LMFDB - Embedded newform 13.9.f.a.11.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,9,Mod(2,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.2"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	13.11
Dual form			13.9.f.a.6.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.75454 - 28.9403i) q^{2} +(32.8317 + 56.8661i) q^{3} +(-555.707 - 320.838i) q^{4} +(-552.313 - 552.313i) q^{5} +(1900.32 - 509.189i) q^{6} +(-156.442 - 583.848i) q^{7} +(-8170.84 + 8170.84i) q^{8} +(1124.66 - 1947.97i) q^{9} +(-20267.1 + 11701.2i) q^{10} +(23687.0 + 6346.91i) q^{11} -42134.5i q^{12} +(-207.500 - 28560.2i) q^{13} -18109.9 q^{14} +(13274.5 - 49541.3i) q^{15} +(90971.2 + 157567. i) q^{16} +(-35251.5 - 20352.5i) q^{17} +(-47653.8 - 47653.8i) q^{18} +(83073.8 - 22259.5i) q^{19} +(129722. + 484127. i) q^{20} +(28064.9 - 28064.9i) q^{21} +(367363. - 636292. i) q^{22} +(-160881. + 92884.7i) q^{23} +(-732906. - 196382. i) q^{24} +219475. i q^{25} +(-828152. - 215466. i) q^{26} +578515. q^{27} +(-100385. + 374641. i) q^{28} +(-241730. - 418689. i) q^{29} +(-1.33080e6 - 768339. i) q^{30} +(1.05366e6 + 1.05366e6i) q^{31} +(2.40811e6 - 645251. i) q^{32} +(416759. + 1.55537e6i) q^{33} +(-862367. + 862367. i) q^{34} +(-236062. + 408872. i) q^{35} +(-1.24997e6 + 721669. i) q^{36} +(-2.11273e6 - 566105. i) q^{37} -2.57679e6i q^{38} +(1.61730e6 - 949480. i) q^{39} +9.02572e6 q^{40} +(-240454. + 897388. i) q^{41} +(-594578. - 1.02984e6i) q^{42} +(3.59791e6 + 2.07725e6i) q^{43} +(-1.11267e7 - 1.11267e7i) q^{44} +(-1.69706e6 + 454725. i) q^{45} +(1.44055e6 + 5.37622e6i) q^{46} +(-2.04296e6 + 2.04296e6i) q^{47} +(-5.97347e6 + 1.03464e7i) q^{48} +(4.67606e6 - 2.69972e6i) q^{49} +(6.35168e6 + 1.70193e6i) q^{50} -2.67282e6i q^{51} +(-9.04789e6 + 1.59377e7i) q^{52} +2.17972e6 q^{53} +(4.48612e6 - 1.67424e7i) q^{54} +(-9.57716e6 - 1.65881e7i) q^{55} +(6.04879e6 + 3.49227e6i) q^{56} +(3.99326e6 + 3.99326e6i) q^{57} +(-1.39915e7 + 3.74901e6i) q^{58} +(-1.42024e6 - 5.30042e6i) q^{59} +(-2.32715e7 + 2.32715e7i) q^{60} +(4.76966e6 - 8.26129e6i) q^{61} +(3.86639e7 - 2.23226e7i) q^{62} +(-1.31327e6 - 351888. i) q^{63} -2.81179e7i q^{64} +(-1.56596e7 + 1.58888e7i) q^{65} +4.82446e7 q^{66} +(-3.40019e6 + 1.26897e7i) q^{67} +(1.30597e7 + 2.26200e7i) q^{68} +(-1.05640e7 - 6.09912e6i) q^{69} +(1.00023e7 + 1.00023e7i) q^{70} +(9.80455e6 - 2.62712e6i) q^{71} +(6.72714e6 + 2.51060e7i) q^{72} +(311675. - 311675. i) q^{73} +(-3.27666e7 + 5.67533e7i) q^{74} +(-1.24807e7 + 7.20573e6i) q^{75} +(-5.33064e7 - 1.42834e7i) q^{76} -1.48225e7i q^{77} +(-1.49369e7 - 5.41679e7i) q^{78} -2.60713e7 q^{79} +(3.67816e7 - 1.37271e8i) q^{80} +(1.16147e7 + 2.01173e7i) q^{81} +(2.41061e7 + 1.39177e7i) q^{82} +(3.95551e6 + 3.95551e6i) q^{83} +(-2.46002e7 + 6.59160e6i) q^{84} +(8.22894e6 + 3.07108e7i) q^{85} +(8.80164e7 - 8.80164e7i) q^{86} +(1.58728e7 - 2.74925e7i) q^{87} +(-2.45402e8 + 1.41683e8i) q^{88} +(-2.29479e7 - 6.14886e6i) q^{89} +5.26396e7i q^{90} +(-1.66424e7 + 4.58916e6i) q^{91} +1.19204e8 q^{92} +(-2.53241e7 + 9.45110e7i) q^{93} +(4.32818e7 + 7.49662e7i) q^{94} +(-5.81770e7 - 3.35885e7i) q^{95} +(1.15755e8 + 1.15755e8i) q^{96} +(1.30006e8 - 3.48351e7i) q^{97} +(-4.18702e7 - 1.56262e8i) q^{98} +(3.90035e7 - 3.90035e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) $ 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	7.75454	−	28.9403i	0.484659	−	1.80877i	−0.0969347	−	0.995291i	$-0.530904\pi$
$2$	7.75454	−	28.9403i	0.484659	−	1.80877i	0.581593	−	0.813480i	$-0.302430\pi$
$3$	32.8317	+	56.8661i	0.405329	+	0.702051i	0.994360	−	0.106060i	$-0.0338236\pi$
$3$	32.8317	+	56.8661i	0.405329	+	0.702051i	−0.589031	+	0.808111i	$0.700490\pi$
$4$	−555.707	−	320.838i	−2.17073	−	1.25327i
$5$	−552.313	−	552.313i	−0.883701	−	0.883701i	0.110207	−	0.993909i	$-0.464849\pi$
$5$	−552.313	−	552.313i	−0.883701	−	0.883701i	−0.993909	+	0.110207i	$0.964849\pi$
$6$	1900.32	−	509.189i	1.46630	−	0.392893i
$7$	−156.442	−	583.848i	−0.0651569	−	0.243169i	0.925665	−	0.378345i	$-0.123507\pi$
$7$	−156.442	−	583.848i	−0.0651569	−	0.243169i	−0.990822	+	0.135176i	$0.956840\pi$
$8$	−8170.84	+	8170.84i	−1.99483	+	1.99483i
$9$	1124.66	−	1947.97i	0.171416	−	0.296902i
$10$	−20267.1	+	11701.2i	−2.02671	+	1.17012i
$11$	23687.0	+	6346.91i	1.61785	+	0.433502i	0.950370	−	0.311122i	$-0.100705\pi$
$11$	23687.0	+	6346.91i	1.61785	+	0.433502i	0.667483	+	0.744625i	$0.267372\pi$
$12$		−	42134.5i		−	2.03195i
$13$	−207.500	−	28560.2i	−0.00726517	−	0.999974i
$13$	−207.500	−	28560.2i	−0.00726517	−	0.999974i
$14$	−18109.9			−0.471415
$15$	13274.5	−	49541.3i	0.262213	−	0.978593i
$16$	90971.2	+	157567.i	1.38811	+	2.40428i
$17$	−35251.5	−	20352.5i	−0.422068	−	0.243681i	0.273894	−	0.961760i	$-0.411688\pi$
$17$	−35251.5	−	20352.5i	−0.422068	−	0.243681i	−0.695962	+	0.718079i	$0.745022\pi$
$18$	−47653.8	−	47653.8i	−0.453949	−	0.453949i
$19$	83073.8	−	22259.5i	0.637455	−	0.170806i	0.0744046	−	0.997228i	$-0.476294\pi$
$19$	83073.8	−	22259.5i	0.637455	−	0.170806i	0.563050	+	0.826423i	$0.309628\pi$
$20$	129722.	+	484127.i	0.810760	+	3.02580i
$21$	28064.9	−	28064.9i	0.144307	−	0.144307i
$22$	367363.	−	636292.i	1.56821	−	2.71622i
$23$	−160881.	+	92884.7i	−0.574901	+	0.331919i	−0.759104	−	0.650969i	$-0.774363\pi$
$23$	−160881.	+	92884.7i	−0.574901	+	0.331919i	0.184203	+	0.982888i	$0.441030\pi$
$24$	−732906.	−	196382.i	−2.20904	−	0.591910i
$25$			219475.i			0.561856i
$26$	−828152.	−	215466.i	−1.81224	−	0.471505i
$27$	578515.			1.08858
$28$	−100385.	+	374641.i	−0.163319	+	0.609513i
$29$	−241730.	−	418689.i	−0.341774	−	0.591970i	0.642988	−	0.765876i	$-0.277694\pi$
$29$	−241730.	−	418689.i	−0.341774	−	0.591970i	−0.984762	+	0.173906i	$0.944361\pi$
$30$	−1.33080e6	−	768339.i	−1.64297	−	0.948567i
$31$	1.05366e6	+	1.05366e6i	1.14092	+	1.14092i	0.988283	+	0.152634i	$0.0487755\pi$
$31$	1.05366e6	+	1.05366e6i	1.14092	+	1.14092i	0.152634	+	0.988283i	$0.451224\pi$
$32$	2.40811e6	−	645251.i	2.29655	−	0.615360i
$33$	416759.	+	1.55537e6i	0.351422	+	1.31153i
$34$	−862367.	+	862367.i	−0.645322	+	0.645322i
$35$	−236062.	+	408872.i	−0.157309	+	0.272468i
$36$	−1.24997e6	+	721669.i	−0.744198	+	0.429663i
$37$	−2.11273e6	−	566105.i	−1.12730	−	0.302058i	−0.353464	−	0.935448i	$-0.614996\pi$
$37$	−2.11273e6	−	566105.i	−1.12730	−	0.302058i	−0.773833	+	0.633390i	$0.781663\pi$
$38$		−	2.57679e6i		−	1.23579i
$39$	1.61730e6	−	949480.i	0.699087	−	0.410419i
$40$	9.02572e6			3.52567
$41$	−240454.	+	897388.i	−0.0850936	+	0.317574i	−0.995332	−	0.0965111i	$-0.969232\pi$
$41$	−240454.	+	897388.i	−0.0850936	+	0.317574i	0.910238	+	0.414085i	$0.135898\pi$
$42$	−594578.	−	1.02984e6i	−0.191078	−	0.330958i
$43$	3.59791e6	+	2.07725e6i	1.05239	+	0.607597i	0.923317	−	0.384039i	$-0.125467\pi$
$43$	3.59791e6	+	2.07725e6i	1.05239	+	0.607597i	0.129071	+	0.991635i	$0.458800\pi$
$44$	−1.11267e7	−	1.11267e7i	−2.96863	−	2.96863i
$45$	−1.69706e6	+	454725.i	−0.413854	+	0.110892i
$46$	1.44055e6	+	5.37622e6i	0.321735	+	1.20073i
$47$	−2.04296e6	+	2.04296e6i	−0.418667	+	0.418667i	−0.884744	−	0.466077i	$-0.845667\pi$
$47$	−2.04296e6	+	2.04296e6i	−0.418667	+	0.418667i	0.466077	+	0.884744i	$0.345667\pi$
$48$	−5.97347e6	+	1.03464e7i	−1.12528	+	1.94905i
$49$	4.67606e6	−	2.69972e6i	0.811140	−	0.468312i
$50$	6.35168e6	+	1.70193e6i	1.01627	+	0.272308i
$51$		−	2.67282e6i		−	0.395084i
$52$	−9.04789e6	+	1.59377e7i	−1.23747	+	2.17978i
$53$	2.17972e6			0.276247			0.138123	−	0.990415i	$-0.455893\pi$
$53$	2.17972e6			0.276247			0.138123	+	0.990415i	$0.455893\pi$
$54$	4.48612e6	−	1.67424e7i	0.527589	−	1.96899i
$55$	−9.57716e6	−	1.65881e7i	−1.04661	−	1.81279i
$56$	6.04879e6	+	3.49227e6i	0.615058	+	0.355104i
$57$	3.99326e6	+	3.99326e6i	0.378293	+	0.378293i
$58$	−1.39915e7	+	3.74901e6i	−1.23638	+	0.331288i
$59$	−1.42024e6	−	5.30042e6i	−0.117207	−	0.437424i	0.882235	−	0.470809i	$-0.156038\pi$
$59$	−1.42024e6	−	5.30042e6i	−0.117207	−	0.437424i	−0.999443	+	0.0333852i	$0.989371\pi$
$60$	−2.32715e7	+	2.32715e7i	−1.79564	+	1.79564i
$61$	4.76966e6	−	8.26129e6i	0.344483	−	0.596662i	−0.640777	−	0.767727i	$-0.721388\pi$
$61$	4.76966e6	−	8.26129e6i	0.344483	−	0.596662i	0.985260	+	0.171065i	$0.0547209\pi$
$62$	3.86639e7	−	2.23226e7i	2.61661	−	1.51070i
$63$	−1.31327e6	−	351888.i	−0.0833663	−	0.0223379i
$64$		−	2.81179e7i		−	1.67596i
$65$	−1.56596e7	+	1.58888e7i	−0.877258	+	0.890098i
$66$	4.82446e7			2.54257
$67$	−3.40019e6	+	1.26897e7i	−0.168734	+	0.629725i	0.828800	+	0.559545i	$0.189024\pi$
$67$	−3.40019e6	+	1.26897e7i	−0.168734	+	0.629725i	−0.997534	+	0.0701804i	$0.977643\pi$
$68$	1.30597e7	+	2.26200e7i	0.610797	+	1.05793i
$69$	−1.05640e7	−	6.09912e6i	−0.466049	−	0.269073i
$70$	1.00023e7	+	1.00023e7i	0.416590	+	0.416590i
$71$	9.80455e6	−	2.62712e6i	0.385828	−	0.103382i	−0.0606905	−	0.998157i	$-0.519330\pi$
$71$	9.80455e6	−	2.62712e6i	0.385828	−	0.103382i	0.446519	+	0.894774i	$0.352664\pi$
$72$	6.72714e6	+	2.51060e7i	0.250323	+	0.934217i
$73$	311675.	−	311675.i	0.0109752	−	0.0109752i	−0.701598	−	0.712573i	$-0.747530\pi$
$73$	311675.	−	311675.i	0.0109752	−	0.0109752i	0.712573	+	0.701598i	$0.247530\pi$
$74$	−3.27666e7	+	5.67533e7i	−1.09271	+	1.89262i
$75$	−1.24807e7	+	7.20573e6i	−0.394451	+	0.227737i
$76$	−5.33064e7	−	1.42834e7i	−1.59781	−	0.428132i
$77$		−	1.48225e7i		−	0.421657i
$78$	−1.49369e7	−	5.41679e7i	−0.403535	−	1.46340i
$79$	−2.60713e7			−0.669350			−0.334675	−	0.942334i	$-0.608627\pi$
$79$	−2.60713e7			−0.669350			−0.334675	+	0.942334i	$0.608627\pi$
$80$	3.67816e7	−	1.37271e8i	0.897988	−	3.35134i
$81$	1.16147e7	+	2.01173e7i	0.269816	+	0.467336i
