LMFDB - Embedded newform 585.2.w.g.73.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(73,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("585.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.w (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.14
Character	$\chi$	$=$	585.73
Dual form			585.2.w.g.577.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73623 q^{2} +5.48694 q^{4} +(-1.95975 + 1.07675i) q^{5} +2.18253i q^{7} +9.54105 q^{8} +O(q^{10})$	\(q+2.73623 q^{2} +5.48694 q^{4} +(-1.95975 + 1.07675i) q^{5} +2.18253i q^{7} +9.54105 q^{8} +(-5.36231 + 2.94624i) q^{10} +(0.403236 - 0.403236i) q^{11} +(2.72201 - 2.36446i) q^{13} +5.97189i q^{14} +15.1326 q^{16} +(-4.22719 - 4.22719i) q^{17} +(-0.462512 + 0.462512i) q^{19} +(-10.7530 + 5.90808i) q^{20} +(1.10334 - 1.10334i) q^{22} +(-4.43399 + 4.43399i) q^{23} +(2.68120 - 4.22032i) q^{25} +(7.44802 - 6.46971i) q^{26} +11.9754i q^{28} +4.40973i q^{29} +(-2.06316 - 2.06316i) q^{31} +22.3241 q^{32} +(-11.5665 - 11.5665i) q^{34} +(-2.35004 - 4.27720i) q^{35} -4.58165i q^{37} +(-1.26554 + 1.26554i) q^{38} +(-18.6980 + 10.2734i) q^{40} +(-6.83712 - 6.83712i) q^{41} +(1.21836 - 1.21836i) q^{43} +(2.21253 - 2.21253i) q^{44} +(-12.1324 + 12.1324i) q^{46} -5.28755i q^{47} +2.23658 q^{49} +(7.33638 - 11.5478i) q^{50} +(14.9355 - 12.9737i) q^{52} +(0.277932 + 0.277932i) q^{53} +(-0.356054 + 1.22442i) q^{55} +20.8236i q^{56} +12.0660i q^{58} +(2.41412 + 2.41412i) q^{59} -8.05723 q^{61} +(-5.64528 - 5.64528i) q^{62} +30.8186 q^{64} +(-2.78850 + 7.56467i) q^{65} -6.48209 q^{67} +(-23.1943 - 23.1943i) q^{68} +(-6.43025 - 11.7034i) q^{70} +(-2.32466 - 2.32466i) q^{71} -2.98262 q^{73} -12.5364i q^{74} +(-2.53777 + 2.53777i) q^{76} +(0.880072 + 0.880072i) q^{77} +12.7156i q^{79} +(-29.6560 + 16.2941i) q^{80} +(-18.7079 - 18.7079i) q^{82} +0.553610i q^{83} +(12.8359 + 3.73257i) q^{85} +(3.33370 - 3.33370i) q^{86} +(3.84729 - 3.84729i) q^{88} +(7.56032 + 7.56032i) q^{89} +(5.16050 + 5.94085i) q^{91} +(-24.3290 + 24.3290i) q^{92} -14.4679i q^{94} +(0.408394 - 1.40442i) q^{95} +9.88577 q^{97} +6.11978 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8}+O(q^{10}) $ 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8	$ 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 28 q^{16} - 28 q^{17} - 12 q^{20} - 32 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{31} + 68 q^{32} - 28 q^{34} - 48 q^{40} - 4 q^{41} + 40 q^{44} - 16 q^{46} + 28 q^{49} - 4 q^{50} + 48 q^{52} - 20 q^{53} - 8 q^{55} + 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} - 64 q^{65} + 32 q^{67} - 60 q^{68} - 16 q^{70} - 40 q^{71} + 56 q^{73} - 40 q^{76} - 48 q^{77} + 12 q^{80} - 4 q^{82} + 44 q^{85} - 16 q^{86} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 56 q^{95} + 48 q^{97} + 12 q^{98}+O(q^{100}) $ 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8 + 8 * q^11 + 28 * q^16 - 28 * q^17 - 12 * q^20 - 32 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^31 + 68 * q^32 - 28 * q^34 - 48 * q^40 - 4 * q^41 + 40 * q^44 - 16 * q^46 + 28 * q^49 - 4 * q^50 + 48 * q^52 - 20 * q^53 - 8 * q^55 + 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 - 64 * q^65 + 32 * q^67 - 60 * q^68 - 16 * q^70 - 40 * q^71 + 56 * q^73 - 40 * q^76 - 48 * q^77 + 12 * q^80 - 4 * q^82 + 44 * q^85 - 16 * q^86 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 56 * q^95 + 48 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.73623			1.93480			0.967402	−	0.253245i	$-0.0814979\pi$
$2$	2.73623			1.93480			0.967402	+	0.253245i	$0.0814979\pi$
$3$		0			0
$3$		0			0
$4$	5.48694			2.74347
$5$	−1.95975	+	1.07675i	−0.876425	+	0.481539i
$5$	−1.95975	+	1.07675i	−0.876425	+	0.481539i
$6$		0			0
$7$			2.18253i			0.824918i	0.910976	+	0.412459i	$0.135330\pi$
$7$			2.18253i			0.824918i	−0.910976	+	0.412459i	$0.864670\pi$
$8$	9.54105			3.37327
$9$		0			0
$10$	−5.36231	+	2.94624i	−1.69571	+	0.931683i
$11$	0.403236	−	0.403236i	0.121580	−	0.121580i	−0.643699	−	0.765279i	$-0.722601\pi$
$11$	0.403236	−	0.403236i	0.121580	−	0.121580i	0.765279	+	0.643699i	$0.222601\pi$
$12$		0			0
$13$	2.72201	−	2.36446i	0.754949	−	0.655784i
$13$	2.72201	−	2.36446i	0.754949	−	0.655784i
$14$			5.97189i			1.59605i
$15$		0			0
$16$	15.1326			3.78315
$17$	−4.22719	−	4.22719i	−1.02524	−	1.02524i	−0.999673	−	0.0255708i	$-0.991860\pi$
$17$	−4.22719	−	4.22719i	−1.02524	−	1.02524i	−0.0255708	−	0.999673i	$-0.508140\pi$
$18$		0			0
$19$	−0.462512	+	0.462512i	−0.106108	+	0.106108i	−0.758167	−	0.652060i	$-0.773905\pi$
$19$	−0.462512	+	0.462512i	−0.106108	+	0.106108i	0.652060	+	0.758167i	$0.273905\pi$
$20$	−10.7530	+	5.90808i	−2.40444	+	1.32109i
$21$		0			0
$22$	1.10334	−	1.10334i	0.235234	−	0.235234i
$23$	−4.43399	+	4.43399i	−0.924552	+	0.924552i	−0.997347	−	0.0727952i	$-0.976808\pi$
$23$	−4.43399	+	4.43399i	−0.924552	+	0.924552i	0.0727952	+	0.997347i	$0.476808\pi$
$24$		0			0
$25$	2.68120	−	4.22032i	0.536241	−	0.844065i
$26$	7.44802	−	6.46971i	1.46068	−	1.26881i
$27$		0			0
$28$			11.9754i			2.26313i
$29$			4.40973i			0.818867i	0.912340	+	0.409434i	$0.134274\pi$
$29$			4.40973i			0.818867i	−0.912340	+	0.409434i	$0.865726\pi$
$30$		0			0
$31$	−2.06316	−	2.06316i	−0.370555	−	0.370555i	0.497124	−	0.867679i	$-0.334389\pi$
$31$	−2.06316	−	2.06316i	−0.370555	−	0.370555i	−0.867679	+	0.497124i	$0.834389\pi$
$32$	22.3241			3.94638
$33$		0			0
$34$	−11.5665	−	11.5665i	−1.98365	−	1.98365i
$35$	−2.35004	−	4.27720i	−0.397230	−	0.722978i
$36$		0			0
$37$		−	4.58165i		−	0.753219i	−0.926372	−	0.376609i	$-0.877090\pi$
$37$		−	4.58165i		−	0.753219i	0.926372	−	0.376609i	$-0.122910\pi$
$38$	−1.26554	+	1.26554i	−0.205297	+	0.205297i
$39$		0			0
$40$	−18.6980	+	10.2734i	−2.95642	+	1.62436i
$41$	−6.83712	−	6.83712i	−1.06778	−	1.06778i	−0.997529	−	0.0702494i	$-0.977620\pi$
$41$	−6.83712	−	6.83712i	−1.06778	−	1.06778i	−0.0702494	−	0.997529i	$-0.522380\pi$
$42$		0			0
$43$	1.21836	−	1.21836i	0.185798	−	0.185798i	−0.608079	−	0.793877i	$-0.708060\pi$
$43$	1.21836	−	1.21836i	0.185798	−	0.185798i	0.793877	+	0.608079i	$0.208060\pi$
$44$	2.21253	−	2.21253i	0.333551	−	0.333551i
$45$		0			0
$46$	−12.1324	+	12.1324i	−1.78883	+	1.78883i
$47$		−	5.28755i		−	0.771268i	−0.922652	−	0.385634i	$-0.873983\pi$
$47$		−	5.28755i		−	0.771268i	0.922652	−	0.385634i	$-0.126017\pi$
$48$		0			0
$49$	2.23658			0.319511
$50$	7.33638	−	11.5478i	1.03752	−	1.63310i
$51$		0			0
$52$	14.9355	−	12.9737i	2.07118	−	1.79912i
$53$	0.277932	+	0.277932i	0.0381769	+	0.0381769i	0.725938	−	0.687761i	$-0.241406\pi$
$53$	0.277932	+	0.277932i	0.0381769	+	0.0381769i	−0.687761	+	0.725938i	$0.741406\pi$
$54$		0			0
$55$	−0.356054	+	1.22442i	−0.0480103	+	0.165101i
$56$			20.8236i			2.78267i
$57$		0			0
$58$			12.0660i			1.58435i
$59$	2.41412	+	2.41412i	0.314291	+	0.314291i	0.846569	−	0.532278i	$-0.178664\pi$
$59$	2.41412	+	2.41412i	0.314291	+	0.314291i	−0.532278	+	0.846569i	$0.678664\pi$
$60$		0			0
$61$	−8.05723			−1.03162			−0.515811	−	0.856702i	$-0.672509\pi$
$61$	−8.05723			−1.03162			−0.515811	+	0.856702i	$0.672509\pi$
$62$	−5.64528	−	5.64528i	−0.716951	−	0.716951i
$63$		0			0
$64$	30.8186			3.85233
