LMFDB - Embedded newform 624.2.cn.f.401.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, not 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			401.11
Character	$\chi$	$=$	624.401
Dual form			624.2.cn.f.305.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26859 + 1.17927i) q^{3} +(-1.56802 + 1.56802i) q^{5} +(0.418596 + 1.56222i) q^{7} +(0.218643 + 2.99202i) q^{9} +O(q^{10})$	\(q+(1.26859 + 1.17927i) q^{3} +(-1.56802 + 1.56802i) q^{5} +(0.418596 + 1.56222i) q^{7} +(0.218643 + 2.99202i) q^{9} +(0.781891 - 2.91806i) q^{11} +(-1.23090 + 3.38894i) q^{13} +(-3.83829 + 0.140055i) q^{15} +(-1.03846 + 1.79867i) q^{17} +(1.13167 - 0.303230i) q^{19} +(-1.31126 + 2.47546i) q^{21} +(-2.51856 - 4.36228i) q^{23} +0.0826334i q^{25} +(-3.25104 + 4.05349i) q^{27} +(-6.68935 + 3.86210i) q^{29} +(4.19633 + 4.19633i) q^{31} +(4.43308 - 2.77976i) q^{33} +(-3.10596 - 1.79323i) q^{35} +(1.42771 + 0.382554i) q^{37} +(-5.55798 + 2.84761i) q^{39} +(1.36535 + 0.365846i) q^{41} +(-4.27542 - 2.46841i) q^{43} +(-5.03438 - 4.34871i) q^{45} +(6.89160 + 6.89160i) q^{47} +(3.79686 - 2.19212i) q^{49} +(-3.43850 + 1.05715i) q^{51} -9.85591i q^{53} +(3.34955 + 5.80159i) q^{55} +(1.79321 + 0.949870i) q^{57} +(13.8606 - 3.71393i) q^{59} +(-5.63954 + 9.76798i) q^{61} +(-4.58268 + 1.59402i) q^{63} +(-3.38384 - 7.24399i) q^{65} +(1.67035 - 6.23384i) q^{67} +(1.94928 - 8.50401i) q^{69} +(1.21689 + 4.54151i) q^{71} +(11.7107 - 11.7107i) q^{73} +(-0.0974471 + 0.104828i) q^{75} +4.88595 q^{77} +2.81772 q^{79} +(-8.90439 + 1.30837i) q^{81} +(-7.24736 + 7.24736i) q^{83} +(-1.19202 - 4.44868i) q^{85} +(-13.0405 - 2.98913i) q^{87} +(-1.86361 + 6.95510i) q^{89} +(-5.80952 - 0.504343i) q^{91} +(0.374816 + 10.2720i) q^{93} +(-1.29901 + 2.24995i) q^{95} +(10.6203 - 2.84569i) q^{97} +(8.90184 + 1.70142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^7	$ 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.26859	+	1.17927i	0.732421	+	0.680852i
$3$	1.26859	+	1.17927i	0.732421	+	0.680852i
$4$		0			0
$5$	−1.56802	+	1.56802i	−0.701239	+	0.701239i	−0.964677	−	0.263437i	$-0.915144\pi$
$5$	−1.56802	+	1.56802i	−0.701239	+	0.701239i	0.263437	+	0.964677i	$0.415144\pi$
$6$		0			0
$7$	0.418596	+	1.56222i	0.158214	+	0.590464i	0.998809	+	0.0487989i	$0.0155394\pi$
$7$	0.418596	+	1.56222i	0.158214	+	0.590464i	−0.840594	+	0.541665i	$0.817794\pi$
$8$		0			0
$9$	0.218643	+	2.99202i	0.0728809	+	0.997341i
$10$		0			0
$11$	0.781891	−	2.91806i	0.235749	−	0.879827i	−0.742061	−	0.670332i	$-0.766151\pi$
$11$	0.781891	−	2.91806i	0.235749	−	0.879827i	0.977810	−	0.209495i	$-0.0671818\pi$
$12$		0			0
$13$	−1.23090	+	3.38894i	−0.341390	+	0.939922i
$13$	−1.23090	+	3.38894i	−0.341390	+	0.939922i
$14$		0			0
$15$	−3.83829	+	0.140055i	−0.991043	+	0.0361621i
$16$		0			0
$17$	−1.03846	+	1.79867i	−0.251864	+	0.436242i	−0.964039	−	0.265760i	$-0.914377\pi$
$17$	−1.03846	+	1.79867i	−0.251864	+	0.436242i	0.712175	+	0.702002i	$0.247710\pi$
$18$		0			0
$19$	1.13167	−	0.303230i	0.259623	−	0.0695657i	−0.126660	−	0.991946i	$-0.540426\pi$
$19$	1.13167	−	0.303230i	0.259623	−	0.0695657i	0.386283	+	0.922381i	$0.373759\pi$
$20$		0			0
$21$	−1.31126	+	2.47546i	−0.286139	+	0.540189i
$22$		0			0
$23$	−2.51856	−	4.36228i	−0.525157	−	0.909598i	−0.999571	−	0.0292962i	$-0.990673\pi$
$23$	−2.51856	−	4.36228i	−0.525157	−	0.909598i	0.474414	−	0.880302i	$-0.342660\pi$
$24$		0			0
$25$			0.0826334i			0.0165267i
$26$		0			0
$27$	−3.25104	+	4.05349i	−0.625662	+	0.780094i
$28$		0			0
$29$	−6.68935	+	3.86210i	−1.24218	+	0.717174i	−0.969538	−	0.244941i	$-0.921231\pi$
$29$	−6.68935	+	3.86210i	−1.24218	+	0.717174i	−0.272643	+	0.962115i	$0.587898\pi$
$30$		0			0
$31$	4.19633	+	4.19633i	0.753683	+	0.753683i	0.975165	−	0.221481i	$-0.0710892\pi$
$31$	4.19633	+	4.19633i	0.753683	+	0.753683i	−0.221481	+	0.975165i	$0.571089\pi$
$32$		0			0
$33$	4.43308	−	2.77976i	0.771700	−	0.483894i
$34$		0			0
$35$	−3.10596	−	1.79323i	−0.525003	−	0.303111i
$36$		0			0
$37$	1.42771	+	0.382554i	0.234714	+	0.0628915i	0.374259	−	0.927324i	$-0.377897\pi$
$37$	1.42771	+	0.382554i	0.234714	+	0.0628915i	−0.139545	+	0.990216i	$0.544564\pi$
$38$		0			0
$39$	−5.55798	+	2.84761i	−0.889989	+	0.455982i
$40$		0			0
$41$	1.36535	+	0.365846i	0.213232	+	0.0571355i	0.363854	−	0.931456i	$-0.381461\pi$
$41$	1.36535	+	0.365846i	0.213232	+	0.0571355i	−0.150621	+	0.988592i	$0.548127\pi$
$42$		0			0
$43$	−4.27542	−	2.46841i	−0.651995	−	0.376430i	0.137225	−	0.990540i	$-0.456182\pi$
$43$	−4.27542	−	2.46841i	−0.651995	−	0.376430i	−0.789220	+	0.614110i	$0.789515\pi$
$44$		0			0
$45$	−5.03438	−	4.34871i	−0.750481	−	0.648268i
$46$		0			0
$47$	6.89160	+	6.89160i	1.00524	+	1.00524i	0.999986	+	0.00525705i	$0.00167338\pi$
$47$	6.89160	+	6.89160i	1.00524	+	1.00524i	0.00525705	+	0.999986i	$0.498327\pi$
$48$		0			0
$49$	3.79686	−	2.19212i	0.542409	−	0.313160i
$50$		0			0
$51$	−3.43850	+	1.05715i	−0.481487	+	0.148030i
$52$		0			0
$53$		−	9.85591i		−	1.35381i	−0.736069	−	0.676907i	$-0.763320\pi$
$53$		−	9.85591i		−	1.35381i	0.736069	−	0.676907i	$-0.236680\pi$
$54$		0			0
$55$	3.34955	+	5.80159i	0.451653	+	0.782286i
$56$		0			0
$57$	1.79321	+	0.949870i	0.237517	+	0.125813i
$58$		0			0
$59$	13.8606	−	3.71393i	1.80449	−	0.483513i	0.809829	−	0.586666i	$-0.199560\pi$
$59$	13.8606	−	3.71393i	1.80449	−	0.483513i	0.994665	+	0.103154i	$0.0328934\pi$
$60$		0			0
$61$	−5.63954	+	9.76798i	−0.722070	+	1.25066i	0.238099	+	0.971241i	$0.423476\pi$
$61$	−5.63954	+	9.76798i	−0.722070	+	1.25066i	−0.960169	+	0.279420i	$0.909858\pi$
$62$		0			0
$63$	−4.58268	+	1.59402i	−0.577363	+	0.200827i
$64$		0			0
$65$	−3.38384	−	7.24399i	−0.419714	−	0.898506i
$66$		0			0
$67$	1.67035	−	6.23384i	0.204066	−	0.761585i	−0.785666	−	0.618651i	$-0.787680\pi$
$67$	1.67035	−	6.23384i	0.204066	−	0.761585i	0.989732	−	0.142934i	$-0.0456538\pi$
$68$		0			0
$69$	1.94928	−	8.50401i	0.234666	−	1.02376i
$70$		0			0
$71$	1.21689	+	4.54151i	0.144419	+	0.538978i	0.999781	+	0.0209472i	$0.00666819\pi$
$71$	1.21689	+	4.54151i	0.144419	+	0.538978i	−0.855362	+	0.518031i	$0.826665\pi$
$72$		0			0
$73$	11.7107	−	11.7107i	1.37063	−	1.37063i	0.511130	−	0.859504i	$-0.329227\pi$
$73$	11.7107	−	11.7107i	1.37063	−	1.37063i	0.859504	−	0.511130i	$-0.170773\pi$
$74$		0			0
$75$	−0.0974471	+	0.104828i	−0.0112522	+	0.0121045i
$76$		0			0
$77$	4.88595			0.556805
$78$		0			0
$79$	2.81772			0.317018			0.158509	−	0.987358i	$-0.449331\pi$
$79$	2.81772			0.317018			0.158509	+	0.987358i	$0.449331\pi$
$80$		0			0
$81$	−8.90439	+	1.30837i	−0.989377	+	0.145374i
$82$		0			0
$83$	−7.24736	+	7.24736i	−0.795501	+	0.795501i	−0.982382	−	0.186882i	$-0.940162\pi$
$83$	−7.24736	+	7.24736i	−0.795501	+	0.795501i	0.186882	+	0.982382i	$0.440162\pi$
$84$		0			0
