LMFDB - Embedded newform 76.5.j.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	76.33
Dual form			76.5.j.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.693233 + 0.122236i) q^{3} +(-24.2132 - 20.3173i) q^{5} +(32.5833 + 56.4359i) q^{7} +(-75.6495 - 27.5342i) q^{9} +O(q^{10})$	\(q+(0.693233 + 0.122236i) q^{3} +(-24.2132 - 20.3173i) q^{5} +(32.5833 + 56.4359i) q^{7} +(-75.6495 - 27.5342i) q^{9} +(-96.0822 + 166.419i) q^{11} +(-85.9617 + 15.1574i) q^{13} +(-14.3019 - 17.0443i) q^{15} +(-103.134 + 37.5377i) q^{17} +(-84.7252 - 350.917i) q^{19} +(15.6893 + 43.1061i) q^{21} +(-676.013 + 567.242i) q^{23} +(64.9565 + 368.387i) q^{25} +(-98.4562 - 56.8437i) q^{27} +(-495.669 + 1361.84i) q^{29} +(1387.38 - 801.005i) q^{31} +(-86.9497 + 103.623i) q^{33} +(357.679 - 2028.50i) q^{35} -2397.08i q^{37} -61.4442 q^{39} +(2312.10 + 407.686i) q^{41} +(175.985 + 147.669i) q^{43} +(1272.30 + 2203.68i) q^{45} +(344.708 + 125.464i) q^{47} +(-922.842 + 1598.41i) q^{49} +(-76.0843 + 13.4157i) q^{51} +(-2078.65 - 2477.24i) q^{53} +(5707.64 - 2077.41i) q^{55} +(-15.8397 - 253.624i) q^{57} +(-624.116 - 1714.75i) q^{59} +(-2111.67 + 1771.90i) q^{61} +(-910.993 - 5166.50i) q^{63} +(2389.36 + 1379.50i) q^{65} +(-2010.34 + 5523.36i) q^{67} +(-537.972 + 310.598i) q^{69} +(876.187 - 1044.20i) q^{71} +(-985.246 + 5587.61i) q^{73} +263.318i q^{75} -12522.7 q^{77} +(-4620.95 - 814.799i) q^{79} +(4933.97 + 4140.09i) q^{81} +(-375.320 - 650.073i) q^{83} +(3259.87 + 1186.49i) q^{85} +(-510.079 + 883.483i) q^{87} +(-7669.75 + 1352.38i) q^{89} +(-3656.33 - 4357.45i) q^{91} +(1059.69 - 385.695i) q^{93} +(-5078.21 + 10218.2i) q^{95} +(2188.55 + 6012.99i) q^{97} +(11850.8 - 9943.99i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$1$

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
$3$	0.693233	+	0.122236i	0.0770259	+	0.0135817i	0.212028	−	0.977264i	$-0.431993\pi$
$3$	0.693233	+	0.122236i	0.0770259	+	0.0135817i	−0.135002	+	0.990845i	$0.543104\pi$
$4$		0			0
$5$	−24.2132	−	20.3173i	−0.968527	−	0.812691i	0.0137919	−	0.999905i	$-0.495610\pi$
$5$	−24.2132	−	20.3173i	−0.968527	−	0.812691i	−0.982319	+	0.187214i	$0.940054\pi$
$6$		0			0
$7$	32.5833	+	56.4359i	0.664965	+	1.15175i	0.979295	+	0.202439i	$0.0648869\pi$
$7$	32.5833	+	56.4359i	0.664965	+	1.15175i	−0.314330	+	0.949314i	$0.601780\pi$
$8$		0			0
$9$	−75.6495	−	27.5342i	−0.933944	−	0.339928i
$10$		0			0
$11$	−96.0822	+	166.419i	−0.794068	+	1.37537i	0.129362	+	0.991597i	$0.458707\pi$
$11$	−96.0822	+	166.419i	−0.794068	+	1.37537i	−0.923429	+	0.383768i	$0.874626\pi$
$12$		0			0
$13$	−85.9617	+	15.1574i	−0.508649	+	0.0896885i	−0.422082	−	0.906558i	$-0.638701\pi$
$13$	−85.9617	+	15.1574i	−0.508649	+	0.0896885i	−0.0865667	+	0.996246i	$0.527590\pi$
$14$		0			0
$15$	−14.3019	−	17.0443i	−0.0635639	−	0.0757525i
$16$		0			0
$17$	−103.134	+	37.5377i	−0.356865	+	0.129888i	−0.514230	−	0.857652i	$-0.671922\pi$
$17$	−103.134	+	37.5377i	−0.356865	+	0.129888i	0.157365	+	0.987540i	$0.449700\pi$
$18$		0			0
$19$	−84.7252	−	350.917i	−0.234696	−	0.972069i
$19$	−84.7252	−	350.917i	−0.234696	−	0.972069i
$20$		0			0
$21$	15.6893	+	43.1061i	0.0355767	+	0.0977462i
$22$		0			0
$23$	−676.013	+	567.242i	−1.27791	+	1.07229i	−0.284379	+	0.958712i	$0.591787\pi$
$23$	−676.013	+	567.242i	−1.27791	+	1.07229i	−0.993529	+	0.113580i	$0.963768\pi$
$24$		0			0
$25$	64.9565	+	368.387i	0.103930	+	0.589419i
$26$		0			0
$27$	−98.4562	−	56.8437i	−0.135056	−	0.0779749i
$28$		0			0
$29$	−495.669	+	1361.84i	−0.589380	+	1.61931i	0.182260	+	0.983250i	$0.441659\pi$
$29$	−495.669	+	1361.84i	−0.589380	+	1.61931i	−0.771640	+	0.636059i	$0.780564\pi$
$30$		0			0
$31$	1387.38	−	801.005i	1.44368	−	0.833512i	0.445592	−	0.895236i	$-0.352993\pi$
$31$	1387.38	−	801.005i	1.44368	−	0.833512i	0.998093	+	0.0617246i	$0.0196601\pi$
$32$		0			0
$33$	−86.9497	+	103.623i	−0.0798436	+	0.0951539i
$34$		0			0
$35$	357.679	−	2028.50i	0.291983	−	1.65592i
$36$		0			0
$37$		−	2397.08i		−	1.75097i	−0.483245	−	0.875485i	$-0.660542\pi$
$37$		−	2397.08i		−	1.75097i	0.483245	−	0.875485i	$-0.339458\pi$
$38$		0			0
$39$	−61.4442			−0.0403973
$40$		0			0
$41$	2312.10	+	407.686i	1.37543	+	0.242526i	0.812010	−	0.583643i	$-0.198373\pi$
$41$	2312.10	+	407.686i	1.37543	+	0.242526i	0.563422	+	0.826169i	$0.309485\pi$
$42$		0			0
$43$	175.985	+	147.669i	0.0951785	+	0.0798642i	0.689135	−	0.724633i	$-0.257991\pi$
$43$	175.985	+	147.669i	0.0951785	+	0.0798642i	−0.593957	+	0.804497i	$0.702435\pi$
$44$		0			0
$45$	1272.30	+	2203.68i	0.628294	+	1.08824i
$46$		0			0
$47$	344.708	+	125.464i	0.156047	+	0.0567966i	0.418863	−	0.908050i	$-0.362429\pi$
$47$	344.708	+	125.464i	0.156047	+	0.0567966i	−0.262816	+	0.964846i	$0.584651\pi$
$48$		0			0
$49$	−922.842	+	1598.41i	−0.384357	+	0.665726i
$50$		0			0
$51$	−76.0843	+	13.4157i	−0.0292519	+	0.00515791i
$52$		0			0
$53$	−2078.65	−	2477.24i	−0.739996	−	0.881892i	0.256413	−	0.966567i	$-0.417459\pi$
$53$	−2078.65	−	2477.24i	−0.739996	−	0.881892i	−0.996409	+	0.0846749i	$0.973015\pi$
$54$		0			0
$55$	5707.64	−	2077.41i	1.88682	−	0.686748i
$56$		0			0
$57$	−15.8397	−	253.624i	−0.00487526	−	0.0780620i
$58$		0			0
$59$	−624.116	−	1714.75i	−0.179292	−	0.492602i	0.817194	−	0.576363i	$-0.195529\pi$
$59$	−624.116	−	1714.75i	−0.179292	−	0.492602i	−0.996486	+	0.0837619i	$0.973306\pi$
$60$		0			0
$61$	−2111.67	+	1771.90i	−0.567502	+	0.476191i	−0.880816	−	0.473459i	$-0.843005\pi$
$61$	−2111.67	+	1771.90i	−0.567502	+	0.476191i	0.313314	+	0.949650i	$0.398561\pi$
$62$		0			0
$63$	−910.993	−	5166.50i	−0.229527	−	1.30171i
$64$		0			0
$65$	2389.36	+	1379.50i	0.565529	+	0.326509i
$66$		0			0
$67$	−2010.34	+	5523.36i	−0.447837	+	1.23042i	0.486390	+	0.873742i	$0.338313\pi$
$67$	−2010.34	+	5523.36i	−0.447837	+	1.23042i	−0.934227	+	0.356680i	$0.883909\pi$
$68$		0			0
$69$	−537.972	+	310.598i	−0.112996	+	0.0652380i
$70$		0			0
$71$	876.187	−	1044.20i	0.173812	−	0.207141i	−0.672105	−	0.740456i	$-0.734609\pi$
$71$	876.187	−	1044.20i	0.173812	−	0.207141i	0.845917	+	0.533315i	$0.179054\pi$
$72$		0			0
$73$	−985.246	+	5587.61i	−0.184884	+	1.04853i	0.741221	+	0.671261i	$0.234247\pi$
$73$	−985.246	+	5587.61i	−0.184884	+	1.04853i	−0.926105	+	0.377267i	$0.876864\pi$
$74$		0			0
$75$			263.318i			0.0468121i
$76$		0			0
$77$	−12522.7			−2.11211
$78$		0			0
$79$	−4620.95	−	814.799i	−0.740419	−	0.130556i	−0.209298	−	0.977852i	$-0.567118\pi$
$79$	−4620.95	−	814.799i	−0.740419	−	0.130556i	−0.531121	+	0.847296i	$0.678229\pi$
$80$		0			0
$81$	4933.97	+	4140.09i	0.752014	+	0.631015i
$82$		0			0
$83$	−375.320	−	650.073i	−0.0544810	−	0.0943639i	0.837499	−	0.546439i	$-0.184017\pi$
