LMFDB - Embedded newform 950.2.bb.d.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.d.857.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(0.134247 - 1.53445i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.17995 + 0.990096i) q^{6} +(-1.26063 - 4.70472i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.617895 + 0.108952i) q^{9} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(0.134247 - 1.53445i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.17995 + 0.990096i) q^{6} +(-1.26063 - 4.70472i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.617895 + 0.108952i) q^{9} +(1.46814 + 2.54289i) q^{11} +(-1.48783 + 0.398663i) q^{12} +(5.53868 - 0.484572i) q^{13} +(4.57694 + 1.66587i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.40345 + 1.68292i) q^{17} +(-0.443658 + 0.443658i) q^{18} +(-4.04566 - 1.62255i) q^{19} +(-7.38841 + 1.30278i) q^{21} +(-2.92511 - 0.255914i) q^{22} +(1.05946 + 0.494036i) q^{23} +(0.526819 - 1.44742i) q^{24} +(-2.77992 + 4.81496i) q^{26} +(1.44612 - 5.39700i) q^{27} +(-3.98983 + 2.79371i) q^{28} +(0.884224 - 5.01468i) q^{29} +(-1.09619 - 0.632887i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(4.09905 - 1.91142i) q^{33} +(-2.75713 + 1.00351i) q^{34} +(-0.108952 - 0.617895i) q^{36} +(-3.37366 - 3.37366i) q^{37} +(3.64961 - 2.38335i) q^{38} -8.56391i q^{39} +(0.867993 + 1.03443i) q^{41} +(3.17065 - 6.79947i) q^{42} +(-4.45973 - 9.56393i) q^{43} +(1.88741 - 2.24932i) q^{44} +(-1.01237 + 0.584495i) q^{46} +(-4.23099 - 6.04248i) q^{47} +(0.883489 + 1.26175i) q^{48} +(-14.4830 + 8.36178i) q^{49} +(2.90502 - 3.46206i) q^{51} +(-2.34969 - 5.03893i) q^{52} +(-1.65042 + 3.53934i) q^{53} +(3.59150 + 4.28018i) q^{54} -4.87068i q^{56} +(-3.03285 + 5.99005i) q^{57} +(3.60062 + 3.60062i) q^{58} +(2.43390 + 13.8033i) q^{59} +(9.38589 - 3.41618i) q^{61} +(1.14718 - 0.534940i) q^{62} +(-0.266348 - 3.04437i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.785376 + 4.45409i) q^{66} +(-7.39421 + 5.17748i) q^{67} +(0.759394 - 2.83410i) q^{68} +(0.900307 - 1.55938i) q^{69} +(3.83539 - 10.5377i) q^{71} +(0.568642 + 0.265162i) q^{72} +(6.81865 + 0.596555i) q^{73} +(4.69859 - 0.828488i) q^{74} +(-0.141002 + 4.35662i) q^{76} +(10.1128 - 10.1128i) q^{77} +(7.01514 + 4.91206i) q^{78} +(-7.47094 + 6.26886i) q^{79} +(-6.31854 - 2.29976i) q^{81} +(-1.34522 + 0.117691i) q^{82} +(-10.6273 + 2.84759i) q^{83} +(3.75119 + 6.49726i) q^{84} +(10.3923 + 1.83245i) q^{86} +(-7.57610 - 2.03001i) q^{87} +(0.759966 + 2.83623i) q^{88} +(-9.08115 - 7.61999i) q^{89} +(-9.26198 - 25.4471i) q^{91} +(0.101884 - 1.16454i) q^{92} +(-1.11830 + 1.59709i) q^{93} +7.37650 q^{94} -1.54032 q^{96} +(2.22997 - 3.18473i) q^{97} +(1.45755 - 16.6599i) q^{98} +(0.630105 + 1.73120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{6}+O(q^{10}) $ 96 * q - 12 * q^6	$ 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) $ 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$	0.134247	−	1.53445i	0.0775078	−	0.885918i	−0.853542	−	0.521025i	$-0.825550\pi$
$3$	0.134247	−	1.53445i	0.0775078	−	0.885918i	0.931049	−	0.364893i	$-0.118894\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	1.17995	+	0.990096i	0.481713	+	0.404205i
$7$	−1.26063	−	4.70472i	−0.476472	−	1.77822i	−0.615727	−	0.787960i	$-0.711137\pi$
$7$	−1.26063	−	4.70472i	−0.476472	−	1.77822i	0.139255	−	0.990257i	$-0.455529\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.617895	+	0.108952i	0.205965	+	0.0363172i
$10$		0			0
$11$	1.46814	+	2.54289i	0.442661	+	0.766712i	0.997886	−	0.0649886i	$-0.0207011\pi$
$11$	1.46814	+	2.54289i	0.442661	+	0.766712i	−0.555225	+	0.831700i	$0.687368\pi$
$12$	−1.48783	+	0.398663i	−0.429500	+	0.115084i
$13$	5.53868	−	0.484572i	1.53615	−	0.134396i	0.712575	−	0.701596i	$-0.247529\pi$
$13$	5.53868	−	0.484572i	1.53615	−	0.134396i	0.823580	+	0.567200i	$0.191973\pi$
$14$	4.57694	+	1.66587i	1.22324	+	0.445223i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	2.40345	+	1.68292i	0.582923	+	0.408167i	0.827502	−	0.561462i	$-0.189761\pi$
$17$	2.40345	+	1.68292i	0.582923	+	0.408167i	−0.244579	+	0.969629i	$0.578650\pi$
$18$	−0.443658	+	0.443658i	−0.104571	+	0.104571i
$19$	−4.04566	−	1.62255i	−0.928137	−	0.372238i
$19$	−4.04566	−	1.62255i	−0.928137	−	0.372238i
$20$		0			0
$21$	−7.38841	+	1.30278i	−1.61228	+	0.284289i
$22$	−2.92511	−	0.255914i	−0.623635	−	0.0545610i
$23$	1.05946	+	0.494036i	0.220914	+	0.103014i	0.529925	−	0.848045i	$-0.322220\pi$
$23$	1.05946	+	0.494036i	0.220914	+	0.103014i	−0.309011	+	0.951058i	$0.599998\pi$
$24$	0.526819	−	1.44742i	0.107536	−	0.295454i
$25$		0			0
$26$	−2.77992	+	4.81496i	−0.545187	+	0.944292i
$27$	1.44612	−	5.39700i	0.278306	−	1.03865i
$28$	−3.98983	+	2.79371i	−0.754007	+	0.527961i
$29$	0.884224	−	5.01468i	0.164196	−	0.931203i	−0.785693	−	0.618617i	$-0.787693\pi$
$29$	0.884224	−	5.01468i	0.164196	−	0.931203i	0.949889	−	0.312587i	$-0.101195\pi$
$30$		0			0
$31$	−1.09619	−	0.632887i	−0.196882	−	0.113670i	0.398318	−	0.917247i	$-0.369594\pi$
$31$	−1.09619	−	0.632887i	−0.196882	−	0.113670i	−0.595200	+	0.803577i	$0.702927\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$	4.09905	−	1.91142i	0.713553	−	0.332735i
$34$	−2.75713	+	1.00351i	−0.472844	+	0.172101i
$35$		0			0
$36$	−0.108952	−	0.617895i	−0.0181586	−	0.102983i
$37$	−3.37366	−	3.37366i	−0.554626	−	0.554626i	0.373147	−	0.927772i	$-0.378279\pi$
$37$	−3.37366	−	3.37366i	−0.554626	−	0.554626i	−0.927772	+	0.373147i	$0.878279\pi$
$38$	3.64961	−	2.38335i	0.592045	−	0.386631i
$39$		−	8.56391i		−	1.37132i
$40$		0			0
$41$	0.867993	+	1.03443i	0.135558	+	0.161551i	0.829553	−	0.558428i	$-0.188595\pi$
$41$	0.867993	+	1.03443i	0.135558	+	0.161551i	−0.693995	+	0.719980i	$0.744151\pi$
$42$	3.17065	−	6.79947i	0.489241	−	1.04918i
$43$	−4.45973	−	9.56393i	−0.680103	−	1.45849i	−0.878195	−	0.478303i	$-0.841252\pi$
$43$	−4.45973	−	9.56393i	−0.680103	−	1.45849i	0.198092	−	0.980183i	$-0.436526\pi$
$44$	1.88741	−	2.24932i	0.284537	−	0.339098i
$45$		0			0
$46$	−1.01237	+	0.584495i	−0.149267	+	0.0861791i
$47$	−4.23099	−	6.04248i	−0.617153	−	0.881386i	0.381931	−	0.924191i	$-0.375259\pi$
$47$	−4.23099	−	6.04248i	−0.617153	−	0.881386i	−0.999083	+	0.0428054i	$0.986370\pi$
$48$	0.883489	+	1.26175i	0.127521	+	0.182118i
$49$	−14.4830	+	8.36178i	−2.06900	+	1.19454i
$50$		0			0
$51$	2.90502	−	3.46206i	0.406784	−	0.484786i
$52$	−2.34969	−	5.03893i	−0.325843	−	0.698773i
$53$	−1.65042	+	3.53934i	−0.226703	+	0.486166i	−0.986452	−	0.164051i	$-0.947544\pi$
$53$	−1.65042	+	3.53934i	−0.226703	+	0.486166i	0.759749	+	0.650216i	$0.225322\pi$
$54$	3.59150	+	4.28018i	0.488741	+	0.582459i
$55$		0			0
$56$		−	4.87068i		−	0.650872i
$57$	−3.03285	+	5.99005i	−0.401710	+	0.793402i
$58$	3.60062	+	3.60062i	0.472784	+	0.472784i
$59$	2.43390	+	13.8033i	0.316867	+	1.79704i	0.561554	+	0.827440i	$0.310204\pi$
$59$	2.43390	+	13.8033i	0.316867	+	1.79704i	−0.244687	+	0.969602i	$0.578685\pi$
$60$		0			0
$61$	9.38589	−	3.41618i	1.20174	−	0.437397i	0.337909	−	0.941179i	$-0.390281\pi$
$61$	9.38589	−	3.41618i	1.20174	−	0.437397i	0.863831	+	0.503781i	$0.168058\pi$
$62$	1.14718	−	0.534940i	0.145692	−	0.0679374i
$63$	−0.266348	−	3.04437i	−0.0335567	−	0.383555i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−0.785376	+	4.45409i	−0.0966731	+	0.548261i
$67$	−7.39421	+	5.17748i	−0.903347	+	0.632530i	−0.930178	−	0.367110i	$-0.880347\pi$
$67$	−7.39421	+	5.17748i	−0.903347	+	0.632530i	0.0268310	+	0.999640i	$0.491458\pi$
$68$	0.759394	−	2.83410i	0.0920901	−	0.343685i
$69$	0.900307	−	1.55938i	0.108384	−	0.187727i
$70$		0			0
$71$	3.83539	−	10.5377i	0.455178	−	1.25059i	−0.473859	−	0.880601i	$-0.657139\pi$
$71$	3.83539	−	10.5377i	0.455178	−	1.25059i	0.929036	−	0.369989i	$-0.120639\pi$
$72$	0.568642	+	0.265162i	0.0670151	+	0.0312497i
$73$	6.81865	+	0.596555i	0.798063	+	0.0698215i	0.478890	−	0.877875i	$-0.341039\pi$
$73$	6.81865	+	0.596555i	0.798063	+	0.0698215i	0.319173	+	0.947696i	$0.396595\pi$
$74$	4.69859	−	0.828488i	0.546200	−	0.0963098i
$75$		0			0
$76$	−0.141002	+	4.35662i	−0.0161740	+	0.499738i
$77$	10.1128	−	10.1128i	1.15246	−	1.15246i
$78$	7.01514	+	4.91206i	0.794309	+	0.556181i
$79$	−7.47094	+	6.26886i	−0.840547	+	0.705302i	−0.957687	−	0.287813i	$-0.907072\pi$
$79$	−7.47094	+	6.26886i	−0.840547	+	0.705302i	0.117140	+	0.993115i	$0.462627\pi$
$80$		0			0
