LMFDB - Embedded newform 225.4.e.g.76.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.4
Character	$\chi$	$=$	225.76
Dual form			225.4.e.g.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54370 - 2.67377i) q^{2} +(4.77188 - 2.05649i) q^{3} +(-0.766022 + 1.32679i) q^{4} +(-12.8649 - 9.58430i) q^{6} +(-15.6602 - 27.1243i) q^{7} -19.9692 q^{8} +(18.5417 - 19.6266i) q^{9} +O(q^{10})$	\(q+(-1.54370 - 2.67377i) q^{2} +(4.77188 - 2.05649i) q^{3} +(-0.766022 + 1.32679i) q^{4} +(-12.8649 - 9.58430i) q^{6} +(-15.6602 - 27.1243i) q^{7} -19.9692 q^{8} +(18.5417 - 19.6266i) q^{9} +(9.59684 + 16.6222i) q^{11} +(-0.926840 + 7.90660i) q^{12} +(-10.4955 + 18.1787i) q^{13} +(-48.3493 + 83.7434i) q^{14} +(36.9546 + 64.0072i) q^{16} +6.19137 q^{17} +(-81.0999 - 19.2786i) q^{18} -96.6654 q^{19} +(-130.509 - 97.2287i) q^{21} +(29.6293 - 51.3194i) q^{22} +(81.4928 - 141.150i) q^{23} +(-95.2905 + 41.0664i) q^{24} +64.8074 q^{26} +(48.1169 - 131.787i) q^{27} +47.9842 q^{28} +(-3.82461 - 6.62442i) q^{29} +(-112.512 + 194.877i) q^{31} +(34.2170 - 59.2655i) q^{32} +(79.9784 + 59.5834i) q^{33} +(-9.55763 - 16.5543i) q^{34} +(11.8371 + 39.6354i) q^{36} -155.911 q^{37} +(149.222 + 258.461i) q^{38} +(-12.6989 + 108.330i) q^{39} +(157.611 - 272.989i) q^{41} +(-58.4997 + 499.044i) q^{42} +(-96.3793 - 166.934i) q^{43} -29.4056 q^{44} -503.202 q^{46} +(159.156 + 275.666i) q^{47} +(307.973 + 229.438i) q^{48} +(-318.983 + 552.495i) q^{49} +(29.5445 - 12.7325i) q^{51} +(-16.0795 - 27.8505i) q^{52} -277.459 q^{53} +(-426.645 + 74.7860i) q^{54} +(312.721 + 541.649i) q^{56} +(-461.276 + 198.791i) q^{57} +(-11.8081 + 20.4522i) q^{58} +(214.646 - 371.778i) q^{59} +(44.9674 + 77.8858i) q^{61} +694.741 q^{62} +(-822.725 - 195.573i) q^{63} +379.991 q^{64} +(35.8496 - 305.823i) q^{66} +(291.652 - 505.156i) q^{67} +(-4.74273 + 8.21465i) q^{68} +(98.6014 - 841.139i) q^{69} +132.605 q^{71} +(-370.263 + 391.928i) q^{72} -259.933 q^{73} +(240.680 + 416.871i) q^{74} +(74.0478 - 128.255i) q^{76} +(300.577 - 520.614i) q^{77} +(309.253 - 133.276i) q^{78} +(-62.3245 - 107.949i) q^{79} +(-41.4099 - 727.823i) q^{81} -973.214 q^{82} +(18.3599 + 31.8003i) q^{83} +(228.975 - 98.6790i) q^{84} +(-297.562 + 515.392i) q^{86} +(-31.8736 - 23.7457i) q^{87} +(-191.641 - 331.932i) q^{88} +333.424 q^{89} +657.443 q^{91} +(124.851 + 216.248i) q^{92} +(-136.133 + 1161.31i) q^{93} +(491.379 - 851.093i) q^{94} +(41.4005 - 353.175i) q^{96} +(-514.623 - 891.353i) q^{97} +1969.66 q^{98} +(504.180 + 119.851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	$ 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) $ 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.54370	−	2.67377i	−0.545781	−	0.945320i	−0.998557	−	0.0536957i	$-0.982900\pi$
$2$	−1.54370	−	2.67377i	−0.545781	−	0.945320i	0.452777	−	0.891624i	$-0.350433\pi$
$3$	4.77188	−	2.05649i	0.918349	−	0.395771i
$3$	4.77188	−	2.05649i	0.918349	−	0.395771i
$4$	−0.766022	+	1.32679i	−0.0957528	+	0.165849i
$5$		0			0
$5$		0			0
$6$	−12.8649	−	9.58430i	−0.875347	−	0.652129i
$7$	−15.6602	−	27.1243i	−0.845571	−	1.46457i	−0.885124	−	0.465354i	$-0.845927\pi$
$7$	−15.6602	−	27.1243i	−0.845571	−	1.46457i	0.0395535	−	0.999217i	$-0.487406\pi$
$8$	−19.9692			−0.882521
$9$	18.5417	−	19.6266i	0.686730	−	0.726913i
$10$		0			0
$11$	9.59684	+	16.6222i	0.263051	+	0.455617i	0.967051	−	0.254583i	$-0.0819381\pi$
$11$	9.59684	+	16.6222i	0.263051	+	0.455617i	−0.704000	+	0.710199i	$0.748605\pi$
$12$	−0.926840	+	7.90660i	−0.0222963	+	0.190203i
$13$	−10.4955	+	18.1787i	−0.223917	+	0.387835i	−0.955994	−	0.293387i	$-0.905218\pi$
$13$	−10.4955	+	18.1787i	−0.223917	+	0.387835i	0.732077	+	0.681222i	$0.238551\pi$
$14$	−48.3493	+	83.7434i	−0.922992	+	1.59867i
$15$		0			0
$16$	36.9546	+	64.0072i	0.577416	+	1.00011i
$17$	6.19137			0.0883311			0.0441656	−	0.999024i	$-0.485937\pi$
$17$	6.19137			0.0883311			0.0441656	+	0.999024i	$0.485937\pi$
$18$	−81.0999	−	19.2786i	−1.06197	−	0.252445i
$19$	−96.6654			−1.16719			−0.583594	−	0.812046i	$-0.698354\pi$
$19$	−96.6654			−1.16719			−0.583594	+	0.812046i	$0.698354\pi$
$20$		0			0
$21$	−130.509	−	97.2287i	−1.35616	−	1.01034i
$22$	29.6293	−	51.3194i	0.287136	−	0.497334i
$23$	81.4928	−	141.150i	0.738801	−	1.27964i	−0.214234	−	0.976782i	$-0.568726\pi$
$23$	81.4928	−	141.150i	0.738801	−	1.27964i	0.953035	−	0.302859i	$-0.0979412\pi$
$24$	−95.2905	+	41.0664i	−0.810462	+	0.349277i
$25$		0			0
$26$	64.8074			0.488837
$27$	48.1169	−	131.787i	0.342967	−	0.939348i
$28$	47.9842			0.323863
$29$	−3.82461	−	6.62442i	−0.0244901	−	0.0424181i	0.853521	−	0.521059i	$-0.174463\pi$
$29$	−3.82461	−	6.62442i	−0.0244901	−	0.0424181i	−0.878011	+	0.478641i	$0.841130\pi$
$30$		0			0
$31$	−112.512	+	194.877i	−0.651865	+	1.12906i	0.330805	+	0.943699i	$0.392680\pi$
$31$	−112.512	+	194.877i	−0.651865	+	1.12906i	−0.982670	+	0.185364i	$0.940654\pi$
$32$	34.2170	−	59.2655i	0.189024	−	0.327399i
$33$	79.9784	+	59.5834i	0.421892	+	0.314307i
$34$	−9.55763	−	16.5543i	−0.0482094	−	0.0835011i
$35$		0			0
$36$	11.8371	+	39.6354i	0.0548012	+	0.183497i
$37$	−155.911			−0.692748			−0.346374	−	0.938097i	$-0.612587\pi$
$37$	−155.911			−0.692748			−0.346374	+	0.938097i	$0.612587\pi$
$38$	149.222	+	258.461i	0.637028	+	1.10337i
$39$	−12.6989	+	108.330i	−0.0521396	+	0.444788i
$40$		0			0
$41$	157.611	−	272.989i	0.600357	−	1.03985i	−0.392410	−	0.919790i	$-0.628359\pi$
$41$	157.611	−	272.989i	0.600357	−	1.03985i	0.992767	−	0.120058i	$-0.0383081\pi$
$42$	−58.4997	+	499.044i	−0.214921	+	1.83343i
$43$	−96.3793	−	166.934i	−0.341807	−	0.592027i	0.642961	−	0.765899i	$-0.277706\pi$
$43$	−96.3793	−	166.934i	−0.341807	−	0.592027i	−0.984768	+	0.173871i	$0.944372\pi$
$44$	−29.4056			−0.100751
$45$		0			0
$46$	−503.202			−1.61289
$47$	159.156	+	275.666i	0.493942	+	0.855533i	0.999976	−	0.00698057i	$-0.00222200\pi$
$47$	159.156	+	275.666i	0.493942	+	0.855533i	−0.506033	+	0.862514i	$0.668889\pi$
$48$	307.973	+	229.438i	0.926085	+	0.689928i
$49$	−318.983	+	552.495i	−0.929980	+	1.61077i
$50$		0			0
$51$	29.5445	−	12.7325i	0.0811188	−	0.0349589i
$52$	−16.0795	−	27.8505i	−0.0428813	−	0.0742725i
$53$	−277.459			−0.719093			−0.359547	−	0.933127i	$-0.617069\pi$
$53$	−277.459			−0.719093			−0.359547	+	0.933127i	$0.617069\pi$
$54$	−426.645	+	74.7860i	−1.07517	+	0.188464i
$55$		0			0
$56$	312.721	+	541.649i	0.746234	+	1.29252i
$57$	−461.276	+	198.791i	−1.07189	+	0.461939i
$58$	−11.8081	+	20.4522i	−0.0267324	+	0.0463019i
$59$	214.646	−	371.778i	0.473636	−	0.820362i	−0.525908	−	0.850541i	$-0.676275\pi$
$59$	214.646	−	371.778i	0.473636	−	0.820362i	0.999544	+	0.0301794i	$0.00960786\pi$
$60$		0			0
$61$	44.9674	+	77.8858i	0.0943850	+	0.163480i	0.909352	−	0.416028i	$-0.136578\pi$
$61$	44.9674	+	77.8858i	0.0943850	+	0.163480i	−0.814967	+	0.579508i	$0.803245\pi$
$62$	694.741			1.42310
$63$	−822.725	−	195.573i	−1.64529	−	0.391109i
$64$	379.991			0.742169
$65$		0			0
$66$	35.8496	−	305.823i	0.0668604	−	0.570366i
$67$	291.652	−	505.156i	0.531805	−	0.921113i	−0.467506	−	0.883990i	$-0.654847\pi$
$67$	291.652	−	505.156i	0.531805	−	0.921113i	0.999311	−	0.0371232i	$-0.0118194\pi$
$68$	−4.74273	+	8.21465i	−0.00845795	+	0.0146496i
$69$	98.6014	−	841.139i	0.172032	−	1.46755i
$70$		0			0
$71$	132.605			0.221653			0.110826	−	0.993840i	$-0.464650\pi$
$71$	132.605			0.221653			0.110826	+	0.993840i	$0.464650\pi$
$72$	−370.263	+	391.928i	−0.606054	+	0.641516i
$73$	−259.933			−0.416752			−0.208376	−	0.978049i	$-0.566818\pi$
$73$	−259.933			−0.416752			−0.208376	+	0.978049i	$0.566818\pi$
$74$	240.680	+	416.871i	0.378088	+	0.654868i
$75$		0			0
$76$	74.0478	−	128.255i	0.111761	−	0.193576i
$77$	300.577	−	520.614i	0.444856	−	0.770513i
$78$	309.253	−	133.276i	0.448923	−	0.193468i
$79$	−62.3245	−	107.949i	−0.0887601	−	0.153737i	0.818227	−	0.574895i	$-0.194957\pi$
$79$	−62.3245	−	107.949i	−0.0887601	−	0.153737i	−0.906987	+	0.421158i	$0.861624\pi$
$80$		0			0
$81$	−41.4099	−	727.823i	−0.0568037	−	0.998385i
$82$	−973.214			−1.31065
