LMFDB - Embedded newform 33.4.e.c.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, 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("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (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:	$1.94706303019$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.3
Root			$1.27457 + 3.92271i$ of defining polynomial
Character	$\chi$	$=$	33.31
Dual form			33.4.e.c.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58358 - 4.87376i) q^{2} +(2.42705 - 1.76336i) q^{3} +(-14.7737 - 10.7337i) q^{4} +(4.61569 + 14.2056i) q^{5} +(-4.75075 - 14.6213i) q^{6} +(9.98349 + 7.25343i) q^{7} +(-42.5421 + 30.9086i) q^{8} +(2.78115 - 8.55951i) q^{9} +76.5442 q^{10} +(-31.7200 - 18.0234i) q^{11} -54.7839 q^{12} +(9.43188 - 29.0283i) q^{13} +(51.1612 - 37.1708i) q^{14} +(36.2521 + 26.3387i) q^{15} +(38.1281 + 117.346i) q^{16} +(40.8103 + 125.601i) q^{17} +(-37.3128 - 27.1094i) q^{18} +(18.0466 - 13.1116i) q^{19} +(84.2885 - 259.413i) q^{20} +37.0208 q^{21} +(-138.073 + 126.054i) q^{22} -158.801 q^{23} +(-48.7489 + 150.034i) q^{24} +(-79.3681 + 57.6643i) q^{25} +(-126.541 - 91.9375i) q^{26} +(-8.34346 - 25.6785i) q^{27} +(-69.6368 - 214.320i) q^{28} +(38.6035 + 28.0471i) q^{29} +(185.777 - 134.975i) q^{30} +(21.0238 - 64.7045i) q^{31} +211.617 q^{32} +(-108.768 + 12.1900i) q^{33} +676.778 q^{34} +(-56.9588 + 175.301i) q^{35} +(-132.963 + 96.6036i) q^{36} +(-128.156 - 93.1106i) q^{37} +(-35.3247 - 108.718i) q^{38} +(-28.2956 - 87.0850i) q^{39} +(-635.437 - 461.672i) q^{40} +(-231.508 + 168.200i) q^{41} +(58.6255 - 180.431i) q^{42} +103.549 q^{43} +(275.164 + 606.746i) q^{44} +134.430 q^{45} +(-251.475 + 773.960i) q^{46} +(375.576 - 272.872i) q^{47} +(299.462 + 217.572i) q^{48} +(-58.9350 - 181.383i) q^{49} +(155.356 + 478.138i) q^{50} +(320.529 + 232.878i) q^{51} +(-450.926 + 327.617i) q^{52} +(-1.86904 + 5.75232i) q^{53} -138.364 q^{54} +(109.624 - 533.793i) q^{55} -648.912 q^{56} +(20.6796 - 63.6451i) q^{57} +(197.827 - 143.729i) q^{58} +(179.294 + 130.264i) q^{59} +(-252.866 - 778.240i) q^{60} +(-84.7750 - 260.911i) q^{61} +(-282.061 - 204.930i) q^{62} +(89.8514 - 65.2808i) q^{63} +(30.0884 - 92.6027i) q^{64} +455.900 q^{65} +(-112.831 + 549.412i) q^{66} +187.178 q^{67} +(745.250 - 2293.64i) q^{68} +(-385.419 + 280.023i) q^{69} +(764.178 + 555.208i) q^{70} +(-141.442 - 435.312i) q^{71} +(146.247 + 450.101i) q^{72} +(218.703 + 158.897i) q^{73} +(-656.744 + 477.153i) q^{74} +(-90.9478 + 279.908i) q^{75} -407.352 q^{76} +(-185.945 - 410.015i) q^{77} -469.240 q^{78} +(152.545 - 469.486i) q^{79} +(-1490.99 + 1083.27i) q^{80} +(-65.5304 - 47.6106i) q^{81} +(453.157 + 1394.67i) q^{82} +(-83.7540 - 257.768i) q^{83} +(-546.935 - 397.371i) q^{84} +(-1595.88 + 1159.47i) q^{85} +(163.979 - 504.674i) q^{86} +143.150 q^{87} +(1906.51 - 213.670i) q^{88} -77.4891 q^{89} +(212.881 - 655.181i) q^{90} +(304.718 - 221.391i) q^{91} +(2346.08 + 1704.53i) q^{92} +(-63.0713 - 194.113i) q^{93} +(-735.158 - 2262.58i) q^{94} +(269.556 + 195.844i) q^{95} +(513.605 - 373.156i) q^{96} +(-392.262 + 1207.26i) q^{97} -977.348 q^{98} +(-242.489 + 221.382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 9 q^{3} - 16 q^{4} + 28 q^{5} + 12 q^{7} - 112 q^{8} - 27 q^{9} + 100 q^{10} - 54 q^{11} - 102 q^{12} - 18 q^{13} + 156 q^{14} + 111 q^{15} + 308 q^{16} - 80 q^{17} - 45 q^{18} - 280 q^{19} - 15 q^{20}+ \cdots - 171 q^{99}+O(q^{100}) $ 12 * q + 9 * q^3 - 16 * q^4 + 28 * q^5 + 12 * q^7 - 112 * q^8 - 27 * q^9 + 100 * q^10 - 54 * q^11 - 102 * q^12 - 18 * q^13 + 156 * q^14 + 111 * q^15 + 308 * q^16 - 80 * q^17 - 45 * q^18 - 280 * q^19 - 15 * q^20 - 6 * q^21 - 193 * q^22 - 392 * q^23 - 264 * q^24 + 77 * q^25 + 406 * q^26 + 81 * q^27 - 429 * q^28 + 13 * q^29 + 120 * q^30 + 413 * q^31 + 1314 * q^32 + 177 * q^33 + 1060 * q^34 - 1239 * q^35 - 144 * q^36 + 654 * q^37 + 912 * q^38 + 54 * q^39 - 1803 * q^40 - 1490 * q^41 + 342 * q^42 + 416 * q^43 + 695 * q^44 + 162 * q^45 - 2369 * q^46 - 150 * q^47 + 711 * q^48 - 301 * q^49 - 1878 * q^50 - 1661 * q^52 + 1359 * q^53 - 270 * q^54 + 3300 * q^55 - 858 * q^56 - 1110 * q^57 + 955 * q^58 + 1262 * q^59 + 45 * q^60 - 1044 * q^61 - 701 * q^62 + 108 * q^63 + 78 * q^64 + 4556 * q^65 + 369 * q^66 - 528 * q^67 + 703 * q^68 - 594 * q^69 + 3050 * q^70 + 558 * q^71 + 792 * q^72 - 699 * q^73 - 3224 * q^74 + 1284 * q^75 - 868 * q^76 + 390 * q^77 - 558 * q^78 - 1252 * q^79 - 1914 * q^80 - 243 * q^81 + 2987 * q^82 - 4464 * q^83 - 1443 * q^84 - 2170 * q^85 - 3209 * q^86 - 3474 * q^87 + 1302 * q^88 + 316 * q^89 - 90 * q^90 + 176 * q^91 + 4595 * q^92 - 1239 * q^93 + 1247 * q^94 + 1466 * q^95 + 1398 * q^96 + 1608 * q^97 + 2810 * q^98 - 171 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	$-0.539191\pi$
$2$	1.58358	−	4.87376i	0.559881	−	1.72314i	0.682692	−	0.730706i	$-0.260809\pi$
$3$	2.42705	−	1.76336i	0.467086	−	0.339358i
$3$	2.42705	−	1.76336i	0.467086	−	0.339358i
$4$	−14.7737	−	10.7337i	−1.84671	−	1.34172i
$5$	4.61569	+	14.2056i	0.412840	+	1.27059i	0.914169	+	0.405333i	$0.132845\pi$
$5$	4.61569	+	14.2056i	0.412840	+	1.27059i	−0.501329	+	0.865257i	$0.667155\pi$
$6$	−4.75075	−	14.6213i	−0.323247	−	0.994853i
$7$	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
$9$	2.78115	−	8.55951i	0.103006	−	0.317019i
$10$	76.5442			2.42054
$11$	−31.7200	−	18.0234i	−0.869449	−	0.494023i
$11$	−31.7200	−	18.0234i	−0.869449	−	0.494023i
$12$	−54.7839			−1.31790
$13$	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
$15$	36.2521	+	26.3387i	0.624016	+	0.453375i
$16$	38.1281	+	117.346i	0.595751	+	1.83353i
$17$	40.8103	+	125.601i	0.582233	+	1.79193i	0.610109	+	0.792317i	$0.291126\pi$
$17$	40.8103	+	125.601i	0.582233	+	1.79193i	−0.0278760	+	0.999611i	$0.508874\pi$
$18$	−37.3128	−	27.1094i	−0.488596	−	0.354986i
$19$	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
$21$	37.0208			0.384695
$22$	−138.073	+	126.054i	−1.33806	+	1.22158i
$23$	−158.801			−1.43967			−0.719834	−	0.694147i	$-0.755782\pi$
$23$	−158.801			−1.43967			−0.719834	+	0.694147i	$0.755782\pi$
$24$	−48.7489	+	150.034i	−0.414618	+	1.27606i
$25$	−79.3681	+	57.6643i	−0.634945	+	0.461314i
$26$	−126.541	−	91.9375i	−0.954490	−	0.693478i
$27$	−8.34346	−	25.6785i	−0.0594703	−	0.183031i
$28$	−69.6368	−	214.320i	−0.470004	−	1.44652i
$29$	38.6035	+	28.0471i	0.247189	+	0.179594i	0.704480	−	0.709724i	$-0.251180\pi$
$29$	38.6035	+	28.0471i	0.247189	+	0.179594i	−0.457291	+	0.889317i	$0.651180\pi$
$30$	185.777	−	134.975i	1.13060	−	0.821430i
$31$	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
$33$	−108.768	+	12.1900i	−0.573758	+	0.0643031i
$34$	676.778			3.41372
$35$	−56.9588	+	175.301i	−0.275080	+	0.846609i
$36$	−132.963	+	96.6036i	−0.615571	+	0.447239i
$37$	−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
$39$	−28.2956	−	87.0850i	−0.116178	−	0.357558i
$40$	−635.437	−	461.672i	−2.51179	−	1.82492i
$41$	−231.508	+	168.200i	−0.881839	+	0.640694i	−0.933737	−	0.357959i	$-0.883473\pi$
$41$	−231.508	+	168.200i	−0.881839	+	0.640694i	0.0518980	+	0.998652i	$0.483473\pi$
$42$	58.6255	−	180.431i	0.215384	−	0.662882i
$43$	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
$45$	134.430			0.445326
$46$	−251.475	+	773.960i	−0.806042	+	2.48074i
$47$	375.576	−	272.872i	1.16560	−	0.846861i	0.175128	−	0.984546i	$-0.443966\pi$
$47$	375.576	−	272.872i	1.16560	−	0.846861i	0.990476	+	0.137684i	$0.0439660\pi$
$48$	299.462	+	217.572i	0.900491	+	0.654245i
$49$	−58.9350	−	181.383i	−0.171822	−	0.528815i
$50$	155.356	+	478.138i	0.439414	+	1.35238i
$51$	320.529	+	232.878i	0.880058	+	0.639400i
