LMFDB - Embedded newform 225.4.f.c.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(107,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("225.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 $ x^12 - 16x^10 - 14x^8 - 512x^6 + 3889x^4 + 126224*x^2 + 506944
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.3
Root			$2.02004 + 2.30794i$ of defining polynomial
Character	$\chi$	$=$	225.143
Dual form			225.4.f.c.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.287902 - 0.287902i) q^{2} -7.83422i q^{4} +(-15.0557 + 15.0557i) q^{7} +(-4.55871 + 4.55871i) q^{8} +O(q^{10})$	\(q+(-0.287902 - 0.287902i) q^{2} -7.83422i q^{4} +(-15.0557 + 15.0557i) q^{7} +(-4.55871 + 4.55871i) q^{8} +27.9992i q^{11} +(-2.49862 - 2.49862i) q^{13} +8.66913 q^{14} -60.0489 q^{16} +(67.9104 + 67.9104i) q^{17} +95.2200i q^{19} +(8.06104 - 8.06104i) q^{22} +(121.994 - 121.994i) q^{23} +1.43872i q^{26} +(117.950 + 117.950i) q^{28} +99.0852 q^{29} -28.7800 q^{31} +(53.7578 + 53.7578i) q^{32} -39.1031i q^{34} +(-271.064 + 271.064i) q^{37} +(27.4140 - 27.4140i) q^{38} +453.748i q^{41} +(-30.5679 - 30.5679i) q^{43} +219.352 q^{44} -70.2445 q^{46} +(254.600 + 254.600i) q^{47} -110.348i q^{49} +(-19.5748 + 19.5748i) q^{52} +(-224.021 + 224.021i) q^{53} -137.269i q^{56} +(-28.5268 - 28.5268i) q^{58} -483.263 q^{59} -264.372 q^{61} +(8.28582 + 8.28582i) q^{62} +449.437i q^{64} +(498.817 - 498.817i) q^{67} +(532.025 - 532.025i) q^{68} -609.904i q^{71} +(74.6843 + 74.6843i) q^{73} +156.080 q^{74} +745.975 q^{76} +(-421.548 - 421.548i) q^{77} -406.574i q^{79} +(130.635 - 130.635i) q^{82} +(-652.278 + 652.278i) q^{83} +17.6011i q^{86} +(-127.640 - 127.640i) q^{88} +139.860 q^{89} +75.2369 q^{91} +(-955.726 - 955.726i) q^{92} -146.600i q^{94} +(-557.633 + 557.633i) q^{97} +(-31.7693 + 31.7693i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7}+O(q^{10}) $ 12 * q - 24 * q^7	$ 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97}+O(q^{100}) $ 12 * q - 24 * q^7 + 108 * q^13 - 648 * q^16 - 1056 * q^22 + 576 * q^28 - 1248 * q^31 - 828 * q^37 + 96 * q^43 + 672 * q^46 + 312 * q^52 + 3864 * q^58 + 96 * q^61 - 1632 * q^67 - 3972 * q^73 - 480 * q^76 + 7848 * q^82 - 7968 * q^88 + 4752 * q^91 - 2772 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.287902	−	0.287902i	−0.101789	−	0.101789i	0.654378	−	0.756167i	$-0.272930\pi$
$2$	−0.287902	−	0.287902i	−0.101789	−	0.101789i	−0.756167	+	0.654378i	$0.772930\pi$
$3$		0			0
$3$		0			0
$4$		−	7.83422i		−	0.979278i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−15.0557	+	15.0557i	−0.812931	+	0.812931i	−0.985072	−	0.172141i	$-0.944931\pi$
$7$	−15.0557	+	15.0557i	−0.812931	+	0.812931i	0.172141	+	0.985072i	$0.444931\pi$
$8$	−4.55871	+	4.55871i	−0.201468	+	0.201468i
$9$		0			0
$10$		0			0
$11$			27.9992i			0.767462i	0.923445	+	0.383731i	$0.125361\pi$
$11$			27.9992i			0.767462i	−0.923445	+	0.383731i	$0.874639\pi$
$12$		0			0
$13$	−2.49862	−	2.49862i	−0.0533071	−	0.0533071i	0.679951	−	0.733258i	$-0.262001\pi$
$13$	−2.49862	−	2.49862i	−0.0533071	−	0.0533071i	−0.733258	+	0.679951i	$0.762001\pi$
$14$	8.66913			0.165494
$15$		0			0
$16$	−60.0489			−0.938264
$17$	67.9104	+	67.9104i	0.968864	+	0.968864i	0.999530	−	0.0306653i	$-0.00976260\pi$
$17$	67.9104	+	67.9104i	0.968864	+	0.968864i	−0.0306653	+	0.999530i	$0.509763\pi$
$18$		0			0
$19$			95.2200i			1.14974i	0.818246	+	0.574868i	$0.194946\pi$
$19$			95.2200i			1.14974i	−0.818246	+	0.574868i	$0.805054\pi$
$20$		0			0
$21$		0			0
$22$	8.06104	−	8.06104i	0.0781191	−	0.0781191i
$23$	121.994	−	121.994i	1.10598	−	1.10598i	0.112302	−	0.993674i	$-0.464178\pi$
$23$	121.994	−	121.994i	1.10598	−	1.10598i	0.993674	−	0.112302i	$-0.0358224\pi$
$24$		0			0
$25$		0			0
$26$			1.43872i			0.0108521i
$27$		0			0
$28$	117.950	+	117.950i	0.796085	+	0.796085i
$29$	99.0852			0.634471			0.317235	−	0.948347i	$-0.397245\pi$
$29$	99.0852			0.634471			0.317235	+	0.948347i	$0.397245\pi$
$30$		0			0
$31$	−28.7800			−0.166743			−0.0833716	−	0.996519i	$-0.526569\pi$
$31$	−28.7800			−0.166743			−0.0833716	+	0.996519i	$0.526569\pi$
$32$	53.7578	+	53.7578i	0.296973	+	0.296973i
$33$		0			0
$34$		−	39.1031i		−	0.197239i
$35$		0			0
$36$		0			0
$37$	−271.064	+	271.064i	−1.20439	+	1.20439i	−0.231578	+	0.972816i	$0.574389\pi$
$37$	−271.064	+	271.064i	−1.20439	+	1.20439i	−0.972816	+	0.231578i	$0.925611\pi$
$38$	27.4140	−	27.4140i	0.117030	−	0.117030i
$39$		0			0
$40$		0			0
$41$			453.748i			1.72838i	0.503166	+	0.864190i	$0.332168\pi$
$41$			453.748i			1.72838i	−0.503166	+	0.864190i	$0.667832\pi$
$42$		0			0
$43$	−30.5679	−	30.5679i	−0.108409	−	0.108409i	0.650822	−	0.759230i	$-0.274424\pi$
$43$	−30.5679	−	30.5679i	−0.108409	−	0.108409i	−0.759230	+	0.650822i	$0.774424\pi$
$44$	219.352			0.751559
$45$		0			0
$46$	−70.2445			−0.225152
$47$	254.600	+	254.600i	0.790153	+	0.790153i	0.981519	−	0.191365i	$-0.0612915\pi$
$47$	254.600	+	254.600i	0.790153	+	0.790153i	−0.191365	+	0.981519i	$0.561292\pi$
$48$		0			0
$49$		−	110.348i		−	0.321713i
$50$		0			0
$51$		0			0
$52$	−19.5748	+	19.5748i	−0.0522025	+	0.0522025i
$53$	−224.021	+	224.021i	−0.580598	+	0.580598i	−0.935068	−	0.354470i	$-0.884661\pi$
$53$	−224.021	+	224.021i	−0.580598	+	0.580598i	0.354470	+	0.935068i	$0.384661\pi$
$54$		0			0
$55$		0			0
$56$		−	137.269i		−	0.327560i
$57$		0			0
$58$	−28.5268	−	28.5268i	−0.0645820	−	0.0645820i
$59$	−483.263			−1.06636			−0.533182	−	0.846001i	$-0.679004\pi$
$59$	−483.263			−1.06636			−0.533182	+	0.846001i	$0.679004\pi$
$60$		0			0
$61$	−264.372			−0.554908			−0.277454	−	0.960739i	$-0.589491\pi$
$61$	−264.372			−0.554908			−0.277454	+	0.960739i	$0.589491\pi$
$62$	8.28582	+	8.28582i	0.0169726	+	0.0169726i
$63$		0			0
$64$			449.437i			0.877807i
$65$		0			0
$66$		0			0
$67$	498.817	−	498.817i	0.909556	−	0.909556i	−0.0866805	−	0.996236i	$-0.527626\pi$
$67$	498.817	−	498.817i	0.909556	−	0.909556i	0.996236	+	0.0866805i	$0.0276259\pi$
$68$	532.025	−	532.025i	0.948788	−	0.948788i
$69$		0			0
$70$		0			0
$71$		−	609.904i		−	1.01947i	−0.860332	−	0.509735i	$-0.829744\pi$
$71$		−	609.904i		−	1.01947i	0.860332	−	0.509735i	$-0.170256\pi$
$72$		0			0
$73$	74.6843	+	74.6843i	0.119742	+	0.119742i	0.764438	−	0.644697i	$-0.223016\pi$
$73$	74.6843	+	74.6843i	0.119742	+	0.119742i	−0.644697	+	0.764438i	$0.723016\pi$
