LMFDB - Embedded newform 29.3.c.a.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,3,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$0.790192766645$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 91x^{4} + 126x^{2} + 25 $ x^8 + 18x^6 + 91x^4 + 126*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.1
Root			$2.35663i$ of defining polynomial
Character	$\chi$	$=$	29.12
Dual form			29.3.c.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45515 - 1.45515i) q^{2} +(3.81178 + 3.81178i) q^{3} +0.234947i q^{4} -3.14526i q^{5} -11.0935i q^{6} +0.342313 q^{7} +(-5.47873 + 5.47873i) q^{8} +20.0593i q^{9} +O(q^{10})$	\(q+(-1.45515 - 1.45515i) q^{2} +(3.81178 + 3.81178i) q^{3} +0.234947i q^{4} -3.14526i q^{5} -11.0935i q^{6} +0.342313 q^{7} +(-5.47873 + 5.47873i) q^{8} +20.0593i q^{9} +(-4.57683 + 4.57683i) q^{10} +(-14.0269 - 14.0269i) q^{11} +(-0.895568 + 0.895568i) q^{12} +11.5162i q^{13} +(-0.498119 - 0.498119i) q^{14} +(11.9890 - 11.9890i) q^{15} +16.8846 q^{16} +(-6.37430 - 6.37430i) q^{17} +(29.1894 - 29.1894i) q^{18} +(-6.11703 - 6.11703i) q^{19} +0.738970 q^{20} +(1.30482 + 1.30482i) q^{21} +40.8226i q^{22} +15.8623 q^{23} -41.7674 q^{24} +15.1074 q^{25} +(16.7578 - 16.7578i) q^{26} +(-42.1557 + 42.1557i) q^{27} +0.0804257i q^{28} +(25.6758 + 13.4817i) q^{29} -34.8918 q^{30} +(6.18103 + 6.18103i) q^{31} +(-2.65475 - 2.65475i) q^{32} -106.935i q^{33} +18.5512i q^{34} -1.07666i q^{35} -4.71289 q^{36} +(24.2121 - 24.2121i) q^{37} +17.8024i q^{38} +(-43.8972 + 43.8972i) q^{39} +(17.2320 + 17.2320i) q^{40} +(-34.9536 + 34.9536i) q^{41} -3.79744i q^{42} +(-15.9908 - 15.9908i) q^{43} +(3.29559 - 3.29559i) q^{44} +63.0917 q^{45} +(-23.0820 - 23.0820i) q^{46} +(7.57643 - 7.57643i) q^{47} +(64.3603 + 64.3603i) q^{48} -48.8828 q^{49} +(-21.9835 - 21.9835i) q^{50} -48.5949i q^{51} -2.70570 q^{52} +62.1991 q^{53} +122.686 q^{54} +(-44.1182 + 44.1182i) q^{55} +(-1.87544 + 1.87544i) q^{56} -46.6336i q^{57} +(-17.7443 - 56.9801i) q^{58} -21.4867 q^{59} +(2.81679 + 2.81679i) q^{60} +(13.1414 + 13.1414i) q^{61} -17.9887i q^{62} +6.86658i q^{63} -59.8122i q^{64} +36.2214 q^{65} +(-155.607 + 155.607i) q^{66} -17.8272i q^{67} +(1.49763 - 1.49763i) q^{68} +(60.4635 + 60.4635i) q^{69} +(-1.56671 + 1.56671i) q^{70} +53.0072i q^{71} +(-109.900 - 109.900i) q^{72} +(5.93089 - 5.93089i) q^{73} -70.4647 q^{74} +(57.5859 + 57.5859i) q^{75} +(1.43718 - 1.43718i) q^{76} +(-4.80160 - 4.80160i) q^{77} +127.754 q^{78} +(-81.6782 - 81.6782i) q^{79} -53.1064i q^{80} -140.843 q^{81} +101.726 q^{82} -77.1462 q^{83} +(-0.306565 + 0.306565i) q^{84} +(-20.0488 + 20.0488i) q^{85} +46.5381i q^{86} +(46.4812 + 149.259i) q^{87} +153.699 q^{88} +(27.4315 + 27.4315i) q^{89} +(-91.8082 - 91.8082i) q^{90} +3.94215i q^{91} +3.72680i q^{92} +47.1215i q^{93} -22.0498 q^{94} +(-19.2396 + 19.2396i) q^{95} -20.2387i q^{96} +(48.7308 - 48.7308i) q^{97} +(71.1320 + 71.1320i) q^{98} +(281.370 - 281.370i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8	$ 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8} + 6 q^{10} - 6 q^{11} + 54 q^{12} - 40 q^{14} - 10 q^{15} - 32 q^{16} + 12 q^{17} + 20 q^{18} - 16 q^{19} + 108 q^{20} - 36 q^{21} + 168 q^{24} + 104 q^{25} - 54 q^{26} - 98 q^{27} + 128 q^{29} - 220 q^{30} - 10 q^{31} - 106 q^{32} - 252 q^{36} - 84 q^{37} - 90 q^{39} + 226 q^{40} + 20 q^{41} - 190 q^{43} + 42 q^{44} + 292 q^{45} + 12 q^{46} + 58 q^{47} + 354 q^{48} - 72 q^{49} - 60 q^{50} - 144 q^{52} + 252 q^{53} + 400 q^{54} - 74 q^{55} - 192 q^{56} + 326 q^{58} - 40 q^{59} - 258 q^{60} - 208 q^{61} + 36 q^{65} - 414 q^{66} - 296 q^{68} + 120 q^{69} + 44 q^{70} - 636 q^{72} - 188 q^{73} - 64 q^{74} - 12 q^{75} + 592 q^{76} + 180 q^{77} + 600 q^{78} - 382 q^{79} - 124 q^{81} + 228 q^{82} + 280 q^{83} - 124 q^{84} + 32 q^{85} + 34 q^{87} + 20 q^{88} - 64 q^{89} + 128 q^{90} - 460 q^{94} - 380 q^{95} - 44 q^{97} - 66 q^{98} + 552 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8 + 6 * q^10 - 6 * q^11 + 54 * q^12 - 40 * q^14 - 10 * q^15 - 32 * q^16 + 12 * q^17 + 20 * q^18 - 16 * q^19 + 108 * q^20 - 36 * q^21 + 168 * q^24 + 104 * q^25 - 54 * q^26 - 98 * q^27 + 128 * q^29 - 220 * q^30 - 10 * q^31 - 106 * q^32 - 252 * q^36 - 84 * q^37 - 90 * q^39 + 226 * q^40 + 20 * q^41 - 190 * q^43 + 42 * q^44 + 292 * q^45 + 12 * q^46 + 58 * q^47 + 354 * q^48 - 72 * q^49 - 60 * q^50 - 144 * q^52 + 252 * q^53 + 400 * q^54 - 74 * q^55 - 192 * q^56 + 326 * q^58 - 40 * q^59 - 258 * q^60 - 208 * q^61 + 36 * q^65 - 414 * q^66 - 296 * q^68 + 120 * q^69 + 44 * q^70 - 636 * q^72 - 188 * q^73 - 64 * q^74 - 12 * q^75 + 592 * q^76 + 180 * q^77 + 600 * q^78 - 382 * q^79 - 124 * q^81 + 228 * q^82 + 280 * q^83 - 124 * q^84 + 32 * q^85 + 34 * q^87 + 20 * q^88 - 64 * q^89 + 128 * q^90 - 460 * q^94 - 380 * q^95 - 44 * q^97 - 66 * q^98 + 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.45515	−	1.45515i	−0.727577	−	0.727577i	0.242559	−	0.970137i	$-0.422013\pi$
$2$	−1.45515	−	1.45515i	−0.727577	−	0.727577i	−0.970137	+	0.242559i	$0.922013\pi$
$3$	3.81178	+	3.81178i	1.27059	+	1.27059i	0.945777	+	0.324816i	$0.105302\pi$
$3$	3.81178	+	3.81178i	1.27059	+	1.27059i	0.324816	+	0.945777i	$0.394698\pi$
$4$			0.234947i			0.0587369i
$5$		−	3.14526i		−	0.629051i	−0.949249	−	0.314526i	$-0.898155\pi$
$5$		−	3.14526i		−	0.629051i	0.949249	−	0.314526i	$-0.101845\pi$
$6$		−	11.0935i		−	1.84891i
$7$	0.342313			0.0489019			0.0244510	−	0.999701i	$-0.492216\pi$
$7$	0.342313			0.0489019			0.0244510	+	0.999701i	$0.492216\pi$
$8$	−5.47873	+	5.47873i	−0.684842	+	0.684842i
$9$			20.0593i			2.22881i
$10$	−4.57683	+	4.57683i	−0.457683	+	0.457683i
$11$	−14.0269	−	14.0269i	−1.27517	−	1.27517i	−0.943337	−	0.331837i	$-0.892332\pi$
$11$	−14.0269	−	14.0269i	−1.27517	−	1.27517i	−0.331837	−	0.943337i	$-0.607668\pi$
$12$	−0.895568	+	0.895568i	−0.0746306	+	0.0746306i
$13$			11.5162i			0.885861i	0.896556	+	0.442931i	$0.146061\pi$
$13$			11.5162i			0.885861i	−0.896556	+	0.442931i	$0.853939\pi$
$14$	−0.498119	−	0.498119i	−0.0355799	−	0.0355799i
$15$	11.9890	−	11.9890i	0.799268	−	0.799268i
$16$	16.8846			1.05529
$17$	−6.37430	−	6.37430i	−0.374959	−	0.374959i	0.494321	−	0.869280i	$-0.335417\pi$
$17$	−6.37430	−	6.37430i	−0.374959	−	0.374959i	−0.869280	+	0.494321i	$0.835417\pi$
$18$	29.1894	−	29.1894i	1.62163	−	1.62163i
$19$	−6.11703	−	6.11703i	−0.321949	−	0.321949i	0.527565	−	0.849514i	$-0.323105\pi$
$19$	−6.11703	−	6.11703i	−0.321949	−	0.321949i	−0.849514	+	0.527565i	$0.823105\pi$
$20$	0.738970			0.0369485
$21$	1.30482	+	1.30482i	0.0621345	+	0.0621345i
$22$			40.8226i			1.85557i
$23$	15.8623			0.689664			0.344832	−	0.938664i	$-0.387936\pi$
$23$	15.8623			0.689664			0.344832	+	0.938664i	$0.387936\pi$
$24$	−41.7674			−1.74031
$25$	15.1074			0.604295
$26$	16.7578	−	16.7578i	0.644532	−	0.644532i
$27$	−42.1557	+	42.1557i	−1.56132	+	1.56132i
$28$			0.0804257i			0.00287235i
$29$	25.6758	+	13.4817i	0.885371	+	0.464885i
$29$	25.6758	+	13.4817i	0.885371	+	0.464885i
$30$	−34.8918			−1.16306
$31$	6.18103	+	6.18103i	0.199388	+	0.199388i	0.799738	−	0.600350i	$-0.204972\pi$
$31$	6.18103	+	6.18103i	0.199388	+	0.199388i	−0.600350	+	0.799738i	$0.704972\pi$
$32$	−2.65475	−	2.65475i	−0.0829610	−	0.0829610i
$33$		−	106.935i		−	3.24045i
$34$			18.5512i			0.545623i
$35$		−	1.07666i		−	0.0307618i
$36$	−4.71289			−0.130914
$37$	24.2121	−	24.2121i	0.654381	−	0.654381i	−0.299664	−	0.954045i	$-0.596874\pi$
$37$	24.2121	−	24.2121i	0.654381	−	0.654381i	0.954045	+	0.299664i	$0.0968745\pi$
$38$			17.8024i			0.468485i
$39$	−43.8972	+	43.8972i	−1.12557	+	1.12557i
$40$	17.2320	+	17.2320i	0.430800	+	0.430800i
$41$	−34.9536	+	34.9536i	−0.852526	+	0.852526i	−0.990444	−	0.137917i	$-0.955959\pi$
$41$	−34.9536	+	34.9536i	−0.852526	+	0.852526i	0.137917	+	0.990444i	$0.455959\pi$
$42$		−	3.79744i		−	0.0904152i
$43$	−15.9908	−	15.9908i	−0.371878	−	0.371878i	0.496283	−	0.868161i	$-0.334698\pi$
$43$	−15.9908	−	15.9908i	−0.371878	−	0.371878i	−0.868161	+	0.496283i	$0.834698\pi$
$44$	3.29559	−	3.29559i	0.0748997	−	0.0748997i
$45$	63.0917			1.40204
$46$	−23.0820	−	23.0820i	−0.501784	−	0.501784i
$47$	7.57643	−	7.57643i	0.161201	−	0.161201i	−0.621898	−	0.783098i	$-0.713638\pi$
$47$	7.57643	−	7.57643i	0.161201	−	0.161201i	0.783098	+	0.621898i	$0.213638\pi$
$48$	64.3603	+	64.3603i	1.34084	+	1.34084i
$49$	−48.8828			−0.997609
$50$	−21.9835	−	21.9835i	−0.439671	−	0.439671i