$85$	−1.19202	−	4.44868i	−0.129293	−	0.482527i
$86$		0			0
$87$	−13.0405	−	2.98913i	−1.39809	−	0.320469i
$88$		0			0
$89$	−1.86361	+	6.95510i	−0.197543	+	0.737239i	0.794051	+	0.607851i	$0.207968\pi$
$89$	−1.86361	+	6.95510i	−0.197543	+	0.737239i	−0.991594	+	0.129388i	$0.958699\pi$
$90$		0			0
$91$	−5.80952	−	0.504343i	−0.609003	−	0.0528695i
$92$		0			0
$93$	0.374816	+	10.2720i	0.0388666	+	1.06516i
$94$		0			0
$95$	−1.29901	+	2.24995i	−0.133275	+	0.230840i
$96$		0			0
$97$	10.6203	−	2.84569i	1.07833	−	0.288936i	0.324416	−	0.945915i	$-0.394832\pi$
$97$	10.6203	−	2.84569i	1.07833	−	0.288936i	0.753910	+	0.656978i	$0.228166\pi$
$98$		0			0
$99$	8.90184	+	1.70142i	0.894669	+	0.170999i
$100$		0			0
$101$	4.73271	+	8.19730i	0.470923	+	0.815662i	0.999447	−	0.0332563i	$-0.0105878\pi$
$101$	4.73271	+	8.19730i	0.470923	+	0.815662i	−0.528524	+	0.848918i	$0.677254\pi$
$102$		0			0
$103$		−	14.2389i		−	1.40300i	−0.712671	−	0.701498i	$-0.752515\pi$
$103$		−	14.2389i		−	1.40300i	0.712671	−	0.701498i	$-0.247485\pi$
$104$		0			0
$105$	−1.82549	−	5.93764i	−0.178150	−	0.579454i
$106$		0			0
$107$	−1.98557	+	1.14637i	−0.191952	+	0.110824i	−0.592896	−	0.805279i	$-0.702016\pi$
$107$	−1.98557	+	1.14637i	−0.191952	+	0.110824i	0.400944	+	0.916103i	$0.368682\pi$
$108$		0			0
$109$	3.09877	+	3.09877i	0.296809	+	0.296809i	0.839763	−	0.542954i	$-0.182694\pi$
$109$	3.09877	+	3.09877i	0.296809	+	0.296809i	−0.542954	+	0.839763i	$0.682694\pi$
$110$		0			0
$111$	1.36005	+	2.16896i	0.129090	+	0.205869i
$112$		0			0
$113$	15.6225	+	9.01967i	1.46964	+	0.848499i	0.999420	−	0.0340476i	$-0.0108398\pi$
$113$	15.6225	+	9.01967i	1.46964	+	0.848499i	0.470224	+	0.882547i	$0.344173\pi$
$114$		0			0
$115$	10.7893	+	2.89098i	1.00611	+	0.269585i
$116$		0			0
$117$	−10.4089	−	2.94191i	−0.962303	−	0.271980i
$118$		0			0
$119$	−3.24462	−	0.869393i	−0.297434	−	0.0796972i
$120$		0			0
$121$	1.62258	+	0.936798i	0.147507	+	0.0851634i
$122$		0			0
$123$	1.30064	+	2.07423i	0.117275	+	0.187027i
$124$		0			0
$125$	−7.96967	−	7.96967i	−0.712829	−	0.712829i
$126$		0			0
$127$	15.9524	−	9.21015i	1.41555	−	0.817268i	0.419646	−	0.907688i	$-0.362154\pi$
$127$	15.9524	−	9.21015i	1.41555	−	0.817268i	0.995904	+	0.0904193i	$0.0288207\pi$
$128$		0			0
$129$	−2.51283	−	8.17328i	−0.221242	−	0.719617i
$130$		0			0
$131$		−	10.6125i		−	0.927215i	−0.886041	−	0.463608i	$-0.846555\pi$
$131$		−	10.6125i		−	0.927215i	0.886041	−	0.463608i	$-0.153445\pi$
$132$		0			0
$133$	0.947425	+	1.64099i	0.0821521	+	0.142292i
$134$		0			0
$135$	−1.25826	−	11.4536i	−0.108294	−	0.985772i
$136$		0			0
$137$	−12.5864	+	3.37252i	−1.07533	+	0.288134i	−0.752682	−	0.658384i	$-0.771240\pi$
$137$	−12.5864	+	3.37252i	−1.07533	+	0.288134i	−0.322650	+	0.946519i	$0.604574\pi$
$138$		0			0
$139$	−5.10962	+	8.85012i	−0.433392	+	0.750658i	−0.997163	−	0.0752738i	$-0.976017\pi$
$139$	−5.10962	+	8.85012i	−0.433392	+	0.750658i	0.563771	+	0.825931i	$0.309350\pi$
$140$		0			0
$141$	0.615557	+	16.8697i	0.0518392	+	1.42068i
$142$		0			0
$143$	8.92668	+	6.24161i	0.746486	+	0.521950i
$144$		0			0
$145$	4.43319	−	16.5449i	0.368156	−	1.37398i
$146$		0			0
$147$	7.40177	+	1.69663i	0.610487	+	0.139935i
$148$		0			0
$149$	1.98820	+	7.42006i	0.162880	+	0.607875i	0.998301	+	0.0582651i	$0.0185569\pi$
$149$	1.98820	+	7.42006i	0.162880	+	0.607875i	−0.835422	+	0.549610i	$0.814776\pi$
$150$		0			0
$151$	3.46798	−	3.46798i	0.282220	−	0.282220i	−0.551774	−	0.833994i	$-0.686049\pi$
$151$	3.46798	−	3.46798i	0.282220	−	0.282220i	0.833994	+	0.551774i	$0.186049\pi$
$152$		0			0
$153$	−5.60872	−	2.71384i	−0.453438	−	0.219401i
$154$		0			0
$155$	−13.1599			−1.05702
$156$		0			0
$157$	−3.70701			−0.295852			−0.147926	−	0.988998i	$-0.547260\pi$
$157$	−3.70701			−0.295852			−0.147926	+	0.988998i	$0.547260\pi$
$158$		0			0
$159$	11.6228	−	12.5031i	0.921747	−	0.991561i
$160$		0			0
$161$	5.76059	−	5.76059i	0.453998	−	0.453998i
$162$		0			0
$163$	−3.50600	−	13.0846i	−0.274611	−	1.02486i	−0.956101	−	0.293036i	$-0.905334\pi$
$163$	−3.50600	−	13.0846i	−0.274611	−	1.02486i	0.681490	−	0.731827i	$-0.261332\pi$
$164$		0			0
$165$	−2.59244	+	11.3099i	−0.201821	+	0.880471i
$166$		0			0
$167$	4.18631	−	15.6235i	0.323946	−	1.20898i	−0.591421	−	0.806363i	$-0.701433\pi$
$167$	4.18631	−	15.6235i	0.323946	−	1.20898i	0.915367	−	0.402620i	$-0.131901\pi$
$168$		0			0
$169$	−9.96977	−	8.34288i	−0.766906	−	0.641760i
$170$		0			0
$171$	1.15470	+	3.31968i	0.0883022	+	0.253862i
$172$		0			0
$173$	9.88581	−	17.1227i	0.751604	−	1.30182i	−0.195440	−	0.980716i	$-0.562614\pi$
$173$	9.88581	−	17.1227i	0.751604	−	1.30182i	0.947045	−	0.321101i	$-0.104053\pi$
$174$		0			0
$175$	−0.129092	+	0.0345900i	−0.00975841	+	0.00261476i
$176$		0			0
$177$	21.9631	+	11.6339i	1.65085	+	0.874459i
$178$		0			0
$179$	1.41662	+	2.45366i	0.105883	+	0.183395i	0.914099	−	0.405492i	$-0.132900\pi$
$179$	1.41662	+	2.45366i	0.105883	+	0.183395i	−0.808216	+	0.588887i	$0.799566\pi$
$180$		0			0
$181$		−	8.14854i		−	0.605676i	−0.953042	−	0.302838i	$-0.902066\pi$
$181$		−	8.14854i		−	0.605676i	0.953042	−	0.302838i	$-0.0979341\pi$
$182$		0			0
$183$	−18.6734	+	5.74101i	−1.38037	+	0.424388i
$184$		0			0
$185$	−2.83853	+	1.63883i	−0.208693	+	0.120489i
$186$		0			0
$187$	4.43666	+	4.43666i	0.324441	+	0.324441i
$188$		0			0
$189$	−7.69332	−	3.38206i	−0.559607	−	0.246009i
$190$		0			0
$191$	−14.8793	−	8.59056i	−1.07663	−	0.621591i	−0.146643	−	0.989190i	$-0.546847\pi$
$191$	−14.8793	−	8.59056i	−1.07663	−	0.621591i	−0.929985	+	0.367598i	$0.880180\pi$
$192$		0			0
$193$	−8.63779	−	2.31449i	−0.621762	−	0.166601i	−0.0658334	−	0.997831i	$-0.520971\pi$
$193$	−8.63779	−	2.31449i	−0.621762	−	0.166601i	−0.555929	+	0.831230i	$0.687637\pi$
$194$		0			0
$195$	4.24991	−	13.1801i	0.304343	−	0.943848i
$196$		0			0
$197$	9.64105	+	2.58331i	0.686897	+	0.184053i	0.585354	−	0.810778i	$-0.300956\pi$
$197$	9.64105	+	2.58331i	0.686897	+	0.184053i	0.101543	+	0.994831i	$0.467622\pi$
$198$		0			0
$199$	−2.76369	−	1.59562i	−0.195913	−	0.113110i	0.398835	−	0.917023i	$-0.369415\pi$
$199$	−2.76369	−	1.59562i	−0.195913	−	0.113110i	−0.594748	+	0.803912i	$0.702748\pi$
$200$		0			0
$201$	9.47038	−	5.93840i	0.667989	−	0.418862i
$202$		0			0
$203$	−8.83359	−	8.83359i	−0.619997	−	0.619997i
$204$		0			0
$205$	−2.71455	+	1.56725i	−0.189593	+	0.109461i
$206$		0			0
$207$	12.5014	−	8.48938i	0.868905	−	0.590052i
$208$		0			0
$209$		−	3.53937i		−	0.244823i
$210$		0			0
$211$	1.83361	+	3.17591i	0.126231	+	0.218639i	0.922214	−	0.386681i	$-0.126379\pi$
$211$	1.83361	+	3.17591i	0.126231	+	0.218639i	−0.795982	+	0.605320i	$0.793045\pi$
$212$		0			0
$213$	−3.81193	+	7.19637i	−0.261189	+	0.493087i
$214$		0			0
$215$	10.5745	−	2.83342i	0.721172	−	0.193237i