$74$	156.080			0.245188
$75$		0			0
$76$	745.975			1.12591
$77$	−421.548	−	421.548i	−0.623894	−	0.623894i
$78$		0			0
$79$		−	406.574i		−	0.579027i	−0.957174	−	0.289513i	$-0.906507\pi$
$79$		−	406.574i		−	0.579027i	0.957174	−	0.289513i	$-0.0934935\pi$
$80$		0			0
$81$		0			0
$82$	130.635	−	130.635i	0.175930	−	0.175930i
$83$	−652.278	+	652.278i	−0.862613	+	0.862613i	−0.991641	−	0.129028i	$-0.958814\pi$
$83$	−652.278	+	652.278i	−0.862613	+	0.862613i	0.129028	+	0.991641i	$0.458814\pi$
$84$		0			0
$85$		0			0
$86$			17.6011i			0.0220695i
$87$		0			0
$88$	−127.640	−	127.640i	−0.154619	−	0.154619i
$89$	139.860			0.166575			0.0832873	−	0.996526i	$-0.473458\pi$
$89$	139.860			0.166575			0.0832873	+	0.996526i	$0.473458\pi$
$90$		0			0
$91$	75.2369			0.0866700
$92$	−955.726	−	955.726i	−1.08306	−	1.08306i
$93$		0			0
$94$		−	146.600i		−	0.160857i
$95$		0			0
$96$		0			0
$97$	−557.633	+	557.633i	−0.583701	+	0.583701i	−0.935918	−	0.352217i	$-0.885428\pi$
$97$	−557.633	+	557.633i	−0.583701	+	0.583701i	0.352217	+	0.935918i	$0.385428\pi$
$98$	−31.7693	+	31.7693i	−0.0327468	+	0.0327468i
$99$		0			0
$100$		0			0
$101$		−	299.833i		−	0.295391i	−0.989033	−	0.147695i	$-0.952814\pi$
$101$		−	299.833i		−	0.295391i	0.989033	−	0.147695i	$-0.0471855\pi$
$102$		0			0
$103$	−577.974	−	577.974i	−0.552907	−	0.552907i	0.374372	−	0.927279i	$-0.377858\pi$
$103$	−577.974	−	577.974i	−0.552907	−	0.552907i	−0.927279	+	0.374372i	$0.877858\pi$
$104$	22.7810			0.0214794
$105$		0			0
$106$	128.992			0.118197
$107$	−216.994	−	216.994i	−0.196053	−	0.196053i	0.602253	−	0.798305i	$-0.294270\pi$
$107$	−216.994	−	216.994i	−0.196053	−	0.196053i	−0.798305	+	0.602253i	$0.794270\pi$
$108$		0			0
$109$		−	936.415i		−	0.822865i	−0.911440	−	0.411432i	$-0.865029\pi$
$109$		−	936.415i		−	0.822865i	0.911440	−	0.411432i	$-0.134971\pi$
$110$		0			0
$111$		0			0
$112$	904.077	−	904.077i	0.762743	−	0.762743i
$113$	−1084.00	+	1084.00i	−0.902428	+	0.902428i	−0.995646	−	0.0932173i	$-0.970285\pi$
$113$	−1084.00	+	1084.00i	−0.902428	+	0.902428i	0.0932173	+	0.995646i	$0.470285\pi$
$114$		0			0
$115$		0			0
$116$		−	776.256i		−	0.621323i
$117$		0			0
$118$	139.132	+	139.132i	0.108544	+	0.108544i
$119$	−2044.88			−1.57524
$120$		0			0
$121$	547.043			0.411001
$122$	76.1133	+	76.1133i	0.0564834	+	0.0564834i
$123$		0			0
$124$			225.469i			0.163288i
$125$		0			0
$126$		0			0
$127$	915.574	−	915.574i	0.639717	−	0.639717i	−0.310769	−	0.950486i	$-0.600586\pi$
$127$	915.574	−	915.574i	0.639717	−	0.639717i	0.950486	+	0.310769i	$0.100586\pi$
$128$	559.457	−	559.457i	0.386324	−	0.386324i
$129$		0			0
$130$		0			0
$131$		−	629.329i		−	0.419731i	−0.977730	−	0.209865i	$-0.932697\pi$
$131$		−	629.329i		−	0.419731i	0.977730	−	0.209865i	$-0.0673026\pi$
$132$		0			0
$133$	−1433.60	−	1433.60i	−0.934655	−	0.934655i
$134$	−287.221			−0.185165
$135$		0			0
$136$	−619.167			−0.390391
$137$	660.931	+	660.931i	0.412169	+	0.412169i	0.882494	−	0.470325i	$-0.155863\pi$
$137$	660.931	+	660.931i	0.412169	+	0.412169i	−0.470325	+	0.882494i	$0.655863\pi$
$138$		0			0
$139$			1378.35i			0.841081i	0.907274	+	0.420540i	$0.138160\pi$
$139$			1378.35i			0.841081i	−0.907274	+	0.420540i	$0.861840\pi$
$140$		0			0
$141$		0			0
$142$	−175.593	+	175.593i	−0.103771	+	0.103771i
$143$	69.9595	−	69.9595i	0.0409112	−	0.0409112i
$144$		0			0
$145$		0			0
$146$		−	43.0035i		−	0.0243767i
$147$		0			0
$148$	2123.57	+	2123.57i	1.17944	+	1.17944i
$149$	924.719			0.508429			0.254215	−	0.967148i	$-0.418183\pi$
$149$	924.719			0.508429			0.254215	+	0.967148i	$0.418183\pi$
$150$		0			0
$151$	−401.768			−0.216526			−0.108263	−	0.994122i	$-0.534529\pi$
$151$	−401.768			−0.216526			−0.108263	+	0.994122i	$0.534529\pi$
$152$	−434.080	−	434.080i	−0.231635	−	0.231635i
$153$		0			0
$154$			242.729i			0.127011i
$155$		0			0
$156$		0			0
$157$	−1305.55	+	1305.55i	−0.663659	+	0.663659i	−0.956240	−	0.292582i	$-0.905486\pi$
$157$	−1305.55	+	1305.55i	−0.663659	+	0.663659i	0.292582	+	0.956240i	$0.405486\pi$
$158$	−117.053	+	117.053i	−0.0589384	+	0.0589384i
$159$		0			0
$160$		0			0
$161$			3673.40i			1.79816i
$162$		0			0
$163$	78.8393	+	78.8393i	0.0378845	+	0.0378845i	0.725795	−	0.687911i	$-0.241472\pi$
$163$	78.8393	+	78.8393i	0.0378845	+	0.0378845i	−0.687911	+	0.725795i	$0.741472\pi$
$164$	3554.77			1.69256
$165$		0			0
$166$	375.585			0.175609
$167$	428.116	+	428.116i	0.198375	+	0.198375i	0.799303	−	0.600928i	$-0.205202\pi$
$167$	428.116	+	428.116i	0.198375	+	0.198375i	−0.600928	+	0.799303i	$0.705202\pi$
$168$		0			0
$169$		−	2184.51i		−	0.994317i
$170$		0			0
$171$		0			0
$172$	−239.476	+	239.476i	−0.106162	+	0.106162i
$173$	1390.57	−	1390.57i	0.611114	−	0.611114i	−0.332122	−	0.943236i	$-0.607765\pi$
$173$	1390.57	−	1390.57i	0.611114	−	0.611114i	0.943236	+	0.332122i	$0.107765\pi$
$174$		0			0
$175$		0			0
$176$		−	1681.32i		−	0.720082i
$177$		0			0
$178$	−40.2660	−	40.2660i	−0.0169554	−	0.0169554i
$179$	−110.674			−0.0462131			−0.0231065	−	0.999733i	$-0.507356\pi$
$179$	−110.674			−0.0462131			−0.0231065	+	0.999733i	$0.507356\pi$
$180$		0			0
$181$	700.593			0.287706			0.143853	−	0.989599i	$-0.454051\pi$
$181$	700.593			0.287706			0.143853	+	0.989599i	$0.454051\pi$
$182$	−21.6609	−	21.6609i	−0.00882203	−	0.00882203i
$183$		0			0
$184$			1112.27i			0.445638i
$185$		0			0
$186$		0			0
$187$	−1901.44	+	1901.44i	−0.743567	+	0.743567i
$188$	1994.59	−	1994.59i	0.773780	−	0.773780i
$189$		0			0
$190$		0			0
$191$			2214.32i			0.838862i	0.907787	+	0.419431i	$0.137770\pi$
$191$			2214.32i			0.838862i	−0.907787	+	0.419431i	$0.862230\pi$
$192$		0			0
$193$	1964.16	+	1964.16i	0.732556	+	0.732556i	0.971125	−	0.238569i	$-0.0766785\pi$
$193$	1964.16	+	1964.16i	0.732556	+	0.732556i	−0.238569	+	0.971125i	$0.576678\pi$
$194$	321.087			0.118828
$195$		0			0
$196$	−864.488			−0.315047
$197$	2700.70	+	2700.70i	0.976735	+	0.976735i	0.999735	−	0.0230004i	$-0.00732189\pi$
$197$	2700.70	+	2700.70i	0.976735	+	0.976735i	−0.0230004	+	0.999735i	$0.507322\pi$
$198$		0			0
$199$			841.195i			0.299652i	0.988712	+	0.149826i	$0.0478713\pi$
$199$			841.195i			0.299652i	−0.988712	+	0.149826i	$0.952129\pi$
$200$		0			0
$201$		0			0
$202$	−86.3224	+	86.3224i	−0.0300674	+	0.0300674i