$52$	−450.926	+	327.617i	−1.20254	+	0.873698i
$53$	−1.86904	+	5.75232i	−0.00484402	+	0.0149084i	−0.953449	−	0.301553i	$-0.902495\pi$
$53$	−1.86904	+	5.75232i	−0.00484402	+	0.0149084i	0.948605	+	0.316462i	$0.102495\pi$
$54$	−138.364			−0.348683
$55$	109.624	−	533.793i	0.268758	−	1.30867i
$56$	−648.912			−1.54847
$57$	20.6796	−	63.6451i	0.0480539	−	0.147895i
$58$	197.827	−	143.729i	0.447861	−	0.325390i
$59$	179.294	+	130.264i	0.395628	+	0.287440i	0.767758	−	0.640740i	$-0.221372\pi$
$59$	179.294	+	130.264i	0.395628	+	0.287440i	−0.372130	+	0.928181i	$0.621372\pi$
$60$	−252.866	−	778.240i	−0.544080	−	1.67451i
$61$	−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
$63$	89.8514	−	65.2808i	0.179686	−	0.130549i
$64$	30.0884	−	92.6027i	0.0587665	−	0.180865i
$65$	455.900			0.869961
$66$	−112.831	+	549.412i	−0.210433	+	1.02467i
$67$	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
$69$	−385.419	+	280.023i	−0.672449	+	0.488563i
$70$	764.178	+	555.208i	1.30481	+	0.948000i
$71$	−141.442	−	435.312i	−0.236423	−	0.727635i	−0.996929	−	0.0783045i	$-0.975049\pi$
$71$	−141.442	−	435.312i	−0.236423	−	0.727635i	0.760507	−	0.649330i	$-0.224951\pi$
$72$	146.247	+	450.101i	0.239380	+	0.736735i
$73$	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
$75$	−90.9478	+	279.908i	−0.140023	+	0.430947i
$76$	−407.352			−0.614822
$77$	−185.945	−	410.015i	−0.275200	−	0.606825i
$78$	−469.240			−0.681167
$79$	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
$81$	−65.5304	−	47.6106i	−0.0898908	−	0.0653095i
$82$	453.157	+	1394.67i	0.610278	+	1.87824i
$83$	−83.7540	−	257.768i	−0.110761	−	0.340888i	0.880278	−	0.474458i	$-0.157356\pi$
$83$	−83.7540	−	257.768i	−0.110761	−	0.340888i	−0.991039	+	0.133570i	$0.957356\pi$
$84$	−546.935	−	397.371i	−0.710422	−	0.516152i
$85$	−1595.88	+	1159.47i	−2.03644	+	1.47956i
$86$	163.979	−	504.674i	0.205608	−	0.632795i
$87$	143.150			0.176405
$88$	1906.51	−	213.670i	2.30949	−	0.258833i
$89$	−77.4891			−0.0922902			−0.0461451	−	0.998935i	$-0.514694\pi$
$89$	−77.4891			−0.0922902			−0.0461451	+	0.998935i	$0.514694\pi$
$90$	212.881	−	655.181i	0.249329	−	0.767357i
$91$	304.718	−	221.391i	0.351023	−	0.255033i
$92$	2346.08	+	1704.53i	2.65865	+	1.93163i
$93$	−63.0713	−	194.113i	−0.0703246	−	0.216437i
$94$	−735.158	−	2262.58i	−0.806657	−	2.48264i
$95$	269.556	+	195.844i	0.291115	+	0.211507i
$96$	513.605	−	373.156i	0.546038	−	0.396720i
$97$	−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
$99$	−242.489	+	221.382i	−0.246173	+	0.224745i
$100$	1791.51			1.79151
$101$	−382.582	+	1177.46i	−0.376914	+	1.16002i	0.565265	+	0.824910i	$0.308774\pi$
$101$	−382.582	+	1177.46i	−0.376914	+	1.16002i	−0.942178	+	0.335112i	$0.891226\pi$
$102$	1642.57	−	1193.40i	1.59450	−	1.15847i
$103$	−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
$105$	170.876	+	525.904i	0.158817	+	0.488790i
$106$	25.0757	+	18.2186i	0.0229770	+	0.0166938i
$107$	1280.95	−	930.666i	1.15733	−	0.840849i	0.167892	−	0.985805i	$-0.446304\pi$
$107$	1280.95	−	930.666i	1.15733	−	0.840849i	0.989438	+	0.144956i	$0.0463041\pi$
$108$	−152.363	+	468.924i	−0.135751	+	0.417798i
$109$	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
$111$	−475.228			−0.406366
$112$	−470.511	+	1448.08i	−0.396956	+	1.22170i
$113$	88.5099	−	64.3062i	0.0736842	−	0.0535347i	−0.550333	−	0.834945i	$-0.685499\pi$
$113$	88.5099	−	64.3062i	0.0736842	−	0.0535347i	0.624018	+	0.781410i	$0.285499\pi$
$114$	−277.444	−	201.575i	−0.227938	−	0.165607i
$115$	−732.977	−	2255.87i	−0.594352	−	1.82923i
$116$	−269.267	−	828.719i	−0.215524	−	0.663316i
$117$	−222.237	−	161.464i	−0.175605	−	0.127585i
$118$	918.804	−	667.550i	0.716803	−	0.520788i
$119$	−503.610	+	1549.95i	−0.387949	+	1.19398i
$120$	−2356.33			−1.79252
$121$	681.316	+	1143.40i	0.511883	+	0.859055i
$122$	−1405.86			−1.04329
$123$	−265.284	+	816.461i	−0.194470	+	0.598519i
$124$	−1005.12	+	730.262i	−0.727922	+	0.528867i
$125$	325.007	+	236.132i	0.232556	+	0.168962i
$126$	−175.876	−	541.292i	−0.124352	−	0.382715i
$127$	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
$129$	251.319	−	182.594i	0.171530	−	0.124624i
$130$	721.955	−	2221.95i	0.487074	−	1.49906i
$131$	1515.23			1.01058			0.505291	−	0.862949i	$-0.331385\pi$
$131$	1515.23			1.01058			0.505291	+	0.862949i	$0.331385\pi$
$132$	1737.75	+	987.391i	1.14584	+	0.651071i
$133$	275.272			0.179467
$134$	296.411	−	912.260i	0.191090	−	0.588114i
$135$	326.269	−	237.048i	0.208005	−	0.151125i
$136$	−5618.32	−	4081.95i	−3.54240	−	2.57371i
$137$	−917.808	−	2824.72i	−0.572362	−	1.76155i	−0.644991	−	0.764190i	$-0.723139\pi$
$137$	−917.808	−	2824.72i	−0.572362	−	1.76155i	0.0726287	−	0.997359i	$-0.476861\pi$
$138$	754.424	+	2321.88i	0.465369	+	1.43226i
$139$	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
$141$	430.372	−	1324.55i	0.257049	−	0.791114i
$142$	−2345.59			−1.38618
$143$	−822.368	+	750.784i	−0.480908	+	0.439047i
$144$	1110.47			0.642630
$145$	−220.245	+	677.843i	−0.126140	+	0.388220i
$146$	1120.76	−	814.281i	0.635307	−	0.461578i
$147$	−462.882	−	336.303i	−0.259713	−	0.188693i
$148$	893.912	+	2751.18i	0.496480	+	1.52801i
$149$	−41.0610	−	126.373i	−0.0225761	−	0.0694822i	0.939134	−	0.343552i	$-0.111630\pi$
$149$	−41.0610	−	126.373i	−0.0225761	−	0.0694822i	−0.961710	+	0.274070i	$0.911630\pi$
$150$	1220.18	+	886.516i	0.664184	+	0.482558i
$151$	−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
$153$	1188.59			0.628049
$154$	−2292.77	+	256.959i	−1.19972	+	0.134457i
$155$	1016.21			0.526604
$156$	−516.715	+	1590.29i	−0.265194	+	0.816185i
$157$	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
$159$	5.60713	+	17.2570i	0.00279669	+	0.00860734i
$160$	976.758	+	3006.15i	0.482622	+	1.48536i
$161$	−1585.39	−	1151.85i	−0.776064	−	0.563843i
$162$	−335.816	+	243.984i	−0.162865	+	0.118329i
$163$	−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
$165$	−675.204	−	1488.85i	−0.318573	−	0.702464i
$166$	−1388.93			−0.649410
$167$	−473.826	+	1458.29i	−0.219555	+	0.675722i	0.779243	+	0.626722i	$0.215604\pi$
$167$	−473.826	+	1458.29i	−0.219555	+	0.675722i	−0.998799	+	0.0490007i	$0.984396\pi$
$168$	−1574.94	+	1144.26i	−0.723270	+	0.525487i
$169$	1023.73	+	743.781i	0.465966	+	0.338544i
$170$	3123.79	+	9614.05i	1.40932	+	4.33744i
$171$	−62.0387	−	190.935i	−0.0277440	−	0.0853871i
$172$	−1529.81	−	1111.47i	−0.678178	−	0.492725i
$173$	−2691.34	+	1955.37i	−1.18277	+	0.859331i	−0.992481	−	0.122398i	$-0.960942\pi$
$173$	−2691.34	+	1955.37i	−1.18277	+	0.859331i	−0.190286	+	0.981729i	$0.560942\pi$
$174$	226.689	−	697.678i	0.0987659	−	0.303970i
$175$	−1210.63			−0.522945
$176$	905.551	−	4409.41i	0.387832	−	1.88848i
$177$	664.857			0.282337
$178$	−122.710	+	377.663i	−0.0516715	+	0.159028i
$179$	−3447.54	+	2504.79i	−1.43956	+	1.04590i	−0.451428	+	0.892307i	$0.649085\pi$
$179$	−3447.54	+	2504.79i	−1.43956	+	1.04590i	−0.988134	+	0.153595i	$0.950915\pi$
$180$	−1986.03	−	1442.94i	−0.822389	−	0.597501i
$181$	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
$183$	−665.831	−	483.755i	−0.268960	−	0.195411i
$184$	6755.74	−	4908.33i	2.70674	−	1.96656i
$185$	731.167	−	2250.30i	0.290576	−	0.894300i
$186$	−1045.94			−0.412323
$187$	969.256	−	4719.61i	0.379032	−	1.84563i
$188$	−8477.59			−3.28879
$189$	102.961	−	316.880i	0.0396258	−	0.121956i
$190$	1381.36	−	1003.62i	0.527445	−	0.383211i
$191$	−3342.99	−	2428.82i	−1.26644	−	0.920124i	−0.267386	−	0.963589i	$-0.586160\pi$
$191$	−3342.99	−	2428.82i	−1.26644	−	0.920124i	−0.999055	+	0.0434658i	$0.986160\pi$
$192$	−90.2653	−	277.808i	−0.0339289	−	0.104422i
$193$	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
