LMFDB - Embedded newform 975.2.bl.e.943.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(193,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 7]))

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

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

chi := DirichletCharacter("975.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bl (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.1
Root			$0.159959 - 0.596975i$ of defining polynomial
Character	$\chi$	$=$	975.943
Dual form			975.2.bl.e.457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14412 + 1.98168i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.61803 - 2.80252i) q^{4} +(-0.592242 + 2.21028i) q^{6} +(-4.18930 + 2.41869i) q^{7} +2.82843 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.14412 + 1.98168i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.61803 - 2.80252i) q^{4} +(-0.592242 + 2.21028i) q^{6} +(-4.18930 + 2.41869i) q^{7} +2.82843 q^{8} +(0.866025 - 0.500000i) q^{9} +(0.139809 + 0.521775i) q^{11} +(-2.28825 - 2.28825i) q^{12} +(-3.41542 - 1.15539i) q^{13} -11.0691i q^{14} +(0.590009 - 2.20194i) q^{17} +2.28825i q^{18} +(5.92055 + 1.58641i) q^{19} +(-3.42055 + 3.42055i) q^{21} +(-1.19395 - 0.319918i) q^{22} +(-0.860681 - 3.21210i) q^{23} +(2.73205 - 0.732051i) q^{24} +(6.19728 - 5.44634i) q^{26} +(0.707107 - 0.707107i) q^{27} +(13.5569 + 7.82706i) q^{28} +(-7.24774 - 4.18448i) q^{29} +(-4.00294 - 4.00294i) q^{31} +(2.82843 + 4.89898i) q^{32} +(0.270091 + 0.467811i) q^{33} +(3.68850 + 3.68850i) q^{34} +(-2.80252 - 1.61803i) q^{36} +(4.80659 + 2.77509i) q^{37} +(-9.91759 + 9.91759i) q^{38} +(-3.59808 - 0.232051i) q^{39} +(-1.52178 + 0.407758i) q^{41} +(-2.86490 - 10.6920i) q^{42} +(5.49818 + 1.47323i) q^{43} +(1.23607 - 1.23607i) q^{44} +(7.35008 + 1.96945i) q^{46} -6.74670i q^{47} +(8.20017 - 14.2031i) q^{49} -2.27962i q^{51} +(2.28825 + 11.4412i) q^{52} +(-6.44932 - 6.44932i) q^{53} +(0.592242 + 2.21028i) q^{54} +(-11.8491 + 6.84110i) q^{56} +6.12941 q^{57} +(16.5846 - 9.57513i) q^{58} +(2.70150 - 10.0821i) q^{59} +(-1.29958 - 2.25093i) q^{61} +(12.5124 - 3.35269i) q^{62} +(-2.41869 + 4.18930i) q^{63} -12.9443 q^{64} -1.23607 q^{66} +(4.50763 - 7.80745i) q^{67} +(-7.12564 + 1.90931i) q^{68} +(-1.66271 - 2.87989i) q^{69} +(-0.223275 + 0.833275i) q^{71} +(2.44949 - 1.41421i) q^{72} -2.89418 q^{73} +(-10.9987 + 6.35008i) q^{74} +(-5.13372 - 19.1593i) q^{76} +(-1.84772 - 1.84772i) q^{77} +(4.57649 - 6.86474i) q^{78} +4.18085i q^{79} +(0.500000 - 0.866025i) q^{81} +(0.933051 - 3.48220i) q^{82} -8.52146i q^{83} +(15.1207 + 4.05158i) q^{84} +(-9.21007 + 9.21007i) q^{86} +(-8.08380 - 2.16605i) q^{87} +(0.395440 + 1.47580i) q^{88} +(-16.6117 + 4.45110i) q^{89} +(17.1028 - 3.42055i) q^{91} +(-7.60937 + 7.60937i) q^{92} +(-4.90258 - 2.83051i) q^{93} +(13.3698 + 7.71905i) q^{94} +(4.00000 + 4.00000i) q^{96} +(1.65617 + 2.86857i) q^{97} +(18.7640 + 32.5002i) q^{98} +(0.381966 + 0.381966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 4 q^{6}+O(q^{10}) $ 16 * q - 8 * q^4 + 4 * q^6	$ 16 q - 8 q^{4} + 4 q^{6} - 12 q^{11} + 32 q^{19} + 8 q^{21} + 16 q^{24} - 4 q^{26} - 24 q^{29} - 24 q^{31} + 24 q^{34} - 16 q^{39} - 28 q^{41} - 16 q^{44} + 72 q^{46} + 40 q^{49} - 4 q^{54} - 48 q^{56} + 80 q^{59} - 16 q^{61} - 64 q^{64} + 16 q^{66} + 4 q^{69} - 44 q^{71} - 48 q^{74} + 8 q^{81} + 88 q^{84} + 32 q^{86} - 32 q^{89} - 40 q^{91} + 96 q^{94} + 64 q^{96} + 24 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 4 * q^6 - 12 * q^11 + 32 * q^19 + 8 * q^21 + 16 * q^24 - 4 * q^26 - 24 * q^29 - 24 * q^31 + 24 * q^34 - 16 * q^39 - 28 * q^41 - 16 * q^44 + 72 * q^46 + 40 * q^49 - 4 * q^54 - 48 * q^56 + 80 * q^59 - 16 * q^61 - 64 * q^64 + 16 * q^66 + 4 * q^69 - 44 * q^71 - 48 * q^74 + 8 * q^81 + 88 * q^84 + 32 * q^86 - 32 * q^89 - 40 * q^91 + 96 * q^94 + 64 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.14412	+	1.98168i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$2$	−1.14412	+	1.98168i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−1.61803	−	2.80252i	−0.809017	−	1.40126i
$5$		0			0
$5$		0			0
$6$	−0.592242	+	2.21028i	−0.241782	+	0.902341i
$7$	−4.18930	+	2.41869i	−1.58341	+	0.914181i	−0.589050	+	0.808096i	$0.700498\pi$
$7$	−4.18930	+	2.41869i	−1.58341	+	0.914181i	−0.994357	+	0.106084i	$0.966169\pi$
$8$	2.82843			1.00000
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	0.139809	+	0.521775i	0.0421541	+	0.157321i	0.983795	−	0.179299i	$-0.0573829\pi$
$11$	0.139809	+	0.521775i	0.0421541	+	0.157321i	−0.941641	+	0.336620i	$0.890716\pi$
$12$	−2.28825	−	2.28825i	−0.660560	−	0.660560i
$13$	−3.41542	−	1.15539i	−0.947266	−	0.320449i
$13$	−3.41542	−	1.15539i	−0.947266	−	0.320449i
$14$		−	11.0691i		−	2.95835i
$15$		0			0
$16$		0			0
$17$	0.590009	−	2.20194i	0.143098	−	0.534049i	−0.856735	−	0.515758i	$-0.827511\pi$
$17$	0.590009	−	2.20194i	0.143098	−	0.534049i	0.999833	−	0.0182919i	$-0.00582281\pi$
$18$			2.28825i			0.539345i
$19$	5.92055	+	1.58641i	1.35827	+	0.363947i	0.863180	−	0.504896i	$-0.168469\pi$
$19$	5.92055	+	1.58641i	1.35827	+	0.363947i	0.495088	+	0.868843i	$0.335136\pi$
$20$		0			0
$21$	−3.42055	+	3.42055i	−0.746425	+	0.746425i
$22$	−1.19395	−	0.319918i	−0.254551	−	0.0682067i
$23$	−0.860681	−	3.21210i	−0.179464	−	0.669770i	−0.995748	−	0.0921189i	$-0.970636\pi$
$23$	−0.860681	−	3.21210i	−0.179464	−	0.669770i	0.816284	−	0.577651i	$-0.196031\pi$
$24$	2.73205	−	0.732051i	0.557678	−	0.149429i
$25$		0			0
$26$	6.19728	−	5.44634i	1.21539	−	1.06812i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	13.5569	+	7.82706i	2.56201	+	1.47918i
$29$	−7.24774	−	4.18448i	−1.34587	−	0.777039i	−0.358209	−	0.933641i	$-0.616613\pi$
$29$	−7.24774	−	4.18448i	−1.34587	−	0.777039i	−0.987662	+	0.156602i	$0.949946\pi$
$30$		0			0
$31$	−4.00294	−	4.00294i	−0.718949	−	0.718949i	0.249441	−	0.968390i	$-0.419753\pi$
$31$	−4.00294	−	4.00294i	−0.718949	−	0.718949i	−0.968390	+	0.249441i	$0.919753\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$	0.270091	+	0.467811i	0.0470168	+	0.0814354i
$34$	3.68850	+	3.68850i	0.632573	+	0.632573i
$35$		0			0
$36$	−2.80252	−	1.61803i	−0.467086	−	0.269672i
$37$	4.80659	+	2.77509i	0.790199	+	0.456222i	0.840033	−	0.542536i	$-0.182536\pi$
$37$	4.80659	+	2.77509i	0.790199	+	0.456222i	−0.0498334	+	0.998758i	$0.515869\pi$
$38$	−9.91759	+	9.91759i	−1.60884	+	1.60884i
$39$	−3.59808	−	0.232051i	−0.576153	−	0.0371579i
$40$		0			0
$41$	−1.52178	+	0.407758i	−0.237661	+	0.0636812i	−0.375684	−	0.926748i	$-0.622592\pi$
$41$	−1.52178	+	0.407758i	−0.237661	+	0.0636812i	0.138022	+	0.990429i	$0.455925\pi$
$42$	−2.86490	−	10.6920i	−0.442064	−	1.64981i
$43$	5.49818	+	1.47323i	0.838465	+	0.224666i	0.652403	−	0.757872i	$-0.273761\pi$
$43$	5.49818	+	1.47323i	0.838465	+	0.224666i	0.186062	+	0.982538i	$0.440428\pi$
$44$	1.23607	−	1.23607i	0.186344	−	0.186344i
$45$		0			0
$46$	7.35008	+	1.96945i	1.08371	+	0.290379i
$47$		−	6.74670i		−	0.984107i	−0.870565	−	0.492054i	$-0.836246\pi$
$47$		−	6.74670i		−	0.984107i	0.870565	−	0.492054i	$-0.163754\pi$
$48$		0			0
$49$	8.20017	−	14.2031i	1.17145	−	2.02902i
$50$		0			0
$51$		−	2.27962i		−	0.319210i
$52$	2.28825	+	11.4412i	0.317323	+	1.58661i
$53$	−6.44932	−	6.44932i	−0.885883	−	0.885883i	0.108242	−	0.994125i	$-0.465478\pi$
$53$	−6.44932	−	6.44932i	−0.885883	−	0.885883i	−0.994125	+	0.108242i	$0.965478\pi$
$54$	0.592242	+	2.21028i	0.0805939	+	0.300780i
$55$		0			0
$56$	−11.8491	+	6.84110i	−1.58341	+	0.914181i
$57$	6.12941			0.811860
$58$	16.5846	−	9.57513i	2.17767	−	1.25728i
$59$	2.70150	−	10.0821i	0.351705	−	1.31258i	−0.532875	−	0.846194i	$-0.678888\pi$
$59$	2.70150	−	10.0821i	0.351705	−	1.31258i	0.884580	−	0.466388i	$-0.154445\pi$
$60$		0			0
$61$	−1.29958	−	2.25093i	−0.166394	−	0.288202i	0.770756	−	0.637131i	$-0.219879\pi$
$61$	−1.29958	−	2.25093i	−0.166394	−	0.288202i	−0.937149	+	0.348929i	$0.886546\pi$
$62$	12.5124	−	3.35269i	1.58908	−	0.425792i
$63$	−2.41869	+	4.18930i	−0.304727	+	0.527802i
$64$	−12.9443			−1.61803
$65$		0			0
$66$	−1.23607			−0.152149
$67$	4.50763	−	7.80745i	0.550695	−	0.953831i	−0.447530	−	0.894269i	$-0.647696\pi$
