LMFDB - Embedded newform 1620.2.e.b.971.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, 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("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.3
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37860 - 0.315389i) q^{2} +(1.80106 + 0.869588i) q^{4} +1.00000i q^{5} -2.19567i q^{7} +(-2.20868 - 1.76684i) q^{8} +O(q^{10})$	\(q+(-1.37860 - 0.315389i) q^{2} +(1.80106 + 0.869588i) q^{4} +1.00000i q^{5} -2.19567i q^{7} +(-2.20868 - 1.76684i) q^{8} +(0.315389 - 1.37860i) q^{10} -4.82416 q^{11} -0.728514 q^{13} +(-0.692488 + 3.02694i) q^{14} +(2.48763 + 3.13236i) q^{16} +6.46429i q^{17} -3.21426i q^{19} +(-0.869588 + 1.80106i) q^{20} +(6.65058 + 1.52149i) q^{22} +7.34542 q^{23} -1.00000 q^{25} +(1.00433 + 0.229765i) q^{26} +(1.90932 - 3.95453i) q^{28} -0.275365i q^{29} +0.919454i q^{31} +(-2.44154 - 5.10283i) q^{32} +(2.03876 - 8.91165i) q^{34} +2.19567 q^{35} +8.84637 q^{37} +(-1.01374 + 4.43117i) q^{38} +(1.76684 - 2.20868i) q^{40} -10.0013i q^{41} -1.68465i q^{43} +(-8.68861 - 4.19503i) q^{44} +(-10.1264 - 2.31666i) q^{46} +6.79274 q^{47} +2.17905 q^{49} +(1.37860 + 0.315389i) q^{50} +(-1.31210 - 0.633507i) q^{52} +0.913620i q^{53} -4.82416i q^{55} +(-3.87940 + 4.84952i) q^{56} +(-0.0868468 + 0.379617i) q^{58} -10.2971 q^{59} +8.55918 q^{61} +(0.289985 - 1.26756i) q^{62} +(1.75652 + 7.80478i) q^{64} -0.728514i q^{65} -1.72497i q^{67} +(-5.62126 + 11.6426i) q^{68} +(-3.02694 - 0.692488i) q^{70} +4.71637 q^{71} +8.12623 q^{73} +(-12.1956 - 2.79005i) q^{74} +(2.79508 - 5.78908i) q^{76} +10.5923i q^{77} -2.12374i q^{79} +(-3.13236 + 2.48763i) q^{80} +(-3.15431 + 13.7878i) q^{82} +7.09458 q^{83} -6.46429 q^{85} +(-0.531318 + 2.32245i) q^{86} +(10.6550 + 8.52355i) q^{88} +1.54875i q^{89} +1.59957i q^{91} +(13.2296 + 6.38749i) q^{92} +(-9.36445 - 2.14235i) q^{94} +3.21426 q^{95} +6.15669 q^{97} +(-3.00404 - 0.687248i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.37860	−	0.315389i	−0.974815	−	0.223013i
$2$	−1.37860	−	0.315389i	−0.974815	−	0.223013i
$3$		0			0
$3$		0			0
$4$	1.80106	+	0.869588i	0.900530	+	0.434794i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$		−	2.19567i		−	0.829884i	−0.909848	−	0.414942i	$-0.863802\pi$
$7$		−	2.19567i		−	0.829884i	0.909848	−	0.414942i	$-0.136198\pi$
$8$	−2.20868	−	1.76684i	−0.780886	−	0.624674i
$9$		0			0
$10$	0.315389	−	1.37860i	0.0997346	−	0.435951i
$11$	−4.82416			−1.45454			−0.727270	−	0.686351i	$-0.759211\pi$
$11$	−4.82416			−1.45454			−0.727270	+	0.686351i	$0.759211\pi$
$12$		0			0
$13$	−0.728514			−0.202053			−0.101027	−	0.994884i	$-0.532213\pi$
$13$	−0.728514			−0.202053			−0.101027	+	0.994884i	$0.532213\pi$
$14$	−0.692488	+	3.02694i	−0.185075	+	0.808983i
$15$		0			0
$16$	2.48763	+	3.13236i	0.621909	+	0.783090i
$17$			6.46429i			1.56782i	0.620875	+	0.783910i	$0.286778\pi$
$17$			6.46429i			1.56782i	−0.620875	+	0.783910i	$0.713222\pi$
$18$		0			0
$19$		−	3.21426i		−	0.737403i	−0.929548	−	0.368701i	$-0.879803\pi$
$19$		−	3.21426i		−	0.737403i	0.929548	−	0.368701i	$-0.120197\pi$
$20$	−0.869588	+	1.80106i	−0.194446	+	0.402729i
$21$		0			0
$22$	6.65058	+	1.52149i	1.41791	+	0.324382i
$23$	7.34542			1.53163			0.765813	−	0.643063i	$-0.222337\pi$
$23$	7.34542			1.53163			0.765813	+	0.643063i	$0.222337\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.00433	+	0.229765i	0.196965	+	0.0450606i
$27$		0			0
$28$	1.90932	−	3.95453i	0.360828	−	0.747335i
$29$		−	0.275365i		−	0.0511339i	−0.999673	−	0.0255670i	$-0.991861\pi$
$29$		−	0.275365i		−	0.0511339i	0.999673	−	0.0255670i	$-0.00813910\pi$
$30$		0			0
$31$			0.919454i			0.165139i	0.996585	+	0.0825694i	$0.0263126\pi$
$31$			0.919454i			0.165139i	−0.996585	+	0.0825694i	$0.973687\pi$
$32$	−2.44154	−	5.10283i	−0.431607	−	0.902062i
$33$		0			0
$34$	2.03876	−	8.91165i	0.349645	−	1.52833i
$35$	2.19567			0.371135
$36$		0			0
$37$	8.84637			1.45433			0.727167	−	0.686460i	$-0.240836\pi$
$37$	8.84637			1.45433			0.727167	+	0.686460i	$0.240836\pi$
$38$	−1.01374	+	4.43117i	−0.164451	+	0.718831i
$39$		0			0
$40$	1.76684	−	2.20868i	0.279363	−	0.349223i
$41$		−	10.0013i		−	1.56195i	−0.624564	−	0.780973i	$-0.714723\pi$
$41$		−	10.0013i		−	1.56195i	0.624564	−	0.780973i	$-0.285277\pi$
$42$		0			0
$43$		−	1.68465i		−	0.256906i	−0.991716	−	0.128453i	$-0.958999\pi$
$43$		−	1.68465i		−	0.256906i	0.991716	−	0.128453i	$-0.0410012\pi$
$44$	−8.68861	−	4.19503i	−1.30986	−	0.632425i
$45$		0			0
$46$	−10.1264	−	2.31666i	−1.49305	−	0.341573i
$47$	6.79274			0.990823			0.495411	−	0.868658i	$-0.335017\pi$
$47$	6.79274			0.990823			0.495411	+	0.868658i	$0.335017\pi$
$48$		0			0
$49$	2.17905			0.311293
$50$	1.37860	+	0.315389i	0.194963	+	0.0446027i
$51$		0			0
$52$	−1.31210	−	0.633507i	−0.181955	−	0.0878516i
$53$			0.913620i			0.125495i	0.998029	+	0.0627477i	$0.0199863\pi$
$53$			0.913620i			0.125495i	−0.998029	+	0.0627477i	$0.980014\pi$
$54$		0			0
$55$		−	4.82416i		−	0.650490i
$56$	−3.87940	+	4.84952i	−0.518407	+	0.648044i
$57$		0			0
$58$	−0.0868468	+	0.379617i	−0.0114035	+	0.0498461i
$59$	−10.2971			−1.34057			−0.670285	−	0.742104i	$-0.733828\pi$
$59$	−10.2971			−1.34057			−0.670285	+	0.742104i	$0.733828\pi$
$60$		0			0
$61$	8.55918			1.09589			0.547945	−	0.836514i	$-0.315410\pi$
$61$	8.55918			1.09589			0.547945	+	0.836514i	$0.315410\pi$
$62$	0.289985	−	1.26756i	0.0368282	−	0.160980i
$63$		0			0
$64$	1.75652	+	7.80478i	0.219565	+	0.975598i
$65$		−	0.728514i		−	0.0903610i
$66$		0			0
$67$		−	1.72497i		−	0.210739i	−0.994433	−	0.105370i	$-0.966397\pi$
$67$		−	1.72497i		−	0.210739i	0.994433	−	0.105370i	$-0.0336025\pi$
$68$	−5.62126	+	11.6426i	−0.681678	+	1.41187i
$69$		0			0
$70$	−3.02694	−	0.692488i	−0.361788	−	0.0827681i
$71$	4.71637			0.559731			0.279865	−	0.960039i	$-0.409710\pi$
$71$	4.71637			0.559731			0.279865	+	0.960039i	$0.409710\pi$
$72$		0			0
$73$	8.12623			0.951104			0.475552	−	0.879688i	$-0.342248\pi$
$73$	8.12623			0.951104			0.475552	+	0.879688i	$0.342248\pi$
$74$	−12.1956	−	2.79005i	−1.41771	−	0.324336i
$75$		0			0
$76$	2.79508	−	5.78908i	0.320618	−	0.664053i
$77$			10.5923i			1.20710i
$78$		0			0
$79$		−	2.12374i		−	0.238939i	−0.992838	−	0.119470i	$-0.961881\pi$
$79$		−	2.12374i		−	0.238939i	0.992838	−	0.119470i	$-0.0381194\pi$
$80$	−3.13236	+	2.48763i	−0.350208	+	0.278126i
$81$		0			0
$82$	−3.15431	+	13.7878i	−0.348335	+	1.52261i
$83$	7.09458			0.778731			0.389365	−	0.921083i	$-0.372694\pi$
$83$	7.09458			0.778731			0.389365	+	0.921083i	$0.372694\pi$
$84$		0			0
$85$	−6.46429			−0.701150
$86$	−0.531318	+	2.32245i	−0.0572935	+	0.250436i