$195$	1106.49	−	803.914i	0.406347	−	0.295228i
$196$	−1076.23	+	3312.30i	−0.392213	+	1.20711i
$197$	3059.84			1.10662			0.553310	−	0.832975i	$-0.313364\pi$
$197$	3059.84			1.10662			0.553310	+	0.832975i	$0.313364\pi$
$198$	694.961	+	1532.41i	0.249438	+	0.550019i
$199$	−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
$201$	454.290	−	330.061i	0.159419	−	0.115824i
$202$	5132.84	+	3729.22i	1.78785	+	1.29895i
$203$	181.960	+	560.015i	0.0629118	+	0.193623i
$204$	−2235.75	−	6880.93i	−0.767323	−	2.36158i
$205$	−3457.96	−	2512.35i	−1.17812	−	0.855952i
$206$	−3780.89	+	2746.98i	−1.27877	+	0.929082i
$207$	−441.651	+	1359.26i	−0.148294	+	0.456402i
$208$	3765.98			1.25540
$209$	−808.754	+	90.6399i	−0.267668	+	0.0299985i
$210$	2833.73			0.931170
$211$	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
$213$	−1110.90	−	807.113i	−0.357358	−	0.259636i
$214$	−2507.35	−	7716.84i	−0.800931	−	2.46501i
$215$	477.950	+	1470.98i	0.151609	+	0.466605i
$216$	1148.64	+	834.533i	0.361828	+	0.262883i
$217$	679.220	−	493.482i	0.212481	−	0.154377i
$218$	470.162	−	1447.01i	0.146071	−	0.449559i
$219$	810.996			0.250237
$220$	−7349.14	+	6709.43i	−2.25218	+	2.05613i
$221$	4030.91			1.22692
$222$	−752.562	+	2316.15i	−0.227516	+	0.700224i
$223$	−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
$225$	272.843	+	839.725i	0.0808425	+	0.248807i
$226$	−173.251	−	533.211i	−0.0509932	−	0.156941i
$227$	859.697	+	624.607i	0.251366	+	0.182628i	0.706332	−	0.707881i	$-0.250349\pi$
$227$	859.697	+	624.607i	0.251366	+	0.182628i	−0.454966	+	0.890509i	$0.650349\pi$
$228$	−988.664	+	718.306i	−0.287175	+	0.208645i
$229$	−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
$231$	−1174.30	−	667.240i	−0.334473	−	0.190048i
$232$	−2509.17			−0.710065
$233$	1592.86	−	4902.32i	0.447862	−	1.37838i	−0.431453	−	0.902135i	$-0.641999\pi$
$233$	1592.86	−	4902.32i	0.447862	−	1.37838i	0.879315	−	0.476241i	$-0.158001\pi$
$234$	−1138.87	+	827.437i	−0.318163	+	0.231159i
$235$	5609.86	+	4075.80i	1.55722	+	1.13139i
$236$	−1250.61	−	3848.98i	−0.344948	−	1.06164i
$237$	−457.636	−	1408.46i	−0.125429	−	0.386030i
$238$	6756.60	+	4908.96i	1.84019	+	1.33698i
$239$	100.555	−	73.0575i	0.0272149	−	0.0197728i	−0.574095	−	0.818789i	$-0.694646\pi$
$239$	100.555	−	73.0575i	0.0272149	−	0.0197728i	0.601310	+	0.799016i	$0.294646\pi$
$240$	−1708.52	+	5258.28i	−0.459519	+	1.41425i
$241$	−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
$243$	−243.000			−0.0641500
$244$	−1548.10	+	4764.57i	−0.406177	+	1.25008i
$245$	2304.64	−	1674.42i	0.600971	−	0.436631i
$246$	3559.14	+	2585.86i	0.922448	+	0.670198i
$247$	−210.395	−	647.530i	−0.0541989	−	0.166807i
$248$	1105.53	+	3402.48i	0.283070	+	0.871200i
$249$	−657.812	−	477.928i	−0.167418	−	0.121636i
$250$	1665.53	−	1210.08i	0.421349	−	0.306128i
$251$	454.595	−	1399.10i	0.114318	−	0.351834i	−0.877486	−	0.479602i	$-0.840781\pi$
$251$	454.595	−	1399.10i	0.114318	−	0.351834i	0.991804	+	0.127767i	$0.0407811\pi$
$252$	−2028.15			−0.506989
$253$	5037.17	+	2862.13i	1.25172	+	0.711229i
$254$	7109.70			1.75631
$255$	−1828.71	+	5628.20i	−0.449092	+	1.38216i
$256$	5580.21	−	4054.26i	1.36236	−	0.989809i
$257$	−1183.60	−	859.935i	−0.287280	−	0.208721i	0.434807	−	0.900524i	$-0.356817\pi$
$257$	−1183.60	−	859.935i	−0.287280	−	0.208721i	−0.722086	+	0.691803i	$0.756817\pi$
$258$	−491.936	−	1514.02i	−0.118708	−	0.365345i
$259$	−604.070	−	1859.14i	−0.144923	−	0.446028i
$260$	−6735.34	−	4893.51i	−1.60657	−	1.16724i
$261$	347.431	−	252.424i	0.0823964	−	0.0598645i
$262$	2399.49	−	7384.87i	0.565805	−	1.74137i
$263$	−734.717			−0.172261			−0.0861304	−	0.996284i	$-0.527450\pi$
$263$	−734.717			−0.172261			−0.0861304	+	0.996284i	$0.527450\pi$
$264$	4250.43	−	3880.45i	0.990893	−	0.904640i
$265$	−90.3423			−0.0209422
$266$	435.916	−	1341.61i	0.100480	−	0.309246i
$267$	−188.070	+	136.641i	−0.0431075	+	0.0313194i
$268$	−2765.31	−	2009.11i	−0.630292	−	0.457934i
$269$	1059.09	+	3259.54i	0.240051	+	0.738802i	0.996411	+	0.0846463i	$0.0269760\pi$
$269$	1059.09	+	3259.54i	0.240051	+	0.738802i	−0.756360	+	0.654156i	$0.773024\pi$
$270$	−638.643	−	1965.54i	−0.143950	−	0.443034i
$271$	−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
$273$	349.176	−	1074.65i	0.0774105	−	0.238245i
$274$	−15220.5			−3.35584
$275$	3556.86	−	398.630i	0.779952	−	0.0874120i
$276$	8699.76			1.89733
$277$	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
$279$	−495.368	−	359.906i	−0.106297	−	0.0772294i
$280$	−2995.17	−	9218.20i	−0.639271	−	1.96747i
$281$	1551.48	+	4774.96i	0.329372	+	1.01370i	0.969428	+	0.245374i	$0.0789108\pi$
$281$	1551.48	+	4774.96i	0.329372	+	1.01370i	−0.640057	+	0.768328i	$0.721089\pi$
$282$	−5774.01	−	4195.06i	−1.21928	−	0.885859i
$283$	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
$285$	999.569			0.207752
$286$	2356.86	+	5196.95i	0.487287	+	1.07448i
$287$	−3531.28			−0.726289
$288$	588.539	−	1811.34i	0.120417	−	0.370605i
$289$	−10135.5	+	7363.87i	−2.06300	+	1.49885i
$290$	2954.87	+	2146.84i	0.598332	+	0.434713i
$291$	1176.79	+	3621.77i	0.237060	+	0.729595i
$292$	−1525.50	−	4695.00i	−0.305729	−	0.940939i
$293$	−3892.69	−	2828.20i	−0.776154	−	0.563909i	0.127668	−	0.991817i	$-0.459251\pi$
$293$	−3892.69	−	2828.20i	−0.776154	−	0.563909i	−0.903822	+	0.427908i	$0.859251\pi$
$294$	−2372.07	+	1723.41i	−0.470552	+	0.341876i
$295$	−1022.92	+	3148.24i	−0.201888	+	0.621347i
$296$	8329.93			1.63570
$297$	−198.159	+	964.900i	−0.0387150	+	0.188516i
$298$	−680.934			−0.132367
$299$	−1497.79	+	4609.74i	−0.289698	+	0.891598i
$300$	4348.10	−	3159.08i	0.836792	−	0.607965i
$301$	1033.78	+	751.086i	0.197961	+	0.143827i
$302$	337.274	+	1038.02i	0.0642648	+	0.197787i
$303$	1147.74	+	3532.39i	0.217611	+	0.669739i
$304$	2226.68	+	1617.78i	0.420095	+	0.305217i
$305$	3315.10	−	2408.56i	0.622368	−	0.452177i
$306$	1882.22	−	5792.88i	0.351632	−	1.08221i
$307$	−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
$309$	−2735.89			−0.503688
$310$	1609.25	−	4952.75i	0.294836	−	0.907411i
$311$	−4151.19	+	3016.02i	−0.756889	+	0.549912i	−0.897954	−	0.440088i	$-0.854947\pi$
$311$	−4151.19	+	3016.02i	−0.756889	+	0.549912i	0.141066	+	0.990000i	$0.454947\pi$
$312$	3895.43	+	2830.20i	0.706844	+	0.513553i
$313$	−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
$315$	1342.08	+	975.079i	0.240056	+	0.174411i
$316$	−7293.00	+	5298.67i	−1.29830	+	0.943271i
$317$	2040.57	−	6280.22i	0.361545	−	1.11272i	−0.590572	−	0.806985i	$-0.701098\pi$
$317$	2040.57	−	6280.22i	0.361545	−	1.11272i	0.952116	−	0.305736i	$-0.0989023\pi$
$318$	92.9858			0.0163974
$319$	−719.000	−	1585.42i	−0.126195	−	0.278265i
$320$	1454.36			0.254066
$321$	1467.84	−	4517.55i	0.255224	−	0.785498i
$322$	−8124.46	+	5902.76i	−1.40608	+	1.02158i
$323$	2383.32	+	1731.59i	0.410563	+	0.298291i
$324$	457.088	+	1406.77i	0.0783758	+	0.241216i
$325$	925.308	+	2847.81i	0.157929	+	0.486055i
$326$	2625.44	+	1907.50i	0.446043	+	0.324069i
$327$	720.586	−	523.536i	0.121861	−	0.0885371i
$328$	4649.98	−	14311.2i	0.782781	−	2.40915i
$329$	5728.82			0.960000
$330$	−8325.53	+	933.072i	−1.38880	+	0.155648i
$331$	−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
$333$	−1153.40	+	837.995i	−0.189808	+	0.137903i
$334$	6357.00	+	4618.63i	1.04144	+	0.756648i
$335$	863.954	+	2658.98i	0.140904	+	0.433658i
$336$	1411.53	+	4344.25i	0.229183	+	0.705352i
$337$	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
$339$	101.423	−	312.149i	0.0162494	−	0.0500106i
$340$	36022.5			5.74587
$341$	−1833.07	+	1673.51i	−0.291103	+	0.265764i
$342$	−1028.82			−0.162667
$343$	2035.25	−	6263.87i	0.320389	−	0.986056i
