LMFDB - Embedded newform 495.3.j.c.298.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,3,Mod(298,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.298"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			298.5
Character	$\chi$	$=$	495.298
Dual form			495.3.j.c.397.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89153 + 1.89153i) q^{2} -3.15579i q^{4} +(-3.98330 - 3.02214i) q^{5} +(-9.02252 + 9.02252i) q^{7} +(-1.59685 - 1.59685i) q^{8} +(13.2510 - 1.81805i) q^{10} -3.31662 q^{11} +(-9.63142 - 9.63142i) q^{13} -34.1328i q^{14} +18.6641 q^{16} +(-2.76788 + 2.76788i) q^{17} +34.0632i q^{19} +(-9.53725 + 12.5704i) q^{20} +(6.27350 - 6.27350i) q^{22} +(-20.6705 - 20.6705i) q^{23} +(6.73329 + 24.0762i) q^{25} +36.4363 q^{26} +(28.4732 + 28.4732i) q^{28} -23.7854i q^{29} +27.0328 q^{31} +(-28.9164 + 28.9164i) q^{32} -10.4711i q^{34} +(63.2067 - 8.67201i) q^{35} +(37.1952 - 37.1952i) q^{37} +(-64.4316 - 64.4316i) q^{38} +(1.53481 + 11.1866i) q^{40} +43.6022 q^{41} +(-20.6445 - 20.6445i) q^{43} +10.4666i q^{44} +78.1978 q^{46} +(7.41800 - 7.41800i) q^{47} -113.812i q^{49} +(-58.2771 - 32.8047i) q^{50} +(-30.3947 + 30.3947i) q^{52} +(36.6271 + 36.6271i) q^{53} +(13.2111 + 10.0233i) q^{55} +28.8152 q^{56} +(44.9908 + 44.9908i) q^{58} +102.317i q^{59} -16.6024 q^{61} +(-51.1333 + 51.1333i) q^{62} -34.7362i q^{64} +(9.25725 + 67.4723i) q^{65} +(10.5885 - 10.5885i) q^{67} +(8.73484 + 8.73484i) q^{68} +(-103.154 + 135.961i) q^{70} -17.2149 q^{71} +(8.68911 + 8.68911i) q^{73} +140.712i q^{74} +107.496 q^{76} +(29.9243 - 29.9243i) q^{77} +105.357i q^{79} +(-74.3448 - 56.4058i) q^{80} +(-82.4750 + 82.4750i) q^{82} +(5.74103 + 5.74103i) q^{83} +(19.3902 - 2.66035i) q^{85} +78.0996 q^{86} +(5.29615 + 5.29615i) q^{88} -172.638i q^{89} +173.799 q^{91} +(-65.2318 + 65.2318i) q^{92} +28.0628i q^{94} +(102.944 - 135.684i) q^{95} +(75.1277 - 75.1277i) q^{97} +(215.279 + 215.279i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) $ 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.89153	+	1.89153i	−0.945766	+	0.945766i	−0.998603	−	0.0528369i	$-0.983174\pi$
$2$	−1.89153	+	1.89153i	−0.945766	+	0.945766i	0.0528369	+	0.998603i	$0.483174\pi$
$3$		0			0
$3$		0			0
$4$		−	3.15579i		−	0.788948i
$5$	−3.98330	−	3.02214i	−0.796659	−	0.604429i
$5$	−3.98330	−	3.02214i	−0.796659	−	0.604429i
$6$		0			0
$7$	−9.02252	+	9.02252i	−1.28893	+	1.28893i	−0.353495	+	0.935436i	$0.615007\pi$
$7$	−9.02252	+	9.02252i	−1.28893	+	1.28893i	−0.935436	+	0.353495i	$0.884993\pi$
$8$	−1.59685	−	1.59685i	−0.199606	−	0.199606i
$9$		0			0
$10$	13.2510	−	1.81805i	1.32510	−	0.181805i
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$		0			0
$13$	−9.63142	−	9.63142i	−0.740878	−	0.740878i	0.231869	−	0.972747i	$-0.425516\pi$
$13$	−9.63142	−	9.63142i	−0.740878	−	0.740878i	−0.972747	+	0.231869i	$0.925516\pi$
$14$		−	34.1328i		−	2.43806i
$15$		0			0
$16$	18.6641			1.16651
$17$	−2.76788	+	2.76788i	−0.162816	+	0.162816i	−0.783813	−	0.620997i	$-0.786728\pi$
$17$	−2.76788	+	2.76788i	−0.162816	+	0.162816i	0.620997	+	0.783813i	$0.286728\pi$
$18$		0			0
$19$			34.0632i			1.79280i	0.443249	+	0.896399i	$0.353826\pi$
$19$			34.0632i			1.79280i	−0.443249	+	0.896399i	$0.646174\pi$
$20$	−9.53725	+	12.5704i	−0.476863	+	0.628522i
$21$		0			0
$22$	6.27350	−	6.27350i	0.285159	−	0.285159i
$23$	−20.6705	−	20.6705i	−0.898717	−	0.898717i	0.0966055	−	0.995323i	$-0.469201\pi$
$23$	−20.6705	−	20.6705i	−0.898717	−	0.898717i	−0.995323	+	0.0966055i	$0.969201\pi$
$24$		0			0
$25$	6.73329	+	24.0762i	0.269331	+	0.963048i
$26$	36.4363			1.40139
$27$		0			0
$28$	28.4732	+	28.4732i	1.01690	+	1.01690i
$29$		−	23.7854i		−	0.820186i	−0.912044	−	0.410093i	$-0.865496\pi$
$29$		−	23.7854i		−	0.820186i	0.912044	−	0.410093i	$-0.134504\pi$
$30$		0			0
$31$	27.0328			0.872024			0.436012	−	0.899941i	$-0.356390\pi$
$31$	27.0328			0.872024			0.436012	+	0.899941i	$0.356390\pi$
$32$	−28.9164	+	28.9164i	−0.903639	+	0.903639i
$33$		0			0
$34$		−	10.4711i		−	0.307972i
$35$	63.2067	−	8.67201i	1.80591	−	0.247772i
$36$		0			0
$37$	37.1952	−	37.1952i	1.00528	−	1.00528i	0.00528942	−	0.999986i	$-0.498316\pi$
$37$	37.1952	−	37.1952i	1.00528	−	1.00528i	0.999986	−	0.00528942i	$-0.00168368\pi$
$38$	−64.4316	−	64.4316i	−1.69557	−	1.69557i
$39$		0			0
$40$	1.53481	+	11.1866i	0.0383704	+	0.279666i
$41$	43.6022			1.06347			0.531734	−	0.846911i	$-0.321540\pi$
$41$	43.6022			1.06347			0.531734	+	0.846911i	$0.321540\pi$
$42$		0			0
$43$	−20.6445	−	20.6445i	−0.480105	−	0.480105i	0.425060	−	0.905165i	$-0.360253\pi$
$43$	−20.6445	−	20.6445i	−0.480105	−	0.480105i	−0.905165	+	0.425060i	$0.860253\pi$
$44$			10.4666i			0.237877i
$45$		0			0
$46$	78.1978			1.69995
$47$	7.41800	−	7.41800i	0.157830	−	0.157830i	−0.623775	−	0.781604i	$-0.714402\pi$
$47$	7.41800	−	7.41800i	0.157830	−	0.157830i	0.781604	+	0.623775i	$0.214402\pi$
$48$		0			0
$49$		−	113.812i		−	2.32269i
$50$	−58.2771	−	32.8047i	−1.16554	−	0.656093i
$51$		0			0
$52$	−30.3947	+	30.3947i	−0.584514	+	0.584514i
$53$	36.6271	+	36.6271i	0.691078	+	0.691078i	0.962469	−	0.271391i	$-0.0874838\pi$
$53$	36.6271	+	36.6271i	0.691078	+	0.691078i	−0.271391	+	0.962469i	$0.587484\pi$
$54$		0			0
$55$	13.2111	+	10.0233i	0.240202	+	0.182242i
$56$	28.8152			0.514558
$57$		0			0
$58$	44.9908	+	44.9908i	0.775704	+	0.775704i
$59$			102.317i			1.73418i	0.498150	+	0.867091i	$0.334013\pi$
$59$			102.317i			1.73418i	−0.498150	+	0.867091i	$0.665987\pi$
$60$		0			0
$61$	−16.6024			−0.272171			−0.136086	−	0.990697i	$-0.543452\pi$
$61$	−16.6024			−0.272171			−0.136086	+	0.990697i	$0.543452\pi$
$62$	−51.1333	+	51.1333i	−0.824731	+	0.824731i
$63$		0			0
$64$		−	34.7362i		−	0.542753i
$65$	9.25725	+	67.4723i	0.142419	+	1.03804i
$66$		0			0
$67$	10.5885	−	10.5885i	0.158037	−	0.158037i	−0.623659	−	0.781696i	$-0.714355\pi$
$67$	10.5885	−	10.5885i	0.158037	−	0.158037i	0.781696	+	0.623659i	$0.214355\pi$
$68$	8.73484	+	8.73484i	0.128454	+	0.128454i
$69$		0			0
$70$	−103.154	+	135.961i	−1.47363	+	1.94230i
$71$	−17.2149			−0.242463			−0.121232	−	0.992624i	$-0.538684\pi$
$71$	−17.2149			−0.242463			−0.121232	+	0.992624i	$0.538684\pi$
$72$		0			0
$73$	8.68911	+	8.68911i	0.119029	+	0.119029i	0.764112	−	0.645083i	$-0.223177\pi$
$73$	8.68911	+	8.68911i	0.119029	+	0.119029i	−0.645083	+	0.764112i	$0.723177\pi$
$74$			140.712i			1.90151i
$75$		0			0
$76$	107.496			1.41442
$77$	29.9243	−	29.9243i	0.388627	−	0.388627i
$78$		0			0
$79$			105.357i			1.33363i	0.745222	+	0.666816i	$0.232343\pi$
$79$			105.357i			1.33363i	−0.745222	+	0.666816i	$0.767657\pi$
$80$	−74.3448	−	56.4058i	−0.929310	−	0.705072i
$81$		0			0
$82$	−82.4750	+	82.4750i	−1.00579	+	1.00579i
$83$	5.74103	+	5.74103i	0.0691690	+	0.0691690i	0.740845	−	0.671676i	$-0.234425\pi$
