LMFDB - Embedded newform 99.4.f.d.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$99 = 3^{2} \cdot 11$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	99.f (of order $5$ , degree $4$ , 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:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 3 x^{11} + 21 x^{10} - 26 x^{9} + 281 x^{8} + 486 x^{7} + 3506 x^{6} + 15102 x^{5} + \cdots + 1936$ x^12 - 3x^11 + 21x^10 - 26x^9 + 281x^8 + 486x^7 + 3506x^6 + 15102x^5 + 46669x^4 + 41850x^3 + 16292x^2 + 616*x + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.3
Root			$-1.92306 + 1.39719i$ of defining polynomial
Character	$\chi$	$=$	99.37
Dual form			99.4.f.d.91.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73208 + 1.98497i) q^{2} +(1.05201 + 3.23775i) q^{4} +(11.3314 - 8.23272i) q^{5} +(7.21292 + 22.1991i) q^{7} +(4.79582 - 14.7600i) q^{8} +47.2999 q^{10} +(28.7668 + 22.4382i) q^{11} +(-30.5289 - 22.1805i) q^{13} +(-24.3583 + 74.9671i) q^{14} +(64.4343 - 46.8143i) q^{16} +(6.96027 - 5.05693i) q^{17} +(-27.3586 + 84.2011i) q^{19} +(38.5762 + 28.0273i) q^{20} +(34.0541 + 118.404i) q^{22} -137.456 q^{23} +(21.9951 - 67.6940i) q^{25} +(-39.3796 - 121.198i) q^{26} +(-64.2871 + 46.7073i) q^{28} +(-68.7037 - 211.448i) q^{29} +(-195.350 - 141.930i) q^{31} +144.808 q^{32} +29.0539 q^{34} +(264.491 + 192.164i) q^{35} +(46.5381 + 143.230i) q^{37} +(-241.883 + 175.738i) q^{38} +(-67.1719 - 206.734i) q^{40} +(43.7700 - 134.710i) q^{41} +246.830 q^{43} +(-42.3862 + 116.745i) q^{44} +(-375.540 - 272.846i) q^{46} +(-19.2348 + 59.1987i) q^{47} +(-163.280 + 118.630i) q^{49} +(194.463 - 141.286i) q^{50} +(39.6984 - 122.179i) q^{52} +(-402.378 - 292.345i) q^{53} +(510.694 + 17.4259i) q^{55} +362.251 q^{56} +(232.015 - 714.068i) q^{58} +(181.127 + 557.451i) q^{59} +(-523.089 + 380.046i) q^{61} +(-251.985 - 775.529i) q^{62} +(-119.848 - 87.0744i) q^{64} -528.540 q^{65} -963.421 q^{67} +(23.6954 + 17.2157i) q^{68} +(341.171 + 1050.02i) q^{70} +(-121.205 + 88.0604i) q^{71} +(133.803 + 411.803i) q^{73} +(-157.161 + 483.692i) q^{74} -301.404 q^{76} +(-290.614 + 800.441i) q^{77} +(1004.73 + 729.982i) q^{79} +(344.720 - 1060.94i) q^{80} +(386.979 - 281.157i) q^{82} +(577.135 - 419.313i) q^{83} +(37.2371 - 114.604i) q^{85} +(674.358 + 489.950i) q^{86} +(469.148 - 316.989i) q^{88} -224.035 q^{89} +(272.185 - 837.700i) q^{91} +(-144.605 - 445.047i) q^{92} +(-170.059 + 123.555i) q^{94} +(383.194 + 1179.35i) q^{95} +(979.471 + 711.627i) q^{97} -681.572 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 16 q^{4} - 28 q^{5} + 12 q^{7} + 112 q^{8} + 100 q^{10} + 54 q^{11} - 18 q^{13} - 156 q^{14} + 308 q^{16} + 80 q^{17} - 280 q^{19} + 15 q^{20} - 193 q^{22} + 392 q^{23} + 77 q^{25} - 406 q^{26} - 429 q^{28}+ \cdots - 2810 q^{98}+O(q^{100})$ 12 * q - 16 * q^4 - 28 * q^5 + 12 * q^7 + 112 * q^8 + 100 * q^10 + 54 * q^11 - 18 * q^13 - 156 * q^14 + 308 * q^16 + 80 * q^17 - 280 * q^19 + 15 * q^20 - 193 * q^22 + 392 * q^23 + 77 * q^25 - 406 * q^26 - 429 * q^28 - 13 * q^29 + 413 * q^31 - 1314 * q^32 + 1060 * q^34 + 1239 * q^35 + 654 * q^37 - 912 * q^38 - 1803 * q^40 + 1490 * q^41 + 416 * q^43 - 695 * q^44 - 2369 * q^46 + 150 * q^47 - 301 * q^49 + 1878 * q^50 - 1661 * q^52 - 1359 * q^53 + 3300 * q^55 + 858 * q^56 + 955 * q^58 - 1262 * q^59 - 1044 * q^61 + 701 * q^62 + 78 * q^64 - 4556 * q^65 - 528 * q^67 - 703 * q^68 + 3050 * q^70 - 558 * q^71 - 699 * q^73 + 3224 * q^74 - 868 * q^76 - 390 * q^77 - 1252 * q^79 + 1914 * q^80 + 2987 * q^82 + 4464 * q^83 - 2170 * q^85 + 3209 * q^86 + 1302 * q^88 - 316 * q^89 + 176 * q^91 - 4595 * q^92 + 1247 * q^94 - 1466 * q^95 + 1608 * q^97 - 2810 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$ .

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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

)

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

$2$	2.73208	+	1.98497i	0.965936	+	0.701794i	0.954522	−	0.298141i	$-0.0963666\pi$
$2$	2.73208	+	1.98497i	0.965936	+	0.701794i	0.0114143	+	0.999935i	$0.496367\pi$
$3$		0			0
$3$		0			0
$4$	1.05201	+	3.23775i	0.131501	+	0.404719i
$5$	11.3314	−	8.23272i	1.01351	−	0.736357i	0.0485664	−	0.998820i	$-0.484535\pi$
$5$	11.3314	−	8.23272i	1.01351	−	0.736357i	0.964942	+	0.262463i	$0.0845347\pi$
$6$		0			0
$7$	7.21292	+	22.1991i	0.389461	+	1.19864i	0.933192	+	0.359378i	$0.117011\pi$
$7$	7.21292	+	22.1991i	0.389461	+	1.19864i	−0.543731	+	0.839260i	$0.682989\pi$
$8$	4.79582	−	14.7600i	0.211947	−	0.652307i
$9$		0			0
$10$	47.2999			1.49576
$11$	28.7668	+	22.4382i	0.788502	+	0.615033i
$11$	28.7668	+	22.4382i	0.788502	+	0.615033i
$12$		0			0
$13$	−30.5289	−	22.1805i	−0.651322	−	0.473213i	0.212399	−	0.977183i	$-0.431872\pi$
$13$	−30.5289	−	22.1805i	−0.651322	−	0.473213i	−0.863721	+	0.503970i	$0.831872\pi$
$14$	−24.3583	+	74.9671i	−0.465002	+	1.43113i
$15$		0			0
$16$	64.4343	−	46.8143i	1.00679	−	0.731473i
$17$	6.96027	−	5.05693i	0.0993008	−	0.0721463i	−0.537027	−	0.843565i	$-0.680453\pi$
$17$	6.96027	−	5.05693i	0.0993008	−	0.0721463i	0.636328	+	0.771419i	$0.280453\pi$
$18$		0			0
$19$	−27.3586	+	84.2011i	−0.330342	+	1.01669i	0.638630	+	0.769514i	$0.279502\pi$
$19$	−27.3586	+	84.2011i	−0.330342	+	1.01669i	−0.968971	+	0.247173i	$0.920498\pi$
$20$	38.5762	+	28.0273i	0.431295	+	0.313354i
$21$		0			0
$22$	34.0541	+	118.404i	0.330016	+	1.14745i
$23$	−137.456			−1.24615			−0.623076	−	0.782162i	$-0.714117\pi$
$23$	−137.456			−1.24615			−0.623076	+	0.782162i	$0.714117\pi$
$24$		0			0
$25$	21.9951	−	67.6940i	0.175961	−	0.541552i
$26$	−39.3796	−	121.198i	−0.297038	−	0.914188i
$27$		0			0
$28$	−64.2871	+	46.7073i	−0.433897	+	0.315245i
$29$	−68.7037	−	211.448i	−0.439929	−	1.35396i	−0.887950	−	0.459940i	$-0.847871\pi$
$29$	−68.7037	−	211.448i	−0.439929	−	1.35396i	0.448020	−	0.894023i	$-0.352129\pi$
$30$		0			0
$31$	−195.350	−	141.930i	−1.13180	−	0.822304i	−0.145848	−	0.989307i	$-0.546591\pi$
$31$	−195.350	−	141.930i	−1.13180	−	0.822304i	−0.985956	+	0.167003i	$0.946591\pi$
$32$	144.808			0.799959
$33$		0			0
$34$	29.0539			0.146550
$35$	264.491	+	192.164i	1.27735	+	0.928047i
$36$		0			0
$37$	46.5381	+	143.230i	0.206779	+	0.636400i	0.999636	+	0.0269922i	$0.00859292\pi$
$37$	46.5381	+	143.230i	0.206779	+	0.636400i	−0.792857	+	0.609408i	$0.791407\pi$
$38$	−241.883	+	175.738i	−1.03259	+	0.750223i
$39$		0			0
$40$	−67.1719	−	206.734i	−0.265520	−	0.817187i
$41$	43.7700	−	134.710i	0.166725	−	0.513127i	−0.832434	−	0.554124i	$-0.813053\pi$
$41$	43.7700	−	134.710i	0.166725	−	0.513127i	0.999159	+	0.0409972i	$0.0130535\pi$
$42$		0			0
$43$	246.830			0.875376			0.437688	−	0.899127i	$-0.355797\pi$
$43$	246.830			0.875376			0.437688	+	0.899127i	$0.355797\pi$
$44$	−42.3862	+	116.745i	−0.145226	+	0.399999i
$45$		0			0
$46$	−375.540	−	272.846i	−1.20370	−	0.874541i
$47$	−19.2348	+	59.1987i	−0.0596955	+	0.183724i	−0.976457	−	0.215710i	$-0.930793\pi$
$47$	−19.2348	+	59.1987i	−0.0596955	+	0.183724i	0.916762	+	0.399434i	$0.130793\pi$
$48$		0			0
$49$	−163.280	+	118.630i	−0.476036	+	0.345860i
$50$	194.463	−	141.286i	0.550025	−	0.399616i
$51$		0			0
$52$	39.6984	−	122.179i	0.105869	−	0.325831i
$53$	−402.378	−	292.345i	−1.04285	−	0.757672i	−0.0720072	−	0.997404i	$-0.522940\pi$
