LMFDB - Embedded newform 225.4.p.b.32.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, 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 $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.16
Character	$\chi$	$=$	225.32
Dual form			225.4.p.b.218.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.27515 + 1.41347i) q^{2} +(-1.94123 + 4.81992i) q^{3} +(18.9011 + 10.9125i) q^{4} +(-17.0531 + 22.6819i) q^{6} +(-1.13077 + 4.22008i) q^{7} +(53.3880 + 53.3880i) q^{8} +(-19.4633 - 18.7131i) q^{9} +O(q^{10})$	\(q+(5.27515 + 1.41347i) q^{2} +(-1.94123 + 4.81992i) q^{3} +(18.9011 + 10.9125i) q^{4} +(-17.0531 + 22.6819i) q^{6} +(-1.13077 + 4.22008i) q^{7} +(53.3880 + 53.3880i) q^{8} +(-19.4633 - 18.7131i) q^{9} +(-5.91593 + 3.41556i) q^{11} +(-89.2889 + 69.9180i) q^{12} +(6.54783 + 24.4368i) q^{13} +(-11.9299 + 20.6632i) q^{14} +(118.867 + 205.883i) q^{16} +(36.0612 - 36.0612i) q^{17} +(-76.2213 - 126.225i) q^{18} -59.8443i q^{19} +(-18.1454 - 13.6423i) q^{21} +(-36.0352 + 9.65561i) q^{22} +(-50.9044 + 13.6398i) q^{23} +(-360.964 + 153.688i) q^{24} +138.163i q^{26} +(127.978 - 57.4851i) q^{27} +(-67.4245 + 67.4245i) q^{28} +(22.1046 + 38.2863i) q^{29} +(67.9692 - 117.726i) q^{31} +(179.699 + 670.646i) q^{32} +(-4.97859 - 35.1447i) q^{33} +(241.199 - 139.257i) q^{34} +(-163.669 - 566.092i) q^{36} +(-233.330 - 233.330i) q^{37} +(84.5883 - 315.688i) q^{38} +(-130.494 - 15.8774i) q^{39} +(335.678 + 193.804i) q^{41} +(-76.4365 - 97.6133i) q^{42} +(306.315 + 82.0769i) q^{43} -149.090 q^{44} -287.808 q^{46} +(-316.977 - 84.9338i) q^{47} +(-1223.09 + 173.263i) q^{48} +(280.516 + 161.956i) q^{49} +(103.809 + 243.815i) q^{51} +(-142.907 + 533.336i) q^{52} +(43.1181 + 43.1181i) q^{53} +(756.358 - 122.349i) q^{54} +(-285.671 + 164.932i) q^{56} +(288.445 + 116.171i) q^{57} +(62.4884 + 233.210i) q^{58} +(248.925 - 431.152i) q^{59} +(36.3039 + 62.8801i) q^{61} +(524.950 - 524.950i) q^{62} +(100.979 - 60.9764i) q^{63} +1889.88i q^{64} +(23.4132 - 192.431i) q^{66} +(-178.215 + 47.7525i) q^{67} +(1075.11 - 288.076i) q^{68} +(33.0742 - 271.833i) q^{69} -563.835i q^{71} +(-40.0503 - 2038.16i) q^{72} +(-84.7460 + 84.7460i) q^{73} +(-901.044 - 1560.65i) q^{74} +(653.054 - 1131.12i) q^{76} +(-7.72441 - 28.8279i) q^{77} +(-665.935 - 268.206i) q^{78} +(186.138 - 107.467i) q^{79} +(28.6389 + 728.437i) q^{81} +(1496.82 + 1496.82i) q^{82} +(249.226 - 930.125i) q^{83} +(-194.095 - 455.867i) q^{84} +(1499.84 + 865.935i) q^{86} +(-227.447 + 32.2201i) q^{87} +(-498.190 - 133.490i) q^{88} +288.322 q^{89} -110.529 q^{91} +(-1110.99 - 297.690i) q^{92} +(435.487 + 556.139i) q^{93} +(-1552.05 - 896.076i) q^{94} +(-3581.30 - 435.740i) q^{96} +(425.658 - 1588.58i) q^{97} +(1250.84 + 1250.84i) q^{98} +(179.059 + 44.2274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	$ 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) $ 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	5.27515	+	1.41347i	1.86505	+	0.499738i	0.999998	−	0.00195086i	$-0.000620979\pi$
$2$	5.27515	+	1.41347i	1.86505	+	0.499738i	0.865048	+	0.501689i	$0.167288\pi$
$3$	−1.94123	+	4.81992i	−0.373589	+	0.927594i
$3$	−1.94123	+	4.81992i	−0.373589	+	0.927594i
$4$	18.9011	+	10.9125i	2.36264	+	1.36407i
$5$		0			0
$5$		0			0
$6$	−17.0531	+	22.6819i	−1.16031	+	1.54331i
$7$	−1.13077	+	4.22008i	−0.0610556	+	0.227863i	−0.989711	−	0.143081i	$-0.954299\pi$
$7$	−1.13077	+	4.22008i	−0.0610556	+	0.227863i	0.928655	+	0.370944i	$0.120966\pi$
$8$	53.3880	+	53.3880i	2.35944	+	2.35944i
$9$	−19.4633	−	18.7131i	−0.720862	−	0.693078i
$10$		0			0
$11$	−5.91593	+	3.41556i	−0.162156	+	0.0936210i	−0.578882	−	0.815411i	$-0.696511\pi$
$11$	−5.91593	+	3.41556i	−0.162156	+	0.0936210i	0.416726	+	0.909032i	$0.363178\pi$
$12$	−89.2889	+	69.9180i	−2.14796	+	1.68197i
$13$	6.54783	+	24.4368i	0.139696	+	0.521351i	0.999934	+	0.0114594i	$0.00364774\pi$
$13$	6.54783	+	24.4368i	0.139696	+	0.521351i	−0.860239	+	0.509891i	$0.829686\pi$
$14$	−11.9299	+	20.6632i	−0.227743	+	0.394463i
$15$		0			0
$16$	118.867	+	205.883i	1.85729	+	3.21693i
$17$	36.0612	−	36.0612i	0.514477	−	0.514477i	−0.401418	−	0.915895i	$-0.631482\pi$
$17$	36.0612	−	36.0612i	0.514477	−	0.514477i	0.915895	+	0.401418i	$0.131482\pi$
$18$	−76.2213	−	126.225i	−0.998085	−	1.65287i
$19$		−	59.8443i		−	0.722591i	−0.932451	−	0.361296i	$-0.882335\pi$
$19$		−	59.8443i		−	0.722591i	0.932451	−	0.361296i	$-0.117665\pi$
$20$		0			0
$21$	−18.1454	−	13.6423i	−0.188554	−	0.141762i
$22$	−36.0352	+	9.65561i	−0.349215	+	0.0935719i
$23$	−50.9044	+	13.6398i	−0.461491	+	0.123656i	−0.482071	−	0.876132i	$-0.660115\pi$
$23$	−50.9044	+	13.6398i	−0.461491	+	0.123656i	0.0205799	+	0.999788i	$0.493449\pi$
$24$	−360.964	+	153.688i	−3.07006	+	1.30714i
$25$		0			0
$26$			138.163i			1.04215i
$27$	127.978	−	57.4851i	0.912202	−	0.409741i
$28$	−67.4245	+	67.4245i	−0.455073	+	0.455073i
$29$	22.1046	+	38.2863i	0.141542	+	0.245158i	0.928077	−	0.372387i	$-0.121461\pi$
$29$	22.1046	+	38.2863i	0.141542	+	0.245158i	−0.786535	+	0.617545i	$0.788127\pi$
$30$		0			0
$31$	67.9692	−	117.726i	0.393794	−	0.682072i	−0.599152	−	0.800635i	$-0.704496\pi$
$31$	67.9692	−	117.726i	0.393794	−	0.682072i	0.992946	+	0.118563i	$0.0378289\pi$
$32$	179.699	+	670.646i	0.992706	+	3.70483i
$33$	−4.97859	−	35.1447i	−0.0262625	−	0.185391i
$34$	241.199	−	139.257i	1.21663	−	0.702421i
$35$		0			0
$36$	−163.669	−	566.092i	−0.757729	−	2.62080i
$37$	−233.330	−	233.330i	−1.03674	−	1.03674i	−0.999299	−	0.0374360i	$-0.988081\pi$
$37$	−233.330	−	233.330i	−1.03674	−	1.03674i	−0.0374360	−	0.999299i	$-0.511919\pi$
$38$	84.5883	−	315.688i	0.361106	−	1.34767i
$39$	−130.494	−	15.8774i	−0.535791	−	0.0651902i
$40$		0			0
$41$	335.678	+	193.804i	1.27864	+	0.738221i	0.976598	−	0.215074i	$-0.0689993\pi$
$41$	335.678	+	193.804i	1.27864	+	0.738221i	0.302039	+	0.953295i	$0.402333\pi$
$42$	−76.4365	−	97.6133i	−0.280819	−	0.358620i
$43$	306.315	+	82.0769i	1.08634	+	0.291084i	0.757191	−	0.653194i	$-0.226571\pi$
$43$	306.315	+	82.0769i	1.08634	+	0.291084i	0.329149	+	0.944278i	$0.393238\pi$
$44$	−149.090			−0.510822
$45$		0			0
$46$	−287.808			−0.922499
$47$	−316.977	−	84.9338i	−0.983742	−	0.263593i	−0.269122	−	0.963106i	$-0.586734\pi$
$47$	−316.977	−	84.9338i	−0.983742	−	0.263593i	−0.714620	+	0.699513i	$0.753400\pi$
$48$	−1223.09	+	173.263i	−3.67787	+	0.521007i
$49$	280.516	+	161.956i	0.817832	+	0.472175i
$50$		0			0
$51$	103.809	+	243.815i	0.285023	+	0.669430i
$52$	−142.907	+	533.336i	−0.381108	+	1.42232i
$53$	43.1181	+	43.1181i	0.111749	+	0.111749i	0.760770	−	0.649021i	$-0.224821\pi$
$53$	43.1181	+	43.1181i	0.111749	+	0.111749i	−0.649021	+	0.760770i	$0.724821\pi$
$54$	756.358	−	122.349i	1.90606	−	0.308325i
$55$		0			0
$56$	−285.671	+	164.932i	−0.681685	+	0.393571i
$57$	288.445	+	116.171i	0.670271	+	0.269952i
$58$	62.4884	+	233.210i	0.141468	+	0.527965i
$59$	248.925	−	431.152i	0.549277	−	0.951376i	−0.449047	−	0.893508i	$-0.648237\pi$
$59$	248.925	−	431.152i	0.549277	−	0.951376i	0.998324	−	0.0578676i	$-0.0184301\pi$
$60$		0			0
$61$	36.3039	+	62.8801i	0.0762006	+	0.131983i	0.901608	−	0.432555i	$-0.142388\pi$
$61$	36.3039	+	62.8801i	0.0762006	+	0.131983i	−0.825407	+	0.564538i	$0.809054\pi$
$62$	524.950	−	524.950i	1.07530	−	1.07530i
$63$	100.979	−	60.9764i	0.201939	−	0.121941i
$64$			1889.88i			3.69118i
$65$		0			0
$66$	23.4132	−	192.431i	0.0436662	−	0.358887i
$67$	−178.215	+	47.7525i	−0.324961	+	0.0870730i	−0.417612	−	0.908626i	$-0.637133\pi$
$67$	−178.215	+	47.7525i	−0.324961	+	0.0870730i	0.0926506	+	0.995699i	$0.470466\pi$
$68$	1075.11	−	288.076i	1.91730	−	0.513740i
$69$	33.0742	−	271.833i	0.0577053	−	0.474273i
$70$		0			0
$71$		−	563.835i		−	0.942464i	−0.882009	−	0.471232i	$-0.843809\pi$
$71$		−	563.835i		−	0.942464i	0.882009	−	0.471232i	$-0.156191\pi$
$72$	−40.0503	−	2038.16i	−0.0655552	−	3.33611i
$73$	−84.7460	+	84.7460i	−0.135874	+	0.135874i	−0.771772	−	0.635899i	$-0.780630\pi$
$73$	−84.7460	+	84.7460i	−0.135874	+	0.135874i	0.635899	+	0.771772i	$0.280630\pi$
$74$	−901.044	−	1560.65i	−1.41546	−	2.45165i
$75$		0			0
$76$	653.054	−	1131.12i	0.985663	−	1.70722i
$77$	−7.72441	−	28.8279i	−0.0114322	−	0.0426655i
$78$	−665.935	−	268.206i	−0.966697	−	0.389338i