$87$		0			0
$88$	10.6550	+	8.52355i	1.13583	+	0.908613i
$89$			1.54875i			0.164167i	0.996625	+	0.0820837i	$0.0261575\pi$
$89$			1.54875i			0.164167i	−0.996625	+	0.0820837i	$0.973843\pi$
$90$		0			0
$91$			1.59957i			0.167681i
$92$	13.2296	+	6.38749i	1.37928	+	0.665942i
$93$		0			0
$94$	−9.36445	−	2.14235i	−0.965869	−	0.220967i
$95$	3.21426			0.329776
$96$		0			0
$97$	6.15669			0.625117			0.312559	−	0.949898i	$-0.398814\pi$
$97$	6.15669			0.625117			0.312559	+	0.949898i	$0.398814\pi$
$98$	−3.00404	−	0.687248i	−0.303453	−	0.0694226i
$99$		0			0
$100$	−1.80106	−	0.869588i	−0.180106	−	0.0869588i
$101$		−	7.29104i		−	0.725486i	−0.931889	−	0.362743i	$-0.881840\pi$
$101$		−	7.29104i		−	0.725486i	0.931889	−	0.362743i	$-0.118160\pi$
$102$		0			0
$103$			4.30488i			0.424173i	0.977251	+	0.212086i	$0.0680258\pi$
$103$			4.30488i			0.424173i	−0.977251	+	0.212086i	$0.931974\pi$
$104$	1.60905	+	1.28717i	0.157781	+	0.126217i
$105$		0			0
$106$	0.288145	−	1.25951i	0.0279871	−	0.122335i
$107$	7.99364			0.772774			0.386387	−	0.922337i	$-0.373723\pi$
$107$	7.99364			0.772774			0.386387	+	0.922337i	$0.373723\pi$
$108$		0			0
$109$	−6.59306			−0.631501			−0.315750	−	0.948842i	$-0.602256\pi$
$109$	−6.59306			−0.631501			−0.315750	+	0.948842i	$0.602256\pi$
$110$	−1.52149	+	6.65058i	−0.145068	+	0.634108i
$111$		0			0
$112$	6.87761	−	5.46201i	0.649873	−	0.516112i
$113$			0.175174i			0.0164790i	0.999966	+	0.00823950i	$0.00262274\pi$
$113$			0.175174i			0.0164790i	−0.999966	+	0.00823950i	$0.997377\pi$
$114$		0			0
$115$			7.34542i			0.684964i
$116$	0.239454	−	0.495948i	0.0222327	−	0.0460476i
$117$		0			0
$118$	14.1956	+	3.24759i	1.30681	+	0.298965i
$119$	14.1934			1.30111
$120$		0			0
$121$	12.2726			1.11569
$122$	−11.7997	−	2.69947i	−1.06829	−	0.244398i
$123$		0			0
$124$	−0.799546	+	1.65599i	−0.0718014	+	0.148713i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			2.08592i			0.185095i	0.995708	+	0.0925477i	$0.0295011\pi$
$127$			2.08592i			0.185095i	−0.995708	+	0.0925477i	$0.970499\pi$
$128$	0.0400062	−	11.3136i	0.00353608	−	0.999994i
$129$		0			0
$130$	−0.229765	+	1.00433i	−0.0201517	+	0.0880853i
$131$	11.5118			1.00579			0.502894	−	0.864348i	$-0.332269\pi$
$131$	11.5118			1.00579			0.502894	+	0.864348i	$0.332269\pi$
$132$		0			0
$133$	−7.05745			−0.611958
$134$	−0.544037	+	2.37804i	−0.0469976	+	0.205432i
$135$		0			0
$136$	11.4214	−	14.2775i	0.979376	−	1.22429i
$137$		−	22.1420i		−	1.89172i	−0.324580	−	0.945858i	$-0.605223\pi$
$137$		−	22.1420i		−	1.89172i	0.324580	−	0.945858i	$-0.394777\pi$
$138$		0			0
$139$		−	17.6514i		−	1.49717i	−0.663037	−	0.748586i	$-0.730733\pi$
$139$		−	17.6514i		−	1.49717i	0.663037	−	0.748586i	$-0.269267\pi$
$140$	3.95453	+	1.90932i	0.334218	+	0.161367i
$141$		0			0
$142$	−6.50198	−	1.48749i	−0.545634	−	0.124827i
$143$	3.51447			0.293895
$144$		0			0
$145$	0.275365			0.0228678
$146$	−11.2028	−	2.56292i	−0.927151	−	0.212109i
$147$		0			0
$148$	15.9329	+	7.69270i	1.30967	+	0.632336i
$149$		−	17.7974i		−	1.45802i	−0.684502	−	0.729011i	$-0.739980\pi$
$149$		−	17.7974i		−	1.45802i	0.684502	−	0.729011i	$-0.260020\pi$
$150$		0			0
$151$			20.0264i			1.62972i	0.579656	+	0.814861i	$0.303187\pi$
$151$			20.0264i			1.62972i	−0.579656	+	0.814861i	$0.696813\pi$
$152$	−5.67910	+	7.09927i	−0.460636	+	0.575827i
$153$		0			0
$154$	3.34068	−	14.6024i	0.269199	−	1.17670i
$155$	−0.919454			−0.0738523
$156$		0			0
$157$	−20.0965			−1.60388			−0.801938	−	0.597407i	$-0.796198\pi$
$157$	−20.0965			−1.60388			−0.801938	+	0.597407i	$0.796198\pi$
$158$	−0.669803	+	2.92778i	−0.0532867	+	0.232922i
$159$		0			0
$160$	5.10283	−	2.44154i	0.403414	−	0.193020i
$161$		−	16.1281i		−	1.27107i
$162$		0			0
$163$			17.2735i			1.35297i	0.736457	+	0.676484i	$0.236497\pi$
$163$			17.2735i			1.35297i	−0.736457	+	0.676484i	$0.763503\pi$
$164$	8.69704	−	18.0130i	0.679125	−	1.40658i
$165$		0			0
$166$	−9.78056	−	2.23755i	−0.759119	−	0.173667i
$167$	13.0271			1.00807			0.504034	−	0.863684i	$-0.331848\pi$
$167$	13.0271			1.00807			0.504034	+	0.863684i	$0.331848\pi$
$168$		0			0
$169$	−12.4693			−0.959174
$170$	8.91165	+	2.03876i	0.683492	+	0.156366i
$171$		0			0
$172$	1.46495	−	3.03415i	0.111701	−	0.231352i
$173$			18.9543i			1.44107i	0.693419	+	0.720534i	$0.256103\pi$
$173$			18.9543i			1.44107i	−0.693419	+	0.720534i	$0.743897\pi$
$174$		0			0
$175$			2.19567i			0.165977i
$176$	−12.0008	−	15.1110i	−0.904591	−	1.13904i
$177$		0			0
$178$	0.488459	−	2.13511i	0.0366115	−	0.160033i
$179$	11.2764			0.842841			0.421421	−	0.906865i	$-0.361532\pi$
$179$	11.2764			0.842841			0.421421	+	0.906865i	$0.361532\pi$
$180$		0			0
$181$	−0.836139			−0.0621498			−0.0310749	−	0.999517i	$-0.509893\pi$
$181$	−0.836139			−0.0621498			−0.0310749	+	0.999517i	$0.509893\pi$
$182$	0.504487	−	2.20517i	0.0373951	−	0.163458i
$183$		0			0
$184$	−16.2237	−	12.9782i	−1.19603	−	0.956767i
$185$			8.84637i			0.650398i
$186$		0			0
$187$		−	31.1848i		−	2.28046i
$188$	12.2341	+	5.90688i	0.892266	+	0.430804i
$189$		0			0
$190$	−4.43117	−	1.01374i	−0.321471	−	0.0735446i
$191$	0.208841			0.0151112			0.00755561	−	0.999971i	$-0.497595\pi$
$191$	0.208841			0.0151112			0.00755561	+	0.999971i	$0.497595\pi$
$192$		0			0
$193$	19.2602			1.38638			0.693190	−	0.720755i	$-0.256205\pi$
$193$	19.2602			1.38638			0.693190	+	0.720755i	$0.256205\pi$
$194$	−8.48760	−	1.94175i	−0.609374	−	0.139410i
$195$		0			0
$196$	3.92460	+	1.89488i	0.280329	+	0.135348i
$197$		−	26.2412i		−	1.86961i	−0.355162	−	0.934805i	$-0.615574\pi$
$197$		−	26.2412i		−	1.86961i	0.355162	−	0.934805i	$-0.384426\pi$
$198$		0			0
$199$		−	10.5046i		−	0.744652i	−0.928102	−	0.372326i	$-0.878560\pi$
$199$		−	10.5046i		−	0.744652i	0.928102	−	0.372326i	$-0.121440\pi$
$200$	2.20868	+	1.76684i	0.156177	+	0.124935i
$201$		0			0
$202$	−2.29951	+	10.0514i	−0.161793	+	0.707215i
$203$	−0.604608			−0.0424352
$204$		0			0
$205$	10.0013			0.698524
$206$	1.35771	−	5.93470i	0.0945962	−	0.413490i
$207$		0			0
$208$	−1.81228	−	2.28197i	−0.125659	−	0.158226i
$209$			15.5061i			1.07258i
$210$		0			0
$211$			6.94656i			0.478221i	0.970992	+	0.239110i	$0.0768558\pi$
$211$			6.94656i			0.478221i	−0.970992	+	0.239110i	$0.923144\pi$
$212$	−0.794472	+	1.64548i	−0.0545646	+	0.113012i
$213$		0			0
$214$	−11.0200	−	2.52110i	−0.753312	−	0.172339i
$215$	1.68465			0.114892
$216$		0			0
$217$	2.01881			0.137046
$218$	9.08917	+	2.07938i	0.615596	+	0.140833i
$219$		0			0
$220$	4.19503	−	8.68861i	0.282829	−	0.585786i
$221$		−	4.70932i		−	0.316783i
$222$		0			0
$223$			9.52810i			0.638049i	0.947747	+	0.319024i	$0.103355\pi$
