LMFDB - Embedded newform 925.2.y.c.193.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.15
Character	$\chi$	$=$	925.193
Dual form			925.2.y.c.532.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.420731 - 0.242909i) q^{2} +(0.673179 + 2.51234i) q^{3} +(-0.881990 + 1.52765i) q^{4} +(0.893496 + 0.893496i) q^{6} +(0.277006 + 1.03380i) q^{7} +1.82861i q^{8} +(-3.26059 + 1.88250i) q^{9} +2.08952i q^{11} +(-4.43171 - 1.18747i) q^{12} +(3.17161 + 1.83113i) q^{13} +(0.367665 + 0.367665i) q^{14} +(-1.31980 - 2.28595i) q^{16} +(-0.928076 - 1.60748i) q^{17} +(-0.914554 + 1.58405i) q^{18} +(0.445873 + 1.66402i) q^{19} +(-2.41078 + 1.39187i) q^{21} +(0.507562 + 0.879123i) q^{22} -3.16775i q^{23} +(-4.59408 + 1.23098i) q^{24} +1.77919 q^{26} +(-1.40697 - 1.40697i) q^{27} +(-1.82361 - 0.488634i) q^{28} +(-2.26804 - 2.26804i) q^{29} +(-4.45483 + 4.45483i) q^{31} +(-4.27780 - 2.46979i) q^{32} +(-5.24957 + 1.40662i) q^{33} +(-0.780940 - 0.450876i) q^{34} -6.64140i q^{36} +(2.49171 - 5.54900i) q^{37} +(0.591798 + 0.591798i) q^{38} +(-2.46536 + 9.20083i) q^{39} +(8.68470 + 5.01411i) q^{41} +(-0.676194 + 1.17120i) q^{42} -5.37912i q^{43} +(-3.19205 - 1.84293i) q^{44} +(-0.769476 - 1.33277i) q^{46} +(-1.58980 + 1.58980i) q^{47} +(4.85462 - 4.85462i) q^{48} +(5.07016 - 2.92726i) q^{49} +(3.41376 - 3.41376i) q^{51} +(-5.59466 + 3.23008i) q^{52} +(1.81540 - 6.77518i) q^{53} +(-0.933722 - 0.250190i) q^{54} +(-1.89042 + 0.506536i) q^{56} +(-3.88043 + 2.24037i) q^{57} +(-1.50516 - 0.403306i) q^{58} +(-10.7855 - 2.88997i) q^{59} +(2.94690 + 10.9980i) q^{61} +(-0.792167 + 2.95641i) q^{62} +(-2.84934 - 2.84934i) q^{63} +2.87944 q^{64} +(-1.86697 + 1.86697i) q^{66} +(-10.2284 + 2.74070i) q^{67} +3.27422 q^{68} +(7.95847 - 2.13247i) q^{69} +(0.439137 - 0.760607i) q^{71} +(-3.44237 - 5.96235i) q^{72} +(4.02172 - 4.02172i) q^{73} +(-0.299561 - 2.93989i) q^{74} +(-2.93530 - 0.786511i) q^{76} +(-2.16014 + 0.578809i) q^{77} +(1.19771 + 4.46993i) q^{78} +(1.52669 + 5.69770i) q^{79} +(-3.05987 + 5.29985i) q^{81} +4.87189 q^{82} +(1.64807 - 6.15070i) q^{83} -4.91045i q^{84} +(-1.30664 - 2.26316i) q^{86} +(4.17128 - 7.22487i) q^{87} -3.82091 q^{88} +(-0.569968 + 2.12715i) q^{89} +(-1.01447 + 3.78605i) q^{91} +(4.83923 + 2.79393i) q^{92} +(-14.1909 - 8.19315i) q^{93} +(-0.282701 + 1.05505i) q^{94} +(3.32522 - 12.4099i) q^{96} -0.682762 q^{97} +(1.42212 - 2.46318i) q^{98} +(-3.93352 - 6.81306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 40 q^{4} - 32 q^{14} - 4 q^{16} - 24 q^{19} + 36 q^{21} + 52 q^{24} + 16 q^{26} + 12 q^{29} + 4 q^{31} - 60 q^{34} + 100 q^{39} - 48 q^{41} + 48 q^{44} + 24 q^{46} - 120 q^{49} - 84 q^{51} + 104 q^{54}+ \cdots - 24 q^{99}+O(q^{100}) $ 96 * q + 40 * q^4 - 32 * q^14 - 4 * q^16 - 24 * q^19 + 36 * q^21 + 52 * q^24 + 16 * q^26 + 12 * q^29 + 4 * q^31 - 60 * q^34 + 100 * q^39 - 48 * q^41 + 48 * q^44 + 24 * q^46 - 120 * q^49 - 84 * q^51 + 104 * q^54 - 68 * q^56 - 28 * q^59 + 68 * q^61 + 48 * q^64 + 4 * q^66 + 28 * q^69 + 48 * q^71 - 48 * q^74 - 152 * q^76 - 92 * q^79 - 16 * q^81 + 20 * q^86 - 8 * q^89 - 12 * q^91 + 56 * q^94 + 252 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.420731	−	0.242909i	0.297502	−	0.171763i	−0.343818	−	0.939036i	$-0.611720\pi$
$2$	0.420731	−	0.242909i	0.297502	−	0.171763i	0.641320	+	0.767274i	$0.278387\pi$
$3$	0.673179	+	2.51234i	0.388660	+	1.45050i	0.832316	+	0.554301i	$0.187015\pi$
$3$	0.673179	+	2.51234i	0.388660	+	1.45050i	−0.443656	+	0.896197i	$0.646319\pi$
$4$	−0.881990	+	1.52765i	−0.440995	+	0.763826i
$5$		0			0
$5$		0			0
$6$	0.893496	+	0.893496i	0.364768	+	0.364768i
$7$	0.277006	+	1.03380i	0.104699	+	0.390740i	0.998311	−	0.0580995i	$-0.0185041\pi$
$7$	0.277006	+	1.03380i	0.104699	+	0.390740i	−0.893612	+	0.448840i	$0.851837\pi$
$8$			1.82861i			0.646511i
$9$	−3.26059	+	1.88250i	−1.08686	+	0.627501i
$10$		0			0
$11$			2.08952i			0.630013i	0.949090	+	0.315006i	$0.102007\pi$
$11$			2.08952i			0.630013i	−0.949090	+	0.315006i	$0.897993\pi$
$12$	−4.43171	−	1.18747i	−1.27933	−	0.342794i
$13$	3.17161	+	1.83113i	0.879646	+	0.507864i	0.870542	−	0.492094i	$-0.163769\pi$
$13$	3.17161	+	1.83113i	0.879646	+	0.507864i	0.00910465	+	0.999959i	$0.497102\pi$
$14$	0.367665	+	0.367665i	0.0982626	+	0.0982626i
$15$		0			0
$16$	−1.31980	−	2.28595i	−0.329949	−	0.571488i
$17$	−0.928076	−	1.60748i	−0.225092	−	0.389870i	0.731255	−	0.682104i	$-0.238935\pi$
$17$	−0.928076	−	1.60748i	−0.225092	−	0.389870i	−0.956347	+	0.292234i	$0.905601\pi$
$18$	−0.914554	+	1.58405i	−0.215563	+	0.373365i
$19$	0.445873	+	1.66402i	0.102290	+	0.381753i	0.998024	−	0.0628391i	$-0.0200155\pi$
$19$	0.445873	+	1.66402i	0.102290	+	0.381753i	−0.895733	+	0.444592i	$0.853349\pi$
$20$		0			0
$21$	−2.41078	+	1.39187i	−0.526076	+	0.303730i
$22$	0.507562	+	0.879123i	0.108213	+	0.187430i
$23$		−	3.16775i		−	0.660523i	−0.943890	−	0.330261i	$-0.892863\pi$
$23$		−	3.16775i		−	0.660523i	0.943890	−	0.330261i	$-0.107137\pi$
$24$	−4.59408	+	1.23098i	−0.937764	+	0.251273i
$25$		0			0
$26$	1.77919			0.348928
$27$	−1.40697	−	1.40697i	−0.270772	−	0.270772i
$28$	−1.82361	−	0.488634i	−0.344629	−	0.0923431i
$29$	−2.26804	−	2.26804i	−0.421164	−	0.421164i	0.464440	−	0.885604i	$-0.346255\pi$
$29$	−2.26804	−	2.26804i	−0.421164	−	0.421164i	−0.885604	+	0.464440i	$0.846255\pi$
$30$		0			0
$31$	−4.45483	+	4.45483i	−0.800112	+	0.800112i	−0.983113	−	0.183001i	$-0.941419\pi$
$31$	−4.45483	+	4.45483i	−0.800112	+	0.800112i	0.183001	+	0.983113i	$0.441419\pi$
$32$	−4.27780	−	2.46979i	−0.756216	−	0.436601i
$33$	−5.24957	+	1.40662i	−0.913832	+	0.244861i
$34$	−0.780940	−	0.450876i	−0.133930	−	0.0773246i
$35$		0			0
$36$		−	6.64140i		−	1.10690i
$37$	2.49171	−	5.54900i	0.409635	−	0.912249i
$37$	2.49171	−	5.54900i	0.409635	−	0.912249i
$38$	0.591798	+	0.591798i	0.0960023	+	0.0960023i
$39$	−2.46536	+	9.20083i	−0.394773	+	1.47331i
$40$		0			0
$41$	8.68470	+	5.01411i	1.35632	+	0.783073i	0.989126	−	0.147071i	$-0.0469845\pi$
$41$	8.68470	+	5.01411i	1.35632	+	0.783073i	0.367196	+	0.930144i	$0.380318\pi$
$42$	−0.676194	+	1.17120i	−0.104339	+	0.180720i
$43$		−	5.37912i		−	0.820309i	−0.912016	−	0.410154i	$-0.865475\pi$
$43$		−	5.37912i		−	0.820309i	0.912016	−	0.410154i	$-0.134525\pi$
$44$	−3.19205	−	1.84293i	−0.481220	−	0.277832i
$45$		0			0
$46$	−0.769476	−	1.33277i	−0.113453	−	0.196506i
$47$	−1.58980	+	1.58980i	−0.231896	+	0.231896i	−0.813484	−	0.581588i	$-0.802432\pi$
$47$	−1.58980	+	1.58980i	−0.231896	+	0.231896i	0.581588	+	0.813484i	$0.302432\pi$
$48$	4.85462	−	4.85462i	0.700705	−	0.700705i
$49$	5.07016	−	2.92726i	0.724309	−	0.418180i
$50$		0			0
$51$	3.41376	−	3.41376i	0.478022	−	0.478022i
$52$	−5.59466	+	3.23008i	−0.775840	+	0.447931i
$53$	1.81540	−	6.77518i	0.249365	−	0.930643i	−0.721774	−	0.692129i	$-0.756673\pi$
$53$	1.81540	−	6.77518i	0.249365	−	0.930643i	0.971139	−	0.238514i	$-0.0766603\pi$
$54$	−0.933722	−	0.250190i	−0.127063	−	0.0340466i
$55$		0			0
$56$	−1.89042	+	0.506536i	−0.252618	+	0.0676888i
$57$	−3.88043	+	2.24037i	−0.513975	+	0.296744i
$58$	−1.50516	−	0.403306i	−0.197637	−	0.0529567i
$59$	−10.7855	−	2.88997i	−1.40416	−	0.376242i	−0.524320	−	0.851521i	$-0.675681\pi$
$59$	−10.7855	−	2.88997i	−1.40416	−	0.376242i	−0.879835	+	0.475279i	$0.842347\pi$
$60$		0			0
$61$	2.94690	+	10.9980i	0.377311	+	1.40815i	0.849938	+	0.526882i	$0.176639\pi$
$61$	2.94690	+	10.9980i	0.377311	+	1.40815i	−0.472627	+	0.881263i	$0.656694\pi$
$62$	−0.792167	+	2.95641i	−0.100605	+	0.375464i
$63$	−2.84934	−	2.84934i	−0.358983	−	0.358983i
$64$	2.87944			0.359930
$65$		0			0
$66$	−1.86697	+	1.86697i	−0.229809	+	0.229809i
$67$	−10.2284	+	2.74070i	−1.24960	+	0.334830i	−0.822183	−	0.569223i	$-0.807244\pi$
$67$	−10.2284	+	2.74070i	−1.24960	+	0.334830i	−0.427420	+	0.904053i	$0.640577\pi$
$68$	3.27422			0.397057
$69$	7.95847	−	2.13247i	0.958087	−	0.256719i
$70$		0			0
$71$	0.439137	−	0.760607i	0.0521159	−	0.0902674i	−0.838791	−	0.544454i	$-0.816737\pi$
$71$	0.439137	−	0.760607i	0.0521159	−	0.0902674i	0.890906	+	0.454187i	$0.150070\pi$
$72$	−3.44237	−	5.96235i	−0.405687	−	0.702670i
$73$	4.02172	−	4.02172i	0.470707	−	0.470707i	−0.431437	−	0.902143i	$-0.641993\pi$
