LMFDB - Embedded newform 207.4.i.a.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			82.2
Character	$\chi$	$=$	207.82
Dual form			207.4.i.a.154.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61249 - 1.86092i) q^{2} +(0.275643 - 1.91714i) q^{4} +(3.07518 - 6.73370i) q^{5} +(-11.6919 - 3.43306i) q^{7} +(-20.5838 + 13.2284i) q^{8} +O(q^{10})$	\(q+(-1.61249 - 1.86092i) q^{2} +(0.275643 - 1.91714i) q^{4} +(3.07518 - 6.73370i) q^{5} +(-11.6919 - 3.43306i) q^{7} +(-20.5838 + 13.2284i) q^{8} +(-17.4896 + 5.13540i) q^{10} +(-3.34406 + 3.85925i) q^{11} +(-23.2908 + 6.83879i) q^{13} +(12.4645 + 27.2935i) q^{14} +(42.9410 + 12.6086i) q^{16} +(-9.15745 - 63.6914i) q^{17} +(-7.05564 + 49.0731i) q^{19} +(-12.0618 - 7.75163i) q^{20} +12.5740 q^{22} +(-72.4803 - 83.1481i) q^{23} +(45.9715 + 53.0540i) q^{25} +(50.2827 + 32.3147i) q^{26} +(-9.80444 + 21.4687i) q^{28} +(24.5481 + 170.736i) q^{29} +(-195.491 + 125.634i) q^{31} +(35.5364 + 77.8139i) q^{32} +(-103.758 + 119.743i) q^{34} +(-59.0720 + 68.1728i) q^{35} +(-98.8932 - 216.546i) q^{37} +(102.698 - 66.0001i) q^{38} +(25.7772 + 179.285i) q^{40} +(-129.476 + 283.513i) q^{41} +(442.252 + 284.218i) q^{43} +(6.47693 + 7.47478i) q^{44} +(-37.8577 + 268.956i) q^{46} -407.467 q^{47} +(-163.635 - 105.162i) q^{49} +(24.6002 - 171.098i) q^{50} +(6.69096 + 46.5367i) q^{52} +(461.872 + 135.618i) q^{53} +(15.7035 + 34.3858i) q^{55} +(286.078 - 84.0001i) q^{56} +(278.142 - 320.993i) q^{58} +(-41.1233 + 12.0749i) q^{59} +(-286.232 + 183.950i) q^{61} +(549.024 + 161.208i) q^{62} +(236.234 - 517.281i) q^{64} +(-25.5730 + 177.864i) q^{65} +(-347.288 - 400.792i) q^{67} -124.629 q^{68} +222.117 q^{70} +(-488.573 - 563.843i) q^{71} +(43.0026 - 299.090i) q^{73} +(-243.509 + 533.211i) q^{74} +(92.1349 + 27.0533i) q^{76} +(52.3475 - 33.6417i) q^{77} +(-744.340 + 218.558i) q^{79} +(216.954 - 250.378i) q^{80} +(736.374 - 216.219i) q^{82} +(-121.922 - 266.971i) q^{83} +(-457.040 - 134.199i) q^{85} +(-184.222 - 1281.29i) q^{86} +(17.7817 - 123.674i) q^{88} +(-479.164 - 307.940i) q^{89} +295.792 q^{91} +(-179.385 + 116.035i) q^{92} +(657.038 + 758.262i) q^{94} +(308.746 + 198.419i) q^{95} +(776.529 - 1700.36i) q^{97} +(68.1628 + 474.083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8}+O(q^{10}) $ 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8	$ 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8} + 47 q^{10} + 53 q^{11} - 65 q^{13} - 117 q^{14} - 499 q^{16} + 117 q^{17} + 73 q^{19} - 529 q^{20} + 310 q^{22} - 542 q^{23} + 246 q^{25} - 324 q^{26} - 677 q^{28} + 497 q^{29} - 471 q^{31} + 915 q^{32} - 2751 q^{34} + 737 q^{35} - 1071 q^{37} + 1504 q^{38} + 1479 q^{40} - 569 q^{41} + 1615 q^{43} - 2518 q^{44} + 4041 q^{46} - 2904 q^{47} + 1226 q^{49} - 1322 q^{50} - 2156 q^{52} - 391 q^{53} - 3323 q^{55} + 7028 q^{56} - 5639 q^{58} + 2445 q^{59} - 1059 q^{61} - 1468 q^{62} + 4570 q^{64} - 2641 q^{65} + 27 q^{67} - 8350 q^{68} + 9702 q^{70} - 3465 q^{71} + 435 q^{73} + 994 q^{74} - 3598 q^{76} + 5931 q^{77} - 2559 q^{79} + 14052 q^{80} - 3822 q^{82} + 3967 q^{83} + 299 q^{85} - 721 q^{86} + 5825 q^{88} - 3717 q^{89} + 7238 q^{91} - 9550 q^{92} + 6035 q^{94} - 4551 q^{95} - 2419 q^{97} + 5687 q^{98}+O(q^{100}) $ 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8 + 47 * q^10 + 53 * q^11 - 65 * q^13 - 117 * q^14 - 499 * q^16 + 117 * q^17 + 73 * q^19 - 529 * q^20 + 310 * q^22 - 542 * q^23 + 246 * q^25 - 324 * q^26 - 677 * q^28 + 497 * q^29 - 471 * q^31 + 915 * q^32 - 2751 * q^34 + 737 * q^35 - 1071 * q^37 + 1504 * q^38 + 1479 * q^40 - 569 * q^41 + 1615 * q^43 - 2518 * q^44 + 4041 * q^46 - 2904 * q^47 + 1226 * q^49 - 1322 * q^50 - 2156 * q^52 - 391 * q^53 - 3323 * q^55 + 7028 * q^56 - 5639 * q^58 + 2445 * q^59 - 1059 * q^61 - 1468 * q^62 + 4570 * q^64 - 2641 * q^65 + 27 * q^67 - 8350 * q^68 + 9702 * q^70 - 3465 * q^71 + 435 * q^73 + 994 * q^74 - 3598 * q^76 + 5931 * q^77 - 2559 * q^79 + 14052 * q^80 - 3822 * q^82 + 3967 * q^83 + 299 * q^85 - 721 * q^86 + 5825 * q^88 - 3717 * q^89 + 7238 * q^91 - 9550 * q^92 + 6035 * q^94 - 4551 * q^95 - 2419 * q^97 + 5687 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−1.61249	−	1.86092i	−0.570103	−	0.657934i	0.395344	−	0.918533i	$-0.370625\pi$
$2$	−1.61249	−	1.86092i	−0.570103	−	0.657934i	−0.965447	+	0.260599i	$0.916080\pi$
$3$		0			0
$3$		0			0
$4$	0.275643	−	1.91714i	0.0344553	−	0.239642i
$5$	3.07518	−	6.73370i	0.275052	−	0.602281i	−0.720812	−	0.693130i	$-0.756231\pi$
$5$	3.07518	−	6.73370i	0.275052	−	0.602281i	0.995865	+	0.0908496i	$0.0289582\pi$
$6$		0			0
$7$	−11.6919	−	3.43306i	−0.631305	−	0.185368i	−0.0496020	−	0.998769i	$-0.515795\pi$
$7$	−11.6919	−	3.43306i	−0.631305	−	0.185368i	−0.581703	+	0.813401i	$0.697613\pi$
$8$	−20.5838	+	13.2284i	−0.909682	+	0.584617i
$9$		0			0
$10$	−17.4896	+	5.13540i	−0.553069	+	0.162396i
$11$	−3.34406	+	3.85925i	−0.0916610	+	0.105782i	−0.799727	−	0.600364i	$-0.795022\pi$
$11$	−3.34406	+	3.85925i	−0.0916610	+	0.105782i	0.708066	+	0.706146i	$0.249568\pi$
$12$		0			0
$13$	−23.2908	+	6.83879i	−0.496900	+	0.145903i	−0.520574	−	0.853817i	$-0.674282\pi$
$13$	−23.2908	+	6.83879i	−0.496900	+	0.145903i	0.0236737	+	0.999720i	$0.492464\pi$
$14$	12.4645	+	27.2935i	0.237949	+	0.521036i
$15$		0			0
$16$	42.9410	+	12.6086i	0.670953	+	0.197009i
$17$	−9.15745	−	63.6914i	−0.130647	−	0.908673i	−0.944713	−	0.327900i	$-0.893659\pi$
$17$	−9.15745	−	63.6914i	−0.130647	−	0.908673i	0.814065	−	0.580774i	$-0.197250\pi$
$18$		0			0
$19$	−7.05564	+	49.0731i	−0.0851935	+	0.592534i	0.901846	+	0.432057i	$0.142212\pi$
$19$	−7.05564	+	49.0731i	−0.0851935	+	0.592534i	−0.987040	+	0.160476i	$0.948697\pi$
$20$	−12.0618	−	7.75163i	−0.134855	−	0.0866659i
$21$		0			0
$22$	12.5740			0.121854
$23$	−72.4803	−	83.1481i	−0.657095	−	0.753808i
$23$	−72.4803	−	83.1481i	−0.657095	−	0.753808i
$24$		0			0
$25$	45.9715	+	53.0540i	0.367772	+	0.424432i
$26$	50.2827	+	32.3147i	0.379279	+	0.243748i
$27$		0			0
$28$	−9.80444	+	21.4687i	−0.0661738	+	0.144900i
$29$	24.5481	+	170.736i	0.157189	+	1.09327i	0.903783	+	0.427992i	$0.140779\pi$
$29$	24.5481	+	170.736i	0.157189	+	1.09327i	−0.746594	+	0.665280i	$0.768312\pi$
$30$		0			0
$31$	−195.491	+	125.634i	−1.13262	+	0.727891i	−0.966105	−	0.258148i	$-0.916888\pi$
$31$	−195.491	+	125.634i	−1.13262	+	0.727891i	−0.166515	+	0.986039i	$0.553251\pi$
$32$	35.5364	+	77.8139i	0.196313	+	0.429865i
$33$		0			0
$34$	−103.758	+	119.743i	−0.523364	+	0.603994i
$35$	−59.0720	+	68.1728i	−0.285286	+	0.329237i
$36$		0			0
$37$	−98.8932	−	216.546i	−0.439404	−	0.962161i	−0.991707	−	0.128517i	$-0.958978\pi$
$37$	−98.8932	−	216.546i	−0.439404	−	0.962161i	0.552303	−	0.833643i	$-0.313749\pi$
$38$	102.698	−	66.0001i	0.438417	−	0.281753i
$39$		0			0
$40$	25.7772	+	179.285i	0.101893	+	0.708685i
$41$	−129.476	+	283.513i	−0.493190	+	1.07994i	0.485433	+	0.874274i	$0.338662\pi$
$41$	−129.476	+	283.513i	−0.493190	+	1.07994i	−0.978623	+	0.205662i	$0.934065\pi$
$42$		0			0
$43$	442.252	+	284.218i	1.56844	+	1.00797i	0.979897	+	0.199505i	$0.0639336\pi$
$43$	442.252	+	284.218i	1.56844	+	1.00797i	0.588540	+	0.808468i	$0.299703\pi$
$44$	6.47693	+	7.47478i	0.0221917	+	0.0256106i
$45$		0			0
$46$	−37.8577	+	268.956i	−0.121344	+	0.862073i
$47$	−407.467			−1.26458			−0.632289	−	0.774733i	$-0.717884\pi$
$47$	−407.467			−1.26458			−0.632289	+	0.774733i	$0.717884\pi$
$48$		0			0
$49$	−163.635	−	105.162i	−0.477069	−	0.306593i
$50$	24.6002	−	171.098i	0.0695800	−	0.483940i
$51$		0			0
$52$	6.69096	+	46.5367i	0.0178436	+	0.124105i
$53$	461.872	+	135.618i	1.19704	+	0.351482i	0.818719	−	0.574194i	$-0.194684\pi$
$53$	461.872	+	135.618i	1.19704	+	0.351482i	0.378318	+	0.925676i	$0.376503\pi$
$54$		0			0
$55$	15.7035	+	34.3858i	0.0384991	+	0.0843014i
$56$	286.078	−	84.0001i	0.682657	−	0.200446i
$57$		0			0
$58$	278.142	−	320.993i	0.629687	−	0.726697i
$59$	−41.1233	+	12.0749i	−0.0907423	+	0.0266443i	−0.326789	−	0.945097i	$-0.605966\pi$
