LMFDB - Embedded newform 250.4.e.b.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(49,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.e (of order $10$, degree $4$, not 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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			149.2
Character	$\chi$	$=$	250.149
Dual form			250.4.e.b.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90211 - 0.618034i) q^{2} +(-1.87704 + 2.58353i) q^{3} +(3.23607 + 2.35114i) q^{4} +(5.16706 - 3.75409i) q^{6} -2.29951i q^{7} +(-4.70228 - 6.47214i) q^{8} +(5.19213 + 15.9797i) q^{9} +O(q^{10})$	\(q+(-1.90211 - 0.618034i) q^{2} +(-1.87704 + 2.58353i) q^{3} +(3.23607 + 2.35114i) q^{4} +(5.16706 - 3.75409i) q^{6} -2.29951i q^{7} +(-4.70228 - 6.47214i) q^{8} +(5.19213 + 15.9797i) q^{9} +(2.42614 - 7.46690i) q^{11} +(-12.1485 + 3.94728i) q^{12} +(43.6924 - 14.1965i) q^{13} +(-1.42118 + 4.37394i) q^{14} +(4.94427 + 15.2169i) q^{16} +(-14.6772 - 20.2014i) q^{17} -33.6041i q^{18} +(-53.8228 + 39.1046i) q^{19} +(5.94086 + 4.31629i) q^{21} +(-9.22960 + 12.7034i) q^{22} +(137.701 + 44.7417i) q^{23} +25.5474 q^{24} -91.8817 q^{26} +(-133.032 - 43.2248i) q^{27} +(5.40648 - 7.44138i) q^{28} +(40.9879 + 29.7795i) q^{29} +(-122.193 + 88.7782i) q^{31} -32.0000i q^{32} +(14.7370 + 20.2837i) q^{33} +(15.4325 + 47.4963i) q^{34} +(-20.7685 + 63.9189i) q^{36} +(-358.151 + 116.370i) q^{37} +(126.545 - 41.1170i) q^{38} +(-45.3354 + 139.528i) q^{39} +(111.749 + 343.927i) q^{41} +(-8.63258 - 11.8817i) q^{42} +481.429i q^{43} +(25.4069 - 18.4592i) q^{44} +(-234.270 - 170.207i) q^{46} +(-142.608 + 196.283i) q^{47} +(-48.5940 - 15.7891i) q^{48} +337.712 q^{49} +79.7407 q^{51} +(174.769 + 56.7860i) q^{52} +(-82.8875 + 114.085i) q^{53} +(226.328 + 164.437i) q^{54} +(-14.8828 + 10.8130i) q^{56} -212.454i q^{57} +(-59.5589 - 81.9758i) q^{58} +(38.9115 + 119.757i) q^{59} +(-105.946 + 326.067i) q^{61} +(287.292 - 93.3470i) q^{62} +(36.7456 - 11.9394i) q^{63} +(-19.7771 + 60.8676i) q^{64} +(-15.4954 - 47.6899i) q^{66} +(414.141 + 570.016i) q^{67} -99.8812i q^{68} +(-374.062 + 271.772i) q^{69} +(-270.639 - 196.630i) q^{71} +(79.0081 - 108.745i) q^{72} +(446.124 + 144.955i) q^{73} +753.165 q^{74} -266.115 q^{76} +(-17.1702 - 5.57895i) q^{77} +(172.466 - 237.379i) q^{78} +(-1108.23 - 805.178i) q^{79} +(-5.63528 + 4.09427i) q^{81} -723.252i q^{82} +(-320.625 - 441.302i) q^{83} +(9.07683 + 27.9356i) q^{84} +(297.540 - 915.733i) q^{86} +(-153.872 + 49.9961i) q^{87} +(-59.7352 + 19.4091i) q^{88} +(-56.1852 + 172.920i) q^{89} +(-32.6451 - 100.471i) q^{91} +(340.415 + 468.541i) q^{92} -482.329i q^{93} +(392.565 - 285.215i) q^{94} +(82.6730 + 60.0654i) q^{96} +(-277.504 + 381.952i) q^{97} +(-642.367 - 208.718i) q^{98} +131.916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9	$ 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9} - 106 q^{11} - 80 q^{12} + 56 q^{14} - 128 q^{16} - 320 q^{17} + 110 q^{19} - 36 q^{21} + 360 q^{22} + 370 q^{23} - 192 q^{24} + 808 q^{26} + 1200 q^{27} + 120 q^{28} - 10 q^{29} - 486 q^{31} - 2560 q^{33} + 616 q^{34} - 104 q^{36} - 680 q^{37} + 1012 q^{39} - 96 q^{41} + 1020 q^{42} - 136 q^{44} - 832 q^{46} - 1040 q^{47} - 320 q^{48} - 2076 q^{49} + 884 q^{51} + 2550 q^{53} - 120 q^{54} - 224 q^{56} + 2250 q^{59} + 934 q^{61} - 4200 q^{62} - 4660 q^{63} + 512 q^{64} + 16 q^{66} + 3780 q^{67} - 628 q^{69} - 2616 q^{71} + 600 q^{73} - 2584 q^{74} + 800 q^{76} + 4320 q^{77} + 6640 q^{78} - 2800 q^{79} - 5268 q^{81} - 4050 q^{83} + 624 q^{84} - 692 q^{86} - 9390 q^{87} + 1680 q^{88} + 4520 q^{89} + 3764 q^{91} - 1280 q^{92} + 656 q^{94} - 192 q^{96} - 1710 q^{97} - 3280 q^{98} - 2108 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9 - 106 * q^11 - 80 * q^12 + 56 * q^14 - 128 * q^16 - 320 * q^17 + 110 * q^19 - 36 * q^21 + 360 * q^22 + 370 * q^23 - 192 * q^24 + 808 * q^26 + 1200 * q^27 + 120 * q^28 - 10 * q^29 - 486 * q^31 - 2560 * q^33 + 616 * q^34 - 104 * q^36 - 680 * q^37 + 1012 * q^39 - 96 * q^41 + 1020 * q^42 - 136 * q^44 - 832 * q^46 - 1040 * q^47 - 320 * q^48 - 2076 * q^49 + 884 * q^51 + 2550 * q^53 - 120 * q^54 - 224 * q^56 + 2250 * q^59 + 934 * q^61 - 4200 * q^62 - 4660 * q^63 + 512 * q^64 + 16 * q^66 + 3780 * q^67 - 628 * q^69 - 2616 * q^71 + 600 * q^73 - 2584 * q^74 + 800 * q^76 + 4320 * q^77 + 6640 * q^78 - 2800 * q^79 - 5268 * q^81 - 4050 * q^83 + 624 * q^84 - 692 * q^86 - 9390 * q^87 + 1680 * q^88 + 4520 * q^89 + 3764 * q^91 - 1280 * q^92 + 656 * q^94 - 192 * q^96 - 1710 * q^97 - 3280 * q^98 - 2108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.90211	−	0.618034i	−0.672499	−	0.218508i
$2$	−1.90211	−	0.618034i	−0.672499	−	0.218508i
$3$	−1.87704	+	2.58353i	−0.361237	+	0.497201i	−0.950493	−	0.310746i	$-0.899421\pi$
$3$	−1.87704	+	2.58353i	−0.361237	+	0.497201i	0.589256	+	0.807947i	$0.299421\pi$
$4$	3.23607	+	2.35114i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	5.16706	−	3.75409i	0.351574	−	0.255433i
$7$		−	2.29951i		−	0.124162i	−0.998071	−	0.0620810i	$-0.980226\pi$
$7$		−	2.29951i		−	0.124162i	0.998071	−	0.0620810i	$-0.0197737\pi$
$8$	−4.70228	−	6.47214i	−0.207813	−	0.286031i
$9$	5.19213	+	15.9797i	0.192301	+	0.591841i
$10$		0			0
$11$	2.42614	−	7.46690i	0.0665009	−	0.204669i	−0.912284	−	0.409557i	$-0.865683\pi$
$11$	2.42614	−	7.46690i	0.0665009	−	0.204669i	0.978785	+	0.204889i	$0.0656832\pi$
$12$	−12.1485	+	3.94728i	−0.292247	+	0.0949569i
$13$	43.6924	−	14.1965i	0.932160	−	0.302877i	0.196714	−	0.980461i	$-0.436973\pi$
$13$	43.6924	−	14.1965i	0.932160	−	0.302877i	0.735446	+	0.677584i	$0.236973\pi$
$14$	−1.42118	+	4.37394i	−0.0271304	+	0.0834988i
$15$		0			0
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	−14.6772	−	20.2014i	−0.209396	−	0.288209i	0.691381	−	0.722490i	$-0.257003\pi$
$17$	−14.6772	−	20.2014i	−0.209396	−	0.288209i	−0.900778	+	0.434281i	$0.857003\pi$
$18$		−	33.6041i		−	0.440032i
$19$	−53.8228	+	39.1046i	−0.649884	+	0.472168i	−0.863232	−	0.504808i	$-0.831563\pi$
$19$	−53.8228	+	39.1046i	−0.649884	+	0.472168i	0.213348	+	0.976976i	$0.431563\pi$
$20$		0			0
$21$	5.94086	+	4.31629i	0.0617335	+	0.0448520i
$22$	−9.22960	+	12.7034i	−0.0894435	+	0.123108i
$23$	137.701	+	44.7417i	1.24837	+	0.405621i	0.857338	−	0.514755i	$-0.172117\pi$
$23$	137.701	+	44.7417i	1.24837	+	0.405621i	0.391035	+	0.920376i	$0.372117\pi$
$24$	25.5474			0.217285
$25$		0			0
$26$	−91.8817			−0.693057
$27$	−133.032	−	43.2248i	−0.948225	−	0.308097i
$28$	5.40648	−	7.44138i	0.0364903	−	0.0502246i
$29$	40.9879	+	29.7795i	0.262457	+	0.190686i	0.711230	−	0.702960i	$-0.248139\pi$
$29$	40.9879	+	29.7795i	0.262457	+	0.190686i	−0.448772	+	0.893646i	$0.648139\pi$
$30$		0			0
$31$	−122.193	+	88.7782i	−0.707950	+	0.514356i	−0.882512	−	0.470290i	$-0.844149\pi$
$31$	−122.193	+	88.7782i	−0.707950	+	0.514356i	0.174561	+	0.984646i	$0.444149\pi$
$32$		−	32.0000i		−	0.176777i
$33$	14.7370	+	20.2837i	0.0777388	+	0.106998i
$34$	15.4325	+	47.4963i	0.0778427	+	0.239575i
$35$		0			0
$36$	−20.7685	+	63.9189i	−0.0961505	+	0.295921i
$37$	−358.151	+	116.370i	−1.59134	+	0.517059i	−0.964947	−	0.262446i	$-0.915471\pi$
$37$	−358.151	+	116.370i	−1.59134	+	0.517059i	−0.626396	+	0.779505i	$0.715471\pi$
$38$	126.545	−	41.1170i	0.540219	−	0.175528i
$39$	−45.3354	+	139.528i	−0.186140	+	0.572881i
$40$		0			0
$41$	111.749	+	343.927i	0.425663	+	1.31006i	0.902358	+	0.430987i	$0.141835\pi$
$41$	111.749	+	343.927i	0.425663	+	1.31006i	−0.476695	+	0.879069i	$0.658165\pi$
$42$	−8.63258	−	11.8817i	−0.0317151	−	0.0436522i
$43$			481.429i			1.70738i	0.520783	+	0.853689i	$0.325640\pi$
$43$			481.429i			1.70738i	−0.520783	+	0.853689i	$0.674360\pi$
$44$	25.4069	−	18.4592i	0.0870508	−	0.0632461i
$45$		0			0
$46$	−234.270	−	170.207i	−0.750898	−	0.545559i
$47$	−142.608	+	196.283i	−0.442585	+	0.609165i	−0.970784	−	0.239955i	$-0.922867\pi$
$47$	−142.608	+	196.283i	−0.442585	+	0.609165i	0.528199	+	0.849120i	$0.322867\pi$
$48$	−48.5940	−	15.7891i	−0.146124	−	0.0474784i
$49$	337.712			0.984584
$50$		0			0
$51$	79.7407			0.218940
$52$	174.769	+	56.7860i	0.466080	+	0.151439i
$53$	−82.8875	+	114.085i	−0.214820	+	0.295675i	−0.902805	−	0.430051i	$-0.858496\pi$
$53$	−82.8875	+	114.085i	−0.214820	+	0.295675i	0.687984	+	0.725725i	$0.258496\pi$
$54$	226.328	+	164.437i	0.570358	+	0.414389i
$55$		0			0
$56$	−14.8828	+	10.8130i	−0.0355142	+	0.0258026i
$57$		−	212.454i		−	0.493688i
$58$	−59.5589	−	81.9758i	−0.134836	−	0.185585i
