LMFDB - Embedded newform 225.4.e.g.76.8

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			76.8
Character	$\chi$	$=$	225.76
Dual form			225.4.e.g.151.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.236995 - 0.410487i) q^{2} +(2.45316 - 4.58061i) q^{3} +(3.88767 - 6.73364i) q^{4} +(-2.46167 + 0.0785933i) q^{6} +(4.10329 + 7.10710i) q^{7} -7.47735 q^{8} +(-14.9641 - 22.4739i) q^{9} +O(q^{10})$	\(q+(-0.236995 - 0.410487i) q^{2} +(2.45316 - 4.58061i) q^{3} +(3.88767 - 6.73364i) q^{4} +(-2.46167 + 0.0785933i) q^{6} +(4.10329 + 7.10710i) q^{7} -7.47735 q^{8} +(-14.9641 - 22.4739i) q^{9} +(-2.63291 - 4.56034i) q^{11} +(-21.3071 - 34.3266i) q^{12} +(38.5171 - 66.7136i) q^{13} +(1.94492 - 3.36869i) q^{14} +(-29.3292 - 50.7997i) q^{16} +88.9397 q^{17} +(-5.67885 + 11.4688i) q^{18} -91.7358 q^{19} +(42.6209 - 1.36075i) q^{21} +(-1.24798 + 2.16156i) q^{22} +(-77.2204 + 133.750i) q^{23} +(-18.3431 + 34.2509i) q^{24} -36.5135 q^{26} +(-139.654 + 13.4125i) q^{27} +63.8088 q^{28} +(-84.1517 - 145.755i) q^{29} +(-36.3943 + 63.0367i) q^{31} +(-43.8112 + 75.8832i) q^{32} +(-27.3481 + 0.873138i) q^{33} +(-21.0783 - 36.5086i) q^{34} +(-209.506 + 13.3914i) q^{36} +154.836 q^{37} +(21.7409 + 37.6564i) q^{38} +(-211.101 - 340.091i) q^{39} +(-3.97579 + 6.88627i) q^{41} +(-10.6595 - 17.1728i) q^{42} +(-11.6007 - 20.0930i) q^{43} -40.9436 q^{44} +73.2034 q^{46} +(150.699 + 261.018i) q^{47} +(-304.643 + 9.72629i) q^{48} +(137.826 - 238.722i) q^{49} +(218.183 - 407.398i) q^{51} +(-299.483 - 518.721i) q^{52} +344.542 q^{53} +(38.6029 + 54.1473i) q^{54} +(-30.6817 - 53.1423i) q^{56} +(-225.042 + 420.206i) q^{57} +(-39.8871 + 69.0864i) q^{58} +(-125.779 + 217.855i) q^{59} +(-136.451 - 236.340i) q^{61} +34.5010 q^{62} +(98.3226 - 198.568i) q^{63} -427.736 q^{64} +(6.83978 + 11.0191i) q^{66} +(417.734 - 723.536i) q^{67} +(345.768 - 598.887i) q^{68} +(423.222 + 681.825i) q^{69} +351.152 q^{71} +(111.891 + 168.045i) q^{72} -522.749 q^{73} +(-36.6954 - 63.5584i) q^{74} +(-356.638 + 617.715i) q^{76} +(21.6072 - 37.4248i) q^{77} +(-89.5732 + 167.254i) q^{78} +(350.053 + 606.310i) q^{79} +(-281.154 + 672.602i) q^{81} +3.76897 q^{82} +(120.651 + 208.974i) q^{83} +(156.533 - 292.284i) q^{84} +(-5.49862 + 9.52388i) q^{86} +(-874.085 + 27.9067i) q^{87} +(19.6872 + 34.0993i) q^{88} +1021.39 q^{89} +632.187 q^{91} +(600.414 + 1039.95i) q^{92} +(199.466 + 321.347i) q^{93} +(71.4298 - 123.720i) q^{94} +(240.116 + 386.835i) q^{96} +(-194.642 - 337.130i) q^{97} -130.656 q^{98} +(-63.0897 + 127.413i) 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 $

$2$	−0.236995	−	0.410487i	−0.0837904	−	0.145129i	0.821085	−	0.570806i	$-0.193369\pi$
$2$	−0.236995	−	0.410487i	−0.0837904	−	0.145129i	−0.904875	+	0.425677i	$0.860036\pi$
$3$	2.45316	−	4.58061i	0.472110	−	0.881540i
$3$	2.45316	−	4.58061i	0.472110	−	0.881540i
$4$	3.88767	−	6.73364i	0.485958	−	0.841705i
$5$		0			0
$5$		0			0
$6$	−2.46167	+	0.0785933i	−0.167495	+	0.00534760i
$7$	4.10329	+	7.10710i	0.221557	+	0.383747i	0.955281	−	0.295700i	$-0.0955529\pi$
$7$	4.10329	+	7.10710i	0.221557	+	0.383747i	−0.733724	+	0.679447i	$0.762220\pi$
$8$	−7.47735			−0.330455
$9$	−14.9641	−	22.4739i	−0.554224	−	0.832367i
$10$		0			0
$11$	−2.63291	−	4.56034i	−0.0721685	−	0.125000i	0.827683	−	0.561196i	$-0.189659\pi$
$11$	−2.63291	−	4.56034i	−0.0721685	−	0.125000i	−0.899851	+	0.436196i	$0.856325\pi$
$12$	−21.3071	−	34.3266i	−0.512570	−	0.825769i
$13$	38.5171	−	66.7136i	0.821748	−	1.42331i	−0.0826310	−	0.996580i	$-0.526332\pi$
$13$	38.5171	−	66.7136i	0.821748	−	1.42331i	0.904379	−	0.426730i	$-0.140334\pi$
$14$	1.94492	−	3.36869i	0.0371286	−	0.0643087i
$15$		0			0
$16$	−29.3292	−	50.7997i	−0.458269	−	0.793746i
$17$	88.9397			1.26888			0.634442	−	0.772970i	$-0.281230\pi$
$17$	88.9397			1.26888			0.634442	+	0.772970i	$0.281230\pi$
$18$	−5.67885	+	11.4688i	−0.0743622	+	0.150179i
$19$	−91.7358			−1.10766			−0.553832	−	0.832628i	$-0.686835\pi$
$19$	−91.7358			−1.10766			−0.553832	+	0.832628i	$0.686835\pi$
$20$		0			0
$21$	42.6209	−	1.36075i	0.442888	−	0.0141400i
$22$	−1.24798	+	2.16156i	−0.0120941	+	0.0209475i
$23$	−77.2204	+	133.750i	−0.700068	+	1.21255i	0.268374	+	0.963315i	$0.413514\pi$
$23$	−77.2204	+	133.750i	−0.700068	+	1.21255i	−0.968442	+	0.249238i	$0.919820\pi$
$24$	−18.3431	+	34.2509i	−0.156011	+	0.291309i
$25$		0			0
$26$	−36.5135			−0.275418
$27$	−139.654	+	13.4125i	−0.995420	+	0.0956017i
$28$	63.8088			0.430669
$29$	−84.1517	−	145.755i	−0.538847	−	0.933311i	−0.998966	−	0.0454539i	$-0.985527\pi$
$29$	−84.1517	−	145.755i	−0.538847	−	0.933311i	0.460119	−	0.887857i	$-0.347807\pi$
$30$		0			0
$31$	−36.3943	+	63.0367i	−0.210858	+	0.365217i	−0.951983	−	0.306150i	$-0.900959\pi$
$31$	−36.3943	+	63.0367i	−0.210858	+	0.365217i	0.741125	+	0.671367i	$0.234292\pi$
$32$	−43.8112	+	75.8832i	−0.242025	+	0.419199i
$33$	−27.3481	+	0.873138i	−0.144264	+	0.00460587i
$34$	−21.0783	−	36.5086i	−0.106320	−	0.184152i
$35$		0			0
$36$	−209.506	+	13.3914i	−0.969937	+	0.0619972i
$37$	154.836			0.687971			0.343986	−	0.938975i	$-0.388223\pi$
$37$	154.836			0.687971			0.343986	+	0.938975i	$0.388223\pi$
$38$	21.7409	+	37.6564i	0.0928117	+	0.160754i
$39$	−211.101	−	340.091i	−0.866748	−	1.39636i
$40$		0			0
$41$	−3.97579	+	6.88627i	−0.0151442	+	0.0262306i	−0.873498	−	0.486827i	$-0.838154\pi$
$41$	−3.97579	+	6.88627i	−0.0151442	+	0.0262306i	0.858354	+	0.513058i	$0.171487\pi$
$42$	−10.6595	−	17.1728i	−0.0391618	−	0.0630911i
$43$	−11.6007	−	20.0930i	−0.0411416	−	0.0712594i	0.844721	−	0.535206i	$-0.179766\pi$
$43$	−11.6007	−	20.0930i	−0.0411416	−	0.0712594i	−0.885863	+	0.463947i	$0.846433\pi$
$44$	−40.9436			−0.140284
$45$		0			0
$46$	73.2034			0.234636
$47$	150.699	+	261.018i	0.467696	+	0.810073i	0.999319	−	0.0369081i	$-0.0117509\pi$
$47$	150.699	+	261.018i	0.467696	+	0.810073i	−0.531623	+	0.846981i	$0.678418\pi$
$48$	−304.643	+	9.72629i	−0.916072	+	0.0292473i
$49$	137.826	−	238.722i	0.401825	−	0.695982i
$50$		0			0
$51$	218.183	−	407.398i	0.599053	−	1.11857i
$52$	−299.483	−	518.721i	−0.798671	−	1.38334i
$53$	344.542			0.892952			0.446476	−	0.894796i	$-0.352679\pi$
$53$	344.542			0.892952			0.446476	+	0.894796i	$0.352679\pi$
$54$	38.6029	+	54.1473i	0.0972812	+	0.136454i
$55$		0			0
$56$	−30.6817	−	53.1423i	−0.0732146	−	0.126811i
$57$	−225.042	+	420.206i	−0.522940	+	0.976450i
$58$	−39.8871	+	69.0864i	−0.0903005	+	0.156405i
$59$	−125.779	+	217.855i	−0.277542	+	0.480718i	−0.970773	−	0.239998i	$-0.922853\pi$
$59$	−125.779	+	217.855i	−0.277542	+	0.480718i	0.693231	+	0.720715i	$0.256187\pi$
$60$		0			0
$61$	−136.451	−	236.340i	−0.286406	−	0.496069i	0.686543	−	0.727089i	$-0.259127\pi$
$61$	−136.451	−	236.340i	−0.286406	−	0.496069i	−0.972949	+	0.231020i	$0.925794\pi$
$62$	34.5010			0.0706715
$63$	98.3226	−	198.568i	0.196627	−	0.397099i
$64$	−427.736			−0.835421
$65$		0			0
$66$	6.83978	+	11.0191i	0.0127563	+	0.0205509i
$67$	417.734	−	723.536i	0.761706	−	1.31931i	−0.180265	−	0.983618i	$-0.557695\pi$
$67$	417.734	−	723.536i	0.761706	−	1.31931i	0.941971	−	0.335695i	$-0.108971\pi$
$68$	345.768	−	598.887i	0.616625	−	1.06803i
$69$	423.222	+	681.825i	0.738405	+	1.18960i
$70$		0			0
$71$	351.152			0.586959			0.293479	−	0.955965i	$-0.405187\pi$
$71$	351.152			0.586959			0.293479	+	0.955965i	$0.405187\pi$
$72$	111.891	+	168.045i	0.183146	+	0.275060i
$73$	−522.749			−0.838126			−0.419063	−	0.907957i	$-0.637641\pi$
$73$	−522.749			−0.838126			−0.419063	+	0.907957i	$0.637641\pi$
$74$	−36.6954	−	63.5584i	−0.0576454	−	0.0998448i
$75$		0			0
$76$	−356.638	+	617.715i	−0.538279	+	0.932326i
$77$	21.6072	−	37.4248i	0.0319788	−	0.0553889i
$78$	−89.5732	+	167.254i	−0.130028	+	0.242792i
$79$	350.053	+	606.310i	0.498533	+	0.863484i	0.999999	−	0.00169342i	$-0.000539032\pi$
$79$	350.053	+	606.310i	0.498533	+	0.863484i	−0.501466	+	0.865177i	$0.667206\pi$
$80$		0			0