$79$	186.138	−	107.467i	0.265091	−	0.153050i	−0.361564	−	0.932347i	$-0.617757\pi$
$79$	186.138	−	107.467i	0.265091	−	0.153050i	0.626655	+	0.779297i	$0.284424\pi$
$80$		0			0
$81$	28.6389	+	728.437i	0.0392852	+	0.999228i
$82$	1496.82	+	1496.82i	2.01580	+	2.01580i
$83$	249.226	−	930.125i	0.329592	−	1.23005i	−0.580022	−	0.814601i	$-0.696956\pi$
$83$	249.226	−	930.125i	0.329592	−	1.23005i	0.909614	−	0.415454i	$-0.136377\pi$
$84$	−194.095	−	455.867i	−0.252113	−	0.592133i
$85$		0			0
$86$	1499.84	+	865.935i	1.88061	+	1.08577i
$87$	−227.447	+	32.2201i	−0.280286	+	0.0397052i
$88$	−498.190	−	133.490i	−0.603491	−	0.161705i
$89$	288.322			0.343394			0.171697	−	0.985150i	$-0.445075\pi$
$89$	288.322			0.343394			0.171697	+	0.985150i	$0.445075\pi$
$90$		0			0
$91$	−110.529			−0.127326
$92$	−1110.99	−	297.690i	−1.25901	−	0.337351i
$93$	435.487	+	556.139i	0.485569	+	0.620096i
$94$	−1552.05	−	896.076i	−1.70300	−	0.983226i
$95$		0			0
$96$	−3581.30	−	435.740i	−3.80744	−	0.463255i
$97$	425.658	−	1588.58i	0.445556	−	1.66284i	−0.268907	−	0.963166i	$-0.586662\pi$
$97$	425.658	−	1588.58i	0.445556	−	1.66284i	0.714463	−	0.699673i	$-0.246671\pi$
$98$	1250.84	+	1250.84i	1.28933	+	1.28933i
$99$	179.059	+	44.2274i	0.181779	+	0.0448992i
$100$		0			0
$101$	−1256.46	+	725.417i	−1.23785	+	0.714670i	−0.968653	−	0.248416i	$-0.920090\pi$
$101$	−1256.46	+	725.417i	−1.23785	+	0.714670i	−0.269192	+	0.963087i	$0.586757\pi$
$102$	202.983	+	1432.89i	0.197042	+	1.39095i
$103$	84.4689	+	315.242i	0.0808055	+	0.301570i	0.994487	−	0.104861i	$-0.0334397\pi$
$103$	84.4689	+	315.242i	0.0808055	+	0.301570i	−0.913681	+	0.406431i	$0.866773\pi$
$104$	−955.059	+	1654.21i	−0.900492	+	1.55970i
$105$		0			0
$106$	166.508	+	288.400i	0.152573	+	0.264263i
$107$	−1233.98	+	1233.98i	−1.11489	+	1.11489i	−0.122409	+	0.992480i	$0.539062\pi$
$107$	−1233.98	+	1233.98i	−1.11489	+	1.11489i	−0.992480	+	0.122409i	$0.960938\pi$
$108$	3046.24	+	310.038i	2.71411	+	0.276236i
$109$			577.196i			0.507205i	0.967308	+	0.253603i	$0.0816156\pi$
$109$			577.196i			0.507205i	−0.967308	+	0.253603i	$0.918384\pi$
$110$		0			0
$111$	1577.58	−	671.686i	1.34898	−	0.574357i
$112$	−1003.25	+	268.821i	−0.846417	+	0.226797i
$113$	−1833.26	+	491.221i	−1.52618	+	0.408940i	−0.921772	−	0.387732i	$-0.873259\pi$
$113$	−1833.26	+	491.221i	−1.52618	+	0.408940i	−0.604412	+	0.796672i	$0.706592\pi$
$114$	1357.38	+	1020.53i	1.11518	+	0.838433i
$115$		0			0
$116$			964.869i			0.772292i
$117$	329.847	−	598.152i	0.260636	−	0.472642i
$118$	1922.54	−	1922.54i	1.49987	−	1.49987i
$119$	111.404	+	192.958i	0.0858185	+	0.148642i
$120$		0			0
$121$	−642.168	+	1112.27i	−0.482470	+	0.835663i
$122$	102.629	+	383.017i	0.0761606	+	0.284235i
$123$	−1585.75	+	1241.73i	−1.16245	+	0.910265i
$124$	2569.38	−	1483.43i	1.86078	−	1.07432i
$125$		0			0
$126$	618.869	−	178.928i	0.437565	−	0.126510i
$127$	−1405.14	−	1405.14i	−0.981780	−	0.981780i	0.0180574	−	0.999837i	$-0.494252\pi$
$127$	−1405.14	−	1405.14i	−0.981780	−	0.981780i	−0.999837	+	0.0180574i	$0.994252\pi$
$128$	−1233.71	+	4604.25i	−0.851916	+	3.17939i
$129$	−990.231	+	1317.09i	−0.675853	+	0.898937i
$130$		0			0
$131$	−1336.30	−	771.513i	−0.891244	−	0.514560i	−0.0168950	−	0.999857i	$-0.505378\pi$
$131$	−1336.30	−	771.513i	−0.891244	−	0.514560i	−0.874349	+	0.485297i	$0.838711\pi$
$132$	289.417	−	718.602i	0.190837	−	0.473835i
$133$	252.548	+	67.6700i	0.164652	+	0.0441183i
$134$	−1007.61			−0.649581
$135$		0			0
$136$	3850.47			2.42776
$137$	−119.427	−	32.0003i	−0.0744767	−	0.0199560i	0.221388	−	0.975186i	$-0.428941\pi$
$137$	−119.427	−	32.0003i	−0.0744767	−	0.0199560i	−0.295865	+	0.955230i	$0.595608\pi$
$138$	558.700	−	1387.21i	0.344635	−	0.855704i
$139$	−308.354	−	178.028i	−0.188160	−	0.108634i	0.402961	−	0.915217i	$-0.367981\pi$
$139$	−308.354	−	178.028i	−0.188160	−	0.108634i	−0.591121	+	0.806583i	$0.701314\pi$
$140$		0			0
$141$	1024.70	−	1362.93i	0.612022	−	0.814038i
$142$	796.965	−	2974.32i	0.470985	−	1.75774i
$143$	−122.202	−	122.202i	−0.0714619	−	0.0714619i
$144$	1539.18	−	6231.54i	0.890729	−	3.60621i
$145$		0			0
$146$	−566.834	+	327.262i	−0.321312	+	0.185509i
$147$	−1325.16	+	1037.67i	−0.743520	+	0.582217i
$148$	−1863.96	−	6956.41i	−1.03525	−	3.86360i
$149$	−601.701	+	1042.18i	−0.330827	+	0.573009i	−0.982674	−	0.185341i	$-0.940661\pi$
$149$	−601.701	+	1042.18i	−0.330827	+	0.573009i	0.651847	+	0.758350i	$0.273994\pi$
$150$		0			0
$151$	−820.064	−	1420.39i	−0.441959	−	0.765496i	0.555876	−	0.831265i	$-0.312383\pi$
$151$	−820.064	−	1420.39i	−0.441959	−	0.765496i	−0.997835	+	0.0657697i	$0.979050\pi$
$152$	3194.97	−	3194.97i	1.70491	−	1.70491i
$153$	−1376.69	+	27.0521i	−0.727441	+	0.0142944i
$154$		−	162.990i		−	0.0852862i
$155$		0			0
$156$	−2293.22	−	1724.13i	−1.17695	−	0.884876i
$157$	3385.35	−	907.102i	1.72089	−	0.461112i	0.742842	−	0.669467i	$-0.233478\pi$
$157$	3385.35	−	907.102i	1.72089	−	0.461112i	0.978053	+	0.208355i	$0.0668109\pi$
$158$	1133.81	−	303.803i	0.570892	−	0.152970i
$159$	−291.528	+	124.124i	−0.145407	+	0.0619098i
$160$		0			0
$161$		−	230.244i		−	0.112707i
$162$	−878.551	+	3883.09i	−0.426083	+	1.88324i
$163$	−1206.55	+	1206.55i	−0.579781	+	0.579781i	−0.934843	−	0.355062i	$-0.884460\pi$
$163$	−1206.55	+	1206.55i	−0.579781	+	0.579781i	0.355062	+	0.934843i	$0.384460\pi$
$164$	4229.79	+	7326.20i	2.01397	+	3.48830i
$165$		0			0
$166$	2629.41	−	4554.27i	1.22941	−	2.12940i
$167$	−88.3316	−	329.658i	−0.0409299	−	0.152753i	0.942437	−	0.334385i	$-0.108529\pi$
$167$	−88.3316	−	329.658i	−0.0409299	−	0.152753i	−0.983367	+	0.181632i	$0.941862\pi$
$168$	−240.408	−	1697.08i	−0.110404	−	0.779361i
$169$	1348.37	−	778.483i	0.613734	−	0.354339i
$170$		0			0
$171$	−1119.87	+	1164.77i	−0.500812	+	0.520889i
$172$	4894.02	+	4894.02i	2.16957	+	2.16957i
$173$	−192.001	+	716.558i	−0.0843790	+	0.314907i	−0.995196	−	0.0979039i	$-0.968786\pi$
$173$	−192.001	+	716.558i	−0.0843790	+	0.314907i	0.910817	+	0.412811i	$0.135453\pi$
$174$	−1245.36	−	151.524i	−0.542588	−	0.0660172i
$175$		0			0
$176$	−1406.42	−	811.995i	−0.602344	−	0.347764i
$177$	1594.90	+	2036.76i	0.677287	+	0.864930i
$178$	1520.94	+	407.535i	0.640445	+	0.171607i
$179$	−2527.65			−1.05545			−0.527725	−	0.849416i	$-0.676955\pi$
$179$	−2527.65			−1.05545			−0.527725	+	0.849416i	$0.676955\pi$
$180$		0			0
$181$	−2223.82			−0.913232			−0.456616	−	0.889664i	$-0.650939\pi$
$181$	−2223.82			−0.913232			−0.456616	+	0.889664i	$0.650939\pi$
$182$	−583.059	−	156.230i	−0.237468	−	0.0636294i
$183$	−373.551	+	52.9172i	−0.150895	+	0.0213757i
$184$	−3445.89	−	1989.48i	−1.38062	−	0.797101i
$185$		0			0
$186$	1511.17	+	3549.26i	0.595723	+	1.39916i
$187$	−90.1661	+	336.505i	−0.0352599	+	0.131592i
$188$	−5064.37	−	5064.37i	−1.96466	−	1.96466i
$189$	97.8781	+	605.081i	0.0376698	+	0.232874i
$190$		0			0
$191$	−2292.92	+	1323.82i	−0.868639	+	0.501509i	−0.866896	−	0.498490i	$-0.833888\pi$
$191$	−2292.92	+	1323.82i	−0.868639	+	0.501509i	−0.00174321	+	0.999998i	$0.500555\pi$
$192$	−9109.09	−	3668.69i	−3.42392	−	1.37898i
$193$	265.955	+	992.559i	0.0991911	+	0.370186i	0.997622	−	0.0689296i	$-0.0219584\pi$
$193$	265.955	+	992.559i	0.0991911	+	0.370186i	−0.898430	+	0.439116i	$0.855292\pi$
$194$	4490.81	−	7778.32i	1.66197	−	2.87861i
$195$		0			0
$196$	3534.71	+	6122.29i	1.28816	+	2.23116i
$197$	−1735.07	+	1735.07i	−0.627507	+	0.627507i	−0.947440	−	0.319933i	$-0.896340\pi$
$197$	−1735.07	+	1735.07i	−0.627507	+	0.627507i	0.319933	+	0.947440i	$0.396340\pi$
$198$	882.050	+	486.401i	0.316589	+	0.174581i
$199$		−	764.080i		−	0.272182i	−0.990696	−	0.136091i	$-0.956546\pi$
$199$		−	764.080i		−	0.272182i	0.990696	−	0.136091i	$-0.0434539\pi$
$200$		0			0
$201$	115.792	−	951.679i	0.0406334	−	0.333961i
$202$	−7653.36	+	2050.71i	−2.66579	+	0.714295i
$203$	−186.566	+	49.9902i	−0.0645043	+	0.0172839i
$204$	−698.536	+	5741.19i	−0.239742	+	1.97041i
$205$		0			0
$206$			1782.34i			0.602824i
$207$	1246.01	+	687.105i	0.418375	+	0.230710i
$208$	−4252.82	+	4252.82i	−1.41769	+	1.41769i
$209$	204.402	+	354.035i	0.0676497	+	0.117173i
$210$		0			0
$211$	1529.60	−	2649.34i	0.499061	−	0.864398i	−0.500939	−	0.865483i	$-0.667012\pi$
$211$	1529.60	−	2649.34i	0.499061	−	0.864398i	0.999999	+	0.00108439i	$0.000345174\pi$
$212$	344.450	+	1285.51i	0.111589	+	0.416457i
