LMFDB - Embedded newform 225.4.h.d.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.3
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31991 + 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(-4.79821 + 10.0984i) q^{5} +33.6094 q^{7} +(7.75447 - 5.63395i) q^{8} +O(q^{10})$	\(q+(-1.31991 + 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(-4.79821 + 10.0984i) q^{5} +33.6094 q^{7} +(7.75447 - 5.63395i) q^{8} +(-34.6890 - 32.8205i) q^{10} +(-9.92549 + 30.5475i) q^{11} +(23.5572 + 72.5016i) q^{13} +(-44.3613 + 136.530i) q^{14} +(-12.6733 - 39.0045i) q^{16} +(-33.4899 + 24.3319i) q^{17} +(-2.91326 + 2.11660i) q^{19} +(100.571 - 54.8000i) q^{20} +(-110.991 - 80.6398i) q^{22} +(38.2254 - 117.646i) q^{23} +(-78.9543 - 96.9083i) q^{25} -325.613 q^{26} +(-278.542 - 202.372i) q^{28} +(153.999 + 111.887i) q^{29} +(-267.535 + 194.376i) q^{31} +251.854 q^{32} +(-54.6386 - 168.160i) q^{34} +(-161.265 + 339.400i) q^{35} +(-39.9391 - 122.920i) q^{37} +(-4.75296 - 14.6281i) q^{38} +(19.6862 + 105.340i) q^{40} +(-129.358 - 398.124i) q^{41} -41.9887 q^{43} +(266.195 - 193.402i) q^{44} +(427.452 + 310.562i) q^{46} +(-375.583 - 272.877i) q^{47} +786.592 q^{49} +(497.878 - 192.823i) q^{50} +(241.321 - 742.710i) q^{52} +(200.790 + 145.882i) q^{53} +(-260.856 - 246.805i) q^{55} +(260.623 - 189.354i) q^{56} +(-657.777 + 477.903i) q^{58} +(66.6949 + 205.266i) q^{59} +(57.9582 - 178.377i) q^{61} +(-436.482 - 1343.35i) q^{62} +(-231.037 + 711.060i) q^{64} +(-845.181 - 109.989i) q^{65} +(-223.332 + 162.260i) q^{67} +424.061 q^{68} +(-1165.88 - 1103.08i) q^{70} +(328.894 + 238.955i) q^{71} +(-161.479 + 496.983i) q^{73} +552.048 q^{74} +36.8887 q^{76} +(-333.590 + 1026.68i) q^{77} +(295.531 + 214.716i) q^{79} +(454.691 + 59.1718i) q^{80} +1788.02 q^{82} +(-550.242 + 399.774i) q^{83} +(-85.0205 - 454.944i) q^{85} +(55.4211 - 170.569i) q^{86} +(95.1364 + 292.800i) q^{88} +(-91.6049 + 281.931i) q^{89} +(791.743 + 2436.73i) q^{91} +(-1025.18 + 744.835i) q^{92} +(1604.23 - 1165.54i) q^{94} +(-7.39584 - 39.5751i) q^{95} +(-185.918 - 135.077i) q^{97} +(-1038.23 + 3195.33i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.31991	+	4.06225i	−0.466657	+	1.43622i	0.390229	+	0.920718i	$0.372396\pi$
$2$	−1.31991	+	4.06225i	−0.466657	+	1.43622i	−0.856886	+	0.515506i	$0.827604\pi$
$3$		0			0
$3$		0			0
$4$	−8.28762	−	6.02131i	−1.03595	−	0.752663i
$5$	−4.79821	+	10.0984i	−0.429165	+	0.903226i
$5$	−4.79821	+	10.0984i	−0.429165	+	0.903226i
$6$		0			0
$7$	33.6094			1.81474			0.907368	−	0.420336i	$-0.138088\pi$
$7$	33.6094			1.81474			0.907368	+	0.420336i	$0.138088\pi$
$8$	7.75447	−	5.63395i	0.342702	−	0.248988i
$9$		0			0
$10$	−34.6890	−	32.8205i	−1.09696	−	1.03787i
$11$	−9.92549	+	30.5475i	−0.272059	+	0.837312i	0.717924	+	0.696122i	$0.245093\pi$
$11$	−9.92549	+	30.5475i	−0.272059	+	0.837312i	−0.989983	+	0.141190i	$0.954907\pi$
$12$		0			0
$13$	23.5572	+	72.5016i	0.502584	+	1.54679i	0.804795	+	0.593553i	$0.202275\pi$
$13$	23.5572	+	72.5016i	0.502584	+	1.54679i	−0.302211	+	0.953241i	$0.597725\pi$
$14$	−44.3613	+	136.530i	−0.846860	+	2.60637i
$15$		0			0
$16$	−12.6733	−	39.0045i	−0.198021	−	0.609445i
$17$	−33.4899	+	24.3319i	−0.477794	+	0.347138i	−0.800471	−	0.599371i	$-0.795417\pi$
$17$	−33.4899	+	24.3319i	−0.477794	+	0.347138i	0.322677	+	0.946509i	$0.395417\pi$
$18$		0			0
$19$	−2.91326	+	2.11660i	−0.0351761	+	0.0255570i	−0.605234	−	0.796047i	$-0.706921\pi$
$19$	−2.91326	+	2.11660i	−0.0351761	+	0.0255570i	0.570058	+	0.821604i	$0.306921\pi$
$20$	100.571	−	54.8000i	1.12442	−	0.612682i
$21$		0			0
$22$	−110.991	−	80.6398i	−1.07561	−	0.781475i
$23$	38.2254	−	117.646i	0.346545	−	1.06656i	−0.614206	−	0.789146i	$-0.710524\pi$
$23$	38.2254	−	117.646i	0.346545	−	1.06656i	0.960751	−	0.277411i	$-0.0894764\pi$
$24$		0			0
$25$	−78.9543	−	96.9083i	−0.631635	−	0.775266i
$26$	−325.613			−2.45608
$27$		0			0
$28$	−278.542	−	202.372i	−1.87998	−	1.36589i
$29$	153.999	+	111.887i	0.986100	+	0.716444i	0.959064	−	0.283191i	$-0.0913929\pi$
$29$	153.999	+	111.887i	0.986100	+	0.716444i	0.0270367	+	0.999634i	$0.491393\pi$
$30$		0			0
$31$	−267.535	+	194.376i	−1.55002	+	1.12616i	−0.606390	+	0.795168i	$0.707383\pi$
$31$	−267.535	+	194.376i	−1.55002	+	1.12616i	−0.943634	+	0.330990i	$0.892617\pi$
$32$	251.854			1.39131
$33$		0			0
$34$	−54.6386	−	168.160i	−0.275601	−	0.848214i
$35$	−161.265	+	339.400i	−0.778822	+	1.63912i
$36$		0			0
$37$	−39.9391	−	122.920i	−0.177458	−	0.546160i	0.822279	−	0.569084i	$-0.192702\pi$
$37$	−39.9391	−	122.920i	−0.177458	−	0.546160i	−0.999737	+	0.0229247i	$0.992702\pi$
$38$	−4.75296	−	14.6281i	−0.0202903	−	0.0624471i
$39$		0			0
$40$	19.6862	+	105.340i	0.0778165	+	0.416395i
$41$	−129.358	−	398.124i	−0.492741	−	1.51650i	−0.820448	−	0.571721i	$-0.806276\pi$
$41$	−129.358	−	398.124i	−0.492741	−	1.51650i	0.327708	−	0.944779i	$-0.393724\pi$
$42$		0			0
$43$	−41.9887			−0.148912			−0.0744559	−	0.997224i	$-0.523722\pi$
$43$	−41.9887			−0.148912			−0.0744559	+	0.997224i	$0.523722\pi$
$44$	266.195	−	193.402i	0.912054	−	0.662646i
$45$		0			0
$46$	427.452	+	310.562i	1.37010	+	0.995433i
$47$	−375.583	−	272.877i	−1.16563	−	0.846877i	−0.175147	−	0.984542i	$-0.556040\pi$
$47$	−375.583	−	272.877i	−1.16563	−	0.846877i	−0.990479	+	0.137666i	$0.956040\pi$
$48$		0			0
$49$	786.592			2.29327
$50$	497.878	−	192.823i	1.40821	−	0.545385i
$51$		0			0
$52$	241.321	−	742.710i	0.643562	−	1.98068i
$53$	200.790	+	145.882i	0.520388	+	0.378084i	0.816750	−	0.576992i	$-0.195774\pi$
$53$	200.790	+	145.882i	0.520388	+	0.378084i	−0.296362	+	0.955076i	$0.595774\pi$
$54$		0			0
$55$	−260.856	−	246.805i	−0.639523	−	0.605076i
$56$	260.623	−	189.354i	0.621915	−	0.451848i
$57$		0			0
$58$	−657.777	+	477.903i	−1.48914	+	1.08193i
$59$	66.6949	+	205.266i	0.147169	+	0.452938i	0.997283	−	0.0736590i	$-0.0234676\pi$
$59$	66.6949	+	205.266i	0.147169	+	0.452938i	−0.850115	+	0.526597i	$0.823468\pi$
$60$		0			0
$61$	57.9582	−	178.377i	0.121652	−	0.374407i	−0.871624	−	0.490175i	$-0.836933\pi$
$61$	57.9582	−	178.377i	0.121652	−	0.374407i	0.993276	+	0.115768i	$0.0369329\pi$
$62$	−436.482	−	1343.35i	−0.894085	−	2.75171i
$63$		0			0
$64$	−231.037	+	711.060i	−0.451245	+	1.38879i
$65$	−845.181	−	109.989i	−1.61280	−	0.209883i
$66$		0			0
$67$	−223.332	+	162.260i	−0.407228	+	0.295869i	−0.772479	−	0.635041i	$-0.780983\pi$
$67$	−223.332	+	162.260i	−0.407228	+	0.295869i	0.365250	+	0.930909i	$0.380983\pi$
$68$	424.061			0.756250
$69$		0			0
$70$	−1165.88	−	1103.08i	−1.99070	−	1.88347i
$71$	328.894	+	238.955i	0.549754	+	0.399419i	0.827695	−	0.561179i	$-0.189652\pi$
$71$	328.894	+	238.955i	0.549754	+	0.399419i	−0.277941	+	0.960598i	$0.589652\pi$
$72$		0			0
$73$	−161.479	+	496.983i	−0.258901	+	0.796814i	0.734136	+	0.679003i	$0.237588\pi$
$73$	−161.479	+	496.983i	−0.258901	+	0.796814i	−0.993036	+	0.117811i	$0.962412\pi$
$74$	552.048			0.867219
$75$		0			0
$76$	36.8887			0.0556766
$77$	−333.590	+	1026.68i	−0.493716	+	1.51950i
$78$		0			0
$79$	295.531	+	214.716i	0.420884	+	0.305790i	0.777993	−	0.628273i	$-0.216238\pi$
$79$	295.531	+	214.716i	0.420884	+	0.305790i	−0.357109	+	0.934063i	$0.616238\pi$
$80$	454.691	+	59.1718i	0.635450	+	0.0826951i
$81$		0			0
$82$	1788.02			2.40797