$67$	4.50763	−	7.80745i	0.550695	−	0.953831i	0.998225	−	0.0595624i	$-0.0189705\pi$
$68$	−7.12564	+	1.90931i	−0.864110	+	0.231538i
$69$	−1.66271	−	2.87989i	−0.200166	−	0.346699i
$70$		0			0
$71$	−0.223275	+	0.833275i	−0.0264979	+	0.0988916i	−0.977908	−	0.209034i	$-0.932968\pi$
$71$	−0.223275	+	0.833275i	−0.0264979	+	0.0988916i	0.951410	+	0.307925i	$0.0996348\pi$
$72$	2.44949	−	1.41421i	0.288675	−	0.166667i
$73$	−2.89418			−0.338738			−0.169369	−	0.985553i	$-0.554173\pi$
$73$	−2.89418			−0.338738			−0.169369	+	0.985553i	$0.554173\pi$
$74$	−10.9987	+	6.35008i	−1.27857	+	0.738182i
$75$		0			0
$76$	−5.13372	−	19.1593i	−0.588878	−	2.19772i
$77$	−1.84772	−	1.84772i	−0.210567	−	0.210567i
$78$	4.57649	−	6.86474i	0.518186	−	0.777278i
$79$			4.18085i			0.470382i	0.971949	+	0.235191i	$0.0755716\pi$
$79$			4.18085i			0.470382i	−0.971949	+	0.235191i	$0.924428\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.933051	−	3.48220i	0.103038	−	0.384544i
$83$		−	8.52146i		−	0.935352i	−0.883900	−	0.467676i	$-0.845091\pi$
$83$		−	8.52146i		−	0.935352i	0.883900	−	0.467676i	$-0.154909\pi$
$84$	15.1207	+	4.05158i	1.64981	+	0.442064i
$85$		0			0
$86$	−9.21007	+	9.21007i	−0.993147	+	0.993147i
$87$	−8.08380	−	2.16605i	−0.866674	−	0.232225i
$88$	0.395440	+	1.47580i	0.0421541	+	0.157321i
$89$	−16.6117	+	4.45110i	−1.76084	+	0.471816i	−0.986885	−	0.161424i	$-0.948391\pi$
$89$	−16.6117	+	4.45110i	−1.76084	+	0.471816i	−0.773956	+	0.633240i	$0.781725\pi$
$90$		0			0
$91$	17.1028	−	3.42055i	1.79286	−	0.358571i
$92$	−7.60937	+	7.60937i	−0.793331	+	0.793331i
$93$	−4.90258	−	2.83051i	−0.508374	−	0.293510i
$94$	13.3698	+	7.71905i	1.37899	+	0.796159i
$95$		0			0
$96$	4.00000	+	4.00000i	0.408248	+	0.408248i
$97$	1.65617	+	2.86857i	0.168159	+	0.291259i	0.937772	−	0.347250i	$-0.112885\pi$
$97$	1.65617	+	2.86857i	0.168159	+	0.291259i	−0.769614	+	0.638510i	$0.779551\pi$
$98$	18.7640	+	32.5002i	1.89545	+	3.28302i
$99$	0.381966	+	0.381966i	0.0383890	+	0.0383890i
$100$		0			0
$101$	15.8547	+	9.15373i	1.57760	+	0.910830i	0.995193	+	0.0979348i	$0.0312237\pi$
$101$	15.8547	+	9.15373i	1.57760	+	0.910830i	0.582410	+	0.812895i	$0.302110\pi$
$102$	4.51747	+	2.60816i	0.447296	+	0.258247i
$103$	−7.33765	+	7.33765i	−0.723000	+	0.723000i	−0.969215	−	0.246215i	$-0.920813\pi$
$103$	−7.33765	+	7.33765i	−0.723000	+	0.723000i	0.246215	+	0.969215i	$0.420813\pi$
$104$	−9.66025	−	3.26795i	−0.947266	−	0.320449i
$105$		0			0
$106$	20.1593	−	5.40167i	1.95804	−	0.524657i
$107$	−3.27112	−	12.2080i	−0.316232	−	1.18019i	−0.922838	−	0.385189i	$-0.874136\pi$
$107$	−3.27112	−	12.2080i	−0.316232	−	1.18019i	0.606606	−	0.795003i	$-0.292531\pi$
$108$	−3.12580	−	0.837556i	−0.300780	−	0.0805939i
$109$	−8.46704	+	8.46704i	−0.810996	+	0.810996i	−0.984783	−	0.173788i	$-0.944399\pi$
$109$	−8.46704	+	8.46704i	−0.810996	+	0.810996i	0.173788	+	0.984783i	$0.444399\pi$
$110$		0			0
$111$	5.36106	+	1.43649i	0.508849	+	0.136346i
$112$		0			0
$113$	−0.438538	+	1.63665i	−0.0412542	+	0.153963i	−0.983480	−	0.181014i	$-0.942062\pi$
$113$	−0.438538	+	1.63665i	−0.0412542	+	0.153963i	0.942226	+	0.334977i	$0.108729\pi$
$114$	−7.01279	+	12.1465i	−0.656808	+	1.13763i
$115$		0			0
$116$			27.0825i			2.51455i
$117$	−3.53553	+	0.707107i	−0.326860	+	0.0653720i
$118$	16.8887	+	16.8887i	1.55473	+	1.55473i
$119$	2.85410	+	10.6517i	0.261635	+	0.976435i
$120$		0			0
$121$	9.27358	−	5.35410i	0.843052	−	0.486737i
$122$	5.94750			0.538461
$123$	−1.36439	+	0.787729i	−0.123023	+	0.0710271i
$124$	−4.74142	+	17.6952i	−0.425792	+	1.58908i
$125$		0			0
$126$	−5.53457	−	9.58615i	−0.493058	−	0.854002i
$127$	3.87715	−	1.03888i	0.344041	−	0.0921855i	−0.0826612	−	0.996578i	$-0.526342\pi$
$127$	3.87715	−	1.03888i	0.344041	−	0.0921855i	0.426702	+	0.904392i	$0.359675\pi$
$128$	9.15298	−	15.8534i	0.809017	−	1.40126i
$129$	5.69214			0.501165
$130$		0			0
$131$	−22.8129			−1.99317			−0.996584	−	0.0825824i	$-0.973683\pi$
$131$	−22.8129			−1.99317			−0.996584	+	0.0825824i	$0.973683\pi$
$132$	0.874032	−	1.51387i	0.0760747	−	0.131765i
$133$	−28.6400	+	7.67407i	−2.48340	+	0.665426i
$134$	10.3146	+	17.8654i	0.891043	+	1.54333i
$135$		0			0
$136$	1.66880	−	6.22803i	0.143098	−	0.534049i
$137$	−9.18888	+	5.30520i	−0.785059	+	0.453254i	−0.838220	−	0.545332i	$-0.816404\pi$
$137$	−9.18888	+	5.30520i	−0.785059	+	0.453254i	0.0531614	+	0.998586i	$0.483070\pi$
$138$	7.60937			0.647752
$139$	3.16171	−	1.82542i	0.268173	−	0.154830i	−0.359884	−	0.932997i	$-0.617184\pi$
$139$	3.16171	−	1.82542i	0.268173	−	0.154830i	0.628057	+	0.778167i	$0.283850\pi$
$140$		0			0
$141$	−1.74617	−	6.51681i	−0.147054	−	0.548814i
$142$	−1.39583	−	1.39583i	−0.117135	−	0.117135i
$143$	0.125350	−	1.94361i	0.0104823	−	0.162533i
$144$		0			0
$145$		0			0
$146$	3.31129	−	5.73533i	0.274045	−	0.474659i
$147$	4.24472	−	15.8415i	0.350099	−	1.30659i
$148$		−	17.9608i		−	1.47636i
$149$	−0.192517	−	0.0515849i	−0.0157716	−	0.00422600i	0.250925	−	0.968007i	$-0.419265\pi$
$149$	−0.192517	−	0.0515849i	−0.0157716	−	0.00422600i	−0.266696	+	0.963781i	$0.585932\pi$
$150$		0			0
$151$	−3.36603	+	3.36603i	−0.273923	+	0.273923i	−0.830677	−	0.556754i	$-0.812047\pi$
$151$	−3.36603	+	3.36603i	−0.273923	+	0.273923i	0.556754	+	0.830677i	$0.312047\pi$
$152$	16.7458	+	4.48704i	1.35827	+	0.363947i
$153$	−0.590009	−	2.20194i	−0.0476994	−	0.178016i
$154$	5.77560	−	1.54757i	0.465411	−	0.124707i
$155$		0			0
$156$	5.17148	+	10.4591i	0.414050	+	0.837401i
$157$	−4.46033	+	4.46033i	−0.355973	+	0.355973i	−0.862326	−	0.506353i	$-0.830993\pi$
$157$	−4.46033	+	4.46033i	−0.355973	+	0.355973i	0.506353	+	0.862326i	$0.330993\pi$
$158$	−8.28510	−	4.78340i	−0.659127	−	0.380547i
$159$	−7.89878	−	4.56036i	−0.626414	−	0.361660i
$160$		0			0
$161$	11.3748	+	11.3748i	0.896456	+	0.896456i
$162$	1.14412	+	1.98168i	0.0898908	+	0.155695i
$163$	−7.83323	−	13.5676i	−0.613546	−	1.06269i	−0.990638	−	0.136517i	$-0.956409\pi$
$163$	−7.83323	−	13.5676i	−0.613546	−	1.06269i	0.377092	−	0.926176i	$-0.376924\pi$
$164$	3.60503	+	3.60503i	0.281506	+	0.281506i
$165$		0			0
$166$	16.8868	+	9.74960i	1.31067	+	0.756716i
$167$	12.6613	+	7.31000i	0.979761	+	0.565665i	0.902198	−	0.431322i	$-0.141953\pi$
$167$	12.6613	+	7.31000i	0.979761	+	0.565665i	0.0775628	+	0.996987i	$0.475286\pi$
$168$	−9.67478	+	9.67478i	−0.746425	+	0.746425i
$169$	10.3301	+	7.89230i	0.794625	+	0.607100i
$170$		0			0
$171$	5.92055	−	1.58641i	0.452756	−	0.121316i
$172$	−4.76748	−	17.7925i	−0.363517	−	1.35666i
$173$	−10.9872	−	2.94400i	−0.835339	−	0.223828i	−0.184297	−	0.982871i	$-0.559001\pi$
$173$	−10.9872	−	2.94400i	−0.835339	−	0.223828i	−0.651042	+	0.759042i	$0.725668\pi$
$174$	13.5413	−	13.5413i	1.02656	−	1.02656i
$175$		0			0
$176$		0			0
$177$		−	10.4378i		−	0.784553i
$178$	10.1852	−	38.0117i	0.763414	−	2.84910i
$179$	10.8220	−	18.7443i	0.808875	−	1.40101i	−0.104768	−	0.994497i	$-0.533410\pi$
$179$	10.8220	−	18.7443i	0.808875	−	1.40101i	0.913643	−	0.406516i	$-0.133257\pi$
$180$		0			0
$181$			21.4636i			1.59538i	0.603070	+	0.797688i	$0.293944\pi$
$181$			21.4636i			1.59538i	−0.603070	+	0.797688i	$0.706056\pi$
$182$	−12.7892	+	37.8057i	−0.948000	+	2.80234i
$183$	−1.83788	−	1.83788i	−0.135860	−	0.135860i
$184$	−2.43437	−	9.08520i	−0.179464	−	0.669770i
$185$		0			0
$186$	11.2183	−	6.47689i	0.822566	−	0.474909i
$187$	1.23141			0.0900495
$188$	−18.9077	+	10.9164i	−1.37899	+	0.796159i
$189$	−1.25201	+	4.67256i	−0.0910702	+	0.339879i
$190$		0			0
$191$	−8.61307	−	14.9183i	−0.623220	−	1.07945i	−0.988882	−	0.148701i	$-0.952491\pi$
$191$	−8.61307	−	14.9183i	−0.623220	−	1.07945i	0.365662	−	0.930748i	$-0.380842\pi$
$192$	−12.5032	+	3.35022i	−0.902341	+	0.241782i
$193$	−9.50785	+	16.4681i	−0.684390	+	1.18540i	0.289238	+	0.957257i	$0.406598\pi$
$193$	−9.50785	+	16.4681i	−0.684390	+	1.18540i	−0.973628	+	0.228141i	$0.926735\pi$
$194$	−7.57945			−0.544173
$195$		0			0
$196$	−53.0726			−3.79090
$197$	2.04070	−	3.53459i	0.145394	−	0.251829i	−0.784126	−	0.620602i	$-0.786888\pi$
$197$	2.04070	−	3.53459i	0.145394	−	0.251829i	0.929520	+	0.368772i	$0.120222\pi$
$198$	−1.19395	+	0.319918i	−0.0848503	+	0.0227356i