$213$	2717.64	+	1094.53i	0.874224	+	0.352094i
$214$	−8253.61	+	4765.22i	−2.63647	+	1.52217i
$215$		0			0
$216$	9901.53	+	3763.49i	3.11904	+	1.18552i
$217$	419.956	+	419.956i	0.131375	+	0.131375i
$218$	−815.851	+	3044.80i	−0.253470	+	0.945962i
$219$	−243.958	−	572.980i	−0.0752747	−	0.176796i
$220$		0			0
$221$	1117.34	+	645.099i	0.340093	+	0.196353i
$222$	9271.36	−	1313.38i	2.80294	−	0.397064i
$223$	4196.27	+	1124.39i	1.26010	+	0.337644i	0.826231	−	0.563331i	$-0.190480\pi$
$223$	4196.27	+	1124.39i	1.26010	+	0.337644i	0.433872	+	0.900975i	$0.357147\pi$
$224$	−3033.37			−0.904803
$225$		0			0
$226$	−10365.1			−3.05077
$227$	−2591.73	−	694.451i	−0.757793	−	0.203050i	−0.140821	−	0.990035i	$-0.544974\pi$
$227$	−2591.73	−	694.451i	−0.757793	−	0.203050i	−0.616972	+	0.786985i	$0.711641\pi$
$228$	4184.20	+	5343.43i	1.21537	+	1.55209i
$229$	4176.87	+	2411.52i	1.20531	+	0.695884i	0.961731	−	0.273997i	$-0.0883459\pi$
$229$	4176.87	+	2411.52i	1.20531	+	0.695884i	0.243577	+	0.969882i	$0.421679\pi$
$230$		0			0
$231$	153.943	+	18.7304i	0.0438472	+	0.00533493i
$232$	−863.908	+	3224.15i	−0.244475	+	0.912395i
$233$	−1004.66	−	1004.66i	−0.282479	−	0.282479i	0.551618	−	0.834097i	$-0.314011\pi$
$233$	−1004.66	−	1004.66i	−0.282479	−	0.282479i	−0.834097	+	0.551618i	$0.814011\pi$
$234$	2585.46	−	2689.11i	0.722295	−	0.751250i
$235$		0			0
$236$	9409.92	−	5432.82i	2.59548	−	1.49850i
$237$	156.646	+	1105.79i	0.0429335	+	0.303075i
$238$	314.933	+	1175.35i	0.0857735	+	0.320111i
$239$	−3310.25	+	5733.51i	−0.895908	+	1.55176i	−0.0632311	+	0.997999i	$0.520141\pi$
$239$	−3310.25	+	5733.51i	−0.895908	+	1.55176i	−0.832677	+	0.553759i	$0.813193\pi$
$240$		0			0
$241$	−1226.12	−	2123.69i	−0.327722	−	0.567631i	0.654337	−	0.756203i	$-0.272948\pi$
$241$	−1226.12	−	2123.69i	−0.327722	−	0.567631i	−0.982059	+	0.188571i	$0.939614\pi$
$242$	−4959.69	+	4959.69i	−1.31744	+	1.31744i
$243$	−3566.60	−	1276.02i	−0.941555	−	0.336860i
$244$			1584.67i			0.415771i
$245$		0			0
$246$	−10120.2	+	4308.88i	−2.62293	+	1.11676i
$247$	1462.41	−	391.851i	0.376723	−	0.100943i
$248$	9913.90	−	2656.42i	2.53844	−	0.680173i
$249$	3999.33	+	3006.83i	1.01786	+	0.765262i
$250$		0			0
$251$			6563.11i			1.65044i	0.564814	+	0.825219i	$0.308948\pi$
$251$			6563.11i			1.65044i	−0.564814	+	0.825219i	$0.691052\pi$
$252$	2574.02	−	50.5801i	0.643446	−	0.0126438i
$253$	254.559	−	254.559i	0.0632569	−	0.0632569i
$254$	−5426.20	−	9398.45i	−1.34043	−	2.32170i
$255$		0			0
$256$	−5456.43	+	9450.81i	−1.33214	+	2.30733i
$257$	−807.694	−	3014.35i	−0.196041	−	0.731635i	−0.991995	−	0.126278i	$-0.959697\pi$
$257$	−807.694	−	3014.35i	−0.196041	−	0.731635i	0.795954	−	0.605357i	$-0.206970\pi$
$258$	−7085.28	+	5548.16i	−1.70973	+	1.33881i
$259$	1248.51	−	720.829i	0.299532	−	0.172935i
$260$		0			0
$261$	286.227	−	1158.82i	0.0678813	−	0.274825i
$262$	−5958.66	−	5958.66i	−1.40507	−	1.40507i
$263$	1215.51	−	4536.33i	0.284986	−	1.06358i	−0.663863	−	0.747854i	$-0.731084\pi$
$263$	1215.51	−	4536.33i	0.284986	−	1.06358i	0.948849	−	0.315729i	$-0.102249\pi$
$264$	1610.51	−	2142.10i	0.375454	−	0.499384i
$265$		0			0
$266$	1236.58	+	713.938i	0.285035	+	0.164565i
$267$	−559.698	+	1389.69i	−0.128288	+	0.318530i
$268$	−3889.55	−	1042.20i	−0.886538	−	0.237547i
$269$	−4107.03			−0.930893			−0.465446	−	0.885076i	$-0.654106\pi$
$269$	−4107.03			−0.930893			−0.465446	+	0.885076i	$0.654106\pi$
$270$		0			0
$271$	−358.244			−0.0803017			−0.0401508	−	0.999194i	$-0.512784\pi$
$271$	−358.244			−0.0803017			−0.0401508	+	0.999194i	$0.512784\pi$
$272$	11710.9	+	3137.92i	2.61057	+	0.699501i
$273$	214.563	−	532.743i	0.0475675	−	0.118107i
$274$	−584.762	−	337.612i	−0.128930	−	0.0744376i
$275$		0			0
$276$	3591.53	−	4777.02i	0.783278	−	1.04182i
$277$	−433.653	+	1618.41i	−0.0940637	+	0.351051i	−0.996876	−	0.0789846i	$-0.974832\pi$
$277$	−433.653	+	1618.41i	−0.0940637	+	0.351051i	0.902812	+	0.430035i	$0.141499\pi$
$278$	−1374.97	−	1374.97i	−0.296638	−	0.296638i
$279$	−3525.92	+	1019.42i	−0.756601	+	0.218750i
$280$		0			0
$281$	3329.19	−	1922.11i	0.706771	−	0.408054i	−0.103094	−	0.994672i	$-0.532874\pi$
$281$	3329.19	−	1922.11i	0.706771	−	0.408054i	0.809864	+	0.586617i	$0.199541\pi$
$282$	7331.90	−	5741.27i	1.54826	−	1.21237i
$283$	−293.688	−	1096.06i	−0.0616888	−	0.230226i	0.928198	−	0.372087i	$-0.121358\pi$
$283$	−293.688	−	1096.06i	−0.0616888	−	0.230226i	−0.989886	+	0.141862i	$0.954691\pi$
$284$	6152.88	−	10657.1i	1.28559	−	2.22670i
$285$		0			0
$286$	−471.905	−	817.363i	−0.0975676	−	0.168992i
$287$	−1197.44	+	1197.44i	−0.246281	+	0.246281i
$288$	9052.33	−	16415.7i	1.85213	−	3.35869i
$289$			2312.18i			0.470626i
$290$		0			0
$291$	6830.51	+	5135.42i	1.37599	+	1.03451i
$292$	−2526.59	+	676.997i	−0.506360	+	0.135679i
$293$	−434.952	+	116.545i	−0.0867241	+	0.0232377i	−0.301920	−	0.953333i	$-0.597628\pi$
$293$	−434.952	+	116.545i	−0.0867241	+	0.0232377i	0.215196	+	0.976571i	$0.430961\pi$
$294$	−8457.14	+	3600.80i	−1.67766	+	0.714296i
$295$		0			0
$296$		−	24914.0i		−	4.89223i
$297$	−560.767	+	777.196i	−0.109559	+	0.151843i
$298$	−4647.15	+	4647.15i	−0.903362	+	0.903362i
$299$	−666.627	−	1154.63i	−0.128937	−	0.223325i
$300$		0			0
$301$	−692.742	+	1199.86i	−0.132654	+	0.229764i
$302$	−2318.27	−	8651.91i	−0.441727	−	1.64855i
$303$	−1057.38	−	7464.23i	−0.200479	−	1.41521i
$304$	12321.0	−	7113.51i	2.32452	−	1.34206i
$305$		0			0
$306$	−7300.46	−	1803.20i	−1.36385	−	0.336870i
$307$	−1217.81	−	1217.81i	−0.226398	−	0.226398i	0.584788	−	0.811186i	$-0.301178\pi$
$307$	−1217.81	−	1217.81i	−0.226398	−	0.226398i	−0.811186	+	0.584788i	$0.801178\pi$
$308$	168.586	−	629.171i	0.0311886	−	0.116397i
$309$	−1683.42	−	204.823i	−0.309923	−	0.0377086i
$310$		0			0
$311$	−4660.61	−	2690.81i	−0.849772	−	0.490616i	0.0108020	−	0.999942i	$-0.496562\pi$
$311$	−4660.61	−	2690.81i	−0.849772	−	0.490616i	−0.860574	+	0.509326i	$0.829895\pi$
$312$	−6119.18	−	7814.50i	−1.11035	−	1.41798i
$313$	4661.02	+	1248.92i	0.841714	+	0.225537i	0.653817	−	0.756652i	$-0.273166\pi$
$313$	4661.02	+	1248.92i	0.841714	+	0.225537i	0.187896	+	0.982189i	$0.439833\pi$
$314$	19140.4			3.43998
$315$		0			0
$316$	4690.95			0.835084
$317$	3721.99	+	997.303i	0.659456	+	0.176701i	0.573001	−	0.819555i	$-0.305779\pi$
$317$	3721.99	+	997.303i	0.659456	+	0.176701i	0.0864556	+	0.996256i	$0.472446\pi$
$318$	−1713.30	+	242.705i	−0.302129	+	0.0427995i
$319$	−261.538	−	150.999i	−0.0459039	−	0.0265026i
$320$		0			0
$321$	−3552.25	−	8343.11i	−0.617654	−	1.45068i
$322$	325.443	−	1214.57i	0.0563238	−	0.210203i
$323$	−2158.06	−	2158.06i	−0.371757	−	0.371757i
$324$	−7407.80	+	14080.8i	−1.27020	+	2.41440i
$325$		0			0
$326$	−8070.15	+	4659.30i	−1.37106	+	0.791579i
$327$	−2782.04	−	1120.47i	−0.470481	−	0.189486i
$328$	7574.39	+	28268.0i	1.27508	+	4.75865i
$329$	716.854	−	1241.63i	0.120126	−	0.208064i
$330$		0			0
$331$	2384.56	+	4130.18i	0.395974	+	0.685847i	0.993225	−	0.116207i	$-0.0370737\pi$
$331$	2384.56	+	4130.18i	0.395974	+	0.685847i	−0.597251	+	0.802054i	$0.703740\pi$
$332$	14860.7	−	14860.7i	2.45658	−	2.45658i
$333$	175.038	+	8907.69i	0.0288049	+	1.46588i
$334$		−	1863.85i		−	0.305345i
$335$		0			0
$336$	651.846	−	5357.45i	0.105837	−	0.869860i
$337$	9743.49	−	2610.76i	1.57496	−	0.422009i	0.637599	−	0.770368i	$-0.279928\pi$
$337$	9743.49	−	2610.76i	1.57496	−	0.422009i	0.937361	+	0.348359i	$0.113261\pi$
$338$	8213.23	−	2200.73i	1.32172	−	0.354153i
$339$	1191.13	−	9789.75i	0.190835	−	1.56846i
$340$		0			0
$341$			928.612i			0.147470i
$342$	−7553.86	+	4561.41i	−1.19435	+	0.721207i
$343$	−2060.30	+	2060.30i	−0.324332	+	0.324332i
$344$	11971.6	+	20735.5i	1.87636	+	3.24995i
$345$		0			0
$346$	−2025.67	+	3508.56i	−0.314742	+	0.545148i
$347$	2600.02	+	9703.39i	0.402237	+	1.50117i	0.809095	+	0.587677i	$0.199958\pi$
$347$	2600.02	+	9703.39i	0.402237	+	1.50117i	−0.406858	+	0.913491i	$0.633376\pi$
$348$	−4650.59	−	1873.03i	−0.716373	−	0.288520i
$349$	5945.55	−	3432.67i	0.911914	−	0.526494i	0.0308677	−	0.999523i	$-0.490173\pi$
$349$	5945.55	−	3432.67i	0.911914	−	0.526494i	0.881047	+	0.473030i	$0.156840\pi$
$350$		0			0
$351$	2242.74	+	2750.98i	0.341050	+	0.418338i
$352$	−3353.72	−	3353.72i	−0.507823	−	0.507823i
$353$	−2316.48	+	8645.22i	−0.349274	+	1.30351i	0.538265	+	0.842776i	$0.319080\pi$