$223$			9.52810i			0.638049i	−0.947747	+	0.319024i	$0.896645\pi$
$224$	−11.2041	+	5.36080i	−0.748606	+	0.358183i
$225$		0			0
$226$	0.0552479	−	0.241494i	0.00367504	−	0.0160640i
$227$	9.97048			0.661764			0.330882	−	0.943672i	$-0.392654\pi$
$227$	9.97048			0.661764			0.330882	+	0.943672i	$0.392654\pi$
$228$		0			0
$229$	23.8168			1.57386			0.786931	−	0.617041i	$-0.211669\pi$
$229$	23.8168			1.57386			0.786931	+	0.617041i	$0.211669\pi$
$230$	2.31666	−	10.1264i	0.152756	−	0.667714i
$231$		0			0
$232$	−0.486526	+	0.608192i	−0.0319420	+	0.0399297i
$233$			13.3809i			0.876613i	0.898825	+	0.438307i	$0.144422\pi$
$233$			13.3809i			0.876613i	−0.898825	+	0.438307i	$0.855578\pi$
$234$		0			0
$235$			6.79274i			0.443109i
$236$	−18.5457	−	8.95424i	−1.20722	−	0.582872i
$237$		0			0
$238$	−19.5670	−	4.47644i	−1.26834	−	0.290164i
$239$	21.9509			1.41988			0.709941	−	0.704261i	$-0.248721\pi$
$239$	21.9509			1.41988			0.709941	+	0.704261i	$0.248721\pi$
$240$		0			0
$241$	5.69338			0.366743			0.183372	−	0.983044i	$-0.441299\pi$
$241$	5.69338			0.366743			0.183372	+	0.983044i	$0.441299\pi$
$242$	−16.9189	−	3.87063i	−1.08759	−	0.248813i
$243$		0			0
$244$	15.4156	+	7.44295i	0.986882	+	0.476486i
$245$			2.17905i			0.139215i
$246$		0			0
$247$			2.34164i			0.148995i
$248$	1.62453	−	2.03078i	0.103158	−	0.128955i
$249$		0			0
$250$	−0.315389	+	1.37860i	−0.0199469	+	0.0871901i
$251$	1.53762			0.0970540			0.0485270	−	0.998822i	$-0.484547\pi$
$251$	1.53762			0.0970540			0.0485270	+	0.998822i	$0.484547\pi$
$252$		0			0
$253$	−35.4355			−2.22781
$254$	0.657875	−	2.87564i	0.0412788	−	0.180434i
$255$		0			0
$256$	−3.62334	+	15.5843i	−0.226459	+	0.974021i
$257$			17.7232i			1.10554i	0.833333	+	0.552772i	$0.186430\pi$
$257$			17.7232i			1.10554i	−0.833333	+	0.552772i	$0.813570\pi$
$258$		0			0
$259$		−	19.4237i		−	1.20693i
$260$	0.633507	−	1.31210i	0.0392884	−	0.0813728i
$261$		0			0
$262$	−15.8701	−	3.63068i	−0.980457	−	0.224304i
$263$	2.57174			0.158580			0.0792900	−	0.996852i	$-0.474735\pi$
$263$	2.57174			0.158580			0.0792900	+	0.996852i	$0.474735\pi$
$264$		0			0
$265$	−0.913620			−0.0561232
$266$	9.72938	+	2.22584i	0.596546	+	0.136475i
$267$		0			0
$268$	1.50002	−	3.10678i	0.0916281	−	0.189777i
$269$		−	10.1758i		−	0.620431i	−0.950666	−	0.310216i	$-0.899599\pi$
$269$		−	10.1758i		−	0.620431i	0.950666	−	0.310216i	$-0.100401\pi$
$270$		0			0
$271$			3.25876i			0.197956i	0.995090	+	0.0989778i	$0.0315573\pi$
$271$			3.25876i			0.197956i	−0.995090	+	0.0989778i	$0.968443\pi$
$272$	−20.2485	+	16.0808i	−1.22774	+	0.975041i
$273$		0			0
$274$	−6.98333	+	30.5249i	−0.421878	+	1.84407i
$275$	4.82416			0.290908
$276$		0			0
$277$	−3.51678			−0.211303			−0.105652	−	0.994403i	$-0.533693\pi$
$277$	−3.51678			−0.211303			−0.105652	+	0.994403i	$0.533693\pi$
$278$	−5.56705	+	24.3342i	−0.333890	+	1.45947i
$279$		0			0
$280$	−4.84952	−	3.87940i	−0.289814	−	0.231838i
$281$			18.5000i			1.10362i	0.833971	+	0.551809i	$0.186062\pi$
$281$			18.5000i			1.10362i	−0.833971	+	0.551809i	$0.813938\pi$
$282$		0			0
$283$			1.38833i			0.0825276i	0.999148	+	0.0412638i	$0.0131384\pi$
$283$			1.38833i			0.0825276i	−0.999148	+	0.0412638i	$0.986862\pi$
$284$	8.49447	+	4.10130i	0.504054	+	0.243367i
$285$		0			0
$286$	−4.84504	−	1.10842i	−0.286493	−	0.0655425i
$287$	−21.9596			−1.29623
$288$		0			0
$289$	−24.7870			−1.45806
$290$	−0.379617	−	0.0868468i	−0.0222919	−	0.00509982i
$291$		0			0
$292$	14.6358	+	7.06647i	0.856498	+	0.413534i
$293$			3.27282i			0.191200i	0.995420	+	0.0956001i	$0.0304770\pi$
$293$			3.27282i			0.191200i	−0.995420	+	0.0956001i	$0.969523\pi$
$294$		0			0
$295$		−	10.2971i		−	0.599521i
$296$	−19.5388	−	15.6302i	−1.13567	−	0.908485i
$297$		0			0
$298$	−5.61311	+	24.5355i	−0.325159	+	1.42130i
$299$	−5.35124			−0.309470
$300$		0			0
$301$	−3.69892			−0.213202
$302$	6.31609	−	27.6083i	0.363450	−	1.58868i
$303$		0			0
$304$	10.0682	−	7.99591i	0.577452	−	0.458597i
$305$			8.55918i			0.490097i
$306$		0			0
$307$		−	18.9762i		−	1.08303i	−0.840692	−	0.541514i	$-0.817851\pi$
$307$		−	18.9762i		−	1.08303i	0.840692	−	0.541514i	$-0.182149\pi$
$308$	−9.21089	+	19.0773i	−0.524839	+	1.08703i
$309$		0			0
$310$	1.26756	+	0.289985i	0.0719924	+	0.0164701i
$311$	−3.60251			−0.204280			−0.102140	−	0.994770i	$-0.532569\pi$
$311$	−3.60251			−0.204280			−0.102140	+	0.994770i	$0.532569\pi$
$312$		0			0
$313$	13.2853			0.750930			0.375465	−	0.926837i	$-0.377483\pi$
$313$	13.2853			0.750930			0.375465	+	0.926837i	$0.377483\pi$
$314$	27.7050	+	6.33821i	1.56348	+	0.357686i
$315$		0			0
$316$	1.84678	−	3.82498i	0.103889	−	0.215172i
$317$		−	13.3108i		−	0.747611i	−0.927507	−	0.373805i	$-0.878053\pi$
$317$		−	13.3108i		−	0.747611i	0.927507	−	0.373805i	$-0.121947\pi$
$318$		0			0
$319$			1.32840i			0.0743763i
$320$	−7.80478	+	1.75652i	−0.436301	+	0.0981924i
$321$		0			0
$322$	−5.08662	+	22.2341i	−0.283466	+	1.23906i
$323$	20.7779			1.15611
$324$		0			0
$325$	0.728514			0.0404107
$326$	5.44788	−	23.8132i	0.301730	−	1.31889i
$327$		0			0
$328$	−17.6708	+	22.0897i	−0.975707	+	1.21970i
$329$		−	14.9146i		−	0.822268i
$330$		0			0
$331$			22.5040i			1.23693i	0.785811	+	0.618466i	$0.212246\pi$
$331$			22.5040i			1.23693i	−0.785811	+	0.618466i	$0.787754\pi$
$332$	12.7778	+	6.16935i	0.701270	+	0.338587i
$333$		0			0
$334$	−17.9591	−	4.10860i	−0.982681	−	0.224813i
$335$	1.72497			0.0942454
$336$		0			0
$337$	−13.4968			−0.735220			−0.367610	−	0.929980i	$-0.619824\pi$
$337$	−13.4968			−0.735220			−0.367610	+	0.929980i	$0.619824\pi$
$338$	17.1901	+	3.93266i	0.935018	+	0.213909i
$339$		0			0
$340$	−11.6426	−	5.62126i	−0.631407	−	0.304856i
$341$		−	4.43560i		−	0.240201i
$342$		0			0
$343$		−	20.1541i		−	1.08822i
$344$	−2.97651	+	3.72084i	−0.160483	+	0.200614i
$345$		0			0
$346$	5.97797	−	26.1303i	0.321378	−	1.40478i
$347$	−14.7330			−0.790908			−0.395454	−	0.918486i	$-0.629413\pi$
$347$	−14.7330			−0.790908			−0.395454	+	0.918486i	$0.629413\pi$
$348$		0			0
$349$	−27.0104			−1.44583			−0.722917	−	0.690935i	$-0.757199\pi$
$349$	−27.0104			−1.44583			−0.722917	+	0.690935i	$0.757199\pi$
$350$	0.692488	−	3.02694i	0.0370150	−	0.161797i
$351$		0			0
$352$	11.7784	+	24.6169i	0.627789	+	1.31209i
$353$			9.19009i			0.489139i	0.969632	+	0.244570i	$0.0786466\pi$
$353$			9.19009i			0.489139i	−0.969632	+	0.244570i	$0.921353\pi$
$354$		0			0
$355$			4.71637i			0.250319i
$356$	−1.34678	+	2.78940i	−0.0713790	+	0.147838i
$357$		0			0
$358$	−15.5457	−	3.55646i	−0.821615	−	0.187965i
$359$	−16.1509			−0.852413			−0.426206	−	0.904626i	$-0.640150\pi$
