LMFDB - Embedded newform 1620.2.e.b.971.29

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			971.29
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.390365 - 1.35927i) q^{2} +(-1.69523 - 1.06122i) q^{4} -1.00000i q^{5} +1.67328i q^{7} +(-2.10425 + 1.89001i) q^{8} +O(q^{10})$	\(q+(0.390365 - 1.35927i) q^{2} +(-1.69523 - 1.06122i) q^{4} -1.00000i q^{5} +1.67328i q^{7} +(-2.10425 + 1.89001i) q^{8} +(-1.35927 - 0.390365i) q^{10} +4.67706 q^{11} -0.142398 q^{13} +(2.27444 + 0.653189i) q^{14} +(1.74761 + 3.59803i) q^{16} +7.09789i q^{17} +0.158590i q^{19} +(-1.06122 + 1.69523i) q^{20} +(1.82576 - 6.35739i) q^{22} -0.185297 q^{23} -1.00000 q^{25} +(-0.0555873 + 0.193558i) q^{26} +(1.77572 - 2.83659i) q^{28} +3.22202i q^{29} +5.91637i q^{31} +(5.57291 - 0.970932i) q^{32} +(9.64795 + 2.77077i) q^{34} +1.67328 q^{35} +0.634278 q^{37} +(0.215567 + 0.0619082i) q^{38} +(1.89001 + 2.10425i) q^{40} +10.8109i q^{41} -8.39571i q^{43} +(-7.92870 - 4.96341i) q^{44} +(-0.0723333 + 0.251868i) q^{46} +9.55743 q^{47} +4.20014 q^{49} +(-0.390365 + 1.35927i) q^{50} +(0.241398 + 0.151116i) q^{52} -7.27280i q^{53} -4.67706i q^{55} +(-3.16252 - 3.52099i) q^{56} +(4.37959 + 1.25776i) q^{58} -6.46738 q^{59} +6.27622 q^{61} +(8.04194 + 2.30954i) q^{62} +(0.855709 - 7.95410i) q^{64} +0.142398i q^{65} -8.44369i q^{67} +(7.53244 - 12.0326i) q^{68} +(0.653189 - 2.27444i) q^{70} +15.4118 q^{71} -4.30972 q^{73} +(0.247600 - 0.862156i) q^{74} +(0.168300 - 0.268847i) q^{76} +7.82603i q^{77} -13.8943i q^{79} +(3.59803 - 1.74761i) q^{80} +(14.6949 + 4.22020i) q^{82} -6.56384 q^{83} +7.09789 q^{85} +(-11.4120 - 3.27739i) q^{86} +(-9.84169 + 8.83971i) q^{88} +11.0790i q^{89} -0.238272i q^{91} +(0.314120 + 0.196641i) q^{92} +(3.73089 - 12.9911i) q^{94} +0.158590 q^{95} +3.53268 q^{97} +(1.63959 - 5.70912i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.390365	−	1.35927i	0.276030	−	0.961149i
$2$	0.390365	−	1.35927i	0.276030	−	0.961149i
$3$		0			0
$3$		0			0
$4$	−1.69523	−	1.06122i	−0.847615	−	0.530611i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$			1.67328i			0.632440i	0.948686	+	0.316220i	$0.102414\pi$
$7$			1.67328i			0.632440i	−0.948686	+	0.316220i	$0.897586\pi$
$8$	−2.10425	+	1.89001i	−0.743964	+	0.668220i
$9$		0			0
$10$	−1.35927	−	0.390365i	−0.429839	−	0.123444i
$11$	4.67706			1.41019			0.705094	−	0.709114i	$-0.250905\pi$
$11$	4.67706			1.41019			0.705094	+	0.709114i	$0.250905\pi$
$12$		0			0
$13$	−0.142398			−0.0394942			−0.0197471	−	0.999805i	$-0.506286\pi$
$13$	−0.142398			−0.0394942			−0.0197471	+	0.999805i	$0.506286\pi$
$14$	2.27444	+	0.653189i	0.607869	+	0.174572i
$15$		0			0
$16$	1.74761	+	3.59803i	0.436903	+	0.899509i
$17$			7.09789i			1.72149i	0.509035	+	0.860746i	$0.330002\pi$
$17$			7.09789i			1.72149i	−0.509035	+	0.860746i	$0.669998\pi$
$18$		0			0
$19$			0.158590i			0.0363832i	0.999835	+	0.0181916i	$0.00579088\pi$
$19$			0.158590i			0.0363832i	−0.999835	+	0.0181916i	$0.994209\pi$
$20$	−1.06122	+	1.69523i	−0.237297	+	0.379065i
$21$		0			0
$22$	1.82576	−	6.35739i	0.389254	−	1.35540i
$23$	−0.185297			−0.0386370			−0.0193185	−	0.999813i	$-0.506150\pi$
$23$	−0.185297			−0.0386370			−0.0193185	+	0.999813i	$0.506150\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.0555873	+	0.193558i	−0.0109016	+	0.0379598i
$27$		0			0
$28$	1.77572	−	2.83659i	0.335580	−	0.536066i
$29$			3.22202i			0.598314i	0.954204	+	0.299157i	$0.0967054\pi$
$29$			3.22202i			0.598314i	−0.954204	+	0.299157i	$0.903295\pi$
$30$		0			0
$31$			5.91637i			1.06261i	0.847180	+	0.531305i	$0.178298\pi$
$31$			5.91637i			1.06261i	−0.847180	+	0.531305i	$0.821702\pi$
$32$	5.57291	−	0.970932i	0.985160	−	0.171638i
$33$		0			0
$34$	9.64795	+	2.77077i	1.65461	+	0.475183i
$35$	1.67328			0.282836
$36$		0			0
$37$	0.634278			0.104275			0.0521374	−	0.998640i	$-0.483397\pi$
$37$	0.634278			0.104275			0.0521374	+	0.998640i	$0.483397\pi$
$38$	0.215567	+	0.0619082i	0.0349696	+	0.0100428i
$39$		0			0
$40$	1.89001	+	2.10425i	0.298837	+	0.332711i
$41$			10.8109i			1.68838i	0.536045	+	0.844189i	$0.319918\pi$
$41$			10.8109i			1.68838i	−0.536045	+	0.844189i	$0.680082\pi$
$42$		0			0
$43$		−	8.39571i		−	1.28033i	−0.768236	−	0.640167i	$-0.778865\pi$
$43$		−	8.39571i		−	1.28033i	0.768236	−	0.640167i	$-0.221135\pi$
$44$	−7.92870	−	4.96341i	−1.19530	−	0.748262i
$45$		0			0
$46$	−0.0723333	+	0.251868i	−0.0106650	+	0.0371359i
$47$	9.55743			1.39409			0.697047	−	0.717025i	$-0.254497\pi$
$47$	9.55743			1.39409			0.697047	+	0.717025i	$0.254497\pi$
$48$		0			0
$49$	4.20014			0.600020
$50$	−0.390365	+	1.35927i	−0.0552059	+	0.192230i
$51$		0			0
$52$	0.241398	+	0.151116i	0.0334759	+	0.0209561i
$53$		−	7.27280i		−	0.998996i	−0.866315	−	0.499498i	$-0.833518\pi$
$53$		−	7.27280i		−	0.998996i	0.866315	−	0.499498i	$-0.166482\pi$
$54$		0			0
$55$		−	4.67706i		−	0.630655i
$56$	−3.16252	−	3.52099i	−0.422609	−	0.470512i
$57$		0			0
$58$	4.37959	+	1.25776i	0.575069	+	0.165152i
$59$	−6.46738			−0.841981			−0.420991	−	0.907065i	$-0.638317\pi$
$59$	−6.46738			−0.841981			−0.420991	+	0.907065i	$0.638317\pi$
$60$		0			0
$61$	6.27622			0.803587			0.401794	−	0.915730i	$-0.368387\pi$
$61$	6.27622			0.803587			0.401794	+	0.915730i	$0.368387\pi$
$62$	8.04194	+	2.30954i	1.02133	+	0.293312i
$63$		0			0
$64$	0.855709	−	7.95410i	0.106964	−	0.994263i
$65$			0.142398i			0.0176623i
$66$		0			0
$67$		−	8.44369i		−	1.03156i	−0.856721	−	0.515781i	$-0.827502\pi$
$67$		−	8.44369i		−	1.03156i	0.856721	−	0.515781i	$-0.172498\pi$
$68$	7.53244	−	12.0326i	0.913443	−	1.45916i
$69$		0			0
$70$	0.653189	−	2.27444i	0.0780711	−	0.271847i
$71$	15.4118			1.82904			0.914520	−	0.404541i	$-0.132569\pi$
$71$	15.4118			1.82904			0.914520	+	0.404541i	$0.132569\pi$
$72$		0			0
$73$	−4.30972			−0.504414			−0.252207	−	0.967673i	$-0.581156\pi$
$73$	−4.30972			−0.504414			−0.252207	+	0.967673i	$0.581156\pi$
$74$	0.247600	−	0.862156i	0.0287829	−	0.100224i
$75$		0			0
$76$	0.168300	−	0.268847i	0.0193053	−	0.0308389i
$77$			7.82603i			0.891859i
$78$		0			0
$79$		−	13.8943i		−	1.56323i	−0.623759	−	0.781617i	$-0.714395\pi$
$79$		−	13.8943i		−	1.56323i	0.623759	−	0.781617i	$-0.285605\pi$
$80$	3.59803	−	1.74761i	0.402272	−	0.195389i
$81$		0			0
$82$	14.6949	+	4.22020i	1.62278	+	0.466043i
$83$	−6.56384			−0.720475			−0.360237	−	0.932861i	$-0.617304\pi$
$83$	−6.56384			−0.720475			−0.360237	+	0.932861i	$0.617304\pi$
$84$		0			0
$85$	7.09789			0.769875
$86$	−11.4120	−	3.27739i	−1.23059	−	0.353410i
$87$		0			0
$88$	−9.84169	+	8.83971i	−1.04913	+	0.942316i
$89$			11.0790i			1.17437i	0.809451	+	0.587187i	$0.199765\pi$
