i
$807$		−	43.8854i		−	1.54484i
$808$	−7.74739	+	10.6634i	−0.272552	+	0.375136i
$809$	14.1830	−	43.6508i	0.498648	−	1.53468i	−0.312546	−	0.949903i	$-0.601182\pi$
$809$	14.1830	−	43.6508i	0.498648	−	1.53468i	0.811194	−	0.584778i	$-0.198818\pi$
$810$		0			0
$811$	12.1734	+	37.4660i	0.427467	+	1.31561i	0.900612	+	0.434623i	$0.143119\pi$
$811$	12.1734	+	37.4660i	0.427467	+	1.31561i	−0.473145	+	0.880984i	$0.656881\pi$
$812$	−13.2246	−	4.29692i	−0.464091	−	0.150792i
$813$	−35.4249	−	11.5102i	−1.24240	−	0.403682i
$814$	−0.744923	−	2.29264i	−0.0261096	−	0.0803569i
$815$		0			0
$816$	2.55266	−	7.85627i	0.0893609	−	0.275025i
$817$	−4.23216	+	5.82507i	−0.148065	+	0.203794i
$818$		−	38.7628i		−	1.35531i
$819$	−20.7993	−	15.1116i	−0.726788	−	0.528042i
$820$		0			0
$821$	−22.0672	+	16.0328i	−0.770152	+	0.559548i	−0.902007	−	0.431721i	$-0.857907\pi$
$821$	−22.0672	+	16.0328i	−0.770152	+	0.559548i	0.131855	+	0.991269i	$0.457907\pi$
$822$	−34.0413	−	46.8538i	−1.18733	−	1.63421i
$823$	−5.83841	+	1.89701i	−0.203514	+	0.0661258i	−0.409000	−	0.912534i	$-0.634122\pi$
$823$	−5.83841	+	1.89701i	−0.203514	+	0.0661258i	0.205486	+	0.978660i	$0.434122\pi$
$824$	2.63318			0.0917311
$825$		0			0
$826$	−16.6110			−0.577971
$827$	41.9087	−	13.6170i	1.45731	−	0.473508i	0.530062	−	0.847959i	$-0.322169\pi$
$827$	41.9087	−	13.6170i	1.45731	−	0.473508i	0.927247	+	0.374451i	$0.122169\pi$
$828$	26.4755	+	36.4404i	0.920088	+	1.26639i
$829$	3.80236	−	2.76257i	0.132061	−	0.0959481i	−0.519794	−	0.854292i	$-0.673991\pi$
$829$	3.80236	−	2.76257i	0.132061	−	0.0959481i	0.651855	+	0.758344i	$0.273991\pi$
$830$		0			0
$831$	15.1958	+	11.0404i	0.527136	+	0.382987i
$832$			2.41785i			0.0838238i
$833$	−5.95589	+	8.19758i	−0.206359	+	0.284029i
$834$	7.29228	−	22.4433i	0.252511	−	0.777149i
$835$		0			0
$836$	0.947439	+	2.91592i	0.0327679	+	0.100849i
$837$	41.8183	+	13.5876i	1.44545	+	0.469656i
$838$	−17.9848	−	5.84362i	−0.621275	−	0.201864i
$839$	14.2747	+	43.9331i	0.492819	+	1.51674i	0.820328	+	0.571893i	$0.193791\pi$
$839$	14.2747	+	43.9331i	0.492819	+	1.51674i	−0.327509	+	0.944848i	$0.606209\pi$
$840$		0			0
$841$	8.81451	−	27.1283i	0.303949	−	0.935458i
$842$	12.9625	−	17.8414i	0.446718	−	0.614855i
$843$		−	59.5937i		−	2.05252i
$844$	17.2356	+	12.5224i	0.593274	+	0.431039i
$845$		0			0
$846$	−8.60242	+	6.25003i	−0.295757	+	0.214880i
$847$	−8.23173	−	11.3300i	−0.282846	−	0.389304i
$848$	6.19839	−	2.01398i	0.212854	−	0.0691604i
$849$	−5.38938			−0.184963
$850$		0			0
$851$	10.2116			0.350048
$852$	0.861899	−	0.280048i	0.0295282	−	0.00959429i
$853$	−7.43121	−	10.2282i	−0.254440	−	0.350206i	0.662620	−	0.748956i	$-0.269444\pi$
$853$	−7.43121	−	10.2282i	−0.254440	−	0.350206i	−0.917060	+	0.398749i	$0.869444\pi$
$854$	3.83849	−	2.78883i	0.131350	−	0.0954317i
$855$		0			0
$856$	−15.2131	−	11.0530i	−0.519974	−	0.377783i
$857$			19.4162i			0.663245i	0.943412	+	0.331623i	$0.107596\pi$
