LMFDB - Embedded newform 225.4.h.d.46.14

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			46.14
Character	$\chi$	$=$	225.46
Dual form			225.4.h.d.181.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31991 - 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(4.79821 - 10.0984i) q^{5} +33.6094 q^{7} +(-7.75447 + 5.63395i) q^{8} +O(q^{10})$	\(q+(1.31991 - 4.06225i) q^{2} +(-8.28762 - 6.02131i) q^{4} +(4.79821 - 10.0984i) q^{5} +33.6094 q^{7} +(-7.75447 + 5.63395i) q^{8} +(-34.6890 - 32.8205i) q^{10} +(9.92549 - 30.5475i) q^{11} +(23.5572 + 72.5016i) q^{13} +(44.3613 - 136.530i) q^{14} +(-12.6733 - 39.0045i) q^{16} +(33.4899 - 24.3319i) q^{17} +(-2.91326 + 2.11660i) q^{19} +(-100.571 + 54.8000i) q^{20} +(-110.991 - 80.6398i) q^{22} +(-38.2254 + 117.646i) q^{23} +(-78.9543 - 96.9083i) q^{25} +325.613 q^{26} +(-278.542 - 202.372i) q^{28} +(-153.999 - 111.887i) q^{29} +(-267.535 + 194.376i) q^{31} -251.854 q^{32} +(-54.6386 - 168.160i) q^{34} +(161.265 - 339.400i) q^{35} +(-39.9391 - 122.920i) q^{37} +(4.75296 + 14.6281i) q^{38} +(19.6862 + 105.340i) q^{40} +(129.358 + 398.124i) q^{41} -41.9887 q^{43} +(-266.195 + 193.402i) q^{44} +(427.452 + 310.562i) q^{46} +(375.583 + 272.877i) q^{47} +786.592 q^{49} +(-497.878 + 192.823i) q^{50} +(241.321 - 742.710i) q^{52} +(-200.790 - 145.882i) q^{53} +(-260.856 - 246.805i) q^{55} +(-260.623 + 189.354i) q^{56} +(-657.777 + 477.903i) q^{58} +(-66.6949 - 205.266i) q^{59} +(57.9582 - 178.377i) q^{61} +(436.482 + 1343.35i) q^{62} +(-231.037 + 711.060i) q^{64} +(845.181 + 109.989i) q^{65} +(-223.332 + 162.260i) q^{67} -424.061 q^{68} +(-1165.88 - 1103.08i) q^{70} +(-328.894 - 238.955i) q^{71} +(-161.479 + 496.983i) q^{73} -552.048 q^{74} +36.8887 q^{76} +(333.590 - 1026.68i) q^{77} +(295.531 + 214.716i) q^{79} +(-454.691 - 59.1718i) q^{80} +1788.02 q^{82} +(550.242 - 399.774i) q^{83} +(-85.0205 - 454.944i) q^{85} +(-55.4211 + 170.569i) q^{86} +(95.1364 + 292.800i) q^{88} +(91.6049 - 281.931i) q^{89} +(791.743 + 2436.73i) q^{91} +(1025.18 - 744.835i) q^{92} +(1604.23 - 1165.54i) q^{94} +(7.39584 + 39.5751i) q^{95} +(-185.918 - 135.077i) q^{97} +(1038.23 - 3195.33i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.627604\pi$
$2$	1.31991	−	4.06225i	0.466657	−	1.43622i	0.856886	−	0.515506i	$-0.172396\pi$
$3$		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	$-0.754907\pi$
$11$	9.92549	−	30.5475i	0.272059	−	0.837312i	0.989983	−	0.141190i	$-0.0450927\pi$
$12$		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	−0.322677	−	0.946509i	$-0.604583\pi$
$17$	33.4899	−	24.3319i	0.477794	−	0.347138i	0.800471	+	0.599371i	$0.204583\pi$
$18$		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	$0.289476\pi$
$23$	−38.2254	+	117.646i	−0.346545	+	1.06656i	−0.960751	+	0.277411i	$0.910524\pi$
$24$		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	−0.0270367	−	0.999634i	$-0.508607\pi$
$29$	−153.999	−	111.887i	−0.986100	−	0.716444i	−0.959064	+	0.283191i	$0.908607\pi$
$30$		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	$0.193724\pi$
$41$	129.358	+	398.124i	0.492741	+	1.51650i	−0.327708	+	0.944779i	$0.606276\pi$
$42$		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	0.990479	−	0.137666i	$-0.0439599\pi$
$47$	375.583	+	272.877i	1.16563	+	0.846877i	0.175147	+	0.984542i	$0.443960\pi$
$48$		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	0.296362	−	0.955076i	$-0.404226\pi$
