LMFDB - Embedded newform 624.2.cn.f.401.7

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			401.7
Character	$\chi$	$=$	624.401
Dual form			624.2.cn.f.305.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0464265 - 1.73143i) q^{3} +(-1.33870 + 1.33870i) q^{5} +(-0.566234 - 2.11322i) q^{7} +(-2.99569 - 0.160768i) q^{9} +O(q^{10})$	\(q+(0.0464265 - 1.73143i) q^{3} +(-1.33870 + 1.33870i) q^{5} +(-0.566234 - 2.11322i) q^{7} +(-2.99569 - 0.160768i) q^{9} +(-0.256724 + 0.958107i) q^{11} +(-3.27036 - 1.51814i) q^{13} +(2.25572 + 2.38002i) q^{15} +(-2.36097 + 4.08932i) q^{17} +(-1.44252 + 0.386521i) q^{19} +(-3.68517 + 0.882285i) q^{21} +(-1.71229 - 2.96577i) q^{23} +1.41574i q^{25} +(-0.417438 + 5.17936i) q^{27} +(0.733696 - 0.423600i) q^{29} +(-3.66157 - 3.66157i) q^{31} +(1.64698 + 0.488981i) q^{33} +(3.58699 + 2.07095i) q^{35} +(-10.5491 - 2.82661i) q^{37} +(-2.78039 + 5.59191i) q^{39} +(8.93255 + 2.39347i) q^{41} +(-6.05002 - 3.49298i) q^{43} +(4.22556 - 3.79512i) q^{45} +(-0.384064 - 0.384064i) q^{47} +(1.91712 - 1.10685i) q^{49} +(6.97075 + 4.27770i) q^{51} +10.3968i q^{53} +(-0.938944 - 1.62630i) q^{55} +(0.602263 + 2.51556i) q^{57} +(-11.7285 + 3.14264i) q^{59} +(2.83411 - 4.90882i) q^{61} +(1.35652 + 6.42157i) q^{63} +(6.41038 - 2.34570i) q^{65} +(-1.52023 + 5.67359i) q^{67} +(-5.21452 + 2.82702i) q^{69} +(-2.69283 - 10.0498i) q^{71} +(-0.393272 + 0.393272i) q^{73} +(2.45126 + 0.0657280i) q^{75} +2.17005 q^{77} +10.0483 q^{79} +(8.94831 + 0.963224i) q^{81} +(-2.25706 + 2.25706i) q^{83} +(-2.31375 - 8.63503i) q^{85} +(-0.699369 - 1.29001i) q^{87} +(4.60143 - 17.1728i) q^{89} +(-1.35637 + 7.77060i) q^{91} +(-6.50974 + 6.16976i) q^{93} +(1.41367 - 2.44854i) q^{95} +(8.28096 - 2.21888i) q^{97} +(0.923099 - 2.82892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.0464265	−	1.73143i	0.0268043	−	0.999641i
$3$	0.0464265	−	1.73143i	0.0268043	−	0.999641i
$4$		0			0
$5$	−1.33870	+	1.33870i	−0.598687	+	0.598687i	−0.939963	−	0.341276i	$-0.889141\pi$
$5$	−1.33870	+	1.33870i	−0.598687	+	0.598687i	0.341276	+	0.939963i	$0.389141\pi$
$6$		0			0
$7$	−0.566234	−	2.11322i	−0.214016	−	0.798720i	−0.986510	−	0.163698i	$-0.947658\pi$
$7$	−0.566234	−	2.11322i	−0.214016	−	0.798720i	0.772494	−	0.635022i	$-0.219009\pi$
$8$		0			0
$9$	−2.99569	−	0.160768i	−0.998563	−	0.0535894i
$10$		0			0
$11$	−0.256724	+	0.958107i	−0.0774052	+	0.288880i	−0.993768	−	0.111469i	$-0.964444\pi$
$11$	−0.256724	+	0.958107i	−0.0774052	+	0.288880i	0.916363	+	0.400349i	$0.131111\pi$
$12$		0			0
$13$	−3.27036	−	1.51814i	−0.907034	−	0.421057i
$13$	−3.27036	−	1.51814i	−0.907034	−	0.421057i
$14$		0			0
$15$	2.25572	+	2.38002i	0.582424	+	0.614519i
$16$		0			0
$17$	−2.36097	+	4.08932i	−0.572619	+	0.991806i	0.423677	+	0.905814i	$0.360739\pi$
$17$	−2.36097	+	4.08932i	−0.572619	+	0.991806i	−0.996296	+	0.0859920i	$0.972594\pi$
$18$		0			0
$19$	−1.44252	+	0.386521i	−0.330936	+	0.0886741i	−0.420461	−	0.907310i	$-0.638132\pi$
$19$	−1.44252	+	0.386521i	−0.330936	+	0.0886741i	0.0895251	+	0.995985i	$0.471465\pi$
$20$		0			0
$21$	−3.68517	+	0.882285i	−0.804170	+	0.192530i
$22$		0			0
$23$	−1.71229	−	2.96577i	−0.357037	−	0.618407i	0.630427	−	0.776248i	$-0.282880\pi$
$23$	−1.71229	−	2.96577i	−0.357037	−	0.618407i	−0.987464	+	0.157842i	$0.949546\pi$
$24$		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	$-0.641602\pi$
$29$	0.733696	−	0.423600i	0.136244	−	0.0786605i	0.566573	+	0.824012i	$0.308269\pi$
$30$		0			0
$31$	−3.66157	−	3.66157i	−0.657638	−	0.657638i	0.297183	−	0.954821i	$-0.403953\pi$
$31$	−3.66157	−	3.66157i	−0.657638	−	0.657638i	−0.954821	+	0.297183i	$0.903953\pi$
$32$		0			0
$33$	1.64698	+	0.488981i	0.286702	+	0.0851207i
$34$		0			0
$35$	3.58699	+	2.07095i	0.606312	+	0.350054i
$36$		0			0
$37$	−10.5491	−	2.82661i	−1.73425	−	0.464692i	−0.753098	−	0.657909i	$-0.771441\pi$
$37$	−10.5491	−	2.82661i	−1.73425	−	0.464692i	−0.981156	+	0.193217i	$0.938108\pi$
$38$		0			0
$39$	−2.78039	+	5.59191i	−0.445218	+	0.895422i
$40$		0			0
$41$	8.93255	+	2.39347i	1.39503	+	0.373797i	0.876558	−	0.481297i	$-0.159834\pi$
$41$	8.93255	+	2.39347i	1.39503	+	0.373797i	0.518473	+	0.855094i	$0.326501\pi$
$42$		0			0
$43$	−6.05002	−	3.49298i	−0.922620	−	0.532675i	−0.0381501	−	0.999272i	$-0.512146\pi$
$43$	−6.05002	−	3.49298i	−0.922620	−	0.532675i	−0.884470	+	0.466597i	$0.845480\pi$
$44$		0			0
$45$	4.22556	−	3.79512i	0.629910	−	0.565743i
$46$		0			0
$47$	−0.384064	−	0.384064i	−0.0560215	−	0.0560215i	0.678541	−	0.734563i	$-0.262613\pi$
$47$	−0.384064	−	0.384064i	−0.0560215	−	0.0560215i	−0.734563	+	0.678541i	$0.762613\pi$
$48$		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
$57$	0.602263	+	2.51556i	0.0797717	+	0.333194i
$58$		0			0
$59$	−11.7285	+	3.14264i	−1.52692	+	0.409137i	−0.922013	−	0.387159i	$-0.873457\pi$
$59$	−11.7285	+	3.14264i	−1.52692	+	0.409137i	−0.604908	+	0.796296i	$0.706790\pi$
$60$		0			0
$61$	2.83411	−	4.90882i	0.362870	−	0.628510i	−0.625562	−	0.780175i	$-0.715130\pi$
$61$	2.83411	−	4.90882i	0.362870	−	0.628510i	0.988432	+	0.151665i	$0.0484635\pi$
$62$		0			0
$63$	1.35652	+	6.42157i	0.170906	+	0.809042i
$64$		0			0
$65$	6.41038	−	2.34570i	0.795110	−	0.290948i
$66$		0			0
$67$	−1.52023	+	5.67359i	−0.185726	+	0.693139i	0.808748	+	0.588155i	$0.200146\pi$
$67$	−1.52023	+	5.67359i	−0.185726	+	0.693139i	−0.994474	+	0.104984i	$0.966521\pi$
$68$		0			0
$69$	−5.21452	+	2.82702i	−0.627755	+	0.340333i
$70$		0			0
$71$	−2.69283	−	10.0498i	−0.319580	−	1.19269i	−0.919649	−	0.392741i	$-0.871527\pi$
$71$	−2.69283	−	10.0498i	−0.319580	−	1.19269i	0.600069	−	0.799948i	$-0.295140\pi$
$72$		0			0
$73$	−0.393272	+	0.393272i	−0.0460290	+	0.0460290i	−0.729747	−	0.683718i	$-0.760362\pi$
$73$	−0.393272	+	0.393272i	−0.0460290	+	0.0460290i	0.683718	+	0.729747i	$0.260362\pi$