$203$	−1491.80	+	1491.80i	−0.515781	+	0.515781i
$204$		0			0
$205$		0			0
$206$			332.800i			0.112559i
$207$		0			0
$208$	150.039	+	150.039i	0.0500161	+	0.0500161i
$209$	−2666.09			−0.882379
$210$		0			0
$211$	−3970.06			−1.29531			−0.647654	−	0.761934i	$-0.724250\pi$
$211$	−3970.06			−1.29531			−0.647654	+	0.761934i	$0.724250\pi$
$212$	1755.03	+	1755.03i	0.568567	+	0.568567i
$213$		0			0
$214$			124.946i			0.0399119i
$215$		0			0
$216$		0			0
$217$	433.303	−	433.303i	0.135551	−	0.135551i
$218$	−269.596	+	269.596i	−0.0837584	+	0.0837584i
$219$		0			0
$220$		0			0
$221$		−	339.365i		−	0.103295i
$222$		0			0
$223$	−3600.34	−	3600.34i	−1.08115	−	1.08115i	−0.996402	−	0.0847496i	$-0.972991\pi$
$223$	−3600.34	−	3600.34i	−1.08115	−	1.08115i	−0.0847496	−	0.996402i	$-0.527009\pi$
$224$	−1618.72			−0.482837
$225$		0			0
$226$	624.173			0.183714
$227$	1734.81	+	1734.81i	0.507239	+	0.507239i	0.913678	−	0.406439i	$-0.133230\pi$
$227$	1734.81	+	1734.81i	0.507239	+	0.507239i	−0.406439	+	0.913678i	$0.633230\pi$
$228$		0			0
$229$			3467.74i			1.00067i	0.865831	+	0.500337i	$0.166791\pi$
$229$			3467.74i			1.00067i	−0.865831	+	0.500337i	$0.833209\pi$
$230$		0			0
$231$		0			0
$232$	−451.700	+	451.700i	−0.127826	+	0.127826i
$233$	1070.17	−	1070.17i	0.300899	−	0.300899i	−0.540467	−	0.841365i	$-0.681752\pi$
$233$	1070.17	−	1070.17i	0.300899	−	0.300899i	0.841365	+	0.540467i	$0.181752\pi$
$234$		0			0
$235$		0			0
$236$			3785.99i			1.04427i
$237$		0			0
$238$	588.724	+	588.724i	0.160342	+	0.160342i
$239$	3909.44			1.05808			0.529038	−	0.848598i	$-0.322553\pi$
$239$	3909.44			1.05808			0.529038	+	0.848598i	$0.322553\pi$
$240$		0			0
$241$	−4787.09			−1.27952			−0.639759	−	0.768576i	$-0.720966\pi$
$241$	−4787.09			−1.27952			−0.639759	+	0.768576i	$0.720966\pi$
$242$	−157.495	−	157.495i	−0.0418353	−	0.0418353i
$243$		0			0
$244$			2071.15i			0.543409i
$245$		0			0
$246$		0			0
$247$	237.919	−	237.919i	0.0612891	−	0.0612891i
$248$	131.200	−	131.200i	0.0335935	−	0.0335935i
$249$		0			0
$250$		0			0
$251$		−	2337.42i		−	0.587794i	−0.955837	−	0.293897i	$-0.905048\pi$
$251$		−	2337.42i		−	0.587794i	0.955837	−	0.293897i	$-0.0949523\pi$
$252$		0			0
$253$	3415.73	+	3415.73i	0.848795	+	0.848795i
$254$	−527.191			−0.130232
$255$		0			0
$256$	3273.36			0.799160
$257$	−977.764	−	977.764i	−0.237320	−	0.237320i	0.578419	−	0.815740i	$-0.303670\pi$
$257$	−977.764	−	977.764i	−0.237320	−	0.237320i	−0.815740	+	0.578419i	$0.803670\pi$
$258$		0			0
$259$		−	8162.10i		−	1.95818i
$260$		0			0
$261$		0			0
$262$	−181.185	+	181.185i	−0.0427239	+	0.0427239i
$263$	−790.690	+	790.690i	−0.185384	+	0.185384i	−0.793697	−	0.608313i	$-0.791847\pi$
$263$	−790.690	+	790.690i	−0.185384	+	0.185384i	0.608313	+	0.793697i	$0.291847\pi$
$264$		0			0
$265$		0			0
$266$			825.474i			0.190275i
$267$		0			0
$268$	−3907.85	−	3907.85i	−0.890708	−	0.890708i
$269$	3954.49			0.896317			0.448159	−	0.893954i	$-0.352080\pi$
$269$	3954.49			0.896317			0.448159	+	0.893954i	$0.352080\pi$
$270$		0			0
$271$	7863.30			1.76259			0.881295	−	0.472567i	$-0.156673\pi$
$271$	7863.30			1.76259			0.881295	+	0.472567i	$0.156673\pi$
$272$	−4077.94	−	4077.94i	−0.909050	−	0.909050i
$273$		0			0
$274$		−	380.567i		−	0.0839083i
$275$		0			0
$276$		0			0
$277$	−908.009	+	908.009i	−0.196957	+	0.196957i	−0.798694	−	0.601737i	$-0.794475\pi$
$277$	−908.009	+	908.009i	−0.196957	+	0.196957i	0.601737	+	0.798694i	$0.294475\pi$
$278$	396.830	−	396.830i	0.0856126	−	0.0856126i
$279$		0			0
$280$		0			0
$281$		−	7102.70i		−	1.50787i	−0.656949	−	0.753935i	$-0.728153\pi$
$281$		−	7102.70i		−	1.50787i	0.656949	−	0.753935i	$-0.271847\pi$
$282$		0			0
$283$	4721.93	+	4721.93i	0.991837	+	0.991837i	0.999967	−	0.00813014i	$-0.00258793\pi$
$283$	4721.93	+	4721.93i	0.991837	+	0.991837i	−0.00813014	+	0.999967i	$0.502588\pi$
$284$	−4778.13			−0.998344
$285$		0			0
$286$	−40.2829			−0.00832860
$287$	−6831.49	−	6831.49i	−1.40505	−	1.40505i
$288$		0			0
$289$			4310.65i			0.877396i
$290$		0			0
$291$		0			0
$292$	585.094	−	585.094i	0.117260	−	0.117260i
$293$	2078.57	−	2078.57i	0.414442	−	0.414442i	−0.468841	−	0.883283i	$-0.655328\pi$
$293$	2078.57	−	2078.57i	0.414442	−	0.414442i	0.883283	+	0.468841i	$0.155328\pi$
$294$		0			0
$295$		0			0
$296$		−	2471.40i		−	0.485294i
$297$		0			0
$298$	−266.229	−	266.229i	−0.0517524	−	0.0517524i
$299$	−609.632			−0.117913
$300$		0			0
$301$	920.443			0.176257
$302$	115.670	+	115.670i	0.0220399	+	0.0220399i
$303$		0			0
$304$		−	5717.85i		−	1.07875i
$305$		0			0
$306$		0			0
$307$	5325.58	−	5325.58i	0.990056	−	0.990056i	−0.00989542	−	0.999951i	$-0.503150\pi$
$307$	5325.58	−	5325.58i	0.990056	−	0.990056i	0.999951	+	0.00989542i	$0.00314986\pi$
$308$	−3302.50	+	3302.50i	−0.610966	+	0.610966i
$309$		0			0
$310$		0			0
$311$			2005.56i			0.365676i	0.983143	+	0.182838i	$0.0585283\pi$
$311$			2005.56i			0.365676i	−0.983143	+	0.182838i	$0.941472\pi$
$312$		0			0
$313$	−5026.49	−	5026.49i	−0.907713	−	0.907713i	0.0883746	−	0.996087i	$-0.471833\pi$
$313$	−5026.49	−	5026.49i	−0.907713	−	0.907713i	−0.996087	+	0.0883746i	$0.971833\pi$
$314$	751.742			0.135106
$315$		0			0
$316$	−3185.19			−0.567028
$317$	3137.15	+	3137.15i	0.555836	+	0.555836i	0.928119	−	0.372283i	$-0.121425\pi$
$317$	3137.15	+	3137.15i	0.555836	+	0.555836i	−0.372283	+	0.928119i	$0.621425\pi$
$318$		0			0
$319$			2774.31i			0.486933i
$320$		0			0
$321$		0			0
$322$	1057.58	−	1057.58i	0.183033	−	0.183033i
$323$	−6466.43	+	6466.43i	−1.11394	+	1.11394i
$324$		0			0
$325$		0			0
$326$		−	45.3960i		−	0.00771243i
$327$		0			0
$328$	−2068.50	−	2068.50i	−0.348214	−	0.348214i
$329$	−7666.35			−1.28468
$330$		0			0
$331$	2978.02			0.494523			0.247261	−	0.968949i	$-0.420469\pi$
$331$	2978.02			0.494523			0.247261	+	0.968949i	$0.420469\pi$
$332$	5110.10	+	5110.10i	0.844738	+	0.844738i
$333$		0			0
$334$		−	246.511i		−	0.0403847i
$335$		0			0
$336$		0			0
$337$	5985.73	−	5985.73i	0.967547	−	0.967547i	−0.0319428	−	0.999490i	$-0.510169\pi$
$337$	5985.73	−	5985.73i	0.967547	−	0.967547i	0.999490	+	0.0319428i	$0.0101694\pi$
$338$	−628.926	+	628.926i	−0.101210	+	0.101210i
$339$		0			0
$340$		0			0
$341$		−	805.818i		−	0.127969i
$342$		0			0
$343$	−3502.74	−	3502.74i	−0.551400	−	0.551400i
$344$	278.701			0.0436818
$345$		0			0