$53$	−402.378	−	292.345i	−1.04285	−	0.757672i	−0.970839	+	0.239732i	$0.922940\pi$
$54$		0			0
$55$	510.694	+	17.4259i	1.25204	+	0.0427219i
$56$	362.251			0.864425
$57$		0			0
$58$	232.015	−	714.068i	0.525259	−	1.61658i
$59$	181.127	+	557.451i	0.399673	+	1.23007i	0.925262	+	0.379329i	$0.123845\pi$
$59$	181.127	+	557.451i	0.399673	+	1.23007i	−0.525589	+	0.850739i	$0.676155\pi$
$60$		0			0
$61$	−523.089	+	380.046i	−1.09795	+	0.797704i	−0.980723	−	0.195402i	$-0.937399\pi$
$61$	−523.089	+	380.046i	−1.09795	+	0.797704i	−0.117222	+	0.993106i	$0.537399\pi$
$62$	−251.985	−	775.529i	−0.516163	−	1.58859i
$63$		0			0
$64$	−119.848	−	87.0744i	−0.234077	−	0.170067i
$65$	−528.540			−1.00857
$66$		0			0
$67$	−963.421			−1.75673			−0.878363	−	0.477995i	$-0.841364\pi$
$67$	−963.421			−1.75673			−0.878363	+	0.477995i	$0.841364\pi$
$68$	23.6954	+	17.2157i	0.0422571	+	0.0307016i
$69$		0			0
$70$	341.171	+	1050.02i	0.582538	+	1.79287i
$71$	−121.205	+	88.0604i	−0.202597	+	0.147195i	−0.684458	−	0.729053i	$-0.739961\pi$
$71$	−121.205	+	88.0604i	−0.202597	+	0.147195i	0.481861	+	0.876248i	$0.339961\pi$
$72$		0			0
$73$	133.803	+	411.803i	0.214527	+	0.660246i	0.999187	+	0.0403194i	$0.0128376\pi$
$73$	133.803	+	411.803i	0.214527	+	0.660246i	−0.784660	+	0.619926i	$0.787162\pi$
$74$	−157.161	+	483.692i	−0.246886	+	0.759838i
$75$		0			0
$76$	−301.404			−0.454913
$77$	−290.614	+	800.441i	−0.430111	+	1.18466i
$78$		0			0
$79$	1004.73	+	729.982i	1.43090	+	1.03961i	0.989847	+	0.142133i	$0.0453962\pi$
$79$	1004.73	+	729.982i	1.43090	+	1.03961i	0.441057	+	0.897479i	$0.354604\pi$
$80$	344.720	−	1060.94i	0.481761	−	1.48271i
$81$		0			0
$82$	386.979	−	281.157i	0.521155	−	0.378641i
$83$	577.135	−	419.313i	0.763239	−	0.554525i	−0.136663	−	0.990618i	$-0.543638\pi$
$83$	577.135	−	419.313i	0.763239	−	0.554525i	0.899902	+	0.436092i	$0.143638\pi$
$84$		0			0
$85$	37.2371	−	114.604i	0.0475168	−	0.146242i
$86$	674.358	+	489.950i	0.845557	+	0.614333i
$87$		0			0
$88$	469.148	−	316.989i	0.568311	−	0.383990i
$89$	−224.035			−0.266828			−0.133414	−	0.991060i	$-0.542594\pi$
$89$	−224.035			−0.266828			−0.133414	+	0.991060i	$0.542594\pi$
$90$		0			0
$91$	272.185	−	837.700i	0.313547	−	0.964998i
$92$	−144.605	−	445.047i	−0.163870	−	0.504341i
$93$		0			0
$94$	−170.059	+	123.555i	−0.186598	+	0.135571i
$95$	383.194	+	1179.35i	0.413841	+	1.27367i
$96$		0			0
$97$	979.471	+	711.627i	1.02526	+	0.744895i	0.967354	−	0.253427i	$-0.0815578\pi$
$97$	979.471	+	711.627i	1.02526	+	0.744895i	0.0579053	+	0.998322i	$0.481558\pi$
$98$	−681.572			−0.702543
$99$		0			0
$100$	242.315			0.242315
$101$	877.948	+	637.867i	0.864942	+	0.628417i	0.929225	−	0.369515i	$-0.120476\pi$
$101$	877.948	+	637.867i	0.864942	+	0.628417i	−0.0642832	+	0.997932i	$0.520476\pi$
$102$		0			0
$103$	−325.959	−	1003.20i	−0.311823	−	0.959692i	−0.977043	−	0.213044i	$-0.931662\pi$
$103$	−325.959	−	1003.20i	−0.311823	−	0.959692i	0.665220	−	0.746648i	$-0.268338\pi$
$104$	−473.796	+	344.233i	−0.446726	+	0.324566i
$105$		0			0
$106$	−519.033	−	1597.42i	−0.475593	−	1.46373i
$107$	166.413	−	512.166i	0.150353	−	0.462737i	−0.847308	−	0.531102i	$-0.821778\pi$
$107$	166.413	−	512.166i	0.150353	−	0.462737i	0.997660	+	0.0683645i	$0.0217781\pi$
$108$		0			0
$109$	−125.822			−0.110565			−0.0552825	−	0.998471i	$-0.517606\pi$
$109$	−125.822			−0.110565			−0.0552825	+	0.998471i	$0.517606\pi$
$110$	1360.67	+	1061.32i	1.17941	+	0.919938i
$111$		0			0
$112$	1503.99	+	1092.72i	1.26888	+	0.921892i
$113$	525.463	−	1617.21i	0.437446	−	1.34632i	−0.453114	−	0.891453i	$-0.649687\pi$
$113$	525.463	−	1617.21i	0.437446	−	1.34632i	0.890559	−	0.454867i	$-0.150313\pi$
$114$		0			0
$115$	−1557.56	+	1131.63i	−1.26298	+	0.917612i
$116$	612.340	−	444.891i	0.490124	−	0.356096i
$117$		0			0
$118$	−611.672	+	1882.53i	−0.477195	+	1.46866i
$119$	162.463	+	118.036i	0.125151	+	0.0909276i
$120$		0			0
$121$	324.059	+	1290.95i	0.243470	+	0.969908i
$122$	−2183.50			−1.62037
$123$		0			0
$124$	254.025	−	781.807i	0.183968	−	0.566196i
$125$	232.954	+	716.958i	0.166688	+	0.513013i
$126$		0			0
$127$	1392.16	−	1011.46i	0.972708	−	0.706714i	0.0166406	−	0.999862i	$-0.494703\pi$
$127$	1392.16	−	1011.46i	0.972708	−	0.706714i	0.956067	+	0.293148i	$0.0947029\pi$
$128$	−512.578	−	1577.55i	−0.353953	−	1.08935i
$129$		0			0
$130$	−1444.01	−	1049.14i	−0.974219	−	0.707811i
$131$	676.499			0.451191			0.225595	−	0.974221i	$-0.427567\pi$
$131$	676.499			0.451191			0.225595	+	0.974221i	$0.427567\pi$
$132$		0			0
$133$	−2066.52			−1.34730
$134$	−2632.14	−	1912.36i	−1.69688	−	1.23286i
$135$		0			0
$136$	−41.2602	−	126.986i	−0.0260149	−	0.0800658i
$137$	228.143	−	165.755i	0.142274	−	0.103368i	−0.514372	−	0.857567i	$-0.671975\pi$
$137$	228.143	−	165.755i	0.142274	−	0.103368i	0.656646	+	0.754199i	$0.271975\pi$
$138$		0			0
$139$	−157.254	−	483.978i	−0.0959577	−	0.295327i	0.891544	−	0.452933i	$-0.149622\pi$
$139$	−157.254	−	483.978i	−0.0959577	−	0.295327i	−0.987502	+	0.157606i	$0.949622\pi$
$140$	−343.932	+	1058.52i	−0.207626	+	0.639006i
$141$		0			0
$142$	−505.939			−0.298996
$143$	−380.528	−	1323.07i	−0.222527	−	0.773714i
$144$		0			0
$145$	−2519.30	−	1830.38i	−1.44287	−	1.04831i
$146$	−451.858	+	1390.68i	−0.256137	+	0.788309i
$147$		0			0
$148$	−414.784	+	301.358i	−0.230372	+	0.167375i
$149$	−181.653	+	131.979i	−0.0998765	+	0.0725646i	−0.636603	−	0.771192i	$-0.719661\pi$
$149$	−181.653	+	131.979i	−0.0998765	+	0.0725646i	0.536726	+	0.843757i	$0.319661\pi$
$150$		0			0
$151$	816.077	−	2511.63i	0.439811	−	1.35360i	−0.448265	−	0.893901i	$-0.647958\pi$
$151$	816.077	−	2511.63i	0.439811	−	1.35360i	0.888075	−	0.459698i	$-0.152042\pi$
$152$	1111.60	+	807.627i	0.593177	+	0.430968i
$153$		0			0
$154$	−2382.83	+	1610.01i	−1.24685	+	0.842456i
$155$	−3382.06			−1.75260
$156$		0			0
$157$	97.3353	−	299.567i	0.0494790	−	0.152281i	−0.923264	−	0.384165i	$-0.874489\pi$
$157$	97.3353	−	299.567i	0.0494790	−	0.152281i	0.972743	+	0.231885i	$0.0744892\pi$
$158$	1296.02	+	3988.74i	0.652568	+	2.00840i
$159$		0			0
$160$	1640.87	−	1192.16i	0.810765	−	0.589055i
$161$	−991.456	−	3051.39i	−0.485327	−	1.49368i
$162$		0			0
$163$	1131.07	+	821.767i	0.543509	+	0.394882i	0.825386	−	0.564568i	$-0.190957\pi$
$163$	1131.07	+	821.767i	0.543509	+	0.394882i	−0.281878	+	0.959450i	$0.590957\pi$
$164$	482.204			0.229597
$165$		0			0
$166$	2409.10			1.12640
$167$	−936.191	−	680.182i	−0.433800	−	0.315174i	0.349367	−	0.936986i	$-0.386397\pi$
$167$	−936.191	−	680.182i	−0.433800	−	0.315174i	−0.783167	+	0.621812i	$0.786397\pi$
$168$		0			0
$169$	−238.874	−	735.177i	−0.108727	−	0.334628i
$170$	329.220	−	239.193i	0.148530	−	0.107913i
$171$		0			0
$172$	259.667	+	799.173i	0.115113	+	0.354281i
$173$	−219.309	+	674.963i	−0.0963799	+	0.296627i	−0.987611	−	0.156923i	$-0.949843\pi$
$173$	−219.309	+	674.963i	−0.0963799	+	0.296627i	0.891231	+	0.453550i	$0.149843\pi$
$174$		0			0
$175$	1661.39			0.717654
$176$	2904.00	+	99.0899i	1.24373	+	0.0424385i
$177$		0			0
$178$	−612.083	−	444.704i	−0.257739	−	0.187258i
$179$	123.274	−	379.400i	0.0514747	−	0.158423i	−0.922015	−	0.387155i	$-0.873458\pi$
$179$	123.274	−	379.400i	0.0514747	−	0.158423i	0.973489	+	0.228732i	$0.0734579\pi$
$180$		0			0