$83$	−375.320	−	650.073i	−0.0544810	−	0.0943639i	−0.891980	+	0.452075i	$0.850684\pi$
$84$		0			0
$85$	3259.87	+	1186.49i	0.451192	+	0.164221i
$86$		0			0
$87$	−510.079	+	883.483i	−0.0673906	+	0.116724i
$88$		0			0
$89$	−7669.75	+	1352.38i	−0.968281	+	0.170734i	−0.635356	−	0.772219i	$-0.719147\pi$
$89$	−7669.75	+	1352.38i	−0.968281	+	0.170734i	−0.332925	+	0.942953i	$0.608036\pi$
$90$		0			0
$91$	−3656.33	−	4357.45i	−0.441533	−	0.526198i
$92$		0			0
$93$	1059.69	−	385.695i	0.122522	−	0.0445942i
$94$		0			0
$95$	−5078.21	+	10218.2i	−0.562682	+	1.13221i
$96$		0			0
$97$	2188.55	+	6012.99i	0.232602	+	0.639068i	0.999998	−	0.00210552i	$-0.000670207\pi$
$97$	2188.55	+	6012.99i	0.232602	+	0.639068i	−0.767396	+	0.641173i	$0.778448\pi$
$98$		0			0
$99$	11850.8	−	9943.99i	1.20914	−	1.01459i
$100$		0			0
$101$	−683.910	−	3878.65i	−0.0670435	−	0.380222i	−0.999805	−	0.0197293i	$-0.993720\pi$
$101$	−683.910	−	3878.65i	−0.0670435	−	0.380222i	0.932762	−	0.360493i	$-0.117392\pi$
$102$		0			0
$103$	−10478.4	−	6049.68i	−0.987685	−	0.570240i	−0.0831035	−	0.996541i	$-0.526483\pi$
$103$	−10478.4	−	6049.68i	−0.987685	−	0.570240i	−0.904582	+	0.426301i	$0.859817\pi$
$104$		0			0
$105$	495.909	−	1362.50i	0.0449804	−	0.123583i
$106$		0			0
$107$	−66.4411	+	38.3598i	−0.00580322	+	0.00335049i	−0.502899	−	0.864345i	$-0.667733\pi$
$107$	−66.4411	+	38.3598i	−0.00580322	+	0.00335049i	0.497096	+	0.867696i	$0.334400\pi$
$108$		0			0
$109$	4428.59	−	5277.79i	0.372746	−	0.444221i	−0.546765	−	0.837286i	$-0.684141\pi$
$109$	4428.59	−	5277.79i	0.372746	−	0.444221i	0.919511	+	0.393065i	$0.128585\pi$
$110$		0			0
$111$	293.008	−	1661.73i	0.0237812	−	0.134870i
$112$		0			0
$113$			18412.6i			1.44197i	0.692948	+	0.720987i	$0.256311\pi$
$113$			18412.6i			1.44197i	−0.692948	+	0.720987i	$0.743689\pi$
$114$		0			0
$115$	27893.2			2.10913
$116$		0			0
$117$	6920.30	+	1220.24i	0.505537	+	0.0891399i
$118$		0			0
$119$	−5478.92	−	4597.36i	−0.386902	−	0.324649i
$120$		0			0
$121$	−11143.1	−	19300.4i	−0.761087	−	1.31824i
$122$		0			0
$123$	1552.99	+	565.243i	0.102650	+	0.0373615i
$124$		0			0
$125$	−3965.71	+	6868.81i	−0.253805	+	0.439604i
$126$		0			0
$127$	9768.85	−	1722.51i	0.605670	−	0.106796i	0.137601	−	0.990488i	$-0.456061\pi$
$127$	9768.85	−	1722.51i	0.605670	−	0.106796i	0.468069	+	0.883692i	$0.344950\pi$
$128$		0			0
$129$	103.948	+	123.881i	0.00624651	+	0.00744430i
$130$		0			0
$131$	−6000.91	+	2184.15i	−0.349683	+	0.127274i	−0.510889	−	0.859647i	$-0.670684\pi$
$131$	−6000.91	+	2184.15i	−0.349683	+	0.127274i	0.161206	+	0.986921i	$0.448462\pi$
$132$		0			0
$133$	17043.7	−	16215.6i	0.963519	−	0.916703i
$134$		0			0
$135$	1229.03	+	3376.73i	0.0674364	+	0.185280i
$136$		0			0
$137$	3234.82	−	2714.34i	0.172349	−	0.144618i	−0.552533	−	0.833491i	$-0.686339\pi$
$137$	3234.82	−	2714.34i	0.172349	−	0.144618i	0.724882	+	0.688873i	$0.241894\pi$
$138$		0			0
$139$	2765.31	+	15682.9i	0.143125	+	0.811700i	0.968854	+	0.247634i	$0.0796529\pi$
$139$	2765.31	+	15682.9i	0.143125	+	0.811700i	−0.825729	+	0.564067i	$0.809236\pi$
$140$		0			0
$141$	223.627	+	129.111i	0.0112483	+	0.00649420i
$142$		0			0
$143$	5736.91	−	15762.0i	0.280547	−	0.770797i
$144$		0			0
$145$	39670.6	−	22903.8i	1.88683	−	1.08936i
$146$		0			0
$147$	−835.127	+	995.265i	−0.0386472	+	0.0460579i
$148$		0			0
$149$	2527.38	−	14333.5i	0.113841	−	0.645622i	−0.873477	−	0.486865i	$-0.838140\pi$
$149$	2527.38	−	14333.5i	0.113841	−	0.645622i	0.987318	−	0.158757i	$-0.0507486\pi$
$150$		0			0
$151$			29961.2i			1.31403i	0.753878	+	0.657014i	$0.228181\pi$
$151$			29961.2i			1.31403i	−0.753878	+	0.657014i	$0.771819\pi$
$152$		0			0
$153$	8835.60			0.377445
$154$		0			0
$155$	−49867.1	−	8792.92i	−2.07564	−	0.365991i
$156$		0			0
$157$	9032.84	+	7579.45i	0.366459	+	0.307495i	0.807359	−	0.590061i	$-0.200896\pi$
$157$	9032.84	+	7579.45i	0.366459	+	0.307495i	−0.440900	+	0.897556i	$0.645341\pi$
$158$		0			0
$159$	−1138.18	−	1971.39i	−0.0450212	−	0.0779790i
$160$		0			0
$161$	−54039.6	−	19668.8i	−2.08478	−	0.758798i
$162$		0			0
$163$	−2502.29	+	4334.09i	−0.0941807	+	0.163126i	−0.909266	−	0.416215i	$-0.863356\pi$
$163$	−2502.29	+	4334.09i	−0.0941807	+	0.163126i	0.815086	+	0.579340i	$0.196690\pi$
$164$		0			0
$165$	4210.66	−	742.453i	0.154661	−	0.0272710i
$166$		0			0
$167$	24384.0	+	29059.7i	0.874323	+	1.04198i	0.998762	+	0.0497499i	$0.0158424\pi$
$167$	24384.0	+	29059.7i	0.874323	+	1.04198i	−0.124439	+	0.992227i	$0.539713\pi$
$168$		0			0
$169$	−19678.9	+	7162.53i	−0.689013	+	0.250780i
$170$		0			0
$171$	−3252.79	+	28879.5i	−0.111241	+	0.987638i
$172$		0			0
$173$	1148.94	+	3156.69i	0.0383889	+	0.105473i	0.957406	−	0.288745i	$-0.0932379\pi$
$173$	1148.94	+	3156.69i	0.0383889	+	0.105473i	−0.919017	+	0.394217i	$0.871016\pi$
$174$		0			0
$175$	−18673.7	+	15669.1i	−0.609755	+	0.511645i
$176$		0			0
$177$	−223.055	−	1265.01i	−0.00711976	−	0.0403782i
$178$		0			0
$179$	4338.08	+	2504.59i	0.135392	+	0.0781684i	0.566166	−	0.824291i	$-0.308426\pi$
$179$	4338.08	+	2504.59i	0.135392	+	0.0781684i	−0.430774	+	0.902460i	$0.641759\pi$
$180$		0			0
$181$	4371.44	−	12010.4i	0.133434	−	0.366608i	−0.854924	−	0.518754i	$-0.826396\pi$
$181$	4371.44	−	12010.4i	0.133434	−	0.366608i	0.988358	+	0.152146i	$0.0486184\pi$
$182$		0			0
$183$	−1680.47	+	970.221i	−0.0501798	+	0.0289713i
$184$		0			0
$185$	−48702.1	+	58040.9i	−1.42300	+	1.69586i
$186$		0			0
$187$	3662.34	−	20770.2i	0.104731	−	0.593960i
$188$		0			0
$189$		−	7408.62i		−	0.207402i
$190$		0			0
$191$	17413.4			0.477327			0.238664	−	0.971102i	$-0.423291\pi$
$191$	17413.4			0.477327			0.238664	+	0.971102i	$0.423291\pi$
$192$		0			0
$193$	30690.7	+	5411.60i	0.823933	+	0.145282i	0.569691	−	0.821859i	$-0.307063\pi$
$193$	30690.7	+	5411.60i	0.823933	+	0.145282i	0.254242	+	0.967141i	$0.418174\pi$
$194$		0			0
$195$	1487.76	+	1248.38i	0.0391258	+	0.0328305i
$196$		0			0
$197$	−23799.8	−	41222.5i	−0.613255	−	1.06219i	−0.990688	−	0.136152i	$-0.956526\pi$
$197$	−23799.8	−	41222.5i	−0.613255	−	1.06219i	0.377433	−	0.926037i	$-0.376807\pi$
$198$		0			0
$199$	−49214.5	−	17912.6i	−1.24276	−	0.452327i	−0.364810	−	0.931082i	$-0.618866\pi$
$199$	−49214.5	−	17912.6i	−1.24276	−	0.452327i	−0.877948	+	0.478755i	$0.841088\pi$
$200$		0			0
$201$	−2068.78	+	3583.24i	−0.0512063	+	0.0886919i
$202$		0			0
$203$	−93007.2	+	16399.7i	−2.25696	+	0.397963i
$204$		0			0
$205$	−47700.3	−	56847.0i	−1.13505	−	1.35269i
$206$		0			0
$207$	66758.6	−	24298.1i	1.55800	−	0.567064i
$208$		0			0
$209$	66539.9	+	19617.0i	1.52331	+	0.449096i
$210$		0			0
$211$	15504.7	+	42598.8i	0.348255	+	0.956824i	0.982920	+	0.184036i	$0.0589163\pi$