$359$	−16.1509			−0.852413			−0.426206	+	0.904626i	$0.640150\pi$
$360$		0			0
$361$	8.66851			0.456238
$362$	1.15270	+	0.263709i	0.0605845	+	0.0138602i
$363$		0			0
$364$	−1.39097	+	2.88093i	−0.0729066	+	0.151002i
$365$			8.12623i			0.425347i
$366$		0			0
$367$			34.6147i			1.80687i	0.428725	+	0.903435i	$0.358963\pi$
$367$			34.6147i			1.80687i	−0.428725	+	0.903435i	$0.641037\pi$
$368$	18.2727	+	23.0085i	0.952532	+	1.19940i
$369$		0			0
$370$	2.79005	−	12.1956i	0.145048	−	0.634018i
$371$	2.00600			0.104147
$372$		0			0
$373$	−3.79523			−0.196510			−0.0982548	−	0.995161i	$-0.531326\pi$
$373$	−3.79523			−0.196510			−0.0982548	+	0.995161i	$0.531326\pi$
$374$	−9.83532	+	42.9912i	−0.508572	+	2.22302i
$375$		0			0
$376$	−15.0030	−	12.0017i	−0.773719	−	0.618941i
$377$			0.200607i			0.0103318i
$378$		0			0
$379$			15.6511i			0.803944i	0.915652	+	0.401972i	$0.131675\pi$
$379$			15.6511i			0.803944i	−0.915652	+	0.401972i	$0.868325\pi$
$380$	5.78908	+	2.79508i	0.296974	+	0.143385i
$381$		0			0
$382$	−0.287908	−	0.0658661i	−0.0147306	−	0.00337000i
$383$	−11.7722			−0.601530			−0.300765	−	0.953698i	$-0.597242\pi$
$383$	−11.7722			−0.601530			−0.300765	+	0.953698i	$0.597242\pi$
$384$		0			0
$385$	−10.5923			−0.539831
$386$	−26.5521	−	6.07445i	−1.35146	−	0.309181i
$387$		0			0
$388$	11.0886	+	5.35378i	0.562937	+	0.271797i
$389$		−	4.88563i		−	0.247711i	−0.992300	−	0.123856i	$-0.960474\pi$
$389$		−	4.88563i		−	0.247711i	0.992300	−	0.123856i	$-0.0395260\pi$
$390$		0			0
$391$			47.4829i			2.40131i
$392$	−4.81283	−	3.85005i	−0.243084	−	0.194457i
$393$		0			0
$394$	−8.27618	+	36.1761i	−0.416948	+	1.82252i
$395$	2.12374			0.106857
$396$		0			0
$397$	1.82795			0.0917420			0.0458710	−	0.998947i	$-0.485394\pi$
$397$	1.82795			0.0917420			0.0458710	+	0.998947i	$0.485394\pi$
$398$	−3.31303	+	14.4816i	−0.166067	+	0.725898i
$399$		0			0
$400$	−2.48763	−	3.13236i	−0.124382	−	0.156618i
$401$			11.6839i			0.583466i	0.956500	+	0.291733i	$0.0942319\pi$
$401$			11.6839i			0.583466i	−0.956500	+	0.291733i	$0.905768\pi$
$402$		0			0
$403$		−	0.669835i		−	0.0333669i
$404$	6.34020	−	13.1316i	0.315437	−	0.653322i
$405$		0			0
$406$	0.833511	+	0.190687i	0.0413665	+	0.00946362i
$407$	−42.6764			−2.11539
$408$		0			0
$409$	−24.4552			−1.20923			−0.604616	−	0.796517i	$-0.706673\pi$
$409$	−24.4552			−1.20923			−0.604616	+	0.796517i	$0.706673\pi$
$410$	−13.7878	−	3.15431i	−0.680932	−	0.155780i
$411$		0			0
$412$	−3.74347	+	7.75336i	−0.184428	+	0.381980i
$413$			22.6090i			1.11252i
$414$		0			0
$415$			7.09458i			0.348259i
$416$	1.77869	+	3.71748i	0.0872076	+	0.182265i
$417$		0			0
$418$	4.89046	−	21.3767i	0.239200	−	1.04557i
$419$	−14.7488			−0.720526			−0.360263	−	0.932851i	$-0.617313\pi$
$419$	−14.7488			−0.720526			−0.360263	+	0.932851i	$0.617313\pi$
$420$		0			0
$421$	−33.3676			−1.62624			−0.813119	−	0.582097i	$-0.802232\pi$
$421$	−33.3676			−1.62624			−0.813119	+	0.582097i	$0.802232\pi$
$422$	2.19086	−	9.57650i	0.106650	−	0.466177i
$423$		0			0
$424$	1.61422	−	2.01789i	0.0783937	−	0.0979975i
$425$		−	6.46429i		−	0.313564i
$426$		0			0
$427$		−	18.7931i		−	0.909461i
$428$	14.3970	+	6.95117i	0.695907	+	0.335998i
$429$		0			0
$430$	−2.32245	−	0.531318i	−0.111998	−	0.0256224i
$431$	−22.7945			−1.09797			−0.548987	−	0.835831i	$-0.684987\pi$
$431$	−22.7945			−1.09797			−0.548987	+	0.835831i	$0.684987\pi$
$432$		0			0
$433$	20.9817			1.00831			0.504157	−	0.863612i	$-0.331803\pi$
$433$	20.9817			1.00831			0.504157	+	0.863612i	$0.331803\pi$
$434$	−2.78313	−	0.636711i	−0.133595	−	0.0305631i
$435$		0			0
$436$	−11.8745	−	5.73324i	−0.568685	−	0.274573i
$437$		−	23.6101i		−	1.12943i
$438$		0			0
$439$		−	0.253179i		−	0.0120836i	−0.999982	−	0.00604178i	$-0.998077\pi$
$439$		−	0.253179i		−	0.0120836i	0.999982	−	0.00604178i	$-0.00192317\pi$
$440$	−8.52355	+	10.6550i	−0.406344	+	0.507958i
$441$		0			0
$442$	−1.48527	+	6.49226i	−0.0706469	+	0.308805i
$443$	16.7800			0.797240			0.398620	−	0.917116i	$-0.369489\pi$
$443$	16.7800			0.797240			0.398620	+	0.917116i	$0.369489\pi$
$444$		0			0
$445$	−1.54875			−0.0734179
$446$	3.00505	−	13.1354i	0.142293	−	0.621980i
$447$		0			0
$448$	17.1367	−	3.85673i	0.809633	−	0.182213i
$449$		−	3.01918i		−	0.142484i	−0.997459	−	0.0712419i	$-0.977304\pi$
$449$		−	3.01918i		−	0.142484i	0.997459	−	0.0712419i	$-0.0226962\pi$
$450$		0			0
$451$			48.2481i			2.27191i
$452$	−0.152329	+	0.315499i	−0.00716496	+	0.0148398i
$453$		0			0
$454$	−13.7453	−	3.14457i	−0.645097	−	0.147582i
$455$	−1.59957			−0.0749891
$456$		0			0
$457$	1.37539			0.0643382			0.0321691	−	0.999482i	$-0.489758\pi$
$457$	1.37539			0.0643382			0.0321691	+	0.999482i	$0.489758\pi$
$458$	−32.8338	−	7.51156i	−1.53422	−	0.350992i
$459$		0			0
$460$	−6.38749	+	13.2296i	−0.297818	+	0.616831i
$461$		−	32.0443i		−	1.49245i	−0.665694	−	0.746225i	$-0.731864\pi$
$461$		−	32.0443i		−	1.49245i	0.665694	−	0.746225i	$-0.268136\pi$
$462$		0			0
$463$		−	33.3711i		−	1.55089i	−0.631417	−	0.775444i	$-0.717526\pi$
$463$		−	33.3711i		−	1.55089i	0.631417	−	0.775444i	$-0.282474\pi$
$464$	0.862541	−	0.685006i	0.0400424	−	0.0318006i
$465$		0			0
$466$	4.22019	−	18.4469i	0.195497	−	0.854536i
$467$	13.1201			0.607126			0.303563	−	0.952811i	$-0.401824\pi$
$467$	13.1201			0.607126			0.303563	+	0.952811i	$0.401824\pi$
$468$		0			0
$469$	−3.78747			−0.174889
$470$	2.14235	−	9.36445i	0.0988193	−	0.431950i
$471$		0			0
$472$	22.7430	+	18.1934i	1.04683	+	0.837419i
$473$			8.12701i			0.373680i
$474$		0			0
$475$			3.21426i			0.147481i
$476$	25.5632	+	12.3424i	1.17169	+	0.565714i
$477$		0			0
$478$	−30.2614	−	6.92305i	−1.38412	−	0.316653i
$479$	−7.56315			−0.345569			−0.172785	−	0.984960i	$-0.555276\pi$
$479$	−7.56315			−0.345569			−0.172785	+	0.984960i	$0.555276\pi$
$480$		0			0
$481$	−6.44471			−0.293853
$482$	−7.84888	−	1.79563i	−0.357507	−	0.0817886i
$483$		0			0
$484$	22.1036	+	10.6721i	1.00471	+	0.485094i
$485$			6.15669i			0.279561i
$486$		0			0
$487$		−	31.7053i		−	1.43671i	−0.695679	−	0.718353i	$-0.744896\pi$
$487$		−	31.7053i		−	1.43671i	0.695679	−	0.718353i	$-0.255104\pi$
$488$	−18.9045	−	15.1227i	−0.855765	−	0.684574i
$489$		0			0
$490$	0.687248	−	3.00404i	0.0310467	−	0.135708i
$491$	−37.4562			−1.69037			−0.845187	−	0.534470i	$-0.820511\pi$
$491$	−37.4562			−1.69037			−0.845187	+	0.534470i	$0.820511\pi$
$492$		0			0
$493$	1.78004			0.0801687
$494$	0.738525	−	3.22817i	0.0332278	−	0.145242i
$495$		0			0
$496$	−2.88006	+	2.28727i	−0.129319	+	0.102701i
$497$		−	10.3556i		−	0.464511i
$498$		0			0