$51$		−	48.5949i		−	0.952840i
$52$	−2.70570			−0.0520327
$53$	62.1991			1.17357			0.586784	−	0.809743i	$-0.300394\pi$
$53$	62.1991			1.17357			0.586784	+	0.809743i	$0.300394\pi$
$54$	122.686			2.27197
$55$	−44.1182	+	44.1182i	−0.802150	+	0.802150i
$56$	−1.87544	+	1.87544i	−0.0334901	+	0.0334901i
$57$		−	46.6336i		−	0.818133i
$58$	−17.7443	−	56.9801i	−0.305936	−	0.982415i
$59$	−21.4867			−0.364182			−0.182091	−	0.983282i	$-0.558287\pi$
$59$	−21.4867			−0.364182			−0.182091	+	0.983282i	$0.558287\pi$
$60$	2.81679	+	2.81679i	0.0469465	+	0.0469465i
$61$	13.1414	+	13.1414i	0.215432	+	0.215432i	0.806570	−	0.591138i	$-0.201321\pi$
$61$	13.1414	+	13.1414i	0.215432	+	0.215432i	−0.591138	+	0.806570i	$0.701321\pi$
$62$		−	17.9887i		−	0.290141i
$63$			6.86658i			0.108993i
$64$		−	59.8122i		−	0.934566i
$65$	36.2214			0.557252
$66$	−155.607	+	155.607i	−2.35768	+	2.35768i
$67$		−	17.8272i		−	0.266078i	−0.991111	−	0.133039i	$-0.957526\pi$
$67$		−	17.8272i		−	0.266078i	0.991111	−	0.133039i	$-0.0424736\pi$
$68$	1.49763	−	1.49763i	0.0220239	−	0.0220239i
$69$	60.4635	+	60.4635i	0.876282	+	0.876282i
$70$	−1.56671	+	1.56671i	−0.0223816	+	0.0223816i
$71$			53.0072i			0.746580i	0.927715	+	0.373290i	$0.121770\pi$
$71$			53.0072i			0.746580i	−0.927715	+	0.373290i	$0.878230\pi$
$72$	−109.900	−	109.900i	−1.52638	−	1.52638i
$73$	5.93089	−	5.93089i	0.0812450	−	0.0812450i	−0.665316	−	0.746561i	$-0.731703\pi$
$73$	5.93089	−	5.93089i	0.0812450	−	0.0812450i	0.746561	+	0.665316i	$0.231703\pi$
$74$	−70.4647			−0.952226
$75$	57.5859	+	57.5859i	0.767813	+	0.767813i
$76$	1.43718	−	1.43718i	0.0189103	−	0.0189103i
$77$	−4.80160	−	4.80160i	−0.0623584	−	0.0623584i
$78$	127.754			1.63788
$79$	−81.6782	−	81.6782i	−1.03390	−	1.03390i	−0.999405	−	0.0344966i	$-0.989017\pi$
$79$	−81.6782	−	81.6782i	−1.03390	−	1.03390i	−0.0344966	−	0.999405i	$-0.510983\pi$
$80$		−	53.1064i		−	0.663829i
$81$	−140.843			−1.73880
$82$	101.726			1.24056
$83$	−77.1462			−0.929472			−0.464736	−	0.885449i	$-0.653851\pi$
$83$	−77.1462			−0.929472			−0.464736	+	0.885449i	$0.653851\pi$
$84$	−0.306565	+	0.306565i	−0.00364958	+	0.00364958i
$85$	−20.0488	+	20.0488i	−0.235868	+	0.235868i
$86$			46.5381i			0.541140i
$87$	46.4812	+	149.259i	0.534267	+	1.71563i
$88$	153.699			1.74658
$89$	27.4315	+	27.4315i	0.308219	+	0.308219i	0.844218	−	0.535999i	$-0.180065\pi$
$89$	27.4315	+	27.4315i	0.308219	+	0.308219i	−0.535999	+	0.844218i	$0.680065\pi$
$90$	−91.8082	−	91.8082i	−1.02009	−	1.02009i
$91$			3.94215i			0.0433203i
$92$			3.72680i			0.0405087i
$93$			47.1215i			0.506683i
$94$	−22.0498			−0.234572
$95$	−19.2396	+	19.2396i	−0.202522	+	0.202522i
$96$		−	20.2387i		−	0.210819i
$97$	48.7308	−	48.7308i	0.502379	−	0.502379i	−0.409797	−	0.912177i	$-0.634401\pi$
$97$	48.7308	−	48.7308i	0.502379	−	0.502379i	0.912177	+	0.409797i	$0.134401\pi$
$98$	71.1320	+	71.1320i	0.725837	+	0.725837i
$99$	281.370	−	281.370i	2.84213	−	2.84213i
$100$			3.54944i			0.0354944i
$101$	−36.0686	−	36.0686i	−0.357115	−	0.357115i	0.505633	−	0.862748i	$-0.331259\pi$
$101$	−36.0686	−	36.0686i	−0.357115	−	0.357115i	−0.862748	+	0.505633i	$0.831259\pi$
$102$	−70.7130	+	70.7130i	−0.693265	+	0.693265i
$103$	−38.7846			−0.376549			−0.188275	−	0.982116i	$-0.560289\pi$
$103$	−38.7846			−0.376549			−0.188275	+	0.982116i	$0.560289\pi$
$104$	−63.0941	−	63.0941i	−0.606674	−	0.606674i
$105$	4.10400	−	4.10400i	0.0390857	−	0.0390857i
$106$	−90.5093	−	90.5093i	−0.853861	−	0.853861i
$107$	100.580			0.940004			0.470002	−	0.882665i	$-0.344253\pi$
$107$	100.580			0.940004			0.470002	+	0.882665i	$0.344253\pi$
$108$	−9.90438	−	9.90438i	−0.0917072	−	0.0917072i
$109$			43.4896i			0.398988i	0.979899	+	0.199494i	$0.0639298\pi$
$109$			43.4896i			0.398988i	−0.979899	+	0.199494i	$0.936070\pi$
$110$	128.398			1.16725
$111$	184.582			1.66290
$112$	5.77982			0.0516056
$113$	−106.279	+	106.279i	−0.940525	+	0.940525i	−0.998328	−	0.0578028i	$-0.981591\pi$
$113$	−106.279	+	106.279i	−0.940525	+	0.940525i	0.0578028	+	0.998328i	$0.481591\pi$
$114$	−67.8590	+	67.8590i	−0.595254	+	0.595254i
$115$		−	49.8909i		−	0.433834i
$116$	−3.16748	+	6.03245i	−0.0273059	+	0.0520039i
$117$	−231.007			−1.97442
$118$	31.2665	+	31.2665i	0.264970	+	0.264970i
$119$	−2.18201	−	2.18201i	−0.0183362	−	0.0183362i
$120$			131.369i			1.09474i
$121$			272.508i			2.25214i
$122$		−	38.2454i		−	0.313487i
$123$	−266.471			−2.16643
$124$	−1.45222	+	1.45222i	−0.0117114	+	0.0117114i
$125$		−	126.148i		−	1.00918i
$126$	9.99193	−	9.99193i	0.0793010	−	0.0793010i
$127$	−43.0879	−	43.0879i	−0.339275	−	0.339275i	0.516820	−	0.856094i	$-0.327116\pi$
$127$	−43.0879	−	43.0879i	−0.339275	−	0.339275i	−0.856094	+	0.516820i	$0.827116\pi$
$128$	−97.6550	+	97.6550i	−0.762930	+	0.762930i
$129$		−	121.907i		−	0.945012i
$130$	−52.7077	−	52.7077i	−0.405444	−	0.405444i
$131$	21.6703	−	21.6703i	0.165422	−	0.165422i	−0.619542	−	0.784964i	$-0.712682\pi$
$131$	21.6703	−	21.6703i	0.165422	−	0.165422i	0.784964	+	0.619542i	$0.212682\pi$
$132$	25.1241			0.190334
$133$	−2.09394	−	2.09394i	−0.0157439	−	0.0157439i
$134$	−25.9414	+	25.9414i	−0.193592	+	0.193592i
$135$	132.591	+	132.591i	0.982152	+	0.982152i
$136$	69.8462			0.513575
$137$	64.9871	+	64.9871i	0.474359	+	0.474359i	0.903322	−	0.428963i	$-0.141121\pi$
$137$	64.9871	+	64.9871i	0.474359	+	0.474359i	−0.428963	+	0.903322i	$0.641121\pi$
$138$		−	175.967i		−	1.27513i
$139$	−73.6837			−0.530099			−0.265049	−	0.964235i	$-0.585388\pi$
$139$	−73.6837			−0.530099			−0.265049	+	0.964235i	$0.585388\pi$
$140$	0.252959			0.00180685
$141$	57.7594			0.409641
$142$	77.1336	−	77.1336i	0.543195	−	0.543195i
$143$	161.537	−	161.537i	1.12963	−	1.12963i
$144$			338.693i			2.35204i
$145$	42.4033	−	80.7568i	0.292436	−	0.556944i
$146$	−17.2607			−0.118224
$147$	−186.331	−	186.331i	−1.26755	−	1.26755i
$148$	5.68857	+	5.68857i	0.0384363	+	0.0384363i
$149$		−	94.7514i		−	0.635915i	−0.948105	−	0.317958i	$-0.897003\pi$
$149$		−	94.7514i		−	0.635915i	0.948105	−	0.317958i	$-0.102997\pi$
$150$		−	167.593i		−	1.11729i
$151$		−	174.343i		−	1.15459i	−0.816537	−	0.577293i	$-0.804109\pi$
$151$		−	174.343i		−	1.15459i	0.816537	−	0.577293i	$-0.195891\pi$
$152$	67.0272			0.440968
$153$	127.864	−	127.864i	0.835713	−	0.835713i
$154$			13.9741i			0.0907412i
$155$	19.4409	−	19.4409i	0.125425	−	0.125425i
$156$	−10.3135	−	10.3135i	−0.0661124	−	0.0661124i
$157$	−204.862	+	204.862i	−1.30486	+	1.30486i	−0.379777	+	0.925078i	$0.623999\pi$
$157$	−204.862	+	204.862i	−1.30486	+	1.30486i	−0.925078	+	0.379777i	$0.876001\pi$
$158$			237.709i			1.50449i
$159$	237.089	+	237.089i	1.49113	+	1.49113i
$160$	−8.34988	+	8.34988i	−0.0521867	+	0.0521867i
$161$	5.42987			0.0337259
$162$	204.948	+	204.948i	1.26511	+	1.26511i
$163$	−128.935	+	128.935i	−0.791012	+	0.791012i	−0.981659	−	0.190647i	$-0.938942\pi$
$163$	−128.935	+	128.935i	−0.791012	+	0.791012i	0.190647	+	0.981659i	$0.438942\pi$
$164$	−8.21225	−	8.21225i	−0.0500747	−	0.0500747i
$165$	−336.338			−2.03841
$166$	112.260	+	112.260i	0.676263	+	0.676263i
$167$			266.891i			1.59815i	0.601230	+	0.799076i	$0.294678\pi$
$167$			266.891i			1.59815i	−0.601230	+	0.799076i	$0.705322\pi$
$168$	−14.2976			−0.0851045
$169$	36.3773			0.215250
$170$	58.3482			0.343225
$171$	122.704	−	122.704i	0.717565	−	0.717565i
$172$	3.75699	−	3.75699i	0.0218430	−	0.0218430i
$173$		−	264.180i		−	1.52705i	−0.645779	−	0.763525i	$-0.723467\pi$
$173$		−	264.180i		−	1.52705i	0.645779	−	0.763525i	$-0.276533\pi$
$174$	149.558	−	284.833i	0.859530	−	1.63697i
$175$	5.17145			0.0295512
$176$	−236.839	−	236.839i	−1.34567	−	1.34567i
$177$	−81.9027	−	81.9027i	−0.462727	−	0.462727i
$178$		−	79.8341i		−	0.448506i
$179$		−	79.9849i		−	0.446843i	−0.974722	−	0.223421i	$-0.928277\pi$
$179$		−	79.9849i		−	0.446843i	0.974722	−	0.223421i	$-0.0717226\pi$
$180$			14.8232i			0.0823513i
$181$	116.758			0.645074			0.322537	−	0.946557i	$-0.395464\pi$
$181$	116.758			0.645074			0.322537	+	0.946557i	$0.395464\pi$
$182$	5.73643	−	5.73643i	0.0315189	−	0.0315189i
$183$			100.184i			0.547454i
$184$	−86.9051	+	86.9051i	−0.472310	+	0.472310i
$185$	−76.1533	−	76.1533i	−0.411639	−	0.411639i
$186$	68.5690	−	68.5690i	0.368651	−	0.368651i
$187$			178.823i			0.956275i
$188$	1.78006	+	1.78006i	0.00946842	+	0.00946842i
$189$	−14.4305	+	14.4305i	−0.0763517	+	0.0763517i
$190$	55.9933			0.294701
$191$	−60.0672	−	60.0672i	−0.314488	−	0.314488i	0.532157	−	0.846645i	$-0.321381\pi$