$211$	15504.7	+	42598.8i	0.348255	+	0.956824i	−0.634664	+	0.772788i	$0.718862\pi$
$212$		0			0
$213$	735.040	−	616.772i	0.0162014	−	0.0135946i
$214$		0			0
$215$	−1260.93	−	7151.07i	−0.0272780	−	0.154701i
$216$		0			0
$217$	90410.9	+	52198.7i	1.92000	+	1.10851i
$218$		0			0
$219$	−1366.01	+	3753.08i	−0.0284817	+	0.0782528i
$220$		0			0
$221$	8296.60	−	4790.04i	0.169870	−	0.0980742i
$222$		0			0
$223$	−30355.7	+	36176.5i	−0.610422	+	0.727473i	−0.979392	−	0.201969i	$-0.935266\pi$
$223$	−30355.7	+	36176.5i	−0.610422	+	0.727473i	0.368970	+	0.929441i	$0.379711\pi$
$224$		0			0
$225$	5229.29	−	29656.8i	0.103295	−	0.585813i
$226$		0			0
$227$			12826.9i			0.248926i	0.992224	+	0.124463i	$0.0397207\pi$
$227$			12826.9i			0.248926i	−0.992224	+	0.124463i	$0.960279\pi$
$228$		0			0
$229$	−70554.2			−1.34540			−0.672701	−	0.739915i	$-0.734866\pi$
$229$	−70554.2			−1.34540			−0.672701	+	0.739915i	$0.734866\pi$
$230$		0			0
$231$	−8681.15	−	1530.72i	−0.162687	−	0.0286861i
$232$		0			0
$233$	17559.4	+	14734.1i	0.323443	+	0.271401i	0.790022	−	0.613079i	$-0.210069\pi$
$233$	17559.4	+	14734.1i	0.323443	+	0.271401i	−0.466579	+	0.884480i	$0.654514\pi$
$234$		0			0
$235$	−5797.41	−	10041.4i	−0.104978	−	0.181827i
$236$		0			0
$237$	−3103.80	−	1129.69i	−0.0552582	−	0.0201124i
$238$		0			0
$239$	21648.2	−	37495.7i	0.378988	−	0.656426i	−0.611927	−	0.790914i	$-0.709606\pi$
$239$	21648.2	−	37495.7i	0.378988	−	0.656426i	0.990915	+	0.134488i	$0.0429388\pi$
$240$		0			0
$241$	38715.2	−	6826.54i	0.666573	−	0.117535i	0.169885	−	0.985464i	$-0.445660\pi$
$241$	38715.2	−	6826.54i	0.666573	−	0.117535i	0.496688	+	0.867929i	$0.334549\pi$
$242$		0			0
$243$	8833.55	+	10527.4i	0.149597	+	0.178283i
$244$		0			0
$245$	54820.2	−	19952.9i	0.913290	−	0.332410i
$246$		0			0
$247$	12602.1	+	28881.2i	0.206561	+	0.473392i
$248$		0			0
$249$	−180.722	−	496.529i	−0.00291482	−	0.00800841i
$250$		0			0
$251$	48070.5	−	40336.0i	0.763012	−	0.640243i	−0.175897	−	0.984409i	$-0.556282\pi$
$251$	48070.5	−	40336.0i	0.763012	−	0.640243i	0.938909	+	0.344165i	$0.111838\pi$
$252$		0			0
$253$	−29447.2	−	167003.i	−0.460048	−	2.60906i
$254$		0			0
$255$	2114.81	+	1220.99i	0.0325231	+	0.0187772i
$256$		0			0
$257$	−27288.3	+	74974.0i	−0.413152	+	1.13513i	0.542352	+	0.840151i	$0.317534\pi$
$257$	−27288.3	+	74974.0i	−0.413152	+	1.13513i	−0.955505	+	0.294976i	$0.904688\pi$
$258$		0			0
$259$	135281.	−	78104.7i	2.01669	−	1.16433i
$260$		0			0
$261$	74994.2	−	89374.6i	1.10090	−	1.31200i
$262$		0			0
$263$	9564.63	−	54243.7i	0.138279	−	0.784220i	−0.834241	−	0.551400i	$-0.814094\pi$
$263$	9564.63	−	54243.7i	0.138279	−	0.784220i	0.972520	−	0.232819i	$-0.0747951\pi$
$264$		0			0
$265$			102214.i			1.45552i
$266$		0			0
$267$	−5482.24			−0.0769016
$268$		0			0
$269$	−31645.8	−	5580.00i	−0.437332	−	0.0771134i	−0.0493523	−	0.998781i	$-0.515716\pi$
$269$	−31645.8	−	5580.00i	−0.437332	−	0.0771134i	−0.387979	+	0.921668i	$0.626827\pi$
$270$		0			0
$271$	40261.4	+	33783.3i	0.548214	+	0.460006i	0.874336	−	0.485321i	$-0.161297\pi$
$271$	40261.4	+	33783.3i	0.548214	+	0.460006i	−0.326121	+	0.945328i	$0.605742\pi$
$272$		0			0
$273$	−2002.06	−	3467.66i	−0.0268628	−	0.0465277i
$274$		0			0
$275$	−67547.8	−	24585.4i	−0.893194	−	0.325096i
$276$		0			0
$277$	−64329.5	+	111422.i	−0.838399	+	1.45215i	0.0528337	+	0.998603i	$0.483175\pi$
$277$	−64329.5	+	111422.i	−0.838399	+	1.45215i	−0.891233	+	0.453546i	$0.850159\pi$
$278$		0			0
$279$	−127010.	+	22395.2i	−1.63165	+	0.287705i
$280$		0			0
$281$	18278.5	+	21783.4i	0.231487	+	0.275876i	0.869267	−	0.494343i	$-0.164591\pi$
$281$	18278.5	+	21783.4i	0.231487	+	0.275876i	−0.637780	+	0.770219i	$0.720147\pi$
$282$		0			0
$283$	105516.	−	38404.9i	1.31749	−	0.479527i	0.414837	−	0.909896i	$-0.363839\pi$
$283$	105516.	−	38404.9i	1.31749	−	0.479527i	0.902653	+	0.430369i	$0.141616\pi$
$284$		0			0
$285$	−4769.41	+	6462.85i	−0.0587185	+	0.0795673i
$286$		0			0
$287$	52327.7	+	143769.i	0.635284	+	1.74543i
$288$		0			0
$289$	−54753.3	+	45943.4i	−0.655563	+	0.550082i
$290$		0			0
$291$	782.172	+	4435.92i	0.00923669	+	0.0523839i
$292$		0			0
$293$	−115335.	−	66588.6i	−1.34346	−	0.775647i	−0.356147	−	0.934430i	$-0.615910\pi$
$293$	−115335.	−	66588.6i	−1.34346	−	0.775647i	−0.987314	+	0.158782i	$0.949243\pi$
$294$		0			0
$295$	−19727.1	+	54199.8i	−0.226683	+	0.622807i
$296$		0			0
$297$	18919.8	−	10923.3i	0.214488	−	0.123835i
$298$		0			0
$299$	49513.3	−	59007.7i	0.553834	−	0.660034i
$300$		0			0
$301$	−2599.66	+	14743.4i	−0.0286935	+	0.162729i
$302$		0			0
$303$		−	2772.41i		−	0.0301975i
$304$		0			0
$305$	87130.6			0.936637
$306$		0			0
$307$	−5220.79	−	920.566i	−0.0553936	−	0.00976738i	0.145883	−	0.989302i	$-0.453398\pi$
$307$	−5220.79	−	920.566i	−0.0553936	−	0.00976738i	−0.201276	+	0.979535i	$0.564509\pi$
$308$		0			0
$309$	−6524.45	−	5474.66i	−0.0683324	−	0.0573377i
$310$		0			0
$311$	−74776.9	−	129517.i	−0.773120	−	1.33908i	−0.935845	−	0.352411i	$-0.885362\pi$
$311$	−74776.9	−	129517.i	−0.773120	−	1.33908i	0.162725	−	0.986671i	$-0.447972\pi$
$312$		0			0
$313$	30999.8	+	11283.0i	0.316424	+	0.115169i	0.495350	−	0.868694i	$-0.335040\pi$
$313$	30999.8	+	11283.0i	0.316424	+	0.115169i	−0.178926	+	0.983863i	$0.557262\pi$
$314$		0			0
$315$	−82911.1	+	143606.i	−0.835587	+	1.44728i
$316$		0			0
$317$	−407.501	+	71.8534i	−0.00405518	+	0.000715038i	−0.175675	−	0.984448i	$-0.556211\pi$
$317$	−407.501	+	71.8534i	−0.00405518	+	0.000715038i	0.171620	+	0.985163i	$0.445100\pi$
$318$		0			0
$319$	−179011.	−	213337.i	−1.75913	−	2.09646i
$320$		0			0
$321$	−50.7481	+	18.4708i	−0.000492504	+	0.000179257i
$322$		0			0
$323$	21910.7	+	33011.1i	0.210015	+	0.316413i
$324$		0			0
$325$	−11167.5	−	30682.6i	−0.105728	−	0.290486i
$326$		0			0
$327$	3715.18	−	3117.41i	0.0347444	−	0.0291540i
$328$		0			0
$329$	4151.08	+	23541.9i	0.0383504	+	0.217496i
$330$		0			0
$331$	−114465.	−	66086.3i	−1.04476	−	0.603191i	−0.123581	−	0.992335i	$-0.539438\pi$
$331$	−114465.	−	66086.3i	−1.04476	−	0.603191i	−0.921177	+	0.389143i	$0.872771\pi$
$332$		0			0
$333$	−66001.5	+	181338.i	−0.595204	+	1.63531i
$334$		0			0
$335$	160896.	−	92893.5i	1.43369	−	0.827744i
$336$		0			0
$337$	−111287.	+	132626.i	−0.979905	+	1.16780i	0.00591259	+	0.999983i	$0.498118\pi$
$337$	−111287.	+	132626.i	−0.979905	+	1.16780i	−0.985817	+	0.167822i	$0.946326\pi$
$338$		0			0
$339$	−2250.67	+	12764.2i	−0.0195845	+	0.111069i
$340$		0			0
$341$			307849.i			2.64746i
$342$		0			0
$343$	36188.1			0.307594
$344$		0			0
$345$	19336.5	+	3409.55i	0.162458	+	0.0286457i
$346$		0			0
$347$	30558.2	+	25641.4i	0.253787	+	0.212953i	0.760801	−	0.648985i	$-0.224806\pi$