$59$	−41.1233	+	12.0749i	−0.0907423	+	0.0266443i	0.236046	+	0.971742i	$0.424148\pi$
$60$		0			0
$61$	−286.232	+	183.950i	−0.600791	+	0.386105i	−0.805394	−	0.592740i	$-0.798046\pi$
$61$	−286.232	+	183.950i	−0.600791	+	0.386105i	0.204603	+	0.978845i	$0.434410\pi$
$62$	549.024	+	161.208i	1.12461	+	0.330216i
$63$		0			0
$64$	236.234	−	517.281i	0.461395	−	1.01031i
$65$	−25.5730	+	177.864i	−0.0487990	+	0.339404i
$66$		0			0
$67$	−347.288	−	400.792i	−0.633254	−	0.730814i	0.344913	−	0.938635i	$-0.387908\pi$
$67$	−347.288	−	400.792i	−0.633254	−	0.730814i	−0.978167	+	0.207821i	$0.933363\pi$
$68$	−124.629			−0.222258
$69$		0			0
$70$	222.117			0.379258
$71$	−488.573	−	563.843i	−0.816661	−	0.942477i	0.182509	−	0.983204i	$-0.441578\pi$
$71$	−488.573	−	563.843i	−0.816661	−	0.942477i	−0.999170	+	0.0407268i	$0.987033\pi$
$72$		0			0
$73$	43.0026	−	299.090i	0.0689462	−	0.479532i	−0.925870	−	0.377842i	$-0.876666\pi$
$73$	43.0026	−	299.090i	0.0689462	−	0.479532i	0.994816	−	0.101689i	$-0.0324248\pi$
$74$	−243.509	+	533.211i	−0.382532	+	0.837629i
$75$		0			0
$76$	92.1349	+	27.0533i	0.139061	+	0.0408319i
$77$	52.3475	−	33.6417i	0.0774747	−	0.0497900i
$78$		0			0
$79$	−744.340	+	218.558i	−1.06006	+	0.311262i	−0.764876	−	0.644178i	$-0.777200\pi$
$79$	−744.340	+	218.558i	−1.06006	+	0.311262i	−0.295185	+	0.955440i	$0.595381\pi$
$80$	216.954	−	250.378i	0.303202	−	0.349914i
$81$		0			0
$82$	736.374	−	216.219i	0.991695	−	0.291188i
$83$	−121.922	−	266.971i	−0.161236	−	0.353059i	0.811720	−	0.584047i	$-0.198531\pi$
$83$	−121.922	−	266.971i	−0.161236	−	0.353059i	−0.972957	+	0.230988i	$0.925804\pi$
$84$		0			0
$85$	−457.040	−	134.199i	−0.583211	−	0.171246i
$86$	−184.222	−	1281.29i	−0.230991	−	1.60658i
$87$		0			0
$88$	17.7817	−	123.674i	0.0215401	−	0.149815i
$89$	−479.164	−	307.940i	−0.570689	−	0.366760i	0.223246	−	0.974762i	$-0.428335\pi$
$89$	−479.164	−	307.940i	−0.570689	−	0.366760i	−0.793935	+	0.608003i	$0.791971\pi$
$90$		0			0
$91$	295.792			0.340741
$92$	−179.385	+	116.035i	−0.203284	+	0.131495i
$93$		0			0
$94$	657.038	+	758.262i	0.720939	+	0.832008i
$95$	308.746	+	198.419i	0.333439	+	0.214288i
$96$		0			0
$97$	776.529	−	1700.36i	0.812830	−	1.77985i	0.218097	−	0.975927i	$-0.430015\pi$
$97$	776.529	−	1700.36i	0.812830	−	1.77985i	0.594733	−	0.803923i	$-0.297258\pi$
$98$	68.1628	+	474.083i	0.0702600	+	0.488669i
$99$		0			0
$100$	114.383	−	73.5098i	0.114383	−	0.0735098i
$101$	−727.853	−	1593.78i	−0.717070	−	1.57016i	−0.817966	−	0.575267i	$-0.804898\pi$
$101$	−727.853	−	1593.78i	−0.717070	−	1.57016i	0.100896	−	0.994897i	$-0.467829\pi$
$102$		0			0
$103$	−542.427	+	625.994i	−0.518902	+	0.598845i	−0.953356	−	0.301849i	$-0.902396\pi$
$103$	−542.427	+	625.994i	−0.518902	+	0.598845i	0.434453	+	0.900694i	$0.356942\pi$
$104$	388.946	−	448.867i	0.366724	−	0.423222i
$105$		0			0
$106$	−492.392	−	1078.19i	−0.451183	−	0.987952i
$107$	53.3004	−	34.2541i	0.0481565	−	0.0309483i	−0.516341	−	0.856383i	$-0.672706\pi$
$107$	53.3004	−	34.2541i	0.0481565	−	0.0309483i	0.564498	+	0.825435i	$0.309070\pi$
$108$		0			0
$109$	−206.529	−	1436.44i	−0.181485	−	1.26226i	−0.853254	−	0.521495i	$-0.825374\pi$
$109$	−206.529	−	1436.44i	−0.181485	−	1.26226i	0.671769	−	0.740761i	$-0.265535\pi$
$110$	38.6673	−	84.6697i	0.0335162	−	0.0733903i
$111$		0			0
$112$	−458.777	−	294.838i	−0.387057	−	0.248746i
$113$	495.556	+	571.902i	0.412549	+	0.476107i	0.923553	−	0.383472i	$-0.125272\pi$
$113$	495.556	+	571.902i	0.412549	+	0.476107i	−0.511004	+	0.859578i	$0.670726\pi$
$114$		0			0
$115$	−782.785	+	232.366i	−0.634740	+	0.188419i
$116$	334.091			0.267410
$117$		0			0
$118$	88.7814	+	57.0563i	0.0692626	+	0.0445124i
$119$	−111.588	+	776.114i	−0.0859604	+	0.597868i
$120$		0			0
$121$	185.710	+	1291.64i	0.139527	+	0.970429i
$122$	803.863	+	236.036i	0.596544	+	0.175161i
$123$		0			0
$124$	186.973	+	409.413i	0.135408	+	0.296503i
$125$	1386.47	−	407.105i	0.992078	−	0.291301i
$126$		0			0
$127$	785.716	−	906.764i	0.548984	−	0.633562i	−0.411662	−	0.911337i	$-0.635052\pi$
$127$	785.716	−	906.764i	0.548984	−	0.633562i	0.960646	+	0.277775i	$0.0895970\pi$
$128$	−686.909	+	201.695i	−0.474334	+	0.139277i
$129$		0			0
$130$	372.226	−	239.215i	0.251126	−	0.161389i
$131$	−270.130	−	79.3174i	−0.180163	−	0.0529007i	0.190407	−	0.981705i	$-0.439019\pi$
$131$	−270.130	−	79.3174i	−0.180163	−	0.0529007i	−0.370570	+	0.928805i	$0.620838\pi$
$132$		0			0
$133$	250.965	−	549.537i	0.163620	−	0.358277i
$134$	−185.840	+	1292.55i	−0.119807	+	0.833278i
$135$		0			0
$136$	1031.03	+	1189.87i	0.650074	+	0.750225i
$137$	−1327.07			−0.827586			−0.413793	−	0.910371i	$-0.635796\pi$
$137$	−1327.07			−0.827586			−0.413793	+	0.910371i	$0.635796\pi$
$138$		0			0
$139$	−452.323			−0.276011			−0.138006	−	0.990431i	$-0.544069\pi$
$139$	−452.323			−0.276011			−0.138006	+	0.990431i	$0.544069\pi$
$140$	114.414	+	132.040i	0.0690694	+	0.0797104i
$141$		0			0
$142$	−261.445	+	1818.39i	−0.154507	+	1.07462i
$143$	51.4931	−	112.754i	0.0301124	−	0.0659369i
$144$		0			0
$145$	1225.18	+	359.744i	0.701692	+	0.206035i
$146$	−625.923	+	402.256i	−0.354806	+	0.228020i
$147$		0			0
$148$	−442.407	+	129.902i	−0.245714	+	0.0721481i
$149$	219.055	−	252.803i	0.120441	−	0.138996i	−0.692327	−	0.721584i	$-0.743414\pi$
$149$	219.055	−	252.803i	0.120441	−	0.138996i	0.812768	+	0.582588i	$0.197960\pi$
$150$		0			0
$151$	−982.460	+	288.476i	−0.529480	+	0.155469i	−0.535536	−	0.844512i	$-0.679890\pi$
$151$	−982.460	+	288.476i	−0.529480	+	0.155469i	0.00605610	+	0.999982i	$0.498072\pi$
$152$	−503.926	−	1103.44i	−0.268906	−	0.588823i
$153$		0			0
$154$	−147.014	−	43.1673i	−0.0769270	−	0.0225878i
$155$	244.815	+	1702.73i	0.126865	+	0.882364i
$156$		0			0
$157$	−381.839	+	2655.75i	−0.194102	+	1.35001i	0.626906	+	0.779095i	$0.284321\pi$
$157$	−381.839	+	2655.75i	−0.194102	+	1.35001i	−0.821008	+	0.570916i	$0.806588\pi$
$158$	1606.96	+	1032.73i	0.809133	+	0.519998i
$159$		0			0
$160$	633.257			0.312896
$161$	561.982	+	1220.99i	0.275096	+	0.597687i
$162$		0			0
$163$	−1333.13	−	1538.51i	−0.640605	−	0.739297i	0.338877	−	0.940831i	$-0.389953\pi$
$163$	−1333.13	−	1538.51i	−0.640605	−	0.739297i	−0.979482	+	0.201533i	$0.935408\pi$
$164$	507.844	+	326.372i	0.241805	+	0.155399i
$165$		0			0
$166$	−300.213	+	657.375i	−0.140368	+	0.307363i
$167$	98.5196	+	685.219i	0.0456508	+	0.317508i	0.999833	+	0.0182815i	$0.00581951\pi$
$167$	98.5196	+	685.219i	0.0456508	+	0.317508i	−0.954182	+	0.299226i	$0.903271\pi$
$168$		0			0
$169$	−1352.54	+	869.226i	−0.615632	+	0.395642i
$170$	487.241	+	1066.91i	0.219822	+	0.481342i
$171$		0			0
$172$	666.788	−	769.515i	0.295594	−	0.341133i
$173$	241.913	−	279.183i	0.106314	−	0.122693i	−0.700099	−	0.714046i	$-0.746861\pi$
$173$	241.913	−	279.183i	0.106314	−	0.122693i	0.806413	+	0.591353i	$0.201406\pi$
$174$		0			0
$175$	−355.359	−	778.127i	−0.153501	−	0.336119i
$176$	−192.257	+	123.556i	−0.0823403	+	0.0529169i
$177$		0			0
$178$	199.598	+	1388.24i	0.0840479	+	0.584566i
$179$	466.422	−	1021.32i	0.194760	−	0.426464i	−0.786906	−	0.617072i	$-0.788319\pi$
$179$	466.422	−	1021.32i	0.194760	−	0.426464i	0.981666	+	0.190608i	$0.0610459\pi$
$180$		0			0
$181$	−1083.48	−	696.308i	−0.444940	−	0.285946i	0.298924	−	0.954277i	$-0.403372\pi$
$181$	−1083.48	−	696.308i	−0.444940	−	0.285946i	−0.743864	+	0.668332i	$0.767009\pi$
$182$	−476.963	−	550.445i	−0.194258	−	0.224185i
$183$		0			0
$184$	2591.83	+	752.704i	1.03844	+	0.301576i
$185$	−1762.27			−0.700350
$186$		0			0
$187$	276.424	+	177.647i	0.108097	+	0.0694697i
$188$	−112.315	+	781.169i	−0.0435714	+	0.303046i
$189$		0			0
$190$	−128.610	−	894.501i	−0.0491070	−	0.341547i
$191$	−2354.65	−	691.386i	−0.892022	−	0.261921i	−0.196566	−	0.980490i	$-0.562979\pi$
$191$	−2354.65	−	691.386i	−0.892022	−	0.261921i	−0.695455	+	0.718569i	$0.744797\pi$
$192$		0			0
$193$	272.302	+	596.258i	0.101558	+	0.222381i	0.953590	−	0.301109i	$-0.0973569\pi$
$193$	272.302	+	596.258i	0.101558	+	0.222381i	−0.852032	+	0.523490i	$0.824630\pi$
