LMFDB - Embedded newform 37.2.h.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(3,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("37.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.h (of order $18$, degree $6$, 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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 30x^{16} + 333x^{14} + 1826x^{12} + 5490x^{10} + 9432x^{8} + 9385x^{6} + 5316x^{4} + 1584x^{2} + 192 $ x^18 + 30x^16 + 333x^14 + 1826x^12 + 5490x^10 + 9432x^8 + 9385x^6 + 5316x^4 + 1584x^2 + 192
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.2
Root			$0.885952i$ of defining polynomial
Character	$\chi$	$=$	37.3
Dual form			37.2.h.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.256873 + 0.306129i) q^{2} +(-0.0473670 + 0.0397456i) q^{3} +(0.319565 + 1.81234i) q^{4} +(0.853756 - 2.34567i) q^{5} -0.0247100i q^{6} +(-4.17818 - 1.52073i) q^{7} +(-1.32907 - 0.767337i) q^{8} +(-0.520281 + 2.95066i) q^{9} +O(q^{10})$	\(q+(-0.256873 + 0.306129i) q^{2} +(-0.0473670 + 0.0397456i) q^{3} +(0.319565 + 1.81234i) q^{4} +(0.853756 - 2.34567i) q^{5} -0.0247100i q^{6} +(-4.17818 - 1.52073i) q^{7} +(-1.32907 - 0.767337i) q^{8} +(-0.520281 + 2.95066i) q^{9} +(0.498773 + 0.863900i) q^{10} +(1.37021 - 2.37328i) q^{11} +(-0.0871695 - 0.0731439i) q^{12} +(0.327564 - 0.0577584i) q^{13} +(1.53880 - 0.888429i) q^{14} +(0.0527905 + 0.145041i) q^{15} +(-2.88233 + 1.04908i) q^{16} +(4.31543 + 0.760927i) q^{17} +(-0.769637 - 0.917218i) q^{18} +(2.41593 + 2.87919i) q^{19} +(4.52400 + 0.797703i) q^{20} +(0.258350 - 0.0940319i) q^{21} +(0.374560 + 1.02909i) q^{22} +(-3.45049 + 1.99214i) q^{23} +(0.0934523 - 0.0164782i) q^{24} +(-0.943068 - 0.791328i) q^{25} +(-0.0664608 + 0.115114i) q^{26} +(-0.185381 - 0.321090i) q^{27} +(1.42089 - 8.05827i) q^{28} +(-3.90301 - 2.25340i) q^{29} +(-0.0579617 - 0.0210963i) q^{30} +2.06457i q^{31} +(1.46902 - 4.03609i) q^{32} +(0.0294246 + 0.166875i) q^{33} +(-1.34146 + 1.12562i) q^{34} +(-7.13429 + 8.50232i) q^{35} -5.51387 q^{36} +(5.31217 + 2.96325i) q^{37} -1.50199 q^{38} +(-0.0132201 + 0.0157551i) q^{39} +(-2.93462 + 2.46244i) q^{40} +(-1.71389 - 9.71996i) q^{41} +(-0.0375774 + 0.103243i) q^{42} -5.17722i q^{43} +(4.73907 + 1.72488i) q^{44} +(6.47709 + 3.73955i) q^{45} +(0.276485 - 1.56802i) q^{46} +(-2.89453 - 5.01347i) q^{47} +(0.0948308 - 0.164252i) q^{48} +(9.78226 + 8.20829i) q^{49} +(0.484498 - 0.0854300i) q^{50} +(-0.234653 + 0.135477i) q^{51} +(0.209356 + 0.575201i) q^{52} +(-4.30830 + 1.56809i) q^{53} +(0.145915 + 0.0257287i) q^{54} +(-4.39711 - 5.24028i) q^{55} +(4.38617 + 5.22723i) q^{56} +(-0.228871 - 0.0403561i) q^{57} +(1.69241 - 0.615987i) q^{58} +(4.68580 + 12.8741i) q^{59} +(-0.245993 + 0.142024i) q^{60} +(1.55470 - 0.274136i) q^{61} +(-0.632024 - 0.530331i) q^{62} +(6.66099 - 11.5372i) q^{63} +(-2.20909 - 3.82626i) q^{64} +(0.144177 - 0.817670i) q^{65} +(-0.0586438 - 0.0338580i) q^{66} +(-4.41138 - 1.60561i) q^{67} +8.06420i q^{68} +(0.0842603 - 0.231503i) q^{69} +(-0.770202 - 4.36803i) q^{70} +(2.88449 - 2.42037i) q^{71} +(2.95564 - 3.52239i) q^{72} -8.59102 q^{73} +(-2.27169 + 0.865033i) q^{74} +0.0761221 q^{75} +(-4.44604 + 5.29858i) q^{76} +(-9.33413 + 7.83226i) q^{77} +(-0.00142721 - 0.00809411i) q^{78} +(2.58096 - 7.09112i) q^{79} +7.65666i q^{80} +(-8.42491 - 3.06642i) q^{81} +(3.41582 + 1.97212i) q^{82} +(-0.340027 + 1.92839i) q^{83} +(0.252978 + 0.438170i) q^{84} +(5.46921 - 9.47295i) q^{85} +(1.58490 + 1.32989i) q^{86} +(0.274437 - 0.0483906i) q^{87} +(-3.64221 + 2.10283i) q^{88} +(-4.13545 - 11.3621i) q^{89} +(-2.80858 + 1.02224i) q^{90} +(-1.45646 - 0.256813i) q^{91} +(-4.71309 - 5.61684i) q^{92} +(-0.0820575 - 0.0977923i) q^{93} +(2.27830 + 0.401725i) q^{94} +(8.81626 - 3.20886i) q^{95} +(0.0908341 + 0.249565i) q^{96} +(-0.861683 + 0.497493i) q^{97} +(-5.02560 + 0.886148i) q^{98} +(6.28984 + 5.27780i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.256873	+	0.306129i	−0.181637	+	0.216466i	−0.849178	−	0.528106i	$-0.822902\pi$
$2$	−0.256873	+	0.306129i	−0.181637	+	0.216466i	0.667542	+	0.744573i	$0.267347\pi$
$3$	−0.0473670	+	0.0397456i	−0.0273474	+	0.0229472i	−0.656359	−	0.754449i	$-0.727904\pi$
$3$	−0.0473670	+	0.0397456i	−0.0273474	+	0.0229472i	0.629012	+	0.777396i	$0.283460\pi$
$4$	0.319565	+	1.81234i	0.159782	+	0.906171i
$5$	0.853756	−	2.34567i	0.381811	−	1.04902i	−0.588782	−	0.808292i	$-0.700392\pi$
$5$	0.853756	−	2.34567i	0.381811	−	1.04902i	0.970593	−	0.240726i	$-0.0773854\pi$
$6$		−	0.0247100i		−	0.0100878i
$7$	−4.17818	−	1.52073i	−1.57920	−	0.574783i	−0.604173	−	0.796853i	$-0.706497\pi$
$7$	−4.17818	−	1.52073i	−1.57920	−	0.574783i	−0.975031	+	0.222070i	$0.928719\pi$
$8$	−1.32907	−	0.767337i	−0.469896	−	0.271295i
$9$	−0.520281	+	2.95066i	−0.173427	+	0.983553i
$10$	0.498773	+	0.863900i	0.157726	+	0.273189i
$11$	1.37021	−	2.37328i	0.413135	−	0.715571i	−0.582096	−	0.813120i	$-0.697767\pi$
$11$	1.37021	−	2.37328i	0.413135	−	0.715571i	0.995231	+	0.0975494i	$0.0311004\pi$
$12$	−0.0871695	−	0.0731439i	−0.0251637	−	0.0211148i
$13$	0.327564	−	0.0577584i	0.0908499	−	0.0160193i	−0.128038	−	0.991769i	$-0.540868\pi$
$13$	0.327564	−	0.0577584i	0.0908499	−	0.0160193i	0.218888	+	0.975750i	$0.429757\pi$
$14$	1.53880	−	0.888429i	0.411263	−	0.237443i
$15$	0.0527905	+	0.145041i	0.0136304	+	0.0374493i
$16$	−2.88233	+	1.04908i	−0.720582	+	0.262270i
$17$	4.31543	+	0.760927i	1.04665	+	0.184552i	0.670424	−	0.741978i	$-0.266112\pi$
$17$	4.31543	+	0.760927i	1.04665	+	0.184552i	0.376221	+	0.926530i	$0.377223\pi$
$18$	−0.769637	−	0.917218i	−0.181405	−	0.216190i
$19$	2.41593	+	2.87919i	0.554252	+	0.660532i	0.968320	−	0.249714i	$-0.0803367\pi$
$19$	2.41593	+	2.87919i	0.554252	+	0.660532i	−0.414067	+	0.910246i	$0.635892\pi$
$20$	4.52400	+	0.797703i	1.01160	+	0.178372i
$21$	0.258350	−	0.0940319i	0.0563767	−	0.0205194i
$22$	0.374560	+	1.02909i	0.0798564	+	0.219404i
$23$	−3.45049	+	1.99214i	−0.719476	+	0.415390i	−0.814560	−	0.580080i	$-0.803021\pi$
$23$	−3.45049	+	1.99214i	−0.719476	+	0.415390i	0.0950838	+	0.995469i	$0.469688\pi$
$24$	0.0934523	−	0.0164782i	0.0190759	−	0.00336359i
$25$	−0.943068	−	0.791328i	−0.188614	−	0.158266i
$26$	−0.0664608	+	0.115114i	−0.0130340	+	0.0225756i
$27$	−0.185381	−	0.321090i	−0.0356767	−	0.0617938i
$28$	1.42089	−	8.05827i	0.268523	−	1.52287i
$29$	−3.90301	−	2.25340i	−0.724770	−	0.418446i	0.0917356	−	0.995783i	$-0.470759\pi$
$29$	−3.90301	−	2.25340i	−0.724770	−	0.418446i	−0.816506	+	0.577337i	$0.804092\pi$
$30$	−0.0579617	−	0.0210963i	−0.0105823	−	0.00385164i
$31$			2.06457i			0.370807i	0.982662	+	0.185403i	$0.0593592\pi$
$31$			2.06457i			0.370807i	−0.982662	+	0.185403i	$0.940641\pi$
$32$	1.46902	−	4.03609i	0.259688	−	0.713487i
$33$	0.0294246	+	0.166875i	0.00512217	+	0.0290492i
$34$	−1.34146	+	1.12562i	−0.230059	+	0.193042i
$35$	−7.13429	+	8.50232i	−1.20592	+	1.43715i
$36$	−5.51387			−0.918978
$37$	5.31217	+	2.96325i	0.873315	+	0.487155i
$37$	5.31217	+	2.96325i	0.873315	+	0.487155i
$38$	−1.50199			−0.243655
$39$	−0.0132201	+	0.0157551i	−0.00211691	+	0.00252283i
$40$	−2.93462	+	2.46244i	−0.464005	+	0.389346i
$41$	−1.71389	−	9.71996i	−0.267665	−	1.51800i	−0.761338	−	0.648355i	$-0.775457\pi$
$41$	−1.71389	−	9.71996i	−0.267665	−	1.51800i	0.493673	−	0.869648i	$-0.335654\pi$
$42$	−0.0375774	+	0.103243i	−0.00579831	+	0.0159307i
$43$		−	5.17722i		−	0.789519i	−0.918784	−	0.394760i	$-0.870828\pi$
$43$		−	5.17722i		−	0.789519i	0.918784	−	0.394760i	$-0.129172\pi$
$44$	4.73907	+	1.72488i	0.714442	+	0.260035i
$45$	6.47709	+	3.73955i	0.965548	+	0.557459i
$46$	0.276485	−	1.56802i	0.0407654	−	0.231192i
$47$	−2.89453	−	5.01347i	−0.422210	−	0.731290i	0.573945	−	0.818894i	$-0.305412\pi$
$47$	−2.89453	−	5.01347i	−0.422210	−	0.731290i	−0.996155	+	0.0876040i	$0.972079\pi$
$48$	0.0948308	−	0.164252i	0.0136877	−	0.0237077i
$49$	9.78226	+	8.20829i	1.39747	+	1.17261i
$50$	0.484498	−	0.0854300i	0.0685183	−	0.0120816i
$51$	−0.234653	+	0.135477i	−0.0328579	+	0.0189705i
$52$	0.209356	+	0.575201i	0.0290324	+	0.0797660i
$53$	−4.30830	+	1.56809i	−0.591791	+	0.215394i	−0.620517	−	0.784193i	$-0.713077\pi$
$53$	−4.30830	+	1.56809i	−0.591791	+	0.215394i	0.0287259	+	0.999587i	$0.490855\pi$
$54$	0.145915	+	0.0257287i	0.0198565	+	0.00350123i
$55$	−4.39711	−	5.24028i	−0.592907	−	0.706599i
$56$	4.38617	+	5.22723i	0.586126	+	0.698518i
$57$	−0.228871	−	0.0403561i	−0.0303147	−	0.00534529i
$58$	1.69241	−	0.615987i	0.222224	−	0.0808831i
$59$	4.68580	+	12.8741i	0.610040	+	1.67607i	0.730131	+	0.683307i	$0.239459\pi$
$59$	4.68580	+	12.8741i	0.610040	+	1.67607i	−0.120091	+	0.992763i	$0.538319\pi$
$60$	−0.245993	+	0.142024i	−0.0317576	+	0.0183353i
$61$	1.55470	−	0.274136i	0.199059	−	0.0350995i	−0.0732294	−	0.997315i	$-0.523331\pi$
$61$	1.55470	−	0.274136i	0.199059	−	0.0350995i	0.272289	+	0.962216i	$0.412219\pi$
$62$	−0.632024	−	0.530331i	−0.0802672	−	0.0673521i
$63$	6.66099	−	11.5372i	0.839206	−	1.45355i
$64$	−2.20909	−	3.82626i	−0.276137	−	0.478283i
$65$	0.144177	−	0.817670i	0.0178830	−	0.101419i
$66$	−0.0586438	−	0.0338580i	−0.00721855	−	0.00416763i
$67$	−4.41138	−	1.60561i	−0.538936	−	0.196157i	0.0581879	−	0.998306i	$-0.481468\pi$
$67$	−4.41138	−	1.60561i	−0.538936	−	0.196157i	−0.597124	+	0.802149i	$0.703690\pi$
$68$			8.06420i			0.977928i
$69$	0.0842603	−	0.231503i	0.0101438	−	0.0278697i
$70$	−0.770202	−	4.36803i	−0.0920568	−	0.522080i
$71$	2.88449	−	2.42037i	0.342325	−	0.287245i	−0.455374	−	0.890300i	$-0.650495\pi$
