LMFDB - Embedded newform 1170.2.m.i.577.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(73,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 396x^{12} + 2412x^{10} + 7716x^{8} + 12984x^{6} + 10756x^{4} + 3648x^{2} + 256 $ x^16 + 32x^14 + 396x^12 + 2412x^10 + 7716x^8 + 12984x^6 + 10756x^4 + 3648*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.7
Root			$1.63314i$ of defining polynomial
Character	$\chi$	$=$	1170.577
Dual form			1170.2.m.i.73.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.15480 + 1.91479i) q^{5} -4.24302i q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.15480 + 1.91479i) q^{5} -4.24302i q^{7} -1.00000 q^{8} +(-1.15480 - 1.91479i) q^{10} +(3.39024 + 3.39024i) q^{11} +(-1.41217 + 3.31749i) q^{13} +4.24302i q^{14} +1.00000 q^{16} +(-3.15929 + 3.15929i) q^{17} +(1.72284 + 1.72284i) q^{19} +(1.15480 + 1.91479i) q^{20} +(-3.39024 - 3.39024i) q^{22} +(-2.37369 - 2.37369i) q^{23} +(-2.33286 + 4.42242i) q^{25} +(1.41217 - 3.31749i) q^{26} -4.24302i q^{28} +5.12623i q^{29} +(7.44803 - 7.44803i) q^{31} -1.00000 q^{32} +(3.15929 - 3.15929i) q^{34} +(8.12450 - 4.89985i) q^{35} +6.10529i q^{37} +(-1.72284 - 1.72284i) q^{38} +(-1.15480 - 1.91479i) q^{40} +(2.65467 - 2.65467i) q^{41} +(4.36740 + 4.36740i) q^{43} +(3.39024 + 3.39024i) q^{44} +(2.37369 + 2.37369i) q^{46} +2.73426i q^{47} -11.0032 q^{49} +(2.33286 - 4.42242i) q^{50} +(-1.41217 + 3.31749i) q^{52} +(9.40073 - 9.40073i) q^{53} +(-2.57655 + 10.4067i) q^{55} +4.24302i q^{56} -5.12623i q^{58} +(-2.65192 + 2.65192i) q^{59} +8.63287 q^{61} +(-7.44803 + 7.44803i) q^{62} +1.00000 q^{64} +(-7.98309 + 1.12703i) q^{65} -1.55388 q^{67} +(-3.15929 + 3.15929i) q^{68} +(-8.12450 + 4.89985i) q^{70} +(-5.27828 + 5.27828i) q^{71} -9.05558 q^{73} -6.10529i q^{74} +(1.72284 + 1.72284i) q^{76} +(14.3849 - 14.3849i) q^{77} +4.42018i q^{79} +(1.15480 + 1.91479i) q^{80} +(-2.65467 + 2.65467i) q^{82} +10.3276i q^{83} +(-9.69775 - 2.40103i) q^{85} +(-4.36740 - 4.36740i) q^{86} +(-3.39024 - 3.39024i) q^{88} +(-6.62584 + 6.62584i) q^{89} +(14.0762 + 5.99188i) q^{91} +(-2.37369 - 2.37369i) q^{92} -2.73426i q^{94} +(-1.30934 + 5.28841i) q^{95} +6.15558 q^{97} +11.0032 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	$ 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} - 4 q^{11} + 4 q^{13} + 16 q^{16} - 4 q^{17} + 4 q^{19} + 4 q^{22} - 16 q^{23} - 16 q^{25} - 4 q^{26} + 12 q^{31} - 16 q^{32} + 4 q^{34} + 12 q^{35} - 4 q^{38} - 4 q^{41} - 16 q^{43} - 4 q^{44} + 16 q^{46} - 80 q^{49} + 16 q^{50} + 4 q^{52} + 44 q^{53} - 20 q^{55} - 12 q^{59} - 32 q^{61} - 12 q^{62} + 16 q^{64} + 44 q^{65} - 32 q^{67} - 4 q^{68} - 12 q^{70} - 16 q^{71} + 4 q^{76} + 32 q^{77} + 4 q^{82} - 64 q^{85} + 16 q^{86} + 4 q^{88} - 4 q^{89} + 76 q^{91} - 16 q^{92} - 40 q^{95} - 8 q^{97} + 80 q^{98}+O(q^{100}) $ 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 - 4 * q^11 + 4 * q^13 + 16 * q^16 - 4 * q^17 + 4 * q^19 + 4 * q^22 - 16 * q^23 - 16 * q^25 - 4 * q^26 + 12 * q^31 - 16 * q^32 + 4 * q^34 + 12 * q^35 - 4 * q^38 - 4 * q^41 - 16 * q^43 - 4 * q^44 + 16 * q^46 - 80 * q^49 + 16 * q^50 + 4 * q^52 + 44 * q^53 - 20 * q^55 - 12 * q^59 - 32 * q^61 - 12 * q^62 + 16 * q^64 + 44 * q^65 - 32 * q^67 - 4 * q^68 - 12 * q^70 - 16 * q^71 + 4 * q^76 + 32 * q^77 + 4 * q^82 - 64 * q^85 + 16 * q^86 + 4 * q^88 - 4 * q^89 + 76 * q^91 - 16 * q^92 - 40 * q^95 - 8 * q^97 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.15480	+	1.91479i	0.516443	+	0.856321i
$5$	1.15480	+	1.91479i	0.516443	+	0.856321i
$6$		0			0
$7$		−	4.24302i		−	1.60371i	−0.597518	−	0.801855i	$-0.703847\pi$
$7$		−	4.24302i		−	1.60371i	0.597518	−	0.801855i	$-0.296153\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.15480	−	1.91479i	−0.365181	−	0.605511i
$11$	3.39024	+	3.39024i	1.02220	+	1.02220i	0.999748	+	0.0224483i	$0.00714612\pi$
$11$	3.39024	+	3.39024i	1.02220	+	1.02220i	0.0224483	+	0.999748i	$0.492854\pi$
$12$		0			0
$13$	−1.41217	+	3.31749i	−0.391666	+	0.920107i
$13$	−1.41217	+	3.31749i	−0.391666	+	0.920107i
$14$			4.24302i			1.13399i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.15929	+	3.15929i	−0.766241	+	0.766241i	−0.977443	−	0.211201i	$-0.932262\pi$
$17$	−3.15929	+	3.15929i	−0.766241	+	0.766241i	0.211201	+	0.977443i	$0.432262\pi$
$18$		0			0
$19$	1.72284	+	1.72284i	0.395246	+	0.395246i	0.876552	−	0.481307i	$-0.159838\pi$
$19$	1.72284	+	1.72284i	0.395246	+	0.395246i	−0.481307	+	0.876552i	$0.659838\pi$
$20$	1.15480	+	1.91479i	0.258222	+	0.428161i
$21$		0			0
$22$	−3.39024	−	3.39024i	−0.722802	−	0.722802i
$23$	−2.37369	−	2.37369i	−0.494949	−	0.494949i	0.414912	−	0.909861i	$-0.363812\pi$
$23$	−2.37369	−	2.37369i	−0.494949	−	0.494949i	−0.909861	+	0.414912i	$0.863812\pi$
$24$		0			0
$25$	−2.33286	+	4.42242i	−0.466572	+	0.884483i
$26$	1.41217	−	3.31749i	0.276950	−	0.650614i
$27$		0			0
$28$		−	4.24302i		−	0.801855i
$29$			5.12623i			0.951917i	0.879468	+	0.475958i	$0.157899\pi$
$29$			5.12623i			0.951917i	−0.879468	+	0.475958i	$0.842101\pi$
$30$		0			0
$31$	7.44803	−	7.44803i	1.33771	−	1.33771i	0.439429	−	0.898277i	$-0.355181\pi$
$31$	7.44803	−	7.44803i	1.33771	−	1.33771i	0.898277	−	0.439429i	$-0.144819\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	3.15929	−	3.15929i	0.541814	−	0.541814i
$35$	8.12450	−	4.89985i	1.37329	−	0.828226i
$36$		0			0
$37$			6.10529i			1.00370i	0.864954	+	0.501852i	$0.167348\pi$
$37$			6.10529i			1.00370i	−0.864954	+	0.501852i	$0.832652\pi$
$38$	−1.72284	−	1.72284i	−0.279481	−	0.279481i
$39$		0			0
$40$	−1.15480	−	1.91479i	−0.182590	−	0.302755i
$41$	2.65467	−	2.65467i	0.414589	−	0.414589i	−0.468745	−	0.883334i	$-0.655294\pi$
$41$	2.65467	−	2.65467i	0.414589	−	0.414589i	0.883334	+	0.468745i	$0.155294\pi$
$42$		0			0
$43$	4.36740	+	4.36740i	0.666022	+	0.666022i	0.956793	−	0.290771i	$-0.0939117\pi$
$43$	4.36740	+	4.36740i	0.666022	+	0.666022i	−0.290771	+	0.956793i	$0.593912\pi$
$44$	3.39024	+	3.39024i	0.511098	+	0.511098i
$45$		0			0
$46$	2.37369	+	2.37369i	0.349982	+	0.349982i
$47$			2.73426i			0.398833i	0.979915	+	0.199416i	$0.0639046\pi$
$47$			2.73426i			0.398833i	−0.979915	+	0.199416i	$0.936095\pi$
$48$		0			0
$49$	−11.0032			−1.57189
$50$	2.33286	−	4.42242i	0.329916	−	0.625424i
$51$		0			0
$52$	−1.41217	+	3.31749i	−0.195833	+	0.460054i
$53$	9.40073	−	9.40073i	1.29129	−	1.29129i	0.357300	−	0.933990i	$-0.383698\pi$
$53$	9.40073	−	9.40073i	1.29129	−	1.29129i	0.933990	−	0.357300i	$-0.116302\pi$
$54$		0			0
$55$	−2.57655	+	10.4067i	−0.347422	+	1.40324i
$56$			4.24302i			0.566997i
$57$		0			0
$58$		−	5.12623i		−	0.673107i
$59$	−2.65192	+	2.65192i	−0.345250	+	0.345250i	−0.858337	−	0.513087i	$-0.828502\pi$
$59$	−2.65192	+	2.65192i	−0.345250	+	0.345250i	0.513087	+	0.858337i	$0.328502\pi$
$60$		0			0
$61$	8.63287			1.10533			0.552663	−	0.833405i	$-0.313612\pi$
$61$	8.63287			1.10533			0.552663	+	0.833405i	$0.313612\pi$
$62$	−7.44803	+	7.44803i	−0.945901	+	0.945901i
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.98309	+	1.12703i	−0.990181	+	0.139791i
$66$		0			0
$67$	−1.55388			−0.189837			−0.0949184	−	0.995485i	$-0.530259\pi$
$67$	−1.55388			−0.189837			−0.0949184	+	0.995485i	$0.530259\pi$