$191$	−60.0672	−	60.0672i	−0.314488	−	0.314488i	−0.846645	+	0.532157i	$0.821381\pi$
$192$	227.991	−	227.991i	1.18745	−	1.18745i
$193$	155.411	+	155.411i	0.805241	+	0.805241i	0.983909	−	0.178669i	$-0.0571790\pi$
$193$	155.411	+	155.411i	0.805241	+	0.805241i	−0.178669	+	0.983909i	$0.557179\pi$
$194$	−141.822			−0.731039
$195$	138.068	+	138.068i	0.708040	+	0.708040i
$196$		−	11.4849i		−	0.0585964i
$197$	127.935			0.649415			0.324708	−	0.945814i	$-0.394734\pi$
$197$	127.935			0.649415			0.324708	+	0.945814i	$0.394734\pi$
$198$	−818.875			−4.13573
$199$	−365.503			−1.83670			−0.918349	−	0.395772i	$-0.870477\pi$
$199$	−365.503			−1.83670			−0.918349	+	0.395772i	$0.870477\pi$
$200$	−82.7692	+	82.7692i	−0.413846	+	0.413846i
$201$	67.9535	−	67.9535i	0.338077	−	0.338077i
$202$			104.971i			0.519657i
$203$	8.78916	+	4.61496i	0.0432963	+	0.0227338i
$204$	11.4172			0.0559668
$205$	109.938	+	109.938i	0.536283	+	0.536283i
$206$	56.4375	+	56.4375i	0.273969	+	0.273969i
$207$			318.186i			1.53713i
$208$			194.446i			0.934837i
$209$			171.606i			0.821082i
$210$	−11.9439			−0.0568758
$211$	235.633	−	235.633i	1.11674	−	1.11674i	0.124527	−	0.992216i	$-0.460259\pi$
$211$	235.633	−	235.633i	1.11674	−	1.11674i	0.992216	−	0.124527i	$-0.0397415\pi$
$212$			14.6135i			0.0689317i
$213$	−202.052	+	202.052i	−0.948600	+	0.948600i
$214$	−146.360	−	146.360i	−0.683925	−	0.683925i
$215$	−50.2950	+	50.2950i	−0.233930	+	0.233930i
$216$		−	461.920i		−	2.13852i
$217$	2.11585	+	2.11585i	0.00975047	+	0.00975047i
$218$	63.2841	−	63.2841i	0.290294	−	0.290294i
$219$	45.2145			0.206459
$220$	−10.3655	−	10.3655i	−0.0471157	−	0.0471157i
$221$	73.4077	−	73.4077i	0.332161	−	0.332161i
$222$	−268.596	−	268.596i	−1.20989	−	1.20989i
$223$	404.109			1.81215			0.906074	−	0.423119i	$-0.139065\pi$
$223$	404.109			1.81215			0.906074	+	0.423119i	$0.139065\pi$
$224$	−0.908758	−	0.908758i	−0.00405695	−	0.00405695i
$225$			303.044i			1.34686i
$226$	309.306			1.36861
$227$	12.2558			0.0539905			0.0269952	−	0.999636i	$-0.491406\pi$
$227$	12.2558			0.0539905			0.0269952	+	0.999636i	$0.491406\pi$
$228$	10.9564			0.0480545
$229$	207.308	−	207.308i	0.905275	−	0.905275i	−0.0906117	−	0.995886i	$-0.528882\pi$
$229$	207.308	−	207.308i	0.905275	−	0.905275i	0.995886	+	0.0906117i	$0.0288822\pi$
$230$	−72.5989	+	72.5989i	−0.315648	+	0.315648i
$231$		−	36.6053i		−	0.158464i
$232$	−214.533	+	66.8082i	−0.924711	+	0.287966i
$233$	240.593			1.03259			0.516293	−	0.856412i	$-0.327311\pi$
$233$	240.593			1.03259			0.516293	+	0.856412i	$0.327311\pi$
$234$	336.151	+	336.151i	1.43654	+	1.43654i
$235$	−23.8298	−	23.8298i	−0.101403	−	0.101403i
$236$		−	5.04825i		−	0.0213909i
$237$		−	622.679i		−	2.62734i
$238$			6.35032i			0.0266820i
$239$	−265.870			−1.11243			−0.556213	−	0.831040i	$-0.687746\pi$
$239$	−265.870			−1.11243			−0.556213	+	0.831040i	$0.687746\pi$
$240$	202.430	−	202.430i	0.843457	−	0.843457i
$241$			423.682i			1.75802i	0.476806	+	0.879008i	$0.341794\pi$
$241$			423.682i			1.75802i	−0.476806	+	0.879008i	$0.658206\pi$
$242$	396.542	−	396.542i	1.63860	−	1.63860i
$243$	−157.460	−	157.460i	−0.647982	−	0.647982i
$244$	−3.08753	+	3.08753i	−0.0126538	+	0.0126538i
$245$			153.749i			0.627547i
$246$	387.756	+	387.756i	1.57624	+	1.57624i
$247$	70.4449	−	70.4449i	0.285202	−	0.285202i
$248$	−67.7285			−0.273099
$249$	−294.064	−	294.064i	−1.18098	−	1.18098i
$250$	−183.565	+	183.565i	−0.734259	+	0.734259i
$251$	−211.437	−	211.437i	−0.842379	−	0.842379i	0.146789	−	0.989168i	$-0.453106\pi$
$251$	−211.437	−	211.437i	−0.842379	−	0.842379i	−0.989168	+	0.146789i	$0.953106\pi$
$252$	−1.61328			−0.00640192
$253$	−222.499	−	222.499i	−0.879441	−	0.879441i
$254$			125.399i			0.493697i
$255$	−152.843			−0.599385
$256$	44.9573			0.175615
$257$	158.690			0.617471			0.308735	−	0.951148i	$-0.400094\pi$
$257$	158.690			0.617471			0.308735	+	0.951148i	$0.400094\pi$
$258$	−177.393	+	177.393i	−0.687569	+	0.687569i
$259$	8.28813	−	8.28813i	0.0320005	−	0.0320005i
$260$			8.51012i			0.0327312i
$261$	−270.433	+	515.038i	−1.03614	+	1.97333i
$262$	−63.0671			−0.240714
$263$	40.2518	+	40.2518i	0.153049	+	0.153049i	0.779478	−	0.626429i	$-0.215484\pi$
$263$	40.2518	+	40.2518i	0.153049	+	0.153049i	−0.626429	+	0.779478i	$0.715484\pi$
$264$	585.868	+	585.868i	2.21920	+	2.21920i
$265$		−	195.632i		−	0.738234i
$266$			6.09402i			0.0229098i
$267$			209.126i			0.783242i
$268$	4.18846			0.0156286
$269$	−141.040	+	141.040i	−0.524311	+	0.524311i	−0.918870	−	0.394559i	$-0.870897\pi$
$269$	−141.040	+	141.040i	−0.524311	+	0.524311i	0.394559	+	0.918870i	$0.370897\pi$
$270$		−	385.879i		−	1.42918i
$271$	24.3687	−	24.3687i	0.0899215	−	0.0899215i	−0.660715	−	0.750637i	$-0.729747\pi$
$271$	24.3687	−	24.3687i	0.0899215	−	0.0899215i	0.750637	+	0.660715i	$0.229747\pi$
$272$	−107.627	−	107.627i	−0.395689	−	0.395689i
$273$	−15.0266	+	15.0266i	−0.0550425	+	0.0550425i
$274$		−	189.133i		−	0.690265i
$275$	−211.910	−	211.910i	−0.770581	−	0.770581i
$276$	−14.2057	+	14.2057i	−0.0514701	+	0.0514701i
$277$	57.9976			0.209378			0.104689	−	0.994505i	$-0.466615\pi$
$277$	57.9976			0.209378			0.104689	+	0.994505i	$0.466615\pi$
$278$	107.221	+	107.221i	0.385688	+	0.385688i
$279$	−123.987	+	123.987i	−0.444399	+	0.444399i
$280$	5.89875	+	5.89875i	0.0210670	+	0.0210670i
$281$	−352.000			−1.25267			−0.626334	−	0.779554i	$-0.715446\pi$
$281$	−352.000			−1.25267			−0.626334	+	0.779554i	$0.715446\pi$
$282$	−84.0488	−	84.0488i	−0.298045	−	0.298045i
$283$		−	446.547i		−	1.57790i	−0.614455	−	0.788952i	$-0.710624\pi$
$283$		−	446.547i		−	1.57790i	0.614455	−	0.788952i	$-0.289376\pi$
$284$	−12.4539			−0.0438518
$285$	−146.674			−0.514647
$286$	−470.121			−1.64378
$287$	−11.9651	+	11.9651i	−0.0416902	+	0.0416902i
$288$	53.2526	−	53.2526i	0.184905	−	0.184905i
$289$		−	207.737i		−	0.718812i
$290$	−179.217	+	55.8103i	−0.617990	+	0.192449i
$291$	371.502			1.27664
$292$	1.39345	+	1.39345i	0.00477208	+	0.00477208i
$293$	14.9522	+	14.9522i	0.0510313	+	0.0510313i	0.732162	−	0.681131i	$-0.238511\pi$
$293$	14.9522	+	14.9522i	0.0510313	+	0.0510313i	−0.681131	+	0.732162i	$0.738511\pi$
$294$			542.279i			1.84449i
$295$			67.5813i			0.229089i
$296$			265.303i			0.896295i
$297$	1182.63			3.98192
$298$	−137.878	+	137.878i	−0.462677	+	0.462677i
$299$			182.673i			0.610946i
$300$	−13.5297	+	13.5297i	−0.0450989	+	0.0450989i
$301$	−5.47385	−	5.47385i	−0.0181856	−	0.0181856i
$302$	−253.695	+	253.695i	−0.840051	+	0.840051i
$303$		−	274.971i		−	0.907496i
$304$	−103.284	−	103.284i	−0.339749	−	0.339749i
$305$	41.3330	−	41.3330i	0.135518	−	0.135518i
$306$	−372.124			−1.21609
$307$	10.2622	+	10.2622i	0.0334274	+	0.0334274i	0.723623	−	0.690196i	$-0.242475\pi$
$307$	10.2622	+	10.2622i	0.0334274	+	0.0334274i	−0.690196	+	0.723623i	$0.742475\pi$
$308$	1.12812	−	1.12812i	0.00366274	−	0.00366274i
$309$	−147.838	−	147.838i	−0.478441	−	0.478441i
$310$	−56.5791			−0.182513
$311$	325.442	+	325.442i	1.04644	+	1.04644i	0.998868	+	0.0475694i	$0.0151475\pi$
$311$	325.442	+	325.442i	1.04644	+	1.04644i	0.0475694	+	0.998868i	$0.484852\pi$
$312$		−	481.002i		−	1.54167i
$313$	−279.640			−0.893417			−0.446709	−	0.894680i	$-0.647404\pi$
$313$	−279.640			−0.893417			−0.446709	+	0.894680i	$0.647404\pi$
$314$	596.212			1.89877
$315$	21.5971			0.0685624
$316$	19.1901	−	19.1901i	0.0607281	−	0.0607281i
$317$	195.785	−	195.785i	0.617619	−	0.617619i	−0.327301	−	0.944920i	$-0.606139\pi$
$317$	195.785	−	195.785i	0.617619	−	0.617619i	0.944920	+	0.327301i	$0.106139\pi$
$318$		−	690.003i		−	2.16982i
$319$	−171.045	−	549.258i	−0.536193	−	1.72181i
$320$	−188.125			−0.587890
$321$	383.390	+	383.390i	1.19436	+	1.19436i
$322$	−7.90130	−	7.90130i	−0.0245382	−	0.0245382i
$323$			77.9836i			0.241435i
$324$		−	33.0906i		−	0.102132i
$325$			173.979i			0.535321i
$326$	375.241			1.15104
$327$	−165.773	+	165.773i	−0.506951	+	0.506951i
$328$		−	383.003i		−	1.16769i
$329$	2.59351	−	2.59351i	0.00788302	−	0.00788302i
$330$	489.423	+	489.423i	1.48310	+	1.48310i
$331$	177.780	−	177.780i	0.537100	−	0.537100i	−0.385576	−	0.922676i	$-0.625997\pi$
$331$	177.780	−	177.780i	0.537100	−	0.537100i	0.922676	+	0.385576i	$0.125997\pi$
$332$		−	18.1253i		−	0.0545943i
$333$	485.679	+	485.679i	1.45849	+	1.45849i
$334$	388.368	−	388.368i	1.16278	−	1.16278i
$335$	−56.0712			−0.167377
$336$	22.0314	+	22.0314i	0.0655697	+	0.0655697i