$499$		−	4.02507i		−	0.180187i	−0.995933	−	0.0900935i	$-0.971283\pi$
$499$		−	4.02507i		−	0.180187i	0.995933	−	0.0900935i	$-0.0287166\pi$
$500$	0.869588	−	1.80106i	0.0388891	−	0.0805459i
$501$		0			0
$502$	−2.11976	−	0.484949i	−0.0946097	−	0.0216443i
$503$	−7.54669			−0.336490			−0.168245	−	0.985745i	$-0.553810\pi$
$503$	−7.54669			−0.336490			−0.168245	+	0.985745i	$0.553810\pi$
$504$		0			0
$505$	7.29104			0.324447
$506$	48.8513	+	11.1760i	2.17171	+	0.496832i
$507$		0			0
$508$	−1.81389	+	3.75687i	−0.0804783	+	0.166684i
$509$			16.1548i			0.716047i	0.933713	+	0.358023i	$0.116549\pi$
$509$			16.1548i			0.716047i	−0.933713	+	0.358023i	$0.883451\pi$
$510$		0			0
$511$		−	17.8425i		−	0.789305i
$512$	9.91025	−	20.3418i	0.437975	−	0.898987i
$513$		0			0
$514$	5.58970	−	24.4332i	0.246551	−	1.07770i
$515$	−4.30488			−0.189696
$516$		0			0
$517$	−32.7693			−1.44119
$518$	−6.12601	+	26.7774i	−0.269161	+	1.17653i
$519$		0			0
$520$	−1.28717	+	1.60905i	−0.0564462	+	0.0705616i
$521$			18.6893i			0.818794i	0.912356	+	0.409397i	$0.134261\pi$
$521$			18.6893i			0.818794i	−0.912356	+	0.409397i	$0.865739\pi$
$522$		0			0
$523$		−	2.11497i		−	0.0924812i	−0.998930	−	0.0462406i	$-0.985276\pi$
$523$		−	2.11497i		−	0.0924812i	0.998930	−	0.0462406i	$-0.0147241\pi$
$524$	20.7334	+	10.0105i	0.905742	+	0.437310i
$525$		0			0
$526$	−3.54539	−	0.811096i	−0.154586	−	0.0353655i
$527$	−5.94362			−0.258908
$528$		0			0
$529$	30.9553			1.34588
$530$	1.25951	+	0.288145i	0.0547098	+	0.0125162i
$531$		0			0
$532$	−12.7109	−	6.13707i	−0.551087	−	0.266076i
$533$			7.28611i			0.315597i
$534$		0			0
$535$			7.99364i			0.345595i
$536$	−3.04776	+	3.80991i	−0.131643	+	0.164563i
$537$		0			0
$538$	−3.20934	+	14.0284i	−0.138364	+	0.604806i
$539$	−10.5121			−0.452789
$540$		0			0
$541$	−8.06577			−0.346775			−0.173387	−	0.984854i	$-0.555471\pi$
$541$	−8.06577			−0.346775			−0.173387	+	0.984854i	$0.555471\pi$
$542$	1.02778	−	4.49252i	0.0441467	−	0.192970i
$543$		0			0
$544$	32.9862	−	15.7828i	1.41427	−	0.676681i
$545$		−	6.59306i		−	0.282416i
$546$		0			0
$547$		−	12.8782i		−	0.550633i	−0.961354	−	0.275316i	$-0.911217\pi$
$547$		−	12.8782i		−	0.550633i	0.961354	−	0.275316i	$-0.0887826\pi$
$548$	19.2544	−	39.8790i	0.822507	−	1.70355i
$549$		0			0
$550$	−6.65058	−	1.52149i	−0.283582	−	0.0648764i
$551$	−0.885094			−0.0377063
$552$		0			0
$553$	−4.66302			−0.198292
$554$	4.84823	+	1.10915i	0.205982	+	0.0471234i
$555$		0			0
$556$	15.3494	−	31.7912i	0.650961	−	1.34825i
$557$			12.3332i			0.522577i	0.965261	+	0.261288i	$0.0841473\pi$
$557$			12.3332i			0.522577i	−0.965261	+	0.261288i	$0.915853\pi$
$558$		0			0
$559$			1.22729i			0.0519088i
$560$	5.46201	+	6.87761i	0.230812	+	0.290632i
$561$		0			0
$562$	5.83469	−	25.5040i	0.246121	−	1.07582i
$563$	7.80567			0.328970			0.164485	−	0.986380i	$-0.447404\pi$
$563$	7.80567			0.328970			0.164485	+	0.986380i	$0.447404\pi$
$564$		0			0
$565$	−0.175174			−0.00736963
$566$	0.437863	−	1.91395i	0.0184048	−	0.0804492i
$567$		0			0
$568$	−10.4170	−	8.33310i	−0.437086	−	0.349649i
$569$			25.1262i			1.05334i	0.850069	+	0.526672i	$0.176560\pi$
$569$			25.1262i			1.05334i	−0.850069	+	0.526672i	$0.823440\pi$
$570$		0			0
$571$		−	30.9290i		−	1.29434i	−0.762347	−	0.647168i	$-0.775953\pi$
$571$		−	30.9290i		−	1.29434i	0.762347	−	0.647168i	$-0.224047\pi$
$572$	6.32977	+	3.05614i	0.264661	+	0.127784i
$573$		0			0
$574$	30.2734	+	6.92581i	1.26359	+	0.289078i
$575$	−7.34542			−0.306325
$576$		0			0
$577$	0.766500			0.0319098			0.0159549	−	0.999873i	$-0.494921\pi$
$577$	0.766500			0.0319098			0.0159549	+	0.999873i	$0.494921\pi$
$578$	34.1713	+	7.81753i	1.42134	+	0.325166i
$579$		0			0
$580$	0.495948	+	0.239454i	0.0205931	+	0.00994277i
$581$		−	15.5773i		−	0.646256i
$582$		0			0
$583$		−	4.40745i		−	0.182538i
$584$	−17.9482	−	14.3578i	−0.742703	−	0.594130i
$585$		0			0
$586$	1.03221	−	4.51190i	0.0426402	−	0.186385i
$587$	−20.8042			−0.858681			−0.429340	−	0.903143i	$-0.641254\pi$
$587$	−20.8042			−0.858681			−0.429340	+	0.903143i	$0.641254\pi$
$588$		0			0
$589$	2.95537			0.121774
$590$	−3.24759	+	14.1956i	−0.133701	+	0.584423i
$591$		0			0
$592$	22.0065	+	27.7100i	0.904464	+	1.13887i
$593$		−	20.4111i		−	0.838184i	−0.907944	−	0.419092i	$-0.862348\pi$
$593$		−	20.4111i		−	0.838184i	0.907944	−	0.419092i	$-0.137652\pi$
$594$		0			0
$595$			14.1934i			0.581873i
$596$	15.4764	−	32.0542i	0.633939	−	1.31299i
$597$		0			0
$598$	7.37721	+	1.68772i	0.301677	+	0.0690160i
$599$	25.8845			1.05761			0.528806	−	0.848742i	$-0.322640\pi$
$599$	25.8845			1.05761			0.528806	+	0.848742i	$0.322640\pi$
$600$		0			0
$601$	26.7414			1.09081			0.545403	−	0.838174i	$-0.316377\pi$
$601$	26.7414			1.09081			0.545403	+	0.838174i	$0.316377\pi$
$602$	5.09932	+	1.16660i	0.207833	+	0.0475470i
$603$		0			0
$604$	−17.4147	+	36.0687i	−0.708593	+	1.46761i
$605$			12.2726i			0.498951i
$606$		0			0
$607$		−	19.9630i		−	0.810272i	−0.914256	−	0.405136i	$-0.867224\pi$
$607$		−	19.9630i		−	0.810272i	0.914256	−	0.405136i	$-0.132776\pi$
$608$	−16.4018	+	7.84774i	−0.665183	+	0.318268i
$609$		0			0
$610$	2.69947	−	11.7997i	0.109298	−	0.477754i
$611$	−4.94860			−0.200199
$612$		0			0
$613$	32.2198			1.30135			0.650673	−	0.759358i	$-0.274487\pi$
$613$	32.2198			1.30135			0.650673	+	0.759358i	$0.274487\pi$
$614$	−5.98487	+	26.1605i	−0.241530	+	1.05575i
$615$		0			0
$616$	18.7149	−	23.3949i	0.754043	−	0.942606i
$617$		−	12.8570i		−	0.517604i	−0.965930	−	0.258802i	$-0.916672\pi$
$617$		−	12.8570i		−	0.517604i	0.965930	−	0.258802i	$-0.0833277\pi$
$618$		0			0
$619$		−	2.93813i		−	0.118093i	−0.998255	−	0.0590466i	$-0.981194\pi$
$619$		−	2.93813i		−	0.118093i	0.998255	−	0.0590466i	$-0.0188061\pi$
$620$	−1.65599	−	0.799546i	−0.0665063	−	0.0321105i
$621$		0			0
$622$	4.96641	+	1.13619i	0.199135	+	0.0455571i
$623$	3.40054			0.136240
$624$		0			0
$625$	1.00000			0.0400000
$626$	−18.3151	−	4.19003i	−0.732018	−	0.167467i
$627$		0			0
$628$	−36.1950	−	17.4757i	−1.44434	−	0.697355i
$629$			57.1855i			2.28013i
$630$		0			0
$631$			11.5694i			0.460572i	0.973123	+	0.230286i	$0.0739661\pi$
$631$			11.5694i			0.460572i	−0.973123	+	0.230286i	$0.926034\pi$
$632$	−3.75232	+	4.69066i	−0.149259	+	0.186584i
$633$		0			0
$634$	−4.19808	+	18.3503i	−0.166727	+	0.728783i
$635$	−2.08592			−0.0827772
$636$		0			0
$637$	−1.58747			−0.0628979
$638$	0.418963	−	1.83133i	0.0165869	−	0.0725032i
$639$		0			0
$640$	11.3136	+	0.0400062i	0.447211	+	0.00158138i
$641$		−	31.3366i		−	1.23772i	−0.785500	−	0.618861i	$-0.787594\pi$
$641$		−	31.3366i		−	1.23772i	0.785500	−	0.618861i	$-0.212406\pi$
$642$		0			0
