LMFDB - Embedded newform 624.2.cn.f.305.3

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			305.3
Character	$\chi$	$=$	624.305
Dual form			624.2.cn.f.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52267 + 0.825508i) q^{3} +(1.33870 + 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(1.63707 - 2.51396i) q^{9} +O(q^{10})$	\(q+(-1.52267 + 0.825508i) q^{3} +(1.33870 + 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(1.63707 - 2.51396i) q^{9} +(0.256724 + 0.958107i) q^{11} +(-3.27036 + 1.51814i) q^{13} +(-3.14352 - 0.933300i) q^{15} +(2.36097 + 4.08932i) q^{17} +(-1.44252 - 0.386521i) q^{19} +(-0.882285 - 3.68517i) q^{21} +(1.71229 - 2.96577i) q^{23} -1.41574i q^{25} +(-0.417438 + 5.17936i) q^{27} +(-0.733696 - 0.423600i) q^{29} +(-3.66157 + 3.66157i) q^{31} +(-1.18183 - 1.24696i) q^{33} +(-3.58699 + 2.07095i) q^{35} +(-10.5491 + 2.82661i) q^{37} +(3.72645 - 5.01134i) q^{39} +(-8.93255 + 2.39347i) q^{41} +(-6.05002 + 3.49298i) q^{43} +(5.55700 - 1.17389i) q^{45} +(0.384064 - 0.384064i) q^{47} +(1.91712 + 1.10685i) q^{49} +(-6.97075 - 4.27770i) q^{51} +10.3968i q^{53} +(-0.938944 + 1.62630i) q^{55} +(2.51556 - 0.602263i) q^{57} +(11.7285 + 3.14264i) q^{59} +(2.83411 + 4.90882i) q^{61} +(4.38557 + 4.88298i) q^{63} +(-6.41038 - 2.34570i) q^{65} +(-1.52023 - 5.67359i) q^{67} +(-0.158991 + 5.92942i) q^{69} +(2.69283 - 10.0498i) q^{71} +(-0.393272 - 0.393272i) q^{73} +(1.16871 + 2.15572i) q^{75} -2.17005 q^{77} +10.0483 q^{79} +(-3.63998 - 8.23107i) q^{81} +(2.25706 + 2.25706i) q^{83} +(-2.31375 + 8.63503i) q^{85} +(1.46686 + 0.0393325i) q^{87} +(-4.60143 - 17.1728i) q^{89} +(-1.35637 - 7.77060i) q^{91} +(2.55273 - 8.59804i) q^{93} +(-1.41367 - 2.44854i) q^{95} +(8.28096 + 2.21888i) q^{97} +(2.82892 + 0.923099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

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
$3$	−1.52267	+	0.825508i	−0.879116	+	0.476607i
$3$	−1.52267	+	0.825508i	−0.879116	+	0.476607i
$4$		0			0
$5$	1.33870	+	1.33870i	0.598687	+	0.598687i	0.939963	−	0.341276i	$-0.110859\pi$
$5$	1.33870	+	1.33870i	0.598687	+	0.598687i	−0.341276	+	0.939963i	$0.610859\pi$
$6$		0			0
$7$	−0.566234	+	2.11322i	−0.214016	+	0.798720i	0.772494	+	0.635022i	$0.219009\pi$
$7$	−0.566234	+	2.11322i	−0.214016	+	0.798720i	−0.986510	+	0.163698i	$0.947658\pi$
$8$		0			0
$9$	1.63707	−	2.51396i	0.545691	−	0.837986i
$10$		0			0
$11$	0.256724	+	0.958107i	0.0774052	+	0.288880i	0.993768	−	0.111469i	$-0.0355555\pi$
$11$	0.256724	+	0.958107i	0.0774052	+	0.288880i	−0.916363	+	0.400349i	$0.868889\pi$
$12$		0			0
$13$	−3.27036	+	1.51814i	−0.907034	+	0.421057i
$13$	−3.27036	+	1.51814i	−0.907034	+	0.421057i
$14$		0			0
$15$	−3.14352	−	0.933300i	−0.811653	−	0.240977i
$16$		0			0
$17$	2.36097	+	4.08932i	0.572619	+	0.991806i	0.996296	+	0.0859920i	$0.0274060\pi$
$17$	2.36097	+	4.08932i	0.572619	+	0.991806i	−0.423677	+	0.905814i	$0.639261\pi$
$18$		0			0
$19$	−1.44252	−	0.386521i	−0.330936	−	0.0886741i	0.0895251	−	0.995985i	$-0.471465\pi$
$19$	−1.44252	−	0.386521i	−0.330936	−	0.0886741i	−0.420461	+	0.907310i	$0.638132\pi$
$20$		0			0
$21$	−0.882285	−	3.68517i	−0.192530	−	0.804170i
$22$		0			0
$23$	1.71229	−	2.96577i	0.357037	−	0.618407i	−0.630427	−	0.776248i	$-0.717120\pi$
$23$	1.71229	−	2.96577i	0.357037	−	0.618407i	0.987464	+	0.157842i	$0.0504536\pi$
$24$		0			0
$25$		−	1.41574i		−	0.283149i
$26$		0			0
$27$	−0.417438	+	5.17936i	−0.0803360	+	0.996768i
$28$		0			0
$29$	−0.733696	−	0.423600i	−0.136244	−	0.0786605i	0.430329	−	0.902672i	$-0.358398\pi$
$29$	−0.733696	−	0.423600i	−0.136244	−	0.0786605i	−0.566573	+	0.824012i	$0.691731\pi$
$30$		0			0
$31$	−3.66157	+	3.66157i	−0.657638	+	0.657638i	−0.954821	−	0.297183i	$-0.903953\pi$
$31$	−3.66157	+	3.66157i	−0.657638	+	0.657638i	0.297183	+	0.954821i	$0.403953\pi$
$32$		0			0
$33$	−1.18183	−	1.24696i	−0.205731	−	0.217067i
$34$		0			0
$35$	−3.58699	+	2.07095i	−0.606312	+	0.350054i
$36$		0			0
$37$	−10.5491	+	2.82661i	−1.73425	+	0.464692i	−0.981156	−	0.193217i	$-0.938108\pi$
$37$	−10.5491	+	2.82661i	−1.73425	+	0.464692i	−0.753098	+	0.657909i	$0.771441\pi$
$38$		0			0
$39$	3.72645	−	5.01134i	0.596710	−	0.802457i
$40$		0			0
$41$	−8.93255	+	2.39347i	−1.39503	+	0.373797i	−0.876558	−	0.481297i	$-0.840166\pi$
$41$	−8.93255	+	2.39347i	−1.39503	+	0.373797i	−0.518473	+	0.855094i	$0.673499\pi$
$42$		0			0
$43$	−6.05002	+	3.49298i	−0.922620	+	0.532675i	−0.884470	−	0.466597i	$-0.845480\pi$
$43$	−6.05002	+	3.49298i	−0.922620	+	0.532675i	−0.0381501	+	0.999272i	$0.512146\pi$
$44$		0			0
$45$	5.55700	−	1.17389i	0.828389	−	0.174993i
$46$		0			0
$47$	0.384064	−	0.384064i	0.0560215	−	0.0560215i	−0.678541	−	0.734563i	$-0.737387\pi$
$47$	0.384064	−	0.384064i	0.0560215	−	0.0560215i	0.734563	+	0.678541i	$0.237387\pi$
$48$		0			0
$49$	1.91712	+	1.10685i	0.273874	+	0.158121i
$50$		0			0
$51$	−6.97075	−	4.27770i	−0.976100	−	0.598998i
$52$		0			0
$53$			10.3968i			1.42811i	0.700090	+	0.714054i	$0.253143\pi$
$53$			10.3968i			1.42811i	−0.700090	+	0.714054i	$0.746857\pi$
$54$		0			0
$55$	−0.938944	+	1.62630i	−0.126607	+	0.219290i
$56$		0			0
$57$	2.51556	−	0.602263i	0.333194	−	0.0797717i
$58$		0			0
$59$	11.7285	+	3.14264i	1.52692	+	0.409137i	0.922013	−	0.387159i	$-0.126543\pi$
$59$	11.7285	+	3.14264i	1.52692	+	0.409137i	0.604908	+	0.796296i	$0.293210\pi$
$60$		0			0
$61$	2.83411	+	4.90882i	0.362870	+	0.628510i	0.988432	−	0.151665i	$-0.0484635\pi$
$61$	2.83411	+	4.90882i	0.362870	+	0.628510i	−0.625562	+	0.780175i	$0.715130\pi$
$62$		0			0
$63$	4.38557	+	4.88298i	0.552530	+	0.615198i
$64$		0			0
$65$	−6.41038	−	2.34570i	−0.795110	−	0.290948i
$66$		0			0
$67$	−1.52023	−	5.67359i	−0.185726	−	0.693139i	−0.994474	−	0.104984i	$-0.966521\pi$
$67$	−1.52023	−	5.67359i	−0.185726	−	0.693139i	0.808748	−	0.588155i	$-0.200146\pi$
$68$		0			0
$69$	−0.158991	+	5.92942i	−0.0191403	+	0.713818i
$70$		0			0
$71$	2.69283	−	10.0498i	0.319580	−	1.19269i	−0.600069	−	0.799948i	$-0.704860\pi$
$71$	2.69283	−	10.0498i	0.319580	−	1.19269i	0.919649	−	0.392741i	$-0.128473\pi$
$72$		0			0
$73$	−0.393272	−	0.393272i	−0.0460290	−	0.0460290i	0.683718	−	0.729747i	$-0.260362\pi$
$73$	−0.393272	−	0.393272i	−0.0460290	−	0.0460290i	−0.729747	+	0.683718i	$0.760362\pi$
$74$		0			0
$75$	1.16871	+	2.15572i	0.134951	+	0.248921i
$76$		0			0
$77$	−2.17005			−0.247300
$78$		0			0
$79$	10.0483			1.13052			0.565261	−	0.824912i	$-0.308775\pi$
$79$	10.0483			1.13052			0.565261	+	0.824912i	$0.308775\pi$
$80$		0			0
$81$	−3.63998	−	8.23107i	−0.404442	−	0.914564i
$82$		0			0
$83$	2.25706	+	2.25706i	0.247745	+	0.247745i	0.820045	−	0.572300i	$-0.193949\pi$
$83$	2.25706	+	2.25706i	0.247745	+	0.247745i	−0.572300	+	0.820045i	$0.693949\pi$