$347$	30558.2	+	25641.4i	0.253787	+	0.212953i	−0.507014	+	0.861938i	$0.669251\pi$
$348$		0			0
$349$	−50857.7	−	88088.0i	−0.417547	−	0.723213i	0.578145	−	0.815934i	$-0.303777\pi$
$349$	−50857.7	−	88088.0i	−0.417547	−	0.723213i	−0.995692	+	0.0927212i	$0.970443\pi$
$350$		0			0
$351$	9325.06	+	3394.04i	0.0756898	+	0.0275488i
$352$		0			0
$353$	−69157.7	+	119785.i	−0.554998	+	0.961284i	0.442906	+	0.896568i	$0.353947\pi$
$353$	−69157.7	+	119785.i	−0.554998	+	0.961284i	−0.997904	+	0.0647160i	$0.979386\pi$
$354$		0			0
$355$	−42430.5	+	7481.65i	−0.336684	+	0.0593664i
$356$		0			0
$357$	−3236.21	−	3856.76i	−0.0253922	−	0.0302612i
$358$		0			0
$359$	44126.7	−	16060.8i	0.342384	−	0.124617i	−0.165105	−	0.986276i	$-0.552796\pi$
$359$	44126.7	−	16060.8i	0.342384	−	0.124617i	0.507488	+	0.861659i	$0.330574\pi$
$360$		0			0
$361$	−115964.	+	59463.0i	−0.889836	+	0.456281i
$362$		0			0
$363$	−5365.55	−	14741.7i	−0.0407194	−	0.111876i
$364$		0			0
$365$	137381.	−	115276.i	1.03119	−	0.865275i
$366$		0			0
$367$	1580.16	+	8961.54i	0.0117319	+	0.0665351i	0.990112	−	0.140282i	$-0.0448008\pi$
$367$	1580.16	+	8961.54i	0.0117319	+	0.0665351i	−0.978380	+	0.206817i	$0.933690\pi$
$368$		0			0
$369$	−163684.	−	94503.0i	−1.20214	−	0.694053i
$370$		0			0
$371$	72075.9	−	198027.i	0.523651	−	1.43872i
$372$		0			0
$373$	190559.	−	110019.i	1.36966	−	0.790771i	0.378771	−	0.925490i	$-0.376347\pi$
$373$	190559.	−	110019.i	1.36966	−	0.790771i	0.990884	+	0.134719i	$0.0430133\pi$
$374$		0			0
$375$	−3588.77	+	4276.93i	−0.0255202	+	0.0304138i
$376$		0			0
$377$	21966.6	−	124579.i	0.154554	−	0.876521i
$378$		0			0
$379$			2519.18i			0.0175380i	0.999962	+	0.00876900i	$0.00279130\pi$
$379$			2519.18i			0.0175380i	−0.999962	+	0.00876900i	$0.997209\pi$
$380$		0			0
$381$	6982.64			0.0481027
$382$		0			0
$383$	−82852.9	−	14609.2i	−0.564820	−	0.0995930i	−0.116055	−	0.993243i	$-0.537025\pi$
$383$	−82852.9	−	14609.2i	−0.564820	−	0.0995930i	−0.448765	+	0.893650i	$0.648136\pi$
$384$		0			0
$385$	303214.	+	254427.i	2.04564	+	1.71649i
$386$		0			0
$387$	−9247.23	−	16016.7i	−0.0617433	−	0.106943i
$388$		0			0
$389$	−190672.	−	69399.0i	−1.26005	−	0.458621i	−0.376265	−	0.926512i	$-0.622792\pi$
$389$	−190672.	−	69399.0i	−1.26005	−	0.458621i	−0.883786	+	0.467891i	$0.845014\pi$
$390$		0			0
$391$	48427.0	−	83877.9i	0.316762	−	0.548649i
$392$		0			0
$393$	−4427.01	+	780.601i	−0.0286632	+	0.00505410i
$394$		0			0
$395$	95333.5	+	113614.i	0.611014	+	0.728179i
$396$		0			0
$397$	173205.	−	63041.5i	1.09896	−	0.399987i	0.272024	−	0.962290i	$-0.412307\pi$
$397$	173205.	−	63041.5i	1.09896	−	0.399987i	0.826931	+	0.562303i	$0.190085\pi$
$398$		0			0
$399$	13797.4	−	9157.82i	0.0866663	−	0.0575236i
$400$		0			0
$401$	−19800.2	−	54400.7i	−0.123135	−	0.338311i	0.862775	−	0.505588i	$-0.168725\pi$
$401$	−19800.2	−	54400.7i	−0.123135	−	0.338311i	−0.985910	+	0.167278i	$0.946502\pi$
$402$		0			0
$403$	−107120.	+	89884.8i	−0.659572	+	0.553447i
$404$		0			0
$405$	−35351.7	−	200489.i	−0.215526	−	1.22231i
$406$		0			0
$407$	398920.	+	230317.i	2.40822	+	1.39039i
$408$		0			0
$409$	15173.5	−	41688.8i	0.0907065	−	0.249214i	−0.886041	−	0.463607i	$-0.846555\pi$
$409$	15173.5	−	41688.8i	0.0907065	−	0.249214i	0.976748	+	0.214393i	$0.0687772\pi$
$410$		0			0
$411$	2574.28	−	1486.26i	0.0152395	−	0.00879854i
$412$		0			0
$413$	76437.5	−	91094.6i	0.448132	−	0.534063i
$414$		0			0
$415$	−4120.02	+	23365.8i	−0.0239223	+	0.135670i
$416$		0			0
$417$			11209.9i			0.0644658i
$418$		0			0
$419$	107796.			0.614006			0.307003	−	0.951709i	$-0.400674\pi$
$419$	107796.			0.614006			0.307003	+	0.951709i	$0.400674\pi$
$420$		0			0
$421$	−185201.	−	32655.9i	−1.04491	−	0.184246i	−0.375257	−	0.926921i	$-0.622446\pi$
$421$	−185201.	−	32655.9i	−1.04491	−	0.184246i	−0.669652	+	0.742675i	$0.733557\pi$
$422$		0			0
$423$	−22622.5	−	18982.5i	−0.126433	−	0.106090i
$424$		0			0
$425$	−20527.6	−	35554.9i	−0.113648	−	0.196844i
$426$		0			0
$427$	−168804.	−	61439.8i	−0.925823	−	0.336972i
$428$		0			0
$429$	5903.70	−	10225.5i	0.0320782	−	0.0555610i
$430$		0			0
$431$	83201.5	−	14670.7i	0.447895	−	0.0789760i	0.0548489	−	0.998495i	$-0.482532\pi$
$431$	83201.5	−	14670.7i	0.447895	−	0.0789760i	0.393046	+	0.919519i	$0.371421\pi$
$432$		0			0
$433$	−197252.	−	235076.i	−1.05207	−	1.25381i	−0.966278	−	0.257500i	$-0.917101\pi$
$433$	−197252.	−	235076.i	−1.05207	−	1.25381i	−0.0857960	−	0.996313i	$-0.527343\pi$
$434$		0			0
$435$	30300.6	−	11028.5i	0.160130	−	0.0582826i
$436$		0			0
$437$	256330.	+	189165.i	1.34226	+	0.990552i
$438$		0			0
$439$	11453.1	+	31467.2i	0.0594286	+	0.163279i	0.965854	−	0.259088i	$-0.0834218\pi$
$439$	11453.1	+	31467.2i	0.0594286	+	0.163279i	−0.906425	+	0.422366i	$0.861200\pi$
$440$		0			0
$441$	113823.	−	95509.1i	0.585267	−	0.491097i
$442$		0			0
$443$	−19837.3	−	112503.i	−0.101082	−	0.573265i	−0.992713	−	0.120502i	$-0.961549\pi$
$443$	−19837.3	−	112503.i	−0.101082	−	0.573265i	0.891631	−	0.452763i	$-0.149562\pi$
$444$		0			0
$445$	213186.	+	123083.i	1.07656	+	0.621553i
$446$		0			0
$447$	3504.12	−	9627.49i	0.0175373	−	0.0481835i
$448$		0			0
$449$	−28145.4	+	16249.7i	−0.139609	+	0.0806035i	−0.568178	−	0.822906i	$-0.692351\pi$
$449$	−28145.4	+	16249.7i	−0.139609	+	0.0806035i	0.428568	+	0.903509i	$0.359018\pi$
$450$		0			0
$451$	−289999.	+	345607.i	−1.42575	+	1.69914i
$452$		0			0
$453$	−3662.32	+	20770.1i	−0.0178468	+	0.101214i
$454$		0			0
$455$			179794.i			0.868467i
$456$		0			0
$457$	180019.			0.861956			0.430978	−	0.902362i	$-0.358169\pi$
$457$	180019.			0.861956			0.430978	+	0.902362i	$0.358169\pi$
$458$		0			0
$459$	12288.0	+	2166.70i	0.0583250	+	0.0102843i
$460$		0			0
$461$	−227440.	−	190845.i	−1.07020	−	0.898005i	−0.0751296	−	0.997174i	$-0.523937\pi$
$461$	−227440.	−	190845.i	−1.07020	−	0.898005i	−0.995071	+	0.0991692i	$0.968381\pi$
$462$		0			0
$463$	−30464.3	−	52765.7i	−0.142112	−	0.246144i	0.786180	−	0.617998i	$-0.212056\pi$
$463$	−30464.3	−	52765.7i	−0.142112	−	0.246144i	−0.928292	+	0.371853i	$0.878723\pi$
$464$		0			0
$465$	−33494.7	−	12191.1i	−0.154907	−	0.0563815i
$466$		0			0
$467$	127334.	−	220550.i	0.583864	−	1.01128i	−0.411152	−	0.911567i	$-0.634873\pi$
$467$	127334.	−	220550.i	0.583864	−	1.01128i	0.995016	−	0.0997156i	$-0.0317933\pi$
$468$		0			0
$469$	−377219.	+	66514.0i	−1.71494	+	0.302390i
$470$		0			0
$471$	5335.38	+	6358.46i	0.0240505	+	0.0286622i
$472$		0			0
$473$	−41484.0	+	15098.9i	−0.185421	+	0.0674876i
$474$		0			0
$475$	123770.	−	54006.0i	0.548564	−	0.239362i
$476$		0			0
$477$	89040.0	+	244635.i	0.391335	+	1.07518i
$478$		0			0
$479$	−44696.4	+	37504.7i	−0.194806	+	0.163461i	−0.734973	−	0.678096i	$-0.762805\pi$
