LMFDB - Embedded newform 312.4.m.a.181.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.32
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04560 + 2.62807i) q^{2} +3.00000i q^{3} +(-5.81346 - 5.49579i) q^{4} -7.49353 q^{5} +(-7.88420 - 3.13679i) q^{6} -9.78456i q^{7} +(20.5218 - 9.53176i) q^{8} -9.00000 q^{9} +(7.83521 - 19.6935i) q^{10} +72.0538 q^{11} +(16.4874 - 17.4404i) q^{12} +(-46.8270 + 2.05771i) q^{13} +(25.7145 + 10.2307i) q^{14} -22.4806i q^{15} +(3.59252 + 63.8991i) q^{16} +14.0519 q^{17} +(9.41037 - 23.6526i) q^{18} +126.824 q^{19} +(43.5633 + 41.1829i) q^{20} +29.3537 q^{21} +(-75.3392 + 189.362i) q^{22} -74.7533 q^{23} +(28.5953 + 61.5655i) q^{24} -68.8471 q^{25} +(43.5543 - 125.216i) q^{26} -27.0000i q^{27} +(-53.7739 + 56.8821i) q^{28} +177.389i q^{29} +(59.0804 + 23.5056i) q^{30} +204.084i q^{31} +(-171.687 - 57.3713i) q^{32} +216.161i q^{33} +(-14.6926 + 36.9292i) q^{34} +73.3208i q^{35} +(52.3211 + 49.4621i) q^{36} +262.345 q^{37} +(-132.606 + 333.301i) q^{38} +(-6.17314 - 140.481i) q^{39} +(-153.781 + 71.4265i) q^{40} -376.047i q^{41} +(-30.6921 + 77.1434i) q^{42} +179.424i q^{43} +(-418.882 - 395.993i) q^{44} +67.4417 q^{45} +(78.1618 - 196.457i) q^{46} +4.21422i q^{47} +(-191.697 + 10.7776i) q^{48} +247.262 q^{49} +(71.9863 - 180.935i) q^{50} +42.1556i q^{51} +(283.535 + 245.389i) q^{52} +102.044i q^{53} +(70.9578 + 28.2311i) q^{54} -539.937 q^{55} +(-93.2640 - 200.797i) q^{56} +380.471i q^{57} +(-466.189 - 185.477i) q^{58} +231.843 q^{59} +(-123.549 + 130.690i) q^{60} +876.661i q^{61} +(-536.346 - 213.389i) q^{62} +88.0610i q^{63} +(330.291 - 391.218i) q^{64} +(350.899 - 15.4195i) q^{65} +(-568.086 - 226.018i) q^{66} -597.074 q^{67} +(-81.6899 - 77.2262i) q^{68} -224.260i q^{69} +(-192.692 - 76.6640i) q^{70} +576.462i q^{71} +(-184.696 + 85.7858i) q^{72} +657.628i q^{73} +(-274.307 + 689.461i) q^{74} -206.541i q^{75} +(-737.284 - 696.996i) q^{76} -705.014i q^{77} +(375.648 + 130.663i) q^{78} -137.370 q^{79} +(-26.9206 - 478.829i) q^{80} +81.0000 q^{81} +(988.277 + 393.194i) q^{82} +1087.78 q^{83} +(-170.646 - 161.322i) q^{84} -105.298 q^{85} +(-471.537 - 187.605i) q^{86} -532.166 q^{87} +(1478.68 - 686.799i) q^{88} -269.127i q^{89} +(-70.5169 + 177.241i) q^{90} +(20.1338 + 458.181i) q^{91} +(434.575 + 410.829i) q^{92} -612.251 q^{93} +(-11.0752 - 4.40637i) q^{94} -950.356 q^{95} +(172.114 - 515.062i) q^{96} +1734.37i q^{97} +(-258.537 + 649.822i) q^{98} -648.484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.04560	+	2.62807i	−0.369674	+	0.929161i
$2$	−1.04560	+	2.62807i	−0.369674	+	0.929161i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−5.81346	−	5.49579i	−0.726682	−	0.686974i
$5$	−7.49353			−0.670241			−0.335121	−	0.942175i	$-0.608777\pi$
$5$	−7.49353			−0.670241			−0.335121	+	0.942175i	$0.608777\pi$
$6$	−7.88420	−	3.13679i	−0.536452	−	0.213432i
$7$		−	9.78456i		−	0.528316i	−0.964479	−	0.264158i	$-0.914906\pi$
$7$		−	9.78456i		−	0.528316i	0.964479	−	0.264158i	$-0.0850941\pi$
$8$	20.5218	−	9.53176i	0.906945	−	0.421248i
$9$	−9.00000			−0.333333
$10$	7.83521	−	19.6935i	0.247771	−	0.622762i
$11$	72.0538			1.97500			0.987502	−	0.157608i	$-0.0503781\pi$
$11$	72.0538			1.97500			0.987502	+	0.157608i	$0.0503781\pi$
$12$	16.4874	−	17.4404i	0.396625	−	0.419550i
$13$	−46.8270	+	2.05771i	−0.999036	+	0.0439005i
$13$	−46.8270	+	2.05771i	−0.999036	+	0.0439005i
$14$	25.7145	+	10.2307i	0.490891	+	0.195305i
$15$		−	22.4806i		−	0.386964i
$16$	3.59252	+	63.8991i	0.0561331	+	0.998423i
$17$	14.0519			0.200475			0.100238	−	0.994964i	$-0.468040\pi$
$17$	14.0519			0.200475			0.100238	+	0.994964i	$0.468040\pi$
$18$	9.41037	−	23.6526i	0.123225	−	0.309720i
$19$	126.824			1.53133			0.765667	−	0.643237i	$-0.222409\pi$
$19$	126.824			1.53133			0.765667	+	0.643237i	$0.222409\pi$
$20$	43.5633	+	41.1829i	0.487052	+	0.460438i
$21$	29.3537			0.305024
$22$	−75.3392	+	189.362i	−0.730108	+	1.83510i
$23$	−74.7533			−0.677702			−0.338851	−	0.940840i	$-0.610038\pi$
$23$	−74.7533			−0.677702			−0.338851	+	0.940840i	$0.610038\pi$
$24$	28.5953	+	61.5655i	0.243208	+	0.523625i
$25$	−68.8471			−0.550777
$26$	43.5543	−	125.216i	0.328527	−	0.944495i
$27$		−	27.0000i		−	0.192450i
$28$	−53.7739	+	56.8821i	−0.362940	+	0.383918i
$29$			177.389i			1.13587i	0.823073	+	0.567936i	$0.192258\pi$
$29$			177.389i			1.13587i	−0.823073	+	0.567936i	$0.807742\pi$
$30$	59.0804	+	23.5056i	0.359552	+	0.143051i
$31$			204.084i			1.18240i	0.806523	+	0.591202i	$0.201346\pi$
$31$			204.084i			1.18240i	−0.806523	+	0.591202i	$0.798654\pi$
$32$	−171.687	−	57.3713i	−0.948447	−	0.316935i
$33$			216.161i			1.14027i
$34$	−14.6926	+	36.9292i	−0.0741105	+	0.186274i
$35$			73.3208i			0.354099i
$36$	52.3211	+	49.4621i	0.242227	+	0.228991i
$37$	262.345			1.16566			0.582828	−	0.812595i	$-0.301946\pi$
$37$	262.345			1.16566			0.582828	+	0.812595i	$0.301946\pi$
$38$	−132.606	+	333.301i	−0.566095	+	1.42286i
$39$	−6.17314	−	140.481i	−0.0253460	−	0.576794i
$40$	−153.781	+	71.4265i	−0.607872	+	0.282338i
$41$		−	376.047i		−	1.43241i	−0.697891	−	0.716204i	$-0.745878\pi$
$41$		−	376.047i		−	1.43241i	0.697891	−	0.716204i	$-0.254122\pi$
$42$	−30.6921	+	77.1434i	−0.112759	+	0.283416i
$43$			179.424i			0.636322i	0.948037	+	0.318161i	$0.103065\pi$
$43$			179.424i			0.636322i	−0.948037	+	0.318161i	$0.896935\pi$
$44$	−418.882	−	395.993i	−1.43520	−	1.35678i
$45$	67.4417			0.223414
$46$	78.1618	−	196.457i	0.250529	−	0.629694i
$47$			4.21422i			0.0130789i	0.999979	+	0.00653943i	$0.00208158\pi$
$47$			4.21422i			0.0130789i	−0.999979	+	0.00653943i	$0.997918\pi$
$48$	−191.697	+	10.7776i	−0.576440	+	0.0324085i
$49$	247.262			0.720882
$50$	71.9863	−	180.935i	0.203608	−	0.511760i
$51$			42.1556i			0.115744i
$52$	283.535	+	245.389i	0.756140	+	0.654410i
$53$			102.044i			0.264468i	0.991219	+	0.132234i	$0.0422150\pi$
$53$			102.044i			0.264468i	−0.991219	+	0.132234i	$0.957785\pi$
$54$	70.9578	+	28.2311i	0.178817	+	0.0711438i
$55$	−539.937			−1.32373
$56$	−93.2640	−	200.797i	−0.222552	−	0.479154i
$57$			380.471i			0.884116i
$58$	−466.189	−	185.477i	−1.05541	−	0.419902i
$59$	231.843			0.511584			0.255792	−	0.966732i	$-0.417664\pi$
$59$	231.843			0.511584			0.255792	+	0.966732i	$0.417664\pi$
$60$	−123.549	+	130.690i	−0.265834	+	0.281200i
$61$			876.661i			1.84008i	0.391824	+	0.920040i	$0.371844\pi$
$61$			876.661i			1.84008i	−0.391824	+	0.920040i	$0.628156\pi$
$62$	−536.346	−	213.389i	−1.09864	−	0.437104i
$63$			88.0610i			0.176105i
$64$	330.291	−	391.218i	0.645100	−	0.764098i
$65$	350.899	−	15.4195i	0.669595	−	0.0294240i
$66$	−568.086	−	226.018i	−1.05949	−	0.421528i
$67$	−597.074			−1.08872			−0.544360	−	0.838852i	$-0.683227\pi$
$67$	−597.074			−1.08872			−0.544360	+	0.838852i	$0.683227\pi$
$68$	−81.6899	−	77.2262i	−0.145682	−	0.137721i
$69$		−	224.260i		−	0.391271i
$70$	−192.692	−	76.6640i	−0.329016	−	0.130901i
$71$			576.462i			0.963570i	0.876289	+	0.481785i	$0.160011\pi$
$71$			576.462i			0.963570i	−0.876289	+	0.481785i	$0.839989\pi$
$72$	−184.696	+	85.7858i	−0.302315	+	0.140416i
$73$			657.628i			1.05438i	0.849748	+	0.527189i	$0.176754\pi$
$73$			657.628i			1.05438i	−0.849748	+	0.527189i	$0.823246\pi$
$74$	−274.307	+	689.461i	−0.430913	+	1.08308i
$75$		−	206.541i		−	0.317991i
$76$	−737.284	−	696.996i	−1.11279	−	1.05199i
$77$		−	705.014i		−	1.04343i
$78$	375.648	+	130.663i	0.545304	+	0.189675i
$79$	−137.370			−0.195637			−0.0978185	−	0.995204i	$-0.531186\pi$
$79$	−137.370			−0.195637			−0.0978185	+	0.995204i	$0.531186\pi$
$80$	−26.9206	−	478.829i	−0.0376227	−	0.669185i
$81$	81.0000			0.111111
$82$	988.277	+	393.194i	1.33094	+	0.529524i
$83$	1087.78			1.43855			0.719273	−	0.694727i	$-0.244475\pi$
