LMFDB - Embedded newform 207.4.i.a.154.2

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			154.2
Character	$\chi$	$=$	207.154
Dual form			207.4.i.a.82.2

$q$-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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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	−0.965447	−	0.260599i	$-0.916080\pi$
$2$	−1.61249	+	1.86092i	−0.570103	+	0.657934i	0.395344	+	0.918533i	$0.370625\pi$
$3$		0			0
$3$		0			0
$4$	0.275643	+	1.91714i	0.0344553	+	0.239642i
$5$	3.07518	+	6.73370i	0.275052	+	0.602281i	0.995865	−	0.0908496i	$-0.0289582\pi$
$5$	3.07518	+	6.73370i	0.275052	+	0.602281i	−0.720812	+	0.693130i	$0.756231\pi$
$6$		0			0
$7$	−11.6919	+	3.43306i	−0.631305	+	0.185368i	−0.581703	−	0.813401i	$-0.697613\pi$
$7$	−11.6919	+	3.43306i	−0.631305	+	0.185368i	−0.0496020	+	0.998769i	$0.515795\pi$
$8$	−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	0.708066	−	0.706146i	$-0.249568\pi$
$11$	−3.34406	−	3.85925i	−0.0916610	−	0.105782i	−0.799727	+	0.600364i	$0.795022\pi$
$12$		0			0
$13$	−23.2908	−	6.83879i	−0.496900	−	0.145903i	0.0236737	−	0.999720i	$-0.492464\pi$
$13$	−23.2908	−	6.83879i	−0.496900	−	0.145903i	−0.520574	+	0.853817i	$0.674282\pi$
$14$	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	0.814065	+	0.580774i	$0.197250\pi$
$17$	−9.15745	+	63.6914i	−0.130647	+	0.908673i	−0.944713	+	0.327900i	$0.893659\pi$
$18$		0			0
$19$	−7.05564	−	49.0731i	−0.0851935	−	0.592534i	−0.987040	−	0.160476i	$-0.948697\pi$
$19$	−7.05564	−	49.0731i	−0.0851935	−	0.592534i	0.901846	−	0.432057i	$-0.142212\pi$
$20$	−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	−0.746594	−	0.665280i	$-0.768312\pi$
$29$	24.5481	−	170.736i	0.157189	−	1.09327i	0.903783	−	0.427992i	$-0.140779\pi$
$30$		0			0
$31$	−195.491	−	125.634i	−1.13262	−	0.727891i	−0.166515	−	0.986039i	$-0.553251\pi$
$31$	−195.491	−	125.634i	−1.13262	−	0.727891i	−0.966105	+	0.258148i	$0.916888\pi$
$32$	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	0.552303	+	0.833643i	$0.313749\pi$
$37$	−98.8932	+	216.546i	−0.439404	+	0.962161i	−0.991707	+	0.128517i	$0.958978\pi$
$38$	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	−0.978623	−	0.205662i	$-0.934065\pi$
$41$	−129.476	−	283.513i	−0.493190	−	1.07994i	0.485433	−	0.874274i	$-0.338662\pi$
$42$		0			0
$43$	442.252	−	284.218i	1.56844	−	1.00797i	0.588540	−	0.808468i	$-0.299703\pi$
$43$	442.252	−	284.218i	1.56844	−	1.00797i	0.979897	−	0.199505i	$-0.0639336\pi$
$44$	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	0.378318	−	0.925676i	$-0.376503\pi$
$53$	461.872	−	135.618i	1.19704	−	0.351482i	0.818719	+	0.574194i	$0.194684\pi$
$54$		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	0.236046	−	0.971742i	$-0.424148\pi$
$59$	−41.1233	−	12.0749i	−0.0907423	−	0.0266443i	−0.326789	+	0.945097i	$0.605966\pi$
$60$		0			0
$61$	−286.232	−	183.950i	−0.600791	−	0.386105i	0.204603	−	0.978845i	$-0.434410\pi$
$61$	−286.232	−	183.950i	−0.600791	−	0.386105i	−0.805394	+	0.592740i	$0.798046\pi$
$62$	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	−0.978167	−	0.207821i	$-0.933363\pi$
$67$	−347.288	+	400.792i	−0.633254	+	0.730814i	0.344913	+	0.938635i	$0.387908\pi$
$68$	−124.629			−0.222258
$69$		0			0
$70$	222.117			0.379258
$71$	−488.573	+	563.843i	−0.816661	+	0.942477i	−0.999170	−	0.0407268i	$-0.987033\pi$
$71$	−488.573	+	563.843i	−0.816661	+	0.942477i	0.182509	+	0.983204i	$0.441578\pi$
$72$		0			0
$73$	43.0026	+	299.090i	0.0689462	+	0.479532i	0.994816	+	0.101689i	$0.0324248\pi$
$73$	43.0026	+	299.090i	0.0689462	+	0.479532i	−0.925870	+	0.377842i	$0.876666\pi$