$84$		0			0
$85$	−2.31375	+	8.63503i	−0.250961	+	0.936600i
$86$		0			0
$87$	1.46686	+	0.0393325i	0.157264	+	0.00421689i
$88$		0			0
$89$	−4.60143	−	17.1728i	−0.487750	−	1.82031i	−0.567342	−	0.823482i	$-0.692028\pi$
$89$	−4.60143	−	17.1728i	−0.487750	−	1.82031i	0.0795919	−	0.996828i	$-0.474638\pi$
$90$		0			0
$91$	−1.35637	−	7.77060i	−0.142186	−	0.814580i
$92$		0			0
$93$	2.55273	−	8.59804i	0.264705	−	0.891575i
$94$		0			0
$95$	−1.41367	−	2.44854i	−0.145039	−	0.251215i
$96$		0			0
$97$	8.28096	+	2.21888i	0.840804	+	0.225293i	0.653422	−	0.756994i	$-0.273333\pi$
$97$	8.28096	+	2.21888i	0.840804	+	0.225293i	0.187383	+	0.982287i	$0.440000\pi$
$98$		0			0
$99$	2.82892	+	0.923099i	0.284317	+	0.0927749i
$100$		0			0
$101$	−1.02109	+	1.76859i	−0.101603	+	0.175981i	−0.912345	−	0.409422i	$-0.865730\pi$
$101$	−1.02109	+	1.76859i	−0.101603	+	0.175981i	0.810742	+	0.585403i	$0.199064\pi$
$102$		0			0
$103$			14.3415i			1.41311i	0.707656	+	0.706557i	$0.249753\pi$
$103$			14.3415i			1.41311i	−0.707656	+	0.706557i	$0.750247\pi$
$104$		0			0
$105$	3.75223	−	6.11447i	0.366180	−	0.596711i
$106$		0			0
$107$	−0.334916	−	0.193364i	−0.0323776	−	0.0186932i	0.483724	−	0.875221i	$-0.339284\pi$
$107$	−0.334916	−	0.193364i	−0.0323776	−	0.0186932i	−0.516101	+	0.856527i	$0.672617\pi$
$108$		0			0
$109$	−8.24097	+	8.24097i	−0.789342	+	0.789342i	−0.981386	−	0.192044i	$-0.938488\pi$
$109$	−8.24097	+	8.24097i	−0.789342	+	0.789342i	0.192044	+	0.981386i	$0.438488\pi$
$110$		0			0
$111$	13.7294	−	13.0123i	1.30314	−	1.23508i
$112$		0			0
$113$	10.3438	−	5.97200i	0.973063	−	0.561798i	0.0728946	−	0.997340i	$-0.476776\pi$
$113$	10.3438	−	5.97200i	0.973063	−	0.561798i	0.900169	+	0.435541i	$0.143443\pi$
$114$		0			0
$115$	6.26254	−	1.67804i	0.583985	−	0.156478i
$116$		0			0
$117$	−1.53727	+	10.7069i	−0.142121	+	0.989849i
$118$		0			0
$119$	−9.97847	+	2.67372i	−0.914725	+	0.245100i
$120$		0			0
$121$	8.67422	−	5.00806i	0.788565	−	0.455278i
$122$		0			0
$123$	11.6255	−	11.0184i	1.04824	−	0.993493i
$124$		0			0
$125$	8.58878	−	8.58878i	0.768204	−	0.768204i
$126$		0			0
$127$	0.109854	+	0.0634245i	0.00974800	+	0.00562801i	0.504866	−	0.863198i	$-0.331542\pi$
$127$	0.109854	+	0.0634245i	0.00974800	+	0.00562801i	−0.495118	+	0.868826i	$0.664875\pi$
$128$		0			0
$129$	6.32873	−	10.3130i	0.557214	−	0.908011i
$130$		0			0
$131$		−	20.8758i		−	1.82392i	−0.410274	−	0.911962i	$-0.634567\pi$
$131$		−	20.8758i		−	1.82392i	0.410274	−	0.911962i	$-0.365433\pi$
$132$		0			0
$133$	1.63361	−	2.82949i	0.141652	−	0.245348i
$134$		0			0
$135$	−7.49245	+	6.37480i	−0.644848	+	0.548655i
$136$		0			0
$137$	12.2978	+	3.29520i	1.05068	+	0.281528i	0.742531	−	0.669812i	$-0.233625\pi$
$137$	12.2978	+	3.29520i	1.05068	+	0.281528i	0.308145	+	0.951340i	$0.400292\pi$
$138$		0			0
$139$	9.15970	+	15.8651i	0.776915	+	1.34566i	0.933712	+	0.358026i	$0.116550\pi$
$139$	9.15970	+	15.8651i	0.776915	+	1.34566i	−0.156796	+	0.987631i	$0.550117\pi$
$140$		0			0
$141$	−0.267757	+	0.901853i	−0.0225492	+	0.0759497i
$142$		0			0
$143$	−2.29412	−	2.74361i	−0.191844	−	0.229432i
$144$		0			0
$145$	−0.415127	−	1.54928i	−0.0344744	−	0.128660i
$146$		0			0
$147$	−3.83286	−	0.102774i	−0.316129	−	0.00847669i
$148$		0			0
$149$	0.550277	−	2.05366i	0.0450804	−	0.168242i	−0.939716	−	0.341957i	$-0.888910\pi$
$149$	0.550277	−	2.05366i	0.0450804	−	0.168242i	0.984796	+	0.173714i	$0.0555770\pi$
$150$		0			0
$151$	−2.93665	−	2.93665i	−0.238981	−	0.238981i	0.577447	−	0.816428i	$-0.304049\pi$
$151$	−2.93665	−	2.93665i	−0.238981	−	0.238981i	−0.816428	+	0.577447i	$0.804049\pi$
$152$		0			0
$153$	14.1455	+	0.759138i	1.14359	+	0.0613727i
$154$		0			0
$155$	−9.80352			−0.787438
$156$		0			0
$157$	16.1940			1.29242			0.646211	−	0.763159i	$-0.276353\pi$
$157$	16.1940			1.29242			0.646211	+	0.763159i	$0.276353\pi$
$158$		0			0
$159$	−8.58263	−	15.8309i	−0.680647	−	1.25547i
$160$		0			0
$161$	5.29776	+	5.29776i	0.417522	+	0.417522i
$162$		0			0
$163$	−0.995027	+	3.71349i	−0.0779365	+	0.290863i	−0.993883	−	0.110437i	$-0.964775\pi$
$163$	−0.995027	+	3.71349i	−0.0779365	+	0.290863i	0.915947	+	0.401300i	$0.131442\pi$
$164$		0			0
$165$	0.0871838	−	3.25143i	0.00678725	−	0.253123i
$166$		0			0
$167$	6.12521	+	22.8596i	0.473983	+	1.76893i	0.625238	+	0.780434i	$0.285002\pi$
$167$	6.12521	+	22.8596i	0.473983	+	1.76893i	−0.151255	+	0.988495i	$0.548332\pi$
$168$		0			0
$169$	8.39049	−	9.92974i	0.645422	−	0.763826i
$170$		0			0
$171$	−3.33321	+	2.99367i	−0.254897	+	0.228931i
$172$		0			0
$173$	7.36150	+	12.7505i	0.559684	+	0.969401i	0.997523	+	0.0703477i	$0.0224109\pi$
$173$	7.36150	+	12.7505i	0.559684	+	0.969401i	−0.437838	+	0.899054i	$0.644256\pi$
$174$		0			0
$175$	2.99177	+	0.801643i	0.226157	+	0.0605985i
$176$		0			0
$177$	−20.4530	+	4.89675i	−1.53734	+	0.368062i
$178$		0			0
$179$	−8.53187	+	14.7776i	−0.637702	+	1.10453i	0.348234	+	0.937408i	$0.386782\pi$
$179$	−8.53187	+	14.7776i	−0.637702	+	1.10453i	−0.985936	+	0.167125i	$0.946552\pi$
$180$		0			0
$181$		−	3.51901i		−	0.261566i	−0.991411	−	0.130783i	$-0.958251\pi$
$181$		−	3.51901i		−	0.261566i	0.991411	−	0.130783i	$-0.0417491\pi$
$182$		0			0
$183$	−8.36769	−	5.13495i	−0.618557	−	0.379587i
$184$		0			0
$185$	−17.9061	−	10.3381i	−1.31648	−	0.760070i
$186$		0			0
$187$	−3.31189	+	3.31189i	−0.242189	+	0.242189i
$188$		0			0
$189$	−10.7087	−	3.81487i	−0.778945	−	0.277491i
$190$		0			0
$191$	−18.6177	+	10.7490i	−1.34713	+	0.777767i	−0.987842	−	0.155459i	$-0.950314\pi$
$191$	−18.6177	+	10.7490i	−1.34713	+	0.777767i	−0.359290	+	0.933226i	$0.616981\pi$
$192$		0			0
$193$	−3.88032	+	1.03973i	−0.279312	+	0.0748413i	−0.395755	−	0.918356i	$-0.629517\pi$
$193$	−3.88032	+	1.03973i	−0.279312	+	0.0748413i	0.116444	+	0.993197i	$0.462851\pi$
$194$		0			0
$195$	11.6973	−	1.72009i	0.837662	−	0.123178i
$196$		0			0
$197$	7.74656	−	2.07569i	0.551920	−	0.147886i	0.0279283	−	0.999610i	$-0.491109\pi$
$197$	7.74656	−	2.07569i	0.551920	−	0.147886i	0.523992	+	0.851723i	$0.324442\pi$
$198$		0			0
$199$	−9.75011	+	5.62923i	−0.691167	+	0.399046i	−0.804049	−	0.594563i	$-0.797325\pi$
$199$	−9.75011	+	5.62923i	−0.691167	+	0.399046i	0.112882	+	0.993608i	$0.463992\pi$
$200$		0			0
$201$	6.99841	+	7.38406i	0.493630	+	0.520831i
$202$		0			0
$203$	1.31060	−	1.31060i	0.0919862	−	0.0919862i
$204$		0			0
$205$	−15.1622	−	8.75390i	−1.05897	−	0.611399i
$206$		0			0
$207$	−4.65269	−	9.15982i	−0.323384	−	0.636651i
$208$		0			0
$209$		−	1.48132i		−	0.102465i
$210$		0			0
$211$	11.9794	−	20.7489i	0.824696	−	1.42842i	−0.0774545	−	0.996996i	$-0.524679\pi$
$211$	11.9794	−	20.7489i	0.824696	−	1.42842i	0.902151	−	0.431420i	$-0.141987\pi$
$212$		0			0