$74$		0			0
$75$	2.45126	+	0.0657280i	0.283047	+	0.00758962i
$76$		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
$81$	8.94831	+	0.963224i	0.994256	+	0.107025i
$82$		0			0
$83$	−2.25706	+	2.25706i	−0.247745	+	0.247745i	−0.820045	−	0.572300i	$-0.806051\pi$
$83$	−2.25706	+	2.25706i	−0.247745	+	0.247745i	0.572300	+	0.820045i	$0.306051\pi$
$84$		0			0
$85$	−2.31375	−	8.63503i	−0.250961	−	0.936600i
$86$		0			0
$87$	−0.699369	−	1.29001i	−0.0749803	−	0.138303i
$88$		0			0
$89$	4.60143	−	17.1728i	0.487750	−	1.82031i	−0.0795919	−	0.996828i	$-0.525362\pi$
$89$	4.60143	−	17.1728i	0.487750	−	1.82031i	0.567342	−	0.823482i	$-0.307972\pi$
$90$		0			0
$91$	−1.35637	+	7.77060i	−0.142186	+	0.814580i
$92$		0			0
$93$	−6.50974	+	6.16976i	−0.675029	+	0.639774i
$94$		0			0
$95$	1.41367	−	2.44854i	0.145039	−	0.251215i
$96$		0			0
$97$	8.28096	−	2.21888i	0.840804	−	0.225293i	0.187383	−	0.982287i	$-0.440000\pi$
$97$	8.28096	−	2.21888i	0.840804	−	0.225293i	0.653422	+	0.756994i	$0.273333\pi$
$98$		0			0
$99$	0.923099	−	2.82892i	0.0927749	−	0.284317i
$100$		0			0
$101$	1.02109	+	1.76859i	0.101603	+	0.175981i	0.912345	−	0.409422i	$-0.134270\pi$
$101$	1.02109	+	1.76859i	0.101603	+	0.175981i	−0.810742	+	0.585403i	$0.800936\pi$
$102$		0			0
$103$		−	14.3415i		−	1.41311i	−0.707656	−	0.706557i	$-0.750247\pi$
$103$		−	14.3415i		−	1.41311i	0.707656	−	0.706557i	$-0.249753\pi$
$104$		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	$-0.660716\pi$
$107$	0.334916	−	0.193364i	0.0323776	−	0.0186932i	0.516101	+	0.856527i	$0.327383\pi$
$108$		0			0
$109$	−8.24097	−	8.24097i	−0.789342	−	0.789342i	0.192044	−	0.981386i	$-0.438488\pi$
$109$	−8.24097	−	8.24097i	−0.789342	−	0.789342i	−0.981386	+	0.192044i	$0.938488\pi$
$110$		0			0
$111$	−5.38383	+	18.1337i	−0.511010	+	1.72117i
$112$		0			0
$113$	−10.3438	−	5.97200i	−0.973063	−	0.561798i	−0.0728946	−	0.997340i	$-0.523224\pi$
$113$	−10.3438	−	5.97200i	−0.973063	−	0.561798i	−0.900169	+	0.435541i	$0.856557\pi$
$114$		0			0
$115$	6.26254	+	1.67804i	0.583985	+	0.156478i
$116$		0			0
$117$	9.55291	+	5.07365i	0.883167	+	0.469059i
$118$		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
$123$	4.55883	−	15.3550i	0.411056	−	1.38451i
$124$		0			0
$125$	−8.58878	−	8.58878i	−0.768204	−	0.768204i
$126$		0			0
$127$	0.109854	−	0.0634245i	0.00974800	−	0.00562801i	−0.495118	−	0.868826i	$-0.664875\pi$
$127$	0.109854	−	0.0634245i	0.00974800	−	0.00562801i	0.504866	+	0.863198i	$0.331542\pi$
$128$		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
$135$	−6.37480	−	7.49245i	−0.548655	−	0.644848i
$136$		0			0
$137$	−12.2978	+	3.29520i	−1.05068	+	0.281528i	−0.742531	−	0.669812i	$-0.766375\pi$
$137$	−12.2978	+	3.29520i	−1.05068	+	0.281528i	−0.308145	+	0.951340i	$0.599708\pi$
$138$		0			0
$139$	9.15970	−	15.8651i	0.776915	−	1.34566i	−0.156796	−	0.987631i	$-0.550117\pi$
$139$	9.15970	−	15.8651i	0.776915	−	1.34566i	0.933712	−	0.358026i	$-0.116550\pi$
$140$		0			0
$141$	−0.682810	+	0.647149i	−0.0575030	+	0.0544998i
$142$		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
$147$	−1.82743	−	3.37074i	−0.150724	−	0.278014i
$148$		0			0
$149$	−0.550277	−	2.05366i	−0.0450804	−	0.168242i	0.939716	−	0.341957i	$-0.111090\pi$
$149$	−0.550277	−	2.05366i	−0.0450804	−	0.168242i	−0.984796	+	0.173714i	$0.944423\pi$
$150$		0			0
$151$	−2.93665	+	2.93665i	−0.238981	+	0.238981i	−0.816428	−	0.577447i	$-0.804049\pi$
$151$	−2.93665	+	2.93665i	−0.238981	+	0.238981i	0.577447	+	0.816428i	$0.304049\pi$
$152$		0			0
$153$	7.73016	−	11.8708i	0.624947	−	0.959694i
$154$		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
$159$	18.0013	+	0.482686i	1.42760	+	0.0382795i
$160$		0			0
$161$	−5.29776	+	5.29776i	−0.417522	+	0.417522i
$162$		0			0
$163$	−0.995027	−	3.71349i	−0.0779365	−	0.290863i	0.915947	−	0.401300i	$-0.131442\pi$
$163$	−0.995027	−	3.71349i	−0.0779365	−	0.290863i	−0.993883	+	0.110437i	$0.964775\pi$
$164$		0			0
$165$	−2.85941	+	1.55021i	−0.222605	+	0.120684i
$166$		0			0
$167$	−6.12521	+	22.8596i	−0.473983	+	1.76893i	0.151255	+	0.988495i	$0.451668\pi$
$167$	−6.12521	+	22.8596i	−0.473983	+	1.76893i	−0.625238	+	0.780434i	$0.714998\pi$
$168$		0			0
$169$	8.39049	+	9.92974i	0.645422	+	0.763826i
$170$		0			0
$171$	4.38347	−	0.925987i	0.335213	−	0.0708120i
$172$		0			0
$173$	−7.36150	+	12.7505i	−0.559684	+	0.969401i	0.437838	+	0.899054i	$0.355744\pi$
$173$	−7.36150	+	12.7505i	−0.559684	+	0.969401i	−0.997523	+	0.0703477i	$0.977589\pi$
$174$		0			0
$175$	2.99177	−	0.801643i	0.226157	−	0.0605985i
$176$		0			0
$177$	4.89675	+	20.4530i	0.368062	+	1.53734i
$178$		0			0
$179$	8.53187	+	14.7776i	0.637702	+	1.10453i	0.985936	+	0.167125i	$0.0534483\pi$
$179$	8.53187	+	14.7776i	0.637702	+	1.10453i	−0.348234	+	0.937408i	$0.613218\pi$
$180$		0			0
$181$			3.51901i			0.261566i	0.991411	+	0.130783i	$0.0417491\pi$
$181$			3.51901i			0.261566i	−0.991411	+	0.130783i	$0.958251\pi$
$182$		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
$189$	11.1815	−	2.05059i	0.813332	−	0.149159i
$190$		0			0
$191$	18.6177	+	10.7490i	1.34713	+	0.777767i	0.987842	−	0.155459i	$-0.0496857\pi$
$191$	18.6177	+	10.7490i	1.34713	+	0.777767i	0.359290	+	0.933226i	$0.383019\pi$
$192$		0			0
$193$	−3.88032	−	1.03973i	−0.279312	−	0.0748413i	0.116444	−	0.993197i	$-0.462851\pi$
$193$	−3.88032	−	1.03973i	−0.279312	−	0.0748413i	−0.395755	+	0.918356i	$0.629517\pi$
$194$		0			0
$195$	−3.76380	−	11.2080i	−0.269531	−	0.802623i
$196$		0			0
$197$	−7.74656	−	2.07569i	−0.551920	−	0.147886i	−0.0279283	−	0.999610i	$-0.508891\pi$
$197$	−7.74656	−	2.07569i	−0.551920	−	0.147886i	−0.523992	+	0.851723i	$0.675558\pi$
$198$		0			0
$199$	−9.75011	−	5.62923i	−0.691167	−	0.399046i	0.112882	−	0.993608i	$-0.463992\pi$
$199$	−9.75011	−	5.62923i	−0.691167	−	0.399046i	−0.804049	+	0.594563i	$0.797325\pi$
