LMFDB - Embedded newform 756.2.e.b.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(323,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("756.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.e (of order $2$, degree $1$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.4
Character	$\chi$	$=$	756.323
Dual form			756.2.e.b.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38801 + 0.270968i) q^{2} +(1.85315 - 0.752213i) q^{4} +1.41649i q^{5} -1.00000i q^{7} +(-2.36837 + 1.54622i) q^{8} +O(q^{10})$	\(q+(-1.38801 + 0.270968i) q^{2} +(1.85315 - 0.752213i) q^{4} +1.41649i q^{5} -1.00000i q^{7} +(-2.36837 + 1.54622i) q^{8} +(-0.383823 - 1.96611i) q^{10} -0.0560930 q^{11} -1.75730 q^{13} +(0.270968 + 1.38801i) q^{14} +(2.86835 - 2.78793i) q^{16} +7.23711i q^{17} +2.28327i q^{19} +(1.06550 + 2.62497i) q^{20} +(0.0778578 - 0.0151994i) q^{22} -3.19553 q^{23} +2.99355 q^{25} +(2.43915 - 0.476171i) q^{26} +(-0.752213 - 1.85315i) q^{28} -4.78374i q^{29} +6.33960i q^{31} +(-3.22587 + 4.64691i) q^{32} +(-1.96102 - 10.0452i) q^{34} +1.41649 q^{35} -5.24245 q^{37} +(-0.618692 - 3.16921i) q^{38} +(-2.19021 - 3.35478i) q^{40} +3.58882i q^{41} +3.12243i q^{43} +(-0.103949 + 0.0421939i) q^{44} +(4.43544 - 0.865886i) q^{46} +5.27725 q^{47} -1.00000 q^{49} +(-4.15509 + 0.811156i) q^{50} +(-3.25654 + 1.32186i) q^{52} +5.18039i q^{53} -0.0794553i q^{55} +(1.54622 + 2.36837i) q^{56} +(1.29624 + 6.63988i) q^{58} -3.27326 q^{59} +8.82741 q^{61} +(-1.71783 - 8.79944i) q^{62} +(3.21838 - 7.32407i) q^{64} -2.48920i q^{65} +15.8030i q^{67} +(5.44384 + 13.4115i) q^{68} +(-1.96611 + 0.383823i) q^{70} -14.2854 q^{71} -5.03219 q^{73} +(7.27658 - 1.42053i) q^{74} +(1.71750 + 4.23125i) q^{76} +0.0560930i q^{77} +12.1925i q^{79} +(3.94908 + 4.06300i) q^{80} +(-0.972455 - 4.98133i) q^{82} -1.28060 q^{83} -10.2513 q^{85} +(-0.846076 - 4.33396i) q^{86} +(0.132849 - 0.0867324i) q^{88} +6.02678i q^{89} +1.75730i q^{91} +(-5.92181 + 2.40372i) q^{92} +(-7.32489 + 1.42996i) q^{94} -3.23423 q^{95} -16.4261 q^{97} +(1.38801 - 0.270968i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4}+O(q^{10}) $ 24 * q + 4 * q^4	$ 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) $ 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.38801	+	0.270968i	−0.981472	+	0.191603i
$2$	−1.38801	+	0.270968i	−0.981472	+	0.191603i
$3$		0			0
$3$		0			0
$4$	1.85315	−	0.752213i	0.926577	−	0.376106i
$5$			1.41649i			0.633474i	0.948513	+	0.316737i	$0.102587\pi$
$5$			1.41649i			0.633474i	−0.948513	+	0.316737i	$0.897413\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.36837	+	1.54622i	−0.837346	+	0.546673i
$9$		0			0
$10$	−0.383823	−	1.96611i	−0.121376	−	0.621737i
$11$	−0.0560930			−0.0169127			−0.00845634	−	0.999964i	$-0.502692\pi$
$11$	−0.0560930			−0.0169127			−0.00845634	+	0.999964i	$0.502692\pi$
$12$		0			0
$13$	−1.75730			−0.487386			−0.243693	−	0.969852i	$-0.578359\pi$
$13$	−1.75730			−0.487386			−0.243693	+	0.969852i	$0.578359\pi$
$14$	0.270968	+	1.38801i	0.0724192	+	0.370962i
$15$		0			0
$16$	2.86835	−	2.78793i	0.717088	−	0.696983i
$17$			7.23711i			1.75526i	0.479342	+	0.877628i	$0.340875\pi$
$17$			7.23711i			1.75526i	−0.479342	+	0.877628i	$0.659125\pi$
$18$		0			0
$19$			2.28327i			0.523818i	0.965093	+	0.261909i	$0.0843521\pi$
$19$			2.28327i			0.523818i	−0.965093	+	0.261909i	$0.915648\pi$
$20$	1.06550	+	2.62497i	0.238254	+	0.586962i
$21$		0			0
$22$	0.0778578	−	0.0151994i	0.0165993	−	0.00324052i
$23$	−3.19553			−0.666315			−0.333157	−	0.942871i	$-0.608114\pi$
$23$	−3.19553			−0.666315			−0.333157	+	0.942871i	$0.608114\pi$
$24$		0			0
$25$	2.99355			0.598711
$26$	2.43915	−	0.476171i	0.478356	−	0.0933847i
$27$		0			0
$28$	−0.752213	−	1.85315i	−0.142155	−	0.350213i
$29$		−	4.78374i		−	0.888317i	−0.895948	−	0.444159i	$-0.853503\pi$
$29$		−	4.78374i		−	0.888317i	0.895948	−	0.444159i	$-0.146497\pi$
$30$		0			0
$31$			6.33960i			1.13863i	0.822121	+	0.569313i	$0.192791\pi$
$31$			6.33960i			1.13863i	−0.822121	+	0.569313i	$0.807209\pi$
$32$	−3.22587	+	4.64691i	−0.570258	+	0.821465i
$33$		0			0
$34$	−1.96102	−	10.0452i	−0.336313	−	1.72274i
$35$	1.41649			0.239431
$36$		0			0
$37$	−5.24245			−0.861853			−0.430927	−	0.902387i	$-0.641813\pi$
$37$	−5.24245			−0.861853			−0.430927	+	0.902387i	$0.641813\pi$
$38$	−0.618692	−	3.16921i	−0.100365	−	0.514113i
$39$		0			0
$40$	−2.19021	−	3.35478i	−0.346303	−	0.530437i
$41$			3.58882i			0.560480i	0.959930	+	0.280240i	$0.0904141\pi$
$41$			3.58882i			0.560480i	−0.959930	+	0.280240i	$0.909586\pi$
$42$		0			0
$43$			3.12243i			0.476165i	0.971245	+	0.238083i	$0.0765189\pi$
$43$			3.12243i			0.476165i	−0.971245	+	0.238083i	$0.923481\pi$
$44$	−0.103949	+	0.0421939i	−0.0156709	+	0.00636097i
$45$		0			0
$46$	4.43544	−	0.865886i	0.653969	−	0.127668i
$47$	5.27725			0.769766			0.384883	−	0.922965i	$-0.374242\pi$
$47$	5.27725			0.769766			0.384883	+	0.922965i	$0.374242\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−4.15509	+	0.811156i	−0.587618	+	0.114715i
$51$		0			0
$52$	−3.25654	+	1.32186i	−0.451601	+	0.183309i
$53$			5.18039i			0.711582i	0.934566	+	0.355791i	$0.115788\pi$
$53$			5.18039i			0.711582i	−0.934566	+	0.355791i	$0.884212\pi$
$54$		0			0
$55$		−	0.0794553i		−	0.0107137i
$56$	1.54622	+	2.36837i	0.206623	+	0.316487i
$57$		0			0
$58$	1.29624	+	6.63988i	0.170204	+	0.871859i
$59$	−3.27326			−0.426143			−0.213071	−	0.977037i	$-0.568347\pi$
$59$	−3.27326			−0.426143			−0.213071	+	0.977037i	$0.568347\pi$
$60$		0			0
$61$	8.82741			1.13023			0.565117	−	0.825011i	$-0.308831\pi$
$61$	8.82741			1.13023			0.565117	+	0.825011i	$0.308831\pi$
$62$	−1.71783	−	8.79944i	−0.218164	−	1.11753i
$63$		0			0
$64$	3.21838	−	7.32407i	0.402297	−	0.915509i
$65$		−	2.48920i		−	0.308747i
$66$		0			0
$67$			15.8030i			1.93065i	0.261060	+	0.965323i	$0.415928\pi$
$67$			15.8030i			1.93065i	−0.261060	+	0.965323i	$0.584072\pi$
$68$	5.44384	+	13.4115i	0.660163	+	1.62638i
$69$		0			0
$70$	−1.96611	+	0.383823i	−0.234995	+	0.0458757i
$71$	−14.2854			−1.69537			−0.847685	−	0.530500i	$-0.822004\pi$
$71$	−14.2854			−1.69537			−0.847685	+	0.530500i	$0.822004\pi$
$72$		0			0
$73$	−5.03219			−0.588973			−0.294486	−	0.955656i	$-0.595149\pi$
$73$	−5.03219			−0.588973			−0.294486	+	0.955656i	$0.595149\pi$
$74$	7.27658	−	1.42053i	0.845885	−	0.165134i
$75$		0			0
$76$	1.71750	+	4.23125i	0.197011	+	0.485358i
$77$			0.0560930i			0.00639239i
$78$		0			0
$79$			12.1925i			1.37177i	0.727711	+	0.685884i	$0.240584\pi$