$83$	−550.242	+	399.774i	−0.727673	+	0.528686i	−0.888827	−	0.458244i	$-0.848479\pi$
$83$	−550.242	+	399.774i	−0.727673	+	0.528686i	0.161153	+	0.986929i	$0.448479\pi$
$84$		0			0
$85$	−85.0205	−	454.944i	−0.108491	−	0.580536i
$86$	55.4211	−	170.569i	0.0694908	−	0.213871i
$87$		0			0
$88$	95.1364	+	292.800i	0.115245	+	0.354688i
$89$	−91.6049	+	281.931i	−0.109102	+	0.335782i	−0.990671	−	0.136273i	$-0.956488\pi$
$89$	−91.6049	+	281.931i	−0.109102	+	0.335782i	0.881569	+	0.472055i	$0.156488\pi$
$90$		0			0
$91$	791.743	+	2436.73i	0.912058	+	2.80702i
$92$	−1025.18	+	744.835i	−1.16176	+	0.844070i
$93$		0			0
$94$	1604.23	−	1165.54i	1.76025	−	1.27890i
$95$	−7.39584	−	39.5751i	−0.00798734	−	0.0427402i
$96$		0			0
$97$	−185.918	−	135.077i	−0.194609	−	0.141392i	0.486214	−	0.873840i	$-0.338378\pi$
$97$	−185.918	−	135.077i	−0.194609	−	0.141392i	−0.680823	+	0.732448i	$0.738378\pi$
$98$	−1038.23	+	3195.33i	−1.07017	+	3.29365i
$99$		0			0
$100$	70.8289	+	1278.55i	0.0708289	+	1.27855i
$101$	514.024			0.506409			0.253205	−	0.967413i	$-0.418515\pi$
$101$	514.024			0.506409			0.253205	+	0.967413i	$0.418515\pi$
$102$		0			0
$103$	77.0965	+	56.0139i	0.0737528	+	0.0535846i	0.624051	−	0.781384i	$-0.285486\pi$
$103$	77.0965	+	56.0139i	0.0737528	+	0.0535846i	−0.550298	+	0.834968i	$0.685486\pi$
$104$	591.144	+	429.491i	0.557370	+	0.404953i
$105$		0			0
$106$	−857.634	+	623.107i	−0.785856	+	0.570958i
$107$	−780.381			−0.705068			−0.352534	−	0.935799i	$-0.614680\pi$
$107$	−780.381			−0.705068			−0.352534	+	0.935799i	$0.614680\pi$
$108$		0			0
$109$	190.124	+	585.140i	0.167069	+	0.514186i	0.999183	−	0.0404192i	$-0.0128693\pi$
$109$	190.124	+	585.140i	0.167069	+	0.514186i	−0.832114	+	0.554605i	$0.812869\pi$
$110$	1346.89	−	733.903i	1.16746	−	0.636136i
$111$		0			0
$112$	−425.943	−	1310.92i	−0.359356	−	1.10598i
$113$	−130.179	−	400.650i	−0.108374	−	0.333539i	0.882134	−	0.470999i	$-0.156106\pi$
$113$	−130.179	−	400.650i	−0.108374	−	0.333539i	−0.990507	+	0.137459i	$0.956106\pi$
$114$		0			0
$115$	1004.62	+	950.503i	0.814617	+	0.770738i
$116$	−602.580	−	1854.55i	−0.482312	−	1.48440i
$117$		0			0
$118$	−921.873			−0.719198
$119$	−1125.58	+	817.780i	−0.867071	+	0.629964i
$120$		0			0
$121$	242.165	+	175.943i	0.181942	+	0.132189i
$122$	648.113	+	470.882i	0.480962	+	0.349440i
$123$		0			0
$124$	3387.62			2.45337
$125$	1357.46	−	332.324i	0.971316	−	0.237792i
$126$		0			0
$127$	354.912	−	1092.31i	0.247979	−	0.763202i	−0.747153	−	0.664652i	$-0.768580\pi$
$127$	354.912	−	1092.31i	0.247979	−	0.763202i	0.995132	−	0.0985497i	$-0.0314204\pi$
$128$	−953.522	−	692.775i	−0.658440	−	0.478384i
$129$		0			0
$130$	1562.36	−	3288.16i	1.05406	−	2.21839i
$131$	−241.102	+	175.171i	−0.160803	+	0.116830i	−0.665277	−	0.746597i	$-0.731686\pi$
$131$	−241.102	+	175.171i	−0.160803	+	0.116830i	0.504474	+	0.863427i	$0.331686\pi$
$132$		0			0
$133$	−97.9127	+	71.1378i	−0.0638354	+	0.0463792i
$134$	−364.364	−	1121.40i	−0.234898	−	0.722940i
$135$		0			0
$136$	−122.612	+	377.362i	−0.0773082	+	0.237930i
$137$	674.262	+	2075.17i	0.420483	+	1.29411i	0.907254	+	0.420583i	$0.138174\pi$
$137$	674.262	+	2075.17i	0.420483	+	1.29411i	−0.486771	+	0.873529i	$0.661826\pi$
$138$		0			0
$139$	−656.504	+	2020.51i	−0.400604	+	1.23293i	0.523907	+	0.851775i	$0.324474\pi$
$139$	−656.504	+	2020.51i	−0.400604	+	1.23293i	−0.924511	+	0.381156i	$0.875526\pi$
$140$	3380.14	−	1841.79i	2.04053	−	1.11186i
$141$		0			0
$142$	−1404.81	+	1020.65i	−0.830202	+	0.603177i
$143$	−2448.56			−1.43188
$144$		0			0
$145$	−1868.80	+	1018.28i	−1.07031	+	0.583199i
$146$	−1805.73	−	1311.94i	−1.02359	−	0.743678i
$147$		0			0
$148$	−409.138	+	1259.20i	−0.227236	+	0.699361i
$149$	2893.87			1.59111			0.795554	−	0.605882i	$-0.207180\pi$
$149$	2893.87			1.59111			0.795554	+	0.605882i	$0.207180\pi$
$150$		0			0
$151$	2519.50			1.35784			0.678921	−	0.734212i	$-0.262448\pi$
$151$	2519.50			1.35784			0.678921	+	0.734212i	$0.262448\pi$
$152$	−10.6659	+	32.8263i	−0.00569157	+	0.0175169i
$153$		0			0
$154$	−3730.34	−	2710.25i	−1.95195	−	1.41817i
$155$	−679.188	−	3634.33i	−0.351959	−	1.88333i
$156$		0			0
$157$	2190.79			1.11366			0.556828	−	0.830628i	$-0.312018\pi$
$157$	2190.79			1.11366			0.556828	+	0.830628i	$0.312018\pi$
$158$	−1262.30	+	917.117i	−0.635591	+	0.461784i
$159$		0			0
$160$	−1208.45	+	2543.32i	−0.597102	+	1.25667i
$161$	1284.73	−	3954.00i	0.628889	−	1.93552i
$162$		0			0
$163$	−150.794	−	464.095i	−0.0724605	−	0.223010i	0.908267	−	0.418391i	$-0.137406\pi$
$163$	−150.794	−	464.095i	−0.0724605	−	0.223010i	−0.980728	+	0.195381i	$0.937406\pi$
$164$	−1325.15	+	4078.40i	−0.630958	+	1.94189i
$165$		0			0
$166$	−897.716	−	2762.89i	−0.419737	−	1.29182i
$167$	2984.57	−	2168.42i	1.38295	−	1.00477i	0.386354	−	0.922351i	$-0.373734\pi$
$167$	2984.57	−	2168.42i	1.38295	−	1.00477i	0.996597	−	0.0824226i	$-0.0262657\pi$
$168$		0			0
$169$	−2924.13	+	2124.50i	−1.33096	+	0.967002i
$170$	1960.32	+	255.108i	0.884408	+	0.115093i
$171$		0			0
$172$	347.986	+	252.827i	0.154266	+	0.112080i
$173$	969.377	−	2983.44i	0.426014	−	1.31114i	−0.476007	−	0.879442i	$-0.657916\pi$
$173$	969.377	−	2983.44i	0.426014	−	1.31114i	0.902020	−	0.431693i	$-0.142084\pi$
$174$		0			0
$175$	−2653.61	−	3257.03i	−1.14625	−	1.40690i
$176$	1317.28			0.564169
$177$		0			0
$178$	−1024.37	−	744.245i	−0.431345	−	0.313391i
$179$	771.743	+	560.704i	0.322250	+	0.234128i	0.737135	−	0.675745i	$-0.236178\pi$
$179$	771.743	+	560.704i	0.322250	+	0.234128i	−0.414885	+	0.909874i	$0.636178\pi$
$180$		0			0
$181$	125.543	−	91.2125i	0.0515556	−	0.0374573i	−0.561709	−	0.827335i	$-0.689856\pi$
$181$	125.543	−	91.2125i	0.0515556	−	0.0374573i	0.613265	+	0.789878i	$0.289856\pi$
$182$	−10943.7			−4.45713
$183$		0			0
$184$	−366.392	−	1127.64i	−0.146798	−	0.451797i
$185$	1432.93	+	186.476i	0.569464	+	0.0741079i
$186$		0			0
$187$	−410.874	−	1264.54i	−0.160674	−	0.494505i
$188$	1469.61	+	4523.00i	0.570119	+	1.75465i
$189$		0			0
$190$	170.526	+	22.1916i	0.0651118	+	0.00847340i
$191$	424.396	+	1306.16i	0.160776	+	0.494818i	0.998700	−	0.0509689i	$-0.0162309\pi$
$191$	424.396	+	1306.16i	0.160776	+	0.494818i	−0.837924	+	0.545787i	$0.816231\pi$
$192$		0			0
$193$	2565.08			0.956676			0.478338	−	0.878176i	$-0.341239\pi$
$193$	2565.08			0.956676			0.478338	+	0.878176i	$0.341239\pi$
$194$	794.113	−	576.957i	0.293887	−	0.213521i
$195$		0			0
$196$	−6518.97	−	4736.31i	−2.37572	−	1.72606i
$197$	−1114.76	−	809.922i	−0.403165	−	0.292917i	0.367664	−	0.929959i	$-0.380158\pi$
$197$	−1114.76	−	809.922i	−0.403165	−	0.292917i	−0.770829	+	0.637042i	$0.780158\pi$
$198$		0			0
$199$	−988.966			−0.352291			−0.176146	−	0.984364i	$-0.556363\pi$
$199$	−988.966			−0.352291			−0.176146	+	0.984364i	$0.556363\pi$
$200$	−1158.23	−	306.647i	−0.409495	−	0.108416i
$201$		0			0
$202$	−678.464	+	2088.10i	−0.236320	+	0.727317i
$203$	5175.82	+	3760.45i	1.78951	+	1.30016i
$204$		0			0
$205$	4641.09	+	603.974i	1.58121	+	0.205773i
$206$	−329.303	+	239.252i	−0.111377	+	0.0809199i
$207$		0			0
$208$	2529.34	−	1837.67i	0.843164	−	0.612595i
$209$	−35.7415	−	110.001i	−0.0118292	−	0.0364064i
$210$		0			0
$211$	606.537	−	1866.73i	0.197895	−	0.609057i	−0.802036	−	0.597276i	$-0.796250\pi$
$211$	606.537	−	1866.73i	0.197895	−	0.609057i	0.999931	−	0.0117812i	$-0.00375017\pi$