$194$	−4416.38	+	1296.77i	−1.63442	+	0.479909i
$195$		0			0
$196$	−246.714	+	284.723i	−0.0899102	+	0.103762i
$197$	3285.04	−	964.574i	1.18807	−	0.348848i	0.372788	−	0.927917i	$-0.378402\pi$
$197$	3285.04	−	964.574i	1.18807	−	0.348848i	0.815279	+	0.579069i	$0.196584\pi$
$198$		0			0
$199$	−2651.88	+	1704.26i	−0.944656	+	0.607094i	−0.919711	−	0.392595i	$-0.871577\pi$
$199$	−2651.88	+	1704.26i	−0.944656	+	0.607094i	−0.0249449	+	0.999689i	$0.507941\pi$
$200$	−1648.09	−	483.922i	−0.582686	−	0.171092i
$201$		0			0
$202$	−1792.23	+	3924.43i	−0.624260	+	1.36694i
$203$	299.132	−	2080.51i	0.103423	−	0.719326i
$204$		0			0
$205$	1510.93	+	1743.71i	0.514771	+	0.594078i
$206$	2039.58			0.689828
$207$		0			0
$208$	−1086.36			−0.362141
$209$	−165.791	−	191.333i	−0.0548707	−	0.0633242i
$210$		0			0
$211$	156.184	−	1086.29i	0.0509581	−	0.354422i	−0.948350	−	0.317226i	$-0.897249\pi$
$211$	156.184	−	1086.29i	0.0509581	−	0.354422i	0.999308	−	0.0371954i	$-0.0118424\pi$
$212$	387.309	−	848.089i	0.125474	−	0.274750i
$213$		0			0
$214$	−149.691	−	43.9531i	−0.0478160	−	0.0140401i
$215$	3273.85	−	2103.97i	1.03849	−	0.667394i
$216$		0			0
$217$	2716.98	−	797.777i	0.849957	−	0.249570i
$218$	−2340.07	+	2700.58i	−0.727016	+	0.839021i
$219$		0			0
$220$	70.2507	−	20.6275i	0.0215286	−	0.00632138i
$221$	648.857	+	1420.80i	0.197497	+	0.432458i
$222$		0			0
$223$	2984.08	+	876.206i	0.896094	+	0.263117i	0.697177	−	0.716899i	$-0.254439\pi$
$223$	2984.08	+	876.206i	0.896094	+	0.263117i	0.198918	+	0.980016i	$0.436257\pi$
$224$	−148.350	−	1031.79i	−0.0442501	−	0.307766i
$225$		0			0
$226$	265.182	−	1844.38i	0.0780514	−	0.542859i
$227$	−2485.44	−	1597.29i	−0.726714	−	0.467031i	0.124252	−	0.992251i	$-0.460347\pi$
$227$	−2485.44	−	1597.29i	−0.726714	−	0.467031i	−0.850967	+	0.525220i	$0.823983\pi$
$228$		0			0
$229$	−5467.66			−1.57779			−0.788893	−	0.614530i	$-0.789346\pi$
$229$	−5467.66			−1.57779			−0.788893	+	0.614530i	$0.789346\pi$
$230$	1694.65	+	1082.01i	0.485834	+	0.310198i
$231$		0			0
$232$	−2763.85	−	3189.66i	−0.782138	−	0.902635i
$233$	−3936.30	−	2529.71i	−1.10676	−	0.711273i	−0.146177	−	0.989258i	$-0.546697\pi$
$233$	−3936.30	−	2529.71i	−1.10676	−	0.711273i	−0.960585	+	0.277985i	$0.910333\pi$
$234$		0			0
$235$	−1253.03	+	2743.76i	−0.347825	+	0.761631i
$236$	11.8139	+	82.1673i	0.00325855	+	0.0226637i
$237$		0			0
$238$	1624.22	−	1043.82i	0.442364	−	0.284290i
$239$	1953.01	+	4276.50i	0.528577	+	1.15742i	0.966089	+	0.258210i	$0.0831325\pi$
$239$	1953.01	+	4276.50i	0.528577	+	1.15742i	−0.437512	+	0.899213i	$0.644140\pi$
$240$		0			0
$241$	4543.72	−	5243.73i	1.21447	−	1.40157i	0.324288	−	0.945959i	$-0.394875\pi$
$241$	4543.72	−	5243.73i	1.21447	−	1.40157i	0.890179	−	0.455611i	$-0.150579\pi$
$242$	2104.18	−	2428.35i	0.558933	−	0.645044i
$243$		0			0
$244$	273.760	+	599.450i	0.0718265	+	0.157278i
$245$	−1211.33	+	778.476i	−0.315874	+	0.203000i
$246$		0			0
$247$	−171.269	−	1191.20i	−0.0441198	−	0.306860i
$248$	2362.00	−	5172.06i	0.604787	−	1.32430i
$249$		0			0
$250$	−2993.27	−	1923.66i	−0.757243	−	0.486651i
$251$	4657.01	+	5374.48i	1.17111	+	1.35153i	0.923931	+	0.382559i	$0.124957\pi$
$251$	4657.01	+	5374.48i	1.17111	+	1.35153i	0.247176	+	0.968970i	$0.420497\pi$
$252$		0			0
$253$	563.267	−	1.66740i	0.139970	−	0.000414342i
$254$	−2954.38			−0.729819
$255$		0			0
$256$	−2344.19	−	1506.52i	−0.572313	−	0.367803i
$257$	435.206	−	3026.92i	0.105632	−	0.734686i	−0.866317	−	0.499494i	$-0.833519\pi$
$257$	435.206	−	3026.92i	0.105632	−	0.734686i	0.971949	−	0.235191i	$-0.0755717\pi$
$258$		0			0
$259$	412.838	+	2871.35i	0.0990443	+	0.688868i
$260$	333.940	+	98.0536i	0.0796542	+	0.0233886i
$261$		0			0
$262$	287.980	+	630.589i	0.0679064	+	0.148694i
$263$	−6992.15	+	2053.08i	−1.63937	+	0.481363i	−0.966129	−	0.258060i	$-0.916917\pi$
$263$	−6992.15	+	2053.08i	−1.63937	+	0.481363i	−0.673242	+	0.739423i	$0.735099\pi$
$264$		0			0
$265$	2333.55	−	2693.06i	0.540939	−	0.624277i
$266$	−1427.32	+	419.100i	−0.329003	+	0.0966039i
$267$		0			0
$268$	−864.100	+	555.323i	−0.196953	+	0.126574i
$269$	−453.585	−	133.184i	−0.102809	−	0.0301874i	0.229924	−	0.973209i	$-0.426152\pi$
$269$	−453.585	−	133.184i	−0.102809	−	0.0301874i	−0.332732	+	0.943021i	$0.607971\pi$
$270$		0			0
$271$	1041.19	−	2279.88i	0.233386	−	0.511045i	−0.756312	−	0.654211i	$-0.773001\pi$
$271$	1041.19	−	2279.88i	0.233386	−	0.511045i	0.989699	+	0.143166i	$0.0457282\pi$
$272$	409.831	−	2850.43i	0.0913589	−	0.635415i
$273$		0			0
$274$	2139.89	+	2469.57i	0.471809	+	0.544497i
$275$	−358.480			−0.0786078
$276$		0			0
$277$	694.569			0.150659			0.0753296	−	0.997159i	$-0.475999\pi$
$277$	694.569			0.150659			0.0753296	+	0.997159i	$0.475999\pi$
$278$	729.368	+	841.736i	0.157355	+	0.181597i
$279$		0			0
$280$	314.110	−	2184.68i	0.0670415	−	0.466284i
$281$	407.100	−	891.425i	0.0864255	−	0.189245i	−0.861484	−	0.507784i	$-0.830465\pi$
$281$	407.100	−	891.425i	0.0864255	−	0.189245i	0.947910	+	0.318539i	$0.103192\pi$
$282$		0			0
$283$	7016.80	+	2060.32i	1.47387	+	0.432768i	0.917355	−	0.398070i	$-0.130320\pi$
$283$	7016.80	+	2060.32i	1.47387	+	0.432768i	0.556516	+	0.830837i	$0.312138\pi$
$284$	−1215.64	+	781.242i	−0.253995	+	0.163233i
$285$		0			0
$286$	−292.858	+	85.9910i	−0.0605492	+	0.0177789i
$287$	2487.15	−	2870.32i	0.511539	−	0.590347i
$288$		0			0
$289$	741.249	−	217.650i	0.150875	−	0.0443009i
$290$	−1306.13	−	2860.04i	−0.264479	−	0.579128i
$291$		0			0
$292$	−561.542	−	164.884i	−0.112540	−	0.0330448i
$293$	739.718	+	5144.85i	0.147491	+	1.02582i	0.920309	+	0.391193i	$0.127938\pi$
$293$	739.718	+	5144.85i	0.147491	+	1.02582i	−0.772818	+	0.634628i	$0.781153\pi$
$294$		0			0
$295$	−45.1528	+	314.044i	−0.00891151	+	0.0619809i
$296$	4900.15	+	3149.13i	0.962214	+	0.618377i
$297$		0			0
$298$	−823.672			−0.160114
$299$	2256.76	+	1440.91i	0.436493	+	0.278695i
$300$		0			0
$301$	−4195.04	−	4841.34i	−0.803317	−	0.927077i
$302$	2121.04	+	1363.11i	0.404147	+	0.259729i
$303$		0			0
$304$	−921.719	+	2018.28i	−0.173895	+	0.380778i
$305$	358.451	+	2493.08i	0.0672946	+	0.468044i
$306$		0			0
$307$	−520.294	+	334.373i	−0.0967256	+	0.0621618i	−0.588109	−	0.808781i	$-0.700128\pi$
$307$	−520.294	+	334.373i	−0.0967256	+	0.0621618i	0.491384	+	0.870943i	$0.336491\pi$
$308$	−50.0665	−	109.630i	−0.00926235	−	0.0202817i
$309$		0			0
$310$	2773.87	−	3201.22i	0.508211	−	0.586507i
$311$	2653.68	−	3062.51i	0.483847	−	0.558389i	−0.460364	−	0.887730i	$-0.652281\pi$
$311$	2653.68	−	3062.51i	0.483847	−	0.558389i	0.944211	+	0.329341i	$0.106827\pi$
$312$		0			0
$313$	−1558.02	−	3411.58i	−0.281356	−	0.616083i	0.715208	−	0.698912i	$-0.246332\pi$
$313$	−1558.02	−	3411.58i	−0.281356	−	0.616083i	−0.996564	+	0.0828284i	$0.973605\pi$
$314$	5557.84	−	3571.81i	0.998876	−	0.641939i
$315$		0			0
$316$	213.834	+	1487.25i	0.0380667	+	0.264760i
$317$	1110.05	−	2430.66i	0.196677	−	0.430662i	−0.785439	−	0.618939i	$-0.787563\pi$
$317$	1110.05	−	2430.66i	0.196677	−	0.430662i	0.982116	+	0.188277i	$0.0602903\pi$
$318$		0			0
$319$	−741.003	−	476.213i	−0.130057	−	0.0835826i
$320$	−2756.75	−	3181.46i	−0.481585	−	0.555779i
$321$		0			0
$322$	1365.97	−	3014.64i	0.236406	−	0.521738i
$323$	3190.15			0.549550
$324$		0			0
$325$	−1433.54	−	921.279i	−0.244672	−	0.157241i
$326$	−713.382	+	4961.68i	−0.121198	+	0.842951i
$327$		0			0
$328$	−1085.32	−	7548.53i	−0.182703	−	1.27073i
$329$	4764.08	+	1398.86i	0.798334	+	0.234412i
$330$		0			0
$331$	3009.73	+	6590.40i	0.499788	+	1.09438i	0.976538	+	0.215345i	$0.0690876\pi$
$331$	3009.73	+	6590.40i	0.499788	+	1.09438i	−0.476750	+	0.879039i	$0.658185\pi$
$332$	−545.426	+	160.152i	−0.0901631	+	0.0264743i
$333$		0			0
$334$	1116.27	−	1288.25i	0.182874	−	0.211047i
$335$	−3766.79	+	1106.03i	−0.614333	+	0.180384i
$336$		0			0
$337$	2227.44	−	1431.49i	0.360049	−	0.231389i	−0.348092	−	0.937460i	$-0.613170\pi$
$337$	2227.44	−	1431.49i	0.360049	−	0.231389i	0.708141	+	0.706071i	$0.249534\pi$
$338$	3798.52	+	1115.35i	0.611280	+	0.179488i