$53$	−200.790	−	145.882i	−0.520388	−	0.378084i	−0.816750	+	0.576992i	$0.804226\pi$
$54$		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	0.850115	−	0.526597i	$-0.176532\pi$
$59$	−66.6949	−	205.266i	−0.147169	−	0.452938i	−0.997283	+	0.0736590i	$0.976532\pi$
$60$		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	0.277941	−	0.960598i	$-0.410348\pi$
$71$	−328.894	−	238.955i	−0.549754	−	0.399419i	−0.827695	+	0.561179i	$0.810348\pi$
$72$		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	−0.161153	−	0.986929i	$-0.551521\pi$
$83$	550.242	−	399.774i	0.727673	−	0.528686i	0.888827	+	0.458244i	$0.151521\pi$
$84$		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	−0.881569	−	0.472055i	$-0.843512\pi$
$89$	91.6049	−	281.931i	0.109102	−	0.335782i	0.990671	+	0.136273i	$0.0435124\pi$
$90$		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	$-0.581485\pi$
$101$	−514.024			−0.506409			−0.253205	+	0.967413i	$0.581485\pi$
$102$		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	$-0.385320\pi$
$107$	780.381			0.705068			0.352534	+	0.935799i	$0.385320\pi$
$108$		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	0.990507	−	0.137459i	$-0.0438936\pi$
$113$	130.179	+	400.650i	0.108374	+	0.333539i	−0.882134	+	0.470999i	$0.843894\pi$
$114$		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	−0.504474	−	0.863427i	$-0.668314\pi$
$131$	241.102	−	175.171i	0.160803	−	0.116830i	0.665277	+	0.746597i	$0.268314\pi$
$132$		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	$-0.861826\pi$
$137$	−674.262	−	2075.17i	−0.420483	−	1.29411i	0.486771	−	0.873529i	$-0.338174\pi$
$138$		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	$-0.792820\pi$
$149$	−2893.87			−1.59111			−0.795554	+	0.605882i	$0.792820\pi$
$150$		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	$0.626266\pi$
$167$	−2984.57	+	2168.42i	−1.38295	+	1.00477i	−0.996597	+	0.0824226i	$0.973734\pi$
$168$		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	$0.342084\pi$
$173$	−969.377	+	2983.44i	−0.426014	+	1.31114i	−0.902020	+	0.431693i	$0.857916\pi$
$174$		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	0.414885	−	0.909874i	$-0.363822\pi$
$179$	−771.743	−	560.704i	−0.322250	−	0.234128i	−0.737135	+	0.675745i	$0.763822\pi$
$180$		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	0.837924	−	0.545787i	$-0.183769\pi$
$191$	−424.396	−	1306.16i	−0.160776	−	0.494818i	−0.998700	+	0.0509689i	$0.983769\pi$
$192$		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	0.770829	−	0.637042i	$-0.219842\pi$
$197$	1114.76	+	809.922i	0.403165	+	0.292917i	−0.367664	+	0.929959i	$0.619842\pi$
$198$		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	−0.997803	−	0.0662496i	$-0.978897\pi$
$227$	−518.565	+	1595.98i	−0.151623	+	0.466647i	0.846180	+	0.532897i	$0.178897\pi$
$228$		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	−0.180070	−	0.983654i	$-0.557632\pi$
$233$	2488.89	−	1808.28i	0.699796	−	0.508431i	0.879866	+	0.475223i	$0.157632\pi$
$234$		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	−0.931165	−	0.364597i	$-0.881207\pi$
$239$	134.744	−	414.700i	0.0364681	−	0.112237i	0.967633	+	0.252360i	$0.0812067\pi$
$240$		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	$-0.298424\pi$
$251$	4706.56			1.18357			0.591784	+	0.806097i	$0.298424\pi$
$252$		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	$-0.522163\pi$