$73$	4.02172	−	4.02172i	0.470707	−	0.470707i	0.902143	+	0.431437i	$0.141993\pi$
$74$	−0.299561	−	2.93989i	−0.0348233	−	0.341756i
$75$		0			0
$76$	−2.93530	−	0.786511i	−0.336702	−	0.0902190i
$77$	−2.16014	+	0.578809i	−0.246171	+	0.0659614i
$78$	1.19771	+	4.46993i	0.135614	+	0.506120i
$79$	1.52669	+	5.69770i	0.171766	+	0.641041i	0.997080	+	0.0763662i	$0.0243318\pi$
$79$	1.52669	+	5.69770i	0.171766	+	0.641041i	−0.825313	+	0.564675i	$0.809002\pi$
$80$		0			0
$81$	−3.05987	+	5.29985i	−0.339985	+	0.588872i
$82$	4.87189			0.538011
$83$	1.64807	−	6.15070i	0.180900	−	0.675127i	−0.814571	−	0.580063i	$-0.803028\pi$
$83$	1.64807	−	6.15070i	0.180900	−	0.675127i	0.995471	−	0.0950638i	$-0.0303055\pi$
$84$		−	4.91045i		−	0.535774i
$85$		0			0
$86$	−1.30664	−	2.26316i	−0.140898	−	0.244043i
$87$	4.17128	−	7.22487i	0.447208	−	0.774587i
$88$	−3.82091			−0.407310
$89$	−0.569968	+	2.12715i	−0.0604164	+	0.225477i	−0.989532	−	0.144311i	$-0.953903\pi$
$89$	−0.569968	+	2.12715i	−0.0604164	+	0.225477i	0.929116	+	0.369789i	$0.120570\pi$
$90$		0			0
$91$	−1.01447	+	3.78605i	−0.106345	+	0.396886i
$92$	4.83923	+	2.79393i	0.504524	+	0.291287i
$93$	−14.1909	−	8.19315i	−1.47153	−	0.849590i
$94$	−0.282701	+	1.05505i	−0.0291583	+	0.108820i
$95$		0			0
$96$	3.32522	−	12.4099i	0.339379	−	1.26658i
$97$	−0.682762			−0.0693240			−0.0346620	−	0.999399i	$-0.511035\pi$
$97$	−0.682762			−0.0693240			−0.0346620	+	0.999399i	$0.511035\pi$
$98$	1.42212	−	2.46318i	0.143655	−	0.248818i
$99$	−3.93352	−	6.81306i	−0.395334	−	0.684738i
$100$		0			0
$101$			13.2653i			1.31994i	0.751291	+	0.659972i	$0.229432\pi$
$101$			13.2653i			1.31994i	−0.751291	+	0.659972i	$0.770568\pi$
$102$	0.607041	−	2.26551i	0.0601060	−	0.224319i
$103$	−2.82512			−0.278368			−0.139184	−	0.990267i	$-0.544448\pi$
$103$	−2.82512			−0.278368			−0.139184	+	0.990267i	$0.544448\pi$
$104$	−3.34842	+	5.79964i	−0.328340	+	0.568701i
$105$		0			0
$106$	−0.881956	−	3.29151i	−0.0856632	−	0.319699i
$107$	2.56972	+	9.59031i	0.248424	+	0.927131i	0.971632	+	0.236500i	$0.0760003\pi$
$107$	2.56972	+	9.59031i	0.248424	+	0.927131i	−0.723208	+	0.690631i	$0.757333\pi$
$108$	3.39030	−	0.908428i	0.326232	−	0.0874135i
$109$	4.78161	+	1.28123i	0.457995	+	0.122719i	0.480438	−	0.877029i	$-0.340478\pi$
$109$	4.78161	+	1.28123i	0.457995	+	0.122719i	−0.0224428	+	0.999748i	$0.507144\pi$
$110$		0			0
$111$	15.6183	+	2.52456i	1.48243	+	0.239620i
$112$	1.99763	−	1.99763i	0.188758	−	0.188758i
$113$	4.03041	+	6.98088i	0.379149	+	0.656706i	0.990939	−	0.134315i	$-0.0428833\pi$
$113$	4.03041	+	6.98088i	0.379149	+	0.656706i	−0.611789	+	0.791021i	$0.709550\pi$
$114$	−1.08841	+	1.88518i	−0.101939	+	0.176563i
$115$		0			0
$116$	5.46516	−	1.46439i	0.507427	−	0.135965i
$117$	−13.7884			−1.27474
$118$	−5.23980	+	1.40400i	−0.482363	+	0.129249i
$119$	1.40473	−	1.40473i	0.128771	−	0.128771i
$120$		0			0
$121$	6.63393			0.603084
$122$	3.91135	+	3.91135i	0.354117	+	0.354117i
$123$	−6.75079	+	25.1943i	−0.608698	+	2.27169i
$124$	−2.87632	−	10.7346i	−0.258301	−	0.963992i
$125$		0			0
$126$	−1.89094	−	0.506675i	−0.168458	−	0.0451382i
$127$	19.7751	+	5.29873i	1.75476	+	0.470187i	0.985632	−	0.168907i	$-0.0540239\pi$
$127$	19.7751	+	5.29873i	1.75476	+	0.470187i	0.769129	+	0.639094i	$0.220691\pi$
$128$	9.76707	−	5.63902i	0.863296	−	0.498424i
$129$	13.5142	−	3.62111i	1.18986	−	0.318821i
$130$		0			0
$131$	−9.44396	−	2.53050i	−0.825123	−	0.221091i	−0.178538	−	0.983933i	$-0.557137\pi$
$131$	−9.44396	−	2.53050i	−0.825123	−	0.221091i	−0.646585	+	0.762842i	$0.723803\pi$
$132$	2.48125	−	9.26013i	0.215965	−	0.805991i
$133$	−1.59676	+	0.921888i	−0.138456	+	0.0799379i
$134$	−3.63768	+	3.63768i	−0.314248	+	0.314248i
$135$		0			0
$136$	2.93944	−	1.69709i	0.252055	−	0.145524i
$137$	11.1133	−	11.1133i	0.949474	−	0.949474i	−0.0493096	−	0.998784i	$-0.515702\pi$
$137$	11.1133	−	11.1133i	0.949474	−	0.949474i	0.998784	+	0.0493096i	$0.0157021\pi$
$138$	2.83038	−	2.83038i	0.240938	−	0.240938i
$139$	4.61807	+	7.99874i	0.391700	+	0.678444i	0.992674	−	0.120824i	$-0.0385538\pi$
$139$	4.61807	+	7.99874i	0.391700	+	0.678444i	−0.600974	+	0.799269i	$0.705220\pi$
$140$		0			0
$141$	−5.06433	−	2.92389i	−0.426493	−	0.246236i
$142$		−	0.426681i		−	0.0358063i
$143$	−3.82617	+	6.62713i	−0.319961	+	0.554188i
$144$	8.60663	+	4.96904i	0.717219	+	0.414087i
$145$		0			0
$146$	0.715149	−	2.66897i	0.0591862	−	0.220886i
$147$	10.7674	+	10.7674i	0.888080	+	0.888080i
$148$	6.27927	+	8.70063i	0.516153	+	0.715188i
$149$		−	6.04883i		−	0.495539i	−0.968819	−	0.247770i	$-0.920302\pi$
$149$		−	6.04883i		−	0.495539i	0.968819	−	0.247770i	$-0.0796976\pi$
$150$		0			0
$151$	5.70690	+	3.29488i	0.464421	+	0.268134i	0.713901	−	0.700246i	$-0.246926\pi$
$151$	5.70690	+	3.29488i	0.464421	+	0.268134i	−0.249480	+	0.968380i	$0.580260\pi$
$152$	−3.04284	+	0.815328i	−0.246807	+	0.0661318i
$153$	6.05216	+	3.49421i	0.489288	+	0.282491i
$154$	−0.768241	+	0.768241i	−0.0619066	+	0.0619066i
$155$		0			0
$156$	−11.8813	−	11.8813i	−0.951262	−	0.951262i
$157$	6.65438	+	1.78303i	0.531077	+	0.142302i	0.514386	−	0.857559i	$-0.328020\pi$
$157$	6.65438	+	1.78303i	0.531077	+	0.142302i	0.0166914	+	0.999861i	$0.494687\pi$
$158$	2.02635	+	2.02635i	0.161208	+	0.161208i
$159$	18.2436			1.44681
$160$		0			0
$161$	3.27483	−	0.877488i	0.258093	−	0.0691557i
$162$			2.97308i			0.233587i
$163$	12.4793	+	21.6148i	0.977455	+	1.69300i	0.671585	+	0.740928i	$0.265614\pi$
$163$	12.4793	+	21.6148i	0.977455	+	1.69300i	0.305870	+	0.952073i	$0.401053\pi$
$164$	−15.3196	+	8.84480i	−1.19626	+	0.690663i
$165$		0			0
$166$	−0.800665	−	2.98812i	−0.0621436	−	0.231923i
$167$	−2.59212	+	4.48968i	−0.200584	+	0.347422i	−0.948717	−	0.316127i	$-0.897617\pi$
$167$	−2.59212	+	4.48968i	−0.200584	+	0.347422i	0.748133	+	0.663549i	$0.230951\pi$
$168$	−2.54518	−	4.40838i	−0.196365	−	0.340114i
$169$	0.206075	+	0.356933i	0.0158520	+	0.0274564i
$170$		0			0
$171$	−4.58634	−	4.58634i	−0.350726	−	0.350726i
$172$	8.21743	+	4.74434i	0.626573	+	0.361752i
$173$	20.3446	+	5.45131i	1.54677	+	0.414455i	0.928445	−	0.371469i	$-0.121146\pi$
$173$	20.3446	+	5.45131i	1.54677	+	0.414455i	0.618323	+	0.785924i	$0.287812\pi$
$174$		−	4.05297i		−	0.307255i
$175$		0			0
$176$	4.77653	−	2.75773i	0.360045	−	0.207872i
$177$		−	29.0423i		−	2.18296i
$178$	0.276901	+	1.03341i	0.0207546	+	0.0774571i
$179$	−14.6472	−	14.6472i	−1.09478	−	1.09478i	−0.995010	−	0.0997713i	$-0.968189\pi$
$179$	−14.6472	−	14.6472i	−1.09478	−	1.09478i	−0.0997713	−	0.995010i	$-0.531811\pi$
$180$		0			0
$181$	−10.9090	+	18.8950i	−0.810862	+	1.40445i	0.101400	+	0.994846i	$0.467668\pi$
$181$	−10.9090	+	18.8950i	−0.810862	+	1.40445i	−0.912262	+	0.409608i	$0.865666\pi$
$182$	0.492847	+	1.83933i	0.0365323	+	0.136340i
$183$	−25.6468	+	14.8072i	−1.89587	+	1.09458i
$184$	5.79259			0.427035
$185$		0			0
$186$	−7.96076			−0.583711
$187$	3.35884	−	1.93923i	0.245623	−	0.141810i
$188$	−1.02647	−	3.83084i	−0.0748631	−	0.279393i
$189$	1.06479	−	1.84427i	0.0774520	−	0.134151i
$190$		0			0
$191$	−17.9295	−	17.9295i	−1.29733	−	1.29733i	−0.930149	−	0.367183i	$-0.880322\pi$
$191$	−17.9295	−	17.9295i	−1.29733	−	1.29733i	−0.367183	−	0.930149i	$-0.619678\pi$
$192$	1.93838	+	7.23413i	0.139891	+	0.522078i
$193$		−	2.76514i		−	0.199039i	−0.995036	−	0.0995196i	$-0.968269\pi$
$193$		−	2.76514i		−	0.199039i	0.995036	−	0.0995196i	$-0.0317306\pi$
$194$	−0.287259	+	0.165849i	−0.0206240	+	0.0119073i
$195$		0			0
$196$			10.3273i			0.737662i
$197$	13.2102	+	3.53967i	0.941189	+	0.252191i	0.696619	−	0.717441i	$-0.254687\pi$
$197$	13.2102	+	3.53967i	0.941189	+	0.252191i	0.244570	+	0.969632i	$0.421353\pi$
$198$	−3.30991	−	1.91098i	−0.235225	−	0.135807i
$199$	2.86901	+	2.86901i	0.203378	+	0.203378i	0.801446	−	0.598067i	$-0.204065\pi$
$199$	2.86901	+	2.86901i	0.203378	+	0.203378i	−0.598067	+	0.801446i	$0.704065\pi$
$200$		0			0
$201$	−13.7711	−	23.8523i	−0.971341	−	1.68241i
$202$	3.22225	+	5.58111i	0.226717	+	0.392685i
$203$	1.71644	−	2.97296i	0.120470	−	0.208661i
$204$	2.20413	+	8.22594i	0.154320	+	0.575931i
$205$		0			0
$206$	−1.18862	+	0.686248i	−0.0828148	+	0.0478132i
$207$	5.96331	+	10.3288i	0.414479	+	0.717898i