$83$	5.74103	+	5.74103i	0.0691690	+	0.0691690i	−0.671676	+	0.740845i	$0.734425\pi$
$84$		0			0
$85$	19.3902	−	2.66035i	0.228120	−	0.0312982i
$86$	78.0996			0.908134
$87$		0			0
$88$	5.29615	+	5.29615i	0.0601836	+	0.0601836i
$89$		−	172.638i		−	1.93975i	−0.243609	−	0.969874i	$-0.578331\pi$
$89$		−	172.638i		−	1.93975i	0.243609	−	0.969874i	$-0.421669\pi$
$90$		0			0
$91$	173.799			1.90988
$92$	−65.2318	+	65.2318i	−0.709041	+	0.709041i
$93$		0			0
$94$			28.0628i			0.298540i
$95$	102.944	−	135.684i	1.08362	−	1.42825i
$96$		0			0
$97$	75.1277	−	75.1277i	0.774512	−	0.774512i	−0.204380	−	0.978892i	$-0.565518\pi$
$97$	75.1277	−	75.1277i	0.774512	−	0.774512i	0.978892	+	0.204380i	$0.0655177\pi$
$98$	215.279	+	215.279i	2.19672	+	2.19672i
$99$		0			0
$100$	75.9794	−	21.2488i	0.759794	−	0.212488i
$101$	−28.6221			−0.283387			−0.141693	−	0.989911i	$-0.545255\pi$
$101$	−28.6221			−0.283387			−0.141693	+	0.989911i	$0.545255\pi$
$102$		0			0
$103$	−52.5309	−	52.5309i	−0.510009	−	0.510009i	0.404520	−	0.914529i	$-0.367439\pi$
$103$	−52.5309	−	52.5309i	−0.510009	−	0.510009i	−0.914529	+	0.404520i	$0.867439\pi$
$104$			30.7599i			0.295768i
$105$		0			0
$106$	−138.563			−1.30720
$107$	−106.333	+	106.333i	−0.993765	+	0.993765i	−0.999981	−	0.00621527i	$-0.998022\pi$
$107$	−106.333	+	106.333i	−0.993765	+	0.993765i	0.00621527	+	0.999981i	$0.498022\pi$
$108$		0			0
$109$		−	101.439i		−	0.930629i	−0.885146	−	0.465314i	$-0.845941\pi$
$109$		−	101.439i		−	0.930629i	0.885146	−	0.465314i	$-0.154059\pi$
$110$	−43.9487	+	6.02978i	−0.399533	+	0.0548162i
$111$		0			0
$112$	−168.398	+	168.398i	−1.50355	+	1.50355i
$113$	135.825	+	135.825i	1.20199	+	1.20199i	0.973561	+	0.228428i	$0.0733584\pi$
$113$	135.825	+	135.825i	1.20199	+	1.20199i	0.228428	+	0.973561i	$0.426642\pi$
$114$		0			0
$115$	19.8675	+	144.806i	0.172761	+	1.25918i
$116$	−75.0617			−0.647084
$117$		0			0
$118$	−193.535	−	193.535i	−1.64013	−	1.64013i
$119$		−	49.9465i		−	0.419718i
$120$		0			0
$121$	11.0000			0.0909091
$122$	31.4041	−	31.4041i	0.257410	−	0.257410i
$123$		0			0
$124$		−	85.3097i		−	0.687982i
$125$	45.9410	−	116.252i	0.367528	−	0.930012i
$126$		0			0
$127$	16.2124	−	16.2124i	0.127657	−	0.127657i	−0.640392	−	0.768048i	$-0.721228\pi$
$127$	16.2124	−	16.2124i	0.127657	−	0.127657i	0.768048	+	0.640392i	$0.221228\pi$
$128$	−49.9611	−	49.9611i	−0.390321	−	0.390321i
$129$		0			0
$130$	−145.136	−	110.116i	−1.11643	−	0.847044i
$131$	−60.6113			−0.462682			−0.231341	−	0.972873i	$-0.574311\pi$
$131$	−60.6113			−0.462682			−0.231341	+	0.972873i	$0.574311\pi$
$132$		0			0
$133$	−307.336	−	307.336i	−2.31079	−	2.31079i
$134$			40.0569i			0.298932i
$135$		0			0
$136$	8.83977			0.0649983
$137$	−10.1705	+	10.1705i	−0.0742372	+	0.0742372i	−0.743250	−	0.669013i	$-0.766717\pi$
$137$	−10.1705	+	10.1705i	−0.0742372	+	0.0742372i	0.669013	+	0.743250i	$0.266717\pi$
$138$		0			0
$139$		−	159.552i		−	1.14786i	−0.818905	−	0.573928i	$-0.805419\pi$
$139$		−	159.552i		−	1.14786i	0.818905	−	0.573928i	$-0.194581\pi$
$140$	−27.3670	−	199.467i	−0.195479	−	1.42477i
$141$		0			0
$142$	32.5625	−	32.5625i	0.229314	−	0.229314i
$143$	31.9438	+	31.9438i	0.223383	+	0.223383i
$144$		0			0
$145$	−71.8829	+	94.7442i	−0.495744	+	0.653408i
$146$	−32.8715			−0.225147
$147$		0			0
$148$	−117.380	−	117.380i	−0.793110	−	0.793110i
$149$		−	112.746i		−	0.756684i	−0.925666	−	0.378342i	$-0.876494\pi$
$149$		−	112.746i		−	0.756684i	0.925666	−	0.378342i	$-0.123506\pi$
$150$		0			0
$151$	271.977			1.80117			0.900585	−	0.434680i	$-0.143138\pi$
$151$	271.977			1.80117			0.900585	+	0.434680i	$0.143138\pi$
$152$	54.3937	−	54.3937i	0.357854	−	0.357854i
$153$		0			0
$154$			113.206i			0.735102i
$155$	−107.679	−	81.6969i	−0.694706	−	0.527077i
$156$		0			0
$157$	−43.5369	+	43.5369i	−0.277305	+	0.277305i	−0.832032	−	0.554727i	$-0.812823\pi$
$157$	−43.5369	+	43.5369i	−0.277305	+	0.277305i	0.554727	+	0.832032i	$0.312823\pi$
$158$	−199.286	−	199.286i	−1.26130	−	1.26130i
$159$		0			0
$160$	202.572	−	27.7931i	1.26608	−	0.173707i
$161$	373.000			2.31677
$162$		0			0
$163$	52.9791	+	52.9791i	0.325025	+	0.325025i	0.850691	−	0.525666i	$-0.176184\pi$
$163$	52.9791	+	52.9791i	0.325025	+	0.325025i	−0.525666	+	0.850691i	$0.676184\pi$
$164$		−	137.599i		−	0.839021i
$165$		0			0
$166$	−21.7187			−0.130835
$167$	−64.9985	+	64.9985i	−0.389213	+	0.389213i	−0.874407	−	0.485194i	$-0.838749\pi$
$167$	−64.9985	+	64.9985i	−0.389213	+	0.389213i	0.485194	+	0.874407i	$0.338749\pi$
$168$		0			0
$169$			16.5283i			0.0978007i
$170$	−31.6450	+	41.7093i	−0.186147	+	0.245349i
$171$		0			0
$172$	−65.1498	+	65.1498i	−0.378778	+	0.378778i
$173$	−70.4358	−	70.4358i	−0.407143	−	0.407143i	0.473598	−	0.880741i	$-0.342955\pi$
$173$	−70.4358	−	70.4358i	−0.407143	−	0.407143i	−0.880741	+	0.473598i	$0.842955\pi$
$174$		0			0
$175$	−277.979	−	156.477i	−1.58845	−	0.894153i
$176$	−61.9020			−0.351716
$177$		0			0
$178$	326.549	+	326.549i	1.83455	+	1.83455i
$179$		−	320.667i		−	1.79144i	−0.444620	−	0.895719i	$-0.646661\pi$
$179$		−	320.667i		−	1.79144i	0.444620	−	0.895719i	$-0.353339\pi$
$180$		0			0
$181$	−149.775			−0.827485			−0.413742	−	0.910394i	$-0.635779\pi$
$181$	−149.775			−0.827485			−0.413742	+	0.910394i	$0.635779\pi$
$182$	−328.747	+	328.747i	−1.80630	+	1.80630i
$183$		0			0
$184$			66.0154i			0.358779i
$185$	−260.569	+	35.7502i	−1.40848	+	0.193244i
$186$		0			0
$187$	9.18001	−	9.18001i	0.0490910	−	0.0490910i
$188$	−23.4096	−	23.4096i	−0.124519	−	0.124519i
$189$		0			0
$190$	61.9285	+	451.371i	0.325939	+	2.37564i
$191$	−362.459			−1.89769			−0.948845	−	0.315741i	$-0.897747\pi$
$191$	−362.459			−1.89769			−0.948845	+	0.315741i	$0.897747\pi$
$192$		0			0
$193$	68.5121	+	68.5121i	0.354985	+	0.354985i	0.861960	−	0.506976i	$-0.169237\pi$
$193$	68.5121	+	68.5121i	0.354985	+	0.354985i	−0.506976	+	0.861960i	$0.669237\pi$
$194$			284.213i			1.46501i
$195$		0			0
$196$	−359.166			−1.83248
$197$	154.787	−	154.787i	0.785719	−	0.785719i	−0.195070	−	0.980789i	$-0.562493\pi$
$197$	154.787	−	154.787i	0.785719	−	0.785719i	0.980789	+	0.195070i	$0.0624934\pi$
$198$		0			0
$199$		−	272.319i		−	1.36844i	−0.729277	−	0.684219i	$-0.760143\pi$
$199$		−	272.319i		−	1.36844i	0.729277	−	0.684219i	$-0.239857\pi$
$200$	27.6940	−	49.1981i	0.138470	−	0.245991i
$201$		0			0
$202$	54.1395	−	54.1395i	0.268018	−	0.268018i
$203$	214.604	+	214.604i	1.05716	+	1.05716i
$204$		0			0
$205$	−173.681	−	131.772i	−0.847222	−	0.642791i
$206$	198.728			0.964698
$207$		0			0
$208$	−179.762	−	179.762i	−0.864241	−	0.864241i
$209$		−	112.975i		−	0.540549i
$210$		0			0
$211$	38.2636			0.181344			0.0906720	−	0.995881i	$-0.471098\pi$
$211$	38.2636			0.181344			0.0906720	+	0.995881i	$0.471098\pi$