$216$		0			0
$217$	−4.79903	+	8.31217i	−0.325780	+	0.564267i
$218$		0			0
$219$	28.6662	−	1.04600i	1.93708	−	0.0706820i
$220$		0			0
$221$	−4.81734	−	5.73327i	−0.324049	−	0.385661i
$222$		0			0
$223$	1.91856	−	7.16015i	0.128476	−	0.479479i	−0.871464	−	0.490460i	$-0.836829\pi$
$223$	1.91856	−	7.16015i	0.128476	−	0.479479i	0.999940	+	0.0109811i	$0.00349546\pi$
$224$		0			0
$225$	−0.247241	+	0.0180672i	−0.0164827	+	0.00120448i
$226$		0			0
$227$	5.55618	+	20.7360i	0.368777	+	1.37629i	0.862228	+	0.506520i	$0.169068\pi$
$227$	5.55618	+	20.7360i	0.368777	+	1.37629i	−0.493451	+	0.869773i	$0.664265\pi$
$228$		0			0
$229$	0.0939698	−	0.0939698i	0.00620970	−	0.00620970i	−0.703995	−	0.710205i	$-0.748602\pi$
$229$	0.0939698	−	0.0939698i	0.00620970	−	0.00620970i	0.710205	+	0.703995i	$0.248602\pi$
$230$		0			0
$231$	6.19827	+	5.76185i	0.407816	+	0.379102i
$232$		0			0
$233$	28.0075			1.83483			0.917416	−	0.397929i	$-0.130271\pi$
$233$	28.0075			1.83483			0.917416	+	0.397929i	$0.130271\pi$
$234$		0			0
$235$	−21.6123			−1.40983
$236$		0			0
$237$	3.57453	+	3.32285i	0.232191	+	0.215842i
$238$		0			0
$239$	−5.71723	+	5.71723i	−0.369817	+	0.369817i	−0.867410	−	0.497594i	$-0.834217\pi$
$239$	−5.71723	+	5.71723i	−0.369817	+	0.369817i	0.497594	+	0.867410i	$0.334217\pi$
$240$		0			0
$241$	3.57550	+	13.3439i	0.230318	+	0.859559i	0.980204	+	0.197991i	$0.0634418\pi$
$241$	3.57550	+	13.3439i	0.230318	+	0.859559i	−0.749886	+	0.661568i	$0.769891\pi$
$242$		0			0
$243$	−12.8389	−	8.84090i	−0.823618	−	0.567144i
$244$		0			0
$245$	−2.51627	+	9.39084i	−0.160758	+	0.599959i
$246$		0			0
$247$	−0.365345	+	4.20840i	−0.0232463	+	0.267774i
$248$		0			0
$249$	−17.7405	+	0.647333i	−1.12426	+	0.0410231i
$250$		0			0
$251$	−11.7510	+	20.3533i	−0.741716	+	1.28469i	0.209997	+	0.977702i	$0.432654\pi$
$251$	−11.7510	+	20.3533i	−0.741716	+	1.28469i	−0.951713	+	0.306988i	$0.900679\pi$
$252$		0			0
$253$	−14.6986	+	3.93848i	−0.924094	+	0.247610i
$254$		0			0
$255$	3.73401	−	7.04927i	0.233833	−	0.441442i
$256$		0			0
$257$	1.32637	+	2.29733i	0.0827365	+	0.143304i	0.904424	−	0.426634i	$-0.140301\pi$
$257$	1.32637	+	2.29733i	0.0827365	+	0.143304i	−0.821688	+	0.569938i	$0.806967\pi$
$258$		0			0
$259$			2.39054i			0.148541i
$260$		0			0
$261$	−13.0181	−	19.1703i	−0.805798	−	1.18661i
$262$		0			0
$263$	−17.6013	+	10.1621i	−1.08534	+	0.626622i	−0.932332	−	0.361603i	$-0.882230\pi$
$263$	−17.6013	+	10.1621i	−1.08534	+	0.626622i	−0.153009	+	0.988225i	$0.548896\pi$
$264$		0			0
$265$	15.4543	+	15.4543i	0.949347	+	0.949347i
$266$		0			0
$267$	−10.5661	+	6.62546i	−0.646635	+	0.405472i
$268$		0			0
$269$	−21.7665	−	12.5669i	−1.32712	−	0.766216i	−0.342271	−	0.939601i	$-0.611196\pi$
$269$	−21.7665	−	12.5669i	−1.32712	−	0.766216i	−0.984854	+	0.173386i	$0.944529\pi$
$270$		0			0
$271$	9.61536	+	2.57643i	0.584092	+	0.156507i	0.538752	−	0.842465i	$-0.318896\pi$
$271$	9.61536	+	2.57643i	0.584092	+	0.156507i	0.0453401	+	0.998972i	$0.485563\pi$
$272$		0			0
$273$	−6.77514	−	7.49080i	−0.410050	−	0.453364i
$274$		0			0
$275$	0.241129	+	0.0646103i	0.0145406	+	0.00389615i
$276$		0			0
$277$	11.9001	+	6.87054i	0.715009	+	0.412811i	0.812913	−	0.582385i	$-0.197880\pi$
$277$	11.9001	+	6.87054i	0.715009	+	0.412811i	−0.0979039	+	0.995196i	$0.531214\pi$
$278$		0			0
$279$	−11.6380	+	13.4730i	−0.696750	+	0.806608i
$280$		0			0
$281$	−3.32284	−	3.32284i	−0.198224	−	0.198224i	0.601014	−	0.799238i	$-0.294763\pi$
$281$	−3.32284	−	3.32284i	−0.198224	−	0.198224i	−0.799238	+	0.601014i	$0.794763\pi$
$282$		0			0
$283$	−26.2042	+	15.1290i	−1.55768	+	0.899326i	−0.560201	+	0.828357i	$0.689276\pi$
$283$	−26.2042	+	15.1290i	−1.55768	+	0.899326i	−0.997478	+	0.0709694i	$0.977391\pi$
$284$		0			0
$285$	−4.30121	+	1.32238i	−0.254782	+	0.0783311i
$286$		0			0
$287$			2.28613i			0.134946i
$288$		0			0
$289$	6.34319	+	10.9867i	0.373129	+	0.646278i
$290$		0			0
$291$	16.8286	+	8.91415i	0.986511	+	0.522557i
$292$		0			0
$293$	−15.2022	+	4.07340i	−0.888119	+	0.237971i	−0.673907	−	0.738816i	$-0.735385\pi$
$293$	−15.2022	+	4.07340i	−0.888119	+	0.237971i	−0.214212	+	0.976787i	$0.568718\pi$
$294$		0			0
$295$	−15.9101	+	27.5572i	−0.926324	+	1.60444i
$296$		0			0
$297$	9.28635	+	12.6561i	0.538849	+	0.734381i
$298$		0			0
$299$	17.8836	−	3.16572i	1.03423	−	0.183078i
$300$		0			0
$301$	2.06654	−	7.71242i	0.119113	−	0.444537i
$302$		0			0
$303$	−3.66296	+	15.9802i	−0.210432	+	0.918036i
$304$		0			0
$305$	−6.47346	−	24.1593i	−0.370669	−	1.38336i
$306$		0			0
$307$	11.5169	−	11.5169i	0.657305	−	0.657305i	−0.297437	−	0.954742i	$-0.596132\pi$
$307$	11.5169	−	11.5169i	0.657305	−	0.657305i	0.954742	+	0.297437i	$0.0961318\pi$
$308$		0			0
$309$	16.7915	−	18.0633i	0.955233	−	1.02758i
$310$		0			0
$311$	−7.59902			−0.430901			−0.215450	−	0.976515i	$-0.569122\pi$
$311$	−7.59902			−0.430901			−0.215450	+	0.976515i	$0.569122\pi$
$312$		0			0
$313$	−13.2916			−0.751284			−0.375642	−	0.926765i	$-0.622578\pi$
$313$	−13.2916			−0.751284			−0.375642	+	0.926765i	$0.622578\pi$
$314$		0			0
$315$	4.68628	−	9.68518i	0.264042	−	0.545698i
$316$		0			0
$317$	8.03620	−	8.03620i	0.451358	−	0.451358i	−0.444447	−	0.895805i	$-0.646600\pi$
$317$	8.03620	−	8.03620i	0.451358	−	0.451358i	0.895805	+	0.444447i	$0.146600\pi$
$318$		0			0
$319$	6.03948	+	22.5396i	0.338146	+	1.26198i
$320$		0			0
$321$	−3.87075	−	0.887251i	−0.216044	−	0.0495215i
$322$		0			0
$323$	−0.629786	+	2.35039i	−0.0350422	+	0.130779i
$324$		0			0
$325$	−0.280039	−	0.101713i	−0.0155338	−	0.00564204i
$326$		0			0
$327$	0.276782	+	7.58537i	0.0153061	+	0.419472i
$328$		0			0
$329$	−7.88141	+	13.6510i	−0.434516	+	0.752604i
$330$		0			0
$331$	−22.5940	+	6.05406i	−1.24188	+	0.332761i	−0.819195	−	0.573515i	$-0.805579\pi$
$331$	−22.5940	+	6.05406i	−1.24188	+	0.332761i	−0.422686	+	0.906276i	$0.638913\pi$
$332$		0			0
$333$	−0.832452	+	4.35539i	−0.0456181	+	0.238674i
$334$		0			0
$335$	7.15564	+	12.3939i	0.390954	+	0.677153i
$336$		0			0
$337$			3.48612i			0.189901i	0.995482	+	0.0949505i	$0.0302693\pi$
$337$			3.48612i			0.189901i	−0.995482	+	0.0949505i	$0.969731\pi$
$338$		0			0
$339$	9.18196	+	29.8655i	0.498696	+	1.62207i
$340$		0			0
$341$	15.5262	−	8.96406i	0.840791	−	0.485431i
$342$		0			0
$343$	13.0193	+	13.0193i	0.702977	+	0.702977i
$344$		0			0
$345$	10.2779	+	16.3910i	0.553346	+	0.882460i
$346$		0			0
$347$	6.26164	+	3.61516i	0.336142	+	0.194072i	0.658565	−	0.752524i	$-0.271164\pi$
$347$	6.26164	+	3.61516i	0.336142	+	0.194072i	−0.322422	+	0.946596i	$0.604497\pi$
$348$		0			0
$349$	9.00361	+	2.41251i	0.481952	+	0.129139i	0.491611	−	0.870815i	$-0.336408\pi$
$349$	9.00361	+	2.41251i	0.481952	+	0.129139i	−0.00965939	+	0.999953i	$0.503075\pi$
$350$		0			0
$351$	−9.73532	−	16.0070i	−0.519633	−	0.854390i
