LMFDB - Embedded newform 3150.2.bf.f.1151.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3150.1151");

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.bf (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.11
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.f.1601.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.54232 - 0.732536i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.54232 - 0.732536i) q^{7} -1.00000i q^{8} +(2.07577 + 1.19845i) q^{11} +5.67714i q^{13} +(-2.56798 + 0.636766i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.03596 - 1.79434i) q^{17} +(5.12164 - 2.95698i) q^{19} +2.39690 q^{22} +(-1.61233 + 0.930877i) q^{23} +(2.83857 + 4.91654i) q^{26} +(-1.90555 + 1.83545i) q^{28} -4.88913i q^{29} +(-3.92008 - 2.26326i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.07192i q^{34} +(1.48455 + 2.57132i) q^{37} +(2.95698 - 5.12164i) q^{38} +7.04428 q^{41} +8.55956 q^{43} +(2.07577 - 1.19845i) q^{44} +(-0.930877 + 1.61233i) q^{46} +(2.78941 + 4.83140i) q^{47} +(5.92678 + 3.72468i) q^{49} +(4.91654 + 2.83857i) q^{52} +(3.62931 + 2.09538i) q^{53} +(-0.732536 + 2.54232i) q^{56} +(-2.44457 - 4.23411i) q^{58} +(-1.00312 + 1.73746i) q^{59} +(10.7862 - 6.22739i) q^{61} -4.52651 q^{62} -1.00000 q^{64} +(-3.81111 + 6.60103i) q^{67} +(-1.03596 - 1.79434i) q^{68} +9.14126i q^{71} +(-0.937339 - 0.541173i) q^{73} +(2.57132 + 1.48455i) q^{74} -5.91397i q^{76} +(-4.39937 - 4.56742i) q^{77} +(-8.38392 - 14.5214i) q^{79} +(6.10053 - 3.52214i) q^{82} +13.6122 q^{83} +(7.41279 - 4.27978i) q^{86} +(1.19845 - 2.07577i) q^{88} +(6.63129 + 11.4857i) q^{89} +(4.15870 - 14.4331i) q^{91} +1.86175i q^{92} +(4.83140 + 2.78941i) q^{94} -12.8260i q^{97} +(6.99508 + 0.262276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 - 48 * q^19 + 24 * q^31 - 16 * q^46 + 56 * q^49 + 48 * q^61 - 32 * q^64 - 8 * q^79 - 56 * q^91 + 120 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.54232	−	0.732536i	−0.960907	−	0.276872i
$7$	−2.54232	−	0.732536i	−0.960907	−	0.276872i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	2.07577	+	1.19845i	0.625869	+	0.361346i	0.779150	−	0.626837i	$-0.215651\pi$
$11$	2.07577	+	1.19845i	0.625869	+	0.361346i	−0.153282	+	0.988183i	$0.548984\pi$
$12$		0			0
$13$			5.67714i			1.57455i	0.616599	+	0.787277i	$0.288510\pi$
$13$			5.67714i			1.57455i	−0.616599	+	0.787277i	$0.711490\pi$
$14$	−2.56798	+	0.636766i	−0.686322	+	0.170183i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.03596	−	1.79434i	0.251258	−	0.435191i	−0.712615	−	0.701556i	$-0.752489\pi$
$17$	1.03596	−	1.79434i	0.251258	−	0.435191i	0.963872	+	0.266365i	$0.0858225\pi$
$18$		0			0
$19$	5.12164	−	2.95698i	1.17499	−	0.678378i	0.220136	−	0.975469i	$-0.429350\pi$
$19$	5.12164	−	2.95698i	1.17499	−	0.678378i	0.954849	+	0.297091i	$0.0960164\pi$
$20$		0			0
$21$		0			0
$22$	2.39690			0.511020
$23$	−1.61233	+	0.930877i	−0.336193	+	0.194101i	−0.658587	−	0.752504i	$-0.728846\pi$
$23$	−1.61233	+	0.930877i	−0.336193	+	0.194101i	0.322394	+	0.946606i	$0.395512\pi$
$24$		0			0
$25$		0			0
$26$	2.83857	+	4.91654i	0.556689	+	0.964214i
$27$		0			0
$28$	−1.90555	+	1.83545i	−0.360116	+	0.346867i
$29$		−	4.88913i		−	0.907889i	−0.891030	−	0.453944i	$-0.850016\pi$
$29$		−	4.88913i		−	0.907889i	0.891030	−	0.453944i	$-0.149984\pi$
$30$		0			0
$31$	−3.92008	−	2.26326i	−0.704067	−	0.406493i	0.104794	−	0.994494i	$-0.466582\pi$
$31$	−3.92008	−	2.26326i	−0.704067	−	0.406493i	−0.808860	+	0.588001i	$0.799915\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	2.07192i		−	0.355332i
$35$		0			0
$36$		0			0
$37$	1.48455	+	2.57132i	0.244059	+	0.422723i	0.961867	−	0.273519i	$-0.0881875\pi$
$37$	1.48455	+	2.57132i	0.244059	+	0.422723i	−0.717807	+	0.696242i	$0.754854\pi$
$38$	2.95698	−	5.12164i	0.479686	−	0.830840i
$39$		0			0
$40$		0			0
$41$	7.04428			1.10013			0.550066	−	0.835121i	$-0.314603\pi$
$41$	7.04428			1.10013			0.550066	+	0.835121i	$0.314603\pi$
$42$		0			0
$43$	8.55956			1.30532			0.652660	−	0.757651i	$-0.273653\pi$
$43$	8.55956			1.30532			0.652660	+	0.757651i	$0.273653\pi$
$44$	2.07577	−	1.19845i	0.312934	−	0.180673i
$45$		0			0
$46$	−0.930877	+	1.61233i	−0.137250	+	0.237725i
$47$	2.78941	+	4.83140i	0.406877	+	0.704732i	0.994538	−	0.104375i	$-0.0332843\pi$
$47$	2.78941	+	4.83140i	0.406877	+	0.704732i	−0.587661	+	0.809107i	$0.699951\pi$
$48$		0			0
$49$	5.92678	+	3.72468i	0.846683	+	0.532097i
$50$		0			0
$51$		0			0
$52$	4.91654	+	2.83857i	0.681802	+	0.393639i
$53$	3.62931	+	2.09538i	0.498524	+	0.287823i	0.728104	−	0.685467i	$-0.240402\pi$
$53$	3.62931	+	2.09538i	0.498524	+	0.287823i	−0.229580	+	0.973290i	$0.573735\pi$
$54$		0			0
$55$		0			0
$56$	−0.732536	+	2.54232i	−0.0978892	+	0.339732i
$57$		0			0
$58$	−2.44457	−	4.23411i	−0.320987	−	0.555966i
$59$	−1.00312	+	1.73746i	−0.130595	+	0.226198i	−0.923906	−	0.382619i	$-0.875022\pi$
$59$	−1.00312	+	1.73746i	−0.130595	+	0.226198i	0.793311	+	0.608817i	$0.208356\pi$
$60$		0			0
$61$	10.7862	−	6.22739i	1.38103	−	0.797335i	0.388744	−	0.921346i	$-0.372909\pi$
$61$	10.7862	−	6.22739i	1.38103	−	0.797335i	0.992281	+	0.124011i	$0.0395757\pi$
$62$	−4.52651			−0.574868
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−3.81111	+	6.60103i	−0.465601	+	0.806445i	−0.999228	−	0.0392750i	$-0.987495\pi$
$67$	−3.81111	+	6.60103i	−0.465601	+	0.806445i	0.533627	+	0.845720i	$0.320829\pi$
$68$	−1.03596	−	1.79434i	−0.125629	−	0.217596i
$69$		0			0
$70$		0			0
$71$			9.14126i			1.08487i	0.840099	+	0.542434i	$0.182497\pi$
$71$			9.14126i			1.08487i	−0.840099	+	0.542434i	$0.817503\pi$
$72$		0			0
$73$	−0.937339	−	0.541173i	−0.109707	−	0.0633395i	0.444142	−	0.895956i	$-0.353508\pi$
$73$	−0.937339	−	0.541173i	−0.109707	−	0.0633395i	−0.553850	+	0.832617i	$0.686842\pi$
$74$	2.57132	+	1.48455i	0.298910	+	0.172576i
$75$		0			0
$76$		−	5.91397i		−	0.678378i
$77$	−4.39937	−	4.56742i	−0.501355	−	0.520505i
$78$		0			0
$79$	−8.38392	−	14.5214i	−0.943265	−	1.63378i	−0.759189	−	0.650870i	$-0.774404\pi$
$79$	−8.38392	−	14.5214i	−0.943265	−	1.63378i	−0.184076	−	0.982912i	$-0.558929\pi$
$80$		0			0
$81$		0			0
$82$	6.10053	−	3.52214i	0.673690	−	0.388955i
$83$	13.6122			1.49414			0.747068	−	0.664747i	$-0.231461\pi$
$83$	13.6122			1.49414			0.747068	+	0.664747i	$0.231461\pi$
$84$		0			0
$85$		0			0
$86$	7.41279	−	4.27978i	0.799342	−	0.461500i
$87$		0			0
$88$	1.19845	−	2.07577i	0.127755	−	0.221278i
$89$	6.63129	+	11.4857i	0.702916	+	1.21749i	0.967438	+	0.253106i	$0.0814523\pi$
$89$	6.63129	+	11.4857i	0.702916	+	1.21749i	−0.264523	+	0.964379i	$0.585214\pi$
$90$		0			0