$257$	−573.257			−0.139139			−0.0695696	+	0.997577i	$0.522163\pi$
$258$		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	$-0.917703\pi$
$263$	−1428.46	−	4396.36i	−0.334915	−	1.03076i	0.631848	−	0.775092i	$-0.282297\pi$
$264$		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	0.248321	−	0.968678i	$-0.420121\pi$
$269$	5498.69	−	3995.03i	1.24632	−	0.905507i	0.998003	+	0.0631703i	$0.0201211\pi$
$270$		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	−0.761663	−	0.647973i	$-0.775617\pi$
$281$	−1793.59	+	1303.12i	−0.380771	+	0.276646i	0.380892	+	0.924619i	$0.375617\pi$
$282$		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	$-0.818459\pi$
$293$	−8443.08			−1.68345			−0.841724	+	0.539908i	$0.818459\pi$
$294$		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	$-0.688996\pi$
$311$	2085.97	−	6419.96i	0.380336	−	1.17055i	0.939807	−	0.341705i	$-0.111004\pi$
$312$		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	−0.799523	−	0.600635i	$-0.794914\pi$
$317$	−2682.89	+	1949.24i	−0.475351	+	0.345363i	0.324172	+	0.945998i	$0.394914\pi$
$318$		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	−0.271619	−	0.962405i	$-0.587559\pi$
$347$	−8214.67	−	5968.31i	−1.27086	−	0.923330i	−0.999236	+	0.0390745i	$0.987559\pi$
$348$		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	0.592628	−	0.805476i	$-0.298090\pi$
$353$	64.3813	+	46.7758i	0.00970728	+	0.00705275i	−0.582921	+	0.812529i	$0.698090\pi$
$354$		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	$0.0520739\pi$
$359$	1932.90	+	5948.86i	0.284163	+	0.874565i	−0.702485	+	0.711699i	$0.747926\pi$
$360$		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	$-0.371257\pi$
$383$	10414.5	−	7566.60i	1.38945	−	1.00949i	0.995926	−	0.0901754i	$-0.0287428\pi$
$384$		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	$-0.595813\pi$
$389$	3872.47	−	11918.2i	0.504735	−	1.55341i	0.801216	−	0.598376i	$-0.204187\pi$
$390$		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	$-0.400056\pi$
$401$	4960.15			0.617700			0.308850	+	0.951111i	$0.400056\pi$
$402$		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	0.107688	−	0.994185i	$-0.465655\pi$
$419$	9318.52	−	6770.30i	1.08649	−	0.789382i	0.978803	+	0.204803i	$0.0656554\pi$
$420$		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	−0.909364	−	0.416001i	$-0.863431\pi$
$431$	−7111.10	+	5166.51i	−0.794732	+	0.577407i	0.114632	+	0.993408i	$0.463431\pi$
$432$		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	$-0.433860\pi$
$443$	3847.00			0.412588			0.206294	+	0.978490i	$0.433860\pi$
$444$		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	$-0.528325\pi$
$449$	−1690.99			−0.177735			−0.0888674	+	0.996043i	$0.528325\pi$
$450$		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	−0.983673	−	0.179964i	$-0.942402\pi$
$461$	−812.481	+	2500.56i	−0.0820846	+	0.252630i	0.901589	+	0.432595i	$0.142402\pi$
$462$		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	−0.933837	−	0.357698i	$-0.883562\pi$
$467$	−8903.30	+	6468.62i	−0.882217	+	0.640968i	0.0516199	+	0.998667i	$0.483562\pi$
$468$		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	−0.0813995	−	0.996682i	$-0.525939\pi$
$479$	−11054.3	−	8031.41i	−1.05445	−	0.766106i	−0.973054	+	0.230576i	$0.925939\pi$
$480$		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	0.944681	−	0.327990i	$-0.106371\pi$
