LMFDB - Embedded newform 3150.2.m.l.2843.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1457,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("3150.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2843.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.2843
Dual form			3150.2.m.l.1457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.41421i q^{11} +(-1.43916 - 1.43916i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.54258 - 1.54258i) q^{17} -2.04989i q^{19} +(2.41421 - 2.41421i) q^{22} +(-1.15660 + 1.15660i) q^{23} +2.03528i q^{26} +(-0.707107 - 0.707107i) q^{28} +8.04524 q^{29} -6.37429 q^{31} +(0.707107 + 0.707107i) q^{32} +2.18154i q^{34} +(0.0498881 - 0.0498881i) q^{37} +(-1.44949 + 1.44949i) q^{38} +7.94887i q^{41} +(-4.65357 - 4.65357i) q^{43} -3.41421 q^{44} +1.63567 q^{46} +(-1.39960 - 1.39960i) q^{47} -1.00000i q^{49} +(1.43916 - 1.43916i) q^{52} +(2.97506 - 2.97506i) q^{53} +1.00000i q^{56} +(-5.68885 - 5.68885i) q^{58} -4.25725 q^{59} -6.88953 q^{61} +(4.50731 + 4.50731i) q^{62} -1.00000i q^{64} +(5.84304 - 5.84304i) q^{67} +(1.54258 - 1.54258i) q^{68} -2.92820i q^{71} +(-5.97469 - 5.97469i) q^{73} -0.0705524 q^{74} +2.04989 q^{76} +(-2.41421 - 2.41421i) q^{77} -11.6410i q^{79} +(5.62070 - 5.62070i) q^{82} +(-1.52797 + 1.52797i) q^{83} +6.58114i q^{86} +(2.41421 + 2.41421i) q^{88} +5.72741 q^{89} +2.03528 q^{91} +(-1.15660 - 1.15660i) q^{92} +1.97934i q^{94} +(9.64564 - 9.64564i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{22} + 16 q^{23} - 16 q^{37} + 8 q^{38} - 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{47} - 8 q^{52} + 32 q^{53} - 8 q^{58} + 8 q^{59} - 32 q^{61} + 32 q^{62} + 16 q^{67} + 16 q^{74} - 8 q^{77} - 8 q^{82} - 8 q^{83} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 16 q^{92} + 16 q^{97}+O(q^{100}) $ 8 * q + 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^22 + 16 * q^23 - 16 * q^37 + 8 * q^38 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^47 - 8 * q^52 + 32 * q^53 - 8 * q^58 + 8 * q^59 - 32 * q^61 + 32 * q^62 + 16 * q^67 + 16 * q^74 - 8 * q^77 - 8 * q^82 - 8 * q^83 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 16 * q^92 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$			3.41421i			1.02942i	0.857363	+	0.514712i	$0.172101\pi$
$11$			3.41421i			1.02942i	−0.857363	+	0.514712i	$0.827899\pi$
$12$		0			0
$13$	−1.43916	−	1.43916i	−0.399150	−	0.399150i	0.478783	−	0.877933i	$-0.341078\pi$
$13$	−1.43916	−	1.43916i	−0.399150	−	0.399150i	−0.877933	+	0.478783i	$0.841078\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.54258	−	1.54258i	−0.374131	−	0.374131i	0.494848	−	0.868979i	$-0.335224\pi$
$17$	−1.54258	−	1.54258i	−0.374131	−	0.374131i	−0.868979	+	0.494848i	$0.835224\pi$
$18$		0			0
$19$		−	2.04989i		−	0.470277i	−0.971962	−	0.235138i	$-0.924446\pi$
$19$		−	2.04989i		−	0.470277i	0.971962	−	0.235138i	$-0.0755543\pi$
$20$		0			0
$21$		0			0
$22$	2.41421	−	2.41421i	0.514712	−	0.514712i
$23$	−1.15660	+	1.15660i	−0.241167	+	0.241167i	−0.817333	−	0.576166i	$-0.804548\pi$
$23$	−1.15660	+	1.15660i	−0.241167	+	0.241167i	0.576166	+	0.817333i	$0.304548\pi$
$24$		0			0
$25$		0			0
$26$			2.03528i			0.399150i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	8.04524			1.49396			0.746982	−	0.664844i	$-0.231502\pi$
$29$	8.04524			1.49396			0.746982	+	0.664844i	$0.231502\pi$
$30$		0			0
$31$	−6.37429			−1.14486			−0.572428	−	0.819955i	$-0.693999\pi$
$31$	−6.37429			−1.14486			−0.572428	+	0.819955i	$0.693999\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			2.18154i			0.374131i
$35$		0			0
$36$		0			0
$37$	0.0498881	−	0.0498881i	0.00820155	−	0.00820155i	−0.702994	−	0.711196i	$-0.748154\pi$
$37$	0.0498881	−	0.0498881i	0.00820155	−	0.00820155i	0.711196	+	0.702994i	$0.248154\pi$
$38$	−1.44949	+	1.44949i	−0.235138	+	0.235138i
$39$		0			0
$40$		0			0
$41$			7.94887i			1.24140i	0.784046	+	0.620702i	$0.213152\pi$
$41$			7.94887i			1.24140i	−0.784046	+	0.620702i	$0.786848\pi$
$42$		0			0
$43$	−4.65357	−	4.65357i	−0.709663	−	0.709663i	0.256801	−	0.966464i	$-0.417331\pi$
$43$	−4.65357	−	4.65357i	−0.709663	−	0.709663i	−0.966464	+	0.256801i	$0.917331\pi$
$44$	−3.41421			−0.514712
$45$		0			0
$46$	1.63567			0.241167
$47$	−1.39960	−	1.39960i	−0.204153	−	0.204153i	0.597624	−	0.801777i	$-0.296112\pi$
$47$	−1.39960	−	1.39960i	−0.204153	−	0.204153i	−0.801777	+	0.597624i	$0.796112\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		0			0
$52$	1.43916	−	1.43916i	0.199575	−	0.199575i
$53$	2.97506	−	2.97506i	0.408655	−	0.408655i	−0.472614	−	0.881269i	$-0.656690\pi$
$53$	2.97506	−	2.97506i	0.408655	−	0.408655i	0.881269	+	0.472614i	$0.156690\pi$
$54$		0			0
$55$		0			0
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−5.68885	−	5.68885i	−0.746982	−	0.746982i
$59$	−4.25725			−0.554247			−0.277124	−	0.960834i	$-0.589381\pi$
$59$	−4.25725			−0.554247			−0.277124	+	0.960834i	$0.589381\pi$
$60$		0			0
$61$	−6.88953			−0.882114			−0.441057	−	0.897479i	$-0.645396\pi$
$61$	−6.88953			−0.882114			−0.441057	+	0.897479i	$0.645396\pi$
$62$	4.50731	+	4.50731i	0.572428	+	0.572428i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	5.84304	−	5.84304i	0.713841	−	0.713841i	−0.253496	−	0.967337i	$-0.581580\pi$
$67$	5.84304	−	5.84304i	0.713841	−	0.713841i	0.967337	+	0.253496i	$0.0815804\pi$
$68$	1.54258	−	1.54258i	0.187066	−	0.187066i
$69$		0			0
$70$		0			0
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$		0			0
$73$	−5.97469	−	5.97469i	−0.699285	−	0.699285i	0.264971	−	0.964256i	$-0.414637\pi$
$73$	−5.97469	−	5.97469i	−0.699285	−	0.699285i	−0.964256	+	0.264971i	$0.914637\pi$
$74$	−0.0705524			−0.00820155
$75$		0			0
$76$	2.04989			0.235138
$77$	−2.41421	−	2.41421i	−0.275125	−	0.275125i
$78$		0			0
$79$		−	11.6410i		−	1.30971i	−0.755753	−	0.654857i	$-0.772729\pi$
$79$		−	11.6410i		−	1.30971i	0.755753	−	0.654857i	$-0.227271\pi$
$80$		0			0
$81$		0			0
$82$	5.62070	−	5.62070i	0.620702	−	0.620702i
$83$	−1.52797	+	1.52797i	−0.167717	+	0.167717i	−0.785975	−	0.618258i	$-0.787839\pi$
$83$	−1.52797	+	1.52797i	−0.167717	+	0.167717i	0.618258	+	0.785975i	$0.287839\pi$
$84$		0			0
$85$		0			0