$74$	−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	−0.295185	−	0.955440i	$-0.595381\pi$
$79$	−744.340	−	218.558i	−1.06006	−	0.311262i	−0.764876	+	0.644178i	$0.777200\pi$
$80$	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	−0.972957	−	0.230988i	$-0.925804\pi$
$83$	−121.922	+	266.971i	−0.161236	+	0.353059i	0.811720	+	0.584047i	$0.198531\pi$
$84$		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	−0.793935	−	0.608003i	$-0.791971\pi$
$89$	−479.164	+	307.940i	−0.570689	+	0.366760i	0.223246	+	0.974762i	$0.428335\pi$
$90$		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	0.594733	+	0.803923i	$0.297258\pi$
$97$	776.529	+	1700.36i	0.812830	+	1.77985i	0.218097	+	0.975927i	$0.430015\pi$
$98$	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	0.100896	+	0.994897i	$0.467829\pi$
$101$	−727.853	+	1593.78i	−0.717070	+	1.57016i	−0.817966	+	0.575267i	$0.804898\pi$
$102$		0			0
$103$	−542.427	−	625.994i	−0.518902	−	0.598845i	0.434453	−	0.900694i	$-0.356942\pi$
$103$	−542.427	−	625.994i	−0.518902	−	0.598845i	−0.953356	+	0.301849i	$0.902396\pi$
$104$	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	0.564498	−	0.825435i	$-0.309070\pi$
$107$	53.3004	+	34.2541i	0.0481565	+	0.0309483i	−0.516341	+	0.856383i	$0.672706\pi$
$108$		0			0
$109$	−206.529	+	1436.44i	−0.181485	+	1.26226i	0.671769	+	0.740761i	$0.265535\pi$
$109$	−206.529	+	1436.44i	−0.181485	+	1.26226i	−0.853254	+	0.521495i	$0.825374\pi$
$110$	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	−0.511004	−	0.859578i	$-0.670726\pi$
$113$	495.556	−	571.902i	0.412549	−	0.476107i	0.923553	+	0.383472i	$0.125272\pi$
$114$		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	0.960646	−	0.277775i	$-0.0895970\pi$
$127$	785.716	+	906.764i	0.548984	+	0.633562i	−0.411662	+	0.911337i	$0.635052\pi$
$128$	−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	−0.370570	−	0.928805i	$-0.620838\pi$
$131$	−270.130	+	79.3174i	−0.180163	+	0.0529007i	0.190407	+	0.981705i	$0.439019\pi$
$132$		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	0.812768	−	0.582588i	$-0.197960\pi$
$149$	219.055	+	252.803i	0.120441	+	0.138996i	−0.692327	+	0.721584i	$0.743414\pi$
$150$		0			0
$151$	−982.460	−	288.476i	−0.529480	−	0.155469i	0.00605610	−	0.999982i	$-0.498072\pi$
$151$	−982.460	−	288.476i	−0.529480	−	0.155469i	−0.535536	+	0.844512i	$0.679890\pi$
$152$	−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	−0.821008	−	0.570916i	$-0.806588\pi$
$157$	−381.839	−	2655.75i	−0.194102	−	1.35001i	0.626906	−	0.779095i	$-0.284321\pi$
$158$	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	−0.979482	−	0.201533i	$-0.935408\pi$
$163$	−1333.13	+	1538.51i	−0.640605	+	0.739297i	0.338877	+	0.940831i	$0.389953\pi$
$164$	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	−0.954182	−	0.299226i	$-0.903271\pi$
$167$	98.5196	−	685.219i	0.0456508	−	0.317508i	0.999833	−	0.0182815i	$-0.00581951\pi$
$168$		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	0.806413	−	0.591353i	$-0.201406\pi$
$173$	241.913	+	279.183i	0.106314	+	0.122693i	−0.700099	+	0.714046i	$0.746861\pi$
$174$		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	0.981666	−	0.190608i	$-0.0610459\pi$
$179$	466.422	+	1021.32i	0.194760	+	0.426464i	−0.786906	+	0.617072i	$0.788319\pi$
$180$		0			0
$181$	−1083.48	+	696.308i	−0.444940	+	0.285946i	−0.743864	−	0.668332i	$-0.767009\pi$
$181$	−1083.48	+	696.308i	−0.444940	+	0.285946i	0.298924	+	0.954277i	$0.403372\pi$
$182$	−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	−0.695455	−	0.718569i	$-0.744797\pi$