$181$	−274.375	+	199.345i	−0.112675	+	0.0818629i	−0.642696	−	0.766122i	$-0.722184\pi$
$181$	−274.375	+	199.345i	−0.112675	+	0.0818629i	0.530021	+	0.847984i	$0.322184\pi$
$182$	2406.44	−	1748.38i	0.980095	−	0.712081i
$183$		0			0
$184$	−659.212	+	2028.85i	−0.264118	+	0.812873i
$185$	1706.51	+	1239.85i	0.678190	+	0.492734i
$186$		0			0
$187$	313.693	+	10.7038i	0.122671	+	0.00418577i
$188$	−211.906			−0.0822065
$189$		0			0
$190$	−1294.06	+	3982.71i	−0.494110	+	1.52072i
$191$	463.401	+	1426.20i	0.175553	+	0.540295i	0.999658	−	0.0261409i	$-0.00832186\pi$
$191$	463.401	+	1426.20i	0.175553	+	0.540295i	−0.824106	+	0.566436i	$0.808322\pi$
$192$		0			0
$193$	1027.08	−	746.216i	0.383061	−	0.278310i	−0.379545	−	0.925173i	$-0.623920\pi$
$193$	1027.08	−	746.216i	0.383061	−	0.278310i	0.762606	+	0.646863i	$0.223920\pi$
$194$	1263.43	+	3888.44i	0.467573	+	1.43904i
$195$		0			0
$196$	−555.867	−	403.861i	−0.202576	−	0.147180i
$197$	−1970.86			−0.712782			−0.356391	−	0.934337i	$-0.615993\pi$
$197$	−1970.86			−0.712782			−0.356391	+	0.934337i	$0.615993\pi$
$198$		0			0
$199$	3706.78			1.32044			0.660218	−	0.751074i	$-0.270464\pi$
$199$	3706.78			1.32044			0.660218	+	0.751074i	$0.270464\pi$
$200$	−893.679	−	649.296i	−0.315963	−	0.229561i
$201$		0			0
$202$	1132.48	+	3485.41i	0.394459	+	1.21402i
$203$	4198.40	−	3050.32i	1.45158	−	1.05463i
$204$		0			0
$205$	−613.057	−	1886.80i	−0.208867	−	0.642827i
$206$	1100.78	−	3387.84i	0.372305	−	1.14584i
$207$		0			0
$208$	−3005.47			−1.00189
$209$	−2676.34	+	1808.32i	−0.885771	+	0.598489i
$210$		0			0
$211$	2345.94	+	1704.43i	0.765409	+	0.556102i	0.900565	−	0.434722i	$-0.143153\pi$
$211$	2345.94	+	1704.43i	0.765409	+	0.556102i	−0.135156	+	0.990824i	$0.543153\pi$
$212$	523.234	−	1610.35i	0.169509	−	0.521694i
$213$		0			0
$214$	1471.29	−	1068.95i	0.469977	−	0.341458i
$215$	2796.92	−	2032.08i	0.887201	−	0.644589i
$216$		0			0
$217$	1741.68	−	5360.33i	0.544851	−	1.67688i
$218$	−343.757	−	249.754i	−0.106799	−	0.0775939i
$219$		0			0
$220$	480.835	+	1671.83i	0.147354	+	0.512341i
$221$	−324.655			−0.0988174
$222$		0			0
$223$	−1937.82	+	5964.01i	−0.581912	+	1.79094i	0.0294221	+	0.999567i	$0.490633\pi$
$223$	−1937.82	+	5964.01i	−0.581912	+	1.79094i	−0.611334	+	0.791373i	$0.709367\pi$
$224$	1044.49	+	3214.61i	0.311553	+	0.958861i
$225$		0			0
$226$	4645.72	−	3375.31i	1.36738	−	0.993462i
$227$	−463.712	−	1427.16i	−0.135584	−	0.417286i	0.860096	−	0.510132i	$-0.170404\pi$
$227$	−463.712	−	1427.16i	−0.135584	−	0.417286i	−0.995680	+	0.0928461i	$0.970404\pi$
$228$		0			0
$229$	1747.29	+	1269.48i	0.504212	+	0.366331i	0.810623	−	0.585568i	$-0.199128\pi$
$229$	1747.29	+	1269.48i	0.504212	+	0.366331i	−0.306412	+	0.951899i	$0.599128\pi$
$230$	−6501.64			−1.86394
$231$		0			0
$232$	−3450.47			−0.976441
$233$	1618.62	+	1176.00i	0.455105	+	0.330653i	0.791608	−	0.611029i	$-0.209244\pi$
$233$	1618.62	+	1176.00i	0.455105	+	0.330653i	−0.336503	+	0.941682i	$0.609244\pi$
$234$		0			0
$235$	269.409	+	829.157i	0.0747844	+	0.230163i
$236$	−1614.34	+	1172.89i	−0.445274	+	0.323511i
$237$		0			0
$238$	209.563	+	644.970i	0.0570755	+	0.175660i
$239$	−545.558	+	1679.05i	−0.147653	+	0.454431i	−0.997343	−	0.0728532i	$-0.976790\pi$
$239$	−545.558	+	1679.05i	−0.147653	+	0.454431i	0.849689	+	0.527284i	$0.176790\pi$
$240$		0			0
$241$	−2787.34			−0.745014			−0.372507	−	0.928029i	$-0.621502\pi$
$241$	−2787.34			−0.745014			−0.372507	+	0.928029i	$0.621502\pi$
$242$	−1677.14	+	4170.22i	−0.445499	+	1.10774i
$243$		0			0
$244$	−1780.79	−	1293.82i	−0.467227	−	0.339460i
$245$	−873.541	+	2688.48i	−0.227790	+	0.701065i
$246$		0			0
$247$	2702.85	−	1963.74i	0.696269	−	0.505869i
$248$	−3031.76	+	2202.70i	−0.776277	+	0.563998i
$249$		0			0
$250$	−786.693	+	2421.19i	−0.199019	+	0.612519i
$251$	−829.428	−	602.614i	−0.208578	−	0.151541i	0.478592	−	0.878037i	$-0.341147\pi$
$251$	−829.428	−	602.614i	−0.208578	−	0.151541i	−0.687170	+	0.726497i	$0.741147\pi$
$252$		0			0
$253$	−3954.16	−	3084.25i	−0.982592	−	0.766423i
$254$	5811.20			1.43554
$255$		0			0
$256$	1364.77	−	4200.34i	0.333197	−	1.02547i
$257$	−523.409	−	1610.89i	−0.127040	−	0.390990i	0.867227	−	0.497913i	$-0.165900\pi$
$257$	−523.409	−	1610.89i	−0.127040	−	0.390990i	−0.994267	+	0.106923i	$0.965900\pi$
$258$		0			0
$259$	−2843.89	+	2066.21i	−0.682281	+	0.495706i
$260$	−556.029	−	1711.28i	−0.132629	−	0.408189i
$261$		0			0
$262$	1848.25	+	1342.83i	0.435821	+	0.316643i
$263$	1139.53			0.267172			0.133586	−	0.991037i	$-0.457351\pi$
$263$	1139.53			0.267172			0.133586	+	0.991037i	$0.457351\pi$
$264$		0			0
$265$	−6966.29			−1.61485
$266$	−5645.91	−	4101.99i	−1.30140	−	0.945523i
$267$		0			0
$268$	−1013.53	−	3119.32i	−0.231011	−	0.710980i
$269$	−4312.13	+	3132.94i	−0.977379	+	0.710107i	−0.957121	−	0.289687i	$-0.906449\pi$
$269$	−4312.13	+	3132.94i	−0.977379	+	0.710107i	−0.0202577	+	0.999795i	$0.506449\pi$
$270$		0			0
$271$	−470.366	−	1447.64i	−0.105434	−	0.324494i	0.884398	−	0.466734i	$-0.154569\pi$
$271$	−470.366	−	1447.64i	−0.105434	−	0.324494i	−0.989832	+	0.142240i	$0.954569\pi$
$272$	211.744	−	651.680i	0.0472017	−	0.145272i
$273$		0			0
$274$	952.324			0.209971
$275$	2151.66	−	1453.81i	0.471817	−	0.318793i
$276$		0			0
$277$	−2207.79	−	1604.05i	−0.478892	−	0.347935i	0.322005	−	0.946738i	$-0.395643\pi$
$277$	−2207.79	−	1604.05i	−0.478892	−	0.347935i	−0.800897	+	0.598803i	$0.795643\pi$
$278$	531.053	−	1634.41i	0.114570	−	0.352610i
$279$		0			0
$280$	4104.80	−	2982.31i	0.876102	−	0.636525i
$281$	5566.19	−	4044.08i	1.18168	−	0.858538i	0.189317	−	0.981916i	$-0.439373\pi$
$281$	5566.19	−	4044.08i	1.18168	−	0.858538i	0.992360	+	0.123378i	$0.0393726\pi$
$282$		0			0
$283$	−269.323	+	828.892i	−0.0565711	+	0.174108i	−0.975349	−	0.220666i	$-0.929177\pi$
$283$	−269.323	+	828.892i	−0.0565711	+	0.174108i	0.918778	+	0.394774i	$0.129177\pi$
$284$	−412.626	−	299.791i	−0.0862143	−	0.0626384i
$285$		0			0
$286$	1586.63	−	4370.08i	0.328040	−	0.903526i
$287$	3306.15			0.679986
$288$		0			0
$289$	−1495.33	+	4602.15i	−0.304361	+	0.936728i
$290$	−3249.68	−	10001.5i	−0.658027	−	2.02520i
$291$		0			0
$292$	−1192.56	+	866.442i	−0.239003	+	0.173646i
$293$	−1409.39	−	4337.65i	−0.281015	−	0.864874i	−0.987565	−	0.157211i	$-0.949750\pi$
$293$	−1409.39	−	4337.65i	−0.281015	−	0.864874i	0.706550	−	0.707663i	$-0.250250\pi$
$294$		0			0
$295$	6641.76	+	4825.52i	1.31084	+	0.952382i
$296$	2337.26			0.458954
$297$		0			0
$298$	−758.265			−0.147400
$299$	4196.37	+	3048.84i	0.811646	+	0.589695i
$300$		0			0
$301$	1780.36	+	5479.39i	0.340925	+	1.04926i
$302$	7215.10	−	5242.08i	1.37478	−	0.998833i
$303$		0			0
$304$	2178.98	+	6706.22i	0.411096	+	1.26522i
$305$	−2798.50	+	8612.89i	−0.525382	+	1.61696i
$306$		0			0
$307$	−4841.69			−0.900097			−0.450048	−	0.893004i	$-0.648593\pi$
$307$	−4841.69			−0.900097			−0.450048	+	0.893004i	$0.648593\pi$
$308$	−2897.36	−	98.8634i	−0.536014	−	0.0182898i
$309$		0			0
$310$	−9240.05	−	6713.29i	−1.69290	−	1.22996i
$311$	−2246.74	+	6914.76i	−0.409650	+	1.26077i	0.507300	+	0.861769i	$0.330643\pi$
$311$	−2246.74	+	6914.76i	−0.409650	+	1.26077i	−0.916950	+	0.399002i	$0.869357\pi$
$312$		0			0
$313$	−1814.17	+	1318.07i	−0.327613	+	0.238025i	−0.739417	−	0.673248i	$-0.764899\pi$