$89$			11.0790i			1.17437i	−0.809451	+	0.587187i	$0.800235\pi$
$90$		0			0
$91$		−	0.238272i		−	0.0249777i
$92$	0.314120	+	0.196641i	0.0327493	+	0.0205012i
$93$		0			0
$94$	3.73089	−	12.9911i	0.384811	−	1.33993i
$95$	0.158590			0.0162710
$96$		0			0
$97$	3.53268			0.358689			0.179345	−	0.983786i	$-0.442602\pi$
$97$	3.53268			0.358689			0.179345	+	0.983786i	$0.442602\pi$
$98$	1.63959	−	5.70912i	0.165623	−	0.576708i
$99$		0			0
$100$	1.69523	+	1.06122i	0.169523	+	0.106122i
$101$			8.17796i			0.813737i	0.913487	+	0.406869i	$0.133379\pi$
$101$			8.17796i			0.813737i	−0.913487	+	0.406869i	$0.866621\pi$
$102$		0			0
$103$			8.33846i			0.821613i	0.911723	+	0.410806i	$0.134753\pi$
$103$			8.33846i			0.821613i	−0.911723	+	0.410806i	$0.865247\pi$
$104$	0.299641	−	0.269134i	0.0293822	−	0.0263908i
$105$		0			0
$106$	−9.88570	−	2.83905i	−0.960184	−	0.275753i
$107$	−16.4383			−1.58915			−0.794575	−	0.607166i	$-0.792306\pi$
$107$	−16.4383			−1.58915			−0.794575	+	0.607166i	$0.792306\pi$
$108$		0			0
$109$	17.8541			1.71011			0.855056	−	0.518536i	$-0.173523\pi$
$109$	17.8541			1.71011			0.855056	+	0.518536i	$0.173523\pi$
$110$	−6.35739	−	1.82576i	−0.606154	−	0.174080i
$111$		0			0
$112$	−6.02051	+	2.92424i	−0.568885	+	0.276315i
$113$			0.164278i			0.0154540i	0.999970	+	0.00772700i	$0.00245961\pi$
$113$			0.164278i			0.0154540i	−0.999970	+	0.00772700i	$0.997540\pi$
$114$		0			0
$115$			0.185297i			0.0172790i
$116$	3.41928	−	5.46206i	0.317472	−	0.507140i
$117$		0			0
$118$	−2.52464	+	8.79092i	−0.232412	+	0.809269i
$119$	−11.8768			−1.08874
$120$		0			0
$121$	10.8749			0.988629
$122$	2.45002	−	8.53108i	0.221814	−	0.772367i
$123$		0			0
$124$	6.27858	−	10.0296i	0.563833	−	0.900685i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	0.353351i		−	0.0313548i	−0.999877	−	0.0156774i	$-0.995010\pi$
$127$		−	0.353351i		−	0.0313548i	0.999877	−	0.0156774i	$-0.00499048\pi$
$128$	−10.4777	−	4.26814i	−0.926110	−	0.377254i
$129$		0			0
$130$	0.193558	+	0.0555873i	0.0169761	+	0.00487533i
$131$	−2.99466			−0.261645			−0.130822	−	0.991406i	$-0.541762\pi$
$131$	−2.99466			−0.261645			−0.130822	+	0.991406i	$0.541762\pi$
$132$		0			0
$133$	−0.265366			−0.0230102
$134$	−11.4773	−	3.29612i	−0.991484	−	0.284742i
$135$		0			0
$136$	−13.4151	−	14.9357i	−1.15034	−	1.28073i
$137$			7.65817i			0.654282i	0.944976	+	0.327141i	$0.106085\pi$
$137$			7.65817i			0.654282i	−0.944976	+	0.327141i	$0.893915\pi$
$138$		0			0
$139$		−	9.70927i		−	0.823529i	−0.911290	−	0.411765i	$-0.864913\pi$
$139$		−	9.70927i		−	0.823529i	0.911290	−	0.411765i	$-0.135087\pi$
$140$	−2.83659	−	1.77572i	−0.239736	−	0.150076i
$141$		0			0
$142$	6.01621	−	20.9488i	0.504869	−	1.75798i
$143$	−0.666006			−0.0556942
$144$		0			0
$145$	3.22202			0.267574
$146$	−1.68236	+	5.85807i	−0.139233	+	0.484817i
$147$		0			0
$148$	−1.07525	−	0.673111i	−0.0883848	−	0.0553293i
$149$		−	2.51116i		−	0.205722i	−0.994696	−	0.102861i	$-0.967200\pi$
$149$		−	2.51116i		−	0.205722i	0.994696	−	0.102861i	$-0.0327997\pi$
$150$		0			0
$151$		−	3.64503i		−	0.296628i	−0.988940	−	0.148314i	$-0.952615\pi$
$151$		−	3.64503i		−	0.296628i	0.988940	−	0.148314i	$-0.0473846\pi$
$152$	−0.299738	−	0.333714i	−0.0243120	−	0.0270677i
$153$		0			0
$154$	10.6377	+	3.05501i	0.857210	+	0.246180i
$155$	5.91637			0.475214
$156$		0			0
$157$	−16.9489			−1.35267			−0.676336	−	0.736593i	$-0.736433\pi$
$157$	−16.9489			−1.35267			−0.676336	+	0.736593i	$0.736433\pi$
$158$	−18.8861	−	5.42386i	−1.50250	−	0.431499i
$159$		0			0
$160$	−0.970932	−	5.57291i	−0.0767589	−	0.440577i
$161$		−	0.310053i		−	0.0244356i
$162$		0			0
$163$			7.71414i			0.604218i	0.953273	+	0.302109i	$0.0976907\pi$
$163$			7.71414i			0.604218i	−0.953273	+	0.302109i	$0.902309\pi$
$164$	11.4728	−	18.3270i	0.895873	−	1.43110i
$165$		0			0
$166$	−2.56229	+	8.92203i	−0.198872	+	0.692484i
$167$	20.5191			1.58781			0.793906	−	0.608040i	$-0.208044\pi$
$167$	20.5191			1.58781			0.793906	+	0.608040i	$0.208044\pi$
$168$		0			0
$169$	−12.9797			−0.998440
$170$	2.77077	−	9.64795i	0.212508	−	0.739964i
$171$		0			0
$172$	−8.90972	+	14.2327i	−0.679359	+	1.08523i
$173$			4.16852i			0.316927i	0.987365	+	0.158463i	$0.0506540\pi$
$173$			4.16852i			0.316927i	−0.987365	+	0.158463i	$0.949346\pi$
$174$		0			0
$175$		−	1.67328i		−	0.126488i
$176$	8.17370	+	16.8282i	0.616115	+	1.26848i
$177$		0			0
$178$	15.0594	+	4.32486i	1.12875	+	0.324162i
$179$	14.5799			1.08975			0.544876	−	0.838517i	$-0.316577\pi$
$179$	14.5799			1.08975			0.544876	+	0.838517i	$0.316577\pi$
$180$		0			0
$181$	−1.43621			−0.106753			−0.0533764	−	0.998574i	$-0.516998\pi$
$181$	−1.43621			−0.106753			−0.0533764	+	0.998574i	$0.516998\pi$
$182$	−0.323876	−	0.0930130i	−0.0240073	−	0.00689458i
$183$		0			0
$184$	0.389910	−	0.350213i	0.0287445	−	0.0258180i
$185$		−	0.634278i		−	0.0466331i
$186$		0			0
$187$			33.1973i			2.42763i
$188$	−16.2020	−	10.1426i	−1.18166	−	0.739722i
$189$		0			0
$190$	0.0619082	−	0.215567i	0.00449129	−	0.0156389i
$191$	−12.9901			−0.939927			−0.469964	−	0.882686i	$-0.655733\pi$
$191$	−12.9901			−0.939927			−0.469964	+	0.882686i	$0.655733\pi$
$192$		0			0
$193$	−7.48894			−0.539066			−0.269533	−	0.962991i	$-0.586869\pi$
$193$	−7.48894			−0.539066			−0.269533	+	0.962991i	$0.586869\pi$
$194$	1.37903	−	4.80187i	0.0990089	−	0.344754i
$195$		0			0
$196$	−7.12020	−	4.45728i	−0.508586	−	0.318377i
$197$			12.9422i			0.922097i	0.887375	+	0.461048i	$0.152527\pi$
$197$			12.9422i			0.922097i	−0.887375	+	0.461048i	$0.847473\pi$
$198$		0			0
$199$			11.0097i			0.780456i	0.920718	+	0.390228i	$0.127604\pi$
$199$			11.0097i			0.780456i	−0.920718	+	0.390228i	$0.872396\pi$
$200$	2.10425	−	1.89001i	0.148793	−	0.133644i
$201$		0			0
$202$	11.1161	+	3.19239i	0.782123	+	0.224616i
$203$	−5.39133			−0.378397
$204$		0			0
$205$	10.8109			0.755066
$206$	11.3342	+	3.25504i	0.789692	+	0.226789i
$207$		0			0
$208$	−0.248857	−	0.512354i	−0.0172551	−	0.0355253i
$209$			0.741738i			0.0513071i
$210$		0			0
$211$			1.03904i			0.0715303i	0.999360	+	0.0357651i	$0.0113868\pi$
$211$			1.03904i			0.0715303i	−0.999360	+	0.0357651i	$0.988613\pi$
$212$	−7.71806	+	12.3291i	−0.530079	+	0.846764i
$213$		0			0
$214$	−6.41693	+	22.3441i	−0.438652	+	1.52741i
$215$	−8.39571			−0.572583
$216$		0			0
$217$	−9.89973			−0.672037
$218$	6.96961	−	24.2685i	0.472042	−	1.64367i
$219$		0			0
$220$	−4.96341	+	7.92870i	−0.334633	+	0.534553i
$221$		−	1.01073i		−	0.0679889i
$222$		0			0
$223$			16.2305i			1.08687i	0.839450	+	0.543437i	$0.182877\pi$
$223$			16.2305i			1.08687i	−0.839450	+	0.543437i	$0.817123\pi$