$191$	−2354.65	+	691.386i	−0.892022	+	0.261921i	−0.196566	+	0.980490i	$0.562979\pi$
$192$		0			0
$193$	272.302	−	596.258i	0.101558	−	0.222381i	−0.852032	−	0.523490i	$-0.824630\pi$
$193$	272.302	−	596.258i	0.101558	−	0.222381i	0.953590	+	0.301109i	$0.0973569\pi$
$194$	−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	0.815279	−	0.579069i	$-0.196584\pi$
$197$	3285.04	+	964.574i	1.18807	+	0.348848i	0.372788	+	0.927917i	$0.378402\pi$
$198$		0			0
$199$	−2651.88	−	1704.26i	−0.944656	−	0.607094i	−0.0249449	−	0.999689i	$-0.507941\pi$
$199$	−2651.88	−	1704.26i	−0.944656	−	0.607094i	−0.919711	+	0.392595i	$0.871577\pi$
$200$	−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	0.999308	+	0.0371954i	$0.0118424\pi$
$211$	156.184	+	1086.29i	0.0509581	+	0.354422i	−0.948350	+	0.317226i	$0.897249\pi$
$212$	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	0.198918	−	0.980016i	$-0.436257\pi$
$223$	2984.08	−	876.206i	0.896094	−	0.263117i	0.697177	+	0.716899i	$0.254439\pi$
$224$	−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	−0.850967	−	0.525220i	$-0.823983\pi$
$227$	−2485.44	+	1597.29i	−0.726714	+	0.467031i	0.124252	+	0.992251i	$0.460347\pi$
$228$		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	−0.960585	−	0.277985i	$-0.910333\pi$
$233$	−3936.30	+	2529.71i	−1.10676	+	0.711273i	−0.146177	+	0.989258i	$0.546697\pi$
$234$		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	−0.437512	−	0.899213i	$-0.644140\pi$
$239$	1953.01	−	4276.50i	0.528577	−	1.15742i	0.966089	−	0.258210i	$-0.0831325\pi$
$240$		0			0
$241$	4543.72	+	5243.73i	1.21447	+	1.40157i	0.890179	+	0.455611i	$0.150579\pi$
$241$	4543.72	+	5243.73i	1.21447	+	1.40157i	0.324288	+	0.945959i	$0.394875\pi$
$242$	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	0.247176	−	0.968970i	$-0.420497\pi$
$251$	4657.01	−	5374.48i	1.17111	−	1.35153i	0.923931	−	0.382559i	$-0.124957\pi$
$252$		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	0.971949	+	0.235191i	$0.0755717\pi$
$257$	435.206	+	3026.92i	0.105632	+	0.734686i	−0.866317	+	0.499494i	$0.833519\pi$
$258$		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	−0.673242	−	0.739423i	$-0.735099\pi$
$263$	−6992.15	−	2053.08i	−1.63937	−	0.481363i	−0.966129	+	0.258060i	$0.916917\pi$
$264$		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	−0.332732	−	0.943021i	$-0.607971\pi$
$269$	−453.585	+	133.184i	−0.102809	+	0.0301874i	0.229924	+	0.973209i	$0.426152\pi$
$270$		0			0
$271$	1041.19	+	2279.88i	0.233386	+	0.511045i	0.989699	−	0.143166i	$-0.0457282\pi$
$271$	1041.19	+	2279.88i	0.233386	+	0.511045i	−0.756312	+	0.654211i	$0.773001\pi$
$272$	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	0.947910	−	0.318539i	$-0.103192\pi$
$281$	407.100	+	891.425i	0.0864255	+	0.189245i	−0.861484	+	0.507784i	$0.830465\pi$
$282$		0			0
$283$	7016.80	−	2060.32i	1.47387	−	0.432768i	0.556516	−	0.830837i	$-0.312138\pi$
$283$	7016.80	−	2060.32i	1.47387	−	0.432768i	0.917355	+	0.398070i	$0.130320\pi$
$284$	−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	−0.772818	−	0.634628i	$-0.781153\pi$
$293$	739.718	−	5144.85i	0.147491	−	1.02582i	0.920309	−	0.391193i	$-0.127938\pi$
$294$		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	0.491384	−	0.870943i	$-0.336491\pi$
$307$	−520.294	−	334.373i	−0.0967256	−	0.0621618i	−0.588109	+	0.808781i	$0.700128\pi$
$308$	−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	0.944211	−	0.329341i	$-0.106827\pi$
$311$	2653.68	+	3062.51i	0.483847	+	0.558389i	−0.460364	+	0.887730i	$0.652281\pi$
$312$		0			0
$313$	−1558.02	+	3411.58i	−0.281356	+	0.616083i	−0.996564	−	0.0828284i	$-0.973605\pi$
