LMFDB - Embedded newform 169.4.e.h.147.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.1
Character	$\chi$	$=$	169.147
Dual form			169.4.e.h.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.70109 - 2.71418i) q^{2} +(-0.837548 + 1.45068i) q^{3} +(10.7335 + 18.5910i) q^{4} +7.70909i q^{5} +(7.87478 - 4.54651i) q^{6} +(13.0120 - 7.51249i) q^{7} -73.1038i q^{8} +(12.0970 + 20.9527i) q^{9} +O(q^{10})$	\(q+(-4.70109 - 2.71418i) q^{2} +(-0.837548 + 1.45068i) q^{3} +(10.7335 + 18.5910i) q^{4} +7.70909i q^{5} +(7.87478 - 4.54651i) q^{6} +(13.0120 - 7.51249i) q^{7} -73.1038i q^{8} +(12.0970 + 20.9527i) q^{9} +(20.9238 - 36.2412i) q^{10} +(-2.17375 - 1.25501i) q^{11} -35.9593 q^{12} -81.5609 q^{14} +(-11.1834 - 6.45673i) q^{15} +(-112.549 + 194.940i) q^{16} +(-1.03238 - 1.78814i) q^{17} -131.334i q^{18} +(-81.7897 + 47.2213i) q^{19} +(-143.320 + 82.7456i) q^{20} +25.1683i q^{21} +(6.81266 + 11.7999i) q^{22} +(17.9370 - 31.0678i) q^{23} +(106.050 + 61.2279i) q^{24} +65.5699 q^{25} -85.7549 q^{27} +(279.329 + 161.271i) q^{28} +(70.0990 - 121.415i) q^{29} +(35.0494 + 60.7074i) q^{30} +264.013i q^{31} +(551.724 - 318.538i) q^{32} +(3.64124 - 2.10227i) q^{33} +11.2083i q^{34} +(57.9145 + 100.311i) q^{35} +(-259.687 + 449.791i) q^{36} +(222.398 + 128.402i) q^{37} +512.668 q^{38} +563.564 q^{40} +(-341.360 - 197.084i) q^{41} +(68.3111 - 118.318i) q^{42} +(128.333 + 222.280i) q^{43} -53.8828i q^{44} +(-161.526 + 93.2571i) q^{45} +(-168.647 + 97.3685i) q^{46} +415.204i q^{47} +(-188.530 - 326.543i) q^{48} +(-58.6251 + 101.542i) q^{49} +(-308.250 - 177.968i) q^{50} +3.45868 q^{51} -504.917 q^{53} +(403.142 + 232.754i) q^{54} +(9.67502 - 16.7576i) q^{55} +(-549.191 - 951.227i) q^{56} -158.200i q^{57} +(-659.083 + 380.522i) q^{58} +(-104.209 + 60.1650i) q^{59} -277.214i q^{60} +(376.415 + 651.969i) q^{61} +(716.577 - 1241.15i) q^{62} +(314.813 + 181.758i) q^{63} -1657.50 q^{64} -22.8237 q^{66} +(-183.557 - 105.977i) q^{67} +(22.1622 - 38.3860i) q^{68} +(30.0462 + 52.0416i) q^{69} -628.760i q^{70} +(-355.532 + 205.267i) q^{71} +(1531.72 - 884.339i) q^{72} -17.4680i q^{73} +(-697.010 - 1207.26i) q^{74} +(-54.9179 + 95.1206i) q^{75} +(-1755.78 - 1013.70i) q^{76} -37.7131 q^{77} -174.953 q^{79} +(-1502.81 - 867.647i) q^{80} +(-254.796 + 441.319i) q^{81} +(1069.84 + 1853.02i) q^{82} +963.151i q^{83} +(-467.903 + 270.144i) q^{84} +(13.7849 - 7.95873i) q^{85} -1393.28i q^{86} +(117.422 + 203.382i) q^{87} +(-91.7463 + 158.909i) q^{88} +(413.644 + 238.817i) q^{89} +1012.47 q^{90} +770.109 q^{92} +(-382.997 - 221.123i) q^{93} +(1126.94 - 1951.91i) q^{94} +(-364.033 - 630.525i) q^{95} +1067.16i q^{96} +(906.730 - 523.501i) q^{97} +(551.204 - 318.238i) q^{98} -60.7278i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	$ 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) $ 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.70109	−	2.71418i	−1.66209	−	0.959606i	−0.971716	−	0.236151i	$-0.924114\pi$
$2$	−4.70109	−	2.71418i	−1.66209	−	0.959606i	−0.690371	−	0.723456i	$-0.742553\pi$
$3$	−0.837548	+	1.45068i	−0.161186	+	0.279183i	−0.935294	−	0.353871i	$-0.884865\pi$
$3$	−0.837548	+	1.45068i	−0.161186	+	0.279183i	0.774108	+	0.633053i	$0.218199\pi$
$4$	10.7335	+	18.5910i	1.34169	+	2.32387i
$5$			7.70909i			0.689522i	0.938690	+	0.344761i	$0.112040\pi$
$5$			7.70909i			0.689522i	−0.938690	+	0.344761i	$0.887960\pi$
$6$	7.87478	−	4.54651i	0.535811	−	0.309351i
$7$	13.0120	−	7.51249i	0.702583	−	0.405636i	−0.105726	−	0.994395i	$-0.533717\pi$
$7$	13.0120	−	7.51249i	0.702583	−	0.405636i	0.808309	+	0.588759i	$0.200383\pi$
$8$		−	73.1038i		−	3.23076i
$9$	12.0970	+	20.9527i	0.448038	+	0.776025i
$10$	20.9238	−	36.2412i	0.661670	−	1.14605i
$11$	−2.17375	−	1.25501i	−0.0595827	−	0.0344001i	0.469913	−	0.882713i	$-0.344285\pi$
$11$	−2.17375	−	1.25501i	−0.0595827	−	0.0344001i	−0.529495	+	0.848313i	$0.677619\pi$
$12$	−35.9593			−0.865047
$13$		0			0
$13$		0			0
$14$	−81.5609			−1.55700
$15$	−11.1834	−	6.45673i	−0.192503	−	0.111141i
$16$	−112.549	+	194.940i	−1.75857	+	3.04593i
$17$	−1.03238	−	1.78814i	−0.0147288	−	0.0255110i	0.858567	−	0.512701i	$-0.171355\pi$
$17$	−1.03238	−	1.78814i	−0.0147288	−	0.0255110i	−0.873296	+	0.487190i	$0.838022\pi$
$18$		−	131.334i		−	1.71976i
$19$	−81.7897	+	47.2213i	−0.987571	+	0.570174i	−0.904547	−	0.426373i	$-0.859791\pi$
$19$	−81.7897	+	47.2213i	−0.987571	+	0.570174i	−0.0830237	+	0.996548i	$0.526458\pi$
$20$	−143.320	+	82.7456i	−1.60236	+	0.925124i
$21$			25.1683i			0.261532i
$22$	6.81266	+	11.7999i	0.0660211	+	0.114352i
$23$	17.9370	−	31.0678i	0.162614	−	0.281656i	−0.773191	−	0.634173i	$-0.781341\pi$
$23$	17.9370	−	31.0678i	0.162614	−	0.281656i	0.935805	+	0.352517i	$0.114674\pi$
$24$	106.050	+	61.2279i	0.901972	+	0.520754i
$25$	65.5699			0.524559
$26$		0			0
$27$	−85.7549			−0.611242
$28$	279.329	+	161.271i	1.88529	+	1.08848i
$29$	70.0990	−	121.415i	0.448864	−	0.777455i	−0.549449	−	0.835528i	$-0.685162\pi$
$29$	70.0990	−	121.415i	0.448864	−	0.777455i	0.998312	+	0.0580727i	$0.0184955\pi$
$30$	35.0494	+	60.7074i	0.213304	+	0.369453i
$31$			264.013i			1.52961i	0.644259	+	0.764807i	$0.277166\pi$
$31$			264.013i			1.52961i	−0.644259	+	0.764807i	$0.722834\pi$
$32$	551.724	−	318.538i	3.04787	−	1.75969i
$33$	3.64124	−	2.10227i	0.0192078	−	0.0110896i
$34$			11.2083i			0.0565354i
$35$	57.9145	+	100.311i	0.279695	+	0.484446i
$36$	−259.687	+	449.791i	−1.20226	+	2.08237i
$37$	222.398	+	128.402i	0.988164	+	0.570517i	0.904725	−	0.425996i	$-0.140076\pi$
$37$	222.398	+	128.402i	0.988164	+	0.570517i	0.0834390	+	0.996513i	$0.473410\pi$
$38$	512.668			2.18857
$39$		0			0
