LMFDB - Embedded newform 207.4.i.a.55.4

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			55.4
Character	$\chi$	$=$	207.55
Dual form			207.4.i.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.49786 - 0.733439i) q^{2} +(-1.02864 + 0.661064i) q^{4} +(-2.23195 - 15.5235i) q^{5} +(-2.46994 + 5.40842i) q^{7} +(-15.7230 + 18.1453i) q^{8} +O(q^{10})$	\(q+(2.49786 - 0.733439i) q^{2} +(-1.02864 + 0.661064i) q^{4} +(-2.23195 - 15.5235i) q^{5} +(-2.46994 + 5.40842i) q^{7} +(-15.7230 + 18.1453i) q^{8} +(-16.9607 - 37.1386i) q^{10} +(-20.9837 - 6.16138i) q^{11} +(-14.2612 - 31.2277i) q^{13} +(-2.20284 + 15.3211i) q^{14} +(-21.9019 + 47.9585i) q^{16} +(-108.865 - 69.9635i) q^{17} +(-23.4761 + 15.0872i) q^{19} +(12.5579 + 14.4926i) q^{20} -56.9335 q^{22} +(18.9488 + 108.664i) q^{23} +(-116.061 + 34.0787i) q^{25} +(-58.5263 - 67.5429i) q^{26} +(-1.03464 - 7.19609i) q^{28} +(-10.5650 - 6.78974i) q^{29} +(-10.3460 + 11.9399i) q^{31} +(7.80215 - 54.2651i) q^{32} +(-323.245 - 94.9132i) q^{34} +(89.4705 + 26.2709i) q^{35} +(33.6066 - 233.739i) q^{37} +(-47.5745 + 54.9039i) q^{38} +(316.772 + 203.577i) q^{40} +(-53.6680 - 373.269i) q^{41} +(-310.499 - 358.335i) q^{43} +(25.6577 - 7.53378i) q^{44} +(127.030 + 257.531i) q^{46} +547.089 q^{47} +(201.467 + 232.505i) q^{49} +(-264.911 + 170.248i) q^{50} +(35.3132 + 22.6944i) q^{52} +(-192.699 + 421.952i) q^{53} +(-48.8118 + 339.493i) q^{55} +(-59.3027 - 129.855i) q^{56} +(-31.3699 - 9.21104i) q^{58} +(248.087 + 543.235i) q^{59} +(-181.560 + 209.532i) q^{61} +(-17.0857 + 37.4124i) q^{62} +(-80.3376 - 558.760i) q^{64} +(-452.934 + 291.083i) q^{65} +(164.674 - 48.3526i) q^{67} +158.233 q^{68} +242.753 q^{70} +(218.486 - 64.1534i) q^{71} +(784.252 - 504.008i) q^{73} +(-87.4886 - 608.496i) q^{74} +(14.1748 - 31.0384i) q^{76} +(85.1520 - 98.2707i) q^{77} +(97.3133 + 213.086i) q^{79} +(793.369 + 232.954i) q^{80} +(-407.826 - 893.014i) q^{82} +(129.907 - 903.521i) q^{83} +(-843.098 + 1846.13i) q^{85} +(-1038.40 - 667.340i) q^{86} +(441.728 - 283.881i) q^{88} +(-451.850 - 521.462i) q^{89} +204.117 q^{91} +(-91.3256 - 99.2497i) q^{92} +(1366.55 - 401.256i) q^{94} +(286.603 + 330.758i) q^{95} +(-12.2538 - 85.2267i) q^{97} +(673.765 + 433.003i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	2.49786	−	0.733439i	0.883128	−	0.259310i	0.191439	−	0.981505i	$-0.438685\pi$
$2$	2.49786	−	0.733439i	0.883128	−	0.259310i	0.691690	+	0.722195i	$0.256867\pi$
$3$		0			0
$3$		0			0
$4$	−1.02864	+	0.661064i	−0.128579	+	0.0826330i
$5$	−2.23195	−	15.5235i	−0.199631	−	1.38847i	−0.805356	−	0.592792i	$-0.798026\pi$
$5$	−2.23195	−	15.5235i	−0.199631	−	1.38847i	0.605725	−	0.795674i	$-0.292883\pi$
$6$		0			0
$7$	−2.46994	+	5.40842i	−0.133364	+	0.292027i	−0.964519	−	0.264014i	$-0.914953\pi$
$7$	−2.46994	+	5.40842i	−0.133364	+	0.292027i	0.831154	+	0.556042i	$0.187681\pi$
$8$	−15.7230	+	18.1453i	−0.694866	+	0.801918i
$9$		0			0
$10$	−16.9607	−	37.1386i	−0.536343	−	1.17443i
$11$	−20.9837	−	6.16138i	−0.575167	−	0.168884i	−0.0188033	−	0.999823i	$-0.505986\pi$
$11$	−20.9837	−	6.16138i	−0.575167	−	0.168884i	−0.556364	+	0.830939i	$0.687804\pi$
$12$		0			0
$13$	−14.2612	−	31.2277i	−0.304258	−	0.666232i	0.694313	−	0.719673i	$-0.255708\pi$
$13$	−14.2612	−	31.2277i	−0.304258	−	0.666232i	−0.998571	+	0.0534411i	$0.982981\pi$
$14$	−2.20284	+	15.3211i	−0.0420523	+	0.292480i
$15$		0			0
$16$	−21.9019	+	47.9585i	−0.342217	+	0.749352i
$17$	−108.865	−	69.9635i	−1.55316	−	0.998155i	−0.984460	−	0.175610i	$-0.943810\pi$
$17$	−108.865	−	69.9635i	−1.55316	−	0.998155i	−0.568700	−	0.822545i	$-0.692553\pi$
$18$		0			0
$19$	−23.4761	+	15.0872i	−0.283462	+	0.182170i	−0.674644	−	0.738143i	$-0.735703\pi$
$19$	−23.4761	+	15.0872i	−0.283462	+	0.182170i	0.391182	+	0.920313i	$0.372066\pi$
$20$	12.5579	+	14.4926i	0.140402	+	0.162032i
$21$		0			0
$22$	−56.9335			−0.551740
$23$	18.9488	+	108.664i	0.171787	+	0.985134i
$23$	18.9488	+	108.664i	0.171787	+	0.985134i
$24$		0			0
$25$	−116.061	+	34.0787i	−0.928492	+	0.272630i
$26$	−58.5263	−	67.5429i	−0.441459	−	0.509471i
$27$		0			0
$28$	−1.03464	−	7.19609i	−0.00698317	−	0.0485690i
$29$	−10.5650	−	6.78974i	−0.0676510	−	0.0434767i	0.506378	−	0.862312i	$-0.330984\pi$
$29$	−10.5650	−	6.78974i	−0.0676510	−	0.0434767i	−0.574029	+	0.818835i	$0.694620\pi$
$30$		0			0
$31$	−10.3460	+	11.9399i	−0.0599418	+	0.0691765i	−0.784929	−	0.619586i	$-0.787300\pi$
$31$	−10.3460	+	11.9399i	−0.0599418	+	0.0691765i	0.724987	+	0.688763i	$0.241846\pi$
$32$	7.80215	−	54.2651i	0.0431012	−	0.299775i
$33$		0			0
$34$	−323.245	−	94.9132i	−1.63047	−	0.478749i
$35$	89.4705	+	26.2709i	0.432094	+	0.126874i
$36$		0			0
$37$	33.6066	−	233.739i	0.149321	−	1.03855i	−0.768013	−	0.640434i	$-0.778754\pi$
$37$	33.6066	−	233.739i	0.149321	−	1.03855i	0.917334	−	0.398118i	$-0.130337\pi$
$38$	−47.5745	+	54.9039i	−0.203095	+	0.234384i
$39$		0			0
$40$	316.772	+	203.577i	1.25215	+	0.804710i
$41$	−53.6680	−	373.269i	−0.204428	−	1.42183i	−0.790944	−	0.611889i	$-0.790410\pi$
$41$	−53.6680	−	373.269i	−0.204428	−	1.42183i	0.586516	−	0.809938i	$-0.300499\pi$
$42$		0			0
$43$	−310.499	−	358.335i	−1.10118	−	1.27083i	−0.959743	−	0.280880i	$-0.909374\pi$
$43$	−310.499	−	358.335i	−1.10118	−	1.27083i	−0.141435	−	0.989948i	$-0.545172\pi$
$44$	25.6577	−	7.53378i	0.0879101	−	0.0258127i
$45$		0			0
$46$	127.030	+	257.531i	0.407165	+	0.825454i
$47$	547.089			1.69790			0.848948	−	0.528476i	$-0.177236\pi$
$47$	547.089			1.69790			0.848948	+	0.528476i	$0.177236\pi$
$48$		0			0
$49$	201.467	+	232.505i	0.587367	+	0.677857i
$50$	−264.911	+	170.248i	−0.749282	+	0.481534i
$51$		0			0
$52$	35.3132	+	22.6944i	0.0941741	+	0.0605220i
$53$	−192.699	+	421.952i	−0.499420	+	1.09358i	0.477238	+	0.878774i	$0.341638\pi$
$53$	−192.699	+	421.952i	−0.499420	+	1.09358i	−0.976658	+	0.214802i	$0.931089\pi$
$54$		0			0
$55$	−48.8118	+	339.493i	−0.119669	+	0.832314i
$56$	−59.3027	−	129.855i	−0.141512	−	0.309867i
$57$		0			0
$58$	−31.3699	−	9.21104i	−0.0710185	−	0.0208529i
$59$	248.087	+	543.235i	0.547426	+	1.19870i	0.957973	+	0.286857i	$0.0926106\pi$
$59$	248.087	+	543.235i	0.547426	+	1.19870i	−0.410547	+	0.911840i	$0.634662\pi$
$60$		0			0
$61$	−181.560	+	209.532i	−0.381089	+	0.439800i	−0.913595	−	0.406626i	$-0.866705\pi$
$61$	−181.560	+	209.532i	−0.381089	+	0.439800i	0.532505	+	0.846427i	$0.321251\pi$
$62$	−17.0857	+	37.4124i	−0.0349981	+	0.0766352i
$63$		0			0
$64$	−80.3376	−	558.760i	−0.156909	−	1.09133i
$65$	−452.934	+	291.083i	−0.864301	+	0.555452i
$66$		0			0
$67$	164.674	−	48.3526i	0.300271	−	0.0881674i	−0.128127	−	0.991758i	$-0.540896\pi$
$67$	164.674	−	48.3526i	0.300271	−	0.0881674i	0.428398	+	0.903590i	$0.359078\pi$
$68$	158.233			0.282185
$69$		0			0
$70$	242.753			0.414494
$71$	218.486	−	64.1534i	0.365205	−	0.107234i	−0.0939811	−	0.995574i	$-0.529959\pi$
$71$	218.486	−	64.1534i	0.365205	−	0.107234i	0.459186	+	0.888340i	$0.348141\pi$
$72$		0			0
$73$	784.252	−	504.008i	1.25739	−	0.808078i	0.269468	−	0.963009i	$-0.413152\pi$
$73$	784.252	−	504.008i	1.25739	−	0.808078i	0.987925	+	0.154931i	$0.0495157\pi$
$74$	−87.4886	−	608.496i	−0.137437	−	0.955895i
$75$		0			0
$76$	14.1748	−	31.0384i	0.0213942	−	0.0468467i
$77$	85.1520	−	98.2707i	0.126026	−	0.145441i
$78$		0			0
$79$	97.3133	+	213.086i	0.138590	+	0.303470i	0.966182	−	0.257860i	$-0.0830173\pi$
$79$	97.3133	+	213.086i	0.138590	+	0.303470i	−0.827592	+	0.561330i	$0.810290\pi$
$80$	793.369	+	232.954i	1.10877	+	0.325563i
$81$		0			0
$82$	−407.826	−	893.014i	−0.549230	−	1.20265i