$224$	1.62464	+	9.32503i	0.108551	+	0.623055i
$225$		0			0
$226$	0.223299	+	0.0641285i	0.0148536	+	0.00426576i
$227$	20.0353			1.32979			0.664896	−	0.746936i	$-0.268476\pi$
$227$	20.0353			1.32979			0.664896	+	0.746936i	$0.268476\pi$
$228$		0			0
$229$	1.87177			0.123690			0.0618451	−	0.998086i	$-0.480302\pi$
$229$	1.87177			0.123690			0.0618451	+	0.998086i	$0.480302\pi$
$230$	0.251868	+	0.0723333i	0.0166077	+	0.00476951i
$231$		0			0
$232$	−6.08965	−	6.77992i	−0.399805	−	0.445124i
$233$			8.06531i			0.528376i	0.964471	+	0.264188i	$0.0851039\pi$
$233$			8.06531i			0.528376i	−0.964471	+	0.264188i	$0.914896\pi$
$234$		0			0
$235$		−	9.55743i		−	0.623458i
$236$	10.9637	+	6.86333i	0.713676	+	0.446765i
$237$		0			0
$238$	−4.63627	+	16.1437i	−0.300525	+	1.04644i
$239$	17.3649			1.12324			0.561621	−	0.827394i	$-0.310178\pi$
$239$	17.3649			1.12324			0.561621	+	0.827394i	$0.310178\pi$
$240$		0			0
$241$	2.65606			0.171092			0.0855458	−	0.996334i	$-0.472737\pi$
$241$	2.65606			0.171092			0.0855458	+	0.996334i	$0.472737\pi$
$242$	4.24519	−	14.7820i	0.272891	−	0.950220i
$243$		0			0
$244$	−10.6396	−	6.66047i	−0.681133	−	0.426393i
$245$		−	4.20014i		−	0.268337i
$246$		0			0
$247$		−	0.0225830i		−	0.00143692i
$248$	−11.1820	−	12.4495i	−0.710058	−	0.790544i
$249$		0			0
$250$	1.35927	+	0.390365i	0.0859678	+	0.0246888i
$251$	−4.95818			−0.312958			−0.156479	−	0.987681i	$-0.550014\pi$
$251$	−4.95818			−0.312958			−0.156479	+	0.987681i	$0.550014\pi$
$252$		0			0
$253$	−0.866644			−0.0544854
$254$	−0.480300	−	0.137936i	−0.0301367	−	0.00865487i
$255$		0			0
$256$	−9.89170	+	12.5759i	−0.618231	+	0.785996i
$257$		−	6.78630i		−	0.423318i	−0.977344	−	0.211659i	$-0.932113\pi$
$257$		−	6.78630i		−	0.423318i	0.977344	−	0.211659i	$-0.0678866\pi$
$258$		0			0
$259$			1.06132i			0.0659475i
$260$	0.151116	−	0.241398i	0.00937183	−	0.0149709i
$261$		0			0
$262$	−1.16901	+	4.07055i	−0.0722217	+	0.251480i
$263$	−13.1379			−0.810119			−0.405059	−	0.914290i	$-0.632749\pi$
$263$	−13.1379			−0.810119			−0.405059	+	0.914290i	$0.632749\pi$
$264$		0			0
$265$	−7.27280			−0.446765
$266$	−0.103590	+	0.360704i	−0.00635149	+	0.0221162i
$267$		0			0
$268$	−8.96064	+	14.3140i	−0.547358	+	0.874367i
$269$		−	13.3786i		−	0.815710i	−0.913047	−	0.407855i	$-0.866277\pi$
$269$		−	13.3786i		−	0.815710i	0.913047	−	0.407855i	$-0.133723\pi$
$270$		0			0
$271$		−	22.1173i		−	1.34353i	−0.740763	−	0.671766i	$-0.765536\pi$
$271$		−	22.1173i		−	1.34353i	0.740763	−	0.671766i	$-0.234464\pi$
$272$	−25.5385	+	12.4044i	−1.54850	+	0.752125i
$273$		0			0
$274$	10.4095	+	2.98948i	0.628862	+	0.180601i
$275$	−4.67706			−0.282038
$276$		0			0
$277$	−7.75626			−0.466028			−0.233014	−	0.972473i	$-0.574859\pi$
$277$	−7.75626			−0.466028			−0.233014	+	0.972473i	$0.574859\pi$
$278$	−13.1975	−	3.79016i	−0.791534	−	0.227318i
$279$		0			0
$280$	−3.52099	+	3.16252i	−0.210420	+	0.188997i
$281$			19.2696i			1.14953i	0.818319	+	0.574765i	$0.194906\pi$
$281$			19.2696i			1.14953i	−0.818319	+	0.574765i	$0.805094\pi$
$282$		0			0
$283$		−	20.1379i		−	1.19707i	−0.801095	−	0.598537i	$-0.795749\pi$
$283$		−	20.1379i		−	1.19707i	0.801095	−	0.598537i	$-0.204251\pi$
$284$	−26.1265	−	16.3553i	−1.55032	−	0.970509i
$285$		0			0
$286$	−0.259985	+	0.905281i	−0.0153732	+	0.0535304i
$287$	−18.0897			−1.06780
$288$		0			0
$289$	−33.3801			−1.96353
$290$	1.25776	−	4.37959i	0.0738584	−	0.257179i
$291$		0			0
$292$	7.30596	+	4.57357i	0.427549	+	0.267648i
$293$		−	1.25219i		−	0.0731539i	−0.999331	−	0.0365769i	$-0.988355\pi$
$293$		−	1.25219i		−	0.0731539i	0.999331	−	0.0365769i	$-0.0116454\pi$
$294$		0			0
$295$			6.46738i			0.376545i
$296$	−1.33468	+	1.19879i	−0.0775766	+	0.0696785i
$297$		0			0
$298$	−3.41335	−	0.980269i	−0.197730	−	0.0567855i
$299$	0.0263859			0.00152594
$300$		0			0
$301$	14.0484			0.809734
$302$	−4.95457	−	1.42289i	−0.285104	−	0.0818781i
$303$		0			0
$304$	−0.570614	+	0.277155i	−0.0327270	+	0.0158959i
$305$		−	6.27622i		−	0.359375i
$306$		0			0
$307$		−	10.4559i		−	0.596749i	−0.954449	−	0.298374i	$-0.903556\pi$
$307$		−	10.4559i		−	0.596749i	0.954449	−	0.298374i	$-0.0964444\pi$
$308$	8.30516	−	13.2669i	0.473230	−	0.755953i
$309$		0			0
$310$	2.30954	−	8.04194i	0.131173	−	0.456751i
$311$	17.3894			0.986062			0.493031	−	0.870012i	$-0.335889\pi$
$311$	17.3894			0.986062			0.493031	+	0.870012i	$0.335889\pi$
$312$		0			0
$313$	−16.3885			−0.926330			−0.463165	−	0.886272i	$-0.653286\pi$
$313$	−16.3885			−0.926330			−0.463165	+	0.886272i	$0.653286\pi$
$314$	−6.61627	+	23.0382i	−0.373377	+	1.30012i
$315$		0			0
$316$	−14.7450	+	23.5541i	−0.829470	+	1.32502i
$317$		−	12.9783i		−	0.728935i	−0.931216	−	0.364467i	$-0.881251\pi$
$317$		−	12.9783i		−	0.728935i	0.931216	−	0.364467i	$-0.118749\pi$
$318$		0			0
$319$			15.0696i			0.843734i
$320$	−7.95410	−	0.855709i	−0.444648	−	0.0478356i
$321$		0			0
$322$	−0.421445	−	0.121034i	−0.0234862	−	0.00674495i
$323$	−1.12566			−0.0626333
$324$		0			0
$325$	0.142398			0.00789883
$326$	10.4856	+	3.01133i	0.580744	+	0.166782i
$327$		0			0
$328$	−20.4327	−	22.7488i	−1.12821	−	1.25609i
$329$			15.9922i			0.881681i
$330$		0			0
$331$		−	0.110031i		−	0.00604788i	−0.999995	−	0.00302394i	$-0.999037\pi$
$331$		−	0.110031i		−	0.00604788i	0.999995	−	0.00302394i	$-0.000962551\pi$
$332$	11.1272	+	6.96569i	0.610686	+	0.382292i
$333$		0			0
$334$	8.00992	−	27.8909i	0.438283	−	1.52612i
$335$	−8.44369			−0.461328
$336$		0			0
$337$	−18.4062			−1.00265			−0.501324	−	0.865259i	$-0.667154\pi$
$337$	−18.4062			−1.00265			−0.501324	+	0.865259i	$0.667154\pi$
$338$	−5.06683	+	17.6429i	−0.275599	+	0.959650i
$339$		0			0
$340$	−12.0326	−	7.53244i	−0.652557	−	0.408504i
$341$			27.6712i			1.49848i
$342$		0			0
$343$			18.7410i			1.01192i
$344$	15.8680	+	17.6666i	0.855545	+	0.952522i
$345$		0			0
$346$	5.66615	+	1.62725i	0.304614	+	0.0874812i
$347$	2.96353			0.159091			0.0795454	−	0.996831i	$-0.474653\pi$
$347$	2.96353			0.159091			0.0795454	+	0.996831i	$0.474653\pi$
$348$		0			0
$349$	25.1111			1.34416			0.672082	−	0.740477i	$-0.265400\pi$
$349$	25.1111			1.34416			0.672082	+	0.740477i	$0.265400\pi$
$350$	−2.27444	−	0.653189i	−0.121574	−	0.0349144i
$351$		0			0
$352$	26.0648	−	4.54111i	1.38926	−	0.242042i
$353$		−	30.2080i		−	1.60781i	−0.594757	−	0.803905i	$-0.702752\pi$
$353$		−	30.2080i		−	1.60781i	0.594757	−	0.803905i	$-0.297248\pi$
$354$		0			0
$355$		−	15.4118i		−	0.817972i
$356$	11.7573	−	18.7815i	0.623136	−	0.995417i
$357$		0			0
$358$	5.69147	−	19.8180i	0.300804	−	1.04741i
$359$	14.8225			0.782301			0.391151	−	0.920327i	$-0.372077\pi$