$86$			6.58114i			0.709663i
$87$		0			0
$88$	2.41421	+	2.41421i	0.257356	+	0.257356i
$89$	5.72741			0.607104			0.303552	−	0.952815i	$-0.401827\pi$
$89$	5.72741			0.607104			0.303552	+	0.952815i	$0.401827\pi$
$90$		0			0
$91$	2.03528			0.213355
$92$	−1.15660	−	1.15660i	−0.120584	−	0.120584i
$93$		0			0
$94$			1.97934i			0.204153i
$95$		0			0
$96$		0			0
$97$	9.64564	−	9.64564i	0.979367	−	0.979367i	−0.0204248	−	0.999791i	$-0.506502\pi$
$97$	9.64564	−	9.64564i	0.979367	−	0.979367i	0.999791	+	0.0204248i	$0.00650187\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$			16.7420i			1.66589i	0.553353	+	0.832947i	$0.313348\pi$
$101$			16.7420i			1.66589i	−0.553353	+	0.832947i	$0.686652\pi$
$102$		0			0
$103$	−8.65597	−	8.65597i	−0.852898	−	0.852898i	0.137591	−	0.990489i	$-0.456064\pi$
$103$	−8.65597	−	8.65597i	−0.852898	−	0.852898i	−0.990489	+	0.137591i	$0.956064\pi$
$104$	−2.03528			−0.199575
$105$		0			0
$106$	−4.20736			−0.408655
$107$	−10.9489	−	10.9489i	−1.05847	−	1.05847i	−0.998181	−	0.0602858i	$-0.980799\pi$
$107$	−10.9489	−	10.9489i	−1.05847	−	1.05847i	−0.0602858	−	0.998181i	$-0.519201\pi$
$108$		0			0
$109$		−	5.23659i		−	0.501574i	−0.968042	−	0.250787i	$-0.919311\pi$
$109$		−	5.23659i		−	0.501574i	0.968042	−	0.250787i	$-0.0806894\pi$
$110$		0			0
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−1.59575	+	1.59575i	−0.150116	+	0.150116i	−0.778170	−	0.628054i	$-0.783852\pi$
$113$	−1.59575	+	1.59575i	−0.150116	+	0.150116i	0.628054	+	0.778170i	$0.283852\pi$
$114$		0			0
$115$		0			0
$116$			8.04524i			0.746982i
$117$		0			0
$118$	3.01033	+	3.01033i	0.277124	+	0.277124i
$119$	2.18154			0.199981
$120$		0			0
$121$	−0.656854			−0.0597140
$122$	4.87163	+	4.87163i	0.441057	+	0.441057i
$123$		0			0
$124$		−	6.37429i		−	0.572428i
$125$		0			0
$126$		0			0
$127$	7.72084	−	7.72084i	0.685114	−	0.685114i	−0.276034	−	0.961148i	$-0.589020\pi$
$127$	7.72084	−	7.72084i	0.685114	−	0.685114i	0.961148	+	0.276034i	$0.0890203\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	7.38426i		−	0.645166i	−0.946541	−	0.322583i	$-0.895449\pi$
$131$		−	7.38426i		−	0.645166i	0.946541	−	0.322583i	$-0.104551\pi$
$132$		0			0
$133$	1.44949	+	1.44949i	0.125687	+	0.125687i
$134$	−8.26330			−0.713841
$135$		0			0
$136$	−2.18154			−0.187066
$137$	−12.2268	−	12.2268i	−1.04460	−	1.04460i	−0.998958	−	0.0456471i	$-0.985465\pi$
$137$	−12.2268	−	12.2268i	−1.04460	−	1.04460i	−0.0456471	−	0.998958i	$-0.514535\pi$
$138$		0			0
$139$			15.2621i			1.29451i	0.762273	+	0.647256i	$0.224083\pi$
$139$			15.2621i			1.29451i	−0.762273	+	0.647256i	$0.775917\pi$
$140$		0			0
$141$		0			0
$142$	−2.07055	+	2.07055i	−0.173757	+	0.173757i
$143$	4.91359	−	4.91359i	0.410895	−	0.410895i
$144$		0			0
$145$		0			0
$146$			8.44949i			0.699285i
$147$		0			0
$148$	0.0498881	+	0.0498881i	0.00410077	+	0.00410077i
$149$	6.01602			0.492852			0.246426	−	0.969162i	$-0.420744\pi$
$149$	6.01602			0.492852			0.246426	+	0.969162i	$0.420744\pi$
$150$		0			0
$151$	−5.12096			−0.416737			−0.208369	−	0.978050i	$-0.566815\pi$
$151$	−5.12096			−0.416737			−0.208369	+	0.978050i	$0.566815\pi$
$152$	−1.44949	−	1.44949i	−0.117569	−	0.117569i
$153$		0			0
$154$			3.41421i			0.275125i
$155$		0			0
$156$		0			0
$157$	−8.79920	+	8.79920i	−0.702253	+	0.702253i	−0.964894	−	0.262641i	$-0.915407\pi$
$157$	−8.79920	+	8.79920i	−0.702253	+	0.702253i	0.262641	+	0.964894i	$0.415407\pi$
$158$	−8.23143	+	8.23143i	−0.654857	+	0.654857i
$159$		0			0
$160$		0			0
$161$		−	1.63567i		−	0.128909i
$162$		0			0
$163$	−2.73998	−	2.73998i	−0.214612	−	0.214612i	0.591611	−	0.806223i	$-0.298492\pi$
$163$	−2.73998	−	2.73998i	−0.214612	−	0.214612i	−0.806223	+	0.591611i	$0.798492\pi$
$164$	−7.94887			−0.620702
$165$		0			0
$166$	2.16088			0.167717
$167$	−6.48477	−	6.48477i	−0.501806	−	0.501806i	0.410193	−	0.911999i	$-0.365461\pi$
$167$	−6.48477	−	6.48477i	−0.501806	−	0.501806i	−0.911999	+	0.410193i	$0.865461\pi$
$168$		0			0
$169$		−	8.85765i		−	0.681358i
$170$		0			0
$171$		0			0
$172$	4.65357	−	4.65357i	0.354831	−	0.354831i
$173$	1.11563	−	1.11563i	0.0848200	−	0.0848200i	−0.663424	−	0.748244i	$-0.730897\pi$
$173$	1.11563	−	1.11563i	0.0848200	−	0.0848200i	0.748244	+	0.663424i	$0.230897\pi$
$174$		0			0
$175$		0			0
$176$		−	3.41421i		−	0.257356i
$177$		0			0
$178$	−4.04989	−	4.04989i	−0.303552	−	0.303552i
$179$	−1.00124			−0.0748365			−0.0374183	−	0.999300i	$-0.511913\pi$
$179$	−1.00124			−0.0748365			−0.0374183	+	0.999300i	$0.511913\pi$
$180$		0			0
$181$	−23.0411			−1.71263			−0.856316	−	0.516452i	$-0.827253\pi$
$181$	−23.0411			−1.71263			−0.856316	+	0.516452i	$0.827253\pi$
$182$	−1.43916	−	1.43916i	−0.106677	−	0.106677i
$183$		0			0
$184$			1.63567i			0.120584i
$185$		0			0
$186$		0			0
$187$	5.26670	−	5.26670i	0.385140	−	0.385140i
$188$	1.39960	−	1.39960i	0.102076	−	0.102076i
$189$		0			0
$190$		0			0
$191$			3.59095i			0.259832i	0.991525	+	0.129916i	$0.0414707\pi$
$191$			3.59095i			0.259832i	−0.991525	+	0.129916i	$0.958529\pi$
$192$		0			0
$193$	4.98539	+	4.98539i	0.358856	+	0.358856i	0.863391	−	0.504535i	$-0.168336\pi$
$193$	4.98539	+	4.98539i	0.358856	+	0.358856i	−0.504535	+	0.863391i	$0.668336\pi$
$194$	−13.6410			−0.979367
$195$		0			0
$196$	1.00000			0.0714286
$197$	−10.0169	−	10.0169i	−0.713675	−	0.713675i	0.253627	−	0.967302i	$-0.418376\pi$
$197$	−10.0169	−	10.0169i	−0.713675	−	0.713675i	−0.967302	+	0.253627i	$0.918376\pi$
$198$		0			0
$199$		−	27.2820i		−	1.93397i	−0.254834	−	0.966985i	$-0.582021\pi$
$199$		−	27.2820i		−	1.93397i	0.254834	−	0.966985i	$-0.417979\pi$
$200$		0			0
$201$		0			0
$202$	11.8384	−	11.8384i	0.832947	−	0.832947i
$203$	−5.68885	+	5.68885i	−0.399279	+	0.399279i
$204$		0			0
$205$		0			0
$206$			12.2414i			0.852898i
$207$		0			0
$208$	1.43916	+	1.43916i	0.0997876	+	0.0997876i
$209$	6.99876			0.484114
$210$		0			0
$211$	−8.70193			−0.599066			−0.299533	−	0.954086i	$-0.596831\pi$
$211$	−8.70193			−0.599066			−0.299533	+	0.954086i	$0.596831\pi$
$212$	2.97506	+	2.97506i	0.204328	+	0.204328i
$213$		0			0
$214$			15.4840i			1.05847i
$215$		0			0
$216$		0			0
$217$	4.50731	−	4.50731i	0.305976	−	0.305976i
$218$	−3.70283	+	3.70283i	−0.250787	+	0.250787i