$81$	−6.31854	−	2.29976i	−0.702060	−	0.255529i
$82$	−1.34522	+	0.117691i	−0.148555	+	0.0129968i
$83$	−10.6273	+	2.84759i	−1.16650	+	0.312564i	−0.789560	−	0.613673i	$-0.789691\pi$
$83$	−10.6273	+	2.84759i	−1.16650	+	0.312564i	−0.376943	+	0.926237i	$0.623025\pi$
$84$	3.75119	+	6.49726i	0.409289	+	0.708909i
$85$		0			0
$86$	10.3923	+	1.83245i	1.12063	+	0.197598i
$87$	−7.57610	−	2.03001i	−0.812243	−	0.217640i
$88$	0.759966	+	2.83623i	0.0810126	+	0.302343i
$89$	−9.08115	−	7.61999i	−0.962600	−	0.807717i	0.0187741	−	0.999824i	$-0.494024\pi$
$89$	−9.08115	−	7.61999i	−0.962600	−	0.807717i	−0.981374	+	0.192106i	$0.938468\pi$
$90$		0			0
$91$	−9.26198	−	25.4471i	−0.970919	−	2.66758i
$92$	0.101884	−	1.16454i	0.0106222	−	0.121412i
$93$	−1.11830	+	1.59709i	−0.115962	+	0.165611i
$94$	7.37650			0.760828
$95$		0			0
$96$	−1.54032			−0.157208
$97$	2.22997	−	3.18473i	0.226419	−	0.323360i	−0.689828	−	0.723973i	$-0.742314\pi$
$97$	2.22997	−	3.18473i	0.226419	−	0.323360i	0.916247	+	0.400613i	$0.131203\pi$
$98$	1.45755	−	16.6599i	0.147235	−	1.68291i
$99$	0.630105	+	1.73120i	0.0633279	+	0.173992i
$100$		0			0
$101$	13.9185	+	11.6790i	1.38494	+	1.16210i	0.967343	+	0.253470i	$0.0815720\pi$
$101$	13.9185	+	11.6790i	1.38494	+	1.16210i	0.417597	+	0.908632i	$0.362872\pi$
$102$	1.16971	+	4.36541i	0.115818	+	0.432240i
$103$	6.07381	+	1.62747i	0.598471	+	0.160360i	0.545322	−	0.838227i	$-0.316408\pi$
$103$	6.07381	+	1.62747i	0.598471	+	0.160360i	0.0531489	+	0.998587i	$0.483074\pi$
$104$	5.47537	+	0.965456i	0.536905	+	0.0946708i
$105$		0			0
$106$	−1.95261	−	3.38203i	−0.189655	−	0.328492i
$107$	−1.90854	+	0.511392i	−0.184506	+	0.0494381i	−0.349889	−	0.936791i	$-0.613781\pi$
$107$	−1.90854	+	0.511392i	−0.184506	+	0.0494381i	0.165383	+	0.986229i	$0.447114\pi$
$108$	−5.56612	+	0.486973i	−0.535600	+	0.0468590i
$109$	3.90560	+	1.42152i	0.374089	+	0.136157i	0.522221	−	0.852810i	$-0.325104\pi$
$109$	3.90560	+	1.42152i	0.374089	+	0.136157i	−0.148132	+	0.988968i	$0.547326\pi$
$110$		0			0
$111$	−5.62963	+	4.72382i	−0.534341	+	0.448365i
$112$	3.98983	+	2.79371i	0.377003	+	0.263981i
$113$	7.01602	−	7.01602i	0.660011	−	0.660011i	−0.295371	−	0.955383i	$-0.595443\pi$
$113$	7.01602	−	7.01602i	0.660011	−	0.660011i	0.955383	+	0.295371i	$0.0954434\pi$
$114$	−3.16719	−	5.92012i	−0.296635	−	0.554470i
$115$		0			0
$116$	−5.01468	+	0.884224i	−0.465602	+	0.0820981i
$117$	3.47512	+	0.304034i	0.321275	+	0.0281079i
$118$	−12.7031	−	5.92354i	−1.16941	−	0.545306i
$119$	4.88779	−	13.4291i	0.448063	−	1.23104i
$120$		0			0
$121$	1.18912	−	2.05962i	0.108102	−	0.187238i
$122$	−2.58515	+	9.64791i	−0.234048	+	0.873481i
$123$	1.70382	−	1.19303i	0.153628	−	0.107571i
$124$	−0.219799	+	1.24654i	−0.0197386	+	0.111943i
$125$		0			0
$126$	2.64657	+	1.52800i	0.235775	+	0.136125i
$127$	0.527359	+	6.02774i	0.0467955	+	0.534875i	0.983023	+	0.183481i	$0.0587367\pi$
$127$	0.527359	+	6.02774i	0.0467955	+	0.534875i	−0.936228	+	0.351394i	$0.885708\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$	−15.2741	+	5.55933i	−1.34481	+	0.489471i
$130$		0			0
$131$	0.412856	+	2.34142i	0.0360714	+	0.204571i	0.997517	−	0.0704236i	$-0.0224351\pi$
$131$	0.412856	+	2.34142i	0.0360714	+	0.204571i	−0.961446	+	0.274994i	$0.911324\pi$
$132$	−3.19810	−	3.19810i	−0.278359	−	0.278359i
$133$	−2.53358	+	21.0791i	−0.219689	+	1.82779i
$134$		−	9.02666i		−	0.779785i
$135$		0			0
$136$	1.88599	+	2.24763i	0.161722	+	0.192733i
$137$	−0.0123729	+	0.0265338i	−0.00105709	+	0.00226693i	−0.906836	−	0.421484i	$-0.861509\pi$
$137$	−0.0123729	+	0.0265338i	−0.00105709	+	0.00226693i	0.905779	+	0.423751i	$0.139287\pi$
$138$	0.760972	+	1.63191i	0.0647783	+	0.138917i
$139$	13.1163	−	15.6315i	1.11251	−	1.32584i	0.172383	−	0.985030i	$-0.444853\pi$
$139$	13.1163	−	15.6315i	1.11251	−	1.32584i	0.940131	−	0.340813i	$-0.110702\pi$
$140$		0			0
$141$	−9.83990	+	5.68107i	−0.828669	+	0.478432i
$142$	6.43205	+	9.18592i	0.539766	+	0.770866i
$143$	9.36378	+	13.3729i	0.783039	+	1.11830i
$144$	−0.543368	+	0.313714i	−0.0452807	+	0.0261428i
$145$		0			0
$146$	−4.39969	+	5.24334i	−0.364121	+	0.433942i
$147$	10.8865	+	23.3461i	0.897900	+	1.92555i
$148$	−2.01634	+	4.32406i	−0.165742	+	0.355436i
$149$	6.53066	+	7.78294i	0.535013	+	0.637603i	0.964062	−	0.265678i	$-0.0855958\pi$
$149$	6.53066	+	7.78294i	0.535013	+	0.637603i	−0.429049	+	0.903281i	$0.641151\pi$
$150$		0			0
$151$			1.46827i			0.119486i	0.998214	+	0.0597431i	$0.0190282\pi$
$151$			1.46827i			0.119486i	−0.998214	+	0.0597431i	$0.980972\pi$
$152$	−3.48786	−	2.61436i	−0.282903	−	0.212052i
$153$	1.30173	+	1.30173i	0.105238	+	0.105238i
$154$	2.48346	+	14.0844i	0.200123	+	1.13496i
$155$		0			0
$156$	−8.04744	+	2.92903i	−0.644311	+	0.234510i
$157$	−6.02081	+	2.80755i	−0.480513	+	0.224067i	−0.647754	−	0.761849i	$-0.724292\pi$
$157$	−6.02081	+	2.80755i	−0.480513	+	0.224067i	0.167242	+	0.985916i	$0.446514\pi$
$158$	−0.849997	−	9.71551i	−0.0676221	−	0.772924i
$159$	5.20939	+	3.00764i	0.413131	+	0.238522i
$160$		0			0
$161$	0.988714	−	5.60728i	0.0779216	−	0.441915i
$162$	5.50802	−	3.85676i	0.432751	−	0.303016i
$163$	−2.48274	+	9.26571i	−0.194463	+	0.725746i	0.797942	+	0.602734i	$0.205922\pi$
$163$	−2.48274	+	9.26571i	−0.194463	+	0.725746i	−0.992405	+	0.123012i	$0.960745\pi$
$164$	0.675178	−	1.16944i	0.0527226	−	0.0913182i
$165$		0			0
$166$	3.76299	−	10.3387i	0.292065	−	0.802441i
$167$	−3.74457	−	1.74612i	−0.289764	−	0.135119i	0.272301	−	0.962212i	$-0.412215\pi$
$167$	−3.74457	−	1.74612i	−0.289764	−	0.135119i	−0.562065	+	0.827093i	$0.689993\pi$
$168$	−7.47384	−	0.653876i	−0.576619	−	0.0504477i
$169$	17.6397	−	3.11036i	1.35690	−	0.239258i
$170$		0			0
$171$	−2.32301	−	1.44335i	−0.177645	−	0.110375i
$172$	−7.46184	+	7.46184i	−0.568960	+	0.568960i
$173$	−14.9517	−	10.4693i	−1.13675	−	0.795964i	−0.155339	−	0.987861i	$-0.549647\pi$
$173$	−14.9517	−	10.4693i	−1.13675	−	0.795964i	−0.981415	+	0.191897i	$0.938536\pi$
$174$	6.00836	−	5.04161i	0.455492	−	0.382204i
$175$		0			0
$176$	−2.75920	−	1.00427i	−0.207983	−	0.0756995i
$177$	21.5073	−	1.88165i	1.61659	−	0.141433i
$178$	11.4507	−	3.06820i	0.858264	−	0.229971i
$179$	2.17597	+	3.76889i	0.162640	+	0.281700i	0.935815	−	0.352493i	$-0.114666\pi$
$179$	2.17597	+	3.76889i	0.162640	+	0.281700i	−0.773175	+	0.634193i	$0.781333\pi$
$180$		0			0
$181$	10.3918	+	1.83235i	0.772415	+	0.136198i	0.545945	−	0.837821i	$-0.316171\pi$
$181$	10.3918	+	1.83235i	0.772415	+	0.136198i	0.226469	+	0.974018i	$0.427282\pi$
$182$	26.1575	+	7.00888i	1.93892	+	0.519533i
$183$	−3.98195	−	14.8608i	−0.294354	−	1.09854i
$184$	0.895498	+	0.751412i	0.0660170	+	0.0553948i
$185$		0			0
$186$	−0.666834	−	1.83211i	−0.0488947	−	0.134337i
$187$	−0.750870	+	8.58249i	−0.0549091	+	0.627614i
$188$	−4.23099	+	6.04248i	−0.308576	+	0.440693i
$189$	−27.2144			−1.97955
$190$		0			0
$191$	17.7578			1.28491			0.642455	−	0.766323i	$-0.277916\pi$
$191$	17.7578			1.28491			0.642455	+	0.766323i	$0.277916\pi$
$192$	0.883489	−	1.26175i	0.0637603	−	0.0910592i
$193$	−1.70640	+	19.5042i	−0.122829	+	1.40394i	0.645437	+	0.763814i	$0.276675\pi$
$193$	−1.70640	+	19.5042i	−0.122829	+	1.40394i	−0.768266	+	0.640131i	$0.778880\pi$
$194$	1.32972	+	3.65337i	0.0954681	+	0.262296i
$195$		0			0
$196$	12.8110	+	10.7497i	0.915070	+	0.767835i
$197$	−2.71406	−	10.1290i	−0.193369	−	0.721662i	−0.992683	−	0.120749i	$-0.961470\pi$
$197$	−2.71406	−	10.1290i	−0.193369	−	0.721662i	0.799314	−	0.600913i	$-0.205196\pi$
$198$	−1.77953	−	0.476823i	−0.126466	−	0.0338864i
$199$	−1.21113	−	0.213554i	−0.0858544	−	0.0151384i	0.130556	−	0.991441i	$-0.458324\pi$
$199$	−1.21113	−	0.213554i	−0.0858544	−	0.0151384i	−0.216410	+	0.976302i	$0.569435\pi$
$200$		0			0
$201$	6.95196	+	12.0411i	0.490353	+	0.849317i
$202$	−17.5502	+	4.70256i	−1.23483	+	0.330871i
$203$	−24.7074	+	2.16161i	−1.73412	+	0.151716i
$204$	−4.24685	−	1.54573i	−0.297339	−	0.108222i
$205$		0			0
$206$	−4.81694	+	4.04190i	−0.335612	+	0.281612i
$207$	0.600812	+	0.420693i	0.0417593	+	0.0292402i
$208$	−3.93140	+	3.93140i	−0.272594	+	0.272594i
$209$	−1.81362	−	12.6698i	−0.125451	−	0.876389i
$210$		0			0
$211$	5.31698	−	0.937527i	0.366036	−	0.0645420i	0.0123947	−	0.999923i	$-0.496055\pi$
$211$	5.31698	−	0.937527i	0.366036	−	0.0645420i	0.353641	+	0.935381i	$0.384943\pi$
$212$	3.89037	+	0.340363i	0.267192	+	0.0233762i