$81$	−281.154	+	672.602i	−0.385671	+	0.922636i
$82$	3.76897			0.00507577
$83$	120.651	+	208.974i	0.159557	+	0.276360i	0.934709	−	0.355414i	$-0.115660\pi$
$83$	120.651	+	208.974i	0.159557	+	0.276360i	−0.775152	+	0.631775i	$0.782327\pi$
$84$	156.533	−	292.284i	0.203323	−	0.379652i
$85$		0			0
$86$	−5.49862	+	9.52388i	−0.00689455	+	0.0119417i
$87$	−874.085	+	27.9067i	−1.07715	+	0.0343898i
$88$	19.6872	+	34.0993i	0.0238485	+	0.0413068i
$89$	1021.39			1.21648			0.608242	−	0.793752i	$-0.291875\pi$
$89$	1021.39			1.21648			0.608242	+	0.793752i	$0.291875\pi$
$90$		0			0
$91$	632.187			0.728255
$92$	600.414	+	1039.95i	0.680408	+	1.17850i
$93$	199.466	+	321.347i	0.222405	+	0.358302i
$94$	71.4298	−	123.720i	0.0783769	−	0.135753i
$95$		0			0
$96$	240.116	+	386.835i	0.255278	+	0.411263i
$97$	−194.642	−	337.130i	−0.203741	−	0.352891i	0.745990	−	0.665958i	$-0.231977\pi$
$97$	−194.642	−	337.130i	−0.203741	−	0.352891i	−0.949731	+	0.313067i	$0.898644\pi$
$98$	−130.656			−0.134676
$99$	−63.0897	+	127.413i	−0.0640480	+	0.129348i
$100$		0			0
$101$	432.260	+	748.696i	0.425856	+	0.737604i	0.996500	−	0.0835936i	$-0.0266397\pi$
$101$	432.260	+	748.696i	0.425856	+	0.737604i	−0.570644	+	0.821197i	$0.693306\pi$
$102$	−218.940	+	6.99006i	−0.212532	+	0.00678548i
$103$	614.103	−	1063.66i	0.587470	−	1.01753i	−0.407093	−	0.913387i	$-0.633457\pi$
$103$	614.103	−	1063.66i	0.587470	−	1.01753i	0.994563	−	0.104141i	$-0.0332092\pi$
$104$	−288.006	+	498.841i	−0.271551	+	0.470340i
$105$		0			0
$106$	−81.6547	−	141.430i	−0.0748208	−	0.129593i
$107$	1860.34			1.68080			0.840402	−	0.541963i	$-0.182319\pi$
$107$	1860.34			1.68080			0.840402	+	0.541963i	$0.182319\pi$
$108$	−452.611	+	992.519i	−0.403264	+	0.884308i
$109$	1037.31			0.911524			0.455762	−	0.890102i	$-0.349367\pi$
$109$	1037.31			0.911524			0.455762	+	0.890102i	$0.349367\pi$
$110$		0			0
$111$	379.838	−	709.246i	0.324798	−	0.606474i
$112$	240.692	−	416.892i	0.203065	−	0.351719i
$113$	−703.867	+	1219.13i	−0.585967	+	1.01492i	0.408787	+	0.912630i	$0.365952\pi$
$113$	−703.867	+	1219.13i	−0.585967	+	1.01492i	−0.994754	+	0.102295i	$0.967381\pi$
$114$	225.823	−	7.20982i	0.185529	−	0.00592334i
$115$		0			0
$116$	−1308.61			−1.04743
$117$	−2075.69	+	132.675i	−1.64015	+	0.104836i
$118$	119.236			0.0930215
$119$	364.945	+	632.103i	0.281130	+	0.486931i
$120$		0			0
$121$	651.636	−	1128.67i	0.489583	−	0.847983i
$122$	−64.6764	+	112.023i	−0.0479961	+	0.0831317i
$123$	21.7901	+	35.1046i	0.0159736	+	0.0257340i
$124$	282.977	+	490.131i	0.204937	+	0.354960i
$125$		0			0
$126$	−104.812	+	6.69943i	−0.0741060	+	0.00473677i
$127$	198.654			0.138801			0.0694005	−	0.997589i	$-0.477891\pi$
$127$	198.654			0.138801			0.0694005	+	0.997589i	$0.477891\pi$
$128$	451.861	+	782.645i	0.312025	+	0.540443i
$129$	−120.497	+	3.84707i	−0.0822414	+	0.00262570i
$130$		0			0
$131$	726.091	−	1257.63i	0.484266	−	0.838773i	−0.515571	−	0.856847i	$-0.672420\pi$
$131$	726.091	−	1257.63i	0.484266	−	0.838773i	0.999837	+	0.0180739i	$0.00575340\pi$
$132$	−100.441	+	187.547i	−0.0662293	+	0.123666i
$133$	−376.418	−	651.975i	−0.245410	−	0.425063i
$134$	−396.003			−0.255295
$135$		0			0
$136$	−665.033			−0.419310
$137$	318.328	+	551.360i	0.198515	+	0.343838i	0.948047	−	0.318130i	$-0.103055\pi$
$137$	318.328	+	551.360i	0.198515	+	0.343838i	−0.749532	+	0.661968i	$0.769721\pi$
$138$	179.579	−	335.316i	0.110774	−	0.206841i
$139$	−761.621	+	1319.17i	−0.464747	+	0.804965i	−0.999190	−	0.0402391i	$-0.987188\pi$
$139$	−761.621	+	1319.17i	−0.464747	+	0.804965i	0.534443	+	0.845204i	$0.320521\pi$
$140$		0			0
$141$	1565.31	−	49.9754i	0.934916	−	0.0298489i
$142$	−83.2213	−	144.143i	−0.0491815	−	0.0851849i
$143$	−405.649			−0.237217
$144$	−702.785	+	1419.31i	−0.406704	+	0.821362i
$145$		0			0
$146$	123.889	+	214.582i	0.0702269	+	0.121637i
$147$	−755.384	−	1216.95i	−0.423830	−	0.682805i
$148$	601.952	−	1042.61i	0.334325	−	0.579069i
$149$	1051.30	−	1820.91i	0.578027	−	1.00117i	−0.417679	−	0.908595i	$-0.637156\pi$
$149$	1051.30	−	1820.91i	0.578027	−	1.00117i	0.995706	−	0.0925770i	$-0.0295104\pi$
$150$		0			0
$151$	1180.25	+	2044.25i	0.636074	+	1.10171i	0.986286	+	0.165043i	$0.0527762\pi$
$151$	1180.25	+	2044.25i	0.636074	+	1.10171i	−0.350212	+	0.936670i	$0.613891\pi$
$152$	685.940			0.366034
$153$	−1330.90	−	1998.82i	−0.703247	−	1.05618i
$154$	−20.4832			−0.0107181
$155$		0			0
$156$	−3110.74	+	99.3160i	−1.59653	+	0.0509721i
$157$	1002.09	−	1735.68i	0.509400	−	0.882306i	−0.490541	−	0.871418i	$-0.663201\pi$
$157$	1002.09	−	1735.68i	0.509400	−	0.882306i	0.999941	−	0.0108880i	$-0.00346583\pi$
$158$	165.922	−	287.385i	0.0835445	−	0.144703i
$159$	845.215	−	1578.21i	0.421572	−	0.787173i
$160$		0			0
$161$	−1267.43			−0.620419
$162$	342.727	−	43.9931i	0.166217	−	0.0213359i
$163$	2772.38			1.33220			0.666102	−	0.745861i	$-0.267962\pi$
$163$	2772.38			1.33220			0.666102	+	0.745861i	$0.267962\pi$
$164$	30.9131	+	53.5430i	0.0147189	+	0.0254939i
$165$		0			0
$166$	57.1875	−	99.0517i	0.0267386	−	0.0463127i
$167$	−923.165	+	1598.97i	−0.427764	+	0.740909i	−0.996674	−	0.0814904i	$-0.974032\pi$
$167$	−923.165	+	1598.97i	−0.427764	+	0.740909i	0.568910	+	0.822400i	$0.307365\pi$
$168$	−318.691	+	10.1748i	−0.146355	+	0.00467263i
$169$	−1868.64	−	3236.57i	−0.850540	−	1.47318i
$170$		0			0
$171$	1372.74	+	2061.66i	0.613895	+	0.921984i
$172$	−180.399			−0.0799725
$173$	96.5861	+	167.292i	0.0424469	+	0.0735201i	0.886468	−	0.462789i	$-0.153151\pi$
$173$	96.5861	+	167.292i	0.0424469	+	0.0735201i	−0.844021	+	0.536309i	$0.819818\pi$
$174$	218.609	+	352.187i	0.0952455	+	0.153444i
$175$		0			0
$176$	−154.443	+	267.503i	−0.0661452	+	0.114567i
$177$	689.356	+	1110.58i	0.292741	+	0.471616i
$178$	−242.064	−	419.268i	−0.101930	−	0.176547i
$179$	−3931.26			−1.64154			−0.820770	−	0.571258i	$-0.806456\pi$
$179$	−3931.26			−1.64154			−0.820770	+	0.571258i	$0.806456\pi$
$180$		0			0
$181$	−1921.32			−0.789007			−0.394503	−	0.918894i	$-0.629083\pi$
$181$	−1921.32			−0.789007			−0.394503	+	0.918894i	$0.629083\pi$
$182$	−149.825	−	259.505i	−0.0610208	−	0.105691i
$183$	−1417.32	+	45.2504i	−0.572520	+	0.0182787i
$184$	577.404	−	1000.09i	0.231341	−	0.400695i
$185$		0			0
$186$	84.6364	−	158.036i	0.0333647	−	0.0622998i
$187$	−234.170	−	405.595i	−0.0915735	−	0.158610i
$188$	2343.47			0.909123
$189$	−668.363	−	937.496i	−0.257229	−	0.360808i
$190$		0			0
$191$	753.915	+	1305.82i	0.285609	+	0.494690i	0.972757	−	0.231828i	$-0.0744707\pi$
$191$	753.915	+	1305.82i	0.285609	+	0.494690i	−0.687147	+	0.726518i	$0.741137\pi$
$192$	−1049.30	+	1959.29i	−0.394411	+	0.736457i
$193$	−2032.83	+	3520.96i	−0.758166	+	1.31318i	0.185619	+	0.982622i	$0.440571\pi$
$193$	−2032.83	+	3520.96i	−0.758166	+	1.31318i	−0.943785	+	0.330561i	$0.892762\pi$
$194$	−92.2585	+	159.796i	−0.0341432	+	0.0591377i
$195$		0			0
$196$	−1071.64	−	1856.14i	−0.390541	−	0.676436i
$197$	−3916.67			−1.41650			−0.708252	−	0.705960i	$-0.750516\pi$
$197$	−3916.67			−1.41650			−0.708252	+	0.705960i	$0.750516\pi$
$198$	67.2534	−	4.29876i	0.0241388	−	0.00154293i
$199$	615.676			0.219317			0.109659	−	0.993969i	$-0.465024\pi$
$199$	615.676			0.219317			0.109659	+	0.993969i	$0.465024\pi$
$200$		0			0
$201$	−2289.47	−	3688.42i	−0.803418	−	1.29433i
$202$	204.887	−	354.874i	0.0713652	−	0.123608i
$203$	690.597	−	1196.15i	0.238770	−	0.413562i
$204$	−1895.05	−	3052.99i	−0.650392	−	1.04780i
$205$		0			0
$206$	−582.157			−0.196897
$207$	4161.41	−	265.992i	1.39728	−	0.0893127i
$208$	−4518.71			−1.50633
$209$	241.532	+	418.346i	0.0799385	+	0.138458i
$210$		0			0
$211$	1116.74	−	1934.26i	0.364360	−	0.631089i	−0.624314	−	0.781174i	$-0.714621\pi$
$211$	1116.74	−	1934.26i	0.364360	−	0.631089i	0.988673	+	0.150085i	$0.0479546\pi$
$212$	1339.46	−	2320.02i	0.433938	−	0.751602i
$213$	861.430	−	1608.49i	0.277109	−	0.517427i
$214$	−440.892	−	763.647i	−0.140835	−	0.243934i
$215$		0			0