$199$	−4.04662	−	7.00895i	−0.286857	−	0.496851i	0.686201	−	0.727412i	$-0.259277\pi$
$199$	−4.04662	−	7.00895i	−0.286857	−	0.496851i	−0.973058	+	0.230561i	$0.925944\pi$
$200$		0			0
$201$	2.33332	−	8.70808i	0.164580	−	0.614220i
$202$	−36.2795	+	20.9460i	−2.55262	+	1.47375i
$203$	40.4840			2.84142
$204$	−6.38867	+	3.68850i	−0.447296	+	0.258247i
$205$		0			0
$206$	−6.14569	−	22.9360i	−0.428191	−	1.59803i
$207$	−2.35142	−	2.35142i	−0.163435	−	0.163435i
$208$		0			0
$209$			3.31099i			0.229026i
$210$		0			0
$211$	−8.26273	+	14.3115i	−0.568830	+	0.985242i	0.427852	+	0.903849i	$0.359270\pi$
$211$	−8.26273	+	14.3115i	−0.568830	+	0.985242i	−0.996682	+	0.0813934i	$0.974063\pi$
$212$	−7.63911	+	28.5096i	−0.524657	+	1.95804i
$213$			0.862670i			0.0591092i
$214$	27.9349	+	7.48514i	1.90959	+	0.511673i
$215$		0			0
$216$	2.00000	−	2.00000i	0.136083	−	0.136083i
$217$	26.4514	+	7.08764i	1.79564	+	0.481140i
$218$	−7.09162	−	26.4663i	−0.480305	−	1.79252i
$219$	−2.79556	+	0.749068i	−0.188906	+	0.0506173i
$220$		0			0
$221$	−4.55924	+	6.83886i	−0.306687	+	0.460031i
$222$	−8.98038	+	8.98038i	−0.602723	+	0.602723i
$223$	−5.15529	−	2.97641i	−0.345224	−	0.199315i	0.317356	−	0.948307i	$-0.397205\pi$
$223$	−5.15529	−	2.97641i	−0.345224	−	0.199315i	−0.662580	+	0.748991i	$0.730538\pi$
$224$	−23.6983	−	13.6822i	−1.58341	−	0.914181i
$225$		0			0
$226$	−2.74157	−	2.74157i	−0.182366	−	0.182366i
$227$	−1.91376	−	3.31473i	−0.127021	−	0.220006i	0.795500	−	0.605953i	$-0.207208\pi$
$227$	−1.91376	−	3.31473i	−0.127021	−	0.220006i	−0.922521	+	0.385947i	$0.873875\pi$
$228$	−9.91759	−	17.1778i	−0.656808	−	1.13763i
$229$	−5.45537	−	5.45537i	−0.360501	−	0.360501i	0.503496	−	0.863997i	$-0.332047\pi$
$229$	−5.45537	−	5.45537i	−0.360501	−	0.360501i	−0.863997	+	0.503496i	$0.832047\pi$
$230$		0			0
$231$	−2.26298	−	1.30653i	−0.148893	−	0.0859636i
$232$	−20.4997	−	11.8355i	−1.34587	−	0.777039i
$233$	14.7647	−	14.7647i	0.967271	−	0.967271i	−0.0322102	−	0.999481i	$-0.510255\pi$
$233$	14.7647	−	14.7647i	0.967271	−	0.967271i	0.999481	+	0.0322102i	$0.0102546\pi$
$234$	2.64383	−	7.81531i	0.172832	−	0.510903i
$235$		0			0
$236$	−32.6265	+	8.74224i	−2.12380	+	0.569071i
$237$	1.08208	+	4.03839i	0.0702889	+	0.262322i
$238$	−24.3736	−	6.53089i	−1.57991	−	0.423334i
$239$	−7.59915	+	7.59915i	−0.491548	+	0.491548i	−0.908794	−	0.417245i	$-0.862996\pi$
$239$	−7.59915	+	7.59915i	−0.491548	+	0.491548i	0.417245	+	0.908794i	$0.362996\pi$
$240$		0			0
$241$	−24.5379	−	6.57492i	−1.58063	−	0.423528i	−0.641508	−	0.767116i	$-0.721691\pi$
$241$	−24.5379	−	6.57492i	−1.58063	−	0.423528i	−0.939120	+	0.343588i	$0.888358\pi$
$242$			24.5030i			1.57511i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−4.20552	+	7.28417i	−0.269231	+	0.466321i
$245$		0			0
$246$		−	3.60503i		−	0.229849i
$247$	−18.3882	−	12.2588i	−1.17001	−	0.780009i
$248$	−11.3220	−	11.3220i	−0.718949	−	0.718949i
$249$	−2.20552	−	8.23110i	−0.139769	−	0.521625i
$250$		0			0
$251$	−10.3573	+	5.97979i	−0.653747	+	0.377441i	−0.789890	−	0.613248i	$-0.789863\pi$
$251$	−10.3573	+	5.97979i	−0.653747	+	0.377441i	0.136143	+	0.990689i	$0.456529\pi$
$252$	15.6541			0.986117
$253$	1.55567	−	0.898164i	0.0978039	−	0.0564671i
$254$	−2.37721	+	8.87186i	−0.149159	+	0.556670i
$255$		0			0
$256$	8.00000	+	13.8564i	0.500000	+	0.866025i
$257$	−7.71781	+	2.06798i	−0.481424	+	0.128997i	−0.491366	−	0.870953i	$-0.663502\pi$
$257$	−7.71781	+	2.06798i	−0.481424	+	0.128997i	0.00994160	+	0.999951i	$0.496835\pi$
$258$	−6.51250	+	11.2800i	−0.405451	+	0.702261i
$259$	−26.8484			−1.66828
$260$		0			0
$261$	−8.36897			−0.518026
$262$	26.1007	−	45.2078i	1.61251	−	2.79294i
$263$	−11.3206	+	3.03335i	−0.698059	+	0.187044i	−0.590361	−	0.807139i	$-0.701015\pi$
$263$	−11.3206	+	3.03335i	−0.698059	+	0.187044i	−0.107698	+	0.994184i	$0.534348\pi$
$264$	0.763932	+	1.32317i	0.0470168	+	0.0814354i
$265$		0			0
$266$	17.5602	−	65.5354i	1.07668	−	4.01823i
$267$	−14.8937	+	8.59887i	−0.911478	+	0.526242i
$268$	−29.1740			−1.78209
$269$	27.8888	−	16.1016i	1.70041	−	0.981734i	0.755077	−	0.655636i	$-0.227600\pi$
$269$	27.8888	−	16.1016i	1.70041	−	0.981734i	0.945336	−	0.326097i	$-0.105734\pi$
$270$		0			0
$271$	−6.24142	−	23.2933i	−0.379139	−	1.41497i	−0.847202	−	0.531271i	$-0.821715\pi$
$271$	−6.24142	−	23.2933i	−0.379139	−	1.41497i	0.468063	−	0.883695i	$-0.344952\pi$
$272$		0			0
$273$	15.6347	−	7.73052i	0.946254	−	0.467872i
$274$		−	24.2792i		−	1.46676i
$275$		0			0
$276$	−5.38064	+	9.31953i	−0.323876	+	0.560970i
$277$	2.31703	−	8.64726i	0.139217	−	0.519564i	−0.860728	−	0.509065i	$-0.829991\pi$
$277$	2.31703	−	8.64726i	0.139217	−	0.519564i	0.999945	−	0.0104989i	$-0.00334198\pi$
$278$			8.35400i			0.501040i
$279$	−5.46812	−	1.46518i	−0.327368	−	0.0877179i
$280$		0			0
$281$	−8.77064	+	8.77064i	−0.523212	+	0.523212i	−0.918540	−	0.395328i	$-0.870631\pi$
$281$	−8.77064	+	8.77064i	−0.523212	+	0.523212i	0.395328	+	0.918540i	$0.370631\pi$
$282$	14.9121	+	3.99567i	0.888000	+	0.237939i
$283$	−0.379069	−	1.41470i	−0.0225333	−	0.0840955i	0.953744	−	0.300621i	$-0.0971941\pi$
$283$	−0.379069	−	1.41470i	−0.0225333	−	0.0840955i	−0.976277	+	0.216526i	$0.930527\pi$
$284$	2.69653	−	0.722534i	0.160010	−	0.0428745i
$285$		0			0
$286$	3.70820	+	2.47214i	0.219271	+	0.146180i
$287$	5.38893	−	5.38893i	0.318099	−	0.318099i
$288$	4.89898	+	2.82843i	0.288675	+	0.166667i
$289$	10.2220	+	5.90167i	0.601294	+	0.347157i
$290$		0			0
$291$	2.34218	+	2.34218i	0.137301	+	0.137301i
$292$	4.68287	+	8.11098i	0.274045	+	0.474659i
$293$	8.10910	+	14.0454i	0.473738	+	0.820539i	0.999548	−	0.0300633i	$-0.00957089\pi$
$293$	8.10910	+	14.0454i	0.473738	+	0.820539i	−0.525810	+	0.850602i	$0.676238\pi$
$294$	26.5363	+	26.5363i	1.54763	+	1.54763i
$295$		0			0
$296$	13.5951	+	7.84914i	0.790199	+	0.456222i
$297$	0.467811	+	0.270091i	0.0271451	+	0.0156723i
$298$	0.322488	−	0.322488i	0.0186812	−	0.0186812i
$299$	−0.771665	+	11.9651i	−0.0446266	+	0.691960i
$300$		0			0
$301$	−26.5968	+	7.12660i	−1.53302	+	0.410771i
$302$	−2.81923	−	10.5215i	−0.162229	−	0.605446i
$303$	17.6836	+	4.73832i	1.01590	+	0.272209i
$304$		0			0
$305$		0			0
$306$	5.03859	+	1.35008i	0.288037	+	0.0771792i
$307$			1.87858i			0.107216i	0.998562	+	0.0536081i	$0.0170722\pi$
$307$			1.87858i			0.107216i	−0.998562	+	0.0536081i	$0.982928\pi$
$308$	−2.18859	+	8.16793i	−0.124707	+	0.465411i
$309$	−5.18850	+	8.98675i	−0.295163	+	0.511238i
$310$		0			0
$311$			1.24825i			0.0707815i	0.999374	+	0.0353908i	$0.0112676\pi$
$311$			1.24825i			0.0707815i	−0.999374	+	0.0353908i	$0.988732\pi$
$312$	−10.1769	−	0.656339i	−0.576153	−	0.0371579i
$313$	−4.54979	−	4.54979i	−0.257169	−	0.257169i	0.566733	−	0.823902i	$-0.308207\pi$
$313$	−4.54979	−	4.54979i	−0.257169	−	0.257169i	−0.823902	+	0.566733i	$0.808207\pi$
$314$	−3.73578	−	13.9421i	−0.210822	−	0.786799i
$315$		0			0
$316$	11.7169	−	6.76475i	0.659127	−	0.380547i
$317$	5.68154			0.319107			0.159554	−	0.987189i	$-0.448995\pi$
$317$	5.68154			0.319107			0.159554	+	0.987189i	$0.448995\pi$
$318$	18.0743	−	10.4352i	1.01356	−	0.585178i
$319$	1.17006	−	4.36672i	0.0655107	−	0.244489i
$320$		0			0
$321$	−6.31933	−	10.9454i	−0.352710	−	0.610912i
$322$	−35.5552	+	9.52699i	−1.98142	+	0.530919i
$323$	6.98635	−	12.1007i	0.388731	−	0.673302i
$324$	−3.23607			−0.179782
$325$		0			0
$326$	35.8487			1.98548
$327$	−5.98710	+	10.3700i	−0.331088	+	0.573460i
$328$	−4.30423	+	1.15332i	−0.237661	+	0.0636812i
$329$	16.3182	+	28.2640i	0.899652	+	1.55824i
$330$		0			0
$331$	−6.79565	+	25.3617i	−0.373523	+	1.39401i	0.481968	+	0.876189i	$0.339922\pi$
$331$	−6.79565	+	25.3617i	−0.373523	+	1.39401i	−0.855491	+	0.517818i	$0.826745\pi$
$332$	−23.8815	+	13.7880i	−1.31067	+	0.756716i
$333$	5.55018			0.304148
$334$	−28.9722	+	16.7271i	−1.58529	+	0.915265i
$335$		0			0
$336$		0			0
$337$	−15.7201	−	15.7201i	−0.856326	−	0.856326i	0.134577	−	0.990903i	$-0.457032\pi$
$337$	−15.7201	−	15.7201i	−0.856326	−	0.856326i	−0.990903	+	0.134577i	$0.957032\pi$
$338$	−27.4589	+	11.4412i	−1.49357	+	0.622321i
$339$			1.69438i			0.0920262i
$340$		0			0
$341$	1.52899	−	2.64828i	0.0827993	−	0.143413i
$342$	−3.63009	+	13.5477i	−0.196293	+	0.732574i
$343$			45.4731i			2.45532i