$83$	18.3599	+	31.8003i	0.0242802	+	0.0420546i	0.877910	−	0.478825i	$-0.158937\pi$
$83$	18.3599	+	31.8003i	0.0242802	+	0.0420546i	−0.853630	+	0.520880i	$0.825604\pi$
$84$	228.975	−	98.6790i	0.297419	−	0.128176i
$85$		0			0
$86$	−297.562	+	515.392i	−0.373103	+	0.646234i
$87$	−31.8736	−	23.7457i	−0.0392783	−	0.0292621i
$88$	−191.641	−	331.932i	−0.232148	−	0.402092i
$89$	333.424			0.397111			0.198555	−	0.980090i	$-0.436375\pi$
$89$	333.424			0.397111			0.198555	+	0.980090i	$0.436375\pi$
$90$		0			0
$91$	657.443			0.757349
$92$	124.851	+	216.248i	0.141485	+	0.245058i
$93$	−136.133	+	1161.31i	−0.151789	+	1.29486i
$94$	491.379	−	851.093i	0.539168	−	0.933867i
$95$		0			0
$96$	41.4005	−	353.175i	0.0440148	−	0.375477i
$97$	−514.623	−	891.353i	−0.538681	−	0.933022i	−0.998975	−	0.0452563i	$-0.985590\pi$
$97$	−514.623	−	891.353i	−0.538681	−	0.933022i	0.460295	−	0.887766i	$-0.347744\pi$
$98$	1969.66			2.03026
$99$	504.180	+	119.851i	0.511838	+	0.121671i
$100$		0			0
$101$	−463.481	−	802.773i	−0.456615	−	0.790880i	0.542165	−	0.840272i	$-0.317605\pi$
$101$	−463.481	−	802.773i	−0.456615	−	0.790880i	−0.998779	+	0.0493922i	$0.984272\pi$
$102$	−79.6516	−	59.3400i	−0.0773204	−	0.0576033i
$103$	843.801	−	1461.51i	0.807205	−	1.39812i	−0.107587	−	0.994196i	$-0.534312\pi$
$103$	843.801	−	1461.51i	0.807205	−	1.39812i	0.914792	−	0.403925i	$-0.132354\pi$
$104$	209.586	−	363.013i	0.197611	−	0.342272i
$105$		0			0
$106$	428.314	+	741.861i	0.392467	+	0.679773i
$107$	750.833			0.678372			0.339186	−	0.940719i	$-0.389848\pi$
$107$	750.833			0.678372			0.339186	+	0.940719i	$0.389848\pi$
$108$	137.995	+	164.793i	0.122950	+	0.146826i
$109$	401.243			0.352589			0.176294	−	0.984338i	$-0.443589\pi$
$109$	401.243			0.352589			0.176294	+	0.984338i	$0.443589\pi$
$110$		0			0
$111$	−743.990	+	320.630i	−0.636184	+	0.274170i
$112$	1157.43	−	2004.73i	0.976492	−	1.69133i
$113$	−110.225	+	190.915i	−0.0917620	+	0.158936i	−0.908253	−	0.418422i	$-0.862583\pi$
$113$	−110.225	+	190.915i	−0.0917620	+	0.158936i	0.816491	+	0.577359i	$0.195917\pi$
$114$	1243.59	+	926.470i	1.02169	+	0.761157i
$115$		0			0
$116$	11.7189			0.00937997
$117$	162.182	+	543.054i	0.128152	+	0.429106i
$118$	−1325.40			−1.03401
$119$	−96.9581	−	167.936i	−0.0746902	−	0.129367i
$120$		0			0
$121$	481.301	−	833.638i	0.361609	−	0.626325i
$122$	138.832	−	240.465i	0.103027	−	0.178448i
$123$	190.699	−	1626.80i	0.139795	−	1.19255i
$124$	−172.374	−	298.560i	−0.124836	−	0.216222i
$125$		0			0
$126$	747.123	+	2501.68i	0.528246	+	1.76879i
$127$	−1185.99			−0.828659			−0.414329	−	0.910127i	$-0.635984\pi$
$127$	−1185.99			−0.828659			−0.414329	+	0.910127i	$0.635984\pi$
$128$	−860.327	−	1490.13i	−0.594085	−	1.02899i
$129$	−803.208	−	598.386i	−0.548206	−	0.408410i
$130$		0			0
$131$	1385.40	−	2399.59i	0.923993	−	1.60040i	0.130822	−	0.991406i	$-0.458239\pi$
$131$	1385.40	−	2399.59i	0.923993	−	1.60040i	0.793172	−	0.608998i	$-0.208428\pi$
$132$	−140.320	+	60.4722i	−0.0925248	+	0.0398745i
$133$	1513.80	+	2621.98i	0.986940	+	1.70943i
$134$	−1800.89			−1.16100
$135$		0			0
$136$	−123.637			−0.0779541
$137$	660.968	+	1144.83i	0.412192	+	0.713937i	0.995129	−	0.0985799i	$-0.0314300\pi$
$137$	660.968	+	1144.83i	0.412192	+	0.713937i	−0.582937	+	0.812517i	$0.698097\pi$
$138$	−2401.22	+	1034.83i	−1.48120	+	0.638337i
$139$	905.223	−	1567.89i	0.552374	−	0.956740i	−0.445729	−	0.895168i	$-0.647055\pi$
$139$	905.223	−	1567.89i	0.552374	−	0.956740i	0.998103	−	0.0615716i	$-0.0196113\pi$
$140$		0			0
$141$	1326.38	+	988.145i	0.792207	+	0.590190i
$142$	−204.703	−	354.556i	−0.120974	−	0.209533i
$143$	−402.893			−0.235606
$144$	1941.45	+	461.509i	1.12352	+	0.267077i
$145$		0			0
$146$	401.259	+	695.001i	0.227455	+	0.393964i
$147$	−385.950	+	3292.43i	−0.216549	+	1.84731i
$148$	119.432	−	206.861i	0.0663325	−	0.114891i
$149$	127.384	−	220.635i	0.0700382	−	0.121310i	−0.828880	−	0.559427i	$-0.811021\pi$
$149$	127.384	−	220.635i	0.0700382	−	0.121310i	0.898918	+	0.438117i	$0.144355\pi$
$150$		0			0
$151$	−1422.37	−	2463.62i	−0.766563	−	1.32773i	−0.939417	−	0.342778i	$-0.888632\pi$
$151$	−1422.37	−	2463.62i	−0.766563	−	1.32773i	0.172854	−	0.984947i	$-0.444701\pi$
$152$	1930.33			1.03007
$153$	114.799	−	121.516i	0.0606596	−	0.0642090i
$154$	−1856.00			−0.971175
$155$		0			0
$156$	−134.004	−	99.8321i	−0.0687749	−	0.0512369i
$157$	−872.568	+	1511.33i	−0.443558	+	0.768264i	−0.997950	−	0.0639909i	$-0.979617\pi$
$157$	−872.568	+	1511.33i	−0.443558	+	0.768264i	0.554393	+	0.832255i	$0.312950\pi$
$158$	−192.421	+	333.282i	−0.0968871	+	0.167813i
$159$	−1324.00	+	570.591i	−0.660379	+	0.284596i
$160$		0			0
$161$	−5104.77			−2.49884
$162$	−1882.10	+	1234.26i	−0.912791	+	0.598597i
$163$	−2607.78			−1.25311			−0.626554	−	0.779378i	$-0.715535\pi$
$163$	−2607.78			−1.25311			−0.626554	+	0.779378i	$0.715535\pi$
$164$	241.466	+	418.232i	0.114972	+	0.199137i
$165$		0			0
$166$	56.6843	−	98.1801i	0.0265034	−	0.0459052i
$167$	−611.660	+	1059.43i	−0.283423	+	0.490904i	−0.972226	−	0.234046i	$-0.924803\pi$
$167$	−611.660	+	1059.43i	−0.283423	+	0.490904i	0.688802	+	0.724949i	$0.258137\pi$
$168$	2606.16	+	1941.58i	1.19684	+	0.891642i
$169$	878.191	+	1521.07i	0.399723	+	0.692340i
$170$		0			0
$171$	−1792.34	+	1897.22i	−0.801543	+	0.848443i
$172$	295.315			0.130916
$173$	1394.97	+	2416.15i	0.613048	+	1.06183i	0.990724	+	0.135893i	$0.0433903\pi$
$173$	1394.97	+	2416.15i	0.613048	+	1.06183i	−0.377675	+	0.925938i	$0.623276\pi$
$174$	−14.2871	+	121.879i	−0.00622472	+	0.0531012i
$175$		0			0
$176$	−709.295	+	1228.53i	−0.303779	+	0.526161i
$177$	259.709	−	2215.50i	0.110288	−	0.940830i
$178$	−514.706	−	891.498i	−0.216735	−	0.375396i
$179$	769.584			0.321349			0.160674	−	0.987007i	$-0.448633\pi$
$179$	769.584			0.321349			0.160674	+	0.987007i	$0.448633\pi$
$180$		0			0
$181$	2302.38			0.945495			0.472747	−	0.881198i	$-0.343262\pi$
$181$	2302.38			0.945495			0.472747	+	0.881198i	$0.343262\pi$
$182$	−1014.90	−	1757.85i	−0.413347	−	0.715937i
$183$	374.750	+	279.187i	0.151379	+	0.112776i
$184$	−1627.34	+	2818.64i	−0.652008	+	1.12931i
$185$		0			0
$186$	3315.22	−	1428.73i	1.30690	−	0.563222i
$187$	59.4176	+	102.914i	0.0232355	+	0.0402451i
$188$	−487.668			−0.189185
$189$	−4328.14	+	758.672i	−1.66574	+	0.291986i
$190$		0			0
$191$	2114.48	+	3662.39i	0.801039	+	1.38744i	0.918933	+	0.394414i	$0.129053\pi$
$191$	2114.48	+	3662.39i	0.801039	+	1.38744i	−0.117893	+	0.993026i	$0.537614\pi$
$192$	1813.27	−	781.446i	0.681570	−	0.293729i
$193$	2182.04	−	3779.41i	0.813818	−	1.40957i	−0.0963548	−	0.995347i	$-0.530718\pi$
$193$	2182.04	−	3779.41i	0.813818	−	1.40957i	0.910173	−	0.414228i	$-0.135948\pi$
$194$	−1588.85	+	2751.96i	−0.588003	+	1.01845i
$195$		0			0
$196$	−488.697	−	846.447i	−0.178096	−	0.308472i
$197$	−1031.50			−0.373052			−0.186526	−	0.982450i	$-0.559723\pi$
$197$	−1031.50			−0.373052			−0.186526	+	0.982450i	$0.559723\pi$
$198$	−457.850	−	1533.07i	−0.164333	−	0.550257i
$199$	1271.59			0.452966			0.226483	−	0.974015i	$-0.427277\pi$
$199$	1271.59			0.452966			0.226483	+	0.974015i	$0.427277\pi$
$200$		0			0
$201$	352.881	−	3010.32i	0.123832	−	1.05638i
$202$	−1430.95	+	2478.48i	−0.498423	+	0.863294i
$203$	−119.788	+	207.479i	−0.0414162	+	0.0717350i
$204$	−5.73842	+	48.9527i	−0.00196946	+	0.0168009i
$205$		0			0
$206$	−5210.30			−1.76223
$207$	−1259.28	−	4216.59i	−0.422830	−	1.41581i
$208$	−1551.42			−0.517172
$209$	−927.682	−	1606.79i	−0.307029	−	0.531790i
$210$		0			0
$211$	−173.148	+	299.900i	−0.0564928	+	0.0978483i	−0.892889	−	0.450277i	$-0.851325\pi$
$211$	−173.148	+	299.900i	−0.0564928	+	0.0978483i	0.836396	+	0.548126i	$0.184658\pi$
$212$	212.540	−	368.130i	0.0688552	−	0.119261i
$213$	632.776	−	272.701i	0.203555	−	0.0877238i
$214$	−1159.06	−	2007.55i	−0.370242	−	0.641278i
$215$		0			0
$216$	−960.855	+	2631.67i	−0.302675	+	0.828994i
$217$	7047.86			2.20479
$218$	−619.400	−	1072.83i	−0.192436	−	0.333309i
$219$	−1240.37	+	534.550i	−0.382724	+	0.164938i
$220$		0			0