$857$			19.4162i			0.663245i	−0.943412	+	0.331623i	$0.892404\pi$
$858$	7.72918	−	10.6383i	0.263870	−	0.363186i
$859$	−2.88593	+	8.88197i	−0.0984665	+	0.303049i	−0.988142	−	0.153545i	$-0.950931\pi$
$859$	−2.88593	+	8.88197i	−0.0984665	+	0.303049i	0.889675	+	0.456594i	$0.150931\pi$
$860$		0			0
$861$	5.90744	+	18.1812i	0.201325	+	0.619615i
$862$	8.75521	+	2.84474i	0.298204	+	0.0968923i
$863$	−15.5445	−	5.05071i	−0.529141	−	0.171928i	0.0322489	−	0.999480i	$-0.489733\pi$
$863$	−15.5445	−	5.05071i	−0.529141	−	0.171928i	−0.561390	+	0.827552i	$0.689733\pi$
$864$	−2.56654	−	7.89900i	−0.0873155	−	0.268729i
$865$		0			0
$866$	10.7529	−	33.0941i	0.365400	−	1.12458i
$867$	16.1210	−	22.1886i	0.547497	−	0.753565i
$868$		−	9.70607i		−	0.329445i
$869$	5.13308	+	3.72940i	0.174128	+	0.126511i
$870$		0			0
$871$	18.5829	−	13.5013i	0.629659	−	0.457474i
$872$	6.05964	+	8.34038i	0.205205	+	0.282441i
$873$	−61.1728	+	19.8763i	−2.07039	+	0.672709i
$874$	−12.9877			−0.439315
$875$		0			0
$876$	44.3426			1.49820
$877$	−33.7673	+	10.9717i	−1.14024	+	0.370487i	−0.817459	−	0.575986i	$-0.804618\pi$
$877$	−33.7673	+	10.9717i	−1.14024	+	0.370487i	−0.322782	+	0.946473i	$0.604618\pi$
$878$	4.90792	+	6.75517i	0.165634	+	0.227976i
$879$	−16.4617	+	11.9601i	−0.555240	+	0.403405i
$880$		0			0
$881$	25.5378	+	18.5543i	0.860390	+	0.625110i	0.927991	−	0.372602i	$-0.121534\pi$
$881$	25.5378	+	18.5543i	0.860390	+	0.625110i	−0.0676008	+	0.997712i	$0.521534\pi$
$882$			21.1042i			0.710615i
$883$	20.5315	−	28.2592i	0.690940	−	0.950997i	−0.309060	−	0.951042i	$-0.600014\pi$
$883$	20.5315	−	28.2592i	0.690940	−	0.950997i	1.00000		4.54670e-5i	$1.44726e-5\pi$
$884$	2.08058	−	6.40337i	0.0699775	−	0.215369i
$885$		0			0
$886$	−0.370470	−	1.14019i	−0.0124462	−	0.0383054i
$887$	40.8311	+	13.2668i	1.37097	+	0.445456i	0.899692	−	0.436526i	$-0.143791\pi$
$887$	40.8311	+	13.2668i	1.37097	+	0.445456i	0.471282	+	0.881982i	$0.343791\pi$
$888$	−3.70957	−	1.20531i	−0.124485	−	0.0404476i
$889$	−0.188810	−	0.581099i	−0.00633250	−	0.0194894i
$890$		0			0
$891$	−4.10085	+	12.6211i	−0.137384	+	0.422823i
$892$	−1.90743	+	2.62535i	−0.0638655	+	0.0879033i
$893$		−	3.06598i		−	0.102599i
$894$	−4.03076	−	2.92852i	−0.134809	−	0.0979442i
$895$		0			0
$896$	−1.48322	+	1.07763i	−0.0495510	+	0.0360009i
$897$	32.7413	+	45.0646i	1.09320	+	1.50466i
$898$	−31.1902	+	10.1343i	−1.04083	+	0.338186i
$899$	40.1532			1.33918
$900$		0			0
$901$	−18.1487			−0.604622
$902$	−6.12896	+	1.99142i	−0.204072	+	0.0663070i
$903$	13.7635	+	18.9438i	0.458020	+	0.630410i
$904$	4.89991	−	3.55999i	0.162968	−	0.118404i
$905$		0			0
$906$	51.0373	+	37.0808i	1.69560	+	1.23193i
$907$			39.8259i			1.32240i	0.750211	+	0.661199i	$0.229952\pi$
$907$			39.8259i			1.32240i	−0.750211	+	0.661199i	$0.770048\pi$
$908$	9.62631	−	13.2495i	0.319460	−	0.439700i
$909$	23.6229	−	72.7038i	0.783522	−	2.41143i
$910$		0			0