$344$	15.5512	+	4.16693i	0.838465	+	0.224666i
$345$		0			0
$346$	18.4047	−	18.4047i	0.989445	−	0.989445i
$347$	10.2670	+	2.75102i	0.551159	+	0.147683i	0.523642	−	0.851939i	$-0.324573\pi$
$347$	10.2670	+	2.75102i	0.551159	+	0.147683i	0.0275176	+	0.999621i	$0.491240\pi$
$348$	7.00948	+	26.1597i	0.375747	+	1.40231i
$349$	32.7284	−	8.76956i	1.75191	−	0.469424i	0.766880	−	0.641790i	$-0.221808\pi$
$349$	32.7284	−	8.76956i	1.75191	−	0.469424i	0.985033	+	0.172366i	$0.0551413\pi$
$350$		0			0
$351$	−3.23205	+	1.59808i	−0.172514	+	0.0852990i
$352$	−2.16073	+	2.16073i	−0.115167	+	0.115167i
$353$	−21.9701	−	12.6844i	−1.16935	−	0.675124i	−0.215822	−	0.976433i	$-0.569243\pi$
$353$	−21.9701	−	12.6844i	−1.16935	−	0.675124i	−0.953527	+	0.301309i	$0.902576\pi$
$354$	20.6844	+	11.9421i	1.09936	+	0.634716i
$355$		0			0
$356$	39.3526	+	39.3526i	2.08569	+	2.08569i
$357$	5.51370	+	9.55001i	0.291816	+	0.505440i
$358$	24.7634	+	42.8915i	1.30879	+	2.26689i
$359$	−20.9349	−	20.9349i	−1.10490	−	1.10490i	−0.993810	−	0.111092i	$-0.964565\pi$
$359$	−20.9349	−	20.9349i	−1.10490	−	1.10490i	−0.111092	−	0.993810i	$-0.535435\pi$
$360$		0			0
$361$	16.0818	+	9.28481i	0.846408	+	0.488674i
$362$	−42.5339	−	24.5570i	−2.23553	−	1.29069i
$363$	7.57184	−	7.57184i	0.397419	−	0.397419i
$364$	−37.2590	−	42.3962i	−1.95290	−	2.22216i
$365$		0			0
$366$	5.74484	−	1.53933i	0.300288	−	0.0804619i
$367$	0.383096	+	1.42973i	0.0199975	+	0.0746315i	0.975203	−	0.221310i	$-0.0710333\pi$
$367$	0.383096	+	1.42973i	0.0199975	+	0.0746315i	−0.955206	+	0.295942i	$0.904367\pi$
$368$		0			0
$369$	−1.11402	+	1.11402i	−0.0579934	+	0.0579934i
$370$		0			0
$371$	42.6171	+	11.4192i	2.21257	+	0.592856i
$372$			18.3194i			0.949818i
$373$	6.88471	−	25.6941i	0.356477	−	1.33039i	−0.522139	−	0.852860i	$-0.674866\pi$
$373$	6.88471	−	25.6941i	0.356477	−	1.33039i	0.878616	−	0.477529i	$-0.158467\pi$
$374$	−1.40888	+	2.44025i	−0.0728515	+	0.126183i
$375$		0			0
$376$		−	19.0825i		−	0.984107i
$377$	19.9193	+	22.6657i	1.02590	+	1.16735i
$378$	−7.82706	−	7.82706i	−0.402581	−	0.402581i
$379$	6.86656	+	25.6263i	0.352711	+	1.31634i	0.883340	+	0.468733i	$0.155289\pi$
$379$	6.86656	+	25.6263i	0.352711	+	1.31634i	−0.530629	+	0.847604i	$0.678044\pi$
$380$		0			0
$381$	3.47615	−	2.00696i	0.178089	−	0.102820i
$382$	39.4176			2.01678
$383$	15.3115	−	8.84009i	0.782380	−	0.451707i	−0.0548931	−	0.998492i	$-0.517482\pi$
$383$	15.3115	−	8.84009i	0.782380	−	0.451707i	0.837273	+	0.546785i	$0.184148\pi$
$384$	4.73793	−	17.6822i	0.241782	−	0.902341i
$385$		0			0
$386$	−21.7563	−	37.6830i	−1.10737	−	1.91802i
$387$	5.49818	−	1.47323i	0.279488	−	0.0748886i
$388$	5.35948	−	9.28289i	0.272086	−	0.471267i
$389$	−13.1956			−0.669046			−0.334523	−	0.942388i	$-0.608575\pi$
$389$	−13.1956			−0.669046			−0.334523	+	0.942388i	$0.608575\pi$
$390$		0			0
$391$	−7.58068			−0.383371
$392$	23.1936	−	40.1725i	1.17145	−	2.02902i
$393$	−22.0355	+	5.90440i	−1.11155	+	0.297838i
$394$	4.66962	+	8.08802i	0.235252	+	0.407468i
$395$		0			0
$396$	0.452432	−	1.68850i	0.0227356	−	0.0848503i
$397$	9.33178	−	5.38770i	0.468348	−	0.270401i	−0.247200	−	0.968965i	$-0.579510\pi$
$397$	9.33178	−	5.38770i	0.468348	−	0.270401i	0.715548	+	0.698563i	$0.246177\pi$
$398$	18.5193			0.928290
$399$	−25.6779	+	14.8252i	−1.28550	+	0.742186i
$400$		0			0
$401$	3.17178	+	11.8373i	0.158391	+	0.591125i	0.998791	+	0.0491574i	$0.0156536\pi$
$401$	3.17178	+	11.8373i	0.158391	+	0.591125i	−0.840400	+	0.541967i	$0.817680\pi$
$402$	14.5870	+	14.5870i	0.727534	+	0.727534i
$403$	9.04673	+	18.2967i	0.450650	+	0.911423i
$404$		−	59.2442i		−	2.94751i
$405$		0			0
$406$	−46.3186	+	80.2262i	−2.29875	+	3.98156i
$407$	−0.775966	+	2.89595i	−0.0384632	+	0.143547i
$408$		−	6.44773i		−	0.319210i
$409$	29.2643	+	7.84136i	1.44703	+	0.387730i	0.894989	−	0.446088i	$-0.147183\pi$
$409$	29.2643	+	7.84136i	1.44703	+	0.387730i	0.552039	+	0.833818i	$0.313850\pi$
$410$		0			0
$411$	−7.50269	+	7.50269i	−0.370080	+	0.370080i
$412$	32.4364	+	8.69132i	1.59803	+	0.428191i
$413$	13.0682	+	48.7712i	0.643045	+	2.39987i
$414$	7.35008	−	1.96945i	0.361237	−	0.0967932i
$415$		0			0
$416$	−4.00000	−	20.0000i	−0.196116	−	0.980581i
$417$	2.58153	−	2.58153i	0.126418	−	0.126418i
$418$	−6.56132	−	3.78818i	−0.320925	−	0.185286i
$419$	10.7224	+	6.19057i	0.523823	+	0.302429i	0.738497	−	0.674256i	$-0.235536\pi$
$419$	10.7224	+	6.19057i	0.523823	+	0.302429i	−0.214675	+	0.976686i	$0.568869\pi$
$420$		0			0
$421$	−14.7075	−	14.7075i	−0.716800	−	0.716800i	0.251148	−	0.967949i	$-0.419192\pi$
$421$	−14.7075	−	14.7075i	−0.716800	−	0.716800i	−0.967949	+	0.251148i	$0.919192\pi$
$422$	−18.9072	−	32.7482i	−0.920386	−	1.59416i
$423$	−3.37335	−	5.84281i	−0.164018	−	0.284087i
$424$	−18.2414	−	18.2414i	−0.885883	−	0.885883i
$425$		0			0
$426$	−1.70953	−	0.987000i	−0.0828272	−	0.0478203i
$427$	10.8886	+	6.28656i	0.526938	+	0.304228i
$428$	−28.9203	+	28.9203i	−1.39792	+	1.39792i
$429$	−0.381966	−	1.90983i	−0.0184415	−	0.0922075i
$430$		0			0
$431$	−17.8877	+	4.79300i	−0.861621	+	0.230871i	−0.662461	−	0.749096i	$-0.730488\pi$
$431$	−17.8877	+	4.79300i	−0.861621	+	0.230871i	−0.199160	+	0.979967i	$0.563821\pi$
$432$		0			0
$433$	4.60368	+	1.23355i	0.221239	+	0.0592808i	0.367736	−	0.929930i	$-0.380133\pi$
$433$	4.60368	+	1.23355i	0.221239	+	0.0592808i	−0.146497	+	0.989211i	$0.546800\pi$
$434$	−44.3091	+	44.3091i	−2.12690	+	2.12690i
$435$		0			0
$436$	37.4290	+	10.0291i	1.79252	+	0.480305i
$437$		−	20.3828i		−	0.975043i
$438$	1.71405	−	6.39693i	0.0819005	−	0.305657i
$439$	−6.21503	+	10.7648i	−0.296627	+	0.513774i	−0.975362	−	0.220610i	$-0.929195\pi$
$439$	−6.21503	+	10.7648i	−0.296627	+	0.513774i	0.678735	+	0.734383i	$0.262529\pi$
$440$		0			0
$441$		−	16.4003i		−	0.780969i
$442$	−8.33609	−	16.8594i	−0.396507	−	0.801922i
$443$	−22.8975	−	22.8975i	−1.08789	−	1.08789i	−0.995745	−	0.0921479i	$-0.970627\pi$
$443$	−22.8975	−	22.8975i	−1.08789	−	1.08789i	−0.0921479	−	0.995745i	$-0.529373\pi$
$444$	−4.64858	−	17.3488i	−0.220612	−	0.823335i
$445$		0			0
$446$	11.7966	−	6.81076i	0.558584	−	0.322499i
$447$	−0.199309			−0.00942698
$448$	54.2275	−	31.3082i	2.56201	−	1.47918i
$449$	1.44492	−	5.39251i	0.0681900	−	0.254488i	−0.923413	−	0.383808i	$-0.874613\pi$
$449$	1.44492	−	5.39251i	0.0681900	−	0.254488i	0.991603	+	0.129319i	$0.0412792\pi$
$450$		0			0
$451$	−0.425517	−	0.737016i	−0.0200368	−	0.0347047i
$452$	5.29630	−	1.41914i	0.249117	−	0.0667507i
$453$	−2.38014	+	4.12252i	−0.111829	+	0.193693i
$454$	8.75831			0.411048
$455$		0			0
$456$	17.3366			0.811860
$457$	−8.53057	+	14.7754i	−0.399043	+	0.691163i	−0.993608	−	0.112885i	$-0.963991\pi$
$457$	−8.53057	+	14.7754i	−0.399043	+	0.691163i	0.594565	+	0.804048i	$0.297324\pi$
$458$	17.0524	−	4.56918i	0.796807	−	0.213504i
$459$	−1.13981	−	1.97421i	−0.0532017	−	0.0921481i
$460$		0			0
$461$	−0.971754	+	3.62663i	−0.0452591	+	0.168909i	−0.984856	−	0.173373i	$-0.944533\pi$
$461$	−0.971754	+	3.62663i	−0.0452591	+	0.168909i	0.939597	+	0.342282i	$0.111200\pi$
$462$	5.17826	−	2.98967i	0.240915	−	0.139092i
$463$	0.416821			0.0193713			0.00968565	−	0.999953i	$-0.496917\pi$
$463$	0.416821			0.0193713			0.00968565	+	0.999953i	$0.496917\pi$
$464$		0			0
$465$		0			0
$466$	12.3663	+	46.1517i	0.572858	+	2.13794i
$467$	4.51606	+	4.51606i	0.208979	+	0.208979i	0.803833	−	0.594855i	$-0.202790\pi$
$467$	4.51606	+	4.51606i	0.208979	+	0.208979i	−0.594855	+	0.803833i	$0.702790\pi$
$468$	7.70229	+	8.76427i	0.356039	+	0.405129i
$469$			43.6103i			2.01374i
$470$		0			0
$471$	−3.15393	+	5.46277i	−0.145326	+	0.251711i
$472$	7.64100	−	28.5166i	0.351705	−	1.31258i
$473$			3.07479i			0.141379i
$474$	−9.24083	−	2.47607i	−0.424445	−	0.113730i
$475$		0			0
$476$	25.2334	−	25.2334i	1.15657	−	1.15657i
$477$	−8.80994	−	2.36062i	−0.403379	−	0.108085i
$478$	−6.36472	−	23.7534i	−0.291115	−	1.08646i
$479$	2.45991	−	0.659131i	0.112396	−	0.0301165i	−0.202183	−	0.979348i	$-0.564803\pi$
$479$	2.45991	−	0.659131i	0.112396	−	0.0301165i	0.314579	+	0.949231i	$0.398137\pi$
$480$		0			0
$481$	−13.2102	−	15.0316i	−0.602333	−	0.685382i
$482$	41.1038	−	41.1038i	1.87223	−	1.87223i