$353$	−2316.48	+	8645.22i	−0.349274	+	1.30351i	−0.887539	+	0.460733i	$0.847587\pi$
$354$	5534.41	+	12998.6i	0.830933	+	1.95160i
$355$		0			0
$356$	5449.59	+	3146.32i	0.811314	+	0.468412i
$357$	−1146.30	+	162.385i	−0.169940	+	0.0240737i
$358$	−13333.7	−	3572.76i	−1.96846	−	0.527448i
$359$	2589.44			0.380684			0.190342	−	0.981718i	$-0.439040\pi$
$359$	2589.44			0.380684			0.190342	+	0.981718i	$0.439040\pi$
$360$		0			0
$361$	3277.66			0.477862
$362$	−11731.0	−	3143.30i	−1.70322	−	0.456376i
$363$	−4114.45	−	5254.36i	−0.594911	−	0.759731i
$364$	−2089.13	−	1206.16i	−0.300824	−	0.173681i
$365$		0			0
$366$	−2045.34	−	248.858i	−0.292108	−	0.0355410i
$367$	2048.55	−	7645.28i	0.291371	−	1.08741i	−0.652686	−	0.757629i	$-0.726358\pi$
$367$	2048.55	−	7645.28i	0.291371	−	1.08741i	0.944057	−	0.329783i	$-0.106976\pi$
$368$	−8859.06	−	8859.06i	−1.25492	−	1.25492i
$369$	−2906.73	−	10053.6i	−0.410076	−	1.41835i
$370$		0			0
$371$	−230.718	+	133.205i	−0.0322865	+	0.0186406i
$372$	2162.28	+	15263.9i	0.301369	+	2.12741i
$373$	−1565.16	−	5841.25i	−0.217268	−	0.810854i	−0.985356	−	0.170510i	$-0.945458\pi$
$373$	−1565.16	−	5841.25i	−0.217268	−	0.810854i	0.768088	−	0.640344i	$-0.221208\pi$
$374$	−951.279	+	1647.66i	−0.131523	+	0.227804i
$375$		0			0
$376$	−12388.3	−	21457.2i	−1.69915	−	2.94301i
$377$	−790.858	+	790.858i	−0.108040	+	0.108040i
$378$	−338.943	+	3330.24i	−0.0461200	+	0.453146i
$379$		−	13501.8i		−	1.82992i	−0.403542	−	0.914961i	$-0.632221\pi$
$379$		−	13501.8i		−	1.82992i	0.403542	−	0.914961i	$-0.367779\pi$
$380$		0			0
$381$	9500.36	−	4044.97i	1.27748	−	0.543911i
$382$	−13966.7	+	3742.36i	−1.87067	+	0.501246i
$383$	9329.14	−	2499.74i	1.24464	−	0.333500i	0.424376	−	0.905486i	$-0.360494\pi$
$383$	9329.14	−	2499.74i	1.24464	−	0.333500i	0.820263	+	0.571986i	$0.193827\pi$
$384$	−19797.2	−	14884.3i	−2.63092	−	1.97802i
$385$		0			0
$386$			5611.82i			0.739984i
$387$	−4425.98	−	7329.59i	−0.581358	−	0.962750i
$388$	25380.8	−	25380.8i	3.32091	−	3.32091i
$389$	−2925.52	−	5067.16i	−0.381311	−	0.660450i	0.609939	−	0.792448i	$-0.291194\pi$
$389$	−2925.52	−	5067.16i	−0.381311	−	0.660450i	−0.991250	+	0.131998i	$0.957861\pi$
$390$		0			0
$391$	−1343.81	+	2327.54i	−0.173809	+	0.301045i
$392$	6329.69	+	23622.7i	0.815555	+	3.04369i
$393$	6312.69	−	4943.18i	0.810262	−	0.634479i
$394$	−11605.2	+	6700.29i	−1.48392	+	0.856741i
$395$		0			0
$396$	2901.78	+	2789.94i	0.368232	+	0.354039i
$397$	−4637.81	−	4637.81i	−0.586309	−	0.586309i	0.350321	−	0.936630i	$-0.386073\pi$
$397$	−4637.81	−	4637.81i	−0.586309	−	0.586309i	−0.936630	+	0.350321i	$0.886073\pi$
$398$	1080.01	−	4030.64i	0.136020	−	0.507632i
$399$	−816.416	+	1085.90i	−0.102436	+	0.136248i
$400$		0			0
$401$	−5746.08	−	3317.50i	−0.715576	−	0.413138i	0.0975465	−	0.995231i	$-0.468901\pi$
$401$	−5746.08	−	3317.50i	−0.715576	−	0.413138i	−0.813122	+	0.582093i	$0.802234\pi$
$402$	1955.99	−	4856.58i	0.242676	−	0.602548i
$403$	3321.90	+	890.102i	0.410610	+	0.110023i
$404$	−31664.6			−3.89944
$405$		0			0
$406$	−1054.82			−0.128941
$407$	2177.32	+	583.410i	0.265173	+	0.0710530i
$408$	−7474.63	+	18559.0i	−0.906983	+	2.25197i
$409$	4763.16	+	2750.01i	0.575851	+	0.332468i	0.759483	−	0.650527i	$-0.225452\pi$
$409$	4763.16	+	2750.01i	0.575851	+	0.332468i	−0.183632	+	0.982995i	$0.558785\pi$
$410$		0			0
$411$	386.073	−	513.507i	0.0463347	−	0.0616288i
$412$	−1843.54	+	6880.19i	−0.220448	+	0.822725i
$413$	1538.02	+	1538.02i	0.183247	+	0.183247i
$414$	5601.68	+	5385.78i	0.664995	+	0.639364i
$415$		0			0
$416$	−15211.8	+	8782.55i	−1.79284	+	1.03510i
$417$	1456.67	−	1140.65i	0.171063	−	0.133952i
$418$	577.833	+	2156.50i	0.0676142	+	0.252340i
$419$	393.101	−	680.870i	0.0458335	−	0.0793859i	−0.842199	−	0.539167i	$-0.818739\pi$
$419$	393.101	−	680.870i	0.0458335	−	0.0793859i	0.888032	+	0.459782i	$0.152072\pi$
$420$		0			0
$421$	7854.61	+	13604.6i	0.909289	+	1.57493i	0.815055	+	0.579384i	$0.196707\pi$
$421$	7854.61	+	13604.6i	0.909289	+	1.57493i	0.0942338	+	0.995550i	$0.469960\pi$
$422$	11813.6	−	11813.6i	1.36274	−	1.36274i
$423$	4580.04	+	7584.72i	0.526452	+	0.871824i
$424$			4603.98i			0.527332i
$425$		0			0
$426$	12788.9	+	9615.13i	1.45451	+	1.09356i
$427$	−306.410	+	82.1024i	−0.0347265	+	0.00930495i
$428$	−36789.3	+	9857.68i	−4.15486	+	1.11329i
$429$	826.226	−	351.783i	0.0929851	−	0.0395903i
$430$		0			0
$431$		−	1343.42i		−	0.150140i	−0.997178	−	0.0750702i	$-0.976082\pi$
$431$		−	1343.42i		−	0.150140i	0.997178	−	0.0750702i	$-0.0239181\pi$
$432$	27047.6	+	19515.5i	3.01234	+	2.17348i
$433$	4364.85	−	4364.85i	0.484437	−	0.484437i	−0.422108	−	0.906545i	$-0.638710\pi$
$433$	4364.85	−	4364.85i	0.484437	−	0.484437i	0.906545	+	0.422108i	$0.138710\pi$
$434$	1621.73	+	2808.93i	0.179368	+	0.310675i
$435$		0			0
$436$	−6298.68	+	10909.6i	−0.691863	+	1.19834i
$437$	816.264	+	3046.34i	0.0893529	+	0.333470i
$438$	−477.023	−	3367.38i	−0.0520389	−	0.367351i
$439$	−6104.30	+	3524.32i	−0.663649	+	0.383158i	−0.793666	−	0.608354i	$-0.791830\pi$
$439$	−6104.30	+	3524.32i	−0.663649	+	0.383158i	0.130017	+	0.991512i	$0.458497\pi$
$440$		0			0
$441$	−2429.06	−	8401.53i	−0.262290	−	0.907195i
$442$	4982.32	+	4982.32i	0.536165	+	0.536165i
$443$	1521.13	−	5676.94i	0.163140	−	0.608848i	−0.835130	−	0.550053i	$-0.814608\pi$
$443$	1521.13	−	5676.94i	0.163140	−	0.608848i	0.998270	−	0.0587949i	$-0.0187258\pi$
$444$	37147.7	+	4519.80i	3.97061	+	0.483109i
$445$		0			0
$446$	20546.7	+	11862.6i	2.18142	+	1.25944i
$447$	−3855.17	−	4923.25i	−0.407927	−	0.520943i
$448$	−7975.46	−	2137.02i	−0.841083	−	0.225367i
$449$	9280.82			0.975477			0.487738	−	0.872990i	$-0.337822\pi$
$449$	9280.82			0.975477			0.487738	+	0.872990i	$0.337822\pi$
$450$		0			0
$451$	−2647.80			−0.276452
$452$	−40011.1	−	10720.9i	−4.16364	−	1.11564i
$453$	8438.11	−	1195.34i	0.875181	−	0.123978i
$454$	−12690.2	−	7326.67i	−1.31185	−	0.757395i
$455$		0			0
$456$	9197.34	+	21601.7i	0.944529	+	2.21840i
$457$	−790.554	+	2950.39i	−0.0809203	+	0.301999i	−0.994510	−	0.104638i	$-0.966632\pi$
$457$	−790.554	+	2950.39i	−0.0809203	+	0.301999i	0.913590	+	0.406636i	$0.133298\pi$
$458$	18625.0	+	18625.0i	1.90019	+	1.90019i
$459$	2542.07	−	6688.03i	0.258504	−	0.680110i
$460$		0			0
$461$	6729.62	−	3885.35i	0.679890	−	0.392535i	−0.119923	−	0.992783i	$-0.538265\pi$
$461$	6729.62	−	3885.35i	0.679890	−	0.392535i	0.799814	+	0.600248i	$0.204932\pi$
$462$	785.597	+	316.400i	0.0791110	+	0.0318620i
$463$	−990.276	−	3695.76i	−0.0993997	−	0.370965i	0.898250	−	0.439485i	$-0.144839\pi$
$463$	−990.276	−	3695.76i	−0.0993997	−	0.370965i	−0.997650	+	0.0685201i	$0.978172\pi$
$464$	−5255.00	+	9101.94i	−0.525770	+	0.910661i
$465$		0			0
$466$	−3879.68	−	6719.80i	−0.385671	−	0.668002i
$467$	−3050.23	+	3050.23i	−0.302243	+	0.302243i	−0.841891	−	0.539648i	$-0.818557\pi$
$467$	−3050.23	+	3050.23i	−0.302243	+	0.302243i	0.539648	+	0.841891i	$0.318557\pi$
$468$	12761.8	−	7706.24i	1.26050	−	0.761156i
$469$		−	806.077i		−	0.0793628i
$470$		0			0
$471$	−2199.57	+	18078.0i	−0.215182	+	1.76856i
$472$	36308.0	−	9728.69i	3.54070	−	0.948727i
$473$	−2092.48	+	560.678i	−0.203409	+	0.0545032i
$474$	−736.671	+	6054.62i	−0.0713849	+	0.586704i
$475$		0			0
$476$			4862.81i			0.468249i
$477$	−32.3460	−	1646.09i	−0.00310487	−	0.158007i
$478$	−25566.2	+	25566.2i	−2.44638	+	2.44638i
$479$	1094.98	+	1896.57i	0.104449	+	0.180911i	0.913513	−	0.406810i	$-0.133359\pi$
$479$	1094.98	+	1896.57i	0.104449	+	0.180911i	−0.809064	+	0.587721i	$0.800025\pi$
$480$		0			0
$481$	4174.04	−	7229.65i	0.395675	−	0.685330i
$482$	−3466.16	−	12935.9i	−0.327550	−	1.22243i
$483$	1109.76	+	446.956i	0.104546	+	0.0421060i
$484$	−24275.3	+	14015.4i	−2.27980	+	1.31624i
$485$		0			0
$486$	−17010.7	−	11772.5i	−1.58770	−	1.09879i
$487$	1824.01	+	1824.01i	0.169721	+	0.169721i	0.786857	−	0.617136i	$-0.211707\pi$
$487$	1824.01	+	1824.01i	0.169721	+	0.169721i	−0.617136	+	0.786857i	$0.711707\pi$
$488$	−1418.85	+	5295.24i	−0.131616	+	0.491197i
$489$	−3473.29	−	8157.66i	−0.321201	−	0.754401i
$490$		0			0
$491$	−2339.22	−	1350.55i	−0.215005	−	0.124133i	0.388630	−	0.921394i	$-0.372948\pi$
$491$	−2339.22	−	1350.55i	−0.215005	−	0.124133i	−0.603635	+	0.797260i	$0.706282\pi$