$40$	563.564			2.22768
$41$	−341.360	−	197.084i	−1.30028	−	0.750717i	−0.319829	−	0.947475i	$-0.603625\pi$
$41$	−341.360	−	197.084i	−1.30028	−	0.750717i	−0.980452	+	0.196758i	$0.936959\pi$
$42$	68.3111	−	118.318i	0.250968	−	0.434689i
$43$	128.333	+	222.280i	0.455131	+	0.788310i	0.998696	−	0.0510575i	$-0.0162592\pi$
$43$	128.333	+	222.280i	0.455131	+	0.788310i	−0.543565	+	0.839367i	$0.682926\pi$
$44$		−	53.8828i		−	0.184617i
$45$	−161.526	+	93.2571i	−0.535086	+	0.308932i
$46$	−168.647	+	97.3685i	−0.540558	+	0.312091i
$47$			415.204i			1.28859i	0.764777	+	0.644295i	$0.222849\pi$
$47$			415.204i			1.28859i	−0.764777	+	0.644295i	$0.777151\pi$
$48$	−188.530	−	326.543i	−0.566914	−	0.981925i
$49$	−58.6251	+	101.542i	−0.170919	+	0.296040i
$50$	−308.250	−	177.968i	−0.871863	−	0.503370i
$51$	3.45868			0.00949631
$52$		0			0
$53$	−504.917			−1.30860			−0.654299	−	0.756236i	$-0.727036\pi$
$53$	−504.917			−1.30860			−0.654299	+	0.756236i	$0.727036\pi$
$54$	403.142	+	232.754i	1.01594	+	0.586552i
$55$	9.67502	−	16.7576i	0.0237196	−	0.0410836i
$56$	−549.191	−	951.227i	−1.31051	−	2.26988i
$57$		−	158.200i		−	0.367617i
$58$	−659.083	+	380.522i	−1.49210	+	0.861465i
$59$	−104.209	+	60.1650i	−0.229946	+	0.132760i	−0.610547	−	0.791980i	$-0.709050\pi$
$59$	−104.209	+	60.1650i	−0.229946	+	0.132760i	0.380601	+	0.924739i	$0.375717\pi$
$60$		−	277.214i		−	0.596469i
$61$	376.415	+	651.969i	0.790081	+	1.36846i	0.925916	+	0.377730i	$0.123295\pi$
$61$	376.415	+	651.969i	0.790081	+	1.36846i	−0.135835	+	0.990732i	$0.543372\pi$
$62$	716.577	−	1241.15i	1.46783	−	2.54235i
$63$	314.813	+	181.758i	0.629567	+	0.363481i
$64$	−1657.50			−3.23730
$65$		0			0
$66$	−22.8237			−0.0425668
$67$	−183.557	−	105.977i	−0.334702	−	0.193240i	0.323225	−	0.946322i	$-0.395233\pi$
$67$	−183.557	−	105.977i	−0.334702	−	0.193240i	−0.657927	+	0.753082i	$0.728566\pi$
$68$	22.1622	−	38.3860i	0.0395229	−	0.0684557i
$69$	30.0462	+	52.0416i	0.0524223	+	0.0907981i
$70$		−	628.760i		−	1.07359i
$71$	−355.532	+	205.267i	−0.594281	+	0.343108i	−0.766788	−	0.641900i	$-0.778146\pi$
$71$	−355.532	+	205.267i	−0.594281	+	0.343108i	0.172508	+	0.985008i	$0.444813\pi$
$72$	1531.72	−	884.339i	2.50715	−	1.44750i
$73$		−	17.4680i		−	0.0280065i	−0.999902	−	0.0140032i	$-0.995542\pi$
$73$		−	17.4680i		−	0.0280065i	0.999902	−	0.0140032i	$-0.00445752\pi$
$74$	−697.010	−	1207.26i	−1.09494	−	1.89650i
$75$	−54.9179	+	95.1206i	−0.0845517	+	0.146448i
$76$	−1755.78	−	1013.70i	−2.65003	−	1.52999i
$77$	−37.7131			−0.0558157
$78$		0			0
$79$	−174.953			−0.249162			−0.124581	−	0.992209i	$-0.539759\pi$
$79$	−174.953			−0.249162			−0.124581	+	0.992209i	$0.539759\pi$
$80$	−1502.81	−	867.647i	−2.10024	−	1.21257i
$81$	−254.796	+	441.319i	−0.349514	+	0.605376i
$82$	1069.84	+	1853.02i	1.44079	+	2.49552i
$83$			963.151i			1.27373i	0.770976	+	0.636865i	$0.219769\pi$
$83$			963.151i			1.27373i	−0.770976	+	0.636865i	$0.780231\pi$
$84$	−467.903	+	270.144i	−0.607767	+	0.350894i
$85$	13.7849	−	7.95873i	0.0175904	−	0.0101558i
$86$		−	1393.28i		−	1.74699i
$87$	117.422	+	203.382i	0.144701	+	0.250630i
$88$	−91.7463	+	158.909i	−0.111139	+	0.192498i
$89$	413.644	+	238.817i	0.492654	+	0.284434i	0.725675	−	0.688038i	$-0.241528\pi$
$89$	413.644	+	238.817i	0.492654	+	0.284434i	−0.233021	+	0.972472i	$0.574861\pi$
$90$	1012.47			1.18581
$91$		0			0
$92$	770.109			0.872711
$93$	−382.997	−	221.123i	−0.427042	−	0.246553i
$94$	1126.94	−	1951.91i	1.23654	−	2.14175i
$95$	−364.033	−	630.525i	−0.393148	−	0.680952i
$96$			1067.16i			1.13455i
$97$	906.730	−	523.501i	0.949119	−	0.547974i	0.0563117	−	0.998413i	$-0.482066\pi$
$97$	906.730	−	523.501i	0.949119	−	0.547974i	0.892807	+	0.450439i	$0.148733\pi$
$98$	551.204	−	318.238i	0.568163	−	0.328029i
$99$		−	60.7278i		−	0.0616502i
$100$	703.795	+	1219.01i	0.703795	+	1.21901i
$101$	−196.629	+	340.571i	−0.193716	+	0.335525i	−0.946479	−	0.322766i	$-0.895387\pi$
$101$	−196.629	+	340.571i	−0.193716	+	0.335525i	0.752763	+	0.658292i	$0.228721\pi$
$102$	−16.2596	−	9.38746i	−0.0157837	−	0.00911272i
$103$	−1629.16			−1.55851			−0.779254	−	0.626708i	$-0.784402\pi$
$103$	−1629.16			−1.55851			−0.779254	+	0.626708i	$0.784402\pi$
$104$		0			0
$105$	−194.025			−0.180332
$106$	2373.66	+	1370.43i	2.17500	+	1.25574i
$107$	−33.6007	+	58.1981i	−0.0303580	+	0.0525815i	−0.880805	−	0.473479i	$-0.842998\pi$
$107$	−33.6007	+	58.1981i	−0.0303580	+	0.0525815i	0.850447	+	0.526060i	$0.176331\pi$
$108$	−920.452	−	1594.27i	−0.820097	−	1.42045i
$109$			330.138i			0.290105i	0.989424	+	0.145053i	$0.0463352\pi$
$109$			330.138i			0.290105i	−0.989424	+	0.145053i	$0.953665\pi$
$110$	−90.9663	+	52.5194i	−0.0788482	+	0.0455230i
$111$	−372.539	+	215.085i	−0.318557	+	0.183919i
$112$			3382.08i			2.85336i
$113$	−244.487	−	423.464i	−0.203535	−	0.352533i	0.746130	−	0.665800i	$-0.231910\pi$
$113$	−244.487	−	423.464i	−0.203535	−	0.352533i	−0.949665	+	0.313268i	$0.898576\pi$
$114$	−429.384	+	743.715i	−0.352768	+	0.611011i
$115$	239.505	+	138.278i	0.194208	+	0.112126i
$116$	3009.63			2.40894
$117$		0			0
$118$	653.194			0.509588
$119$	−26.8667	−	15.5115i	−0.0206964	−	0.0119491i
$120$	−472.012	+	817.548i	−0.359071	+	0.621930i
$121$	−662.350	−	1147.22i	−0.497633	−	0.861926i
$122$		−	4086.62i		−	3.03267i
$123$	571.811	−	330.135i	0.419174	−	0.242010i
$124$	−4908.26	+	2833.78i	−3.55463	+	2.05227i
$125$			1469.12i			1.05122i
$126$	−986.644	−	1708.92i	−0.697597	−	1.20827i
$127$	211.426	−	366.201i	0.147725	−	0.255867i	−0.782661	−	0.622448i	$-0.786138\pi$
$127$	211.426	−	366.201i	0.147725	−	0.255867i	0.930386	+	0.366581i	$0.119472\pi$
$128$	3378.26	+	1950.44i	2.33280	+	1.34684i