$212$	−785.666	−	2418.03i	−0.254527	−	0.783354i
$213$		0			0
$214$	1030.03	−	3170.11i	0.329025	−	1.01264i
$215$	201.470	−	424.017i	0.0639078	−	0.134501i
$216$		0			0
$217$	−8991.70	+	6532.85i	−2.81289	+	2.04368i
$218$	−2627.93			−0.816450
$219$		0			0
$220$	675.785	+	3616.12i	0.207097	+	1.10818i
$221$	−2553.03	−	1854.88i	−0.777083	−	0.564584i
$222$		0			0
$223$	1063.53	−	3273.20i	0.319368	−	0.982913i	−0.654551	−	0.756018i	$-0.727142\pi$
$223$	1063.53	−	3273.20i	0.319368	−	0.982913i	0.973919	−	0.226895i	$-0.0728576\pi$
$224$	8464.67			2.52486
$225$		0			0
$226$	1799.36			0.529610
$227$	518.565	−	1595.98i	0.151623	−	0.466647i	−0.846180	−	0.532897i	$-0.821103\pi$
$227$	518.565	−	1595.98i	0.151623	−	0.466647i	0.997803	+	0.0662496i	$0.0211034\pi$
$228$		0			0
$229$	436.125	+	316.863i	0.125851	+	0.0914363i	0.648930	−	0.760848i	$-0.275217\pi$
$229$	436.125	+	316.863i	0.125851	+	0.0914363i	−0.523079	+	0.852284i	$0.675217\pi$
$230$	−5187.18	+	2826.43i	−1.48710	+	0.810301i
$231$		0			0
$232$	1824.55			0.516325
$233$	−2488.89	+	1808.28i	−0.699796	+	0.508431i	−0.879866	−	0.475223i	$-0.842368\pi$
$233$	−2488.89	+	1808.28i	−0.699796	+	0.508431i	0.180070	+	0.983654i	$0.442368\pi$
$234$		0			0
$235$	4557.74	−	2483.46i	1.26517	−	0.689374i
$236$	683.227	−	2102.76i	0.188450	−	0.579990i
$237$		0			0
$238$	−1836.37	−	5651.77i	−0.500144	−	1.53929i
$239$	−134.744	+	414.700i	−0.0364681	+	0.112237i	−0.967633	−	0.252360i	$-0.918793\pi$
$239$	−134.744	+	414.700i	−0.0364681	+	0.112237i	0.931165	+	0.364597i	$0.118793\pi$
$240$		0			0
$241$	1239.98	+	3816.27i	0.331429	+	1.02003i	0.968455	+	0.249190i	$0.0801644\pi$
$241$	1239.98	+	3816.27i	0.331429	+	1.02003i	−0.637026	+	0.770842i	$0.719836\pi$
$242$	−1034.36	+	751.508i	−0.274758	+	0.199623i
$243$		0			0
$244$	−1554.40	+	1129.34i	−0.407828	+	0.296305i
$245$	−3774.23	+	7943.30i	−0.984191	+	2.07134i
$246$		0			0
$247$	−222.085	−	161.354i	−0.0572103	−	0.0415657i
$248$	−979.490	+	3014.56i	−0.250797	+	0.771874i
$249$		0			0
$250$	−441.729	+	5952.97i	−0.111750	+	1.50599i
$251$	−4706.56			−1.18357			−0.591784	−	0.806097i	$-0.701576\pi$
$251$	−4706.56			−1.18357			−0.591784	+	0.806097i	$0.701576\pi$
$252$		0			0
$253$	3214.38	+	2335.38i	0.798760	+	0.580333i
$254$	3968.78	+	2883.49i	0.980407	+	0.712308i
$255$		0			0
$256$	−766.121	+	556.620i	−0.187041	+	0.135893i
$257$	573.257			0.139139			0.0695696	−	0.997577i	$-0.477837\pi$
$257$	573.257			0.139139			0.0695696	+	0.997577i	$0.477837\pi$
$258$		0			0
$259$	−1342.33	−	4131.26i	−0.322040	−	0.991136i
$260$	6342.26	+	6000.63i	1.51281	+	1.43132i
$261$		0			0
$262$	−393.357	−	1210.63i	−0.0927544	−	0.285469i
$263$	1428.46	+	4396.36i	0.334915	+	1.03076i	0.966764	+	0.255672i	$0.0822966\pi$
$263$	1428.46	+	4396.36i	0.334915	+	1.03076i	−0.631848	+	0.775092i	$0.717703\pi$
$264$		0			0
$265$	−2436.60	+	1327.67i	−0.564828	+	0.307768i
$266$	−159.744	−	491.642i	−0.0368216	−	0.113325i
$267$		0			0
$268$	2827.90			0.644559
$269$	−5498.69	+	3995.03i	−1.24632	+	0.905507i	−0.998003	−	0.0631703i	$-0.979879\pi$
$269$	−5498.69	+	3995.03i	−1.24632	+	0.905507i	−0.248321	+	0.968678i	$0.579879\pi$
$270$		0			0
$271$	−4062.81	−	2951.81i	−0.910695	−	0.661659i	0.0304957	−	0.999535i	$-0.490291\pi$
$271$	−4062.81	−	2951.81i	−0.910695	−	0.661659i	−0.941190	+	0.337876i	$0.890291\pi$
$272$	1373.48	+	997.893i	0.306175	+	0.222449i
$273$		0			0
$274$	−9319.81			−2.05486
$275$	3743.97	−	1450.00i	0.820981	−	0.317957i
$276$		0			0
$277$	−1967.28	+	6054.66i	−0.426723	+	1.31332i	0.474612	+	0.880195i	$0.342589\pi$
$277$	−1967.28	+	6054.66i	−0.426723	+	1.31332i	−0.901335	+	0.433123i	$0.857411\pi$
$278$	−7341.30	−	5333.77i	−1.58382	−	1.15071i
$279$		0			0
$280$	661.641	+	3540.43i	0.141216	+	0.755647i
$281$	1793.59	−	1303.12i	0.380771	−	0.276646i	−0.380892	−	0.924619i	$-0.624383\pi$
$281$	1793.59	−	1303.12i	0.380771	−	0.276646i	0.761663	+	0.647973i	$0.224383\pi$
$282$		0			0
$283$	5646.82	−	4102.66i	1.18611	−	0.861759i	0.193261	−	0.981147i	$-0.438093\pi$
$283$	5646.82	−	4102.66i	1.18611	−	0.861759i	0.992848	+	0.119389i	$0.0380935\pi$
$284$	−1286.92	−	3960.74i	−0.268890	−	0.827559i
$285$		0			0
$286$	3231.87	−	9946.68i	0.668198	−	2.05650i
$287$	−4347.65	−	13380.7i	−0.894195	−	2.75205i
$288$		0			0
$289$	−988.664	+	3042.79i	−0.201234	+	0.619335i
$290$	−1669.89	−	8935.56i	−0.338136	−	1.80936i
$291$		0			0
$292$	4330.76	−	3146.48i	0.867941	−	0.630596i
$293$	8443.08			1.68345			0.841724	−	0.539908i	$-0.181541\pi$
$293$	8443.08			1.68345			0.841724	+	0.539908i	$0.181541\pi$
$294$		0			0
$295$	−2392.87	−	311.399i	−0.472265	−	0.0614588i
$296$	−1002.23	−	728.164i	−0.196802	−	0.142985i
$297$		0			0
$298$	−3819.64	+	11755.6i	−0.742503	+	2.28519i
$299$	9429.98			1.82391
$300$		0			0
$301$	−1411.21			−0.270236
$302$	−3325.50	+	10234.8i	−0.633647	+	1.95016i
$303$		0			0
$304$	119.478	+	86.8056i	0.0225412	+	0.0163771i
$305$	1523.22	+	1441.17i	0.285965	+	0.270562i
$306$		0			0
$307$	−2853.33			−0.530450			−0.265225	−	0.964187i	$-0.585446\pi$
$307$	−2853.33			−0.530450			−0.265225	+	0.964187i	$0.585446\pi$
$308$	8946.64	−	6500.12i	1.65514	−	1.20253i
$309$		0			0
$310$	15660.0	+	2037.94i	2.86913	+	0.373377i
$311$	−2085.97	+	6419.96i	−0.380336	+	1.17055i	0.559471	+	0.828850i	$0.311004\pi$
$311$	−2085.97	+	6419.96i	−0.380336	+	1.17055i	−0.939807	+	0.341705i	$0.888996\pi$
$312$		0			0
$313$	1021.84	+	3144.90i	0.184530	+	0.567924i	0.999940	−	0.0109593i	$-0.00348854\pi$
$313$	1021.84	+	3144.90i	0.184530	+	0.567924i	−0.815410	+	0.578884i	$0.803489\pi$
$314$	−2891.64	+	8899.54i	−0.519696	+	1.59946i
$315$		0			0
$316$	−1156.38	−	3558.96i	−0.205859	−	0.633568i
$317$	2682.89	−	1949.24i	0.475351	−	0.345363i	−0.324172	−	0.945998i	$-0.605086\pi$
$317$	2682.89	−	1949.24i	0.475351	−	0.345363i	0.799523	+	0.600635i	$0.205086\pi$
$318$		0			0
$319$	−4946.39	+	3593.76i	−0.868164	+	0.630758i
$320$	−6071.98	−	5744.92i	−1.06073	−	1.00360i
$321$		0			0
$322$	14366.4	+	10437.8i	2.48636	+	1.80645i
$323$	46.0638	−	141.770i	0.00793517	−	0.0244219i
$324$		0			0
$325$	5166.06	−	8007.20i	0.881728	−	1.36665i
$326$	2084.30			0.354107
$327$		0			0
$328$	−3246.12	−	2358.44i	−0.546454	−	0.397022i
$329$	−12623.1	−	9171.23i	−2.11530	−	1.53686i
$330$		0			0
$331$	6061.25	−	4403.76i	1.00651	−	0.731276i	0.0430396	−	0.999073i	$-0.486296\pi$
$331$	6061.25	−	4403.76i	1.00651	−	0.731276i	0.963475	+	0.267798i	$0.0862958\pi$
$332$	6967.36			1.15176
$333$		0			0
$334$	4869.31	+	14986.2i	0.797714	+	2.45511i
$335$	−566.969	−	3033.84i	−0.0924682	−	0.494796i
$336$		0			0
$337$	−2497.93	−	7687.83i	−0.403771	−	1.24268i	−0.921917	−	0.387387i	$-0.873378\pi$
$337$	−2497.93	−	7687.83i	−0.403771	−	1.24268i	0.518146	−	0.855292i	$-0.326622\pi$
$338$	−4770.70	−	14682.7i	−0.767727	−	2.36282i
$339$		0			0
$340$	−2034.74	+	4282.33i	−0.324556	+	0.683065i
$341$	−3282.28	−	10101.8i	−0.521247	−	1.60423i
$342$		0			0
$343$	14908.8			2.34694
$344$	−325.600	+	236.562i	−0.0510325	+	0.0370773i
$345$		0			0
$346$	10840.0	+	7875.71i	1.68428	+	1.22370i
$347$	8214.67	+	5968.31i	1.27086	+	0.923330i	0.999236	−	0.0390745i	$-0.0124410\pi$
$347$	8214.67	+	5968.31i	1.27086	+	0.923330i	0.271619	+	0.962405i	$0.412441\pi$
$348$		0			0
$349$	915.035			0.140346			0.0701729	−	0.997535i	$-0.477645\pi$