$213$	−15.6547	−	7.29989i	−1.07264	−	0.500180i
$214$	0.675786	−	1.85671i	0.0461958	−	0.126922i
$215$		0			0
$216$	2.79369	−	4.83882i	0.190087	−	0.329240i
$217$	−1.59567	+	5.95511i	−0.108321	+	0.404259i
$218$	−3.40461	+	2.38393i	−0.230589	+	0.161460i
$219$	1.83077	−	10.3828i	0.123712	−	0.701606i
$220$		0			0
$221$	14.1275	+	8.15649i	0.950316	+	0.548665i
$222$	−0.640504	−	7.32099i	−0.0429878	−	0.491353i
$223$	0.360006	−	0.167873i	0.0241078	−	0.0112416i	−0.410527	−	0.911848i	$-0.634655\pi$
$223$	0.360006	−	0.167873i	0.0241078	−	0.0112416i	0.434635	+	0.900607i	$0.356877\pi$
$224$	−4.57694	+	1.66587i	−0.305810	+	0.111306i
$225$		0			0
$226$	1.72296	+	9.77140i	0.114610	+	0.649984i
$227$	18.1669	+	18.1669i	1.20578	+	1.20578i	0.972381	+	0.233401i	$0.0749855\pi$
$227$	18.1669	+	18.1669i	1.20578	+	1.20578i	0.233401	+	0.972381i	$0.425014\pi$
$228$	6.66610	+	0.801225i	0.441473	+	0.0530624i
$229$			6.74272i			0.445571i	0.974867	+	0.222786i	$0.0715150\pi$
$229$			6.74272i			0.445571i	−0.974867	+	0.222786i	$0.928485\pi$
$230$		0			0
$231$	−14.1601	−	16.8753i	−0.931663	−	1.11031i
$232$	2.15199	−	4.61496i	0.141285	−	0.302987i
$233$	−2.82372	−	6.05549i	−0.184988	−	0.396708i	0.791842	−	0.610726i	$-0.209123\pi$
$233$	−2.82372	−	6.05549i	−0.184988	−	0.396708i	−0.976830	+	0.214018i	$0.931345\pi$
$234$	−2.24230	+	2.67227i	−0.146584	+	0.174692i
$235$		0			0
$236$	12.1385	−	7.00814i	0.790146	−	0.456191i
$237$	8.61633	+	12.3054i	0.559691	+	0.799321i
$238$	8.19695	+	11.7065i	0.531329	+	0.758817i
$239$	−5.36570	+	3.09789i	−0.347078	+	0.200386i	−0.663398	−	0.748267i	$-0.730886\pi$
$239$	−5.36570	+	3.09789i	−0.347078	+	0.200386i	0.316320	+	0.948653i	$0.397553\pi$
$240$		0			0
$241$	−19.0147	+	22.6608i	−1.22484	+	1.45971i	−0.379754	+	0.925087i	$0.623991\pi$
$241$	−19.0147	+	22.6608i	−1.22484	+	1.45971i	−0.845090	+	0.534625i	$0.820453\pi$
$242$	1.00509	+	2.15542i	0.0646097	+	0.138556i
$243$	2.70686	−	5.80489i	0.173645	−	0.372384i
$244$	−6.42032	−	7.65145i	−0.411019	−	0.489834i
$245$		0			0
$246$			2.07998i			0.132614i
$247$	−23.1939	−	7.02638i	−1.47579	−	0.447078i
$248$	−0.895038	−	0.895038i	−0.0568350	−	0.0568350i
$249$	2.94280	+	16.6895i	0.186493	+	1.05765i
$250$		0			0
$251$	−26.2096	+	9.53952i	−1.65434	+	0.602129i	−0.989458	−	0.144823i	$-0.953739\pi$
$251$	−26.2096	+	9.53952i	−1.65434	+	0.602129i	−0.664878	+	0.746952i	$0.731516\pi$
$252$	−2.76968	+	1.29152i	−0.174473	+	0.0813582i
$253$	0.299161	+	3.41942i	0.0188081	+	0.214977i
$254$	−5.24012	−	3.02538i	−0.328794	−	0.189829i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−16.1402	+	11.3015i	−1.00680	+	0.704966i	−0.955886	−	0.293737i	$-0.905101\pi$
$257$	−16.1402	+	11.3015i	−1.00680	+	0.704966i	−0.0509093	+	0.998703i	$0.516212\pi$
$258$	4.20694	−	15.7005i	0.261913	−	0.977472i
$259$	−11.6192	+	20.1250i	−0.721981	+	1.25051i
$260$		0			0
$261$	1.09272	−	3.00221i	0.0676374	−	0.185832i
$262$	−2.15478	−	1.00479i	−0.133123	−	0.0620763i
$263$	26.2763	+	2.29888i	1.62027	+	0.141755i	0.860854	−	0.508853i	$-0.169930\pi$
$263$	26.2763	+	2.29888i	1.62027	+	0.141755i	0.759414	+	0.650608i	$0.225486\pi$
$264$	4.45409	−	0.785376i	0.274130	−	0.0483366i
$265$		0			0
$266$	−15.8138	−	14.1659i	−0.969605	−	0.868565i
$267$	−12.9116	+	12.9116i	−0.790180	+	0.790180i
$268$	7.39421	+	5.17748i	0.451673	+	0.316265i
$269$	10.5396	−	8.84373i	0.642608	−	0.539212i	−0.262210	−	0.965011i	$-0.584451\pi$
$269$	10.5396	−	8.84373i	0.642608	−	0.539212i	0.904818	+	0.425799i	$0.140007\pi$
$270$		0			0
$271$	−6.42054	−	2.33689i	−0.390020	−	0.141956i	0.139564	−	0.990213i	$-0.455430\pi$
$271$	−6.42054	−	2.33689i	−0.390020	−	0.141956i	−0.529584	+	0.848257i	$0.677652\pi$
$272$	−2.92291	+	0.255721i	−0.177227	+	0.0155054i
$273$	−40.2908	+	10.7959i	−2.43851	+	0.653397i
$274$	−0.0146384	−	0.0253544i	−0.000884337	−	0.00153172i
$275$		0			0
$276$	−1.77326	−	0.312673i	−0.106738	−	0.0188207i
$277$	0.561690	+	0.150504i	0.0337487	+	0.00904292i	0.275654	−	0.961257i	$-0.411106\pi$
$277$	0.561690	+	0.150504i	0.0337487	+	0.00904292i	−0.241905	+	0.970300i	$0.577772\pi$
$278$	5.28131	+	19.7101i	0.316752	+	1.18213i
$279$	−0.608378	−	0.510490i	−0.0364227	−	0.0305622i
$280$		0			0
$281$	−0.394358	−	1.08349i	−0.0235254	−	0.0646355i	0.927374	−	0.374136i	$-0.122061\pi$
$281$	−0.394358	−	1.08349i	−0.0235254	−	0.0646355i	−0.950899	+	0.309500i	$0.899838\pi$
$282$	0.990276	−	11.3189i	0.0589701	−	0.674031i
$283$	3.71840	−	5.31043i	0.221036	−	0.315672i	−0.693284	−	0.720664i	$-0.743837\pi$
$283$	3.71840	−	5.31043i	0.221036	−	0.315672i	0.914320	+	0.404992i	$0.132726\pi$
$284$	−11.2139			−0.665425
$285$		0			0
$286$	−16.3253			−0.965333
$287$	3.77250	−	5.38769i	0.222684	−	0.318026i
$288$	0.0546839	−	0.625040i	0.00322228	−	0.0368308i
$289$	−2.86996	−	7.88515i	−0.168821	−	0.463833i
$290$		0			0
$291$	−4.58745	−	3.84933i	−0.268921	−	0.225652i
$292$	−1.77154	−	6.61147i	−0.103671	−	0.386907i
$293$	−9.69556	−	2.59792i	−0.566420	−	0.151772i	−0.0357660	−	0.999360i	$-0.511387\pi$
$293$	−9.69556	−	2.59792i	−0.566420	−	0.151772i	−0.530654	+	0.847588i	$0.678054\pi$
$294$	−25.3682	−	4.47310i	−1.47950	−	0.260876i
$295$		0			0
$296$	−2.38554	−	4.13187i	−0.138656	−	0.240160i
$297$	15.8471	−	4.24622i	0.919543	−	0.246391i
$298$	−10.1212	+	0.885494i	−0.586308	+	0.0512953i
$299$	6.10744	+	2.22292i	0.353202	+	0.128555i
$300$		0			0
$301$	−39.3736	+	33.0383i	−2.26945	+	1.90430i
$302$	−1.20274	−	0.842166i	−0.0692098	−	0.0484612i
$303$	19.7894	−	19.7894i	1.13687	−	1.13687i
$304$	4.14211	−	1.35755i	0.237566	−	0.0778610i
$305$		0			0
$306$	−1.81295	+	0.319672i	−0.103640	+	0.0182744i
$307$	24.0315	+	2.10248i	1.37155	+	0.119995i	0.748992	−	0.662579i	$-0.230538\pi$
$307$	24.0315	+	2.10248i	1.37155	+	0.119995i	0.622558	+	0.782574i	$0.286094\pi$
$308$	−12.9617	−	6.04416i	−0.738564	−	0.344398i
$309$	3.31268	−	9.10151i	0.188452	−	0.517767i
$310$		0			0
$311$	6.78673	−	11.7550i	0.384840	−	0.666563i	−0.606907	−	0.794773i	$-0.707590\pi$
$311$	6.78673	−	11.7550i	0.384840	−	0.666563i	0.991747	+	0.128210i	$0.0409233\pi$
$312$	2.21650	−	8.27210i	0.125485	−	0.468316i
$313$	4.45274	−	3.11784i	0.251683	−	0.176231i	−0.440926	−	0.897543i	$-0.645350\pi$
$313$	4.45274	−	3.11784i	0.251683	−	0.176231i	0.692609	+	0.721313i	$0.256461\pi$
$314$	1.15358	−	6.54230i	0.0651005	−	0.369203i
$315$		0			0
$316$	8.44602	+	4.87631i	0.475126	+	0.274314i
$317$	2.14459	+	24.5127i	0.120452	+	1.37677i	0.780315	+	0.625386i	$0.215059\pi$
$317$	2.14459	+	24.5127i	0.120452	+	1.37677i	−0.659864	+	0.751385i	$0.729386\pi$
$318$	−5.45170	+	2.54217i	−0.305716	+	0.142558i
$319$	14.0500	−	5.11377i	0.786648	−	0.286316i
$320$		0			0
$321$	0.528491	+	2.99722i	0.0294975	+	0.167289i
$322$	4.02611	+	4.02611i	0.224366	+	0.224366i
$323$	−6.99293	−	10.7082i	−0.389097	−	0.595821i
$324$			6.72405i			0.373558i
$325$		0			0
$326$	−6.16598	−	7.34833i	−0.341502	−	0.406986i
$327$	2.70558	−	5.80213i	0.149619	−	0.320859i
$328$	0.570685	+	1.22384i	0.0315108	+	0.0675752i
$329$	−23.0945	+	27.5229i	−1.27324	+	1.51739i
$330$		0			0
$331$	10.4535	−	6.03532i	0.574576	−	0.331731i	−0.184399	−	0.982851i	$-0.559034\pi$
$331$	10.4535	−	6.03532i	0.574576	−	0.331731i	0.758975	+	0.651120i	$0.225701\pi$
$332$	6.31063	+	9.01251i	0.346341	+	0.494626i
$333$	−1.71700	−	2.45213i	−0.0940911	−	0.134376i
$334$	3.57814	−	2.06584i	0.195787	−	0.113038i
$335$		0			0
$336$	4.82244	−	5.74716i	0.263086	−	0.313533i
$337$	3.51803	+	7.54445i	0.191639	+	0.410972i	0.978525	−	0.206126i	$-0.0660858\pi$
$337$	3.51803	+	7.54445i	0.191639	+	0.410972i	−0.786886	+	0.617098i	$0.788308\pi$
$338$	−7.56987	+	16.2336i	−0.411746	+	0.882993i
$339$	−9.82387	−	11.7076i	−0.533560	−	0.635872i
$340$		0			0
$341$		−	3.71667i		−	0.201269i
$342$	2.51475	−	1.07503i	0.135982	−	0.0581310i
$343$	33.4888	+	33.4888i	1.80823	+	1.80823i
$344$	−1.83245	−	10.3923i	−0.0987988	−	0.560316i
$345$		0			0
$346$	17.1518	−	6.24276i	0.922089	−	0.335613i
$347$	25.6092	−	11.9418i	1.37478	−	0.641068i	0.411954	−	0.911205i	$-0.364847\pi$
$347$	25.6092	−	11.9418i	1.37478	−	0.641068i	0.962822	+	0.270136i	$0.0870688\pi$
$348$	0.683593	+	7.81351i	0.0366445	+	0.418848i
$349$	−18.7493	−	10.8249i	−1.00363	−	0.579444i	−0.0943071	−	0.995543i	$-0.530064\pi$
$349$	−18.7493	−	10.8249i	−1.00363	−	0.579444i	−0.909319	+	0.416099i	$0.863397\pi$
$350$		0			0
$351$	5.39437	−	30.5930i	0.287930	−	1.63293i