$79$			12.1925i			1.37177i	−0.727711	+	0.685884i	$0.759416\pi$
$80$	3.94908	+	4.06300i	0.441520	+	0.454257i
$81$		0			0
$82$	−0.972455	−	4.98133i	−0.107390	−	0.550096i
$83$	−1.28060			−0.140564			−0.0702822	−	0.997527i	$-0.522390\pi$
$83$	−1.28060			−0.140564			−0.0702822	+	0.997527i	$0.522390\pi$
$84$		0			0
$85$	−10.2513			−1.11191
$86$	−0.846076	−	4.33396i	−0.0912348	−	0.467343i
$87$		0			0
$88$	0.132849	−	0.0867324i	0.0141618	−	0.00924571i
$89$			6.02678i			0.638838i	0.947614	+	0.319419i	$0.103488\pi$
$89$			6.02678i			0.638838i	−0.947614	+	0.319419i	$0.896512\pi$
$90$		0			0
$91$			1.75730i			0.184215i
$92$	−5.92181	+	2.40372i	−0.617391	+	0.250605i
$93$		0			0
$94$	−7.32489	+	1.42996i	−0.755504	+	0.147490i
$95$	−3.23423			−0.331825
$96$		0			0
$97$	−16.4261			−1.66782			−0.833911	−	0.551899i	$-0.813903\pi$
$97$	−16.4261			−1.66782			−0.833911	+	0.551899i	$0.813903\pi$
$98$	1.38801	−	0.270968i	0.140210	−	0.0273719i
$99$		0			0
$100$	5.54751	−	2.25179i	0.554751	−	0.225179i
$101$		−	13.6763i		−	1.36084i	−0.732821	−	0.680422i	$-0.761797\pi$
$101$		−	13.6763i		−	1.36084i	0.732821	−	0.680422i	$-0.238203\pi$
$102$		0			0
$103$			14.2835i			1.40739i	0.710500	+	0.703697i	$0.248469\pi$
$103$			14.2835i			1.40739i	−0.710500	+	0.703697i	$0.751531\pi$
$104$	4.16193	−	2.71718i	0.408111	−	0.266441i
$105$		0			0
$106$	−1.40372	−	7.19045i	−0.136341	−	0.698398i
$107$	6.75443			0.652975			0.326488	−	0.945202i	$-0.394135\pi$
$107$	6.75443			0.652975			0.326488	+	0.945202i	$0.394135\pi$
$108$		0			0
$109$	18.3307			1.75577			0.877883	−	0.478875i	$-0.158955\pi$
$109$	18.3307			1.75577			0.877883	+	0.478875i	$0.158955\pi$
$110$	0.0215298	+	0.110285i	0.00205279	+	0.0105152i
$111$		0			0
$112$	−2.78793	−	2.86835i	−0.263435	−	0.271034i
$113$		−	4.42856i		−	0.416604i	−0.978065	−	0.208302i	$-0.933206\pi$
$113$		−	4.42856i		−	0.416604i	0.978065	−	0.208302i	$-0.0667936\pi$
$114$		0			0
$115$		−	4.52644i		−	0.422093i
$116$	−3.59839	−	8.86499i	−0.334102	−	0.823094i
$117$		0			0
$118$	4.54333	−	0.886949i	0.418247	−	0.0816503i
$119$	7.23711			0.663425
$120$		0			0
$121$	−10.9969			−0.999714
$122$	−12.2526	+	2.39194i	−1.10929	+	0.216556i
$123$		0			0
$124$	4.76873	+	11.7483i	0.428245	+	1.05502i
$125$			11.3228i			1.01274i
$126$		0			0
$127$		−	3.95033i		−	0.350535i	−0.984521	−	0.175267i	$-0.943921\pi$
$127$		−	3.95033i		−	0.350535i	0.984521	−	0.175267i	$-0.0560790\pi$
$128$	−2.48256	+	11.0380i	−0.219430	+	0.975628i
$129$		0			0
$130$	0.674491	+	3.45503i	0.0591568	+	0.303026i
$131$	15.3032			1.33705			0.668524	−	0.743691i	$-0.266926\pi$
$131$	15.3032			1.33705			0.668524	+	0.743691i	$0.266926\pi$
$132$		0			0
$133$	2.28327			0.197985
$134$	−4.28210	−	21.9348i	−0.369918	−	1.89488i
$135$		0			0
$136$	−11.1902	−	17.1402i	−0.959551	−	1.46976i
$137$		−	1.68670i		−	0.144104i	−0.997401	−	0.0720521i	$-0.977045\pi$
$137$		−	1.68670i		−	0.144104i	0.997401	−	0.0720521i	$-0.0229548\pi$
$138$		0			0
$139$			1.00403i			0.0851603i	0.999093	+	0.0425801i	$0.0135578\pi$
$139$			1.00403i			0.0851603i	−0.999093	+	0.0425801i	$0.986442\pi$
$140$	2.62497	−	1.06550i	0.221851	−	0.0900514i
$141$		0			0
$142$	19.8284	−	3.87089i	1.66396	−	0.324838i
$143$	0.0985721			0.00824301
$144$		0			0
$145$	6.77612			0.562726
$146$	6.98473	−	1.36356i	0.578061	−	0.112849i
$147$		0			0
$148$	−9.71506	+	3.94344i	−0.798573	+	0.324148i
$149$		−	20.5173i		−	1.68085i	−0.541932	−	0.840423i	$-0.682307\pi$
$149$		−	20.5173i		−	1.68085i	0.541932	−	0.840423i	$-0.317693\pi$
$150$		0			0
$151$		−	7.14060i		−	0.581093i	−0.956861	−	0.290547i	$-0.906163\pi$
$151$		−	7.14060i		−	0.581093i	0.956861	−	0.290547i	$-0.0938372\pi$
$152$	−3.53045	−	5.40764i	−0.286357	−	0.438617i
$153$		0			0
$154$	−0.0151994	−	0.0778578i	−0.00122480	−	0.00627396i
$155$	−8.97999			−0.721290
$156$		0			0
$157$	10.2629			0.819068			0.409534	−	0.912295i	$-0.365691\pi$
$157$	10.2629			0.819068			0.409534	+	0.912295i	$0.365691\pi$
$158$	−3.30378	−	16.9234i	−0.262835	−	1.34635i
$159$		0			0
$160$	−6.58231	−	4.56941i	−0.520377	−	0.361244i
$161$			3.19553i			0.251843i
$162$		0			0
$163$		−	14.7928i		−	1.15866i	−0.815093	−	0.579330i	$-0.803314\pi$
$163$		−	14.7928i		−	1.15866i	0.815093	−	0.579330i	$-0.196686\pi$
$164$	2.69956	+	6.65064i	0.210800	+	0.519328i
$165$		0			0
$166$	1.77749	−	0.347002i	0.137960	−	0.0269326i
$167$	18.5537			1.43573			0.717863	−	0.696184i	$-0.245120\pi$
$167$	18.5537			1.43573			0.717863	+	0.696184i	$0.245120\pi$
$168$		0			0
$169$	−9.91191			−0.762454
$170$	14.2289	−	2.77777i	1.09131	−	0.213045i
$171$		0			0
$172$	2.34873	+	5.78633i	0.179089	+	0.441204i
$173$		−	15.6538i		−	1.19014i	−0.803675	−	0.595068i	$-0.797125\pi$
$173$		−	15.6538i		−	1.19014i	0.803675	−	0.595068i	$-0.202875\pi$
$174$		0			0
$175$		−	2.99355i		−	0.226291i
$176$	−0.160895	+	0.156383i	−0.0121279	+	0.0117878i
$177$		0			0
$178$	−1.63306	−	8.36525i	−0.122403	−	0.627002i
$179$	−1.56032			−0.116624			−0.0583121	−	0.998298i	$-0.518572\pi$
$179$	−1.56032			−0.116624			−0.0583121	+	0.998298i	$0.518572\pi$
$180$		0			0
$181$	−3.21313			−0.238830			−0.119415	−	0.992844i	$-0.538102\pi$
$181$	−3.21313			−0.238830			−0.119415	+	0.992844i	$0.538102\pi$
$182$	−0.476171	−	2.43915i	−0.0352961	−	0.180802i
$183$		0			0
$184$	7.56821	−	4.94101i	0.557936	−	0.364256i
$185$		−	7.42588i		−	0.545962i
$186$		0			0
$187$		−	0.405951i		−	0.0296861i
$188$	9.77955	−	3.96961i	0.713247	−	0.289514i
$189$		0			0
$190$	4.48915	−	0.876372i	0.325677	−	0.0635787i
$191$	16.2170			1.17342			0.586711	−	0.809797i	$-0.300423\pi$
$191$	16.2170			1.17342			0.586711	+	0.809797i	$0.300423\pi$
$192$		0			0
$193$	11.8957			0.856269			0.428135	−	0.903715i	$-0.359171\pi$
$193$	11.8957			0.856269			0.428135	+	0.903715i	$0.359171\pi$
$194$	22.7997	−	4.45095i	1.63692	−	0.319560i
$195$		0			0
$196$	−1.85315	+	0.752213i	−0.132368	+	0.0537295i
$197$		−	9.99565i		−	0.712160i	−0.934455	−	0.356080i	$-0.884113\pi$
$197$		−	9.99565i		−	0.712160i	0.934455	−	0.356080i	$-0.115887\pi$
$198$		0			0
$199$		−	4.64109i		−	0.328998i	−0.986377	−	0.164499i	$-0.947399\pi$
$199$		−	4.64109i		−	0.328998i	0.986377	−	0.164499i	$-0.0526007\pi$
$200$	−7.08985	+	4.62870i	−0.501328	+	0.327299i
$201$		0			0
$202$	3.70584	+	18.9829i	0.260742	+	1.33563i
$203$	−4.78374			−0.335752
$204$		0			0
$205$	−5.08354			−0.355050
$206$	−3.87036	−	19.8256i	−0.269661	−	1.38132i
$207$		0			0
$208$	−5.04055	+	4.89922i	−0.349499	+	0.339700i
$209$		−	0.128076i		−	0.00885917i
$210$		0			0
$211$		−	9.39925i		−	0.647071i	−0.946216	−	0.323535i	$-0.895128\pi$