$492$	−43522.7	+	6165.42i	−3.98812	+	0.564957i
$493$	2177.76	+	583.530i	0.198948	+	0.0533081i
$494$	8268.28			0.753052
$495$		0			0
$496$	32317.1			2.92557
$497$	2379.43	+	637.566i	0.214753	+	0.0575428i
$498$	16847.0	+	21514.4i	1.51592	+	1.93591i
$499$	14609.9	+	8435.02i	1.31068	+	0.756720i	0.982208	−	0.187795i	$-0.0601340\pi$
$499$	14609.9	+	8435.02i	1.31068	+	0.756720i	0.328469	+	0.944515i	$0.393467\pi$
$500$		0			0
$501$	1760.40	+	214.189i	0.156983	+	0.0191003i
$502$	−9276.77	+	34621.4i	−0.824786	+	3.07814i
$503$	−3851.44	−	3851.44i	−0.341406	−	0.341406i	0.515490	−	0.856896i	$-0.327610\pi$
$503$	−3851.44	−	3851.44i	−0.341406	−	0.341406i	−0.856896	+	0.515490i	$0.827610\pi$
$504$	8646.49	+	2135.67i	0.764177	+	0.188751i
$505$		0			0
$506$	1702.65	−	983.026i	0.149589	−	0.0863653i
$507$	1134.73	+	8010.26i	0.0993989	+	0.701673i
$508$	−11225.0	−	41892.3i	−0.980373	−	3.65880i
$509$	1119.01	−	1938.18i	0.0974443	−	0.168779i	−0.813182	−	0.582010i	$-0.802267\pi$
$509$	1119.01	−	1938.18i	0.0974443	−	0.168779i	0.910626	+	0.413231i	$0.135600\pi$
$510$		0			0
$511$	−261.807	−	453.463i	−0.0226647	−	0.0392564i
$512$	−15177.5	+	15177.5i	−1.31007	+	1.31007i
$513$	−3440.16	−	7658.78i	−0.296075	−	0.659149i
$514$		−	17042.8i		−	1.46250i
$515$		0			0
$516$	−33089.2	+	14088.4i	−2.82300	+	1.20195i
$517$	2165.31	−	580.193i	0.184198	−	0.0493557i
$518$	7604.96	−	2037.74i	0.645063	−	0.172844i
$519$	−3081.03	−	2316.43i	−0.260583	−	0.195915i
$520$		0			0
$521$		−	11295.2i		−	0.949810i	−0.880037	−	0.474905i	$-0.842482\pi$
$521$		−	11295.2i		−	0.949810i	0.880037	−	0.474905i	$-0.157518\pi$
$522$	3147.85	−	5708.38i	0.263942	−	0.478638i
$523$	−7883.52	+	7883.52i	−0.659125	+	0.659125i	−0.955173	−	0.296048i	$-0.904331\pi$
$523$	−7883.52	+	7883.52i	−0.659125	+	0.659125i	0.296048	+	0.955173i	$0.404331\pi$
$524$	−16838.3	−	29164.8i	−1.40379	−	2.43144i
$525$		0			0
$526$	12824.0	−	22211.7i	1.06302	−	1.84121i
$527$	−1794.29	−	6696.39i	−0.148312	−	0.553509i
$528$	6643.92	−	5202.55i	0.547613	−	0.428811i
$529$	−8131.72	+	4694.85i	−0.668342	+	0.385867i
$530$		0			0
$531$	−12913.1	+	3733.46i	−1.05533	+	0.305119i
$532$	4034.97	+	4034.97i	0.328831	+	0.328831i
$533$	−2537.99	+	9471.91i	−0.206252	+	0.769745i
$534$	−4916.77	+	6539.69i	−0.398445	+	0.529963i
$535$		0			0
$536$	−12063.9	−	6965.12i	−0.972169	−	0.561282i
$537$	4906.74	−	12183.1i	0.394304	−	0.979029i
$538$	−21665.2	−	5805.17i	−1.73616	−	0.465202i
$539$	−2212.69			−0.176822
$540$		0			0
$541$	−9200.65			−0.731177			−0.365588	−	0.930777i	$-0.619132\pi$
$541$	−9200.65			−0.731177			−0.365588	+	0.930777i	$0.619132\pi$
$542$	−1889.79	−	506.367i	−0.149766	−	0.0401298i
$543$	4316.93	−	10718.6i	0.341173	−	0.847109i
$544$	30664.4	+	17704.1i	2.41678	+	1.39533i
$545$		0			0
$546$	1884.87	−	2507.02i	0.147738	−	0.196503i
$547$	−4617.23	+	17231.7i	−0.360911	+	1.34694i	0.511969	+	0.859004i	$0.328916\pi$
$547$	−4617.23	+	17231.7i	−0.360911	+	1.34694i	−0.872880	+	0.487934i	$0.837751\pi$
$548$	−1908.09	−	1908.09i	−0.148740	−	0.148740i
$549$	470.091	−	1903.21i	0.0365446	−	0.147955i
$550$		0			0
$551$	2291.22	−	1322.83i	0.177149	−	0.102277i
$552$	16278.4	−	12746.9i	1.25517	−	0.982867i
$553$	243.040	+	907.038i	0.0186892	+	0.0697490i
$554$	−4575.16	+	7924.41i	−0.350866	+	0.607719i
$555$		0			0
$556$	−3885.48	−	6729.85i	−0.296369	−	0.513326i
$557$	9243.69	−	9243.69i	0.703174	−	0.703174i	−0.261917	−	0.965091i	$-0.584355\pi$
$557$	9243.69	−	9243.69i	0.703174	−	0.703174i	0.965091	+	0.261917i	$0.0843545\pi$
$558$	−20040.7	+	393.804i	−1.52041	+	0.0298764i
$559$			8022.80i			0.607027i
$560$		0			0
$561$	−1446.89	−	1087.82i	−0.108891	−	0.0818681i
$562$	20278.8	−	5433.68i	1.52208	−	0.407840i
$563$	−14763.8	+	3955.94i	−1.10518	+	0.296133i	−0.764874	−	0.644180i	$-0.777199\pi$
$563$	−14763.8	+	3955.94i	−1.10518	+	0.296133i	−0.340310	+	0.940313i	$0.610532\pi$
$564$	34240.9	−	14578.8i	2.55639	−	1.08843i
$565$		0			0
$566$		−	6196.99i		−	0.460210i
$567$	−3106.45	−	702.834i	−0.230085	−	0.0520569i
$568$	30102.1	−	30102.1i	2.22369	−	2.22369i
$569$	7749.24	+	13422.1i	0.570941	+	0.988898i	0.996470	+	0.0839534i	$0.0267547\pi$
$569$	7749.24	+	13422.1i	0.570941	+	0.988898i	−0.425529	+	0.904945i	$0.639912\pi$
$570$		0			0
$571$	986.984	−	1709.51i	0.0723362	−	0.125290i	−0.827589	−	0.561335i	$-0.810288\pi$
$571$	986.984	−	1709.51i	0.0723362	−	0.125290i	0.899925	+	0.436045i	$0.143621\pi$
$572$	−976.216	−	3643.29i	−0.0713595	−	0.266317i
$573$	−1929.63	−	13621.5i	−0.140683	−	0.993103i
$574$	−8009.23	+	4624.13i	−0.582402	+	0.336250i
$575$		0			0
$576$	35365.6	−	36783.4i	2.55828	−	2.66083i
$577$	2600.22	+	2600.22i	0.187606	+	0.187606i	0.794660	−	0.607055i	$-0.207649\pi$
$577$	2600.22	+	2600.22i	0.187606	+	0.187606i	−0.607055	+	0.794660i	$0.707649\pi$
$578$	−3268.21	+	12197.1i	−0.235189	+	0.877739i
$579$	−5300.34	−	644.897i	−0.380439	−	0.0462884i
$580$		0			0
$581$	3643.38	+	2103.51i	0.260160	+	0.150203i
$582$	28773.2	+	36744.8i	2.04929	+	2.61705i
$583$	−402.356	−	107.811i	−0.0285830	−	0.00765879i
$584$	−9048.84			−0.641171
$585$		0			0
$586$	−2459.17			−0.173357
$587$	20290.6	+	5436.85i	1.42672	+	0.382288i	0.887862	−	0.460110i	$-0.152190\pi$
$587$	20290.6	+	5436.85i	1.42672	+	0.382288i	0.538856	+	0.842398i	$0.318857\pi$
$588$	−36370.6	+	5152.26i	−2.55085	+	0.361353i
$589$	−7045.24	−	4067.57i	−0.492859	−	0.284552i
$590$		0			0
$591$	−4994.75	−	11731.1i	−0.347642	−	0.816502i
$592$	20303.6	−	75774.0i	1.40958	−	5.26063i
$593$	−1706.61	−	1706.61i	−0.118182	−	0.118182i	0.645542	−	0.763725i	$-0.276631\pi$
$593$	−1706.61	−	1706.61i	−0.118182	−	0.118182i	−0.763725	+	0.645542i	$0.776631\pi$
$594$	−4056.67	+	3307.20i	−0.280214	+	0.228444i
$595$		0			0
$596$	−22745.6	+	13132.2i	−1.56325	+	0.902541i
$597$	3682.81	+	1483.25i	0.252474	+	0.101684i
$598$	−1884.52	−	7033.11i	−0.128869	−	0.480945i
$599$	−6939.25	+	12019.1i	−0.473339	+	0.819847i	−0.999534	−	0.0305164i	$-0.990285\pi$
$599$	−6939.25	+	12019.1i	−0.473339	+	0.819847i	0.526195	+	0.850364i	$0.323618\pi$
$600$		0			0
$601$	11793.6	+	20427.2i	0.800454	+	1.38643i	0.919318	+	0.393516i	$0.128741\pi$
$601$	11793.6	+	20427.2i	0.800454	+	1.38643i	−0.118864	+	0.992911i	$0.537925\pi$
$602$	−5350.29	+	5350.29i	−0.362228	+	0.362228i
$603$	4362.24	+	2405.53i	0.294601	+	0.162456i
$604$		−	35795.9i		−	2.41145i
$605$		0			0
$606$	4972.63	−	40869.5i	0.333332	−	2.73962i
$607$	−25746.1	+	6898.66i	−1.72159	+	0.461298i	−0.978218	−	0.207583i	$-0.933440\pi$
$607$	−25746.1	+	6898.66i	−1.72159	+	0.461298i	−0.743370	+	0.668881i	$0.766774\pi$
$608$	40134.3	−	10754.0i	2.67708	−	0.717320i
$609$	121.218	−	996.276i	0.00806568	−	0.0662909i
$610$		0			0
$611$		−	8302.05i		−	0.549697i
$612$	−26316.0	−	14511.8i	−1.73818	−	0.958506i
$613$	−2171.14	+	2171.14i	−0.143053	+	0.143053i	−0.775006	−	0.631953i	$-0.782253\pi$
$613$	−2171.14	+	2171.14i	−0.143053	+	0.143053i	0.631953	+	0.775006i	$0.282253\pi$
$614$	−4702.80	−	8145.49i	−0.309103	−	0.535383i
$615$		0			0
$616$	1126.67	−	1951.45i	0.0736931	−	0.127640i
$617$	−250.327	−	934.234i	−0.0163335	−	0.0609576i	0.957278	−	0.289169i	$-0.0933789\pi$
$617$	−250.327	−	934.234i	−0.0163335	−	0.0609576i	−0.973612	+	0.228211i	$0.926712\pi$
$618$	−8590.76	−	3459.93i	−0.559176	−	0.225209i
$619$	−5225.86	+	3017.15i	−0.339330	+	0.195912i	−0.659976	−	0.751287i	$-0.729433\pi$
$619$	−5225.86	+	3017.15i	−0.339330	+	0.195912i	0.320646	+	0.947199i	$0.396100\pi$
$620$		0			0
$621$	−5730.58	+	4671.84i	−0.370306	+	0.301892i
$622$	−20782.0	−	20782.0i	−1.33968	−	1.33968i
$623$	−326.025	+	1216.74i	−0.0209661	+	0.0782466i
$624$	−12242.6	−	28753.9i	−0.785409	−	1.84468i
$625$		0			0
$626$	22822.3	+	13176.4i	1.45713	+	0.841272i
$627$	−2103.21	+	297.941i	−0.133962	+	0.0189770i
$628$	73885.6	+	19797.6i	4.69484	+	1.25798i
$629$	−16828.3			−1.06675
$630$		0			0
$631$	−15462.3			−0.975505			−0.487753	−	0.872982i	$-0.662183\pi$
$631$	−15462.3			−0.975505			−0.487753	+	0.872982i	$0.662183\pi$
$632$	15675.0	+	4200.10i	0.986579	+	0.264353i
$633$	9800.31	+	12515.5i	0.615367	+	0.785856i
$634$	18224.4	+	10521.8i	1.14161	+	0.659110i
$635$		0			0
$636$	−6864.69	−	835.234i	−0.427992	−	0.0520742i
$637$	−2120.92	+	7915.39i	−0.131922	+	0.492338i
$638$	−1166.22	−	1166.22i	−0.0723685	−	0.0723685i