$219$		0			0
$220$		0			0
$221$			4.44004i			0.298669i
$222$		0			0
$223$	2.80813	+	2.80813i	0.188046	+	0.188046i	0.794851	−	0.606805i	$-0.207549\pi$
$223$	2.80813	+	2.80813i	0.188046	+	0.188046i	−0.606805	+	0.794851i	$0.707549\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	2.25674			0.150116
$227$	−2.88573	−	2.88573i	−0.191532	−	0.191532i	0.604826	−	0.796358i	$-0.293243\pi$
$227$	−2.88573	−	2.88573i	−0.191532	−	0.191532i	−0.796358	+	0.604826i	$0.793243\pi$
$228$		0			0
$229$		−	9.16228i		−	0.605461i	−0.953076	−	0.302730i	$-0.902102\pi$
$229$		−	9.16228i		−	0.605461i	0.953076	−	0.302730i	$-0.0978982\pi$
$230$		0			0
$231$		0			0
$232$	5.68885	−	5.68885i	0.373491	−	0.373491i
$233$	−4.67611	+	4.67611i	−0.306342	+	0.306342i	−0.843489	−	0.537147i	$-0.819502\pi$
$233$	−4.67611	+	4.67611i	−0.306342	+	0.306342i	0.537147	+	0.843489i	$0.319502\pi$
$234$		0			0
$235$		0			0
$236$		−	4.25725i		−	0.277124i
$237$		0			0
$238$	−1.54258	−	1.54258i	−0.0999907	−	0.0999907i
$239$	16.4853			1.06634			0.533172	−	0.846007i	$-0.321000\pi$
$239$	16.4853			1.06634			0.533172	+	0.846007i	$0.321000\pi$
$240$		0			0
$241$	−8.50419			−0.547803			−0.273901	−	0.961758i	$-0.588314\pi$
$241$	−8.50419			−0.547803			−0.273901	+	0.961758i	$0.588314\pi$
$242$	0.464466	+	0.464466i	0.0298570	+	0.0298570i
$243$		0			0
$244$		−	6.88953i		−	0.441057i
$245$		0			0
$246$		0			0
$247$	−2.95011	+	2.95011i	−0.187711	+	0.187711i
$248$	−4.50731	+	4.50731i	−0.286214	+	0.286214i
$249$		0			0
$250$		0			0
$251$		−	18.9250i		−	1.19453i	−0.802043	−	0.597267i	$-0.796253\pi$
$251$		−	18.9250i		−	1.19453i	0.802043	−	0.597267i	$-0.203747\pi$
$252$		0			0
$253$	−3.94887	−	3.94887i	−0.248263	−	0.248263i
$254$	−10.9189			−0.685114
$255$		0			0
$256$	1.00000			0.0625000
$257$	16.8697	+	16.8697i	1.05230	+	1.05230i	0.998555	+	0.0537457i	$0.0171160\pi$
$257$	16.8697	+	16.8697i	1.05230	+	1.05230i	0.0537457	+	0.998555i	$0.482884\pi$
$258$		0			0
$259$			0.0705524i			0.00438391i
$260$		0			0
$261$		0			0
$262$	−5.22146	+	5.22146i	−0.322583	+	0.322583i
$263$	−8.32817	+	8.32817i	−0.513537	+	0.513537i	−0.915608	−	0.402071i	$-0.868290\pi$
$263$	−8.32817	+	8.32817i	−0.513537	+	0.513537i	0.402071	+	0.915608i	$0.368290\pi$
$264$		0			0
$265$		0			0
$266$		−	2.04989i		−	0.125687i
$267$		0			0
$268$	5.84304	+	5.84304i	0.356920	+	0.356920i
$269$	−16.3218			−0.995155			−0.497577	−	0.867420i	$-0.665777\pi$
$269$	−16.3218			−0.995155			−0.497577	+	0.867420i	$0.665777\pi$
$270$		0			0
$271$	−27.3911			−1.66389			−0.831944	−	0.554859i	$-0.812772\pi$
$271$	−27.3911			−1.66389			−0.831944	+	0.554859i	$0.812772\pi$
$272$	1.54258	+	1.54258i	0.0935328	+	0.0935328i
$273$		0			0
$274$			17.2913i			1.04460i
$275$		0			0
$276$		0			0
$277$	0.564607	−	0.564607i	0.0339239	−	0.0339239i	−0.689941	−	0.723865i	$-0.742364\pi$
$277$	0.564607	−	0.564607i	0.0339239	−	0.0339239i	0.723865	+	0.689941i	$0.242364\pi$
$278$	10.7919	−	10.7919i	0.647256	−	0.647256i
$279$		0			0
$280$		0			0
$281$		−	6.14214i		−	0.366409i	−0.983075	−	0.183205i	$-0.941353\pi$
$281$		−	6.14214i		−	0.366409i	0.983075	−	0.183205i	$-0.0586471\pi$
$282$		0			0
$283$	10.9959	+	10.9959i	0.653637	+	0.653637i	0.953867	−	0.300230i	$-0.0970635\pi$
$283$	10.9959	+	10.9959i	0.653637	+	0.653637i	−0.300230	+	0.953867i	$0.597063\pi$
$284$	2.92820			0.173757
$285$		0			0
$286$	−6.94887			−0.410895
$287$	−5.62070	−	5.62070i	−0.331779	−	0.331779i
$288$		0			0
$289$		−	12.2409i		−	0.720052i
$290$		0			0
$291$		0			0
$292$	5.97469	−	5.97469i	0.349642	−	0.349642i
$293$	17.4135	−	17.4135i	1.01731	−	1.01731i	0.0174591	−	0.999848i	$-0.494442\pi$
$293$	17.4135	−	17.4135i	1.01731	−	1.01731i	0.999848	−	0.0174591i	$-0.00555767\pi$
$294$		0			0
$295$		0			0
$296$		−	0.0705524i		−	0.00410077i
$297$		0			0
$298$	−4.25397	−	4.25397i	−0.246426	−	0.246426i
$299$	3.32905			0.192524
$300$		0			0
$301$	6.58114			0.379331
$302$	3.62106	+	3.62106i	0.208369	+	0.208369i
$303$		0			0
$304$			2.04989i			0.117569i
$305$		0			0
$306$		0			0
$307$	−17.2979	+	17.2979i	−0.987241	+	0.987241i	−0.999920	−	0.0126790i	$-0.995964\pi$
$307$	−17.2979	+	17.2979i	−0.987241	+	0.987241i	0.0126790	+	0.999920i	$0.495964\pi$
$308$	2.41421	−	2.41421i	0.137563	−	0.137563i
$309$		0			0
$310$		0			0
$311$		−	12.3046i		−	0.697732i	−0.937173	−	0.348866i	$-0.886567\pi$
$311$		−	12.3046i		−	0.697732i	0.937173	−	0.348866i	$-0.113433\pi$
$312$		0			0
$313$	−16.8031	−	16.8031i	−0.949768	−	0.949768i	0.0490289	−	0.998797i	$-0.484387\pi$
$313$	−16.8031	−	16.8031i	−0.949768	−	0.949768i	−0.998797	+	0.0490289i	$0.984387\pi$
$314$	12.4440			0.702253
$315$		0			0
$316$	11.6410			0.654857
$317$	3.16781	+	3.16781i	0.177922	+	0.177922i	0.790449	−	0.612527i	$-0.209847\pi$
$317$	3.16781	+	3.16781i	0.177922	+	0.177922i	−0.612527	+	0.790449i	$0.709847\pi$
$318$		0			0
$319$			27.4682i			1.53792i
$320$		0			0
$321$		0			0
$322$	−1.15660	+	1.15660i	−0.0644546	+	0.0644546i
$323$	−3.16212	+	3.16212i	−0.175945	+	0.175945i
$324$		0			0
$325$		0			0
$326$			3.87492i			0.214612i
$327$		0			0
$328$	5.62070	+	5.62070i	0.310351	+	0.310351i
$329$	1.97934			0.109124
$330$		0			0
$331$	−13.4986			−0.741953			−0.370976	−	0.928642i	$-0.620977\pi$
$331$	−13.4986			−0.741953			−0.370976	+	0.928642i	$0.620977\pi$
$332$	−1.52797	−	1.52797i	−0.0838583	−	0.0838583i
$333$		0			0
$334$			9.17084i			0.501806i
$335$		0			0
$336$		0			0
$337$	18.1303	−	18.1303i	0.987620	−	0.987620i	−0.0123043	−	0.999924i	$-0.503917\pi$
$337$	18.1303	−	18.1303i	0.987620	−	0.987620i	0.999924	+	0.0123043i	$0.00391669\pi$
$338$	−6.26330	+	6.26330i	−0.340679	+	0.340679i
$339$		0			0
$340$		0			0
$341$		−	21.7632i		−	1.17854i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−6.58114			−0.354831
$345$		0			0
$346$	−1.57774			−0.0848200
$347$	−18.2259	−	18.2259i	−0.978417	−	0.978417i	0.0213548	−	0.999772i	$-0.493202\pi$
$347$	−18.2259	−	18.2259i	−0.978417	−	0.978417i	−0.999772	+	0.0213548i	$0.993202\pi$
$348$		0			0
$349$			0.538551i			0.0288280i	0.999896	+	0.0144140i	$0.00458827\pi$
$349$			0.538551i			0.0288280i	−0.999896	+	0.0144140i	$0.995412\pi$
$350$		0			0
$351$		0			0
$352$	−2.41421	+	2.41421i	−0.128678	+	0.128678i
