LMFDB - Embedded newform 144.4.k.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.4
Root			$1.97476 - 0.316760i$ of defining polynomial
Character	$\chi$	$=$	144.37
Dual form			144.4.k.a.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.29152 - 1.65800i) q^{2} +(2.50210 - 7.59865i) q^{4} +(-8.67959 - 8.67959i) q^{5} +1.63924i q^{7} +(-6.86495 - 21.5609i) q^{8} +O(q^{10})$	\(q+(2.29152 - 1.65800i) q^{2} +(2.50210 - 7.59865i) q^{4} +(-8.67959 - 8.67959i) q^{5} +1.63924i q^{7} +(-6.86495 - 21.5609i) q^{8} +(-34.2802 - 5.49869i) q^{10} +(-18.2021 - 18.2021i) q^{11} +(-9.34700 + 9.34700i) q^{13} +(2.71786 + 3.75636i) q^{14} +(-51.4790 - 38.0251i) q^{16} -53.6113 q^{17} +(70.9870 - 70.9870i) q^{19} +(-87.6704 + 44.2360i) q^{20} +(-71.8893 - 11.5314i) q^{22} +25.1189i q^{23} +25.6706i q^{25} +(-5.92151 + 36.9161i) q^{26} +(12.4560 + 4.10155i) q^{28} +(181.094 - 181.094i) q^{29} +132.684 q^{31} +(-181.011 - 1.78308i) q^{32} +(-122.851 + 88.8874i) q^{34} +(14.2280 - 14.2280i) q^{35} +(174.872 + 174.872i) q^{37} +(44.9717 - 280.364i) q^{38} +(-127.555 + 246.725i) q^{40} +198.660i q^{41} +(-285.717 - 285.717i) q^{43} +(-183.854 + 92.7678i) q^{44} +(41.6471 + 57.5605i) q^{46} -78.3629 q^{47} +340.313 q^{49} +(42.5617 + 58.8245i) q^{50} +(47.6375 + 94.4117i) q^{52} +(525.776 + 525.776i) q^{53} +315.973i q^{55} +(35.3436 - 11.2533i) q^{56} +(114.727 - 715.232i) q^{58} +(-46.5301 - 46.5301i) q^{59} +(193.318 - 193.318i) q^{61} +(304.047 - 219.990i) q^{62} +(-417.745 + 296.029i) q^{64} +162.256 q^{65} +(282.182 - 282.182i) q^{67} +(-134.141 + 407.374i) q^{68} +(9.01370 - 56.1935i) q^{70} -727.536i q^{71} -106.065i q^{73} +(690.659 + 110.785i) q^{74} +(-361.789 - 717.022i) q^{76} +(29.8376 - 29.8376i) q^{77} -58.9970 q^{79} +(116.775 + 776.859i) q^{80} +(329.378 + 455.233i) q^{82} +(410.156 - 410.156i) q^{83} +(465.324 + 465.324i) q^{85} +(-1128.44 - 181.007i) q^{86} +(-267.497 + 517.409i) q^{88} +768.959i q^{89} +(-15.3220 - 15.3220i) q^{91} +(190.870 + 62.8500i) q^{92} +(-179.570 + 129.925i) q^{94} -1232.28 q^{95} -809.953 q^{97} +(779.833 - 564.238i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	$ 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	2.29152	−	1.65800i	0.810173	−	0.586190i
$2$	2.29152	−	1.65800i	0.810173	−	0.586190i
$3$		0			0
$3$		0			0
$4$	2.50210	−	7.59865i	0.312762	−	0.949832i
$5$	−8.67959	−	8.67959i	−0.776326	−	0.776326i	0.202878	−	0.979204i	$-0.434971\pi$
$5$	−8.67959	−	8.67959i	−0.776326	−	0.776326i	−0.979204	+	0.202878i	$0.934971\pi$
$6$		0			0
$7$			1.63924i			0.0885109i	0.999020	+	0.0442554i	$0.0140915\pi$
$7$			1.63924i			0.0885109i	−0.999020	+	0.0442554i	$0.985908\pi$
$8$	−6.86495	−	21.5609i	−0.303391	−	0.952866i
$9$		0			0
$10$	−34.2802	−	5.49869i	−1.08403	−	0.173884i
$11$	−18.2021	−	18.2021i	−0.498921	−	0.498921i	0.412181	−	0.911102i	$-0.364767\pi$
$11$	−18.2021	−	18.2021i	−0.498921	−	0.498921i	−0.911102	+	0.412181i	$0.864767\pi$
$12$		0			0
$13$	−9.34700	+	9.34700i	−0.199415	+	0.199415i	−0.799749	−	0.600334i	$-0.795034\pi$
$13$	−9.34700	+	9.34700i	−0.199415	+	0.199415i	0.600334	+	0.799749i	$0.295034\pi$
$14$	2.71786	+	3.75636i	0.0518842	+	0.0717092i
$15$		0			0
$16$	−51.4790	−	38.0251i	−0.804360	−	0.594142i
$17$	−53.6113			−0.764862			−0.382431	−	0.923984i	$-0.624913\pi$
$17$	−53.6113			−0.764862			−0.382431	+	0.923984i	$0.624913\pi$
$18$		0			0
$19$	70.9870	−	70.9870i	0.857133	−	0.857133i	−0.133866	−	0.990999i	$-0.542739\pi$
$19$	70.9870	−	70.9870i	0.857133	−	0.857133i	0.990999	+	0.133866i	$0.0427392\pi$
$20$	−87.6704	+	44.2360i	−0.980184	+	0.494574i
$21$		0			0
$22$	−71.8893	−	11.5314i	−0.696675	−	0.111750i
$23$			25.1189i			0.227724i	0.993497	+	0.113862i	$0.0363222\pi$
$23$			25.1189i			0.227724i	−0.993497	+	0.113862i	$0.963678\pi$
$24$		0			0
$25$			25.6706i			0.205365i
$26$	−5.92151	+	36.9161i	−0.0446656	+	0.278456i
$27$		0			0
$28$	12.4560	+	4.10155i	0.0840704	+	0.0276828i
$29$	181.094	−	181.094i	1.15960	−	1.15960i	0.175033	−	0.984563i	$-0.443997\pi$
$29$	181.094	−	181.094i	1.15960	−	1.15960i	0.984563	−	0.175033i	$-0.0560031\pi$
$30$		0			0
$31$	132.684			0.768733			0.384367	−	0.923180i	$-0.374420\pi$
$31$	132.684			0.768733			0.384367	+	0.923180i	$0.374420\pi$
$32$	−181.011	−	1.78308i	−0.999951	−	0.00985023i
$33$		0			0
$34$	−122.851	+	88.8874i	−0.619671	+	0.448355i
$35$	14.2280	−	14.2280i	0.0687133	−	0.0687133i
$36$		0			0
$37$	174.872	+	174.872i	0.776994	+	0.776994i	0.979319	−	0.202324i	$-0.0648495\pi$
$37$	174.872	+	174.872i	0.776994	+	0.776994i	−0.202324	+	0.979319i	$0.564849\pi$
$38$	44.9717	−	280.364i	0.191983	−	1.19687i
$39$		0			0
$40$	−127.555	+	246.725i	−0.504205	+	0.975265i
$41$			198.660i			0.756720i	0.925658	+	0.378360i	$0.123512\pi$
$41$			198.660i			0.756720i	−0.925658	+	0.378360i	$0.876488\pi$
$42$		0			0
$43$	−285.717	−	285.717i	−1.01329	−	1.01329i	−0.999911	−	0.0133770i	$-0.995742\pi$
$43$	−285.717	−	285.717i	−1.01329	−	1.01329i	−0.0133770	−	0.999911i	$-0.504258\pi$
$44$	−183.854	+	92.7678i	−0.629934	+	0.317847i
$45$		0			0
$46$	41.6471	+	57.5605i	0.133490	+	0.184496i
$47$	−78.3629			−0.243200			−0.121600	−	0.992579i	$-0.538803\pi$
$47$	−78.3629			−0.243200			−0.121600	+	0.992579i	$0.538803\pi$
$48$		0			0
$49$	340.313			0.992166
$50$	42.5617	+	58.8245i	0.120383	+	0.166381i
$51$		0			0
$52$	47.6375	+	94.4117i	0.127041	+	0.251780i
$53$	525.776	+	525.776i	1.36266	+	1.36266i	0.870515	+	0.492143i	$0.163786\pi$
$53$	525.776	+	525.776i	1.36266	+	1.36266i	0.492143	+	0.870515i	$0.336214\pi$
$54$		0			0
$55$			315.973i			0.774650i
$56$	35.3436	−	11.2533i	0.0843390	−	0.0268534i
$57$		0			0
$58$	114.727	−	715.232i	0.259730	−	1.61922i
$59$	−46.5301	−	46.5301i	−0.102673	−	0.102673i	0.653904	−	0.756577i	$-0.273130\pi$
$59$	−46.5301	−	46.5301i	−0.102673	−	0.102673i	−0.756577	+	0.653904i	$0.773130\pi$
$60$		0			0
$61$	193.318	−	193.318i	0.405767	−	0.405767i	−0.474493	−	0.880259i	$-0.657368\pi$
$61$	193.318	−	193.318i	0.405767	−	0.405767i	0.880259	+	0.474493i	$0.157368\pi$
$62$	304.047	−	219.990i	0.622807	−	0.450624i
$63$		0			0
$64$	−417.745	+	296.029i	−0.815908	+	0.578181i
$65$	162.256			0.309622
$66$		0			0
$67$	282.182	−	282.182i	0.514538	−	0.514538i	−0.401375	−	0.915914i	$-0.631468\pi$
$67$	282.182	−	282.182i	0.514538	−	0.514538i	0.915914	+	0.401375i	$0.131468\pi$
$68$	−134.141	+	407.374i	−0.239220	+	0.726490i
$69$		0			0
$70$	9.01370	−	56.1935i	0.0153906	−	0.0959488i
$71$		−	727.536i		−	1.21609i	−0.793901	−	0.608046i	$-0.791953\pi$
$71$		−	727.536i		−	1.21609i	0.793901	−	0.608046i	$-0.208047\pi$
$72$		0			0
$73$		−	106.065i		−	0.170054i	−0.996379	−	0.0850270i	$-0.972902\pi$
$73$		−	106.065i		−	0.170054i	0.996379	−	0.0850270i	$-0.0270977\pi$
$74$	690.659	+	110.785i	1.08497	+	0.174034i
$75$		0			0
$76$	−361.789	−	717.022i	−0.546054	−	1.08221i
$77$	29.8376	−	29.8376i	0.0441599	−	0.0441599i
$78$		0			0
$79$	−58.9970			−0.0840213			−0.0420107	−	0.999117i	$-0.513376\pi$
$79$	−58.9970			−0.0840213			−0.0420107	+	0.999117i	$0.513376\pi$
$80$	116.775	+	776.859i	0.163198	+	1.08569i
$81$		0			0
$82$	329.378	+	455.233i	0.443582	+	0.613075i
$83$	410.156	−	410.156i	0.542416	−	0.542416i	−0.381821	−	0.924236i	$-0.624703\pi$
$83$	410.156	−	410.156i	0.542416	−	0.542416i	0.924236	+	0.381821i	$0.124703\pi$
$84$		0			0
$85$	465.324	+	465.324i	0.593783	+	0.593783i
$86$	−1128.44	−	181.007i	−1.41492	−	0.226959i
