LMFDB - Embedded newform 350.4.e.n.151.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,4,Mod(51,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.51"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-12,-7,-24,0,28,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 93 x^{10} + 40 x^{9} + 6374 x^{8} + 1920 x^{7} + 179828 x^{6} + 77536 x^{5} + \cdots + 60840000 $ x^12 - x^11 + 93x^10 + 40x^9 + 6374x^8 + 1920x^7 + 179828x^6 + 77536x^5 + 3757776x^4 + 574880x^3 + 16511200x^2 - 624000x + 60840000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.3
Root			$1.03379 - 1.79059i$ of defining polynomial
Character	$\chi$	$=$	350.151
Dual form			350.4.e.n.51.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.53379 + 2.65661i) q^{3} +(-2.00000 + 3.46410i) q^{4} +6.13518 q^{6} +(18.4345 + 1.78031i) q^{7} +8.00000 q^{8} +(8.79495 + 15.2333i) q^{9} +(24.7508 - 42.8697i) q^{11} +(-6.13518 - 10.6264i) q^{12} -44.6154 q^{13} +(-15.3509 - 33.7098i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-19.6456 + 34.0272i) q^{17} +(17.5899 - 30.4666i) q^{18} +(28.1578 + 48.7708i) q^{19} +(-33.0043 + 46.2426i) q^{21} -99.0033 q^{22} +(-45.8301 - 79.3801i) q^{23} +(-12.2704 + 21.2529i) q^{24} +(44.6154 + 77.2761i) q^{26} -136.783 q^{27} +(-43.0362 + 60.2983i) q^{28} +281.845 q^{29} +(-35.2827 + 61.1114i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(75.9254 + 131.507i) q^{33} +78.5824 q^{34} -70.3596 q^{36} +(98.5446 + 170.684i) q^{37} +(56.3157 - 97.5416i) q^{38} +(68.4308 - 118.526i) q^{39} +399.021 q^{41} +(113.099 + 10.9225i) q^{42} +203.567 q^{43} +(99.0033 + 171.479i) q^{44} +(-91.6603 + 158.760i) q^{46} +(34.2494 + 59.3217i) q^{47} +49.0814 q^{48} +(336.661 + 65.6384i) q^{49} +(-60.2646 - 104.381i) q^{51} +(89.2307 - 154.552i) q^{52} +(-308.743 + 534.758i) q^{53} +(136.783 + 236.916i) q^{54} +(147.476 + 14.2425i) q^{56} -172.753 q^{57} +(-281.845 - 488.169i) q^{58} +(-240.256 + 416.136i) q^{59} +(11.7487 + 20.3493i) q^{61} +141.131 q^{62} +(135.010 + 296.476i) q^{63} +64.0000 q^{64} +(151.851 - 263.013i) q^{66} +(126.062 - 218.346i) q^{67} +(-78.5824 - 136.109i) q^{68} +281.176 q^{69} +835.640 q^{71} +(70.3596 + 121.866i) q^{72} +(-128.893 + 223.249i) q^{73} +(197.089 - 341.369i) q^{74} -225.263 q^{76} +(532.590 - 746.216i) q^{77} -273.723 q^{78} +(386.850 + 670.044i) q^{79} +(-27.6658 + 47.9185i) q^{81} +(-399.021 - 691.125i) q^{82} +1341.21 q^{83} +(-94.1805 - 206.816i) q^{84} +(-203.567 - 352.588i) q^{86} +(-432.292 + 748.752i) q^{87} +(198.007 - 342.957i) q^{88} +(-650.558 - 1126.80i) q^{89} +(-822.462 - 79.4293i) q^{91} +366.641 q^{92} +(-108.233 - 187.465i) q^{93} +(68.4988 - 118.643i) q^{94} +(-49.0814 - 85.0115i) q^{96} +323.729 q^{97} +(-222.972 - 648.752i) q^{98} +870.729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 7 q^{3} - 24 q^{4} + 28 q^{6} - 9 q^{7} + 96 q^{8} - 31 q^{9} - 31 q^{11} - 28 q^{12} + 118 q^{13} + 42 q^{14} - 96 q^{16} - 68 q^{17} - 62 q^{18} - 93 q^{19} + 175 q^{21} + 124 q^{22}+ \cdots + 8546 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 - 7 * q^3 - 24 * q^4 + 28 * q^6 - 9 * q^7 + 96 * q^8 - 31 * q^9 - 31 * q^11 - 28 * q^12 + 118 * q^13 + 42 * q^14 - 96 * q^16 - 68 * q^17 - 62 * q^18 - 93 * q^19 + 175 * q^21 + 124 * q^22 + 94 * q^23 - 56 * q^24 - 118 * q^26 + 770 * q^27 - 48 * q^28 + 338 * q^29 - 326 * q^31 - 192 * q^32 - 400 * q^33 + 272 * q^34 + 248 * q^36 + 253 * q^37 - 186 * q^38 + 434 * q^39 + 396 * q^41 - 154 * q^42 - 198 * q^43 - 124 * q^44 + 188 * q^46 - 901 * q^47 + 224 * q^48 - 801 * q^49 - 724 * q^51 - 236 * q^52 - 233 * q^53 - 770 * q^54 - 72 * q^56 - 1036 * q^57 - 338 * q^58 - 668 * q^59 - 157 * q^61 + 1304 * q^62 + 2413 * q^63 + 768 * q^64 - 800 * q^66 - 1193 * q^67 - 272 * q^68 - 90 * q^69 + 2216 * q^71 - 248 * q^72 - 1458 * q^73 + 506 * q^74 + 744 * q^76 + 655 * q^77 - 1736 * q^78 + 886 * q^79 + 614 * q^81 - 396 * q^82 + 3598 * q^83 - 392 * q^84 + 198 * q^86 - 789 * q^87 - 248 * q^88 - 3047 * q^89 - 2182 * q^91 - 752 * q^92 - 1902 * q^93 - 1802 * q^94 - 224 * q^96 + 6808 * q^97 + 1452 * q^98 + 8546 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−1.53379	+	2.65661i	−0.295179	+	0.511265i	−0.975027	−	0.222089i	$-0.928713\pi$
$3$	−1.53379	+	2.65661i	−0.295179	+	0.511265i	0.679848	+	0.733353i	$0.262046\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	6.13518			0.417446
$7$	18.4345	+	1.78031i	0.995369	+	0.0961279i
$7$	18.4345	+	1.78031i	0.995369	+	0.0961279i
$8$	8.00000			0.353553
$9$	8.79495	+	15.2333i	0.325739	+	0.564196i
$10$		0			0
$11$	24.7508	−	42.8697i	0.678423	−	1.17506i	−0.297033	−	0.954867i	$-0.595997\pi$
$11$	24.7508	−	42.8697i	0.678423	−	1.17506i	0.975456	−	0.220196i	$-0.0706696\pi$
$12$	−6.13518	−	10.6264i	−0.147589	−	0.255632i
$13$	−44.6154			−0.951852			−0.475926	−	0.879485i	$-0.657887\pi$
$13$	−44.6154			−0.951852			−0.475926	+	0.879485i	$0.657887\pi$
$14$	−15.3509	−	33.7098i	−0.293050	−	0.643523i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−19.6456	+	34.0272i	−0.280280	+	0.485459i	−0.971454	−	0.237230i	$-0.923761\pi$
$17$	−19.6456	+	34.0272i	−0.280280	+	0.485459i	0.691174	+	0.722689i	$0.257094\pi$
$18$	17.5899	−	30.4666i	0.230332	−	0.398947i
$19$	28.1578	+	48.7708i	0.339992	+	0.588884i	0.984431	−	0.175772i	$-0.0562422\pi$
$19$	28.1578	+	48.7708i	0.339992	+	0.588884i	−0.644439	+	0.764656i	$0.722909\pi$
$20$		0			0
$21$	−33.0043	+	46.2426i	−0.342959	+	0.480522i
$22$	−99.0033			−0.959435
$23$	−45.8301	−	79.3801i	−0.415489	−	0.719648i	0.579991	−	0.814623i	$-0.303056\pi$
$23$	−45.8301	−	79.3801i	−0.415489	−	0.719648i	−0.995480	+	0.0949751i	$0.969723\pi$
$24$	−12.2704	+	21.2529i	−0.104362	+	0.180759i
$25$		0			0
$26$	44.6154	+	77.2761i	0.336530	+	0.582888i
$27$	−136.783			−0.974963
$28$	−43.0362	+	60.2983i	−0.290467	+	0.406975i
$29$	281.845			1.80473			0.902367	−	0.430969i	$-0.141828\pi$
$29$	281.845			1.80473			0.902367	+	0.430969i	$0.141828\pi$
$30$		0			0
$31$	−35.2827	+	61.1114i	−0.204418	+	0.354063i	−0.949947	−	0.312411i	$-0.898864\pi$
$31$	−35.2827	+	61.1114i	−0.204418	+	0.354063i	0.745529	+	0.666473i	$0.232197\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	75.9254	+	131.507i	0.400512	+	0.693708i
$34$	78.5824			0.396376
$35$		0			0
$36$	−70.3596			−0.325739
$37$	98.5446	+	170.684i	0.437855	+	0.758387i	0.997524	−	0.0703292i	$-0.0224050\pi$
$37$	98.5446	+	170.684i	0.437855	+	0.758387i	−0.559669	+	0.828716i	$0.689072\pi$
$38$	56.3157	−	97.5416i	0.240411	−	0.416404i
$39$	68.4308	−	118.526i	0.280967	−	0.486649i
$40$		0			0
$41$	399.021			1.51992			0.759959	−	0.649971i	$-0.225219\pi$
$41$	399.021			1.51992			0.759959	+	0.649971i	$0.225219\pi$
$42$	113.099	+	10.9225i	0.415513	+	0.0401282i
$43$	203.567			0.721946			0.360973	−	0.932576i	$-0.382445\pi$
$43$	203.567			0.721946			0.360973	+	0.932576i	$0.382445\pi$
$44$	99.0033	+	171.479i	0.339211	+	0.587531i
$45$		0			0
$46$	−91.6603	+	158.760i	−0.293795	+	0.508868i
$47$	34.2494	+	59.3217i	0.106293	+	0.184106i	0.914266	−	0.405115i	$-0.132768\pi$
$47$	34.2494	+	59.3217i	0.106293	+	0.184106i	−0.807972	+	0.589220i	$0.799435\pi$
$48$	49.0814			0.147589
$49$	336.661	+	65.6384i	0.981519	+	0.191365i
$50$		0			0
$51$	−60.2646	−	104.381i	−0.165465	−	0.286595i
$52$	89.2307	−	154.552i	0.237963	−	0.412164i
$53$	−308.743	+	534.758i	−0.800172	+	1.38594i	0.119331	+	0.992855i	$0.461925\pi$
$53$	−308.743	+	534.758i	−0.800172	+	1.38594i	−0.919503	+	0.393084i	$0.871408\pi$
$54$	136.783	+	236.916i	0.344701	+	0.597040i
$55$		0			0
$56$	147.476	+	14.2425i	0.351916	+	0.0339863i
$57$	−172.753			−0.401434
$58$	−281.845	−	488.169i	−0.638070	−	1.10517i
$59$	−240.256	+	416.136i	−0.530147	+	0.918242i	0.469234	+	0.883074i	$0.344530\pi$
$59$	−240.256	+	416.136i	−0.530147	+	0.918242i	−0.999381	+	0.0351685i	$0.988803\pi$
$60$		0			0
$61$	11.7487	+	20.3493i	0.0246601	+	0.0427125i	0.878092	−	0.478492i	$-0.158816\pi$
$61$	11.7487	+	20.3493i	0.0246601	+	0.0427125i	−0.853432	+	0.521204i	$0.825483\pi$