$213$	4.19587	+	17.5255i	0.287496	+	1.20083i
$214$		0			0
$215$	−12.7753	−	3.42312i	−0.871266	−	0.233455i
$216$		0			0
$217$	−5.66438	−	9.81100i	−0.384523	−	0.666014i
$218$		0			0
$219$	0.923475	+	0.274176i	0.0624027	+	0.0185271i
$220$		0			0
$221$	−13.9294	−	9.78925i	−0.936992	−	0.658496i
$222$		0			0
$223$	0.495422	+	1.84894i	0.0331759	+	0.123814i	0.980528	−	0.196380i	$-0.0629185\pi$
$223$	0.495422	+	1.84894i	0.0331759	+	0.123814i	−0.947352	+	0.320194i	$0.896252\pi$
$224$		0			0
$225$	−3.55912	−	2.31768i	−0.237275	−	0.154512i
$226$		0			0
$227$	2.83237	−	10.5705i	0.187991	−	0.701591i	−0.805980	−	0.591943i	$-0.798361\pi$
$227$	2.83237	−	10.5705i	0.187991	−	0.701591i	0.993970	−	0.109648i	$-0.0349723\pi$
$228$		0			0
$229$	2.18006	+	2.18006i	0.144063	+	0.144063i	0.775460	−	0.631397i	$-0.217518\pi$
$229$	2.18006	+	2.18006i	0.144063	+	0.144063i	−0.631397	+	0.775460i	$0.717518\pi$
$230$		0			0
$231$	3.30428	−	1.79140i	0.217406	−	0.117865i
$232$		0			0
$233$	7.80150			0.511093			0.255546	−	0.966797i	$-0.417745\pi$
$233$	7.80150			0.511093			0.255546	+	0.966797i	$0.417745\pi$
$234$		0			0
$235$	1.02830			0.0670787
$236$		0			0
$237$	−15.3003	+	8.29495i	−0.993861	+	0.538815i
$238$		0			0
$239$	14.8365	+	14.8365i	0.959695	+	0.959695i	0.999219	−	0.0395239i	$-0.0125841\pi$
$239$	14.8365	+	14.8365i	0.959695	+	0.959695i	−0.0395239	+	0.999219i	$0.512584\pi$
$240$		0			0
$241$	−4.24837	+	15.8551i	−0.273661	+	1.02132i	0.683072	+	0.730351i	$0.260644\pi$
$241$	−4.24837	+	15.8551i	−0.273661	+	1.02132i	−0.956733	+	0.290967i	$0.906023\pi$
$242$		0			0
$243$	12.3373	+	9.52841i	0.791439	+	0.611248i
$244$		0			0
$245$	1.08471	+	4.04820i	0.0692997	+	0.258630i
$246$		0			0
$247$	5.30434	−	0.925883i	0.337507	−	0.0589125i
$248$		0			0
$249$	−5.29999	−	1.57355i	−0.335873	−	0.0997196i
$250$		0			0
$251$	2.11649	+	3.66588i	0.133592	+	0.231388i	0.925059	−	0.379824i	$-0.124016\pi$
$251$	2.11649	+	3.66588i	0.133592	+	0.231388i	−0.791467	+	0.611212i	$0.790682\pi$
$252$		0			0
$253$	3.28112	+	0.879172i	0.206282	+	0.0552731i
$254$		0			0
$255$	−3.60520	−	15.0583i	−0.225766	−	0.942990i
$256$		0			0
$257$	−3.01424	+	5.22082i	−0.188023	+	0.325666i	−0.944591	−	0.328249i	$-0.893541\pi$
$257$	−3.01424	+	5.22082i	−0.188023	+	0.325666i	0.756568	+	0.653915i	$0.226875\pi$
$258$		0			0
$259$		−	23.8929i		−	1.48464i
$260$		0			0
$261$	−2.26603	+	1.15102i	−0.140264	+	0.0712462i
$262$		0			0
$263$	16.9076	+	9.76159i	1.04257	+	0.601925i	0.920559	−	0.390604i	$-0.127734\pi$
$263$	16.9076	+	9.76159i	1.04257	+	0.601925i	0.122006	+	0.992529i	$0.461067\pi$
$264$		0			0
$265$	−13.9182	+	13.9182i	−0.854989	+	0.854989i
$266$		0			0
$267$	21.1827	+	22.3500i	1.29636	+	1.36780i
$268$		0			0
$269$	22.7011	−	13.1065i	1.38411	−	0.799118i	0.391469	−	0.920191i	$-0.371967\pi$
$269$	22.7011	−	13.1065i	1.38411	−	0.799118i	0.992644	+	0.121074i	$0.0386337\pi$
$270$		0			0
$271$	−13.9542	+	3.73902i	−0.847657	+	0.227129i	−0.656402	−	0.754411i	$-0.727923\pi$
$271$	−13.9542	+	3.73902i	−0.847657	+	0.227129i	−0.191255	+	0.981540i	$0.561256\pi$
$272$		0			0
$273$	8.48000	+	10.7124i	0.513233	+	0.648343i
$274$		0			0
$275$	1.35643	−	0.363456i	0.0817961	−	0.0219172i
$276$		0			0
$277$	−4.00445	+	2.31197i	−0.240604	+	0.138913i	−0.615454	−	0.788172i	$-0.711028\pi$
$277$	−4.00445	+	2.31197i	−0.240604	+	0.138913i	0.374850	+	0.927085i	$0.377694\pi$
$278$		0			0
$279$	3.21078	+	15.1993i	0.192224	+	0.909959i
$280$		0			0
$281$	−2.83565	+	2.83565i	−0.169161	+	0.169161i	−0.786611	−	0.617450i	$-0.788166\pi$
$281$	−2.83565	+	2.83565i	−0.169161	+	0.169161i	0.617450	+	0.786611i	$0.288166\pi$
$282$		0			0
$283$	−21.9372	−	12.6654i	−1.30403	−	0.752883i	−0.322938	−	0.946420i	$-0.604671\pi$
$283$	−21.9372	−	12.6654i	−1.30403	−	0.752883i	−0.981093	+	0.193537i	$0.938004\pi$
$284$		0			0
$285$	4.17384	+	2.56134i	0.247237	+	0.151721i
$286$		0			0
$287$		−	20.2317i		−	1.19424i
$288$		0			0
$289$	−2.64835	+	4.58708i	−0.155785	+	0.269828i
$290$		0			0
$291$	−14.4409	+	3.45737i	−0.846541	+	0.202675i
$292$		0			0
$293$	−17.0816	−	4.57700i	−0.997917	−	0.267391i	−0.277345	−	0.960770i	$-0.589454\pi$
$293$	−17.0816	−	4.57700i	−0.997917	−	0.267391i	−0.720573	+	0.693379i	$0.756121\pi$
$294$		0			0
$295$	11.4939	+	19.9081i	0.669202	+	1.15909i
$296$		0			0
$297$	−5.06955	+	0.929715i	−0.294165	+	0.0539475i
$298$		0			0
$299$	−1.09734	+	12.2986i	−0.0634607	+	0.711249i
$300$		0			0
$301$	−3.95569	−	14.7628i	−0.228002	−	0.850917i
$302$		0			0
$303$	0.0948117	−	3.53591i	0.00544679	−	0.203132i
$304$		0			0
$305$	−2.77742	+	10.3655i	−0.159035	+	0.593526i
$306$		0			0
$307$	−16.5562	−	16.5562i	−0.944910	−	0.944910i	0.0536497	−	0.998560i	$-0.482915\pi$
$307$	−16.5562	−	16.5562i	−0.944910	−	0.944910i	−0.998560	+	0.0536497i	$0.982915\pi$
$308$		0			0
$309$	−11.8390	−	21.8375i	−0.673500	−	1.24229i
$310$		0			0
$311$	27.9565			1.58527			0.792635	−	0.609697i	$-0.208709\pi$
$311$	27.9565			1.58527			0.792635	+	0.609697i	$0.208709\pi$
$312$		0			0
$313$	22.1801			1.25369			0.626846	−	0.779144i	$-0.284346\pi$
$313$	22.1801			1.25369			0.626846	+	0.779144i	$0.284346\pi$
$314$		0			0
$315$	−0.665886	+	12.4078i	−0.0375184	+	0.699103i
$316$		0			0
$317$	5.44471	+	5.44471i	0.305805	+	0.305805i	0.843280	−	0.537475i	$-0.180622\pi$
$317$	5.44471	+	5.44471i	0.305805	+	0.305805i	−0.537475	+	0.843280i	$0.680622\pi$
$318$		0			0
$319$	0.217496	−	0.811708i	0.0121775	−	0.0454469i
$320$		0			0
$321$	0.669592	+	0.0179544i	0.0373730	+	0.00100212i
$322$		0			0
$323$	−1.82513	−	6.81148i	−0.101553	−	0.379001i
$324$		0			0
$325$	2.14930	+	4.62999i	0.119222	+	0.256826i
$326$		0			0
$327$	5.74533	−	19.3513i	0.317717	−	1.07013i
$328$		0			0
$329$	0.594140	+	1.02908i	0.0327560	+	0.0567350i
$330$		0			0
$331$	−5.61987	−	1.50584i	−0.308896	−	0.0827684i	0.101041	−	0.994882i	$-0.467783\pi$
$331$	−5.61987	−	1.50584i	−0.308896	−	0.0827684i	−0.409937	+	0.912114i	$0.634449\pi$
$332$		0			0
$333$	−10.1636	+	31.1473i	−0.556962	+	1.70686i
$334$		0			0
$335$	5.56011	−	9.63039i	0.303781	−	0.526165i
$336$		0			0
$337$		−	15.0629i		−	0.820528i	−0.911967	−	0.410264i	$-0.865436\pi$
$337$		−	15.0629i		−	0.820528i	0.911967	−	0.410264i	$-0.134564\pi$
$338$		0			0
$339$	−10.8203	+	17.6323i	−0.587679	+	0.957655i
$340$		0			0
$341$	−4.44819	−	2.56817i	−0.240883	−	0.139074i
$342$		0			0
$343$	−14.2534	+	14.2534i	−0.769612	+	0.769612i
$344$		0			0
$345$	−8.15058	+	7.72489i	−0.438812	+	0.415894i
$346$		0			0
$347$	−6.58502	+	3.80186i	−0.353502	+	0.204095i	−0.666227	−	0.745749i	$-0.732092\pi$
$347$	−6.58502	+	3.80186i	−0.353502	+	0.204095i	0.312724	+	0.949844i	$0.398758\pi$
$348$		0			0
$349$	−13.2155	+	3.54107i	−0.707407	+	0.189549i	−0.594546	−	0.804062i	$-0.702668\pi$