$71$	2.88449	−	2.42037i	0.342325	−	0.287245i	0.797700	+	0.603055i	$0.206050\pi$
$72$	2.95564	−	3.52239i	0.348325	−	0.415118i
$73$	−8.59102			−1.00550			−0.502751	−	0.864431i	$-0.667679\pi$
$73$	−8.59102			−1.00550			−0.502751	+	0.864431i	$0.667679\pi$
$74$	−2.27169	+	0.865033i	−0.264079	+	0.100558i
$75$	0.0761221			0.00878983
$76$	−4.44604	+	5.29858i	−0.509995	+	0.607789i
$77$	−9.33413	+	7.83226i	−1.06372	+	0.892569i
$78$	−0.00142721	−	0.00809411i	−0.000161600	−	0.000916478i
$79$	2.58096	−	7.09112i	0.290380	−	0.797813i	−0.705631	−	0.708580i	$-0.749336\pi$
$79$	2.58096	−	7.09112i	0.290380	−	0.797813i	0.996011	−	0.0892330i	$-0.0284416\pi$
$80$			7.65666i			0.856041i
$81$	−8.42491	−	3.06642i	−0.936101	−	0.340713i
$82$	3.41582	+	1.97212i	0.377214	+	0.217785i
$83$	−0.340027	+	1.92839i	−0.0373228	+	0.211668i	−0.997766	−	0.0668085i	$-0.978718\pi$
$83$	−0.340027	+	1.92839i	−0.0373228	+	0.211668i	0.960443	+	0.278477i	$0.0898295\pi$
$84$	0.252978	+	0.438170i	0.0276021	+	0.0478083i
$85$	5.46921	−	9.47295i	0.593219	−	1.02749i
$86$	1.58490	+	1.32989i	0.170904	+	0.143406i
$87$	0.274437	−	0.0483906i	0.0294227	−	0.00518802i
$88$	−3.64221	+	2.10283i	−0.388261	+	0.224163i
$89$	−4.13545	−	11.3621i	−0.438357	−	1.20438i	−0.940561	−	0.339626i	$-0.889699\pi$
$89$	−4.13545	−	11.3621i	−0.438357	−	1.20438i	0.502204	−	0.864749i	$-0.332523\pi$
$90$	−2.80858	+	1.02224i	−0.296050	+	0.107753i
$91$	−1.45646	−	0.256813i	−0.152678	−	0.0269213i
$92$	−4.71309	−	5.61684i	−0.491374	−	0.585596i
$93$	−0.0820575	−	0.0977923i	−0.00850896	−	0.0101406i
$94$	2.27830	+	0.401725i	0.234988	+	0.0414348i
$95$	8.81626	−	3.20886i	0.904529	−	0.329222i
$96$	0.0908341	+	0.249565i	0.00927072	+	0.0254711i
$97$	−0.861683	+	0.497493i	−0.0874906	+	0.0505127i	−0.543107	−	0.839663i	$-0.682752\pi$
$97$	−0.861683	+	0.497493i	−0.0874906	+	0.0505127i	0.455616	+	0.890176i	$0.349419\pi$
$98$	−5.02560	+	0.886148i	−0.507662	+	0.0895145i
$99$	6.28984	+	5.27780i	0.632153	+	0.530439i
$100$	1.13279	−	1.96204i	0.113279	−	0.196204i
$101$	2.79934	+	4.84860i	0.278545	+	0.482454i	0.971023	−	0.238985i	$-0.0768146\pi$
$101$	2.79934	+	4.84860i	0.278545	+	0.482454i	−0.692478	+	0.721439i	$0.743481\pi$
$102$	0.0188025	−	0.106634i	0.00186173	−	0.0105584i
$103$	13.7205	+	7.92156i	1.35193	+	0.780534i	0.988519	−	0.151096i	$-0.0482804\pi$
$103$	13.7205	+	7.92156i	1.35193	+	0.780534i	0.363406	+	0.931631i	$0.381614\pi$
$104$	−0.479675	−	0.174587i	−0.0470360	−	0.0171197i
$105$		−	0.686286i		−	0.0669747i
$106$	0.626648	−	1.72170i	0.0608654	−	0.167226i
$107$	1.44409	+	8.18985i	0.139606	+	0.791743i	0.971541	+	0.236871i	$0.0761218\pi$
$107$	1.44409	+	8.18985i	0.139606	+	0.791743i	−0.831936	+	0.554872i	$0.812767\pi$
$108$	0.522684	−	0.438584i	0.0502953	−	0.0422028i
$109$	−5.85979	+	6.98343i	−0.561266	+	0.668891i	−0.969814	−	0.243846i	$-0.921591\pi$
$109$	−5.85979	+	6.98343i	−0.561266	+	0.668891i	0.408548	+	0.912737i	$0.366035\pi$
$110$	2.73370			0.260648
$111$	−0.369398	+	0.0707753i	−0.0350617	+	0.00671770i
$112$	13.6383			1.28869
$113$	3.68222	−	4.38830i	0.346394	−	0.412816i	−0.564516	−	0.825422i	$-0.690937\pi$
$113$	3.68222	−	4.38830i	0.346394	−	0.412816i	0.910909	+	0.412606i	$0.135381\pi$
$114$	0.0711449	−	0.0596977i	0.00666333	−	0.00559120i
$115$	1.72704	+	9.79452i	0.161047	+	0.913343i
$116$	2.83667	−	7.79370i	0.263378	−	0.723626i
$117$			0.996580i			0.0921338i
$118$	−5.14481	−	1.87256i	−0.473618	−	0.172383i
$119$	−16.8735	−	9.74191i	−1.54679	−	0.893039i
$120$	0.0411330	−	0.233277i	0.00375491	−	0.0212952i
$121$	1.74503	+	3.02248i	0.158639	+	0.274771i
$122$	−0.315440	+	0.546359i	−0.0285586	+	0.0494650i
$123$	0.467508	+	0.392286i	0.0421538	+	0.0353712i
$124$	−3.74170	+	0.659763i	−0.336015	+	0.0592484i
$125$	8.14758	−	4.70401i	0.728742	−	0.420739i
$126$	1.82084	+	5.00272i	0.162213	+	0.445677i
$127$	−5.88137	+	2.14064i	−0.521887	+	0.189951i	−0.589512	−	0.807759i	$-0.700680\pi$
$127$	−5.88137	+	2.14064i	−0.521887	+	0.189951i	0.0676251	+	0.997711i	$0.478458\pi$
$128$	10.1985	+	1.79827i	0.901431	+	0.158947i
$129$	0.205772	+	0.245230i	0.0181172	+	0.0215913i
$130$	0.213278	+	0.254174i	0.0187057	+	0.0222926i
$131$	6.60854	+	1.16526i	0.577391	+	0.101810i	0.454715	−	0.890637i	$-0.349741\pi$
$131$	6.60854	+	1.16526i	0.577391	+	0.101810i	0.122676	+	0.992447i	$0.460852\pi$
$132$	−0.293032	+	0.106655i	−0.0255052	+	0.00928312i
$133$	−5.71571	−	15.7038i	−0.495615	−	1.36169i
$134$	1.62469	−	0.938016i	0.140352	−	0.0810322i
$135$	−0.911444	+	0.160712i	−0.0784446	+	0.0138319i
$136$	−5.15161	−	4.32271i	−0.441747	−	0.370670i
$137$	−8.96680	+	15.5310i	−0.766086	+	1.32690i	0.173585	+	0.984819i	$0.444465\pi$
$137$	−8.96680	+	15.5310i	−0.766086	+	1.32690i	−0.939671	+	0.342081i	$0.888868\pi$
$138$	0.0492258	+	0.0852616i	0.00419038	+	0.00725795i
$139$	0.564477	−	3.20131i	0.0478783	−	0.271531i	−0.951465	−	0.307756i	$-0.900422\pi$
$139$	0.564477	−	3.20131i	0.0478783	−	0.271531i	0.999344	+	0.0362245i	$0.0115331\pi$
$140$	−17.6890	−	10.2127i	−1.49499	−	0.863134i
$141$	0.336369	+	0.122428i	0.0283274	+	0.0103103i
$142$			1.50475i			0.126276i
$143$	0.311756	−	0.856542i	0.0260703	−	0.0716277i
$144$	−1.59586	−	9.05058i	−0.132988	−	0.754215i
$145$	−8.61796	+	7.23133i	−0.715683	+	0.600529i
$146$	2.20680	−	2.62996i	0.182636	−	0.217657i
$147$	−0.789600			−0.0651251
$148$	−3.67284	+	10.5744i	−0.301906	+	0.869212i
$149$	−14.2944			−1.17104			−0.585522	−	0.810656i	$-0.699111\pi$
$149$	−14.2944			−1.17104			−0.585522	+	0.810656i	$0.699111\pi$
$150$	−0.0195537	+	0.0233032i	−0.00159656	+	0.00190270i
$151$	9.71891	−	8.15513i	0.790913	−	0.663655i	−0.155058	−	0.987905i	$-0.549556\pi$
$151$	9.71891	−	8.15513i	0.790913	−	0.663655i	0.945971	+	0.324250i	$0.105112\pi$
$152$	−1.00162	−	5.68047i	−0.0812422	−	0.460747i
$153$	−4.49047	+	12.3375i	−0.363033	+	0.997425i
$154$		−	4.86935i		−	0.392383i
$155$	4.84280	+	1.76263i	0.388983	+	0.141578i
$156$	−0.0327783	−	0.0189245i	−0.00262436	−	0.00151518i
$157$	0.0232755	−	0.132002i	0.00185758	−	0.0105349i	−0.983865	−	0.178913i	$-0.942742\pi$
$157$	0.0232755	−	0.132002i	0.00185758	−	0.0105349i	0.985722	+	0.168378i	$0.0538530\pi$
$158$	1.50782	+	2.61162i	0.119956	+	0.207770i
$159$	0.141747	−	0.245512i	0.0112412	−	0.0194704i
$160$	−8.21318	−	6.89167i	−0.649309	−	0.544835i
$161$	17.4463	−	3.07625i	1.37496	−	0.242442i
$162$	3.10285	−	1.79143i	0.243783	−	0.140748i
$163$	3.64225	+	10.0070i	0.285283	+	0.783809i	0.996710	+	0.0810488i	$0.0258270\pi$
$163$	3.64225	+	10.0070i	0.285283	+	0.783809i	−0.711427	+	0.702760i	$0.751951\pi$
$164$	17.0682	−	6.21232i	1.33280	−	0.485100i
$165$	0.416556	+	0.0734501i	0.0324289	+	0.00571808i
$166$	−0.502993	−	0.599443i	−0.0390398	−	0.0465258i
$167$	2.62423	+	3.12744i	0.203069	+	0.242009i	0.857962	−	0.513713i	$-0.171731\pi$
$167$	2.62423	+	3.12744i	0.203069	+	0.242009i	−0.654892	+	0.755722i	$0.727286\pi$
$168$	−0.415519	−	0.0732673i	−0.0320580	−	0.00565269i
$169$	−12.1120	+	4.40842i	−0.931696	+	0.339109i
$170$	1.49506	+	4.10763i	0.114666	+	0.315041i
$171$	−9.75247	+	5.63059i	−0.745790	+	0.430582i
$172$	9.38290	−	1.65446i	0.715440	−	0.126151i
$173$	−2.81503	−	2.36209i	−0.214023	−	0.179587i	0.529473	−	0.848327i	$-0.322390\pi$
$173$	−2.81503	−	2.36209i	−0.214023	−	0.179587i	−0.743496	+	0.668740i	$0.766834\pi$
$174$	−0.0556816	+	0.0964434i	−0.00422121	+	0.00731135i
$175$	2.73691	+	4.74047i	0.206891	+	0.358346i
$176$	−1.45964	+	8.27804i	−0.110025	+	0.623981i
$177$	−0.733643	−	0.423569i	−0.0551440	−	0.0318374i
$178$	4.54055	+	1.65262i	0.340328	+	0.123869i
$179$		−	20.7101i		−	1.54795i	−0.633219	−	0.773973i	$-0.718267\pi$
$179$		−	20.7101i		−	1.54795i	0.633219	−	0.773973i	$-0.281733\pi$
$180$	−4.70750	+	12.9337i	−0.350876	+	0.964024i
$181$	1.32621	+	7.52131i	0.0985765	+	0.559055i	0.993593	+	0.113021i	$0.0360528\pi$
$181$	1.32621	+	7.52131i	0.0985765	+	0.559055i	−0.895016	+	0.446034i	$0.852836\pi$
$182$	0.452742	−	0.379896i	0.0335595	−	0.0281598i
$183$	−0.0627459	+	0.0747777i	−0.00463831	+	0.00552773i
$184$	6.11457			0.450772
$185$	11.4861	−	9.93073i	0.844476	−	0.730122i
$186$	0.0510155			0.00374063
$187$	7.71896	−	9.19909i	0.564466	−	0.672704i
$188$	8.16114	−	6.84801i	0.595212	−	0.499442i
$189$	0.286265	+	1.62349i	0.0208227	+	0.118091i
$190$	−1.28234	+	3.52319i	−0.0930304	+	0.255599i
$191$		−	2.35688i		−	0.170538i	−0.996358	−	0.0852689i	$-0.972825\pi$
$191$		−	2.35688i		−	0.170538i	0.996358	−	0.0852689i	$-0.0271749\pi$
$192$	0.256715	+	0.0934368i	0.0185268	+	0.00674322i
$193$	13.1725	+	7.60512i	0.948174	+	0.547428i	0.892513	−	0.451021i	$-0.148940\pi$
$193$	13.1725	+	7.60512i	0.948174	+	0.547428i	0.0556607	+	0.998450i	$0.482273\pi$
$194$	0.0690459	−	0.391579i	0.00495721	−	0.0281137i
$195$	0.0256696	+	0.0444610i	0.00183824	+	0.00318392i
$196$	−11.7502	+	20.3519i	−0.839297	+	1.45371i
$197$	−9.17555	−	7.69920i	−0.653731	−	0.548545i	0.254470	−	0.967081i	$-0.418099\pi$
$197$	−9.17555	−	7.69920i	−0.653731	−	0.548545i	−0.908200	+	0.418536i	$0.862544\pi$
$198$	−3.23138	+	0.569780i	−0.229644	+	0.0404925i
$199$	7.75592	−	4.47788i	0.549803	−	0.317429i	−0.199240	−	0.979951i	$-0.563847\pi$
$199$	7.75592	−	4.47788i	0.549803	−	0.317429i	0.749042	+	0.662522i	$0.230514\pi$
$200$	0.646185	+	1.77538i	0.0456922	+	0.125538i
$201$	0.272770	−	0.0992802i	0.0192397	−	0.00700268i
$202$	−2.20338	−	0.388515i	−0.155029	−	0.0273358i
$203$	12.8806	+	15.3506i	0.904044	+	1.07740i
$204$	−0.320517	−	0.381977i	−0.0224407	−	0.0267438i