$483$	13.9312	+	8.04317i	0.633890	+	0.365977i
$484$	−30.0099	−	17.3262i	−1.36409	−	0.787556i
$485$		0			0
$486$	1.61803	+	1.61803i	0.0733955	+	0.0733955i
$487$	−4.48717	−	7.77200i	−0.203333	−	0.352183i	0.746267	−	0.665646i	$-0.231844\pi$
$487$	−4.48717	−	7.77200i	−0.203333	−	0.352183i	−0.949600	+	0.313463i	$0.898511\pi$
$488$	−3.67576	−	6.36660i	−0.166394	−	0.288202i
$489$	−11.0779	−	11.0779i	−0.500958	−	0.500958i
$490$		0			0
$491$	4.07277	+	2.35142i	0.183802	+	0.106118i	0.589078	−	0.808076i	$-0.299491\pi$
$491$	4.07277	+	2.35142i	0.183802	+	0.106118i	−0.405276	+	0.914194i	$0.632825\pi$
$492$	4.41525	+	2.54914i	0.199055	+	0.114924i
$493$	−13.4902	+	13.4902i	−0.607569	+	0.607569i
$494$	45.3314	−	22.4140i	2.03956	−	1.00845i
$495$		0			0
$496$		0			0
$497$	−1.08007	−	4.03088i	−0.0484478	−	0.180809i
$498$	18.8348	+	5.04677i	0.844007	+	0.226151i
$499$	−1.36239	+	1.36239i	−0.0609890	+	0.0609890i	−0.736943	−	0.675954i	$-0.763732\pi$
$499$	−1.36239	+	1.36239i	−0.0609890	+	0.0609890i	0.675954	+	0.736943i	$0.263732\pi$
$500$		0			0
$501$	14.1218	+	3.78394i	0.630917	+	0.169054i
$502$		−	27.3664i		−	1.22142i
$503$	−5.10187	+	19.0404i	−0.227481	+	0.848970i	0.753914	+	0.656973i	$0.228163\pi$
$503$	−5.10187	+	19.0404i	−0.227481	+	0.848970i	−0.981395	+	0.191998i	$0.938503\pi$
$504$	−6.84110	+	11.8491i	−0.304727	+	0.527802i
$505$		0			0
$506$			4.11044i			0.182731i
$507$	12.0208	+	4.94975i	0.533863	+	0.219826i
$508$	−9.18483	−	9.18483i	−0.407511	−	0.407511i
$509$	4.53590	+	16.9282i	0.201050	+	0.750329i	0.990617	+	0.136665i	$0.0436385\pi$
$509$	4.53590	+	16.9282i	0.201050	+	0.750329i	−0.789567	+	0.613664i	$0.789695\pi$
$510$		0			0
$511$	12.1246	−	7.00013i	0.536360	−	0.309667i
$512$		0			0
$513$	5.30822	−	3.06470i	0.234364	−	0.135310i
$514$	4.73205	−	17.6603i	0.208722	−	0.778960i
$515$		0			0
$516$	−9.21007	−	15.9523i	−0.405451	−	0.702261i
$517$	3.52026	−	0.943251i	0.154821	−	0.0414841i
$518$	30.7178	−	53.2049i	1.34966	−	2.33769i
$519$	−11.3748			−0.499296
$520$		0			0
$521$	3.83962			0.168217			0.0841084	−	0.996457i	$-0.473196\pi$
$521$	3.83962			0.168217			0.0841084	+	0.996457i	$0.473196\pi$
$522$	9.57513	−	16.5846i	0.419092	−	0.725888i
$523$	34.3282	−	9.19820i	1.50107	−	0.402209i	0.587609	−	0.809145i	$-0.300069\pi$
$523$	34.3282	−	9.19820i	1.50107	−	0.402209i	0.913457	+	0.406936i	$0.133403\pi$
$524$	36.9120	+	63.9334i	1.61251	+	2.79294i
$525$		0			0
$526$	6.94105	−	25.9044i	0.302644	−	1.12948i
$527$	−11.1760	+	6.45248i	−0.486835	+	0.281074i
$528$		0			0
$529$	10.3417	−	5.97081i	0.449641	−	0.259600i
$530$		0			0
$531$	−2.70150	−	10.0821i	−0.117235	−	0.437527i
$532$	67.8472	+	67.8472i	2.94155	+	2.94155i
$533$	5.66862	+	0.365586i	0.245535	+	0.0158353i
$534$		−	39.3526i		−	1.70296i
$535$		0			0
$536$	12.7495	−	22.0828i	0.550695	−	0.953831i
$537$	5.60189	−	20.9065i	0.241739	−	0.902183i
$538$			73.6890i			3.17696i
$539$	8.55729	+	2.29292i	0.368589	+	0.0987630i
$540$		0			0
$541$	26.6416	−	26.6416i	1.14541	−	1.14541i	0.157967	−	0.987444i	$-0.449506\pi$
$541$	26.6416	−	26.6416i	1.14541	−	1.14541i	0.987444	−	0.157967i	$-0.0504940\pi$
$542$	53.3007	+	14.2819i	2.28946	+	0.613460i
$543$	5.55519	+	20.7322i	0.238396	+	0.889706i
$544$	12.4561	−	3.33759i	0.534049	−	0.143098i
$545$		0			0
$546$	−2.56860	+	39.8276i	−0.109926	+	1.70446i
$547$	2.29294	−	2.29294i	0.0980392	−	0.0980392i	−0.656386	−	0.754425i	$-0.727916\pi$
$547$	2.29294	−	2.29294i	0.0980392	−	0.0980392i	0.754425	+	0.656386i	$0.227916\pi$
$548$	29.7358	+	17.1680i	1.27025	+	0.733380i
$549$	−2.25093	−	1.29958i	−0.0960674	−	0.0554646i
$550$		0			0
$551$	−36.2723	−	36.2723i	−1.54525	−	1.54525i
$552$	−4.70285	−	8.14557i	−0.200166	−	0.346699i
$553$	−10.1122	−	17.5148i	−0.430014	−	0.744807i
$554$	14.4851	+	14.4851i	0.615414	+	0.615414i
$555$		0			0
$556$	−10.2315	−	5.90717i	−0.433913	−	0.250520i
$557$	−23.9365	−	13.8198i	−1.01422	−	0.585562i	−0.101798	−	0.994805i	$-0.532459\pi$
$557$	−23.9365	−	13.8198i	−1.01422	−	0.585562i	−0.912425	+	0.409243i	$0.865793\pi$
$558$	9.15971	−	9.15971i	0.387762	−	0.387762i
$559$	−17.0764	−	11.3843i	−0.722255	−	0.481503i
$560$		0			0
$561$	1.18945	−	0.318712i	0.0502186	−	0.0134560i
$562$	−7.34590	−	27.4153i	−0.309868	−	1.15644i
$563$	24.1829	+	6.47979i	1.01919	+	0.273091i	0.729464	−	0.684020i	$-0.239770\pi$
$563$	24.1829	+	6.47979i	1.01919	+	0.273091i	0.289724	+	0.957110i	$0.406436\pi$
$564$	−15.4381	+	15.4381i	−0.650061	+	0.650061i
$565$		0			0
$566$	3.23719	+	0.867403i	0.136069	+	0.0364597i
$567$			4.83739i			0.203151i
$568$	−0.631518	+	2.35686i	−0.0264979	+	0.0988916i
$569$	−0.824675	+	1.42838i	−0.0345722	+	0.0598807i	−0.882794	−	0.469761i	$-0.844340\pi$
$569$	−0.824675	+	1.42838i	−0.0345722	+	0.0598807i	0.848222	+	0.529641i	$0.177674\pi$
$570$		0			0
$571$			16.0708i			0.672541i	0.941765	+	0.336271i	$0.109166\pi$
$571$			16.0708i			0.672541i	−0.941765	+	0.336271i	$0.890834\pi$
$572$	−5.64983	+	2.79354i	−0.236231	+	0.116804i
$573$	−12.1807	−	12.1807i	−0.508857	−	0.508857i
$574$	4.51353	+	16.8447i	0.188391	+	0.703086i
$575$		0			0
$576$	−11.2101	+	6.47214i	−0.467086	+	0.269672i
$577$	6.92615			0.288339			0.144170	−	0.989553i	$-0.453949\pi$
$577$	6.92615			0.288339			0.144170	+	0.989553i	$0.453949\pi$
$578$	−23.3904	+	13.5045i	−0.972914	+	0.561712i
$579$	−4.92163	+	18.3678i	−0.204536	+	0.763338i
$580$		0			0
$581$	20.6108	+	35.6990i	0.855081	+	1.48104i
$582$	−7.32119	+	1.96171i	−0.303473	+	0.0813153i
$583$	2.46342	−	4.26677i	0.102025	−	0.176712i
$584$	−8.18597			−0.338738
$585$		0			0
$586$	−37.1112			−1.53305
$587$	13.1070	−	22.7019i	0.540982	−	0.937009i	−0.457866	−	0.889021i	$-0.651386\pi$
$587$	13.1070	−	22.7019i	0.540982	−	0.937009i	0.998848	−	0.0479876i	$-0.0152808\pi$
$588$	−51.2642	+	13.7362i	−2.11410	+	0.566471i
$589$	−17.3493	−	30.0499i	−0.714866	−	1.23818i
$590$		0			0
$591$	1.05634	−	3.94233i	0.0434522	−	0.162166i
$592$		0			0
$593$	−12.3090			−0.505472			−0.252736	−	0.967535i	$-0.581330\pi$
$593$	−12.3090			−0.505472			−0.252736	+	0.967535i	$0.581330\pi$
$594$	−1.07047	+	0.618034i	−0.0439218	+	0.0253582i
$595$		0			0
$596$	0.166932	+	0.622999i	0.00683781	+	0.0255191i
$597$	−5.72278	−	5.72278i	−0.234218	−	0.234218i
$598$	−22.8281	−	15.2187i	−0.933511	−	0.622340i
$599$		−	46.6193i		−	1.90481i	−0.304830	−	0.952407i	$-0.598599\pi$
$599$		−	46.6193i		−	1.90481i	0.304830	−	0.952407i	$-0.401401\pi$
$600$		0			0
$601$	15.2241	−	26.3690i	0.621006	−	1.07561i	−0.368293	−	0.929710i	$-0.620058\pi$
$601$	15.2241	−	26.3690i	0.621006	−	1.07561i	0.989299	−	0.145904i	$-0.0466090\pi$
$602$	16.3074	−	60.8601i	0.664641	−	2.48047i
$603$		−	9.01526i		−	0.367130i
$604$	14.8797	+	3.98700i	0.605446	+	0.162229i
$605$		0			0
$606$	−29.6221	+	29.6221i	−1.20331	+	1.20331i
$607$	1.01718	+	0.272554i	0.0412863	+	0.0110626i	0.279403	−	0.960174i	$-0.409863\pi$
$607$	1.01718	+	0.272554i	0.0412863	+	0.0110626i	−0.238117	+	0.971237i	$0.576530\pi$
$608$	8.97407	+	33.4917i	0.363947	+	1.35827i
$609$	39.1045	−	10.4780i	1.58459	−	0.424591i
$610$		0			0
$611$	−7.79510	+	23.0428i	−0.315356	+	0.932211i
$612$	−5.21633	+	5.21633i	−0.210858	+	0.210858i
$613$	−25.5137	−	14.7304i	−1.03049	−	0.594953i	−0.113365	−	0.993553i	$-0.536163\pi$
$613$	−25.5137	−	14.7304i	−1.03049	−	0.594953i	−0.917125	+	0.398600i	$0.869496\pi$
$614$	−3.72274	−	2.14933i	−0.150238	−	0.0867397i
$615$		0			0
$616$	−5.22614	−	5.22614i	−0.210567	−	0.210567i
$617$	18.2917	+	31.6822i	0.736398	+	1.27548i	0.954107	+	0.299465i	$0.0968081\pi$
$617$	18.2917	+	31.6822i	0.736398	+	1.27548i	−0.217710	+	0.976014i	$0.569859\pi$
$618$	−11.8726	−	20.5639i	−0.477585	−	0.827201i
$619$	−33.3064	−	33.3064i	−1.33870	−	1.33870i	−0.897322	−	0.441377i	$-0.854490\pi$
$619$	−33.3064	−	33.3064i	−1.33870	−	1.33870i	−0.441377	−	0.897322i	$-0.645510\pi$
$620$		0			0
$621$	−2.87989	−	1.66271i	−0.115566	−	0.0667222i
$622$	−2.47362	−	1.42815i	−0.0991832	−	0.0572634i
$623$	58.8257	−	58.8257i	2.35680	−	2.35680i
$624$		0			0
$625$		0			0
$626$	14.2217	−	3.81070i	0.568415	−	0.152306i
$627$	0.856948	+	3.19817i	0.0342232	+	0.127723i
$628$	19.7171	+	5.28319i	0.786799	+	0.210822i
$629$	8.94652	−	8.94652i	0.356721	−	0.356721i
$630$		0			0