$129$	−429.941			−0.293443
$130$		0			0
$131$	1743.96			1.16313			0.581567	−	0.813498i	$-0.302440\pi$
$131$	1743.96			1.16313			0.581567	+	0.813498i	$0.302440\pi$
$132$	78.1665	+	45.1295i	0.0515418	+	0.0297577i
$133$	−709.499	+	1228.89i	−0.462567	+	0.801189i
$134$	575.278	+	996.412i	0.370869	+	0.642365i
$135$		−	661.093i		−	0.421465i
$136$	−130.720	+	75.4710i	−0.0824200	+	0.0475852i
$137$	1865.58	−	1077.09i	1.16341	−	0.671696i	0.211293	−	0.977423i	$-0.432233\pi$
$137$	1865.58	−	1077.09i	1.16341	−	0.671696i	0.952119	+	0.305726i	$0.0988993\pi$
$138$		−	326.203i		−	0.201219i
$139$	−644.835	−	1116.89i	−0.393483	−	0.681533i	0.599423	−	0.800433i	$-0.295397\pi$
$139$	−644.835	−	1116.89i	−0.393483	−	0.681533i	−0.992906	+	0.118899i	$0.962063\pi$
$140$	−1243.25	+	2153.37i	−0.750528	+	1.29995i
$141$	−602.326	−	347.753i	−0.359752	−	0.207703i
$142$	2228.52			1.31700
$143$		0			0
$144$	−5446.01			−3.15163
$145$	935.999	+	540.399i	0.536072	+	0.309502i
$146$	−47.4112	+	82.1187i	−0.0268752	+	0.0465492i
$147$	−98.2026	−	170.092i	−0.0550994	−	0.0954350i
$148$			5512.81i			3.06182i
$149$	1621.69	−	936.283i	0.891638	−	0.514787i	0.0171599	−	0.999853i	$-0.494538\pi$
$149$	1621.69	−	936.283i	0.891638	−	0.514787i	0.874478	+	0.485065i	$0.161204\pi$
$150$	516.348	−	298.114i	0.281065	−	0.162273i
$151$		−	1558.07i		−	0.839695i	−0.907595	−	0.419847i	$-0.862084\pi$
$151$		−	1558.07i		−	0.839695i	0.907595	−	0.419847i	$-0.137916\pi$
$152$	3452.06	+	5979.14i	1.84210	+	3.19061i
$153$	24.9775	−	43.2623i	0.0131981	−	0.0228598i
$154$	177.293	+	102.360i	0.0927705	+	0.0535611i
$155$	−2035.30			−1.05470
$156$		0			0
$157$	2301.74			1.17006			0.585028	−	0.811013i	$-0.301084\pi$
$157$	2301.74			1.17006			0.585028	+	0.811013i	$0.301084\pi$
$158$	822.472	+	474.854i	0.414129	+	0.239097i
$159$	422.892	−	732.471i	0.210928	−	0.365338i
$160$	2455.64	+	4253.29i	1.21335	+	2.10158i
$161$		−	539.007i		−	0.263849i
$162$	2395.64	−	1383.12i	1.16185	−	0.670792i
$163$	273.232	−	157.751i	0.131296	−	0.0758035i	−0.432914	−	0.901435i	$-0.642514\pi$
$163$	273.232	−	157.751i	0.131296	−	0.0758035i	0.564209	+	0.825632i	$0.309181\pi$
$164$		−	8461.63i		−	4.02892i
$165$	16.2066	+	28.0706i	0.00764655	+	0.0132442i
$166$	2614.16	−	4527.86i	1.22228	−	2.11705i
$167$	−641.899	−	370.601i	−0.297435	−	0.171724i	0.343855	−	0.939023i	$-0.388267\pi$
$167$	−641.899	−	370.601i	−0.297435	−	0.171724i	−0.641290	+	0.767299i	$0.721600\pi$
$168$	1839.90			0.844947
$169$		0			0
$170$	−86.4056			−0.0389824
$171$	−1978.83	−	1142.48i	−0.884939	−	0.510920i
$172$	−2754.93	+	4771.68i	−1.22129	+	2.11533i
$173$	754.606	+	1307.02i	0.331628	+	0.574397i	0.982831	−	0.184507i	$-0.0590688\pi$
$173$	754.606	+	1307.02i	0.331628	+	0.574397i	−0.651203	+	0.758903i	$0.725735\pi$
$174$		−	1274.82i		−	0.555425i
$175$	853.196	−	492.593i	0.368546	−	0.212780i
$176$	489.304	−	282.500i	0.209561	−	0.120990i
$177$		−	201.564i		−	0.0855960i
$178$	−1296.39	−	2245.41i	−0.545889	−	0.945507i
$179$	−1882.69	+	3260.92i	−0.786139	+	1.36163i	0.142177	+	0.989841i	$0.454590\pi$
$179$	−1882.69	+	3260.92i	−0.786139	+	1.36163i	−0.928316	+	0.371792i	$0.878743\pi$
$180$	−3467.48	−	2001.95i	−1.43584	−	0.828982i
$181$	−1947.48			−0.799753			−0.399876	−	0.916569i	$-0.630947\pi$
$181$	−1947.48			−0.799753			−0.399876	+	0.916569i	$0.630947\pi$
$182$		0			0
$183$	−1261.06			−0.509401
$184$	−2271.18	−	1311.26i	−0.909964	−	0.525368i
$185$	−989.861	+	1714.49i	−0.393384	+	0.681361i
$186$	1200.33	+	2079.04i	0.473187	+	0.819584i
$187$			5.18262i			0.00202669i
$188$	−7719.05	+	4456.60i	−2.99452	+	1.72889i
$189$	−1115.84	+	644.233i	−0.429448	+	0.247942i
$190$			3952.21i			1.50907i
$191$	−1228.68	−	2128.13i	−0.465465	−	0.806209i	0.533757	−	0.845638i	$-0.320780\pi$
$191$	−1228.68	−	2128.13i	−0.465465	−	0.806209i	−0.999222	+	0.0394284i	$0.987446\pi$
$192$	1388.23	−	2404.49i	0.521808	−	0.903798i
$193$	−1042.73	−	602.021i	−0.388899	−	0.224531i	0.292784	−	0.956179i	$-0.405418\pi$
$193$	−1042.73	−	602.021i	−0.388899	−	0.224531i	−0.681683	+	0.731648i	$0.738752\pi$
$194$	−5683.50			−2.10336
$195$		0			0
$196$	−2517.01			−0.917278
$197$	346.323	+	199.949i	0.125251	+	0.0723137i	0.561317	−	0.827601i	$-0.310295\pi$
$197$	346.323	+	199.949i	0.125251	+	0.0723137i	−0.436065	+	0.899915i	$0.643628\pi$
$198$	−164.826	+	285.487i	−0.0591599	+	0.102468i
$199$	−1881.09	−	3258.14i	−0.670085	−	1.16062i	−0.977880	−	0.209169i	$-0.932924\pi$
$199$	−1881.09	−	3258.14i	−0.670085	−	1.16062i	0.307794	−	0.951453i	$-0.400409\pi$
$200$		−	4793.41i		−	1.69473i
$201$	307.475	−	177.521i	0.107899	−	0.0622953i
$202$	1848.74	−	1067.37i	0.643945	−	0.371782i
$203$		−	2106.47i		−	0.728302i
$204$	37.1238	+	64.3002i	0.0127411	+	0.0220682i
$205$	1519.34	−	2631.58i	0.517636	−	0.896572i
$206$	7658.85	+	4421.84i	2.59038	+	1.49555i
$207$	867.939			0.291429
$208$		0			0
$209$	237.054			0.0784562
$210$	912.127	+	526.617i	0.299727	+	0.173048i
$211$	1226.14	−	2123.74i	0.400053	−	0.692912i	−0.593679	−	0.804702i	$-0.702325\pi$
$211$	1226.14	−	2123.74i	0.400053	−	0.692912i	0.993732	+	0.111790i	$0.0356585\pi$
$212$	−5419.53	−	9386.91i	−1.75573	−	3.04102i
$213$		−	687.683i		−	0.221217i
$214$	315.920	−	182.397i	0.100915	−	0.0582634i
$215$	−1713.57	+	989.332i	−0.543557	+	0.313823i
$216$			6269.01i			1.97478i
$217$	1983.39	+	3435.33i	0.620467	+	1.07468i
$218$	896.053	−	1552.01i	0.278387	−	0.482180i
$219$	25.3404	+	14.6303i	0.00781893	+	0.00451426i
$220$	415.388			0.127297
$221$		0			0
$222$	2335.12			0.705959
$223$	3992.65	+	2305.16i	1.19896	+	0.692219i	0.960323	−	0.278890i	$-0.0899666\pi$
$223$	3992.65	+	2305.16i	1.19896	+	0.692219i	0.238635	+	0.971109i	$0.423300\pi$