$87$		0			0
$88$	−267.497	+	517.409i	−0.324037	+	0.626772i
$89$			768.959i			0.915837i	0.888994	+	0.457918i	$0.151405\pi$
$89$			768.959i			0.915837i	−0.888994	+	0.457918i	$0.848595\pi$
$90$		0			0
$91$	−15.3220	−	15.3220i	−0.0176504	−	0.0176504i
$92$	190.870	+	62.8500i	0.216300	+	0.0712235i
$93$		0			0
$94$	−179.570	+	129.925i	−0.197034	+	0.142562i
$95$	−1232.28			−1.33083
$96$		0			0
$97$	−809.953			−0.847817			−0.423908	−	0.905705i	$-0.639342\pi$
$97$	−809.953			−0.847817			−0.423908	+	0.905705i	$0.639342\pi$
$98$	779.833	−	564.238i	0.803826	−	0.581598i
$99$		0			0
$100$	195.062	+	64.2302i	0.195062	+	0.0642302i
$101$	303.189	+	303.189i	0.298698	+	0.298698i	0.840504	−	0.541806i	$-0.182259\pi$
$101$	303.189	+	303.189i	0.298698	+	0.298698i	−0.541806	+	0.840504i	$0.682259\pi$
$102$		0			0
$103$			962.201i			0.920471i	0.887797	+	0.460235i	$0.152235\pi$
$103$			962.201i			0.920471i	−0.887797	+	0.460235i	$0.847765\pi$
$104$	265.697	+	137.363i	0.250516	+	0.129515i
$105$		0			0
$106$	2076.56	+	333.089i	1.90277	+	0.305212i
$107$	−728.337	−	728.337i	−0.658046	−	0.658046i	0.296871	−	0.954918i	$-0.404057\pi$
$107$	−728.337	−	728.337i	−0.658046	−	0.658046i	−0.954918	+	0.296871i	$0.904057\pi$
$108$		0			0
$109$	−593.258	+	593.258i	−0.521319	+	0.521319i	−0.917970	−	0.396651i	$-0.870172\pi$
$109$	−593.258	+	593.258i	−0.521319	+	0.521319i	0.396651	+	0.917970i	$0.370172\pi$
$110$	523.882	+	724.057i	0.454092	+	0.627601i
$111$		0			0
$112$	62.3324	−	84.3867i	0.0525880	−	0.0711946i
$113$	−351.938			−0.292987			−0.146493	−	0.989212i	$-0.546799\pi$
$113$	−351.938			−0.292987			−0.146493	+	0.989212i	$0.546799\pi$
$114$		0			0
$115$	218.022	−	218.022i	0.176788	−	0.176788i
$116$	−922.955	−	1829.18i	−0.738743	−	1.46410i
$117$		0			0
$118$	−183.771	−	29.4778i	−0.143369	−	0.0229970i
$119$		−	87.8821i		−	0.0676986i
$120$		0			0
$121$		−	668.370i		−	0.502157i
$122$	122.471	−	763.510i	0.0908849	−	0.566598i
$123$		0			0
$124$	331.988	−	1008.22i	0.240431	−	0.730167i
$125$	−862.139	+	862.139i	−0.616896	+	0.616896i
$126$		0			0
$127$	−2365.81			−1.65301			−0.826504	−	0.562931i	$-0.809674\pi$
$127$	−2365.81			−1.65301			−0.826504	+	0.562931i	$0.809674\pi$
$128$	−466.455	+	1370.97i	−0.322103	+	0.946705i
$129$		0			0
$130$	371.813	−	269.020i	0.250847	−	0.181497i
$131$	−403.454	+	403.454i	−0.269083	+	0.269083i	−0.828731	−	0.559647i	$-0.810937\pi$
$131$	−403.454	+	403.454i	−0.269083	+	0.269083i	0.559647	+	0.828731i	$0.310937\pi$
$132$		0			0
$133$	116.365	+	116.365i	0.0758656	+	0.0758656i
$134$	178.768	−	1114.48i	0.115248	−	0.718483i
$135$		0			0
$136$	368.039	+	1155.91i	0.232052	+	0.728811i
$137$		−	856.850i		−	0.534348i	−0.963648	−	0.267174i	$-0.913910\pi$
$137$		−	856.850i		−	0.534348i	0.963648	−	0.267174i	$-0.0860898\pi$
$138$		0			0
$139$	−1689.33	−	1689.33i	−1.03084	−	1.03084i	−0.999509	−	0.0313345i	$-0.990024\pi$
$139$	−1689.33	−	1689.33i	−1.03084	−	1.03084i	−0.0313345	−	0.999509i	$-0.509976\pi$
$140$	−72.5137	−	143.713i	−0.0437752	−	0.0867570i
$141$		0			0
$142$	−1206.25	−	1667.16i	−0.712862	−	0.985246i
$143$	340.269			0.198984
$144$		0			0
$145$	−3143.64			−1.80045
$146$	−175.855	−	243.049i	−0.0996840	−	0.137773i
$147$		0			0
$148$	1766.34	−	891.246i	0.981028	−	0.495000i
$149$	32.2208	+	32.2208i	0.0177156	+	0.0177156i	0.715909	−	0.698193i	$-0.246012\pi$
$149$	32.2208	+	32.2208i	0.0177156	+	0.0177156i	−0.698193	+	0.715909i	$0.746012\pi$
$150$		0			0
$151$		−	1077.06i		−	0.580460i	−0.956957	−	0.290230i	$-0.906268\pi$
$151$		−	1077.06i		−	0.580460i	0.956957	−	0.290230i	$-0.0937319\pi$
$152$	−2017.87	−	1043.22i	−1.07678	−	0.556687i
$153$		0			0
$154$	18.9027	−	117.844i	0.00989107	−	0.0616633i
$155$	−1151.64	−	1151.64i	−0.596788	−	0.596788i
$156$		0			0
$157$	1905.61	−	1905.61i	0.968691	−	0.968691i	−0.0308332	−	0.999525i	$-0.509816\pi$
$157$	1905.61	−	1905.61i	0.968691	−	0.968691i	0.999525	+	0.0308332i	$0.00981607\pi$
$158$	−135.193	+	97.8169i	−0.0680718	+	0.0492525i
$159$		0			0
$160$	1555.62	+	1586.57i	0.768641	+	0.783935i
$161$	−41.1761			−0.0201561
$162$		0			0
$163$	709.828	−	709.828i	0.341092	−	0.341092i	−0.515686	−	0.856778i	$-0.672463\pi$
$163$	709.828	−	709.828i	0.341092	−	0.341092i	0.856778	+	0.515686i	$0.172463\pi$
$164$	1509.55	+	497.067i	0.718757	+	0.236673i
$165$		0			0
$166$	259.842	−	1619.92i	0.121492	−	0.757410i
$167$			3460.66i			1.60356i	0.597623	+	0.801778i	$0.296112\pi$
$167$			3460.66i			1.60356i	−0.597623	+	0.801778i	$0.703888\pi$
$168$		0			0
$169$			2022.27i			0.920467i
$170$	1837.80	+	294.792i	0.829136	+	0.132997i
$171$		0			0
$172$	−2885.95	+	1456.17i	−1.27937	+	0.645535i
$173$	1303.54	−	1303.54i	0.572871	−	0.572871i	−0.360059	−	0.932930i	$-0.617243\pi$
$173$	1303.54	−	1303.54i	0.572871	−	0.572871i	0.932930	+	0.360059i	$0.117243\pi$
$174$		0			0
$175$	−42.0803			−0.0181770
$176$	244.889	+	1629.16i	0.104882	+	0.697742i
$177$		0			0
$178$	1274.93	+	1762.08i	0.536855	+	0.741987i
$179$	1082.35	−	1082.35i	0.451947	−	0.451947i	−0.444054	−	0.896000i	$-0.646460\pi$
$179$	1082.35	−	1082.35i	0.451947	−	0.451947i	0.896000	+	0.444054i	$0.146460\pi$
$180$		0			0
$181$	2943.93	+	2943.93i	1.20895	+	1.20895i	0.971366	+	0.237588i	$0.0763567\pi$
$181$	2943.93	+	2943.93i	1.20895	+	1.20895i	0.237588	+	0.971366i	$0.423643\pi$
$182$	−60.5145	−	9.70681i	−0.0246463	−	0.00395339i
$183$		0			0
$184$	541.587	−	172.440i	0.216991	−	0.0690895i
$185$		−	3035.64i		−	1.20640i
$186$		0			0
$187$	975.837	+	975.837i	0.381606	+	0.381606i
$188$	−196.072	+	595.453i	−0.0760637	+	0.230999i
$189$		0			0
$190$	−2823.78	+	2043.11i	−1.07820	+	0.780120i
$191$	430.650			0.163145			0.0815726	−	0.996667i	$-0.474006\pi$
$191$	430.650			0.163145			0.0815726	+	0.996667i	$0.474006\pi$
$192$		0			0
$193$	−2266.98			−0.845497			−0.422749	−	0.906247i	$-0.638935\pi$
$193$	−2266.98			−0.845497			−0.422749	+	0.906247i	$0.638935\pi$
$194$	−1856.02	+	1342.90i	−0.686879	+	0.496982i
$195$		0			0
$196$	851.495	−	2585.92i	0.310312	−	0.942390i
$197$	1039.41	+	1039.41i	0.375913	+	0.375913i	0.869625	−	0.493712i	$-0.164360\pi$
$197$	1039.41	+	1039.41i	0.375913	+	0.375913i	−0.493712	+	0.869625i	$0.664360\pi$
$198$		0			0
$199$			4989.44i			1.77735i	0.458540	+	0.888674i	$0.348373\pi$
$199$			4989.44i			1.77735i	−0.458540	+	0.888674i	$0.651627\pi$
$200$	553.481	−	176.227i	0.195685	−	0.0623057i
$201$		0			0
$202$	1197.45	+	192.077i	0.417091	+	0.0669033i
$203$	296.857	+	296.857i	0.102637	+	0.102637i
$204$		0			0
$205$	1724.29	−	1724.29i	0.587462	−	0.587462i
$206$	1595.33	+	2204.90i	0.539571	+	0.745741i
$207$		0			0
$208$	836.596	−	125.754i	0.278882	−	0.0419205i
$209$	−2584.22			−0.855283
$210$		0			0
$211$	2651.50	−	2651.50i	0.865103	−	0.865103i	−0.126823	−	0.991925i	$-0.540478\pi$
$211$	2651.50	−	2651.50i	0.865103	−	0.865103i	0.991925	+	0.126823i	$0.0404779\pi$
$212$	5310.73	−	2679.65i	1.72048	−	0.868108i
$213$		0			0
$214$	−2876.58	−	461.416i	−0.918872	−	0.147391i
$215$			4959.80i			1.57328i
$216$		0			0
$217$			217.501i			0.0680413i
$218$	−375.841	+	2343.08i	−0.116767	+	0.727951i
$219$		0			0
$220$	2400.97	+	790.594i	0.735787	+	0.242281i
$221$	501.105	−	501.105i	0.152525	−	0.152525i
$222$		0			0
$223$	3690.85			1.10833			0.554165	−	0.832407i	$-0.313038\pi$
$223$	3690.85			1.10833			0.554165	+	0.832407i	$0.313038\pi$
$224$	2.92291	−	296.721i	0.000871853	−	0.0885066i