$83$	1087.78			1.43855			0.719273	+	0.694727i	$0.244475\pi$
$84$	−170.646	−	161.322i	−0.221655	−	0.209543i
$85$	−105.298			−0.134367
$86$	−471.537	−	187.605i	−0.591246	−	0.235232i
$87$	−532.166			−0.655795
$88$	1478.68	−	686.799i	1.79122	−	0.831967i
$89$		−	269.127i		−	0.320532i	−0.987074	−	0.160266i	$-0.948765\pi$
$89$		−	269.127i		−	0.320532i	0.987074	−	0.160266i	$-0.0512352\pi$
$90$	−70.5169	+	177.241i	−0.0825903	+	0.207587i
$91$	20.1338	+	458.181i	0.0231934	+	0.527807i
$92$	434.575	+	410.829i	0.492474	+	0.465564i
$93$	−612.251			−0.682661
$94$	−11.0752	−	4.40637i	−0.0121524	−	0.00483492i
$95$	−950.356			−1.02636
$96$	172.114	−	515.062i	0.182982	−	0.547586i
$97$			1734.37i			1.81545i	0.419570	+	0.907723i	$0.362181\pi$
$97$			1734.37i			1.81545i	−0.419570	+	0.907723i	$0.637819\pi$
$98$	−258.537	+	649.822i	−0.266491	+	0.669816i
$99$	−648.484			−0.658335
$100$	400.239	+	378.369i	0.400239	+	0.378369i
$101$		−	239.851i		−	0.236297i	−0.992996	−	0.118149i	$-0.962304\pi$
$101$		−	239.851i		−	0.236297i	0.992996	−	0.118149i	$-0.0376959\pi$
$102$	−110.788	−	44.0778i	−0.107545	−	0.0427877i
$103$	530.863			0.507839			0.253920	−	0.967225i	$-0.418280\pi$
$103$	530.863			0.507839			0.253920	+	0.967225i	$0.418280\pi$
$104$	−941.362	+	488.571i	−0.887578	+	0.460657i
$105$	−219.962			−0.204439
$106$	−268.178	−	106.697i	−0.245733	−	0.0977669i
$107$		−	740.028i		−	0.668609i	−0.942465	−	0.334305i	$-0.891499\pi$
$107$		−	740.028i		−	0.668609i	0.942465	−	0.334305i	$-0.108501\pi$
$108$	−148.386	+	156.963i	−0.132208	+	0.139850i
$109$	1064.00			0.934977			0.467489	−	0.883999i	$-0.345159\pi$
$109$	1064.00			0.934977			0.467489	+	0.883999i	$0.345159\pi$
$110$	564.556	−	1418.99i	0.489349	−	1.22996i
$111$			787.036i			0.672992i
$112$	625.224	−	35.1512i	0.527483	−	0.0296561i
$113$	115.266			0.0959581			0.0479791	−	0.998848i	$-0.484722\pi$
$113$	115.266			0.0959581			0.0479791	+	0.998848i	$0.484722\pi$
$114$	−999.902	−	397.819i	−0.821486	−	0.326835i
$115$	560.166			0.454224
$116$	974.892	−	1031.24i	0.780314	−	0.825417i
$117$	421.443	−	18.5194i	0.333012	−	0.0146335i
$118$	−242.415	+	609.300i	−0.189119	+	0.475344i
$119$		−	137.491i		−	0.105914i
$120$	−214.279	−	461.343i	−0.163008	−	0.350955i
$121$	3860.75			2.90064
$122$	−2303.92	−	916.634i	−1.70973	−	0.680230i
$123$	1128.14			0.827001
$124$	1121.60	−	1186.43i	0.812281	−	0.859232i
$125$	1452.60			1.03939
$126$	−231.430	−	92.0763i	−0.163630	−	0.0651017i
$127$	1036.50			0.724210			0.362105	−	0.932137i	$-0.382058\pi$
$127$	1036.50			0.724210			0.362105	+	0.932137i	$0.382058\pi$
$128$	682.796	+	1277.08i	0.471494	+	0.881869i
$129$	−538.271			−0.367380
$130$	−326.375	+	938.309i	−0.220192	+	0.633039i
$131$			1820.97i			1.21449i	0.794513	+	0.607247i	$0.207726\pi$
$131$			1820.97i			1.21449i	−0.794513	+	0.607247i	$0.792274\pi$
$132$	1187.98	−	1256.64i	0.783335	−	0.828613i
$133$		−	1240.91i		−	0.809029i
$134$	624.299	−	1569.15i	0.402472	−	1.01160i
$135$			202.325i			0.128988i
$136$	288.370	−	133.939i	0.181820	−	0.0844498i
$137$		−	475.278i		−	0.296392i	−0.988958	−	0.148196i	$-0.952653\pi$
$137$		−	475.278i		−	0.296392i	0.988958	−	0.148196i	$-0.0473467\pi$
$138$	589.370	+	234.485i	0.363554	+	0.144643i
$139$		−	1722.61i		−	1.05115i	−0.850748	−	0.525574i	$-0.823851\pi$
$139$		−	1722.61i		−	1.05115i	0.850748	−	0.525574i	$-0.176149\pi$
$140$	402.956	−	426.247i	0.243257	−	0.257318i
$141$	−12.6426			−0.00755109
$142$	−1514.98	−	602.747i	−0.895312	−	0.356207i
$143$	−3374.06	+	148.266i	−1.97310	+	0.0867037i
$144$	−32.3327	−	575.092i	−0.0187110	−	0.332808i
$145$		−	1329.27i		−	0.761308i
$146$	−1728.29	−	687.614i	−0.979687	−	0.389776i
$147$			741.787i			0.416201i
$148$	−1525.13	−	1441.80i	−0.847062	−	0.800776i
$149$	1885.30			1.03658			0.518289	−	0.855206i	$-0.326569\pi$
$149$	1885.30			1.03658			0.518289	+	0.855206i	$0.326569\pi$
$150$	542.804	+	215.959i	0.295465	+	0.117553i
$151$			2416.05i			1.30209i	0.759041	+	0.651043i	$0.225668\pi$
$151$			2416.05i			1.30209i	−0.759041	+	0.651043i	$0.774332\pi$
$152$	2602.65	−	1208.85i	1.38884	−	0.645071i
$153$	−126.467			−0.0668251
$154$	1852.82	+	737.161i	0.969512	+	0.385728i
$155$		−	1529.31i		−	0.792496i
$156$	−736.167	+	850.606i	−0.377824	+	0.436558i
$157$		−	2426.92i		−	1.23369i	−0.787085	−	0.616845i	$-0.788411\pi$
$157$		−	2426.92i		−	1.23369i	0.787085	−	0.616845i	$-0.211589\pi$
$158$	143.634	−	361.017i	0.0723220	−	0.181778i
$159$	−306.131			−0.152690
$160$	1286.54	+	429.913i	0.635689	+	0.212423i
$161$			731.428i			0.358041i
$162$	−84.6933	+	212.873i	−0.0410749	+	0.103240i
$163$	−1149.46			−0.552348			−0.276174	−	0.961108i	$-0.589067\pi$
$163$	−1149.46			−0.552348			−0.276174	+	0.961108i	$0.589067\pi$
$164$	−2066.68	+	2186.13i	−0.984027	+	1.04090i
$165$		−	1619.81i		−	0.764255i
$166$	−1137.38	+	2858.76i	−0.531793	+	1.33664i
$167$		−	2356.30i		−	1.09183i	−0.837840	−	0.545916i	$-0.816182\pi$
$167$		−	2356.30i		−	1.09183i	0.837840	−	0.545916i	$-0.183818\pi$
$168$	602.391	−	279.792i	0.276640	−	0.128491i
$169$	2188.53	−	192.713i	0.996145	−	0.0877164i
$170$	110.099	−	276.730i	0.0496719	−	0.124848i
$171$	−1141.41			−0.510445
$172$	986.075	−	1043.07i	0.437137	−	0.462403i
$173$		−	3329.62i		−	1.46327i	−0.681694	−	0.731637i	$-0.738756\pi$
$173$		−	3329.62i		−	1.46327i	0.681694	−	0.731637i	$-0.261244\pi$
$174$	556.431	−	1398.57i	0.242431	−	0.609340i
$175$			673.638i			0.290984i
$176$	258.855	+	4604.17i	0.110863	+	1.97189i
$177$			695.530i			0.295363i
$178$	707.282	+	281.398i	0.297826	+	0.118492i
$179$			2221.93i			0.927793i	0.885889	+	0.463897i	$0.153549\pi$
$179$			2221.93i			0.927793i	−0.885889	+	0.463897i	$0.846451\pi$
$180$	−392.069	−	370.646i	−0.162351	−	0.153479i
$181$			1776.63i			0.729592i	0.931088	+	0.364796i	$0.118861\pi$
$181$			1776.63i			0.729592i	−0.931088	+	0.364796i	$0.881139\pi$
$182$	−1225.18	−	426.160i	−0.498992	−	0.173566i
$183$	−2629.98			−1.06237
$184$	−1534.07	+	712.530i	−0.614639	+	0.285481i
$185$	−1965.89			−0.781271
$186$	640.168	−	1609.04i	0.252362	−	0.634303i
$187$	1012.49			0.395939
$188$	23.1605	−	24.4992i	0.00898484	−	0.00950417i
$189$	−264.183			−0.101675
$190$	993.689	−	2497.60i	0.379420	−	0.953657i
$191$	2034.25			0.770647			0.385323	−	0.922782i	$-0.374090\pi$
$191$	2034.25			0.770647			0.385323	+	0.922782i	$0.374090\pi$
$192$	1173.65	+	990.874i	0.441152	+	0.372449i
$193$		−	1853.76i		−	0.691381i	−0.938349	−	0.345690i	$-0.887645\pi$
$193$		−	1853.76i		−	0.691381i	0.938349	−	0.345690i	$-0.112355\pi$
$194$	−4558.03	−	1813.45i	−1.68684	−	0.671124i
$195$	46.2586	+	1052.70i	0.0169879	+	0.386591i
$196$	−1437.45	−	1358.90i	−0.523852	−	0.495227i
$197$	−497.507			−0.179928			−0.0899642	−	0.995945i	$-0.528675\pi$
$197$	−497.507			−0.179928			−0.0899642	+	0.995945i	$0.528675\pi$
$198$	678.053	−	1704.26i	0.243369	−	0.611699i
$199$	−3080.62			−1.09738			−0.548691	−	0.836025i	$-0.684874\pi$
$199$	−3080.62			−1.09738			−0.548691	+	0.836025i	$0.684874\pi$
$200$	−1412.87	+	656.234i	−0.499524	+	0.232014i
$201$		−	1791.22i		−	0.628573i
$202$	630.343	+	250.787i	0.219558	+	0.0873530i
$203$	1735.67			0.600099
$204$	231.678	−	245.070i	0.0795134	−	0.0841094i
$205$			2817.92i			0.960059i
$206$	−555.068	+	1395.14i	−0.187735	+	0.471865i
$207$	672.780			0.225901
$208$	−299.713	−	2984.81i	−0.0999103	−	0.994996i
$209$	9138.13			3.02439
$210$	229.992	−	578.076i	0.0755760	−	0.189957i
$211$			5026.60i			1.64003i	0.572344	+	0.820013i	$0.306034\pi$
$211$			5026.60i			1.64003i	−0.572344	+	0.820013i	$0.693966\pi$
$212$	560.811	−	593.227i	0.181682	−	0.192184i
$213$	−1729.39			−0.556318
$214$	1944.84	+	773.771i	0.621246	+	0.247168i
$215$		−	1344.51i		−	0.426489i
$216$	−257.357	−	554.089i	−0.0810692	−	0.174542i
$217$	1996.87			0.624683