$313$	−1814.17	+	1318.07i	−0.327613	+	0.238025i	0.411804	+	0.911272i	$0.364899\pi$
$314$	860.560	−	625.233i	0.154663	−	0.112369i
$315$		0			0
$316$	−1306.51	+	4021.03i	−0.232585	+	0.715824i
$317$	4400.59	+	3197.22i	0.779691	+	0.566479i	0.904886	−	0.425654i	$-0.139956\pi$
$317$	4400.59	+	3197.22i	0.779691	+	0.566479i	−0.125195	+	0.992132i	$0.539956\pi$
$318$		0			0
$319$	2768.12	−	7624.27i	0.485847	−	1.33817i
$320$	−2074.90			−0.362470
$321$		0			0
$322$	3348.18	−	10304.6i	0.579463	−	1.78340i
$323$	235.376	+	724.413i	0.0405470	+	0.124791i
$324$		0			0
$325$	−2172.97	+	1578.76i	−0.370877	+	0.269458i
$326$	1458.98	+	4490.27i	0.247869	+	0.762862i
$327$		0			0
$328$	−1778.41	−	1292.09i	−0.299379	−	0.217512i
$329$	−1452.90			−0.243467
$330$		0			0
$331$	8447.66			1.40280			0.701398	−	0.712770i	$-0.252560\pi$
$331$	8447.66			1.40280			0.701398	+	0.712770i	$0.252560\pi$
$332$	1964.78	+	1427.50i	0.324794	+	0.235976i
$333$		0			0
$334$	−1207.60	−	3716.62i	−0.197836	−	0.608876i
$335$	−10916.9	+	7931.58i	−1.78046	+	1.29358i
$336$		0			0
$337$	−963.009	−	2963.84i	−0.155663	−	0.479082i	0.842564	−	0.538596i	$-0.181045\pi$
$337$	−963.009	−	2963.84i	−0.155663	−	0.479082i	−0.998227	+	0.0595139i	$0.981045\pi$
$338$	806.685	−	2482.72i	0.129816	−	0.399533i
$339$		0			0
$340$	410.233			0.0654353
$341$	−2434.95	−	8466.18i	−0.386686	−	1.34448i
$342$		0			0
$343$	2665.89	+	1936.88i	0.419663	+	0.304903i
$344$	1183.75	−	3643.21i	0.185534	−	0.571014i
$345$		0			0
$346$	−1938.95	+	1408.73i	−0.301268	+	0.218884i
$347$	3085.35	−	2241.64i	0.477321	−	0.346794i	−0.322966	−	0.946410i	$-0.604680\pi$
$347$	3085.35	−	2241.64i	0.477321	−	0.346794i	0.800288	+	0.599616i	$0.204680\pi$
$348$		0			0
$349$	−620.100	+	1908.47i	−0.0951094	+	0.292717i	−0.987282	−	0.158978i	$-0.949180\pi$
$349$	−620.100	+	1908.47i	−0.0951094	+	0.292717i	0.892173	+	0.451694i	$0.149180\pi$
$350$	4539.06	+	3297.82i	0.693208	+	0.503645i
$351$		0			0
$352$	4165.67	+	3249.23i	0.630769	+	0.492001i
$353$	−7986.75			−1.20423			−0.602113	−	0.798411i	$-0.705674\pi$
$353$	−7986.75			−1.20423			−0.602113	+	0.798411i	$0.705674\pi$
$354$		0			0
$355$	−648.439	+	1995.69i	−0.0969453	+	0.298367i
$356$	−235.687	−	725.371i	−0.0350882	−	0.107990i
$357$		0			0
$358$	1089.89	−	791.854i	0.160901	−	0.116902i
$359$	159.034	+	489.457i	0.0233802	+	0.0719569i	0.962066	−	0.272817i	$-0.0879555\pi$
$359$	159.034	+	489.457i	0.0233802	+	0.0719569i	−0.938686	+	0.344774i	$0.887955\pi$
$360$		0			0
$361$	−792.285	−	575.629i	−0.115510	−	0.0839232i
$362$	−1145.31			−0.166287
$363$		0			0
$364$	2998.61			0.431785
$365$	4906.43	+	3564.73i	0.703601	+	0.511196i
$366$		0			0
$367$	−851.393	−	2620.32i	−0.121096	−	0.372696i	0.872073	−	0.489375i	$-0.162775\pi$
$367$	−851.393	−	2620.32i	−0.121096	−	0.372696i	−0.993170	+	0.116679i	$0.962775\pi$
$368$	−8856.86	+	6434.89i	−1.25461	+	0.911526i
$369$		0			0
$370$	2201.25	+	6774.75i	0.309291	+	0.951899i
$371$	3587.46	−	11041.1i	0.502027	−	1.54508i
$372$		0			0
$373$	191.959			0.0266468			0.0133234	−	0.999911i	$-0.495759\pi$
$373$	191.959			0.0266468			0.0133234	+	0.999911i	$0.495759\pi$
$374$	835.788	+	651.916i	0.115555	+	0.0901330i
$375$		0			0
$376$	781.527	+	567.812i	0.107192	+	0.0778795i
$377$	−2592.59	+	7979.16i	−0.354178	+	1.09005i
$378$		0			0
$379$	−1271.27	+	923.632i	−0.172298	+	0.125182i	−0.670592	−	0.741826i	$-0.733960\pi$
$379$	−1271.27	+	923.632i	−0.172298	+	0.125182i	0.498294	+	0.867008i	$0.333960\pi$
$380$	−3415.32	+	2481.37i	−0.461058	+	0.334978i
$381$		0			0
$382$	−1564.92	+	4816.34i	−0.209603	+	0.645092i
$383$	−11608.0	−	8433.73i	−1.54868	−	1.12518i	−0.944587	−	0.328261i	$-0.893537\pi$
$383$	−11608.0	−	8433.73i	−1.54868	−	1.12518i	−0.604089	−	0.796917i	$-0.706463\pi$
$384$		0			0
$385$	3296.76	+	11462.6i	0.436412	+	1.51738i
$386$	4287.28			0.565328
$387$		0			0
$388$	−1273.66	+	3919.92i	−0.166650	+	0.512897i
$389$	−2330.94	−	7173.91i	−0.303814	−	0.935043i	−0.980117	−	0.198419i	$-0.936419\pi$
$389$	−2330.94	−	7173.91i	−0.303814	−	0.935043i	0.676303	−	0.736623i	$-0.263581\pi$
$390$		0			0
$391$	−956.728	+	695.104i	−0.123744	+	0.0899051i
$392$	967.919	+	2978.95i	0.124713	+	0.383826i
$393$		0			0
$394$	−5384.55	−	3912.10i	−0.688502	−	0.500226i
$395$	17394.8			2.21576
$396$		0			0
$397$	−3008.38			−0.380319			−0.190159	−	0.981753i	$-0.560900\pi$
$397$	−3008.38			−0.380319			−0.190159	+	0.981753i	$0.560900\pi$
$398$	10127.2	+	7357.86i	1.27546	+	0.926674i
$399$		0			0
$400$	−1751.81	−	5391.50i	−0.218976	−	0.673938i
$401$	10661.6	−	7746.09i	1.32772	−	0.964642i	0.327914	−	0.944708i	$-0.393654\pi$
$401$	10661.6	−	7746.09i	1.32772	−	0.964642i	0.999801	−	0.0199341i	$-0.00634564\pi$
$402$		0			0
$403$	2815.73	+	8665.94i	0.348044	+	1.07117i
$404$	−1141.64	+	3513.62i	−0.140591	+	0.432696i
$405$		0			0
$406$	17525.2			2.14226
$407$	−1875.06	+	5164.49i	−0.228361	+	0.628979i
$408$		0			0
$409$	8699.67	+	6320.68i	1.05176	+	0.764151i	0.972547	−	0.232707i	$-0.0747582\pi$
$409$	8699.67	+	6320.68i	1.05176	+	0.764151i	0.0792163	+	0.996857i	$0.474758\pi$
$410$	2070.32	−	6371.78i	0.249380	−	0.767512i
$411$		0			0
$412$	2905.20	−	2110.75i	0.347400	−	0.252401i
$413$	−11068.5	+	8041.71i	−1.31875	+	0.958127i
$414$		0			0
$415$	3087.64	−	9502.79i	0.365220	−	1.12403i
$416$	−4420.83	−	3211.92i	−0.521031	−	0.378551i
$417$		0			0
$418$	−10901.4	−	371.978i	−1.27561	−	0.0435264i
$419$	−440.292			−0.0513358			−0.0256679	−	0.999671i	$-0.508171\pi$
$419$	−440.292			−0.0513358			−0.0256679	+	0.999671i	$0.508171\pi$
$420$		0			0
$421$	3393.63	−	10444.5i	0.392863	−	1.20911i	−0.537750	−	0.843105i	$-0.680725\pi$
$421$	3393.63	−	10444.5i	0.392863	−	1.20911i	0.930613	−	0.366005i	$-0.119275\pi$
$422$	3026.06	+	9313.26i	0.349067	+	1.07432i
$423$		0			0
$424$	−6244.74	+	4537.07i	−0.715263	+	0.519669i
$425$	−189.232	−	582.396i	−0.0215979	−	0.0664715i
$426$		0			0
$427$	−12209.7	−	8870.85i	−1.38377	−	1.00536i
$428$	1833.33			0.207050
$429$		0			0
$430$	11675.0			1.30935
$431$	3488.79	+	2534.76i	0.389905	+	0.283283i	0.765417	−	0.643535i	$-0.222533\pi$
$431$	3488.79	+	2534.76i	0.389905	+	0.283283i	−0.375511	+	0.926818i	$0.622533\pi$
$432$		0			0
$433$	3376.82	+	10392.8i	0.374780	+	1.15345i	0.943627	+	0.331011i	$0.107390\pi$
$433$	3376.82	+	10392.8i	0.374780	+	1.15345i	−0.568847	+	0.822444i	$0.692610\pi$
$434$	15398.5	−	11187.7i	1.70311	−	1.23738i
$435$		0			0
$436$	−132.366	−	407.382i	−0.0145394	−	0.0447478i
$437$	3760.59	−	11573.9i	0.411656	−	1.26695i
$438$		0			0
$439$	−5655.67			−0.614876			−0.307438	−	0.951568i	$-0.599472\pi$
$439$	−5655.67			−0.614876			−0.307438	+	0.951568i	$0.599472\pi$
$440$	2706.40	−	7454.29i	0.293234	−	0.807657i
$441$		0			0
$442$	−886.983	−	644.431i	−0.0954513	−	0.0693494i
$443$	−897.124	+	2761.06i	−0.0962159	+	0.296122i	−0.987569	−	0.157188i	$-0.949757\pi$
$443$	−897.124	+	2761.06i	−0.0962159	+	0.296122i	0.891353	+	0.453310i	$0.149757\pi$
$444$		0			0
$445$	−2538.63	+	1844.42i	−0.270433	+	0.196481i
$446$	−17132.7	+	12447.6i	−1.81896	+	1.32155i
$447$		0			0
$448$	1068.52	−	3288.57i	0.112685	−	0.346809i
$449$	2813.36	+	2044.02i	0.295703	+	0.214841i	0.725738	−	0.687972i	$-0.241499\pi$
$449$	2813.36	+	2044.02i	0.295703	+	0.214841i	−0.430035	+	0.902812i	$0.641499\pi$