$337$	−312.630	+	312.630i	−0.927686	+	0.927686i	−0.997556	−	0.0698697i	$-0.977742\pi$
$337$	−312.630	+	312.630i	−0.927686	+	0.927686i	0.0698697	+	0.997556i	$0.477742\pi$
$338$	−52.9346	−	52.9346i	−0.156611	−	0.156611i
$339$	−810.227			−2.39005
$340$	−4.71041	−	4.71041i	−0.0138542	−	0.0138542i
$341$		−	173.402i		−	0.508509i
$342$	−357.105			−1.04417
$343$	−33.5066			−0.0976869
$344$	175.218			0.509355
$345$	190.173	−	190.173i	0.551226	−	0.551226i
$346$	−384.422	+	384.422i	−1.11105	+	1.11105i
$347$			307.039i			0.884840i	0.896808	+	0.442420i	$0.145880\pi$
$347$			307.039i			0.884840i	−0.896808	+	0.442420i	$0.854120\pi$
$348$	−35.0681	+	10.9206i	−0.100770	+	0.0313811i
$349$	463.827			1.32902			0.664509	−	0.747280i	$-0.268641\pi$
$349$	463.827			1.32902			0.664509	+	0.747280i	$0.268641\pi$
$350$	−7.52526	−	7.52526i	−0.0215008	−	0.0215008i
$351$	−485.473	−	485.473i	−1.38311	−	1.38311i
$352$			74.4760i			0.211579i
$353$		−	322.072i		−	0.912385i	−0.889881	−	0.456192i	$-0.849213\pi$
$353$		−	322.072i		−	0.912385i	0.889881	−	0.456192i	$-0.150787\pi$
$354$			238.362i			0.673339i
$355$	166.721			0.469637
$356$	−6.44496	+	6.44496i	−0.0181038	+	0.0181038i
$357$		−	16.6347i		−	0.0465957i
$358$	−116.390	+	116.390i	−0.325113	+	0.325113i
$359$	410.933	+	410.933i	1.14466	+	1.14466i	0.987587	+	0.157072i	$0.0502055\pi$
$359$	410.933	+	410.933i	1.14466	+	1.14466i	0.157072	+	0.987587i	$0.449795\pi$
$360$	−345.663	+	345.663i	−0.960174	+	0.960174i
$361$		−	286.164i		−	0.792698i
$362$	−169.902	−	169.902i	−0.469341	−	0.469341i
$363$	−1038.74	+	1038.74i	−2.86155	+	2.86155i
$364$	−0.926197			−0.00254450
$365$	−18.6542	−	18.6542i	−0.0511073	−	0.0511073i
$366$	145.783	−	145.783i	0.398315	−	0.398315i
$367$	309.094	+	309.094i	0.842218	+	0.842218i	0.989147	−	0.146929i	$-0.0469390\pi$
$367$	309.094	+	309.094i	0.842218	+	0.842218i	−0.146929	+	0.989147i	$0.546939\pi$
$368$	267.828			0.727793
$369$	−701.145	−	701.145i	−1.90012	−	1.90012i
$370$			221.629i			0.598999i
$371$	21.2916			0.0573897
$372$	−11.0711			−0.0297609
$373$	210.646			0.564734			0.282367	−	0.959306i	$-0.408880\pi$
$373$	210.646			0.564734			0.282367	+	0.959306i	$0.408880\pi$
$374$	260.216	−	260.216i	0.695764	−	0.695764i
$375$	480.848	−	480.848i	1.28226	−	1.28226i
$376$			83.0185i			0.220794i
$377$	−155.257	+	295.687i	−0.411824	+	0.784316i
$378$	41.9971			0.111103
$379$	−229.599	−	229.599i	−0.605803	−	0.605803i	0.336043	−	0.941847i	$-0.390911\pi$
$379$	−229.599	−	229.599i	−0.605803	−	0.605803i	−0.941847	+	0.336043i	$0.890911\pi$
$380$	−4.52030	−	4.52030i	−0.0118955	−	0.0118955i
$381$		−	328.483i		−	0.862160i
$382$			174.814i			0.457628i
$383$			248.070i			0.647701i	0.946108	+	0.323851i	$0.104978\pi$
$383$			248.070i			0.647701i	−0.946108	+	0.323851i	$0.895022\pi$
$384$	−744.479			−1.93875
$385$	−15.1023	+	15.1023i	−0.0392267	+	0.0392267i
$386$		−	452.295i		−	1.17175i
$387$	320.764	−	320.764i	0.828847	−	0.828847i
$388$	11.4492	+	11.4492i	0.0295082	+	0.0295082i
$389$	78.1188	−	78.1188i	0.200820	−	0.200820i	−0.599532	−	0.800351i	$-0.704646\pi$
$389$	78.1188	−	78.1188i	0.200820	−	0.200820i	0.800351	+	0.599532i	$0.204646\pi$
$390$		−	401.820i		−	1.03031i
$391$	−101.111	−	101.111i	−0.258596	−	0.258596i
$392$	267.816	−	267.816i	0.683204	−	0.683204i
$393$	165.204			0.420368
$394$	−186.165	−	186.165i	−0.472500	−	0.472500i
$395$	−256.899	+	256.899i	−0.650377	+	0.650377i
$396$	66.1072	+	66.1072i	0.166937	+	0.166937i
$397$	399.382			1.00600			0.503000	−	0.864287i	$-0.332230\pi$
$397$	399.382			1.00600			0.503000	+	0.864287i	$0.332230\pi$
$398$	531.863	+	531.863i	1.33634	+	1.33634i
$399$		−	15.9633i		−	0.0400083i
$400$	255.082			0.637704
$401$	−585.895			−1.46109			−0.730543	−	0.682867i	$-0.760733\pi$
$401$	−585.895			−1.46109			−0.730543	+	0.682867i	$0.760733\pi$
$402$	−197.766			−0.491954
$403$	−71.1820	+	71.1820i	−0.176630	+	0.176630i
$404$	8.47423	−	8.47423i	0.0209758	−	0.0209758i
$405$			442.986i			1.09379i
$406$	−6.07411	−	19.5051i	−0.0149609	−	0.0480420i
$407$	−679.242			−1.66890
$408$	266.238	+	266.238i	0.652545	+	0.652545i
$409$	243.027	+	243.027i	0.594198	+	0.594198i	0.938763	−	0.344564i	$-0.111973\pi$
$409$	243.027	+	243.027i	0.594198	+	0.594198i	−0.344564	+	0.938763i	$0.611973\pi$
$410$		−	319.953i		−	0.780374i
$411$			495.433i			1.20543i
$412$		−	9.11233i		−	0.0221173i
$413$	−7.35520			−0.0178092
$414$	463.010	−	463.010i	1.11838	−	1.11838i
$415$			242.645i			0.584686i
$416$	30.5726	−	30.5726i	0.0734919	−	0.0734919i
$417$	−280.866	−	280.866i	−0.673540	−	0.673540i
$418$	249.713	−	249.713i	0.597400	−	0.597400i
$419$			548.833i			1.30987i	0.755687	+	0.654933i	$0.227303\pi$
$419$			548.833i			1.30987i	−0.755687	+	0.654933i	$0.772697\pi$
$420$	0.964225	+	0.964225i	0.00229577	+	0.00229577i
$421$	−126.907	+	126.907i	−0.301442	+	0.301442i	−0.841578	−	0.540136i	$-0.818373\pi$
$421$	−126.907	+	126.907i	−0.301442	+	0.301442i	0.540136	+	0.841578i	$0.318373\pi$
$422$	−685.764			−1.62503
$423$	151.978	+	151.978i	0.359286	+	0.359286i
$424$	−340.772	+	340.772i	−0.803708	+	0.803708i
$425$	−96.2989	−	96.2989i	−0.226586	−	0.226586i
$426$	588.033			1.38036
$427$	4.49847	+	4.49847i	0.0105351	+	0.0105351i
$428$			23.6311i			0.0552129i
$429$	1231.48			2.87059
$430$	146.374			0.340405
$431$	334.232			0.775480			0.387740	−	0.921769i	$-0.373256\pi$
$431$	334.232			0.775480			0.387740	+	0.921769i	$0.373256\pi$
$432$	−711.782	+	711.782i	−1.64764	+	1.64764i
$433$	−321.593	+	321.593i	−0.742710	+	0.742710i	−0.973099	−	0.230389i	$-0.926000\pi$
$433$	−321.593	+	321.593i	−0.742710	+	0.742710i	0.230389	+	0.973099i	$0.426000\pi$
$434$		−	6.15778i		−	0.0141884i
$435$	469.459	−	146.195i	1.07922	−	0.336081i
$436$	−10.2178			−0.0234353
$437$	−97.0300	−	97.0300i	−0.222037	−	0.222037i
$438$	−65.7940	−	65.7940i	−0.150215	−	0.150215i
$439$			493.002i			1.12301i	0.827473	+	0.561506i	$0.189778\pi$
$439$			493.002i			1.12301i	−0.827473	+	0.561506i	$0.810222\pi$
$440$		−	483.424i		−	1.09869i
$441$		−	980.556i		−	2.22348i
$442$	−213.639			−0.483346
$443$	305.073	−	305.073i	0.688653	−	0.688653i	−0.273281	−	0.961934i	$-0.588109\pi$
$443$	305.073	−	305.073i	0.688653	−	0.688653i	0.961934	+	0.273281i	$0.0881089\pi$
$444$			43.3672i			0.0976738i
$445$	86.2791	−	86.2791i	0.193886	−	0.193886i
$446$	−588.041	−	588.041i	−1.31848	−	1.31848i
$447$	361.171	−	361.171i	0.807990	−	0.807990i
$448$		−	20.4745i		−	0.0457021i
$449$	−604.469	−	604.469i	−1.34626	−	1.34626i	−0.889689	−	0.456567i	$-0.849079\pi$
$449$	−604.469	−	604.469i	−1.34626	−	1.34626i	−0.456567	−	0.889689i	$-0.650921\pi$
$450$	440.975	−	440.975i	0.979945	−	0.979945i
$451$	980.582			2.17424
$452$	−24.9701	−	24.9701i	−0.0552435	−	0.0552435i
$453$	664.556	−	664.556i	1.46701	−	1.46701i
$454$	−17.8341	−	17.8341i	−0.0392822	−	0.0392822i
$455$	12.3991			0.0272507
$456$	255.493	+	255.493i	0.560291	+	0.560291i
$457$			563.383i			1.23278i	0.787439	+	0.616392i	$0.211406\pi$
$457$			563.383i			1.23278i	−0.787439	+	0.616392i	$0.788594\pi$
$458$	−603.330			−1.31731
$459$	537.426			1.17086
$460$	11.7217			0.0254820
$461$	−371.986	+	371.986i	−0.806911	+	0.806911i	−0.984165	−	0.177254i	$-0.943279\pi$
$461$	−371.986	+	371.986i	−0.806911	+	0.806911i	0.177254	+	0.984165i	$0.443279\pi$
$462$	−53.2663	+	53.2663i	−0.115295	+	0.115295i
$463$			13.1023i			0.0282986i	0.999900	+	0.0141493i	$0.00450402\pi$
$463$			13.1023i			0.0282986i	−0.999900	+	0.0141493i	$0.995496\pi$
$464$	433.525	+	227.632i	0.934320	+	0.490587i
$465$	148.209			0.318729
$466$	−350.100	−	350.100i	−0.751287	−	0.751287i
$467$	−192.103	−	192.103i	−0.411356	−	0.411356i	0.470854	−	0.882211i	$-0.343946\pi$
$467$	−192.103	−	192.103i	−0.411356	−	0.411356i	−0.882211	+	0.470854i	$0.843946\pi$
$468$		−	54.2745i		−	0.115971i
$469$		−	6.10250i		−	0.0130117i
$470$			69.3521i			0.147558i
$471$	−1561.78			−3.31588
$472$	117.720	−	117.720i	0.249407	−	0.249407i
$473$			448.602i			0.948419i
$474$	−906.093	+	906.093i	−1.91159	+	1.91159i
$475$	−92.4122	−	92.4122i	−0.194552	−	0.194552i
$476$	0.512657	−	0.512657i	0.00107701	−	0.00107701i
$477$			1247.67i			2.61566i
$478$	386.882	+	386.882i	0.809376	+	0.809376i
$479$	237.779	−	237.779i	0.496407	−	0.496407i	−0.413911	−	0.910317i	$-0.635837\pi$
$479$	237.779	−	237.779i	0.496407	−	0.496407i	0.910317	+	0.413911i	$0.135837\pi$
$480$	−63.6558			−0.132616
$481$	278.831	+	278.831i	0.579691	+	0.579691i
$482$	616.523	−	616.523i	1.27909	−	1.27909i