$83$	129.907	−	903.521i	0.171797	−	1.19487i	−0.703289	−	0.710904i	$-0.748286\pi$
$83$	129.907	−	903.521i	0.171797	−	1.19487i	0.875086	−	0.483967i	$-0.160805\pi$
$84$		0			0
$85$	−843.098	+	1846.13i	−1.07585	+	2.35577i
$86$	−1038.40	−	667.340i	−1.30202	−	0.836757i
$87$		0			0
$88$	441.728	−	283.881i	0.535095	−	0.343885i
$89$	−451.850	−	521.462i	−0.538157	−	0.621066i	0.419926	−	0.907559i	$-0.362056\pi$
$89$	−451.850	−	521.462i	−0.538157	−	0.621066i	−0.958083	+	0.286492i	$0.907511\pi$
$90$		0			0
$91$	204.117			0.235135
$92$	−91.3256	−	99.2497i	−0.103493	−	0.112473i
$93$		0			0
$94$	1366.55	−	401.256i	1.49946	−	0.440281i
$95$	286.603	+	330.758i	0.309525	+	0.357211i
$96$		0			0
$97$	−12.2538	−	85.2267i	−0.0128266	−	0.0892109i	0.982403	−	0.186776i	$-0.0598038\pi$
$97$	−12.2538	−	85.2267i	−0.0128266	−	0.0892109i	−0.995229	+	0.0975648i	$0.968895\pi$
$98$	673.765	+	433.003i	0.694495	+	0.446325i
$99$		0			0
$100$	96.8568	−	111.779i	0.0968568	−	0.111779i
$101$	68.9206	−	479.353i	0.0678995	−	0.472252i	−0.927295	−	0.374332i	$-0.877872\pi$
$101$	68.9206	−	479.353i	0.0678995	−	0.472252i	0.995194	−	0.0979197i	$-0.0312188\pi$
$102$		0			0
$103$	121.652	+	35.7202i	0.116376	+	0.0341710i	0.339402	−	0.940641i	$-0.389775\pi$
$103$	121.652	+	35.7202i	0.116376	+	0.0341710i	−0.223026	+	0.974812i	$0.571594\pi$
$104$	790.867	+	232.220i	0.745682	+	0.218952i
$105$		0			0
$106$	−171.860	+	1195.31i	−0.157476	+	1.09527i
$107$	−1242.80	+	1434.27i	−1.12286	+	1.29585i	−0.172392	+	0.985029i	$0.555149\pi$
$107$	−1242.80	+	1434.27i	−1.12286	+	1.29585i	−0.950468	+	0.310821i	$0.899396\pi$
$108$		0			0
$109$	−718.784	−	461.934i	−0.631624	−	0.405920i	0.185287	−	0.982685i	$-0.440679\pi$
$109$	−718.784	−	461.934i	−0.631624	−	0.405920i	−0.816910	+	0.576765i	$0.804315\pi$
$110$	127.073	+	883.809i	0.110144	+	0.766072i
$111$		0			0
$112$	−205.283	−	236.910i	−0.173192	−	0.199874i
$113$	545.831	−	160.270i	0.454402	−	0.133425i	−0.0465190	−	0.998917i	$-0.514813\pi$
$113$	545.831	−	160.270i	0.454402	−	0.133425i	0.500921	+	0.865493i	$0.332995\pi$
$114$		0			0
$115$	1644.56	−	536.685i	1.33353	−	0.435184i
$116$	15.3560			0.0122911
$117$		0			0
$118$	1018.12	+	1174.97i	0.794282	+	0.916650i
$119$	647.283	−	415.984i	0.498625	−	0.320447i
$120$		0			0
$121$	−717.354	−	461.015i	−0.538958	−	0.346368i
$122$	−299.834	+	656.546i	−0.222506	+	0.487220i
$123$		0			0
$124$	2.74921	−	19.1212i	0.00199102	−	0.0138479i
$125$	−26.3125	−	57.6163i	−0.0188277	−	0.0412268i
$126$		0			0
$127$	−1021.39	−	299.907i	−0.713651	−	0.209547i	−0.0952996	−	0.995449i	$-0.530381\pi$
$127$	−1021.39	−	299.907i	−0.713651	−	0.209547i	−0.618351	+	0.785902i	$0.712199\pi$
$128$	−428.294	−	937.832i	−0.295751	−	0.647605i
$129$		0			0
$130$	−917.876	+	1059.29i	−0.619254	+	0.714658i
$131$	−296.727	+	649.742i	−0.197902	+	0.433345i	−0.982401	−	0.186785i	$-0.940193\pi$
$131$	−296.727	+	649.742i	−0.197902	+	0.433345i	0.784499	+	0.620131i	$0.212920\pi$
$132$		0			0
$133$	−23.6131	−	164.233i	−0.0153949	−	0.107074i
$134$	375.870	−	241.557i	0.242315	−	0.155726i
$135$		0			0
$136$	2981.20	−	875.360i	1.87968	−	0.551923i
$137$	−442.264			−0.275804			−0.137902	−	0.990446i	$-0.544036\pi$
$137$	−442.264			−0.275804			−0.137902	+	0.990446i	$0.544036\pi$
$138$		0			0
$139$	−1903.69			−1.16164			−0.580822	−	0.814030i	$-0.697269\pi$
$139$	−1903.69			−1.16164			−0.580822	+	0.814030i	$0.697269\pi$
$140$	−109.399	+	32.1226i	−0.0660424	+	0.0193918i
$141$		0			0
$142$	498.696	−	320.493i	0.294716	−	0.189402i
$143$	106.848	+	743.144i	0.0624830	+	0.434579i
$144$		0			0
$145$	−81.8201	+	179.161i	−0.0468606	+	0.102610i
$146$	1589.30	−	1834.14i	0.900897	−	1.03969i
$147$		0			0
$148$	119.947	+	262.648i	0.0666191	+	0.145875i
$149$	404.216	+	118.688i	0.222246	+	0.0652573i	0.390960	−	0.920408i	$-0.372143\pi$
$149$	404.216	+	118.688i	0.222246	+	0.0652573i	−0.168714	+	0.985665i	$0.553961\pi$
$150$		0			0
$151$	367.181	+	804.014i	0.197886	+	0.433310i	0.982397	−	0.186805i	$-0.0598133\pi$
$151$	367.181	+	804.014i	0.197886	+	0.433310i	−0.784511	+	0.620115i	$0.787086\pi$
$152$	95.3533	−	663.197i	0.0508827	−	0.353897i
$153$		0			0
$154$	140.623	−	307.921i	0.0735824	−	0.161123i
$155$	208.441	+	133.957i	0.108015	+	0.0694173i
$156$		0			0
$157$	−1897.61	+	1219.52i	−0.964623	+	0.619926i	−0.925274	−	0.379300i	$-0.876165\pi$
$157$	−1897.61	+	1219.52i	−0.964623	+	0.619926i	−0.0393494	+	0.999226i	$0.512529\pi$
$158$	399.361	+	460.888i	0.201085	+	0.232065i
$159$		0			0
$160$	−859.800			−0.424832
$161$	−634.505	−	165.912i	−0.310596	−	0.0812153i
$162$		0			0
$163$	−112.176	+	32.9379i	−0.0539038	+	0.0158276i	−0.308573	−	0.951201i	$-0.599852\pi$
$163$	−112.176	+	32.9379i	−0.0539038	+	0.0158276i	0.254669	+	0.967028i	$0.418033\pi$
$164$	301.960	+	348.480i	0.143775	+	0.165925i
$165$		0			0
$166$	−338.188	−	2352.15i	−0.158123	−	1.09977i
$167$	−1242.29	−	798.372i	−0.575637	−	0.369939i	0.220196	−	0.975456i	$-0.429330\pi$
$167$	−1242.29	−	798.372i	−0.575637	−	0.369939i	−0.795833	+	0.605516i	$0.792967\pi$
$168$		0			0
$169$	666.940	−	769.690i	0.303569	−	0.350337i
$170$	−751.923	+	5229.74i	−0.339234	+	2.35943i
$171$		0			0
$172$	556.273	+	163.336i	0.246601	+	0.0724086i
$173$	455.044	+	133.613i	0.199979	+	0.0587191i	0.380188	−	0.924909i	$-0.375859\pi$
$173$	455.044	+	133.613i	0.199979	+	0.0587191i	−0.180209	+	0.983628i	$0.557677\pi$
$174$		0			0
$175$	102.353	−	711.882i	0.0442124	−	0.307504i
$176$	755.075	−	871.403i	0.323386	−	0.373207i
$177$		0			0
$178$	−1511.12	−	971.138i	−0.636310	−	0.408932i
$179$	−318.315	−	2213.93i	−0.132916	−	0.924452i	−0.941726	−	0.336382i	$-0.890797\pi$
$179$	−318.315	−	2213.93i	−0.132916	−	0.924452i	0.808810	−	0.588071i	$-0.200112\pi$
$180$		0			0
$181$	−1861.65	−	2148.45i	−0.764503	−	0.882283i	0.231386	−	0.972862i	$-0.425674\pi$
$181$	−1861.65	−	2148.45i	−0.764503	−	0.882283i	−0.995889	+	0.0905785i	$0.971128\pi$
$182$	509.857	−	149.708i	0.207655	−	0.0609729i
$183$		0			0
$184$	−2269.68	−	1364.70i	−0.909366	−	0.546777i
$185$	−3703.46			−1.47180
$186$		0			0
$187$	1853.33	+	2138.86i	0.724753	+	0.836410i
$188$	−562.755	+	361.661i	−0.218315	+	0.140302i
$189$		0			0
$190$	958.486	+	615.982i	0.365978	+	0.235200i
$191$	180.457	−	395.146i	0.0683634	−	0.149695i	−0.872366	−	0.488854i	$-0.837415\pi$
$191$	180.457	−	395.146i	0.0683634	−	0.149695i	0.940729	+	0.339159i	$0.110142\pi$
$192$		0			0
$193$	−460.744	+	3204.55i	−0.171840	+	1.19517i	0.703153	+	0.711038i	$0.251775\pi$
$193$	−460.744	+	3204.55i	−0.171840	+	1.19517i	−0.874993	+	0.484135i	$0.839134\pi$
$194$	−93.1168	−	203.897i	−0.0344608	−	0.0754586i
$195$		0			0
$196$	−360.937	−	105.981i	−0.131537	−	0.0386227i
$197$	−1336.28	−	2926.04i	−0.483278	−	1.05823i	−0.981549	−	0.191209i	$-0.938759\pi$
$197$	−1336.28	−	2926.04i	−0.483278	−	1.05823i	0.498272	−	0.867021i	$-0.333968\pi$
$198$		0			0
$199$	−391.536	+	451.857i	−0.139474	+	0.160961i	−0.821189	−	0.570656i	$-0.806689\pi$
$199$	−391.536	+	451.857i	−0.139474	+	0.160961i	0.681715	+	0.731618i	$0.261234\pi$
$200$	1206.47	−	2641.79i	0.426551	−	0.934016i
$201$		0			0
$202$	−179.422	−	1247.91i	−0.0624955	−	0.434666i
$203$	62.8169	−	40.3700i	0.0217186	−	0.0139577i
$204$		0			0
$205$	−5674.67	+	1666.23i	−1.93335	+	0.567682i
$206$	330.068			0.111636
$207$		0			0
$208$	1809.98			0.603364
$209$	585.574	−	171.940i	0.193804	−	0.0569059i
$210$		0			0
$211$	−3839.77	+	2467.67i	−1.25280	+	0.805125i	−0.987282	−	0.158981i	$-0.949179\pi$
$211$	−3839.77	+	2467.67i	−1.25280	+	0.805125i	−0.265518	+	0.964106i	$0.585543\pi$