$221$	−64.9813	+	112.551i	−0.0197788	+	0.0342579i
$222$	2005.79	+	1494.30i	0.606395	+	0.451761i
$223$	2019.66	+	3498.16i	0.606487	+	1.05047i	0.991815	+	0.127687i	$0.0407552\pi$
$223$	2019.66	+	3498.16i	0.606487	+	1.05047i	−0.385327	+	0.922780i	$0.625911\pi$
$224$	−2143.38			−0.639332
$225$		0			0
$226$	680.618			0.200328
$227$	−431.226	−	746.905i	−0.126086	−	0.218387i	0.796071	−	0.605203i	$-0.206908\pi$
$227$	−431.226	−	746.905i	−0.126086	−	0.218387i	−0.922157	+	0.386816i	$0.873575\pi$
$228$	89.5934	−	764.294i	0.0260240	−	0.222003i
$229$	−479.108	+	829.840i	−0.138255	+	0.239464i	−0.926836	−	0.375466i	$-0.877483\pi$
$229$	−479.108	+	829.840i	−0.138255	+	0.239464i	0.788581	+	0.614931i	$0.210816\pi$
$230$		0			0
$231$	363.680	−	3102.44i	0.103586	−	0.883661i
$232$	76.3743	+	132.284i	0.0216130	+	0.0374348i
$233$	−1159.05			−0.325887			−0.162944	−	0.986635i	$-0.552099\pi$
$233$	−1159.05			−0.325887			−0.162944	+	0.986635i	$0.552099\pi$
$234$	1201.64	−	1271.95i	0.335699	−	0.355342i
$235$		0			0
$236$	328.847	+	569.580i	0.0907039	+	0.157104i
$237$	−519.401	−	386.951i	−0.142358	−	0.106056i
$238$	−299.349	+	518.487i	−0.0815289	+	0.141212i
$239$	2023.20	−	3504.29i	0.547573	−	0.948424i	−0.450867	−	0.892591i	$-0.648885\pi$
$239$	2023.20	−	3504.29i	0.547573	−	0.948424i	0.998440	−	0.0558333i	$-0.0177815\pi$
$240$		0			0
$241$	1212.74	+	2100.53i	0.324148	+	0.561441i	0.981340	−	0.192283i	$-0.0615890\pi$
$241$	1212.74	+	2100.53i	0.324148	+	0.561441i	−0.657191	+	0.753724i	$0.728256\pi$
$242$	−2971.94			−0.789436
$243$	−1694.36	−	3387.93i	−0.447298	−	0.894385i
$244$	−137.784			−0.0361505
$245$		0			0
$246$	−4644.06	+	2001.40i	−1.20364	+	0.518719i
$247$	1014.55	−	1757.25i	0.261353	−	0.452676i
$248$	2246.78	−	3891.53i	0.575284	−	0.996422i
$249$	153.008	+	113.990i	0.0389417	+	0.0290114i
$250$		0			0
$251$	7272.75			1.82889			0.914445	−	0.404709i	$-0.132627\pi$
$251$	7272.75			1.82889			0.914445	+	0.404709i	$0.132627\pi$
$252$	889.709	−	941.769i	0.222406	−	0.235420i
$253$	3128.29			0.777368
$254$	1830.81	+	3171.06i	0.452266	+	0.783347i
$255$		0			0
$256$	−1136.21	+	1967.98i	−0.277396	+	0.480464i
$257$	1617.09	−	2800.88i	0.392495	−	0.679822i	−0.600283	−	0.799788i	$-0.704945\pi$
$257$	1617.09	−	2800.88i	0.392495	−	0.679822i	0.992778	+	0.119966i	$0.0382787\pi$
$258$	−360.032	+	3071.32i	−0.0868782	+	0.741132i
$259$	2441.60	+	4228.98i	0.585767	+	1.01458i
$260$		0			0
$261$	−200.930	−	47.7638i	−0.0476523	−	0.0113276i
$262$	−8554.58			−2.01719
$263$	528.308	+	915.056i	0.123866	+	0.214543i	0.921289	−	0.388878i	$-0.127137\pi$
$263$	528.308	+	915.056i	0.123866	+	0.214543i	−0.797423	+	0.603421i	$0.793804\pi$
$264$	−1597.10	−	1189.83i	−0.372329	−	0.277383i
$265$		0			0
$266$	4673.70	−	8095.09i	1.07731	−	1.86595i
$267$	1591.06	−	685.682i	0.364686	−	0.157165i
$268$	446.823	+	773.921i	0.101844	+	0.176398i
$269$	−1528.13			−0.346363			−0.173182	−	0.984890i	$-0.555405\pi$
$269$	−1528.13			−0.346363			−0.173182	+	0.984890i	$0.555405\pi$
$270$		0			0
$271$	−7368.77			−1.65174			−0.825869	−	0.563862i	$-0.809315\pi$
$271$	−7368.77			−1.65174			−0.825869	+	0.563862i	$0.809315\pi$
$272$	228.800	+	396.293i	0.0510038	+	0.0883411i
$273$	3137.24	−	1352.02i	0.695511	−	0.299737i
$274$	2040.67	−	3534.55i	0.449933	−	0.779306i
$275$		0			0
$276$	1040.48	+	775.154i	0.226919	+	0.169054i
$277$	927.160	+	1605.89i	0.201111	+	0.348334i	0.948887	−	0.315617i	$-0.102212\pi$
$277$	927.160	+	1605.89i	0.201111	+	0.348334i	−0.747776	+	0.663951i	$0.768878\pi$
$278$	−5589.57			−1.20590
$279$	1738.61	+	5821.59i	0.373075	+	1.24921i
$280$		0			0
$281$	−207.566	−	359.515i	−0.0440653	−	0.0763233i	0.843152	−	0.537676i	$-0.180698\pi$
$281$	−207.566	−	359.515i	−0.0440653	−	0.0763233i	−0.887217	+	0.461353i	$0.847364\pi$
$282$	594.538	−	5071.83i	0.125547	−	1.07100i
$283$	−2058.11	+	3564.75i	−0.432303	+	0.748771i	−0.997071	−	0.0764785i	$-0.975632\pi$
$283$	−2058.11	+	3564.75i	−0.432303	+	0.748771i	0.564768	+	0.825250i	$0.308966\pi$
$284$	−101.579	+	175.939i	−0.0212239	+	0.0367608i
$285$		0			0
$286$	621.946	+	1077.24i	0.128589	+	0.222723i
$287$	−9872.84			−2.03058
$288$	−528.742	−	1770.45i	−0.108182	−	0.362238i
$289$	−4874.67			−0.992198
$290$		0			0
$291$	−4288.78	−	3195.11i	−0.863961	−	0.643646i
$292$	199.115	−	344.877i	0.0399051	−	0.0691177i
$293$	−2453.10	+	4248.89i	−0.489118	+	0.847177i	−0.999922	−	0.0125203i	$-0.996015\pi$
$293$	−2453.10	+	4248.89i	−0.489118	+	0.847177i	0.510804	+	0.859697i	$0.329348\pi$
$294$	9398.98	−	4050.58i	1.86449	−	0.803519i
$295$		0			0
$296$	3113.42			0.611364
$297$	2652.36	−	464.928i	0.518200	−	0.0908344i
$298$	−786.570			−0.152902
$299$	1710.61	+	2962.86i	0.330860	+	0.573066i
$300$		0			0
$301$	−3018.64	+	5228.43i	−0.578045	+	1.00120i
$302$	−4391.43	+	7606.18i	−0.836750	+	1.44929i
$303$	−3862.57	−	2877.59i	−0.732340	−	0.545589i
$304$	−3572.23	−	6187.29i	−0.673952	−	1.16732i
$305$		0			0
$306$	−502.120	−	119.361i	−0.0938049	−	0.0222987i
$307$	6909.30			1.28448			0.642239	−	0.766504i	$-0.278006\pi$
$307$	6909.30			1.28448			0.642239	+	0.766504i	$0.278006\pi$
$308$	460.497	+	797.604i	0.0851923	+	0.147557i
$309$	1020.95	−	8709.40i	0.187960	−	1.60343i
$310$		0			0
$311$	2686.93	−	4653.90i	0.489910	−	0.848549i	−0.510023	−	0.860161i	$-0.670363\pi$
$311$	2686.93	−	4653.90i	0.489910	−	0.848549i	0.999933	+	0.0116121i	$0.00369633\pi$
$312$	253.586	−	2163.26i	0.0460143	−	0.392534i
$313$	−1196.30	−	2072.06i	−0.216035	−	0.374184i	0.737557	−	0.675285i	$-0.235979\pi$
$313$	−1196.30	−	2072.06i	−0.216035	−	0.374184i	−0.953592	+	0.301101i	$0.902646\pi$
$314$	5387.94			0.968340
$315$		0			0
$316$	190.968			0.0339961
$317$	591.841	+	1025.10i	0.104861	+	0.181625i	0.913682	−	0.406431i	$-0.133227\pi$
$317$	591.841	+	1025.10i	0.104861	+	0.181625i	−0.808820	+	0.588056i	$0.799893\pi$
$318$	3569.49	+	2659.25i	0.629456	+	0.468942i
$319$	73.4083	−	127.147i	0.0128843	−	0.0223162i
$320$		0			0
$321$	3582.89	−	1544.08i	0.622982	−	0.268480i
$322$	7880.24	+	13649.0i	1.36382	+	2.36220i
$323$	−598.492			−0.103099
$324$	997.389	+	502.586i	0.171020	+	0.0861773i
$325$		0			0
$326$	4025.62	+	6972.59i	0.683922	+	1.18459i
$327$	1914.69	−	825.153i	0.323799	−	0.139544i
$328$	−3147.35	+	5451.37i	−0.529827	+	0.917688i
$329$	4984.83	−	8633.98i	0.835327	−	1.44683i
$330$		0			0
$331$	4693.21	+	8128.88i	0.779342	+	1.34986i	0.932321	+	0.361631i	$0.117780\pi$
$331$	4693.21	+	8128.88i	0.779342	+	1.34986i	−0.152979	+	0.988229i	$0.548887\pi$
$332$	−56.2563			−0.00929960
$333$	−2890.86	+	3060.02i	−0.475731	+	0.503567i
$334$	3776.88			0.618748
$335$		0			0
$336$	1400.42	−	11946.6i	0.227379	−	1.93970i
$337$	−6085.81	+	10540.9i	−0.983724	+	1.70386i	−0.336250	+	0.941773i	$0.609159\pi$
$337$	−6085.81	+	10540.9i	−0.983724	+	1.70386i	−0.647474	+	0.762088i	$0.724174\pi$
$338$	2711.33	−	4696.16i	0.436322	−	0.755731i
$339$	−133.366	+	1137.70i	−0.0213671	+	0.182276i
$340$		0			0
$341$	−4319.05			−0.685893
$342$	7839.56	+	1863.57i	1.23952	+	0.294650i
$343$	9238.47			1.45432
$344$	1924.62	+	3333.53i	0.301652	+	0.522477i
$345$		0			0
$346$	4306.82	−	7459.63i	0.669180	−	1.15905i
$347$	−1392.78	+	2412.37i	−0.215471	+	0.373207i	−0.953418	−	0.301651i	$-0.902462\pi$
$347$	−1392.78	+	2412.37i	−0.215471	+	0.373207i	0.737947	+	0.674859i	$0.235795\pi$
$348$	55.9214	−	24.0999i	0.00861409	−	0.00371232i
$349$	1679.88	+	2909.63i	0.257656	+	0.446273i	0.965613	−	0.259982i	$-0.0837167\pi$
$349$	1679.88	+	2909.63i	0.257656	+	0.446273i	−0.707958	+	0.706255i	$0.750383\pi$
$350$		0			0
$351$	1890.70	+	2257.86i	0.287516	+	0.343350i
$352$	1313.50			0.198891
$353$	−2713.84	−	4700.51i	−0.409188	−	0.708734i	0.585611	−	0.810592i	$-0.300854\pi$
$353$	−2713.84	−	4700.51i	−0.409188	−	0.708734i	−0.994799	+	0.101858i	$0.967521\pi$
$354$	−6324.64	+	2725.66i	−0.949578	+	0.409230i
$355$		0			0
$356$	−255.410	+	442.383i	−0.0380244	+	0.0658603i
$357$	−808.032	−	601.979i	−0.119792	−	0.0892440i
$358$	−1188.01	−	2057.69i	−0.175386	−	0.303777i
$359$	−3920.74			−0.576404			−0.288202	−	0.957570i	$-0.593057\pi$