$483$	20.6975	+	20.6975i	0.0428519	+	0.0428519i
$484$	−64.0252			−0.132283
$485$	−153.271	−	153.271i	−0.316022	−	0.316022i
$486$			458.256i			0.942914i
$487$	−754.182			−1.54863			−0.774314	−	0.632802i	$-0.781905\pi$
$487$	−754.182			−1.54863			−0.774314	+	0.632802i	$0.781905\pi$
$488$	−143.996			−0.295074
$489$	−982.943			−2.01011
$490$	223.728	−	223.728i	0.456589	−	0.456589i
$491$	451.910	−	451.910i	0.920388	−	0.920388i	−0.0766690	−	0.997057i	$-0.524428\pi$
$491$	451.910	−	451.910i	0.920388	−	0.920388i	0.997057	+	0.0766690i	$0.0244285\pi$
$492$		−	62.6066i		−	0.127249i
$493$	−77.7288	−	249.601i	−0.157665	−	0.506290i
$494$	−205.016			−0.415013
$495$	−884.982	−	884.982i	−1.78784	−	1.78784i
$496$	104.364	+	104.364i	0.210412	+	0.210412i
$497$			18.1451i			0.0365092i
$498$			855.818i			1.71851i
$499$		−	292.373i		−	0.585918i	−0.956125	−	0.292959i	$-0.905360\pi$
$499$		−	292.373i		−	0.585918i	0.956125	−	0.292959i	$-0.0946399\pi$
$500$	29.6381			0.0592763
$501$	−1017.33	+	1017.33i	−2.03060	+	2.03060i
$502$			615.347i			1.22579i
$503$	510.905	−	510.905i	1.01572	−	1.01572i	0.0158408	−	0.999875i	$-0.494958\pi$
$503$	510.905	−	510.905i	1.01572	−	1.01572i	0.999875	−	0.0158408i	$-0.00504249\pi$
$504$	−37.6201	−	37.6201i	−0.0746431	−	0.0746431i
$505$	−113.445	+	113.445i	−0.224644	+	0.224644i
$506$			647.540i			1.27972i
$507$	138.662	+	138.662i	0.273496	+	0.273496i
$508$	10.1234	−	10.1234i	0.0199279	−	0.0199279i
$509$	−10.9652			−0.0215427			−0.0107714	−	0.999942i	$-0.503429\pi$
$509$	−10.9652			−0.0215427			−0.0107714	+	0.999942i	$0.503429\pi$
$510$	222.410	+	222.410i	0.436099	+	0.436099i
$511$	2.03022	−	2.03022i	0.00397304	−	0.00397304i
$512$	325.200	+	325.200i	0.635157	+	0.635157i
$513$	515.736			1.00533
$514$	−230.918	−	230.918i	−0.449257	−	0.449257i
$515$			121.987i			0.236869i
$516$	28.6416			0.0555070
$517$	−212.548			−0.411118
$518$	−24.1210			−0.0465657
$519$	1006.99	−	1006.99i	1.94026	−	1.94026i
$520$	−198.447	+	198.447i	−0.381629	+	0.381629i
$521$		−	93.8560i		−	0.180146i	−0.995935	−	0.0900729i	$-0.971290\pi$
$521$		−	93.8560i		−	0.180146i	0.995935	−	0.0900729i	$-0.0287100\pi$
$522$	1142.98	−	355.938i	2.18962	−	0.681874i
$523$	32.4183			0.0619853			0.0309926	−	0.999520i	$-0.490133\pi$
$523$	32.4183			0.0619853			0.0309926	+	0.999520i	$0.490133\pi$
$524$	5.09137	+	5.09137i	0.00971636	+	0.00971636i
$525$	19.7124	+	19.7124i	0.0375475	+	0.0375475i
$526$		−	117.145i		−	0.222709i
$527$		−	78.7995i		−	0.149525i
$528$		−	1805.55i		−	3.41961i
$529$	−277.388			−0.524364
$530$	−284.675	+	284.675i	−0.537122	+	0.537122i
$531$		−	431.009i		−	0.811694i
$532$	0.491966	−	0.491966i	0.000924749	−	0.000924749i
$533$	−402.532	−	402.532i	−0.755220	−	0.755220i
$534$	304.310	−	304.310i	0.569869	−	0.569869i
$535$		−	316.351i		−	0.591311i
$536$	97.6706	+	97.6706i	0.182221	+	0.182221i
$537$	304.885	−	304.885i	0.567756	−	0.567756i
$538$	410.469			0.762953
$539$	685.675	+	685.675i	1.27212	+	1.27212i
$540$	−31.1518	+	31.1518i	−0.0576885	+	0.0576885i
$541$	−249.329	−	249.329i	−0.460867	−	0.460867i	0.438072	−	0.898940i	$-0.355661\pi$
$541$	−249.329	−	249.329i	−0.460867	−	0.460867i	−0.898940	+	0.438072i	$0.855661\pi$
$542$	−70.9205			−0.130850
$543$	445.058	+	445.058i	0.819627	+	0.819627i
$544$			33.8444i			0.0622139i
$545$	136.786			0.250984
$546$	43.7320			0.0800953
$547$	387.586			0.708566			0.354283	−	0.935138i	$-0.384725\pi$
$547$	387.586			0.708566			0.354283	+	0.935138i	$0.384725\pi$
$548$	−15.2686	+	15.2686i	−0.0278623	+	0.0278623i
$549$	−263.607	+	263.607i	−0.480159	+	0.480159i
$550$			616.723i			1.12131i
$551$	−74.5917	−	239.527i	−0.135375	−	0.434714i
$552$	−662.526			−1.20023
$553$	−27.9596	−	27.9596i	−0.0505598	−	0.0505598i
$554$	−84.3955	−	84.3955i	−0.152338	−	0.152338i
$555$		−	580.559i		−	1.04605i
$556$		−	17.3118i		−	0.0311363i
$557$			352.548i			0.632941i	0.948602	+	0.316471i	$0.102498\pi$
$557$			352.548i			0.632941i	−0.948602	+	0.316471i	$0.897502\pi$
$558$	360.841			0.646669
$559$	184.153	−	184.153i	0.329432	−	0.329432i
$560$		−	18.1790i		−	0.0324625i
$561$	−681.636	+	681.636i	−1.21504	+	1.21504i
$562$	512.214	+	512.214i	0.911413	+	0.911413i
$563$	−151.066	+	151.066i	−0.268324	+	0.268324i	−0.828425	−	0.560101i	$-0.810762\pi$
$563$	−151.066	+	151.066i	−0.268324	+	0.268324i	0.560101	+	0.828425i	$0.310762\pi$
$564$			13.5704i			0.0240610i
$565$	334.276	+	334.276i	0.591638	+	0.591638i
$566$	−649.795	+	649.795i	−1.14805	+	1.14805i
$567$	−48.2123			−0.0850306
$568$	−290.412	−	290.412i	−0.511289	−	0.511289i
$569$	431.698	−	431.698i	0.758697	−	0.758697i	−0.217389	−	0.976085i	$-0.569754\pi$
$569$	431.698	−	431.698i	0.758697	−	0.758697i	0.976085	+	0.217389i	$0.0697539\pi$
$570$	213.434	+	213.434i	0.374446	+	0.374446i
$571$	66.0488			0.115672			0.0578361	−	0.998326i	$-0.481580\pi$
$571$	66.0488			0.115672			0.0578361	+	0.998326i	$0.481580\pi$
$572$	37.9526	+	37.9526i	0.0663507	+	0.0663507i
$573$		−	457.926i		−	0.799172i
$574$	34.8221			0.0606656
$575$	239.637			0.416760
$576$	1199.79			2.08297
$577$	−392.139	+	392.139i	−0.679616	+	0.679616i	−0.959913	−	0.280297i	$-0.909567\pi$
$577$	−392.139	+	392.139i	−0.679616	+	0.679616i	0.280297	+	0.959913i	$0.409567\pi$
$578$	−302.289	+	302.289i	−0.522991	+	0.522991i
$579$			1184.79i			2.04627i
$580$	18.9736	+	9.96254i	0.0327131	+	0.0171768i
$581$	−26.4082			−0.0454530
$582$	−540.593	−	540.593i	−0.928853	−	0.928853i
$583$	−872.461	−	872.461i	−1.49650	−	1.49650i
$584$			64.9875i			0.111280i
$585$			726.576i			1.24201i
$586$		−	43.5154i		−	0.0742584i
$587$	195.193			0.332527			0.166263	−	0.986081i	$-0.446830\pi$
$587$	195.193			0.332527			0.166263	+	0.986081i	$0.446830\pi$
$588$	43.7779	−	43.7779i	0.0744522	−	0.0744522i
$589$		−	75.6192i		−	0.128386i
$590$	98.3412	−	98.3412i	0.166680	−	0.166680i
$591$	487.659	+	487.659i	0.825143	+	0.825143i
$592$	408.811	−	408.811i	0.690560	−	0.690560i
$593$			128.271i			0.216309i	0.994134	+	0.108155i	$0.0344942\pi$
$593$			128.271i			0.216309i	−0.994134	+	0.108155i	$0.965506\pi$
$594$	−1720.91	−	1720.91i	−2.89715	−	2.89715i
$595$	−6.86298	+	6.86298i	−0.0115344	+	0.0115344i
$596$	22.2616			0.0373517
$597$	−1393.22	−	1393.22i	−2.33370	−	2.33370i
$598$	265.817	−	265.817i	0.444511	−	0.444511i
$599$	717.619	+	717.619i	1.19803	+	1.19803i	0.974756	+	0.223271i	$0.0716736\pi$
$599$	717.619	+	717.619i	1.19803	+	1.19803i	0.223271	+	0.974756i	$0.428326\pi$
$600$	−630.996			−1.05166
$601$	−9.96872	−	9.96872i	−0.0165869	−	0.0165869i	0.698765	−	0.715352i	$-0.253733\pi$
$601$	−9.96872	−	9.96872i	−0.0165869	−	0.0165869i	−0.715352	+	0.698765i	$0.753733\pi$
$602$			15.9306i			0.0264628i
$603$	357.602			0.593038
$604$	40.9613			0.0678168
$605$	857.109			1.41671
$606$	−400.126	+	400.126i	−0.660273	+	0.660273i
$607$	−162.407	+	162.407i	−0.267556	+	0.267556i	−0.828115	−	0.560559i	$-0.810586\pi$
$607$	−162.407	+	162.407i	−0.267556	+	0.267556i	0.560559	+	0.828115i	$0.310586\pi$
$608$			32.4784i			0.0534184i
$609$	15.9111	+	51.0935i	0.0261267	+	0.0838974i
$610$	−120.292			−0.197200
$611$	87.2517	+	87.2517i	0.142801	+	0.142801i
$612$	30.0414	+	30.0414i	0.0490872	+	0.0490872i
$613$		−	376.150i		−	0.613621i	−0.951771	−	0.306811i	$-0.900738\pi$
$613$		−	376.150i		−	0.613621i	0.951771	−	0.306811i	$-0.0992619\pi$
$614$		−	29.8662i		−	0.0486420i
$615$			838.118i			1.36279i
$616$	52.6134			0.0854113
$617$	373.217	−	373.217i	0.604889	−	0.604889i	−0.336717	−	0.941606i	$-0.609316\pi$
$617$	373.217	−	373.217i	0.604889	−	0.604889i	0.941606	+	0.336717i	$0.109316\pi$
$618$			430.255i			0.696205i
$619$	−196.763	+	196.763i	−0.317872	+	0.317872i	−0.847949	−	0.530077i	$-0.822163\pi$
$619$	−196.763	+	196.763i	−0.317872	+	0.317872i	0.530077	+	0.847949i	$0.322163\pi$
$620$	4.56760	+	4.56760i	0.00736709	+	0.00736709i
$621$	−668.685	+	668.685i	−1.07679	+	1.07679i
$622$		−	947.137i		−	1.52273i
$623$	9.39017	+	9.39017i	0.0150725	+	0.0150725i
$624$	−741.186	+	741.186i	−1.18780	+	1.18780i
$625$	−19.0833			−0.0305333
$626$	406.919	+	406.919i	0.650030	+	0.650030i
$627$	−654.125	+	654.125i	−1.04326	+	1.04326i
$628$	−48.1319	−	48.1319i	−0.0766431	−	0.0766431i
$629$	−308.670			−0.490732
$630$	−31.4272	−	31.4272i	−0.0498844	−	0.0498844i
$631$		−	335.146i		−	0.531135i	−0.964092	−	0.265567i	$-0.914441\pi$
$631$		−	335.146i		−	0.531135i	0.964092	−	0.265567i	$-0.0855592\pi$
$632$	894.986			1.41612
$633$	1796.36			2.83785