$212$	−80.7202	−	561.421i	−0.0261504	−	0.181880i
$213$		0			0
$214$	−2052.40	+	4494.12i	−0.655603	+	1.43557i
$215$	−4869.60	+	5619.82i	−1.54467	+	1.78264i
$216$		0			0
$217$	−39.0221	−	85.4464i	−0.0122073	−	0.0267303i
$218$	−2134.22	−	626.665i	−0.663064	−	0.194693i
$219$		0			0
$220$	−174.217	−	381.483i	−0.0533897	−	0.116907i
$221$	−632.248	+	4397.38i	−0.192442	+	1.33846i
$222$		0			0
$223$	1555.81	−	3406.75i	0.467196	−	1.02302i	−0.518592	−	0.855022i	$-0.673543\pi$
$223$	1555.81	−	3406.75i	0.467196	−	1.02302i	0.985788	−	0.167995i	$-0.0537293\pi$
$224$	274.218	+	176.229i	0.0817945	+	0.0525661i
$225$		0			0
$226$	1245.86	−	800.667i	0.366697	−	0.235662i
$227$	−2177.84	−	2513.36i	−0.636777	−	0.734880i	0.342024	−	0.939691i	$-0.388887\pi$
$227$	−2177.84	−	2513.36i	−0.636777	−	0.734880i	−0.978802	+	0.204811i	$0.934342\pi$
$228$		0			0
$229$	1285.35			0.370909			0.185454	−	0.982653i	$-0.440624\pi$
$229$	1285.35			0.370909			0.185454	+	0.982653i	$0.440624\pi$
$230$	3714.26	−	2546.75i	1.06483	−	0.730121i
$231$		0			0
$232$	289.317	−	84.9510i	0.0818731	−	0.0240401i
$233$	3646.65	+	4208.46i	1.02532	+	1.18328i	0.982892	+	0.184184i	$0.0589643\pi$
$233$	3646.65	+	4208.46i	1.02532	+	1.18328i	0.0424293	+	0.999099i	$0.486490\pi$
$234$		0			0
$235$	−1221.07	−	8492.75i	−0.338953	−	2.35747i
$236$	−614.304	−	394.789i	−0.169440	−	0.108892i
$237$		0			0
$238$	1311.73	−	1513.81i	0.357255	−	0.412294i
$239$	146.770	−	1020.81i	0.0397230	−	0.276279i	−0.960273	−	0.279062i	$-0.909977\pi$
$239$	146.770	−	1020.81i	0.0397230	−	0.276279i	0.999996	+	0.00278236i	$0.000885654\pi$
$240$		0			0
$241$	3131.22	+	919.409i	0.836928	+	0.245744i	0.671990	−	0.740560i	$-0.265440\pi$
$241$	3131.22	+	919.409i	0.836928	+	0.245744i	0.164937	+	0.986304i	$0.447258\pi$
$242$	−2129.98	−	625.418i	−0.565786	−	0.166130i
$243$		0			0
$244$	48.2456	−	335.555i	0.0126582	−	0.0880398i
$245$	3159.63	−	3646.41i	0.823925	−	0.950860i
$246$		0			0
$247$	805.935	+	517.943i	0.207613	+	0.133425i
$248$	−53.9834	−	375.463i	−0.0138224	−	0.0961368i
$249$		0			0
$250$	−107.983	−	124.619i	−0.0273178	−	0.0315264i
$251$	3225.71	−	947.155i	0.811176	−	0.238183i	0.150264	−	0.988646i	$-0.451988\pi$
$251$	3225.71	−	947.155i	0.811176	−	0.238183i	0.660912	+	0.750463i	$0.270169\pi$
$252$		0			0
$253$	271.905	−	2396.94i	0.0675673	−	0.595629i
$254$	−2771.26			−0.684583
$255$		0			0
$256$	1199.72	+	1384.55i	0.292900	+	0.338025i
$257$	−1072.38	+	689.177i	−0.260285	+	0.167275i	−0.664275	−	0.747489i	$-0.731259\pi$
$257$	−1072.38	+	689.177i	−0.260285	+	0.167275i	0.403990	+	0.914763i	$0.367623\pi$
$258$		0			0
$259$	1181.15	+	759.081i	0.283372	+	0.182112i
$260$	273.480	−	598.837i	0.0652327	−	0.142840i
$261$		0			0
$262$	−264.638	+	1840.60i	−0.0624023	+	0.434018i
$263$	−2176.10	−	4765.00i	−0.510206	−	1.11720i	−0.973016	−	0.230738i	$-0.925886\pi$
$263$	−2176.10	−	4765.00i	−0.510206	−	1.11720i	0.462809	−	0.886458i	$-0.346841\pi$
$264$		0			0
$265$	6980.27	+	2049.59i	1.61809	+	0.475115i
$266$	−179.437	−	392.913i	−0.0413609	−	0.0905678i
$267$		0			0
$268$	−137.425	+	158.597i	−0.0313231	+	0.0361488i
$269$	−2612.67	+	5720.95i	−0.592184	+	1.29670i	0.341930	+	0.939726i	$0.388920\pi$
$269$	−2612.67	+	5720.95i	−0.592184	+	1.29670i	−0.934113	+	0.356976i	$0.883808\pi$
$270$		0			0
$271$	69.9139	+	486.262i	0.0156715	+	0.108997i	0.996156	−	0.0876002i	$-0.0279198\pi$
$271$	69.9139	+	486.262i	0.0156715	+	0.108997i	−0.980484	+	0.196598i	$0.937011\pi$
$272$	5739.70	−	3688.68i	1.27949	−	0.822277i
$273$		0			0
$274$	−1104.71	+	324.374i	−0.243570	+	0.0715187i
$275$	2645.38			0.580081
$276$		0			0
$277$	−4007.70			−0.869312			−0.434656	−	0.900597i	$-0.643130\pi$
$277$	−4007.70			−0.869312			−0.434656	+	0.900597i	$0.643130\pi$
$278$	−4755.15	+	1396.24i	−1.02588	+	0.301226i
$279$		0			0
$280$	−1883.44	+	1210.41i	−0.401990	+	0.258343i
$281$	230.352	+	1602.13i	0.0489026	+	0.340125i	0.999554	+	0.0298640i	$0.00950743\pi$
$281$	230.352	+	1602.13i	0.0489026	+	0.340125i	−0.950651	+	0.310261i	$0.899583\pi$
$282$		0			0
$283$	1539.90	−	3371.91i	0.323454	−	0.708265i	−0.676140	−	0.736773i	$-0.736348\pi$
$283$	1539.90	−	3371.91i	0.323454	−	0.708265i	0.999594	+	0.0285085i	$0.00907576\pi$
$284$	−182.333	+	210.424i	−0.0380968	+	0.0439661i
$285$		0			0
$286$	811.942	+	1777.91i	0.167871	+	0.367587i
$287$	2151.36	+	631.695i	0.442476	+	0.129923i
$288$		0			0
$289$	4915.83	+	10764.2i	1.00058	+	2.19096i
$290$	−72.9718	+	507.530i	−0.0147760	+	0.102770i
$291$		0			0
$292$	−473.528	+	1036.88i	−0.0949011	+	0.207804i
$293$	4224.80	+	2715.12i	0.842374	+	0.541361i	0.889188	−	0.457543i	$-0.151270\pi$
$293$	4224.80	+	2715.12i	0.842374	+	0.541361i	−0.0468135	+	0.998904i	$0.514907\pi$
$294$		0			0
$295$	7879.20	−	5063.65i	1.55507	−	0.999380i
$296$	3712.87	+	4284.88i	0.729076	+	0.841398i
$297$		0			0
$298$	1096.73			0.213194
$299$	3123.11	−	2141.42i	0.604060	−	0.414185i
$300$		0			0
$301$	2704.94	−	794.243i	0.517974	−	0.152091i
$302$	1506.86	+	1739.01i	0.287120	+	0.331354i
$303$		0			0
$304$	−209.386	−	1456.31i	−0.0395037	−	0.274755i
$305$	3657.91	+	2350.79i	0.686725	+	0.441331i
$306$		0			0
$307$	−2900.34	+	3347.17i	−0.539189	+	0.622258i	−0.958330	−	0.285664i	$-0.907786\pi$
$307$	−2900.34	+	3347.17i	−0.539189	+	0.622258i	0.419141	+	0.907921i	$0.362331\pi$
$308$	−22.6272	+	157.376i	−0.00418606	+	0.0291147i
$309$		0			0
$310$	618.907	+	181.728i	0.113392	+	0.0332949i
$311$	8812.64	+	2587.62i	1.60681	+	0.471803i	0.957432	−	0.288660i	$-0.0932097\pi$
$311$	8812.64	+	2587.62i	1.60681	+	0.471803i	0.649381	+	0.760463i	$0.275028\pi$
$312$		0			0
$313$	354.613	−	2466.39i	0.0640381	−	0.445395i	−0.932425	−	0.361363i	$-0.882311\pi$
$313$	354.613	−	2466.39i	0.0640381	−	0.445395i	0.996463	−	0.0840312i	$-0.0267795\pi$
$314$	−3845.53	+	4437.98i	−0.691133	+	0.797610i
$315$		0			0
$316$	−240.964	−	154.858i	−0.0428964	−	0.0275679i
$317$	−709.513	−	4934.77i	−0.125710	−	0.874335i	−0.950904	−	0.309485i	$-0.899843\pi$
$317$	−709.513	−	4934.77i	−0.125710	−	0.874335i	0.825194	−	0.564850i	$-0.191066\pi$
$318$		0			0
$319$	179.860	+	207.570i	0.0315681	+	0.0364315i
$320$	−8494.61	+	2494.24i	−1.48395	+	0.435726i
$321$		0			0
$322$	−1706.59	+	50.9465i	−0.295356	+	0.00881719i
$323$	3611.28			0.622096
$324$		0			0
$325$	2719.38	+	3138.33i	0.464136	+	0.535641i
$326$	−256.043	+	164.549i	−0.0434997	+	0.0279556i
$327$		0			0
$328$	7616.92	+	4895.10i	1.28224	+	0.824044i
$329$	−1351.28	+	2958.89i	−0.226439	+	0.495832i
$330$		0			0
$331$	894.512	−	6221.47i	0.148540	−	1.03312i	−0.770071	−	0.637958i	$-0.779779\pi$
$331$	894.512	−	6221.47i	0.148540	−	1.03312i	0.918611	−	0.395162i	$-0.129312\pi$
$332$	463.659	+	1015.27i	0.0766463	+	0.167832i
$333$		0			0
$334$	−3688.63	−	1083.08i	−0.604290	−	0.177436i
$335$	−1118.15	−	2448.40i	−0.182361	−	0.399315i
$336$		0			0
$337$	2107.49	−	2432.17i	0.340659	−	0.393141i	−0.559408	−	0.828892i	$-0.688972\pi$
$337$	2107.49	−	2432.17i	0.340659	−	0.393141i	0.900067	+	0.435751i	$0.143517\pi$
$338$	1101.41	−	2411.74i	0.177244	−	0.388111i
$339$		0			0
$340$	−353.168	−	2456.34i	−0.0563330	−	0.391804i
$341$	290.664	−	186.798i	0.0461594	−	0.0296648i
$342$		0			0
$343$	−3711.87	+	1089.90i	−0.584321	+	0.171572i
$344$	11384.1			1.78427
$345$		0			0
$346$	1234.64			0.191834
$347$	−7565.23	+	2221.35i	−1.17038	+	0.343655i	−0.808459	−	0.588552i	$-0.799698\pi$
$347$	−7565.23	+	2221.35i	−1.17038	+	0.343655i	−0.361924	+	0.932208i	$0.617880\pi$
$348$		0			0
$349$	−372.034	+	239.092i	−0.0570617	+	0.0366713i	−0.568861	−	0.822434i	$-0.692616\pi$