$211$		−	9.39925i		−	0.647071i	0.946216	−	0.323535i	$-0.104872\pi$
$212$	3.89676	+	9.60006i	0.267630	+	0.659335i
$213$		0			0
$214$	−9.37522	+	1.83023i	−0.640877	+	0.125112i
$215$	−4.42289			−0.301638
$216$		0			0
$217$	6.33960			0.430360
$218$	−25.4433	+	4.96704i	−1.72324	+	0.336410i
$219$		0			0
$220$	−0.0597673	−	0.147243i	−0.00402951	−	0.00992711i
$221$		−	12.7177i		−	0.855488i
$222$		0			0
$223$		−	20.2192i		−	1.35398i	−0.735994	−	0.676988i	$-0.763285\pi$
$223$		−	20.2192i		−	1.35398i	0.735994	−	0.676988i	$-0.236715\pi$
$224$	4.64691	+	3.22587i	0.310485	+	0.215537i
$225$		0			0
$226$	1.20000	+	6.14689i	0.0798225	+	0.408885i
$227$	−15.0538			−0.999154			−0.499577	−	0.866270i	$-0.666511\pi$
$227$	−15.0538			−0.999154			−0.499577	+	0.866270i	$0.666511\pi$
$228$		0			0
$229$	13.1310			0.867722			0.433861	−	0.900980i	$-0.357151\pi$
$229$	13.1310			0.867722			0.433861	+	0.900980i	$0.357151\pi$
$230$	1.22652	+	6.28276i	0.0808743	+	0.414273i
$231$		0			0
$232$	7.39673	+	11.3297i	0.485619	+	0.743829i
$233$			26.9126i			1.76310i	0.472090	+	0.881550i	$0.343500\pi$
$233$			26.9126i			1.76310i	−0.472090	+	0.881550i	$0.656500\pi$
$234$		0			0
$235$			7.47518i			0.487627i
$236$	−6.06586	+	2.46219i	−0.394854	+	0.160275i
$237$		0			0
$238$	−10.0452	+	1.96102i	−0.651133	+	0.127114i
$239$	−10.5149			−0.680151			−0.340076	−	0.940398i	$-0.610453\pi$
$239$	−10.5149			−0.680151			−0.340076	+	0.940398i	$0.610453\pi$
$240$		0			0
$241$	27.2307			1.75408			0.877041	−	0.480416i	$-0.159514\pi$
$241$	27.2307			1.75408			0.877041	+	0.480416i	$0.159514\pi$
$242$	15.2638	−	2.97979i	0.981192	−	0.191548i
$243$		0			0
$244$	16.3585	−	6.64009i	1.04725	−	0.425088i
$245$		−	1.41649i		−	0.0904963i
$246$		0			0
$247$		−	4.01238i		−	0.255302i
$248$	−9.80245	−	15.0145i	−0.622456	−	0.953425i
$249$		0			0
$250$	−3.06811	−	15.7162i	−0.194044	−	0.993978i
$251$	16.0425			1.01259			0.506297	−	0.862359i	$-0.331014\pi$
$251$	16.0425			1.01259			0.506297	+	0.862359i	$0.331014\pi$
$252$		0			0
$253$	0.179247			0.0112692
$254$	1.07041	+	5.48310i	0.0671636	+	0.344040i
$255$		0			0
$256$	0.454892	−	15.9935i	0.0284307	−	0.999596i
$257$			13.4054i			0.836205i	0.908400	+	0.418103i	$0.137305\pi$
$257$			13.4054i			0.836205i	−0.908400	+	0.418103i	$0.862695\pi$
$258$		0			0
$259$			5.24245i			0.325750i
$260$	−1.87240	−	4.61286i	−0.116122	−	0.286077i
$261$		0			0
$262$	−21.2410	+	4.14668i	−1.31228	+	0.256182i
$263$	−7.94818			−0.490106			−0.245053	−	0.969510i	$-0.578805\pi$
$263$	−7.94818			−0.490106			−0.245053	+	0.969510i	$0.578805\pi$
$264$		0			0
$265$	−7.33798			−0.450769
$266$	−3.16921	+	0.618692i	−0.194316	+	0.0379345i
$267$		0			0
$268$	11.8872	+	29.2854i	0.726128	+	1.78889i
$269$			2.93491i			0.178944i	0.995989	+	0.0894722i	$0.0285180\pi$
$269$			2.93491i			0.178944i	−0.995989	+	0.0894722i	$0.971482\pi$
$270$		0			0
$271$		−	20.2473i		−	1.22993i	−0.788553	−	0.614967i	$-0.789169\pi$
$271$		−	20.2473i		−	1.22993i	0.788553	−	0.614967i	$-0.210831\pi$
$272$	20.1765	+	20.7586i	1.22338	+	1.25867i
$273$		0			0
$274$	0.457040	+	2.34115i	0.0276108	+	0.141434i
$275$	−0.167917			−0.0101258
$276$		0			0
$277$	−5.47011			−0.328667			−0.164334	−	0.986405i	$-0.552547\pi$
$277$	−5.47011			−0.328667			−0.164334	+	0.986405i	$0.552547\pi$
$278$	−0.272058	−	1.39360i	−0.0163170	−	0.0835825i
$279$		0			0
$280$	−3.35478	+	2.19021i	−0.200486	+	0.130890i
$281$		−	5.13169i		−	0.306131i	−0.988216	−	0.153065i	$-0.951085\pi$
$281$		−	5.13169i		−	0.306131i	0.988216	−	0.153065i	$-0.0489145\pi$
$282$		0			0
$283$		−	20.5692i		−	1.22271i	−0.791357	−	0.611355i	$-0.790625\pi$
$283$		−	20.5692i		−	1.22271i	0.791357	−	0.611355i	$-0.209375\pi$
$284$	−26.4731	+	10.7457i	−1.57089	+	0.637639i
$285$		0			0
$286$	−0.136819	+	0.0267099i	−0.00809029	+	0.00157939i
$287$	3.58882			0.211842
$288$		0			0
$289$	−35.3757			−2.08092
$290$	−9.40533	+	1.83611i	−0.552300	+	0.107820i
$291$		0			0
$292$	−9.32541	+	3.78527i	−0.545728	+	0.221516i
$293$		−	7.05752i		−	0.412305i	−0.978520	−	0.206152i	$-0.933906\pi$
$293$		−	7.05752i		−	0.412305i	0.978520	−	0.206152i	$-0.0660942\pi$
$294$		0			0
$295$		−	4.63655i		−	0.269950i
$296$	12.4161	−	8.10600i	0.721669	−	0.471152i
$297$		0			0
$298$	5.55953	+	28.4783i	0.322055	+	1.64970i
$299$	5.61550			0.324753
$300$		0			0
$301$	3.12243			0.179974
$302$	1.93487	+	9.91123i	0.111339	+	0.570327i
$303$		0			0
$304$	6.36560	+	6.54922i	0.365092	+	0.375624i
$305$			12.5040i			0.715974i
$306$		0			0
$307$			15.1933i			0.867126i	0.901123	+	0.433563i	$0.142744\pi$
$307$			15.1933i			0.867126i	−0.901123	+	0.433563i	$0.857256\pi$
$308$	0.0421939	+	0.103949i	0.00240422	+	0.00592304i
$309$		0			0
$310$	12.4643	−	2.43329i	0.707927	−	0.138201i
$311$	−13.8748			−0.786766			−0.393383	−	0.919375i	$-0.628695\pi$
$311$	−13.8748			−0.786766			−0.393383	+	0.919375i	$0.628695\pi$
$312$		0			0
$313$	16.2779			0.920083			0.460042	−	0.887897i	$-0.347834\pi$
$313$	16.2779			0.920083			0.460042	+	0.887897i	$0.347834\pi$
$314$	−14.2450	+	2.78091i	−0.803893	+	0.156936i
$315$		0			0
$316$	9.17138	+	22.5946i	0.515931	+	1.27105i
$317$			26.5682i			1.49222i	0.665823	+	0.746109i	$0.268080\pi$
$317$			26.5682i			1.49222i	−0.665823	+	0.746109i	$0.731920\pi$
$318$		0			0
$319$			0.268334i			0.0150238i
$320$	10.3745	+	4.55881i	0.579951	+	0.254845i
$321$		0			0
$322$	−0.865886	−	4.43544i	−0.0482539	−	0.247177i
$323$	−16.5243			−0.919435
$324$		0			0
$325$	−5.26056			−0.291803
$326$	4.00837	+	20.5326i	0.222003	+	1.13719i
$327$		0			0
$328$	−5.54913	−	8.49967i	−0.306399	−	0.469316i
$329$		−	5.27725i		−	0.290944i
$330$		0			0
$331$		−	30.2688i		−	1.66373i	−0.554982	−	0.831863i	$-0.687275\pi$
$331$		−	30.2688i		−	1.66373i	0.554982	−	0.831863i	$-0.312725\pi$
$332$	−2.37315	+	0.963285i	−0.130244	+	0.0528671i
$333$		0			0
$334$	−25.7527	+	5.02745i	−1.40913	+	0.275090i
$335$	−22.3848			−1.22301
$336$		0			0
$337$	0.793186			0.0432076			0.0216038	−	0.999767i	$-0.493123\pi$
$337$	0.793186			0.0432076			0.0216038	+	0.999767i	$0.493123\pi$
$338$	13.7578	−	2.68581i	0.748328	−	0.146089i
$339$		0			0
$340$	−18.9972	+	7.71116i	−1.03027	+	0.418196i
$341$		−	0.355608i		−	0.0192572i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−4.82797	−	7.39507i	−0.260307	−	0.398715i
$345$		0			0
$346$	4.24167	+	21.7277i	0.228034	+	1.16809i
$347$	−14.3681			−0.771321			−0.385660	−	0.922641i	$-0.626026\pi$
$347$	−14.3681			−0.771321			−0.385660	+	0.922641i	$0.626026\pi$
$348$		0			0