$491$	−134.582	−	414.201i	−0.0123699	−	0.0380705i	−0.957051	+	0.289920i	$0.906371\pi$
$492$		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	0.734551	−	0.678553i	$-0.237393\pi$
$503$	3567.05	+	2591.62i	0.316197	+	0.229731i	−0.418354	+	0.908284i	$0.637393\pi$
$504$		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	0.998020	−	0.0629024i	$-0.0200357\pi$
$509$	1764.24	+	5429.77i	0.153632	+	0.472830i	−0.844388	+	0.535732i	$0.820036\pi$
$510$		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	0.654635	−	0.755945i	$-0.272822\pi$
$521$	1640.89	+	1192.18i	0.137982	+	0.100250i	−0.516653	+	0.856195i	$0.672822\pi$
$522$		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	$-0.283841\pi$
$557$	16513.1			1.25616			0.628080	+	0.778149i	$0.283841\pi$
$558$		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	$0.132175\pi$
$563$	5502.05	+	16933.6i	0.411872	+	1.26761i	−0.503147	+	0.864201i	$0.667825\pi$
$564$		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	−0.724819	−	0.688939i	$-0.758077\pi$
$569$	−3984.70	+	2895.05i	−0.293580	+	0.213299i	0.431239	+	0.902238i	$0.358077\pi$
$570$		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	0.849375	−	0.527790i	$-0.176979\pi$
$587$	−2104.99	−	6478.50i	−0.148011	−	0.455530i	−0.997386	+	0.0722593i	$0.976979\pi$
$588$		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	$-0.753438\pi$
$593$	−20641.3			−1.42941			−0.714703	+	0.699428i	$0.753438\pi$
$594$		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	$-0.679220\pi$
$599$	−15650.0			−1.06751			−0.533757	+	0.845638i	$0.679220\pi$
$600$		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	$0.759148\pi$
$617$	−24594.0	+	17868.6i	−1.60473	+	1.16590i	−0.877593	+	0.479406i	$0.840852\pi$
$618$		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	$0.0804897\pi$
$641$	5387.35	+	16580.5i	0.331962	+	1.02167i	−0.636238	+	0.771493i	$0.719510\pi$
$642$		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	0.623227	−	0.782041i	$-0.285821\pi$
$647$	1185.75	+	861.499i	0.0720506	+	0.0523478i	−0.551177	+	0.834388i	$0.685821\pi$
$648$		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	0.413244	−	0.910620i	$-0.364395\pi$
$653$	−5424.96	−	3941.46i	−0.325107	−	0.236204i	−0.738352	+	0.674416i	$0.764395\pi$
$654$		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	0.939821	−	0.341667i	$-0.110992\pi$
$659$	−360.964	−	1110.93i	−0.0213371	−	0.0656689i	−0.961158	+	0.275998i	$0.910992\pi$
$660$		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	−0.979826	−	0.199852i	$-0.935954\pi$
$677$	−1227.06	+	3776.51i	−0.0696600	+	0.214392i	0.910166	+	0.414244i	$0.135954\pi$
$678$		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	−0.820092	−	0.572231i	$-0.806078\pi$
$683$	−9447.69	+	6864.15i	−0.529291	+	0.384552i	0.290802	+	0.956783i	$0.406078\pi$
$684$		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	$-0.743206\pi$
$701$	−25681.6			−1.38371			−0.691855	+	0.722036i	$0.743206\pi$
$702$		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	−0.696797	−	0.717268i	$-0.745392\pi$
$719$	−4433.43	+	3221.08i	−0.229957	+	0.167074i	0.466840	+	0.884342i	$0.345392\pi$
$720$		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	$-0.568395\pi$
$743$	−8636.53			−0.426438			−0.213219	+	0.977004i	$0.568395\pi$
$744$		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	$0.354029\pi$