$212$	115.587	−	115.587i	0.545224	−	0.545224i
$213$		0			0
$214$		−	402.264i		−	1.87974i
$215$	19.8425	+	144.624i	0.0922907	+	0.672670i
$216$		0			0
$217$	−243.904	+	243.904i	−1.12398	+	1.12398i
$218$	191.874	+	191.874i	0.880157	+	0.880157i
$219$		0			0
$220$	31.6315	−	41.6915i	0.143780	−	0.189507i
$221$	53.3171			0.241254
$222$		0			0
$223$	28.1568	+	28.1568i	0.126264	+	0.126264i	0.767415	−	0.641151i	$-0.221543\pi$
$223$	28.1568	+	28.1568i	0.126264	+	0.126264i	−0.641151	+	0.767415i	$0.721543\pi$
$224$		−	521.798i		−	2.32946i
$225$		0			0
$226$	−513.834			−2.27360
$227$	28.0968	−	28.0968i	0.123775	−	0.123775i	−0.642506	−	0.766281i	$-0.722105\pi$
$227$	28.0968	−	28.0968i	0.123775	−	0.123775i	0.766281	+	0.642506i	$0.222105\pi$
$228$		0			0
$229$		−	159.216i		−	0.695268i	−0.937630	−	0.347634i	$-0.886985\pi$
$229$		−	159.216i		−	0.695268i	0.937630	−	0.347634i	$-0.113015\pi$
$230$	−311.485	−	236.325i	−1.35428	−	1.02750i
$231$		0			0
$232$	−37.9817	+	37.9817i	−0.163714	+	0.163714i
$233$	8.00096	+	8.00096i	0.0343389	+	0.0343389i	0.724068	−	0.689729i	$-0.242270\pi$
$233$	8.00096	+	8.00096i	0.0343389	+	0.0343389i	−0.689729	+	0.724068i	$0.742270\pi$
$234$		0			0
$235$	−51.9663	+	7.12982i	−0.221133	+	0.0303396i
$236$	322.890			1.36818
$237$		0			0
$238$	94.4753	+	94.4753i	0.396955	+	0.396955i
$239$		−	91.1272i		−	0.381285i	−0.981659	−	0.190643i	$-0.938943\pi$
$239$		−	91.1272i		−	0.381285i	0.981659	−	0.190643i	$-0.0610572\pi$
$240$		0			0
$241$	159.288			0.660946			0.330473	−	0.943816i	$-0.392792\pi$
$241$	159.288			0.660946			0.330473	+	0.943816i	$0.392792\pi$
$242$	−20.8069	+	20.8069i	−0.0859787	+	0.0859787i
$243$		0			0
$244$			52.3938i			0.214729i
$245$	−343.956	+	453.346i	−1.40390	+	1.85039i
$246$		0			0
$247$	328.076	−	328.076i	1.32824	−	1.32824i
$248$	−43.1673	−	43.1673i	−0.174062	−	0.174062i
$249$		0			0
$250$	132.995	+	306.793i	0.531978	+	1.22717i
$251$	24.3526			0.0970225			0.0485112	−	0.998823i	$-0.484552\pi$
$251$	24.3526			0.0970225			0.0485112	+	0.998823i	$0.484552\pi$
$252$		0			0
$253$	68.5563	+	68.5563i	0.270973	+	0.270973i
$254$			61.3325i			0.241467i
$255$		0			0
$256$	327.951			1.28106
$257$	−251.126	+	251.126i	−0.977144	+	0.977144i	−0.999745	−	0.0226003i	$-0.992805\pi$
$257$	−251.126	+	251.126i	−0.977144	+	0.977144i	0.0226003	+	0.999745i	$0.492805\pi$
$258$		0			0
$259$			671.189i			2.59146i
$260$	212.928	−	29.2139i	0.818955	−	0.112361i
$261$		0			0
$262$	114.648	−	114.648i	0.437589	−	0.437589i
$263$	124.748	+	124.748i	0.474326	+	0.474326i	0.903311	−	0.428986i	$-0.141129\pi$
$263$	124.748	+	124.748i	0.474326	+	0.474326i	−0.428986	+	0.903311i	$0.641129\pi$
$264$		0			0
$265$	−35.2042	−	256.589i	−0.132846	−	0.968261i
$266$	1162.67			4.37094
$267$		0			0
$268$	−33.4150	−	33.4150i	−0.124683	−	0.124683i
$269$			4.21663i			0.0156752i	0.999969	+	0.00783760i	$0.00249481\pi$
$269$			4.21663i			0.0156752i	−0.999969	+	0.00783760i	$0.997505\pi$
$270$		0			0
$271$	287.404			1.06053			0.530267	−	0.847831i	$-0.322092\pi$
$271$	287.404			1.06053			0.530267	+	0.847831i	$0.322092\pi$
$272$	−51.6601	+	51.6601i	−0.189927	+	0.189927i
$273$		0			0
$274$		−	38.4756i		−	0.140422i
$275$	−22.3318	−	79.8517i	−0.0812065	−	0.290370i
$276$		0			0
$277$	151.000	−	151.000i	0.545126	−	0.545126i	−0.379901	−	0.925027i	$-0.624042\pi$
$277$	151.000	−	151.000i	0.545126	−	0.545126i	0.925027	+	0.379901i	$0.124042\pi$
$278$	301.798	+	301.798i	1.08560	+	1.08560i
$279$		0			0
$280$	−114.780	−	87.0838i	−0.409927	−	0.311014i
$281$	−14.4957			−0.0515863			−0.0257931	−	0.999667i	$-0.508211\pi$
$281$	−14.4957			−0.0515863			−0.0257931	+	0.999667i	$0.508211\pi$
$282$		0			0
$283$	−167.596	−	167.596i	−0.592213	−	0.592213i	0.346015	−	0.938229i	$-0.387535\pi$
$283$	−167.596	−	167.596i	−0.592213	−	0.592213i	−0.938229	+	0.346015i	$0.887535\pi$
$284$			54.3266i			0.191291i
$285$		0			0
$286$	−120.845			−0.422536
$287$	−393.402	+	393.402i	−1.37074	+	1.37074i
$288$		0			0
$289$			273.678i			0.946982i
$290$	−43.2430	−	315.181i	−0.149114	−	1.08683i
$291$		0			0
$292$	27.4210	−	27.4210i	0.0939076	−	0.0939076i
$293$	89.8118	+	89.8118i	0.306525	+	0.306525i	0.843560	−	0.537035i	$-0.180456\pi$
$293$	89.8118	+	89.8118i	0.306525	+	0.306525i	−0.537035	+	0.843560i	$0.680456\pi$
$294$		0			0
$295$	309.216	−	407.558i	1.04819	−	1.38155i
$296$	−118.790			−0.401319
$297$		0			0
$298$	213.263	+	213.263i	0.715646	+	0.715646i
$299$			398.172i			1.33168i
$300$		0			0
$301$	372.531			1.23765
$302$	−514.453	+	514.453i	−1.70349	+	1.70349i
$303$		0			0
$304$			635.760i			2.09131i
$305$	66.1324	+	50.1750i	0.216828	+	0.164508i
$306$		0			0
$307$	−34.6779	+	34.6779i	−0.112957	+	0.112957i	−0.761326	−	0.648369i	$-0.775451\pi$
$307$	−34.6779	+	34.6779i	−0.112957	+	0.112957i	0.648369	+	0.761326i	$0.275451\pi$
$308$	−94.4349	−	94.4349i	−0.306607	−	0.306607i
$309$		0			0
$310$	358.212	−	49.1469i	1.15552	−	0.158538i
$311$	362.566			1.16581			0.582903	−	0.812542i	$-0.301917\pi$
$311$	362.566			1.16581			0.582903	+	0.812542i	$0.301917\pi$
$312$		0			0
$313$	−17.9680	−	17.9680i	−0.0574059	−	0.0574059i	0.677821	−	0.735227i	$-0.262924\pi$
$313$	−17.9680	−	17.9680i	−0.0574059	−	0.0574059i	−0.735227	+	0.677821i	$0.762924\pi$
$314$		−	164.703i		−	0.524531i
$315$		0			0
$316$	332.484			1.05217
$317$	−30.4366	+	30.4366i	−0.0960146	+	0.0960146i	−0.753483	−	0.657468i	$-0.771628\pi$
$317$	−30.4366	+	30.4366i	−0.0960146	+	0.0960146i	0.657468	+	0.753483i	$0.271628\pi$
$318$		0			0
$319$			78.8872i			0.247295i
$320$	−104.978	+	138.365i	−0.328056	+	0.432389i
$321$		0			0
$322$	−705.542	+	705.542i	−2.19112	+	2.19112i
$323$	−94.2826	−	94.2826i	−0.291897	−	0.291897i
$324$		0			0
$325$	167.037	−	296.739i	0.513959	−	0.913043i
$326$	−200.423			−0.614796
$327$		0			0
$328$	−69.6262	−	69.6262i	−0.212275	−	0.212275i
$329$			133.858i			0.406863i
$330$		0			0
$331$	−484.224			−1.46291			−0.731455	−	0.681889i	$-0.761159\pi$
$331$	−484.224			−1.46291			−0.731455	+	0.681889i	$0.761159\pi$
$332$	18.1175	−	18.1175i	0.0545707	−	0.0545707i
$333$		0			0
$334$		−	245.894i		−	0.736209i
$335$	−74.1769	+	10.1771i	−0.221424	+	0.0303795i
$336$		0			0
$337$	345.058	−	345.058i	1.02391	−	1.02391i	0.0242030	−	0.999707i	$-0.492295\pi$
$337$	345.058	−	345.058i	1.02391	−	1.02391i	0.999707	−	0.0242030i	$-0.00770481\pi$
$338$	−31.2638	−	31.2638i	−0.0924966	−	0.0924966i
$339$		0			0
$340$	−8.39550	−	61.1914i	−0.0246926	−	0.179975i
$341$	−89.6575			−0.262925
$342$		0			0
$343$	584.766	+	584.766i	1.70486	+	1.70486i
$344$			65.9324i			0.191664i
$345$		0			0
$346$	266.463			0.770125
$347$	308.727	−	308.727i	0.889704	−	0.889704i	−0.104790	−	0.994494i	$-0.533417\pi$