$349$	915.035			0.140346			0.0701729	+	0.997535i	$0.477645\pi$
$350$	16733.4	−	6480.65i	2.55554	−	0.989730i
$351$		0			0
$352$	−2499.78	+	7693.52i	−0.378519	+	1.16496i
$353$	−64.3813	−	46.7758i	−0.00970728	−	0.00705275i	0.582921	−	0.812529i	$-0.301910\pi$
$353$	−64.3813	−	46.7758i	−0.00970728	−	0.00705275i	−0.592628	+	0.805476i	$0.701910\pi$
$354$		0			0
$355$	−3991.16	+	2174.73i	−0.596701	+	0.325135i
$356$	2456.78	−	1784.95i	0.365756	−	0.265737i
$357$		0			0
$358$	−3296.35	+	2394.94i	−0.486641	+	0.353565i
$359$	−1932.90	−	5948.86i	−0.284163	−	0.874565i	−0.986648	−	0.162866i	$-0.947926\pi$
$359$	−1932.90	−	5948.86i	−0.284163	−	0.874565i	0.702485	−	0.711699i	$-0.252074\pi$
$360$		0			0
$361$	−2115.54	+	6510.96i	−0.308433	+	0.949259i
$362$	204.823	+	630.380i	0.0297383	+	0.0915250i
$363$		0			0
$364$	8110.66	−	24962.1i	1.16790	−	3.59441i
$365$	−4243.90	−	4015.31i	−0.608592	−	0.575810i
$366$		0			0
$367$	2077.48	−	1509.38i	0.295487	−	0.214684i	−0.430157	−	0.902754i	$-0.641542\pi$
$367$	2077.48	−	1509.38i	0.295487	−	0.214684i	0.725644	+	0.688070i	$0.241542\pi$
$368$	−5073.15			−0.718631
$369$		0			0
$370$	−2648.84	+	5574.78i	−0.372180	+	0.783295i
$371$	6748.41	+	4903.01i	0.944367	+	0.686123i
$372$		0			0
$373$	2876.24	−	8852.16i	0.399266	−	1.22881i	−0.526323	−	0.850285i	$-0.676430\pi$
$373$	2876.24	−	8852.16i	0.399266	−	1.22881i	0.925589	−	0.378530i	$-0.123570\pi$
$374$	5679.20			0.785199
$375$		0			0
$376$	−4449.82			−0.610325
$377$	−4484.19	+	13800.9i	−0.612593	+	1.88537i
$378$		0			0
$379$	1786.14	+	1297.71i	0.242079	+	0.175880i	0.702209	−	0.711971i	$-0.252197\pi$
$379$	1786.14	+	1297.71i	0.242079	+	0.175880i	−0.460130	+	0.887851i	$0.652197\pi$
$380$	−177.000	+	372.515i	−0.0238944	+	0.0502885i
$381$		0			0
$382$	−5866.10			−0.785696
$383$	−10414.5	+	7566.60i	−1.38945	+	1.00949i	−0.393520	+	0.919316i	$0.628743\pi$
$383$	−10414.5	+	7566.60i	−1.38945	+	1.00949i	−0.995926	+	0.0901754i	$0.971257\pi$
$384$		0			0
$385$	−8767.21	−	8294.96i	−1.16057	−	1.09805i
$386$	−3385.66	+	10420.0i	−0.446440	+	1.37400i
$387$		0			0
$388$	727.475	+	2238.94i	0.0951855	+	0.292951i
$389$	−3872.47	+	11918.2i	−0.504735	+	1.55341i	0.296481	+	0.955039i	$0.404187\pi$
$389$	−3872.47	+	11918.2i	−0.504735	+	1.55341i	−0.801216	+	0.598376i	$0.795813\pi$
$390$		0			0
$391$	1582.37	+	4870.04i	0.204665	+	0.629894i
$392$	6099.60	−	4431.62i	0.785909	−	0.570996i
$393$		0			0
$394$	4761.49	−	3459.43i	0.608834	−	0.442344i
$395$	−3586.30	+	1954.13i	−0.456826	+	0.248919i
$396$		0			0
$397$	−10322.4	−	7499.67i	−1.30496	−	0.948105i	−0.304964	−	0.952364i	$-0.598645\pi$
$397$	−10322.4	−	7499.67i	−1.30496	−	0.948105i	−0.999991	+	0.00425835i	$0.998645\pi$
$398$	1305.34	−	4017.43i	0.164399	−	0.505969i
$399$		0			0
$400$	−2779.24	+	4307.72i	−0.347405	+	0.538466i
$401$	−4960.15			−0.617700			−0.308850	−	0.951111i	$-0.599944\pi$
$401$	−4960.15			−0.617700			−0.308850	+	0.951111i	$0.599944\pi$
$402$		0			0
$403$	−20394.9	−	14817.8i	−2.52095	−	1.83158i
$404$	−4260.04	−	3095.10i	−0.524616	−	0.381156i
$405$		0			0
$406$	−22107.5	+	16062.0i	−2.70241	+	1.96341i
$407$	4151.31			0.505585
$408$		0			0
$409$	3499.05	+	10769.0i	0.423025	+	1.30194i	0.904873	+	0.425682i	$0.139966\pi$
$409$	3499.05	+	10769.0i	0.423025	+	1.30194i	−0.481848	+	0.876255i	$0.660034\pi$
$410$	−8579.30	+	18056.1i	−1.03342	+	2.17494i
$411$		0			0
$412$	−301.669	−	928.443i	−0.0360733	−	0.111022i
$413$	2241.58	+	6898.86i	0.267072	+	0.821963i
$414$		0			0
$415$	−1396.89	−	7474.75i	−0.165231	−	0.884147i
$416$	5932.98	+	18259.8i	0.699251	+	2.15207i
$417$		0			0
$418$	494.028			0.0578079
$419$	−9318.52	+	6770.30i	−1.08649	+	0.789382i	−0.978803	−	0.204803i	$-0.934345\pi$
$419$	−9318.52	+	6770.30i	−1.08649	+	0.789382i	−0.107688	+	0.994185i	$0.534345\pi$
$420$		0			0
$421$	1968.58	+	1430.26i	0.227892	+	0.165574i	0.695872	−	0.718166i	$-0.255018\pi$
$421$	1968.58	+	1430.26i	0.227892	+	0.165574i	−0.467980	+	0.883739i	$0.655018\pi$
$422$	6782.56	+	4927.82i	0.782393	+	0.568442i
$423$		0			0
$424$	2378.91			0.272477
$425$	5002.14	+	1324.35i	0.570916	+	0.151153i
$426$		0			0
$427$	1947.94	−	5995.14i	0.220767	−	0.679450i
$428$	6467.50	+	4698.91i	0.730417	+	0.530679i
$429$		0			0
$430$	1456.54	+	1378.09i	0.163351	+	0.154552i
$431$	7111.10	−	5166.51i	0.794732	−	0.577407i	−0.114632	−	0.993408i	$-0.536569\pi$
$431$	7111.10	−	5166.51i	0.794732	−	0.577407i	0.909364	+	0.416001i	$0.136569\pi$
$432$		0			0
$433$	−6196.51	+	4502.03i	−0.687726	+	0.499662i	−0.875912	−	0.482471i	$-0.839739\pi$
$433$	−6196.51	+	4502.03i	−0.687726	+	0.499662i	0.188186	+	0.982133i	$0.439739\pi$
$434$	−14669.9	−	45149.3i	−1.62253	−	4.99363i
$435$		0			0
$436$	1947.64	−	5994.21i	0.213933	−	0.658419i
$437$	137.649	+	423.640i	0.0150678	+	0.0463740i
$438$		0			0
$439$	1589.15	−	4890.90i	0.172770	−	0.531731i	−0.826755	−	0.562563i	$-0.809815\pi$
$439$	1589.15	−	4890.90i	0.172770	−	0.531731i	0.999525	+	0.0308313i	$0.00981546\pi$
$440$	−3413.29	−	444.192i	−0.369823	−	0.0481273i
$441$		0			0
$442$	10904.8	−	7922.78i	1.17350	−	0.852598i
$443$	−3847.00			−0.412588			−0.206294	−	0.978490i	$-0.566140\pi$
$443$	−3847.00			−0.412588			−0.206294	+	0.978490i	$0.566140\pi$
$444$		0			0
$445$	−2407.50	−	2277.83i	−0.256464	−	0.242650i
$446$	11892.8	+	8640.63i	1.26265	+	0.917367i
$447$		0			0
$448$	−7765.02	+	23898.3i	−0.818890	+	2.52029i
$449$	1690.99			0.177735			0.0888674	−	0.996043i	$-0.471675\pi$
$449$	1690.99			0.177735			0.0888674	+	0.996043i	$0.471675\pi$
$450$		0			0
$451$	13445.6			1.40384
$452$	−1333.56	+	4104.28i	−0.138773	+	0.427100i
$453$		0			0
$454$	5798.82	+	4213.09i	0.599454	+	0.435529i
$455$	−28406.0	−	3696.65i	−2.92680	−	0.380883i
$456$		0			0
$457$	−369.186			−0.0377895			−0.0188947	−	0.999821i	$-0.506015\pi$
$457$	−369.186			−0.0377895			−0.0188947	+	0.999821i	$0.506015\pi$
$458$	−1862.82	+	1353.42i	−0.190052	+	0.138081i
$459$		0			0
$460$	−2602.60	−	13926.5i	−0.263798	−	1.41158i
$461$	812.481	−	2500.56i	0.0820846	−	0.252630i	−0.901589	−	0.432595i	$-0.857598\pi$
$461$	812.481	−	2500.56i	0.0820846	−	0.252630i	0.983673	+	0.179964i	$0.0575982\pi$
$462$		0			0
$463$	587.970	+	1809.58i	0.0590178	+	0.181638i	0.976219	−	0.216786i	$-0.0695573\pi$
$463$	587.970	+	1809.58i	0.0590178	+	0.181638i	−0.917201	+	0.398424i	$0.869557\pi$
$464$	2412.41	−	7424.64i	0.241365	−	0.742845i
$465$		0			0
$466$	−4060.60	−	12497.2i	−0.403656	−	1.24233i
$467$	8903.30	−	6468.62i	0.882217	−	0.640968i	−0.0516199	−	0.998667i	$-0.516438\pi$
$467$	8903.30	−	6468.62i	0.882217	−	0.640968i	0.933837	+	0.357698i	$0.116438\pi$
$468$		0			0
$469$	−7506.04	+	5453.46i	−0.739012	+	0.536924i
$470$	4072.64	+	21792.6i	0.399695	+	2.13876i
$471$		0			0
$472$	1673.64	+	1215.97i	0.163211	+	0.118580i
$473$	416.758	−	1282.65i	0.0405128	−	0.124686i
$474$		0			0
$475$	435.131	+	115.203i	0.0420319	+	0.0111282i
$476$	14252.5			1.37239
$477$		0			0
$478$	−1506.77	−	1094.73i	−0.144180	−	0.104753i
$479$	11054.3	+	8031.41i	1.05445	+	0.766106i	0.973054	−	0.230576i	$-0.0740610\pi$
$479$	11054.3	+	8031.41i	1.05445	+	0.766106i	0.0813995	+	0.996682i	$0.474061\pi$
$480$		0			0
$481$	7971.03	−	5791.30i	0.755609	−	0.548982i
$482$	−17139.3			−1.61966
$483$		0			0
$484$	−947.564	−	2916.30i	−0.0889899	−	0.273883i