$225$		0			0
$226$	−806.471	+	583.512i	−0.237370	+	0.171746i
$227$	1710.42	−	1710.42i	0.500108	−	0.500108i	−0.411363	−	0.911471i	$-0.634947\pi$
$227$	1710.42	−	1710.42i	0.500108	−	0.500108i	0.911471	+	0.411363i	$0.134947\pi$
$228$		0			0
$229$	−91.8012	−	91.8012i	−0.0264908	−	0.0264908i	0.693737	−	0.720228i	$-0.255963\pi$
$229$	−91.8012	−	91.8012i	−0.0264908	−	0.0264908i	−0.720228	+	0.693737i	$0.755963\pi$
$230$	138.121	−	861.081i	0.0395976	−	0.246861i
$231$		0			0
$232$	−5147.74	−	2661.35i	−1.45675	−	0.753129i
$233$			4259.71i			1.19769i	0.800863	+	0.598847i	$0.204374\pi$
$233$			4259.71i			1.19769i	−0.800863	+	0.598847i	$0.795626\pi$
$234$		0			0
$235$	680.158	+	680.158i	0.188803	+	0.188803i
$236$	−469.989	+	237.144i	−0.129634	+	0.0654099i
$237$		0			0
$238$	−145.708	−	201.383i	−0.0396843	−	0.0548476i
$239$	5053.12			1.36761			0.683806	−	0.729664i	$-0.260324\pi$
$239$	5053.12			1.36761			0.683806	+	0.729664i	$0.260324\pi$
$240$		0			0
$241$	48.8379			0.0130536			0.00652681	−	0.999979i	$-0.497922\pi$
$241$	48.8379			0.0130536			0.00652681	+	0.999979i	$0.497922\pi$
$242$	−1108.16	−	1531.58i	−0.294359	−	0.406834i
$243$		0			0
$244$	−985.254	−	1952.65i	−0.258502	−	0.512319i
$245$	−2953.78	−	2953.78i	−0.770244	−	0.770244i
$246$		0			0
$247$			1327.03i			0.341850i
$248$	−910.868	−	2860.79i	−0.233227	−	0.732500i
$249$		0			0
$250$	−546.182	+	3405.03i	−0.138174	+	0.861412i
$251$	2604.76	+	2604.76i	0.655025	+	0.655025i	0.954199	−	0.299174i	$-0.0967111\pi$
$251$	2604.76	+	2604.76i	0.655025	+	0.655025i	−0.299174	+	0.954199i	$0.596711\pi$
$252$		0			0
$253$	457.216	−	457.216i	0.113616	−	0.113616i
$254$	−5421.30	+	3922.51i	−1.33922	+	0.968977i
$255$		0			0
$256$	1204.18	+	3914.99i	0.293990	+	0.955808i
$257$	−739.054			−0.179381			−0.0896905	−	0.995970i	$-0.528588\pi$
$257$	−739.054			−0.179381			−0.0896905	+	0.995970i	$0.528588\pi$
$258$		0			0
$259$	−286.658	+	286.658i	−0.0687724	+	0.0687724i
$260$	405.981	−	1232.93i	0.0968379	−	0.294089i
$261$		0			0
$262$	−255.596	+	1593.45i	−0.0602701	+	0.375738i
$263$		−	2448.30i		−	0.574025i	−0.957927	−	0.287012i	$-0.907338\pi$
$263$		−	2448.30i		−	0.574025i	0.957927	−	0.287012i	$-0.0926621\pi$
$264$		0			0
$265$		−	9127.03i		−	2.11573i
$266$	459.585	+	73.7196i	0.105936	+	0.0169926i
$267$		0			0
$268$	−1438.16	−	2850.25i	−0.327797	−	0.649653i
$269$	829.952	−	829.952i	0.188116	−	0.188116i	−0.606765	−	0.794881i	$-0.707533\pi$
$269$	829.952	−	829.952i	0.188116	−	0.188116i	0.794881	+	0.606765i	$0.207533\pi$
$270$		0			0
$271$	1404.85			0.314902			0.157451	−	0.987527i	$-0.449672\pi$
$271$	1404.85			0.314902			0.157451	+	0.987527i	$0.449672\pi$
$272$	2759.86	+	2038.58i	0.615225	+	0.454437i
$273$		0			0
$274$	−1420.65	−	1963.49i	−0.313229	−	0.432914i
$275$	467.257	−	467.257i	0.102461	−	0.102461i
$276$		0			0
$277$	−2245.69	−	2245.69i	−0.487112	−	0.487112i	0.420281	−	0.907394i	$-0.361931\pi$
$277$	−2245.69	−	2245.69i	−0.487112	−	0.487112i	−0.907394	+	0.420281i	$0.861931\pi$
$278$	−6672.04	−	1070.23i	−1.43943	−	0.230892i
$279$		0			0
$280$	−404.442	−	209.094i	−0.0863216	−	0.0446276i
$281$		−	6045.97i		−	1.28353i	−0.766900	−	0.641766i	$-0.778202\pi$
$281$		−	6045.97i		−	1.28353i	0.766900	−	0.641766i	$-0.221798\pi$
$282$		0			0
$283$	2459.63	+	2459.63i	0.516643	+	0.516643i	0.916554	−	0.399911i	$-0.130959\pi$
$283$	2459.63	+	2459.63i	0.516643	+	0.516643i	−0.399911	+	0.916554i	$0.630959\pi$
$284$	−5528.29	−	1820.36i	−1.15508	−	0.380347i
$285$		0			0
$286$	779.733	−	564.165i	0.161212	−	0.116643i
$287$	−325.653			−0.0669780
$288$		0			0
$289$	−2038.82			−0.414986
$290$	−7203.70	+	5212.14i	−1.45868	+	1.05541i
$291$		0			0
$292$	−805.950	−	265.384i	−0.161523	−	0.0531864i
$293$	1852.49	+	1852.49i	0.369364	+	0.369364i	0.867245	−	0.497881i	$-0.165888\pi$
$293$	1852.49	+	1852.49i	0.369364	+	0.369364i	−0.497881	+	0.867245i	$0.665888\pi$
$294$		0			0
$295$			807.725i			0.159415i
$296$	2569.91	−	4970.89i	0.504639	−	0.976105i
$297$		0			0
$298$	127.256	+	20.4125i	0.0247375	+	0.00396801i
$299$	−234.787	−	234.787i	−0.0454116	−	0.0454116i
$300$		0			0
$301$	468.359	−	468.359i	0.0896870	−	0.0896870i
$302$	−1785.75	−	2468.09i	−0.340260	−	0.470274i
$303$		0			0
$304$	−6353.63	+	955.055i	−1.19870	+	0.180185i
$305$	−3355.83			−0.630015
$306$		0			0
$307$	2107.35	−	2107.35i	0.391768	−	0.391768i	−0.483549	−	0.875317i	$-0.660653\pi$
$307$	2107.35	−	2107.35i	0.391768	−	0.391768i	0.875317	+	0.483549i	$0.160653\pi$
$308$	−152.069	−	301.382i	−0.0281329	−	0.0557560i
$309$		0			0
$310$	−4548.43	−	729.588i	−0.833333	−	0.133670i
$311$		−	5294.90i		−	0.965422i	−0.875780	−	0.482711i	$-0.839652\pi$
$311$		−	5294.90i		−	0.965422i	0.875780	−	0.482711i	$-0.160348\pi$
$312$		0			0
$313$			4005.87i			0.723403i	0.932294	+	0.361702i	$0.117804\pi$
$313$			4005.87i			0.723403i	−0.932294	+	0.361702i	$0.882196\pi$
$314$	1207.24	−	7526.25i	0.216971	−	1.35265i
$315$		0			0
$316$	−147.616	+	448.298i	−0.0262787	+	0.0798061i
$317$	−809.240	+	809.240i	−0.143380	+	0.143380i	−0.775153	−	0.631773i	$-0.782327\pi$
$317$	−809.240	+	809.240i	−0.143380	+	0.143380i	0.631773	+	0.775153i	$0.282327\pi$
$318$		0			0
$319$	−6592.56			−1.15709
$320$	6195.27	+	1056.45i	1.08227	+	0.184554i
$321$		0			0
$322$	−94.3557	+	68.2698i	−0.0163299	+	0.0118153i
$323$	−3805.71	+	3805.71i	−0.655589	+	0.655589i
$324$		0			0
$325$	−239.943	−	239.943i	−0.0409527	−	0.0409527i
$326$	449.690	−	2803.47i	0.0763989	−	0.476289i
$327$		0			0
$328$	4283.30	−	1363.79i	0.721053	−	0.229582i
$329$		−	128.456i		−	0.0215259i
$330$		0			0
$331$	−4229.66	−	4229.66i	−0.702366	−	0.702366i	0.262552	−	0.964918i	$-0.415436\pi$
$331$	−4229.66	−	4229.66i	−0.702366	−	0.702366i	−0.964918	+	0.262552i	$0.915436\pi$
$332$	−2090.39	−	4142.89i	−0.345557	−	0.684851i
$333$		0			0
$334$	5737.76	+	7930.15i	0.939988	+	1.29916i
$335$	−4898.46			−0.798899
$336$		0			0
$337$	10002.6			1.61684			0.808419	−	0.588607i	$-0.200323\pi$
$337$	10002.6			1.61684			0.808419	+	0.588607i	$0.200323\pi$
$338$	3352.91	+	4634.06i	0.539569	+	0.745738i
$339$		0			0
$340$	4700.12	−	2371.55i	0.749706	−	0.378281i
$341$	−2415.12	−	2415.12i	−0.383537	−	0.383537i
$342$		0			0
$343$			1120.12i			0.176328i
$344$	−4198.88	+	8121.74i	−0.658106	+	1.27295i
$345$		0			0
$346$	825.821	−	5148.37i	0.128313	−	0.799936i
$347$	6409.49	+	6409.49i	0.991583	+	0.991583i	0.999965	−	0.00838198i	$-0.00266810\pi$
$347$	6409.49	+	6409.49i	0.991583	+	0.991583i	−0.00838198	+	0.999965i	$0.502668\pi$
$348$		0			0
$349$	−5503.23	+	5503.23i	−0.844071	+	0.844071i	−0.989386	−	0.145314i	$-0.953581\pi$
$349$	−5503.23	+	5503.23i	−0.844071	+	0.844071i	0.145314	+	0.989386i	$0.453581\pi$
$350$	−96.4278	+	69.7691i	−0.0147265	+	0.0106552i
$351$		0			0
$352$	3262.31	+	3327.22i	0.493982	+	0.503811i
$353$	1411.35			0.212800			0.106400	−	0.994323i	$-0.466068\pi$
$353$	1411.35			0.212800			0.106400	+	0.994323i	$0.466068\pi$
$354$		0			0
$355$	−6314.71	+	6314.71i	−0.944085	+	0.944085i
$356$	5843.05	+	1924.01i	0.869891	+	0.286439i
$357$		0			0
$358$	685.689	−	4274.75i	0.101228	−	0.631082i
$359$			2160.73i			0.317658i	0.987306	+	0.158829i	$0.0507718\pi$
$359$			2160.73i			0.317658i	−0.987306	+	0.158829i	$0.949228\pi$
$360$		0			0
$361$		−	3219.31i		−	0.469355i
$362$	11627.1	+	1865.04i	1.68814	+	0.270785i
$363$		0			0
$364$	−154.764	+	78.0896i	−0.0222853	+	0.0112445i