$349$	−13.2155	+	3.54107i	−0.707407	+	0.189549i	−0.112861	+	0.993611i	$0.536002\pi$
$350$		0			0
$351$	−6.49783	−	17.5721i	−0.346828	−	0.937929i
$352$		0			0
$353$	−6.31893	+	1.69315i	−0.336323	+	0.0901174i	−0.423028	−	0.906117i	$-0.639033\pi$
$353$	−6.31893	+	1.69315i	−0.336323	+	0.0901174i	0.0867052	+	0.996234i	$0.472366\pi$
$354$		0			0
$355$	17.0586	−	9.84877i	0.905375	−	0.522719i
$356$		0			0
$357$	12.9868	−	12.3085i	0.687334	−	0.651436i
$358$		0			0
$359$	−11.5879	+	11.5879i	−0.611588	+	0.611588i	−0.943360	−	0.331772i	$-0.892354\pi$
$359$	−11.5879	+	11.5879i	−0.611588	+	0.611588i	0.331772	+	0.943360i	$0.392354\pi$
$360$		0			0
$361$	−14.5230	−	8.38487i	−0.764370	−	0.441309i
$362$		0			0
$363$	−9.07381	+	14.7863i	−0.476252	+	0.776078i
$364$		0			0
$365$		−	1.05295i		−	0.0551139i
$366$		0			0
$367$	10.4529	−	18.1049i	0.545635	−	0.945068i	−0.452931	−	0.891545i	$-0.649622\pi$
$367$	10.4529	−	18.1049i	0.545635	−	0.945068i	0.998567	−	0.0535227i	$-0.0170449\pi$
$368$		0			0
$369$	−8.60617	+	26.3744i	−0.448019	+	1.37299i
$370$		0			0
$371$	−21.9707	−	5.88702i	−1.14066	−	0.305639i
$372$		0			0
$373$	11.5708	+	20.0412i	0.599114	+	1.03770i	0.992952	+	0.118516i	$0.0378138\pi$
$373$	11.5708	+	20.0412i	0.599114	+	1.03770i	−0.393838	+	0.919180i	$0.628853\pi$
$374$		0			0
$375$	−5.98781	+	20.1680i	−0.309209	+	1.04147i
$376$		0			0
$377$	3.04253	+	0.271468i	0.156698	+	0.0139813i
$378$		0			0
$379$	3.41564	+	12.7474i	0.175450	+	0.654788i	0.996475	+	0.0838951i	$0.0267361\pi$
$379$	3.41564	+	12.7474i	0.175450	+	0.654788i	−0.821025	+	0.570893i	$0.806597\pi$
$380$		0			0
$381$	−0.219630	−	0.00588915i	−0.0112520	−	0.000301710i
$382$		0			0
$383$	2.61140	−	9.74587i	0.133436	−	0.497991i	−0.866563	−	0.499067i	$-0.833676\pi$
$383$	2.61140	−	9.74587i	0.133436	−	0.497991i	0.999999	+	0.00107658i	$0.000342686\pi$
$384$		0			0
$385$	−2.90506	−	2.90506i	−0.148055	−	0.148055i
$386$		0			0
$387$	−1.12312	+	20.9278i	−0.0570915	+	1.06382i
$388$		0			0
$389$	−21.6943			−1.09994			−0.549971	−	0.835184i	$-0.685361\pi$
$389$	−21.6943			−1.09994			−0.549971	+	0.835184i	$0.685361\pi$
$390$		0			0
$391$	16.1707			0.817786
$392$		0			0
$393$	17.2331	+	31.7870i	0.869295	+	1.60344i
$394$		0			0
$395$	13.4517	+	13.4517i	0.676829	+	0.676829i
$396$		0			0
$397$	4.57617	−	17.0785i	0.229672	−	0.857146i	−0.750807	−	0.660521i	$-0.770335\pi$
$397$	4.57617	−	17.0785i	0.229672	−	0.857146i	0.980479	−	0.196625i	$-0.0629980\pi$
$398$		0			0
$399$	−0.151685	+	5.65694i	−0.00759376	+	0.283201i
$400$		0			0
$401$	1.42326	+	5.31167i	0.0710741	+	0.265252i	0.992314	−	0.123742i	$-0.0394894\pi$
$401$	1.42326	+	5.31167i	0.0710741	+	0.265252i	−0.921240	+	0.388994i	$0.872823\pi$
$402$		0			0
$403$	6.41587	−	17.5334i	0.319597	−	0.873403i
$404$		0			0
$405$	6.14612	−	15.8918i	0.305403	−	0.789671i
$406$		0			0
$407$	−5.41639	−	9.38147i	−0.268481	−	0.465022i
$408$		0			0
$409$	−19.7035	−	5.27954i	−0.974275	−	0.261056i	−0.263643	−	0.964620i	$-0.584924\pi$
$409$	−19.7035	−	5.27954i	−0.974275	−	0.261056i	−0.710632	+	0.703564i	$0.751591\pi$
$410$		0			0
$411$	−21.4458	+	5.13445i	−1.05784	+	0.253264i
$412$		0			0
$413$	−13.2822	+	23.0054i	−0.653572	+	1.13202i
$414$		0			0
$415$			6.04308i			0.296643i
$416$		0			0
$417$	−27.0440	−	16.5959i	−1.32435	−	0.812706i
$418$		0			0
$419$	30.6973	+	17.7231i	1.49966	+	0.865831i	1.00000		0.000389131i	$-0.000123864\pi$
$419$	30.6973	+	17.7231i	1.49966	+	0.865831i	0.499663	+	0.866220i	$0.333457\pi$
$420$		0			0
$421$	26.7150	−	26.7150i	1.30201	−	1.30201i	0.374972	−	0.927036i	$-0.377652\pi$
$421$	26.7150	−	26.7150i	1.30201	−	1.30201i	0.927036	−	0.374972i	$-0.122348\pi$
$422$		0			0
$423$	−0.336780	−	1.59426i	−0.0163748	−	0.0775157i
$424$		0			0
$425$	5.78943	−	3.34253i	0.280829	−	0.162136i
$426$		0			0
$427$	−11.9782	+	3.20954i	−0.579664	+	0.155320i
$428$		0			0
$429$	5.75807	+	2.28381i	0.278002	+	0.110263i
$430$		0			0
$431$	−25.5938	+	6.85785i	−1.23281	+	0.330331i	−0.815674	−	0.578512i	$-0.803634\pi$
$431$	−25.5938	+	6.85785i	−1.23281	+	0.330331i	−0.417138	+	0.908843i	$0.636967\pi$
$432$		0			0
$433$	−22.5129	+	12.9978i	−1.08190	+	0.624636i	−0.931409	−	0.363975i	$-0.881419\pi$
$433$	−22.5129	+	12.9978i	−1.08190	+	0.624636i	−0.150493	+	0.988611i	$0.548086\pi$
$434$		0			0
$435$	1.91104	+	2.01635i	0.0916275	+	0.0966767i
$436$		0			0
$437$	−3.61634	+	3.61634i	−0.172993	+	0.172993i
$438$		0			0
$439$	21.2539	+	12.2710i	1.01440	+	0.585661i	0.912476	−	0.409131i	$-0.134168\pi$
$439$	21.2539	+	12.2710i	1.01440	+	0.585661i	0.101920	+	0.994793i	$0.467501\pi$
$440$		0			0
$441$	5.92104	−	3.00757i	0.281955	−	0.143217i
$442$		0			0
$443$		−	24.7493i		−	1.17587i	−0.808907	−	0.587937i	$-0.799940\pi$
$443$		−	24.7493i		−	1.17587i	0.808907	−	0.587937i	$-0.200060\pi$
$444$		0			0
$445$	16.8293	−	29.1492i	0.797785	−	1.38180i
$446$		0			0
$447$	0.857420	+	3.58131i	0.0405546	+	0.169390i
$448$		0			0
$449$	18.0387	+	4.83346i	0.851300	+	0.228105i	0.657985	−	0.753031i	$-0.271409\pi$
$449$	18.0387	+	4.83346i	0.851300	+	0.228105i	0.193316	+	0.981137i	$0.438076\pi$
$450$		0			0
$451$	−4.58640	−	7.94388i	−0.215965	−	0.374063i
$452$		0			0
$453$	6.89579	+	2.04733i	0.323992	+	0.0961921i
$454$		0			0
$455$	8.58675	−	12.2183i	0.402553	−	0.572803i
$456$		0			0
$457$	0.610148	+	2.27710i	0.0285415	+	0.106518i	0.978727	−	0.205166i	$-0.0657735\pi$
$457$	0.610148	+	2.27710i	0.0285415	+	0.106518i	−0.950186	+	0.311685i	$0.899107\pi$
$458$		0			0
$459$	−22.1656	+	10.5213i	−1.03460	+	0.491091i
$460$		0			0
$461$	3.36375	−	12.5537i	0.156665	−	0.584683i	−0.842292	−	0.539022i	$-0.818794\pi$
$461$	3.36375	−	12.5537i	0.156665	−	0.584683i	0.998957	−	0.0456608i	$-0.0145393\pi$
$462$		0			0
$463$	−1.03011	−	1.03011i	−0.0478733	−	0.0478733i	0.682765	−	0.730638i	$-0.260777\pi$
$463$	−1.03011	−	1.03011i	−0.0478733	−	0.0478733i	−0.730638	+	0.682765i	$0.760777\pi$
$464$		0			0
$465$	14.9276	−	8.09288i	0.692250	−	0.375298i
$466$		0			0
$467$	−36.9118			−1.70808			−0.854038	−	0.520211i	$-0.825853\pi$
$467$	−36.9118			−1.70808			−0.854038	+	0.520211i	$0.825853\pi$
$468$		0			0
$469$	12.8503			0.593373
$470$		0			0
$471$	−24.6582	+	13.3683i	−1.13619	+	0.615977i
$472$		0			0
$473$	−4.89984	−	4.89984i	−0.225295	−	0.225295i
$474$		0			0
$475$	−0.547215	+	2.04224i	−0.0251080	+	0.0937042i
$476$		0			0
$477$	26.1371	+	17.0203i	1.19674	+	0.779307i
$478$		0			0
$479$	−2.40863	−	8.98914i	−0.110053	−	0.410724i	0.888816	−	0.458264i	$-0.151529\pi$
$479$	−2.40863	−	8.98914i	−0.110053	−	0.410724i	−0.998869	+	0.0475398i	$0.984862\pi$
$480$		0			0
$481$	30.2080	−	25.2590i	1.37737	−	1.15171i
$482$		0			0
$483$	−12.4401	−	3.69342i	−0.566045	−	0.168057i
$484$		0			0