$62$	141.131			0.289091
$63$	135.010	+	296.476i	0.269995	+	0.592896i
$64$	64.0000			0.125000
$65$		0			0
$66$	151.851	−	263.013i	0.283205	−	0.490525i
$67$	126.062	−	218.346i	0.229865	−	0.398137i	−0.727903	−	0.685680i	$-0.759505\pi$
$67$	126.062	−	218.346i	0.229865	−	0.398137i	0.957768	+	0.287543i	$0.0928383\pi$
$68$	−78.5824	−	136.109i	−0.140140	−	0.242729i
$69$	281.176			0.490574
$70$		0			0
$71$	835.640			1.39679			0.698396	−	0.715711i	$-0.253897\pi$
$71$	835.640			1.39679			0.698396	+	0.715711i	$0.253897\pi$
$72$	70.3596	+	121.866i	0.115166	+	0.199473i
$73$	−128.893	+	223.249i	−0.206654	+	0.357936i	−0.950659	−	0.310239i	$-0.899591\pi$
$73$	−128.893	+	223.249i	−0.206654	+	0.357936i	0.744004	+	0.668175i	$0.232924\pi$
$74$	197.089	−	341.369i	0.309610	−	0.536261i
$75$		0			0
$76$	−225.263			−0.339992
$77$	532.590	−	746.216i	0.788237	−	1.10441i
$78$	−273.723			−0.397347
$79$	386.850	+	670.044i	0.550937	+	0.954251i	0.998207	+	0.0598520i	$0.0190629\pi$
$79$	386.850	+	670.044i	0.550937	+	0.954251i	−0.447270	+	0.894399i	$0.647604\pi$
$80$		0			0
$81$	−27.6658	+	47.9185i	−0.0379503	+	0.0657318i
$82$	−399.021	−	691.125i	−0.537372	−	0.930756i
$83$	1341.21			1.77369			0.886846	−	0.462065i	$-0.152891\pi$
$83$	1341.21			1.77369			0.886846	+	0.462065i	$0.152891\pi$
$84$	−94.1805	−	206.816i	−0.122333	−	0.268636i
$85$		0			0
$86$	−203.567	−	352.588i	−0.255246	−	0.442100i
$87$	−432.292	+	748.752i	−0.532719	+	0.922697i
$88$	198.007	−	342.957i	0.239859	−	0.415448i
$89$	−650.558	−	1126.80i	−0.774821	−	1.34203i	−0.934895	−	0.354924i	$-0.884507\pi$
$89$	−650.558	−	1126.80i	−0.774821	−	1.34203i	0.160075	−	0.987105i	$-0.448827\pi$
$90$		0			0
$91$	−822.462	−	79.4293i	−0.947444	−	0.0914995i
$92$	366.641			0.415489
$93$	−108.233	−	187.465i	−0.120680	−	0.209024i
$94$	68.4988	−	118.643i	0.0751608	−	0.130182i
$95$		0			0
$96$	−49.0814	−	85.0115i	−0.0521808	−	0.0903797i
$97$	323.729			0.338862			0.169431	−	0.985542i	$-0.445807\pi$
$97$	323.729			0.338862			0.169431	+	0.985542i	$0.445807\pi$
$98$	−222.972	−	648.752i	−0.229832	−	0.668713i
$99$	870.729			0.883955
$100$		0			0
$101$	−590.509	+	1022.79i	−0.581761	+	1.00764i	0.413510	+	0.910500i	$0.364303\pi$
$101$	−590.509	+	1022.79i	−0.581761	+	1.00764i	−0.995271	+	0.0971395i	$0.969031\pi$
$102$	−120.529	+	208.763i	−0.117002	+	0.202653i
$103$	−366.021	−	633.967i	−0.350147	−	0.606472i	0.636128	−	0.771583i	$-0.280535\pi$
$103$	−366.021	−	633.967i	−0.350147	−	0.606472i	−0.986275	+	0.165111i	$0.947202\pi$
$104$	−356.923			−0.336530
$105$		0			0
$106$	1234.97			1.13161
$107$	669.021	+	1158.78i	0.604455	+	1.04695i	0.992137	+	0.125154i	$0.0399425\pi$
$107$	669.021	+	1158.78i	0.604455	+	1.04695i	−0.387682	+	0.921793i	$0.626724\pi$
$108$	273.567	−	473.832i	0.243741	−	0.422171i
$109$	25.8786	−	44.8230i	0.0227405	−	0.0393877i	−0.854431	−	0.519565i	$-0.826094\pi$
$109$	25.8786	−	44.8230i	0.0227405	−	0.0393877i	0.877172	+	0.480177i	$0.159428\pi$
$110$		0			0
$111$	−604.589			−0.516982
$112$	−122.807	−	269.678i	−0.103609	−	0.227520i
$113$	−471.803			−0.392774			−0.196387	−	0.980526i	$-0.562921\pi$
$113$	−471.803			−0.392774			−0.196387	+	0.980526i	$0.562921\pi$
$114$	172.753	+	299.218i	0.141928	+	0.245827i
$115$		0			0
$116$	−563.690	+	976.339i	−0.451183	+	0.781472i
$117$	−392.390	−	679.639i	−0.310055	−	0.537031i
$118$	961.025			0.749742
$119$	−422.736	+	592.298i	−0.325648	+	0.456268i
$120$		0			0
$121$	−559.706	−	969.439i	−0.420515	−	0.728354i
$122$	23.4974	−	40.6987i	0.0174373	−	0.0302023i
$123$	−612.017	+	1060.04i	−0.448648	+	0.777081i
$124$	−141.131	−	244.446i	−0.102209	−	0.177031i
$125$		0			0
$126$	378.501	−	530.321i	0.267615	−	0.374958i
$127$	−202.294			−0.141344			−0.0706721	−	0.997500i	$-0.522514\pi$
$127$	−202.294			−0.141344			−0.0706721	+	0.997500i	$0.522514\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−312.230	+	540.798i	−0.213103	+	0.369106i
$130$		0			0
$131$	584.478	+	1012.35i	0.389817	+	0.675184i	0.992425	−	0.122854i	$-0.0392048\pi$
$131$	584.478	+	1012.35i	0.389817	+	0.675184i	−0.602607	+	0.798038i	$0.705871\pi$
$132$	−607.403			−0.400512
$133$	432.248	+	949.195i	0.281810	+	0.618839i
$134$	−504.248			−0.325078
$135$		0			0
$136$	−157.165	+	272.217i	−0.0990939	+	0.171636i
$137$	73.3588	−	127.061i	0.0457479	−	0.0792377i	−0.842245	−	0.539095i	$-0.818766\pi$
$137$	73.3588	−	127.061i	0.0457479	−	0.0792377i	0.887993	+	0.459858i	$0.152100\pi$
$138$	−281.176	−	487.011i	−0.173444	−	0.300414i
$139$	−2505.64			−1.52896			−0.764479	−	0.644648i	$-0.777004\pi$
$139$	−2505.64			−1.52896			−0.764479	+	0.644648i	$0.777004\pi$
$140$		0			0
$141$	−210.126			−0.125502
$142$	−835.640	−	1447.37i	−0.493841	−	0.855357i
$143$	−1104.27	+	1912.65i	−0.645758	+	1.11849i
$144$	140.719	−	243.733i	0.0814347	−	0.141049i
$145$		0			0
$146$	515.571			0.292253
$147$	−690.744	+	793.701i	−0.387562	+	0.445329i
$148$	−788.357			−0.437855
$149$	−1054.09	−	1825.74i	−0.579559	−	1.00383i	−0.995530	−	0.0944481i	$-0.969891\pi$
$149$	−1054.09	−	1825.74i	−0.579559	−	1.00383i	0.415970	−	0.909378i	$-0.363442\pi$
$150$		0			0
$151$	1107.75	−	1918.68i	0.597004	−	1.03404i	−0.396256	−	0.918140i	$-0.629691\pi$
$151$	1107.75	−	1918.68i	0.597004	−	1.03404i	0.993261	−	0.115902i	$-0.0369758\pi$
$152$	225.263	+	390.166i	0.120205	+	0.208202i
$153$	−691.128			−0.365192
$154$	−1825.07	−	176.257i	−0.954992	−	0.0922285i
$155$		0			0
$156$	273.723	+	474.103i	0.140483	+	0.243324i
$157$	−1131.01	+	1958.97i	−0.574935	+	0.995816i	0.421114	+	0.907008i	$0.361639\pi$
$157$	−1131.01	+	1958.97i	−0.574935	+	0.995816i	−0.996049	+	0.0888082i	$0.971694\pi$
$158$	773.700	−	1340.09i	0.389571	−	0.674757i
$159$	−947.097	−	1640.42i	−0.472388	−	0.818200i
$160$		0			0
$161$	−703.534	−	1544.92i	−0.344387	−	0.756255i
$162$	110.663			0.0536698
$163$	43.8579	+	75.9641i	0.0210750	+	0.0365029i	0.876371	−	0.481638i	$-0.159958\pi$
$163$	43.8579	+	75.9641i	0.0210750	+	0.0365029i	−0.855296	+	0.518140i	$0.826624\pi$
$164$	−798.043	+	1382.25i	−0.379980	+	0.658144i
$165$		0			0
$166$	−1341.21	−	2323.04i	−0.627095	−	1.08616i
$167$	1851.38			0.857868			0.428934	−	0.903336i	$-0.358889\pi$
$167$	1851.38			0.857868			0.428934	+	0.903336i	$0.358889\pi$
$168$	−264.035	+	369.941i	−0.121254	+	0.169890i
$169$	−206.469			−0.0939779
$170$		0			0
$171$	−495.293	+	857.873i	−0.221497	+	0.383645i
$172$	−407.134	+	705.177i	−0.180486	+	0.312612i
$173$	921.039	+	1595.29i	0.404771	+	0.701083i	0.994295	−	0.106668i	$-0.0340181\pi$
$173$	921.039	+	1595.29i	0.404771	+	0.701083i	−0.589524	+	0.807751i	$0.700685\pi$
$174$	1729.17			0.753379
$175$		0			0
$176$	−792.026			−0.339211
$177$	−737.008	−	1276.53i	−0.312977	−	0.542092i
$178$	−1301.12	+	2253.60i	−0.547881	+	0.948958i
$179$	−374.266	+	648.248i	−0.156279	+	0.270683i	−0.933524	−	0.358515i	$-0.883283\pi$
$179$	−374.266	+	648.248i	−0.156279	+	0.270683i	0.777245	+	0.629198i	$0.216617\pi$
$180$		0			0
$181$	−1393.90			−0.572418			−0.286209	−	0.958167i	$-0.592395\pi$
$181$	−1393.90			−0.572418			−0.286209	+	0.958167i	$0.592395\pi$
$182$	684.886	+	1503.97i	0.278940	+	0.612539i
$183$	−72.0803			−0.0291166
$184$	−366.641	−	635.041i	−0.146898	−	0.254434i
$185$		0			0
$186$	−216.466	+	374.930i	−0.0853335	+	0.147802i
$187$	972.489	+	1684.40i	0.380297	+	0.658693i
$188$	−273.995			−0.106293
$189$	−2521.53	−	243.518i	−0.970448	−	0.0937211i
$190$		0			0
$191$	479.087	+	829.803i	0.181495	+	0.314358i	0.942390	−	0.334517i	$-0.108573\pi$
$191$	479.087	+	829.803i	0.181495	+	0.314358i	−0.760895	+	0.648875i	$0.775240\pi$
$192$	−98.1629	+	170.023i	−0.0368974	+	0.0639081i
$193$	2288.52	−	3963.83i	0.853530	−	1.47836i	−0.0244729	−	0.999700i	$-0.507791\pi$
$193$	2288.52	−	3963.83i	0.853530	−	1.47836i	0.878002	−	0.478656i	$-0.158876\pi$
$194$	−323.729	−	560.714i	−0.119806	−	0.207510i
$195$		0			0
$196$	−900.700	+	1034.95i	−0.328243	+	0.377169i
$197$	−3429.27			−1.24023			−0.620115	−	0.784511i	$-0.712914\pi$
$197$	−3429.27			−1.24023			−0.620115	+	0.784511i	$0.712914\pi$