$68$	−3.15929	+	3.15929i	−0.383121	+	0.383121i
$69$		0			0
$70$	−8.12450	+	4.89985i	−0.971064	+	0.585644i
$71$	−5.27828	+	5.27828i	−0.626417	+	0.626417i	−0.947165	−	0.320748i	$-0.896066\pi$
$71$	−5.27828	+	5.27828i	−0.626417	+	0.626417i	0.320748	+	0.947165i	$0.396066\pi$
$72$		0			0
$73$	−9.05558			−1.05988			−0.529938	−	0.848037i	$-0.677785\pi$
$73$	−9.05558			−1.05988			−0.529938	+	0.848037i	$0.677785\pi$
$74$		−	6.10529i		−	0.709725i
$75$		0			0
$76$	1.72284	+	1.72284i	0.197623	+	0.197623i
$77$	14.3849	−	14.3849i	1.63931	−	1.63931i
$78$		0			0
$79$			4.42018i			0.497309i	0.968592	+	0.248654i	$0.0799883\pi$
$79$			4.42018i			0.497309i	−0.968592	+	0.248654i	$0.920012\pi$
$80$	1.15480	+	1.91479i	0.129111	+	0.214080i
$81$		0			0
$82$	−2.65467	+	2.65467i	−0.293159	+	0.293159i
$83$			10.3276i			1.13360i	0.823856	+	0.566799i	$0.191818\pi$
$83$			10.3276i			1.13360i	−0.823856	+	0.566799i	$0.808182\pi$
$84$		0			0
$85$	−9.69775	−	2.40103i	−1.05187	−	0.260428i
$86$	−4.36740	−	4.36740i	−0.470949	−	0.470949i
$87$		0			0
$88$	−3.39024	−	3.39024i	−0.361401	−	0.361401i
$89$	−6.62584	+	6.62584i	−0.702338	+	0.702338i	−0.964912	−	0.262574i	$-0.915429\pi$
$89$	−6.62584	+	6.62584i	−0.702338	+	0.702338i	0.262574	+	0.964912i	$0.415429\pi$
$90$		0			0
$91$	14.0762	+	5.99188i	1.47559	+	0.628119i
$92$	−2.37369	−	2.37369i	−0.247475	−	0.247475i
$93$		0			0
$94$		−	2.73426i		−	0.282017i
$95$	−1.30934	+	5.28841i	−0.134335	+	0.542579i
$96$		0			0
$97$	6.15558			0.625005			0.312502	−	0.949917i	$-0.398833\pi$
$97$	6.15558			0.625005			0.312502	+	0.949917i	$0.398833\pi$
$98$	11.0032			1.11149
$99$		0			0
$100$	−2.33286	+	4.42242i	−0.233286	+	0.442242i
$101$			6.65138i			0.661837i	0.943659	+	0.330919i	$0.107359\pi$
$101$			6.65138i			0.661837i	−0.943659	+	0.330919i	$0.892641\pi$
$102$		0			0
$103$	7.54915	+	7.54915i	0.743840	+	0.743840i	0.973315	−	0.229475i	$-0.0737009\pi$
$103$	7.54915	+	7.54915i	0.743840	+	0.743840i	−0.229475	+	0.973315i	$0.573701\pi$
$104$	1.41217	−	3.31749i	0.138475	−	0.325307i
$105$		0			0
$106$	−9.40073	+	9.40073i	−0.913080	+	0.913080i
$107$	−3.29470	−	3.29470i	−0.318511	−	0.318511i	0.529684	−	0.848195i	$-0.322311\pi$
$107$	−3.29470	−	3.29470i	−0.318511	−	0.318511i	−0.848195	+	0.529684i	$0.822311\pi$
$108$		0			0
$109$	10.2873	+	10.2873i	0.985348	+	0.985348i	0.999894	−	0.0145461i	$-0.00463033\pi$
$109$	10.2873	+	10.2873i	0.985348	+	0.985348i	−0.0145461	+	0.999894i	$0.504630\pi$
$110$	2.57655	−	10.4067i	0.245664	−	0.992237i
$111$		0			0
$112$		−	4.24302i		−	0.400928i
$113$	2.75960	−	2.75960i	0.259602	−	0.259602i	−0.565290	−	0.824892i	$-0.691236\pi$
$113$	2.75960	−	2.75960i	0.259602	−	0.259602i	0.824892	+	0.565290i	$0.191236\pi$
$114$		0			0
$115$	1.80398	−	7.28628i	0.168222	−	0.679449i
$116$			5.12623i			0.475958i
$117$		0			0
$118$	2.65192	−	2.65192i	0.244129	−	0.244129i
$119$	13.4049	+	13.4049i	1.22883	+	1.22883i
$120$		0			0
$121$			11.9875i			1.08977i
$122$	−8.63287			−0.781584
$123$		0			0
$124$	7.44803	−	7.44803i	0.668853	−	0.668853i
$125$	−11.1620	+	0.640071i	−0.998360	+	0.0572497i
$126$		0			0
$127$	8.07990	−	8.07990i	0.716975	−	0.716975i	−0.251009	−	0.967985i	$-0.580762\pi$
$127$	8.07990	−	8.07990i	0.716975	−	0.716975i	0.967985	+	0.251009i	$0.0807625\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	7.98309	−	1.12703i	0.700164	−	0.0988473i
$131$	20.9685			1.83203			0.916013	−	0.401148i	$-0.131389\pi$
$131$	20.9685			1.83203			0.916013	+	0.401148i	$0.131389\pi$
$132$		0			0
$133$	7.31002	−	7.31002i	0.633860	−	0.633860i
$134$	1.55388			0.134235
$135$		0			0
$136$	3.15929	−	3.15929i	0.270907	−	0.270907i
$137$		−	7.84662i		−	0.670382i	−0.942150	−	0.335191i	$-0.891199\pi$
$137$		−	7.84662i		−	0.670382i	0.942150	−	0.335191i	$-0.108801\pi$
$138$		0			0
$139$		−	20.1452i		−	1.70869i	−0.519703	−	0.854347i	$-0.673957\pi$
$139$		−	20.1452i		−	1.70869i	0.519703	−	0.854347i	$-0.326043\pi$
$140$	8.12450	−	4.89985i	0.686646	−	0.414113i
$141$		0			0
$142$	5.27828	−	5.27828i	0.442943	−	0.442943i
$143$	−16.0347	+	6.45950i	−1.34089	+	0.540170i
$144$		0			0
$145$	−9.81567	+	5.91978i	−0.815147	+	0.491611i
$146$	9.05558			0.749445
$147$		0			0
$148$			6.10529i			0.501852i
$149$	−3.60161	−	3.60161i	−0.295055	−	0.295055i	0.544018	−	0.839074i	$-0.316902\pi$
$149$	−3.60161	−	3.60161i	−0.295055	−	0.295055i	−0.839074	+	0.544018i	$0.816902\pi$
$150$		0			0
$151$	8.97545	+	8.97545i	0.730412	+	0.730412i	0.970701	−	0.240289i	$-0.0772423\pi$
$151$	8.97545	+	8.97545i	0.730412	+	0.730412i	−0.240289	+	0.970701i	$0.577242\pi$
$152$	−1.72284	−	1.72284i	−0.139740	−	0.139740i
$153$		0			0
$154$	−14.3849	+	14.3849i	−1.15917	+	1.15917i
$155$	22.8624	+	5.66043i	1.83636	+	0.454657i
$156$		0			0
$157$	10.3982	+	10.3982i	0.829865	+	0.829865i	0.987498	−	0.157633i	$-0.0503862\pi$
$157$	10.3982	+	10.3982i	0.829865	+	0.829865i	−0.157633	+	0.987498i	$0.550386\pi$
$158$		−	4.42018i		−	0.351650i
$159$		0			0
$160$	−1.15480	−	1.91479i	−0.0912952	−	0.151378i
$161$	−10.0716	+	10.0716i	−0.793755	+	0.793755i
$162$		0			0
$163$	−13.4484			−1.05336			−0.526680	−	0.850064i	$-0.676563\pi$
$163$	−13.4484			−1.05336			−0.526680	+	0.850064i	$0.676563\pi$
$164$	2.65467	−	2.65467i	0.207295	−	0.207295i
$165$		0			0
$166$		−	10.3276i		−	0.801575i
$167$		−	0.456413i		−	0.0353183i	−0.999844	−	0.0176592i	$-0.994379\pi$
$167$		−	0.456413i		−	0.0353183i	0.999844	−	0.0176592i	$-0.00562138\pi$
$168$		0			0
$169$	−9.01154	−	9.36975i	−0.693195	−	0.720750i
$170$	9.69775	+	2.40103i	0.743784	+	0.184151i
$171$		0			0
$172$	4.36740	+	4.36740i	0.333011	+	0.333011i
$173$	−10.8079	−	10.8079i	−0.821713	−	0.821713i	0.164641	−	0.986354i	$-0.447353\pi$
$173$	−10.8079	−	10.8079i	−0.821713	−	0.821713i	−0.986354	+	0.164641i	$0.947353\pi$
$174$		0			0
$175$	18.7644	+	9.89838i	1.41845	+	0.748247i
$176$	3.39024	+	3.39024i	0.255549	+	0.255549i
$177$		0			0
$178$	6.62584	−	6.62584i	0.496628	−	0.496628i
$179$	−16.0336			−1.19840			−0.599202	−	0.800598i	$-0.704515\pi$
$179$	−16.0336			−1.19840			−0.599202	+	0.800598i	$0.704515\pi$
$180$		0			0
$181$		−	4.28132i		−	0.318228i	−0.987260	−	0.159114i	$-0.949136\pi$
$181$		−	4.28132i		−	0.318228i	0.987260	−	0.159114i	$-0.0508637\pi$
$182$	−14.0762	−	5.99188i	−1.04340	−	0.444147i
$183$		0			0
$184$	2.37369	+	2.37369i	0.174991	+	0.174991i
$185$	−11.6904	+	7.05040i	−0.859493	+	0.518356i
$186$		0			0
$187$	−21.4215			−1.56650
$188$			2.73426i			0.199416i
$189$		0			0
$190$	1.30934	−	5.28841i	0.0949894	−	0.383661i
$191$	4.94792			0.358019			0.179009	−	0.983847i	$-0.442711\pi$
$191$	4.94792			0.358019			0.179009	+	0.983847i	$0.442711\pi$
$192$		0			0
$193$	6.31053			0.454242			0.227121	−	0.973867i	$-0.427069\pi$
$193$	6.31053			0.454242			0.227121	+	0.973867i	$0.427069\pi$
$194$	−6.15558			−0.441945
$195$		0			0
$196$	−11.0032			−0.785944
$197$	8.20699			0.584724			0.292362	−	0.956308i	$-0.405559\pi$
$197$	8.20699			0.584724			0.292362	+	0.956308i	$0.405559\pi$
$198$		0			0
$199$	−13.6919			−0.970590			−0.485295	−	0.874351i	$-0.661288\pi$
$199$	−13.6919			−0.970590			−0.485295	+	0.874351i	$0.661288\pi$
$200$	2.33286	−	4.42242i	0.164958	−	0.312712i
$201$		0			0