$339$		0			0
$340$	−383.258	+	839.217i	−0.0611325	+	0.133862i
$341$	168.879	−	1174.58i	0.0268190	−	0.186531i
$342$		0			0
$343$	4289.26	+	4950.07i	0.675214	+	0.779238i
$344$	−12863.0			−2.01606
$345$		0			0
$346$	−909.619			−0.141334
$347$	−5343.17	−	6166.35i	−0.826618	−	0.953968i	0.172902	−	0.984939i	$-0.444686\pi$
$347$	−5343.17	−	6166.35i	−0.826618	−	0.953968i	−0.999520	+	0.0309706i	$0.990140\pi$
$348$		0			0
$349$	−301.911	+	2099.84i	−0.0463064	+	0.322068i	0.953481	+	0.301453i	$0.0974716\pi$
$349$	−301.911	+	2099.84i	−0.0463064	+	0.322068i	−0.999787	+	0.0206153i	$0.993437\pi$
$350$	−875.016	+	1916.02i	−0.133633	+	0.292616i
$351$		0			0
$352$	−419.139	−	123.070i	−0.0634664	−	0.0186354i
$353$	−191.567	+	123.113i	−0.0288841	+	0.0185627i	−0.555003	−	0.831848i	$-0.687283\pi$
$353$	−191.567	+	123.113i	−0.0288841	+	0.0185627i	0.526119	+	0.850411i	$0.323647\pi$
$354$		0			0
$355$	−5299.20	+	1555.99i	−0.792261	+	0.232629i
$356$	−722.441	+	833.742i	−0.107554	+	0.124124i
$357$		0			0
$358$	−2652.70	+	778.902i	−0.391618	+	0.114990i
$359$	−1120.81	−	2454.23i	−0.164774	−	0.360805i	0.809176	−	0.587566i	$-0.199914\pi$
$359$	−1120.81	−	2454.23i	−0.164774	−	0.360805i	−0.973950	+	0.226761i	$0.927186\pi$
$360$		0			0
$361$	4222.78	+	1239.92i	0.615655	+	0.180773i
$362$	451.327	+	3139.05i	0.0655283	+	0.455759i
$363$		0			0
$364$	81.5330	−	567.074i	0.0117404	−	0.0816559i
$365$	−1881.74	−	1209.32i	−0.269849	−	0.173421i
$366$		0			0
$367$	−7082.81			−1.00741			−0.503705	−	0.863876i	$-0.668030\pi$
$367$	−7082.81			−1.00741			−0.503705	+	0.863876i	$0.668030\pi$
$368$	−2063.99	−	4484.34i	−0.292372	−	0.635223i
$369$		0			0
$370$	2841.65	+	3279.44i	0.399272	+	0.460784i
$371$	−4934.59	−	3171.27i	−0.690542	−	0.443785i
$372$		0			0
$373$	3321.90	−	7273.95i	0.461130	−	1.00973i	−0.526098	−	0.850424i	$-0.676346\pi$
$373$	3321.90	−	7273.95i	0.461130	−	1.00973i	0.987229	−	0.159310i	$-0.0509271\pi$
$374$	−115.146	−	800.857i	−0.0159199	−	0.110725i
$375$		0			0
$376$	8387.20	−	5390.13i	1.15036	−	0.739294i
$377$	−1739.37	−	3808.70i	−0.237619	−	0.520313i
$378$		0			0
$379$	−7982.32	+	9212.09i	−1.08186	+	1.24853i	−0.114960	+	0.993370i	$0.536674\pi$
$379$	−7982.32	+	9212.09i	−1.08186	+	1.24853i	−0.966898	+	0.255161i	$0.917871\pi$
$380$	465.500	−	537.216i	0.0628412	−	0.0725226i
$381$		0			0
$382$	2510.24	+	5496.66i	0.336217	+	0.736213i
$383$	−3830.50	+	2461.71i	−0.511042	+	0.328427i	−0.770620	−	0.637295i	$-0.780053\pi$
$383$	−3830.50	+	2461.71i	−0.511042	+	0.328427i	0.259577	+	0.965722i	$0.416417\pi$
$384$		0			0
$385$	−65.5553	−	455.947i	−0.00867794	−	0.0603564i
$386$	670.501	−	1468.19i	0.0884135	−	0.193599i
$387$		0			0
$388$	−3045.78	−	1957.40i	−0.398521	−	0.256114i
$389$	5159.85	+	5954.79i	0.672532	+	0.776143i	0.984770	−	0.173860i	$-0.0556242\pi$
$389$	5159.85	+	5954.79i	0.672532	+	0.776143i	−0.312238	+	0.950004i	$0.601079\pi$
$390$		0			0
$391$	−4632.09	+	5377.80i	−0.599117	+	0.695568i
$392$	4759.33			0.613221
$393$		0			0
$394$	−7092.09	−	4557.81i	−0.906839	−	0.582790i
$395$	−817.275	+	5684.27i	−0.104105	+	0.724068i
$396$		0			0
$397$	794.424	+	5525.34i	0.100431	+	0.698511i	0.976373	+	0.216094i	$0.0693318\pi$
$397$	794.424	+	5525.34i	0.100431	+	0.698511i	−0.875942	+	0.482417i	$0.839759\pi$
$398$	7447.62	+	2186.82i	0.937978	+	0.275415i
$399$		0			0
$400$	1305.13	+	2857.83i	0.163141	+	0.357228i
$401$	6034.23	−	1771.81i	0.751459	−	0.220648i	0.116497	−	0.993191i	$-0.462834\pi$
$401$	6034.23	−	1771.81i	0.751459	−	0.220648i	0.634963	+	0.772543i	$0.281015\pi$
$402$		0			0
$403$	3693.95	−	4263.05i	0.456598	−	0.526942i
$404$	−3256.11	+	956.080i	−0.400984	+	0.117740i
$405$		0			0
$406$	−4354.01	+	2798.15i	−0.532231	+	0.342044i
$407$	1166.41	+	342.489i	0.142056	+	0.0417114i
$408$		0			0
$409$	6732.02	−	14741.1i	0.813880	−	1.78215i	0.224137	−	0.974558i	$-0.428044\pi$
$409$	6732.02	−	14741.1i	0.813880	−	1.78215i	0.589743	−	0.807591i	$-0.299229\pi$
$410$	808.529	−	5623.44i	0.0973912	−	0.677371i
$411$		0			0
$412$	1050.60	+	1212.46i	0.125630	+	0.144984i
$413$	522.265			0.0622251
$414$		0			0
$415$	−2172.63			−0.256989
$416$	−1359.82	−	1569.32i	−0.160266	−	0.184957i
$417$		0			0
$418$	−88.7177	+	617.045i	−0.0103812	+	0.0722026i
$419$	−4627.57	+	10133.0i	−0.539550	+	1.18145i	0.421943	+	0.906622i	$0.361348\pi$
$419$	−4627.57	+	10133.0i	−0.539550	+	1.18145i	−0.961493	+	0.274828i	$0.911379\pi$
$420$		0			0
$421$	4972.49	+	1460.05i	0.575639	+	0.169023i	0.556578	−	0.830795i	$-0.312114\pi$
$421$	4972.49	+	1460.05i	0.575639	+	0.169023i	0.0190613	+	0.999818i	$0.493932\pi$
$422$	−2273.33	+	1460.98i	−0.262237	+	0.168530i
$423$		0			0
$424$	−11301.1	+	3318.29i	−1.29441	+	0.380072i
$425$	2958.10	−	3413.83i	0.337621	−	0.389636i
$426$		0			0
$427$	3978.12	−	1168.08i	0.450854	−	0.132383i
$428$	−50.9779	−	111.626i	−0.00575726	−	0.0126066i
$429$		0			0
$430$	−9194.37	−	2699.71i	−1.03114	−	0.302771i
$431$	340.940	+	2371.29i	0.0381032	+	0.265014i	0.999964	−	0.00852704i	$-0.00271427\pi$
$431$	340.940	+	2371.29i	0.0381032	+	0.265014i	−0.961860	+	0.273541i	$0.911805\pi$
$432$		0			0
$433$	−1167.33	+	8118.95i	−0.129557	+	0.901090i	0.816559	+	0.577262i	$0.195879\pi$
$433$	−1167.33	+	8118.95i	−0.129557	+	0.901090i	−0.946116	+	0.323828i	$0.895030\pi$
$434$	−5865.71	−	3769.66i	−0.648763	−	0.416935i
$435$		0			0
$436$	−2810.78			−0.308743
$437$	4591.73	−	2970.17i	0.502637	−	0.325131i
$438$		0			0
$439$	6908.50	+	7972.83i	0.751081	+	0.866794i	0.994673	−	0.103084i	$-0.0328710\pi$
$439$	6908.50	+	7972.83i	0.751081	+	0.866794i	−0.243591	+	0.969878i	$0.578326\pi$
$440$	−778.104	−	500.057i	−0.0843060	−	0.0541802i
$441$		0			0
$442$	1597.71	−	3498.50i	0.171935	−	0.376485i
$443$	1246.82	+	8671.80i	0.133720	+	0.930045i	0.940645	+	0.339391i	$0.110221\pi$
$443$	1246.82	+	8671.80i	0.133720	+	0.930045i	−0.806925	+	0.590654i	$0.798870\pi$
$444$		0			0
$445$	−3547.10	+	2279.58i	−0.377862	+	0.242837i
$446$	−3181.27	−	6966.01i	−0.337752	−	0.739574i
$447$		0			0
$448$	−4537.89	+	5237.01i	−0.478561	+	0.552289i
$449$	−2124.44	+	2451.73i	−0.223293	+	0.257694i	−0.856332	−	0.516426i	$-0.827262\pi$
$449$	−2124.44	+	2451.73i	−0.223293	+	0.257694i	0.633039	+	0.774120i	$0.281807\pi$
$450$		0			0
$451$	−661.172	−	1447.76i	−0.0690319	−	0.151159i
$452$	1233.01	−	792.408i	0.128310	−	0.0824596i
$453$		0			0
$454$	1035.32	+	7200.82i	0.107026	+	0.744386i
$455$	909.615	−	1991.78i	0.0937218	−	0.205222i
$456$		0			0
$457$	2503.50	+	1608.90i	0.256255	+	0.164685i	0.662461	−	0.749096i	$-0.269512\pi$
$457$	2503.50	+	1608.90i	0.256255	+	0.164685i	−0.406206	+	0.913782i	$0.633148\pi$
$458$	8816.57	+	10174.9i	0.899500	+	1.03808i
$459$		0			0
$460$	229.708	+	1564.75i	0.0232830	+	0.158602i
$461$	−19088.5			−1.92850			−0.964252	−	0.264986i	$-0.914633\pi$
$461$	−19088.5			−1.92850			−0.964252	+	0.264986i	$0.914633\pi$
$462$		0			0
$463$	1080.69	+	694.517i	0.108475	+	0.0697126i	0.593753	−	0.804647i	$-0.297645\pi$
$463$	1080.69	+	694.517i	0.108475	+	0.0697126i	−0.485279	+	0.874360i	$0.661282\pi$
$464$	−1098.62	+	7641.09i	−0.109919	+	0.764501i
$465$		0			0
$466$	1639.69	+	11404.3i	0.162998	+	1.13367i
$467$	5390.32	+	1582.74i	0.534121	+	0.156832i	0.537660	−	0.843162i	$-0.319308\pi$
$467$	5390.32	+	1582.74i	0.534121	+	0.156832i	−0.00353939	+	0.999994i	$0.501127\pi$
$468$		0			0
$469$	2684.53	+	5878.29i	0.264307	+	0.578751i
$470$	7126.42	−	2092.51i	0.699399	−	0.205362i
$471$		0			0
$472$	686.741	−	792.541i	0.0669699	−	0.0772874i
$473$	−2575.78	+	756.318i	−0.250390	+	0.0735212i
$474$		0			0
$475$	−2927.88	+	1881.64i	−0.282822	+	0.181759i
$476$	1457.16	+	427.860i	0.140312	+	0.0411995i
$477$		0			0
$478$	4808.99	−	10530.2i	0.460164	−	1.00762i
$479$	−850.347	+	5914.29i	−0.0811135	+	0.564157i	0.908221	+	0.418492i	$0.137441\pi$
$479$	−850.347	+	5914.29i	−0.0811135	+	0.564157i	−0.989334	+	0.145665i	$0.953468\pi$
$480$		0			0
$481$	3784.21	+	4367.22i	0.358722	+	0.413987i
$482$	−17084.9			−1.61451
$483$		0			0