$200$		0			0
$201$	9.75283	+	2.89558i	0.687912	+	0.204238i
$202$		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	0.902151	+	0.431420i	$0.141987\pi$
$211$	11.9794	+	20.7489i	0.824696	+	1.42842i	−0.0774545	+	0.996996i	$0.524679\pi$
$212$		0			0
$213$	−17.5255	+	4.19587i	−1.20083	+	0.287496i
$214$		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
$219$	0.662665	+	0.699181i	0.0447787	+	0.0472463i
$220$		0			0
$221$	13.9294	−	9.78925i	0.936992	−	0.658496i
$222$		0			0
$223$	0.495422	−	1.84894i	0.0331759	−	0.123814i	−0.947352	−	0.320194i	$-0.896252\pi$
$223$	0.495422	−	1.84894i	0.0331759	−	0.123814i	0.980528	+	0.196380i	$0.0629185\pi$
$224$		0			0
$225$	0.227607	−	4.24113i	0.0151738	−	0.282742i
$226$		0			0
$227$	−2.83237	−	10.5705i	−0.187991	−	0.701591i	−0.993970	−	0.109648i	$-0.965028\pi$
$227$	−2.83237	−	10.5705i	−0.187991	−	0.701591i	0.805980	−	0.591943i	$-0.201639\pi$
$228$		0			0
$229$	2.18006	−	2.18006i	0.144063	−	0.144063i	−0.631397	−	0.775460i	$-0.717518\pi$
$229$	2.18006	−	2.18006i	0.144063	−	0.144063i	0.775460	+	0.631397i	$0.217518\pi$
$230$		0			0
$231$	0.100748	−	3.75729i	0.00662873	−	0.247212i
$232$		0			0
$233$	−7.80150			−0.511093			−0.255546	−	0.966797i	$-0.582255\pi$
$233$	−7.80150			−0.511093			−0.255546	+	0.966797i	$0.582255\pi$
$234$		0			0
$235$	1.02830			0.0670787
$236$		0			0
$237$	0.466508	−	17.3979i	0.0303029	−	1.13012i
$238$		0			0
$239$	−14.8365	+	14.8365i	−0.959695	+	0.959695i	−0.999219	−	0.0395239i	$-0.987416\pi$
$239$	−14.8365	+	14.8365i	−0.959695	+	0.959695i	0.0395239	+	0.999219i	$0.487416\pi$
$240$		0			0
$241$	−4.24837	−	15.8551i	−0.273661	−	1.02132i	−0.956733	−	0.290967i	$-0.906023\pi$
$241$	−4.24837	−	15.8551i	−0.273661	−	1.02132i	0.683072	−	0.730351i	$-0.260644\pi$
$242$		0			0
$243$	2.08319	−	15.4486i	0.133637	−	0.991030i
$244$		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
$249$	3.80316	+	4.01273i	0.241015	+	0.254296i
$250$		0			0
$251$	−2.11649	+	3.66588i	−0.133592	+	0.231388i	−0.925059	−	0.379824i	$-0.875984\pi$
$251$	−2.11649	+	3.66588i	−0.133592	+	0.231388i	0.791467	+	0.611212i	$0.209318\pi$
$252$		0			0
$253$	3.28112	−	0.879172i	0.206282	−	0.0552731i
$254$		0			0
$255$	−15.0583	+	3.60520i	−0.942990	+	0.225766i
$256$		0			0
$257$	3.01424	+	5.22082i	0.188023	+	0.325666i	0.944591	−	0.328249i	$-0.106459\pi$
$257$	3.01424	+	5.22082i	0.188023	+	0.325666i	−0.756568	+	0.653915i	$0.773125\pi$
$258$		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	$-0.872266\pi$
$263$	−16.9076	+	9.76159i	−1.04257	+	0.601925i	−0.122006	+	0.992529i	$0.538933\pi$
$264$		0			0
$265$	−13.9182	−	13.9182i	−0.854989	−	0.854989i
$266$		0			0
$267$	−29.5198	−	8.76432i	−1.80658	−	0.536367i
$268$		0			0
$269$	−22.7011	−	13.1065i	−1.38411	−	0.799118i	−0.391469	−	0.920191i	$-0.628033\pi$
$269$	−22.7011	−	13.1065i	−1.38411	−	0.799118i	−0.992644	+	0.121074i	$0.961366\pi$
$270$		0			0
$271$	−13.9542	−	3.73902i	−0.847657	−	0.227129i	−0.191255	−	0.981540i	$-0.561256\pi$
$271$	−13.9542	−	3.73902i	−0.847657	−	0.227129i	−0.656402	+	0.754411i	$0.727923\pi$
$272$		0			0
$273$	13.3913	+	2.70922i	0.810476	+	0.163970i
$274$		0			0
$275$	−1.35643	−	0.363456i	−0.0817961	−	0.0219172i
$276$		0			0
$277$	−4.00445	−	2.31197i	−0.240604	−	0.138913i	0.374850	−	0.927085i	$-0.377694\pi$
$277$	−4.00445	−	2.31197i	−0.240604	−	0.138913i	−0.615454	+	0.788172i	$0.711028\pi$
$278$		0			0
$279$	10.3803	+	11.5576i	0.621450	+	0.691935i
$280$		0			0
$281$	2.83565	+	2.83565i	0.169161	+	0.169161i	0.786611	−	0.617450i	$-0.211834\pi$
$281$	2.83565	+	2.83565i	0.169161	+	0.169161i	−0.617450	+	0.786611i	$0.711834\pi$
$282$		0			0
$283$	−21.9372	+	12.6654i	−1.30403	+	0.752883i	−0.981093	−	0.193537i	$-0.938004\pi$
$283$	−21.9372	+	12.6654i	−1.30403	+	0.752883i	−0.322938	+	0.946420i	$0.604671\pi$
$284$		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
$291$	−3.45737	−	14.4409i	−0.202675	−	0.846541i
$292$		0			0
$293$	17.0816	−	4.57700i	0.997917	−	0.267391i	0.277345	−	0.960770i	$-0.410546\pi$
$293$	17.0816	−	4.57700i	0.997917	−	0.267391i	0.720573	+	0.693379i	$0.243879\pi$
$294$		0			0
$295$	11.4939	−	19.9081i	0.669202	−	1.15909i
$296$		0			0
$297$	−4.85521	−	1.72962i	−0.281728	−	0.100363i
$298$		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
$303$	3.10959	−	1.68584i	0.178641	−	0.0968492i
$304$		0			0
$305$	2.77742	+	10.3655i	0.159035	+	0.593526i
$306$		0			0
$307$	−16.5562	+	16.5562i	−0.944910	+	0.944910i	−0.998560	−	0.0536497i	$-0.982915\pi$
$307$	−16.5562	+	16.5562i	−0.944910	+	0.944910i	0.0536497	+	0.998560i	$0.482915\pi$
$308$		0			0
$309$	−24.8313	−	0.665827i	−1.41261	−	0.0378776i
$310$		0			0
$311$	−27.9565			−1.58527			−0.792635	−	0.609697i	$-0.791291\pi$
$311$	−27.9565			−1.58527			−0.792635	+	0.609697i	$0.791291\pi$
$312$		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
$315$	−10.4126	−	6.78059i	−0.586681	−	0.382043i
$316$		0			0
$317$	−5.44471	+	5.44471i	−0.305805	+	0.305805i	−0.843280	−	0.537475i	$-0.819378\pi$
$317$	−5.44471	+	5.44471i	−0.305805	+	0.305805i	0.537475	+	0.843280i	$0.319378\pi$
$318$		0			0
$319$	0.217496	+	0.811708i	0.0121775	+	0.0454469i
$320$		0			0
$321$	−0.319247	−	0.588861i	−0.0178186	−	0.0328670i
$322$		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
$327$	−14.6513	+	13.8861i	−0.810216	+	0.767900i
$328$		0			0
$329$	−0.594140	+	1.02908i	−0.0327560	+	0.0567350i
$330$		0			0
$331$	−5.61987	+	1.50584i	−0.308896	+	0.0827684i	−0.409937	−	0.912114i	$-0.634449\pi$
$331$	−5.61987	+	1.50584i	−0.308896	+	0.0827684i	0.101041	+	0.994882i	$0.467783\pi$
$332$		0			0
$333$	31.1473	+	10.1636i	1.70686	+	0.556962i
$334$		0			0
$335$	−5.56011	−	9.63039i	−0.303781	−	0.526165i
$336$		0			0
$337$			15.0629i			0.820528i	0.911967	+	0.410264i	$0.134564\pi$