$313$	−1558.02	+	3411.58i	−0.281356	+	0.616083i	0.715208	+	0.698912i	$0.246332\pi$
$314$	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	0.982116	−	0.188277i	$-0.0602903\pi$
$317$	1110.05	+	2430.66i	0.196677	+	0.430662i	−0.785439	+	0.618939i	$0.787563\pi$
$318$		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	−0.476750	−	0.879039i	$-0.658185\pi$
$331$	3009.73	−	6590.40i	0.499788	−	1.09438i	0.976538	−	0.215345i	$-0.0690876\pi$
$332$	−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	0.708141	−	0.706071i	$-0.249534\pi$
$337$	2227.44	+	1431.49i	0.360049	+	0.231389i	−0.348092	+	0.937460i	$0.613170\pi$
$338$	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	−0.999520	−	0.0309706i	$-0.990140\pi$
$347$	−5343.17	+	6166.35i	−0.826618	+	0.953968i	0.172902	+	0.984939i	$0.444686\pi$
$348$		0			0
$349$	−301.911	−	2099.84i	−0.0463064	−	0.322068i	−0.999787	−	0.0206153i	$-0.993437\pi$
$349$	−301.911	−	2099.84i	−0.0463064	−	0.322068i	0.953481	−	0.301453i	$-0.0974716\pi$
$350$	−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	0.526119	−	0.850411i	$-0.323647\pi$
$353$	−191.567	−	123.113i	−0.0288841	−	0.0185627i	−0.555003	+	0.831848i	$0.687283\pi$
$354$		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	−0.973950	−	0.226761i	$-0.927186\pi$
$359$	−1120.81	+	2454.23i	−0.164774	+	0.360805i	0.809176	+	0.587566i	$0.199914\pi$
$360$		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	0.987229	+	0.159310i	$0.0509271\pi$
$373$	3321.90	+	7273.95i	0.461130	+	1.00973i	−0.526098	+	0.850424i	$0.676346\pi$
$374$	−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	−0.966898	−	0.255161i	$-0.917871\pi$
$379$	−7982.32	−	9212.09i	−1.08186	−	1.24853i	−0.114960	−	0.993370i	$-0.536674\pi$
$380$	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	0.259577	−	0.965722i	$-0.416417\pi$
$383$	−3830.50	−	2461.71i	−0.511042	−	0.328427i	−0.770620	+	0.637295i	$0.780053\pi$
$384$		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	−0.312238	−	0.950004i	$-0.601079\pi$
$389$	5159.85	−	5954.79i	0.672532	−	0.776143i	0.984770	+	0.173860i	$0.0556242\pi$
$390$		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	−0.875942	−	0.482417i	$-0.839759\pi$
$397$	794.424	−	5525.34i	0.100431	−	0.698511i	0.976373	−	0.216094i	$-0.0693318\pi$
$398$	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	0.634963	−	0.772543i	$-0.281015\pi$
$401$	6034.23	+	1771.81i	0.751459	+	0.220648i	0.116497	+	0.993191i	$0.462834\pi$
$402$		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	0.589743	+	0.807591i	$0.299229\pi$
$409$	6732.02	+	14741.1i	0.813880	+	1.78215i	0.224137	+	0.974558i	$0.428044\pi$
$410$	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	−0.961493	−	0.274828i	$-0.911379\pi$
$419$	−4627.57	−	10133.0i	−0.539550	−	1.18145i	0.421943	−	0.906622i	$-0.361348\pi$
$420$		0			0
$421$	4972.49	−	1460.05i	0.575639	−	0.169023i	0.0190613	−	0.999818i	$-0.493932\pi$
$421$	4972.49	−	1460.05i	0.575639	−	0.169023i	0.556578	+	0.830795i	$0.312114\pi$
$422$	−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	−0.961860	−	0.273541i	$-0.911805\pi$
$431$	340.940	−	2371.29i	0.0381032	−	0.265014i	0.999964	+	0.00852704i	$0.00271427\pi$
$432$		0			0
$433$	−1167.33	−	8118.95i	−0.129557	−	0.901090i	−0.946116	−	0.323828i	$-0.895030\pi$
$433$	−1167.33	−	8118.95i	−0.129557	−	0.901090i	0.816559	−	0.577262i	$-0.195879\pi$
$434$	−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	−0.243591	−	0.969878i	$-0.578326\pi$
$439$	6908.50	−	7972.83i	0.751081	−	0.866794i	0.994673	+	0.103084i	$0.0328710\pi$