$216$	1044.24	−	100.290i	0.328942	−	0.0315921i
$217$	−597.344			−0.186868
$218$	−245.837	−	425.802i	−0.0763769	−	0.132289i
$219$	−1282.39	+	2394.51i	−0.395687	+	0.738841i
$220$		0			0
$221$	3425.70	−	5933.49i	1.04270	−	1.80602i
$222$	−381.156	+	12.1691i	−0.115232	+	0.00367899i
$223$	2315.22	+	4010.08i	0.695240	+	1.20419i	0.970100	+	0.242707i	$0.0780353\pi$
$223$	2315.22	+	4010.08i	0.695240	+	1.20419i	−0.274860	+	0.961484i	$0.588631\pi$
$224$	−719.079			−0.214489
$225$		0			0
$226$	667.252			0.196394
$227$	−233.846	−	405.034i	−0.0683741	−	0.118427i	0.829812	−	0.558044i	$-0.188448\pi$
$227$	−233.846	−	405.034i	−0.0683741	−	0.118427i	−0.898186	+	0.439616i	$0.855114\pi$
$228$	1954.63	+	3148.97i	0.567756	+	0.914675i
$229$	−728.574	+	1261.93i	−0.210242	+	0.364150i	−0.951790	−	0.306749i	$-0.900759\pi$
$229$	−728.574	+	1261.93i	−0.210242	+	0.364150i	0.741548	+	0.670900i	$0.234092\pi$
$230$		0			0
$231$	−118.423	−	190.783i	−0.0337300	−	0.0543403i
$232$	629.232	+	1089.86i	0.178065	+	0.308418i
$233$	−2617.43			−0.735938			−0.367969	−	0.929838i	$-0.619947\pi$
$233$	−2617.43			−0.735938			−0.367969	+	0.929838i	$0.619947\pi$
$234$	546.389	+	820.601i	0.152644	+	0.229249i
$235$		0			0
$236$	977.972	+	1693.90i	0.269748	+	0.467217i
$237$	3636.01	−	116.086i	0.996558	−	0.0318169i
$238$	172.980	−	299.610i	0.0471119	−	0.0816003i
$239$	1855.58	−	3213.96i	0.502207	−	0.869847i	−0.497790	−	0.867298i	$-0.665855\pi$
$239$	1855.58	−	3213.96i	0.502207	−	0.869847i	0.999997	−	0.00254992i	$-0.000811665\pi$
$240$		0			0
$241$	922.053	+	1597.04i	0.246451	+	0.426865i	0.962539	−	0.271145i	$-0.0874023\pi$
$241$	922.053	+	1597.04i	0.246451	+	0.426865i	−0.716088	+	0.698010i	$0.754069\pi$
$242$	−617.737			−0.164090
$243$	2391.22	+	2937.86i	0.631261	+	0.775570i
$244$	−2121.90			−0.556725
$245$		0			0
$246$	9.24586	−	17.2642i	0.00239632	−	0.00447449i
$247$	−3533.40	+	6120.02i	−0.910222	+	1.57655i
$248$	272.133	−	471.347i	0.0696792	−	0.120688i
$249$	1253.21	−	40.0109i	0.318951	−	0.0101831i
$250$		0			0
$251$	−7204.10			−1.81163			−0.905815	−	0.423674i	$-0.860740\pi$
$251$	−7204.10			−1.81163			−0.905815	+	0.423674i	$0.860740\pi$
$252$	−954.839	−	1434.03i	−0.238687	−	0.358475i
$253$	813.259			0.202091
$254$	−47.0801	−	81.5451i	−0.0116302	−	0.0201441i
$255$		0			0
$256$	−1496.77	+	2592.47i	−0.365421	+	0.632928i
$257$	878.573	−	1521.73i	0.213245	−	0.369351i	−0.739484	−	0.673175i	$-0.764930\pi$
$257$	878.573	−	1521.73i	0.213245	−	0.369351i	0.952728	+	0.303824i	$0.0982635\pi$
$258$	30.1363	+	48.5506i	0.00727210	+	0.0117156i
$259$	635.338	+	1100.44i	0.152425	+	0.264007i
$260$		0			0
$261$	−2016.44	+	4072.30i	−0.478215	+	0.965783i
$262$	−688.319			−0.162307
$263$	−2678.45	−	4639.22i	−0.627987	−	1.08771i	−0.987955	−	0.154741i	$-0.950546\pi$
$263$	−2678.45	−	4639.22i	−0.627987	−	1.08771i	0.359968	−	0.932965i	$-0.382788\pi$
$264$	204.491	−	6.52876i	0.0476726	−	0.00152204i
$265$		0			0
$266$	−178.418	+	309.030i	−0.0411261	+	0.0712324i
$267$	2505.63	−	4678.59i	0.574314	−	1.07238i
$268$	−3248.02	−	5625.73i	−0.740315	−	1.28226i
$269$	−1040.60			−0.235860			−0.117930	−	0.993022i	$-0.537626\pi$
$269$	−1040.60			−0.235860			−0.117930	+	0.993022i	$0.537626\pi$
$270$		0			0
$271$	−1531.38			−0.343265			−0.171632	−	0.985161i	$-0.554904\pi$
$271$	−1531.38			−0.343265			−0.171632	+	0.985161i	$0.554904\pi$
$272$	−2608.53	−	4518.11i	−0.581491	−	1.00717i
$273$	1550.85	−	2895.80i	0.343816	−	0.641986i
$274$	150.884	−	261.339i	0.0332673	−	0.0576207i
$275$		0			0
$276$	6236.51	−	199.112i	1.36012	−	0.0434244i
$277$	3115.55	+	5396.29i	0.675794	+	1.17051i	0.976236	+	0.216710i	$0.0695326\pi$
$277$	3115.55	+	5396.29i	0.675794	+	1.17051i	−0.300442	+	0.953800i	$0.597134\pi$
$278$	722.001			0.155765
$279$	1961.29	−	125.363i	0.420857	−	0.0269007i
$280$		0			0
$281$	4556.98	+	7892.92i	0.967425	+	1.67563i	0.702953	+	0.711236i	$0.251864\pi$
$281$	4556.98	+	7892.92i	0.967425	+	1.67563i	0.264472	+	0.964393i	$0.414802\pi$
$282$	−391.486	−	630.697i	−0.0826689	−	0.133183i
$283$	757.546	−	1312.11i	0.159122	−	0.275607i	−0.775431	−	0.631433i	$-0.782467\pi$
$283$	757.546	−	1312.11i	0.159122	−	0.275607i	0.934552	+	0.355826i	$0.115800\pi$
$284$	1365.16	−	2364.53i	0.285238	−	0.494046i
$285$		0			0
$286$	96.1368	+	166.514i	0.0198765	+	0.0344272i
$287$	−65.2552			−0.0134212
$288$	2360.99	−	150.911i	0.483064	−	0.0308768i
$289$	2997.26			0.610067
$290$		0			0
$291$	−2021.75	+	64.5481i	−0.407275	+	0.0130030i
$292$	−2032.27	+	3520.00i	−0.407294	+	0.705454i
$293$	−692.150	+	1198.84i	−0.138006	+	0.239034i	−0.926742	−	0.375699i	$-0.877403\pi$
$293$	−692.150	+	1198.84i	−0.138006	+	0.239034i	0.788736	+	0.614733i	$0.210736\pi$
$294$	−320.520	+	598.487i	−0.0635821	+	0.118723i
$295$		0			0
$296$	−1157.77			−0.227344
$297$	428.862	+	601.554i	0.0837881	+	0.117528i
$298$	−996.613			−0.193732
$299$	5948.61	+	10303.3i	1.15056	+	1.99283i
$300$		0			0
$301$	95.2020	−	164.895i	0.0182304	−	0.0315760i
$302$	559.426	−	968.954i	0.106594	−	0.184626i
$303$	4489.89	−	143.348i	0.851278	−	0.0271786i
$304$	2690.54	+	4660.15i	0.507609	+	0.879204i
$305$		0			0
$306$	−505.075	+	1020.03i	−0.0943570	+	0.190559i
$307$	−1628.16			−0.302685			−0.151342	−	0.988481i	$-0.548360\pi$
$307$	−1628.16			−0.302685			−0.151342	+	0.988481i	$0.548360\pi$
$308$	−168.003	−	290.990i	−0.0310807	−	0.0538334i
$309$	−3365.72	−	5422.29i	−0.619640	−	0.998263i
$310$		0			0
$311$	703.314	−	1218.17i	0.128236	−	0.222110i	−0.794758	−	0.606927i	$-0.792402\pi$
$311$	703.314	−	1218.17i	0.128236	−	0.222110i	0.922993	+	0.384817i	$0.125735\pi$
$312$	1578.47	+	2542.98i	0.286422	+	0.461435i
$313$	2715.77	+	4703.85i	0.490429	+	0.849448i	0.999939	−	0.0110164i	$-0.00350668\pi$
$313$	2715.77	+	4703.85i	0.490429	+	0.849448i	−0.509510	+	0.860465i	$0.670173\pi$
$314$	−949.964			−0.170731
$315$		0			0
$316$	5443.56			0.969065
$317$	−3840.80	−	6652.46i	−0.680507	−	1.17867i	−0.974826	−	0.222966i	$-0.928426\pi$
$317$	−3840.80	−	6652.46i	−0.680507	−	1.17867i	0.294319	−	0.955707i	$-0.404907\pi$
$318$	−848.148	+	27.0787i	−0.149565	+	0.00477515i
$319$	−443.128	+	767.521i	−0.0777756	+	0.134711i
$320$		0			0
$321$	4563.71	−	8521.51i	0.793525	−	1.48170i
$322$	300.374	+	520.264i	0.0519851	+	0.0900409i
$323$	−8158.95			−1.40550
$324$	3436.02	+	4508.04i	0.589167	+	0.772984i
$325$		0			0
$326$	−657.039	−	1138.03i	−0.111626	−	0.193342i
$327$	2544.68	−	4751.51i	0.430339	−	0.803544i
$328$	29.7284	−	51.4910i	0.00500449	−	0.00866804i
$329$	−1236.72	+	2142.07i	−0.207242	+	0.358954i
$330$		0			0
$331$	−2064.44	−	3575.71i	−0.342815	−	0.593773i	0.642139	−	0.766588i	$-0.278047\pi$
$331$	−2064.44	−	3575.71i	−0.342815	−	0.593773i	−0.984954	+	0.172815i	$0.944714\pi$
$332$	1876.21			0.310152
$333$	−2316.98	−	3479.78i	−0.381290	−	0.572645i
$334$	875.142			0.143370
$335$		0			0
$336$	−1319.16	−	2125.22i	−0.214185	−	0.345060i
$337$	−1312.08	+	2272.58i	−0.212087	+	0.367345i	−0.952367	−	0.304953i	$-0.901359\pi$
$337$	−1312.08	+	2272.58i	−0.212087	+	0.367345i	0.740281	+	0.672298i	$0.234693\pi$
$338$	−885.715	+	1534.10i	−0.142534	+	0.246877i
$339$	3857.69	+	6214.87i	0.618055	+	0.995709i
$340$		0			0
$341$	383.292			0.0608693
$342$	520.954	−	1052.10i	0.0823683	−	0.166347i
$343$	5077.01			0.799221
$344$	86.7425	+	150.242i	0.0135955	+	0.0235480i
$345$		0			0
$346$	45.7809	−	79.2948i	0.00711328	−	0.0123206i
$347$	−3457.40	+	5988.40i	−0.534880	+	0.926439i	0.464290	+	0.885683i	$0.346310\pi$
$347$	−3457.40	+	5988.40i	−0.534880	+	0.926439i	−0.999169	+	0.0407551i	$0.987024\pi$
$348$	−3210.24	+	5994.26i	−0.494502	+	0.923351i
$349$	1330.20	+	2303.98i	0.204024	+	0.353379i	0.949821	−	0.312793i	$-0.101265\pi$
$349$	1330.20	+	2303.98i	0.204024	+	0.353379i	−0.745798	+	0.666173i	$0.767931\pi$
$350$		0			0
$351$	−4484.25	+	9833.40i	−0.681914	+	1.49535i
$352$	461.404			0.0698663
$353$	2258.75	+	3912.26i	0.340569	+	0.589883i	0.984539	−	0.175168i	$-0.0560469\pi$