$359$	14.8225			0.782301			0.391151	+	0.920327i	$0.372077\pi$
$360$		0			0
$361$	18.9748			0.998676
$362$	−0.560646	+	1.95220i	−0.0294669	+	0.102605i
$363$		0			0
$364$	−0.252860	+	0.403926i	−0.0132534	+	0.0211715i
$365$			4.30972i			0.225581i
$366$		0			0
$367$			7.01934i			0.366407i	0.983075	+	0.183203i	$0.0586467\pi$
$367$			7.01934i			0.366407i	−0.983075	+	0.183203i	$0.941353\pi$
$368$	−0.323827	−	0.666703i	−0.0168806	−	0.0347543i
$369$		0			0
$370$	−0.862156	−	0.247600i	−0.0448213	−	0.0128721i
$371$	12.1694			0.631805
$372$		0			0
$373$	−15.7441			−0.815198			−0.407599	−	0.913161i	$-0.633634\pi$
$373$	−15.7441			−0.815198			−0.407599	+	0.913161i	$0.633634\pi$
$374$	45.1241	+	12.9591i	2.33331	+	0.670097i
$375$		0			0
$376$	−20.1112	+	18.0637i	−1.03716	+	0.931562i
$377$		−	0.458810i		−	0.0236299i
$378$		0			0
$379$			2.42034i			0.124325i	0.998066	+	0.0621624i	$0.0197997\pi$
$379$			2.42034i			0.124325i	−0.998066	+	0.0621624i	$0.980200\pi$
$380$	−0.268847	−	0.168300i	−0.0137916	−	0.00863360i
$381$		0			0
$382$	−5.07086	+	17.6570i	−0.259448	+	0.903410i
$383$	−9.59157			−0.490106			−0.245053	−	0.969510i	$-0.578805\pi$
$383$	−9.59157			−0.490106			−0.245053	+	0.969510i	$0.578805\pi$
$384$		0			0
$385$	7.82603			0.398851
$386$	−2.92342	+	10.1795i	−0.148798	+	0.518123i
$387$		0			0
$388$	−5.98871	−	3.74896i	−0.304031	−	0.190325i
$389$			22.9068i			1.16142i	0.814111	+	0.580709i	$0.197225\pi$
$389$			22.9068i			1.16142i	−0.814111	+	0.580709i	$0.802775\pi$
$390$		0			0
$391$		−	1.31521i		−	0.0665133i
$392$	−8.83813	+	7.93831i	−0.446393	+	0.400945i
$393$		0			0
$394$	17.5920	+	5.05220i	0.886273	+	0.254526i
$395$	−13.8943			−0.699100
$396$		0			0
$397$	−36.9587			−1.85490			−0.927451	−	0.373945i	$-0.878005\pi$
$397$	−36.9587			−1.85490			−0.927451	+	0.373945i	$0.878005\pi$
$398$	14.9651	+	4.29779i	0.750134	+	0.215429i
$399$		0			0
$400$	−1.74761	−	3.59803i	−0.0873806	−	0.179902i
$401$			16.6312i			0.830521i	0.909703	+	0.415260i	$0.136310\pi$
$401$			16.6312i			0.830521i	−0.909703	+	0.415260i	$0.863690\pi$
$402$		0			0
$403$		−	0.842480i		−	0.0419669i
$404$	8.67864	−	13.8635i	0.431778	−	0.689736i
$405$		0			0
$406$	−2.10459	+	7.32828i	−0.104449	+	0.363696i
$407$	2.96656			0.147047
$408$		0			0
$409$	−26.5521			−1.31292			−0.656458	−	0.754362i	$-0.727946\pi$
$409$	−26.5521			−1.31292			−0.656458	+	0.754362i	$0.727946\pi$
$410$	4.22020	−	14.6949i	0.208421	−	0.725731i
$411$		0			0
$412$	8.84896	−	14.1356i	0.435957	−	0.696412i
$413$		−	10.8217i		−	0.532503i
$414$		0			0
$415$			6.56384i			0.322206i
$416$	−0.793572	+	0.138259i	−0.0389081	+	0.00677870i
$417$		0			0
$418$	1.00822	+	0.289548i	0.0493137	+	0.0141623i
$419$	3.27372			0.159931			0.0799657	−	0.996798i	$-0.474519\pi$
$419$	3.27372			0.159931			0.0799657	+	0.996798i	$0.474519\pi$
$420$		0			0
$421$	−0.844144			−0.0411411			−0.0205705	−	0.999788i	$-0.506548\pi$
$421$	−0.844144			−0.0411411			−0.0205705	+	0.999788i	$0.506548\pi$
$422$	1.41233	+	0.405604i	0.0687513	+	0.0197445i
$423$		0			0
$424$	13.7457	+	15.3038i	0.667549	+	0.743217i
$425$		−	7.09789i		−	0.344298i
$426$		0			0
$427$			10.5019i			0.508221i
$428$	27.8667	+	17.4447i	1.34699	+	0.843221i
$429$		0			0
$430$	−3.27739	+	11.4120i	−0.158050	+	0.550337i
$431$	−2.94486			−0.141849			−0.0709244	−	0.997482i	$-0.522595\pi$
$431$	−2.94486			−0.141849			−0.0709244	+	0.997482i	$0.522595\pi$
$432$		0			0
$433$	4.61848			0.221950			0.110975	−	0.993823i	$-0.464603\pi$
$433$	4.61848			0.221950			0.110975	+	0.993823i	$0.464603\pi$
$434$	−3.86451	+	13.4564i	−0.185502	+	0.645928i
$435$		0			0
$436$	−30.2668	−	18.9472i	−1.44952	−	0.907405i
$437$		−	0.0293863i		−	0.00140574i
$438$		0			0
$439$		−	34.0889i		−	1.62697i	−0.581583	−	0.813487i	$-0.697566\pi$
$439$		−	34.0889i		−	1.62697i	0.581583	−	0.813487i	$-0.302434\pi$
$440$	8.83971	+	9.84169i	0.421416	+	0.469184i
$441$		0			0
$442$	−1.37385	−	0.394553i	−0.0653475	−	0.0187669i
$443$	13.9781			0.664121			0.332060	−	0.943258i	$-0.392256\pi$
$443$	13.9781			0.664121			0.332060	+	0.943258i	$0.392256\pi$
$444$		0			0
$445$	11.0790			0.525196
$446$	22.0616	+	6.33581i	1.04465	+	0.300009i
$447$		0			0
$448$	13.3094	+	1.43184i	0.628812	+	0.0676480i
$449$		−	19.8321i		−	0.935935i	−0.883746	−	0.467967i	$-0.844986\pi$
$449$		−	19.8321i		−	0.935935i	0.883746	−	0.467967i	$-0.155014\pi$
$450$		0			0
$451$			50.5633i			2.38093i
$452$	0.174336	−	0.278490i	0.00820007	−	0.0130991i
$453$		0			0
$454$	7.82109	−	27.2334i	0.367062	−	1.27813i
$455$	−0.238272			−0.0111704
$456$		0			0
$457$	−34.6189			−1.61940			−0.809701	−	0.586843i	$-0.800371\pi$
$457$	−34.6189			−1.61940			−0.809701	+	0.586843i	$0.800371\pi$
$458$	0.730674	−	2.54424i	0.0341422	−	0.118885i
$459$		0			0
$460$	0.196641	−	0.314120i	0.00916843	−	0.0146459i
$461$		−	0.452176i		−	0.0210599i	−0.999945	−	0.0105300i	$-0.996648\pi$
$461$		−	0.452176i		−	0.0210599i	0.999945	−	0.0105300i	$-0.00335186\pi$
$462$		0			0
$463$			37.5587i			1.74550i	0.488168	+	0.872750i	$0.337665\pi$
$463$			37.5587i			1.74550i	−0.488168	+	0.872750i	$0.662335\pi$
$464$	−11.5929	+	5.63084i	−0.538188	+	0.261405i
$465$		0			0
$466$	10.9629	+	3.14841i	0.507848	+	0.145847i
$467$	30.5224			1.41241			0.706204	−	0.708008i	$-0.250406\pi$
$467$	30.5224			1.41241			0.706204	+	0.708008i	$0.250406\pi$
$468$		0			0
$469$	14.1287			0.652401
$470$	−12.9911	−	3.73089i	−0.599236	−	0.172093i
$471$		0			0
$472$	13.6090	−	12.2234i	0.626403	−	0.562629i
$473$		−	39.2673i		−	1.80551i
$474$		0			0
$475$		−	0.158590i		−	0.00727663i
$476$	20.1338	+	12.6039i	0.922833	+	0.577698i
$477$		0			0
$478$	6.77865	−	23.6036i	0.310048	−	1.07960i
$479$	−2.01263			−0.0919594			−0.0459797	−	0.998942i	$-0.514641\pi$
$479$	−2.01263			−0.0919594			−0.0459797	+	0.998942i	$0.514641\pi$
$480$		0			0
$481$	−0.0903201			−0.00411824
$482$	1.03683	−	3.61030i	0.0472264	−	0.164445i
$483$		0			0
$484$	−18.4355	−	11.5407i	−0.837977	−	0.524578i
$485$		−	3.53268i		−	0.160411i
$486$		0			0
$487$		−	8.48364i		−	0.384430i	−0.981353	−	0.192215i	$-0.938433\pi$
$487$		−	8.48364i		−	0.384430i	0.981353	−	0.192215i	$-0.0615671\pi$
$488$	−13.2067	+	11.8621i	−0.597840	+	0.536973i
$489$		0			0
$490$	−5.70912	−	1.63959i	−0.257912	−	0.0740690i
$491$	−13.0738			−0.590012			−0.295006	−	0.955495i	$-0.595322\pi$
$491$	−13.0738			−0.590012			−0.295006	+	0.955495i	$0.595322\pi$
$492$		0			0
$493$	−22.8695			−1.02999
$494$	−0.0306964	−	0.00881561i	−0.00138110	−	0.000396633i
$495$		0			0
$496$	−21.2873	+	10.3395i	−0.955827	+	0.464258i
$497$			25.7882i			1.15676i
$498$		0			0
$499$			18.3461i			0.821285i	0.911796	+	0.410642i	$0.134696\pi$