$634$	−569.795			−0.898730
$635$	−135.522	+	135.522i	−0.213421	+	0.213421i
$636$	−55.7035	+	55.7035i	−0.0875841	+	0.0875841i
$637$		−	562.944i		−	0.883743i
$638$	−550.357	+	1048.15i	−0.862629	+	1.64287i
$639$	−1063.29			−1.66399
$640$	307.150	+	307.150i	0.479922	+	0.479922i
$641$	−343.144	−	343.144i	−0.535326	−	0.535326i	0.386827	−	0.922152i	$-0.373571\pi$
$641$	−343.144	−	343.144i	−0.535326	−	0.535326i	−0.922152	+	0.386827i	$0.873571\pi$
$642$		−	1115.78i		−	1.73798i
$643$			561.006i			0.872482i	0.899830	+	0.436241i	$0.143690\pi$
$643$			561.006i			0.872482i	−0.899830	+	0.436241i	$0.856310\pi$
$644$			1.27573i			0.00198095i
$645$	−383.427			−0.594461
$646$	113.478	−	113.478i	0.175663	−	0.175663i
$647$		−	930.722i		−	1.43852i	−0.694741	−	0.719260i	$-0.744481\pi$
$647$		−	930.722i		−	1.43852i	0.694741	−	0.719260i	$-0.255519\pi$
$648$	771.639	−	771.639i	1.19080	−	1.19080i
$649$	301.393	+	301.393i	0.464395	+	0.464395i
$650$	253.167	−	253.167i	0.389487	−	0.389487i
$651$			16.1303i			0.0247777i
$652$	−30.2929	−	30.2929i	−0.0464616	−	0.0464616i
$653$	168.866	−	168.866i	0.258600	−	0.258600i	−0.565885	−	0.824484i	$-0.691465\pi$
$653$	168.866	−	168.866i	0.258600	−	0.258600i	0.824484	+	0.565885i	$0.191465\pi$
$654$	482.450			0.737692
$655$	−68.1585	−	68.1585i	−0.104059	−	0.104059i
$656$	−590.177	+	590.177i	−0.899660	+	0.899660i
$657$	118.970	+	118.970i	0.181080	+	0.181080i
$658$	−7.54793			−0.0114710
$659$	−414.083	−	414.083i	−0.628350	−	0.628350i	0.319303	−	0.947653i	$-0.396551\pi$
$659$	−414.083	−	414.083i	−0.628350	−	0.628350i	−0.947653	+	0.319303i	$0.896551\pi$
$660$		−	79.0217i		−	0.119730i
$661$	−732.973			−1.10888			−0.554442	−	0.832222i	$-0.687068\pi$
$661$	−732.973			−1.10888			−0.554442	+	0.832222i	$0.687068\pi$
$662$	−517.395			−0.781563
$663$	559.628			0.844084
$664$	422.663	−	422.663i	0.636541	−	0.636541i
$665$	−6.58598	+	6.58598i	−0.00990374	+	0.00990374i
$666$		−	1413.47i		−	2.12233i
$667$	407.276	+	213.850i	0.610608	+	0.320614i
$668$	−62.7054			−0.0938704
$669$	1540.37	+	1540.37i	2.30250	+	2.30250i
$670$	81.5922	+	81.5922i	0.121779	+	0.121779i
$671$		−	368.666i		−	0.549427i
$672$		−	6.92797i		−	0.0103095i
$673$		−	503.554i		−	0.748223i	−0.927384	−	0.374112i	$-0.877948\pi$
$673$		−	503.554i		−	0.748223i	0.927384	−	0.374112i	$-0.122052\pi$
$674$	909.851			1.34993
$675$	−636.862	+	636.862i	−0.943499	+	0.943499i
$676$			8.54675i			0.0126431i
$677$	257.461	−	257.461i	0.380298	−	0.380298i	−0.490912	−	0.871209i	$-0.663336\pi$
$677$	257.461	−	257.461i	0.380298	−	0.380298i	0.871209	+	0.490912i	$0.163336\pi$
$678$	1179.01	+	1179.01i	1.73895	+	1.73895i
$679$	16.6812	−	16.6812i	0.0245673	−	0.0245673i
$680$		−	219.684i		−	0.323065i
$681$	46.7165	+	46.7165i	0.0685999	+	0.0685999i
$682$	−252.326	+	252.326i	−0.369980	+	0.369980i
$683$	−840.114			−1.23004			−0.615018	−	0.788513i	$-0.710851\pi$
$683$	−840.114			−1.23004			−0.615018	+	0.788513i	$0.710851\pi$
$684$	28.8289	+	28.8289i	0.0421475	+	0.0421475i
$685$	204.401	−	204.401i	0.298396	−	0.298396i
$686$	48.7573	+	48.7573i	0.0710748	+	0.0710748i
$687$	1580.42			2.30047
$688$	−269.997	−	269.997i	−0.392438	−	0.392438i
$689$			716.297i			1.03962i
$690$	−553.462			−0.802119
$691$	−347.277			−0.502571			−0.251286	−	0.967913i	$-0.580853\pi$
$691$	−347.277			−0.502571			−0.251286	+	0.967913i	$0.580853\pi$
$692$	62.0683			0.0896941
$693$	96.3169	−	96.3169i	0.138985	−	0.138985i
$694$	446.790	−	446.790i	0.643789	−	0.643789i
$695$			231.754i			0.333459i
$696$	−1072.41	−	563.095i	−1.54082	−	0.809044i
$697$	445.609			0.639325
$698$	−674.940	−	674.940i	−0.966963	−	0.966963i
$699$	917.087	+	917.087i	1.31200	+	1.31200i
$700$			1.21502i			0.00173574i
$701$		−	384.210i		−	0.548088i	−0.961717	−	0.274044i	$-0.911639\pi$
$701$		−	384.210i		−	0.548088i	0.961717	−	0.274044i	$-0.0883615\pi$
$702$			1412.88i			2.01265i
$703$	−296.212			−0.421355
$704$	−838.981	+	838.981i	−1.19173	+	1.19173i
$705$		−	181.668i		−	0.257685i
$706$	−468.664	+	468.664i	−0.663830	+	0.663830i
$707$	−12.3468	−	12.3468i	−0.0174636	−	0.0174636i
$708$	19.2428	−	19.2428i	0.0271791	−	0.0271791i
$709$		−	689.774i		−	0.972883i	−0.873713	−	0.486442i	$-0.838295\pi$
$709$		−	689.774i		−	0.972883i	0.873713	−	0.486442i	$-0.161705\pi$
$710$	−242.605	−	242.605i	−0.341697	−	0.341697i
$711$	1638.41	−	1638.41i	2.30437	−	2.30437i
$712$	−300.580			−0.422162
$713$	98.0452	+	98.0452i	0.137511	+	0.137511i
$714$	−24.2060	+	24.2060i	−0.0339020	+	0.0339020i
$715$	−508.074	−	508.074i	−0.710593	−	0.710593i
$716$	18.7922			0.0262461
$717$	−1013.44	−	1013.44i	−1.41344	−	1.41344i
$718$		−	1195.94i		−	1.66566i
$719$	−1313.45			−1.82677			−0.913387	−	0.407092i	$-0.866543\pi$
$719$	−1313.45			−1.82677			−0.913387	+	0.407092i	$0.866543\pi$
$720$	1065.28			1.47955
$721$	−13.2765			−0.0184140
$722$	−416.413	+	416.413i	−0.576749	+	0.576749i
$723$	−1614.98	+	1614.98i	−2.23372	+	2.23372i
$724$			27.4321i			0.0378896i
$725$	387.893	+	203.672i	0.535025	+	0.280928i
$726$	3023.06			4.16399
$727$	767.639	+	767.639i	1.05590	+	1.05590i	0.998342	+	0.0575571i	$0.0183311\pi$
$727$	767.639	+	767.639i	1.05590	+	1.05590i	0.0575571	+	0.998342i	$0.481669\pi$
$728$	−21.5980	−	21.5980i	−0.0296675	−	0.0296675i
$729$			67.1807i			0.0921546i
$730$			54.2894i			0.0743690i
$731$			203.860i			0.278878i
$732$	−23.5380			−0.0321557
$733$	−640.227	+	640.227i	−0.873434	+	0.873434i	−0.992845	−	0.119411i	$-0.961899\pi$
$733$	−640.227	+	640.227i	−0.873434	+	0.873434i	0.119411	+	0.992845i	$0.461899\pi$
$734$		−	899.559i		−	1.22556i
$735$	−586.057	+	586.057i	−0.797357	+	0.797357i
$736$	−42.1104	−	42.1104i	−0.0572152	−	0.0572152i
$737$	−250.061	+	250.061i	−0.339296	+	0.339296i
$738$			2040.55i			2.76497i
$739$	−126.689	−	126.689i	−0.171433	−	0.171433i	0.616175	−	0.787609i	$-0.288681\pi$
$739$	−126.689	−	126.689i	−0.171433	−	0.171433i	−0.787609	+	0.616175i	$0.788681\pi$
$740$	17.8920	−	17.8920i	0.0241784	−	0.0241784i
$741$	537.041			0.724752
$742$	−30.9825	−	30.9825i	−0.0417555	−	0.0417555i
$743$	547.079	−	547.079i	0.736310	−	0.736310i	−0.235551	−	0.971862i	$-0.575690\pi$
$743$	547.079	−	547.079i	0.736310	−	0.736310i	0.971862	+	0.235551i	$0.0756896\pi$
$744$	−258.166	−	258.166i	−0.346997	−	0.346997i
$745$	−298.017			−0.400023
$746$	−306.522	−	306.522i	−0.410887	−	0.410887i
$747$		−	1547.50i		−	2.07162i
$748$	−42.0141			−0.0561686
$749$	34.4300			0.0459680
$750$	−1399.42			−1.86589
$751$	−819.975	+	819.975i	−1.09184	+	1.09184i	−0.0965128	+	0.995332i	$0.530769\pi$
$751$	−819.975	+	819.975i	−1.09184	+	1.09184i	−0.995332	+	0.0965128i	$0.969231\pi$
$752$	127.925	−	127.925i	0.170113	−	0.170113i
$753$		−	1611.90i		−	2.14064i
$754$	656.194	−	204.347i	0.870283	−	0.271017i
$755$	−548.352			−0.726294
$756$	−3.39040	−	3.39040i	−0.00448466	−	0.00448466i
$757$	499.757	+	499.757i	0.660181	+	0.660181i	0.955423	−	0.295242i	$-0.0954003\pi$
$757$	499.757	+	499.757i	0.660181	+	0.660181i	−0.295242	+	0.955423i	$0.595400\pi$
$758$			668.205i			0.881537i
$759$		−	1696.23i		−	2.23482i
$760$		−	210.818i		−	0.277392i
$761$	1105.01			1.45205			0.726023	−	0.687670i	$-0.241367\pi$
$761$	1105.01			1.45205			0.726023	+	0.687670i	$0.241367\pi$
$762$	−477.993	+	477.993i	−0.627288	+	0.627288i
$763$			14.8871i			0.0195113i
$764$	14.1126	−	14.1126i	0.0184720	−	0.0184720i
$765$	−402.165	−	402.165i	−0.525707	−	0.525707i
$766$	360.980	−	360.980i	0.471253	−	0.471253i
$767$		−	247.445i		−	0.322615i
$768$	171.367	+	171.367i	0.223135	+	0.223135i
$769$	−379.661	+	379.661i	−0.493707	+	0.493707i	−0.909472	−	0.415765i	$-0.863514\pi$
$769$	−379.661	+	379.661i	−0.493707	+	0.493707i	0.415765	+	0.909472i	$0.363514\pi$
$770$	43.9522			0.0570808
$771$	604.891	+	604.891i	0.784554	+	0.784554i
$772$	−36.5135	+	36.5135i	−0.0472973	+	0.0472973i
$773$	−912.108	−	912.108i	−1.17996	−	1.17996i	−0.979754	−	0.200204i	$-0.935840\pi$
$773$	−912.108	−	912.108i	−1.17996	−	1.17996i	−0.200204	−	0.979754i	$-0.564160\pi$
$774$	−933.522			−1.20610
$775$	93.3791	+	93.3791i	0.120489	+	0.120489i
$776$			533.966i			0.688100i
$777$	63.1850			0.0813192
$778$	−227.350			−0.292223
$779$	427.624			0.548940
$780$	−32.4387	+	32.4387i	−0.0415881	+	0.0415881i
$781$	743.527	−	743.527i	0.952019	−	0.952019i
$782$			294.264i			0.376296i
$783$	−1650.71	+	514.051i	−2.10819	+	0.656514i
$784$	−825.366			−1.05276
$785$	644.344	+	644.344i	0.820821	+	0.820821i
$786$	−240.398	−	240.398i	−0.305850	−	0.305850i