$205$	−24.2631	−	4.27824i	−1.69461	−	0.298805i
$206$	−5.94946	+	2.16543i	−0.414519	+	0.150872i
$207$	−4.08290	−	11.2177i	−0.283781	−	0.779682i
$208$	−0.883554	+	0.510120i	−0.0612634	+	0.0353705i
$209$	10.1435	−	1.78857i	0.701639	−	0.123718i
$210$	0.210092	+	0.176289i	0.0144978	+	0.0121651i
$211$	0.554188	−	0.959881i	0.0381519	−	0.0660810i	−0.846319	−	0.532676i	$-0.821186\pi$
$211$	0.554188	−	0.959881i	0.0381519	−	0.0660810i	0.884471	+	0.466595i	$0.154520\pi$
$212$	−4.21871	−	7.30702i	−0.289742	−	0.501848i
$213$	−0.0404303	+	0.229291i	−0.00277024	+	0.0157108i
$214$	−2.87810	−	1.66167i	−0.196743	−	0.113590i
$215$	−12.1441	−	4.42008i	−0.828220	−	0.301447i
$216$			0.569001i			0.0387156i
$217$	3.13965	−	8.62613i	0.213134	−	0.585580i
$218$	−0.632610	−	3.58771i	−0.0428457	−	0.242990i
$219$	0.406931	−	0.341456i	0.0274978	−	0.0230734i
$220$	8.09201	−	9.64369i	0.545564	−	0.650177i
$221$	1.45753			0.0980440
$222$	0.0732220	−	0.131264i	0.00491434	−	0.00880985i
$223$	−6.10088			−0.408545			−0.204272	−	0.978914i	$-0.565483\pi$
$223$	−6.10088			−0.408545			−0.204272	+	0.978914i	$0.565483\pi$
$224$	−12.2756	+	14.6295i	−0.820201	+	0.977477i
$225$	2.82560	−	2.37096i	0.188373	−	0.158064i
$226$	0.397524	+	2.25447i	0.0264429	+	0.149965i
$227$	−0.988854	+	2.71685i	−0.0656326	+	0.180324i	−0.968173	−	0.250280i	$-0.919477\pi$
$227$	−0.988854	+	2.71685i	−0.0656326	+	0.180324i	0.902541	+	0.430604i	$0.141699\pi$
$228$		−	0.427688i		−	0.0283244i
$229$	13.7138	+	4.99142i	0.906234	+	0.329842i	0.752748	−	0.658309i	$-0.228728\pi$
$229$	13.7138	+	4.99142i	0.906234	+	0.329842i	0.153486	+	0.988151i	$0.450950\pi$
$230$	−3.44202	−	1.98725i	−0.226960	−	0.131035i
$231$	0.130831	−	0.741982i	0.00860807	−	0.0488188i
$232$	3.45824	+	5.98985i	0.227045	+	0.393253i
$233$	−5.60552	+	9.70905i	−0.367230	+	0.636061i	−0.989131	−	0.147035i	$-0.953027\pi$
$233$	−5.60552	+	9.70905i	−0.367230	+	0.636061i	0.621901	+	0.783095i	$0.286360\pi$
$234$	−0.305082	−	0.255995i	−0.0199439	−	0.0167349i
$235$	−14.2312	+	2.50934i	−0.928341	+	0.163691i
$236$	−21.8349	+	12.6064i	−1.42133	+	0.820607i
$237$	0.159589	+	0.438467i	0.0103664	+	0.0284815i
$238$	7.31663	−	2.66304i	0.474267	−	0.172619i
$239$	−25.6636	−	4.52519i	−1.66004	−	0.292710i	−0.736566	−	0.676366i	$-0.763554\pi$
$239$	−25.6636	−	4.52519i	−1.66004	−	0.292710i	−0.923476	+	0.383655i	$0.874665\pi$
$240$	−0.304319	−	0.362673i	−0.0196437	−	0.0234105i
$241$	−17.3955	−	20.7312i	−1.12054	−	1.33541i	−0.935762	−	0.352632i	$-0.885287\pi$
$241$	−17.3955	−	20.7312i	−1.12054	−	1.33541i	−0.184781	−	0.982780i	$-0.559158\pi$
$242$	−1.37352	−	0.242189i	−0.0882932	−	0.0155685i
$243$	1.56615	−	0.570032i	0.100469	−	0.0365676i
$244$	0.993657	+	2.73005i	0.0636124	+	0.174774i
$245$	27.6056	−	15.9381i	1.76366	−	1.01825i
$246$	−0.240180	+	0.0423503i	−0.0153133	+	0.00270016i
$247$	0.957669	+	0.803580i	0.0609350	+	0.0511305i
$248$	1.58422	−	2.74395i	0.100598	−	0.174241i
$249$	−0.0605390	−	0.104857i	−0.00383650	−	0.00664501i
$250$	−0.652859	+	3.70255i	−0.0412904	+	0.234170i
$251$	17.0602	+	9.84973i	1.07683	+	0.621710i	0.930040	−	0.367458i	$-0.119772\pi$
$251$	17.0602	+	9.84973i	1.07683	+	0.621710i	0.146793	+	0.989167i	$0.453105\pi$
$252$	23.0379	+	8.38512i	1.45125	+	0.528213i
$253$			10.9186i			0.686448i
$254$	0.855452	−	2.35033i	0.0536758	−	0.147473i
$255$	0.117448	+	0.666083i	0.00735490	+	0.0417117i
$256$	3.59883	−	3.01977i	0.224927	−	0.188736i
$257$	11.2418	−	13.3975i	0.701247	−	0.835714i	−0.291420	−	0.956595i	$-0.594128\pi$
$257$	11.2418	−	13.3975i	0.701247	−	0.835714i	0.992667	+	0.120882i	$0.0385721\pi$
$258$	−0.127929			−0.00796453
$259$	−17.6889	−	20.4594i	−1.09913	−	1.27128i
$260$	1.52797			0.0947608
$261$	8.67968	−	10.3440i	0.537259	−	0.640280i
$262$	−2.05428	+	1.72374i	−0.126914	+	0.106493i
$263$	2.49709	+	14.1617i	0.153977	+	0.873248i	0.959715	+	0.280976i	$0.0906580\pi$
$263$	2.49709	+	14.1617i	0.153977	+	0.873248i	−0.805738	+	0.592272i	$0.798231\pi$
$264$	0.0889423	−	0.244367i	0.00547402	−	0.0150397i
$265$			11.4446i			0.703039i
$266$	6.27560	+	2.28413i	0.384782	+	0.140049i
$267$	0.647476	+	0.373820i	0.0396249	+	0.0228774i
$268$	1.50020	−	8.50803i	0.0916390	−	0.519711i
$269$	0.0849430	+	0.147126i	0.00517907	+	0.00897041i	0.868603	−	0.495508i	$-0.165018\pi$
$269$	0.0849430	+	0.147126i	0.00517907	+	0.00897041i	−0.863424	+	0.504478i	$0.831685\pi$
$270$	0.184927	−	0.320302i	0.0112543	−	0.0194930i
$271$	5.06300	+	4.24836i	0.307556	+	0.258070i	0.783481	−	0.621416i	$-0.213442\pi$
$271$	5.06300	+	4.24836i	0.307556	+	0.258070i	−0.475925	+	0.879486i	$0.657887\pi$
$272$	−13.2368	+	2.33400i	−0.802597	+	0.141519i
$273$	0.0791952	−	0.0457234i	0.00479311	−	0.00276730i
$274$	−2.45115	−	6.73449i	−0.148080	−	0.406845i
$275$	−3.17025	+	1.15388i	−0.191173	+	0.0695813i
$276$	0.446490	+	0.0787282i	0.0268755	+	0.00473888i
$277$	15.0810	+	17.9728i	0.906127	+	1.07988i	0.996468	+	0.0839692i	$0.0267597\pi$
$277$	15.0810	+	17.9728i	0.906127	+	1.07988i	−0.0903414	+	0.995911i	$0.528796\pi$
$278$	0.835015	+	0.995132i	0.0500809	+	0.0596841i
$279$	−6.09183	−	1.07415i	−0.364708	−	0.0643079i
$280$	16.0061	−	5.82575i	0.956548	−	0.348155i
$281$	0.934879	+	2.56856i	0.0557702	+	0.153227i	0.964449	−	0.264268i	$-0.0851303\pi$
$281$	0.934879	+	2.56856i	0.0557702	+	0.153227i	−0.908679	+	0.417495i	$0.862908\pi$
$282$	−0.123883	+	0.0715239i	−0.00737712	+	0.00425918i
$283$	−22.1983	+	3.91415i	−1.31955	+	0.232672i	−0.788692	−	0.614788i	$-0.789241\pi$
$283$	−22.1983	+	3.91415i	−1.31955	+	0.232672i	−0.530858	+	0.847461i	$0.678130\pi$
$284$	5.30832	+	4.45421i	0.314991	+	0.264309i
$285$	−0.290062	+	0.502402i	−0.0171818	+	0.0297597i
$286$	0.182131	+	0.315460i	0.0107696	+	0.0186536i
$287$	−7.62052	+	43.2181i	−0.449825	+	2.55109i
$288$	11.1448	+	6.43447i	0.656715	+	0.379155i
$289$	2.06916	+	0.753111i	0.121715	+	0.0443007i
$290$		−	4.49575i		−	0.263999i
$291$	0.0210422	−	0.0578129i	0.00123351	−	0.00338905i
$292$	−2.74539	−	15.5699i	−0.160662	−	0.911158i
$293$	17.8330	−	14.9636i	1.04181	−	0.874186i	0.0496047	−	0.998769i	$-0.484204\pi$
$293$	17.8330	−	14.9636i	1.04181	−	0.874186i	0.992209	+	0.124583i	$0.0397594\pi$
$294$	0.202827	−	0.241720i	0.0118291	−	0.0140974i
$295$	34.1991			1.99115
$296$	−4.78642	−	8.01459i	−0.278205	−	0.465838i
$297$	−1.01605			−0.0589572
$298$	3.67185	−	4.37594i	0.212705	−	0.253492i
$299$	−1.01519	+	0.851847i	−0.0587101	+	0.0492636i
$300$	0.0243260	+	0.137959i	0.00140446	+	0.00796509i
$301$	−7.87318	+	21.6314i	−0.453802	+	1.24681i
$302$			5.07008i			0.291750i
$303$	−0.325307	−	0.118402i	−0.0186884	−	0.00680203i
$304$	−9.98401	−	5.76427i	−0.572622	−	0.330604i
$305$	0.684303	−	3.88087i	0.0391831	−	0.222218i
$306$	−2.62338	−	4.54383i	−0.149969	−	0.259753i
$307$	9.00760	−	15.6016i	0.514091	−	0.890432i	−0.485775	−	0.874084i	$-0.661463\pi$
$307$	9.00760	−	15.6016i	0.514091	−	0.890432i	0.999866	−	0.0163480i	$-0.00520395\pi$
$308$	−17.1776	−	14.4137i	−0.978785	−	0.821298i
$309$	−0.964748	+	0.170111i	−0.0548826	+	0.00967729i
$310$	−1.78358	+	1.02975i	−0.101300	+	0.0584859i
$311$	−3.82316	−	10.5040i	−0.216791	−	0.595629i	0.782855	−	0.622204i	$-0.213762\pi$
$311$	−3.82316	−	10.5040i	−0.216791	−	0.595629i	−0.999647	+	0.0265742i	$0.991540\pi$
$312$	0.0296598	−	0.0107953i	0.00167916	−	0.000611164i
$313$	−16.4255	−	2.89625i	−0.928422	−	0.163706i	−0.311065	−	0.950389i	$-0.600686\pi$
$313$	−16.4255	−	2.89625i	−0.928422	−	0.163706i	−0.617357	+	0.786683i	$0.711797\pi$
$314$	0.0344308	+	0.0410330i	0.00194304	+	0.00231563i
$315$	−21.3756	−	25.4744i	−1.20438	−	1.43532i
$316$	13.6763	+	2.41150i	0.769353	+	0.135658i
$317$	−13.2496	+	4.82245i	−0.744171	+	0.270856i	−0.686151	−	0.727459i	$-0.740701\pi$
$317$	−13.2496	+	4.82245i	−0.744171	+	0.270856i	−0.0580201	+	0.998315i	$0.518479\pi$
$318$	0.0387476	+	0.106458i	0.00217286	+	0.00596988i
$319$	−10.6959	+	6.17529i	−0.598856	+	0.345750i
$320$	−10.8612	+	1.91512i	−0.607159	+	0.107059i
$321$	−0.393913	−	0.330532i	−0.0219861	−	0.0184485i
$322$	−3.53975	+	6.13102i	−0.197262	+	0.341668i
$323$	8.23492	+	14.2633i	0.458203	+	0.793631i
$324$	2.86509	−	16.2487i	0.159172	−	0.902708i
$325$	−0.354621	−	0.204740i	−0.0196708	−	0.0113570i
$326$	−3.99903	−	1.45553i	−0.221486	−	0.0806143i
$327$		−	0.563685i		−	0.0311719i
$328$	−5.18061	+	14.2336i	−0.286051	+	0.785920i
$329$	4.46971	+	25.3490i	0.246423	+	1.39754i
$330$	−0.129487	+	0.108653i	−0.00712804	+	0.00598114i
$331$	11.6522	−	13.8865i	0.640463	−	0.763274i	−0.343981	−	0.938977i	$-0.611775\pi$
$331$	11.6522	−	13.8865i	0.640463	−	0.763274i	0.984443	+	0.175703i	$0.0562199\pi$
$332$	−3.60356			−0.197771
$333$	−11.5074	+	14.1327i	−0.630599	+	0.774466i
$334$	−1.63150			−0.0892715
$335$	−7.53249	+	8.97687i	−0.411544	+	0.490459i
$336$	−0.646004	+	0.542061i	−0.0352424	+	0.0295719i
$337$	−3.34661	−	18.9796i	−0.182301	−	1.03388i	−0.929374	−	0.369140i	$-0.879652\pi$
$337$	−3.34661	−	18.9796i	−0.182301	−	1.03388i	0.747072	−	0.664743i	$-0.231459\pi$
$338$	1.76171	−	4.84026i	0.0958244	−	0.263275i
$339$			0.354213i			0.0192382i
$340$	18.9160	+	6.88486i	1.02586	+	0.373384i
$341$	4.89979	+	2.82890i	0.265339	+	0.153193i
$342$	0.781458	−	4.43187i	0.0422564	−	0.239648i
$343$	−12.8273	−	22.2175i	−0.692608	−	1.19963i
$344$	−3.97268	+	6.88088i	−0.214192	+	0.370992i
$345$	−0.471094	−	0.395295i	−0.0253628	−	0.0212819i
$346$	1.44621	−	0.255006i	0.0777489	−	0.0137092i
$347$	−18.0438	+	10.4176i	−0.968641	+	0.559245i	−0.898822	−	0.438314i	$-0.855576\pi$