$82$	2.41061e7	+	1.39177e7i	0.533177	+	0.307830i
$83$	3.95551e6	+	3.95551e6i	0.0833470	+	0.0833470i	0.747551	−	0.664204i	$-0.231229\pi$
$83$	3.95551e6	+	3.95551e6i	0.0833470	+	0.0833470i	−0.664204	+	0.747551i	$0.731229\pi$
$84$	−2.46002e7	+	6.59160e6i	−0.494107	+	0.132396i
$85$	8.22894e6	+	3.07108e7i	0.157641	+	0.588323i
$86$	8.80164e7	−	8.80164e7i	1.60905	−	1.60905i
$87$	1.58728e7	−	2.74925e7i	0.277062	−	0.479886i
$88$	−2.45402e8	+	1.41683e8i	−4.09211	+	2.36258i
$89$	−2.29479e7	−	6.14886e6i	−0.365748	−	0.0980020i	0.0712640	−	0.997457i	$-0.477297\pi$
$89$	−2.29479e7	−	6.14886e6i	−0.365748	−	0.0980020i	−0.437012	+	0.899456i	$0.643963\pi$
$90$			5.26396e7i			0.802311i
$91$	−1.66424e7	+	4.58916e6i	−0.242689	+	0.0669218i
$92$	1.19204e8			1.66394
$93$	−2.53241e7	+	9.45110e7i	−0.338535	+	1.26343i
$94$	4.32818e7	+	7.49662e7i	0.554362	+	0.960184i
$95$	−5.81770e7	−	3.35885e7i	−0.714261	−	0.412379i
$96$	1.15755e8	+	1.15755e8i	1.36287	+	1.36287i
$97$	1.30006e8	−	3.48351e7i	1.46851	−	0.393487i	0.566091	−	0.824343i	$-0.308455\pi$
$97$	1.30006e8	−	3.48351e7i	1.46851	−	0.393487i	0.902421	+	0.430856i	$0.141788\pi$
$98$	−4.18702e7	−	1.56262e8i	−0.453943	−	1.69414i
$99$	3.90035e7	−	3.90035e7i	0.406034	−	0.406034i
$100$	7.04159e7	−	1.21964e8i	0.704159	−	1.21964i
$101$	3.97300e7	−	2.29382e7i	0.381798	−	0.220431i	−0.296802	−	0.954939i	$-0.595920\pi$
$101$	3.97300e7	−	2.29382e7i	0.381798	−	0.220431i	0.678600	+	0.734508i	$0.262587\pi$
$102$	−7.73524e7	−	2.07265e7i	−0.714617	−	0.191481i
$103$		−	1.00259e8i		−	0.890790i	−0.895334	−	0.445395i	$-0.853063\pi$
$103$		−	1.00259e8i		−	0.890790i	0.895334	−	0.445395i	$-0.146937\pi$
$104$	2.35057e8	+	2.31666e8i	2.00927	+	1.98029i
$105$	−3.10013e7			−0.255048
$106$	1.69027e7	−	6.30818e7i	0.133885	−	0.499667i
$107$	−5.95823e6	−	1.03200e7i	−0.0454550	−	0.0787304i	0.842403	−	0.538848i	$-0.181140\pi$
$107$	−5.95823e6	−	1.03200e7i	−0.0454550	−	0.0787304i	−0.887858	+	0.460118i	$0.847807\pi$
$108$	−3.21485e8	−	1.85610e8i	−2.36301	−	1.36429i
$109$	1.49469e8	+	1.49469e8i	1.05888	+	1.05888i	0.998155	+	0.0607202i	$0.0193397\pi$
$109$	1.49469e8	+	1.49469e8i	1.05888	+	1.05888i	0.0607202	+	0.998155i	$0.480660\pi$
$110$	−5.54332e8	+	1.48533e8i	−3.78616	+	1.01450i
$111$	−3.71724e7	−	1.38729e8i	−0.244866	−	0.913852i
$112$	7.77634e7	−	7.77634e7i	0.494200	−	0.494200i
$113$	4.18169e7	−	7.24291e7i	0.256471	−	0.444221i	−0.708823	−	0.705386i	$-0.750773\pi$
$113$	4.18169e7	−	7.24291e7i	0.256471	−	0.444221i	0.965294	+	0.261165i	$0.0841068\pi$
$114$	1.46532e8	−	8.46005e7i	0.867589	−	0.500903i
$115$	1.40158e8	+	3.75553e7i	0.801359	+	0.214723i
$116$			3.10225e8i			1.71334i
$117$	−5.58680e7	−	3.17165e7i	−0.298140	−	0.169255i
$118$	−1.64409e8			−0.848004
$119$	−6.36795e6	+	2.37655e7i	−0.0317550	+	0.118511i
$120$	2.96330e8	+	5.13258e8i	1.42906	+	2.47520i
$121$	3.35150e8	+	1.93499e8i	1.56350	+	0.902687i
$122$	−2.02098e8	−	2.02098e8i	−0.912268	−	0.912268i
$123$	−5.89255e7	+	1.57890e7i	−0.257444	+	0.0689819i
$124$	−2.47473e8	−	9.23581e8i	−1.04674	−	3.90650i
$125$	−9.45284e7	+	9.45284e7i	−0.387188	+	0.387188i
$126$	−2.03675e7	+	3.52776e7i	−0.0808084	+	0.139964i
$127$	−4.35127e8	+	2.51221e8i	−1.67263	+	0.965696i	−0.706479	+	0.707734i	$0.749718\pi$
$127$	−4.35127e8	+	2.51221e8i	−1.67263	+	0.965696i	−0.966155	+	0.257962i	$0.916949\pi$
$128$	−1.97264e8	−	5.28568e7i	−0.734866	−	0.196907i
$129$			2.72799e8i			0.985107i
$130$	3.38394e8	+	5.76404e8i	1.18481	+	2.01815i
$131$	1.94278e7			0.0659688			0.0329844	−	0.999456i	$-0.489499\pi$
$131$	1.94278e7			0.0659688			0.0329844	+	0.999456i	$0.489499\pi$
$132$	2.67424e8	−	9.98040e8i	0.880856	−	3.28740i
$133$	−2.59924e7	−	4.50202e7i	−0.0830692	−	0.143880i
$134$	3.40876e8	+	1.96805e8i	1.05725	+	0.610404i
$135$	−3.19522e8	−	3.19522e8i	−0.961979	−	0.961979i
$136$	4.54331e8	−	1.21738e8i	1.32806	−	0.355852i
$137$	4.46775e7	+	1.66739e8i	0.126825	+	0.473319i	0.999898	−	0.0142712i	$-0.00454281\pi$
$137$	4.46775e7	+	1.66739e8i	0.126825	+	0.473319i	−0.873073	+	0.487590i	$0.837876\pi$
$138$	−2.58429e8	+	2.58429e8i	−0.712566	+	0.712566i
$139$	−2.70308e7	+	4.68188e7i	−0.0724102	+	0.125418i	−0.899957	−	0.435978i	$-0.856402\pi$
$139$	−2.70308e7	+	4.68188e7i	−0.0724102	+	0.125418i	0.827547	+	0.561397i	$0.189736\pi$
$140$	2.62363e8	−	1.51475e8i	0.682953	−	0.394303i
$141$	−1.83249e8	−	4.91015e7i	−0.463624	−	0.124228i
$142$		−	3.04119e8i		−	0.747980i
$143$	1.76354e8	−	6.77823e8i	0.421737	−	1.62096i
$144$	4.09248e8			0.951780
$145$	−9.77368e7	+	3.64759e8i	−0.221099	+	0.825151i
$146$	−6.60308e6	−	1.14369e7i	−0.0145323	−	0.0251707i
$147$	3.07046e8	+	1.77273e8i	0.657557	+	0.379641i
$148$	9.92434e8	+	9.92434e8i	2.06850	+	2.06850i
$149$	−7.10272e8	+	1.90317e8i	−1.44105	+	0.386129i	−0.892902	−	0.450252i	$-0.851334\pi$
$149$	−7.10272e8	+	1.90317e8i	−1.44105	+	0.386129i	−0.548150	+	0.836380i	$0.684668\pi$
$150$	1.11754e8	+	4.17072e8i	0.220749	+	0.823847i
$151$	2.00003e8	−	2.00003e8i	0.384705	−	0.384705i	−0.488089	−	0.872794i	$-0.662306\pi$
$151$	2.00003e8	−	2.00003e8i	0.384705	−	0.384705i	0.872794	+	0.488089i	$0.162306\pi$
$152$	−4.96903e8	+	8.60661e8i	−0.930888	+	1.61234i
$153$	−7.92922e7	+	4.57794e7i	−0.144699	+	0.0835419i
$154$	−4.28969e8	−	1.14942e8i	−0.762681	−	0.204360i
$155$		−	1.16390e9i		−	2.01646i
$156$	−1.20337e9	+	8.74294e6i	−2.03190	+	0.0147625i
$157$	6.20122e8			1.02065			0.510327	−	0.859981i	$-0.329525\pi$
$157$	6.20122e8			1.02065			0.510327	+	0.859981i	$0.329525\pi$
$158$	−2.02171e8	+	7.54511e8i	−0.324406	+	1.21070i
$159$	7.15638e7	+	1.23952e8i	0.111971	+	0.193939i
$160$	−1.68641e9	−	9.73651e8i	−2.57326	−	1.48567i
$161$	7.93990e7	+	7.93990e7i	0.118171	+	0.118171i
$162$	6.72267e8	−	1.80133e8i	0.976072	−	0.261538i
$163$	1.25521e8	+	4.68453e8i	0.177815	+	0.663613i	0.996055	+	0.0887372i	$0.0282831\pi$
$163$	1.25521e8	+	4.68453e8i	0.177815	+	0.663613i	−0.818240	+	0.574876i	$0.805050\pi$
$164$	4.21538e8	−	4.21538e8i	0.582722	−	0.582722i
$165$	6.28868e8	−	1.08923e9i	0.848445	−	1.46955i
$166$	1.45147e8	−	8.38006e7i	0.191151	−	0.110361i
$167$	−1.80855e8	−	4.84599e7i	−0.232522	−	0.0623041i	0.140676	−	0.990056i	$-0.455072\pi$
$167$	−1.80855e8	−	4.84599e7i	−0.232522	−	0.0623041i	−0.373198	+	0.927752i	$0.621739\pi$
$168$			4.58628e8i			0.575736i
$169$	−8.15645e8	+	1.18525e7i	−0.999894	+	0.0145300i
$170$	9.52593e8			1.14054
$171$	5.00690e7	−	1.86860e8i	0.0585578	−	0.218541i
$172$	−1.33292e9	−	2.30869e9i	−1.52297	−	2.63786i
$173$	−8.68873e8	−	5.01644e8i	−0.970001	−	0.560030i	−0.0707643	−	0.997493i	$-0.522544\pi$
$173$	−8.68873e8	−	5.01644e8i	−0.970001	−	0.560030i	−0.899237	+	0.437463i	$0.855877\pi$
$174$	−6.72557e8	−	6.72557e8i	−0.733722	−	0.733722i
$175$	1.28140e8	−	3.43350e7i	0.136626	−	0.0366088i
$176$	1.15477e9	+	4.30967e9i	1.20350	+	4.49152i
$177$	2.54785e8	−	2.54785e8i	0.259586	−	0.259586i
$178$	−3.55900e8	+	6.16437e8i	−0.354526	+	0.614057i
$179$	−9.33533e8	+	5.38975e8i	−0.909322	+	0.524997i	−0.880213	−	0.474579i	$-0.842600\pi$
$179$	−9.33533e8	+	5.38975e8i	−0.909322	+	0.524997i	−0.0291088	+	0.999576i	$0.509267\pi$
$180$	1.08896e9	+	2.91786e8i	1.03734	+	0.277955i
$181$			1.64210e8i			0.152998i	0.997070	+	0.0764989i	$0.0243742\pi$
$181$			1.64210e8i			0.152998i	−0.997070	+	0.0764989i	$0.975626\pi$
$182$	3.75781e6	+	5.17223e8i	0.00342491	+	0.471403i
$183$	6.26383e8			0.558516
$184$	5.55587e8	−	2.07348e9i	0.484708	−	1.80896i
$185$	8.54224e8	+	1.47956e9i	0.729264	+	1.26312i
$186$	2.53880e9	+	1.46578e9i	2.12118	+	1.22466i
$187$	−7.05827e8	−	7.05827e8i	−0.577208	−	0.577208i
$188$	1.79075e9	−	4.79830e8i	1.43352	−	0.384110i
$189$	−9.05039e7	−	3.37765e8i	−0.0709284	−	0.264708i
$190$	−1.42320e9	+	1.42320e9i	−1.09207	+	1.09207i
$191$	−3.35766e8	+	5.81565e8i	−0.252292	+	0.436983i	−0.964157	−	0.265334i	$-0.914518\pi$
$191$	−3.35766e8	+	5.81565e8i	−0.252292	+	0.436983i	0.711864	+	0.702317i	$0.247851\pi$
$192$	1.59895e9	−	9.23157e8i	1.17661	−	0.679314i
$193$	2.29826e9	+	6.15818e8i	1.65642	+	0.443837i	0.961400	−	0.275153i	$-0.0887285\pi$
$193$	2.29826e9	+	6.15818e8i	1.65642	+	0.443837i	0.695021	+	0.718990i	$0.255395\pi$
$194$		−	4.03256e9i		−	2.84691i
$195$	−1.41767e9	−	3.68844e8i	−0.980472	−	0.255097i
$196$	−3.46469e9			−2.34769
$197$	−6.80031e8	+	2.53791e9i	−0.451507	+	1.68505i	0.246654	+	0.969104i	$0.420669\pi$
$197$	−6.80031e8	+	2.53791e9i	−0.451507	+	1.68505i	−0.698160	+	0.715942i	$0.745998\pi$
$198$	−8.26320e8	−	1.43123e9i	−0.537635	−	0.931211i
$199$	1.72221e9	+	9.94317e8i	1.09818	+	0.634034i	0.935742	−	0.352685i	$-0.114731\pi$
$199$	1.72221e9	+	9.94317e8i	1.09818	+	0.634034i	0.162437	+	0.986719i	$0.448065\pi$
$200$	−1.79329e9	−	1.79329e9i	−1.12081	−	1.12081i
$201$	−8.33246e8	+	2.23268e8i	−0.510492	+	0.136786i
$202$	−3.55750e8	−	1.32768e9i	−0.213668	−	0.797419i
$203$	−2.06634e8	+	2.06634e8i	−0.121680	+	0.121680i
$204$	−8.57543e8	+	1.48531e9i	−0.495148	+	0.857622i
$205$	6.28445e8	−	3.62833e8i	0.355838	−	0.205443i
$206$	−2.90153e9	−	7.77463e8i	−1.61123	−	0.431729i
$207$			4.17856e8i			0.227586i
$208$	4.48127e9	−	2.63086e9i	2.39413	−	1.40554i
$209$	2.10905e9			1.10535
$210$	−2.40401e8	+	8.97187e8i	−0.123611	+	0.461324i
$211$	3.07563e7	+	5.32715e7i	0.0155169	+	0.0268760i	0.873680	−	0.486502i	$-0.161727\pi$
$211$	3.07563e7	+	5.32715e7i	0.0155169	+	0.0268760i	−0.858163	+	0.513378i	$0.828394\pi$
$212$	−1.21129e9	−	6.99336e8i	−0.599657	−	0.346212i
$213$	4.71294e8	+	4.71294e8i	0.228967	+	0.228967i
$214$	−3.44866e8	+	9.24066e7i	−0.164435	+	0.0440603i
$215$	−8.39877e8	−	3.13446e9i	−0.393063	−	1.46693i