$353$	−16.3830	+	16.3830i	−0.871980	+	0.871980i	−0.992688	−	0.120708i	$-0.961484\pi$
$353$	−16.3830	+	16.3830i	−0.871980	+	0.871980i	0.120708	+	0.992688i	$0.461484\pi$
$354$		0			0
$355$		0			0
$356$			5.72741i			0.303552i
$357$		0			0
$358$	0.707987	+	0.707987i	0.0374183	+	0.0374183i
$359$	−31.9223			−1.68480			−0.842398	−	0.538856i	$-0.818857\pi$
$359$	−31.9223			−1.68480			−0.842398	+	0.538856i	$0.818857\pi$
$360$		0			0
$361$	14.7980			0.778840
$362$	16.2925	+	16.2925i	0.856316	+	0.856316i
$363$		0			0
$364$			2.03528i			0.106677i
$365$		0			0
$366$		0			0
$367$	−24.5854	+	24.5854i	−1.28335	+	1.28335i	−0.344598	+	0.938750i	$0.611985\pi$
$367$	−24.5854	+	24.5854i	−1.28335	+	1.28335i	−0.938750	+	0.344598i	$0.888015\pi$
$368$	1.15660	−	1.15660i	0.0602918	−	0.0602918i
$369$		0			0
$370$		0			0
$371$			4.20736i			0.218435i
$372$		0			0
$373$	2.79796	+	2.79796i	0.144873	+	0.144873i	0.775823	−	0.630950i	$-0.217335\pi$
$373$	2.79796	+	2.79796i	0.144873	+	0.144873i	−0.630950	+	0.775823i	$0.717335\pi$
$374$	−7.44825			−0.385140
$375$		0			0
$376$	−1.97934			−0.102076
$377$	−11.5784	−	11.5784i	−0.596317	−	0.596317i
$378$		0			0
$379$			26.4390i			1.35808i	0.734102	+	0.679039i	$0.237603\pi$
$379$			26.4390i			1.35808i	−0.734102	+	0.679039i	$0.762397\pi$
$380$		0			0
$381$		0			0
$382$	2.53918	−	2.53918i	0.129916	−	0.129916i
$383$	−17.2280	+	17.2280i	−0.880311	+	0.880311i	−0.993566	−	0.113255i	$-0.963872\pi$
$383$	−17.2280	+	17.2280i	−0.880311	+	0.880311i	0.113255	+	0.993566i	$0.463872\pi$
$384$		0			0
$385$		0			0
$386$		−	7.05040i		−	0.358856i
$387$		0			0
$388$	9.64564	+	9.64564i	0.489683	+	0.489683i
$389$	32.8766			1.66691			0.833454	−	0.552589i	$-0.186360\pi$
$389$	32.8766			1.66691			0.833454	+	0.552589i	$0.186360\pi$
$390$		0			0
$391$	3.56829			0.180456
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$			14.1660i			0.713675i
$395$		0			0
$396$		0			0
$397$	−5.39783	+	5.39783i	−0.270909	+	0.270909i	−0.829466	−	0.558557i	$-0.811355\pi$
$397$	−5.39783	+	5.39783i	−0.270909	+	0.270909i	0.558557	+	0.829466i	$0.311355\pi$
$398$	−19.2913	+	19.2913i	−0.966985	+	0.966985i
$399$		0			0
$400$		0			0
$401$			14.4760i			0.722897i	0.932392	+	0.361448i	$0.117718\pi$
$401$			14.4760i			0.722897i	−0.932392	+	0.361448i	$0.882282\pi$
$402$		0			0
$403$	9.17361	+	9.17361i	0.456970	+	0.456970i
$404$	−16.7420			−0.832947
$405$		0			0
$406$	8.04524			0.399279
$407$	0.170328	+	0.170328i	0.00844287	+	0.00844287i
$408$		0			0
$409$		−	16.5156i		−	0.816642i	−0.912838	−	0.408321i	$-0.866114\pi$
$409$		−	16.5156i		−	0.816642i	0.912838	−	0.408321i	$-0.133886\pi$
$410$		0			0
$411$		0			0
$412$	8.65597	−	8.65597i	0.426449	−	0.426449i
$413$	3.01033	−	3.01033i	0.148129	−	0.148129i
$414$		0			0
$415$		0			0
$416$		−	2.03528i		−	0.0997876i
$417$		0			0
$418$	−4.94887	−	4.94887i	−0.242057	−	0.242057i
$419$	12.0421			0.588294			0.294147	−	0.955760i	$-0.404964\pi$
$419$	12.0421			0.588294			0.294147	+	0.955760i	$0.404964\pi$
$420$		0			0
$421$	32.4894			1.58343			0.791717	−	0.610888i	$-0.209187\pi$
$421$	32.4894			1.58343			0.791717	+	0.610888i	$0.209187\pi$
$422$	6.15320	+	6.15320i	0.299533	+	0.299533i
$423$		0			0
$424$		−	4.20736i		−	0.204328i
$425$		0			0
$426$		0			0
$427$	4.87163	−	4.87163i	0.235755	−	0.235755i
$428$	10.9489	−	10.9489i	0.529233	−	0.529233i
$429$		0			0
$430$		0			0
$431$		−	8.50883i		−	0.409856i	−0.978777	−	0.204928i	$-0.934304\pi$
$431$		−	8.50883i		−	0.409856i	0.978777	−	0.204928i	$-0.0656960\pi$
$432$		0			0
$433$	−3.55532	−	3.55532i	−0.170858	−	0.170858i	0.616498	−	0.787356i	$-0.288551\pi$
$433$	−3.55532	−	3.55532i	−0.170858	−	0.170858i	−0.787356	+	0.616498i	$0.788551\pi$
$434$	−6.37429			−0.305976
$435$		0			0
$436$	5.23659			0.250787
$437$	2.37089	+	2.37089i	0.113415	+	0.113415i
$438$		0			0
$439$		−	13.2309i		−	0.631477i	−0.948846	−	0.315739i	$-0.897748\pi$
$439$		−	13.2309i		−	0.631477i	0.948846	−	0.315739i	$-0.102252\pi$
$440$		0			0
$441$		0			0
$442$	3.13958	−	3.13958i	0.149335	−	0.149335i
$443$	−23.9223	+	23.9223i	−1.13658	+	1.13658i	−0.147525	+	0.989058i	$0.547131\pi$
$443$	−23.9223	+	23.9223i	−1.13658	+	1.13658i	−0.989058	+	0.147525i	$0.952869\pi$
$444$		0			0
$445$		0			0
$446$		−	3.97129i		−	0.188046i
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	4.09905			0.193446			0.0967230	−	0.995311i	$-0.469164\pi$
$449$	4.09905			0.193446			0.0967230	+	0.995311i	$0.469164\pi$
$450$		0			0
$451$	−27.1391			−1.27793
$452$	−1.59575	−	1.59575i	−0.0750580	−	0.0750580i
$453$		0			0
$454$			4.08104i			0.191532i
$455$		0			0
$456$		0			0
$457$	−23.4150	+	23.4150i	−1.09531	+	1.09531i	−0.100356	+	0.994952i	$0.531998\pi$
$457$	−23.4150	+	23.4150i	−1.09531	+	1.09531i	−0.994952	+	0.100356i	$0.968002\pi$
$458$	−6.47871	+	6.47871i	−0.302730	+	0.302730i
$459$		0			0
$460$		0			0
$461$		−	19.4974i		−	0.908085i	−0.890980	−	0.454042i	$-0.849981\pi$
$461$		−	19.4974i		−	0.908085i	0.890980	−	0.454042i	$-0.150019\pi$
$462$		0			0
$463$	9.62033	+	9.62033i	0.447095	+	0.447095i	0.894388	−	0.447293i	$-0.147612\pi$
$463$	9.62033	+	9.62033i	0.447095	+	0.447095i	−0.447293	+	0.894388i	$0.647612\pi$
$464$	−8.04524			−0.373491
$465$		0			0
$466$	6.61302			0.306342
$467$	14.8643	+	14.8643i	0.687839	+	0.687839i	0.961754	−	0.273915i	$-0.0883186\pi$
$467$	14.8643	+	14.8643i	0.687839	+	0.687839i	−0.273915	+	0.961754i	$0.588319\pi$
$468$		0			0
$469$			8.26330i			0.381564i
$470$		0			0
$471$		0			0
$472$	−3.01033	+	3.01033i	−0.138562	+	0.138562i
$473$	15.8883	−	15.8883i	0.730544	−	0.730544i
$474$		0			0
$475$		0			0
$476$			2.18154i			0.0999907i
$477$		0			0
$478$	−11.6569	−	11.6569i	−0.533172	−	0.533172i
$479$	−11.6065			−0.530313			−0.265157	−	0.964205i	$-0.585424\pi$
$479$	−11.6065			−0.530313			−0.265157	+	0.964205i	$0.585424\pi$
$480$		0			0
$481$	−0.143594			−0.00654730
$482$	6.01337	+	6.01337i	0.273901	+	0.273901i
$483$		0			0
$484$		−	0.656854i		−	0.0298570i
$485$		0			0
$486$		0			0
$487$	−26.5745	+	26.5745i	−1.20421	+	1.20421i	−0.231332	+	0.972875i	$0.574308\pi$
$487$	−26.5745	+	26.5745i	−1.20421	+	1.20421i	−0.972875	+	0.231332i	$0.925692\pi$