$65$	−2.78850	+	7.56467i	−0.345870	+	0.938282i
$66$		0			0
$67$	−6.48209			−0.791914			−0.395957	−	0.918269i	$-0.629587\pi$
$67$	−6.48209			−0.791914			−0.395957	+	0.918269i	$0.629587\pi$
$68$	−23.1943	−	23.1943i	−2.81272	−	2.81272i
$69$		0			0
$70$	−6.43025	−	11.7034i	−0.768562	−	1.39882i
$71$	−2.32466	−	2.32466i	−0.275887	−	0.275887i	0.555578	−	0.831465i	$-0.312497\pi$
$71$	−2.32466	−	2.32466i	−0.275887	−	0.275887i	−0.831465	+	0.555578i	$0.812497\pi$
$72$		0			0
$73$	−2.98262			−0.349089			−0.174545	−	0.984649i	$-0.555845\pi$
$73$	−2.98262			−0.349089			−0.174545	+	0.984649i	$0.555845\pi$
$74$		−	12.5364i		−	1.45733i
$75$		0			0
$76$	−2.53777	+	2.53777i	−0.291103	+	0.291103i
$77$	0.880072	+	0.880072i	0.100294	+	0.100294i
$78$		0			0
$79$			12.7156i			1.43062i	0.698810	+	0.715308i	$0.253713\pi$
$79$			12.7156i			1.43062i	−0.698810	+	0.715308i	$0.746287\pi$
$80$	−29.6560	+	16.2941i	−3.31564	+	1.82173i
$81$		0			0
$82$	−18.7079	−	18.7079i	−2.06594	−	2.06594i
$83$			0.553610i			0.0607666i	0.999538	+	0.0303833i	$0.00967279\pi$
$83$			0.553610i			0.0607666i	−0.999538	+	0.0303833i	$0.990327\pi$
$84$		0			0
$85$	12.8359	+	3.73257i	1.39224	+	0.404854i
$86$	3.33370	−	3.33370i	0.359482	−	0.359482i
$87$		0			0
$88$	3.84729	−	3.84729i	0.410122	−	0.410122i
$89$	7.56032	+	7.56032i	0.801393	+	0.801393i	0.983313	−	0.181920i	$-0.0582314\pi$
$89$	7.56032	+	7.56032i	0.801393	+	0.801393i	−0.181920	+	0.983313i	$0.558231\pi$
$90$		0			0
$91$	5.16050	+	5.94085i	0.540968	+	0.622770i
$92$	−24.3290	+	24.3290i	−2.53648	+	2.53648i
$93$		0			0
$94$		−	14.4679i		−	1.49225i
$95$	0.408394	−	1.40442i	0.0419004	−	0.144090i
$96$		0			0
$97$	9.88577			1.00375			0.501874	−	0.864941i	$-0.332644\pi$
$97$	9.88577			1.00375			0.501874	+	0.864941i	$0.332644\pi$
$98$	6.11978			0.618191
$99$		0			0
$100$	14.7116	−	23.1567i	1.47116	−	2.31567i
$101$			6.83452i			0.680060i	0.940415	+	0.340030i	$0.110437\pi$
$101$			6.83452i			0.680060i	−0.940415	+	0.340030i	$0.889563\pi$
$102$		0			0
$103$	−8.57596	+	8.57596i	−0.845014	+	0.845014i	−0.989506	−	0.144492i	$-0.953845\pi$
$103$	−8.57596	+	8.57596i	−0.845014	+	0.845014i	0.144492	+	0.989506i	$0.453845\pi$
$104$	25.9708	−	22.5594i	2.54664	−	2.21214i
$105$		0			0
$106$	0.760484	+	0.760484i	0.0738648	+	0.0738648i
$107$	10.1957	−	10.1957i	0.985655	−	0.985655i	−0.0142431	−	0.999899i	$-0.504534\pi$
$107$	10.1957	−	10.1957i	0.985655	−	0.985655i	0.999899	+	0.0142431i	$0.00453387\pi$
$108$		0			0
$109$	−3.71769	+	3.71769i	−0.356090	+	0.356090i	−0.862369	−	0.506280i	$-0.831020\pi$
$109$	−3.71769	+	3.71769i	−0.356090	+	0.356090i	0.506280	+	0.862369i	$0.331020\pi$
$110$	−0.974244	+	3.35030i	−0.0928905	+	0.319439i
$111$		0			0
$112$			33.0273i			3.12079i
$113$	6.07606	+	6.07606i	0.571587	+	0.571587i	0.932572	−	0.360985i	$-0.117559\pi$
$113$	6.07606	+	6.07606i	0.571587	+	0.571587i	−0.360985	+	0.932572i	$0.617559\pi$
$114$		0			0
$115$	3.91518	−	13.4638i	0.365093	−	1.25551i
$116$			24.1959i			2.24654i
$117$		0			0
$118$	6.60557	+	6.60557i	0.608092	+	0.608092i
$119$	9.22595	−	9.22595i	0.845742	−	0.845742i
$120$		0			0
$121$			10.6748i			0.970437i
$122$	−22.0464			−1.99599
$123$		0			0
$124$	−11.3204	−	11.3204i	−1.01661	−	1.01661i
$125$	−0.710229	+	11.1578i	−0.0635248	+	0.997980i
$126$		0			0
$127$	6.69689	+	6.69689i	0.594253	+	0.594253i	0.938777	−	0.344524i	$-0.111960\pi$
$127$	6.69689	+	6.69689i	0.594253	+	0.594253i	−0.344524	+	0.938777i	$0.611960\pi$
$128$	39.6785			3.50712
$129$		0			0
$130$	−7.62996	+	20.6987i	−0.669191	+	1.81539i
$131$	11.8946			1.03923			0.519617	−	0.854400i	$-0.326075\pi$
$131$	11.8946			1.03923			0.519617	+	0.854400i	$0.326075\pi$
$132$		0			0
$133$	−1.00944	−	1.00944i	−0.0875300	−	0.0875300i
$134$	−17.7365			−1.53220
$135$		0			0
$136$	−40.3318	−	40.3318i	−3.45842	−	3.45842i
$137$		−	20.1238i		−	1.71929i	−0.510892	−	0.859645i	$-0.670685\pi$
$137$		−	20.1238i		−	1.71929i	0.510892	−	0.859645i	$-0.329315\pi$
$138$		0			0
$139$		−	1.95472i		−	0.165797i	−0.996558	−	0.0828985i	$-0.973582\pi$
$139$		−	1.95472i		−	0.165797i	0.996558	−	0.0828985i	$-0.0264177\pi$
$140$	−12.8945	−	23.4687i	−1.08979	−	1.98347i
$141$		0			0
$142$	−6.36081	−	6.36081i	−0.533787	−	0.533787i
$143$	0.144174	−	2.05105i	0.0120564	−	0.171517i
$144$		0			0
$145$	−4.74820	−	8.64196i	−0.394316	−	0.717675i
$146$	−8.16112			−0.675419
$147$		0			0
$148$		−	25.1392i		−	2.06643i
$149$	−8.07404	+	8.07404i	−0.661451	+	0.661451i	−0.955722	−	0.294271i	$-0.904923\pi$
$149$	−8.07404	+	8.07404i	−0.661451	+	0.661451i	0.294271	+	0.955722i	$0.404923\pi$
$150$		0			0
$151$	6.07785	−	6.07785i	0.494608	−	0.494608i	−0.415146	−	0.909755i	$-0.636270\pi$
$151$	6.07785	−	6.07785i	0.494608	−	0.494608i	0.909755	+	0.415146i	$0.136270\pi$
$152$	−4.41285	+	4.41285i	−0.357929	+	0.357929i
$153$		0			0
$154$	2.40808	+	2.40808i	0.194048	+	0.194048i
$155$	6.26479	+	1.82176i	0.503200	+	0.146327i
$156$		0			0
$157$	−6.06202	+	6.06202i	−0.483802	+	0.483802i	−0.906343	−	0.422542i	$-0.861138\pi$
$157$	−6.06202	+	6.06202i	−0.483802	+	0.483802i	0.422542	+	0.906343i	$0.361138\pi$
$158$			34.7927i			2.76796i
$159$		0			0
$160$	−43.7496	+	24.0376i	−3.45871	+	1.90034i
$161$	−9.67731	−	9.67731i	−0.762679	−	0.762679i
$162$		0			0
$163$	−1.10175			−0.0862953			−0.0431477	−	0.999069i	$-0.513739\pi$
$163$	−1.10175			−0.0862953			−0.0431477	+	0.999069i	$0.513739\pi$
$164$	−37.5148	−	37.5148i	−2.92942	−	2.92942i
$165$		0			0
$166$			1.51480i			0.117571i
$167$			19.4106i			1.50204i	0.660280	+	0.751020i	$0.270438\pi$
$167$			19.4106i			1.50204i	−0.660280	+	0.751020i	$0.729562\pi$
$168$		0			0
$169$	1.81863	−	12.8722i	0.139895	−	0.990166i
$170$	35.1218	+	10.2132i	2.69372	+	0.783314i
$171$		0			0
$172$	6.68505	−	6.68505i	0.509730	−	0.509730i
$173$	12.9851	−	12.9851i	0.987237	−	0.987237i	−0.0126824	−	0.999920i	$-0.504037\pi$
$173$	12.9851	−	12.9851i	0.987237	−	0.987237i	0.999920	+	0.0126824i	$0.00403703\pi$
$174$		0			0
$175$	9.21097	+	5.85180i	0.696284	+	0.442355i
$176$	6.10200	−	6.10200i	0.459956	−	0.459956i
$177$		0			0
$178$	20.6868	+	20.6868i	1.55054	+	1.55054i
$179$	−6.05315			−0.452433			−0.226217	−	0.974077i	$-0.572636\pi$
$179$	−6.05315			−0.452433			−0.226217	+	0.974077i	$0.572636\pi$
$180$		0			0
$181$			0.642386i			0.0477482i	0.999715	+	0.0238741i	$0.00760009\pi$
$181$			0.642386i			0.0477482i	−0.999715	+	0.0238741i	$0.992400\pi$
$182$	14.1203	+	16.2555i	1.04667	+	1.20494i
$183$		0			0
$184$	−42.3049	+	42.3049i	−3.11876	+	3.11876i
$185$	4.93331	+	8.97887i	0.362704	+	0.660140i
$186$		0			0
$187$	−3.40911			−0.249298
$188$		−	29.0124i		−	2.11595i
$189$		0			0
$190$	1.11746	−	3.84280i	0.0810690	−	0.278786i
$191$	24.0434			1.73972			0.869861	−	0.493298i	$-0.164209\pi$
$191$	24.0434			1.73972			0.869861	+	0.493298i	$0.164209\pi$
$192$		0			0
$193$	−15.5465			−1.11906			−0.559531	−	0.828810i	$-0.689019\pi$
$193$	−15.5465			−1.11906			−0.559531	+	0.828810i	$0.689019\pi$
$194$	27.0497			1.94206
$195$		0			0
$196$	12.2720			0.876568
$197$	3.65831			0.260644			0.130322	−	0.991472i	$-0.458399\pi$
$197$	3.65831			0.260644			0.130322	+	0.991472i	$0.458399\pi$
$198$		0			0
$199$	16.5387			1.17240			0.586199	−	0.810167i	$-0.300624\pi$