$485$	8.11534	+	14.0562i	0.368498	+	0.638258i
$486$		0			0
$487$	−16.0328	−	4.29597i	−0.726515	−	0.194669i	−0.123438	−	0.992352i	$-0.539392\pi$
$487$	−16.0328	−	4.29597i	−0.726515	−	0.194669i	−0.603077	+	0.797683i	$0.706059\pi$
$488$		0			0
$489$	−1.55041	−	6.47584i	−0.0701121	−	0.292848i
$490$		0			0
$491$	12.3545	−	21.3987i	0.557553	−	0.965709i	−0.440147	−	0.897926i	$-0.645074\pi$
$491$	12.3545	−	21.3987i	0.557553	−	0.965709i	0.997700	−	0.0677839i	$-0.0215928\pi$
$492$		0			0
$493$		−	4.00042i		−	0.180170i
$494$		0			0
$495$	2.55133	+	5.02284i	0.114674	+	0.225760i
$496$		0			0
$497$	19.7126	+	11.3811i	0.884229	+	0.510510i
$498$		0			0
$499$	4.69214	−	4.69214i	0.210049	−	0.210049i	−0.594239	−	0.804288i	$-0.702547\pi$
$499$	4.69214	−	4.69214i	0.210049	−	0.210049i	0.804288	+	0.594239i	$0.202547\pi$
$500$		0			0
$501$	−28.1975	−	29.7513i	−1.25977	−	1.32919i
$502$		0			0
$503$	31.1321	−	17.9741i	1.38811	−	0.801427i	0.395010	−	0.918677i	$-0.370741\pi$
$503$	31.1321	−	17.9741i	1.38811	−	0.801427i	0.993102	+	0.117249i	$0.0374077\pi$
$504$		0			0
$505$	−3.73456	+	1.00067i	−0.166186	+	0.0445293i
$506$		0			0
$507$	−4.57891	+	22.0462i	−0.203357	+	0.979105i
$508$		0			0
$509$	−17.0359	+	4.56477i	−0.755105	+	0.202330i	−0.615781	−	0.787917i	$-0.711160\pi$
$509$	−17.0359	+	4.56477i	−0.755105	+	0.202330i	−0.139324	+	0.990247i	$0.544493\pi$
$510$		0			0
$511$	1.05375	−	0.608385i	0.0466153	−	0.0269134i
$512$		0			0
$513$	2.60409	−	7.30996i	0.114974	−	0.322743i
$514$		0			0
$515$	−19.1991	+	19.1991i	−0.846012	+	0.846012i
$516$		0			0
$517$	0.466573	+	0.269376i	0.0205199	+	0.0118472i
$518$		0			0
$519$	−21.7348	−	13.3379i	−0.954051	−	0.585467i
$520$		0			0
$521$			22.9129i			1.00383i	0.864917	+	0.501915i	$0.167371\pi$
$521$			22.9129i			1.00383i	−0.864917	+	0.501915i	$0.832629\pi$
$522$		0			0
$523$	−6.11740	+	10.5957i	−0.267495	+	0.463316i	−0.968214	−	0.250122i	$-0.919529\pi$
$523$	−6.11740	+	10.5957i	−0.267495	+	0.463316i	0.700719	+	0.713437i	$0.252863\pi$
$524$		0			0
$525$	−5.21726	+	1.24909i	−0.227700	+	0.0545147i
$526$		0			0
$527$	−23.6182	−	6.32848i	−1.02882	−	0.275673i
$528$		0			0
$529$	5.63612	+	9.76205i	0.245049	+	0.424437i
$530$		0			0
$531$	27.1009	−	24.3402i	1.17608	−	1.05628i
$532$		0			0
$533$	25.5790	−	21.3884i	1.10795	−	0.926434i
$534$		0			0
$535$	−0.189497	−	0.707211i	−0.00819266	−	0.0305754i
$536$		0			0
$537$	0.792210	−	29.5447i	0.0341864	−	1.27495i
$538$		0			0
$539$	−0.568310	+	2.12096i	−0.0244789	+	0.0913563i
$540$		0			0
$541$	−17.8177	−	17.8177i	−0.766042	−	0.766042i	0.211365	−	0.977407i	$-0.432209\pi$
$541$	−17.8177	−	17.8177i	−0.766042	−	0.766042i	−0.977407	+	0.211365i	$0.932209\pi$
$542$		0			0
$543$	2.90497	+	5.35831i	0.124664	+	0.229947i
$544$		0			0
$545$	−22.0644			−0.945137
$546$		0			0
$547$	19.4843			0.833087			0.416543	−	0.909116i	$-0.363241\pi$
$547$	19.4843			0.833087			0.416543	+	0.909116i	$0.363241\pi$
$548$		0			0
$549$	16.9802	+	0.911269i	0.724698	+	0.0388920i
$550$		0			0
$551$	0.894639	+	0.894639i	0.0381129	+	0.0381129i
$552$		0			0
$553$	−5.68970	+	21.2342i	−0.241950	+	0.902971i
$554$		0			0
$555$	35.7992	+	0.959920i	1.51959	+	0.0407463i
$556$		0			0
$557$	1.33172	+	4.97004i	0.0564267	+	0.210587i	0.988383	−	0.151983i	$-0.0485659\pi$
$557$	1.33172	+	4.97004i	0.0564267	+	0.210587i	−0.931956	+	0.362570i	$0.881899\pi$
$558$		0			0
$559$	14.4829	−	20.6081i	0.612562	−	0.871630i
$560$		0			0
$561$	2.30894	−	7.77692i	0.0974834	−	0.328342i
$562$		0			0
$563$	1.28809	+	2.23104i	0.0542866	+	0.0940271i	0.891892	−	0.452249i	$-0.149378\pi$
$563$	1.28809	+	2.23104i	0.0542866	+	0.0940271i	−0.837605	+	0.546276i	$0.816045\pi$
$564$		0			0
$565$	21.8420	+	5.85255i	0.918901	+	0.246219i
$566$		0			0
$567$	19.4551	−	3.03134i	0.817038	−	0.127304i
$568$		0			0
$569$	2.81100	−	4.86880i	0.117843	−	0.204111i	−0.801069	−	0.598572i	$-0.795735\pi$
$569$	2.81100	−	4.86880i	0.117843	−	0.204111i	0.918913	+	0.394461i	$0.129069\pi$
$570$		0			0
$571$		−	33.8079i		−	1.41482i	−0.706806	−	0.707408i	$-0.749864\pi$
$571$		−	33.8079i		−	1.41482i	0.706806	−	0.707408i	$-0.250136\pi$
$572$		0			0
$573$	19.4754	−	31.7362i	0.813597	−	1.32580i
$574$		0			0
$575$	−4.19878	−	2.42417i	−0.175101	−	0.101095i
$576$		0			0
$577$	−5.78457	+	5.78457i	−0.240815	+	0.240815i	−0.817187	−	0.576372i	$-0.804468\pi$
$577$	−5.78457	+	5.78457i	−0.240815	+	0.240815i	0.576372	+	0.817187i	$0.304468\pi$
$578$		0			0
$579$	5.05016	−	4.78640i	0.209877	−	0.198916i
$580$		0			0
$581$	−6.04769	+	3.49163i	−0.250900	+	0.144857i
$582$		0			0
$583$	−9.96124	+	2.66911i	−0.412552	+	0.110543i
$584$		0			0
$585$	−16.3913	+	12.2754i	−0.677695	+	0.507524i
$586$		0			0
$587$	39.0455	−	10.4622i	1.61158	−	0.431822i	0.663068	−	0.748559i	$-0.269254\pi$
$587$	39.0455	−	10.4622i	1.61158	−	0.431822i	0.948514	+	0.316737i	$0.102587\pi$
$588$		0			0
$589$	6.69716	−	3.86661i	0.275952	−	0.159321i
$590$		0			0
$591$	−10.0820	+	9.55544i	−0.414718	+	0.393058i
$592$		0			0
$593$	8.23055	−	8.23055i	0.337988	−	0.337988i	−0.517621	−	0.855610i	$-0.673182\pi$
$593$	8.23055	−	8.23055i	0.337988	−	0.337988i	0.855610	+	0.517621i	$0.173182\pi$
$594$		0			0
$595$	−16.9375	−	9.77890i	−0.694372	−	0.400896i
$596$		0			0
$597$	10.1993	−	16.6203i	0.417428	−	0.680223i
$598$		0			0
$599$			7.22852i			0.295349i	0.989036	+	0.147675i	$0.0471789\pi$
$599$			7.22852i			0.295349i	−0.989036	+	0.147675i	$0.952821\pi$
$600$		0			0
$601$	−1.92099	+	3.32725i	−0.0783587	+	0.135721i	−0.902542	−	0.430602i	$-0.858301\pi$
$601$	−1.92099	+	3.32725i	−0.0783587	+	0.135721i	0.824183	+	0.566323i	$0.191635\pi$
$602$		0			0
$603$	−16.7519	−	5.46628i	−0.682190	−	0.222604i
$604$		0			0
$605$	18.3165	+	4.90790i	0.744672	+	0.199534i
$606$		0			0
$607$	6.01621	+	10.4204i	0.244190	+	0.422950i	0.961904	−	0.273389i	$-0.0881445\pi$
$607$	6.01621	+	10.4204i	0.244190	+	0.422950i	−0.717713	+	0.696339i	$0.754811\pi$
$608$		0			0
$609$	−0.913707	+	3.07753i	−0.0370253	+	0.124708i
$610$		0			0
$611$	−0.672964	+	1.83909i	−0.0272252	+	0.0744017i
$612$		0			0
$613$	6.43463	+	24.0144i	0.259892	+	0.969931i	0.965303	+	0.261133i	$0.0840960\pi$
$613$	6.43463	+	24.0144i	0.259892	+	0.969931i	−0.705411	+	0.708799i	$0.749237\pi$
$614$		0			0
$615$	30.3135	+	0.812825i	1.22236	+	0.0327763i
$616$		0			0
$617$	−11.6729	+	43.5637i	−0.469932	+	1.75381i	0.170066	+	0.985433i	$0.445602\pi$
$617$	−11.6729	+	43.5637i	−0.469932	+	1.75381i	−0.639997	+	0.768377i	$0.721065\pi$
$618$		0			0
$619$	24.4865	+	24.4865i	0.984197	+	0.984197i	0.999877	−	0.0156805i	$-0.00499147\pi$
$619$	24.4865	+	24.4865i	0.984197	+	0.984197i	−0.0156805	+	0.999877i	$0.504991\pi$
$620$		0			0
$621$	14.6460	+	10.1066i	0.587725	+	0.405564i