$218$	−1112.51	+	2796.26i	−0.345637	+	0.868745i
$219$	−1972.89			−0.608745
$220$	3138.90	+	2967.38i	0.961930	+	0.909368i
$221$	−658.007	+	28.9147i	−0.200282	+	0.00880097i
$222$	−2068.38	−	822.922i	−0.625318	−	0.248788i
$223$		−	5076.03i		−	1.52429i	−0.647408	−	0.762143i	$-0.724147\pi$
$223$		−	5076.03i		−	1.52429i	0.647408	−	0.762143i	$-0.275853\pi$
$224$	−561.353	+	1679.88i	−0.167442	+	0.501080i
$225$	619.624			0.183592
$226$	−120.521	+	302.925i	−0.0354733	+	0.0891606i
$227$	1300.80			0.380340			0.190170	−	0.981751i	$-0.439096\pi$
$227$	1300.80			0.380340			0.190170	+	0.981751i	$0.439096\pi$
$228$	2090.99	−	2211.85i	0.607365	−	0.642471i
$229$	−6698.62			−1.93300			−0.966500	−	0.256667i	$-0.917376\pi$
$229$	−6698.62			−1.93300			−0.966500	+	0.256667i	$0.917376\pi$
$230$	−585.708	+	1472.15i	−0.167915	+	0.422047i
$231$	2115.04			0.602423
$232$	1690.83	+	3640.34i	0.478484	+	1.03017i
$233$	−4160.62			−1.16983			−0.584917	−	0.811093i	$-0.698873\pi$
$233$	−4160.62			−1.16983			−0.584917	+	0.811093i	$0.698873\pi$
$234$	−391.989	+	1126.94i	−0.109509	+	0.314832i
$235$		−	31.5793i		−	0.00876600i
$236$	−1347.81	−	1274.16i	−0.371759	−	0.351445i
$237$		−	412.110i		−	0.112951i
$238$	361.336	+	143.760i	0.0984115	+	0.0391538i
$239$		−	1312.20i		−	0.355144i	−0.984108	−	0.177572i	$-0.943176\pi$
$239$		−	1312.20i		−	0.355144i	0.984108	−	0.177572i	$-0.0568243\pi$
$240$	1436.49	−	80.7619i	0.386354	−	0.0217215i
$241$			3560.36i			0.951629i	0.879546	+	0.475815i	$0.157847\pi$
$241$			3560.36i			0.951629i	−0.879546	+	0.475815i	$0.842153\pi$
$242$	−4036.79	+	10146.3i	−1.07229	+	2.69516i
$243$			243.000i			0.0641500i
$244$	4817.95	−	5096.43i	1.26409	−	1.33715i
$245$	−1852.87			−0.483165
$246$	−1179.58	+	2964.83i	−0.305721	+	0.768418i
$247$	−5938.77	+	260.967i	−1.52986	+	0.0672264i
$248$	1945.28	+	4188.17i	0.498086	+	1.07238i
$249$			3263.34i			0.830545i
$250$	−1518.83	+	3817.52i	−0.384237	+	0.965765i
$251$			6122.00i			1.53951i	0.638339	+	0.769755i	$0.279622\pi$
$251$			6122.00i			1.53951i	−0.638339	+	0.769755i	$0.720378\pi$
$252$	483.965	−	511.939i	0.120980	−	0.127973i
$253$	−5386.26			−1.33846
$254$	−1083.76	+	2723.99i	−0.267722	+	0.672908i
$255$		−	315.894i		−	0.0775767i
$256$	−4070.19	+	459.118i	−0.993698	+	0.112089i
$257$	−164.036			−0.0398143			−0.0199071	−	0.999802i	$-0.506337\pi$
$257$	−164.036			−0.0398143			−0.0199071	+	0.999802i	$0.506337\pi$
$258$	562.814	−	1414.61i	0.135811	−	0.341356i
$259$		−	2566.93i		−	0.615836i
$260$	−2124.68	−	1838.83i	−0.506796	−	0.438613i
$261$		−	1596.50i		−	0.378624i
$262$	−4785.62	−	1904.00i	−1.12846	−	0.448967i
$263$	−1372.59			−0.321815			−0.160908	−	0.986969i	$-0.551442\pi$
$263$	−1372.59			−0.321815			−0.160908	+	0.986969i	$0.551442\pi$
$264$	2060.40	+	4436.03i	0.480336	+	1.03416i
$265$		−	764.667i		−	0.177257i
$266$	3261.20	+	1297.49i	0.751718	+	0.299077i
$267$	807.380			0.185059
$268$	3471.06	+	3281.40i	0.791153	+	0.747922i
$269$		−	3566.60i		−	0.808400i	−0.914671	−	0.404200i	$-0.867550\pi$
$269$		−	3566.60i		−	0.808400i	0.914671	−	0.404200i	$-0.132450\pi$
$270$	−531.724	−	211.551i	−0.119851	−	0.0476835i
$271$		−	4351.15i		−	0.975326i	−0.873032	−	0.487663i	$-0.837849\pi$
$271$		−	4351.15i		−	0.975326i	0.873032	−	0.487663i	$-0.162151\pi$
$272$	50.4816	+	897.902i	0.0112533	+	0.200159i
$273$	−1374.54	+	60.4014i	−0.304730	+	0.0133907i
$274$	1249.06	+	496.949i	0.275396	+	0.109569i
$275$	−4960.69			−1.08779
$276$	−1232.49	+	1303.72i	−0.268793	+	0.284330i
$277$			4899.77i			1.06281i	0.847118	+	0.531405i	$0.178336\pi$
$277$			4899.77i			1.06281i	−0.847118	+	0.531405i	$0.821664\pi$
$278$	4527.12	+	1801.15i	0.976687	+	0.388583i
$279$		−	1836.75i		−	0.394135i
$280$	698.876	+	1504.68i	0.149164	+	0.321149i
$281$		−	4827.29i		−	1.02481i	−0.858743	−	0.512406i	$-0.828754\pi$
$281$		−	4827.29i		−	1.02481i	0.858743	−	0.512406i	$-0.171246\pi$
$282$	13.2191	−	33.2257i	0.00279144	−	0.00701618i
$283$		−	5713.48i		−	1.20011i	−0.799959	−	0.600055i	$-0.795145\pi$
$283$		−	5713.48i		−	1.20011i	0.799959	−	0.600055i	$-0.204855\pi$
$284$	3168.12	−	3351.24i	0.661948	−	0.700209i
$285$		−	2851.07i		−	0.592571i
$286$	3138.26	−	9022.28i	0.648842	−	1.86538i
$287$	−3679.46			−0.756765
$288$	1545.19	+	516.342i	0.316149	+	0.105645i
$289$	−4715.54			−0.959810
$290$	3493.40	+	1389.88i	0.707378	+	0.281436i
$291$	−5203.10			−1.04815
$292$	3614.19	−	3823.09i	0.724330	−	0.766197i
$293$	8943.28			1.78318			0.891590	−	0.452843i	$-0.149590\pi$
$293$	8943.28			1.78318			0.891590	+	0.452843i	$0.149590\pi$
$294$	−1949.47	−	775.610i	−0.386718	−	0.153859i
$295$	−1737.32			−0.342885
$296$	5383.81	−	2500.61i	1.05719	−	0.491031i
$297$		−	1945.45i		−	0.380090i
$298$	−1971.27	+	4954.70i	−0.383196	+	0.963148i
$299$	3500.47	−	153.821i	0.677048	−	0.0297515i
$300$	−1135.11	+	1200.72i	−0.218452	+	0.231078i
$301$	1755.58			0.336179
$302$	−6349.53	−	2526.21i	−1.20985	−	0.481348i
$303$	719.552			0.136426
$304$	455.617	+	8103.92i	0.0859586	+	1.52892i
$305$		−	6569.28i		−	1.23330i
$306$	132.233	−	332.363i	0.0247035	−	0.0620913i
$307$	−6562.74			−1.22005			−0.610025	−	0.792382i	$-0.708841\pi$
$307$	−6562.74			−1.22005			−0.610025	+	0.792382i	$0.708841\pi$
$308$	−3874.61	+	4098.57i	−0.716807	+	0.758239i
$309$			1592.59i			0.293201i
$310$	4019.12	+	1599.04i	0.736357	+	0.292965i
$311$	−3224.79			−0.587979			−0.293989	−	0.955809i	$-0.594983\pi$
$311$	−3224.79			−0.587979			−0.293989	+	0.955809i	$0.594983\pi$
$312$	−1465.71	−	2824.09i	−0.265961	−	0.512443i
$313$	3942.86			0.712024			0.356012	−	0.934481i	$-0.384136\pi$
$313$	3942.86			0.712024			0.356012	+	0.934481i	$0.384136\pi$
$314$	6378.10	+	2537.58i	1.14630	+	0.456063i
$315$		−	659.887i		−	0.118033i
$316$	798.594	+	754.957i	0.142166	+	0.134398i
$317$	−1635.90			−0.289846			−0.144923	−	0.989443i	$-0.546293\pi$
$317$	−1635.90			−0.289846			−0.144923	+	0.989443i	$0.546293\pi$
$318$	320.090	−	804.533i	0.0564457	−	0.141874i
$319$			12781.5i			2.24335i
$320$	−2475.05	+	2931.60i	−0.432373	+	0.512130i
$321$	2220.08			0.386022
$322$	−1922.24	−	764.779i	−0.332678	−	0.132359i
$323$	1782.11			0.306994
$324$	−470.890	−	445.159i	−0.0807424	−	0.0763305i
$325$	3223.90	−	141.668i	0.550246	−	0.0241794i
$326$	1201.87	−	3020.86i	0.204189	−	0.513220i
$327$			3191.99i			0.539809i
$328$	−3584.39	−	7717.18i	−0.603399	−	1.29912i
$329$	41.2342			0.00690978
$330$	4256.97	+	1693.67i	0.710117	+	0.282526i
$331$	−7588.23			−1.26008			−0.630040	−	0.776563i	$-0.716962\pi$
$331$	−7588.23			−1.26008			−0.630040	+	0.776563i	$0.716962\pi$
$332$	−6323.76	−	5978.21i	−1.04537	−	0.988244i
$333$	−2361.11			−0.388552
$334$	6192.51	+	2463.74i	1.01449	+	0.403622i
$335$	4474.19			0.729705
$336$	105.454	+	1875.67i	0.0171219	+	0.304543i
$337$	−2341.44			−0.378475			−0.189238	−	0.981931i	$-0.560602\pi$
$337$	−2341.44			−0.378475			−0.189238	+	0.981931i	$0.560602\pi$
$338$	−1781.86	+	5953.10i	−0.286747	+	0.958006i
$339$			345.797i			0.0554015i
$340$	612.145	+	578.696i	0.0976419	+	0.0923065i
$341$			14705.0i			2.33525i
$342$	1193.46	−	2999.71i	0.188698	−	0.474285i
$343$		−	5775.46i		−	0.909170i
$344$	1710.22	+	3682.10i	0.268049	+	0.577109i
$345$			1680.50i			0.262246i
$346$	8750.47	+	3481.44i	1.35962	+	0.540935i
$347$			2305.05i			0.356604i	0.983976	+	0.178302i	$0.0570604\pi$
$347$			2305.05i			0.356604i	−0.983976	+	0.178302i	$0.942940\pi$
$348$	3093.72	+	2924.68i	0.476555	+	0.450515i
$349$	5388.45			0.826467			0.413234	−	0.910625i	$-0.364399\pi$
$349$	5388.45			0.826467			0.413234	+	0.910625i	$0.364399\pi$
$350$	−1770.36	−	704.354i	−0.270371	−	0.107569i
$351$	55.5583	+	1264.33i	0.00844866	+	0.192265i
$352$	−12370.7	−	4133.82i	−1.87319	−	0.625947i