$346$	−800.693			−0.124409
$347$	−8183.37	−	8183.37i	−1.26601	−	1.26601i	−0.948130	−	0.317881i	$-0.897029\pi$
$347$	−8183.37	−	8183.37i	−1.26601	−	1.26601i	−0.317881	−	0.948130i	$-0.602971\pi$
$348$		0			0
$349$			1421.22i			0.217983i	0.994043	+	0.108991i	$0.0347621\pi$
$349$			1421.22i			0.217983i	−0.994043	+	0.108991i	$0.965238\pi$
$350$		0			0
$351$		0			0
$352$	−1505.18	+	1505.18i	−0.227916	+	0.227916i
$353$	1399.56	−	1399.56i	0.211023	−	0.211023i	−0.593679	−	0.804702i	$-0.702325\pi$
$353$	1399.56	−	1399.56i	0.211023	−	0.211023i	0.804702	+	0.593679i	$0.202325\pi$
$354$		0			0
$355$		0			0
$356$		−	1095.70i		−	0.163123i
$357$		0			0
$358$	31.8632	+	31.8632i	0.00470397	+	0.00470397i
$359$	−4313.98			−0.634215			−0.317108	−	0.948390i	$-0.602712\pi$
$359$	−4313.98			−0.634215			−0.317108	+	0.948390i	$0.602712\pi$
$360$		0			0
$361$	−2207.85			−0.321891
$362$	−201.702	−	201.702i	−0.0292852	−	0.0292852i
$363$		0			0
$364$		−	589.423i		−	0.0848740i
$365$		0			0
$366$		0			0
$367$	−4533.34	+	4533.34i	−0.644792	+	0.644792i	−0.951730	−	0.306938i	$-0.900696\pi$
$367$	−4533.34	+	4533.34i	−0.644792	+	0.644792i	0.306938	+	0.951730i	$0.400696\pi$
$368$	−7325.59	+	7325.59i	−1.03770	+	1.03770i
$369$		0			0
$370$		0			0
$371$		−	6745.59i		−	0.943972i
$372$		0			0
$373$	2787.95	+	2787.95i	0.387010	+	0.387010i	0.873620	−	0.486609i	$-0.161766\pi$
$373$	2787.95	+	2787.95i	0.387010	+	0.387010i	−0.486609	+	0.873620i	$0.661766\pi$
$374$	1094.86			0.151374
$375$		0			0
$376$	−2321.29			−0.318382
$377$	−247.576	−	247.576i	−0.0338218	−	0.0338218i
$378$		0			0
$379$		−	8409.09i		−	1.13970i	−0.821749	−	0.569849i	$-0.807002\pi$
$379$		−	8409.09i		−	1.13970i	0.821749	−	0.569849i	$-0.192998\pi$
$380$		0			0
$381$		0			0
$382$	637.508	−	637.508i	0.0853868	−	0.0853868i
$383$	8507.38	−	8507.38i	1.13500	−	1.13500i	0.145672	−	0.989333i	$-0.453466\pi$
$383$	8507.38	−	8507.38i	1.13500	−	1.13500i	0.989333	−	0.145672i	$-0.0465343\pi$
$384$		0			0
$385$		0			0
$386$		−	1130.97i		−	0.149132i
$387$		0			0
$388$	4368.62	+	4368.62i	0.571606	+	0.571606i
$389$	8641.23			1.12629			0.563146	−	0.826357i	$-0.309591\pi$
$389$	8641.23			1.12629			0.563146	+	0.826357i	$0.309591\pi$
$390$		0			0
$391$	16569.3			2.14308
$392$	503.042	+	503.042i	0.0648150	+	0.0648150i
$393$		0			0
$394$		−	1555.07i		−	0.198841i
$395$		0			0
$396$		0			0
$397$	−1902.21	+	1902.21i	−0.240476	+	0.240476i	−0.817047	−	0.576571i	$-0.804390\pi$
$397$	−1902.21	+	1902.21i	−0.240476	+	0.240476i	0.576571	+	0.817047i	$0.304390\pi$
$398$	242.182	−	242.182i	0.0305012	−	0.0305012i
$399$		0			0
$400$		0			0
$401$			13640.1i			1.69864i	0.527882	+	0.849318i	$0.322986\pi$
$401$			13640.1i			1.69864i	−0.527882	+	0.849318i	$0.677014\pi$
$402$		0			0
$403$	71.9103	+	71.9103i	0.00888860	+	0.00888860i
$404$	−2348.96			−0.289270
$405$		0			0
$406$	858.982			0.105001
$407$	−7589.57	−	7589.57i	−0.924327	−	0.924327i
$408$		0			0
$409$			6395.02i			0.773138i	0.922260	+	0.386569i	$0.126340\pi$
$409$			6395.02i			0.773138i	−0.922260	+	0.386569i	$0.873660\pi$
$410$		0			0
$411$		0			0
$412$	−4527.98	+	4527.98i	−0.541450	+	0.541450i
$413$	7275.86	−	7275.86i	0.866880	−	0.866880i
$414$		0			0
$415$		0			0
$416$		−	268.641i		−	0.0316615i
$417$		0			0
$418$	767.572	+	767.572i	0.0898162	+	0.0898162i
$419$	8474.94			0.988133			0.494067	−	0.869424i	$-0.335510\pi$
$419$	8474.94			0.988133			0.494067	+	0.869424i	$0.335510\pi$
$420$		0			0
$421$	−9069.21			−1.04990			−0.524948	−	0.851134i	$-0.675915\pi$
$421$	−9069.21			−1.04990			−0.524948	+	0.851134i	$0.675915\pi$
$422$	1142.99	+	1142.99i	0.131848	+	0.131848i
$423$		0			0
$424$		−	2042.49i		−	0.233944i
$425$		0			0
$426$		0			0
$427$	3980.30	−	3980.30i	0.451102	−	0.451102i
$428$	−1699.98	+	1699.98i	−0.191990	+	0.191990i
$429$		0			0
$430$		0			0
$431$		−	8388.11i		−	0.937450i	−0.883344	−	0.468725i	$-0.844713\pi$
$431$		−	8388.11i		−	0.937450i	0.883344	−	0.468725i	$-0.155287\pi$
$432$		0			0
$433$	4132.17	+	4132.17i	0.458613	+	0.458613i	0.898200	−	0.439587i	$-0.144875\pi$
$433$	4132.17	+	4132.17i	0.458613	+	0.458613i	−0.439587	+	0.898200i	$0.644875\pi$
$434$	−249.498			−0.0275951
$435$		0			0
$436$	−7336.08			−0.805814
$437$	11616.2	+	11616.2i	1.27158	+	1.27158i
$438$		0			0
$439$			10498.9i			1.14143i	0.821149	+	0.570714i	$0.193333\pi$
$439$			10498.9i			1.14143i	−0.821149	+	0.570714i	$0.806667\pi$
$440$		0			0
$441$		0			0
$442$	−97.7038	+	97.7038i	−0.0105142	+	0.0105142i
$443$	1465.93	−	1465.93i	0.157220	−	0.157220i	−0.624114	−	0.781333i	$-0.714540\pi$
$443$	1465.93	−	1465.93i	0.157220	−	0.157220i	0.781333	+	0.624114i	$0.214540\pi$
$444$		0			0
$445$		0			0
$446$			2073.09i			0.220098i
$447$		0			0
$448$	−6766.58	−	6766.58i	−0.713596	−	0.713596i
$449$	6295.42			0.661691			0.330846	−	0.943685i	$-0.392666\pi$
$449$	6295.42			0.661691			0.330846	+	0.943685i	$0.392666\pi$
$450$		0			0
$451$	−12704.6			−1.32647
$452$	8492.32	+	8492.32i	0.883728	+	0.883728i
$453$		0			0
$454$		−	998.909i		−	0.103262i
$455$		0			0
$456$		0			0
$457$	−9065.09	+	9065.09i	−0.927893	+	0.927893i	−0.997570	−	0.0696767i	$-0.977803\pi$
$457$	−9065.09	+	9065.09i	−0.927893	+	0.927893i	0.0696767	+	0.997570i	$0.477803\pi$
$458$	998.368	−	998.368i	0.101857	−	0.101857i
$459$		0			0
$460$		0			0
$461$			13305.5i			1.34424i	0.740440	+	0.672122i	$0.234617\pi$
$461$			13305.5i			1.34424i	−0.740440	+	0.672122i	$0.765383\pi$
$462$		0			0
$463$	3124.86	+	3124.86i	0.313660	+	0.313660i	0.846326	−	0.532666i	$-0.178810\pi$
$463$	3124.86	+	3124.86i	0.313660	+	0.313660i	−0.532666	+	0.846326i	$0.678810\pi$
$464$	−5949.95			−0.595301
$465$		0			0
$466$	−616.210			−0.0612562
$467$	4255.07	+	4255.07i	0.421629	+	0.421629i	0.885764	−	0.464135i	$-0.153635\pi$
$467$	4255.07	+	4255.07i	0.421629	+	0.421629i	−0.464135	+	0.885764i	$0.653635\pi$
$468$		0			0
$469$			15020.1i			1.47881i
$470$		0			0
$471$		0			0
$472$	2203.05	−	2203.05i	0.214838	−	0.214838i
$473$	855.879	−	855.879i	0.0831995	−	0.0831995i
$474$		0			0
$475$		0			0
$476$			16020.0i			1.54260i
$477$		0			0
$478$	−1125.53	−	1125.53i	−0.107700	−	0.107700i
$479$	−10625.2			−1.01352			−0.506761	−	0.862087i	$-0.669157\pi$
$479$	−10625.2			−1.01352			−0.506761	+	0.862087i	$0.669157\pi$
$480$		0			0
$481$	1354.57			0.128406
