LMFDB - Embedded newform 99.4.f.d.64.1

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			64.1
Root			$1.27457 + 3.92271i$ of defining polynomial
Character	$\chi$	$=$	99.64
Dual form			99.4.f.d.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.58358 + 4.87376i) q^{2} +(-14.7737 - 10.7337i) q^{4} +(-4.61569 - 14.2056i) q^{5} +(9.98349 + 7.25343i) q^{7} +(42.5421 - 30.9086i) q^{8} +76.5442 q^{10} +(31.7200 + 18.0234i) q^{11} +(9.43188 - 29.0283i) q^{13} +(-51.1612 + 37.1708i) q^{14} +(38.1281 + 117.346i) q^{16} +(-40.8103 - 125.601i) q^{17} +(18.0466 - 13.1116i) q^{19} +(-84.2885 + 259.413i) q^{20} +(-138.073 + 126.054i) q^{22} +158.801 q^{23} +(-79.3681 + 57.6643i) q^{25} +(126.541 + 91.9375i) q^{26} +(-69.6368 - 214.320i) q^{28} +(-38.6035 - 28.0471i) q^{29} +(21.0238 - 64.7045i) q^{31} -211.617 q^{32} +676.778 q^{34} +(56.9588 - 175.301i) q^{35} +(-128.156 - 93.1106i) q^{37} +(35.3247 + 108.718i) q^{38} +(-635.437 - 461.672i) q^{40} +(231.508 - 168.200i) q^{41} +103.549 q^{43} +(-275.164 - 606.746i) q^{44} +(-251.475 + 773.960i) q^{46} +(-375.576 + 272.872i) q^{47} +(-58.9350 - 181.383i) q^{49} +(-155.356 - 478.138i) q^{50} +(-450.926 + 327.617i) q^{52} +(1.86904 - 5.75232i) q^{53} +(109.624 - 533.793i) q^{55} +648.912 q^{56} +(197.827 - 143.729i) q^{58} +(-179.294 - 130.264i) q^{59} +(-84.7750 - 260.911i) q^{61} +(282.061 + 204.930i) q^{62} +(30.0884 - 92.6027i) q^{64} -455.900 q^{65} +187.178 q^{67} +(-745.250 + 2293.64i) q^{68} +(764.178 + 555.208i) q^{70} +(141.442 + 435.312i) q^{71} +(218.703 + 158.897i) q^{73} +(656.744 - 477.153i) q^{74} -407.352 q^{76} +(185.945 + 410.015i) q^{77} +(152.545 - 469.486i) q^{79} +(1490.99 - 1083.27i) q^{80} +(453.157 + 1394.67i) q^{82} +(83.7540 + 257.768i) q^{83} +(-1595.88 + 1159.47i) q^{85} +(-163.979 + 504.674i) q^{86} +(1906.51 - 213.670i) q^{88} +77.4891 q^{89} +(304.718 - 221.391i) q^{91} +(-2346.08 - 1704.53i) q^{92} +(-735.158 - 2262.58i) q^{94} +(-269.556 - 195.844i) q^{95} +(-392.262 + 1207.26i) q^{97} +977.348 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−1.58358	+	4.87376i	−0.559881	+	1.72314i	0.122812	+	0.992430i	$0.460809\pi$
$2$	−1.58358	+	4.87376i	−0.559881	+	1.72314i	−0.682692	+	0.730706i	$0.739191\pi$
$3$		0			0
$3$		0			0
$4$	−14.7737	−	10.7337i	−1.84671	−	1.34172i
$5$	−4.61569	−	14.2056i	−0.412840	−	1.27059i	−0.914169	−	0.405333i	$-0.867155\pi$
$5$	−4.61569	−	14.2056i	−0.412840	−	1.27059i	0.501329	−	0.865257i	$-0.332845\pi$
$6$		0			0
$7$	9.98349	+	7.25343i	0.539058	+	0.391648i	0.823735	−	0.566975i	$-0.191886\pi$
$7$	9.98349	+	7.25343i	0.539058	+	0.391648i	−0.284677	+	0.958623i	$0.591886\pi$
$8$	42.5421	−	30.9086i	1.88011	−	1.36598i
$9$		0			0
$10$	76.5442			2.42054
$11$	31.7200	+	18.0234i	0.869449	+	0.494023i
$11$	31.7200	+	18.0234i	0.869449	+	0.494023i
$12$		0			0
$13$	9.43188	−	29.0283i	0.201226	−	0.619308i	−0.798622	−	0.601833i	$-0.794437\pi$
$13$	9.43188	−	29.0283i	0.201226	−	0.619308i	0.999847	−	0.0174752i	$-0.00556282\pi$
$14$	−51.1612	+	37.1708i	−0.976671	+	0.709593i
$15$		0			0
$16$	38.1281	+	117.346i	0.595751	+	1.83353i
$17$	−40.8103	−	125.601i	−0.582233	−	1.79193i	−0.610109	−	0.792317i	$-0.708874\pi$
$17$	−40.8103	−	125.601i	−0.582233	−	1.79193i	0.0278760	−	0.999611i	$-0.491126\pi$
$18$		0			0
$19$	18.0466	−	13.1116i	0.217904	−	0.158316i	−0.473479	−	0.880805i	$-0.657002\pi$
$19$	18.0466	−	13.1116i	0.217904	−	0.158316i	0.691383	+	0.722489i	$0.257002\pi$
$20$	−84.2885	+	259.413i	−0.942374	+	2.90033i
$21$		0			0
$22$	−138.073	+	126.054i	−1.33806	+	1.22158i
$23$	158.801			1.43967			0.719834	−	0.694147i	$-0.244218\pi$
$23$	158.801			1.43967			0.719834	+	0.694147i	$0.244218\pi$
$24$		0			0
$25$	−79.3681	+	57.6643i	−0.634945	+	0.461314i
$26$	126.541	+	91.9375i	0.954490	+	0.693478i
$27$		0			0
$28$	−69.6368	−	214.320i	−0.470004	−	1.44652i
$29$	−38.6035	−	28.0471i	−0.247189	−	0.179594i	0.457291	−	0.889317i	$-0.348820\pi$
$29$	−38.6035	−	28.0471i	−0.247189	−	0.179594i	−0.704480	+	0.709724i	$0.748820\pi$
$30$		0			0
$31$	21.0238	−	64.7045i	0.121806	−	0.374880i	−0.871500	−	0.490396i	$-0.836852\pi$
$31$	21.0238	−	64.7045i	0.121806	−	0.374880i	0.993306	+	0.115516i	$0.0368522\pi$
$32$	−211.617			−1.16903
$33$		0			0
$34$	676.778			3.41372
$35$	56.9588	−	175.301i	0.275080	−	0.846609i
$36$		0			0
$37$	−128.156	−	93.1106i	−0.569424	−	0.413710i	0.265472	−	0.964119i	$-0.414472\pi$
$37$	−128.156	−	93.1106i	−0.569424	−	0.413710i	−0.834896	+	0.550408i	$0.814472\pi$
$38$	35.3247	+	108.718i	0.150801	+	0.464116i
$39$		0			0
$40$	−635.437	−	461.672i	−2.51179	−	1.82492i
$41$	231.508	−	168.200i	0.881839	−	0.640694i	−0.0518980	−	0.998652i	$-0.516527\pi$
$41$	231.508	−	168.200i	0.881839	−	0.640694i	0.933737	+	0.357959i	$0.116527\pi$
$42$		0			0
$43$	103.549			0.367235			0.183617	−	0.982998i	$-0.441219\pi$
$43$	103.549			0.367235			0.183617	+	0.982998i	$0.441219\pi$
$44$	−275.164	−	606.746i	−0.942785	−	2.07887i
$45$		0			0
$46$	−251.475	+	773.960i	−0.806042	+	2.48074i
$47$	−375.576	+	272.872i	−1.16560	+	0.846861i	−0.990476	−	0.137684i	$-0.956034\pi$
$47$	−375.576	+	272.872i	−1.16560	+	0.846861i	−0.175128	+	0.984546i	$0.556034\pi$
$48$		0			0
$49$	−58.9350	−	181.383i	−0.171822	−	0.528815i
$50$	−155.356	−	478.138i	−0.439414	−	1.35238i
$51$		0			0
$52$	−450.926	+	327.617i	−1.20254	+	0.873698i
$53$	1.86904	−	5.75232i	0.00484402	−	0.0149084i	−0.948605	−	0.316462i	$-0.897505\pi$
$53$	1.86904	−	5.75232i	0.00484402	−	0.0149084i	0.953449	+	0.301553i	$0.0975051\pi$
$54$		0			0
$55$	109.624	−	533.793i	0.268758	−	1.30867i
$56$	648.912			1.54847
$57$		0			0
$58$	197.827	−	143.729i	0.447861	−	0.325390i
$59$	−179.294	−	130.264i	−0.395628	−	0.287440i	0.372130	−	0.928181i	$-0.378628\pi$
$59$	−179.294	−	130.264i	−0.395628	−	0.287440i	−0.767758	+	0.640740i	$0.778628\pi$
$60$		0			0
$61$	−84.7750	−	260.911i	−0.177940	−	0.547642i	0.821816	−	0.569753i	$-0.192961\pi$
$61$	−84.7750	−	260.911i	−0.177940	−	0.547642i	−0.999756	+	0.0221111i	$0.992961\pi$
$62$	282.061	+	204.930i	0.577772	+	0.419776i
$63$		0			0
$64$	30.0884	−	92.6027i	0.0587665	−	0.180865i
$65$	−455.900			−0.869961
$66$		0			0
$67$	187.178			0.341304			0.170652	−	0.985331i	$-0.445413\pi$
$67$	187.178			0.341304			0.170652	+	0.985331i	$0.445413\pi$
$68$	−745.250	+	2293.64i	−1.32904	+	4.09037i
$69$		0			0
$70$	764.178	+	555.208i	1.30481	+	0.948000i
$71$	141.442	+	435.312i	0.236423	+	0.727635i	0.996929	+	0.0783045i	$0.0249506\pi$
$71$	141.442	+	435.312i	0.236423	+	0.727635i	−0.760507	+	0.649330i	$0.775049\pi$
$72$		0			0
$73$	218.703	+	158.897i	0.350647	+	0.254760i	0.749141	−	0.662411i	$-0.230467\pi$
$73$	218.703	+	158.897i	0.350647	+	0.254760i	−0.398493	+	0.917171i	$0.630467\pi$
$74$	656.744	−	477.153i	1.03169	−	0.749566i
$75$		0			0
$76$	−407.352			−0.614822
$77$	185.945	+	410.015i	0.275200	+	0.606825i
$78$		0			0
$79$	152.545	−	469.486i	0.217249	−	0.668624i	−0.781737	−	0.623608i	$-0.785666\pi$
$79$	152.545	−	469.486i	0.217249	−	0.668624i	0.998986	−	0.0450161i	$-0.0143339\pi$
$80$	1490.99	−	1083.27i	2.08372	−	1.51391i
$81$		0			0
$82$	453.157	+	1394.67i	0.610278	+	1.87824i
$83$	83.7540	+	257.768i	0.110761	+	0.340888i	0.991039	−	0.133570i	$-0.0426440\pi$