$91$	4.15870	−	14.4331i	0.435951	−	1.51300i
$92$			1.86175i			0.194101i
$93$		0			0
$94$	4.83140	+	2.78941i	0.498321	+	0.287706i
$95$		0			0
$96$		0			0
$97$		−	12.8260i		−	1.30229i	−0.758955	−	0.651143i	$-0.774290\pi$
$97$		−	12.8260i		−	1.30229i	0.758955	−	0.651143i	$-0.225710\pi$
$98$	6.99508	+	0.262276i	0.706610	+	0.0264939i
$99$		0			0
$100$		0			0
$101$	4.45573	−	7.71756i	0.443362	−	0.767926i	−0.554574	−	0.832134i	$-0.687119\pi$
$101$	4.45573	−	7.71756i	0.443362	−	0.767926i	0.997937	+	0.0642084i	$0.0204523\pi$
$102$		0			0
$103$	9.37021	−	5.40989i	0.923274	−	0.533053i	0.0385960	−	0.999255i	$-0.487711\pi$
$103$	9.37021	−	5.40989i	0.923274	−	0.533053i	0.884678	+	0.466202i	$0.154378\pi$
$104$	5.67714			0.556689
$105$		0			0
$106$	4.19077			0.407043
$107$	4.82989	−	2.78854i	0.466923	−	0.269578i	−0.248028	−	0.968753i	$-0.579782\pi$
$107$	4.82989	−	2.78854i	0.466923	−	0.269578i	0.714951	+	0.699175i	$0.246449\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$		0			0
$112$	0.636766	+	2.56798i	0.0601687	+	0.242651i
$113$		−	14.5030i		−	1.36432i	−0.731202	−	0.682161i	$-0.761040\pi$
$113$		−	14.5030i		−	1.36432i	0.731202	−	0.682161i	$-0.238960\pi$
$114$		0			0
$115$		0			0
$116$	−4.23411	−	2.44457i	−0.393127	−	0.226972i
$117$		0			0
$118$			2.00624i			0.184690i
$119$	−3.94816	+	3.80290i	−0.361928	+	0.348612i
$120$		0			0
$121$	−2.62745	−	4.55087i	−0.238859	−	0.413715i
$122$	6.22739	−	10.7862i	0.563801	−	0.976532i
$123$		0			0
$124$	−3.92008	+	2.26326i	−0.352033	+	0.203247i
$125$		0			0
$126$		0			0
$127$	−19.2462			−1.70783			−0.853913	−	0.520416i	$-0.825777\pi$
$127$	−19.2462			−1.70783			−0.853913	+	0.520416i	$0.825777\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	−2.34970	−	4.06980i	−0.205294	−	0.355580i	0.744932	−	0.667140i	$-0.232482\pi$
$131$	−2.34970	−	4.06980i	−0.205294	−	0.355580i	−0.950226	+	0.311560i	$0.899149\pi$
$132$		0			0
$133$	−15.1870	+	3.76581i	−1.31688	+	0.326537i
$134$			7.62222i			0.658459i
$135$		0			0
$136$	−1.79434	−	1.03596i	−0.153863	−	0.0888330i
$137$	19.8185	+	11.4422i	1.69321	+	0.977577i	0.951896	+	0.306421i	$0.0991317\pi$
$137$	19.8185	+	11.4422i	1.69321	+	0.977577i	0.741317	+	0.671155i	$0.234202\pi$
$138$		0			0
$139$			9.13862i			0.775127i	0.921843	+	0.387564i	$0.126683\pi$
$139$			9.13862i			0.775127i	−0.921843	+	0.387564i	$0.873317\pi$
$140$		0			0
$141$		0			0
$142$	4.57063	+	7.91656i	0.383559	+	0.664343i
$143$	−6.80375	+	11.7844i	−0.568958	+	0.985465i
$144$		0			0
$145$		0			0
$146$	−1.08235			−0.0895756
$147$		0			0
$148$	2.96911			0.244059
$149$	9.05052	−	5.22532i	0.741448	−	0.428075i	−0.0811477	−	0.996702i	$-0.525859\pi$
$149$	9.05052	−	5.22532i	0.741448	−	0.428075i	0.822596	+	0.568627i	$0.192525\pi$
$150$		0			0
$151$	8.85937	−	15.3449i	0.720965	−	1.24875i	−0.239648	−	0.970860i	$-0.577032\pi$
$151$	8.85937	−	15.3449i	0.720965	−	1.24875i	0.960613	−	0.277888i	$-0.0896346\pi$
$152$	−2.95698	−	5.12164i	−0.239843	−	0.415420i
$153$		0			0
$154$	−6.09368	−	1.75581i	−0.491042	−	0.141487i
$155$		0			0
$156$		0			0
$157$	−5.26801	−	3.04149i	−0.420433	−	0.242737i	0.274830	−	0.961493i	$-0.411379\pi$
$157$	−5.26801	−	3.04149i	−0.420433	−	0.242737i	−0.695263	+	0.718756i	$0.744712\pi$
$158$	−14.5214	−	8.38392i	−1.15526	−	0.666989i
$159$		0			0
$160$		0			0
$161$	4.78095	−	1.18550i	0.376792	−	0.0934305i
$162$		0			0
$163$	0.468670	+	0.811759i	0.0367090	+	0.0635819i	0.883796	−	0.467872i	$-0.154979\pi$
$163$	0.468670	+	0.811759i	0.0367090	+	0.0635819i	−0.847087	+	0.531454i	$0.821646\pi$
$164$	3.52214	−	6.10053i	0.275033	−	0.476371i
$165$		0			0
$166$	11.7885	−	6.80611i	0.914968	−	0.528257i
$167$	−17.2101			−1.33176			−0.665879	−	0.746060i	$-0.731943\pi$
$167$	−17.2101			−1.33176			−0.665879	+	0.746060i	$0.731943\pi$
$168$		0			0
$169$	−19.2299			−1.47922
$170$		0			0
$171$		0			0
$172$	4.27978	−	7.41279i	0.326330	−	0.565220i
$173$	0.988114	+	1.71146i	0.0751249	+	0.130120i	0.901141	−	0.433527i	$-0.142731\pi$
$173$	0.988114	+	1.71146i	0.0751249	+	0.130120i	−0.826016	+	0.563647i	$0.809398\pi$
$174$		0			0
$175$		0			0
$176$		−	2.39690i		−	0.180673i
$177$		0			0
$178$	11.4857	+	6.63129i	0.860893	+	0.497037i
$179$	0.768461	+	0.443671i	0.0574375	+	0.0331615i	0.528444	−	0.848968i	$-0.322776\pi$
$179$	0.768461	+	0.443671i	0.0574375	+	0.0331615i	−0.471006	+	0.882130i	$0.656109\pi$
$180$		0			0
$181$		−	4.89973i		−	0.364194i	−0.983281	−	0.182097i	$-0.941712\pi$
$181$		−	4.89973i		−	0.364194i	0.983281	−	0.182097i	$-0.0582885\pi$
$182$	−3.61500	−	14.5788i	−0.267962	−	1.08065i
$183$		0			0
$184$	0.930877	+	1.61233i	0.0686252	+	0.118862i
$185$		0			0
$186$		0			0
$187$	4.30084	−	2.48309i	0.314509	−	0.181582i
$188$	5.57882			0.406877
$189$		0			0
$190$		0			0
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	−9.74828	+	16.8845i	−0.701697	+	1.21537i	0.266174	+	0.963925i	$0.414240\pi$
$193$	−9.74828	+	16.8845i	−0.701697	+	1.21537i	−0.967871	+	0.251449i	$0.919093\pi$
$194$	−6.41301	−	11.1077i	−0.460428	−	0.797484i
$195$		0			0
$196$	6.18906	−	3.27040i	0.442076	−	0.233600i
$197$			27.1576i			1.93490i	0.253069	+	0.967448i	$0.418560\pi$
$197$			27.1576i			1.93490i	−0.253069	+	0.967448i	$0.581440\pi$
$198$		0			0
$199$	3.00000	+	1.73205i	0.212664	+	0.122782i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	3.00000	+	1.73205i	0.212664	+	0.122782i	−0.389885	+	0.920864i	$0.627485\pi$
$200$		0			0
$201$		0			0
$202$		−	8.91147i		−	0.627009i
$203$	−3.58146	+	12.4297i	−0.251369	+	0.872396i
$204$		0			0
$205$		0			0
$206$	5.40989	−	9.37021i	0.376925	−	0.652853i
$207$		0			0
$208$	4.91654	−	2.83857i	0.340901	−	0.196819i
$209$	14.1752			0.980516
$210$		0			0
$211$	−4.06071			−0.279551			−0.139775	−	0.990183i	$-0.544638\pi$
$211$	−4.06071			−0.279551			−0.139775	+	0.990183i	$0.544638\pi$
$212$	3.62931	−	2.09538i	0.249262	−	0.143912i
$213$		0			0
$214$	2.78854	−	4.82989i	0.190620	−	0.330164i
$215$		0			0
$216$		0			0
$217$	8.30817	+	8.62552i	0.563996	+	0.585538i
$218$		−	2.00000i		−	0.135457i
$219$		0			0
$220$		0			0
$221$	10.1867	+	5.88130i	0.685232	+	0.395619i
$222$		0			0
$223$		−	16.1486i		−	1.08139i	−0.841218	−	0.540696i	$-0.818161\pi$
$223$		−	16.1486i		−	1.08139i	0.841218	−	0.540696i	$-0.181839\pi$
$224$	1.83545	+	1.90555i	0.122636	+	0.127320i
$225$		0			0
$226$	−7.25148	−	12.5599i	−0.482361	−	0.835474i
$227$	−0.839901	+	1.45475i	−0.0557462	+	0.0965552i	−0.892552	−	0.450945i	$-0.851087\pi$
$227$	−0.839901	+	1.45475i	−0.0557462	+	0.0965552i	0.836806	+	0.547500i	$0.184420\pi$
$228$		0			0
$229$	10.9143	−	6.30136i	0.721236	−	0.416406i	−0.0939717	−	0.995575i	$-0.529956\pi$