$352$		0			0
$353$	3.97036	+	1.06385i	0.211321	+	0.0566233i	0.362926	−	0.931818i	$-0.381778\pi$
$353$	3.97036	+	1.06385i	0.211321	+	0.0566233i	−0.151605	+	0.988441i	$0.548444\pi$
$354$		0			0
$355$	−9.02929	−	5.21306i	−0.479225	−	0.276681i
$356$		0			0
$357$	−3.09084	−	4.92919i	−0.163585	−	0.260880i
$358$		0			0
$359$	0.612655	+	0.612655i	0.0323347	+	0.0323347i	0.723089	−	0.690755i	$-0.242722\pi$
$359$	0.612655	+	0.612655i	0.0323347	+	0.0323347i	−0.690755	+	0.723089i	$0.742722\pi$
$360$		0			0
$361$	−15.2658	+	8.81369i	−0.803461	+	0.463878i
$362$		0			0
$363$	0.953653	+	3.10187i	0.0500538	+	0.162806i
$364$		0			0
$365$			36.7252i			1.92228i
$366$		0			0
$367$	6.17281	+	10.6916i	0.322218	+	0.558098i	0.980945	−	0.194284i	$-0.0622382\pi$
$367$	6.17281	+	10.6916i	0.322218	+	0.558098i	−0.658727	+	0.752382i	$0.728905\pi$
$368$		0			0
$369$	−0.796093	+	4.16516i	−0.0414430	+	0.216829i
$370$		0			0
$371$	15.3971	−	4.12565i	0.799379	−	0.214193i
$372$		0			0
$373$	−16.8205	+	29.1340i	−0.870934	+	1.50850i	−0.00990208	+	0.999951i	$0.503152\pi$
$373$	−16.8205	+	29.1340i	−0.870934	+	1.50850i	−0.861032	+	0.508551i	$0.830181\pi$
$374$		0			0
$375$	−0.711849	−	19.5086i	−0.0367597	−	1.00742i
$376$		0			0
$377$	−4.85449	−	27.4236i	−0.250019	−	1.41239i
$378$		0			0
$379$	6.81176	−	25.4219i	0.349897	−	1.30583i	−0.536889	−	0.843653i	$-0.680401\pi$
$379$	6.81176	−	25.4219i	0.349897	−	1.30583i	0.886786	−	0.462180i	$-0.152933\pi$
$380$		0			0
$381$	31.0984	+	7.12834i	1.59322	+	0.365196i
$382$		0			0
$383$	−9.04647	−	33.7619i	−0.462253	−	1.72515i	−0.665840	−	0.746094i	$-0.731927\pi$
$383$	−9.04647	−	33.7619i	−0.462253	−	1.72515i	0.203587	−	0.979057i	$-0.434740\pi$
$384$		0			0
$385$	−7.66126	+	7.66126i	−0.390454	+	0.390454i
$386$		0			0
$387$	6.45076	−	13.3318i	0.327911	−	0.677696i
$388$		0			0
$389$	4.41992			0.224099			0.112049	−	0.993703i	$-0.464259\pi$
$389$	4.41992			0.224099			0.112049	+	0.993703i	$0.464259\pi$
$390$		0			0
$391$	10.4617			0.529073
$392$		0			0
$393$	12.5150	−	13.4629i	0.631296	−	0.679112i
$394$		0			0
$395$	−4.41824	+	4.41824i	−0.222306	+	0.222306i
$396$		0			0
$397$	−9.03870	−	33.7329i	−0.453639	−	1.69300i	−0.692058	−	0.721842i	$-0.743296\pi$
$397$	−9.03870	−	33.7329i	−0.453639	−	1.69300i	0.238419	−	0.971162i	$-0.423371\pi$
$398$		0			0
$399$	−0.733275	+	3.19901i	−0.0367096	+	0.160151i
$400$		0			0
$401$	−2.67186	+	9.97150i	−0.133426	+	0.497953i	−0.999999	−	0.00109677i	$-0.999651\pi$
$401$	−2.67186	+	9.97150i	−0.133426	+	0.497953i	0.866573	+	0.499050i	$0.166318\pi$
$402$		0			0
$403$	−19.3864	+	9.05584i	−0.965703	+	0.451103i
$404$		0			0
$405$	11.9107	−	16.0138i	0.591848	−	0.795732i
$406$		0			0
$407$	2.23263	−	3.86703i	0.110667	−	0.191681i
$408$		0			0
$409$	−27.8715	+	7.46816i	−1.37816	+	0.369277i	−0.870452	−	0.492253i	$-0.836173\pi$
$409$	−27.8715	+	7.46816i	−1.37816	+	0.369277i	−0.507707	+	0.861530i	$0.669507\pi$
$410$		0			0
$411$	−19.9441	−	10.5645i	−0.983772	−	0.521106i
$412$		0			0
$413$	11.6040	+	20.0987i	0.570994	+	0.988991i
$414$		0			0
$415$		−	22.7280i		−	1.11567i
$416$		0			0
$417$	−16.9187	+	5.20156i	−0.828512	+	0.254721i
$418$		0			0
$419$	10.1249	−	5.84561i	0.494633	−	0.285577i	−0.231861	−	0.972749i	$-0.574482\pi$
$419$	10.1249	−	5.84561i	0.494633	−	0.285577i	0.726494	+	0.687172i	$0.241148\pi$
$420$		0			0
$421$	13.5303	+	13.5303i	0.659424	+	0.659424i	0.955244	−	0.295820i	$-0.0955928\pi$
$421$	13.5303	+	13.5303i	0.659424	+	0.659424i	−0.295820	+	0.955244i	$0.595593\pi$
$422$		0			0
$423$	−19.1130	+	22.1266i	−0.929307	+	1.07583i
$424$		0			0
$425$	−0.148630	−	0.0858117i	−0.00720963	−	0.00416248i
$426$		0			0
$427$	−17.6204	−	4.72138i	−0.852713	−	0.228484i
$428$		0			0
$429$	3.96375	+	18.4450i	0.191372	+	0.890534i
$430$		0			0
$431$	4.33330	+	1.16110i	0.208728	+	0.0559284i	0.361668	−	0.932307i	$-0.382207\pi$
$431$	4.33330	+	1.16110i	0.208728	+	0.0559284i	−0.152940	+	0.988235i	$0.548874\pi$
$432$		0			0
$433$	−20.2735	−	11.7049i	−0.974280	−	0.562501i	−0.0737418	−	0.997277i	$-0.523494\pi$
$433$	−20.2735	−	11.7049i	−0.974280	−	0.562501i	−0.900538	+	0.434776i	$0.856827\pi$
$434$		0			0
$435$	25.1348	−	15.7607i	1.20512	−	0.755670i
$436$		0			0
$437$	−4.17295	−	4.17295i	−0.199619	−	0.199619i
$438$		0			0
$439$	−12.1163	+	6.99536i	−0.578281	+	0.333870i	−0.760450	−	0.649397i	$-0.775021\pi$
$439$	−12.1163	+	6.99536i	−0.578281	+	0.333870i	0.182169	+	0.983267i	$0.441688\pi$
$440$		0			0
$441$	7.38903	+	10.8810i	0.351858	+	0.518143i
$442$		0			0
$443$		−	26.3319i		−	1.25107i	−0.780198	−	0.625533i	$-0.784882\pi$
$443$		−	26.3319i		−	1.25107i	0.780198	−	0.625533i	$-0.215118\pi$
$444$		0			0
$445$	−7.98354	−	13.8279i	−0.378456	−	0.655505i
$446$		0			0
$447$	−6.22804	+	11.7576i	−0.294576	+	0.556117i
$448$		0			0
$449$	−27.1589	+	7.27720i	−1.28171	+	0.343432i	−0.834505	−	0.551001i	$-0.814246\pi$
$449$	−27.1589	+	7.27720i	−1.28171	+	0.343432i	−0.447202	+	0.894433i	$0.647579\pi$
$450$		0			0
$451$	2.13512	−	3.69813i	0.100539	−	0.174138i
$452$		0			0
$453$	8.48912	−	0.309759i	0.398854	−	0.0145538i
$454$		0			0
$455$	9.90026	−	8.31862i	0.464131	−	0.389983i
$456$		0			0
$457$	3.28100	−	12.2448i	0.153478	−	0.572790i	−0.845752	−	0.533576i	$-0.820848\pi$
$457$	3.28100	−	12.2448i	0.153478	−	0.572790i	0.999231	−	0.0392139i	$-0.0124854\pi$
$458$		0			0
$459$	−3.91481	−	10.0569i	−0.182728	−	0.469418i
$460$		0			0
$461$	0.145136	+	0.541655i	0.00675966	+	0.0252274i	0.969223	−	0.246183i	$-0.0791765\pi$
$461$	0.145136	+	0.541655i	0.00675966	+	0.0252274i	−0.962464	+	0.271411i	$0.912510\pi$
$462$		0			0
$463$	13.7097	−	13.7097i	0.637143	−	0.637143i	−0.312707	−	0.949850i	$-0.601236\pi$
$463$	13.7097	−	13.7097i	0.637143	−	0.637143i	0.949850	+	0.312707i	$0.101236\pi$
$464$		0			0
$465$	−16.6945	−	15.5190i	−0.774187	−	0.719678i
$466$		0			0
$467$	4.97267			0.230108			0.115054	−	0.993359i	$-0.463296\pi$
$467$	4.97267			0.230108			0.115054	+	0.993359i	$0.463296\pi$
$468$		0			0
$469$	10.4379			0.481975
$470$		0			0
$471$	−4.70268	−	4.37157i	−0.216688	−	0.201431i
$472$		0			0
$473$	−10.5459	+	10.5459i	−0.484900	+	0.484900i
$474$		0			0
$475$	0.0250569	+	0.0935137i	0.00114969	+	0.00429070i
$476$		0			0
$477$	29.4891	−	2.15492i	1.35021	−	0.0986671i
$478$		0			0
$479$	1.36129	−	5.08042i	0.0621991	−	0.232130i	−0.927828	−	0.373009i	$-0.878326\pi$
$479$	1.36129	−	5.08042i	0.0621991	−	0.232130i	0.990027	+	0.140879i	$0.0449927\pi$
$480$		0			0
$481$	−3.05382	+	4.36754i	−0.139242	+	0.199143i
$482$		0			0
$483$	14.1011	−	0.514535i	0.641623	−	0.0234121i
$484$		0			0
$485$	−12.1907	+	21.1149i	−0.553551	+	0.958778i
$486$		0			0
$487$	−29.0847	+	7.79321i	−1.31795	+	0.353144i	−0.848210	−	0.529660i	$-0.822320\pi$