$349$	−372.034	+	239.092i	−0.0570617	+	0.0366713i	0.511799	+	0.859105i	$0.328979\pi$
$350$	−266.458	−	1853.25i	−0.0406936	−	0.283030i
$351$		0			0
$352$	−498.067	+	1090.61i	−0.0754177	+	0.165142i
$353$	3049.03	−	3518.77i	0.459727	−	0.530553i	−0.477799	−	0.878469i	$-0.658565\pi$
$353$	3049.03	−	3518.77i	0.459727	−	0.530553i	0.937526	+	0.347916i	$0.113111\pi$
$354$		0			0
$355$	−1483.54	−	3248.49i	−0.221797	−	0.485667i
$356$	809.509	+	237.693i	0.120517	+	0.0353868i
$357$		0			0
$358$	−2418.89	−	5296.63i	−0.357102	−	0.781943i
$359$	1235.41	−	8592.44i	0.181622	−	1.26321i	−0.671306	−	0.741180i	$-0.734266\pi$
$359$	1235.41	−	8592.44i	0.181622	−	1.26321i	0.852928	−	0.522028i	$-0.174824\pi$
$360$		0			0
$361$	−2525.83	+	5530.79i	−0.368250	+	0.806355i
$362$	−6225.90	−	4001.14i	−0.903939	−	0.580926i
$363$		0			0
$364$	−209.962	+	134.935i	−0.0302336	+	0.0194299i
$365$	−9574.39	−	11049.4i	−1.37300	−	1.58453i
$366$		0			0
$367$	5699.85			0.810708			0.405354	−	0.914160i	$-0.367148\pi$
$367$	5699.85			0.810708			0.405354	+	0.914160i	$0.367148\pi$
$368$	−5626.39	−	1471.20i	−0.797000	−	0.208401i
$369$		0			0
$370$	−9250.74	+	2716.26i	−1.29979	+	0.381653i
$371$	−1806.14	−	2084.40i	−0.252750	−	0.291688i
$372$		0			0
$373$	1048.79	+	7294.49i	0.145588	+	1.01258i	0.923332	+	0.384004i	$0.125455\pi$
$373$	1048.79	+	7294.49i	0.145588	+	1.01258i	−0.777744	+	0.628581i	$0.783636\pi$
$374$	6198.09	+	3983.27i	0.856940	+	0.550722i
$375$		0			0
$376$	−8601.89	+	9927.11i	−1.17981	+	1.36157i
$377$	−61.3578	+	426.753i	−0.00838219	+	0.0582994i
$378$		0			0
$379$	7502.22	+	2202.85i	1.01679	+	0.298556i	0.747328	−	0.664455i	$-0.231336\pi$
$379$	7502.22	+	2202.85i	1.01679	+	0.298556i	0.269461	+	0.963011i	$0.413154\pi$
$380$	−513.462	−	150.766i	−0.0693159	−	0.0203530i
$381$		0			0
$382$	160.942	−	1119.37i	0.0215563	−	0.149927i
$383$	5045.50	−	5822.82i	0.673141	−	0.776847i	−0.311723	−	0.950173i	$-0.600906\pi$
$383$	5045.50	−	5822.82i	0.673141	−	0.776847i	0.984864	+	0.173326i	$0.0554516\pi$
$384$		0			0
$385$	−1715.56	−	1102.52i	−0.227099	−	0.145948i
$386$	1199.46	+	8342.45i	0.158163	+	1.10005i
$387$		0			0
$388$	68.9450	+	79.5667i	0.00902101	+	0.0104108i
$389$	−4252.51	+	1248.65i	−0.554269	+	0.162748i	−0.546860	−	0.837224i	$-0.684177\pi$
$389$	−4252.51	+	1248.65i	−0.554269	+	0.162748i	−0.00740987	+	0.999973i	$0.502359\pi$
$390$		0			0
$391$	5539.67	−	13155.5i	0.716504	−	1.70154i
$392$	−7386.55			−0.951727
$393$		0			0
$394$	−5483.90	−	6328.76i	−0.701206	−	0.809235i
$395$	3090.65	−	1986.24i	0.393690	−	0.253009i
$396$		0			0
$397$	−7687.49	−	4940.45i	−0.971849	−	0.624570i	−0.0445963	−	0.999005i	$-0.514200\pi$
$397$	−7687.49	−	4940.45i	−0.971849	−	0.624570i	−0.927253	+	0.374436i	$0.877837\pi$
$398$	−646.595	+	1415.85i	−0.0814343	+	0.178316i
$399$		0			0
$400$	907.604	−	6312.52i	0.113450	−	0.789065i
$401$	1663.49	+	3642.53i	0.207159	+	0.453614i	0.984482	−	0.175487i	$-0.0561501\pi$
$401$	1663.49	+	3642.53i	0.207159	+	0.453614i	−0.777323	+	0.629102i	$0.783423\pi$
$402$		0			0
$403$	520.403	+	152.804i	0.0643254	+	0.0188876i
$404$	245.989	+	538.641i	0.0302931	+	0.0663326i
$405$		0			0
$406$	127.299	−	146.911i	0.0155610	−	0.0179583i
$407$	−2145.35	+	4697.65i	−0.261280	+	0.572123i
$408$		0			0
$409$	−273.427	−	1901.73i	−0.0330565	−	0.229913i	0.966595	−	0.256308i	$-0.0825062\pi$
$409$	−273.427	−	1901.73i	−0.0330565	−	0.229913i	−0.999652	+	0.0263954i	$0.991597\pi$
$410$	−12952.5	+	8324.05i	−1.56019	+	1.00267i
$411$		0			0
$412$	−148.749	+	43.6766i	−0.0177872	+	0.00522279i
$413$	−3550.80			−0.423060
$414$		0			0
$415$	−14315.8			−1.69333
$416$	−1805.85	+	530.244i	−0.212834	+	0.0624937i
$417$		0			0
$418$	1336.58	−	858.965i	0.156397	−	0.100510i
$419$	186.435	+	1296.69i	0.0217374	+	0.151187i	0.997799	−	0.0663058i	$-0.0211213\pi$
$419$	186.435	+	1296.69i	0.0217374	+	0.151187i	−0.976062	+	0.217493i	$0.930212\pi$
$420$		0			0
$421$	1382.79	−	3027.89i	0.160078	−	0.350523i	−0.812549	−	0.582893i	$-0.801921\pi$
$421$	1382.79	−	3027.89i	0.160078	−	0.350523i	0.972627	+	0.232370i	$0.0746480\pi$
$422$	−7781.34	+	8980.14i	−0.897606	+	1.03589i
$423$		0			0
$424$	−4626.65	−	10130.9i	−0.529929	−	1.16038i
$425$	15019.3	+	4410.07i	1.71422	+	0.503341i
$426$		0			0
$427$	−684.793	−	1499.49i	−0.0776100	−	0.169942i
$428$	330.246	−	2296.91i	0.0372968	−	0.259405i
$429$		0			0
$430$	−8041.81	+	17609.1i	−0.901885	+	1.97485i
$431$	−13194.8	−	8479.78i	−1.47464	−	0.947695i	−0.997631	−	0.0687975i	$-0.978084\pi$
$431$	−13194.8	−	8479.78i	−1.47464	−	0.947695i	−0.477011	−	0.878897i	$-0.658280\pi$
$432$		0			0
$433$	7857.80	−	5049.90i	0.872106	−	0.560469i	−0.0262902	−	0.999654i	$-0.508369\pi$
$433$	7857.80	−	5049.90i	0.872106	−	0.560469i	0.898396	+	0.439186i	$0.144733\pi$
$434$	−160.142	−	184.813i	−0.0177121	−	0.0204408i
$435$		0			0
$436$	1044.73			0.114756
$437$	−2084.28	−	2265.13i	−0.228157	−	0.247954i
$438$		0			0
$439$	−1895.04	+	556.435i	−0.206026	+	0.0604948i	−0.383117	−	0.923700i	$-0.625149\pi$
$439$	−1895.04	+	556.435i	−0.206026	+	0.0604948i	0.177091	+	0.984194i	$0.443331\pi$
$440$	−5392.75	−	6223.57i	−0.584294	−	0.674311i
$441$		0			0
$442$	1645.94	+	11447.8i	0.177126	+	1.23194i
$443$	10980.2	+	7056.57i	1.17762	+	0.756812i	0.974948	−	0.222434i	$-0.0714004\pi$
$443$	10980.2	+	7056.57i	1.17762	+	0.756812i	0.202674	+	0.979246i	$0.435037\pi$
$444$		0			0
$445$	−7086.43	+	8178.17i	−0.754896	+	0.871197i
$446$	1387.56	−	9650.69i	0.147316	−	1.02460i
$447$		0			0
$448$	3220.44	+	945.606i	0.339624	+	0.0997225i
$449$	2820.42	+	828.149i	0.296445	+	0.0870440i	0.426573	−	0.904453i	$-0.359721\pi$
$449$	2820.42	+	828.149i	0.296445	+	0.0870440i	−0.130128	+	0.991497i	$0.541539\pi$
$450$		0			0
$451$	−1173.70	+	8163.26i	−0.122544	+	0.852312i
$452$	−455.512	+	525.689i	−0.0474015	+	0.0547043i
$453$		0			0
$454$	−7283.35	−	4680.73i	−0.752918	−	0.483871i
$455$	−455.579	−	3168.62i	−0.0469403	−	0.326477i
$456$		0			0
$457$	−3183.49	−	3673.94i	−0.325859	−	0.376061i	0.569056	−	0.822299i	$-0.307309\pi$
$457$	−3183.49	−	3673.94i	−0.325859	−	0.376061i	−0.894914	+	0.446238i	$0.852763\pi$
$458$	3210.62	−	942.724i	0.327560	−	0.0961803i
$459$		0			0
$460$	−1336.87	+	1639.21i	−0.135504	+	0.166149i
$461$	−5249.19			−0.530323			−0.265162	−	0.964204i	$-0.585425\pi$
$461$	−5249.19			−0.530323			−0.265162	+	0.964204i	$0.585425\pi$
$462$		0			0
$463$	2696.87	+	3112.35i	0.270700	+	0.312404i	0.874781	−	0.484518i	$-0.161005\pi$
$463$	2696.87	+	3112.35i	0.270700	+	0.312404i	−0.604081	+	0.796923i	$0.706460\pi$
$464$	557.021	−	357.975i	0.0557307	−	0.0358159i
$465$		0			0
$466$	12195.5	+	7837.56i	1.21233	+	0.779115i
$467$	−6146.84	+	13459.7i	−0.609083	+	1.33371i	0.314116	+	0.949385i	$0.398292\pi$
$467$	−6146.84	+	13459.7i	−0.609083	+	1.33371i	−0.923199	+	0.384322i	$0.874435\pi$
$468$		0			0
$469$	−145.224	+	1010.06i	−0.0142981	+	0.0994456i
$470$	−9278.98	−	20318.1i	−0.910655	−	1.99406i
$471$		0			0
$472$	−13757.8	−	4039.67i	−1.34164	−	0.393942i
$473$	4307.59	+	9432.31i	0.418738	+	0.916909i
$474$		0			0
$475$	2210.52	−	2551.07i	0.213527	−	0.246424i
$476$	−390.827	+	855.792i	−0.0376335	+	0.0824058i
$477$		0			0
$478$	−382.090	−	2657.49i	−0.0365615	−	0.254291i
$479$	3712.79	−	2386.07i	0.354158	−	0.227604i	−0.351449	−	0.936207i	$-0.614311\pi$
$479$	3712.79	−	2386.07i	0.354158	−	0.227604i	0.705607	+	0.708604i	$0.250674\pi$
$480$		0			0
$481$	−7778.41	+	2283.95i	−0.737349	+	0.216505i
$482$	8495.69			0.802839
$483$		0			0
$484$	1042.66			0.0979204