$202$		−	6.65138i		−	0.467990i
$203$	21.7507			1.52660
$204$		0			0
$205$	8.14875	+	2.01752i	0.569133	+	0.140910i
$206$	−7.54915	−	7.54915i	−0.525974	−	0.525974i
$207$		0			0
$208$	−1.41217	+	3.31749i	−0.0979166	+	0.230027i
$209$			11.6817i			0.808037i
$210$		0			0
$211$	−5.75300			−0.396053			−0.198027	−	0.980197i	$-0.563453\pi$
$211$	−5.75300			−0.396053			−0.198027	+	0.980197i	$0.563453\pi$
$212$	9.40073	−	9.40073i	0.645645	−	0.645645i
$213$		0			0
$214$	3.29470	+	3.29470i	0.225221	+	0.225221i
$215$	−3.31918	+	13.4061i	−0.226366	+	0.914291i
$216$		0			0
$217$	−31.6021	−	31.6021i	−2.14529	−	2.14529i
$218$	−10.2873	−	10.2873i	−0.696746	−	0.696746i
$219$		0			0
$220$	−2.57655	+	10.4067i	−0.173711	+	0.701618i
$221$	−6.01947	−	14.9424i	−0.404913	−	1.00514i
$222$		0			0
$223$		−	8.52784i		−	0.571066i	−0.958369	−	0.285533i	$-0.907829\pi$
$223$		−	8.52784i		−	0.571066i	0.958369	−	0.285533i	$-0.0921706\pi$
$224$			4.24302i			0.283499i
$225$		0			0
$226$	−2.75960	+	2.75960i	−0.183566	+	0.183566i
$227$	−14.3219			−0.950578			−0.475289	−	0.879830i	$-0.657657\pi$
$227$	−14.3219			−0.950578			−0.475289	+	0.879830i	$0.657657\pi$
$228$		0			0
$229$	−6.57430	+	6.57430i	−0.434442	+	0.434442i	−0.890136	−	0.455694i	$-0.849391\pi$
$229$	−6.57430	+	6.57430i	−0.434442	+	0.434442i	0.455694	+	0.890136i	$0.349391\pi$
$230$	−1.80398	+	7.28628i	−0.118951	+	0.480443i
$231$		0			0
$232$		−	5.12623i		−	0.336553i
$233$	−12.2743	−	12.2743i	−0.804119	−	0.804119i	0.179617	−	0.983737i	$-0.442514\pi$
$233$	−12.2743	−	12.2743i	−0.804119	−	0.804119i	−0.983737	+	0.179617i	$0.942514\pi$
$234$		0			0
$235$	−5.23554	+	3.15753i	−0.341529	+	0.205975i
$236$	−2.65192	+	2.65192i	−0.172625	+	0.172625i
$237$		0			0
$238$	−13.4049	−	13.4049i	−0.868913	−	0.868913i
$239$	−8.10072	−	8.10072i	−0.523992	−	0.523992i	0.394782	−	0.918775i	$-0.370820\pi$
$239$	−8.10072	−	8.10072i	−0.523992	−	0.523992i	−0.918775	+	0.394782i	$0.870820\pi$
$240$		0			0
$241$	−19.9744	−	19.9744i	−1.28666	−	1.28666i	−0.936802	−	0.349859i	$-0.886229\pi$
$241$	−19.9744	−	19.9744i	−1.28666	−	1.28666i	−0.349859	−	0.936802i	$-0.613771\pi$
$242$		−	11.9875i		−	0.770584i
$243$		0			0
$244$	8.63287			0.552663
$245$	−12.7065	−	21.0689i	−0.811791	−	1.34604i
$246$		0			0
$247$	−8.14844	+	3.28256i	−0.518473	+	0.208864i
$248$	−7.44803	+	7.44803i	−0.472951	+	0.472951i
$249$		0			0
$250$	11.1620	−	0.640071i	0.705947	−	0.0404816i
$251$			7.31908i			0.461976i	0.972957	+	0.230988i	$0.0741959\pi$
$251$			7.31908i			0.461976i	−0.972957	+	0.230988i	$0.925804\pi$
$252$		0			0
$253$		−	16.0948i		−	1.01187i
$254$	−8.07990	+	8.07990i	−0.506978	+	0.506978i
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.4521	−	12.4521i	0.776742	−	0.776742i	−0.202534	−	0.979275i	$-0.564918\pi$
$257$	12.4521	−	12.4521i	0.776742	−	0.776742i	0.979275	+	0.202534i	$0.0649175\pi$
$258$		0			0
$259$	25.9049			1.60965
$260$	−7.98309	+	1.12703i	−0.495091	+	0.0698956i
$261$		0			0
$262$	−20.9685			−1.29544
$263$	−2.46033	+	2.46033i	−0.151710	+	0.151710i	−0.778882	−	0.627171i	$-0.784213\pi$
$263$	−2.46033	+	2.46033i	−0.151710	+	0.151710i	0.627171	+	0.778882i	$0.284213\pi$
$264$		0			0
$265$	28.8564	+	7.14446i	1.77264	+	0.438881i
$266$	−7.31002	+	7.31002i	−0.448206	+	0.448206i
$267$		0			0
$268$	−1.55388			−0.0949184
$269$		−	4.72839i		−	0.288295i	−0.989556	−	0.144148i	$-0.953956\pi$
$269$		−	4.72839i		−	0.288295i	0.989556	−	0.144148i	$-0.0460440\pi$
$270$		0			0
$271$	−5.22916	−	5.22916i	−0.317649	−	0.317649i	0.530215	−	0.847863i	$-0.322111\pi$
$271$	−5.22916	−	5.22916i	−0.317649	−	0.317649i	−0.847863	+	0.530215i	$0.822111\pi$
$272$	−3.15929	+	3.15929i	−0.191560	+	0.191560i
$273$		0			0
$274$			7.84662i			0.474032i
$275$	−22.9020	+	7.08409i	−1.38104	+	0.427187i
$276$		0			0
$277$	14.4045	−	14.4045i	0.865484	−	0.865484i	−0.126484	−	0.991969i	$-0.540369\pi$
$277$	14.4045	−	14.4045i	0.865484	−	0.865484i	0.991969	+	0.126484i	$0.0403693\pi$
$278$			20.1452i			1.20823i
$279$		0			0
$280$	−8.12450	+	4.89985i	−0.485532	+	0.292822i
$281$	2.95771	+	2.95771i	0.176442	+	0.176442i	0.789803	−	0.613361i	$-0.210183\pi$
$281$	2.95771	+	2.95771i	0.176442	+	0.176442i	−0.613361	+	0.789803i	$0.710183\pi$
$282$		0			0
$283$	0.451466	+	0.451466i	0.0268368	+	0.0268368i	0.720398	−	0.693561i	$-0.243959\pi$
$283$	0.451466	+	0.451466i	0.0268368	+	0.0268368i	−0.693561	+	0.720398i	$0.743959\pi$
$284$	−5.27828	+	5.27828i	−0.313208	+	0.313208i
$285$		0			0
$286$	16.0347	−	6.45950i	0.948153	−	0.381958i
$287$	−11.2638	−	11.2638i	−0.664881	−	0.664881i
$288$		0			0
$289$		−	2.96227i		−	0.174251i
$290$	9.81567	−	5.91978i	0.576396	−	0.347622i
$291$		0			0
$292$	−9.05558			−0.529938
$293$	9.67515			0.565229			0.282614	−	0.959234i	$-0.408798\pi$
$293$	9.67515			0.565229			0.282614	+	0.959234i	$0.408798\pi$
$294$		0			0
$295$	−8.14031	−	2.01543i	−0.473947	−	0.117343i
$296$		−	6.10529i		−	0.354863i
$297$		0			0
$298$	3.60161	+	3.60161i	0.208636	+	0.208636i
$299$	11.2268	−	4.52265i	0.649262	−	0.261552i
$300$		0			0
$301$	18.5309	−	18.5309i	1.06811	−	1.06811i
$302$	−8.97545	−	8.97545i	−0.516479	−	0.516479i
$303$		0			0
$304$	1.72284	+	1.72284i	0.0988114	+	0.0988114i
$305$	9.96927	+	16.5302i	0.570838	+	0.946514i
$306$		0			0
$307$			14.0489i			0.801816i	0.916118	+	0.400908i	$0.131305\pi$
$307$			14.0489i			0.801816i	−0.916118	+	0.400908i	$0.868695\pi$
$308$	14.3849	−	14.3849i	0.819653	−	0.819653i
$309$		0			0
$310$	−22.8624	−	5.66043i	−1.29850	−	0.321491i
$311$		−	27.9773i		−	1.58645i	−0.608931	−	0.793223i	$-0.708401\pi$
$311$		−	27.9773i		−	1.58645i	0.608931	−	0.793223i	$-0.291599\pi$
$312$		0			0
$313$	23.6402	−	23.6402i	1.33622	−	1.33622i	0.436531	−	0.899689i	$-0.356207\pi$
$313$	23.6402	−	23.6402i	1.33622	−	1.33622i	0.899689	−	0.436531i	$-0.143793\pi$
$314$	−10.3982	−	10.3982i	−0.586803	−	0.586803i
$315$		0			0
$316$			4.42018i			0.248654i
$317$	−4.56873			−0.256605			−0.128303	−	0.991735i	$-0.540953\pi$
$317$	−4.56873			−0.256605			−0.128303	+	0.991735i	$0.540953\pi$
$318$		0			0
$319$	−17.3792	+	17.3792i	−0.973046	+	0.973046i
$320$	1.15480	+	1.91479i	0.0645554	+	0.107040i
$321$		0			0
$322$	10.0716	−	10.0716i	0.561270	−	0.561270i
$323$	−10.8859			−0.605707
$324$		0			0
$325$	−11.3769	−	13.9845i	−0.631079	−	0.775719i
$326$	13.4484			0.744838
$327$		0			0
$328$	−2.65467	+	2.65467i	−0.146579	+	0.146579i
$329$	11.6015			0.639612
$330$		0			0
$331$	8.63600	−	8.63600i	0.474678	−	0.474678i	−0.428747	−	0.903425i	$-0.641045\pi$
$331$	8.63600	−	8.63600i	0.474678	−	0.474678i	0.903425	+	0.428747i	$0.141045\pi$
$332$			10.3276i			0.566799i
$333$		0			0
$334$			0.456413i			0.0249738i
$335$	−1.79443	−	2.97536i	−0.0980400	−	0.162561i
$336$		0			0
$337$	−19.0445	+	19.0445i	−1.03742	+	1.03742i	−0.0381471	+	0.999272i	$0.512146\pi$
$337$	−19.0445	+	19.0445i	−1.03742	+	1.03742i	−0.999272	+	0.0381471i	$0.987854\pi$
$338$	9.01154	+	9.36975i	0.490163	+	0.509647i
$339$		0			0
$340$	−9.69775	−	2.40103i	−0.525934	−	0.130214i
$341$	50.5013			2.73480
$342$		0			0
$343$			16.9857i			0.917141i
$344$	−4.36740	−	4.36740i	−0.235474	−	0.235474i
$345$		0			0
$346$	10.8079	+	10.8079i	0.581039	+	0.581039i