$349$	−21.7493			−1.16421			−0.582107	−	0.813112i	$-0.697772\pi$
$349$	−21.7493			−1.16421			−0.582107	+	0.813112i	$0.697772\pi$
$350$	0.811156	+	4.15509i	0.0433581	+	0.222099i
$351$		0			0
$352$	0.180949	−	0.260659i	0.00964460	−	0.0138932i
$353$			14.3636i			0.764498i	0.924059	+	0.382249i	$0.124850\pi$
$353$			14.3636i			0.764498i	−0.924059	+	0.382249i	$0.875150\pi$
$354$		0			0
$355$		−	20.2352i		−	1.07397i
$356$	4.53342	+	11.1686i	0.240271	+	0.591932i
$357$		0			0
$358$	2.16575	−	0.422798i	0.114463	−	0.0223455i
$359$	0.0765874			0.00404213			0.00202106	−	0.999998i	$-0.499357\pi$
$359$	0.0765874			0.00404213			0.00202106	+	0.999998i	$0.499357\pi$
$360$		0			0
$361$	13.7867			0.725615
$362$	4.45987	−	0.870656i	0.234405	−	0.0457606i
$363$		0			0
$364$	1.32186	+	3.25654i	0.0692843	+	0.170689i
$365$		−	7.12805i		−	0.373099i
$366$		0			0
$367$			25.6120i			1.33693i	0.743742	+	0.668467i	$0.233049\pi$
$367$			25.6120i			1.33693i	−0.743742	+	0.668467i	$0.766951\pi$
$368$	−9.16591	+	8.90892i	−0.477806	+	0.464410i
$369$		0			0
$370$	2.01217	+	10.3072i	0.104608	+	0.535846i
$371$	5.18039			0.268953
$372$		0			0
$373$	−28.4421			−1.47267			−0.736337	−	0.676615i	$-0.763446\pi$
$373$	−28.4421			−1.47267			−0.736337	+	0.676615i	$0.763446\pi$
$374$	0.110000	+	0.563465i	0.00568795	+	0.0291361i
$375$		0			0
$376$	−12.4985	+	8.15981i	−0.644561	+	0.420810i
$377$			8.40644i			0.432954i
$378$		0			0
$379$			22.0571i			1.13300i	0.824062	+	0.566499i	$0.191702\pi$
$379$			22.0571i			1.13300i	−0.824062	+	0.566499i	$0.808298\pi$
$380$	−5.99353	+	2.43283i	−0.307461	+	0.124802i
$381$		0			0
$382$	−22.5094	+	4.39428i	−1.15168	+	0.224831i
$383$	16.4721			0.841683			0.420841	−	0.907134i	$-0.361735\pi$
$383$	16.4721			0.841683			0.420841	+	0.907134i	$0.361735\pi$
$384$		0			0
$385$	−0.0794553			−0.00404942
$386$	−16.5113	+	3.22334i	−0.840405	+	0.164064i
$387$		0			0
$388$	−30.4402	+	12.3559i	−1.54536	+	0.627278i
$389$		−	28.1771i		−	1.42863i	−0.699822	−	0.714317i	$-0.746737\pi$
$389$		−	28.1771i		−	1.42863i	0.699822	−	0.714317i	$-0.253263\pi$
$390$		0			0
$391$		−	23.1264i		−	1.16955i
$392$	2.36837	−	1.54622i	0.119621	−	0.0780961i
$393$		0			0
$394$	2.70850	+	13.8741i	0.136452	+	0.698966i
$395$	−17.2706			−0.868980
$396$		0			0
$397$	2.87558			0.144321			0.0721606	−	0.997393i	$-0.477011\pi$
$397$	2.87558			0.144321			0.0721606	+	0.997393i	$0.477011\pi$
$398$	1.25758	+	6.44188i	0.0630370	+	0.322902i
$399$		0			0
$400$	8.58656	−	8.34582i	0.429328	−	0.417291i
$401$			27.0712i			1.35187i	0.736960	+	0.675937i	$0.236261\pi$
$401$			27.0712i			1.35187i	−0.736960	+	0.675937i	$0.763739\pi$
$402$		0			0
$403$		−	11.1406i		−	0.554951i
$404$	−10.2875	−	25.3443i	−0.511822	−	1.26093i
$405$		0			0
$406$	6.63988	−	1.29624i	0.329532	−	0.0643312i
$407$	0.294065			0.0145763
$408$		0			0
$409$	34.0123			1.68180			0.840901	−	0.541189i	$-0.182026\pi$
$409$	34.0123			1.68180			0.840901	+	0.541189i	$0.182026\pi$
$410$	7.05601	−	1.37747i	0.348471	−	0.0680286i
$411$		0			0
$412$	10.7442	+	26.4695i	0.529330	+	1.30406i
$413$			3.27326i			0.161067i
$414$		0			0
$415$		−	1.81396i		−	0.0890439i
$416$	5.66881	−	8.16600i	0.277936	−	0.400371i
$417$		0			0
$418$	0.0347043	+	0.177770i	0.00169744	+	0.00869503i
$419$	38.4327			1.87756			0.938779	−	0.344520i	$-0.111958\pi$
$419$	38.4327			1.87756			0.938779	+	0.344520i	$0.111958\pi$
$420$		0			0
$421$	−0.0923307			−0.00449992			−0.00224996	−	0.999997i	$-0.500716\pi$
$421$	−0.0923307			−0.00449992			−0.00224996	+	0.999997i	$0.500716\pi$
$422$	2.54689	+	13.0463i	0.123981	+	0.635082i
$423$		0			0
$424$	−8.01005	−	12.2691i	−0.389003	−	0.595840i
$425$			21.6647i			1.05089i
$426$		0			0
$427$		−	8.82741i		−	0.427188i
$428$	12.5170	−	5.08076i	0.605031	−	0.245588i
$429$		0			0
$430$	6.13902	−	1.19846i	0.296050	−	0.0577949i
$431$	20.8904			1.00625			0.503126	−	0.864213i	$-0.332183\pi$
$431$	20.8904			1.00625			0.503126	+	0.864213i	$0.332183\pi$
$432$		0			0
$433$	6.82055			0.327775			0.163887	−	0.986479i	$-0.447597\pi$
$433$	6.82055			0.327775			0.163887	+	0.986479i	$0.447597\pi$
$434$	−8.79944	+	1.71783i	−0.422387	+	0.0824584i
$435$		0			0
$436$	33.9697	−	13.7886i	1.62685	−	0.660355i
$437$		−	7.29626i		−	0.349028i
$438$		0			0
$439$			25.6109i			1.22234i	0.791499	+	0.611170i	$0.209301\pi$
$439$			25.6109i			1.22234i	−0.791499	+	0.611170i	$0.790699\pi$
$440$	0.122856	+	0.188180i	0.00585692	+	0.00897112i
$441$		0			0
$442$	3.44610	+	17.6524i	0.163914	+	0.839638i
$443$	35.6884			1.69561			0.847804	−	0.530310i	$-0.177924\pi$
$443$	35.6884			1.69561			0.847804	+	0.530310i	$0.177924\pi$
$444$		0			0
$445$	−8.53688			−0.404687
$446$	5.47874	+	28.0645i	0.259426	+	1.32889i
$447$		0			0
$448$	−7.32407	−	3.21838i	−0.346030	−	0.152054i
$449$			34.3779i			1.62239i	0.584773	+	0.811197i	$0.301183\pi$
$449$			34.3779i			1.62239i	−0.584773	+	0.811197i	$0.698817\pi$
$450$		0			0
$451$		−	0.201308i		−	0.00947922i
$452$	−3.33122	−	8.20679i	−0.156687	−	0.386015i
$453$		0			0
$454$	20.8948	−	4.07908i	0.980642	−	0.191441i
$455$	−2.48920			−0.116695
$456$		0			0
$457$	−14.8444			−0.694391			−0.347196	−	0.937793i	$-0.612866\pi$
$457$	−14.8444			−0.694391			−0.347196	+	0.937793i	$0.612866\pi$
$458$	−18.2260	+	3.55808i	−0.851646	+	0.166258i
$459$		0			0
$460$	−3.40485	−	8.38819i	−0.158752	−	0.391101i
$461$		−	20.8391i		−	0.970574i	−0.874355	−	0.485287i	$-0.838715\pi$
$461$		−	20.8391i		−	0.970574i	0.874355	−	0.485287i	$-0.161285\pi$
$462$		0			0
$463$		−	15.4010i		−	0.715744i	−0.933771	−	0.357872i	$-0.883502\pi$
$463$		−	15.4010i		−	0.715744i	0.933771	−	0.357872i	$-0.116498\pi$
$464$	−13.3367	−	13.7214i	−0.619142	−	0.637002i
$465$		0			0
$466$	−7.29243	−	37.3549i	−0.337815	−	1.73043i
$467$	−22.3860			−1.03590			−0.517951	−	0.855411i	$-0.673305\pi$
$467$	−22.3860			−1.03590			−0.517951	+	0.855411i	$0.673305\pi$
$468$		0			0
$469$	15.8030			0.729715
$470$	−2.02553	−	10.3756i	−0.0934308	−	0.478592i
$471$		0			0
$472$	7.75231	−	5.06120i	0.356829	−	0.232961i
$473$		−	0.175146i		−	0.00805324i
$474$		0			0
$475$			6.83509i			0.313615i
$476$	13.4115	−	5.44384i	0.614714	−	0.249518i
$477$		0			0
$478$	14.5948	−	2.84919i	0.667550	−	0.130319i
$479$	17.0781			0.780318			0.390159	−	0.920747i	$-0.372420\pi$
$479$	17.0781			0.780318			0.390159	+	0.920747i	$0.372420\pi$
$480$		0			0
$481$	9.21254			0.420056
$482$	−37.7965	+	7.37863i	−1.72158	+	0.336087i
$483$		0			0
$484$	−20.3789	+	8.27197i	−0.926311	+	0.375999i
$485$		−	23.2675i		−	1.05652i
$486$		0			0