$482$	1378.21	+	1378.21i	0.130241	+	0.130241i
$483$		0			0
$484$		−	4285.66i		−	0.402485i
$485$		0			0
$486$		0			0
$487$	3269.03	−	3269.03i	0.304177	−	0.304177i	−0.538469	−	0.842645i	$-0.680997\pi$
$487$	3269.03	−	3269.03i	0.304177	−	0.304177i	0.842645	+	0.538469i	$0.180997\pi$
$488$	1205.19	−	1205.19i	0.111796	−	0.111796i
$489$		0			0
$490$		0			0
$491$		−	18791.1i		−	1.72715i	−0.504220	−	0.863575i	$-0.668220\pi$
$491$		−	18791.1i		−	1.72715i	0.504220	−	0.863575i	$-0.331780\pi$
$492$		0			0
$493$	6728.92	+	6728.92i	0.614716	+	0.614716i
$494$	−136.995			−0.0124771
$495$		0			0
$496$	1728.21			0.156449
$497$	9182.53	+	9182.53i	0.828758	+	0.828758i
$498$		0			0
$499$		−	7220.67i		−	0.647778i	−0.946095	−	0.323889i	$-0.895010\pi$
$499$		−	7220.67i		−	0.647778i	0.946095	−	0.323889i	$-0.104990\pi$
$500$		0			0
$501$		0			0
$502$	−672.947	+	672.947i	−0.0598308	+	0.0598308i
$503$	2081.38	−	2081.38i	0.184501	−	0.184501i	−0.608813	−	0.793314i	$-0.708354\pi$
$503$	2081.38	−	2081.38i	0.184501	−	0.184501i	0.793314	+	0.608813i	$0.208354\pi$
$504$		0			0
$505$		0			0
$506$		−	1966.79i		−	0.172796i
$507$		0			0
$508$	−7172.81	−	7172.81i	−0.626461	−	0.626461i
$509$	12624.1			1.09932			0.549659	−	0.835389i	$-0.314758\pi$
$509$	12624.1			1.09932			0.549659	+	0.835389i	$0.314758\pi$
$510$		0			0
$511$	−2248.85			−0.194683
$512$	−5418.06	−	5418.06i	−0.467669	−	0.467669i
$513$		0			0
$514$			563.001i			0.0483130i
$515$		0			0
$516$		0			0
$517$	−7128.60	+	7128.60i	−0.606413	+	0.606413i
$518$	−2349.89	+	2349.89i	−0.199321	+	0.199321i
$519$		0			0
$520$		0			0
$521$			11837.5i			0.995409i	0.867347	+	0.497705i	$0.165824\pi$
$521$			11837.5i			0.995409i	−0.867347	+	0.497705i	$0.834176\pi$
$522$		0			0
$523$	5538.72	+	5538.72i	0.463081	+	0.463081i	0.899664	−	0.436583i	$-0.143811\pi$
$523$	5538.72	+	5538.72i	0.463081	+	0.463081i	−0.436583	+	0.899664i	$0.643811\pi$
$524$	−4930.31			−0.411033
$525$		0			0
$526$	455.282			0.0377400
$527$	−1954.46	−	1954.46i	−0.161552	−	0.161552i
$528$		0			0
$529$		−	17597.9i		−	1.44637i
$530$		0			0
$531$		0			0
$532$	−11231.2	+	11231.2i	−0.915287	+	0.915287i
$533$	1133.74	−	1133.74i	0.0921349	−	0.0921349i
$534$		0			0
$535$		0			0
$536$			4547.92i			0.366493i
$537$		0			0
$538$	−1138.51	−	1138.51i	−0.0912350	−	0.0912350i
$539$	3089.65			0.246903
$540$		0			0
$541$	5207.24			0.413820			0.206910	−	0.978360i	$-0.433659\pi$
$541$	5207.24			0.413820			0.206910	+	0.978360i	$0.433659\pi$
$542$	−2263.86	−	2263.86i	−0.179412	−	0.179412i
$543$		0			0
$544$			7301.44i			0.575453i
$545$		0			0
$546$		0			0
$547$	3940.59	−	3940.59i	0.308021	−	0.308021i	−0.536121	−	0.844141i	$-0.680111\pi$
$547$	3940.59	−	3940.59i	0.308021	−	0.308021i	0.844141	+	0.536121i	$0.180111\pi$
$548$	5177.88	−	5177.88i	0.403628	−	0.403628i
$549$		0			0
$550$		0			0
$551$			9434.89i			0.729473i
$552$		0			0
$553$	6121.25	+	6121.25i	0.470709	+	0.470709i
$554$	522.836			0.0400959
$555$		0			0
$556$	10798.3			0.823652
$557$	−2850.64	−	2850.64i	−0.216850	−	0.216850i	0.590320	−	0.807170i	$-0.299002\pi$
$557$	−2850.64	−	2850.64i	−0.216850	−	0.216850i	−0.807170	+	0.590320i	$0.799002\pi$
$558$		0			0
$559$			152.755i			0.0115579i
$560$		0			0
$561$		0			0
$562$	−2044.88	+	2044.88i	−0.153484	+	0.153484i
$563$	−12845.3	+	12845.3i	−0.961569	+	0.961569i	−0.999288	−	0.0377198i	$-0.987991\pi$
$563$	−12845.3	+	12845.3i	−0.961569	+	0.961569i	0.0377198	+	0.999288i	$0.487991\pi$
$564$		0			0
$565$		0			0
$566$		−	2718.91i		−	0.201916i
$567$		0			0
$568$	2780.38	+	2780.38i	0.205391	+	0.205391i
$569$	25072.7			1.84728			0.923639	−	0.383263i	$-0.125200\pi$
$569$	25072.7			1.84728			0.923639	+	0.383263i	$0.125200\pi$
$570$		0			0
$571$	−3587.24			−0.262909			−0.131455	−	0.991322i	$-0.541965\pi$
$571$	−3587.24			−0.262909			−0.131455	+	0.991322i	$0.541965\pi$
$572$	−548.078	−	548.078i	−0.0400635	−	0.0400635i
$573$		0			0
$574$			3933.60i			0.286037i
$575$		0			0
$576$		0			0
$577$	−760.083	+	760.083i	−0.0548400	+	0.0548400i	−0.733995	−	0.679155i	$-0.762346\pi$
$577$	−760.083	+	760.083i	−0.0548400	+	0.0548400i	0.679155	+	0.733995i	$0.262346\pi$
$578$	1241.04	−	1241.04i	0.0893091	−	0.0893091i
$579$		0			0
$580$		0			0
$581$		−	19641.0i		−	1.40249i
$582$		0			0
$583$	−6272.43	−	6272.43i	−0.445587	−	0.445587i
$584$	−680.928			−0.0482483
$585$		0			0
$586$	−1196.85			−0.0843711
$587$	−8165.43	−	8165.43i	−0.574146	−	0.574146i	0.359139	−	0.933284i	$-0.383071\pi$
$587$	−8165.43	−	8165.43i	−0.574146	−	0.574146i	−0.933284	+	0.359139i	$0.883071\pi$
$588$		0			0
$589$		−	2740.43i		−	0.191711i
$590$		0			0
$591$		0			0
$592$	16277.1	−	16277.1i	1.13004	−	1.13004i
$593$	9861.32	−	9861.32i	0.682893	−	0.682893i	−0.277758	−	0.960651i	$-0.589591\pi$
$593$	9861.32	−	9861.32i	0.682893	−	0.682893i	0.960651	+	0.277758i	$0.0895913\pi$
$594$		0			0
$595$		0			0
$596$		−	7244.46i		−	0.497893i
$597$		0			0
$598$	175.514	+	175.514i	0.0120022	+	0.0120022i
$599$	−20769.5			−1.41673			−0.708363	−	0.705848i	$-0.750566\pi$
$599$	−20769.5			−1.41673			−0.708363	+	0.705848i	$0.750566\pi$
$600$		0			0
$601$	−11642.9			−0.790222			−0.395111	−	0.918633i	$-0.629294\pi$
$601$	−11642.9			−0.790222			−0.395111	+	0.918633i	$0.629294\pi$
$602$	−264.997	−	264.997i	−0.0179410	−	0.0179410i
$603$		0			0
$604$			3147.54i			0.212039i
$605$		0			0
$606$		0			0
$607$	17174.6	−	17174.6i	1.14843	−	1.14843i	0.161565	−	0.986862i	$-0.448346\pi$
$607$	17174.6	−	17174.6i	1.14843	−	1.14843i	0.986862	−	0.161565i	$-0.0516540\pi$
$608$	−5118.82	+	5118.82i	−0.341440	+	0.341440i
$609$		0			0
$610$		0			0
$611$		−	1272.30i		−	0.0842416i
$612$		0			0
$613$	−11694.1	−	11694.1i	−0.770504	−	0.770504i	0.207691	−	0.978195i	$-0.433405\pi$
$613$	−11694.1	−	11694.1i	−0.770504	−	0.770504i	−0.978195	+	0.207691i	$0.933405\pi$
$614$	−3066.49			−0.201553
$615$		0			0
$616$	3843.43			0.251390
$617$	−5586.69	−	5586.69i	−0.364525	−	0.364525i	0.500951	−	0.865476i	$-0.332984\pi$
$617$	−5586.69	−	5586.69i	−0.364525	−	0.364525i	−0.865476	+	0.500951i	$0.832984\pi$
$618$		0			0
$619$			16137.1i			1.04783i	0.851771	+	0.523914i	$0.175529\pi$
$619$			16137.1i			1.04783i	−0.851771	+	0.523914i	$0.824471\pi$
$620$		0			0
$621$		0			0
$622$	577.406	−	577.406i	0.0372217	−	0.0372217i
$623$	−2105.69	+	2105.69i	−0.135414	+	0.135414i