$499$			18.3461i			0.821285i	−0.911796	+	0.410642i	$0.865304\pi$
$500$	1.06122	−	1.69523i	0.0474593	−	0.0758130i
$501$		0			0
$502$	−1.93550	+	6.73951i	−0.0863856	+	0.300799i
$503$	17.1874			0.766347			0.383174	−	0.923676i	$-0.374831\pi$
$503$	17.1874			0.766347			0.383174	+	0.923676i	$0.374831\pi$
$504$		0			0
$505$	8.17796			0.363914
$506$	−0.338307	+	1.17800i	−0.0150396	+	0.0523686i
$507$		0			0
$508$	−0.374984	+	0.599012i	−0.0166372	+	0.0265768i
$509$			11.5031i			0.509867i	0.966959	+	0.254933i	$0.0820535\pi$
$509$			11.5031i			0.509867i	−0.966959	+	0.254933i	$0.917946\pi$
$510$		0			0
$511$		−	7.21136i		−	0.319012i
$512$	13.2327	+	18.3547i	0.584810	+	0.811171i
$513$		0			0
$514$	−9.22441	−	2.64913i	−0.406871	−	0.116848i
$515$	8.33846			0.367436
$516$		0			0
$517$	44.7007			1.96593
$518$	1.44263	+	0.414304i	0.0633854	+	0.0182035i
$519$		0			0
$520$	−0.269134	−	0.299641i	−0.0118023	−	0.0131401i
$521$			14.3960i			0.630700i	0.948975	+	0.315350i	$0.102122\pi$
$521$			14.3960i			0.630700i	−0.948975	+	0.315350i	$0.897878\pi$
$522$		0			0
$523$		−	18.3747i		−	0.803469i	−0.915756	−	0.401735i	$-0.868407\pi$
$523$		−	18.3747i		−	0.803469i	0.915756	−	0.401735i	$-0.131593\pi$
$524$	5.07664	+	3.17800i	0.221774	+	0.138832i
$525$		0			0
$526$	−5.12858	+	17.8580i	−0.223617	+	0.778645i
$527$	−41.9937			−1.82928
$528$		0			0
$529$	−22.9657			−0.998507
$530$	−2.83905	+	9.88570i	−0.123320	+	0.429407i
$531$		0			0
$532$	0.449857	+	0.281613i	0.0195038	+	0.0122095i
$533$		−	1.53945i		−	0.0666811i
$534$		0			0
$535$			16.4383i			0.710689i
$536$	15.9587	+	17.7676i	0.689310	+	0.767444i
$537$		0			0
$538$	−18.1852	−	5.22255i	−0.784019	−	0.225160i
$539$	19.6443			0.846140
$540$		0			0
$541$	44.3078			1.90494			0.952470	−	0.304633i	$-0.0985337\pi$
$541$	44.3078			1.90494			0.952470	+	0.304633i	$0.0985337\pi$
$542$	−30.0634	−	8.63383i	−1.29134	−	0.370855i
$543$		0			0
$544$	6.89157	+	39.5559i	0.295474	+	1.69595i
$545$		−	17.8541i		−	0.764785i
$546$		0			0
$547$		−	6.78472i		−	0.290094i	−0.989425	−	0.145047i	$-0.953667\pi$
$547$		−	6.78472i		−	0.290094i	0.989425	−	0.145047i	$-0.0463333\pi$
$548$	8.12702	−	12.9824i	0.347169	−	0.554579i
$549$		0			0
$550$	−1.82576	+	6.35739i	−0.0778507	+	0.271080i
$551$	−0.510981			−0.0217685
$552$		0			0
$553$	23.2491			0.988652
$554$	−3.02777	+	10.5429i	−0.128638	+	0.447923i
$555$		0			0
$556$	−10.3037	+	16.4594i	−0.436974	+	0.698036i
$557$		−	4.60175i		−	0.194983i	−0.995236	−	0.0974913i	$-0.968918\pi$
$557$		−	4.60175i		−	0.194983i	0.995236	−	0.0974913i	$-0.0310818\pi$
$558$		0			0
$559$			1.19553i			0.0505657i
$560$	2.92424	+	6.02051i	0.123572	+	0.254413i
$561$		0			0
$562$	26.1926	+	7.52218i	1.10487	+	0.317304i
$563$	−18.5156			−0.780339			−0.390169	−	0.920743i	$-0.627584\pi$
$563$	−18.5156			−0.780339			−0.390169	+	0.920743i	$0.627584\pi$
$564$		0			0
$565$	0.164278			0.00691124
$566$	−27.3728	−	7.86113i	−1.15057	−	0.330428i
$567$		0			0
$568$	−32.4302	+	29.1284i	−1.36074	+	1.22220i
$569$		−	17.8082i		−	0.746559i	−0.927719	−	0.373280i	$-0.878233\pi$
$569$		−	17.8082i		−	0.746559i	0.927719	−	0.373280i	$-0.121767\pi$
$570$		0			0
$571$		−	27.2209i		−	1.13916i	−0.821937	−	0.569579i	$-0.807106\pi$
$571$		−	27.2209i		−	1.13916i	0.821937	−	0.569579i	$-0.192894\pi$
$572$	1.12903	+	0.706780i	0.0472072	+	0.0295520i
$573$		0			0
$574$	−7.06156	+	24.5887i	−0.294744	+	1.02631i
$575$	0.185297			0.00772740
$576$		0			0
$577$	−0.104229			−0.00433911			−0.00216956	−	0.999998i	$-0.500691\pi$
$577$	−0.104229			−0.00433911			−0.00216956	+	0.999998i	$0.500691\pi$
$578$	−13.0304	+	45.3726i	−0.541994	+	1.88725i
$579$		0			0
$580$	−5.46206	−	3.41928i	−0.226800	−	0.141978i
$581$		−	10.9831i		−	0.455657i
$582$		0			0
$583$		−	34.0154i		−	1.40877i
$584$	9.06871	−	8.14542i	0.375266	−	0.337060i
$585$		0			0
$586$	−1.70207	−	0.488812i	−0.0703118	−	0.0201926i
$587$	−26.2935			−1.08525			−0.542625	−	0.839975i	$-0.682570\pi$
$587$	−26.2935			−1.08525			−0.542625	+	0.839975i	$0.682570\pi$
$588$		0			0
$589$	−0.938279			−0.0386611
$590$	8.79092	+	2.52464i	0.361916	+	0.103938i
$591$		0			0
$592$	1.10847	+	2.28216i	0.0455580	+	0.0937960i
$593$		−	42.9299i		−	1.76292i	−0.472261	−	0.881459i	$-0.656562\pi$
$593$		−	42.9299i		−	1.76292i	0.472261	−	0.881459i	$-0.343438\pi$
$594$		0			0
$595$			11.8768i			0.486899i
$596$	−2.66490	+	4.25700i	−0.109159	+	0.174373i
$597$		0			0
$598$	0.0103001	−	0.0358656i	0.000421204	−	0.00146665i
$599$	−31.9413			−1.30509			−0.652543	−	0.757752i	$-0.726298\pi$
$599$	−31.9413			−1.30509			−0.652543	+	0.757752i	$0.726298\pi$
$600$		0			0
$601$	24.1690			0.985873			0.492936	−	0.870065i	$-0.335924\pi$
$601$	24.1690			0.985873			0.492936	+	0.870065i	$0.335924\pi$
$602$	5.48399	−	19.0955i	0.223511	−	0.778275i
$603$		0			0
$604$	−3.86818	+	6.17916i	−0.157394	+	0.251426i
$605$		−	10.8749i		−	0.442128i
$606$		0			0
$607$			10.4954i			0.425994i	0.977053	+	0.212997i	$0.0683224\pi$
$607$			10.4954i			0.425994i	−0.977053	+	0.212997i	$0.931678\pi$
$608$	0.153981	+	0.883810i	0.00624474	+	0.0358432i
$609$		0			0
$610$	−8.53108	−	2.45002i	−0.345413	−	0.0991982i
$611$	−1.36096			−0.0550586
$612$		0			0
$613$	−2.69967			−0.109039			−0.0545193	−	0.998513i	$-0.517363\pi$
$613$	−2.69967			−0.109039			−0.0545193	+	0.998513i	$0.517363\pi$
$614$	−14.2124	−	4.08161i	−0.573564	−	0.164720i
$615$		0			0
$616$	−14.7913	−	16.4679i	−0.595958	−	0.663511i
$617$			13.1231i			0.528317i	0.964479	+	0.264159i	$0.0850942\pi$
$617$			13.1231i			0.528317i	−0.964479	+	0.264159i	$0.914906\pi$
$618$		0			0
$619$			6.41600i			0.257881i	0.991652	+	0.128940i	$0.0411576\pi$
$619$			6.41600i			0.257881i	−0.991652	+	0.128940i	$0.958842\pi$
$620$	−10.0296	−	6.27858i	−0.402799	−	0.252154i
$621$		0			0
$622$	6.78821	−	23.6369i	0.272182	−	0.947752i
$623$	−18.5383			−0.742721
$624$		0			0
$625$	1.00000			0.0400000
$626$	−6.39748	+	22.2763i	−0.255695	+	0.890341i
$627$		0			0
$628$	28.7323	+	17.9866i	1.14654	+	0.717743i
$629$			4.50204i			0.179508i
$630$		0			0
$631$		−	38.2596i		−	1.52309i	−0.648111	−	0.761546i	$-0.724441\pi$
$631$		−	38.2596i		−	1.52309i	0.648111	−	0.761546i	$-0.275559\pi$
$632$	26.2605	+	29.2371i	1.04458	+	1.16299i
$633$		0			0
$634$	−17.6410	−	5.06628i	−0.700615	−	0.201208i
$635$	−0.353351			−0.0140223
$636$		0			0
$637$	−0.598092			−0.0236973
$638$	20.4836	+	5.88263i	0.810955	+	0.232896i
$639$		0			0
$640$	−4.26814	+	10.4777i	−0.168713	+	0.414169i
$641$		−	11.6381i		−	0.459678i	−0.973229	−	0.229839i	$-0.926180\pi$
$641$		−	11.6381i		−	0.459678i	0.973229	−	0.229839i	$-0.0738199\pi$