$229$	10.9143	−	6.30136i	0.721236	−	0.416406i	0.815207	+	0.579169i	$0.196623\pi$
$230$		0			0
$231$		0			0
$232$	−4.88913			−0.320987
$233$	−12.5715	+	7.25818i	−0.823589	+	0.475499i	−0.851653	−	0.524107i	$-0.824399\pi$
$233$	−12.5715	+	7.25818i	−0.823589	+	0.475499i	0.0280635	+	0.999606i	$0.491066\pi$
$234$		0			0
$235$		0			0
$236$	1.00312	+	1.73746i	0.0652977	+	0.113099i
$237$		0			0
$238$	−1.51776	+	5.26749i	−0.0983816	+	0.341441i
$239$			0.207089i			0.0133955i	0.999978	+	0.00669774i	$0.00213197\pi$
$239$			0.207089i			0.0133955i	−0.999978	+	0.00669774i	$0.997868\pi$
$240$		0			0
$241$	9.04172	+	5.22024i	0.582428	+	0.336265i	0.762098	−	0.647462i	$-0.224169\pi$
$241$	9.04172	+	5.22024i	0.582428	+	0.336265i	−0.179669	+	0.983727i	$0.557503\pi$
$242$	−4.55087	−	2.62745i	−0.292541	−	0.168899i
$243$		0			0
$244$		−	12.4548i		−	0.797335i
$245$		0			0
$246$		0			0
$247$	16.7872	+	29.0763i	1.06814	+	1.85008i
$248$	−2.26326	+	3.92008i	−0.143717	+	0.248925i
$249$		0			0
$250$		0			0
$251$	28.6464			1.80815			0.904074	−	0.427377i	$-0.140562\pi$
$251$	28.6464			1.80815			0.904074	+	0.427377i	$0.140562\pi$
$252$		0			0
$253$	−4.46243			−0.280551
$254$	−16.6677	+	9.62311i	−1.04583	+	0.603808i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.4595	+	21.5805i	0.777202	+	1.34615i	0.933548	+	0.358452i	$0.116695\pi$
$257$	12.4595	+	21.5805i	0.777202	+	1.34615i	−0.156346	+	0.987702i	$0.549971\pi$
$258$		0			0
$259$	−1.89063	−	7.62462i	−0.117478	−	0.473771i
$260$		0			0
$261$		0			0
$262$	−4.06980	−	2.34970i	−0.251433	−	0.145165i
$263$	−16.6197	−	9.59538i	−1.02481	−	0.591677i	−0.109319	−	0.994007i	$-0.534867\pi$
$263$	−16.6197	−	9.59538i	−1.02481	−	0.591677i	−0.915495	+	0.402330i	$0.868200\pi$
$264$		0			0
$265$		0			0
$266$	−11.2694	+	10.8548i	−0.690970	+	0.665548i
$267$		0			0
$268$	3.81111	+	6.60103i	0.232801	+	0.403222i
$269$	−2.42744	+	4.20446i	−0.148004	+	0.256350i	−0.930490	−	0.366318i	$-0.880618\pi$
$269$	−2.42744	+	4.20446i	−0.148004	+	0.256350i	0.782486	+	0.622668i	$0.213951\pi$
$270$		0			0
$271$	−11.8344	+	6.83257i	−0.718886	+	0.415049i	−0.814342	−	0.580385i	$-0.802902\pi$
$271$	−11.8344	+	6.83257i	−0.718886	+	0.415049i	0.0954567	+	0.995434i	$0.469569\pi$
$272$	−2.07192			−0.125629
$273$		0			0
$274$	22.8845			1.38250
$275$		0			0
$276$		0			0
$277$	−6.06491	+	10.5047i	−0.364405	+	0.631168i	−0.988680	−	0.150036i	$-0.952061\pi$
$277$	−6.06491	+	10.5047i	−0.364405	+	0.631168i	0.624276	+	0.781204i	$0.285394\pi$
$278$	4.56931	+	7.91427i	0.274049	+	0.474667i
$279$		0			0
$280$		0			0
$281$			32.6206i			1.94598i	0.230839	+	0.972992i	$0.425853\pi$
$281$			32.6206i			1.94598i	−0.230839	+	0.972992i	$0.574147\pi$
$282$		0			0
$283$	−10.9647	−	6.33045i	−0.651781	−	0.376306i	0.137357	−	0.990522i	$-0.456139\pi$
$283$	−10.9647	−	6.33045i	−0.651781	−	0.376306i	−0.789138	+	0.614216i	$0.789473\pi$
$284$	7.91656	+	4.57063i	0.469761	+	0.271217i
$285$		0			0
$286$			13.6075i			0.804628i
$287$	−17.9088	−	5.16019i	−1.05712	−	0.304596i
$288$		0			0
$289$	6.35357	+	11.0047i	0.373739	+	0.647335i
$290$		0			0
$291$		0			0
$292$	−0.937339	+	0.541173i	−0.0548536	+	0.0316698i
$293$	25.1151			1.46724			0.733621	−	0.679559i	$-0.237829\pi$
$293$	25.1151			1.46724			0.733621	+	0.679559i	$0.237829\pi$
$294$		0			0
$295$		0			0
$296$	2.57132	−	1.48455i	0.149455	−	0.0862880i
$297$		0			0
$298$	5.22532	−	9.05052i	0.302695	−	0.524283i
$299$	−5.28472	−	9.15340i	−0.305623	−	0.529355i
$300$		0			0
$301$	−21.7611	−	6.27018i	−1.25429	−	0.361407i
$302$		−	17.7187i		−	1.01960i
$303$		0			0
$304$	−5.12164	−	2.95698i	−0.293746	−	0.169595i
$305$		0			0
$306$		0			0
$307$		−	18.5674i		−	1.05970i	−0.848092	−	0.529849i	$-0.822249\pi$
$307$		−	18.5674i		−	1.05970i	0.848092	−	0.529849i	$-0.177751\pi$
$308$	−6.15518	+	1.52626i	−0.350724	+	0.0869668i
$309$		0			0
$310$		0			0
$311$	−6.21831	+	10.7704i	−0.352608	+	0.610735i	−0.986706	−	0.162518i	$-0.948038\pi$
$311$	−6.21831	+	10.7704i	−0.352608	+	0.610735i	0.634098	+	0.773253i	$0.281372\pi$
$312$		0			0
$313$	−10.7504	+	6.20675i	−0.607649	+	0.350826i	−0.772045	−	0.635568i	$-0.780766\pi$
$313$	−10.7504	+	6.20675i	−0.607649	+	0.350826i	0.164396	+	0.986394i	$0.447433\pi$
$314$	−6.08297			−0.343282
$315$		0			0
$316$	−16.7678			−0.943265
$317$	−21.3444	+	12.3232i	−1.19882	+	0.692141i	−0.960293	−	0.278995i	$-0.909999\pi$
$317$	−21.3444	+	12.3232i	−1.19882	+	0.692141i	−0.238530	+	0.971135i	$0.576665\pi$
$318$		0			0
$319$	5.85937	−	10.1487i	0.328062	−	0.568219i
$320$		0			0
$321$		0			0
$322$	3.54767	−	3.41715i	0.197704	−	0.190430i
$323$		−	12.2533i		−	0.681791i
$324$		0			0
$325$		0			0
$326$	0.811759	+	0.468670i	0.0449592	+	0.0259572i
$327$		0			0
$328$		−	7.04428i		−	0.388955i
$329$	−3.55240	−	14.3263i	−0.195850	−	0.789835i
$330$		0			0
$331$	12.5788	+	21.7871i	0.691392	+	1.19753i	0.971382	+	0.237524i	$0.0763357\pi$
$331$	12.5788	+	21.7871i	0.691392	+	1.19753i	−0.279989	+	0.960003i	$0.590331\pi$
$332$	6.80611	−	11.7885i	0.373534	−	0.646980i
$333$		0			0
$334$	−14.9044	+	8.60505i	−0.815531	+	0.470847i
$335$		0			0
$336$		0			0
$337$	−14.4214			−0.785584			−0.392792	−	0.919627i	$-0.628491\pi$
$337$	−14.4214			−0.785584			−0.392792	+	0.919627i	$0.628491\pi$
$338$	−16.6536	+	9.61494i	−0.905834	+	0.522984i
$339$		0			0
$340$		0			0
$341$	−5.42479	−	9.39601i	−0.293769	−	0.508823i
$342$		0			0
$343$	−12.3393	−	13.8109i	−0.666261	−	0.745719i
$344$		−	8.55956i		−	0.461500i
$345$		0			0
$346$	1.71146	+	0.988114i	0.0920088	+	0.0531213i
$347$	−12.5457	−	7.24329i	−0.673491	−	0.388840i	0.123907	−	0.992294i	$-0.460457\pi$
$347$	−12.5457	−	7.24329i	−0.673491	−	0.388840i	−0.797398	+	0.603454i	$0.793791\pi$
$348$		0			0
$349$		−	2.12483i		−	0.113739i	−0.998382	−	0.0568697i	$-0.981888\pi$
$349$		−	2.12483i		−	0.113739i	0.998382	−	0.0568697i	$-0.0181119\pi$
$350$		0			0
$351$		0			0
$352$	−1.19845	−	2.07577i	−0.0638775	−	0.110639i
$353$	−7.26335	+	12.5805i	−0.386589	+	0.669592i	−0.991988	−	0.126330i	$-0.959680\pi$
$353$	−7.26335	+	12.5805i	−0.386589	+	0.669592i	0.605399	+	0.795922i	$0.293013\pi$
$354$		0			0
$355$		0			0
$356$	13.2626			0.702916
$357$		0			0
$358$	0.887342			0.0468975
$359$	−3.42054	+	1.97485i	−0.180529	+	0.104228i	−0.587541	−	0.809194i	$-0.699904\pi$
$359$	−3.42054	+	1.97485i	−0.180529	+	0.104228i	0.407012	+	0.913423i	$0.366571\pi$
$360$		0			0
$361$	7.98749	−	13.8347i	0.420394	−	0.728144i
$362$	−2.44986	−	4.24329i	−0.128762	−	0.223022i
$363$		0			0
$364$	−10.4201	−	10.8181i	−0.546160	−	0.567022i
$365$		0			0
$366$		0			0