$337$			15.0629i			0.820528i	−0.911967	+	0.410264i	$0.865436\pi$
$338$		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
$345$	3.19616	−	10.7652i	0.172075	−	0.579581i
$346$		0			0
$347$	6.58502	+	3.80186i	0.353502	+	0.204095i	0.666227	−	0.745749i	$-0.267908\pi$
$347$	6.58502	+	3.80186i	0.353502	+	0.204095i	−0.312724	+	0.949844i	$0.601242\pi$
$348$		0			0
$349$	−13.2155	−	3.54107i	−0.707407	−	0.189549i	−0.112861	−	0.993611i	$-0.536002\pi$
$349$	−13.2155	−	3.54107i	−0.707407	−	0.189549i	−0.594546	+	0.804062i	$0.702668\pi$
$350$		0			0
$351$	9.22817	−	16.3046i	0.492563	−	0.870277i
$352$		0			0
$353$	6.31893	+	1.69315i	0.336323	+	0.0901174i	0.423028	−	0.906117i	$-0.360967\pi$
$353$	6.31893	+	1.69315i	0.336323	+	0.0901174i	−0.0867052	+	0.996234i	$0.527634\pi$
$354$		0			0
$355$	17.0586	+	9.84877i	0.905375	+	0.522719i
$356$		0			0
$357$	5.09263	−	17.1529i	0.269530	−	0.907827i
$358$		0			0
$359$	11.5879	+	11.5879i	0.611588	+	0.611588i	0.943360	−	0.331772i	$-0.107646\pi$
$359$	11.5879	+	11.5879i	0.611588	+	0.611588i	−0.331772	+	0.943360i	$0.607646\pi$
$360$		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	0.998567	+	0.0535227i	$0.0170449\pi$
$367$	10.4529	+	18.1049i	0.545635	+	0.945068i	−0.452931	+	0.891545i	$0.649622\pi$
$368$		0			0
$369$	−26.3744	−	8.60617i	−1.37299	−	0.448019i
$370$		0			0
$371$	21.9707	−	5.88702i	1.14066	−	0.305639i
$372$		0			0
$373$	11.5708	−	20.0412i	0.599114	−	1.03770i	−0.393838	−	0.919180i	$-0.628853\pi$
$373$	11.5708	−	20.0412i	0.599114	−	1.03770i	0.992952	−	0.118516i	$-0.0378138\pi$
$374$		0			0
$375$	−15.2696	+	14.4721i	−0.788519	+	0.747337i
$376$		0			0
$377$	−3.04253	+	0.271468i	−0.156698	+	0.0139813i
$378$		0			0
$379$	3.41564	−	12.7474i	0.175450	−	0.654788i	−0.821025	−	0.570893i	$-0.806597\pi$
$379$	3.41564	−	12.7474i	0.175450	−	0.654788i	0.996475	−	0.0838951i	$-0.0267361\pi$
$380$		0			0
$381$	−0.104715	−	0.193150i	−0.00536470	−	0.00989536i
$382$		0			0
$383$	−2.61140	−	9.74587i	−0.133436	−	0.497991i	0.866563	−	0.499067i	$-0.166324\pi$
$383$	−2.61140	−	9.74587i	−0.133436	−	0.497991i	−0.999999	+	0.00107658i	$0.999657\pi$
$384$		0			0
$385$	−2.90506	+	2.90506i	−0.148055	+	0.148055i
$386$		0			0
$387$	17.5624	+	11.4365i	0.892749	+	0.581352i
$388$		0			0
$389$	21.6943			1.09994			0.549971	−	0.835184i	$-0.314639\pi$
$389$	21.6943			1.09994			0.549971	+	0.835184i	$0.314639\pi$
$390$		0			0
$391$	16.1707			0.817786
$392$		0			0
$393$	−36.1449	−	0.969189i	−1.82327	−	0.0488891i
$394$		0			0
$395$	−13.4517	+	13.4517i	−0.676829	+	0.676829i
$396$		0			0
$397$	4.57617	+	17.0785i	0.229672	+	0.857146i	0.980479	+	0.196625i	$0.0629980\pi$
$397$	4.57617	+	17.0785i	0.229672	+	0.857146i	−0.750807	+	0.660521i	$0.770335\pi$
$398$		0			0
$399$	4.97490	−	2.69711i	0.249056	−	0.135024i
$400$		0			0
$401$	−1.42326	+	5.31167i	−0.0710741	+	0.265252i	−0.992314	−	0.123742i	$-0.960511\pi$
$401$	−1.42326	+	5.31167i	−0.0710741	+	0.265252i	0.921240	+	0.388994i	$0.127177\pi$
$402$		0			0
$403$	6.41587	+	17.5334i	0.319597	+	0.873403i
$404$		0			0
$405$	−13.2686	+	10.6897i	−0.659322	+	0.531174i
$406$		0			0
$407$	5.41639	−	9.38147i	0.268481	−	0.465022i
$408$		0			0
$409$	−19.7035	+	5.27954i	−0.974275	+	0.261056i	−0.710632	−	0.703564i	$-0.751591\pi$
$409$	−19.7035	+	5.27954i	−0.974275	+	0.261056i	−0.263643	+	0.964620i	$0.584924\pi$
$410$		0			0
$411$	5.13445	+	21.4458i	0.253264	+	1.05784i
$412$		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	$-0.999876\pi$
$419$	−30.6973	+	17.7231i	−1.49966	+	0.865831i	−0.499663	+	0.866220i	$0.666543\pi$
$420$		0			0
$421$	26.7150	+	26.7150i	1.30201	+	1.30201i	0.927036	+	0.374972i	$0.122348\pi$
$421$	26.7150	+	26.7150i	1.30201	+	1.30201i	0.374972	+	0.927036i	$0.377652\pi$
$422$		0			0
$423$	1.08879	+	1.21228i	0.0529389	+	0.0589432i
$424$		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
$429$	−4.64386	−	4.09949i	−0.224208	−	0.197925i
$430$		0			0
$431$	25.5938	+	6.85785i	1.23281	+	0.330331i	0.815674	−	0.578512i	$-0.196366\pi$
$431$	25.5938	+	6.85785i	1.23281	+	0.330331i	0.417138	+	0.908843i	$0.363033\pi$
$432$		0			0
$433$	−22.5129	−	12.9978i	−1.08190	−	0.624636i	−0.150493	−	0.988611i	$-0.548086\pi$
$433$	−22.5129	−	12.9978i	−1.08190	−	0.624636i	−0.931409	+	0.363975i	$0.881419\pi$
$434$		0			0
$435$	2.66319	+	0.790691i	0.127690	+	0.0379107i
$436$		0			0
$437$	3.61634	+	3.61634i	0.172993	+	0.172993i
$438$		0			0
$439$	21.2539	−	12.2710i	1.01440	−	0.585661i	0.101920	−	0.994793i	$-0.467501\pi$
$439$	21.2539	−	12.2710i	1.01440	−	0.585661i	0.912476	+	0.409131i	$0.134168\pi$
$440$		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
$447$	−3.58131	+	0.857420i	−0.169390	+	0.0405546i
$448$		0			0
$449$	−18.0387	+	4.83346i	−0.851300	+	0.228105i	−0.657985	−	0.753031i	$-0.728591\pi$
$449$	−18.0387	+	4.83346i	−0.851300	+	0.228105i	−0.193316	+	0.981137i	$0.561924\pi$
$450$		0			0
$451$	−4.58640	+	7.94388i	−0.215965	+	0.374063i
$452$		0			0
$453$	4.94826	+	5.22094i	0.232490	+	0.245301i
$454$		0			0
$455$	−8.58675	−	12.2183i	−0.402553	−	0.572803i
$456$		0			0
$457$	0.610148	−	2.27710i	0.0285415	−	0.106518i	−0.950186	−	0.311685i	$-0.899107\pi$
$457$	0.610148	−	2.27710i	0.0285415	−	0.106518i	0.978727	+	0.205166i	$0.0657735\pi$
$458$		0			0
$459$	−20.1945	−	13.9353i	−0.942598	−	0.650446i
$460$		0			0
$461$	−3.36375	−	12.5537i	−0.156665	−	0.584683i	−0.998957	−	0.0456608i	$-0.985461\pi$
$461$	−3.36375	−	12.5537i	−0.156665	−	0.584683i	0.842292	−	0.539022i	$-0.181206\pi$
$462$		0			0
$463$	−1.03011	+	1.03011i	−0.0478733	+	0.0478733i	−0.730638	−	0.682765i	$-0.760777\pi$
$463$	−1.03011	+	1.03011i	−0.0478733	+	0.0478733i	0.682765	+	0.730638i	$0.260777\pi$
$464$		0			0
$465$	0.455143	−	16.9741i	0.0211068	−	0.787155i
$466$		0			0
$467$	36.9118			1.70808			0.854038	−	0.520211i	$-0.174147\pi$