$440$	−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	−0.806925	−	0.590654i	$-0.798870\pi$
$443$	1246.82	−	8671.80i	0.133720	−	0.930045i	0.940645	−	0.339391i	$-0.110221\pi$
$444$		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	0.633039	−	0.774120i	$-0.281807\pi$
$449$	−2124.44	−	2451.73i	−0.223293	−	0.257694i	−0.856332	+	0.516426i	$0.827262\pi$
$450$		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	−0.406206	−	0.913782i	$-0.633148\pi$
$457$	2503.50	−	1608.90i	0.256255	−	0.164685i	0.662461	+	0.749096i	$0.269512\pi$
$458$	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	−0.485279	−	0.874360i	$-0.661282\pi$
$463$	1080.69	−	694.517i	0.108475	−	0.0697126i	0.593753	+	0.804647i	$0.297645\pi$
$464$	−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	−0.00353939	−	0.999994i	$-0.501127\pi$
$467$	5390.32	−	1582.74i	0.534121	−	0.156832i	0.537660	+	0.843162i	$0.319308\pi$
$468$		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	−0.989334	−	0.145665i	$-0.953468\pi$
$479$	−850.347	−	5914.29i	−0.0811135	−	0.564157i	0.908221	−	0.418492i	$-0.137441\pi$
$480$		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	0.990977	−	0.134035i	$-0.0427935\pi$
$487$	25.5727	+	177.862i	0.00237948	+	0.0165497i	−0.988597	+	0.150585i	$0.951884\pi$
$488$	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	0.695468	−	0.718557i	$-0.255197\pi$
$491$	3598.54	+	2312.64i	0.330753	+	0.212562i	−0.364715	+	0.931119i	$0.618833\pi$
$492$		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	−0.747812	−	0.663910i	$-0.768896\pi$
$499$	−11347.2	+	3331.83i	−1.01798	+	0.298905i	−0.270163	+	0.962815i	$0.587078\pi$
$500$	−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	−0.303132	−	0.952949i	$-0.598032\pi$
$503$	4938.59	−	3173.84i	0.437775	−	0.281341i	0.740907	+	0.671608i	$0.234396\pi$
$504$		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	−0.00283219	−	0.999996i	$-0.500902\pi$
$509$	10399.7	−	6683.51i	0.905620	−	0.582006i	0.908452	+	0.417990i	$0.137265\pi$
$510$		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	0.999215	+	0.0396159i	$0.0126134\pi$
$521$	17247.5	+	11084.3i	1.45034	+	0.932077i	0.451125	+	0.892461i	$0.351023\pi$
$522$		0			0
$523$	975.984	−	6788.12i	0.0816000	−	0.567540i	−0.907473	−	0.420111i	$-0.861991\pi$
$523$	975.984	−	6788.12i	0.0816000	−	0.567540i	0.989073	−	0.147429i	$-0.0470998\pi$
$524$	−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	0.999998	−	0.00217860i	$-0.000693472\pi$
$541$	10765.4	+	12423.9i	0.855527	+	0.987330i	−0.144471	+	0.989509i	$0.546148\pi$
$542$	−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	0.980147	+	0.198274i	$0.0635334\pi$
$547$	6244.80	+	13674.2i	0.488132	+	1.06886i	−0.492014	+	0.870587i	$0.663739\pi$
$548$	−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	0.980864	−	0.194695i	$-0.0623716\pi$
$557$	2516.00	+	5509.28i	0.191394	+	0.419095i	−0.789470	+	0.613789i	$0.789644\pi$
$558$		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	0.510407	−	0.859933i	$-0.329495\pi$
$563$	−5522.61	−	6373.43i	−0.413411	−	0.477102i	−0.923818	+	0.382831i	$0.874949\pi$
$564$		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	0.856300	+	0.516479i	$0.172758\pi$
$569$	−1504.17	+	10461.7i	−0.110823	+	0.770790i	−0.967123	+	0.254311i	$0.918151\pi$
$570$		0			0
$571$	−1363.76	−	9485.16i	−0.0999502	−	0.695169i	−0.976761	−	0.214333i	$-0.931242\pi$
$571$	−1363.76	−	9485.16i	−0.0999502	−	0.695169i	0.876810	−	0.480836i	$-0.159667\pi$
$572$	−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	−0.972568	−	0.232620i	$-0.925270\pi$