$643$			47.4872i			1.87271i	0.351050	+	0.936357i	$0.385825\pi$
$643$			47.4872i			1.87271i	−0.351050	+	0.936357i	$0.614175\pi$
$644$	14.0248	−	29.0477i	0.552654	−	1.14464i
$645$		0			0
$646$	−28.6444	−	6.55312i	−1.12700	−	0.257829i
$647$	−16.8575			−0.662738			−0.331369	−	0.943501i	$-0.607510\pi$
$647$	−16.8575			−0.662738			−0.331369	+	0.943501i	$0.607510\pi$
$648$		0			0
$649$	49.6750			1.94991
$650$	−1.00433	−	0.229765i	−0.0393930	−	0.00901212i
$651$		0			0
$652$	−15.0209	+	31.1107i	−0.588262	+	1.21839i
$653$			20.1924i			0.790189i	0.918641	+	0.395094i	$0.129288\pi$
$653$			20.1924i			0.790189i	−0.918641	+	0.395094i	$0.870712\pi$
$654$		0			0
$655$			11.5118i			0.449802i
$656$	31.3278	−	24.8797i	1.22314	−	0.971388i
$657$		0			0
$658$	−4.70389	+	20.5612i	−0.183377	+	0.801559i
$659$	−26.6309			−1.03739			−0.518696	−	0.854959i	$-0.673582\pi$
$659$	−26.6309			−1.03739			−0.518696	+	0.854959i	$0.673582\pi$
$660$		0			0
$661$	−13.9742			−0.543534			−0.271767	−	0.962363i	$-0.587608\pi$
$661$	−13.9742			−0.543534			−0.271767	+	0.962363i	$0.587608\pi$
$662$	7.09751	−	31.0240i	0.275853	−	1.20578i
$663$		0			0
$664$	−15.6696	−	12.5350i	−0.608100	−	0.486453i
$665$		−	7.05745i		−	0.273676i
$666$		0			0
$667$		−	2.02267i		−	0.0783181i
$668$	23.4626	+	11.3282i	0.907796	+	0.438302i
$669$		0			0
$670$	−2.37804	−	0.544037i	−0.0918719	−	0.0210180i
$671$	−41.2909			−1.59402
$672$		0			0
$673$	−4.27163			−0.164659			−0.0823297	−	0.996605i	$-0.526236\pi$
$673$	−4.27163			−0.164659			−0.0823297	+	0.996605i	$0.526236\pi$
$674$	18.6067	+	4.25675i	0.716704	+	0.163964i
$675$		0			0
$676$	−22.4579	−	10.8431i	−0.863765	−	0.417043i
$677$			13.2478i			0.509155i	0.967052	+	0.254577i	$0.0819363\pi$
$677$			13.2478i			0.509155i	−0.967052	+	0.254577i	$0.918064\pi$
$678$		0			0
$679$		−	13.5180i		−	0.518775i
$680$	14.2775	+	11.4214i	0.547518	+	0.437990i
$681$		0			0
$682$	−1.39894	+	6.11490i	−0.0535681	+	0.234152i
$683$	16.3799			0.626758			0.313379	−	0.949628i	$-0.398539\pi$
$683$	16.3799			0.626758			0.313379	+	0.949628i	$0.398539\pi$
$684$		0			0
$685$	22.1420			0.846001
$686$	−6.35638	+	27.7844i	−0.242688	+	1.06081i
$687$		0			0
$688$	5.27692	−	4.19079i	0.201181	−	0.159772i
$689$		−	0.665585i		−	0.0253568i
$690$		0			0
$691$			5.73918i			0.218329i	0.994024	+	0.109164i	$0.0348175\pi$
$691$			5.73918i			0.218329i	−0.994024	+	0.109164i	$0.965183\pi$
$692$	−16.4824	+	34.1378i	−0.626568	+	1.29773i
$693$		0			0
$694$	20.3108	+	4.64661i	0.770989	+	0.176383i
$695$	17.6514			0.669556
$696$		0			0
$697$	64.6515			2.44885
$698$	37.2364	+	8.51877i	1.40942	+	0.322440i
$699$		0			0
$700$	−1.90932	+	3.95453i	−0.0721656	+	0.149467i
$701$		−	4.94578i		−	0.186800i	−0.995629	−	0.0933998i	$-0.970227\pi$
$701$		−	4.94578i		−	0.186800i	0.995629	−	0.0933998i	$-0.0297735\pi$
$702$		0			0
$703$		−	28.4346i		−	1.07243i
$704$	−8.47374	−	37.6516i	−0.319366	−	1.41905i
$705$		0			0
$706$	2.89845	−	12.6694i	0.109085	−	0.476820i
$707$	−16.0087			−0.602069
$708$		0			0
$709$	20.5684			0.772464			0.386232	−	0.922402i	$-0.373776\pi$
$709$	20.5684			0.772464			0.386232	+	0.922402i	$0.373776\pi$
$710$	1.48749	−	6.50198i	0.0558245	−	0.244015i
$711$		0			0
$712$	2.73641	−	3.42070i	0.102551	−	0.128196i
$713$			6.75378i			0.252931i
$714$		0			0
$715$			3.51447i			0.131434i
$716$	20.3096	+	9.80586i	0.759004	+	0.366462i
$717$		0			0
$718$	22.2656	+	5.09382i	0.830945	+	0.190100i
$719$	18.0292			0.672378			0.336189	−	0.941795i	$-0.390862\pi$
$719$	18.0292			0.672378			0.336189	+	0.941795i	$0.390862\pi$
$720$		0			0
$721$	9.45209			0.352014
$722$	−11.9504	−	2.73395i	−0.444747	−	0.101747i
$723$		0			0
$724$	−1.50594	−	0.727096i	−0.0559677	−	0.0270223i
$725$			0.275365i			0.0102268i
$726$		0			0
$727$		−	37.5346i		−	1.39208i	−0.718003	−	0.696040i	$-0.754944\pi$
$727$		−	37.5346i		−	1.39208i	0.718003	−	0.696040i	$-0.245056\pi$
$728$	2.82620	−	3.53294i	0.104746	−	0.130940i
$729$		0			0
$730$	2.56292	−	11.2028i	0.0948580	−	0.414634i
$731$	10.8900			0.402783
$732$		0			0
$733$	1.46517			0.0541173			0.0270586	−	0.999634i	$-0.491386\pi$
$733$	1.46517			0.0541173			0.0270586	+	0.999634i	$0.491386\pi$
$734$	10.9171	−	47.7197i	0.402956	−	1.76136i
$735$		0			0
$736$	−17.9341	−	37.4825i	−0.661060	−	1.38162i
$737$			8.32156i			0.306529i
$738$		0			0
$739$		−	37.3913i		−	1.37546i	−0.725965	−	0.687732i	$-0.758607\pi$
$739$		−	37.3913i		−	1.37546i	0.725965	−	0.687732i	$-0.241393\pi$
$740$	−7.69270	+	15.9329i	−0.282789	+	0.585703i
$741$		0			0
$742$	−2.76547	−	0.632671i	−0.101524	−	0.0232261i
$743$	23.7432			0.871055			0.435527	−	0.900175i	$-0.356562\pi$
$743$	23.7432			0.871055			0.435527	+	0.900175i	$0.356562\pi$
$744$		0			0
$745$	17.7974			0.652048
$746$	5.23209	+	1.19697i	0.191561	+	0.0438243i
$747$		0			0
$748$	27.1179	−	56.1657i	0.991528	−	2.05362i
$749$		−	17.5514i		−	0.641313i
$750$		0			0
$751$			39.6991i			1.44864i	0.689464	+	0.724320i	$0.257846\pi$
$751$			39.6991i			1.44864i	−0.689464	+	0.724320i	$0.742154\pi$
$752$	16.8979	+	21.2773i	0.616201	+	0.775903i
$753$		0			0
$754$	0.0632691	−	0.276556i	0.00230413	−	0.0100716i
$755$	−20.0264			−0.728834
$756$		0			0
$757$	−36.1118			−1.31251			−0.656253	−	0.754541i	$-0.727860\pi$
$757$	−36.1118			−1.31251			−0.656253	+	0.754541i	$0.727860\pi$
$758$	4.93619	−	21.5766i	0.179290	−	0.783697i
$759$		0			0
$760$	−7.09927	−	5.67910i	−0.257518	−	0.206003i
$761$		−	15.6269i		−	0.566475i	−0.959050	−	0.283237i	$-0.908592\pi$
$761$		−	15.6269i		−	0.566475i	0.959050	−	0.283237i	$-0.0914084\pi$
$762$		0			0
$763$			14.4762i			0.524072i
$764$	0.376136	+	0.181606i	0.0136081	+	0.00657026i
$765$		0			0
$766$	16.2291	+	3.71281i	0.586380	+	0.134149i
$767$	7.50159			0.270867
$768$		0			0
$769$	12.6313			0.455497			0.227748	−	0.973720i	$-0.426864\pi$
$769$	12.6313			0.455497			0.227748	+	0.973720i	$0.426864\pi$
$770$	14.6024	+	3.34068i	0.526236	+	0.120390i
$771$		0			0
$772$	34.6888	+	16.7484i	1.24848	+	0.602790i
$773$			26.2292i			0.943400i	0.881759	+	0.471700i	$0.156359\pi$
$773$			26.2292i			0.943400i	−0.881759	+	0.471700i	$0.843641\pi$
$774$		0			0
$775$		−	0.919454i		−	0.0330278i
$776$	−13.5982	−	10.8779i	−0.488145	−	0.390495i
$777$		0			0
$778$	−1.54087	+	6.73531i	−0.0552429	+	0.241473i
$779$	−32.1469			−1.15178
$780$		0			0
$781$	−22.7526			−0.814151
$782$	14.9756	−	65.4598i	0.535525	−	2.34084i
$783$		0			0
$784$	5.42069	+	6.82557i	0.193596	+	0.243771i
$785$		−	20.0965i		−	0.717275i
$786$		0			0
$787$			3.65636i			0.130335i	0.997874	+	0.0651676i	$0.0207582\pi$
$787$			3.65636i			0.130335i	−0.997874	+	0.0651676i	$0.979242\pi$