$83$	83.7540	+	257.768i	0.110761	+	0.340888i	−0.880278	+	0.474458i	$0.842644\pi$
$84$		0			0
$85$	−1595.88	+	1159.47i	−2.03644	+	1.47956i
$86$	−163.979	+	504.674i	−0.205608	+	0.632795i
$87$		0			0
$88$	1906.51	−	213.670i	2.30949	−	0.258833i
$89$	77.4891			0.0922902			0.0461451	−	0.998935i	$-0.485306\pi$
$89$	77.4891			0.0922902			0.0461451	+	0.998935i	$0.485306\pi$
$90$		0			0
$91$	304.718	−	221.391i	0.351023	−	0.255033i
$92$	−2346.08	−	1704.53i	−2.65865	−	1.93163i
$93$		0			0
$94$	−735.158	−	2262.58i	−0.806657	−	2.48264i
$95$	−269.556	−	195.844i	−0.291115	−	0.211507i
$96$		0			0
$97$	−392.262	+	1207.26i	−0.410600	+	1.26370i	0.505528	+	0.862810i	$0.331298\pi$
$97$	−392.262	+	1207.26i	−0.410600	+	1.26370i	−0.916128	+	0.400886i	$0.868702\pi$
$98$	977.348			1.00742
$99$		0			0
$100$	1791.51			1.79151
$101$	382.582	−	1177.46i	0.376914	−	1.16002i	−0.565265	−	0.824910i	$-0.691226\pi$
$101$	382.582	−	1177.46i	0.376914	−	1.16002i	0.942178	−	0.335112i	$-0.108774\pi$
$102$		0			0
$103$	−737.795	−	536.039i	−0.705797	−	0.512791i	0.176018	−	0.984387i	$-0.443678\pi$
$103$	−737.795	−	536.039i	−0.705797	−	0.512791i	−0.881815	+	0.471595i	$0.843678\pi$
$104$	−495.974	−	1526.45i	−0.467637	−	1.43924i
$105$		0			0
$106$	25.0757	+	18.2186i	0.0229770	+	0.0166938i
$107$	−1280.95	+	930.666i	−1.15733	+	0.840849i	−0.989438	−	0.144956i	$-0.953696\pi$
$107$	−1280.95	+	930.666i	−1.15733	+	0.840849i	−0.167892	+	0.985805i	$0.553696\pi$
$108$		0			0
$109$	296.898			0.260896			0.130448	−	0.991455i	$-0.458358\pi$
$109$	296.898			0.260896			0.130448	+	0.991455i	$0.458358\pi$
$110$	2427.98	+	1379.58i	2.10454	+	1.19580i
$111$		0			0
$112$	−470.511	+	1448.08i	−0.396956	+	1.22170i
$113$	−88.5099	+	64.3062i	−0.0736842	+	0.0535347i	−0.624018	−	0.781410i	$-0.714501\pi$
$113$	−88.5099	+	64.3062i	−0.0736842	+	0.0535347i	0.550333	+	0.834945i	$0.314501\pi$
$114$		0			0
$115$	−732.977	−	2255.87i	−0.594352	−	1.82923i
$116$	269.267	+	828.719i	0.215524	+	0.663316i
$117$		0			0
$118$	918.804	−	667.550i	0.716803	−	0.520788i
$119$	503.610	−	1549.95i	0.387949	−	1.19398i
$120$		0			0
$121$	681.316	+	1143.40i	0.511883	+	0.859055i
$122$	1405.86			1.04329
$123$		0			0
$124$	−1005.12	+	730.262i	−0.727922	+	0.528867i
$125$	−325.007	−	236.132i	−0.232556	−	0.168962i
$126$		0			0
$127$	428.722	+	1319.47i	0.299550	+	0.921921i	0.981655	+	0.190667i	$0.0610649\pi$
$127$	428.722	+	1319.47i	0.299550	+	0.921921i	−0.682104	+	0.731255i	$0.738935\pi$
$128$	−965.938	−	701.795i	−0.667013	−	0.484613i
$129$		0			0
$130$	721.955	−	2221.95i	0.487074	−	1.49906i
$131$	−1515.23			−1.01058			−0.505291	−	0.862949i	$-0.668615\pi$
$131$	−1515.23			−1.01058			−0.505291	+	0.862949i	$0.668615\pi$
$132$		0			0
$133$	275.272			0.179467
$134$	−296.411	+	912.260i	−0.191090	+	0.588114i
$135$		0			0
$136$	−5618.32	−	4081.95i	−3.54240	−	2.57371i
$137$	917.808	+	2824.72i	0.572362	+	1.76155i	0.644991	+	0.764190i	$0.276861\pi$
$137$	917.808	+	2824.72i	0.572362	+	1.76155i	−0.0726287	+	0.997359i	$0.523139\pi$
$138$		0			0
$139$	1741.07	+	1264.96i	1.06241	+	0.771890i	0.974534	−	0.224241i	$-0.0719904\pi$
$139$	1741.07	+	1264.96i	1.06241	+	0.771890i	0.0878812	+	0.996131i	$0.471990\pi$
$140$	−2723.13	+	1978.47i	−1.64390	+	1.19437i
$141$		0			0
$142$	−2345.59			−1.38618
$143$	822.368	−	750.784i	0.480908	−	0.439047i
$144$		0			0
$145$	−220.245	+	677.843i	−0.126140	+	0.388220i
$146$	−1120.76	+	814.281i	−0.635307	+	0.461578i
$147$		0			0
$148$	893.912	+	2751.18i	0.496480	+	1.52801i
$149$	41.0610	+	126.373i	0.0225761	+	0.0694822i	0.961710	−	0.274070i	$-0.0883699\pi$
$149$	41.0610	+	126.373i	0.0225761	+	0.0694822i	−0.939134	+	0.343552i	$0.888370\pi$
$150$		0			0
$151$	−172.306	+	125.188i	−0.0928613	+	0.0674677i	−0.633247	−	0.773950i	$-0.718278\pi$
$151$	−172.306	+	125.188i	−0.0928613	+	0.0674677i	0.540386	+	0.841417i	$0.318278\pi$
$152$	362.478	−	1115.59i	0.193426	−	0.595305i
$153$		0			0
$154$	−2292.77	+	256.959i	−1.19972	+	0.134457i
$155$	−1016.21			−0.526604
$156$		0			0
$157$	2366.45	−	1719.32i	1.20295	−	0.873994i	0.208378	−	0.978048i	$-0.433182\pi$
$157$	2366.45	−	1719.32i	1.20295	−	0.873994i	0.994572	+	0.104055i	$0.0331817\pi$
$158$	2046.60	+	1486.94i	1.03050	+	0.748700i
$159$		0			0
$160$	976.758	+	3006.15i	0.482622	+	1.48536i
$161$	1585.39	+	1151.85i	0.776064	+	0.563843i
$162$		0			0
$163$	−195.690	+	602.273i	−0.0940346	+	0.289409i	−0.987001	−	0.160715i	$-0.948620\pi$
$163$	−195.690	+	602.273i	−0.0940346	+	0.289409i	0.892966	+	0.450124i	$0.148620\pi$
$164$	−5225.64			−2.48813
$165$		0			0
$166$	−1388.93			−0.649410
$167$	473.826	−	1458.29i	0.219555	−	0.675722i	−0.779243	−	0.626722i	$-0.784396\pi$
$167$	473.826	−	1458.29i	0.219555	−	0.675722i	0.998799	−	0.0490007i	$-0.0156036\pi$
$168$		0			0
$169$	1023.73	+	743.781i	0.465966	+	0.338544i
$170$	−3123.79	−	9614.05i	−1.40932	−	4.33744i
$171$		0			0
$172$	−1529.81	−	1111.47i	−0.678178	−	0.492725i
$173$	2691.34	−	1955.37i	1.18277	−	0.859331i	0.190286	−	0.981729i	$-0.439058\pi$
$173$	2691.34	−	1955.37i	1.18277	−	0.859331i	0.992481	+	0.122398i	$0.0390583\pi$
$174$		0			0
$175$	−1210.63			−0.522945
$176$	−905.551	+	4409.41i	−0.387832	+	1.88848i
$177$		0			0
$178$	−122.710	+	377.663i	−0.0516715	+	0.159028i
$179$	3447.54	−	2504.79i	1.43956	−	1.04590i	0.451428	−	0.892307i	$-0.350915\pi$
$179$	3447.54	−	2504.79i	1.43956	−	1.04590i	0.988134	−	0.153595i	$-0.0490853\pi$
$180$		0			0
$181$	229.269	+	705.618i	0.0941516	+	0.289769i	0.987032	−	0.160526i	$-0.0513190\pi$
$181$	229.269	+	705.618i	0.0941516	+	0.289769i	−0.892880	+	0.450295i	$0.851319\pi$
$182$	596.459	+	1835.71i	0.242926	+	0.747649i
$183$		0			0
$184$	6755.74	−	4908.33i	2.70674	−	1.96656i
$185$	−731.167	+	2250.30i	−0.290576	+	0.894300i
$186$		0			0
$187$	969.256	−	4719.61i	0.379032	−	1.84563i
$188$	8477.59			3.28879
$189$		0			0
$190$	1381.36	−	1003.62i	0.527445	−	0.383211i
$191$	3342.99	+	2428.82i	1.26644	+	0.920124i	0.999055	−	0.0434658i	$-0.0138400\pi$
$191$	3342.99	+	2428.82i	1.26644	+	0.920124i	0.267386	+	0.963589i	$0.413840\pi$
$192$		0			0
$193$	952.321	+	2930.94i	0.355179	+	1.09313i	0.955906	+	0.293674i	$0.0948781\pi$
$193$	952.321	+	2930.94i	0.355179	+	1.09313i	−0.600726	+	0.799455i	$0.705122\pi$
$194$	−5262.71	−	3823.58i	−1.94763	−	1.41504i
$195$		0			0
$196$	−1076.23	+	3312.30i	−0.392213	+	1.20711i
$197$	−3059.84			−1.10662			−0.553310	−	0.832975i	$-0.686636\pi$
$197$	−3059.84			−1.10662			−0.553310	+	0.832975i	$0.686636\pi$
$198$		0			0
$199$	−971.928			−0.346222			−0.173111	−	0.984902i	$-0.555382\pi$
$199$	−971.928			−0.346222			−0.173111	+	0.984902i	$0.555382\pi$
$200$	−1594.16	+	4906.32i	−0.563621	+	1.73465i
$201$		0			0
$202$	5132.84	+	3729.22i	1.78785	+	1.29895i
$203$	−181.960	−	560.015i	−0.0629118	−	0.193623i
$204$		0			0
$205$	−3457.96	−	2512.35i	−1.17812	−	0.855952i
$206$	3780.89	−	2746.98i	1.27877	−	0.929082i
$207$		0			0
$208$	3765.98			1.25540
$209$	808.754	−	90.6399i	0.267668	−	0.0299985i
$210$		0			0
$211$	1028.15	−	3164.32i	0.335453	−	1.03242i	−0.631045	−	0.775746i	$-0.717374\pi$
$211$	1028.15	−	3164.32i	0.335453	−	1.03242i	0.966498	−	0.256673i	$-0.0826264\pi$
$212$	−89.3566	+	64.9214i	−0.0289483	+	0.0210322i
$213$		0			0
$214$	−2507.35	−	7716.84i	−0.800931	−	2.46501i