$224$	4786.03	−	8289.64i	1.42759	−	2.47266i
$225$	793.201	+	1373.86i	0.235022	+	0.407071i
$226$			2654.33i			0.781253i
$227$	−1375.77	+	794.300i	−0.402260	+	0.232245i	−0.687458	−	0.726224i	$-0.741274\pi$
$227$	−1375.77	+	794.300i	−0.402260	+	0.232245i	0.285199	+	0.958468i	$0.407940\pi$
$228$	2941.10	−	1698.05i	0.854295	−	0.493228i
$229$			353.354i			0.101966i	0.998700	+	0.0509832i	$0.0162355\pi$
$229$			353.354i			0.101966i	−0.998700	+	0.0509832i	$0.983764\pi$
$230$	−750.623	−	1300.12i	−0.215194	−	0.372727i
$231$	31.5865	−	54.7095i	0.00899672	−	0.0155828i
$232$	−8875.89	−	5124.50i	−2.51177	−	1.45017i
$233$	6622.95			1.86216			0.931081	−	0.364812i	$-0.118867\pi$
$233$	6622.95			1.86216			0.931081	+	0.364812i	$0.118867\pi$
$234$		0			0
$235$	−3200.85			−0.888511
$236$	−2237.05	−	1291.56i	−0.617033	−	0.356244i
$237$	146.532	−	253.801i	0.0401614	−	0.0695617i
$238$	84.2020	+	145.842i	0.0229328	+	0.0397208i
$239$			1852.86i			0.501471i	0.968056	+	0.250736i	$0.0806724\pi$
$239$			1852.86i			0.501471i	−0.968056	+	0.250736i	$0.919328\pi$
$240$	2517.35	−	1453.39i	0.677059	−	0.390900i
$241$	1438.26	−	830.377i	0.384424	−	0.221947i	−0.295317	−	0.955399i	$-0.595425\pi$
$241$	1438.26	−	830.377i	0.384424	−	0.221947i	0.679741	+	0.733452i	$0.262092\pi$
$242$			7190.94i			1.91013i
$243$	−1584.50	−	2744.43i	−0.418295	−	0.724508i
$244$	−8080.50	+	13995.8i	−2.12009	+	3.67210i
$245$	−782.793	−	451.946i	−0.204126	−	0.117852i
$246$	−3584.18			−0.928939
$247$		0			0
$248$	19300.3			4.94182
$249$	−1397.22	−	806.685i	−0.355603	−	0.205307i
$250$	3987.45	−	6906.47i	1.00875	−	1.74721i
$251$	3280.75	+	5682.43i	0.825017	+	1.42897i	0.901907	+	0.431931i	$0.142168\pi$
$251$	3280.75	+	5682.43i	0.825017	+	1.42897i	−0.0768900	+	0.997040i	$0.524499\pi$
$252$			7803.59i			1.95071i
$253$	−77.9812	+	45.0224i	−0.0193780	+	0.0111879i
$254$	−1987.87	+	1147.70i	−0.491063	+	0.283516i
$255$			26.6633i			0.00654791i
$256$	−3957.68	−	6854.90i	−0.966230	−	1.67356i
$257$	990.429	−	1715.47i	0.240394	−	0.416375i	−0.720433	−	0.693525i	$-0.756057\pi$
$257$	990.429	−	1715.47i	0.240394	−	0.416375i	0.960827	+	0.277150i	$0.0893900\pi$
$258$	2021.19	+	1166.93i	0.487728	+	0.281590i
$259$	3858.47			0.925689
$260$		0			0
$261$	3391.96			0.804432
$262$	−8198.53	−	4733.42i	−1.93323	−	1.11615i
$263$	165.643	−	286.902i	0.0388364	−	0.0672667i	−0.845954	−	0.533256i	$-0.820968\pi$
$263$	165.643	−	286.902i	0.0388364	−	0.0672667i	0.884790	+	0.465989i	$0.154302\pi$
$264$	−153.684	−	266.188i	−0.0358280	−	0.0620559i
$265$		−	3892.45i		−	0.902307i
$266$	6670.84	−	3851.41i	1.53765	−	0.887764i
$267$	−692.893	+	400.042i	−0.158818	+	0.0916935i
$268$		−	4550.00i		−	1.03707i
$269$	2891.96	+	5009.02i	0.655487	+	1.13534i	0.981772	+	0.190065i	$0.0608698\pi$
$269$	2891.96	+	5009.02i	0.655487	+	1.13534i	−0.326285	+	0.945271i	$0.605797\pi$
$270$	−1794.32	+	3107.86i	−0.404441	+	0.700512i
$271$	3712.68	+	2143.52i	0.832211	+	0.480478i	0.854609	−	0.519272i	$-0.173797\pi$
$271$	3712.68	+	2143.52i	0.832211	+	0.480478i	−0.0223978	+	0.999749i	$0.507130\pi$
$272$	464.772			0.103606
$273$		0			0
$274$	−11693.7			−2.57826
$275$	−142.532	−	82.2912i	−0.0312547	−	0.0180449i
$276$	−645.003	+	1117.18i	−0.140669	+	0.243646i
$277$	17.2524	+	29.8821i	0.00374223	+	0.00648173i	0.867890	−	0.496756i	$-0.165475\pi$
$277$	17.2524	+	29.8821i	0.00374223	+	0.00648173i	−0.864148	+	0.503237i	$0.832142\pi$
$278$			7000.79i			1.51036i
$279$	−5531.77	+	3193.77i	−1.18702	+	0.685326i
$280$	7333.10	−	4233.77i	1.56513	−	0.903628i
$281$			4215.51i			0.894933i	0.894301	+	0.447466i	$0.147674\pi$
$281$			4215.51i			0.894933i	−0.894301	+	0.447466i	$0.852326\pi$
$282$	1887.73	+	3269.64i	0.398626	+	0.690441i
$283$	312.943	−	542.032i	0.0657332	−	0.113853i	−0.831286	−	0.555845i	$-0.812395\pi$
$283$	312.943	−	542.032i	0.0657332	−	0.113853i	0.897019	+	0.441992i	$0.145728\pi$
$284$	−7632.22	−	4406.47i	−1.59468	−	0.920689i
$285$	1219.58			0.253480
$286$		0			0
$287$	−5922.38			−1.21807
$288$	13348.4	+	7706.73i	2.73113	+	1.57682i
$289$	2454.37	−	4251.09i	0.499566	−	0.865274i
$290$	−2933.48	−	5080.93i	−0.593999	−	1.02884i
$291$			1753.83i			0.353303i
$292$	324.747	−	187.493i	0.0650836	−	0.0375760i
$293$	−769.474	+	444.256i	−0.153424	+	0.0885792i	−0.574746	−	0.818332i	$-0.694899\pi$
$293$	−769.474	+	444.256i	−0.153424	+	0.0885792i	0.421323	+	0.906911i	$0.361566\pi$
$294$			1066.16i			0.211495i
$295$	−463.817	−	803.355i	−0.0915407	−	0.158553i
$296$	9386.66	−	16258.2i	1.84320	−	3.19252i
$297$	186.410	+	107.624i	0.0364195	+	0.0210268i
$298$	−10165.0			−1.97597
$299$		0			0
$300$	−2357.85			−0.453768
$301$	3339.74	+	1928.20i	0.639534	+	0.369235i
$302$	−4228.88	+	7324.63i	−0.805777	+	1.39565i
$303$	−329.372	−	570.489i	−0.0624486	−	0.108164i
$304$		−	21258.8i		−	4.01077i
$305$	−5026.09	+	2901.82i	−0.943584	+	0.544779i
$306$	−234.843	+	135.587i	−0.0438728	+	0.0253300i
$307$		−	4467.87i		−	0.830601i	−0.909684	−	0.415301i	$-0.863676\pi$
$307$		−	4467.87i		−	0.830601i	0.909684	−	0.415301i	$-0.136324\pi$
$308$	−404.794	−	701.124i	−0.0748873	−	0.129709i
$309$	1364.50	−	2363.39i	0.251210	−	0.435108i
$310$	9568.12	+	5524.16i	1.75301	+	1.01210i
$311$	2722.79			0.496448			0.248224	−	0.968703i	$-0.420153\pi$
$311$	2722.79			0.496448			0.248224	+	0.968703i	$0.420153\pi$
$312$		0			0
$313$	−2513.73			−0.453944			−0.226972	−	0.973901i	$-0.572883\pi$
$313$	−2513.73			−0.453944			−0.226972	+	0.973901i	$0.572883\pi$
$314$	−10820.7	−	6247.32i	−1.94473	−	1.12279i
$315$	−1401.19	+	2426.92i	−0.250628	+	0.434101i
$316$	−1877.86	−	3252.56i	−0.334298	−	0.579021i