$59$	38.9115	+	119.757i	0.0858617	+	0.264255i	0.984765	−	0.173893i	$-0.0556346\pi$
$59$	38.9115	+	119.757i	0.0858617	+	0.264255i	−0.898903	+	0.438148i	$0.855635\pi$
$60$		0			0
$61$	−105.946	+	326.067i	−0.222376	+	0.684403i	0.776171	+	0.630522i	$0.217159\pi$
$61$	−105.946	+	326.067i	−0.222376	+	0.684403i	−0.998547	+	0.0538811i	$0.982841\pi$
$62$	287.292	−	93.3470i	0.588487	−	0.191211i
$63$	36.7456	−	11.9394i	0.0734843	−	0.0238765i
$64$	−19.7771	+	60.8676i	−0.0386271	+	0.118882i
$65$		0			0
$66$	−15.4954	−	47.6899i	−0.0288992	−	0.0889427i
$67$	414.141	+	570.016i	0.755155	+	1.03938i	0.997602	+	0.0692168i	$0.0220500\pi$
$67$	414.141	+	570.016i	0.755155	+	1.03938i	−0.242447	+	0.970165i	$0.577950\pi$
$68$		−	99.8812i		−	0.178123i
$69$	−374.062	+	271.772i	−0.652634	+	0.474166i
$70$		0			0
$71$	−270.639	−	196.630i	−0.452379	−	0.328672i	0.338155	−	0.941090i	$-0.390197\pi$
$71$	−270.639	−	196.630i	−0.452379	−	0.328672i	−0.790534	+	0.612418i	$0.790197\pi$
$72$	79.0081	−	108.745i	0.129322	−	0.177997i
$73$	446.124	+	144.955i	0.715273	+	0.232406i	0.643972	−	0.765049i	$-0.277285\pi$
$73$	446.124	+	144.955i	0.715273	+	0.232406i	0.0713002	+	0.997455i	$0.477285\pi$
$74$	753.165			1.18316
$75$		0			0
$76$	−266.115			−0.401650
$77$	−17.1702	−	5.57895i	−0.0254121	−	0.00825689i
$78$	172.466	−	237.379i	0.250358	−	0.344589i
$79$	−1108.23	−	805.178i	−1.57830	−	1.14670i	−0.918609	−	0.395168i	$-0.870686\pi$
$79$	−1108.23	−	805.178i	−1.57830	−	1.14670i	−0.659693	−	0.751535i	$-0.729314\pi$
$80$		0			0
$81$	−5.63528	+	4.09427i	−0.00773015	+	0.00561628i
$82$		−	723.252i		−	0.974022i
$83$	−320.625	−	441.302i	−0.424014	−	0.583605i	0.542552	−	0.840022i	$-0.317458\pi$
$83$	−320.625	−	441.302i	−0.424014	−	0.583605i	−0.966566	+	0.256417i	$0.917458\pi$
$84$	9.07683	+	27.9356i	0.0117900	+	0.0362860i
$85$		0			0
$86$	297.540	−	915.733i	0.373076	−	1.14821i
$87$	−153.872	+	49.9961i	−0.189619	+	0.0616109i
$88$	−59.7352	+	19.4091i	−0.0723613	+	0.0235116i
$89$	−56.1852	+	172.920i	−0.0669171	+	0.205950i	−0.978924	−	0.204226i	$-0.934532\pi$
$89$	−56.1852	+	172.920i	−0.0669171	+	0.205950i	0.912007	+	0.410175i	$0.134532\pi$
$90$		0			0
$91$	−32.6451	−	100.471i	−0.0376059	−	0.115739i
$92$	340.415	+	468.541i	0.385768	+	0.530965i
$93$		−	482.329i		−	0.537798i
$94$	392.565	−	285.215i	0.430745	−	0.312955i
$95$		0			0
$96$	82.6730	+	60.0654i	0.0878935	+	0.0638584i
$97$	−277.504	+	381.952i	−0.290477	+	0.399807i	−0.929169	−	0.369655i	$-0.879476\pi$
$97$	−277.504	+	381.952i	−0.290477	+	0.399807i	0.638692	+	0.769463i	$0.279476\pi$
$98$	−642.367	−	208.718i	−0.662131	−	0.215139i
$99$	131.916			0.133920
$100$		0			0
$101$	1777.51			1.75117			0.875586	−	0.483061i	$-0.160475\pi$
$101$	1777.51			1.75117			0.875586	+	0.483061i	$0.160475\pi$
$102$	−151.676	−	49.2824i	−0.147237	−	0.0478401i
$103$	−502.009	+	690.956i	−0.480237	+	0.660990i	−0.978550	−	0.206007i	$-0.933953\pi$
$103$	−502.009	+	690.956i	−0.480237	+	0.660990i	0.498313	+	0.866997i	$0.333953\pi$
$104$	−297.336	−	216.027i	−0.280348	−	0.203684i
$105$		0			0
$106$	228.170	−	165.775i	0.209074	−	0.151901i
$107$		−	1574.38i		−	1.42244i	−0.702970	−	0.711220i	$-0.748143\pi$
$107$		−	1574.38i		−	1.42244i	0.702970	−	0.711220i	$-0.251857\pi$
$108$	−328.874	−	452.656i	−0.293018	−	0.403304i
$109$	−647.998	−	1994.33i	−0.569422	−	1.75250i	−0.654434	−	0.756119i	$-0.727093\pi$
$109$	−647.998	−	1994.33i	−0.569422	−	1.75250i	0.0850122	−	0.996380i	$-0.472907\pi$
$110$		0			0
$111$	371.619	−	1143.73i	0.317771	−	0.977998i
$112$	34.9915	−	11.3694i	0.0295213	−	0.00959205i
$113$	−241.729	+	78.5427i	−0.201239	+	0.0653865i	−0.407902	−	0.913026i	$-0.633740\pi$
$113$	−241.729	+	78.5427i	−0.201239	+	0.0653865i	0.206663	+	0.978412i	$0.433740\pi$
$114$	−131.304	+	404.111i	−0.107875	+	0.332004i
$115$		0			0
$116$	62.6239	+	192.737i	0.0501249	+	0.154269i
$117$	453.713	+	624.482i	0.358511	+	0.493448i
$118$		−	251.840i		−	0.196473i
$119$	−46.4534	+	33.7504i	−0.0357847	+	0.0259991i
$120$		0			0
$121$	1026.93	+	746.111i	0.771550	+	0.560564i
$122$	403.041	−	554.738i	0.299095	−	0.411669i
$123$	−1098.30	−	356.860i	−0.805126	−	0.261601i
$124$	−604.154			−0.437537
$125$		0			0
$126$	−77.2732			−0.0546353
$127$	−306.900	−	99.7177i	−0.214433	−	0.0696734i	0.199831	−	0.979830i	$-0.435961\pi$
$127$	−306.900	−	99.7177i	−0.214433	−	0.0696734i	−0.414263	+	0.910157i	$0.635961\pi$
$128$	75.2365	−	103.554i	0.0519534	−	0.0715077i
$129$	−1243.79	−	903.664i	−0.848909	−	0.616769i
$130$		0			0
$131$	−50.1564	+	36.4407i	−0.0334518	+	0.0243041i	−0.604386	−	0.796692i	$-0.706581\pi$
$131$	−50.1564	+	36.4407i	−0.0334518	+	0.0243041i	0.570934	+	0.820996i	$0.306581\pi$
$132$			100.288i			0.0661286i
$133$	89.9215	+	123.766i	0.0586254	+	0.0806909i
$134$	−435.454	−	1340.19i	−0.280727	−	0.863990i
$135$		0			0
$136$	−61.7300	+	189.985i	−0.0389213	+	0.119788i
$137$	1817.01	−	590.382i	1.13312	−	0.368173i	0.318359	−	0.947970i	$-0.396868\pi$
$137$	1817.01	−	590.382i	1.13312	−	0.368173i	0.814761	+	0.579797i	$0.196868\pi$
$138$	879.472	−	285.758i	0.542505	−	0.176270i
$139$	−672.409	+	2069.46i	−0.410310	+	1.26280i	0.506070	+	0.862492i	$0.331098\pi$
$139$	−672.409	+	2069.46i	−0.410310	+	1.26280i	−0.916380	+	0.400311i	$0.868902\pi$
$140$		0			0
$141$	−239.421	−	736.863i	−0.142999	−	0.440107i
$142$	393.261	+	541.277i	0.232407	+	0.319880i
$143$		−	360.689i		−	0.210926i
$144$	−217.491	+	158.016i	−0.125863	+	0.0914445i
$145$		0			0
$146$	−758.992	−	551.440i	−0.430237	−	0.312586i
$147$	−633.901	+	872.490i	−0.355669	+	0.489536i
$148$	−1432.60	−	465.482i	−0.795672	−	0.258529i
$149$	3058.26			1.68149			0.840746	−	0.541430i	$-0.182117\pi$
$149$	3058.26			1.68149			0.840746	+	0.541430i	$0.182117\pi$
$150$		0			0
$151$	−96.5972			−0.0520594			−0.0260297	−	0.999661i	$-0.508286\pi$
$151$	−96.5972			−0.0520594			−0.0260297	+	0.999661i	$0.508286\pi$
$152$	506.180	+	164.468i	0.270109	+	0.0877638i
$153$	246.607	−	339.425i	0.130307	−	0.179352i
$154$	29.2118	+	21.2236i	0.0152854	+	0.0111055i
$155$		0			0
$156$	−474.759	+	344.932i	−0.243661	+	0.177030i
$157$		−	1642.60i		−	0.834994i	−0.908678	−	0.417497i	$-0.862907\pi$
$157$		−	1642.60i		−	0.834994i	0.908678	−	0.417497i	$-0.137093\pi$
$158$	1610.36	+	2216.46i	0.810842	+	1.11603i
$159$	−139.158	−	428.285i	−0.0694086	−	0.213618i
$160$		0			0
$161$	102.884	−	316.645i	0.0503627	−	0.155001i
$162$	13.2493	−	4.30497i	0.00642571	−	0.00208784i
$163$	−1609.79	+	523.052i	−0.773548	+	0.251341i	−0.669083	−	0.743188i	$-0.733313\pi$
$163$	−1609.79	+	523.052i	−0.773548	+	0.251341i	−0.104465	+	0.994529i	$0.533313\pi$
$164$	−446.994	+	1375.71i	−0.212832	+	0.655028i
$165$		0			0
$166$	337.125	+	1037.56i	0.157626	+	0.485124i
$167$	835.295	+	1149.69i	0.387048	+	0.532726i	0.957435	−	0.288650i	$-0.0932065\pi$
$167$	835.295	+	1149.69i	0.387048	+	0.532726i	−0.570386	+	0.821377i	$0.693206\pi$
$168$		−	58.7465i		−	0.0269785i
$169$	−69.9282	+	50.8058i	−0.0318290	+	0.0231251i
$170$		0			0
$171$	−904.335	−	657.037i	−0.404422	−	0.293830i
$172$	−1131.91	+	1557.94i	−0.501786	+	0.690649i
$173$	3333.54	+	1083.13i	1.46500	+	0.476007i	0.929593	−	0.368588i	$-0.120159\pi$
$173$	3333.54	+	1083.13i	1.46500	+	0.476007i	0.535406	+	0.844595i	$0.320159\pi$
$174$	323.582			0.140981
$175$		0			0
$176$	125.619			0.0538003
$177$	−382.435	−	124.261i	−0.162404	−	0.0527684i
$178$	213.741	−	294.189i	0.0900032	−	0.123879i
$179$	2530.42	+	1838.46i	1.05661	+	0.767669i	0.973457	−	0.228868i	$-0.0735024\pi$
$179$	2530.42	+	1838.46i	1.05661	+	0.767669i	0.0831486	+	0.996537i	$0.473502\pi$
$180$		0			0
$181$	−2127.12	+	1545.44i	−0.873522	+	0.634651i	−0.931530	−	0.363665i	$-0.881525\pi$
$181$	−2127.12	+	1545.44i	−0.873522	+	0.634651i	0.0580074	+	0.998316i	$0.481525\pi$
$182$			211.283i			0.0860514i
$183$	−643.539	−	885.756i	−0.259955	−	0.357798i
$184$	−357.933	−	1101.61i	−0.143409	−	0.441366i
$185$		0			0
$186$	−298.096	+	917.445i	−0.117513	+	0.361668i
$187$	−186.451	+	60.5815i	−0.0729125	+	0.0236907i
$188$	−922.977	+	299.893i	−0.358058	+	0.116340i
$189$	−99.3960	+	305.910i	−0.0382540	+	0.117734i
$190$		0			0
$191$	−729.436	−	2244.97i	−0.276336	−	0.850474i	−0.988863	−	0.148829i	$-0.952449\pi$
$191$	−729.436	−	2244.97i	−0.276336	−	0.850474i	0.712527	−	0.701645i	$-0.247551\pi$
$192$	−120.131	−	165.346i	−0.0451547	−	0.0621501i
$193$		−	947.301i		−	0.353307i	−0.984273	−	0.176653i	$-0.943473\pi$