$622$		0			0
$623$	38.8952			1.55830
$624$		0			0
$625$	15.9169			0.636678
$626$		0			0
$627$	1.22284	+	2.25556i	0.0488354	+	0.0900784i
$628$		0			0
$629$	−36.4649	−	36.4649i	−1.45395	−	1.45395i
$630$		0			0
$631$	−3.56833	+	13.3172i	−0.142053	+	0.530149i	0.857816	+	0.513957i	$0.171821\pi$
$631$	−3.56833	+	13.3172i	−0.142053	+	0.530149i	−0.999869	+	0.0161917i	$0.994846\pi$
$632$		0			0
$633$	−1.11232	+	41.4830i	−0.0442109	+	1.64880i
$634$		0			0
$635$	0.0621559	+	0.231969i	0.00246658	+	0.00920541i
$636$		0			0
$637$	−7.95003	−	0.709336i	−0.314992	−	0.0281049i
$638$		0			0
$639$	−20.8564	−	23.2219i	−0.825065	−	0.918644i
$640$		0			0
$641$	−18.7773	−	32.5233i	−0.741659	−	1.28459i	−0.951739	−	0.306908i	$-0.900706\pi$
$641$	−18.7773	−	32.5233i	−0.741659	−	1.28459i	0.210080	−	0.977684i	$-0.432628\pi$
$642$		0			0
$643$	33.9096	+	9.08605i	1.33726	+	0.358319i	0.855418	−	0.517937i	$-0.173300\pi$
$643$	33.9096	+	9.08605i	1.33726	+	0.358319i	0.481845	+	0.876256i	$0.339967\pi$
$644$		0			0
$645$	22.2784	−	5.33378i	0.877210	−	0.210017i
$646$		0			0
$647$	4.67261	−	8.09319i	0.183699	−	0.318176i	−0.759438	−	0.650579i	$-0.774526\pi$
$647$	4.67261	−	8.09319i	0.183699	−	0.318176i	0.943137	+	0.332403i	$0.107859\pi$
$648$		0			0
$649$			12.0440i			0.472767i
$650$		0			0
$651$	16.7241	+	10.2630i	0.655468	+	0.402237i
$652$		0			0
$653$	−4.78580	−	2.76309i	−0.187283	−	0.108128i	0.403427	−	0.915012i	$-0.367819\pi$
$653$	−4.78580	−	2.76309i	−0.187283	−	0.108128i	−0.590710	+	0.806884i	$0.701152\pi$
$654$		0			0
$655$	27.9465	−	27.9465i	1.09196	−	1.09196i
$656$		0			0
$657$	−1.63249	+	0.344855i	−0.0636894	+	0.0134541i
$658$		0			0
$659$	30.1079	−	17.3828i	1.17284	−	0.677138i	0.218491	−	0.975839i	$-0.429887\pi$
$659$	30.1079	−	17.3828i	1.17284	−	0.677138i	0.954347	+	0.298701i	$0.0965533\pi$
$660$		0			0
$661$	−10.7464	+	2.87948i	−0.417985	+	0.111999i	−0.461681	−	0.887046i	$-0.652753\pi$
$661$	−10.7464	+	2.87948i	−0.417985	+	0.111999i	0.0436959	+	0.999045i	$0.486087\pi$
$662$		0			0
$663$	29.2910	+	3.40703i	1.13757	+	0.132318i
$664$		0			0
$665$	5.97476	−	1.60093i	0.231691	−	0.0620815i
$666$		0			0
$667$	−2.51260	+	1.45065i	−0.0972883	+	0.0561694i
$668$		0			0
$669$	−2.28068	−	2.40636i	−0.0881763	−	0.0930353i
$670$		0			0
$671$	−3.97559	+	3.97559i	−0.153476	+	0.153476i
$672$		0			0
$673$	38.4396	+	22.1931i	1.48174	+	0.855482i	0.999785	−	0.0207144i	$-0.00659408\pi$
$673$	38.4396	+	22.1931i	1.48174	+	0.855482i	0.481954	+	0.876197i	$0.339927\pi$
$674$		0			0
$675$	7.33265	+	0.590986i	0.282234	+	0.0227470i
$676$		0			0
$677$		−	20.7036i		−	0.795704i	−0.917450	−	0.397852i	$-0.869756\pi$
$677$		−	20.7036i		−	0.795704i	0.917450	−	0.397852i	$-0.130244\pi$
$678$		0			0
$679$	−9.37793	+	16.2430i	−0.359892	+	0.623351i
$680$		0			0
$681$	4.41329	+	18.4336i	0.169117	+	0.706378i
$682$		0			0
$683$	3.10117	+	0.830957i	0.118663	+	0.0317957i	0.317662	−	0.948204i	$-0.397102\pi$
$683$	3.10117	+	0.830957i	0.118663	+	0.0317957i	−0.198999	+	0.980000i	$0.563769\pi$
$684$		0			0
$685$	12.0519	+	20.8745i	0.460478	+	0.797572i
$686$		0			0
$687$	−5.11918	−	1.51987i	−0.195309	−	0.0579865i
$688$		0			0
$689$	−15.7838	−	34.0012i	−0.601315	−	1.29534i
$690$		0			0
$691$	0.553429	+	2.06543i	0.0210534	+	0.0785725i	0.975653	−	0.219319i	$-0.0703834\pi$
$691$	0.553429	+	2.06543i	0.0210534	+	0.0785725i	−0.954600	+	0.297891i	$0.903717\pi$
$692$		0			0
$693$	−3.55254	+	5.45542i	−0.134950	+	0.207234i
$694$		0			0
$695$	−8.97649	+	33.5007i	−0.340498	+	1.27076i
$696$		0			0
$697$	−30.8772	−	30.8772i	−1.16956	−	1.16956i
$698$		0			0
$699$	−11.8791	+	6.44019i	−0.449310	+	0.243591i
$700$		0			0
$701$	−21.3084			−0.804808			−0.402404	−	0.915462i	$-0.631825\pi$
$701$	−21.3084			−0.804808			−0.402404	+	0.915462i	$0.631825\pi$
$702$		0			0
$703$	16.3097			0.615133
$704$		0			0
$705$	−1.56576	+	0.848867i	−0.0589700	+	0.0319702i
$706$		0			0
$707$	−3.15923	−	3.15923i	−0.118815	−	0.118815i
$708$		0			0
$709$	7.30917	−	27.2782i	0.274502	−	1.02445i	−0.681673	−	0.731657i	$-0.738747\pi$
$709$	7.30917	−	27.2782i	0.274502	−	1.02445i	0.956175	−	0.292797i	$-0.0945859\pi$
$710$		0			0
$711$	16.4498	−	25.2610i	0.616917	−	0.947363i
$712$		0			0
$713$	4.58972	+	17.1291i	0.171886	+	0.641489i
$714$		0			0
$715$	0.601732	−	6.74403i	0.0225035	−	0.252213i
$716$		0			0
$717$	−34.8389	−	10.3435i	−1.30108	−	0.386286i
$718$		0			0
$719$	−2.67277	−	4.62937i	−0.0996774	−	0.172646i	0.811874	−	0.583833i	$-0.198448\pi$
$719$	−2.67277	−	4.62937i	−0.0996774	−	0.172646i	−0.911551	+	0.411187i	$0.865114\pi$
$720$		0			0
$721$	−30.3068	−	8.12067i	−1.12868	−	0.302430i
$722$		0			0
$723$	−6.61964	−	27.6492i	−0.246187	−	1.02829i
$724$		0			0
$725$	−0.599709	+	1.03873i	−0.0222726	+	0.0385773i
$726$		0			0
$727$			3.49159i			0.129496i	0.997902	+	0.0647480i	$0.0206244\pi$
$727$			3.49159i			0.129496i	−0.997902	+	0.0647480i	$0.979376\pi$
$728$		0			0
$729$	−26.6515	−	4.32412i	−0.987092	−	0.160153i
$730$		0			0
$731$	−28.5678	−	16.4937i	−1.05662	−	0.610040i
$732$		0			0
$733$	−1.07662	+	1.07662i	−0.0397658	+	0.0397658i	−0.726710	−	0.686944i	$-0.758952\pi$
$733$	−1.07662	+	1.07662i	−0.0397658	+	0.0397658i	0.686944	+	0.726710i	$0.258952\pi$
$734$		0			0
$735$	−4.99349	−	5.26865i	−0.184187	−	0.194337i
$736$		0			0
$737$	5.04562	−	2.91309i	0.185858	−	0.107305i
$738$		0			0
$739$	−32.6118	+	8.73832i	−1.19965	+	0.321444i	−0.802692	−	0.596394i	$-0.796599\pi$
$739$	−32.6118	+	8.73832i	−1.19965	+	0.321444i	−0.396954	+	0.917838i	$0.629933\pi$
$740$		0			0
$741$	−7.31246	+	5.78859i	−0.268630	+	0.212649i
$742$		0			0
$743$	9.87756	−	2.64668i	0.362372	−	0.0970974i	−0.0730388	−	0.997329i	$-0.523270\pi$
$743$	9.87756	−	2.64668i	0.362372	−	0.0970974i	0.435411	+	0.900232i	$0.356603\pi$
$744$		0			0
$745$	3.48590	−	2.01259i	0.127713	−	0.0737354i
$746$		0			0
$747$	9.36914	−	1.97918i	0.342799	−	0.0724146i
$748$		0			0
$749$	0.598261	−	0.598261i	0.0218600	−	0.0218600i
$750$		0			0
$751$	−29.4768	−	17.0185i	−1.07563	−	0.621012i	−0.145912	−	0.989298i	$-0.546612\pi$
$751$	−29.4768	−	17.0185i	−1.07563	−	0.621012i	−0.929713	+	0.368285i	$0.879945\pi$
$752$		0			0
$753$	−6.24894	−	3.83475i	−0.227724	−	0.139746i
$754$		0			0
$755$		−	7.86261i		−	0.286150i
$756$		0			0
$757$	4.15573	−	7.19794i	0.151043	−	0.261614i	−0.780568	−	0.625070i	$-0.785070\pi$
$757$	4.15573	−	7.19794i	0.151043	−	0.261614i	0.931611	+	0.363457i	$0.118404\pi$
$758$		0			0
$759$	−5.72183	+	1.36989i	−0.207689	+	0.0497240i
$760$		0			0
$761$	30.3530	+	8.13305i	1.10029	+	0.294823i	0.762884	−	0.646535i	$-0.223783\pi$
$761$	30.3530	+	8.13305i	1.10029	+	0.294823i	0.337409	+	0.941358i	$0.390449\pi$
$762$		0			0
$763$	−12.7486	−	22.0813i	−0.461531	−	0.799395i