$359$	−3920.74			−0.576404			−0.288202	+	0.957570i	$0.593057\pi$
$360$		0			0
$361$	2485.20			0.362327
$362$	−3554.18	−	6156.03i	−0.516033	−	0.893795i
$363$	582.345	−	4967.81i	0.0842017	−	0.718299i
$364$	−503.616	+	872.289i	−0.0725183	+	0.125605i
$365$		0			0
$366$	167.979	−	1432.98i	0.0239901	−	0.204653i
$367$	−838.603	−	1452.50i	−0.119277	−	0.206594i	0.800204	−	0.599728i	$-0.204724\pi$
$367$	−838.603	−	1452.50i	−0.119277	−	0.206594i	−0.919481	+	0.393133i	$0.871391\pi$
$368$	12046.1			1.70638
$369$	−2435.50	−	8155.05i	−0.343596	−	1.15050i
$370$		0			0
$371$	4345.06	+	7525.87i	0.608044	+	1.05316i
$372$	−1436.53	−	1070.21i	−0.200217	−	0.149161i
$373$	−478.168	+	828.211i	−0.0663769	+	0.114968i	−0.897304	−	0.441413i	$-0.854477\pi$
$373$	−478.168	+	828.211i	−0.0663769	+	0.114968i	0.830927	+	0.556381i	$0.187811\pi$
$374$	183.446	−	317.738i	0.0253630	−	0.0439300i
$375$		0			0
$376$	−3178.21	−	5504.83i	−0.435915	−	0.755026i
$377$	160.564			0.0219349
$378$	8709.86	+	10401.3i	1.18515	+	1.41530i
$379$	10019.0			1.35789			0.678943	−	0.734191i	$-0.262438\pi$
$379$	10019.0			1.35789			0.678943	+	0.734191i	$0.262438\pi$
$380$		0			0
$381$	−5659.41	+	2438.98i	−0.760998	+	0.327959i
$382$	6528.25	−	11307.3i	0.874383	−	1.51448i
$383$	−6443.10	+	11159.8i	−0.859600	+	1.48887i	0.0127104	+	0.999919i	$0.495954\pi$
$383$	−6443.10	+	11159.8i	−0.859600	+	1.48887i	−0.872311	+	0.488952i	$0.837379\pi$
$384$	−7169.82	−	5341.47i	−0.952821	−	0.709846i
$385$		0			0
$386$	−13473.7			−1.77667
$387$	−5063.39	−	1203.64i	−0.665081	−	0.158099i
$388$	1576.85			0.206321
$389$	344.243	+	596.247i	0.0448684	+	0.0777144i	0.887587	−	0.460639i	$-0.152380\pi$
$389$	344.243	+	596.247i	0.0448684	+	0.0777144i	−0.842719	+	0.538354i	$0.819046\pi$
$390$		0			0
$391$	504.553	−	873.911i	0.0652591	−	0.113032i
$392$	6369.83	−	11032.9i	0.820727	−	1.42154i
$393$	1676.25	−	14299.6i	0.215155	−	1.83542i
$394$	1592.32	+	2757.99i	0.203604	+	0.352653i
$395$		0			0
$396$	−545.230	+	577.132i	−0.0691889	+	0.0732374i
$397$	−7893.06			−0.997837			−0.498918	−	0.866649i	$-0.666269\pi$
$397$	−7893.06			−0.997837			−0.498918	+	0.866649i	$0.666269\pi$
$398$	−1962.95	−	3399.92i	−0.247220	−	0.428198i
$399$	12615.7	+	9398.65i	1.58290	+	1.17925i
$400$		0			0
$401$	−2096.41	+	3631.09i	−0.261072	+	0.452190i	−0.966527	−	0.256565i	$-0.917409\pi$
$401$	−2096.41	+	3631.09i	−0.261072	+	0.452190i	0.705455	+	0.708755i	$0.250743\pi$
$402$	−8593.64	+	3703.51i	−1.06620	+	0.459489i
$403$	−2361.74	−	4090.65i	−0.291927	−	0.505632i
$404$	1420.15			0.174889
$405$		0			0
$406$	739.669			0.0904166
$407$	−1496.26	−	2591.59i	−0.182228	−	0.315628i
$408$	−589.979	+	254.257i	−0.0715890	+	0.0308520i
$409$	−4505.02	+	7802.92i	−0.544642	+	0.943348i	0.453987	+	0.891008i	$0.350001\pi$
$409$	−4505.02	+	7802.92i	−0.544642	+	0.943348i	−0.998629	+	0.0523398i	$0.983332\pi$
$410$		0			0
$411$	5508.39	+	4103.72i	0.661092	+	0.492510i
$412$	1292.74	+	2239.09i	0.154584	+	0.267748i
$413$	−13445.6			−1.60197
$414$	−9330.23	+	9876.17i	−1.10762	+	1.17243i
$415$		0			0
$416$	718.245	+	1244.04i	0.0846511	+	0.146620i
$417$	1095.26	−	9343.37i	0.128622	−	1.09723i
$418$	−2864.13	+	4960.81i	−0.335141	+	0.580482i
$419$	−3429.90	+	5940.76i	−0.399908	+	0.692662i	−0.993714	−	0.111947i	$-0.964291\pi$
$419$	−3429.90	+	5940.76i	−0.399908	+	0.692662i	0.593806	+	0.804608i	$0.297625\pi$
$420$		0			0
$421$	−6297.30	−	10907.2i	−0.729007	−	1.26268i	−0.957303	−	0.289085i	$-0.906649\pi$
$421$	−6297.30	−	10907.2i	−0.729007	−	1.26268i	0.228297	−	0.973592i	$-0.426684\pi$
$422$	1069.15			0.123331
$423$	8361.43	+	1987.63i	0.961103	+	0.228468i
$424$	5540.63			0.634615
$425$		0			0
$426$	−1705.96	−	1270.93i	−0.194023	−	0.144546i
$427$	1408.40	−	2439.41i	0.159618	−	0.276467i
$428$	−575.155	+	996.197i	−0.0649560	+	0.112507i
$429$	−1922.56	+	828.544i	−0.216368	+	0.0932459i
$430$		0			0
$431$	−8470.15			−0.946619			−0.473310	−	0.880896i	$-0.656941\pi$
$431$	−8470.15			−0.946619			−0.473310	+	0.880896i	$0.656941\pi$
$432$	10213.5	−	1790.30i	1.13749	−	0.199388i
$433$	8182.86			0.908183			0.454092	−	0.890955i	$-0.349964\pi$
$433$	8182.86			0.908183			0.454092	+	0.890955i	$0.349964\pi$
$434$	−10879.8	−	18844.3i	−1.20333	−	2.08423i
$435$		0			0
$436$	−307.361	+	532.366i	−0.0337613	+	0.0584763i
$437$	−7877.54	+	13644.3i	−0.862320	+	1.49358i
$438$	3344.02	+	2491.28i	0.364803	+	0.271776i
$439$	−4176.79	−	7234.42i	−0.454094	−	0.786514i	0.544541	−	0.838734i	$-0.316704\pi$
$439$	−4176.79	−	7234.42i	−0.454094	−	0.786514i	−0.998636	+	0.0522196i	$0.983370\pi$
$440$		0			0
$441$	4929.13	+	16504.8i	0.532246	+	1.78218i
$442$	401.247			0.0431795
$443$	1111.30	+	1924.82i	0.119186	+	0.206436i	0.919445	−	0.393218i	$-0.128638\pi$
$443$	1111.30	+	1924.82i	0.119186	+	0.206436i	−0.800260	+	0.599654i	$0.795305\pi$
$444$	144.505	−	1232.73i	0.0154457	−	0.131763i
$445$		0			0
$446$	6235.51	−	10800.2i	0.662018	−	1.14665i
$447$	154.127	−	1314.81i	0.0163086	−	0.139124i
$448$	−5950.73	−	10307.0i	−0.627557	−	1.08696i
$449$	−5455.02			−0.573360			−0.286680	−	0.958026i	$-0.592552\pi$
$449$	−5455.02			−0.573360			−0.286680	+	0.958026i	$0.592552\pi$
$450$		0			0
$451$	6050.25			0.631697
$452$	−168.870	−	292.491i	−0.0175729	−	0.0304372i
$453$	−11853.8	−	8831.01i	−1.22945	−	0.915932i
$454$	−1331.37	+	2305.99i	−0.137630	+	0.238382i
$455$		0			0
$456$	9211.30	−	3969.70i	0.945962	−	0.407671i
$457$	−3487.07	−	6039.78i	−0.356932	−	0.618225i	0.630514	−	0.776178i	$-0.282844\pi$
$457$	−3487.07	−	6039.78i	−0.356932	−	0.618225i	−0.987447	+	0.157953i	$0.949511\pi$
$458$	2958.40			0.301827
$459$	297.910	−	815.941i	0.0302946	−	0.0829736i
$460$		0			0
$461$	−2811.55	−	4869.75i	−0.284050	−	0.491988i	0.688329	−	0.725399i	$-0.258345\pi$
$461$	−2811.55	−	4869.75i	−0.284050	−	0.491988i	−0.972378	+	0.233411i	$0.925011\pi$
$462$	−8856.62	+	3816.85i	−0.891877	+	0.384363i
$463$	−1440.80	+	2495.54i	−0.144621	+	0.250491i	−0.929232	−	0.369498i	$-0.879530\pi$
$463$	−1440.80	+	2495.54i	−0.144621	+	0.250491i	0.784610	+	0.619989i	$0.212863\pi$
$464$	282.674	−	489.606i	0.0282819	−	0.0489857i
$465$		0			0
$466$	1789.22	+	3099.03i	0.177863	+	0.308068i
$467$	16877.2			1.67234			0.836172	−	0.548468i	$-0.184789\pi$
$467$	16877.2			1.67234			0.836172	+	0.548468i	$0.184789\pi$
$468$	−844.753	−	200.810i	−0.0834375	−	0.0198342i
$469$	−18269.3			−1.79872
$470$		0			0
$471$	−1055.75	+	9006.33i	−0.103284	+	0.881082i
$472$	−4286.30	+	7424.10i	−0.417994	+	0.723987i
$473$	1849.87	−	3204.08i	0.179825	−	0.311466i
$474$	−232.817	+	1986.09i	−0.0225605	+	0.192456i
$475$		0			0
$476$	297.088			0.0286072
$477$	−5144.57	+	5445.59i	−0.493823	+	0.522718i
$478$	−12492.9			−1.19542
$479$	9544.08	+	16530.8i	0.910397	+	1.57685i	0.813505	+	0.581558i	$0.197557\pi$
$479$	9544.08	+	16530.8i	0.910397	+	1.57685i	0.0968921	+	0.995295i	$0.469110\pi$
$480$		0			0
$481$	1636.36	−	2834.26i	0.155118	−	0.268672i
$482$	3744.23	−	6485.19i	0.353828	−	0.612847i
$483$	−24359.4	+	10497.9i	−2.29480	+	0.988968i
$484$	737.375	+	1277.17i	0.0692501	+	0.119945i
$485$		0			0
$486$	−6442.94	+	9760.27i	−0.601353	+	0.910977i
$487$	12553.6			1.16809			0.584044	−	0.811722i	$-0.301470\pi$
$487$	12553.6			1.16809			0.584044	+	0.811722i	$0.301470\pi$
$488$	−897.962	−	1555.32i	−0.0832967	−	0.144274i
$489$	−12444.0	+	5362.86i	−1.15079	+	0.495945i
$490$		0			0
$491$	−784.659	+	1359.07i	−0.0721205	+	0.124916i	−0.899830	−	0.436240i	$-0.856310\pi$
$491$	−784.659	+	1359.07i	−0.0721205	+	0.124916i	0.827710	+	0.561156i	$0.189643\pi$
$492$	2012.34	+	1499.18i	0.184397	+	0.137375i
$493$	−23.6796	−	41.0143i	−0.00216324	−	0.00374683i
$494$	−6264.63			−0.570565
$495$		0			0
$496$	−16631.4			−1.50559
$497$	−2076.62	−	3596.82i	−0.187423	−	0.324626i
$498$	68.5846	−	585.075i	0.00617138	−	0.0526462i
$499$	5357.34	−	9279.18i	0.480616	−	0.832451i	−0.519137	−	0.854691i	$-0.673746\pi$
$499$	5357.34	−	9279.18i	0.480616	−	0.832451i	0.999753	+	0.0222401i	$0.00707983\pi$
$500$		0			0
$501$	−740.072	+	6313.33i	−0.0659960	+	0.562992i