$347$	308.727	−	308.727i	0.889704	−	0.889704i	0.994494	+	0.104790i	$0.0334172\pi$
$348$		0			0
$349$			235.849i			0.675784i	0.941185	+	0.337892i	$0.109714\pi$
$349$			235.849i			0.675784i	−0.941185	+	0.337892i	$0.890286\pi$
$350$	821.787	−	229.826i	2.34796	−	0.656645i
$351$		0			0
$352$	95.9050	−	95.9050i	0.272457	−	0.272457i
$353$	144.951	+	144.951i	0.410626	+	0.410626i	0.881956	−	0.471331i	$-0.156226\pi$
$353$	144.951	+	144.951i	0.410626	+	0.410626i	−0.471331	+	0.881956i	$0.656226\pi$
$354$		0			0
$355$	68.5720	+	52.0259i	0.193161	+	0.146552i
$356$	−544.808			−1.53036
$357$		0			0
$358$	606.553	+	606.553i	1.69428	+	1.69428i
$359$		−	118.990i		−	0.331450i	−0.986172	−	0.165725i	$-0.947004\pi$
$359$		−	118.990i		−	0.331450i	0.986172	−	0.165725i	$-0.0529963\pi$
$360$		0			0
$361$	−799.298			−2.21412
$362$	283.304	−	283.304i	0.782607	−	0.782607i
$363$		0			0
$364$		−	548.474i		−	1.50680i
$365$	−8.35155	−	60.8711i	−0.0228810	−	0.166770i
$366$		0			0
$367$	148.169	−	148.169i	0.403730	−	0.403730i	−0.475815	−	0.879545i	$-0.657847\pi$
$367$	148.169	−	148.169i	0.403730	−	0.403730i	0.879545	+	0.475815i	$0.157847\pi$
$368$	−385.797	−	385.797i	−1.04836	−	1.04836i
$369$		0			0
$370$	425.251	−	560.497i	1.14933	−	1.51486i
$371$	−660.938			−1.78150
$372$		0			0
$373$	−28.9818	−	28.9818i	−0.0776993	−	0.0776993i	0.667189	−	0.744888i	$-0.267497\pi$
$373$	−28.9818	−	28.9818i	−0.0776993	−	0.0776993i	−0.744888	+	0.667189i	$0.767497\pi$
$374$			34.7286i			0.0928571i
$375$		0			0
$376$	−23.6909			−0.0630076
$377$	−229.087	+	229.087i	−0.607658	+	0.607658i
$378$		0			0
$379$		−	106.926i		−	0.282126i	−0.990001	−	0.141063i	$-0.954948\pi$
$379$		−	106.926i		−	0.282126i	0.990001	−	0.141063i	$-0.0450520\pi$
$380$	−428.189	−	324.869i	−1.12681	−	0.854918i
$381$		0			0
$382$	685.603	−	685.603i	1.79477	−	1.79477i
$383$	311.497	+	311.497i	0.813309	+	0.813309i	0.985128	−	0.171819i	$-0.0549646\pi$
$383$	311.497	+	311.497i	0.813309	+	0.813309i	−0.171819	+	0.985128i	$0.554965\pi$
$384$		0			0
$385$	−209.633	+	28.7618i	−0.544501	+	0.0747060i
$386$	−259.186			−0.671465
$387$		0			0
$388$	−237.087	−	237.087i	−0.611050	−	0.611050i
$389$			416.377i			1.07038i	0.844733	+	0.535189i	$0.179759\pi$
$389$			416.377i			1.07038i	−0.844733	+	0.535189i	$0.820241\pi$
$390$		0			0
$391$	114.427			0.292652
$392$	−181.740	+	181.740i	−0.463623	+	0.463623i
$393$		0			0
$394$			585.568i			1.48621i
$395$	318.404	−	419.668i	0.806086	−	1.06245i
$396$		0			0
$397$	54.0423	−	54.0423i	0.136127	−	0.136127i	−0.635760	−	0.771887i	$-0.719313\pi$
$397$	54.0423	−	54.0423i	0.136127	−	0.136127i	0.771887	+	0.635760i	$0.219313\pi$
$398$	515.100	+	515.100i	1.29422	+	1.29422i
$399$		0			0
$400$	125.671	+	449.362i	0.314178	+	1.12340i
$401$	36.2893			0.0904971			0.0452485	−	0.998976i	$-0.485592\pi$
$401$	36.2893			0.0904971			0.0452485	+	0.998976i	$0.485592\pi$
$402$		0			0
$403$	−260.364	−	260.364i	−0.646064	−	0.646064i
$404$			90.3252i			0.223577i
$405$		0			0
$406$	−811.861			−1.99966
$407$	−123.362	+	123.362i	−0.303102	+	0.303102i
$408$		0			0
$409$			642.763i			1.57155i	0.618514	+	0.785774i	$0.287735\pi$
$409$			642.763i			1.57155i	−0.618514	+	0.785774i	$0.712265\pi$
$410$	577.774	−	79.2709i	1.40920	−	0.193344i
$411$		0			0
$412$	−165.777	+	165.777i	−0.402370	+	0.402370i
$413$	−923.155	−	923.155i	−2.23524	−	2.23524i
$414$		0			0
$415$	−5.51800	−	40.2184i	−0.0132964	−	0.0969119i
$416$	557.013			1.33897
$417$		0			0
$418$	213.695	+	213.695i	0.511233	+	0.511233i
$419$			216.828i			0.517489i	0.965946	+	0.258745i	$0.0833088\pi$
$419$			216.828i			0.517489i	−0.965946	+	0.258745i	$0.916691\pi$
$420$		0			0
$421$	419.087			0.995457			0.497728	−	0.867333i	$-0.334168\pi$
$421$	419.087			0.995457			0.497728	+	0.867333i	$0.334168\pi$
$422$	−72.3769	+	72.3769i	−0.171509	+	0.171509i
$423$		0			0
$424$		−	116.976i		−	0.275887i
$425$	−85.2768	−	48.0030i	−0.200651	−	0.112948i
$426$		0			0
$427$	149.796	−	149.796i	0.350810	−	0.350810i
$428$	335.564	+	335.564i	0.784029	+	0.784029i
$429$		0			0
$430$	−311.094	−	236.028i	−0.723474	−	0.548903i
$431$	−299.101			−0.693970			−0.346985	−	0.937871i	$-0.612795\pi$
$431$	−299.101			−0.693970			−0.346985	+	0.937871i	$0.612795\pi$
$432$		0			0
$433$	282.647	+	282.647i	0.652764	+	0.652764i	0.953658	−	0.300893i	$-0.0972849\pi$
$433$	282.647	+	282.647i	0.652764	+	0.652764i	−0.300893	+	0.953658i	$0.597285\pi$
$434$		−	922.703i		−	2.12604i
$435$		0			0
$436$	−320.119			−0.734217
$437$	704.102	−	704.102i	1.61122	−	1.61122i
$438$		0			0
$439$			129.560i			0.295126i	0.989053	+	0.147563i	$0.0471430\pi$
$439$			129.560i			0.295126i	−0.989053	+	0.147563i	$0.952857\pi$
$440$	−5.09040	−	37.1019i	−0.0115691	−	0.0843225i
$441$		0			0
$442$	−100.851	+	100.851i	−0.228170	+	0.228170i
$443$	−535.163	−	535.163i	−1.20804	−	1.20804i	−0.971660	−	0.236384i	$-0.924038\pi$
$443$	−535.163	−	535.163i	−1.20804	−	1.20804i	−0.236384	−	0.971660i	$-0.575962\pi$
$444$		0			0
$445$	−521.735	+	687.666i	−1.17244	+	1.54532i
$446$	−106.519			−0.238832
$447$		0			0
$448$	313.408	+	313.408i	0.699571	+	0.699571i
$449$		−	90.9277i		−	0.202512i	−0.994860	−	0.101256i	$-0.967714\pi$
$449$		−	90.9277i		−	0.202512i	0.994860	−	0.101256i	$-0.0322861\pi$
$450$		0			0
$451$	−144.612			−0.320648
$452$	428.634	−	428.634i	0.948306	−	0.948306i
$453$		0			0
$454$			106.292i			0.234124i
$455$	−692.294	−	525.247i	−1.52153	−	1.15439i
$456$		0			0
$457$	104.188	−	104.188i	0.227982	−	0.227982i	−0.583867	−	0.811849i	$-0.698461\pi$
$457$	104.188	−	104.188i	0.227982	−	0.227982i	0.811849	+	0.583867i	$0.198461\pi$
$458$	301.163	+	301.163i	0.657561	+	0.657561i
$459$		0			0
$460$	456.977	−	62.6976i	0.993429	−	0.136299i
$461$	399.301			0.866163			0.433081	−	0.901355i	$-0.357426\pi$
$461$	399.301			0.866163			0.433081	+	0.901355i	$0.357426\pi$
$462$		0			0
$463$	163.597	+	163.597i	0.353342	+	0.353342i	0.861352	−	0.508009i	$-0.169618\pi$
$463$	163.597	+	163.597i	0.353342	+	0.353342i	−0.508009	+	0.861352i	$0.669618\pi$
$464$		−	443.934i		−	0.956754i
$465$		0			0
$466$	−30.2682			−0.0649531
$467$	426.533	−	426.533i	0.913347	−	0.913347i	−0.0831872	−	0.996534i	$-0.526510\pi$
$467$	426.533	−	426.533i	0.913347	−	0.913347i	0.996534	+	0.0831872i	$0.0265099\pi$
$468$		0			0
$469$			191.069i			0.407398i
$470$	84.8097	−	111.782i	0.180446	−	0.237835i
$471$		0			0
$472$	163.385	−	163.385i	0.346154	−	0.346154i
$473$	68.4701	+	68.4701i	0.144757	+	0.144757i
$474$		0			0
$475$	−820.111	+	229.357i	−1.72655	+	0.482857i
$476$	−157.621			−0.331136
$477$		0			0
$478$	172.370	+	172.370i	0.360607	+	0.360607i
$479$		−	151.509i		−	0.316302i	−0.987415	−	0.158151i	$-0.949447\pi$
$479$		−	151.509i		−	0.316302i	0.987415	−	0.158151i	$-0.0505533\pi$
$480$		0			0