$485$	2256.14	−	1229.34i	0.211229	−	0.115096i
$486$		0			0
$487$	−1524.98	−	4693.40i	−0.141896	−	0.436711i	0.854703	−	0.519118i	$-0.173739\pi$
$487$	−1524.98	−	4693.40i	−0.141896	−	0.436711i	−0.996599	+	0.0824064i	$0.973739\pi$
$488$	−555.532	−	1709.75i	−0.0515323	−	0.158600i
$489$		0			0
$490$	−27286.0	−	25816.3i	−2.51563	−	2.38013i
$491$	134.582	+	414.201i	0.0123699	+	0.0380705i	0.957051	−	0.289920i	$-0.0936287\pi$
$491$	134.582	+	414.201i	0.0123699	+	0.0380705i	−0.944681	+	0.327990i	$0.893629\pi$
$492$		0			0
$493$	−7879.84			−0.719858
$494$	948.594	−	689.194i	0.0863953	−	0.0627698i
$495$		0			0
$496$	10972.1	+	7971.69i	0.993269	+	0.721652i
$497$	11053.9	+	8031.14i	0.997658	+	0.724841i
$498$		0			0
$499$	3428.76			0.307600			0.153800	−	0.988102i	$-0.450849\pi$
$499$	3428.76			0.307600			0.153800	+	0.988102i	$0.450849\pi$
$500$	−13251.1	−	5419.48i	−1.18521	−	0.484733i
$501$		0			0
$502$	6212.22	−	19119.2i	0.552320	−	1.69987i
$503$	−3567.05	−	2591.62i	−0.316197	−	0.229731i	0.418354	−	0.908284i	$-0.362607\pi$
$503$	−3567.05	−	2591.62i	−0.316197	−	0.229731i	−0.734551	+	0.678553i	$0.762607\pi$
$504$		0			0
$505$	−2466.40	+	5190.81i	−0.217333	+	0.457402i
$506$	−13729.6	+	9975.13i	−1.20623	+	0.876381i
$507$		0			0
$508$	−9518.50	+	6915.59i	−0.831329	+	0.603996i
$509$	−1764.24	−	5429.77i	−0.153632	−	0.472830i	0.844388	−	0.535732i	$-0.179964\pi$
$509$	−1764.24	−	5429.77i	−0.153632	−	0.472830i	−0.998020	+	0.0629024i	$0.979964\pi$
$510$		0			0
$511$	−5427.23	+	16703.3i	−0.469836	+	1.44601i
$512$	−4163.63	−	12814.3i	−0.359391	−	1.10609i
$513$		0			0
$514$	−756.645	+	2328.72i	−0.0649303	+	0.199835i
$515$	−935.574	+	509.783i	−0.0800511	+	0.0436189i
$516$		0			0
$517$	12063.6	−	8764.69i	1.02622	−	0.745592i
$518$	18554.0			1.57377
$519$		0			0
$520$	−7173.60	+	3908.81i	−0.604968	+	0.329639i
$521$	−1640.89	−	1192.18i	−0.137982	−	0.100250i	0.516653	−	0.856195i	$-0.327178\pi$
$521$	−1640.89	−	1192.18i	−0.137982	−	0.100250i	−0.654635	+	0.755945i	$0.727178\pi$
$522$		0			0
$523$	−1067.09	+	3284.16i	−0.0892171	+	0.274582i	−0.985703	−	0.168489i	$-0.946111\pi$
$523$	−1067.09	+	3284.16i	−0.0892171	+	0.274582i	0.896486	+	0.443071i	$0.146111\pi$
$524$	3052.92			0.254518
$525$		0			0
$526$	−19744.5			−1.63670
$527$	4230.21	−	13019.3i	0.349660	−	1.07614i
$528$		0			0
$529$	−2536.00	−	1842.51i	−0.208433	−	0.151435i
$530$	−2177.26	−	11650.5i	−0.178442	−	0.954841i
$531$		0			0
$532$	1239.81			0.101038
$533$	25817.3	−	18757.4i	2.09807	−	1.52434i
$534$		0			0
$535$	3744.43	−	7880.58i	0.302591	−	0.636836i
$536$	−817.654	+	2516.48i	−0.0658904	+	0.202790i
$537$		0			0
$538$	−8971.08	−	27610.2i	−0.718905	−	2.21256i
$539$	−7807.31	+	24028.4i	−0.623905	+	1.92018i
$540$		0			0
$541$	6762.35	+	20812.4i	0.537405	+	1.65396i	0.738394	+	0.674370i	$0.235585\pi$
$541$	6762.35	+	20812.4i	0.537405	+	1.65396i	−0.200988	+	0.979594i	$0.564415\pi$
$542$	17353.5	−	12608.1i	1.37527	−	0.999194i
$543$		0			0
$544$	−8434.58	+	6128.08i	−0.664761	+	0.482977i
$545$	−6821.22	−	887.687i	−0.536126	−	0.0697694i
$546$		0			0
$547$	−6842.63	−	4971.46i	−0.534862	−	0.388600i	0.287311	−	0.957837i	$-0.407239\pi$
$547$	−6842.63	−	4971.46i	−0.534862	−	0.388600i	−0.822173	+	0.569237i	$0.807239\pi$
$548$	6907.18	−	21258.1i	0.538431	−	1.65712i
$549$		0			0
$550$	948.569	+	17122.8i	0.0735402	+	1.32749i
$551$	−685.459			−0.0529973
$552$		0			0
$553$	9932.62	+	7216.47i	0.763793	+	0.554928i
$554$	−21998.9	−	15983.2i	−1.68709	−	1.22574i
$555$		0			0
$556$	17607.0	−	12792.2i	1.34299	−	0.975738i
$557$	−16513.1			−1.25616			−0.628080	−	0.778149i	$-0.716159\pi$
$557$	−16513.1			−1.25616			−0.628080	+	0.778149i	$0.716159\pi$
$558$		0			0
$559$	−989.135	−	3044.24i	−0.0748407	−	0.230336i
$560$	15281.9	+	1988.73i	1.15318	+	0.150070i
$561$		0			0
$562$	2926.23	+	9006.01i	0.219636	+	0.675971i
$563$	−5502.05	−	16933.6i	−0.411872	−	1.26761i	−0.915019	−	0.403410i	$-0.867825\pi$
$563$	−5502.05	−	16933.6i	−0.411872	−	1.26761i	0.503147	−	0.864201i	$-0.332175\pi$
$564$		0			0
$565$	4670.54	+	607.806i	0.347772	+	0.0452577i
$566$	9212.76	+	28354.0i	0.684172	+	2.10566i
$567$		0			0
$568$	3896.66			0.287853
$569$	3984.70	−	2895.05i	0.293580	−	0.213299i	−0.431239	−	0.902238i	$-0.641923\pi$
$569$	3984.70	−	2895.05i	0.293580	−	0.213299i	0.724819	+	0.688939i	$0.241923\pi$
$570$		0			0
$571$	−10205.8	−	7414.97i	−0.747987	−	0.543444i	0.147215	−	0.989104i	$-0.452969\pi$
$571$	−10205.8	−	7414.97i	−0.747987	−	0.543444i	−0.895202	+	0.445660i	$0.852969\pi$
$572$	20292.7	+	14743.5i	1.48336	+	1.07772i
$573$		0			0
$574$	60094.3			4.36984
$575$	−14418.9	+	5584.28i	−1.04576	+	0.405009i
$576$		0			0
$577$	3968.83	−	12214.8i	0.286351	−	0.881297i	−0.699640	−	0.714496i	$-0.746656\pi$
$577$	3968.83	−	12214.8i	0.286351	−	0.881297i	0.985991	−	0.166801i	$-0.0533439\pi$
$578$	−11055.7	−	8032.41i	−0.795597	−	0.578035i
$579$		0			0
$580$	21619.3	+	2813.45i	1.54774	+	0.201417i
$581$	−18493.3	+	13436.2i	−1.32054	+	0.959425i
$582$		0			0
$583$	−6449.27	+	4685.67i	−0.458150	+	0.332866i
$584$	1547.79	+	4763.61i	0.109671	+	0.337533i
$585$		0			0
$586$	−11144.1	+	34297.9i	−0.785593	+	2.41781i
$587$	2104.99	+	6478.50i	0.148011	+	0.455530i	0.997386	−	0.0722593i	$-0.0230209\pi$
$587$	2104.99	+	6478.50i	0.148011	+	0.455530i	−0.849375	+	0.527790i	$0.823021\pi$
$588$		0			0
$589$	367.982	−	1132.53i	0.0257427	−	0.0792278i
$590$	4423.34	−	9309.42i	0.308655	−	0.649598i
$591$		0			0
$592$	−4288.27	+	3115.61i	−0.297714	+	0.216302i
$593$	20641.3			1.42941			0.714703	−	0.699428i	$-0.246562\pi$
$593$	20641.3			1.42941			0.714703	+	0.699428i	$0.246562\pi$
$594$		0			0
$595$	−2857.49	−	15290.4i	−0.196883	−	1.05352i
$596$	−23983.3	−	17424.9i	−1.64831	−	1.19757i
$597$		0			0
$598$	−12446.7	+	38307.0i	−0.851142	+	2.61955i
$599$	15650.0			1.06751			0.533757	−	0.845638i	$-0.320780\pi$
$599$	15650.0			1.06751			0.533757	+	0.845638i	$0.320780\pi$
$600$		0			0
$601$	−17812.8			−1.20898			−0.604491	−	0.796612i	$-0.706623\pi$
$601$	−17812.8			−1.20898			−0.604491	+	0.796612i	$0.706623\pi$
$602$	1862.67	−	5732.71i	0.126108	−	0.388119i
$603$		0			0
$604$	−20880.6	−	15170.7i	−1.40666	−	1.02200i
$605$	−2938.70	+	1601.26i	−0.197480	+	0.107604i
$606$		0			0
$607$	−22919.5			−1.53258			−0.766290	−	0.642495i	$-0.777899\pi$
$607$	−22919.5			−1.53258			−0.766290	+	0.642495i	$0.777899\pi$
$608$	−733.716	+	533.076i	−0.0489409	+	0.0355577i
$609$		0			0
$610$	−7864.93	+	4285.50i	−0.522035	+	0.284450i
$611$	10936.3	−	33658.6i	0.724119	−	2.22861i
$612$		0			0
$613$	−2407.59	−	7409.79i	−0.158632	−	0.488220i	0.839879	−	0.542774i	$-0.182626\pi$
$613$	−2407.59	−	7409.79i	−0.158632	−	0.488220i	−0.998511	+	0.0545546i	$0.982626\pi$
$614$	3766.13	−	11591.0i	0.247538	−	0.761845i
$615$		0			0
$616$	3197.48	+	9840.82i	0.209140	+	0.643666i
$617$	24594.0	−	17868.6i	1.60473	−	1.16590i	0.727134	−	0.686496i	$-0.240852\pi$
$617$	24594.0	−	17868.6i	1.60473	−	1.16590i	0.877593	−	0.479406i	$-0.159148\pi$
$618$		0			0
$619$	16760.8	−	12177.5i	1.08833	−	0.790716i	0.109212	−	0.994019i	$-0.465167\pi$
$619$	16760.8	−	12177.5i	1.08833	−	0.790716i	0.979116	+	0.203302i	$0.0651674\pi$
$620$	−16254.5	+	34209.5i	−1.05290	+	2.21595i
$621$		0			0
$622$	−23326.2	−	16947.5i	−1.50369	−	1.09250i