$215$	−477.950	−	1470.98i	−0.151609	−	0.466605i
$216$		0			0
$217$	679.220	−	493.482i	0.212481	−	0.154377i
$218$	−470.162	+	1447.01i	−0.146071	+	0.449559i
$219$		0			0
$220$	−7349.14	+	6709.43i	−2.25218	+	2.05613i
$221$	−4030.91			−1.22692
$222$		0			0
$223$	−3976.34	+	2888.98i	−1.19406	+	0.867535i	−0.993687	−	0.112185i	$-0.964215\pi$
$223$	−3976.34	+	2888.98i	−1.19406	+	0.867535i	−0.200372	+	0.979720i	$0.564215\pi$
$224$	−2112.68	−	1534.95i	−0.630175	−	0.457849i
$225$		0			0
$226$	−173.251	−	533.211i	−0.0509932	−	0.156941i
$227$	−859.697	−	624.607i	−0.251366	−	0.182628i	0.454966	−	0.890509i	$-0.349651\pi$
$227$	−859.697	−	624.607i	−0.251366	−	0.182628i	−0.706332	+	0.707881i	$0.749651\pi$
$228$		0			0
$229$	−1332.75	+	4101.80i	−0.384589	+	1.18364i	0.552189	+	0.833719i	$0.313793\pi$
$229$	−1332.75	+	4101.80i	−0.384589	+	1.18364i	−0.936778	+	0.349924i	$0.886207\pi$
$230$	12155.3			3.48477
$231$		0			0
$232$	−2509.17			−0.710065
$233$	−1592.86	+	4902.32i	−0.447862	+	1.37838i	0.431453	+	0.902135i	$0.358001\pi$
$233$	−1592.86	+	4902.32i	−0.447862	+	1.37838i	−0.879315	+	0.476241i	$0.841999\pi$
$234$		0			0
$235$	5609.86	+	4075.80i	1.55722	+	1.13139i
$236$	1250.61	+	3848.98i	0.344948	+	1.06164i
$237$		0			0
$238$	6756.60	+	4908.96i	1.84019	+	1.33698i
$239$	−100.555	+	73.0575i	−0.0272149	+	0.0197728i	−0.601310	−	0.799016i	$-0.705354\pi$
$239$	−100.555	+	73.0575i	−0.0272149	+	0.0197728i	0.574095	+	0.818789i	$0.305354\pi$
$240$		0			0
$241$	−445.539			−0.119086			−0.0595429	−	0.998226i	$-0.518964\pi$
$241$	−445.539			−0.119086			−0.0595429	+	0.998226i	$0.518964\pi$
$242$	−6651.59	+	1509.90i	−1.76686	+	0.401075i
$243$		0			0
$244$	−1548.10	+	4764.57i	−0.406177	+	1.25008i
$245$	−2304.64	+	1674.42i	−0.600971	+	0.436631i
$246$		0			0
$247$	−210.395	−	647.530i	−0.0541989	−	0.166807i
$248$	−1105.53	−	3402.48i	−0.283070	−	0.871200i
$249$		0			0
$250$	1665.53	−	1210.08i	0.421349	−	0.306128i
$251$	−454.595	+	1399.10i	−0.114318	+	0.351834i	−0.991804	−	0.127767i	$-0.959219\pi$
$251$	−454.595	+	1399.10i	−0.114318	+	0.351834i	0.877486	+	0.479602i	$0.159219\pi$
$252$		0			0
$253$	5037.17	+	2862.13i	1.25172	+	0.711229i
$254$	−7109.70			−1.75631
$255$		0			0
$256$	5580.21	−	4054.26i	1.36236	−	0.989809i
$257$	1183.60	+	859.935i	0.287280	+	0.208721i	0.722086	−	0.691803i	$-0.243183\pi$
$257$	1183.60	+	859.935i	0.287280	+	0.208721i	−0.434807	+	0.900524i	$0.643183\pi$
$258$		0			0
$259$	−604.070	−	1859.14i	−0.144923	−	0.446028i
$260$	6735.34	+	4893.51i	1.60657	+	1.16724i
$261$		0			0
$262$	2399.49	−	7384.87i	0.565805	−	1.74137i
$263$	734.717			0.172261			0.0861304	−	0.996284i	$-0.472550\pi$
$263$	734.717			0.172261			0.0861304	+	0.996284i	$0.472550\pi$
$264$		0			0
$265$	−90.3423			−0.0209422
$266$	−435.916	+	1341.61i	−0.100480	+	0.309246i
$267$		0			0
$268$	−2765.31	−	2009.11i	−0.630292	−	0.457934i
$269$	−1059.09	−	3259.54i	−0.240051	−	0.738802i	−0.996411	−	0.0846463i	$-0.973024\pi$
$269$	−1059.09	−	3259.54i	−0.240051	−	0.738802i	0.756360	−	0.654156i	$-0.226976\pi$
$270$		0			0
$271$	−1390.98	−	1010.61i	−0.311793	−	0.226531i	0.420872	−	0.907120i	$-0.361724\pi$
$271$	−1390.98	−	1010.61i	−0.311793	−	0.226531i	−0.732666	+	0.680589i	$0.761724\pi$
$272$	13182.8	−	9577.87i	2.93870	−	2.13509i
$273$		0			0
$274$	−15220.5			−3.35584
$275$	−3556.86	+	398.630i	−0.779952	+	0.0874120i
$276$		0			0
$277$	1593.31	−	4903.72i	0.345607	−	1.06367i	−0.615652	−	0.788018i	$-0.711107\pi$
$277$	1593.31	−	4903.72i	0.345607	−	1.06367i	0.961258	−	0.275649i	$-0.0888928\pi$
$278$	−8922.25	+	6482.40i	−1.92490	+	1.39852i
$279$		0			0
$280$	−2995.17	−	9218.20i	−0.639271	−	1.96747i
$281$	−1551.48	−	4774.96i	−0.329372	−	1.01370i	−0.969428	−	0.245374i	$-0.921089\pi$
$281$	−1551.48	−	4774.96i	−0.329372	−	1.01370i	0.640057	−	0.768328i	$-0.278911\pi$
$282$		0			0
$283$	1519.35	−	1103.87i	0.319138	−	0.231868i	−0.416669	−	0.909058i	$-0.636803\pi$
$283$	1519.35	−	1103.87i	0.319138	−	0.231868i	0.735808	+	0.677190i	$0.236803\pi$
$284$	2582.91	−	7949.37i	0.539674	−	1.66095i
$285$		0			0
$286$	2356.86	+	5196.95i	0.487287	+	1.07448i
$287$	3531.28			0.726289
$288$		0			0
$289$	−10135.5	+	7363.87i	−2.06300	+	1.49885i
$290$	−2954.87	−	2146.84i	−0.598332	−	0.434713i
$291$		0			0
$292$	−1525.50	−	4695.00i	−0.305729	−	0.940939i
$293$	3892.69	+	2828.20i	0.776154	+	0.563909i	0.903822	−	0.427908i	$-0.140749\pi$
$293$	3892.69	+	2828.20i	0.776154	+	0.563909i	−0.127668	+	0.991817i	$0.540749\pi$
$294$		0			0
$295$	−1022.92	+	3148.24i	−0.201888	+	0.621347i
$296$	−8329.93			−1.63570
$297$		0			0
$298$	−680.934			−0.132367
$299$	1497.79	−	4609.74i	0.289698	−	0.891598i
$300$		0			0
$301$	1033.78	+	751.086i	0.197961	+	0.143827i
$302$	−337.274	−	1038.02i	−0.0642648	−	0.197787i
$303$		0			0
$304$	2226.68	+	1617.78i	0.420095	+	0.305217i
$305$	−3315.10	+	2408.56i	−0.622368	+	0.452177i
$306$		0			0
$307$	−598.905			−0.111340			−0.0556699	−	0.998449i	$-0.517729\pi$
$307$	−598.905			−0.111340			−0.0556699	+	0.998449i	$0.517729\pi$
$308$	1653.89	−	8053.32i	0.305972	−	1.48987i
$309$		0			0
$310$	1609.25	−	4952.75i	0.294836	−	0.907411i
$311$	4151.19	−	3016.02i	0.756889	−	0.549912i	−0.141066	−	0.990000i	$-0.545053\pi$
$311$	4151.19	−	3016.02i	0.756889	−	0.549912i	0.897954	+	0.440088i	$0.145053\pi$
$312$		0			0
$313$	−2948.47	−	9074.46i	−0.532452	−	1.63872i	−0.749092	−	0.662466i	$-0.769510\pi$
$313$	−2948.47	−	9074.46i	−0.532452	−	1.63872i	0.216640	−	0.976251i	$-0.430490\pi$
$314$	4632.12	+	14256.2i	0.832502	+	2.56218i
$315$		0			0
$316$	−7293.00	+	5298.67i	−1.29830	+	0.943271i
$317$	−2040.57	+	6280.22i	−0.361545	+	1.11272i	0.590572	+	0.806985i	$0.298902\pi$
$317$	−2040.57	+	6280.22i	−0.361545	+	1.11272i	−0.952116	+	0.305736i	$0.901098\pi$
$318$		0			0
$319$	−719.000	−	1585.42i	−0.126195	−	0.278265i
$320$	−1454.36			−0.254066
$321$		0			0
$322$	−8124.46	+	5902.76i	−1.40608	+	1.02158i
$323$	−2383.32	−	1731.59i	−0.410563	−	0.298291i
$324$		0			0
$325$	925.308	+	2847.81i	0.157929	+	0.486055i
$326$	−2625.44	−	1907.50i	−0.446043	−	0.324069i
$327$		0			0
$328$	4649.98	−	14311.2i	0.782781	−	2.40915i
$329$	−5728.82			−0.960000
$330$		0			0
$331$	−6549.79			−1.08764			−0.543820	−	0.839202i	$-0.683023\pi$
$331$	−6549.79			−1.08764			−0.543820	+	0.839202i	$0.683023\pi$
$332$	1529.46	−	4707.18i	0.252831	−	0.778134i
$333$		0			0
$334$	6357.00	+	4618.63i	1.04144	+	0.756648i
$335$	−863.954	−	2658.98i	−0.140904	−	0.433658i
$336$		0			0
$337$	2176.56	+	1581.36i	0.351824	+	0.255615i	0.749634	−	0.661853i	$-0.230230\pi$
$337$	2176.56	+	1581.36i	0.351824	+	0.255615i	−0.397810	+	0.917468i	$0.630230\pi$
$338$	−5246.17	+	3811.56i	−0.844242	+	0.613378i
$339$		0			0
$340$	36022.5			5.74587
$341$	1833.07	−	1673.51i	0.291103	−	0.265764i
$342$		0			0
$343$	2035.25	−	6263.87i	0.320389	−	0.986056i
$344$	4405.20	−	3200.56i	0.690443	−	0.501636i
$345$		0			0
$346$	5268.07	+	16213.5i	0.818535	+	2.51919i
$347$	240.519	+	740.240i	0.0372095	+	0.114519i	0.967936	−	0.251197i	$-0.0808241\pi$
$347$	240.519	+	740.240i	0.0372095	+	0.114519i	−0.930726	+	0.365716i	$0.880824\pi$
$348$		0			0
$349$	4381.68	−	3183.48i	0.672052	−	0.488274i	−0.198660	−	0.980069i	$-0.563659\pi$