$481$	−716.485			−1.48957
$482$	−301.298	+	301.298i	−0.625100	+	0.625100i
$483$		0			0
$484$		−	34.7137i		−	0.0717225i
$485$	−526.302	+	72.2091i	−1.08516	+	0.148885i
$486$		0			0
$487$	360.092	−	360.092i	0.739408	−	0.739408i	−0.233056	−	0.972463i	$-0.574872\pi$
$487$	360.092	−	360.092i	0.739408	−	0.739408i	0.972463	+	0.233056i	$0.0748724\pi$
$488$	26.5116	+	26.5116i	0.0543271	+	0.0543271i
$489$		0			0
$490$	−206.915	−	1508.12i	−0.422276	−	3.07780i
$491$	60.0286			0.122258			0.0611289	−	0.998130i	$-0.480530\pi$
$491$	60.0286			0.122258			0.0611289	+	0.998130i	$0.480530\pi$
$492$		0			0
$493$	65.8350	+	65.8350i	0.133540	+	0.133540i
$494$			1241.13i			2.51242i
$495$		0			0
$496$	504.543			1.01722
$497$	155.322	−	155.322i	0.312519	−	0.312519i
$498$		0			0
$499$		−	148.056i		−	0.296705i	−0.988935	−	0.148352i	$-0.952603\pi$
$499$		−	148.056i		−	0.296705i	0.988935	−	0.148352i	$-0.0473970\pi$
$500$	−366.865	−	144.980i	−0.733731	−	0.289961i
$501$		0			0
$502$	−46.0638	+	46.0638i	−0.0917606	+	0.0917606i
$503$	481.606	+	481.606i	0.957467	+	0.957467i	0.999132	−	0.0416643i	$-0.0132660\pi$
$503$	481.606	+	481.606i	0.957467	+	0.957467i	−0.0416643	+	0.999132i	$0.513266\pi$
$504$		0			0
$505$	114.010	+	86.5000i	0.225763	+	0.171287i
$506$	−259.353			−0.512555
$507$		0			0
$508$	−51.1629	−	51.1629i	−0.100714	−	0.100714i
$509$			16.6842i			0.0327783i	0.999866	+	0.0163892i	$0.00521707\pi$
$509$			16.6842i			0.0327783i	−0.999866	+	0.0163892i	$0.994783\pi$
$510$		0			0
$511$	−156.795			−0.306840
$512$	−420.485	+	420.485i	−0.821261	+	0.821261i
$513$		0			0
$514$		−	950.026i		−	1.84830i
$515$	50.4901	+	368.002i	0.0980391	+	0.714567i
$516$		0			0
$517$	−24.6027	+	24.6027i	−0.0475875	+	0.0475875i
$518$	−1269.58	−	1269.58i	−2.45092	−	2.45092i
$519$		0			0
$520$	92.9607	−	122.526i	0.178771	−	0.235626i
$521$	−693.350			−1.33081			−0.665404	−	0.746484i	$-0.731741\pi$
$521$	−693.350			−1.33081			−0.665404	+	0.746484i	$0.731741\pi$
$522$		0			0
$523$	−107.263	−	107.263i	−0.205091	−	0.205091i	0.597086	−	0.802177i	$-0.296325\pi$
$523$	−107.263	−	107.263i	−0.205091	−	0.205091i	−0.802177	+	0.597086i	$0.796325\pi$
$524$			191.277i			0.365032i
$525$		0			0
$526$	−471.928			−0.897202
$527$	−74.8233	+	74.8233i	−0.141980	+	0.141980i
$528$		0			0
$529$			325.539i			0.615385i
$530$	551.936	+	418.757i	1.04139	+	0.790107i
$531$		0			0
$532$	−969.886	+	969.886i	−1.82309	+	1.82309i
$533$	−419.951	−	419.951i	−0.787901	−	0.787901i
$534$		0			0
$535$	744.909	−	102.202i	1.39235	−	0.191032i
$536$	−33.8164			−0.0630903
$537$		0			0
$538$	−7.97589	−	7.97589i	−0.0148251	−	0.0148251i
$539$			377.471i			0.700317i
$540$		0			0
$541$	−331.077			−0.611972			−0.305986	−	0.952036i	$-0.598986\pi$
$541$	−331.077			−0.611972			−0.305986	+	0.952036i	$0.598986\pi$
$542$	−543.635	+	543.635i	−1.00302	+	1.00302i
$543$		0			0
$544$		−	160.074i		−	0.294254i
$545$	−306.562	+	404.060i	−0.562499	+	0.741394i
$546$		0			0
$547$	−536.209	+	536.209i	−0.980273	+	0.980273i	−0.999809	−	0.0195366i	$-0.993781\pi$
$547$	−536.209	+	536.209i	−0.980273	+	0.980273i	0.0195366	+	0.999809i	$0.493781\pi$
$548$	32.0959	+	32.0959i	0.0585692	+	0.0585692i
$549$		0			0
$550$	193.283	+	108.801i	0.351424	+	0.197820i
$551$	810.205			1.47043
$552$		0			0
$553$	−950.585	−	950.585i	−1.71896	−	1.71896i
$554$			571.243i			1.03112i
$555$		0			0
$556$	−503.513			−0.905599
$557$	167.861	−	167.861i	0.301366	−	0.301366i	−0.540182	−	0.841548i	$-0.681645\pi$
$557$	167.861	−	167.861i	0.301366	−	0.301366i	0.841548	+	0.540182i	$0.181645\pi$
$558$		0			0
$559$			397.672i			0.711399i
$560$	1179.70	−	161.856i	2.10661	−	0.289028i
$561$		0			0
$562$	27.4192	−	27.4192i	0.0487886	−	0.0487886i
$563$	627.439	+	627.439i	1.11446	+	1.11446i	0.992541	+	0.121915i	$0.0389036\pi$
$563$	627.439	+	627.439i	1.11446	+	1.11446i	0.121915	+	0.992541i	$0.461096\pi$
$564$		0			0
$565$	−130.548	−	951.512i	−0.231059	−	1.68409i
$566$	634.028			1.12019
$567$		0			0
$568$	27.4896	+	27.4896i	0.0483972	+	0.0483972i
$569$		−	96.3156i		−	0.169272i	−0.996412	−	0.0846358i	$-0.973027\pi$
$569$		−	96.3156i		−	0.169272i	0.996412	−	0.0846358i	$-0.0269727\pi$
$570$		0			0
$571$	613.950			1.07522			0.537609	−	0.843194i	$-0.319327\pi$
$571$	613.950			1.07522			0.537609	+	0.843194i	$0.319327\pi$
$572$	100.808	−	100.808i	0.176238	−	0.176238i
$573$		0			0
$574$		−	1488.27i		−	2.59280i
$575$	358.486	−	636.847i	0.623455	−	1.10756i
$576$		0			0
$577$	5.29825	−	5.29825i	0.00918241	−	0.00918241i	−0.702501	−	0.711683i	$-0.747933\pi$
$577$	5.29825	−	5.29825i	0.00918241	−	0.00918241i	0.711683	+	0.702501i	$0.247933\pi$
$578$	−517.670	−	517.670i	−0.895623	−	0.895623i
$579$		0			0
$580$	298.993	+	226.847i	0.515505	+	0.391116i
$581$	−103.597			−0.178308
$582$		0			0
$583$	−121.478	−	121.478i	−0.208368	−	0.208368i
$584$		−	27.7504i		−	0.0475178i
$585$		0			0
$586$	−339.764			−0.579802
$587$	574.839	−	574.839i	0.979283	−	0.979283i	−0.0205069	−	0.999790i	$-0.506528\pi$
$587$	574.839	−	574.839i	0.979283	−	0.979283i	0.999790	+	0.0205069i	$0.00652802\pi$
$588$		0			0
$589$			920.821i			1.56336i
$590$	186.017	+	1355.80i	0.315283	+	2.29797i
$591$		0			0
$592$	694.217	−	694.217i	1.17266	−	1.17266i
$593$	142.619	+	142.619i	0.240505	+	0.240505i	0.817059	−	0.576554i	$-0.195603\pi$
$593$	142.619	+	142.619i	0.240505	+	0.240505i	−0.576554	+	0.817059i	$0.695603\pi$
$594$		0			0
$595$	−150.945	+	198.951i	−0.253690	+	0.334372i
$596$	−355.802			−0.596984
$597$		0			0
$598$	−753.156	−	753.156i	−1.25946	−	1.25946i
$599$		−	809.182i		−	1.35089i	−0.737412	−	0.675444i	$-0.763952\pi$
$599$		−	809.182i		−	1.35089i	0.737412	−	0.675444i	$-0.236048\pi$
$600$		0			0
$601$	−571.827			−0.951459			−0.475729	−	0.879592i	$-0.657816\pi$
$601$	−571.827			−0.951459			−0.475729	+	0.879592i	$0.657816\pi$
$602$	−704.655	+	704.655i	−1.17052	+	1.17052i
$603$		0			0
$604$		−	858.301i		−	1.42103i
$605$	−43.8163	−	33.2436i	−0.0724236	−	0.0549481i
$606$		0			0
$607$	746.235	−	746.235i	1.22938	−	1.22938i	0.265184	−	0.964198i	$-0.414567\pi$
$607$	746.235	−	746.235i	1.22938	−	1.22938i	0.964198	−	0.265184i	$-0.0854327\pi$
$608$	−984.985	−	984.985i	−1.62004	−	1.62004i
$609$		0			0
$610$	−219.999	+	30.1840i	−0.360655	+	0.0494820i
$611$	−142.892			−0.233865
$612$		0			0
$613$	−606.293	−	606.293i	−0.989059	−	0.989059i	0.0108820	−	0.999941i	$-0.496536\pi$
$613$	−606.293	−	606.293i	−0.989059	−	0.989059i	−0.999941	+	0.0108820i	$0.996536\pi$
$614$		−	131.189i		−	0.213663i
$615$		0			0
$616$	−95.5693			−0.155145
$617$	−745.890	+	745.890i	−1.20890	+	1.20890i	−0.237514	+	0.971384i	$0.576332\pi$
$617$	−745.890	+	745.890i	−1.20890	+	1.20890i	−0.971384	+	0.237514i	$0.923668\pi$
$618$		0			0
$619$			680.541i			1.09942i	0.835356	+	0.549710i	$0.185262\pi$