$216$	−4.72696e9	+	4.72696e9i	−2.17153	+	2.17153i
$217$	4.50342e8	−	7.80014e8i	0.203097	−	0.351774i
$218$	5.48474e9	−	3.16662e9i	2.42845	−	1.40207i
$219$	2.79566e7	+	7.49094e6i	0.0121537	+	0.00325656i
$220$			1.22909e10i			5.24676i
$221$	−5.73957e8	+	1.01102e9i	−0.240608	+	0.423827i
$222$	−4.30312e9			−1.77162
$223$	−8.34045e8	+	3.11270e9i	−0.337264	+	1.25869i	0.564130	+	0.825686i	$0.309212\pi$
$223$	−8.34045e8	+	3.11270e9i	−0.337264	+	1.25869i	−0.901394	+	0.433001i	$0.857455\pi$
$224$	−7.53458e8	−	1.30503e9i	−0.299273	−	0.518355i
$225$	4.27532e8	+	2.46835e8i	0.166816	+	0.0963114i
$226$	−1.77185e9	−	1.77185e9i	−0.679193	−	0.679193i
$227$	−2.47573e9	+	6.63371e8i	−0.932396	+	0.249835i	−0.692876	−	0.721057i	$-0.743657\pi$
$227$	−2.47573e9	+	6.63371e8i	−0.932396	+	0.249835i	−0.239520	+	0.970891i	$0.576990\pi$
$228$	−9.37896e8	−	3.50028e9i	−0.347069	−	1.29528i
$229$	1.80497e9	−	1.80497e9i	0.656340	−	0.656340i	−0.298172	−	0.954512i	$-0.596377\pi$
$229$	1.80497e9	−	1.80497e9i	0.656340	−	0.656340i	0.954512	+	0.298172i	$0.0963771\pi$
$230$	2.17372e9	−	3.76500e9i	0.776771	−	1.34541i
$231$	8.42900e8	−	4.86648e8i	0.296025	−	0.170910i
$232$	5.39618e9	+	1.44590e9i	1.86266	+	0.499099i
$233$		−	4.48123e9i		−	1.52045i	−0.649658	−	0.760227i	$-0.725088\pi$
$233$		−	4.48123e9i		−	1.52045i	0.649658	−	0.760227i	$-0.274912\pi$
$234$	−1.35111e9	+	1.37089e9i	−0.450639	+	0.457235i
$235$	2.25671e9			0.739954
$236$	−9.11335e8	+	3.40115e9i	−0.293785	+	1.09642i
$237$	−8.55963e8	−	1.48257e9i	−0.271307	−	0.469918i
$238$	6.38402e8	+	3.68581e8i	0.198969	+	0.114875i
$239$	3.08389e9	+	3.08389e9i	0.945164	+	0.945164i	0.998573	−	0.0534090i	$-0.0170087\pi$
$239$	3.08389e9	+	3.08389e9i	0.945164	+	0.945164i	−0.0534090	+	0.998573i	$0.517009\pi$
$240$	9.01366e9	−	2.41520e9i	2.71679	−	0.727962i
$241$	−1.00432e9	−	3.74817e9i	−0.297717	−	1.11109i	−0.939036	−	0.343819i	$-0.888279\pi$
$241$	−1.00432e9	−	3.74817e9i	−0.297717	−	1.11109i	0.641319	−	0.767274i	$-0.278387\pi$
$242$	8.19885e9	−	8.19885e9i	2.39052	−	2.39052i
$243$	1.13516e9	−	1.96615e9i	0.325560	−	0.563887i
$244$	−5.30107e9	+	3.06057e9i	−1.49556	+	0.863462i
$245$	−4.07374e9	−	1.09156e9i	−1.13065	−	0.302958i
$246$			1.82776e9i			0.499090i
$247$	−6.52976e8	−	2.36799e9i	−0.175432	−	0.636197i
$248$	−1.72186e10			−4.55188
$249$	−9.50685e7	+	3.54801e8i	−0.0247309	+	0.0922969i
$250$	2.00266e9	+	3.46871e9i	0.512681	+	0.887989i
$251$	4.11348e9	+	2.37492e9i	1.03637	+	0.598348i	0.918803	−	0.394717i	$-0.129157\pi$
$251$	4.11348e9	+	2.37492e9i	1.03637	+	0.598348i	0.117566	+	0.993065i	$0.462491\pi$
$252$	6.16892e8	+	6.16892e8i	0.152970	+	0.152970i
$253$	−4.40032e9	+	1.17906e9i	−1.07399	+	0.287776i
$254$	3.89620e9	+	1.45408e10i	0.936066	+	3.49344i
$255$	−1.47624e9	+	1.47624e9i	−0.349136	+	0.349136i
$256$	5.39704e8	−	9.34794e8i	0.125660	−	0.217649i
$257$	−4.70131e9	+	2.71430e9i	−1.07767	+	0.622194i	−0.930267	−	0.366882i	$-0.880425\pi$
$257$	−4.70131e9	+	2.71430e9i	−1.07767	+	0.622194i	−0.147404	+	0.989076i	$0.547092\pi$
$258$	7.89488e9	+	2.11543e9i	1.78183	+	0.477440i
$259$			1.32208e9i			0.293804i
$260$	1.37999e10	−	3.80534e9i	3.01983	−	0.832721i
$261$	−1.08746e9			−0.234343
$262$	1.50654e8	−	5.62247e8i	0.0319724	−	0.119322i
$263$	2.06784e8	+	3.58160e8i	0.0432208	+	0.0748607i	0.886827	−	0.462102i	$-0.152905\pi$
$263$	2.06784e8	+	3.58160e8i	0.0432208	+	0.0748607i	−0.843606	+	0.536963i	$0.819571\pi$
$264$	−1.61139e10	−	9.30338e9i	−3.31731	−	1.91525i
$265$	−1.20389e9	−	1.20389e9i	−0.244120	−	0.244120i
$266$	−1.50446e9	+	4.03118e8i	−0.300506	+	0.0805204i
$267$	−4.03755e8	−	1.50683e9i	−0.0794461	−	0.296497i
$268$	5.96083e9	−	5.96083e9i	1.15549	−	1.15549i
$269$	2.72974e9	−	4.72804e9i	0.521329	−	0.902968i	−0.478363	−	0.878162i	$-0.658770\pi$
$269$	2.72974e9	−	4.72804e9i	0.521329	−	0.902968i	0.999692	−	0.0248061i	$-0.00789683\pi$
$270$	−1.17248e10	+	6.76932e9i	−2.20623	+	1.27377i
$271$	6.26447e8	+	1.67856e8i	0.116147	+	0.0311214i	0.316424	−	0.948618i	$-0.397518\pi$
$271$	6.26447e8	+	1.67856e8i	0.116147	+	0.0311214i	−0.200278	+	0.979739i	$0.564184\pi$
$272$		−	7.40596e9i		−	1.35302i
$273$	−8.07365e8	−	7.95718e8i	−0.145351	−	0.143255i
$274$	5.17192e9			0.917592
$275$	−1.39299e9	+	5.19870e9i	−0.243566	+	0.909000i
$276$	3.91365e9	+	6.77864e9i	0.674444	+	1.16817i
$277$	−1.60551e9	−	9.26939e8i	−0.272705	−	0.157446i	0.357411	−	0.933947i	$-0.383659\pi$
$277$	−1.60551e9	−	9.26939e8i	−0.272705	−	0.157446i	−0.630116	+	0.776501i	$0.716993\pi$
$278$	1.14534e9	+	1.14534e9i	0.191759	+	0.191759i
$279$	3.23752e9	−	8.67490e8i	0.534312	−	0.143169i
$280$	−1.41200e9	−	5.26965e9i	−0.229722	−	0.857334i
$281$	−6.46294e9	+	6.46294e9i	−1.03659	+	1.03659i	−0.0372803	+	0.999305i	$0.511869\pi$
$281$	−6.46294e9	+	6.46294e9i	−1.03659	+	1.03659i	−0.999305	+	0.0372803i	$0.988131\pi$
$282$	−2.84203e9	+	4.92253e9i	−0.449398	+	0.778381i
$283$	−1.32073e9	+	7.62523e8i	−0.205905	+	0.118880i	−0.599407	−	0.800444i	$-0.704597\pi$
$283$	−1.32073e9	+	7.62523e8i	−0.205905	+	0.118880i	0.393502	+	0.919324i	$0.371264\pi$
$284$	−6.29134e9	−	1.68576e9i	−0.967096	−	0.259133i
$285$		−	4.41107e9i		−	0.668597i
$286$	−1.82489e10	−	1.03600e10i	−2.72755	−	1.54844i
$287$	5.61555e8			0.0827685
$288$	1.45138e9	−	5.41663e9i	0.210965	−	0.787334i
$289$	−2.65943e9	−	4.60627e9i	−0.381239	−	0.660326i
$290$	9.79833e9	+	5.65707e9i	1.38535	+	0.799833i
$291$	6.24926e9	+	6.24926e9i	0.871478	+	0.871478i
$292$	−2.73197e8	+	7.32030e7i	−0.0375790	+	0.0100693i
$293$	−5.55146e7	−	2.07183e8i	−0.00753246	−	0.0281115i	0.962057	−	0.272847i	$-0.0879654\pi$
$293$	−5.55146e7	−	2.07183e8i	−0.00753246	−	0.0281115i	−0.969590	+	0.244736i	$0.921299\pi$
$294$	7.51133e9	−	7.51133e9i	1.00537	−	1.00537i
$295$	−2.14307e9	+	3.71191e9i	−0.282976	+	0.490128i
$296$	2.18884e10	−	1.26373e10i	2.85132	−	1.64621i
$297$	1.37033e10	+	3.67178e9i	1.76116	+	0.471902i
$298$			2.20313e10i			2.79367i
$299$	2.68619e9	+	4.57553e9i	0.336087	+	0.572475i
$300$	9.24748e9			1.14166
$301$	6.49938e8	−	2.42560e9i	0.0791782	−	0.295497i
$302$	−4.23721e9	−	7.33907e9i	−0.509393	−	0.882294i
$303$	2.60881e9	+	1.50620e9i	0.309508	+	0.178694i
$304$	1.10647e10	+	1.10647e10i	1.29552	+	1.29552i
$305$	−7.19716e9	+	1.92847e9i	−0.831691	+	0.222851i
$306$	7.09996e8	+	2.64974e9i	0.0809786	+	0.302216i
$307$	−3.42258e9	+	3.42258e9i	−0.385301	+	0.385301i	−0.873008	−	0.487707i	$-0.837834\pi$
$307$	−3.42258e9	+	3.42258e9i	−0.385301	+	0.385301i	0.487707	+	0.873008i	$0.337834\pi$
$308$	−4.75563e9	+	8.23699e9i	−0.528451	+	0.915304i
$309$	5.70135e9	−	3.29167e9i	0.625379	−	0.361063i
$310$	−3.36837e10	−	9.02552e9i	−3.64731	−	0.977294i
$311$		−	8.67756e9i		−	0.927590i	−0.885943	−	0.463795i	$-0.846487\pi$
$311$		−	8.67756e9i		−	0.927590i	0.885943	−	0.463795i	$-0.153513\pi$
$312$	−5.45663e9	+	2.09727e10i	−0.575845	+	2.21328i
$313$	−5.13097e8			−0.0534591			−0.0267296	−	0.999643i	$-0.508509\pi$
$313$	−5.13097e8			−0.0534591			−0.0267296	+	0.999643i	$0.508509\pi$
$314$	4.80876e9	−	1.79465e10i	0.494668	−	1.84613i
$315$	5.30981e8	+	9.19687e8i	0.0539308	+	0.0934109i
$316$	1.44880e10	+	8.36464e9i	1.45298	+	0.838878i
$317$	−9.84226e9	−	9.84226e9i	−0.974671	−	0.974671i	0.0250162	−	0.999687i	$-0.492036\pi$
$317$	−9.84226e9	−	9.84226e9i	−0.974671	−	0.974671i	−0.999687	+	0.0250162i	$0.992036\pi$
$318$	4.14216e9	−	1.10989e9i	0.405059	−	0.108535i
$319$	−3.06848e9	−	1.14517e10i	−0.296320	−	1.10588i
$320$	−1.55299e10	+	1.55299e10i	−1.48104	+	1.48104i
$321$	3.91237e8	−	6.77642e8i	0.0368485	−	0.0638235i
$322$	2.91354e9	−	1.68213e9i	0.271017	−	0.156472i
$323$	−3.38151e9	−	9.06074e8i	−0.310671	−	0.0832441i
$324$		−	1.49057e10i		−	1.35261i
$325$	6.26826e9	−	4.55412e7i	0.561841	−	0.00408198i
$326$	1.45305e10			1.28650
$327$	−3.59240e9	+	1.34070e10i	−0.314191	+	1.17258i
$328$	−5.36770e9	−	9.29712e9i	−0.463759	−	0.803254i
$329$	1.51238e9	+	8.73176e8i	0.129086	+	0.0745278i
$330$	−2.66461e10	−	2.66461e10i	−2.24687	−	2.24687i
$331$	8.97712e9	−	2.40541e9i	0.747868	−	0.200391i	0.135296	−	0.990805i	$-0.456802\pi$
$331$	8.97712e9	−	2.40541e9i	0.747868	−	0.200391i	0.612572	+	0.790415i	$0.290135\pi$
$332$	−9.29029e8	−	3.46718e9i	−0.0764675	−	0.285381i
$333$	−3.47887e9	+	3.47887e9i	−0.282919	+	0.282919i
$334$	−2.80489e9	+	4.85821e9i	−0.225388	+	0.390383i
$335$	8.88665e9	−	5.13071e9i	0.705600	−	0.407378i
$336$	6.97520e9	+	1.86900e9i	0.547268	+	0.146640i
$337$		−	2.22118e10i		−	1.72212i	−0.508501	−	0.861061i	$-0.669800\pi$
$337$		−	2.22118e10i		−	1.72212i	0.508501	−	0.861061i	$-0.330200\pi$
$338$	−5.98193e9	+	2.36969e10i	−0.458326	+	1.81562i
$339$	5.49168e9			0.415821
$340$	5.28031e9	−	1.97064e10i	0.395134	−	1.47466i
$341$	1.82706e10	+	3.16455e10i	1.35125	+	2.34043i
$342$	−5.01953e9	−	2.89803e9i	−0.366909	−	0.211835i
$343$	−4.77167e9	−	4.77167e9i	−0.344742	−	0.344742i
$344$	−4.63708e10	+	1.24250e10i	−3.31139	+	0.887285i
$345$	2.46600e9	+	9.20325e9i	0.174067	+	0.649628i
$346$	−2.12555e10	+	2.12555e10i	−1.48309	+	1.48309i
$347$	−1.14883e10	+	1.98982e10i	−0.792385	+	1.37245i	0.132102	+	0.991236i	$0.457827\pi$
$347$	−1.14883e10	+	1.98982e10i	−0.792385	+	1.37245i	−0.924487	+	0.381214i	$0.875506\pi$
$348$	−1.76413e10	+	1.01852e10i	−1.20285	+	0.694469i
$349$	2.47465e10	+	6.63079e9i	1.66806	+	0.446955i	0.964586	−	0.263768i	$-0.0849653\pi$
$349$	2.47465e10	+	6.63079e9i	1.66806	+	0.446955i	0.703472	+	0.710723i	$0.251632\pi$
$350$		−	3.97467e9i		−	0.264868i
$351$	−1.20042e8	−	1.65225e10i	−0.00790871	−	1.08855i
$352$	6.11362e10			3.98225
$353$	5.97969e9	−	2.23165e10i	0.385106	−	1.43723i	−0.452894	−	0.891564i	$-0.649608\pi$