$450$		0			0
$451$	4281.77	−	2893.06i	0.447052	−	0.302060i
$452$	5788.91			0.602406
$453$		0			0
$454$	1565.97	−	4819.57i	0.161883	−	0.498224i
$455$	−3812.32	−	11733.1i	−0.392801	−	1.20892i
$456$		0			0
$457$	−2953.10	+	2145.55i	−0.302276	+	0.219616i	−0.728575	−	0.684966i	$-0.759817\pi$
$457$	−2953.10	+	2145.55i	−0.302276	+	0.219616i	0.426299	+	0.904582i	$0.359817\pi$
$458$	2253.86	+	6936.66i	0.229947	+	0.707705i
$459$		0			0
$460$	−5302.52	−	3852.50i	−0.537459	−	0.390487i
$461$	−11721.5			−1.18422			−0.592111	−	0.805856i	$-0.701705\pi$
$461$	−11721.5			−1.18422			−0.592111	+	0.805856i	$0.701705\pi$
$462$		0			0
$463$	−7337.56			−0.736512			−0.368256	−	0.929724i	$-0.620045\pi$
$463$	−7337.56			−0.736512			−0.368256	+	0.929724i	$0.620045\pi$
$464$	−14325.7	−	10408.2i	−1.43330	−	1.04136i
$465$		0			0
$466$	2087.88	+	6425.84i	0.207552	+	0.638779i
$467$	−8516.50	+	6187.60i	−0.843890	+	0.613122i	−0.923455	−	0.383708i	$-0.874647\pi$
$467$	−8516.50	+	6187.60i	−0.843890	+	0.613122i	0.0795645	+	0.996830i	$0.474647\pi$
$468$		0			0
$469$	−6949.08	−	21387.1i	−0.684176	−	2.10568i
$470$	−909.806	+	2800.09i	−0.0892898	+	0.274806i
$471$		0			0
$472$	9096.64			0.887091
$473$	7100.50	+	5538.40i	0.690236	+	0.538385i
$474$		0			0
$475$	5098.15	+	3704.02i	0.492462	+	0.357794i
$476$	−211.260	+	650.191i	−0.0203426	+	0.0626081i
$477$		0			0
$478$	−4823.38	+	3504.39i	−0.461540	+	0.335329i
$479$	−8519.68	+	6189.91i	−0.812681	+	0.590447i	−0.914607	−	0.404345i	$-0.867500\pi$
$479$	−8519.68	+	6189.91i	−0.812681	+	0.590447i	0.101926	+	0.994792i	$0.467500\pi$
$480$		0			0
$481$	1756.15	−	5404.88i	0.166473	−	0.512352i
$482$	−7615.23	−	5532.79i	−0.719635	−	0.522846i
$483$		0			0
$484$	−3838.86	+	2407.31i	−0.360524	+	0.226081i
$485$	16957.4			1.58762
$486$		0			0
$487$	260.953	−	803.130i	0.0242811	−	0.0747295i	−0.938182	−	0.346143i	$-0.887491\pi$
$487$	260.953	−	803.130i	0.0242811	−	0.0747295i	0.962463	+	0.271414i	$0.0874911\pi$
$488$	3100.85	+	9543.43i	0.287641	+	0.885268i
$489$		0			0
$490$	−7723.15	+	5611.20i	−0.712033	+	0.517323i
$491$	4083.24	+	12566.9i	0.375303	+	1.15507i	0.943274	+	0.332016i	$0.107729\pi$
$491$	4083.24	+	12566.9i	0.375303	+	1.15507i	−0.567970	+	0.823049i	$0.692271\pi$
$492$		0			0
$493$	−1547.48	−	1124.31i	−0.141369	−	0.102710i
$494$	11282.4			1.02757
$495$		0			0
$496$	−19231.6			−1.74098
$497$	−2829.10	−	2055.46i	−0.255337	−	0.185513i
$498$		0			0
$499$	−5250.64	−	16159.8i	−0.471044	−	1.44972i	−0.851219	−	0.524810i	$-0.824136\pi$
$499$	−5250.64	−	16159.8i	−0.471044	−	1.44972i	0.380176	−	0.924914i	$-0.375864\pi$
$500$	−2076.26	+	1508.49i	−0.185707	+	0.134924i
$501$		0			0
$502$	−1069.89	−	3292.78i	−0.0951225	−	0.292757i
$503$	−794.495	+	2445.20i	−0.0704270	+	0.216752i	−0.980075	−	0.198628i	$-0.936351\pi$
$503$	−794.495	+	2445.20i	−0.0704270	+	0.216752i	0.909648	+	0.415380i	$0.136351\pi$
$504$		0			0
$505$	15199.7			1.33936
$506$	−4680.93	−	16275.3i	−0.411250	−	1.42989i
$507$		0			0
$508$	4739.42	+	3443.39i	0.413933	+	0.300740i
$509$	6460.29	−	19882.7i	0.562569	−	1.73141i	−0.112499	−	0.993652i	$-0.535885\pi$
$509$	6460.29	−	19882.7i	0.562569	−	1.73141i	0.675067	−	0.737756i	$-0.264115\pi$
$510$		0			0
$511$	−8176.55	+	5940.61i	−0.707846	+	0.514280i
$512$	1330.65	−	966.775i	0.114857	−	0.0834489i
$513$		0			0
$514$	1767.57	−	5440.02i	0.151681	−	0.466827i
$515$	−11952.6	−	8684.10i	−1.02271	−	0.743043i
$516$		0			0
$517$	−1881.63	+	1271.36i	−0.160066	+	0.108152i
$518$	−11871.1			−1.00692
$519$		0			0
$520$	−2534.78	+	7801.26i	−0.213765	+	0.657900i
$521$	−227.454	−	700.032i	−0.0191266	−	0.0588656i	0.941038	−	0.338302i	$-0.109852\pi$
$521$	−227.454	−	700.032i	−0.0191266	−	0.0588656i	−0.960164	+	0.279436i	$0.909852\pi$
$522$		0			0
$523$	−10651.2	+	7738.58i	−0.890528	+	0.647007i	−0.936016	−	0.351958i	$-0.885516\pi$
$523$	−10651.2	+	7738.58i	−0.890528	+	0.647007i	0.0454874	+	0.998965i	$0.485516\pi$
$524$	711.683	+	2190.34i	0.0593321	+	0.182605i
$525$		0			0
$526$	3113.28	+	2261.93i	0.258071	+	0.187499i
$527$	−2077.42			−0.171715
$528$		0			0
$529$	6727.04			0.552892
$530$	−19032.4	−	13827.9i	−1.55984	−	1.13329i
$531$		0			0
$532$	−2174.00	−	6690.89i	−0.177171	−	0.545276i
$533$	−4324.19	+	3141.71i	−0.351410	+	0.255314i
$534$		0			0
$535$	−2330.83	−	7173.57i	−0.188356	−	0.579702i
$536$	−4620.39	+	14220.1i	−0.372333	+	1.14592i
$537$		0			0
$538$	−17999.9			−1.44243
$539$	−7358.90	−	251.100i	−0.588071	−	0.0200661i
$540$		0			0
$541$	17769.9	+	12910.6i	1.41218	+	1.02601i	0.993001	+	0.118106i	$0.0376823\pi$
$541$	17769.9	+	12910.6i	1.41218	+	1.02601i	0.419180	+	0.907903i	$0.362318\pi$
$542$	1588.44	−	4888.73i	0.125885	−	0.387433i
$543$		0			0
$544$	1007.90	−	732.285i	0.0794366	−	0.0577141i
$545$	−1425.74	+	1035.86i	−0.112059	+	0.0814154i
$546$		0			0
$547$	−5332.99	+	16413.3i	−0.416860	+	1.28296i	0.493717	+	0.869623i	$0.335638\pi$
$547$	−5332.99	+	16413.3i	−0.416860	+	1.28296i	−0.910577	+	0.413340i	$0.864362\pi$
$548$	776.683	+	564.293i	0.0605443	+	0.0439880i
$549$		0			0
$550$	8764.27	+	299.054i	0.679472	+	0.0231849i
$551$	19683.8			1.52188
$552$		0			0
$553$	−8957.87	+	27569.5i	−0.688838	+	2.12002i
$554$	−2847.85	−	8764.79i	−0.218400	−	0.672167i
$555$		0			0
$556$	1401.57	−	1018.30i	0.106906	−	0.0776718i
$557$	−5616.20	−	17284.9i	−0.427228	−	1.31487i	−0.900845	−	0.434141i	$-0.857052\pi$
$557$	−5616.20	−	17284.9i	−0.427228	−	1.31487i	0.473617	−	0.880731i	$-0.342948\pi$
$558$		0			0
$559$	−7535.44	−	5474.81i	−0.570152	−	0.414240i
$560$	26038.3			1.96486
$561$		0			0
$562$	23234.7			1.74394
$563$	18160.5	+	13194.4i	1.35946	+	0.987702i	0.998479	+	0.0551274i	$0.0175565\pi$
$563$	18160.5	+	13194.4i	1.35946	+	0.987702i	0.360976	+	0.932575i	$0.382443\pi$
$564$		0			0
$565$	−7359.81	−	22651.2i	−0.548017	−	1.68662i
$566$	−2381.14	+	1730.00i	−0.176832	+	0.128476i
$567$		0			0
$568$	718.497	+	2211.31i	0.0530765	+	0.163353i
$569$	−2899.51	+	8923.77i	−0.213627	+	0.657476i	0.785621	+	0.618708i	$0.212343\pi$
$569$	−2899.51	+	8923.77i	−0.213627	+	0.657476i	−0.999248	+	0.0387685i	$0.987657\pi$
$570$		0			0
$571$	7968.11			0.583984			0.291992	−	0.956421i	$-0.405682\pi$
$571$	7968.11			0.583984			0.291992	+	0.956421i	$0.405682\pi$
$572$	3883.47	−	2623.94i	0.283874	−	0.191805i
$573$		0			0
$574$	9032.67	+	6562.62i	0.656823	+	0.477210i
$575$	−3023.35	+	9304.92i	−0.219274	+	0.674855i
$576$		0			0
$577$	3988.11	−	2897.53i	0.287742	−	0.209057i	−0.434545	−	0.900650i	$-0.643091\pi$
$577$	3988.11	−	2897.53i	0.287742	−	0.209057i	0.722287	+	0.691593i	$0.243091\pi$
$578$	−13220.5	+	9605.24i	−0.951384	+	0.691221i
$579$		0			0
$580$	3275.99	−	10082.4i	0.234531	−	0.721812i
$581$	13471.2	+	9787.40i	0.961927	+	0.698881i
$582$		0			0
$583$	−5015.45	−	17438.4i	−0.356293	−	1.23881i
$584$	6719.92			0.476151
$585$		0			0
$586$	4759.55	−	14648.4i	0.335521	−	1.03263i
$587$	740.099	+	2277.79i	0.0520395	+	0.160161i	0.973699	−	0.227839i	$-0.0731660\pi$
$587$	740.099	+	2277.79i	0.0520395	+	0.160161i	−0.921659	+	0.388000i	$0.873166\pi$
$588$		0			0
$589$	17295.2	−	12565.7i	1.20991	−	0.879049i
$590$	8567.29	+	26367.4i	0.597813	+	1.83988i
$591$		0			0
$592$	9703.85	+	7050.26i	0.673692	+	0.489466i