$484$	2527.44			0.237363
$485$	−9061.76	−	10457.8i	−0.848399	−	0.979104i
$486$		0			0
$487$	25.5727	−	177.862i	0.00237948	−	0.0165497i	−0.988597	−	0.150585i	$-0.951884\pi$
$487$	25.5727	−	177.862i	0.00237948	−	0.0165497i	0.990977	+	0.134035i	$0.0427935\pi$
$488$	3458.37	−	7572.77i	0.320805	−	0.702466i
$489$		0			0
$490$	3401.94	+	998.901i	0.313641	+	0.0920934i
$491$	3598.54	−	2312.64i	0.330753	−	0.212562i	−0.364715	−	0.931119i	$-0.618833\pi$
$491$	3598.54	−	2312.64i	0.330753	−	0.212562i	0.695468	+	0.718557i	$0.255197\pi$
$492$		0			0
$493$	10649.6	−	3127.01i	0.972890	−	0.285666i
$494$	−1940.56	+	2239.52i	−0.176741	+	0.203970i
$495$		0			0
$496$	−9978.65	+	2930.00i	−0.903336	+	0.265243i
$497$	3776.66	+	8269.72i	0.340857	+	0.746374i
$498$		0			0
$499$	−11347.2	−	3331.83i	−1.01798	−	0.298905i	−0.270163	−	0.962815i	$-0.587078\pi$
$499$	−11347.2	−	3331.83i	−1.01798	−	0.298905i	−0.747812	+	0.663910i	$0.768896\pi$
$500$	−398.305	−	2770.27i	−0.0356255	−	0.247781i
$501$		0			0
$502$	2492.06	−	17332.6i	0.221565	−	1.54102i
$503$	4938.59	+	3173.84i	0.437775	+	0.281341i	0.740907	−	0.671608i	$-0.234396\pi$
$503$	4938.59	+	3173.84i	0.437775	+	0.281341i	−0.303132	+	0.952949i	$0.598032\pi$
$504$		0			0
$505$	−12970.3			−1.14291
$506$	−911.368	−	1045.50i	−0.0800696	−	0.0918545i
$507$		0			0
$508$	−1521.81	−	1756.27i	−0.132913	−	0.153389i
$509$	10399.7	+	6683.51i	0.905620	+	0.582006i	0.908452	−	0.417990i	$-0.137265\pi$
$509$	10399.7	+	6683.51i	0.905620	+	0.582006i	−0.00283219	+	0.999996i	$0.500902\pi$
$510$		0			0
$511$	−1529.58	+	3349.31i	−0.132416	+	0.289950i
$512$	1791.56	+	12460.6i	0.154642	+	1.07556i
$513$		0			0
$514$	−6334.62	+	4071.01i	−0.543595	+	0.349348i
$515$	2547.20	+	5577.59i	0.217948	+	0.477239i
$516$		0			0
$517$	1362.59	−	1572.51i	0.115912	−	0.133770i
$518$	4677.64	−	5398.29i	0.396764	−	0.457890i
$519$		0			0
$520$	−1826.46	−	3999.39i	−0.154030	−	0.337279i
$521$	17247.5	−	11084.3i	1.45034	−	0.932077i	0.451125	−	0.892461i	$-0.351023\pi$
$521$	17247.5	−	11084.3i	1.45034	−	0.932077i	0.999215	−	0.0396159i	$-0.0126134\pi$
$522$		0			0
$523$	975.984	+	6788.12i	0.0816000	+	0.567540i	0.989073	+	0.147429i	$0.0470998\pi$
$523$	975.984	+	6788.12i	0.0816000	+	0.567540i	−0.907473	+	0.420111i	$0.861991\pi$
$524$	−226.522	+	496.013i	−0.0188848	+	0.0413520i
$525$		0			0
$526$	15095.4	+	9701.23i	1.25131	+	0.804171i
$527$	9792.04	+	11300.6i	0.809389	+	0.934085i
$528$		0			0
$529$	−1660.21	+	12053.2i	−0.136452	+	0.990647i
$530$	−8774.40			−0.719123
$531$		0			0
$532$	−984.360	−	632.610i	−0.0802207	−	0.0515547i
$533$	1076.71	−	7488.71i	0.0875003	−	0.608578i
$534$		0			0
$535$	−66.7486	−	464.246i	−0.00539400	−	0.0375161i
$536$	12450.3	+	3655.75i	1.00331	+	0.294597i
$537$		0			0
$538$	483.557	+	1058.84i	0.0387502	+	0.0848512i
$539$	953.047	−	279.840i	0.0761607	−	0.0223628i
$540$		0			0
$541$	10765.4	−	12423.9i	0.855527	−	0.987330i	−0.144471	−	0.989509i	$-0.546148\pi$
$541$	10765.4	−	12423.9i	0.855527	−	0.987330i	0.999998	+	0.00217860i	$0.000693472\pi$
$542$	−5921.59	+	1738.74i	−0.469288	+	0.137795i
$543$		0			0
$544$	4630.66	−	2975.94i	0.364959	−	0.234545i
$545$	−10307.7	−	3026.60i	−0.810151	−	0.237882i
$546$		0			0
$547$	6244.80	−	13674.2i	0.488132	−	1.06886i	−0.492014	−	0.870587i	$-0.663739\pi$
$547$	6244.80	−	13674.2i	0.488132	−	1.06886i	0.980147	−	0.198274i	$-0.0635334\pi$
$548$	−365.797	+	2544.17i	−0.0285147	+	0.198324i
$549$		0			0
$550$	578.046	+	667.101i	0.0448145	+	0.0517187i
$551$	−8551.75			−0.661192
$552$		0			0
$553$	9453.10			0.726920
$554$	−1119.99	−	1292.53i	−0.0858912	−	0.0991237i
$555$		0			0
$556$	−124.679	+	867.165i	−0.00951005	+	0.0661438i
$557$	2516.00	−	5509.28i	0.191394	−	0.419095i	−0.789470	−	0.613789i	$-0.789644\pi$
$557$	2516.00	−	5509.28i	0.191394	−	0.419095i	0.980864	+	0.194695i	$0.0623716\pi$
$558$		0			0
$559$	−12244.1	−	3595.19i	−0.926423	−	0.272022i
$560$	−3396.17	+	2182.59i	−0.256276	+	0.164699i
$561$		0			0
$562$	−2315.32	+	679.838i	−0.173782	+	0.0510271i
$563$	−5522.61	+	6373.43i	−0.413411	+	0.477102i	−0.923818	−	0.382831i	$-0.874949\pi$
$563$	−5522.61	+	6373.43i	−0.413411	+	0.477102i	0.510407	+	0.859933i	$0.329495\pi$
$564$		0			0
$565$	5374.95	−	1578.23i	0.400222	−	0.117516i
$566$	−7480.47	−	16379.9i	−0.555525	−	1.21643i
$567$		0			0
$568$	17515.4	+	5142.99i	1.29389	+	0.379921i
$569$	−1504.17	−	10461.7i	−0.110823	−	0.770790i	−0.967123	−	0.254311i	$-0.918151\pi$
$569$	−1504.17	−	10461.7i	−0.110823	−	0.770790i	0.856300	−	0.516479i	$-0.172758\pi$
$570$		0			0
$571$	−1363.76	+	9485.16i	−0.0999502	+	0.695169i	0.876810	+	0.480836i	$0.159667\pi$
$571$	−1363.76	+	9485.16i	−0.0999502	+	0.695169i	−0.976761	+	0.214333i	$0.931242\pi$
$572$	−201.971	−	129.799i	−0.0147637	−	0.00948807i
$573$		0			0
$574$	−9351.94			−0.680039
$575$	1079.31	−	7667.82i	0.0782787	−	0.556122i
$576$		0			0
$577$	−8370.12	−	9659.63i	−0.603904	−	0.696942i	0.368664	−	0.929563i	$-0.379815\pi$
$577$	−8370.12	−	9659.63i	−0.603904	−	0.696942i	−0.972568	+	0.232620i	$0.925270\pi$
$578$	−1600.29	−	1028.44i	−0.115161	−	0.0740096i
$579$		0			0
$580$	1027.39	−	2249.67i	0.0735517	−	0.161056i
$581$	508.971	+	3539.97i	0.0363437	+	0.252776i
$582$		0			0
$583$	−2067.91	+	1328.96i	−0.146902	+	0.0944083i
$584$	3071.32	+	6725.25i	0.217623	+	0.476529i
$585$		0			0
$586$	8381.36	−	9672.60i	0.590837	−	0.681862i
$587$	10232.3	−	11808.8i	0.719479	−	0.830323i	−0.271765	−	0.962364i	$-0.587607\pi$
$587$	10232.3	−	11808.8i	0.719479	−	0.830323i	0.991244	+	0.132041i	$0.0421529\pi$
$588$		0			0
$589$	−4785.96	−	10479.8i	−0.334808	−	0.733127i
$590$	657.219	−	422.369i	0.0458598	−	0.0294723i
$591$		0			0
$592$	−1516.23	−	10545.6i	−0.105265	−	0.732131i
$593$	9024.22	−	19760.3i	0.624925	−	1.36839i	−0.286958	−	0.957943i	$-0.592644\pi$
$593$	9024.22	−	19760.3i	0.624925	−	1.36839i	0.911883	−	0.410451i	$-0.134629\pi$
$594$		0			0
$595$	4882.97	+	3138.09i	0.336441	+	0.216217i
$596$	−424.278	−	489.642i	−0.0291595	−	0.0336519i
$597$		0			0
$598$	−957.596	−	6523.09i	−0.0654833	−	0.446068i
$599$	−24421.4			−1.66583			−0.832915	−	0.553401i	$-0.813330\pi$
$599$	−24421.4			−1.66583			−0.832915	+	0.553401i	$0.813330\pi$
$600$		0			0
$601$	−6732.69	−	4326.84i	−0.456959	−	0.293669i	0.291840	−	0.956467i	$-0.405733\pi$
$601$	−6732.69	−	4326.84i	−0.456959	−	0.293669i	−0.748798	+	0.662798i	$0.769369\pi$
$602$	−2244.85	+	15613.3i	−0.151982	+	1.05706i
$603$		0			0
$604$	282.241	+	1963.03i	0.0190136	+	0.132242i
$605$	9268.62	+	2721.51i	0.622848	+	0.182885i
$606$		0			0
$607$	−6781.63	−	14849.7i	−0.453472	−	0.992966i	−0.988927	−	0.148402i	$-0.952587\pi$
$607$	−6781.63	−	14849.7i	−0.453472	−	0.992966i	0.535455	−	0.844564i	$-0.320140\pi$
$608$	−4069.30	+	1194.85i	−0.271434	+	0.0797002i
$609$		0			0
$610$	4061.42	−	4687.13i	0.269577	−	0.311108i
$611$	9490.22	−	2786.58i	0.628369	−	0.184506i
$612$		0			0
$613$	9852.75	−	6331.98i	0.649183	−	0.417204i	−0.174185	−	0.984713i	$-0.555729\pi$
$613$	9852.75	−	6331.98i	0.649183	−	0.417204i	0.823367	+	0.567509i	$0.192093\pi$
$614$	1461.21	+	429.050i	0.0960419	+	0.0282004i
$615$		0			0
$616$	−632.484	+	1384.95i	−0.0413693	+	0.0905861i
$617$	2585.91	−	17985.4i	0.168727	−	1.17352i	−0.712792	−	0.701375i	$-0.752570\pi$
$617$	2585.91	−	17985.4i	0.168727	−	1.17352i	0.881519	−	0.472148i	$-0.156521\pi$
$618$		0			0
$619$	−9589.91	−	11067.3i	−0.622700	−	0.718634i	0.353518	−	0.935428i	$-0.384985\pi$
$619$	−9589.91	−	11067.3i	−0.622700	−	0.718634i	−0.976217	+	0.216794i	$0.930440\pi$
$620$	3331.84			0.215823
$621$		0			0
$622$	−9978.12			−0.643226
$623$	4545.18	+	5245.42i	0.292293	+	0.337325i
$624$		0			0
$625$	273.505	−	1902.27i	0.0175043	−	0.121745i
$626$	−3836.38	+	8400.50i	−0.244940	+	0.536344i
$627$		0			0
$628$	4986.18	+	1464.07i	0.316832	+	0.0930301i
$629$	−12886.5	+	8281.66i	−0.816882	+	0.524978i
$630$		0			0
$631$	9282.21	−	2725.50i	0.585609	−	0.171950i	0.0245107	−	0.999700i	$-0.492197\pi$
$631$	9282.21	−	2725.50i	0.585609	−	0.171950i	0.561098	+	0.827749i	$0.310379\pi$