$365$	−920.599	+	920.599i	−0.132017	+	0.132017i
$366$		0			0
$367$	10757.7			1.53010			0.765052	−	0.643969i	$-0.222713\pi$
$367$	10757.7			1.53010			0.765052	+	0.643969i	$0.222713\pi$
$368$	955.150	−	1293.10i	0.135301	−	0.183172i
$369$		0			0
$370$	−5033.07	−	6956.21i	−0.707181	−	0.977395i
$371$	−861.875	+	861.875i	−0.120610	+	0.120610i
$372$		0			0
$373$	1406.99	+	1406.99i	0.195312	+	0.195312i	0.797987	−	0.602675i	$-0.205898\pi$
$373$	1406.99	+	1406.99i	0.195312	+	0.195312i	−0.602675	+	0.797987i	$0.705898\pi$
$374$	3854.08	+	618.212i	0.532860	+	0.0854732i
$375$		0			0
$376$	537.957	+	1689.58i	0.0737847	+	0.231737i
$377$			3385.37i			0.462481i
$378$		0			0
$379$	−1146.95	−	1146.95i	−0.155449	−	0.155449i	0.625098	−	0.780547i	$-0.285059\pi$
$379$	−1146.95	−	1146.95i	−0.155449	−	0.155449i	−0.780547	+	0.625098i	$0.785059\pi$
$380$	−3083.27	+	9363.64i	−0.416233	+	1.26406i
$381$		0			0
$382$	986.842	−	714.016i	0.132176	−	0.0956342i
$383$	−9042.17			−1.20635			−0.603176	−	0.797608i	$-0.706098\pi$
$383$	−9042.17			−1.20635			−0.603176	+	0.797608i	$0.706098\pi$
$384$		0			0
$385$	−517.957			−0.0685650
$386$	−5194.83	+	3758.65i	−0.684999	+	0.495622i
$387$		0			0
$388$	−2026.58	+	6154.55i	−0.265165	+	0.805283i
$389$	−2575.34	−	2575.34i	−0.335668	−	0.335668i	0.519066	−	0.854734i	$-0.326280\pi$
$389$	−2575.34	−	2575.34i	−0.335668	−	0.335668i	−0.854734	+	0.519066i	$0.826280\pi$
$390$		0			0
$391$		−	1346.66i		−	0.174178i
$392$	−2336.23	−	7337.45i	−0.301014	−	0.945401i
$393$		0			0
$394$	4105.16	+	658.486i	0.524911	+	0.0841981i
$395$	512.070	+	512.070i	0.0652279	+	0.0652279i
$396$		0			0
$397$	−7121.46	+	7121.46i	−0.900292	+	0.900292i	−0.995461	−	0.0951695i	$-0.969661\pi$
$397$	−7121.46	+	7121.46i	−0.900292	+	0.900292i	0.0951695	+	0.995461i	$0.469661\pi$
$398$	8272.48	+	11433.4i	1.04186	+	1.43996i
$399$		0			0
$400$	976.126	−	1321.50i	0.122016	−	0.165187i
$401$	3025.14			0.376729			0.188365	−	0.982099i	$-0.439681\pi$
$401$	3025.14			0.376729			0.188365	+	0.982099i	$0.439681\pi$
$402$		0			0
$403$	−1240.20	+	1240.20i	−0.153297	+	0.153297i
$404$	3062.44	−	1545.22i	0.377134	−	0.190291i
$405$		0			0
$406$	1172.44	+	188.065i	0.143318	+	0.0229889i
$407$		−	6366.06i		−	0.775317i
$408$		0			0
$409$			9440.21i			1.14129i	0.821196	+	0.570646i	$0.193307\pi$
$409$			9440.21i			1.14129i	−0.821196	+	0.570646i	$0.806693\pi$
$410$	1092.37	−	6810.11i	0.131581	−	0.820310i
$411$		0			0
$412$	7311.43	+	2407.52i	0.874292	+	0.287888i
$413$	76.2743	−	76.2743i	0.00908768	−	0.00908768i
$414$		0			0
$415$	−7119.98			−0.842183
$416$	1708.57	−	1675.24i	0.201369	−	0.197441i
$417$		0			0
$418$	−5921.78	+	4284.63i	−0.692928	+	0.501359i
$419$	3255.69	−	3255.69i	0.379597	−	0.379597i	−0.491360	−	0.870957i	$-0.663500\pi$
$419$	3255.69	−	3255.69i	0.379597	−	0.379597i	0.870957	+	0.491360i	$0.163500\pi$
$420$		0			0
$421$	−9438.04	−	9438.04i	−1.09259	−	1.09259i	−0.995251	−	0.0973423i	$-0.968966\pi$
$421$	−9438.04	−	9438.04i	−1.09259	−	1.09259i	−0.0973423	−	0.995251i	$-0.531034\pi$
$422$	1679.78	−	10472.1i	0.193768	−	1.20800i
$423$		0			0
$424$	7726.77	−	14945.6i	0.885013	−	1.71185i
$425$		−	1376.23i		−	0.157076i
$426$		0			0
$427$	316.895	+	316.895i	0.0359148	+	0.0359148i
$428$	−7356.75	+	3712.01i	−0.830845	+	0.419221i
$429$		0			0
$430$	8223.34	+	11365.5i	0.922243	+	1.27463i
$431$	10617.7			1.18663			0.593314	−	0.804971i	$-0.297819\pi$
$431$	10617.7			1.18663			0.593314	+	0.804971i	$0.297819\pi$
$432$		0			0
$433$	706.479			0.0784093			0.0392046	−	0.999231i	$-0.487518\pi$
$433$	706.479			0.0784093			0.0392046	+	0.999231i	$0.487518\pi$
$434$	360.617	+	498.408i	0.0398851	+	0.0551252i
$435$		0			0
$436$	3023.57	+	5992.35i	0.332117	+	0.658214i
$437$	1783.12	+	1783.12i	0.195190	+	0.195190i
$438$		0			0
$439$		−	13611.8i		−	1.47985i	−0.672688	−	0.739926i	$-0.734860\pi$
$439$		−	13611.8i		−	1.47985i	0.672688	−	0.739926i	$-0.265140\pi$
$440$	6812.66	−	2169.14i	0.738138	−	0.235022i
$441$		0			0
$442$	317.460	−	1979.12i	0.0341630	−	0.212980i
$443$	−3126.97	−	3126.97i	−0.335366	−	0.335366i	0.519254	−	0.854620i	$-0.326210\pi$
$443$	−3126.97	−	3126.97i	−0.335366	−	0.335366i	−0.854620	+	0.519254i	$0.826210\pi$
$444$		0			0
$445$	6674.25	−	6674.25i	0.710988	−	0.710988i
$446$	8457.64	−	6119.42i	0.897939	−	0.649692i
$447$		0			0
$448$	−485.264	−	684.786i	−0.0511753	−	0.0722167i
$449$	5231.76			0.549893			0.274947	−	0.961460i	$-0.411340\pi$
$449$	5231.76			0.549893			0.274947	+	0.961460i	$0.411340\pi$
$450$		0			0
$451$	3616.03	−	3616.03i	0.377543	−	0.377543i
$452$	−880.582	+	2674.25i	−0.0916352	+	0.278288i
$453$		0			0
$454$	1083.58	−	6755.32i	0.112016	−	0.698333i
$455$			265.978i			0.0274049i
$456$		0			0
$457$			6833.10i			0.699429i	0.936856	+	0.349715i	$0.113721\pi$
$457$			6833.10i			0.699429i	−0.936856	+	0.349715i	$0.886279\pi$
$458$	−362.570	−	58.1579i	−0.0369908	−	0.00593350i
$459$		0			0
$460$	−1111.16	−	2202.19i	−0.112627	−	0.223212i
$461$	5975.90	−	5975.90i	0.603742	−	0.603742i	−0.337561	−	0.941304i	$-0.609602\pi$
$461$	5975.90	−	5975.90i	0.603742	−	0.603742i	0.941304	+	0.337561i	$0.109602\pi$
$462$		0			0
$463$	−4273.38			−0.428943			−0.214472	−	0.976730i	$-0.568803\pi$
$463$	−4273.38			−0.428943			−0.214472	+	0.976730i	$0.568803\pi$
$464$	−16208.6	+	2436.42i	−1.62170	+	0.243768i
$465$		0			0
$466$	7062.59	+	9761.20i	0.702077	+	0.970341i
$467$	−12245.6	+	12245.6i	−1.21340	+	1.21340i	−0.243500	+	0.969901i	$0.578296\pi$
$467$	−12245.6	+	12245.6i	−1.21340	+	1.21340i	−0.969901	+	0.243500i	$0.921704\pi$
$468$		0			0
$469$	462.566	+	462.566i	0.0455422	+	0.0455422i
$470$	2686.29	+	430.894i	0.263637	+	0.0422886i
$471$		0			0
$472$	−683.805	+	1322.66i	−0.0666836	+	0.128984i
$473$			10401.3i			1.01110i
$474$		0			0
$475$	1822.28	+	1822.28i	0.176025	+	0.176025i
$476$	−667.785	−	219.889i	−0.0643023	−	0.0211736i
$477$		0			0
$478$	11579.3	−	8378.05i	1.10800	−	0.801681i
$479$	4067.97			0.388038			0.194019	−	0.980998i	$-0.437848\pi$
$479$	4067.97			0.388038			0.194019	+	0.980998i	$0.437848\pi$
$480$		0			0
$481$	−3269.06			−0.309888
$482$	111.913	−	80.9730i	0.0105757	−	0.00765191i
$483$		0			0
$484$	−5078.71	−	1672.33i	−0.476964	−	0.157055i
$485$	7030.06	+	7030.06i	0.658182	+	0.658182i
$486$		0			0
$487$		−	16174.3i		−	1.50499i	−0.658600	−	0.752493i	$-0.728851\pi$
$487$		−	16174.3i		−	1.50499i	0.658600	−	0.752493i	$-0.271149\pi$
$488$	−5495.22	−	2840.99i	−0.509747	−	0.263536i
$489$		0			0
$490$	−11666.0	−	1871.28i	−1.07554	−	0.172522i
$491$	−13596.7	−	13596.7i	−1.24971	−	1.24971i	−0.955847	−	0.293866i	$-0.905058\pi$
$491$	−13596.7	−	13596.7i	−1.24971	−	1.24971i	−0.293866	−	0.955847i	$-0.594942\pi$
$492$		0			0
$493$	−9708.68	+	9708.68i	−0.886931	+	0.886931i
$494$	2200.21	+	3040.91i	0.200389	+	0.276958i
$495$		0			0
$496$	−6830.44	−	5045.32i	−0.618338	−	0.456737i
$497$	1192.61			0.107637
$498$		0			0
$499$	−14646.7	+	14646.7i	−1.31398	+	1.31398i	−0.395530	+	0.918453i	$0.629439\pi$
$499$	−14646.7	+	14646.7i	−1.31398	+	1.31398i	−0.918453	+	0.395530i	$0.870561\pi$
$500$	4393.94	+	8708.25i	0.393006	+	0.778889i
$501$		0			0
$502$	10287.5	+	1650.17i	0.914652	+	0.146714i
$503$			9828.84i			0.871265i	0.900125	+	0.435632i	$0.143475\pi$
$503$			9828.84i			0.871265i	−0.900125	+	0.435632i	$0.856525\pi$
$504$		0			0
$505$		−	5263.12i		−	0.463774i
$506$	289.656	−	1805.78i	0.0254482	−	0.158650i
$507$		0			0