$208$		−	9.66687i		−	0.670277i
$209$	−3.47700	+	0.931658i	−0.240509	+	0.0644442i
$210$		0			0
$211$	6.57006			0.452301			0.226151	−	0.974092i	$-0.427386\pi$
$211$	6.57006			0.452301			0.226151	+	0.974092i	$0.427386\pi$
$212$	8.74895	+	8.74895i	0.600880	+	0.600880i
$213$	2.20652	+	0.591235i	0.151188	+	0.0405107i
$214$	3.41073	+	3.41073i	0.233153	+	0.233153i
$215$		0			0
$216$	2.57280	−	2.57280i	0.175057	−	0.175057i
$217$	−5.83943	−	3.37140i	−0.396407	−	0.228865i
$218$	2.32299	−	0.622444i	0.157333	−	0.0421572i
$219$	12.8113	+	7.39658i	0.865704	+	0.499815i
$220$		0			0
$221$		−	6.79771i		−	0.457264i
$222$	7.18435	−	2.73167i	0.482182	−	0.183338i
$223$	−18.9226	−	18.9226i	−1.26715	−	1.26715i	−0.947555	−	0.319593i	$-0.896454\pi$
$223$	−18.9226	−	18.9226i	−1.26715	−	1.26715i	−0.319593	−	0.947555i	$-0.603546\pi$
$224$	1.36829	−	5.10655i	0.0914230	−	0.341195i
$225$		0			0
$226$	3.39144	+	1.95805i	0.225595	+	0.130247i
$227$	−5.82737	+	10.0933i	−0.386776	+	0.669916i	−0.992014	−	0.126129i	$-0.959745\pi$
$227$	−5.82737	+	10.0933i	−0.386776	+	0.669916i	0.605238	+	0.796045i	$0.293078\pi$
$228$		−	7.90393i		−	0.523450i
$229$	14.4306	+	8.33150i	0.953600	+	0.550561i	0.894197	−	0.447673i	$-0.147747\pi$
$229$	14.4306	+	8.33150i	0.953600	+	0.550561i	0.0594025	+	0.998234i	$0.481080\pi$
$230$		0			0
$231$	−2.90833	−	5.03737i	−0.191354	−	0.331435i
$232$	4.14736	−	4.14736i	0.272287	−	0.272287i
$233$	−2.60164	+	2.60164i	−0.170439	+	0.170439i	−0.787172	−	0.616733i	$-0.788456\pi$
$233$	−2.60164	+	2.60164i	−0.170439	+	0.170439i	0.616733	+	0.787172i	$0.288456\pi$
$234$	−5.80122	+	3.34934i	−0.379238	+	0.218953i
$235$		0			0
$236$	13.9276	−	13.9276i	0.906610	−	0.906610i
$237$	−13.2868	+	7.67114i	−0.863071	+	0.498294i
$238$	0.249791	−	0.932233i	0.0161916	−	0.0604277i
$239$	7.01240	+	1.87897i	0.453594	+	0.121540i	0.478381	−	0.878153i	$-0.341224\pi$
$239$	7.01240	+	1.87897i	0.453594	+	0.121540i	−0.0247864	+	0.999693i	$0.507891\pi$
$240$		0			0
$241$	−24.1435	+	6.46922i	−1.55522	+	0.416719i	−0.931145	−	0.364649i	$-0.881189\pi$
$241$	−24.1435	+	6.46922i	−1.55522	+	0.416719i	−0.624071	+	0.781368i	$0.714522\pi$
$242$	2.79110	−	1.61144i	0.179419	−	0.103587i
$243$	−21.1407	−	5.66464i	−1.35618	−	0.363387i
$244$	−19.4002	−	5.19827i	−1.24197	−	0.332785i
$245$		0			0
$246$	3.27965	+	12.2398i	0.209103	+	0.780384i
$247$	−1.63290	+	6.09408i	−0.103899	+	0.387757i
$248$	−8.14615	−	8.14615i	−0.517281	−	0.517281i
$249$	16.5621			1.04958
$250$		0			0
$251$	3.06212	−	3.06212i	0.193279	−	0.193279i	−0.603832	−	0.797111i	$-0.706360\pi$
$251$	3.06212	−	3.06212i	0.193279	−	0.193279i	0.797111	+	0.603832i	$0.206360\pi$
$252$	6.86589	−	1.83971i	0.432511	−	0.115891i
$253$	6.61907			0.416137
$254$	9.60712	−	2.57422i	0.602804	−	0.161521i
$255$		0			0
$256$	−0.139904	+	0.242321i	−0.00874400	+	0.0151450i
$257$	−15.4811	−	26.8141i	−0.965687	−	1.67262i	−0.707757	−	0.706456i	$-0.750293\pi$
$257$	−15.4811	−	26.8141i	−0.965687	−	1.67262i	−0.257931	−	0.966163i	$-0.583041\pi$
$258$	4.80623	−	4.80623i	0.299223	−	0.299223i
$259$	6.42678	+	1.03883i	0.399341	+	0.0645497i
$260$		0			0
$261$	11.6647	+	3.12556i	0.722029	+	0.193467i
$262$	−4.58805	+	1.22936i	−0.283451	+	0.0759503i
$263$	3.28492	+	12.2595i	0.202557	+	0.755953i	0.990180	+	0.139796i	$0.0446446\pi$
$263$	3.28492	+	12.2595i	0.202557	+	0.755953i	−0.787623	+	0.616157i	$0.788689\pi$
$264$	−2.57215	−	9.59941i	−0.158305	−	0.590803i
$265$		0			0
$266$	−0.447870	+	0.775734i	−0.0274607	+	0.0475633i
$267$	−5.72780			−0.350536
$268$	4.83455	−	18.0428i	0.295317	−	1.10214i
$269$		−	16.7531i		−	1.02145i	−0.859744	−	0.510726i	$-0.829377\pi$
$269$		−	16.7531i		−	1.02145i	0.859744	−	0.510726i	$-0.170623\pi$
$270$		0			0
$271$	−9.55233	−	16.5451i	−0.580263	−	1.00504i	−0.995448	−	0.0953075i	$-0.969617\pi$
$271$	−9.55233	−	16.5451i	−0.580263	−	1.00504i	0.415185	−	0.909737i	$-0.363717\pi$
$272$	−2.44974	+	4.24308i	−0.148537	+	0.257274i
$273$	−10.1948			−0.617015
$274$	1.97619	−	7.37523i	0.119386	−	0.445554i
$275$		0			0
$276$	−3.76163	+	14.0386i	−0.226423	+	0.845024i
$277$	−14.5711	−	8.41266i	−0.875495	−	0.505468i	−0.00632489	−	0.999980i	$-0.502013\pi$
$277$	−14.5711	−	8.41266i	−0.875495	−	0.505468i	−0.869171	+	0.494512i	$0.835347\pi$
$278$	3.88593	+	2.24354i	0.233063	+	0.134559i
$279$	6.13916	−	22.9116i	0.367542	−	1.37168i
$280$		0			0
$281$	5.84495	−	21.8136i	0.348680	−	1.30129i	−0.539573	−	0.841939i	$-0.681414\pi$
$281$	5.84495	−	21.8136i	0.348680	−	1.30129i	0.888253	−	0.459354i	$-0.151919\pi$
$282$	−2.84096			−0.169177
$283$	2.18654	−	3.78721i	0.129977	−	0.225126i	−0.793691	−	0.608322i	$-0.791843\pi$
$283$	2.18654	−	3.78721i	0.129977	−	0.225126i	0.923667	+	0.383196i	$0.125176\pi$
$284$	0.774628	+	1.34170i	0.0459657	+	0.0796150i
$285$		0			0
$286$			3.71765i			0.219829i
$287$	−2.77788	+	10.3672i	−0.163973	+	0.611956i
$288$	18.5976			1.09587
$289$	6.77735	−	11.7387i	0.398668	−	0.690513i
$290$		0			0
$291$	−0.459621	−	1.71533i	−0.0269435	−	0.100554i
$292$	2.59667	+	9.69091i	0.151959	+	0.567117i
$293$	27.6145	−	7.39929i	1.61326	−	0.432271i	0.664247	−	0.747513i	$-0.268752\pi$
$293$	27.6145	−	7.39929i	1.61326	−	0.432271i	0.949011	+	0.315242i	$0.102086\pi$
$294$	7.14567	+	1.91468i	0.416744	+	0.111666i
$295$		0			0
$296$	10.1470	+	4.55637i	0.589780	+	0.264834i
$297$	2.93989	−	2.93989i	0.170590	−	0.170590i
$298$	−1.46931	−	2.54493i	−0.0851151	−	0.147424i
$299$	5.80057	−	10.0469i	0.335456	−	0.581026i
$300$		0			0
$301$	5.56095	−	1.49005i	0.320528	−	0.0858851i
$302$	3.20142			0.184221
$303$	−33.3268	+	8.92989i	−1.91458	+	0.513009i
$304$	3.21541	−	3.21541i	0.184416	−	0.184416i
$305$		0			0
$306$	3.39510			0.194085
$307$	−0.859218	−	0.859218i	−0.0490382	−	0.0490382i	0.682162	−	0.731201i	$-0.261040\pi$
$307$	−0.859218	−	0.859218i	−0.0490382	−	0.0490382i	−0.731201	+	0.682162i	$0.761040\pi$
$308$	1.02101	−	3.81045i	0.0581773	−	0.217121i
$309$	−1.90181	−	7.09766i	−0.108190	−	0.403772i
$310$		0			0
$311$	27.8607	+	7.46525i	1.57983	+	0.423315i	0.938875	−	0.344259i	$-0.111870\pi$
$311$	27.8607	+	7.46525i	1.57983	+	0.423315i	0.640959	+	0.767575i	$0.278537\pi$
$312$	−16.8247	−	4.50817i	−0.952513	−	0.255225i
$313$	1.16260	−	0.671228i	0.0657141	−	0.0379400i	−0.466783	−	0.884372i	$-0.654587\pi$
$313$	1.16260	−	0.671228i	0.0657141	−	0.0379400i	0.532497	+	0.846432i	$0.321254\pi$
$314$	3.23282	−	0.866230i	0.182438	−	0.0488842i
$315$		0			0
$316$	−10.0506	−	2.69306i	−0.565392	−	0.151496i
$317$	−3.82182	+	14.2632i	−0.214655	+	0.801102i	0.771633	+	0.636068i	$0.219440\pi$
$317$	−3.82182	+	14.2632i	−0.214655	+	0.801102i	−0.986288	+	0.165034i	$0.947227\pi$
$318$	7.67566	−	4.43154i	0.430429	−	0.248509i
$319$	4.73910	−	4.73910i	0.265339	−	0.265339i
$320$		0			0
$321$	−22.3642	+	12.9120i	−1.24825	+	0.720677i
$322$	1.16467	−	1.16467i	0.0649046	−	0.0649046i
$323$	2.26107	−	2.26107i	0.125809	−	0.125809i
$324$	−5.39755	−	9.34883i	−0.299864	−	0.519380i
$325$		0			0
$326$	10.5009	+	6.06267i	0.581589	+	0.335780i
$327$			12.8755i			0.712017i
$328$	−9.16886	+	15.8809i	−0.506265	+	0.876877i
$329$	−2.08392	−	1.20315i	−0.114890	−	0.0663319i
$330$		0			0
$331$	−4.83434	+	18.0420i	−0.265719	+	0.991678i	0.696089	+	0.717955i	$0.254922\pi$
$331$	−4.83434	+	18.0420i	−0.265719	+	0.991678i	−0.961809	+	0.273723i	$0.911745\pi$
$332$	7.94254	+	7.94254i	0.435904	+	0.435904i
$333$	2.32155	+	22.7837i	0.127220	+	1.24854i
$334$			2.51860i			0.137811i
$335$		0			0
$336$	6.36348	+	3.67396i	0.347156	+	0.200431i
$337$	−5.89849	+	1.58050i	−0.321311	+	0.0860951i	−0.415870	−	0.909424i	$-0.636523\pi$
$337$	−5.89849	+	1.58050i	−0.321311	+	0.0860951i	0.0945584	+	0.995519i	$0.469856\pi$
$338$	0.173405	+	0.100115i	0.00943197	+	0.00544555i
$339$	−14.8251	+	14.8251i	−0.805191	+	0.805191i
$340$		0			0
$341$	−9.30844	−	9.30844i	−0.504081	−	0.504081i
$342$	−3.04367	−	0.815550i	−0.164583	−	0.0440999i
$343$	9.72824	+	9.72824i	0.525276	+	0.525276i
$344$	9.83632			0.530339
$345$		0			0
$346$	9.88376	−	2.64834i	0.531354	−	0.142376i
$347$		−	36.4201i		−	1.95513i	−0.210632	−	0.977565i	$-0.567552\pi$
$347$		−	36.4201i		−	1.95513i	0.210632	−	0.977565i	$-0.432448\pi$
$348$	7.35806	+	12.7445i	0.394433	+	0.683179i