$764$		0			0
$765$	17.9203	+	19.9528i	0.647911	+	0.721397i
$766$		0			0
$767$	−43.1274	+	7.52796i	−1.55724	+	0.271819i
$768$		0			0
$769$	12.2950	+	45.8856i	0.443370	+	1.65468i	0.720205	+	0.693761i	$0.244048\pi$
$769$	12.2950	+	45.8856i	0.443370	+	1.65468i	−0.276835	+	0.960917i	$0.589286\pi$
$770$		0			0
$771$	0.279882	−	10.4379i	0.0100797	−	0.375912i
$772$		0			0
$773$	2.09638	−	7.82380i	0.0754015	−	0.281402i	−0.917923	−	0.396760i	$-0.870135\pi$
$773$	2.09638	−	7.82380i	0.0754015	−	0.281402i	0.993324	+	0.115357i	$0.0368013\pi$
$774$		0			0
$775$	5.18385	+	5.18385i	0.186209	+	0.186209i
$776$		0			0
$777$	19.7238	+	36.3812i	0.707588	+	1.30517i
$778$		0			0
$779$	13.8105			0.494812
$780$		0			0
$781$	10.3201			0.369281
$782$		0			0
$783$	2.50025	−	3.62325i	0.0893515	−	0.129484i
$784$		0			0
$785$	21.6790	+	21.6790i	0.773755	+	0.773755i
$786$		0			0
$787$	5.53321	−	20.6502i	0.197238	−	0.736101i	−0.794439	−	0.607344i	$-0.792235\pi$
$787$	5.53321	−	20.6502i	0.197238	−	0.736101i	0.991676	−	0.128756i	$-0.0410985\pi$
$788$		0			0
$789$	−33.8030	−	0.906392i	−1.20342	−	0.0322684i
$790$		0			0
$791$	6.76310	+	25.2402i	0.240468	+	0.897439i
$792$		0			0
$793$	−16.7208	−	11.7510i	−0.593774	−	0.417291i
$794$		0			0
$795$	9.70332	−	32.6825i	0.344141	−	1.15913i
$796$		0			0
$797$	−7.33180	−	12.6990i	−0.259706	−	0.449823i	0.706457	−	0.707756i	$-0.250292\pi$
$797$	−7.33180	−	12.6990i	−0.259706	−	0.449823i	−0.966163	+	0.257932i	$0.916959\pi$
$798$		0			0
$799$	2.47732	+	0.663797i	0.0876414	+	0.0234835i
$800$		0			0
$801$	−50.7045	−	16.5453i	−1.79156	−	0.584599i
$802$		0			0
$803$	0.275835	−	0.477760i	0.00973399	−	0.0168598i
$804$		0			0
$805$			14.1843i			0.499930i
$806$		0			0
$807$	−23.7469	+	38.6969i	−0.835931	+	1.36220i
$808$		0			0
$809$	11.8733	+	6.85508i	0.417445	+	0.241012i	0.693983	−	0.719991i	$-0.255854\pi$
$809$	11.8733	+	6.85508i	0.417445	+	0.241012i	−0.276539	+	0.961003i	$0.589187\pi$
$810$		0			0
$811$	−16.9177	+	16.9177i	−0.594060	+	0.594060i	−0.938726	−	0.344666i	$-0.887992\pi$
$811$	−16.9177	+	16.9177i	−0.594060	+	0.594060i	0.344666	+	0.938726i	$0.387992\pi$
$812$		0			0
$813$	18.1611	−	17.2126i	0.636938	−	0.603672i
$814$		0			0
$815$	−6.30331	+	3.63922i	−0.220795	+	0.127476i
$816$		0			0
$817$	10.0774	−	2.70023i	0.352563	−	0.0944689i
$818$		0			0
$819$	−21.7554	−	9.31118i	−0.760196	−	0.325359i
$820$		0			0
$821$	−5.16766	+	1.38467i	−0.180353	+	0.0483253i	−0.347865	−	0.937545i	$-0.613093\pi$
$821$	−5.16766	+	1.38467i	−0.180353	+	0.0483253i	0.167512	+	0.985870i	$0.446427\pi$
$822$		0			0
$823$	−40.3992	+	23.3245i	−1.40823	+	0.813040i	−0.995217	−	0.0976860i	$-0.968856\pi$
$823$	−40.3992	+	23.3245i	−1.40823	+	0.813040i	−0.413010	+	0.910726i	$0.635523\pi$
$824$		0			0
$825$	−1.76537	+	1.67317i	−0.0614624	+	0.0582524i
$826$		0			0
$827$	−21.8472	+	21.8472i	−0.759703	+	0.759703i	−0.976268	−	0.216565i	$-0.930515\pi$
$827$	−21.8472	+	21.8472i	−0.759703	+	0.759703i	0.216565	+	0.976268i	$0.430515\pi$
$828$		0			0
$829$	−44.5299	−	25.7093i	−1.54659	−	0.892922i	−0.998399	−	0.0565657i	$-0.981985\pi$
$829$	−44.5299	−	25.7093i	−1.54659	−	0.892922i	−0.548187	−	0.836356i	$-0.684682\pi$
$830$		0			0
$831$	4.18893	−	6.82609i	0.145312	−	0.236794i
$832$		0			0
$833$			10.4530i			0.362174i
$834$		0			0
$835$	−22.4024	+	38.8021i	−0.775267	+	1.34280i
$836$		0			0
$837$	−17.4361	−	20.4931i	−0.602680	−	0.708344i
$838$		0			0
$839$	−23.3739	−	6.26302i	−0.806957	−	0.216223i	−0.168321	−	0.985732i	$-0.553834\pi$
$839$	−23.3739	−	6.26302i	−0.806957	−	0.216223i	−0.638636	+	0.769509i	$0.720501\pi$
$840$		0			0
$841$	−14.1411	−	24.4932i	−0.487625	−	0.844591i
$842$		0			0
$843$	1.97692	−	6.65863i	0.0680889	−	0.229336i
$844$		0			0
$845$	24.5254	−	2.06059i	0.843698	−	0.0708866i
$846$		0			0
$847$	5.67147	+	21.1662i	0.194874	+	0.727280i
$848$		0			0
$849$	43.8586	+	1.17602i	1.50522	+	0.0403611i
$850$		0			0
$851$	−9.67996	+	36.1261i	−0.331825	+	1.23839i
$852$		0			0
$853$	16.9446	+	16.9446i	0.580173	+	0.580173i	0.934951	−	0.354778i	$-0.115444\pi$
$853$	16.9446	+	16.9446i	0.580173	+	0.580173i	−0.354778	+	0.934951i	$0.615444\pi$
$854$		0			0
$855$	−8.46981	−	0.454545i	−0.289661	−	0.0155451i
$856$		0			0
$857$	−23.5591			−0.804762			−0.402381	−	0.915472i	$-0.631817\pi$
$857$	−23.5591			−0.804762			−0.402381	+	0.915472i	$0.631817\pi$
$858$		0			0
$859$	46.8413			1.59821			0.799103	−	0.601194i	$-0.205308\pi$
$859$	46.8413			1.59821			0.799103	+	0.601194i	$0.205308\pi$
$860$		0			0
$861$	16.7014	+	30.8063i	0.569182	+	1.04987i
$862$		0			0
$863$	−14.5673	−	14.5673i	−0.495875	−	0.495875i	0.414276	−	0.910151i	$-0.364035\pi$
$863$	−14.5673	−	14.5673i	−0.495875	−	0.495875i	−0.910151	+	0.414276i	$0.864035\pi$
$864$		0			0
$865$	−7.21426	+	26.9240i	−0.245292	+	0.915443i
$866$		0			0
$867$	0.245907	−	9.17087i	0.00835146	−	0.311459i
$868$		0			0
$869$	2.57964	+	9.62736i	0.0875084	+	0.326586i
$870$		0			0
$871$	13.5850	+	16.2467i	0.460311	+	0.550500i
$872$		0			0
$873$	19.1347	−	17.1855i	0.647612	−	0.581642i
$874$		0			0
$875$	13.2867	+	23.0132i	0.449172	+	0.777988i
$876$		0			0
$877$	4.37238	+	1.17158i	0.147645	+	0.0395613i	0.331884	−	0.943320i	$-0.392316\pi$
$877$	4.37238	+	1.17158i	0.147645	+	0.0395613i	−0.184240	+	0.982881i	$0.558982\pi$
$878$		0			0
$879$	29.7881	−	7.13171i	1.00473	−	0.240547i
$880$		0			0
$881$	3.84672	−	6.66271i	0.129599	−	0.224473i	−0.793922	−	0.608019i	$-0.791964\pi$
$881$	3.84672	−	6.66271i	0.129599	−	0.224473i	0.923521	+	0.383547i	$0.125298\pi$
$882$		0			0
$883$			15.0647i			0.506967i	0.967340	+	0.253484i	$0.0815764\pi$
$883$			15.0647i			0.506967i	−0.967340	+	0.253484i	$0.918424\pi$
$884$		0			0
$885$	−33.9358	−	20.8252i	−1.14074	−	0.700030i
$886$		0			0
$887$	−19.2421	−	11.1094i	−0.646086	−	0.373018i	0.140869	−	0.990028i	$-0.455010\pi$
$887$	−19.2421	−	11.1094i	−0.646086	−	0.373018i	−0.786955	+	0.617010i	$0.788344\pi$
$888$		0			0
$889$	−0.196233	+	0.196233i	−0.00658144	+	0.00658144i
$890$		0			0
$891$	6.95178	−	5.60060i	0.232893	−	0.187627i
$892$		0			0
$893$	−0.702468	+	0.405570i	−0.0235072	+	0.0135719i
$894$		0			0
$895$	−31.2045	+	8.36123i	−1.04305	+	0.279485i
$896$		0			0
$897$	−8.48174	−	19.6327i	−0.283197	−	0.655517i
$898$		0			0
$899$	4.23752	−	1.13544i	0.141329	−	0.0378691i
$900$		0			0
$901$	−42.5158	+	24.5465i	−1.41641	+	0.817762i
$902$		0			0
$903$	18.2101	+	19.2136i	0.605994	+	0.639387i
$904$		0			0
$905$	4.71091	−	4.71091i	0.156596	−	0.156596i
$906$		0			0
$907$	8.02812	+	4.63504i	0.266569	+	0.153904i	0.627328	−	0.778755i	$-0.284149\pi$
$907$	8.02812	+	4.63504i	0.266569	+	0.153904i	−0.360758	+	0.932659i	$0.617482\pi$
$908$		0			0