$619$			680.541i			1.09942i	−0.835356	+	0.549710i	$0.814738\pi$
$620$	−257.818	+	339.814i	−0.415836	+	0.548087i
$621$		0			0
$622$	−685.805	+	685.805i	−1.10258	+	1.10258i
$623$	1557.63	+	1557.63i	2.50020	+	2.50020i
$624$		0			0
$625$	−534.326	+	324.224i	−0.854921	+	0.518758i
$626$	67.9742			0.108585
$627$		0			0
$628$	137.393	+	137.393i	0.218779	+	0.218779i
$629$			205.903i			0.327350i
$630$		0			0
$631$	645.293			1.02265			0.511326	−	0.859387i	$-0.329155\pi$
$631$	645.293			1.02265			0.511326	+	0.859387i	$0.329155\pi$
$632$	168.239	−	168.239i	0.266201	−	0.266201i
$633$		0			0
$634$		−	115.144i		−	0.181615i
$635$	−113.575	+	15.5826i	−0.178858	+	0.0245395i
$636$		0			0
$637$	−1096.17	+	1096.17i	−1.72083	+	1.72083i
$638$	−149.218	−	149.218i	−0.233884	−	0.233884i
$639$		0			0
$640$	48.0202	+	350.000i	0.0750316	+	0.546875i
$641$	948.999			1.48050			0.740249	−	0.672333i	$-0.234708\pi$
$641$	948.999			1.48050			0.740249	+	0.672333i	$0.234708\pi$
$642$		0			0
$643$	161.270	+	161.270i	0.250808	+	0.250808i	0.821302	−	0.570494i	$-0.193248\pi$
$643$	161.270	+	161.270i	0.250808	+	0.250808i	−0.570494	+	0.821302i	$0.693248\pi$
$644$		−	1177.11i		−	1.82781i
$645$		0			0
$646$	356.677			0.552132
$647$	469.948	−	469.948i	0.726350	−	0.726350i	−0.243541	−	0.969891i	$-0.578309\pi$
$647$	469.948	−	469.948i	0.726350	−	0.726350i	0.969891	+	0.243541i	$0.0783091\pi$
$648$		0			0
$649$		−	339.346i		−	0.522876i
$650$	245.336	+	877.246i	0.377440	+	1.34961i
$651$		0			0
$652$	167.191	−	167.191i	0.256428	−	0.256428i
$653$	652.446	+	652.446i	0.999152	+	0.999152i	1.00000		0.000847636i	$-0.000269811\pi$
$653$	652.446	+	652.446i	0.999152	+	0.999152i	−0.000847636		1.00000i	$0.500270\pi$
$654$		0			0
$655$	241.433	+	183.176i	0.368600	+	0.279658i
$656$	813.798			1.24055
$657$		0			0
$658$	−253.197	−	253.197i	−0.384798	−	0.384798i
$659$			725.168i			1.10041i	0.835031	+	0.550204i	$0.185450\pi$
$659$			725.168i			1.10041i	−0.835031	+	0.550204i	$0.814550\pi$
$660$		0			0
$661$	−353.874			−0.535362			−0.267681	−	0.963508i	$-0.586257\pi$
$661$	−353.874			−0.535362			−0.267681	+	0.963508i	$0.586257\pi$
$662$	915.925	−	915.925i	1.38357	−	1.38357i
$663$		0			0
$664$		−	18.3351i		−	0.0276131i
$665$	295.396	+	2153.02i	0.444204	+	3.23762i
$666$		0			0
$667$	−491.656	+	491.656i	−0.737115	+	0.737115i
$668$	205.122	+	205.122i	0.307068	+	0.307068i
$669$		0			0
$670$	121.058	−	159.558i	0.180683	−	0.238147i
$671$	55.0641			0.0820627
$672$		0			0
$673$	−455.680	−	455.680i	−0.677087	−	0.677087i	0.282253	−	0.959340i	$-0.408918\pi$
$673$	−455.680	−	455.680i	−0.677087	−	0.677087i	−0.959340	+	0.282253i	$0.908918\pi$
$674$			1305.38i			1.93676i
$675$		0			0
$676$	52.1599			0.0771596
$677$	338.927	−	338.927i	0.500631	−	0.500631i	−0.411003	−	0.911634i	$-0.634822\pi$
$677$	338.927	−	338.927i	0.500631	−	0.500631i	0.911634	+	0.411003i	$0.134822\pi$
$678$		0			0
$679$			1355.68i			1.99659i
$680$	−35.2114	−	26.7151i	−0.0517815	−	0.0392868i
$681$		0			0
$682$	169.590	−	169.590i	0.248666	−	0.248666i
$683$	−299.595	−	299.595i	−0.438645	−	0.438645i	0.452911	−	0.891556i	$-0.350386\pi$
$683$	−299.595	−	299.595i	−0.438645	−	0.438645i	−0.891556	+	0.452911i	$0.850386\pi$
$684$		0			0
$685$	71.2488	−	9.77538i	0.104013	−	0.0142706i
$686$	−2212.21			−3.22479
$687$		0			0
$688$	−385.312	−	385.312i	−0.560047	−	0.560047i
$689$		−	705.542i		−	1.02401i
$690$		0			0
$691$	526.110			0.761375			0.380688	−	0.924704i	$-0.375687\pi$
$691$	526.110			0.761375			0.380688	+	0.924704i	$0.375687\pi$
$692$	−222.281	+	222.281i	−0.321215	+	0.321215i
$693$		0			0
$694$			1167.94i			1.68290i
$695$	−482.189	+	635.543i	−0.693798	+	0.914451i
$696$		0			0
$697$	−120.686	+	120.686i	−0.173150	+	0.173150i
$698$	−446.115	−	446.115i	−0.639134	−	0.639134i
$699$		0			0
$700$	−493.808	+	877.244i	−0.705440	+	1.25321i
$701$	−44.3857			−0.0633177			−0.0316589	−	0.999499i	$-0.510079\pi$
$701$	−44.3857			−0.0633177			−0.0316589	+	0.999499i	$0.510079\pi$
$702$		0			0
$703$	1266.99	+	1266.99i	1.80226	+	1.80226i
$704$			115.207i			0.163646i
$705$		0			0
$706$	−548.359			−0.776712
$707$	258.243	−	258.243i	0.365266	−	0.365266i
$708$		0			0
$709$		−	742.204i		−	1.04683i	−0.852077	−	0.523416i	$-0.824657\pi$
$709$		−	742.204i		−	1.04683i	0.852077	−	0.523416i	$-0.175343\pi$
$710$	−228.115	+	31.2975i	−0.321289	+	0.0440810i
$711$		0			0
$712$	−275.676	+	275.676i	−0.387186	+	0.387186i
$713$	−558.781	−	558.781i	−0.783703	−	0.783703i
$714$		0			0
$715$	−30.7028	−	223.780i	−0.0429410	−	0.312979i
$716$	−1011.96			−1.41335
$717$		0			0
$718$	225.074	+	225.074i	0.313474	+	0.313474i
$719$		−	864.622i		−	1.20253i	−0.799048	−	0.601267i	$-0.794663\pi$
$719$		−	864.622i		−	1.20253i	0.799048	−	0.601267i	$-0.205337\pi$
$720$		0			0
$721$	947.923			1.31473
$722$	1511.90	−	1511.90i	2.09404	−	2.09404i
$723$		0			0
$724$			472.658i			0.652842i
$725$	572.661	−	160.154i	0.789878	−	0.220902i
$726$		0			0
$727$	−467.068	+	467.068i	−0.642460	+	0.642460i	−0.951160	−	0.308700i	$-0.900106\pi$
$727$	−467.068	+	467.068i	−0.642460	+	0.642460i	0.308700	+	0.951160i	$0.400106\pi$
$728$	−277.531	−	277.531i	−0.381224	−	0.381224i
$729$		0			0
$730$	130.937	+	99.3424i	0.179365	+	0.136085i
$731$	114.283			0.156338
$732$		0			0
$733$	−273.279	−	273.279i	−0.372822	−	0.372822i	0.495682	−	0.868504i	$-0.334918\pi$
$733$	−273.279	−	273.279i	−0.372822	−	0.372822i	−0.868504	+	0.495682i	$0.834918\pi$
$734$			560.533i			0.763669i
$735$		0			0
$736$	1195.43			1.62423
$737$	−35.1180	+	35.1180i	−0.0476499	+	0.0476499i
$738$		0			0
$739$		−	665.220i		−	0.900162i	−0.892988	−	0.450081i	$-0.851395\pi$
$739$		−	665.220i		−	0.900162i	0.892988	−	0.450081i	$-0.148605\pi$
$740$	112.820	+	822.300i	0.152460	+	1.11122i
$741$		0			0
$742$	1250.19	−	1250.19i	1.68489	−	1.68489i
$743$	462.551	+	462.551i	0.622545	+	0.622545i	0.946181	−	0.323637i	$-0.104906\pi$
$743$	462.551	+	462.551i	0.622545	+	0.622545i	−0.323637	+	0.946181i	$0.604906\pi$
$744$		0			0
$745$	−340.734	+	449.100i	−0.457362	+	0.602819i
$746$	109.640			0.146971
$747$		0			0
$748$	−28.9702	−	28.9702i	−0.0387302	−	0.0387302i
$749$		−	1918.78i		−	2.56179i
$750$		0			0
$751$	799.748			1.06491			0.532455	−	0.846458i	$-0.321269\pi$
$751$	799.748			1.06491			0.532455	+	0.846458i	$0.321269\pi$
$752$	138.451	−	138.451i	0.184110	−	0.184110i
$753$		0			0
$754$		−	866.651i		−	1.14940i
$755$	−1083.36	−	821.953i	−1.43492	−	1.08868i
$756$		0			0
$757$	518.456	−	518.456i	0.684883	−	0.684883i	−0.276214	−	0.961096i	$-0.589080\pi$
$757$	518.456	−	518.456i	0.684883	−	0.684883i	0.961096	+	0.276214i	$0.0890797\pi$
$758$	202.253	+	202.253i	0.266825	+	0.266825i
$759$		0			0
$760$	−381.052	+	52.2806i	−0.501384	+	0.0687903i