$344$	−4405.20	+	3200.56i	−0.690443	+	0.501636i
$345$	−5756.88	−	4182.61i	−0.898376	−	0.652708i
$346$	5268.07	+	16213.5i	0.818535	+	2.51919i
$347$	−240.519	−	740.240i	−0.0372095	−	0.114519i	0.930726	−	0.365716i	$-0.119176\pi$
$347$	−240.519	−	740.240i	−0.0372095	−	0.114519i	−0.967936	+	0.251197i	$0.919176\pi$
$348$	−2114.85	−	1536.53i	−0.325770	−	0.236686i
$349$	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
$351$	−824.099			−0.125320
$352$	−6712.49	−	3814.05i	−1.01641	−	0.577528i
$353$	−4504.51			−0.679181			−0.339591	−	0.940573i	$-0.610289\pi$
$353$	−4504.51			−0.679181			−0.339591	+	0.940573i	$0.610289\pi$
$354$	1052.86	−	3240.36i	0.158075	−	0.486506i
$355$	5531.03	−	4018.53i	0.826920	−	0.600793i
$356$	1144.80	+	831.747i	0.170434	+	0.123827i
$357$	1510.83	+	4649.86i	0.223982	+	0.689347i
$358$	6748.28	+	20769.1i	0.996250	+	3.06614i
$359$	−6948.18	−	5048.15i	−1.02148	−	0.742147i	−0.0548930	−	0.998492i	$-0.517482\pi$
$359$	−6948.18	−	5048.15i	−1.02148	−	0.742147i	−0.966585	+	0.256345i	$0.917482\pi$
$360$	−5718.94	+	4155.05i	−0.837262	+	0.608307i
$361$	−1965.78	+	6050.06i	−0.286599	+	0.882061i
$362$	3802.08			0.552025
$363$	3669.81	+	1573.69i	0.530621	+	0.227541i
$364$	−6878.16			−0.990422
$365$	−1247.77	+	3840.23i	−0.178935	+	0.550704i
$366$	−3412.11	+	2479.04i	−0.487305	+	0.354048i
$367$	−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
$369$	795.852	+	2449.38i	0.112278	+	0.345555i
$370$	−9809.58	−	7127.08i	−1.37831	−	1.00140i
$371$	−60.3836	+	43.8713i	−0.00845003	+	0.00613931i
$372$	−1151.76	+	3544.77i	−0.160527	+	0.494052i
$373$	−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
$375$	1205.19			0.165963
$376$	−7543.69	+	23217.1i	−1.03467	+	3.18439i
$377$	1178.26	−	856.058i	0.160965	−	0.116948i
$378$	−1381.35	−	1003.61i	−0.187960	−	0.136561i
$379$	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
$381$	3367.22	+	2446.43i	0.452777	+	0.328962i
$382$	−17131.4	+	12446.7i	−2.29455	+	1.66709i
$383$	3496.23	−	10760.3i	0.466446	−	1.43557i	−0.390708	−	0.920515i	$-0.627770\pi$
$383$	3496.23	−	10760.3i	0.466446	−	1.43557i	0.857154	−	0.515060i	$-0.172230\pi$
$384$	3581.90			0.476010
$385$	4966.25	−	4533.96i	0.657412	−	0.600187i
$386$	15792.8			2.08247
$387$	287.986	−	886.330i	0.0378273	−	0.116420i
$388$	18753.5	−	13625.2i	2.45378	−	1.78278i
$389$	2391.30	+	1737.38i	0.311681	+	0.226449i	0.732617	−	0.680641i	$-0.238299\pi$
$389$	2391.30	+	1737.38i	0.311681	+	0.226449i	−0.420937	+	0.907090i	$0.638299\pi$
$390$	−2165.87	−	6665.85i	−0.281213	−	0.865483i
$391$	−6480.73	−	19945.6i	−0.838222	−	2.57978i
$392$	8113.53	+	5894.83i	1.04540	+	0.759525i
$393$	3677.54	−	2671.89i	0.472029	−	0.342949i
$394$	4845.50	−	14912.9i	0.619576	−	1.90686i
$395$	7373.45			0.939236
$396$	5958.72	−	667.815i	0.756154	−	0.0847449i
$397$	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
$399$	668.100	−	485.403i	0.0838266	−	0.0609036i
$400$	−9792.84	−	7114.91i	−1.22410	−	0.889364i
$401$	2346.26	+	7221.04i	0.292186	+	0.899255i	0.984152	+	0.177326i	$0.0567446\pi$
$401$	2346.26	+	7221.04i	0.292186	+	0.899255i	−0.691967	+	0.721930i	$0.743255\pi$
$402$	−889.234	−	2736.78i	−0.110326	−	0.339548i
$403$	−1679.97	−	1220.57i	−0.207656	−	0.150871i
$404$	18290.7	−	13289.0i	2.25247	−	1.63652i
$405$	373.871	−	1150.66i	0.0458711	−	0.141177i
$406$	3017.53			0.368861
$407$	2386.93	+	5263.27i	0.290702	+	0.641008i
$408$	−20833.9			−2.52802
$409$	−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
$411$	−7208.56	−	5237.32i	−0.865138	−	0.628560i
$412$	5146.27	+	15838.6i	0.615384	+	1.89396i
$413$	845.112	+	2600.99i	0.100691	+	0.309894i
$414$	5925.33	+	4305.00i	0.703415	+	0.511061i
$415$	3275.18	−	2379.55i	0.387403	−	0.281464i
$416$	1995.95	−	6142.89i	0.235239	−	0.723990i
$417$	6456.24			0.758186
$418$	−838.970	+	4085.21i	−0.0981707	+	0.478024i
$419$	11095.7			1.29370			0.646851	−	0.762616i	$-0.276085\pi$
$419$	11095.7			1.29370			0.646851	+	0.762616i	$0.276085\pi$
$420$	3120.43	−	9603.69i	0.362527	−	1.11574i
$421$	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
$423$	−1291.12	−	3973.65i	−0.148407	−	0.456750i
$424$	−98.2835	−	302.485i	−0.0112572	−	0.0346462i
$425$	−10481.8	−	7615.44i	−1.19633	−	0.869184i
$426$	−5692.87	+	4136.12i	−0.647466	+	0.470412i
$427$	1046.15	−	3219.71i	0.118563	−	0.364900i
$428$	−28913.9			−3.26544
$429$	−672.028	+	3272.32i	−0.0756313	+	0.368273i
$430$	7926.09			0.888906
$431$	−4461.49	+	13731.1i	−0.498613	+	1.53457i	0.312635	+	0.949873i	$0.398788\pi$
$431$	−4461.49	+	13731.1i	−0.498613	+	1.53457i	−0.811249	+	0.584701i	$0.801212\pi$
$432$	2695.16	−	1958.15i	0.300164	−	0.218082i
$433$	−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
$435$	660.734	+	2033.53i	0.0728271	+	0.224139i
$436$	−4386.28	−	3186.82i	−0.481800	−	0.350048i
$437$	−2865.82	+	2082.14i	−0.313709	+	0.227923i
$438$	1284.28	−	3952.60i	0.140103	−	0.431193i
$439$	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
$441$	−1716.46			−0.185343
$442$	6383.28	−	19645.7i	0.686927	−	2.11414i
$443$	−3881.15	+	2819.82i	−0.416251	+	0.302424i	−0.776127	−	0.630576i	$-0.782819\pi$
$443$	−3881.15	+	2819.82i	−0.416251	+	0.302424i	0.359877	+	0.933000i	$0.382819\pi$
$444$	7020.88	+	5100.96i	0.750441	+	0.545228i
$445$	−357.665	−	1100.78i	−0.0381010	−	0.117263i
$446$	7783.34	+	23954.7i	0.826350	+	2.54324i
$447$	−322.497	−	234.308i	−0.0341244	−	0.0247928i
$448$	972.075	−	706.254i	0.102514	−	0.0744807i
$449$	−2835.91	+	8728.03i	−0.298073	+	0.917375i	0.684099	+	0.729390i	$0.260196\pi$
$449$	−2835.91	+	8728.03i	−0.298073	+	0.917375i	−0.982172	+	0.187985i	$0.939804\pi$
$450$	4524.69			0.473991
$451$	10375.0	−	1162.76i	1.08323	−	0.121402i
$452$	−1997.87			−0.207902
$453$	−197.445	+	607.674i	−0.0204785	+	0.0630265i
$454$	4405.59	−	3200.85i	0.455428	−	0.330888i
$455$	4551.47	+	3306.84i	0.468959	+	0.340719i
$456$	1087.43	+	3346.77i	0.111675	+	0.343700i
$457$	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
$459$	2884.76	−	2095.90i	0.293353	−	0.213133i
$460$	−13385.1	+	41195.2i	−1.35671	+	4.17551i
$461$	−16827.2			−1.70004			−0.850022	−	0.526747i	$-0.823411\pi$
$461$	−16827.2			−1.70004			−0.850022	+	0.526747i	$0.823411\pi$
$462$	−5111.57	+	4666.63i	−0.514744	+	0.469938i
$463$	−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
$465$	2466.39	−	1791.93i	0.245970	−	0.178707i
$466$	−21370.3	−	15526.5i	−2.12438	−	1.54345i
$467$	−5188.30	−	15968.0i	−0.514103	−	1.58225i	−0.784908	−	0.619612i	$-0.787290\pi$
$467$	−5188.30	−	15968.0i	−0.514103	−	1.58225i	0.270805	−	0.962634i	$-0.412710\pi$
$468$	1550.15	+	4770.86i	0.153110	+	0.471224i
$469$	1868.69	+	1357.68i	0.183983	+	0.133671i
$470$	28748.2	−	20886.8i	2.82139	−	2.04986i
$471$	2711.71	−	8345.78i	0.265284	−	0.816461i
$472$	−11653.8			−1.13646
$473$	−3284.58	−	1866.30i	−0.319292	−	0.181422i
$474$	−7589.20			−0.735408
$475$	−676.252	+	2081.29i	−0.0653233	+	0.201044i
$476$	24077.0	−	17493.0i	2.31842	−	1.68443i
$477$	44.0390	+	31.9962i	0.00422727	+	0.00307129i
$478$	−196.828	−	605.774i	−0.0188341	−	0.0579654i
$479$	−1438.96	−	4428.65i	−0.137260	−	0.422443i	0.858675	−	0.512521i	$-0.171288\pi$
$479$	−1438.96	−	4428.65i	−0.137260	−	0.422443i	−0.995935	+	0.0900778i	$0.971288\pi$
$480$	7671.56	+	5573.71i	0.729494	+	0.530008i
$481$	−3911.59	+	2841.94i	−0.370797	+	0.269400i
$482$	−705.547	+	2171.45i	−0.0666739	+	0.205201i
$483$	−5878.95			−0.553833
$484$	2207.41	−	24205.4i	0.207308	−	2.27323i
$485$	−18960.4			−1.77515
$486$	−384.810	+	1184.32i	−0.0359164	+	0.110539i
$487$	−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
$489$	587.071	+	1806.82i	0.0542909	+	0.167090i