$353$		−	888.251i		−	0.133929i	−0.997755	−	0.0669644i	$-0.978669\pi$
$353$		−	888.251i		−	0.133929i	0.997755	−	0.0669644i	$-0.0213314\pi$
$354$	−1827.90	−	727.244i	−0.274440	−	0.109188i
$355$		−	4319.73i		−	0.645825i
$356$	−1479.06	+	1564.56i	−0.220197	+	0.232925i
$357$	412.474			0.0611497
$358$	−5839.38	−	2323.24i	−0.862070	−	0.342981i
$359$		−	4027.76i		−	0.592136i	−0.955167	−	0.296068i	$-0.904325\pi$
$359$		−	4027.76i		−	0.592136i	0.955167	−	0.296068i	$-0.0956755\pi$
$360$	1384.03	−	642.838i	0.202624	−	0.0941126i
$361$	9225.24			1.34498
$362$	−4669.11	−	1857.64i	−0.677908	−	0.269711i
$363$			11582.3i			1.67468i
$364$	2401.02	−	2774.27i	0.345736	−	0.399481i
$365$		−	4927.96i		−	0.706688i
$366$	2749.90	−	6911.77i	0.392731	−	0.987114i
$367$	2485.79			0.353562			0.176781	−	0.984250i	$-0.443432\pi$
$367$	2485.79			0.353562			0.176781	+	0.984250i	$0.443432\pi$
$368$	−268.553	−	4776.67i	−0.0380415	−	0.676633i
$369$			3384.43i			0.477469i
$370$	2055.53	−	5166.49i	0.288816	−	0.725927i
$371$	998.452			0.139723
$372$	3559.30	+	3364.81i	0.496078	+	0.468971i
$373$			9505.46i			1.31950i	0.751484	+	0.659751i	$0.229338\pi$
$373$			9505.46i			1.31950i	−0.751484	+	0.659751i	$0.770662\pi$
$374$	−1058.66	+	2660.89i	−0.146369	+	0.367892i
$375$			4357.79i			0.600095i
$376$	40.1689	+	86.4834i	0.00550945	+	0.0118618i
$377$	−365.015	−	8306.58i	−0.0498654	−	1.13478i
$378$	276.229	−	694.290i	0.0375865	−	0.0944721i
$379$	7001.77			0.948963			0.474482	−	0.880265i	$-0.342636\pi$
$379$	7001.77			0.948963			0.474482	+	0.880265i	$0.342636\pi$
$380$	5524.85	+	5222.96i	0.745839	+	0.705085i
$381$			3109.50i			0.418123i
$382$	−2127.01	+	5346.16i	−0.284888	+	0.716055i
$383$		−	9798.88i		−	1.30731i	−0.756793	−	0.653655i	$-0.773235\pi$
$383$		−	9798.88i		−	1.30731i	0.756793	−	0.653655i	$-0.226765\pi$
$384$	−3831.25	+	2048.39i	−0.509148	+	0.272217i
$385$			5283.04i			0.699348i
$386$	4871.80	+	1938.28i	0.642404	+	0.255586i
$387$		−	1614.81i		−	0.212107i
$388$	9531.72	−	10082.7i	1.24716	−	1.31925i
$389$		−	10473.6i		−	1.36512i	−0.730831	−	0.682559i	$-0.760867\pi$
$389$		−	10473.6i		−	1.36512i	0.730831	−	0.682559i	$-0.239133\pi$
$390$	−2814.93	−	979.126i	−0.365485	−	0.127128i
$391$	−1050.42			−0.135862
$392$	5074.28	−	2356.85i	0.653800	−	0.303670i
$393$	−5462.90			−0.701188
$394$	520.192	−	1307.48i	0.0665149	−	0.167183i
$395$	1029.39			0.131124
$396$	3769.93	+	3563.94i	0.478400	+	0.452259i
$397$	−8777.00			−1.10958			−0.554792	−	0.831989i	$-0.687202\pi$
$397$	−8777.00			−1.10958			−0.554792	+	0.831989i	$0.687202\pi$
$398$	3221.08	−	8096.06i	0.405674	−	1.01965i
$399$	3722.74			0.467093
$400$	−247.334	−	4399.27i	−0.0309168	−	0.549908i
$401$			1609.88i			0.200483i	0.994963	+	0.100242i	$0.0319616\pi$
$401$			1609.88i			0.200483i	−0.994963	+	0.100242i	$0.968038\pi$
$402$	4707.45	+	1872.90i	0.584045	+	0.232367i
$403$	−419.946	−	9556.63i	−0.0519082	−	1.18126i
$404$	−1318.17	+	1394.36i	−0.162330	+	0.171713i
$405$	−606.976			−0.0744713
$406$	−1814.81	+	4561.45i	−0.221841	+	0.557589i
$407$	18903.0			2.30218
$408$	401.817	+	865.110i	0.0487571	+	0.104974i
$409$		−	8418.60i		−	1.01778i	−0.860831	−	0.508891i	$-0.830056\pi$
$409$		−	8418.60i		−	1.01778i	0.860831	−	0.508891i	$-0.169944\pi$
$410$	−7405.68	−	2946.41i	−0.892050	−	0.354909i
$411$	1425.83			0.171122
$412$	−3086.15	−	2917.51i	−0.369038	−	0.348873i
$413$		−	2268.49i		−	0.270278i
$414$	−703.456	+	1768.11i	−0.0835096	+	0.209898i
$415$	−8151.31			−0.964173
$416$	8157.65	+	2333.24i	0.961447	+	0.274992i
$417$	5167.82			0.606881
$418$	−9554.79	+	24015.6i	−1.11804	+	2.81015i
$419$		−	10178.1i		−	1.18671i	−0.804940	−	0.593357i	$-0.797802\pi$
$419$		−	10178.1i		−	1.18671i	0.804940	−	0.593357i	$-0.202198\pi$
$420$	1278.74	+	1208.87i	0.148562	+	0.140445i
$421$	−784.561			−0.0908246			−0.0454123	−	0.998968i	$-0.514460\pi$
$421$	−784.561			−0.0908246			−0.0454123	+	0.998968i	$0.514460\pi$
$422$	−13210.2	−	5255.80i	−1.52385	−	0.606276i
$423$		−	37.9279i		−	0.00435962i
$424$	972.656	+	2094.12i	0.111406	+	0.239858i
$425$	−967.430			−0.110417
$426$	1808.24	−	4544.94i	0.205656	−	0.516909i
$427$	8577.74			0.972145
$428$	−4067.04	+	4302.12i	−0.459317	+	0.485866i
$429$	−444.798	−	10122.2i	−0.0500584	−	1.13917i
$430$	3533.47	+	1405.82i	0.396277	+	0.157662i
$431$		−	580.743i		−	0.0649035i	−0.999473	−	0.0324517i	$-0.989668\pi$
$431$		−	580.743i		−	0.0649035i	0.999473	−	0.0324517i	$-0.0103315\pi$
$432$	1725.28	−	96.9980i	0.192147	−	0.0108028i
$433$	−10988.6			−1.21958			−0.609788	−	0.792565i	$-0.708745\pi$
$433$	−10988.6			−1.21958			−0.609788	+	0.792565i	$0.708745\pi$
$434$	−2087.92	+	5247.90i	−0.230929	+	0.580432i
$435$	3987.80			0.439541
$436$	−6185.50	−	5847.51i	−0.679431	−	0.642305i
$437$	−9480.49			−1.03779
$438$	2062.84	−	5184.87i	0.225038	−	0.565623i
$439$	−4957.49			−0.538971			−0.269486	−	0.963004i	$-0.586854\pi$
$439$	−4957.49			−0.538971			−0.269486	+	0.963004i	$0.586854\pi$
$440$	−11080.5	+	5146.55i	−1.20055	+	0.557618i
$441$	−2225.36			−0.240294
$442$	612.020	−	1759.52i	0.0658616	−	0.189348i
$443$			3219.87i			0.345328i	0.984981	+	0.172664i	$0.0552376\pi$
$443$			3219.87i			0.345328i	−0.984981	+	0.172664i	$0.944762\pi$
$444$	4325.39	−	4575.40i	0.462328	−	0.489051i
$445$			2016.71i			0.214834i
$446$	13340.1	+	5307.48i	1.41631	+	0.563490i
$447$			5655.91i			0.598468i
$448$	−3827.90	−	3231.75i	−0.403686	−	0.340817i
$449$			6166.53i			0.648144i	0.946032	+	0.324072i	$0.105052\pi$
$449$			6166.53i			0.648144i	−0.946032	+	0.324072i	$0.894948\pi$
$450$	−647.876	+	1628.41i	−0.0678693	+	0.170587i
$451$		−	27095.6i		−	2.82901i
$452$	−670.091	−	633.475i	−0.0697310	−	0.0659208i
$453$	−7248.14			−0.751760
$454$	−1360.11	+	3418.59i	−0.140602	+	0.353397i
$455$	−150.873	−	3433.39i	−0.0155452	−	0.353758i
$456$	3626.56	+	7807.96i	0.372432	+	0.801845i
$457$			3680.41i			0.376723i	0.982100	+	0.188361i	$0.0603177\pi$
$457$			3680.41i			0.376723i	−0.982100	+	0.188361i	$0.939682\pi$
$458$	7004.05	−	17604.4i	0.714580	−	1.79607i
$459$		−	379.400i		−	0.0385815i
$460$	−3256.50	−	3078.56i	−0.330076	−	0.312040i
$461$	17220.4			1.73977			0.869886	−	0.493252i	$-0.164192\pi$
$461$	17220.4			1.73977			0.869886	+	0.493252i	$0.164192\pi$
$462$	−2211.48	+	5558.47i	−0.222700	+	0.559748i
$463$			15319.2i			1.53768i	0.639444	+	0.768838i	$0.279165\pi$
$463$			15319.2i			1.53768i	−0.639444	+	0.768838i	$0.720835\pi$
$464$	−11335.0	+	637.273i	−1.13408	+	0.0637600i
$465$	4587.92			0.457548
$466$	4350.33	−	10934.4i	0.432458	−	1.08696i
$467$		−	3787.04i		−	0.375254i	−0.982240	−	0.187627i	$-0.939920\pi$
$467$		−	3787.04i		−	0.375254i	0.982240	−	0.187627i	$-0.0600796\pi$
$468$	−2551.82	−	2208.50i	−0.252047	−	0.218137i
$469$			5842.11i			0.575188i
$470$	82.9926	+	33.0193i	0.00814502	+	0.00324056i
$471$	7280.76			0.712271
$472$	4757.85	−	2209.88i	0.463979	−	0.215504i
$473$			12928.1i			1.25674i
$474$	1083.05	+	430.901i	0.104950	+	0.0417551i
$475$	−8731.44			−0.843423
$476$	−755.624	+	799.299i	−0.0727604	+	0.0769660i
$477$		−	918.393i		−	0.0881559i
$478$	3448.56	+	1372.04i	0.329986	+	0.131288i
$479$		−	10733.6i		−	1.02386i	−0.859027	−	0.511930i	$-0.828931\pi$
$479$		−	10733.6i		−	1.02386i	0.859027	−	0.511930i	$-0.171069\pi$
$480$	−1289.74	+	3859.63i	−0.122642	+	0.367015i
$481$	−12284.8	+	539.832i	−1.16453	+	0.0511730i
$482$	−9356.85	−	3722.70i	−0.884217	−	0.351793i
$483$	−2194.28			−0.206715
$484$	−22444.3	−	21217.9i	−2.10784	−	1.99266i
$485$		−	12996.5i		−	1.21679i
$486$	−638.620	−	254.080i	−0.0596057	−	0.0237146i
$487$		−	1390.84i		−	0.129415i	−0.997904	−	0.0647074i	$-0.979389\pi$
$487$		−	1390.84i		−	0.129415i	0.997904	−	0.0647074i	$-0.0206114\pi$
$488$	8356.12	+	17990.7i	0.775131	+	1.66885i
$489$		−	3448.38i		−	0.318898i