$488$	−4.87163	+	4.87163i	−0.220528	+	0.220528i
$489$		0			0
$490$		0			0
$491$		−	33.5029i		−	1.51197i	−0.654591	−	0.755983i	$-0.727159\pi$
$491$		−	33.5029i		−	1.51197i	0.654591	−	0.755983i	$-0.272841\pi$
$492$		0			0
$493$	−12.4104	−	12.4104i	−0.558939	−	0.558939i
$494$	4.17209			0.187711
$495$		0			0
$496$	6.37429			0.286214
$497$	2.07055	+	2.07055i	0.0928770	+	0.0928770i
$498$		0			0
$499$		−	6.58504i		−	0.294787i	−0.989078	−	0.147393i	$-0.952912\pi$
$499$		−	6.58504i		−	0.294787i	0.989078	−	0.147393i	$-0.0470883\pi$
$500$		0			0
$501$		0			0
$502$	−13.3820	+	13.3820i	−0.597267	+	0.597267i
$503$	26.4682	−	26.4682i	1.18016	−	1.18016i	0.200455	−	0.979703i	$-0.435758\pi$
$503$	26.4682	−	26.4682i	1.18016	−	1.18016i	0.979703	−	0.200455i	$-0.0642420\pi$
$504$		0			0
$505$		0			0
$506$			5.58454i			0.248263i
$507$		0			0
$508$	7.72084	+	7.72084i	0.342557	+	0.342557i
$509$	11.6050			0.514381			0.257191	−	0.966361i	$-0.417203\pi$
$509$	11.6050			0.514381			0.257191	+	0.966361i	$0.417203\pi$
$510$		0			0
$511$	8.44949			0.373783
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	23.8573i		−	1.05230i
$515$		0			0
$516$		0			0
$517$	4.77854	−	4.77854i	0.210160	−	0.210160i
$518$	0.0498881	−	0.0498881i	0.00219196	−	0.00219196i
$519$		0			0
$520$		0			0
$521$			27.9474i			1.22440i	0.790704	+	0.612199i	$0.209715\pi$
$521$			27.9474i			1.22440i	−0.790704	+	0.612199i	$0.790285\pi$
$522$		0			0
$523$	21.4247	+	21.4247i	0.936837	+	0.936837i	0.998120	−	0.0612838i	$-0.0195195\pi$
$523$	21.4247	+	21.4247i	0.936837	+	0.936837i	−0.0612838	+	0.998120i	$0.519519\pi$
$524$	7.38426			0.322583
$525$		0			0
$526$	11.7778			0.513537
$527$	9.83287	+	9.83287i	0.428327	+	0.428327i
$528$		0			0
$529$			20.3246i			0.883677i
$530$		0			0
$531$		0			0
$532$	−1.44949	+	1.44949i	−0.0628434	+	0.0628434i
$533$	11.4397	−	11.4397i	0.495507	−	0.495507i
$534$		0			0
$535$		0			0
$536$		−	8.26330i		−	0.356920i
$537$		0			0
$538$	11.5412	+	11.5412i	0.497577	+	0.497577i
$539$	3.41421			0.147061
$540$		0			0
$541$	32.4705			1.39601			0.698007	−	0.716091i	$-0.254070\pi$
$541$	32.4705			1.39601			0.698007	+	0.716091i	$0.254070\pi$
$542$	19.3684	+	19.3684i	0.831944	+	0.831944i
$543$		0			0
$544$		−	2.18154i		−	0.0935328i
$545$		0			0
$546$		0			0
$547$	6.60441	−	6.60441i	0.282384	−	0.282384i	−0.551675	−	0.834059i	$-0.686011\pi$
$547$	6.60441	−	6.60441i	0.282384	−	0.282384i	0.834059	+	0.551675i	$0.186011\pi$
$548$	12.2268	−	12.2268i	0.522302	−	0.522302i
$549$		0			0
$550$		0			0
$551$		−	16.4918i		−	0.702576i
$552$		0			0
$553$	8.23143	+	8.23143i	0.350036	+	0.350036i
$554$	−0.798474			−0.0339239
$555$		0			0
$556$	−15.2621			−0.647256
$557$	−25.2207	−	25.2207i	−1.06864	−	1.06864i	−0.997464	−	0.0711727i	$-0.977326\pi$
$557$	−25.2207	−	25.2207i	−1.06864	−	1.06864i	−0.0711727	−	0.997464i	$-0.522674\pi$
$558$		0			0
$559$			13.3944i			0.566525i
$560$		0			0
$561$		0			0
$562$	−4.34315	+	4.34315i	−0.183205	+	0.183205i
$563$	−0.0225400	+	0.0225400i	−0.000949948	+	0.000949948i	−0.707582	−	0.706632i	$-0.750214\pi$
$563$	−0.0225400	+	0.0225400i	−0.000949948	+	0.000949948i	0.706632	+	0.707582i	$0.250214\pi$
$564$		0			0
$565$		0			0
$566$		−	15.5505i		−	0.653637i
$567$		0			0
$568$	−2.07055	−	2.07055i	−0.0868784	−	0.0868784i
$569$	16.4767			0.690740			0.345370	−	0.938467i	$-0.387753\pi$
$569$	16.4767			0.690740			0.345370	+	0.938467i	$0.387753\pi$
$570$		0			0
$571$	28.9560			1.21177			0.605884	−	0.795553i	$-0.292819\pi$
$571$	28.9560			1.21177			0.605884	+	0.795553i	$0.292819\pi$
$572$	4.91359	+	4.91359i	0.205448	+	0.205448i
$573$		0			0
$574$			7.94887i			0.331779i
$575$		0			0
$576$		0			0
$577$	−30.3424	+	30.3424i	−1.26317	+	1.26317i	−0.313624	+	0.949547i	$0.601543\pi$
$577$	−30.3424	+	30.3424i	−1.26317	+	1.26317i	−0.949547	+	0.313624i	$0.898457\pi$
$578$	−8.65561	+	8.65561i	−0.360026	+	0.360026i
$579$		0			0
$580$		0			0
$581$		−	2.16088i		−	0.0896483i
$582$		0			0
$583$	10.1575	+	10.1575i	0.420680	+	0.420680i
$584$	−8.44949			−0.349642
$585$		0			0
$586$	−24.6264			−1.01731
$587$	−5.98778	−	5.98778i	−0.247142	−	0.247142i	0.572655	−	0.819797i	$-0.305914\pi$
$587$	−5.98778	−	5.98778i	−0.247142	−	0.247142i	−0.819797	+	0.572655i	$0.805914\pi$
$588$		0			0
$589$			13.0666i			0.538399i
$590$		0			0
$591$		0			0
$592$	−0.0498881	+	0.0498881i	−0.00205039	+	0.00205039i
$593$	33.1306	−	33.1306i	1.36051	−	1.36051i	0.487243	−	0.873266i	$-0.338003\pi$
$593$	33.1306	−	33.1306i	1.36051	−	1.36051i	0.873266	−	0.487243i	$-0.161997\pi$
$594$		0			0
$595$		0			0
$596$			6.01602i			0.246426i
$597$		0			0
$598$	−2.35399	−	2.35399i	−0.0962619	−	0.0962619i
$599$	0.303973			0.0124200			0.00620999	−	0.999981i	$-0.498023\pi$
$599$	0.303973			0.0124200			0.00620999	+	0.999981i	$0.498023\pi$
$600$		0			0
$601$	17.2813			0.704918			0.352459	−	0.935827i	$-0.385346\pi$
$601$	17.2813			0.704918			0.352459	+	0.935827i	$0.385346\pi$
$602$	−4.65357	−	4.65357i	−0.189665	−	0.189665i
$603$		0			0
$604$		−	5.12096i		−	0.208369i
$605$		0			0
$606$		0			0
$607$	16.4243	−	16.4243i	0.666644	−	0.666644i	−0.290294	−	0.956938i	$-0.593753\pi$
$607$	16.4243	−	16.4243i	0.666644	−	0.666644i	0.956938	+	0.290294i	$0.0937531\pi$
$608$	1.44949	−	1.44949i	0.0587846	−	0.0587846i
$609$		0			0
$610$		0			0
$611$			4.02849i			0.162975i
$612$		0			0
$613$	−14.6330	−	14.6330i	−0.591019	−	0.591019i	0.346887	−	0.937907i	$-0.387239\pi$
$613$	−14.6330	−	14.6330i	−0.591019	−	0.591019i	−0.937907	+	0.346887i	$0.887239\pi$
$614$	24.4629			0.987241
$615$		0			0
$616$	−3.41421			−0.137563
$617$	32.8831	+	32.8831i	1.32382	+	1.32382i	0.910653	+	0.413171i	$0.135579\pi$
$617$	32.8831	+	32.8831i	1.32382	+	1.32382i	0.413171	+	0.910653i	$0.364421\pi$
$618$		0			0
$619$		−	28.1001i		−	1.12944i	−0.825283	−	0.564719i	$-0.808984\pi$
$619$		−	28.1001i		−	1.12944i	0.825283	−	0.564719i	$-0.191016\pi$
$620$		0			0
$621$		0			0
$622$	−8.70069	+	8.70069i	−0.348866	+	0.348866i
$623$	−4.04989	+	4.04989i	−0.162255	+	0.162255i
$624$		0			0
$625$		0			0
$626$			23.7632i			0.949768i
$627$		0			0
$628$	−8.79920	−	8.79920i	−0.351126	−	0.351126i
$629$	−0.153913			−0.00613691
$630$		0			0