$490$	−4511.14	−	13883.8i	−0.415903	−	1.28002i
$491$	12098.6	+	8790.18i	1.11203	+	0.807934i	0.982981	−	0.183705i	$-0.0588092\pi$
$491$	12098.6	+	8790.18i	1.11203	+	0.807934i	0.129044	+	0.991639i	$0.458809\pi$
$492$	12682.9	−	9214.67i	1.16217	−	0.844368i
$493$	−1947.33	+	5993.26i	−0.177897	+	0.547511i
$494$	−3489.09			−0.317776
$495$	−4264.12	−	2422.88i	−0.387188	−	0.220001i
$496$	8394.41			0.759920
$497$	1745.43	−	5371.87i	0.157531	−	0.484831i
$498$	−3371.01	+	2449.18i	−0.303330	+	0.220382i
$499$	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
$501$	1421.48	+	4374.86i	0.126760	+	0.390128i
$502$	−6098.99	−	4431.18i	−0.542254	−	0.393971i
$503$	−9572.63	+	6954.92i	−0.848554	+	0.616510i	−0.924747	−	0.380583i	$-0.875723\pi$
$503$	−9572.63	+	6954.92i	−0.848554	+	0.616510i	0.0761930	+	0.997093i	$0.475723\pi$
$504$	−1804.72	+	5554.37i	−0.159501	+	0.490895i
$505$	−18492.5			−1.62952
$506$	21926.1	−	20017.6i	1.92636	−	1.75868i
$507$	3796.19			0.332534
$508$	7829.02	−	24095.3i	0.683773	−	2.10444i
$509$	10979.7	−	7977.19i	0.956119	−	0.694661i	0.00387285	−	0.999993i	$-0.498767\pi$
$509$	10979.7	−	7977.19i	0.956119	−	0.694661i	0.952246	+	0.305331i	$0.0987672\pi$
$510$	24534.6	+	17825.4i	2.13022	+	1.54769i
$511$	1030.87	+	3172.69i	0.0892427	+	0.274661i
$512$	−7971.14	−	24532.6i	−0.688043	−	2.11758i
$513$	−487.258	−	354.014i	−0.0419356	−	0.0304680i
$514$	−6065.45	+	4406.81i	−0.520497	+	0.378163i
$515$	4209.34	−	12955.0i	0.360167	−	1.10848i
$516$	−5672.83			−0.483977
$517$	−16831.3	+	1886.35i	−1.43180	+	0.160467i
$518$	−10017.6			−0.849706
$519$	−3084.00	+	9491.58i	−0.260834	+	0.802763i
$520$	−19394.9	+	14091.3i	−1.63562	+	1.18835i
$521$	1718.71	+	1248.72i	0.144526	+	0.105004i	0.657699	−	0.753281i	$-0.271530\pi$
$521$	1718.71	+	1248.72i	0.144526	+	0.105004i	−0.513173	+	0.858285i	$0.671530\pi$
$522$	−680.068	−	2093.03i	−0.0570225	−	0.175497i
$523$	−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
$525$	−2938.27	+	2134.78i	−0.244260	+	0.177466i
$526$	−1163.48	+	3580.84i	−0.0964455	+	0.296829i
$527$	8984.95			0.742677
$528$	−5577.55	−	12298.7i	−0.459719	−	1.01370i
$529$	13050.8			1.07264
$530$	−143.064	+	440.307i	−0.0117251	+	0.0360863i
$531$	1613.64	−	1172.38i	0.131876	−	0.0958135i
$532$	−4066.79	−	2954.70i	−0.331424	−	0.240794i
$533$	2699.02	+	8306.72i	0.219339	+	0.675055i
$534$	368.131	+	1132.99i	0.0298325	+	0.0918151i
$535$	19133.2	+	13901.1i	1.54617	+	1.12336i
$536$	−7962.93	+	5785.41i	−0.641691	+	0.466215i
$537$	−3950.53	+	12158.5i	−0.317464	+	0.977054i
$538$	17563.4			1.40746
$539$	−1399.72	+	6815.69i	−0.111856	+	0.544661i
$540$	−7364.61			−0.586893
$541$	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
$543$	1800.70	+	1308.29i	0.142312	+	0.103396i
$544$	8636.16	+	26579.4i	0.680648	+	2.09482i
$545$	1370.39	+	4217.62i	0.107708	+	0.331492i
$546$	−4684.65	−	3403.60i	−0.367188	−	0.266778i
$547$	−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
$549$	−2469.04			−0.191942
$550$	3689.75	−	17966.6i	0.286057	−	1.39290i
$551$	1064.40			0.0822961
$552$	7741.38	−	23825.5i	0.596912	−	1.83710i
$553$	4928.32	−	3580.63i	0.378975	−	0.275342i
$554$	−21376.4	−	15530.9i	−1.63935	−	1.19105i
$555$	−2193.50	−	6750.91i	−0.167764	−	0.516324i
$556$	−12144.3	−	37376.4i	−0.926320	−	2.85092i
$557$	6895.70	+	5010.02i	0.524560	+	0.381115i	0.818319	−	0.574764i	$-0.194906\pi$
$557$	6895.70	+	5010.02i	0.524560	+	0.381115i	−0.293759	+	0.955880i	$0.594906\pi$
$558$	−2538.55	+	1844.37i	−0.192591	+	0.139925i
$559$	976.663	−	3005.86i	0.0738970	−	0.227432i
$560$	−22742.7			−1.71616
$561$	−5969.92	−	13163.9i	−0.449288	−	0.990694i
$562$	25728.9			1.93115
$563$	7620.38	−	23453.1i	0.570445	−	1.75565i	−0.0807448	−	0.996735i	$-0.525730\pi$
$563$	7620.38	−	23453.1i	0.570445	−	1.75565i	0.651190	−	0.758915i	$-0.274270\pi$
$564$	−20575.5	+	14949.0i	−1.53615	+	1.11608i
$565$	1322.04	+	960.522i	0.0984404	+	0.0715212i
$566$	−2974.00	−	9153.05i	−0.220860	−	0.679737i
$567$	−308.882	−	950.640i	−0.0228780	−	0.0704111i
$568$	19472.1	+	14147.3i	1.43844	+	1.04509i
$569$	−5078.13	+	3689.48i	−0.374141	+	0.271829i	−0.758926	−	0.651177i	$-0.774276\pi$
$569$	−5078.13	+	3689.48i	−0.374141	+	0.271829i	0.384785	+	0.923006i	$0.374276\pi$
$570$	1582.90	−	4871.67i	0.116316	−	0.357985i
$571$	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
$573$	−12396.5			−0.903789
$574$	−5592.07	+	17210.6i	−0.406635	+	1.25149i
$575$	12603.8	−	9157.16i	0.914109	−	0.664139i
$576$	−708.953	−	515.085i	−0.0512842	−	0.0372602i
$577$	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
$579$	7479.63	+	5434.27i	0.536861	+	0.390053i
$580$	10529.6	−	7650.22i	0.753825	−	0.547686i
$581$	1033.55	−	3180.93i	0.0738016	−	0.227138i
$582$	19515.2			1.38992
$583$	162.962	−	148.777i	0.0115767	−	0.0105690i
$584$	−14215.4			−1.00725
$585$	1267.93	−	3902.28i	0.0896109	−	0.275794i
$586$	−19948.4	+	14493.3i	−1.40625	+	1.02170i
$587$	−3121.98	−	2268.25i	−0.219519	−	0.159490i	0.472591	−	0.881282i	$-0.343319\pi$
$587$	−3121.98	−	2268.25i	−0.219519	−	0.159490i	−0.692110	+	0.721792i	$0.743319\pi$
$588$	3228.69	+	9936.90i	0.226444	+	0.696923i
$589$	−468.973	−	1443.35i	−0.0328076	−	0.100972i
$590$	13723.9	+	9970.98i	0.957633	+	0.695761i
$591$	7426.38	−	5395.58i	0.516887	−	0.375540i
$592$	6039.84	−	18588.7i	0.419317	−	1.29053i
$593$	26982.6			1.86854			0.934270	−	0.356567i	$-0.116053\pi$
$593$	26982.6			1.86854			0.934270	+	0.356567i	$0.116053\pi$
$594$	4388.89	+	2493.78i	0.303162	+	0.172258i
$595$	−24342.6			−1.67722
$596$	−749.827	+	2307.73i	−0.0515337	+	0.158605i
$597$	−2358.92	+	1713.85i	−0.161715	+	0.117493i
$598$	20094.9	+	14599.8i	1.37415	+	0.998377i
$599$	−7080.31	−	21791.0i	−0.482961	−	1.48640i	−0.834912	−	0.550383i	$-0.814482\pi$
$599$	−7080.31	−	21791.0i	−0.482961	−	1.48640i	0.351951	−	0.936018i	$-0.385518\pi$
$600$	−4782.48	−	14719.0i	−0.325407	−	1.00150i
$601$	−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
$603$	520.570	−	1602.15i	0.0351563	−	0.108200i
$604$	3889.33			0.262011
$605$	−13098.0	+	14956.1i	−0.880182	+	1.00505i
$606$	19033.6			1.27589
$607$	−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
$609$	1429.13	+	1038.33i	0.0950926	+	0.0690888i
$610$	−6489.03	−	19971.2i	−0.430710	−	1.32559i
$611$	−4378.63	−	13476.0i	−0.289919	−	0.892279i
$612$	−17559.8	−	12758.0i	−1.15983	−	0.842663i
$613$	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
$615$	−12822.8			−0.840757
$616$	20583.5	+	11695.6i	1.34632	+	0.764981i
$617$	23885.0			1.55847			0.779235	−	0.626732i	$-0.215608\pi$
$617$	23885.0			1.55847			0.779235	+	0.626732i	$0.215608\pi$
$618$	−4332.51	+	13334.1i	−0.282005	+	0.867923i
$619$	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
$621$	1324.95	+	4077.78i	0.0856175	+	0.263504i
$622$	8125.60	+	25008.0i	0.523805	+	1.61211i
$623$	−773.611	−	562.061i	−0.0497497	−	0.0361453i
$624$	9140.23	−	6640.77i	0.586381	−	0.426031i
$625$	−5643.76	+	17369.7i	−0.361200	+	1.11166i
$626$	−48895.9			−3.12184
$627$	−1803.06	+	1646.11i	−0.114844	+	0.104847i
$628$	−53416.0			−3.39415
$629$	6464.73	−	19896.4i	0.409803	−	1.26124i
$630$	6877.60	−	4996.87i	0.434937	−	0.316000i
$631$	−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
$633$	−3084.45	−	9492.95i	−0.193674	−	0.596068i
$634$	−27376.9	−	19890.5i	−1.71495	−	1.24598i
$635$	−16765.0	+	12180.5i	−1.04772	+	0.761211i
$636$	102.394	−	315.135i	0.00638391	−	0.0196477i
$637$	−5821.13			−0.362074
$638$	−8865.55	+	993.594i	−0.550142	+	0.0616564i
$639$	−4119.43			−0.255027
$640$	−5510.97	+	16961.0i	−0.340375	+	1.04757i
$641$	−815.075	+	592.187i	−0.0502239	+	0.0364898i	−0.612614	−	0.790382i	$-0.709882\pi$