$367$	−23.9826	−	13.8464i	−1.25188	−	0.722775i	−0.280400	−	0.959883i	$-0.590467\pi$
$367$	−23.9826	−	13.8464i	−1.25188	−	0.722775i	−0.971483	+	0.237109i	$0.923800\pi$
$368$	1.61233	+	0.930877i	0.0840483	+	0.0485253i
$369$		0			0
$370$		0			0
$371$	−7.69193	−	7.98574i	−0.399345	−	0.414599i
$372$		0			0
$373$	−6.06491	−	10.5047i	−0.314029	−	0.543914i	0.665202	−	0.746664i	$-0.268346\pi$
$373$	−6.06491	−	10.5047i	−0.314029	−	0.543914i	−0.979231	+	0.202750i	$0.935012\pi$
$374$	2.48309	−	4.30084i	0.128398	−	0.222391i
$375$		0			0
$376$	4.83140	−	2.78941i	0.249160	−	0.143853i
$377$	27.7563			1.42952
$378$		0			0
$379$	18.6821			0.959636			0.479818	−	0.877368i	$-0.340703\pi$
$379$	18.6821			0.959636			0.479818	+	0.877368i	$0.340703\pi$
$380$		0			0
$381$		0			0
$382$	−1.41421	+	2.44949i	−0.0723575	+	0.125327i
$383$	5.51463	+	9.55162i	0.281784	+	0.488065i	0.971824	−	0.235706i	$-0.0757404\pi$
$383$	5.51463	+	9.55162i	0.281784	+	0.488065i	−0.690040	+	0.723771i	$0.742407\pi$
$384$		0			0
$385$		0			0
$386$			19.4966i			0.992349i
$387$		0			0
$388$	−11.1077	−	6.41301i	−0.563906	−	0.325571i
$389$	−29.7662	−	17.1855i	−1.50921	−	0.871341i	−0.999942	−	0.0107299i	$-0.996584\pi$
$389$	−29.7662	−	17.1855i	−1.50921	−	0.871341i	−0.509264	−	0.860611i	$-0.670082\pi$
$390$		0			0
$391$			3.85741i			0.195078i
$392$	3.72468	−	5.92678i	0.188125	−	0.299348i
$393$		0			0
$394$	13.5788	+	23.5191i	0.684089	+	1.18488i
$395$		0			0
$396$		0			0
$397$	26.8561	−	15.5054i	1.34787	−	0.778191i	0.359920	−	0.932983i	$-0.382804\pi$
$397$	26.8561	−	15.5054i	1.34787	−	0.778191i	0.987947	+	0.154792i	$0.0494706\pi$
$398$	3.46410			0.173640
$399$		0			0
$400$		0			0
$401$	8.20771	−	4.73872i	0.409873	−	0.236641i	−0.280862	−	0.959748i	$-0.590620\pi$
$401$	8.20771	−	4.73872i	0.409873	−	0.236641i	0.690735	+	0.723108i	$0.257287\pi$
$402$		0			0
$403$	12.8488	−	22.2548i	0.640045	−	1.10859i
$404$	−4.45573	−	7.71756i	−0.221681	−	0.383963i
$405$		0			0
$406$	3.11323	+	12.5552i	0.154507	+	0.623104i
$407$			7.11665i			0.352759i
$408$		0			0
$409$	−8.20805	−	4.73892i	−0.405862	−	0.234324i	0.283148	−	0.959076i	$-0.408621\pi$
$409$	−8.20805	−	4.73892i	−0.405862	−	0.234324i	−0.689010	+	0.724752i	$0.741954\pi$
$410$		0			0
$411$		0			0
$412$		−	10.8198i		−	0.533053i
$413$	3.82301	−	3.68235i	0.188118	−	0.181197i
$414$		0			0
$415$		0			0
$416$	2.83857	−	4.91654i	0.139172	−	0.241053i
$417$		0			0
$418$	12.2760	−	7.08758i	0.600441	−	0.346665i
$419$	2.54445			0.124305			0.0621523	−	0.998067i	$-0.480204\pi$
$419$	2.54445			0.124305			0.0621523	+	0.998067i	$0.480204\pi$
$420$		0			0
$421$	−5.08573			−0.247863			−0.123932	−	0.992291i	$-0.539550\pi$
$421$	−5.08573			−0.247863			−0.123932	+	0.992291i	$0.539550\pi$
$422$	−3.51668	+	2.03035i	−0.171189	+	0.0988361i
$423$		0			0
$424$	2.09538	−	3.62931i	0.101761	−	0.176255i
$425$		0			0
$426$		0			0
$427$	−31.9836	+	7.93077i	−1.54780	+	0.383797i
$428$		−	5.57707i		−	0.269578i
$429$		0			0
$430$		0			0
$431$	−11.5164	−	6.64902i	−0.554727	−	0.320272i	0.196299	−	0.980544i	$-0.437108\pi$
$431$	−11.5164	−	6.64902i	−0.554727	−	0.320272i	−0.751027	+	0.660272i	$0.770441\pi$
$432$		0			0
$433$			12.7895i			0.614626i	0.951608	+	0.307313i	$0.0994299\pi$
$433$			12.7895i			0.614626i	−0.951608	+	0.307313i	$0.900570\pi$
$434$	11.5078	+	3.31583i	0.552394	+	0.159165i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−5.50517	+	9.53524i	−0.263348	+	0.456132i
$438$		0			0
$439$	−0.323211	+	0.186606i	−0.0154260	+	0.00890623i	−0.507693	−	0.861538i	$-0.669502\pi$
$439$	−0.323211	+	0.186606i	−0.0154260	+	0.00890623i	0.492267	+	0.870444i	$0.336168\pi$
$440$		0			0
$441$		0			0
$442$	11.7626			0.559490
$443$	−21.3328	+	12.3165i	−1.01355	+	0.585175i	−0.912230	−	0.409679i	$-0.865641\pi$
$443$	−21.3328	+	12.3165i	−1.01355	+	0.585175i	−0.101323	+	0.994854i	$0.532307\pi$
$444$		0			0
$445$		0			0
$446$	−8.07432	−	13.9851i	−0.382330	−	0.662215i
$447$		0			0
$448$	2.54232	+	0.732536i	0.120113	+	0.0346091i
$449$			40.6223i			1.91708i	0.284950	+	0.958542i	$0.408023\pi$
$449$			40.6223i			1.91708i	−0.284950	+	0.958542i	$0.591977\pi$
$450$		0			0
$451$	14.6223	+	8.44220i	0.688538	+	0.397528i
$452$	−12.5599	−	7.25148i	−0.590769	−	0.341081i
$453$		0			0
$454$			1.67980i			0.0788370i
$455$		0			0
$456$		0			0
$457$	−0.495276	−	0.857843i	−0.0231680	−	0.0401282i	0.854209	−	0.519930i	$-0.174042\pi$
$457$	−0.495276	−	0.857843i	−0.0231680	−	0.0401282i	−0.877377	+	0.479802i	$0.840709\pi$
$458$	6.30136	−	10.9143i	0.294443	−	0.509991i
$459$		0			0
$460$		0			0
$461$	−20.7397			−0.965945			−0.482972	−	0.875636i	$-0.660443\pi$
$461$	−20.7397			−0.965945			−0.482972	+	0.875636i	$0.660443\pi$
$462$		0			0
$463$	−1.46421			−0.0680476			−0.0340238	−	0.999421i	$-0.510832\pi$
$463$	−1.46421			−0.0680476			−0.0340238	+	0.999421i	$0.510832\pi$
$464$	−4.23411	+	2.44457i	−0.196564	+	0.113486i
$465$		0			0
$466$	−7.25818	+	12.5715i	−0.336229	+	0.582365i
$467$	18.1340	+	31.4090i	0.839142	+	1.45344i	0.890613	+	0.454762i	$0.150276\pi$
$467$	18.1340	+	31.4090i	0.839142	+	1.45344i	−0.0514705	+	0.998675i	$0.516391\pi$
$468$		0			0
$469$	14.5246	−	13.9902i	0.670682	−	0.646006i
$470$		0			0
$471$		0			0
$472$	1.73746	+	1.00312i	0.0799730	+	0.0461724i
$473$	17.7677	+	10.2582i	0.816959	+	0.471672i
$474$		0			0
$475$		0			0
$476$	1.31933	+	5.32066i	0.0604714	+	0.243872i
$477$		0			0
$478$	0.103545	+	0.179344i	0.00473602	+	0.00820302i
$479$	5.16288	−	8.94237i	0.235898	−	0.408587i	−0.723635	−	0.690183i	$-0.757530\pi$
$479$	5.16288	−	8.94237i	0.235898	−	0.408587i	0.959533	+	0.281595i	$0.0908635\pi$
$480$		0			0
$481$	−14.5978	+	8.42802i	−0.665600	+	0.384285i
$482$	10.4405			0.475551
$483$		0			0
$484$	−5.25489			−0.238859
$485$		0			0
$486$		0			0
$487$	10.1645	−	17.6055i	0.460599	−	0.797781i	−0.538392	−	0.842695i	$-0.680968\pi$
$487$	10.1645	−	17.6055i	0.460599	−	0.797781i	0.998991	+	0.0449135i	$0.0143012\pi$
$488$	−6.22739	−	10.7862i	−0.281901	−	0.488266i
$489$		0			0
$490$		0			0
$491$		−	34.6034i		−	1.56163i	−0.624764	−	0.780814i	$-0.714805\pi$
$491$		−	34.6034i		−	1.56163i	0.624764	−	0.780814i	$-0.285195\pi$
$492$		0			0
$493$	−8.77276	−	5.06495i	−0.395105	−	0.228114i
$494$	29.0763	+	16.7872i	1.30820	+	0.755292i
$495$		0			0
$496$			4.52651i			0.203247i
$497$	6.69630	−	23.2400i	0.300370	−	1.04246i
$498$		0			0
$499$	1.47545	+	2.55555i	0.0660501	+	0.114402i	0.897159	−	0.441707i	$-0.145627\pi$
$499$	1.47545	+	2.55555i	0.0660501	+	0.114402i	−0.831109	+	0.556109i	$0.812294\pi$
$500$		0			0
$501$		0			0
$502$	24.8085	−	14.3232i	1.10726	−	0.639277i