$347$	−18.0438	+	10.4176i	−0.968641	+	0.559245i	−0.0698194	+	0.997560i	$0.522242\pi$
$348$	0.175401	+	0.481909i	0.00940246	+	0.0258331i
$349$	25.2607	−	9.19415i	1.35218	−	0.492151i	0.438549	−	0.898707i	$-0.355493\pi$
$349$	25.2607	−	9.19415i	1.35218	−	0.492151i	0.913626	+	0.406556i	$0.133270\pi$
$350$	−2.15424	−	0.379850i	−0.115149	−	0.0203038i
$351$	−0.0792699	−	0.0944702i	−0.00423112	−	0.00504245i
$352$	−7.56591	−	9.01670i	−0.403264	−	0.480592i
$353$	−9.86105	−	1.73877i	−0.524851	−	0.0925454i	−0.0950560	−	0.995472i	$-0.530303\pi$
$353$	−9.86105	−	1.73877i	−0.524851	−	0.0925454i	−0.429795	+	0.902927i	$0.641414\pi$
$354$	0.318120	−	0.115786i	0.0169079	−	0.00615397i
$355$	−3.21476	−	8.83247i	−0.170622	−	0.468779i
$356$	19.2704	−	11.1258i	1.02133	−	0.589664i
$357$	1.18644	−	0.209202i	0.0627933	−	0.0110722i
$358$	6.33997	+	5.31987i	0.335078	+	0.281164i
$359$	−9.39048	+	16.2648i	−0.495611	+	0.858423i	−0.999987	−	0.00506107i	$-0.998389\pi$
$359$	−9.39048	+	16.2648i	−0.495611	+	0.858423i	0.504377	+	0.863484i	$0.331722\pi$
$360$	−5.73899	−	9.94023i	−0.302472	−	0.523896i
$361$	0.846281	−	4.79950i	0.0445411	−	0.252605i
$362$	−2.64316	−	1.52603i	−0.138922	−	0.0802064i
$363$	−0.202787	−	0.0738084i	−0.0106436	−	0.00387394i
$364$		−	2.72167i		−	0.142654i
$365$	−7.33463	+	20.1517i	−0.383912	+	1.05479i
$366$	−0.00677391	−	0.0384168i	−0.000354078	−	0.00200808i
$367$	−3.56491	+	2.99132i	−0.186087	+	0.156146i	−0.731072	−	0.682300i	$-0.760980\pi$
$367$	−3.56491	+	2.99132i	−0.186087	+	0.156146i	0.544985	+	0.838446i	$0.316535\pi$
$368$	7.85551	−	9.36184i	0.409497	−	0.488020i
$369$	29.5720			1.53946
$370$	0.0896152	+	6.06718i	0.00465887	+	0.315417i
$371$	20.3855			1.05836
$372$	0.151010	−	0.179967i	0.00782953	−	0.00933087i
$373$	8.97635	−	7.53206i	0.464778	−	0.389995i	−0.380107	−	0.924942i	$-0.624113\pi$
$373$	8.97635	−	7.53206i	0.464778	−	0.389995i	0.844885	+	0.534947i	$0.179669\pi$
$374$	0.833321	+	4.72600i	0.0430900	+	0.244376i
$375$	−0.198963	+	0.546645i	−0.0102744	+	0.0282286i
$376$			8.88432i			0.458174i
$377$	−1.40864	−	0.512702i	−0.0725485	−	0.0264055i
$378$	−0.570531	−	0.329397i	−0.0293450	−	0.0169423i
$379$	−0.507599	+	2.87874i	−0.0260736	+	0.147871i	−0.995065	−	0.0992227i	$-0.968364\pi$
$379$	−0.507599	+	2.87874i	−0.0260736	+	0.147871i	0.968992	+	0.247094i	$0.0794755\pi$
$380$	8.63292	+	14.9526i	0.442859	+	0.767055i
$381$	0.193502	−	0.335155i	0.00991339	−	0.0171705i
$382$	0.721511	+	0.605419i	0.0369157	+	0.0309759i
$383$	13.4269	−	2.36752i	0.686081	−	0.120975i	0.180268	−	0.983618i	$-0.442304\pi$
$383$	13.4269	−	2.36752i	0.686081	−	0.120975i	0.505813	+	0.862643i	$0.331192\pi$
$384$	−0.554547	+	0.320168i	−0.0282991	+	0.0163385i
$385$	10.4029	+	28.5817i	0.530180	+	1.45666i
$386$	−5.71180	+	2.07893i	−0.290723	+	0.105815i
$387$	15.2762	+	2.69361i	0.776534	+	0.136924i
$388$	−1.17699	−	1.40268i	−0.0597527	−	0.0712105i
$389$	20.6405	+	24.5984i	1.04652	+	1.24719i	0.968178	+	0.250262i	$0.0805169\pi$
$389$	20.6405	+	24.5984i	1.04652	+	1.24719i	0.0783380	+	0.996927i	$0.475039\pi$
$390$	−0.0202046	−	0.00356262i	−0.00102310	−	0.000180400i
$391$	−16.4062	+	5.97137i	−0.829697	+	0.301985i
$392$	−6.70275	−	18.4157i	−0.338540	−	0.930131i
$393$	−0.359341	+	0.207465i	−0.0181263	+	0.0104652i
$394$	4.71390	−	0.831188i	0.237483	−	0.0418747i
$395$	−14.4299	−	12.1082i	−0.726049	−	0.609228i
$396$	−7.55518	+	13.0860i	−0.379662	+	0.657594i
$397$	−5.76052	−	9.97751i	−0.289112	−	0.500757i	0.684486	−	0.729026i	$-0.260027\pi$
$397$	−5.76052	−	9.97751i	−0.289112	−	0.500757i	−0.973598	+	0.228269i	$0.926693\pi$
$398$	−0.621476	+	3.52456i	−0.0311518	+	0.176670i
$399$	0.894892	+	0.516666i	0.0448007	+	0.0258657i
$400$	3.54840	+	1.29151i	0.177420	+	0.0645756i
$401$		−	28.4569i		−	1.42107i	−0.703663	−	0.710534i	$-0.748454\pi$
$401$		−	28.4569i		−	1.42107i	0.703663	−	0.710534i	$-0.251546\pi$
$402$	−0.0396747	+	0.109005i	−0.00197879	+	0.00543669i
$403$	0.119246	+	0.676277i	0.00594006	+	0.0336878i
$404$	−7.89276	+	6.62281i	−0.392679	+	0.329497i
$405$	−14.3856	+	17.1441i	−0.714828	+	0.851899i
$406$	−8.00795			−0.397428
$407$	14.3114	−	8.54698i	0.709391	−	0.423658i
$408$	0.415825			0.0205864
$409$	4.49941	−	5.36219i	0.222482	−	0.265143i	−0.643245	−	0.765660i	$-0.722412\pi$
$409$	4.49941	−	5.36219i	0.222482	−	0.265143i	0.865727	+	0.500517i	$0.166857\pi$
$410$	7.54224	−	6.32869i	0.372484	−	0.312552i
$411$	−0.192557	−	1.09205i	−0.00949815	−	0.0538667i
$412$	−9.97198	+	27.3978i	−0.491284	+	1.34979i
$413$		−	60.9163i		−	2.99750i
$414$	4.48285	+	1.63162i	0.220320	+	0.0801899i
$415$	4.23307	+	2.44396i	0.207793	+	0.119970i
$416$	0.248079	−	1.40693i	0.0121631	−	0.0689802i
$417$	0.100500	+	0.174072i	0.00492153	+	0.00852433i
$418$	−2.05805	+	3.56465i	−0.100663	+	0.174353i
$419$	−5.14057	−	4.31345i	−0.251133	−	0.210726i	0.508527	−	0.861046i	$-0.330190\pi$
$419$	−5.14057	−	4.31345i	−0.251133	−	0.210726i	−0.759660	+	0.650320i	$0.774635\pi$
$420$	1.24379	−	0.219313i	0.0606905	−	0.0107014i
$421$	10.0127	−	5.78081i	0.487987	−	0.281740i	−0.235752	−	0.971813i	$-0.575755\pi$
$421$	10.0127	−	5.78081i	0.487987	−	0.281740i	0.723739	+	0.690074i	$0.242422\pi$
$422$	0.151492	+	0.416221i	0.00737452	+	0.0202613i
$423$	16.2990	−	5.93235i	0.792485	−	0.288441i
$424$	6.92928	+	1.22182i	0.336516	+	0.0593368i
$425$	−3.46760	−	4.13253i	−0.168203	−	0.200457i
$426$	−0.0598074	−	0.0712757i	−0.00289768	−	0.00345332i
$427$	−6.91272	−	1.21890i	−0.334530	−	0.0589867i
$428$	−14.3813	+	5.23438i	−0.695148	+	0.253013i
$429$	0.0192769	+	0.0529628i	0.000930696	+	0.00255707i
$430$	4.47261	−	2.58226i	0.215688	−	0.124528i
$431$	7.98373	−	1.40775i	0.384563	−	0.0678088i	0.0219752	−	0.999759i	$-0.493005\pi$
$431$	7.98373	−	1.40775i	0.384563	−	0.0678088i	0.362587	+	0.931950i	$0.381893\pi$
$432$	0.871180	+	0.731007i	0.0419147	+	0.0351706i
$433$	4.38098	−	7.58808i	0.210537	−	0.364660i	−0.741346	−	0.671123i	$-0.765812\pi$
$433$	4.38098	−	7.58808i	0.210537	−	0.364660i	0.951883	+	0.306463i	$0.0991456\pi$
$434$	1.83422	+	3.17696i	0.0880453	+	0.152499i
$435$	0.120793	−	0.685053i	0.00579160	−	0.0328458i
$436$	−14.5289	−	8.38829i	−0.695810	−	0.401726i
$437$	−14.0719	−	5.12175i	−0.673149	−	0.245006i
$438$			0.212284i			0.0101433i
$439$	−5.13798	+	14.1165i	−0.245222	+	0.673743i	0.754623	+	0.656159i	$0.227820\pi$
$439$	−5.13798	+	14.1165i	−0.245222	+	0.673743i	−0.999845	+	0.0175845i	$0.994402\pi$
$440$	1.82300	+	10.3388i	0.0869082	+	0.492881i
$441$	−29.3094	+	24.5935i	−1.39568	+	1.17112i
$442$	−0.374400	+	0.446193i	−0.0178084	+	0.0212232i
$443$	−16.4147			−0.779888			−0.389944	−	0.920839i	$-0.627506\pi$
$443$	−16.4147			−0.779888			−0.389944	+	0.920839i	$0.627506\pi$
$444$	−0.246316	−	0.646858i	−0.0116896	−	0.0306985i
$445$	−30.1824			−1.43078
$446$	1.56715	−	1.86766i	0.0742067	−	0.0884362i
$447$	0.677084	−	0.568141i	0.0320250	−	0.0268721i
$448$	3.41127	+	19.3463i	0.161167	+	0.914025i
$449$	1.65327	−	4.54232i	0.0780226	−	0.214365i	−0.894549	−	0.446971i	$-0.852503\pi$
$449$	1.65327	−	4.54232i	0.0780226	−	0.214365i	0.972571	+	0.232605i	$0.0747251\pi$
$450$			1.47403i			0.0694866i
$451$	−25.4166	−	9.25088i	−1.19682	−	0.435607i
$452$	9.12980	+	5.27109i	0.429430	+	0.247931i
$453$	−0.136225	+	0.772568i	−0.00640039	+	0.0362984i
$454$	−0.577699	−	1.00060i	−0.0271128	−	0.0469607i
$455$	−1.84586	+	3.19712i	−0.0865351	+	0.149883i
$456$	0.273218	+	0.229257i	0.0127946	+	0.0107359i
$457$	20.6088	−	3.63389i	0.964039	−	0.169986i	0.330593	−	0.943773i	$-0.392751\pi$
$457$	20.6088	−	3.63389i	0.964039	−	0.169986i	0.633445	+	0.773787i	$0.281640\pi$
$458$	−5.05073	+	2.91604i	−0.236005	+	0.136258i
$459$	−0.555675	−	1.52670i	−0.0259367	−	0.0712604i
$460$	−17.1991	+	6.25997i	−0.801913	+	0.291872i
$461$	−9.23292	−	1.62801i	−0.430020	−	0.0758241i	−0.0455509	−	0.998962i	$-0.514504\pi$
$461$	−9.23292	−	1.62801i	−0.430020	−	0.0758241i	−0.384469	+	0.923138i	$0.625615\pi$
$462$	0.193535	+	0.230647i	0.00900408	+	0.0107306i
$463$	1.61881	+	1.92923i	0.0752327	+	0.0896588i	0.802348	−	0.596857i	$-0.203584\pi$
$463$	1.61881	+	1.92923i	0.0752327	+	0.0896588i	−0.727115	+	0.686515i	$0.759139\pi$
$464$	13.6138	+	2.40047i	0.632003	+	0.111439i
$465$	−0.299446	+	0.108989i	−0.0138865	+	0.00505426i
$466$	−1.53232	−	4.21001i	−0.0709832	−	0.195025i
$467$	14.5441	−	8.39703i	0.673020	−	0.388568i	−0.124200	−	0.992257i	$-0.539637\pi$
$467$	14.5441	−	8.39703i	0.673020	−	0.388568i	0.797220	+	0.603689i	$0.206303\pi$
$468$	−1.80614	+	0.318472i	−0.0834890	+	0.0147214i
$469$	15.9898	+	13.4171i	0.738342	+	0.619543i
$470$	2.88743	−	5.00117i	0.133187	−	0.230687i
$471$	0.00414400	+	0.00717762i	0.000190946	+	0.000330727i
$472$	3.65106	−	20.7062i	0.168054	−	0.953080i
$473$	−12.2870	−	7.09390i	−0.564957	−	0.326178i
$474$	−0.175222	−	0.0637755i	−0.00804820	−	0.00292930i
$475$		−	4.62707i		−	0.212304i
$476$	12.2635	−	33.6937i	0.562097	−	1.54435i
$477$	−2.38538	−	13.5282i	−0.109219	−	0.619413i
$478$	7.97759	−	6.69399i	0.364887	−	0.306176i
$479$	5.99256	−	7.14165i	0.273807	−	0.326310i	−0.611565	−	0.791194i	$-0.709460\pi$
$479$	5.99256	−	7.14165i	0.273807	−	0.326310i	0.885372	+	0.464884i	$0.153904\pi$
$480$	0.662947			0.0302593
$481$	1.91123	+	0.663832i	0.0871445	+	0.0302681i
$482$	10.8149			0.492603
$483$	−0.704110	+	0.839126i	−0.0320381	+	0.0381815i
$484$	−4.92011	+	4.12847i	−0.223642	+	0.187658i
$485$	0.431290	+	2.44596i	0.0195839	+	0.111066i
$486$	−0.227798	+	0.625870i	−0.0103331	+	0.0283901i