$490$	1937.35	−	4869.46i	0.178614	−	0.448938i
$491$			13956.7i			1.28280i	0.767206	+	0.641401i	$0.221646\pi$
$491$			13956.7i			1.28280i	−0.767206	+	0.641401i	$0.778354\pi$
$492$	−6558.40	−	6200.03i	−0.600967	−	0.568128i
$493$			2492.64i			0.227714i
$494$	5523.72	−	15880.3i	0.503085	−	1.44634i
$495$	4859.43			0.441243
$496$	−13040.8	+	733.175i	−1.18054	+	0.0663720i
$497$	5640.43			0.509070
$498$	−8576.27	−	3412.14i	−0.771710	−	0.307031i
$499$	4676.41			0.419529			0.209764	−	0.977752i	$-0.432730\pi$
$499$	4676.41			0.419529			0.209764	+	0.977752i	$0.432730\pi$
$500$	−8444.61	−	7983.18i	−0.755309	−	0.714037i
$501$	7068.90			0.630370
$502$	−16089.0	−	6401.14i	−1.43045	−	0.569117i
$503$	8410.46			0.745534			0.372767	−	0.927925i	$-0.378409\pi$
$503$	8410.46			0.745534			0.372767	+	0.927925i	$0.378409\pi$
$504$	839.376	+	1807.17i	0.0741841	+	0.159718i
$505$			1797.33i			0.158376i
$506$	5631.86	−	14155.4i	0.494795	−	1.24365i
$507$	578.139	+	6565.59i	0.0506431	+	0.575125i
$508$	−6025.66	−	5696.40i	−0.526270	−	0.497513i
$509$	10217.4			0.889745			0.444873	−	0.895594i	$-0.353249\pi$
$509$	10217.4			0.889745			0.444873	+	0.895594i	$0.353249\pi$
$510$	830.190	+	330.298i	0.0720813	+	0.0286781i
$511$	6434.60			0.557045
$512$	3049.18	−	11176.8i	0.263196	−	0.964742i
$513$		−	3424.24i		−	0.294705i
$514$	171.515	−	431.097i	0.0147183	−	0.0369939i
$515$	−3978.03			−0.340375
$516$	3129.21	+	2958.22i	0.266969	+	0.252381i
$517$			303.650i			0.0258308i
$518$	6746.07	+	2683.98i	0.572211	+	0.227659i
$519$	9988.87			0.844822
$520$	7054.12	−	3661.12i	0.594891	−	0.308752i
$521$	−14540.2			−1.22268			−0.611341	−	0.791367i	$-0.709370\pi$
$521$	−14540.2			−1.22268			−0.611341	+	0.791367i	$0.709370\pi$
$522$	4195.70	+	1669.29i	0.351803	+	0.139967i
$523$			1680.47i			0.140500i	0.997529	+	0.0702502i	$0.0223798\pi$
$523$			1680.47i			0.140500i	−0.997529	+	0.0702502i	$0.977620\pi$
$524$	10007.7	−	10586.1i	0.834326	−	0.882550i
$525$	−2020.91			−0.168000
$526$	1435.17	−	3607.25i	0.118967	−	0.299018i
$527$			2867.76i			0.237043i
$528$	−13812.5	+	776.564i	−1.13847	+	0.0640069i
$529$	−6578.94			−0.540720
$530$	2009.60	+	799.534i	0.164700	+	0.0655274i
$531$	−2086.59			−0.170528
$532$	−6819.80	+	7213.99i	−0.555782	+	0.587906i
$533$	773.798	+	17609.2i	0.0628835	+	1.43103i
$534$	−844.194	+	2121.85i	−0.0684117	+	0.171950i
$535$			5545.42i			0.448129i
$536$	−12253.1	+	5691.17i	−0.987409	+	0.458621i
$537$	−6665.80			−0.535662
$538$	9373.26	+	3729.23i	0.751134	+	0.298845i
$539$	17816.2			1.42374
$540$	1111.94	−	1176.21i	0.0886114	−	0.0937332i
$541$	11384.5			0.904730			0.452365	−	0.891833i	$-0.350580\pi$
$541$	11384.5			0.904730			0.452365	+	0.891833i	$0.350580\pi$
$542$	11435.1	+	4549.55i	0.906235	+	0.360553i
$543$	−5329.90			−0.421230
$544$	−2412.53	−	806.174i	−0.190140	−	0.0635375i
$545$	−7973.09			−0.626660
$546$	1278.48	−	3675.55i	0.100209	−	0.288093i
$547$			1662.17i			0.129926i	0.997888	+	0.0649629i	$0.0206929\pi$
$547$			1662.17i			0.129926i	−0.997888	+	0.0649629i	$0.979307\pi$
$548$	−2612.03	+	2763.01i	−0.203614	+	0.215383i
$549$		−	7889.95i		−	0.613360i
$550$	5186.88	−	13037.0i	0.402126	−	1.01073i
$551$			22497.1i			1.73940i
$552$	−2137.59	−	4602.22i	−0.164822	−	0.354862i
$553$			1344.10i			0.103358i
$554$	−12876.9	−	5123.18i	−0.987523	−	0.392894i
$555$		−	5897.67i		−	0.451067i
$556$	−9467.09	+	10014.3i	−0.722112	+	0.763851i
$557$	305.728			0.0232569			0.0116285	−	0.999932i	$-0.496298\pi$
$557$	305.728			0.0232569			0.0116285	+	0.999932i	$0.496298\pi$
$558$	4827.11	+	1920.50i	0.366215	+	0.145701i
$559$	−369.202	−	8401.86i	−0.0279349	−	0.635708i
$560$	−4685.13	+	263.407i	−0.353541	+	0.0198767i
$561$			3037.47i			0.228596i
$562$	12686.4	+	5047.40i	0.952216	+	0.378847i
$563$			7612.68i			0.569869i	0.958547	+	0.284935i	$0.0919719\pi$
$563$			7612.68i			0.569869i	−0.958547	+	0.284935i	$0.908028\pi$
$564$	73.4975	+	69.4814i	0.00548724	+	0.00518740i
$565$	−863.745			−0.0643151
$566$	15015.4	+	5973.99i	1.11510	+	0.443650i
$567$		−	792.549i		−	0.0587018i
$568$	5494.70	+	11830.1i	0.405902	+	0.873906i
$569$	−8655.06			−0.637679			−0.318839	−	0.947809i	$-0.603293\pi$
$569$	−8655.06			−0.637679			−0.318839	+	0.947809i	$0.603293\pi$
$570$	7492.80	+	2981.07i	0.550594	+	0.219058i
$571$		−	13397.0i		−	0.981872i	−0.871196	−	0.490936i	$-0.836655\pi$
$571$		−	13397.0i		−	0.981872i	0.871196	−	0.490936i	$-0.163345\pi$
$572$	20429.8	+	17681.2i	1.49338	+	1.29246i
$573$			6102.76i			0.444933i
$574$	3847.23	−	9669.85i	0.279756	−	0.703156i
$575$	5146.55			0.373262
$576$	−2972.62	+	3520.96i	−0.215033	+	0.254699i
$577$			8080.93i			0.583039i	0.956565	+	0.291520i	$0.0941608\pi$
$577$			8080.93i			0.583039i	−0.956565	+	0.291520i	$0.905839\pi$
$578$	4930.56	−	12392.8i	0.354817	−	0.891818i
$579$	5561.28			0.399169
$580$	−7305.38	+	7727.63i	−0.522999	+	0.553229i
$581$		−	10643.4i		−	0.760007i
$582$	5440.34	−	13674.1i	0.387473	−	0.973899i
$583$			7352.64i			0.522324i
$584$	6268.35	+	13495.7i	0.444155	+	0.956263i
$585$	−3158.09	+	138.776i	−0.223198	+	0.00980799i
$586$	−9351.06	+	23503.5i	−0.659196	+	1.65686i
$587$	5614.17			0.394756			0.197378	−	0.980327i	$-0.436757\pi$
$587$	5614.17			0.394756			0.197378	+	0.980327i	$0.436757\pi$
$588$	4076.71	−	4312.35i	0.285920	−	0.302446i
$589$			25882.6i			1.81066i
$590$	1816.54	−	4565.80i	0.126756	−	0.318595i
$591$		−	1492.52i		−	0.103882i
$592$	942.481	+	16763.6i	0.0654320	+	1.16382i
$593$			25941.9i			1.79647i	0.439517	+	0.898234i	$0.355150\pi$
$593$			25941.9i			1.79647i	−0.439517	+	0.898234i	$0.644850\pi$
$594$	5112.78	+	2034.16i	0.353165	+	0.140509i
$595$			1030.29i			0.0709882i
$596$	−10960.1	−	10361.2i	−0.753262	−	0.712102i
$597$		−	9241.85i		−	0.633574i
$598$	−3255.83	+	9360.30i	−0.222643	+	0.640086i
$599$	26297.4			1.79379			0.896896	−	0.442241i	$-0.145816\pi$
$599$	26297.4			1.79379			0.896896	+	0.442241i	$0.145816\pi$
$600$	−1968.70	−	4238.60i	−0.133953	−	0.288400i
$601$	−6750.22			−0.458148			−0.229074	−	0.973409i	$-0.573570\pi$
$601$	−6750.22			−0.458148			−0.229074	+	0.973409i	$0.573570\pi$
$602$	−1835.63	+	4613.78i	−0.124277	+	0.312365i
$603$	5373.67			0.362907
$604$	13278.1	−	14045.6i	0.894500	−	0.946203i
$605$	−28930.6			−1.94413
$606$	−752.361	+	1891.03i	−0.0504333	+	0.126762i
$607$	9596.56			0.641700			0.320850	−	0.947130i	$-0.396031\pi$
$607$	9596.56			0.641700			0.320850	+	0.947130i	$0.396031\pi$
$608$	−21774.0	−	7276.04i	−1.45239	−	0.485333i
$609$			5207.01i			0.346467i
$610$	17264.5	+	6868.82i	1.14593	+	0.455919i
$611$	−8.67165	−	197.339i	−0.000574169	−	0.0130663i
$612$	735.209	+	695.035i	0.0485606	+	0.0459071i
$613$	25871.6			1.70464			0.852319	−	0.523023i	$-0.175196\pi$
$613$	25871.6			1.70464			0.852319	+	0.523023i	$0.175196\pi$
$614$	6861.98	−	17247.3i	0.451021	−	1.13362i
$615$	−8453.76			−0.554290
$616$	−6720.03	−	14468.2i	−0.439542	−	0.946331i
$617$		−	16910.5i		−	1.10339i	−0.834047	−	0.551694i	$-0.813982\pi$
$617$		−	16910.5i		−	1.10339i	0.834047	−	0.551694i	$-0.186018\pi$
$618$	−4185.43	−	1665.21i	−0.272431	−	0.108389i
$619$	20847.7			1.35370			0.676849	−	0.736122i	$-0.263345\pi$
$619$	20847.7			1.35370			0.676849	+	0.736122i	$0.263345\pi$
$620$	−8404.75	+	8890.56i	−0.544424	+	0.575893i
$621$			2018.34i			0.130424i
$622$	3371.83	−	8474.97i	0.217361	−	0.546327i
$623$	−2633.28			−0.169342
$624$	8954.43	−	899.139i	0.574461	−	0.0576833i
$625$	−2279.20			−0.145869
$626$	−4122.64	+	10362.1i	−0.263217	+	0.661585i
$627$			27414.4i			1.74613i
$628$	−13337.8	+	14108.8i	−0.847513	+	0.896500i
$629$	3686.44			0.233685
$630$	1734.23	+	689.976i	0.109672	+	0.0436338i
$631$		−	7426.08i		−	0.468506i	−0.972176	−	0.234253i	$-0.924736\pi$
$631$		−	7426.08i		−	0.468506i	0.972176	−	0.234253i	$-0.0752645\pi$