$349$	−5.28579	+	3.05175i	−0.282942	+	0.163357i	−0.634754	−	0.772714i	$-0.718899\pi$
$349$	−5.28579	+	3.05175i	−0.282942	+	0.163357i	0.351813	+	0.936070i	$0.385565\pi$
$350$		0			0
$351$	−1.88602	−	7.03871i	−0.100668	−	0.375699i
$352$	5.16066	−	8.93853i	0.275064	−	0.476425i
$353$	−11.6679	−	20.2094i	−0.621021	−	1.07564i	−0.989296	−	0.145923i	$-0.953385\pi$
$353$	−11.6679	−	20.2094i	−0.621021	−	1.07564i	0.368275	−	0.929717i	$-0.379948\pi$
$354$	−7.05465	−	12.2190i	−0.374950	−	0.649433i
$355$		0			0
$356$	−2.74684	−	2.74684i	−0.145582	−	0.145582i
$357$	4.47478	+	2.58352i	0.236831	+	0.136734i
$358$	−9.72045	−	2.60459i	−0.513742	−	0.137657i
$359$			13.7535i			0.725881i	0.931812	+	0.362941i	$0.118227\pi$
$359$			13.7535i			0.725881i	−0.931812	+	0.362941i	$0.881773\pi$
$360$		0			0
$361$	13.8843	−	8.01612i	0.730754	−	0.421901i
$362$			10.5996i			0.557103i
$363$	4.46582	+	16.6667i	0.234395	+	0.874773i
$364$	−4.88902	−	4.88902i	−0.256254	−	0.256254i
$365$		0			0
$366$	−7.19360	+	12.4597i	−0.376016	+	0.651278i
$367$	−1.51502	−	5.65412i	−0.0790832	−	0.295143i	0.915045	−	0.403352i	$-0.132155\pi$
$367$	−1.51502	−	5.65412i	−0.0790832	−	0.295143i	−0.994128	+	0.108209i	$0.965488\pi$
$368$	−7.24134	+	4.18079i	−0.377481	+	0.217939i
$369$	−37.7563			−1.96552
$370$		0			0
$371$	7.50707			0.389748
$372$	25.0326	−	14.4526i	1.29788	−	0.749330i
$373$	−7.08637	−	26.4467i	−0.366918	−	1.36936i	−0.864802	−	0.502114i	$-0.832556\pi$
$373$	−7.08637	−	26.4467i	−0.366918	−	1.36936i	0.497883	−	0.867244i	$-0.334111\pi$
$374$	0.942113	−	1.63179i	0.0487155	−	0.0843777i
$375$		0			0
$376$	−2.90712	−	2.90712i	−0.149923	−	0.149923i
$377$	−3.04026	−	11.3464i	−0.156581	−	0.584369i
$378$		−	1.03459i		−	0.0532134i
$379$	−14.5045	+	8.37420i	−0.745048	+	0.430154i	−0.823902	−	0.566733i	$-0.808207\pi$
$379$	−14.5045	+	8.37420i	−0.745048	+	0.430154i	0.0788540	+	0.996886i	$0.474874\pi$
$380$		0			0
$381$			53.2488i			2.72802i
$382$	−11.8987	−	3.18825i	−0.608791	−	0.163125i
$383$	27.3880	+	15.8124i	1.39946	+	0.807978i	0.994336	−	0.106284i	$-0.0338952\pi$
$383$	27.3880	+	15.8124i	1.39946	+	0.807978i	0.405123	+	0.914262i	$0.367229\pi$
$384$	20.7421	+	20.7421i	1.05849	+	1.05849i
$385$		0			0
$386$	−0.671677	−	1.16338i	−0.0341875	−	0.0592144i
$387$	10.1262	+	17.5391i	0.514745	+	0.891564i
$388$	0.602190	−	1.04302i	0.0305716	−	0.0529515i
$389$	9.26758	+	34.5871i	0.469885	+	1.75364i	0.640163	+	0.768239i	$0.278867\pi$
$389$	9.26758	+	34.5871i	0.469885	+	1.75364i	−0.170278	+	0.985396i	$0.554467\pi$
$390$		0			0
$391$	−5.09209	+	2.93992i	−0.257518	+	0.148678i
$392$	5.35282	+	9.27135i	0.270358	+	0.468274i
$393$		−	25.4299i		−	1.28277i
$394$	6.41776	−	1.71963i	0.323322	−	0.0866339i
$395$		0			0
$396$	13.8773			0.697361
$397$	−15.6873	−	15.6873i	−0.787325	−	0.787325i	0.193730	−	0.981055i	$-0.437941\pi$
$397$	−15.6873	−	15.6873i	−0.787325	−	0.787325i	−0.981055	+	0.193730i	$0.937941\pi$
$398$	1.90399	+	0.510172i	0.0954382	+	0.0255726i
$399$	−3.39100	−	3.39100i	−0.169762	−	0.169762i
$400$		0			0
$401$	14.8433	−	14.8433i	0.741241	−	0.741241i	−0.231576	−	0.972817i	$-0.574388\pi$
$401$	14.8433	−	14.8433i	0.741241	−	0.741241i	0.972817	+	0.231576i	$0.0743882\pi$
$402$	−11.5879	−	6.69027i	−0.577951	−	0.333680i
$403$	−22.2864	+	5.97162i	−1.11016	+	0.297468i
$404$	−20.2647	−	11.6998i	−1.00821	−	0.582089i
$405$		0			0
$406$		−	1.66776i		−	0.0827693i
$407$	11.5947	+	5.20647i	0.574729	+	0.258075i
$408$	6.24243	+	6.24243i	0.309046	+	0.309046i
$409$	−9.15489	+	34.1665i	−0.452680	+	1.68943i	0.242139	+	0.970242i	$0.422151\pi$
$409$	−9.15489	+	34.1665i	−0.452680	+	1.68943i	−0.694819	+	0.719185i	$0.744516\pi$
$410$		0			0
$411$	35.4016	+	20.4391i	1.74623	+	1.00819i
$412$	2.49173	−	4.31581i	0.122759	−	0.212625i
$413$		−	11.9506i		−	0.588052i
$414$	5.01790	+	2.89708i	0.246616	+	0.142384i
$415$		0			0
$416$	−9.04501	−	15.6664i	−0.443468	−	0.768110i
$417$	−16.9867	+	16.9867i	−0.831844	+	0.831844i
$418$	−1.23657	+	1.23657i	−0.0604827	+	0.0604827i
$419$	−12.8247	+	7.40437i	−0.626530	+	0.361727i	−0.779407	−	0.626518i	$-0.784479\pi$
$419$	−12.8247	+	7.40437i	−0.626530	+	0.361727i	0.152877	+	0.988245i	$0.451146\pi$
$420$		0			0
$421$	−13.0213	+	13.0213i	−0.634620	+	0.634620i	−0.949223	−	0.314603i	$-0.898129\pi$
$421$	−13.0213	+	13.0213i	−0.634620	+	0.634620i	0.314603	+	0.949223i	$0.398129\pi$
$422$	2.76423	−	1.59593i	0.134560	−	0.0776885i
$423$	2.19088	−	8.17648i	0.106524	−	0.397554i
$424$	12.3892	+	3.31967i	0.601671	+	0.161217i
$425$		0			0
$426$	1.07197	−	0.287233i	0.0519369	−	0.0139165i
$427$	−10.5534	+	6.09301i	−0.510715	+	0.294861i
$428$	−16.9171	−	4.53293i	−0.817720	−	0.219107i
$429$	−19.2253	−	5.15140i	−0.928205	−	0.248712i
$430$		0			0
$431$	−9.92884	−	37.0549i	−0.478255	−	1.78487i	−0.608681	−	0.793415i	$-0.708301\pi$
$431$	−9.92884	−	37.0549i	−0.478255	−	1.78487i	0.130425	−	0.991458i	$-0.458366\pi$
$432$	−1.35936	+	5.07318i	−0.0654020	+	0.244084i
$433$	10.7074	+	10.7074i	0.514566	+	0.514566i	0.915922	−	0.401356i	$-0.131461\pi$
$433$	10.7074	+	10.7074i	0.514566	+	0.514566i	−0.401356	+	0.915922i	$0.631461\pi$
$434$	−3.27577			−0.157242
$435$		0			0
$436$	−6.17461	+	6.17461i	−0.295710	+	0.295710i
$437$	5.27121	−	1.41242i	0.252156	−	0.0675650i
$438$	7.18678			0.343398
$439$	5.94424	−	1.59276i	0.283703	−	0.0760181i	−0.114161	−	0.993462i	$-0.536418\pi$
$439$	5.94424	−	1.59276i	0.283703	−	0.0760181i	0.397865	+	0.917444i	$0.369751\pi$
$440$		0			0
$441$	−11.0212	+	19.0892i	−0.524817	+	0.909010i
$442$	−1.65123	−	2.86001i	−0.0785408	−	0.136037i
$443$	2.15090	−	2.15090i	0.102192	−	0.102192i	−0.654162	−	0.756354i	$-0.726979\pi$
$443$	2.15090	−	2.15090i	0.102192	−	0.102192i	0.756354	+	0.654162i	$0.226979\pi$
$444$	−17.6319	+	21.6327i	−0.836771	+	1.02664i
$445$		0			0
$446$	−12.5578	−	3.36484i	−0.594627	−	0.159330i
$447$	15.1967	−	4.07194i	0.718779	−	0.192596i
$448$	0.797624	+	2.97677i	0.0376842	+	0.140639i
$449$	−5.83410	−	21.7731i	−0.275328	−	1.02754i	−0.955621	−	0.294598i	$-0.904814\pi$
$449$	−5.83410	−	21.7731i	−0.275328	−	1.02754i	0.680293	−	0.732940i	$-0.261852\pi$
$450$		0			0
$451$	−10.4771	+	18.1468i	−0.493346	+	0.854500i
$452$	−14.2191			−0.668812
$453$	−4.43609	+	16.5557i	−0.208426	+	0.777855i
$454$			5.66208i			0.265735i
$455$		0			0
$456$	−4.09676	−	7.09579i	−0.191848	−	0.332291i
$457$	2.92148	−	5.06014i	0.136661	−	0.236704i	−0.789570	−	0.613661i	$-0.789696\pi$
$457$	2.92148	−	5.06014i	0.136661	−	0.236704i	0.926231	+	0.376957i	$0.123030\pi$
$458$	8.09519			0.378263
$459$	−0.955895	+	3.56745i	−0.0446173	+	0.166514i
$460$		0			0
$461$	2.21024	−	8.24872i	0.102941	−	0.384181i	−0.895162	−	0.445740i	$-0.852941\pi$
$461$	2.21024	−	8.24872i	0.102941	−	0.384181i	0.998103	+	0.0615588i	$0.0196072\pi$
$462$	−2.44724	−	1.41292i	−0.113856	−	0.0657349i
$463$	−4.45024	−	2.56935i	−0.206820	−	0.119408i	0.393012	−	0.919533i	$-0.371433\pi$
$463$	−4.45024	−	2.56935i	−0.206820	−	0.119408i	−0.599833	+	0.800125i	$0.704766\pi$
$464$	−2.19128	+	8.17797i	−0.101728	+	0.379653i
$465$		0			0
$466$	−0.462628	+	1.72655i	−0.0214308	+	0.0799810i
$467$	−10.8145			−0.500436			−0.250218	−	0.968189i	$-0.580502\pi$
$467$	−10.8145			−0.500436			−0.250218	+	0.968189i	$0.580502\pi$
$468$	12.1613	−	21.0639i	0.562155	−	0.973681i
$469$	−5.66669	−	9.81499i	−0.261663	−	0.453214i
$470$		0			0
$471$			17.9183i			0.825633i
$472$	5.28463	−	19.7225i	0.243245	−	0.907802i
$473$	11.2398			0.516805
$474$	−3.72678	+	6.45497i	−0.171177	+	0.296487i
$475$		0			0
$476$	0.906979	+	3.38489i	0.0415713	+	0.155146i
$477$	6.83501	+	25.5086i	0.312954	+	1.16796i
$478$	3.40675	−	0.912836i	0.155821	−	0.0417521i
$479$	3.94037	+	1.05582i	0.180040	+	0.0482416i	0.347713	−	0.937601i	$-0.386958\pi$
$479$	3.94037	+	1.05582i	0.180040	+	0.0482416i	−0.167673	+	0.985843i	$0.553625\pi$
$480$		0			0
$481$	18.0637	−	13.0366i	0.823633	−	0.594418i
$482$	−8.58646	+	8.58646i	−0.391103	+	0.391103i
$483$	4.40909	+	7.63677i	0.200621	+	0.347485i
$484$	−5.85106	+	10.1343i	−0.265957	+	0.460651i
$485$		0			0
$486$	−10.2705	+	2.75198i	−0.465881	+	0.124833i
$487$	−10.4321			−0.472725			−0.236363	−	0.971665i	$-0.575955\pi$