$487$		−	31.8466i		−	1.44311i	−0.692359	−	0.721553i	$-0.743429\pi$
$487$		−	31.8466i		−	1.44311i	0.692359	−	0.721553i	$-0.256571\pi$
$488$	−20.9066	+	13.6492i	−0.946398	+	0.617869i
$489$		0			0
$490$	0.383823	+	1.96611i	0.0173394	+	0.0888196i
$491$	−18.5201			−0.835799			−0.417900	−	0.908493i	$-0.637234\pi$
$491$	−18.5201			−0.835799			−0.417900	+	0.908493i	$0.637234\pi$
$492$		0			0
$493$	34.6204			1.55922
$494$	1.08723	+	5.56924i	0.0489166	+	0.250572i
$495$		0			0
$496$	17.6744	+	18.1842i	0.793603	+	0.816496i
$497$			14.2854i			0.640790i
$498$		0			0
$499$			4.89961i			0.219337i	0.993968	+	0.109668i	$0.0349789\pi$
$499$			4.89961i			0.219337i	−0.993968	+	0.109668i	$0.965021\pi$
$500$	8.51715	+	20.9829i	0.380899	+	0.938383i
$501$		0			0
$502$	−22.2672	+	4.34700i	−0.993833	+	0.194016i
$503$	3.38502			0.150931			0.0754653	−	0.997148i	$-0.475956\pi$
$503$	3.38502			0.150931			0.0754653	+	0.997148i	$0.475956\pi$
$504$		0			0
$505$	19.3724			0.862059
$506$	−0.248797	+	0.0485702i	−0.0110604	+	0.00215921i
$507$		0			0
$508$	−2.97149	−	7.32056i	−0.131838	−	0.324797i
$509$			14.4845i			0.642012i	0.947077	+	0.321006i	$0.104021\pi$
$509$			14.4845i			0.642012i	−0.947077	+	0.321006i	$0.895979\pi$
$510$		0			0
$511$			5.03219i			0.222611i
$512$	3.70234	+	22.3225i	0.163622	+	0.986523i
$513$		0			0
$514$	−3.63243	−	18.6068i	−0.160219	−	0.820712i
$515$	−20.2324			−0.891547
$516$		0			0
$517$	−0.296017			−0.0130188
$518$	−1.42053	−	7.27658i	−0.0624147	−	0.319715i
$519$		0			0
$520$	3.84885	+	5.89534i	0.168783	+	0.258528i
$521$		−	9.34153i		−	0.409260i	−0.978839	−	0.204630i	$-0.934401\pi$
$521$		−	9.34153i		−	0.409260i	0.978839	−	0.204630i	$-0.0655991\pi$
$522$		0			0
$523$			14.6595i			0.641014i	0.947246	+	0.320507i	$0.103853\pi$
$523$			14.6595i			0.641014i	−0.947246	+	0.320507i	$0.896147\pi$
$524$	28.3592	−	11.5113i	1.23888	−	0.502872i
$525$		0			0
$526$	11.0322	−	2.15370i	0.481025	−	0.0939058i
$527$	−45.8804			−1.99858
$528$		0			0
$529$	−12.7886			−0.556025
$530$	10.1852	−	1.98836i	0.442417	−	0.0863687i
$531$		0			0
$532$	4.23125	−	1.71750i	0.183448	−	0.0744633i
$533$		−	6.30663i		−	0.273170i
$534$		0			0
$535$			9.56759i			0.413643i
$536$	−24.4350	−	37.4274i	−1.05543	−	1.61662i
$537$		0			0
$538$	−0.795265	−	4.07369i	−0.0342863	−	0.175629i
$539$	0.0560930			0.00241610
$540$		0			0
$541$	−44.5037			−1.91336			−0.956682	−	0.291137i	$-0.905967\pi$
$541$	−44.5037			−1.91336			−0.956682	+	0.291137i	$0.905967\pi$
$542$	5.48635	+	28.1034i	0.235659	+	1.20715i
$543$		0			0
$544$	−33.6302	−	23.3460i	−1.44188	−	1.00095i
$545$			25.9653i			1.11223i
$546$		0			0
$547$		−	24.5838i		−	1.05113i	−0.850754	−	0.525564i	$-0.823854\pi$
$547$		−	24.5838i		−	1.05113i	0.850754	−	0.525564i	$-0.176146\pi$
$548$	−1.26875	−	3.12570i	−0.0541985	−	0.133523i
$549$		0			0
$550$	0.233071	−	0.0455002i	0.00993820	−	0.00194014i
$551$	10.9226			0.465317
$552$		0			0
$553$	12.1925			0.518480
$554$	7.59258	−	1.48222i	0.322578	−	0.0629736i
$555$		0			0
$556$	0.755240	+	1.86061i	0.0320293	+	0.0789075i
$557$			13.6793i			0.579612i	0.957085	+	0.289806i	$0.0935908\pi$
$557$			13.6793i			0.579612i	−0.957085	+	0.289806i	$0.906409\pi$
$558$		0			0
$559$		−	5.48703i		−	0.232077i
$560$	4.06300	−	3.94908i	0.171693	−	0.166879i
$561$		0			0
$562$	1.39052	+	7.12284i	0.0586556	+	0.300459i
$563$	10.4078			0.438636			0.219318	−	0.975653i	$-0.429617\pi$
$563$	10.4078			0.438636			0.219318	+	0.975653i	$0.429617\pi$
$564$		0			0
$565$	6.27301			0.263908
$566$	5.57358	+	28.5502i	0.234275	+	1.20006i
$567$		0			0
$568$	33.8333	−	22.0885i	1.41961	−	0.926813i
$569$		−	36.6819i		−	1.53778i	−0.639379	−	0.768892i	$-0.720808\pi$
$569$		−	36.6819i		−	1.53778i	0.639379	−	0.768892i	$-0.279192\pi$
$570$		0			0
$571$		−	28.8754i		−	1.20840i	−0.796834	−	0.604198i	$-0.793494\pi$
$571$		−	28.8754i		−	1.20840i	0.796834	−	0.604198i	$-0.206506\pi$
$572$	0.182669	−	0.0741472i	0.00763778	−	0.00310025i
$573$		0			0
$574$	−4.98133	+	0.972455i	−0.207917	+	0.0405895i
$575$	−9.56599			−0.398930
$576$		0			0
$577$	−27.5486			−1.14686			−0.573432	−	0.819253i	$-0.694388\pi$
$577$	−27.5486			−1.14686			−0.573432	+	0.819253i	$0.694388\pi$
$578$	49.1019	−	9.58568i	2.04237	−	0.398712i
$579$		0			0
$580$	12.5572	−	5.09708i	0.521409	−	0.211645i
$581$			1.28060i			0.0531283i
$582$		0			0
$583$		−	0.290584i		−	0.0120348i
$584$	11.9181	−	7.78089i	0.493174	−	0.321975i
$585$		0			0
$586$	1.91236	+	9.79592i	0.0789988	+	0.404666i
$587$	−41.3991			−1.70872			−0.854362	−	0.519678i	$-0.826052\pi$
$587$	−41.3991			−1.70872			−0.854362	+	0.519678i	$0.826052\pi$
$588$		0			0
$589$	−14.4750			−0.596433
$590$	1.25636	+	6.43559i	0.0517233	+	0.264949i
$591$		0			0
$592$	−15.0372	+	14.6156i	−0.618025	+	0.600697i
$593$		−	21.8909i		−	0.898952i	−0.893292	−	0.449476i	$-0.851611\pi$
$593$		−	21.8909i		−	0.898952i	0.893292	−	0.449476i	$-0.148389\pi$
$594$		0			0
$595$			10.2513i			0.420262i
$596$	−15.4334	−	38.0218i	−0.632176	−	1.55743i
$597$		0			0
$598$	−7.79438	+	1.52162i	−0.318736	+	0.0622236i
$599$	15.5382			0.634872			0.317436	−	0.948280i	$-0.397178\pi$
$599$	15.5382			0.634872			0.317436	+	0.948280i	$0.397178\pi$
$600$		0			0
$601$	23.3128			0.950950			0.475475	−	0.879729i	$-0.342276\pi$
$601$	23.3128			0.950950			0.475475	+	0.879729i	$0.342276\pi$
$602$	−4.33396	+	0.846076i	−0.176639	+	0.0344835i
$603$		0			0
$604$	−5.37125	−	13.2326i	−0.218553	−	0.538428i
$605$		−	15.5769i		−	0.633293i
$606$		0			0
$607$		−	3.50712i		−	0.142350i	−0.997464	−	0.0711748i	$-0.977325\pi$
$607$		−	3.50712i		−	0.142350i	0.997464	−	0.0711748i	$-0.0226748\pi$
$608$	−10.6102	−	7.36553i	−0.430299	−	0.298712i
$609$		0			0
$610$	−3.38817	−	17.3556i	−0.137183	−	0.702709i
$611$	−9.27370			−0.375174
$612$		0			0
$613$	5.41525			0.218720			0.109360	−	0.994002i	$-0.465120\pi$
$613$	5.41525			0.218720			0.109360	+	0.994002i	$0.465120\pi$
$614$	−4.11688	−	21.0884i	−0.166144	−	0.851060i
$615$		0			0
$616$	−0.0867324	−	0.132849i	−0.00349455	−	0.00535265i
$617$			23.7193i			0.954904i	0.878658	+	0.477452i	$0.158440\pi$
$617$			23.7193i			0.954904i	−0.878658	+	0.477452i	$0.841560\pi$
$618$		0			0
$619$			37.5876i			1.51077i	0.655279	+	0.755387i	$0.272551\pi$
$619$			37.5876i			1.51077i	−0.655279	+	0.755387i	$0.727449\pi$
$620$	−16.6413	+	6.75486i	−0.668331	+	0.271282i
$621$		0			0
$622$	19.2583	−	3.75961i	0.772189	−	0.150747i
$623$	6.02678			0.241458
$624$		0			0
$625$	−1.07088			−0.0428350
$626$	−22.5940	+	4.41079i	−0.903036	+	0.176291i
$627$		0			0