$198$	−870.729	−	1508.15i	−0.312525	−	0.541309i
$199$	73.0079	−	126.453i	0.0260070	−	0.0450454i	−0.852729	−	0.522354i	$-0.825054\pi$
$199$	73.0079	−	126.453i	0.0260070	−	0.0450454i	0.878736	+	0.477308i	$0.158387\pi$
$200$		0			0
$201$	386.707	+	669.795i	0.135702	+	0.235043i
$202$	2362.04			0.822734
$203$	5195.67	+	501.772i	1.79638	+	0.173485i
$204$	482.117			0.165465
$205$		0			0
$206$	−732.042	+	1267.93i	−0.247591	+	0.428840i
$207$	806.147	−	1396.29i	0.270682	−	0.468835i
$208$	356.923	+	618.209i	0.118981	+	0.206082i
$209$	2787.72			0.922634
$210$		0			0
$211$	−705.410			−0.230154			−0.115077	−	0.993357i	$-0.536711\pi$
$211$	−705.410			−0.230154			−0.115077	+	0.993357i	$0.536711\pi$
$212$	−1234.97	−	2139.03i	−0.400086	−	0.692969i
$213$	−1281.70	+	2219.97i	−0.412304	+	0.714131i
$214$	1338.04	−	2317.56i	0.427414	−	0.740303i
$215$		0			0
$216$	−1094.27			−0.344701
$217$	−759.216	+	1063.74i	−0.237507	+	0.332773i
$218$	−103.514			−0.0321600
$219$	−395.390	−	684.836i	−0.122000	−	0.211310i
$220$		0			0
$221$	876.496	−	1518.13i	0.266785	−	0.462085i
$222$	604.589	+	1047.18i	0.182781	+	0.316586i
$223$	−2232.07			−0.670271			−0.335135	−	0.942170i	$-0.608782\pi$
$223$	−2232.07			−0.670271			−0.335135	+	0.942170i	$0.608782\pi$
$224$	−344.289	+	482.387i	−0.102696	+	0.143888i
$225$		0			0
$226$	471.803	+	817.186i	0.138867	+	0.240524i
$227$	2732.48	−	4732.79i	0.798947	−	1.38382i	−0.121355	−	0.992609i	$-0.538724\pi$
$227$	2732.48	−	4732.79i	0.798947	−	1.38382i	0.920302	−	0.391208i	$-0.127943\pi$
$228$	345.507	−	598.435i	0.100359	−	0.173826i
$229$	−971.944	−	1683.46i	−0.280471	−	0.485790i	0.691030	−	0.722826i	$-0.257157\pi$
$229$	−971.944	−	1683.46i	−0.280471	−	0.485790i	−0.971501	+	0.237036i	$0.923824\pi$
$230$		0			0
$231$	1165.52	+	2559.43i	0.331973	+	0.728996i
$232$	2254.76			0.638070
$233$	−1653.62	−	2864.16i	−0.464946	−	0.805311i	0.534253	−	0.845325i	$-0.320593\pi$
$233$	−1653.62	−	2864.16i	−0.464946	−	0.805311i	−0.999199	+	0.0400141i	$0.987260\pi$
$234$	−784.780	+	1359.28i	−0.219242	+	0.379738i
$235$		0			0
$236$	−961.025	−	1664.54i	−0.265074	−	0.459121i
$237$	−2373.39			−0.650500
$238$	1448.63	+	139.901i	0.394540	+	0.0381028i
$239$	6107.99			1.65311			0.826554	−	0.562857i	$-0.190298\pi$
$239$	6107.99			1.65311			0.826554	+	0.562857i	$0.190298\pi$
$240$		0			0
$241$	1981.30	−	3431.71i	0.529571	−	0.917245i	−0.469834	−	0.882755i	$-0.655686\pi$
$241$	1981.30	−	3431.71i	0.529571	−	0.917245i	0.999405	−	0.0344896i	$-0.0109805\pi$
$242$	−1119.41	+	1938.88i	−0.297349	+	0.515024i
$243$	−1931.44	−	3345.36i	−0.509886	−	0.883148i
$244$	−93.9895			−0.0246601
$245$		0			0
$246$	2448.07			0.634484
$247$	−1256.27	−	2175.93i	−0.323622	−	0.560530i
$248$	−282.262	+	488.892i	−0.0722727	+	0.125180i
$249$	−2057.13	+	3563.06i	−0.523556	+	0.906826i
$250$		0			0
$251$	−3.92299			−0.000986522			−0.000493261	−	1.00000i	$-0.500157\pi$
$251$	−3.92299			−0.000986522			−0.000493261		1.00000i	$0.500157\pi$
$252$	−1297.04	−	125.262i	−0.324230	−	0.0313126i
$253$	−4537.33			−1.12751
$254$	202.294	+	350.384i	0.0499727	+	0.0865553i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	109.797	+	190.175i	0.0266497	+	0.0461586i	0.879043	−	0.476743i	$-0.158183\pi$
$257$	109.797	+	190.175i	0.0266497	+	0.0461586i	−0.852393	+	0.522902i	$0.824849\pi$
$258$	1248.92			0.301373
$259$	1512.75	+	3321.92i	0.362925	+	0.796965i
$260$		0			0
$261$	2478.81	+	4293.42i	0.587872	+	1.01822i
$262$	1168.96	−	2024.69i	0.275643	−	0.477427i
$263$	2733.86	−	4735.18i	0.640977	−	1.11020i	−0.344238	−	0.938882i	$-0.611863\pi$
$263$	2733.86	−	4735.18i	0.640977	−	1.11020i	0.985215	−	0.171322i	$-0.0548039\pi$
$264$	607.403	+	1052.05i	0.141602	+	0.245263i
$265$		0			0
$266$	1211.81	−	1697.87i	0.279325	−	0.391365i
$267$	3991.29			0.914843
$268$	504.248	+	873.383i	0.114932	+	0.199069i
$269$	145.866	−	252.647i	0.0330616	−	0.0572644i	−0.849021	−	0.528359i	$-0.822808\pi$
$269$	145.866	−	252.647i	0.0330616	−	0.0572644i	0.882083	+	0.471094i	$0.156141\pi$
$270$		0			0
$271$	−1330.51	−	2304.51i	−0.298239	−	0.516565i	0.677494	−	0.735528i	$-0.263066\pi$
$271$	−1330.51	−	2304.51i	−0.298239	−	0.516565i	−0.975733	+	0.218963i	$0.929733\pi$
$272$	628.659			0.140140
$273$	1472.50	−	2063.13i	0.326446	−	0.457386i
$274$	−293.435			−0.0646973
$275$		0			0
$276$	−562.352	+	974.023i	−0.122644	+	0.212425i
$277$	2251.33	−	3899.41i	0.488336	−	0.845824i	−0.511574	−	0.859240i	$-0.670937\pi$
$277$	2251.33	−	3899.41i	0.488336	−	0.845824i	0.999910	+	0.0134159i	$0.00427054\pi$
$278$	2505.64	+	4339.89i	0.540568	+	0.936292i
$279$	−1241.24			−0.266348
$280$		0			0
$281$	−462.388			−0.0981628			−0.0490814	−	0.998795i	$-0.515629\pi$
$281$	−462.388			−0.0981628			−0.0490814	+	0.998795i	$0.515629\pi$
$282$	210.126	+	363.949i	0.0443718	+	0.0768542i
$283$	−3572.86	+	6188.37i	−0.750474	+	1.29986i	0.197118	+	0.980380i	$0.436842\pi$
$283$	−3572.86	+	6188.37i	−0.750474	+	1.29986i	−0.947593	+	0.319480i	$0.896492\pi$
$284$	−1671.28	+	2894.74i	−0.349198	+	0.604829i
$285$		0			0
$286$	4417.07			0.913240
$287$	7355.75	+	710.383i	1.51288	+	0.146107i
$288$	−562.877			−0.115166
$289$	1684.60	+	2917.81i	0.342886	+	0.593897i
$290$		0			0
$291$	−496.533	+	860.021i	−0.100025	+	0.173248i
$292$	−515.571	−	892.996i	−0.103327	−	0.178968i
$293$	8656.21			1.72594			0.862971	−	0.505254i	$-0.168601\pi$
$293$	8656.21			1.72594			0.862971	+	0.505254i	$0.168601\pi$
$294$	2065.48	+	402.703i	0.409731	+	0.0798848i
$295$		0			0
$296$	788.357	+	1365.47i	0.154805	+	0.268130i
$297$	−3385.50	+	5863.86i	−0.661437	+	1.14564i
$298$	−2108.18	+	3651.47i	−0.409810	+	0.709812i
$299$	2044.73	+	3541.57i	0.395484	+	0.684998i
$300$		0			0
$301$	3752.65	+	362.413i	0.718603	+	0.0693991i
$302$	−4431.01			−0.844291
$303$	−1811.44	−	3137.50i	−0.343447	−	0.594868i
$304$	450.525	−	780.333i	0.0849981	−	0.147221i
$305$		0			0
$306$	691.128	+	1197.07i	0.129115	+	0.223634i
$307$	4296.26			0.798699			0.399349	−	0.916799i	$-0.369236\pi$
$307$	4296.26			0.798699			0.399349	+	0.916799i	$0.369236\pi$
$308$	1519.79	+	3337.38i	0.281162	+	0.617418i
$309$	2245.60			0.413424
$310$		0			0
$311$	−1967.56	+	3407.92i	−0.358747	+	0.621368i	−0.987752	−	0.156034i	$-0.950129\pi$
$311$	−1967.56	+	3407.92i	−0.358747	+	0.621368i	0.629005	+	0.777401i	$0.283463\pi$
$312$	547.446	−	948.205i	0.0993367	−	0.172056i
$313$	−5249.47	−	9092.34i	−0.947979	−	1.64195i	−0.749674	−	0.661807i	$-0.769790\pi$
$313$	−5249.47	−	9092.34i	−0.947979	−	1.64195i	−0.198304	−	0.980140i	$-0.563543\pi$
$314$	4524.05			0.813080
$315$		0			0
$316$	−3094.80			−0.550937
$317$	−2873.59	−	4977.20i	−0.509138	−	0.881853i	−0.999944	−	0.0105840i	$-0.996631\pi$
$317$	−2873.59	−	4977.20i	−0.509138	−	0.881853i	0.490806	−	0.871269i	$-0.336702\pi$
$318$	−1894.19	+	3280.84i	−0.334029	+	0.578554i
$319$	6975.89	−	12082.6i	1.22437	−	2.12068i
$320$		0			0
$321$	−4104.56			−0.713690
$322$	−1972.35	+	2763.48i	−0.341351	+	0.478270i
$323$	−2212.71			−0.381172
$324$	−110.663	−	191.674i	−0.0189751	−	0.0328659i
$325$		0			0
$326$	87.7158	−	151.928i	0.0149022	−	0.0258114i
$327$	79.3848	+	137.499i	0.0134250	+	0.0232529i
$328$	3192.17			0.537372
$329$	525.759	+	1154.54i	0.0881035	+	0.193471i
$330$		0			0
$331$	−4704.04	−	8147.64i	−0.781141	−	1.35298i	−0.931277	−	0.364311i	$-0.881305\pi$
$331$	−4704.04	−	8147.64i	−0.781141	−	1.35298i	0.150136	−	0.988665i	$-0.452029\pi$
$332$	−2682.41	+	4646.07i	−0.443423	+	0.768031i
$333$	−1733.39	+	3002.32i	−0.285253	+	0.494072i
$334$	−1851.38	−	3206.68i	−0.303302	−	0.525335i
$335$		0			0
$336$	904.791	+	87.3803i	0.146906	+	0.0141875i
$337$	−4501.95			−0.727706			−0.363853	−	0.931456i	$-0.618539\pi$
$337$	−4501.95			−0.727706			−0.363853	+	0.931456i	$0.618539\pi$
$338$	206.469	+	357.615i	0.0332262	+	0.0575495i
$339$	723.649	−	1253.40i	0.115939	−	0.200812i
$340$		0			0
$341$	1746.55	+	3025.12i	0.277364	+	0.480408i
$342$	1981.17			0.313244
$343$	6089.32	+	1809.37i	0.958578	+	0.284831i