$485$	−1295.67	+	380.443i	−0.121306	+	0.0356186i
$486$		0			0
$487$	11848.7	−	7614.70i	1.10250	−	0.708532i	0.142852	−	0.989744i	$-0.454373\pi$
$487$	11848.7	−	7614.70i	1.10250	−	0.708532i	0.959646	+	0.281212i	$0.0907364\pi$
$488$	−947.348	−	6588.95i	−0.0878779	−	0.611204i
$489$		0			0
$490$	5217.92	−	11425.6i	0.481064	−	1.05338i
$491$	3643.28	−	4204.57i	0.334865	−	0.386455i	−0.563197	−	0.826322i	$-0.690429\pi$
$491$	3643.28	−	4204.57i	0.334865	−	0.386455i	0.898063	+	0.439867i	$0.144974\pi$
$492$		0			0
$493$	675.133	+	1478.33i	0.0616764	+	0.135052i
$494$	2393.00	+	702.647i	0.217947	+	0.0639951i
$495$		0			0
$496$	−346.023	−	757.685i	−0.0313244	−	0.0685909i
$497$	−192.680	+	1340.12i	−0.0173901	+	0.120951i
$498$		0			0
$499$	3154.77	−	6907.98i	0.283020	−	0.619727i	−0.713718	−	0.700433i	$-0.752990\pi$
$499$	3154.77	−	6907.98i	0.283020	−	0.619727i	0.996738	+	0.0807061i	$0.0257175\pi$
$500$	65.1540	+	41.8719i	0.00582755	+	0.00374514i
$501$		0			0
$502$	7362.71	−	4731.73i	0.654610	−	0.420692i
$503$	9122.39	+	10527.8i	0.808643	+	0.933223i	0.998822	−	0.0485260i	$-0.0154524\pi$
$503$	9122.39	+	10527.8i	0.808643	+	0.933223i	−0.190179	+	0.981749i	$0.560907\pi$
$504$		0			0
$505$	−7595.07			−0.669260
$506$	−1078.82	−	6186.65i	−0.0947818	−	0.543537i
$507$		0			0
$508$	1248.90	−	366.709i	0.109076	−	0.0320277i
$509$	3672.49	+	4238.28i	0.319804	+	0.369074i	0.892776	−	0.450502i	$-0.148755\pi$
$509$	3672.49	+	4238.28i	0.319804	+	0.369074i	−0.572971	+	0.819575i	$0.694209\pi$
$510$		0			0
$511$	788.831	+	5486.44i	0.0682893	+	0.474962i
$512$	10950.9	+	7037.71i	0.945245	+	0.607472i
$513$		0			0
$514$	−2173.19	+	2508.00i	−0.186489	+	0.215220i
$515$	282.983	−	1968.19i	0.0242130	−	0.168405i
$516$		0			0
$517$	−11480.0	−	3370.82i	−0.976574	−	0.286748i
$518$	3507.10	+	1029.78i	0.297477	+	0.0873471i
$519$		0			0
$520$	1839.69	−	12795.3i	0.155146	−	1.07906i
$521$	5797.01	−	6690.10i	0.487469	−	0.562569i	−0.457718	−	0.889097i	$-0.651333\pi$
$521$	5797.01	−	6690.10i	0.487469	−	0.562569i	0.945188	+	0.326528i	$0.105879\pi$
$522$		0			0
$523$	16279.0	+	10461.9i	1.36105	+	0.874694i	0.998362	−	0.0572166i	$-0.0182226\pi$
$523$	16279.0	+	10461.9i	1.36105	+	0.874694i	0.362688	+	0.931910i	$0.381859\pi$
$524$	−124.297	−	864.504i	−0.0103625	−	0.0720726i
$525$		0			0
$526$	−8930.45	−	10306.3i	−0.740278	−	0.854326i
$527$	1961.68	−	576.001i	0.162148	−	0.0476110i
$528$		0			0
$529$	−11448.9	+	4118.13i	−0.940978	+	0.338467i
$530$	18939.0			1.55219
$531$		0			0
$532$	132.858	+	153.326i	0.0108273	+	0.0124954i
$533$	−10891.0	+	6999.21i	−0.885067	+	0.568798i
$534$		0			0
$535$	25038.7	+	16091.4i	2.02340	+	1.30036i
$536$	−1711.80	+	3748.31i	−0.137945	+	0.302057i
$537$		0			0
$538$	−2330.13	+	16206.4i	−0.186727	+	1.29871i
$539$	−2794.97	−	6120.14i	−0.223355	−	0.489078i
$540$		0			0
$541$	12885.0	+	3783.39i	1.02398	+	0.300666i	0.750259	−	0.661144i	$-0.229929\pi$
$541$	12885.0	+	3783.39i	1.02398	+	0.300666i	0.273717	+	0.961810i	$0.411747\pi$
$542$	531.279	+	1163.34i	0.0421040	+	0.0921950i
$543$		0			0
$544$	−4645.96	+	5361.73i	−0.366165	+	0.422577i
$545$	−5566.56	+	12189.1i	−0.437514	+	0.958022i
$546$		0			0
$547$	−2147.26	−	14934.5i	−0.167843	−	1.16737i	−0.883332	−	0.468749i	$-0.844705\pi$
$547$	−2147.26	−	14934.5i	−0.167843	−	1.16737i	0.715489	−	0.698624i	$-0.246204\pi$
$548$	454.928	−	292.365i	0.0354627	−	0.0227905i
$549$		0			0
$550$	6607.79	−	1940.22i	0.512286	−	0.150421i
$551$	350.464			0.0270967
$552$		0			0
$553$	−1392.82			−0.107104
$554$	−10010.7	+	2939.40i	−0.767714	+	0.225421i
$555$		0			0
$556$	1958.20	−	1258.46i	0.149364	−	0.0959902i
$557$	−1131.61	−	7870.50i	−0.0860821	−	0.598714i	−0.986509	−	0.163707i	$-0.947655\pi$
$557$	−1131.61	−	7870.50i	−0.0860821	−	0.598714i	0.900427	−	0.435007i	$-0.143254\pi$
$558$		0			0
$559$	−6761.89	+	14806.5i	−0.511623	+	1.12030i
$560$	−3219.49	+	3715.49i	−0.242943	+	0.280372i
$561$		0			0
$562$	1750.45	+	3832.96i	0.131385	+	0.287693i
$563$	2919.31	+	857.188i	0.218534	+	0.0641673i	0.389167	−	0.921167i	$-0.372763\pi$
$563$	2919.31	+	857.188i	0.218534	+	0.0641673i	−0.170633	+	0.985335i	$0.554581\pi$
$564$		0			0
$565$	−3706.23	−	8115.50i	−0.275968	−	0.604286i
$566$	1373.37	−	9551.98i	0.101991	−	0.709363i
$567$		0			0
$568$	−2271.18	+	4973.19i	−0.167776	+	0.367378i
$569$	−9864.81	−	6339.73i	−0.726809	−	0.467092i	0.124190	−	0.992258i	$-0.460367\pi$
$569$	−9864.81	−	6339.73i	−0.726809	−	0.467092i	−0.850999	+	0.525167i	$0.824003\pi$
$570$		0			0
$571$	3776.73	−	2427.16i	0.276797	−	0.177887i	−0.394876	−	0.918735i	$-0.629212\pi$
$571$	3776.73	−	2427.16i	0.276797	−	0.177887i	0.671673	+	0.740848i	$0.265576\pi$
$572$	−601.173	−	693.791i	−0.0439446	−	0.0507148i
$573$		0			0
$574$	5837.10			0.424453
$575$	−5902.37	−	11966.0i	−0.428080	−	0.867855i
$576$		0			0
$577$	−19260.5	+	5655.40i	−1.38965	+	0.408037i	−0.889116	−	0.457681i	$-0.848680\pi$
$577$	−19260.5	+	5655.40i	−1.38965	+	0.408037i	−0.500531	+	0.865719i	$0.666862\pi$
$578$	20173.9	+	23282.0i	1.45177	+	1.67544i
$579$		0			0
$580$	−34.2738	−	238.380i	−0.00245370	−	0.0170658i
$581$	4565.76	+	2934.24i	0.326024	+	0.209523i
$582$		0			0
$583$	6643.35	−	7666.84i	0.471938	−	0.544645i
$584$	−3185.41	+	22155.0i	−0.225708	+	1.56983i
$585$		0			0
$586$	12544.4	+	3683.36i	0.884305	+	0.259655i
$587$	−9112.34	−	2675.63i	−0.640727	−	0.188134i	−0.0547987	−	0.998497i	$-0.517452\pi$
$587$	−9112.34	−	2675.63i	−0.640727	−	0.188134i	−0.585928	+	0.810363i	$0.699270\pi$
$588$		0			0
$589$	62.7440	−	436.394i	0.00438934	−	0.0305285i
$590$	15967.3	−	18427.2i	1.11417	−	1.28583i
$591$		0			0
$592$	10473.7	+	6731.05i	0.727140	+	0.467305i
$593$	−1793.07	−	12471.1i	−0.124170	−	0.863621i	−0.952751	−	0.303752i	$-0.901761\pi$
$593$	−1793.07	−	12471.1i	−0.124170	−	0.863621i	0.828581	−	0.559869i	$-0.189148\pi$
$594$		0			0
$595$	−7902.23	−	9119.66i	−0.544471	−	0.628352i
$596$	−494.252	+	145.125i	−0.0339687	+	0.00997410i
$597$		0			0
$598$	6230.50	−	7639.58i	0.426060	−	0.522417i
$599$	−5827.00			−0.397471			−0.198735	−	0.980053i	$-0.563683\pi$
$599$	−5827.00			−0.397471			−0.198735	+	0.980053i	$0.563683\pi$
$600$		0			0
$601$	15847.0	+	18288.4i	1.07556	+	1.24126i	0.969027	+	0.246953i	$0.0794294\pi$
$601$	15847.0	+	18288.4i	1.07556	+	1.24126i	0.106533	+	0.994309i	$0.466025\pi$
$602$	6174.05	−	3967.82i	0.417999	−	0.268632i
$603$		0			0
$604$	−909.201	−	584.308i	−0.0612497	−	0.0393628i
$605$	−5555.48	+	12164.8i	−0.373327	+	0.817471i
$606$		0			0
$607$	340.180	−	2366.00i	0.0227471	−	0.158209i	−0.975282	−	0.220964i	$-0.929080\pi$
$607$	340.180	−	2366.00i	0.0227471	−	0.158209i	0.998029	+	0.0627550i	$0.0199887\pi$
$608$	635.543	+	1391.64i	0.0423925	+	0.0928267i
$609$		0			0
$610$	10861.1	+	3189.11i	0.720908	+	0.211678i
$611$	−7802.16	−	17084.3i	−0.516598	−	1.13119i
$612$		0			0
$613$	14588.9	−	16836.5i	0.961241	−	1.10933i	−0.0327049	−	0.999465i	$-0.510412\pi$
$613$	14588.9	−	16836.5i	0.961241	−	1.10933i	0.993946	−	0.109867i	$-0.0350424\pi$
$614$	−4789.71	+	10488.0i	−0.314816	+	0.689351i
$615$		0			0
$616$	444.307	+	3090.22i	0.0290611	+	0.202124i
$617$	3446.25	−	2214.77i	0.224864	−	0.144511i	−0.423359	−	0.905962i	$-0.639149\pi$
$617$	3446.25	−	2214.77i	0.224864	−	0.144511i	0.648222	+	0.761451i	$0.275513\pi$
$618$		0			0
$619$	−11720.2	+	3441.36i	−0.761024	+	0.223457i	−0.639143	−	0.769088i	$-0.720711\pi$
$619$	−11720.2	+	3441.36i	−0.761024	+	0.223457i	−0.121881	+	0.992545i	$0.538893\pi$
$620$	−302.964			−0.0196247
$621$		0			0
$622$	23910.6			1.54137