$502$	−11226.9	−	19445.6i	−0.998173	−	1.72889i
$503$	19016.8			1.68572			0.842862	−	0.538130i	$-0.180869\pi$
$503$	19016.8			1.68572			0.842862	+	0.538130i	$0.180869\pi$
$504$	16429.1	+	3905.43i	1.45201	+	0.345162i
$505$		0			0
$506$	−4829.15	−	8364.33i	−0.424273	−	0.734862i
$507$	7318.69	+	5452.38i	0.641093	+	0.477611i
$508$	908.495	−	1573.56i	0.0793464	−	0.137432i
$509$	−8205.73	+	14212.7i	−0.714563	+	1.23766i	0.248564	+	0.968615i	$0.420041\pi$
$509$	−8205.73	+	14212.7i	−0.714563	+	1.23766i	−0.963128	+	0.269045i	$0.913292\pi$
$510$		0			0
$511$	4070.60	+	7050.49i	0.352393	+	0.610363i
$512$	−6749.35			−0.582582
$513$	−4651.24	+	12739.2i	−0.400307	+	1.09639i
$514$	−9985.20			−0.856865
$515$		0			0
$516$	1409.21	−	607.311i	0.120227	−	0.0518128i
$517$	−3054.79	+	5291.05i	−0.259864	+	0.450097i
$518$	7538.20	−	13056.5i	0.639401	−	1.10747i
$519$	11625.4	+	8660.87i	0.983235	+	0.732504i
$520$		0			0
$521$	−9319.21			−0.783651			−0.391826	−	0.920040i	$-0.628156\pi$
$521$	−9319.21			−0.783651			−0.391826	+	0.920040i	$0.628156\pi$
$522$	182.466	+	610.973i	0.0152995	+	0.0512290i
$523$	19719.6			1.64871			0.824357	−	0.566071i	$-0.191537\pi$
$523$	19719.6			1.64871			0.824357	+	0.566071i	$0.191537\pi$
$524$	2122.50	+	3676.27i	0.176950	+	0.306486i
$525$		0			0
$526$	1631.10	−	2825.14i	0.135208	−	0.234187i
$527$	−696.606	+	1206.56i	−0.0575799	+	0.0997313i
$528$	−858.204	+	7321.08i	−0.0707358	+	0.603426i
$529$	−7198.67	−	12468.5i	−0.591655	−	1.02478i
$530$		0			0
$531$	−3316.84	−	11106.2i	−0.271071	−	0.907659i
$532$	−4638.41			−0.378009
$533$	3308.39	+	5730.30i	0.268860	+	0.465679i
$534$	−4289.47	−	3195.63i	−0.347610	−	0.258967i
$535$		0			0
$536$	−5824.04	+	10087.5i	−0.469329	+	0.812902i
$537$	3672.36	−	1582.64i	0.295110	−	0.127181i
$538$	2358.98	+	4085.87i	0.189038	+	0.327424i
$539$	−12244.9			−0.978527
$540$		0			0
$541$	16592.1			1.31857			0.659287	−	0.751891i	$-0.270858\pi$
$541$	16592.1			1.31857			0.659287	+	0.751891i	$0.270858\pi$
$542$	11375.2	+	19702.4i	0.901487	+	1.56142i
$543$	10986.7	−	4734.82i	0.868294	−	0.374200i
$544$	211.850	−	366.935i	0.0166967	−	0.0289195i
$545$		0			0
$546$	−8457.96	−	6301.14i	−0.662944	−	0.493890i
$547$	−6132.23	−	10621.3i	−0.479333	−	0.830230i	0.520386	−	0.853931i	$-0.325788\pi$
$547$	−6132.23	−	10621.3i	−0.479333	−	0.830230i	−0.999719	+	0.0237015i	$0.992455\pi$
$548$	−2025.26			−0.157874
$549$	2362.41	+	561.577i	0.183652	+	0.0436567i
$550$		0			0
$551$	369.708	+	640.352i	0.0285845	+	0.0495098i
$552$	−1968.99	+	16796.8i	−0.151822	+	1.29515i
$553$	−1952.03	+	3381.01i	−0.150106	+	0.259991i
$554$	2862.51	−	4958.02i	0.219524	−	0.380228i
$555$		0			0
$556$	1386.84	+	2402.08i	0.105783	+	0.183221i
$557$	1623.54			0.123504			0.0617518	−	0.998092i	$-0.480331\pi$
$557$	1623.54			0.123504			0.0617518	+	0.998092i	$0.480331\pi$
$558$	12881.7	−	13635.4i	0.977286	−	1.03447i
$559$	4046.18			0.306145
$560$		0			0
$561$	495.176	+	368.903i	0.0372662	+	0.0277631i
$562$	−640.839	+	1109.97i	−0.0481000	+	0.0833116i
$563$	−3421.15	+	5925.60i	−0.256100	+	0.443578i	−0.965194	−	0.261536i	$-0.915771\pi$
$563$	−3421.15	+	5925.60i	−0.256100	+	0.443578i	0.709094	+	0.705114i	$0.249104\pi$
$564$	−2327.10	+	1002.88i	−0.173738	+	0.0748742i
$565$		0			0
$566$	12708.4			0.943771
$567$	−19093.2	+	12521.1i	−1.41418	+	0.927399i
$568$	−2648.02			−0.195613
$569$	4538.29	+	7860.55i	0.334367	+	0.579141i	0.983363	−	0.181651i	$-0.0581440\pi$
$569$	4538.29	+	7860.55i	0.334367	+	0.579141i	−0.648996	+	0.760792i	$0.724811\pi$
$570$		0			0
$571$	2750.80	−	4764.52i	0.201606	−	0.349193i	−0.747440	−	0.664330i	$-0.768717\pi$
$571$	2750.80	−	4764.52i	0.201606	−	0.349193i	0.949046	+	0.315137i	$0.102050\pi$
$572$	308.625	−	534.554i	0.0225599	−	0.0390749i
$573$	17621.7	+	13128.1i	1.28474	+	0.957127i
$574$	15240.7	+	26397.7i	1.10825	+	1.91954i
$575$		0			0
$576$	7045.68	−	7457.94i	0.509670	−	0.539492i
$577$	13600.1			0.981245			0.490622	−	0.871372i	$-0.336769\pi$
$577$	13600.1			0.981245			0.490622	+	0.871372i	$0.336769\pi$
$578$	7525.03	+	13033.7i	0.541522	+	0.937944i
$579$	2640.14	−	22522.2i	0.189500	−	1.61657i
$580$		0			0
$581$	575.039	−	995.996i	0.0410613	−	0.0711203i
$582$	−1922.41	+	16399.5i	−0.136918	+	1.16801i
$583$	−2662.73	−	4611.98i	−0.189158	−	0.327631i
$584$	5190.65			0.367792
$585$		0			0
$586$	15147.4			1.06780
$587$	10608.1	+	18373.7i	0.745896	+	1.29193i	0.949775	+	0.312934i	$0.101312\pi$
$587$	10608.1	+	18373.7i	0.745896	+	1.29193i	−0.203878	+	0.978996i	$0.565355\pi$
$588$	−4072.71	−	3034.15i	−0.285639	−	0.212800i
$589$	10876.0	−	18837.9i	0.760848	−	1.31783i
$590$		0			0
$591$	−4922.19	+	2121.26i	−0.342592	+	0.147643i
$592$	−5761.64	−	9979.45i	−0.400003	−	0.692826i
$593$	−14973.6			−1.03692			−0.518458	−	0.855103i	$-0.673494\pi$
$593$	−14973.6			−1.03692			−0.518458	+	0.855103i	$0.673494\pi$
$594$	−5337.56	−	6374.08i	−0.368691	−	0.440289i
$595$		0			0
$596$	195.158	+	338.023i	0.0134127	+	0.0232315i
$597$	6067.86	−	2615.00i	0.415981	−	0.179271i
$598$	5281.34	−	9147.54i	0.361154	−	0.625536i
$599$	8952.39	−	15506.0i	0.610659	−	1.05769i	−0.380471	−	0.924793i	$-0.624238\pi$
$599$	8952.39	−	15506.0i	0.610659	−	1.05769i	0.991130	−	0.132899i	$-0.0424286\pi$
$600$		0			0
$601$	−8227.51	−	14250.5i	−0.558414	−	0.967202i	−0.997629	−	0.0688199i	$-0.978077\pi$
$601$	−8227.51	−	14250.5i	−0.558414	−	0.967202i	0.439215	−	0.898382i	$-0.355257\pi$
$602$	18639.5			1.26194
$603$	−4506.79	−	15090.6i	−0.304362	−	1.01913i
$604$	4358.27			0.293602
$605$		0			0
$606$	−1731.37	+	14769.8i	−0.116059	+	0.990067i
$607$	2728.75	−	4726.33i	0.182465	−	0.316039i	−0.760254	−	0.649626i	$-0.774926\pi$
$607$	2728.75	−	4726.33i	0.182465	−	0.316039i	0.942719	+	0.333587i	$0.108259\pi$
$608$	−3307.60	+	5728.93i	−0.220626	+	0.382136i
$609$	−144.937	+	1236.41i	−0.00964388	+	0.0822691i
$610$		0			0
$611$	−6681.66			−0.442408
$612$	73.2876	+	245.397i	0.00484065	+	0.0162085i
$613$	−10945.3			−0.721167			−0.360584	−	0.932727i	$-0.617422\pi$
$613$	−10945.3			−0.721167			−0.360584	+	0.932727i	$0.617422\pi$
$614$	−10665.9	−	18473.9i	−0.701043	−	1.21424i
$615$		0			0
$616$	−6002.27	+	10396.2i	−0.392595	+	0.679994i
$617$	12767.0	−	22113.1i	0.833032	−	1.44285i	−0.0625911	−	0.998039i	$-0.519936\pi$
$617$	12767.0	−	22113.1i	0.833032	−	1.44285i	0.895623	−	0.444814i	$-0.146730\pi$
$618$	−24862.9	+	10714.9i	−1.61834	+	0.697439i
$619$	3947.91	+	6837.98i	0.256349	+	0.444009i	0.965261	−	0.261288i	$-0.0841472\pi$
$619$	3947.91	+	6837.98i	0.256349	+	0.444009i	−0.708912	+	0.705297i	$0.750814\pi$
$620$		0			0
$621$	−14680.5	−	17531.4i	−0.948644	−	1.13287i
$622$	−16591.3			−1.06953
$623$	−5221.48	−	9043.87i	−0.335785	−	0.581597i
$624$	−7403.20	+	3190.48i	−0.474944	+	0.204682i
$625$		0			0
$626$	−3693.46	+	6397.27i	−0.235815	+	0.408444i
$627$	−7731.14	−	5759.66i	−0.492428	−	0.366856i
$628$	−1336.81	−	2315.43i	−0.0849437	−	0.147127i
$629$	−965.305			−0.0611912
$630$		0			0
$631$	−5659.61			−0.357061			−0.178531	−	0.983934i	$-0.557134\pi$
$631$	−5659.61			−0.357061			−0.178531	+	0.983934i	$0.557134\pi$
$632$	1244.57	+	2155.66i	0.0783327	+	0.135676i
$633$	−209.498	+	1787.17i	−0.0131545	+	0.112217i
$634$	1827.25	−	3164.89i	0.114463	−	0.198255i
$635$		0			0
$636$	257.160	−	2193.76i	0.0160331	−	0.136774i
$637$	−6695.75	−	11597.4i	−0.416476	−	0.721358i
$638$	−453.282			−0.0281279
$639$	2458.73	−	2602.59i	0.152216	−	0.161122i
$640$		0			0
$641$	8041.46	+	13928.2i	0.495505	+	0.858240i	0.999987	−	0.00518258i	$-0.00164967\pi$
$641$	8041.46	+	13928.2i	0.495505	+	0.858240i	−0.504482	+	0.863422i	$0.668316\pi$
$642$	−9659.41	−	7196.21i	−0.593811	−	0.442386i
$643$	33.3745	−	57.8064i	0.00204691	−	0.00354535i	−0.865000	−	0.501772i	$-0.832682\pi$
$643$	33.3745	−	57.8064i	0.00204691	−	0.00354535i	0.867047	+	0.498226i	$0.166015\pi$
$644$	3910.37	−	6772.96i	0.239270	−	0.414429i
$645$		0			0
$646$	923.892	+	1600.23i	0.0562694	+	0.0974615i
$647$	1263.42			0.0767697			0.0383849	−	0.999263i	$-0.487779\pi$