$349$	4381.68	−	3183.48i	0.672052	−	0.488274i	0.870711	+	0.491794i	$0.163659\pi$
$350$	1917.14	−	5900.35i	0.292787	−	0.901105i
$351$		0			0
$352$	−6712.49	−	3814.05i	−1.01641	−	0.577528i
$353$	4504.51			0.679181			0.339591	−	0.940573i	$-0.389711\pi$
$353$	4504.51			0.679181			0.339591	+	0.940573i	$0.389711\pi$
$354$		0			0
$355$	5531.03	−	4018.53i	0.826920	−	0.600793i
$356$	−1144.80	−	831.747i	−0.170434	−	0.123827i
$357$		0			0
$358$	6748.28	+	20769.1i	0.996250	+	3.06614i
$359$	6948.18	+	5048.15i	1.02148	+	0.742147i	0.966585	−	0.256345i	$-0.0825182\pi$
$359$	6948.18	+	5048.15i	1.02148	+	0.742147i	0.0548930	+	0.998492i	$0.482518\pi$
$360$		0			0
$361$	−1965.78	+	6050.06i	−0.286599	+	0.882061i
$362$	−3802.08			−0.552025
$363$		0			0
$364$	−6878.16			−0.990422
$365$	1247.77	−	3840.23i	0.178935	−	0.550704i
$366$		0			0
$367$	−1762.10	−	1280.24i	−0.250629	−	0.182093i	0.455376	−	0.890299i	$-0.349505\pi$
$367$	−1762.10	−	1280.24i	−0.250629	−	0.182093i	−0.706006	+	0.708206i	$0.749505\pi$
$368$	6054.78	+	18634.7i	0.857683	+	2.63968i
$369$		0			0
$370$	−9809.58	−	7127.08i	−1.37831	−	1.00140i
$371$	60.3836	−	43.8713i	0.00845003	−	0.00613931i
$372$		0			0
$373$	−12814.7			−1.77888			−0.889440	−	0.457052i	$-0.848905\pi$
$373$	−12814.7			−1.77888			−0.889440	+	0.457052i	$0.848905\pi$
$374$	21467.4	+	12197.8i	2.96805	+	1.68646i
$375$		0			0
$376$	−7543.69	+	23217.1i	−1.03467	+	3.18439i
$377$	−1178.26	+	856.058i	−0.160965	+	0.116948i
$378$		0			0
$379$	2256.70	+	6945.39i	0.305854	+	0.941322i	0.979357	+	0.202137i	$0.0647888\pi$
$379$	2256.70	+	6945.39i	0.305854	+	0.941322i	−0.673503	+	0.739184i	$0.735211\pi$
$380$	1880.21	+	5786.69i	0.253823	+	0.781186i
$381$		0			0
$382$	−17131.4	+	12446.7i	−2.29455	+	1.66709i
$383$	−3496.23	+	10760.3i	−0.466446	+	1.43557i	0.390708	+	0.920515i	$0.372230\pi$
$383$	−3496.23	+	10760.3i	−0.466446	+	1.43557i	−0.857154	+	0.515060i	$0.827770\pi$
$384$		0			0
$385$	4966.25	−	4533.96i	0.657412	−	0.600187i
$386$	−15792.8			−2.08247
$387$		0			0
$388$	18753.5	−	13625.2i	2.45378	−	1.78278i
$389$	−2391.30	−	1737.38i	−0.311681	−	0.226449i	0.420937	−	0.907090i	$-0.361701\pi$
$389$	−2391.30	−	1737.38i	−0.311681	−	0.226449i	−0.732617	+	0.680641i	$0.761701\pi$
$390$		0			0
$391$	−6480.73	−	19945.6i	−0.838222	−	2.57978i
$392$	−8113.53	−	5894.83i	−1.04540	−	0.759525i
$393$		0			0
$394$	4845.50	−	14912.9i	0.619576	−	1.90686i
$395$	−7373.45			−0.939236
$396$		0			0
$397$	12391.9			1.56658			0.783288	−	0.621659i	$-0.213541\pi$
$397$	12391.9			1.56658			0.783288	+	0.621659i	$0.213541\pi$
$398$	1539.13	−	4736.95i	0.193843	−	0.596587i
$399$		0			0
$400$	−9792.84	−	7114.91i	−1.22410	−	0.889364i
$401$	−2346.26	−	7221.04i	−0.292186	−	0.899255i	−0.984152	−	0.177326i	$-0.943255\pi$
$401$	−2346.26	−	7221.04i	−0.292186	−	0.899255i	0.691967	−	0.721930i	$-0.256745\pi$
$402$		0			0
$403$	−1679.97	−	1220.57i	−0.207656	−	0.150871i
$404$	−18290.7	+	13289.0i	−2.25247	+	1.63652i
$405$		0			0
$406$	3017.53			0.368861
$407$	−2386.93	−	5263.27i	−0.290702	−	0.641008i
$408$		0			0
$409$	−2248.34	+	6919.67i	−0.271817	+	0.836567i	0.718227	+	0.695809i	$0.244954\pi$
$409$	−2248.34	+	6919.67i	−0.271817	+	0.836567i	−0.990044	+	0.140758i	$0.955046\pi$
$410$	17720.6	−	12874.7i	2.13453	−	1.55083i
$411$		0			0
$412$	5146.27	+	15838.6i	0.615384	+	1.89396i
$413$	−845.112	−	2600.99i	−0.100691	−	0.309894i
$414$		0			0
$415$	3275.18	−	2379.55i	0.387403	−	0.281464i
$416$	−1995.95	+	6142.89i	−0.235239	+	0.723990i
$417$		0			0
$418$	−838.970	+	4085.21i	−0.0981707	+	0.478024i
$419$	−11095.7			−1.29370			−0.646851	−	0.762616i	$-0.723915\pi$
$419$	−11095.7			−1.29370			−0.646851	+	0.762616i	$0.723915\pi$
$420$		0			0
$421$	4128.85	−	2999.79i	0.477976	−	0.347270i	−0.322565	−	0.946547i	$-0.604545\pi$
$421$	4128.85	−	2999.79i	0.477976	−	0.347270i	0.800542	+	0.599277i	$0.204545\pi$
$422$	13794.0	+	10021.9i	1.59119	+	1.15606i
$423$		0			0
$424$	−98.2835	−	302.485i	−0.0112572	−	0.0346462i
$425$	10481.8	+	7615.44i	1.19633	+	0.869184i
$426$		0			0
$427$	1046.15	−	3219.71i	0.118563	−	0.364900i
$428$	28913.9			3.26544
$429$		0			0
$430$	7926.09			0.888906
$431$	4461.49	−	13731.1i	0.498613	−	1.53457i	−0.312635	−	0.949873i	$-0.601212\pi$
$431$	4461.49	−	13731.1i	0.498613	−	1.53457i	0.811249	−	0.584701i	$-0.198788\pi$
$432$		0			0
$433$	−3427.67	−	2490.35i	−0.380423	−	0.276394i	0.381097	−	0.924535i	$-0.375546\pi$
$433$	−3427.67	−	2490.35i	−0.380423	−	0.276394i	−0.761520	+	0.648142i	$0.775546\pi$
$434$	1329.51	+	4091.83i	0.147048	+	0.452567i
$435$		0			0
$436$	−4386.28	−	3186.82i	−0.481800	−	0.350048i
$437$	2865.82	−	2082.14i	0.313709	−	0.227923i
$438$		0			0
$439$	1809.83			0.196761			0.0983807	−	0.995149i	$-0.468634\pi$
$439$	1809.83			0.196761			0.0983807	+	0.995149i	$0.468634\pi$
$440$	−11835.2	−	26097.0i	−1.28232	−	2.82756i
$441$		0			0
$442$	6383.28	−	19645.7i	0.686927	−	2.11414i
$443$	3881.15	−	2819.82i	0.416251	−	0.302424i	−0.359877	−	0.933000i	$-0.617181\pi$
$443$	3881.15	−	2819.82i	0.416251	−	0.302424i	0.776127	+	0.630576i	$0.217181\pi$
$444$		0			0
$445$	−357.665	−	1100.78i	−0.0381010	−	0.117263i
$446$	−7783.34	−	23954.7i	−0.826350	−	2.54324i
$447$		0			0
$448$	972.075	−	706.254i	0.102514	−	0.0744807i
$449$	2835.91	−	8728.03i	0.298073	−	0.917375i	−0.684099	−	0.729390i	$-0.739804\pi$
$449$	2835.91	−	8728.03i	0.298073	−	0.917375i	0.982172	−	0.187985i	$-0.0601958\pi$
$450$		0			0
$451$	10375.0	−	1162.76i	1.08323	−	0.121402i
$452$	1997.87			0.207902
$453$		0			0
$454$	4405.59	−	3200.85i	0.455428	−	0.330888i
$455$	−4551.47	−	3306.84i	−0.468959	−	0.340719i
$456$		0			0
$457$	1909.56	+	5877.02i	0.195461	+	0.601566i	0.999971	+	0.00762708i	$0.00242780\pi$
$457$	1909.56	+	5877.02i	0.195461	+	0.601566i	−0.804510	+	0.593939i	$0.797572\pi$
$458$	−17880.7	−	12991.1i	−1.82425	−	1.32540i
$459$		0			0
$460$	−13385.1	+	41195.2i	−1.35671	+	4.17551i
$461$	16827.2			1.70004			0.850022	−	0.526747i	$-0.176589\pi$
$461$	16827.2			1.70004			0.850022	+	0.526747i	$0.176589\pi$
$462$		0			0
$463$	−818.694			−0.0821770			−0.0410885	−	0.999156i	$-0.513083\pi$
$463$	−818.694			−0.0821770			−0.0410885	+	0.999156i	$0.513083\pi$
$464$	1819.34	−	5599.35i	0.182027	−	0.560223i
$465$		0			0
$466$	−21370.3	−	15526.5i	−2.12438	−	1.54345i
$467$	5188.30	+	15968.0i	0.514103	+	1.58225i	0.784908	+	0.619612i	$0.212710\pi$
$467$	5188.30	+	15968.0i	0.514103	+	1.58225i	−0.270805	+	0.962634i	$0.587290\pi$
$468$		0			0
$469$	1868.69	+	1357.68i	0.183983	+	0.133671i
$470$	−28748.2	+	20886.8i	−2.82139	+	2.04986i
$471$		0			0
$472$	−11653.8			−1.13646
$473$	3284.58	+	1866.30i	0.319292	+	0.181422i
$474$		0			0
$475$	−676.252	+	2081.29i	−0.0653233	+	0.201044i
$476$	−24077.0	+	17493.0i	−2.31842	+	1.68443i
$477$		0			0
$478$	−196.828	−	605.774i	−0.0188341	−	0.0579654i
$479$	1438.96	+	4428.65i	0.137260	+	0.422443i	0.995935	−	0.0900778i	$-0.0287116\pi$
$479$	1438.96	+	4428.65i	0.137260	+	0.422443i	−0.858675	+	0.512521i	$0.828712\pi$
$480$		0			0
$481$	−3911.59	+	2841.94i	−0.370797	+	0.269400i
$482$	705.547	−	2171.45i	0.0666739	−	0.205201i
$483$		0			0
$484$	2207.41	−	24205.4i	0.207308	−	2.27323i
$485$	18960.4			1.77515
$486$		0			0
$487$	−14260.7	+	10361.0i	−1.32693	+	0.964072i	−0.327114	+	0.944985i	$0.606076\pi$