$487$	−29.0847	+	7.79321i	−1.31795	+	0.353144i	−0.469741	+	0.882804i	$0.655653\pi$
$488$		0			0
$489$	10.9826	−	20.7335i	0.496649	−	0.937601i
$490$		0			0
$491$	−16.1436	−	27.9615i	−0.728549	−	1.26188i	−0.957497	−	0.288444i	$-0.906862\pi$
$491$	−16.1436	−	27.9615i	−0.728549	−	1.26188i	0.228948	−	0.973439i	$-0.426471\pi$
$492$		0			0
$493$		−	16.0426i		−	0.722522i
$494$		0			0
$495$	−16.6261	+	11.2904i	−0.747289	+	0.507465i
$496$		0			0
$497$	−6.58546	+	3.80212i	−0.295398	+	0.170548i
$498$		0			0
$499$	15.8520	+	15.8520i	0.709634	+	0.709634i	0.966458	−	0.256824i	$-0.0826761\pi$
$499$	15.8520	+	15.8520i	0.709634	+	0.709634i	−0.256824	+	0.966458i	$0.582676\pi$
$500$		0			0
$501$	23.7350	−	14.8830i	1.06040	−	0.664925i
$502$		0			0
$503$	18.7253	+	10.8111i	0.834921	+	0.482042i	0.855535	−	0.517745i	$-0.173229\pi$
$503$	18.7253	+	10.8111i	0.834921	+	0.482042i	−0.0206133	+	0.999788i	$0.506562\pi$
$504$		0			0
$505$	−20.2745	−	5.43254i	−0.902204	−	0.241745i
$506$		0			0
$507$	−2.80905	−	22.3408i	−0.124754	−	0.992188i
$508$		0			0
$509$	20.7682	+	5.56482i	0.920534	+	0.246656i	0.687814	−	0.725887i	$-0.258571\pi$
$509$	20.7682	+	5.56482i	0.920534	+	0.246656i	0.232721	+	0.972544i	$0.425237\pi$
$510$		0			0
$511$	23.1968	+	13.3927i	1.02616	+	0.592456i
$512$		0			0
$513$	−2.44996	+	5.57302i	−0.108168	+	0.246055i
$514$		0			0
$515$	22.3268	+	22.3268i	0.983837	+	0.983837i
$516$		0			0
$517$	25.4986	−	14.7216i	1.12143	−	0.647455i
$518$		0			0
$519$	32.7334	−	10.0637i	1.43684	−	0.441747i
$520$		0			0
$521$			28.4493i			1.24638i	0.782069	+	0.623192i	$0.214165\pi$
$521$			28.4493i			1.24638i	−0.782069	+	0.623192i	$0.785835\pi$
$522$		0			0
$523$	−22.4493	−	38.8833i	−0.981639	−	1.70025i	−0.656011	−	0.754751i	$-0.727758\pi$
$523$	−22.4493	−	38.8833i	−0.981639	−	1.70025i	−0.325628	−	0.945498i	$-0.605576\pi$
$524$		0			0
$525$	−0.204555	−	0.108353i	−0.00892753	−	0.00472893i
$526$		0			0
$527$	−11.9056	+	3.19008i	−0.518614	+	0.138962i
$528$		0			0
$529$	−1.18632	+	2.05476i	−0.0515791	+	0.0893376i
$530$		0			0
$531$	14.1427	+	40.6591i	0.613740	+	1.76446i
$532$		0			0
$533$	−2.92044	+	4.17678i	−0.126498	+	0.180916i
$534$		0			0
$535$	1.31588	−	4.91094i	0.0568906	−	0.212318i
$536$		0			0
$537$	−1.09642	+	4.78327i	−0.0473138	+	0.206413i
$538$		0			0
$539$	−3.42800	−	12.7935i	−0.147654	−	0.551053i
$540$		0			0
$541$	10.3303	−	10.3303i	0.444135	−	0.444135i	−0.449264	−	0.893399i	$-0.648314\pi$
$541$	10.3303	−	10.3303i	0.444135	−	0.444135i	0.893399	+	0.449264i	$0.148314\pi$
$542$		0			0
$543$	9.60933	−	10.3372i	0.412376	−	0.443610i
$544$		0			0
$545$	−9.71787			−0.416268
$546$		0			0
$547$	4.88585			0.208904			0.104452	−	0.994530i	$-0.466691\pi$
$547$	4.88585			0.208904			0.104452	+	0.994530i	$0.466691\pi$
$548$		0			0
$549$	−30.4590	−	14.7379i	−1.29996	−	0.629000i
$550$		0			0
$551$	−6.39903	+	6.39903i	−0.272608	+	0.272608i
$552$		0			0
$553$	1.17949	+	4.40190i	0.0501568	+	0.187188i
$554$		0			0
$555$	−5.53355	−	1.26840i	−0.234886	−	0.0538404i
$556$		0			0
$557$	8.70865	−	32.5011i	0.368997	−	1.37712i	−0.492923	−	0.870073i	$-0.664071\pi$
$557$	8.70865	−	32.5011i	0.368997	−	1.37712i	0.861920	−	0.507044i	$-0.169262\pi$
$558$		0			0
$559$	13.6279	−	11.4508i	0.576399	−	0.484315i
$560$		0			0
$561$	0.396282	+	10.8603i	0.0167310	+	0.458523i
$562$		0			0
$563$	12.3927	−	21.4647i	0.522288	−	0.904630i	−0.477376	−	0.878699i	$-0.658412\pi$
$563$	12.3927	−	21.4647i	0.522288	−	0.904630i	0.999664	−	0.0259303i	$-0.00825479\pi$
$564$		0			0
$565$	−38.6394	+	10.3534i	−1.62557	+	0.435571i
$566$		0			0
$567$	−5.77130	−	13.3630i	−0.242372	−	0.561191i
$568$		0			0
$569$	−3.35537	−	5.81167i	−0.140664	−	0.243638i	0.787083	−	0.616848i	$-0.211591\pi$
$569$	−3.35537	−	5.81167i	−0.140664	−	0.243638i	−0.927747	+	0.373210i	$0.878257\pi$
$570$		0			0
$571$			26.7992i			1.12151i	0.827982	+	0.560755i	$0.189489\pi$
$571$			26.7992i			1.12151i	−0.827982	+	0.560755i	$0.810511\pi$
$572$		0			0
$573$	−8.74513	−	28.4446i	−0.365333	−	1.18829i
$574$		0			0
$575$	0.360470	−	0.208117i	0.0150326	−	0.00867909i
$576$		0			0
$577$	30.5894	+	30.5894i	1.27345	+	1.27345i	0.944264	+	0.329189i	$0.106775\pi$
$577$	30.5894	+	30.5894i	1.27345	+	1.27345i	0.329189	+	0.944264i	$0.393225\pi$
$578$		0			0
$579$	−8.22841	−	13.1224i	−0.341961	−	0.545350i
$580$		0			0
$581$	−14.3557	−	8.28826i	−0.595575	−	0.343855i
$582$		0			0
$583$	−28.7601	−	7.70625i	−1.19112	−	0.319160i
$584$		0			0
$585$	20.9343	−	11.7084i	0.865528	−	0.484082i
$586$		0			0
$587$	21.5900	+	5.78501i	0.891113	+	0.238773i	0.675196	−	0.737639i	$-0.264059\pi$
$587$	21.5900	+	5.78501i	0.891113	+	0.238773i	0.215918	+	0.976412i	$0.430726\pi$
$588$		0			0
$589$	6.02131	+	3.47641i	0.248104	+	0.143243i
$590$		0			0
$591$	9.18412	+	14.6466i	0.377784	+	0.602480i
$592$		0			0
$593$	−8.05590	−	8.05590i	−0.330816	−	0.330816i	0.522080	−	0.852896i	$-0.325156\pi$
$593$	−8.05590	−	8.05590i	−0.330816	−	0.330816i	−0.852896	+	0.522080i	$0.825156\pi$
$594$		0			0
$595$	6.45085	−	3.72440i	0.264459	−	0.152686i
$596$		0			0
$597$	−1.62433	−	5.28332i	−0.0664792	−	0.216232i
$598$		0			0
$599$		−	25.2313i		−	1.03092i	−0.856913	−	0.515461i	$-0.827621\pi$
$599$		−	25.2313i		−	1.03092i	0.856913	−	0.515461i	$-0.172379\pi$
$600$		0			0
$601$	5.19058	+	8.99035i	0.211728	+	0.366724i	0.952255	−	0.305302i	$-0.0987575\pi$
$601$	5.19058	+	8.99035i	0.211728	+	0.366724i	−0.740527	+	0.672026i	$0.765424\pi$
$602$		0			0
$603$	19.0170	+	3.63475i	0.774432	+	0.148018i
$604$		0			0
$605$	−4.01315	+	1.07532i	−0.163158	+	0.0437180i
$606$		0			0
$607$	11.5164	−	19.9470i	0.467437	−	0.809624i	−0.531871	−	0.846825i	$-0.678511\pi$
$607$	11.5164	−	19.9470i	0.467437	−	0.809624i	0.999308	+	0.0372012i	$0.0118442\pi$
$608$		0			0
$609$	−0.789015	−	21.6234i	−0.0319725	−	0.876224i
$610$		0			0
$611$	−31.8381	+	14.8723i	−1.28803	+	0.601670i
$612$		0			0
$613$	8.72938	−	32.5785i	0.352576	−	1.31583i	−0.530931	−	0.847415i	$-0.678158\pi$
$613$	8.72938	−	32.5785i	0.352576	−	1.31583i	0.883507	−	0.468418i	$-0.155176\pi$
$614$		0			0
$615$	−5.29187	−	1.21300i	−0.213389	−	0.0489128i
$616$		0			0
$617$	2.65220	+	9.89815i	0.106774	+	0.398485i	0.998540	−	0.0540108i	$-0.0172005\pi$
$617$	2.65220	+	9.89815i	0.106774	+	0.398485i	−0.891767	+	0.452495i	$0.850534\pi$
$618$		0			0
$619$	−11.5373	+	11.5373i	−0.463723	+	0.463723i	−0.899874	−	0.436151i	$-0.856341\pi$
$619$	−11.5373	+	11.5373i	−0.463723	+	0.463723i	0.436151	+	0.899874i	$0.356341\pi$
$620$		0			0
$621$	25.8704	+	3.97296i	1.03814	+	0.159429i
$622$		0			0
$623$	−11.6455			−0.466567
$624$		0			0
$625$	24.5800			0.983200
$626$		0			0
$627$	4.17387	−	4.49001i	0.166688	−	0.179314i
$628$		0			0
$629$	−2.17072	+	2.17072i	−0.0865521	+	0.0865521i
$630$		0			0