$503$	−31.8907			−1.42193			−0.710967	−	0.703225i	$-0.751742\pi$
$503$	−31.8907			−1.42193			−0.710967	+	0.703225i	$0.751742\pi$
$504$		0			0
$505$		0			0
$506$	−3.86458	+	2.23121i	−0.171801	+	0.0991896i
$507$		0			0
$508$	−9.62311	+	16.6677i	−0.426957	+	0.739510i
$509$	−0.421199	−	0.729538i	−0.0186693	−	0.0323362i	0.856540	−	0.516081i	$-0.172610\pi$
$509$	−0.421199	−	0.729538i	−0.0186693	−	0.0323362i	−0.875209	+	0.483745i	$0.839276\pi$
$510$		0			0
$511$	1.98659	+	2.06247i	0.0878815	+	0.0912383i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	21.5805	+	12.4595i	0.951875	+	0.549565i
$515$		0			0
$516$		0			0
$517$			13.3718i			0.588093i
$518$	−5.44964	−	5.65780i	−0.239443	−	0.248589i
$519$		0			0
$520$		0			0
$521$	−2.81499	+	4.87571i	−0.123327	+	0.213609i	−0.921078	−	0.389379i	$-0.872690\pi$
$521$	−2.81499	+	4.87571i	−0.123327	+	0.213609i	0.797751	+	0.602987i	$0.206023\pi$
$522$		0			0
$523$	15.4482	−	8.91899i	0.675500	−	0.390000i	−0.122657	−	0.992449i	$-0.539142\pi$
$523$	15.4482	−	8.91899i	0.675500	−	0.390000i	0.798158	+	0.602449i	$0.205808\pi$
$524$	−4.69940			−0.205294
$525$		0			0
$526$	−19.1908			−0.836757
$527$	−8.12210	+	4.68930i	−0.353804	+	0.204269i
$528$		0			0
$529$	−9.76694	+	16.9168i	−0.424649	+	0.735514i
$530$		0			0
$531$		0			0
$532$	−4.33219	+	15.0352i	−0.187824	+	0.651858i
$533$			39.9913i			1.73222i
$534$		0			0
$535$		0			0
$536$	6.60103	+	3.81111i	0.285121	+	0.164615i
$537$		0			0
$538$			4.85489i			0.209309i
$539$	7.83882	+	14.8345i	0.337642	+	0.638968i
$540$		0			0
$541$	12.7120	+	22.0179i	0.546533	+	0.946623i	0.998509	+	0.0545925i	$0.0173860\pi$
$541$	12.7120	+	22.0179i	0.546533	+	0.946623i	−0.451976	+	0.892030i	$0.649281\pi$
$542$	−6.83257	+	11.8344i	−0.293484	+	0.508329i
$543$		0			0
$544$	−1.79434	+	1.03596i	−0.0769316	+	0.0444165i
$545$		0			0
$546$		0			0
$547$	12.1182			0.518138			0.259069	−	0.965859i	$-0.416584\pi$
$547$	12.1182			0.518138			0.259069	+	0.965859i	$0.416584\pi$
$548$	19.8185	−	11.4422i	0.846606	−	0.488788i
$549$		0			0
$550$		0			0
$551$	−14.4571	−	25.0404i	−0.615892	−	1.06676i
$552$		0			0
$553$	10.6772	+	43.0595i	0.454040	+	1.83108i
$554$			12.1298i			0.515346i
$555$		0			0
$556$	7.91427	+	4.56931i	0.335640	+	0.193782i
$557$	1.33331	+	0.769786i	0.0564941	+	0.0326169i	0.527981	−	0.849256i	$-0.322949\pi$
$557$	1.33331	+	0.769786i	0.0564941	+	0.0326169i	−0.471487	+	0.881873i	$0.656283\pi$
$558$		0			0
$559$			48.5938i			2.05530i
$560$		0			0
$561$		0			0
$562$	16.3103	+	28.2503i	0.688009	+	1.19167i
$563$	11.2322	−	19.4548i	0.473381	−	0.819920i	−0.526155	−	0.850389i	$-0.676367\pi$
$563$	11.2322	−	19.4548i	0.473381	−	0.819920i	0.999536	+	0.0304689i	$0.00970005\pi$
$564$		0			0
$565$		0			0
$566$	−12.6609			−0.532177
$567$		0			0
$568$	9.14126			0.383559
$569$	9.35810	−	5.40290i	0.392312	−	0.226501i	−0.290849	−	0.956769i	$-0.593938\pi$
$569$	9.35810	−	5.40290i	0.392312	−	0.226501i	0.683161	+	0.730267i	$0.260605\pi$
$570$		0			0
$571$	3.98169	−	6.89649i	0.166629	−	0.288609i	−0.770604	−	0.637314i	$-0.780045\pi$
$571$	3.98169	−	6.89649i	0.166629	−	0.288609i	0.937232	+	0.348705i	$0.113379\pi$
$572$	6.80375	+	11.7844i	0.284479	+	0.492732i
$573$		0			0
$574$	−18.0896	+	4.48555i	−0.755045	+	0.187223i
$575$		0			0
$576$		0			0
$577$	−21.2980	−	12.2964i	−0.886648	−	0.511906i	−0.0138033	−	0.999905i	$-0.504394\pi$
$577$	−21.2980	−	12.2964i	−0.886648	−	0.511906i	−0.872845	+	0.487998i	$0.837727\pi$
$578$	11.0047	+	6.35357i	0.457735	+	0.264274i
$579$		0			0
$580$		0			0
$581$	−34.6066	−	9.97144i	−1.43573	−	0.413685i
$582$		0			0
$583$	5.02242	+	8.69908i	0.208007	+	0.360279i
$584$	−0.541173	+	0.937339i	−0.0223939	+	0.0387874i
$585$		0			0
$586$	21.7503	−	12.5576i	0.898498	−	0.518748i
$587$	12.8469			0.530248			0.265124	−	0.964214i	$-0.414587\pi$
$587$	12.8469			0.530248			0.265124	+	0.964214i	$0.414587\pi$
$588$		0			0
$589$	−26.7696			−1.10302
$590$		0			0
$591$		0			0
$592$	1.48455	−	2.57132i	0.0610148	−	0.105681i
$593$	8.58155	+	14.8637i	0.352402	+	0.610379i	0.986670	−	0.162735i	$-0.0520316\pi$
$593$	8.58155	+	14.8637i	0.352402	+	0.610379i	−0.634268	+	0.773114i	$0.718698\pi$
$594$		0			0
$595$		0			0
$596$		−	10.4506i		−	0.428075i
$597$		0			0
$598$	−9.15340	−	5.28472i	−0.374310	−	0.216108i
$599$	−16.9813	−	9.80416i	−0.693837	−	0.400587i	0.111211	−	0.993797i	$-0.464527\pi$
$599$	−16.9813	−	9.80416i	−0.693837	−	0.400587i	−0.805048	+	0.593210i	$0.797860\pi$
$600$		0			0
$601$			28.2340i			1.15169i	0.817560	+	0.575844i	$0.195326\pi$
$601$			28.2340i			1.15169i	−0.817560	+	0.575844i	$0.804674\pi$
$602$	−21.9808	+	5.45043i	−0.895870	+	0.222143i
$603$		0			0
$604$	−8.85937	−	15.3449i	−0.360483	−	0.624374i
$605$		0			0
$606$		0			0
$607$	−8.35987	+	4.82657i	−0.339316	+	0.195904i	−0.659970	−	0.751292i	$-0.729431\pi$
$607$	−8.35987	+	4.82657i	−0.339316	+	0.195904i	0.320653	+	0.947197i	$0.396098\pi$
$608$	−5.91397			−0.239843
$609$		0			0
$610$		0			0
$611$	−27.4285	+	15.8359i	−1.10964	+	0.640650i
$612$		0			0
$613$	4.52794	−	7.84262i	0.182882	−	0.316761i	−0.759979	−	0.649948i	$-0.774791\pi$
$613$	4.52794	−	7.84262i	0.182882	−	0.316761i	0.942861	+	0.333187i	$0.108124\pi$
$614$	−9.28370	−	16.0798i	−0.374660	−	0.648930i
$615$		0			0
$616$	−4.56742	+	4.39937i	−0.184026	+	0.177256i
$617$		−	25.3122i		−	1.01903i	−0.860462	−	0.509515i	$-0.829825\pi$
$617$		−	25.3122i		−	1.01903i	0.860462	−	0.509515i	$-0.170175\pi$
$618$		0			0
$619$	−33.6634	−	19.4356i	−1.35304	−	0.781181i	−0.364370	−	0.931254i	$-0.618716\pi$
$619$	−33.6634	−	19.4356i	−1.35304	−	0.781181i	−0.988675	+	0.150073i	$0.952049\pi$
$620$		0			0
$621$		0			0
$622$			12.4366i			0.498663i
$623$	−8.44516	−	34.0581i	−0.338348	−	1.36451i
$624$		0			0
$625$		0			0
$626$	−6.20675	+	10.7504i	−0.248072	+	0.429673i
$627$		0			0
$628$	−5.26801	+	3.04149i	−0.210216	+	0.121369i
$629$	6.15177			0.245287
$630$		0			0
$631$	−23.8670			−0.950129			−0.475065	−	0.879951i	$-0.657575\pi$
$631$	−23.8670			−0.950129			−0.475065	+	0.879951i	$0.657575\pi$
$632$	−14.5214	+	8.38392i	−0.577629	+	0.333494i
$633$		0			0
$634$	−12.3232	+	21.3444i	−0.489417	+	0.847696i
$635$		0			0
$636$		0			0
$637$	−21.1455	+	33.6472i	−0.837816	+	1.33315i
$638$		−	11.7187i		−	0.463949i
$639$		0			0
$640$		0			0
$641$	−30.2066	−	17.4398i	−1.19309	−	0.688830i	−0.234083	−	0.972217i	$-0.575209\pi$
$641$	−30.2066	−	17.4398i	−1.19309	−	0.688830i	−0.959006	+	0.283386i	$0.908542\pi$
$642$		0			0
$643$			6.25944i			0.246848i	0.992354	+	0.123424i	$0.0393875\pi$
$643$			6.25944i			0.246848i	−0.992354	+	0.123424i	$0.960612\pi$