$577$	−8370.12	+	9659.63i	−0.603904	+	0.696942i	0.368664	+	0.929563i	$0.379815\pi$
$578$	−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	0.991244	−	0.132041i	$-0.0421529\pi$
$587$	10232.3	+	11808.8i	0.719479	+	0.830323i	−0.271765	+	0.962364i	$0.587607\pi$
$588$		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	0.911883	+	0.410451i	$0.134629\pi$
$593$	9024.22	+	19760.3i	0.624925	+	1.36839i	−0.286958	+	0.957943i	$0.592644\pi$
$594$		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	−0.748798	−	0.662798i	$-0.769369\pi$
$601$	−6732.69	+	4326.84i	−0.456959	+	0.293669i	0.291840	+	0.956467i	$0.405733\pi$
$602$	−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	0.535455	+	0.844564i	$0.320140\pi$
$607$	−6781.63	+	14849.7i	−0.453472	+	0.992966i	−0.988927	+	0.148402i	$0.952587\pi$
$608$	−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	0.823367	−	0.567509i	$-0.192093\pi$
$613$	9852.75	+	6331.98i	0.649183	+	0.417204i	−0.174185	+	0.984713i	$0.555729\pi$
$614$	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	0.881519	+	0.472148i	$0.156521\pi$
$617$	2585.91	+	17985.4i	0.168727	+	1.17352i	−0.712792	+	0.701375i	$0.752570\pi$
$618$		0			0
$619$	−9589.91	+	11067.3i	−0.622700	+	0.718634i	−0.976217	−	0.216794i	$-0.930440\pi$
$619$	−9589.91	+	11067.3i	−0.622700	+	0.718634i	0.353518	+	0.935428i	$0.384985\pi$
$620$	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	0.561098	−	0.827749i	$-0.310379\pi$
$631$	9282.21	+	2725.50i	0.585609	+	0.171950i	0.0245107	+	0.999700i	$0.492197\pi$
$632$	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	0.00386677	−	0.999993i	$-0.498769\pi$
$641$	14851.0	−	9544.14i	0.915098	−	0.588098i	0.911232	+	0.411895i	$0.135133\pi$
$642$		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	−0.539465	+	0.842008i	$0.681373\pi$
$647$	−25171.1	+	16176.5i	−1.52948	+	0.982940i	−0.990019	+	0.140931i	$0.954990\pi$
$648$		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	−0.922276	−	0.386532i	$-0.873673\pi$
$653$	−437.066	+	957.040i	−0.0261925	+	0.0573536i	0.896084	+	0.443885i	$0.146400\pi$
$654$		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	0.555072	−	0.831803i	$-0.312691\pi$
$659$	490.976	+	315.531i	0.0290223	+	0.0186515i	−0.526049	+	0.850454i	$0.676327\pi$
$660$		0			0
$661$	−2295.98	+	15968.9i	−0.135103	+	0.939663i	0.803657	+	0.595092i	$0.202885\pi$
$661$	−2295.98	+	15968.9i	−0.135103	+	0.939663i	−0.938760	+	0.344571i	$0.888025\pi$
$662$	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	−0.967824	−	0.251629i	$-0.919034\pi$
$673$	553.254	−	3847.97i	0.0316885	−	0.220398i	0.999512	+	0.0312309i	$0.00994271\pi$
$674$	−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	0.217637	−	0.976030i	$-0.430165\pi$
$677$	−2236.35	−	656.650i	−0.126957	−	0.0372779i	−0.344594	+	0.938752i	$0.611983\pi$
$678$		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	−0.750117	−	0.661306i	$-0.770003\pi$
$683$	−18271.4	+	5364.97i	−1.02363	+	0.300564i	−0.273509	+	0.961869i	$0.588184\pi$
$684$		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	−0.996478	−	0.0838528i	$-0.973277\pi$
$701$	−17403.0	−	20084.1i	−0.937664	−	1.08212i	0.0588143	−	0.998269i	$-0.481268\pi$
$702$		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	0.999830	+	0.0184294i	$0.00586660\pi$
$709$	862.606	+	5999.56i	0.0456923	+	0.317797i	−0.954138	+	0.299368i	$0.903224\pi$
$710$	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	−0.908414	−	0.418072i	$-0.862706\pi$
$719$	1561.39	−	10859.7i	0.0809874	−	0.563280i	0.989401	−	0.145207i	$-0.0463850\pi$