$624$		0			0
$625$		0			0
$626$			2894.27i			0.184790i
$627$		0			0
$628$	10228.0	+	10228.0i	0.649906	+	0.649906i
$629$	−36816.1			−2.33379
$630$		0			0
$631$	25292.3			1.59567			0.797837	−	0.602874i	$-0.205978\pi$
$631$	25292.3			1.59567			0.797837	+	0.602874i	$0.205978\pi$
$632$	1853.45	+	1853.45i	0.116656	+	0.116656i
$633$		0			0
$634$		−	1806.38i		−	0.113156i
$635$		0			0
$636$		0			0
$637$	−275.717	+	275.717i	−0.0171496	+	0.0171496i
$638$	798.729	−	798.729i	0.0495643	−	0.0495643i
$639$		0			0
$640$		0			0
$641$		−	8057.35i		−	0.496484i	−0.968698	−	0.248242i	$-0.920147\pi$
$641$		−	8057.35i		−	0.496484i	0.968698	−	0.248242i	$-0.0798528\pi$
$642$		0			0
$643$	−15024.4	−	15024.4i	−0.921471	−	0.921471i	0.0756629	−	0.997133i	$-0.475893\pi$
$643$	−15024.4	−	15024.4i	−0.921471	−	0.921471i	−0.997133	+	0.0756629i	$0.975893\pi$
$644$	28778.2			1.76090
$645$		0			0
$646$	3723.40			0.226773
$647$	−2396.69	−	2396.69i	−0.145631	−	0.145631i	0.630532	−	0.776163i	$-0.282837\pi$
$647$	−2396.69	−	2396.69i	−0.145631	−	0.145631i	−0.776163	+	0.630532i	$0.782837\pi$
$648$		0			0
$649$		−	13531.0i		−	0.818394i
$650$		0			0
$651$		0			0
$652$	617.645	−	617.645i	0.0370995	−	0.0370995i
$653$	−10852.1	+	10852.1i	−0.650343	+	0.650343i	−0.953076	−	0.302732i	$-0.902101\pi$
$653$	−10852.1	+	10852.1i	−0.650343	+	0.650343i	0.302732	+	0.953076i	$0.402101\pi$
$654$		0			0
$655$		0			0
$656$		−	27247.1i		−	1.62168i
$657$		0			0
$658$	2207.16	+	2207.16i	0.130766	+	0.130766i
$659$	−21164.7			−1.25108			−0.625538	−	0.780193i	$-0.715121\pi$
$659$	−21164.7			−1.25108			−0.625538	+	0.780193i	$0.715121\pi$
$660$		0			0
$661$	−6399.33			−0.376558			−0.188279	−	0.982116i	$-0.560291\pi$
$661$	−6399.33			−0.376558			−0.188279	+	0.982116i	$0.560291\pi$
$662$	−857.380	−	857.380i	−0.0503369	−	0.0503369i
$663$		0			0
$664$		−	5947.09i		−	0.347578i
$665$		0			0
$666$		0			0
$667$	12087.8	−	12087.8i	0.701710	−	0.701710i
$668$	3353.96	−	3353.96i	0.194264	−	0.194264i
$669$		0			0
$670$		0			0
$671$		−	7402.22i		−	0.425871i
$672$		0			0
$673$	1618.29	+	1618.29i	0.0926903	+	0.0926903i	0.751932	−	0.659241i	$-0.229122\pi$
$673$	1618.29	+	1618.29i	0.0926903	+	0.0926903i	−0.659241	+	0.751932i	$0.729122\pi$
$674$	−3446.61			−0.196971
$675$		0			0
$676$	−17114.0			−0.973713
$677$	−16119.8	−	16119.8i	−0.915118	−	0.915118i	0.0815511	−	0.996669i	$-0.474013\pi$
$677$	−16119.8	−	16119.8i	−0.915118	−	0.915118i	−0.996669	+	0.0815511i	$0.974013\pi$
$678$		0			0
$679$		−	16791.1i		−	0.949017i
$680$		0			0
$681$		0			0
$682$	−231.997	+	231.997i	−0.0130258	+	0.0130258i
$683$	−23612.1	+	23612.1i	−1.32283	+	1.32283i	−0.411351	+	0.911477i	$0.634943\pi$
$683$	−23612.1	+	23612.1i	−1.32283	+	1.32283i	−0.911477	+	0.411351i	$0.865057\pi$
$684$		0			0
$685$		0			0
$686$			2016.89i			0.112253i
$687$		0			0
$688$	1835.57	+	1835.57i	0.101716	+	0.101716i
$689$	1119.49			0.0619000
$690$		0			0
$691$	12036.1			0.662624			0.331312	−	0.943521i	$-0.392509\pi$
$691$	12036.1			0.662624			0.331312	+	0.943521i	$0.392509\pi$
$692$	−10894.0	−	10894.0i	−0.598451	−	0.598451i
$693$		0			0
$694$			4712.02i			0.257732i
$695$		0			0
$696$		0			0
$697$	−30814.2	+	30814.2i	−1.67457	+	1.67457i
$698$	409.171	−	409.171i	0.0221882	−	0.0221882i
$699$		0			0
$700$		0			0
$701$			33366.3i			1.79776i	0.438200	+	0.898878i	$0.355616\pi$
$701$			33366.3i			1.79776i	−0.438200	+	0.898878i	$0.644384\pi$
$702$		0			0
$703$	−25810.7	−	25810.7i	−1.38473	−	1.38473i
$704$	−12583.9			−0.673684
$705$		0			0
$706$	−805.875			−0.0429596
$707$	4514.19	+	4514.19i	0.240132	+	0.240132i
$708$		0			0
$709$		−	4987.22i		−	0.264173i	−0.991238	−	0.132087i	$-0.957832\pi$
$709$		−	4987.22i		−	0.264173i	0.991238	−	0.132087i	$-0.0421677\pi$
$710$		0			0
$711$		0			0
$712$	−637.581	+	637.581i	−0.0335595	+	0.0335595i
$713$	−3510.98	+	3510.98i	−0.184414	+	0.184414i
$714$		0			0
$715$		0			0
$716$			867.043i			0.0452555i
$717$		0			0
$718$	1242.00	+	1242.00i	0.0645560	+	0.0645560i
$719$	33618.4			1.74375			0.871873	−	0.489732i	$-0.162905\pi$
$719$	33618.4			1.74375			0.871873	+	0.489732i	$0.162905\pi$
$720$		0			0
$721$	17403.6			0.898951
$722$	635.644	+	635.644i	0.0327649	+	0.0327649i
$723$		0			0
$724$		−	5488.61i		−	0.281744i
$725$		0			0
$726$		0			0
$727$	10057.9	−	10057.9i	0.513106	−	0.513106i	−0.402371	−	0.915477i	$-0.631814\pi$
$727$	10057.9	−	10057.9i	0.513106	−	0.513106i	0.915477	+	0.402371i	$0.131814\pi$
$728$	−342.983	+	342.983i	−0.0174613	+	0.0174613i
$729$		0			0
$730$		0			0
$731$		−	4151.76i		−	0.210066i
$732$		0			0
$733$	4209.55	+	4209.55i	0.212119	+	0.212119i	0.805167	−	0.593048i	$-0.202076\pi$
$733$	4209.55	+	4209.55i	0.212119	+	0.212119i	−0.593048	+	0.805167i	$0.702076\pi$
$734$	2610.32			0.131265
$735$		0			0
$736$	13116.2			0.656890
$737$	13966.5	+	13966.5i	0.698050	+	0.698050i
$738$		0			0
$739$		−	4750.38i		−	0.236462i	−0.992986	−	0.118231i	$-0.962278\pi$
$739$		−	4750.38i		−	0.236462i	0.992986	−	0.118231i	$-0.0377223\pi$
$740$		0			0
$741$		0			0
$742$	−1942.07	+	1942.07i	−0.0960857	+	0.0960857i
$743$	16266.1	−	16266.1i	0.803159	−	0.803159i	−0.180429	−	0.983588i	$-0.557749\pi$
$743$	16266.1	−	16266.1i	0.803159	−	0.803159i	0.983588	+	0.180429i	$0.0577487\pi$
$744$		0			0
$745$		0			0
$746$		−	1605.32i		−	0.0787866i
$747$		0			0
$748$	14896.3	+	14896.3i	0.728159	+	0.728159i
$749$	6534.00			0.318754
$750$		0			0
$751$	−32690.2			−1.58839			−0.794197	−	0.607660i	$-0.792108\pi$
$751$	−32690.2			−1.58839			−0.794197	+	0.607660i	$0.792108\pi$
$752$	−15288.4	−	15288.4i	−0.741372	−	0.741372i
$753$		0			0
$754$			142.555i			0.00688536i
$755$		0			0
$756$		0			0
$757$	6722.97	−	6722.97i	0.322788	−	0.322788i	−0.527048	−	0.849836i	$-0.676701\pi$
$757$	6722.97	−	6722.97i	0.322788	−	0.322788i	0.849836	+	0.527048i	$0.176701\pi$
$758$	−2420.99	+	2420.99i	−0.116008	+	0.116008i
$759$		0			0
$760$		0			0
$761$			7001.94i			0.333535i	0.985996	+	0.166767i	$0.0533329\pi$
$761$			7001.94i			0.333535i	−0.985996	+	0.166767i	$0.946667\pi$
$762$		0			0
$763$	14098.4	+	14098.4i	0.668932	+	0.668932i
$764$	17347.5			0.821480
$765$		0			0
$766$	−4898.58			−0.231061
$767$	1207.49	+	1207.49i	0.0568448	+	0.0568448i
$768$		0			0
$769$			25176.4i			1.18060i	0.807183	+	0.590301i	$0.200991\pi$