$317$		−	3069.18i		−	0.543792i	−0.962327	−	0.271896i	$-0.912349\pi$
$317$		−	3069.18i		−	0.543792i	0.962327	−	0.271896i	$-0.0876507\pi$
$318$	−3976.11	+	2295.61i	−0.701161	+	0.404816i
$319$	−304.755	+	175.950i	−0.0534890	+	0.0308819i
$320$		−	12777.8i		−	2.23219i
$321$	−56.2844	−	97.4874i	−0.00978657	−	0.0169508i
$322$	−1462.96	+	2533.92i	−0.253191	+	0.438540i
$323$	168.876	+	97.5009i	0.0290914	+	0.0167960i
$324$	−10939.4			−1.87576
$325$		0			0
$326$	−1712.65			−0.290966
$327$	−478.923	−	276.506i	−0.0809923	−	0.0467610i
$328$	−14407.6	+	24954.7i	−2.42539	+	4.20090i
$329$	3119.22	+	5402.64i	0.522699	+	0.905341i
$330$		−	175.950i		−	0.0293507i
$331$	−8174.52	+	4719.56i	−1.35744	+	0.783718i	−0.989278	−	0.146045i	$-0.953346\pi$
$331$	−8174.52	+	4719.56i	−1.35744	+	0.783718i	−0.368161	+	0.929762i	$0.620012\pi$
$332$	−17905.9	+	10338.0i	−2.95999	+	1.70895i
$333$			6213.12i			1.02245i
$334$	2011.75	+	3484.46i	0.329575	+	0.570841i
$335$	816.983	−	1415.06i	0.133243	−	0.230784i
$336$	−4906.30	−	2832.65i	−0.796608	−	0.459922i
$337$	5601.75			0.905480			0.452740	−	0.891643i	$-0.350447\pi$
$337$	5601.75			0.905480			0.452740	+	0.891643i	$0.350447\pi$
$338$		0			0
$339$	819.079			0.131228
$340$	295.921	+	170.850i	0.0472017	+	0.0272519i
$341$	331.340	−	573.897i	0.0526189	−	0.0911386i
$342$	6201.76	+	10741.8i	0.980564	+	1.69839i
$343$			6915.25i			1.08860i
$344$	16249.5	−	9381.64i	2.54684	−	1.47042i
$345$	−401.193	+	231.629i	−0.0626073	+	0.0361464i
$346$		−	8192.54i		−	1.27293i
$347$	−4986.79	−	8637.38i	−0.771485	−	1.33625i	−0.936749	−	0.350001i	$-0.886181\pi$
$347$	−4986.79	−	8637.38i	−0.771485	−	1.33625i	0.165265	−	0.986249i	$-0.447152\pi$
$348$	−2520.71	+	4366.00i	−0.388288	+	0.672535i
$349$	−5488.37	−	3168.71i	−0.841792	−	0.486009i	0.0160809	−	0.999871i	$-0.494881\pi$
$349$	−5488.37	−	3168.71i	−0.841792	−	0.486009i	−0.857873	+	0.513862i	$0.828214\pi$
$350$	−5347.94			−0.816741
$351$		0			0
$352$	−1599.08			−0.242134
$353$	−5101.56	−	2945.39i	−0.769203	−	0.444100i	0.0633871	−	0.997989i	$-0.479810\pi$
$353$	−5101.56	−	2945.39i	−0.769203	−	0.444100i	−0.832590	+	0.553889i	$0.813143\pi$
$354$	−547.081	+	947.572i	−0.0821385	+	0.142268i
$355$	−1582.42	−	2740.83i	−0.236581	−	0.409770i
$356$			10253.4i			1.52649i
$357$	45.0043	−	25.9833i	0.00667194	−	0.00385205i
$358$	17701.4	−	10219.9i	2.61326	−	1.50877i
$359$		−	7743.25i		−	1.13837i	−0.822211	−	0.569183i	$-0.807260\pi$
$359$		−	7743.25i		−	1.13837i	0.822211	−	0.569183i	$-0.192740\pi$
$360$	6817.45	+	11808.2i	0.998086	+	1.72874i
$361$	1030.21	−	1784.37i	0.150198	−	0.260150i
$362$	9155.30	+	5285.81i	1.32926	+	0.767448i
$363$	2219.00			0.320846
$364$		0			0
$365$	134.662			0.0193111
$366$	5928.37	+	3422.74i	0.846668	+	0.488824i
$367$	5657.54	−	9799.14i	0.804690	−	1.39376i	−0.111811	−	0.993730i	$-0.535665\pi$
$367$	5657.54	−	9799.14i	0.804690	−	1.39376i	0.916500	−	0.400034i	$-0.131002\pi$
$368$	4037.57	+	6993.28i	0.571937	+	0.990624i
$369$		−	9536.54i		−	1.34540i
$370$	9306.86	−	5373.32i	1.30768	−	0.754988i
$371$	−6569.99	+	3793.18i	−0.919398	+	0.530815i
$372$		−	9493.71i		−	1.32319i
$373$	5189.68	+	8988.79i	0.720406	+	1.24778i	0.960837	+	0.277114i	$0.0893779\pi$
$373$	5189.68	+	8988.79i	0.720406	+	1.24778i	−0.240431	+	0.970666i	$0.577289\pi$
$374$	14.0665	−	24.3640i	0.00194482	−	0.00336853i
$375$	−2131.22	−	1230.46i	−0.293482	−	0.169442i
$376$	30353.0			4.16313
$377$		0			0
$378$	6994.25			0.951707
$379$	6087.46	+	3514.60i	0.825044	+	0.476339i	0.852153	−	0.523293i	$-0.175297\pi$
$379$	6087.46	+	3514.60i	0.825044	+	0.476339i	−0.0271087	+	0.999632i	$0.508630\pi$
$380$	7814.72	−	13535.5i	1.05496	−	1.82725i
$381$	354.160	+	613.422i	0.0476224	+	0.0824845i
$382$			13339.4i			1.78665i
$383$	4616.21	−	2665.17i	0.615868	−	0.355572i	−0.159391	−	0.987216i	$-0.550953\pi$
$383$	4616.21	−	2665.17i	0.615868	−	0.355572i	0.775259	+	0.631644i	$0.217620\pi$
$384$	−5658.91	+	3267.17i	−0.752031	+	0.434185i
$385$		−	290.734i		−	0.0384862i
$386$	3267.98	+	5660.32i	0.430922	+	0.746380i
$387$	−3104.90	+	5377.84i	−0.407832	+	0.706385i
$388$	19464.8	+	11238.0i	2.54684	+	1.47042i
$389$	226.100			0.0294697			0.0147348	−	0.999891i	$-0.495310\pi$
$389$	226.100			0.0294697			0.0147348	+	0.999891i	$0.495310\pi$
$390$		0			0
$391$	−74.0714			−0.00958044
$392$	7423.07	+	4285.71i	0.956433	+	0.552197i
$393$	−1460.65	+	2529.92i	−0.187481	+	0.324727i
$394$	−1085.40	−	1879.96i	−0.138785	−	0.240384i
$395$		−	1348.73i		−	0.171803i
$396$	1128.99	−	651.822i	0.143267	−	0.0827154i
$397$	10984.5	−	6341.91i	1.38866	−	0.801742i	0.395493	−	0.918469i	$-0.370574\pi$
$397$	10984.5	−	6341.91i	1.38866	−	0.801742i	0.993164	+	0.116727i	$0.0372403\pi$
$398$			20422.5i			2.57207i
$399$	−1188.48	−	2058.51i	−0.149119	−	0.258281i
$400$	−7379.79	+	12782.2i	−0.922474	+	1.59777i
$401$	−8913.86	−	5146.42i	−1.11007	−	0.640898i	−0.171220	−	0.985233i	$-0.554771\pi$
$401$	−8913.86	−	5146.42i	−1.11007	−	0.640898i	−0.938847	+	0.344335i	$0.888104\pi$
$402$	−1927.29			−0.239116
$403$		0			0
$404$	−8442.07			−1.03963
$405$	−3402.17	−	1964.24i	−0.417420	−	0.240998i
$406$	−5717.33	+	9902.71i	−0.698883	+	1.21050i
$407$	−322.292	−	558.226i	−0.0392517	−	0.0679859i
$408$		−	252.842i		−	0.0306803i
$409$	9987.52	−	5766.30i	1.20746	−	0.697128i	0.245257	−	0.969458i	$-0.421128\pi$
$409$	9987.52	−	5766.30i	1.20746	−	0.697128i	0.962204	+	0.272331i	$0.0877944\pi$
$410$	−14285.1	+	8247.52i	−1.72071	+	0.993454i
$411$			3608.47i			0.433073i
$412$	−17486.7	−	30287.8i	−2.09103	−	3.62178i
$413$	−903.978	+	1565.74i	−0.107704	+	0.186549i
$414$	−4080.26	−	2355.74i	−0.484381	−	0.279658i
$415$	−7425.02			−0.878264
$416$		0			0