$487$	−14260.7	+	10361.0i	−1.32693	+	0.964072i	−0.999818	+	0.0190875i	$0.993924\pi$
$488$	−11670.9	−	8479.40i	−1.08262	−	0.786566i
$489$		0			0
$490$	−4511.14	−	13883.8i	−0.415903	−	1.28002i
$491$	−12098.6	−	8790.18i	−1.11203	−	0.807934i	−0.129044	−	0.991639i	$-0.541191\pi$
$491$	−12098.6	−	8790.18i	−1.11203	−	0.807934i	−0.982981	+	0.183705i	$0.941191\pi$
$492$		0			0
$493$	−1947.33	+	5993.26i	−0.177897	+	0.547511i
$494$	3489.09			0.317776
$495$		0			0
$496$	8394.41			0.759920
$497$	−1745.43	+	5371.87i	−0.157531	+	0.484831i
$498$		0			0
$499$	17373.4	+	12622.5i	1.55859	+	1.13239i	0.937150	+	0.348928i	$0.113454\pi$
$499$	17373.4	+	12622.5i	1.55859	+	1.13239i	0.621445	+	0.783458i	$0.286546\pi$
$500$	2266.99	+	6977.08i	0.202766	+	0.624049i
$501$		0			0
$502$	−6098.99	−	4431.18i	−0.542254	−	0.393971i
$503$	9572.63	−	6954.92i	0.848554	−	0.616510i	−0.0761930	−	0.997093i	$-0.524277\pi$
$503$	9572.63	−	6954.92i	0.848554	−	0.616510i	0.924747	+	0.380583i	$0.124277\pi$
$504$		0			0
$505$	−18492.5			−1.62952
$506$	−21926.1	+	20017.6i	−1.92636	+	1.75868i
$507$		0			0
$508$	7829.02	−	24095.3i	0.683773	−	2.10444i
$509$	−10979.7	+	7977.19i	−0.956119	+	0.694661i	−0.952246	−	0.305331i	$-0.901233\pi$
$509$	−10979.7	+	7977.19i	−0.956119	+	0.694661i	−0.00387285	+	0.999993i	$0.501233\pi$
$510$		0			0
$511$	1030.87	+	3172.69i	0.0892427	+	0.274661i
$512$	7971.14	+	24532.6i	0.688043	+	2.11758i
$513$		0			0
$514$	−6065.45	+	4406.81i	−0.520497	+	0.378163i
$515$	−4209.34	+	12955.0i	−0.360167	+	1.10848i
$516$		0			0
$517$	−16831.3	+	1886.35i	−1.43180	+	0.160467i
$518$	10017.6			0.849706
$519$		0			0
$520$	−19394.9	+	14091.3i	−1.63562	+	1.18835i
$521$	−1718.71	−	1248.72i	−0.144526	−	0.105004i	0.513173	−	0.858285i	$-0.328470\pi$
$521$	−1718.71	−	1248.72i	−0.144526	−	0.105004i	−0.657699	+	0.753281i	$0.728470\pi$
$522$		0			0
$523$	−1717.70	−	5286.52i	−0.143613	−	0.441995i	0.853217	−	0.521556i	$-0.174648\pi$
$523$	−1717.70	−	5286.52i	−0.143613	−	0.441995i	−0.996830	+	0.0795607i	$0.974648\pi$
$524$	22385.6	+	16264.1i	1.86626	+	1.35591i
$525$		0			0
$526$	−1163.48	+	3580.84i	−0.0964455	+	0.296829i
$527$	−8984.95			−0.742677
$528$		0			0
$529$	13050.8			1.07264
$530$	143.064	−	440.307i	0.0117251	−	0.0360863i
$531$		0			0
$532$	−4066.79	−	2954.70i	−0.331424	−	0.240794i
$533$	−2699.02	−	8306.72i	−0.219339	−	0.675055i
$534$		0			0
$535$	19133.2	+	13901.1i	1.54617	+	1.12336i
$536$	7962.93	−	5785.41i	0.641691	−	0.466215i
$537$		0			0
$538$	17563.4			1.40746
$539$	1399.72	−	6815.69i	0.111856	−	0.544661i
$540$		0			0
$541$	4074.70	−	12540.6i	0.323817	−	0.996605i	−0.648155	−	0.761508i	$-0.724459\pi$
$541$	4074.70	−	12540.6i	0.323817	−	0.996605i	0.971972	−	0.235097i	$-0.0755408\pi$
$542$	7128.18	−	5178.93i	0.564911	−	0.410432i
$543$		0			0
$544$	8636.16	+	26579.4i	0.680648	+	2.09482i
$545$	−1370.39	−	4217.62i	−0.107708	−	0.331492i
$546$		0			0
$547$	−16488.3	+	11979.4i	−1.28883	+	0.936388i	−0.999781	−	0.0209272i	$-0.993338\pi$
$547$	−16488.3	+	11979.4i	−1.28883	+	0.936388i	−0.289046	+	0.957315i	$0.593338\pi$
$548$	16760.4	−	51583.1i	1.30651	−	4.02103i
$549$		0			0
$550$	3689.75	−	17966.6i	0.286057	−	1.39290i
$551$	−1064.40			−0.0822961
$552$		0			0
$553$	4928.32	−	3580.63i	0.378975	−	0.275342i
$554$	21376.4	+	15530.9i	1.63935	+	1.19105i
$555$		0			0
$556$	−12144.3	−	37376.4i	−0.926320	−	2.85092i
$557$	−6895.70	−	5010.02i	−0.524560	−	0.381115i	0.293759	−	0.955880i	$-0.405094\pi$
$557$	−6895.70	−	5010.02i	−0.524560	−	0.381115i	−0.818319	+	0.574764i	$0.805094\pi$
$558$		0			0
$559$	976.663	−	3005.86i	0.0738970	−	0.227432i
$560$	22742.7			1.71616
$561$		0			0
$562$	25728.9			1.93115
$563$	−7620.38	+	23453.1i	−0.570445	+	1.75565i	0.0807448	+	0.996735i	$0.474270\pi$
$563$	−7620.38	+	23453.1i	−0.570445	+	1.75565i	−0.651190	+	0.758915i	$0.725730\pi$
$564$		0			0
$565$	1322.04	+	960.522i	0.0984404	+	0.0715212i
$566$	2974.00	+	9153.05i	0.220860	+	0.679737i
$567$		0			0
$568$	19472.1	+	14147.3i	1.43844	+	1.04509i
$569$	5078.13	−	3689.48i	0.374141	−	0.271829i	−0.384785	−	0.923006i	$-0.625724\pi$
$569$	5078.13	−	3689.48i	0.374141	−	0.271829i	0.758926	+	0.651177i	$0.225724\pi$
$570$		0			0
$571$	13032.1			0.955127			0.477563	−	0.878597i	$-0.341520\pi$
$571$	13032.1			0.955127			0.477563	+	0.878597i	$0.341520\pi$
$572$	−20208.1	+	2264.80i	−1.47718	+	0.165552i
$573$		0			0
$574$	−5592.07	+	17210.6i	−0.406635	+	1.25149i
$575$	−12603.8	+	9157.16i	−0.914109	+	0.664139i
$576$		0			0
$577$	2386.86	+	7346.00i	0.172212	+	0.530014i	0.999495	−	0.0317713i	$-0.0101148\pi$
$577$	2386.86	+	7346.00i	0.172212	+	0.530014i	−0.827283	+	0.561785i	$0.810115\pi$
$578$	−19839.4	−	61059.4i	−1.42770	−	4.39400i
$579$		0			0
$580$	10529.6	−	7650.22i	0.753825	−	0.547686i
$581$	−1033.55	+	3180.93i	−0.0738016	+	0.227138i
$582$		0			0
$583$	162.962	−	148.777i	0.0115767	−	0.0105690i
$584$	14215.4			1.00725
$585$		0			0
$586$	−19948.4	+	14493.3i	−1.40625	+	1.02170i
$587$	3121.98	+	2268.25i	0.219519	+	0.159490i	0.692110	−	0.721792i	$-0.256681\pi$
$587$	3121.98	+	2268.25i	0.219519	+	0.159490i	−0.472591	+	0.881282i	$0.656681\pi$
$588$		0			0
$589$	−468.973	−	1443.35i	−0.0328076	−	0.100972i
$590$	−13723.9	−	9970.98i	−0.957633	−	0.695761i
$591$		0			0
$592$	6039.84	−	18588.7i	0.419317	−	1.29053i
$593$	−26982.6			−1.86854			−0.934270	−	0.356567i	$-0.883947\pi$
$593$	−26982.6			−1.86854			−0.934270	+	0.356567i	$0.883947\pi$
$594$		0			0
$595$	−24342.6			−1.67722
$596$	749.827	−	2307.73i	0.0515337	−	0.158605i
$597$		0			0
$598$	20094.9	+	14599.8i	1.37415	+	0.998377i
$599$	7080.31	+	21791.0i	0.482961	+	1.48640i	0.834912	+	0.550383i	$0.185518\pi$
$599$	7080.31	+	21791.0i	0.482961	+	1.48640i	−0.351951	+	0.936018i	$0.614482\pi$
$600$		0			0
$601$	−2501.39	−	1817.36i	−0.169773	−	0.123348i	0.499654	−	0.866225i	$-0.333460\pi$
$601$	−2501.39	−	1817.36i	−0.169773	−	0.123348i	−0.669427	+	0.742878i	$0.733460\pi$
$602$	−5297.69	+	3849.00i	−0.358668	+	0.260587i
$603$		0			0
$604$	3889.33			0.262011
$605$	13098.0	−	14956.1i	0.880182	−	1.00505i
$606$		0			0
$607$	−4035.44	+	12419.8i	−0.269841	+	0.830486i	0.720697	+	0.693250i	$0.243822\pi$
$607$	−4035.44	+	12419.8i	−0.269841	+	0.830486i	−0.990538	+	0.137236i	$0.956178\pi$
$608$	−3818.97	+	2774.64i	−0.254736	+	0.185077i
$609$		0			0
$610$	−6489.03	−	19971.2i	−0.430710	−	1.32559i
$611$	4378.63	+	13476.0i	0.289919	+	0.892279i
$612$		0			0
$613$	21863.9	−	15885.0i	1.44058	−	1.04664i	0.452654	−	0.891686i	$-0.350477\pi$
$613$	21863.9	−	15885.0i	1.44058	−	1.04664i	0.987922	−	0.154953i	$-0.0495227\pi$
$614$	948.415	−	2918.92i	0.0623370	−	0.191854i
$615$		0			0
$616$	20583.5	+	11695.6i	1.34632	+	0.764981i
$617$	−23885.0			−1.55847			−0.779235	−	0.626732i	$-0.784392\pi$
$617$	−23885.0			−1.55847			−0.779235	+	0.626732i	$0.784392\pi$
$618$		0			0
$619$	11607.5	−	8433.32i	0.753705	−	0.547599i	−0.143268	−	0.989684i	$-0.545761\pi$
$619$	11607.5	−	8433.32i	0.753705	−	0.547599i	0.896973	+	0.442085i	$0.145761\pi$
$620$	15013.1	+	10907.7i	0.972488	+	0.706554i
$621$		0			0
$622$	8125.60	+	25008.0i	0.523805	+	1.61211i
$623$	773.611	+	562.061i	0.0497497	+	0.0361453i
$624$		0			0
$625$	−5643.76	+	17369.7i	−0.361200	+	1.11166i