$353$	5.97969e9	−	2.23165e10i	0.385106	−	1.43723i	0.838000	−	0.545670i	$-0.183725\pi$
$354$	−5.39783e9	−	9.34931e9i	−0.343721	−	0.595342i
$355$	−6.86617e9	−	3.96419e9i	−0.432316	−	0.249598i
$356$	1.07795e10	+	1.07795e10i	0.671118	+	0.671118i
$357$	−1.56052e9	+	4.18141e8i	−0.0960722	+	0.0257425i
$358$	8.35901e9	+	3.11963e10i	0.508889	+	1.89920i
$359$	−9.06987e8	+	9.06987e8i	−0.0546039	+	0.0546039i	−0.733881	−	0.679278i	$-0.762293\pi$
$359$	−9.06987e8	+	9.06987e8i	−0.0546039	+	0.0546039i	0.679278	+	0.733881i	$0.262293\pi$
$360$	1.01509e10	−	1.75819e10i	0.604358	−	1.04678i
$361$	−8.30243e9	+	4.79341e9i	−0.488851	+	0.282238i
$362$	4.75229e9	+	1.27337e9i	0.276738	+	0.0741517i
$363$			2.54116e10i			1.46354i
$364$	1.07207e10	+	2.78928e9i	0.610684	+	0.158886i
$365$	−3.44285e8			−0.0193975
$366$	4.85731e9	−	1.81277e10i	0.270690	−	1.01023i
$367$	−1.63366e10	−	2.82958e10i	−0.900528	−	1.55976i	−0.826810	−	0.562481i	$-0.809847\pi$
$367$	−1.63366e10	−	2.82958e10i	−0.900528	−	1.55976i	−0.0737176	−	0.997279i	$-0.523486\pi$
$368$	−2.92711e10	−	1.68997e10i	−1.59605	−	0.921481i
$369$	1.47766e9	+	1.47766e9i	0.0797018	+	0.0797018i
$370$	4.94430e10	−	1.32482e10i	2.63814	−	0.706888i
$371$	−3.40999e8	−	1.27263e9i	−0.0179994	−	0.0671746i
$372$	4.43955e10	−	4.43955e10i	2.31829	−	2.31829i
$373$	−5.18060e9	+	8.97306e9i	−0.267636	+	0.463559i	−0.968251	−	0.249980i	$-0.919576\pi$
$373$	−5.18060e9	+	8.97306e9i	−0.267636	+	0.463559i	0.700615	+	0.713540i	$0.252909\pi$
$374$	−2.59002e10	+	1.49535e10i	−1.32378	+	0.764287i
$375$	−8.47899e9	−	2.27194e9i	−0.428765	−	0.114887i
$376$		−	3.33854e10i		−	1.67034i
$377$	−1.19077e10	+	6.99076e9i	−0.589472	+	0.346066i
$378$	−1.04769e10			−0.513173
$379$	−6.72809e9	+	2.51096e10i	−0.326088	+	1.21698i	0.587125	+	0.809496i	$0.300260\pi$
$379$	−6.72809e9	+	2.51096e10i	−0.326088	+	1.21698i	−0.913213	+	0.407482i	$0.866407\pi$
$380$	2.15529e10	+	3.73307e10i	1.03365	+	1.79033i
$381$	−2.85719e10	−	1.64960e10i	−1.35594	−	0.782850i
$382$	1.42270e10	+	1.42270e10i	0.668126	+	0.668126i
$383$	1.14461e10	−	3.06697e9i	0.531939	−	0.142533i	0.0171554	−	0.999853i	$-0.494539\pi$
$383$	1.14461e10	−	3.06697e9i	0.531939	−	0.142533i	0.514783	+	0.857320i	$0.327872\pi$
$384$	−3.47075e9	−	1.29530e10i	−0.159624	−	0.595725i
$385$	−8.18668e9	+	8.18668e9i	−0.372619	+	0.372619i
$386$	3.56440e10	−	6.17371e10i	1.60560	−	2.78098i
$387$	8.09286e9	−	4.67242e9i	0.360793	−	0.208304i
$388$	−8.34218e10	−	2.23528e10i	−3.68089	−	0.986292i
$389$			2.48132e10i			1.08364i	0.840495	+	0.541819i	$0.182264\pi$
$389$			2.48132e10i			1.08364i	−0.840495	+	0.541819i	$0.817736\pi$
$390$	−2.16678e10	+	3.81675e10i	−0.936606	+	1.64981i
$391$	7.56173e9			0.323530
$392$	−1.61483e10	+	6.02663e10i	−0.683885	+	2.55229i
$393$	6.37847e8	+	1.10478e9i	0.0267391	+	0.0463135i
$394$	6.81747e10	+	3.93607e10i	2.82903	+	1.63334i
$395$	1.43995e10	+	1.43995e10i	0.591506	+	0.591506i
$396$	−3.41883e10	+	9.16073e9i	−1.39026	+	0.372520i
$397$	−9.48699e8	−	3.54059e9i	−0.0381915	−	0.142533i	0.944197	−	0.329380i	$-0.106840\pi$
$397$	−9.48699e8	−	3.54059e9i	−0.0381915	−	0.142533i	−0.982389	+	0.186847i	$0.940173\pi$
$398$	4.21308e10	−	4.21308e10i	1.67906	−	1.67906i
$399$	1.70675e9	−	2.95617e9i	0.0673407	−	0.116638i
$400$	−3.45820e10	+	1.99659e10i	−1.35086	+	0.779918i
$401$	−2.04838e10	−	5.48861e9i	−0.792196	−	0.212268i	−0.160041	−	0.987110i	$-0.551163\pi$
$401$	−2.04838e10	−	5.48861e9i	−0.792196	−	0.212268i	−0.632155	+	0.774842i	$0.717829\pi$
$402$			2.58458e10i			0.989658i
$403$	2.98742e10	−	3.03114e10i	1.13260	−	1.14918i
$404$	−2.94377e10			−1.10504
$405$	4.69608e9	−	1.75260e10i	0.174548	−	0.651422i
$406$	4.37771e9	+	7.58242e9i	0.161118	+	0.279064i
$407$	−4.64513e10	−	2.68187e10i	−1.69286	−	0.977371i
$408$	2.18392e10	+	2.18392e10i	0.788127	+	0.788127i
$409$	5.58159e9	−	1.49558e9i	0.199464	−	0.0534463i	−0.157704	−	0.987486i	$-0.550409\pi$
$409$	5.58159e9	−	1.49558e9i	0.199464	−	0.0534463i	0.357168	+	0.934040i	$0.383742\pi$
$410$	−5.62720e9	−	2.10010e10i	−0.199139	−	0.743198i
$411$	−8.01494e9	+	8.01494e9i	−0.280888	+	0.280888i
$412$	−3.21669e10	+	5.57147e10i	−1.11640	+	1.93366i
$413$	−2.87246e9	+	1.65841e9i	−0.0987309	+	0.0570023i
$414$	1.20929e10	+	3.24028e9i	0.411650	+	0.110301i
$415$		−	4.36936e9i		−	0.147308i
$416$	−1.89282e10	−	6.86423e10i	−0.632028	−	2.29202i
$417$	−3.54987e9			−0.117400
$418$	1.63547e10	−	6.10365e10i	0.535719	−	1.99933i
$419$	−1.41659e10	−	2.45361e10i	−0.459610	−	0.796067i	0.539331	−	0.842094i	$-0.318677\pi$
$419$	−1.41659e10	−	2.45361e10i	−0.459610	−	0.796067i	−0.998940	+	0.0460269i	$0.985344\pi$
$420$	1.72276e10	+	9.94638e9i	0.553641	+	0.319645i
$421$	3.93997e10	+	3.93997e10i	1.25419	+	1.25419i	0.953822	+	0.300372i	$0.0971110\pi$
$421$	3.93997e10	+	3.93997e10i	1.25419	+	1.25419i	0.300372	+	0.953822i	$0.402889\pi$
$422$	1.78020e9	−	4.77002e8i	0.0561329	−	0.0150408i
$423$	1.68199e9	+	6.27728e9i	0.0525367	+	0.196070i
$424$	−1.78101e10	+	1.78101e10i	−0.551066	+	0.551066i
$425$	4.46686e9	−	7.73683e9i	0.136914	−	0.237141i
$426$	1.72941e10	−	9.98473e9i	0.525120	−	0.303178i
$427$	−5.56951e9	−	1.49235e9i	−0.167535	−	0.0448909i
$428$			7.64649e9i			0.227870i
$429$	4.43352e10	−	1.22255e10i	1.30894	−	0.360942i
$430$	−9.72253e10			−2.84384
$431$	1.50141e10	−	5.60333e10i	0.435101	−	1.62382i	−0.305725	−	0.952120i	$-0.598899\pi$
$431$	1.50141e10	−	5.60333e10i	0.435101	−	1.62382i	0.740826	−	0.671697i	$-0.234434\pi$
$432$	5.26282e10	+	9.11548e10i	1.51107	+	2.61725i
$433$	−2.61653e10	−	1.51065e10i	−0.744344	−	0.429747i	0.0793027	−	0.996851i	$-0.474731\pi$
$433$	−2.61653e10	−	1.51065e10i	−0.744344	−	0.429747i	−0.823647	+	0.567103i	$0.808064\pi$
$434$	−1.90817e10	−	1.90817e10i	−0.537846	−	0.537846i
$435$	−2.39513e10	+	6.41772e9i	−0.668916	+	0.179235i
$436$	−3.51057e10	−	1.31016e11i	−0.971474	−	3.62559i
$437$	−1.12974e10	+	1.12974e10i	−0.309780	+	0.309780i
$438$	4.33580e8	−	7.50983e8i	0.0117808	−	0.0204049i
$439$	2.68548e10	−	1.55046e10i	0.723041	−	0.417448i	−0.0928297	−	0.995682i	$-0.529591\pi$
$439$	2.68548e10	−	1.55046e10i	0.723041	−	0.417448i	0.815871	+	0.578234i	$0.196258\pi$
$440$	2.13792e11	+	5.72855e10i	5.70402	+	1.52839i
$441$		−	1.21451e10i		−	0.321105i
$442$	2.48084e10	+	2.44505e10i	0.649993	+	0.640616i
$443$	9.52449e8			0.0247301			0.0123651	−	0.999924i	$-0.496064\pi$
$443$	9.52449e8			0.0247301			0.0123651	+	0.999924i	$0.496064\pi$
$444$	−2.38526e10	+	8.90191e10i	−0.613767	+	2.29061i
$445$	9.27831e9	+	1.60705e10i	0.236608	+	0.409817i
$446$	8.36149e10	+	4.82751e10i	2.11322	+	1.22007i
$447$	−3.41420e10	−	3.41420e10i	−0.855182	−	0.855182i
$448$	−1.64166e10	+	4.39881e9i	−0.407540	+	0.109200i
$449$	8.70444e9	+	3.24854e10i	0.214168	+	0.799288i	0.986458	+	0.164016i	$0.0524450\pi$
$449$	8.70444e9	+	3.24854e10i	0.214168	+	0.799288i	−0.772289	+	0.635271i	$0.780888\pi$
$450$	1.04588e10	−	1.04588e10i	0.255054	−	0.255054i
$451$	−1.13913e10	+	1.97303e10i	−0.275338	+	0.476899i
$452$	−4.64759e10	+	2.68329e10i	−1.11346	+	0.642856i
$453$	1.79398e10	+	4.80695e9i	0.426015	+	0.114150i
$454$			7.67927e10i			1.80758i
$455$	1.17265e10	+	6.65716e9i	0.273604	+	0.155326i
$456$	−6.52566e10			−1.50926
$457$	−1.35053e10	+	5.04024e10i	−0.309627	+	1.15554i	0.619262	+	0.785185i	$0.287432\pi$
$457$	−1.35053e10	+	5.04024e10i	−0.309627	+	1.15554i	−0.928889	+	0.370359i	$0.879235\pi$
$458$	−3.82398e10	−	6.62332e10i	−0.869067	−	1.50527i
$459$	−2.03936e10	−	1.17742e10i	−0.459454	−	0.265266i
$460$	−6.58377e10	−	6.58377e10i	−1.47043	−	1.47043i
$461$	−3.04054e10	+	8.14711e9i	−0.673205	+	0.180385i	−0.579198	−	0.815187i	$-0.696634\pi$
$461$	−3.04054e10	+	8.14711e9i	−0.673205	+	0.180385i	−0.0940068	+	0.995572i	$0.529968\pi$
$462$	−7.54747e9	−	2.81675e10i	−0.165666	−	0.618274i
$463$	−5.93614e9	+	5.93614e9i	−0.129176	+	0.129176i	−0.768739	−	0.639563i	$-0.779115\pi$
$463$	−5.93614e9	+	5.93614e9i	−0.129176	+	0.129176i	0.639563	+	0.768739i	$0.279115\pi$
$464$	4.39810e10	−	7.61773e10i	0.948841	−	1.64344i
$465$	6.61866e10	−	3.82128e10i	1.41566	−	0.817330i
$466$	−1.29688e11	−	3.47498e10i	−2.75015	−	0.736901i
$467$			1.26471e10i			0.265903i	0.991123	+	0.132951i	$0.0424454\pi$
$467$			1.26471e10i			0.265903i	−0.991123	+	0.132951i	$0.957555\pi$
$468$	2.08704e10	+	3.55496e10i	0.435058	+	0.741057i
$469$	7.94078e9			0.164124
$470$	1.74997e10	−	6.53100e10i	0.358625	−	1.33841i
$471$	2.03596e10	+	3.52639e10i	0.413701	+	0.716550i
$472$	5.49135e10	+	3.17043e10i	1.10640	+	0.638778i
$473$	7.20394e10	+	7.20394e10i	1.43921	+	1.43921i
$474$	−4.95437e10	+	1.32752e10i	−0.981465	+	0.262983i
$475$	4.88541e9	+	1.82326e10i	0.0959681	+	0.358158i
$476$	1.11636e10	−	1.11636e10i	0.217458	−	0.217458i
$477$	2.45145e9	−	4.24604e9i	0.0473532	−	0.0820182i
$478$	1.13163e11	−	6.53346e10i	2.16767	−	1.25150i
$479$	2.90021e10	+	7.77109e9i	0.550919	+	0.147618i	0.523531	−	0.852007i	$-0.324614\pi$
$479$	2.90021e10	+	7.77109e9i	0.550919	+	0.147618i	0.0273879	+	0.999625i	$0.491281\pi$
$480$		−	1.27866e11i		−	2.40875i
$481$	−1.57297e10	+	6.04577e10i	−0.293860	+	1.12946i
$482$	−1.16261e11			−2.15400
$483$	−1.90831e9	+	7.12192e9i	−0.0350640	+	0.130860i
$484$	−1.24163e11	−	2.15057e11i	−2.26262	−	3.91898i
$485$	−9.10441e10	−	5.25643e10i	−1.64545	−	0.950001i
$486$	−4.80985e10	−	4.80985e10i	−0.862157	−	0.862157i
$487$	9.58747e10	−	2.56896e10i	1.70447	−	0.456710i	0.730408	−	0.683011i	$-0.239330\pi$
$487$	9.58747e10	−	2.56896e10i	1.70447	−	0.456710i	0.974058	+	0.226300i	$0.0726631\pi$
$488$	2.85296e10	+	1.06474e11i	0.503055	+	1.87743i
$489$	−2.25180e10	+	2.25180e10i	−0.393817	+	0.393817i
$490$	−6.31800e10	+	1.09431e11i	−1.09596	+	1.89826i