$467$	36.9118			1.70808			0.854038	+	0.520211i	$0.174147\pi$
$468$		0			0
$469$	12.8503			0.593373
$470$		0			0
$471$	0.751830	−	28.0387i	0.0346425	−	1.29196i
$472$		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
$477$	1.67147	−	31.1455i	0.0765315	−	1.42606i
$478$		0			0
$479$	2.40863	−	8.98914i	0.110053	−	0.410724i	−0.888816	−	0.458264i	$-0.848471\pi$
$479$	2.40863	−	8.98914i	0.110053	−	0.410724i	0.998869	+	0.0475398i	$0.0151381\pi$
$480$		0			0
$481$	30.2080	+	25.2590i	1.37737	+	1.15171i
$482$		0			0
$483$	8.92674	+	9.41865i	0.406181	+	0.428563i
$484$		0			0
$485$	−8.11534	+	14.0562i	−0.368498	+	0.638258i
$486$		0			0
$487$	−16.0328	+	4.29597i	−0.726515	+	0.194669i	−0.603077	−	0.797683i	$-0.706059\pi$
$487$	−16.0328	+	4.29597i	−0.726515	+	0.194669i	−0.123438	+	0.992352i	$0.539392\pi$
$488$		0			0
$489$	−6.47584	+	1.55041i	−0.292848	+	0.0701121i
$490$		0			0
$491$	−12.3545	−	21.3987i	−0.557553	−	0.965709i	−0.997700	−	0.0677839i	$-0.978407\pi$
$491$	−12.3545	−	21.3987i	−0.557553	−	0.965709i	0.440147	−	0.897926i	$-0.354926\pi$
$492$		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	0.804288	−	0.594239i	$-0.202547\pi$
$499$	4.69214	+	4.69214i	0.210049	+	0.210049i	−0.594239	+	0.804288i	$0.702547\pi$
$500$		0			0
$501$	39.2954	+	11.6667i	1.75559	+	0.521228i
$502$		0			0
$503$	−31.1321	−	17.9741i	−1.38811	−	0.801427i	−0.395010	−	0.918677i	$-0.629259\pi$
$503$	−31.1321	−	17.9741i	−1.38811	−	0.801427i	−0.993102	+	0.117249i	$0.962592\pi$
$504$		0			0
$505$	−3.73456	−	1.00067i	−0.166186	−	0.0445293i
$506$		0			0
$507$	17.5822	−	14.0665i	0.780852	−	0.624717i
$508$		0			0
$509$	17.0359	+	4.56477i	0.755105	+	0.202330i	0.615781	−	0.787917i	$-0.288840\pi$
$509$	17.0359	+	4.56477i	0.755105	+	0.202330i	0.139324	+	0.990247i	$0.455507\pi$
$510$		0			0
$511$	1.05375	+	0.608385i	0.0466153	+	0.0269134i
$512$		0			0
$513$	−1.39977	−	7.63266i	−0.0618014	−	0.336990i
$514$		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	0.700719	−	0.713437i	$-0.252863\pi$
$523$	−6.11740	−	10.5957i	−0.267495	−	0.463316i	−0.968214	+	0.250122i	$0.919529\pi$
$524$		0			0
$525$	−1.24909	−	5.21726i	−0.0545147	−	0.227700i
$526$		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
$531$	35.6402	−	7.52881i	1.54665	−	0.326722i
$532$		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
$537$	25.9825	−	14.0863i	1.12123	−	0.607867i
$538$		0			0
$539$	0.568310	+	2.12096i	0.0244789	+	0.0913563i
$540$		0			0
$541$	−17.8177	+	17.8177i	−0.766042	+	0.766042i	−0.977407	−	0.211365i	$-0.932209\pi$
$541$	−17.8177	+	17.8177i	−0.766042	+	0.766042i	0.211365	+	0.977407i	$0.432209\pi$
$542$		0			0
$543$	6.09291	+	0.163375i	0.261472	+	0.00701110i
$544$		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
$549$	−9.27929	+	14.2497i	−0.396030	+	0.608161i
$550$		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
$555$	−17.0683	−	31.4830i	−0.724509	−	1.33638i
$556$		0			0
$557$	−1.33172	+	4.97004i	−0.0564267	+	0.210587i	−0.988383	−	0.151983i	$-0.951434\pi$
$557$	−1.33172	+	4.97004i	−0.0564267	+	0.210587i	0.931956	+	0.362570i	$0.118101\pi$
$558$		0			0
$559$	14.4829	+	20.6081i	0.612562	+	0.871630i
$560$		0			0
$561$	−5.88806	+	5.58054i	−0.248594	+	0.235611i
$562$		0			0
$563$	−1.28809	+	2.23104i	−0.0542866	+	0.0940271i	−0.891892	−	0.452249i	$-0.850622\pi$
$563$	−1.28809	+	2.23104i	−0.0542866	+	0.0940271i	0.837605	+	0.546276i	$0.183955\pi$
$564$		0			0
$565$	21.8420	−	5.85255i	0.918901	−	0.246219i
$566$		0			0
$567$	−3.03134	−	19.4551i	−0.127304	−	0.817038i
$568$		0			0
$569$	−2.81100	−	4.86880i	−0.117843	−	0.204111i	0.801069	−	0.598572i	$-0.204265\pi$
$569$	−2.81100	−	4.86880i	−0.117843	−	0.204111i	−0.918913	+	0.394461i	$0.870931\pi$
$570$		0			0
$571$			33.8079i			1.41482i	0.706806	+	0.707408i	$0.250136\pi$
$571$			33.8079i			1.41482i	−0.706806	+	0.707408i	$0.749864\pi$
$572$		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	0.576372	−	0.817187i	$-0.304468\pi$
$577$	−5.78457	−	5.78457i	−0.240815	−	0.240815i	−0.817187	+	0.576372i	$0.804468\pi$
$578$		0			0
$579$	−1.98037	+	6.67022i	−0.0823012	+	0.277205i
$580$		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
$585$	−19.5806	+	5.99640i	−0.809559	+	0.247921i
$586$		0			0
$587$	−39.0455	−	10.4622i	−1.61158	−	0.431822i	−0.663068	−	0.748559i	$-0.730746\pi$
$587$	−39.0455	−	10.4622i	−1.61158	−	0.431822i	−0.948514	+	0.316737i	$0.897413\pi$
$588$		0			0
$589$	6.69716	+	3.86661i	0.275952	+	0.159321i
$590$		0			0
$591$	−3.95355	+	13.3163i	−0.162627	+	0.547758i
$592$		0			0
$593$	−8.23055	−	8.23055i	−0.337988	−	0.337988i	0.517621	−	0.855610i	$-0.326818\pi$
$593$	−8.23055	−	8.23055i	−0.337988	−	0.337988i	−0.855610	+	0.517621i	$0.826818\pi$
$594$		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	0.824183	−	0.566323i	$-0.191635\pi$
$601$	−1.92099	−	3.32725i	−0.0783587	−	0.135721i	−0.902542	+	0.430602i	$0.858301\pi$
$602$		0			0
$603$	5.46628	−	16.7519i	0.222604	−	0.682190i
$604$		0			0
$605$	−18.3165	+	4.90790i	−0.744672	+	0.199534i
$606$		0			0
$607$	6.01621	−	10.4204i	0.244190	−	0.422950i	−0.717713	−	0.696339i	$-0.754811\pi$
$607$	6.01621	−	10.4204i	0.244190	−	0.422950i	0.961904	+	0.273389i	$0.0881445\pi$
$608$		0			0
$609$	−2.33006	+	2.20837i	−0.0944187	+	0.0894875i
$610$		0			0
$611$	0.672964	+	1.83909i	0.0272252	+	0.0744017i
$612$		0			0
$613$	6.43463	−	24.0144i	0.259892	−	0.969931i	−0.705411	−	0.708799i	$-0.749237\pi$
$613$	6.43463	−	24.0144i	0.259892	−	0.969931i	0.965303	−	0.261133i	$-0.0840960\pi$
$614$		0			0
$615$	14.4528	+	26.6587i	0.582794	+	1.07498i
$616$		0			0
$617$	11.6729	+	43.5637i	0.469932	+	1.75381i	0.639997	+	0.768377i	$0.278935\pi$
$617$	11.6729	+	43.5637i	0.469932	+	1.75381i	−0.170066	+	0.985433i	$0.554398\pi$
$618$		0			0