$193$		−	947.301i		−	0.353307i	0.984273	−	0.176653i	$-0.0565272\pi$
$194$	763.903	−	555.008i	0.282706	−	0.205398i
$195$		0			0
$196$	1092.86	+	794.009i	0.398273	+	0.289362i
$197$	217.553	−	299.436i	0.0786802	−	0.108294i	−0.767863	−	0.640614i	$-0.778680\pi$
$197$	217.553	−	299.436i	0.0786802	−	0.108294i	0.846543	+	0.532320i	$0.178680\pi$
$198$	−250.919	−	81.5284i	−0.0900607	−	0.0292625i
$199$	4873.99			1.73622			0.868110	−	0.496371i	$-0.165334\pi$
$199$	4873.99			1.73622			0.868110	+	0.496371i	$0.165334\pi$
$200$		0			0
$201$	−2250.02			−0.789571
$202$	−3381.02	−	1098.56i	−1.17766	−	0.382645i
$203$	68.4783	−	94.2523i	0.0236760	−	0.0325872i
$204$	258.046	+	187.482i	0.0885630	+	0.0643448i
$205$		0			0
$206$	1381.91	−	1004.02i	0.467390	−	0.339579i
$207$			2432.72i			0.816840i
$208$	432.054	+	594.671i	0.144027	+	0.198236i
$209$	161.408	+	496.763i	0.0534202	+	0.164410i
$210$		0			0
$211$	−1228.43	+	3780.73i	−0.400800	+	1.23354i	0.523552	+	0.851994i	$0.324607\pi$
$211$	−1228.43	+	3780.73i	−0.400800	+	1.23354i	−0.924352	+	0.381542i	$0.875393\pi$
$212$	−536.459	+	174.306i	−0.173793	+	0.0564688i
$213$	1016.00	−	330.119i	0.326832	−	0.106194i
$214$	−973.020	+	2994.65i	−0.310814	+	0.956588i
$215$		0			0
$216$	345.798	+	1064.26i	0.108929	+	0.335248i
$217$	204.147	+	280.984i	0.0638635	+	0.0879006i
$218$			4193.93i			1.30298i
$219$	−1211.89	+	880.489i	−0.373936	+	0.271680i
$220$		0			0
$221$	−928.070	−	674.282i	−0.282483	−	0.205236i
$222$	−1413.72	+	1945.82i	−0.427401	+	0.588267i
$223$	1410.44	+	458.280i	0.423543	+	0.137617i	0.513030	−	0.858371i	$-0.328523\pi$
$223$	1410.44	+	458.280i	0.423543	+	0.137617i	−0.0894874	+	0.995988i	$0.528523\pi$
$224$	−73.5844			−0.0219490
$225$		0			0
$226$	508.339			0.149620
$227$	−3793.27	−	1232.51i	−1.10911	−	0.360372i	−0.303508	−	0.952829i	$-0.598158\pi$
$227$	−3793.27	−	1232.51i	−1.10911	−	0.360372i	−0.805602	+	0.592457i	$0.798158\pi$
$228$	499.509	−	687.515i	0.145091	−	0.199701i
$229$	−3146.62	−	2286.15i	−0.908012	−	0.659709i	0.0324997	−	0.999472i	$-0.489653\pi$
$229$	−3146.62	−	2286.15i	−0.908012	−	0.659709i	−0.940511	+	0.339763i	$0.889653\pi$
$230$		0			0
$231$	46.6427	−	33.8879i	0.0132851	−	0.00965221i
$232$		−	405.311i		−	0.114698i
$233$	2025.92	+	2788.44i	0.569625	+	0.784022i	0.992510	−	0.122161i	$-0.0389826\pi$
$233$	2025.92	+	2788.44i	0.569625	+	0.784022i	−0.422885	+	0.906183i	$0.638983\pi$
$234$	−477.062	−	1468.24i	−0.133276	−	0.410180i
$235$		0			0
$236$	−155.646	+	479.029i	−0.0429309	+	0.132128i
$237$	4160.40	−	1351.80i	1.14028	−	0.370501i
$238$	109.219	−	35.4872i	0.0297462	−	0.00966511i
$239$	−1870.32	+	5756.25i	−0.506196	+	1.55791i	0.292555	+	0.956249i	$0.405495\pi$
$239$	−1870.32	+	5756.25i	−0.506196	+	1.55791i	−0.798751	+	0.601662i	$0.794505\pi$
$240$		0			0
$241$	944.344	+	2906.39i	0.252409	+	0.776834i	0.994329	+	0.106346i	$0.0339152\pi$
$241$	944.344	+	2906.39i	0.252409	+	0.776834i	−0.741920	+	0.670488i	$0.766085\pi$
$242$	−1492.22	−	2053.87i	−0.396379	−	0.545568i
$243$		−	3798.96i		−	1.00289i
$244$	−1109.48	+	806.082i	−0.291094	+	0.211492i
$245$		0			0
$246$	1868.54	+	1357.58i	0.484284	+	0.351853i
$247$	−1796.50	+	2472.67i	−0.462787	+	0.636972i
$248$	1149.17	+	373.388i	0.294243	+	0.0956054i
$249$	1741.95			0.443339
$250$		0			0
$251$	−2919.95			−0.734285			−0.367142	−	0.930165i	$-0.619664\pi$
$251$	−2919.95			−0.734285			−0.367142	+	0.930165i	$0.619664\pi$
$252$	146.982	+	47.7575i	0.0367421	+	0.0119382i
$253$	668.163	−	919.647i	0.166036	−	0.228529i
$254$	522.129	+	379.349i	0.128981	+	0.0937105i
$255$		0			0
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$		−	4819.54i		−	1.16978i	−0.811111	−	0.584892i	$-0.801137\pi$
$257$		−	4819.54i		−	1.16978i	0.811111	−	0.584892i	$-0.198863\pi$
$258$	1807.33	+	2487.57i	0.436121	+	0.600270i
$259$	267.595	+	823.574i	0.0641991	+	0.197584i
$260$		0			0
$261$	−263.053	+	809.594i	−0.0623853	+	0.192002i
$262$	117.925	−	38.3160i	0.0278069	−	0.00903501i
$263$	−236.409	+	76.8139i	−0.0554281	+	0.0180097i	−0.336600	−	0.941648i	$-0.609277\pi$
$263$	−236.409	+	76.8139i	−0.0554281	+	0.0180097i	0.281172	+	0.959657i	$0.409277\pi$
$264$	61.9815	−	190.760i	0.0144496	−	0.0444714i
$265$		0			0
$266$	−94.5490	−	290.992i	−0.0217939	−	0.0670747i
$267$	−341.283	−	469.735i	−0.0782253	−	0.107668i
$268$			2818.32i			0.642373i
$269$	−87.0192	+	63.2231i	−0.0197236	+	0.0143300i	−0.597603	−	0.801792i	$-0.703880\pi$
$269$	−87.0192	+	63.2231i	−0.0197236	+	0.0143300i	0.577880	+	0.816122i	$0.303880\pi$
$270$		0			0
$271$	−1667.50	−	1211.51i	−0.373776	−	0.271564i	0.384999	−	0.922917i	$-0.374202\pi$
$271$	−1667.50	−	1211.51i	−0.373776	−	0.271564i	−0.758775	+	0.651353i	$0.774202\pi$
$272$	234.835	−	323.222i	0.0523491	−	0.0720524i
$273$	320.847	+	104.249i	0.0711301	+	0.0231116i
$274$	−3821.03			−0.842470
$275$		0			0
$276$	−1849.46			−0.403350
$277$	−4301.78	−	1397.73i	−0.933100	−	0.303183i	−0.197270	−	0.980349i	$-0.563208\pi$
$277$	−4301.78	−	1397.73i	−0.933100	−	0.303183i	−0.735830	+	0.677167i	$0.763208\pi$
$278$	2558.00	−	3520.78i	0.551865	−	0.759577i
$279$	−2053.09	−	1491.66i	−0.440557	−	0.320083i
$280$		0			0
$281$	5570.74	−	4047.38i	1.18264	−	0.859240i	0.190175	−	0.981750i	$-0.439095\pi$
$281$	5570.74	−	4047.38i	1.18264	−	0.859240i	0.992467	+	0.122511i	$0.0390946\pi$
$282$			1549.57i			0.327218i
$283$	−4089.83	−	5629.17i	−0.859064	−	1.18240i	−0.981792	−	0.189960i	$-0.939164\pi$
$283$	−4089.83	−	5629.17i	−0.859064	−	1.18240i	0.122728	−	0.992440i	$-0.460836\pi$
$284$	−413.499	−	1272.62i	−0.0863967	−	0.265902i
$285$		0			0
$286$	−222.918	+	686.072i	−0.0460889	+	0.141847i
$287$	790.864	−	256.967i	0.162659	−	0.0528512i
$288$	511.351	−	166.148i	0.104624	−	0.0339943i
$289$	1325.52	−	4079.54i	0.269799	−	0.830357i
$290$		0			0
$291$	−465.896	−	1433.88i	−0.0938533	−	0.288851i
$292$	1102.88	+	1517.98i	0.221031	+	0.304224i
$293$		−	1534.47i		−	0.305954i	−0.988230	−	0.152977i	$-0.951114\pi$
$293$		−	1534.47i		−	0.305954i	0.988230	−	0.152977i	$-0.0488860\pi$
$294$	1744.98	−	1267.80i	0.346154	−	0.251496i
$295$		0			0
$296$	2437.29	+	1770.80i	0.478597	+	0.347721i
$297$	−645.510	+	888.469i	−0.126116	+	0.173583i
$298$	−5817.15	−	1890.11i	−1.13080	−	0.367419i
$299$	6651.64			1.28654
$300$		0			0
$301$	1107.05			0.211992
$302$	183.739	+	59.7003i	0.0350099	+	0.0113754i
$303$	−3336.46	+	4592.24i	−0.632589	+	0.870684i
$304$	−861.165	−	625.673i	−0.162471	−	0.118042i
$305$		0			0
$306$	−678.851	+	493.214i	−0.126821	+	0.0921411i
$307$			5810.26i			1.08016i	0.841614	+	0.540080i	$0.181606\pi$
$307$			5810.26i			1.08016i	−0.841614	+	0.540080i	$0.818394\pi$
$308$	−42.4472	−	58.4235i	−0.00785276	−	0.0108084i
$309$	−842.813	−	2593.91i	−0.155165	−	0.477549i
$310$		0			0
$311$	2323.98	−	7152.46i	0.423732	−	1.30411i	−0.480471	−	0.877010i	$-0.659534\pi$
$311$	2323.98	−	7152.46i	0.423732	−	1.30411i	0.904203	−	0.427102i	$-0.140466\pi$
$312$	1116.22	−	362.683i	0.202544	−	0.0658106i
$313$	2461.89	−	799.917i	0.444583	−	0.144454i	−0.0781662	−	0.996940i	$-0.524906\pi$
$313$	2461.89	−	799.917i	0.444583	−	0.144454i	0.522749	+	0.852487i	$0.324906\pi$
$314$	−1015.19	+	3124.42i	−0.182453	+	0.561532i
$315$		0			0
$316$	−1693.23	−	5211.22i	−0.301429	−	0.927703i
$317$	−1756.33	−	2417.37i	−0.311183	−	0.428307i	0.624567	−	0.780972i	$-0.285276\pi$
$317$	−1756.33	−	2417.37i	−0.311183	−	0.428307i	−0.935750	+	0.352665i	$0.885276\pi$
$318$			900.651i			0.158824i
$319$	321.803	−	233.803i	0.0564812	−	0.0410360i
$320$		0			0
$321$	4067.46	+	2955.18i	0.707238	+	0.513838i
$322$	−391.394	+	538.708i	−0.0677377	+	0.0932330i
$323$	1579.93	+	513.352i	0.272167	+	0.0884323i
$324$	−27.8623			−0.00477749
$325$		0			0
$326$	3385.26			0.575130
$327$	6368.74	+	2069.33i	1.07704	+	0.349952i
$328$	1700.47	−	2340.49i	0.286258	−	0.394000i
$329$	451.355	+	327.928i	0.0756352	+	0.0549522i
$330$		0			0
$331$	1556.35	−	1130.75i	0.258443	−	0.187769i	−0.451018	−	0.892515i	$-0.648939\pi$
$331$	1556.35	−	1130.75i	0.258443	−	0.187769i	0.709460	+	0.704746i	$0.248939\pi$
$332$		−	2181.92i		−	0.360688i
$333$	−3719.13	−	5118.95i	−0.612034	−	0.842392i
$334$	−878.281	−	2703.07i	−0.143884	−	0.442831i
$335$		0			0
$336$	−36.3073	+	111.742i	−0.00589502	+	0.0181430i
$337$	10840.4	−	3522.27i	1.75227	−	0.569348i	0.755918	−	0.654666i	$-0.227191\pi$
$337$	10840.4	−	3522.27i	1.75227	−	0.569348i	0.996354	+	0.0853185i	$0.0271908\pi$
$338$	164.411	−	53.4204i	0.0264579	−	0.00859671i