$769$			25176.4i			1.18060i	−0.807183	+	0.590301i	$0.799009\pi$
$770$		0			0
$771$		0			0
$772$	15387.7	−	15387.7i	0.717376	−	0.717376i
$773$	7322.13	−	7322.13i	0.340697	−	0.340697i	−0.515932	−	0.856629i	$-0.672554\pi$
$773$	7322.13	−	7322.13i	0.340697	−	0.340697i	0.856629	+	0.515932i	$0.172554\pi$
$774$		0			0
$775$		0			0
$776$		−	5084.17i		−	0.235195i
$777$		0			0
$778$	−2487.83	−	2487.83i	−0.114644	−	0.114644i
$779$	−43205.9			−1.98718
$780$		0			0
$781$	17076.9			0.782405
$782$	−4770.33	−	4770.33i	−0.218142	−	0.218142i
$783$		0			0
$784$			6626.25i			0.301852i
$785$		0			0
$786$		0			0
$787$	−16794.5	+	16794.5i	−0.760683	+	0.760683i	−0.976446	−	0.215763i	$-0.930776\pi$
$787$	−16794.5	+	16794.5i	−0.760683	+	0.760683i	0.215763	+	0.976446i	$0.430776\pi$
$788$	21157.9	−	21157.9i	0.956495	−	0.956495i
$789$		0			0
$790$		0			0
$791$		−	32640.8i		−	1.46722i
$792$		0			0
$793$	660.565	+	660.565i	0.0295805	+	0.0295805i
$794$	1095.30			0.0489556
$795$		0			0
$796$	6590.11			0.293443
$797$	18950.9	+	18950.9i	0.842251	+	0.842251i	0.989151	−	0.146900i	$-0.0469296\pi$
$797$	18950.9	+	18950.9i	0.842251	+	0.842251i	−0.146900	+	0.989151i	$0.546930\pi$
$798$		0			0
$799$			34580.0i			1.53110i
$800$		0			0
$801$		0			0
$802$	3927.01	−	3927.01i	0.172902	−	0.172902i
$803$	−2091.10	+	2091.10i	−0.0918972	+	0.0918972i
$804$		0			0
$805$		0			0
$806$		−	41.4062i		−	0.00180952i
$807$		0			0
$808$	1366.85	+	1366.85i	0.0595118	+	0.0595118i
$809$	−3967.32			−0.172415			−0.0862074	−	0.996277i	$-0.527475\pi$
$809$	−3967.32			−0.172415			−0.0862074	+	0.996277i	$0.527475\pi$
$810$		0			0
$811$	−23204.4			−1.00471			−0.502353	−	0.864663i	$-0.667532\pi$
$811$	−23204.4			−1.00471			−0.502353	+	0.864663i	$0.667532\pi$
$812$	11687.1	+	11687.1i	0.505093	+	0.505093i
$813$		0			0
$814$			4370.11i			0.188172i
$815$		0			0
$816$		0			0
$817$	2910.68	−	2910.68i	0.124641	−	0.124641i
$818$	1841.14	−	1841.14i	0.0786968	−	0.0786968i
$819$		0			0
$820$		0			0
$821$			5783.29i			0.245844i	0.992416	+	0.122922i	$0.0392265\pi$
$821$			5783.29i			0.245844i	−0.992416	+	0.122922i	$0.960773\pi$
$822$		0			0
$823$	−2021.92	−	2021.92i	−0.0856375	−	0.0856375i	0.662990	−	0.748628i	$-0.269287\pi$
$823$	−2021.92	−	2021.92i	−0.0856375	−	0.0856375i	−0.748628	+	0.662990i	$0.769287\pi$
$824$	5269.62			0.222786
$825$		0			0
$826$	−4189.47			−0.176477
$827$	18025.3	+	18025.3i	0.757922	+	0.757922i	0.975944	−	0.218022i	$-0.0699605\pi$
$827$	18025.3	+	18025.3i	0.757922	+	0.757922i	−0.218022	+	0.975944i	$0.569961\pi$
$828$		0			0
$829$		−	42400.5i		−	1.77640i	−0.459462	−	0.888198i	$-0.651958\pi$
$829$		−	42400.5i		−	1.77640i	0.459462	−	0.888198i	$-0.348042\pi$
$830$		0			0
$831$		0			0
$832$	1122.97	−	1122.97i	0.0467933	−	0.0467933i
$833$	7493.75	−	7493.75i	0.311696	−	0.311696i
$834$		0			0
$835$		0			0
$836$			20886.7i			0.864094i
$837$		0			0
$838$	−2439.95	−	2439.95i	−0.100581	−	0.100581i
$839$	38073.9			1.56670			0.783348	−	0.621584i	$-0.213510\pi$
$839$	38073.9			1.56670			0.783348	+	0.621584i	$0.213510\pi$
$840$		0			0
$841$	−14571.1			−0.597447
$842$	2611.04	+	2611.04i	0.106868	+	0.106868i
$843$		0			0
$844$			31102.3i			1.26847i
$845$		0			0
$846$		0			0
$847$	−8236.11	+	8236.11i	−0.334116	+	0.334116i
$848$	13452.2	−	13452.2i	0.544754	−	0.544754i
$849$		0			0
$850$		0			0
$851$			66136.1i			2.66406i
$852$		0			0
$853$	26447.7	+	26447.7i	1.06161	+	1.06161i	0.997973	+	0.0636372i	$0.0202701\pi$
$853$	26447.7	+	26447.7i	1.06161	+	1.06161i	0.0636372	+	0.997973i	$0.479730\pi$
$854$	−2291.88			−0.0918342
$855$		0			0
$856$	1978.43			0.0789967
$857$	18997.5	+	18997.5i	0.757227	+	0.757227i	0.975817	−	0.218590i	$-0.0701457\pi$
$857$	18997.5	+	18997.5i	0.757227	+	0.757227i	−0.218590	+	0.975817i	$0.570146\pi$
$858$		0			0
$859$		−	29326.5i		−	1.16485i	−0.812885	−	0.582425i	$-0.802104\pi$
$859$		−	29326.5i		−	1.16485i	0.812885	−	0.582425i	$-0.197896\pi$
$860$		0			0
$861$		0			0
$862$	−2414.95	+	2414.95i	−0.0954219	+	0.0954219i
$863$	−23070.8	+	23070.8i	−0.910011	+	0.910011i	−0.996273	−	0.0862616i	$-0.972508\pi$
$863$	−23070.8	+	23070.8i	−0.910011	+	0.910011i	0.0862616	+	0.996273i	$0.472508\pi$
$864$		0			0
$865$		0			0
$866$		−	2379.32i		−	0.0933633i
$867$		0			0
$868$	−3394.59	−	3394.59i	−0.132742	−	0.132742i
$869$	11383.8			0.444381
$870$		0			0
$871$	−2492.71			−0.0969716
$872$	4268.84	+	4268.84i	0.165781	+	0.165781i
$873$		0			0
$874$		−	6688.68i		−	0.258865i
$875$		0			0
$876$		0			0
$877$	−20252.6	+	20252.6i	−0.779795	+	0.779795i	−0.979796	−	0.200001i	$-0.935906\pi$
$877$	−20252.6	+	20252.6i	−0.779795	+	0.779795i	0.200001	+	0.979796i	$0.435906\pi$
$878$	3022.67	−	3022.67i	0.116185	−	0.116185i
$879$		0			0
$880$		0			0
$881$		−	15547.7i		−	0.594569i	−0.954789	−	0.297284i	$-0.903919\pi$
$881$		−	15547.7i		−	0.594569i	0.954789	−	0.297284i	$-0.0960809\pi$
$882$		0			0
$883$	−17599.2	−	17599.2i	−0.670737	−	0.670737i	0.287149	−	0.957886i	$-0.407293\pi$
$883$	−17599.2	−	17599.2i	−0.670737	−	0.670737i	−0.957886	+	0.287149i	$0.907293\pi$
$884$	−2658.66			−0.101154
$885$		0			0
$886$	−844.087			−0.0320064
$887$	−9099.97	−	9099.97i	−0.344472	−	0.344472i	0.513573	−	0.858046i	$-0.328321\pi$
$887$	−9099.97	−	9099.97i	−0.344472	−	0.344472i	−0.858046	+	0.513573i	$0.828321\pi$
$888$		0			0
$889$			27569.2i			1.04009i
$890$		0			0
$891$		0			0
$892$	−28205.9	+	28205.9i	−1.05875	+	1.05875i
$893$	−24243.0	+	24243.0i	−0.908467	+	0.908467i
$894$		0			0
$895$		0			0
$896$			16846.0i			0.628109i
$897$		0			0
$898$	−1812.47	−	1812.47i	−0.0673528	−	0.0673528i
$899$	−2851.67			−0.105794
$900$		0			0
$901$	−30426.8			−1.12504
$902$	3657.68	+	3657.68i	0.135019	+	0.135019i
$903$		0			0
$904$		−	9883.30i		−	0.363621i
$905$		0			0
$906$		0			0
$907$	−28827.2	+	28827.2i	−1.05534	+	1.05534i	−0.0569624	+	0.998376i	$0.518142\pi$
$907$	−28827.2	+	28827.2i	−1.05534	+	1.05534i	−0.998376	+	0.0569624i	$0.981858\pi$
$908$	13590.9	−	13590.9i	0.496728	−	0.496728i
$909$		0			0
$910$		0			0
$911$			32922.1i			1.19732i	0.801003	+	0.598660i	$0.204300\pi$
$911$			32922.1i			1.19732i	−0.801003	+	0.598660i	$0.795700\pi$
$912$		0			0
$913$	−18263.3	−	18263.3i	−0.662023	−	0.662023i
$914$	5219.72			0.188898
$915$		0			0
$916$	27167.0			0.979938
$917$	9474.99	+	9474.99i	0.341212	+	0.341212i
$918$		0			0