$347$	17.2413	+	17.2413i	0.925564	+	0.925564i	0.997415	−	0.0718517i	$-0.0228908\pi$
$347$	17.2413	+	17.2413i	0.925564	+	0.925564i	−0.0718517	+	0.997415i	$0.522891\pi$
$348$		0			0
$349$	−12.6310	+	12.6310i	−0.676122	+	0.676122i	−0.959120	−	0.282999i	$-0.908671\pi$
$349$	−12.6310	+	12.6310i	−0.676122	+	0.676122i	0.282999	+	0.959120i	$0.408671\pi$
$350$	−18.7644	−	9.89838i	−1.00300	−	0.529090i
$351$		0			0
$352$	−3.39024	−	3.39024i	−0.180700	−	0.180700i
$353$		−	15.2675i		−	0.812606i	−0.913738	−	0.406303i	$-0.866818\pi$
$353$		−	15.2675i		−	0.812606i	0.913738	−	0.406303i	$-0.133182\pi$
$354$		0			0
$355$	−16.2022	−	4.01144i	−0.859923	−	0.212905i
$356$	−6.62584	+	6.62584i	−0.351169	+	0.351169i
$357$		0			0
$358$	16.0336			0.847400
$359$	25.2263	−	25.2263i	1.33139	−	1.33139i	0.427264	−	0.904127i	$-0.359477\pi$
$359$	25.2263	−	25.2263i	1.33139	−	1.33139i	0.904127	−	0.427264i	$-0.140523\pi$
$360$		0			0
$361$		−	13.0637i		−	0.687562i
$362$			4.28132i			0.225021i
$363$		0			0
$364$	14.0762	+	5.99188i	0.737793	+	0.314060i
$365$	−10.4574	−	17.3396i	−0.547366	−	0.907594i
$366$		0			0
$367$	−8.15472	−	8.15472i	−0.425673	−	0.425673i	0.461479	−	0.887151i	$-0.347319\pi$
$367$	−8.15472	−	8.15472i	−0.425673	−	0.425673i	−0.887151	+	0.461479i	$0.847319\pi$
$368$	−2.37369	−	2.37369i	−0.123737	−	0.123737i
$369$		0			0
$370$	11.6904	−	7.05040i	0.607753	−	0.366533i
$371$	−39.8875	−	39.8875i	−2.07085	−	2.07085i
$372$		0			0
$373$	−25.1341	+	25.1341i	−1.30140	+	1.30140i	−0.373945	+	0.927451i	$0.621995\pi$
$373$	−25.1341	+	25.1341i	−1.30140	+	1.30140i	−0.927451	+	0.373945i	$0.878005\pi$
$374$	21.4215			1.10768
$375$		0			0
$376$		−	2.73426i		−	0.141009i
$377$	−17.0062	−	7.23912i	−0.875866	−	0.372834i
$378$		0			0
$379$	12.6119	+	12.6119i	0.647832	+	0.647832i	0.952469	−	0.304637i	$-0.0985351\pi$
$379$	12.6119	+	12.6119i	0.647832	+	0.647832i	−0.304637	+	0.952469i	$0.598535\pi$
$380$	−1.30934	+	5.28841i	−0.0671676	+	0.271290i
$381$		0			0
$382$	−4.94792			−0.253157
$383$		−	7.06697i		−	0.361105i	−0.983565	−	0.180553i	$-0.942211\pi$
$383$		−	7.06697i		−	0.361105i	0.983565	−	0.180553i	$-0.0577886\pi$
$384$		0			0
$385$	44.1557	+	10.9323i	2.25038	+	0.557164i
$386$	−6.31053			−0.321198
$387$		0			0
$388$	6.15558			0.312502
$389$	2.02343			0.102592			0.0512960	−	0.998683i	$-0.483665\pi$
$389$	2.02343			0.102592			0.0512960	+	0.998683i	$0.483665\pi$
$390$		0			0
$391$	14.9984			0.758501
$392$	11.0032			0.555746
$393$		0			0
$394$	−8.20699			−0.413462
$395$	−8.46372	+	5.10443i	−0.425856	+	0.256832i
$396$		0			0
$397$			4.50938i			0.226320i	0.993577	+	0.113160i	$0.0360972\pi$
$397$			4.50938i			0.226320i	−0.993577	+	0.113160i	$0.963903\pi$
$398$	13.6919			0.686310
$399$		0			0
$400$	−2.33286	+	4.42242i	−0.116643	+	0.221121i
$401$	−4.61446	−	4.61446i	−0.230435	−	0.230435i	0.582439	−	0.812874i	$-0.302098\pi$
$401$	−4.61446	−	4.61446i	−0.230435	−	0.230435i	−0.812874	+	0.582439i	$0.802098\pi$
$402$		0			0
$403$	14.1909	+	35.2267i	0.706899	+	1.75477i
$404$			6.65138i			0.330919i
$405$		0			0
$406$	−21.7507			−1.07947
$407$	−20.6984	+	20.6984i	−1.02598	+	1.02598i
$408$		0			0
$409$	−3.91373	−	3.91373i	−0.193522	−	0.193522i	0.603694	−	0.797216i	$-0.293695\pi$
$409$	−3.91373	−	3.91373i	−0.193522	−	0.193522i	−0.797216	+	0.603694i	$0.793695\pi$
$410$	−8.14875	−	2.01752i	−0.402438	−	0.0996382i
$411$		0			0
$412$	7.54915	+	7.54915i	0.371920	+	0.371920i
$413$	11.2521	+	11.2521i	0.553681	+	0.553681i
$414$		0			0
$415$	−19.7752	+	11.9263i	−0.970724	+	0.585439i
$416$	1.41217	−	3.31749i	0.0692375	−	0.162654i
$417$		0			0
$418$		−	11.6817i		−	0.571369i
$419$		−	30.2004i		−	1.47539i	−0.675136	−	0.737694i	$-0.735915\pi$
$419$		−	30.2004i		−	1.47539i	0.675136	−	0.737694i	$-0.264085\pi$
$420$		0			0
$421$	−16.6746	+	16.6746i	−0.812671	+	0.812671i	−0.985034	−	0.172362i	$-0.944860\pi$
$421$	−16.6746	+	16.6746i	−0.812671	+	0.812671i	0.172362	+	0.985034i	$0.444860\pi$
$422$	5.75300			0.280052
$423$		0			0
$424$	−9.40073	+	9.40073i	−0.456540	+	0.456540i
$425$	−6.60151	−	21.3419i	−0.320220	−	1.03523i
$426$		0			0
$427$		−	36.6294i		−	1.77262i
$428$	−3.29470	−	3.29470i	−0.159256	−	0.159256i
$429$		0			0
$430$	3.31918	−	13.4061i	0.160065	−	0.646502i
$431$	0.949294	−	0.949294i	0.0457259	−	0.0457259i	−0.683874	−	0.729600i	$-0.739706\pi$
$431$	0.949294	−	0.949294i	0.0457259	−	0.0457259i	0.729600	+	0.683874i	$0.239706\pi$
$432$		0			0
$433$	−12.7434	−	12.7434i	−0.612408	−	0.612408i	0.331165	−	0.943573i	$-0.392558\pi$
$433$	−12.7434	−	12.7434i	−0.612408	−	0.612408i	−0.943573	+	0.331165i	$0.892558\pi$
$434$	31.6021	+	31.6021i	1.51695	+	1.51695i
$435$		0			0
$436$	10.2873	+	10.2873i	0.492674	+	0.492674i
$437$		−	8.17897i		−	0.391253i
$438$		0			0
$439$	9.01553			0.430288			0.215144	−	0.976582i	$-0.430978\pi$
$439$	9.01553			0.430288			0.215144	+	0.976582i	$0.430978\pi$
$440$	2.57655	−	10.4067i	0.122832	−	0.496119i
$441$		0			0
$442$	6.01947	+	14.9424i	0.286317	+	0.710738i
$443$	14.4156	−	14.4156i	0.684904	−	0.684904i	−0.276197	−	0.961101i	$-0.589074\pi$
$443$	14.4156	−	14.4156i	0.684904	−	0.684904i	0.961101	+	0.276197i	$0.0890742\pi$
$444$		0			0
$445$	−20.3386	−	5.03557i	−0.964144	−	0.238709i
$446$			8.52784i			0.403805i
$447$		0			0
$448$		−	4.24302i		−	0.200464i
$449$	−10.2569	+	10.2569i	−0.484052	+	0.484052i	−0.906423	−	0.422371i	$-0.861198\pi$
$449$	−10.2569	+	10.2569i	−0.484052	+	0.484052i	0.422371	+	0.906423i	$0.361198\pi$
$450$		0			0
$451$	17.9999			0.847583
$452$	2.75960	−	2.75960i	0.129801	−	0.129801i
$453$		0			0
$454$	14.3219			0.672160
$455$	4.78202	+	33.8724i	0.224185	+	1.58796i
$456$		0			0
$457$	−2.74265			−0.128296			−0.0641478	−	0.997940i	$-0.520433\pi$
$457$	−2.74265			−0.128296			−0.0641478	+	0.997940i	$0.520433\pi$
$458$	6.57430	−	6.57430i	0.307197	−	0.307197i
$459$		0			0
$460$	1.80398	−	7.28628i	0.0841112	−	0.339725i
$461$	1.58645	−	1.58645i	0.0738882	−	0.0738882i	−0.669197	−	0.743085i	$-0.733362\pi$
$461$	1.58645	−	1.58645i	0.0738882	−	0.0738882i	0.743085	+	0.669197i	$0.233362\pi$
$462$		0			0
$463$	8.38165			0.389528			0.194764	−	0.980850i	$-0.437606\pi$
$463$	8.38165			0.389528			0.194764	+	0.980850i	$0.437606\pi$
$464$			5.12623i			0.237979i
$465$		0			0
$466$	12.2743	+	12.2743i	0.568598	+	0.568598i
$467$	11.9372	−	11.9372i	0.552388	−	0.552388i	−0.374741	−	0.927129i	$-0.622268\pi$
$467$	11.9372	−	11.9372i	0.552388	−	0.552388i	0.927129	+	0.374741i	$0.122268\pi$
$468$		0			0
$469$			6.59315i			0.304443i
$470$	5.23554	−	3.15753i	0.241497	−	0.145646i
$471$		0			0
$472$	2.65192	−	2.65192i	0.122064	−	0.122064i
$473$			29.6131i			1.36161i
$474$		0			0
$475$	−11.6382	+	3.59996i	−0.533999	+	0.165177i
$476$	13.4049	+	13.4049i	0.614415	+	0.614415i
$477$		0			0
$478$	8.10072	+	8.10072i	0.370518	+	0.370518i
$479$	−9.99726	+	9.99726i	−0.456786	+	0.456786i	−0.897599	−	0.440813i	$-0.854690\pi$
$479$	−9.99726	+	9.99726i	−0.456786	+	0.456786i	0.440813	+	0.897599i	$0.354690\pi$
$480$		0			0
$481$	−20.2543	−	8.62172i	−0.923515	−	0.393117i
$482$	19.9744	+	19.9744i	0.909807	+	0.909807i
$483$		0			0
$484$			11.9875i			0.544885i
$485$	7.10848	+	11.7867i	0.322780	+	0.535205i
$486$		0			0