$491$	−4.06982e10	+	2.34971e10i	−0.700244	+	0.404286i	−0.807438	−	0.589952i	$-0.799147\pi$
$491$	−4.06982e10	+	2.34971e10i	−0.700244	+	0.404286i	0.107195	+	0.994238i	$0.465813\pi$
$492$	3.78110e10	+	1.01314e10i	0.645295	+	0.172906i
$493$			1.96793e10i			0.333136i
$494$	−7.35939e10	+	5.34686e8i	−1.23576	+	0.00897823i
$495$	−4.30843e10			−0.717626
$496$	−7.01691e10	+	2.61875e11i	−1.15936	+	4.32680i
$497$	−3.06768e9	−	5.31338e9i	−0.0502787	−	0.0870853i
$498$	9.53083e9	+	5.50263e9i	0.154958	+	0.0894649i
$499$	2.28657e10	+	2.28657e10i	0.368792	+	0.368792i	0.867037	−	0.498244i	$-0.166022\pi$
$499$	2.28657e10	+	2.28657e10i	0.368792	+	0.368792i	−0.498244	+	0.867037i	$0.666022\pi$
$500$	8.28584e10	−	2.22018e10i	1.32573	−	0.355230i
$501$	−3.18204e9	−	1.18755e10i	−0.0505073	−	0.188496i
$502$	1.00629e11	−	1.00629e11i	1.58456	−	1.58456i
$503$	−4.02972e9	+	6.97968e9i	−0.0629511	+	0.109034i	−0.895783	−	0.444491i	$-0.853385\pi$
$503$	−4.02972e9	+	6.97968e9i	−0.0629511	+	0.109034i	0.832832	+	0.553526i	$0.186718\pi$
$504$	1.36057e10	−	7.85526e9i	0.210862	−	0.121741i
$505$	−3.46125e10	−	9.27439e9i	−0.532191	−	0.142600i
$506$			1.36490e11i			2.08208i
$507$	−2.74530e10	−	4.59934e10i	−0.415487	−	0.696087i
$508$	3.22404e11			4.84112
$509$	1.90144e10	−	7.09626e10i	0.283277	−	1.05720i	−0.666813	−	0.745225i	$-0.732342\pi$
$509$	1.90144e10	−	7.09626e10i	0.283277	−	1.05720i	0.950090	−	0.311977i	$-0.100991\pi$
$510$	3.12752e10	+	5.41703e10i	0.462296	+	0.800720i
$511$	−2.30730e8	−	1.33212e8i	−0.00338392	−	0.00195371i
$512$	−5.98364e10	−	5.98364e10i	−0.870734	−	0.870734i
$513$	4.80595e10	−	1.28775e10i	0.693920	−	0.185935i
$514$	4.20963e10	+	1.57106e11i	0.603103	+	2.25081i
$515$	−5.53745e10	+	5.53745e10i	−0.787192	+	0.787192i
$516$	8.75241e10	−	1.51596e11i	1.23461	−	2.13840i
$517$	−6.13581e10	+	3.54251e10i	−0.858835	+	0.495849i
$518$	3.82614e10	+	1.02521e10i	0.531425	+	0.142395i
$519$		−	6.58793e10i		−	0.907987i
$520$	−1.87284e9	−	2.57777e11i	−0.0256146	−	3.52558i
$521$	1.25560e11			1.70412			0.852062	−	0.523441i	$-0.175352\pi$
$521$	1.25560e11			1.70412			0.852062	+	0.523441i	$0.175352\pi$
$522$	−8.43276e9	+	3.14715e10i	−0.113576	+	0.423872i
$523$	2.08988e10	+	3.61977e10i	0.279328	+	0.483810i	0.971218	−	0.238193i	$-0.0765551\pi$
$523$	2.08988e10	+	3.61977e10i	0.279328	+	0.483810i	−0.691890	+	0.722003i	$0.743222\pi$
$524$	−1.07962e10	−	6.23317e9i	−0.143201	−	0.0826769i
$525$	6.15955e9	+	6.15955e9i	0.0810797	+	0.0810797i
$526$	1.19688e10	−	3.20702e9i	0.156353	−	0.0418947i
$527$	−1.56985e10	−	5.85878e10i	−0.203525	−	0.759564i
$528$	−2.07161e11	+	2.07161e11i	−2.66546	+	2.66546i
$529$	−2.19004e10	+	3.79326e10i	−0.279659	+	0.484384i
$530$	−4.41765e10	+	2.55053e10i	−0.559871	+	0.323242i
$531$	−1.19224e10	−	3.19459e9i	−0.149963	−	0.0401825i
$532$			3.33574e10i			0.416433i
$533$	2.56795e10	+	6.68123e9i	0.318184	+	0.0827842i
$534$	−4.67392e10			−0.574799
$535$	−2.40904e9	+	8.99065e9i	−0.0294055	+	0.109743i
$536$	−7.59029e10	−	1.31468e11i	−0.919600	−	1.59279i
$537$	−6.12989e10	−	3.53909e10i	−0.737149	−	0.425593i
$538$	−1.15663e11	−	1.15663e11i	−1.38060	−	1.38060i
$539$	1.27897e11	−	3.42698e10i	1.51532	−	0.406029i
$540$	7.50459e10	+	2.80075e11i	0.882576	+	3.29382i
$541$	4.25882e10	−	4.25882e10i	0.497164	−	0.497164i	−0.413390	−	0.910554i	$-0.635655\pi$
$541$	4.25882e10	−	4.25882e10i	0.497164	−	0.497164i	0.910554	+	0.413390i	$0.135655\pi$
$542$	9.71561e9	−	1.68279e10i	0.112583	−	0.194999i
$543$	−9.33798e9	+	5.39129e9i	−0.107412	+	0.0620145i
$544$	−9.80220e10	−	2.62649e10i	−1.11925	−	0.299903i
$545$		−	1.65107e11i		−	1.87146i
$546$	−2.92891e10	+	1.71950e10i	−0.329561	+	0.193478i
$547$	−7.03713e10			−0.786043			−0.393022	−	0.919529i	$-0.628570\pi$
$547$	−7.03713e10			−0.786043			−0.393022	+	0.919529i	$0.628570\pi$
$548$	2.86684e10	−	1.06992e11i	0.317893	−	1.18639i
$549$	−1.07285e10	−	1.85823e10i	−0.118100	−	0.204555i
$550$	1.39650e11	+	8.06270e10i	1.52613	+	0.881110i
$551$	−2.94013e10	−	2.94013e10i	−0.318977	−	0.318977i
$552$	1.36151e11	−	3.64817e10i	1.46645	−	0.392933i
$553$	4.07863e9	+	1.52217e10i	0.0436128	+	0.162765i
$554$	−3.92759e10	+	3.92759e10i	−0.416953	+	0.416953i
$555$	−5.60912e10	+	9.71528e10i	−0.591184	+	1.02396i
$556$	3.00424e10	−	1.73450e10i	0.314366	−	0.181499i
$557$	−2.26414e10	−	6.06674e9i	−0.235224	−	0.0630282i	0.139281	−	0.990253i	$-0.455521\pi$
$557$	−2.26414e10	−	6.06674e9i	−0.235224	−	0.0630282i	−0.374505	+	0.927225i	$0.622188\pi$
$558$		−	1.00422e11i		−	1.03584i
$559$	5.85803e10	−	1.03188e11i	0.599935	−	1.05677i
$560$	−8.58995e10			−0.873451
$561$	1.69642e10	−	6.33111e10i	0.171270	−	0.639188i
$562$	1.36923e11	+	2.37157e11i	1.37255	+	2.37733i
$563$	1.06973e10	+	6.17608e9i	0.106473	+	0.0614723i	0.552291	−	0.833651i	$-0.313754\pi$
$563$	1.06973e10	+	6.17608e9i	0.106473	+	0.0614723i	−0.445818	+	0.895124i	$0.647087\pi$
$564$	8.60793e10	+	8.60793e10i	0.850712	+	0.850712i
$565$	−6.30996e10	+	1.69075e10i	−0.619203	+	0.165915i
$566$	1.18260e10	+	4.41353e10i	0.115232	+	0.430052i
$567$	9.92841e9	−	9.92841e9i	0.0960611	−	0.0960611i
$568$	−5.86456e10	+	1.01577e11i	−0.563433	+	0.975894i
$569$	−4.09054e9	+	2.36167e9i	−0.0390239	+	0.0225305i	−0.519385	−	0.854540i	$-0.673839\pi$
$569$	−4.09054e9	+	2.36167e9i	−0.0390239	+	0.0225305i	0.480361	+	0.877071i	$0.340506\pi$
$570$	−1.27658e11	−	3.42058e10i	−1.20934	−	0.324041i
$571$		−	5.07669e9i		−	0.0477569i	−0.999715	−	0.0238784i	$-0.992399\pi$
$571$		−	5.07669e9i		−	0.0477569i	0.999715	−	0.0238784i	$-0.00760147\pi$
$572$	−3.15473e11	+	3.20090e11i	−2.94698	+	2.99012i
$573$	−4.40951e10			−0.409046
$574$	4.35460e9	−	1.62516e10i	0.0401145	−	0.149709i
$575$	−2.03859e10	−	3.53093e10i	−0.186491	−	0.323012i
$576$	−5.47729e10	−	3.16231e10i	−0.497595	−	0.287286i
$577$	−6.35562e10	−	6.35562e10i	−0.573396	−	0.573396i	0.359679	−	0.933076i	$-0.382886\pi$
$577$	−6.35562e10	−	6.35562e10i	−0.573396	−	0.573396i	−0.933076	+	0.359679i	$0.882886\pi$
$578$	−1.53930e11	+	4.12453e10i	−1.37915	+	0.369542i
$579$	4.04367e10	+	1.50912e11i	0.359800	+	1.34279i
$580$	1.71341e11	−	1.71341e11i	1.51408	−	1.51408i
$581$	1.69061e9	−	2.92823e9i	0.0148368	−	0.0256980i
$582$	2.29316e11	−	1.32396e11i	1.99867	−	1.15393i
$583$	5.16310e10	+	1.38345e10i	0.446927	+	0.119754i
$584$			5.09329e9i			0.0437872i
$585$	1.33392e10	+	4.83741e10i	0.113896	+	0.413037i
$586$	−6.42644e9			−0.0544979
$587$	−4.33025e10	+	1.61607e11i	−0.364721	+	1.36116i	0.503078	+	0.864241i	$0.332201\pi$
$587$	−4.33025e10	+	1.61607e11i	−0.364721	+	1.36116i	−0.867799	+	0.496915i	$0.834466\pi$
$588$	−1.13752e11	−	1.97024e11i	−0.951587	−	1.64820i
$589$	1.10986e11	+	6.40775e10i	0.922158	+	0.532408i
$590$	9.08054e10	+	9.08054e10i	0.749383	+	0.749383i
$591$	−1.66648e11	+	4.46531e10i	−1.36600	+	0.366018i
$592$	−1.02999e11	−	3.84396e11i	−0.838580	−	3.12962i
$593$	−1.38142e11	+	1.38142e11i	−1.11714	+	1.11714i	−0.124981	+	0.992159i	$0.539887\pi$
$593$	−1.38142e11	+	1.38142e11i	−1.11714	+	1.11714i	−0.992159	+	0.124981i	$0.960113\pi$
$594$	2.12525e11	−	3.68105e11i	1.70712	−	2.95682i
$595$	1.66431e10	−	9.60891e9i	0.132790	−	0.0766666i
$596$	4.55764e11	+	1.22122e11i	3.61206	+	0.967848i
$597$			1.30580e11i			1.02797i
$598$	1.53247e11	−	4.22582e10i	1.19836	−	0.330450i
$599$	−1.05467e10			−0.0819237			−0.0409619	−	0.999161i	$-0.513042\pi$
$599$	−1.05467e10			−0.0819237			−0.0409619	+	0.999161i	$0.513042\pi$
$600$	4.31008e10	−	1.60855e11i	0.332568	−	1.24116i
$601$	−4.92533e10	−	8.53093e10i	−0.377518	−	0.653880i	0.613182	−	0.789941i	$-0.289889\pi$
$601$	−4.92533e10	−	8.53093e10i	−0.377518	−	0.653880i	−0.990700	+	0.136061i	$0.956556\pi$
$602$	−6.51577e10	−	3.76188e10i	−0.496112	−	0.286430i
$603$	2.08951e10	+	2.08951e10i	0.158043	+	0.158043i
$604$	−1.75311e11	+	4.69745e10i	−1.31723	+	0.352951i
$605$	−7.82357e10	−	2.91980e11i	−0.583961	−	2.17937i
$606$	6.38199e10	−	6.38199e10i	0.473223	−	0.473223i
$607$	4.33909e10	−	7.51552e10i	0.319627	−	0.553611i	−0.660783	−	0.750577i	$-0.729776\pi$
$607$	4.33909e10	−	7.51552e10i	0.319627	−	0.553611i	0.980410	+	0.196966i	$0.0631090\pi$
$608$	1.85688e11	−	1.07207e11i	1.35884	−	0.784528i
$609$	−1.85346e10	−	4.96634e9i	−0.134746	−	0.0361050i
$610$			2.23243e11i			1.61234i
$611$	5.87714e10	+	5.79236e10i	0.421698	+	0.415615i
$612$	5.87510e10			0.418803
$613$	−9.53124e8	+	3.55711e9i	−0.00675006	+	0.0251916i	−0.969219	−	0.246201i	$-0.920818\pi$
$613$	−9.53124e8	+	3.55711e9i	−0.00675006	+	0.0251916i	0.962469	+	0.271393i	$0.0874842\pi$
$614$	7.25101e10	+	1.25591e11i	0.510182	+	0.883660i
$615$	4.12658e10	+	2.38248e10i	0.288463	+	0.166544i
$616$	1.21112e11	+	1.21112e11i	0.841136	+	0.841136i
$617$	1.64889e10	−	4.41820e9i	0.113776	−	0.0304863i	−0.201482	−	0.979492i	$-0.564576\pi$
$617$	1.64889e10	−	4.41820e9i	0.113776	−	0.0304863i	0.315258	+	0.949006i	$0.397909\pi$
$618$	−5.10508e10	−	1.90524e11i	−0.349985	−	1.30616i
$619$	−1.14693e11	+	1.14693e11i	−0.781219	+	0.781219i	−0.980037	−	0.198817i	$-0.936290\pi$
$619$	−1.14693e11	+	1.14693e11i	−0.781219	+	0.781219i	0.198817	+	0.980037i	$0.436290\pi$
$620$	−3.73423e11	+	6.46788e11i	−2.52717	+	4.37719i
$621$	−9.30721e10	+	5.37352e10i	−0.625825	+	0.361320i
$622$	−2.51131e11	−	6.72905e10i	−1.67780	−	0.449565i
$623$			1.43600e10i			0.0953241i
$624$	2.96734e11	+	1.68457e11i	1.95717	+	1.11109i
$625$	1.90151e11			1.24617
$626$	−3.97883e9	+	1.48492e10i	−0.0259094	+	0.0966953i
$627$	6.92435e10	+	1.19933e11i	0.448032	+	0.776014i
$628$	−3.44606e11	−	1.98958e11i	−2.21556	−	1.27916i
$629$	6.29555e10	+	6.29555e10i	0.402190	+	0.402190i