$787$			1254.47i			1.59399i	0.603984	+	0.796996i	$0.293579\pi$
$787$			1254.47i			1.59399i	−0.603984	+	0.796996i	$0.706421\pi$
$788$			30.0579i			0.0381446i
$789$			306.862i			0.388925i
$790$	747.655			0.946399
$791$	−36.3809	+	36.3809i	−0.0459935	+	0.0459935i
$792$			3083.11i			3.89281i
$793$	−151.339	+	151.339i	−0.190843	+	0.190843i
$794$	−581.162	−	581.162i	−0.731942	−	0.731942i
$795$	745.706	−	745.706i	0.937995	−	0.937995i
$796$		−	85.8740i		−	0.107882i
$797$	222.524	+	222.524i	0.279202	+	0.279202i	0.832790	−	0.553588i	$-0.186742\pi$
$797$	222.524	+	222.524i	0.279202	+	0.279202i	−0.553588	+	0.832790i	$0.686742\pi$
$798$	−23.2291	+	23.2291i	−0.0291091	+	0.0291091i
$799$	−96.5889			−0.120887
$800$	−40.1063	−	40.1063i	−0.0501329	−	0.0501329i
$801$	−550.257	+	550.257i	−0.686963	+	0.686963i
$802$	852.568	+	852.568i	1.06305	+	1.06305i
$803$	−166.384			−0.207203
$804$	15.9655	+	15.9655i	0.0198576	+	0.0198576i
$805$		−	17.0783i		−	0.0212153i
$806$	207.161			0.257024
$807$	−1075.22			−1.33237
$808$	395.221			0.489134
$809$	−393.131	+	393.131i	−0.485947	+	0.485947i	−0.907025	−	0.421078i	$-0.861652\pi$
$809$	−393.131	+	393.131i	−0.485947	+	0.485947i	0.421078	+	0.907025i	$0.361652\pi$
$810$	644.613	−	644.613i	0.795819	−	0.795819i
$811$		−	1199.23i		−	1.47870i	−0.673320	−	0.739351i	$-0.735132\pi$
$811$		−	1199.23i		−	1.47870i	0.673320	−	0.739351i	$-0.264868\pi$
$812$	−1.08427	+	2.06499i	−0.00133531	+	0.00254309i
$813$	185.776			0.228507
$814$	988.402	+	988.402i	1.21425	+	1.21425i
$815$	405.533	+	405.533i	0.497587	+	0.497587i
$816$		−	820.504i		−	1.00552i
$817$			195.632i			0.239452i
$818$		−	707.284i		−	0.864650i
$819$	−79.0768			−0.0965529
$820$	−25.8296	+	25.8296i	−0.0314996	+	0.0314996i
$821$		−	1035.60i		−	1.26139i	−0.776032	−	0.630693i	$-0.782771\pi$
$821$		−	1035.60i		−	1.26139i	0.776032	−	0.630693i	$-0.217229\pi$
$822$	720.932	−	720.932i	0.877046	−	0.877046i
$823$	−738.936	−	738.936i	−0.897857	−	0.897857i	0.0973894	−	0.995246i	$-0.468951\pi$
$823$	−738.936	−	738.936i	−0.897857	−	0.897857i	−0.995246	+	0.0973894i	$0.968951\pi$
$824$	212.490	−	212.490i	0.257877	−	0.257877i
$825$		−	1615.51i		−	1.95819i
$826$	10.7029	+	10.7029i	0.0129576	+	0.0129576i
$827$	38.9897	−	38.9897i	0.0471459	−	0.0471459i	−0.683141	−	0.730287i	$-0.739386\pi$
$827$	38.9897	−	38.9897i	0.0471459	−	0.0471459i	0.730287	+	0.683141i	$0.239386\pi$
$828$	−74.7571			−0.0902863
$829$	562.619	+	562.619i	0.678672	+	0.678672i	0.959700	−	0.281028i	$-0.0906752\pi$
$829$	562.619	+	562.619i	0.678672	+	0.678672i	−0.281028	+	0.959700i	$0.590675\pi$
$830$	353.085	−	353.085i	0.425404	−	0.425404i
$831$	221.074	+	221.074i	0.266034	+	0.266034i
$832$	688.809			0.827895
$833$	311.594	+	311.594i	0.374062	+	0.374062i
$834$			817.407i			0.980104i
$835$	839.442			1.00532
$836$	−40.3184			−0.0482278
$837$	−521.132			−0.622619
$838$	798.637	−	798.637i	0.953028	−	0.953028i
$839$	42.1944	−	42.1944i	0.0502913	−	0.0502913i	−0.681514	−	0.731805i	$-0.738678\pi$
$839$	42.1944	−	42.1944i	0.0502913	−	0.0502913i	0.731805	+	0.681514i	$0.238678\pi$
$840$			44.9695i			0.0535351i
$841$	477.489	+	692.304i	0.567764	+	0.823191i
$842$	369.338			0.438644
$843$	−1341.75	−	1341.75i	−1.59163	−	1.59163i
$844$	55.3613	+	55.3613i	0.0655940	+	0.0655940i
$845$		−	114.416i		−	0.135403i
$846$		−	442.303i		−	0.522817i
$847$			93.2833i			0.110134i
$848$	1050.21			1.23845
$849$	1702.14	−	1702.14i	2.00487	−	2.00487i
$850$			280.259i			0.329717i
$851$	384.059	−	384.059i	0.451303	−	0.451303i
$852$	−47.4715	−	47.4715i	−0.0557178	−	0.0557178i
$853$	−946.645	+	946.645i	−1.10978	+	1.10978i	−0.116604	+	0.993178i	$0.537201\pi$
$853$	−946.645	+	946.645i	−1.10978	+	1.10978i	−0.993178	+	0.116604i	$0.962799\pi$
$854$		−	13.0919i		−	0.0153301i
$855$	−385.934	−	385.934i	−0.451385	−	0.451385i
$856$	−551.053	+	551.053i	−0.643754	+	0.643754i
$857$	390.149			0.455250			0.227625	−	0.973749i	$-0.426904\pi$
$857$	390.149			0.455250			0.227625	+	0.973749i	$0.426904\pi$
$858$	−1792.00	−	1792.00i	−2.08858	−	2.08858i
$859$	579.404	−	579.404i	0.674510	−	0.674510i	−0.284242	−	0.958752i	$-0.591742\pi$
$859$	579.404	−	579.404i	0.674510	−	0.674510i	0.958752	+	0.284242i	$0.0917420\pi$
$860$	−11.8167	−	11.8167i	−0.0137403	−	0.0137403i
$861$	−91.2165			−0.105943
$862$	−486.359	−	486.359i	−0.564222	−	0.564222i
$863$			1539.24i			1.78360i	0.452434	+	0.891798i	$0.350556\pi$
$863$			1539.24i			1.78360i	−0.452434	+	0.891798i	$0.649444\pi$
$864$	223.826			0.259058
$865$	−830.912			−0.960592
$866$	935.936			1.08076
$867$	791.846	−	791.846i	0.913317	−	0.913317i
$868$	−0.497114	+	0.497114i	−0.000572712	+	0.000572712i
$869$			2291.39i			2.63681i
$870$	−895.872	−	470.399i	−1.02974	−	0.540688i
$871$	205.302			0.235708
$872$	−238.268	−	238.268i	−0.273243	−	0.273243i
$873$	977.507	+	977.507i	1.11971	+	1.11971i
$874$			282.387i			0.323098i
$875$		−	43.1821i		−	0.0493510i
$876$			10.6230i			0.0121267i
$877$	−909.345			−1.03688			−0.518441	−	0.855114i	$-0.673487\pi$
$877$	−909.345			−1.03688			−0.518441	+	0.855114i	$0.673487\pi$
$878$	717.395	−	717.395i	0.817078	−	0.817078i
$879$			113.989i			0.129680i
$880$	−744.918	+	744.918i	−0.846498	+	0.846498i
$881$	949.796	+	949.796i	1.07809	+	1.07809i	0.996681	+	0.0814077i	$0.0259416\pi$
$881$	949.796	+	949.796i	1.07809	+	1.07809i	0.0814077	+	0.996681i	$0.474058\pi$
$882$	−1426.86	+	1426.86i	−1.61776	+	1.61776i
$883$			226.833i			0.256889i	0.991717	+	0.128445i	$0.0409985\pi$
$883$			226.833i			0.256889i	−0.991717	+	0.128445i	$0.959002\pi$
$884$	17.2469	+	17.2469i	0.0195101	+	0.0195101i
$885$	−257.605	+	257.605i	−0.291079	+	0.291079i
$886$	−887.857			−1.00210
$887$	−575.636	−	575.636i	−0.648969	−	0.648969i	0.303775	−	0.952744i	$-0.401753\pi$
$887$	−575.636	−	575.636i	−0.648969	−	0.648969i	−0.952744	+	0.303775i	$0.901753\pi$
$888$	−1011.28	+	1011.28i	−1.13883	+	1.13883i
$889$	−14.7496	−	14.7496i	−0.0165912	−	0.0165912i
$890$	−251.099			−0.282133
$891$	1975.59	+	1975.59i	2.21727	+	2.21727i
$892$			94.9444i			0.106440i
$893$	−92.6906			−0.103797
$894$	−1051.12			−1.17575
$895$	−251.573			−0.281087
$896$	−33.4286	+	33.4286i	−0.0373087	+	0.0373087i
$897$	−696.309	+	696.309i	−0.776264	+	0.776264i
$898$			1759.19i			1.95901i
$899$	75.3721	+	242.033i	0.0838399	+	0.269225i
$900$	−71.1993			−0.0791103
$901$	−396.476	−	396.476i	−0.440040	−	0.440040i
$902$	−1426.90	−	1426.90i	−1.58193	−	1.58193i
$903$		−	41.7302i		−	0.0462129i
$904$		−	1164.55i		−	1.28822i
$905$		−	367.235i		−	0.405785i
$906$	−1934.06			−2.13473
$907$	123.661	−	123.661i	0.136341	−	0.136341i	−0.635643	−	0.771983i	$-0.719265\pi$
$907$	123.661	−	123.661i	0.136341	−	0.136341i	0.771983	+	0.635643i	$0.219265\pi$
$908$			2.87948i			0.00317123i
$909$	723.512	−	723.512i	0.795943	−	0.795943i
$910$	−18.0425	−	18.0425i	−0.0198270	−	0.0198270i
$911$	−22.7492	+	22.7492i	−0.0249716	+	0.0249716i	−0.719482	−	0.694511i	$-0.755621\pi$
$911$	−22.7492	+	22.7492i	−0.0249716	+	0.0249716i	0.694511	+	0.719482i	$0.255621\pi$
$912$		−	787.388i		−	0.863364i
$913$	1082.12	+	1082.12i	1.18524	+	1.18524i
$914$	819.808	−	819.808i	0.896946	−	0.896946i
$915$	315.104			0.344376
$916$	48.7064	+	48.7064i	0.0531730	+	0.0531730i
$917$	7.41802	−	7.41802i	0.00808944	−	0.00808944i
$918$	−782.038	−	782.038i	−0.851893	−	0.851893i
$919$	−1114.91			−1.21318			−0.606591	−	0.795014i	$-0.707463\pi$
$919$	−1114.91			−1.21318			−0.606591	+	0.795014i	$0.707463\pi$
$920$	273.339	+	273.339i	0.297107	+	0.297107i
$921$			78.2346i			0.0849452i
$922$	1082.59			1.17418
$923$	−610.441			−0.661366
$924$	8.60032			0.00930770
$925$	365.781	−	365.781i	0.395439	−	0.395439i
$926$	19.0658	−	19.0658i	0.0205894	−	0.0205894i
$927$		−	777.992i		−	0.839258i
$928$	−32.3723	−	103.953i	−0.0348840	−	0.112019i
$929$	−1298.02			−1.39722			−0.698611	−	0.715502i	$-0.746198\pi$
$929$	−1298.02			−1.39722			−0.698611	+	0.715502i	$0.746198\pi$
$930$	−215.667	−	215.667i	−0.231900	−	0.231900i
$931$	299.018	+	299.018i	0.321179	+	0.321179i
$932$			56.5266i			0.0606509i
$933$			2481.03i			2.65919i
$934$			559.080i			0.598587i
$935$	562.446			0.601546
$936$	1265.63	−	1265.63i	1.35216	−	1.35216i
$937$		−	965.994i		−	1.03094i	−0.856907	−	0.515472i	$-0.827617\pi$
$937$		−	965.994i		−	1.03094i	0.856907	−	0.515472i	$-0.172383\pi$
$938$	−8.88008	+	8.88008i	−0.00946703	+	0.00946703i
$939$	−1065.92	−	1065.92i	−1.13517	−	1.13517i