$487$	−10.4321			−0.472725			−0.236363	+	0.971665i	$0.575955\pi$
$488$	−20.1110	+	5.38872i	−0.910382	+	0.243936i
$489$	−45.9028	+	45.9028i	−2.07580	+	2.07580i
$490$		0			0
$491$	−7.43200			−0.335401			−0.167701	−	0.985838i	$-0.553634\pi$
$491$	−7.43200			−0.335401			−0.167701	+	0.985838i	$0.553634\pi$
$492$	−32.5340	−	32.5340i	−1.46674	−	1.46674i
$493$	−1.54090	+	5.75073i	−0.0693987	+	0.259000i
$494$	0.793294	+	2.96061i	0.0356920	+	0.133204i
$495$		0			0
$496$	16.0630	+	4.30407i	0.721250	+	0.193258i
$497$	0.907960	+	0.243287i	0.0407276	+	0.0109129i
$498$	6.96818	−	4.02308i	0.312251	−	0.180278i
$499$	−24.1425	+	6.46895i	−1.08077	+	0.289590i	−0.754909	−	0.655829i	$-0.772319\pi$
$499$	−24.1425	+	6.46895i	−1.08077	+	0.289590i	−0.325856	+	0.945419i	$0.605652\pi$
$500$		0			0
$501$	−13.0246	−	3.48992i	−0.581894	−	0.155918i
$502$	0.544511	−	2.03214i	0.0243027	−	0.0906990i
$503$	18.0415	−	10.4163i	0.804431	−	0.464438i	−0.0405874	−	0.999176i	$-0.512923\pi$
$503$	18.0415	−	10.4163i	0.804431	−	0.464438i	0.845018	+	0.534738i	$0.179590\pi$
$504$	5.21033	−	5.21033i	0.232087	−	0.232087i
$505$		0			0
$506$	2.78485	−	1.60783i	0.123802	−	0.0714769i
$507$	−0.758011	+	0.758011i	−0.0336645	+	0.0336645i
$508$	−25.5361	+	25.5361i	−1.13298	+	1.13298i
$509$	−8.54631	−	14.8026i	−0.378808	−	0.656115i	0.612081	−	0.790795i	$-0.290333\pi$
$509$	−8.54631	−	14.8026i	−0.378808	−	0.656115i	−0.990889	+	0.134680i	$0.956999\pi$
$510$		0			0
$511$	5.27170	+	3.04362i	0.233206	+	0.134642i
$512$			22.6920i			1.00286i
$513$	1.71390	−	2.96856i	0.0756705	−	0.131065i
$514$	−13.0268	−	7.52102i	−0.574587	−	0.331738i
$515$		0			0
$516$	−6.38757	+	23.8387i	−0.281197	+	1.04944i
$517$	−3.32191	−	3.32191i	−0.146097	−	0.146097i
$518$	2.95629	−	1.12406i	0.129892	−	0.0493882i
$519$			54.7821i			2.40467i
$520$		0			0
$521$	29.6690	+	17.1294i	1.29982	+	0.750453i	0.980373	−	0.197150i	$-0.0631686\pi$
$521$	29.6690	+	17.1294i	1.29982	+	0.750453i	0.319450	+	0.947603i	$0.396502\pi$
$522$	5.66694	−	1.51845i	0.248035	−	0.0664608i
$523$	11.7635	+	6.79166i	0.514382	+	0.296979i	0.734633	−	0.678465i	$-0.237354\pi$
$523$	11.7635	+	6.79166i	0.514382	+	0.296979i	−0.220251	+	0.975443i	$0.570688\pi$
$524$	12.1952	−	12.1952i	0.532750	−	0.532750i
$525$		0			0
$526$	4.36001	+	4.36001i	0.190105	+	0.190105i
$527$	11.2955	+	3.02661i	0.492038	+	0.131841i
$528$	10.1438	+	10.1438i	0.441453	+	0.441453i
$529$	12.9653			0.563710
$530$		0			0
$531$	40.6076	−	10.8808i	1.76222	−	0.472185i
$532$		−	3.25239i		−	0.141009i
$533$	18.3630	+	31.8056i	0.795389	+	1.37765i
$534$	−2.40986	+	1.39134i	−0.104285	+	0.0602090i
$535$		0			0
$536$	−5.01168	−	18.7038i	−0.216471	−	0.807882i
$537$	26.9385	−	46.6588i	1.16248	−	2.01348i
$538$	−4.06947	−	7.04853i	−0.175447	−	0.303883i
$539$	6.11656	+	10.5942i	0.263459	+	0.456324i
$540$		0			0
$541$	−14.8341	−	14.8341i	−0.637767	−	0.637767i	0.312237	−	0.950004i	$-0.398922\pi$
$541$	−14.8341	−	14.8341i	−0.637767	−	0.637767i	−0.950004	+	0.312237i	$0.898922\pi$
$542$	−8.03792	−	4.64069i	−0.345258	−	0.199335i
$543$	−54.8143	−	14.6874i	−2.35231	−	0.630299i
$544$			9.16861i			0.393101i
$545$		0			0
$546$	−4.28925	+	2.47640i	−0.183563	+	0.105980i
$547$			23.4215i			1.00143i	0.865612	+	0.500715i	$0.166930\pi$
$547$			23.4215i			1.00143i	−0.865612	+	0.500715i	$0.833070\pi$
$548$	7.17544	+	26.7791i	0.306520	+	1.14395i
$549$	−30.3123	−	30.3123i	−1.29370	−	1.29370i
$550$		0			0
$551$	2.76280	−	4.78532i	0.117699	−	0.203861i
$552$	3.89945	+	14.5529i	0.165971	+	0.619414i
$553$	−5.46739	+	3.15660i	−0.232497	+	0.134232i
$554$	−8.17404			−0.347282
$555$		0			0
$556$	−16.2924			−0.690951
$557$	10.6258	−	6.13483i	0.450231	−	0.259941i	−0.257697	−	0.966226i	$-0.582964\pi$
$557$	10.6258	−	6.13483i	0.450231	−	0.259941i	0.707928	+	0.706285i	$0.249630\pi$
$558$	−2.98251	−	11.1309i	−0.126260	−	0.471208i
$559$	9.84988	−	17.0605i	0.416605	−	0.721582i
$560$		0			0
$561$	7.13310	+	7.13310i	0.301160	+	0.301160i
$562$	−2.83958	−	10.5975i	−0.119780	−	0.447027i
$563$		−	2.53059i		−	0.106652i	−0.998577	−	0.0533258i	$-0.983018\pi$
$563$		−	2.53059i		−	0.106652i	0.998577	−	0.0533258i	$-0.0169822\pi$
$564$	8.93337	−	5.15769i	0.376163	−	0.217178i
$565$		0			0
$566$		−	2.12453i		−	0.0893005i
$567$	−6.32660	−	1.69521i	−0.265692	−	0.0711920i
$568$	1.39085	+	0.803009i	0.0583589	+	0.0336935i
$569$	−24.7731	−	24.7731i	−1.03854	−	1.03854i	−0.999227	−	0.0393138i	$-0.987483\pi$
$569$	−24.7731	−	24.7731i	−1.03854	−	1.03854i	−0.0393138	−	0.999227i	$-0.512517\pi$
$570$		0			0
$571$	−20.6850	−	35.8275i	−0.865642	−	1.49934i	−0.866408	−	0.499336i	$-0.833577\pi$
$571$	−20.6850	−	35.8275i	−0.865642	−	1.49934i	0.000766004	−	1.00000i	$-0.499756\pi$
$572$	−6.74930	−	11.6901i	−0.282202	−	0.488789i
$573$	32.9752	−	57.1146i	1.37756	−	2.38600i
$574$	1.34954	+	5.03657i	0.0563289	+	0.210222i
$575$		0			0
$576$	−9.38869	+	5.42056i	−0.391195	+	0.225857i
$577$	−16.4321	−	28.4613i	−0.684078	−	1.18486i	−0.973725	−	0.227725i	$-0.926871\pi$
$577$	−16.4321	−	28.4613i	−0.684078	−	1.18486i	0.289647	−	0.957134i	$-0.406462\pi$
$578$		−	6.58512i		−	0.273905i
$579$	6.94696	−	1.86143i	0.288706	−	0.0773585i
$580$		0			0
$581$	6.81513			0.282739
$582$	−0.610046	−	0.610046i	−0.0252872	−	0.0252872i
$583$	14.1568	+	3.79331i	0.586317	+	0.157103i
$584$	7.35416	+	7.35416i	0.304317	+	0.304317i
$585$		0			0
$586$	9.82093	−	9.82093i	0.405699	−	0.405699i
$587$	17.8170	+	10.2866i	0.735385	+	0.424574i	0.820389	−	0.571806i	$-0.193757\pi$
$587$	17.8170	+	10.2866i	0.735385	+	0.424574i	−0.0850042	+	0.996381i	$0.527090\pi$
$588$	−25.9456	+	6.95209i	−1.06998	+	0.286700i
$589$	−9.39923	−	5.42665i	−0.387288	−	0.223601i
$590$		0			0
$591$			35.5714i			1.46321i
$592$	−15.9733	+	1.62760i	−0.656498	+	0.0668941i
$593$	−14.5325	−	14.5325i	−0.596779	−	0.596779i	0.342675	−	0.939454i	$-0.388667\pi$
$593$	−14.5325	−	14.5325i	−0.596779	−	0.596779i	−0.939454	+	0.342675i	$0.888667\pi$
$594$	0.522776	−	1.95103i	0.0214498	−	0.0800516i
$595$		0			0
$596$	9.24050	+	5.33501i	0.378506	+	0.218530i
$597$	−5.27656	+	9.13926i	−0.215955	+	0.374045i
$598$		−	5.63604i		−	0.230475i
$599$	18.6453	+	10.7649i	0.761827	+	0.439841i	0.829951	−	0.557836i	$-0.188368\pi$
$599$	18.6453	+	10.7649i	0.761827	+	0.439841i	−0.0681245	+	0.997677i	$0.521701\pi$
$600$		0			0
$601$	−6.57451	−	11.3874i	−0.268180	−	0.464501i	0.700212	−	0.713935i	$-0.253089\pi$
$601$	−6.57451	−	11.3874i	−0.268180	−	0.464501i	−0.968392	+	0.249434i	$0.919755\pi$
$602$	1.97771	−	1.97771i	0.0806056	−	0.0806056i
$603$	28.1914	−	28.1914i	1.14804	−	1.14804i
$604$	−10.0669	+	5.81211i	−0.409615	+	0.236491i
$605$		0			0
$606$	−11.8525	+	11.8525i	−0.481474	+	0.481474i
$607$	−1.41563	+	0.817317i	−0.0574588	+	0.0331739i	−0.528454	−	0.848962i	$-0.677228\pi$
$607$	−1.41563	+	0.817317i	−0.0574588	+	0.0331739i	0.470995	+	0.882136i	$0.343895\pi$
$608$	2.20243	−	8.21956i	0.0893201	−	0.333347i
$609$	8.62455	+	2.31094i	0.349484	+	0.0936441i
$610$		0			0
$611$	−7.95335	+	2.13109i	−0.321758	+	0.0862148i
$612$	−10.6759	+	6.16373i	−0.431547	+	0.249154i
$613$	−32.2668	−	8.64586i	−1.30324	−	0.349203i	−0.460568	−	0.887625i	$-0.652354\pi$
$613$	−32.2668	−	8.64586i	−1.30324	−	0.349203i	−0.842676	+	0.538422i	$0.819021\pi$
$614$	−0.570211	−	0.152788i	−0.0230119	−	0.00616601i
$615$		0			0
$616$	−1.05842	−	3.95006i	−0.0426448	−	0.159152i
$617$	−2.14484	+	8.00465i	−0.0863480	+	0.322255i	−0.995566	−	0.0940651i	$-0.970014\pi$
$617$	−2.14484	+	8.00465i	−0.0863480	+	0.322255i	0.909218	+	0.416320i	$0.136680\pi$
$618$	−2.52424	−	2.52424i	−0.101540	−	0.101540i
$619$	35.3283			1.41997			0.709983	−	0.704219i	$-0.248703\pi$
$619$	35.3283			1.41997			0.709983	+	0.704219i	$0.248703\pi$
$620$		0			0
$621$	−4.45694	+	4.45694i	−0.178851	+	0.178851i
$622$	13.5352	−	3.62675i	0.542713	−	0.145419i
$623$	−2.35693			−0.0944286
$624$	24.2864	−	6.50753i	0.972235	−	0.260510i
$625$		0			0
$626$	0.326095	−	0.564812i	0.0130334	−	0.0225744i
$627$	−4.68128	−	8.10821i	−0.186952	−	0.323811i
$628$	−8.59295	+	8.59295i	−0.342896	+	0.342896i
$629$	−11.2324	+	1.14453i	−0.447864	+	0.0456352i
$630$		0			0
$631$	16.9880	+	4.55192i	0.676281	+	0.181209i	0.580583	−	0.814201i	$-0.302825\pi$