$344$	1628.54			0.255246
$345$		0			0
$346$	1842.08	−	3190.57i	0.286216	−	0.495741i
$347$	−2496.68	+	4324.38i	−0.386250	+	0.669005i	−0.991942	−	0.126695i	$-0.959563\pi$
$347$	−2496.68	+	4324.38i	−0.386250	+	0.669005i	0.605692	+	0.795700i	$0.292897\pi$
$348$	−1729.17	−	2995.01i	−0.266360	−	0.461348i
$349$	6675.06			1.02381			0.511903	−	0.859044i	$-0.328941\pi$
$349$	6675.06			1.02381			0.511903	+	0.859044i	$0.328941\pi$
$350$		0			0
$351$	6102.65			0.928020
$352$	792.026	+	1371.83i	0.119929	+	0.207724i
$353$	−1419.66	+	2458.93i	−0.214054	+	0.370752i	−0.952979	−	0.303035i	$-0.902000\pi$
$353$	−1419.66	+	2458.93i	−0.214054	+	0.370752i	0.738926	+	0.673787i	$0.235333\pi$
$354$	−1474.02	+	2553.07i	−0.221308	+	0.383317i
$355$		0			0
$356$	5204.47			0.774821
$357$	−925.116	−	2031.51i	−0.137149	−	0.301173i
$358$	1497.06			0.221012
$359$	4242.21	+	7347.72i	0.623663	+	1.08022i	0.988798	+	0.149262i	$0.0476897\pi$
$359$	4242.21	+	7347.72i	0.623663	+	1.08022i	−0.365134	+	0.930955i	$0.618977\pi$
$360$		0			0
$361$	1843.77	−	3193.51i	0.268811	−	0.465594i
$362$	1393.90	+	2414.30i	0.202380	+	0.350533i
$363$	3433.90			0.496509
$364$	1920.07	−	2690.23i	0.276481	−	0.387380i
$365$		0			0
$366$	72.0803	+	124.847i	0.0102943	+	0.0178302i
$367$	−5659.86	+	9803.17i	−0.805020	+	1.39434i	0.111257	+	0.993792i	$0.464512\pi$
$367$	−5659.86	+	9803.17i	−0.805020	+	1.39434i	−0.916277	+	0.400544i	$0.868821\pi$
$368$	−733.282	+	1270.08i	−0.103872	+	0.179912i
$369$	3509.37	+	6078.41i	0.495096	+	0.857532i
$370$		0			0
$371$	−6643.56	+	9308.34i	−0.929693	+	1.30260i
$372$	865.863			0.120680
$373$	−5653.09	−	9791.45i	−0.784735	−	1.35920i	−0.929157	−	0.369684i	$-0.879466\pi$
$373$	−5653.09	−	9791.45i	−0.784735	−	1.35920i	0.144423	−	0.989516i	$-0.453868\pi$
$374$	1944.98	−	3368.80i	0.268910	−	0.465766i
$375$		0			0
$376$	273.995	+	474.574i	0.0375804	+	0.0650912i
$377$	−12574.6			−1.71784
$378$	2099.75	+	4610.94i	0.285713	+	0.627411i
$379$	−10626.4			−1.44022			−0.720109	−	0.693861i	$-0.755908\pi$
$379$	−10626.4			−1.44022			−0.720109	+	0.693861i	$0.755908\pi$
$380$		0			0
$381$	310.278	−	537.417i	0.0417218	−	0.0722644i
$382$	958.174	−	1659.61i	0.128336	−	0.222285i
$383$	3791.44	+	6566.96i	0.505832	+	0.876126i	0.999977	+	0.00674681i	$0.00214759\pi$
$383$	3791.44	+	6566.96i	0.505832	+	0.876126i	−0.494146	+	0.869379i	$0.664519\pi$
$384$	392.651			0.0521808
$385$		0			0
$386$	−9154.08			−1.20707
$387$	1790.36	+	3101.00i	0.235166	+	0.407319i
$388$	−647.457	+	1121.43i	−0.0847156	+	0.146732i
$389$	−1606.41	+	2782.39i	−0.209379	+	0.362655i	−0.951519	−	0.307590i	$-0.900478\pi$
$389$	−1606.41	+	2782.39i	−0.209379	+	0.362655i	0.742140	+	0.670245i	$0.233811\pi$
$390$		0			0
$391$	3601.44			0.465813
$392$	2693.29	+	525.107i	0.347019	+	0.0676579i
$393$	−3585.88			−0.460264
$394$	3429.27	+	5939.67i	0.438488	+	0.759483i
$395$		0			0
$396$	−1741.46	+	3016.29i	−0.220989	+	0.382764i
$397$	−6590.40	−	11414.9i	−0.833155	−	1.44307i	−0.895524	−	0.445014i	$-0.853199\pi$
$397$	−6590.40	−	11414.9i	−0.833155	−	1.44307i	0.0623685	−	0.998053i	$-0.480135\pi$
$398$	−292.031			−0.0367794
$399$	−3184.62	−	307.555i	−0.399575	−	0.0385890i
$400$		0			0
$401$	3597.12	+	6230.39i	0.447959	+	0.775887i	0.998253	−	0.0590837i	$-0.0188179\pi$
$401$	3597.12	+	6230.39i	0.447959	+	0.775887i	−0.550295	+	0.834971i	$0.685485\pi$
$402$	773.413	−	1339.59i	0.0959561	−	0.166201i
$403$	1574.15	−	2726.51i	0.194576	−	0.337015i
$404$	−2362.04	−	4091.17i	−0.290880	−	0.503820i
$405$		0			0
$406$	−4326.57	−	9500.93i	−0.528877	−	1.16139i
$407$	9756.24			1.18820
$408$	−482.117	−	835.051i	−0.0585009	−	0.101326i
$409$	544.577	−	943.234i	0.0658376	−	0.114034i	−0.831228	−	0.555932i	$-0.812361\pi$
$409$	544.577	−	943.234i	0.0658376	−	0.114034i	0.897065	+	0.441898i	$0.145695\pi$
$410$		0			0
$411$	225.035	+	389.771i	0.0270076	+	0.0467786i
$412$	2928.17			0.350147
$413$	−5169.85	+	7243.53i	−0.615961	+	0.863028i
$414$	−3224.59			−0.382802
$415$		0			0
$416$	713.846	−	1236.42i	0.0841326	−	0.145722i
$417$	3843.13	−	6656.50i	0.451316	−	0.781703i
$418$	−2787.72	−	4828.47i	−0.326200	−	0.564996i
$419$	−12514.5			−1.45913			−0.729563	−	0.683914i	$-0.760276\pi$
$419$	−12514.5			−1.45913			−0.729563	+	0.683914i	$0.760276\pi$
$420$		0			0
$421$	−827.022			−0.0957401			−0.0478701	−	0.998854i	$-0.515243\pi$
$421$	−827.022			−0.0957401			−0.0478701	+	0.998854i	$0.515243\pi$
$422$	705.410	+	1221.81i	0.0813716	+	0.140940i
$423$	−602.444	+	1043.46i	−0.0692478	+	0.119941i
$424$	−2469.94	+	4278.07i	−0.282903	+	0.490003i
$425$		0			0
$426$	5126.80			0.583085
$427$	180.353	+	396.046i	0.0204400	+	0.0448853i
$428$	−5352.17			−0.604455
$429$	−3387.44	−	5867.21i	−0.381228	−	0.660307i
$430$		0			0
$431$	840.220	−	1455.30i	0.0939025	−	0.162644i	−0.815248	−	0.579113i	$-0.803399\pi$
$431$	840.220	−	1455.30i	0.0939025	−	0.162644i	0.909150	+	0.416469i	$0.136732\pi$
$432$	1094.27	+	1895.33i	0.121870	+	0.211086i
$433$	7421.56			0.823689			0.411845	−	0.911254i	$-0.364885\pi$
$433$	7421.56			0.823689			0.411845	+	0.911254i	$0.364885\pi$
$434$	2601.68	+	251.257i	0.287752	+	0.0277897i
$435$		0			0
$436$	103.514	+	179.292i	0.0113703	+	0.0196939i
$437$	2580.96	−	4470.35i	0.282526	−	0.489349i
$438$	−790.781	+	1369.67i	−0.0862671	+	0.149419i
$439$	−2399.11	−	4155.39i	−0.260828	−	0.451767i	0.705634	−	0.708576i	$-0.250662\pi$
$439$	−2399.11	−	4155.39i	−0.260828	−	0.451767i	−0.966462	+	0.256809i	$0.917329\pi$
$440$		0			0
$441$	1961.03	+	5705.74i	0.211751	+	0.616104i
$442$	−3505.98			−0.377291
$443$	−7967.80	−	13800.6i	−0.854541	−	1.48011i	−0.877070	−	0.480362i	$-0.840505\pi$
$443$	−7967.80	−	13800.6i	−0.854541	−	1.48011i	0.0225292	−	0.999746i	$-0.492828\pi$
$444$	1209.18	−	2094.36i	0.129246	−	0.223860i
$445$		0			0
$446$	2232.07	+	3866.06i	0.236977	+	0.410455i
$447$	6467.03			0.684295
$448$	1179.81	+	113.940i	0.124421	+	0.0120160i
$449$	−9352.06			−0.982964			−0.491482	−	0.870888i	$-0.663545\pi$
$449$	−9352.06			−0.982964			−0.491482	+	0.870888i	$0.663545\pi$
$450$		0			0
$451$	9876.10	−	17105.9i	1.03115	−	1.78600i
$452$	943.606	−	1634.37i	0.0981935	−	0.170076i
$453$	3398.13	+	5885.73i	0.352446	+	0.610455i
$454$	−10929.9			−1.12988
$455$		0			0
$456$	−1382.03			−0.141928
$457$	4288.61	+	7428.09i	0.438977	+	0.760331i	0.997611	−	0.0690835i	$-0.0220075\pi$
$457$	4288.61	+	7428.09i	0.438977	+	0.760331i	−0.558633	+	0.829415i	$0.688674\pi$
$458$	−1943.89	+	3366.91i	−0.198323	+	0.343506i
$459$	2687.19	−	4654.36i	0.273262	−	0.473304i
$460$		0			0
$461$	−8463.98			−0.855113			−0.427556	−	0.903989i	$-0.640625\pi$
$461$	−8463.98			−0.855113			−0.427556	+	0.903989i	$0.640625\pi$
$462$	3267.54	−	4578.17i	0.329047	−	0.461030i
$463$	4297.74			0.431388			0.215694	−	0.976461i	$-0.430799\pi$
$463$	4297.74			0.431388			0.215694	+	0.976461i	$0.430799\pi$
$464$	−2254.76	−	3905.36i	−0.225592	−	0.390736i
$465$		0			0
$466$	−3307.25	+	5728.32i	−0.328767	+	0.569441i
$467$	−515.064	−	892.116i	−0.0510371	−	0.0883988i	0.839378	−	0.543548i	$-0.182919\pi$
$467$	−515.064	−	892.116i	−0.0510371	−	0.0883988i	−0.890415	+	0.455149i	$0.849586\pi$
$468$	3139.12			0.310055
$469$	2712.61	−	3800.66i	0.267072	−	0.374197i
$470$		0			0
$471$	−3469.49	−	6009.33i	−0.339417	−	0.587888i
$472$	−1922.05	+	3329.09i	−0.187435	+	0.324648i
$473$	5038.45	−	8726.85i	0.489785	−	0.848332i
$474$	2373.39	+	4110.84i	0.229986	+	0.398348i
$475$		0			0
$476$	−1206.31	−	2649.00i	−0.116158	−	0.255077i
$477$	−10861.5			−1.04259
$478$	−6107.99	−	10579.3i	−0.584462	−	1.01232i
$479$	−2568.74	+	4449.19i	−0.245029	+	0.424402i	−0.962140	−	0.272557i	$-0.912131\pi$
$479$	−2568.74	+	4449.19i	−0.245029	+	0.424402i	0.717111	+	0.696959i	$0.245464\pi$
$480$		0			0
$481$	−4396.60	−	7615.14i	−0.416773	−	0.721872i
$482$	−7925.20			−0.748927
$483$	5183.34	+	500.582i	0.488303	+	0.0471579i
$484$	4477.65			0.420515
$485$		0			0
$486$	−3862.89	+	6690.72i	−0.360544	+	0.624480i
$487$	263.269	−	455.995i	0.0244966	−	0.0424294i	−0.853517	−	0.521065i	$-0.825535\pi$