$911$	−0.522189	−	1.60713i	−0.0173009	−	0.0532467i	0.942033	−	0.335519i	$-0.108912\pi$
$911$	−0.522189	−	1.60713i	−0.0173009	−	0.0532467i	−0.959334	+	0.282273i	$0.908912\pi$
$912$	4.71806	+	1.53299i	0.156230	+	0.0507623i
$913$	11.1115	+	3.61034i	0.367737	+	0.119485i
$914$	−6.11496	−	18.8199i	−0.202265	−	0.622508i
$915$		0			0
$916$	−1.57289	+	4.84085i	−0.0519697	+	0.159946i
$917$	5.57995	−	7.68015i	0.184266	−	0.253621i
$918$			23.1281i			0.763340i
$919$	−24.2013	−	17.5833i	−0.798327	−	0.580019i	0.112096	−	0.993697i	$-0.464244\pi$
$919$	−24.2013	−	17.5833i	−0.798327	−	0.580019i	−0.910423	+	0.413679i	$0.864244\pi$
$920$		0			0
$921$	6.94836	−	5.04828i	0.228956	−	0.166346i
$922$	5.52504	+	7.60456i	0.181957	+	0.250443i
$923$	0.702504	−	0.228257i	0.0231232	−	0.00751318i
$924$	9.97091			0.328019
$925$		0			0
$926$	17.7329			0.582739
$927$	−14.5245	+	4.71929i	−0.477047	+	0.155002i
$928$	−4.45805	−	6.13597i	−0.146343	−	0.201423i
$929$	−12.8664	+	9.34795i	−0.422131	+	0.306696i	−0.778495	−	0.627651i	$-0.784017\pi$
$929$	−12.8664	+	9.34795i	−0.422131	+	0.306696i	0.356363	+	0.934347i	$0.384017\pi$
$930$		0			0
$931$	−4.92303	−	3.57679i	−0.161346	−	0.117225i
$932$			1.66296i			0.0544721i
$933$	−36.0043	+	49.5557i	−1.17873	+	1.62238i
$934$	−6.75535	+	20.7908i	−0.221042	+	0.680297i
$935$		0			0
$936$	−4.33337	−	13.3367i	−0.141640	−	0.435925i
$937$	−44.0026	−	14.2973i	−1.43750	−	0.467073i	−0.516384	−	0.856357i	$-0.672722\pi$
$937$	−44.0026	−	14.2973i	−1.43750	−	0.467073i	−0.921118	+	0.389284i	$0.872722\pi$
$938$	16.5647	+	5.38220i	0.540856	+	0.175735i
$939$	−15.0585	−	46.3454i	−0.491417	−	1.51243i
$940$		0			0
$941$	−3.60650	+	11.0997i	−0.117569	+	0.361839i	−0.992474	−	0.122455i	$-0.960923\pi$
$941$	−3.60650	+	11.0997i	−0.117569	+	0.361839i	0.874906	+	0.484294i	$0.160923\pi$
$942$	−18.2234	+	25.0824i	−0.593751	+	0.817228i
$943$		−	27.2988i		−	0.888971i
$944$	−7.33001	−	5.32556i	−0.238571	−	0.173332i
$945$		0			0
$946$	−6.38602	+	4.63972i	−0.207628	+	0.150850i
$947$	−1.72435	−	2.37336i	−0.0560337	−	0.0771238i	0.780081	−	0.625679i	$-0.215178\pi$
$947$	−1.72435	−	2.37336i	−0.0560337	−	0.0771238i	−0.836114	+	0.548555i	$0.815178\pi$
$948$	9.76370	−	3.17242i	0.317110	−	0.103035i
$949$	36.1421			1.17322
$950$		0			0
$951$	48.9638			1.58776
$952$	4.85544	−	1.57763i	0.157366	−	0.0511313i
$953$	5.84085	+	8.03924i	0.189204	+	0.260417i	0.893072	−	0.449914i	$-0.148545\pi$
$953$	5.84085	+	8.03924i	0.189204	+	0.260417i	−0.703868	+	0.710331i	$0.748545\pi$
$954$	−30.5805	+	22.2180i	−0.990080	+	0.719335i
$955$		0			0
$956$	−10.3553	−	7.52354i	−0.334913	−	0.243329i
$957$			41.2488i			1.33339i
$958$	−3.59168	+	4.94352i	−0.116042	+	0.159718i
$959$	11.0607	−	34.0413i	0.357168	−	1.09925i
$960$		0			0
$961$	−0.918471	−	2.82676i	−0.0296281	−	0.0911859i
$962$	−3.02354	−	0.982407i	−0.0974828	−	0.0316741i
$963$	103.725	+	33.7021i	3.34248	+	1.08604i