$631$	−16.9867			−0.676228			−0.338114	−	0.941105i	$-0.609789\pi$
$631$	−16.9867			−0.676228			−0.338114	+	0.941105i	$0.609789\pi$
$632$	−8.23143	−	8.23143i	−0.327429	−	0.327429i
$633$		0			0
$634$		−	4.47996i		−	0.177922i
$635$		0			0
$636$		0			0
$637$	−1.43916	+	1.43916i	−0.0570215	+	0.0570215i
$638$	19.4229	−	19.4229i	0.768961	−	0.768961i
$639$		0			0
$640$		0			0
$641$		−	12.1607i		−	0.480319i	−0.970733	−	0.240160i	$-0.922800\pi$
$641$		−	12.1607i		−	0.480319i	0.970733	−	0.240160i	$-0.0771998\pi$
$642$		0			0
$643$	2.93285	+	2.93285i	0.115660	+	0.115660i	0.762568	−	0.646908i	$-0.223938\pi$
$643$	2.93285	+	2.93285i	0.115660	+	0.115660i	−0.646908	+	0.762568i	$0.723938\pi$
$644$	1.63567			0.0644546
$645$		0			0
$646$	4.47191			0.175945
$647$	29.4705	+	29.4705i	1.15860	+	1.15860i	0.984776	+	0.173827i	$0.0556133\pi$
$647$	29.4705	+	29.4705i	1.15860	+	1.15860i	0.173827	+	0.984776i	$0.444387\pi$
$648$		0			0
$649$		−	14.5352i		−	0.570555i
$650$		0			0
$651$		0			0
$652$	2.73998	−	2.73998i	0.107306	−	0.107306i
$653$	−7.46337	+	7.46337i	−0.292064	+	0.292064i	−0.837895	−	0.545831i	$-0.816214\pi$
$653$	−7.46337	+	7.46337i	−0.292064	+	0.292064i	0.545831	+	0.837895i	$0.316214\pi$
$654$		0			0
$655$		0			0
$656$		−	7.94887i		−	0.310351i
$657$		0			0
$658$	−1.39960	−	1.39960i	−0.0545622	−	0.0545622i
$659$	24.7639			0.964666			0.482333	−	0.875988i	$-0.339789\pi$
$659$	24.7639			0.964666			0.482333	+	0.875988i	$0.339789\pi$
$660$		0			0
$661$	10.3827			0.403840			0.201920	−	0.979402i	$-0.435282\pi$
$661$	10.3827			0.403840			0.201920	+	0.979402i	$0.435282\pi$
$662$	9.54499	+	9.54499i	0.370976	+	0.370976i
$663$		0			0
$664$			2.16088i			0.0838583i
$665$		0			0
$666$		0			0
$667$	−9.30510	+	9.30510i	−0.360295	+	0.360295i
$668$	6.48477	−	6.48477i	0.250903	−	0.250903i
$669$		0			0
$670$		0			0
$671$		−	23.5223i		−	0.908069i
$672$		0			0
$673$	11.8380	+	11.8380i	0.456321	+	0.456321i	0.897446	−	0.441125i	$-0.145420\pi$
$673$	11.8380	+	11.8380i	0.456321	+	0.456321i	−0.441125	+	0.897446i	$0.645420\pi$
$674$	−25.6401			−0.987620
$675$		0			0
$676$	8.85765			0.340679
$677$	12.7408	+	12.7408i	0.489668	+	0.489668i	0.908201	−	0.418534i	$-0.137456\pi$
$677$	12.7408	+	12.7408i	0.489668	+	0.489668i	−0.418534	+	0.908201i	$0.637456\pi$
$678$		0			0
$679$			13.6410i			0.523493i
$680$		0			0
$681$		0			0
$682$	−15.3889	+	15.3889i	−0.589272	+	0.589272i
$683$	5.61177	−	5.61177i	0.214729	−	0.214729i	−0.591544	−	0.806273i	$-0.701481\pi$
$683$	5.61177	−	5.61177i	0.214729	−	0.214729i	0.806273	+	0.591544i	$0.201481\pi$
$684$		0			0
$685$		0			0
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	4.65357	+	4.65357i	0.177416	+	0.177416i
$689$	−8.56315			−0.326230
$690$		0			0
$691$	31.6347			1.20344			0.601721	−	0.798706i	$-0.294482\pi$
$691$	31.6347			1.20344			0.601721	+	0.798706i	$0.294482\pi$
$692$	1.11563	+	1.11563i	0.0424100	+	0.0424100i
$693$		0			0
$694$			25.7753i			0.978417i
$695$		0			0
$696$		0			0
$697$	12.2618	−	12.2618i	0.464448	−	0.464448i
$698$	0.380813	−	0.380813i	0.0144140	−	0.0144140i
$699$		0			0
$700$		0			0
$701$		−	32.7205i		−	1.23583i	−0.786243	−	0.617917i	$-0.787977\pi$
$701$		−	32.7205i		−	1.23583i	0.786243	−	0.617917i	$-0.212023\pi$
$702$		0			0
$703$	−0.102265	−	0.102265i	−0.00385699	−	0.00385699i
$704$	3.41421			0.128678
$705$		0			0
$706$	23.1691			0.871980
$707$	−11.8384	−	11.8384i	−0.445229	−	0.445229i
$708$		0			0
$709$		−	47.0878i		−	1.76842i	−0.467091	−	0.884209i	$-0.654698\pi$
$709$		−	47.0878i		−	1.76842i	0.467091	−	0.884209i	$-0.345302\pi$
$710$		0			0
$711$		0			0
$712$	4.04989	−	4.04989i	0.151776	−	0.151776i
$713$	7.37249	−	7.37249i	0.276102	−	0.276102i
$714$		0			0
$715$		0			0
$716$		−	1.00124i		−	0.0374183i
$717$		0			0
$718$	22.5725	+	22.5725i	0.842398	+	0.842398i
$719$	−13.9350			−0.519687			−0.259844	−	0.965651i	$-0.583671\pi$
$719$	−13.9350			−0.519687			−0.259844	+	0.965651i	$0.583671\pi$
$720$		0			0
$721$	12.2414			0.455893
$722$	−10.4637	−	10.4637i	−0.389420	−	0.389420i
$723$		0			0
$724$		−	23.0411i		−	0.856316i
$725$		0			0
$726$		0			0
$727$	−0.199188	+	0.199188i	−0.00738746	+	0.00738746i	−0.710791	−	0.703403i	$-0.751663\pi$
$727$	−0.199188	+	0.199188i	−0.00738746	+	0.00738746i	0.703403	+	0.710791i	$0.251663\pi$
$728$	1.43916	−	1.43916i	0.0533387	−	0.0533387i
$729$		0			0
$730$		0			0
$731$			14.3570i			0.531014i
$732$		0			0
$733$	10.2245	+	10.2245i	0.377650	+	0.377650i	0.870254	−	0.492603i	$-0.163955\pi$
$733$	10.2245	+	10.2245i	0.377650	+	0.377650i	−0.492603	+	0.870254i	$0.663955\pi$
$734$	34.7690			1.28335
$735$		0			0
$736$	−1.63567			−0.0602918
$737$	19.9494	+	19.9494i	0.734845	+	0.734845i
$738$		0			0
$739$			35.1993i			1.29483i	0.762139	+	0.647414i	$0.224149\pi$
$739$			35.1993i			1.29483i	−0.762139	+	0.647414i	$0.775851\pi$
$740$		0			0
$741$		0			0
$742$	2.97506	−	2.97506i	0.109218	−	0.109218i
$743$	−12.2052	+	12.2052i	−0.447767	+	0.447767i	−0.894612	−	0.446845i	$-0.852548\pi$
$743$	−12.2052	+	12.2052i	−0.447767	+	0.447767i	0.446845	+	0.894612i	$0.352548\pi$
$744$		0			0
$745$		0			0
$746$		−	3.95691i		−	0.144873i
$747$		0			0
$748$	5.26670	+	5.26670i	0.192570	+	0.192570i
$749$	15.4840			0.565774
$750$		0			0
$751$	−3.73294			−0.136217			−0.0681085	−	0.997678i	$-0.521696\pi$
$751$	−3.73294			−0.136217			−0.0681085	+	0.997678i	$0.521696\pi$
$752$	1.39960	+	1.39960i	0.0510382	+	0.0510382i
$753$		0			0
$754$			16.3743i			0.596317i
$755$		0			0
$756$		0			0
$757$	−0.363597	+	0.363597i	−0.0132151	+	0.0132151i	−0.713683	−	0.700468i	$-0.752974\pi$
$757$	−0.363597	+	0.363597i	−0.0132151	+	0.0132151i	0.700468	+	0.713683i	$0.252974\pi$
$758$	18.6952	−	18.6952i	0.679039	−	0.679039i
$759$		0			0
$760$		0			0
$761$			26.1799i			0.949022i	0.880250	+	0.474511i	$0.157375\pi$
$761$			26.1799i			0.949022i	−0.880250	+	0.474511i	$0.842625\pi$
$762$		0			0
$763$	3.70283	+	3.70283i	0.134051	+	0.134051i
$764$	−3.59095			−0.129916
$765$		0			0
$766$	24.3641			0.880311
$767$	6.12686	+	6.12686i	0.221228	+	0.221228i
$768$		0			0
$769$			28.9756i			1.04489i	0.852674	+	0.522443i	$0.174979\pi$
$769$			28.9756i			1.04489i	−0.852674	+	0.522443i	$0.825021\pi$
$770$		0			0