$199$	16.5387			1.17240			0.586199	+	0.810167i	$0.300624\pi$
$200$	25.5815	−	40.2663i	1.80888	−	2.84726i
$201$		0			0
$202$			18.7008i			1.31578i
$203$	−9.62436			−0.675498
$204$		0			0
$205$	20.7609	+	6.03712i	1.45000	+	0.421651i
$206$	−23.4658	+	23.4658i	−1.63494	+	1.63494i
$207$		0			0
$208$	41.1910	−	35.7805i	2.85608	−	2.48093i
$209$			0.373003i			0.0258011i
$210$		0			0
$211$	6.29230			0.433180			0.216590	−	0.976263i	$-0.430507\pi$
$211$	6.29230			0.433180			0.216590	+	0.976263i	$0.430507\pi$
$212$	1.52499	+	1.52499i	0.104737	+	0.104737i
$213$		0			0
$214$	27.8977	−	27.8977i	1.90705	−	1.90705i
$215$	−1.07580	+	3.69954i	−0.0733690	+	0.252307i
$216$		0			0
$217$	4.50291	−	4.50291i	0.305677	−	0.305677i
$218$	−10.1724	+	10.1724i	−0.688964	+	0.688964i
$219$		0			0
$220$	−1.95364	+	6.71834i	−0.131715	+	0.452950i
$221$	−21.5015	−	1.51140i	−1.44634	−	0.101668i
$222$		0			0
$223$		−	26.7096i		−	1.78861i	−0.447459	−	0.894304i	$-0.647671\pi$
$223$		−	26.7096i		−	1.78861i	0.447459	−	0.894304i	$-0.352329\pi$
$224$			48.7230i			3.25544i
$225$		0			0
$226$	16.6255	+	16.6255i	1.10591	+	1.10591i
$227$	−15.1974			−1.00869			−0.504343	−	0.863503i	$-0.668265\pi$
$227$	−15.1974			−1.00869			−0.504343	+	0.863503i	$0.668265\pi$
$228$		0			0
$229$	2.32027	+	2.32027i	0.153328	+	0.153328i	0.779602	−	0.626275i	$-0.215421\pi$
$229$	2.32027	+	2.32027i	0.153328	+	0.153328i	−0.626275	+	0.779602i	$0.715421\pi$
$230$	10.7128	−	36.8401i	0.706383	−	2.42916i
$231$		0			0
$232$			42.0735i			2.76226i
$233$	−3.25148	+	3.25148i	−0.213011	+	0.213011i	−0.805545	−	0.592534i	$-0.798128\pi$
$233$	−3.25148	+	3.25148i	−0.213011	+	0.213011i	0.592534	+	0.805545i	$0.298128\pi$
$234$		0			0
$235$	5.69338	+	10.3622i	0.371395	+	0.675958i
$236$	13.2461	+	13.2461i	0.862247	+	0.862247i
$237$		0			0
$238$	25.2443	−	25.2443i	1.63634	−	1.63634i
$239$	10.0778	−	10.0778i	0.651877	−	0.651877i	−0.301567	−	0.953445i	$-0.597510\pi$
$239$	10.0778	−	10.0778i	0.651877	−	0.651877i	0.953445	+	0.301567i	$0.0975098\pi$
$240$		0			0
$241$	−1.54296	+	1.54296i	−0.0993911	+	0.0993911i	−0.755054	−	0.655663i	$-0.772389\pi$
$241$	−1.54296	+	1.54296i	−0.0993911	+	0.0993911i	0.655663	+	0.755054i	$0.272389\pi$
$242$			29.2087i			1.87760i
$243$		0			0
$244$	−44.2095			−2.83022
$245$	−4.38312	+	2.40824i	−0.280027	+	0.153857i
$246$		0			0
$247$	−0.165368	+	2.35255i	−0.0105221	+	0.149689i
$248$	−19.6847	−	19.6847i	−1.24998	−	1.24998i
$249$		0			0
$250$	−1.94335	+	30.5302i	−0.122908	+	1.93090i
$251$			17.9493i			1.13295i	0.824078	+	0.566476i	$0.191694\pi$
$251$			17.9493i			1.13295i	−0.824078	+	0.566476i	$0.808306\pi$
$252$		0			0
$253$			3.57589i			0.224814i
$254$	18.3242	+	18.3242i	1.14976	+	1.14976i
$255$		0			0
$256$	46.9322			2.93326
$257$	6.15242	+	6.15242i	0.383778	+	0.383778i	0.872461	−	0.488684i	$-0.162523\pi$
$257$	6.15242	+	6.15242i	0.383778	+	0.383778i	−0.488684	+	0.872461i	$0.662523\pi$
$258$		0			0
$259$	9.99958			0.621344
$260$	−15.3003	+	41.5069i	−0.948884	+	2.57415i
$261$		0			0
$262$	32.5462			2.01071
$263$	7.67855	+	7.67855i	0.473480	+	0.473480i	0.903039	−	0.429559i	$-0.141331\pi$
$263$	7.67855	+	7.67855i	0.473480	+	0.473480i	−0.429559	+	0.903039i	$0.641331\pi$
$264$		0			0
$265$	−0.843939	−	0.245412i	−0.0518428	−	0.0150755i
$266$	−2.76207	−	2.76207i	−0.169353	−	0.169353i
$267$		0			0
$268$	−35.5668			−2.17259
$269$		−	15.3699i		−	0.937121i	−0.883431	−	0.468561i	$-0.844773\pi$
$269$		−	15.3699i		−	0.937121i	0.883431	−	0.468561i	$-0.155227\pi$
$270$		0			0
$271$	−14.9961	+	14.9961i	−0.910946	+	0.910946i	−0.996347	−	0.0854010i	$-0.972783\pi$
$271$	−14.9961	+	14.9961i	−0.910946	+	0.910946i	0.0854010	+	0.996347i	$0.472783\pi$
$272$	−63.9683	−	63.9683i	−3.87865	−	3.87865i
$273$		0			0
$274$		−	55.0632i		−	3.32649i
$275$	−0.620628	−	2.78294i	−0.0374253	−	0.167818i
$276$		0			0
$277$	−21.1916	−	21.1916i	−1.27328	−	1.27328i	−0.944358	−	0.328920i	$-0.893315\pi$
$277$	−21.1916	−	21.1916i	−1.27328	−	1.27328i	−0.328920	−	0.944358i	$-0.606685\pi$
$278$		−	5.34855i		−	0.320785i
$279$		0			0
$280$	−22.4219	−	40.8089i	−1.33996	−	2.43880i
$281$	5.73727	−	5.73727i	0.342257	−	0.342257i	−0.514958	−	0.857215i	$-0.672193\pi$
$281$	5.73727	−	5.73727i	0.342257	−	0.342257i	0.857215	+	0.514958i	$0.172193\pi$
$282$		0			0
$283$	−11.7247	+	11.7247i	−0.696964	+	0.696964i	−0.963754	−	0.266791i	$-0.914037\pi$
$283$	−11.7247	+	11.7247i	−0.696964	+	0.696964i	0.266791	+	0.963754i	$0.414037\pi$
$284$	−12.7553	−	12.7553i	−0.756886	−	0.756886i
$285$		0			0
$286$	0.394493	−	5.61212i	0.0233269	−	0.331852i
$287$	14.9222	−	14.9222i	0.880830	−	0.880830i
$288$		0			0
$289$			18.7382i			1.10225i
$290$	−12.9921	−	23.6464i	−0.762925	−	1.38856i
$291$		0			0
$292$	−16.3654			−0.957715
$293$	−24.9122			−1.45539			−0.727693	−	0.685903i	$-0.759408\pi$
$293$	−24.9122			−1.45539			−0.727693	+	0.685903i	$0.759408\pi$
$294$		0			0
$295$	−7.33046	−	2.13164i	−0.426796	−	0.124109i
$296$		−	43.7137i		−	2.54081i
$297$		0			0
$298$	−22.0924	+	22.0924i	−1.27978	+	1.27978i
$299$	−1.58534	+	22.5534i	−0.0916829	+	1.30430i
$300$		0			0
$301$	2.65910	+	2.65910i	0.153268	+	0.153268i
$302$	16.6304	−	16.6304i	0.956971	−	0.956971i
$303$		0			0
$304$	−6.99901	+	6.99901i	−0.401420	+	0.401420i
$305$	15.7901	−	8.67565i	0.904139	−	0.496766i
$306$		0			0
$307$		−	17.4397i		−	0.995334i	−0.867368	−	0.497667i	$-0.834190\pi$
$307$		−	17.4397i		−	0.995334i	0.867368	−	0.497667i	$-0.165810\pi$
$308$	4.82890	+	4.82890i	0.275152	+	0.275152i
$309$		0			0
$310$	17.1419	+	4.98474i	0.973593	+	0.283114i
$311$			17.2745i			0.979549i	0.871849	+	0.489774i	$0.162921\pi$
$311$			17.2745i			0.979549i	−0.871849	+	0.489774i	$0.837079\pi$
$312$		0			0
$313$	−4.81994	−	4.81994i	−0.272439	−	0.272439i	0.557642	−	0.830081i	$-0.311706\pi$
$313$	−4.81994	−	4.81994i	−0.272439	−	0.272439i	−0.830081	+	0.557642i	$0.811706\pi$
$314$	−16.5870	+	16.5870i	−0.936061	+	0.936061i
$315$		0			0
$316$			69.7696i			3.92485i
$317$	−6.98466			−0.392298			−0.196149	−	0.980574i	$-0.562844\pi$
$317$	−6.98466			−0.392298			−0.196149	+	0.980574i	$0.562844\pi$
$318$		0			0
$319$	1.77816	+	1.77816i	0.0995579	+	0.0995579i
$320$	−60.3967	+	33.1841i	−3.37628	+	1.85505i
$321$		0			0
$322$	−26.4793	−	26.4793i	−1.47563	−	1.47563i
$323$	3.91025			0.217572
$324$		0			0
$325$	−2.68055	−	17.8274i	−0.148690	−	0.988884i
$326$	−3.01462			−0.166965
$327$		0			0
$328$	−65.2333	−	65.2333i	−3.60191	−	3.60191i
$329$	11.5402			0.636232
$330$		0			0
$331$	−2.71466	−	2.71466i	−0.149211	−	0.149211i	0.628554	−	0.777766i	$-0.283647\pi$
$331$	−2.71466	−	2.71466i	−0.149211	−	0.149211i	−0.777766	+	0.628554i	$0.783647\pi$
$332$			3.03762i			0.166711i
$333$		0			0
$334$			53.1119i			2.90615i
$335$	12.7033	−	6.97961i	0.694053	−	0.381337i
$336$		0			0
$337$	−24.3781	−	24.3781i	−1.32796	−	1.32796i	−0.907150	−	0.420808i	$-0.861747\pi$
$337$	−24.3781	−	24.3781i	−1.32796	−	1.32796i	−0.420808	−	0.907150i	$-0.638253\pi$
$338$	4.97619	−	35.2212i	0.270669	−	1.91578i
$339$		0			0
$340$	70.4295	+	20.4804i	3.81958	+	1.11071i
$341$	−1.66388			−0.0901042
$342$		0			0
$343$			20.1591i			1.08849i