$479$	−44696.4	+	37504.7i	−0.194806	+	0.163461i	0.540168	+	0.841558i	$0.318361\pi$
$480$		0			0
$481$	36333.4	+	206057.i	0.157042	+	0.890629i
$482$		0			0
$483$	−35057.8	−	20240.6i	−0.150276	−	0.0867620i
$484$		0			0
$485$	69175.8	−	190059.i	0.294084	−	0.807988i
$486$		0			0
$487$	−64126.5	+	37023.4i	−0.270383	+	0.156106i	−0.629062	−	0.777355i	$-0.716561\pi$
$487$	−64126.5	+	37023.4i	−0.270383	+	0.156106i	0.358679	+	0.933461i	$0.383227\pi$
$488$		0			0
$489$	−2264.45	+	2698.66i	−0.00946988	+	0.0112858i
$490$		0			0
$491$	34828.9	−	197524.i	0.144470	−	0.819328i	−0.823322	−	0.567575i	$-0.807882\pi$
$491$	34828.9	−	197524.i	0.144470	−	0.819328i	0.967792	−	0.251753i	$-0.0810071\pi$
$492$		0			0
$493$		−	159058.i		−	0.654428i
$494$		0			0
$495$	−488980.			−1.99563
$496$		0			0
$497$	87479.4	+	15425.0i	0.354155	+	0.0624470i
$498$		0			0
$499$	−129561.	−	108714.i	−0.520322	−	0.436602i	0.344422	−	0.938815i	$-0.388075\pi$
$499$	−129561.	−	108714.i	−0.520322	−	0.436602i	−0.864744	+	0.502213i	$0.832519\pi$
$500$		0			0
$501$	13351.6	+	23125.7i	0.0531936	+	0.0921340i
$502$		0			0
$503$	−128080.	−	46617.4i	−0.506228	−	0.184252i	0.0762650	−	0.997088i	$-0.475700\pi$
$503$	−128080.	−	46617.4i	−0.506228	−	0.184252i	−0.582493	+	0.812836i	$0.697923\pi$
$504$		0			0
$505$	−62243.9	+	107810.i	−0.244070	+	0.422741i
$506$		0			0
$507$	−14517.6	+	2559.84i	−0.0564779	+	0.00995857i
$508$		0			0
$509$	301408.	+	359204.i	1.16337	+	1.38645i	0.907663	+	0.419699i	$0.137864\pi$
$509$	301408.	+	359204.i	1.16337	+	1.38645i	0.255708	+	0.966754i	$0.417691\pi$
$510$		0			0
$511$	−347444.	+	126459.i	−1.33059	+	0.484294i
$512$		0			0
$513$	−11605.7	+	39366.0i	−0.0440998	+	0.149585i
$514$		0			0
$515$	130801.	+	359373.i	0.493171	+	1.35498i
$516$		0			0
$517$	−53999.9	+	45311.3i	−0.202028	+	0.169522i
$518$		0			0
$519$	410.623	+	2328.76i	0.00152444	+	0.00864550i
$520$		0			0
$521$	−72663.0	−	41952.0i	−0.267694	−	0.154553i	0.360145	−	0.932896i	$-0.382727\pi$
$521$	−72663.0	−	41952.0i	−0.267694	−	0.154553i	−0.627839	+	0.778343i	$0.716060\pi$
$522$		0			0
$523$	−150695.	+	414032.i	−0.550930	+	1.51367i	0.281514	+	0.959557i	$0.409164\pi$
$523$	−150695.	+	414032.i	−0.550930	+	1.51367i	−0.832443	+	0.554110i	$0.813059\pi$
$524$		0			0
$525$	−14860.6	+	8579.76i	−0.0539160	+	0.0311284i
$526$		0			0
$527$	−113018.	+	134690.i	−0.406937	+	0.484969i
$528$		0			0
$529$	86636.0	−	491337.i	0.309590	−	1.75577i
$530$		0			0
$531$			146904.i			0.521009i
$532$		0			0
$533$	−204932.			−0.721364
$534$		0			0
$535$	2388.12	+	421.089i	0.00834349	+	0.00147118i
$536$		0			0
$537$	2701.15	+	2266.54i	0.00936700	+	0.00785985i
$538$		0			0
$539$	−177337.	−	307157.i	−0.610411	−	1.05726i
$540$		0			0
$541$	−234761.	−	85446.1i	−0.802106	−	0.291943i	−0.0917472	−	0.995782i	$-0.529245\pi$
$541$	−234761.	−	85446.1i	−0.802106	−	0.291943i	−0.710359	+	0.703840i	$0.751467\pi$
$542$		0			0
$543$	4498.53	−	7791.68i	0.0152571	−	0.0264260i
$544$		0			0
$545$	−214461.	+	37815.2i	−0.722029	+	0.127313i
$546$		0			0
$547$	284604.	+	339177.i	0.951187	+	1.13358i	0.990931	+	0.134370i	$0.0429011\pi$
$547$	284604.	+	339177.i	0.951187	+	1.13358i	−0.0397445	+	0.999210i	$0.512654\pi$
$548$		0			0
$549$	208535.	−	75900.5i	0.691885	−	0.251826i
$550$		0			0
$551$	519888.	+	58556.6i	1.71241	+	0.192873i
$552$		0			0
$553$	−104582.	−	287337.i	−0.341985	−	0.939595i
$554$		0			0
$555$	−40856.6	+	34282.7i	−0.132640	+	0.111299i
$556$		0			0
$557$	18753.5	+	106357.i	0.0604467	+	0.342810i	1.00000		0.000407388i	$0.000129676\pi$
$557$	18753.5	+	106357.i	0.0604467	+	0.342810i	−0.939553	+	0.342403i	$0.888759\pi$
$558$		0			0
$559$	−17366.2	−	10026.4i	−0.0555753	−	0.0320864i
$560$		0			0
$561$	5077.72	−	13950.9i	0.0161340	−	0.0443279i
$562$		0			0
$563$	17056.8	−	9847.76i	0.0538123	−	0.0310685i	−0.472852	−	0.881142i	$-0.656776\pi$
$563$	17056.8	−	9847.76i	0.0538123	−	0.0310685i	0.526665	+	0.850073i	$0.323442\pi$
$564$		0			0
$565$	374093.	−	445827.i	1.17188	−	1.39659i
$566$		0			0
$567$	−72884.9	+	413351.i	−0.226710	+	1.28574i
$568$		0			0
$569$		−	558758.i		−	1.72584i	−0.505344	−	0.862918i	$-0.668635\pi$
$569$		−	558758.i		−	1.72584i	0.505344	−	0.862918i	$-0.331365\pi$
$570$		0			0
$571$	538854.			1.65272			0.826359	−	0.563144i	$-0.190408\pi$
$571$	538854.			1.65272			0.826359	+	0.563144i	$0.190408\pi$
$572$		0			0
$573$	12071.5	+	2128.53i	0.0367665	+	0.00648293i
$574$		0			0
$575$	−252876.	−	212188.i	−0.764843	−	0.641779i
$576$		0			0
$577$	140861.	+	243978.i	0.423096	+	0.732824i	0.996240	−	0.0866306i	$-0.0276100\pi$
$577$	140861.	+	243978.i	0.423096	+	0.732824i	−0.573145	+	0.819454i	$0.694277\pi$
$578$		0			0
$579$	20614.3	+	7502.99i	0.0614910	+	0.0223809i
$580$		0			0
$581$	24458.3	−	42363.0i	0.0724559	−	0.125497i
$582$		0			0
$583$	611981.	−	107909.i	1.80053	−	0.317482i
$584$		0			0
$585$	−142771.	−	170147.i	−0.417184	−	0.497180i
$586$		0			0
$587$	−303711.	+	110542.i	−0.881423	+	0.320812i	−0.742784	−	0.669531i	$-0.766495\pi$
$587$	−303711.	+	110542.i	−0.881423	+	0.320812i	−0.138639	+	0.990343i	$0.544273\pi$
$588$		0			0
$589$	−398632.	−	418990.i	−1.14906	−	1.20774i
$590$		0			0
$591$	−11460.0	−	31486.0i	−0.0328101	−	0.0901451i
$592$		0			0
$593$	−65213.6	+	54720.7i	−0.185451	+	0.155612i	−0.730787	−	0.682606i	$-0.760847\pi$
$593$	−65213.6	+	54720.7i	−0.185451	+	0.155612i	0.545336	+	0.838218i	$0.316402\pi$
$594$		0			0
$595$	39256.3	+	222633.i	0.110886	+	0.628863i
$596$		0			0
$597$	−31927.5	−	18433.4i	−0.0895811	−	0.0517197i
$598$		0			0
$599$	129481.	−	355746.i	0.360871	−	0.991485i	−0.617851	−	0.786295i	$-0.711997\pi$
$599$	129481.	−	355746.i	0.360871	−	0.991485i	0.978722	−	0.205190i	$-0.0657813\pi$
$600$		0			0
$601$	334921.	−	193367.i	0.927244	−	0.535345i	0.0413051	−	0.999147i	$-0.486848\pi$
$601$	334921.	−	193367.i	0.927244	−	0.535345i	0.885939	+	0.463802i	$0.153515\pi$
$602$		0			0
$603$	304162.	−	362486.i	0.836509	−	0.996913i
$604$		0			0
$605$	−122322.	+	693721.i	−0.334189	+	1.89528i
$606$		0			0
$607$			243144.i			0.659912i	0.943996	+	0.329956i	$0.107034\pi$
$607$			243144.i			0.659912i	−0.943996	+	0.329956i	$0.892966\pi$
$608$		0			0
$609$	−66480.3			−0.179250
$610$		0			0
$611$	−31533.4	−	5560.19i	−0.0844673	−	0.0148939i
$612$		0			0
$613$	177368.	+	148829.i	0.472012	+	0.396065i	0.847528	−	0.530751i	$-0.178090\pi$
$613$	177368.	+	148829.i	0.472012	+	0.396065i	−0.375516	+	0.926816i	$0.622534\pi$
$614$		0			0
$615$	−26118.7	−	45238.9i	−0.0690559	−	0.119608i
$616$		0			0
$617$	512867.	+	186668.i	1.34721	+	0.490343i	0.912075	−	0.410023i	$-0.134479\pi$