$508$	−5919.49	+	17977.0i	−0.516998	+	1.57008i
$509$	−13456.1	+	13456.1i	−1.17177	+	1.17177i	−0.189985	+	0.981787i	$0.560844\pi$
$509$	−13456.1	+	13456.1i	−1.17177	+	1.17177i	−0.981787	+	0.189985i	$0.939156\pi$
$510$		0			0
$511$	173.866			0.0150516
$512$	9250.45	+	6974.74i	0.798469	+	0.602037i
$513$		0			0
$514$	−1693.55	+	1225.35i	−0.145330	+	0.105151i
$515$	8351.51	−	8351.51i	0.714585	−	0.714585i
$516$		0			0
$517$	1426.37	+	1426.37i	0.121338	+	0.121338i
$518$	−181.604	+	1132.16i	−0.0154039	+	0.0960313i
$519$		0			0
$520$	−1113.88	−	3498.39i	−0.0939364	−	0.295028i
$521$			10607.1i			0.891950i	0.895045	+	0.445975i	$0.147143\pi$
$521$			10607.1i			0.891950i	−0.895045	+	0.445975i	$0.852857\pi$
$522$		0			0
$523$	3903.15	+	3903.15i	0.326334	+	0.326334i	0.851191	−	0.524857i	$-0.175881\pi$
$523$	3903.15	+	3903.15i	0.326334	+	0.326334i	−0.524857	+	0.851191i	$0.675881\pi$
$524$	2056.22	+	4075.18i	0.171425	+	0.339743i
$525$		0			0
$526$	−4059.27	−	5610.32i	−0.336488	−	0.465060i
$527$	−7113.36			−0.587975
$528$		0			0
$529$	11536.0			0.948142
$530$	−15132.6	−	20914.7i	−1.24022	−	1.71411i
$531$		0			0
$532$	1175.37	−	593.061i	0.0957874	−	0.0483317i
$533$	−1856.88	−	1856.88i	−0.150901	−	0.150901i
$534$		0			0
$535$			12643.3i			1.02172i
$536$	−8021.28	−	4146.94i	−0.646392	−	0.334180i
$537$		0			0
$538$	525.791	−	3277.91i	0.0421347	−	0.262678i
$539$	−6194.39	−	6194.39i	−0.495012	−	0.495012i
$540$		0			0
$541$	9532.77	−	9532.77i	0.757570	−	0.757570i	−0.218309	−	0.975880i	$-0.570054\pi$
$541$	9532.77	−	9532.77i	0.757570	−	0.757570i	0.975880	+	0.218309i	$0.0700541\pi$
$542$	3219.23	−	2329.23i	0.255125	−	0.184592i
$543$		0			0
$544$	9704.22	+	95.5934i	0.764825	+	0.00753407i
$545$	10298.5			0.809427
$546$		0			0
$547$	−1232.88	+	1232.88i	−0.0963693	+	0.0963693i	−0.753648	−	0.657278i	$-0.771708\pi$
$547$	−1232.88	+	1232.88i	−0.0963693	+	0.0963693i	0.657278	+	0.753648i	$0.271708\pi$
$548$	−6510.90	−	2143.92i	−0.507540	−	0.167124i
$549$		0			0
$550$	296.017	−	1845.44i	0.0229494	−	0.143072i
$551$		−	25710.6i		−	1.98786i
$552$		0			0
$553$		−	96.7105i		−	0.00743680i
$554$	−8869.36	−	1422.69i	−0.680186	−	0.109105i
$555$		0			0
$556$	−17063.5	+	8609.78i	−1.30154	+	0.656719i
$557$	2889.57	−	2889.57i	0.219812	−	0.219812i	−0.588607	−	0.808419i	$-0.700324\pi$
$557$	2889.57	−	2889.57i	0.219812	−	0.219812i	0.808419	+	0.588607i	$0.200324\pi$
$558$		0			0
$559$	5341.19			0.404129
$560$	−1273.46	+	191.422i	−0.0960957	+	0.0144448i
$561$		0			0
$562$	−10024.2	−	13854.4i	−0.752394	−	1.03988i
$563$	−70.0753	+	70.0753i	−0.00524569	+	0.00524569i	−0.709725	−	0.704479i	$-0.751181\pi$
$563$	−70.0753	+	70.0753i	−0.00524569	+	0.00524569i	0.704479	+	0.709725i	$0.251181\pi$
$564$		0			0
$565$	3054.68	+	3054.68i	0.227453	+	0.227453i
$566$	9714.35	+	1558.23i	0.721422	+	0.115719i
$567$		0			0
$568$	−15686.3	+	4994.49i	−1.15877	+	0.368951i
$569$		−	8915.23i		−	0.656847i	−0.944531	−	0.328423i	$-0.893483\pi$
$569$		−	8915.23i		−	0.656847i	0.944531	−	0.328423i	$-0.106517\pi$
$570$		0			0
$571$	4946.30	+	4946.30i	0.362515	+	0.362515i	0.864738	−	0.502223i	$-0.167484\pi$
$571$	4946.30	+	4946.30i	0.362515	+	0.362515i	−0.502223	+	0.864738i	$0.667484\pi$
$572$	851.386	−	2585.59i	0.0622347	−	0.189002i
$573$		0			0
$574$	−746.239	+	539.931i	−0.0542638	+	0.0392618i
$575$	−644.818			−0.0467665
$576$		0			0
$577$	17911.5			1.29232			0.646159	−	0.763203i	$-0.276374\pi$
$577$	17911.5			1.29232			0.646159	+	0.763203i	$0.276374\pi$
$578$	−4672.00	+	3380.36i	−0.336210	+	0.243261i
$579$		0			0
$580$	−7865.68	+	23887.4i	−0.563112	+	1.71012i
$581$	672.347	+	672.347i	0.0480097	+	0.0480097i
$582$		0			0
$583$		−	19140.4i		−	1.35972i
$584$	−2286.85	+	728.129i	−0.162039	+	0.0515928i
$585$		0			0
$586$	7316.44	+	1173.59i	0.515767	+	0.0827314i
$587$	−7940.26	−	7940.26i	−0.558312	−	0.558312i	0.370514	−	0.928827i	$-0.379181\pi$
$587$	−7940.26	−	7940.26i	−0.558312	−	0.558312i	−0.928827	+	0.370514i	$0.879181\pi$
$588$		0			0
$589$	9418.83	−	9418.83i	0.658907	−	0.658907i
$590$	1339.21	+	1850.92i	0.0934478	+	0.129154i
$591$		0			0
$592$	−2352.72	−	15651.8i	−0.163338	−	1.08663i
$593$	7006.26			0.485181			0.242591	−	0.970129i	$-0.422003\pi$
$593$	7006.26			0.485181			0.242591	+	0.970129i	$0.422003\pi$
$594$		0			0
$595$	−762.780	+	762.780i	−0.0525562	+	0.0525562i
$596$	325.454	−	164.215i	0.0223677	−	0.0112861i
$597$		0			0
$598$	−927.294	−	148.742i	−0.0634111	−	0.0101714i
$599$		−	8502.74i		−	0.579987i	−0.957029	−	0.289994i	$-0.906347\pi$
$599$		−	8502.74i		−	0.579987i	0.957029	−	0.289994i	$-0.0936532\pi$
$600$		0			0
$601$			11936.2i			0.810127i	0.914289	+	0.405063i	$0.132751\pi$
$601$			11936.2i			0.810127i	−0.914289	+	0.405063i	$0.867249\pi$
$602$	296.715	−	1849.79i	0.0200884	−	0.125236i
$603$		0			0
$604$	−8184.17	−	2694.89i	−0.551340	−	0.181546i
$605$	−5801.18	+	5801.18i	−0.389837	+	0.389837i
$606$		0			0
$607$	−3850.00			−0.257441			−0.128721	−	0.991681i	$-0.541087\pi$
$607$	−3850.00			−0.257441			−0.128721	+	0.991681i	$0.541087\pi$
$608$	−12976.0	+	12722.8i	−0.865535	+	0.848649i
$609$		0			0
$610$	−7689.95	+	5563.96i	−0.510421	+	0.369309i
$611$	732.459	−	732.459i	0.0484977	−	0.0484977i
$612$		0			0
$613$	−6320.36	−	6320.36i	−0.416439	−	0.416439i	0.467536	−	0.883974i	$-0.345142\pi$
$613$	−6320.36	−	6320.36i	−0.416439	−	0.416439i	−0.883974	+	0.467536i	$0.845142\pi$
$614$	1335.05	−	8323.01i	0.0877494	−	0.547051i
$615$		0			0
$616$	−848.160	−	438.492i	−0.0554762	−	0.0286808i
$617$		−	2585.09i		−	0.168674i	−0.996437	−	0.0843370i	$-0.973123\pi$
$617$		−	2585.09i		−	0.168674i	0.996437	−	0.0843370i	$-0.0268772\pi$
$618$		0			0
$619$	7325.02	+	7325.02i	0.475634	+	0.475634i	0.903732	−	0.428098i	$-0.140816\pi$
$619$	7325.02	+	7325.02i	0.475634	+	0.475634i	−0.428098	+	0.903732i	$0.640816\pi$
$620$	−11632.4	+	5869.41i	−0.753501	+	0.380195i
$621$		0			0
$622$	−8778.92	−	12133.3i	−0.565921	−	0.782159i
$623$	−1260.51			−0.0810615
$624$		0			0
$625$	18174.8			1.16319
$626$	6641.72	+	9179.52i	0.424052	+	0.586082i
$627$		0			0
$628$	−9712.07	−	19248.1i	−0.617124	−	1.22306i
$629$	−9375.13	−	9375.13i	−0.594294	−	0.594294i
$630$		0			0
$631$		−	14411.5i		−	0.909210i	−0.890693	−	0.454605i	$-0.849780\pi$
$631$		−	14411.5i		−	0.909210i	0.890693	−	0.454605i	$-0.150220\pi$
$632$	405.011	+	1272.03i	0.0254913	+	0.0800611i
$633$		0			0
$634$	−512.670	+	3196.10i	−0.0321147	+	0.200211i
$635$	20534.3	+	20534.3i	1.28327	+	1.28327i
$636$		0			0
$637$	−3180.91	+	3180.91i	−0.197853	+	0.197853i
$638$	−15107.0	+	10930.4i	−0.937445	+	0.678276i
$639$		0			0
$640$	15948.1	−	7850.86i	0.985008	−	0.484895i
$641$	25724.0			1.58508			0.792542	−	0.609818i	$-0.208757\pi$
$641$	25724.0			1.58508			0.792542	+	0.609818i	$0.208757\pi$
$642$		0			0
$643$	−7835.74	+	7835.74i	−0.480578	+	0.480578i	−0.905316	−	0.424738i	$-0.860366\pi$
$643$	−7835.74	+	7835.74i	−0.480578	+	0.480578i	0.424738	+	0.905316i	$0.360366\pi$
$644$	−103.026	+	312.883i	−0.00630406	+	0.0191449i
$645$		0			0
$646$	−2410.99	+	15030.7i	−0.146841	+	0.915441i
$647$		−	1247.43i		−	0.0757981i	−0.999282	−	0.0378991i	$-0.987933\pi$
$647$		−	1247.43i		−	0.0757981i	0.999282	−	0.0378991i	$-0.0120665\pi$
$648$		0			0
$649$			1693.89i			0.102451i
$650$	−947.658	−	152.009i	−0.0571849	−	0.00917272i
$651$		0			0
$652$	−3617.68	−	7169.79i	−0.217299	−	0.430661i