$352$	2.40526	−	1.68418i	0.128201	−	0.0897672i
$353$	9.14390	−	34.1255i	0.486681	−	1.81632i	−0.0856892	−	0.996322i	$-0.527309\pi$
$353$	9.14390	−	34.1255i	0.486681	−	1.81632i	0.572370	−	0.819996i	$-0.306024\pi$
$354$	−10.7948	+	18.6971i	−0.573735	+	0.993737i
$355$		0			0
$356$	−4.05451	+	11.1397i	−0.214889	+	0.590402i
$357$	−19.9502	−	9.30291i	−1.05587	−	0.492362i
$358$	−4.33538	−	0.379297i	−0.229132	−	0.0200465i
$359$	33.8187	−	5.96315i	1.78488	−	0.314723i	0.819018	−	0.573768i	$-0.194519\pi$
$359$	33.8187	−	5.96315i	1.78488	−	0.314723i	0.965865	+	0.259045i	$0.0834079\pi$
$360$		0			0
$361$	13.7347	+	13.1286i	0.722877	+	0.690977i
$362$	−7.46145	+	7.46145i	−0.392165	+	0.392165i
$363$	−3.00076	−	2.10116i	−0.157499	−	0.110282i
$364$	−20.7447	+	17.4068i	−1.08732	+	0.912366i
$365$		0			0
$366$	14.4572	+	5.26200i	0.755692	+	0.275049i
$367$	−12.8358	+	1.12299i	−0.670024	+	0.0586195i	−0.417092	−	0.908864i	$-0.636951\pi$
$367$	−12.8358	+	1.12299i	−0.670024	+	0.0586195i	−0.252932	+	0.967484i	$0.581395\pi$
$368$	−1.12916	+	0.302557i	−0.0588614	+	0.0157719i
$369$	0.423625	+	0.733741i	0.0220531	+	0.0381970i
$370$		0			0
$371$	18.7322	+	3.30298i	0.972525	+	0.171482i
$372$	1.88326	+	0.504618i	0.0976424	+	0.0261632i
$373$	1.97031	+	7.35328i	0.102019	+	0.380738i	0.997990	−	0.0633735i	$-0.0201859\pi$
$373$	1.97031	+	7.35328i	0.102019	+	0.380738i	−0.895971	+	0.444112i	$0.853519\pi$
$374$	−6.59968	−	5.53779i	−0.341261	−	0.286352i
$375$		0			0
$376$	−2.52291	−	6.93164i	−0.130109	−	0.357472i
$377$	2.46746	−	28.2032i	0.127081	−	1.45254i
$378$	15.6095	−	22.2927i	0.802867	−	1.14661i
$379$	28.5908			1.46861			0.734305	−	0.678820i	$-0.237508\pi$
$379$	28.5908			1.46861			0.734305	+	0.678820i	$0.237508\pi$
$380$		0			0
$381$	9.32009			0.477483
$382$	−10.1855	+	14.5463i	−0.521134	+	0.744256i
$383$	−2.70398	+	30.9066i	−0.138167	+	1.57925i	0.538282	+	0.842765i	$0.319073\pi$
$383$	−2.70398	+	30.9066i	−0.138167	+	1.57925i	−0.676449	+	0.736489i	$0.736482\pi$
$384$	0.526819	+	1.44742i	0.0268841	+	0.0738635i
$385$		0			0
$386$	−14.9982	−	12.5850i	−0.763387	−	0.640558i
$387$	−1.71364	−	6.39540i	−0.0871094	−	0.325097i
$388$	−3.75536	−	1.00625i	−0.190649	−	0.0510844i
$389$	−7.78944	−	1.37349i	−0.394940	−	0.0696387i	−0.0273488	−	0.999626i	$-0.508706\pi$
$389$	−7.78944	−	1.37349i	−0.394940	−	0.0696387i	−0.367592	+	0.929987i	$0.619818\pi$
$390$		0			0
$391$	1.71495	+	2.97038i	0.0867288	+	0.150219i
$392$	−16.1537	+	4.32837i	−0.815886	+	0.218616i
$393$	3.64823	−	0.319179i	0.184029	−	0.0161004i
$394$	9.85392	+	3.58654i	0.496434	+	0.180687i
$395$		0			0
$396$	1.41129	−	1.18421i	0.0709198	−	0.0595088i
$397$	10.7534	+	7.52964i	0.539700	+	0.377902i	0.811410	−	0.584477i	$-0.198700\pi$
$397$	10.7534	+	7.52964i	0.539700	+	0.377902i	−0.271710	+	0.962379i	$0.587589\pi$
$398$	0.869606	−	0.869606i	0.0435894	−	0.0435894i
$399$	32.0048	+	6.71748i	1.60224	+	0.336295i
$400$		0			0
$401$	23.8657	−	4.20816i	1.19179	−	0.210146i	0.457646	−	0.889135i	$-0.348693\pi$
$401$	23.8657	−	4.20816i	1.19179	−	0.210146i	0.734148	+	0.678989i	$0.237582\pi$
$402$	−13.8510	−	1.21181i	−0.690825	−	0.0604394i
$403$	−6.37815	−	2.97418i	−0.317718	−	0.148154i
$404$	6.21426	−	17.0735i	0.309171	−	0.849440i
$405$		0			0
$406$	12.4009	−	21.4789i	0.615445	−	1.06598i
$407$	3.62585	−	13.5319i	0.179727	−	0.670749i
$408$	3.70208	−	2.59222i	0.183280	−	0.128334i
$409$	−1.07767	+	6.11175i	−0.0532872	+	0.302207i	−0.999790	−	0.0204886i	$-0.993478\pi$
$409$	−1.07767	+	6.11175i	−0.0532872	+	0.302207i	0.946503	+	0.322695i	$0.104589\pi$
$410$		0			0
$411$	0.0390538	+	0.0225477i	0.00192638	+	0.00111220i
$412$	−0.548042	−	6.26415i	−0.0270001	−	0.308612i
$413$	61.8726	−	28.8517i	3.04455	−	1.41970i
$414$	−0.689223	+	0.250857i	−0.0338735	+	0.0123289i
$415$		0			0
$416$	−0.965456	−	5.47537i	−0.0473354	−	0.268452i
$417$	−22.2249	−	22.2249i	−1.08836	−	1.08836i
$418$	11.4188	+	5.78147i	0.558509	+	0.282781i
$419$			23.1337i			1.13016i	0.825037	+	0.565079i	$0.191154\pi$
$419$			23.1337i			1.13016i	−0.825037	+	0.565079i	$0.808846\pi$
$420$		0			0
$421$	9.66828	+	11.5222i	0.471203	+	0.561558i	0.948334	−	0.317274i	$-0.102768\pi$
$421$	9.66828	+	11.5222i	0.471203	+	0.561558i	−0.477131	+	0.878832i	$0.658323\pi$
$422$	−2.28172	+	4.89316i	−0.111072	+	0.238195i
$423$	−1.95597	−	4.19459i	−0.0951025	−	0.203948i
$424$	−2.51023	+	2.99158i	−0.121908	+	0.145284i
$425$		0			0
$426$	14.9589	−	8.63651i	0.724759	−	0.418440i
$427$	−27.9043	−	39.8514i	−1.35038	−	1.92855i
$428$	1.13331	+	1.61853i	0.0547806	+	0.0782348i
$429$	21.7771	−	12.5730i	1.05141	−	0.607032i
$430$		0			0
$431$	−15.8409	+	18.8785i	−0.763032	+	0.909346i	−0.998036	−	0.0626488i	$-0.980045\pi$
$431$	−15.8409	+	18.8785i	−0.763032	+	0.909346i	0.235004	+	0.971994i	$0.424490\pi$
$432$	2.36133	+	5.06389i	0.113610	+	0.243636i
$433$	−11.0857	+	23.7733i	−0.532743	+	1.14247i	0.437251	+	0.899340i	$0.355952\pi$
$433$	−11.0857	+	23.7733i	−0.532743	+	1.14247i	−0.969993	+	0.243131i	$0.921826\pi$
$434$	−3.96291	−	4.72281i	−0.190226	−	0.226702i
$435$		0			0
$436$		−	4.15626i		−	0.199049i
$437$	−3.48463	−	3.71774i	−0.166693	−	0.177843i
$438$	7.45503	+	7.45503i	0.356215	+	0.356215i
$439$	3.87397	+	21.9704i	0.184894	+	1.04859i	0.926091	+	0.377300i	$0.123148\pi$
$439$	3.87397	+	21.9704i	0.184894	+	1.04859i	−0.741196	+	0.671288i	$0.765741\pi$
$440$		0			0
$441$	−9.86002	+	3.58875i	−0.469525	+	0.170893i
$442$	−14.7846	+	6.89417i	−0.703231	+	0.327922i
$443$	−2.74263	−	31.3484i	−0.130306	−	1.48941i	−0.726833	−	0.686814i	$-0.759009\pi$
$443$	−2.74263	−	31.3484i	−0.130306	−	1.48941i	0.596527	−	0.802593i	$-0.296547\pi$
$444$	6.36438	+	3.67448i	0.302040	+	0.174383i
$445$		0			0
$446$	−0.0689770	+	0.391188i	−0.00326615	+	0.0185233i
$447$	12.8193	−	8.97616i	0.606332	−	0.424558i
$448$	1.26063	−	4.70472i	0.0595590	−	0.222277i
$449$	4.30806	−	7.46177i	0.203310	−	0.352143i	−0.746283	−	0.665629i	$-0.768164\pi$
$449$	4.30806	−	7.46177i	0.203310	−	0.352143i	0.949593	+	0.313486i	$0.101497\pi$
$450$		0			0
$451$	−1.35612	+	3.72591i	−0.0638572	+	0.175446i
$452$	−8.99252	−	4.19328i	−0.422972	−	0.197235i
$453$	2.25300	+	0.197112i	0.105855	+	0.00926111i
$454$	−25.3016	+	4.46136i	−1.18746	+	0.209382i
$455$		0			0
$456$	−4.47984	+	5.00099i	−0.209788	+	0.234193i
$457$	−0.588441	+	0.588441i	−0.0275261	+	0.0275261i	−0.720736	−	0.693210i	$-0.756196\pi$
$457$	−0.588441	+	0.588441i	−0.0275261	+	0.0275261i	0.693210	+	0.720736i	$0.256196\pi$
$458$	−5.52331	−	3.86746i	−0.258087	−	0.180715i
$459$	12.5584	−	10.5377i	0.586175	−	0.491859i
$460$		0			0
$461$	11.4264	+	4.15885i	0.532178	+	0.193697i	0.594111	−	0.804383i	$-0.297504\pi$
$461$	11.4264	+	4.15885i	0.532178	+	0.193697i	−0.0619323	+	0.998080i	$0.519726\pi$
$462$	21.9453	−	1.91997i	1.02099	−	0.0893249i
$463$	−34.1850	+	9.15984i	−1.58871	+	0.425694i	−0.941608	−	0.336710i	$-0.890686\pi$
$463$	−34.1850	+	9.15984i	−1.58871	+	0.425694i	−0.647102	+	0.762403i	$0.724019\pi$
$464$	2.54602	+	4.40984i	0.118196	+	0.204722i
$465$		0			0
$466$	6.57998	+	1.16023i	0.304812	+	0.0537465i
$467$	18.5337	+	4.96610i	0.857638	+	0.229804i	0.660735	−	0.750619i	$-0.270245\pi$
$467$	18.5337	+	4.96610i	0.857638	+	0.229804i	0.196904	+	0.980423i	$0.436911\pi$
$468$	−0.902863	−	3.36953i	−0.0417349	−	0.155757i
$469$	33.6799	+	28.2608i	1.55519	+	1.30496i
$470$		0			0
$471$	3.49978	+	9.61556i	0.161261	+	0.443061i
$472$	−1.22160	+	13.9629i	−0.0562287	+	0.642697i
$473$	17.7726	−	25.3818i	0.817183	−	1.16706i
$474$	−15.0221			−0.689989
$475$		0			0
$476$	−14.2909			−0.655025
$477$	−1.40540	+	2.00713i	−0.0643490	+	0.0918999i
$478$	0.539997	−	6.17220i	0.0246989	−	0.282310i
$479$	6.80316	+	18.6915i	0.310845	+	0.854038i	0.992487	+	0.122353i	$0.0390439\pi$
$479$	6.80316	+	18.6915i	0.310845	+	0.854038i	−0.681642	+	0.731686i	$0.738734\pi$
$480$		0			0
$481$	−20.3204	−	17.0508i	−0.926531	−	0.777451i
$482$	−7.65628	−	28.5736i	−0.348734	−	1.30149i
$483$	−8.47138	−	2.26990i	−0.385461	−	0.103284i
$484$	−2.34212	−	0.412978i	−0.106460	−	0.0187717i
$485$		0			0
$486$	3.20249	+	5.54688i	0.145268	+	0.251612i
$487$	−4.21160	+	1.12850i	−0.190846	+	0.0511370i	−0.352976	−	0.935632i	$-0.614830\pi$
$487$	−4.21160	+	1.12850i	−0.190846	+	0.0511370i	0.162130	+	0.986769i	$0.448164\pi$
$488$	9.95024	−	0.870534i	0.450426	−	0.0394072i
$489$	13.8845	+	5.05355i	0.627879	+	0.228529i