$720$		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	−0.600248	−	0.799814i	$-0.704932\pi$
$727$	7787.70	−	17052.7i	0.397290	−	0.869943i	0.997538	−	0.0701294i	$-0.0223412\pi$
$728$	−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	−0.424934	+	0.905224i	$0.639703\pi$
$733$	−28277.0	+	18172.6i	−1.42488	+	0.915714i	−0.999945	+	0.0104903i	$0.996661\pi$
$734$	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	−0.673160	−	0.739496i	$-0.735064\pi$
$739$	−5627.68	+	3616.69i	−0.280132	+	0.180030i	0.393029	+	0.919526i	$0.371427\pi$
$740$	−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	0.315587	−	0.948896i	$-0.397798\pi$
$743$	22158.3	−	6506.25i	1.09409	−	0.321253i	0.778501	+	0.627643i	$0.215980\pi$
$744$		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	0.940120	−	0.340843i	$-0.110713\pi$
$751$	21005.0	+	13499.1i	1.02062	+	0.655911i	0.0804980	+	0.996755i	$0.474349\pi$
$752$	−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	−0.470260	−	0.882528i	$-0.655840\pi$
$757$	9793.45	−	11302.2i	0.470210	−	0.542651i	0.940470	+	0.339877i	$0.110385\pi$
$758$	30014.4			1.43822
$759$		0			0
$760$	−8979.93			−0.428600
$761$	21740.9	−	25090.4i	1.03562	−	1.19517i	0.0551574	−	0.998478i	$-0.482434\pi$
$761$	21740.9	−	25090.4i	1.03562	−	1.19517i	0.980465	−	0.196694i	$-0.0630206\pi$
$762$		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	−0.613459	−	0.789727i	$-0.710222\pi$
$769$	−33192.2	−	9746.12i	−1.55649	−	0.457027i	−0.943033	+	0.332699i	$0.892041\pi$
$770$	−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	0.212512	+	0.977159i	$0.431836\pi$
$773$	−14295.0	+	31301.6i	−0.665141	+	1.45646i	−0.877653	+	0.479297i	$0.840892\pi$
$774$		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	−0.731622	−	0.681710i	$-0.761236\pi$
$787$	−16949.7	−	37114.6i	−0.767714	−	1.68106i	−0.0360916	−	0.999348i	$-0.511491\pi$
$788$	−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	0.541743	−	0.840544i	$-0.317765\pi$
$797$	49.6073	+	31.8807i	0.00220474	+	0.00141690i	−0.539538	+	0.841961i	$0.681401\pi$
$798$		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	−0.940987	−	0.338444i	$-0.890100\pi$
$809$	−3071.12	−	21360.1i	−0.133467	−	0.928285i	0.807519	−	0.589841i	$-0.200810\pi$
$810$		0			0
$811$	1474.00	−	10251.9i	0.0638215	−	0.443889i	−0.932707	−	0.360635i	$-0.882560\pi$
$811$	1474.00	−	10251.9i	0.0638215	−	0.443889i	0.996528	−	0.0832532i	$-0.0265310\pi$
$812$	−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	−0.378577	−	0.925570i	$-0.623586\pi$
$821$	−4626.14	+	1358.36i	−0.196655	+	0.0577430i	0.181922	+	0.983313i	$0.441768\pi$
$822$		0			0
$823$	−14726.3	−	32246.2i	−0.623727	−	1.36577i	−0.912777	−	0.408458i	$-0.866066\pi$
$823$	−14726.3	−	32246.2i	−0.623727	−	1.36577i	0.289049	−	0.957314i	$-0.406661\pi$
$824$	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	0.586668	−	0.809828i	$-0.300439\pi$
$839$	−7251.94	−	8369.18i	−0.298408	−	0.344382i	−0.885076	+	0.465446i	$0.845894\pi$
$840$		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	−0.996067	−	0.0886014i	$-0.971760\pi$
$853$	−19098.5	+	22040.9i	−0.766612	+	0.884718i	0.229455	+	0.973319i	$0.426306\pi$
$854$	−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	0.953572	+	0.301165i	$0.0973754\pi$
$857$	−1159.62	+	8065.34i	−0.0462216	+	0.321478i	−0.999794	+	0.0203132i	$0.993534\pi$
$858$		0			0
$859$	−6179.53	−	3971.34i	−0.245452	−	0.157742i	0.412131	−	0.911125i	$-0.364785\pi$
$859$	−6179.53	−	3971.34i	−0.245452	−	0.157742i	−0.657583	+	0.753382i	$0.728421\pi$
$860$	−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	0.975062	−	0.221932i	$-0.0712364\pi$