$623$	3936.33	−	1155.81i	0.253139	−	0.0743284i
$624$		0			0
$625$	−13555.6	+	8711.63i	−0.867556	+	0.557544i
$626$	−923.170	−	6420.79i	−0.0589414	−	0.409946i
$627$		0			0
$628$	1145.77	−	2508.89i	0.0728044	−	0.159419i
$629$	−20011.8	+	23094.8i	−1.26856	+	1.46399i
$630$		0			0
$631$	−11749.4	−	25727.6i	−0.741263	−	1.62314i	−0.781467	−	0.623947i	$-0.785528\pi$
$631$	−11749.4	−	25727.6i	−0.741263	−	1.62314i	0.0402042	−	0.999191i	$-0.487199\pi$
$632$	−5396.58	−	1584.58i	−0.339659	−	0.0997329i
$633$		0			0
$634$	−5391.62	−	11806.0i	−0.337742	−	0.739552i
$635$	−2375.93	+	16524.9i	−0.148482	+	1.03271i
$636$		0			0
$637$	4387.44	−	9607.16i	0.272899	−	0.597566i
$638$	601.505	+	386.564i	0.0373257	+	0.0239878i
$639$		0			0
$640$	−13602.5	+	8741.82i	−0.840136	+	0.539923i
$641$	−7835.51	−	9042.66i	−0.482814	−	0.557198i	0.461117	−	0.887339i	$-0.347449\pi$
$641$	−7835.51	−	9042.66i	−0.482814	−	0.557198i	−0.943931	+	0.330142i	$0.892903\pi$
$642$		0			0
$643$	2342.99			0.143699			0.0718495	−	0.997415i	$-0.477110\pi$
$643$	2342.99			0.143699			0.0718495	+	0.997415i	$0.477110\pi$
$644$	762.353	−	248.786i	0.0466474	−	0.0152229i
$645$		0			0
$646$	9020.49	−	2648.65i	0.549391	−	0.161316i
$647$	4155.18	+	4795.33i	0.252484	+	0.291382i	0.867816	−	0.496886i	$-0.165523\pi$
$647$	4155.18	+	4795.33i	0.252484	+	0.291382i	−0.615332	+	0.788268i	$0.710978\pi$
$648$		0			0
$649$	−1858.72	−	12927.7i	−0.112421	−	0.781902i
$650$	9094.42	+	5844.63i	0.548788	+	0.352685i
$651$		0			0
$652$	93.6144	−	108.037i	0.00562304	−	0.00648933i
$653$	−404.813	+	2815.54i	−0.0242597	+	0.168730i	−0.998349	−	0.0574321i	$-0.981709\pi$
$653$	−404.813	+	2815.54i	−0.0242597	+	0.168730i	0.974090	+	0.226162i	$0.0726178\pi$
$654$		0			0
$655$	10748.6	+	3156.06i	0.641193	+	0.188271i
$656$	19076.9	+	5601.47i	1.13541	+	0.333385i
$657$		0			0
$658$	−1205.15	+	8381.98i	−0.0714005	+	0.496601i
$659$	12062.7	−	13921.1i	0.713043	−	0.822895i	−0.277409	−	0.960752i	$-0.589476\pi$
$659$	12062.7	−	13921.1i	0.713043	−	0.822895i	0.990452	+	0.137857i	$0.0440213\pi$
$660$		0			0
$661$	1083.59	+	696.383i	0.0637623	+	0.0409776i	0.572134	−	0.820160i	$-0.306116\pi$
$661$	1083.59	+	696.383i	0.0637623	+	0.0409776i	−0.508371	+	0.861138i	$0.669752\pi$
$662$	−2328.70	−	16196.5i	−0.136718	−	0.950896i
$663$		0			0
$664$	14352.2	+	16563.3i	0.838813	+	0.968042i
$665$	−2496.77	+	733.118i	−0.145595	+	0.0427505i
$666$		0			0
$667$	537.608	−	1276.70i	0.0312088	−	0.0741141i
$668$	1805.64			0.104584
$669$		0			0
$670$	−4588.73	−	5295.68i	−0.264594	−	0.305358i
$671$	5100.82	−	3278.10i	0.293465	−	0.188599i
$672$		0			0
$673$	−12279.3	−	7891.40i	−0.703314	−	0.451993i	0.139483	−	0.990225i	$-0.455456\pi$
$673$	−12279.3	−	7891.40i	−0.703314	−	0.451993i	−0.842797	+	0.538232i	$0.819092\pi$
$674$	3480.37	−	7620.94i	0.198900	−	0.435531i
$675$		0			0
$676$	−177.224	+	1232.62i	−0.0100833	+	0.0701309i
$677$	−2129.42	−	4662.78i	−0.120887	−	0.264705i	0.839509	−	0.543347i	$-0.182843\pi$
$677$	−2129.42	−	4662.78i	−0.120887	−	0.264705i	−0.960395	+	0.278642i	$0.910116\pi$
$678$		0			0
$679$	491.208	+	144.232i	0.0277626	+	0.00815185i
$680$	−20242.5	−	44325.0i	−1.14157	−	2.49969i
$681$		0			0
$682$	589.034	−	679.782i	0.0330723	−	0.0381674i
$683$	14549.2	−	31858.4i	0.815096	−	1.78481i	0.231359	−	0.972868i	$-0.425683\pi$
$683$	14549.2	−	31858.4i	0.815096	−	1.78481i	0.583737	−	0.811943i	$-0.301590\pi$
$684$		0			0
$685$	987.108	+	6865.49i	0.0550591	+	0.382944i
$686$	−8472.37	+	5444.86i	−0.471540	+	0.303041i
$687$		0			0
$688$	23985.7	−	7042.84i	1.32914	−	0.390270i
$689$	15924.7			0.880528
$690$		0			0
$691$	−21001.1			−1.15618			−0.578090	−	0.815973i	$-0.696202\pi$
$691$	−21001.1			−1.15618			−0.578090	+	0.815973i	$0.696202\pi$
$692$	−556.401	+	163.374i	−0.0305653	+	0.00897479i
$693$		0			0
$694$	−17267.7	+	11097.3i	−0.944485	+	0.606984i
$695$	4248.92	+	29551.9i	0.231901	+	1.61290i
$696$		0			0
$697$	−20272.6	+	44390.9i	−1.10169	+	2.41237i
$698$	−753.932	+	870.083i	−0.0408836	+	0.0471822i
$699$		0			0
$700$	365.316	+	799.930i	0.0197252	+	0.0431921i
$701$	−6542.50	−	1921.05i	−0.352506	−	0.103505i	0.100685	−	0.994918i	$-0.467896\pi$
$701$	−6542.50	−	1921.05i	−0.352506	−	0.103505i	−0.453192	+	0.891413i	$0.649715\pi$
$702$		0			0
$703$	2737.50	+	5994.30i	0.146866	+	0.321592i
$704$	−1756.95	+	12219.9i	−0.0940591	+	0.654195i
$705$		0			0
$706$	5035.26	−	11025.7i	0.268420	−	0.587758i
$707$	2422.31	+	1556.73i	0.128855	+	0.0828101i
$708$		0			0
$709$	−30459.3	+	19575.0i	−1.61343	+	1.03689i	−0.653395	+	0.757017i	$0.726656\pi$
$709$	−30459.3	+	19575.0i	−1.61343	+	1.03689i	−0.960037	+	0.279872i	$0.909708\pi$
$710$	−6088.24	−	7026.20i	−0.321813	−	0.371392i
$711$		0			0
$712$	16566.5			0.871991
$713$	−1493.49	−	897.993i	−0.0784454	−	0.0471671i
$714$		0			0
$715$	11297.7	−	3317.31i	0.590924	−	0.173511i
$716$	1790.98	+	2066.90i	0.0934806	+	0.107882i
$717$		0			0
$718$	−3216.15	−	22368.8i	−0.167167	−	1.16267i
$719$	−28861.0	−	18547.8i	−1.49699	−	0.962056i	−0.995283	−	0.0970170i	$-0.969070\pi$
$719$	−28861.0	−	18547.8i	−1.49699	−	0.962056i	−0.501705	−	0.865039i	$-0.667294\pi$
$720$		0			0
$721$	−493.663	+	569.717i	−0.0254993	+	0.0294277i
$722$	−2252.68	+	15667.7i	−0.116116	+	0.807606i
$723$		0			0
$724$	3335.22	+	979.309i	0.171205	+	0.0502704i
$725$	1457.58	+	427.984i	0.0746665	+	0.0219241i
$726$		0			0
$727$	260.604	−	1812.54i	0.0132947	−	0.0924669i	−0.982094	−	0.188393i	$-0.939672\pi$
$727$	260.604	−	1812.54i	0.0132947	−	0.0924669i	0.995388	+	0.0959260i	$0.0305812\pi$
$728$	−3209.34	+	3703.78i	−0.163387	+	0.188559i
$729$		0			0
$730$	−32019.6	−	20577.7i	−1.62342	−	1.04331i
$731$	8732.21	+	60733.8i	0.441823	+	3.07294i
$732$		0			0
$733$	5525.61	+	6376.90i	0.278436	+	0.321332i	0.877692	−	0.479226i	$-0.159082\pi$
$733$	5525.61	+	6376.90i	0.278436	+	0.321332i	−0.599256	+	0.800557i	$0.704537\pi$
$734$	14237.5	−	4180.50i	0.715960	−	0.210225i
$735$		0			0
$736$	6044.53	−	180.446i	0.302723	−	0.00903711i
$737$	−3753.40			−0.187596
$738$		0			0
$739$	−3963.33	−	4573.93i	−0.197285	−	0.227679i	0.648484	−	0.761228i	$-0.275403\pi$
$739$	−3963.33	−	4573.93i	−0.197285	−	0.227679i	−0.845769	+	0.533549i	$0.820858\pi$
$740$	3809.51	−	2448.22i	0.189244	−	0.121620i
$741$		0			0
$742$	−6040.27	−	3881.84i	−0.298848	−	0.192058i
$743$	−7421.71	+	16251.3i	−0.366455	+	0.802424i	0.633142	+	0.774036i	$0.281765\pi$
$743$	−7421.71	+	16251.3i	−0.366455	+	0.802424i	−0.999597	+	0.0283886i	$0.990962\pi$
$744$		0			0
$745$	940.275	−	6539.76i	0.0462403	−	0.321608i
$746$	7969.79	+	17451.4i	0.391146	+	0.856490i
$747$		0			0
$748$	−3320.32	−	974.935i	−0.162304	−	0.0476566i
$749$	−4687.48	−	10264.1i	−0.228674	−	0.500726i
$750$		0			0
$751$	−11455.2	+	13220.0i	−0.556601	+	0.642351i	−0.962408	−	0.271607i	$-0.912445\pi$
$751$	−11455.2	+	13220.0i	−0.556601	+	0.642351i	0.405808	+	0.913959i	$0.366990\pi$
$752$	−11982.3	+	26237.6i	−0.581050	+	1.27232i
$753$		0			0
$754$	159.734	+	1110.97i	0.00771506	+	0.0536594i
$755$	11661.6	−	7494.46i	0.562131	−	0.361260i
$756$		0			0
$757$	34877.2	−	10240.9i	1.67455	−	0.491691i	0.699676	−	0.714460i	$-0.253328\pi$
$757$	34877.2	−	10240.9i	1.67455	−	0.491691i	0.974871	+	0.222769i	$0.0715096\pi$
$758$	20355.2			0.975374
$759$		0			0
$760$	−10508.0			−0.501532
$761$	−21810.5	+	6404.14i	−1.03894	+	0.305059i	−0.756339	−	0.654180i	$-0.773014\pi$
$761$	−21810.5	+	6404.14i	−1.03894	+	0.305059i	−0.282597	+	0.959239i	$0.591196\pi$
$762$		0			0
$763$	4273.69	−	2746.53i	0.202776	−	0.130316i
$764$	75.5921	+	525.755i	0.00357962	+	0.0248968i