$593$	7389.73			0.511737			0.255868	−	0.966712i	$-0.417639\pi$
$593$	7389.73			0.511737			0.255868	+	0.966712i	$0.417639\pi$
$594$		0			0
$595$	2812.69			0.193797
$596$	−618.415	−	449.305i	−0.0425021	−	0.0308796i
$597$		0			0
$598$	5412.95	+	16659.3i	0.370154	+	1.13922i
$599$	17663.1	−	12833.0i	1.20484	−	0.875364i	0.210084	−	0.977683i	$-0.432626\pi$
$599$	17663.1	−	12833.0i	1.20484	−	0.875364i	0.994752	+	0.102319i	$0.0326263\pi$
$600$		0			0
$601$	−1478.65	−	4550.80i	−0.100358	−	0.308871i	0.888255	−	0.459351i	$-0.151918\pi$
$601$	−1478.65	−	4550.80i	−0.100358	−	0.308871i	−0.988613	+	0.150480i	$0.951918\pi$
$602$	−6012.35	+	18504.1i	−0.407052	+	1.25278i
$603$		0			0
$604$	8990.55			0.605663
$605$	14300.0	+	11960.3i	0.960958	+	0.803730i
$606$		0			0
$607$	13630.6	+	9903.20i	0.911447	+	0.662205i	0.941380	−	0.337347i	$-0.109529\pi$
$607$	13630.6	+	9903.20i	0.911447	+	0.662205i	−0.0299333	+	0.999552i	$0.509529\pi$
$608$	−3961.75	+	12193.0i	−0.264260	+	0.813308i
$609$		0			0
$610$	−24742.1	+	17976.2i	−1.64226	+	1.19317i
$611$	1900.28	−	1380.63i	0.125822	−	0.0914147i
$612$		0			0
$613$	1062.30	−	3269.42i	0.0699933	−	0.215417i	−0.909941	−	0.414737i	$-0.863873\pi$
$613$	1062.30	−	3269.42i	0.0699933	−	0.215417i	0.979934	+	0.199320i	$0.0638734\pi$
$614$	−13227.9	−	9610.62i	−0.869436	−	0.631682i
$615$		0			0
$616$	10420.8	+	8128.24i	0.681600	+	0.531649i
$617$	−12049.1			−0.786186			−0.393093	−	0.919499i	$-0.628595\pi$
$617$	−12049.1			−0.786186			−0.393093	+	0.919499i	$0.628595\pi$
$618$		0			0
$619$	6812.82	−	20967.7i	0.442375	−	1.36149i	−0.442962	−	0.896541i	$-0.646072\pi$
$619$	6812.82	−	20967.7i	0.442375	−	1.36149i	0.885337	−	0.464950i	$-0.153928\pi$
$620$	−3557.96	−	10950.3i	−0.230469	−	0.709311i
$621$		0			0
$622$	−19863.9	+	14432.0i	−1.28050	+	0.930335i
$623$	−1615.95	−	4973.38i	−0.103919	−	0.319830i
$624$		0			0
$625$	15740.2	+	11435.9i	1.00737	+	0.731899i
$626$	−7572.78			−0.483497
$627$		0			0
$628$	1072.32			0.0681374
$629$	1048.22	+	761.577i	0.0664472	+	0.0482767i
$630$		0			0
$631$	880.012	+	2708.40i	0.0555194	+	0.170871i	0.974971	−	0.222332i	$-0.0713669\pi$
$631$	880.012	+	2708.40i	0.0555194	+	0.170871i	−0.919452	+	0.393203i	$0.871367\pi$
$632$	15593.1	−	11329.0i	0.981422	−	0.713045i
$633$		0			0
$634$	5676.38	+	17470.1i	0.355580	+	1.09436i
$635$	7447.96	−	22922.5i	0.465454	−	1.43252i
$636$		0			0
$637$	7616.05			0.473719
$638$	22696.7	−	15335.5i	1.40842	−	0.951626i
$639$		0			0
$640$	−18795.8	−	13655.9i	−1.16089	−	0.843434i
$641$	−3145.57	+	9681.08i	−0.193826	+	0.596536i	0.806162	+	0.591695i	$0.201541\pi$
$641$	−3145.57	+	9681.08i	−0.193826	+	0.596536i	−0.999988	+	0.00484133i	$0.998459\pi$
$642$		0			0
$643$	12706.0	−	9231.45i	0.779278	−	0.566178i	−0.125484	−	0.992096i	$-0.540048\pi$
$643$	12706.0	−	9231.45i	0.779278	−	0.566178i	0.904762	+	0.425917i	$0.140048\pi$
$644$	8836.62	−	6420.18i	0.540701	−	0.392842i
$645$		0			0
$646$	−794.874	+	2446.37i	−0.0484116	+	0.148996i
$647$	−2754.53	−	2001.28i	−0.167375	−	0.121605i	0.500944	−	0.865479i	$-0.332986\pi$
$647$	−2754.53	−	2001.28i	−0.167375	−	0.121605i	−0.668320	+	0.743874i	$0.732986\pi$
$648$		0			0
$649$	−7297.74	+	20100.3i	−0.441389	+	1.21572i
$650$	−9070.53			−0.547347
$651$		0			0
$652$	−1470.79	+	4526.62i	−0.0883443	+	0.271896i
$653$	−7928.85	−	24402.5i	−0.475161	−	1.46239i	−0.845741	−	0.533594i	$-0.820841\pi$
$653$	−7928.85	−	24402.5i	−0.475161	−	1.46239i	0.370580	−	0.928801i	$-0.379159\pi$
$654$		0			0
$655$	7665.66	−	5569.43i	0.457286	−	0.332237i
$656$	−3486.07	−	10729.0i	−0.207482	−	0.638564i
$657$		0			0
$658$	−3969.43	−	2883.96i	−0.235174	−	0.170864i
$659$	−30937.0			−1.82873			−0.914367	−	0.404887i	$-0.867311\pi$
$659$	−30937.0			−1.82873			−0.914367	+	0.404887i	$0.867311\pi$
$660$		0			0
$661$	−17637.6			−1.03786			−0.518928	−	0.854818i	$-0.673669\pi$
$661$	−17637.6			−1.03786			−0.518928	+	0.854818i	$0.673669\pi$
$662$	23079.7	+	16768.4i	1.35501	+	0.984473i
$663$		0			0
$664$	−3421.23	−	10529.5i	−0.199954	−	0.615396i
$665$	−23416.5	+	17013.1i	−1.36550	+	0.992090i
$666$		0			0
$667$	9443.71	+	29064.7i	0.548219	+	1.68724i
$668$	1217.38	−	3746.71i	0.0705118	−	0.217013i
$669$		0			0
$670$	−45569.7			−2.62763
$671$	−23575.1	−	804.429i	−1.35635	−	0.0462811i
$672$		0			0
$673$	−22173.8	−	16110.2i	−1.27004	−	0.922738i	−0.270835	−	0.962626i	$-0.587300\pi$
$673$	−22173.8	−	16110.2i	−1.27004	−	0.922738i	−0.999204	+	0.0398882i	$0.987300\pi$
$674$	3252.12	−	10009.0i	0.185856	−	0.572006i
$675$		0			0
$676$	2129.02	−	1546.83i	0.121132	−	0.0880079i
$677$	1490.85	−	1083.16i	0.0846351	−	0.0614910i	−0.544663	−	0.838655i	$-0.683342\pi$
$677$	1490.85	−	1083.16i	0.0846351	−	0.0614910i	0.629298	+	0.777164i	$0.283342\pi$
$678$		0			0
$679$	−8732.63	+	26876.3i	−0.493560	+	1.51902i
$680$	−1512.97	−	1099.24i	−0.0853234	−	0.0619911i
$681$		0			0
$682$	10152.6	−	27963.6i	0.570037	−	1.57006i
$683$	−9024.46			−0.505580			−0.252790	−	0.967521i	$-0.581348\pi$
$683$	−9024.46			−0.505580			−0.252790	+	0.967521i	$0.581348\pi$
$684$		0			0
$685$	1220.55	−	3756.47i	0.0680801	−	0.209529i
$686$	3438.77	+	10583.4i	0.191389	+	0.589034i
$687$		0			0
$688$	15904.3	−	11555.2i	0.881317	−	0.640314i
$689$	5799.79	+	17849.9i	0.320688	+	0.986978i
$690$		0			0
$691$	−6227.01	−	4524.19i	−0.342817	−	0.249071i	0.403032	−	0.915186i	$-0.367956\pi$
$691$	−6227.01	−	4524.19i	−0.342817	−	0.249071i	−0.745850	+	0.666114i	$0.767956\pi$
$692$	−2416.08			−0.132725
$693$		0			0
$694$	12879.0			0.704440
$695$	−5766.36	−	4189.51i	−0.314720	−	0.228658i
$696$		0			0
$697$	−376.569	−	1158.96i	−0.0204642	−	0.0629825i
$698$	−5482.42	+	3983.21i	−0.297296	+	0.215998i
$699$		0			0
$700$	1747.80	+	5379.18i	0.0943724	+	0.290448i
$701$	4124.93	−	12695.2i	0.222249	−	0.684011i	−0.776310	−	0.630351i	$-0.782911\pi$
$701$	4124.93	−	12695.2i	0.222249	−	0.684011i	0.998559	−	0.0536607i	$-0.0170889\pi$
$702$		0			0
$703$	−13333.3			−0.715328
$704$	−1493.85	−	5194.01i	−0.0799736	−	0.278063i
$705$		0			0
$706$	−21820.4	−	15853.5i	−1.16321	−	0.845118i
$707$	−7827.49	+	24090.5i	−0.416383	+	1.28150i
$708$		0			0
$709$	19619.8	−	14254.6i	1.03926	−	0.755067i	0.0691197	−	0.997608i	$-0.477981\pi$
$709$	19619.8	−	14254.6i	1.03926	−	0.755067i	0.970141	+	0.242541i	$0.0779809\pi$
$710$	−5732.98	+	4165.25i	−0.303035	+	0.220168i
$711$		0			0
$712$	−1074.43	+	3306.77i	−0.0565535	+	0.174054i
$713$	26852.0	+	19509.1i	1.41040	+	1.02471i
$714$		0			0
$715$	−15204.4	−	11859.5i	−0.795263	−	0.620306i
$716$	1358.09			0.0708857
$717$		0			0
$718$	−537.064	+	1652.91i	−0.0279151	+	0.0859139i
$719$	4397.77	+	13534.9i	0.228107	+	0.702042i	0.997961	+	0.0638217i	$0.0203289\pi$
$719$	4397.77	+	13534.9i	0.228107	+	0.702042i	−0.769854	+	0.638220i	$0.779671\pi$
$720$		0			0
$721$	19919.0	−	14472.0i	1.02888	−	0.747525i
$722$	−1021.98	−	3145.33i	−0.0526788	−	0.162129i
$723$		0			0
$724$	−934.073	−	678.644i	−0.0479483	−	0.0348365i
$725$	−15824.9			−0.810652
$726$		0			0
$727$	−9582.44			−0.488849			−0.244424	−	0.969668i	$-0.578599\pi$
$727$	−9582.44			−0.488849			−0.244424	+	0.969668i	$0.578599\pi$
$728$	−11059.1	−	8034.91i	−0.563019	−	0.409057i
$729$		0			0
$730$	6328.87	+	19478.3i	0.320880	+	0.987566i
$731$	1718.00	−	1248.20i	0.0869256	−	0.0631551i