$626$	48895.9			3.12184
$627$		0			0
$628$	−53416.0			−3.39415
$629$	−6464.73	+	19896.4i	−0.409803	+	1.26124i
$630$		0			0
$631$	−3780.07	−	2746.38i	−0.238482	−	0.173267i	0.462125	−	0.886815i	$-0.347087\pi$
$631$	−3780.07	−	2746.38i	−0.238482	−	0.173267i	−0.700607	+	0.713548i	$0.747087\pi$
$632$	−8021.58	−	24687.9i	−0.504876	−	1.55385i
$633$		0			0
$634$	−27376.9	−	19890.5i	−1.71495	−	1.24598i
$635$	16765.0	−	12180.5i	1.04772	−	0.761211i
$636$		0			0
$637$	−5821.13			−0.362074
$638$	8865.55	−	993.594i	0.550142	−	0.0616564i
$639$		0			0
$640$	−5510.97	+	16961.0i	−0.340375	+	1.04757i
$641$	815.075	−	592.187i	0.0502239	−	0.0364898i	−0.562390	−	0.826872i	$-0.690118\pi$
$641$	815.075	−	592.187i	0.0502239	−	0.0364898i	0.612614	+	0.790382i	$0.290118\pi$
$642$		0			0
$643$	−73.7377	−	226.941i	−0.00452244	−	0.0139187i	0.948770	−	0.315968i	$-0.102329\pi$
$643$	−73.7377	−	226.941i	−0.00452244	−	0.0139187i	−0.953292	+	0.302049i	$0.902329\pi$
$644$	−11058.4	−	34034.3i	−0.676650	−	2.08251i
$645$		0			0
$646$	12213.5	−	8873.65i	0.743862	−	0.540448i
$647$	−2481.51	+	7637.29i	−0.150785	+	0.464070i	−0.997710	−	0.0676441i	$-0.978452\pi$
$647$	−2481.51	+	7637.29i	−0.150785	+	0.464070i	0.846924	+	0.531714i	$0.178452\pi$
$648$		0			0
$649$	−3339.39	−	7363.46i	−0.201976	−	0.445364i
$650$	−15344.8			−0.925960
$651$		0			0
$652$	9355.70	−	6797.32i	0.561960	−	0.408288i
$653$	236.274	+	171.663i	0.0141594	+	0.0102874i	0.594842	−	0.803842i	$-0.297214\pi$
$653$	236.274	+	171.663i	0.0141594	+	0.0102874i	−0.580683	+	0.814130i	$0.697214\pi$
$654$		0			0
$655$	6993.83	+	21524.8i	0.417208	+	1.28403i
$656$	28564.6	+	20753.4i	1.70009	+	1.23519i
$657$		0			0
$658$	9072.05	−	27920.9i	0.537485	−	1.65421i
$659$	9034.21			0.534025			0.267013	−	0.963693i	$-0.413963\pi$
$659$	9034.21			0.534025			0.267013	+	0.963693i	$0.413963\pi$
$660$		0			0
$661$	11884.6			0.699332			0.349666	−	0.936874i	$-0.386295\pi$
$661$	11884.6			0.699332			0.349666	+	0.936874i	$0.386295\pi$
$662$	10372.1	−	31922.1i	0.608949	−	1.87415i
$663$		0			0
$664$	11530.3	+	8377.27i	0.673891	+	0.489610i
$665$	−1270.57	−	3910.41i	−0.0740911	−	0.228029i
$666$		0			0
$667$	−6130.28	−	4453.91i	−0.355870	−	0.258555i
$668$	−22653.0	+	16458.4i	−1.31208	+	0.953285i
$669$		0			0
$670$	14327.4			0.826141
$671$	2013.43	−	9804.01i	0.115838	−	0.564053i
$672$		0			0
$673$	−2312.52	+	7117.22i	−0.132454	+	0.407650i	−0.995185	−	0.0980118i	$-0.968752\pi$
$673$	−2312.52	+	7117.22i	−0.132454	+	0.407650i	0.862732	+	0.505662i	$0.168752\pi$
$674$	−11154.0	+	8103.82i	−0.637440	+	0.463127i
$675$		0			0
$676$	−7140.70	−	21976.8i	−0.406276	−	1.25039i
$677$	9795.40	+	30147.2i	0.556083	+	1.71145i	0.693067	+	0.720873i	$0.256259\pi$
$677$	9795.40	+	30147.2i	0.556083	+	1.71145i	−0.136984	+	0.990573i	$0.543741\pi$
$678$		0			0
$679$	−12672.9	+	9207.40i	−0.716261	+	0.520394i
$680$	−32054.2	+	98652.8i	−1.80768	+	5.56347i
$681$		0			0
$682$	5253.46	+	11584.1i	0.294964	+	0.650406i
$683$	7905.89			0.442914			0.221457	−	0.975170i	$-0.428919\pi$
$683$	7905.89			0.442914			0.221457	+	0.975170i	$0.428919\pi$
$684$		0			0
$685$	35890.6	−	26076.1i	2.00191	−	1.45447i
$686$	27305.6	+	19838.7i	1.51973	+	1.10415i
$687$		0			0
$688$	3948.13	+	12151.1i	0.218781	+	0.673337i
$689$	−149.352	−	108.510i	−0.00825813	−	0.00599988i
$690$		0			0
$691$	−2133.15	+	6565.17i	−0.117437	+	0.361434i	−0.992448	−	0.122670i	$-0.960854\pi$
$691$	−2133.15	+	6565.17i	−0.117437	+	0.361434i	0.875010	+	0.484104i	$0.160854\pi$
$692$	−60749.5			−3.33721
$693$		0			0
$694$	−3988.64			−0.218165
$695$	9933.34	−	30571.7i	0.542148	−	1.66856i
$696$		0			0
$697$	−30574.1	−	22213.4i	−1.66151	−	1.20716i
$698$	8576.77	+	26396.6i	0.465094	+	1.43141i
$699$		0			0
$700$	17885.6	+	12994.6i	0.965730	+	0.701644i
$701$	16748.4	−	12168.4i	0.902393	−	0.655627i	−0.0366868	−	0.999327i	$-0.511680\pi$
$701$	16748.4	−	12168.4i	0.902393	−	0.655627i	0.939079	+	0.343700i	$0.111680\pi$
$702$		0			0
$703$	−3533.61			−0.189577
$704$	2623.42	−	2395.06i	0.140446	−	0.128221i
$705$		0			0
$706$	−7133.27	+	21953.9i	−0.380261	+	1.17032i
$707$	12360.2	−	8980.18i	0.657498	−	0.477701i
$708$		0			0
$709$	−1947.48	−	5993.72i	−0.103158	−	0.317488i	0.886136	−	0.463426i	$-0.153380\pi$
$709$	−1947.48	−	5993.72i	−0.103158	−	0.317488i	−0.989294	+	0.145938i	$0.953380\pi$
$710$	10826.5	+	33320.6i	0.572271	+	1.76127i
$711$		0			0
$712$	3296.55	−	2395.08i	0.173516	−	0.126067i
$713$	3338.60	−	10275.2i	0.175360	−	0.539702i
$714$		0			0
$715$	−14461.2	−	8216.86i	−0.756387	−	0.429781i
$716$	−77818.7			−4.06176
$717$		0			0
$718$	−35606.5	+	25869.6i	−1.85073	+	1.34463i
$719$	1121.07	+	814.505i	0.0581486	+	0.0422474i	0.616480	−	0.787371i	$-0.288558\pi$
$719$	1121.07	+	814.505i	0.0581486	+	0.0422474i	−0.558331	+	0.829618i	$0.688558\pi$
$720$		0			0
$721$	−3477.64	−	10703.1i	−0.179631	−	0.552848i
$722$	−26373.6	−	19161.5i	−1.35945	−	0.987698i
$723$		0			0
$724$	4186.76	−	12885.5i	0.214916	−	0.661445i
$725$	4681.20			0.239801
$726$		0			0
$727$	−11818.1			−0.602900			−0.301450	−	0.953482i	$-0.597471\pi$
$727$	−11818.1			−0.602900			−0.301450	+	0.953482i	$0.597471\pi$
$728$	6120.46	−	18836.8i	0.311592	−	0.958982i
$729$		0			0
$730$	16740.5	+	12162.6i	0.848756	+	0.616657i
$731$	−4225.88	−	13005.9i	−0.213816	−	0.658059i
$732$		0			0
$733$	7716.12	+	5606.09i	0.388815	+	0.282491i	0.764970	−	0.644066i	$-0.222754\pi$
$733$	7716.12	+	5606.09i	0.388815	+	0.282491i	−0.376155	+	0.926557i	$0.622754\pi$
$734$	9030.03	−	6560.70i	0.454093	−	0.329918i
$735$		0			0
$736$	−33605.1			−1.68301
$737$	5937.27	+	3373.57i	0.296747	+	0.168612i
$738$		0			0
$739$	−1054.22	+	3244.54i	−0.0524763	+	0.161505i	−0.973860	−	0.227148i	$-0.927060\pi$
$739$	−1054.22	+	3244.54i	−0.0524763	+	0.161505i	0.921384	+	0.388654i	$0.127060\pi$
$740$	34956.2	−	25397.2i	1.73651	−	1.26165i
$741$		0			0
$742$	118.196	+	363.769i	0.00584785	+	0.0179978i
$743$	757.991	+	2332.86i	0.0374266	+	0.115187i	0.968024	−	0.250856i	$-0.0807121\pi$
$743$	757.991	+	2332.86i	0.0374266	+	0.115187i	−0.930598	+	0.366044i	$0.880712\pi$
$744$		0			0
$745$	1605.68	−	1166.59i	0.0789631	−	0.0573700i
$746$	20293.2	−	62456.0i	0.995961	−	3.06525i
$747$		0			0
$748$	−64978.6	+	59322.5i	−3.17627	+	2.89979i
$749$	−19538.9			−0.953185
$750$		0			0
$751$	9349.05	−	6792.49i	0.454263	−	0.330042i	−0.337013	−	0.941500i	$-0.609417\pi$
$751$	9349.05	−	6792.49i	0.454263	−	0.330042i	0.791277	+	0.611458i	$0.209417\pi$
$752$	−46340.5	−	33668.3i	−2.24716	−	1.63266i
$753$		0			0
$754$	−2306.35	−	7098.22i	−0.111396	−	0.342841i
$755$	2573.68	+	1869.89i	0.124061	+	0.0901353i
$756$		0			0
$757$	7924.05	−	24387.7i	0.380455	−	1.17092i	−0.559269	−	0.828986i	$-0.688918\pi$
$757$	7924.05	−	24387.7i	0.380455	−	1.17092i	0.939724	−	0.341934i	$-0.111082\pi$
$758$	−37423.9			−1.79327
$759$		0			0
$760$	−17520.8			−0.836243
$761$	1870.80	−	5757.72i	0.0891147	−	0.274267i	−0.896561	−	0.442921i	$-0.853942\pi$
$761$	1870.80	−	5757.72i	0.0891147	−	0.274267i	0.985675	+	0.168654i	$0.0539422\pi$
$762$		0			0
$763$	2964.07	+	2153.53i	0.140638	+	0.102179i
$764$	−23318.0	−	71765.5i	−1.10421	−	3.39841i
$765$		0			0
$766$	−46906.5	−	34079.6i	−2.21254	−	1.60750i
$767$	−5472.43	+	3975.96i	−0.257625	+	0.187175i