$642$		0			0
$643$			10.2928i			0.405909i	0.979188	+	0.202955i	$0.0650544\pi$
$643$			10.2928i			0.405909i	−0.979188	+	0.202955i	$0.934946\pi$
$644$	−0.329035	+	0.525611i	−0.0129658	+	0.0207120i
$645$		0			0
$646$	−0.439417	+	1.53007i	−0.0172886	+	0.0601999i
$647$	2.32166			0.0912740			0.0456370	−	0.998958i	$-0.485468\pi$
$647$	2.32166			0.0912740			0.0456370	+	0.998958i	$0.485468\pi$
$648$		0			0
$649$	−30.2483			−1.18735
$650$	0.0555873	−	0.193558i	0.00218031	−	0.00759196i
$651$		0			0
$652$	8.18642	−	13.0772i	0.320605	−	0.512144i
$653$		−	17.7803i		−	0.695796i	−0.937532	−	0.347898i	$-0.886896\pi$
$653$		−	17.7803i		−	0.695796i	0.937532	−	0.347898i	$-0.113104\pi$
$654$		0			0
$655$			2.99466i			0.117011i
$656$	−38.8980	+	18.8933i	−1.51871	+	0.737658i
$657$		0			0
$658$	21.7378	+	6.24281i	0.847427	+	0.243370i
$659$	19.4318			0.756957			0.378478	−	0.925610i	$-0.376447\pi$
$659$	19.4318			0.756957			0.378478	+	0.925610i	$0.376447\pi$
$660$		0			0
$661$	6.73746			0.262057			0.131028	−	0.991379i	$-0.458172\pi$
$661$	6.73746			0.262057			0.131028	+	0.991379i	$0.458172\pi$
$662$	−0.149562	−	0.0429524i	−0.00581291	−	0.00166939i
$663$		0			0
$664$	13.8119	−	12.4057i	0.536007	−	0.481436i
$665$			0.265366i			0.0102905i
$666$		0			0
$667$		−	0.597029i		−	0.0231170i
$668$	−34.7845	−	21.7753i	−1.34585	−	0.842511i
$669$		0			0
$670$	−3.29612	+	11.4773i	−0.127340	+	0.443405i
$671$	29.3543			1.13321
$672$		0			0
$673$	40.7962			1.57258			0.786290	−	0.617858i	$-0.211999\pi$
$673$	40.7962			1.57258			0.786290	+	0.617858i	$0.211999\pi$
$674$	−7.18513	+	25.0190i	−0.276761	+	0.963695i
$675$		0			0
$676$	22.0036	+	13.7744i	0.846293	+	0.529784i
$677$		−	50.2514i		−	1.93132i	−0.259815	−	0.965658i	$-0.583662\pi$
$677$		−	50.2514i		−	1.93132i	0.259815	−	0.965658i	$-0.416338\pi$
$678$		0			0
$679$			5.91116i			0.226850i
$680$	−14.9357	+	13.4151i	−0.572759	+	0.514446i
$681$		0			0
$682$	37.6127	+	10.8019i	1.44026	+	0.413625i
$683$	−27.9871			−1.07090			−0.535448	−	0.844568i	$-0.679857\pi$
$683$	−27.9871			−1.07090			−0.535448	+	0.844568i	$0.679857\pi$
$684$		0			0
$685$	7.65817			0.292604
$686$	25.4740	+	7.31581i	0.972603	+	0.279319i
$687$		0			0
$688$	30.2080	−	14.6724i	1.15167	−	0.559382i
$689$			1.03563i			0.0394545i
$690$		0			0
$691$		−	16.7968i		−	0.638980i	−0.947590	−	0.319490i	$-0.896488\pi$
$691$		−	16.7968i		−	0.638980i	0.947590	−	0.319490i	$-0.103512\pi$
$692$	4.42373	−	7.06661i	0.168165	−	0.268632i
$693$		0			0
$694$	1.15686	−	4.02824i	0.0439138	−	0.152910i
$695$	−9.70927			−0.368293
$696$		0			0
$697$	−76.7346			−2.90653
$698$	9.80248	−	34.1327i	0.371029	−	1.29194i
$699$		0			0
$700$	−1.77572	+	2.83659i	−0.0671160	+	0.107213i
$701$		−	37.5112i		−	1.41678i	−0.705822	−	0.708389i	$-0.749422\pi$
$701$		−	37.5112i		−	1.41678i	0.705822	−	0.708389i	$-0.250578\pi$
$702$		0			0
$703$			0.100591i			0.00379384i
$704$	4.00220	−	37.2018i	0.150839	−	1.40210i
$705$		0			0
$706$	−41.0609	−	11.7922i	−1.54535	−	0.443803i
$707$	−13.6840			−0.514640
$708$		0			0
$709$	−33.2804			−1.24987			−0.624936	−	0.780676i	$-0.714875\pi$
$709$	−33.2804			−1.24987			−0.624936	+	0.780676i	$0.714875\pi$
$710$	−20.9488	−	6.01621i	−0.786193	−	0.225784i
$711$		0			0
$712$	−20.9395	−	23.3130i	−0.784740	−	0.873691i
$713$		−	1.09628i		−	0.0410561i
$714$		0			0
$715$			0.666006i			0.0249072i
$716$	−24.7162	−	15.4725i	−0.923690	−	0.578234i
$717$		0			0
$718$	5.78618	−	20.1478i	0.215938	−	0.751908i
$719$	−48.1986			−1.79751			−0.898753	−	0.438456i	$-0.855526\pi$
$719$	−48.1986			−1.79751			−0.898753	+	0.438456i	$0.855526\pi$
$720$		0			0
$721$	−13.9526			−0.519621
$722$	7.40711	−	25.7919i	0.275664	−	0.959877i
$723$		0			0
$724$	2.43471	+	1.52414i	0.0904853	+	0.0566442i
$725$		−	3.22202i		−	0.119663i
$726$		0			0
$727$		−	42.7566i		−	1.58576i	−0.609381	−	0.792878i	$-0.708582\pi$
$727$		−	42.7566i		−	1.58576i	0.609381	−	0.792878i	$-0.291418\pi$
$728$	0.450337	+	0.501383i	0.0166906	+	0.0185825i
$729$		0			0
$730$	5.85807	+	1.68236i	0.216817	+	0.0622670i
$731$	59.5918			2.20408
$732$		0			0
$733$	45.8724			1.69434			0.847168	−	0.531326i	$-0.178306\pi$
$733$	45.8724			1.69434			0.847168	+	0.531326i	$0.178306\pi$
$734$	9.54118	+	2.74011i	0.352171	+	0.101139i
$735$		0			0
$736$	−1.03264	+	0.179910i	−0.0380636	+	0.00663158i
$737$		−	39.4917i		−	1.45469i
$738$		0			0
$739$			2.47344i			0.0909869i	0.998965	+	0.0454935i	$0.0144860\pi$
$739$			2.47344i			0.0909869i	−0.998965	+	0.0454935i	$0.985514\pi$
$740$	−0.673111	+	1.07525i	−0.0247440	+	0.0395269i
$741$		0			0
$742$	4.75052	−	16.5415i	0.174397	−	0.607259i
$743$	21.6982			0.796031			0.398016	−	0.917379i	$-0.369699\pi$
$743$	21.6982			0.796031			0.398016	+	0.917379i	$0.369699\pi$
$744$		0			0
$745$	−2.51116			−0.0920018
$746$	−6.14594	+	21.4005i	−0.225019	+	0.783527i
$747$		0			0
$748$	35.2297	−	56.2771i	1.28813	−	2.05769i
$749$		−	27.5058i		−	1.00504i
$750$		0			0
$751$		−	50.9055i		−	1.85757i	−0.370623	−	0.928784i	$-0.620856\pi$
$751$		−	50.9055i		−	1.85757i	0.370623	−	0.928784i	$-0.379144\pi$
$752$	16.7027	+	34.3880i	0.609084	+	1.25400i
$753$		0			0
$754$	−0.623646	−	0.179103i	−0.0227119	−	0.00652255i
$755$	−3.64503			−0.132656
$756$		0			0
$757$	5.47413			0.198961			0.0994803	−	0.995040i	$-0.468282\pi$
$757$	5.47413			0.198961			0.0994803	+	0.995040i	$0.468282\pi$
$758$	3.28990	+	0.944817i	0.119495	+	0.0343173i
$759$		0			0
$760$	−0.333714	+	0.299738i	−0.0121051	+	0.0108726i
$761$		−	31.7356i		−	1.15042i	−0.818007	−	0.575208i	$-0.804921\pi$
$761$		−	31.7356i		−	1.15042i	0.818007	−	0.575208i	$-0.195079\pi$
$762$		0			0
$763$			29.8749i			1.08154i
$764$	22.0211	+	13.7853i	0.796697	+	0.498736i
$765$		0			0
$766$	−3.74421	+	13.0375i	−0.135284	+	0.471065i
$767$	0.920943			0.0332533
$768$		0			0
$769$	8.46048			0.305093			0.152546	−	0.988296i	$-0.451253\pi$
$769$	8.46048			0.305093			0.152546	+	0.988296i	$0.451253\pi$
$770$	3.05501	−	10.6377i	0.110095	−	0.383356i
$771$		0			0
$772$	12.6955	+	7.94744i	0.456921	+	0.286035i
$773$			6.99215i			0.251490i	0.992063	+	0.125745i	$0.0401322\pi$
$773$			6.99215i			0.251490i	−0.992063	+	0.125745i	$0.959868\pi$
$774$		0			0
$775$		−	5.91637i		−	0.212522i
$776$	−7.43363	+	6.67681i	−0.266852	+	0.239684i
$777$		0			0
$778$	31.1365	+	8.94200i	1.11630	+	0.320586i
$779$	−1.71451			−0.0614285
$780$		0			0
$781$	72.0818			2.57929
$782$	−1.78773	−	0.513414i	−0.0639292	−	0.0183596i
$783$		0			0
$784$	7.34021	+	15.1122i	0.262151	+	0.539723i
$785$			16.9489i			0.604933i
$786$		0			0
$787$			12.2962i			0.438311i	0.975690	+	0.219155i	$0.0703302\pi$