$632$	12430.2	−	14345.2i	0.782350	−	0.902880i
$633$		0			0
$634$	−6313.21	+	1853.73i	−0.395473	+	0.116121i
$635$	−3689.67	−	8079.24i	−0.230583	−	0.504905i
$636$		0			0
$637$	4530.35	+	1330.23i	0.281788	+	0.0827405i
$638$	308.668	+	2146.84i	0.0191541	+	0.133220i
$639$		0			0
$640$	−754.217	+	5245.69i	−0.0465829	+	0.323991i
$641$	14851.0	+	9544.14i	0.915098	+	0.588098i	0.911232	−	0.411895i	$-0.135133\pi$
$641$	14851.0	+	9544.14i	0.915098	+	0.588098i	0.00386677	+	0.999993i	$0.498769\pi$
$642$		0			0
$643$	−1015.03			−0.0622533			−0.0311267	−	0.999515i	$-0.509910\pi$
$643$	−1015.03			−0.0622533			−0.0311267	+	0.999515i	$0.509910\pi$
$644$	2495.71	−	740.839i	0.152709	−	0.0453310i
$645$		0			0
$646$	−5144.09	−	5936.60i	−0.313300	−	0.361567i
$647$	−25171.1	−	16176.5i	−1.52948	−	0.982940i	−0.990019	−	0.140931i	$-0.954990\pi$
$647$	−25171.1	−	16176.5i	−1.52948	−	0.982940i	−0.539465	−	0.842008i	$-0.681373\pi$
$648$		0			0
$649$	90.9186	−	199.084i	0.00549902	−	0.0120412i
$650$	597.148	+	4153.25i	0.0360339	+	0.250622i
$651$		0			0
$652$	−3317.00	+	2131.71i	−0.199239	+	0.128043i
$653$	−437.066	−	957.040i	−0.0261925	−	0.0573536i	0.896084	−	0.443885i	$-0.146400\pi$
$653$	−437.066	−	957.040i	−0.0261925	−	0.0573536i	−0.922276	+	0.386532i	$0.873673\pi$
$654$		0			0
$655$	−1364.80	+	1575.06i	−0.0814155	+	0.0939584i
$656$	−9134.54	+	10541.8i	−0.543664	+	0.627422i
$657$		0			0
$658$	−5078.88	−	11121.2i	−0.300905	−	0.658890i
$659$	490.976	−	315.531i	0.0290223	−	0.0186515i	−0.526049	−	0.850454i	$-0.676327\pi$
$659$	490.976	−	315.531i	0.0290223	−	0.0186515i	0.555072	+	0.831803i	$0.312691\pi$
$660$		0			0
$661$	−2295.98	−	15968.9i	−0.135103	−	0.939663i	−0.938760	−	0.344571i	$-0.888025\pi$
$661$	−2295.98	−	15968.9i	−0.135103	−	0.939663i	0.803657	−	0.595092i	$-0.202885\pi$
$662$	7411.01	−	16227.8i	0.435101	−	0.952739i
$663$		0			0
$664$	6041.20	+	3882.44i	0.353078	+	0.226910i
$665$	−2928.66	−	3379.85i	−0.170780	−	0.197090i
$666$		0			0
$667$	12417.1	−	14416.1i	0.720829	−	0.836874i
$668$	1340.81			0.0776612
$669$		0			0
$670$	8132.15	+	5226.22i	0.468914	+	0.301353i
$671$	247.267	−	1719.78i	0.0142260	−	0.0989438i
$672$		0			0
$673$	553.254	+	3847.97i	0.0316885	+	0.220398i	0.999512	−	0.0312309i	$-0.00994271\pi$
$673$	553.254	+	3847.97i	0.0316885	+	0.220398i	−0.967824	+	0.251629i	$0.919034\pi$
$674$	−6255.62	−	1836.81i	−0.357503	−	0.104972i
$675$		0			0
$676$	1293.61	+	2832.60i	0.0736007	+	0.161163i
$677$	−2236.35	+	656.650i	−0.126957	+	0.0372779i	−0.344594	−	0.938752i	$-0.611983\pi$
$677$	−2236.35	+	656.650i	−0.126957	+	0.0372779i	0.217637	+	0.976030i	$0.430165\pi$
$678$		0			0
$679$	−14916.6	+	17214.6i	−0.843071	+	0.972956i
$680$	11182.8	−	3283.58i	0.630651	−	0.185176i
$681$		0			0
$682$	−2458.11	+	1579.73i	−0.138014	+	0.0886964i
$683$	−18271.4	−	5364.97i	−1.02363	−	0.300564i	−0.273509	−	0.961869i	$-0.588184\pi$
$683$	−18271.4	−	5364.97i	−1.02363	−	0.300564i	−0.750117	+	0.661306i	$0.770003\pi$
$684$		0			0
$685$	−4080.98	+	8936.10i	−0.227630	+	0.498439i
$686$	2295.26	−	15963.9i	0.127746	−	0.888491i
$687$		0			0
$688$	15407.1	+	17780.8i	0.853767	+	0.985299i
$689$	−11684.8			−0.646090
$690$		0			0
$691$	−31012.9			−1.70736			−0.853681	−	0.520796i	$-0.825635\pi$
$691$	−31012.9			−1.70736			−0.853681	+	0.520796i	$0.825635\pi$
$692$	−468.549	−	540.735i	−0.0257393	−	0.0297047i
$693$		0			0
$694$	−2859.23	+	19886.4i	−0.156391	+	1.08772i
$695$	−1390.97	+	3045.81i	−0.0759175	+	0.166236i
$696$		0			0
$697$	19243.0	+	5650.27i	1.04574	+	0.307058i
$698$	4394.46	−	2824.15i	0.238299	−	0.153145i
$699$		0			0
$700$	−1589.73	+	466.786i	−0.0858372	+	0.0252041i
$701$	−17403.0	+	20084.1i	−0.937664	+	1.08212i	0.0588143	+	0.998269i	$0.481268\pi$
$701$	−17403.0	+	20084.1i	−0.937664	+	1.08212i	−0.996478	+	0.0838528i	$0.973277\pi$
$702$		0			0
$703$	11324.3	−	3325.13i	0.607547	−	0.178392i
$704$	1206.33	+	2641.50i	0.0645815	+	0.141414i
$705$		0			0
$706$	538.004	+	157.972i	0.0286800	+	0.00842119i
$707$	3038.48	+	21133.1i	0.161632	+	1.12417i
$708$		0			0
$709$	862.606	−	5999.56i	0.0456923	−	0.317797i	−0.954138	−	0.299368i	$-0.903224\pi$
$709$	862.606	−	5999.56i	0.0456923	−	0.317797i	0.999830	−	0.0184294i	$-0.00586660\pi$
$710$	11440.5	+	7352.36i	0.604724	+	0.388633i
$711$		0			0
$712$	13936.6			0.733560
$713$	24615.5	+	7148.69i	1.29293	+	0.375485i
$714$		0			0
$715$	−600.903	−	693.479i	−0.0314301	−	0.0362722i
$716$	−1829.45	−	1175.71i	−0.0954883	−	0.0613666i
$717$		0			0
$718$	−2759.82	+	6043.15i	−0.143448	+	0.314106i
$719$	1561.39	+	10859.7i	0.0809874	+	0.563280i	0.989401	+	0.145207i	$0.0463850\pi$
$719$	1561.39	+	10859.7i	0.0809874	+	0.563280i	−0.908414	+	0.418072i	$0.862706\pi$
$720$		0			0
$721$	8491.10	−	5456.90i	0.438593	−	0.281866i
$722$	−4501.82	−	9857.60i	−0.232050	−	0.508119i
$723$		0			0
$724$	−1633.57	+	1885.24i	−0.0838551	+	0.0967739i
$725$	−7929.71	+	9151.37i	−0.406210	+	0.468791i
$726$		0			0
$727$	7787.70	+	17052.7i	0.397290	+	0.869943i	0.997538	+	0.0701294i	$0.0223412\pi$
$727$	7787.70	+	17052.7i	0.397290	+	0.869943i	−0.600248	+	0.799814i	$0.704932\pi$
$728$	−6088.52	+	3912.85i	−0.309966	+	0.199203i
$729$		0			0
$730$	783.849	+	5451.79i	0.0397419	+	0.276411i
$731$	14052.4	−	30770.4i	0.711006	−	1.55689i
$732$		0			0
$733$	−28277.0	−	18172.6i	−1.42488	−	0.915714i	−0.999945	−	0.0104903i	$-0.996661\pi$
$733$	−28277.0	−	18172.6i	−1.42488	−	0.915714i	−0.424934	−	0.905224i	$-0.639703\pi$
$734$	11421.0	+	13180.5i	0.574327	+	0.662809i
$735$		0			0
$736$	3894.39	−	8594.76i	0.195039	−	0.430444i
$737$	2708.11			0.135352
$738$		0			0
$739$	−5627.68	−	3616.69i	−0.280132	−	0.180030i	0.393029	−	0.919526i	$-0.371427\pi$
$739$	−5627.68	−	3616.69i	−0.280132	−	0.180030i	−0.673160	+	0.739496i	$0.735064\pi$
$740$	−485.757	+	3378.51i	−0.0241308	+	0.167833i
$741$		0			0
$742$	2055.53	+	14296.5i	0.101699	+	0.707334i
$743$	22158.3	+	6506.25i	1.09409	+	0.321253i	0.778501	−	0.627643i	$-0.215980\pi$
$743$	22158.3	+	6506.25i	1.09409	+	0.321253i	0.315587	+	0.948896i	$0.397798\pi$
$744$		0			0
$745$	−1028.67	−	2252.47i	−0.0505873	−	0.110771i
$746$	−18892.8	+	5547.42i	−0.927230	+	0.272259i
$747$		0			0
$748$	416.767	−	480.975i	0.0203724	−	0.0235110i
$749$	−740.781	+	217.513i	−0.0361382	+	0.0106111i
$750$		0			0
$751$	21005.0	−	13499.1i	1.02062	−	0.655911i	0.0804980	−	0.996755i	$-0.474349\pi$
$751$	21005.0	−	13499.1i	1.02062	−	0.655911i	0.940120	+	0.340843i	$0.110713\pi$
$752$	−17497.0	−	5137.59i	−0.848472	−	0.249134i
$753$		0			0
$754$	−4282.94	+	9378.33i	−0.206864	+	0.452969i
$755$	−1078.73	+	7502.72i	−0.0519986	+	0.361658i
$756$		0			0
$757$	9793.45	+	11302.2i	0.470210	+	0.542651i	0.940470	−	0.339877i	$-0.110385\pi$
$757$	9793.45	+	11302.2i	0.470210	+	0.542651i	−0.470260	+	0.882528i	$0.655840\pi$
$758$	30014.4			1.43822
$759$		0			0
$760$	−8979.93			−0.428600
$761$	21740.9	+	25090.4i	1.03562	+	1.19517i	0.980465	+	0.196694i	$0.0630206\pi$
$761$	21740.9	+	25090.4i	1.03562	+	1.19517i	0.0551574	+	0.998478i	$0.482434\pi$
$762$		0			0
$763$	−2516.66	+	17503.8i	−0.119409	+	0.830510i
$764$	−1974.52	+	4323.60i	−0.0935022	+	0.204741i
$765$		0			0
$766$	10757.7	+	3158.74i	0.507430	+	0.148995i
$767$	875.216	−	562.467i	0.0412024	−	0.0264791i
$768$		0			0
$769$	−33192.2	+	9746.12i	−1.55649	+	0.457027i	−0.943033	−	0.332699i	$-0.892041\pi$
$769$	−33192.2	+	9746.12i	−1.55649	+	0.457027i	−0.613459	+	0.789727i	$0.710222\pi$
$770$	−742.772	+	857.205i	−0.0347632	+	0.0401189i
$771$		0			0
$772$	1218.17	−	357.686i	0.0567911	−	0.0166754i
$773$	−14295.0	−	31301.6i	−0.665141	−	1.45646i	−0.877653	−	0.479297i	$-0.840892\pi$
$773$	−14295.0	−	31301.6i	−0.665141	−	1.45646i	0.212512	−	0.977159i	$-0.431836\pi$
$774$		0			0
$775$	−15652.4	−	4595.97i	−0.725487	−	0.213022i
$776$	6509.14	+	45272.0i	0.301114	+	2.09429i
$777$		0			0
$778$	2761.14	−	19204.1i	0.127238	−	0.884963i
$779$	−12999.3	−	8354.17i	−0.597881	−	0.384235i
$780$		0			0
$781$	3809.83			0.174553