$487$			34.3471i			1.55641i	0.628007	+	0.778207i	$0.283871\pi$
$487$			34.3471i			1.55641i	−0.628007	+	0.778207i	$0.716129\pi$
$488$	−2.27666	−	0.828637i	−0.103060	−	0.0375106i
$489$	−0.570257	−	0.329238i	−0.0257879	−	0.0148887i
$490$	−2.21202	+	12.5450i	−0.0999287	+	0.566724i
$491$	14.0975	+	24.4175i	0.636210	+	1.10195i	0.986257	+	0.165216i	$0.0528321\pi$
$491$	14.0975	+	24.4175i	0.636210	+	1.10195i	−0.350047	+	0.936732i	$0.613835\pi$
$492$	−0.561557	+	0.972645i	−0.0253169	+	0.0438502i
$493$	−15.1285	−	12.6943i	−0.681353	−	0.571723i
$494$	−0.491999	+	0.0867527i	−0.0221361	+	0.00390319i
$495$	17.7500	−	10.2480i	0.797803	−	0.460612i
$496$	−2.16590	−	5.95076i	−0.0972517	−	0.267197i
$497$	−15.7326	+	5.72621i	−0.705705	+	0.256856i
$498$	0.0476505	+	0.00840207i	0.00213527	+	0.000376506i
$499$	1.93772	+	2.30929i	0.0867444	+	0.103378i	0.807671	−	0.589634i	$-0.200728\pi$
$499$	1.93772	+	2.30929i	0.0867444	+	0.103378i	−0.720926	+	0.693012i	$0.756283\pi$
$500$	11.1290	+	13.2630i	0.497702	+	0.593138i
$501$	−0.248604	−	0.0438356i	−0.0111068	−	0.00195843i
$502$	−7.39761	+	2.69251i	−0.330172	+	0.120173i
$503$	5.50358	+	15.1210i	0.245392	+	0.674210i	0.999841	+	0.0178504i	$0.00568227\pi$
$503$	5.50358	+	15.1210i	0.245392	+	0.674210i	−0.754448	+	0.656359i	$0.772096\pi$
$504$	−17.7058	+	10.2225i	−0.788680	+	0.455344i
$505$	13.7632	−	2.42682i	0.612454	−	0.107992i
$506$	−3.34251	−	2.80470i	−0.148593	−	0.124684i
$507$	0.398496	−	0.690215i	0.0176978	−	0.0306535i
$508$	−5.75906	−	9.97498i	−0.255517	−	0.442568i
$509$	0.241578	−	1.37006i	0.0107078	−	0.0607267i	−0.978986	−	0.203929i	$-0.934629\pi$
$509$	0.241578	−	1.37006i	0.0107078	−	0.0607267i	0.989693	+	0.143202i	$0.0457399\pi$
$510$	−0.234077	−	0.135144i	−0.0103651	−	0.00598429i
$511$	35.8948	+	13.0647i	1.58789	+	0.577946i
$512$			22.5891i			0.998307i
$513$	0.476612	−	1.30948i	0.0210429	−	0.0578150i
$514$	1.21364	+	6.88292i	0.0535316	+	0.303593i
$515$	30.2954	−	25.4209i	1.33497	−	1.12018i
$516$	−0.378683	+	0.451296i	−0.0166706	+	0.0198672i
$517$	−15.8645			−0.697720
$518$	10.8070	−	0.159625i	0.474833	−	0.00701353i
$519$	0.227223			0.00997397
$520$	−0.819050	+	0.976106i	−0.0359177	+	0.0428051i
$521$	10.7791	−	9.04477i	0.472243	−	0.396259i	−0.375369	−	0.926875i	$-0.622484\pi$
$521$	10.7791	−	9.04477i	0.472243	−	0.396259i	0.847612	+	0.530617i	$0.178040\pi$
$522$	0.937039	+	5.31421i	0.0410131	+	0.232597i
$523$	12.1470	−	33.3735i	0.531150	−	1.45932i	−0.326554	−	0.945178i	$-0.605888\pi$
$523$	12.1470	−	33.3735i	0.531150	−	1.45932i	0.857704	−	0.514144i	$-0.171890\pi$
$524$			12.3493i			0.539482i
$525$	−0.318052	−	0.115762i	−0.0138809	−	0.00505225i
$526$	−4.97675	−	2.87333i	−0.216997	−	0.125283i
$527$	−1.57098	+	8.90949i	−0.0684331	+	0.388103i
$528$	−0.259877	−	0.450120i	−0.0113097	−	0.0195890i
$529$	−3.56277	+	6.17089i	−0.154903	+	0.268300i
$530$	−3.50354	−	2.93982i	−0.152184	−	0.127698i
$531$	−40.4251	+	7.12804i	−1.75430	+	0.309331i
$532$	26.6341	−	15.3772i	1.15473	−	0.666686i
$533$	−1.12282	−	3.08492i	−0.0486346	−	0.133623i
$534$	−0.280757	+	0.102187i	−0.0121495	+	0.00442207i
$535$	20.4436	+	3.60476i	0.883855	+	0.155848i
$536$	4.63098	+	5.51899i	0.200028	+	0.238384i
$537$	0.823136	+	0.980976i	0.0355210	+	0.0423322i
$538$	−0.0668591	−	0.0117891i	−0.00288250	−	0.000508262i
$539$	32.8843	−	11.9689i	1.41643	−	0.515538i
$540$	−0.582531	−	1.60049i	−0.0250681	−	0.0688741i
$541$	−38.6207	+	22.2977i	−1.66044	+	0.958653i	−0.687929	+	0.725778i	$0.741480\pi$
$541$	−38.6207	+	22.2977i	−1.66044	+	0.958653i	−0.972507	+	0.232875i	$0.925187\pi$
$542$	−2.60110	+	0.458644i	−0.111727	+	0.0197004i
$543$	−0.361758	−	0.303551i	−0.0155245	−	0.0130266i
$544$	9.41061	−	16.2997i	0.403477	−	0.698842i
$545$	11.3780	+	19.7073i	0.487381	+	0.844168i
$546$	−0.00634585	+	0.0359891i	−0.000271577	+	0.00154019i
$547$	10.8346	+	6.25534i	0.463252	+	0.267459i	0.713411	−	0.700746i	$-0.247149\pi$
$547$	10.8346	+	6.25534i	0.463252	+	0.267459i	−0.250158	+	0.968205i	$0.580483\pi$
$548$	−31.0129	−	11.2878i	−1.32481	−	0.482190i
$549$			4.73003i			0.201873i
$550$	0.461116	−	1.26691i	0.0196621	−	0.0540211i
$551$	−2.94141	−	16.6816i	−0.125308	−	0.710659i
$552$	−0.289629	+	0.243027i	−0.0123274	+	0.0103439i
$553$	−21.5674	+	25.7030i	−0.917139	+	1.09300i
$554$	−9.37589			−0.398343
$555$	−0.149360	+	0.926912i	−0.00633996	+	0.0393452i
$556$	5.98225			0.253704
$557$	2.38646	−	2.84407i	0.101117	−	0.120507i	−0.713112	−	0.701050i	$-0.752715\pi$
$557$	2.38646	−	2.84407i	0.101117	−	0.120507i	0.814230	+	0.580543i	$0.197160\pi$
$558$	1.89366	−	1.58897i	0.0801649	−	0.0672663i
$559$	−0.299028	−	1.69587i	−0.0126475	−	0.0717277i
$560$	11.6437	−	31.9909i	0.492038	−	1.35186i
$561$			0.742528i			0.0313496i
$562$	−1.02646	−	0.373600i	−0.0432985	−	0.0157594i
$563$	−24.8675	−	14.3573i	−1.04804	−	0.605087i	−0.125941	−	0.992038i	$-0.540195\pi$
$563$	−24.8675	−	14.3573i	−1.04804	−	0.605087i	−0.922100	+	0.386951i	$0.873528\pi$
$564$	−0.114390	+	0.648739i	−0.00481670	+	0.0273168i
$565$	−7.14980	−	12.3838i	−0.300794	−	0.520991i
$566$	4.50390	−	7.80099i	0.189313	−	0.327900i
$567$	30.5376	+	25.6241i	1.28246	+	1.07611i
$568$	−5.69092	+	1.00346i	−0.238786	+	0.0421043i
$569$	−28.1460	+	16.2501i	−1.17994	+	0.681239i	−0.956001	−	0.293364i	$-0.905225\pi$
$569$	−28.1460	+	16.2501i	−1.17994	+	0.681239i	−0.223940	+	0.974603i	$0.571892\pi$
$570$	−0.0792909	−	0.217850i	−0.00332113	−	0.00912473i
$571$	−22.3596	+	8.13821i	−0.935718	+	0.340574i	−0.764474	−	0.644655i	$-0.777001\pi$
$571$	−22.3596	+	8.13821i	−0.935718	+	0.340574i	−0.171245	+	0.985229i	$0.554779\pi$
$572$	1.65197	+	0.291288i	0.0690725	+	0.0121793i
$573$	0.0936757	+	0.111638i	0.00391336	+	0.00466376i
$574$	−11.2728	−	13.4344i	−0.470519	−	0.560743i
$575$	4.83048	+	0.851744i	0.201445	+	0.0355202i
$576$	12.4393	−	4.52755i	0.518306	−	0.188648i
$577$	10.5312	+	28.9343i	0.438420	+	1.20455i	0.940519	+	0.339740i	$0.110339\pi$
$577$	10.5312	+	28.9343i	0.438420	+	1.20455i	−0.502099	+	0.864810i	$0.667439\pi$
$578$	−0.762060	+	0.439976i	−0.0316975	+	0.0183006i
$579$	−0.926210	+	0.163316i	−0.0384920	+	0.00678717i
$580$	−15.8596	−	13.3078i	−0.658536	−	0.552577i
$581$	4.35326	−	7.54007i	0.180604	−	0.312815i
$582$	0.0122931	+	0.0212922i	0.000509564	+	0.000882590i
$583$	−2.18177	+	12.3734i	−0.0903597	+	0.512455i
$584$	11.4180	+	6.59221i	0.472482	+	0.272788i
$585$	2.33765	+	0.850836i	0.0966500	+	0.0351777i
$586$			9.30296i			0.384302i
$587$	12.9265	−	35.5153i	0.533534	−	1.46587i	−0.321304	−	0.946976i	$-0.604121\pi$
$587$	12.9265	−	35.5153i	0.533534	−	1.46587i	0.854837	−	0.518896i	$-0.173657\pi$
$588$	−0.252328	−	1.43103i	−0.0104058	−	0.0590145i
$589$	−5.94428	+	4.98784i	−0.244930	+	0.205521i
$590$	−8.78482	+	10.4693i	−0.361665	+	0.431016i
$591$	0.740628			0.0304654
$592$	−18.4201	−	2.96816i	−0.757062	−	0.121991i
$593$	−16.6117			−0.682160			−0.341080	−	0.940034i	$-0.610793\pi$
$593$	−16.6117			−0.682160			−0.341080	+	0.940034i	$0.610793\pi$
$594$	0.260996	−	0.311043i	0.0107088	−	0.0127622i
$595$	−37.2572	+	31.2625i	−1.52740	+	1.28164i
$596$	−4.56800	−	25.9064i	−0.187112	−	1.06117i
$597$	−0.189398	+	0.520368i	−0.00775156	+	0.0212972i
$598$		−	0.529597i		−	0.0216568i
$599$	−32.3280	−	11.7664i	−1.32089	−	0.480763i	−0.417143	−	0.908841i	$-0.636969\pi$
$599$	−32.3280	−	11.7664i	−1.32089	−	0.480763i	−0.903742	+	0.428078i	$0.859191\pi$
$600$	−0.101171	−	0.0584114i	−0.00413031	−	0.00238463i
$601$	−0.137007	+	0.777005i	−0.00558863	+	0.0316947i	−0.987475	−	0.157778i	$-0.949567\pi$
$601$	−0.137007	+	0.777005i	−0.00558863	+	0.0316947i	0.981886	+	0.189473i	$0.0606780\pi$
$602$	−4.59959	−	7.96673i	−0.187465	−	0.324700i
$603$	7.03277	−	12.1811i	0.286396	−	0.496053i
$604$	17.8857	+	15.0079i	0.727759	+	0.610663i
$605$	8.57957	−	1.51281i	0.348809	−	0.0615045i
$606$	0.119809	−	0.0691718i	0.00486691	−	0.00280991i
$607$	−12.6726	−	34.8176i	−0.514364	−	1.41320i	−0.876646	−	0.481135i	$-0.840225\pi$
$607$	−12.6726	−	34.8176i	−0.514364	−	1.41320i	0.362283	−	0.932068i	$-0.381998\pi$
$608$	15.1697	−	5.52133i	0.615214	−	0.223919i
$609$	−1.22024	−	0.215160i	−0.0494464	−	0.00871874i
$610$	1.01227	+	1.20638i	0.0409857	+	0.0488448i
$611$	−1.23771	−	1.47505i	−0.0500725	−	0.0596741i
$612$	−23.7947	−	4.19565i	−0.961844	−	0.169599i
$613$	36.6373	−	13.3349i	1.47977	−	0.538591i	0.529032	−	0.848602i	$-0.322555\pi$
$613$	36.6373	−	13.3349i	1.47977	−	0.538591i	0.950733	+	0.310011i	$0.100333\pi$
$614$	2.46231	+	6.76513i	0.0993706	+	0.273018i
$615$	1.31931	−	0.761705i	0.0531998	−	0.0307149i
$616$	18.4157	−	3.24718i	0.741989	−	0.130833i
$617$	−21.6442	−	18.1616i	−0.871361	−	0.731159i	0.0930232	−	0.995664i	$-0.470347\pi$
$617$	−21.6442	−	18.1616i	−0.871361	−	0.731159i	−0.964384	+	0.264505i	$0.914791\pi$
$618$	0.195742	−	0.339035i	0.00787389	−	0.0136380i
$619$	−0.667259	−	1.15573i	−0.0268194	−	0.0464526i	0.852304	−	0.523046i	$-0.175205\pi$
$619$	−0.667259	−	1.15573i	−0.0268194	−	0.0464526i	−0.879124	+	0.476594i	$0.841871\pi$
$620$	−1.64691	+	9.34009i	−0.0661415	+	0.375107i
$621$	1.27931	+	0.738611i	0.0513370	+	0.0296394i
$622$	4.19766	+	1.52782i	0.168311	+	0.0612602i
$623$			53.7616i			2.15391i
$624$	0.0215762	−	0.0592803i	0.000863741	−	0.00237311i
$625$	−5.14691	−	29.1896i	−0.205876	−	1.16758i
$626$	5.10589	−	4.28435i	0.204072	−	0.171237i
$627$	−0.409378	+	0.487878i	−0.0163490	+	0.0194840i
$628$	0.246670			0.00984322
$629$	20.6695	+	16.8299i	0.824146	+	0.671051i
$630$	13.2893			0.529458