$631$	16.9880	+	4.55192i	0.676281	+	0.181209i	0.0956987	+	0.995410i	$0.469491\pi$
$632$	−10.4189	+	2.79173i	−0.414440	+	0.111049i
$633$	4.42282	+	16.5062i	0.175791	+	0.656062i
$634$	1.85671	+	6.92933i	0.0737393	+	0.275199i
$635$		0			0
$636$	−16.0907	+	27.8699i	−0.638038	+	1.10511i
$637$	21.4408			0.849515
$638$	0.842715	−	3.14505i	0.0333634	−	0.124514i
$639$			3.30671i			0.130811i
$640$		0			0
$641$	−1.89712	−	3.28591i	−0.0749317	−	0.129785i	0.826125	−	0.563487i	$-0.190541\pi$
$641$	−1.89712	−	3.28591i	−0.0749317	−	0.129785i	−0.901057	+	0.433702i	$0.857207\pi$
$642$	−6.27288	+	10.8649i	−0.247571	+	0.428805i
$643$	12.8924			0.508428			0.254214	−	0.967148i	$-0.418183\pi$
$643$	12.8924			0.508428			0.254214	+	0.967148i	$0.418183\pi$
$644$	−1.54787	+	5.77674i	−0.0609947	+	0.227635i
$645$		0			0
$646$	0.402067	−	1.50053i	0.0158191	−	0.0590377i
$647$	−3.72562	−	2.15099i	−0.146469	−	0.0845640i	0.424974	−	0.905205i	$-0.360283\pi$
$647$	−3.72562	−	2.15099i	−0.146469	−	0.0845640i	−0.571444	+	0.820641i	$0.693616\pi$
$648$	−9.69136	−	5.59531i	−0.380712	−	0.219804i
$649$	6.03864	−	22.5365i	0.237037	−	0.884636i
$650$		0			0
$651$	4.53911	−	16.9402i	0.177902	−	0.663938i
$652$	−44.0265			−1.72421
$653$	1.00320	−	1.73760i	0.0392584	−	0.0679976i	−0.845729	−	0.533613i	$-0.820834\pi$
$653$	1.00320	−	1.73760i	0.0392584	−	0.0679976i	0.884987	+	0.465616i	$0.154167\pi$
$654$	3.12758	+	5.41712i	0.122298	+	0.211826i
$655$		0			0
$656$		−	26.4704i		−	1.03350i
$657$	−5.54229	+	20.6841i	−0.216225	+	0.806963i
$658$	−1.16903			−0.0455733
$659$	20.0335	−	34.6990i	0.780394	−	1.35168i	−0.151319	−	0.988485i	$-0.548352\pi$
$659$	20.0335	−	34.6990i	0.780394	−	1.35168i	0.931713	−	0.363197i	$-0.118315\pi$
$660$		0			0
$661$	8.62310	+	32.1818i	0.335400	+	1.25173i	0.903435	+	0.428725i	$0.141037\pi$
$661$	8.62310	+	32.1818i	0.335400	+	1.25173i	−0.568036	+	0.823004i	$0.692296\pi$
$662$	2.34861	+	8.76513i	0.0912813	+	0.340666i
$663$	17.0781	−	4.57608i	0.663260	−	0.177720i
$664$	11.2472	+	3.01369i	0.436477	+	0.116954i
$665$		0			0
$666$	6.51111	+	9.02187i	0.252300	+	0.349590i
$667$	−7.18459	+	7.18459i	−0.278188	+	0.278188i
$668$	−4.57245	−	7.91971i	−0.176913	−	0.306423i
$669$	34.8016	−	60.2781i	1.34551	−	2.33049i
$670$		0			0
$671$	−22.9804	+	6.15758i	−0.887149	+	0.237711i
$672$	13.7505			0.530436
$673$	−39.3491	+	10.5436i	−1.51680	+	0.406424i	−0.918686	−	0.394989i	$-0.870748\pi$
$673$	−39.3491	+	10.5436i	−1.51680	+	0.406424i	−0.598111	+	0.801414i	$0.704082\pi$
$674$	−2.09776	+	2.09776i	−0.0808027	+	0.0808027i
$675$		0			0
$676$	−0.727026			−0.0279626
$677$	−11.1292	−	11.1292i	−0.427732	−	0.427732i	0.460123	−	0.887855i	$-0.347805\pi$
$677$	−11.1292	−	11.1292i	−0.427732	−	0.427732i	−0.887855	+	0.460123i	$0.847805\pi$
$678$	−2.63623	+	9.83855i	−0.101244	+	0.377847i
$679$	−0.189129	−	0.705841i	−0.00725812	−	0.0270877i
$680$		0			0
$681$	−29.2806	−	7.84572i	−1.12204	−	0.300649i
$682$	−6.17745	−	1.65524i	−0.236547	−	0.0633826i
$683$	20.3675	−	11.7592i	0.779340	−	0.449952i	−0.0568564	−	0.998382i	$-0.518108\pi$
$683$	20.3675	−	11.7592i	0.779340	−	0.449952i	0.836196	+	0.548430i	$0.184774\pi$
$684$	11.0514	−	2.96122i	0.422562	−	0.113225i
$685$		0			0
$686$	6.45605	+	1.72989i	0.246493	+	0.0660476i
$687$	−11.2172	+	41.8631i	−0.427962	+	1.59718i
$688$	−12.2964	+	7.09934i	−0.468797	+	0.270660i
$689$	18.1640	−	18.1640i	0.691993	−	0.691993i
$690$		0			0
$691$	34.9969	−	20.2055i	1.33135	−	0.768653i	0.345840	−	0.938294i	$-0.387594\pi$
$691$	34.9969	−	20.2055i	1.33135	−	0.768653i	0.985506	+	0.169641i	$0.0542607\pi$
$692$	−26.2714	+	26.2714i	−0.998689	+	0.998689i
$693$	5.95374	−	5.95374i	0.226164	−	0.226164i
$694$	−8.84676	−	15.3230i	−0.335818	−	0.581655i
$695$		0			0
$696$	13.2115	+	7.62764i	0.500779	+	0.289125i
$697$		−	18.6139i		−	0.705052i
$698$	−1.48260	+	2.56793i	−0.0561171	+	0.0971977i
$699$	−8.28757	−	4.78483i	−0.313465	−	0.180979i
$700$		0			0
$701$	−1.40325	+	5.23699i	−0.0529999	+	0.197798i	−0.987349	−	0.158560i	$-0.949315\pi$
$701$	−1.40325	+	5.23699i	−0.0529999	+	0.197798i	0.934350	+	0.356358i	$0.115982\pi$
$702$	−2.50327	−	2.50327i	−0.0944799	−	0.0944799i
$703$	10.3446	+	1.67211i	0.390155	+	0.0630649i
$704$			6.01664i			0.226761i
$705$		0			0
$706$	−9.81811	−	5.66849i	−0.369509	−	0.213336i
$707$	−13.7137	+	3.67456i	−0.515755	+	0.138196i
$708$	44.3666	+	25.6151i	1.66740	+	0.962673i
$709$	−27.6470	+	27.6470i	−1.03830	+	1.03830i	−0.0390675	+	0.999237i	$0.512439\pi$
$709$	−27.6470	+	27.6470i	−1.03830	+	1.03830i	−0.999237	+	0.0390675i	$0.987561\pi$
$710$		0			0
$711$	−15.7039	−	15.7039i	−0.588941	−	0.588941i
$712$	−3.88972	−	1.04225i	−0.145774	−	0.0390599i
$713$	14.1118	+	14.1118i	0.528492	+	0.528492i
$714$	2.51024			0.0939433
$715$		0			0
$716$	35.2945	−	9.45712i	1.31902	−	0.353429i
$717$			18.8824i			0.705176i
$718$	3.34085	+	5.78652i	0.124679	+	0.215951i
$719$	−17.5989	+	10.1607i	−0.656328	+	0.378931i	−0.790877	−	0.611976i	$-0.790375\pi$
$719$	−17.5989	+	10.1607i	−0.656328	+	0.378931i	0.134548	+	0.990907i	$0.457042\pi$
$720$		0			0
$721$	−0.782577	−	2.92062i	−0.0291447	−	0.108769i
$722$	3.89437	−	6.74525i	0.144934	−	0.251032i
$723$	−32.5057	−	56.3016i	−1.20890	−	2.09388i
$724$	−19.2433	−	33.3304i	−0.715172	−	1.23871i
$725$		0			0
$726$	5.92739	+	5.92739i	0.219986	+	0.219986i
$727$	29.5637	+	17.0686i	1.09646	+	0.633039i	0.935288	−	0.353888i	$-0.115140\pi$
$727$	29.5637	+	17.0686i	1.09646	+	0.633039i	0.161168	+	0.986927i	$0.448474\pi$
$728$	−6.92321	−	1.85507i	−0.256591	−	0.0687534i
$729$		−	38.5667i		−	1.42840i
$730$		0			0
$731$	−8.64681	+	4.99224i	−0.319814	+	0.184645i
$732$		−	52.2392i		−	1.93082i
$733$	5.30156	+	19.7857i	0.195818	+	0.730802i	0.992054	+	0.125815i	$0.0401547\pi$
$733$	5.30156	+	19.7857i	0.195818	+	0.730802i	−0.796236	+	0.604986i	$0.793179\pi$
$734$	−2.01085	−	2.01085i	−0.0742218	−	0.0742218i
$735$		0			0
$736$	−7.82369	+	13.5510i	−0.288385	+	0.499497i
$737$	−5.72674	−	21.3725i	−0.210947	−	0.787266i
$738$	−15.8853	+	9.17136i	−0.584744	+	0.337602i
$739$	36.2323			1.33283			0.666414	−	0.745582i	$-0.267828\pi$
$739$	36.2323			1.33283			0.666414	+	0.745582i	$0.267828\pi$
$740$		0			0
$741$	−16.4096			−0.602822
$742$	3.15846	−	1.82354i	0.115951	−	0.0669441i
$743$	−8.68941	−	32.4293i	−0.318784	−	1.18972i	−0.920415	−	0.390943i	$-0.872149\pi$
$743$	−8.68941	−	32.4293i	−0.318784	−	1.18972i	0.601631	−	0.798774i	$-0.294518\pi$
$744$	14.9821	−	25.9497i	0.549269	−	0.951362i
$745$		0			0
$746$	−9.40559	−	9.40559i	−0.344363	−	0.344363i
$747$	6.20502	+	23.1574i	0.227030	+	0.847286i
$748$			6.84153i			0.250151i
$749$	−9.20265	+	5.31315i	−0.336258	+	0.194138i
$750$		0			0
$751$			33.4106i			1.21917i	0.792721	+	0.609585i	$0.208664\pi$
$751$			33.4106i			1.21917i	−0.792721	+	0.609585i	$0.791336\pi$
$752$	5.73241	+	1.53599i	0.209039	+	0.0560119i
$753$	9.75443	+	5.63172i	0.355471	+	0.205231i
$754$	−4.03527	−	4.03527i	−0.146956	−	0.146956i
$755$		0			0
$756$	1.87827	+	3.25325i	0.0683119	+	0.118320i
$757$	7.24176	+	12.5431i	0.263206	+	0.455886i	0.967092	−	0.254427i	$-0.0818867\pi$
$757$	7.24176	+	12.5431i	0.263206	+	0.455886i	−0.703886	+	0.710313i	$0.748553\pi$
$758$	−4.06834	+	7.04656i	−0.147769	+	0.255943i
$759$	4.45582	+	16.6293i	0.161736	+	0.603607i
$760$		0			0
$761$	18.3530	−	10.5961i	0.665296	−	0.384109i	−0.128996	−	0.991645i	$-0.541175\pi$
$761$	18.3530	−	10.5961i	0.665296	−	0.384109i	0.794292	+	0.607536i	$0.207842\pi$
$762$	12.9346	+	22.4034i	0.468572	+	0.811590i
$763$			5.29814i			0.191806i
$764$	43.2036	−	11.5764i	1.56305	−	0.418819i
$765$		0			0
$766$	15.3639			0.555122
$767$	−28.9156	−	28.9156i	−1.04408	−	1.04408i
$768$	−0.702972	−	0.188361i	−0.0253663	−	0.00679688i
$769$	27.0019	+	27.0019i	0.973712	+	0.973712i	0.999663	−	0.0259516i	$-0.00826157\pi$
$769$	27.0019	+	27.0019i	0.973712	+	0.973712i	−0.0259516	+	0.999663i	$0.508262\pi$
$770$		0			0
$771$	56.9446	−	56.9446i	2.05081	−	2.05081i
$772$	4.22417	+	2.43883i	0.152031	+	0.0877753i
$773$	−8.85179	+	2.37183i	−0.318377	+	0.0853088i	−0.414468	−	0.910064i	$-0.636032\pi$
$773$	−8.85179	+	2.37183i	−0.318377	+	0.0853088i	0.0960916	+	0.995372i	$0.469366\pi$