$617$	512867.	+	186668.i	1.34721	+	0.490343i	0.435132	+	0.900366i	$0.356702\pi$
$618$		0			0
$619$	−265793.	+	460367.i	−0.693685	+	1.20150i	0.276937	+	0.960888i	$0.410681\pi$
$619$	−265793.	+	460367.i	−0.693685	+	1.20150i	−0.970622	+	0.240610i	$0.922653\pi$
$620$		0			0
$621$	98801.8	−	17421.4i	0.256202	−	0.0451752i
$622$		0			0
$623$	−326229.	−	388784.i	−0.840517	−	1.00169i
$624$		0			0
$625$	455272.	−	165705.i	1.16550	−	0.424206i
$626$		0			0
$627$	43729.8	+	21732.7i	0.111235	+	0.0552813i
$628$		0			0
$629$	89980.8	+	247220.i	0.227430	+	0.624860i
$630$		0			0
$631$	208648.	−	175076.i	0.524029	−	0.439712i	−0.342005	−	0.939698i	$-0.611106\pi$
$631$	208648.	−	175076.i	0.524029	−	0.439712i	0.866033	+	0.499986i	$0.166662\pi$
$632$		0			0
$633$	5541.27	+	31426.1i	0.0138293	+	0.0784301i
$634$		0			0
$635$	−271532.	−	156769.i	−0.673400	−	0.388788i
$636$		0			0
$637$	55101.4	−	151390.i	0.135795	−	0.373093i
$638$		0			0
$639$	−95034.2	+	54868.0i	−0.232744	+	0.134375i
$640$		0			0
$641$	−277020.	+	330140.i	−0.674210	+	0.803492i	−0.989351	−	0.145553i	$-0.953504\pi$
$641$	−277020.	+	330140.i	−0.674210	+	0.803492i	0.315140	+	0.949045i	$0.397948\pi$
$642$		0			0
$643$	84349.0	−	478367.i	0.204013	−	1.15702i	−0.694972	−	0.719037i	$-0.744583\pi$
$643$	84349.0	−	478367.i	0.204013	−	1.15702i	0.898985	−	0.437979i	$-0.144306\pi$
$644$		0			0
$645$		−	5111.49i		−	0.0122865i
$646$		0			0
$647$	95597.5			0.228369			0.114185	−	0.993460i	$-0.463574\pi$
$647$	95597.5			0.228369			0.114185	+	0.993460i	$0.463574\pi$
$648$		0			0
$649$	345333.	+	60891.6i	0.819877	+	0.144567i
$650$		0			0
$651$	56295.2	+	47237.3i	0.132834	+	0.111461i
$652$		0			0
$653$	251342.	+	435337.i	0.589438	+	1.02094i	0.994306	+	0.106561i	$0.0339841\pi$
$653$	251342.	+	435337.i	0.589438	+	1.02094i	−0.404868	+	0.914375i	$0.632683\pi$
$654$		0			0
$655$	189677.	+	69036.8i	0.442112	+	0.160916i
$656$		0			0
$657$	228383.	−	395572.i	0.529095	−	0.916419i
$658$		0			0
$659$	240961.	−	42488.0i	0.554851	−	0.0978352i	0.110810	−	0.993842i	$-0.464656\pi$
$659$	240961.	−	42488.0i	0.554851	−	0.0978352i	0.444041	+	0.896006i	$0.353544\pi$
$660$		0			0
$661$	35563.9	+	42383.4i	0.0813967	+	0.0970048i	0.805206	−	0.592996i	$-0.202055\pi$
$661$	35563.9	+	42383.4i	0.0813967	+	0.0970048i	−0.723809	+	0.690000i	$0.757610\pi$
$662$		0			0
$663$	6336.99	−	2306.48i	0.0144164	−	0.00524713i
$664$		0			0
$665$	−742138.	+	46349.2i	−1.67819	+	0.104809i
$666$		0			0
$667$	−437414.	−	1.20179e6i	−0.983198	−	2.70132i
$668$		0			0
$669$	−25465.6	+	21368.2i	−0.0568987	+	0.0477436i
$670$		0			0
$671$	−91984.8	−	521672.i	−0.204301	−	1.15865i
$672$		0			0
$673$	−371361.	−	214405.i	−0.819909	−	0.473375i	0.0304761	−	0.999535i	$-0.490298\pi$
$673$	−371361.	−	214405.i	−0.819909	−	0.473375i	−0.850385	+	0.526161i	$0.823631\pi$
$674$		0			0
$675$	14545.1	−	39962.3i	0.0319234	−	0.0877088i
$676$		0			0
$677$	−743727.	+	429391.i	−1.62269	+	0.936862i	−0.636497	+	0.771279i	$0.719617\pi$
$677$	−743727.	+	429391.i	−1.62269	+	0.936862i	−0.986196	+	0.165583i	$0.947049\pi$
$678$		0			0
$679$	−268038.	+	319436.i	−0.581376	+	0.692857i
$680$		0			0
$681$	−1567.90	+	8892.02i	−0.00338084	+	0.0191737i
$682$		0			0
$683$			231818.i			0.496942i	0.968639	+	0.248471i	$0.0799281\pi$
$683$			231818.i			0.496942i	−0.968639	+	0.248471i	$0.920072\pi$
$684$		0			0
$685$	−133473.			−0.284455
$686$		0			0
$687$	−48910.5	−	8624.24i	−0.103631	−	0.0182729i
$688$		0			0
$689$	216232.	+	181441.i	0.455494	+	0.382205i
$690$		0			0
$691$	300258.	+	520062.i	0.628837	+	1.08918i	0.987785	+	0.155821i	$0.0498022\pi$
$691$	300258.	+	520062.i	0.628837	+	1.08918i	−0.358948	+	0.933358i	$0.616864\pi$
$692$		0			0
$693$	947335.	+	344802.i	1.97259	+	0.717965i
$694$		0			0
$695$	251676.	−	435916.i	0.521041	−	0.902470i
$696$		0			0
$697$	−253760.	+	44744.7i	−0.522345	+	0.0921035i
$698$		0			0
$699$	10371.7	+	12360.5i	0.0212274	+	0.0252978i
$700$		0			0
$701$	−256747.	+	93448.3i	−0.522480	+	0.190167i	−0.589777	−	0.807566i	$-0.700785\pi$
$701$	−256747.	+	93448.3i	−0.522480	+	0.190167i	0.0672977	+	0.997733i	$0.478562\pi$
$702$		0			0
$703$	−841175.	+	203093.i	−1.70206	+	0.410945i
$704$		0			0
$705$	−2791.54	−	7669.68i	−0.00561649	−	0.0154312i
$706$		0			0
$707$	196611.	−	164976.i	0.393341	−	0.330052i
$708$		0			0
$709$	71493.5	+	405460.i	0.142224	+	0.806595i	0.969554	+	0.244878i	$0.0787478\pi$
$709$	71493.5	+	405460.i	0.142224	+	0.806595i	−0.827330	+	0.561717i	$0.810141\pi$
$710$		0			0
$711$	327138.	+	188873.i	0.647130	+	0.373621i
$712$		0			0
$713$	−483524.	+	1.32847e6i	−0.951128	+	2.61320i
$714$		0			0
$715$	−459150.	+	265091.i	−0.898137	+	0.518540i
$716$		0			0
$717$	19590.5	−	23347.1i	0.0381073	−	0.0454145i
$718$		0			0
$719$	−123960.	+	703011.i	−0.239786	+	1.35989i	0.592511	+	0.805562i	$0.298137\pi$
$719$	−123960.	+	703011.i	−0.239786	+	1.35989i	−0.832297	+	0.554330i	$0.812975\pi$
$720$		0			0
$721$		−	788474.i		−	1.51676i
$722$		0			0
$723$	27673.1			0.0529397
$724$		0			0
$725$	−533880.	−	94137.5i	−1.01571	−	0.179096i
$726$		0			0
$727$	767353.	+	643885.i	1.45186	+	1.21826i	0.931205	+	0.364495i	$0.118758\pi$
$727$	767353.	+	643885.i	1.45186	+	1.21826i	0.520660	+	0.853764i	$0.325686\pi$
$728$		0			0
$729$	−256017.	−	443434.i	−0.481741	−	0.834400i
$730$		0			0
$731$	−23693.2	−	8623.61i	−0.0443393	−	0.0161382i
$732$		0			0
$733$	−201153.	+	348407.i	−0.374385	+	0.648454i	−0.990235	−	0.139410i	$-0.955480\pi$
$733$	−201153.	+	348407.i	−0.374385	+	0.648454i	0.615850	+	0.787864i	$0.288813\pi$
$734$		0			0
$735$	40442.2	−	7131.04i	0.0748617	−	0.0132001i
$736$		0			0
$737$	−726036.	−	865256.i	−1.33667	−	1.59298i
$738$		0			0
$739$	−840729.	+	306000.i	−1.53946	+	0.560316i	−0.965915	−	0.258860i	$-0.916653\pi$
$739$	−840729.	+	306000.i	−1.53946	+	0.560316i	−0.573541	+	0.819177i	$0.694431\pi$
$740$		0			0
$741$	5205.87	+	21561.8i	0.00948106	+	0.0392689i
$742$		0			0
$743$	−188375.	−	517555.i	−0.341228	−	0.937516i	−0.985039	−	0.172332i	$-0.944870\pi$
$743$	−188375.	−	517555.i	−0.341228	−	0.937516i	0.643811	−	0.765185i	$-0.277352\pi$
$744$		0			0
$745$	−352413.	+	295709.i	−0.634949	+	0.532785i
$746$		0			0
$747$	10493.5	+	59511.8i	0.0188053	+	0.106650i
$748$		0			0
$749$	−4329.74	−	2499.77i	−0.00771788	−	0.00445592i
$750$		0			0
$751$	348702.	−	958051.i	0.618265	−	1.69867i	−0.0929277	−	0.995673i	$-0.529623\pi$
$751$	348702.	−	958051.i	0.618265	−	1.69867i	0.711193	−	0.702997i	$-0.248155\pi$
$752$		0			0
$753$	38254.6	−	22086.3i	0.0674673	−	0.0389523i
$754$		0			0
$755$	608729.	−	725455.i	1.06790	−	1.27267i
$756$		0			0
$757$	−81811.7	+	463977.i	−0.142766	+	0.809664i	0.826368	+	0.563130i	$0.190403\pi$