$768$		0			0
$769$	23509.7			1.10245			0.551224	−	0.834357i	$-0.314161\pi$
$769$	23509.7			1.10245			0.551224	+	0.834357i	$0.314161\pi$
$770$	14233.0	+	31384.3i	0.666132	+	1.46884i
$771$		0			0
$772$	17390.6	−	53522.9i	0.810755	−	2.49525i
$773$	4033.24	−	2930.32i	0.187666	−	0.136347i	−0.489986	−	0.871731i	$-0.662998\pi$
$773$	4033.24	−	2930.32i	0.187666	−	0.136347i	0.677651	+	0.735384i	$0.262998\pi$
$774$		0			0
$775$	2062.52	+	6347.79i	0.0955974	+	0.294219i
$776$	20627.1	+	63483.6i	0.954212	+	2.93676i
$777$		0			0
$778$	12254.4	−	8903.35i	0.564707	−	0.410284i
$779$	1972.55	−	6070.88i	0.0907239	−	0.279219i
$780$		0			0
$781$	−3359.27	+	16357.4i	−0.153911	+	0.749439i
$782$	107473.			4.91462
$783$		0			0
$784$	19037.6	−	13831.6i	0.867236	−	0.630084i
$785$	−35346.9	−	25681.0i	−1.60711	−	1.16764i
$786$		0			0
$787$	7136.30	+	21963.3i	0.323230	+	0.994798i	0.972233	+	0.234013i	$0.0751859\pi$
$787$	7136.30	+	21963.3i	0.323230	+	0.994798i	−0.649004	+	0.760785i	$0.724814\pi$
$788$	45205.1	+	32843.4i	2.04361	+	1.48477i
$789$		0			0
$790$	11676.5	−	35936.4i	0.525860	−	1.61843i
$791$	−1350.08			−0.0606868
$792$		0			0
$793$	−8373.39			−0.374965
$794$	−19623.6	+	60395.1i	−0.877096	+	2.69942i
$795$		0			0
$796$	14359.0	+	10432.4i	0.639373	+	0.464531i
$797$	−5369.64	−	16526.1i	−0.238648	−	0.734483i	−0.996617	−	0.0821918i	$-0.973808\pi$
$797$	−5369.64	−	16526.1i	−0.238648	−	0.734483i	0.757969	−	0.652291i	$-0.226192\pi$
$798$		0			0
$799$	49600.5	+	36036.8i	2.19617	+	1.59561i
$800$	16795.6	−	12202.8i	0.742270	−	0.539291i
$801$		0			0
$802$	38909.1			1.71313
$803$	4073.40	+	8981.98i	0.179013	+	0.394729i
$804$		0			0
$805$	9045.13	−	27838.1i	0.396024	−	1.21884i
$806$	8609.14	−	6254.90i	0.376233	−	0.273349i
$807$		0			0
$808$	−20118.0	−	61916.9i	−0.875927	−	2.69583i
$809$	−1030.68	−	3172.12i	−0.0447922	−	0.137856i	0.926159	−	0.377132i	$-0.123090\pi$
$809$	−1030.68	−	3172.12i	−0.0447922	−	0.137856i	−0.970952	+	0.239276i	$0.923090\pi$
$810$		0			0
$811$	−3942.93	+	2864.71i	−0.170721	+	0.124036i	−0.669865	−	0.742483i	$-0.733648\pi$
$811$	−3942.93	+	2864.71i	−0.170721	+	0.124036i	0.499144	+	0.866519i	$0.333648\pi$
$812$	−3322.83	+	10226.6i	−0.143606	+	0.441975i
$813$		0			0
$814$	29431.8	−	3298.53i	1.26730	−	0.142031i
$815$	9458.91			0.406541
$816$		0			0
$817$	1868.71	−	1357.70i	0.0800219	−	0.0581393i
$818$	−30164.4	−	21915.7i	−1.28933	−	0.936755i
$819$		0			0
$820$	24119.9	+	74233.5i	1.02720	+	3.16140i
$821$	15080.4	+	10956.5i	0.641058	+	0.465756i	0.860214	−	0.509934i	$-0.170330\pi$
$821$	15080.4	+	10956.5i	0.641058	+	0.465756i	−0.219155	+	0.975690i	$0.570330\pi$
$822$		0			0
$823$	5815.65	−	17898.7i	0.246319	−	0.758093i	−0.749097	−	0.662460i	$-0.769512\pi$
$823$	5815.65	−	17898.7i	0.246319	−	0.758093i	0.995417	−	0.0956332i	$-0.0304876\pi$
$824$	−47955.6			−2.02744
$825$		0			0
$826$	14014.9			0.590364
$827$	10812.3	−	33276.8i	0.454632	−	1.39921i	−0.416935	−	0.908936i	$-0.636896\pi$
$827$	10812.3	−	33276.8i	0.454632	−	1.39921i	0.871567	−	0.490277i	$-0.163104\pi$
$828$		0			0
$829$	−11513.8	−	8365.25i	−0.482377	−	0.350467i	0.319868	−	0.947462i	$-0.396361\pi$
$829$	−11513.8	−	8365.25i	−0.482377	−	0.350467i	−0.802245	+	0.596995i	$0.796361\pi$
$830$	6410.88	+	19730.7i	0.268102	+	0.825134i
$831$		0			0
$832$	−2404.31	−	1746.83i	−0.100186	−	0.0727892i
$833$	−20376.8	+	14804.6i	−0.847558	+	0.615787i
$834$		0			0
$835$	−22902.9			−0.949207
$836$	−12921.2	−	7341.85i	−0.534556	−	0.303736i
$837$		0			0
$838$	17571.0	−	54077.9i	0.724319	−	2.22923i
$839$	−20512.2	+	14903.0i	−0.844054	+	0.613241i	−0.923500	−	0.383598i	$-0.874685\pi$
$839$	−20512.2	+	14903.0i	−0.844054	+	0.613241i	0.0794461	+	0.996839i	$0.474685\pi$
$840$		0			0
$841$	−6833.02	−	21029.9i	−0.280168	−	0.862269i
$842$	8081.88	+	24873.5i	0.330784	+	1.01805i
$843$		0			0
$844$	−49154.5	+	35712.8i	−2.00470	+	1.45650i
$845$	5840.67	−	17975.7i	0.237781	−	0.731816i
$846$		0			0
$847$	−1491.68	+	16357.0i	−0.0605133	+	0.663558i
$848$	746.276			0.0302208
$849$		0			0
$850$	−53714.6	+	39025.9i	−2.16752	+	1.57480i
$851$	−20351.3	−	14786.1i	−0.819781	−	0.595605i
$852$		0			0
$853$	−2986.46	−	9191.39i	−0.119876	−	0.368942i	0.873056	−	0.487619i	$-0.162135\pi$
$853$	−2986.46	−	9191.39i	−0.119876	−	0.368942i	−0.992933	+	0.118678i	$0.962135\pi$
$854$	14035.4	+	10197.3i	0.562392	+	0.408602i
$855$		0			0
$856$	−25728.7	+	79184.9i	−1.02733	+	3.16178i
$857$	38619.7			1.53935			0.769676	−	0.638435i	$-0.220418\pi$
$857$	38619.7			1.53935			0.769676	+	0.638435i	$0.220418\pi$
$858$		0			0
$859$	−30501.9			−1.21154			−0.605769	−	0.795641i	$-0.707134\pi$
$859$	−30501.9			−1.21154			−0.605769	+	0.795641i	$0.707134\pi$
$860$	−8728.00	+	26862.0i	−0.346073	+	1.06510i
$861$		0			0
$862$	59856.8	+	43488.5i	2.36512	+	1.71836i
$863$	9135.64	+	28116.6i	0.360349	+	1.10904i	0.952843	+	0.303464i	$0.0981433\pi$
$863$	9135.64	+	28116.6i	0.360349	+	1.10904i	−0.592494	+	0.805575i	$0.701857\pi$
$864$		0			0
$865$	−40199.7	−	29206.8i	−1.58015	−	1.14805i
$866$	17565.4	−	12762.0i	0.689255	−	0.500773i
$867$		0			0
$868$	−15331.5			−0.599522
$869$	13300.5	−	12142.7i	0.519203	−	0.474009i
$870$		0			0
$871$	1765.44	−	5433.46i	0.0686792	−	0.211373i
$872$	12630.6	−	9176.70i	0.490513	−	0.356379i
$873$		0			0
$874$	5609.60	+	17264.6i	0.217103	+	0.668173i
$875$	−1531.94	−	4714.84i	−0.0591876	−	0.182161i
$876$		0			0
$877$	18613.5	−	13523.5i	0.716685	−	0.520702i	−0.168638	−	0.985678i	$-0.553937\pi$
$877$	18613.5	−	13523.5i	0.716685	−	0.520702i	0.885323	+	0.464976i	$0.153937\pi$
$878$	−2866.01	+	8820.67i	−0.110163	+	0.339047i
$879$		0			0
$880$	66818.2	−	7488.56i	2.55959	−	0.286863i
$881$	−34057.4			−1.30241			−0.651205	−	0.758902i	$-0.725736\pi$
$881$	−34057.4			−1.30241			−0.651205	+	0.758902i	$0.725736\pi$
$882$		0			0
$883$	−28035.4	+	20368.9i	−1.06848	+	0.776295i	−0.975638	−	0.219386i	$-0.929595\pi$
$883$	−28035.4	+	20368.9i	−1.06848	+	0.776295i	−0.0928400	+	0.995681i	$0.529595\pi$
$884$	59551.6	+	43266.7i	2.26576	+	1.64617i
$885$		0			0
$886$	7597.02	+	23381.2i	0.288067	+	0.886578i
$887$	−4164.73	−	3025.86i	−0.157653	−	0.114541i	0.506162	−	0.862438i	$-0.331064\pi$
$887$	−4164.73	−	3025.86i	−0.157653	−	0.114541i	−0.663815	+	0.747897i	$0.731064\pi$
$888$		0			0
$889$	−5290.54	+	16282.6i	−0.199594	+	0.614287i
$890$	5931.34			0.223392
$891$		0			0
$892$	89754.8			3.36907
$893$	−3200.08	+	9848.82i	−0.119918	+	0.369069i
$894$		0			0
$895$	−51494.9	−	37413.2i	−1.92322	−	1.39730i
$896$	−4553.01	−	14012.7i	−0.169760	−	0.522469i
$897$		0			0
$898$	38047.5	+	27643.1i	1.41388	+	1.02724i
$899$	−2626.36	+	1908.16i	−0.0974350	+	0.0707907i
$900$		0			0
$901$	−798.776			−0.0295351
$902$	−10762.6	+	52406.4i	−0.397289	+	1.93453i
$903$		0			0
$904$	−1777.78	+	5471.44i	−0.0654072	+	0.201303i
$905$	8965.51	−	6513.82i	0.329308	−	0.239256i
$906$		0			0
$907$	12572.1	+	38693.0i	0.460254	+	1.41652i	0.864855	+	0.502022i	$0.167411\pi$
$907$	12572.1	+	38693.0i	0.460254	+	1.41652i	−0.404601	+	0.914493i	$0.632589\pi$
$908$	5996.56	+	18455.5i	0.219166	+	0.674524i
$909$		0			0
$910$	23324.4	−	16946.2i	0.849666	−	0.617318i
$911$	−7794.32	+	23988.5i	−0.283466	+	0.872418i	0.703388	+	0.710806i	$0.251669\pi$