$344$	11.6244	−	11.6244i	0.626746	−	0.626746i
$345$		0			0
$346$	35.5301	−	35.5301i	1.91011	−	1.91011i
$347$	13.2149	−	13.2149i	0.709412	−	0.709412i	−0.257000	−	0.966411i	$-0.582734\pi$
$347$	13.2149	−	13.2149i	0.709412	−	0.709412i	0.966411	+	0.257000i	$0.0827340\pi$
$348$		0			0
$349$	23.3899	+	23.3899i	1.25203	+	1.25203i	0.954807	+	0.297228i	$0.0960621\pi$
$349$	23.3899	+	23.3899i	1.25203	+	1.25203i	0.297228	+	0.954807i	$0.403938\pi$
$350$	25.2033	+	16.0119i	1.34717	+	0.855869i
$351$		0			0
$352$	9.00187	−	9.00187i	0.479802	−	0.479802i
$353$		−	7.41087i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$353$		−	7.41087i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$354$		0			0
$355$	7.05884	+	2.05266i	0.374644	+	0.108944i
$356$	41.4830	+	41.4830i	2.19860	+	2.19860i
$357$		0			0
$358$	−16.5628			−0.875370
$359$	10.9837	+	10.9837i	0.579700	+	0.579700i	0.934821	−	0.355120i	$-0.115560\pi$
$359$	10.9837	+	10.9837i	0.579700	+	0.579700i	−0.355120	+	0.934821i	$0.615560\pi$
$360$		0			0
$361$			18.5722i			0.977482i
$362$			1.75771i			0.0923834i
$363$		0			0
$364$	28.3153	+	32.5971i	1.48413	+	1.70855i
$365$	5.84517	−	3.21154i	0.305950	−	0.168100i
$366$		0			0
$367$	10.6094	−	10.6094i	0.553807	−	0.553807i	−0.373730	−	0.927537i	$-0.621921\pi$
$367$	10.6094	−	10.6094i	0.553807	−	0.553807i	0.927537	+	0.373730i	$0.121921\pi$
$368$	−67.0978	+	67.0978i	−3.49772	+	3.49772i
$369$		0			0
$370$	13.4987	+	24.5682i	0.701761	+	1.27724i
$371$	−0.606593	+	0.606593i	−0.0314928	+	0.0314928i
$372$		0			0
$373$	−2.17179	−	2.17179i	−0.112451	−	0.112451i	0.648642	−	0.761093i	$-0.275337\pi$
$373$	−2.17179	−	2.17179i	−0.112451	−	0.112451i	−0.761093	+	0.648642i	$0.775337\pi$
$374$	−9.32808			−0.482344
$375$		0			0
$376$		−	50.4487i		−	2.60169i
$377$	10.4267	+	12.0033i	0.537000	+	0.618203i
$378$		0			0
$379$	−18.8444	+	18.8444i	−0.967974	+	0.967974i	−0.999503	−	0.0315286i	$-0.989962\pi$
$379$	−18.8444	+	18.8444i	−0.967974	+	0.967974i	0.0315286	+	0.999503i	$0.489962\pi$
$380$	2.24083	−	7.70595i	0.114952	−	0.395307i
$381$		0			0
$382$	65.7883			3.36602
$383$			13.3355i			0.681410i	0.940170	+	0.340705i	$0.110666\pi$
$383$			13.3355i			0.681410i	−0.940170	+	0.340705i	$0.889334\pi$
$384$		0			0
$385$	−2.67234	−	0.777097i	−0.136195	−	0.0396045i
$386$	−42.5388			−2.16517
$387$		0			0
$388$	54.2426			2.75375
$389$	−14.5958			−0.740038			−0.370019	−	0.929024i	$-0.620649\pi$
$389$	−14.5958			−0.740038			−0.370019	+	0.929024i	$0.620649\pi$
$390$		0			0
$391$	37.4867			1.89578
$392$	21.3393			1.07780
$393$		0			0
$394$	10.0100			0.504295
$395$	−13.6916	−	24.9193i	−0.688897	−	1.25383i
$396$		0			0
$397$			2.66580i			0.133793i	0.997760	+	0.0668963i	$0.0213097\pi$
$397$			2.66580i			0.133793i	−0.997760	+	0.0668963i	$0.978690\pi$
$398$	45.2537			2.26836
$399$		0			0
$400$	40.5736	−	63.8645i	2.02868	−	3.19322i
$401$	3.94441	−	3.94441i	0.196974	−	0.196974i	−0.601727	−	0.798702i	$-0.705521\pi$
$401$	3.94441	−	3.94441i	0.196974	−	0.196974i	0.798702	+	0.601727i	$0.205521\pi$
$402$		0			0
$403$	−10.4942	−	0.737670i	−0.522754	−	0.0367459i
$404$			37.5006i			1.86572i
$405$		0			0
$406$	−26.3344			−1.30696
$407$	−1.84748	−	1.84748i	−0.0915764	−	0.0915764i
$408$		0			0
$409$	−6.46298	+	6.46298i	−0.319574	+	0.319574i	−0.848603	−	0.529030i	$-0.822556\pi$
$409$	−6.46298	+	6.46298i	−0.319574	+	0.319574i	0.529030	+	0.848603i	$0.322556\pi$
$410$	56.8066	+	16.5189i	2.80548	+	0.815812i
$411$		0			0
$412$	−47.0557	+	47.0557i	−2.31827	+	2.31827i
$413$	−5.26887	+	5.26887i	−0.259264	+	0.259264i
$414$		0			0
$415$	−0.596101	−	1.08493i	−0.0292615	−	0.0532573i
$416$	60.7664	−	52.7845i	2.97932	−	2.58797i
$417$		0			0
$418$			1.02062i			0.0499201i
$419$			4.68103i			0.228683i	0.993441	+	0.114342i	$0.0364759\pi$
$419$			4.68103i			0.228683i	−0.993441	+	0.114342i	$0.963524\pi$
$420$		0			0
$421$	−14.8900	−	14.8900i	−0.725692	−	0.725692i	0.244066	−	0.969759i	$-0.421519\pi$
$421$	−14.8900	−	14.8900i	−0.725692	−	0.725692i	−0.969759	+	0.244066i	$0.921519\pi$
$422$	17.2171			0.838118
$423$		0			0
$424$	2.65176	+	2.65176i	0.128781	+	0.128781i
$425$	−29.1741	+	6.50615i	−1.41515	+	0.315595i
$426$		0			0
$427$		−	17.5851i		−	0.851003i
$428$	55.9431	−	55.9431i	2.70411	−	2.70411i
$429$		0			0
$430$	−2.94363	+	10.1228i	−0.141955	+	0.488164i
$431$	8.23888	+	8.23888i	0.396853	+	0.396853i	0.877122	−	0.480269i	$-0.159461\pi$
$431$	8.23888	+	8.23888i	0.396853	+	0.396853i	−0.480269	+	0.877122i	$0.659461\pi$
$432$		0			0
$433$	−20.2068	+	20.2068i	−0.971076	+	0.971076i	−0.999593	−	0.0285175i	$-0.990921\pi$
$433$	−20.2068	+	20.2068i	−0.971076	+	0.971076i	0.0285175	+	0.999593i	$0.490921\pi$
$434$	12.3210	−	12.3210i	0.591425	−	0.591425i
$435$		0			0
$436$	−20.3987	+	20.3987i	−0.976921	+	0.976921i
$437$		−	4.10155i		−	0.196204i
$438$		0			0
$439$	14.1906			0.677282			0.338641	−	0.940916i	$-0.390033\pi$
$439$	14.1906			0.677282			0.338641	+	0.940916i	$0.390033\pi$
$440$	−3.39713	+	11.6823i	−0.161952	+	0.556931i
$441$		0			0
$442$	−58.8329	−	4.13554i	−2.79839	−	0.196708i
$443$	−7.40061	−	7.40061i	−0.351613	−	0.351613i	0.509096	−	0.860710i	$-0.329980\pi$
$443$	−7.40061	−	7.40061i	−0.351613	−	0.351613i	−0.860710	+	0.509096i	$0.829980\pi$
$444$		0			0
$445$	−22.9569	−	6.67571i	−1.08826	−	0.316459i
$446$		−	73.0836i		−	3.46061i
$447$		0			0
$448$			67.2625i			3.17785i
$449$	−14.0038	−	14.0038i	−0.660879	−	0.660879i	0.294709	−	0.955587i	$-0.404777\pi$
$449$	−14.0038	−	14.0038i	−0.660879	−	0.660879i	−0.955587	+	0.294709i	$0.904777\pi$
$450$		0			0
$451$	−5.51394			−0.259641
$452$	33.3389	+	33.3389i	1.56813	+	1.56813i
$453$		0			0
$454$	−41.5835			−1.95161
$455$	−16.5101	−	6.08597i	−0.774006	−	0.285315i
$456$		0			0
$457$	−10.1902			−0.476680			−0.238340	−	0.971182i	$-0.576603\pi$
$457$	−10.1902			−0.476680			−0.238340	+	0.971182i	$0.576603\pi$
$458$	6.34879	+	6.34879i	0.296659	+	0.296659i
$459$		0			0
$460$	21.4824	−	73.8751i	1.00162	−	3.44444i
$461$	8.03629	+	8.03629i	0.374288	+	0.374288i	0.869036	−	0.494749i	$-0.164740\pi$
$461$	8.03629	+	8.03629i	0.374288	+	0.374288i	−0.494749	+	0.869036i	$0.664740\pi$
$462$		0			0
$463$	14.2791			0.663606			0.331803	−	0.943349i	$-0.392343\pi$
$463$	14.2791			0.663606			0.331803	+	0.943349i	$0.392343\pi$
$464$			66.7307i			3.09790i
$465$		0			0
$466$	−8.89678	+	8.89678i	−0.412135	+	0.412135i
$467$	−25.6127	−	25.6127i	−1.18521	−	1.18521i	−0.978375	−	0.206840i	$-0.933682\pi$
$467$	−25.6127	−	25.6127i	−1.18521	−	1.18521i	−0.206840	−	0.978375i	$-0.566318\pi$
$468$		0			0
$469$		−	14.1473i		−	0.653263i
$470$	15.5784	+	28.3534i	0.718577	+	1.30785i
$471$		0			0
$472$	23.0332	+	23.0332i	1.06019	+	1.06019i
$473$		−	0.982570i		−	0.0451786i
$474$		0			0
$475$	0.711862	+	3.19204i	0.0326625	+	0.146461i
$476$	50.6222	−	50.6222i	2.32027	−	2.32027i
$477$		0			0
$478$	27.5751	−	27.5751i	1.26126	−	1.26126i
$479$	6.00774	+	6.00774i	0.274500	+	0.274500i	0.830909	−	0.556408i	$-0.187821\pi$
$479$	6.00774	+	6.00774i	0.274500	+	0.274500i	−0.556408	+	0.830909i	$0.687821\pi$
$480$		0			0
$481$	−10.8331	−	12.4713i	−0.493949	−	0.568642i
$482$	−4.22190	+	4.22190i	−0.192302	+	0.192302i
$483$		0			0
$484$			58.5720i			2.66236i