$647$	1263.42			0.0767697			0.0383849	+	0.999263i	$0.487779\pi$
$648$	826.921	+	14534.0i	0.0501305	+	0.881096i
$649$	8239.69			0.498361
$650$		0			0
$651$	33631.5	−	14493.8i	2.02477	−	0.872593i
$652$	1997.61	−	3459.97i	0.119989	−	0.207826i
$653$	10933.7	−	18937.7i	0.655235	−	1.13490i	−0.326600	−	0.945163i	$-0.605903\pi$
$653$	10933.7	−	18937.7i	0.655235	−	1.13490i	0.981835	−	0.189737i	$-0.0607636\pi$
$654$	−5161.97	−	3845.64i	−0.308638	−	0.229933i
$655$		0			0
$656$	23297.7			1.38662
$657$	−4819.61	+	5101.61i	−0.286196	+	0.302942i
$658$	−30780.3			−1.82362
$659$	−181.247	−	313.928i	−0.0107138	−	0.0185568i	0.860619	−	0.509250i	$-0.170077\pi$
$659$	−181.247	−	313.928i	−0.0107138	−	0.0185568i	−0.871333	+	0.490693i	$0.836744\pi$
$660$		0			0
$661$	199.371	−	345.320i	0.0117316	−	0.0203198i	−0.860100	−	0.510125i	$-0.829599\pi$
$661$	199.371	−	345.320i	0.0117316	−	0.0203198i	0.871832	+	0.489806i	$0.162932\pi$
$662$	14489.8	−	25097.1i	0.850700	−	1.47346i
$663$	−78.6234	+	670.713i	−0.00460555	+	0.0392886i
$664$	−366.632	−	635.025i	−0.0214278	−	0.0371141i
$665$		0			0
$666$	12644.4	+	3005.75i	0.735676	+	0.174880i
$667$	−1246.71			−0.0723732
$668$	−937.091	−	1623.09i	−0.0542771	−	0.0940108i
$669$	16831.5	+	12539.4i	0.972712	+	0.724665i
$670$		0			0
$671$	−863.090	+	1494.92i	−0.0496560	+	0.0860068i
$672$	−10227.9	+	4407.83i	−0.587130	+	0.253029i
$673$	−1552.09	−	2688.30i	−0.0888986	−	0.153977i	0.818147	−	0.575009i	$-0.195001\pi$
$673$	−1552.09	−	2688.30i	−0.0888986	−	0.153977i	−0.907046	+	0.421032i	$0.861668\pi$
$674$	37578.7			2.14759
$675$		0			0
$676$	−2690.85			−0.153098
$677$	−12282.7	−	21274.2i	−0.697285	−	1.20773i	−0.969404	−	0.245470i	$-0.921058\pi$
$677$	−12282.7	−	21274.2i	−0.697285	−	1.20773i	0.272119	−	0.962264i	$-0.412276\pi$
$678$	3247.83	−	1399.68i	0.183971	−	0.0792839i
$679$	−16118.2	+	27917.5i	−0.910986	+	1.57787i
$680$		0			0
$681$	−3593.76	−	2677.33i	−0.202222	−	0.150654i
$682$	6667.32	+	11548.1i	0.374347	+	0.648388i
$683$	8921.93			0.499836			0.249918	−	0.968267i	$-0.419596\pi$
$683$	8921.93			0.499836			0.249918	+	0.968267i	$0.419596\pi$
$684$	−1144.23	−	3831.37i	−0.0639632	−	0.214176i
$685$		0			0
$686$	−14261.4	−	24701.5i	−0.793737	−	1.37479i
$687$	−579.692	+	4945.18i	−0.0321931	+	0.274629i
$688$	7123.32	−	12338.0i	0.394730	−	0.683692i
$689$	2912.06	−	5043.84i	0.161017	−	0.278889i
$690$		0			0
$691$	3344.10	+	5792.16i	0.184104	+	0.318877i	0.943274	−	0.332015i	$-0.107728\pi$
$691$	3344.10	+	5792.16i	0.184104	+	0.318877i	−0.759170	+	0.650892i	$0.774395\pi$
$692$	−4274.30			−0.234804
$693$	−4644.70	−	15552.4i	−0.254600	−	0.852506i
$694$	8600.17			0.470400
$695$		0			0
$696$	636.490	+	474.182i	0.0346639	+	0.0258244i
$697$	975.826	−	1690.18i	0.0530302	−	0.0918509i
$698$	5186.46	−	8983.21i	0.281247	−	0.487134i
$699$	−5530.84	+	2383.57i	−0.299278	+	0.128977i
$700$		0			0
$701$	33422.0			1.80076			0.900380	−	0.435105i	$-0.143289\pi$
$701$	33422.0			1.80076			0.900380	+	0.435105i	$0.143289\pi$
$702$	3118.33	−	8540.76i	0.167655	−	0.459188i
$703$	15071.2			0.808567
$704$	3646.71	+	6316.28i	0.195228	+	0.338145i
$705$		0			0
$706$	−8378.72	+	14512.4i	−0.446653	+	0.773626i
$707$	−14516.4	+	25143.2i	−0.772201	+	1.33749i
$708$	2740.55	+	2041.70i	0.145475	+	0.108378i
$709$	−14646.8	−	25368.9i	−0.775840	−	1.34380i	−0.934321	−	0.356433i	$-0.883993\pi$
$709$	−14646.8	−	25368.9i	−0.775840	−	1.34380i	0.158481	−	0.987362i	$-0.449340\pi$
$710$		0			0
$711$	−3274.28	−	778.342i	−0.172708	−	0.0410550i
$712$	−6658.20			−0.350459
$713$	18337.9	+	31762.2i	0.963197	+	1.66831i
$714$	−362.194	+	3089.77i	−0.0189843	+	0.161949i
$715$		0			0
$716$	−589.518	+	1021.08i	−0.0307700	+	0.0532952i
$717$	2447.95	−	20882.7i	0.127504	−	1.08770i
$718$	6052.45	+	10483.2i	0.314590	+	0.544886i
$719$	29311.2			1.52034			0.760169	−	0.649725i	$-0.225116\pi$
$719$	29311.2			1.52034			0.760169	+	0.649725i	$0.225116\pi$
$720$		0			0
$721$	−52856.3			−2.73020
$722$	−3836.41	−	6644.85i	−0.197751	−	0.342515i
$723$	10106.8	+	7529.51i	0.519884	+	0.387310i
$724$	−1763.67	+	3054.77i	−0.0905337	+	0.156809i
$725$		0			0
$726$	−14181.7	+	6111.76i	−0.724978	+	0.312436i
$727$	2465.84	+	4270.96i	0.125795	+	0.217883i	0.922043	−	0.387087i	$-0.126519\pi$
$727$	2465.84	+	4270.96i	0.125795	+	0.217883i	−0.796248	+	0.604970i	$0.793185\pi$
$728$	−13128.6			−0.668377
$729$	−15052.5	−	12682.3i	−0.764748	−	0.644330i
$730$		0			0
$731$	−596.720	−	1033.55i	−0.0301922	−	0.0522944i
$732$	−657.489	+	283.351i	−0.0331988	+	0.0143073i
$733$	4112.78	−	7123.54i	0.207243	−	0.358955i	−0.743602	−	0.668622i	$-0.766884\pi$
$733$	4112.78	−	7123.54i	0.207243	−	0.358955i	0.950845	+	0.309667i	$0.100218\pi$
$734$	−2589.10	+	4484.46i	−0.130198	+	0.225510i
$735$		0			0
$736$	−5576.88	−	9659.43i	−0.279302	−	0.483765i
$737$	11195.7			0.559566
$738$	−18045.0	+	19100.9i	−0.900064	+	0.952729i
$739$	17847.1			0.888382			0.444191	−	0.895932i	$-0.353491\pi$
$739$	17847.1			0.888382			0.444191	+	0.895932i	$0.353491\pi$
$740$		0			0
$741$	1227.54	−	10471.8i	0.0608567	−	0.519151i
$742$	13415.0	−	23235.4i	0.663717	−	1.14959i
$743$	−11905.3	+	20620.6i	−0.587838	+	1.01817i	0.406677	+	0.913572i	$0.366687\pi$
$743$	−11905.3	+	20620.6i	−0.587838	+	1.01817i	−0.994515	+	0.104593i	$0.966646\pi$
$744$	2718.46	−	23190.4i	0.133957	−	1.14274i
$745$		0			0
$746$	2952.59			0.144909
$747$	964.556	+	229.288i	0.0472440	+	0.0112305i
$748$	−182.061			−0.00889947
$749$	−11758.2	−	20365.8i	−0.573611	−	0.993524i
$750$		0			0
$751$	−10647.9	+	18442.7i	−0.517374	+	0.896119i	0.482422	+	0.875939i	$0.339757\pi$
$751$	−10647.9	+	18442.7i	−0.517374	+	0.896119i	−0.999796	+	0.0201799i	$0.993576\pi$
$752$	−11763.1	+	20374.3i	−0.570420	+	0.987997i
$753$	34704.7	−	14956.3i	1.67956	−	0.723823i
$754$	−247.863	−	429.311i	−0.0119717	−	0.0207355i
$755$		0			0
$756$	2308.85	−	6323.69i	0.111074	−	0.304220i
$757$	−13423.0			−0.644472			−0.322236	−	0.946659i	$-0.604435\pi$
$757$	−13423.0			−0.644472			−0.322236	+	0.946659i	$0.604435\pi$
$758$	−15466.3	−	26788.4i	−0.741108	−	1.28364i
$759$	14927.9	−	6433.30i	0.713896	−	0.307660i
$760$		0			0
$761$	12050.1	−	20871.4i	0.574003	−	0.994202i	−0.422146	−	0.906528i	$-0.638723\pi$
$761$	12050.1	−	20871.4i	0.574003	−	0.994202i	0.996149	−	0.0876745i	$-0.0279436\pi$
$762$	15257.7	+	11366.9i	0.725364	+	0.540392i
$763$	−6283.55	−	10883.4i	−0.298139	−	0.516391i
$764$	−6478.96			−0.306807
$765$		0			0
$766$	39784.8			1.87661
$767$	4505.62	+	7803.95i	0.212110	+	0.367385i
$768$	−1374.75	+	11727.6i	−0.0645924	+	0.551019i
$769$	493.380	−	854.559i	0.0231362	−	0.0400730i	−0.854225	−	0.519903i	$-0.825968\pi$
$769$	493.380	−	854.559i	0.0231362	−	0.0400730i	0.877362	+	0.479830i	$0.159302\pi$
$770$		0			0
$771$	1956.58	−	16691.0i	0.0913936	−	0.779652i
$772$	3342.99	+	5790.22i	0.155851	+	0.269941i
$773$	7277.05			0.338599			0.169300	−	0.985565i	$-0.445849\pi$
$773$	7277.05			0.338599			0.169300	+	0.985565i	$0.445849\pi$
$774$	4598.11	+	15396.4i	0.213534	+	0.715002i
$775$		0			0
$776$	10276.6	+	17799.6i	0.475397	+	0.823412i
$777$	20347.9	+	15159.1i	0.939480	+	0.699908i
$778$	1062.82	−	1840.85i	0.0489766	−	0.0848300i
$779$	−15235.5	+	26388.6i	−0.700729	+	1.21370i
$780$		0			0
$781$	1272.59	+	2204.19i	0.0583059	+	0.100989i
$782$	−3115.51			−0.142469
$783$	−1057.04	+	185.287i	−0.0482446	+	0.00845671i
$784$	−47151.6			−2.14794
$785$		0			0
$786$	−40821.5	+	17592.4i	−1.85249	+	0.798346i
$787$	2469.72	−	4277.68i	0.111863	−	0.193752i	−0.804659	−	0.593738i	$-0.797652\pi$
$787$	2469.72	−	4277.68i	0.111863	−	0.193752i	0.916521	+	0.399986i	$0.130985\pi$
$788$	790.150	−	1368.58i	0.0357207	−	0.0618701i
$789$	4402.82	+	3280.08i	0.198662	+	0.148002i
$790$		0			0
$791$	6904.59			0.310365
$792$	−10068.1	−	2393.32i	−0.451708	−	0.107377i
$793$	−1887.81			−0.0845375
$794$	12184.5	+	21104.2i	0.544600	+	0.943275i
$795$		0			0
$796$	−974.063	+	1687.13i	−0.0433728	+	0.0751239i
$797$	6223.79	−	10779.9i	0.276610	−	0.479102i	−0.693930	−	0.720042i	$-0.744122\pi$