$863$	15632.8	+	18041.2i	0.616623	+	0.711621i	−0.358439	+	0.933553i	$0.616691\pi$
$864$		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	−0.762502	−	0.646986i	$-0.776029\pi$
$877$	−12745.3	+	8190.90i	−0.490738	+	0.315378i	0.271764	+	0.962364i	$0.412393\pi$
$878$	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	−0.433280	−	0.901259i	$-0.642644\pi$
$881$	−8120.00	+	2384.25i	−0.310522	+	0.0911774i	0.122759	+	0.992437i	$0.460826\pi$
$882$		0			0
$883$	−20456.4	+	44793.3i	−0.779629	+	1.70715i	−0.0754261	+	0.997151i	$0.524032\pi$
$883$	−20456.4	+	44793.3i	−0.779629	+	1.70715i	−0.704203	+	0.709999i	$0.748696\pi$
$884$	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	0.760354	−	0.649509i	$-0.225026\pi$
$887$	27707.7	+	8135.70i	1.04885	+	0.307971i	0.288499	+	0.957480i	$0.406844\pi$
$888$		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	0.294273	−	0.955722i	$-0.404923\pi$
$907$	686.398	+	201.545i	0.0251284	+	0.00737837i	−0.269144	+	0.963100i	$0.586741\pi$
$908$	−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	−0.745862	−	0.666101i	$-0.767962\pi$
$911$	6763.57	−	14810.2i	0.245979	−	0.538620i	0.991841	+	0.127481i	$0.0406893\pi$
$912$		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	0.454650	+	0.890670i	$0.349764\pi$
$929$	−14616.6	+	32005.9i	−0.516206	+	1.13033i	−0.970856	+	0.239663i	$0.922963\pi$
$930$		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	−0.765016	−	0.644011i	$-0.777269\pi$
$937$	4315.22	−	30013.0i	0.150450	−	1.04640i	0.915467	−	0.402394i	$-0.131822\pi$
$938$	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	−0.919300	−	0.393557i	$-0.871245\pi$
$941$	−11515.2	+	13289.2i	−0.398919	+	0.460378i	0.520381	+	0.853934i	$0.325790\pi$
$942$		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	−0.916606	−	0.399793i	$-0.869082\pi$
$947$	−4364.47	−	30355.5i	−0.149764	−	1.04163i	0.766842	−	0.641836i	$-0.221827\pi$
$948$		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	−0.130838	−	0.991404i	$-0.541767\pi$
$953$	−22856.2	−	6711.18i	−0.776899	−	0.228118i	−0.646061	+	0.763286i	$0.723585\pi$
$954$		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	0.974616	+	0.223882i	$0.0718731\pi$
$971$	15297.4	+	33496.5i	0.505577	+	1.10706i	−0.469039	+	0.883178i	$0.655400\pi$
$972$		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	0.227732	−	0.973724i	$-0.426869\pi$
$977$	−23468.2	−	27083.8i	−0.768491	−	0.886885i	−0.996222	+	0.0868385i	$0.972324\pi$
$978$		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	0.842726	+	0.538343i	$0.180950\pi$
$983$	−3622.33	+	25193.9i	−0.117533	+	0.817457i	−0.960258	+	0.279113i	$0.909959\pi$
$984$		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	−0.932818	−	0.360348i	$-0.882658\pi$
$991$	−13832.2	+	15963.2i	−0.443383	+	0.511692i	0.489434	+	0.872040i	$0.337203\pi$
$992$	−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	0.643235	−	0.765669i	$-0.277592\pi$
$997$	6735.84	+	4328.86i	0.213968	+	0.137509i	−0.429267	+	0.903178i	$0.641228\pi$
$998$	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.154.2		50
3.2	odd	2		23.4.c.a.16.4	yes	50
23.13	even	11	inner	207.4.i.a.82.2		50
69.17	even	22		529.4.a.m.1.8		25
69.29	odd	22		529.4.a.n.1.8		25
69.59	odd	22		23.4.c.a.13.4	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.13.4	✓	50	69.59	odd	22
23.4.c.a.16.4	yes	50	3.2	odd	2
207.4.i.a.82.2		50	23.13	even	11	inner
207.4.i.a.154.2		50	1.1	even	1	trivial
529.4.a.m.1.8		25	69.17	even	22
529.4.a.n.1.8		25	69.29	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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