$644$	1.36380	−	4.73317i	0.0537413	−	0.186513i
$645$		0			0
$646$	−6.12664	−	10.6117i	−0.241050	−	0.417510i
$647$	18.7511	−	32.4778i	0.737181	−	1.27683i	−0.216579	−	0.976265i	$-0.569490\pi$
$647$	18.7511	−	32.4778i	0.737181	−	1.27683i	0.953760	−	0.300570i	$-0.0971768\pi$
$648$		0			0
$649$	−4.16451	+	2.40438i	−0.163471	+	0.0943801i
$650$		0			0
$651$		0			0
$652$	0.937339			0.0367090
$653$	22.9077	−	13.2258i	0.896449	−	0.517565i	0.0204023	−	0.999792i	$-0.493505\pi$
$653$	22.9077	−	13.2258i	0.896449	−	0.517565i	0.876046	+	0.482227i	$0.160172\pi$
$654$		0			0
$655$		0			0
$656$	−3.52214	−	6.10053i	−0.137516	−	0.238186i
$657$		0			0
$658$	−10.2396	−	10.6307i	−0.399182	−	0.414430i
$659$		−	19.9524i		−	0.777234i	−0.921399	−	0.388617i	$-0.872953\pi$
$659$		−	19.9524i		−	0.777234i	0.921399	−	0.388617i	$-0.127047\pi$
$660$		0			0
$661$	4.71203	+	2.72049i	0.183277	+	0.105815i	0.588831	−	0.808256i	$-0.299588\pi$
$661$	4.71203	+	2.72049i	0.183277	+	0.105815i	−0.405555	+	0.914071i	$0.632922\pi$
$662$	21.7871	+	12.5788i	0.846779	+	0.488888i
$663$		0			0
$664$		−	13.6122i		−	0.528257i
$665$		0			0
$666$		0			0
$667$	4.55118	+	7.88287i	0.176222	+	0.305226i
$668$	−8.60505	+	14.9044i	−0.332939	+	0.576668i
$669$		0			0
$670$		0			0
$671$	29.8528			1.15245
$672$		0			0
$673$	−8.50635			−0.327896			−0.163948	−	0.986469i	$-0.552423\pi$
$673$	−8.50635			−0.327896			−0.163948	+	0.986469i	$0.552423\pi$
$674$	−12.4893	+	7.21070i	−0.481070	+	0.277746i
$675$		0			0
$676$	−9.61494	+	16.6536i	−0.369805	+	0.640522i
$677$	−2.54320	−	4.40495i	−0.0977430	−	0.169296i	0.813007	−	0.582254i	$-0.197829\pi$
$677$	−2.54320	−	4.40495i	−0.0977430	−	0.169296i	−0.910750	+	0.412958i	$0.864496\pi$
$678$		0			0
$679$	−9.39552	+	32.6079i	−0.360567	+	1.25138i
$680$		0			0
$681$		0			0
$682$	−9.39601	−	5.42479i	−0.359792	−	0.207726i
$683$	−18.1991	−	10.5073i	−0.696370	−	0.402050i	0.109624	−	0.993973i	$-0.465035\pi$
$683$	−18.1991	−	10.5073i	−0.696370	−	0.402050i	−0.805994	+	0.591924i	$0.798369\pi$
$684$		0			0
$685$		0			0
$686$	−17.5916	−	5.79094i	−0.671651	−	0.221099i
$687$		0			0
$688$	−4.27978	−	7.41279i	−0.163165	−	0.282610i
$689$	−11.8958	+	20.6041i	−0.453193	+	0.784953i
$690$		0			0
$691$	−21.5723	+	12.4548i	−0.820649	+	0.473802i	−0.850640	−	0.525748i	$-0.823785\pi$
$691$	−21.5723	+	12.4548i	−0.820649	+	0.473802i	0.0299912	+	0.999550i	$0.490452\pi$
$692$	1.97623			0.0751249
$693$		0			0
$694$	−14.4866			−0.549903
$695$		0			0
$696$		0			0
$697$	7.29761	−	12.6398i	0.276417	−	0.478767i
$698$	−1.06241	−	1.84015i	−0.0402129	−	0.0696508i
$699$		0			0
$700$		0			0
$701$			22.5321i			0.851025i	0.904953	+	0.425512i	$0.139906\pi$
$701$			22.5321i			0.851025i	−0.904953	+	0.425512i	$0.860094\pi$
$702$		0			0
$703$	15.2067	+	8.77961i	0.573532	+	0.331129i
$704$	−2.07577	−	1.19845i	−0.0782336	−	0.0451682i
$705$		0			0
$706$			14.5267i			0.546719i
$707$	−16.9813	+	16.3565i	−0.638647	+	0.615150i
$708$		0			0
$709$	12.4504	+	21.5648i	0.467586	+	0.809882i	0.999314	−	0.0370327i	$-0.0117906\pi$
$709$	12.4504	+	21.5648i	0.467586	+	0.809882i	−0.531728	+	0.846915i	$0.678457\pi$
$710$		0			0
$711$		0			0
$712$	11.4857	−	6.63129i	0.430446	−	0.248518i
$713$	8.42726			0.315603
$714$		0			0
$715$		0			0
$716$	0.768461	−	0.443671i	0.0287187	−	0.0165808i
$717$		0			0
$718$	−1.97485	+	3.42054i	−0.0737007	+	0.127653i
$719$	19.9241	+	34.5096i	0.743045	+	1.28699i	0.951103	+	0.308875i	$0.0999526\pi$
$719$	19.9241	+	34.5096i	0.743045	+	1.28699i	−0.208057	+	0.978117i	$0.566714\pi$
$720$		0			0
$721$	−27.7850	+	6.88967i	−1.03477	+	0.256585i
$722$		−	15.9750i		−	0.594527i
$723$		0			0
$724$	−4.24329	−	2.44986i	−0.157701	−	0.0910485i
$725$		0			0
$726$		0			0
$727$			0.124004i			0.00459906i	0.999997	+	0.00229953i	$0.000731964\pi$
$727$			0.124004i			0.00459906i	−0.999997	+	0.00229953i	$0.999268\pi$
$728$	−14.4331	−	4.15870i	−0.534926	−	0.154132i
$729$		0			0
$730$		0			0
$731$	8.86738	−	15.3587i	0.327972	−	0.568064i
$732$		0			0
$733$	24.7231	−	14.2739i	0.913168	−	0.527218i	0.0317189	−	0.999497i	$-0.489902\pi$
$733$	24.7231	−	14.2739i	0.913168	−	0.527218i	0.881449	+	0.472279i	$0.156569\pi$
$734$	−27.6927			−1.02216
$735$		0			0
$736$	1.86175			0.0686252
$737$	−15.8220	+	9.13483i	−0.582811	+	0.336486i
$738$		0			0
$739$	−9.51807	+	16.4858i	−0.350128	+	0.606439i	−0.986272	−	0.165131i	$-0.947195\pi$
$739$	−9.51807	+	16.4858i	−0.350128	+	0.606439i	0.636144	+	0.771571i	$0.280529\pi$
$740$		0			0
$741$		0			0
$742$	−10.6543	−	3.06989i	−0.391131	−	0.112699i
$743$			17.0800i			0.626605i	0.949653	+	0.313303i	$0.101435\pi$
$743$			17.0800i			0.626605i	−0.949653	+	0.313303i	$0.898565\pi$
$744$		0			0
$745$		0			0
$746$	−10.5047	−	6.06491i	−0.384605	−	0.222052i
$747$		0			0
$748$		−	4.96618i		−	0.181582i
$749$	−14.3218	+	3.55129i	−0.523308	+	0.129761i
$750$		0			0
$751$	8.44463	+	14.6265i	0.308149	+	0.533730i	0.977957	−	0.208804i	$-0.0669572\pi$
$751$	8.44463	+	14.6265i	0.308149	+	0.533730i	−0.669809	+	0.742534i	$0.733624\pi$
$752$	2.78941	−	4.83140i	0.101719	−	0.176183i
$753$		0			0
$754$	24.0376	−	13.8781i	0.875399	−	0.505412i
$755$		0			0
$756$		0			0
$757$	−33.4057			−1.21415			−0.607076	−	0.794644i	$-0.707658\pi$
$757$	−33.4057			−1.21415			−0.607076	+	0.794644i	$0.707658\pi$
$758$	16.1792	−	9.34106i	0.587655	−	0.339282i
$759$		0			0
$760$		0			0
$761$	−16.3074	−	28.2453i	−0.591143	−	1.02389i	−0.994079	−	0.108662i	$-0.965343\pi$
$761$	−16.3074	−	28.2453i	−0.591143	−	1.02389i	0.402935	−	0.915228i	$-0.367990\pi$
$762$		0			0
$763$	−3.81111	+	3.67089i	−0.137971	+	0.132895i
$764$			2.82843i			0.102329i
$765$		0			0
$766$	9.55162	+	5.51463i	0.345114	+	0.199252i
$767$	−9.86379	−	5.69486i	−0.356161	−	0.205630i
$768$		0			0
$769$		−	22.4396i		−	0.809192i	−0.914495	−	0.404596i	$-0.867412\pi$
$769$		−	22.4396i		−	0.809192i	0.914495	−	0.404596i	$-0.132588\pi$
$770$		0			0
$771$		0			0
$772$	9.74828	+	16.8845i	0.350848	+	0.607687i
$773$	19.9165	−	34.4965i	0.716348	−	1.24075i	−0.246089	−	0.969247i	$-0.579145\pi$
$773$	19.9165	−	34.4965i	0.716348	−	1.24075i	0.962437	−	0.271505i	$-0.0875212\pi$
$774$		0			0
$775$		0			0
$776$	−12.8260			−0.460428
$777$		0			0
$778$	−34.3710			−1.23226
$779$	36.0783	−	20.8298i	1.29264	−	0.746306i
$780$		0			0
$781$	−10.9553	+	18.9752i	−0.392012	+	0.678985i
$782$	1.92871	+	3.34062i	0.0689704	+	0.119460i
$783$		0			0
$784$	0.262276	−	6.99508i	0.00936701	−	0.249824i
$785$		0			0
$786$		0			0
$787$	−14.4912	−	8.36649i	−0.516555	−	0.298233i	0.218969	−	0.975732i	$-0.429731\pi$
$787$	−14.4912	−	8.36649i	−0.516555	−	0.298233i	−0.735524	+	0.677499i	$0.763064\pi$