$632$	−2819.08	+	1309.38i	−0.177432	+	0.0824117i
$633$	−15079.8			−0.946870
$634$	1710.49	−	4299.25i	0.107149	−	0.269314i
$635$	−7767.05			−0.485395
$636$	1779.68	+	1682.43i	0.110957	+	0.104894i
$637$	−11578.6	+	508.795i	−0.720187	+	0.0316471i
$638$	−33590.7	−	13364.3i	−2.08443	−	0.829309i
$639$		−	5188.16i		−	0.321190i
$640$	−5116.55	−	9569.86i	−0.316015	−	0.591065i
$641$	−12901.9			−0.795002			−0.397501	−	0.917602i	$-0.630122\pi$
$641$	−12901.9			−0.795002			−0.397501	+	0.917602i	$0.630122\pi$
$642$	−2321.31	+	5834.52i	−0.142702	+	0.358676i
$643$	−3893.05			−0.238767			−0.119383	−	0.992848i	$-0.538092\pi$
$643$	−3893.05			−0.238767			−0.119383	+	0.992848i	$0.538092\pi$
$644$	4019.78	−	4252.12i	0.245965	−	0.260182i
$645$	4033.54			0.246234
$646$	−1863.37	+	4683.50i	−0.113488	+	0.285247i
$647$	−8327.09			−0.505984			−0.252992	−	0.967468i	$-0.581415\pi$
$647$	−8327.09			−0.505984			−0.252992	+	0.967468i	$0.581415\pi$
$648$	1662.27	−	772.072i	0.100772	−	0.0468053i
$649$	16705.2			1.01038
$650$	−2998.59	+	8620.75i	−0.180945	+	0.520205i
$651$			5990.61i			0.360661i
$652$	6682.33	+	6317.19i	0.401381	+	0.379449i
$653$			17563.3i			1.05254i	0.850319	+	0.526268i	$0.176409\pi$
$653$			17563.3i			1.05254i	−0.850319	+	0.526268i	$0.823591\pi$
$654$	−8388.77	−	3337.54i	−0.501570	−	0.199554i
$655$		−	13645.5i		−	0.814004i
$656$	24029.1	−	1350.96i	1.43015	−	0.0804055i
$657$		−	5918.66i		−	0.351459i
$658$	−43.1144	+	108.366i	−0.00255437	+	0.00642030i
$659$			26423.6i			1.56194i	0.624571	+	0.780968i	$0.285274\pi$
$659$			26423.6i			1.56194i	−0.624571	+	0.780968i	$0.714726\pi$
$660$	−8902.15	+	9416.70i	−0.525024	+	0.555371i
$661$	1578.33			0.0928746			0.0464373	−	0.998921i	$-0.485213\pi$
$661$	1578.33			0.0928746			0.0464373	+	0.998921i	$0.485213\pi$
$662$	7934.22	−	19942.4i	0.465819	−	1.17082i
$663$	−86.7442	−	1974.02i	−0.00508124	−	0.115633i
$664$	22323.2	−	10368.5i	1.30468	−	0.605985i
$665$			9298.81i			0.542244i
$666$	2468.77	−	6205.15i	0.143638	−	0.361028i
$667$		−	13260.4i		−	0.769782i
$668$	−12949.7	+	13698.3i	−0.750061	+	0.793415i
$669$	15228.1			0.880047
$670$	−4678.20	+	11758.5i	−0.269753	+	0.678014i
$671$			63166.8i			3.63417i
$672$	−5039.65	−	1684.06i	−0.289299	−	0.0966725i
$673$	27226.4			1.55943			0.779717	−	0.626132i	$-0.215363\pi$
$673$	27226.4			1.55943			0.779717	+	0.626132i	$0.215363\pi$
$674$	2448.20	−	6153.45i	0.139913	−	0.351665i
$675$			1858.87i			0.105997i
$676$	−13782.0	−	10907.4i	−0.784140	−	0.620584i
$677$			5715.23i			0.324452i	0.986754	+	0.162226i	$0.0518674\pi$
$677$			5715.23i			0.324452i	−0.986754	+	0.162226i	$0.948133\pi$
$678$	−908.776	−	361.564i	−0.0514769	−	0.0204805i
$679$	16970.0			0.959130
$680$	−2160.91	+	1003.68i	−0.121863	+	0.0566018i
$681$			3902.40i			0.219590i
$682$	−38645.7	−	15375.5i	−2.16983	−	0.863283i
$683$	−20426.9			−1.14438			−0.572191	−	0.820120i	$-0.693906\pi$
$683$	−20426.9			−1.14438			−0.572191	+	0.820120i	$0.693906\pi$
$684$	6635.55	+	6272.97i	0.370931	+	0.350662i
$685$			3561.51i			0.198654i
$686$	15178.3	+	6038.80i	0.844766	+	0.336097i
$687$		−	20095.8i		−	1.11602i
$688$	−11465.0	+	644.583i	−0.635318	+	0.0357187i
$689$	−209.977	−	4778.40i	−0.0116103	−	0.264213i
$690$	−4416.46	−	1757.12i	−0.243669	−	0.0969457i
$691$	−18026.4			−0.992413			−0.496207	−	0.868204i	$-0.665274\pi$
$691$	−18026.4			−0.992413			−0.496207	+	0.868204i	$0.665274\pi$
$692$	−18298.9	+	19356.6i	−1.00523	+	1.06334i
$693$			6345.13i			0.347809i
$694$	−6057.82	−	2410.15i	−0.331342	−	0.131827i
$695$			12908.4i			0.704523i
$696$	−10921.0	+	5072.48i	−0.594771	+	0.276253i
$697$		−	5284.17i		−	0.287162i
$698$	−5634.15	+	14161.2i	−0.305524	+	0.767922i
$699$		−	12481.9i		−	0.675404i
$700$	3702.17	−	3916.16i	0.199899	−	0.211453i
$701$		−	15181.2i		−	0.817955i	−0.912544	−	0.408978i	$-0.865885\pi$
$701$		−	15181.2i		−	0.817955i	0.912544	−	0.408978i	$-0.134115\pi$
$702$	−3380.83	−	1175.97i	−0.181768	−	0.0632251i
$703$	33271.6			1.78501
$704$	23798.7	−	28188.8i	1.27407	−	1.50910i
$705$	94.7380			0.00506105
$706$	2334.38	+	928.753i	0.124441	+	0.0495100i
$707$	−2346.83			−0.124840
$708$	3822.49	−	4043.43i	0.202907	−	0.214635i
$709$	−15371.5			−0.814228			−0.407114	−	0.913377i	$-0.633465\pi$
$709$	−15371.5			−0.814228			−0.407114	+	0.913377i	$0.633465\pi$
$710$	11352.5	+	4516.70i	0.600075	+	0.238745i
$711$	1236.33			0.0652123
$712$	−2565.25	−	5522.97i	−0.135024	−	0.290705i
$713$		−	15255.9i		−	0.801317i
$714$	−431.281	+	1084.01i	−0.0226055	+	0.0568179i
$715$	25283.6	−	1111.04i	1.32245	−	0.0581124i
$716$	12211.3	−	12917.1i	0.637370	−	0.674211i
$717$	3936.61			0.205043
$718$	10585.2	+	4211.41i	0.550190	+	0.218897i
$719$	−15590.7			−0.808670			−0.404335	−	0.914611i	$-0.632497\pi$
$719$	−15590.7			−0.808670			−0.404335	+	0.914611i	$0.632497\pi$
$720$	242.286	+	4309.47i	0.0125409	+	0.223062i
$721$		−	5194.26i		−	0.268300i
$722$	−9645.88	+	24244.5i	−0.497206	+	1.24971i
$723$	−10681.1			−0.549423
$724$	9764.01	−	10328.4i	0.501211	−	0.530181i
$725$		−	12212.7i		−	0.625611i
$726$	−30438.9	−	12110.4i	−1.55605	−	0.619088i
$727$	−22081.0			−1.12646			−0.563231	−	0.826299i	$-0.690442\pi$
$727$	−22081.0			−1.12646			−0.563231	+	0.826299i	$0.690442\pi$
$728$	4780.45	+	9210.81i	0.243373	+	0.468922i
$729$	−729.000			−0.0370370
$730$	12951.0	+	5152.65i	0.656627	+	0.261244i
$731$			2521.24i			0.127567i
$732$	15289.3	+	14453.8i	0.772006	+	0.729821i
$733$	−5519.68			−0.278136			−0.139068	−	0.990283i	$-0.544411\pi$
$733$	−5519.68			−0.278136			−0.139068	+	0.990283i	$0.544411\pi$
$734$	−2599.14	+	6532.83i	−0.130703	+	0.328516i
$735$		−	5558.60i		−	0.278955i
$736$	12834.2	+	4288.69i	0.642764	+	0.214787i
$737$	−43021.5			−2.15023
$738$	−8894.49	−	3538.74i	−0.443646	−	0.176508i
$739$	14356.2			0.714617			0.357309	−	0.933986i	$-0.383694\pi$
$739$	14356.2			0.714617			0.357309	+	0.933986i	$0.383694\pi$
$740$	11428.6	+	10804.1i	0.567736	+	0.536713i
$741$	−782.900	−	17816.3i	−0.0388132	−	0.883264i
$742$	−1043.98	+	2624.00i	−0.0516518	+	0.129825i
$743$		−	9478.13i		−	0.467993i	−0.972237	−	0.233996i	$-0.924820\pi$
$743$		−	9478.13i		−	0.467993i	0.972237	−	0.233996i	$-0.0751804\pi$
$744$	−12564.5	+	5835.83i	−0.619137	+	0.287570i
$745$	−14127.6			−0.694757
$746$	−24981.0	−	9938.88i	−1.22603	−	0.487786i
$747$	−9790.02			−0.479515
$748$	−5886.07	−	5564.44i	−0.287722	−	0.272000i
$749$	−7240.84			−0.353237
$750$	−11452.6	−	4556.50i	−0.557585	−	0.221840i
$751$	−26690.4			−1.29686			−0.648432	−	0.761273i	$-0.724575\pi$
$751$	−26690.4			−1.29686			−0.648432	+	0.761273i	$0.724575\pi$
$752$	−269.285	+	15.1397i	−0.0130582	+	0.000734158i
$753$	−18366.0			−0.888837
$754$	22211.9	+	7726.05i	1.07282	+	0.373165i
$755$		−	18104.7i		−	0.872712i
$756$	1535.82	+	1451.90i	0.0738850	+	0.0698478i
$757$			21871.3i			1.05010i	0.851071	+	0.525050i	$0.175953\pi$
$757$			21871.3i			1.05010i	−0.851071	+	0.525050i	$0.824047\pi$
$758$	−7321.03	+	18401.1i	−0.350807	+	0.881740i
$759$		−	16158.8i		−	0.772762i
$760$	−19503.1	+	9058.57i	−0.930855	+	0.432354i
$761$		−	19183.4i		−	0.913796i	−0.889519	−	0.456898i	$-0.848960\pi$
$761$		−	19183.4i		−	0.913796i	0.889519	−	0.456898i	$-0.151040\pi$
$762$	−8171.98	−	3251.29i	−0.388504	−	0.154569i
$763$		−	10410.7i		−	0.493964i
$764$	−11826.0	−	11179.8i	−0.560015	−	0.529414i
$765$	947.682			0.0447889
$766$	25752.1	+	10245.7i	1.21470	+	0.483278i
$767$	−10856.5	+	477.067i	−0.511091	+	0.0224588i
$768$	−1377.35	−	12210.6i	−0.0647148	−	0.573712i
$769$		−	2171.49i		−	0.101828i	−0.998703	−	0.0509141i	$-0.983787\pi$
$769$		−	2171.49i		−	0.101828i	0.998703	−	0.0509141i	$-0.0162135\pi$
$770$	−13884.2	−	5523.93i	−0.649807	−	0.258531i
$771$		−	492.107i		−	0.0229868i