$487$	−21.2763			−0.964120			−0.482060	−	0.876138i	$-0.660111\pi$
$487$	−21.2763			−0.964120			−0.482060	+	0.876138i	$0.660111\pi$
$488$	−8.63287			−0.390792
$489$		0			0
$490$	12.7065	+	21.0689i	0.574023	+	0.951794i
$491$			6.15126i			0.277602i	0.990320	+	0.138801i	$0.0443249\pi$
$491$			6.15126i			0.277602i	−0.990320	+	0.138801i	$0.955675\pi$
$492$		0			0
$493$	−16.1953	−	16.1953i	−0.729398	−	0.729398i
$494$	8.14844	−	3.28256i	0.366616	−	0.147689i
$495$		0			0
$496$	7.44803	−	7.44803i	0.334427	−	0.334427i
$497$	22.3958	+	22.3958i	1.00459	+	1.00459i
$498$		0			0
$499$	−0.842453	−	0.842453i	−0.0377134	−	0.0377134i	0.687999	−	0.725712i	$-0.258490\pi$
$499$	−0.842453	−	0.842453i	−0.0377134	−	0.0377134i	−0.725712	+	0.687999i	$0.758490\pi$
$500$	−11.1620	+	0.640071i	−0.499180	+	0.0286248i
$501$		0			0
$502$		−	7.31908i		−	0.326667i
$503$	−29.7635	+	29.7635i	−1.32709	+	1.32709i	−0.419188	+	0.907899i	$0.637685\pi$
$503$	−29.7635	+	29.7635i	−1.32709	+	1.32709i	−0.907899	+	0.419188i	$0.862315\pi$
$504$		0			0
$505$	−12.7360	+	7.68103i	−0.566745	+	0.341801i
$506$			16.0948i			0.715501i
$507$		0			0
$508$	8.07990	−	8.07990i	0.358488	−	0.358488i
$509$	−30.6991	−	30.6991i	−1.36071	−	1.36071i	−0.873010	−	0.487702i	$-0.837835\pi$
$509$	−30.6991	−	30.6991i	−1.36071	−	1.36071i	−0.487702	−	0.873010i	$-0.662165\pi$
$510$		0			0
$511$			38.4230i			1.69973i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−12.4521	+	12.4521i	−0.549239	+	0.549239i
$515$	−5.73728	+	23.1728i	−0.252815	+	1.02112i
$516$		0			0
$517$	−9.26980	+	9.26980i	−0.407685	+	0.407685i
$518$	−25.9049			−1.13819
$519$		0			0
$520$	7.98309	−	1.12703i	0.350082	−	0.0494237i
$521$	16.9557			0.742843			0.371421	−	0.928464i	$-0.378871\pi$
$521$	16.9557			0.742843			0.371421	+	0.928464i	$0.378871\pi$
$522$		0			0
$523$	14.4343	−	14.4343i	0.631166	−	0.631166i	−0.317194	−	0.948361i	$-0.602741\pi$
$523$	14.4343	−	14.4343i	0.631166	−	0.631166i	0.948361	+	0.317194i	$0.102741\pi$
$524$	20.9685			0.916013
$525$		0			0
$526$	2.46033	−	2.46033i	0.107275	−	0.107275i
$527$			47.0610i			2.05001i
$528$		0			0
$529$		−	11.7312i		−	0.510050i
$530$	−28.8564	−	7.14446i	−1.25344	−	0.310335i
$531$		0			0
$532$	7.31002	−	7.31002i	0.316930	−	0.316930i
$533$	5.05799	+	12.5557i	0.219086	+	0.543847i
$534$		0			0
$535$	2.50394	−	10.1134i	0.108255	−	0.437241i
$536$	1.55388			0.0671175
$537$		0			0
$538$			4.72839i			0.203855i
$539$	−37.3035	−	37.3035i	−1.60678	−	1.60678i
$540$		0			0
$541$	−19.1123	−	19.1123i	−0.821702	−	0.821702i	0.164650	−	0.986352i	$-0.447350\pi$
$541$	−19.1123	−	19.1123i	−0.821702	−	0.821702i	−0.986352	+	0.164650i	$0.947350\pi$
$542$	5.22916	+	5.22916i	0.224611	+	0.224611i
$543$		0			0
$544$	3.15929	−	3.15929i	0.135454	−	0.135454i
$545$	−7.81827	+	31.5780i	−0.334898	+	1.35265i
$546$		0			0
$547$	−22.6746	−	22.6746i	−0.969494	−	0.969494i	0.0300538	−	0.999548i	$-0.490432\pi$
$547$	−22.6746	−	22.6746i	−0.969494	−	0.969494i	−0.999548	+	0.0300538i	$0.990432\pi$
$548$		−	7.84662i		−	0.335191i
$549$		0			0
$550$	22.9020	−	7.08409i	0.976545	−	0.302067i
$551$	−8.83165	+	8.83165i	−0.376241	+	0.376241i
$552$		0			0
$553$	18.7549			0.797539
$554$	−14.4045	+	14.4045i	−0.611990	+	0.611990i
$555$		0			0
$556$		−	20.1452i		−	0.854347i
$557$			17.9235i			0.759443i	0.925101	+	0.379722i	$0.123980\pi$
$557$			17.9235i			0.759443i	−0.925101	+	0.379722i	$0.876020\pi$
$558$		0			0
$559$	−20.6563	+	8.32130i	−0.873670	+	0.351953i
$560$	8.12450	−	4.89985i	0.343323	−	0.207056i
$561$		0			0
$562$	−2.95771	−	2.95771i	−0.124764	−	0.124764i
$563$	16.9376	+	16.9376i	0.713834	+	0.713834i	0.967335	−	0.253501i	$-0.0815822\pi$
$563$	16.9376	+	16.9376i	0.713834	+	0.713834i	−0.253501	+	0.967335i	$0.581582\pi$
$564$		0			0
$565$	8.47086	+	2.09727i	0.356372	+	0.0882328i
$566$	−0.451466	−	0.451466i	−0.0189765	−	0.0189765i
$567$		0			0
$568$	5.27828	−	5.27828i	0.221472	−	0.221472i
$569$	−6.54249			−0.274275			−0.137138	−	0.990552i	$-0.543790\pi$
$569$	−6.54249			−0.274275			−0.137138	+	0.990552i	$0.543790\pi$
$570$		0			0
$571$			32.8449i			1.37452i	0.726414	+	0.687258i	$0.241186\pi$
$571$			32.8449i			1.37452i	−0.726414	+	0.687258i	$0.758814\pi$
$572$	−16.0347	+	6.45950i	−0.670445	+	0.270085i
$573$		0			0
$574$	11.2638	+	11.2638i	0.470142	+	0.470142i
$575$	16.0350	−	4.95996i	0.668704	−	0.206845i
$576$		0			0
$577$	21.8568			0.909909			0.454954	−	0.890515i	$-0.349656\pi$
$577$	21.8568			0.909909			0.454954	+	0.890515i	$0.349656\pi$
$578$			2.96227i			0.123214i
$579$		0			0
$580$	−9.81567	+	5.91978i	−0.407573	+	0.245806i
$581$	43.8201			1.81796
$582$		0			0
$583$	63.7415			2.63990
$584$	9.05558			0.374722
$585$		0			0
$586$	−9.67515			−0.399677
$587$	17.7060			0.730806			0.365403	−	0.930849i	$-0.380931\pi$
$587$	17.7060			0.730806			0.365403	+	0.930849i	$0.380931\pi$
$588$		0			0
$589$	25.6635			1.05745
$590$	8.14031	+	2.01543i	0.335131	+	0.0829739i
$591$		0			0
$592$			6.10529i			0.250926i
$593$	−18.4502			−0.757658			−0.378829	−	0.925467i	$-0.623673\pi$
$593$	−18.4502			−0.757658			−0.378829	+	0.925467i	$0.623673\pi$
$594$		0			0
$595$	−10.1876	+	41.1477i	−0.417652	+	1.68689i
$596$	−3.60161	−	3.60161i	−0.147528	−	0.147528i
$597$		0			0
$598$	−11.2268	+	4.52265i	−0.459097	+	0.184945i
$599$			0.0140262i			0.000573094i	1.00000		0.000286547i	$9.12107e-5\pi$
$599$			0.0140262i			0.000573094i	−1.00000		0.000286547i	$0.999909\pi$
$600$		0			0
$601$	36.0578			1.47083			0.735415	−	0.677617i	$-0.236987\pi$
$601$	36.0578			1.47083			0.735415	+	0.677617i	$0.236987\pi$
$602$	−18.5309	+	18.5309i	−0.755265	+	0.755265i
$603$		0			0
$604$	8.97545	+	8.97545i	0.365206	+	0.365206i
$605$	−22.9535	+	13.8432i	−0.933194	+	0.562805i
$606$		0			0
$607$	3.42677	+	3.42677i	0.139088	+	0.139088i	0.773223	−	0.634135i	$-0.218643\pi$
$607$	3.42677	+	3.42677i	0.139088	+	0.139088i	−0.634135	+	0.773223i	$0.718643\pi$
$608$	−1.72284	−	1.72284i	−0.0698702	−	0.0698702i
$609$		0			0
$610$	−9.96927	−	16.5302i	−0.403644	−	0.669287i
$611$	−9.07089	−	3.86125i	−0.366969	−	0.156209i
$612$		0			0
$613$			2.44865i			0.0989002i	0.998777	+	0.0494501i	$0.0157469\pi$
$613$			2.44865i			0.0989002i	−0.998777	+	0.0494501i	$0.984253\pi$
$614$		−	14.0489i		−	0.566969i
$615$		0			0
$616$	−14.3849	+	14.3849i	−0.579583	+	0.579583i
$617$	7.23444			0.291247			0.145624	−	0.989340i	$-0.453481\pi$
$617$	7.23444			0.291247			0.145624	+	0.989340i	$0.453481\pi$
$618$		0			0
$619$	19.3510	−	19.3510i	0.777781	−	0.777781i	−0.201672	−	0.979453i	$-0.564638\pi$
$619$	19.3510	−	19.3510i	0.777781	−	0.777781i	0.979453	+	0.201672i	$0.0646376\pi$
$620$	22.8624	+	5.66043i	0.918178	+	0.227328i
$621$		0			0
$622$			27.9773i			1.12179i
$623$	28.1136	+	28.1136i	1.12635	+	1.12635i
$624$		0			0
$625$	−14.1155	−	20.6338i	−0.564621	−	0.825351i
$626$	−23.6402	+	23.6402i	−0.944850	+	0.944850i
$627$		0			0
$628$	10.3982	+	10.3982i	0.414933	+	0.414933i
$629$	−19.2884	−	19.2884i	−0.769079	−	0.769079i
$630$		0			0
$631$	−15.0478	−	15.0478i	−0.599042	−	0.599042i	0.341016	−	0.940058i	$-0.389229\pi$
$631$	−15.0478	−	15.0478i	−0.599042	−	0.599042i	−0.940058	+	0.341016i	$0.889229\pi$
$632$		−	4.42018i		−	0.175825i
$633$		0			0