$653$	−8302.21	+	8302.21i	−0.497535	+	0.497535i	−0.910670	−	0.413135i	$-0.864434\pi$
$653$	−8302.21	+	8302.21i	−0.497535	+	0.497535i	0.413135	+	0.910670i	$0.364434\pi$
$654$		0			0
$655$	7003.63			0.417793
$656$	7554.08	−	10226.8i	0.449599	−	0.608675i
$657$		0			0
$658$	−212.980	−	294.359i	−0.0126182	−	0.0174397i
$659$	−1696.16	+	1696.16i	−0.100262	+	0.100262i	−0.755459	−	0.655196i	$-0.772586\pi$
$659$	−1696.16	+	1696.16i	−0.100262	+	0.100262i	0.655196	+	0.755459i	$0.272586\pi$
$660$		0			0
$661$	−8788.30	−	8788.30i	−0.517134	−	0.517134i	0.399569	−	0.916703i	$-0.369160\pi$
$661$	−8788.30	−	8788.30i	−0.517134	−	0.517134i	−0.916703	+	0.399569i	$0.869160\pi$
$662$	−16705.1	−	2679.57i	−0.980758	−	0.157318i
$663$		0			0
$664$	−11659.0	−	6027.64i	−0.681414	−	0.352286i
$665$		−	2020.00i		−	0.117793i
$666$		0			0
$667$	4548.88	+	4548.88i	0.264068	+	0.264068i
$668$	26296.3	+	8658.89i	1.52311	+	0.501531i
$669$		0			0
$670$	−11224.9	+	8121.62i	−0.647247	+	0.468307i
$671$	−7037.56			−0.404891
$672$		0			0
$673$	−23869.3			−1.36716			−0.683578	−	0.729878i	$-0.739577\pi$
$673$	−23869.3			−1.36716			−0.683578	+	0.729878i	$0.739577\pi$
$674$	22921.1	−	16584.2i	1.30992	−	0.947775i
$675$		0			0
$676$	15366.5	+	5059.90i	0.874289	+	0.287887i
$677$	5663.30	+	5663.30i	0.321504	+	0.321504i	0.849344	−	0.527840i	$-0.176998\pi$
$677$	5663.30	+	5663.30i	0.321504	+	0.321504i	−0.527840	+	0.849344i	$0.676998\pi$
$678$		0			0
$679$		−	1327.71i		−	0.0750410i
$680$	6838.39	−	13227.2i	0.385647	−	0.745943i
$681$		0			0
$682$	−9538.55	−	1530.03i	−0.535557	−	0.0859058i
$683$	9152.80	+	9152.80i	0.512770	+	0.512770i	0.915374	−	0.402604i	$-0.131895\pi$
$683$	9152.80	+	9152.80i	0.512770	+	0.512770i	−0.402604	+	0.915374i	$0.631895\pi$
$684$		0			0
$685$	−7437.11	+	7437.11i	−0.414828	+	0.414828i
$686$	1857.15	+	2566.77i	0.103362	+	0.142857i
$687$		0			0
$688$	3844.01	+	25572.8i	0.213011	+	1.41708i
$689$	−9828.85			−0.543468
$690$		0			0
$691$	17057.9	−	17057.9i	0.939091	−	0.939091i	−0.0591580	−	0.998249i	$-0.518842\pi$
$691$	17057.9	−	17057.9i	0.939091	−	0.939091i	0.998249	+	0.0591580i	$0.0188416\pi$
$692$	−6643.59	−	13166.8i	−0.364959	−	0.723303i
$693$		0			0
$694$	25314.3	+	4060.54i	1.38461	+	0.222098i
$695$			29325.4i			1.60054i
$696$		0			0
$697$		−	10650.4i		−	0.578787i
$698$	−3486.40	+	21735.1i	−0.189058	+	1.17863i
$699$		0			0
$700$	−105.289	+	319.754i	−0.00568507	+	0.0172651i
$701$	7720.44	−	7720.44i	0.415973	−	0.415973i	−0.467840	−	0.883813i	$-0.654968\pi$
$701$	7720.44	−	7720.44i	0.415973	−	0.415973i	0.883813	+	0.467840i	$0.154968\pi$
$702$		0			0
$703$	24827.3			1.33198
$704$	12992.2	+	2215.48i	0.695540	+	0.118607i
$705$		0			0
$706$	3234.13	−	2340.01i	0.172405	−	0.124741i
$707$	−497.001	+	497.001i	−0.0264380	+	0.0264380i
$708$		0			0
$709$	4577.66	+	4577.66i	0.242479	+	0.242479i	0.817875	−	0.575396i	$-0.195152\pi$
$709$	4577.66	+	4577.66i	0.242479	+	0.242479i	−0.575396	+	0.817875i	$0.695152\pi$
$710$	−4000.50	+	24940.0i	−0.211459	+	1.31829i
$711$		0			0
$712$	16579.4	−	5278.86i	0.872670	−	0.277856i
$713$			3332.88i			0.175059i
$714$		0			0
$715$	−2953.40	−	2953.40i	−0.154477	−	0.154477i
$716$	−5516.25	−	10932.5i	−0.287921	−	0.570625i
$717$		0			0
$718$	3582.49	+	4951.36i	0.186208	+	0.257358i
$719$	30210.0			1.56696			0.783479	−	0.621418i	$-0.213443\pi$
$719$	30210.0			1.56696			0.783479	+	0.621418i	$0.213443\pi$
$720$		0			0
$721$	−1577.28			−0.0814717
$722$	−5337.60	−	7377.10i	−0.275132	−	0.380259i
$723$		0			0
$724$	29735.9	−	15003.9i	1.52642	−	0.770188i
$725$	4648.78	+	4648.78i	0.238140	+	0.238140i
$726$		0			0
$727$			20721.3i			1.05710i	0.848903	+	0.528549i	$0.177264\pi$
$727$			20721.3i			1.05710i	−0.848903	+	0.528549i	$0.822736\pi$
$728$	−225.172	+	435.541i	−0.0114635	+	0.0221734i
$729$		0			0
$730$	−583.218	+	3635.92i	−0.0295697	+	0.184344i
$731$	15317.6	+	15317.6i	0.775025	+	0.775025i
$732$		0			0
$733$	−13879.8	+	13879.8i	−0.699404	+	0.699404i	−0.964282	−	0.264878i	$-0.914668\pi$
$733$	−13879.8	+	13879.8i	−0.699404	+	0.699404i	0.264878	+	0.964282i	$0.414668\pi$
$734$	24651.5	−	17836.2i	1.23965	−	0.896932i
$735$		0			0
$736$	44.7891	−	4546.79i	0.00224314	−	0.227713i
$737$	−10272.6			−0.513428
$738$		0			0
$739$	8793.93	−	8793.93i	0.437740	−	0.437740i	−0.453511	−	0.891251i	$-0.649829\pi$
$739$	8793.93	−	8793.93i	0.437740	−	0.437740i	0.891251	+	0.453511i	$0.149829\pi$
$740$	−23066.7	−	7595.45i	−1.14588	−	0.377317i
$741$		0			0
$742$	−546.015	+	3403.98i	−0.0270146	+	0.168415i
$743$		−	7669.27i		−	0.378678i	−0.981912	−	0.189339i	$-0.939365\pi$
$743$		−	7669.27i		−	0.378678i	0.981912	−	0.189339i	$-0.0606346\pi$
$744$		0			0
$745$		−	559.327i		−	0.0275062i
$746$	5556.94	+	891.359i	0.272727	+	0.0437466i
$747$		0			0
$748$	9856.68	−	4973.41i	0.481813	−	0.243109i
$749$	1193.92	−	1193.92i	0.0582443	−	0.0582443i
$750$		0			0
$751$	−26531.8			−1.28916			−0.644580	−	0.764537i	$-0.722968\pi$
$751$	−26531.8			−1.28916			−0.644580	+	0.764537i	$0.722968\pi$
$752$	4034.05	+	2979.76i	0.195620	+	0.144495i
$753$		0			0
$754$	5612.93	+	7757.63i	0.271102	+	0.374690i
$755$	−9348.40	+	9348.40i	−0.450627	+	0.450627i
$756$		0			0
$757$	−79.4192	−	79.4192i	−0.00381313	−	0.00381313i	0.705198	−	0.709011i	$-0.250858\pi$
$757$	−79.4192	−	79.4192i	−0.00381313	−	0.00381313i	−0.709011	+	0.705198i	$0.750858\pi$
$758$	−4529.91	−	726.619i	−0.217063	−	0.0348179i
$759$		0			0
$760$	8459.51	+	26569.0i	0.403761	+	1.26810i
$761$		−	36991.3i		−	1.76207i	−0.473055	−	0.881033i	$-0.656849\pi$
$761$		−	36991.3i		−	1.76207i	0.473055	−	0.881033i	$-0.343151\pi$
$762$		0			0
$763$	−972.494	−	972.494i	−0.0461424	−	0.0461424i
$764$	1077.53	−	3272.36i	0.0510256	−	0.154961i
$765$		0			0
$766$	−20720.3	+	14991.9i	−0.977355	+	0.707152i
$767$	869.835			0.0409490
$768$		0			0
$769$	26637.0			1.24910			0.624548	−	0.780987i	$-0.285283\pi$
$769$	26637.0			1.24910			0.624548	+	0.780987i	$0.285283\pi$
$770$	−1186.91	+	858.770i	−0.0555495	+	0.0401921i
$771$		0			0
$772$	−5672.20	+	17226.0i	−0.264439	+	0.803080i
$773$	−19743.6	−	19743.6i	−0.918667	−	0.918667i	0.0782657	−	0.996933i	$-0.475062\pi$
$773$	−19743.6	−	19743.6i	−0.918667	−	0.918667i	−0.996933	+	0.0782657i	$0.975062\pi$
$774$		0			0
$775$			3406.07i			0.157871i
$776$	5560.28	+	17463.3i	0.257220	+	0.807856i
$777$		0			0
$778$	−10171.3	−	1631.53i	−0.468715	−	0.0751840i
$779$	14102.3	+	14102.3i	0.648610	+	0.648610i
$780$		0			0
$781$	−13242.6	+	13242.6i	−0.606734	+	0.606734i
$782$	−2232.76	−	3085.89i	−0.102101	−	0.141114i
$783$		0			0
$784$	−17519.0	−	12940.4i	−0.798058	−	0.589488i
$785$	−33079.9			−1.50404
$786$		0			0
$787$	−28878.1	+	28878.1i	−1.30800	+	1.30800i	−0.385136	+	0.922860i	$0.625845\pi$
$787$	−28878.1	+	28878.1i	−1.30800	+	1.30800i	−0.922860	+	0.385136i	$0.874155\pi$
$788$	10498.8	−	5297.41i	0.474625	−	0.239483i
$789$		0			0
$790$	2022.43	+	324.407i	0.0910819	+	0.0146100i
$791$		−	576.912i		−	0.0259325i
$792$		0			0
$793$			3613.88i			0.161832i
$794$	−4511.59	+	28126.3i	−0.201650	+	1.25713i
$795$		0			0
$796$	37913.0	+	12484.1i	1.68818	+	0.555887i
$797$	16656.0	−	16656.0i	0.740257	−	0.740257i	−0.232371	−	0.972627i	$-0.574648\pi$
$797$	16656.0	−	16656.0i	0.740257	−	0.740257i	0.972627	+	0.232371i	$0.0746483\pi$
$798$		0			0
$799$	4201.14			0.186015
$800$	45.7727	−	4646.64i	0.00202289	−	0.205355i
$801$		0			0
$802$	6932.16	−	5015.68i	0.305216	−	0.220835i