$339$	250.820	−	771.943i	0.0401848	−	0.123676i
$340$		0			0
$341$	366.441	+	1127.79i	0.0581932	+	0.179100i
$342$	1314.07	+	1808.67i	0.207769	+	0.285970i
$343$		−	1565.31i		−	0.246410i
$344$	3115.87	−	2263.82i	0.488362	−	0.354816i
$345$		0			0
$346$	−5671.37	−	4120.49i	−0.881198	−	0.640228i
$347$	2710.11	−	3730.14i	0.419269	−	0.577074i	−0.546180	−	0.837668i	$-0.683918\pi$
$347$	2710.11	−	3730.14i	0.419269	−	0.577074i	0.965448	+	0.260594i	$0.0839185\pi$
$348$	−615.489	−	199.985i	−0.0948094	−	0.0308054i
$349$	−3259.11			−0.499874			−0.249937	−	0.968262i	$-0.580410\pi$
$349$	−3259.11			−0.499874			−0.249937	+	0.968262i	$0.580410\pi$
$350$		0			0
$351$	−6426.14			−0.977213
$352$	−238.941	−	77.6366i	−0.0361806	−	0.0117558i
$353$	−6298.41	+	8669.02i	−0.949662	+	1.30710i	0.00201504	+	0.999998i	$0.499359\pi$
$353$	−6298.41	+	8669.02i	−0.949662	+	1.30710i	−0.951677	+	0.307100i	$0.900641\pi$
$354$	650.637	+	472.716i	0.0976864	+	0.0709733i
$355$		0			0
$356$	−588.379	+	427.482i	−0.0875956	+	0.0636419i
$357$		−	183.365i		−	0.0271840i
$358$	−3676.92	−	5060.84i	−0.542824	−	0.747133i
$359$	1475.99	+	4542.64i	0.216992	+	0.667832i	0.999006	+	0.0445715i	$0.0141922\pi$
$359$	1475.99	+	4542.64i	0.216992	+	0.667832i	−0.782015	+	0.623260i	$0.785808\pi$
$360$		0			0
$361$	−751.820	+	2313.86i	−0.109611	+	0.337347i
$362$	5001.16	−	1624.97i	0.726119	−	0.235930i
$363$	−3855.20	+	1252.63i	−0.557426	+	0.181119i
$364$	130.580	−	401.885i	0.0188029	−	0.0578695i
$365$		0			0
$366$	676.657	+	2082.54i	0.0966378	+	0.297421i
$367$	3718.61	+	5118.23i	0.528910	+	0.727983i	0.986964	−	0.160942i	$-0.0514532\pi$
$367$	3718.61	+	5118.23i	0.528910	+	0.727983i	−0.458054	+	0.888925i	$0.651453\pi$
$368$			2316.59i			0.328154i
$369$	−4915.64	+	3571.42i	−0.693490	+	0.503850i
$370$		0			0
$371$	262.340	+	190.601i	0.0367116	+	0.0266725i
$372$	1134.02	−	1560.85i	0.158055	−	0.217544i
$373$	7305.63	+	2373.74i	1.01413	+	0.329511i	0.768498	−	0.639852i	$-0.221004\pi$
$373$	7305.63	+	2373.74i	1.01413	+	0.329511i	0.245633	+	0.969363i	$0.421004\pi$
$374$	392.092			0.0542101
$375$		0			0
$376$	1940.95			0.266215
$377$	2213.62	+	719.250i	0.302407	+	0.0982579i
$378$	378.125	−	520.444i	0.0514515	−	0.0708168i
$379$	−10596.6	−	7698.89i	−1.43618	−	1.04344i	−0.988824	−	0.149088i	$-0.952366\pi$
$379$	−10596.6	−	7698.89i	−1.43618	−	1.04344i	−0.447355	−	0.894357i	$-0.647634\pi$
$380$		0			0
$381$	833.688	−	605.710i	0.112103	−	0.0814474i
$382$			4721.01i			0.632324i
$383$	1884.08	+	2593.21i	0.251363	+	0.345971i	0.915988	−	0.401206i	$-0.131409\pi$
$383$	1884.08	+	2593.21i	0.251363	+	0.345971i	−0.664625	+	0.747177i	$0.731409\pi$
$384$	126.313	+	388.752i	0.0167862	+	0.0516625i
$385$		0			0
$386$	−585.464	+	1801.87i	−0.0772004	+	0.237598i
$387$	−7693.10	+	2499.64i	−1.01050	+	0.328330i
$388$	−1796.04	+	583.570i	−0.235001	+	0.0763564i
$389$	4285.06	−	13188.0i	0.558512	−	1.71892i	−0.127973	−	0.991778i	$-0.540847\pi$
$389$	4285.06	−	13188.0i	0.558512	−	1.71892i	0.686485	−	0.727144i	$-0.259153\pi$
$390$		0			0
$391$	−1117.21	−	3438.43i	−0.144501	−	0.444728i
$392$	−1588.02	−	2185.72i	−0.204610	−	0.281621i
$393$		−	197.981i		−	0.0254118i
$394$	−598.871	+	435.106i	−0.0765754	+	0.0556353i
$395$		0			0
$396$	426.888	+	310.153i	0.0541716	+	0.0393580i
$397$	2557.74	−	3520.43i	0.323348	−	0.445051i	−0.616138	−	0.787639i	$-0.711303\pi$
$397$	2557.74	−	3520.43i	0.323348	−	0.445051i	0.939486	+	0.342588i	$0.111303\pi$
$398$	−9270.88	−	3012.29i	−1.16761	−	0.379378i
$399$	−488.541			−0.0612973
$400$		0			0
$401$	10359.1			1.29005			0.645023	−	0.764163i	$-0.276848\pi$
$401$	10359.1			1.29005			0.645023	+	0.764163i	$0.276848\pi$
$402$	4279.78	+	1390.59i	0.530986	+	0.172528i
$403$	−4078.55	+	5613.64i	−0.504137	+	0.693884i
$404$	5752.13	+	4179.17i	0.708364	+	0.514657i
$405$		0			0
$406$	−188.505	+	136.957i	−0.0230427	+	0.0167415i
$407$			2956.61i			0.360083i
$408$	−374.963	−	516.092i	−0.0454986	−	0.0626235i
$409$	1000.84	+	3080.26i	0.120998	+	0.372394i	0.993151	−	0.116840i	$-0.0372765\pi$
$409$	1000.84	+	3080.26i	0.120998	+	0.372394i	−0.872153	+	0.489234i	$0.837277\pi$
$410$		0			0
$411$	−1885.34	+	5802.47i	−0.226270	+	0.696386i
$412$	−3249.07	+	1055.69i	−0.388520	+	0.126238i
$413$	275.383	−	89.4774i	0.0328105	−	0.0106608i
$414$	1503.51	−	4627.31i	0.178486	−	0.549324i
$415$		0			0
$416$	−454.288	−	1398.16i	−0.0535416	−	0.164784i
$417$	−4084.38	−	5621.67i	−0.479647	−	0.660178i
$418$		−	1044.65i		−	0.122239i
$419$	−4434.10	+	3221.56i	−0.516993	+	0.375617i	−0.815470	−	0.578799i	$-0.803521\pi$
$419$	−4434.10	+	3221.56i	−0.516993	+	0.375617i	0.298477	+	0.954417i	$0.403521\pi$
$420$		0			0
$421$	2450.28	+	1780.23i	0.283657	+	0.206089i	0.720511	−	0.693444i	$-0.243907\pi$
$421$	2450.28	+	1780.23i	0.283657	+	0.206089i	−0.436854	+	0.899532i	$0.643907\pi$
$422$	4673.24	−	6432.16i	0.539075	−	0.741973i
$423$	−3876.98	−	1259.71i	−0.445639	−	0.144797i
$424$	1128.13			0.129215
$425$		0			0
$426$	−2136.57			−0.242999
$427$	749.795	+	243.623i	0.0849769	+	0.0276107i
$428$	3701.59	−	5094.80i	0.418044	−	0.575389i
$429$	931.852	+	677.030i	0.104872	+	0.0761942i
$430$		0			0
$431$	2722.97	−	1978.35i	0.304317	−	0.221099i	−0.425137	−	0.905129i	$-0.639774\pi$
$431$	2722.97	−	1978.35i	0.304317	−	0.221099i	0.729454	+	0.684030i	$0.239774\pi$
$432$		−	2238.05i		−	0.249256i
$433$	−824.752	−	1135.17i	−0.0915359	−	0.125988i	0.760793	−	0.648995i	$-0.224810\pi$
$433$	−824.752	−	1135.17i	−0.0915359	−	0.125988i	−0.852329	+	0.523007i	$0.824810\pi$
$434$	−214.653	−	660.633i	−0.0237411	−	0.0730677i
$435$		0			0
$436$	2591.99	−	7977.33i	0.284711	−	0.876250i
$437$	−9161.04	+	2976.60i	−1.00282	+	0.325836i
$438$	2849.32	−	925.801i	0.310836	−	0.100997i
$439$	1060.43	−	3263.66i	0.115288	−	0.354820i	−0.876719	−	0.481003i	$-0.840273\pi$
$439$	1060.43	−	3263.66i	0.115288	−	0.354820i	0.992007	+	0.126183i	$0.0402726\pi$
$440$		0			0
$441$	1753.44	+	5396.55i	0.189336	+	0.582718i
$442$	1348.56	+	1856.14i	0.145124	+	0.199746i
$443$			184.590i			0.0197972i	0.999951	+	0.00989860i	$0.00315087\pi$
$443$			184.590i			0.0197972i	−0.999951	+	0.00989860i	$0.996849\pi$
$444$	3891.65	−	2827.45i	0.415967	−	0.302218i
$445$		0			0
$446$	−2399.58	−	1743.40i	−0.254761	−	0.185095i
$447$	−5740.49	+	7901.10i	−0.607418	+	0.836039i
$448$	139.966	+	45.4777i	0.0147606	+	0.00479602i
$449$	−14097.0			−1.48169			−0.740845	−	0.671676i	$-0.765575\pi$
$449$	−14097.0			−1.48169			−0.740845	+	0.671676i	$0.765575\pi$
$450$		0			0
$451$	2839.18			0.296434
$452$	−966.918	−	314.171i	−0.100619	−	0.0326932i
$453$	181.317	−	249.562i	0.0188058	−	0.0258840i
$454$	6453.49	+	4688.73i	0.667130	+	0.484699i
$455$		0			0
$456$	−1375.03	+	999.018i	−0.141210	+	0.102595i
$457$			1943.27i			0.198911i	0.995042	+	0.0994555i	$0.0317101\pi$
$457$			1943.27i			0.198911i	−0.995042	+	0.0994555i	$0.968290\pi$
$458$	4572.31	+	6293.24i	0.466485	+	0.642061i
$459$	1079.34	+	3321.86i	0.109758	+	0.337802i
$460$		0			0
$461$	2141.01	−	6589.35i	0.216305	−	0.665720i	−0.782753	−	0.622333i	$-0.786185\pi$
$461$	2141.01	−	6589.35i	0.216305	−	0.665720i	0.999058	−	0.0433870i	$-0.0138148\pi$
$462$	−109.664	+	35.6318i	−0.0110433	+	0.00358819i
$463$	5933.23	−	1927.82i	0.595552	−	0.193507i	0.00429657	−	0.999991i	$-0.498632\pi$
$463$	5933.23	−	1927.82i	0.595552	−	0.193507i	0.591256	+	0.806484i	$0.298632\pi$
$464$	−250.496	+	770.947i	−0.0250624	+	0.0771343i
$465$		0			0
$466$	−2130.18	−	6556.03i	−0.211757	−	0.651721i
$467$	−5238.48	−	7210.14i	−0.519074	−	0.714445i	0.466342	−	0.884604i	$-0.345572\pi$
$467$	−5238.48	−	7210.14i	−0.519074	−	0.714445i	−0.985416	+	0.170160i	$0.945572\pi$
$468$			3087.61i			0.304967i
$469$	1310.76	−	952.323i	0.129052	−	0.0937616i
$470$		0			0
$471$	4243.72	+	3083.24i	0.415160	+	0.301631i
$472$	592.112	−	814.972i	0.0577419	−	0.0794749i
$473$	3594.78	+	1168.02i	0.349447	+	0.113542i
$474$	−8749.01			−0.847796
$475$		0			0
$476$	−229.678			−0.0221161
$477$	−2253.41	−	732.176i	−0.216303	−	0.0702810i
$478$	7115.11	−	9793.11i	0.680832	−	0.937085i
$479$	7185.70	+	5220.72i	0.685435	+	0.497997i	0.875156	−	0.483841i	$-0.160759\pi$
$479$	7185.70	+	5220.72i	0.685435	+	0.497997i	−0.189722	+	0.981838i	$0.560759\pi$
$480$		0			0
$481$	−13996.4	+	10169.0i	−1.32678	+	0.963963i
$482$		−	6111.92i		−	0.577573i
$483$	624.943	+	860.160i	0.0588735	+	0.0810324i
$484$	1569.01	+	4828.93i	0.147353	+	0.453506i
$485$		0			0
$486$	−2347.89	+	7226.05i	−0.219141	+	0.674445i