$628$	19.0187	−	7.71988i	0.758929	−	0.308057i
$629$		−	37.9402i		−	1.51277i
$630$		0			0
$631$			16.2032i			0.645040i	0.946563	+	0.322520i	$0.104530\pi$
$631$			16.2032i			0.645040i	−0.946563	+	0.322520i	$0.895470\pi$
$632$	−18.8524	−	28.8765i	−0.749909	−	1.14864i
$633$		0			0
$634$	−7.19912	−	36.8770i	−0.285914	−	1.46457i
$635$	5.59560			0.222055
$636$		0			0
$637$	1.75730			0.0696266
$638$	−0.0727099	−	0.372451i	−0.00287861	−	0.0147455i
$639$		0			0
$640$	−15.6352	−	3.51653i	−0.618035	−	0.139003i
$641$			35.0779i			1.38549i	0.721180	+	0.692747i	$0.243600\pi$
$641$			35.0779i			1.38549i	−0.721180	+	0.692747i	$0.756400\pi$
$642$		0			0
$643$			9.55599i			0.376852i	0.982087	+	0.188426i	$0.0603385\pi$
$643$			9.55599i			0.376852i	−0.982087	+	0.188426i	$0.939662\pi$
$644$	2.40372	+	5.92181i	0.0947198	+	0.233352i
$645$		0			0
$646$	22.9359	−	4.47754i	0.902400	−	0.176167i
$647$	36.1415			1.42087			0.710435	−	0.703763i	$-0.248498\pi$
$647$	36.1415			1.42087			0.710435	+	0.703763i	$0.248498\pi$
$648$		0			0
$649$	0.183607			0.00720722
$650$	7.30172	−	1.42544i	0.286397	−	0.0559104i
$651$		0			0
$652$	−11.1273	−	27.4133i	−0.435779	−	1.07359i
$653$		−	18.9760i		−	0.742589i	−0.928515	−	0.371294i	$-0.878914\pi$
$653$		−	18.9760i		−	0.742589i	0.928515	−	0.371294i	$-0.121086\pi$
$654$		0			0
$655$			21.6769i			0.846985i
$656$	10.0054	+	10.2940i	0.390645	+	0.401914i
$657$		0			0
$658$	1.42996	+	7.32489i	0.0557458	+	0.285554i
$659$	47.9319			1.86716			0.933581	−	0.358365i	$-0.116666\pi$
$659$	47.9319			1.86716			0.933581	+	0.358365i	$0.116666\pi$
$660$		0			0
$661$	34.6710			1.34855			0.674273	−	0.738483i	$-0.264457\pi$
$661$	34.6710			1.34855			0.674273	+	0.738483i	$0.264457\pi$
$662$	8.20187	+	42.0135i	0.318775	+	1.63290i
$663$		0			0
$664$	3.03294	−	1.98010i	0.117701	−	0.0768427i
$665$			3.23423i			0.125418i
$666$		0			0
$667$			15.2866i			0.591899i
$668$	34.3828	−	13.9563i	1.33031	−	0.539986i
$669$		0			0
$670$	31.0704	−	6.06556i	1.20035	−	0.234333i
$671$	−0.495156			−0.0191153
$672$		0			0
$673$	−44.2185			−1.70450			−0.852248	−	0.523138i	$-0.824761\pi$
$673$	−44.2185			−1.70450			−0.852248	+	0.523138i	$0.824761\pi$
$674$	−1.10095	+	0.214928i	−0.0424071	+	0.00827871i
$675$		0			0
$676$	−18.3683	+	7.45586i	−0.706472	+	0.286764i
$677$		−	8.86027i		−	0.340528i	−0.985398	−	0.170264i	$-0.945538\pi$
$677$		−	8.86027i		−	0.340528i	0.985398	−	0.170264i	$-0.0544621\pi$
$678$		0			0
$679$			16.4261i			0.630377i
$680$	24.2789	−	15.8508i	0.931053	−	0.607851i
$681$		0			0
$682$	0.0963582	+	0.493588i	0.00368974	+	0.0189004i
$683$	14.7455			0.564221			0.282110	−	0.959382i	$-0.408966\pi$
$683$	14.7455			0.564221			0.282110	+	0.959382i	$0.408966\pi$
$684$		0			0
$685$	2.38919			0.0912862
$686$	−0.270968	−	1.38801i	−0.0103456	−	0.0529945i
$687$		0			0
$688$	8.70510	+	8.95622i	0.331879	+	0.341453i
$689$		−	9.10349i		−	0.346815i
$690$		0			0
$691$		−	23.1595i		−	0.881031i	−0.897745	−	0.440515i	$-0.854796\pi$
$691$		−	23.1595i		−	0.881031i	0.897745	−	0.440515i	$-0.145204\pi$
$692$	−11.7750	−	29.0089i	−0.447618	−	1.10275i
$693$		0			0
$694$	19.9431	−	3.89329i	0.757030	−	0.147787i
$695$	−1.42219			−0.0539468
$696$		0			0
$697$	−25.9727			−0.983786
$698$	30.1883	−	5.89336i	1.14264	−	0.223067i
$699$		0			0
$700$	−2.25179	−	5.54751i	−0.0851096	−	0.209676i
$701$		−	39.7059i		−	1.49967i	−0.661625	−	0.749835i	$-0.730133\pi$
$701$		−	39.7059i		−	1.49967i	0.661625	−	0.749835i	$-0.269867\pi$
$702$		0			0
$703$		−	11.9699i		−	0.451454i
$704$	−0.180529	+	0.410829i	−0.00680393	+	0.0154837i
$705$		0			0
$706$	−3.89208	−	19.9369i	−0.146480	−	0.750334i
$707$	−13.6763			−0.514350
$708$		0			0
$709$	−28.0024			−1.05165			−0.525826	−	0.850592i	$-0.676244\pi$
$709$	−28.0024			−1.05165			−0.525826	+	0.850592i	$0.676244\pi$
$710$	5.48309	+	28.0867i	0.205777	+	1.05407i
$711$		0			0
$712$	−9.31876	−	14.2737i	−0.349235	−	0.534928i
$713$		−	20.2584i		−	0.758683i
$714$		0			0
$715$			0.139626i			0.00522173i
$716$	−2.89152	+	1.17370i	−0.108061	+	0.0438631i
$717$		0			0
$718$	−0.106304	+	0.0207527i	−0.00396724	+	0.000774484i
$719$	−7.04858			−0.262867			−0.131434	−	0.991325i	$-0.541958\pi$
$719$	−7.04858			−0.262867			−0.131434	+	0.991325i	$0.541958\pi$
$720$		0			0
$721$	14.2835			0.531945
$722$	−19.1361	+	3.73574i	−0.712171	+	0.139030i
$723$		0			0
$724$	−5.95443	+	2.41696i	−0.221295	+	0.0898256i
$725$		−	14.3204i		−	0.531845i
$726$		0			0
$727$			37.0164i			1.37286i	0.727196	+	0.686430i	$0.240823\pi$
$727$			37.0164i			1.37286i	−0.727196	+	0.686430i	$0.759177\pi$
$728$	−2.71718	−	4.16193i	−0.100705	−	0.154252i
$729$		0			0
$730$	1.93147	+	9.89381i	0.0714869	+	0.366186i
$731$	−22.5973			−0.835792
$732$		0			0
$733$	10.2423			0.378309			0.189154	−	0.981947i	$-0.439425\pi$
$733$	10.2423			0.378309			0.189154	+	0.981947i	$0.439425\pi$
$734$	−6.94001	−	35.5497i	−0.256161	−	1.31216i
$735$		0			0
$736$	10.3084	−	14.8494i	0.379971	−	0.547354i
$737$		−	0.886439i		−	0.0326524i
$738$		0			0
$739$			51.1454i			1.88141i	0.339219	+	0.940707i	$0.389837\pi$
$739$			51.1454i			1.88141i	−0.339219	+	0.940707i	$0.610163\pi$
$740$	−5.58584	−	13.7613i	−0.205340	−	0.505875i
$741$		0			0
$742$	−7.19045	+	1.40372i	−0.263970	+	0.0515322i
$743$	−0.512623			−0.0188063			−0.00940316	−	0.999956i	$-0.502993\pi$
$743$	−0.512623			−0.0188063			−0.00940316	+	0.999956i	$0.502993\pi$
$744$		0			0
$745$	29.0626			1.06477
$746$	39.4779	−	7.70688i	1.44539	−	0.282169i
$747$		0			0
$748$	−0.305362	−	0.752290i	−0.0111651	−	0.0275064i
$749$		−	6.75443i		−	0.246801i
$750$		0			0
$751$			2.56484i			0.0935925i	0.998904	+	0.0467962i	$0.0149011\pi$
$751$			2.56484i			0.0935925i	−0.998904	+	0.0467962i	$0.985099\pi$
$752$	15.1370	−	14.7126i	0.551990	−	0.536514i
$753$		0			0
$754$	−2.27787	−	11.6682i	−0.0829553	−	0.424932i
$755$	10.1146			0.368108
$756$		0			0
$757$	27.8759			1.01317			0.506584	−	0.862191i	$-0.330908\pi$
$757$	27.8759			1.01317			0.506584	+	0.862191i	$0.330908\pi$
$758$	−5.97676	−	30.6155i	−0.217086	−	1.11201i
$759$		0			0
$760$	7.65987	−	5.00085i	0.277853	−	0.181400i
$761$		−	6.94222i		−	0.251655i	−0.992052	−	0.125828i	$-0.959841\pi$
$761$		−	6.94222i		−	0.251655i	0.992052	−	0.125828i	$-0.0401586\pi$
$762$		0			0
$763$		−	18.3307i		−	0.663617i
$764$	30.0526	−	12.1986i	1.08726	−	0.441331i
$765$		0			0
$766$	−22.8634	+	4.46339i	−0.826088	+	0.161269i
$767$	5.75210			0.207696
$768$		0			0
$769$	−36.0326			−1.29937			−0.649684	−	0.760204i	$-0.725099\pi$
$769$	−36.0326			−1.29937			−0.649684	+	0.760204i	$0.725099\pi$