$631$	−12.3380	+	14.7039i	−0.491169	+	0.585352i	−0.953514	−	0.301348i	$-0.902563\pi$
$631$	−12.3380	+	14.7039i	−0.491169	+	0.585352i	0.462346	+	0.886700i	$0.347008\pi$
$632$	−8.87154	+	7.44411i	−0.352891	+	0.296111i
$633$	0.0119009	+	0.0674933i	0.000473018	+	0.00268262i
$634$	1.92717	−	5.29485i	0.0765376	−	0.210285i
$635$			15.6234i			0.619994i
$636$	0.490250	+	0.178436i	0.0194397	+	0.00707546i
$637$	3.67841	+	2.12373i	0.145744	+	0.0841453i
$638$	0.857055	−	4.86060i	0.0339311	−	0.192433i
$639$	5.64094	+	9.77040i	0.223152	+	0.386511i
$640$	12.9252	−	22.3871i	0.510914	−	0.884929i
$641$	23.3832	+	19.6209i	0.923583	+	0.774978i	0.974654	−	0.223717i	$-0.0718191\pi$
$641$	23.3832	+	19.6209i	0.923583	+	0.774978i	−0.0510713	+	0.998695i	$0.516264\pi$
$642$	0.202371	−	0.0356835i	0.00798696	−	0.00140832i
$643$	32.3880	−	18.6992i	1.27726	−	0.737425i	0.300914	−	0.953651i	$-0.402708\pi$
$643$	32.3880	−	18.6992i	1.27726	−	0.737425i	0.976343	+	0.216227i	$0.0693750\pi$
$644$	11.1504	+	30.6355i	0.439388	+	1.20721i
$645$	0.750908	−	0.273308i	0.0295670	−	0.0107615i
$646$	−6.48175	−	1.14291i	−0.255021	−	0.0449671i
$647$	−13.9069	−	16.5736i	−0.546738	−	0.651577i	0.419946	−	0.907549i	$-0.362049\pi$
$647$	−13.9069	−	16.5736i	−0.546738	−	0.651577i	−0.966684	+	0.255972i	$0.917604\pi$
$648$	8.84430	+	10.5402i	0.347437	+	0.414059i
$649$	36.9745	+	6.51960i	1.45138	+	0.255917i
$650$	0.153770	−	0.0559676i	0.00603134	−	0.00219523i
$651$	0.194135	+	0.533381i	0.00760875	+	0.0209049i
$652$	−16.9722	+	9.79889i	−0.664682	+	0.383754i
$653$	−22.4942	+	3.96633i	−0.880266	+	0.155215i	−0.595474	−	0.803375i	$-0.703036\pi$
$653$	−22.4942	+	3.96633i	−0.880266	+	0.155215i	−0.284792	+	0.958589i	$0.591924\pi$
$654$	0.172561	+	0.144796i	0.00674765	+	0.00566195i
$655$	8.37540	−	14.5066i	0.327254	−	0.566821i
$656$	15.1370	+	26.2181i	0.591002	+	1.02364i
$657$	4.46974	−	25.3492i	0.174381	−	0.988965i
$658$	−8.90822	−	5.14317i	−0.347279	−	0.200501i
$659$	−10.1105	−	3.67992i	−0.393849	−	0.143349i	0.137501	−	0.990502i	$-0.456093\pi$
$659$	−10.1105	−	3.67992i	−0.393849	−	0.143349i	−0.531350	+	0.847152i	$0.678315\pi$
$660$			0.778415i			0.0302998i
$661$	1.59612	−	4.38531i	0.0620820	−	0.170569i	−0.904774	−	0.425893i	$-0.859960\pi$
$661$	1.59612	−	4.38531i	0.0620820	−	0.170569i	0.966856	+	0.255324i	$0.0821822\pi$
$662$	1.25794	+	7.13416i	0.0488914	+	0.277277i
$663$	−0.0690388	+	0.0579304i	−0.00268125	+	0.00224983i
$664$	1.93164	−	2.30204i	0.0749623	−	0.0893366i
$665$	−41.7158			−1.61767
$666$	−1.37050	−	7.15304i	−0.0531057	−	0.277175i
$667$	17.9564			0.695273
$668$	−4.82938	+	5.75543i	−0.186854	+	0.222684i
$669$	0.288980	−	0.242483i	0.0111726	−	0.00937494i
$670$	−0.813190	−	4.61183i	−0.0314163	−	0.178171i
$671$	1.47967	−	4.06537i	0.0571222	−	0.156942i
$672$		−	1.18086i		−	0.0455527i
$673$	31.3187	+	11.3991i	1.20725	+	0.439402i	0.865748	−	0.500480i	$-0.166843\pi$
$673$	31.3187	+	11.3991i	1.20725	+	0.439402i	0.341499	+	0.939882i	$0.389065\pi$
$674$	6.66986	+	3.85084i	0.256913	+	0.148329i
$675$	−0.0792603	+	0.449507i	−0.00305073	+	0.0173016i
$676$	−11.8602	−	20.5424i	−0.456160	−	0.790092i
$677$	−15.5408	+	26.9174i	−0.597280	+	1.03452i	0.395941	+	0.918276i	$0.370418\pi$
$677$	−15.5408	+	26.9174i	−0.597280	+	1.03452i	−0.993221	+	0.116243i	$0.962915\pi$
$678$	−0.108435	−	0.0909877i	−0.00416442	−	0.00349436i
$679$	4.35682	−	0.768225i	0.167199	−	0.0294818i
$680$	−14.5379	+	8.39346i	−0.557503	+	0.321874i
$681$	−0.0611441	−	0.167992i	−0.00234305	−	0.00643746i
$682$	−2.12463	+	0.773303i	−0.0813564	+	0.0296113i
$683$	31.4568	+	5.54669i	1.20366	+	0.212238i	0.739281	−	0.673397i	$-0.235165\pi$
$683$	31.4568	+	5.54669i	1.20366	+	0.212238i	0.464382	+	0.885635i	$0.346277\pi$
$684$	−13.3211	−	15.8755i	−0.509345	−	0.607014i
$685$	28.7751	+	34.2929i	1.09944	+	1.31026i
$686$	10.0964	+	1.78027i	0.385483	+	0.0679710i
$687$	−0.847969	+	0.308635i	−0.0323520	+	0.0117752i
$688$	5.43133	+	14.9225i	0.207068	+	0.568913i
$689$	−1.32067	+	0.762492i	−0.0503137	+	0.0290486i
$690$	0.242023	−	0.0426751i	0.00921365	−	0.00162461i
$691$	31.8951	+	26.7631i	1.21335	+	1.01812i	0.999146	+	0.0413276i	$0.0131587\pi$
$691$	31.8951	+	26.7631i	1.21335	+	1.01812i	0.214200	+	0.976790i	$0.431286\pi$
$692$	3.38134	−	5.85665i	0.128539	−	0.222636i
$693$	−18.2540	−	31.6168i	−0.693411	−	1.20102i
$694$	1.44583	−	8.19973i	0.0548831	−	0.311258i
$695$	−7.02730	−	4.05721i	−0.266561	−	0.153899i
$696$	−0.401877	−	0.146271i	−0.0152331	−	0.00554440i
$697$		−	43.2500i		−	1.63821i
$698$	−3.67420	+	10.0948i	−0.139070	+	0.382093i
$699$	−0.120376	−	0.682683i	−0.00455302	−	0.0258215i
$700$	−7.71673	+	6.47511i	−0.291665	+	0.244736i
$701$	−10.1818	+	12.1342i	−0.384562	+	0.458303i	−0.923249	−	0.384203i	$-0.874476\pi$
$701$	−10.1818	+	12.1342i	−0.384562	+	0.458303i	0.538686	+	0.842506i	$0.318921\pi$
$702$	0.0492824			0.00186005
$703$	4.30206	+	22.4538i	0.162255	+	0.846860i
$704$	−12.1077			−0.456327
$705$	0.574353	−	0.684488i	0.0216314	−	0.0257793i
$706$	3.06533	−	2.57212i	0.115365	−	0.0968029i
$707$	−4.32273	−	24.5154i	−0.162573	−	0.921996i
$708$	0.533206	−	1.46497i	0.0200391	−	0.0550570i
$709$		−	23.7592i		−	0.892294i	−0.894960	−	0.446147i	$-0.852796\pi$
$709$		−	23.7592i		−	0.892294i	0.894960	−	0.446147i	$-0.147204\pi$
$710$	3.52966	+	1.28469i	0.132466	+	0.0482136i
$711$	19.5806	+	11.3049i	0.734331	+	0.423966i
$712$	−3.22224	+	18.2742i	−0.120759	+	0.684856i
$713$	−4.11290	−	7.12375i	−0.154029	−	0.266787i
$714$	−0.240723	+	0.416944i	−0.00900882	+	0.0156037i
$715$	−1.74301	−	1.46256i	−0.0651847	−	0.0546965i
$716$	37.5338	−	6.61822i	1.40270	−	0.247335i
$717$	1.39547	−	0.805673i	0.0521146	−	0.0300884i
$718$	−2.56697	−	7.05269i	−0.0957984	−	0.263204i
$719$	−34.7188	+	12.6366i	−1.29479	+	0.471266i	−0.895297	−	0.445470i	$-0.853037\pi$
$719$	−34.7188	+	12.6366i	−1.29479	+	0.471266i	−0.399495	+	0.916735i	$0.630814\pi$
$720$	−22.5922	−	3.98361i	−0.841961	−	0.148461i
$721$	−45.2803	−	53.9630i	−1.68633	−	2.00969i
$722$	1.25188	+	1.49193i	0.0465902	+	0.0555240i
$723$	1.64795	+	0.290577i	0.0612878	+	0.0108067i
$724$	−13.2074	+	4.80710i	−0.490849	+	0.178654i
$725$	1.89762	+	5.21367i	0.0704759	+	0.193631i
$726$	0.0746855	−	0.0431197i	0.00277184	−	0.00160032i
$727$	−11.2092	+	1.97649i	−0.415728	+	0.0733041i	−0.377600	−	0.925969i	$-0.623251\pi$
$727$	−11.2092	+	1.97649i	−0.415728	+	0.0733041i	−0.0381280	+	0.999273i	$0.512139\pi$
$728$	1.73867	+	1.45892i	0.0644393	+	0.0540710i
$729$	13.3969	−	23.2041i	0.496181	−	0.859410i
$730$	−4.28497	−	7.42179i	−0.158594	−	0.274693i
$731$	3.93949	−	22.3419i	0.145707	−	0.826347i
$732$	−0.155574	−	0.0898208i	−0.00575019	−	0.00331987i
$733$	−30.7666	−	11.1981i	−1.13639	−	0.413612i	−0.295782	−	0.955256i	$-0.595580\pi$
$733$	−30.7666	−	11.1981i	−1.13639	−	0.413612i	−0.840608	+	0.541643i	$0.817802\pi$
$734$		−	1.85971i		−	0.0686433i
$735$	−0.674125	+	1.85214i	−0.0248655	+	0.0683174i
$736$	2.97163	+	16.8530i	0.109536	+	0.621208i
$737$	−9.85510	+	8.26941i	−0.363017	+	0.304608i
$738$	−7.59625	+	9.05285i	−0.279622	+	0.333240i
$739$	−43.6845			−1.60696			−0.803479	−	0.595333i	$-0.797020\pi$
$739$	−43.6845			−1.60696			−0.803479	+	0.595333i	$0.797020\pi$
$740$	21.6684	+	17.6433i	0.796548	+	0.648579i
$741$	−0.0773007			−0.00283971
$742$	−5.23649	+	6.24061i	−0.192238	+	0.229100i
$743$	−29.1093	+	24.4256i	−1.06792	+	0.896089i	−0.994862	−	0.101238i	$-0.967719\pi$
$743$	−29.1093	+	24.4256i	−1.06792	+	0.896089i	−0.0730556	+	0.997328i	$0.523275\pi$
$744$	0.0340202	+	0.192938i	0.00124724	+	0.00707346i
$745$	−12.2039	+	33.5301i	−0.447118	+	1.22845i
$746$			4.68271i			0.171446i
$747$	−5.51310	−	2.00661i	−0.201714	−	0.0734179i
$748$	19.1386	+	11.0497i	0.699777	+	0.404016i
$749$	6.42091	−	36.4148i	0.234615	−	1.33057i
$750$	−0.116236	−	0.201327i	−0.00424434	−	0.00735142i
$751$	20.8011	−	36.0285i	0.759043	−	1.31470i	−0.184297	−	0.982871i	$-0.559001\pi$
$751$	20.8011	−	36.0285i	0.759043	−	1.31470i	0.943339	−	0.331830i	$-0.107666\pi$
$752$	13.6025	+	11.4139i	0.496033	+	0.416221i
$753$	−1.19958	+	0.211518i	−0.0437150	+	0.00770813i
$754$	0.518794	−	0.299526i	0.0188934	−	0.0109081i
$755$	−10.8317	−	29.7599i	−0.394206	−	1.08307i
$756$	−2.85084	+	1.03762i	−0.103684	+	0.0377379i
$757$	21.6968	+	3.82573i	0.788583	+	0.139049i	0.553414	−	0.832906i	$-0.313325\pi$
$757$	21.6968	+	3.82573i	0.788583	+	0.139049i	0.235169	+	0.971955i	$0.424436\pi$
$758$	−0.750878	−	0.894862i	−0.0272731	−	0.0325028i
$759$	−0.433968	−	0.517183i	−0.0157520	−	0.0187725i
$760$	−14.1797	−	2.50026i	−0.514351	−	0.0906940i
$761$	−29.6836	+	10.8040i	−1.07603	+	0.391643i	−0.818429	−	0.574608i	$-0.805154\pi$
$761$	−29.6836	+	10.8040i	−1.07603	+	0.391643i	−0.257602	+	0.966251i	$0.582932\pi$
$762$	0.0528954	+	0.145329i	0.00191620	+	0.00526471i
$763$	35.1032	−	20.2668i	1.27082	−	0.733709i
$764$	4.27148	−	0.753176i	0.154537	−	0.0272490i
$765$	25.1059	+	21.0664i	0.907706	+	0.761656i
$766$	−2.72424	+	4.71852i	−0.0984307	+	0.170487i
$767$	2.27849	+	3.94646i	0.0822715	+	0.142498i
$768$	−0.0504428	+	0.286075i	−0.00182020	+	0.0103229i
$769$	−7.59056	−	4.38241i	−0.273723	−	0.158034i	0.356856	−	0.934160i	$-0.383849\pi$
$769$	−7.59056	−	4.38241i	−0.273723	−	0.158034i	−0.630578	+	0.776126i	$0.717182\pi$
$770$	−11.4219	−	4.15724i	−0.411617	−	0.149816i
$771$			1.08141i			0.0389462i
$772$	−9.57363	+	26.3033i	−0.344562	+	0.946677i
$773$	7.22588	+	40.9800i	0.259897	+	1.47395i	0.783183	+	0.621791i	$0.213595\pi$
$773$	7.22588	+	40.9800i	0.259897	+	1.47395i	−0.523286	+	0.852157i	$0.675294\pi$