$630$	3.07336e10	−	8.23503e9i	0.195097	−	0.0522761i
$631$	−2.51263e10	−	9.37725e10i	−0.158493	−	0.591505i	−0.998781	−	0.0493638i	$-0.984281\pi$
$631$	−2.51263e10	−	9.37725e10i	−0.158493	−	0.591505i	0.840288	−	0.542141i	$-0.182386\pi$
$632$	2.13024e11	−	2.13024e11i	1.33524	−	1.33524i
$633$	−2.01956e9	+	3.49798e9i	−0.0125789	+	0.0217873i
$634$	−3.61161e11	+	2.08516e11i	−2.23534	+	1.29057i
$635$	3.79079e11	+	1.01574e11i	2.33150	+	0.624722i
$636$		−	9.18415e10i		−	0.561320i
$637$	−7.80751e10	−	1.32989e11i	−0.474192	−	0.807716i
$638$	−3.55211e11			−2.14390
$639$	5.90925e9	−	2.20536e10i	0.0354429	−	0.132275i
$640$	7.97581e10	+	1.38145e11i	0.475395	+	0.823409i
$641$	1.32053e11	+	7.62406e10i	0.782195	+	0.451600i	0.837207	−	0.546885i	$-0.184187\pi$
$641$	1.32053e11	+	7.62406e10i	0.782195	+	0.451600i	−0.0550129	+	0.998486i	$0.517520\pi$
$642$	−1.65773e10	−	1.65773e10i	−0.0975831	−	0.0975831i
$643$	−2.13933e11	+	5.73232e10i	−1.25151	+	0.335341i	−0.822920	−	0.568158i	$-0.807656\pi$
$643$	−2.13933e11	+	5.73232e10i	−1.25151	+	0.335341i	−0.428591	+	0.903499i	$0.640990\pi$
$644$	−1.86484e10	−	6.95968e10i	−0.108417	−	0.404619i
$645$	1.50670e11	−	1.50670e11i	0.870540	−	0.870540i
$646$	−5.24442e10	+	9.08360e10i	−0.301139	+	0.521588i
$647$	1.32612e11	−	7.65635e10i	0.756773	−	0.436923i	−0.0713631	−	0.997450i	$-0.522735\pi$
$647$	1.32612e11	−	7.65635e10i	0.756773	−	0.436923i	0.828136	+	0.560527i	$0.189402\pi$
$648$	−2.59277e11	−	6.94730e10i	−1.47050	−	0.394018i
$649$		−	1.34565e11i		−	0.758497i
$650$	4.72895e10	−	1.81759e11i	0.264918	−	1.01822i
$651$	5.91419e10			0.329284
$652$	8.05440e10	−	3.00594e11i	0.445700	−	1.66338i
$653$	1.75994e10	+	3.04831e10i	0.0967933	+	0.167651i	0.910356	−	0.413827i	$-0.135808\pi$
$653$	1.75994e10	+	3.04831e10i	0.0967933	+	0.167651i	−0.813562	+	0.581478i	$0.802475\pi$
$654$	3.60146e11	+	2.07931e11i	1.96865	+	1.13660i
$655$	−1.07302e10	−	1.07302e10i	−0.0582967	−	0.0582967i
$656$	−1.63273e11	+	4.37488e10i	−0.881655	+	0.236239i
$657$	−2.56605e8	−	9.57664e8i	−0.00137722	−	0.00513987i
$658$	3.69978e10	−	3.69978e10i	0.197366	−	0.197366i
$659$	1.58218e11	−	2.74041e11i	0.838906	−	1.45303i	−0.0519050	−	0.998652i	$-0.516529\pi$
$659$	1.58218e11	−	2.74041e11i	0.838906	−	1.45303i	0.890811	−	0.454375i	$-0.150137\pi$
$660$	−6.98933e11	+	4.03529e11i	−3.68349	+	2.12667i
$661$	−1.47788e11	−	3.95995e10i	−0.774162	−	0.207436i	−0.149953	−	0.988693i	$-0.547912\pi$
$661$	−1.47788e11	−	3.95995e10i	−0.774162	−	0.207436i	−0.624209	+	0.781257i	$0.714579\pi$
$662$		−	2.78454e11i		−	1.44984i
$663$	−7.63365e10	+	5.54612e8i	−0.395074	+	0.00287035i
$664$	−6.46397e10			−0.332527
$665$	−1.05093e10	+	3.92212e10i	−0.0537386	+	0.200555i
$666$	7.37027e10	+	1.27657e11i	0.374616	+	0.648854i
$667$	7.77796e10	+	4.49061e10i	0.392973	+	0.226883i
$668$	8.49545e10	+	8.49545e10i	0.426659	+	0.426659i
$669$	−2.04390e11	+	5.47662e10i	−1.02037	+	0.273406i
$670$	−7.95725e10	−	2.96969e11i	−0.394879	−	1.47371i
$671$	1.65412e11	−	1.65412e11i	0.815977	−	0.815977i
$672$	4.94745e10	−	8.56924e10i	0.242608	−	0.420209i
$673$	−1.02455e11	+	5.91524e10i	−0.499428	+	0.288345i	−0.728477	−	0.685070i	$-0.759772\pi$
$673$	−1.02455e11	+	5.91524e10i	−0.499428	+	0.288345i	0.229049	+	0.973415i	$0.426438\pi$
$674$	−6.42817e11	−	1.72242e11i	−3.11493	−	0.834642i
$675$			1.26970e11i			0.611625i
$676$	4.57062e11	+	2.55103e11i	2.18871	+	1.22160i
$677$	−5.96062e10			−0.283751			−0.141875	−	0.989885i	$-0.545313\pi$
$677$	−5.96062e10			−0.283751			−0.141875	+	0.989885i	$0.545313\pi$
$678$	4.25854e10	−	1.58931e11i	0.201531	−	0.752125i
$679$	−4.06768e10	−	7.04543e10i	−0.191367	−	0.331458i
$680$	−3.18171e11	−	1.83696e11i	−1.48807	−	0.859140i
$681$	−1.19006e11	−	1.19006e11i	−0.553324	−	0.553324i
$682$	1.05751e12	−	2.83359e11i	4.88819	−	1.30979i
$683$	7.96968e10	+	2.97433e11i	0.366234	+	1.36680i	0.865741	+	0.500493i	$0.166848\pi$
$683$	7.96968e10	+	2.97433e11i	0.366234	+	1.36680i	−0.499507	+	0.866310i	$0.666486\pi$
$684$	−8.77754e10	+	8.77754e10i	−0.401004	+	0.401004i
$685$	6.74160e10	−	1.16768e11i	0.306197	−	0.530348i
$686$	−1.75096e11	+	1.01092e11i	−0.790642	+	0.456477i
$687$	1.61902e11	+	4.33815e10i	0.726817	+	0.194750i
$688$			7.55880e11i			3.37364i
$689$	−4.52293e8	−	6.22533e10i	−0.00200698	−	0.276239i
$690$	2.85468e11			1.25939
$691$	−1.07997e11	+	4.03049e11i	−0.473694	+	1.76785i	0.152627	+	0.988284i	$0.451227\pi$
$691$	−1.07997e11	+	4.03049e11i	−0.473694	+	1.76785i	−0.626321	+	0.779565i	$0.715440\pi$
$692$	3.21893e11	+	5.57535e11i	1.40374	+	2.43135i
$693$	−2.88739e10	−	1.66704e10i	−0.125191	−	0.0722790i
$694$	4.86775e11	+	4.86775e11i	2.09841	+	2.09841i
$695$	4.07881e10	−	1.09291e10i	0.174821	−	0.0468432i
$696$	9.49428e10	+	3.54331e11i	0.404599	+	1.50998i
$697$	2.67404e10	−	2.67404e10i	0.113302	−	0.113302i
$698$	3.83795e11	−	6.64752e11i	1.61688	−	2.80051i
$699$	2.54830e11	−	1.47126e11i	1.06744	−	0.616284i
$700$	−8.22244e10	−	2.20320e10i	−0.342459	−	0.0917616i
$701$			4.67953e10i			0.193789i	0.995295	+	0.0968947i	$0.0308910\pi$
$701$			4.67953e10i			0.193789i	−0.995295	+	0.0968947i	$0.969109\pi$
$702$	−4.79099e11	−	1.24651e11i	−1.97277	−	0.513270i
$703$	−1.88114e11			−0.770194
$704$	1.78462e11	−	6.66028e11i	0.726531	−	2.71145i
$705$	7.40916e10	+	1.28330e11i	0.299925	+	0.519485i
$706$	−5.99478e11	−	3.46109e11i	−2.41298	−	1.39314i
$707$	−1.96078e10	−	1.96078e10i	−0.0784788	−	0.0784788i
$708$	−2.23331e11	+	5.98413e10i	−0.888824	+	0.238160i
$709$	−8.31071e10	−	3.10160e11i	−0.328892	−	1.22744i	−0.910341	−	0.413859i	$-0.864181\pi$
$709$	−8.31071e10	−	3.10160e11i	−0.328892	−	1.22744i	0.581449	−	0.813583i	$-0.302486\pi$
$710$	−1.67969e11	+	1.67969e11i	−0.660991	+	0.660991i
$711$	−2.93214e10	+	5.07861e10i	−0.114738	+	0.198731i
$712$	2.37745e11	−	1.37262e11i	0.925105	−	0.534109i
$713$	−2.67383e11	−	7.16450e10i	−1.03461	−	0.277222i
$714$			4.84046e10i			0.186249i
$715$	−4.71774e11	+	2.76968e11i	−1.80513	+	1.05975i
$716$	6.91695e11			2.63186
$717$	−7.41196e10	+	2.76618e11i	−0.280450	+	1.04666i
$718$	1.92152e10	+	3.32818e10i	0.0723016	+	0.125230i
$719$	−4.33237e10	−	2.50129e10i	−0.162110	−	0.0935943i	0.416750	−	0.909021i	$-0.363169\pi$
$719$	−4.33237e10	−	2.50129e10i	−0.162110	−	0.0935943i	−0.578860	+	0.815427i	$0.696502\pi$
$720$	−2.26033e11	−	2.26033e11i	−0.841089	−	0.841089i
$721$	−5.85361e10	+	1.56847e10i	−0.216612	+	0.0580411i
$722$	7.43414e10	+	2.77446e11i	0.273578	+	1.02101i
$723$	1.80170e11	−	1.80170e11i	0.659371	−	0.659371i
$724$	5.26847e10	−	9.12527e10i	0.191748	−	0.332117i
$725$	9.18918e10	−	5.30538e10i	0.332602	−	0.192028i
$726$	7.35419e11	+	1.97055e11i	2.64721	+	0.709318i
$727$		−	3.31129e11i		−	1.18538i	−0.805429	−	0.592692i	$-0.798065\pi$
$727$		−	3.31129e11i		−	1.18538i	0.805429	−	0.592692i	$-0.201935\pi$
$728$	9.84850e10	−	1.73480e11i	0.350626	−	0.617622i
$729$	3.01485e11			1.06747
$730$	−2.66977e9	+	9.96371e9i	−0.00940117	+	0.0350857i
$731$	−8.45545e10	−	1.46453e11i	−0.296120	−	0.512894i
$732$	−3.48086e11	−	2.00967e11i	−1.21239	−	0.699973i
$733$	8.00241e10	+	8.00241e10i	0.277207	+	0.277207i	0.831993	−	0.554786i	$-0.187200\pi$
$733$	8.00241e10	+	8.00241e10i	0.277207	+	0.277207i	−0.554786	+	0.831993i	$0.687200\pi$
$734$	−9.45573e11	+	2.53365e11i	−3.25770	+	0.872897i
$735$	−7.16752e10	−	2.67496e11i	−0.245595	−	0.916573i
$736$	−3.27485e11	+	3.27485e11i	−1.11604	+	1.11604i
$737$	−1.61080e11	+	2.78999e11i	−0.545975	+	0.945657i
$738$	5.42224e10	−	3.13053e10i	0.182791	−	0.105534i
$739$	−1.74647e11	−	4.67965e10i	−0.585576	−	0.156905i	−0.0461455	−	0.998935i	$-0.514694\pi$
$739$	−1.74647e11	−	4.67965e10i	−0.585576	−	0.156905i	−0.539431	+	0.842030i	$0.681360\pi$
$740$		−	1.09627e12i		−	3.65586i
$741$	1.13220e11	−	1.14877e11i	0.375535	−	0.381032i
$742$	−3.94745e10			−0.130227
$743$	−6.23044e10	+	2.32523e11i	−0.204439	+	0.762976i	0.785181	+	0.619266i	$0.212570\pi$
$743$	−6.23044e10	+	2.32523e11i	−0.204439	+	0.762976i	−0.989620	+	0.143710i	$0.954097\pi$
$744$	−5.65315e11	−	9.79154e11i	−1.84501	−	3.19565i
$745$	4.97407e11	+	2.87178e11i	1.61468	+	0.932237i
$746$	2.19510e11	+	2.19510e11i	0.708760	+	0.708760i
$747$	1.21539e10	−	3.25661e9i	0.0390330	−	0.0104588i
$748$	1.65777e11	+	6.18689e11i	0.529564	+	1.97636i
$749$	−5.09317e9	+	5.09317e9i	−0.0161831	+	0.0161831i
$750$	−1.31501e11	+	2.27767e11i	−0.415609	+	0.719856i
$751$	−1.50685e11	+	8.69978e10i	−0.473706	+	0.273494i	−0.717790	−	0.696260i	$-0.754846\pi$
$751$	−1.50685e11	+	8.69978e10i	−0.473706	+	0.273494i	0.244084	+	0.969754i	$0.421513\pi$
$752$	−5.07754e11	−	1.36052e11i	−1.58775	−	0.425436i
$753$			3.11890e11i			0.970111i
$754$	1.09976e11	+	3.98823e11i	0.340261	+	1.23394i
$755$	−2.20928e11			−0.679929
$756$	−5.80741e10	+	2.16736e11i	−0.177785	+	0.663503i
$757$	2.02434e11	+	3.50626e11i	0.616452	+	1.06773i	0.990128	+	0.140167i	$0.0447641\pi$
$757$	2.02434e11	+	3.50626e11i	0.616452	+	1.06773i	−0.373675	+	0.927560i	$0.621903\pi$
$758$	6.74507e11	+	3.89427e11i	2.04319	+	1.17964i
$759$	−2.11518e11	−	2.11518e11i	−0.637354	−	0.637354i
$760$	7.49801e11	−	2.00909e11i	2.24746	−	0.602205i
$761$	6.74464e10	+	2.51714e11i	0.201104	+	0.750530i	0.990602	+	0.136777i	$0.0436743\pi$
$761$	6.74464e10	+	2.51714e11i	0.201104	+	0.750530i	−0.789498	+	0.613753i	$0.789659\pi$
$762$	−6.98961e11	+	6.98961e11i	−2.07316	+	2.07316i
$763$	6.38840e10	−	1.10650e11i	0.188492	−	0.326478i
$764$	3.73176e11	−	2.15453e11i	1.09532	−	0.632382i
$765$	6.90787e10	+	1.85096e10i	0.201697	+	0.0540444i
$766$		−	3.55036e11i		−	1.03123i
$767$	−1.51087e11	+	4.16623e10i	−0.436561	+	0.120382i
$768$	7.08775e10			0.203734