$782$	17476.9	−	51.7355i	0.799196	−	0.00236580i
$783$		0			0
$784$	−5700.68	−	6578.94i	−0.259689	−	0.299697i
$785$	16708.8	+	10738.1i	0.759698	+	0.488228i
$786$		0			0
$787$	−16949.7	+	37114.6i	−0.767714	+	1.68106i	−0.0360916	+	0.999348i	$0.511491\pi$
$787$	−16949.7	+	37114.6i	−0.767714	+	1.68106i	−0.731622	+	0.681710i	$0.761236\pi$
$788$	−943.723	−	6563.74i	−0.0426634	−	0.296730i
$789$		0			0
$790$	11895.8	−	7644.97i	0.535739	−	0.344299i
$791$	−3830.63	−	8387.92i	−0.172189	−	0.377042i
$792$		0			0
$793$	5408.57	−	6241.82i	0.242199	−	0.279513i
$794$	9001.20	−	10387.9i	0.402318	−	0.464300i
$795$		0			0
$796$	2536.32	+	5553.77i	0.112937	+	0.247297i
$797$	49.6073	−	31.8807i	0.00220474	−	0.00141690i	−0.539538	−	0.841961i	$-0.681401\pi$
$797$	49.6073	−	31.8807i	0.00220474	−	0.00141690i	0.541743	+	0.840544i	$0.317765\pi$
$798$		0			0
$799$	3731.36	+	25952.1i	0.165214	+	1.14909i
$800$	−2494.67	+	5462.57i	−0.110250	+	0.241414i
$801$		0			0
$802$	−13027.4	−	8372.17i	−0.573581	−	0.368618i
$803$	1010.46	+	1166.13i	0.0444063	+	0.0512476i
$804$		0			0
$805$	9949.99	−	29.4543i	0.435641	−	0.00128960i
$806$	−13889.7			−0.607000
$807$		0			0
$808$	36065.0	+	23177.6i	1.57025	+	1.00914i
$809$	−3071.12	+	21360.1i	−0.133467	+	0.928285i	0.807519	+	0.589841i	$0.200810\pi$
$809$	−3071.12	+	21360.1i	−0.133467	+	0.928285i	−0.940987	+	0.338444i	$0.890100\pi$
$810$		0			0
$811$	1474.00	+	10251.9i	0.0638215	+	0.443889i	0.996528	+	0.0832532i	$0.0265310\pi$
$811$	1474.00	+	10251.9i	0.0638215	+	0.443889i	−0.932707	+	0.360635i	$0.882560\pi$
$812$	−3906.17	−	1146.95i	−0.168817	−	0.0495692i
$813$		0			0
$814$	−1243.48	−	2722.85i	−0.0535431	−	0.117243i
$815$	−14459.5	+	4245.69i	−0.621464	+	0.182478i
$816$		0			0
$817$	−17067.8	+	19697.3i	−0.730879	+	0.843479i
$818$	−38287.2	+	11242.1i	−1.63653	+	0.480529i
$819$		0			0
$820$	3759.40	−	2416.02i	0.160103	−	0.102892i
$821$	−4626.14	−	1358.36i	−0.196655	−	0.0577430i	0.181922	−	0.983313i	$-0.441768\pi$
$821$	−4626.14	−	1358.36i	−0.196655	−	0.0577430i	−0.378577	+	0.925570i	$0.623586\pi$
$822$		0			0
$823$	−14726.3	+	32246.2i	−0.623727	+	1.36577i	0.289049	+	0.957314i	$0.406661\pi$
$823$	−14726.3	+	32246.2i	−0.623727	+	1.36577i	−0.912777	+	0.408458i	$0.866066\pi$
$824$	2884.30	−	20060.8i	0.121941	−	0.848118i
$825$		0			0
$826$	−842.148	−	971.891i	−0.0354747	−	0.0409400i
$827$	−23791.2			−1.00037			−0.500183	−	0.865920i	$-0.666734\pi$
$827$	−23791.2			−1.00037			−0.500183	+	0.865920i	$0.666734\pi$
$828$		0			0
$829$	−14874.3			−0.623167			−0.311584	−	0.950219i	$-0.600859\pi$
$829$	−14874.3			−0.623167			−0.311584	+	0.950219i	$0.600859\pi$
$830$	3503.36	+	4043.09i	0.146510	+	0.169082i
$831$		0			0
$832$	−1964.50	+	13663.4i	−0.0818593	+	0.569344i
$833$	−5199.41	+	11385.1i	−0.216265	+	0.473555i
$834$		0			0
$835$	4917.03	+	1443.77i	0.203785	+	0.0598368i
$836$	−412.510	+	265.104i	−0.0170657	+	0.0109675i
$837$		0			0
$838$	26318.5	−	7727.82i	1.08491	−	0.318560i
$839$	−7251.94	+	8369.18i	−0.298408	+	0.344382i	−0.885076	−	0.465446i	$-0.845894\pi$
$839$	−7251.94	+	8369.18i	−0.298408	+	0.344382i	0.586668	+	0.809828i	$0.300439\pi$
$840$		0			0
$841$	−5147.10	+	1511.33i	−0.211042	+	0.0619675i
$842$	−5301.06	−	11607.7i	−0.216968	−	0.475093i
$843$		0			0
$844$	−2039.51	−	598.853i	−0.0831785	−	0.0244234i
$845$	1693.80	+	11780.6i	0.0689569	+	0.479606i
$846$		0			0
$847$	2262.98	−	15739.3i	0.0918026	−	0.638501i
$848$	18123.3	+	11647.1i	0.733910	+	0.471655i
$849$		0			0
$850$	−11122.8			−0.448833
$851$	−10837.6	+	23918.1i	−0.436554	+	0.963457i
$852$		0			0
$853$	−19098.5	−	22040.9i	−0.766612	−	0.884718i	0.229455	−	0.973319i	$-0.426306\pi$
$853$	−19098.5	−	22040.9i	−0.766612	−	0.884718i	−0.996067	+	0.0886014i	$0.971760\pi$
$854$	−8588.39	−	5519.42i	−0.344132	−	0.221160i
$855$		0			0
$856$	−643.996	+	1410.16i	−0.0257142	+	0.0563062i
$857$	−1159.62	−	8065.34i	−0.0462216	−	0.321478i	−0.999794	−	0.0203132i	$-0.993534\pi$
$857$	−1159.62	−	8065.34i	−0.0462216	−	0.321478i	0.953572	−	0.301165i	$-0.0973754\pi$
$858$		0			0
$859$	−6179.53	+	3971.34i	−0.245452	+	0.157742i	−0.657583	−	0.753382i	$-0.728421\pi$
$859$	−6179.53	+	3971.34i	−0.245452	+	0.157742i	0.412131	+	0.911125i	$0.364785\pi$
$860$	−3131.19	−	6856.35i	−0.124154	−	0.271860i
$861$		0			0
$862$	3863.01	−	4458.15i	0.152639	−	0.176154i
$863$	15632.8	−	18041.2i	0.616623	−	0.711621i	−0.358439	−	0.933553i	$-0.616691\pi$
$863$	15632.8	−	18041.2i	0.616623	−	0.711621i	0.975062	+	0.221932i	$0.0712364\pi$
$864$		0			0
$865$	−1136.01	−	2487.51i	−0.0446536	−	0.0977778i
$866$	16991.0	−	10919.5i	0.666718	−	0.428474i
$867$		0			0
$868$	−780.532	−	5428.72i	−0.0305219	−	0.212284i
$869$	1645.65	−	3603.46i	0.0642402	−	0.140666i
$870$		0			0
$871$	10829.5	+	6959.73i	0.421292	+	0.270748i
$872$	23252.9	+	26835.3i	0.903031	+	1.04215i
$873$		0			0
$874$	−12931.4	−	3755.45i	−0.500469	−	0.145343i
$875$	−17608.2			−0.680302
$876$		0			0
$877$	−12745.3	−	8190.90i	−0.490738	−	0.315378i	0.271764	−	0.962364i	$-0.412393\pi$
$877$	−12745.3	−	8190.90i	−0.490738	−	0.315378i	−0.762502	+	0.646986i	$0.776029\pi$
$878$	3696.87	−	25712.3i	0.142099	−	0.988323i
$879$		0			0
$880$	240.765	+	1674.56i	0.00922293	+	0.0641469i
$881$	−8120.00	−	2384.25i	−0.310522	−	0.0911774i	0.122759	−	0.992437i	$-0.460826\pi$
$881$	−8120.00	−	2384.25i	−0.310522	−	0.0911774i	−0.433280	+	0.901259i	$0.642644\pi$
$882$		0			0
$883$	−20456.4	−	44793.3i	−0.779629	−	1.70715i	−0.704203	−	0.709999i	$-0.748696\pi$
$883$	−20456.4	−	44793.3i	−0.779629	−	1.70715i	−0.0754261	−	0.997151i	$-0.524032\pi$
$884$	2902.71	−	852.314i	0.110440	−	0.0324281i
$885$		0			0
$886$	14127.0	−	16303.5i	0.535673	−	0.618200i
$887$	27707.7	−	8135.70i	1.04885	−	0.307971i	0.288499	−	0.957480i	$-0.406844\pi$
$887$	27707.7	−	8135.70i	1.04885	−	0.307971i	0.760354	+	0.649509i	$0.225026\pi$
$888$		0			0
$889$	−12299.5	+	7904.42i	−0.464019	+	0.298207i
$890$	9961.78	+	2925.04i	0.375191	+	0.110166i
$891$		0			0
$892$	2502.35	−	5479.38i	0.0939291	−	0.205676i
$893$	2874.94	−	19995.7i	0.107734	−	0.749305i
$894$		0			0
$895$	−5442.94	−	6281.49i	−0.203282	−	0.234600i
$896$	8723.73			0.325267
$897$		0			0
$898$	7988.12			0.296845
$899$	−26249.3	−	30293.3i	−0.973818	−	1.12385i
$900$		0			0
$901$	4408.13	−	30659.2i	0.162992	−	1.13364i
$902$	−1628.03	+	3564.90i	−0.0600971	+	0.131594i
$903$		0			0
$904$	−17765.8	−	5216.50i	−0.653628	−	0.191923i
$905$	−8020.61	+	5154.54i	−0.294601	+	0.189329i
$906$		0			0
$907$	686.398	−	201.545i	0.0251284	−	0.00737837i	−0.269144	−	0.963100i	$-0.586741\pi$
$907$	686.398	−	201.545i	0.0251284	−	0.00737837i	0.294273	+	0.955722i	$0.404923\pi$
$908$	−3747.32	+	4324.64i	−0.136959	+	0.158060i
$909$		0			0
$910$	−5173.28	+	1519.01i	−0.188453	+	0.0553349i
$911$	6763.57	+	14810.2i	0.245979	+	0.538620i	0.991841	−	0.127481i	$-0.0406893\pi$
$911$	6763.57	+	14810.2i	0.245979	+	0.538620i	−0.745862	+	0.666101i	$0.767962\pi$
$912$		0			0
$913$	1438.02	+	422.240i	0.0521265	+	0.0153057i
$914$	−1042.84	−	7253.14i	−0.0377398	−	0.262486i
$915$		0			0
$916$	−1507.12	+	10482.2i	−0.0543631	+	0.378104i
$917$	2886.04	+	1854.75i	0.103932	+	0.0667930i
$918$		0			0
$919$	43308.7			1.55454			0.777270	−	0.629167i	$-0.216604\pi$
$919$	43308.7			1.55454			0.777270	+	0.629167i	$0.216604\pi$
$920$	13038.8	−	15137.9i	0.467258	−	0.542481i
$921$		0			0
$922$	30780.1	+	35522.1i	1.09945	+	1.26883i
$923$	15235.3	+	9791.10i	0.543309	+	0.349164i
$924$		0			0
$925$	6942.35	−	15201.6i	0.246771	−	0.540353i
$926$	−450.167	−	3130.98i	−0.0159756	−	0.111113i
$927$		0			0
$928$	−12413.3	+	7977.53i	−0.439101	+	0.282193i
$929$	−14616.6	−	32005.9i	−0.516206	−	1.13033i	−0.970856	−	0.239663i	$-0.922963\pi$
$929$	−14616.6	−	32005.9i	−0.516206	−	1.13033i	0.454650	−	0.890670i	$-0.349764\pi$
$930$		0			0
$931$	6315.15	−	7288.07i	0.222310	−	0.256559i
$932$	−5934.80	+	6849.13i	−0.208585	+	0.240720i
$933$		0			0
$934$	−5746.51	−	12583.1i	−0.201319	−	0.440826i
$935$	2046.27	−	1315.06i	0.0715726	−	0.0459969i