$770$	0.110285	−	0.0215298i	0.00397439	−	0.000775881i
$771$		0			0
$772$	22.0445	−	8.94807i	0.793399	−	0.322048i
$773$		−	8.15857i		−	0.293443i	−0.989178	−	0.146722i	$-0.953128\pi$
$773$		−	8.15857i		−	0.293443i	0.989178	−	0.146722i	$-0.0468722\pi$
$774$		0			0
$775$			18.9779i			0.681708i
$776$	38.9032	−	25.3985i	1.39654	−	0.911753i
$777$		0			0
$778$	7.63508	+	39.1101i	0.273731	+	1.40217i
$779$	−8.19426			−0.293590
$780$		0			0
$781$	0.801314			0.0286733
$782$	6.26651	+	32.0997i	0.224090	+	1.14788i
$783$		0			0
$784$	−2.86835	+	2.78793i	−0.102441	+	0.0995689i
$785$			14.5373i			0.518858i
$786$		0			0
$787$			29.7365i			1.05999i	0.848000	+	0.529997i	$0.177807\pi$
$787$			29.7365i			1.05999i	−0.848000	+	0.529997i	$0.822193\pi$
$788$	−7.51885	−	18.5235i	−0.267848	−	0.659871i
$789$		0			0
$790$	23.9718	−	4.67978i	0.852880	−	0.166499i
$791$	−4.42856			−0.157461
$792$		0			0
$793$	−15.5124			−0.550861
$794$	−3.99134	+	0.779189i	−0.141647	+	0.0276524i
$795$		0			0
$796$	−3.49108	−	8.60064i	−0.123738	−	0.304842i
$797$		−	7.06876i		−	0.250388i	−0.992132	−	0.125194i	$-0.960045\pi$
$797$		−	7.06876i		−	0.250388i	0.992132	−	0.125194i	$-0.0399554\pi$
$798$		0			0
$799$			38.1920i			1.35114i
$800$	−9.65681	+	13.9108i	−0.341420	+	0.491820i
$801$		0			0
$802$	−7.33543	−	37.5752i	−0.259023	−	1.32683i
$803$	0.282271			0.00996111
$804$		0			0
$805$	−4.52644			−0.159536
$806$	3.01873	+	15.4632i	0.106330	+	0.544669i
$807$		0			0
$808$	21.1466	+	32.3906i	0.743936	+	1.13950i
$809$		−	44.0446i		−	1.54853i	−0.632864	−	0.774263i	$-0.718121\pi$
$809$		−	44.0446i		−	1.54853i	0.632864	−	0.774263i	$-0.281879\pi$
$810$		0			0
$811$			26.9807i			0.947420i	0.880681	+	0.473710i	$0.157086\pi$
$811$			26.9807i			0.947420i	−0.880681	+	0.473710i	$0.842914\pi$
$812$	−8.86499	+	3.59839i	−0.311100	+	0.126279i
$813$		0			0
$814$	−0.408165	+	0.0796820i	−0.0143062	+	0.00279285i
$815$	20.9538			0.733981
$816$		0			0
$817$	−7.12934			−0.249424
$818$	−47.2095	+	9.21625i	−1.65064	+	0.322238i
$819$		0			0
$820$	−9.42057	+	3.82390i	−0.328981	+	0.133536i
$821$			16.1090i			0.562206i	0.959678	+	0.281103i	$0.0907003\pi$
$821$			16.1090i			0.562206i	−0.959678	+	0.281103i	$0.909300\pi$
$822$		0			0
$823$			11.1358i			0.388169i	0.980985	+	0.194085i	$0.0621736\pi$
$823$			11.1358i			0.388169i	−0.980985	+	0.194085i	$0.937826\pi$
$824$	−22.0855	−	33.8286i	−0.769384	−	1.17848i
$825$		0			0
$826$	−0.886949	−	4.54333i	−0.0308609	−	0.158083i
$827$	31.6149			1.09936			0.549678	−	0.835376i	$-0.314750\pi$
$827$	31.6149			1.09936			0.549678	+	0.835376i	$0.314750\pi$
$828$		0			0
$829$	−16.0132			−0.556161			−0.278081	−	0.960558i	$-0.589698\pi$
$829$	−16.0132			−0.556161			−0.278081	+	0.960558i	$0.589698\pi$
$830$	0.491525	+	2.51780i	0.0170611	+	0.0873941i
$831$		0			0
$832$	−5.65565	+	12.8706i	−0.196074	+	0.446207i
$833$		−	7.23711i		−	0.250751i
$834$		0			0
$835$			26.2811i			0.909496i
$836$	−0.0963400	−	0.237344i	−0.00333199	−	0.00820870i
$837$		0			0
$838$	−53.3450	+	10.4140i	−1.84277	+	0.359746i
$839$	−47.1044			−1.62622			−0.813112	−	0.582107i	$-0.802228\pi$
$839$	−47.1044			−1.62622			−0.813112	+	0.582107i	$0.802228\pi$
$840$		0			0
$841$	6.11587			0.210892
$842$	0.128156	−	0.0250186i	0.00441655	−	0.000862199i
$843$		0			0
$844$	−7.07023	−	17.4182i	−0.243367	−	0.599561i
$845$		−	14.0401i		−	0.482995i
$846$		0			0
$847$			10.9969i			0.377856i
$848$	14.4426	+	14.8592i	0.495960	+	0.510267i
$849$		0			0
$850$	−5.87042	−	30.0708i	−0.201354	−	1.03142i
$851$	16.7524			0.574265
$852$		0			0
$853$	−25.1550			−0.861290			−0.430645	−	0.902521i	$-0.641714\pi$
$853$	−25.1550			−0.861290			−0.430645	+	0.902521i	$0.641714\pi$
$854$	2.39194	+	12.2526i	0.0818506	+	0.419274i
$855$		0			0
$856$	−15.9970	+	10.4439i	−0.546766	+	0.356964i
$857$			54.0514i			1.84636i	0.384369	+	0.923180i	$0.374419\pi$
$857$			54.0514i			1.84636i	−0.384369	+	0.923180i	$0.625581\pi$
$858$		0			0
$859$			48.1801i			1.64388i	0.569571	+	0.821942i	$0.307109\pi$
$859$			48.1801i			1.64388i	−0.569571	+	0.821942i	$0.692891\pi$
$860$	−8.19629	+	3.32695i	−0.279491	+	0.113448i
$861$		0			0
$862$	−28.9961	+	5.66061i	−0.987609	+	0.192801i
$863$	−33.1426			−1.12819			−0.564094	−	0.825711i	$-0.690774\pi$
$863$	−33.1426			−1.12819			−0.564094	+	0.825711i	$0.690774\pi$
$864$		0			0
$865$	22.1735			0.753920
$866$	−9.46700	+	1.84815i	−0.321702	+	0.0628026i
$867$		0			0
$868$	11.7483	−	4.76873i	0.398762	−	0.161861i
$869$		−	0.683917i		−	0.0232003i
$870$		0			0
$871$		−	27.7706i		−	0.940970i
$872$	−43.4140	+	28.3434i	−1.47018	+	0.959830i
$873$		0			0
$874$	1.97705	+	10.1273i	0.0668748	+	0.342561i
$875$	11.3228			0.382780
$876$		0			0
$877$	16.2824			0.549819			0.274909	−	0.961470i	$-0.411352\pi$
$877$	16.2824			0.549819			0.274909	+	0.961470i	$0.411352\pi$
$878$	−6.93972	−	35.5482i	−0.234204	−	1.19969i
$879$		0			0
$880$	−0.221516	−	0.227906i	−0.00746729	−	0.00768270i
$881$			16.4202i			0.553212i	0.960983	+	0.276606i	$0.0892096\pi$
$881$			16.4202i			0.553212i	−0.960983	+	0.276606i	$0.910790\pi$
$882$		0			0
$883$		−	6.06477i		−	0.204096i	−0.994779	−	0.102048i	$-0.967461\pi$
$883$		−	6.06477i		−	0.204096i	0.994779	−	0.102048i	$-0.0325395\pi$
$884$	−9.56645	−	23.5679i	−0.321754	−	0.792675i
$885$		0			0
$886$	−49.5359	+	9.67041i	−1.66419	+	0.324884i
$887$	−17.4930			−0.587358			−0.293679	−	0.955904i	$-0.594880\pi$
$887$	−17.4930			−0.587358			−0.293679	+	0.955904i	$0.594880\pi$
$888$		0			0
$889$	−3.95033			−0.132490
$890$	11.8493	−	2.31322i	0.397189	−	0.0775393i
$891$		0			0
$892$	−15.2091	−	37.4692i	−0.509239	−	1.25456i
$893$			12.0494i			0.403217i
$894$		0			0
$895$		−	2.21019i		−	0.0738784i
$896$	11.0380	+	2.48256i	0.368753	+	0.0829366i
$897$		0			0
$898$	−9.31530	−	47.7169i	−0.310856	−	1.59233i
$899$	30.3270			1.01146
$900$		0			0
$901$	−37.4911			−1.24901
$902$	0.0545480	+	0.279418i	0.00181625	+	0.00930360i
$903$		0			0
$904$	6.84754	+	10.4885i	0.227746	+	0.348841i
$905$		−	4.55138i		−	0.151293i
$906$		0			0
$907$		−	20.3074i		−	0.674297i	−0.941452	−	0.337148i	$-0.890538\pi$
$907$		−	20.3074i		−	0.674297i	0.941452	−	0.337148i	$-0.109462\pi$
$908$	−27.8969	+	11.3236i	−0.925792	+	0.375788i
$909$		0			0
$910$	3.45503	−	0.674491i	0.114533	−	0.0223592i
$911$	34.7262			1.15053			0.575265	−	0.817967i	$-0.304899\pi$
$911$	34.7262			1.15053			0.575265	+	0.817967i	$0.304899\pi$
$912$		0			0
$913$	0.0718328			0.00237732
$914$	20.6042	−	4.02235i	0.681526	−	0.133048i
$915$		0			0