$634$	4.56873			0.181447
$635$	24.8020	+	6.14065i	0.984239	+	0.243684i
$636$		0			0
$637$	15.5384	−	36.5031i	0.615655	−	1.44630i
$638$	17.3792	−	17.3792i	0.688047	−	0.688047i
$639$		0			0
$640$	−1.15480	−	1.91479i	−0.0456476	−	0.0756888i
$641$		−	16.6347i		−	0.657031i	−0.944499	−	0.328516i	$-0.893452\pi$
$641$		−	16.6347i		−	0.657031i	0.944499	−	0.328516i	$-0.106548\pi$
$642$		0			0
$643$		−	14.3034i		−	0.564071i	−0.959404	−	0.282035i	$-0.908990\pi$
$643$		−	14.3034i		−	0.564071i	0.959404	−	0.282035i	$-0.0910095\pi$
$644$	−10.0716	+	10.0716i	−0.396878	+	0.396878i
$645$		0			0
$646$	10.8859			0.428300
$647$	20.6899	−	20.6899i	0.813404	−	0.813404i	−0.171739	−	0.985143i	$-0.554938\pi$
$647$	20.6899	−	20.6899i	0.813404	−	0.813404i	0.985143	+	0.171739i	$0.0549385\pi$
$648$		0			0
$649$	−17.9813			−0.705827
$650$	11.3769	+	13.9845i	0.446240	+	0.548516i
$651$		0			0
$652$	−13.4484			−0.526680
$653$	27.6266	−	27.6266i	1.08111	−	1.08111i	0.0847049	−	0.996406i	$-0.473005\pi$
$653$	27.6266	−	27.6266i	1.08111	−	1.08111i	0.996406	−	0.0847049i	$-0.0269947\pi$
$654$		0			0
$655$	24.2145	+	40.1503i	0.946138	+	1.56880i
$656$	2.65467	−	2.65467i	0.103647	−	0.103647i
$657$		0			0
$658$	−11.6015			−0.452274
$659$		−	19.0665i		−	0.742726i	−0.928488	−	0.371363i	$-0.878891\pi$
$659$		−	19.0665i		−	0.742726i	0.928488	−	0.371363i	$-0.121109\pi$
$660$		0			0
$661$	−10.0738	−	10.0738i	−0.391825	−	0.391825i	0.483513	−	0.875337i	$-0.339361\pi$
$661$	−10.0738	−	10.0738i	−0.391825	−	0.391825i	−0.875337	+	0.483513i	$0.839361\pi$
$662$	−8.63600	+	8.63600i	−0.335648	+	0.335648i
$663$		0			0
$664$		−	10.3276i		−	0.400787i
$665$	22.4388	+	5.55555i	0.870140	+	0.215435i
$666$		0			0
$667$	12.1681	−	12.1681i	0.471151	−	0.471151i
$668$		−	0.456413i		−	0.0176592i
$669$		0			0
$670$	1.79443	+	2.97536i	0.0693247	+	0.114948i
$671$	29.2675	+	29.2675i	1.12986	+	1.12986i
$672$		0			0
$673$	−23.3780	−	23.3780i	−0.901156	−	0.901156i	0.0943805	−	0.995536i	$-0.469913\pi$
$673$	−23.3780	−	23.3780i	−0.901156	−	0.901156i	−0.995536	+	0.0943805i	$0.969913\pi$
$674$	19.0445	−	19.0445i	0.733566	−	0.733566i
$675$		0			0
$676$	−9.01154	−	9.36975i	−0.346598	−	0.360375i
$677$	−25.6726	−	25.6726i	−0.986677	−	0.986677i	0.0132355	−	0.999912i	$-0.495787\pi$
$677$	−25.6726	−	25.6726i	−0.986677	−	0.986677i	−0.999912	+	0.0132355i	$0.995787\pi$
$678$		0			0
$679$		−	26.1183i		−	1.00233i
$680$	9.69775	+	2.40103i	0.371892	+	0.0920753i
$681$		0			0
$682$	−50.5013			−1.93379
$683$	31.4365			1.20288			0.601442	−	0.798917i	$-0.294593\pi$
$683$	31.4365			1.20288			0.601442	+	0.798917i	$0.294593\pi$
$684$		0			0
$685$	15.0246	−	9.06130i	0.574062	−	0.346214i
$686$		−	16.9857i		−	0.648517i
$687$		0			0
$688$	4.36740	+	4.36740i	0.166505	+	0.166505i
$689$	17.9114	+	44.4623i	0.682370	+	1.69388i
$690$		0			0
$691$	1.05801	−	1.05801i	0.0402487	−	0.0402487i	−0.686696	−	0.726945i	$-0.740940\pi$
$691$	1.05801	−	1.05801i	0.0402487	−	0.0402487i	0.726945	+	0.686696i	$0.240940\pi$
$692$	−10.8079	−	10.8079i	−0.410856	−	0.410856i
$693$		0			0
$694$	−17.2413	−	17.2413i	−0.654472	−	0.654472i
$695$	38.5739	−	23.2637i	1.46319	−	0.882444i
$696$		0			0
$697$			16.7737i			0.635351i
$698$	12.6310	−	12.6310i	0.478090	−	0.478090i
$699$		0			0
$700$	18.7644	+	9.89838i	0.709227	+	0.374123i
$701$			44.1096i			1.66600i	0.553275	+	0.832999i	$0.313378\pi$
$701$			44.1096i			1.66600i	−0.553275	+	0.832999i	$0.686622\pi$
$702$		0			0
$703$	−10.5184	+	10.5184i	−0.396709	+	0.396709i
$704$	3.39024	+	3.39024i	0.127775	+	0.127775i
$705$		0			0
$706$			15.2675i			0.574599i
$707$	28.2219			1.06140
$708$		0			0
$709$	4.04833	−	4.04833i	0.152038	−	0.152038i	−0.626990	−	0.779028i	$-0.715713\pi$
$709$	4.04833	−	4.04833i	0.152038	−	0.152038i	0.779028	+	0.626990i	$0.215713\pi$
$710$	16.2022	+	4.01144i	0.608057	+	0.150547i
$711$		0			0
$712$	6.62584	−	6.62584i	0.248314	−	0.248314i
$713$	−35.3587			−1.32419
$714$		0			0
$715$	−30.8855	−	23.2437i	−1.15505	−	0.869265i
$716$	−16.0336			−0.599202
$717$		0			0
$718$	−25.2263	+	25.2263i	−0.941436	+	0.941436i
$719$	12.9678			0.483619			0.241809	−	0.970324i	$-0.422259\pi$
$719$	12.9678			0.483619			0.241809	+	0.970324i	$0.422259\pi$
$720$		0			0
$721$	32.0312	−	32.0312i	1.19290	−	1.19290i
$722$			13.0637i			0.486180i
$723$		0			0
$724$		−	4.28132i		−	0.159114i
$725$	−22.6703	−	11.9588i	−0.841954	−	0.444138i
$726$		0			0
$727$	18.6879	−	18.6879i	0.693096	−	0.693096i	−0.269816	−	0.962912i	$-0.586963\pi$
$727$	18.6879	−	18.6879i	0.693096	−	0.693096i	0.962912	+	0.269816i	$0.0869629\pi$
$728$	−14.0762	−	5.99188i	−0.521698	−	0.222074i
$729$		0			0
$730$	10.4574	+	17.3396i	0.387046	+	0.641766i
$731$	−27.5958			−1.02067
$732$		0			0
$733$		−	12.0069i		−	0.443486i	−0.975105	−	0.221743i	$-0.928825\pi$
$733$		−	12.0069i		−	0.443486i	0.975105	−	0.221743i	$-0.0711746\pi$
$734$	8.15472	+	8.15472i	0.300996	+	0.300996i
$735$		0			0
$736$	2.37369	+	2.37369i	0.0874955	+	0.0874955i
$737$	−5.26803	−	5.26803i	−0.194050	−	0.194050i
$738$		0			0
$739$	−18.5175	+	18.5175i	−0.681176	+	0.681176i	−0.960265	−	0.279090i	$-0.909967\pi$
$739$	−18.5175	+	18.5175i	−0.681176	+	0.681176i	0.279090	+	0.960265i	$0.409967\pi$
$740$	−11.6904	+	7.05040i	−0.429746	+	0.259178i
$741$		0			0
$742$	39.8875	+	39.8875i	1.46432	+	1.46432i
$743$		−	26.0394i		−	0.955293i	−0.878552	−	0.477647i	$-0.841490\pi$
$743$		−	26.0394i		−	0.955293i	0.878552	−	0.477647i	$-0.158510\pi$
$744$		0			0
$745$	2.73719	−	11.0555i	0.100283	−	0.405042i
$746$	25.1341	−	25.1341i	0.920226	−	0.920226i
$747$		0			0
$748$	−21.4215			−0.783249
$749$	−13.9795	+	13.9795i	−0.510800	+	0.510800i
$750$		0			0
$751$			14.2734i			0.520842i	0.965495	+	0.260421i	$0.0838614\pi$
$751$			14.2734i			0.520842i	−0.965495	+	0.260421i	$0.916139\pi$
$752$			2.73426i			0.0997082i
$753$		0			0
$754$	17.0062	+	7.23912i	0.619331	+	0.263633i
$755$	−6.82125	+	27.5510i	−0.248251	+	1.00268i
$756$		0			0
$757$	34.0930	+	34.0930i	1.23913	+	1.23913i	0.960357	+	0.278774i	$0.0899282\pi$
$757$	34.0930	+	34.0930i	1.23913	+	1.23913i	0.278774	+	0.960357i	$0.410072\pi$
$758$	−12.6119	−	12.6119i	−0.458086	−	0.458086i
$759$		0			0
$760$	1.30934	−	5.28841i	0.0474947	−	0.191831i
$761$	−29.2663	−	29.2663i	−1.06090	−	1.06090i	−0.998021	−	0.0628807i	$-0.979971\pi$
$761$	−29.2663	−	29.2663i	−1.06090	−	1.06090i	−0.0628807	−	0.998021i	$-0.520029\pi$
$762$		0			0
$763$	43.6494	−	43.6494i	1.58021	−	1.58021i
$764$	4.94792			0.179009
$765$		0			0
$766$			7.06697i			0.255340i
$767$	−5.05275	−	12.5427i	−0.182444	−	0.452890i
$768$		0			0
$769$	10.0320	+	10.0320i	0.361764	+	0.361764i	0.864462	−	0.502698i	$-0.167659\pi$
$769$	10.0320	+	10.0320i	0.361764	+	0.361764i	−0.502698	+	0.864462i	$0.667659\pi$
$770$	−44.1557	−	10.9323i	−1.59126	−	0.393975i
$771$		0			0
$772$	6.31053			0.227121
$773$			45.9949i			1.65432i	0.561964	+	0.827162i	$0.310046\pi$
$773$			45.9949i			1.65432i	−0.561964	+	0.827162i	$0.689954\pi$
$774$		0			0
$775$	15.5631	+	50.3135i	0.559042	+	1.80732i
$776$	−6.15558			−0.220973
$777$		0			0
$778$	−2.02343			−0.0725434
$779$	9.14711			0.327729
$780$		0			0
$781$	−35.7893			−1.28064
$782$	−14.9984			−0.536341
$783$		0			0