$490$		0			0
$491$	20.5365	−	17.2321i	0.926797	−	0.777675i	−0.0484424	−	0.998826i	$-0.515426\pi$
$491$	20.5365	−	17.2321i	0.926797	−	0.777675i	0.975240	+	0.221151i	$0.0709813\pi$
$492$	−1.70382	−	1.19303i	−0.0768140	−	0.0537857i
$493$	10.5645	−	10.5645i	0.475800	−	0.475800i
$494$	19.0591	−	14.9691i	0.857510	−	0.673493i
$495$		0			0
$496$	1.24654	−	0.219799i	0.0559715	−	0.00986929i
$497$	−54.4117	−	4.76041i	−2.44070	−	0.213533i
$498$	−15.3591	−	7.16208i	−0.688259	−	0.320941i
$499$	14.9961	−	41.2015i	0.671319	−	1.84443i	0.155274	−	0.987871i	$-0.450374\pi$
$499$	14.9961	−	41.2015i	0.671319	−	1.84443i	0.516045	−	0.856562i	$-0.327404\pi$
$500$		0			0
$501$	−3.18204	+	5.51146i	−0.142163	+	0.246234i
$502$	7.21890	−	26.9413i	0.322195	−	1.20245i
$503$	−8.09458	+	5.66789i	−0.360919	+	0.252719i	−0.739945	−	0.672668i	$-0.765148\pi$
$503$	−8.09458	+	5.66789i	−0.360919	+	0.252719i	0.379025	+	0.925386i	$0.376259\pi$
$504$	0.530669	−	3.00957i	0.0236379	−	0.134057i
$505$		0			0
$506$	−2.97262	−	1.71624i	−0.132149	−	0.0762963i
$507$	−2.40462	−	27.4849i	−0.106793	−	1.22065i
$508$	5.48386	−	2.55716i	0.243307	−	0.113456i
$509$	28.6884	−	10.4417i	1.27159	−	0.462822i	0.383950	−	0.923354i	$-0.374564\pi$
$509$	28.6884	−	10.4417i	1.27159	−	0.462822i	0.887643	+	0.460532i	$0.152341\pi$
$510$		0			0
$511$	−5.78915	−	32.8319i	−0.256097	−	1.45240i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−14.6074	+	19.4880i	−0.644933	+	0.860416i
$514$		−	19.7035i		−	0.869084i
$515$		0			0
$516$	10.4481	+	12.4516i	0.459953	+	0.548150i
$517$	9.15369	−	19.6302i	0.402579	−	0.863333i
$518$	−9.82096	−	21.0611i	−0.431508	−	0.925373i
$519$	−18.0718	+	21.5372i	−0.793266	+	0.945377i
$520$		0			0
$521$	−11.1954	+	6.46369i	−0.490481	+	0.283179i	−0.724774	−	0.688987i	$-0.758056\pi$
$521$	−11.1954	+	6.46369i	−0.490481	+	0.283179i	0.234293	+	0.972166i	$0.424723\pi$
$522$	1.83251	+	2.61710i	0.0802069	+	0.114547i
$523$	18.8709	+	26.9505i	0.825169	+	1.17846i	0.981633	+	0.190780i	$0.0611016\pi$
$523$	18.8709	+	26.9505i	0.825169	+	1.17846i	−0.156464	+	0.987684i	$0.550010\pi$
$524$	2.05901	−	1.18877i	0.0899483	−	0.0519317i
$525$		0			0
$526$	−16.9546	+	20.2057i	−0.739256	+	0.881011i
$527$	−1.56955	−	3.36592i	−0.0683708	−	0.146622i
$528$	−1.91142	+	4.09905i	−0.0831838	+	0.178388i
$529$	−13.9057	−	16.5722i	−0.604597	−	0.720530i
$530$		0			0
$531$			8.79420i			0.381636i
$532$	20.6744	−	4.82869i	0.896349	−	0.209350i
$533$	5.30879	+	5.30879i	0.229949	+	0.229949i
$534$	−3.17079	−	17.9824i	−0.137213	−	0.778175i
$535$		0			0
$536$	−8.48229	+	3.08730i	−0.366379	+	0.133351i
$537$	6.07531	−	2.83297i	0.262169	−	0.122251i
$538$	1.19912	+	13.7061i	0.0516979	+	0.590910i
$539$	−42.5262	−	24.5525i	−1.83173	−	1.05755i
$540$		0			0
$541$	0.0567126	−	0.321633i	0.00243827	−	0.0138281i	−0.983564	−	0.180558i	$-0.942210\pi$
$541$	0.0567126	−	0.321633i	0.00243827	−	0.0138281i	0.986003	+	0.166730i	$0.0533208\pi$
$542$	5.59693	−	3.91902i	0.240409	−	0.168336i
$543$	4.20673	−	15.6997i	0.180528	−	0.673739i
$544$	1.46704	−	2.54098i	0.0628987	−	0.108944i
$545$		0			0
$546$	14.2664	−	39.1965i	0.610544	−	1.67746i
$547$	−15.8020	−	7.36861i	−0.675647	−	0.315059i	0.0543382	−	0.998523i	$-0.482695\pi$
$547$	−15.8020	−	7.36861i	−0.675647	−	0.315059i	−0.729985	+	0.683463i	$0.760473\pi$
$548$	0.0291654	+	0.00255164i	0.00124588	+	0.000109001i
$549$	6.17169	−	1.08824i	0.263401	−	0.0464448i
$550$		0			0
$551$	−11.7138	+	18.8530i	−0.499026	+	0.803164i
$552$	1.27323	−	1.27323i	0.0541921	−	0.0541921i
$553$	38.9113	+	27.2460i	1.65468	+	1.15862i
$554$	−0.445458	+	0.373783i	−0.0189257	+	0.0158805i
$555$		0			0
$556$	−19.1748	−	6.97906i	−0.813193	−	0.295978i
$557$	−10.0612	+	0.880241i	−0.426307	+	0.0372970i	−0.298291	−	0.954475i	$-0.596416\pi$
$557$	−10.0612	+	0.880241i	−0.426307	+	0.0372970i	−0.128016	+	0.991772i	$0.540861\pi$
$558$	0.767121	−	0.205549i	0.0324748	−	0.00870160i
$559$	−29.3355	−	50.8105i	−1.24076	−	2.14906i
$560$		0			0
$561$	13.0686	+	2.30435i	0.551758	+	0.0972898i
$562$	1.11374	+	0.298425i	0.0469801	+	0.0125883i
$563$	−5.14948	−	19.2181i	−0.217025	−	0.809947i	−0.985444	−	0.170000i	$-0.945623\pi$
$563$	−5.14948	−	19.2181i	−0.217025	−	0.809947i	0.768419	−	0.639947i	$-0.221044\pi$
$564$	8.70390	+	7.30344i	0.366500	+	0.307530i
$565$		0			0
$566$	2.21726	+	6.09187i	0.0931984	+	0.256061i
$567$	−2.85441	+	32.6261i	−0.119874	+	1.37017i
$568$	6.43205	−	9.18592i	0.269883	−	0.385433i
$569$	−31.9875			−1.34098			−0.670492	−	0.741917i	$-0.733917\pi$
$569$	−31.9875			−1.34098			−0.670492	+	0.741917i	$0.733917\pi$
$570$		0			0
$571$	−21.3990			−0.895521			−0.447760	−	0.894154i	$-0.647778\pi$
$571$	−21.3990			−0.895521			−0.447760	+	0.894154i	$0.647778\pi$
$572$	9.36378	−	13.3729i	0.391520	−	0.559148i
$573$	2.38394	−	27.2485i	0.0995905	−	1.13832i
$574$	2.24952	+	6.18051i	0.0938932	+	0.257969i
$575$		0			0
$576$	0.480637	+	0.403303i	0.0200266	+	0.0168043i
$577$	−5.01536	−	18.7176i	−0.208792	−	0.779223i	−0.988260	−	0.152781i	$-0.951177\pi$
$577$	−5.01536	−	18.7176i	−0.208792	−	0.779223i	0.779468	−	0.626442i	$-0.215490\pi$
$578$	8.10528	+	2.17180i	0.337135	+	0.0903351i
$579$	29.6993	+	5.23678i	1.23426	+	0.217633i
$580$		0			0
$581$	26.7942	+	46.4089i	1.11161	+	1.92537i
$582$	5.78444	−	1.54994i	0.239773	−	0.0642469i
$583$	−11.4232	+	0.999402i	−0.473101	+	0.0413910i
$584$	6.43191	+	2.34102i	0.266154	+	0.0968723i
$585$		0			0
$586$	7.68923	−	6.45203i	0.317639	−	0.266531i
$587$	13.0910	+	9.16640i	0.540323	+	0.378338i	0.811645	−	0.584150i	$-0.198572\pi$
$587$	13.0910	+	9.16640i	0.540323	+	0.378338i	−0.271323	+	0.962488i	$0.587461\pi$
$588$	18.2148	−	18.2148i	0.751164	−	0.751164i
$589$	3.40793	+	4.33907i	0.140421	+	0.178788i
$590$		0			0
$591$	−15.9069	+	2.80481i	−0.654321	+	0.115374i
$592$	4.75292	+	0.415826i	0.195344	+	0.0170904i
$593$	−15.4032	−	7.18261i	−0.632532	−	0.294955i	0.0797853	−	0.996812i	$-0.474577\pi$
$593$	−15.4032	−	7.18261i	−0.632532	−	0.294955i	−0.712317	+	0.701858i	$0.752354\pi$
$594$	−5.61123	+	15.4167i	−0.230231	+	0.632556i
$595$		0			0
$596$	5.07995	−	8.79874i	0.208083	−	0.360410i
$597$	−0.490279	+	1.82975i	−0.0200658	+	0.0748866i
$598$	−5.32400	+	3.72790i	−0.217714	+	0.152445i
$599$	−3.65873	+	20.7497i	−0.149492	+	0.847809i	0.814159	+	0.580642i	$0.197198\pi$
$599$	−3.65873	+	20.7497i	−0.149492	+	0.847809i	−0.963650	+	0.267167i	$0.913913\pi$
$600$		0			0
$601$	−27.9043	−	16.1105i	−1.13824	−	0.657162i	−0.192245	−	0.981347i	$-0.561577\pi$
$601$	−27.9043	−	16.1105i	−1.13824	−	0.657162i	−0.945994	+	0.324185i	$0.894910\pi$
$602$	−4.47968	−	51.2029i	−0.182578	−	2.08688i
$603$	−5.13294	+	2.39353i	−0.209030	+	0.0974721i
$604$	1.37972	−	0.502178i	0.0561402	−	0.0204333i
$605$		0			0
$606$	4.85979	+	27.5612i	0.197416	+	1.11960i
$607$	16.3979	+	16.3979i	0.665570	+	0.665570i	0.956687	−	0.291117i	$-0.0940269\pi$
$607$	16.3979	+	16.3979i	0.665570	+	0.665570i	−0.291117	+	0.956687i	$0.594027\pi$
$608$	−1.26377	+	4.17168i	−0.0512528	+	0.169184i
$609$			38.2025i			1.54804i
$610$		0			0
$611$	−26.3621	−	31.4171i	−1.06650	−	1.27100i
$612$	0.778006	−	1.66844i	0.0314490	−	0.0674426i
$613$	12.2853	+	26.3460i	0.496200	+	1.06410i	0.981799	+	0.189923i	$0.0608238\pi$
$613$	12.2853	+	26.3460i	0.496200	+	1.06410i	−0.485599	+	0.874182i	$0.661398\pi$
$614$	−15.5062	+	18.4795i	−0.625777	+	0.745772i
$615$		0			0
$616$	12.3856	−	7.15085i	0.499031	−	0.288116i
$617$	12.3514	+	17.6396i	0.497248	+	0.710143i	0.986820	−	0.161819i	$-0.0517362\pi$
$617$	12.3514	+	17.6396i	0.497248	+	0.710143i	−0.489573	+	0.871962i	$0.662847\pi$
$618$	5.55544	+	7.93399i	0.223473	+	0.319152i
$619$	6.88077	−	3.97261i	0.276561	−	0.159673i	−0.355304	−	0.934751i	$-0.615623\pi$
$619$	6.88077	−	3.97261i	0.276561	−	0.159673i	0.631866	+	0.775078i	$0.282289\pi$
$620$		0			0
$621$	4.19843	−	5.00349i	0.168477	−	0.200783i
$622$	5.73639	+	12.3017i	0.230008	+	0.493254i
$623$	−24.4020	+	52.3302i	−0.977645	+	2.09657i
$624$	5.50478	+	6.56034i	0.220367	+	0.262624i
$625$		0			0
$626$			5.43579i			0.217258i
$627$	−19.6847	+	1.08203i	−0.786132	+	0.0432121i
$628$	4.69747	+	4.69747i	0.187449	+	0.187449i
$629$	−2.43085	−	13.7860i	−0.0969242	−	0.549684i
$630$		0			0
$631$	35.4560	−	12.9049i	1.41148	−	0.513737i	0.479917	−	0.877314i	$-0.340667\pi$
$631$	35.4560	−	12.9049i	1.41148	−	0.513737i	0.931564	+	0.363577i	$0.118445\pi$