$732$		0			0
$733$	5812.90	+	17890.3i	0.292912	+	0.901491i	0.983915	+	0.178638i	$0.0571692\pi$
$733$	5812.90	+	17890.3i	0.292912	+	0.901491i	−0.691003	+	0.722852i	$0.742831\pi$
$734$	2875.19	−	8848.91i	0.144585	−	0.444985i
$735$		0			0
$736$	−19904.7			−0.996870
$737$	−27714.5	−	21617.4i	−1.38518	−	1.08044i
$738$		0			0
$739$	−11667.0	−	8476.60i	−0.580756	−	0.421944i	0.258240	−	0.966081i	$-0.416857\pi$
$739$	−11667.0	−	8476.60i	−0.580756	−	0.421944i	−0.838997	+	0.544136i	$0.816857\pi$
$740$	−2219.07	+	6829.60i	−0.110236	+	0.339272i
$741$		0			0
$742$	31717.5	−	23044.1i	1.56925	−	1.14013i
$743$	7563.70	−	5495.35i	0.373466	−	0.271339i	−0.385181	−	0.922841i	$-0.625861\pi$
$743$	7563.70	−	5495.35i	0.373466	−	0.271339i	0.758647	+	0.651502i	$0.225861\pi$
$744$		0			0
$745$	−971.835	+	2991.00i	−0.0477923	+	0.147090i
$746$	524.447	+	381.033i	0.0257391	+	0.0187006i
$747$		0			0
$748$	295.352	+	1026.92i	0.0144373	+	0.0501978i
$749$	12569.9			0.613211
$750$		0			0
$751$	−2379.38	+	7322.96i	−0.115612	+	0.355817i	−0.992074	−	0.125653i	$-0.959897\pi$
$751$	−2379.38	+	7322.96i	−0.115612	+	0.355817i	0.876462	+	0.481471i	$0.159897\pi$
$752$	1531.96	+	4714.89i	0.0742884	+	0.228636i
$753$		0			0
$754$	−22921.6	+	16653.5i	−1.10710	+	0.804356i
$755$	−11430.3	−	35178.7i	−0.550980	−	1.69574i
$756$		0			0
$757$	−32243.5	−	23426.3i	−1.54810	−	1.12476i	−0.944991	−	0.327097i	$-0.893930\pi$
$757$	−32243.5	−	23426.3i	−1.54810	−	1.12476i	−0.603106	−	0.797661i	$-0.706070\pi$
$758$	−5306.60			−0.254280
$759$		0			0
$760$	19244.9			0.918536
$761$	23628.2	+	17166.9i	1.12552	+	0.817737i	0.985036	−	0.172346i	$-0.0551347\pi$
$761$	23628.2	+	17166.9i	1.12552	+	0.817737i	0.140482	+	0.990083i	$0.455135\pi$
$762$		0			0
$763$	−907.547	−	2793.14i	−0.0430608	−	0.132528i
$764$	−4130.19	+	3000.76i	−0.195582	+	0.142099i
$765$		0			0
$766$	−14973.4	−	46083.2i	−0.706278	−	2.17370i
$767$	6834.97	−	21035.9i	0.321768	−	0.990301i
$768$		0			0
$769$	19737.4			0.925553			0.462777	−	0.886475i	$-0.346853\pi$
$769$	19737.4			0.925553			0.462777	+	0.886475i	$0.346853\pi$
$770$	−13746.0	+	37860.8i	−0.643340	+	1.77196i
$771$		0			0
$772$	3496.56	+	2540.40i	0.163010	+	0.118434i
$773$	11172.5	−	34385.3i	0.519852	−	1.59994i	−0.254424	−	0.967093i	$-0.581886\pi$
$773$	11172.5	−	34385.3i	0.519852	−	1.59994i	0.774276	−	0.632848i	$-0.218114\pi$
$774$		0			0
$775$	−13904.6	+	10102.3i	−0.644473	+	0.468237i
$776$	15201.0	−	11044.2i	0.703201	−	0.510905i
$777$		0			0
$778$	7871.68	−	24226.5i	0.362742	−	1.11641i
$779$	10145.3	+	7370.96i	0.466613	+	0.339014i
$780$		0			0
$781$	−5462.59	−	186.394i	−0.250278	−	0.00853995i
$782$	−3993.62			−0.182623
$783$		0			0
$784$	−4967.28	+	15287.7i	−0.226279	+	0.696415i
$785$	−1363.31	−	4195.84i	−0.0619855	−	0.190772i
$786$		0			0
$787$	−8525.61	+	6194.22i	−0.386157	+	0.280559i	−0.763879	−	0.645360i	$-0.776707\pi$
$787$	−8525.61	+	6194.22i	−0.386157	+	0.280559i	0.377722	+	0.925919i	$0.376707\pi$
$788$	−2073.36	−	6381.16i	−0.0937317	−	0.288476i
$789$		0			0
$790$	47523.9	+	34528.1i	2.14028	+	1.55501i
$791$	39690.7			1.78412
$792$		0			0
$793$	24398.9			1.09260
$794$	−8219.15	−	5971.56i	−0.367363	−	0.266905i
$795$		0			0
$796$	3899.57	+	12001.6i	0.173639	+	0.534406i
$797$	−22288.7	+	16193.7i	−0.990597	+	0.719711i	−0.960052	−	0.279823i	$-0.909724\pi$
$797$	−22288.7	+	16193.7i	−0.990597	+	0.719711i	−0.0305449	+	0.999533i	$0.509724\pi$
$798$		0			0
$799$	165.484	+	509.308i	0.00732717	+	0.0225507i
$800$	3185.07	−	9802.63i	0.140761	−	0.433219i
$801$		0			0
$802$	44504.1			1.95947
$803$	−5391.02	+	14848.6i	−0.236918	+	0.652546i
$804$		0			0
$805$	−36355.8	−	26414.0i	−1.59177	−	1.15649i
$806$	−9508.84	+	29265.2i	−0.415552	+	1.27894i
$807$		0			0
$808$	13625.4	−	9899.43i	0.593243	−	0.431016i
$809$	34358.5	−	24962.9i	1.49318	−	1.08486i	0.520174	−	0.854060i	$-0.325867\pi$
$809$	34358.5	−	24962.9i	1.49318	−	1.08486i	0.973002	−	0.230796i	$-0.0741330\pi$
$810$		0			0
$811$	−956.111	+	2942.61i	−0.0413978	+	0.127409i	−0.969619	−	0.244618i	$-0.921337\pi$
$811$	−956.111	+	2942.61i	−0.0413978	+	0.127409i	0.928222	+	0.372028i	$0.121337\pi$
$812$	14292.9	+	10384.4i	0.617714	+	0.448795i
$813$		0			0
$814$	−15374.2	+	10387.9i	−0.661996	+	0.447291i
$815$	19581.9			0.841625
$816$		0			0
$817$	−6752.91	+	20783.3i	−0.289173	+	0.889984i
$818$	11221.8	+	34537.2i	0.479660	+	1.47624i
$819$		0			0
$820$	5464.04	−	3969.85i	0.232698	−	0.169065i
$821$	9187.58	+	28276.5i	0.390559	+	1.20202i	0.932367	+	0.361514i	$0.117740\pi$
$821$	9187.58	+	28276.5i	0.390559	+	1.20202i	−0.541808	+	0.840502i	$0.682260\pi$
$822$		0			0
$823$	23522.1	+	17089.8i	0.996268	+	0.723831i	0.961285	−	0.275557i	$-0.0888622\pi$
$823$	23522.1	+	17089.8i	0.996268	+	0.723831i	0.0349832	+	0.999388i	$0.488862\pi$
$824$	−16370.5			−0.692103
$825$		0			0
$826$	−46202.5			−1.94623
$827$	−28084.0	−	20404.3i	−1.18087	−	0.857951i	−0.188599	−	0.982054i	$-0.560395\pi$
$827$	−28084.0	−	20404.3i	−1.18087	−	0.857951i	−0.992269	+	0.124103i	$0.960395\pi$
$828$		0			0
$829$	11291.2	+	34750.7i	0.473051	+	1.45590i	0.848568	+	0.529086i	$0.177465\pi$
$829$	11291.2	+	34750.7i	0.473051	+	1.45590i	−0.375517	+	0.926815i	$0.622535\pi$
$830$	27298.4	−	19833.5i	1.14162	−	0.829434i
$831$		0			0
$832$	1727.46	+	5316.57i	0.0719818	+	0.221537i
$833$	−536.571	+	1651.40i	−0.0223182	+	0.0686884i
$834$		0			0
$835$	−16208.1			−0.671741
$836$	−8670.42	−	6762.94i	−0.358700	−	0.279786i
$837$		0			0
$838$	−1202.91	−	873.968i	−0.0495871	−	0.0360271i
$839$	−1495.43	+	4602.45i	−0.0615350	+	0.189385i	−0.977098	−	0.212789i	$-0.931745\pi$
$839$	−1495.43	+	4602.45i	−0.0615350	+	0.189385i	0.915563	+	0.402174i	$0.131745\pi$
$840$		0			0
$841$	−20259.0	+	14719.1i	−0.830663	+	0.603512i
$842$	30003.8	−	21799.0i	1.22803	−	0.892213i
$843$		0			0
$844$	−3050.56	+	9388.65i	−0.124413	+	0.382904i
$845$	−8759.28	−	6363.99i	−0.356601	−	0.259086i
$846$		0			0
$847$	−26320.5	+	16505.3i	−1.06775	+	0.669574i
$848$	−39612.9			−1.60414
$849$		0			0
$850$	639.043	−	1966.77i	0.0257871	−	0.0793644i
$851$	−6396.93	−	19687.7i	−0.257678	−	0.793051i
$852$		0			0
$853$	34422.9	−	25009.7i	1.38173	−	1.00389i	0.385015	−	0.922910i	$-0.374196\pi$
$853$	34422.9	−	25009.7i	1.38173	−	1.00389i	0.996716	−	0.0809764i	$-0.0258038\pi$
$854$	−15749.4	−	48471.7i	−0.631071	−	1.94224i
$855$		0			0
$856$	−6761.48	−	4912.51i	−0.269980	−	0.196152i
$857$	−4754.94			−0.189528			−0.0947640	−	0.995500i	$-0.530210\pi$
$857$	−4754.94			−0.189528			−0.0947640	+	0.995500i	$0.530210\pi$
$858$		0			0
$859$	−15180.5			−0.602972			−0.301486	−	0.953471i	$-0.597483\pi$
$859$	−15180.5			−0.602972			−0.301486	+	0.953471i	$0.597483\pi$
$860$	9521.76	+	6917.96i	0.377546	+	0.274303i
$861$		0			0
$862$	4500.24	+	13850.3i	0.177818	+	0.547266i
$863$	−26671.9	+	19378.3i	−1.05206	+	0.764363i	−0.972602	−	0.232476i	$-0.925317\pi$
$863$	−26671.9	+	19378.3i	−1.05206	+	0.764363i	−0.0794529	+	0.996839i	$0.525317\pi$
$864$		0			0
$865$	3071.71	+	9453.76i	0.120741	+	0.371604i
$866$	−11403.7	+	35096.9i	−0.447474	+	1.37718i
$867$		0			0
$868$	19187.7			0.750313
$869$	12523.5	+	43543.6i	0.488875	+	1.69979i
$870$		0			0
$871$	29412.2	+	21369.2i	1.14419	+	0.831306i
$872$	−603.421	+	1857.14i	−0.0234340	+	0.0721223i