$631$	−7.07557	−	26.4064i	−0.281674	−	1.05122i	−0.951236	−	0.308465i	$-0.900185\pi$
$631$	−7.07557	−	26.4064i	−0.281674	−	1.05122i	0.669562	−	0.742756i	$-0.266482\pi$
$632$		0			0
$633$	−1.41915	+	6.19126i	−0.0564063	+	0.246080i
$634$		0			0
$635$	−10.5720	+	39.4554i	−0.419539	+	1.56574i
$636$		0			0
$637$	2.75540	+	15.5656i	0.109173	+	0.616732i
$638$		0			0
$639$	−13.3222	+	4.63394i	−0.527020	+	0.183316i
$640$		0			0
$641$	11.6077	−	20.1051i	0.458476	−	0.794103i	−0.540405	−	0.841405i	$-0.681729\pi$
$641$	11.6077	−	20.1051i	0.458476	−	0.794103i	0.998881	+	0.0473020i	$0.0150623\pi$
$642$		0			0
$643$	−9.86387	+	2.64302i	−0.388993	+	0.104230i	−0.448014	−	0.894026i	$-0.647869\pi$
$643$	−9.86387	+	2.64302i	−0.388993	+	0.104230i	0.0590213	+	0.998257i	$0.481202\pi$
$644$		0			0
$645$	16.7560	+	8.87570i	0.659768	+	0.349480i
$646$		0			0
$647$	12.8120	+	22.1911i	0.503692	+	0.872420i	0.999991	+	0.00426847i	$0.00135870\pi$
$647$	12.8120	+	22.1911i	0.503692	+	0.872420i	−0.496299	+	0.868152i	$0.665308\pi$
$648$		0			0
$649$		−	43.3498i		−	1.70163i
$650$		0			0
$651$	−15.8903	+	4.88538i	−0.622790	+	0.191473i
$652$		0			0
$653$	20.3016	−	11.7212i	0.794465	−	0.458685i	−0.0470671	−	0.998892i	$-0.514987\pi$
$653$	20.3016	−	11.7212i	0.794465	−	0.458685i	0.841532	+	0.540207i	$0.181654\pi$
$654$		0			0
$655$	16.6405	+	16.6405i	0.650200	+	0.650200i
$656$		0			0
$657$	37.5991	+	32.4782i	1.46688	+	1.26710i
$658$		0			0
$659$	4.19864	+	2.42408i	0.163556	+	0.0944289i	0.579544	−	0.814941i	$-0.303231\pi$
$659$	4.19864	+	2.42408i	0.163556	+	0.0944289i	−0.415988	+	0.909370i	$0.636564\pi$
$660$		0			0
$661$	35.3299	+	9.46662i	1.37417	+	0.368209i	0.869002	−	0.494809i	$-0.164762\pi$
$661$	35.3299	+	9.46662i	1.37417	+	0.368209i	0.505173	+	0.863018i	$0.331429\pi$
$662$		0			0
$663$	0.649847	−	12.9541i	0.0252380	−	0.503096i
$664$		0			0
$665$	−4.05868	−	1.08752i	−0.157389	−	0.0421722i
$666$		0			0
$667$	33.6951	+	19.4539i	1.30468	+	0.753257i
$668$		0			0
$669$	10.8776	−	6.82080i	0.420553	−	0.263707i
$670$		0			0
$671$	24.0940	+	24.0940i	0.930138	+	0.930138i
$672$		0			0
$673$	−43.5065	+	25.1185i	−1.67705	+	0.968248i	−0.713530	+	0.700624i	$0.752905\pi$
$673$	−43.5065	+	25.1185i	−1.67705	+	0.968248i	−0.963524	+	0.267623i	$0.913762\pi$
$674$		0			0
$675$	−0.334953	−	0.268644i	−0.0128924	−	0.0103401i
$676$		0			0
$677$		−	21.2309i		−	0.815970i	−0.912989	−	0.407985i	$-0.866232\pi$
$677$		−	21.2309i		−	0.815970i	0.912989	−	0.407985i	$-0.133768\pi$
$678$		0			0
$679$	8.89121	+	15.4000i	0.341213	+	0.590999i
$680$		0			0
$681$	−17.4048	+	32.8577i	−0.666953	+	1.25911i
$682$		0			0
$683$	−13.3137	+	3.56740i	−0.509435	+	0.136503i	−0.504375	−	0.863484i	$-0.668277\pi$
$683$	−13.3137	+	3.56740i	−0.509435	+	0.136503i	−0.00505974	+	0.999987i	$0.501611\pi$
$684$		0			0
$685$	14.4476	−	25.0239i	0.552014	−	0.956116i
$686$		0			0
$687$	0.230025	−	0.00839337i	0.00877600	−	0.000320227i
$688$		0			0
$689$	33.4010	+	12.1316i	1.27248	+	0.462178i
$690$		0			0
$691$	12.6969	−	47.3855i	0.483013	−	1.80263i	−0.105834	−	0.994384i	$-0.533751\pi$
$691$	12.6969	−	47.3855i	0.483013	−	1.80263i	0.588847	−	0.808245i	$-0.299582\pi$
$692$		0			0
$693$	1.06828	+	14.6189i	0.0405805	+	0.555325i
$694$		0			0
$695$	−5.86518	−	21.8891i	−0.222479	−	0.830302i
$696$		0			0
$697$	−2.07591	+	2.07591i	−0.0786306	+	0.0786306i
$698$		0			0
$699$	35.5301	+	33.0284i	1.34387	+	1.24925i
$700$		0			0
$701$	−22.4699			−0.848677			−0.424338	−	0.905504i	$-0.639493\pi$
$701$	−22.4699			−0.848677			−0.424338	+	0.905504i	$0.639493\pi$
$702$		0			0
$703$	1.73170			0.0653123
$704$		0			0
$705$	−27.4172	−	25.4868i	−1.03259	−	0.959887i
$706$		0			0
$707$	−10.8249	+	10.8249i	−0.407113	+	0.407113i
$708$		0			0
$709$	2.76758	+	10.3287i	0.103939	+	0.387904i	0.998223	−	0.0595959i	$-0.0189812\pi$
$709$	2.76758	+	10.3287i	0.103939	+	0.387904i	−0.894284	+	0.447500i	$0.852315\pi$
$710$		0			0
$711$	0.616073	+	8.43067i	0.0231045	+	0.316175i
$712$		0			0
$713$	7.73684	−	28.8743i	0.289747	−	1.08135i
$714$		0			0
$715$	−23.7842	+	4.21023i	−0.889477	+	0.157454i
$716$		0			0
$717$	−13.9950	+	0.510662i	−0.522652	+	0.0190710i
$718$		0			0
$719$	7.22594	−	12.5157i	0.269482	−	0.466757i	−0.699246	−	0.714881i	$-0.746481\pi$
$719$	7.22594	−	12.5157i	0.269482	−	0.466757i	0.968728	+	0.248124i	$0.0798142\pi$
$720$		0			0
$721$	22.2443	−	5.96033i	0.828420	−	0.221974i
$722$		0			0
$723$	−11.2003	+	21.1445i	−0.416543	+	0.786372i
$724$		0			0
$725$	−0.319138	−	0.552764i	−0.0118525	−	0.0205291i
$726$		0			0
$727$		−	14.7369i		−	0.546560i	−0.961935	−	0.273280i	$-0.911892\pi$
$727$		−	14.7369i		−	0.546560i	0.961935	−	0.273280i	$-0.0881085\pi$
$728$		0			0
$729$	−5.86154	−	26.3561i	−0.217094	−	0.976151i
$730$		0			0
$731$	8.87973	−	5.12672i	0.328429	−	0.189618i
$732$		0			0
$733$	−26.4060	−	26.4060i	−0.975328	−	0.975328i	0.0243745	−	0.999703i	$-0.492241\pi$
$733$	−26.4060	−	26.4060i	−0.975328	−	0.975328i	−0.999703	+	0.0243745i	$0.992241\pi$
$734$		0			0
$735$	−14.2665	+	8.94577i	−0.526226	+	0.329970i
$736$		0			0
$737$	−16.8847	−	9.74837i	−0.621955	−	0.359086i
$738$		0			0
$739$	0.773003	+	0.207126i	0.0284354	+	0.00761924i	0.273009	−	0.962012i	$-0.411981\pi$
$739$	0.773003	+	0.207126i	0.0284354	+	0.00761924i	−0.244573	+	0.969631i	$0.578648\pi$
$740$		0			0
$741$	−5.42631	+	4.90790i	−0.199341	+	0.180296i
$742$		0			0
$743$	−8.82884	−	2.36568i	−0.323899	−	0.0867885i	0.0932059	−	0.995647i	$-0.470289\pi$
$743$	−8.82884	−	2.36568i	−0.323899	−	0.0867885i	−0.417105	+	0.908858i	$0.636955\pi$
$744$		0			0
$745$	−14.7523	−	8.51726i	−0.540483	−	0.312048i
$746$		0			0
$747$	−23.2688	−	20.0997i	−0.851362	−	0.735408i
$748$		0			0
$749$	−2.62203	−	2.62203i	−0.0958071	−	0.0958071i
$750$		0			0
$751$	16.1851	−	9.34448i	0.590603	−	0.340985i	−0.174733	−	0.984616i	$-0.555906\pi$
$751$	16.1851	−	9.34448i	0.590603	−	0.340985i	0.765336	+	0.643631i	$0.222573\pi$
$752$		0			0
$753$	−38.9093	+	11.9624i	−1.41793	+	0.435935i
$754$		0			0
$755$			10.8757i			0.395808i
$756$		0			0
$757$	−5.18418	−	8.97927i	−0.188422	−	0.326357i	0.756302	−	0.654223i	$-0.227004\pi$
$757$	−5.18418	−	8.97927i	−0.188422	−	0.326357i	−0.944724	+	0.327866i	$0.893671\pi$
$758$		0			0
$759$	−23.2911	−	12.3373i	−0.845412	−	0.447816i
$760$		0			0
$761$	19.8250	−	5.31209i	0.718655	−	0.192563i	0.119083	−	0.992884i	$-0.462004\pi$
$761$	19.8250	−	5.31209i	0.718655	−	0.192563i	0.599571	+	0.800321i	$0.295338\pi$
$762$		0			0
$763$	−3.54384	+	6.13811i	−0.128296	+	0.222214i
$764$		0			0
$765$	13.0499	−	4.53922i	0.471821	−	0.164116i
$766$		0			0
$767$	−4.47471	+	51.5441i	−0.161572	+	1.86115i
$768$		0			0
$769$	−6.30665	+	23.5367i	−0.227424	+	0.848756i	0.753995	+	0.656880i	$0.228124\pi$