$641$	−815.075	+	592.187i	−0.0502239	+	0.0364898i	0.562390	+	0.826872i	$0.309882\pi$
$642$	−19693.0	−	14307.8i	−1.21063	−	0.879571i
$643$	−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
$645$	3753.87	+	2727.35i	0.229161	+	0.166495i
$646$	12213.5	−	8873.65i	0.743862	−	0.540448i
$647$	2481.51	−	7637.29i	0.150785	−	0.464070i	−0.846924	−	0.531714i	$-0.821548\pi$
$647$	2481.51	−	7637.29i	0.150785	−	0.464070i	0.997710	+	0.0676441i	$0.0215482\pi$
$648$	4259.38			0.258216
$649$	−3339.39	−	7363.46i	−0.201976	−	0.445364i
$650$	15344.8			0.925960
$651$	778.316	−	2395.41i	0.0468581	−	0.144214i
$652$	9355.70	−	6797.32i	0.561960	−	0.408288i
$653$	−236.274	−	171.663i	−0.0141594	−	0.0102874i	0.580683	−	0.814130i	$-0.302786\pi$
$653$	−236.274	−	171.663i	−0.0141594	−	0.0102874i	−0.594842	+	0.803842i	$0.702786\pi$
$654$	−1410.49	−	4341.03i	−0.0843339	−	0.259553i
$655$	6993.83	+	21524.8i	0.417208	+	1.28403i
$656$	−28564.6	−	20753.4i	−1.70009	−	1.23519i
$657$	1968.33	−	1430.07i	0.116882	−	0.0849201i
$658$	9072.05	−	27920.9i	0.537485	−	1.65421i
$659$	−9034.21			−0.534025			−0.267013	−	0.963693i	$-0.586037\pi$
$659$	−9034.21			−0.534025			−0.267013	+	0.963693i	$0.586037\pi$
$660$	−6005.62	+	29243.3i	−0.354195	+	1.72469i
$661$	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
$663$	9783.23	−	7107.94i	0.573076	−	0.416364i
$664$	11530.3	+	8377.27i	0.673891	+	0.489610i
$665$	1270.57	+	3910.41i	0.0740911	+	0.228029i
$666$	2257.69	+	6948.44i	0.131357	+	0.404274i
$667$	−6130.28	−	4453.91i	−0.355870	−	0.258555i
$668$	22653.0	−	16458.4i	1.31208	−	0.953285i
$669$	−4556.48	+	14023.4i	−0.263324	+	0.810427i
$670$	14327.4			0.826141
$671$	−2013.43	+	9804.01i	−0.115838	+	0.564053i
$672$	7834.23			0.449720
$673$	−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
$675$	2142.94	+	1556.94i	0.122195	+	0.0887800i
$676$	−7140.70	−	21976.8i	−0.406276	−	1.25039i
$677$	−9795.40	−	30147.2i	−0.556083	−	1.71145i	−0.693067	−	0.720873i	$-0.743741\pi$
$677$	−9795.40	−	30147.2i	−0.556083	−	1.71145i	0.136984	−	0.990573i	$-0.456259\pi$
$678$	−1360.73	−	988.627i	−0.0770774	−	0.0560000i
$679$	−12672.9	+	9207.40i	−0.716261	+	0.520394i
$680$	32054.2	−	98652.8i	1.80768	−	5.56347i
$681$	3187.93			0.179386
$682$	5253.46	+	11584.1i	0.294964	+	0.650406i
$683$	−7905.89			−0.442914			−0.221457	−	0.975170i	$-0.571081\pi$
$683$	−7905.89			−0.442914			−0.221457	+	0.975170i	$0.571081\pi$
$684$	−1132.91	+	3486.73i	−0.0633301	+	0.194910i
$685$	35890.6	−	26076.1i	2.00191	−	1.45447i
$686$	−27305.6	−	19838.7i	−1.51973	−	1.10415i
$687$	3998.26	+	12305.4i	0.222043	+	0.683377i
$688$	3948.13	+	12151.1i	0.218781	+	0.673337i
$689$	149.352	+	108.510i	0.00825813	+	0.00599988i
$690$	−29501.6	+	21434.1i	−1.62769	+	1.18259i
$691$	−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
$693$	−4026.67	+	451.283i	−0.220722	+	0.0247371i
$694$	−3988.64			−0.218165
$695$	−9933.34	+	30571.7i	−0.542148	+	1.66856i
$696$	−6089.88	+	4424.56i	−0.331662	+	0.240966i
$697$	−30574.1	−	22213.4i	−1.66151	−	1.20716i
$698$	−8576.77	−	26396.6i	−0.465094	−	1.43141i
$699$	−4778.58	−	14707.0i	−0.258573	−	0.795806i
$700$	17885.6	+	12994.6i	0.965730	+	0.701644i
$701$	−16748.4	+	12168.4i	−0.902393	+	0.655627i	−0.939079	−	0.343700i	$-0.888320\pi$
$701$	−16748.4	+	12168.4i	−0.902393	+	0.655627i	0.0366868	+	0.999327i	$0.488320\pi$
$702$	−1305.03	+	4016.47i	−0.0701640	+	0.215943i
$703$	−3533.61			−0.189577
$704$	−2623.42	+	2395.06i	−0.140446	+	0.128221i
$705$	20802.5			1.11130
$706$	−7133.27	+	21953.9i	−0.380261	+	1.17032i
$707$	−12360.2	+	8980.18i	−0.657498	+	0.477701i
$708$	−9822.41	−	7136.40i	−0.521396	−	0.378817i
$709$	−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
$711$	−3594.32	−	2611.43i	−0.189589	−	0.137744i
$712$	3296.55	−	2395.08i	0.173516	−	0.126067i
$713$	−3338.60	+	10275.2i	−0.175360	+	0.539702i
$714$	25054.9			1.31324
$715$	−14461.2	−	8216.86i	−0.756387	−	0.429781i
$716$	77818.7			4.06176
$717$	115.226	−	354.629i	0.00600166	−	0.0184712i
$718$	−35606.5	+	25869.6i	−1.85073	+	1.34463i
$719$	−1121.07	−	814.505i	−0.0581486	−	0.0422474i	0.558331	−	0.829618i	$-0.311442\pi$
$719$	−1121.07	−	814.505i	−0.0581486	−	0.0422474i	−0.616480	+	0.787371i	$0.711442\pi$
$720$	5125.56	+	15774.9i	0.265303	+	0.816520i
$721$	−3477.64	−	10703.1i	−0.179631	−	0.552848i
$722$	26373.6	+	19161.5i	1.35945	+	0.987698i
$723$	−1081.35	+	785.644i	−0.0556233	+	0.0404127i
$724$	4186.76	−	12885.5i	0.214916	−	0.661445i
$725$	−4681.20			−0.239801
$726$	13481.3	−	15393.7i	0.689169	−	0.786935i
$727$	−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
$729$	−589.773	+	428.495i	−0.0299636	+	0.0217698i
$730$	16740.5	+	12162.6i	0.848756	+	0.616657i
$731$	4225.88	+	13005.9i	0.213816	+	0.658059i
$732$	4644.31	+	14293.7i	0.234506	+	0.721736i
$733$	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
$735$	2640.88	−	8127.80i	0.132531	−	0.407889i
$736$	−33605.1			−1.68301
$737$	−5937.27	−	3373.57i	−0.296747	−	0.168612i
$738$	13198.0			0.658300
$739$	−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
$741$	−1652.47	−	1200.59i	−0.0819228	−	0.0595204i
$742$	118.196	+	363.769i	0.00584785	+	0.0179978i
$743$	−757.991	−	2332.86i	−0.0374266	−	0.115187i	0.930598	−	0.366044i	$-0.119288\pi$
$743$	−757.991	−	2332.86i	−0.0374266	−	0.115187i	−0.968024	+	0.250856i	$0.919288\pi$
$744$	8682.96	+	6308.54i	0.427867	+	0.310863i
$745$	1605.68	−	1166.59i	0.0789631	−	0.0573700i
$746$	−20293.2	+	62456.0i	−0.995961	+	3.06525i
$747$	−2439.30			−0.119477
$748$	−64978.6	+	59322.5i	−3.17627	+	2.89979i
$749$	19538.9			0.953185
$750$	1908.52	−	5873.83i	0.0929192	−	0.285976i
$751$	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
$753$	−1363.79	−	4197.30i	−0.0660015	−	0.203132i
$754$	−2306.35	−	7098.22i	−0.111396	−	0.342841i
$755$	−2573.68	−	1869.89i	−0.124061	−	0.0901353i
$756$	−4922.41	+	3576.34i	−0.236807	+	0.172051i
$757$	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
$759$	17272.4	−	1935.78i	0.826021	−	0.0925751i
$760$	−17520.8			−0.836243
$761$	−1870.80	+	5757.72i	−0.0891147	+	0.274267i	−0.985675	−	0.168654i	$-0.946058\pi$
$761$	−1870.80	+	5757.72i	−0.0891147	+	0.274267i	0.896561	+	0.442921i	$0.146058\pi$
$762$	17255.6	−	12536.9i	0.820347	−	0.596017i
$763$	2964.07	+	2153.53i	0.140638	+	0.102179i
$764$	23318.0	+	71765.5i	1.10421	+	3.39841i
$765$	5486.14	+	16884.6i	0.259283	+	0.797992i
$766$	−46906.5	−	34079.6i	−2.21254	−	1.60750i
$767$	5472.43	−	3975.96i	0.257625	−	0.187175i
$768$	6394.35	−	19679.8i	0.300438	−	0.924652i
$769$	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
$771$	−4389.03			−0.205015
$772$	17390.6	−	53522.9i	0.810755	−	2.49525i
$773$	−4033.24	+	2930.32i	−0.187666	+	0.136347i	−0.677651	−	0.735384i	$-0.737002\pi$
$773$	−4033.24	+	2930.32i	−0.187666	+	0.136347i	0.489986	+	0.871731i	$0.337002\pi$
$774$	−3863.71	−	2807.15i	−0.179429	−	0.130363i
$775$	2062.52	+	6347.79i	0.0955974	+	0.294219i
$776$	−20627.1	−	63483.6i	−0.954212	−	2.93676i
$777$	−4744.43	−	3447.03i	−0.219055	−	0.159152i
$778$	12254.4	−	8903.35i	0.564707	−	0.410284i
$779$	−1972.55	+	6070.88i	−0.0907239	+	0.279219i
$780$	−24976.0			−1.14652
$781$	−3359.27	+	16357.4i	−0.153911	+	0.749439i
$782$	−107473.			−4.91462
$783$	398.121	−	1225.29i	0.0181707	−	0.0559238i
$784$	19037.6	−	13831.6i	0.867236	−	0.630084i
$785$	35346.9	+	25681.0i	1.60711	+	1.16764i
$786$	−7198.47	−	22154.6i	−0.326668	−	1.00538i
$787$	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
$789$	−1783.20	+	1295.57i	−0.0804606	+	0.0584581i
$790$	11676.5	−	35936.4i	0.525860	−	1.61843i
$791$	1350.08			0.0606868