$803$	−1930.60	+	1930.60i	−0.0848435	+	0.0848435i
$804$		0			0
$805$	357.391	+	357.391i	0.0156477	+	0.0156477i
$806$	−785.690	+	4898.18i	−0.0343359	+	0.214058i
$807$		0			0
$808$	4455.66	−	8618.42i	0.193997	−	0.375241i
$809$			34940.4i			1.51847i	0.650819	+	0.759233i	$0.274426\pi$
$809$			34940.4i			1.51847i	−0.650819	+	0.759233i	$0.725574\pi$
$810$		0			0
$811$	−15168.2	−	15168.2i	−0.656753	−	0.656753i	0.297857	−	0.954610i	$-0.403728\pi$
$811$	−15168.2	−	15168.2i	−0.656753	−	0.656753i	−0.954610	+	0.297857i	$0.903728\pi$
$812$	2998.48	−	1512.95i	0.129589	−	0.0653868i
$813$		0			0
$814$	−10554.9	−	14587.9i	−0.454483	−	0.628141i
$815$	−12322.0			−0.529597
$816$		0			0
$817$	−40564.3			−1.73705
$818$	15651.8	+	21632.4i	0.669014	+	0.924644i
$819$		0			0
$820$	−8787.94	−	17416.6i	−0.374254	−	0.741725i
$821$	−8710.55	−	8710.55i	−0.370280	−	0.370280i	0.497299	−	0.867579i	$-0.334325\pi$
$821$	−8710.55	−	8710.55i	−0.370280	−	0.370280i	−0.867579	+	0.497299i	$0.834325\pi$
$822$		0			0
$823$			24493.5i			1.03741i	0.854952	+	0.518707i	$0.173586\pi$
$823$			24493.5i			1.03741i	−0.854952	+	0.518707i	$0.826414\pi$
$824$	20745.9	−	6605.46i	0.877085	−	0.279262i
$825$		0			0
$826$	48.3213	−	301.246i	0.00203549	−	0.0126897i
$827$	−26328.0	−	26328.0i	−1.10703	−	1.10703i	−0.993539	−	0.113492i	$-0.963796\pi$
$827$	−26328.0	−	26328.0i	−1.10703	−	1.10703i	−0.113492	−	0.993539i	$-0.536204\pi$
$828$		0			0
$829$	9108.25	−	9108.25i	0.381596	−	0.381596i	−0.490081	−	0.871677i	$-0.663033\pi$
$829$	9108.25	−	9108.25i	0.381596	−	0.381596i	0.871677	+	0.490081i	$0.163033\pi$
$830$	−16315.6	+	11804.9i	−0.682315	+	0.493680i
$831$		0			0
$832$	1137.68	−	6671.65i	0.0474062	−	0.278002i
$833$	−18244.6			−0.758870
$834$		0			0
$835$	30037.1	−	30037.1i	1.24488	−	1.24488i
$836$	−6465.96	+	19636.6i	−0.267500	+	0.812375i
$837$		0			0
$838$	2062.55	−	12858.4i	0.0850233	−	0.530055i
$839$		−	1394.89i		−	0.0573982i	−0.999588	−	0.0286991i	$-0.990864\pi$
$839$		−	1394.89i		−	0.0573982i	0.999588	−	0.0286991i	$-0.00913646\pi$
$840$		0			0
$841$		−	41200.9i		−	1.68932i
$842$	−37275.6	−	5979.18i	−1.52566	−	0.244722i
$843$		0			0
$844$	−13513.5	−	26782.1i	−0.551131	−	1.09227i
$845$	17552.4	−	17552.4i	0.714583	−	0.714583i
$846$		0			0
$847$	1095.62			0.0444463
$848$	−7073.75	−	47059.1i	−0.286455	−	1.90568i
$849$		0			0
$850$	−2281.79	−	3153.66i	−0.0920762	−	0.127258i
$851$	−4392.60	+	4392.60i	−0.176941	+	0.176941i
$852$		0			0
$853$	15284.7	+	15284.7i	0.613527	+	0.613527i	0.943863	−	0.330337i	$-0.107162\pi$
$853$	15284.7	+	15284.7i	0.613527	+	0.613527i	−0.330337	+	0.943863i	$0.607162\pi$
$854$	1251.58	+	200.759i	0.0501501	+	0.00804430i
$855$		0			0
$856$	−10703.6	+	20703.6i	−0.427385	+	0.826675i
$857$			2273.70i			0.0906277i	0.998973	+	0.0453139i	$0.0144288\pi$
$857$			2273.70i			0.0906277i	−0.998973	+	0.0453139i	$0.985571\pi$
$858$		0			0
$859$	−21674.3	−	21674.3i	−0.860905	−	0.860905i	0.130538	−	0.991443i	$-0.458329\pi$
$859$	−21674.3	−	21674.3i	−0.860905	−	0.860905i	−0.991443	+	0.130538i	$0.958329\pi$
$860$	37687.8	+	12409.9i	1.49435	+	0.492063i
$861$		0			0
$862$	24330.6	−	17604.1i	0.961374	−	0.695589i
$863$	−23721.7			−0.935686			−0.467843	−	0.883812i	$-0.654969\pi$
$863$	−23721.7			−0.935686			−0.467843	+	0.883812i	$0.654969\pi$
$864$		0			0
$865$	−22628.5			−0.889469
$866$	1618.91	−	1171.34i	0.0635251	−	0.0459628i
$867$		0			0
$868$	1652.72	+	544.209i	0.0646277	+	0.0212807i
$869$	1073.87	+	1073.87i	0.0419200	+	0.0419200i
$870$		0			0
$871$			5275.12i			0.205213i
$872$	16863.9	+	8718.49i	0.654911	+	0.338584i
$873$		0			0
$874$	7042.45	+	1129.64i	0.272557	+	0.0437193i
$875$	−1413.26	−	1413.26i	−0.0546020	−	0.0546020i
$876$		0			0
$877$	22429.6	−	22429.6i	0.863617	−	0.863617i	−0.128139	−	0.991756i	$-0.540900\pi$
$877$	22429.6	−	22429.6i	0.863617	−	0.863617i	0.991756	+	0.128139i	$0.0409004\pi$
$878$	−22568.3	−	31191.6i	−0.867475	−	1.19894i
$879$		0			0
$880$	12014.9	−	16266.0i	0.460252	−	0.623098i
$881$	−24603.0			−0.940859			−0.470429	−	0.882438i	$-0.655901\pi$
$881$	−24603.0			−0.940859			−0.470429	+	0.882438i	$0.655901\pi$
$882$		0			0
$883$	−23486.7	+	23486.7i	−0.895120	+	0.895120i	−0.995000	−	0.0998799i	$-0.968154\pi$
$883$	−23486.7	+	23486.7i	−0.895120	+	0.895120i	0.0998799	+	0.995000i	$0.468154\pi$
$884$	−2553.91	−	5061.54i	−0.0971690	−	0.192577i
$885$		0			0
$886$	−12350.0	−	1981.00i	−0.468293	−	0.0751163i
$887$			39722.9i			1.50368i	0.659345	+	0.751841i	$0.270834\pi$
$887$			39722.9i			1.50368i	−0.659345	+	0.751841i	$0.729166\pi$
$888$		0			0
$889$		−	3878.15i		−	0.146309i
$890$	4228.27	−	26360.0i	0.159249	−	0.992798i
$891$		0			0
$892$	9234.86	−	28045.5i	0.346643	−	1.05273i
$893$	−5562.75	+	5562.75i	−0.208455	+	0.208455i
$894$		0			0
$895$	−18788.7			−0.701716
$896$	−2247.36	−	764.633i	−0.0837937	−	0.0285096i
$897$		0			0
$898$	11988.7	−	8674.24i	0.445509	−	0.322342i
$899$	24028.2	−	24028.2i	0.891420	−	0.891420i
$900$		0			0
$901$	−28187.5	−	28187.5i	−1.04225	−	1.04225i
$902$	2290.82	−	14281.5i	0.0845633	−	0.527188i
$903$		0			0
$904$	2416.03	+	7588.10i	0.0888895	+	0.279177i
$905$		−	51104.2i		−	1.87708i
$906$		0			0
$907$	4565.44	+	4565.44i	0.167136	+	0.167136i	0.785719	−	0.618583i	$-0.212293\pi$
$907$	4565.44	+	4565.44i	0.167136	+	0.167136i	−0.618583	+	0.785719i	$0.712293\pi$
$908$	−8717.25	−	17276.5i	−0.318604	−	0.631433i
$909$		0			0
$910$	440.990	+	609.492i	0.0160645	+	0.0222027i
$911$	2013.95			0.0732438			0.0366219	−	0.999329i	$-0.488340\pi$
$911$	2013.95			0.0732438			0.0366219	+	0.999329i	$0.488340\pi$
$912$		0			0
$913$	−14931.4			−0.541245
$914$	11329.3	+	15658.2i	0.409999	+	0.566659i
$915$		0			0
$916$	−927.261	+	467.870i	−0.0334471	+	0.0168765i
$917$	−661.359	−	661.359i	−0.0238168	−	0.0238168i
$918$		0			0
$919$			37746.5i			1.35489i	0.735575	+	0.677443i	$0.236912\pi$
$919$			37746.5i			1.35489i	−0.735575	+	0.677443i	$0.763088\pi$
$920$	−6197.46	−	3204.04i	−0.222092	−	0.114820i
$921$		0			0
$922$	3785.85	−	23601.9i	0.135228	−	0.843044i
$923$	6800.28	+	6800.28i	0.242507	+	0.242507i
$924$		0			0
$925$	−4489.07	+	4489.07i	−0.159567	+	0.159567i
$926$	−9792.51	+	7085.24i	−0.347518	+	0.251442i
$927$		0			0
$928$	−33102.8	+	32457.0i	−1.17096	+	1.14812i
$929$	−45643.5			−1.61197			−0.805983	−	0.591939i	$-0.798363\pi$
$929$	−45643.5			−1.61197			−0.805983	+	0.591939i	$0.798363\pi$
$930$		0			0
$931$	24157.8	−	24157.8i	0.850418	−	0.850418i
$932$	32368.1	+	10658.2i	1.13761	+	0.374593i
$933$		0			0
$934$	−7757.82	+	48364.1i	−0.271781	+	1.69435i
$935$		−	16939.7i		−	0.592501i
$936$		0			0
$937$			47317.5i			1.64973i	0.565331	+	0.824864i	$0.308748\pi$
$937$			47317.5i			1.64973i	−0.565331	+	0.824864i	$0.691252\pi$
$938$	1826.91	+	293.045i	0.0635935	+	0.0102007i
$939$		0			0
$940$	6870.11	−	3466.46i	0.238381	−	0.120280i
$941$	−15074.7	+	15074.7i	−0.522234	+	0.522234i	−0.918246	−	0.396012i	$-0.870394\pi$
$941$	−15074.7	+	15074.7i	−0.522234	+	0.522234i	0.396012	+	0.918246i	$0.370394\pi$
$942$		0			0
$943$	−4990.14			−0.172324
$944$	626.013	+	4164.64i	0.0215837	+	0.143588i
$945$		0			0
$946$	17245.2	+	23834.7i	0.592697	+	0.819166i
$947$	−14567.7	+	14567.7i	−0.499880	+	0.499880i	−0.911400	−	0.411521i	$-0.864998\pi$
$947$	−14567.7	+	14567.7i	−0.499880	+	0.499880i	0.411521	+	0.911400i	$0.364998\pi$
$948$		0			0
$949$	991.388	+	991.388i	0.0339113	+	0.0339113i