$487$	−15689.8	+	5097.92i	−1.45990	+	0.474351i	−0.928040	−	0.372480i	$-0.878507\pi$
$487$	−15689.8	+	5097.92i	−1.45990	+	0.474351i	−0.531862	+	0.846831i	$0.678507\pi$
$488$	2608.54	−	847.565i	0.241973	−	0.0786218i
$489$	1670.32	−	5140.73i	0.154468	−	0.475402i
$490$		0			0
$491$	1011.45	+	3112.91i	0.0929652	+	0.286117i	0.986718	−	0.162442i	$-0.0519371\pi$
$491$	1011.45	+	3112.91i	0.0929652	+	0.286117i	−0.893753	+	0.448560i	$0.851937\pi$
$492$	−2715.15	−	3737.08i	−0.248798	−	0.342441i
$493$		−	1265.09i		−	0.115572i
$494$	4945.33	−	3592.99i	0.450407	−	0.327240i
$495$		0			0
$496$	−1955.08	−	1420.45i	−0.176988	−	0.128589i
$497$	−452.154	+	622.337i	−0.0408087	+	0.0561683i
$498$	−3313.38	−	1076.58i	−0.298145	−	0.0968731i
$499$	−3641.51			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$499$	−3641.51			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$500$		0			0
$501$	−4538.13			−0.404688
$502$	5554.07	+	1804.63i	0.493805	+	0.160447i
$503$	1692.47	−	2329.49i	0.150027	−	0.206495i	−0.727388	−	0.686226i	$-0.759266\pi$
$503$	1692.47	−	2329.49i	0.150027	−	0.206495i	0.877415	+	0.479732i	$0.159266\pi$
$504$	−250.061	−	181.680i	−0.0221004	−	0.0160569i
$505$		0			0
$506$	−1839.29	+	1336.33i	−0.161594	+	0.117405i
$507$		−	276.026i		−	0.0241790i
$508$	−758.697	−	1044.26i	−0.0662633	−	0.0912036i
$509$	2891.28	+	8898.45i	0.251776	+	0.774886i	0.994448	+	0.105231i	$0.0335581\pi$
$509$	2891.28	+	8898.45i	0.251776	+	0.774886i	−0.742672	+	0.669655i	$0.766442\pi$
$510$		0			0
$511$	333.325	−	1025.87i	0.0288560	−	0.0888097i
$512$	486.941	−	158.217i	0.0420312	−	0.0136568i
$513$	8850.45	−	2875.69i	0.761710	−	0.247494i
$514$	−2978.64	+	9167.31i	−0.255607	+	0.786678i
$515$		0			0
$516$	−1900.34	−	5848.64i	−0.162127	−	0.498976i
$517$	1119.64	+	1541.05i	0.0952448	+	0.131093i
$518$		−	1731.91i		−	0.146903i
$519$	−9055.52	+	6579.22i	−0.765883	+	0.556447i
$520$		0			0
$521$	−3981.75	−	2892.91i	−0.334824	−	0.243264i	0.407650	−	0.913138i	$-0.366348\pi$
$521$	−3981.75	−	2892.91i	−0.334824	−	0.243264i	−0.742475	+	0.669874i	$0.766348\pi$
$522$	1000.71	−	1377.36i	0.0839081	−	0.115490i
$523$	10044.0	+	3263.49i	0.839758	+	0.272854i	0.697150	−	0.716925i	$-0.254451\pi$
$523$	10044.0	+	3263.49i	0.839758	+	0.272854i	0.142608	+	0.989779i	$0.454451\pi$
$524$	−247.987			−0.0206743
$525$		0			0
$526$	497.150			0.0412106
$527$	3586.89	+	1165.45i	0.296485	+	0.0963337i
$528$	−235.792	+	324.539i	−0.0194347	+	0.0267496i
$529$	7116.35	+	5170.33i	0.584890	+	0.424947i
$530$		0			0
$531$	−1711.65	+	1243.59i	−0.139886	+	0.101633i
$532$			611.934i			0.0498697i
$533$	9765.11	+	13440.5i	0.793572	+	1.09226i
$534$	358.846	+	1104.41i	0.0290801	+	0.0894994i
$535$		0			0
$536$	1741.81	−	5360.75i	0.140364	−	0.431995i
$537$	−9499.42	+	3086.55i	−0.763371	+	0.248034i
$538$	204.594	−	66.4767i	0.0163953	−	0.00532717i
$539$	819.338	−	2521.66i	0.0654757	−	0.201513i
$540$		0			0
$541$	4371.04	+	13452.7i	0.347367	+	1.06909i	0.960304	+	0.278955i	$0.0899880\pi$
$541$	4371.04	+	13452.7i	0.347367	+	1.06909i	−0.612937	+	0.790132i	$0.710012\pi$
$542$	2423.01	+	3334.99i	0.192025	+	0.264299i
$543$		−	8396.34i		−	0.663576i
$544$	−646.445	+	469.670i	−0.0509487	+	0.0370164i
$545$		0			0
$546$	−545.857	−	396.588i	−0.0427848	−	0.0310850i
$547$	11310.7	−	15567.9i	0.884116	−	1.21688i	−0.0911483	−	0.995837i	$-0.529054\pi$
$547$	11310.7	−	15567.9i	0.884116	−	1.21688i	0.975264	−	0.221043i	$-0.0709463\pi$
$548$	7268.03	+	2361.53i	0.566560	+	0.184087i
$549$	−5760.54			−0.447821
$550$		0			0
$551$	−3370.60			−0.260603
$552$	3517.89	+	1143.03i	0.271252	+	0.0881352i
$553$	−1851.52	+	2548.39i	−0.142377	+	0.195965i
$554$	7318.62	+	5317.29i	0.561261	+	0.407780i
$555$		0			0
$556$	−7041.56	+	5116.00i	−0.537102	+	0.390228i
$557$			5217.98i			0.396935i	0.980107	+	0.198468i	$0.0635965\pi$
$557$			5217.98i			0.396935i	−0.980107	+	0.198468i	$0.936403\pi$
$558$	2983.32	+	4106.18i	0.226333	+	0.311521i
$559$	6834.61	+	21034.8i	0.517126	+	1.59155i
$560$		0			0
$561$	193.462	−	595.416i	0.0145597	−	0.0448101i
$562$	−13097.6	+	4255.66i	−0.983076	+	0.319421i
$563$	−17171.7	+	5579.44i	−1.28544	+	0.417665i	−0.870493	−	0.492181i	$-0.836200\pi$
$563$	−17171.7	+	5579.44i	−1.28544	+	0.417665i	−0.414947	+	0.909846i	$0.636200\pi$
$564$	957.685	−	2947.45i	0.0714997	−	0.220053i
$565$		0			0
$566$	4300.30	+	13235.0i	0.319355	+	0.982875i
$567$	9.41483	+	12.9584i	0.000697329	+	0.000959791i
$568$			2676.22i			0.197697i
$569$	6298.18	−	4575.90i	0.464031	−	0.337138i	−0.331080	−	0.943603i	$-0.607413\pi$
$569$	6298.18	−	4575.90i	0.464031	−	0.337138i	0.795110	+	0.606465i	$0.207413\pi$
$570$		0			0
$571$	−4980.74	−	3618.72i	−0.365039	−	0.265217i	0.390112	−	0.920768i	$-0.372436\pi$
$571$	−4980.74	−	3618.72i	−0.365039	−	0.265217i	−0.755151	+	0.655551i	$0.772436\pi$
$572$	848.031	−	1167.22i	0.0619895	−	0.0853212i
$573$	7169.14	+	2329.39i	0.522679	+	0.169829i
$574$	−1663.13			−0.120937
$575$		0			0
$576$	−1075.33			−0.0777874
$577$	11734.1	+	3812.64i	0.846616	+	0.275082i	0.700028	−	0.714115i	$-0.253171\pi$
$577$	11734.1	+	3812.64i	0.846616	+	0.275082i	0.146588	+	0.989198i	$0.453171\pi$
$578$	−5042.59	+	6940.53i	−0.362879	+	0.499460i
$579$	2447.38	+	1778.13i	0.175664	+	0.127628i
$580$		0			0
$581$	−1014.78	+	737.282i	−0.0724616	+	0.0526465i
$582$			3015.34i			0.214759i
$583$	650.763	+	895.699i	0.0462296	+	0.0636296i
$584$	−1159.64	−	3568.99i	−0.0821680	−	0.252887i
$585$		0			0
$586$	−948.352	+	2918.73i	−0.0668534	+	0.205754i
$587$	−18172.8	+	5904.71i	−1.27781	+	0.415184i	−0.867807	−	0.496901i	$-0.834471\pi$
$587$	−18172.8	+	5904.71i	−1.27781	+	0.415184i	−0.409999	+	0.912086i	$0.634471\pi$
$588$	−4102.69	+	1333.05i	−0.287742	+	0.0934930i
$589$	3105.12	−	9556.58i	0.217223	−	0.668544i
$590$		0			0
$591$	365.245	+	1124.11i	0.0254216	+	0.0782397i
$592$	−3541.59	−	4874.59i	−0.245876	−	0.338419i
$593$		−	3305.14i		−	0.228880i	−0.993430	−	0.114440i	$-0.963493\pi$
$593$		−	3305.14i		−	0.228880i	0.993430	−	0.114440i	$-0.0365074\pi$
$594$	1776.94	−	1291.02i	0.122742	−	0.0891772i
$595$		0			0
$596$	9896.73	+	7190.40i	0.680178	+	0.494178i
$597$	−9148.70	+	12592.1i	−0.627188	+	0.863250i
$598$	−12652.2	−	4110.94i	−0.865194	−	0.281119i
$599$	−10582.2			−0.721830			−0.360915	−	0.932599i	$-0.617536\pi$
$599$	−10582.2			−0.721830			−0.360915	+	0.932599i	$0.617536\pi$
$600$		0			0
$601$	7836.60			0.531883			0.265941	−	0.963989i	$-0.414317\pi$
$601$	7836.60			0.531883			0.265941	+	0.963989i	$0.414317\pi$
$602$	−2105.74	−	684.196i	−0.142564	−	0.0463219i
$603$	−6958.43	+	9577.45i	−0.469932	+	0.646806i
$604$	−312.595	−	227.114i	−0.0210585	−	0.0152999i
$605$		0			0
$606$	9184.48	−	6672.92i	0.615667	−	0.447308i
$607$		−	10685.1i		−	0.714487i	−0.934011	−	0.357243i	$-0.883717\pi$
$607$		−	10685.1i		−	0.714487i	0.934011	−	0.357243i	$-0.116283\pi$
$608$	1251.35	+	1722.33i	0.0834684	+	0.114884i
$609$	114.967	+	353.831i	0.00764974	+	0.0235435i
$610$		0			0
$611$	−3444.34	+	10600.6i	−0.228057	+	0.701889i
$612$	1596.07	−	518.596i	0.105421	−	0.0342533i
$613$	−3699.58	+	1202.07i	−0.243760	+	0.0792023i	−0.428349	−	0.903613i	$-0.640905\pi$
$613$	−3699.58	+	1202.07i	−0.243760	+	0.0792023i	0.184589	+	0.982816i	$0.440905\pi$
$614$	3590.94	−	11051.8i	0.236024	−	0.726406i
$615$		0			0
$616$	44.6316	+	137.362i	0.00291925	+	0.00898453i
$617$	3473.50	+	4780.86i	0.226641	+	0.311945i	0.907160	−	0.420786i	$-0.138246\pi$
$617$	3473.50	+	4780.86i	0.226641	+	0.311945i	−0.680519	+	0.732731i	$0.738246\pi$
$618$			5454.80i			0.355055i
$619$	18706.7	−	13591.2i	1.21468	−	0.882518i	0.219034	−	0.975717i	$-0.429710\pi$
$619$	18706.7	−	13591.2i	1.21468	−	0.882518i	0.995647	+	0.0931998i	$0.0297095\pi$
$620$		0			0
$621$	−16384.7	−	11904.2i	−1.05877	−	0.769240i
$622$	−8840.93	+	12168.5i	−0.569918	+	0.784425i
$623$	397.632	+	129.199i	0.0255711	+	0.00830856i
$624$	−2347.34			−0.150591
$625$		0			0
$626$	−5177.17			−0.330546
$627$	−1586.37	−	515.443i	−0.101042	−	0.0328307i
$628$	3861.99	−	5315.58i	0.245399	−	0.337762i
$629$	7607.49	+	5527.17i	0.482243	+	0.350370i
$630$		0			0
$631$	−3138.76	+	2280.44i	−0.198022	+	0.143871i	−0.682378	−	0.731000i	$-0.739054\pi$
$631$	−3138.76	+	2280.44i	−0.198022	+	0.143871i	0.484356	+	0.874871i	$0.339054\pi$
$632$			10958.8i			0.689743i
$633$	−7461.80	−	10270.3i	−0.468531	−	0.644877i
$634$	1846.71	+	5683.59i	0.115682	+	0.356032i
$635$		0			0
$636$	556.633	−	1713.14i	0.0347043	−	0.106809i