$417$	2160.32			0.253696
$418$	−1114.41	−	643.406i	−0.130401	−	0.0752871i
$419$	−2086.61	+	3614.12i	−0.243288	+	0.421387i	−0.961649	−	0.274283i	$-0.911559\pi$
$419$	−2086.61	+	3614.12i	−0.243288	+	0.421387i	0.718361	+	0.695671i	$0.244893\pi$
$420$	−2082.56	−	3607.11i	−0.241949	−	0.419069i
$421$		−	1949.71i		−	0.225708i	−0.993612	−	0.112854i	$-0.964001\pi$
$421$		−	1949.71i		−	0.225708i	0.993612	−	0.112854i	$-0.0359993\pi$
$422$	−11528.4	+	6655.93i	−1.32984	+	0.767786i
$423$	−8699.63	+	5022.73i	−0.999978	+	0.577337i
$424$			36911.4i			4.22777i
$425$	−67.6932	−	117.248i	−0.00772612	−	0.0133820i
$426$	−1866.49	+	3232.86i	−0.212281	+	0.367682i
$427$	9795.82	+	5655.62i	1.11019	+	0.640971i
$428$	−1442.61			−0.162924
$429$		0			0
$430$	10740.9			1.20459
$431$	1002.49	+	578.786i	0.112037	+	0.0646848i	0.554972	−	0.831869i	$-0.312729\pi$
$431$	1002.49	+	578.786i	0.112037	+	0.0646848i	−0.442934	+	0.896554i	$0.646062\pi$
$432$	9651.59	−	16717.0i	1.07491	−	1.86180i
$433$	−5573.38	−	9653.37i	−0.618567	−	1.07139i	−0.989747	−	0.142828i	$-0.954380\pi$
$433$	−5573.38	−	9653.37i	−0.618567	−	1.07139i	0.371181	−	0.928561i	$-0.378953\pi$
$434$		−	21533.1i		−	2.38162i
$435$	−1567.89	+	905.221i	−0.172815	+	0.0997747i
$436$	−6137.59	+	3543.54i	−0.674168	+	0.389231i
$437$			3388.04i			0.370874i
$438$	−79.4183	−	137.557i	−0.00866383	−	0.0150062i
$439$	1672.77	−	2897.33i	0.181861	−	0.314993i	−0.760653	−	0.649159i	$-0.775121\pi$
$439$	1672.77	−	2897.33i	0.181861	−	0.314993i	0.942514	+	0.334166i	$0.108454\pi$
$440$	−1225.05	−	707.281i	−0.132731	−	0.0766325i
$441$	−2836.76			−0.306312
$442$		0			0
$443$	12320.7			1.32139			0.660696	−	0.750654i	$-0.270261\pi$
$443$	12320.7			1.32139			0.660696	+	0.750654i	$0.270261\pi$
$444$	−7997.30	−	4617.24i	−0.854808	−	0.493524i
$445$	−1841.07	+	3188.82i	−0.196123	+	0.339696i
$446$	−12513.2	−	21673.5i	−1.32852	−	2.30106i
$447$			3136.73i			0.331906i
$448$	−21567.4	+	12451.9i	−2.27447	+	1.31317i
$449$	12314.6	−	7109.83i	1.29435	−	0.747291i	0.314924	−	0.949117i	$-0.398021\pi$
$449$	12314.6	−	7109.83i	1.29435	−	0.747291i	0.979421	+	0.201826i	$0.0646875\pi$
$450$		−	8611.55i		−	0.902116i
$451$	494.687	+	856.824i	0.0516495	+	0.0894596i
$452$	5248.41	−	9090.52i	0.546161	−	0.945978i
$453$	2260.25	+	1304.96i	0.234428	+	0.135347i
$454$	8623.48			0.891454
$455$		0			0
$456$	−11565.1			−1.18768
$457$	13238.3	+	7643.16i	1.35506	+	0.782346i	0.988953	−	0.148226i	$-0.0473565\pi$
$457$	13238.3	+	7643.16i	1.35506	+	0.782346i	0.366109	+	0.930572i	$0.380690\pi$
$458$	959.067	−	1661.15i	0.0978477	−	0.169477i
$459$	88.5318	+	153.342i	0.00900286	+	0.0155934i
$460$			5936.84i			0.601754i
$461$	6150.99	−	3551.27i	0.621432	−	0.358784i	−0.155995	−	0.987758i	$-0.549858\pi$
$461$	6150.99	−	3551.27i	0.621432	−	0.358784i	0.777426	+	0.628974i	$0.216525\pi$
$462$	−296.982	+	171.463i	−0.0299067	+	0.0172666i
$463$		−	13129.1i		−	1.31785i	−0.752211	−	0.658923i	$-0.771012\pi$
$463$		−	13129.1i		−	1.31785i	0.752211	−	0.658923i	$-0.228988\pi$
$464$	15779.1	+	27330.1i	1.57872	+	2.73442i
$465$	1704.66	−	2952.56i	0.170004	−	0.294455i
$466$	−31135.1	−	17975.9i	−3.09508	−	1.78694i
$467$	−12669.7			−1.25542			−0.627712	−	0.778445i	$-0.716009\pi$
$467$	−12669.7			−1.25542			−0.627712	+	0.778445i	$0.716009\pi$
$468$		0			0
$469$	−3184.59			−0.313541
$470$	15047.5	+	8687.66i	1.47678	+	0.852621i
$471$	−1927.82	+	3339.07i	−0.188597	+	0.326659i
$472$	4398.29	+	7618.06i	0.428915	+	0.742902i
$473$		−	644.240i		−	0.0626262i
$474$	−1377.72	+	795.426i	−0.133504	+	0.0770784i
$475$	−5362.94	+	3096.30i	−0.518039	+	0.299090i
$476$		−	665.972i		−	0.0641277i
$477$	−6108.00	−	10579.4i	−0.586302	−	1.01550i
$478$	5028.99	−	8710.47i	0.481215	−	0.833489i
$479$	−136.847	−	79.0087i	−0.0130537	−	0.00753654i	0.493459	−	0.869769i	$-0.335732\pi$
$479$	−136.847	−	79.0087i	−0.0130537	−	0.00753654i	−0.506513	+	0.862233i	$0.669066\pi$
$480$	−8226.86			−0.782298
$481$		0			0
$482$	−9015.16			−0.851928
$483$	781.924	+	451.444i	0.0736620	+	0.0425288i
$484$	14218.7	−	24627.5i	1.33534	−	2.31287i
$485$	4035.72	+	6990.07i	0.377840	+	0.654438i
$486$			17202.4i			1.60559i
$487$	11091.6	−	6403.71i	1.03205	−	0.595852i	0.114476	−	0.993426i	$-0.463481\pi$
$487$	11091.6	−	6403.71i	1.03205	−	0.595852i	0.917570	+	0.397574i	$0.130148\pi$
$488$	47661.4	−	27517.3i	4.42117	−	2.55256i
$489$			528.494i			0.0488739i
$490$	2453.32	+	4249.28i	0.226183	+	0.391761i
$491$	−7117.26	+	12327.5i	−0.654170	+	1.13306i	0.327931	+	0.944702i	$0.393649\pi$
$491$	−7117.26	+	12327.5i	−0.654170	+	1.13306i	−0.982101	+	0.188354i	$0.939685\pi$
$492$	12275.1	+	7087.02i	1.12480	+	0.649406i
$493$	−289.476			−0.0264449
$494$		0			0
$495$	468.156			0.0425092
$496$	−51466.5	−	29714.2i	−4.65910	−	2.68994i
$497$	−3084.13	+	5341.87i	−0.278354	+	0.482124i
$498$	4378.97	+	7584.60i	0.394029	+	0.682478i
$499$		−	379.793i		−	0.0340719i	−0.999855	−	0.0170360i	$-0.994577\pi$
$499$		−	379.793i		−	0.0340719i	0.999855	−	0.0170360i	$-0.00542298\pi$
$500$	−27312.4	+	15768.8i	−2.44290	+	1.41041i
$501$	1075.24	−	620.792i	0.0958849	−	0.0553591i
$502$		−	35618.2i		−	3.16677i
$503$	−6542.73	−	11332.3i	−0.579972	−	1.00454i	−0.995482	−	0.0949520i	$-0.969730\pi$
$503$	−6542.73	−	11332.3i	−0.579972	−	1.00454i	0.415510	−	0.909589i	$-0.363603\pi$
$504$	13287.2	−	23014.0i	1.17432	−	2.03398i
$505$	−2625.49	−	1515.83i	−0.231352	−	0.133571i
$506$	488.795			0.0429439
$507$		0			0
$508$	9077.40			0.792804
$509$	−13289.3	−	7672.55i	−1.15724	−	0.668134i	−0.206600	−	0.978425i	$-0.566240\pi$
$509$	−13289.3	−	7672.55i	−1.15724	−	0.668134i	−0.950641	+	0.310292i	$0.899573\pi$