$774$	8.52083	+	4.91950i	0.306275	+	0.176828i
$775$		0			0
$776$		−	1.24851i		−	0.0448187i
$777$	1.71648	+	16.8456i	0.0615785	+	0.604331i
$778$	12.3007	+	12.3007i	0.441001	+	0.441001i
$779$	−4.47131	+	16.6872i	−0.160201	+	0.597880i
$780$		0			0
$781$	1.58930	+	0.917582i	0.0568696	+	0.0328337i
$782$	−1.42827	+	2.47383i	−0.0510747	+	0.0884639i
$783$			6.38213i			0.228079i
$784$	−13.3832	−	7.72677i	−0.477970	−	0.275956i
$785$		0			0
$786$	−6.17715	−	10.6991i	−0.220332	−	0.381626i
$787$	2.37899	−	2.37899i	0.0848017	−	0.0848017i	−0.663434	−	0.748235i	$-0.730901\pi$
$787$	2.37899	−	2.37899i	0.0848017	−	0.0848017i	0.748235	+	0.663434i	$0.230901\pi$
$788$	−17.0587	+	17.0587i	−0.607690	+	0.607690i
$789$	−28.5886	+	16.5057i	−1.01778	+	0.587617i
$790$		0			0
$791$	−6.10040	+	6.10040i	−0.216905	+	0.216905i
$792$	12.4584	−	7.19287i	0.442691	−	0.255588i
$793$	−10.7923	+	40.2774i	−0.383246	+	1.43029i
$794$	−10.4107	−	2.78955i	−0.369463	−	0.0989974i
$795$		0			0
$796$	−6.91328	+	1.85241i	−0.245035	+	0.0656568i
$797$	47.5375	−	27.4458i	1.68386	−	0.972179i	0.724811	−	0.688947i	$-0.241927\pi$
$797$	47.5375	−	27.4458i	1.68386	−	0.972179i	0.959052	−	0.283231i	$-0.0914065\pi$
$798$	−2.25040	−	0.602993i	−0.0796633	−	0.0213457i
$799$	4.03101	+	1.08011i	0.142607	+	0.0382114i
$800$		0			0
$801$	−2.14593	−	8.00873i	−0.0758228	−	0.282975i
$802$	2.63947	−	9.85063i	0.0932028	−	0.347838i
$803$	8.40344	+	8.40344i	0.296551	+	0.296551i
$804$	48.5841			1.71343
$805$		0			0
$806$	−7.92601	+	7.92601i	−0.279182	+	0.279182i
$807$	42.0893	−	11.2778i	1.48161	−	0.396997i
$808$	−24.2570			−0.853358
$809$	−1.18348	+	0.317113i	−0.0416090	+	0.0111491i	−0.279563	−	0.960127i	$-0.590190\pi$
$809$	−1.18348	+	0.317113i	−0.0416090	+	0.0111491i	0.237955	+	0.971276i	$0.423523\pi$
$810$		0			0
$811$	16.2208	−	28.0952i	0.569588	−	0.986556i	−0.427018	−	0.904243i	$-0.640436\pi$
$811$	16.2208	−	28.0952i	0.569588	−	0.986556i	0.996607	−	0.0823128i	$-0.0262307\pi$
$812$	3.02777	+	5.24425i	0.106254	+	0.184037i
$813$	35.1365	−	35.1365i	1.23229	−	1.23229i
$814$	6.14295	−	0.625938i	0.215310	−	0.0219391i
$815$		0			0
$816$	−12.3091	−	3.29823i	−0.430906	−	0.115461i
$817$	8.95097	−	2.39841i	0.313155	−	0.0839096i
$818$	4.44761	+	16.5987i	0.155507	+	0.580361i
$819$	−3.81948	−	14.2545i	−0.133464	−	0.498093i
$820$		0			0
$821$	−15.4623	+	26.7814i	−0.539637	+	0.934678i	0.459287	+	0.888288i	$0.348105\pi$
$821$	−15.4623	+	26.7814i	−0.539637	+	0.934678i	−0.998923	+	0.0463901i	$0.985228\pi$
$822$	19.8594			0.692676
$823$	5.46402	−	20.3920i	0.190464	−	0.710820i	−0.802931	−	0.596072i	$-0.796727\pi$
$823$	5.46402	−	20.3920i	0.190464	−	0.710820i	0.993395	−	0.114748i	$-0.0366061\pi$
$824$		−	5.16605i		−	0.179968i
$825$		0			0
$826$	−2.90292	−	5.02800i	−0.101005	−	0.174946i
$827$	4.82781	−	8.36201i	0.167879	−	0.290776i	−0.769795	−	0.638292i	$-0.779641\pi$
$827$	4.82781	−	8.36201i	0.167879	−	0.290776i	0.937674	+	0.347516i	$0.112975\pi$
$828$	−21.0383			−0.731133
$829$	3.28514	−	12.2603i	0.114097	−	0.425818i	−0.885120	−	0.465362i	$-0.845924\pi$
$829$	3.28514	−	12.2603i	0.114097	−	0.425818i	0.999218	+	0.0395446i	$0.0125907\pi$
$830$		0			0
$831$	11.3264	−	42.2709i	0.392910	−	1.46636i
$832$	9.13247	+	5.27263i	0.316611	+	0.182796i
$833$	−9.41100	−	5.43344i	−0.326072	−	0.188258i
$834$	−3.02061	+	11.2731i	−0.104595	+	0.390355i
$835$		0			0
$836$	1.64343	−	6.13335i	0.0568391	−	0.212127i
$837$	12.5356			0.433295
$838$	−3.59718	+	6.23049i	−0.124262	+	0.215229i
$839$	−9.34812	−	16.1914i	−0.322733	−	0.558990i	0.658318	−	0.752740i	$-0.271268\pi$
$839$	−9.34812	−	16.1914i	−0.322733	−	0.558990i	−0.981051	+	0.193750i	$0.937935\pi$
$840$		0			0
$841$		−	18.7120i		−	0.645242i
$842$	−2.31547	+	8.64147i	−0.0797965	+	0.297805i
$843$	58.7379			2.02304
$844$	−5.79473	+	10.0368i	−0.199463	+	0.345480i
$845$		0			0
$846$	−1.06437	−	3.97228i	−0.0365938	−	0.136570i
$847$	1.83764	+	6.85816i	0.0631420	+	0.235649i
$848$	−17.8837	+	4.79192i	−0.614129	+	0.164555i
$849$	10.9867	+	2.94387i	0.377062	+	0.101033i
$850$		0			0
$851$	−17.5779	−	7.89313i	−0.602561	−	0.270573i
$852$	−2.84933	+	2.84933i	−0.0976164	+	0.0976164i
$853$	−4.08446	−	7.07448i	−0.139849	−	0.242226i	0.787590	−	0.616199i	$-0.211328\pi$
$853$	−4.08446	−	7.07448i	−0.139849	−	0.242226i	−0.927439	+	0.373974i	$0.877995\pi$
$854$	−2.96009	+	5.12703i	−0.101292	+	0.175444i
$855$		0			0
$856$	−17.5369	+	4.69901i	−0.599400	+	0.160609i
$857$	−1.03295			−0.0352847			−0.0176424	−	0.999844i	$-0.505616\pi$
$857$	−1.03295			−0.0352847			−0.0176424	+	0.999844i	$0.505616\pi$
$858$	−9.33999	+	2.50264i	−0.318862	+	0.0854388i
$859$	−20.1427	+	20.1427i	−0.687259	+	0.687259i	−0.961625	−	0.274367i	$-0.911532\pi$
$859$	−20.1427	+	20.1427i	−0.687259	+	0.687259i	0.274367	+	0.961625i	$0.411532\pi$
$860$		0			0
$861$	−27.9159			−0.951371
$862$	−13.1783	−	13.1783i	−0.448856	−	0.448856i
$863$	−6.82233	+	25.4613i	−0.232235	+	0.866712i	0.747141	+	0.664665i	$0.231426\pi$
$863$	−6.82233	+	25.4613i	−0.232235	+	0.866712i	−0.979376	+	0.202046i	$0.935241\pi$
$864$	2.54382	+	9.49367i	0.0865425	+	0.322981i
$865$		0			0
$866$	7.10587	+	1.90401i	0.241467	+	0.0647010i
$867$	34.0540	+	9.12473i	1.15653	+	0.309892i
$868$	10.3006	−	5.94708i	0.349627	−	0.201857i
$869$	−11.9054	+	3.19005i	−0.403864	+	0.108215i
$870$		0			0
$871$	−37.4592	−	10.0372i	−1.26926	−	0.340096i
$872$	−2.34287	+	8.74370i	−0.0793395	+	0.296099i
$873$	2.22621	−	1.28530i	0.0753458	−	0.0435009i
$874$	1.87467	−	1.87467i	0.0634117	−	0.0634117i
$875$		0			0
$876$	−22.5988	+	13.0474i	−0.763543	+	0.440832i
$877$	−34.9927	+	34.9927i	−1.18162	+	1.18162i	−0.202294	+	0.979325i	$0.564840\pi$
$877$	−34.9927	+	34.9927i	−1.18162	+	1.18162i	−0.979325	+	0.202294i	$0.935160\pi$
$878$	2.11403	−	2.11403i	0.0713451	−	0.0713451i
$879$	37.1790	+	64.3960i	1.25402	+	2.17202i
$880$		0			0
$881$	17.4478	+	10.0735i	0.587831	+	0.339384i	0.764239	−	0.644933i	$-0.223115\pi$
$881$	17.4478	+	10.0735i	0.587831	+	0.339384i	−0.176408	+	0.984317i	$0.556448\pi$
$882$			10.7086i			0.360576i
$883$	11.3483	−	19.6558i	0.381901	−	0.661471i	−0.609433	−	0.792837i	$-0.708603\pi$
$883$	11.3483	−	19.6558i	0.381901	−	0.661471i	0.991334	+	0.131366i	$0.0419363\pi$
$884$	10.3845	+	5.99552i	0.349270	+	0.201651i
$885$		0			0
$886$	0.382476	−	1.42742i	0.0128495	−	0.0479552i
$887$	−11.4898	−	11.4898i	−0.385791	−	0.385791i	0.487392	−	0.873183i	$-0.337948\pi$
$887$	−11.4898	−	11.4898i	−0.385791	−	0.385791i	−0.873183	+	0.487392i	$0.837948\pi$
$888$	−4.61643	+	28.5598i	−0.154917	+	0.958405i
$889$			21.9114i			0.734883i
$890$		0			0
$891$	−11.0741	−	6.39364i	−0.370997	−	0.214195i
$892$	45.5966	−	12.2176i	1.52669	−	0.409074i
$893$	−3.35430	−	1.93661i	−0.112247	−	0.0648061i
$894$	5.40460	−	5.40460i	0.180757	−	0.180757i
$895$		0			0
$896$	8.53517	+	8.53517i	0.285140	+	0.285140i
$897$	29.1460	+	7.80964i	0.973156	+	0.260756i
$898$	−7.74348	−	7.74348i	−0.258403	−	0.258403i
$899$	20.2075			0.673957
$900$		0			0
$901$	−12.5758	+	3.36967i	−0.418960	+	0.112260i
$902$			10.1799i			0.338953i
$903$	7.48702	+	12.9679i	0.249153	+	0.431545i
$904$	−12.7653	+	7.37005i	−0.424568	+	0.245124i
$905$		0			0
$906$	2.15513	+	8.04306i	0.0715994	+	0.267213i
$907$	9.73301	−	16.8581i	0.323179	−	0.559763i	−0.657963	−	0.753050i	$-0.728582\pi$
$907$	9.73301	−	16.8581i	0.323179	−	0.559763i	0.981142	+	0.193287i	$0.0619150\pi$
$908$	−10.2794	−	17.8044i	−0.341133	−	0.590859i
$909$	−24.9719	−	43.2526i	−0.828266	−	1.43460i
$910$		0			0
$911$	−10.7957	−	10.7957i	−0.357678	−	0.357678i	0.505279	−	0.862956i	$-0.331390\pi$
$911$	−10.7957	−	10.7957i	−0.357678	−	0.357678i	−0.862956	+	0.505279i	$0.831390\pi$
$912$	10.2427	+	5.91365i	0.339171	+	0.195820i
$913$	12.8520	+	3.44368i	0.425338	+	0.113969i
$914$		−	2.83861i		−	0.0938929i
$915$		0			0
$916$	−25.4553	+	14.6966i	−0.841066	+	0.485590i
$917$		−	10.4642i		−	0.345557i
$918$	0.464391	+	1.73313i	0.0153272	+	0.0572018i
$919$	0.633274	+	0.633274i	0.0208898	+	0.0208898i	0.717475	−	0.696585i	$-0.245298\pi$
$919$	0.633274	+	0.633274i	0.0208898	+	0.0208898i	−0.696585	+	0.717475i	$0.745298\pi$
$920$		0			0
$921$	1.58024	−	2.73705i	0.0520706	−	0.0901890i