$916$	24.3338	−	9.87732i	0.804011	−	0.326356i
$917$		−	15.3032i		−	0.505357i
$918$		0			0
$919$		−	41.4965i		−	1.36884i	−0.729087	−	0.684421i	$-0.760055\pi$
$919$		−	41.4965i		−	1.36884i	0.729087	−	0.684421i	$-0.239945\pi$
$920$	6.99890	+	10.7203i	0.230747	+	0.353438i
$921$		0			0
$922$	5.64672	+	28.9249i	0.185965	+	0.952591i
$923$	25.1038			0.826300
$924$		0			0
$925$	−15.6935			−0.516001
$926$	4.17317	+	21.3767i	0.137139	+	0.702483i
$927$		0			0
$928$	22.2296	+	15.4317i	0.729722	+	0.506570i
$929$			26.1549i			0.858115i	0.903277	+	0.429057i	$0.141154\pi$
$929$			26.1549i			0.858115i	−0.903277	+	0.429057i	$0.858846\pi$
$930$		0			0
$931$		−	2.28327i		−	0.0748312i
$932$	20.2440	+	49.8731i	0.663113	+	1.63365i
$933$		0			0
$934$	31.0720	−	6.06589i	1.01671	−	0.198482i
$935$	0.575026			0.0188054
$936$		0			0
$937$	−8.61565			−0.281461			−0.140730	−	0.990048i	$-0.544945\pi$
$937$	−8.61565			−0.281461			−0.140730	+	0.990048i	$0.544945\pi$
$938$	−21.9348	+	4.28210i	−0.716195	+	0.139816i
$939$		0			0
$940$	5.62292	+	13.8527i	0.183400	+	0.451824i
$941$			58.7826i			1.91626i	0.286335	+	0.958130i	$0.407563\pi$
$941$			58.7826i			1.91626i	−0.286335	+	0.958130i	$0.592437\pi$
$942$		0			0
$943$		−	11.4682i		−	0.373456i
$944$	−9.38888	+	9.12563i	−0.305582	+	0.297014i
$945$		0			0
$946$	0.0474590	+	0.243105i	0.00154302	+	0.00790403i
$947$	29.3460			0.953618			0.476809	−	0.879007i	$-0.341793\pi$
$947$	29.3460			0.953618			0.476809	+	0.879007i	$0.341793\pi$
$948$		0			0
$949$	8.84304			0.287057
$950$	−1.85209	−	9.48719i	−0.0600897	−	0.307805i
$951$		0			0
$952$	−17.1402	+	11.1902i	−0.555516	+	0.362676i
$953$		−	47.2690i		−	1.53119i	−0.643322	−	0.765596i	$-0.722444\pi$
$953$		−	47.2690i		−	1.53119i	0.643322	−	0.765596i	$-0.277556\pi$
$954$		0			0
$955$			22.9712i			0.743332i
$956$	−19.4857	+	7.90943i	−0.630212	+	0.255809i
$957$		0			0
$958$	−23.7046	+	4.62761i	−0.765861	+	0.149511i
$959$	−1.68670			−0.0544662
$960$		0			0
$961$	−9.19058			−0.296470
$962$	−12.7871	+	2.49630i	−0.412273	+	0.0804839i
$963$		0			0
$964$	50.4626	−	20.4832i	1.62529	−	0.659721i
$965$			16.8501i			0.542424i
$966$		0			0
$967$			58.9579i			1.89596i	0.318331	+	0.947980i	$0.396878\pi$
$967$			58.9579i			1.89596i	−0.318331	+	0.947980i	$0.603122\pi$
$968$	26.0446	−	17.0036i	0.837107	−	0.546517i
$969$		0			0
$970$	6.30474	+	32.2955i	0.202433	+	1.03695i
$971$	−10.4565			−0.335565			−0.167782	−	0.985824i	$-0.553661\pi$
$971$	−10.4565			−0.335565			−0.167782	+	0.985824i	$0.553661\pi$
$972$		0			0
$973$	1.00403			0.0321876
$974$	8.62939	+	44.2034i	0.276504	+	1.41637i
$975$		0			0
$976$	25.3201	−	24.6102i	0.810478	−	0.787754i
$977$			45.6350i			1.45999i	0.683452	+	0.729996i	$0.260478\pi$
$977$			45.6350i			1.45999i	−0.683452	+	0.729996i	$0.739522\pi$
$978$		0			0
$979$		−	0.338061i		−	0.0108045i
$980$	−1.06550	−	2.62497i	−0.0340362	−	0.0838517i
$981$		0			0
$982$	25.7061	−	5.01834i	0.820314	−	0.160142i
$983$	−28.1758			−0.898667			−0.449333	−	0.893364i	$-0.648338\pi$
$983$	−28.1758			−0.898667			−0.449333	+	0.893364i	$0.648338\pi$
$984$		0			0
$985$	14.1587			0.451135
$986$	−48.0535	+	9.38101i	−1.53034	+	0.298752i
$987$		0			0
$988$	−3.01817	−	7.43556i	−0.0960206	−	0.236557i
$989$		−	9.97781i		−	0.317276i
$990$		0			0
$991$			7.28831i			0.231521i	0.993277	+	0.115760i	$0.0369305\pi$
$991$			7.28831i			0.231521i	−0.993277	+	0.115760i	$0.963070\pi$
$992$	−29.4596	−	20.4507i	−0.935342	−	0.649311i
$993$		0			0
$994$	−3.87089	−	19.8284i	−0.122777	−	0.628917i
$995$	6.57406			0.208412
$996$		0			0
$997$	21.3792			0.677086			0.338543	−	0.940951i	$-0.390066\pi$
$997$	21.3792			0.677086			0.338543	+	0.940951i	$0.390066\pi$
$998$	−1.32764	−	6.80072i	−0.0420256	−	0.215273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.e.b.323.4	yes	24
3.2	odd	2	inner	756.2.e.b.323.21	yes	24
4.3	odd	2	inner	756.2.e.b.323.22	yes	24
12.11	even	2	inner	756.2.e.b.323.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.e.b.323.3	✓	24	12.11	even	2	inner
756.2.e.b.323.4	yes	24	1.1	even	1	trivial
756.2.e.b.323.21	yes	24	3.2	odd	2	inner
756.2.e.b.323.22	yes	24	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38801 + 0.270968i) q^{2} +(1.85315 - 0.752213i) q^{4} +1.41649i q^{5} -1.00000i q^{7} +(-2.36837 + 1.54622i) q^{8} +O(q^{10})\)	\(q+(-1.38801 + 0.270968i) q^{2} +(1.85315 - 0.752213i) q^{4} +1.41649i q^{5} -1.00000i q^{7} +(-2.36837 + 1.54622i) q^{8} +(-0.383823 - 1.96611i) q^{10} -0.0560930 q^{11} -1.75730 q^{13} +(0.270968 + 1.38801i) q^{14} +(2.86835 - 2.78793i) q^{16} +7.23711i q^{17} +2.28327i q^{19} +(1.06550 + 2.62497i) q^{20} +(0.0778578 - 0.0151994i) q^{22} -3.19553 q^{23} +2.99355 q^{25} +(2.43915 - 0.476171i) q^{26} +(-0.752213 - 1.85315i) q^{28} -4.78374i q^{29} +6.33960i q^{31} +(-3.22587 + 4.64691i) q^{32} +(-1.96102 - 10.0452i) q^{34} +1.41649 q^{35} -5.24245 q^{37} +(-0.618692 - 3.16921i) q^{38} +(-2.19021 - 3.35478i) q^{40} +3.58882i q^{41} +3.12243i q^{43} +(-0.103949 + 0.0421939i) q^{44} +(4.43544 - 0.865886i) q^{46} +5.27725 q^{47} -1.00000 q^{49} +(-4.15509 + 0.811156i) q^{50} +(-3.25654 + 1.32186i) q^{52} +5.18039i q^{53} -0.0794553i q^{55} +(1.54622 + 2.36837i) q^{56} +(1.29624 + 6.63988i) q^{58} -3.27326 q^{59} +8.82741 q^{61} +(-1.71783 - 8.79944i) q^{62} +(3.21838 - 7.32407i) q^{64} -2.48920i q^{65} +15.8030i q^{67} +(5.44384 + 13.4115i) q^{68} +(-1.96611 + 0.383823i) q^{70} -14.2854 q^{71} -5.03219 q^{73} +(7.27658 - 1.42053i) q^{74} +(1.71750 + 4.23125i) q^{76} +0.0560930i q^{77} +12.1925i q^{79} +(3.94908 + 4.06300i) q^{80} +(-0.972455 - 4.98133i) q^{82} -1.28060 q^{83} -10.2513 q^{85} +(-0.846076 - 4.33396i) q^{86} +(0.132849 - 0.0867324i) q^{88} +6.02678i q^{89} +1.75730i q^{91} +(-5.92181 + 2.40372i) q^{92} +(-7.32489 + 1.42996i) q^{94} -3.23423 q^{95} -16.4261 q^{97} +(1.38801 - 0.270968i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4}+O(q^{10}) \) 24 * q + 4 * q^4	\( 24 q + 4 q^{4} + 20 q^{10} + 20 q^{16} - 8 q^{22} - 24 q^{25} - 8 q^{28} - 20 q^{34} + 16 q^{37} - 32 q^{40} + 36 q^{46} - 24 q^{49} + 16 q^{52} - 52 q^{58} + 16 q^{61} + 4 q^{64} + 12 q^{70} + 4 q^{82} - 64 q^{85} - 16 q^{88} + 12 q^{94}+O(q^{100}) \) 24 * q + 4 * q^4 + 20 * q^10 + 20 * q^16 - 8 * q^22 - 24 * q^25 - 8 * q^28 - 20 * q^34 + 16 * q^37 - 32 * q^40 + 36 * q^46 - 24 * q^49 + 16 * q^52 - 52 * q^58 + 16 * q^61 + 4 * q^64 + 12 * q^70 + 4 * q^82 - 64 * q^85 - 16 * q^88 + 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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