$619$	24.4865	−	24.4865i	0.984197	−	0.984197i	−0.0156805	−	0.999877i	$-0.504991\pi$
$619$	24.4865	−	24.4865i	0.984197	−	0.984197i	0.999877	+	0.0156805i	$0.00499147\pi$
$620$		0			0
$621$	16.0756	−	7.63054i	0.645091	−	0.306203i
$622$		0			0
$623$	−38.8952			−1.55830
$624$		0			0
$625$	15.9169			0.636678
$626$		0			0
$627$	−2.56479	−	0.0687723i	−0.102428	−	0.00274650i
$628$		0			0
$629$	36.4649	−	36.4649i	1.45395	−	1.45395i
$630$		0			0
$631$	−3.56833	−	13.3172i	−0.142053	−	0.530149i	−0.999869	−	0.0161917i	$-0.994846\pi$
$631$	−3.56833	−	13.3172i	−0.142053	−	0.530149i	0.857816	−	0.513957i	$-0.171821\pi$
$632$		0			0
$633$	36.4815	−	19.7782i	1.45001	−	0.786112i
$634$		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
$639$	6.45119	+	30.5389i	0.255205	+	1.20810i
$640$		0			0
$641$	18.7773	−	32.5233i	0.741659	−	1.28459i	−0.210080	−	0.977684i	$-0.567372\pi$
$641$	18.7773	−	32.5233i	0.741659	−	1.28459i	0.951739	−	0.306908i	$-0.0992942\pi$
$642$		0			0
$643$	33.9096	−	9.08605i	1.33726	−	0.358319i	0.481845	−	0.876256i	$-0.339967\pi$
$643$	33.9096	−	9.08605i	1.33726	−	0.358319i	0.855418	+	0.517937i	$0.173300\pi$
$644$		0			0
$645$	−5.33378	−	22.2784i	−0.210017	−	0.877210i
$646$		0			0
$647$	−4.67261	−	8.09319i	−0.183699	−	0.318176i	0.759438	−	0.650579i	$-0.225474\pi$
$647$	−4.67261	−	8.09319i	−0.183699	−	0.318176i	−0.943137	+	0.332403i	$0.892141\pi$
$648$		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	$-0.632181\pi$
$653$	4.78580	−	2.76309i	0.187283	−	0.108128i	0.590710	+	0.806884i	$0.298848\pi$
$654$		0			0
$655$	27.9465	+	27.9465i	1.09196	+	1.09196i
$656$		0			0
$657$	1.24135	−	1.11490i	0.0484296	−	0.0434962i
$658$		0			0
$659$	−30.1079	−	17.3828i	−1.17284	−	0.677138i	−0.218491	−	0.975839i	$-0.570113\pi$
$659$	−30.1079	−	17.3828i	−1.17284	−	0.677138i	−0.954347	+	0.298701i	$0.903447\pi$
$660$		0			0
$661$	−10.7464	−	2.87948i	−0.417985	−	0.111999i	0.0436959	−	0.999045i	$-0.486087\pi$
$661$	−10.7464	−	2.87948i	−0.417985	−	0.111999i	−0.461681	+	0.887046i	$0.652753\pi$
$662$		0			0
$663$	−16.3027	−	24.5722i	−0.633144	−	0.954306i
$664$		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
$669$	−3.17831	−	0.943628i	−0.122881	−	0.0364828i
$670$		0			0
$671$	3.97559	+	3.97559i	0.153476	+	0.153476i
$672$		0			0
$673$	38.4396	−	22.1931i	1.48174	−	0.855482i	0.481954	−	0.876197i	$-0.339927\pi$
$673$	38.4396	−	22.1931i	1.48174	−	0.855482i	0.999785	+	0.0207144i	$0.00659408\pi$
$674$		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
$681$	−18.4336	+	4.41329i	−0.706378	+	0.169117i
$682$		0			0
$683$	−3.10117	+	0.830957i	−0.118663	+	0.0317957i	−0.317662	−	0.948204i	$-0.602898\pi$
$683$	−3.10117	+	0.830957i	−0.118663	+	0.0317957i	0.198999	+	0.980000i	$0.436231\pi$
$684$		0			0
$685$	12.0519	−	20.8745i	0.460478	−	0.797572i
$686$		0			0
$687$	−3.67341	−	3.87584i	−0.140149	−	0.147872i
$688$		0			0
$689$	15.7838	−	34.0012i	0.601315	−	1.29534i
$690$		0			0
$691$	0.553429	−	2.06543i	0.0210534	−	0.0785725i	−0.954600	−	0.297891i	$-0.903717\pi$
$691$	0.553429	−	2.06543i	0.0210534	−	0.0785725i	0.975653	+	0.219319i	$0.0703834\pi$
$692$		0			0
$693$	−6.50080	−	0.348876i	−0.246945	−	0.0132527i
$694$		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
$699$	−0.362196	+	13.5077i	−0.0136995	+	0.510909i
$700$		0			0
$701$	21.3084			0.804808			0.402404	−	0.915462i	$-0.368175\pi$
$701$	21.3084			0.804808			0.402404	+	0.915462i	$0.368175\pi$
$702$		0			0
$703$	16.3097			0.615133
$704$		0			0
$705$	0.0477402	−	1.78042i	0.00179800	−	0.0670546i
$706$		0			0
$707$	3.15923	−	3.15923i	0.118815	−	0.118815i
$708$		0			0
$709$	7.30917	+	27.2782i	0.274502	+	1.02445i	0.956175	+	0.292797i	$0.0945859\pi$
$709$	7.30917	+	27.2782i	0.274502	+	1.02445i	−0.681673	+	0.731657i	$0.738747\pi$
$710$		0			0
$711$	−30.1016	−	1.61545i	−1.12890	−	0.0605841i
$712$		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
$717$	24.9996	+	26.3772i	0.933626	+	0.985074i
$718$		0			0
$719$	2.67277	−	4.62937i	0.0996774	−	0.172646i	−0.811874	−	0.583833i	$-0.801552\pi$
$719$	2.67277	−	4.62937i	0.0996774	−	0.172646i	0.911551	+	0.411187i	$0.134886\pi$
$720$		0			0
$721$	−30.3068	+	8.12067i	−1.12868	+	0.302430i
$722$		0			0
$723$	−27.6492	+	6.61964i	−1.02829	+	0.246187i
$724$		0			0
$725$	0.599709	+	1.03873i	0.0222726	+	0.0385773i
$726$		0			0
$727$		−	3.49159i		−	0.129496i	−0.997902	−	0.0647480i	$-0.979376\pi$
$727$		−	3.49159i		−	0.129496i	0.997902	−	0.0647480i	$-0.0206244\pi$
$728$		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	0.686944	−	0.726710i	$-0.258952\pi$
$733$	−1.07662	−	1.07662i	−0.0397658	−	0.0397658i	−0.726710	+	0.686944i	$0.758952\pi$
$734$		0			0
$735$	6.95881	+	2.06605i	0.256680	+	0.0762072i
$736$		0			0
$737$	−5.04562	−	2.91309i	−0.185858	−	0.107305i
$738$		0			0
$739$	−32.6118	−	8.73832i	−1.19965	−	0.321444i	−0.396954	−	0.917838i	$-0.629933\pi$
$739$	−32.6118	−	8.73832i	−1.19965	−	0.321444i	−0.802692	+	0.596394i	$0.796599\pi$
$740$		0			0
$741$	1.84936	−	9.14111i	0.0679380	−	0.335807i
$742$		0			0
$743$	−9.87756	−	2.64668i	−0.362372	−	0.0970974i	0.0730388	−	0.997329i	$-0.476730\pi$
$743$	−9.87756	−	2.64668i	−0.362372	−	0.0970974i	−0.435411	+	0.900232i	$0.643397\pi$
$744$		0			0
$745$	3.48590	+	2.01259i	0.127713	+	0.0737354i
$746$		0			0
$747$	7.12432	−	6.39859i	0.260665	−	0.234112i
$748$		0			0
$749$	−0.598261	−	0.598261i	−0.0218600	−	0.0218600i
$750$		0			0
$751$	−29.4768	+	17.0185i	−1.07563	+	0.621012i	−0.929713	−	0.368285i	$-0.879945\pi$
$751$	−29.4768	+	17.0185i	−1.07563	+	0.621012i	−0.145912	+	0.989298i	$0.546612\pi$
$752$		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	0.931611	−	0.363457i	$-0.118404\pi$
$757$	4.15573	+	7.19794i	0.151043	+	0.261614i	−0.780568	+	0.625070i	$0.785070\pi$
$758$		0			0
$759$	−1.36989	−	5.72183i	−0.0497240	−	0.207689i