$765$		0			0
$766$	8332.30	−	18245.2i	0.393026	−	0.860607i
$767$	13426.0	−	15494.4i	0.632051	−	0.729426i
$768$		0			0
$769$	8565.11	+	18755.0i	0.401646	+	0.879482i	0.997101	+	0.0760934i	$0.0242447\pi$
$769$	8565.11	+	18755.0i	0.401646	+	0.879482i	−0.595455	+	0.803389i	$0.703028\pi$
$770$	−5093.87	−	1495.70i	−0.238403	−	0.0700015i
$771$		0			0
$772$	−1644.47	−	3600.90i	−0.0766657	−	0.167874i
$773$	3452.38	−	24011.8i	0.160638	−	1.11726i	−0.736796	−	0.676115i	$-0.763662\pi$
$773$	3452.38	−	24011.8i	0.160638	−	1.11726i	0.897434	−	0.441148i	$-0.145429\pi$
$774$		0			0
$775$	793.874	−	1738.34i	0.0367959	−	0.0805717i
$776$	1739.13	+	1117.67i	0.0804526	+	0.0517038i
$777$		0			0
$778$	−9706.38	+	6237.91i	−0.447289	+	0.287455i
$779$	6891.49	+	7953.20i	0.316962	+	0.365793i
$780$		0			0
$781$	−4979.93			−0.228164
$782$	4188.57	−	36923.7i	0.191538	−	1.68848i
$783$		0			0
$784$	−15563.1	+	4569.74i	−0.708961	+	0.208170i
$785$	23166.6	+	26735.7i	1.05331	+	1.21559i
$786$		0			0
$787$	1422.46	+	9893.39i	0.0644283	+	0.448109i	0.996344	+	0.0854333i	$0.0272275\pi$
$787$	1422.46	+	9893.39i	0.0644283	+	0.448109i	−0.931916	+	0.362675i	$0.881863\pi$
$788$	3308.84	+	2126.46i	0.149584	+	0.0961320i
$789$		0			0
$790$	6263.25	−	7228.17i	0.282071	−	0.325528i
$791$	−481.362	+	3347.94i	−0.0216375	+	0.150492i
$792$		0			0
$793$	9132.48	+	2681.54i	0.408958	+	0.120081i
$794$	−22825.8	−	6702.27i	−1.02022	−	0.299565i
$795$		0			0
$796$	104.042	−	723.627i	0.00463274	−	0.0322214i
$797$	−970.728	+	1120.28i	−0.0431430	+	0.0497897i	−0.776911	−	0.629611i	$-0.783214\pi$
$797$	−970.728	+	1120.28i	−0.0431430	+	0.0497897i	0.733768	+	0.679400i	$0.237760\pi$
$798$		0			0
$799$	−59559.0	−	38276.2i	−2.63710	−	1.69476i
$800$	943.758	+	6563.98i	0.0417086	+	0.290090i
$801$		0			0
$802$	6826.74	+	7878.48i	0.300574	+	0.346881i
$803$	−19561.9	+	5743.90i	−0.859683	+	0.252426i
$804$		0			0
$805$	−1159.35	+	10220.1i	−0.0507599	+	0.447466i
$806$	1411.97			0.0617053
$807$		0			0
$808$	7614.38	+	8787.47i	0.331526	+	0.382601i
$809$	30775.6	−	19778.3i	1.33747	−	0.859540i	0.340726	−	0.940163i	$-0.389327\pi$
$809$	30775.6	−	19778.3i	1.33747	−	0.859540i	0.996745	+	0.0806228i	$0.0256909\pi$
$810$		0			0
$811$	−8468.09	−	5442.11i	−0.366652	−	0.235633i	0.344321	−	0.938852i	$-0.388109\pi$
$811$	−8468.09	−	5442.11i	−0.366652	−	0.235633i	−0.710973	+	0.703219i	$0.751745\pi$
$812$	−37.9286	+	83.0520i	−0.00163920	+	0.00358935i
$813$		0			0
$814$	−1913.34	+	13307.6i	−0.0823865	+	0.573010i
$815$	761.683	+	1667.85i	0.0327369	+	0.0716839i
$816$		0			0
$817$	12695.6	+	3727.75i	0.543649	+	0.159630i
$818$	−2077.78	−	4549.71i	−0.0888118	−	0.194471i
$819$		0			0
$820$	4735.68	−	5465.27i	0.201680	−	0.232751i
$821$	−6798.44	+	14886.5i	−0.288998	+	0.632817i	−0.997327	−	0.0730653i	$-0.976722\pi$
$821$	−6798.44	+	14886.5i	−0.288998	+	0.632817i	0.708329	+	0.705882i	$0.249449\pi$
$822$		0			0
$823$	3011.07	+	20942.4i	0.127532	+	0.887007i	0.948668	+	0.316274i	$0.102432\pi$
$823$	3011.07	+	20942.4i	0.127532	+	0.887007i	−0.821136	+	0.570733i	$0.806659\pi$
$824$	−2560.89	+	1645.78i	−0.108268	+	0.0695795i
$825$		0			0
$826$	−8869.42	+	2604.30i	−0.373616	+	0.109704i
$827$	−7331.71			−0.308281			−0.154141	−	0.988049i	$-0.549261\pi$
$827$	−7331.71			−0.308281			−0.154141	+	0.988049i	$0.549261\pi$
$828$		0			0
$829$	3353.85			0.140511			0.0702557	−	0.997529i	$-0.477618\pi$
$829$	3353.85			0.140511			0.0702557	+	0.997529i	$0.477618\pi$
$830$	−35758.8	+	10499.7i	−1.49543	+	0.439098i
$831$		0			0
$832$	−16303.1	+	10477.4i	−0.679337	+	0.436583i
$833$	−5665.88	−	39407.1i	−0.235668	−	1.63910i
$834$		0			0
$835$	−9620.82	+	21066.7i	−0.398733	+	0.873104i
$836$	−488.679	+	563.965i	−0.0202169	+	0.0233315i
$837$		0			0
$838$	1416.73	+	3102.21i	0.0584011	+	0.127881i
$839$	−45444.9	−	13343.8i	−1.87000	−	0.549082i	−0.998250	−	0.0591332i	$-0.981166\pi$
$839$	−45444.9	−	13343.8i	−1.87000	−	0.549082i	−0.871751	−	0.489949i	$-0.837016\pi$
$840$		0			0
$841$	−10066.0	−	22041.5i	−0.412729	−	0.903750i
$842$	1233.25	−	8577.44i	0.0504758	−	0.351067i
$843$		0			0
$844$	2318.44	−	5076.67i	0.0945544	−	0.207045i
$845$	−13436.9	−	8635.35i	−0.547033	−	0.351556i
$846$		0			0
$847$	4265.19	−	2741.07i	0.173027	−	0.111198i
$848$	−16015.7	−	18483.1i	−0.648563	−	0.748482i
$849$		0			0
$850$	40750.8			1.64440
$851$	26035.9	−	777.242i	1.04876	−	0.0313085i
$852$		0			0
$853$	−18377.2	+	5396.02i	−0.737658	+	0.216596i	−0.628915	−	0.777474i	$-0.716501\pi$
$853$	−18377.2	+	5396.02i	−0.737658	+	0.216596i	−0.108743	+	0.994070i	$0.534683\pi$
$854$	−2810.30	−	3243.26i	−0.112607	−	0.129956i
$855$		0			0
$856$	−6484.70	−	45102.0i	−0.258928	−	1.80088i
$857$	5162.69	+	3317.86i	0.205781	+	0.132247i	0.639472	−	0.768814i	$-0.279153\pi$
$857$	5162.69	+	3317.86i	0.205781	+	0.132247i	−0.433691	+	0.901061i	$0.642789\pi$
$858$		0			0
$859$	19685.2	−	22717.9i	0.781897	−	0.902358i	−0.215348	−	0.976537i	$-0.569088\pi$
$859$	19685.2	−	22717.9i	0.781897	−	0.902358i	0.997245	+	0.0741799i	$0.0236339\pi$
$860$	1293.99	−	8999.87i	0.0513076	−	0.356852i
$861$		0			0
$862$	−39178.2	−	11503.8i	−1.54804	−	0.454547i
$863$	40937.8	+	12020.4i	1.61476	+	0.474137i	0.959604	−	0.281354i	$-0.0907837\pi$
$863$	40937.8	+	12020.4i	1.61476	+	0.474137i	0.655158	+	0.755491i	$0.272602\pi$
$864$		0			0
$865$	1058.51	−	7362.10i	0.0416074	−	0.289386i
$866$	15923.9	−	18377.2i	0.624847	−	0.721111i
$867$		0			0
$868$	96.6251	+	62.0972i	0.00377842	+	0.00242824i
$869$	−729.090	−	5070.94i	−0.0284611	−	0.197951i
$870$		0			0
$871$	−3858.40	−	4452.83i	−0.150100	−	0.173224i
$872$	19683.4	−	5779.57i	0.764408	−	0.224451i
$873$		0			0
$874$	−6867.58	−	4129.29i	−0.265789	−	0.159812i
$875$	376.603			0.0145503
$876$		0			0
$877$	−2345.39	−	2706.72i	−0.0903057	−	0.104218i	0.708798	−	0.705411i	$-0.249238\pi$
$877$	−2345.39	−	2706.72i	−0.0903057	−	0.104218i	−0.799104	+	0.601193i	$0.794692\pi$
$878$	−4325.45	+	2779.80i	−0.166261	+	0.106849i
$879$		0			0
$880$	−15212.5	−	9776.49i	−0.582743	−	0.374506i
$881$	−11158.7	+	24434.2i	−0.426728	+	0.934403i	0.567119	+	0.823636i	$0.308058\pi$
$881$	−11158.7	+	24434.2i	−0.426728	+	0.934403i	−0.993846	+	0.110767i	$0.964669\pi$
$882$		0			0
$883$	−1576.66	+	10965.9i	−0.0600892	+	0.417930i	0.937468	+	0.348072i	$0.113164\pi$
$883$	−1576.66	+	10965.9i	−0.0600892	+	0.417930i	−0.997557	+	0.0698575i	$0.977746\pi$
$884$	−2256.60	−	4941.26i	−0.0858570	−	0.188001i
$885$		0			0
$886$	32602.7	+	9573.01i	1.23624	+	0.362993i
$887$	−1694.57	−	3710.59i	−0.0641466	−	0.140461i	0.874843	−	0.484406i	$-0.160964\pi$
$887$	−1694.57	−	3710.59i	−0.0641466	−	0.140461i	−0.938990	+	0.343944i	$0.888237\pi$
$888$		0			0
$889$	4144.80	−	4783.35i	0.156369	−	0.180460i
$890$	−11702.7	+	25625.4i	−0.440760	+	0.965131i
$891$		0			0
$892$	651.718	+	4532.80i	0.0244631	+	0.170145i
$893$	−12843.5	+	8254.02i	−0.481289	+	0.309306i
$894$		0			0
$895$	−33657.5	+	9882.74i	−1.25704	+	0.369099i
$896$	6130.06			0.228561
$897$		0			0
$898$	7652.41			0.284370
$899$	190.375	−	55.8991i	0.00706269	−	0.00207379i
$900$		0			0
$901$	50499.5	−	32454.0i	1.86724	−	1.20000i
$902$	3055.51	+	21251.5i	0.112791	+	0.784478i
$903$		0			0
$904$	−5673.95	+	12424.2i	−0.208753	+	0.457106i
$905$	−29196.5	+	33694.5i	−1.07240	+	1.23762i
$906$		0			0
$907$	2334.63	+	5112.13i	0.0854687	+	0.187150i	0.947540	−	0.319636i	$-0.103561\pi$
$907$	2334.63	+	5112.13i	0.0854687	+	0.187150i	−0.862072	+	0.506786i	$0.830833\pi$
$908$	3901.70	+	1145.64i	0.142602	+	0.0418717i
$909$		0			0