$911$	−7794.32	+	23988.5i	−0.283466	+	0.872418i	−0.986854	+	0.161613i	$0.948331\pi$
$912$		0			0
$913$	−1989.18	+	9685.93i	−0.0721053	+	0.351104i
$914$	−31667.2			−1.14601
$915$		0			0
$916$	63717.3	−	46293.3i	2.29834	−	1.66984i
$917$	−15127.3	−	10990.6i	−0.544762	−	0.395793i
$918$		0			0
$919$	−2842.41	−	8748.04i	−0.102027	−	0.314006i	0.886994	−	0.461780i	$-0.152789\pi$
$919$	−2842.41	−	8748.04i	−0.102027	−	0.314006i	−0.989021	+	0.147774i	$0.952789\pi$
$920$	−100908.	−	73314.1i	−3.61614	−	2.62728i
$921$		0			0
$922$	−26647.2	+	82011.7i	−0.951822	+	2.92941i
$923$	13970.4			0.498205
$924$		0			0
$925$	15540.6			0.552403
$926$	1296.47	−	3990.12i	0.0460093	−	0.141602i
$927$		0			0
$928$	8169.16	+	5935.24i	0.288972	+	0.209950i
$929$	10339.7	+	31822.2i	0.365160	+	1.12385i	0.949881	+	0.312612i	$0.101204\pi$
$929$	10339.7	+	31822.2i	0.365160	+	1.12385i	−0.584721	+	0.811235i	$0.698796\pi$
$930$		0			0
$931$	−3441.81	−	2500.62i	−0.121161	−	0.0880285i
$932$	76152.7	−	55328.1i	2.67646	−	1.94456i
$933$		0			0
$934$	−86040.2			−3.01426
$935$	−71518.8	+	8015.37i	−2.50151	+	0.280354i
$936$		0			0
$937$	−9594.58	+	29529.1i	−0.334516	+	1.02953i	0.632445	+	0.774606i	$0.282052\pi$
$937$	−9594.58	+	29529.1i	−0.334516	+	1.02953i	−0.966960	+	0.254928i	$0.917948\pi$
$938$	−9576.23	+	6957.54i	−0.333342	+	0.242187i
$939$		0			0
$940$	−39129.9	−	120429.i	−1.35774	−	4.17870i
$941$	−6687.39	−	20581.7i	−0.231671	−	0.713011i	−0.997546	−	0.0700208i	$-0.977693\pi$
$941$	−6687.39	−	20581.7i	−0.231671	−	0.713011i	0.765874	−	0.642991i	$-0.222307\pi$
$942$		0			0
$943$	36763.7	−	26710.4i	1.26956	−	0.922386i
$944$	8449.91	−	26006.1i	0.291336	−	0.896640i
$945$		0			0
$946$	−14297.3	+	13052.8i	−0.491381	+	0.448608i
$947$	31725.1			1.08862			0.544311	−	0.838883i	$-0.316791\pi$
$947$	31725.1			1.08862			0.544311	+	0.838883i	$0.316791\pi$
$948$		0			0
$949$	6675.30	−	4849.89i	0.228334	−	0.165895i
$950$	−9072.81	−	6591.78i	−0.309854	−	0.225122i
$951$		0			0
$952$	−26482.3	−	81504.2i	−0.901572	−	2.77475i
$953$	42127.7	+	30607.6i	1.43195	+	1.04037i	0.989649	+	0.143508i	$0.0458383\pi$
$953$	42127.7	+	30607.6i	1.43195	+	1.04037i	0.442303	+	0.896866i	$0.354162\pi$
$954$		0			0
$955$	19072.8	−	58700.0i	0.646262	−	1.98899i
$956$	2269.75			0.0767877
$957$		0			0
$958$	−23862.9			−0.804777
$959$	−11326.0	+	34857.8i	−0.381372	+	1.17374i
$960$		0			0
$961$	20356.8	+	14790.0i	0.683319	+	0.496460i
$962$	−7656.61	−	23564.6i	−0.256610	−	0.789765i
$963$		0			0
$964$	6582.26	+	4782.29i	0.219917	+	0.159779i
$965$	37240.3	−	27056.6i	1.24229	−	0.902574i
$966$		0			0
$967$	−4519.31			−0.150291			−0.0751454	−	0.997173i	$-0.523942\pi$
$967$	−4519.31			−0.150291			−0.0751454	+	0.997173i	$0.523942\pi$
$968$	64325.6	+	27584.2i	2.13585	+	0.915898i
$969$		0			0
$970$	−30025.4	+	92408.6i	−0.993873	+	3.05883i
$971$	20189.6	−	14668.6i	0.667265	−	0.484796i	−0.201844	−	0.979418i	$-0.564693\pi$
$971$	20189.6	−	14668.6i	0.667265	−	0.484796i	0.869109	+	0.494621i	$0.164693\pi$
$972$		0			0
$973$	8206.64	+	25257.5i	0.270394	+	0.832186i
$974$	−27914.2	−	85911.0i	−0.918304	−	2.82625i
$975$		0			0
$976$	27384.5	−	19896.0i	0.898112	−	0.652517i
$977$	−17549.0	+	54010.4i	−0.574661	+	1.76862i	0.0626715	+	0.998034i	$0.480038\pi$
$977$	−17549.0	+	54010.4i	−0.574661	+	1.76862i	−0.637332	+	0.770589i	$0.719962\pi$
$978$		0			0
$979$	2457.95	+	1396.61i	0.0802416	+	0.0455935i
$980$	52020.8			1.69566
$981$		0			0
$982$	62000.5	−	45046.0i	2.01478	−	1.46382i
$983$	−25471.5	−	18506.2i	−0.826466	−	0.600463i	0.0920914	−	0.995751i	$-0.470645\pi$
$983$	−25471.5	−	18506.2i	−0.826466	−	0.600463i	−0.918557	+	0.395288i	$0.870645\pi$
$984$		0			0
$985$	14123.2	+	43466.9i	0.456857	+	1.40606i
$986$	−26126.0	−	18981.6i	−0.843835	−	0.613082i
$987$		0			0
$988$	−3842.09	+	11824.7i	−0.123718	+	0.380764i
$989$	16443.7			0.528696
$990$		0			0
$991$	9490.27			0.304206			0.152103	−	0.988365i	$-0.451395\pi$
$991$	9490.27			0.304206			0.152103	+	0.988365i	$0.451395\pi$
$992$	−4448.99	+	13692.6i	−0.142395	+	0.438246i
$993$		0			0
$994$	−23417.2	−	17013.6i	−0.747232	−	0.542896i
$995$	4486.12	+	13806.8i	0.142934	+	0.439906i
$996$		0			0
$997$	−33078.7	−	24033.1i	−1.05077	−	0.763427i	−0.0784085	−	0.996921i	$-0.524984\pi$
$997$	−33078.7	−	24033.1i	−1.05077	−	0.763427i	−0.972358	+	0.233495i	$0.924984\pi$
$998$	−89031.2	+	64685.0i	−2.82388	+	2.05167i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.d.64.1		12
3.2	odd	2		33.4.e.c.31.3	yes	12
11.4	even	5		1089.4.a.bi.1.1		6
11.5	even	5	inner	99.4.f.d.82.1		12
11.7	odd	10		1089.4.a.bk.1.6		6
33.5	odd	10		33.4.e.c.16.3	✓	12
33.26	odd	10		363.4.a.v.1.6		6
33.29	even	10		363.4.a.u.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.c.16.3	✓	12	33.5	odd	10
33.4.e.c.31.3	yes	12	3.2	odd	2
99.4.f.d.64.1		12	1.1	even	1	trivial
99.4.f.d.82.1		12	11.5	even	5	inner
363.4.a.u.1.1		6	33.29	even	10
363.4.a.v.1.6		6	33.26	odd	10
1089.4.a.bi.1.1		6	11.4	even	5
1089.4.a.bk.1.6		6	11.7	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58358 + 4.87376i) q^{2} +(-14.7737 - 10.7337i) q^{4} +(-4.61569 - 14.2056i) q^{5} +(9.98349 + 7.25343i) q^{7} +(42.5421 - 30.9086i) q^{8} +76.5442 q^{10} +(31.7200 + 18.0234i) q^{11} +(9.43188 - 29.0283i) q^{13} +(-51.1612 + 37.1708i) q^{14} +(38.1281 + 117.346i) q^{16} +(-40.8103 - 125.601i) q^{17} +(18.0466 - 13.1116i) q^{19} +(-84.2885 + 259.413i) q^{20} +(-138.073 + 126.054i) q^{22} +158.801 q^{23} +(-79.3681 + 57.6643i) q^{25} +(126.541 + 91.9375i) q^{26} +(-69.6368 - 214.320i) q^{28} +(-38.6035 - 28.0471i) q^{29} +(21.0238 - 64.7045i) q^{31} -211.617 q^{32} +676.778 q^{34} +(56.9588 - 175.301i) q^{35} +(-128.156 - 93.1106i) q^{37} +(35.3247 + 108.718i) q^{38} +(-635.437 - 461.672i) q^{40} +(231.508 - 168.200i) q^{41} +103.549 q^{43} +(-275.164 - 606.746i) q^{44} +(-251.475 + 773.960i) q^{46} +(-375.576 + 272.872i) q^{47} +(-58.9350 - 181.383i) q^{49} +(-155.356 - 478.138i) q^{50} +(-450.926 + 327.617i) q^{52} +(1.86904 - 5.75232i) q^{53} +(109.624 - 533.793i) q^{55} +648.912 q^{56} +(197.827 - 143.729i) q^{58} +(-179.294 - 130.264i) q^{59} +(-84.7750 - 260.911i) q^{61} +(282.061 + 204.930i) q^{62} +(30.0884 - 92.6027i) q^{64} -455.900 q^{65} +187.178 q^{67} +(-745.250 + 2293.64i) q^{68} +(764.178 + 555.208i) q^{70} +(141.442 + 435.312i) q^{71} +(218.703 + 158.897i) q^{73} +(656.744 - 477.153i) q^{74} -407.352 q^{76} +(185.945 + 410.015i) q^{77} +(152.545 - 469.486i) q^{79} +(1490.99 - 1083.27i) q^{80} +(453.157 + 1394.67i) q^{82} +(83.7540 + 257.768i) q^{83} +(-1595.88 + 1159.47i) q^{85} +(-163.979 + 504.674i) q^{86} +(1906.51 - 213.670i) q^{88} +77.4891 q^{89} +(304.718 - 221.391i) q^{91} +(-2346.08 - 1704.53i) q^{92} +(-735.158 - 2262.58i) q^{94} +(-269.556 - 195.844i) q^{95} +(-392.262 + 1207.26i) q^{97} +977.348 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 28 q^{5} + 12 q^{7} + 112 q^{8} + 100 q^{10} + 54 q^{11} - 18 q^{13} - 156 q^{14} + 308 q^{16} + 80 q^{17} - 280 q^{19} + 15 q^{20} - 193 q^{22} + 392 q^{23} + 77 q^{25} - 406 q^{26} - 429 q^{28}+ \cdots - 2810 q^{98}+O(q^{100}) \) 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

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