$761$	1045.23			1.37350			0.686748	−	0.726895i	$-0.259037\pi$
$761$	1045.23			1.37350			0.686748	+	0.726895i	$0.259037\pi$
$762$		0			0
$763$	915.231	+	915.231i	1.19952	+	1.19952i
$764$			1143.84i			1.49718i
$765$		0			0
$766$	−1178.41			−1.53840
$767$	985.455	−	985.455i	1.28482	−	1.28482i
$768$		0			0
$769$		−	641.987i		−	0.834834i	−0.908715	−	0.417417i	$-0.862935\pi$
$769$		−	641.987i		−	0.834834i	0.908715	−	0.417417i	$-0.137065\pi$
$770$	342.124	−	450.932i	0.444317	−	0.585625i
$771$		0			0
$772$	216.210	−	216.210i	0.280064	−	0.280064i
$773$	29.6724	+	29.6724i	0.0383860	+	0.0383860i	0.726039	−	0.687653i	$-0.241359\pi$
$773$	29.6724	+	29.6724i	0.0383860	+	0.0383860i	−0.687653	+	0.726039i	$0.741359\pi$
$774$		0			0
$775$	182.019	+	650.846i	0.234864	+	0.839801i
$776$	−239.935			−0.309195
$777$		0			0
$778$	−787.590	−	787.590i	−1.01233	−	1.01233i
$779$			1485.23i			1.90658i
$780$		0			0
$781$	57.0953			0.0731054
$782$	−216.442	+	216.442i	−0.276780	+	0.276780i
$783$		0			0
$784$		−	2124.20i		−	2.70944i
$785$	304.995	−	41.8455i	0.388528	−	0.0533064i
$786$		0			0
$787$	−219.821	+	219.821i	−0.279316	+	0.279316i	−0.832836	−	0.553520i	$-0.813284\pi$
$787$	−219.821	+	219.821i	−0.279316	+	0.279316i	0.553520	+	0.832836i	$0.313284\pi$
$788$	−488.474	−	488.474i	−0.619891	−	0.619891i
$789$		0			0
$790$	191.544	+	1396.09i	0.242461	+	1.76720i
$791$	−2450.96			−3.09856
$792$		0			0
$793$	159.905	+	159.905i	0.201646	+	0.201646i
$794$			204.445i			0.257488i
$795$		0			0
$796$	−859.382			−1.07963
$797$	−952.391	+	952.391i	−1.19497	+	1.19497i	−0.219316	+	0.975654i	$0.570383\pi$
$797$	−952.391	+	952.391i	−1.19497	+	1.19497i	−0.975654	+	0.219316i	$0.929617\pi$
$798$		0			0
$799$			41.0642i			0.0513945i
$800$	−890.900	−	501.495i	−1.11363	−	0.626869i
$801$		0			0
$802$	−68.6425	+	68.6425i	−0.0855891	+	0.0855891i
$803$	−28.8185	−	28.8185i	−0.0358886	−	0.0358886i
$804$		0			0
$805$	−1485.77	−	1127.26i	−1.84568	−	1.40032i
$806$	984.973			1.22205
$807$		0			0
$808$	45.7051	+	45.7051i	0.0565658	+	0.0565658i
$809$		−	334.364i		−	0.413305i	−0.978414	−	0.206652i	$-0.933743\pi$
$809$		−	334.364i		−	0.413305i	0.978414	−	0.206652i	$-0.0662569\pi$
$810$		0			0
$811$	−99.7762			−0.123029			−0.0615143	−	0.998106i	$-0.519593\pi$
$811$	−99.7762			−0.123029			−0.0615143	+	0.998106i	$0.519593\pi$
$812$	677.246	−	677.246i	0.834046	−	0.834046i
$813$		0			0
$814$		−	466.688i		−	0.573327i
$815$	−50.9209	−	371.142i	−0.0624797	−	0.455389i
$816$		0			0
$817$	703.217	−	703.217i	0.860731	−	0.860731i
$818$	−1215.81	−	1215.81i	−1.48632	−	1.48632i
$819$		0			0
$820$	−415.845	+	548.099i	−0.507129	+	0.668414i
$821$	−1427.05			−1.73819			−0.869094	−	0.494647i	$-0.835297\pi$
$821$	−1427.05			−1.73819			−0.869094	+	0.494647i	$0.835297\pi$
$822$		0			0
$823$	640.882	+	640.882i	0.778714	+	0.778714i	0.979612	−	0.200898i	$-0.0643859\pi$
$823$	640.882	+	640.882i	0.778714	+	0.778714i	−0.200898	+	0.979612i	$0.564386\pi$
$824$			167.768i			0.203602i
$825$		0			0
$826$	3492.36			4.22803
$827$	405.808	−	405.808i	0.490699	−	0.490699i	−0.417827	−	0.908526i	$-0.637208\pi$
$827$	405.808	−	405.808i	0.490699	−	0.490699i	0.908526	+	0.417827i	$0.137208\pi$
$828$		0			0
$829$		−	1270.58i		−	1.53266i	−0.642446	−	0.766331i	$-0.722081\pi$
$829$		−	1270.58i		−	1.53266i	0.642446	−	0.766331i	$-0.277919\pi$
$830$	86.5119	+	65.6370i	0.104231	+	0.0790807i
$831$		0			0
$832$	−334.559	+	334.559i	−0.402114	+	0.402114i
$833$	315.017	+	315.017i	0.378172	+	0.378172i
$834$		0			0
$835$	455.343	−	62.4734i	0.545321	−	0.0748184i
$836$	−356.524			−0.426465
$837$		0			0
$838$	−410.137	−	410.137i	−0.489424	−	0.489424i
$839$		−	1131.65i		−	1.34881i	−0.738363	−	0.674403i	$-0.764401\pi$
$839$		−	1131.65i		−	1.34881i	0.738363	−	0.674403i	$-0.235599\pi$
$840$		0			0
$841$	275.255			0.327295
$842$	−792.717	+	792.717i	−0.941470	+	0.941470i
$843$		0			0
$844$		−	120.752i		−	0.143071i
$845$	49.9509	−	65.8372i	0.0591135	−	0.0779138i
$846$		0			0
$847$	−99.2477	+	99.2477i	−0.117176	+	0.117176i
$848$	683.614	+	683.614i	0.806148	+	0.806148i
$849$		0			0
$850$	252.103	−	70.5046i	0.296592	−	0.0829466i
$851$	−1537.69			−1.80692
$852$		0			0
$853$	−1069.18	−	1069.18i	−1.25343	−	1.25343i	−0.954171	−	0.299261i	$-0.903260\pi$
$853$	−1069.18	−	1069.18i	−1.25343	−	1.25343i	−0.299261	−	0.954171i	$-0.596740\pi$
$854$			566.688i			0.663569i
$855$		0			0
$856$	339.595			0.396724
$857$	1180.15	−	1180.15i	1.37708	−	1.37708i	0.527557	−	0.849520i	$-0.323108\pi$
$857$	1180.15	−	1180.15i	1.37708	−	1.37708i	0.849520	−	0.527557i	$-0.176892\pi$
$858$		0			0
$859$			866.921i			1.00922i	0.863347	+	0.504610i	$0.168364\pi$
$859$			866.921i			1.00922i	−0.863347	+	0.504610i	$0.831636\pi$
$860$	456.403	−	62.6188i	0.530701	−	0.0728125i
$861$		0			0
$862$	565.760	−	565.760i	0.656334	−	0.656334i
$863$	−886.055	−	886.055i	−1.02671	−	1.02671i	−0.999633	−	0.0270816i	$-0.991379\pi$
$863$	−886.055	−	886.055i	−1.02671	−	1.02671i	−0.0270816	−	0.999633i	$-0.508621\pi$
$864$		0			0
$865$	67.6995	+	493.434i	0.0782653	+	0.570444i
$866$	−1069.27			−1.23472
$867$		0			0
$868$	769.709	+	769.709i	0.886761	+	0.886761i
$869$		−	349.429i		−	0.402105i
$870$		0			0
$871$	−203.964			−0.234172
$872$	−161.982	+	161.982i	−0.185759	+	0.185759i
$873$		0			0
$874$			2663.66i			3.04767i
$875$	634.378	+	1463.39i	0.725003	+	1.67244i
$876$		0			0
$877$	131.956	−	131.956i	0.150463	−	0.150463i	−0.627862	−	0.778325i	$-0.716070\pi$
$877$	131.956	−	131.956i	0.150463	−	0.150463i	0.778325	+	0.627862i	$0.216070\pi$
$878$	−245.068	−	245.068i	−0.279121	−	0.279121i
$879$		0			0
$880$	246.574	+	187.077i	0.280198	+	0.212587i
$881$	1098.23			1.24658			0.623288	−	0.781992i	$-0.285796\pi$
$881$	1098.23			1.24658			0.623288	+	0.781992i	$0.285796\pi$
$882$		0			0
$883$	−589.293	−	589.293i	−0.667376	−	0.667376i	0.289732	−	0.957108i	$-0.406434\pi$
$883$	−589.293	−	589.293i	−0.667376	−	0.667376i	−0.957108	+	0.289732i	$0.906434\pi$
$884$		−	168.258i		−	0.190337i
$885$		0			0
$886$	2024.56			2.28505
$887$	−379.152	+	379.152i	−0.427454	+	0.427454i	−0.887760	−	0.460306i	$-0.847740\pi$
$887$	−379.152	+	379.152i	−0.427454	+	0.427454i	0.460306	+	0.887760i	$0.347740\pi$
$888$		0			0
$889$			292.553i			0.329081i
$890$	−313.863	−	2287.62i	−0.352655	−	2.57036i
$891$		0			0
$892$	88.8570	−	88.8570i	0.0996155	−	0.0996155i
$893$	252.680	+	252.680i	0.282957	+	0.282957i
$894$		0			0
$895$	−969.103	+	1277.31i	−1.08280	+	1.42717i
$896$	901.551			1.00620
$897$		0			0
$898$	171.993	+	171.993i	0.191529	+	0.191529i
$899$		−	642.985i		−	0.715222i
$900$		0			0
$901$	−202.759			−0.225037
$902$	273.539	−	273.539i	0.303258	−	0.303258i
$903$		0			0
$904$		−	433.783i		−	0.479849i