$760$		0			0
$761$	−30.3530	+	8.13305i	−1.10029	+	0.294823i	−0.762884	−	0.646535i	$-0.776217\pi$
$761$	−30.3530	+	8.13305i	−1.10029	+	0.294823i	−0.337409	+	0.941358i	$0.609551\pi$
$762$		0			0
$763$	−12.7486	+	22.0813i	−0.461531	+	0.799395i
$764$		0			0
$765$	5.54303	+	26.2398i	0.200409	+	0.948703i
$766$		0			0
$767$	43.1274	+	7.52796i	1.55724	+	0.271819i
$768$		0			0
$769$	12.2950	−	45.8856i	0.443370	−	1.65468i	−0.276835	−	0.960917i	$-0.589286\pi$
$769$	12.2950	−	45.8856i	0.443370	−	1.65468i	0.720205	−	0.693761i	$-0.244048\pi$
$770$		0			0
$771$	9.17942	−	4.97656i	0.330589	−	0.179227i
$772$		0			0
$773$	−2.09638	−	7.82380i	−0.0754015	−	0.281402i	0.917923	−	0.396760i	$-0.129865\pi$
$773$	−2.09638	−	7.82380i	−0.0754015	−	0.281402i	−0.993324	+	0.115357i	$0.963199\pi$
$774$		0			0
$775$	5.18385	−	5.18385i	0.186209	−	0.186209i
$776$		0			0
$777$	41.3689	+	1.10927i	1.48410	+	0.0397947i
$778$		0			0
$779$	−13.8105			−0.494812
$780$		0			0
$781$	10.3201			0.369281
$782$		0			0
$783$	1.88770	+	3.97690i	0.0674609	+	0.142123i
$784$		0			0
$785$	−21.6790	+	21.6790i	−0.773755	+	0.773755i
$786$		0			0
$787$	5.53321	+	20.6502i	0.197238	+	0.736101i	0.991676	+	0.128756i	$0.0410985\pi$
$787$	5.53321	+	20.6502i	0.197238	+	0.736101i	−0.794439	+	0.607344i	$0.792235\pi$
$788$		0			0
$789$	16.1165	+	29.7274i	0.573764	+	1.05832i
$790$		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
$795$	−24.7446	+	23.4522i	−0.877600	+	0.831765i
$796$		0			0
$797$	7.33180	−	12.6990i	0.259706	−	0.449823i	−0.706457	−	0.707756i	$-0.749708\pi$
$797$	7.33180	−	12.6990i	0.259706	−	0.449823i	0.966163	+	0.257932i	$0.0830411\pi$
$798$		0			0
$799$	2.47732	−	0.663797i	0.0876414	−	0.0234835i
$800$		0			0
$801$	−16.5453	+	50.7045i	−0.584599	+	1.79156i
$802$		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	$-0.744146\pi$
$809$	−11.8733	+	6.85508i	−0.417445	+	0.241012i	0.276539	+	0.961003i	$0.410813\pi$
$810$		0			0
$811$	−16.9177	−	16.9177i	−0.594060	−	0.594060i	0.344666	−	0.938726i	$-0.387992\pi$
$811$	−16.9177	−	16.9177i	−0.594060	−	0.594060i	−0.938726	+	0.344666i	$0.887992\pi$
$812$		0			0
$813$	−7.12169	+	23.9871i	−0.249768	+	0.841265i
$814$		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
$819$	5.31253	−	23.0602i	0.185635	−	0.805790i
$820$		0			0
$821$	5.16766	+	1.38467i	0.180353	+	0.0483253i	0.347865	−	0.937545i	$-0.386907\pi$
$821$	5.16766	+	1.38467i	0.180353	+	0.0483253i	−0.167512	+	0.985870i	$0.553573\pi$
$822$		0			0
$823$	−40.3992	−	23.3245i	−1.40823	−	0.813040i	−0.413010	−	0.910726i	$-0.635523\pi$
$823$	−40.3992	−	23.3245i	−1.40823	−	0.813040i	−0.995217	+	0.0976860i	$0.968856\pi$
$824$		0			0
$825$	−0.692272	+	2.33170i	−0.0241018	+	0.0811792i
$826$		0			0
$827$	21.8472	+	21.8472i	0.759703	+	0.759703i	0.976268	−	0.216565i	$-0.0694854\pi$
$827$	21.8472	+	21.8472i	0.759703	+	0.759703i	−0.216565	+	0.976268i	$0.569485\pi$
$828$		0			0
$829$	−44.5299	+	25.7093i	−1.54659	+	0.892922i	−0.548187	+	0.836356i	$0.684682\pi$
$829$	−44.5299	+	25.7093i	−1.54659	+	0.892922i	−0.998399	+	0.0565657i	$0.981985\pi$
$830$		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
$837$	20.4931	−	17.4361i	0.708344	−	0.602680i
$838$		0			0
$839$	23.3739	−	6.26302i	0.806957	−	0.216223i	0.168321	−	0.985732i	$-0.446166\pi$
$839$	23.3739	−	6.26302i	0.806957	−	0.216223i	0.638636	+	0.769509i	$0.279499\pi$
$840$		0			0
$841$	−14.1411	+	24.4932i	−0.487625	+	0.844591i
$842$		0			0
$843$	5.04138	−	4.77808i	0.173634	−	0.164566i
$844$		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
$849$	20.9109	+	38.5707i	0.717659	+	1.32374i
$850$		0			0
$851$	9.67996	+	36.1261i	0.331825	+	1.23839i
$852$		0			0
$853$	16.9446	−	16.9446i	0.580173	−	0.580173i	−0.354778	−	0.934951i	$-0.615444\pi$
$853$	16.9446	−	16.9446i	0.580173	−	0.580173i	0.934951	+	0.354778i	$0.115444\pi$
$854$		0			0
$855$	−4.62855	+	7.10780i	−0.158293	+	0.243081i
$856$		0			0
$857$	23.5591			0.804762			0.402381	−	0.915472i	$-0.368183\pi$
$857$	23.5591			0.804762			0.402381	+	0.915472i	$0.368183\pi$
$858$		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
$861$	−35.0297	−	0.939286i	−1.19381	−	0.0320108i
$862$		0			0
$863$	14.5673	−	14.5673i	0.495875	−	0.495875i	−0.414276	−	0.910151i	$-0.635965\pi$
$863$	14.5673	−	14.5673i	0.495875	−	0.495875i	0.910151	+	0.414276i	$0.135965\pi$
$864$		0			0
$865$	−7.21426	−	26.9240i	−0.245292	−	0.915443i
$866$		0			0
$867$	−8.06516	+	4.37247i	−0.273907	+	0.148497i
$868$		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
$873$	−25.1639	+	5.31575i	−0.851669	+	0.179911i
$874$		0			0
$875$	−13.2867	+	23.0132i	−0.449172	+	0.777988i
$876$		0			0
$877$	4.37238	−	1.17158i	0.147645	−	0.0395613i	−0.184240	−	0.982881i	$-0.558982\pi$
$877$	4.37238	−	1.17158i	0.147645	−	0.0395613i	0.331884	+	0.943320i	$0.392316\pi$
$878$		0			0
$879$	−7.13171	−	29.7881i	−0.240547	−	1.00473i
$880$		0			0
$881$	−3.84672	−	6.66271i	−0.129599	−	0.224473i	0.793922	−	0.608019i	$-0.208036\pi$
$881$	−3.84672	−	6.66271i	−0.129599	−	0.224473i	−0.923521	+	0.383547i	$0.874702\pi$
$882$		0			0
$883$		−	15.0647i		−	0.506967i	−0.967340	−	0.253484i	$-0.918424\pi$
$883$		−	15.0647i		−	0.506967i	0.967340	−	0.253484i	$-0.0815764\pi$
$884$		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	$-0.544990\pi$
$887$	19.2421	−	11.1094i	0.646086	−	0.373018i	0.786955	+	0.617010i	$0.211656\pi$
$888$		0			0
$889$	−0.196233	−	0.196233i	−0.00658144	−	0.00658144i
$890$		0			0
$891$	−3.22012	+	8.32616i	−0.107878	+	0.278937i
$892$		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
$897$	21.3452	−	1.32898i	0.712694	−	0.0443733i
$898$		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
$903$	25.3772	+	7.53439i	0.844499	+	0.250729i
$904$		0			0
$905$	−4.71091	−	4.71091i	−0.156596	−	0.156596i