$631$	9.79825	+	2.62543i	0.390062	+	0.104517i	0.448519	−	0.893773i	$-0.351952\pi$
$631$	9.79825	+	2.62543i	0.390062	+	0.104517i	−0.0584574	+	0.998290i	$0.518618\pi$
$632$			11.8252i			0.470382i
$633$	−4.27710	+	15.9624i	−0.170000	+	0.634447i
$634$	−6.50038	+	11.2590i	−0.258163	+	0.447152i
$635$		0			0
$636$			29.5153i			1.17036i
$637$	−44.4172	+	39.0351i	−1.75987	+	1.54663i
$638$	7.31474	+	7.31474i	0.289594	+	0.289594i
$639$	0.223275	+	0.833275i	0.00883264	+	0.0329639i
$640$		0			0
$641$	−25.1611	+	14.5268i	−0.993805	+	0.573774i	−0.906410	−	0.422400i	$-0.861188\pi$
$641$	−25.1611	+	14.5268i	−0.993805	+	0.573774i	−0.0873957	+	0.996174i	$0.527854\pi$
$642$	28.9203			1.14139
$643$	−28.4469	+	16.4238i	−1.12184	+	0.647693i	−0.941869	−	0.335979i	$-0.890933\pi$
$643$	−28.4469	+	16.4238i	−1.12184	+	0.647693i	−0.179968	+	0.983672i	$0.557600\pi$
$644$	13.4732	−	50.2827i	0.530919	−	1.98142i
$645$		0			0
$646$	15.9865	+	27.6894i	0.628980	+	1.08943i
$647$	24.0917	−	6.45536i	0.947144	−	0.253787i	0.247994	−	0.968762i	$-0.420229\pi$
$647$	24.0917	−	6.45536i	0.947144	−	0.253787i	0.699150	+	0.714975i	$0.253562\pi$
$648$	1.41421	−	2.44949i	0.0555556	−	0.0962250i
$649$	5.63830			0.221323
$650$		0			0
$651$	27.3845			1.07328
$652$	−25.3489	+	43.9055i	−0.992739	+	1.71947i
$653$	34.5295	−	9.25216i	1.35125	−	0.362065i	0.490651	−	0.871356i	$-0.336759\pi$
$653$	34.5295	−	9.25216i	1.35125	−	0.362065i	0.860594	+	0.509291i	$0.170092\pi$
$654$	−13.7000	−	23.7290i	−0.535711	−	0.927879i
$655$		0			0
$656$		0			0
$657$	−2.50643	+	1.44709i	−0.0977851	+	0.0564563i
$658$	−74.6801			−2.91133
$659$	−8.68241	+	5.01279i	−0.338219	+	0.195271i	−0.659484	−	0.751719i	$-0.729225\pi$
$659$	−8.68241	+	5.01279i	−0.338219	+	0.195271i	0.321265	+	0.946989i	$0.395892\pi$
$660$		0			0
$661$	1.89161	+	7.05959i	0.0735751	+	0.274586i	0.992906	−	0.118898i	$-0.0379362\pi$
$661$	1.89161	+	7.05959i	0.0735751	+	0.274586i	−0.919331	+	0.393484i	$0.871270\pi$
$662$	−42.4837	−	42.4837i	−1.65118	−	1.65118i
$663$	−2.63386	+	7.78584i	−0.102291	+	0.302377i
$664$		−	24.1023i		−	0.935352i
$665$		0			0
$666$	−6.35008	+	10.9987i	−0.246061	+	0.426190i
$667$	−7.20301	+	26.8820i	−0.278902	+	1.04088i
$668$		−	47.3113i		−	1.83053i
$669$	−5.74998	−	1.54070i	−0.222307	−	0.0595670i
$670$		0			0
$671$	0.992788	−	0.992788i	0.0383262	−	0.0383262i
$672$	−26.4320	−	7.08243i	−1.01964	−	0.273211i
$673$	8.59144	+	32.0637i	0.331176	+	1.23596i	0.907956	+	0.419065i	$0.137642\pi$
$673$	8.59144	+	32.0637i	0.331176	+	1.23596i	−0.576781	+	0.816899i	$0.695691\pi$
$674$	49.1378	−	13.1664i	1.89272	−	0.507152i
$675$		0			0
$676$	5.40382	−	41.7204i	0.207839	−	1.60463i
$677$	−29.7190	+	29.7190i	−1.14220	+	1.14220i	−0.154147	+	0.988048i	$0.549263\pi$
$677$	−29.7190	+	29.7190i	−1.14220	+	1.14220i	−0.988048	+	0.154147i	$0.950737\pi$
$678$	−3.35772	−	1.93858i	−0.128952	−	0.0744507i
$679$	−13.8764	−	8.01154i	−0.532527	−	0.307455i
$680$		0			0
$681$	−2.70647	−	2.70647i	−0.103712	−	0.103712i
$682$	3.49870	+	6.05992i	0.133972	+	0.232046i
$683$	10.0731	+	17.4471i	0.385436	+	0.667594i	0.991830	−	0.127570i	$-0.0407178\pi$
$683$	10.0731	+	17.4471i	0.385436	+	0.667594i	−0.606394	+	0.795165i	$0.707384\pi$
$684$	−14.0256	−	14.0256i	−0.536282	−	0.536282i
$685$		0			0
$686$	−90.1131	−	52.0268i	−3.44053	−	1.98639i
$687$	−6.68144	−	3.85753i	−0.254913	−	0.147174i
$688$		0			0
$689$	14.5756	+	29.4786i	0.555286	+	1.12305i
$690$		0			0
$691$	−0.351033	+	0.0940590i	−0.0133539	+	0.00357817i	−0.265490	−	0.964114i	$-0.585534\pi$
$691$	−0.351033	+	0.0940590i	−0.0133539	+	0.00357817i	0.252136	+	0.967692i	$0.418867\pi$
$692$	9.52699	+	35.5552i	0.362162	+	1.35161i
$693$	−2.52403	−	0.676312i	−0.0958800	−	0.0256910i
$694$	−17.1983	+	17.1983i	−0.652839	+	0.652839i
$695$		0			0
$696$	−22.8644	−	6.12651i	−0.866674	−	0.232225i
$697$			3.59144i			0.136036i
$698$	−20.0669	+	74.8907i	−0.759544	+	2.83466i
$699$	10.4403	−	18.0831i	0.394887	−	0.683964i
$700$		0			0
$701$			2.77509i			0.104814i	0.998626	+	0.0524069i	$0.0166893\pi$
$701$			2.77509i			0.104814i	−0.998626	+	0.0524069i	$0.983311\pi$
$702$	0.530989	−	8.23328i	0.0200409	−	0.310745i
$703$	24.0553	+	24.0553i	0.907262	+	0.907262i
$704$	−1.80973	−	6.75400i	−0.0682067	−	0.254551i
$705$		0			0
$706$	50.2729	−	29.0251i	1.89205	−	1.09237i
$707$	−88.5603			−3.33065
$708$	−29.2521	+	16.8887i	−1.09936	+	0.634716i
$709$	−2.88810	+	10.7785i	−0.108465	+	0.404797i	−0.998715	−	0.0506751i	$-0.983863\pi$
$709$	−2.88810	+	10.7785i	−0.108465	+	0.404797i	0.890250	+	0.455472i	$0.150529\pi$
$710$		0			0
$711$	2.09042	+	3.62072i	0.0783970	+	0.135788i
$712$	−46.9851	+	12.5896i	−1.76084	+	0.471816i
$713$	−9.41261	+	16.3031i	−0.352505	+	0.610557i
$714$	−25.2334			−0.944337
$715$		0			0
$716$	−70.0415			−2.61758
$717$	−5.37341	+	9.30702i	−0.200674	+	0.347577i
$718$	65.4384	−	17.5342i	2.44214	−	0.654369i
$719$	−9.45550	−	16.3774i	−0.352631	−	0.610774i	0.634079	−	0.773268i	$-0.281379\pi$
$719$	−9.45550	−	16.3774i	−0.352631	−	0.610774i	−0.986710	+	0.162494i	$0.948046\pi$
$720$		0			0
$721$	12.9921	−	48.4872i	0.483851	−	1.80576i
$722$	−36.7990	+	21.2459i	−1.36952	+	0.790691i
$723$	−25.4036			−0.944768
$724$	60.1521	−	34.7288i	2.23553	−	1.29069i
$725$		0			0
$726$	6.34184	+	23.6681i	0.235368	+	0.878405i
$727$	0.240056	+	0.240056i	0.00890317	+	0.00890317i	0.711544	−	0.702641i	$-0.247996\pi$
$727$	0.240056	+	0.240056i	0.00890317	+	0.00890317i	−0.702641	+	0.711544i	$0.747996\pi$
$728$	48.3739	−	9.67478i	1.79286	−	0.358571i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	6.48795	−	11.2375i	0.239965	−	0.415632i
$732$	−2.17694	+	8.12444i	−0.0804619	+	0.300288i
$733$			21.8432i			0.806795i	0.915025	+	0.403398i	$0.132171\pi$
$733$			21.8432i			0.806795i	−0.915025	+	0.403398i	$0.867829\pi$
$734$	−3.27158	−	0.876618i	−0.120756	−	0.0323566i
$735$		0			0
$736$	13.3017	−	13.3017i	0.490306	−	0.490306i
$737$	4.70394	+	1.26042i	0.173272	+	0.0464281i
$738$	−0.933051	−	3.48220i	−0.0343461	−	0.128181i
$739$	28.5692	−	7.65510i	1.05094	−	0.281597i	0.308298	−	0.951290i	$-0.400241\pi$
$739$	28.5692	−	7.65510i	1.05094	−	0.281597i	0.742639	+	0.669692i	$0.233574\pi$
$740$		0			0
$741$	−20.9345	−	7.08188i	−0.769047	−	0.260159i
$742$	−71.3884	+	71.3884i	−2.62075	+	2.62075i
$743$	−5.98408	−	3.45491i	−0.219535	−	0.126748i	0.386200	−	0.922415i	$-0.373787\pi$
$743$	−5.98408	−	3.45491i	−0.219535	−	0.126748i	−0.605735	+	0.795667i	$0.707121\pi$
$744$	−13.8666	−	8.00588i	−0.508374	−	0.293510i
$745$		0			0
$746$	43.0405	+	43.0405i	1.57582	+	1.57582i
$747$	−4.26073	−	7.37980i	−0.155892	−	0.270013i
$748$	−1.99246	−	3.45104i	−0.0728515	−	0.126183i
$749$	43.2312	+	43.2312i	1.57963	+	1.57963i
$750$		0			0
$751$	20.8236	+	12.0225i	0.759864	+	0.438708i	0.829247	−	0.558882i	$-0.188770\pi$
$751$	20.8236	+	12.0225i	0.759864	+	0.438708i	−0.0693827	+	0.997590i	$0.522103\pi$
$752$		0			0
$753$	−8.45670	+	8.45670i	−0.308179	+	0.308179i
$754$	−67.7064	+	13.5413i	−2.46572	+	0.493144i
$755$		0			0
$756$	15.1207	−	4.05158i	0.549935	−	0.147355i
$757$	1.04829	+	3.91228i	0.0381008	+	0.142194i	0.982356	−	0.187020i	$-0.0598829\pi$
$757$	1.04829	+	3.91228i	0.0381008	+	0.142194i	−0.944255	+	0.329214i	$0.893216\pi$
$758$	−58.6394	−	15.7124i	−2.12988	−	0.570699i
$759$	1.27020	−	1.27020i	0.0461052	−	0.0461052i
$760$		0			0
$761$	9.44327	+	2.53032i	0.342318	+	0.0917239i	0.425883	−	0.904778i	$-0.359964\pi$
$761$	9.44327	+	2.53032i	0.342318	+	0.0917239i	−0.0835641	+	0.996502i	$0.526630\pi$
$762$			9.18483i			0.332731i
$763$	14.9918	−	55.9502i	0.542740	−	2.02553i
$764$	−27.8725	+	48.2765i	−1.00839	+	1.74658i
$765$		0			0
$766$			40.4566i			1.46176i
$767$	−20.8756	+	31.3134i	−0.753774	+	1.13066i
$768$	11.3137	+	11.3137i	0.408248	+	0.408248i
$769$	−6.95307	−	25.9492i	−0.250734	−	0.935752i	−0.970414	−	0.241446i	$-0.922378\pi$
$769$	−6.95307	−	25.9492i	−0.250734	−	0.935752i	0.719680	−	0.694306i	$-0.244288\pi$
$770$		0			0
$771$	−6.91960	+	3.99503i	−0.249203	+	0.143878i
$772$	61.5361			2.21473
$773$	−9.36218	+	5.40526i	−0.336734	+	0.194414i	−0.658827	−	0.752295i	$-0.728947\pi$
$773$	−9.36218	+	5.40526i	−0.336734	+	0.194414i	0.322093	+	0.946708i	$0.395614\pi$