$910$	−3461.96	−	7580.64i	−0.126113	−	0.276149i
$911$	2135.16	−	14850.3i	0.0776519	−	0.540081i	−0.913447	−	0.406957i	$-0.866590\pi$
$911$	2135.16	−	14850.3i	0.0776519	−	0.540081i	0.991099	−	0.133124i	$-0.0425009\pi$
$912$		0			0
$913$	−8292.87	+	18158.8i	−0.300607	+	0.658237i
$914$	−10646.5	−	6842.11i	−0.385291	−	0.247612i
$915$		0			0
$916$	−1322.15	+	849.697i	−0.0476913	+	0.0306493i
$917$	−2781.18	−	3209.65i	−0.100156	−	0.115586i
$918$		0			0
$919$	−11481.3			−0.412114			−0.206057	−	0.978540i	$-0.566063\pi$
$919$	−11481.3			−0.412114			−0.206057	+	0.978540i	$0.566063\pi$
$920$	−16119.1	+	38279.4i	−0.577643	+	1.37178i
$921$		0			0
$922$	−13111.8	+	3849.96i	−0.468343	+	0.137518i
$923$	−5119.25	−	5907.93i	−0.182559	−	0.210684i
$924$		0			0
$925$	4065.09	+	28273.3i	0.144497	+	1.00500i
$926$	9019.13	+	5796.24i	0.320072	+	0.205698i
$927$		0			0
$928$	−450.876	+	520.339i	−0.0159491	+	0.0184062i
$929$	−6380.24	+	44375.6i	−0.225327	+	1.56719i	0.492092	+	0.870543i	$0.336232\pi$
$929$	−6380.24	+	44375.6i	−0.225327	+	1.56719i	−0.717419	+	0.696642i	$0.754677\pi$
$930$		0			0
$931$	−8237.49	−	2418.75i	−0.289982	−	0.0851463i
$932$	−6533.13	−	1918.30i	−0.229614	−	0.0674206i
$933$		0			0
$934$	−5482.10	+	38128.8i	−0.192055	+	1.33577i
$935$	29066.1	−	33544.0i	1.01664	−	1.17327i
$936$		0			0
$937$	776.251	+	498.866i	0.0270641	+	0.0173930i	0.554103	−	0.832448i	$-0.313061\pi$
$937$	776.251	+	498.866i	0.0270641	+	0.0173930i	−0.527039	+	0.849841i	$0.676698\pi$
$938$	378.064	+	2629.49i	0.0131602	+	0.0915309i
$939$		0			0
$940$	6870.29	+	7928.74i	0.238387	+	0.275114i
$941$	7539.84	−	2213.90i	0.261203	−	0.0766961i	−0.148509	−	0.988911i	$-0.547447\pi$
$941$	7539.84	−	2213.90i	0.261203	−	0.0766961i	0.409712	+	0.912215i	$0.365629\pi$
$942$		0			0
$943$	39544.1	−	12904.8i	1.36557	−	0.445640i
$944$	−31486.3			−1.08558
$945$		0			0
$946$	17677.8	+	20401.3i	0.607563	+	0.701166i
$947$	−8280.87	+	5321.80i	−0.284152	+	0.182614i	−0.674951	−	0.737863i	$-0.735835\pi$
$947$	−8280.87	+	5321.80i	−0.284152	+	0.182614i	0.390799	+	0.920476i	$0.372199\pi$
$948$		0			0
$949$	−26923.4	−	17302.6i	−0.920939	−	0.591852i
$950$	3650.51	−	7993.51i	0.124672	−	0.272993i
$951$		0			0
$952$	−2629.09	+	18285.7i	−0.0895054	+	0.622524i
$953$	−15987.1	−	35006.9i	−0.543414	−	1.18991i	−0.959790	−	0.280718i	$-0.909427\pi$
$953$	−15987.1	−	35006.9i	−0.543414	−	1.18991i	0.416376	−	0.909192i	$-0.363300\pi$
$954$		0			0
$955$	−6536.82	−	1919.38i	−0.221494	−	0.0650365i
$956$	523.848	+	1147.07i	0.0177222	+	0.0388063i
$957$		0			0
$958$	7524.01	−	8683.17i	0.253747	−	0.292840i
$959$	1092.37	−	2391.95i	0.0367824	−	0.0805423i
$960$		0			0
$961$	4204.18	+	29240.7i	0.141122	+	0.981528i
$962$	−17754.3	+	11410.0i	−0.595032	+	0.382404i
$963$		0			0
$964$	−3828.67	+	1124.20i	−0.127918	+	0.0375602i
$965$	50774.2			1.69376
$966$		0			0
$967$	27609.5			0.918161			0.459081	−	0.888395i	$-0.348179\pi$
$967$	27609.5			0.918161			0.459081	+	0.888395i	$0.348179\pi$
$968$	19644.2	−	5768.07i	0.652262	−	0.191521i
$969$		0			0
$970$	−2957.37	+	1900.59i	−0.0978923	+	0.0629116i
$971$	−2076.46	−	14442.1i	−0.0686269	−	0.477310i	−0.994933	−	0.100539i	$-0.967943\pi$
$971$	−2076.46	−	14442.1i	−0.0686269	−	0.477310i	0.926306	−	0.376771i	$-0.122966\pi$
$972$		0			0
$973$	4702.00	−	10295.9i	0.154922	−	0.339232i
$974$	24011.5	−	27710.8i	0.789917	−	0.911613i
$975$		0			0
$976$	−6072.32	−	13296.5i	−0.199150	−	0.436077i
$977$	34572.2	+	10151.3i	1.13210	+	0.332415i	0.793533	−	0.608527i	$-0.208239\pi$
$977$	34572.2	+	10151.3i	1.13210	+	0.332415i	0.338568	+	0.940942i	$0.390057\pi$
$978$		0			0
$979$	6268.57	+	13726.2i	0.204642	+	0.448103i
$980$	−839.601	+	5839.55i	−0.0273674	+	0.190345i
$981$		0			0
$982$	6016.62	−	13174.6i	0.195518	−	0.428124i
$983$	−50763.4	−	32623.6i	−1.64710	−	1.05853i	−0.933879	−	0.357590i	$-0.883599\pi$
$983$	−50763.4	−	32623.6i	−1.64710	−	1.05853i	−0.713223	−	0.700938i	$-0.752765\pi$
$984$		0			0
$985$	−42439.9	+	27274.4i	−1.37284	+	0.882270i
$986$	2770.66	+	3197.51i	0.0894886	+	0.103275i
$987$		0			0
$988$	−1171.41			−0.0377201
$989$	33054.6	−	40530.2i	1.06277	−	1.30312i
$990$		0			0
$991$	19132.1	−	5617.70i	0.613272	−	0.180073i	0.0396776	−	0.999213i	$-0.487367\pi$
$991$	19132.1	−	5617.70i	0.613272	−	0.180073i	0.573594	+	0.819140i	$0.305549\pi$
$992$	567.200	+	654.584i	0.0181539	+	0.0209507i
$993$		0			0
$994$	501.608	+	3488.76i	0.0160061	+	0.111325i
$995$	7888.30	+	5069.50i	0.251332	+	0.161522i
$996$		0			0
$997$	25001.8	−	28853.7i	0.794199	−	0.916555i	−0.203849	−	0.979002i	$-0.565345\pi$
$997$	25001.8	−	28853.7i	0.794199	−	0.916555i	0.998048	+	0.0624477i	$0.0198907\pi$
$998$	2813.60	−	19569.0i	0.0892415	−	0.620688i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.i.a.55.4		50
3.2	odd	2		23.4.c.a.9.2	✓	50
23.18	even	11	inner	207.4.i.a.64.4		50
69.8	odd	22		529.4.a.n.1.19		25
69.38	even	22		529.4.a.m.1.19		25
69.41	odd	22		23.4.c.a.18.2	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.9.2	✓	50	3.2	odd	2
23.4.c.a.18.2	yes	50	69.41	odd	22
207.4.i.a.55.4		50	1.1	even	1	trivial
207.4.i.a.64.4		50	23.18	even	11	inner
529.4.a.m.1.19		25	69.38	even	22
529.4.a.n.1.19		25	69.8	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)

\(f(q)\)	\(=\)	\(q+(2.49786 - 0.733439i) q^{2} +(-1.02864 + 0.661064i) q^{4} +(-2.23195 - 15.5235i) q^{5} +(-2.46994 + 5.40842i) q^{7} +(-15.7230 + 18.1453i) q^{8} +O(q^{10})\)	\(q+(2.49786 - 0.733439i) q^{2} +(-1.02864 + 0.661064i) q^{4} +(-2.23195 - 15.5235i) q^{5} +(-2.46994 + 5.40842i) q^{7} +(-15.7230 + 18.1453i) q^{8} +(-16.9607 - 37.1386i) q^{10} +(-20.9837 - 6.16138i) q^{11} +(-14.2612 - 31.2277i) q^{13} +(-2.20284 + 15.3211i) q^{14} +(-21.9019 + 47.9585i) q^{16} +(-108.865 - 69.9635i) q^{17} +(-23.4761 + 15.0872i) q^{19} +(12.5579 + 14.4926i) q^{20} -56.9335 q^{22} +(18.9488 + 108.664i) q^{23} +(-116.061 + 34.0787i) q^{25} +(-58.5263 - 67.5429i) q^{26} +(-1.03464 - 7.19609i) q^{28} +(-10.5650 - 6.78974i) q^{29} +(-10.3460 + 11.9399i) q^{31} +(7.80215 - 54.2651i) q^{32} +(-323.245 - 94.9132i) q^{34} +(89.4705 + 26.2709i) q^{35} +(33.6066 - 233.739i) q^{37} +(-47.5745 + 54.9039i) q^{38} +(316.772 + 203.577i) q^{40} +(-53.6680 - 373.269i) q^{41} +(-310.499 - 358.335i) q^{43} +(25.6577 - 7.53378i) q^{44} +(127.030 + 257.531i) q^{46} +547.089 q^{47} +(201.467 + 232.505i) q^{49} +(-264.911 + 170.248i) q^{50} +(35.3132 + 22.6944i) q^{52} +(-192.699 + 421.952i) q^{53} +(-48.8118 + 339.493i) q^{55} +(-59.3027 - 129.855i) q^{56} +(-31.3699 - 9.21104i) q^{58} +(248.087 + 543.235i) q^{59} +(-181.560 + 209.532i) q^{61} +(-17.0857 + 37.4124i) q^{62} +(-80.3376 - 558.760i) q^{64} +(-452.934 + 291.083i) q^{65} +(164.674 - 48.3526i) q^{67} +158.233 q^{68} +242.753 q^{70} +(218.486 - 64.1534i) q^{71} +(784.252 - 504.008i) q^{73} +(-87.4886 - 608.496i) q^{74} +(14.1748 - 31.0384i) q^{76} +(85.1520 - 98.2707i) q^{77} +(97.3133 + 213.086i) q^{79} +(793.369 + 232.954i) q^{80} +(-407.826 - 893.014i) q^{82} +(129.907 - 903.521i) q^{83} +(-843.098 + 1846.13i) q^{85} +(-1038.40 - 667.340i) q^{86} +(441.728 - 283.881i) q^{88} +(-451.850 - 521.462i) q^{89} +204.117 q^{91} +(-91.3256 - 99.2497i) q^{92} +(1366.55 - 401.256i) q^{94} +(286.603 + 330.758i) q^{95} +(-12.2538 - 85.2267i) q^{97} +(673.765 + 433.003i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 11 q^{2} - 27 q^{4} + 19 q^{5} - 19 q^{7} - 28 q^{8}+O(q^{10}) \) 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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