$353$	2258.75	+	3912.26i	0.340569	+	0.589883i	−0.643969	+	0.765051i	$0.722714\pi$
$354$	292.504	−	546.173i	0.0439164	−	0.0820022i
$355$		0			0
$356$	3970.82	−	6877.67i	0.591161	−	1.02392i
$357$	3790.69	−	121.025i	0.561973	−	0.0179420i
$358$	931.688	+	1613.73i	0.137545	+	0.238236i
$359$	2702.34			0.397281			0.198640	−	0.980072i	$-0.436347\pi$
$359$	2702.34			0.397281			0.198640	+	0.980072i	$0.436347\pi$
$360$		0			0
$361$	1556.45			0.226921
$362$	455.342	+	788.676i	0.0661112	+	0.114508i
$363$	−3571.42	−	5753.68i	−0.516394	−	0.831929i
$364$	2457.73	−	4256.92i	0.353902	−	0.612976i
$365$		0			0
$366$	354.472	+	571.067i	0.0506244	+	0.0815577i
$367$	1769.15	+	3064.27i	0.251632	+	0.435840i	0.963975	−	0.265991i	$-0.0856993\pi$
$367$	1769.15	+	3064.27i	0.251632	+	0.435840i	−0.712343	+	0.701832i	$0.752366\pi$
$368$	9059.26			1.28328
$369$	214.255	−	13.6949i	0.0302268	−	0.00193206i
$370$		0			0
$371$	1413.75	+	2448.69i	0.197839	+	0.342668i
$372$	2939.29	−	93.8422i	0.409664	−	0.0130793i
$373$	−2864.94	+	4962.23i	−0.397697	+	0.688832i	−0.993441	−	0.114342i	$-0.963524\pi$
$373$	−2864.94	+	4962.23i	−0.397697	+	0.688832i	0.595744	+	0.803174i	$0.296857\pi$
$374$	−110.994	+	192.248i	−0.0153460	+	0.0265800i
$375$		0			0
$376$	−1126.83	−	1951.73i	−0.154553	−	0.267693i
$377$	−12965.1			−1.77119
$378$	−226.432	+	496.536i	−0.0308105	+	0.0675637i
$379$	−8727.59			−1.18287			−0.591433	−	0.806354i	$-0.701437\pi$
$379$	−8727.59			−1.18287			−0.591433	+	0.806354i	$0.701437\pi$
$380$		0			0
$381$	487.330	−	909.959i	0.0655293	−	0.122359i
$382$	357.348	−	618.945i	0.0478626	−	0.0829005i
$383$	−2281.40	+	3951.50i	−0.304371	+	0.527186i	−0.977121	−	0.212684i	$-0.931780\pi$
$383$	−2281.40	+	3951.50i	−0.304371	+	0.527186i	0.672750	+	0.739870i	$0.265113\pi$
$384$	4693.48	−	149.848i	0.623732	−	0.0199138i
$385$		0			0
$386$	1927.08			0.254108
$387$	−277.975	+	561.386i	−0.0365123	+	0.0737386i
$388$	−3026.82			−0.396039
$389$	−6042.19	−	10465.4i	−0.787536	−	1.36405i	−0.927472	−	0.373891i	$-0.878023\pi$
$389$	−6042.19	−	10465.4i	−0.787536	−	1.36405i	0.139937	−	0.990160i	$-0.455310\pi$
$390$		0			0
$391$	−6867.95	+	11895.6i	−0.888305	+	1.53859i
$392$	−1030.57	+	1785.01i	−0.132785	+	0.229991i
$393$	−3979.49	−	6411.09i	−0.510785	−	0.822893i
$394$	928.232	+	1607.74i	0.118689	+	0.205576i
$395$		0			0
$396$	612.682	+	920.163i	0.0777485	+	0.116767i
$397$	5880.63			0.743426			0.371713	−	0.928348i	$-0.378770\pi$
$397$	5880.63			0.743426			0.371713	+	0.928348i	$0.378770\pi$
$398$	−145.912	−	252.727i	−0.0183767	−	0.0318293i
$399$	−3909.86	+	124.829i	−0.490571	+	0.0156624i
$400$		0			0
$401$	−1647.56	+	2853.65i	−0.205175	+	0.355373i	−0.950188	−	0.311676i	$-0.899110\pi$
$401$	−1647.56	+	2853.65i	−0.205175	+	0.355373i	0.745014	+	0.667049i	$0.232443\pi$
$402$	−971.458	+	1813.94i	−0.120527	+	0.225052i
$403$	2803.60	+	4855.98i	0.346545	+	0.600233i
$404$	6721.92			0.827793
$405$		0			0
$406$	−654.672			−0.0800267
$407$	−407.671	−	706.107i	−0.0496499	−	0.0859961i
$408$	−1631.43	+	3046.26i	−0.197960	+	0.369638i
$409$	3108.71	−	5384.45i	0.375834	−	0.650963i	−0.614618	−	0.788825i	$-0.710690\pi$
$409$	3108.71	−	5384.45i	0.375834	−	0.650963i	0.990451	+	0.137862i	$0.0440231\pi$
$410$		0			0
$411$	3306.48	−	105.565i	0.396828	−	0.0126695i
$412$	−4774.86	−	8270.29i	−0.570972	−	0.988952i
$413$	−2064.42			−0.245965
$414$	−1095.42	−	1645.17i	−0.130041	−	0.195303i
$415$		0			0
$416$	3374.96	+	5845.60i	0.397767	+	0.688953i
$417$	4174.22	+	6724.81i	0.490197	+	0.789725i
$418$	114.484	−	198.292i	0.0133962	−	0.0232028i
$419$	−870.140	+	1507.13i	−0.101454	+	0.175723i	−0.912284	−	0.409559i	$-0.865683\pi$
$419$	−870.140	+	1507.13i	−0.101454	+	0.175723i	0.810830	+	0.585282i	$0.199016\pi$
$420$		0			0
$421$	642.288	+	1112.48i	0.0743544	+	0.128786i	0.900805	−	0.434223i	$-0.142977\pi$
$421$	642.288	+	1112.48i	0.0743544	+	0.128786i	−0.826451	+	0.563009i	$0.809644\pi$
$422$	−1058.65			−0.122119
$423$	3611.04	−	7292.69i	0.415070	−	0.838257i
$424$	−2576.26			−0.295081
$425$		0			0
$426$	−864.420	+	27.5982i	−0.0983129	+	0.00313882i
$427$	1119.79	−	1939.54i	0.126910	−	0.219815i
$428$	7232.39	−	12526.9i	0.816801	−	1.41474i
$429$	−995.120	+	1858.12i	−0.111993	+	0.209117i
$430$		0			0
$431$	−11917.4			−1.33189			−0.665943	−	0.746003i	$-0.731970\pi$
$431$	−11917.4			−1.33189			−0.665943	+	0.746003i	$0.731970\pi$
$432$	4777.28	+	6700.98i	0.532054	+	0.746299i
$433$	−1603.61			−0.177978			−0.0889889	−	0.996033i	$-0.528364\pi$
$433$	−1603.61			−0.177978			−0.0889889	+	0.996033i	$0.528364\pi$
$434$	141.568	+	245.202i	0.0156577	+	0.0271200i
$435$		0			0
$436$	4032.71	−	6984.85i	0.442963	−	0.767234i
$437$	7083.87	−	12269.6i	0.775440	−	1.34310i
$438$	1286.84	−	41.0846i	0.140382	−	0.00448196i
$439$	−908.226	−	1573.09i	−0.0987409	−	0.171024i	0.812423	−	0.583069i	$-0.198148\pi$
$439$	−908.226	−	1573.09i	−0.0987409	−	0.171024i	−0.911164	+	0.412044i	$0.864815\pi$
$440$		0			0
$441$	−7427.45	+	474.754i	−0.802014	+	0.0512638i
$442$	−3247.49			−0.349474
$443$	−1132.64	−	1961.79i	−0.121475	−	0.210401i	0.798875	−	0.601498i	$-0.205429\pi$
$443$	−1132.64	−	1961.79i	−0.121475	−	0.210401i	−0.920350	+	0.391097i	$0.872096\pi$
$444$	−3299.12	−	5315.00i	−0.352634	−	0.568105i
$445$		0			0
$446$	1097.39	−	1900.74i	0.116509	−	0.201799i
$447$	−5761.87	−	9282.58i	−0.609680	−	0.982217i
$448$	−1755.12	−	3039.96i	−0.185093	−	0.320591i
$449$	−13259.9			−1.39371			−0.696854	−	0.717213i	$-0.745417\pi$
$449$	−13259.9			−1.39371			−0.696854	+	0.717213i	$0.745417\pi$
$450$		0			0
$451$	41.8716			0.00437175
$452$	5472.80	+	9479.17i	0.569511	+	0.986422i
$453$	12259.3	−	391.399i	1.27150	−	0.0405950i
$454$	−110.841	+	191.982i	−0.0114582	+	0.0198462i
$455$		0			0
$456$	1682.72	−	3142.03i	0.172808	−	0.322673i
$457$	65.9288	+	114.192i	0.00674840	+	0.0116886i	0.869380	−	0.494144i	$-0.164519\pi$
$457$	65.9288	+	114.192i	0.00674840	+	0.0116886i	−0.862631	+	0.505833i	$0.831185\pi$
$458$	690.673			0.0704652
$459$	−12420.7	+	1192.91i	−1.26307	+	0.121307i
$460$		0			0
$461$	−6391.25	−	11070.0i	−0.645705	−	1.11839i	−0.984138	−	0.177404i	$-0.943230\pi$
$461$	−6391.25	−	11070.0i	−0.645705	−	1.11839i	0.338433	−	0.940990i	$-0.390103\pi$
$462$	−50.2485	+	93.8256i	−0.00506011	+	0.00944840i
$463$	2310.71	−	4002.26i	0.231939	−	0.401729i	−0.726440	−	0.687230i	$-0.758826\pi$
$463$	2310.71	−	4002.26i	0.231939	−	0.401729i	0.958379	+	0.285500i	$0.0921598\pi$
$464$	−4936.21	+	8549.77i	−0.493875	+	0.855416i
$465$		0			0
$466$	620.318	+	1074.42i	0.0616645	+	0.106806i
$467$	5550.68			0.550010			0.275005	−	0.961443i	$-0.411320\pi$
$467$	5550.68			0.550010			0.275005	+	0.961443i	$0.411320\pi$
$468$	−7176.20	+	14492.7i	−0.708803	+	1.43147i
$469$	6856.32			0.675044
$470$		0			0
$471$	−5492.17	−	8848.09i	−0.537295	−	0.865602i
$472$	940.492	−	1628.98i	0.0917154	−	0.158856i
$473$	−61.0873	+	105.806i	−0.00593826	+	0.0102854i
$474$	−909.368	−	1465.02i	−0.0881195	−	0.141964i
$475$		0			0
$476$	5675.13			0.546469
$477$	−5155.74	−	7743.21i	−0.494896	−	0.743264i
$478$	−1759.05			−0.168320
$479$	−970.694	−	1681.29i	−0.0925932	−	0.160376i	0.816008	−	0.578040i	$-0.196182\pi$
$479$	−970.694	−	1681.29i	−0.0925932	−	0.160376i	−0.908602	+	0.417664i	$0.862849\pi$
$480$		0			0
$481$	5963.85	−	10329.7i	0.565339	−	0.979196i
$482$	437.044	−	756.982i	0.0413004	−	0.0715344i
$483$	−3109.20	+	5805.60i	−0.292906	+	0.546924i
$484$	−5066.68	−	8775.75i	−0.475834	−	0.824169i
$485$		0			0
$486$	639.247	−	1677.82i	0.0596642	−	0.156600i
$487$	−178.136			−0.0165752			−0.00828761	−	0.999966i	$-0.502638\pi$
$487$	−178.136			−0.0165752			−0.00828761	+	0.999966i	$0.502638\pi$
$488$	1020.29	+	1767.20i	0.0946443	+	0.163929i
$489$	6801.07	−	12699.2i	0.628947	−	1.17439i
$490$		0			0
$491$	2795.80	−	4842.46i	0.256971	−	0.445086i	−0.708458	−	0.705753i	$-0.750609\pi$
$491$	2795.80	−	4842.46i	0.256971	−	0.445086i	0.965429	+	0.260667i	$0.0839423\pi$