$623$	−3078.79	+	9475.53i	−0.197992	+	0.609356i
$624$		0			0
$625$	−3157.43	+	15302.7i	−0.202075	+	0.979370i
$626$	−14124.1			−0.901778
$627$		0			0
$628$	−18156.4	−	13191.4i	−1.15369	−	0.838208i
$629$	4328.43	+	3144.79i	0.274381	+	0.199350i
$630$		0			0
$631$	18557.5	−	13482.8i	1.17078	−	0.850624i	0.179681	−	0.983725i	$-0.442493\pi$
$631$	18557.5	−	13482.8i	1.17078	−	0.850624i	0.991102	+	0.133101i	$0.0424935\pi$
$632$	3501.38			0.220376
$633$		0			0
$634$	4377.12	+	13471.4i	0.274192	+	0.843876i
$635$	9327.59	+	8825.16i	0.582920	+	0.551521i
$636$		0			0
$637$	18529.9	+	57029.1i	1.15256	+	3.54722i
$638$	−8070.00	−	24836.9i	−0.500775	−	1.54123i
$639$		0			0
$640$	11571.1	−	6304.95i	0.714669	−	0.389414i
$641$	−5387.35	−	16580.5i	−0.331962	−	1.02167i	−0.968199	−	0.250180i	$-0.919510\pi$
$641$	−5387.35	−	16580.5i	−0.331962	−	1.02167i	0.636238	−	0.771493i	$-0.280490\pi$
$642$		0			0
$643$	29188.0			1.79014			0.895072	−	0.445921i	$-0.147124\pi$
$643$	29188.0			1.79014			0.895072	+	0.445921i	$0.147124\pi$
$644$	−34455.6	+	25033.5i	−2.10829	+	1.53176i
$645$		0			0
$646$	515.105	+	374.246i	0.0313724	+	0.0227934i
$647$	−1185.75	−	861.499i	−0.0720506	−	0.0523478i	0.551177	−	0.834388i	$-0.314179\pi$
$647$	−1185.75	−	861.499i	−0.0720506	−	0.0523478i	−0.623227	+	0.782041i	$0.714179\pi$
$648$		0			0
$649$	−6932.35			−0.419289
$650$	25708.6	+	31554.6i	1.55134	+	1.90411i
$651$		0			0
$652$	−1544.74	+	4754.21i	−0.0927862	+	0.285567i
$653$	5424.96	+	3941.46i	0.325107	+	0.236204i	0.738352	−	0.674416i	$-0.235605\pi$
$653$	5424.96	+	3941.46i	0.325107	+	0.236204i	−0.413244	+	0.910620i	$0.635605\pi$
$654$		0			0
$655$	−612.083	−	3275.25i	−0.0365131	−	0.195381i
$656$	−13889.2	+	10091.1i	−0.826651	+	0.600597i
$657$		0			0
$658$	53917.2	−	39173.1i	3.19439	−	2.32086i
$659$	360.964	+	1110.93i	0.0213371	+	0.0656689i	0.961158	−	0.275998i	$-0.0890084\pi$
$659$	360.964	+	1110.93i	0.0213371	+	0.0656689i	−0.939821	+	0.341667i	$0.889008\pi$
$660$		0			0
$661$	811.577	−	2497.78i	0.0477559	−	0.146978i	−0.924335	−	0.381582i	$-0.875379\pi$
$661$	811.577	−	2497.78i	0.0477559	−	0.146978i	0.972091	+	0.234604i	$0.0753794\pi$
$662$	9888.89	+	30434.9i	0.580578	+	1.78684i
$663$		0			0
$664$	−2014.53	+	6200.07i	−0.117739	+	0.362364i
$665$	−248.570	−	1330.09i	−0.0144949	−	0.0775621i
$666$		0			0
$667$	19049.7	−	13840.4i	1.10586	−	0.803452i
$668$	−37791.7			−2.18893
$669$		0			0
$670$	13072.6	+	1701.22i	0.753788	+	0.0980951i
$671$	4873.71	+	3540.96i	0.280399	+	0.203722i
$672$		0			0
$673$	−6129.43	+	18864.4i	−0.351073	+	1.08049i	0.607179	+	0.794565i	$0.292301\pi$
$673$	−6129.43	+	18864.4i	−0.351073	+	1.08049i	−0.958252	+	0.285926i	$0.907699\pi$
$674$	34527.0			1.97319
$675$		0			0
$676$	37026.4			2.10664
$677$	1227.06	−	3776.51i	0.0696600	−	0.214392i	−0.910166	−	0.414244i	$-0.864046\pi$
$677$	1227.06	−	3776.51i	0.0696600	−	0.214392i	0.979826	+	0.199852i	$0.0640462\pi$
$678$		0			0
$679$	−6248.59	−	4539.87i	−0.353165	−	0.256589i
$680$	−3222.42	−	3048.85i	−0.181727	−	0.171938i
$681$		0			0
$682$	45368.4			2.54728
$683$	9447.69	−	6864.15i	0.529291	−	0.384552i	−0.290802	−	0.956783i	$-0.593922\pi$
$683$	9447.69	−	6864.15i	0.529291	−	0.384552i	0.820092	+	0.572231i	$0.193922\pi$
$684$		0			0
$685$	−24191.1	−	3148.13i	−1.34933	−	0.175597i
$686$	−19678.3	+	60563.5i	−1.09522	+	3.37074i
$687$		0			0
$688$	532.136	+	1637.75i	0.0294876	+	0.0907536i
$689$	−5846.65	+	17994.1i	−0.323279	+	0.994952i
$690$		0			0
$691$	−10114.6	−	31129.6i	−0.556844	−	1.71379i	−0.691024	−	0.722831i	$-0.742840\pi$
$691$	−10114.6	−	31129.6i	−0.556844	−	1.71379i	0.134181	−	0.990957i	$-0.457160\pi$
$692$	−25998.0	+	18888.7i	−1.42817	+	1.03763i
$693$		0			0
$694$	−35087.4	+	25492.5i	−1.91916	+	1.39435i
$695$	−17253.8	−	16324.5i	−0.941691	−	0.890967i
$696$		0			0
$697$	14019.3	+	10185.6i	0.761863	+	0.553526i
$698$	−1207.76	+	3717.10i	−0.0654934	+	0.201568i
$699$		0			0
$700$	2380.52	+	42971.2i	0.128536	+	2.32023i
$701$	25681.6			1.38371			0.691855	−	0.722036i	$-0.256794\pi$
$701$	25681.6			1.38371			0.691855	+	0.722036i	$0.256794\pi$
$702$		0			0
$703$	376.525	+	273.562i	0.0202005	+	0.0146765i
$704$	−19428.0	−	14115.2i	−1.04008	−	0.755665i
$705$		0			0
$706$	274.992	−	199.794i	0.0146593	−	0.0106506i
$707$	17276.0			0.918999
$708$		0			0
$709$	8535.60	+	26269.9i	0.452132	+	1.39152i	0.874470	+	0.485080i	$0.161209\pi$
$709$	8535.60	+	26269.9i	0.452132	+	1.39152i	−0.422338	+	0.906438i	$0.638791\pi$
$710$	−3566.36	−	19083.6i	−0.188512	−	1.00872i
$711$		0			0
$712$	878.038	+	2702.32i	0.0462161	+	0.142239i
$713$	12640.8	+	38904.4i	0.663958	+	2.04345i
$714$		0			0
$715$	11748.7	−	24726.5i	0.614513	−	1.29331i
$716$	−3019.74	−	9293.80i	−0.157616	−	0.485092i
$717$		0			0
$718$	26717.0			1.38868
$719$	4433.43	−	3221.08i	0.229957	−	0.167074i	−0.466840	−	0.884342i	$-0.654608\pi$
$719$	4433.43	−	3221.08i	0.229957	−	0.167074i	0.696797	+	0.717268i	$0.254608\pi$
$720$		0			0
$721$	2591.17	+	1882.59i	0.133842	+	0.0972419i
$722$	−23656.9	−	17187.7i	−1.21942	−	0.885957i
$723$		0			0
$724$	−1589.67			−0.0816018
$725$	−1316.13	−	23757.7i	−0.0674205	−	1.21702i
$726$		0			0
$727$	−7275.89	+	22392.9i	−0.371180	+	1.14237i	0.574840	+	0.818266i	$0.305064\pi$
$727$	−7275.89	+	22392.9i	−0.371180	+	1.14237i	−0.946020	+	0.324109i	$0.894936\pi$
$728$	19868.0	+	14434.9i	1.01148	+	0.734883i
$729$		0			0
$730$	21912.8	−	11940.0i	1.11100	−	0.605368i
$731$	1406.20	−	1021.66i	0.0711493	−	0.0516930i
$732$		0			0
$733$	−6158.96	+	4474.74i	−0.310350	+	0.225482i	−0.732046	−	0.681255i	$-0.761435\pi$
$733$	−6158.96	+	4474.74i	−0.310350	+	0.225482i	0.421697	+	0.906737i	$0.361435\pi$
$734$	3389.40	+	10431.5i	0.170443	+	0.524570i
$735$		0			0
$736$	9627.22	−	29629.5i	0.482152	−	1.48391i
$737$	−2739.96	−	8432.74i	−0.136944	−	0.421471i
$738$		0			0
$739$	−3949.52	+	12155.4i	−0.196597	+	0.605064i	0.803357	+	0.595498i	$0.203045\pi$
$739$	−3949.52	+	12155.4i	−0.196597	+	0.605064i	−0.999954	+	0.00956656i	$0.996955\pi$
$740$	−10752.7	−	10173.5i	−0.534159	−	0.505387i
$741$		0			0
$742$	−28824.5	+	20942.3i	−1.42612	+	1.03614i
$743$	8636.53			0.426438			0.213219	−	0.977004i	$-0.431605\pi$
$743$	8636.53			0.426438			0.213219	+	0.977004i	$0.431605\pi$
$744$		0			0
$745$	−13885.4	+	29223.4i	−0.682848	+	1.43713i
$746$	32163.4	+	23368.1i	1.57853	+	1.14687i
$747$		0			0
$748$	−4209.02	+	12954.0i	−0.205745	+	0.633217i
$749$	−26228.1			−1.27951
$750$		0			0
$751$	−13862.3			−0.673558			−0.336779	−	0.941584i	$-0.609338\pi$
$751$	−13862.3			−0.673558			−0.336779	+	0.941584i	$0.609338\pi$
$752$	−5883.54	+	18107.7i	−0.285307	+	0.878084i
$753$		0			0
$754$	−50144.1	−	36431.8i	−2.42194	−	1.75964i
$755$	−12089.1	+	25442.9i	−0.582738	+	1.22644i
$756$		0			0
$757$	−34297.7			−1.64673			−0.823364	−	0.567514i	$-0.807905\pi$
$757$	−34297.7			−1.64673			−0.823364	+	0.567514i	$0.807905\pi$
$758$	−7629.15	+	5542.90i	−0.365571	+	0.265603i
$759$		0			0
$760$	−280.315	−	265.216i	−0.0133791	−	0.0126584i
$761$	9289.71	−	28590.8i	0.442512	−	1.36191i	−0.442678	−	0.896681i	$-0.645971\pi$
$761$	9289.71	−	28590.8i	0.442512	−	1.36191i	0.885189	−	0.465231i	$-0.154029\pi$
$762$		0			0
$763$	6389.94	+	19666.2i	0.303186	+	0.933112i
$764$	4347.54	−	13380.3i	0.205875	−	0.633618i
$765$		0			0