$487$	263.269	−	455.995i	0.0244966	−	0.0424294i	0.878014	+	0.478635i	$0.158868\pi$
$488$	93.9895	+	162.795i	0.00871866	+	0.0151012i
$489$	−269.076			−0.0248835
$490$		0			0
$491$	−1546.87			−0.142178			−0.0710889	−	0.997470i	$-0.522647\pi$
$491$	−1546.87			−0.142178			−0.0710889	+	0.997470i	$0.522647\pi$
$492$	−2448.07	−	4240.18i	−0.224324	−	0.388540i
$493$	−5537.01	+	9590.38i	−0.505830	+	0.876124i
$494$	−2512.54	+	4351.85i	−0.228835	+	0.396355i
$495$		0			0
$496$	1129.05			0.102209
$497$	15404.6	+	1487.70i	1.39032	+	0.134271i
$498$	8228.54			0.740421
$499$	−4746.42	−	8221.04i	−0.425809	−	0.737524i	0.570686	−	0.821168i	$-0.306677\pi$
$499$	−4746.42	−	8221.04i	−0.425809	−	0.737524i	−0.996496	+	0.0836446i	$0.973344\pi$
$500$		0			0
$501$	−2839.64	+	4918.39i	−0.253225	+	0.438598i
$502$	3.92299	+	6.79482i	0.000348788	+	0.000604119i
$503$	9819.97			0.870479			0.435239	−	0.900315i	$-0.356664\pi$
$503$	9819.97			0.870479			0.435239	+	0.900315i	$0.356664\pi$
$504$	1080.08	+	2371.81i	0.0954578	+	0.209620i
$505$		0			0
$506$	4537.33	+	7858.89i	0.398635	+	0.690455i
$507$	316.682	−	548.509i	0.0277403	−	0.0480476i
$508$	404.589	−	700.768i	0.0353361	−	0.0612039i
$509$	1319.03	+	2284.62i	0.114862	+	0.198947i	0.917725	−	0.397217i	$-0.130024\pi$
$509$	1319.03	+	2284.62i	0.114862	+	0.198947i	−0.802863	+	0.596164i	$0.796691\pi$
$510$		0			0
$511$	−2773.53	+	3886.01i	−0.240105	+	0.336413i
$512$	512.000			0.0441942
$513$	−3851.53	−	6671.04i	−0.331480	−	0.574140i
$514$	219.595	−	380.349i	0.0188442	−	0.0326391i
$515$		0			0
$516$	−1248.92	−	2163.19i	−0.106552	−	0.184553i
$517$	3390.80			0.288448
$518$	4240.98	−	5942.08i	0.359726	−	0.504015i
$519$	−5650.74			−0.477919
$520$		0			0
$521$	−2213.18	+	3833.33i	−0.186106	+	0.322344i	−0.943949	−	0.330093i	$-0.892920\pi$
$521$	−2213.18	+	3833.33i	−0.186106	+	0.322344i	0.757843	+	0.652437i	$0.226253\pi$
$522$	4957.62	−	8586.85i	0.415688	−	0.719993i
$523$	452.882	+	784.415i	0.0378645	+	0.0655833i	0.884337	−	0.466850i	$-0.154611\pi$
$523$	452.882	+	784.415i	0.0378645	+	0.0655833i	−0.846472	+	0.532433i	$0.821278\pi$
$524$	−4675.82			−0.389817
$525$		0			0
$526$	−10935.4			−0.906478
$527$	−1386.30	−	2401.14i	−0.114589	−	0.198473i
$528$	1214.81	−	2104.11i	0.100128	−	0.173427i
$529$	1882.70	−	3260.92i	0.154738	−	0.268014i
$530$		0			0
$531$	−8452.16			−0.690758
$532$	−4152.60	−	401.038i	−0.338418	−	0.0326827i
$533$	−17802.5			−1.44674
$534$	−3991.29	−	6913.12i	−0.323446	−	0.560225i
$535$		0			0
$536$	1008.50	−	1746.77i	0.0812694	−	0.140763i
$537$	−1148.09	−	1988.56i	−0.0922606	−	0.159800i
$538$	−583.462			−0.0467562
$539$	11146.5	−	12807.9i	0.890751	−	1.02352i
$540$		0			0
$541$	−9810.32	−	16992.0i	−0.779628	−	1.35035i	−0.932157	−	0.362056i	$-0.882075\pi$
$541$	−9810.32	−	16992.0i	−0.779628	−	1.35035i	0.152529	−	0.988299i	$-0.451258\pi$
$542$	−2661.02	+	4609.02i	−0.210887	+	0.365267i
$543$	2137.96	−	3703.05i	0.168966	−	0.292657i
$544$	−628.659	−	1088.87i	−0.0495470	−	0.0858178i
$545$		0			0
$546$	−5045.95	−	487.313i	−0.395507	−	0.0381961i
$547$	−6717.26			−0.525062			−0.262531	−	0.964923i	$-0.584557\pi$
$547$	−6717.26			−0.525062			−0.262531	+	0.964923i	$0.584557\pi$
$548$	293.435	+	508.244i	0.0228740	+	0.0396188i
$549$	−206.658	+	357.943i	−0.0160655	+	0.0278263i
$550$		0			0
$551$	7936.14	+	13745.8i	0.613595	+	1.06278i
$552$	2249.41			0.173444
$553$	5938.49	+	13040.6i	0.456655	+	1.00279i
$554$	−9005.31			−0.690612
$555$		0			0
$556$	5011.27	−	8679.78i	0.382240	−	0.662058i
$557$	−6551.98	+	11348.4i	−0.498413	+	0.863277i	−0.999998	−	0.00183114i	$-0.999417\pi$
$557$	−6551.98	+	11348.4i	−0.498413	+	0.863277i	0.501585	+	0.865108i	$0.332750\pi$
$558$	1241.24	+	2149.89i	0.0941681	+	0.163104i
$559$	−9082.21			−0.687186
$560$		0			0
$561$	−5966.40			−0.449022
$562$	462.388	+	800.879i	0.0347058	+	0.0601122i
$563$	−8324.35	+	14418.2i	−0.623143	+	1.07932i	0.365754	+	0.930712i	$0.380811\pi$
$563$	−8324.35	+	14418.2i	−0.623143	+	1.07932i	−0.988897	+	0.148604i	$0.952522\pi$
$564$	420.253	−	727.899i	0.0313756	−	0.0543441i
$565$		0			0
$566$	14291.4			1.06133
$567$	−595.314	+	834.099i	−0.0440932	+	0.0617793i
$568$	6685.12			0.493841
$569$	−7348.85	−	12728.6i	−0.541441	−	0.937803i	−0.998822	−	0.0485321i	$-0.984546\pi$
$569$	−7348.85	−	12728.6i	−0.541441	−	0.937803i	0.457381	−	0.889271i	$-0.348788\pi$
$570$		0			0
$571$	−1498.89	+	2596.15i	−0.109854	+	0.190272i	−0.915711	−	0.401838i	$-0.868372\pi$
$571$	−1498.89	+	2596.15i	−0.109854	+	0.190272i	0.805857	+	0.592110i	$0.201705\pi$
$572$	−4417.07	−	7650.58i	−0.322879	−	0.559243i
$573$	−2939.28			−0.214294
$574$	−6125.34	−	13450.9i	−0.445412	−	0.978102i
$575$		0			0
$576$	562.877	+	974.931i	0.0407173	+	0.0705245i
$577$	2436.64	−	4220.38i	0.175803	−	0.304500i	−0.764636	−	0.644463i	$-0.777081\pi$
$577$	2436.64	−	4220.38i	0.175803	−	0.304500i	0.940439	+	0.339963i	$0.110414\pi$
$578$	3369.20	−	5835.63i	0.242457	−	0.419948i
$579$	7020.24	+	12159.4i	0.503888	+	0.872759i
$580$		0			0
$581$	24724.4	+	2387.77i	1.76548	+	0.170501i
$582$	1986.13			0.141457
$583$	15283.3	+	26471.4i	1.08571	+	1.88050i
$584$	−1031.14	+	1785.99i	−0.0730634	+	0.126549i
$585$		0			0
$586$	−8656.21	−	14993.0i	−0.610213	−	1.05692i
$587$	23971.4			1.68553			0.842764	−	0.538283i	$-0.180927\pi$
$587$	23971.4			1.68553			0.842764	+	0.538283i	$0.180927\pi$
$588$	−1367.97	−	3980.21i	−0.0959426	−	0.279152i
$589$	−3973.94			−0.278002
$590$		0			0
$591$	5259.80	−	9110.24i	0.366090	−	0.634086i
$592$	1576.71	−	2730.95i	0.109464	−	0.189597i
$593$	−780.834	−	1352.44i	−0.0540726	−	0.0936564i	0.837722	−	0.546097i	$-0.183887\pi$
$593$	−780.834	−	1352.44i	−0.0540726	−	0.0936564i	−0.891795	+	0.452440i	$0.850554\pi$
$594$	13542.0			0.935413
$595$		0			0
$596$	8432.71			0.579559
$597$	223.958	+	387.907i	0.0153534	+	0.0265929i
$598$	4089.46	−	7083.15i	0.279649	−	0.484367i
$599$	−8700.70	+	15070.1i	−0.593491	+	1.02796i	0.400267	+	0.916398i	$0.368917\pi$
$599$	−8700.70	+	15070.1i	−0.593491	+	1.02796i	−0.993758	+	0.111557i	$0.964416\pi$
$600$		0			0
$601$	−26823.7			−1.82057			−0.910283	−	0.413987i	$-0.864136\pi$
$601$	−26823.7			−1.82057			−0.910283	+	0.413987i	$0.864136\pi$
$602$	−3124.94	−	6862.20i	−0.211566	−	0.464589i
$603$	4434.84			0.299503
$604$	4431.01	+	7674.74i	0.298502	+	0.517021i
$605$		0			0
$606$	−3622.88	+	6275.01i	−0.242854	+	0.420635i
$607$	11360.7	+	19677.3i	0.759665	+	1.31578i	0.943022	+	0.332731i	$0.107970\pi$
$607$	11360.7	+	19677.3i	0.759665	+	1.31578i	−0.183357	+	0.983046i	$0.558696\pi$
$608$	−1802.10			−0.120205
$609$	−9302.10	+	13033.2i	−0.618949	+	0.867215i
$610$		0			0
$611$	−1528.05	−	2646.66i	−0.101176	−	0.175241i
$612$	1382.26	−	2394.14i	0.0912980	−	0.158133i
$613$	−11465.8	+	19859.3i	−0.755462	+	1.30850i	0.189682	+	0.981846i	$0.439254\pi$
$613$	−11465.8	+	19859.3i	−0.755462	+	1.30850i	−0.945144	+	0.326653i	$0.894079\pi$
$614$	−4296.26	−	7441.34i	−0.282383	−	0.489101i
$615$		0			0
$616$	4260.72	−	5969.73i	0.278684	−	0.390466i
$617$	−4299.04			−0.280507			−0.140253	−	0.990116i	$-0.544792\pi$
$617$	−4299.04			−0.280507			−0.140253	+	0.990116i	$0.544792\pi$
$618$	−2245.60	−	3889.50i	−0.146167	−	0.253169i
$619$	2660.95	−	4608.89i	0.172783	−	0.299268i	−0.766609	−	0.642114i	$-0.778058\pi$
$619$	2660.95	−	4608.89i	0.172783	−	0.299268i	0.939392	+	0.342846i	$0.111391\pi$
$620$		0			0
$621$	6268.81	+	10857.9i	0.405086	+	0.701630i
$622$	7870.25			0.507345
$623$	−9986.65	−	21930.2i	−0.642226	−	1.41030i
$624$	−2189.79			−0.140483
$625$		0			0
$626$	−10498.9	+	18184.7i	−0.670322	+	1.16103i
$627$	−4275.79	+	7405.88i	−0.272342	+	0.471710i
$628$	−4524.05	−	7835.89i	−0.287467	−	0.497908i
$629$	−7743.87			−0.490888
$630$		0			0
$631$	19486.3			1.22938			0.614688	−	0.788771i	$-0.289282\pi$
$631$	19486.3			1.22938			0.614688	+	0.788771i	$0.289282\pi$
$632$	3094.80	+	5360.35i	0.194786	+	0.337379i
$633$	1081.95	−	1874.00i	0.0679365	−	0.117670i
$634$	−5747.17	+	9954.40i	−0.360015	+	0.623564i