$792$	3473.40	−	16913.1i	0.155836	−	0.758812i
$793$	−8373.39			−0.374965
$794$	19623.6	−	60395.1i	0.877096	−	2.69942i
$795$	−219.265	+	159.306i	−0.00978181	+	0.00710690i
$796$	14359.0	+	10432.4i	0.639373	+	0.464531i
$797$	5369.64	+	16526.1i	0.238648	+	0.734483i	0.996617	+	0.0821918i	$0.0261920\pi$
$797$	5369.64	+	16526.1i	0.238648	+	0.734483i	−0.757969	+	0.652291i	$0.773808\pi$
$798$	−1307.75	−	4024.83i	−0.0580123	−	0.178543i
$799$	49600.5	+	36036.8i	2.19617	+	1.59561i
$800$	−16795.6	+	12202.8i	−0.742270	+	0.539291i
$801$	−215.509	+	663.268i	−0.00950641	+	0.0292577i
$802$	38909.1			1.71313
$803$	−4073.40	−	8981.98i	−0.179013	−	0.394729i
$804$	−10254.3			−0.449804
$805$	9045.13	−	27838.1i	0.396024	−	1.21884i
$806$	−8609.14	+	6254.90i	−0.376233	+	0.273349i
$807$	8318.20	+	6043.52i	0.362843	+	0.263621i
$808$	−20118.0	−	61916.9i	−0.875927	−	2.69583i
$809$	1030.68	+	3172.12i	0.0447922	+	0.137856i	0.970952	−	0.239276i	$-0.0769101\pi$
$809$	1030.68	+	3172.12i	0.0447922	+	0.137856i	−0.926159	+	0.377132i	$0.876910\pi$
$810$	−5015.97	−	3644.32i	−0.217584	−	0.158084i
$811$	−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
$813$	−5158.03			−0.222509
$814$	29431.8	−	3298.53i	1.26730	−	0.142031i
$815$	−9458.91			−0.406541
$816$	−15106.2	+	46492.0i	−0.648065	+	1.99454i
$817$	1868.71	−	1357.70i	0.0800219	−	0.0581393i
$818$	30164.4	+	21915.7i	1.28933	+	0.936755i
$819$	−1047.53	−	3223.96i	−0.0446930	−	0.137551i
$820$	24119.9	+	74233.5i	1.02720	+	3.16140i
$821$	−15080.4	−	10956.5i	−0.641058	−	0.465756i	0.219155	−	0.975690i	$-0.429670\pi$
$821$	−15080.4	−	10956.5i	−0.641058	−	0.465756i	−0.860214	+	0.509934i	$0.829670\pi$
$822$	−36940.8	+	26839.1i	−1.56747	+	1.13883i
$823$	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
$825$	7929.76	−	7239.51i	0.334641	−	0.305512i
$826$	14014.9			0.590364
$827$	−10812.3	+	33276.8i	−0.454632	+	1.39921i	0.416935	+	0.908936i	$0.363104\pi$
$827$	−10812.3	+	33276.8i	−0.454632	+	1.39921i	−0.871567	+	0.490277i	$0.836896\pi$
$828$	21114.8	−	15340.8i	0.886218	−	0.643875i
$829$	−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
$831$	−4779.94	−	14711.2i	−0.199536	−	0.614109i
$832$	−2404.31	−	1746.83i	−0.100186	−	0.0727892i
$833$	20376.8	−	14804.6i	0.847558	−	0.615787i
$834$	10224.0	−	31466.2i	0.424494	−	1.30646i
$835$	−22902.9			−0.949207
$836$	12921.2	+	7341.85i	0.534556	+	0.303736i
$837$	−1836.93			−0.0758584
$838$	17571.0	−	54077.9i	0.724319	−	2.22923i
$839$	20512.2	−	14903.0i	0.844054	−	0.613241i	−0.0794461	−	0.996839i	$-0.525315\pi$
$839$	20512.2	−	14903.0i	0.844054	−	0.613241i	0.923500	+	0.383598i	$0.125315\pi$
$840$	−23524.4	−	17091.5i	−0.966273	−	0.702038i
$841$	−6833.02	−	21029.9i	−0.280168	−	0.862269i
$842$	−8081.88	−	24873.5i	−0.330784	−	1.01805i
$843$	12185.5	+	8853.26i	0.497853	+	0.361711i
$844$	−49154.5	+	35712.8i	−2.00470	+	1.45650i
$845$	−5840.67	+	17975.7i	−0.237781	+	0.731816i
$846$	−21411.2			−0.870133
$847$	−1491.68	+	16357.0i	−0.0605133	+	0.663558i
$848$	−746.276			−0.0302208
$849$	1741.02	−	5358.32i	0.0703790	−	0.216604i
$850$	−53714.6	+	39025.9i	−2.16752	+	1.57480i
$851$	20351.3	+	14786.1i	0.819781	+	0.595605i
$852$	7748.72	+	23848.1i	0.311581	+	0.958947i
$853$	−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
$855$	2426.01	−	1762.60i	0.0970382	−	0.0705024i
$856$	−25728.7	+	79184.9i	−1.02733	+	3.16178i
$857$	−38619.7			−1.53935			−0.769676	−	0.638435i	$-0.779582\pi$
$857$	−38619.7			−1.53935			−0.769676	+	0.638435i	$0.779582\pi$
$858$	14884.3	+	8457.29i	0.592239	+	0.336512i
$859$	−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
$861$	−8570.60	+	6226.90i	−0.339239	+	0.246472i
$862$	59856.8	+	43488.5i	2.36512	+	1.71836i
$863$	−9135.64	−	28116.6i	−0.360349	−	1.10904i	−0.952843	−	0.303464i	$-0.901857\pi$
$863$	−9135.64	−	28116.6i	−0.360349	−	1.10904i	0.592494	−	0.805575i	$-0.298143\pi$
$864$	−1765.62	−	5434.01i	−0.0695226	−	0.213969i
$865$	−40199.7	−	29206.8i	−1.58015	−	1.14805i
$866$	−17565.4	+	12762.0i	−0.689255	+	0.500773i
$867$	−11614.3	+	35745.0i	−0.454949	+	1.40019i
$868$	−15331.5			−0.599522
$869$	−13300.5	+	12142.7i	−0.519203	+	0.474009i
$870$	10957.3			0.426996
$871$	1765.44	−	5433.46i	0.0686792	−	0.211373i
$872$	−12630.6	+	9176.70i	−0.490513	+	0.356379i
$873$	9242.60	+	6715.14i	0.358321	+	0.260336i
$874$	5609.60	+	17264.6i	0.217103	+	0.668173i
$875$	1531.94	+	4714.84i	0.0591876	+	0.182161i
$876$	−11981.4	−	8705.01i	−0.462117	−	0.335748i
$877$	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
$879$	−14434.9			−0.553898
$880$	66818.2	−	7488.56i	2.55959	−	0.286863i
$881$	34057.4			1.30241			0.651205	−	0.758902i	$-0.274264\pi$
$881$	34057.4			1.30241			0.651205	+	0.758902i	$0.274264\pi$
$882$	−2718.16	+	8365.62i	−0.103770	+	0.319371i
$883$	−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
$885$	3068.77	+	9444.71i	0.116560	+	0.358735i
$886$	7597.02	+	23381.2i	0.288067	+	0.886578i
$887$	4164.73	+	3025.86i	0.157653	+	0.114541i	0.663815	−	0.747897i	$-0.268936\pi$
$887$	4164.73	+	3025.86i	0.157653	+	0.114541i	−0.506162	+	0.862438i	$0.668936\pi$
$888$	20217.2	−	14688.6i	0.764013	−	0.555088i
$889$	−5290.54	+	16282.6i	−0.199594	+	0.614287i
$890$	−5931.34			−0.223392
$891$	1220.52	+	2691.29i	0.0458911	+	0.101191i
$892$	89754.8			3.36907
$893$	3200.08	−	9848.82i	0.119918	−	0.369069i
$894$	−1652.66	+	1200.73i	−0.0618269	+	0.0449199i
$895$	−51494.9	−	37413.2i	−1.92322	−	1.39730i
$896$	4553.01	+	14012.7i	0.169760	+	0.522469i
$897$	4493.38	+	13829.2i	0.167257	+	0.514764i
$898$	38047.5	+	27643.1i	1.41388	+	1.02724i
$899$	2626.36	−	1908.16i	0.0974350	−	0.0707907i
$900$	4982.48	−	15334.5i	0.184536	−	0.567944i
$901$	−798.776			−0.0295351
$902$	10762.6	−	52406.4i	0.397289	−	1.93453i
$903$	3833.47			0.141273
$904$	−1777.78	+	5471.44i	−0.0654072	+	0.201303i
$905$	−8965.51	+	6513.82i	−0.329308	+	0.239256i
$906$	2648.99	+	1924.60i	0.0971376	+	0.0705746i
$907$	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
$909$	9014.50	+	6549.42i	0.328924	+	0.238977i
$910$	23324.4	−	16946.2i	0.849666	−	0.617318i
$911$	7794.32	−	23988.5i	0.283466	−	0.872418i	−0.703388	−	0.710806i	$-0.748331\pi$
$911$	7794.32	−	23988.5i	0.283466	−	0.872418i	0.986854	−	0.161613i	$-0.0516695\pi$
$912$	8256.98			0.299798
$913$	−1989.18	+	9685.93i	−0.0721053	+	0.351104i
$914$	31667.2			1.14601
$915$	3798.77	−	11691.4i	0.137250	−	0.422411i
$916$	63717.3	−	46293.3i	2.29834	−	1.66984i
$917$	15127.3	+	10990.6i	0.544762	+	0.395793i
$918$	−5646.67	−	17378.7i	−0.203015	−	0.624816i
$919$	−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
$921$	−1453.57	+	1056.08i	−0.0520053	+	0.0377840i
$922$	−26647.2	+	82011.7i	−0.951822	+	2.92941i
$923$	−13970.4			−0.498205
$924$	10186.8	+	22462.2i	0.362685	+	0.799733i
$925$	15540.6			0.552403
$926$	−1296.47	+	3990.12i	−0.0460093	+	0.141602i
$927$	−6640.15	+	4824.35i	−0.235266	+	0.170930i
$928$	8169.16	+	5935.24i	0.288972	+	0.209950i
$929$	−10339.7	−	31822.2i	−0.365160	−	1.12385i	−0.949881	−	0.312612i	$-0.898796\pi$
$929$	−10339.7	−	31822.2i	−0.365160	−	1.12385i	0.584721	−	0.811235i	$-0.301204\pi$
$930$	−4827.74	−	14858.3i	−0.170223	−	0.523894i
$931$	−3441.81	−	2500.62i	−0.121161	−	0.0880285i
$932$	−76152.7	+	55328.1i	−2.67646	+	1.94456i
$933$	−4756.84	+	14640.1i	−0.166915	+	0.513713i
$934$	−86040.2			−3.01426
$935$	71518.8	−	8015.37i	2.50151	−	0.280354i
$936$	14445.1			0.504435
$937$	−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
$939$	−23157.6	−	16825.0i	−0.804813	−	0.584731i
$940$	−39129.9	−	120429.i	−1.35774	−	4.17870i
$941$	6687.39	+	20581.7i	0.231671	+	0.713011i	0.997546	+	0.0700208i	$0.0223066\pi$