$639$	−10551.1	+	10974.1i	−0.653201	+	0.679387i
$640$		0			0
$641$	1917.34	−	1106.98i	0.118144	−	0.0682105i	−0.439763	−	0.898114i	$-0.644938\pi$
$641$	1917.34	−	1106.98i	0.118144	−	0.0682105i	0.557908	+	0.829903i	$0.311604\pi$
$642$	−6945.88	−	49032.1i	−0.426997	−	3.01424i
$643$	−1472.27	−	5494.59i	−0.0902965	−	0.336991i	0.905968	−	0.423346i	$-0.139145\pi$
$643$	−1472.27	−	5494.59i	−0.0902965	−	0.336991i	−0.996264	+	0.0863552i	$0.972478\pi$
$644$	2512.55	−	4351.86i	0.153740	−	0.266285i
$645$		0			0
$646$	−8333.71	−	14434.4i	−0.507563	−	0.879125i
$647$	−8395.00	+	8395.00i	−0.510110	+	0.510110i	−0.914560	−	0.404450i	$-0.867463\pi$
$647$	−8395.00	+	8395.00i	−0.510110	+	0.510110i	0.404450	+	0.914560i	$0.367463\pi$
$648$	−37360.8	+	40418.8i	−2.26493	+	2.45031i
$649$			3400.88i			0.205695i
$650$		0			0
$651$	−2839.38	+	1208.93i	−0.170944	+	0.0727827i
$652$	−35971.6	+	9638.56i	−2.16067	+	0.578950i
$653$	−4064.57	+	1089.10i	−0.243582	+	0.0652676i	−0.378544	−	0.925583i	$-0.623575\pi$
$653$	−4064.57	+	1089.10i	−0.243582	+	0.0652676i	0.134962	+	0.990851i	$0.456909\pi$
$654$	−13091.9	−	9842.97i	−0.782775	−	0.588518i
$655$		0			0
$656$			92147.4i			5.48438i
$657$	3235.30	−	63.5743i	0.192117	−	0.00377514i
$658$	5536.52	−	5536.52i	0.328018	−	0.328018i
$659$	15566.0	+	26961.1i	0.920129	+	1.59371i	0.799214	+	0.601047i	$0.205249\pi$
$659$	15566.0	+	26961.1i	0.920129	+	1.59371i	0.120915	+	0.992663i	$0.461417\pi$
$660$		0			0
$661$	7194.58	−	12461.4i	0.423354	−	0.733270i	−0.572911	−	0.819617i	$-0.694186\pi$
$661$	7194.58	−	12461.4i	0.423354	−	0.733270i	0.996265	+	0.0863471i	$0.0275194\pi$
$662$	6741.02	+	25157.8i	0.395766	+	1.47702i
$663$	−5278.34	+	4133.23i	−0.309191	+	0.242113i
$664$	62963.2	−	36351.8i	3.67989	−	2.12459i
$665$		0			0
$666$	−11667.4	+	47236.8i	−0.678834	+	2.74833i
$667$	−1647.44	−	1647.44i	−0.0956357	−	0.0956357i
$668$	1927.84	−	7194.81i	0.111662	−	0.416730i
$669$	−13565.4	+	18043.0i	−0.783957	+	1.04272i
$670$		0			0
$671$	−429.542	−	247.996i	−0.0247128	−	0.0142679i
$672$	5888.46	−	14620.6i	0.338024	−	0.839290i
$673$	−18240.0	−	4887.41i	−1.04473	−	0.279934i	−0.304657	−	0.952462i	$-0.598542\pi$
$673$	−18240.0	−	4887.41i	−1.04473	−	0.279934i	−0.740072	+	0.672528i	$0.765208\pi$
$674$	55088.6			3.14827
$675$		0			0
$676$	33980.9			1.93337
$677$	20847.9	+	5586.18i	1.18353	+	0.317126i	0.796326	−	0.604867i	$-0.206774\pi$
$677$	20847.9	+	5586.18i	1.18353	+	0.317126i	0.387205	+	0.921994i	$0.373441\pi$
$678$	20120.9	−	49958.8i	1.13973	−	2.82987i
$679$	6222.59	+	3592.62i	0.351695	+	0.203051i
$680$		0			0
$681$	8378.33	−	11143.8i	0.471451	−	0.627067i
$682$	−1312.57	+	4898.57i	−0.0736962	+	0.275038i
$683$	13485.0	+	13485.0i	0.755474	+	0.755474i	0.975495	−	0.220021i	$-0.0706126\pi$
$683$	13485.0	+	13485.0i	0.755474	+	0.755474i	−0.220021	+	0.975495i	$0.570613\pi$
$684$	−33877.4	+	9794.69i	−1.89376	+	0.547528i
$685$		0			0
$686$	−13780.6	+	7956.21i	−0.766974	+	0.442813i
$687$	−19731.6	+	15450.9i	−1.09579	+	0.858061i
$688$	19512.4	+	72821.4i	1.08126	+	4.03531i
$689$	−771.339	+	1336.00i	−0.0426498	+	0.0738716i
$690$		0			0
$691$	9014.75	+	15614.0i	0.496291	+	0.859602i	0.999991	−	0.00427721i	$-0.00136148\pi$
$691$	9014.75	+	15614.0i	0.496291	+	0.859602i	−0.503700	+	0.863879i	$0.668028\pi$
$692$	−11448.5	+	11448.5i	−0.628911	+	0.628911i
$693$	−389.117	+	705.633i	−0.0213295	+	0.0386794i
$694$			54861.9i			3.00076i
$695$		0			0
$696$	−13863.1	−	10422.8i	−0.754999	−	0.567635i
$697$	19093.7	−	5116.15i	1.03763	−	0.278032i
$698$	36215.6	−	9703.95i	1.96387	−	0.526218i
$699$	6792.67	−	2892.12i	0.367557	−	0.156495i
$700$		0			0
$701$			5187.88i			0.279520i	0.990185	+	0.139760i	$0.0446331\pi$
$701$			5187.88i			0.279520i	−0.990185	+	0.139760i	$0.955367\pi$
$702$	7942.33	+	17681.9i	0.427014	+	0.950655i
$703$	−13963.5	+	13963.5i	−0.749135	+	0.749135i
$704$	−6455.02	−	11180.4i	−0.345572	−	0.598548i
$705$		0			0
$706$	−24439.5	+	42330.5i	−1.30282	+	2.25656i
$707$	−1640.55	−	6122.63i	−0.0872693	−	0.325694i
$708$	7918.99	+	55901.4i	0.420358	+	2.96738i
$709$	−3337.90	+	1927.14i	−0.176809	+	0.102081i	−0.585793	−	0.810461i	$-0.699217\pi$
$709$	−3337.90	+	1927.14i	−0.176809	+	0.102081i	0.408984	+	0.912542i	$0.365883\pi$
$710$		0			0
$711$	−5633.90	−	1391.57i	−0.297170	−	0.0734005i
$712$	15392.9	+	15392.9i	0.810217	+	0.810217i
$713$	−1854.17	+	6919.86i	−0.0973903	+	0.363465i
$714$	−6276.44	−	763.660i	−0.328977	−	0.0400270i
$715$		0			0
$716$	−47775.3	−	27583.1i	−2.49364	−	1.43970i
$717$	−21209.2	−	27085.2i	−1.10470	−	1.41076i
$718$	13659.7	+	3660.11i	0.709994	+	0.190242i
$719$	−9734.47			−0.504916			−0.252458	−	0.967608i	$-0.581239\pi$
$719$	−9734.47			−0.504916			−0.252458	+	0.967608i	$0.581239\pi$
$720$		0			0
$721$	−1425.86			−0.0736503
$722$	17290.1	+	4632.88i	0.891235	+	0.238806i
$723$	12616.2	−	1787.21i	0.648965	−	0.0919323i
$724$	−42032.5	−	24267.5i	−2.15763	−	1.24571i
$725$		0			0
$726$	−14277.4	−	33533.2i	−0.729870	−	1.71423i
$727$	−3115.30	+	11626.5i	−0.158927	+	0.593125i	0.839810	+	0.542881i	$0.182666\pi$
$727$	−3115.30	+	11626.5i	−0.158927	+	0.593125i	−0.998737	+	0.0502438i	$0.984000\pi$
$728$	−5900.95	−	5900.95i	−0.300417	−	0.300417i
$729$	13073.9	−	14713.7i	0.664224	−	0.747534i
$730$		0			0
$731$	14005.9	−	8086.29i	0.708654	−	0.409141i
$732$	−7637.99	−	3076.20i	−0.385667	−	0.155327i
$733$	6750.61	+	25193.6i	0.340163	+	1.26951i	0.898162	+	0.439664i	$0.144903\pi$
$733$	6750.61	+	25193.6i	0.340163	+	1.26951i	−0.557999	+	0.829842i	$0.688431\pi$
$734$	21612.8	−	37434.4i	1.08684	−	1.88246i
$735$		0			0
$736$	−18294.9	−	31687.8i	−0.916250	−	1.58699i
$737$	891.204	−	891.204i	0.0445426	−	0.0445426i
$738$	−1122.87	−	57143.0i	−0.0560074	−	2.85022i
$739$		−	24108.3i		−	1.20005i	−0.799981	−	0.600025i	$-0.795157\pi$
$739$		−	24108.3i		−	1.20005i	0.799981	−	0.600025i	$-0.204843\pi$
$740$		0			0
$741$	−950.172	+	7809.35i	−0.0471058	+	0.387158i
$742$	−1405.35	+	376.563i	−0.0695312	+	0.0186308i
$743$	1607.80	−	430.808i	0.0793867	−	0.0212716i	−0.218907	−	0.975746i	$-0.570249\pi$
$743$	1607.80	−	430.808i	0.0793867	−	0.0212716i	0.298294	+	0.954474i	$0.403582\pi$
$744$	−6441.38	+	52940.9i	−0.317409	+	2.60875i
$745$		0			0
$746$		−	33025.8i		−	1.62086i
$747$	−22256.3	+	13439.5i	−1.09011	+	0.658267i
$748$	−5376.36	+	5376.36i	−0.262806	+	0.262806i
$749$	−3812.14	−	6602.82i	−0.185971	−	0.322112i
$750$		0			0
$751$	−11016.0	+	19080.3i	−0.535259	+	0.927096i	0.463892	+	0.885892i	$0.346453\pi$
$751$	−11016.0	+	19080.3i	−0.535259	+	0.927096i	−0.999151	+	0.0412042i	$0.986881\pi$
$752$	−20191.6	−	75356.1i	−0.979139	−	3.65420i
$753$	−31633.7	−	12740.5i	−1.53094	−	0.616585i
$754$	−5289.75	+	3054.04i	−0.255492	+	0.147509i
$755$		0			0
$756$	−4752.97	+	12504.8i	−0.228656	+	0.601580i
$757$	25360.2	+	25360.2i	1.21761	+	1.21761i	0.968466	+	0.249145i	$0.0801494\pi$
$757$	25360.2	+	25360.2i	1.21761	+	1.21761i	0.249145	+	0.968466i	$0.419851\pi$
$758$	19084.4	−	71224.0i	0.914481	−	3.41289i
$759$	732.799	+	1721.11i	0.0350447	+	0.0823089i
$760$		0			0
$761$	−14614.3	−	8437.57i	−0.696147	−	0.401921i	0.109763	−	0.993958i	$-0.464991\pi$
$761$	−14614.3	−	8437.57i	−0.696147	−	0.401921i	−0.805911	+	0.592037i	$0.798324\pi$
$762$	55833.2	−	7909.33i	2.65436	−	0.376017i
$763$	−2435.81	−	652.674i	−0.115573	−	0.0309678i
$764$	−57784.9			−2.73637
$765$		0			0
$766$	52745.9			2.48797
$767$	12165.9	+	3259.84i	0.572732	+	0.153463i
$768$	−34960.0	−	44645.7i	−1.64259	−	2.09767i
$769$	−4117.86	−	2377.45i	−0.193100	−	0.111486i	0.400333	−	0.916370i	$-0.368894\pi$
$769$	−4117.86	−	2377.45i	−0.193100	−	0.111486i	−0.593433	+	0.804883i	$0.702228\pi$
$770$		0			0
$771$	16096.9	+	1958.52i	0.751900	+	0.0914844i
$772$	−5804.50	+	21662.7i	−0.270607	+	1.00992i
$773$	15286.0	+	15286.0i	0.711252	+	0.711252i	0.966797	−	0.255545i	$-0.0822549\pi$
$773$	15286.0	+	15286.0i	0.711252	+	0.711252i	−0.255545	+	0.966797i	$0.582255\pi$
$774$	−12987.5	−	44920.7i	−0.603137	−	2.08610i
$775$		0			0
$776$	107536.	−	62085.9i	4.97463	−	2.87210i
$777$	1050.69	+	7417.02i	0.0485115	+	0.342451i
$778$	−8270.29	−	30865.1i	−0.381111	−	1.42233i
$779$	11598.1	−	20088.4i	0.533432	−	0.923932i
$780$		0			0
$781$	1925.82	+	3335.61i	0.0882345	+	0.152827i
$782$	−10378.7	+	10378.7i	−0.474605	+	0.474605i