$769$	−6.30665	+	23.5367i	−0.227424	+	0.848756i	−0.981419	+	0.191877i	$0.938543\pi$
$770$		0			0
$771$	−1.02656	+	4.47852i	−0.0369707	+	0.161290i
$772$		0			0
$773$	2.24882	+	8.39271i	0.0808844	+	0.301865i	0.994503	−	0.104707i	$-0.0333906\pi$
$773$	2.24882	+	8.39271i	0.0808844	+	0.301865i	−0.913619	+	0.406572i	$0.866724\pi$
$774$		0			0
$775$	−0.346757	+	0.346757i	−0.0124559	+	0.0124559i
$776$		0			0
$777$	−2.81909	+	3.03261i	−0.101134	+	0.108794i
$778$		0			0
$779$	1.65606			0.0593347
$780$		0			0
$781$	14.2039			0.508254
$782$		0			0
$783$	6.09234	−	39.6710i	0.217723	−	1.41773i
$784$		0			0
$785$	5.81267	−	5.81267i	0.207463	−	0.207463i
$786$		0			0
$787$	1.02627	+	3.83008i	0.0365824	+	0.136528i	0.981802	−	0.189908i	$-0.0608190\pi$
$787$	1.02627	+	3.83008i	0.0365824	+	0.136528i	−0.945219	+	0.326436i	$0.894152\pi$
$788$		0			0
$789$	−34.3127	−	7.86512i	−1.22156	−	0.280006i
$790$		0			0
$791$	−7.55120	+	28.1815i	−0.268490	+	1.00202i
$792$		0			0
$793$	−26.1613	−	31.1355i	−0.929016	−	1.10565i
$794$		0			0
$795$	1.38037	+	37.8299i	0.0489567	+	1.34169i
$796$		0			0
$797$	−24.6204	+	42.6438i	−0.872100	+	1.51052i	−0.0122797	+	0.999925i	$0.503909\pi$
$797$	−24.6204	+	42.6438i	−0.872100	+	1.51052i	−0.859820	+	0.510597i	$0.829424\pi$
$798$		0			0
$799$	−19.5524	+	5.23905i	−0.691714	+	0.185344i
$800$		0			0
$801$	−21.2173	−	4.05529i	−0.749675	−	0.143287i
$802$		0			0
$803$	−25.0160	−	43.3290i	−0.882795	−	1.52905i
$804$		0			0
$805$			18.0654i			0.636722i
$806$		0			0
$807$	−12.7930	−	41.6108i	−0.450334	−	1.46477i
$808$		0			0
$809$	25.2106	−	14.5553i	0.886357	−	0.511739i	0.0136080	−	0.999907i	$-0.495668\pi$
$809$	25.2106	−	14.5553i	0.886357	−	0.511739i	0.872749	+	0.488169i	$0.162335\pi$
$810$		0			0
$811$	−11.4094	−	11.4094i	−0.400639	−	0.400639i	0.477819	−	0.878458i	$-0.341427\pi$
$811$	−11.4094	−	11.4094i	−0.400639	−	0.400639i	−0.878458	+	0.477819i	$0.841427\pi$
$812$		0			0
$813$	9.15965	+	14.6075i	0.321243	+	0.512309i
$814$		0			0
$815$	26.0143	+	15.0194i	0.911243	+	0.526106i
$816$		0			0
$817$	−5.58686	−	1.49699i	−0.195459	−	0.0523732i
$818$		0			0
$819$	0.238796	−	17.4925i	0.00834422	−	0.611237i
$820$		0			0
$821$	−0.492396	−	0.131937i	−0.0171847	−	0.00460464i	0.250216	−	0.968190i	$-0.419498\pi$
$821$	−0.492396	−	0.131937i	−0.0171847	−	0.00460464i	−0.267401	+	0.963585i	$0.586165\pi$
$822$		0			0
$823$	−16.2968	−	9.40898i	−0.568072	−	0.327976i	0.188307	−	0.982110i	$-0.439700\pi$
$823$	−16.2968	−	9.40898i	−0.568072	−	0.327976i	−0.756379	+	0.654134i	$0.773033\pi$
$824$		0			0
$825$	0.229701	+	0.366320i	0.00799715	+	0.0127536i
$826$		0			0
$827$	−13.7947	−	13.7947i	−0.479688	−	0.479688i	0.425344	−	0.905032i	$-0.360153\pi$
$827$	−13.7947	−	13.7947i	−0.479688	−	0.479688i	−0.905032	+	0.425344i	$0.860153\pi$
$828$		0			0
$829$	11.0322	−	6.36943i	0.383163	−	0.221219i	−0.296030	−	0.955179i	$-0.595663\pi$
$829$	11.0322	−	6.36943i	0.383163	−	0.221219i	0.679194	+	0.733959i	$0.262330\pi$
$830$		0			0
$831$	6.99416	+	22.7494i	0.242625	+	0.789167i
$832$		0			0
$833$			9.10575i			0.315495i
$834$		0			0
$835$	17.9337	+	31.0622i	0.620623	+	1.07495i
$836$		0			0
$837$	−30.6522	+	3.36736i	−1.05950	+	0.116393i
$838$		0			0
$839$	20.6957	−	5.54539i	0.714494	−	0.191448i	0.116780	−	0.993158i	$-0.462743\pi$
$839$	20.6957	−	5.54539i	0.714494	−	0.191448i	0.597714	+	0.801710i	$0.296076\pi$
$840$		0			0
$841$	15.3316	−	26.5551i	0.528676	−	0.915694i
$842$		0			0
$843$	−0.296795	−	8.13384i	−0.0102222	−	0.280144i
$844$		0			0
$845$	28.7146	−	2.55100i	0.987812	−	0.0877571i
$846$		0			0
$847$	−0.784280	+	2.92697i	−0.0269482	+	0.100572i
$848$		0			0
$849$	−51.0836	−	11.7093i	−1.75319	−	0.401864i
$850$		0			0
$851$	−1.92697	−	7.19156i	−0.0660558	−	0.246524i
$852$		0			0
$853$	7.24525	−	7.24525i	0.248073	−	0.248073i	−0.572107	−	0.820179i	$-0.693874\pi$
$853$	7.24525	−	7.24525i	0.248073	−	0.248073i	0.820179	+	0.572107i	$0.193874\pi$
$854$		0			0
$855$	−7.01592	−	3.39473i	−0.239939	−	0.116097i
$856$		0			0
$857$	6.48368			0.221478			0.110739	−	0.993850i	$-0.464678\pi$
$857$	6.48368			0.221478			0.110739	+	0.993850i	$0.464678\pi$
$858$		0			0
$859$	31.3981			1.07129			0.535644	−	0.844444i	$-0.320069\pi$
$859$	31.3981			1.07129			0.535644	+	0.844444i	$0.320069\pi$
$860$		0			0
$861$	−2.69596	+	2.90016i	−0.0918782	+	0.0988372i
$862$		0			0
$863$	24.0869	−	24.0869i	0.819927	−	0.819927i	−0.166170	−	0.986097i	$-0.553140\pi$
$863$	24.0869	−	24.0869i	0.819927	−	0.819927i	0.986097	+	0.166170i	$0.0531402\pi$
$864$		0			0
$865$	11.3476	+	42.3499i	0.385831	+	1.43994i
$866$		0			0
$867$	−4.90941	+	21.4180i	−0.166732	+	0.727393i
$868$		0			0
$869$	2.20315	−	8.22226i	0.0747367	−	0.278921i
$870$		0			0
$871$	19.0701	+	13.3340i	0.646164	+	0.451804i
$872$		0			0
$873$	10.8364	+	31.1539i	0.366757	+	1.05440i
$874$		0			0
$875$	9.11431	−	15.7865i	0.308120	−	0.533680i
$876$		0			0
$877$	−23.7637	+	6.36747i	−0.802444	+	0.215014i	−0.636657	−	0.771147i	$-0.719683\pi$
$877$	−23.7637	+	6.36747i	−0.802444	+	0.215014i	−0.165787	+	0.986162i	$0.553016\pi$
$878$		0			0
$879$	−24.0889	−	12.7600i	−0.812500	−	0.430383i
$880$		0			0
$881$	0.578074	+	1.00125i	0.0194758	+	0.0337331i	0.875599	−	0.483039i	$-0.160467\pi$
$881$	0.578074	+	1.00125i	0.0194758	+	0.0337331i	−0.856123	+	0.516772i	$0.827134\pi$
$882$		0			0
$883$		−	3.10113i		−	0.104361i	−0.998638	−	0.0521806i	$-0.983383\pi$
$883$		−	3.10113i		−	0.104361i	0.998638	−	0.0521806i	$-0.0166171\pi$
$884$		0			0
$885$	−52.6808	+	16.1964i	−1.77085	+	0.544436i
$886$		0			0
$887$	−39.2130	+	22.6396i	−1.31664	+	0.760165i	−0.983187	−	0.182600i	$-0.941549\pi$
$887$	−39.2130	+	22.6396i	−1.31664	+	0.760165i	−0.333457	+	0.942765i	$0.608215\pi$
$888$		0			0
$889$	21.0659	+	21.0659i	0.706528	+	0.706528i
$890$		0			0
$891$	−3.14437	+	27.0065i	−0.105340	+	0.904752i
$892$		0			0
$893$	9.88875	+	5.70927i	0.330914	+	0.191054i
$894$		0			0
$895$	−6.06867	−	1.62610i	−0.202853	−	0.0543544i
$896$		0			0
$897$	26.4202	+	17.0736i	0.882144	+	0.570070i
$898$		0			0
$899$	−44.2774	−	11.8641i	−1.47673	−	0.395689i
$900$		0			0
$901$	17.7275	+	10.2350i	0.590590	+	0.340977i
$902$		0			0
$903$	11.7166	−	7.34690i	0.389905	−	0.244489i
$904$		0			0
$905$	12.7771	+	12.7771i	0.424724	+	0.424724i
$906$		0			0
$907$	−7.35502	+	4.24642i	−0.244219	+	0.141000i	−0.617114	−	0.786873i	$-0.711698\pi$
$907$	−7.35502	+	4.24642i	−0.244219	+	0.141000i	0.372895	+	0.927873i	$0.378365\pi$
$908$		0			0
$909$	−23.4917	+	15.9527i	−0.779172	+	0.529116i
$910$		0			0
$911$		−	29.1375i		−	0.965367i	−0.875795	−	0.482684i	$-0.839662\pi$
$911$		−	29.1375i		−	0.965367i	0.875795	−	0.482684i	$-0.160338\pi$
$912$		0			0
$913$	15.4816	+	26.8148i	0.512365	+	0.887442i
$914$		0			0
$915$	20.2782	−	38.2822i	0.670375	−	1.26557i