$941$	6687.39	+	20581.7i	0.231671	+	0.713011i	−0.765874	+	0.642991i	$0.777693\pi$
$942$	−36381.1	−	26432.4i	−1.25835	−	0.914242i
$943$	36763.7	−	26710.4i	1.26956	−	0.922386i
$944$	−8449.91	+	26006.1i	−0.291336	+	0.896640i
$945$	4976.71			0.171315
$946$	−14297.3	+	13052.8i	−0.491381	+	0.448608i
$947$	−31725.1			−1.08862			−0.544311	−	0.838883i	$-0.683209\pi$
$947$	−31725.1			−1.08862			−0.544311	+	0.838883i	$0.683209\pi$
$948$	−8357.03	+	25720.3i	−0.286312	+	0.881178i
$949$	6675.30	−	4849.89i	0.228334	−	0.165895i
$950$	9072.81	+	6591.78i	0.309854	+	0.225122i
$951$	−6121.70	−	18840.7i	−0.208738	−	0.642430i
$952$	−26482.3	−	81504.2i	−0.901572	−	2.77475i
$953$	−42127.7	−	30607.6i	−1.43195	−	1.04037i	−0.989649	−	0.143508i	$-0.954162\pi$
$953$	−42127.7	−	30607.6i	−1.43195	−	1.04037i	−0.442303	−	0.896866i	$-0.645838\pi$
$954$	225.681	−	163.967i	0.00765901	−	0.00556460i
$955$	19072.8	−	58700.0i	0.646262	−	1.98899i
$956$	−2269.75			−0.0767877
$957$	−4540.71	−	2580.04i	−0.153375	−	0.0871482i
$958$	−23862.9			−0.804777
$959$	11326.0	−	34857.8i	0.381372	−	1.17374i
$960$	3529.80	−	2564.55i	0.118671	−	0.0862193i
$961$	20356.8	+	14790.0i	0.683319	+	0.496460i
$962$	7656.61	+	23564.6i	0.256610	+	0.789765i
$963$	−4403.52	−	13552.6i	−0.147354	−	0.453508i
$964$	6582.26	+	4782.29i	0.219917	+	0.159779i
$965$	−37240.3	+	27056.6i	−1.24229	+	0.902574i
$966$	−9309.80	+	28652.6i	−0.310081	+	0.954330i
$967$	−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
$969$	8837.85			0.292996
$970$	−30025.4	+	92408.6i	−0.993873	+	3.05883i
$971$	−20189.6	+	14668.6i	−0.667265	+	0.484796i	−0.869109	−	0.494621i	$-0.835307\pi$
$971$	−20189.6	+	14668.6i	−0.667265	+	0.484796i	0.201844	+	0.979418i	$0.435307\pi$
$972$	3590.01	+	2608.30i	0.118467	+	0.0860711i
$973$	8206.64	+	25257.5i	0.270394	+	0.832186i
$974$	27914.2	+	85911.0i	0.918304	+	2.82625i
$975$	7267.47	+	5280.12i	0.238713	+	0.173435i
$976$	27384.5	−	19896.0i	0.898112	−	0.652517i
$977$	17549.0	−	54010.4i	0.574661	−	1.76862i	−0.0626715	−	0.998034i	$-0.519962\pi$
$977$	17549.0	−	54010.4i	0.574661	−	1.76862i	0.637332	−	0.770589i	$-0.280038\pi$
$978$	9735.68			0.318316
$979$	2457.95	+	1396.61i	0.0802416	+	0.0455935i
$980$	−52020.8			−1.69566
$981$	825.718	−	2541.30i	0.0268738	−	0.0827089i
$982$	62000.5	−	45046.0i	2.01478	−	1.46382i
$983$	25471.5	+	18506.2i	0.826466	+	0.600463i	0.918557	−	0.395288i	$-0.129355\pi$
$983$	25471.5	+	18506.2i	0.826466	+	0.600463i	−0.0920914	+	0.995751i	$0.529355\pi$
$984$	−13949.9	−	42933.5i	−0.451939	−	1.39092i
$985$	14123.2	+	43466.9i	0.456857	+	1.40606i
$986$	26126.0	+	18981.6i	0.843835	+	0.613082i
$987$	13904.1	−	10101.9i	0.448403	−	0.325784i
$988$	−3842.09	+	11824.7i	−0.123718	+	0.380764i
$989$	−16443.7			−0.528696
$990$	−18561.2	+	16945.5i	−0.595871	+	0.544003i
$991$	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
$993$	−15896.7	+	11549.6i	−0.508022	+	0.369100i
$994$	−23417.2	−	17013.6i	−0.747232	−	0.542896i
$995$	−4486.12	−	13806.8i	−0.142934	−	0.439906i
$996$	4588.37	+	14121.6i	0.145972	+	0.449256i
$997$	−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
$999$	−1321.68	+	4067.71i	−0.0418580	+	0.128826i

Twists

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

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58358 - 4.87376i) q^{2} +(2.42705 - 1.76336i) q^{3} +(-14.7737 - 10.7337i) q^{4} +(4.61569 + 14.2056i) q^{5} +(-4.75075 - 14.6213i) q^{6} +(9.98349 + 7.25343i) q^{7} +(-42.5421 + 30.9086i) q^{8} +(2.78115 - 8.55951i) q^{9} +76.5442 q^{10} +(-31.7200 - 18.0234i) q^{11} -54.7839 q^{12} +(9.43188 - 29.0283i) q^{13} +(51.1612 - 37.1708i) q^{14} +(36.2521 + 26.3387i) q^{15} +(38.1281 + 117.346i) q^{16} +(40.8103 + 125.601i) q^{17} +(-37.3128 - 27.1094i) q^{18} +(18.0466 - 13.1116i) q^{19} +(84.2885 - 259.413i) q^{20} +37.0208 q^{21} +(-138.073 + 126.054i) q^{22} -158.801 q^{23} +(-48.7489 + 150.034i) q^{24} +(-79.3681 + 57.6643i) q^{25} +(-126.541 - 91.9375i) q^{26} +(-8.34346 - 25.6785i) q^{27} +(-69.6368 - 214.320i) q^{28} +(38.6035 + 28.0471i) q^{29} +(185.777 - 134.975i) q^{30} +(21.0238 - 64.7045i) q^{31} +211.617 q^{32} +(-108.768 + 12.1900i) q^{33} +676.778 q^{34} +(-56.9588 + 175.301i) q^{35} +(-132.963 + 96.6036i) q^{36} +(-128.156 - 93.1106i) q^{37} +(-35.3247 - 108.718i) q^{38} +(-28.2956 - 87.0850i) q^{39} +(-635.437 - 461.672i) q^{40} +(-231.508 + 168.200i) q^{41} +(58.6255 - 180.431i) q^{42} +103.549 q^{43} +(275.164 + 606.746i) q^{44} +134.430 q^{45} +(-251.475 + 773.960i) q^{46} +(375.576 - 272.872i) q^{47} +(299.462 + 217.572i) q^{48} +(-58.9350 - 181.383i) q^{49} +(155.356 + 478.138i) q^{50} +(320.529 + 232.878i) q^{51} +(-450.926 + 327.617i) q^{52} +(-1.86904 + 5.75232i) q^{53} -138.364 q^{54} +(109.624 - 533.793i) q^{55} -648.912 q^{56} +(20.6796 - 63.6451i) q^{57} +(197.827 - 143.729i) q^{58} +(179.294 + 130.264i) q^{59} +(-252.866 - 778.240i) q^{60} +(-84.7750 - 260.911i) q^{61} +(-282.061 - 204.930i) q^{62} +(89.8514 - 65.2808i) q^{63} +(30.0884 - 92.6027i) q^{64} +455.900 q^{65} +(-112.831 + 549.412i) q^{66} +187.178 q^{67} +(745.250 - 2293.64i) q^{68} +(-385.419 + 280.023i) q^{69} +(764.178 + 555.208i) q^{70} +(-141.442 - 435.312i) q^{71} +(146.247 + 450.101i) q^{72} +(218.703 + 158.897i) q^{73} +(-656.744 + 477.153i) q^{74} +(-90.9478 + 279.908i) q^{75} -407.352 q^{76} +(-185.945 - 410.015i) q^{77} -469.240 q^{78} +(152.545 - 469.486i) q^{79} +(-1490.99 + 1083.27i) q^{80} +(-65.5304 - 47.6106i) q^{81} +(453.157 + 1394.67i) q^{82} +(-83.7540 - 257.768i) q^{83} +(-546.935 - 397.371i) q^{84} +(-1595.88 + 1159.47i) q^{85} +(163.979 - 504.674i) q^{86} +143.150 q^{87} +(1906.51 - 213.670i) q^{88} -77.4891 q^{89} +(212.881 - 655.181i) q^{90} +(304.718 - 221.391i) q^{91} +(2346.08 + 1704.53i) q^{92} +(-63.0713 - 194.113i) q^{93} +(-735.158 - 2262.58i) q^{94} +(269.556 + 195.844i) q^{95} +(513.605 - 373.156i) q^{96} +(-392.262 + 1207.26i) q^{97} -977.348 q^{98} +(-242.489 + 221.382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 9 q^{3} - 16 q^{4} + 28 q^{5} + 12 q^{7} - 112 q^{8} - 27 q^{9} + 100 q^{10} - 54 q^{11} - 102 q^{12} - 18 q^{13} + 156 q^{14} + 111 q^{15} + 308 q^{16} - 80 q^{17} - 45 q^{18} - 280 q^{19} - 15 q^{20}+ \cdots - 171 q^{99}+O(q^{100}) \) 12 * q + 9 * q^3 - 16 * q^4 + 28 * q^5 + 12 * q^7 - 112 * q^8 - 27 * q^9 + 100 * q^10 - 54 * q^11 - 102 * q^12 - 18 * q^13 + 156 * q^14 + 111 * q^15 + 308 * q^16 - 80 * q^17 - 45 * q^18 - 280 * q^19 - 15 * q^20 - 6 * q^21 - 193 * q^22 - 392 * q^23 - 264 * q^24 + 77 * q^25 + 406 * q^26 + 81 * q^27 - 429 * q^28 + 13 * q^29 + 120 * q^30 + 413 * q^31 + 1314 * q^32 + 177 * q^33 + 1060 * q^34 - 1239 * q^35 - 144 * q^36 + 654 * q^37 + 912 * q^38 + 54 * q^39 - 1803 * q^40 - 1490 * q^41 + 342 * q^42 + 416 * q^43 + 695 * q^44 + 162 * q^45 - 2369 * q^46 - 150 * q^47 + 711 * q^48 - 301 * q^49 - 1878 * q^50 - 1661 * q^52 + 1359 * q^53 - 270 * q^54 + 3300 * q^55 - 858 * q^56 - 1110 * q^57 + 955 * q^58 + 1262 * q^59 + 45 * q^60 - 1044 * q^61 - 701 * q^62 + 108 * q^63 + 78 * q^64 + 4556 * q^65 + 369 * q^66 - 528 * q^67 + 703 * q^68 - 594 * q^69 + 3050 * q^70 + 558 * q^71 + 792 * q^72 - 699 * q^73 - 3224 * q^74 + 1284 * q^75 - 868 * q^76 + 390 * q^77 - 558 * q^78 - 1252 * q^79 - 1914 * q^80 - 243 * q^81 + 2987 * q^82 - 4464 * q^83 - 1443 * q^84 - 2170 * q^85 - 3209 * q^86 - 3474 * q^87 + 1302 * q^88 + 316 * q^89 - 90 * q^90 + 176 * q^91 + 4595 * q^92 - 1239 * q^93 + 1247 * q^94 + 1466 * q^95 + 1398 * q^96 + 1608 * q^97 + 2810 * q^98 - 171 * q^99

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