$485$	−19.3736	+	10.6445i	−0.879709	+	0.483343i
$486$		0			0
$487$	43.1824			1.95678			0.978391	−	0.206761i	$-0.0662923\pi$
$487$	43.1824			1.95678			0.978391	+	0.206761i	$0.0662923\pi$
$488$	−76.8744			−3.47994
$489$		0			0
$490$	−11.9932	+	6.58949i	−0.541798	+	0.297683i
$491$			35.5626i			1.60492i	0.596706	+	0.802460i	$0.296476\pi$
$491$			35.5626i			1.60492i	−0.596706	+	0.802460i	$0.703524\pi$
$492$		0			0
$493$	18.6408	−	18.6408i	0.839538	−	0.839538i
$494$	−0.452484	+	6.43712i	−0.0203582	+	0.289620i
$495$		0			0
$496$	−31.2210	−	31.2210i	−1.40186	−	1.40186i
$497$	5.07364	−	5.07364i	0.227584	−	0.227584i
$498$		0			0
$499$	8.05960	−	8.05960i	0.360797	−	0.360797i	−0.503309	−	0.864106i	$-0.667884\pi$
$499$	8.05960	−	8.05960i	0.360797	−	0.360797i	0.864106	+	0.503309i	$0.167884\pi$
$500$	−3.89698	+	61.2219i	−0.174278	+	2.73793i
$501$		0			0
$502$			49.1134i			2.19204i
$503$	0.598343	+	0.598343i	0.0266788	+	0.0266788i	0.720320	−	0.693642i	$-0.243995\pi$
$503$	0.598343	+	0.598343i	0.0266788	+	0.0266788i	−0.693642	+	0.720320i	$0.743995\pi$
$504$		0			0
$505$	−7.35909	−	13.3939i	−0.327475	−	0.596022i
$506$			9.78444i			0.434971i
$507$		0			0
$508$	36.7454	+	36.7454i	1.63031	+	1.63031i
$509$	−10.1171	+	10.1171i	−0.448434	+	0.448434i	−0.894834	−	0.446400i	$-0.852706\pi$
$509$	−10.1171	+	10.1171i	−0.448434	+	0.448434i	0.446400	+	0.894834i	$0.352706\pi$
$510$		0			0
$511$		−	6.50964i		−	0.287970i
$512$	49.0601			2.16817
$513$		0			0
$514$	16.8344	+	16.8344i	0.742534	+	0.742534i
$515$	7.57250	−	26.0409i	0.333684	−	1.14750i
$516$		0			0
$517$	−2.13213	−	2.13213i	−0.0937708	−	0.0937708i
$518$	27.3611			1.20218
$519$		0			0
$520$	−26.6052	+	72.1749i	−1.16671	+	3.16508i
$521$	17.8118			0.780350			0.390175	−	0.920741i	$-0.372414\pi$
$521$	17.8118			0.780350			0.390175	+	0.920741i	$0.372414\pi$
$522$		0			0
$523$	8.40927	+	8.40927i	0.367712	+	0.367712i	0.866642	−	0.498930i	$-0.166274\pi$
$523$	8.40927	+	8.40927i	0.367712	+	0.367712i	−0.498930	+	0.866642i	$0.666274\pi$
$524$	65.2647			2.85110
$525$		0			0
$526$	21.0103	+	21.0103i	0.916091	+	0.916091i
$527$			17.4427i			0.759818i
$528$		0			0
$529$		−	16.3206i		−	0.709592i
$530$	−2.30921	−	0.671502i	−0.100306	−	0.0291682i
$531$		0			0
$532$	−5.53876	−	5.53876i	−0.240136	−	0.240136i
$533$	−34.7768	−	2.44457i	−1.50635	−	0.105886i
$534$		0			0
$535$	−9.00272	+	30.9592i	−0.389222	+	1.33848i
$536$	−61.8459			−2.67134
$537$		0			0
$538$		−	42.0556i		−	1.81315i
$539$	0.901867	−	0.901867i	0.0388462	−	0.0388462i
$540$		0			0
$541$	7.53385	−	7.53385i	0.323906	−	0.323906i	−0.526358	−	0.850263i	$-0.676443\pi$
$541$	7.53385	−	7.53385i	0.323906	−	0.323906i	0.850263	+	0.526358i	$0.176443\pi$
$542$	−41.0326	+	41.0326i	−1.76250	+	1.76250i
$543$		0			0
$544$	−94.3682	−	94.3682i	−4.04600	−	4.04600i
$545$	3.28269	−	11.2887i	0.140615	−	0.483557i
$546$		0			0
$547$	2.00219	−	2.00219i	0.0856074	−	0.0856074i	−0.663006	−	0.748614i	$-0.730720\pi$
$547$	2.00219	−	2.00219i	0.0856074	−	0.0856074i	0.748614	+	0.663006i	$0.230720\pi$
$548$		−	110.418i		−	4.71682i
$549$		0			0
$550$	−1.69818	−	7.61476i	−0.0724106	−	0.324694i
$551$	−2.03955	−	2.03955i	−0.0868880	−	0.0868880i
$552$		0			0
$553$	−27.7521			−1.18014
$554$	−57.9849	−	57.9849i	−2.46354	−	2.46354i
$555$		0			0
$556$		−	10.7254i		−	0.454859i
$557$			10.8795i			0.460977i	0.973075	+	0.230489i	$0.0740325\pi$
$557$			10.8795i			0.460977i	−0.973075	+	0.230489i	$0.925968\pi$
$558$		0			0
$559$	0.435616	−	6.19714i	0.0184246	−	0.262111i
$560$	−35.5622	−	64.7251i	−1.50278	−	2.73513i
$561$		0			0
$562$	15.6985	−	15.6985i	0.662200	−	0.662200i
$563$	7.54907	−	7.54907i	0.318155	−	0.318155i	−0.529903	−	0.848058i	$-0.677772\pi$
$563$	7.54907	−	7.54907i	0.318155	−	0.318155i	0.848058	+	0.529903i	$0.177772\pi$
$564$		0			0
$565$	−18.4499	−	5.36511i	−0.776195	−	0.225712i
$566$	−32.0816	+	32.0816i	−1.34849	+	1.34849i
$567$		0			0
$568$	−22.1797	−	22.1797i	−0.930640	−	0.930640i
$569$	−18.9891			−0.796063			−0.398031	−	0.917372i	$-0.630307\pi$
$569$	−18.9891			−0.796063			−0.398031	+	0.917372i	$0.630307\pi$
$570$		0			0
$571$		−	11.6537i		−	0.487690i	−0.969814	−	0.243845i	$-0.921591\pi$
$571$		−	11.6537i		−	0.487690i	0.969814	−	0.243845i	$-0.0784089\pi$
$572$	0.791074	−	11.2540i	0.0330765	−	0.470551i
$573$		0			0
$574$	40.8305	−	40.8305i	1.70423	−	1.70423i
$575$	6.82445	+	30.6013i	0.284599	+	1.27616i
$576$		0			0
$577$	−44.8098			−1.86545			−0.932727	−	0.360583i	$-0.882578\pi$
$577$	−44.8098			−1.86545			−0.932727	+	0.360583i	$0.882578\pi$
$578$			51.2721i			2.13264i
$579$		0			0
$580$	−26.0530	−	47.4179i	−1.08179	−	1.96892i
$581$	−1.20827			−0.0501274
$582$		0			0
$583$	0.224144			0.00928309
$584$	−28.4573			−1.17757
$585$		0			0
$586$	−68.1654			−2.81589
$587$	−40.6108			−1.67619			−0.838094	−	0.545526i	$-0.816330\pi$
$587$	−40.6108			−1.67619			−0.838094	+	0.545526i	$0.816330\pi$
$588$		0			0
$589$	1.90847			0.0786373
$590$	−20.0578	−	5.83266i	−0.825766	−	0.240127i
$591$		0			0
$592$		−	69.3323i		−	2.84954i
$593$	37.0717			1.52235			0.761177	−	0.648544i	$-0.224622\pi$
$593$	37.0717			1.52235			0.761177	+	0.648544i	$0.224622\pi$
$594$		0			0
$595$	−8.14644	+	28.0146i	−0.333972	+	1.14849i
$596$	−44.3017	+	44.3017i	−1.81467	+	1.81467i
$597$		0			0
$598$	−4.33786	+	61.7111i	−0.177388	+	2.52356i
$599$		−	17.5005i		−	0.715052i	−0.933903	−	0.357526i	$-0.883620\pi$
$599$		−	17.5005i		−	0.715052i	0.933903	−	0.357526i	$-0.116380\pi$
$600$		0			0
$601$	12.1303			0.494806			0.247403	−	0.968913i	$-0.420423\pi$
$601$	12.1303			0.494806			0.247403	+	0.968913i	$0.420423\pi$
$602$	7.27590	+	7.27590i	0.296543	+	0.296543i
$603$		0			0
$604$	33.3488	−	33.3488i	1.35694	−	1.35694i
$605$	−11.4941	−	20.9199i	−0.467303	−	0.850515i
$606$		0			0
$607$	21.4794	−	21.4794i	0.871823	−	0.871823i	−0.120848	−	0.992671i	$-0.538561\pi$
$607$	21.4794	−	21.4794i	0.871823	−	0.871823i	0.992671	+	0.120848i	$0.0385613\pi$
$608$	−10.3252	+	10.3252i	−0.418741	+	0.418741i
$609$		0			0
$610$	43.2053	−	23.7385i	1.74933	−	0.961145i
$611$	−12.5022	−	14.3927i	−0.505785	−	0.582268i
$612$		0			0
$613$			0.726110i			0.0293273i	0.999892	+	0.0146637i	$0.00466775\pi$
$613$			0.726110i			0.0293273i	−0.999892	+	0.0146637i	$0.995332\pi$
$614$		−	47.7188i		−	1.92578i
$615$		0			0
$616$	8.39681	+	8.39681i	0.338317	+	0.338317i
$617$	−5.15654			−0.207595			−0.103797	−	0.994598i	$-0.533099\pi$
$617$	−5.15654			−0.207595			−0.103797	+	0.994598i	$0.533099\pi$
$618$		0			0
$619$	−9.30732	−	9.30732i	−0.374093	−	0.374093i	0.494873	−	0.868966i	$-0.335215\pi$
$619$	−9.30732	−	9.30732i	−0.374093	−	0.374093i	−0.868966	+	0.494873i	$0.835215\pi$
$620$	34.3745	+	9.99585i	1.38051	+	0.401443i
$621$		0			0
$622$			47.2670i			1.89524i
$623$	−16.5006	+	16.5006i	−0.661083	+	0.661083i
$624$		0			0
$625$	−10.6223	−	22.6311i	−0.424891	−	0.905244i
$626$	−13.1885	−	13.1885i	−0.527117	−	0.527117i
$627$		0			0
$628$	−33.2619	+	33.2619i	−1.32729	+	1.32729i
$629$	−19.3675	+	19.3675i	−0.772233	+	0.772233i
$630$		0			0
$631$	12.6202	−	12.6202i	0.502401	−	0.502401i	−0.409783	−	0.912183i	$-0.634395\pi$
$631$	12.6202	−	12.6202i	0.502401	−	0.502401i	0.912183	+	0.409783i	$0.134395\pi$