$905$	596.597	+	452.641i	0.659223	+	0.500156i
$906$		0			0
$907$	−647.760	+	647.760i	−0.714178	+	0.714178i	−0.967407	−	0.253228i	$-0.918508\pi$
$907$	−647.760	+	647.760i	−0.714178	+	0.714178i	0.253228	+	0.967407i	$0.418508\pi$
$908$	−88.6678	−	88.6678i	−0.0976517	−	0.0976517i
$909$		0			0
$910$	2303.02	−	315.976i	2.53079	−	0.347226i
$911$	431.203			0.473330			0.236665	−	0.971591i	$-0.423946\pi$
$911$	431.203			0.473330			0.236665	+	0.971591i	$0.423946\pi$
$912$		0			0
$913$	−19.0408	−	19.0408i	−0.0208552	−	0.0208552i
$914$			394.150i			0.431236i
$915$		0			0
$916$	−502.453			−0.548530
$917$	546.867	−	546.867i	0.596365	−	0.596365i
$918$		0			0
$919$		−	1641.19i		−	1.78584i	−0.450212	−	0.892921i	$-0.648652\pi$
$919$		−	1641.19i		−	1.78584i	0.450212	−	0.892921i	$-0.351348\pi$
$920$	199.508	−	262.959i	0.216857	−	0.285825i
$921$		0			0
$922$	−755.291	+	755.291i	−0.819188	+	0.819188i
$923$	165.804	+	165.804i	0.179636	+	0.179636i
$924$		0			0
$925$	1145.96	+	645.073i	1.23888	+	0.697376i
$926$	−618.900			−0.668358
$927$		0			0
$928$	687.789	+	687.789i	0.741152	+	0.741152i
$929$			775.197i			0.834442i	0.908805	+	0.417221i	$0.136996\pi$
$929$			775.197i			0.834442i	−0.908805	+	0.417221i	$0.863004\pi$
$930$		0			0
$931$	3876.79			4.16411
$932$	25.2494	−	25.2494i	0.0270916	−	0.0270916i
$933$		0			0
$934$			1613.60i			1.72763i
$935$	−64.3100	+	8.82338i	−0.0687807	+	0.00943677i
$936$		0			0
$937$	−1109.99	+	1109.99i	−1.18462	+	1.18462i	−0.206082	+	0.978535i	$0.566071\pi$
$937$	−1109.99	+	1109.99i	−1.18462	+	1.18462i	−0.978535	+	0.206082i	$0.933929\pi$
$938$	−361.414	−	361.414i	−0.385303	−	0.385303i
$939$		0			0
$940$	22.5002	+	163.995i	0.0239364	+	0.174463i
$941$	−632.362			−0.672011			−0.336005	−	0.941860i	$-0.609076\pi$
$941$	−632.362			−0.672011			−0.336005	+	0.941860i	$0.609076\pi$
$942$		0			0
$943$	−901.280	−	901.280i	−0.955758	−	0.955758i
$944$			1909.65i			2.02294i
$945$		0			0
$946$	−259.027			−0.273813
$947$	693.863	−	693.863i	0.732696	−	0.732696i	−0.238457	−	0.971153i	$-0.576642\pi$
$947$	693.863	−	693.863i	0.732696	−	0.732696i	0.971153	+	0.238457i	$0.0766417\pi$
$948$		0			0
$949$		−	167.377i		−	0.176372i
$950$	1117.43	−	1985.10i	1.17624	−	2.08958i
$951$		0			0
$952$	−79.7570	+	79.7570i	−0.0837784	+	0.0837784i
$953$	−827.010	−	827.010i	−0.867796	−	0.867796i	0.124432	−	0.992228i	$-0.460289\pi$
$953$	−827.010	−	827.010i	−0.867796	−	0.867796i	−0.992228	+	0.124432i	$0.960289\pi$
$954$		0			0
$955$	1443.78	+	1095.40i	1.51181	+	1.14702i
$956$	−287.578			−0.300814
$957$		0			0
$958$	286.584	+	286.584i	0.299148	+	0.299148i
$959$		−	183.527i		−	0.191373i
$960$		0			0
$961$	−230.230			−0.239573
$962$	1355.25	−	1355.25i	1.40879	−	1.40879i
$963$		0			0
$964$		−	502.679i		−	0.521451i
$965$	−65.8504	−	479.957i	−0.0682388	−	0.497365i
$966$		0			0
$967$	−315.855	+	315.855i	−0.326634	+	0.326634i	−0.851305	−	0.524671i	$-0.824188\pi$
$967$	−315.855	+	315.855i	−0.326634	+	0.326634i	0.524671	+	0.851305i	$0.324188\pi$
$968$	−17.5654	−	17.5654i	−0.0181460	−	0.0181460i
$969$		0			0
$970$	858.932	−	1132.10i	0.885497	−	1.16712i
$971$	445.544			0.458851			0.229425	−	0.973326i	$-0.426315\pi$
$971$	445.544			0.458851			0.229425	+	0.973326i	$0.426315\pi$
$972$		0			0
$973$	1439.56	+	1439.56i	1.47951	+	1.47951i
$974$			1362.25i			1.39861i
$975$		0			0
$976$	−309.870			−0.317490
$977$	562.840	−	562.840i	0.576091	−	0.576091i	−0.357733	−	0.933824i	$-0.616450\pi$
$977$	562.840	−	562.840i	0.576091	−	0.576091i	0.933824	+	0.357733i	$0.116450\pi$
$978$		0			0
$979$			572.574i			0.584856i
$980$	1430.66	+	1085.45i	1.45986	+	1.10760i
$981$		0			0
$982$	−113.546	+	113.546i	−0.115627	+	0.115627i
$983$	817.886	+	817.886i	0.832031	+	0.832031i	0.987794	−	0.155763i	$-0.0497838\pi$
$983$	817.886	+	817.886i	0.832031	+	0.832031i	−0.155763	+	0.987794i	$0.549784\pi$
$984$		0			0
$985$	−1084.35	+	148.773i	−1.10086	+	0.151039i
$986$	−249.058			−0.252594
$987$		0			0
$988$	−1035.34	−	1035.34i	−1.04792	−	1.04792i
$989$			853.465i			0.862958i
$990$		0			0
$991$	−1479.24			−1.49268			−0.746339	−	0.665566i	$-0.768190\pi$
$991$	−1479.24			−1.49268			−0.746339	+	0.665566i	$0.768190\pi$
$992$	−781.691	+	781.691i	−0.787995	+	0.787995i
$993$		0			0
$994$			587.592i			0.591139i
$995$	−822.987	+	1084.73i	−0.827123	+	1.09018i
$996$		0			0
$997$	−73.9474	+	73.9474i	−0.0741699	+	0.0741699i	−0.743219	−	0.669049i	$-0.766702\pi$
$997$	−73.9474	+	73.9474i	−0.0741699	+	0.0741699i	0.669049	+	0.743219i	$0.266702\pi$
$998$	280.052	+	280.052i	0.280614	+	0.280614i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.j.c.298.5	✓	40
3.2	odd	2	inner	495.3.j.c.298.16	yes	40
5.2	odd	4	inner	495.3.j.c.397.5	yes	40
15.2	even	4	inner	495.3.j.c.397.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.3.j.c.298.5	✓	40	1.1	even	1	trivial
495.3.j.c.298.16	yes	40	3.2	odd	2	inner
495.3.j.c.397.5	yes	40	5.2	odd	4	inner
495.3.j.c.397.16	yes	40	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89153 + 1.89153i) q^{2} -3.15579i q^{4} +(-3.98330 - 3.02214i) q^{5} +(-9.02252 + 9.02252i) q^{7} +(-1.59685 - 1.59685i) q^{8} +(13.2510 - 1.81805i) q^{10} -3.31662 q^{11} +(-9.63142 - 9.63142i) q^{13} -34.1328i q^{14} +18.6641 q^{16} +(-2.76788 + 2.76788i) q^{17} +34.0632i q^{19} +(-9.53725 + 12.5704i) q^{20} +(6.27350 - 6.27350i) q^{22} +(-20.6705 - 20.6705i) q^{23} +(6.73329 + 24.0762i) q^{25} +36.4363 q^{26} +(28.4732 + 28.4732i) q^{28} -23.7854i q^{29} +27.0328 q^{31} +(-28.9164 + 28.9164i) q^{32} -10.4711i q^{34} +(63.2067 - 8.67201i) q^{35} +(37.1952 - 37.1952i) q^{37} +(-64.4316 - 64.4316i) q^{38} +(1.53481 + 11.1866i) q^{40} +43.6022 q^{41} +(-20.6445 - 20.6445i) q^{43} +10.4666i q^{44} +78.1978 q^{46} +(7.41800 - 7.41800i) q^{47} -113.812i q^{49} +(-58.2771 - 32.8047i) q^{50} +(-30.3947 + 30.3947i) q^{52} +(36.6271 + 36.6271i) q^{53} +(13.2111 + 10.0233i) q^{55} +28.8152 q^{56} +(44.9908 + 44.9908i) q^{58} +102.317i q^{59} -16.6024 q^{61} +(-51.1333 + 51.1333i) q^{62} -34.7362i q^{64} +(9.25725 + 67.4723i) q^{65} +(10.5885 - 10.5885i) q^{67} +(8.73484 + 8.73484i) q^{68} +(-103.154 + 135.961i) q^{70} -17.2149 q^{71} +(8.68911 + 8.68911i) q^{73} +140.712i q^{74} +107.496 q^{76} +(29.9243 - 29.9243i) q^{77} +105.357i q^{79} +(-74.3448 - 56.4058i) q^{80} +(-82.4750 + 82.4750i) q^{82} +(5.74103 + 5.74103i) q^{83} +(19.3902 - 2.66035i) q^{85} +78.0996 q^{86} +(5.29615 + 5.29615i) q^{88} -172.638i q^{89} +173.799 q^{91} +(-65.2318 + 65.2318i) q^{92} +28.0628i q^{94} +(102.944 - 135.684i) q^{95} +(75.1277 - 75.1277i) q^{97} +(215.279 + 215.279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) \) 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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