$783$	5029.80	+	3629.13i	0.229566	+	0.165638i
$784$			77004.9i			3.50788i
$785$		0			0
$786$	40287.4	−	17153.2i	1.82825	−	0.778414i
$787$	5913.74	−	1584.58i	0.267855	−	0.0717716i	−0.122392	−	0.992482i	$-0.539056\pi$
$787$	5913.74	−	1584.58i	0.267855	−	0.0717716i	0.390247	+	0.920710i	$0.372390\pi$
$788$	−51728.8	+	13860.7i	−2.33853	+	0.626608i
$789$	19505.2	+	14664.7i	0.880106	+	0.661695i
$790$		0			0
$791$		−	8291.97i		−	0.372729i
$792$	7198.41	+	11920.8i	0.322960	+	0.534834i
$793$	−1298.88	+	1298.88i	−0.0581647	+	0.0581647i
$794$	−17909.7	−	31020.5i	−0.800493	−	1.38649i
$795$		0			0
$796$	8338.06	−	14441.9i	0.371275	−	0.643067i
$797$	−1366.45	−	5099.67i	−0.0607305	−	0.226649i	0.928890	−	0.370356i	$-0.120764\pi$
$797$	−1366.45	−	5099.67i	−0.0607305	−	0.226649i	−0.989620	+	0.143707i	$0.954098\pi$
$798$	−5841.60	+	4574.29i	−0.259136	+	0.202917i
$799$	−14493.4	+	8367.75i	−0.641726	+	0.370500i
$800$		0			0
$801$	−5611.69	−	5395.40i	−0.247540	−	0.237999i
$802$	−25622.2	−	25622.2i	−1.12812	−	1.12812i
$803$	211.896	−	790.807i	0.00931214	−	0.0347534i
$804$	12573.8	−	16724.2i	0.551548	−	0.733602i
$805$		0			0
$806$	16265.4	+	9390.83i	0.710824	+	0.410395i
$807$	7972.68	−	19795.6i	0.347771	−	0.863491i
$808$	−105808.	−	28351.3i	−4.60684	−	1.23440i
$809$	5052.91			0.219593			0.109797	−	0.993954i	$-0.464980\pi$
$809$	5052.91			0.219593			0.109797	+	0.993954i	$0.464980\pi$
$810$		0			0
$811$	−35887.2			−1.55385			−0.776923	−	0.629595i	$-0.783221\pi$
$811$	−35887.2			−1.55385			−0.776923	+	0.629595i	$0.783221\pi$
$812$	−4071.82	−	1091.04i	−0.175977	−	0.0471528i
$813$	695.432	−	1726.71i	0.0299998	−	0.0744874i
$814$	10661.0	+	6155.15i	0.459053	+	0.265034i
$815$		0			0
$816$	−37858.0	+	50354.1i	−1.62414	+	2.16023i
$817$	4911.84	−	18331.2i	0.210335	−	0.784979i
$818$	21239.3	+	21239.3i	0.907843	+	0.907843i
$819$	2151.27	+	2068.35i	0.0917843	+	0.0882466i
$820$		0			0
$821$	−34969.2	+	20189.5i	−1.48652	+	0.858243i	−0.999882	−	0.0153613i	$-0.995110\pi$
$821$	−34969.2	+	20189.5i	−1.48652	+	0.858243i	−0.486638	+	0.873604i	$0.661777\pi$
$822$	2762.42	−	2163.12i	0.117215	−	0.0917854i
$823$	−11363.1	−	42407.7i	−0.481280	−	1.79616i	−0.596258	−	0.802793i	$-0.703347\pi$
$823$	−11363.1	−	42407.7i	−0.481280	−	1.79616i	0.114979	−	0.993368i	$-0.463320\pi$
$824$	−12320.5	+	21339.8i	−0.520881	+	0.902192i
$825$		0			0
$826$	5939.32	+	10287.2i	0.250188	+	0.433339i
$827$	−104.564	+	104.564i	−0.00439667	+	0.00439667i	−0.709302	−	0.704905i	$-0.750990\pi$
$827$	−104.564	+	104.564i	−0.00439667	+	0.00439667i	0.704905	+	0.709302i	$0.250990\pi$
$828$	16052.9	+	26584.2i	0.673763	+	1.11578i
$829$			22880.1i			0.958575i	0.877658	+	0.479288i	$0.159105\pi$
$829$			22880.1i			0.958575i	−0.877658	+	0.479288i	$0.840895\pi$
$830$		0			0
$831$	−6958.81	−	5231.88i	−0.290491	−	0.218402i
$832$	−46182.8	+	12374.6i	−1.92440	+	0.515641i
$833$	15956.1	−	4275.42i	0.663680	−	0.177832i
$834$	9296.41	−	3958.13i	0.385981	−	0.164339i
$835$		0			0
$836$			8922.19i			0.369115i
$837$	1931.09	−	18973.6i	0.0797468	−	0.783541i
$838$	3036.06	−	3036.06i	0.125154	−	0.125154i
$839$	−8316.09	−	14403.9i	−0.342197	−	0.592703i	0.642643	−	0.766165i	$-0.277838\pi$
$839$	−8316.09	−	14403.9i	−0.342197	−	0.592703i	−0.984840	+	0.173463i	$0.944504\pi$
$840$		0			0
$841$	11217.3	−	19428.9i	0.459932	−	0.796625i
$842$	22204.5	+	82868.5i	0.908812	+	3.39173i
$843$	2801.70	+	19777.7i	0.114467	+	0.808041i
$844$	57822.1	−	33383.6i	2.35820	−	1.36151i
$845$		0			0
$846$	13439.6	+	46484.3i	0.546174	+	1.88908i
$847$	−3967.71	−	3967.71i	−0.160959	−	0.160959i
$848$	−3751.99	+	14002.6i	−0.151938	+	0.567042i
$849$	5853.03	+	712.143i	0.236602	+	0.0287876i
$850$		0			0
$851$	15060.1	+	8694.95i	0.606643	+	0.350246i
$852$	39422.3	+	50344.2i	1.58519	+	2.02437i
$853$	23270.6	+	6235.35i	0.934081	+	0.250286i	0.693594	−	0.720366i	$-0.256026\pi$
$853$	23270.6	+	6235.35i	0.934081	+	0.250286i	0.240487	+	0.970652i	$0.422693\pi$
$854$	−1732.41			−0.0694166
$855$		0			0
$856$	−131759.			−5.26103
$857$	−21805.1	−	5842.65i	−0.869133	−	0.232883i	−0.203420	−	0.979092i	$-0.565206\pi$
$857$	−21805.1	−	5842.65i	−0.869133	−	0.232883i	−0.665713	+	0.746208i	$0.731872\pi$
$858$	4855.70	−	687.858i	0.193206	−	0.0273696i
$859$	5394.56	+	3114.55i	0.214272	+	0.123710i	0.603295	−	0.797518i	$-0.293854\pi$
$859$	5394.56	+	3114.55i	0.214272	+	0.123710i	−0.389023	+	0.921228i	$0.627187\pi$
$860$		0			0
$861$	−3447.07	−	8096.07i	−0.136441	−	0.320457i
$862$	1898.89	−	7086.77i	0.0750308	−	0.280019i
$863$	−27165.1	−	27165.1i	−1.07151	−	1.07151i	−0.997238	−	0.0742697i	$-0.976337\pi$
$863$	−27165.1	−	27165.1i	−1.07151	−	1.07151i	−0.0742697	−	0.997238i	$-0.523663\pi$
$864$	61549.7	+	75498.1i	2.42357	+	2.97280i
$865$		0			0
$866$	29194.8	−	16855.6i	1.14559	−	0.661406i
$867$	−11144.5	−	4488.47i	−0.436550	−	0.175821i
$868$	3354.83	+	12520.4i	0.131187	+	0.489597i
$869$	−734.121	+	1271.53i	−0.0286575	+	0.0496362i
$870$		0			0
$871$	−2333.84	−	4042.33i	−0.0907912	−	0.157255i
$872$	−30815.4	+	30815.4i	−1.19672	+	1.19672i
$873$	−38011.9	+	22953.5i	−1.47366	+	0.889873i
$874$			17223.7i			0.666589i
$875$		0			0
$876$	1641.60	−	13492.1i	0.0633158	−	0.520385i
$877$	−37586.2	+	10071.2i	−1.44720	+	0.387777i	−0.895050	−	0.445966i	$-0.852860\pi$
$877$	−37586.2	+	10071.2i	−1.44720	+	0.387777i	−0.552153	+	0.833743i	$0.686194\pi$
$878$	−37182.6	+	9963.04i	−1.42922	+	0.382957i
$879$	282.602	−	2322.67i	0.0108441	−	0.0891261i
$880$		0			0
$881$		−	1863.97i		−	0.0712812i	−0.999365	−	0.0356406i	$-0.988653\pi$
$881$		−	1863.97i		−	0.0712812i	0.999365	−	0.0356406i	$-0.0113472\pi$
$882$	−938.351	−	47752.7i	−0.0358230	−	1.82304i
$883$	−5893.85	+	5893.85i	−0.224625	+	0.224625i	−0.810443	−	0.585818i	$-0.800773\pi$
$883$	−5893.85	+	5893.85i	−0.224625	+	0.224625i	0.585818	+	0.810443i	$0.300773\pi$
$884$	14079.3	+	24386.1i	0.535678	+	0.927821i
$885$		0			0
$886$	16048.4	−	27796.6i	0.608528	−	1.05400i
$887$	−8210.50	−	30642.0i	−0.310802	−	1.15993i	−0.927835	−	0.372992i	$-0.878332\pi$
$887$	−8210.50	−	30642.0i	−0.310802	−	1.15993i	0.617032	−	0.786938i	$-0.288335\pi$
$888$	120084.	+	48363.8i	4.53800	+	1.82768i
$889$	7518.68	−	4340.91i	0.283654	−	0.163768i
$890$		0			0
$891$	−2657.45	−	4211.57i	−0.0999191	−	0.158353i
$892$	67044.1	+	67044.1i	2.51659	+	2.51659i
$893$	−5082.80	+	18969.3i	−0.190470	+	0.710843i
$894$	−13377.7	−	31420.0i	−0.500467	−	1.17544i
$895$		0			0
$896$	−18035.3	−	10412.7i	−0.672451	−	0.388240i
$897$	6859.31	−	971.689i	0.255324	−	0.0361692i
$898$	48957.7	+	13118.2i	1.81931	+	0.487482i
$899$	6009.72			0.222954
$900$		0			0
$901$	3109.78			0.114985
$902$	−13967.5	−	3742.59i	−0.515596	−	0.138154i
$903$	−4438.48	−	5668.17i	−0.163570	−	0.208887i
$904$	−124100.	−	71648.9i	−4.56581	−	2.63607i
$905$		0			0
$906$	46201.8	+	5621.42i	1.69421	+	0.206136i
$907$	10920.7	−	40756.7i	0.399798	−	1.49207i	−0.413653	−	0.910434i	$-0.635747\pi$
$907$	10920.7	−	40756.7i	0.399798	−	1.49207i	0.813452	−	0.581633i	$-0.197586\pi$
$908$	−41408.2	−	41408.2i	−1.51341	−	1.51341i
$909$	38029.6	+	9393.26i	1.38764	+	0.342745i
$910$		0			0
$911$	16299.0	−	9410.22i	0.592766	−	0.342233i	−0.173425	−	0.984847i	$-0.555483\pi$
$911$	16299.0	−	9410.22i	0.592766	−	0.342233i	0.766190	+	0.642614i	$0.222150\pi$
$912$	10368.8	+	73195.0i	0.376475	+	2.65760i
$913$	1702.50	+	6353.80i	0.0617135	+	0.230318i
$914$	−8340.58	+	14446.3i	−0.301840	+	0.522802i
$915$		0			0
$916$	52631.6	+	91160.6i	1.89847	+	3.28824i
$917$	4766.89	−	4766.89i	0.171665	−	0.171665i
$918$	22863.1	−	31687.2i	0.821999	−	1.13925i
$919$		−	44356.0i		−	1.59213i	−0.605211	−	0.796065i	$-0.706911\pi$
$919$		−	44356.0i		−	1.59213i	0.605211	−	0.796065i	$-0.293089\pi$
$920$		0			0
$921$	8233.81	−	3505.71i	0.294586	−	0.125426i
$922$	40991.5	−	10983.7i	1.46419	−	0.392329i
$923$	13778.4	−	3691.90i	0.491354	−	0.131658i
$924$	2705.29	+	2033.93i	0.0963177	+	0.0724151i
$925$		0			0
$926$		−	20895.4i		−	0.741540i
$927$	4255.12	−	7716.33i	0.150762	−	0.273395i
$928$	−21704.3	+	21704.3i	−0.767758	+	0.767758i
$929$	13518.2	+	23414.2i	0.477415	+	0.826907i	0.999665	−	0.0258858i	$-0.00824061\pi$
$929$	13518.2	+	23414.2i	0.477415	+	0.826907i	−0.522250	+	0.852792i	$0.674907\pi$
$930$		0			0