$788$	22.8190	−	47.2620i	0.812895	−	1.68364i
$789$		0			0
$790$	−2.92778	−	0.669803i	−0.104166	−	0.0238305i
$791$	0.384624			0.0136756
$792$		0			0
$793$	−6.23548			−0.221428
$794$	−2.52000	−	0.576514i	−0.0894316	−	0.0204597i
$795$		0			0
$796$	9.13468	−	18.9194i	0.323770	−	0.670582i
$797$			7.05066i			0.249747i	0.992173	+	0.124874i	$0.0398525\pi$
$797$			7.05066i			0.249747i	−0.992173	+	0.124874i	$0.960147\pi$
$798$		0			0
$799$			43.9102i			1.55343i
$800$	2.44154	+	5.10283i	0.0863213	+	0.180412i
$801$		0			0
$802$	3.68497	−	16.1074i	0.130121	−	0.568772i
$803$	−39.2023			−1.38342
$804$		0			0
$805$	16.1281			0.568441
$806$	−0.211258	+	0.923433i	−0.00744126	+	0.0325265i
$807$		0			0
$808$	−12.8821	+	16.1036i	−0.453192	+	0.566522i
$809$		−	45.8745i		−	1.61286i	−0.591329	−	0.806430i	$-0.701397\pi$
$809$		−	45.8745i		−	1.61286i	0.591329	−	0.806430i	$-0.298603\pi$
$810$		0			0
$811$		−	0.247904i		−	0.00870507i	−0.999991	−	0.00435254i	$-0.998615\pi$
$811$		−	0.247904i		−	0.00870507i	0.999991	−	0.00435254i	$-0.00138546\pi$
$812$	−1.08894	−	0.525760i	−0.0382142	−	0.0184506i
$813$		0			0
$814$	58.8335	+	13.4596i	2.06211	+	0.471760i
$815$	−17.2735			−0.605066
$816$		0			0
$817$	−5.41490			−0.189443
$818$	33.7139	+	7.71289i	1.17878	+	0.269675i
$819$		0			0
$820$	18.0130	+	8.69704i	0.629042	+	0.303714i
$821$			16.8315i			0.587423i	0.955894	+	0.293711i	$0.0948904\pi$
$821$			16.8315i			0.587423i	−0.955894	+	0.293711i	$0.905110\pi$
$822$		0			0
$823$		−	17.9212i		−	0.624692i	−0.949968	−	0.312346i	$-0.898885\pi$
$823$		−	17.9212i		−	0.624692i	0.949968	−	0.312346i	$-0.101115\pi$
$824$	7.60606	−	9.50811i	0.264970	−	0.331231i
$825$		0			0
$826$	7.13063	−	31.1687i	0.248106	−	1.08450i
$827$	17.5414			0.609973			0.304986	−	0.952357i	$-0.401348\pi$
$827$	17.5414			0.609973			0.304986	+	0.952357i	$0.401348\pi$
$828$		0			0
$829$	−20.0056			−0.694822			−0.347411	−	0.937713i	$-0.612939\pi$
$829$	−20.0056			−0.694822			−0.347411	+	0.937713i	$0.612939\pi$
$830$	2.23755	−	9.78056i	0.0776664	−	0.339488i
$831$		0			0
$832$	−1.27965	−	5.68589i	−0.0443639	−	0.197123i
$833$			14.0860i			0.488052i
$834$		0			0
$835$			13.0271i			0.450822i
$836$	−13.4839	+	27.9275i	−0.466352	+	0.965892i
$837$		0			0
$838$	20.3327	+	4.65160i	0.702380	+	0.160687i
$839$	−20.2953			−0.700672			−0.350336	−	0.936624i	$-0.613933\pi$
$839$	−20.2953			−0.700672			−0.350336	+	0.936624i	$0.613933\pi$
$840$		0			0
$841$	28.9242			0.997385
$842$	46.0005	+	10.5238i	1.58528	+	0.362673i
$843$		0			0
$844$	−6.04064	+	12.5112i	−0.207927	+	0.430652i
$845$		−	12.4693i		−	0.428956i
$846$		0			0
$847$		−	26.9464i		−	0.925891i
$848$	−2.86179	+	2.27275i	−0.0982741	+	0.0780466i
$849$		0			0
$850$	−2.03876	+	8.91165i	−0.0699290	+	0.305667i
$851$	64.9804			2.22750
$852$		0			0
$853$	−36.7109			−1.25696			−0.628478	−	0.777827i	$-0.716322\pi$
$853$	−36.7109			−1.25696			−0.628478	+	0.777827i	$0.716322\pi$
$854$	−5.92713	+	25.9081i	−0.202822	+	0.886557i
$855$		0			0
$856$	−17.6554	−	14.1235i	−0.603448	−	0.482732i
$857$			56.4515i			1.92835i	0.265276	+	0.964173i	$0.414537\pi$
$857$			56.4515i			1.92835i	−0.265276	+	0.964173i	$0.585463\pi$
$858$		0			0
$859$			45.0442i			1.53689i	0.639917	+	0.768444i	$0.278969\pi$
$859$			45.0442i			1.53689i	−0.639917	+	0.768444i	$0.721031\pi$
$860$	3.03415	+	1.46495i	0.103464	+	0.0499543i
$861$		0			0
$862$	31.4245	+	7.18914i	1.07032	+	0.244863i
$863$	−56.4258			−1.92076			−0.960378	−	0.278700i	$-0.910097\pi$
$863$	−56.4258			−1.92076			−0.960378	+	0.278700i	$0.910097\pi$
$864$		0			0
$865$	−18.9543			−0.644466
$866$	−28.9252	−	6.61737i	−0.982920	−	0.224867i
$867$		0			0
$868$	3.63601	+	1.75554i	0.123414	+	0.0595868i
$869$			10.2453i			0.347547i
$870$		0			0
$871$			1.25667i			0.0425806i
$872$	14.5619	+	11.6489i	0.493130	+	0.394482i
$873$		0			0
$874$	−7.44636	+	32.5489i	−0.251877	+	1.10098i
$875$	−2.19567			−0.0742270
$876$		0			0
$877$	−21.1390			−0.713814			−0.356907	−	0.934140i	$-0.616169\pi$
$877$	−21.1390			−0.713814			−0.356907	+	0.934140i	$0.616169\pi$
$878$	−0.0798497	+	0.349032i	−0.00269480	+	0.0117792i
$879$		0			0
$880$	15.1110	−	12.0008i	0.509392	−	0.404546i
$881$		−	13.9427i		−	0.469742i	−0.972027	−	0.234871i	$-0.924533\pi$
$881$		−	13.9427i		−	0.469742i	0.972027	−	0.234871i	$-0.0754667\pi$
$882$		0			0
$883$			13.9169i			0.468340i	0.972196	+	0.234170i	$0.0752372\pi$
$883$			13.9169i			0.468340i	−0.972196	+	0.234170i	$0.924763\pi$
$884$	4.09517	−	8.48177i	0.137735	−	0.285273i
$885$		0			0
$886$	−23.1328	−	5.29221i	−0.777162	−	0.177795i
$887$	49.0199			1.64593			0.822963	−	0.568095i	$-0.192319\pi$
$887$	49.0199			1.64593			0.822963	+	0.568095i	$0.192319\pi$
$888$		0			0
$889$	4.57998			0.153608
$890$	2.13511	+	0.488459i	0.0715689	+	0.0163732i
$891$		0			0
$892$	−8.28551	+	17.1607i	−0.277420	+	0.574582i
$893$		−	21.8336i		−	0.730635i
$894$		0			0
$895$			11.2764i			0.376930i
$896$	−24.8410	−	0.0878402i	−0.829878	−	0.00293454i
$897$		0			0
$898$	−0.952214	+	4.16223i	−0.0317758	+	0.138895i
$899$	0.253185			0.00844420
$900$		0			0
$901$	−5.90590			−0.196754
$902$	15.2169	−	66.5147i	0.506667	−	2.21470i
$903$		0			0
$904$	0.309505	−	0.386903i	0.0102940	−	0.0128682i
$905$		−	0.836139i		−	0.0277942i
$906$		0			0
$907$		−	27.1024i		−	0.899922i	−0.893048	−	0.449961i	$-0.851438\pi$
$907$		−	27.1024i		−	0.899922i	0.893048	−	0.449961i	$-0.148562\pi$
$908$	17.9574	+	8.67020i	0.595938	+	0.287731i
$909$		0			0
$910$	2.20517	+	0.504487i	0.0731006	+	0.0167236i
$911$	10.4534			0.346338			0.173169	−	0.984892i	$-0.444599\pi$
$911$	10.4534			0.346338			0.173169	+	0.984892i	$0.444599\pi$
$912$		0			0
$913$	−34.2254			−1.13270
$914$	−1.89611	−	0.433783i	−0.0627178	−	0.0143483i
$915$		0			0
$916$	42.8956	+	20.7108i	1.41731	+	0.684305i
$917$		−	25.2760i		−	0.834687i
$918$		0			0
$919$		−	25.6632i		−	0.846550i	−0.906001	−	0.423275i	$-0.860880\pi$
$919$		−	25.6632i		−	0.846550i	0.906001	−	0.423275i	$-0.139120\pi$
$920$	12.9782	−	16.2237i	0.427879	−	0.534879i
$921$		0			0
$922$	−10.1064	+	44.1761i	−0.332836	+	1.45486i
$923$	−3.43594			−0.113095
$924$		0			0
$925$	−8.84637			−0.290867
$926$	−10.5249	+	46.0053i	−0.345869	+	1.51183i
$927$		0			0
$928$	−1.40514	+	0.672313i	−0.0461260	+	0.0220697i
$929$		−	25.4349i		−	0.834493i	−0.908793	−	0.417246i	$-0.862995\pi$
$929$		−	25.4349i		−	0.834493i	0.908793	−	0.417246i	$-0.137005\pi$
$930$		0			0
$931$		−	7.00405i		−	0.229548i
$932$	−11.6359	+	24.0998i	−0.381146	+	0.789417i
$933$		0			0
$934$	−18.0873	−	4.13793i	−0.591836	−	0.135397i