$632$	−8.83888	+	4.12164i	−0.351592	+	0.163950i
$633$	−0.724802	−	8.28452i	−0.0288083	−	0.329280i
$634$	−21.3097	−	12.3032i	−0.846317	−	0.488622i
$635$		0			0
$636$	1.04454	−	5.92390i	0.0414188	−	0.234898i
$637$	−76.1650	+	53.3313i	−3.01777	+	2.11306i
$638$	−3.86978	+	14.4422i	−0.153206	+	0.571773i
$639$	3.51797	−	6.09330i	0.139169	−	0.241047i
$640$		0			0
$641$	−12.5298	+	34.4253i	−0.494897	+	1.35972i	0.401252	+	0.915967i	$0.368575\pi$
$641$	−12.5298	+	34.4253i	−0.494897	+	1.35972i	−0.896150	+	0.443752i	$0.853647\pi$
$642$	−2.75831	−	1.28622i	−0.108862	−	0.0507631i
$643$	−17.9540	−	1.57077i	−0.708036	−	0.0619451i	−0.272551	−	0.962141i	$-0.587867\pi$
$643$	−17.9540	−	1.57077i	−0.708036	−	0.0619451i	−0.435485	+	0.900196i	$0.643423\pi$
$644$	−5.60728	+	0.988714i	−0.220958	+	0.0389608i
$645$		0			0
$646$	12.7826	+	0.413710i	0.502926	+	0.0162772i
$647$	−2.57400	+	2.57400i	−0.101194	+	0.101194i	−0.755891	−	0.654697i	$-0.772796\pi$
$647$	−2.57400	+	2.57400i	−0.101194	+	0.101194i	0.654697	+	0.755891i	$0.272796\pi$
$648$	−5.50802	−	3.85676i	−0.216376	−	0.151508i
$649$	−31.5271	+	26.4544i	−1.23755	+	1.03843i
$650$		0			0
$651$	8.92364	+	3.24794i	0.349745	+	0.127297i
$652$	9.55606	−	0.836047i	0.374244	−	0.0327421i
$653$	23.5631	−	6.31372i	0.922097	−	0.247075i	0.233615	−	0.972329i	$-0.424944\pi$
$653$	23.5631	−	6.31372i	0.922097	−	0.247075i	0.688481	+	0.725254i	$0.258278\pi$
$654$	3.20097	+	5.54425i	0.125168	+	0.216797i
$655$		0			0
$656$	−1.32984	−	0.234487i	−0.0519216	−	0.00915518i
$657$	4.14822	+	1.11151i	0.161837	+	0.0433642i
$658$	−9.29900	−	34.7044i	−0.362513	−	1.35292i
$659$	34.6005	+	29.0333i	1.34784	+	1.13098i	0.979535	+	0.201273i	$0.0645077\pi$
$659$	34.6005	+	29.0333i	1.34784	+	1.13098i	0.368309	+	0.929703i	$0.379937\pi$
$660$		0			0
$661$	−4.52803	−	12.4407i	−0.176120	−	0.483885i	0.819952	−	0.572432i	$-0.194000\pi$
$661$	−4.52803	−	12.4407i	−0.176120	−	0.483885i	−0.996072	+	0.0885467i	$0.971778\pi$
$662$	−1.05203	+	12.0247i	−0.0408882	+	0.467354i
$663$	14.4123	−	20.5830i	0.559729	−	0.799376i
$664$	−11.0022			−0.426970
$665$		0			0
$666$	2.99350			0.115996
$667$	3.41424	−	4.87604i	0.132200	−	0.188801i
$668$	−0.360099	+	4.11596i	−0.0139327	+	0.159251i
$669$	−0.209264	−	0.574949i	−0.00809063	−	0.0222288i
$670$		0			0
$671$	22.4668	+	18.8519i	0.867321	+	0.727769i
$672$	1.94176	+	7.24675i	0.0749051	+	0.279550i
$673$	−34.0514	−	9.12406i	−1.31259	−	0.351706i	−0.466391	−	0.884579i	$-0.654446\pi$
$673$	−34.0514	−	9.12406i	−1.31259	−	0.351706i	−0.846196	+	0.532872i	$0.821113\pi$
$674$	−8.19791	−	1.44551i	−0.315772	−	0.0556791i
$675$		0			0
$676$	−8.95591	−	15.5121i	−0.344458	−	0.596619i
$677$	34.2186	−	9.16886i	1.31513	−	0.352388i	0.467978	−	0.883740i	$-0.344983\pi$
$677$	34.2186	−	9.16886i	1.31513	−	0.352388i	0.847151	+	0.531352i	$0.178316\pi$
$678$	15.2251	−	1.33202i	0.584716	−	0.0511560i
$679$	−17.7944	−	6.47663i	−0.682886	−	0.248550i
$680$		0			0
$681$	30.3152	−	25.4375i	1.16168	−	0.974766i
$682$	3.04452	+	2.13180i	0.116581	+	0.0816307i
$683$	6.85231	−	6.85231i	0.262196	−	0.262196i	−0.563749	−	0.825946i	$-0.690642\pi$
$683$	6.85231	−	6.85231i	0.262196	−	0.262196i	0.825946	+	0.563749i	$0.190642\pi$
$684$	−0.561785	+	2.67657i	−0.0214804	+	0.102341i
$685$		0			0
$686$	−46.6408	+	8.22404i	−1.78075	+	0.313995i
$687$	10.3464	+	0.905192i	0.394740	+	0.0345352i
$688$	9.56393	+	4.45973i	0.364621	+	0.170026i
$689$	−7.42610	+	20.4030i	−0.282912	+	0.777293i
$690$		0			0
$691$	−6.39401	+	11.0748i	−0.243240	+	0.421303i	−0.961635	−	0.274331i	$-0.911543\pi$
$691$	−6.39401	+	11.0748i	−0.243240	+	0.421303i	0.718396	+	0.695635i	$0.244877\pi$
$692$	−4.72412	+	17.6307i	−0.179584	+	0.670218i
$693$	7.35048	−	5.14686i	0.279222	−	0.195513i
$694$	−4.90672	+	27.8274i	−0.186256	+	1.05631i
$695$		0			0
$696$	−6.79254	−	3.92168i	−0.257471	−	0.148651i
$697$	0.345315	+	3.94697i	0.0130797	+	0.149502i
$698$	19.6214	−	9.14961i	0.742681	−	0.346318i
$699$	−9.67094	+	3.51994i	−0.365789	+	0.133136i
$700$		0			0
$701$	3.36083	+	19.0602i	0.126937	+	0.719894i	0.980139	+	0.198313i	$0.0635463\pi$
$701$	3.36083	+	19.0602i	0.126937	+	0.719894i	−0.853202	+	0.521581i	$0.825343\pi$
$702$	21.9662	+	21.9662i	0.829063	+	0.829063i
$703$	8.17473	+	19.1226i	0.308316	+	0.721222i
$704$			2.93628i			0.110665i
$705$		0			0
$706$	22.7093	+	27.0638i	0.854674	+	1.01856i
$707$	37.4004	−	80.2053i	1.40659	−	3.01643i
$708$	−9.12412	−	19.5667i	−0.342905	−	0.735363i
$709$	13.9660	−	16.6440i	0.524503	−	0.625079i	−0.437136	−	0.899395i	$-0.644007\pi$
$709$	13.9660	−	16.6440i	0.524503	−	0.625079i	0.961639	+	0.274317i	$0.0884516\pi$
$710$		0			0
$711$	−5.29926	+	3.05953i	−0.198738	+	0.114741i
$712$	−6.79952	−	9.71072i	−0.254823	−	0.363925i
$713$	−0.848708	−	1.21208i	−0.0317844	−	0.0453928i
$714$	19.0634	−	11.0063i	0.713432	−	0.411900i
$715$		0			0
$716$	2.79737	−	3.33378i	0.104543	−	0.124589i
$717$	4.03323	+	8.64930i	0.150624	+	0.323014i
$718$	−14.5129	+	31.1230i	−0.541616	+	1.16150i
$719$	1.43612	+	1.71150i	0.0535581	+	0.0638280i	0.792158	−	0.610316i	$-0.208957\pi$
$719$	1.43612	+	1.71150i	0.0535581	+	0.0638280i	−0.738600	+	0.674144i	$0.764513\pi$
$720$		0			0
$721$		−	30.6272i		−	1.14062i
$722$	−18.6322	+	3.72055i	−0.693417	+	0.138465i
$723$	32.2193	+	32.2193i	1.19825	+	1.19825i
$724$	−1.83235	−	10.3918i	−0.0680988	−	0.386207i
$725$		0			0
$726$	3.44233	−	1.25291i	0.127757	−	0.0464997i
$727$	10.7340	−	5.00534i	0.398101	−	0.185638i	−0.213249	−	0.976998i	$-0.568405\pi$
$727$	10.7340	−	5.00534i	0.398101	−	0.185638i	0.611350	+	0.791360i	$0.290627\pi$
$728$	−2.36020	−	26.9772i	−0.0874747	−	0.999841i
$729$	−26.0135	−	15.0189i	−0.963465	−	0.556257i
$730$		0			0
$731$	5.37653	−	30.4918i	0.198858	−	1.12778i
$732$	−12.6027	+	8.82451i	−0.465809	+	0.326163i
$733$	2.68673	−	10.0270i	0.0992367	−	0.370356i	−0.898391	−	0.439197i	$-0.855263\pi$
$733$	2.68673	−	10.0270i	0.0992367	−	0.370356i	0.997628	+	0.0688402i	$0.0219299\pi$
$734$	6.44242	−	11.1586i	0.237794	−	0.411872i
$735$		0			0
$736$	0.399818	−	1.09849i	0.0147375	−	0.0404909i
$737$	−24.0215	−	11.2014i	−0.884845	−	0.412610i
$738$	−0.844027	−	0.0738428i	−0.0310691	−	0.00271819i
$739$	−38.7923	+	6.84014i	−1.42700	+	0.251619i	−0.833190	−	0.552987i	$-0.813488\pi$
$739$	−38.7923	+	6.84014i	−1.42700	+	0.251619i	−0.593810	+	0.804606i	$0.702377\pi$
$740$		0			0
$741$	−13.8954	+	34.6466i	−0.510459	+	1.27278i
$742$	−13.4500	+	13.4500i	−0.493764	+	0.493764i
$743$	−29.4992	−	20.6556i	−1.08222	−	0.757779i	−0.110491	−	0.993877i	$-0.535242\pi$
$743$	−29.4992	−	20.6556i	−1.08222	−	0.757779i	−0.971729	+	0.236098i	$0.924131\pi$
$744$	−1.49355	+	1.25324i	−0.0547563	+	0.0459459i
$745$		0			0
$746$	−7.15357	−	2.60369i	−0.261911	−	0.0953278i
$747$	−6.87684	+	0.601645i	−0.251610	+	0.0220131i
$748$	8.32171	−	2.22980i	0.304272	−	0.0815294i
$749$	4.81191	+	8.33447i	0.175823	+	0.304535i
$750$		0			0
$751$	−33.2841	−	5.86888i	−1.21455	−	0.214158i	−0.470573	−	0.882361i	$-0.655953\pi$
$751$	−33.2841	−	5.86888i	−1.21455	−	0.214158i	−0.743979	+	0.668203i	$0.767064\pi$
$752$	7.12515	+	1.90918i	0.259828	+	0.0696206i
$753$	11.1194	+	41.4981i	0.405213	+	1.51227i
$754$	21.6874	+	18.1979i	0.789810	+	0.662729i
$755$		0			0
$756$	9.30786	+	25.5731i	0.338524	+	0.930086i
$757$	1.92995	−	22.0594i	0.0701451	−	0.801762i	−0.876902	−	0.480669i	$-0.840394\pi$
$757$	1.92995	−	22.0594i	0.0701451	−	0.801762i	0.947047	−	0.321094i	$-0.104050\pi$
$758$	−16.3990	+	23.4202i	−0.595638	+	0.850659i
$759$	5.28711			0.191910
$760$		0			0
$761$	−14.7174			−0.533505			−0.266752	−	0.963765i	$-0.585951\pi$
$761$	−14.7174			−0.533505			−0.266752	+	0.963765i	$0.585951\pi$
$762$	−5.34578	+	7.63457i	−0.193657	+	0.276571i
$763$	1.76436	−	20.1668i	0.0638743	−	0.730086i
$764$	−6.07353	−	16.6869i	−0.219733	−	0.603710i
$765$		0			0
$766$	−23.7663	−	19.9423i	−0.858710	−	0.720544i
$767$	20.1693	+	75.2730i	0.728272	+	2.71795i
$768$	−1.48783	−	0.398663i	−0.0536875	−	0.0143855i
$769$	−49.6365	−	8.75226i	−1.78994	−	0.315615i	−0.822509	−	0.568753i	$-0.807426\pi$
$769$	−49.6365	−	8.75226i	−1.78994	−	0.315615i	−0.967430	+	0.253138i	$0.918537\pi$
$770$		0			0
$771$	15.1748	+	26.2835i	0.546507	+	0.946578i
$772$	18.9116	−	5.06735i	0.680643	−	0.182378i
$773$	−47.6815	+	4.17159i	−1.71499	+	0.150042i	−0.901855	−	0.432039i	$-0.857794\pi$