$797$	6223.79	−	10779.9i	0.276610	−	0.479102i	0.970540	+	0.240940i	$0.0774558\pi$
$798$	5654.90	−	48240.2i	0.250854	−	2.13996i
$799$	985.395	+	1706.75i	0.0436305	+	0.0755702i
$800$		0			0
$801$	6182.25	−	6543.99i	0.272708	−	0.288665i
$802$	12944.9			0.569952
$803$	−2494.54	−	4320.66i	−0.109627	−	0.189879i
$804$	3723.75	+	2774.17i	0.163341	+	0.121688i
$805$		0			0
$806$	−7291.62	+	12629.5i	−0.318656	+	0.551928i
$807$	−7292.06	+	3142.58i	−0.318082	+	0.137081i
$808$	9255.34	+	16030.7i	0.402972	+	0.697968i
$809$	−37250.9			−1.61888			−0.809438	−	0.587205i	$-0.800228\pi$
$809$	−37250.9			−1.61888			−0.809438	+	0.587205i	$0.800228\pi$
$810$		0			0
$811$	7201.80			0.311824			0.155912	−	0.987771i	$-0.450168\pi$
$811$	7201.80			0.311824			0.155912	+	0.987771i	$0.450168\pi$
$812$	−183.521	−	317.868i	−0.00793143	−	0.0137376i
$813$	−35162.9	+	15153.8i	−1.51687	+	0.653711i
$814$	−4619.54	+	8001.28i	−0.198913	+	0.344527i
$815$		0			0
$816$	1906.78	+	1420.54i	0.0818021	+	0.0609421i
$817$	9316.55	+	16136.7i	0.398953	+	0.691007i
$818$	27817.6			1.18902
$819$	12190.1	−	12903.4i	0.520095	−	0.550527i
$820$		0			0
$821$	−5412.30	−	9374.37i	−0.230074	−	0.398499i	0.727756	−	0.685836i	$-0.240563\pi$
$821$	−5412.30	−	9374.37i	−0.230074	−	0.398499i	−0.957830	+	0.287337i	$0.907230\pi$
$822$	2469.09	−	21063.1i	0.104768	−	0.893746i
$823$	−9015.67	+	15615.6i	−0.381855	+	0.661392i	−0.991327	−	0.131415i	$-0.958048\pi$
$823$	−9015.67	+	15615.6i	−0.381855	+	0.661392i	0.609472	+	0.792807i	$0.291381\pi$
$824$	−16850.0	+	29185.1i	−0.712376	+	1.23387i
$825$		0			0
$826$	20756.0	+	35950.4i	0.874325	+	1.51438i
$827$	13172.5			0.553873			0.276937	−	0.960888i	$-0.410681\pi$
$827$	13172.5			0.553873			0.276937	+	0.960888i	$0.410681\pi$
$828$	6559.16	+	1559.20i	0.275298	+	0.0654421i
$829$	−11929.1			−0.499776			−0.249888	−	0.968275i	$-0.580394\pi$
$829$	−11929.1			−0.499776			−0.249888	+	0.968275i	$0.580394\pi$
$830$		0			0
$831$	7726.79	+	5756.41i	0.322550	+	0.240298i
$832$	−3988.17	+	6907.72i	−0.166184	+	0.287839i
$833$	−1974.94	+	3420.70i	−0.0821462	+	0.142281i
$834$	−26672.8	+	11494.9i	−1.10744	+	0.477261i
$835$		0			0
$836$	2842.50			0.117596
$837$	20268.5	+	24204.5i	0.837014	+	0.999558i
$838$	21179.0			0.873049
$839$	−12696.7	−	21991.3i	−0.522453	−	0.904915i	−0.999659	−	0.0261237i	$-0.991684\pi$
$839$	−12696.7	−	21991.3i	−0.522453	−	0.904915i	0.477206	−	0.878792i	$-0.341650\pi$
$840$		0			0
$841$	12165.2	−	21070.8i	0.498800	−	0.863948i
$842$	−19442.3	+	33675.1i	−0.795755	+	1.37829i
$843$	−1729.82	−	1288.71i	−0.0706739	−	0.0526517i
$844$	−265.270	−	459.461i	−0.0108187	−	0.0187385i
$845$		0			0
$846$	−7593.09	−	25424.8i	−0.308577	−	1.03324i
$847$	−30149.1			−1.22306
$848$	−10253.4	−	17759.4i	−0.415216	−	0.719175i
$849$	−2490.19	+	21243.0i	−0.100663	+	0.858727i
$850$		0			0
$851$	−12705.7	+	22006.8i	−0.511803	+	0.886469i
$852$	−122.904	+	1048.46i	−0.00494204	+	0.0421591i
$853$	19686.8	+	34098.5i	0.790225	+	1.36871i	0.925827	+	0.377947i	$0.123370\pi$
$853$	19686.8	+	34098.5i	0.790225	+	1.36871i	−0.135602	+	0.990763i	$0.543297\pi$
$854$	−8696.57			−0.348466
$855$		0			0
$856$	−14993.5			−0.598677
$857$	2620.42	+	4538.69i	0.104448	+	0.180909i	0.913512	−	0.406811i	$-0.133359\pi$
$857$	2620.42	+	4538.69i	0.104448	+	0.180909i	−0.809065	+	0.587720i	$0.800026\pi$
$858$	5183.19	+	3861.45i	0.206237	+	0.153645i
$859$	4154.47	−	7195.75i	0.165016	−	0.285816i	−0.771645	−	0.636053i	$-0.780566\pi$
$859$	4154.47	−	7195.75i	0.165016	−	0.285816i	0.936661	+	0.350238i	$0.113899\pi$
$860$		0			0
$861$	−47112.0	+	20303.4i	−1.86478	+	0.803644i
$862$	13075.4	+	22647.2i	0.516646	+	0.894858i
$863$	−5719.30			−0.225593			−0.112797	−	0.993618i	$-0.535981\pi$
$863$	−5719.30			−0.225593			−0.112797	+	0.993618i	$0.535981\pi$
$864$	−6164.00	−	7361.02i	−0.242712	−	0.289846i
$865$		0			0
$866$	−12631.9	−	21879.1i	−0.495669	−	0.858523i
$867$	−23261.3	+	10024.7i	−0.911184	+	0.392683i
$868$	−5398.81	+	9351.02i	−0.211115	+	0.365662i
$869$	1196.24	−	2071.94i	0.0466968	−	0.0808812i
$870$		0			0
$871$	6122.04	+	10603.7i	0.238160	+	0.412505i
$872$	−8012.50			−0.311167
$873$	−27036.3	−	6426.89i	−1.04815	−	0.249161i
$874$	48642.2			1.88255
$875$		0			0
$876$	240.917	−	2055.19i	0.00929203	−	0.0792675i
$877$	−6158.81	+	10667.4i	−0.237136	+	0.410731i	−0.959891	−	0.280373i	$-0.909542\pi$
$877$	−6158.81	+	10667.4i	−0.237136	+	0.410731i	0.722755	+	0.691104i	$0.242875\pi$
$878$	−12895.4	+	22335.5i	−0.495672	+	0.858529i
$879$	−2968.10	+	25320.0i	−0.113893	+	0.971583i
$880$		0			0
$881$	−4540.33			−0.173630			−0.0868148	−	0.996224i	$-0.527669\pi$
$881$	−4540.33			−0.173630			−0.0868148	+	0.996224i	$0.527669\pi$
$882$	36520.8	−	38657.8i	1.39424	−	1.47582i
$883$	−19437.5			−0.740796			−0.370398	−	0.928873i	$-0.620779\pi$
$883$	−19437.5			−0.740796			−0.370398	+	0.928873i	$0.620779\pi$
$884$	−99.5542	−	172.433i	−0.00378775	−	0.00656057i
$885$		0			0
$886$	3431.02	−	5942.69i	0.130098	−	0.225337i
$887$	1312.83	−	2273.89i	0.0496962	−	0.0860764i	−0.840107	−	0.542420i	$-0.817508\pi$
$887$	1312.83	−	2273.89i	0.0496962	−	0.0860764i	0.889803	+	0.456344i	$0.150841\pi$
$888$	14856.9	−	6402.71i	0.561446	−	0.241961i
$889$	18572.8	+	32169.1i	0.700690	+	1.21363i
$890$		0			0
$891$	11700.6	−	7673.12i	0.439939	−	0.288507i
$892$	−6188.43			−0.232291
$893$	−15384.9	−	26647.4i	−0.576524	−	0.998568i
$894$	−3753.42	+	1617.57i	−0.140417	+	0.0605142i
$895$		0			0
$896$	−26945.8	+	46671.5i	−1.00468	+	1.74016i
$897$	14255.9	+	10620.6i	0.530648	+	0.395330i
$898$	8420.92	+	14585.5i	0.312929	+	0.542008i
$899$	1721.26			0.0638569
$900$		0			0
$901$	−1717.85			−0.0635183
$902$	−9339.77	−	16177.0i	−0.344768	−	0.597155i
$903$	−3652.37	+	31157.3i	−0.134599	+	1.14823i
$904$	2201.10	−	3812.42i	0.0809819	−	0.140265i
$905$		0			0
$906$	−5313.37	+	45326.7i	−0.194840	+	1.66212i
$907$	22440.3	+	38867.7i	0.821519	+	1.42291i	0.904551	+	0.426365i	$0.140206\pi$
$907$	22440.3	+	38867.7i	0.821519	+	1.42291i	−0.0830325	+	0.996547i	$0.526461\pi$
$908$	1321.31			0.0482922
$909$	−24349.5	−	5788.21i	−0.888472	−	0.211202i
$910$		0			0
$911$	−26383.0	−	45696.7i	−0.959503	−	1.66191i	−0.723709	−	0.690105i	$-0.757564\pi$
$911$	−26383.0	−	45696.7i	−0.959503	−	1.66191i	−0.235794	−	0.971803i	$-0.575769\pi$
$912$	−29770.3	−	22178.7i	−1.08092	−	0.805276i
$913$	−352.394	+	610.364i	−0.0127739	+	0.0221250i
$914$	−10766.0	+	18647.2i	−0.389614	+	0.674830i
$915$		0			0
$916$	−734.015	−	1271.35i	−0.0264766	−	0.0458588i
$917$	−86782.7			−3.12521
$918$	−2641.52	+	463.028i	−0.0949708	+	0.0166473i
$919$	−33853.3			−1.21514			−0.607571	−	0.794265i	$-0.707856\pi$
$919$	−33853.3			−1.21514			−0.607571	+	0.794265i	$0.707856\pi$
$920$		0			0
$921$	32970.4	−	14208.9i	1.17960	−	0.508360i
$922$	−8680.38	+	15034.9i	−0.310058	+	0.537035i
$923$	−1391.75	+	2410.59i	−0.0496317	+	0.0859647i
$924$	3837.70	+	2859.07i	0.136635	+	0.101793i
$925$		0			0
$926$	8896.65			0.315726
$927$	−13038.9	−	43659.8i	−0.461979	−	1.54690i
$928$	−523.466			−0.0185168
$929$	2701.11	+	4678.46i	0.0953935	+	0.165226i	0.909773	−	0.415107i	$-0.136256\pi$
$929$	2701.11	+	4678.46i	0.0953935	+	0.165226i	−0.814379	+	0.580333i	$0.802922\pi$
$930$		0			0
$931$	30834.6	−	53407.2i	1.08546	−	1.88007i
$932$	887.857	−	1537.81i	0.0312046	−	0.0540480i
$933$	3251.03	−	27733.5i	0.114077	−	0.973156i
$934$	−26053.4	−	45125.7i	−0.912732	−	1.58090i
$935$		0			0
$936$	−3238.65	−	10844.3i	−0.113097	−	0.378695i
$937$	37756.4			1.31638			0.658190	−	0.752852i	$-0.271323\pi$
$937$	37756.4			1.31638			0.658190	+	0.752852i	$0.271323\pi$
$938$	28202.3	+	48847.8i	0.981704	+	1.70036i
$939$	−9969.77	−	7427.42i	−0.346487	−	0.258131i
$940$		0			0
$941$	−1585.09	+	2745.46i	−0.0549123	+	0.0951109i	−0.892175	−	0.451690i	$-0.850821\pi$
$941$	−1585.09	+	2745.46i	−0.0549123	+	0.0951109i	0.837263	+	0.546801i	$0.184155\pi$
$942$	25710.6	−	11080.2i	0.889274	−	0.383241i
$943$	−25688.3	−	44493.4i	−0.887089	−	1.53648i
$944$	31728.6			1.09394
$945$		0			0