$935$	31.1848			1.01985
$936$		0			0
$937$	−20.7864			−0.679064			−0.339532	−	0.940595i	$-0.610269\pi$
$937$	−20.7864			−0.679064			−0.339532	+	0.940595i	$0.610269\pi$
$938$	5.22139	+	1.19452i	0.170484	+	0.0390026i
$939$		0			0
$940$	−5.90688	+	12.2341i	−0.192661	+	0.399033i
$941$		−	14.8842i		−	0.485210i	−0.970125	−	0.242605i	$-0.921998\pi$
$941$		−	14.8842i		−	0.485210i	0.970125	−	0.242605i	$-0.0780018\pi$
$942$		0			0
$943$		−	73.4641i		−	2.39232i
$944$	−25.6155	−	32.2543i	−0.833712	−	1.04979i
$945$		0			0
$946$	2.56317	−	11.2039i	0.0833357	−	0.364269i
$947$	16.7267			0.543546			0.271773	−	0.962361i	$-0.412390\pi$
$947$	16.7267			0.543546			0.271773	+	0.962361i	$0.412390\pi$
$948$		0			0
$949$	−5.92007			−0.192174
$950$	1.01374	−	4.43117i	0.0328901	−	0.143766i
$951$		0			0
$952$	−31.3487	−	25.0775i	−1.01602	−	0.812768i
$953$		−	29.3976i		−	0.952283i	−0.879369	−	0.476141i	$-0.842035\pi$
$953$		−	29.3976i		−	0.952283i	0.879369	−	0.476141i	$-0.157965\pi$
$954$		0			0
$955$			0.208841i			0.00675794i
$956$	39.5348	+	19.0882i	1.27865	+	0.617356i
$957$		0			0
$958$	10.4265	+	2.38533i	0.336866	+	0.0770665i
$959$	−48.6164			−1.56990
$960$		0			0
$961$	30.1546			0.972729
$962$	8.88465	+	2.03259i	0.286453	+	0.0655332i
$963$		0			0
$964$	10.2541	+	4.95090i	0.330263	+	0.159458i
$965$			19.2602i			0.620008i
$966$		0			0
$967$		−	58.2692i		−	1.87381i	−0.349581	−	0.936906i	$-0.613676\pi$
$967$		−	58.2692i		−	1.87381i	0.349581	−	0.936906i	$-0.386324\pi$
$968$	−27.1061	−	21.6837i	−0.871224	−	0.696941i
$969$		0			0
$970$	1.94175	−	8.48760i	0.0623459	−	0.272520i
$971$	−30.0040			−0.962873			−0.481436	−	0.876481i	$-0.659885\pi$
$971$	−30.0040			−0.962873			−0.481436	+	0.876481i	$0.659885\pi$
$972$		0			0
$973$	−38.7566			−1.24248
$974$	−9.99950	+	43.7089i	−0.320405	+	1.40052i
$975$		0			0
$976$	21.2921	+	26.8104i	0.681544	+	0.858180i
$977$		−	16.1313i		−	0.516086i	−0.966133	−	0.258043i	$-0.916922\pi$
$977$		−	16.1313i		−	0.516086i	0.966133	−	0.258043i	$-0.0830776\pi$
$978$		0			0
$979$		−	7.47144i		−	0.238788i
$980$	−1.89488	+	3.92460i	−0.0605296	+	0.125367i
$981$		0			0
$982$	51.6370	+	11.8133i	1.64780	+	0.376976i
$983$	−39.3905			−1.25636			−0.628182	−	0.778067i	$-0.716201\pi$
$983$	−39.3905			−1.25636			−0.628182	+	0.778067i	$0.716201\pi$
$984$		0			0
$985$	26.2412			0.836115
$986$	−2.45395	−	0.561403i	−0.0781497	−	0.0178787i
$987$		0			0
$988$	−2.03626	+	4.21743i	−0.0647820	+	0.134174i
$989$		−	12.3744i		−	0.393484i
$990$		0			0
$991$			61.1451i			1.94234i	0.238389	+	0.971170i	$0.423381\pi$
$991$			61.1451i			1.94234i	−0.238389	+	0.971170i	$0.576619\pi$
$992$	4.69182	−	2.24488i	0.148965	−	0.0712750i
$993$		0			0
$994$	−3.26603	+	14.2762i	−0.103592	+	0.452813i
$995$	10.5046			0.333019
$996$		0			0
$997$	16.7194			0.529509			0.264755	−	0.964316i	$-0.414709\pi$
$997$	16.7194			0.529509			0.264755	+	0.964316i	$0.414709\pi$
$998$	−1.26946	+	5.54895i	−0.0401841	+	0.175649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.3		48
3.2	odd	2	inner	1620.2.e.b.971.46		48
4.3	odd	2	inner	1620.2.e.b.971.45		48
9.2	odd	6		540.2.q.a.71.10		48
9.4	even	3		540.2.q.a.251.18		48
9.5	odd	6		180.2.q.a.11.7	✓	48
9.7	even	3		180.2.q.a.131.15	yes	48
12.11	even	2	inner	1620.2.e.b.971.4		48
36.7	odd	6		180.2.q.a.131.7	yes	48
36.11	even	6		540.2.q.a.71.18		48
36.23	even	6		180.2.q.a.11.15	yes	48
36.31	odd	6		540.2.q.a.251.10		48
45.7	odd	12		900.2.o.b.599.4		48
45.14	odd	6		900.2.r.f.551.18		48
45.23	even	12		900.2.o.b.299.20		48
45.32	even	12		900.2.o.c.299.5		48
45.34	even	6		900.2.r.f.851.10		48
45.43	odd	12		900.2.o.c.599.21		48
180.7	even	12		900.2.o.b.599.20		48
180.23	odd	12		900.2.o.b.299.4		48
180.43	even	12		900.2.o.c.599.5		48
180.59	even	6		900.2.r.f.551.10		48
180.79	odd	6		900.2.r.f.851.18		48
180.167	odd	12		900.2.o.c.299.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.7	✓	48	9.5	odd	6
180.2.q.a.11.15	yes	48	36.23	even	6
180.2.q.a.131.7	yes	48	36.7	odd	6
180.2.q.a.131.15	yes	48	9.7	even	3
540.2.q.a.71.10		48	9.2	odd	6
540.2.q.a.71.18		48	36.11	even	6
540.2.q.a.251.10		48	36.31	odd	6
540.2.q.a.251.18		48	9.4	even	3
900.2.o.b.299.4		48	180.23	odd	12
900.2.o.b.299.20		48	45.23	even	12
900.2.o.b.599.4		48	45.7	odd	12
900.2.o.b.599.20		48	180.7	even	12
900.2.o.c.299.5		48	45.32	even	12
900.2.o.c.299.21		48	180.167	odd	12
900.2.o.c.599.5		48	180.43	even	12
900.2.o.c.599.21		48	45.43	odd	12
900.2.r.f.551.10		48	180.59	even	6
900.2.r.f.551.18		48	45.14	odd	6
900.2.r.f.851.10		48	45.34	even	6
900.2.r.f.851.18		48	180.79	odd	6
1620.2.e.b.971.3		48	1.1	even	1	trivial
1620.2.e.b.971.4		48	12.11	even	2	inner
1620.2.e.b.971.45		48	4.3	odd	2	inner
1620.2.e.b.971.46		48	3.2	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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37860 - 0.315389i) q^{2} +(1.80106 + 0.869588i) q^{4} +1.00000i q^{5} -2.19567i q^{7} +(-2.20868 - 1.76684i) q^{8} +O(q^{10})\)	\(q+(-1.37860 - 0.315389i) q^{2} +(1.80106 + 0.869588i) q^{4} +1.00000i q^{5} -2.19567i q^{7} +(-2.20868 - 1.76684i) q^{8} +(0.315389 - 1.37860i) q^{10} -4.82416 q^{11} -0.728514 q^{13} +(-0.692488 + 3.02694i) q^{14} +(2.48763 + 3.13236i) q^{16} +6.46429i q^{17} -3.21426i q^{19} +(-0.869588 + 1.80106i) q^{20} +(6.65058 + 1.52149i) q^{22} +7.34542 q^{23} -1.00000 q^{25} +(1.00433 + 0.229765i) q^{26} +(1.90932 - 3.95453i) q^{28} -0.275365i q^{29} +0.919454i q^{31} +(-2.44154 - 5.10283i) q^{32} +(2.03876 - 8.91165i) q^{34} +2.19567 q^{35} +8.84637 q^{37} +(-1.01374 + 4.43117i) q^{38} +(1.76684 - 2.20868i) q^{40} -10.0013i q^{41} -1.68465i q^{43} +(-8.68861 - 4.19503i) q^{44} +(-10.1264 - 2.31666i) q^{46} +6.79274 q^{47} +2.17905 q^{49} +(1.37860 + 0.315389i) q^{50} +(-1.31210 - 0.633507i) q^{52} +0.913620i q^{53} -4.82416i q^{55} +(-3.87940 + 4.84952i) q^{56} +(-0.0868468 + 0.379617i) q^{58} -10.2971 q^{59} +8.55918 q^{61} +(0.289985 - 1.26756i) q^{62} +(1.75652 + 7.80478i) q^{64} -0.728514i q^{65} -1.72497i q^{67} +(-5.62126 + 11.6426i) q^{68} +(-3.02694 - 0.692488i) q^{70} +4.71637 q^{71} +8.12623 q^{73} +(-12.1956 - 2.79005i) q^{74} +(2.79508 - 5.78908i) q^{76} +10.5923i q^{77} -2.12374i q^{79} +(-3.13236 + 2.48763i) q^{80} +(-3.15431 + 13.7878i) q^{82} +7.09458 q^{83} -6.46429 q^{85} +(-0.531318 + 2.32245i) q^{86} +(10.6550 + 8.52355i) q^{88} +1.54875i q^{89} +1.59957i q^{91} +(13.2296 + 6.38749i) q^{92} +(-9.36445 - 2.14235i) q^{94} +3.21426 q^{95} +6.15669 q^{97} +(-3.00404 - 0.687248i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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