$510$	72.3688	−	125.346i	0.00628342	−	0.0108832i
$511$	−131.228	−	227.294i	−0.0113604	−	0.0196769i
$512$			11760.4i			1.01512i
$513$	7013.87	−	4049.46i	0.603645	−	0.348515i
$514$	−9312.20	+	5376.40i	−0.799112	+	0.461367i
$515$		−	12559.4i		−	1.07463i
$516$	−4614.77	−	7993.02i	−0.393709	−	0.681925i
$517$	521.087	−	902.549i	0.0443276	−	0.0767777i
$518$	−18139.0	−	10472.6i	−1.53858	−	0.888297i
$519$	−2528.08			−0.213815
$520$		0			0
$521$	19946.6			1.67731			0.838653	−	0.544666i	$-0.183343\pi$
$521$	19946.6			1.67731			0.838653	+	0.544666i	$0.183343\pi$
$522$	−15945.9	−	9206.37i	−1.33704	−	0.771938i
$523$	416.467	−	721.343i	0.0348200	−	0.0603100i	−0.848090	−	0.529852i	$-0.822248\pi$
$523$	416.467	−	721.343i	0.0348200	−	0.0603100i	0.882910	+	0.469542i	$0.155581\pi$
$524$	18718.8	+	32422.0i	1.56057	+	2.70298i
$525$			1650.28i			0.137189i
$526$	−1557.41	+	899.169i	−0.129099	+	0.0745354i
$527$	472.091	−	272.562i	0.0390220	−	0.0225294i
$528$			946.429i			0.0780076i
$529$	5440.03	+	9422.40i	0.447113	+	0.774423i
$530$	−10564.8	+	18298.8i	−0.865860	+	1.49971i
$531$	−2521.23	−	1455.64i	−0.206049	−	0.118963i
$532$	−30461.7			−2.48248
$533$		0			0
$534$	4343.14			0.351959
$535$	−448.655	−	259.031i	−0.0362561	−	0.0209325i
$536$	−7747.29	+	13418.7i	−0.624313	+	1.08134i
$537$	−3153.69	−	5462.35i	−0.253430	−	0.438953i
$538$		−	31397.2i		−	2.51604i
$539$	254.872	−	147.151i	0.0203676	−	0.0117592i
$540$	12290.4	−	7095.85i	0.979432	−	0.565475i
$541$			9717.26i			0.772232i	0.922450	+	0.386116i	$0.126184\pi$
$541$			9717.26i			0.772232i	−0.922450	+	0.386116i	$0.873816\pi$
$542$	−11635.8	−	20153.7i	−0.922139	−	1.59719i
$543$	1631.11	−	2825.17i	0.128909	−	0.223277i
$544$	−1139.18	−	657.706i	−0.0897830	−	0.0518362i
$545$	−2545.06			−0.200034
$546$		0			0
$547$	−17069.7			−1.33427			−0.667137	−	0.744935i	$-0.732481\pi$
$547$	−17069.7			−1.33427			−0.667137	+	0.744935i	$0.732481\pi$
$548$	40048.5	+	23122.0i	3.12188	+	1.80242i
$549$	−9107.00	+	15773.8i	−0.707973	+	1.22625i
$550$	446.706	+	773.717i	0.0346320	+	0.0599843i
$551$			13240.7i			1.02372i
$552$	3804.44	−	2196.49i	0.293347	−	0.169364i
$553$	−2276.49	+	1314.33i	−0.175057	+	0.101069i
$554$		−	187.305i		−	0.0143643i
$555$	−1658.11	−	2871.93i	−0.126816	−	0.219652i
$556$	13842.7	−	23976.2i	1.05587	−	1.82881i
$557$	7047.15	+	4068.67i	0.536081	+	0.309507i	0.743489	−	0.668748i	$-0.233169\pi$
$557$	7047.15	+	4068.67i	0.536081	+	0.309507i	−0.207408	+	0.978255i	$0.566503\pi$
$558$	34673.8			2.63057
$559$		0			0
$560$	−26072.7			−1.96745
$561$	−7.51829	−	4.34069i	−0.000565816	−	0.000326674i
$562$	11441.6	−	19817.5i	0.858783	−	1.48746i
$563$	−2484.78	−	4303.76i	−0.186005	−	0.322170i	0.757910	−	0.652360i	$-0.226221\pi$
$563$	−2484.78	−	4303.76i	−0.186005	−	0.322170i	−0.943915	+	0.330189i	$0.892887\pi$
$564$		−	14930.5i		−	1.11469i
$565$	3264.53	−	1884.77i	0.243079	−	0.140342i
$566$	−2942.34	+	1698.76i	−0.218509	+	0.126156i
$567$			7656.60i			0.567103i
$568$	15005.8	+	25990.8i	1.10850	+	1.91998i
$569$	−222.421	+	385.245i	−0.0163873	+	0.0283836i	−0.874103	−	0.485741i	$-0.838550\pi$
$569$	−222.421	+	385.245i	−0.0163873	+	0.0283836i	0.857715	+	0.514125i	$0.171883\pi$
$570$	−5733.37	−	3310.16i	−0.421306	−	0.243241i
$571$	−22724.7			−1.66550			−0.832750	−	0.553650i	$-0.813235\pi$
$571$	−22724.7			−1.66550			−0.832750	+	0.553650i	$0.813235\pi$
$572$		0			0
$573$	4116.30			0.300106
$574$	27841.6	+	16074.4i	2.02454	+	1.16887i
$575$	1176.13	−	2037.11i	0.0853008	−	0.147745i
$576$	−20050.8	−	34729.0i	−1.45043	−	2.51223i
$577$			3282.72i			0.236848i	0.992963	+	0.118424i	$0.0377843\pi$
$577$			3282.72i			0.236848i	−0.992963	+	0.118424i	$0.962216\pi$
$578$	−23076.4	+	13323.2i	−1.66064	+	0.958774i
$579$	1746.67	−	1008.44i	0.125370	−	0.0723825i
$580$			23201.5i			1.66102i
$581$	7235.66	+	12532.5i	0.516671	+	0.894900i
$582$	4760.20	−	8244.91i	0.339032	−	0.587221i
$583$	1097.56	+	633.678i	0.0779698	+	0.0450159i
$584$	−1276.98			−0.0904823
$585$		0			0
$586$	4823.16			0.340005
$587$	−9315.72	−	5378.43i	−0.655027	−	0.378180i	0.135353	−	0.990798i	$-0.456783\pi$
$587$	−9315.72	−	5378.43i	−0.655027	−	0.378180i	−0.790380	+	0.612617i	$0.790117\pi$
$588$	2108.12	−	3651.37i	0.147853	−	0.256088i
$589$	−12467.0	−	21593.5i	−0.872147	−	1.51060i
$590$			5035.53i			0.351372i
$591$	−580.123	+	334.934i	−0.0403775	+	0.0233119i
$592$	−50061.2	+	28902.9i	−3.47551	+	2.00659i
$593$			9838.16i			0.681290i	0.940192	+	0.340645i	$0.110645\pi$
$593$			9838.16i			0.681290i	−0.940192	+	0.340645i	$0.889355\pi$
$594$	−584.219	−	1011.90i	−0.0403549	−	0.0698967i
$595$	119.580	−	207.118i	0.00823914	−	0.0142706i
$596$	34812.9	+	20099.2i	2.39260	+	1.38137i
$597$	6302.01			0.432034
$598$		0			0
$599$	439.112			0.0299527			0.0149763	−	0.999888i	$-0.495233\pi$
$599$	439.112			0.0299527			0.0149763	+	0.999888i	$0.495233\pi$
$600$	6953.68	+	4014.71i	0.473138	+	0.273166i
$601$	−958.258	+	1659.75i	−0.0650386	+	0.112650i	−0.896711	−	0.442616i	$-0.854050\pi$
$601$	−958.258	+	1659.75i	−0.0650386	+	0.112650i	0.831673	+	0.555266i	$0.187384\pi$
$602$	−10467.0	−	18129.3i	−0.708641	−	1.22740i
$603$		−	5128.01i		−	0.346316i
$604$	28966.1	−	16723.6i	1.95135	−	1.12661i
$605$	8844.05	−	5106.12i	0.594317	−	0.343129i
$606$			3575.89i			0.239704i
$607$	2333.50	+	4041.73i	0.156036	+	0.270262i	0.933436	−	0.358745i	$-0.116795\pi$
$607$	2333.50	+	4041.73i	0.156036	+	0.270262i	−0.777400	+	0.629007i	$0.783462\pi$
$608$	−30083.6	+	52106.3i	−2.00666	+	3.47564i
$609$	3055.80	+	1764.27i	0.203329	+	0.117392i
$610$	31504.2			2.09109
$611$		0			0
$612$	1072.39			0.0708311
$613$	−5750.98	−	3320.33i	−0.378923	−	0.218771i	0.298427	−	0.954433i	$-0.403538\pi$