$635$		0			0
$636$	7576.77			0.472388
$637$	−15020.3	−	2928.48i	−0.934261	−	0.182152i
$638$	−27903.6			−1.73152
$639$	7349.41	+	12729.6i	0.454989	+	0.788065i
$640$		0			0
$641$	14287.3	−	24746.4i	0.880368	−	1.52484i	0.0294367	−	0.999567i	$-0.490629\pi$
$641$	14287.3	−	24746.4i	0.880368	−	1.52484i	0.850932	−	0.525276i	$-0.176038\pi$
$642$	4104.56	+	7109.31i	0.252327	+	0.437044i
$643$	6347.10			0.389277			0.194639	−	0.980875i	$-0.437647\pi$
$643$	6347.10			0.389277			0.194639	+	0.980875i	$0.437647\pi$
$644$	6758.84	+	652.736i	0.413565	+	0.0399401i
$645$		0			0
$646$	2212.71	+	3832.53i	0.134765	+	0.233419i
$647$	−1324.85	+	2294.70i	−0.0805024	+	0.139434i	−0.903466	−	0.428660i	$-0.858986\pi$
$647$	−1324.85	+	2294.70i	−0.0805024	+	0.139434i	0.822963	+	0.568094i	$0.192319\pi$
$648$	−221.326	+	383.348i	−0.0134175	+	0.0232397i
$649$	11893.1	+	20599.4i	0.719328	+	1.24591i
$650$		0			0
$651$	−1661.47	−	3648.51i	−0.100028	−	0.219656i
$652$	−350.863			−0.0210750
$653$	3530.81	+	6115.54i	0.211595	+	0.366493i	0.952214	−	0.305432i	$-0.0988010\pi$
$653$	3530.81	+	6115.54i	0.211595	+	0.366493i	−0.740619	+	0.671925i	$0.765468\pi$
$654$	158.770	−	274.997i	0.00949294	−	0.0164423i
$655$		0			0
$656$	−3192.17	−	5529.00i	−0.189990	−	0.329072i
$657$	−4534.42			−0.269261
$658$	1473.96	−	2065.18i	0.0873269	−	0.122354i
$659$	11227.0			0.663646			0.331823	−	0.943342i	$-0.392336\pi$
$659$	11227.0			0.663646			0.331823	+	0.943342i	$0.392336\pi$
$660$		0			0
$661$	−14375.0	+	24898.2i	−0.845873	+	1.46509i	0.0389881	+	0.999240i	$0.487587\pi$
$661$	−14375.0	+	24898.2i	−0.845873	+	1.46509i	−0.884861	+	0.465855i	$0.845747\pi$
$662$	−9408.09	+	16295.3i	−0.552350	+	0.956698i
$663$	2688.73	+	4657.01i	0.157499	+	0.272796i
$664$	10729.6			0.627095
$665$		0			0
$666$	6933.56			0.403408
$667$	−12917.0	−	22372.9i	−0.749847	−	1.29877i
$668$	−3702.76	+	6413.36i	−0.214467	+	0.371468i
$669$	3423.54	−	5929.74i	0.197850	−	0.342686i
$670$		0			0
$671$	1163.16			0.0669199
$672$	−753.444	−	1654.52i	−0.0432511	−	0.0949772i
$673$	4440.57			0.254341			0.127170	−	0.991881i	$-0.459411\pi$
$673$	4440.57			0.254341			0.127170	+	0.991881i	$0.459411\pi$
$674$	4501.95	+	7797.61i	0.257283	+	0.445627i
$675$		0			0
$676$	412.939	−	715.231i	0.0234945	−	0.0406936i
$677$	−8154.92	−	14124.7i	−0.462953	−	0.801857i	0.536154	−	0.844120i	$-0.319877\pi$
$677$	−8154.92	−	14124.7i	−0.462953	−	0.801857i	−0.999107	+	0.0422629i	$0.986543\pi$
$678$	−2894.59			−0.163962
$679$	5967.77	+	576.338i	0.337293	+	0.0325741i
$680$		0			0
$681$	8382.13	+	14518.3i	0.471665	+	0.816948i
$682$	3493.10	−	6050.23i	0.196126	−	0.339700i
$683$	2433.22	−	4214.46i	0.136317	−	0.236108i	−0.789783	−	0.613387i	$-0.789807\pi$
$683$	2433.22	−	4214.46i	0.136317	−	0.236108i	0.926100	+	0.377279i	$0.123140\pi$
$684$	−1981.17	−	3431.49i	−0.110749	−	0.191822i
$685$		0			0
$686$	−2955.39	−	12356.4i	−0.164486	−	0.687709i
$687$	5963.05			0.331157
$688$	−1628.54	−	2820.71i	−0.0902432	−	0.156306i
$689$	13774.7	−	23858.4i	0.761645	−	1.31921i
$690$		0			0
$691$	7513.56	+	13013.9i	0.413646	+	0.716455i	0.995285	−	0.0969914i	$-0.0309219\pi$
$691$	7513.56	+	13013.9i	0.413646	+	0.716455i	−0.581640	+	0.813447i	$0.697589\pi$
$692$	−7368.31			−0.404771
$693$	16051.4	+	1550.17i	0.879861	+	0.0849727i
$694$	9986.72			0.546240
$695$		0			0
$696$	−3458.34	+	5990.01i	−0.188345	+	0.326223i
$697$	−7839.01	+	13577.6i	−0.426003	+	0.737858i
$698$	−6675.06	−	11561.5i	−0.361970	−	0.626950i
$699$	10145.3			0.548970
$700$		0			0
$701$	−10821.8			−0.583073			−0.291536	−	0.956560i	$-0.594166\pi$
$701$	−10821.8			−0.583073			−0.291536	+	0.956560i	$0.594166\pi$
$702$	−6102.65	−	10570.1i	−0.328105	−	0.568294i
$703$	−5549.61	+	9612.20i	−0.297735	+	0.515691i
$704$	1584.05	−	2743.66i	0.0848029	−	0.146883i
$705$		0			0
$706$	5678.64			0.302718
$707$	−12706.6	+	17803.3i	−0.675929	+	0.947049i
$708$	5896.06			0.312977
$709$	−10251.4	−	17755.9i	−0.543016	−	0.940532i	−0.998729	−	0.0504047i	$-0.983949\pi$
$709$	−10251.4	−	17755.9i	−0.543016	−	0.940532i	0.455713	−	0.890127i	$-0.349384\pi$
$710$		0			0
$711$	−6804.65	+	11786.0i	−0.358923	+	0.621673i
$712$	−5204.47	−	9014.40i	−0.273940	−	0.474479i
$713$	6468.05			0.339734
$714$	−2593.56	+	3633.86i	−0.135940	+	0.190467i
$715$		0			0
$716$	−1497.06	−	2592.99i	−0.0781396	−	0.135342i
$717$	−9368.40	+	16226.5i	−0.487963	+	0.845176i
$718$	8484.41	−	14695.4i	0.440997	−	0.763828i
$719$	−136.829	−	236.995i	−0.00709717	−	0.0122927i	0.862455	−	0.506134i	$-0.168926\pi$
$719$	−136.829	−	236.995i	−0.00709717	−	0.0122927i	−0.869552	+	0.493841i	$0.835592\pi$
$720$		0			0
$721$	−5618.75	−	12338.5i	−0.290226	−	0.637322i
$722$	−7375.09			−0.380156
$723$	6077.81	+	10527.1i	0.312637	+	0.541503i
$724$	2787.80	−	4828.61i	0.143105	−	0.247864i
$725$		0			0
$726$	−3433.90	−	5947.68i	−0.175542	−	0.304049i
$727$	−1244.59			−0.0634931			−0.0317465	−	0.999496i	$-0.510107\pi$
$727$	−1244.59			−0.0634931			−0.0317465	+	0.999496i	$0.510107\pi$
$728$	−6579.69	−	635.435i	−0.334972	−	0.0323500i
$729$	10355.8			0.526129
$730$		0			0
$731$	−3999.20	+	6926.81i	−0.202347	+	0.350475i
$732$	144.161	−	249.694i	0.00727914	−	0.0126078i
$733$	−7826.61	−	13556.1i	−0.394383	−	0.683091i	0.598640	−	0.801019i	$-0.295708\pi$
$733$	−7826.61	−	13556.1i	−0.394383	−	0.683091i	−0.993022	+	0.117928i	$0.962375\pi$
$734$	22639.5			1.13847
$735$		0			0
$736$	2933.13			0.146898
$737$	−6240.28	−	10808.5i	−0.311891	−	0.540211i
$738$	7018.74	−	12156.8i	0.350086	−	0.606367i
$739$	2683.14	−	4647.34i	0.133560	−	0.231333i	−0.791486	−	0.611187i	$-0.790692\pi$
$739$	2683.14	−	4647.34i	0.133560	−	0.231333i	0.925047	+	0.379854i	$0.124026\pi$
$740$		0			0
$741$	7707.46			0.382106
$742$	22766.1	+	2198.64i	1.12637	+	0.108780i
$743$	−7927.48			−0.391428			−0.195714	−	0.980661i	$-0.562702\pi$
$743$	−7927.48			−0.391428			−0.195714	+	0.980661i	$0.562702\pi$
$744$	−865.863	−	1499.72i	−0.0426668	−	0.0739010i
$745$		0			0
$746$	−11306.2	+	19582.9i	−0.554891	+	0.961100i
$747$	11795.8	+	20431.0i	0.577760	+	1.00071i
$748$	−7779.91			−0.380297
$749$	10270.1	+	22552.6i	0.501015	+	1.10020i
$750$		0			0
$751$	−3693.26	−	6396.92i	−0.179453	−	0.310821i	0.762240	−	0.647294i	$-0.224099\pi$
$751$	−3693.26	−	6396.92i	−0.179453	−	0.310821i	−0.941693	+	0.336473i	$0.890766\pi$
$752$	547.991	−	949.148i	0.0265734	−	0.0460264i
$753$	6.01707	−	10.4219i	0.000291201	−	0.000504374i
$754$	12574.6	+	21779.9i	0.607348	+	1.05196i
$755$		0			0
$756$	5886.64	−	8247.82i	0.283194	−	0.396786i
$757$	13406.0			0.643659			0.321829	−	0.946798i	$-0.395702\pi$
$757$	13406.0			0.643659			0.321829	+	0.946798i	$0.395702\pi$
$758$	10626.4	+	18405.5i	0.509194	+	0.881949i
$759$	6959.34	−	12053.9i	0.332817	−	0.576456i
$760$		0			0
$761$	12942.5	+	22417.0i	0.616510	+	1.06783i	0.990117	+	0.140240i	$0.0447875\pi$
$761$	12942.5	+	22417.0i	0.616510	+	1.06783i	−0.373607	+	0.927587i	$0.621879\pi$
$762$	−1241.11			−0.0590036
$763$	556.857	−	780.217i	0.0264215	−	0.0370193i
$764$	−3832.69			−0.181495
$765$		0			0
$766$	7582.88	−	13133.9i	0.357677	−	0.619515i
$767$	10719.1	−	18566.1i	0.504622	−	0.874031i
$768$	−392.651	−	680.092i	−0.0184487	−	0.0319541i
$769$	11600.6			0.543991			0.271996	−	0.962299i	$-0.412316\pi$
$769$	11600.6			0.543991			0.271996	+	0.962299i	$0.412316\pi$
$770$		0			0
$771$	−673.626			−0.0314657
$772$	9154.08	+	15855.3i	0.426765	+	0.739178i
$773$	14123.7	−	24462.9i	0.657170	−	1.13825i	−0.324175	−	0.945997i	$-0.605087\pi$
$773$	14123.7	−	24462.9i	0.657170	−	1.13825i	0.981345	−	0.192255i	$-0.0615801\pi$
$774$	3580.72	−	6201.99i	0.166287	−	0.288018i
$775$		0			0
$776$	2589.83			0.119806
$777$	−11145.3	−	1076.36i	−0.514588	−	0.0496964i
$778$	6425.65			0.296106
$779$	11235.6	+	19460.6i	0.516760	+	0.895055i
$780$		0			0
$781$	20682.8	−	35823.6i	0.947616	−	1.64132i
$782$	−3601.44	−	6237.88i	−0.164690	−	0.285251i
$783$	−38551.7			−1.75955
$784$	−1783.78	−	5190.02i	−0.0812580	−	0.236426i
$785$		0			0