$637$	14755.4	−	4794.34i	0.917790	−	0.298208i
$638$	−756.604	+	245.835i	−0.0469502	+	0.0152550i
$639$	1736.91	−	5345.66i	0.107529	−	0.330941i
$640$		0			0
$641$	−3137.90	−	9657.46i	−0.193354	−	0.595081i	−0.999992	−	0.00403564i	$-0.998715\pi$
$641$	−3137.90	−	9657.46i	−0.193354	−	0.595081i	0.806638	−	0.591045i	$-0.201285\pi$
$642$	−5910.36	−	8134.92i	−0.363339	−	0.500093i
$643$			12133.7i			0.744177i	0.928197	+	0.372088i	$0.121358\pi$
$643$			12133.7i			0.744177i	−0.928197	+	0.372088i	$0.878642\pi$
$644$	1077.42	−	782.789i	0.0659257	−	0.0478978i
$645$		0			0
$646$	−2687.94	−	1952.91i	−0.163709	−	0.118941i
$647$	19126.7	−	26325.6i	1.16221	−	1.59964i	0.459466	−	0.888196i	$-0.348041\pi$
$647$	19126.7	−	26325.6i	1.16221	−	1.59964i	0.702741	−	0.711445i	$-0.251959\pi$
$648$	52.9973	+	17.2199i	0.00321286	+	0.00104392i
$649$	988.620			0.0597946
$650$		0			0
$651$	−1109.12			−0.0667741
$652$	−6439.15	−	2092.21i	−0.386774	−	0.125671i
$653$	8150.20	−	11217.8i	0.488426	−	0.672261i	−0.491671	−	0.870781i	$-0.663614\pi$
$653$	8150.20	−	11217.8i	0.488426	−	0.672261i	0.980097	+	0.198521i	$0.0636137\pi$
$654$	−10835.1	−	7872.20i	−0.647841	−	0.470684i
$655$		0			0
$656$	−4680.98	+	3400.93i	−0.278600	+	0.202415i
$657$			7881.56i			0.468020i
$658$	−655.857	−	902.710i	−0.0388571	−	0.0534822i
$659$	−3501.07	−	10775.2i	−0.206953	−	0.636937i	−0.999628	−	0.0272913i	$-0.991312\pi$
$659$	−3501.07	−	10775.2i	−0.206953	−	0.636937i	0.792674	−	0.609645i	$-0.208688\pi$
$660$		0			0
$661$	188.793	−	581.044i	0.0111092	−	0.0341906i	−0.945348	−	0.326062i	$-0.894278\pi$
$661$	188.793	−	581.044i	0.0111092	−	0.0341906i	0.956457	+	0.291872i	$0.0942780\pi$
$662$	−3659.19	+	1188.94i	−0.214831	+	0.0698029i
$663$	3484.06	−	1132.04i	0.204087	−	0.0663119i
$664$	−1348.50	+	4150.26i	−0.0788132	+	0.242562i
$665$		0			0
$666$	3910.53	+	12035.4i	0.227522	+	0.700242i
$667$	4311.68	+	5934.52i	0.250298	+	0.344506i
$668$			5684.36i			0.329243i
$669$	−3831.44	+	2783.70i	−0.221423	+	0.160873i
$670$		0			0
$671$	2177.67	+	1582.17i	0.125288	+	0.0910268i
$672$	138.121	−	190.108i	0.00792879	−	0.0109130i
$673$	−2409.94	−	783.038i	−0.138033	−	0.0448498i	0.239186	−	0.970974i	$-0.423120\pi$
$673$	−2409.94	−	783.038i	−0.138033	−	0.0448498i	−0.377219	+	0.926124i	$0.623120\pi$
$674$	−22796.6			−1.30281
$675$		0			0
$676$	−345.744			−0.0196714
$677$	9282.87	+	3016.19i	0.526986	+	0.171228i	0.560414	−	0.828213i	$-0.310642\pi$
$677$	9282.87	+	3016.19i	0.526986	+	0.171228i	−0.0334272	+	0.999441i	$0.510642\pi$
$678$	−954.175	+	1313.31i	−0.0540485	+	0.0743913i
$679$	878.303	+	638.124i	0.0496409	+	0.0360662i
$680$		0			0
$681$	10304.3	−	7486.55i	0.579829	−	0.421270i
$682$		−	2371.66i		−	0.133160i
$683$	−1760.61	−	2423.27i	−0.0986351	−	0.135760i	0.756847	−	0.653592i	$-0.226739\pi$
$683$	−1760.61	−	2423.27i	−0.0986351	−	0.135760i	−0.855482	+	0.517833i	$0.826739\pi$
$684$	−1381.70	−	4252.44i	−0.0772378	−	0.237713i
$685$		0			0
$686$	−967.413	+	2977.39i	−0.0538426	+	0.165710i
$687$	11812.7	−	3838.18i	0.656016	−	0.213152i
$688$	−7325.86	+	2380.32i	−0.405953	+	0.131902i
$689$	−2001.94	+	6161.35i	−0.110694	+	0.340680i
$690$		0			0
$691$	−5114.72	−	15741.5i	−0.281582	−	0.866619i	−0.987402	−	0.158229i	$-0.949422\pi$
$691$	−5114.72	−	15741.5i	−0.281582	−	0.866619i	0.705821	−	0.708390i	$-0.250578\pi$
$692$	8240.98	+	11342.7i	0.452709	+	0.623101i
$693$		−	303.342i		−	0.0166277i
$694$	−7460.29	+	5420.21i	−0.408053	+	0.296468i
$695$		0			0
$696$	1047.13	+	760.786i	0.0570280	+	0.0414332i
$697$	5307.65	−	7305.35i	0.288438	−	0.397001i
$698$	6199.19	+	2014.24i	0.336164	+	0.109226i
$699$	−11006.8			−0.595586
$700$		0			0
$701$	−2272.93			−0.122464			−0.0612320	−	0.998124i	$-0.519503\pi$
$701$	−2272.93			−0.122464			−0.0612320	+	0.998124i	$0.519503\pi$
$702$	12223.2	+	3971.57i	0.657174	+	0.213529i
$703$	14726.1	−	20268.7i	0.790050	−	1.08741i
$704$	406.510	+	295.347i	0.0217627	+	0.0158115i
$705$		0			0
$706$	17338.0	−	12596.8i	0.924258	−	0.671513i
$707$		−	4087.40i		−	0.217429i
$708$	−945.431	−	1301.27i	−0.0501857	−	0.0690747i
$709$	913.364	+	2811.04i	0.0483809	+	0.148901i	0.972328	−	0.233618i	$-0.0750565\pi$
$709$	913.364	+	2811.04i	0.0483809	+	0.148901i	−0.923947	+	0.382519i	$0.875057\pi$
$710$		0			0
$711$	7112.43	−	21889.8i	0.375158	−	1.15462i
$712$	1383.36	−	449.482i	0.0728142	−	0.0236588i
$713$	−20798.1	+	6757.72i	−1.09242	+	0.354949i
$714$	−113.326	+	348.780i	−0.00593992	+	0.0182812i
$715$		0			0
$716$	3866.14	+	11898.7i	0.201794	+	0.621057i
$717$	−11360.8	−	15636.8i	−0.591737	−	0.814457i
$718$		−	9552.84i		−	0.496530i
$719$	7819.14	−	5680.94i	0.405570	−	0.294664i	−0.366236	−	0.930522i	$-0.619354\pi$
$719$	7819.14	−	5680.94i	0.405570	−	0.294664i	0.771806	+	0.635858i	$0.219354\pi$
$720$		0			0
$721$	1588.86	+	1154.38i	0.0820699	+	0.0596272i
$722$	2860.09	−	3936.58i	0.147426	−	0.202915i
$723$	−9281.33	−	3015.69i	−0.477422	−	0.155124i
$724$	−10517.1			−0.539867
$725$		0			0
$726$	8107.19			0.414444
$727$	24153.6	+	7847.98i	1.23220	+	0.400365i	0.851510	−	0.524338i	$-0.175687\pi$
$727$	24153.6	+	7847.98i	1.23220	+	0.400365i	0.380688	+	0.924704i	$0.375687\pi$
$728$	−496.757	+	683.727i	−0.0252899	+	0.0348085i
$729$	9662.58	+	7020.27i	0.490910	+	0.356667i
$730$		0			0
$731$	9725.54	−	7066.02i	0.492082	−	0.357519i
$732$		−	4379.42i		−	0.221131i
$733$	−16004.9	−	22028.9i	−0.806487	−	1.11003i	−0.991856	−	0.127365i	$-0.959348\pi$
$733$	−16004.9	−	22028.9i	−0.806487	−	1.11003i	0.185369	−	0.982669i	$-0.440652\pi$
$734$	−3909.98	−	12033.7i	−0.196621	−	0.605138i
$735$		0			0
$736$	1431.73	−	4406.42i	0.0717043	−	0.220683i
$737$	5261.02	−	1709.41i	0.262947	−	0.0854367i
$738$	11557.4	−	3755.21i	0.576466	−	0.187305i
$739$	10252.8	−	31554.9i	0.510359	−	1.57072i	−0.281211	−	0.959646i	$-0.590736\pi$
$739$	10252.8	−	31554.9i	0.510359	−	1.57072i	0.791570	−	0.611078i	$-0.209264\pi$
$740$		0			0
$741$	−3016.10	−	9282.61i	−0.149527	−	0.460196i
$742$	−381.202	−	524.679i	−0.0188603	−	0.0259590i
$743$		−	29934.4i		−	1.47804i	−0.673682	−	0.739021i	$-0.735288\pi$
$743$		−	29934.4i		−	1.47804i	0.673682	−	0.739021i	$-0.264712\pi$
$744$	−3121.70	+	2268.05i	−0.153827	+	0.111762i
$745$		0			0
$746$	−12429.1	−	9030.25i	−0.610001	−	0.443192i
$747$	5387.16	−	7414.80i	0.263864	−	0.363177i
$748$	−745.803	−	242.326i	−0.0364562	−	0.0118453i
$749$	−3620.31			−0.176613
$750$		0			0
$751$	28659.1			1.39253			0.696263	−	0.717787i	$-0.254845\pi$
$751$	28659.1			1.39253			0.696263	+	0.717787i	$0.254845\pi$
$752$	−3691.91	−	1199.57i	−0.179029	−	0.0581701i
$753$	5480.87	−	7543.78i	0.265251	−	0.365087i
$754$	−3766.04	−	2736.19i	−0.181898	−	0.132157i
$755$		0			0
$756$	−1040.89	+	756.250i	−0.0500751	+	0.0363817i
$757$			4822.42i			0.231538i	0.993276	+	0.115769i	$0.0369332\pi$
$757$			4822.42i			0.231538i	−0.993276	+	0.115769i	$0.963067\pi$
$758$	15397.8	+	21193.2i	0.737827	+	1.01553i
$759$	1121.77	+	3452.44i	0.0536463	+	0.165106i
$760$		0			0
$761$	5641.16	−	17361.7i	0.268715	−	0.827019i	−0.722100	−	0.691789i	$-0.756823\pi$
$761$	5641.16	−	17361.7i	0.268715	−	0.827019i	0.990814	−	0.135230i	$-0.0431772\pi$
$762$	−1960.12	+	636.881i	−0.0931858	+	0.0302779i
$763$	−4586.00	+	1490.08i	−0.217594	+	0.0707006i
$764$	2917.74	−	8979.89i	0.138168	−	0.425237i
$765$		0			0
$766$	−1981.04	−	6097.01i	−0.0934437	−	0.287590i
$767$	3400.27	+	4680.07i	0.160074	+	0.220323i
$768$		−	817.515i		−	0.0384109i
$769$	−8875.39	+	6448.34i	−0.416196	+	0.302384i	−0.776105	−	0.630603i	$-0.782808\pi$
$769$	−8875.39	+	6448.34i	−0.416196	+	0.302384i	0.359910	+	0.932987i	$0.382808\pi$
$770$		0			0
$771$	12451.4	+	9046.49i	0.581618	+	0.422570i
$772$	2227.24	−	3065.53i	0.103834	−	0.142916i
$773$	−38530.9	−	12519.4i	−1.79283	−	0.582527i	−0.793183	−	0.608984i	$-0.791577\pi$
$773$	−38530.9	−	12519.4i	−1.79283	−	0.582527i	−0.999650	+	0.0264571i	$0.991577\pi$
$774$	16178.0			0.751301
$775$		0			0
$776$	3776.95			0.174722
$777$	−2630.02	−	854.544i	−0.121430	−	0.0394551i
$778$	−16301.3	+	22436.8i	−0.751196	+	1.03393i
$779$	−19463.7	−	14141.2i	−0.895199	−	0.650400i
$780$		0			0
$781$	−2124.83	+	1543.78i	−0.0973525	+	0.0707307i
$782$			7230.76i			0.330654i
$783$	−4165.50	−	5733.32i	−0.190119	−	0.261676i
$784$	1669.74	+	5138.93i	0.0760633	+	0.234099i
$785$		0			0
$786$	−122.359	+	376.583i	−0.00555268	+	0.0170894i
$787$	7455.41	−	2422.41i	0.337683	−	0.109720i	−0.135267	−	0.990809i	$-0.543189\pi$