$936$		0			0
$937$	4315.22	+	30013.0i	0.150450	+	1.04640i	0.915467	+	0.402394i	$0.131822\pi$
$937$	4315.22	+	30013.0i	0.150450	+	1.04640i	−0.765016	+	0.644011i	$0.777269\pi$
$938$	6610.24	−	14474.4i	0.230098	−	0.503844i
$939$		0			0
$940$	4914.77	+	3158.53i	0.170534	+	0.109596i
$941$	−11515.2	−	13289.2i	−0.398919	−	0.460378i	0.520381	−	0.853934i	$-0.325790\pi$
$941$	−11515.2	−	13289.2i	−0.398919	−	0.460378i	−0.919300	+	0.393557i	$0.871245\pi$
$942$		0			0
$943$	32958.1	−	9783.43i	1.13814	−	0.337850i
$944$	−1918.12			−0.0661330
$945$		0			0
$946$	5560.88	+	3573.76i	0.191120	+	0.122826i
$947$	−4364.47	+	30355.5i	−0.149764	+	1.04163i	0.766842	+	0.641836i	$0.221827\pi$
$947$	−4364.47	+	30355.5i	−0.149764	+	1.04163i	−0.916606	+	0.399793i	$0.869082\pi$
$948$		0			0
$949$	1043.85	+	7260.12i	0.0357057	+	0.248339i
$950$	8222.76	+	2414.42i	0.280823	+	0.0824570i
$951$		0			0
$952$	−7969.83	−	17451.5i	−0.271327	−	0.594124i
$953$	−22856.2	+	6711.18i	−0.776899	+	0.228118i	−0.646061	−	0.763286i	$-0.723585\pi$
$953$	−22856.2	+	6711.18i	−0.776899	+	0.228118i	−0.130838	+	0.991404i	$0.541767\pi$
$954$		0			0
$955$	−11896.6	+	13729.4i	−0.403103	+	0.465206i
$956$	8736.97	−	2565.41i	0.295579	−	0.0867899i
$957$		0			0
$958$	12377.2	−	7954.34i	0.417421	−	0.268260i
$959$	15516.0	+	4555.92i	0.522459	+	0.153408i
$960$		0			0
$961$	10057.1	−	22022.0i	0.337589	−	0.739217i
$962$	2025.00	−	14084.2i	0.0678678	−	0.472031i
$963$		0			0
$964$	−8800.50	−	10156.3i	−0.294030	−	0.339329i
$965$	4852.40			0.161870
$966$		0			0
$967$	−3825.29			−0.127211			−0.0636055	−	0.997975i	$-0.520260\pi$
$967$	−3825.29			−0.127211			−0.0636055	+	0.997975i	$0.520260\pi$
$968$	−20908.9	−	24130.2i	−0.694255	−	0.801213i
$969$		0			0
$970$	−4849.12	+	33726.4i	−0.160511	+	1.11638i
$971$	15297.4	−	33496.5i	0.505577	−	1.10706i	−0.469039	−	0.883178i	$-0.655400\pi$
$971$	15297.4	−	33496.5i	0.505577	−	1.10706i	0.974616	−	0.223882i	$-0.0718731\pi$
$972$		0			0
$973$	5288.53	+	1552.85i	0.174247	+	0.0511636i
$974$	−372.222	+	239.212i	−0.0122451	+	0.00786947i
$975$		0			0
$976$	−14610.4	+	4290.01i	−0.479168	+	0.140697i
$977$	−23468.2	+	27083.8i	−0.768491	+	0.886885i	−0.996222	−	0.0868385i	$-0.972324\pi$
$977$	−23468.2	+	27083.8i	−0.768491	+	0.886885i	0.227732	+	0.973724i	$0.426869\pi$
$978$		0			0
$979$	2790.77	−	819.444i	0.0911066	−	0.0267513i
$980$	1158.55	+	2536.87i	0.0377638	+	0.0826911i
$981$		0			0
$982$	−10106.3	−	2967.47i	−0.328415	−	0.0964314i
$983$	−3622.33	−	25193.9i	−0.117533	−	0.817457i	−0.960258	−	0.279113i	$-0.909959\pi$
$983$	−3622.33	−	25193.9i	−0.117533	−	0.817457i	0.842726	−	0.538343i	$-0.180950\pi$
$984$		0			0
$985$	3606.92	−	25086.7i	0.116676	−	0.811501i
$986$	−22991.6	−	14775.8i	−0.742597	−	0.477238i
$987$		0			0
$988$	−2330.91			−0.0750567
$989$	−8422.36	−	57372.6i	−0.270794	−	1.84463i
$990$		0			0
$991$	−13832.2	−	15963.2i	−0.443383	−	0.511692i	0.489434	−	0.872040i	$-0.337203\pi$
$991$	−13832.2	−	15963.2i	−0.443383	−	0.511692i	−0.932818	+	0.360348i	$0.882658\pi$
$992$	−16723.2	−	10747.3i	−0.535243	−	0.343980i
$993$		0			0
$994$	9299.43	−	20362.9i	0.296741	−	0.649771i
$995$	3320.97	+	23097.9i	0.105811	+	0.735931i
$996$		0			0
$997$	6735.84	−	4328.86i	0.213968	−	0.137509i	−0.429267	−	0.903178i	$-0.641228\pi$
$997$	6735.84	−	4328.86i	0.213968	−	0.137509i	0.643235	+	0.765669i	$0.277592\pi$
$998$	12097.0	+	26488.7i	0.383691	+	0.840167i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.a.82.2		50
3.2	odd	2		23.4.c.a.13.4	✓	50
23.16	even	11	inner	207.4.i.a.154.2		50
69.50	odd	22		529.4.a.n.1.8		25
69.62	odd	22		23.4.c.a.16.4	yes	50
69.65	even	22		529.4.a.m.1.8		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.13.4	✓	50	3.2	odd	2
23.4.c.a.16.4	yes	50	69.62	odd	22
207.4.i.a.82.2		50	1.1	even	1	trivial
207.4.i.a.154.2		50	23.16	even	11	inner
529.4.a.m.1.8		25	69.65	even	22
529.4.a.n.1.8		25	69.50	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61249 - 1.86092i) q^{2} +(0.275643 - 1.91714i) q^{4} +(3.07518 - 6.73370i) q^{5} +(-11.6919 - 3.43306i) q^{7} +(-20.5838 + 13.2284i) q^{8} +O(q^{10})\)	\(q+(-1.61249 - 1.86092i) q^{2} +(0.275643 - 1.91714i) q^{4} +(3.07518 - 6.73370i) q^{5} +(-11.6919 - 3.43306i) q^{7} +(-20.5838 + 13.2284i) q^{8} +(-17.4896 + 5.13540i) q^{10} +(-3.34406 + 3.85925i) q^{11} +(-23.2908 + 6.83879i) q^{13} +(12.4645 + 27.2935i) q^{14} +(42.9410 + 12.6086i) q^{16} +(-9.15745 - 63.6914i) q^{17} +(-7.05564 + 49.0731i) q^{19} +(-12.0618 - 7.75163i) q^{20} +12.5740 q^{22} +(-72.4803 - 83.1481i) q^{23} +(45.9715 + 53.0540i) q^{25} +(50.2827 + 32.3147i) q^{26} +(-9.80444 + 21.4687i) q^{28} +(24.5481 + 170.736i) q^{29} +(-195.491 + 125.634i) q^{31} +(35.5364 + 77.8139i) q^{32} +(-103.758 + 119.743i) q^{34} +(-59.0720 + 68.1728i) q^{35} +(-98.8932 - 216.546i) q^{37} +(102.698 - 66.0001i) q^{38} +(25.7772 + 179.285i) q^{40} +(-129.476 + 283.513i) q^{41} +(442.252 + 284.218i) q^{43} +(6.47693 + 7.47478i) q^{44} +(-37.8577 + 268.956i) q^{46} -407.467 q^{47} +(-163.635 - 105.162i) q^{49} +(24.6002 - 171.098i) q^{50} +(6.69096 + 46.5367i) q^{52} +(461.872 + 135.618i) q^{53} +(15.7035 + 34.3858i) q^{55} +(286.078 - 84.0001i) q^{56} +(278.142 - 320.993i) q^{58} +(-41.1233 + 12.0749i) q^{59} +(-286.232 + 183.950i) q^{61} +(549.024 + 161.208i) q^{62} +(236.234 - 517.281i) q^{64} +(-25.5730 + 177.864i) q^{65} +(-347.288 - 400.792i) q^{67} -124.629 q^{68} +222.117 q^{70} +(-488.573 - 563.843i) q^{71} +(43.0026 - 299.090i) q^{73} +(-243.509 + 533.211i) q^{74} +(92.1349 + 27.0533i) q^{76} +(52.3475 - 33.6417i) q^{77} +(-744.340 + 218.558i) q^{79} +(216.954 - 250.378i) q^{80} +(736.374 - 216.219i) q^{82} +(-121.922 - 266.971i) q^{83} +(-457.040 - 134.199i) q^{85} +(-184.222 - 1281.29i) q^{86} +(17.7817 - 123.674i) q^{88} +(-479.164 - 307.940i) q^{89} +295.792 q^{91} +(-179.385 + 116.035i) q^{92} +(657.038 + 758.262i) q^{94} +(308.746 + 198.419i) q^{95} +(776.529 - 1700.36i) q^{97} +(68.1628 + 474.083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8}+O(q^{10}) \) 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8	\( 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8} + 47 q^{10} + 53 q^{11} - 65 q^{13} - 117 q^{14} - 499 q^{16} + 117 q^{17} + 73 q^{19} - 529 q^{20} + 310 q^{22} - 542 q^{23} + 246 q^{25} - 324 q^{26} - 677 q^{28} + 497 q^{29} - 471 q^{31} + 915 q^{32} - 2751 q^{34} + 737 q^{35} - 1071 q^{37} + 1504 q^{38} + 1479 q^{40} - 569 q^{41} + 1615 q^{43} - 2518 q^{44} + 4041 q^{46} - 2904 q^{47} + 1226 q^{49} - 1322 q^{50} - 2156 q^{52} - 391 q^{53} - 3323 q^{55} + 7028 q^{56} - 5639 q^{58} + 2445 q^{59} - 1059 q^{61} - 1468 q^{62} + 4570 q^{64} - 2641 q^{65} + 27 q^{67} - 8350 q^{68} + 9702 q^{70} - 3465 q^{71} + 435 q^{73} + 994 q^{74} - 3598 q^{76} + 5931 q^{77} - 2559 q^{79} + 14052 q^{80} - 3822 q^{82} + 3967 q^{83} + 299 q^{85} - 721 q^{86} + 5825 q^{88} - 3717 q^{89} + 7238 q^{91} - 9550 q^{92} + 6035 q^{94} - 4551 q^{95} - 2419 q^{97} + 5687 q^{98}+O(q^{100}) \) 50 * q + 11 * q^2 - 27 * q^4 + 19 * q^5 - 19 * q^7 - 28 * q^8 + 47 * q^10 + 53 * q^11 - 65 * q^13 - 117 * q^14 - 499 * q^16 + 117 * q^17 + 73 * q^19 - 529 * q^20 + 310 * q^22 - 542 * q^23 + 246 * q^25 - 324 * q^26 - 677 * q^28 + 497 * q^29 - 471 * q^31 + 915 * q^32 - 2751 * q^34 + 737 * q^35 - 1071 * q^37 + 1504 * q^38 + 1479 * q^40 - 569 * q^41 + 1615 * q^43 - 2518 * q^44 + 4041 * q^46 - 2904 * q^47 + 1226 * q^49 - 1322 * q^50 - 2156 * q^52 - 391 * q^53 - 3323 * q^55 + 7028 * q^56 - 5639 * q^58 + 2445 * q^59 - 1059 * q^61 - 1468 * q^62 + 4570 * q^64 - 2641 * q^65 + 27 * q^67 - 8350 * q^68 + 9702 * q^70 - 3465 * q^71 + 435 * q^73 + 994 * q^74 - 3598 * q^76 + 5931 * q^77 - 2559 * q^79 + 14052 * q^80 - 3822 * q^82 + 3967 * q^83 + 299 * q^85 - 721 * q^86 + 5825 * q^88 - 3717 * q^89 + 7238 * q^91 - 9550 * q^92 + 6035 * q^94 - 4551 * q^95 - 2419 * q^97 + 5687 * q^98

Introduction

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