$492$	321.094	−	10.2515i	0.0294229	−	0.000939379i
$493$	−7484.42	−	12963.4i	−0.683735	−	1.18426i
$494$	3349.59			0.305071
$495$		0			0
$496$	4269.66			0.386519
$497$	1440.88	+	2495.67i	0.130045	+	0.225244i
$498$	−313.428	−	504.943i	−0.0282029	−	0.0454358i
$499$	−5683.52	+	9844.15i	−0.509879	+	0.883136i	0.490056	+	0.871691i	$0.336976\pi$
$499$	−5683.52	+	9844.15i	−0.509879	+	0.883136i	−0.999935	+	0.0114449i	$0.996357\pi$
$500$		0			0
$501$	5059.59	+	8151.18i	0.451189	+	0.726882i
$502$	1707.34	+	2957.19i	0.151797	+	0.262920i
$503$	−9225.98			−0.817825			−0.408913	−	0.912574i	$-0.634092\pi$
$503$	−9225.98			−0.817825			−0.408913	+	0.912574i	$0.634092\pi$
$504$	−735.192	+	1484.76i	−0.0649763	+	0.131223i
$505$		0			0
$506$	−192.738	−	333.832i	−0.0169333	−	0.0293294i
$507$	−19409.6	+	619.685i	−1.70021	+	0.0542824i
$508$	772.302	−	1337.67i	0.0674515	−	0.116829i
$509$	9156.72	−	15859.9i	0.797376	−	1.38110i	−0.123944	−	0.992289i	$-0.539554\pi$
$509$	9156.72	−	15859.9i	0.797376	−	1.38110i	0.921320	−	0.388806i	$-0.127112\pi$
$510$		0			0
$511$	−2144.99	−	3715.23i	−0.185692	−	0.321628i
$512$	8648.67			0.746525
$513$	12811.2	−	1230.41i	1.10259	−	0.105895i
$514$	−832.870			−0.0714714
$515$		0			0
$516$	−442.546	+	826.337i	−0.0377558	+	0.0704989i
$517$	793.555	−	1374.48i	0.0675058	−	0.116924i
$518$	301.144	−	521.596i	0.0255434	−	0.0442425i
$519$	1003.24	−	32.0303i	0.0848505	−	0.00270901i
$520$		0			0
$521$	−11305.4			−0.950670			−0.475335	−	0.879805i	$-0.657673\pi$
$521$	−11305.4			−0.950670			−0.475335	+	0.879805i	$0.657673\pi$
$522$	2149.51	−	137.394i	0.180233	−	0.0115203i
$523$	2825.92			0.236269			0.118135	−	0.992998i	$-0.462309\pi$
$523$	2825.92			0.236269			0.118135	+	0.992998i	$0.462309\pi$
$524$	−5645.60	−	9778.46i	−0.470666	−	0.815218i
$525$		0			0
$526$	−1269.56	+	2198.94i	−0.105239	+	0.182279i
$527$	−3236.89	+	5606.46i	−0.267555	+	0.463418i
$528$	846.455	+	1363.67i	0.0697674	+	0.112398i
$529$	−5842.47	−	10119.5i	−0.480190	−	0.831714i
$530$		0			0
$531$	6778.22	−	433.256i	0.553954	−	0.0354081i
$532$	−5853.55			−0.477037
$533$	306.272	+	530.478i	0.0248895	+	0.0431099i
$534$	−2514.32	+	80.2744i	−0.203756	+	0.00650526i
$535$		0			0
$536$	−3123.54	+	5410.13i	−0.251710	+	0.435974i
$537$	−9643.98	+	18007.6i	−0.774988	+	1.44708i
$538$	246.616	+	427.152i	0.0197628	+	0.0342302i
$539$	−1451.54			−0.115997
$540$		0			0
$541$	−20588.2			−1.63615			−0.818075	−	0.575112i	$-0.804959\pi$
$541$	−20588.2			−1.63615			−0.818075	+	0.575112i	$0.804959\pi$
$542$	362.929	+	628.612i	0.0287623	+	0.0498177i
$543$	−4713.29	+	8800.80i	−0.372498	+	0.695541i
$544$	−3896.55	+	6749.02i	−0.307101	+	0.531915i
$545$		0			0
$546$	−1556.24	+	49.6856i	−0.121979	+	0.00389441i
$547$	−2176.97	−	3770.63i	−0.170166	−	0.294736i	0.768312	−	0.640076i	$-0.221097\pi$
$547$	−2176.97	−	3770.63i	−0.170166	−	0.294736i	−0.938478	+	0.345340i	$0.887764\pi$
$548$	4950.21			0.385881
$549$	−3269.62	+	6603.19i	−0.254179	+	0.513328i
$550$		0			0
$551$	7719.72	+	13370.9i	0.596862	+	1.03380i
$552$	−3164.58	−	5098.25i	−0.244010	−	0.393108i
$553$	−2872.74	+	4975.73i	−0.220906	+	0.382621i
$554$	1476.74	−	2557.79i	0.113250	−	0.196155i
$555$		0			0
$556$	5921.85	+	10257.0i	0.451695	+	0.782359i
$557$	22267.5			1.69390			0.846951	−	0.531672i	$-0.178436\pi$
$557$	22267.5			1.69390			0.846951	+	0.531672i	$0.178436\pi$
$558$	−516.275	−	775.373i	−0.0391679	−	0.0588247i
$559$	−1787.30			−0.135232
$560$		0			0
$561$	−2432.33	+	77.6566i	−0.183054	+	0.00584432i
$562$	2159.96	−	3741.16i	0.162122	−	0.280803i
$563$	−11505.4	+	19927.9i	−0.861270	+	1.49176i	0.00943368	+	0.999956i	$0.496997\pi$
$563$	−11505.4	+	19927.9i	−0.861270	+	1.49176i	−0.870704	+	0.491808i	$0.836336\pi$
$564$	5748.90	−	10734.5i	0.429206	−	0.801428i
$565$		0			0
$566$	−718.139			−0.0533315
$567$	−5933.90	+	761.688i	−0.439507	+	0.0564160i
$568$	−2625.69			−0.193964
$569$	7121.98	+	12335.6i	0.524726	+	0.908852i	0.999585	+	0.0287902i	$0.00916546\pi$
$569$	7121.98	+	12335.6i	0.524726	+	0.908852i	−0.474860	+	0.880062i	$0.657501\pi$
$570$		0			0
$571$	2396.71	−	4151.22i	0.175655	−	0.304244i	−0.764733	−	0.644348i	$-0.777129\pi$
$571$	2396.71	−	4151.22i	0.175655	−	0.304244i	0.940388	+	0.340104i	$0.110462\pi$
$572$	−1577.03	+	2731.49i	−0.115278	+	0.199667i
$573$	7830.92	−	250.016i	0.570928	−	0.0182279i
$574$	15.4651	+	26.7864i	0.00112457	+	0.00194781i
$575$		0			0
$576$	6400.66	+	9612.90i	0.463011	+	0.695377i
$577$	6617.46			0.477450			0.238725	−	0.971087i	$-0.423271\pi$
$577$	6617.46			0.477450			0.238725	+	0.971087i	$0.423271\pi$
$578$	−710.336	−	1230.34i	−0.0511178	−	0.0885386i
$579$	11141.3	+	17949.1i	0.799684	+	1.28832i
$580$		0			0
$581$	−990.134	+	1714.96i	−0.0707017	+	0.122459i
$582$	505.641	+	814.606i	0.0360129	+	0.0580180i
$583$	−907.149	−	1571.23i	−0.0644430	−	0.111619i
$584$	3908.78			0.276963
$585$		0			0
$586$	656.145			0.0462544
$587$	8227.71	+	14250.8i	0.578524	+	1.00203i	0.995649	+	0.0931841i	$0.0297045\pi$
$587$	8227.71	+	14250.8i	0.578524	+	1.00203i	−0.417125	+	0.908849i	$0.636962\pi$
$588$	−11131.2	+	355.383i	−0.780684	+	0.0249247i
$589$	3338.65	−	5782.72i	0.233560	−	0.404538i
$590$		0			0
$591$	−9608.21	+	17940.8i	−0.668746	+	1.24870i
$592$	−4541.23	−	7865.65i	−0.315276	−	0.546074i
$593$	15990.1			1.10731			0.553655	−	0.832746i	$-0.313233\pi$
$593$	15990.1			1.10731			0.553655	+	0.832746i	$0.313233\pi$
$594$	145.292	−	318.607i	0.0100360	−	0.0220078i
$595$		0			0
$596$	−8174.22	−	14158.2i	−0.561794	−	0.973056i
$597$	1510.35	−	2820.17i	0.103542	−	0.193337i
$598$	2819.58	−	4883.66i	0.192812	−	0.333959i
$599$	−10230.4	+	17719.6i	−0.697836	+	1.20869i	0.271379	+	0.962473i	$0.412520\pi$
$599$	−10230.4	+	17719.6i	−0.697836	+	1.20869i	−0.969215	+	0.246215i	$0.920813\pi$
$600$		0			0
$601$	320.870	+	555.762i	0.0217779	+	0.0377205i	0.876709	−	0.481021i	$-0.159734\pi$
$601$	320.870	+	555.762i	0.0217779	+	0.0377205i	−0.854931	+	0.518742i	$0.826401\pi$
$602$	−90.2496			−0.00611013
$603$	−22511.7	+	1438.92i	−1.52031	+	0.0971763i
$604$	18353.6			1.23642
$605$		0			0
$606$	−1122.92	−	1809.07i	−0.0752733	−	0.121268i
$607$	9375.63	−	16239.1i	0.626928	−	1.08587i	−0.361237	−	0.932474i	$-0.617645\pi$
$607$	9375.63	−	16239.1i	0.626928	−	1.08587i	0.988165	−	0.153397i	$-0.0490212\pi$
$608$	4019.05	−	6961.20i	0.268082	−	0.464332i
$609$	−3784.95	−	6097.70i	−0.251846	−	0.405733i
$610$		0			0
$611$	23218.0			1.53731
$612$	−18633.4	+	1191.03i	−1.23074	+	0.0786673i
$613$	24213.4			1.59538			0.797690	−	0.603067i	$-0.206055\pi$
$613$	24213.4			1.59538			0.797690	+	0.603067i	$0.206055\pi$
$614$	385.866	+	668.340i	0.0253621	+	0.0439284i
$615$		0			0
$616$	−161.565	+	279.838i	−0.0105676	+	0.0183036i
$617$	−7935.46	+	13744.6i	−0.517779	+	0.896819i	0.482008	+	0.876167i	$0.339908\pi$
$617$	−7935.46	+	13744.6i	−0.517779	+	0.896819i	−0.999787	+	0.0206523i	$0.993426\pi$
$618$	−1428.12	+	2666.64i	−0.0929572	+	0.173573i
$619$	12217.1	+	21160.6i	0.793289	+	1.37402i	0.923920	+	0.382585i	$0.124966\pi$
$619$	12217.1	+	21160.6i	0.793289	+	1.37402i	−0.130631	+	0.991431i	$0.541700\pi$
$620$		0			0
$621$	8990.17	−	19714.3i	0.580939	−	1.27393i
$622$	−666.727			−0.0429796
$623$	4191.05	+	7259.12i	0.269520	+	0.466822i
$624$	−11085.1	+	20698.5i	−0.711153	+	1.32789i
$625$		0			0
$626$	1287.25	−	2229.58i	0.0821865	−	0.142351i
$627$	2508.80	−	80.0980i	0.159796	−	0.00510176i
$628$	−7791.61	−	13495.5i	−0.495094	−	0.857528i
$629$	13771.1			0.872956
$630$		0			0
$631$	22573.7			1.42416			0.712079	−	0.702099i	$-0.247754\pi$
$631$	22573.7			1.42416			0.712079	+	0.702099i	$0.247754\pi$
$632$	−2617.47	−	4533.59i	−0.164743	−	0.285343i
$633$	−6120.54	−	9860.41i	−0.384312	−	0.619141i
$634$	−1820.50	+	3153.20i	−0.114040	+	0.197523i
$635$		0			0
$636$	−7341.20	−	11826.9i	−0.457701	−	0.737372i
$637$	−10617.3	−	18389.8i	−0.660399	−	1.14384i