$761$	−9289.71	+	28590.8i	−0.442512	+	1.36191i	−0.885189	+	0.465231i	$0.845971\pi$
$762$		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	−0.921907	−	0.387412i	$-0.873369\pi$
$773$	1109.96	−	3416.11i	0.0516463	−	0.158951i	0.973553	+	0.228461i	$0.0733692\pi$
$774$		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	0.609673	−	0.792653i	$-0.291301\pi$
$797$	994.815	+	722.775i	0.0442135	+	0.0321230i	−0.565459	+	0.824776i	$0.691301\pi$
$798$		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	$0.200823\pi$
$809$	11526.7	+	35475.6i	0.500938	+	1.54173i	−0.306557	+	0.951852i	$0.599177\pi$
$810$		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	0.0886674	−	0.996061i	$-0.471739\pi$
$821$	−19554.3	−	14207.1i	−0.831243	−	0.603934i	−0.919911	+	0.392128i	$0.871739\pi$
$822$		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	−0.843756	−	0.536727i	$-0.819660\pi$
$827$	3670.53	−	11296.7i	0.154337	−	0.475001i	0.998093	+	0.0617260i	$0.0196605\pi$
$828$		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	$0.247166\pi$
$839$	−6699.29	+	20618.3i	−0.275668	+	0.848418i	−0.989042	+	0.147635i	$0.952834\pi$
$840$		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	$-0.740846\pi$
$857$	−34445.3			−1.37296			−0.686482	+	0.727147i	$0.740846\pi$
$858$		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	$-0.870167\pi$
$863$	−10355.6	−	31871.3i	−0.408470	−	1.25714i	0.509494	−	0.860474i	$-0.329833\pi$
$864$		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	$-0.353281\pi$
$881$	37499.2	−	27244.8i	1.43403	−	1.04188i	0.989248	−	0.146246i	$-0.0467192\pi$
$882$		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	0.982754	−	0.184919i	$-0.0592023\pi$
$887$	2086.86	+	6422.69i	0.0789965	+	0.243126i	−0.903757	+	0.428045i	$0.859202\pi$
$888$		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	−0.992386	−	0.123166i	$-0.960695\pi$
$911$	−3220.77	+	9912.52i	−0.117134	+	0.360501i	0.875252	+	0.483667i	$0.160695\pi$
$912$		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	$-0.982432\pi$
$929$	−38494.5	−	27967.9i	−1.35949	−	0.987726i	−0.361010	−	0.932562i	$-0.617568\pi$
$930$		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	$-0.974676\pi$
$941$	−6843.90	−	21063.4i	−0.237093	−	0.729698i	0.759744	−	0.650223i	$-0.225324\pi$
$942$		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	0.887548	−	0.460716i	$-0.152407\pi$
$947$	21088.8	+	15321.9i	0.723648	+	0.525761i	−0.163900	+	0.986477i	$0.552407\pi$
$948$		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	0.946682	−	0.322168i	$-0.104412\pi$
$953$	27443.4	+	19938.8i	0.932823	+	0.677736i	−0.0138594	+	0.999904i	$0.504412\pi$
$954$		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	$0.0316635\pi$
$971$	42269.2	+	30710.4i	1.39700	+	1.01498i	0.401939	+	0.915667i	$0.368336\pi$
$972$		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	$0.324483\pi$
$977$	−12234.1	+	37652.6i	−0.400617	+	1.23297i	−0.924500	+	0.381183i	$0.875517\pi$
$978$		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	−0.194454	−	0.980912i	$-0.562293\pi$
$983$	20906.9	−	15189.8i	0.678359	−	0.492857i	0.872813	+	0.488055i	$0.162293\pi$
$984$		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.46.14	yes	64
3.2	odd	2	inner	225.4.h.d.46.3	✓	64
25.6	even	5	inner	225.4.h.d.181.14	yes	64
75.56	odd	10	inner	225.4.h.d.181.3	yes	64

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