$766$	−16991.2	−	52293.7i	−0.801460	−	2.46664i
$767$	−13311.0	+	9670.98i	−0.626638	+	0.455279i
$768$		0			0
$769$	6704.47	−	4871.08i	0.314395	−	0.228421i	−0.419385	−	0.907808i	$-0.637754\pi$
$769$	6704.47	−	4871.08i	0.314395	−	0.228421i	0.733780	+	0.679387i	$0.237754\pi$
$770$	45268.1	−	24666.0i	2.11864	−	1.15442i
$771$		0			0
$772$	−21258.4	−	15445.1i	−0.991070	−	0.720055i
$773$	−1109.96	+	3416.11i	−0.0516463	+	0.158951i	−0.973553	−	0.228461i	$-0.926631\pi$
$773$	−1109.96	+	3416.11i	−0.0516463	+	0.158951i	0.921907	+	0.387412i	$0.126631\pi$
$774$		0			0
$775$	39959.7	+	10579.6i	1.85212	+	0.490360i
$776$	−2202.72			−0.101898
$777$		0			0
$778$	−43303.6	−	31461.9i	−1.99551	−	1.44982i
$779$	1219.52	+	886.036i	0.0560898	+	0.0407516i
$780$		0			0
$781$	−10563.9	+	7675.14i	−0.484004	+	0.351649i
$782$	−21871.9			−1.00018
$783$		0			0
$784$	−9968.73	−	30680.6i	−0.454115	−	1.39762i
$785$	−10511.9	+	22123.4i	−0.477942	+	1.00588i
$786$		0			0
$787$	692.596	+	2131.59i	0.0313702	+	0.0965477i	0.965516	−	0.260345i	$-0.0838362\pi$
$787$	692.596	+	2131.59i	0.0313702	+	0.0965477i	−0.934145	+	0.356893i	$0.883836\pi$
$788$	4361.93	+	13424.7i	0.197192	+	0.606895i
$789$		0			0
$790$	−3204.59	−	17147.7i	−0.144322	−	0.772264i
$791$	−4375.24	−	13465.6i	−0.196669	−	0.605286i
$792$		0			0
$793$	14297.9			0.640271
$794$	44090.2	−	32033.4i	1.97066	−	1.43177i
$795$		0			0
$796$	8196.17	+	5954.87i	0.364957	+	0.265157i
$797$	−994.815	−	722.775i	−0.0442135	−	0.0321230i	0.565459	−	0.824776i	$-0.308699\pi$
$797$	−994.815	−	722.775i	−0.0442135	−	0.0321230i	−0.609673	+	0.792653i	$0.708699\pi$
$798$		0			0
$799$	19217.9			0.850913
$800$	−19885.0	−	24406.8i	−0.878800	−	1.07864i
$801$		0			0
$802$	6546.93	−	20149.4i	0.288254	−	0.887156i
$803$	−13578.8	−	9865.60i	−0.596745	−	0.433561i
$804$		0			0
$805$	33764.5	+	31945.8i	1.47832	+	1.39869i
$806$	87113.0	−	63291.3i	3.80698	−	2.76593i
$807$		0			0
$808$	3985.99	−	2895.99i	0.173548	−	0.126090i
$809$	−11526.7	−	35475.6i	−0.500938	−	1.54173i	−0.807495	−	0.589875i	$-0.799177\pi$
$809$	−11526.7	−	35475.6i	−0.500938	−	1.54173i	0.306557	−	0.951852i	$-0.400823\pi$
$810$		0			0
$811$	−2563.92	+	7890.95i	−0.111013	+	0.341663i	−0.991095	−	0.133159i	$-0.957488\pi$
$811$	−2563.92	+	7890.95i	−0.111013	+	0.341663i	0.880082	+	0.474823i	$0.157488\pi$
$812$	−20252.4	−	62330.3i	−0.875269	−	2.69380i
$813$		0			0
$814$	−5479.35	+	16863.7i	−0.235935	+	0.726133i
$815$	5410.14	+	704.055i	0.232526	+	0.0302601i
$816$		0			0
$817$	122.324	−	88.8733i	0.00523814	−	0.00380573i
$818$	−48364.8			−2.06728
$819$		0			0
$820$	−34826.9	−	32950.9i	−1.48318	−	1.40329i
$821$	19554.3	+	14207.1i	0.831243	+	0.603934i	0.919911	−	0.392128i	$-0.128261\pi$
$821$	19554.3	+	14207.1i	0.831243	+	0.603934i	−0.0886674	+	0.996061i	$0.528261\pi$
$822$		0			0
$823$	8334.88	−	25652.1i	0.353020	−	1.08648i	−0.604128	−	0.796887i	$-0.706479\pi$
$823$	8334.88	−	25652.1i	0.353020	−	1.08648i	0.957149	−	0.289598i	$-0.0935215\pi$
$824$	913.422			0.0386172
$825$		0			0
$826$	−30983.6			−1.30515
$827$	−3670.53	+	11296.7i	−0.154337	+	0.475001i	−0.998093	−	0.0617260i	$-0.980340\pi$
$827$	−3670.53	+	11296.7i	−0.154337	+	0.475001i	0.843756	+	0.536727i	$0.180340\pi$
$828$		0			0
$829$	−21788.3	−	15830.1i	−0.912833	−	0.663212i	0.0288964	−	0.999582i	$-0.490801\pi$
$829$	−21788.3	−	15830.1i	−0.912833	−	0.663212i	−0.941730	+	0.336370i	$0.890801\pi$
$830$	32208.1	+	4191.44i	1.34694	+	0.175285i
$831$		0			0
$832$	−56995.5			−2.37496
$833$	−26342.9	+	19139.2i	−1.09571	+	0.796081i
$834$		0			0
$835$	7576.89	+	40543.8i	0.314023	+	1.68033i
$836$	−366.138	+	1126.86i	−0.0151473	+	0.0466186i
$837$		0			0
$838$	−15203.1	−	46790.4i	−0.626710	−	1.92881i
$839$	6699.29	−	20618.3i	0.275668	−	0.848418i	−0.713374	−	0.700783i	$-0.752834\pi$
$839$	6699.29	−	20618.3i	0.275668	−	0.848418i	0.989042	−	0.147635i	$-0.0471659\pi$
$840$		0			0
$841$	3660.43	+	11265.6i	0.150085	+	0.461915i
$842$	−8408.41	+	6109.07i	−0.344148	+	0.250038i
$843$		0			0
$844$	−16266.9	+	11818.6i	−0.663424	+	0.482006i
$845$	−7423.45	−	39722.8i	−0.302218	−	1.61717i
$846$		0			0
$847$	8139.03	+	5913.35i	0.330178	+	0.239888i
$848$	3145.39	−	9680.51i	0.127374	−	0.392016i
$849$		0			0
$850$	−11982.2	+	18571.9i	−0.483512	+	0.749426i
$851$	−15987.7			−0.644007
$852$		0			0
$853$	−22494.3	−	16343.1i	−0.902919	−	0.656009i	0.0362948	−	0.999341i	$-0.488444\pi$
$853$	−22494.3	−	16343.1i	−0.902919	−	0.656009i	−0.939214	+	0.343332i	$0.888444\pi$
$854$	21782.7	+	15826.1i	0.872820	+	0.634141i
$855$		0			0
$856$	−6051.45	+	4396.63i	−0.241629	+	0.175553i
$857$	34445.3			1.37296			0.686482	−	0.727147i	$-0.259154\pi$
$857$	34445.3			1.37296			0.686482	+	0.727147i	$0.259154\pi$
$858$		0			0
$859$	−7164.69	−	22050.7i	−0.284582	−	0.875854i	−0.986524	−	0.163619i	$-0.947683\pi$
$859$	−7164.69	−	22050.7i	−0.284582	−	0.875854i	0.701941	−	0.712235i	$-0.252317\pi$
$860$	−4222.85	+	2300.98i	−0.167439	+	0.0912356i
$861$		0			0
$862$	11601.7	+	35706.4i	0.458417	+	1.41086i
$863$	10355.6	+	31871.3i	0.408470	+	1.25714i	0.917963	+	0.396666i	$0.129833\pi$
$863$	10355.6	+	31871.3i	0.408470	+	1.25714i	−0.509494	+	0.860474i	$0.670167\pi$
$864$		0			0
$865$	25476.6	+	24104.3i	1.00142	+	0.947480i
$866$	−10109.6	−	31114.0i	−0.396694	−	1.22090i
$867$		0			0
$868$	113856.			4.45222
$869$	−9492.33	+	6896.58i	−0.370547	+	0.269218i
$870$		0			0
$871$	−17025.2	−	12369.5i	−0.662314	−	0.481200i
$872$	4770.96	+	3466.31i	0.185281	+	0.134615i
$873$		0			0
$874$	−1902.62			−0.0736349
$875$	45623.3	−	11169.2i	1.76268	−	0.431529i
$876$		0			0
$877$	−1943.07	+	5980.14i	−0.0748149	+	0.230257i	−0.981470	−	0.191616i	$-0.938627\pi$
$877$	−1943.07	+	5980.14i	−0.0748149	+	0.230257i	0.906655	+	0.421873i	$0.138627\pi$
$878$	17770.6	+	12911.1i	0.683061	+	0.496273i
$879$		0			0
$880$	−6320.59	+	13302.4i	−0.242122	+	0.509572i
$881$	−37499.2	+	27244.8i	−1.43403	+	1.04188i	−0.444783	+	0.895638i	$0.646719\pi$
$881$	−37499.2	+	27244.8i	−1.43403	+	1.04188i	−0.989248	+	0.146246i	$0.953281\pi$
$882$		0			0
$883$	5645.20	−	4101.48i	0.215149	−	0.156315i	−0.474992	−	0.879990i	$-0.657549\pi$
$883$	5645.20	−	4101.48i	0.215149	−	0.156315i	0.690140	+	0.723676i	$0.257549\pi$
$884$	9989.70	+	30745.1i	0.380079	+	1.16976i
$885$		0			0
$886$	5077.69	−	15627.5i	0.192537	−	0.592569i
$887$	−2086.86	−	6422.69i	−0.0789965	−	0.243126i	0.903757	−	0.428045i	$-0.140798\pi$
$887$	−2086.86	−	6422.69i	−0.0789965	−	0.243126i	−0.982754	+	0.184919i	$0.940798\pi$
$888$		0			0
$889$	11928.4	−	36711.8i	0.450017	−	1.38501i
$890$	12430.8	−	6773.38i	0.468181	−	0.255106i
$891$		0			0
$892$	−28523.0	+	20723.2i	−1.07065	+	0.777874i
$893$	1671.74			0.0626458
$894$		0			0
$895$	−9365.18	+	5102.97i	−0.349769	+	0.190585i
$896$	−32047.3	−	23283.7i	−1.19489	−	0.868142i
$897$		0			0
$898$	−2231.95	+	6869.25i	−0.0829413	+	0.255267i
$899$	−62948.3			−2.33531
$900$		0			0
$901$	−10274.0			−0.379886
$902$	−17747.0	+	54619.6i	−0.655111	+	2.01622i
$903$		0			0
$904$	−3266.71	−	2373.40i	−0.120187	−	0.0873211i
$905$	318.715	+	1705.44i	0.0117066	+	0.0626417i
$906$		0			0
$907$	50129.5			1.83519			0.917597	−	0.397511i	$-0.130126\pi$
$907$	50129.5			1.83519			0.917597	+	0.397511i	$0.130126\pi$
$908$	−13907.6	+	10104.4i	−0.508302	+	0.369303i
$909$		0			0