$638$	420.077			0.0260674
$639$	−5254.66	−	7891.76i	−0.325307	−	0.488565i
$640$		0			0
$641$	1861.15	+	3223.61i	0.114682	+	0.198635i	0.917653	−	0.397384i	$-0.130082\pi$
$641$	1861.15	+	3223.61i	0.114682	+	0.198635i	−0.802971	+	0.596019i	$0.796748\pi$
$642$	−4579.55	+	146.210i	−0.281527	+	0.00898826i
$643$	1499.38	−	2597.00i	0.0919593	−	0.159278i	−0.816376	−	0.577520i	$-0.804020\pi$
$643$	1499.38	−	2597.00i	0.0919593	−	0.159278i	0.908335	+	0.418242i	$0.137354\pi$
$644$	−4927.34	+	8534.41i	−0.301498	+	0.522209i
$645$		0			0
$646$	1933.63	+	3349.15i	0.117767	+	0.203979i
$647$	−4302.38			−0.261428			−0.130714	−	0.991420i	$-0.541727\pi$
$647$	−4302.38			−0.261428			−0.130714	+	0.991420i	$0.541727\pi$
$648$	2102.29	−	5029.28i	0.127447	−	0.304890i
$649$	1324.66			0.0801193
$650$		0			0
$651$	−1465.38	+	2736.20i	−0.0882223	+	0.164732i
$652$	10778.1	−	18668.2i	0.647396	−	1.12132i
$653$	−400.641	+	693.930i	−0.0240096	+	0.0415859i	−0.877781	−	0.479063i	$-0.840977\pi$
$653$	−400.641	+	693.930i	−0.0240096	+	0.0415859i	0.853771	+	0.520649i	$0.174310\pi$
$654$	−2553.51	+	81.5254i	−0.152676	+	0.00487446i
$655$		0			0
$656$	466.427			0.0277606
$657$	7822.45	+	11748.2i	0.464510	+	0.697628i
$658$	1172.39			0.0694596
$659$	3728.20	+	6457.43i	0.220379	+	0.381708i	0.954923	−	0.296853i	$-0.0959372\pi$
$659$	3728.20	+	6457.43i	0.220379	+	0.381708i	−0.734544	+	0.678561i	$0.762604\pi$
$660$		0			0
$661$	−1332.53	+	2308.01i	−0.0784106	+	0.135811i	−0.902564	−	0.430555i	$-0.858318\pi$
$661$	−1332.53	+	2308.01i	−0.0784106	+	0.135811i	0.824154	+	0.566366i	$0.191651\pi$
$662$	−978.524	+	1694.85i	−0.0574492	+	0.0995050i
$663$	−18775.2	−	30247.6i	−1.09980	−	1.77182i
$664$	−902.152	−	1562.57i	−0.0527264	−	0.0913247i
$665$		0			0
$666$	−879.293	+	1775.78i	−0.0511590	+	0.103319i
$667$	25992.9			1.50892
$668$	7177.91	+	12432.5i	0.415751	+	0.720102i
$669$	24048.2	−	767.783i	1.38977	−	0.0443710i
$670$		0			0
$671$	−718.527	+	1244.53i	−0.0413389	+	0.0716011i
$672$	−1764.01	+	3293.82i	−0.101262	+	0.189080i
$673$	11774.9	+	20394.7i	0.674427	+	1.16814i	0.976636	+	0.214900i	$0.0689424\pi$
$673$	11774.9	+	20394.7i	0.674427	+	1.16814i	−0.302210	+	0.953242i	$0.597724\pi$
$674$	1243.82			0.0710834
$675$		0			0
$676$	−29058.6			−1.65331
$677$	4969.86	+	8608.04i	0.282138	+	0.488677i	0.971911	−	0.235349i	$-0.0756232\pi$
$677$	4969.86	+	8608.04i	0.282138	+	0.488677i	−0.689773	+	0.724025i	$0.742290\pi$
$678$	1636.87	−	3056.43i	0.0927194	−	0.173129i
$679$	1597.34	−	2766.68i	0.0902805	−	0.156370i
$680$		0			0
$681$	−2428.97	+	77.5491i	−0.136679	+	0.00436371i
$682$	−90.8382	−	157.336i	−0.00510026	−	0.00883391i
$683$	11680.3			0.654371			0.327185	−	0.944960i	$-0.393900\pi$
$683$	11680.3			0.654371			0.327185	+	0.944960i	$0.393900\pi$
$684$	19219.2	−	1228.47i	1.07437	−	0.0686721i
$685$		0			0
$686$	−1203.23	−	2084.05i	−0.0669671	−	0.115990i
$687$	3993.09	+	6433.02i	0.221756	+	0.357256i
$688$	−680.479	+	1178.63i	−0.0377079	+	0.0653120i
$689$	13270.8	−	22985.6i	0.733782	−	1.27095i
$690$		0			0
$691$	6178.47	+	10701.4i	0.340145	+	0.589148i	0.984459	−	0.175613i	$-0.0561906\pi$
$691$	6178.47	+	10701.4i	0.340145	+	0.589148i	−0.644315	+	0.764761i	$0.722857\pi$
$692$	1501.98			0.0825096
$693$	−1164.41	+	74.4278i	−0.0638274	+	0.00407977i
$694$	3277.55			0.179271
$695$		0			0
$696$	6535.84	−	208.668i	0.355949	−	0.0113643i
$697$	−353.605	+	612.462i	−0.0192163	+	0.0332836i
$698$	630.504	−	1092.06i	0.0341904	−	0.0592195i
$699$	−6420.96	+	11989.4i	−0.347444	+	0.648759i
$700$		0			0
$701$	10659.6			0.574333			0.287167	−	0.957881i	$-0.407287\pi$
$701$	10659.6			0.574333			0.287167	+	0.957881i	$0.407287\pi$
$702$	5099.23	−	489.738i	0.274157	−	0.0263305i
$703$	−14204.0			−0.762042
$704$	1126.19	+	1950.62i	0.0602911	+	0.104427i
$705$		0			0
$706$	1070.62	−	1854.37i	0.0570729	−	0.0988531i
$707$	−3547.37	+	6144.22i	−0.188702	+	0.326842i
$708$	10158.2	−	324.319i	0.539221	−	0.0172156i
$709$	−9669.28	−	16747.7i	−0.512183	−	0.887126i	−0.999900	−	0.0141250i	$-0.995504\pi$
$709$	−9669.28	−	16747.7i	−0.512183	−	0.887126i	0.487718	−	0.873002i	$-0.337830\pi$
$710$		0			0
$711$	8387.95	−	16939.9i	0.442437	−	0.893526i
$712$	−7637.29			−0.401994
$713$	−5620.76	−	9735.43i	−0.295230	−	0.511353i
$714$	−948.053	−	1527.35i	−0.0496918	−	0.0800553i
$715$		0			0
$716$	−15283.4	+	26471.6i	−0.797720	+	1.38169i
$717$	−10169.9	−	16384.0i	−0.529708	−	0.853379i
$718$	−640.440	−	1109.27i	−0.0332883	−	0.0576571i
$719$	−27300.1			−1.41603			−0.708013	−	0.706199i	$-0.750408\pi$
$719$	−27300.1			−1.41603			−0.708013	+	0.706199i	$0.750408\pi$
$720$		0			0
$721$	10079.4			0.520631
$722$	−368.871	−	638.904i	−0.0190138	−	0.0329329i
$723$	9577.37	−	305.775i	0.492651	−	0.0157288i
$724$	−7469.43	+	12937.4i	−0.383424	+	0.664111i
$725$		0			0
$726$	−1515.41	+	2829.62i	−0.0774683	+	0.144651i
$727$	882.466	+	1528.48i	0.0450191	+	0.0779753i	0.887657	−	0.460505i	$-0.152332\pi$
$727$	882.466	+	1528.48i	0.0450191	+	0.0779753i	−0.842638	+	0.538481i	$0.818998\pi$
$728$	−4727.08			−0.240656
$729$	19323.2	−	3746.22i	0.981721	−	0.190328i
$730$		0			0
$731$	−1031.76	−	1787.06i	−0.0522040	−	0.0904199i
$732$	−5205.36	+	9719.62i	−0.262835	+	0.490775i
$733$	8652.75	−	14987.0i	0.436012	−	0.755195i	−0.561366	−	0.827568i	$-0.689724\pi$
$733$	8652.75	−	14987.0i	0.436012	−	0.755195i	0.997378	+	0.0723730i	$0.0230572\pi$
$734$	838.561	−	1452.43i	0.0421688	−	0.0730384i
$735$		0			0
$736$	−6766.23	−	11719.5i	−0.338868	−	0.586936i
$737$	−4399.43			−0.219885
$738$	−56.3990	−	84.7035i	−0.00281311	−	0.00422490i
$739$	−1456.60			−0.0725058			−0.0362529	−	0.999343i	$-0.511542\pi$
$739$	−1456.60			−0.0725058			−0.0362529	+	0.999343i	$0.511542\pi$
$740$		0			0
$741$	19365.5	+	31198.5i	0.960067	+	1.54670i
$742$	670.105	−	1160.66i	0.0331541	−	0.0574246i
$743$	8468.55	−	14668.0i	0.418144	−	0.724246i	−0.577609	−	0.816314i	$-0.696014\pi$
$743$	8468.55	−	14668.0i	0.418144	−	0.724246i	0.995753	+	0.0920673i	$0.0293475\pi$
$744$	−1491.48	−	2402.82i	−0.0734949	−	0.118403i
$745$		0			0
$746$	2715.91			0.133293
$747$	2891.04	−	5838.61i	0.141603	−	0.285975i
$748$	−3641.51			−0.178004
$749$	7633.51	+	13221.6i	0.372393	+	0.645004i
$750$		0			0
$751$	−6467.80	+	11202.6i	−0.314265	+	0.544323i	−0.979281	−	0.202506i	$-0.935091\pi$
$751$	−6467.80	+	11202.6i	−0.314265	+	0.544323i	0.665016	+	0.746829i	$0.268425\pi$
$752$	8839.78	−	15310.9i	0.428661	−	0.742463i
$753$	−17672.8	+	32999.2i	−0.855288	+	1.59702i
$754$	3072.67	+	5322.02i	0.148409	+	0.257051i
$755$		0			0
$756$	−8911.13	+	855.839i	−0.428696	+	0.0411727i
$757$	−37371.9			−1.79433			−0.897164	−	0.441697i	$-0.854377\pi$
$757$	−37371.9			−1.79433			−0.897164	+	0.441697i	$0.854377\pi$
$758$	2068.39	+	3582.56i	0.0991128	+	0.171668i
$759$	1995.05	−	3725.22i	0.0954094	−	0.178152i
$760$		0			0
$761$	6999.67	−	12123.8i	0.333427	−	0.577513i	−0.649754	−	0.760144i	$-0.725128\pi$
$761$	6999.67	−	12123.8i	0.333427	−	0.577513i	0.983181	+	0.182632i	$0.0584616\pi$
$762$	−489.021	+	15.6129i	−0.0232485	+	0.000742251i
$763$	4256.37	+	7372.25i	0.201954	+	0.349795i
$764$	11723.9			0.555177
$765$		0			0
$766$	2162.72			0.102013
$767$	9689.27	+	16782.3i	0.456140	+	0.790058i
$768$	8203.32	+	13215.8i	0.385432	+	0.620945i
$769$	5221.26	−	9043.49i	0.244842	−	0.424079i	−0.717245	−	0.696821i	$-0.754597\pi$
$769$	5221.26	−	9043.49i	0.244842	−	0.424079i	0.962087	+	0.272742i	$0.0879306\pi$
$770$		0			0
$771$	−4815.20	−	7757.45i	−0.224922	−	0.362358i
$772$	15805.9	+	27376.6i	0.736874	+	1.27630i
$773$	−23092.7			−1.07450			−0.537249	−	0.843424i	$-0.680537\pi$
$773$	−23092.7			−1.07450			−0.537249	+	0.843424i	$0.680537\pi$
$774$	296.321	−	18.9405i	0.0137610	−	0.000879587i
$775$		0			0
$776$	1455.41	+	2520.84i	0.0673274	+	0.116615i
$777$	6599.26	−	210.693i	0.304694	−	0.00972791i
$778$	−2863.94	+	4960.49i	−0.131976	+	0.228589i
$779$	364.722	−	631.717i	0.0167747	−	0.0290547i