$787$	7455.41	−	2422.41i	0.337683	−	0.109720i	0.472950	+	0.881089i	$0.343189\pi$
$788$	1408.03	−	457.497i	0.0636536	−	0.0206823i
$789$	245.299	−	754.953i	0.0110683	−	0.0340647i
$790$		0			0
$791$	180.610	+	555.860i	0.00811852	+	0.0249862i
$792$	−620.305	−	853.777i	−0.0278303	−	0.0383051i
$793$			15750.7i			0.705326i
$794$	−7040.85	+	5115.48i	−0.314698	+	0.228642i
$795$		0			0
$796$	15772.6	+	11459.4i	0.702316	+	0.510262i
$797$	−13007.8	+	17903.7i	−0.578118	+	0.795711i	−0.993487	−	0.113942i	$-0.963652\pi$
$797$	−13007.8	+	17903.7i	−0.578118	+	0.795711i	0.415370	+	0.909653i	$0.363652\pi$
$798$	929.259	+	301.935i	0.0412223	+	0.0133939i
$799$	6058.26			0.268243
$800$		0			0
$801$	−3054.94			−0.134758
$802$	−19704.2	−	6402.27i	−0.867554	−	0.281885i
$803$	2164.72	−	2979.48i	0.0951325	−	0.130939i
$804$	−7281.20	−	5290.10i	−0.319388	−	0.232049i
$805$		0			0
$806$	11227.3	−	8157.10i	0.490650	−	0.356478i
$807$		−	343.489i		−	0.0149831i
$808$	−8358.33	−	11504.3i	−0.363917	−	0.500889i
$809$	565.841	+	1741.48i	0.0245908	+	0.0756826i	0.962599	−	0.270931i	$-0.0873315\pi$
$809$	565.841	+	1741.48i	0.0245908	+	0.0756826i	−0.938008	+	0.346614i	$0.887332\pi$
$810$		0			0
$811$	−8606.01	+	26486.6i	−0.372624	+	1.14682i	0.572444	+	0.819944i	$0.305995\pi$
$811$	−8606.01	+	26486.6i	−0.372624	+	1.14682i	−0.945068	+	0.326875i	$0.894005\pi$
$812$	443.201	−	144.005i	0.0191543	−	0.00622361i
$813$	6259.93	−	2033.98i	0.270044	−	0.0877425i
$814$	1827.29	−	5623.81i	0.0786810	−	0.242155i
$815$		0			0
$816$	394.260	+	1213.41i	0.0169140	+	0.0520560i
$817$	−18826.1	−	25911.9i	−0.806170	−	1.10960i
$818$		−	6477.55i		−	0.276873i
$819$	1436.00	−	1043.32i	0.0612675	−	0.0445134i
$820$		0			0
$821$	−6794.96	−	4936.83i	−0.288850	−	0.209862i	0.433918	−	0.900952i	$-0.357131\pi$
$821$	−6794.96	−	4936.83i	−0.288850	−	0.209862i	−0.722768	+	0.691090i	$0.757131\pi$
$822$	7172.24	−	9871.75i	0.304332	−	0.418877i
$823$	33921.0	+	11021.6i	1.43671	+	0.466815i	0.920870	−	0.389870i	$-0.127480\pi$
$823$	33921.0	+	11021.6i	1.43671	+	0.466815i	0.515840	+	0.856685i	$0.327480\pi$
$824$	6832.55			0.288863
$825$		0			0
$826$	−579.110			−0.0243945
$827$	−14916.9	−	4846.79i	−0.627220	−	0.203796i	−0.0218769	−	0.999761i	$-0.506964\pi$
$827$	−14916.9	−	4846.79i	−0.627220	−	0.203796i	−0.605343	+	0.795964i	$0.706964\pi$
$828$	−5719.67	+	7872.46i	−0.240063	+	0.330419i
$829$	−1413.23	−	1026.77i	−0.0592081	−	0.0430172i	0.557788	−	0.829984i	$-0.311650\pi$
$829$	−1413.23	−	1026.77i	−0.0592081	−	0.0430172i	−0.616996	+	0.786967i	$0.711650\pi$
$830$		0			0
$831$	11685.7	−	8490.17i	0.487813	−	0.354417i
$832$			2940.22i			0.122516i
$833$	−4956.66	−	6822.26i	−0.206168	−	0.283766i
$834$	4294.57	+	13217.3i	0.178308	+	0.548775i
$835$		0			0
$836$	−645.632	+	1987.05i	−0.0267101	+	0.0822052i
$837$	20093.0	−	6528.61i	0.829768	−	0.269608i
$838$	10425.2	−	3387.35i	0.429752	−	0.139635i
$839$	−9852.56	+	30323.1i	−0.405421	+	1.24776i	0.515122	+	0.857117i	$0.327747\pi$
$839$	−9852.56	+	30323.1i	−0.405421	+	1.24776i	−0.920543	+	0.390641i	$0.872253\pi$
$840$		0			0
$841$	−6743.42	−	20754.1i	−0.276494	−	0.850962i
$842$	−3560.47	−	4900.57i	−0.145727	−	0.200576i
$843$			21989.3i			0.898400i
$844$	−12864.3	+	9346.47i	−0.524654	+	0.381183i
$845$		0			0
$846$	6595.91	+	4792.21i	0.268052	+	0.194751i
$847$	1715.69	−	2361.45i	0.0696008	−	0.0957973i
$848$	−2145.84	−	697.225i	−0.0868966	−	0.0282344i
$849$	22219.9			0.898216
$850$		0			0
$851$	−54524.3			−2.19632
$852$	4064.01	+	1320.48i	0.163416	+	0.0530971i
$853$	−15351.7	+	21129.8i	−0.616215	+	0.848147i	−0.997071	−	0.0764878i	$-0.975629\pi$
$853$	−15351.7	+	21129.8i	−0.616215	+	0.848147i	0.380856	+	0.924634i	$0.375629\pi$
$854$	−1275.63	−	926.798i	−0.0511137	−	0.0371363i
$855$		0			0
$856$	−10189.6	+	7403.18i	−0.406861	+	0.295602i
$857$			33953.0i			1.35334i	0.736287	+	0.676669i	$0.236577\pi$
$857$			33953.0i			1.35334i	−0.736287	+	0.676669i	$0.763423\pi$
$858$	−1354.06	−	1863.70i	−0.0538774	−	0.0741559i
$859$	−14082.2	−	43340.6i	−0.559346	−	1.72149i	−0.684180	−	0.729314i	$-0.739840\pi$
$859$	−14082.2	−	43340.6i	−0.559346	−	1.72149i	0.124833	−	0.992178i	$-0.460160\pi$
$860$		0			0
$861$	−820.604	+	2525.56i	−0.0324810	+	0.0999661i
$862$	−6402.08	+	2080.16i	−0.252965	+	0.0821932i
$863$	44450.7	−	14442.9i	1.75333	−	0.569690i	0.756852	−	0.653586i	$-0.226736\pi$
$863$	44450.7	−	14442.9i	1.75333	−	0.569690i	0.996475	+	0.0838958i	$0.0267363\pi$
$864$	−1383.19	+	4257.03i	−0.0544644	+	0.167624i
$865$		0			0
$866$	867.195	+	2668.95i	0.0340283	+	0.104728i
$867$	8051.55	+	11082.0i	0.315392	+	0.434100i
$868$			1389.26i			0.0543256i
$869$	−8700.91	+	6321.58i	−0.339653	+	0.246772i
$870$		0			0
$871$	26187.0	+	19026.0i	1.01873	+	0.740151i
$872$	−9860.52	+	13571.8i	−0.382935	+	0.527065i
$873$	−7544.32	−	2451.30i	−0.292482	−	0.0950330i
$874$	19265.0			0.745592
$875$		0			0
$876$	−5991.91			−0.231105
$877$	−7364.40	−	2392.84i	−0.283555	−	0.0921327i	0.163786	−	0.986496i	$-0.447629\pi$
$877$	−7364.40	−	2392.84i	−0.283555	−	0.0921327i	−0.447342	+	0.894363i	$0.647629\pi$
$878$	−4034.11	+	5552.48i	−0.155062	+	0.213425i
$879$	3964.34	+	2880.26i	0.152120	+	0.110522i
$880$		0			0
$881$	−37825.3	+	27481.7i	−1.44650	+	1.05094i	−0.459866	+	0.887988i	$0.652103\pi$
$881$	−37825.3	+	27481.7i	−1.44650	+	1.05094i	−0.986633	+	0.162955i	$0.947897\pi$
$882$		−	11348.5i		−	0.433248i
$883$	16544.5	+	22771.6i	0.630540	+	0.867864i	0.998067	−	0.0621488i	$-0.0197953\pi$
$883$	16544.5	+	22771.6i	0.630540	+	0.867864i	−0.367527	+	0.930013i	$0.619795\pi$
$884$	−1417.96	−	4364.05i	−0.0539495	−	0.166039i
$885$		0			0
$886$	114.083	−	351.112i	0.00432585	−	0.0133136i
$887$	−917.776	+	298.203i	−0.0347417	+	0.0112883i	−0.326336	−	0.945254i	$-0.605814\pi$
$887$	−917.776	+	298.203i	−0.0347417	+	0.0112883i	0.291595	+	0.956542i	$0.405814\pi$
$888$	−9149.82	+	2972.96i	−0.345774	+	0.112349i
$889$	−229.302	+	705.720i	−0.00865079	+	0.0266244i
$890$		0			0
$891$	16.8995	+	52.0113i	0.000635415	+	0.00195561i
$892$	3486.80	+	4799.17i	0.130882	+	0.180144i
$893$		−	16141.1i		−	0.604861i
$894$	15802.2	−	11481.0i	0.591169	−	0.429509i
$895$		0			0
$896$	−238.124	−	173.007i	−0.00887854	−	0.00645064i
$897$	−12485.4	+	17184.7i	−0.464745	+	0.639667i
$898$	26814.1	+	8712.43i	0.996434	+	0.323761i
$899$	−7652.19			−0.283888
$900$		0			0
$901$	3521.23			0.130199
$902$	−5400.45	−	1754.71i	−0.199352	−	0.0647733i
$903$	−2077.99	+	2860.10i	−0.0765793	+	0.105402i
$904$	1645.02	+	1195.18i	0.0605227	+	0.0439723i
$905$		0			0
$906$	−499.124	+	362.634i	−0.0183027	+	0.0132977i
$907$		−	17595.6i		−	0.644159i	−0.946713	−	0.322080i	$-0.895618\pi$
$907$		−	17595.6i		−	0.644159i	0.946713	−	0.322080i	$-0.104382\pi$
$908$	−9377.47	−	12907.0i	−0.342734	−	0.471732i
$909$	9229.04	+	28404.0i	0.336752	+	1.03642i
$910$		0			0
$911$	−10233.3	+	31494.9i	−0.372167	+	1.14541i	0.573203	+	0.819414i	$0.305701\pi$
$911$	−10233.3	+	31494.9i	−0.372167	+	1.14541i	−0.945370	+	0.326000i	$0.894299\pi$
$912$	3232.89	−	1050.43i	0.117381	−	0.0381395i
$913$	−4073.04	+	1323.41i	−0.147643	+	0.0479721i
$914$	1201.01	−	3696.32i	0.0434636	−	0.133767i
$915$		0			0
$916$	−4807.61	−	14796.3i	−0.173415	−	0.533716i
$917$	83.7959	+	115.335i	0.00301765	+	0.00415344i
$918$		−	6985.61i		−	0.251154i
$919$	−3450.13	+	2506.66i	−0.123840	+	0.0899752i	−0.647981	−	0.761656i	$-0.724386\pi$
$919$	−3450.13	+	2506.66i	−0.123840	+	0.0899752i	0.524141	+	0.851632i	$0.324386\pi$
$920$		0			0
$921$	−15011.0	−	10906.1i	−0.537056	−	0.390194i
$922$	−8144.89	+	11210.5i	−0.290930	+	0.400431i
$923$	−14616.3	−	4749.13i	−0.521237	−	0.169360i
$924$	230.614			0.00821066
$925$		0			0
$926$	−12477.1			−0.442791
$927$	−13647.8	−	4434.43i	−0.483551	−	0.157115i
$928$	952.943	−	1311.61i	0.0337089	−	0.0463963i
$929$	9279.10	+	6741.66i	0.327704	+	0.238091i	0.739456	−	0.673205i	$-0.235083\pi$
$929$	9279.10	+	6741.66i	0.327704	+	0.238091i	−0.411751	+	0.911296i	$0.635083\pi$
$930$		0			0
$931$	−18176.6	+	13206.1i	−0.639865	+	0.464889i
$932$			13786.8i			0.484552i
$933$	14116.4	+	19429.6i	0.495338	+	0.681774i
$934$	5508.06	+	16952.1i	0.192965	+	0.593885i
$935$		0			0
$936$	1908.25	−	5872.98i	0.0666378	−	0.205090i
$937$	3567.54	−	1159.16i	0.124382	−	0.0404143i	−0.246164	−	0.969228i	$-0.579170\pi$
$937$	3567.54	−	1159.16i	0.124382	−	0.0404143i	0.370547	+	0.928814i	$0.379170\pi$
$938$	−3081.78	+	1001.33i	−0.107275	+	0.0348557i