$773$	−47.6815	+	4.17159i	−1.71499	+	0.150042i	−0.813131	+	0.582081i	$0.802239\pi$
$774$	6.22171	+	2.26452i	0.223635	+	0.0813964i
$775$		0			0
$776$	2.97825	−	2.49905i	0.106913	−	0.0897107i
$777$	29.3211	+	20.5308i	1.05189	+	0.736540i
$778$	5.59294	−	5.59294i	0.200517	−	0.200517i
$779$	−1.83318	−	5.59332i	−0.0656805	−	0.200402i
$780$		0			0
$781$	32.4271	−	5.71777i	1.16033	−	0.204598i
$782$	−3.41685	−	0.298936i	−0.122186	−	0.0106899i
$783$	−25.7855	−	12.0240i	−0.921500	−	0.429703i
$784$	5.71979	−	15.7150i	0.204278	−	0.561250i
$785$		0			0
$786$	−1.83108	+	3.17153i	−0.0653125	+	0.113125i
$787$	3.97960	−	14.8521i	0.141857	−	0.529419i	−0.858018	−	0.513620i	$-0.828304\pi$
$787$	3.97960	−	14.8521i	0.141857	−	0.529419i	0.999875	−	0.0157990i	$-0.00502920\pi$
$788$	−8.58990	+	6.01471i	−0.306002	+	0.214265i
$789$	7.05505	−	40.0112i	0.251167	−	1.42444i
$790$		0			0
$791$	−41.8529	−	24.1638i	−1.48812	−	0.859166i
$792$	0.160567	+	1.83529i	0.00570551	+	0.0652143i
$793$	50.3301	−	23.4693i	1.78727	−	0.833419i
$794$	−12.3358	+	4.48988i	−0.437783	+	0.159340i
$795$		0			0
$796$	0.213554	+	1.21113i	0.00756922	+	0.0429272i
$797$	12.9442	+	12.9442i	0.458507	+	0.458507i	0.898165	−	0.439658i	$-0.144900\pi$
$797$	12.9442	+	12.9442i	0.458507	+	0.458507i	−0.439658	+	0.898165i	$0.644900\pi$
$798$	−23.8598	+	22.3638i	−0.844629	+	0.791670i
$799$		−	21.6432i		−	0.765681i
$800$		0			0
$801$	−4.78099	−	5.69776i	−0.168928	−	0.201321i
$802$	−10.2417	+	21.9633i	−0.361646	+	0.775551i
$803$	8.49377	+	18.2149i	0.299739	+	0.642791i
$804$	8.93726	−	10.6510i	0.315193	−	0.375632i
$805$		0			0
$806$	6.09466	−	3.51875i	0.214675	−	0.123943i
$807$	−12.1554	−	17.3597i	−0.427890	−	0.611091i
$808$	10.4215	+	14.8834i	0.366626	+	0.523596i
$809$	−27.7692	+	16.0326i	−0.976314	+	0.563675i	−0.901155	−	0.433496i	$-0.857280\pi$
$809$	−27.7692	+	16.0326i	−0.976314	+	0.563675i	−0.0751587	+	0.997172i	$0.523946\pi$
$810$		0			0
$811$	−4.24844	+	5.06310i	−0.149183	+	0.177789i	−0.835461	−	0.549550i	$-0.814799\pi$
$811$	−4.24844	+	5.06310i	−0.149183	+	0.177789i	0.686278	+	0.727340i	$0.259244\pi$
$812$	10.4817	+	22.4780i	0.367834	+	0.788823i
$813$	−4.44778	+	9.53830i	−0.155991	+	0.334523i
$814$	9.00495	+	10.7317i	0.315623	+	0.376145i
$815$		0			0
$816$			4.51940i			0.158211i
$817$	2.52460	+	45.9285i	0.0883246	+	1.60684i
$818$	−4.38833	−	4.38833i	−0.153434	−	0.153434i
$819$	−2.95043	−	16.7327i	−0.103096	−	0.584689i
$820$		0			0
$821$	3.32711	−	1.21097i	0.116117	−	0.0422631i	−0.283308	−	0.959029i	$-0.591432\pi$
$821$	3.32711	−	1.21097i	0.116117	−	0.0422631i	0.399425	+	0.916766i	$0.369210\pi$
$822$	−0.0408704	+	0.0190582i	−0.00142552	+	0.000664730i
$823$	−2.15880	−	24.6752i	−0.0752510	−	0.860123i	−0.936208	−	0.351446i	$-0.885690\pi$
$823$	−2.15880	−	24.6752i	−0.0752510	−	0.860123i	0.860957	−	0.508677i	$-0.169865\pi$
$824$	5.44563	+	3.14404i	0.189708	+	0.109528i
$825$		0			0
$826$	−11.8548	+	67.2317i	−0.412480	+	2.33929i
$827$	−3.67760	+	2.57508i	−0.127883	+	0.0895444i	−0.635768	−	0.771880i	$-0.719316\pi$
$827$	−3.67760	+	2.57508i	−0.127883	+	0.0895444i	0.507885	+	0.861425i	$0.330427\pi$
$828$	0.189832	−	0.708464i	0.00659713	−	0.0246208i
$829$	8.11745	−	14.0598i	0.281931	−	0.488318i	−0.689929	−	0.723877i	$-0.742358\pi$
$829$	8.11745	−	14.0598i	0.281931	−	0.488318i	0.971860	+	0.235558i	$0.0756918\pi$
$830$		0			0
$831$	0.306347	−	0.841682i	0.0106271	−	0.0291976i
$832$	5.03893	+	2.34969i	0.174693	+	0.0814609i
$833$	−48.8814	−	4.27657i	−1.69364	−	0.148174i
$834$	30.9533	−	5.45790i	1.07182	−	0.188992i
$835$		0			0
$836$	−11.2854	+	6.03758i	−0.390315	+	0.208814i
$837$	−5.00092	+	5.00092i	−0.172857	+	0.172857i
$838$	−18.9501	−	13.2690i	−0.654619	−	0.458369i
$839$	−4.47696	+	3.75661i	−0.154562	+	0.129693i	−0.716789	−	0.697290i	$-0.754389\pi$
$839$	−4.47696	+	3.75661i	−0.154562	+	0.129693i	0.562227	+	0.826983i	$0.309945\pi$
$840$		0			0
$841$	2.88588	+	1.05037i	0.0995131	+	0.0362198i
$842$	−14.9839	+	1.31093i	−0.516381	+	0.0451775i
$843$	−1.71551	+	0.459668i	−0.0590851	+	0.0158318i
$844$	−2.69950	−	4.67567i	−0.0929206	−	0.160943i
$845$		0			0
$846$	4.55790	+	0.803682i	0.156704	+	0.0276311i
$847$	−11.1890	−	2.99808i	−0.384458	−	0.103015i
$848$	−1.01075	−	3.77216i	−0.0347092	−	0.129537i
$849$	−7.64942	−	6.41863i	−0.262528	−	0.220287i
$850$		0			0
$851$	−1.90756	−	5.24098i	−0.0653904	−	0.179659i
$852$	−1.50544	+	17.2073i	−0.0515756	+	0.589512i
$853$	−10.2609	+	14.6541i	−0.351328	+	0.501748i	−0.955454	−	0.295141i	$-0.904634\pi$
$853$	−10.2609	+	14.6541i	−0.351328	+	0.501748i	0.604126	+	0.796889i	$0.293522\pi$
$854$	48.6496			1.66476
$855$		0			0
$856$	−1.97587			−0.0675337
$857$	−7.76048	+	11.0831i	−0.265093	+	0.378592i	−0.929526	−	0.368756i	$-0.879784\pi$
$857$	−7.76048	+	11.0831i	−0.265093	+	0.378592i	0.664434	+	0.747347i	$0.268673\pi$
$858$	−2.19162	+	25.0504i	−0.0748208	+	0.855205i
$859$	7.01619	+	19.2768i	0.239389	+	0.657717i	0.999964	+	0.00846646i	$0.00269499\pi$
$859$	7.01619	+	19.2768i	0.239389	+	0.657717i	−0.760575	+	0.649250i	$0.775083\pi$
$860$		0			0
$861$	−7.76072	−	6.51202i	−0.264485	−	0.221929i
$862$	−6.37837	−	23.8044i	−0.217248	−	0.810781i
$863$	12.0591	+	3.23124i	0.410498	+	0.109993i	0.458158	−	0.888871i	$-0.348510\pi$
$863$	12.0591	+	3.23124i	0.410498	+	0.109993i	−0.0476594	+	0.998864i	$0.515176\pi$
$864$	−5.50250	−	0.970239i	−0.187199	−	0.0330082i
$865$		0			0
$866$	−13.1155	−	22.7166i	−0.445681	−	0.771943i
$867$	−12.4847	+	3.34526i	−0.424002	+	0.113611i
$868$	6.14173	−	0.537331i	0.208464	−	0.0182382i
$869$	−26.9095	−	9.79424i	−0.912841	−	0.332247i
$870$		0			0
$871$	−38.4453	+	32.2595i	−1.30267	+	1.09307i
$872$	3.40461	+	2.38393i	0.115295	+	0.0807301i
$873$	1.72487	−	1.72487i	0.0583779	−	0.0583779i
$874$	5.04409	−	0.722037i	0.170619	−	0.0244233i
$875$		0			0
$876$	−10.3828	+	1.83077i	−0.350803	+	0.0618561i
$877$	44.0244	+	3.85163i	1.48660	+	0.130060i	0.801326	−	0.598227i	$-0.204128\pi$
$877$	44.0244	+	3.85163i	1.48660	+	0.130060i	0.685271	+	0.728288i	$0.259684\pi$
$878$	−20.2191	−	9.42832i	−0.682361	−	0.318190i
$879$	−5.28799	+	14.5286i	−0.178359	+	0.490038i
$880$		0			0
$881$	−8.82414	+	15.2839i	−0.297293	+	0.514927i	−0.975516	−	0.219930i	$-0.929417\pi$
$881$	−8.82414	+	15.2839i	−0.297293	+	0.514927i	0.678223	+	0.734856i	$0.262750\pi$
$882$	2.71574	−	10.1353i	0.0914437	−	0.341273i
$883$	−1.54638	+	1.08279i	−0.0520398	+	0.0364386i	−0.599307	−	0.800519i	$-0.704557\pi$
$883$	−1.54638	+	1.08279i	−0.0520398	+	0.0364386i	0.547267	+	0.836958i	$0.315668\pi$
$884$	2.83272	−	16.0652i	0.0952747	−	0.540330i
$885$		0			0
$886$	27.2522	+	15.7341i	0.915555	+	0.528596i
$887$	2.96137	+	33.8487i	0.0994332	+	1.13653i	0.867935	+	0.496678i	$0.165447\pi$
$887$	2.96137	+	33.8487i	0.0994332	+	1.13653i	−0.768501	+	0.639848i	$0.778997\pi$
$888$	−6.66042	+	3.10580i	−0.223509	+	0.104224i
$889$	27.6940	−	10.0798i	0.928828	−	0.338066i
$890$		0			0
$891$	−3.42846	−	19.4438i	−0.114858	−	0.651391i
$892$	−0.280879	−	0.280879i	−0.00940452	−	0.00940452i
$893$	7.31290	+	31.3108i	0.244717	+	1.04777i
$894$			15.6495i			0.523396i
$895$		0			0
$896$	3.13081	+	3.73116i	0.104593	+	0.124649i
$897$	4.23088	−	9.07316i	0.141265	−	0.302944i
$898$	3.64133	+	7.80885i	0.121513	+	0.260585i
$899$	−4.14301	+	4.93745i	−0.138177	+	0.164673i
$900$		0			0
$901$	−9.92312	+	5.72912i	−0.330587	+	0.190865i
$902$	−2.27425	−	3.24796i	−0.0757241	−	0.108145i
$903$	45.4100	+	64.8522i	1.51115	+	2.15815i
$904$	8.59283	−	4.96107i	0.285793	−	0.165003i
$905$		0			0
$906$	−1.45373	+	1.73249i	−0.0482969	+	0.0575580i
$907$	−6.46866	−	13.8721i	−0.214788	−	0.460615i	0.769163	−	0.639053i	$-0.220673\pi$
$907$	−6.46866	−	13.8721i	−0.214788	−	0.460615i	−0.983951	+	0.178438i	$0.942896\pi$
$908$	10.8579	−	23.2848i	0.360331	−	0.772733i
$909$	7.32772	+	8.73283i	0.243045	+	0.289650i
$910$		0			0
$911$		−	5.01227i		−	0.166064i	−0.996547	−	0.0830320i	$-0.973540\pi$
$911$		−	5.01227i		−	0.166064i	0.996547	−	0.0830320i	$-0.0264604\pi$
$912$	−1.52704	−	6.53812i	−0.0505652	−	0.216499i
$913$	−22.8436	−	22.8436i	−0.756012	−	0.756012i
$914$	−0.144507	−	0.819539i	−0.00477986	−	0.0271079i
$915$		0			0
$916$	6.33608	−	2.30615i	0.209350	−	0.0761972i
$917$	10.4953	−	4.89402i	0.346584	−	0.161615i
$918$	1.42881	+	16.3314i	0.0471579	+	0.539017i
$919$	34.6531	+	20.0070i	1.14310	+	0.659969i	0.947196	−	0.320655i	$-0.103903\pi$