$784$	−11.0032			−0.392972
$785$	−7.90251	+	31.9182i	−0.282053	+	1.13921i
$786$		0			0
$787$			50.3402i			1.79443i	0.441590	+	0.897217i	$0.354415\pi$
$787$			50.3402i			1.79443i	−0.441590	+	0.897217i	$0.645585\pi$
$788$	8.20699			0.292362
$789$		0			0
$790$	8.46372	−	5.10443i	0.301126	−	0.181608i
$791$	−11.7090	−	11.7090i	−0.416326	−	0.416326i
$792$		0			0
$793$	−12.1911	+	28.6395i	−0.432919	+	1.01702i
$794$		−	4.50938i		−	0.160032i
$795$		0			0
$796$	−13.6919			−0.485295
$797$	−19.5517	+	19.5517i	−0.692558	+	0.692558i	−0.962794	−	0.270236i	$-0.912898\pi$
$797$	−19.5517	+	19.5517i	−0.692558	+	0.692558i	0.270236	+	0.962794i	$0.412898\pi$
$798$		0			0
$799$	−8.63833	−	8.63833i	−0.305602	−	0.305602i
$800$	2.33286	−	4.42242i	0.0824791	−	0.156356i
$801$		0			0
$802$	4.61446	+	4.61446i	0.162942	+	0.162942i
$803$	−30.7006	−	30.7006i	−1.08340	−	1.08340i
$804$		0			0
$805$	−30.9158	−	7.65434i	−1.08964	−	0.269780i
$806$	−14.1909	−	35.2267i	−0.499853	−	1.24081i
$807$		0			0
$808$		−	6.65138i		−	0.233995i
$809$			22.5160i			0.791620i	0.918332	+	0.395810i	$0.129536\pi$
$809$			22.5160i			0.791620i	−0.918332	+	0.395810i	$0.870464\pi$
$810$		0			0
$811$	−32.6131	+	32.6131i	−1.14520	+	1.14520i	−0.157718	+	0.987484i	$0.550414\pi$
$811$	−32.6131	+	32.6131i	−1.14520	+	1.14520i	−0.987484	+	0.157718i	$0.949586\pi$
$812$	21.7507			0.763299
$813$		0			0
$814$	20.6984	−	20.6984i	0.725479	−	0.725479i
$815$	−15.5302	−	25.7509i	−0.544001	−	0.902014i
$816$		0			0
$817$			15.0486i			0.526484i
$818$	3.91373	+	3.91373i	0.136840	+	0.136840i
$819$		0			0
$820$	8.14875	+	2.01752i	0.284567	+	0.0704548i
$821$	−6.98285	+	6.98285i	−0.243703	+	0.243703i	−0.818380	−	0.574677i	$-0.805128\pi$
$821$	−6.98285	+	6.98285i	−0.243703	+	0.243703i	0.574677	+	0.818380i	$0.305128\pi$
$822$		0			0
$823$	−7.60792	−	7.60792i	−0.265195	−	0.265195i	0.561965	−	0.827161i	$-0.310045\pi$
$823$	−7.60792	−	7.60792i	−0.265195	−	0.265195i	−0.827161	+	0.561965i	$0.810045\pi$
$824$	−7.54915	−	7.54915i	−0.262987	−	0.262987i
$825$		0			0
$826$	−11.2521	−	11.2521i	−0.391512	−	0.391512i
$827$			25.4262i			0.884157i	0.896976	+	0.442079i	$0.145759\pi$
$827$			25.4262i			0.884157i	−0.896976	+	0.442079i	$0.854241\pi$
$828$		0			0
$829$	8.70961			0.302497			0.151249	−	0.988496i	$-0.451671\pi$
$829$	8.70961			0.302497			0.151249	+	0.988496i	$0.451671\pi$
$830$	19.7752	−	11.9263i	0.686406	−	0.413968i
$831$		0			0
$832$	−1.41217	+	3.31749i	−0.0489583	+	0.115013i
$833$	34.7624	−	34.7624i	1.20444	−	1.20444i
$834$		0			0
$835$	0.873937	−	0.527068i	0.0302438	−	0.0182399i
$836$			11.6817i			0.404019i
$837$		0			0
$838$			30.2004i			1.04326i
$839$	29.2217	−	29.2217i	1.00884	−	1.00884i	0.00888323	−	0.999961i	$-0.497172\pi$
$839$	29.2217	−	29.2217i	1.00884	−	1.00884i	0.999961	−	0.00888323i	$-0.00282766\pi$
$840$		0			0
$841$	2.72177			0.0938543
$842$	16.6746	−	16.6746i	0.574645	−	0.574645i
$843$		0			0
$844$	−5.75300			−0.198027
$845$	7.53458	−	28.0754i	0.259198	−	0.965824i
$846$		0			0
$847$	50.8631			1.74768
$848$	9.40073	−	9.40073i	0.322822	−	0.322822i
$849$		0			0
$850$	6.60151	+	21.3419i	0.226430	+	0.732021i
$851$	14.4921	−	14.4921i	0.496782	−	0.496782i
$852$		0			0
$853$	−25.2776			−0.865489			−0.432745	−	0.901517i	$-0.642455\pi$
$853$	−25.2776			−0.865489			−0.432745	+	0.901517i	$0.642455\pi$
$854$			36.6294i			1.25343i
$855$		0			0
$856$	3.29470	+	3.29470i	0.112611	+	0.112611i
$857$	−15.8319	+	15.8319i	−0.540808	+	0.540808i	−0.923766	−	0.382958i	$-0.874906\pi$
$857$	−15.8319	+	15.8319i	−0.540808	+	0.540808i	0.382958	+	0.923766i	$0.374906\pi$
$858$		0			0
$859$		−	32.9838i		−	1.12539i	−0.826664	−	0.562696i	$-0.809764\pi$
$859$		−	32.9838i		−	1.12539i	0.826664	−	0.562696i	$-0.190236\pi$
$860$	−3.31918	+	13.4061i	−0.113183	+	0.457146i
$861$		0			0
$862$	−0.949294	+	0.949294i	−0.0323331	+	0.0323331i
$863$			11.3846i			0.387535i	0.981047	+	0.193768i	$0.0620707\pi$
$863$			11.3846i			0.387535i	−0.981047	+	0.193768i	$0.937929\pi$
$864$		0			0
$865$	8.21393	−	33.1760i	0.279282	−	1.12802i
$866$	12.7434	+	12.7434i	0.433037	+	0.433037i
$867$		0			0
$868$	−31.6021	−	31.6021i	−1.07265	−	1.07265i
$869$	−14.9855	+	14.9855i	−0.508347	+	0.508347i
$870$		0			0
$871$	2.19435	−	5.15499i	0.0743527	−	0.174670i
$872$	−10.2873	−	10.2873i	−0.348373	−	0.348373i
$873$		0			0
$874$			8.17897i			0.276658i
$875$	2.71583	+	47.3606i	0.0918119	+	1.60108i
$876$		0			0
$877$	−27.4605			−0.927274			−0.463637	−	0.886025i	$-0.653456\pi$
$877$	−27.4605			−0.927274			−0.463637	+	0.886025i	$0.653456\pi$
$878$	−9.01553			−0.304260
$879$		0			0
$880$	−2.57655	+	10.4067i	−0.0868555	+	0.350809i
$881$		−	40.2705i		−	1.35675i	−0.734717	−	0.678374i	$-0.762685\pi$
$881$		−	40.2705i		−	1.35675i	0.734717	−	0.678374i	$-0.237315\pi$
$882$		0			0
$883$	−0.818356	−	0.818356i	−0.0275399	−	0.0275399i	0.693203	−	0.720743i	$-0.256199\pi$
$883$	−0.818356	−	0.818356i	−0.0275399	−	0.0275399i	−0.720743	+	0.693203i	$0.756199\pi$
$884$	−6.01947	−	14.9424i	−0.202457	−	0.502568i
$885$		0			0
$886$	−14.4156	+	14.4156i	−0.484300	+	0.484300i
$887$	−8.39474	−	8.39474i	−0.281868	−	0.281868i	0.551986	−	0.833854i	$-0.313870\pi$
$887$	−8.39474	−	8.39474i	−0.281868	−	0.281868i	−0.833854	+	0.551986i	$0.813870\pi$
$888$		0			0
$889$	−34.2832	−	34.2832i	−1.14982	−	1.14982i
$890$	20.3386	+	5.03557i	0.681753	+	0.168793i
$891$		0			0
$892$		−	8.52784i		−	0.285533i
$893$	−4.71068	+	4.71068i	−0.157637	+	0.157637i
$894$		0			0
$895$	−18.5156	−	30.7009i	−0.618908	−	1.02622i
$896$			4.24302i			0.141749i
$897$		0			0
$898$	10.2569	−	10.2569i	0.342276	−	0.342276i
$899$	38.1803	+	38.1803i	1.27339	+	1.27339i
$900$		0			0
$901$			59.3993i			1.97888i
$902$	−17.9999			−0.599332
$903$		0			0
$904$	−2.75960	+	2.75960i	−0.0917830	+	0.0917830i
$905$	8.19784	−	4.94408i	0.272505	−	0.164347i
$906$		0			0
$907$	−1.17966	+	1.17966i	−0.0391701	+	0.0391701i	−0.726421	−	0.687250i	$-0.758817\pi$
$907$	−1.17966	+	1.17966i	−0.0391701	+	0.0391701i	0.687250	+	0.726421i	$0.258817\pi$
$908$	−14.3219			−0.475289
$909$		0			0
$910$	−4.78202	−	33.8724i	−0.158522	−	1.12286i
$911$	−19.9767			−0.661858			−0.330929	−	0.943656i	$-0.607362\pi$
$911$	−19.9767			−0.661858			−0.330929	+	0.943656i	$0.607362\pi$
$912$		0			0
$913$	−35.0130	+	35.0130i	−1.15876	+	1.15876i
$914$	2.74265			0.0907187
$915$		0			0
$916$	−6.57430	+	6.57430i	−0.217221	+	0.217221i
$917$		−	88.9697i		−	2.93804i
$918$		0			0
$919$			32.3664i			1.06767i	0.845589	+	0.533834i	$0.179249\pi$
$919$			32.3664i			1.06767i	−0.845589	+	0.533834i	$0.820751\pi$
$920$	−1.80398	+	7.28628i	−0.0594756	+	0.240222i
$921$		0			0
$922$	−1.58645	+	1.58645i	−0.0522468	+	0.0522468i
$923$	−10.0568	−	24.9645i	−0.331024	−	0.821717i
$924$		0			0
$925$	−27.0001	−	14.2428i	−0.887759	−	0.468300i
$926$	−8.38165			−0.275438
$927$		0			0
$928$		−	5.12623i		−	0.168277i
$929$	−21.3629	−	21.3629i	−0.700895	−	0.700895i	0.263708	−	0.964603i	$-0.415055\pi$
$929$	−21.3629	−	21.3629i	−0.700895	−	0.700895i	−0.964603	+	0.263708i	$0.915055\pi$
$930$		0			0
$931$	−18.9567	−	18.9567i	−0.621282	−	0.621282i
$932$	−12.2743	−	12.2743i	−0.402060	−	0.402060i
$933$		0			0