$774$	−3.37112	+	12.5812i	−0.121172	+	0.452221i
$775$		0			0
$776$	4.68436	+	8.11354i	0.168159	+	0.291259i
$777$	−25.9335	+	6.94887i	−0.930360	+	0.249289i
$778$	15.0974	−	26.1495i	0.541269	−	0.937506i
$779$	−9.65662			−0.345984
$780$		0			0
$781$	−0.465998			−0.0166747
$782$	8.67323	−	15.0225i	0.310154	−	0.537202i
$783$	−8.08380	+	2.16605i	−0.288891	+	0.0774082i
$784$		0			0
$785$		0			0
$786$	13.5107	−	50.4227i	0.481911	−	1.79852i
$787$	6.86284	−	3.96226i	0.244634	−	0.141239i	−0.372671	−	0.927964i	$-0.621558\pi$
$787$	6.86284	−	3.96226i	0.244634	−	0.141239i	0.617305	+	0.786724i	$0.288225\pi$
$788$	−13.2077			−0.470504
$789$	−10.1498	+	5.85998i	−0.361342	+	0.208621i
$790$		0			0
$791$	−2.12138	−	7.91710i	−0.0754276	−	0.281500i
$792$	1.08036	+	1.08036i	0.0383890	+	0.0383890i
$793$	1.83788	+	9.18939i	0.0652650	+	0.326325i
$794$			24.6568i			0.875036i
$795$		0			0
$796$	−13.0951	+	22.6814i	−0.464145	+	0.803922i
$797$	−6.08750	+	22.7189i	−0.215630	+	0.804743i	0.770313	+	0.637666i	$0.220100\pi$
$797$	−6.08750	+	22.7189i	−0.215630	+	0.804743i	−0.985944	+	0.167078i	$0.946567\pi$
$798$		−	67.8472i		−	2.40177i
$799$	−14.8558	−	3.98061i	−0.525562	−	0.140824i
$800$		0			0
$801$	−12.1606	+	12.1606i	−0.429675	+	0.429675i
$802$	−27.0866	−	7.25782i	−0.956460	−	0.256283i
$803$	−0.404633	−	1.51011i	−0.0142792	−	0.0532906i
$804$	−28.1799	+	7.55079i	−0.993829	+	0.266296i
$805$		0			0
$806$	−46.6087	−	3.00594i	−1.64172	−	0.105880i
$807$	22.7711	−	22.7711i	0.801582	−	0.801582i
$808$	44.8439	+	25.8906i	1.57760	+	0.910830i
$809$	19.5303	+	11.2758i	0.686649	+	0.396437i	0.802356	−	0.596846i	$-0.203580\pi$
$809$	19.5303	+	11.2758i	0.686649	+	0.396437i	−0.115706	+	0.993283i	$0.536913\pi$
$810$		0			0
$811$	0.704313	+	0.704313i	0.0247318	+	0.0247318i	0.719365	−	0.694633i	$-0.244433\pi$
$811$	0.704313	+	0.704313i	0.0247318	+	0.0247318i	−0.694633	+	0.719365i	$0.744433\pi$
$812$	−65.5044	−	113.457i	−2.29875	−	3.98156i
$813$	−12.0575	−	20.8842i	−0.422875	−	0.732440i
$814$	−4.85103	−	4.85103i	−0.170029	−	0.170029i
$815$		0			0
$816$		0			0
$817$	30.2151	+	17.4447i	1.05709	+	0.610313i
$818$	−49.0210	+	49.0210i	−1.71398	+	1.71398i
$819$	13.1011	−	11.5137i	0.457791	−	0.402320i
$820$		0			0
$821$	15.0071	−	4.02113i	0.523750	−	0.140338i	0.0127492	−	0.999919i	$-0.495942\pi$
$821$	15.0071	−	4.02113i	0.523750	−	0.140338i	0.511001	+	0.859580i	$0.329275\pi$
$822$	−6.28392	−	23.4519i	−0.219177	−	0.817979i
$823$	23.4232	+	6.27623i	0.816481	+	0.218775i	0.642807	−	0.766028i	$-0.277770\pi$
$823$	23.4232	+	6.27623i	0.816481	+	0.218775i	0.173674	+	0.984803i	$0.444436\pi$
$824$	−20.7540	+	20.7540i	−0.723000	+	0.723000i
$825$		0			0
$826$	−111.601	−	29.9033i	−3.88308	−	1.04047i
$827$		−	47.6927i		−	1.65844i	−0.558923	−	0.829219i	$-0.688785\pi$
$827$		−	47.6927i		−	1.65844i	0.558923	−	0.829219i	$-0.311215\pi$
$828$	−2.78522	+	10.3946i	−0.0967932	+	0.361237i
$829$	2.60409	−	4.51041i	0.0904436	−	0.156653i	−0.817254	−	0.576277i	$-0.804505\pi$
$829$	2.60409	−	4.51041i	0.0904436	−	0.156653i	0.907698	+	0.419624i	$0.137838\pi$
$830$		0			0
$831$		−	8.95231i		−	0.310552i
$832$	44.2101	+	14.9557i	1.53271	+	0.518497i
$833$	−26.4363	−	26.4363i	−0.915962	−	0.915962i
$834$	2.16217	+	8.06934i	0.0748700	+	0.279418i
$835$		0			0
$836$	9.27911	−	5.35730i	0.320925	−	0.185286i
$837$	−5.66101			−0.195673
$838$	−24.5355	+	14.1655i	−0.847563	+	0.489341i
$839$	5.20173	−	19.4131i	0.179584	−	0.670216i	−0.816142	−	0.577852i	$-0.803891\pi$
$839$	5.20173	−	19.4131i	0.179584	−	0.670216i	0.995725	−	0.0923637i	$-0.0294423\pi$
$840$		0			0
$841$	20.5198	+	35.5413i	0.707579	+	1.22556i
$842$	45.9728	−	12.3184i	1.58433	−	0.424519i
$843$	−6.20178	+	10.7418i	−0.213601	+	0.369967i
$844$	53.4775			1.84077
$845$		0			0
$846$	15.4381			0.530773
$847$	−25.8999	+	44.8599i	−0.889930	+	1.54140i
$848$		0			0
$849$	−0.732305	−	1.26839i	−0.0251326	−	0.0435310i
$850$		0			0
$851$	4.77693	−	17.8278i	0.163751	−	0.611127i
$852$	2.41765	−	1.39583i	0.0828272	−	0.0478203i
$853$	−19.8228			−0.678721			−0.339360	−	0.940656i	$-0.610211\pi$
$853$	−19.8228			−0.678721			−0.339360	+	0.940656i	$0.610211\pi$
$854$	−24.9159	+	14.3852i	−0.852604	+	0.492251i
$855$		0			0
$856$	−9.25214	−	34.5294i	−0.316232	−	1.18019i
$857$	20.4173	+	20.4173i	0.697440	+	0.697440i	0.963858	−	0.266417i	$-0.0858399\pi$
$857$	20.4173	+	20.4173i	0.697440	+	0.697440i	−0.266417	+	0.963858i	$0.585840\pi$
$858$	4.22169	+	1.42815i	0.144126	+	0.0487561i
$859$			37.4788i			1.27876i	0.768890	+	0.639381i	$0.220809\pi$
$859$			37.4788i			1.27876i	−0.768890	+	0.639381i	$0.779191\pi$
$860$		0			0
$861$	3.81055	−	6.60007i	0.129863	−	0.224930i
$862$	10.9676	−	40.9315i	0.373557	−	1.39413i
$863$		−	37.3841i		−	1.27257i	−0.771455	−	0.636284i	$-0.780471\pi$
$863$		−	37.3841i		−	1.27257i	0.771455	−	0.636284i	$-0.219529\pi$
$864$	5.46410	+	1.46410i	0.185893	+	0.0498097i
$865$		0			0
$866$	−7.71169	+	7.71169i	−0.262054	+	0.262054i
$867$	11.4012	+	3.05493i	0.387203	+	0.103751i
$868$	−22.9361	−	85.5986i	−0.778501	−	2.90541i
$869$	−2.18146	+	0.584521i	−0.0740011	+	0.0198285i
$870$		0			0
$871$	−24.4161	+	21.4576i	−0.827309	+	0.727062i
$872$	−23.9484	+	23.9484i	−0.810996	+	0.810996i
$873$	2.86857	+	1.65617i	0.0970864	+	0.0560529i
$874$	40.3922	+	23.3205i	1.36629	+	0.788826i
$875$		0			0
$876$	6.62259	+	6.62259i	0.223756	+	0.223756i
$877$	−2.19892	−	3.80864i	−0.0742523	−	0.128609i	0.826509	−	0.562924i	$-0.190324\pi$
$877$	−2.19892	−	3.80864i	−0.0742523	−	0.128609i	−0.900761	+	0.434315i	$0.856990\pi$
$878$	−14.2215	−	24.6324i	−0.479953	−	0.831303i
$879$	11.4680	+	11.4680i	0.386806	+	0.386806i
$880$		0			0
$881$	−22.2900	−	12.8691i	−0.750969	−	0.433572i	0.0750747	−	0.997178i	$-0.476080\pi$
$881$	−22.2900	−	12.8691i	−0.750969	−	0.433572i	−0.826044	+	0.563606i	$0.809414\pi$
$882$	32.5002	+	18.7640i	1.09434	+	0.631817i
$883$	34.0469	−	34.0469i	1.14577	−	1.14577i	0.158392	−	0.987376i	$-0.449369\pi$
$883$	34.0469	−	34.0469i	1.14577	−	1.14577i	0.987376	−	0.158392i	$-0.0506308\pi$
$884$	26.5430	+	1.71184i	0.892738	+	0.0575754i
$885$		0			0
$886$	71.5731	−	19.1779i	2.40454	−	0.644296i
$887$	3.17404	+	11.8457i	0.106574	+	0.397739i	0.998519	−	0.0544047i	$-0.0173261\pi$
$887$	3.17404	+	11.8457i	0.106574	+	0.397739i	−0.891945	+	0.452144i	$0.850659\pi$
$888$	15.1634	+	4.06301i	0.508849	+	0.136346i
$889$	−13.7298	+	13.7298i	−0.460483	+	0.460483i
$890$		0			0
$891$	0.521775	+	0.139809i	0.0174801	+	0.00468379i
$892$			19.2637i			0.644998i
$893$	10.7030	−	39.9442i	0.358163	−	1.33668i
$894$	0.228034	−	0.394966i	0.00762659	−	0.0132096i
$895$		0			0
$896$			88.5531i			2.95835i
$897$	2.35142	+	11.7571i	0.0785118	+	0.392559i
$898$	9.03306	+	9.03306i	0.301437	+	0.301437i
$899$	12.2620	+	45.7625i	0.408961	+	1.52626i
$900$		0			0
$901$	−18.0062	+	10.3959i	−0.599873	+	0.346337i
$902$	1.94737			0.0648404
$903$	−23.8461	+	13.7675i	−0.793548	+	0.458155i
$904$	−1.24037	+	4.62914i	−0.0412542	+	0.153963i
$905$		0			0
$906$	−5.44634	−	9.43334i	−0.180943	−	0.313402i
$907$	44.4756	−	11.9172i	1.47679	−	0.395704i	0.571535	−	0.820578i	$-0.306348\pi$
$907$	44.4756	−	11.9172i	1.47679	−	0.395704i	0.905253	+	0.424873i	$0.139681\pi$
$908$	−6.19306	+	10.7267i	−0.205524	+	0.355978i
$909$	18.3075			0.607220
$910$		0			0
$911$	18.1814			0.602375			0.301188	−	0.953565i	$-0.402617\pi$
$911$	18.1814			0.602375			0.301188	+	0.953565i	$0.402617\pi$
$912$		0			0
$913$	4.44629	−	1.19138i	0.147151	−	0.0394289i
$914$	−19.5200	−	33.8097i	−0.645665	−	1.11832i
$915$		0			0
$916$	−6.46180	+	24.1158i	−0.213504	+	0.796807i
$917$	95.5700	−	55.1773i	3.15600	−	1.82212i
$918$	5.21633			0.172164
$919$	−23.2033	+	13.3965i	−0.765407	+	0.441908i	−0.831234	−	0.555923i	$-0.812365\pi$
$919$	−23.2033	+	13.3965i	−0.765407	+	0.441908i	0.0658265	+	0.997831i	$0.479032\pi$
$920$		0			0
$921$	0.486212	+	1.81457i	0.0160212	+	0.0597921i
$922$	−6.07502	−	6.07502i	−0.200070	−	0.200070i
$923$	1.72534	−	2.58801i	0.0567902	−	0.0851854i
$924$			8.45607i			0.278184i
$925$		0			0
$926$	−0.476894	+	0.826005i	−0.0156717	+	0.0271442i
$927$	−2.68577	+	10.0234i	−0.0882121	+	0.329212i