$774$	−4.74864	+	3.98458i	−0.170686	+	0.143223i
$775$	1.63375	−	1.94703i	0.0586860	−	0.0699392i
$776$	1.52698			0.0548154
$777$	1.65104	+	0.266044i	0.0592308	+	0.00954426i
$778$	−12.8323			−0.460060
$779$	23.8450	−	28.4174i	0.854336	−	1.01816i
$780$	−0.0723755	+	0.0607302i	−0.00259146	+	0.00217449i
$781$	−1.79186	−	10.1621i	−0.0641176	−	0.363629i
$782$	2.38630	−	6.55631i	0.0853339	−	0.234453i
$783$			1.67096i			0.0597151i
$784$	−36.8068	−	13.3966i	−1.31453	−	0.478450i
$785$	−0.289761	−	0.167294i	−0.0103420	−	0.00597097i
$786$	0.0287937	−	0.163297i	0.00102704	−	0.00582461i
$787$	22.3316	+	38.6794i	0.796034	+	1.37877i	0.922180	+	0.386760i	$0.126406\pi$
$787$	22.3316	+	38.6794i	0.796034	+	1.37877i	−0.126146	+	0.992012i	$0.540261\pi$
$788$	11.0214	−	19.0896i	0.392621	−	0.680040i
$789$	−0.681146	−	0.571549i	−0.0242494	−	0.0203477i
$790$	7.41333	−	1.30717i	0.263754	−	0.0465070i
$791$	−22.0584	+	12.7354i	−0.784307	+	0.452820i
$792$	−4.30977	−	11.8410i	−0.153141	−	0.420751i
$793$	0.493431	−	0.179594i	0.0175223	−	0.00637758i
$794$	4.53413	+	0.799490i	0.160910	+	0.0283728i
$795$	−0.454875	−	0.542099i	−0.0161327	−	0.0192263i
$796$	10.5940	+	12.6254i	0.375494	+	0.447496i
$797$	36.5416	+	6.44326i	1.29437	+	0.228232i	0.778071	−	0.628177i	$-0.216199\pi$
$797$	36.5416	+	6.44326i	1.29437	+	0.228232i	0.516298	+	0.856409i	$0.327310\pi$
$798$	−0.388041	+	0.141235i	−0.0137365	+	0.00499967i
$799$	−8.67625	−	23.8378i	−0.306944	−	0.843321i
$800$	−4.57926	+	2.64383i	−0.161901	+	0.0934737i
$801$	35.6771	−	6.29084i	1.26059	−	0.222276i
$802$	8.71148	+	7.30980i	0.307613	+	0.258118i
$803$	−11.7715	+	20.3889i	−0.415408	+	0.719509i
$804$	0.267097	+	0.462626i	0.00941980	+	0.0163156i
$805$	7.67897	−	43.5496i	0.270648	−	1.53492i
$806$	−0.237659	−	0.137213i	−0.00837120	−	0.00483311i
$807$	−0.00987110	−	0.00359279i	−0.000347479	−	0.000126472i
$808$		−	8.59216i		−	0.302271i
$809$	3.62316	−	9.95454i	0.127383	−	0.349983i	−0.859564	−	0.511029i	$-0.829264\pi$
$809$	3.62316	−	9.95454i	0.127383	−	0.349983i	0.986947	+	0.161046i	$0.0514867\pi$
$810$	−1.55304	−	8.80773i	−0.0545683	−	0.309472i
$811$	−34.8710	+	29.2602i	−1.22448	+	1.02746i	−0.225907	+	0.974149i	$0.572535\pi$
$811$	−34.8710	+	29.2602i	−1.22448	+	1.02746i	−0.998578	+	0.0533159i	$0.983021\pi$
$812$	−23.7043	+	28.2496i	−0.831857	+	0.991368i
$813$	−0.408673			−0.0143328
$814$	−1.05974	+	6.57664i	−0.0371438	+	0.230511i
$815$	26.5828			0.931153
$816$	0.534220	−	0.636658i	0.0187014	−	0.0222875i
$817$	14.9062	−	12.5078i	0.521503	−	0.437593i
$818$	0.485747	+	2.75481i	0.0169837	+	0.0963196i
$819$	1.51553	−	4.16389i	0.0529570	−	0.145498i
$820$		−	45.3402i		−	1.58335i
$821$	26.6246	+	9.69057i	0.929206	+	0.338203i	0.761895	−	0.647701i	$-0.224269\pi$
$821$	26.6246	+	9.69057i	0.929206	+	0.338203i	0.167311	+	0.985904i	$0.446492\pi$
$822$	0.383770	+	0.221570i	0.0133855	+	0.00772814i
$823$	−2.85659	+	16.2005i	−0.0995745	+	0.564715i	0.893675	+	0.448715i	$0.148118\pi$
$823$	−2.85659	+	16.2005i	−0.0995745	+	0.564715i	−0.993249	+	0.116000i	$0.962993\pi$
$824$	−12.1570	−	21.0566i	−0.423510	−	0.733541i
$825$	0.104304	−	0.180659i	0.00363139	−	0.00628975i
$826$	18.6483	+	15.6478i	0.648857	+	0.544456i
$827$	18.3394	−	3.23372i	0.637722	−	0.112448i	0.154567	−	0.987982i	$-0.450602\pi$
$827$	18.3394	−	3.23372i	0.637722	−	0.112448i	0.483155	+	0.875535i	$0.339491\pi$
$828$	19.0255	−	10.9844i	0.661182	−	0.381734i
$829$	14.9927	+	41.1920i	0.520717	+	1.43066i	0.869724	+	0.493538i	$0.164297\pi$
$829$	14.9927	+	41.1920i	0.520717	+	1.43066i	−0.349007	+	0.937120i	$0.613481\pi$
$830$	−1.83553	+	0.668079i	−0.0637122	+	0.0231894i
$831$	−1.42868	−	0.251915i	−0.0495603	−	0.00873883i
$832$	−0.944618	−	1.12575i	−0.0327487	−	0.0390284i
$833$	35.9687	+	42.8659i	1.24624	+	1.48521i
$834$	−0.0791043	−	0.0139482i	−0.00273916	−	0.000482988i
$835$	9.57641	−	3.48553i	0.331405	−	0.120622i
$836$	6.48299	+	17.8119i	0.224219	+	0.616037i
$837$	0.662912	−	0.382732i	0.0229136	−	0.0132292i
$838$	2.64095	−	0.465671i	0.0912301	−	0.0160863i
$839$	−42.7059	−	35.8345i	−1.47437	−	1.23714i	−0.911955	−	0.410291i	$-0.865427\pi$
$839$	−42.7059	−	35.8345i	−1.47437	−	1.23714i	−0.562417	−	0.826854i	$-0.690128\pi$
$840$	−0.526613	+	0.912121i	−0.0181699	+	0.0314712i
$841$	−4.34436	−	7.52464i	−0.149805	−	0.259470i
$842$	−0.802306	+	4.55010i	−0.0276493	+	0.156807i
$843$	−0.146371	−	0.0845076i	−0.00504130	−	0.00291060i
$844$	1.91673	+	0.697634i	0.0659767	+	0.0240135i
$845$			32.1746i			1.10684i
$846$	−2.37071	+	6.51347i	−0.0815066	+	0.223938i
$847$	−2.69466	−	15.2822i	−0.0925896	−	0.525102i
$848$	10.7729	−	9.03953i	0.369942	−	0.310419i
$849$	0.895895	−	1.06769i	0.0307470	−	0.0366429i
$850$	2.15582			0.0739441
$851$	−24.2328	+	0.357930i	−0.830689	+	0.0122697i
$852$	−0.428475			−0.0146793
$853$	−17.7871	+	21.1978i	−0.609017	+	0.725798i	−0.979141	−	0.203184i	$-0.934871\pi$
$853$	−17.7871	+	21.1978i	−0.609017	+	0.725798i	0.370123	+	0.928983i	$0.379315\pi$
$854$	2.14883	−	1.80309i	0.0735316	−	0.0617003i
$855$	4.88131	+	27.6833i	0.166937	+	0.946748i
$856$	4.36509	−	11.9930i	0.149196	−	0.409911i
$857$			11.0988i			0.379126i	0.981869	+	0.189563i	$0.0607072\pi$
$857$			11.0988i			0.379126i	−0.981869	+	0.189563i	$0.939293\pi$
$858$	−0.0211652	−	0.00770350i	−0.000722567	−	0.000262993i
$859$	−4.91745	−	2.83909i	−0.167781	−	0.0968686i	0.413758	−	0.910387i	$-0.364216\pi$
$859$	−4.91745	−	2.83909i	−0.167781	−	0.0968686i	−0.581539	+	0.813518i	$0.697549\pi$
$860$	4.12989	−	23.4217i	0.140828	−	0.798675i
$861$	−1.35677	−	2.35000i	−0.0462386	−	0.0800876i
$862$	−1.61985	+	2.80567i	−0.0551724	+	0.0955614i
$863$	−28.6008	−	23.9989i	−0.973583	−	0.816933i	0.00952592	−	0.999955i	$-0.496968\pi$
$863$	−28.6008	−	23.9989i	−0.973583	−	0.816933i	−0.983109	+	0.183022i	$0.941412\pi$
$864$	−1.56828	+	0.276530i	−0.0533539	+	0.00940773i
$865$	−7.94406	+	4.58650i	−0.270106	+	0.155946i
$866$	1.19758	+	3.29032i	0.0406954	+	0.111810i
$867$	−0.127943	+	0.0465673i	−0.00434516	+	0.00158151i
$868$	16.6368	+	2.93352i	0.564691	+	0.0995702i
$869$	−13.2927	−	15.8417i	−0.450925	−	0.537392i
$870$	0.178686	+	0.212950i	0.00605803	+	0.00721968i
$871$	−1.53775	−	0.271146i	−0.0521046	−	0.00918744i
$872$	13.1467	−	4.78501i	0.445203	−	0.162041i
$873$	−1.01961	−	2.80137i	−0.0345087	−	0.0948119i
$874$	5.18260	−	2.99218i	0.175304	−	0.101212i
$875$	−41.1956	+	7.26390i	−1.39267	+	0.245565i
$876$	0.748875	+	0.628381i	0.0253022	+	0.0212310i
$877$	4.24462	−	7.35189i	0.143331	−	0.248256i	−0.785418	−	0.618965i	$-0.787552\pi$
$877$	4.24462	−	7.35189i	0.143331	−	0.248256i	0.928749	+	0.370710i	$0.120885\pi$
$878$	−3.00166	−	5.19903i	−0.101301	−	0.175459i
$879$	−0.249955	+	1.41757i	−0.00843078	+	0.0478133i
$880$	18.1714	+	10.4913i	0.612558	+	0.353661i
$881$	36.1240	+	13.1481i	1.21705	+	0.442969i	0.869143	−	0.494560i	$-0.164671\pi$
$881$	36.1240	+	13.1481i	1.21705	+	0.442969i	0.347905	+	0.937530i	$0.386893\pi$
$882$		−	15.2899i		−	0.514837i
$883$	1.28694	−	3.53585i	0.0433091	−	0.118991i	−0.916153	−	0.400829i	$-0.868722\pi$
$883$	1.28694	−	3.53585i	0.0433091	−	0.118991i	0.959462	+	0.281839i	$0.0909443\pi$
$884$	0.465775	+	2.64154i	0.0156657	+	0.0888447i
$885$	−1.61991	+	1.35926i	−0.0544526	+	0.0456912i
$886$	4.21650	−	5.02503i	0.141656	−	0.168819i
$887$	35.3539			1.18707			0.593533	−	0.804809i	$-0.297732\pi$
$887$	35.3539			1.18707			0.593533	+	0.804809i	$0.297732\pi$
$888$	0.545263	+	0.189388i	0.0182978	+	0.00635543i
$889$	27.8288			0.933347
$890$	7.75303	−	9.23971i	0.259882	−	0.309716i
$891$	−18.8214	+	15.7930i	−0.630541	+	0.529086i
$892$	−1.94963	−	11.0569i	−0.0652783	−	0.370212i
$893$	7.44177	−	20.4461i	0.249029	−	0.684203i
$894$			0.353215i			0.0118133i
$895$	−48.5792	−	17.6814i	−1.62382	−	0.591023i
$896$	−39.8766	−	23.0228i	−1.33218	−	0.769136i
$897$	0.0142294	−	0.0806989i	0.000475106	−	0.00269446i
$898$	0.965857	+	1.67291i	0.0322311	+	0.0558259i
$899$	4.65230	−	8.05801i	0.155163	−	0.268750i
$900$	5.19995	+	4.36328i	0.173332	+	0.145443i
$901$	−19.7854	+	3.48870i	−0.659147	+	0.116225i
$902$	9.36080	−	5.40446i	0.311681	−	0.179949i
$903$	−0.486824	−	1.33754i	−0.0162005	−	0.0445105i
$904$	−8.26122	+	3.00684i	−0.274764	+	0.100006i
$905$	18.7748	+	3.31051i	0.624096	+	0.110045i
$906$	−0.201513	−	0.240154i	−0.00669484	−	0.00797860i
$907$	−18.1720	−	21.6565i	−0.603390	−	0.719092i	0.374730	−	0.927134i	$-0.377735\pi$
$907$	−18.1720	−	21.6565i	−0.603390	−	0.719092i	−0.978120	+	0.208042i	$0.933291\pi$
$908$	−5.23988	−	0.923931i	−0.173891	−	0.0306617i
$909$	−15.7630	+	5.73727i	−0.522826	+	0.190293i
$910$	−0.504581	−	1.38632i	−0.0167267	−	0.0459562i
$911$	−24.9821	+	14.4234i	−0.827694	+	0.477869i	−0.853063	−	0.521809i	$-0.825257\pi$
$911$	−24.9821	+	14.4234i	−0.827694	+	0.477869i	0.0253684	+	0.999678i	$0.491924\pi$
$912$	0.702017	−	0.123785i	0.0232461	−	0.00409892i
$913$	4.11070	+	3.44928i	0.136044	+	0.114155i
$914$	−4.18140	+	7.24241i	−0.138309	+	0.239557i
$915$	0.121834	+	0.211023i	0.00402772	+	0.00697622i
$916$	−4.66371	+	26.4492i	−0.154093	+	0.873906i
$917$	−25.8396	−	14.9185i	−0.853299	−	0.492652i
$918$	0.610107	+	0.222061i	0.0201365	+	0.00732910i
$919$			52.6532i			1.73687i	0.495805	+	0.868434i	$0.334873\pi$
$919$			52.6532i			1.73687i	−0.495805	+	0.868434i	$0.665127\pi$
$920$	5.22035	−	14.3428i	0.172110	−	0.472868i
$921$	0.193433	+	1.09701i	0.00637384	+	0.0361479i
$922$	2.87007	−	2.40828i	0.0945207	−	0.0793123i
$923$	0.805057	−	0.959429i	0.0264988	−	0.0315800i