$757$	−81811.7	+	463977.i	−0.142766	+	0.809664i	−0.969134	+	0.246534i	$0.920708\pi$
$758$		0			0
$759$		−	119372.i		−	0.207214i
$760$		0			0
$761$	−371141.			−0.640869			−0.320434	−	0.947271i	$-0.603829\pi$
$761$	−371141.			−0.640869			−0.320434	+	0.947271i	$0.603829\pi$
$762$		0			0
$763$	442155.	+	77963.9i	0.759496	+	0.133920i
$764$		0			0
$765$	−213938.	−	179515.i	−0.365565	−	0.306746i
$766$		0			0
$767$	79641.1	+	137942.i	0.135378	+	0.234481i
$768$		0			0
$769$	443948.	+	161584.i	0.750723	+	0.273241i	0.688910	−	0.724847i	$-0.258090\pi$
$769$	443948.	+	161584.i	0.750723	+	0.273241i	0.0618129	+	0.998088i	$0.480312\pi$
$770$		0			0
$771$	−28081.6	+	48638.8i	−0.0472404	+	0.0818228i
$772$		0			0
$773$	891114.	−	157127.i	1.49133	−	0.262962i	0.632236	−	0.774776i	$-0.282137\pi$
$773$	891114.	−	157127.i	1.49133	−	0.262962i	0.859096	+	0.511814i	$0.171026\pi$
$774$		0			0
$775$	385199.	+	459062.i	0.641330	+	0.764308i
$776$		0			0
$777$	103329.	−	37608.6i	0.171151	−	0.0622938i
$778$		0			0
$779$	−52829.3	−	845897.i	−0.0870562	−	1.39393i
$780$		0			0
$781$	89588.8	+	246143.i	0.146876	+	0.403539i
$782$		0			0
$783$	126214.	−	105906.i	0.205865	−	0.172741i
$784$		0			0
$785$	−64720.0	−	367045.i	−0.105027	−	0.595635i
$786$		0			0
$787$	27445.8	+	15845.8i	0.0443125	+	0.0255838i	0.521993	−	0.852950i	$-0.325189\pi$
$787$	27445.8	+	15845.8i	0.0443125	+	0.0255838i	−0.477680	+	0.878534i	$0.658522\pi$
$788$		0			0
$789$	13261.0	−	36434.4i	0.0213021	−	0.0585271i
$790$		0			0
$791$	−1.03913e6	+	599942.i	−1.66080	+	0.958863i
$792$		0			0
$793$	154666.	−	184323.i	0.245950	−	0.293112i
$794$		0			0
$795$	−12494.2	+	70858.3i	−0.0197686	+	0.112113i
$796$		0			0
$797$		−	145767.i		−	0.229478i	−0.993396	−	0.114739i	$-0.963397\pi$
$797$		−	145767.i		−	0.229478i	0.993396	−	0.114739i	$-0.0366032\pi$
$798$		0			0
$799$	−40260.8			−0.0630650
$800$		0			0
$801$	617450.	+	108873.i	0.962358	+	0.169690i
$802$		0			0
$803$	−835221.	−	700833.i	−1.29530	−	1.08689i
$804$		0			0
$805$	908854.	+	1.57418e6i	1.40250	+	2.42920i
$806$		0			0
$807$	−21255.8	−	7736.48i	−0.0326385	−	0.0118794i
$808$		0			0
$809$	−35669.8	+	61781.9i	−0.0545009	+	0.0943984i	−0.891989	−	0.452058i	$-0.850690\pi$
$809$	−35669.8	+	61781.9i	−0.0545009	+	0.0943984i	0.837488	+	0.546456i	$0.184023\pi$
$810$		0			0
$811$	−67074.6	+	11827.1i	−0.101980	+	0.0179819i	−0.224405	−	0.974496i	$-0.572044\pi$
$811$	−67074.6	+	11827.1i	−0.101980	+	0.0179819i	0.122425	+	0.992478i	$0.460933\pi$
$812$		0			0
$813$	23781.0	+	28341.1i	0.0359790	+	0.0428781i
$814$		0			0
$815$	148645.	−	54102.4i	0.223787	−	0.0814520i
$816$		0			0
$817$	36909.2	−	74267.4i	0.0552955	−	0.111264i
$818$		0			0
$819$	156621.	+	430313.i	0.233498	+	0.641529i
$820$		0			0
$821$	−749298.	+	628736.i	−1.11165	+	0.932785i	−0.998153	−	0.0607529i	$-0.980650\pi$
$821$	−749298.	+	628736.i	−1.11165	+	0.932785i	−0.113498	+	0.993538i	$0.536205\pi$
$822$		0			0
$823$	73885.5	+	419026.i	0.109084	+	0.618644i	0.989510	+	0.144462i	$0.0461451\pi$
$823$	73885.5	+	419026.i	0.109084	+	0.618644i	−0.880427	+	0.474182i	$0.842744\pi$
$824$		0			0
$825$	−43821.2	−	25300.2i	−0.0643837	−	0.0371720i
$826$		0			0
$827$	105592.	−	290112.i	0.154391	−	0.424185i	−0.838249	−	0.545287i	$-0.816421\pi$
$827$	105592.	−	290112.i	0.154391	−	0.424185i	0.992640	+	0.121102i	$0.0386429\pi$
$828$		0			0
$829$	327216.	−	188918.i	0.476130	−	0.274894i	−0.242672	−	0.970108i	$-0.578024\pi$
$829$	327216.	−	188918.i	0.476130	−	0.274894i	0.718802	+	0.695214i	$0.244691\pi$
$830$		0			0
$831$	−58215.1	+	69378.0i	−0.0843011	+	0.100466i
$832$		0			0
$833$	35175.8	−	199492.i	0.0506936	−	0.287498i
$834$		0			0
$835$		−	1.19904e6i		−	1.71974i
$836$		0			0
$837$	−182128.			−0.259972
$838$		0			0
$839$	665042.	+	117265.i	0.944768	+	0.166588i	0.624751	−	0.780824i	$-0.285200\pi$
$839$	665042.	+	117265.i	0.944768	+	0.166588i	0.320016	+	0.947412i	$0.396312\pi$
$840$		0			0
$841$	−1.06711e6	−	895411.i	−1.50875	−	1.26599i
$842$		0			0
$843$	10008.5	+	17335.3i	0.0140836	+	0.0243936i
$844$		0			0
$845$	622012.	+	226394.i	0.871135	+	0.317067i
$846$		0			0
$847$	726156.	−	1.25774e6i	1.01219	−	1.75317i
$848$		0			0
$849$	77841.9	−	13725.6i	0.107994	−	0.0190422i
$850$		0			0
$851$	1.35972e6	+	1.62046e6i	1.87755	+	2.23758i
$852$		0			0
$853$	728297.	−	265078.i	1.00095	−	0.364314i	0.210996	−	0.977487i	$-0.432329\pi$
$853$	728297.	−	265078.i	1.00095	−	0.364314i	0.789949	+	0.613173i	$0.210107\pi$
$854$		0			0
$855$	665513.	−	633177.i	0.910384	−	0.866150i
$856$		0			0
$857$	−52799.5	−	145066.i	−0.0718900	−	0.197516i	0.898544	−	0.438884i	$-0.144626\pi$
$857$	−52799.5	−	145066.i	−0.0718900	−	0.197516i	−0.970434	+	0.241368i	$0.922404\pi$
$858$		0			0
$859$	498289.	−	418114.i	0.675297	−	0.566641i	−0.239331	−	0.970938i	$-0.576928\pi$
$859$	498289.	−	418114.i	0.675297	−	0.566641i	0.914628	+	0.404297i	$0.132484\pi$
$860$		0			0
$861$	18701.6	+	106062.i	0.0252274	+	0.143072i
$862$		0			0
$863$	−365470.	−	211004.i	−0.490715	−	0.283315i	0.234156	−	0.972199i	$-0.424767\pi$
$863$	−365470.	−	211004.i	−0.490715	−	0.283315i	−0.724871	+	0.688884i	$0.758101\pi$
$864$		0			0
$865$	36315.8	−	99776.8i	0.0485359	−	0.133351i
$866$		0			0
$867$	−43572.7	+	25156.7i	−0.0579664	+	0.0334669i
$868$		0			0
$869$	579590.	−	690728.i	0.767505	−	0.914677i
$870$		0			0
$871$	89092.5	−	505269.i	0.117437	−	0.666018i
$872$		0			0
$873$		−	515139.i		−	0.675921i
$874$		0			0
$875$	−516864.			−0.675087
$876$		0			0
$877$	−240096.	−	42335.4i	−0.312166	−	0.0550432i	0.0153705	−	0.999882i	$-0.495107\pi$
$877$	−240096.	−	42335.4i	−0.312166	−	0.0550432i	−0.327536	+	0.944839i	$0.606218\pi$
$878$		0			0
$879$	−71814.4	−	60259.4i	−0.0929466	−	0.0779915i
$880$		0			0
$881$	−203870.	−	353113.i	−0.262664	−	0.454948i	0.704285	−	0.709917i	$-0.251268\pi$
$881$	−203870.	−	353113.i	−0.262664	−	0.454948i	−0.966949	+	0.254970i	$0.917934\pi$
$882$		0			0
$883$	−236698.	−	86151.1i	−0.303580	−	0.110494i	0.185739	−	0.982599i	$-0.440532\pi$
$883$	−236698.	−	86151.1i	−0.303580	−	0.110494i	−0.489319	+	0.872105i	$0.662754\pi$
$884$		0			0
$885$	−20300.6	+	35161.7i	−0.0259193	+	0.0448935i
$886$		0			0
$887$	−187497.	+	33060.7i	−0.238312	+	0.0420209i	−0.291529	−	0.956562i	$-0.594164\pi$
$887$	−187497.	+	33060.7i	−0.238312	+	0.0420209i	0.0532163	+	0.998583i	$0.483053\pi$
$888$		0			0
$889$	415513.	+	495189.i	0.525752	+	0.626567i
$890$		0			0
$891$	−1.16306e6	+	423318.i	−1.46503	+	0.533226i
$892$		0			0
$893$	14821.8	−	131594.i	0.0185865	−	0.165019i
$894$		0			0
$895$	−54152.3	−	148782.i	−0.0676038	−	0.185740i
$896$		0			0
$897$	41537.1	−	34853.8i	0.0516240	−	0.0433176i
$898$		0			0