$772$	−10187.9	+	10776.7i	−0.474961	+	0.502414i
$773$	−6860.28			−0.319207			−0.159603	−	0.987181i	$-0.551022\pi$
$773$	−6860.28			−0.319207			−0.159603	+	0.987181i	$0.551022\pi$
$774$	4243.83	+	1688.44i	0.197082	+	0.0784106i
$775$		−	14050.6i		−	0.651240i
$776$	16531.6	+	35592.4i	0.764753	+	1.64651i
$777$	7700.80			0.355553
$778$	27525.2	+	10951.1i	1.26841	+	0.504649i
$779$		−	47691.7i		−	2.19349i
$780$	5516.49	−	6374.04i	0.253233	−	0.292599i
$781$			41536.3i			1.90305i
$782$	1098.32	−	2760.58i	0.0502248	−	0.126238i
$783$	4789.50			0.218598
$784$	888.295	+	15799.8i	0.0404654	+	0.719745i
$785$			18186.2i			0.826870i
$786$	5711.99	−	14356.9i	0.259211	−	0.651517i
$787$	−18310.8			−0.829366			−0.414683	−	0.909966i	$-0.636107\pi$
$787$	−18310.8			−0.829366			−0.414683	+	0.909966i	$0.636107\pi$
$788$	2892.24	+	2734.20i	0.130751	+	0.123606i
$789$		−	4117.76i		−	0.185800i
$790$	−1076.32	+	2705.29i	−0.0484732	+	0.121835i
$791$		−	1127.82i		−	0.0506963i
$792$	−13308.1	+	6181.19i	−0.597074	+	0.277322i
$793$	−1803.92	−	41051.4i	−0.0807805	−	1.83831i
$794$	9177.20	−	23066.5i	0.410185	−	1.03098i
$795$	2294.00			0.102339
$796$	17909.0	+	16930.4i	0.797448	+	0.753874i
$797$		−	34492.7i		−	1.53299i	−0.642249	−	0.766496i	$-0.721998\pi$
$797$		−	34492.7i		−	1.53299i	0.642249	−	0.766496i	$-0.278002\pi$
$798$	−3892.48	+	9783.60i	−0.172672	+	0.434005i
$799$			59.2176i			0.00262199i
$800$	11820.2	+	3949.85i	0.522383	+	0.174560i
$801$			2422.14i			0.106844i
$802$	−4230.88	−	1683.29i	−0.186281	−	0.0741135i
$803$			47384.6i			2.08240i
$804$	−9844.19	+	10413.2i	−0.431813	+	0.456772i
$805$		−	5480.97i		−	0.239974i
$806$	25554.5	+	8888.73i	1.11677	+	0.388452i
$807$	10699.8			0.466730
$808$	−2286.20	−	4922.17i	−0.0995398	−	0.214309i
$809$	33909.8			1.47368			0.736839	−	0.676069i	$-0.236318\pi$
$809$	33909.8			1.47368			0.736839	+	0.676069i	$0.236318\pi$
$810$	634.652	−	1595.17i	0.0275301	−	0.0691958i
$811$	−22972.6			−0.994668			−0.497334	−	0.867559i	$-0.665688\pi$
$811$	−22972.6			−0.994668			−0.497334	+	0.867559i	$0.665688\pi$
$812$	−10090.2	−	9538.88i	−0.436081	−	0.412253i
$813$	13053.4			0.563105
$814$	−19764.9	+	49678.3i	−0.851055	+	2.13909i
$815$	8613.51			0.370206
$816$	−2693.70	+	151.445i	−0.115562	+	0.00649710i
$817$			22755.1i			0.974421i
$818$	22124.6	+	8802.46i	0.945684	+	0.376248i
$819$	−181.204	−	4123.63i	−0.00773113	−	0.175936i
$820$	15486.7	−	16381.9i	0.659536	−	0.697658i
$821$	−17293.0			−0.735115			−0.367558	−	0.930001i	$-0.619806\pi$
$821$	−17293.0			−0.735115			−0.367558	+	0.930001i	$0.619806\pi$
$822$	−1490.85	+	3747.18i	−0.0632594	+	0.159000i
$823$	−3515.45			−0.148895			−0.0744477	−	0.997225i	$-0.523719\pi$
$823$	−3515.45			−0.148895			−0.0744477	+	0.997225i	$0.523719\pi$
$824$	10894.3	−	5060.06i	0.460583	−	0.213926i
$825$		−	14882.1i		−	0.628033i
$826$	5961.73	+	2371.92i	0.251132	+	0.0999149i
$827$	−16950.3			−0.712720			−0.356360	−	0.934349i	$-0.615982\pi$
$827$	−16950.3			−0.712720			−0.356360	+	0.934349i	$0.615982\pi$
$828$	−3911.17	−	3697.46i	−0.164158	−	0.155188i
$829$			15610.6i			0.654013i	0.945022	+	0.327007i	$0.106040\pi$
$829$			15610.6i			0.654013i	−0.945022	+	0.327007i	$0.893960\pi$
$830$	8522.98	−	21422.2i	0.356430	−	0.895872i
$831$	−14699.3			−0.613614
$832$	−14661.5	+	18999.2i	−0.610934	+	0.791682i
$833$	3474.50			0.144519
$834$	−5403.46	+	13581.4i	−0.224348	+	0.563890i
$835$			17657.0i			0.731791i
$836$	−53124.1	−	50221.3i	−2.19777	−	2.07768i
$837$	5510.26			0.227554
$838$	26748.7	+	10642.2i	1.10265	+	0.438698i
$839$			9644.64i			0.396865i	0.980115	+	0.198433i	$0.0635851\pi$
$839$			9644.64i			0.396865i	−0.980115	+	0.198433i	$0.936415\pi$
$840$	−4514.03	+	2096.63i	−0.185415	+	0.0861197i
$841$	−7077.76			−0.290203
$842$	820.334	−	2061.88i	0.0335755	−	0.0843907i
$843$	14481.9			0.591676
$844$	27625.2	−	29221.9i	1.12666	−	1.19178i
$845$	−16399.8	+	1444.10i	−0.667658	+	0.0587912i
$846$	99.6771	+	39.6573i	0.00405079	+	0.00161164i
$847$		−	37775.7i		−	1.53246i
$848$	−6520.50	+	366.594i	−0.264051	+	0.0148454i
$849$	17140.4			0.692884
$850$	1011.54	−	2542.47i	0.0408183	−	0.102595i
$851$	−19611.2			−0.789968
$852$	10053.7	+	9504.35i	0.404266	+	0.382176i
$853$	6268.45			0.251615			0.125808	−	0.992055i	$-0.459848\pi$
$853$	6268.45			0.251615			0.125808	+	0.992055i	$0.459848\pi$
$854$	−8968.85	+	22542.9i	−0.359377	+	0.903279i
$855$	8553.21			0.342121
$856$	−7053.76	−	15186.7i	−0.281650	−	0.606392i
$857$	21936.5			0.874372			0.437186	−	0.899371i	$-0.355975\pi$
$857$	21936.5			0.874372			0.437186	+	0.899371i	$0.355975\pi$
$858$	27066.8	+	9414.77i	1.07698	+	0.374609i
$859$		−	16932.2i		−	0.672549i	−0.941764	−	0.336274i	$-0.890833\pi$
$859$		−	16932.2i		−	0.672549i	0.941764	−	0.336274i	$-0.109167\pi$
$860$	−7389.18	+	7816.28i	−0.292987	+	0.309922i
$861$		−	11038.4i		−	0.436918i
$862$	1526.23	+	607.223i	0.0603058	+	0.0239932i
$863$		−	38618.2i		−	1.52327i	−0.648008	−	0.761634i	$-0.724398\pi$
$863$		−	38618.2i		−	1.52327i	0.648008	−	0.761634i	$-0.275602\pi$
$864$	−1549.03	+	4635.56i	−0.0609941	+	0.182529i
$865$			24950.6i			0.980747i
$866$	11489.6	−	28878.6i	0.450846	−	1.13318i
$867$		−	14146.6i		−	0.554146i
$868$	−11608.7	−	10974.4i	−0.453946	−	0.429141i
$869$	−9898.03			−0.386384
$870$	−4169.63	+	10480.2i	−0.162487	+	0.408405i
$871$	27959.2	−	1228.61i	1.08767	−	0.0477954i
$872$	21835.2	−	10141.8i	0.847973	−	0.393857i
$873$		−	15609.3i		−	0.605149i
$874$	9912.77	−	24915.3i	0.383643	−	0.964272i
$875$		−	14213.0i		−	0.549129i
$876$	11469.3	+	10842.6i	0.442364	+	0.418192i
$877$	28880.1			1.11199			0.555994	−	0.831186i	$-0.312338\pi$
$877$	28880.1			1.11199			0.555994	+	0.831186i	$0.312338\pi$
$878$	5183.54	−	13028.6i	0.199244	−	0.500791i
$879$			26829.8i			1.02952i
$880$	−1939.73	−	34501.5i	−0.0743051	−	1.32164i
$881$	10648.9			0.407230			0.203615	−	0.979051i	$-0.434731\pi$
$881$	10648.9			0.407230			0.203615	+	0.979051i	$0.434731\pi$
$882$	2326.83	−	5848.40i	0.0888305	−	0.223272i
$883$			19439.7i			0.740880i	0.928856	+	0.370440i	$0.120793\pi$
$883$			19439.7i			0.740880i	−0.928856	+	0.370440i	$0.879207\pi$
$884$	3984.20	+	3448.17i	0.151587	+	0.131193i
$885$		−	5211.97i		−	0.197965i
$886$	−8462.02	−	3366.68i	−0.320866	−	0.127659i
$887$	4384.57			0.165975			0.0829873	−	0.996551i	$-0.473554\pi$
$887$	4384.57			0.165975			0.0829873	+	0.996551i	$0.473554\pi$
$888$	7501.84	+	16151.4i	0.283497	+	0.610367i
$889$		−	10141.7i		−	0.382612i
$890$	−5300.04	−	2108.66i	−0.199615	−	0.0794186i
$891$	5836.36			0.219445
$892$	−27896.8	+	29509.3i	−1.04715	+	1.10767i
$893$			534.462i			0.0200281i
$894$	−14864.1	−	5913.80i	−0.556073	−	0.221238i
$895$		−	16650.1i		−	0.621845i
$896$	12495.7	−	6680.85i	0.465906	−	0.249098i
$897$	461.463	+	10501.4i	0.0171770	+	0.390894i
$898$	−16206.0	−	6447.70i	−0.602230	−	0.239602i
$899$	−36202.2			−1.34306
$900$	−3602.15	−	3405.32i	−0.133413	−	0.126123i
$901$			1433.90i			0.0530192i
$902$	71209.1	+	28331.1i	2.62861	+	1.04581i
$903$			5266.74i			0.194093i
$904$	2365.46	−	1098.68i	0.0870288	−	0.0404222i
$905$		−	13313.2i		−	0.489002i
$906$	7578.63	−	19048.6i	0.277906	−	0.698506i
$907$		−	10424.1i		−	0.381618i	−0.981627	−	0.190809i	$-0.938889\pi$
$907$		−	10424.1i		−	0.381618i	0.981627	−	0.190809i	$-0.0611111\pi$
$908$	−7562.15	−	7148.93i	−0.276386	−	0.261284i
$909$			2158.65i			0.0787657i
$910$	9180.93	+	3193.44i	0.334445	+	0.116331i
$911$	2959.87			0.107645			0.0538227	−	0.998551i	$-0.482859\pi$
$911$	2959.87			0.107645			0.0538227	+	0.998551i	$0.482859\pi$
$912$	−24311.7	+	1366.85i	−0.882722	+	0.0496282i
$913$	78378.7			2.84113
$914$	−9672.36	−	3848.23i	−0.350036	−	0.139265i
$915$	19707.8			0.712045
$916$	38942.1	+	36814.2i	1.40468	+	1.32792i