$924$	1.38653			0.0456136
$925$	−2.66484	−	6.99822i	−0.0876192	−	0.230100i
$926$	−1.00642			−0.0330731
$927$	−30.5123	+	36.3632i	−1.00216	+	1.19432i
$928$	−14.8285	+	12.4426i	−0.486770	+	0.408449i
$929$	−3.41242	−	19.3528i	−0.111958	−	0.634945i	−0.988212	−	0.153095i	$-0.951076\pi$
$929$	−3.41242	−	19.3528i	−0.111958	−	0.634945i	0.876254	−	0.481850i	$-0.160035\pi$
$930$	0.0435547	−	0.119666i	0.00142822	−	0.00392399i
$931$			47.9956i			1.57299i
$932$	−19.3874	−	7.05645i	−0.635057	−	0.231142i
$933$	0.598581	+	0.345591i	0.0195967	+	0.0113141i
$934$	−1.16541	+	6.60934i	−0.0381332	+	0.216264i
$935$	−14.9880	−	25.9599i	−0.490159	−	0.848981i
$936$	0.764713	−	1.32452i	0.0249954	−	0.0432934i
$937$	4.66127	+	3.91127i	0.152277	+	0.127776i	0.715743	−	0.698363i	$-0.246088\pi$
$937$	4.66127	+	3.91127i	0.152277	+	0.127776i	−0.563466	+	0.826139i	$0.690533\pi$
$938$	−8.21472	+	1.44848i	−0.268220	+	0.0472945i
$939$	0.893138	−	0.515654i	0.0291465	−	0.0168277i
$940$	−9.09558	−	24.9899i	−0.296665	−	0.815081i
$941$	−4.52635	+	1.64746i	−0.147555	+	0.0537056i	−0.414742	−	0.909939i	$-0.636128\pi$
$941$	−4.52635	+	1.64746i	−0.147555	+	0.0537056i	0.267187	+	0.963645i	$0.413906\pi$
$942$	−0.00326176		0.000575137i	−0.000106274		1.87390e-5i
$943$	25.2773	+	30.1243i	0.823141	+	0.980981i
$944$	−27.0120	−	32.1917i	−0.879167	−	1.04775i
$945$	4.05258	+	0.714579i	0.131830	+	0.0232452i
$946$	5.32785	−	1.93918i	0.173223	−	0.0630482i
$947$	3.09287	+	8.49759i	0.100505	+	0.276134i	0.979747	−	0.200241i	$-0.0641725\pi$
$947$	3.09287	+	8.49759i	0.100505	+	0.276134i	−0.879242	+	0.476375i	$0.841950\pi$
$948$	−0.743653	+	0.429348i	−0.0241527	+	0.0139446i
$949$	−2.81411	+	0.496203i	−0.0913498	+	0.0161074i
$950$	1.41648	+	1.18857i	0.0459567	+	0.0385623i
$951$	0.435922	−	0.755038i	0.0141357	−	0.0244838i
$952$	14.9507	+	25.8953i	0.484554	+	0.839272i
$953$	0.0437565	−	0.248155i	0.00141741	−	0.00803854i	−0.984091	−	0.177666i	$-0.943145\pi$
$953$	0.0437565	−	0.248155i	0.00141741	−	0.00803854i	0.985508	+	0.169627i	$0.0542564\pi$
$954$	4.75412	+	2.74479i	0.153920	+	0.0888659i
$955$	−5.52847	−	2.01220i	−0.178897	−	0.0651133i
$956$		−	47.9574i		−	1.55105i
$957$	0.261193	−	0.717621i	0.00844316	−	0.0231974i
$958$	0.646943	+	3.66900i	0.0209018	+	0.118540i
$959$	61.0834	−	51.2550i	1.97249	−	1.65511i
$960$	0.438345	−	0.522399i	0.0141475	−	0.0168603i
$961$	26.7376			0.862502
$962$	−0.694161	+	0.414563i	−0.0223807	+	0.0133660i
$963$	−24.9168			−0.802932
$964$	32.0130	−	38.1516i	1.03107	−	1.22878i
$965$	29.0852	−	24.4054i	0.936285	−	0.785637i
$966$	−0.0760141	−	0.431098i	−0.00244571	−	0.0138703i
$967$	17.3416	−	47.6455i	0.557667	−	1.53218i	−0.265346	−	0.964153i	$-0.585486\pi$
$967$	17.3416	−	47.6455i	0.557667	−	1.53218i	0.823012	−	0.568023i	$-0.192292\pi$
$968$		−	5.35610i		−	0.172152i
$969$	−0.956967	−	0.348308i	−0.0307422	−	0.0111893i
$970$	−0.859569	−	0.496272i	−0.0275991	−	0.0159343i
$971$	−10.0423	+	56.9526i	−0.322272	+	1.82770i	0.205916	+	0.978570i	$0.433983\pi$
$971$	−10.0423	+	56.9526i	−0.322272	+	1.82770i	−0.528188	+	0.849127i	$0.677128\pi$
$972$	1.53358	+	2.65624i	0.0491896	+	0.0851988i
$973$	−7.22682	+	12.5172i	−0.231681	+	0.401284i
$974$	−10.5147	−	8.82284i	−0.336911	−	0.282702i
$975$	0.0249349	−	0.00439669i	0.000798555	−	0.000140807i
$976$	−4.19357	+	2.42116i	−0.134233	+	0.0774995i
$977$	6.20213	+	17.0402i	0.198424	+	0.545165i	0.998501	−	0.0547321i	$-0.0174305\pi$
$977$	6.20213	+	17.0402i	0.198424	+	0.545165i	−0.800077	+	0.599897i	$0.795208\pi$
$978$	0.247273	−	0.0900001i	0.00790692	−	0.00287788i
$979$	−32.6318	−	5.75387i	−1.04292	−	0.183894i
$980$	37.7071	+	44.9376i	1.20451	+	1.43548i
$981$	−17.5570	−	20.9236i	−0.560551	−	0.668038i
$982$	−11.0962	−	1.95656i	−0.354094	−	0.0624363i
$983$	52.9969	−	19.2893i	1.69034	−	0.615233i	0.695671	−	0.718361i	$-0.255107\pi$
$983$	52.9969	−	19.2893i	1.69034	−	0.615233i	0.994668	+	0.103128i	$0.0328851\pi$
$984$	−0.320334	−	0.880111i	−0.0102119	−	0.0280569i
$985$	−25.8935	+	14.9496i	−0.825035	+	0.476334i
$986$	7.77220	−	1.37045i	0.247517	−	0.0436440i
$987$	−1.21923	−	1.02305i	−0.0388085	−	0.0325642i
$988$	−1.15032	+	1.99242i	−0.0365967	+	0.0633873i
$989$	10.3137	+	17.8639i	0.327958	+	0.568040i
$990$	−1.42229	+	8.06622i	−0.0452034	+	0.256361i
$991$	−13.9955	−	8.08029i	−0.444581	−	0.256679i	0.260958	−	0.965350i	$-0.415962\pi$
$991$	−13.9955	−	8.08029i	−0.444581	−	0.256679i	−0.705539	+	0.708671i	$0.749295\pi$
$992$	8.33278	+	3.03288i	0.264566	+	0.0962941i
$993$			1.12089i			0.0355703i
$994$	2.28833	−	6.28713i	0.0725814	−	0.199416i
$995$	−3.88200	−	22.0159i	−0.123068	−	0.697951i
$996$	0.170690	−	0.143226i	0.00540852	−	0.00453828i
$997$	5.63997	−	6.72145i	0.178620	−	0.212871i	−0.669305	−	0.742988i	$-0.733408\pi$
$997$	5.63997	−	6.72145i	0.178620	−	0.212871i	0.847924	+	0.530118i	$0.177852\pi$
$998$	−1.20469			−0.0381338
$999$	−0.0333077	−	2.25502i	−0.00105381	−	0.0713456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.h.a.3.2	✓	18
3.2	odd	2		333.2.bl.d.262.2		18
4.3	odd	2		592.2.bq.d.225.1		18
5.2	odd	4		925.2.ba.a.299.3		36
5.3	odd	4		925.2.ba.a.299.4		36
5.4	even	2		925.2.bb.a.151.2		18
37.5	odd	36		1369.2.a.m.1.10		18
37.7	even	9		1369.2.b.g.1368.10		18
37.25	even	18	inner	37.2.h.a.25.2	yes	18
37.30	even	18		1369.2.b.g.1368.9		18
37.32	odd	36		1369.2.a.m.1.9		18
111.62	odd	18		333.2.bl.d.136.2		18
148.99	odd	18		592.2.bq.d.321.1		18
185.62	odd	36		925.2.ba.a.99.4		36
185.99	even	18		925.2.bb.a.876.2		18
185.173	odd	36		925.2.ba.a.99.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.3.2	✓	18	1.1	even	1	trivial
37.2.h.a.25.2	yes	18	37.25	even	18	inner
333.2.bl.d.136.2		18	111.62	odd	18
333.2.bl.d.262.2		18	3.2	odd	2
592.2.bq.d.225.1		18	4.3	odd	2
592.2.bq.d.321.1		18	148.99	odd	18
925.2.ba.a.99.3		36	185.173	odd	36
925.2.ba.a.99.4		36	185.62	odd	36
925.2.ba.a.299.3		36	5.2	odd	4
925.2.ba.a.299.4		36	5.3	odd	4
925.2.bb.a.151.2		18	5.4	even	2
925.2.bb.a.876.2		18	185.99	even	18
1369.2.a.m.1.9		18	37.32	odd	36
1369.2.a.m.1.10		18	37.5	odd	36
1369.2.b.g.1368.9		18	37.30	even	18
1369.2.b.g.1368.10		18	37.7	even	9

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.256873 + 0.306129i) q^{2} +(-0.0473670 + 0.0397456i) q^{3} +(0.319565 + 1.81234i) q^{4} +(0.853756 - 2.34567i) q^{5} -0.0247100i q^{6} +(-4.17818 - 1.52073i) q^{7} +(-1.32907 - 0.767337i) q^{8} +(-0.520281 + 2.95066i) q^{9} +O(q^{10})\)	\(q+(-0.256873 + 0.306129i) q^{2} +(-0.0473670 + 0.0397456i) q^{3} +(0.319565 + 1.81234i) q^{4} +(0.853756 - 2.34567i) q^{5} -0.0247100i q^{6} +(-4.17818 - 1.52073i) q^{7} +(-1.32907 - 0.767337i) q^{8} +(-0.520281 + 2.95066i) q^{9} +(0.498773 + 0.863900i) q^{10} +(1.37021 - 2.37328i) q^{11} +(-0.0871695 - 0.0731439i) q^{12} +(0.327564 - 0.0577584i) q^{13} +(1.53880 - 0.888429i) q^{14} +(0.0527905 + 0.145041i) q^{15} +(-2.88233 + 1.04908i) q^{16} +(4.31543 + 0.760927i) q^{17} +(-0.769637 - 0.917218i) q^{18} +(2.41593 + 2.87919i) q^{19} +(4.52400 + 0.797703i) q^{20} +(0.258350 - 0.0940319i) q^{21} +(0.374560 + 1.02909i) q^{22} +(-3.45049 + 1.99214i) q^{23} +(0.0934523 - 0.0164782i) q^{24} +(-0.943068 - 0.791328i) q^{25} +(-0.0664608 + 0.115114i) q^{26} +(-0.185381 - 0.321090i) q^{27} +(1.42089 - 8.05827i) q^{28} +(-3.90301 - 2.25340i) q^{29} +(-0.0579617 - 0.0210963i) q^{30} +2.06457i q^{31} +(1.46902 - 4.03609i) q^{32} +(0.0294246 + 0.166875i) q^{33} +(-1.34146 + 1.12562i) q^{34} +(-7.13429 + 8.50232i) q^{35} -5.51387 q^{36} +(5.31217 + 2.96325i) q^{37} -1.50199 q^{38} +(-0.0132201 + 0.0157551i) q^{39} +(-2.93462 + 2.46244i) q^{40} +(-1.71389 - 9.71996i) q^{41} +(-0.0375774 + 0.103243i) q^{42} -5.17722i q^{43} +(4.73907 + 1.72488i) q^{44} +(6.47709 + 3.73955i) q^{45} +(0.276485 - 1.56802i) q^{46} +(-2.89453 - 5.01347i) q^{47} +(0.0948308 - 0.164252i) q^{48} +(9.78226 + 8.20829i) q^{49} +(0.484498 - 0.0854300i) q^{50} +(-0.234653 + 0.135477i) q^{51} +(0.209356 + 0.575201i) q^{52} +(-4.30830 + 1.56809i) q^{53} +(0.145915 + 0.0257287i) q^{54} +(-4.39711 - 5.24028i) q^{55} +(4.38617 + 5.22723i) q^{56} +(-0.228871 - 0.0403561i) q^{57} +(1.69241 - 0.615987i) q^{58} +(4.68580 + 12.8741i) q^{59} +(-0.245993 + 0.142024i) q^{60} +(1.55470 - 0.274136i) q^{61} +(-0.632024 - 0.530331i) q^{62} +(6.66099 - 11.5372i) q^{63} +(-2.20909 - 3.82626i) q^{64} +(0.144177 - 0.817670i) q^{65} +(-0.0586438 - 0.0338580i) q^{66} +(-4.41138 - 1.60561i) q^{67} +8.06420i q^{68} +(0.0842603 - 0.231503i) q^{69} +(-0.770202 - 4.36803i) q^{70} +(2.88449 - 2.42037i) q^{71} +(2.95564 - 3.52239i) q^{72} -8.59102 q^{73} +(-2.27169 + 0.865033i) q^{74} +0.0761221 q^{75} +(-4.44604 + 5.29858i) q^{76} +(-9.33413 + 7.83226i) q^{77} +(-0.00142721 - 0.00809411i) q^{78} +(2.58096 - 7.09112i) q^{79} +7.65666i q^{80} +(-8.42491 - 3.06642i) q^{81} +(3.41582 + 1.97212i) q^{82} +(-0.340027 + 1.92839i) q^{83} +(0.252978 + 0.438170i) q^{84} +(5.46921 - 9.47295i) q^{85} +(1.58490 + 1.32989i) q^{86} +(0.274437 - 0.0483906i) q^{87} +(-3.64221 + 2.10283i) q^{88} +(-4.13545 - 11.3621i) q^{89} +(-2.80858 + 1.02224i) q^{90} +(-1.45646 - 0.256813i) q^{91} +(-4.71309 - 5.61684i) q^{92} +(-0.0820575 - 0.0977923i) q^{93} +(2.27830 + 0.401725i) q^{94} +(8.81626 - 3.20886i) q^{95} +(0.0908341 + 0.249565i) q^{96} +(-0.861683 + 0.497493i) q^{97} +(-5.02560 + 0.886148i) q^{98} +(6.28984 + 5.27780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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