$899$	403158.	+	2.28642e6i	0.498834	+	2.82903i
$900$		0			0
$901$	307369.	+	177460.i	0.378626	+	0.218600i
$902$		0			0
$903$	−3604.34	+	9902.85i	−0.00442029	+	0.0121446i
$904$		0			0
$905$	−349866.	+	201995.i	−0.427173	+	0.246629i
$906$		0			0
$907$	−351542.	+	418951.i	−0.427329	+	0.509271i	−0.936150	−	0.351601i	$-0.885637\pi$
$907$	−351542.	+	418951.i	−0.427329	+	0.509271i	0.508821	+	0.860873i	$0.330082\pi$
$908$		0			0
$909$	−55057.9	+	312249.i	−0.0666333	+	0.377896i
$910$		0			0
$911$		−	921192.i		−	1.10998i	−0.831858	−	0.554988i	$-0.812723\pi$
$911$		−	921192.i		−	1.10998i	0.831858	−	0.554988i	$-0.187277\pi$
$912$		0			0
$913$	144246.			0.173046
$914$		0			0
$915$	60401.8	+	10650.5i	0.0721453	+	0.0127212i
$916$		0			0
$917$	−318794.	−	267500.i	−0.379115	−	0.318115i
$918$		0			0
$919$	−246580.	−	427090.i	−0.291963	−	0.505694i	0.682311	−	0.731062i	$-0.260975\pi$
$919$	−246580.	−	427090.i	−0.291963	−	0.505694i	−0.974274	+	0.225368i	$0.927642\pi$
$920$		0			0
$921$	−3506.70	−	1276.33i	−0.00413408	−	0.00150468i
$922$		0			0
$923$	−59491.2	+	103042.i	−0.0698312	+	0.120951i
$924$		0			0
$925$	883052.	−	155706.i	1.03205	−	0.181979i
$926$		0			0
$927$	626109.	+	746167.i	0.728602	+	0.868314i
$928$		0			0
$929$	−1.22258e6	+	444983.i	−1.41660	+	0.515599i	−0.933059	−	0.359724i	$-0.882871\pi$
$929$	−1.22258e6	+	444983.i	−1.41660	+	0.515599i	−0.483538	+	0.875323i	$0.660648\pi$
$930$		0			0
$931$	639096.	+	188415.i	0.737339	+	0.217379i
$932$		0			0
$933$	−36006.2	−	98926.2i	−0.0413632	−	0.113644i
$934$		0			0
$935$	−510671.	+	428503.i	−0.584141	+	0.490152i
$936$		0			0
$937$	−74205.2	−	420839.i	−0.0845192	−	0.479332i	−0.997459	−	0.0712385i	$-0.977305\pi$
$937$	−74205.2	−	420839.i	−0.0845192	−	0.479332i	0.912940	−	0.408094i	$-0.133806\pi$
$938$		0			0
$939$	20110.9	+	11611.0i	0.0228087	+	0.0131686i
$940$		0			0
$941$	−359469.	+	987633.i	−0.405959	+	1.11536i	0.553336	+	0.832958i	$0.313355\pi$
$941$	−359469.	+	987633.i	−0.405959	+	1.11536i	−0.959295	+	0.282405i	$0.908868\pi$
$942$		0			0
$943$	−1.79427e6	+	1.03592e6i	−2.01773	+	1.16494i
$944$		0			0
$945$	−150523.	+	179386.i	−0.168554	+	0.200875i
$946$		0			0
$947$	78149.7	−	443209.i	0.0871419	−	0.494207i	−0.909732	−	0.415196i	$-0.863713\pi$
$947$	78149.7	−	443209.i	0.0871419	−	0.494207i	0.996874	−	0.0790103i	$-0.0251760\pi$
$948$		0			0
$949$		−	495254.i		−	0.549915i
$950$		0			0
$951$	−291.276			−0.000322065
$952$		0			0
$953$	1.00103e6	+	176509.i	1.10221	+	0.194349i	0.695016	−	0.718994i	$-0.255397\pi$
$953$	1.00103e6	+	176509.i	1.10221	+	0.194349i	0.407191	+	0.913343i	$0.366508\pi$
$954$		0			0
$955$	−421633.	−	353792.i	−0.462304	−	0.387919i
$956$		0			0
$957$	−98019.1	−	169774.i	−0.107025	−	0.185373i
$958$		0			0
$959$	258587.	+	94118.1i	0.281171	+	0.102338i
$960$		0			0
$961$	821457.	−	1.42281e6i	0.889484	−	1.54063i
$962$		0			0
$963$	6082.44	−	1072.50i	0.00655881	−	0.00115649i
$964$		0			0
$965$	−633170.	−	754583.i	−0.679933	−	0.810312i
$966$		0			0
$967$	−1.51176e6	+	550235.i	−1.61670	+	0.588431i	−0.982749	−	0.184942i	$-0.940790\pi$
$967$	−1.51176e6	+	550235.i	−1.61670	+	0.588431i	−0.633951	+	0.773373i	$0.718568\pi$
$968$		0			0
$969$	11154.1	+	25562.6i	0.0118791	+	0.0272244i
$970$		0			0
$971$	16122.4	+	44295.9i	0.0170998	+	0.0469813i	0.947949	−	0.318423i	$-0.103153\pi$
$971$	16122.4	+	44295.9i	0.0170998	+	0.0469813i	−0.930849	+	0.365404i	$0.880931\pi$
$972$		0			0
$973$	−794974.	+	667062.i	−0.839706	+	0.704597i
$974$		0			0
$975$	−3991.20	−	22635.2i	−0.00419851	−	0.0238109i
$976$		0			0
$977$	−515574.	−	297667.i	−0.540135	−	0.311847i	0.204999	−	0.978762i	$-0.434281\pi$
$977$	−515574.	−	297667.i	−0.540135	−	0.311847i	−0.745134	+	0.666915i	$0.767614\pi$
$978$		0			0
$979$	511864.	−	1.40634e6i	0.534059	−	1.46732i
$980$		0			0
$981$	−480340.	+	277325.i	−0.499127	+	0.288171i
$982$		0			0
$983$	−634961.	+	756716.i	−0.657112	+	0.783116i	−0.986968	−	0.160915i	$-0.948555\pi$
$983$	−634961.	+	756716.i	−0.657112	+	0.783116i	0.329856	+	0.944031i	$0.393000\pi$
$984$		0			0
$985$	−261259.	+	1.48168e6i	−0.269277	+	1.52715i
$986$		0			0
$987$			16827.5i			0.0172737i
$988$		0			0
$989$	−202732.			−0.207267
$990$		0			0
$991$	−1.09494e6	−	193068.i	−1.11492	−	0.196591i	−0.414312	−	0.910135i	$-0.635978\pi$
$991$	−1.09494e6	−	193068.i	−1.11492	−	0.196591i	−0.700611	+	0.713544i	$0.747089\pi$
$992$		0			0
$993$	−71272.6	−	59804.8i	−0.0722810	−	0.0606510i
$994$		0			0
$995$	827703.	+	1.43362e6i	0.836043	+	1.44807i
$996$		0			0
$997$	−185329.	−	67454.3i	−0.186446	−	0.0678608i	0.247110	−	0.968987i	$-0.420519\pi$
$997$	−185329.	−	67454.3i	−0.186446	−	0.0678608i	−0.433556	+	0.901127i	$0.642741\pi$
$998$		0			0
$999$	−136259.	+	236007.i	−0.136532	+	0.236480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.33.4	✓	42
19.15	odd	18	inner	76.5.j.a.53.4	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.33.4	✓	42	1.1	even	1	trivial
76.5.j.a.53.4	yes	42	19.15	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.693233 + 0.122236i) q^{3} +(-24.2132 - 20.3173i) q^{5} +(32.5833 + 56.4359i) q^{7} +(-75.6495 - 27.5342i) q^{9} +O(q^{10})\)	\(q+(0.693233 + 0.122236i) q^{3} +(-24.2132 - 20.3173i) q^{5} +(32.5833 + 56.4359i) q^{7} +(-75.6495 - 27.5342i) q^{9} +(-96.0822 + 166.419i) q^{11} +(-85.9617 + 15.1574i) q^{13} +(-14.3019 - 17.0443i) q^{15} +(-103.134 + 37.5377i) q^{17} +(-84.7252 - 350.917i) q^{19} +(15.6893 + 43.1061i) q^{21} +(-676.013 + 567.242i) q^{23} +(64.9565 + 368.387i) q^{25} +(-98.4562 - 56.8437i) q^{27} +(-495.669 + 1361.84i) q^{29} +(1387.38 - 801.005i) q^{31} +(-86.9497 + 103.623i) q^{33} +(357.679 - 2028.50i) q^{35} -2397.08i q^{37} -61.4442 q^{39} +(2312.10 + 407.686i) q^{41} +(175.985 + 147.669i) q^{43} +(1272.30 + 2203.68i) q^{45} +(344.708 + 125.464i) q^{47} +(-922.842 + 1598.41i) q^{49} +(-76.0843 + 13.4157i) q^{51} +(-2078.65 - 2477.24i) q^{53} +(5707.64 - 2077.41i) q^{55} +(-15.8397 - 253.624i) q^{57} +(-624.116 - 1714.75i) q^{59} +(-2111.67 + 1771.90i) q^{61} +(-910.993 - 5166.50i) q^{63} +(2389.36 + 1379.50i) q^{65} +(-2010.34 + 5523.36i) q^{67} +(-537.972 + 310.598i) q^{69} +(876.187 - 1044.20i) q^{71} +(-985.246 + 5587.61i) q^{73} +263.318i q^{75} -12522.7 q^{77} +(-4620.95 - 814.799i) q^{79} +(4933.97 + 4140.09i) q^{81} +(-375.320 - 650.073i) q^{83} +(3259.87 + 1186.49i) q^{85} +(-510.079 + 883.483i) q^{87} +(-7669.75 + 1352.38i) q^{89} +(-3656.33 - 4357.45i) q^{91} +(1059.69 - 385.695i) q^{93} +(-5078.21 + 10218.2i) q^{95} +(2188.55 + 6012.99i) q^{97} +(11850.8 - 9943.99i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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