$632$			121.320i			4.82585i
$633$		0			0
$634$	−19.1116			−0.759019
$635$	−20.3351	−	5.91330i	−0.806974	−	0.234662i
$636$		0			0
$637$	6.08798	−	5.28830i	0.241214	−	0.209530i
$638$	4.86545	+	4.86545i	0.192625	+	0.192625i
$639$		0			0
$640$	−77.7599	+	42.7240i	−3.07373	+	1.68881i
$641$		−	45.1788i		−	1.78445i	−0.451586	−	0.892227i	$-0.649142\pi$
$641$		−	45.1788i		−	1.78445i	0.451586	−	0.892227i	$-0.350858\pi$
$642$		0			0
$643$		−	4.62889i		−	0.182545i	−0.995826	−	0.0912727i	$-0.970906\pi$
$643$		−	4.62889i		−	0.182545i	0.995826	−	0.0912727i	$-0.0290935\pi$
$644$	−53.0988	−	53.0988i	−2.09239	−	2.09239i
$645$		0			0
$646$	10.6993			0.420960
$647$	−10.9090	−	10.9090i	−0.428875	−	0.428875i	0.459370	−	0.888245i	$-0.348075\pi$
$647$	−10.9090	−	10.9090i	−0.428875	−	0.428875i	−0.888245	+	0.459370i	$0.848075\pi$
$648$		0			0
$649$	1.94691			0.0764231
$650$	−7.33458	−	48.7797i	−0.287686	−	1.91330i
$651$		0			0
$652$	−6.04520			−0.236748
$653$	−12.5146	−	12.5146i	−0.489732	−	0.489732i	0.418489	−	0.908222i	$-0.362560\pi$
$653$	−12.5146	−	12.5146i	−0.489732	−	0.489732i	−0.908222	+	0.418489i	$0.862560\pi$
$654$		0			0
$655$	−23.3103	+	12.8075i	−0.910810	+	0.500431i
$656$	−103.463	−	103.463i	−4.03957	−	4.03957i
$657$		0			0
$658$	31.5766			1.23099
$659$			18.9250i			0.737212i	0.929586	+	0.368606i	$0.120165\pi$
$659$			18.9250i			0.737212i	−0.929586	+	0.368606i	$0.879835\pi$
$660$		0			0
$661$	−19.8468	+	19.8468i	−0.771950	+	0.771950i	−0.978447	−	0.206497i	$-0.933794\pi$
$661$	−19.8468	+	19.8468i	−0.771950	+	0.771950i	0.206497	+	0.978447i	$0.433794\pi$
$662$	−7.42793	−	7.42793i	−0.288695	−	0.288695i
$663$		0			0
$664$			5.28202i			0.204982i
$665$	3.06518	+	0.891332i	0.118863	+	0.0345644i
$666$		0			0
$667$	−19.5527	−	19.5527i	−0.757085	−	0.757085i
$668$			106.505i			4.12080i
$669$		0			0
$670$	34.7590	−	19.0978i	1.34286	−	0.737813i
$671$	−3.24896	+	3.24896i	−0.125425	+	0.125425i
$672$		0			0
$673$	−1.67376	+	1.67376i	−0.0645189	+	0.0645189i	−0.738630	−	0.674111i	$-0.764527\pi$
$673$	−1.67376	+	1.67376i	−0.0645189	+	0.0645189i	0.674111	+	0.738630i	$0.264527\pi$
$674$	−66.7039	−	66.7039i	−2.56934	−	2.56934i
$675$		0			0
$676$	9.97872	−	70.6287i	0.383797	−	2.71649i
$677$	26.4518	−	26.4518i	1.01662	−	1.01662i	0.0167645	−	0.999859i	$-0.494663\pi$
$677$	26.4518	−	26.4518i	1.01662	−	1.01662i	0.999859	−	0.0167645i	$-0.00533657\pi$
$678$		0			0
$679$			21.5760i			0.828009i
$680$	122.467	+	35.6127i	4.69641	+	1.36568i
$681$		0			0
$682$	−4.55275			−0.174334
$683$	7.05381			0.269906			0.134953	−	0.990852i	$-0.456912\pi$
$683$	7.05381			0.269906			0.134953	+	0.990852i	$0.456912\pi$
$684$		0			0
$685$	21.6683	+	39.4375i	0.827905	+	1.50683i
$686$			55.1598i			2.10601i
$687$		0			0
$688$	18.4369	−	18.4369i	0.702901	−	0.702901i
$689$	1.41369	+	0.0993726i	0.0538573	+	0.00378580i
$690$		0			0
$691$	2.82022	+	2.82022i	0.107286	+	0.107286i	0.758712	−	0.651426i	$-0.225829\pi$
$691$	2.82022	+	2.82022i	0.107286	+	0.107286i	−0.651426	+	0.758712i	$0.725829\pi$
$692$	71.2483	−	71.2483i	2.70845	−	2.70845i
$693$		0			0
$694$	36.1589	−	36.1589i	1.37257	−	1.37257i
$695$	2.10475	+	3.83075i	0.0798377	+	0.145309i
$696$		0			0
$697$			57.8036i			2.18947i
$698$	64.0002	+	64.0002i	2.42244	+	2.42244i
$699$		0			0
$700$	50.5400	+	32.1085i	1.91023	+	1.21359i
$701$		−	34.2082i		−	1.29203i	−0.763326	−	0.646013i	$-0.776435\pi$
$701$		−	34.2082i		−	1.29203i	0.763326	−	0.646013i	$-0.223565\pi$
$702$		0			0
$703$	2.11907	+	2.11907i	0.0799222	+	0.0799222i
$704$	12.4272	−	12.4272i	0.468367	−	0.468367i
$705$		0			0
$706$		−	20.2778i		−	0.763166i
$707$	−14.9165			−0.560994
$708$		0			0
$709$	−11.6794	−	11.6794i	−0.438629	−	0.438629i	0.452922	−	0.891550i	$-0.350382\pi$
$709$	−11.6794	−	11.6794i	−0.438629	−	0.438629i	−0.891550	+	0.452922i	$0.850382\pi$
$710$	19.3146	+	5.61654i	0.724863	+	0.210785i
$711$		0			0
$712$	72.1334	+	72.1334i	2.70331	+	2.70331i
$713$	18.2961			0.685194
$714$		0			0
$715$	1.92592	+	4.17477i	0.0720255	+	0.156127i
$716$	−33.2132			−1.24124
$717$		0			0
$718$	30.0540	+	30.0540i	1.12161	+	1.12161i
$719$	−5.64612			−0.210565			−0.105282	−	0.994442i	$-0.533575\pi$
$719$	−5.64612			−0.210565			−0.105282	+	0.994442i	$0.533575\pi$
$720$		0			0
$721$	−18.7173	−	18.7173i	−0.697067	−	0.697067i
$722$			50.8177i			1.89124i
$723$		0			0
$724$			3.52473i			0.130996i
$725$	18.6105	+	11.8234i	0.691177	+	0.439110i
$726$		0			0
$727$	28.2805	+	28.2805i	1.04887	+	1.04887i	0.998743	+	0.0501220i	$0.0159610\pi$
$727$	28.2805	+	28.2805i	1.04887	+	1.04887i	0.0501220	+	0.998743i	$0.484039\pi$
$728$	49.2366	+	56.6819i	1.82483	+	2.10077i
$729$		0			0
$730$	15.9937	−	8.78751i	0.591954	−	0.325240i
$731$	−10.3005			−0.380976
$732$		0			0
$733$		−	11.2999i		−	0.417371i	−0.977983	−	0.208685i	$-0.933082\pi$
$733$		−	11.2999i		−	0.417371i	0.977983	−	0.208685i	$-0.0669184\pi$
$734$	29.0298	−	29.0298i	1.07151	−	1.07151i
$735$		0			0
$736$	−98.9850	+	98.9850i	−3.64863	+	3.64863i
$737$	−2.61381	+	2.61381i	−0.0962809	+	0.0962809i
$738$		0			0
$739$	−29.7175	−	29.7175i	−1.09318	−	1.09318i	−0.995187	−	0.0979893i	$-0.968759\pi$
$739$	−29.7175	−	29.7175i	−1.09318	−	1.09318i	−0.0979893	−	0.995187i	$-0.531241\pi$
$740$	27.0687	+	49.2665i	0.995067	+	1.81107i
$741$		0			0
$742$	−1.65978	+	1.65978i	−0.0609323	+	0.0609323i
$743$			0.480200i			0.0176168i	0.999961	+	0.00880841i	$0.00280384\pi$
$743$			0.480200i			0.0176168i	−0.999961	+	0.00880841i	$0.997196\pi$
$744$		0			0
$745$	7.12931	−	24.5168i	0.261198	−	0.898226i
$746$	−5.94252	−	5.94252i	−0.217571	−	0.217571i
$747$		0			0
$748$	−18.7055			−0.683942
$749$	22.2524	+	22.2524i	0.813085	+	0.813085i
$750$		0			0
$751$			14.4818i			0.528449i	0.964461	+	0.264224i	$0.0851160\pi$
$751$			14.4818i			0.528449i	−0.964461	+	0.264224i	$0.914884\pi$
$752$		−	80.0143i		−	2.91782i
$753$		0			0
$754$	28.5297	+	32.8438i	1.03899	+	1.19610i
$755$	−5.36669	+	18.4554i	−0.195314	+	0.671660i
$756$		0			0
$757$	3.80569	−	3.80569i	0.138320	−	0.138320i	−0.634556	−	0.772877i	$-0.718817\pi$
$757$	3.80569	−	3.80569i	0.138320	−	0.138320i	0.772877	+	0.634556i	$0.218817\pi$
$758$	−51.5627	+	51.5627i	−1.87284	+	1.87284i
$759$		0			0
$760$	3.89651	−	13.3996i	0.141341	−	0.486055i
$761$	7.13165	−	7.13165i	0.258522	−	0.258522i	−0.565931	−	0.824453i	$-0.691483\pi$
$761$	7.13165	−	7.13165i	0.258522	−	0.258522i	0.824453	+	0.565931i	$0.191483\pi$
$762$		0			0
$763$	−8.11395	−	8.11395i	−0.293745	−	0.293745i
$764$	131.925			4.77287
$765$		0			0
$766$			36.4888i			1.31840i
$767$	12.2793	+	0.863151i	0.443381	+	0.0311666i
$768$		0			0
$769$	−6.28641	+	6.28641i	−0.226694	+	0.226694i	−0.811310	−	0.584616i	$-0.801245\pi$
$769$	−6.28641	+	6.28641i	−0.226694	+	0.226694i	0.584616	+	0.811310i	$0.301245\pi$
$770$	−7.31212	−	2.12631i	−0.263511	−	0.0766270i
$771$		0			0
$772$	−85.3027			−3.07011
$773$		−	24.2193i		−	0.871108i	−0.900163	−	0.435554i	$-0.856553\pi$
$773$		−	24.2193i		−	0.871108i	0.900163	−	0.435554i	$-0.143447\pi$
$774$		0			0
$775$	−14.2390	+	3.17545i	−0.511479	+	0.114066i
$776$	94.3206			3.38591
$777$		0			0
$778$	−39.9375			−1.43183
$779$	6.32450			0.226599