$916$		0			0
$917$	16.5790	−	4.44233i	0.547487	−	0.146699i
$918$		0			0
$919$	−11.9109	+	20.6303i	−0.392904	+	0.680530i	−0.992831	−	0.119525i	$-0.961863\pi$
$919$	−11.9109	+	20.6303i	−0.392904	+	0.680530i	0.599927	+	0.800055i	$0.295196\pi$
$920$		0			0
$921$	28.1918	−	1.02869i	0.928951	−	0.0338964i
$922$		0			0
$923$	−16.8888	−	1.46617i	−0.555901	−	0.0482595i
$924$		0			0
$925$	−0.0316117	+	0.117977i	−0.00103939	+	0.00387905i
$926$		0			0
$927$	42.6030	−	3.11322i	1.39927	−	0.102252i
$928$		0			0
$929$	12.2567	+	45.7426i	0.402129	+	1.50077i	0.809290	+	0.587410i	$0.199852\pi$
$929$	12.2567	+	45.7426i	0.402129	+	1.50077i	−0.407160	+	0.913357i	$0.633481\pi$
$930$		0			0
$931$	3.63208	−	3.63208i	0.119037	−	0.119037i
$932$		0			0
$933$	−9.64004	−	8.96129i	−0.315601	−	0.293380i
$934$		0			0
$935$	−13.9135			−0.455021
$936$		0			0
$937$	18.5181			0.604961			0.302480	−	0.953156i	$-0.402185\pi$
$937$	18.5181			0.604961			0.302480	+	0.953156i	$0.402185\pi$
$938$		0			0
$939$	−16.8616	−	15.6744i	−0.550256	−	0.511514i
$940$		0			0
$941$	7.71712	−	7.71712i	0.251571	−	0.251571i	−0.570044	−	0.821614i	$-0.693074\pi$
$941$	7.71712	−	7.71712i	0.251571	−	0.251571i	0.821614	+	0.570044i	$0.193074\pi$
$942$		0			0
$943$	−1.84281	−	6.87746i	−0.0600101	−	0.223961i
$944$		0			0
$945$	17.3664	−	6.76013i	0.564929	−	0.219907i
$946$		0			0
$947$	−2.41686	+	9.01986i	−0.0785375	+	0.293106i	−0.994012	−	0.109270i	$-0.965149\pi$
$947$	−2.41686	+	9.01986i	−0.0785375	+	0.293106i	0.915475	+	0.402376i	$0.131815\pi$
$948$		0			0
$949$	25.2721	+	54.1015i	0.820367	+	1.75621i
$950$		0			0
$951$	19.6715	−	0.717792i	0.637892	−	0.0232760i
$952$		0			0
$953$	5.24649	−	9.08718i	0.169950	−	0.294363i	−0.768452	−	0.639908i	$-0.778973\pi$
$953$	5.24649	−	9.08718i	0.169950	−	0.294363i	0.938402	+	0.345545i	$0.112306\pi$
$954$		0			0
$955$	36.8012	−	9.86084i	1.19086	−	0.319089i
$956$		0			0
$957$	−18.9187	+	35.7157i	−0.611555	+	1.15453i
$958$		0			0
$959$	−10.5373	−	18.2511i	−0.340266	−	0.589358i
$960$		0			0
$961$			4.21839i			0.136077i
$962$		0			0
$963$	−3.86409	−	5.69022i	−0.124519	−	0.183365i
$964$		0			0
$965$	17.1734	−	9.91506i	0.552831	−	0.319177i
$966$		0			0
$967$	13.3894	+	13.3894i	0.430575	+	0.430575i	0.888824	−	0.458249i	$-0.151523\pi$
$967$	13.3894	+	13.3894i	0.430575	+	0.430575i	−0.458249	+	0.888824i	$0.651523\pi$
$968$		0			0
$969$	−3.57069	+	2.23900i	−0.114707	+	0.0719270i
$970$		0			0
$971$	36.1983	+	20.8991i	1.16166	+	0.670684i	0.951701	−	0.307026i	$-0.0993339\pi$
$971$	36.1983	+	20.8991i	1.16166	+	0.670684i	0.209958	+	0.977710i	$0.432667\pi$
$972$		0			0
$973$	−15.9647	−	4.27773i	−0.511806	−	0.137138i
$974$		0			0
$975$	−0.235307	−	0.459275i	−0.00753587	−	0.0147086i
$976$		0			0
$977$	−51.8326	−	13.8885i	−1.65827	−	0.444332i	−0.696360	−	0.717693i	$-0.745198\pi$
$977$	−51.8326	−	13.8885i	−1.65827	−	0.444332i	−0.961912	+	0.273360i	$0.911865\pi$
$978$		0			0
$979$	18.8382	+	10.8763i	0.602072	+	0.347607i
$980$		0			0
$981$	−8.59407	+	9.94912i	−0.274388	+	0.317651i
$982$		0			0
$983$	3.22088	+	3.22088i	0.102730	+	0.102730i	0.756604	−	0.653874i	$-0.226857\pi$
$983$	3.22088	+	3.22088i	0.102730	+	0.102730i	−0.653874	+	0.756604i	$0.726857\pi$
$984$		0			0
$985$	−19.1680	+	11.0667i	−0.610745	+	0.352614i
$986$		0			0
$987$	−26.0965	+	8.02322i	−0.830661	+	0.255382i
$988$		0			0
$989$			24.8674i			0.790738i
$990$		0			0
$991$	−0.213053	−	0.369019i	−0.00676785	−	0.0117223i	0.862622	−	0.505850i	$-0.168821\pi$
$991$	−0.213053	−	0.369019i	−0.00676785	−	0.0117223i	−0.869389	+	0.494127i	$0.835488\pi$
$992$		0			0
$993$	−35.8020	−	18.9644i	−1.13614	−	0.601816i
$994$		0			0
$995$	6.83548	−	1.83156i	0.216699	−	0.0580644i
$996$		0			0
$997$	−20.9763	+	36.3321i	−0.664327	+	1.15065i	0.315140	+	0.949045i	$0.397948\pi$
$997$	−20.9763	+	36.3321i	−0.664327	+	1.15065i	−0.979467	+	0.201603i	$0.935385\pi$
$998$		0			0
$999$	−6.19222	+	4.54351i	−0.195913	+	0.143750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.401.11		56
3.2	odd	2	inner	624.2.cn.f.401.9		56
4.3	odd	2		312.2.bp.a.89.4	✓	56
12.11	even	2		312.2.bp.a.89.6	yes	56
13.6	odd	12	inner	624.2.cn.f.305.9		56
39.32	even	12	inner	624.2.cn.f.305.11		56
52.19	even	12		312.2.bp.a.305.6	yes	56
156.71	odd	12		312.2.bp.a.305.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.4	✓	56	4.3	odd	2
312.2.bp.a.89.6	yes	56	12.11	even	2
312.2.bp.a.305.4	yes	56	156.71	odd	12
312.2.bp.a.305.6	yes	56	52.19	even	12
624.2.cn.f.305.9		56	13.6	odd	12	inner
624.2.cn.f.305.11		56	39.32	even	12	inner
624.2.cn.f.401.9		56	3.2	odd	2	inner
624.2.cn.f.401.11		56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26859 + 1.17927i) q^{3} +(-1.56802 + 1.56802i) q^{5} +(0.418596 + 1.56222i) q^{7} +(0.218643 + 2.99202i) q^{9} +O(q^{10})\)	\(q+(1.26859 + 1.17927i) q^{3} +(-1.56802 + 1.56802i) q^{5} +(0.418596 + 1.56222i) q^{7} +(0.218643 + 2.99202i) q^{9} +(0.781891 - 2.91806i) q^{11} +(-1.23090 + 3.38894i) q^{13} +(-3.83829 + 0.140055i) q^{15} +(-1.03846 + 1.79867i) q^{17} +(1.13167 - 0.303230i) q^{19} +(-1.31126 + 2.47546i) q^{21} +(-2.51856 - 4.36228i) q^{23} +0.0826334i q^{25} +(-3.25104 + 4.05349i) q^{27} +(-6.68935 + 3.86210i) q^{29} +(4.19633 + 4.19633i) q^{31} +(4.43308 - 2.77976i) q^{33} +(-3.10596 - 1.79323i) q^{35} +(1.42771 + 0.382554i) q^{37} +(-5.55798 + 2.84761i) q^{39} +(1.36535 + 0.365846i) q^{41} +(-4.27542 - 2.46841i) q^{43} +(-5.03438 - 4.34871i) q^{45} +(6.89160 + 6.89160i) q^{47} +(3.79686 - 2.19212i) q^{49} +(-3.43850 + 1.05715i) q^{51} -9.85591i q^{53} +(3.34955 + 5.80159i) q^{55} +(1.79321 + 0.949870i) q^{57} +(13.8606 - 3.71393i) q^{59} +(-5.63954 + 9.76798i) q^{61} +(-4.58268 + 1.59402i) q^{63} +(-3.38384 - 7.24399i) q^{65} +(1.67035 - 6.23384i) q^{67} +(1.94928 - 8.50401i) q^{69} +(1.21689 + 4.54151i) q^{71} +(11.7107 - 11.7107i) q^{73} +(-0.0974471 + 0.104828i) q^{75} +4.88595 q^{77} +2.81772 q^{79} +(-8.90439 + 1.30837i) q^{81} +(-7.24736 + 7.24736i) q^{83} +(-1.19202 - 4.44868i) q^{85} +(-13.0405 - 2.98913i) q^{87} +(-1.86361 + 6.95510i) q^{89} +(-5.80952 - 0.504343i) q^{91} +(0.374816 + 10.2720i) q^{93} +(-1.29901 + 2.24995i) q^{95} +(10.6203 - 2.84569i) q^{97} +(8.90184 + 1.70142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^7	\( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 4 * q^7 + 8 * q^13 + 8 * q^15 - 4 * q^19 + 16 * q^21 - 24 * q^27 + 36 * q^31 + 28 * q^33 + 20 * q^37 - 16 * q^39 + 84 * q^43 + 12 * q^45 - 12 * q^49 + 24 * q^55 - 36 * q^57 - 24 * q^61 + 12 * q^63 + 32 * q^67 - 36 * q^69 - 20 * q^73 + 60 * q^75 + 32 * q^79 - 88 * q^85 + 16 * q^87 - 28 * q^91 - 88 * q^93 - 36 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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