$946$	−11422.6			−0.392580
$947$	−20760.6	−	35958.4i	−0.712385	−	1.23389i	−0.963959	−	0.266049i	$-0.914282\pi$
$947$	−20760.6	−	35958.4i	−0.712385	−	1.23389i	0.251574	−	0.967838i	$-0.419052\pi$
$948$	911.275	−	392.723i	0.0312203	−	0.0134547i
$949$	2728.12	−	4725.24i	0.0933176	−	0.161631i
$950$		0			0
$951$	4932.30	+	3674.53i	0.168182	+	0.125294i
$952$	1936.17	+	3353.55i	0.0659157	+	0.114169i
$953$	−18886.5			−0.641965			−0.320982	−	0.947085i	$-0.604013\pi$
$953$	−18886.5			−0.641965			−0.320982	+	0.947085i	$0.604013\pi$
$954$	22501.9	+	5349.02i	0.763654	+	0.181531i
$955$		0			0
$956$	3099.63	+	5368.72i	0.104863	+	0.181629i
$957$	88.8197	−	757.694i	0.00300014	−	0.0255933i
$958$	29466.4	−	51037.3i	0.993754	−	1.72123i
$959$	20701.8	−	35856.5i	0.697075	−	1.20737i
$960$		0			0
$961$	−10422.5	−	18052.3i	−0.349855	−	0.605966i
$962$	−10104.2			−0.338641
$963$	13921.7	−	14736.3i	0.465858	−	0.493117i
$964$	−3715.96			−0.124152
$965$		0			0
$966$	65672.6	+	48925.7i	2.18735	+	1.62956i
$967$	19899.9	−	34467.7i	0.661777	−	1.14623i	−0.318371	−	0.947966i	$-0.603136\pi$
$967$	19899.9	−	34467.7i	0.661777	−	1.14623i	0.980148	−	0.198266i	$-0.0635310\pi$
$968$	−9611.19	+	16647.1i	−0.319127	+	0.552745i
$969$	−2855.93	+	1230.79i	−0.0946808	+	0.0408036i
$970$		0			0
$971$	−39063.6			−1.29105			−0.645525	−	0.763739i	$-0.723361\pi$
$971$	−39063.6			−1.29105			−0.645525	+	0.763739i	$0.723361\pi$
$972$	5792.98	+	347.164i	0.191163	+	0.0114561i
$973$	−56703.8			−1.86829
$974$	−19379.0	−	33565.5i	−0.637520	−	1.10422i
$975$		0			0
$976$	−3323.50	+	5756.48i	−0.108999	+	0.188791i
$977$	2543.57	−	4405.60i	0.0832918	−	0.144266i	−0.821370	−	0.570395i	$-0.806790\pi$
$977$	2543.57	−	4405.60i	0.0832918	−	0.144266i	0.904662	+	0.426130i	$0.140123\pi$
$978$	33548.8	+	24993.7i	1.09691	+	0.817189i
$979$	3199.81	+	5542.24i	0.104460	+	0.180930i
$980$		0			0
$981$	7439.74	−	7875.06i	0.242133	−	0.256301i
$982$	4845.12			0.157448
$983$	−16006.1	−	27723.3i	−0.519343	−	0.899528i	−0.999747	−	0.0224813i	$-0.992843\pi$
$983$	−16006.1	−	27723.3i	−0.519343	−	0.899528i	0.480404	−	0.877047i	$-0.340490\pi$
$984$	−3808.10	+	32485.8i	−0.123372	+	1.05245i
$985$		0			0
$986$	−73.1084	+	126.627i	−0.00236130	+	0.00408990i
$987$	6031.34	−	51451.6i	0.194508	−	1.65929i
$988$	1554.33	+	2692.18i	0.0500505	+	0.0866900i
$989$	−31416.9			−1.01011
$990$		0			0
$991$	3717.85			0.119174			0.0595870	−	0.998223i	$-0.481022\pi$
$991$	3717.85			0.119174			0.0595870	+	0.998223i	$0.481022\pi$
$992$	7699.66	+	13336.2i	0.246436	+	0.426839i
$993$	39112.4	+	29138.5i	1.24994	+	0.931202i
$994$	−6411.37	+	11104.8i	−0.204584	+	0.354349i
$995$		0			0
$996$	−268.448	+	115.690i	−0.00854028	+	0.00368051i
$997$	−2758.56	−	4777.96i	−0.0876272	−	0.151775i	0.818880	−	0.573964i	$-0.194595\pi$
$997$	−2758.56	−	4777.96i	−0.0876272	−	0.151775i	−0.906508	+	0.422189i	$0.861262\pi$
$998$	−33080.5			−1.04924
$999$	−7501.97	+	20547.1i	−0.237589	+	0.650731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.g.76.4		32
5.2	odd	4		45.4.j.a.4.13	yes	32
5.3	odd	4		45.4.j.a.4.4	✓	32
5.4	even	2	inner	225.4.e.g.76.13		32
9.4	even	3		2025.4.a.bk.1.13		16
9.5	odd	6		2025.4.a.bl.1.4		16
9.7	even	3	inner	225.4.e.g.151.4		32
15.2	even	4		135.4.j.a.64.4		32
15.8	even	4		135.4.j.a.64.13		32
45.2	even	12		135.4.j.a.19.13		32
45.4	even	6		2025.4.a.bk.1.4		16
45.7	odd	12		45.4.j.a.34.4	yes	32
45.13	odd	12		405.4.b.e.244.4		16
45.14	odd	6		2025.4.a.bl.1.13		16
45.22	odd	12		405.4.b.e.244.13		16
45.23	even	12		405.4.b.f.244.13		16
45.32	even	12		405.4.b.f.244.4		16
45.34	even	6	inner	225.4.e.g.151.13		32
45.38	even	12		135.4.j.a.19.4		32
45.43	odd	12		45.4.j.a.34.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.4	✓	32	5.3	odd	4
45.4.j.a.4.13	yes	32	5.2	odd	4
45.4.j.a.34.4	yes	32	45.7	odd	12
45.4.j.a.34.13	yes	32	45.43	odd	12
135.4.j.a.19.4		32	45.38	even	12
135.4.j.a.19.13		32	45.2	even	12
135.4.j.a.64.4		32	15.2	even	4
135.4.j.a.64.13		32	15.8	even	4
225.4.e.g.76.4		32	1.1	even	1	trivial
225.4.e.g.76.13		32	5.4	even	2	inner
225.4.e.g.151.4		32	9.7	even	3	inner
225.4.e.g.151.13		32	45.34	even	6	inner
405.4.b.e.244.4		16	45.13	odd	12
405.4.b.e.244.13		16	45.22	odd	12
405.4.b.f.244.4		16	45.32	even	12
405.4.b.f.244.13		16	45.23	even	12
2025.4.a.bk.1.4		16	45.4	even	6
2025.4.a.bk.1.13		16	9.4	even	3
2025.4.a.bl.1.4		16	9.5	odd	6
2025.4.a.bl.1.13		16	45.14	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54370 - 2.67377i) q^{2} +(4.77188 - 2.05649i) q^{3} +(-0.766022 + 1.32679i) q^{4} +(-12.8649 - 9.58430i) q^{6} +(-15.6602 - 27.1243i) q^{7} -19.9692 q^{8} +(18.5417 - 19.6266i) q^{9} +O(q^{10})\)	\(q+(-1.54370 - 2.67377i) q^{2} +(4.77188 - 2.05649i) q^{3} +(-0.766022 + 1.32679i) q^{4} +(-12.8649 - 9.58430i) q^{6} +(-15.6602 - 27.1243i) q^{7} -19.9692 q^{8} +(18.5417 - 19.6266i) q^{9} +(9.59684 + 16.6222i) q^{11} +(-0.926840 + 7.90660i) q^{12} +(-10.4955 + 18.1787i) q^{13} +(-48.3493 + 83.7434i) q^{14} +(36.9546 + 64.0072i) q^{16} +6.19137 q^{17} +(-81.0999 - 19.2786i) q^{18} -96.6654 q^{19} +(-130.509 - 97.2287i) q^{21} +(29.6293 - 51.3194i) q^{22} +(81.4928 - 141.150i) q^{23} +(-95.2905 + 41.0664i) q^{24} +64.8074 q^{26} +(48.1169 - 131.787i) q^{27} +47.9842 q^{28} +(-3.82461 - 6.62442i) q^{29} +(-112.512 + 194.877i) q^{31} +(34.2170 - 59.2655i) q^{32} +(79.9784 + 59.5834i) q^{33} +(-9.55763 - 16.5543i) q^{34} +(11.8371 + 39.6354i) q^{36} -155.911 q^{37} +(149.222 + 258.461i) q^{38} +(-12.6989 + 108.330i) q^{39} +(157.611 - 272.989i) q^{41} +(-58.4997 + 499.044i) q^{42} +(-96.3793 - 166.934i) q^{43} -29.4056 q^{44} -503.202 q^{46} +(159.156 + 275.666i) q^{47} +(307.973 + 229.438i) q^{48} +(-318.983 + 552.495i) q^{49} +(29.5445 - 12.7325i) q^{51} +(-16.0795 - 27.8505i) q^{52} -277.459 q^{53} +(-426.645 + 74.7860i) q^{54} +(312.721 + 541.649i) q^{56} +(-461.276 + 198.791i) q^{57} +(-11.8081 + 20.4522i) q^{58} +(214.646 - 371.778i) q^{59} +(44.9674 + 77.8858i) q^{61} +694.741 q^{62} +(-822.725 - 195.573i) q^{63} +379.991 q^{64} +(35.8496 - 305.823i) q^{66} +(291.652 - 505.156i) q^{67} +(-4.74273 + 8.21465i) q^{68} +(98.6014 - 841.139i) q^{69} +132.605 q^{71} +(-370.263 + 391.928i) q^{72} -259.933 q^{73} +(240.680 + 416.871i) q^{74} +(74.0478 - 128.255i) q^{76} +(300.577 - 520.614i) q^{77} +(309.253 - 133.276i) q^{78} +(-62.3245 - 107.949i) q^{79} +(-41.4099 - 727.823i) q^{81} -973.214 q^{82} +(18.3599 + 31.8003i) q^{83} +(228.975 - 98.6790i) q^{84} +(-297.562 + 515.392i) q^{86} +(-31.8736 - 23.7457i) q^{87} +(-191.641 - 331.932i) q^{88} +333.424 q^{89} +657.443 q^{91} +(124.851 + 216.248i) q^{92} +(-136.133 + 1161.31i) q^{93} +(491.379 - 851.093i) q^{94} +(41.4005 - 353.175i) q^{96} +(-514.623 - 891.353i) q^{97} +1969.66 q^{98} +(504.180 + 119.851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9}+O(q^{10}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9	\( 32 q - 54 q^{4} - 12 q^{6} + 18 q^{9} + 90 q^{11} + 102 q^{14} - 146 q^{16} + 8 q^{19} + 30 q^{21} - 462 q^{24} - 936 q^{26} + 516 q^{29} - 38 q^{31} - 212 q^{34} + 864 q^{36} - 330 q^{39} + 576 q^{41} - 3288 q^{44} - 580 q^{46} + 4 q^{49} + 1260 q^{51} + 3726 q^{54} + 2430 q^{56} + 2202 q^{59} - 20 q^{61} - 644 q^{64} - 5052 q^{66} - 1452 q^{69} - 5904 q^{71} + 4080 q^{74} + 396 q^{76} + 218 q^{79} + 198 q^{81} - 4662 q^{84} + 6108 q^{86} - 8148 q^{89} - 1884 q^{91} + 1078 q^{94} + 11874 q^{96} + 1602 q^{99}+O(q^{100}) \) 32 * q - 54 * q^4 - 12 * q^6 + 18 * q^9 + 90 * q^11 + 102 * q^14 - 146 * q^16 + 8 * q^19 + 30 * q^21 - 462 * q^24 - 936 * q^26 + 516 * q^29 - 38 * q^31 - 212 * q^34 + 864 * q^36 - 330 * q^39 + 576 * q^41 - 3288 * q^44 - 580 * q^46 + 4 * q^49 + 1260 * q^51 + 3726 * q^54 + 2430 * q^56 + 2202 * q^59 - 20 * q^61 - 644 * q^64 - 5052 * q^66 - 1452 * q^69 - 5904 * q^71 + 4080 * q^74 + 396 * q^76 + 218 * q^79 + 198 * q^81 - 4662 * q^84 + 6108 * q^86 - 8148 * q^89 - 1884 * q^91 + 1078 * q^94 + 11874 * q^96 + 1602 * q^99

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