$786$	3585.88	+	6210.92i	0.162728	+	0.281853i
$787$	5252.63	−	9097.82i	0.237911	−	0.412074i	−0.722204	−	0.691680i	$-0.756871\pi$
$787$	5252.63	−	9097.82i	0.237911	−	0.412074i	0.960115	+	0.279606i	$0.0902040\pi$
$788$	6858.54	−	11879.3i	0.310058	−	0.537036i
$789$	8386.36	+	14525.6i	0.378406	+	0.655418i
$790$		0			0
$791$	−8697.45	−	839.957i	−0.390955	−	0.0377566i
$792$	6965.83			0.312525
$793$	−524.172	−	907.893i	−0.0234728	−	0.0406560i
$794$	−13180.8	+	22829.8i	−0.589130	+	1.02040i
$795$		0			0
$796$	292.031	+	505.813i	0.0130035	+	0.0225227i
$797$	2165.99			0.0962651			0.0481325	−	0.998841i	$-0.484673\pi$
$797$	2165.99			0.0962651			0.0481325	+	0.998841i	$0.484673\pi$
$798$	2651.92	+	5823.48i	0.117640	+	0.258332i
$799$	−2691.40			−0.119168
$800$		0			0
$801$	11443.3	−	19820.3i	0.504778	−	0.874302i
$802$	7194.23	−	12460.8i	0.316755	−	0.548635i
$803$	6380.41	+	11051.2i	0.280398	+	0.485664i
$804$	−3093.65			−0.135702
$805$		0			0
$806$	−6296.60			−0.275172
$807$	447.456	+	775.016i	0.0195182	+	0.0338065i
$808$	−4724.07	+	8182.33i	−0.205683	+	0.356254i
$809$	−2674.33	+	4632.08i	−0.116223	+	0.201304i	−0.918268	−	0.395959i	$-0.870412\pi$
$809$	−2674.33	+	4632.08i	−0.116223	+	0.201304i	0.802045	+	0.597264i	$0.203745\pi$
$810$		0			0
$811$	−33841.2			−1.46526			−0.732629	−	0.680628i	$-0.761707\pi$
$811$	−33841.2			−1.46526			−0.732629	+	0.680628i	$0.761707\pi$
$812$	−12129.5	+	16994.8i	−0.524215	+	0.734482i
$813$	8162.92			0.352135
$814$	−9756.24	−	16898.3i	−0.420093	−	0.727623i
$815$		0			0
$816$	−964.234	+	1670.10i	−0.0413664	+	0.0716486i
$817$	5732.01	+	9928.13i	0.245456	+	0.425142i
$818$	−2178.31			−0.0931084
$819$	−6023.54	−	13227.4i	−0.256996	−	0.564349i
$820$		0			0
$821$	−7290.73	−	12627.9i	−0.309925	−	0.536806i	0.668421	−	0.743783i	$-0.266971\pi$
$821$	−7290.73	−	12627.9i	−0.309925	−	0.536806i	−0.978346	+	0.206978i	$0.933637\pi$
$822$	450.069	−	779.543i	0.0190973	−	0.0330775i
$823$	−1539.13	+	2665.86i	−0.0651894	+	0.112911i	−0.896778	−	0.442481i	$-0.854098\pi$
$823$	−1539.13	+	2665.86i	−0.0651894	+	0.112911i	0.831589	+	0.555392i	$0.187432\pi$
$824$	−2928.17	−	5071.74i	−0.123796	−	0.214420i
$825$		0			0
$826$	17716.0	+	1710.93i	0.746270	+	0.0720711i
$827$	40275.0			1.69347			0.846734	−	0.532017i	$-0.178566\pi$
$827$	40275.0			1.69347			0.846734	+	0.532017i	$0.178566\pi$
$828$	3224.59	+	5585.15i	0.135341	+	0.234417i
$829$	−14593.5	+	25276.6i	−0.611402	+	1.05898i	0.379603	+	0.925150i	$0.376061\pi$
$829$	−14593.5	+	25276.6i	−0.611402	+	1.05898i	−0.991004	+	0.133829i	$0.957273\pi$
$830$		0			0
$831$	6906.15	+	11961.8i	0.288293	+	0.499339i
$832$	−2855.38			−0.118981
$833$	−8847.39	+	10166.1i	−0.368000	+	0.422851i
$834$	−15372.5			−0.638258
$835$		0			0
$836$	−5575.44	+	9656.94i	−0.230659	+	0.399512i
$837$	4826.09	−	8359.04i	0.199300	−	0.345198i
$838$	12514.5	+	21675.8i	0.515879	+	0.893528i
$839$	9396.07			0.386637			0.193318	−	0.981136i	$-0.438075\pi$
$839$	9396.07			0.386637			0.193318	+	0.981136i	$0.438075\pi$
$840$		0			0
$841$	55047.5			2.25706
$842$	827.022	+	1432.44i	0.0338493	+	0.0586286i
$843$	709.208	−	1228.38i	0.0289756	−	0.0501872i
$844$	1410.82	−	2443.61i	0.0575384	−	0.0996595i
$845$		0			0
$846$	2409.77			0.0979312
$847$	−8591.99	−	18867.6i	−0.348553	−	0.765404i
$848$	9879.77			0.400086
$849$	−10960.1	−	18983.4i	−0.443049	−	0.767383i
$850$		0			0
$851$	9032.63	−	15645.0i	0.363848	−	0.630203i
$852$	−5126.80	−	8879.88i	−0.206152	−	0.357065i
$853$	−20167.0			−0.809502			−0.404751	−	0.914427i	$-0.632642\pi$
$853$	−20167.0			−0.809502			−0.404751	+	0.914427i	$0.632642\pi$
$854$	505.619	−	708.426i	0.0202599	−	0.0283862i
$855$		0			0
$856$	5352.17	+	9270.23i	0.213707	+	0.370152i
$857$	21239.7	−	36788.3i	0.846599	−	1.46635i	−0.0376269	−	0.999292i	$-0.511980\pi$
$857$	21239.7	−	36788.3i	0.846599	−	1.46635i	0.884226	−	0.467060i	$-0.154687\pi$
$858$	−6774.87	+	11734.4i	−0.269569	+	0.466908i
$859$	−10521.8	−	18224.4i	−0.417929	−	0.723873i	0.577802	−	0.816177i	$-0.303910\pi$
$859$	−10521.8	−	18224.4i	−0.417929	−	0.723873i	−0.995731	+	0.0923032i	$0.970577\pi$
$860$		0			0
$861$	−13169.4	+	18451.8i	−0.521269	+	0.730355i
$862$	−3360.88			−0.132798
$863$	−4225.57	−	7318.91i	−0.166675	−	0.288689i	0.770574	−	0.637350i	$-0.219970\pi$
$863$	−4225.57	−	7318.91i	−0.166675	−	0.288689i	−0.937249	+	0.348662i	$0.886636\pi$
$864$	2188.54	−	3790.66i	0.0861754	−	0.149260i
$865$		0			0
$866$	−7421.56	−	12854.5i	−0.291218	−	0.504405i
$867$	−10335.3			−0.404851
$868$	−2166.49	−	4757.49i	−0.0847181	−	0.186037i
$869$	38299.4			1.49507
$870$		0			0
$871$	−5624.30	+	9741.58i	−0.218797	+	0.378968i
$872$	207.028	−	358.584i	0.00803999	−	0.0139257i
$873$	2847.18	+	4931.45i	0.110381	+	0.191185i
$874$	−10323.8			−0.399552
$875$		0			0
$876$	3163.12			0.122000
$877$	17215.5	+	29818.1i	0.662856	+	1.14810i	0.979862	+	0.199677i	$0.0639893\pi$
$877$	17215.5	+	29818.1i	0.662856	+	1.14810i	−0.317005	+	0.948424i	$0.602677\pi$
$878$	−4798.23	+	8310.78i	−0.184433	+	0.319448i
$879$	−13276.8	+	22996.2i	−0.509462	+	0.882414i
$880$		0			0
$881$	−11602.4			−0.443695			−0.221848	−	0.975081i	$-0.571209\pi$
$881$	−11602.4			−0.443695			−0.221848	+	0.975081i	$0.571209\pi$
$882$	7921.61	−	9102.34i	0.302420	−	0.347496i
$883$	37934.8			1.44576			0.722880	−	0.690974i	$-0.242818\pi$
$883$	37934.8			1.44576			0.722880	+	0.690974i	$0.242818\pi$
$884$	3505.98	+	6072.54i	0.133392	+	0.231043i
$885$		0			0
$886$	−15935.6	+	27601.3i	−0.604252	+	1.04659i
$887$	−12718.1	−	22028.5i	−0.481436	−	0.833871i	0.518337	−	0.855176i	$-0.326551\pi$
$887$	−12718.1	−	22028.5i	−0.481436	−	0.833871i	−0.999773	+	0.0213052i	$0.993218\pi$
$888$	−4836.71			−0.182781
$889$	−3729.19	−	360.147i	−0.140690	−	0.0135871i
$890$		0			0
$891$	1369.50	+	2372.04i	0.0514927	+	0.0891879i
$892$	4464.14	−	7732.12i	0.167568	−	0.290236i
$893$	−1928.78	+	3340.74i	−0.0722779	+	0.125189i
$894$	−6467.03	−	11201.2i	−0.241935	−	0.419043i
$895$		0			0
$896$	−982.457	−	2157.43i	−0.0366313	−	0.0804404i
$897$	−12544.8			−0.466954
$898$	9352.06	+	16198.2i	0.347530	+	0.601940i
$899$	−9944.25	+	17223.9i	−0.368920	+	0.638988i
$900$		0			0
$901$	−12130.9	−	21011.3i	−0.448544	−	0.776901i
$902$	−39504.4			−1.45826
$903$	−6718.59	+	9413.47i	−0.247598	+	0.346911i
$904$	−3774.42			−0.138867
$905$		0			0
$906$	6796.26	−	11771.5i	0.249217	−	0.431657i
$907$	−3015.93	+	5223.74i	−0.110410	+	0.191236i	−0.915936	−	0.401325i	$-0.868550\pi$
$907$	−3015.93	+	5223.74i	−0.110410	+	0.191236i	0.805525	+	0.592561i	$0.201883\pi$
$908$	10929.9	+	18931.2i	0.399474	+	0.691909i
$909$	−20774.0			−0.758008
$910$		0			0
$911$	−21631.5			−0.786699			−0.393349	−	0.919389i	$-0.628684\pi$
$911$	−21631.5			−0.786699			−0.393349	+	0.919389i	$0.628684\pi$
$912$	1382.03	+	2393.74i	0.0501793	+	0.0869130i
$913$	33195.9	−	57497.0i	1.20331	−	2.08420i
$914$	8577.22	−	14856.2i	0.310404	−	0.537635i
$915$		0			0
$916$	7775.56			0.280471
$917$	8972.26	+	19702.6i	0.323108	+	0.709529i
$918$	−10748.8			−0.386451
$919$	14122.3	+	24460.6i	0.506913	+	0.877999i	0.999968	+	0.00800113i	$0.00254687\pi$
$919$	14122.3	+	24460.6i	0.506913	+	0.877999i	−0.493055	+	0.869998i	$0.664120\pi$
$920$		0			0
$921$	−6589.58	+	11413.5i	−0.235759	+	0.408347i
$922$	8463.98	+	14660.0i	0.302328	+	0.523647i
$923$	−37282.4			−1.32954
$924$	−11197.2	−	1081.37i	−0.398658	−	0.0385004i
$925$		0			0
$926$	−4297.74	−	7443.90i	−0.152519	−	0.264170i
$927$	6438.27	−	11151.4i	0.228113	−	0.395103i
$928$	−4509.52	+	7810.71i	−0.159517	+	0.276292i
$929$	−22472.1	−	38922.8i	−0.793633	−	1.37461i	−0.923703	−	0.383109i	$-0.874854\pi$
$929$	−22472.1	−	38922.8i	−0.793633	−	1.37461i	0.130070	−	0.991505i	$-0.458480\pi$
$930$		0			0
$931$	6278.41	+	18267.5i	0.221017	+	0.643063i
$932$	13229.0			0.464946
$933$	−6035.68	−	10454.1i	−0.211789	−	0.366829i
$934$	−1030.13	+	1784.23i	−0.0360886	+	0.0625074i
$935$		0			0
$936$	−3139.12	−	5437.11i	−0.109621	−	0.189869i
$937$	3777.71			0.131710			0.0658551	−	0.997829i	$-0.479022\pi$