$919$	34.6531	+	20.0070i	1.14310	+	0.659969i	0.195903	+	0.980623i	$0.437236\pi$
$920$		0			0
$921$	6.45233	−	36.5930i	0.212611	−	1.20578i
$922$	−9.96062	+	6.97450i	−0.328036	+	0.229693i
$923$	16.1368	−	60.2233i	0.531149	−	1.98227i
$924$	−11.0146	+	19.0778i	−0.362353	+	0.627613i
$925$		0			0
$926$	12.1044	−	33.2566i	0.397775	−	1.09288i
$927$	3.57566	+	1.66736i	0.117440	+	0.0547633i
$928$	−5.07267	−	0.443801i	−0.166518	−	0.0145685i
$929$	6.74661	−	1.18961i	0.221349	−	0.0390298i	−0.0618736	−	0.998084i	$-0.519708\pi$
$929$	6.74661	−	1.18961i	0.221349	−	0.0390298i	0.283223	+	0.959054i	$0.408596\pi$
$930$		0			0
$931$	72.1607	−	10.3295i	2.36497	−	0.338534i
$932$	−4.72453	+	4.72453i	−0.154757	+	0.154757i
$933$	−17.1263	−	11.9920i	−0.560692	−	0.392600i
$934$	−14.6985	+	12.3335i	−0.480949	+	0.403565i
$935$		0			0
$936$	3.27802	+	1.19310i	0.107145	+	0.0389977i
$937$	34.8670	−	3.05047i	1.13906	−	0.0996546i	0.498021	−	0.867165i	$-0.334060\pi$
$937$	34.8670	−	3.05047i	1.13906	−	0.0996546i	0.641036	+	0.767511i	$0.278505\pi$
$938$	−42.4679	+	11.3792i	−1.38663	+	0.371545i
$939$	−4.18641	−	7.25108i	−0.136618	−	0.236630i
$940$		0			0
$941$	−15.6825	−	2.76525i	−0.511234	−	0.0901444i	−0.0879205	−	0.996127i	$-0.528022\pi$
$941$	−15.6825	−	2.76525i	−0.511234	−	0.0901444i	−0.423314	+	0.905983i	$0.639133\pi$
$942$	−9.88399	−	2.64841i	−0.322038	−	0.0862898i
$943$	0.408560	+	1.52477i	0.0133045	+	0.0496532i
$944$	−10.7371	−	9.00949i	−0.349463	−	0.293234i
$945$		0			0
$946$	10.5977	+	29.1168i	0.344560	+	0.946670i
$947$	−2.26861	+	25.9303i	−0.0737198	+	0.842621i	0.865859	+	0.500288i	$0.166773\pi$
$947$	−2.26861	+	25.9303i	−0.0737198	+	0.842621i	−0.939579	+	0.342333i	$0.888783\pi$
$948$	8.61633	−	12.3054i	0.279845	−	0.399661i
$949$	38.0554			1.23533
$950$		0			0
$951$	37.9016			1.22904
$952$	8.19695	−	11.7065i	0.265665	−	0.379409i
$953$	0.282375	−	3.22756i	0.00914701	−	0.104551i	−0.990249	−	0.139311i	$-0.955511\pi$
$953$	0.282375	−	3.22756i	0.00914701	−	0.104551i	0.999396	+	0.0347603i	$0.0110668\pi$
$954$	−0.838034	−	2.30248i	−0.0271324	−	0.0745455i
$955$		0			0
$956$	4.74624	+	3.98257i	0.153504	+	0.128805i
$957$	−5.96068	−	22.2456i	−0.192681	−	0.719097i
$958$	−19.2133	−	5.14820i	−0.620755	−	0.166331i
$959$	0.140432	+	0.0247619i	0.00453477	+	0.000799602i
$960$		0			0
$961$	−14.6989	−	25.4593i	−0.474158	−	0.821266i
$962$	25.6225	−	6.86554i	0.826104	−	0.221354i
$963$	−1.23499	+	0.108048i	−0.0397971	+	0.00348180i
$964$	27.7976	+	10.1175i	0.895301	+	0.325863i
$965$		0			0
$966$	6.71838	−	5.63739i	0.216160	−	0.181380i
$967$	15.2341	+	10.6671i	0.489897	+	0.343030i	0.792281	−	0.610157i	$-0.208894\pi$
$967$	15.2341	+	10.6671i	0.489897	+	0.343030i	−0.302384	+	0.953186i	$0.597782\pi$
$968$	1.68167	−	1.68167i	0.0540511	−	0.0540511i
$969$	−17.3701	+	9.29278i	−0.558007	+	0.298527i
$970$		0			0
$971$	18.1047	−	3.19235i	0.581009	−	0.102447i	0.124583	−	0.992209i	$-0.460241\pi$
$971$	18.1047	−	3.19235i	0.581009	−	0.102447i	0.456425	+	0.889762i	$0.349130\pi$
$972$	−6.38061	−	0.558231i	−0.204658	−	0.0179053i
$973$	−90.0764	−	42.0033i	−2.88772	−	1.34656i
$974$	1.49127	−	4.09722i	0.0477833	−	0.131283i
$975$		0			0
$976$	−4.99413	+	8.65008i	−0.159858	+	0.276882i
$977$	−6.24477	+	23.3058i	−0.199788	+	0.745619i	0.791187	+	0.611574i	$0.209463\pi$
$977$	−6.24477	+	23.3058i	−0.199788	+	0.745619i	−0.990975	+	0.134045i	$0.957203\pi$
$978$	−12.1034	+	8.47492i	−0.387025	+	0.270998i
$979$	6.04442	−	34.2796i	0.193181	−	1.09558i
$980$		0			0
$981$	2.25838	+	1.30387i	0.0721044	+	0.0416295i
$982$	2.33651	+	26.7064i	0.0745610	+	0.852236i
$983$	−19.8352	+	9.24932i	−0.632646	+	0.295008i	−0.712364	−	0.701810i	$-0.752376\pi$
$983$	−19.8352	+	9.24932i	−0.632646	+	0.295008i	0.0797185	+	0.996817i	$0.474598\pi$
$984$	1.95454	−	0.711394i	0.0623084	−	0.0226784i
$985$		0			0
$986$	2.59438	+	14.7135i	0.0826219	+	0.468572i
$987$	39.1323	+	39.1323i	1.24559	+	1.24559i
$988$	1.33013	+	24.1983i	0.0423171	+	0.769849i
$989$		−	12.3359i		−	0.392259i
$990$		0			0
$991$	18.4810	+	22.0248i	0.587069	+	0.699641i	0.975040	−	0.222030i	$-0.0712683\pi$
$991$	18.4810	+	22.0248i	0.587069	+	0.699641i	−0.387971	+	0.921672i	$0.626824\pi$
$992$	−0.534940	+	1.14718i	−0.0169843	+	0.0364231i
$993$	−7.85757	−	16.8506i	−0.249353	−	0.534738i
$994$	35.1088	−	41.8410i	1.11358	−	1.32712i
$995$		0			0
$996$	14.6765	−	8.47346i	0.465042	−	0.268492i
$997$	9.47125	+	13.5263i	0.299957	+	0.428384i	0.940632	−	0.339429i	$-0.110234\pi$
$997$	9.47125	+	13.5263i	0.299957	+	0.428384i	−0.640674	+	0.767813i	$0.721345\pi$
$998$	25.1489	+	35.9163i	0.796074	+	1.13691i
$999$	−23.0863	+	13.3289i	−0.730420	+	0.421708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.143.3	✓	96
5.2	odd	4	inner	950.2.bb.d.257.2	yes	96
5.3	odd	4	inner	950.2.bb.d.257.7	yes	96
5.4	even	2	inner	950.2.bb.d.143.6	yes	96
19.2	odd	18	inner	950.2.bb.d.743.2	yes	96
95.2	even	36	inner	950.2.bb.d.857.3	yes	96
95.59	odd	18	inner	950.2.bb.d.743.7	yes	96
95.78	even	36	inner	950.2.bb.d.857.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.143.3	✓	96	1.1	even	1	trivial
950.2.bb.d.143.6	yes	96	5.4	even	2	inner
950.2.bb.d.257.2	yes	96	5.2	odd	4	inner
950.2.bb.d.257.7	yes	96	5.3	odd	4	inner
950.2.bb.d.743.2	yes	96	19.2	odd	18	inner
950.2.bb.d.743.7	yes	96	95.59	odd	18	inner
950.2.bb.d.857.3	yes	96	95.2	even	36	inner
950.2.bb.d.857.6	yes	96	95.78	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.134247 - 1.53445i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.17995 + 0.990096i) q^{6} +(-1.26063 - 4.70472i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.617895 + 0.108952i) q^{9} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.134247 - 1.53445i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.17995 + 0.990096i) q^{6} +(-1.26063 - 4.70472i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.617895 + 0.108952i) q^{9} +(1.46814 + 2.54289i) q^{11} +(-1.48783 + 0.398663i) q^{12} +(5.53868 - 0.484572i) q^{13} +(4.57694 + 1.66587i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.40345 + 1.68292i) q^{17} +(-0.443658 + 0.443658i) q^{18} +(-4.04566 - 1.62255i) q^{19} +(-7.38841 + 1.30278i) q^{21} +(-2.92511 - 0.255914i) q^{22} +(1.05946 + 0.494036i) q^{23} +(0.526819 - 1.44742i) q^{24} +(-2.77992 + 4.81496i) q^{26} +(1.44612 - 5.39700i) q^{27} +(-3.98983 + 2.79371i) q^{28} +(0.884224 - 5.01468i) q^{29} +(-1.09619 - 0.632887i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(4.09905 - 1.91142i) q^{33} +(-2.75713 + 1.00351i) q^{34} +(-0.108952 - 0.617895i) q^{36} +(-3.37366 - 3.37366i) q^{37} +(3.64961 - 2.38335i) q^{38} -8.56391i q^{39} +(0.867993 + 1.03443i) q^{41} +(3.17065 - 6.79947i) q^{42} +(-4.45973 - 9.56393i) q^{43} +(1.88741 - 2.24932i) q^{44} +(-1.01237 + 0.584495i) q^{46} +(-4.23099 - 6.04248i) q^{47} +(0.883489 + 1.26175i) q^{48} +(-14.4830 + 8.36178i) q^{49} +(2.90502 - 3.46206i) q^{51} +(-2.34969 - 5.03893i) q^{52} +(-1.65042 + 3.53934i) q^{53} +(3.59150 + 4.28018i) q^{54} -4.87068i q^{56} +(-3.03285 + 5.99005i) q^{57} +(3.60062 + 3.60062i) q^{58} +(2.43390 + 13.8033i) q^{59} +(9.38589 - 3.41618i) q^{61} +(1.14718 - 0.534940i) q^{62} +(-0.266348 - 3.04437i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.785376 + 4.45409i) q^{66} +(-7.39421 + 5.17748i) q^{67} +(0.759394 - 2.83410i) q^{68} +(0.900307 - 1.55938i) q^{69} +(3.83539 - 10.5377i) q^{71} +(0.568642 + 0.265162i) q^{72} +(6.81865 + 0.596555i) q^{73} +(4.69859 - 0.828488i) q^{74} +(-0.141002 + 4.35662i) q^{76} +(10.1128 - 10.1128i) q^{77} +(7.01514 + 4.91206i) q^{78} +(-7.47094 + 6.26886i) q^{79} +(-6.31854 - 2.29976i) q^{81} +(-1.34522 + 0.117691i) q^{82} +(-10.6273 + 2.84759i) q^{83} +(3.75119 + 6.49726i) q^{84} +(10.3923 + 1.83245i) q^{86} +(-7.57610 - 2.03001i) q^{87} +(0.759966 + 2.83623i) q^{88} +(-9.08115 - 7.61999i) q^{89} +(-9.26198 - 25.4471i) q^{91} +(0.101884 - 1.16454i) q^{92} +(-1.11830 + 1.59709i) q^{93} +7.37650 q^{94} -1.54032 q^{96} +(2.22997 - 3.18473i) q^{97} +(1.45755 - 16.6599i) q^{98} +(0.630105 + 1.73120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{6}+O(q^{10}) \) 96 * q - 12 * q^6	\( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Introduction

L-functions

Modular forms

Varieties

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Database

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