$964$	−0.122209	−	0.376121i	−0.00393610	−	0.0121141i
$965$		0			0
$966$	−13.0521	+	40.1702i	−0.419944	+	1.29246i
$967$	−26.6781	+	36.7193i	−0.857910	+	1.18081i	0.124153	+	0.992263i	$0.460379\pi$
$967$	−26.6781	+	36.7193i	−0.857910	+	1.18081i	−0.982064	+	0.188549i	$0.939621\pi$
$968$		−	7.63877i		−	0.245519i
$969$	−11.1760	−	8.11987i	−0.359026	−	0.260848i
$970$		0			0
$971$	3.78844	−	2.75246i	0.121577	−	0.0883307i	−0.525335	−	0.850895i	$-0.676060\pi$
$971$	3.78844	−	2.75246i	0.121577	−	0.0883307i	0.646912	+	0.762565i	$0.276060\pi$
$972$	−2.02444	−	2.78640i	−0.0649338	−	0.0893737i
$973$	13.8707	−	4.50688i	0.444675	−	0.144484i
$974$	−5.06189			−0.162194
$975$		0			0
$976$	2.58794			0.0828379
$977$	3.05103	−	0.991339i	0.0976110	−	0.0317157i	−0.259804	−	0.965661i	$-0.583658\pi$
$977$	3.05103	−	0.991339i	0.0976110	−	0.0317157i	0.357415	+	0.933946i	$0.383658\pi$
$978$	−18.1523	−	24.9845i	−0.580447	−	0.798917i
$979$	4.92498	−	3.57820i	0.157403	−	0.114360i
$980$		0			0
$981$	−48.3726	−	35.1448i	−1.54442	−	1.12209i
$982$		−	2.38228i		−	0.0760216i
$983$	11.5038	−	15.8337i	0.366915	−	0.505015i	−0.585144	−	0.810929i	$-0.698962\pi$
$983$	11.5038	−	15.8337i	0.366915	−	0.505015i	0.952059	+	0.305914i	$0.0989621\pi$
$984$	−3.22218	+	9.91686i	−0.102719	+	0.316138i
$985$		0			0
$986$	6.52652	+	20.0866i	0.207847	+	0.639687i
$987$	−9.48290	−	3.08118i	−0.301844	−	0.0980751i
$988$	3.84552	+	1.24949i	0.122342	+	0.0397514i
$989$	−10.3328	−	31.8011i	−0.328564	−	1.01122i
$990$		0			0
$991$	13.9762	−	43.0144i	0.443969	−	1.36640i	−0.439641	−	0.898173i	$-0.644894\pi$
$991$	13.9762	−	43.0144i	0.443969	−	1.36640i	0.883610	−	0.468223i	$-0.155106\pi$
$992$	3.11181	−	4.28304i	0.0988000	−	0.135987i
$993$			81.4913i			2.58605i
$994$	0.453127	+	0.329216i	0.0143723	+	0.0104421i
$995$		0			0
$996$	15.2937	−	11.1115i	0.484598	−	0.352081i
$997$	−34.1335	−	46.9808i	−1.08102	−	1.48790i	−0.858394	−	0.512991i	$-0.828537\pi$
$997$	−34.1335	−	46.9808i	−1.08102	−	1.48790i	−0.222626	−	0.974904i	$-0.571463\pi$
$998$	0.0478679	−	0.0155532i	0.00151523	−	0.000492329i
$999$	10.9206			0.345512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.e.c.99.3		16
5.2	odd	4		50.2.d.b.31.1	yes	8
5.3	odd	4		250.2.d.d.151.2		8
5.4	even	2	inner	250.2.e.c.99.2		16
15.2	even	4		450.2.h.e.181.1		8
20.7	even	4		400.2.u.d.81.2		8
25.2	odd	20		1250.2.a.l.1.4		4
25.3	odd	20		250.2.d.d.101.2		8
25.4	even	10	inner	250.2.e.c.149.3		16
25.11	even	5		1250.2.b.e.1249.4		8
25.14	even	10		1250.2.b.e.1249.5		8
25.21	even	5	inner	250.2.e.c.149.2		16
25.22	odd	20		50.2.d.b.21.1	✓	8
25.23	odd	20		1250.2.a.f.1.1		4
75.47	even	20		450.2.h.e.271.1		8
100.23	even	20		10000.2.a.x.1.4		4
100.27	even	20		10000.2.a.t.1.1		4
100.47	even	20		400.2.u.d.321.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.1	✓	8	25.22	odd	20
50.2.d.b.31.1	yes	8	5.2	odd	4
250.2.d.d.101.2		8	25.3	odd	20
250.2.d.d.151.2		8	5.3	odd	4