$873$		0			0
$874$	33248.1	−	24156.2i	1.28677	−	0.934891i
$875$	−14235.5	+	10342.7i	−0.549999	+	0.399597i
$876$		0			0
$877$	12504.4	−	38484.7i	0.481465	−	1.48180i	−0.355570	−	0.934650i	$-0.615713\pi$
$877$	12504.4	−	38484.7i	0.481465	−	1.48180i	0.837036	−	0.547149i	$-0.184287\pi$
$878$	−15451.7	−	11226.3i	−0.593931	−	0.431516i
$879$		0			0
$880$	33722.0	−	22785.0i	1.29178	−	0.872820i
$881$	33385.1			1.27670			0.638350	−	0.769746i	$-0.279617\pi$
$881$	33385.1			1.27670			0.638350	+	0.769746i	$0.279617\pi$
$882$		0			0
$883$	−4006.70	+	12331.4i	−0.152702	+	0.469969i	−0.997921	−	0.0644514i	$-0.979470\pi$
$883$	−4006.70	+	12331.4i	−0.152702	+	0.469969i	0.845219	+	0.534421i	$0.179470\pi$
$884$	−341.540	−	1051.15i	−0.0129946	−	0.0399933i
$885$		0			0
$886$	−7931.65	+	5762.68i	−0.300755	+	0.218511i
$887$	−4396.87	−	13532.2i	−0.166440	−	0.512251i	0.832699	−	0.553726i	$-0.186794\pi$
$887$	−4396.87	−	13532.2i	−0.166440	−	0.512251i	−0.999140	+	0.0414749i	$0.986794\pi$
$888$		0			0
$889$	32495.0	+	23609.0i	1.22593	+	0.890687i
$890$	−10596.9			−0.399110
$891$		0			0
$892$	−21348.6			−0.801349
$893$	−4458.36	−	3239.19i	−0.167070	−	0.121383i
$894$		0			0
$895$	−1726.62	−	5314.00i	−0.0644857	−	0.198467i
$896$	31323.1	−	22757.5i	1.16789	−	0.848522i
$897$		0			0
$898$	3628.99	+	11168.9i	0.134856	+	0.415045i
$899$	−16589.6	+	51057.6i	−0.615455	+	1.89418i
$900$		0			0
$901$	−4279.03			−0.158219
$902$	17440.8	+	595.113i	0.643808	+	0.0219680i
$903$		0			0
$904$	−21350.0	−	15511.7i	−0.785498	−	0.570697i
$905$	−1467.89	+	4517.70i	−0.0539163	+	0.165937i
$906$		0			0
$907$	−17142.6	+	12454.8i	−0.627576	+	0.455960i	−0.855559	−	0.517705i	$-0.826787\pi$
$907$	−17142.6	+	12454.8i	−0.627576	+	0.455960i	0.227984	+	0.973665i	$0.426787\pi$
$908$	4132.96	−	3002.77i	0.151054	−	0.109747i
$909$		0			0
$910$	12874.3	−	39623.1i	0.468989	−	1.44340i
$911$	−22910.1	−	16645.2i	−0.833200	−	0.605355i	0.0872628	−	0.996185i	$-0.472188\pi$
$911$	−22910.1	−	16645.2i	−0.833200	−	0.605355i	−0.920463	+	0.390830i	$0.872188\pi$
$912$		0			0
$913$	26010.9	+	887.543i	0.942866	+	0.0321724i
$914$	−12327.0			−0.446105
$915$		0			0
$916$	−2272.10	+	6992.81i	−0.0819568	+	0.252237i
$917$	4879.53	+	15017.7i	0.175721	+	0.540814i
$918$		0			0
$919$	5785.49	−	4203.40i	0.207667	−	0.150879i	−0.479091	−	0.877765i	$-0.659033\pi$
$919$	5785.49	−	4203.40i	0.207667	−	0.150879i	0.686757	+	0.726887i	$0.259033\pi$
$920$	9233.15	+	28416.7i	0.330878	+	1.01834i
$921$		0			0
$922$	−32024.2	−	23266.9i	−1.14388	−	0.831080i
$923$	5653.47			0.201610
$924$		0			0
$925$	10719.4			0.381029
$926$	−20046.8	−	14564.8i	−0.711424	−	0.516880i
$927$		0			0
$928$	−9948.85	−	30619.4i	−0.351926	−	1.08312i
$929$	−27003.5	+	19619.2i	−0.953666	+	0.692879i	−0.951671	−	0.307119i	$-0.900635\pi$
$929$	−27003.5	+	19619.2i	−0.953666	+	0.692879i	−0.00199468	+	0.999998i	$0.500635\pi$
$930$		0			0
$931$	−5521.67	−	16993.9i	−0.194377	−	0.598232i
$932$	−2104.78	+	6477.86i	−0.0739747	+	0.227671i
$933$		0			0
$934$	−35550.0			−1.24543
$935$	3642.69	−	2461.26i	0.127410	−	0.0860875i
$936$		0			0
$937$	−8163.43	−	5931.08i	−0.284618	−	0.206787i	0.436311	−	0.899796i	$-0.356285\pi$
$937$	−8163.43	−	5931.08i	−0.284618	−	0.206787i	−0.720929	+	0.693009i	$0.756285\pi$
$938$	23467.3	−	72224.9i	0.816881	−	2.51410i
$939$		0			0
$940$	−2401.18	+	1744.56i	−0.0833170	+	0.0605333i
$941$	16833.5	−	12230.2i	0.583162	−	0.423692i	−0.256701	−	0.966491i	$-0.582635\pi$
$941$	16833.5	−	12230.2i	0.583162	−	0.423692i	0.839863	+	0.542799i	$0.182635\pi$
$942$		0			0
$943$	−6016.43	+	18516.7i	−0.207764	+	0.639433i
$944$	37767.5	+	27439.7i	1.30215	+	0.946066i
$945$		0			0
$946$	8405.56	+	29225.7i	0.288888	+	1.00445i
$947$	−35396.1			−1.21459			−0.607296	−	0.794476i	$-0.707746\pi$
$947$	−35396.1			−1.21459			−0.607296	+	0.794476i	$0.707746\pi$
$948$		0			0
$949$	5049.16	−	15539.7i	0.172711	−	0.531550i
$950$	6576.17	+	20239.4i	0.224589	+	0.691213i
$951$		0			0
$952$	2521.36	−	1831.88i	0.0858381	−	0.0623650i
$953$	9626.73	+	29628.0i	0.327220	+	1.00708i	0.970429	+	0.241388i	$0.0776026\pi$
$953$	9626.73	+	29628.0i	0.327220	+	1.00708i	−0.643209	+	0.765690i	$0.722397\pi$
$954$		0			0
$955$	16992.5	+	12345.8i	0.575774	+	0.418324i
$956$	−6010.29			−0.203333
$957$		0			0
$958$	−35563.3			−1.19937
$959$	5325.19	+	3868.98i	0.179311	+	0.130277i
$960$		0			0
$961$	8811.58	+	27119.2i	0.295780	+	0.910317i
$962$	15526.5	−	11280.7i	0.520368	−	0.378070i
$963$		0			0
$964$	−2932.31	−	9024.71i	−0.0979701	−	0.301521i
$965$	5494.81	−	16911.3i	0.183300	−	0.564139i
$966$		0			0
$967$	−10002.0			−0.332620			−0.166310	−	0.986074i	$-0.553185\pi$
$967$	−10002.0			−0.332620			−0.166310	+	0.986074i	$0.553185\pi$
$968$	20608.5	+	1408.04i	0.684280	+	0.0467523i
$969$		0			0
$970$	46328.9	+	33659.9i	1.53354	+	1.11418i
$971$	−6382.61	+	19643.7i	−0.210945	+	0.649222i	0.788472	+	0.615071i	$0.210873\pi$
$971$	−6382.61	+	19643.7i	−0.210945	+	0.649222i	−0.999417	+	0.0341510i	$0.989127\pi$
$972$		0			0
$973$	9609.62	−	6981.79i	0.316619	−	0.230037i
$974$	2307.13	−	1676.23i	0.0758987	−	0.0551436i
$975$		0			0
$976$	−15913.3	+	48976.1i	−0.521898	+	1.60624i
$977$	−6476.46	−	4705.43i	−0.212078	−	0.154084i	0.476675	−	0.879079i	$-0.341842\pi$
$977$	−6476.46	−	4705.43i	−0.212078	−	0.154084i	−0.688753	+	0.724996i	$0.741842\pi$
$978$		0			0
$979$	−6444.78	−	5026.94i	−0.210394	−	0.164108i
$980$	−9623.62			−0.313689
$981$		0			0
$982$	−13789.2	+	42438.9i	−0.448098	+	1.37910i
$983$	1850.68	+	5695.79i	0.0600482	+	0.184809i	0.976581	−	0.215150i	$-0.0690241\pi$
$983$	1850.68	+	5695.79i	0.0600482	+	0.184809i	−0.916533	+	0.399960i	$0.869024\pi$
$984$		0			0
$985$	−22332.6	+	16225.6i	−0.722411	+	0.524862i
$986$	−1996.11	−	6143.39i	−0.0644717	−	0.198423i
$987$		0			0
$988$	9201.52	+	6685.30i	0.296295	+	0.215271i
$989$	−33928.1			−1.09085
$990$		0			0
$991$	24763.7			0.793787			0.396894	−	0.917865i	$-0.370088\pi$
$991$	24763.7			0.793787			0.396894	+	0.917865i	$0.370088\pi$
$992$	−28288.3	−	20552.6i	−0.905397	−	0.657809i
$993$		0			0
$994$	−3649.30	−	11231.4i	−0.116447	−	0.358388i
$995$	42002.9	−	30516.9i	1.33827	−	0.972313i
$996$		0			0
$997$	−3134.12	−	9645.82i	−0.0995572	−	0.306406i	0.888857	−	0.458184i	$-0.151500\pi$
$997$	−3134.12	−	9645.82i	−0.0995572	−	0.306406i	−0.988415	+	0.151779i	$0.951500\pi$
$998$	17731.6	−	54572.3i	0.562409	−	1.73092i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.d.37.3		12
3.2	odd	2		33.4.e.c.4.1	✓	12
11.3	even	5	inner	99.4.f.d.91.3		12
11.5	even	5		1089.4.a.bi.1.2		6
11.6	odd	10		1089.4.a.bk.1.5		6
33.5	odd	10		363.4.a.v.1.5		6
33.14	odd	10		33.4.e.c.25.1	yes	12
33.17	even	10		363.4.a.u.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.c.4.1	✓	12	3.2	odd	2
33.4.e.c.25.1	yes	12	33.14	odd	10
99.4.f.d.37.3		12	1.1	even	1	trivial
99.4.f.d.91.3		12	11.3	even	5	inner
363.4.a.u.1.2		6	33.17	even	10
363.4.a.v.1.5		6	33.5	odd	10
1089.4.a.bi.1.2		6	11.5	even	5
1089.4.a.bk.1.5		6	11.6	odd	10

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Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	99.4.f.d.37.3

Level	$99$
Weight	$4$
Character	99.37
Analytic conductor	$5.841$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$