$788$	23.5191	+	13.5788i	0.837835	+	0.483724i
$789$		0			0
$790$		0			0
$791$	−10.6239	+	36.8711i	−0.377743	+	1.31099i
$792$		0			0
$793$	35.3537	+	61.2344i	1.25545	+	2.17450i
$794$	15.5054	−	26.8561i	0.550264	−	0.953086i
$795$		0			0
$796$	3.00000	−	1.73205i	0.106332	−	0.0613909i
$797$	2.68812			0.0952182			0.0476091	−	0.998866i	$-0.484840\pi$
$797$	2.68812			0.0952182			0.0476091	+	0.998866i	$0.484840\pi$
$798$		0			0
$799$	11.5589			0.408924
$800$		0			0
$801$		0			0
$802$	4.73872	−	8.20771i	0.167330	−	0.289824i
$803$	−1.29714	−	2.24670i	−0.0457749	−	0.0792845i
$804$		0			0
$805$		0			0
$806$		−	25.6976i		−	0.905161i
$807$		0			0
$808$	−7.71756	−	4.45573i	−0.271503	−	0.156752i
$809$	−27.2213	−	15.7162i	−0.957051	−	0.552554i	−0.0617867	−	0.998089i	$-0.519680\pi$
$809$	−27.2213	−	15.7162i	−0.957051	−	0.552554i	−0.895264	+	0.445536i	$0.853013\pi$
$810$		0			0
$811$			49.3830i			1.73407i	0.498246	+	0.867036i	$0.333978\pi$
$811$			49.3830i			1.73407i	−0.498246	+	0.867036i	$0.666022\pi$
$812$	8.97374	+	9.31651i	0.314916	+	0.326945i
$813$		0			0
$814$	3.55832	+	6.16320i	0.124719	+	0.216020i
$815$		0			0
$816$		0			0
$817$	43.8390	−	25.3105i	1.53373	−	0.885501i
$818$	−9.47784			−0.331385
$819$		0			0
$820$		0			0
$821$	38.7342	−	22.3632i	1.35183	−	0.780480i	0.363325	−	0.931662i	$-0.381641\pi$
$821$	38.7342	−	22.3632i	1.35183	−	0.780480i	0.988506	+	0.151182i	$0.0483080\pi$
$822$		0			0
$823$	−6.57071	+	11.3808i	−0.229041	+	0.396710i	−0.957524	−	0.288353i	$-0.906892\pi$
$823$	−6.57071	+	11.3808i	−0.229041	+	0.396710i	0.728483	+	0.685063i	$0.240226\pi$
$824$	−5.40989	−	9.37021i	−0.188463	−	0.326427i
$825$		0			0
$826$	1.46965	−	5.10052i	0.0511355	−	0.177470i
$827$		−	47.4125i		−	1.64869i	−0.566086	−	0.824346i	$-0.691543\pi$
$827$		−	47.4125i		−	1.64869i	0.566086	−	0.824346i	$-0.308457\pi$
$828$		0			0
$829$	−7.11516	−	4.10794i	−0.247120	−	0.142675i	0.371325	−	0.928503i	$-0.378904\pi$
$829$	−7.11516	−	4.10794i	−0.247120	−	0.142675i	−0.618445	+	0.785828i	$0.712237\pi$
$830$		0			0
$831$		0			0
$832$		−	5.67714i		−	0.196819i
$833$	12.8233	−	6.77603i	0.444300	−	0.234775i
$834$		0			0
$835$		0			0
$836$	7.08758	−	12.2760i	0.245129	−	0.424576i
$837$		0			0
$838$	2.20356	−	1.27223i	0.0761208	−	0.0439483i
$839$	17.6943			0.610875			0.305437	−	0.952212i	$-0.401197\pi$
$839$	17.6943			0.610875			0.305437	+	0.952212i	$0.401197\pi$
$840$		0			0
$841$	5.09640			0.175738
$842$	−4.40437	+	2.54286i	−0.151785	+	0.0876328i
$843$		0			0
$844$	−2.03035	+	3.51668i	−0.0698877	+	0.121049i
$845$		0			0
$846$		0			0
$847$	3.34613	+	13.4945i	0.114975	+	0.463675i
$848$		−	4.19077i		−	0.143912i
$849$		0			0
$850$		0			0
$851$	−4.78717	−	2.76388i	−0.164102	−	0.0947444i
$852$		0			0
$853$		−	40.1129i		−	1.37344i	−0.726922	−	0.686720i	$-0.759050\pi$
$853$		−	40.1129i		−	1.37344i	0.726922	−	0.686720i	$-0.240950\pi$
$854$	−23.7333	+	22.8601i	−0.812135	+	0.782255i
$855$		0			0
$856$	−2.78854	−	4.82989i	−0.0953102	−	0.165082i
$857$	22.0654	−	38.2184i	0.753740	−	1.30552i	−0.192259	−	0.981344i	$-0.561581\pi$
$857$	22.0654	−	38.2184i	0.753740	−	1.30552i	0.945998	−	0.324171i	$-0.105085\pi$
$858$		0			0
$859$	12.4339	−	7.17873i	0.424240	−	0.244935i	−0.272650	−	0.962113i	$-0.587900\pi$
$859$	12.4339	−	7.17873i	0.424240	−	0.244935i	0.696890	+	0.717178i	$0.254567\pi$
$860$		0			0
$861$		0			0
$862$	−13.2980			−0.452933
$863$	11.0876	−	6.40143i	0.377426	−	0.217907i	−0.299272	−	0.954168i	$-0.596744\pi$
$863$	11.0876	−	6.40143i	0.377426	−	0.217907i	0.676698	+	0.736261i	$0.263410\pi$
$864$		0			0
$865$		0			0
$866$	6.39477	+	11.0761i	0.217303	+	0.376380i
$867$		0			0
$868$	11.6240	−	2.88233i	0.394544	−	0.0978326i
$869$		−	40.1908i		−	1.36338i
$870$		0			0
$871$	−37.4750	−	21.6362i	−1.26979	−	0.733114i
$872$	−1.73205	−	1.00000i	−0.0586546	−	0.0338643i
$873$		0			0
$874$			11.0103i			0.372431i
$875$		0			0
$876$		0			0
$877$	29.1360	+	50.4650i	0.983853	+	1.70408i	0.646928	+	0.762551i	$0.276053\pi$
$877$	29.1360	+	50.4650i	0.983853	+	1.70408i	0.336925	+	0.941532i	$0.390613\pi$
$878$	−0.186606	+	0.323211i	−0.00629765	+	0.0109079i
$879$		0			0
$880$		0			0
$881$	1.80667			0.0608682			0.0304341	−	0.999537i	$-0.490311\pi$
$881$	1.80667			0.0608682			0.0304341	+	0.999537i	$0.490311\pi$
$882$		0			0
$883$	−13.8997			−0.467761			−0.233881	−	0.972265i	$-0.575142\pi$
$883$	−13.8997			−0.467761			−0.233881	+	0.972265i	$0.575142\pi$
$884$	10.1867	−	5.88130i	0.342616	−	0.197809i
$885$		0			0
$886$	−12.3165	+	21.3328i	−0.413781	+	0.716690i
$887$	13.2459	+	22.9426i	0.444754	+	0.770337i	0.998035	−	0.0626581i	$-0.0199578\pi$
$887$	13.2459	+	22.9426i	0.444754	+	0.770337i	−0.553281	+	0.832995i	$0.686624\pi$
$888$		0			0
$889$	48.9301	+	14.0985i	1.64106	+	0.472850i
$890$		0			0
$891$		0			0
$892$	−13.9851	−	8.07432i	−0.468257	−	0.270348i
$893$	28.5727	+	16.4965i	0.956150	+	0.552033i
$894$		0			0
$895$		0			0
$896$	2.56798	−	0.636766i	0.0857902	−	0.0212728i
$897$		0			0
$898$	20.3111	+	35.1799i	0.677792	+	1.17397i
$899$	−11.0654	+	19.1658i	−0.369050	+	0.639214i
$900$		0			0
$901$	7.51966	−	4.34148i	0.250516	−	0.144636i
$902$	16.8844			0.562189
$903$		0			0
$904$	−14.5030			−0.482361
$905$		0			0
$906$		0			0
$907$	18.3650	−	31.8091i	0.609800	−	1.05620i	−0.381474	−	0.924380i	$-0.624583\pi$
$907$	18.3650	−	31.8091i	0.609800	−	1.05620i	0.991273	−	0.131824i	$-0.0420834\pi$
$908$	0.839901	+	1.45475i	0.0278731	+	0.0482776i
$909$		0			0
$910$		0			0
$911$			39.8018i			1.31869i	0.751839	+	0.659347i	$0.229167\pi$
$911$			39.8018i			1.31869i	−0.751839	+	0.659347i	$0.770833\pi$
$912$		0			0
$913$	28.2559	+	16.3135i	0.935134	+	0.539900i
$914$	−0.857843	−	0.495276i	−0.0283749	−	0.0163823i
$915$		0			0
$916$		−	12.6027i		−	0.416406i
$917$	2.99242	+	12.0680i	0.0988184	+	0.398520i
$918$		0			0
$919$	−30.1692	−	52.2545i	−0.995189	−	1.72372i	−0.582442	−	0.812872i	$-0.697903\pi$
$919$	−30.1692	−	52.2545i	−0.995189	−	1.72372i	−0.412747	−	0.910846i	$-0.635430\pi$
$920$		0			0
$921$		0			0
$922$	−17.9611	+	10.3699i	−0.591518	+	0.341513i
$923$	−51.8962			−1.70818
$924$		0			0
$925$		0			0
$926$	−1.26804	+	0.732105i	−0.0416705	+	0.0240585i
$927$		0			0
$928$	−2.44457	+	4.23411i	−0.0802468	+	0.138992i
$929$	−22.1749	−	38.4080i	−0.727533	−	1.26012i	−0.957923	−	0.287026i	$-0.907333\pi$
$929$	−22.1749	−	38.4080i	−0.727533	−	1.26012i	0.230389	−	0.973099i	$-0.426000\pi$
$930$		0			0
$931$	41.3687	+	1.55109i	1.35580	+	0.0508350i
$932$			14.5164i			0.475499i
$933$		0			0
$934$	31.4090	+	18.1340i	1.02774	+	0.593363i