$769$	1.67280e11	−	6.24298e11i	0.478343	−	1.78520i	−0.129989	−	0.991515i	$-0.541494\pi$
$769$	1.67280e11	−	6.24298e11i	0.478343	−	1.78520i	0.608331	−	0.793683i	$-0.291839\pi$
$770$	1.73441e11	+	3.00409e11i	0.493389	+	0.854575i
$771$	−3.08704e11	−	1.78230e11i	−0.873624	−	0.504387i
$772$	−1.07958e12	−	1.07958e12i	−3.03940	−	3.03940i
$773$	7.45839e10	−	1.99847e10i	0.208894	−	0.0559731i	−0.152854	−	0.988249i	$-0.548846\pi$
$773$	7.45839e10	−	1.99847e10i	0.208894	−	0.0559731i	0.361749	+	0.932276i	$0.382180\pi$
$774$	−7.24649e10	−	2.70443e11i	−0.201913	−	0.753549i
$775$	−2.31252e11	+	2.31252e11i	−0.641031	+	0.641031i
$776$	−7.77629e11	+	1.34689e12i	−2.14450	+	3.71438i
$777$	−7.51815e10	+	4.34061e10i	−0.206266	+	0.119088i
$778$	7.18102e11	+	1.92415e11i	1.96005	+	0.525195i
$779$			7.99018e10i			0.216973i
$780$	6.69468e11	+	6.59810e11i	1.80864	+	1.78255i
$781$	2.48914e11			0.669030
$782$	5.86377e10	−	2.18839e11i	0.156802	−	0.585191i
$783$	−1.39845e11	−	2.42218e11i	−0.372048	−	0.644406i
$784$	8.50773e11	+	4.91194e11i	2.25190	+	1.30014i
$785$	−3.42501e11	−	3.42501e11i	−0.901953	−	0.901953i
$786$	3.69190e10	−	9.89242e9i	0.0967297	−	0.0259187i
$787$	−1.52094e11	−	5.67624e11i	−0.396474	−	1.47966i	−0.819256	−	0.573428i	$-0.805613\pi$
$787$	−1.52094e11	−	5.67624e11i	−0.396474	−	1.47966i	0.422782	−	0.906231i	$-0.361054\pi$
$788$	1.19216e12	−	1.19216e12i	3.09192	−	3.09192i
$789$	−1.35781e10	+	2.35180e10i	−0.0350373	+	0.0606864i
$790$	5.28388e11	−	3.05065e11i	1.35658	−	0.783220i
$791$	−4.88295e10	−	1.30838e10i	−0.124732	−	0.0334217i
$792$			6.37383e11i			1.61994i
$793$	−2.36934e11	−	1.34508e11i	−0.599149	−	0.340139i
$794$	−1.09823e11			−0.276318
$795$	2.89348e10	−	1.07986e11i	0.0724355	−	0.270333i
$796$	−6.38028e11	−	1.10510e12i	−1.58923	−	2.75263i
$797$	5.50125e11	+	3.17615e11i	1.36342	+	0.787169i	0.990077	−	0.140526i	$-0.0448794\pi$
$797$	5.50125e11	+	3.17615e11i	1.36342	+	0.787169i	0.373339	+	0.927695i	$0.378213\pi$
$798$	−7.23176e10	−	7.23176e10i	−0.178333	−	0.178333i
$799$	1.13597e11	−	3.04382e10i	0.278727	−	0.0746848i
$800$	1.41617e11	+	5.28520e11i	0.345743	+	1.29033i
$801$	−3.77865e10	+	3.77865e10i	−0.0917923	+	0.0917923i
$802$	−3.17684e11	+	5.50246e11i	−0.767889	+	1.33002i
$803$	9.36082e9	−	5.40447e9i	0.0225139	−	0.0129984i
$804$	5.34674e11	+	1.43265e11i	1.27957	+	0.342860i
$805$		−	8.77063e10i		−	0.208856i
$806$	−6.45563e11	−	1.09962e12i	−1.52967	−	2.60557i
$807$	3.58487e11			0.845239
$808$	−1.37204e11	+	5.12052e11i	−0.321900	+	1.20135i
$809$	−3.13763e11	−	5.43453e11i	−0.732499	−	1.26873i	−0.955812	−	0.293979i	$-0.905020\pi$
$809$	−3.13763e11	−	5.43453e11i	−0.732499	−	1.26873i	0.223313	−	0.974747i	$-0.428313\pi$
$810$	−4.70792e11	−	2.71812e11i	−1.09368	−	0.631435i
$811$	1.21445e11	+	1.21445e11i	0.280736	+	0.280736i	0.833402	−	0.552667i	$-0.186390\pi$
$811$	1.21445e11	+	1.21445e11i	0.280736	+	0.280736i	−0.552667	+	0.833402i	$0.686390\pi$
$812$	1.81124e11	−	4.85321e10i	0.416632	−	0.111636i
$813$	1.10220e10	+	4.11346e10i	0.0252288	+	0.0941553i
$814$	−1.13635e12	+	1.13635e12i	−2.58830	+	2.58830i
$815$	1.89405e11	−	3.28060e11i	0.429301	−	0.743571i
$816$	4.21148e11	−	2.43150e11i	0.949892	−	0.548420i
$817$	3.45130e11	+	9.24774e10i	0.774631	+	0.207562i
$818$		−	1.73131e11i		−	0.386688i
$819$	−9.77752e9	+	3.75802e10i	−0.0217317	+	0.0835264i
$820$	−4.65642e11			−1.02990
$821$	−7.26642e10	+	2.71186e11i	−0.159937	+	0.596891i	0.838695	+	0.544601i	$0.183319\pi$
$821$	−7.26642e10	+	2.71186e11i	−0.159937	+	0.596891i	−0.998632	+	0.0522905i	$0.983348\pi$
$822$	1.69803e11	+	2.94107e11i	0.371927	+	0.644196i
$823$	5.13695e11	+	2.96582e11i	1.11971	+	0.646466i	0.941327	−	0.337495i	$-0.109580\pi$
$823$	5.13695e11	+	2.96582e11i	1.11971	+	0.646466i	0.178385	+	0.983961i	$0.442913\pi$
$824$	8.19201e11	+	8.19201e11i	1.77698	+	1.77698i
$825$	−3.41364e11	+	9.14682e10i	−0.736889	+	0.197449i
$826$	2.57205e10	+	9.59901e10i	0.0552533	+	0.206208i
$827$	4.41310e11	−	4.41310e11i	0.943456	−	0.943456i	−0.0550289	−	0.998485i	$-0.517525\pi$
$827$	4.41310e11	−	4.41310e11i	0.943456	−	0.943456i	0.998485	+	0.0550289i	$0.0175251\pi$
$828$	1.34064e11	−	2.32205e11i	0.285227	−	0.494027i
$829$	−5.91248e11	+	3.41357e11i	−1.25185	+	0.722755i	−0.971476	−	0.237136i	$-0.923791\pi$
$829$	−5.91248e11	+	3.41357e11i	−1.25185	+	0.722755i	−0.280372	+	0.959891i	$0.590458\pi$
$830$	−1.26451e11	−	3.38824e10i	−0.266446	−	0.0713940i
$831$		−	1.21732e11i		−	0.255270i
$832$	−8.03053e11	+	5.83447e9i	−1.67591	+	0.0121761i
$833$	−2.19784e11			−0.456475
$834$	−2.75276e10	+	1.02734e11i	−0.0568989	+	0.212350i
$835$	7.31235e10	+	1.26654e11i	0.150422	+	0.260538i
$836$	−1.17201e12	−	6.76662e11i	−2.39942	−	1.38531i
$837$	6.09559e11	+	6.09559e11i	1.24198	+	1.24198i
$838$	−8.19934e11	+	2.19701e11i	−1.66266	+	0.445508i
$839$	2.16519e11	+	8.08060e11i	0.436967	+	1.63078i	0.736316	+	0.676638i	$0.236564\pi$
$839$	2.16519e11	+	8.08060e11i	0.436967	+	1.63078i	−0.299349	+	0.954144i	$0.596770\pi$
$840$	2.53306e11	−	2.53306e11i	0.508779	−	0.508779i
$841$	1.33256e11	−	2.30806e11i	0.266381	−	0.461385i
$842$	1.44577e12	−	8.34714e11i	2.87641	−	1.66069i
$843$	−5.79712e11	−	1.55333e11i	−1.14789	−	0.307577i
$844$		−	3.94711e10i		−	0.0777875i
$845$	4.57038e11	+	4.43945e11i	0.896448	+	0.870768i
$846$	1.94710e11			0.380107
$847$	6.05426e10	−	2.25948e11i	0.117633	−	0.439010i
$848$	1.98292e11	+	3.43451e11i	0.383461	+	0.664174i
$849$	−8.67234e10	−	5.00698e10i	−0.166919	−	0.0963707i
$850$	−1.89268e11	−	1.89268e11i	−0.362578	−	0.362578i
$851$	3.92481e11	−	1.05165e11i	0.748343	−	0.200518i
$852$	−1.10693e11	−	4.13110e11i	−0.210068	−	0.783984i
$853$	9.46184e10	−	9.46184e10i	0.178723	−	0.178723i	−0.612076	−	0.790799i	$-0.709665\pi$
$853$	9.46184e10	−	9.46184e10i	0.178723	−	0.178723i	0.790799	+	0.612076i	$0.209665\pi$
$854$	−8.63780e10	+	1.49611e11i	−0.162395	+	0.281276i
$855$	−1.30859e11	+	7.55515e10i	−0.244872	+	0.141377i
$856$	1.33006e11	+	3.56389e10i	0.247729	+	0.0663789i
$857$			1.19352e10i			0.0221262i	0.999939	+	0.0110631i	$0.00352156\pi$
$857$			1.19352e10i			0.0221262i	−0.999939	+	0.0110631i	$0.996478\pi$
$858$	−1.00108e10	−	1.37788e12i	−0.0184722	−	2.54250i
$859$	−4.75591e11			−0.873497			−0.436748	−	0.899584i	$-0.643870\pi$
$859$	−4.75591e11			−0.873497			−0.436748	+	0.899584i	$0.643870\pi$
$860$	−5.38929e11	+	2.01131e12i	−0.985230	+	3.67693i
$861$	1.84368e10	+	3.19335e10i	0.0335485	+	0.0581077i
$862$	−1.50519e12	−	8.69025e11i	−2.72624	−	1.57399i
$863$	−3.27762e11	−	3.27762e11i	−0.590901	−	0.590901i	0.346974	−	0.937875i	$-0.387209\pi$
$863$	−3.27762e11	−	3.27762e11i	−0.590901	−	0.590901i	−0.937875	+	0.346974i	$0.887209\pi$
$864$	1.39313e12	−	3.73288e11i	2.49998	−	0.669867i
$865$	2.02826e11	+	7.56955e11i	0.362292	+	1.35209i
$866$	−6.40087e11	+	6.40087e11i	−1.13807	+	1.13807i
$867$	1.74627e11	−	3.02463e11i	0.309055	−	0.535298i
$868$	−5.00516e11	+	2.88973e11i	−0.881737	+	0.509071i
$869$	−6.17549e11	−	1.65472e11i	−1.08291	−	0.290165i
$870$			7.42924e11i			1.29678i
$871$	3.63126e11	+	9.44771e10i	0.630935	+	0.164155i
$872$	−2.44257e12			−4.22456
$873$	7.83555e10	−	2.92427e11i	0.134900	−	0.503454i
$874$	2.39345e11	+	4.14557e11i	0.410183	+	0.710458i
$875$	6.99785e10	+	4.04021e10i	0.119380	+	0.0689242i
$876$	−1.31323e10	−	1.31323e10i	−0.0223010	−	0.0223010i
$877$	1.04794e11	−	2.80795e10i	0.177149	−	0.0474669i	−0.169154	−	0.985590i	$-0.554104\pi$
$877$	1.04794e11	−	2.80795e10i	0.177149	−	0.0474669i	0.346303	+	0.938123i	$0.387437\pi$
$878$	−2.40462e11	−	8.97416e11i	−0.404640	−	1.51014i
$879$	9.95907e9	−	9.95907e9i	0.0166826	−	0.0166826i
$880$	1.74249e12	−	3.01808e12i	2.90563	−	5.03269i
$881$	−3.60348e11	+	2.08047e11i	−0.598161	+	0.345348i	−0.768318	−	0.640069i	$-0.778906\pi$
$881$	−3.60348e11	+	2.08047e11i	−0.598161	+	0.345348i	0.170157	+	0.985417i	$0.445573\pi$
$882$	−3.51484e11	−	9.41798e10i	−0.580806	−	0.155626i
$883$		−	2.44422e11i		−	0.402066i	−0.979584	−	0.201033i	$-0.935570\pi$
$883$		−	2.44422e11i		−	0.402066i	0.979584	−	0.201033i	$-0.0644298\pi$
$884$	6.43324e11	−	3.77682e11i	1.05347	−	0.618467i
$885$	−2.81443e11			−0.458793
$886$	7.38580e9	−	2.75642e10i	0.0119857	−	0.0447312i
$887$	4.06264e11	+	7.03670e11i	0.656317	+	1.13677i	0.981562	+	0.191145i	$0.0612199\pi$
$887$	4.06264e11	+	7.03670e11i	0.656317	+	1.13677i	−0.325245	+	0.945630i	$0.605447\pi$
$888$	1.43726e12	+	8.29804e11i	2.31145	+	1.33452i
$889$	2.14747e11	+	2.14747e11i	0.343811	+	0.343811i
$890$	5.37035e11	−	1.43898e11i	0.855938	−	0.229348i
$891$	1.47435e11	+	5.50235e11i	0.233932	+	0.873047i
$892$	1.46216e12	−	1.46216e12i	2.30959	−	2.30959i
$893$	−1.24241e11	+	2.15192e11i	−0.195371	+	0.338392i
$894$	−1.25284e12	+	7.23325e11i	−1.96130	+	1.13236i
$895$	8.13286e11	+	2.17919e11i	1.26751	+	0.339628i
$896$			1.23441e11i			0.191526i
$897$	−1.72000e11	+	3.02975e11i	−0.265680	+	0.467991i
$898$	1.00764e12			1.54953
$899$	1.86455e11	−	6.95858e11i	0.285453	−	1.06532i
$900$	−1.58388e11	−	2.74336e11i	−0.241409	−	0.418132i
$901$	−7.68384e10	−	4.43627e10i	−0.116595	−	0.0673161i
$902$	4.82666e11	+	4.82666e11i	0.729157	+	0.729157i
$903$	1.59273e11	−	4.26771e10i	0.239547	−	0.0641865i
$904$	2.50127e11	+	9.33486e11i	0.374530	+	1.39776i
$905$	9.06953e10	−	9.06953e10i	0.135204	−	0.135204i
$906$	2.78230e11	−	4.81908e11i	0.412943	−	0.715239i
$907$	−6.96593e11	+	4.02178e11i	−1.02932	+	0.594278i	−0.916790	−	0.399371i	$-0.869229\pi$
$907$	−6.96593e11	+	4.02178e11i	−1.02932	+	0.594278i	−0.112530	+	0.993648i	$0.535895\pi$
$908$	1.58862e12	+	4.25669e11i	2.33709	+	0.626222i
$909$		−	1.03191e11i		−	0.151142i