$928$		−	47.3420i		−	1.55408i
$929$	−20.5413	−	5.50402i	−0.673937	−	0.180581i	−0.0944095	−	0.995533i	$-0.530096\pi$
$929$	−20.5413	−	5.50402i	−0.673937	−	0.180581i	−0.579528	+	0.814953i	$0.696763\pi$
$930$		0			0
$931$	71.0814	−	71.0814i	2.32960	−	2.32960i
$932$	−65.2683	−	17.4886i	−2.13794	−	0.572858i
$933$	0.323070	+	1.20571i	0.0105768	+	0.0394733i
$934$	−14.1163	+	3.78246i	−0.461900	+	0.123766i
$935$		0			0
$936$	−10.0000	+	2.00000i	−0.326860	+	0.0653720i
$937$	−21.6443	+	21.6443i	−0.707088	+	0.707088i	−0.965922	−	0.258834i	$-0.916662\pi$
$937$	−21.6443	+	21.6443i	−0.707088	+	0.707088i	0.258834	+	0.965922i	$0.416662\pi$
$938$	−86.4217	−	49.8956i	−2.82177	−	1.62915i
$939$	−5.57233	−	3.21719i	−0.181846	−	0.104989i
$940$		0			0
$941$	32.2254	+	32.2254i	1.05052	+	1.05052i	0.998654	+	0.0518629i	$0.0165159\pi$
$941$	32.2254	+	32.2254i	1.05052	+	1.05052i	0.0518629	+	0.998654i	$0.483484\pi$
$942$	−7.21697	−	12.5002i	−0.235142	−	0.407277i
$943$	2.61953	+	4.53715i	0.0853035	+	0.147750i
$944$		0			0
$945$		0			0
$946$	−6.09324	−	3.51793i	−0.198108	−	0.114378i
$947$	12.1012	+	6.98664i	0.393237	+	0.227035i	0.683562	−	0.729893i	$-0.260430\pi$
$947$	12.1012	+	6.98664i	0.393237	+	0.227035i	−0.290325	+	0.956928i	$0.593763\pi$
$948$	9.56681	−	9.56681i	0.310715	−	0.310715i
$949$	9.88481	+	3.34391i	0.320875	+	0.108548i
$950$		0			0
$951$	5.48795	−	1.47049i	0.177959	−	0.0476839i
$952$	8.07262	+	30.1274i	0.261635	+	0.976435i
$953$	12.5722	+	3.36872i	0.407254	+	0.109123i	0.456630	−	0.889657i	$-0.349056\pi$
$953$	12.5722	+	3.36872i	0.407254	+	0.109123i	−0.0493755	+	0.998780i	$0.515723\pi$
$954$	14.7576	−	14.7576i	0.477796	−	0.477796i
$955$		0			0
$956$	33.5924	+	9.00107i	1.08646	+	0.291115i
$957$		−	4.52076i		−	0.146135i
$958$	−1.50825	+	5.62888i	−0.0487294	+	0.181861i
$959$	25.6633	−	44.4502i	0.828712	−	1.43537i
$960$		0			0
$961$			1.04707i			0.0337764i
$962$	44.9019	−	8.98038i	1.44769	−	0.289539i
$963$	−8.93688	−	8.93688i	−0.287987	−	0.287987i
$964$	21.2769	+	79.4065i	0.685283	+	2.55751i
$965$		0			0
$966$	−31.8779	+	18.4047i	−1.02566	+	0.592163i
$967$	31.5942			1.01600			0.508000	−	0.861357i	$-0.330385\pi$
$967$	31.5942			1.01600			0.508000	+	0.861357i	$0.330385\pi$
$968$	26.2296	−	15.1437i	0.843052	−	0.486737i
$969$	3.61640	−	13.4966i	0.116176	−	0.433573i
$970$		0			0
$971$	−6.20613	−	10.7493i	−0.199164	−	0.344963i	0.749093	−	0.662464i	$-0.230489\pi$
$971$	−6.20613	−	10.7493i	−0.199164	−	0.344963i	−0.948258	+	0.317502i	$0.897156\pi$
$972$	−3.12580	+	0.837556i	−0.100260	+	0.0268646i
$973$	−8.83025	+	15.2944i	−0.283085	+	0.490317i
$974$	20.5355			0.657999
$975$		0			0
$976$		0			0
$977$	−18.6557	+	32.3127i	−0.596850	+	1.03377i	0.396433	+	0.918064i	$0.370248\pi$
$977$	−18.6557	+	32.3127i	−0.596850	+	1.03377i	−0.993283	+	0.115711i	$0.963085\pi$
$978$	34.6272	−	9.27833i	1.10726	−	0.296688i
$979$	−4.64495	−	8.04529i	−0.148453	−	0.257129i
$980$		0			0
$981$	−3.09915	+	11.5662i	−0.0989483	+	0.369280i
$982$	−9.31950	+	5.38062i	−0.297397	+	0.171702i
$983$	−8.10446			−0.258492			−0.129246	−	0.991613i	$-0.541256\pi$
$983$	−8.10446			−0.258492			−0.129246	+	0.991613i	$0.541256\pi$
$984$	−3.85907	+	2.22803i	−0.123023	+	0.0710271i
$985$		0			0
$986$	−11.2988	−	42.1677i	−0.359828	−	1.34289i
$987$	23.0774	+	23.0774i	0.734563	+	0.734563i
$988$	−4.60277	+	71.3685i	−0.146434	+	2.27053i
$989$		−	18.9287i		−	0.601898i
$990$		0			0
$991$	8.48782	−	14.7013i	0.269625	−	0.467003i	−0.699140	−	0.714984i	$-0.746434\pi$
$991$	8.48782	−	14.7013i	0.269625	−	0.467003i	0.968765	+	0.247981i	$0.0797671\pi$
$992$	8.28830	−	30.9324i	0.263154	−	0.982103i
$993$			26.2564i			0.833221i
$994$	9.22363	+	2.47147i	0.292556	+	0.0783901i
$995$		0			0
$996$	−19.4992	+	19.4992i	−0.617856	+	0.617856i
$997$	−17.7104	−	4.74550i	−0.560895	−	0.150291i	−0.0327775	−	0.999463i	$-0.510435\pi$
$997$	−17.7104	−	4.74550i	−0.560895	−	0.150291i	−0.528117	+	0.849171i	$0.677102\pi$
$998$	−1.14108	−	4.25856i	−0.0361202	−	0.134802i
$999$	5.36106	−	1.43649i	0.169616	−	0.0454486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bl.e.943.1	yes	16
5.2	odd	4		975.2.bu.f.7.1	yes	16
5.3	odd	4		975.2.bu.f.7.4	yes	16
5.4	even	2	inner	975.2.bl.e.943.4	yes	16
13.2	odd	12		975.2.bu.f.418.1	yes	16
65.2	even	12	inner	975.2.bl.e.457.1	✓	16
65.28	even	12	inner	975.2.bl.e.457.4	yes	16
65.54	odd	12		975.2.bu.f.418.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.bl.e.457.1	✓	16	65.2	even	12	inner
975.2.bl.e.457.4	yes	16	65.28	even	12	inner
975.2.bl.e.943.1	yes	16	1.1	even	1	trivial
975.2.bl.e.943.4	yes	16	5.4	even	2	inner
975.2.bu.f.7.1	yes	16	5.2	odd	4
975.2.bu.f.7.4	yes	16	5.3	odd	4
975.2.bu.f.418.1	yes	16	13.2	odd	12
975.2.bu.f.418.4	yes	16	65.54	odd	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14412 + 1.98168i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.61803 - 2.80252i) q^{4} +(-0.592242 + 2.21028i) q^{6} +(-4.18930 + 2.41869i) q^{7} +2.82843 q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.14412 + 1.98168i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.61803 - 2.80252i) q^{4} +(-0.592242 + 2.21028i) q^{6} +(-4.18930 + 2.41869i) q^{7} +2.82843 q^{8} +(0.866025 - 0.500000i) q^{9} +(0.139809 + 0.521775i) q^{11} +(-2.28825 - 2.28825i) q^{12} +(-3.41542 - 1.15539i) q^{13} -11.0691i q^{14} +(0.590009 - 2.20194i) q^{17} +2.28825i q^{18} +(5.92055 + 1.58641i) q^{19} +(-3.42055 + 3.42055i) q^{21} +(-1.19395 - 0.319918i) q^{22} +(-0.860681 - 3.21210i) q^{23} +(2.73205 - 0.732051i) q^{24} +(6.19728 - 5.44634i) q^{26} +(0.707107 - 0.707107i) q^{27} +(13.5569 + 7.82706i) q^{28} +(-7.24774 - 4.18448i) q^{29} +(-4.00294 - 4.00294i) q^{31} +(2.82843 + 4.89898i) q^{32} +(0.270091 + 0.467811i) q^{33} +(3.68850 + 3.68850i) q^{34} +(-2.80252 - 1.61803i) q^{36} +(4.80659 + 2.77509i) q^{37} +(-9.91759 + 9.91759i) q^{38} +(-3.59808 - 0.232051i) q^{39} +(-1.52178 + 0.407758i) q^{41} +(-2.86490 - 10.6920i) q^{42} +(5.49818 + 1.47323i) q^{43} +(1.23607 - 1.23607i) q^{44} +(7.35008 + 1.96945i) q^{46} -6.74670i q^{47} +(8.20017 - 14.2031i) q^{49} -2.27962i q^{51} +(2.28825 + 11.4412i) q^{52} +(-6.44932 - 6.44932i) q^{53} +(0.592242 + 2.21028i) q^{54} +(-11.8491 + 6.84110i) q^{56} +6.12941 q^{57} +(16.5846 - 9.57513i) q^{58} +(2.70150 - 10.0821i) q^{59} +(-1.29958 - 2.25093i) q^{61} +(12.5124 - 3.35269i) q^{62} +(-2.41869 + 4.18930i) q^{63} -12.9443 q^{64} -1.23607 q^{66} +(4.50763 - 7.80745i) q^{67} +(-7.12564 + 1.90931i) q^{68} +(-1.66271 - 2.87989i) q^{69} +(-0.223275 + 0.833275i) q^{71} +(2.44949 - 1.41421i) q^{72} -2.89418 q^{73} +(-10.9987 + 6.35008i) q^{74} +(-5.13372 - 19.1593i) q^{76} +(-1.84772 - 1.84772i) q^{77} +(4.57649 - 6.86474i) q^{78} +4.18085i q^{79} +(0.500000 - 0.866025i) q^{81} +(0.933051 - 3.48220i) q^{82} -8.52146i q^{83} +(15.1207 + 4.05158i) q^{84} +(-9.21007 + 9.21007i) q^{86} +(-8.08380 - 2.16605i) q^{87} +(0.395440 + 1.47580i) q^{88} +(-16.6117 + 4.45110i) q^{89} +(17.1028 - 3.42055i) q^{91} +(-7.60937 + 7.60937i) q^{92} +(-4.90258 - 2.83051i) q^{93} +(13.3698 + 7.71905i) q^{94} +(4.00000 + 4.00000i) q^{96} +(1.65617 + 2.86857i) q^{97} +(18.7640 + 32.5002i) q^{98} +(0.381966 + 0.381966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 4 q^{6}+O(q^{10}) \) 16 * q - 8 * q^4 + 4 * q^6	\( 16 q - 8 q^{4} + 4 q^{6} - 12 q^{11} + 32 q^{19} + 8 q^{21} + 16 q^{24} - 4 q^{26} - 24 q^{29} - 24 q^{31} + 24 q^{34} - 16 q^{39} - 28 q^{41} - 16 q^{44} + 72 q^{46} + 40 q^{49} - 4 q^{54} - 48 q^{56} + 80 q^{59} - 16 q^{61} - 64 q^{64} + 16 q^{66} + 4 q^{69} - 44 q^{71} - 48 q^{74} + 8 q^{81} + 88 q^{84} + 32 q^{86} - 32 q^{89} - 40 q^{91} + 96 q^{94} + 64 q^{96} + 24 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 4 * q^6 - 12 * q^11 + 32 * q^19 + 8 * q^21 + 16 * q^24 - 4 * q^26 - 24 * q^29 - 24 * q^31 + 24 * q^34 - 16 * q^39 - 28 * q^41 - 16 * q^44 + 72 * q^46 + 40 * q^49 - 4 * q^54 - 48 * q^56 + 80 * q^59 - 16 * q^61 - 64 * q^64 + 16 * q^66 + 4 * q^69 - 44 * q^71 - 48 * q^74 + 8 * q^81 + 88 * q^84 + 32 * q^86 - 32 * q^89 - 40 * q^91 + 96 * q^94 + 64 * q^96 + 24 * q^99

Introduction

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