$906$		0			0
$907$	8.02812	−	4.63504i	0.266569	−	0.153904i	−0.360758	−	0.932659i	$-0.617482\pi$
$907$	8.02812	−	4.63504i	0.266569	−	0.153904i	0.627328	+	0.778755i	$0.284149\pi$
$908$		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
$915$	18.0760	−	4.32768i	0.597575	−	0.143069i
$916$		0			0
$917$	−44.1150	+	11.8206i	−1.45681	+	0.390350i
$918$		0			0
$919$	−21.3969	+	37.0606i	−0.705819	+	1.22251i	0.260576	+	0.965453i	$0.416088\pi$
$919$	−21.3969	+	37.0606i	−0.705819	+	1.22251i	−0.966395	+	0.257062i	$0.917246\pi$
$920$		0			0
$921$	27.8972	+	29.4345i	0.919243	+	0.969898i
$922$		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
$927$	−2.30566	+	42.9628i	−0.0757280	+	1.41108i
$928$		0			0
$929$	−12.0662	−	45.0318i	−0.395880	−	1.47745i	−0.820275	−	0.571969i	$-0.806180\pi$
$929$	−12.0662	−	45.0318i	−0.395880	−	1.47745i	0.424395	−	0.905477i	$-0.360487\pi$
$930$		0			0
$931$	−2.33766	+	2.33766i	−0.0766137	+	0.0766137i
$932$		0			0
$933$	−1.29792	+	48.4047i	−0.0424921	+	1.58470i
$934$		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
$939$	1.02974	−	38.4032i	0.0336044	−	1.25324i
$940$		0			0
$941$	−6.48909	+	6.48909i	−0.211538	+	0.211538i	−0.804921	−	0.593382i	$-0.797792\pi$
$941$	−6.48909	+	6.48909i	−0.211538	+	0.211538i	0.593382	+	0.804921i	$0.297792\pi$
$942$		0			0
$943$	−8.19663	−	30.5903i	−0.266919	−	0.996156i
$944$		0			0
$945$	−12.2235	+	17.7138i	−0.397632	+	0.576230i
$946$		0			0
$947$	13.7168	−	51.1917i	0.445735	−	1.66351i	−0.268253	−	0.963348i	$-0.586446\pi$
$947$	13.7168	−	51.1917i	0.445735	−	1.66351i	0.713988	−	0.700158i	$-0.246887\pi$
$948$		0			0
$949$	1.88318	−	0.689098i	0.0611308	−	0.0223691i
$950$		0			0
$951$	9.17435	+	9.67991i	0.297499	+	0.313892i
$952$		0			0
$953$	9.11381	−	15.7856i	0.295225	−	0.511345i	−0.679812	−	0.733386i	$-0.737939\pi$
$953$	9.11381	−	15.7856i	0.295225	−	0.511345i	0.975037	+	0.222041i	$0.0712720\pi$
$954$		0			0
$955$	−39.3133	+	10.5340i	−1.27215	+	0.340871i
$956$		0			0
$957$	1.41551	−	0.338895i	0.0457570	−	0.0109549i
$958$		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	0.479707	−	0.877429i	$-0.340743\pi$
$967$	−12.3678	−	12.3678i	−0.397722	−	0.397722i	−0.877429	+	0.479707i	$0.840743\pi$
$968$		0			0
$969$	−11.7089	−	3.47632i	−0.376143	−	0.111675i
$970$		0			0
$971$	−0.0142027	−	0.00819993i	−0.000455786	−	0.000263148i	0.499772	−	0.866157i	$-0.333417\pi$
$971$	−0.0142027	−	0.00819993i	−0.000455786	−	0.000263148i	−0.500228	+	0.865894i	$0.666750\pi$
$972$		0			0
$973$	−38.7128	−	10.3731i	−1.24108	−	0.332545i
$974$		0			0
$975$	−7.91671	−	3.93631i	−0.253538	−	0.126063i
$976$		0			0
$977$	−7.17509	−	1.92256i	−0.229551	−	0.0615081i	0.142210	−	0.989837i	$-0.454579\pi$
$977$	−7.17509	−	1.92256i	−0.229551	−	0.0615081i	−0.371761	+	0.928328i	$0.621246\pi$
$978$		0			0
$979$	15.2721	+	8.81732i	0.488097	+	0.281803i
$980$		0			0
$981$	23.3625	+	26.0123i	0.745907	+	0.830508i
$982$		0			0
$983$	11.5176	+	11.5176i	0.367355	+	0.367355i	0.866512	−	0.499157i	$-0.166357\pi$
$983$	11.5176	+	11.5176i	0.367355	+	0.367355i	−0.499157	+	0.866512i	$0.666357\pi$
$984$		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	0.999956	−	0.00933404i	$-0.00297116\pi$
$991$	15.4849	+	26.8207i	0.491895	+	0.851987i	−0.508062	+	0.861321i	$0.669638\pi$
$992$		0			0
$993$	2.34634	+	9.80031i	0.0744589	+	0.311003i
$994$		0			0
$995$	20.5884	−	5.51664i	0.652696	−	0.174889i
$996$		0			0
$997$	9.87356	−	17.1015i	0.312699	−	0.541610i	−0.666247	−	0.745731i	$-0.732100\pi$
$997$	9.87356	−	17.1015i	0.312699	−	0.541610i	0.978946	+	0.204121i	$0.0654336\pi$
$998$		0			0
$999$	19.0436	−	53.4574i	0.602513	−	1.69132i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bp.a.89.8	✓	56	4.3	odd	2
312.2.bp.a.89.12	yes	56	12.11	even	2
312.2.bp.a.305.8	yes	56	156.71	odd	12
312.2.bp.a.305.12	yes	56	52.19	even	12
624.2.cn.f.305.3		56	13.6	odd	12	inner
624.2.cn.f.305.7		56	39.32	even	12	inner
624.2.cn.f.401.3		56	3.2	odd	2	inner
624.2.cn.f.401.7		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)

\(f(q)\)	\(=\)	\(q+(0.0464265 - 1.73143i) q^{3} +(-1.33870 + 1.33870i) q^{5} +(-0.566234 - 2.11322i) q^{7} +(-2.99569 - 0.160768i) q^{9} +O(q^{10})\)	\(q+(0.0464265 - 1.73143i) q^{3} +(-1.33870 + 1.33870i) q^{5} +(-0.566234 - 2.11322i) q^{7} +(-2.99569 - 0.160768i) q^{9} +(-0.256724 + 0.958107i) q^{11} +(-3.27036 - 1.51814i) q^{13} +(2.25572 + 2.38002i) q^{15} +(-2.36097 + 4.08932i) q^{17} +(-1.44252 + 0.386521i) q^{19} +(-3.68517 + 0.882285i) q^{21} +(-1.71229 - 2.96577i) q^{23} +1.41574i q^{25} +(-0.417438 + 5.17936i) q^{27} +(0.733696 - 0.423600i) q^{29} +(-3.66157 - 3.66157i) q^{31} +(1.64698 + 0.488981i) q^{33} +(3.58699 + 2.07095i) q^{35} +(-10.5491 - 2.82661i) q^{37} +(-2.78039 + 5.59191i) q^{39} +(8.93255 + 2.39347i) q^{41} +(-6.05002 - 3.49298i) q^{43} +(4.22556 - 3.79512i) q^{45} +(-0.384064 - 0.384064i) q^{47} +(1.91712 - 1.10685i) q^{49} +(6.97075 + 4.27770i) q^{51} +10.3968i q^{53} +(-0.938944 - 1.62630i) q^{55} +(0.602263 + 2.51556i) q^{57} +(-11.7285 + 3.14264i) q^{59} +(2.83411 - 4.90882i) q^{61} +(1.35652 + 6.42157i) q^{63} +(6.41038 - 2.34570i) q^{65} +(-1.52023 + 5.67359i) q^{67} +(-5.21452 + 2.82702i) q^{69} +(-2.69283 - 10.0498i) q^{71} +(-0.393272 + 0.393272i) q^{73} +(2.45126 + 0.0657280i) q^{75} +2.17005 q^{77} +10.0483 q^{79} +(8.94831 + 0.963224i) q^{81} +(-2.25706 + 2.25706i) q^{83} +(-2.31375 - 8.63503i) q^{85} +(-0.699369 - 1.29001i) q^{87} +(4.60143 - 17.1728i) q^{89} +(-1.35637 + 7.77060i) q^{91} +(-6.50974 + 6.16976i) q^{93} +(1.41367 - 2.44854i) q^{95} +(8.28096 - 2.21888i) q^{97} +(0.923099 - 2.82892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{7}+O(q^{10}) \) 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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