250.2.e.c.99.2		16	5.4	even	2	inner
250.2.e.c.99.3		16	1.1	even	1	trivial
250.2.e.c.149.2		16	25.21	even	5	inner
250.2.e.c.149.3		16	25.4	even	10	inner
400.2.u.d.81.2		8	20.7	even	4
400.2.u.d.321.2		8	100.47	even	20
450.2.h.e.181.1		8	15.2	even	4
450.2.h.e.271.1		8	75.47	even	20
1250.2.a.f.1.1		4	25.23	odd	20
1250.2.a.l.1.4		4	25.2	odd	20
1250.2.b.e.1249.4		8	25.11	even	5
1250.2.b.e.1249.5		8	25.14	even	10
10000.2.a.t.1.1		4	100.27	even	20
10000.2.a.x.1.4		4	100.23	even	20

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.74363 - 2.39991i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.39991 - 1.74363i) q^{6} -1.83337i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.79224 + 5.51595i) q^{9} +(-0.566541 - 1.74363i) q^{11} +(-2.82126 - 0.916683i) q^{12} +(-2.29951 - 0.747156i) q^{13} +(-0.566541 - 1.74363i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-1.63679 + 2.25284i) q^{17} +5.79981i q^{18} +(-1.35294 - 0.982966i) q^{19} +(-4.39991 + 3.19672i) q^{21} +(-1.07763 - 1.48322i) q^{22} +(7.38615 - 2.39991i) q^{23} -2.96645 q^{24} -2.41785 q^{26} +(7.89900 - 2.56654i) q^{27} +(-1.07763 - 1.48322i) q^{28} +(6.13597 - 4.45805i) q^{29} +(4.28304 + 3.11181i) q^{31} -1.00000i q^{32} +(-3.19672 + 4.39991i) q^{33} +(-0.860510 + 2.64838i) q^{34} +(1.79224 + 5.51595i) q^{36} +(1.25051 + 0.406315i) q^{37} +(-1.59047 - 0.516776i) q^{38} +(2.21640 + 6.82138i) q^{39} +(1.08621 - 3.34301i) q^{41} +(-3.19672 + 4.39991i) q^{42} -4.30550i q^{43} +(-1.48322 - 1.07763i) q^{44} +(6.28304 - 4.56489i) q^{46} +(1.07763 + 1.48322i) q^{47} +(-2.82126 + 0.916683i) q^{48} +3.63877 q^{49} +8.26057 q^{51} +(-2.29951 + 0.747156i) q^{52} +(3.83082 + 5.27267i) q^{53} +(6.71929 - 4.88185i) q^{54} +(-1.48322 - 1.07763i) q^{56} +4.96086i q^{57} +(4.45805 - 6.13597i) q^{58} +(2.79981 - 8.61694i) q^{59} +(0.799717 + 2.46127i) q^{61} +(5.03501 + 1.63597i) q^{62} +(10.1128 + 3.28583i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-1.68061 + 5.17240i) q^{66} +(-5.58402 + 7.68574i) q^{67} +2.78467i q^{68} +(-18.6383 - 13.5415i) q^{69} +(-0.247156 + 0.179569i) q^{71} +(3.40904 + 4.69215i) q^{72} +(-14.2164 + 4.61920i) q^{73} +1.31486 q^{74} -1.67232 q^{76} +(-3.19672 + 1.03868i) q^{77} +(4.21584 + 5.80261i) q^{78} +(-2.79981 + 2.03418i) q^{79} +(-5.85599 - 4.25462i) q^{81} -3.51505i q^{82} +(-3.74572 + 5.15555i) q^{83} +(-1.68061 + 5.17240i) q^{84} +(-1.33047 - 4.09478i) q^{86} +(-21.3978 - 6.95256i) q^{87} +(-1.74363 - 0.566541i) q^{88} +(1.02608 + 3.15794i) q^{89} +(-1.36981 + 4.21584i) q^{91} +(4.56489 - 6.28304i) q^{92} -15.7047i q^{93} +(1.48322 + 1.07763i) q^{94} +(-2.39991 + 1.74363i) q^{96} +(6.51864 + 8.97214i) q^{97} +(3.46068 - 1.12444i) q^{98} +10.6332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46}+ \cdots + 84 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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