$787$			12.2962i			0.438311i	−0.975690	+	0.219155i	$0.929670\pi$
$788$	13.7346	−	21.9401i	0.489275	−	0.781583i
$789$		0			0
$790$	−5.42386	+	18.8861i	−0.192972	+	0.671939i
$791$	−0.274883			−0.00977373
$792$		0			0
$793$	−0.893722			−0.0317370
$794$	−14.4274	+	50.2368i	−0.512008	+	1.78284i
$795$		0			0
$796$	11.6837	−	18.6639i	0.414119	−	0.661526i
$797$		−	5.45171i		−	0.193110i	−0.995328	−	0.0965548i	$-0.969218\pi$
$797$		−	5.45171i		−	0.193110i	0.995328	−	0.0965548i	$-0.0307823\pi$
$798$		0			0
$799$			67.8376i			2.39992i
$800$	−5.57291	+	0.970932i	−0.197032	+	0.0343276i
$801$		0			0
$802$	22.6062	+	6.49222i	0.798254	+	0.229248i
$803$	−20.1568			−0.711319
$804$		0			0
$805$	−0.310053			−0.0109279
$806$	−1.14516	−	0.328875i	−0.0403365	−	0.0115841i
$807$		0			0
$808$	−15.4564	−	17.2084i	−0.543756	−	0.605391i
$809$			14.8748i			0.522970i	0.965207	+	0.261485i	$0.0842122\pi$
$809$			14.8748i			0.522970i	−0.965207	+	0.261485i	$0.915788\pi$
$810$		0			0
$811$		−	1.39680i		−	0.0490483i	−0.999699	−	0.0245241i	$-0.992193\pi$
$811$		−	1.39680i		−	0.0490483i	0.999699	−	0.0245241i	$-0.00780706\pi$
$812$	9.13955	+	5.72141i	0.320735	+	0.200782i
$813$		0			0
$814$	1.15804	−	4.03236i	0.0405893	−	0.141334i
$815$	7.71414			0.270214
$816$		0			0
$817$	1.33148			0.0465826
$818$	−10.3650	+	36.0915i	−0.362404	+	1.26191i
$819$		0			0
$820$	−18.3270	−	11.4728i	−0.640005	−	0.400647i
$821$		−	48.9515i		−	1.70842i	−0.519928	−	0.854210i	$-0.674041\pi$
$821$		−	48.9515i		−	1.70842i	0.519928	−	0.854210i	$-0.325959\pi$
$822$		0			0
$823$		−	28.9724i		−	1.00991i	−0.863144	−	0.504957i	$-0.831508\pi$
$823$		−	28.9724i		−	1.00991i	0.863144	−	0.504957i	$-0.168492\pi$
$824$	−15.7598	−	17.5462i	−0.549018	−	0.611250i
$825$		0			0
$826$	−14.7097	−	4.22442i	−0.511814	−	0.146986i
$827$	3.75398			0.130539			0.0652694	−	0.997868i	$-0.479209\pi$
$827$	3.75398			0.130539			0.0652694	+	0.997868i	$0.479209\pi$
$828$		0			0
$829$	−5.66130			−0.196625			−0.0983126	−	0.995156i	$-0.531345\pi$
$829$	−5.66130			−0.196625			−0.0983126	+	0.995156i	$0.531345\pi$
$830$	8.92203	+	2.56229i	0.309688	+	0.0889385i
$831$		0			0
$832$	−0.121851	+	1.13265i	−0.00422444	+	0.0392676i
$833$			29.8121i			1.03293i
$834$		0			0
$835$		−	20.5191i		−	0.710091i
$836$	0.787149	−	1.25742i	0.0272241	−	0.0434887i
$837$		0			0
$838$	1.27794	−	4.44986i	0.0441458	−	0.153718i
$839$	−24.4974			−0.845744			−0.422872	−	0.906189i	$-0.638978\pi$
$839$	−24.4974			−0.845744			−0.422872	+	0.906189i	$0.638978\pi$
$840$		0			0
$841$	18.6186			0.642021
$842$	−0.329524	+	1.14742i	−0.0113562	+	0.0395427i
$843$		0			0
$844$	1.10265	−	1.76141i	0.0379548	−	0.0606302i
$845$			12.9797i			0.446516i
$846$		0			0
$847$			18.1968i			0.625249i
$848$	26.1678	−	12.7100i	0.898606	−	0.436465i
$849$		0			0
$850$	−9.64795	−	2.77077i	−0.330922	−	0.0950366i
$851$	−0.117530			−0.00402886
$852$		0			0
$853$	30.6539			1.04957			0.524785	−	0.851235i	$-0.324146\pi$
$853$	30.6539			1.04957			0.524785	+	0.851235i	$0.324146\pi$
$854$	14.2749	+	4.09956i	0.488476	+	0.140284i
$855$		0			0
$856$	34.5902	−	31.0686i	1.18227	−	1.06190i
$857$			20.5092i			0.700580i	0.936641	+	0.350290i	$0.113917\pi$
$857$			20.5092i			0.700580i	−0.936641	+	0.350290i	$0.886083\pi$
$858$		0			0
$859$		−	16.8096i		−	0.573535i	−0.958000	−	0.286768i	$-0.907419\pi$
$859$		−	16.8096i		−	0.573535i	0.958000	−	0.286768i	$-0.0925807\pi$
$860$	14.2327	+	8.90972i	0.485330	+	0.303819i
$861$		0			0
$862$	−1.14957	+	4.00286i	−0.0391545	+	0.136338i
$863$	−15.0807			−0.513351			−0.256676	−	0.966498i	$-0.582627\pi$
$863$	−15.0807			−0.513351			−0.256676	+	0.966498i	$0.582627\pi$
$864$		0			0
$865$	4.16852			0.141734
$866$	1.80289	−	6.27777i	0.0612648	−	0.213327i
$867$		0			0
$868$	16.7823	+	10.5058i	0.569629	+	0.356591i
$869$		−	64.9847i		−	2.20445i
$870$		0			0
$871$			1.20237i			0.0407407i
$872$	−37.5694	+	33.7445i	−1.27226	+	1.14273i
$873$		0			0
$874$	−0.0399439	−	0.0114714i	−0.00135112	−	0.000388025i
$875$	−1.67328			−0.0565672
$876$		0			0
$877$	15.0524			0.508284			0.254142	−	0.967167i	$-0.418207\pi$
$877$	15.0524			0.508284			0.254142	+	0.967167i	$0.418207\pi$
$878$	−46.3360	−	13.3071i	−1.56376	−	0.449093i
$879$		0			0
$880$	16.8282	−	8.17370i	0.567280	−	0.275535i
$881$			26.5731i			0.895272i	0.894216	+	0.447636i	$0.147734\pi$
$881$			26.5731i			0.895272i	−0.894216	+	0.447636i	$0.852266\pi$
$882$		0			0
$883$		−	26.3817i		−	0.887816i	−0.896072	−	0.443908i	$-0.853592\pi$
$883$		−	26.3817i		−	0.887816i	0.896072	−	0.443908i	$-0.146408\pi$
$884$	−1.07261	+	1.71342i	−0.0360757	+	0.0576284i
$885$		0			0
$886$	5.45657	−	19.0001i	0.183317	−	0.638319i
$887$	17.9266			0.601916			0.300958	−	0.953637i	$-0.402694\pi$
$887$	17.9266			0.601916			0.300958	+	0.953637i	$0.402694\pi$
$888$		0			0
$889$	0.591255			0.0198301
$890$	4.32486	−	15.0594i	0.144970	−	0.504792i
$891$		0			0
$892$	17.2241	−	27.5144i	0.576707	−	0.921250i
$893$			1.51572i			0.0507216i
$894$		0			0
$895$		−	14.5799i		−	0.487351i
$896$	7.14179	−	17.5322i	0.238591	−	0.585709i
$897$		0			0
$898$	−26.9572	−	7.74176i	−0.899573	−	0.258346i
$899$	−19.0626			−0.635774
$900$		0			0
$901$	51.6216			1.71976
$902$	68.7291	+	19.7381i	2.28843	+	0.657208i
$903$		0			0
$904$	−0.310488	−	0.345682i	−0.0103267	−	0.0114972i
$905$			1.43621i			0.0477413i
$906$		0			0
$907$			26.2767i			0.872504i	0.899825	+	0.436252i	$0.143694\pi$
$907$			26.2767i			0.872504i	−0.899825	+	0.436252i	$0.856306\pi$
$908$	−33.9645	−	21.2619i	−1.12715	−	0.705602i
$909$		0			0
$910$	−0.0930130	+	0.323876i	−0.00308335	+	0.0107364i
$911$	−24.6465			−0.816575			−0.408287	−	0.912853i	$-0.633874\pi$
$911$	−24.6465			−0.816575			−0.408287	+	0.912853i	$0.633874\pi$
$912$		0			0
$913$	−30.6995			−1.01600
$914$	−13.5140	+	47.0564i	−0.447003	+	1.55649i
$915$		0			0
$916$	−3.17309	−	1.98637i	−0.104842	−	0.0656314i
$917$		−	5.01091i		−	0.165475i
$918$		0			0
$919$		−	12.2149i		−	0.402933i	−0.979495	−	0.201467i	$-0.935429\pi$
$919$		−	12.2149i		−	0.402933i	0.979495	−	0.201467i	$-0.0645707\pi$
$920$	−0.350213	−	0.389910i	−0.0115462	−	0.0128549i
$921$		0			0
$922$	−0.614629	−	0.176514i	−0.0202417	−	0.00581317i
$923$	−2.19461			−0.0722364
$924$		0			0
$925$	−0.634278			−0.0208549
$926$	51.0524	+	14.6616i	1.67769	+	0.481810i
$927$		0			0
$928$	3.12836	+	17.9560i	0.102693	+	0.589435i
$929$		−	14.1161i		−	0.463133i	−0.972819	−	0.231567i	$-0.925615\pi$
$929$		−	14.1161i		−	0.463133i	0.972819	−	0.231567i	$-0.0743851\pi$
$930$		0			0
$931$			0.666102i			0.0218306i
$932$	8.55909	−	13.6726i	0.280362	−	0.447860i
$933$		0			0