$937$	3777.71			0.131710			0.0658551	+	0.997829i	$0.479022\pi$
$938$	−9295.56	−	897.720i	−0.323572	−	0.0312490i
$939$	32206.4			1.11929
$940$		0			0
$941$	176.423	−	305.573i	0.00611182	−	0.0105860i	−0.862953	−	0.505284i	$-0.831388\pi$
$941$	176.423	−	305.573i	0.00611182	−	0.0105860i	0.869065	+	0.494698i	$0.164721\pi$
$942$	−6938.97	+	12018.7i	−0.240004	+	0.415699i
$943$	−18287.2	−	31674.4i	−0.631509	−	1.09381i
$944$	7688.20			0.265074
$945$		0			0
$946$	−20153.8			−0.692660
$947$	−6767.42	−	11721.5i	−0.232219	−	0.402215i	0.726242	−	0.687439i	$-0.241265\pi$
$947$	−6767.42	−	11721.5i	−0.232219	−	0.402215i	−0.958461	+	0.285224i	$0.907932\pi$
$948$	4746.79	−	8221.68i	0.162625	−	0.281675i
$949$	5750.60	−	9960.34i	0.196704	−	0.340702i
$950$		0			0
$951$	17630.0			0.601147
$952$	−3381.89	+	4738.39i	−0.115134	+	0.161315i
$953$	51886.1			1.76365			0.881824	−	0.471579i	$-0.156316\pi$
$953$	51886.1			1.76365			0.881824	+	0.471579i	$0.156316\pi$
$954$	10861.5	+	18812.7i	0.368610	+	0.638452i
$955$		0			0
$956$	−12216.0	+	21158.7i	−0.413277	+	0.715817i
$957$	21399.2	+	37064.4i	0.722818	+	1.25196i
$958$	10275.0			0.346523
$959$	1578.54	−	2211.71i	0.0531530	−	0.0744731i
$960$		0			0
$961$	12405.8	+	21487.4i	0.416426	+	0.721272i
$962$	−8793.21	+	15230.3i	−0.294703	+	0.510441i
$963$	−11768.0	+	20382.8i	−0.393789	+	0.682063i
$964$	7925.20	+	13726.8i	0.264786	+	0.458622i
$965$		0			0
$966$	−4316.31	−	9478.39i	−0.143763	−	0.315696i
$967$	−45517.8			−1.51371			−0.756853	−	0.653585i	$-0.773264\pi$
$967$	−45517.8			−1.51371			−0.756853	+	0.653585i	$0.773264\pi$
$968$	−4477.65	−	7755.51i	−0.148675	−	0.257512i
$969$	3393.84	−	5878.31i	0.112514	−	0.194880i
$970$		0			0
$971$	−11699.1	−	20263.5i	−0.386656	−	0.669708i	0.605341	−	0.795966i	$-0.293037\pi$
$971$	−11699.1	−	20263.5i	−0.386656	−	0.669708i	−0.991997	+	0.126258i	$0.959703\pi$
$972$	15451.6			0.509886
$973$	−46190.1	−	4460.82i	−1.52188	−	0.146976i
$974$	−1053.07			−0.0346434
$975$		0			0
$976$	187.979	−	325.589i	0.00616502	−	0.0106781i
$977$	17161.9	−	29725.3i	0.561985	−	0.973386i	−0.435339	−	0.900267i	$-0.643371\pi$
$977$	17161.9	−	29725.3i	0.561985	−	0.973386i	0.997323	−	0.0731191i	$-0.0232953\pi$
$978$	269.076	+	466.054i	0.00879766	+	0.0152380i
$979$	−64407.4			−2.10262
$980$		0			0
$981$	910.402			0.0296299
$982$	1546.87	+	2679.26i	0.0502675	+	0.0870658i
$983$	18578.5	−	32178.9i	0.602809	−	1.04410i	−0.389584	−	0.920991i	$-0.627381\pi$
$983$	18578.5	−	32178.9i	0.602809	−	1.04410i	0.992394	−	0.123106i	$-0.0392854\pi$
$984$	−4896.13	+	8480.35i	−0.158621	+	0.274740i
$985$		0			0
$986$	22148.0			0.715352
$987$	−3873.57	−	374.091i	−0.124921	−	0.0120643i
$988$	10050.2			0.323622
$989$	−9329.50	−	16159.2i	−0.299961	−	0.519547i
$990$		0			0
$991$	5271.25	−	9130.08i	0.168968	−	0.292660i	−0.769090	−	0.639141i	$-0.779290\pi$
$991$	5271.25	−	9130.08i	0.168968	−	0.292660i	0.938057	+	0.346481i	$0.112623\pi$
$992$	−1129.05	−	1955.57i	−0.0361364	−	0.0625900i
$993$	28860.2			0.922306
$994$	−12827.8	−	28169.3i	−0.409330	−	0.898868i
$995$		0			0
$996$	−8228.54	−	14252.2i	−0.261778	−	0.453413i
$997$	−18128.0	+	31398.6i	−0.575846	+	0.997394i	0.420103	+	0.907476i	$0.361994\pi$
$997$	−18128.0	+	31398.6i	−0.575846	+	0.997394i	−0.995949	+	0.0899181i	$0.971339\pi$
$998$	−9492.84	+	16442.1i	−0.301093	+	0.521508i
$999$	−13479.3	−	23346.8i	−0.426892	−	0.739399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.e.n.151.3		12
5.2	odd	4		70.4.i.a.39.10	yes	24
5.3	odd	4		70.4.i.a.39.3	yes	24
5.4	even	2		350.4.e.o.151.4		12
7.2	even	3	inner	350.4.e.n.51.3		12
7.3	odd	6		2450.4.a.cx.1.3		6
7.4	even	3		2450.4.a.cy.1.4		6
35.2	odd	12		70.4.i.a.9.3	✓	24
35.3	even	12		490.4.c.e.99.3		12
35.4	even	6		2450.4.a.cv.1.3		6
35.9	even	6		350.4.e.o.51.4		12
35.17	even	12		490.4.c.e.99.10		12
35.18	odd	12		490.4.c.f.99.4		12
35.23	odd	12		70.4.i.a.9.10	yes	24
35.24	odd	6		2450.4.a.cw.1.4		6
35.32	odd	12		490.4.c.f.99.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.3	✓	24	35.2	odd	12
70.4.i.a.9.10	yes	24	35.23	odd	12
70.4.i.a.39.3	yes	24	5.3	odd	4
70.4.i.a.39.10	yes	24	5.2	odd	4
350.4.e.n.51.3		12	7.2	even	3	inner
350.4.e.n.151.3		12	1.1	even	1	trivial
350.4.e.o.51.4		12	35.9	even	6
350.4.e.o.151.4		12	5.4	even	2
490.4.c.e.99.3		12	35.3	even	12
490.4.c.e.99.10		12	35.17	even	12
490.4.c.f.99.4		12	35.18	odd	12
490.4.c.f.99.9		12	35.32	odd	12
2450.4.a.cv.1.3		6	35.4	even	6
2450.4.a.cw.1.4		6	35.24	odd	6
2450.4.a.cx.1.3		6	7.3	odd	6
2450.4.a.cy.1.4		6	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.53379 + 2.65661i) q^{3} +(-2.00000 + 3.46410i) q^{4} +6.13518 q^{6} +(18.4345 + 1.78031i) q^{7} +8.00000 q^{8} +(8.79495 + 15.2333i) q^{9} +(24.7508 - 42.8697i) q^{11} +(-6.13518 - 10.6264i) q^{12} -44.6154 q^{13} +(-15.3509 - 33.7098i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-19.6456 + 34.0272i) q^{17} +(17.5899 - 30.4666i) q^{18} +(28.1578 + 48.7708i) q^{19} +(-33.0043 + 46.2426i) q^{21} -99.0033 q^{22} +(-45.8301 - 79.3801i) q^{23} +(-12.2704 + 21.2529i) q^{24} +(44.6154 + 77.2761i) q^{26} -136.783 q^{27} +(-43.0362 + 60.2983i) q^{28} +281.845 q^{29} +(-35.2827 + 61.1114i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(75.9254 + 131.507i) q^{33} +78.5824 q^{34} -70.3596 q^{36} +(98.5446 + 170.684i) q^{37} +(56.3157 - 97.5416i) q^{38} +(68.4308 - 118.526i) q^{39} +399.021 q^{41} +(113.099 + 10.9225i) q^{42} +203.567 q^{43} +(99.0033 + 171.479i) q^{44} +(-91.6603 + 158.760i) q^{46} +(34.2494 + 59.3217i) q^{47} +49.0814 q^{48} +(336.661 + 65.6384i) q^{49} +(-60.2646 - 104.381i) q^{51} +(89.2307 - 154.552i) q^{52} +(-308.743 + 534.758i) q^{53} +(136.783 + 236.916i) q^{54} +(147.476 + 14.2425i) q^{56} -172.753 q^{57} +(-281.845 - 488.169i) q^{58} +(-240.256 + 416.136i) q^{59} +(11.7487 + 20.3493i) q^{61} +141.131 q^{62} +(135.010 + 296.476i) q^{63} +64.0000 q^{64} +(151.851 - 263.013i) q^{66} +(126.062 - 218.346i) q^{67} +(-78.5824 - 136.109i) q^{68} +281.176 q^{69} +835.640 q^{71} +(70.3596 + 121.866i) q^{72} +(-128.893 + 223.249i) q^{73} +(197.089 - 341.369i) q^{74} -225.263 q^{76} +(532.590 - 746.216i) q^{77} -273.723 q^{78} +(386.850 + 670.044i) q^{79} +(-27.6658 + 47.9185i) q^{81} +(-399.021 - 691.125i) q^{82} +1341.21 q^{83} +(-94.1805 - 206.816i) q^{84} +(-203.567 - 352.588i) q^{86} +(-432.292 + 748.752i) q^{87} +(198.007 - 342.957i) q^{88} +(-650.558 - 1126.80i) q^{89} +(-822.462 - 79.4293i) q^{91} +366.641 q^{92} +(-108.233 - 187.465i) q^{93} +(68.4988 - 118.643i) q^{94} +(-49.0814 - 85.0115i) q^{96} +323.729 q^{97} +(-222.972 - 648.752i) q^{98} +870.729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 7 q^{3} - 24 q^{4} + 28 q^{6} - 9 q^{7} + 96 q^{8} - 31 q^{9} - 31 q^{11} - 28 q^{12} + 118 q^{13} + 42 q^{14} - 96 q^{16} - 68 q^{17} - 62 q^{18} - 93 q^{19} + 175 q^{21} + 124 q^{22}+ \cdots + 8546 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 7 * q^3 - 24 * q^4 + 28 * q^6 - 9 * q^7 + 96 * q^8 - 31 * q^9 - 31 * q^11 - 28 * q^12 + 118 * q^13 + 42 * q^14 - 96 * q^16 - 68 * q^17 - 62 * q^18 - 93 * q^19 + 175 * q^21 + 124 * q^22 + 94 * q^23 - 56 * q^24 - 118 * q^26 + 770 * q^27 - 48 * q^28 + 338 * q^29 - 326 * q^31 - 192 * q^32 - 400 * q^33 + 272 * q^34 + 248 * q^36 + 253 * q^37 - 186 * q^38 + 434 * q^39 + 396 * q^41 - 154 * q^42 - 198 * q^43 - 124 * q^44 + 188 * q^46 - 901 * q^47 + 224 * q^48 - 801 * q^49 - 724 * q^51 - 236 * q^52 - 233 * q^53 - 770 * q^54 - 72 * q^56 - 1036 * q^57 - 338 * q^58 - 668 * q^59 - 157 * q^61 + 1304 * q^62 + 2413 * q^63 + 768 * q^64 - 800 * q^66 - 1193 * q^67 - 272 * q^68 - 90 * q^69 + 2216 * q^71 - 248 * q^72 - 1458 * q^73 + 506 * q^74 + 744 * q^76 + 655 * q^77 - 1736 * q^78 + 886 * q^79 + 614 * q^81 - 396 * q^82 + 3598 * q^83 - 392 * q^84 + 198 * q^86 - 789 * q^87 - 248 * q^88 - 3047 * q^89 - 2182 * q^91 - 752 * q^92 - 1902 * q^93 - 1802 * q^94 - 224 * q^96 + 6808 * q^97 + 1452 * q^98 + 8546 * q^99

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