$931$	9692.16	−	16787.3i	0.341190	−	0.590958i
$932$	−8025.78	−	29952.6i	−0.282074	−	1.05272i
$933$	22016.8	−	17240.3i	0.772558	−	0.604955i
$934$	−20401.8	+	11779.0i	−0.714740	+	0.412656i
$935$		0			0
$936$	49544.0	−	14324.2i	1.73012	−	0.500216i
$937$	−37452.3	−	37452.3i	−1.30578	−	1.30578i	−0.924432	−	0.381346i	$-0.875461\pi$
$937$	−37452.3	−	37452.3i	−1.30578	−	1.30578i	−0.381346	−	0.924432i	$-0.624539\pi$
$938$	1139.37	−	4252.17i	0.0396606	−	0.148015i
$939$	−15067.8	+	20041.3i	−0.523661	+	0.696511i
$940$		0			0
$941$	−6297.33	−	3635.77i	−0.218158	−	0.125954i	0.386939	−	0.922105i	$-0.373532\pi$
$941$	−6297.33	−	3635.77i	−0.218158	−	0.125954i	−0.605097	+	0.796152i	$0.706866\pi$
$942$	−37155.8	+	92255.2i	−1.28514	+	3.19091i
$943$	−19730.9	−	5286.89i	−0.681366	−	0.182571i
$944$	118356.			4.08068
$945$		0			0
$946$	−11830.6			−0.406604
$947$	−32687.2	−	8758.51i	−1.12164	−	0.300542i	−0.350092	−	0.936715i	$-0.613850\pi$
$947$	−32687.2	−	8758.51i	−1.12164	−	0.300542i	−0.771546	+	0.636173i	$0.780516\pi$
$948$	−9106.20	+	22610.0i	−0.311978	+	0.774620i
$949$	−2625.83	−	1516.02i	−0.0898187	−	0.0518569i
$950$		0			0
$951$	−12032.1	+	16003.7i	−0.410272	+	0.545694i
$952$	−4353.98	+	16249.3i	−0.148228	+	0.553195i
$953$	−14114.4	−	14114.4i	−0.479760	−	0.479760i	0.425295	−	0.905055i	$-0.360170\pi$
$953$	−14114.4	−	14114.4i	−0.479760	−	0.479760i	−0.905055	+	0.425295i	$0.860170\pi$
$954$	2156.07	−	8729.10i	0.0731714	−	0.296242i
$955$		0			0
$956$	−125134.	+	72246.4i	−4.23341	+	2.44416i
$957$	1235.51	−	967.471i	0.0417329	−	0.0326791i
$958$	3095.45	+	11552.4i	0.104394	+	0.389604i
$959$	270.087	−	467.805i	0.00909445	−	0.0157520i
$960$		0			0
$961$	5655.88	+	9796.27i	0.189852	+	0.328833i
$962$	32237.6	−	32237.6i	1.08044	−	1.08044i
$963$	47108.8	−	925.698i	1.57639	−	0.0309763i
$964$		−	53520.1i		−	1.78814i
$965$		0			0
$966$	5222.38	+	3926.37i	0.173941	+	0.130775i
$967$	24896.1	−	6670.89i	0.827926	−	0.221842i	0.180117	−	0.983645i	$-0.442352\pi$
$967$	24896.1	−	6670.89i	0.827926	−	0.221842i	0.647809	+	0.761803i	$0.275686\pi$
$968$	−93665.8	+	25097.7i	−3.11005	+	0.833337i
$969$	14590.9	−	6212.39i	0.483724	−	0.205955i
$970$		0			0
$971$			33741.6i			1.11516i	0.830124	+	0.557579i	$0.188270\pi$
$971$			33741.6i			1.11516i	−0.830124	+	0.557579i	$0.811730\pi$
$972$	−53488.0	−	63039.0i	−1.76505	−	2.08022i
$973$	1099.97	−	1099.97i	0.0362419	−	0.0362419i
$974$	7043.75	+	12200.1i	0.231721	+	0.401353i
$975$		0			0
$976$	−8630.65	+	14948.7i	−0.283054	+	0.490264i
$977$	−4918.86	−	18357.4i	−0.161073	−	0.601132i	−0.998509	−	0.0545961i	$-0.982613\pi$
$977$	−4918.86	−	18357.4i	−0.161073	−	0.601132i	0.837436	−	0.546536i	$-0.184054\pi$
$978$	−6791.49	−	47942.2i	−0.222053	−	1.56751i
$979$	−1705.69	+	984.781i	−0.0556835	+	0.0321489i
$980$		0			0
$981$	10801.1	−	11234.1i	0.351533	−	0.365625i
$982$	−10430.8	−	10430.8i	−0.338961	−	0.338961i
$983$	−6717.95	+	25071.7i	−0.217975	+	0.813493i	0.767123	+	0.641500i	$0.221687\pi$
$983$	−6717.95	+	25071.7i	−0.217975	+	0.813493i	−0.985098	+	0.171994i	$0.944979\pi$
$984$	−150953.	−	18366.6i	−4.89046	−	0.595027i
$985$		0			0
$986$	10663.2	+	6156.42i	0.344408	+	0.198844i
$987$	4592.97	+	5865.46i	0.148122	+	0.189159i
$988$	31917.1	+	8552.17i	1.02775	+	0.275385i
$989$	−16712.3			−0.537331
$990$		0			0
$991$	15779.5			0.505806			0.252903	−	0.967492i	$-0.418615\pi$
$991$	15779.5			0.505806			0.252903	+	0.967492i	$0.418615\pi$
$992$	91166.5	+	24428.0i	2.91788	+	0.781844i
$993$	−24536.1	+	3475.78i	−0.784119	+	0.111078i
$994$	11650.7	+	6726.51i	0.371767	+	0.214640i
$995$		0			0
$996$	42779.4	+	100475.i	1.36096	+	3.19646i
$997$	−14491.4	+	54082.7i	−0.460329	+	1.71797i	0.211603	+	0.977356i	$0.432132\pi$
$997$	−14491.4	+	54082.7i	−0.460329	+	1.71797i	−0.671931	+	0.740614i	$0.734535\pi$
$998$	65146.6	+	65146.6i	2.06631	+	2.06631i
$999$	−43274.2	−	16448.2i	−1.37050	−	0.520918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.p.b.32.16		64
5.2	odd	4		45.4.l.a.23.1	yes	64
5.3	odd	4	inner	225.4.p.b.68.16		64
5.4	even	2		45.4.l.a.32.1	yes	64
9.2	odd	6	inner	225.4.p.b.182.16		64
15.2	even	4		135.4.m.a.98.16		64
15.14	odd	2		135.4.m.a.17.16		64
45.2	even	12		45.4.l.a.38.1	yes	64
45.7	odd	12		135.4.m.a.8.16		64
45.29	odd	6		45.4.l.a.2.1	✓	64
45.34	even	6		135.4.m.a.62.16		64
45.38	even	12	inner	225.4.p.b.218.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.1	✓	64	45.29	odd	6
45.4.l.a.23.1	yes	64	5.2	odd	4
45.4.l.a.32.1	yes	64	5.4	even	2
45.4.l.a.38.1	yes	64	45.2	even	12
135.4.m.a.8.16		64	45.7	odd	12
135.4.m.a.17.16		64	15.14	odd	2
135.4.m.a.62.16		64	45.34	even	6
135.4.m.a.98.16		64	15.2	even	4
225.4.p.b.32.16		64	1.1	even	1	trivial
225.4.p.b.68.16		64	5.3	odd	4	inner
225.4.p.b.182.16		64	9.2	odd	6	inner
225.4.p.b.218.16		64	45.38	even	12	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.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.27515 + 1.41347i) q^{2} +(-1.94123 + 4.81992i) q^{3} +(18.9011 + 10.9125i) q^{4} +(-17.0531 + 22.6819i) q^{6} +(-1.13077 + 4.22008i) q^{7} +(53.3880 + 53.3880i) q^{8} +(-19.4633 - 18.7131i) q^{9} +O(q^{10})\)	\(q+(5.27515 + 1.41347i) q^{2} +(-1.94123 + 4.81992i) q^{3} +(18.9011 + 10.9125i) q^{4} +(-17.0531 + 22.6819i) q^{6} +(-1.13077 + 4.22008i) q^{7} +(53.3880 + 53.3880i) q^{8} +(-19.4633 - 18.7131i) q^{9} +(-5.91593 + 3.41556i) q^{11} +(-89.2889 + 69.9180i) q^{12} +(6.54783 + 24.4368i) q^{13} +(-11.9299 + 20.6632i) q^{14} +(118.867 + 205.883i) q^{16} +(36.0612 - 36.0612i) q^{17} +(-76.2213 - 126.225i) q^{18} -59.8443i q^{19} +(-18.1454 - 13.6423i) q^{21} +(-36.0352 + 9.65561i) q^{22} +(-50.9044 + 13.6398i) q^{23} +(-360.964 + 153.688i) q^{24} +138.163i q^{26} +(127.978 - 57.4851i) q^{27} +(-67.4245 + 67.4245i) q^{28} +(22.1046 + 38.2863i) q^{29} +(67.9692 - 117.726i) q^{31} +(179.699 + 670.646i) q^{32} +(-4.97859 - 35.1447i) q^{33} +(241.199 - 139.257i) q^{34} +(-163.669 - 566.092i) q^{36} +(-233.330 - 233.330i) q^{37} +(84.5883 - 315.688i) q^{38} +(-130.494 - 15.8774i) q^{39} +(335.678 + 193.804i) q^{41} +(-76.4365 - 97.6133i) q^{42} +(306.315 + 82.0769i) q^{43} -149.090 q^{44} -287.808 q^{46} +(-316.977 - 84.9338i) q^{47} +(-1223.09 + 173.263i) q^{48} +(280.516 + 161.956i) q^{49} +(103.809 + 243.815i) q^{51} +(-142.907 + 533.336i) q^{52} +(43.1181 + 43.1181i) q^{53} +(756.358 - 122.349i) q^{54} +(-285.671 + 164.932i) q^{56} +(288.445 + 116.171i) q^{57} +(62.4884 + 233.210i) q^{58} +(248.925 - 431.152i) q^{59} +(36.3039 + 62.8801i) q^{61} +(524.950 - 524.950i) q^{62} +(100.979 - 60.9764i) q^{63} +1889.88i q^{64} +(23.4132 - 192.431i) q^{66} +(-178.215 + 47.7525i) q^{67} +(1075.11 - 288.076i) q^{68} +(33.0742 - 271.833i) q^{69} -563.835i q^{71} +(-40.0503 - 2038.16i) q^{72} +(-84.7460 + 84.7460i) q^{73} +(-901.044 - 1560.65i) q^{74} +(653.054 - 1131.12i) q^{76} +(-7.72441 - 28.8279i) q^{77} +(-665.935 - 268.206i) q^{78} +(186.138 - 107.467i) q^{79} +(28.6389 + 728.437i) q^{81} +(1496.82 + 1496.82i) q^{82} +(249.226 - 930.125i) q^{83} +(-194.095 - 455.867i) q^{84} +(1499.84 + 865.935i) q^{86} +(-227.447 + 32.2201i) q^{87} +(-498.190 - 133.490i) q^{88} +288.322 q^{89} -110.529 q^{91} +(-1110.99 - 297.690i) q^{92} +(435.487 + 556.139i) q^{93} +(-1552.05 - 896.076i) q^{94} +(-3581.30 - 435.740i) q^{96} +(425.658 - 1588.58i) q^{97} +(1250.84 + 1250.84i) q^{98} +(179.059 + 44.2274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7	\( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) 64 * q + 6 * q^2 - 24 * q^6 + 2 * q^7 - 36 * q^11 + 138 * q^12 + 2 * q^13 + 316 * q^16 + 480 * q^18 + 480 * q^21 + 34 * q^22 - 306 * q^23 - 180 * q^27 + 232 * q^28 - 4 * q^31 + 1770 * q^32 + 294 * q^33 - 216 * q^36 - 136 * q^37 - 114 * q^38 + 1992 * q^41 - 1698 * q^42 + 2 * q^43 - 952 * q^46 - 3462 * q^47 - 4326 * q^48 - 2496 * q^51 + 242 * q^52 - 7128 * q^56 + 2544 * q^57 - 534 * q^58 + 32 * q^61 + 4038 * q^63 + 2892 * q^66 - 610 * q^67 + 2694 * q^68 + 1854 * q^72 + 8 * q^73 + 1368 * q^76 + 6486 * q^77 - 1434 * q^78 + 3012 * q^81 + 3784 * q^82 - 2814 * q^83 + 12480 * q^86 - 4830 * q^87 + 1338 * q^88 + 992 * q^91 - 13152 * q^92 - 8310 * q^93 - 7932 * q^96 - 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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