$950$	7197.11	+	1154.45i	0.245795	+	0.0394266i
$951$		0			0
$952$	−1894.82	+	603.306i	−0.0645077	+	0.0205391i
$953$			42987.2i			1.46117i	0.682824	+	0.730583i	$0.260752\pi$
$953$			42987.2i			1.46117i	−0.682824	+	0.730583i	$0.739248\pi$
$954$		0			0
$955$	−3737.87	−	3737.87i	−0.126654	−	0.126654i
$956$	12643.4	−	38396.9i	0.427737	−	1.29900i
$957$		0			0
$958$	9321.81	−	6744.67i	0.314378	−	0.227464i
$959$	1404.59			0.0472956
$960$		0			0
$961$	−12186.0			−0.409049
$962$	−7491.10	+	5420.09i	−0.251063	+	0.181654i
$963$		0			0
$964$	122.197	−	371.102i	0.00408268	−	0.0123987i
$965$	19676.5	+	19676.5i	0.656381	+	0.656381i
$966$		0			0
$967$			44030.7i			1.46425i	0.681170	+	0.732126i	$0.261472\pi$
$967$			44030.7i			1.46425i	−0.681170	+	0.732126i	$0.738528\pi$
$968$	−14410.7	+	4588.33i	−0.478488	+	0.152350i
$969$		0			0
$970$	27765.3	+	4453.68i	0.919062	+	0.147422i
$971$	−35699.8	−	35699.8i	−1.17988	−	1.17988i	−0.979775	−	0.200101i	$-0.935873\pi$
$971$	−35699.8	−	35699.8i	−1.17988	−	1.17988i	−0.200101	−	0.979775i	$-0.564127\pi$
$972$		0			0
$973$	2769.23	−	2769.23i	0.0912409	−	0.0912409i
$974$	−26817.0	−	37063.7i	−0.882208	−	1.21930i
$975$		0			0
$976$	−17302.7	+	2600.88i	−0.567466	+	0.0852994i
$977$	49515.3			1.62143			0.810714	−	0.585442i	$-0.199079\pi$
$977$	49515.3			1.62143			0.810714	+	0.585442i	$0.199079\pi$
$978$		0			0
$979$	13996.6	−	13996.6i	0.456930	−	0.456930i
$980$	−29835.3	+	15054.1i	−0.972505	+	0.490699i
$981$		0			0
$982$	−53700.2	−	8613.76i	−1.74505	−	0.279915i
$983$			40046.2i			1.29936i	0.760206	+	0.649682i	$0.225098\pi$
$983$			40046.2i			1.29936i	−0.760206	+	0.649682i	$0.774902\pi$
$984$		0			0
$985$		−	18043.3i		−	0.583662i
$986$	−6150.64	+	38344.6i	−0.198658	+	1.23848i
$987$		0			0
$988$	10083.7	+	3320.36i	0.324700	+	0.106918i
$989$	7176.90	−	7176.90i	0.230750	−	0.230750i
$990$		0			0
$991$	18673.2			0.598560			0.299280	−	0.954165i	$-0.403254\pi$
$991$	18673.2			0.598560			0.299280	+	0.954165i	$0.403254\pi$
$992$	−24017.2	−	236.586i	−0.768696	−	0.00757220i
$993$		0			0
$994$	2732.88	−	1977.34i	0.0872050	−	0.0630960i
$995$	43306.3	−	43306.3i	1.37980	−	1.37980i
$996$		0			0
$997$	21982.1	+	21982.1i	0.698274	+	0.698274i	0.964038	−	0.265764i	$-0.0856243\pi$
$997$	21982.1	+	21982.1i	0.698274	+	0.698274i	−0.265764	+	0.964038i	$0.585624\pi$
$998$	−9279.00	+	57847.4i	−0.294310	+	1.83480i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.a.37.4		10
3.2	odd	2		16.4.e.a.5.2	✓	10
4.3	odd	2		576.4.k.a.433.1		10
12.11	even	2		64.4.e.a.49.5		10
16.3	odd	4		576.4.k.a.145.1		10
16.13	even	4	inner	144.4.k.a.109.4		10
24.5	odd	2		128.4.e.b.97.5		10
24.11	even	2		128.4.e.a.97.1		10
48.5	odd	4		128.4.e.b.33.5		10
48.11	even	4		128.4.e.a.33.1		10
48.29	odd	4		16.4.e.a.13.2	yes	10
48.35	even	4		64.4.e.a.17.5		10
96.5	odd	8		1024.4.b.j.513.1		10
96.11	even	8		1024.4.b.k.513.1		10
96.29	odd	8		1024.4.a.n.1.1		10
96.35	even	8		1024.4.a.m.1.10		10
96.53	odd	8		1024.4.b.j.513.10		10
96.59	even	8		1024.4.b.k.513.10		10
96.77	odd	8		1024.4.a.n.1.10		10
96.83	even	8		1024.4.a.m.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.2	✓	10	3.2	odd	2
16.4.e.a.13.2	yes	10	48.29	odd	4
64.4.e.a.17.5		10	48.35	even	4
64.4.e.a.49.5		10	12.11	even	2
128.4.e.a.33.1		10	48.11	even	4
128.4.e.a.97.1		10	24.11	even	2
128.4.e.b.33.5		10	48.5	odd	4
128.4.e.b.97.5		10	24.5	odd	2
144.4.k.a.37.4		10	1.1	even	1	trivial
144.4.k.a.109.4		10	16.13	even	4	inner
576.4.k.a.145.1		10	16.3	odd	4
576.4.k.a.433.1		10	4.3	odd	2
1024.4.a.m.1.1		10	96.83	even	8
1024.4.a.m.1.10		10	96.35	even	8
1024.4.a.n.1.1		10	96.29	odd	8
1024.4.a.n.1.10		10	96.77	odd	8
1024.4.b.j.513.1		10	96.5	odd	8
1024.4.b.j.513.10		10	96.53	odd	8
1024.4.b.k.513.1		10	96.11	even	8
1024.4.b.k.513.10		10	96.59	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29152 - 1.65800i) q^{2} +(2.50210 - 7.59865i) q^{4} +(-8.67959 - 8.67959i) q^{5} +1.63924i q^{7} +(-6.86495 - 21.5609i) q^{8} +O(q^{10})\)	\(q+(2.29152 - 1.65800i) q^{2} +(2.50210 - 7.59865i) q^{4} +(-8.67959 - 8.67959i) q^{5} +1.63924i q^{7} +(-6.86495 - 21.5609i) q^{8} +(-34.2802 - 5.49869i) q^{10} +(-18.2021 - 18.2021i) q^{11} +(-9.34700 + 9.34700i) q^{13} +(2.71786 + 3.75636i) q^{14} +(-51.4790 - 38.0251i) q^{16} -53.6113 q^{17} +(70.9870 - 70.9870i) q^{19} +(-87.6704 + 44.2360i) q^{20} +(-71.8893 - 11.5314i) q^{22} +25.1189i q^{23} +25.6706i q^{25} +(-5.92151 + 36.9161i) q^{26} +(12.4560 + 4.10155i) q^{28} +(181.094 - 181.094i) q^{29} +132.684 q^{31} +(-181.011 - 1.78308i) q^{32} +(-122.851 + 88.8874i) q^{34} +(14.2280 - 14.2280i) q^{35} +(174.872 + 174.872i) q^{37} +(44.9717 - 280.364i) q^{38} +(-127.555 + 246.725i) q^{40} +198.660i q^{41} +(-285.717 - 285.717i) q^{43} +(-183.854 + 92.7678i) q^{44} +(41.6471 + 57.5605i) q^{46} -78.3629 q^{47} +340.313 q^{49} +(42.5617 + 58.8245i) q^{50} +(47.6375 + 94.4117i) q^{52} +(525.776 + 525.776i) q^{53} +315.973i q^{55} +(35.3436 - 11.2533i) q^{56} +(114.727 - 715.232i) q^{58} +(-46.5301 - 46.5301i) q^{59} +(193.318 - 193.318i) q^{61} +(304.047 - 219.990i) q^{62} +(-417.745 + 296.029i) q^{64} +162.256 q^{65} +(282.182 - 282.182i) q^{67} +(-134.141 + 407.374i) q^{68} +(9.01370 - 56.1935i) q^{70} -727.536i q^{71} -106.065i q^{73} +(690.659 + 110.785i) q^{74} +(-361.789 - 717.022i) q^{76} +(29.8376 - 29.8376i) q^{77} -58.9970 q^{79} +(116.775 + 776.859i) q^{80} +(329.378 + 455.233i) q^{82} +(410.156 - 410.156i) q^{83} +(465.324 + 465.324i) q^{85} +(-1128.44 - 181.007i) q^{86} +(-267.497 + 517.409i) q^{88} +768.959i q^{89} +(-15.3220 - 15.3220i) q^{91} +(190.870 + 62.8500i) q^{92} +(-179.570 + 129.925i) q^{94} -1232.28 q^{95} -809.953 q^{97} +(779.833 - 564.238i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8}+O(q^{10}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8	\( 10 q + 2 q^{2} + 8 q^{4} + 2 q^{5} + 44 q^{8} - 68 q^{10} - 18 q^{11} - 2 q^{13} - 188 q^{14} + 280 q^{16} + 4 q^{17} - 26 q^{19} + 196 q^{20} - 588 q^{22} + 264 q^{26} + 280 q^{28} + 202 q^{29} + 368 q^{31} - 968 q^{32} + 436 q^{34} - 476 q^{35} - 10 q^{37} + 1232 q^{38} - 1336 q^{40} - 838 q^{43} - 868 q^{44} + 1132 q^{46} + 944 q^{47} + 94 q^{49} - 726 q^{50} - 236 q^{52} + 378 q^{53} + 488 q^{56} + 8 q^{58} - 1706 q^{59} + 910 q^{61} + 80 q^{62} + 512 q^{64} + 492 q^{65} + 1942 q^{67} + 880 q^{68} + 160 q^{70} + 452 q^{74} - 1228 q^{76} + 268 q^{77} - 4416 q^{79} + 2648 q^{80} - 704 q^{82} + 2562 q^{83} - 12 q^{85} - 3764 q^{86} + 1528 q^{88} + 3332 q^{91} - 632 q^{92} - 3248 q^{94} - 6900 q^{95} - 4 q^{97} - 314 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 8 * q^4 + 2 * q^5 + 44 * q^8 - 68 * q^10 - 18 * q^11 - 2 * q^13 - 188 * q^14 + 280 * q^16 + 4 * q^17 - 26 * q^19 + 196 * q^20 - 588 * q^22 + 264 * q^26 + 280 * q^28 + 202 * q^29 + 368 * q^31 - 968 * q^32 + 436 * q^34 - 476 * q^35 - 10 * q^37 + 1232 * q^38 - 1336 * q^40 - 838 * q^43 - 868 * q^44 + 1132 * q^46 + 944 * q^47 + 94 * q^49 - 726 * q^50 - 236 * q^52 + 378 * q^53 + 488 * q^56 + 8 * q^58 - 1706 * q^59 + 910 * q^61 + 80 * q^62 + 512 * q^64 + 492 * q^65 + 1942 * q^67 + 880 * q^68 + 160 * q^70 + 452 * q^74 - 1228 * q^76 + 268 * q^77 - 4416 * q^79 + 2648 * q^80 - 704 * q^82 + 2562 * q^83 - 12 * q^85 - 3764 * q^86 + 1528 * q^88 + 3332 * q^91 - 632 * q^92 - 3248 * q^94 - 6900 * q^95 - 4 * q^97 - 314 * q^98

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