$910$	52510.0	−	110513.i	1.91285	−	4.02580i
$911$	3220.77	−	9912.52i	0.117134	−	0.360501i	−0.875252	−	0.483667i	$-0.839305\pi$
$911$	3220.77	−	9912.52i	0.117134	−	0.360501i	0.992386	+	0.123166i	$0.0393047\pi$
$912$		0			0
$913$	−6750.69	−	20776.5i	−0.244705	−	0.753123i
$914$	487.291	−	1499.73i	0.0176347	−	0.0542741i
$915$		0			0
$916$	−1706.50	−	5252.08i	−0.0615551	−	0.189447i
$917$	−8103.30	+	5887.39i	−0.291815	+	0.212016i
$918$		0			0
$919$	−19295.9	+	14019.3i	−0.692616	+	0.503215i	−0.877519	−	0.479542i	$-0.840803\pi$
$919$	−19295.9	+	14019.3i	−0.692616	+	0.503215i	0.184903	+	0.982757i	$0.440803\pi$
$920$	13145.4	+	1710.69i	0.471076	+	0.0613040i
$921$		0			0
$922$	9085.50	+	6601.00i	0.324528	+	0.235784i
$923$	−9576.83	+	29474.4i	−0.341522	+	1.05110i
$924$		0			0
$925$	−8758.59	+	13575.5i	−0.311330	+	0.482550i
$926$	−8127.05			−0.288414
$927$		0			0
$928$	38785.3	+	28179.2i	1.37197	+	0.996796i
$929$	38494.5	+	27967.9i	1.35949	+	0.987726i	0.998477	+	0.0551637i	$0.0175681\pi$
$929$	38494.5	+	27967.9i	1.35949	+	0.987726i	0.361010	+	0.932562i	$0.382432\pi$
$930$		0			0
$931$	−2291.54	+	1664.90i	−0.0806684	+	0.0586090i
$932$	31515.1			1.10763
$933$		0			0
$934$	14525.7	+	44705.4i	0.508881	+	1.56617i
$935$	14741.3	+	1918.37i	0.515606	+	0.0670989i
$936$		0			0
$937$	−7306.25	−	22486.3i	−0.254733	−	0.783987i	−0.993882	−	0.110446i	$-0.964772\pi$
$937$	−7306.25	−	22486.3i	−0.254733	−	0.783987i	0.739149	−	0.673542i	$-0.235228\pi$
$938$	−12246.1	−	37689.5i	−0.426277	−	1.31195i
$939$		0			0
$940$	−52726.5	−	6861.62i	−1.82952	−	0.238087i
$941$	6843.90	+	21063.4i	0.237093	+	0.729698i	0.996837	+	0.0794751i	$0.0253244\pi$
$941$	6843.90	+	21063.4i	0.237093	+	0.729698i	−0.759744	+	0.650223i	$0.774676\pi$
$942$		0			0
$943$	−51782.3			−1.78819
$944$	7161.05	−	5202.81i	0.246899	−	0.179382i
$945$		0			0
$946$	4660.37	+	3385.95i	0.160171	+	0.116371i
$947$	−21088.8	−	15321.9i	−0.723648	−	0.525761i	0.163900	−	0.986477i	$-0.447593\pi$
$947$	−21088.8	−	15321.9i	−0.723648	−	0.525761i	−0.887548	+	0.460716i	$0.847593\pi$
$948$		0			0
$949$	−39836.0			−1.36263
$950$	−1042.32	+	1615.55i	−0.0355971	+	0.0551742i
$951$		0			0
$952$	−4120.92	+	12682.9i	−0.140294	+	0.431781i
$953$	−27443.4	−	19938.8i	−0.932823	−	0.677736i	0.0138594	−	0.999904i	$-0.495588\pi$
$953$	−27443.4	−	19938.8i	−0.932823	−	0.677736i	−0.946682	+	0.322168i	$0.895588\pi$
$954$		0			0
$955$	−15226.4	−	1981.51i	−0.515932	−	0.0671414i
$956$	3613.74	−	2625.54i	0.122256	−	0.0888242i
$957$		0			0
$958$	−47216.3	+	34304.6i	−1.59237	+	1.15692i
$959$	22661.6	+	69745.1i	0.763065	+	2.34847i
$960$		0			0
$961$	24587.2	−	75671.7i	0.825324	−	2.54009i
$962$	13004.7	+	40024.3i	0.435850	+	1.34141i
$963$		0			0
$964$	12702.5	−	39094.1i	0.424397	−	1.30616i
$965$	−12307.8	+	25903.1i	−0.410572	+	0.864094i
$966$		0			0
$967$	17639.8	−	12816.1i	0.586617	−	0.426202i	−0.254487	−	0.967076i	$-0.581907\pi$
$967$	17639.8	−	12816.1i	0.586617	−	0.426202i	0.841103	+	0.540874i	$0.181907\pi$
$968$	2869.12			0.0952656
$969$		0			0
$970$	2016.00	+	10787.6i	0.0667320	+	0.357082i
$971$	−42269.2	−	30710.4i	−1.39700	−	1.01498i	−0.995057	−	0.0993099i	$-0.968336\pi$
$971$	−42269.2	−	30710.4i	−1.39700	−	1.01498i	−0.401939	−	0.915667i	$-0.631664\pi$
$972$		0			0
$973$	−22064.7	+	67908.1i	−0.726990	+	2.23745i
$974$	21078.6			0.693432
$975$		0			0
$976$	−7692.03			−0.252270
$977$	12234.1	−	37652.6i	0.400617	−	1.23297i	−0.523882	−	0.851791i	$-0.675517\pi$
$977$	12234.1	−	37652.6i	0.400617	−	1.23297i	0.924500	−	0.381183i	$-0.124483\pi$
$978$		0			0
$979$	−7703.07	−	5596.61i	−0.251472	−	0.182705i
$980$	79108.4	−	43105.2i	2.57860	−	1.40505i
$981$		0			0
$982$	−1860.22			−0.0604502
$983$	−20906.9	+	15189.8i	−0.678359	+	0.492857i	−0.872813	−	0.488055i	$-0.837707\pi$
$983$	−20906.9	+	15189.8i	−0.678359	+	0.492857i	0.194454	+	0.980912i	$0.437707\pi$
$984$		0			0
$985$	13527.8	−	7371.11i	0.437594	−	0.238440i
$986$	10400.6	−	32009.9i	0.335927	−	1.03388i
$987$		0			0
$988$	868.993	+	2674.49i	0.0279821	+	0.0861202i
$989$	−1605.03	+	4939.78i	−0.0516047	+	0.158823i
$990$		0			0
$991$	−2506.63	−	7714.61i	−0.0803488	−	0.247288i	0.902811	−	0.430038i	$-0.141500\pi$
$991$	−2506.63	−	7714.61i	−0.0803488	−	0.247288i	−0.983159	+	0.182750i	$0.941500\pi$
$992$	−67379.9	+	48954.3i	−2.15656	+	1.56684i
$993$		0			0
$994$	−47214.7	+	34303.5i	−1.50660	+	1.09461i
$995$	4745.27	−	9986.95i	0.151191	−	0.318199i
$996$		0			0
$997$	−10032.6	−	7289.10i	−0.318691	−	0.231543i	0.416926	−	0.908941i	$-0.363108\pi$
$997$	−10032.6	−	7289.10i	−0.318691	−	0.231543i	−0.735617	+	0.677398i	$0.763108\pi$
$998$	−4525.64	+	13928.5i	−0.143544	+	0.441782i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.46.3	✓	64
3.2	odd	2	inner	225.4.h.d.46.14	yes	64
25.6	even	5	inner	225.4.h.d.181.3	yes	64
75.56	odd	10	inner	225.4.h.d.181.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.46.3	✓	64	1.1	even	1	trivial
225.4.h.d.46.14	yes	64	3.2	odd	2	inner
225.4.h.d.181.3	yes	64	25.6	even	5	inner
225.4.h.d.181.14	yes	64	75.56	odd	10	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.31991 + 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(-4.79821 + 10.0984i) q^{5} +33.6094 q^{7} +(7.75447 - 5.63395i) q^{8} +O(q^{10})\)	\(q+(-1.31991 + 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(-4.79821 + 10.0984i) q^{5} +33.6094 q^{7} +(7.75447 - 5.63395i) q^{8} +(-34.6890 - 32.8205i) q^{10} +(-9.92549 + 30.5475i) q^{11} +(23.5572 + 72.5016i) q^{13} +(-44.3613 + 136.530i) q^{14} +(-12.6733 - 39.0045i) q^{16} +(-33.4899 + 24.3319i) q^{17} +(-2.91326 + 2.11660i) q^{19} +(100.571 - 54.8000i) q^{20} +(-110.991 - 80.6398i) q^{22} +(38.2254 - 117.646i) q^{23} +(-78.9543 - 96.9083i) q^{25} -325.613 q^{26} +(-278.542 - 202.372i) q^{28} +(153.999 + 111.887i) q^{29} +(-267.535 + 194.376i) q^{31} +251.854 q^{32} +(-54.6386 - 168.160i) q^{34} +(-161.265 + 339.400i) q^{35} +(-39.9391 - 122.920i) q^{37} +(-4.75296 - 14.6281i) q^{38} +(19.6862 + 105.340i) q^{40} +(-129.358 - 398.124i) q^{41} -41.9887 q^{43} +(266.195 - 193.402i) q^{44} +(427.452 + 310.562i) q^{46} +(-375.583 - 272.877i) q^{47} +786.592 q^{49} +(497.878 - 192.823i) q^{50} +(241.321 - 742.710i) q^{52} +(200.790 + 145.882i) q^{53} +(-260.856 - 246.805i) q^{55} +(260.623 - 189.354i) q^{56} +(-657.777 + 477.903i) q^{58} +(66.6949 + 205.266i) q^{59} +(57.9582 - 178.377i) q^{61} +(-436.482 - 1343.35i) q^{62} +(-231.037 + 711.060i) q^{64} +(-845.181 - 109.989i) q^{65} +(-223.332 + 162.260i) q^{67} +424.061 q^{68} +(-1165.88 - 1103.08i) q^{70} +(328.894 + 238.955i) q^{71} +(-161.479 + 496.983i) q^{73} +552.048 q^{74} +36.8887 q^{76} +(-333.590 + 1026.68i) q^{77} +(295.531 + 214.716i) q^{79} +(454.691 + 59.1718i) q^{80} +1788.02 q^{82} +(-550.242 + 399.774i) q^{83} +(-85.0205 - 454.944i) q^{85} +(55.4211 - 170.569i) q^{86} +(95.1364 + 292.800i) q^{88} +(-91.6049 + 281.931i) q^{89} +(791.743 + 2436.73i) q^{91} +(-1025.18 + 744.835i) q^{92} +(1604.23 - 1165.54i) q^{94} +(-7.39584 - 39.5751i) q^{95} +(-185.918 - 135.077i) q^{97} +(-1038.23 + 3195.33i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 64 * q - 72 * q^4 + 20 * q^7	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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