$910$	2.83594e11	−	2.87745e11i	0.413553	−	0.419606i
$911$	−1.06366e12			−1.54429			−0.772147	−	0.635444i	$-0.780817\pi$
$911$	−1.06366e12			−1.54429			−0.772147	+	0.635444i	$0.780817\pi$
$912$	−2.65934e11	+	9.92478e11i	−0.384409	+	1.43463i
$913$	6.85889e10	+	1.18799e11i	0.0987121	+	0.170974i
$914$	1.35393e12	+	7.81695e11i	1.94005	+	1.12009i
$915$	−3.45960e11	−	3.45960e11i	−0.493561	−	0.493561i
$916$	−1.58214e12	+	4.23933e11i	−2.24731	+	0.602165i
$917$	−3.03932e9	−	1.13429e10i	−0.00429832	−	0.0160416i
$918$	−4.98893e11	+	4.98893e11i	−0.702484	+	0.702484i
$919$	−1.66868e11	+	2.89025e11i	−0.233944	+	0.405203i	−0.958965	−	0.283523i	$-0.908497\pi$
$919$	−1.66868e11	+	2.89025e11i	−0.233944	+	0.405203i	0.725021	+	0.688727i	$0.241830\pi$
$920$	−1.45207e12	+	8.38351e11i	−2.02691	+	1.17024i
$921$	−3.06998e11	−	8.22598e10i	−0.426675	−	0.114327i
$922$			9.43120e11i			1.30510i
$923$	−7.70656e10	−	2.79475e11i	−0.106183	−	0.385067i
$924$	−6.24541e11			−0.856787
$925$	1.24246e11	−	4.63692e11i	0.169713	−	0.633378i
$926$	1.25762e11	+	2.17826e11i	0.171043	+	0.296255i
$927$	−1.95302e11	−	1.12758e11i	−0.264477	−	0.152696i
$928$	−8.52273e11	−	8.52273e11i	−1.14918	−	1.14918i
$929$	6.83329e11	−	1.83098e11i	0.917418	−	0.245821i	0.230937	−	0.972969i	$-0.425821\pi$
$929$	6.83329e11	−	1.83098e11i	0.917418	−	0.245821i	0.686481	+	0.727147i	$0.259154\pi$
$930$	−5.92646e11	−	2.21178e12i	−0.792252	−	2.95672i
$931$	3.28363e11	−	3.28363e11i	0.437075	−	0.437075i
$932$	−1.43775e12	+	2.49025e12i	−1.90554	+	3.30050i
$933$	4.93459e11	−	2.84899e11i	0.651215	−	0.375979i
$934$	3.66011e11	+	9.80723e10i	0.480957	+	0.128872i
$935$			7.79676e11i			1.02016i
$936$	7.15638e11	−	1.97338e11i	0.932374	−	0.257103i
$937$	3.30322e11			0.428528			0.214264	−	0.976776i	$-0.431265\pi$
$937$	3.30322e11			0.428528			0.214264	+	0.976776i	$0.431265\pi$
$938$	6.15771e10	−	2.29809e11i	0.0795440	−	0.296862i
$939$	−1.68458e10	−	2.91778e10i	−0.0216685	−	0.0375310i
$940$	−1.25407e12	−	7.24038e11i	−1.60624	−	0.927363i
$941$	−3.23067e11	−	3.23067e11i	−0.412035	−	0.412035i	0.470412	−	0.882447i	$-0.344105\pi$
$941$	−3.23067e11	−	3.23067e11i	−0.412035	−	0.412035i	−0.882447	+	0.470412i	$0.844105\pi$
$942$	1.17843e12	−	3.15759e11i	1.49658	−	0.401007i
$943$	−4.46690e10	−	1.66707e11i	−0.0564885	−	0.210818i
$944$	7.05969e11	−	7.05969e11i	0.888991	−	0.888991i
$945$	−1.36566e11	+	2.36539e11i	−0.171244	+	0.296603i
$946$	2.64348e12	−	1.52621e12i	3.30074	−	1.90568i
$947$	−4.80274e11	−	1.28689e11i	−0.597158	−	0.160008i	−0.0524353	−	0.998624i	$-0.516698\pi$
$947$	−4.80274e11	−	1.28689e11i	−0.597158	−	0.160008i	−0.544722	+	0.838616i	$0.683365\pi$
$948$			1.09850e12i			1.36009i
$949$	−8.96619e9	−	8.83684e9i	−0.0110546	−	0.0108951i
$950$	5.65542e11			0.694337
$951$	2.36553e11	−	8.82829e11i	0.289206	−	1.07933i
$952$	−1.42153e11	−	2.46216e11i	−0.173064	−	0.299756i
$953$	−1.19984e12	−	6.92728e11i	−1.45463	−	0.839830i	−0.455889	−	0.890036i	$-0.650679\pi$
$953$	−1.19984e12	−	6.92728e11i	−1.45463	−	0.839830i	−0.998739	+	0.0502065i	$0.984012\pi$
$954$	−1.03872e11	−	1.03872e11i	−0.125402	−	0.125402i
$955$	5.06654e11	−	1.35758e11i	0.609113	−	0.163211i
$956$	−7.24311e11	−	2.70317e12i	−0.867149	−	3.23624i
$957$	5.50472e11	−	5.50472e11i	0.656277	−	0.656277i
$958$	4.49796e11	−	7.79070e11i	0.534015	−	0.924941i
$959$	9.03606e10	−	5.21697e10i	0.106833	−	0.0616800i
$960$	−1.39300e12	−	3.73252e11i	−1.64008	−	0.439458i
$961$			1.36751e12i			1.60338i
$962$	1.62769e12	+	9.24044e11i	1.90051	+	1.07893i
$963$	−2.68040e10			−0.0311670
$964$	−6.44446e11	+	2.40511e12i	−0.746240	+	2.78501i
$965$	−9.29238e11	−	1.60949e12i	−1.07156	−	1.85600i
$966$	1.91313e11	+	1.10454e11i	0.219702	+	0.126845i
$967$	−5.43740e11	−	5.43740e11i	−0.621850	−	0.621850i	0.324155	−	0.946004i	$-0.394920\pi$
$967$	−5.43740e11	−	5.43740e11i	−0.621850	−	0.621850i	−0.946004	+	0.324155i	$0.894920\pi$
$968$	−4.31950e12	+	1.15741e12i	−4.91963	+	1.31821i
$969$	−5.94958e10	−	2.22042e11i	−0.0674826	−	0.251848i
$970$	−2.22723e12	+	2.22723e12i	−2.51582	+	2.51582i
$971$	−3.01525e11	+	5.22257e11i	−0.339193	+	0.587499i	−0.984281	−	0.176609i	$-0.943487\pi$
$971$	−3.01525e11	+	5.22257e11i	−0.339193	+	0.587499i	0.645088	+	0.764108i	$0.276821\pi$
$972$	−1.26163e12	+	7.28404e11i	−1.41341	+	0.816032i
$973$	3.15638e10	+	8.45749e9i	0.0352158	+	0.00943605i
$974$		−	2.97386e12i		−	3.30434i
$975$	2.08387e11	+	3.54956e11i	0.230596	+	0.392786i
$976$	1.73561e12			1.91272
$977$	−1.00926e11	+	3.76661e11i	−0.110771	+	0.413402i	−0.998936	−	0.0461228i	$-0.985313\pi$
$977$	−1.00926e11	+	3.76661e11i	−0.110771	+	0.413402i	0.888165	+	0.459524i	$0.151980\pi$
$978$	4.77062e11	+	8.26295e11i	0.521458	+	0.903191i
$979$	−5.04540e11	−	2.91296e11i	−0.549243	−	0.317106i
$980$	1.91360e12	+	1.91360e12i	2.07466	+	2.07466i
$981$	4.59264e11	−	1.23059e11i	0.495891	−	0.132874i
$982$	3.64418e11	+	1.36003e12i	0.391881	+	1.46252i
$983$	−5.17500e11	+	5.17500e11i	−0.554238	+	0.554238i	−0.927661	−	0.373423i	$-0.878184\pi$
$983$	−5.17500e11	+	5.17500e11i	−0.554238	+	0.554238i	0.373423	+	0.927661i	$0.378184\pi$
$984$	3.52461e11	−	6.10480e11i	0.375950	−	0.651165i
$985$	1.77731e12	−	1.02613e12i	1.88807	−	1.09008i
$986$	5.69524e11	+	1.52604e11i	0.602566	+	0.161457i
$987$			1.14671e11i			0.120833i
$988$	−3.96876e11	+	1.52541e12i	−0.416512	+	1.60088i
$989$	−7.71779e11			−0.806692
$990$	−3.34099e11	+	1.24687e12i	−0.347804	+	1.29802i
$991$	5.34220e11	+	9.25296e11i	0.553893	+	0.959370i	0.997989	+	0.0633910i	$0.0201915\pi$
$991$	5.34220e11	+	9.25296e11i	0.553893	+	0.959370i	−0.444096	+	0.895979i	$0.646475\pi$
$992$	3.21721e12	+	1.85746e12i	3.32225	+	1.91810i
$993$	4.31520e11	+	4.31520e11i	0.443817	+	0.443817i
$994$	−1.77559e11	+	4.75769e10i	−0.181885	+	0.0487361i
$995$	−4.02023e11	−	1.50037e12i	−0.410165	−	1.53076i
$996$	1.66664e11	−	1.66664e11i	0.169357	−	0.169357i
$997$	2.34114e11	−	4.05497e11i	0.236944	−	0.410399i	−0.722892	−	0.690961i	$-0.757187\pi$
$997$	2.34114e11	−	4.05497e11i	0.236944	−	0.410399i	0.959836	+	0.280562i	$0.0905208\pi$
$998$	8.39053e11	−	4.84428e11i	0.845799	−	0.488323i
$999$	−1.22225e12	−	3.27501e11i	−1.22715	−	0.328814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.f.a.11.8	yes	32
13.6	odd	12	inner	13.9.f.a.6.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.f.a.6.8	✓	32	13.6	odd	12	inner
13.9.f.a.11.8	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(7.75454 - 28.9403i) q^{2} +(32.8317 + 56.8661i) q^{3} +(-555.707 - 320.838i) q^{4} +(-552.313 - 552.313i) q^{5} +(1900.32 - 509.189i) q^{6} +(-156.442 - 583.848i) q^{7} +(-8170.84 + 8170.84i) q^{8} +(1124.66 - 1947.97i) q^{9} +(-20267.1 + 11701.2i) q^{10} +(23687.0 + 6346.91i) q^{11} -42134.5i q^{12} +(-207.500 - 28560.2i) q^{13} -18109.9 q^{14} +(13274.5 - 49541.3i) q^{15} +(90971.2 + 157567. i) q^{16} +(-35251.5 - 20352.5i) q^{17} +(-47653.8 - 47653.8i) q^{18} +(83073.8 - 22259.5i) q^{19} +(129722. + 484127. i) q^{20} +(28064.9 - 28064.9i) q^{21} +(367363. - 636292. i) q^{22} +(-160881. + 92884.7i) q^{23} +(-732906. - 196382. i) q^{24} +219475. i q^{25} +(-828152. - 215466. i) q^{26} +578515. q^{27} +(-100385. + 374641. i) q^{28} +(-241730. - 418689. i) q^{29} +(-1.33080e6 - 768339. i) q^{30} +(1.05366e6 + 1.05366e6i) q^{31} +(2.40811e6 - 645251. i) q^{32} +(416759. + 1.55537e6i) q^{33} +(-862367. + 862367. i) q^{34} +(-236062. + 408872. i) q^{35} +(-1.24997e6 + 721669. i) q^{36} +(-2.11273e6 - 566105. i) q^{37} -2.57679e6i q^{38} +(1.61730e6 - 949480. i) q^{39} +9.02572e6 q^{40} +(-240454. + 897388. i) q^{41} +(-594578. - 1.02984e6i) q^{42} +(3.59791e6 + 2.07725e6i) q^{43} +(-1.11267e7 - 1.11267e7i) q^{44} +(-1.69706e6 + 454725. i) q^{45} +(1.44055e6 + 5.37622e6i) q^{46} +(-2.04296e6 + 2.04296e6i) q^{47} +(-5.97347e6 + 1.03464e7i) q^{48} +(4.67606e6 - 2.69972e6i) q^{49} +(6.35168e6 + 1.70193e6i) q^{50} -2.67282e6i q^{51} +(-9.04789e6 + 1.59377e7i) q^{52} +2.17972e6 q^{53} +(4.48612e6 - 1.67424e7i) q^{54} +(-9.57716e6 - 1.65881e7i) q^{55} +(6.04879e6 + 3.49227e6i) q^{56} +(3.99326e6 + 3.99326e6i) q^{57} +(-1.39915e7 + 3.74901e6i) q^{58} +(-1.42024e6 - 5.30042e6i) q^{59} +(-2.32715e7 + 2.32715e7i) q^{60} +(4.76966e6 - 8.26129e6i) q^{61} +(3.86639e7 - 2.23226e7i) q^{62} +(-1.31327e6 - 351888. i) q^{63} -2.81179e7i q^{64} +(-1.56596e7 + 1.58888e7i) q^{65} +4.82446e7 q^{66} +(-3.40019e6 + 1.26897e7i) q^{67} +(1.30597e7 + 2.26200e7i) q^{68} +(-1.05640e7 - 6.09912e6i) q^{69} +(1.00023e7 + 1.00023e7i) q^{70} +(9.80455e6 - 2.62712e6i) q^{71} +(6.72714e6 + 2.51060e7i) q^{72} +(311675. - 311675. i) q^{73} +(-3.27666e7 + 5.67533e7i) q^{74} +(-1.24807e7 + 7.20573e6i) q^{75} +(-5.33064e7 - 1.42834e7i) q^{76} -1.48225e7i q^{77} +(-1.49369e7 - 5.41679e7i) q^{78} -2.60713e7 q^{79} +(3.67816e7 - 1.37271e8i) q^{80} +(1.16147e7 + 2.01173e7i) q^{81} +(2.41061e7 + 1.39177e7i) q^{82} +(3.95551e6 + 3.95551e6i) q^{83} +(-2.46002e7 + 6.59160e6i) q^{84} +(8.22894e6 + 3.07108e7i) q^{85} +(8.80164e7 - 8.80164e7i) q^{86} +(1.58728e7 - 2.74925e7i) q^{87} +(-2.45402e8 + 1.41683e8i) q^{88} +(-2.29479e7 - 6.14886e6i) q^{89} +5.26396e7i q^{90} +(-1.66424e7 + 4.58916e6i) q^{91} +1.19204e8 q^{92} +(-2.53241e7 + 9.45110e7i) q^{93} +(4.32818e7 + 7.49662e7i) q^{94} +(-5.81770e7 - 3.35885e7i) q^{95} +(1.15755e8 + 1.15755e8i) q^{96} +(1.30006e8 - 3.48351e7i) q^{97} +(-4.18702e7 - 1.56262e8i) q^{98} +(3.90035e7 - 3.90035e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) \) 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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