$934$	11.9149	−	41.4882i	0.389867	−	1.35754i
$935$	33.1973			1.08567
$936$		0			0
$937$	−16.6420			−0.543669			−0.271834	−	0.962344i	$-0.587630\pi$
$937$	−16.6420			−0.543669			−0.271834	+	0.962344i	$0.587630\pi$
$938$	5.51533	−	19.2047i	0.180082	−	0.627054i
$939$		0			0
$940$	−10.1426	+	16.2020i	−0.330814	+	0.528453i
$941$			13.9566i			0.454971i	0.973781	+	0.227485i	$0.0730504\pi$
$941$			13.9566i			0.454971i	−0.973781	+	0.227485i	$0.926950\pi$
$942$		0			0
$943$		−	2.00322i		−	0.0652339i
$944$	−11.3025	−	23.2699i	−0.367864	−	0.757369i
$945$		0			0
$946$	−53.3748	−	15.3286i	−1.73536	−	0.498374i
$947$	−37.9845			−1.23433			−0.617165	−	0.786834i	$-0.711719\pi$
$947$	−37.9845			−1.23433			−0.617165	+	0.786834i	$0.711719\pi$
$948$		0			0
$949$	0.613696			0.0199214
$950$	−0.215567	−	0.0619082i	−0.00699393	−	0.00200857i
$951$		0			0
$952$	24.9916	−	22.4472i	0.809983	−	0.727518i
$953$			3.47463i			0.112554i	0.998415	+	0.0562772i	$0.0179230\pi$
$953$			3.47463i			0.112554i	−0.998415	+	0.0562772i	$0.982077\pi$
$954$		0			0
$955$			12.9901i			0.420348i
$956$	−29.4375	−	18.4280i	−0.952078	−	0.596005i
$957$		0			0
$958$	−0.785660	+	2.73571i	−0.0253835	+	0.0883867i
$959$	−12.8143			−0.413794
$960$		0			0
$961$	−4.00338			−0.129141
$962$	−0.0352578	+	0.122769i	−0.00113676	+	0.00395825i
$963$		0			0
$964$	−4.50263	−	2.81867i	−0.145020	−	0.0907832i
$965$			7.48894i			0.241078i
$966$		0			0
$967$			15.5757i			0.500880i	0.968132	+	0.250440i	$0.0805753\pi$
$967$			15.5757i			0.500880i	−0.968132	+	0.250440i	$0.919425\pi$
$968$	−22.8835	+	20.5537i	−0.735504	+	0.660622i
$969$		0			0
$970$	−4.80187	−	1.37903i	−0.154179	−	0.0442781i
$971$	−54.2908			−1.74228			−0.871138	−	0.491038i	$-0.836618\pi$
$971$	−54.2908			−1.74228			−0.871138	+	0.491038i	$0.836618\pi$
$972$		0			0
$973$	16.2463			0.520833
$974$	−11.5316	−	3.31171i	−0.369495	−	0.106114i
$975$		0			0
$976$	10.9684	+	22.5820i	0.351090	+	0.722834i
$977$		−	3.38426i		−	0.108272i	−0.998534	−	0.0541361i	$-0.982760\pi$
$977$		−	3.38426i		−	0.108272i	0.998534	−	0.0541361i	$-0.0172405\pi$
$978$		0			0
$979$			51.8173i			1.65609i
$980$	−4.45728	+	7.12020i	−0.142383	+	0.227446i
$981$		0			0
$982$	−5.10355	+	17.7708i	−0.162861	+	0.567090i
$983$	28.8915			0.921495			0.460747	−	0.887531i	$-0.347581\pi$
$983$	28.8915			0.921495			0.460747	+	0.887531i	$0.347581\pi$
$984$		0			0
$985$	12.9422			0.412374
$986$	−8.92746	+	31.0859i	−0.284308	+	0.989976i
$987$		0			0
$988$	−0.0239656	+	0.0382834i	−0.000762447	+	0.00121796i
$989$			1.55570i			0.0494682i
$990$		0			0
$991$		−	21.1222i		−	0.670968i	−0.942046	−	0.335484i	$-0.891100\pi$
$991$		−	21.1222i		−	0.670968i	0.942046	−	0.335484i	$-0.108900\pi$
$992$	5.74439	+	32.9714i	0.182384	+	1.04684i
$993$		0			0
$994$	35.0531	+	10.0668i	1.11182	+	0.319300i
$995$	11.0097			0.349030
$996$		0			0
$997$	12.3772			0.391989			0.195995	−	0.980605i	$-0.437207\pi$
$997$	12.3772			0.391989			0.195995	+	0.980605i	$0.437207\pi$
$998$	24.9373	+	7.16168i	0.789377	+	0.226699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.29		48
3.2	odd	2	inner	1620.2.e.b.971.20		48
4.3	odd	2	inner	1620.2.e.b.971.19		48
9.2	odd	6		540.2.q.a.71.23		48
9.4	even	3		540.2.q.a.251.19		48
9.5	odd	6		180.2.q.a.11.6	yes	48
9.7	even	3		180.2.q.a.131.2	yes	48
12.11	even	2	inner	1620.2.e.b.971.30		48
36.7	odd	6		180.2.q.a.131.6	yes	48
36.11	even	6		540.2.q.a.71.19		48
36.23	even	6		180.2.q.a.11.2	✓	48
36.31	odd	6		540.2.q.a.251.23		48
45.7	odd	12		900.2.o.c.599.12		48
45.14	odd	6		900.2.r.f.551.19		48
45.23	even	12		900.2.o.c.299.6		48
45.32	even	12		900.2.o.b.299.19		48
45.34	even	6		900.2.r.f.851.23		48
45.43	odd	12		900.2.o.b.599.13		48
180.7	even	12		900.2.o.c.599.6		48
180.23	odd	12		900.2.o.c.299.12		48
180.43	even	12		900.2.o.b.599.19		48
180.59	even	6		900.2.r.f.551.23		48
180.79	odd	6		900.2.r.f.851.19		48
180.167	odd	12		900.2.o.b.299.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.2	✓	48	36.23	even	6
180.2.q.a.11.6	yes	48	9.5	odd	6
180.2.q.a.131.2	yes	48	9.7	even	3
180.2.q.a.131.6	yes	48	36.7	odd	6
540.2.q.a.71.19		48	36.11	even	6
540.2.q.a.71.23		48	9.2	odd	6
540.2.q.a.251.19		48	9.4	even	3
540.2.q.a.251.23		48	36.31	odd	6
900.2.o.b.299.13		48	180.167	odd	12
900.2.o.b.299.19		48	45.32	even	12
900.2.o.b.599.13		48	45.43	odd	12
900.2.o.b.599.19		48	180.43	even	12
900.2.o.c.299.6		48	45.23	even	12
900.2.o.c.299.12		48	180.23	odd	12
900.2.o.c.599.6		48	180.7	even	12
900.2.o.c.599.12		48	45.7	odd	12
900.2.r.f.551.19		48	45.14	odd	6
900.2.r.f.551.23		48	180.59	even	6
900.2.r.f.851.19		48	180.79	odd	6
900.2.r.f.851.23		48	45.34	even	6
1620.2.e.b.971.19		48	4.3	odd	2	inner
1620.2.e.b.971.20		48	3.2	odd	2	inner
1620.2.e.b.971.29		48	1.1	even	1	trivial
1620.2.e.b.971.30		48	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(0.390365 - 1.35927i) q^{2} +(-1.69523 - 1.06122i) q^{4} -1.00000i q^{5} +1.67328i q^{7} +(-2.10425 + 1.89001i) q^{8} +O(q^{10})\)	\(q+(0.390365 - 1.35927i) q^{2} +(-1.69523 - 1.06122i) q^{4} -1.00000i q^{5} +1.67328i q^{7} +(-2.10425 + 1.89001i) q^{8} +(-1.35927 - 0.390365i) q^{10} +4.67706 q^{11} -0.142398 q^{13} +(2.27444 + 0.653189i) q^{14} +(1.74761 + 3.59803i) q^{16} +7.09789i q^{17} +0.158590i q^{19} +(-1.06122 + 1.69523i) q^{20} +(1.82576 - 6.35739i) q^{22} -0.185297 q^{23} -1.00000 q^{25} +(-0.0555873 + 0.193558i) q^{26} +(1.77572 - 2.83659i) q^{28} +3.22202i q^{29} +5.91637i q^{31} +(5.57291 - 0.970932i) q^{32} +(9.64795 + 2.77077i) q^{34} +1.67328 q^{35} +0.634278 q^{37} +(0.215567 + 0.0619082i) q^{38} +(1.89001 + 2.10425i) q^{40} +10.8109i q^{41} -8.39571i q^{43} +(-7.92870 - 4.96341i) q^{44} +(-0.0723333 + 0.251868i) q^{46} +9.55743 q^{47} +4.20014 q^{49} +(-0.390365 + 1.35927i) q^{50} +(0.241398 + 0.151116i) q^{52} -7.27280i q^{53} -4.67706i q^{55} +(-3.16252 - 3.52099i) q^{56} +(4.37959 + 1.25776i) q^{58} -6.46738 q^{59} +6.27622 q^{61} +(8.04194 + 2.30954i) q^{62} +(0.855709 - 7.95410i) q^{64} +0.142398i q^{65} -8.44369i q^{67} +(7.53244 - 12.0326i) q^{68} +(0.653189 - 2.27444i) q^{70} +15.4118 q^{71} -4.30972 q^{73} +(0.247600 - 0.862156i) q^{74} +(0.168300 - 0.268847i) q^{76} +7.82603i q^{77} -13.8943i q^{79} +(3.59803 - 1.74761i) q^{80} +(14.6949 + 4.22020i) q^{82} -6.56384 q^{83} +7.09789 q^{85} +(-11.4120 - 3.27739i) q^{86} +(-9.84169 + 8.83971i) q^{88} +11.0790i q^{89} -0.238272i q^{91} +(0.314120 + 0.196641i) q^{92} +(3.73089 - 12.9911i) q^{94} +0.158590 q^{95} +3.53268 q^{97} +(1.63959 - 5.70912i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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