$771$		0			0
$772$	−4.98539	+	4.98539i	−0.179428	+	0.179428i
$773$	27.3745	−	27.3745i	0.984591	−	0.984591i	−0.0152923	−	0.999883i	$-0.504868\pi$
$773$	27.3745	−	27.3745i	0.984591	−	0.984591i	0.999883	+	0.0152923i	$0.00486787\pi$
$774$		0			0
$775$		0			0
$776$		−	13.6410i		−	0.489683i
$777$		0			0
$778$	−23.2472	−	23.2472i	−0.833454	−	0.833454i
$779$	16.2943			0.583803
$780$		0			0
$781$	9.99751			0.357739
$782$	−2.52316	−	2.52316i	−0.0902281	−	0.0902281i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$		0			0
$786$		0			0
$787$	−26.8559	+	26.8559i	−0.957309	+	0.957309i	−0.999125	−	0.0418162i	$-0.986686\pi$
$787$	−26.8559	+	26.8559i	−0.957309	+	0.957309i	0.0418162	+	0.999125i	$0.486686\pi$
$788$	10.0169	−	10.0169i	0.356837	−	0.356837i
$789$		0			0
$790$		0			0
$791$		−	2.25674i		−	0.0802403i
$792$		0			0
$793$	9.91512	+	9.91512i	0.352096	+	0.352096i
$794$	7.63368			0.270909
$795$		0			0
$796$	27.2820			0.966985
$797$	−5.58506	−	5.58506i	−0.197833	−	0.197833i	0.601237	−	0.799070i	$-0.294675\pi$
$797$	−5.58506	−	5.58506i	−0.197833	−	0.197833i	−0.799070	+	0.601237i	$0.794675\pi$
$798$		0			0
$799$			4.31800i			0.152760i
$800$		0			0
$801$		0			0
$802$	10.2361	−	10.2361i	0.361448	−	0.361448i
$803$	20.3989	−	20.3989i	0.719861	−	0.719861i
$804$		0			0
$805$		0			0
$806$		−	12.9734i		−	0.456970i
$807$		0			0
$808$	11.8384	+	11.8384i	0.416473	+	0.416473i
$809$	−35.7067			−1.25538			−0.627691	−	0.778463i	$-0.716000\pi$
$809$	−35.7067			−1.25538			−0.627691	+	0.778463i	$0.716000\pi$
$810$		0			0
$811$	21.5685			0.757371			0.378685	−	0.925525i	$-0.376376\pi$
$811$	21.5685			0.757371			0.378685	+	0.925525i	$0.376376\pi$
$812$	−5.68885	−	5.68885i	−0.199639	−	0.199639i
$813$		0			0
$814$		−	0.240881i		−	0.00844287i
$815$		0			0
$816$		0			0
$817$	−9.53930	+	9.53930i	−0.333738	+	0.333738i
$818$	−11.6783	+	11.6783i	−0.408321	+	0.408321i
$819$		0			0
$820$		0			0
$821$			45.6237i			1.59228i	0.605114	+	0.796139i	$0.293127\pi$
$821$			45.6237i			1.59228i	−0.605114	+	0.796139i	$0.706873\pi$
$822$		0			0
$823$	24.0562	+	24.0562i	0.838548	+	0.838548i	0.988668	−	0.150120i	$-0.0479660\pi$
$823$	24.0562	+	24.0562i	0.838548	+	0.838548i	−0.150120	+	0.988668i	$0.547966\pi$
$824$	−12.2414			−0.426449
$825$		0			0
$826$	−4.25725			−0.148129
$827$	−30.4601	−	30.4601i	−1.05920	−	1.05920i	−0.998134	−	0.0610692i	$-0.980549\pi$
$827$	−30.4601	−	30.4601i	−1.05920	−	1.05920i	−0.0610692	−	0.998134i	$-0.519451\pi$
$828$		0			0
$829$		−	51.5031i		−	1.78878i	−0.447291	−	0.894388i	$-0.647611\pi$
$829$		−	51.5031i		−	1.78878i	0.447291	−	0.894388i	$-0.352389\pi$
$830$		0			0
$831$		0			0
$832$	−1.43916	+	1.43916i	−0.0498938	+	0.0498938i
$833$	−1.54258	+	1.54258i	−0.0534473	+	0.0534473i
$834$		0			0
$835$		0			0
$836$			6.99876i			0.242057i
$837$		0			0
$838$	−8.51503	−	8.51503i	−0.294147	−	0.294147i
$839$	−26.7154			−0.922319			−0.461159	−	0.887317i	$-0.652566\pi$
$839$	−26.7154			−0.922319			−0.461159	+	0.887317i	$0.652566\pi$
$840$		0			0
$841$	35.7259			1.23193
$842$	−22.9734	−	22.9734i	−0.791717	−	0.791717i
$843$		0			0
$844$		−	8.70193i		−	0.299533i
$845$		0			0
$846$		0			0
$847$	0.464466	−	0.464466i	0.0159592	−	0.0159592i
$848$	−2.97506	+	2.97506i	−0.102164	+	0.102164i
$849$		0			0
$850$		0			0
$851$			0.115401i			0.00395588i
$852$		0			0
$853$	−36.4710	−	36.4710i	−1.24874	−	1.24874i	−0.956276	−	0.292467i	$-0.905524\pi$
$853$	−36.4710	−	36.4710i	−1.24874	−	1.24874i	−0.292467	−	0.956276i	$-0.594476\pi$
$854$	−6.88953			−0.235755
$855$		0			0
$856$	−15.4840			−0.529233
$857$	22.0837	+	22.0837i	0.754364	+	0.754364i	0.975291	−	0.220926i	$-0.0709080\pi$
$857$	22.0837	+	22.0837i	0.754364	+	0.754364i	−0.220926	+	0.975291i	$0.570908\pi$
$858$		0			0
$859$		−	8.42683i		−	0.287520i	−0.989613	−	0.143760i	$-0.954081\pi$
$859$		−	8.42683i		−	0.287520i	0.989613	−	0.143760i	$-0.0459193\pi$
$860$		0			0
$861$		0			0
$862$	−6.01665	+	6.01665i	−0.204928	+	0.204928i
$863$	9.78940	−	9.78940i	0.333235	−	0.333235i	−0.520579	−	0.853814i	$-0.674284\pi$
$863$	9.78940	−	9.78940i	0.333235	−	0.333235i	0.853814	+	0.520579i	$0.174284\pi$
$864$		0			0
$865$		0			0
$866$			5.02798i			0.170858i
$867$		0			0
$868$	4.50731	+	4.50731i	0.152988	+	0.152988i
$869$	39.7449			1.34825
$870$		0			0
$871$	−16.8181			−0.569860
$872$	−3.70283	−	3.70283i	−0.125394	−	0.125394i
$873$		0			0
$874$		−	3.35295i		−	0.113415i
$875$		0			0
$876$		0			0
$877$	−32.7554	+	32.7554i	−1.10607	+	1.10607i	−0.112409	+	0.993662i	$0.535857\pi$
$877$	−32.7554	+	32.7554i	−1.10607	+	1.10607i	−0.993662	+	0.112409i	$0.964143\pi$
$878$	−9.35567	+	9.35567i	−0.315739	+	0.315739i
$879$		0			0
$880$		0			0
$881$			38.0422i			1.28167i	0.767677	+	0.640837i	$0.221412\pi$
$881$			38.0422i			1.28167i	−0.767677	+	0.640837i	$0.778588\pi$
$882$		0			0
$883$	22.6735	+	22.6735i	0.763024	+	0.763024i	0.976868	−	0.213844i	$-0.0685983\pi$
$883$	22.6735	+	22.6735i	0.763024	+	0.763024i	−0.213844	+	0.976868i	$0.568598\pi$
$884$	−4.44004			−0.149335
$885$		0			0
$886$	33.8313			1.13658
$887$	26.7254	+	26.7254i	0.897352	+	0.897352i	0.995201	−	0.0978490i	$-0.0311962\pi$
$887$	26.7254	+	26.7254i	0.897352	+	0.897352i	−0.0978490	+	0.995201i	$0.531196\pi$
$888$		0			0
$889$			10.9189i			0.366209i
$890$		0			0
$891$		0			0
$892$	−2.80813	+	2.80813i	−0.0940231	+	0.0940231i
$893$	−2.86903	+	2.86903i	−0.0960083	+	0.0960083i
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−2.89846	−	2.89846i	−0.0967230	−	0.0967230i
$899$	−51.2827			−1.71038
$900$		0			0
$901$	−9.17854			−0.305781
$902$	19.1903	+	19.1903i	0.638966	+	0.638966i
$903$		0			0
$904$			2.25674i			0.0750580i
$905$		0			0
$906$		0			0
$907$	20.9527	−	20.9527i	0.695722	−	0.695722i	−0.267763	−	0.963485i	$-0.586284\pi$
$907$	20.9527	−	20.9527i	0.695722	−	0.695722i	0.963485	+	0.267763i	$0.0862844\pi$
$908$	2.88573	−	2.88573i	0.0957662	−	0.0957662i
$909$		0			0
$910$		0			0
$911$			7.95403i			0.263529i	0.991281	+	0.131764i	$0.0420642\pi$
$911$			7.95403i			0.263529i	−0.991281	+	0.131764i	$0.957936\pi$
$912$		0			0
$913$	−5.21682	−	5.21682i	−0.172651	−	0.172651i
$914$	33.1138			1.09531
$915$		0			0
$916$	9.16228			0.302730