$919$		−	28643.9i		−	1.02815i	−0.857744	−	0.514077i	$-0.828135\pi$
$919$		−	28643.9i		−	1.02815i	0.857744	−	0.514077i	$-0.171865\pi$
$920$		0			0
$921$		0			0
$922$	3830.67	−	3830.67i	0.136829	−	0.136829i
$923$	−1523.92	+	1523.92i	−0.0543450	+	0.0543450i
$924$		0			0
$925$		0			0
$926$		−	1799.31i		−	0.0638541i
$927$		0			0
$928$	5326.61	+	5326.61i	0.188421	+	0.188421i
$929$	−12080.7			−0.426648			−0.213324	−	0.976981i	$-0.568429\pi$
$929$	−12080.7			−0.426648			−0.213324	+	0.976981i	$0.568429\pi$
$930$		0			0
$931$	10507.3			0.369885
$932$	−8383.98	−	8383.98i	−0.294664	−	0.294664i
$933$		0			0
$934$		−	2450.08i		−	0.0858343i
$935$		0			0
$936$		0			0
$937$	18170.0	−	18170.0i	0.633500	−	0.633500i	−0.315444	−	0.948944i	$-0.602154\pi$
$937$	18170.0	−	18170.0i	0.633500	−	0.633500i	0.948944	+	0.315444i	$0.102154\pi$
$938$	4324.31	−	4324.31i	0.150526	−	0.150526i
$939$		0			0
$940$		0			0
$941$		−	7693.26i		−	0.266518i	−0.991081	−	0.133259i	$-0.957456\pi$
$941$		−	7693.26i		−	0.266518i	0.991081	−	0.133259i	$-0.0425442\pi$
$942$		0			0
$943$	55354.4	+	55354.4i	1.91155	+	1.91155i
$944$	29019.4			1.00053
$945$		0			0
$946$	−492.819			−0.0169375
$947$	−9792.71	−	9792.71i	−0.336030	−	0.336030i	0.518841	−	0.854871i	$-0.326364\pi$
$947$	−9792.71	−	9792.71i	−0.336030	−	0.336030i	−0.854871	+	0.518841i	$0.826364\pi$
$948$		0			0
$949$		−	373.216i		−	0.0127662i
$950$		0			0
$951$		0			0
$952$	9321.99	−	9321.99i	0.317361	−	0.317361i
$953$	22620.8	−	22620.8i	0.768899	−	0.768899i	−0.209014	−	0.977913i	$-0.567025\pi$
$953$	22620.8	−	22620.8i	0.768899	−	0.768899i	0.977913	+	0.209014i	$0.0670254\pi$
$954$		0			0
$955$		0			0
$956$		−	30627.4i		−	1.03615i
$957$		0			0
$958$	3059.01	+	3059.01i	0.103165	+	0.103165i
$959$	−19901.5			−0.670130
$960$		0			0
$961$	−28962.7			−0.972197
$962$	−389.984	−	389.984i	−0.0130702	−	0.0130702i
$963$		0			0
$964$			37503.2i			1.25300i
$965$		0			0
$966$		0			0
$967$	4426.36	−	4426.36i	0.147200	−	0.147200i	−0.629666	−	0.776866i	$-0.716808\pi$
$967$	4426.36	−	4426.36i	0.147200	−	0.147200i	0.776866	+	0.629666i	$0.216808\pi$
$968$	−2493.81	+	2493.81i	−0.0828037	+	0.0828037i
$969$		0			0
$970$		0			0
$971$		−	36943.3i		−	1.22097i	−0.792026	−	0.610487i	$-0.790974\pi$
$971$		−	36943.3i		−	1.22097i	0.792026	−	0.610487i	$-0.209026\pi$
$972$		0			0
$973$	−20752.0	−	20752.0i	−0.683741	−	0.683741i
$974$	−1882.32			−0.0619236
$975$		0			0
$976$	15875.2			0.520650
$977$	14789.2	+	14789.2i	0.484287	+	0.484287i	0.906498	−	0.422211i	$-0.138746\pi$
$977$	14789.2	+	14789.2i	0.484287	+	0.484287i	−0.422211	+	0.906498i	$0.638746\pi$
$978$		0			0
$979$			3915.98i			0.127840i
$980$		0			0
$981$		0			0
$982$	−5410.00	+	5410.00i	−0.175805	+	0.175805i
$983$	12134.8	−	12134.8i	0.393733	−	0.393733i	−0.482283	−	0.876015i	$-0.660192\pi$
$983$	12134.8	−	12134.8i	0.393733	−	0.393733i	0.876015	+	0.482283i	$0.160192\pi$
$984$		0			0
$985$		0			0
$986$		−	3874.54i		−	0.125142i
$987$		0			0
$988$	−1863.91	−	1863.91i	−0.0600190	−	0.0600190i
$989$	−7458.19			−0.239794
$990$		0			0
$991$	29327.6			0.940084			0.470042	−	0.882644i	$-0.344239\pi$
$991$	29327.6			0.940084			0.470042	+	0.882644i	$0.344239\pi$
$992$	−1547.15	−	1547.15i	−0.0495182	−	0.0495182i
$993$		0			0
$994$		−	5287.34i		−	0.168717i
$995$		0			0
$996$		0			0
$997$	44483.8	−	44483.8i	1.41306	−	1.41306i	0.677912	−	0.735143i	$-0.262885\pi$
$997$	44483.8	−	44483.8i	1.41306	−	1.41306i	0.735143	−	0.677912i	$-0.237115\pi$
$998$	−2078.84	+	2078.84i	−0.0659365	+	0.0659365i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.f.c.143.3		12
3.2	odd	2	inner	225.4.f.c.143.4		12
5.2	odd	4	inner	225.4.f.c.107.4		12
5.3	odd	4		45.4.f.a.17.3	yes	12
5.4	even	2		45.4.f.a.8.4	yes	12
15.2	even	4	inner	225.4.f.c.107.3		12
15.8	even	4		45.4.f.a.17.4	yes	12
15.14	odd	2		45.4.f.a.8.3	✓	12
20.3	even	4		720.4.w.d.17.1		12
20.19	odd	2		720.4.w.d.593.6		12
60.23	odd	4		720.4.w.d.17.6		12
60.59	even	2		720.4.w.d.593.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.f.a.8.3	✓	12	15.14	odd	2
45.4.f.a.8.4	yes	12	5.4	even	2
45.4.f.a.17.3	yes	12	5.3	odd	4
45.4.f.a.17.4	yes	12	15.8	even	4
225.4.f.c.107.3		12	15.2	even	4	inner
225.4.f.c.107.4		12	5.2	odd	4	inner
225.4.f.c.143.3		12	1.1	even	1	trivial
225.4.f.c.143.4		12	3.2	odd	2	inner
720.4.w.d.17.1		12	20.3	even	4
720.4.w.d.17.6		12	60.23	odd	4
720.4.w.d.593.1		12	60.59	even	2
720.4.w.d.593.6		12	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.287902 - 0.287902i) q^{2} -7.83422i q^{4} +(-15.0557 + 15.0557i) q^{7} +(-4.55871 + 4.55871i) q^{8} +O(q^{10})\)	\(q+(-0.287902 - 0.287902i) q^{2} -7.83422i q^{4} +(-15.0557 + 15.0557i) q^{7} +(-4.55871 + 4.55871i) q^{8} +27.9992i q^{11} +(-2.49862 - 2.49862i) q^{13} +8.66913 q^{14} -60.0489 q^{16} +(67.9104 + 67.9104i) q^{17} +95.2200i q^{19} +(8.06104 - 8.06104i) q^{22} +(121.994 - 121.994i) q^{23} +1.43872i q^{26} +(117.950 + 117.950i) q^{28} +99.0852 q^{29} -28.7800 q^{31} +(53.7578 + 53.7578i) q^{32} -39.1031i q^{34} +(-271.064 + 271.064i) q^{37} +(27.4140 - 27.4140i) q^{38} +453.748i q^{41} +(-30.5679 - 30.5679i) q^{43} +219.352 q^{44} -70.2445 q^{46} +(254.600 + 254.600i) q^{47} -110.348i q^{49} +(-19.5748 + 19.5748i) q^{52} +(-224.021 + 224.021i) q^{53} -137.269i q^{56} +(-28.5268 - 28.5268i) q^{58} -483.263 q^{59} -264.372 q^{61} +(8.28582 + 8.28582i) q^{62} +449.437i q^{64} +(498.817 - 498.817i) q^{67} +(532.025 - 532.025i) q^{68} -609.904i q^{71} +(74.6843 + 74.6843i) q^{73} +156.080 q^{74} +745.975 q^{76} +(-421.548 - 421.548i) q^{77} -406.574i q^{79} +(130.635 - 130.635i) q^{82} +(-652.278 + 652.278i) q^{83} +17.6011i q^{86} +(-127.640 - 127.640i) q^{88} +139.860 q^{89} +75.2369 q^{91} +(-955.726 - 955.726i) q^{92} -146.600i q^{94} +(-557.633 + 557.633i) q^{97} +(-31.7693 + 31.7693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7}+O(q^{10}) \) 12 * q - 24 * q^7	\( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97}+O(q^{100}) \) 12 * q - 24 * q^7 + 108 * q^13 - 648 * q^16 - 1056 * q^22 + 576 * q^28 - 1248 * q^31 - 828 * q^37 + 96 * q^43 + 672 * q^46 + 312 * q^52 + 3864 * q^58 + 96 * q^61 - 1632 * q^67 - 3972 * q^73 - 480 * q^76 + 7848 * q^82 - 7968 * q^88 + 4752 * q^91 - 2772 * q^97

Introduction

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