$935$		0			0
$936$		0			0
$937$		−	2.54073i		−	0.0830021i	−0.999138	−	0.0415010i	$-0.986786\pi$
$937$		−	2.54073i		−	0.0830021i	0.999138	−	0.0415010i	$-0.0132140\pi$
$938$	5.58355	−	19.3781i	0.182309	−	0.632718i
$939$		0			0
$940$		0			0
$941$	−16.9488	+	29.3563i	−0.552516	+	0.956987i	0.445576	+	0.895244i	$0.352999\pi$
$941$	−16.9488	+	29.3563i	−0.552516	+	0.956987i	−0.998092	+	0.0617423i	$0.980334\pi$
$942$		0			0
$943$	−11.3577	+	6.55736i	−0.369857	+	0.213537i
$944$	2.00624			0.0652977
$945$		0			0
$946$	20.5164			0.667045
$947$	−42.8759	+	24.7544i	−1.39328	+	0.804411i	−0.993677	−	0.112277i	$-0.964186\pi$
$947$	−42.8759	+	24.7544i	−1.39328	+	0.804411i	−0.399604	+	0.916688i	$0.630852\pi$
$948$		0			0
$949$	3.07231	−	5.32140i	0.0997315	−	0.172740i
$950$		0			0
$951$		0			0
$952$	3.80290	+	3.94816i	0.123253	+	0.127961i
$953$			17.0625i			0.552709i	0.961056	+	0.276355i	$0.0891264\pi$
$953$			17.0625i			0.552709i	−0.961056	+	0.276355i	$0.910874\pi$
$954$		0			0
$955$		0			0
$956$	0.179344	+	0.103545i	0.00580041	+	0.00334887i
$957$		0			0
$958$		−	10.3258i		−	0.333610i
$959$	−42.0032	−	43.6076i	−1.35636	−	1.40816i
$960$		0			0
$961$	−5.25533	−	9.10250i	−0.169527	−	0.293629i
$962$	−8.42802	+	14.5978i	−0.271730	+	0.470651i
$963$		0			0
$964$	9.04172	−	5.22024i	0.291214	−	0.168133i
$965$		0			0
$966$		0			0
$967$	49.6639			1.59708			0.798541	−	0.601940i	$-0.205606\pi$
$967$	49.6639			1.59708			0.798541	+	0.601940i	$0.205606\pi$
$968$	−4.55087	+	2.62745i	−0.146270	+	0.0844493i
$969$		0			0
$970$		0			0
$971$	14.2930	+	24.7561i	0.458683	+	0.794462i	0.998892	−	0.0470689i	$-0.0149880\pi$
$971$	14.2930	+	24.7561i	0.458683	+	0.794462i	−0.540209	+	0.841531i	$0.681655\pi$
$972$		0			0
$973$	6.69436	−	23.2333i	0.214611	−	0.744825i
$974$		−	20.3291i		−	0.651386i
$975$		0			0
$976$	−10.7862	−	6.22739i	−0.345256	−	0.199334i
$977$	24.0067	+	13.8603i	0.768042	+	0.443429i	0.832176	−	0.554512i	$-0.187095\pi$
$977$	24.0067	+	13.8603i	0.768042	+	0.443429i	−0.0641335	+	0.997941i	$0.520428\pi$
$978$		0			0
$979$			31.7890i			1.01598i
$980$		0			0
$981$		0			0
$982$	−17.3017	−	29.9674i	−0.552119	−	0.956298i
$983$	21.4134	−	37.0891i	0.682982	−	1.18296i	−0.291085	−	0.956697i	$-0.594016\pi$
$983$	21.4134	−	37.0891i	0.682982	−	1.18296i	0.974067	−	0.226262i	$-0.0726504\pi$
$984$		0			0
$985$		0			0
$986$	−10.1299			−0.322602
$987$		0			0
$988$	33.5744			1.06814
$989$	−13.8008	+	7.96789i	−0.438840	+	0.253364i
$990$		0			0
$991$	−21.3723	+	37.0179i	−0.678914	+	1.17591i	0.296394	+	0.955066i	$0.404216\pi$
$991$	−21.3723	+	37.0179i	−0.678914	+	1.17591i	−0.975308	+	0.220848i	$0.929118\pi$
$992$	2.26326	+	3.92008i	0.0718585	+	0.124463i
$993$		0			0
$994$	−5.82084	−	23.4746i	−0.184626	−	0.744568i
$995$		0			0
$996$		0			0
$997$	−28.4679	−	16.4359i	−0.901587	−	0.520531i	−0.0238722	−	0.999715i	$-0.507599\pi$
$997$	−28.4679	−	16.4359i	−0.901587	−	0.520531i	−0.877715	+	0.479184i	$0.840933\pi$
$998$	2.55555	+	1.47545i	0.0808945	+	0.0467045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.f.1151.11		32
3.2	odd	2	inner	3150.2.bf.f.1151.1		32
5.2	odd	4		630.2.bo.b.269.5	yes	16
5.3	odd	4		630.2.bo.a.269.7	yes	16
5.4	even	2	inner	3150.2.bf.f.1151.2		32
7.5	odd	6	inner	3150.2.bf.f.1601.1		32
15.2	even	4		630.2.bo.a.269.4	yes	16
15.8	even	4		630.2.bo.b.269.2	yes	16
15.14	odd	2	inner	3150.2.bf.f.1151.12		32
21.5	even	6	inner	3150.2.bf.f.1601.11		32
35.3	even	12		4410.2.d.b.4409.15		16
35.12	even	12		630.2.bo.b.89.2	yes	16
35.17	even	12		4410.2.d.a.4409.16		16
35.18	odd	12		4410.2.d.b.4409.2		16
35.19	odd	6	inner	3150.2.bf.f.1601.12		32
35.32	odd	12		4410.2.d.a.4409.1		16
35.33	even	12		630.2.bo.a.89.4	✓	16
105.17	odd	12		4410.2.d.b.4409.1		16
105.32	even	12		4410.2.d.b.4409.16		16
105.38	odd	12		4410.2.d.a.4409.2		16
105.47	odd	12		630.2.bo.a.89.7	yes	16
105.53	even	12		4410.2.d.a.4409.15		16
105.68	odd	12		630.2.bo.b.89.5	yes	16
105.89	even	6	inner	3150.2.bf.f.1601.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.4	✓	16	35.33	even	12
630.2.bo.a.89.7	yes	16	105.47	odd	12
630.2.bo.a.269.4	yes	16	15.2	even	4
630.2.bo.a.269.7	yes	16	5.3	odd	4
630.2.bo.b.89.2	yes	16	35.12	even	12
630.2.bo.b.89.5	yes	16	105.68	odd	12
630.2.bo.b.269.2	yes	16	15.8	even	4
630.2.bo.b.269.5	yes	16	5.2	odd	4
3150.2.bf.f.1151.1		32	3.2	odd	2	inner
3150.2.bf.f.1151.2		32	5.4	even	2	inner
3150.2.bf.f.1151.11		32	1.1	even	1	trivial
3150.2.bf.f.1151.12		32	15.14	odd	2	inner
3150.2.bf.f.1601.1		32	7.5	odd	6	inner
3150.2.bf.f.1601.2		32	105.89	even	6	inner
3150.2.bf.f.1601.11		32	21.5	even	6	inner
3150.2.bf.f.1601.12		32	35.19	odd	6	inner
4410.2.d.a.4409.1		16	35.32	odd	12
4410.2.d.a.4409.2		16	105.38	odd	12
4410.2.d.a.4409.15		16	105.53	even	12
4410.2.d.a.4409.16		16	35.17	even	12
4410.2.d.b.4409.1		16	105.17	odd	12
4410.2.d.b.4409.2		16	35.18	odd	12
4410.2.d.b.4409.15		16	35.3	even	12
4410.2.d.b.4409.16		16	105.32	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.54232 - 0.732536i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-2.54232 - 0.732536i) q^{7} -1.00000i q^{8} +(2.07577 + 1.19845i) q^{11} +5.67714i q^{13} +(-2.56798 + 0.636766i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.03596 - 1.79434i) q^{17} +(5.12164 - 2.95698i) q^{19} +2.39690 q^{22} +(-1.61233 + 0.930877i) q^{23} +(2.83857 + 4.91654i) q^{26} +(-1.90555 + 1.83545i) q^{28} -4.88913i q^{29} +(-3.92008 - 2.26326i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.07192i q^{34} +(1.48455 + 2.57132i) q^{37} +(2.95698 - 5.12164i) q^{38} +7.04428 q^{41} +8.55956 q^{43} +(2.07577 - 1.19845i) q^{44} +(-0.930877 + 1.61233i) q^{46} +(2.78941 + 4.83140i) q^{47} +(5.92678 + 3.72468i) q^{49} +(4.91654 + 2.83857i) q^{52} +(3.62931 + 2.09538i) q^{53} +(-0.732536 + 2.54232i) q^{56} +(-2.44457 - 4.23411i) q^{58} +(-1.00312 + 1.73746i) q^{59} +(10.7862 - 6.22739i) q^{61} -4.52651 q^{62} -1.00000 q^{64} +(-3.81111 + 6.60103i) q^{67} +(-1.03596 - 1.79434i) q^{68} +9.14126i q^{71} +(-0.937339 - 0.541173i) q^{73} +(2.57132 + 1.48455i) q^{74} -5.91397i q^{76} +(-4.39937 - 4.56742i) q^{77} +(-8.38392 - 14.5214i) q^{79} +(6.10053 - 3.52214i) q^{82} +13.6122 q^{83} +(7.41279 - 4.27978i) q^{86} +(1.19845 - 2.07577i) q^{88} +(6.63129 + 11.4857i) q^{89} +(4.15870 - 14.4331i) q^{91} +1.86175i q^{92} +(4.83140 + 2.78941i) q^{94} -12.8260i q^{97} +(6.99508 + 0.262276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 - 48 * q^19 + 24 * q^31 - 16 * q^46 + 56 * q^49 + 48 * q^61 - 32 * q^64 - 8 * q^79 - 56 * q^91 + 120 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more