$780$		0			0
$781$	−1.87477			−0.0670847
$782$	102.572			3.66797
$783$		0			0
$784$	33.8452			1.20876
$785$	5.35271	−	18.4073i	0.191046	−	0.656985i
$786$		0			0
$787$		−	32.7945i		−	1.16900i	−0.811394	−	0.584499i	$-0.801291\pi$
$787$		−	32.7945i		−	1.16900i	0.811394	−	0.584499i	$-0.198709\pi$
$788$	20.0729			0.715069
$789$		0			0
$790$	−37.4632	−	68.1849i	−1.33288	−	2.42591i
$791$	−13.2612	+	13.2612i	−0.471512	+	0.471512i
$792$		0			0
$793$	−21.9318	+	19.0510i	−0.778822	+	0.676521i
$794$			7.29423i			0.258863i
$795$		0			0
$796$	90.7469			3.21644
$797$	3.08683	+	3.08683i	0.109341	+	0.109341i	0.759661	−	0.650320i	$-0.225365\pi$
$797$	3.08683	+	3.08683i	0.109341	+	0.109341i	−0.650320	+	0.759661i	$0.725365\pi$
$798$		0			0
$799$	−22.3515	+	22.3515i	−0.790738	+	0.790738i
$800$	59.8555	−	94.2150i	2.11621	−	3.33100i
$801$		0			0
$802$	10.7928	−	10.7928i	0.381107	−	0.381107i
$803$	−1.20270	+	1.20270i	−0.0424423	+	0.0424423i
$804$		0			0
$805$	29.3851	+	8.54499i	1.03569	+	0.301171i
$806$	−28.7145	−	2.01843i	−1.01143	−	0.0710962i
$807$		0			0
$808$			65.2085i			2.29403i
$809$			27.8780i			0.980140i	0.871683	+	0.490070i	$0.163029\pi$
$809$			27.8780i			0.980140i	−0.871683	+	0.490070i	$0.836971\pi$
$810$		0			0
$811$	26.2382	+	26.2382i	0.921347	+	0.921347i	0.997125	−	0.0757777i	$-0.0241439\pi$
$811$	26.2382	+	26.2382i	0.921347	+	0.921347i	−0.0757777	+	0.997125i	$0.524144\pi$
$812$	−52.8083			−1.85321
$813$		0			0
$814$	−5.05514	−	5.05514i	−0.177182	−	0.177182i
$815$	2.15914	−	1.18631i	0.0756314	−	0.0415545i
$816$		0			0
$817$			1.12701i			0.0394291i
$818$	−17.6842	+	17.6842i	−0.618313	+	0.618313i
$819$		0			0
$820$	113.914	+	33.1253i	3.97804	+	1.15679i
$821$	−23.4557	−	23.4557i	−0.818609	−	0.818609i	0.167298	−	0.985906i	$-0.446496\pi$
$821$	−23.4557	−	23.4557i	−0.818609	−	0.818609i	−0.985906	+	0.167298i	$0.946496\pi$
$822$		0			0
$823$	21.2386	−	21.2386i	0.740333	−	0.740333i	−0.232309	−	0.972642i	$-0.574628\pi$
$823$	21.2386	−	21.2386i	0.740333	−	0.740333i	0.972642	+	0.232309i	$0.0746282\pi$
$824$	−81.8236	+	81.8236i	−2.85046	+	2.85046i
$825$		0			0
$826$	−14.4168	+	14.4168i	−0.501626	+	0.501626i
$827$		−	54.2245i		−	1.88557i	−0.333398	−	0.942786i	$-0.608195\pi$
$827$		−	54.2245i		−	1.88557i	0.333398	−	0.942786i	$-0.391805\pi$
$828$		0			0
$829$	−19.2741			−0.669416			−0.334708	−	0.942322i	$-0.608638\pi$
$829$	−19.2741			−0.669416			−0.334708	+	0.942322i	$0.608638\pi$
$830$	−1.63107	−	2.96863i	−0.0566152	−	0.103042i
$831$		0			0
$832$	83.8885	−	72.8695i	2.90831	−	2.52630i
$833$	−9.45443	−	9.45443i	−0.327577	−	0.327577i
$834$		0			0
$835$	−20.9005	−	38.0399i	−0.723290	−	1.31642i
$836$			2.04664i			0.0707846i
$837$		0			0
$838$			12.8084i			0.442457i
$839$	14.3455	+	14.3455i	0.495261	+	0.495261i	0.909959	−	0.414698i	$-0.136113\pi$
$839$	14.3455	+	14.3455i	0.495261	+	0.495261i	−0.414698	+	0.909959i	$0.636113\pi$
$840$		0			0
$841$	9.55424			0.329457
$842$	−40.7423	−	40.7423i	−1.40407	−	1.40407i
$843$		0			0
$844$	34.5254			1.18841
$845$	10.2961	+	27.1844i	0.354196	+	0.935171i
$846$		0			0
$847$	−23.2980			−0.800530
$848$	4.20583	+	4.20583i	0.144429	+	0.144429i
$849$		0			0
$850$	−79.8269	+	17.8023i	−2.73804	+	0.610614i
$851$	20.3150	+	20.3150i	0.696390	+	0.696390i
$852$		0			0
$853$	48.6784			1.66672			0.833358	−	0.552734i	$-0.186415\pi$
$853$	48.6784			1.66672			0.833358	+	0.552734i	$0.186415\pi$
$854$		−	48.1169i		−	1.64652i
$855$		0			0
$856$	97.2776	−	97.2776i	3.32488	−	3.32488i
$857$	30.4034	+	30.4034i	1.03856	+	1.03856i	0.999226	+	0.0393345i	$0.0125238\pi$
$857$	30.4034	+	30.4034i	1.03856	+	1.03856i	0.0393345	+	0.999226i	$0.487476\pi$
$858$		0			0
$859$		−	41.7176i		−	1.42339i	−0.702490	−	0.711693i	$-0.747929\pi$
$859$		−	41.7176i		−	1.42339i	0.702490	−	0.711693i	$-0.252071\pi$
$860$	−5.90285	+	20.2992i	−0.201285	+	0.692195i
$861$		0			0
$862$	22.5434	+	22.5434i	0.767833	+	0.767833i
$863$		−	46.2439i		−	1.57416i	−0.616851	−	0.787080i	$-0.711592\pi$
$863$		−	46.2439i		−	1.57416i	0.616851	−	0.787080i	$-0.288408\pi$
$864$		0			0
$865$	−11.4657	+	39.4292i	−0.389846	+	1.34063i
$866$	−55.2903	+	55.2903i	−1.87884	+	1.87884i
$867$		0			0
$868$	24.7072	−	24.7072i	0.838615	−	0.838615i
$869$	5.12738	+	5.12738i	0.173934	+	0.173934i
$870$		0			0
$871$	−17.6443	+	15.3267i	−0.597854	+	0.519324i
$872$	−35.4706	+	35.4706i	−1.20119	+	1.20119i
$873$		0			0
$874$		−	11.2228i		−	0.379616i
$875$	−24.3521	−	1.55009i	−0.823251	−	0.0524027i
$876$		0			0
$877$	−43.7565			−1.47755			−0.738776	−	0.673951i	$-0.764596\pi$
$877$	−43.7565			−1.47755			−0.738776	+	0.673951i	$0.764596\pi$
$878$	38.8288			1.31041
$879$		0			0
$880$	−5.38802	+	18.5287i	−0.181630	+	0.624603i
$881$			23.4781i			0.790998i	0.918466	+	0.395499i	$0.129428\pi$
$881$			23.4781i			0.790998i	−0.918466	+	0.395499i	$0.870572\pi$
$882$		0			0
$883$	−32.6644	+	32.6644i	−1.09925	+	1.09925i	−0.104747	+	0.994499i	$0.533403\pi$
$883$	−32.6644	+	32.6644i	−1.09925	+	1.09925i	−0.994499	+	0.104747i	$0.966597\pi$
$884$	−117.977	−	8.29297i	−3.96800	−	0.278923i
$885$		0			0
$886$	−20.2497	−	20.2497i	−0.680303	−	0.680303i
$887$	−19.0826	+	19.0826i	−0.640732	+	0.640732i	−0.950735	−	0.310004i	$-0.899670\pi$
$887$	−19.0826	+	19.0826i	−0.640732	+	0.640732i	0.310004	+	0.950735i	$0.399670\pi$
$888$		0			0
$889$	−14.6161	+	14.6161i	−0.490210	+	0.490210i
$890$	−62.8153	−	18.2662i	−2.10557	−	0.612286i
$891$		0			0
$892$		−	146.554i		−	4.90699i
$893$	2.44555	+	2.44555i	0.0818373	+	0.0818373i
$894$		0			0
$895$	11.8626	−	6.51775i	0.396524	−	0.217864i
$896$			86.5995i			2.89309i
$897$		0			0
$898$	−38.3175	−	38.3175i	−1.27867	−	1.27867i
$899$	9.09799	−	9.09799i	0.303435	−	0.303435i
$900$		0			0
$901$		−	2.34974i		−	0.0782812i
$902$	−15.0874			−0.502355
$903$		0			0
$904$	57.9719	+	57.9719i	1.92812	+	1.92812i
$905$	−0.691692	−	1.25891i	−0.0229926	−	0.0418477i
$906$		0			0
$907$	22.9031	+	22.9031i	0.760486	+	0.760486i	0.976410	−	0.215924i	$-0.0692763\pi$
$907$	22.9031	+	22.9031i	0.760486	+	0.760486i	−0.215924	+	0.976410i	$0.569276\pi$
$908$	−83.3871			−2.76730
$909$		0			0
$910$	−45.1754	−	16.6526i	−1.49755	−	0.552028i
$911$	40.3959			1.33838			0.669188	−	0.743093i	$-0.266642\pi$
$911$	40.3959			1.33838			0.669188	+	0.743093i	$0.266642\pi$
$912$		0			0
$913$	0.223235	+	0.223235i	0.00738800	+	0.00738800i
$914$	−27.8828			−0.922282
$915$		0			0
$916$	12.7312	+	12.7312i	0.420650	+	0.420650i
$917$			25.9602i			0.857282i
$918$		0			0
$919$		−	17.0001i		−	0.560783i	−0.959886	−	0.280391i	$-0.909536\pi$
$919$		−	17.0001i		−	0.560783i	0.959886	−	0.280391i	$-0.0904642\pi$
$920$	37.3549	−	128.459i	1.23156	−	4.23516i
$921$		0			0
$922$	21.9891	+	21.9891i	0.724173	+	0.724173i
$923$	−11.8243	−	0.831168i	−0.389202	−	0.0273582i
$924$		0			0
$925$	−19.3361	−	12.2843i	−0.635766	−	0.403907i
$926$	39.0709			1.28395
$927$		0			0
$928$			98.4434i			3.23156i
$929$	42.8153	−	42.8153i	1.40473	−	1.40473i	0.620594	−	0.784132i	$-0.286892\pi$
$929$	42.8153	−	42.8153i	1.40473	−	1.40473i	0.784132	−	0.620594i	$-0.213108\pi$
$930$		0			0
$931$	−1.03444	+	1.03444i	−0.0339025	+	0.0339025i
$932$	−17.8406	+	17.8406i	−0.584390	+	0.584390i
$933$		0			0