$922$	−1.07377	−	4.00738i	−0.0353629	−	0.131976i
$923$	2.78554	−	1.60823i	0.0916872	−	0.0529356i
$924$	10.2605			0.337544
$925$		0			0
$926$	−2.49647			−0.0820392
$927$	9.21158	−	5.31831i	0.302548	−	0.174676i
$928$	4.10064	+	15.3038i	0.134610	+	0.502372i
$929$	−23.7899	+	41.2053i	−0.780521	+	1.35190i	0.151118	+	0.988516i	$0.451713\pi$
$929$	−23.7899	+	41.2053i	−0.780521	+	1.35190i	−0.931639	+	0.363386i	$0.881621\pi$
$930$		0			0
$931$	7.13167	+	7.13167i	0.233731	+	0.233731i
$932$	−1.67978	−	6.26903i	−0.0550230	−	0.205349i
$933$			75.0209i			2.45607i
$934$	−4.55000	+	2.62694i	−0.148881	+	0.0859563i
$935$		0			0
$936$		−	25.2137i		−	0.824135i
$937$	45.9687	+	12.3173i	1.50173	+	0.402388i	0.913680	−	0.406435i	$-0.133228\pi$
$937$	45.9687	+	12.3173i	1.50173	+	0.402388i	0.588052	+	0.808823i	$0.299895\pi$
$938$	−4.76830	−	2.75298i	−0.155690	−	0.0898879i
$939$	2.46899	+	2.46899i	0.0805724	+	0.0805724i
$940$		0			0
$941$	−16.4063	−	28.4165i	−0.534829	−	0.926351i	−0.999172	−	0.0406953i	$-0.987043\pi$
$941$	−16.4063	−	28.4165i	−0.534829	−	0.926351i	0.464343	−	0.885656i	$-0.346291\pi$
$942$	4.35253	+	7.53880i	0.141813	+	0.245627i
$943$	15.8835	−	27.5110i	0.517237	−	0.895881i
$944$	7.62834	+	28.4694i	0.248281	+	0.926599i
$945$		0			0
$946$	4.72891	−	2.73024i	0.153750	−	0.0887677i
$947$	2.20312	+	3.81592i	0.0715918	+	0.124001i	0.899599	−	0.436717i	$-0.143859\pi$
$947$	2.20312	+	3.81592i	0.0715918	+	0.124001i	−0.828007	+	0.560717i	$0.810525\pi$
$948$		−	27.0635i		−	0.878981i
$949$	20.1196	−	5.39104i	0.653111	−	0.175000i
$950$		0			0
$951$	−38.4068			−1.24543
$952$	2.56870	+	2.56870i	0.0832520	+	0.0832520i
$953$	18.1686	+	4.86825i	0.588538	+	0.157698i	0.540785	−	0.841161i	$-0.318127\pi$
$953$	18.1686	+	4.86825i	0.588538	+	0.157698i	0.0477530	+	0.998859i	$0.484794\pi$
$954$	9.07197	+	9.07197i	0.293716	+	0.293716i
$955$		0			0
$956$	−9.05527	+	9.05527i	−0.292868	+	0.292868i
$957$	15.0965	+	8.71595i	0.488000	+	0.281747i
$958$	1.91430	−	0.512936i	0.0618483	−	0.0165722i
$959$	14.5674	+	8.41050i	0.470406	+	0.271589i
$960$		0			0
$961$		−	8.69111i		−	0.280358i
$962$	4.43324	−	9.87273i	0.142933	−	0.318310i
$963$	−26.4326	−	26.4326i	−0.851779	−	0.851779i
$964$	11.4116	−	42.5886i	0.367542	−	1.37169i
$965$		0			0
$966$	3.71008	+	2.14202i	0.119370	+	0.0689182i
$967$	−13.8632	+	24.0118i	−0.445811	+	0.772167i	−0.998108	−	0.0614801i	$-0.980418\pi$
$967$	−13.8632	+	24.0118i	−0.445811	+	0.772167i	0.552297	+	0.833647i	$0.313751\pi$
$968$			12.1309i			0.389901i
$969$	7.20267	+	4.15846i	0.231383	+	0.133589i
$970$		0			0
$971$	−17.5325	−	30.3673i	−0.562646	−	0.974532i	−0.997264	−	0.0739171i	$-0.976450\pi$
$971$	−17.5325	−	30.3673i	−0.562646	−	0.974532i	0.434618	−	0.900615i	$-0.356883\pi$
$972$	27.2995	−	27.2995i	0.875632	−	0.875632i
$973$	−6.98987	+	6.98987i	−0.224085	+	0.224085i
$974$	−4.38912	+	2.53406i	−0.140637	+	0.0811965i
$975$		0			0
$976$	21.2515	−	21.2515i	0.680245	−	0.680245i
$977$	10.7827	−	6.22537i	0.344968	−	0.199167i	−0.317499	−	0.948259i	$-0.602843\pi$
$977$	10.7827	−	6.22537i	0.344968	−	0.199167i	0.662467	+	0.749091i	$0.269510\pi$
$978$	−8.16252	+	30.4630i	−0.261009	+	0.974098i
$979$	−4.44471	−	1.19096i	−0.142053	−	0.0380631i
$980$		0			0
$981$	−18.0028	+	4.82384i	−0.574785	+	0.154013i
$982$	−3.12687	+	1.80530i	−0.0997825	+	0.0576094i
$983$	−19.2867	−	5.16785i	−0.615150	−	0.164829i	−0.0622280	−	0.998062i	$-0.519821\pi$
$983$	−19.2867	−	5.16785i	−0.615150	−	0.164829i	−0.552922	+	0.833233i	$0.686487\pi$
$984$	−46.0705	−	12.3446i	−1.46867	−	0.393530i
$985$		0			0
$986$	0.748598	+	2.79381i	0.0238402	+	0.0889729i
$987$	1.61987	−	6.04544i	0.0515611	−	0.192429i
$988$	−7.86942	−	7.86942i	−0.250360	−	0.250360i
$989$	−17.0397			−0.541832
$990$		0			0
$991$	0.0857771	−	0.0857771i	0.00272480	−	0.00272480i	−0.705743	−	0.708468i	$-0.749387\pi$
$991$	0.0857771	−	0.0857771i	0.00272480	−	0.00272480i	0.708468	+	0.705743i	$0.249387\pi$
$992$	30.0594	−	8.05439i	0.954387	−	0.255727i
$993$	−48.5820			−1.54170
$994$	0.441103	−	0.118193i	0.0139910	−	0.00374886i
$995$		0			0
$996$	−14.6076	+	25.3011i	−0.462859	+	0.801696i
$997$	14.4932	+	25.1030i	0.459006	+	0.795021i	0.998909	−	0.0467059i	$-0.0148724\pi$
$997$	14.4932	+	25.1030i	0.459006	+	0.795021i	−0.539903	+	0.841727i	$0.681539\pi$
$998$	−8.58611	+	8.58611i	−0.271789	+	0.271789i
$999$	−11.3130	+	4.30151i	−0.357929	+	0.136094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.c.193.15	yes	96
5.2	odd	4		925.2.t.c.82.15	yes	96
5.3	odd	4		925.2.t.c.82.10	✓	96
5.4	even	2	inner	925.2.y.c.193.10	yes	96
37.14	odd	12		925.2.t.c.643.15	yes	96
185.14	odd	12		925.2.t.c.643.10	yes	96
185.88	even	12	inner	925.2.y.c.532.10	yes	96
185.162	even	12	inner	925.2.y.c.532.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.c.82.10	✓	96	5.3	odd	4
925.2.t.c.82.15	yes	96	5.2	odd	4
925.2.t.c.643.10	yes	96	185.14	odd	12
925.2.t.c.643.15	yes	96	37.14	odd	12
925.2.y.c.193.10	yes	96	5.4	even	2	inner
925.2.y.c.193.15	yes	96	1.1	even	1	trivial
925.2.y.c.532.10	yes	96	185.88	even	12	inner
925.2.y.c.532.15	yes	96	185.162	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.420731 - 0.242909i) q^{2} +(0.673179 + 2.51234i) q^{3} +(-0.881990 + 1.52765i) q^{4} +(0.893496 + 0.893496i) q^{6} +(0.277006 + 1.03380i) q^{7} +1.82861i q^{8} +(-3.26059 + 1.88250i) q^{9} +2.08952i q^{11} +(-4.43171 - 1.18747i) q^{12} +(3.17161 + 1.83113i) q^{13} +(0.367665 + 0.367665i) q^{14} +(-1.31980 - 2.28595i) q^{16} +(-0.928076 - 1.60748i) q^{17} +(-0.914554 + 1.58405i) q^{18} +(0.445873 + 1.66402i) q^{19} +(-2.41078 + 1.39187i) q^{21} +(0.507562 + 0.879123i) q^{22} -3.16775i q^{23} +(-4.59408 + 1.23098i) q^{24} +1.77919 q^{26} +(-1.40697 - 1.40697i) q^{27} +(-1.82361 - 0.488634i) q^{28} +(-2.26804 - 2.26804i) q^{29} +(-4.45483 + 4.45483i) q^{31} +(-4.27780 - 2.46979i) q^{32} +(-5.24957 + 1.40662i) q^{33} +(-0.780940 - 0.450876i) q^{34} -6.64140i q^{36} +(2.49171 - 5.54900i) q^{37} +(0.591798 + 0.591798i) q^{38} +(-2.46536 + 9.20083i) q^{39} +(8.68470 + 5.01411i) q^{41} +(-0.676194 + 1.17120i) q^{42} -5.37912i q^{43} +(-3.19205 - 1.84293i) q^{44} +(-0.769476 - 1.33277i) q^{46} +(-1.58980 + 1.58980i) q^{47} +(4.85462 - 4.85462i) q^{48} +(5.07016 - 2.92726i) q^{49} +(3.41376 - 3.41376i) q^{51} +(-5.59466 + 3.23008i) q^{52} +(1.81540 - 6.77518i) q^{53} +(-0.933722 - 0.250190i) q^{54} +(-1.89042 + 0.506536i) q^{56} +(-3.88043 + 2.24037i) q^{57} +(-1.50516 - 0.403306i) q^{58} +(-10.7855 - 2.88997i) q^{59} +(2.94690 + 10.9980i) q^{61} +(-0.792167 + 2.95641i) q^{62} +(-2.84934 - 2.84934i) q^{63} +2.87944 q^{64} +(-1.86697 + 1.86697i) q^{66} +(-10.2284 + 2.74070i) q^{67} +3.27422 q^{68} +(7.95847 - 2.13247i) q^{69} +(0.439137 - 0.760607i) q^{71} +(-3.44237 - 5.96235i) q^{72} +(4.02172 - 4.02172i) q^{73} +(-0.299561 - 2.93989i) q^{74} +(-2.93530 - 0.786511i) q^{76} +(-2.16014 + 0.578809i) q^{77} +(1.19771 + 4.46993i) q^{78} +(1.52669 + 5.69770i) q^{79} +(-3.05987 + 5.29985i) q^{81} +4.87189 q^{82} +(1.64807 - 6.15070i) q^{83} -4.91045i q^{84} +(-1.30664 - 2.26316i) q^{86} +(4.17128 - 7.22487i) q^{87} -3.82091 q^{88} +(-0.569968 + 2.12715i) q^{89} +(-1.01447 + 3.78605i) q^{91} +(4.83923 + 2.79393i) q^{92} +(-14.1909 - 8.19315i) q^{93} +(-0.282701 + 1.05505i) q^{94} +(3.32522 - 12.4099i) q^{96} -0.682762 q^{97} +(1.42212 - 2.46318i) q^{98} +(-3.93352 - 6.81306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 40 q^{4} - 32 q^{14} - 4 q^{16} - 24 q^{19} + 36 q^{21} + 52 q^{24} + 16 q^{26} + 12 q^{29} + 4 q^{31} - 60 q^{34} + 100 q^{39} - 48 q^{41} + 48 q^{44} + 24 q^{46} - 120 q^{49} - 84 q^{51} + 104 q^{54}+ \cdots - 24 q^{99}+O(q^{100}) \) 96 * q + 40 * q^4 - 32 * q^14 - 4 * q^16 - 24 * q^19 + 36 * q^21 + 52 * q^24 + 16 * q^26 + 12 * q^29 + 4 * q^31 - 60 * q^34 + 100 * q^39 - 48 * q^41 + 48 * q^44 + 24 * q^46 - 120 * q^49 - 84 * q^51 + 104 * q^54 - 68 * q^56 - 28 * q^59 + 68 * q^61 + 48 * q^64 + 4 * q^66 + 28 * q^69 + 48 * q^71 - 48 * q^74 - 152 * q^76 - 92 * q^79 - 16 * q^81 + 20 * q^86 - 8 * q^89 - 12 * q^91 + 56 * q^94 + 252 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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