$917$	17817.4			0.641637
$918$	997.089	+	396.700i	0.0358484	+	0.0142626i
$919$	−43513.0			−1.56187			−0.780936	−	0.624611i	$-0.785257\pi$
$919$	−43513.0			−1.56187			−0.780936	+	0.624611i	$0.785257\pi$
$920$	11495.6	−	5339.36i	0.411956	−	0.191341i
$921$		−	19688.2i		−	0.704396i
$922$	−18005.6	+	45256.4i	−0.643149	+	1.61653i
$923$	−1186.19	−	26994.0i	−0.0423013	−	0.962641i
$924$	−12295.7	−	11623.8i	−0.437770	−	0.413849i
$925$	−18061.7			−0.642016
$926$	−40259.9	−	16017.7i	−1.42875	−	0.568439i
$927$	−4777.77			−0.169280
$928$	10177.0	−	30455.4i	0.359997	−	1.07731i
$929$			3863.45i			0.136443i	0.997670	+	0.0682216i	$0.0217325\pi$
$929$			3863.45i			0.136443i	−0.997670	+	0.0682216i	$0.978268\pi$
$930$	−4797.12	+	12057.4i	−0.169144	+	0.425136i
$931$	31358.7			1.10391
$932$	24187.6	+	22865.9i	0.850097	+	0.803646i
$933$		−	9674.38i		−	0.339470i
$934$	9952.60	+	3959.72i	0.348671	+	0.138722i
$935$	−7587.12			−0.265375
$936$	8472.26	−	4397.14i	0.295859	−	0.153552i
$937$	20376.0			0.710411			0.355206	−	0.934788i	$-0.384411\pi$
$937$	20376.0			0.710411			0.355206	+	0.934788i	$0.384411\pi$
$938$	−15353.4	−	6108.49i	−0.534443	−	0.212632i
$939$			11828.6i			0.411087i
$940$	−173.554	+	183.585i	−0.00602201	+	0.00637009i
$941$	−5420.31			−0.187776			−0.0938880	−	0.995583i	$-0.529930\pi$
$941$	−5420.31			−0.187776			−0.0938880	+	0.995583i	$0.529930\pi$
$942$	−7612.74	+	19134.3i	−0.263308	+	0.661815i
$943$			28110.8i			0.970745i
$944$	832.902	+	14814.6i	0.0287168	+	0.510777i
$945$	1979.66			0.0681465
$946$	−33976.0	−	13517.6i	−1.16771	−	0.464584i
$947$	22573.3			0.774587			0.387294	−	0.921956i	$-0.373410\pi$
$947$	22573.3			0.774587			0.387294	+	0.921956i	$0.373410\pi$
$948$	−2264.87	+	2395.78i	−0.0775945	+	0.0820795i
$949$	−1353.21	−	30794.8i	−0.0462878	−	1.05336i
$950$	9129.56	−	22946.8i	0.311792	−	0.783676i
$951$		−	4907.70i		−	0.167343i
$952$	−1310.53	−	2821.57i	−0.0446162	−	0.0960585i
$953$	−18646.7			−0.633815			−0.316908	−	0.948456i	$-0.602645\pi$
$953$	−18646.7			−0.633815			−0.316908	+	0.948456i	$0.602645\pi$
$954$	2413.60	+	960.269i	0.0819110	+	0.0325890i
$955$	−15243.7			−0.516519
$956$	−7211.60	+	7628.44i	−0.243975	+	0.258077i
$957$	−38344.6			−1.29520
$958$	28208.5	+	11223.0i	0.951332	+	0.378495i
$959$	−4650.38			−0.156589
$960$	−8794.81	−	7425.14i	−0.295678	−	0.249630i
$961$	−11859.2			−0.398080
$962$	11426.3	−	32849.8i	0.382950	−	1.10096i
$963$			6660.25i			0.222870i
$964$	19567.0	−	20698.0i	0.653745	−	0.691532i
$965$			13891.2i			0.463392i
$966$	2294.34	−	5766.72i	0.0764172	−	0.192072i
$967$		−	6736.17i		−	0.224013i	−0.993707	−	0.112007i	$-0.964272\pi$
$967$		−	6736.17i		−	0.224013i	0.993707	−	0.112007i	$-0.0357278\pi$
$968$	79229.7	−	36799.7i	2.63072	−	1.22189i
$969$			5346.33i			0.177243i
$970$	34155.7	+	13589.1i	1.13059	+	0.449815i
$971$		−	4629.21i		−	0.152995i	−0.997070	−	0.0764977i	$-0.975626\pi$
$971$		−	4629.21i		−	0.152995i	0.997070	−	0.0764977i	$-0.0243738\pi$
$972$	1335.48	−	1412.67i	0.0440694	−	0.0466167i
$973$	−16854.9			−0.555339
$974$	3655.22	+	1454.26i	0.120247	+	0.0478413i
$975$	425.003	+	9671.70i	0.0139600	+	0.317684i
$976$	−56017.8	+	3149.42i	−1.83718	+	0.103289i
$977$			22621.5i			0.740764i	0.928879	+	0.370382i	$0.120773\pi$
$977$			22621.5i			0.740764i	−0.928879	+	0.370382i	$0.879227\pi$
$978$	9062.57	+	3605.62i	0.296308	+	0.117888i
$979$		−	19391.6i		−	0.633052i
$980$	10771.6	+	10183.0i	0.351107	+	0.331922i
$981$	−9575.98			−0.311659
$982$	−36679.0	−	14593.0i	−1.19193	−	0.474219i
$983$		−	48294.1i		−	1.56698i	−0.621404	−	0.783491i	$-0.713437\pi$
$983$		−	48294.1i		−	1.56698i	0.621404	−	0.783491i	$-0.286563\pi$
$984$	23151.5	−	10753.2i	0.750045	−	0.348373i
$985$	3728.08			0.120596
$986$	−6550.83	−	2606.30i	−0.211583	−	0.0841800i
$987$			123.703i			0.00398936i
$988$	35959.0	+	31121.1i	1.15790	+	1.00212i
$989$		−	13412.5i		−	0.431236i
$990$	−5081.01	+	12770.9i	−0.163116	+	0.409986i
$991$	24859.7			0.796866			0.398433	−	0.917197i	$-0.369554\pi$
$991$	24859.7			0.796866			0.398433	+	0.917197i	$0.369554\pi$
$992$	11708.6	−	35038.6i	0.374745	−	1.12145i
$993$		−	22764.7i		−	0.727508i
$994$	−5897.61	+	14823.4i	−0.188190	+	0.473008i
$995$	23084.7			0.735511
$996$	17934.6	−	18971.3i	0.570563	−	0.603542i
$997$		−	45423.7i		−	1.44291i	−0.692460	−	0.721456i	$-0.743473\pi$
$997$		−	45423.7i		−	1.44291i	0.692460	−	0.721456i	$-0.256527\pi$
$998$	−4889.64	+	12289.9i	−0.155089	+	0.389810i
$999$		−	7083.32i		−	0.224331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.4.m.a.181.32	yes	84
4.3	odd	2		1248.4.m.a.337.41		84
8.3	odd	2		1248.4.m.a.337.44		84
8.5	even	2	inner	312.4.m.a.181.54	yes	84
13.12	even	2	inner	312.4.m.a.181.53	yes	84
52.51	odd	2		1248.4.m.a.337.42		84
104.51	odd	2		1248.4.m.a.337.43		84
104.77	even	2	inner	312.4.m.a.181.31	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.4.m.a.181.31	✓	84	104.77	even	2	inner
312.4.m.a.181.32	yes	84	1.1	even	1	trivial
312.4.m.a.181.53	yes	84	13.12	even	2	inner
312.4.m.a.181.54	yes	84	8.5	even	2	inner
1248.4.m.a.337.41		84	4.3	odd	2
1248.4.m.a.337.42		84	52.51	odd	2
1248.4.m.a.337.43		84	104.51	odd	2
1248.4.m.a.337.44		84	8.3	odd	2

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04560 + 2.62807i) q^{2} +3.00000i q^{3} +(-5.81346 - 5.49579i) q^{4} -7.49353 q^{5} +(-7.88420 - 3.13679i) q^{6} -9.78456i q^{7} +(20.5218 - 9.53176i) q^{8} -9.00000 q^{9} +(7.83521 - 19.6935i) q^{10} +72.0538 q^{11} +(16.4874 - 17.4404i) q^{12} +(-46.8270 + 2.05771i) q^{13} +(25.7145 + 10.2307i) q^{14} -22.4806i q^{15} +(3.59252 + 63.8991i) q^{16} +14.0519 q^{17} +(9.41037 - 23.6526i) q^{18} +126.824 q^{19} +(43.5633 + 41.1829i) q^{20} +29.3537 q^{21} +(-75.3392 + 189.362i) q^{22} -74.7533 q^{23} +(28.5953 + 61.5655i) q^{24} -68.8471 q^{25} +(43.5543 - 125.216i) q^{26} -27.0000i q^{27} +(-53.7739 + 56.8821i) q^{28} +177.389i q^{29} +(59.0804 + 23.5056i) q^{30} +204.084i q^{31} +(-171.687 - 57.3713i) q^{32} +216.161i q^{33} +(-14.6926 + 36.9292i) q^{34} +73.3208i q^{35} +(52.3211 + 49.4621i) q^{36} +262.345 q^{37} +(-132.606 + 333.301i) q^{38} +(-6.17314 - 140.481i) q^{39} +(-153.781 + 71.4265i) q^{40} -376.047i q^{41} +(-30.6921 + 77.1434i) q^{42} +179.424i q^{43} +(-418.882 - 395.993i) q^{44} +67.4417 q^{45} +(78.1618 - 196.457i) q^{46} +4.21422i q^{47} +(-191.697 + 10.7776i) q^{48} +247.262 q^{49} +(71.9863 - 180.935i) q^{50} +42.1556i q^{51} +(283.535 + 245.389i) q^{52} +102.044i q^{53} +(70.9578 + 28.2311i) q^{54} -539.937 q^{55} +(-93.2640 - 200.797i) q^{56} +380.471i q^{57} +(-466.189 - 185.477i) q^{58} +231.843 q^{59} +(-123.549 + 130.690i) q^{60} +876.661i q^{61} +(-536.346 - 213.389i) q^{62} +88.0610i q^{63} +(330.291 - 391.218i) q^{64} +(350.899 - 15.4195i) q^{65} +(-568.086 - 226.018i) q^{66} -597.074 q^{67} +(-81.6899 - 77.2262i) q^{68} -224.260i q^{69} +(-192.692 - 76.6640i) q^{70} +576.462i q^{71} +(-184.696 + 85.7858i) q^{72} +657.628i q^{73} +(-274.307 + 689.461i) q^{74} -206.541i q^{75} +(-737.284 - 696.996i) q^{76} -705.014i q^{77} +(375.648 + 130.663i) q^{78} -137.370 q^{79} +(-26.9206 - 478.829i) q^{80} +81.0000 q^{81} +(988.277 + 393.194i) q^{82} +1087.78 q^{83} +(-170.646 - 161.322i) q^{84} -105.298 q^{85} +(-471.537 - 187.605i) q^{86} -532.166 q^{87} +(1478.68 - 686.799i) q^{88} -269.127i q^{89} +(-70.5169 + 177.241i) q^{90} +(20.1338 + 458.181i) q^{91} +(434.575 + 410.829i) q^{92} -612.251 q^{93} +(-11.0752 - 4.40637i) q^{94} -950.356 q^{95} +(172.114 - 515.062i) q^{96} +1734.37i q^{97} +(-258.537 + 649.822i) q^{98} -648.484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Introduction

L-functions

Modular forms

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