$909$	2.77455	+	5.46230i	0.0920260	+	0.181173i
$910$		0			0
$911$			27.0434i			0.895986i	0.894037	+	0.447993i	$0.147861\pi$
$911$			27.0434i			0.895986i	−0.894037	+	0.447993i	$0.852139\pi$
$912$		0			0
$913$	−1.58307	+	2.74195i	−0.0523918	+	0.0907453i
$914$		0			0
$915$	−4.32768	−	18.0760i	−0.143069	−	0.597575i
$916$		0			0
$917$	44.1150	+	11.8206i	1.45681	+	0.390350i
$918$		0			0
$919$	−21.3969	−	37.0606i	−0.705819	−	1.22251i	−0.966395	−	0.257062i	$-0.917246\pi$
$919$	−21.3969	−	37.0606i	−0.705819	−	1.22251i	0.260576	−	0.965453i	$-0.416088\pi$
$920$		0			0
$921$	38.8769	+	11.5424i	1.28104	+	0.380335i
$922$		0			0
$923$	6.45047	+	36.9545i	0.212320	+	1.21637i
$924$		0			0
$925$	4.00176	+	14.9348i	0.131577	+	0.491052i
$926$		0			0
$927$	36.0540	+	23.4782i	1.18417	+	0.771124i
$928$		0			0
$929$	12.0662	−	45.0318i	0.395880	−	1.47745i	−0.424395	−	0.905477i	$-0.639513\pi$
$929$	12.0662	−	45.0318i	0.395880	−	1.47745i	0.820275	−	0.571969i	$-0.193820\pi$
$930$		0			0
$931$	−2.33766	−	2.33766i	−0.0766137	−	0.0766137i
$932$		0			0
$933$	−42.5687	+	23.0783i	−1.39364	+	0.755551i
$934$		0			0
$935$	−8.86728			−0.289991
$936$		0			0
$937$	−33.1367			−1.08253			−0.541265	−	0.840852i	$-0.682054\pi$
$937$	−33.1367			−1.08253			−0.541265	+	0.840852i	$0.682054\pi$
$938$		0			0
$939$	−33.7730	+	18.3098i	−1.10214	+	0.597518i
$940$		0			0
$941$	6.48909	+	6.48909i	0.211538	+	0.211538i	0.804921	−	0.593382i	$-0.202208\pi$
$941$	6.48909	+	6.48909i	0.211538	+	0.211538i	−0.593382	+	0.804921i	$0.702208\pi$
$942$		0			0
$943$	−8.19663	+	30.5903i	−0.266919	+	0.996156i
$944$		0			0
$945$	−9.22884	−	19.4428i	−0.300214	−	0.632474i
$946$		0			0
$947$	−13.7168	−	51.1917i	−0.445735	−	1.66351i	−0.713988	−	0.700158i	$-0.753113\pi$
$947$	−13.7168	−	51.1917i	−0.445735	−	1.66351i	0.268253	−	0.963348i	$-0.413554\pi$
$948$		0			0
$949$	1.88318	+	0.689098i	0.0611308	+	0.0223691i
$950$		0			0
$951$	−12.7852	−	3.79587i	−0.414588	−	0.123090i
$952$		0			0
$953$	−9.11381	−	15.7856i	−0.295225	−	0.511345i	0.679812	−	0.733386i	$-0.262061\pi$
$953$	−9.11381	−	15.7856i	−0.295225	−	0.511345i	−0.975037	+	0.222041i	$0.928728\pi$
$954$		0			0
$955$	−39.3133	−	10.5340i	−1.27215	−	0.340871i
$956$		0			0
$957$	0.338895	+	1.41551i	0.0109549	+	0.0457570i
$958$		0			0
$959$	−13.9269	+	24.1221i	−0.449724	+	0.778944i
$960$		0			0
$961$			4.18577i			0.135025i
$962$		0			0
$963$	−1.03439	+	0.525415i	−0.0333328	+	0.0169313i
$964$		0			0
$965$	−6.58649	−	3.80271i	−0.212027	−	0.122414i
$966$		0			0
$967$	−12.3678	+	12.3678i	−0.397722	+	0.397722i	−0.877429	−	0.479707i	$-0.840743\pi$
$967$	−12.3678	+	12.3678i	−0.397722	+	0.397722i	0.479707	+	0.877429i	$0.340743\pi$
$968$		0			0
$969$	8.40201	+	8.86500i	0.269911	+	0.284785i
$970$		0			0
$971$	0.0142027	−	0.00819993i	0.000455786	−	0.000263148i	−0.499772	−	0.866157i	$-0.666583\pi$
$971$	0.0142027	−	0.00819993i	0.000455786	−	0.000263148i	0.500228	+	0.865894i	$0.333250\pi$
$972$		0			0
$973$	−38.7128	+	10.3731i	−1.24108	+	0.332545i
$974$		0			0
$975$	−7.09478	−	5.27570i	−0.227215	−	0.168958i
$976$		0			0
$977$	7.17509	−	1.92256i	0.229551	−	0.0615081i	−0.142210	−	0.989837i	$-0.545421\pi$
$977$	7.17509	−	1.92256i	0.229551	−	0.0615081i	0.371761	+	0.928328i	$0.378754\pi$
$978$		0			0
$979$	15.2721	−	8.81732i	0.488097	−	0.281803i
$980$		0			0
$981$	7.22638	+	34.2085i	0.230721	+	1.09219i
$982$		0			0
$983$	−11.5176	+	11.5176i	−0.367355	+	0.367355i	−0.866512	−	0.499157i	$-0.833643\pi$
$983$	−11.5176	+	11.5176i	−0.367355	+	0.367355i	0.499157	+	0.866512i	$0.333643\pi$
$984$		0			0
$985$	13.1491	+	7.59163i	0.418965	+	0.241889i
$986$		0			0
$987$	−1.75420	−	1.07649i	−0.0558367	−	0.0342650i
$988$		0			0
$989$			23.9240i			0.760739i
$990$		0			0
$991$	15.4849	−	26.8207i	0.491895	−	0.851987i	−0.508062	−	0.861321i	$-0.669638\pi$
$991$	15.4849	−	26.8207i	0.491895	−	0.851987i	0.999956	+	0.00933404i	$0.00297116\pi$
$992$		0			0
$993$	9.80031	−	2.34634i	0.311003	−	0.0744589i
$994$		0			0
$995$	−20.5884	−	5.51664i	−0.652696	−	0.174889i
$996$		0			0
$997$	9.87356	+	17.1015i	0.312699	+	0.541610i	0.978946	−	0.204121i	$-0.0654336\pi$
$997$	9.87356	+	17.1015i	0.312699	+	0.541610i	−0.666247	+	0.745731i	$0.732100\pi$
$998$		0			0
$999$	−10.2364	−	55.8173i	−0.323867	−	1.76598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.f.305.3		56
3.2	odd	2	inner	624.2.cn.f.305.7		56
4.3	odd	2		312.2.bp.a.305.12	yes	56
12.11	even	2		312.2.bp.a.305.8	yes	56
13.11	odd	12	inner	624.2.cn.f.401.7		56
39.11	even	12	inner	624.2.cn.f.401.3		56
52.11	even	12		312.2.bp.a.89.8	✓	56
156.11	odd	12		312.2.bp.a.89.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.8	✓	56	52.11	even	12
312.2.bp.a.89.12	yes	56	156.11	odd	12
312.2.bp.a.305.8	yes	56	12.11	even	2
312.2.bp.a.305.12	yes	56	4.3	odd	2
624.2.cn.f.305.3		56	1.1	even	1	trivial
624.2.cn.f.305.7		56	3.2	odd	2	inner
624.2.cn.f.401.3		56	39.11	even	12	inner
624.2.cn.f.401.7		56	13.11	odd	12	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.52267 + 0.825508i) q^{3} +(1.33870 + 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(1.63707 - 2.51396i) q^{9} +O(q^{10})\)	\(q+(-1.52267 + 0.825508i) q^{3} +(1.33870 + 1.33870i) q^{5} +(-0.566234 + 2.11322i) q^{7} +(1.63707 - 2.51396i) q^{9} +(0.256724 + 0.958107i) q^{11} +(-3.27036 + 1.51814i) q^{13} +(-3.14352 - 0.933300i) q^{15} +(2.36097 + 4.08932i) q^{17} +(-1.44252 - 0.386521i) q^{19} +(-0.882285 - 3.68517i) q^{21} +(1.71229 - 2.96577i) q^{23} -1.41574i q^{25} +(-0.417438 + 5.17936i) q^{27} +(-0.733696 - 0.423600i) q^{29} +(-3.66157 + 3.66157i) q^{31} +(-1.18183 - 1.24696i) q^{33} +(-3.58699 + 2.07095i) q^{35} +(-10.5491 + 2.82661i) q^{37} +(3.72645 - 5.01134i) q^{39} +(-8.93255 + 2.39347i) q^{41} +(-6.05002 + 3.49298i) q^{43} +(5.55700 - 1.17389i) q^{45} +(0.384064 - 0.384064i) q^{47} +(1.91712 + 1.10685i) q^{49} +(-6.97075 - 4.27770i) q^{51} +10.3968i q^{53} +(-0.938944 + 1.62630i) q^{55} +(2.51556 - 0.602263i) q^{57} +(11.7285 + 3.14264i) q^{59} +(2.83411 + 4.90882i) q^{61} +(4.38557 + 4.88298i) q^{63} +(-6.41038 - 2.34570i) q^{65} +(-1.52023 - 5.67359i) q^{67} +(-0.158991 + 5.92942i) q^{69} +(2.69283 - 10.0498i) q^{71} +(-0.393272 - 0.393272i) q^{73} +(1.16871 + 2.15572i) q^{75} -2.17005 q^{77} +10.0483 q^{79} +(-3.63998 - 8.23107i) q^{81} +(2.25706 + 2.25706i) q^{83} +(-2.31375 + 8.63503i) q^{85} +(1.46686 + 0.0393325i) q^{87} +(-4.60143 - 17.1728i) q^{89} +(-1.35637 - 7.77060i) q^{91} +(2.55273 - 8.59804i) q^{93} +(-1.41367 - 2.44854i) q^{95} +(8.28096 + 2.21888i) q^{97} +(2.82892 + 0.923099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 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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