$934$	−11.9372	+	11.9372i	−0.390597	+	0.390597i
$935$	−24.7376	−	41.0178i	−0.809008	−	1.34143i
$936$		0			0
$937$	29.7628	+	29.7628i	0.972308	+	0.972308i	0.999627	−	0.0273191i	$-0.00869704\pi$
$937$	29.7628	+	29.7628i	0.972308	+	0.972308i	−0.0273191	+	0.999627i	$0.508697\pi$
$938$		−	6.59315i		−	0.215274i
$939$		0			0
$940$	−5.23554	+	3.15753i	−0.170764	+	0.102987i
$941$	−41.7949	+	41.7949i	−1.36247	+	1.36247i	−0.491720	+	0.870753i	$0.663632\pi$
$941$	−41.7949	+	41.7949i	−1.36247	+	1.36247i	−0.870753	+	0.491720i	$0.836368\pi$
$942$		0			0
$943$	−12.6027			−0.410401
$944$	−2.65192	+	2.65192i	−0.0863125	+	0.0863125i
$945$		0			0
$946$		−	29.6131i		−	0.962804i
$947$		−	27.6501i		−	0.898509i	−0.893404	−	0.449254i	$-0.851690\pi$
$947$		−	27.6501i		−	0.898509i	0.893404	−	0.449254i	$-0.148310\pi$
$948$		0			0
$949$	12.7880	−	30.0418i	0.415117	−	0.975199i
$950$	11.6382	−	3.59996i	0.377594	−	0.116798i
$951$		0			0
$952$	−13.4049	−	13.4049i	−0.434457	−	0.434457i
$953$	24.8697	+	24.8697i	0.805609	+	0.805609i	0.983966	−	0.178357i	$-0.0570783\pi$
$953$	24.8697	+	24.8697i	0.805609	+	0.805609i	−0.178357	+	0.983966i	$0.557078\pi$
$954$		0			0
$955$	5.71387	+	9.47424i	0.184896	+	0.306579i
$956$	−8.10072	−	8.10072i	−0.261996	−	0.261996i
$957$		0			0
$958$	9.99726	−	9.99726i	0.322997	−	0.322997i
$959$	−33.2933			−1.07510
$960$		0			0
$961$		−	79.9464i		−	2.57892i
$962$	20.2543	+	8.62172i	0.653024	+	0.277976i
$963$		0			0
$964$	−19.9744	−	19.9744i	−0.643331	−	0.643331i
$965$	7.28742	+	12.0834i	0.234590	+	0.388977i
$966$		0			0
$967$	44.2904			1.42428			0.712141	−	0.702037i	$-0.247726\pi$
$967$	44.2904			1.42428			0.712141	+	0.702037i	$0.247726\pi$
$968$		−	11.9875i		−	0.385292i
$969$		0			0
$970$	−7.10848	−	11.7867i	−0.228240	−	0.378447i
$971$	−44.8986			−1.44087			−0.720433	−	0.693525i	$-0.756057\pi$
$971$	−44.8986			−1.44087			−0.720433	+	0.693525i	$0.756057\pi$
$972$		0			0
$973$	−85.4765			−2.74025
$974$	21.2763			0.681736
$975$		0			0
$976$	8.63287			0.276332
$977$	23.5480			0.753367			0.376684	−	0.926342i	$-0.377064\pi$
$977$	23.5480			0.753367			0.376684	+	0.926342i	$0.377064\pi$
$978$		0			0
$979$	−44.9264			−1.43585
$980$	−12.7065	−	21.0689i	−0.405895	−	0.673020i
$981$		0			0
$982$		−	6.15126i		−	0.196294i
$983$	30.2435			0.964619			0.482309	−	0.876001i	$-0.339798\pi$
$983$	30.2435			0.964619			0.482309	+	0.876001i	$0.339798\pi$
$984$		0			0
$985$	9.47746	+	15.7147i	0.301977	+	0.500712i
$986$	16.1953	+	16.1953i	0.515762	+	0.515762i
$987$		0			0
$988$	−8.14844	+	3.28256i	−0.259236	+	0.104432i
$989$		−	20.7337i		−	0.659294i
$990$		0			0
$991$	9.77356			0.310467			0.155234	−	0.987878i	$-0.450387\pi$
$991$	9.77356			0.310467			0.155234	+	0.987878i	$0.450387\pi$
$992$	−7.44803	+	7.44803i	−0.236475	+	0.236475i
$993$		0			0
$994$	−22.3958	−	22.3958i	−0.710353	−	0.710353i
$995$	−15.8114	−	26.2171i	−0.501255	−	0.831136i
$996$		0			0
$997$	11.8295	+	11.8295i	0.374644	+	0.374644i	0.869166	−	0.494521i	$-0.164657\pi$
$997$	11.8295	+	11.8295i	0.374644	+	0.374644i	−0.494521	+	0.869166i	$0.664657\pi$
$998$	0.842453	+	0.842453i	0.0266674	+	0.0266674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.m.i.577.7		16
3.2	odd	2		390.2.j.b.187.1	yes	16
5.3	odd	4		1170.2.w.i.343.3		16
13.8	odd	4		1170.2.w.i.307.3		16
15.2	even	4		1950.2.t.e.343.8		16
15.8	even	4		390.2.t.b.343.3	yes	16
15.14	odd	2		1950.2.j.e.1357.8		16
39.8	even	4		390.2.t.b.307.3	yes	16
65.8	even	4	inner	1170.2.m.i.73.7		16
195.8	odd	4		390.2.j.b.73.1	✓	16
195.47	odd	4		1950.2.j.e.1243.5		16
195.164	even	4		1950.2.t.e.307.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.b.73.1	✓	16	195.8	odd	4
390.2.j.b.187.1	yes	16	3.2	odd	2
390.2.t.b.307.3	yes	16	39.8	even	4
390.2.t.b.343.3	yes	16	15.8	even	4
1170.2.m.i.73.7		16	65.8	even	4	inner
1170.2.m.i.577.7		16	1.1	even	1	trivial
1170.2.w.i.307.3		16	13.8	odd	4
1170.2.w.i.343.3		16	5.3	odd	4
1950.2.j.e.1243.5		16	195.47	odd	4
1950.2.j.e.1357.8		16	15.14	odd	2
1950.2.t.e.307.8		16	195.164	even	4
1950.2.t.e.343.8		16	15.2	even	4

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.15480 + 1.91479i) q^{5} -4.24302i q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.15480 + 1.91479i) q^{5} -4.24302i q^{7} -1.00000 q^{8} +(-1.15480 - 1.91479i) q^{10} +(3.39024 + 3.39024i) q^{11} +(-1.41217 + 3.31749i) q^{13} +4.24302i q^{14} +1.00000 q^{16} +(-3.15929 + 3.15929i) q^{17} +(1.72284 + 1.72284i) q^{19} +(1.15480 + 1.91479i) q^{20} +(-3.39024 - 3.39024i) q^{22} +(-2.37369 - 2.37369i) q^{23} +(-2.33286 + 4.42242i) q^{25} +(1.41217 - 3.31749i) q^{26} -4.24302i q^{28} +5.12623i q^{29} +(7.44803 - 7.44803i) q^{31} -1.00000 q^{32} +(3.15929 - 3.15929i) q^{34} +(8.12450 - 4.89985i) q^{35} +6.10529i q^{37} +(-1.72284 - 1.72284i) q^{38} +(-1.15480 - 1.91479i) q^{40} +(2.65467 - 2.65467i) q^{41} +(4.36740 + 4.36740i) q^{43} +(3.39024 + 3.39024i) q^{44} +(2.37369 + 2.37369i) q^{46} +2.73426i q^{47} -11.0032 q^{49} +(2.33286 - 4.42242i) q^{50} +(-1.41217 + 3.31749i) q^{52} +(9.40073 - 9.40073i) q^{53} +(-2.57655 + 10.4067i) q^{55} +4.24302i q^{56} -5.12623i q^{58} +(-2.65192 + 2.65192i) q^{59} +8.63287 q^{61} +(-7.44803 + 7.44803i) q^{62} +1.00000 q^{64} +(-7.98309 + 1.12703i) q^{65} -1.55388 q^{67} +(-3.15929 + 3.15929i) q^{68} +(-8.12450 + 4.89985i) q^{70} +(-5.27828 + 5.27828i) q^{71} -9.05558 q^{73} -6.10529i q^{74} +(1.72284 + 1.72284i) q^{76} +(14.3849 - 14.3849i) q^{77} +4.42018i q^{79} +(1.15480 + 1.91479i) q^{80} +(-2.65467 + 2.65467i) q^{82} +10.3276i q^{83} +(-9.69775 - 2.40103i) q^{85} +(-4.36740 - 4.36740i) q^{86} +(-3.39024 - 3.39024i) q^{88} +(-6.62584 + 6.62584i) q^{89} +(14.0762 + 5.99188i) q^{91} +(-2.37369 - 2.37369i) q^{92} -2.73426i q^{94} +(-1.30934 + 5.28841i) q^{95} +6.15558 q^{97} +11.0032 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8}+O(q^{10}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8	\( 16 q - 16 q^{2} + 16 q^{4} - 16 q^{8} - 4 q^{11} + 4 q^{13} + 16 q^{16} - 4 q^{17} + 4 q^{19} + 4 q^{22} - 16 q^{23} - 16 q^{25} - 4 q^{26} + 12 q^{31} - 16 q^{32} + 4 q^{34} + 12 q^{35} - 4 q^{38} - 4 q^{41} - 16 q^{43} - 4 q^{44} + 16 q^{46} - 80 q^{49} + 16 q^{50} + 4 q^{52} + 44 q^{53} - 20 q^{55} - 12 q^{59} - 32 q^{61} - 12 q^{62} + 16 q^{64} + 44 q^{65} - 32 q^{67} - 4 q^{68} - 12 q^{70} - 16 q^{71} + 4 q^{76} + 32 q^{77} + 4 q^{82} - 64 q^{85} + 16 q^{86} + 4 q^{88} - 4 q^{89} + 76 q^{91} - 16 q^{92} - 40 q^{95} - 8 q^{97} + 80 q^{98}+O(q^{100}) \) 16 * q - 16 * q^2 + 16 * q^4 - 16 * q^8 - 4 * q^11 + 4 * q^13 + 16 * q^16 - 4 * q^17 + 4 * q^19 + 4 * q^22 - 16 * q^23 - 16 * q^25 - 4 * q^26 + 12 * q^31 - 16 * q^32 + 4 * q^34 + 12 * q^35 - 4 * q^38 - 4 * q^41 - 16 * q^43 - 4 * q^44 + 16 * q^46 - 80 * q^49 + 16 * q^50 + 4 * q^52 + 44 * q^53 - 20 * q^55 - 12 * q^59 - 32 * q^61 - 12 * q^62 + 16 * q^64 + 44 * q^65 - 32 * q^67 - 4 * q^68 - 12 * q^70 - 16 * q^71 + 4 * q^76 + 32 * q^77 + 4 * q^82 - 64 * q^85 + 16 * q^86 + 4 * q^88 - 4 * q^89 + 76 * q^91 - 16 * q^92 - 40 * q^95 - 8 * q^97 + 80 * q^98

Introduction

L-functions

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Database

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