$940$	5.59875	−	5.59875i	0.00595612	−	0.00595612i
$941$		−	407.730i		−	0.433295i	−0.976250	−	0.216647i	$-0.930488\pi$
$941$		−	407.730i		−	0.433295i	0.976250	−	0.216647i	$-0.0695121\pi$
$942$	2272.63	+	2272.63i	2.41256	+	2.41256i
$943$	−554.443	+	554.443i	−0.587957	+	0.587957i
$944$	−362.795			−0.384316
$945$	45.3875	+	45.3875i	0.0480291	+	0.0480291i
$946$	652.785	−	652.785i	0.690048	−	0.690048i
$947$	−200.676	−	200.676i	−0.211907	−	0.211907i	0.593170	−	0.805077i	$-0.297876\pi$
$947$	−200.676	−	200.676i	−0.211907	−	0.211907i	−0.805077	+	0.593170i	$0.797876\pi$
$948$	146.297			0.154321
$949$	68.3012	+	68.3012i	0.0719718	+	0.0719718i
$950$			268.948i			0.283103i
$951$	1492.58			1.56948
$952$	23.9093			0.0251148
$953$	−955.349			−1.00246			−0.501232	−	0.865313i	$-0.667120\pi$
$953$	−955.349			−1.00246			−0.501232	+	0.865313i	$0.667120\pi$
$954$	1815.56	−	1815.56i	1.90310	−	1.90310i
$955$	−188.927	+	188.927i	−0.197829	+	0.197829i
$956$		−	62.4654i		−	0.0653404i
$957$	1441.66	−	2745.64i	1.50644	−	2.86900i
$958$	−692.010			−0.722348
$959$	22.2460	+	22.2460i	0.0231970	+	0.0231970i
$960$	−717.090	−	717.090i	−0.746969	−	0.746969i
$961$		−	884.590i		−	0.920489i
$962$		−	811.485i		−	0.843540i
$963$			2017.58i			2.09509i
$964$	−99.5430			−0.103260
$965$	488.809	−	488.809i	0.506538	−	0.506538i
$966$		−	60.2360i		−	0.0623561i
$967$	−148.263	+	148.263i	−0.153322	+	0.153322i	−0.779600	−	0.626278i	$-0.784578\pi$
$967$	−148.263	+	148.263i	−0.153322	+	0.153322i	0.626278	+	0.779600i	$0.284578\pi$
$968$	−1493.00	−	1493.00i	−1.54236	−	1.54236i
$969$	−297.256	+	297.256i	−0.306766	+	0.306766i
$970$			446.065i			0.459861i
$971$	−284.558	−	284.558i	−0.293057	−	0.293057i	0.545230	−	0.838287i	$-0.316442\pi$
$971$	−284.558	−	284.558i	−0.293057	−	0.293057i	−0.838287	+	0.545230i	$0.816442\pi$
$972$	36.9947	−	36.9947i	0.0380604	−	0.0380604i
$973$	−25.2229			−0.0259228
$974$	1097.45	+	1097.45i	1.12675	+	1.12675i
$975$	−663.171	+	663.171i	−0.680175	+	0.680175i
$976$	221.887	+	221.887i	0.227343	+	0.227343i
$977$	−893.603			−0.914639			−0.457320	−	0.889302i	$-0.651190\pi$
$977$	−893.603			−0.914639			−0.457320	+	0.889302i	$0.651190\pi$
$978$	1430.33	+	1430.33i	1.46251	+	1.46251i
$979$		−	769.558i		−	0.786066i
$980$	−36.1229			−0.0368601
$981$	−872.373			−0.889269
$982$	−1315.20			−1.33931
$983$	−263.685	+	263.685i	−0.268245	+	0.268245i	−0.828393	−	0.560148i	$-0.810744\pi$
$983$	−263.685	+	263.685i	−0.268245	+	0.268245i	0.560148	+	0.828393i	$0.310744\pi$
$984$	1459.92	−	1459.92i	1.48366	−	1.48366i
$985$		−	402.388i		−	0.408515i
$986$	−250.101	+	476.316i	−0.253652	+	0.483079i
$987$	19.7718			0.0200322
$988$	16.5509	+	16.5509i	0.0167519	+	0.0167519i
$989$	−253.650	−	253.650i	−0.256471	−	0.256471i
$990$			2575.57i			2.60159i
$991$			905.420i			0.913643i	0.889558	+	0.456821i	$0.151012\pi$
$991$			905.420i			0.913643i	−0.889558	+	0.456821i	$0.848988\pi$
$992$		−	32.8182i		−	0.0330829i
$993$	1355.32			1.36487
$994$	26.4039	−	26.4039i	0.0265633	−	0.0265633i
$995$			1149.60i			1.15538i
$996$	69.0897	−	69.0897i	0.0693671	−	0.0693671i
$997$	1236.12	+	1236.12i	1.23984	+	1.23984i	0.960065	+	0.279776i	$0.0902604\pi$
$997$	1236.12	+	1236.12i	1.23984	+	1.23984i	0.279776	+	0.960065i	$0.409740\pi$
$998$	−425.448	+	425.448i	−0.426300	+	0.426300i
$999$			2041.36i			2.04340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.3.c.a.12.1	✓	8
3.2	odd	2		261.3.f.a.244.4		8
4.3	odd	2		464.3.l.c.273.1		8
29.17	odd	4	inner	29.3.c.a.17.1	yes	8
87.17	even	4		261.3.f.a.46.4		8
116.75	even	4		464.3.l.c.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.c.a.12.1	✓	8	1.1	even	1	trivial
29.3.c.a.17.1	yes	8	29.17	odd	4	inner
261.3.f.a.46.4		8	87.17	even	4
261.3.f.a.244.4		8	3.2	odd	2
464.3.l.c.17.1		8	116.75	even	4
464.3.l.c.273.1		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45515 - 1.45515i) q^{2} +(3.81178 + 3.81178i) q^{3} +0.234947i q^{4} -3.14526i q^{5} -11.0935i q^{6} +0.342313 q^{7} +(-5.47873 + 5.47873i) q^{8} +20.0593i q^{9} +O(q^{10})\)	\(q+(-1.45515 - 1.45515i) q^{2} +(3.81178 + 3.81178i) q^{3} +0.234947i q^{4} -3.14526i q^{5} -11.0935i q^{6} +0.342313 q^{7} +(-5.47873 + 5.47873i) q^{8} +20.0593i q^{9} +(-4.57683 + 4.57683i) q^{10} +(-14.0269 - 14.0269i) q^{11} +(-0.895568 + 0.895568i) q^{12} +11.5162i q^{13} +(-0.498119 - 0.498119i) q^{14} +(11.9890 - 11.9890i) q^{15} +16.8846 q^{16} +(-6.37430 - 6.37430i) q^{17} +(29.1894 - 29.1894i) q^{18} +(-6.11703 - 6.11703i) q^{19} +0.738970 q^{20} +(1.30482 + 1.30482i) q^{21} +40.8226i q^{22} +15.8623 q^{23} -41.7674 q^{24} +15.1074 q^{25} +(16.7578 - 16.7578i) q^{26} +(-42.1557 + 42.1557i) q^{27} +0.0804257i q^{28} +(25.6758 + 13.4817i) q^{29} -34.8918 q^{30} +(6.18103 + 6.18103i) q^{31} +(-2.65475 - 2.65475i) q^{32} -106.935i q^{33} +18.5512i q^{34} -1.07666i q^{35} -4.71289 q^{36} +(24.2121 - 24.2121i) q^{37} +17.8024i q^{38} +(-43.8972 + 43.8972i) q^{39} +(17.2320 + 17.2320i) q^{40} +(-34.9536 + 34.9536i) q^{41} -3.79744i q^{42} +(-15.9908 - 15.9908i) q^{43} +(3.29559 - 3.29559i) q^{44} +63.0917 q^{45} +(-23.0820 - 23.0820i) q^{46} +(7.57643 - 7.57643i) q^{47} +(64.3603 + 64.3603i) q^{48} -48.8828 q^{49} +(-21.9835 - 21.9835i) q^{50} -48.5949i q^{51} -2.70570 q^{52} +62.1991 q^{53} +122.686 q^{54} +(-44.1182 + 44.1182i) q^{55} +(-1.87544 + 1.87544i) q^{56} -46.6336i q^{57} +(-17.7443 - 56.9801i) q^{58} -21.4867 q^{59} +(2.81679 + 2.81679i) q^{60} +(13.1414 + 13.1414i) q^{61} -17.9887i q^{62} +6.86658i q^{63} -59.8122i q^{64} +36.2214 q^{65} +(-155.607 + 155.607i) q^{66} -17.8272i q^{67} +(1.49763 - 1.49763i) q^{68} +(60.4635 + 60.4635i) q^{69} +(-1.56671 + 1.56671i) q^{70} +53.0072i q^{71} +(-109.900 - 109.900i) q^{72} +(5.93089 - 5.93089i) q^{73} -70.4647 q^{74} +(57.5859 + 57.5859i) q^{75} +(1.43718 - 1.43718i) q^{76} +(-4.80160 - 4.80160i) q^{77} +127.754 q^{78} +(-81.6782 - 81.6782i) q^{79} -53.1064i q^{80} -140.843 q^{81} +101.726 q^{82} -77.1462 q^{83} +(-0.306565 + 0.306565i) q^{84} +(-20.0488 + 20.0488i) q^{85} +46.5381i q^{86} +(46.4812 + 149.259i) q^{87} +153.699 q^{88} +(27.4315 + 27.4315i) q^{89} +(-91.8082 - 91.8082i) q^{90} +3.94215i q^{91} +3.72680i q^{92} +47.1215i q^{93} -22.0498 q^{94} +(-19.2396 + 19.2396i) q^{95} -20.2387i q^{96} +(48.7308 - 48.7308i) q^{97} +(71.1320 + 71.1320i) q^{98} +(281.370 - 281.370i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8	\( 8 q + 2 q^{2} - 2 q^{3} - 4 q^{7} - 42 q^{8} + 6 q^{10} - 6 q^{11} + 54 q^{12} - 40 q^{14} - 10 q^{15} - 32 q^{16} + 12 q^{17} + 20 q^{18} - 16 q^{19} + 108 q^{20} - 36 q^{21} + 168 q^{24} + 104 q^{25} - 54 q^{26} - 98 q^{27} + 128 q^{29} - 220 q^{30} - 10 q^{31} - 106 q^{32} - 252 q^{36} - 84 q^{37} - 90 q^{39} + 226 q^{40} + 20 q^{41} - 190 q^{43} + 42 q^{44} + 292 q^{45} + 12 q^{46} + 58 q^{47} + 354 q^{48} - 72 q^{49} - 60 q^{50} - 144 q^{52} + 252 q^{53} + 400 q^{54} - 74 q^{55} - 192 q^{56} + 326 q^{58} - 40 q^{59} - 258 q^{60} - 208 q^{61} + 36 q^{65} - 414 q^{66} - 296 q^{68} + 120 q^{69} + 44 q^{70} - 636 q^{72} - 188 q^{73} - 64 q^{74} - 12 q^{75} + 592 q^{76} + 180 q^{77} + 600 q^{78} - 382 q^{79} - 124 q^{81} + 228 q^{82} + 280 q^{83} - 124 q^{84} + 32 q^{85} + 34 q^{87} + 20 q^{88} - 64 q^{89} + 128 q^{90} - 460 q^{94} - 380 q^{95} - 44 q^{97} - 66 q^{98} + 552 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 4 * q^7 - 42 * q^8 + 6 * q^10 - 6 * q^11 + 54 * q^12 - 40 * q^14 - 10 * q^15 - 32 * q^16 + 12 * q^17 + 20 * q^18 - 16 * q^19 + 108 * q^20 - 36 * q^21 + 168 * q^24 + 104 * q^25 - 54 * q^26 - 98 * q^27 + 128 * q^29 - 220 * q^30 - 10 * q^31 - 106 * q^32 - 252 * q^36 - 84 * q^37 - 90 * q^39 + 226 * q^40 + 20 * q^41 - 190 * q^43 + 42 * q^44 + 292 * q^45 + 12 * q^46 + 58 * q^47 + 354 * q^48 - 72 * q^49 - 60 * q^50 - 144 * q^52 + 252 * q^53 + 400 * q^54 - 74 * q^55 - 192 * q^56 + 326 * q^58 - 40 * q^59 - 258 * q^60 - 208 * q^61 + 36 * q^65 - 414 * q^66 - 296 * q^68 + 120 * q^69 + 44 * q^70 - 636 * q^72 - 188 * q^73 - 64 * q^74 - 12 * q^75 + 592 * q^76 + 180 * q^77 + 600 * q^78 - 382 * q^79 - 124 * q^81 + 228 * q^82 + 280 * q^83 - 124 * q^84 + 32 * q^85 + 34 * q^87 + 20 * q^88 - 64 * q^89 + 128 * q^90 - 460 * q^94 - 380 * q^95 - 44 * q^97 - 66 * q^98 + 552 * q^99

Introduction

L-functions

Modular forms

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Database

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