$780$		0			0
$781$	−924.553	−	1601.37i	−0.0423599	−	0.0733696i
$782$	6510.68			0.297726
$783$	13707.0	+	19226.5i	0.625605	+	0.877522i
$784$	−16169.3			−0.736577
$785$		0			0
$786$	−1688.55	+	3152.93i	−0.0766269	+	0.143080i
$787$	−4258.12	+	7375.28i	−0.192866	+	0.334054i	−0.946199	−	0.323586i	$-0.895112\pi$
$787$	−4258.12	+	7375.28i	−0.192866	+	0.334054i	0.753333	+	0.657639i	$0.228445\pi$
$788$	−15226.7	+	26373.4i	−0.688362	+	1.19228i
$789$	−27821.1	+	888.240i	−1.25533	+	0.0400788i
$790$		0			0
$791$	−11552.7			−0.519299
$792$	471.744	−	952.712i	0.0211650	−	0.0427439i
$793$	−21022.8			−0.941413
$794$	−1393.68	−	2413.92i	−0.0622920	−	0.107893i
$795$		0			0
$796$	2393.54	−	4145.74i	0.106579	−	0.184600i
$797$	14701.1	−	25463.1i	0.653376	−	1.13168i	−0.328922	−	0.944357i	$-0.606685\pi$
$797$	14701.1	−	25463.1i	0.653376	−	1.13168i	0.982298	−	0.187324i	$-0.0599813\pi$
$798$	977.858	+	1575.36i	0.0433782	+	0.0698838i
$799$	13403.1	+	23214.9i	0.593452	+	1.02789i
$800$		0			0
$801$	−15284.1	−	22954.6i	−0.674205	−	1.01256i
$802$	1561.85			0.0687667
$803$	1376.35	+	2383.91i	0.0604863	+	0.104765i
$804$	−33737.2	+	1077.12i	−1.47988	+	0.0472477i
$805$		0			0
$806$	1328.88	−	2301.69i	0.0580742	−	0.100587i
$807$	−2552.75	+	4766.58i	−0.111352	+	0.207920i
$808$	−3232.16	−	5598.26i	−0.140726	−	0.243745i
$809$	−7358.17			−0.319777			−0.159888	−	0.987135i	$-0.551113\pi$
$809$	−7358.17			−0.319777			−0.159888	+	0.987135i	$0.551113\pi$
$810$		0			0
$811$	14069.2			0.609168			0.304584	−	0.952485i	$-0.401483\pi$
$811$	14069.2			0.609168			0.304584	+	0.952485i	$0.401483\pi$
$812$	−5369.62	−	9300.45i	−0.232065	−	0.401948i
$813$	−3756.71	+	7014.66i	−0.162059	+	0.302601i
$814$	−193.232	+	334.688i	−0.00832036	+	0.0144113i
$815$		0			0
$816$	−27094.9	+	865.052i	−1.16239	+	0.0371114i
$817$	1064.20	+	1843.25i	0.0455711	+	0.0789315i
$818$	−2947.00			−0.125965
$819$	−9460.08	−	14207.7i	−0.403617	−	0.606176i
$820$		0			0
$821$	−13340.0	−	23105.6i	−0.567076	−	0.982205i	−0.996853	−	0.0792696i	$-0.974741\pi$
$821$	−13340.0	−	23105.6i	−0.567076	−	0.982205i	0.429777	−	0.902935i	$-0.358592\pi$
$822$	−826.951	−	1332.25i	−0.0350891	−	0.0565298i
$823$	−3807.19	+	6594.24i	−0.161252	+	0.279296i	−0.935318	−	0.353809i	$-0.884886\pi$
$823$	−3807.19	+	6594.24i	−0.161252	+	0.279296i	0.774066	+	0.633105i	$0.218220\pi$
$824$	−4591.86	+	7953.34i	−0.194132	+	0.336247i
$825$		0			0
$826$	489.258	+	847.420i	0.0206095	+	0.0356968i
$827$	−24854.1			−1.04505			−0.522527	−	0.852623i	$-0.675011\pi$
$827$	−24854.1			−1.04505			−0.522527	+	0.852623i	$0.675011\pi$
$828$	14387.1	−	29055.5i	0.603847	−	1.21950i
$829$	−17292.6			−0.724482			−0.362241	−	0.932084i	$-0.617988\pi$
$829$	−17292.6			−0.724482			−0.362241	+	0.932084i	$0.617988\pi$
$830$		0			0
$831$	32361.2	−	1033.19i	1.35090	−	0.0431300i
$832$	−16475.1	+	28535.8i	−0.686506	+	1.18906i
$833$	12258.2	−	21231.8i	0.509870	−	0.883121i
$834$	1771.18	−	3307.21i	0.0735384	−	0.137313i
$835$		0			0
$836$	3755.99			0.155387
$837$	4237.10	−	9291.44i	0.174977	−	0.383703i
$838$	824.876			0.0340034
$839$	−3524.59	−	6104.77i	−0.145033	−	0.251204i	0.784352	−	0.620315i	$-0.212995\pi$
$839$	−3524.59	−	6104.77i	−0.145033	−	0.251204i	−0.929385	+	0.369111i	$0.879662\pi$
$840$		0			0
$841$	−1968.51	+	3409.56i	−0.0807131	+	0.139799i
$842$	304.438	−	527.302i	0.0124604	−	0.0215820i
$843$	47333.4	−	1511.20i	1.93386	−	0.0617421i
$844$	−8683.06	−	15039.5i	−0.354127	−	0.613366i
$845$		0			0
$846$	−3849.36	+	246.046i	−0.156434	+	0.00999910i
$847$	10695.4			0.433882
$848$	−10105.1	−	17502.6i	−0.409213	−	0.708777i
$849$	−4151.88	−	6688.83i	−0.167835	−	0.270389i
$850$		0			0
$851$	−11956.5	+	20709.3i	−0.481627	+	0.834202i
$852$	−7482.04	−	12053.8i	−0.300858	−	0.484692i
$853$	−5634.57	−	9759.36i	−0.226171	−	0.391740i	0.730499	−	0.682914i	$-0.239288\pi$
$853$	−5634.57	−	9759.36i	−0.226171	−	0.391740i	−0.956670	+	0.291174i	$0.905954\pi$
$854$	−1061.54			−0.0425354
$855$		0			0
$856$	−13910.4			−0.555431
$857$	−17077.0	−	29578.3i	−0.680676	−	1.17897i	−0.974775	−	0.223191i	$-0.928353\pi$
$857$	−17077.0	−	29578.3i	−0.680676	−	1.17897i	0.294098	−	0.955775i	$-0.404981\pi$
$858$	998.574	−	31.8813i	0.0397328	−	0.00126854i
$859$	21367.1	−	37008.9i	0.848704	−	1.47000i	−0.0336608	−	0.999433i	$-0.510717\pi$
$859$	21367.1	−	37008.9i	0.848704	−	1.47000i	0.882365	−	0.470566i	$-0.155950\pi$
$860$		0			0
$861$	−160.081	+	298.909i	−0.00633629	+	0.0118313i
$862$	2824.37	+	4891.96i	0.111599	+	0.193295i
$863$	−6893.93			−0.271926			−0.135963	−	0.990714i	$-0.543413\pi$
$863$	−6893.93			−0.271926			−0.135963	+	0.990714i	$0.543413\pi$
$864$	5100.60	−	11185.0i	0.200840	−	0.440417i
$865$		0			0
$866$	380.047	+	658.260i	0.0149128	+	0.0258298i
$867$	7352.75	−	13729.3i	0.288019	−	0.537799i
$868$	−2322.27	+	4022.30i	−0.0908101	+	0.157288i
$869$	1843.32	−	3192.73i	0.0719567	−	0.124633i
$870$		0			0
$871$	−32179.8	−	55737.0i	−1.25186	−	2.16829i
$872$	−7756.32			−0.301218
$873$	−4664.00	+	9419.21i	−0.180816	+	0.365168i
$874$	−6715.37			−0.259898
$875$		0			0
$876$	11138.3	+	17944.2i	0.429598	+	0.692098i
$877$	−23969.2	+	41515.9i	−0.922900	+	1.59851i	−0.127995	+	0.991775i	$0.540854\pi$
$877$	−23969.2	+	41515.9i	−0.922900	+	1.59851i	−0.794905	+	0.606734i	$0.792479\pi$
$878$	−430.490	+	745.630i	−0.0165471	+	0.0286604i
$879$	3793.47	+	6111.41i	0.145564	+	0.234508i
$880$		0			0
$881$	35033.8			1.33975			0.669875	−	0.742474i	$-0.266348\pi$
$881$	35033.8			1.33975			0.669875	+	0.742474i	$0.266348\pi$
$882$	1955.15	+	2936.36i	0.0746409	+	0.112100i
$883$	155.057			0.00590951			0.00295475	−	0.999996i	$-0.499059\pi$
$883$	155.057			0.00590951			0.00295475	+	0.999996i	$0.499059\pi$
$884$	−26636.0	−	46134.8i	−1.01342	−	1.75530i
$885$		0			0
$886$	−536.861	+	929.870i	−0.0203569	+	0.0352591i
$887$	2238.25	−	3876.76i	0.0847272	−	0.146752i	−0.820548	−	0.571578i	$-0.806331\pi$
$887$	2238.25	−	3876.76i	0.0847272	−	0.146752i	0.905275	+	0.424826i	$0.139665\pi$
$888$	−2840.18	+	5303.28i	−0.107331	+	0.200413i
$889$	815.135	+	1411.86i	0.0307523	+	0.0532645i
$890$		0			0
$891$	3807.55	−	488.745i	0.143162	−	0.0183766i
$892$	36003.2			1.35143
$893$	−13824.5	−	23944.7i	−0.518050	−	0.897289i
$894$	−2444.85	+	4565.10i	−0.0914630	+	0.170783i
$895$		0			0
$896$	−3708.23	+	6422.84i	−0.138262	+	0.239478i
$897$	61788.3	−	1972.70i	2.29995	−	0.0734300i
$898$	3142.54	+	5443.03i	0.116779	+	0.202268i
$899$	12250.6			0.454481
$900$		0			0
$901$	30643.4			1.13305
$902$	−9.92337	−	17.1878i	−0.000366310	−	0.000634468i
$903$	−521.774	−	840.596i	−0.0192287	−	0.0309782i
$904$	5263.06	−	9115.89i	0.193636	−	0.335387i
$905$		0			0
$906$	−3066.05	−	4939.51i	−0.112431	−	0.181130i
$907$	−6294.11	−	10901.7i	−0.230422	−	0.399102i	0.727511	−	0.686096i	$-0.240677\pi$
$907$	−6294.11	−	10901.7i	−0.230422	−	0.399102i	−0.957932	+	0.286994i	$0.907344\pi$
$908$	−3636.47			−0.132908
$909$	10357.8	−	20918.1i	0.377938	−	0.763266i
$910$		0			0
$911$	−19956.5	−	34565.7i	−0.725784	−	1.25709i	−0.958651	−	0.284586i	$-0.908144\pi$
$911$	−19956.5	−	34565.7i	−0.725784	−	1.25709i	0.232867	−	0.972509i	$-0.425189\pi$
$912$	27946.7	−	892.248i	1.01470	−	0.0323962i
$913$	635.329	−	1100.42i	0.0230299	−	0.0398890i
$914$	31.2496	−	54.1259i	0.00113090	−	0.00195878i
$915$		0			0
$916$	5664.90	+	9811.90i	0.204338	+	0.353924i
$917$	11917.4			0.429169
$918$	3433.33	+	4815.84i	0.123439	+	0.173144i
$919$	−36540.8			−1.31161			−0.655804	−	0.754931i	$-0.727670\pi$
$919$	−36540.8			−1.31161			−0.655804	+	0.754931i	$0.727670\pi$
$920$		0			0
$921$	−3994.14	+	7457.99i	−0.142900	+	0.266828i
$922$	−3029.39	+	5247.05i	−0.108208	+	0.187421i
$923$	13525.4	−	23426.6i	0.482332	−	0.835424i
$924$	−1745.05	+	55.7139i	−0.0621298	+	0.00198361i
$925$		0			0
$926$	−2190.50			−0.0777369
$927$	−33094.0	+	2115.33i	−1.17255	+	0.0749477i
$928$	14747.1			0.521658