$917$	5.22146	+	5.22146i	0.172428	+	0.172428i
$918$		0			0
$919$		−	22.4684i		−	0.741164i	−0.928800	−	0.370582i	$-0.879158\pi$
$919$		−	22.4684i		−	0.741164i	0.928800	−	0.370582i	$-0.120842\pi$
$920$		0			0
$921$		0			0
$922$	−13.7867	+	13.7867i	−0.454042	+	0.454042i
$923$	−4.21415	+	4.21415i	−0.138710	+	0.138710i
$924$		0			0
$925$		0			0
$926$		−	13.6052i		−	0.447095i
$927$		0			0
$928$	5.68885	+	5.68885i	0.186746	+	0.186746i
$929$	13.2519			0.434782			0.217391	−	0.976085i	$-0.430245\pi$
$929$	13.2519			0.434782			0.217391	+	0.976085i	$0.430245\pi$
$930$		0			0
$931$	−2.04989			−0.0671824
$932$	−4.67611	−	4.67611i	−0.153171	−	0.153171i
$933$		0			0
$934$		−	21.0213i		−	0.687839i
$935$		0			0
$936$		0			0
$937$	29.0638	−	29.0638i	0.949472	−	0.949472i	−0.0493114	−	0.998783i	$-0.515703\pi$
$937$	29.0638	−	29.0638i	0.949472	−	0.949472i	0.998783	+	0.0493114i	$0.0157027\pi$
$938$	5.84304	−	5.84304i	0.190782	−	0.190782i
$939$		0			0
$940$		0			0
$941$			19.1092i			0.622941i	0.950256	+	0.311471i	$0.100822\pi$
$941$			19.1092i			0.622941i	−0.950256	+	0.311471i	$0.899178\pi$
$942$		0			0
$943$	−9.19363	−	9.19363i	−0.299386	−	0.299386i
$944$	4.25725			0.138562
$945$		0			0
$946$	−22.4694			−0.730544
$947$	32.1010	+	32.1010i	1.04314	+	1.04314i	0.999026	+	0.0441149i	$0.0140468\pi$
$947$	32.1010	+	32.1010i	1.04314	+	1.04314i	0.0441149	+	0.999026i	$0.485953\pi$
$948$		0			0
$949$			17.1970i			0.558240i
$950$		0			0
$951$		0			0
$952$	1.54258	−	1.54258i	0.0499954	−	0.0499954i
$953$	31.8179	−	31.8179i	1.03068	−	1.03068i	0.0311686	−	0.999514i	$-0.490077\pi$
$953$	31.8179	−	31.8179i	1.03068	−	1.03068i	0.999514	−	0.0311686i	$-0.00992287\pi$
$954$		0			0
$955$		0			0
$956$			16.4853i			0.533172i
$957$		0			0
$958$	8.20701	+	8.20701i	0.265157	+	0.265157i
$959$	17.2913			0.558365
$960$		0			0
$961$	9.63161			0.310697
$962$	0.101536	+	0.101536i	0.00327365	+	0.00327365i
$963$		0			0
$964$		−	8.50419i		−	0.273901i
$965$		0			0
$966$		0			0
$967$	32.9608	−	32.9608i	1.05995	−	1.05995i	0.0618618	−	0.998085i	$-0.480296\pi$
$967$	32.9608	−	32.9608i	1.05995	−	1.05995i	0.998085	−	0.0618618i	$-0.0197038\pi$
$968$	−0.464466	+	0.464466i	−0.0149285	+	0.0149285i
$969$		0			0
$970$		0			0
$971$		−	36.4536i		−	1.16985i	−0.811087	−	0.584925i	$-0.801124\pi$
$971$		−	36.4536i		−	1.16985i	0.811087	−	0.584925i	$-0.198876\pi$
$972$		0			0
$973$	−10.7919	−	10.7919i	−0.345973	−	0.345973i
$974$	37.5821			1.20421
$975$		0			0
$976$	6.88953			0.220528
$977$	−2.66218	−	2.66218i	−0.0851706	−	0.0851706i	0.663238	−	0.748409i	$-0.269182\pi$
$977$	−2.66218	−	2.66218i	−0.0851706	−	0.0851706i	−0.748409	+	0.663238i	$0.769182\pi$
$978$		0			0
$979$			19.5546i			0.624967i
$980$		0			0
$981$		0			0
$982$	−23.6902	+	23.6902i	−0.755983	+	0.755983i
$983$	−40.9827	+	40.9827i	−1.30714	+	1.30714i	−0.383677	+	0.923468i	$0.625342\pi$
$983$	−40.9827	+	40.9827i	−1.30714	+	1.30714i	−0.923468	+	0.383677i	$0.874658\pi$
$984$		0			0
$985$		0			0
$986$			17.5510i			0.558939i
$987$		0			0
$988$	−2.95011	−	2.95011i	−0.0938556	−	0.0938556i
$989$	10.7646			0.342295
$990$		0			0
$991$	44.8845			1.42580			0.712901	−	0.701264i	$-0.247381\pi$
$991$	44.8845			1.42580			0.712901	+	0.701264i	$0.247381\pi$
$992$	−4.50731	−	4.50731i	−0.143107	−	0.143107i
$993$		0			0
$994$		−	2.92820i		−	0.0928770i
$995$		0			0
$996$		0			0
$997$	−32.9695	+	32.9695i	−1.04416	+	1.04416i	−0.0451765	+	0.998979i	$0.514385\pi$
$997$	−32.9695	+	32.9695i	−1.04416	+	1.04416i	−0.998979	+	0.0451765i	$0.985615\pi$
$998$	−4.65633	+	4.65633i	−0.147393	+	0.147393i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.m.l.2843.1	yes	8
3.2	odd	2		3150.2.m.k.2843.3	yes	8
5.2	odd	4		3150.2.m.k.1457.3	yes	8
5.3	odd	4		3150.2.m.g.1457.2	✓	8
5.4	even	2		3150.2.m.h.2843.4	yes	8
15.2	even	4	inner	3150.2.m.l.1457.1	yes	8
15.8	even	4		3150.2.m.h.1457.4	yes	8
15.14	odd	2		3150.2.m.g.2843.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.m.g.1457.2	✓	8	5.3	odd	4
3150.2.m.g.2843.2	yes	8	15.14	odd	2
3150.2.m.h.1457.4	yes	8	15.8	even	4
3150.2.m.h.2843.4	yes	8	5.4	even	2
3150.2.m.k.1457.3	yes	8	5.2	odd	4
3150.2.m.k.2843.3	yes	8	3.2	odd	2
3150.2.m.l.1457.1	yes	8	15.2	even	4	inner
3150.2.m.l.2843.1	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +3.41421i q^{11} +(-1.43916 - 1.43916i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.54258 - 1.54258i) q^{17} -2.04989i q^{19} +(2.41421 - 2.41421i) q^{22} +(-1.15660 + 1.15660i) q^{23} +2.03528i q^{26} +(-0.707107 - 0.707107i) q^{28} +8.04524 q^{29} -6.37429 q^{31} +(0.707107 + 0.707107i) q^{32} +2.18154i q^{34} +(0.0498881 - 0.0498881i) q^{37} +(-1.44949 + 1.44949i) q^{38} +7.94887i q^{41} +(-4.65357 - 4.65357i) q^{43} -3.41421 q^{44} +1.63567 q^{46} +(-1.39960 - 1.39960i) q^{47} -1.00000i q^{49} +(1.43916 - 1.43916i) q^{52} +(2.97506 - 2.97506i) q^{53} +1.00000i q^{56} +(-5.68885 - 5.68885i) q^{58} -4.25725 q^{59} -6.88953 q^{61} +(4.50731 + 4.50731i) q^{62} -1.00000i q^{64} +(5.84304 - 5.84304i) q^{67} +(1.54258 - 1.54258i) q^{68} -2.92820i q^{71} +(-5.97469 - 5.97469i) q^{73} -0.0705524 q^{74} +2.04989 q^{76} +(-2.41421 - 2.41421i) q^{77} -11.6410i q^{79} +(5.62070 - 5.62070i) q^{82} +(-1.52797 + 1.52797i) q^{83} +6.58114i q^{86} +(2.41421 + 2.41421i) q^{88} +5.72741 q^{89} +2.03528 q^{91} +(-1.15660 - 1.15660i) q^{92} +1.97934i q^{94} +(9.64564 - 9.64564i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{22} + 16 q^{23} - 16 q^{37} + 8 q^{38} - 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{47} - 8 q^{52} + 32 q^{53} - 8 q^{58} + 8 q^{59} - 32 q^{61} + 32 q^{62} + 16 q^{67} + 16 q^{74} - 8 q^{77} - 8 q^{82} - 8 q^{83} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 16 q^{92} + 16 q^{97}+O(q^{100}) \) 8 * q + 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^22 + 16 * q^23 - 16 * q^37 + 8 * q^38 - 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^47 - 8 * q^52 + 32 * q^53 - 8 * q^58 + 8 * q^59 - 32 * q^61 + 32 * q^62 + 16 * q^67 + 16 * q^74 - 8 * q^77 - 8 * q^82 - 8 * q^83 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 16 * q^92 + 16 * q^97

Introduction

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