$934$	−70.0821	−	70.0821i	−2.29316	−	2.29316i
$935$	6.68098	−	3.67077i	0.218491	−	0.120047i
$936$		0			0
$937$	−3.27358	+	3.27358i	−0.106943	+	0.106943i	−0.758554	−	0.651610i	$-0.774094\pi$
$937$	−3.27358	+	3.27358i	−0.106943	+	0.106943i	0.651610	+	0.758554i	$0.274094\pi$
$938$		−	38.7103i		−	1.26394i
$939$		0			0
$940$	31.2392	+	56.8570i	1.01891	+	1.85447i
$941$	1.51052	+	1.51052i	0.0492416	+	0.0492416i	0.731299	−	0.682057i	$-0.238915\pi$
$941$	1.51052	+	1.51052i	0.0492416	+	0.0492416i	−0.682057	+	0.731299i	$0.738915\pi$
$942$		0			0
$943$	60.6315			1.97443
$944$	36.5318	+	36.5318i	1.18901	+	1.18901i
$945$		0			0
$946$		−	2.68854i		−	0.0874118i
$947$			3.23810i			0.105224i	0.998615	+	0.0526120i	$0.0167547\pi$
$947$			3.23810i			0.105224i	−0.998615	+	0.0526120i	$0.983245\pi$
$948$		0			0
$949$	−8.11871	+	7.05229i	−0.263544	+	0.228927i
$950$	1.94781	+	8.73414i	0.0631955	+	0.283373i
$951$		0			0
$952$	88.0252	−	88.0252i	2.85291	−	2.85291i
$953$	13.8263	−	13.8263i	0.447879	−	0.447879i	−0.446770	−	0.894649i	$-0.647426\pi$
$953$	13.8263	−	13.8263i	0.447879	−	0.447879i	0.894649	+	0.446770i	$0.147426\pi$
$954$		0			0
$955$	−47.1190	+	25.8888i	−1.52473	+	0.837743i
$956$	55.2961	−	55.2961i	1.78840	−	1.78840i
$957$		0			0
$958$	16.4385	+	16.4385i	0.531105	+	0.531105i
$959$	43.9207			1.41827
$960$		0			0
$961$		−	22.4867i		−	0.725378i
$962$	−29.6419	−	34.1243i	−0.955694	−	1.10021i
$963$		0			0
$964$	−8.46615	+	8.46615i	−0.272676	+	0.272676i
$965$	30.4672	−	16.7397i	0.980773	−	0.538872i
$966$		0			0
$967$	30.3258			0.975211			0.487605	−	0.873064i	$-0.337871\pi$
$967$	30.3258			0.975211			0.487605	+	0.873064i	$0.337871\pi$
$968$			101.849i			3.27354i
$969$		0			0
$970$	−53.0105	+	29.1259i	−1.70207	+	0.935175i
$971$	48.6798			1.56221			0.781104	−	0.624401i	$-0.214657\pi$
$971$	48.6798			1.56221			0.781104	+	0.624401i	$0.214657\pi$
$972$		0			0
$973$	4.26623			0.136769
$974$	118.157			3.78599
$975$		0			0
$976$	−121.927			−3.90278
$977$	27.4765			0.879051			0.439525	−	0.898230i	$-0.355147\pi$
$977$	27.4765			0.879051			0.439525	+	0.898230i	$0.355147\pi$
$978$		0			0
$979$	6.09718			0.194867
$980$	−24.0499	+	13.2139i	−0.768246	+	0.422101i
$981$		0			0
$982$			97.3075i			3.10521i
$983$	−25.7298			−0.820654			−0.410327	−	0.911938i	$-0.634585\pi$
$983$	−25.7298			−0.820654			−0.410327	+	0.911938i	$0.634585\pi$
$984$		0			0
$985$	−7.16936	+	3.93910i	−0.228435	+	0.125510i
$986$	51.0054	−	51.0054i	1.62434	−	1.62434i
$987$		0			0
$988$	−0.907364	+	12.9083i	−0.0288671	+	0.410668i
$989$			10.8044i			0.343559i
$990$		0			0
$991$	−32.9796			−1.04763			−0.523816	−	0.851831i	$-0.675492\pi$
$991$	−32.9796			−1.04763			−0.523816	+	0.851831i	$0.675492\pi$
$992$	−46.0582	−	46.0582i	−1.46235	−	1.46235i
$993$		0			0
$994$	13.8826	−	13.8826i	0.440330	−	0.440330i
$995$	−32.4117	+	17.8081i	−1.02752	+	0.564555i
$996$		0			0
$997$	37.1254	−	37.1254i	1.17577	−	1.17577i	0.194961	−	0.980811i	$-0.437542\pi$
$997$	37.1254	−	37.1254i	1.17577	−	1.17577i	0.980811	−	0.194961i	$-0.0624581\pi$
$998$	22.0529	−	22.0529i	0.698072	−	0.698072i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.w.g.73.14		28
3.2	odd	2		195.2.t.a.73.1	yes	28
5.2	odd	4		585.2.n.g.307.14		28
13.5	odd	4		585.2.n.g.343.1		28
15.2	even	4		195.2.k.a.112.1	✓	28
15.8	even	4		975.2.k.d.307.14		28
15.14	odd	2		975.2.t.d.268.14		28
39.5	even	4		195.2.k.a.148.14	yes	28
65.57	even	4	inner	585.2.w.g.577.14		28
195.44	even	4		975.2.k.d.343.1		28
195.83	odd	4		975.2.t.d.382.14		28
195.122	odd	4		195.2.t.a.187.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.1	✓	28	15.2	even	4
195.2.k.a.148.14	yes	28	39.5	even	4
195.2.t.a.73.1	yes	28	3.2	odd	2
195.2.t.a.187.1	yes	28	195.122	odd	4
585.2.n.g.307.14		28	5.2	odd	4
585.2.n.g.343.1		28	13.5	odd	4
585.2.w.g.73.14		28	1.1	even	1	trivial
585.2.w.g.577.14		28	65.57	even	4	inner
975.2.k.d.307.14		28	15.8	even	4
975.2.k.d.343.1		28	195.44	even	4
975.2.t.d.268.14		28	15.14	odd	2
975.2.t.d.382.14		28	195.83	odd	4

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.73623 q^{2} +5.48694 q^{4} +(-1.95975 + 1.07675i) q^{5} +2.18253i q^{7} +9.54105 q^{8} +O(q^{10})\)	\(q+2.73623 q^{2} +5.48694 q^{4} +(-1.95975 + 1.07675i) q^{5} +2.18253i q^{7} +9.54105 q^{8} +(-5.36231 + 2.94624i) q^{10} +(0.403236 - 0.403236i) q^{11} +(2.72201 - 2.36446i) q^{13} +5.97189i q^{14} +15.1326 q^{16} +(-4.22719 - 4.22719i) q^{17} +(-0.462512 + 0.462512i) q^{19} +(-10.7530 + 5.90808i) q^{20} +(1.10334 - 1.10334i) q^{22} +(-4.43399 + 4.43399i) q^{23} +(2.68120 - 4.22032i) q^{25} +(7.44802 - 6.46971i) q^{26} +11.9754i q^{28} +4.40973i q^{29} +(-2.06316 - 2.06316i) q^{31} +22.3241 q^{32} +(-11.5665 - 11.5665i) q^{34} +(-2.35004 - 4.27720i) q^{35} -4.58165i q^{37} +(-1.26554 + 1.26554i) q^{38} +(-18.6980 + 10.2734i) q^{40} +(-6.83712 - 6.83712i) q^{41} +(1.21836 - 1.21836i) q^{43} +(2.21253 - 2.21253i) q^{44} +(-12.1324 + 12.1324i) q^{46} -5.28755i q^{47} +2.23658 q^{49} +(7.33638 - 11.5478i) q^{50} +(14.9355 - 12.9737i) q^{52} +(0.277932 + 0.277932i) q^{53} +(-0.356054 + 1.22442i) q^{55} +20.8236i q^{56} +12.0660i q^{58} +(2.41412 + 2.41412i) q^{59} -8.05723 q^{61} +(-5.64528 - 5.64528i) q^{62} +30.8186 q^{64} +(-2.78850 + 7.56467i) q^{65} -6.48209 q^{67} +(-23.1943 - 23.1943i) q^{68} +(-6.43025 - 11.7034i) q^{70} +(-2.32466 - 2.32466i) q^{71} -2.98262 q^{73} -12.5364i q^{74} +(-2.53777 + 2.53777i) q^{76} +(0.880072 + 0.880072i) q^{77} +12.7156i q^{79} +(-29.6560 + 16.2941i) q^{80} +(-18.7079 - 18.7079i) q^{82} +0.553610i q^{83} +(12.8359 + 3.73257i) q^{85} +(3.33370 - 3.33370i) q^{86} +(3.84729 - 3.84729i) q^{88} +(7.56032 + 7.56032i) q^{89} +(5.16050 + 5.94085i) q^{91} +(-24.3290 + 24.3290i) q^{92} -14.4679i q^{94} +(0.408394 - 1.40442i) q^{95} +9.88577 q^{97} +6.11978 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8}+O(q^{10}) \) 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8	\( 28 q + 4 q^{2} + 28 q^{4} + 4 q^{5} + 12 q^{8} + 8 q^{11} + 28 q^{16} - 28 q^{17} - 12 q^{20} - 32 q^{22} + 8 q^{23} + 4 q^{25} - 16 q^{31} + 68 q^{32} - 28 q^{34} - 48 q^{40} - 4 q^{41} + 40 q^{44} - 16 q^{46} + 28 q^{49} - 4 q^{50} + 48 q^{52} - 20 q^{53} - 8 q^{55} + 32 q^{59} + 8 q^{61} + 72 q^{62} + 28 q^{64} - 64 q^{65} + 32 q^{67} - 60 q^{68} - 16 q^{70} - 40 q^{71} + 56 q^{73} - 40 q^{76} - 48 q^{77} + 12 q^{80} - 4 q^{82} + 44 q^{85} - 16 q^{86} - 72 q^{88} - 36 q^{89} - 56 q^{91} + 32 q^{92} + 56 q^{95} + 48 q^{97} + 12 q^{98}+O(q^{100}) \) 28 * q + 4 * q^2 + 28 * q^4 + 4 * q^5 + 12 * q^8 + 8 * q^11 + 28 * q^16 - 28 * q^17 - 12 * q^20 - 32 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^31 + 68 * q^32 - 28 * q^34 - 48 * q^40 - 4 * q^41 + 40 * q^44 - 16 * q^46 + 28 * q^49 - 4 * q^50 + 48 * q^52 - 20 * q^53 - 8 * q^55 + 32 * q^59 + 8 * q^61 + 72 * q^62 + 28 * q^64 - 64 * q^65 + 32 * q^67 - 60 * q^68 - 16 * q^70 - 40 * q^71 + 56 * q^73 - 40 * q^76 - 48 * q^77 + 12 * q^80 - 4 * q^82 + 44 * q^85 - 16 * q^86 - 72 * q^88 - 36 * q^89 - 56 * q^91 + 32 * q^92 + 56 * q^95 + 48 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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