$929$	−9366.27	−	16222.8i	−0.330783	−	0.572933i	0.651883	−	0.758320i	$-0.273979\pi$
$929$	−9366.27	−	16222.8i	−0.330783	−	0.572933i	−0.982666	+	0.185387i	$0.940646\pi$
$930$		0			0
$931$	−12643.6	+	21899.3i	−0.445088	+	0.770915i
$932$	−10175.7	+	17624.8i	−0.357635	+	0.619442i
$933$	−3854.65	−	6209.98i	−0.135258	−	0.217905i
$934$	−1315.48	−	2278.48i	−0.0460856	−	0.0798226i
$935$		0			0
$936$	15520.7	−	992.061i	0.541996	−	0.0346437i
$937$	−41501.3			−1.44695			−0.723473	−	0.690353i	$-0.757455\pi$
$937$	−41501.3			−1.44695			−0.723473	+	0.690353i	$0.757455\pi$
$938$	−1624.91	−	2814.43i	−0.0565622	−	0.0979686i
$939$	28208.7	−	900.615i	0.980359	−	0.0312997i
$940$		0			0
$941$	−13683.3	+	23700.1i	−0.474029	+	0.821043i	−0.999558	−	0.0297333i	$-0.990534\pi$
$941$	−13683.3	+	23700.1i	−0.474029	+	0.821043i	0.525529	+	0.850776i	$0.323868\pi$
$942$	−2330.41	+	4351.42i	−0.0806039	+	0.150506i
$943$	−614.024	−	1063.52i	−0.0212040	−	0.0367264i
$944$	14756.0			0.508757
$945$		0			0
$946$	57.9095			0.00199028
$947$	−25943.9	−	44936.1i	−0.890245	−	1.54195i	−0.839581	−	0.543234i	$-0.817200\pi$
$947$	−25943.9	−	44936.1i	−0.890245	−	1.54195i	−0.0506637	−	0.998716i	$-0.516134\pi$
$948$	13353.9	−	24934.9i	0.457505	−	0.854269i
$949$	−20134.8	+	34874.5i	−0.688728	+	1.19291i
$950$		0			0
$951$	−39894.4	+	1273.70i	−1.36032	+	0.0434307i
$952$	−2728.82	−	4726.45i	−0.0929008	−	0.160909i
$953$	10624.9			0.361150			0.180575	−	0.983561i	$-0.442204\pi$
$953$	10624.9			0.361150			0.180575	+	0.983561i	$0.442204\pi$
$954$	−1956.60	+	3951.47i	−0.0664018	+	0.134102i
$955$		0			0
$956$	−14427.7	−	24989.6i	−0.488103	−	0.845419i
$957$	2428.65	+	3912.65i	0.0820347	+	0.132161i
$958$	−460.099	+	796.915i	−0.0155168	+	0.0268760i
$959$	−2612.38	+	4524.78i	−0.0879647	+	0.152359i
$960$		0			0
$961$	12246.4	+	21211.4i	0.411078	+	0.712008i
$962$	−5653.61			−0.189480
$963$	−27838.3	−	41809.2i	−0.931543	−	1.39905i
$964$	14338.5			0.479059
$965$		0			0
$966$	3119.99	−	99.6114i	0.103917	−	0.00331775i
$967$	11229.2	−	19449.5i	0.373429	−	0.646797i	−0.616662	−	0.787228i	$-0.711515\pi$
$967$	11229.2	−	19449.5i	0.373429	−	0.646797i	0.990090	+	0.140431i	$0.0448488\pi$
$968$	−4872.51	+	8439.43i	−0.161785	+	0.280221i
$969$	−20015.2	+	37373.0i	−0.663550	+	1.23900i
$970$		0			0
$971$	42186.8			1.39427			0.697137	−	0.716938i	$-0.254457\pi$
$971$	42186.8			1.39427			0.697137	+	0.716938i	$0.254457\pi$
$972$	29078.7	−	4680.17i	0.959568	−	0.154441i
$973$	−12500.6			−0.411871
$974$	42.2174	+	73.1228i	0.00138884	+	0.00240555i
$975$		0			0
$976$	−8004.00	+	13863.3i	−0.262502	+	0.454667i
$977$	−14339.7	+	24837.1i	−0.469568	+	0.813315i	−0.999395	−	0.0347907i	$-0.988924\pi$
$977$	−14339.7	+	24837.1i	−0.469568	+	0.813315i	0.529827	+	0.848106i	$0.322257\pi$
$978$	−6824.67	+	217.890i	−0.223138	+	0.00712409i
$979$	−2689.23	−	4657.88i	−0.0877918	−	0.152060i
$980$		0			0
$981$	−15522.3	−	23312.4i	−0.505189	−	0.758723i
$982$	−2650.36			−0.0861267
$983$	26691.2	+	46230.6i	0.866041	+	1.50003i	0.866010	+	0.500027i	$0.166677\pi$
$983$	26691.2	+	46230.6i	0.866041	+	1.50003i	3.14809e−5		1.00000i	$0.499990\pi$
$984$	−162.932	−	262.490i	−0.00527855	−	0.00850393i
$985$		0			0
$986$	−3547.54	+	6144.52i	−0.114581	+	0.198460i
$987$	6778.10	+	10919.8i	0.218591	+	0.352158i
$988$	27473.3	+	47585.2i	0.884659	+	1.53228i
$989$	3583.24			0.115208
$990$		0			0
$991$	−1505.90			−0.0482708			−0.0241354	−	0.999709i	$-0.507683\pi$
$991$	−1505.90			−0.0482708			−0.0241354	+	0.999709i	$0.507683\pi$
$992$	−3188.95	−	5523.42i	−0.102066	−	0.176783i
$993$	−21443.4	+	684.618i	−0.685281	+	0.0218788i
$994$	682.961	−	1182.92i	0.0217930	−	0.0377465i
$995$		0			0
$996$	4602.63	−	8594.19i	0.146426	−	0.273411i
$997$	17760.5	+	30762.1i	0.564174	+	0.977178i	0.997126	+	0.0757610i	$0.0241386\pi$
$997$	17760.5	+	30762.1i	0.564174	+	0.977178i	−0.432952	+	0.901417i	$0.642528\pi$
$998$	5387.87			0.170892
$999$	−21623.4	+	2076.75i	−0.684820	+	0.0657712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.g.76.8		32
5.2	odd	4		45.4.j.a.4.9	yes	32
5.3	odd	4		45.4.j.a.4.8	✓	32
5.4	even	2	inner	225.4.e.g.76.9		32
9.4	even	3		2025.4.a.bk.1.9		16
9.5	odd	6		2025.4.a.bl.1.8		16
9.7	even	3	inner	225.4.e.g.151.8		32
15.2	even	4		135.4.j.a.64.8		32
15.8	even	4		135.4.j.a.64.9		32
45.2	even	12		135.4.j.a.19.9		32
45.4	even	6		2025.4.a.bk.1.8		16
45.7	odd	12		45.4.j.a.34.8	yes	32
45.13	odd	12		405.4.b.e.244.8		16
45.14	odd	6		2025.4.a.bl.1.9		16
45.22	odd	12		405.4.b.e.244.9		16
45.23	even	12		405.4.b.f.244.9		16
45.32	even	12		405.4.b.f.244.8		16
45.34	even	6	inner	225.4.e.g.151.9		32
45.38	even	12		135.4.j.a.19.8		32
45.43	odd	12		45.4.j.a.34.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.j.a.4.8	✓	32	5.3	odd	4
45.4.j.a.4.9	yes	32	5.2	odd	4
45.4.j.a.34.8	yes	32	45.7	odd	12
45.4.j.a.34.9	yes	32	45.43	odd	12
135.4.j.a.19.8		32	45.38	even	12
135.4.j.a.19.9		32	45.2	even	12
135.4.j.a.64.8		32	15.2	even	4
135.4.j.a.64.9		32	15.8	even	4
225.4.e.g.76.8		32	1.1	even	1	trivial
225.4.e.g.76.9		32	5.4	even	2	inner
225.4.e.g.151.8		32	9.7	even	3	inner
225.4.e.g.151.9		32	45.34	even	6	inner
405.4.b.e.244.8		16	45.13	odd	12
405.4.b.e.244.9		16	45.22	odd	12
405.4.b.f.244.8		16	45.32	even	12
405.4.b.f.244.9		16	45.23	even	12
2025.4.a.bk.1.8		16	45.4	even	6
2025.4.a.bk.1.9		16	9.4	even	3
2025.4.a.bl.1.8		16	9.5	odd	6
2025.4.a.bl.1.9		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)

\(f(q)\)	\(=\)	\(q+(-0.236995 - 0.410487i) q^{2} +(2.45316 - 4.58061i) q^{3} +(3.88767 - 6.73364i) q^{4} +(-2.46167 + 0.0785933i) q^{6} +(4.10329 + 7.10710i) q^{7} -7.47735 q^{8} +(-14.9641 - 22.4739i) q^{9} +O(q^{10})\)	\(q+(-0.236995 - 0.410487i) q^{2} +(2.45316 - 4.58061i) q^{3} +(3.88767 - 6.73364i) q^{4} +(-2.46167 + 0.0785933i) q^{6} +(4.10329 + 7.10710i) q^{7} -7.47735 q^{8} +(-14.9641 - 22.4739i) q^{9} +(-2.63291 - 4.56034i) q^{11} +(-21.3071 - 34.3266i) q^{12} +(38.5171 - 66.7136i) q^{13} +(1.94492 - 3.36869i) q^{14} +(-29.3292 - 50.7997i) q^{16} +88.9397 q^{17} +(-5.67885 + 11.4688i) q^{18} -91.7358 q^{19} +(42.6209 - 1.36075i) q^{21} +(-1.24798 + 2.16156i) q^{22} +(-77.2204 + 133.750i) q^{23} +(-18.3431 + 34.2509i) q^{24} -36.5135 q^{26} +(-139.654 + 13.4125i) q^{27} +63.8088 q^{28} +(-84.1517 - 145.755i) q^{29} +(-36.3943 + 63.0367i) q^{31} +(-43.8112 + 75.8832i) q^{32} +(-27.3481 + 0.873138i) q^{33} +(-21.0783 - 36.5086i) q^{34} +(-209.506 + 13.3914i) q^{36} +154.836 q^{37} +(21.7409 + 37.6564i) q^{38} +(-211.101 - 340.091i) q^{39} +(-3.97579 + 6.88627i) q^{41} +(-10.6595 - 17.1728i) q^{42} +(-11.6007 - 20.0930i) q^{43} -40.9436 q^{44} +73.2034 q^{46} +(150.699 + 261.018i) q^{47} +(-304.643 + 9.72629i) q^{48} +(137.826 - 238.722i) q^{49} +(218.183 - 407.398i) q^{51} +(-299.483 - 518.721i) q^{52} +344.542 q^{53} +(38.6029 + 54.1473i) q^{54} +(-30.6817 - 53.1423i) q^{56} +(-225.042 + 420.206i) q^{57} +(-39.8871 + 69.0864i) q^{58} +(-125.779 + 217.855i) q^{59} +(-136.451 - 236.340i) q^{61} +34.5010 q^{62} +(98.3226 - 198.568i) q^{63} -427.736 q^{64} +(6.83978 + 11.0191i) q^{66} +(417.734 - 723.536i) q^{67} +(345.768 - 598.887i) q^{68} +(423.222 + 681.825i) q^{69} +351.152 q^{71} +(111.891 + 168.045i) q^{72} -522.749 q^{73} +(-36.6954 - 63.5584i) q^{74} +(-356.638 + 617.715i) q^{76} +(21.6072 - 37.4248i) q^{77} +(-89.5732 + 167.254i) q^{78} +(350.053 + 606.310i) q^{79} +(-281.154 + 672.602i) q^{81} +3.76897 q^{82} +(120.651 + 208.974i) q^{83} +(156.533 - 292.284i) q^{84} +(-5.49862 + 9.52388i) q^{86} +(-874.085 + 27.9067i) q^{87} +(19.6872 + 34.0993i) q^{88} +1021.39 q^{89} +632.187 q^{91} +(600.414 + 1039.95i) q^{92} +(199.466 + 321.347i) q^{93} +(71.4298 - 123.720i) q^{94} +(240.116 + 386.835i) q^{96} +(-194.642 - 337.130i) q^{97} -130.656 q^{98} +(-63.0897 + 127.413i) 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

Introduction

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