$939$	−2554.47	+	7861.86i	−0.0887775	+	0.273229i
$940$		0			0
$941$	7425.56	+	22853.5i	0.257244	+	0.791715i	0.993379	+	0.114881i	$0.0366485\pi$
$941$	7425.56	+	22853.5i	0.257244	+	0.791715i	−0.736136	+	0.676834i	$0.763351\pi$
$942$	−6166.48	−	8487.44i	−0.213285	−	0.293562i
$943$			52358.7i			1.80810i
$944$	−1629.94	+	1184.22i	−0.0561972	+	0.0408297i
$945$		0			0
$946$	−6115.81	−	4443.40i	−0.210193	−	0.152714i
$947$	−11640.8	+	16022.2i	−0.399445	+	0.549789i	−0.960605	−	0.277919i	$-0.910355\pi$
$947$	−11640.8	+	16022.2i	−0.399445	+	0.549789i	0.561159	+	0.827708i	$0.310355\pi$
$948$	16641.6	+	5407.19i	0.570142	+	0.185250i
$949$	21550.1			0.737139
$950$		0			0
$951$	9542.06			0.325365
$952$	436.874	+	141.949i	0.0148731	+	0.00483256i
$953$	3484.11	−	4795.47i	0.118428	−	0.163002i	−0.745688	−	0.666296i	$-0.767879\pi$
$953$	3484.11	−	4795.47i	0.118428	−	0.163002i	0.864115	+	0.503294i	$0.167879\pi$
$954$	3833.72	+	2785.36i	0.130106	+	0.0945278i
$955$		0			0
$956$	−19586.2	+	14230.2i	−0.662619	+	0.481421i
$957$			1270.25i			0.0429062i
$958$	−10441.4	−	14371.4i	−0.352137	−	0.484675i
$959$	−1357.59	−	4178.23i	−0.0457131	−	0.140691i
$960$		0			0
$961$	−2156.43	+	6636.81i	−0.0723853	+	0.222779i
$962$	32907.6	−	10692.3i	1.10289	−	0.358351i
$963$	25158.1	−	8174.38i	0.841859	−	0.273536i
$964$	−3777.37	+	11625.6i	−0.126204	+	0.388417i
$965$		0			0
$966$	−657.104	−	2022.36i	−0.0218861	−	0.0673585i
$967$	16926.3	+	23297.0i	0.562887	+	0.774748i	0.991690	−	0.128650i	$-0.0410645\pi$
$967$	16926.3	+	23297.0i	0.562887	+	0.774748i	−0.428803	+	0.903398i	$0.641064\pi$
$968$		−	10154.9i		−	0.337180i
$969$	−4291.87	+	3118.22i	−0.142285	+	0.103376i
$970$		0			0
$971$	19218.9	+	13963.3i	0.635184	+	0.461488i	0.858192	−	0.513328i	$-0.171588\pi$
$971$	19218.9	+	13963.3i	0.635184	+	0.461488i	−0.223008	+	0.974817i	$0.571588\pi$
$972$	8931.89	−	12293.7i	0.294743	−	0.405679i
$973$	4758.76	+	1546.21i	0.156792	+	0.0509449i
$974$	32994.4			1.08543
$975$		0			0
$976$	−5485.55			−0.179906
$977$	−31294.2	−	10168.1i	−1.02476	−	0.332965i	−0.252044	−	0.967716i	$-0.581103\pi$
$977$	−31294.2	−	10168.1i	−1.02476	−	0.332965i	−0.772717	+	0.634751i	$0.781103\pi$
$978$	−6354.29	+	8745.93i	−0.207758	+	0.285955i
$979$	1154.86	+	839.058i	0.0377014	+	0.0273916i
$980$		0			0
$981$	28504.4	−	20709.7i	0.927701	−	0.674015i
$982$		−	6546.21i		−	0.212727i
$983$	10666.5	+	14681.2i	0.346091	+	0.476354i	0.946208	−	0.323558i	$-0.104879\pi$
$983$	10666.5	+	14681.2i	0.346091	+	0.476354i	−0.600117	+	0.799912i	$0.704879\pi$
$984$	2854.88	+	8786.41i	0.0924901	+	0.284655i
$985$		0			0
$986$	−781.870	+	2406.35i	−0.0252533	+	0.0777218i
$987$	−1694.43	+	550.552i	−0.0546446	+	0.0177551i
$988$	−11627.2	+	3777.90i	−0.374403	+	0.121651i
$989$	−21539.9	+	66293.1i	−0.692548	+	2.13144i
$990$		0			0
$991$	−8256.85	−	25412.0i	−0.264669	−	0.814569i	−0.991769	−	0.128037i	$-0.959132\pi$
$991$	−8256.85	−	25412.0i	−0.264669	−	0.814569i	0.727100	−	0.686532i	$-0.240868\pi$
$992$	2840.90	+	3910.17i	0.0909262	+	0.125149i
$993$			6143.34i			0.196327i
$994$	1244.67	−	904.309i	0.0397170	−	0.0288561i
$995$		0			0
$996$	5637.06	+	4095.56i	0.179334	+	0.130294i
$997$	−15696.4	+	21604.3i	−0.498606	+	0.686273i	−0.981946	−	0.189160i	$-0.939423\pi$
$997$	−15696.4	+	21604.3i	−0.498606	+	0.686273i	0.483340	+	0.875433i	$0.339423\pi$
$998$	6926.56	+	2250.58i	0.219696	+	0.0713835i
$999$	52675.7			1.66826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.e.b.149.2		32
5.2	odd	4		250.4.d.c.101.6		32
5.3	odd	4		250.4.d.d.101.3		32
5.4	even	2		50.4.e.a.29.7	yes	32
25.6	even	5		50.4.e.a.19.7	✓	32
25.8	odd	20		250.4.d.d.151.3		32
25.12	odd	20		1250.4.a.n.1.6		16
25.13	odd	20		1250.4.a.m.1.11		16
25.17	odd	20		250.4.d.c.151.6		32
25.19	even	10	inner	250.4.e.b.99.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.19.7	✓	32	25.6	even	5
50.4.e.a.29.7	yes	32	5.4	even	2
250.4.d.c.101.6		32	5.2	odd	4
250.4.d.c.151.6		32	25.17	odd	20
250.4.d.d.101.3		32	5.3	odd	4
250.4.d.d.151.3		32	25.8	odd	20
250.4.e.b.99.2		32	25.19	even	10	inner
250.4.e.b.149.2		32	1.1	even	1	trivial
1250.4.a.m.1.11		16	25.13	odd	20
1250.4.a.n.1.6		16	25.12	odd	20

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.90211 - 0.618034i) q^{2} +(-1.87704 + 2.58353i) q^{3} +(3.23607 + 2.35114i) q^{4} +(5.16706 - 3.75409i) q^{6} -2.29951i q^{7} +(-4.70228 - 6.47214i) q^{8} +(5.19213 + 15.9797i) q^{9} +O(q^{10})\)	\(q+(-1.90211 - 0.618034i) q^{2} +(-1.87704 + 2.58353i) q^{3} +(3.23607 + 2.35114i) q^{4} +(5.16706 - 3.75409i) q^{6} -2.29951i q^{7} +(-4.70228 - 6.47214i) q^{8} +(5.19213 + 15.9797i) q^{9} +(2.42614 - 7.46690i) q^{11} +(-12.1485 + 3.94728i) q^{12} +(43.6924 - 14.1965i) q^{13} +(-1.42118 + 4.37394i) q^{14} +(4.94427 + 15.2169i) q^{16} +(-14.6772 - 20.2014i) q^{17} -33.6041i q^{18} +(-53.8228 + 39.1046i) q^{19} +(5.94086 + 4.31629i) q^{21} +(-9.22960 + 12.7034i) q^{22} +(137.701 + 44.7417i) q^{23} +25.5474 q^{24} -91.8817 q^{26} +(-133.032 - 43.2248i) q^{27} +(5.40648 - 7.44138i) q^{28} +(40.9879 + 29.7795i) q^{29} +(-122.193 + 88.7782i) q^{31} -32.0000i q^{32} +(14.7370 + 20.2837i) q^{33} +(15.4325 + 47.4963i) q^{34} +(-20.7685 + 63.9189i) q^{36} +(-358.151 + 116.370i) q^{37} +(126.545 - 41.1170i) q^{38} +(-45.3354 + 139.528i) q^{39} +(111.749 + 343.927i) q^{41} +(-8.63258 - 11.8817i) q^{42} +481.429i q^{43} +(25.4069 - 18.4592i) q^{44} +(-234.270 - 170.207i) q^{46} +(-142.608 + 196.283i) q^{47} +(-48.5940 - 15.7891i) q^{48} +337.712 q^{49} +79.7407 q^{51} +(174.769 + 56.7860i) q^{52} +(-82.8875 + 114.085i) q^{53} +(226.328 + 164.437i) q^{54} +(-14.8828 + 10.8130i) q^{56} -212.454i q^{57} +(-59.5589 - 81.9758i) q^{58} +(38.9115 + 119.757i) q^{59} +(-105.946 + 326.067i) q^{61} +(287.292 - 93.3470i) q^{62} +(36.7456 - 11.9394i) q^{63} +(-19.7771 + 60.8676i) q^{64} +(-15.4954 - 47.6899i) q^{66} +(414.141 + 570.016i) q^{67} -99.8812i q^{68} +(-374.062 + 271.772i) q^{69} +(-270.639 - 196.630i) q^{71} +(79.0081 - 108.745i) q^{72} +(446.124 + 144.955i) q^{73} +753.165 q^{74} -266.115 q^{76} +(-17.1702 - 5.57895i) q^{77} +(172.466 - 237.379i) q^{78} +(-1108.23 - 805.178i) q^{79} +(-5.63528 + 4.09427i) q^{81} -723.252i q^{82} +(-320.625 - 441.302i) q^{83} +(9.07683 + 27.9356i) q^{84} +(297.540 - 915.733i) q^{86} +(-153.872 + 49.9961i) q^{87} +(-59.7352 + 19.4091i) q^{88} +(-56.1852 + 172.920i) q^{89} +(-32.6451 - 100.471i) q^{91} +(340.415 + 468.541i) q^{92} -482.329i q^{93} +(392.565 - 285.215i) q^{94} +(82.6730 + 60.0654i) q^{96} +(-277.504 + 381.952i) q^{97} +(-642.367 - 208.718i) q^{98} +131.916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 12 q^{6} + 26 q^{9} - 106 q^{11} - 80 q^{12} + 56 q^{14} - 128 q^{16} - 320 q^{17} + 110 q^{19} - 36 q^{21} + 360 q^{22} + 370 q^{23} - 192 q^{24} + 808 q^{26} + 1200 q^{27} + 120 q^{28} - 10 q^{29} - 486 q^{31} - 2560 q^{33} + 616 q^{34} - 104 q^{36} - 680 q^{37} + 1012 q^{39} - 96 q^{41} + 1020 q^{42} - 136 q^{44} - 832 q^{46} - 1040 q^{47} - 320 q^{48} - 2076 q^{49} + 884 q^{51} + 2550 q^{53} - 120 q^{54} - 224 q^{56} + 2250 q^{59} + 934 q^{61} - 4200 q^{62} - 4660 q^{63} + 512 q^{64} + 16 q^{66} + 3780 q^{67} - 628 q^{69} - 2616 q^{71} + 600 q^{73} - 2584 q^{74} + 800 q^{76} + 4320 q^{77} + 6640 q^{78} - 2800 q^{79} - 5268 q^{81} - 4050 q^{83} + 624 q^{84} - 692 q^{86} - 9390 q^{87} + 1680 q^{88} + 4520 q^{89} + 3764 q^{91} - 1280 q^{92} + 656 q^{94} - 192 q^{96} - 1710 q^{97} - 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 12 * q^6 + 26 * q^9 - 106 * q^11 - 80 * q^12 + 56 * q^14 - 128 * q^16 - 320 * q^17 + 110 * q^19 - 36 * q^21 + 360 * q^22 + 370 * q^23 - 192 * q^24 + 808 * q^26 + 1200 * q^27 + 120 * q^28 - 10 * q^29 - 486 * q^31 - 2560 * q^33 + 616 * q^34 - 104 * q^36 - 680 * q^37 + 1012 * q^39 - 96 * q^41 + 1020 * q^42 - 136 * q^44 - 832 * q^46 - 1040 * q^47 - 320 * q^48 - 2076 * q^49 + 884 * q^51 + 2550 * q^53 - 120 * q^54 - 224 * q^56 + 2250 * q^59 + 934 * q^61 - 4200 * q^62 - 4660 * q^63 + 512 * q^64 + 16 * q^66 + 3780 * q^67 - 628 * q^69 - 2616 * q^71 + 600 * q^73 - 2584 * q^74 + 800 * q^76 + 4320 * q^77 + 6640 * q^78 - 2800 * q^79 - 5268 * q^81 - 4050 * q^83 + 624 * q^84 - 692 * q^86 - 9390 * q^87 + 1680 * q^88 + 4520 * q^89 + 3764 * q^91 - 1280 * q^92 + 656 * q^94 - 192 * q^96 - 1710 * q^97 - 3280 * q^98 - 2108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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