$613$	−5750.98	−	3320.33i	−0.378923	−	0.218771i	−0.677350	+	0.735661i	$0.736872\pi$
$614$	−12126.6	+	21003.9i	−0.797050	+	1.38053i
$615$	2545.04	+	4408.14i	0.166872	+	0.289030i
$616$			2756.97i			0.180327i
$617$	−3181.17	+	1836.65i	−0.207568	+	0.119839i	−0.600180	−	0.799865i	$-0.704905\pi$
$617$	−3181.17	+	1836.65i	−0.207568	+	0.119839i	0.392613	+	0.919704i	$0.371571\pi$
$618$	−12829.3	+	7407.01i	−0.835066	+	0.482125i
$619$			15843.8i			1.02878i	0.857557	+	0.514390i	$0.171982\pi$
$619$			15843.8i			1.02878i	−0.857557	+	0.514390i	$0.828018\pi$
$620$	−21845.9	−	37838.2i	−1.41508	−	2.45100i
$621$	−1538.19	+	2664.22i	−0.0993967	+	0.172160i
$622$	−12800.1	−	7390.14i	−0.825140	−	0.476395i
$623$	7176.45			0.461506
$624$		0			0
$625$	−3129.35			−0.200278
$626$	11817.3	+	6822.71i	0.754494	+	0.435608i
$627$	−198.544	+	343.888i	−0.0126461	+	0.0219036i
$628$	24705.7	+	42791.6i	1.56985	+	2.71906i
$629$		−	530.239i		−	0.0336121i
$630$	13174.2	−	7606.13i	0.833132	−	0.481009i
$631$	−10257.4	+	5922.12i	−0.647133	+	0.373623i	−0.787357	−	0.616497i	$-0.788551\pi$
$631$	−10257.4	+	5922.12i	−0.647133	+	0.373623i	0.140224	+	0.990120i	$0.455218\pi$
$632$			12789.8i			0.804983i
$633$	2053.91	+	3557.47i	0.128966	+	0.223375i
$634$	−8330.29	+	14428.5i	−0.521827	+	0.903830i
$635$	2823.08	+	1629.91i	0.176426	+	0.101860i
$636$	18156.5			1.13200
$637$		0			0
$638$	1910.24			0.118538
$639$	−8601.77	−	4966.24i	−0.532521	−	0.307451i
$640$	−15036.1	+	26043.3i	−0.928679	+	1.60852i
$641$	13766.8	+	23844.8i	0.848294	+	1.46929i	0.882730	+	0.469881i	$0.155703\pi$
$641$	13766.8	+	23844.8i	0.848294	+	1.46929i	−0.0344363	+	0.999407i	$0.510964\pi$
$642$			611.063i			0.0375650i
$643$	−18818.7	+	10865.0i	−1.15418	+	0.666365i	−0.949902	−	0.312548i	$-0.898817\pi$
$643$	−18818.7	+	10865.0i	−1.15418	+	0.666365i	−0.204276	+	0.978913i	$0.565484\pi$
$644$	10020.7	−	5785.44i	0.613152	−	0.354003i
$645$		−	3314.45i		−	0.202336i
$646$	−529.269	−	916.721i	−0.0322350	−	0.0558327i
$647$	−9121.79	+	15799.4i	−0.554273	+	0.960029i	0.443687	+	0.896182i	$0.353670\pi$
$647$	−9121.79	+	15799.4i	−0.554273	+	0.960029i	−0.997960	+	0.0638468i	$0.979663\pi$
$648$	32262.1	+	18626.5i	1.95583	+	1.12920i
$649$	302.032			0.0182678
$650$		0			0
$651$	−6644.74			−0.400043
$652$	5865.48	+	3386.43i	0.352316	+	0.203410i
$653$	11839.1	−	20506.0i	0.709496	−	1.22888i	−0.255549	−	0.966796i	$-0.582256\pi$
$653$	11839.1	−	20506.0i	0.709496	−	1.22888i	0.965044	−	0.262087i	$-0.0844106\pi$
$654$	1500.97	+	2599.76i	0.0897442	+	0.155442i
$655$			13444.4i			0.802007i
$656$	76839.2	−	44363.1i	4.57327	−	2.64038i
$657$	366.001	−	211.311i	0.0217337	−	0.0125480i
$658$		−	33864.4i		−	2.00634i
$659$	3808.28	+	6596.13i	0.225113	+	0.389907i	0.956353	−	0.292213i	$-0.0943915\pi$
$659$	3808.28	+	6596.13i	0.225113	+	0.389907i	−0.731240	+	0.682120i	$0.761058\pi$
$660$	−347.907	+	602.593i	−0.0205186	+	0.0355392i
$661$	6571.94	+	3794.31i	0.386716	+	0.223270i	0.680736	−	0.732529i	$-0.261660\pi$
$661$	6571.94	+	3794.31i	0.386716	+	0.223270i	−0.294021	+	0.955799i	$0.594993\pi$
$662$	51238.9			3.00824
$663$		0			0
$664$	70410.0			4.11511
$665$	−9473.61	−	5469.59i	−0.552438	−	0.318950i
$666$	16863.5	−	29208.4i	0.981152	−	1.69941i
$667$	−2514.73	−	4355.65i	−0.145983	−	0.252850i
$668$		−	15911.4i		−	0.921602i
$669$	−6688.07	+	3861.36i	−0.386511	+	0.223152i
$670$	−7681.43	+	4434.87i	−0.442925	+	0.255723i
$671$		−	1889.62i		−	0.108716i
$672$	8017.05	+	13885.9i	0.460215	+	0.797116i
$673$	6994.55	−	12114.9i	0.400624	−	0.693901i	−0.593177	−	0.805072i	$-0.702127\pi$
$673$	6994.55	−	12114.9i	0.400624	−	0.693901i	0.993801	+	0.111171i	$0.0354600\pi$
$674$	−26334.3	−	15204.1i	−1.50499	−	0.868904i
$675$	−5622.94			−0.320633
$676$		0			0
$677$	−16112.1			−0.914678			−0.457339	−	0.889292i	$-0.651197\pi$
$677$	−16112.1			−0.914678			−0.457339	+	0.889292i	$0.651197\pi$
$678$	−3850.57	−	2223.13i	−0.218112	−	0.125927i
$679$	7865.59	−	13623.6i	0.444556	−	0.769994i
$680$	−581.813	−	1007.73i	−0.0328110	−	0.0568304i
$681$		−	2661.06i		−	0.149738i
$682$	−3115.32	+	1798.63i	−0.174914	+	0.100987i
$683$	8073.17	−	4661.05i	0.452286	−	0.261127i	−0.256509	−	0.966542i	$-0.582572\pi$
$683$	8073.17	−	4661.05i	0.452286	−	0.261127i	0.708795	+	0.705414i	$0.249239\pi$
$684$		−	49051.1i		−	2.74198i
$685$	8303.42	+	14382.0i	0.463150	+	0.802199i
$686$	18769.2	−	32509.2i	1.04462	−	1.80934i
$687$	−512.603	−	295.951i	−0.0284673	−	0.0164356i
$688$	−57774.8			−3.20152
$689$		0			0
$690$	2514.73			0.138745
$691$	23995.3	+	13853.7i	1.32102	+	0.762689i	0.983891	−	0.178770i	$-0.0572118\pi$
$691$	23995.3	+	13853.7i	1.32102	+	0.762689i	0.337126	+	0.941460i	$0.390545\pi$
$692$	−16199.2	+	28057.8i	−0.889884	+	1.54132i
$693$	−456.217	−	790.190i	−0.0250076	−	0.0433144i
$694$			54140.2i			2.96129i
$695$	8610.19	−	4971.09i	0.469932	−	0.271316i
$696$	14868.0	−	8584.03i	0.809725	−	0.467495i
$697$			813.865i			0.0442286i
$698$	17200.9	+	29792.8i	0.932755	+	1.61558i
$699$	−5547.04	+	9607.75i	−0.300155	+	0.519883i
$700$	18315.6	+	10574.5i	0.988949	+	0.570970i
$701$	−7657.78			−0.412597			−0.206298	−	0.978489i	$-0.566142\pi$
$701$	−7657.78			−0.412597			−0.206298	+	0.978489i	$0.566142\pi$
$702$		0			0
$703$	−24253.2			−1.30118
$704$	3602.98	+	2080.18i	0.192887	+	0.111363i
$705$	2680.86	−	4643.39i	0.143216	−	0.248057i
$706$	15988.6	+	27693.1i	0.852322	+	1.47626i
$707$			5908.68i			0.314312i
$708$	3747.28	−	2163.49i	0.198914	−	0.114843i
$709$	−1961.07	+	1132.22i	−0.103878	+	0.0599740i	−0.551039	−	0.834480i	$-0.685768\pi$
$709$	−1961.07	+	1132.22i	−0.103878	+	0.0599740i	0.447161	+	0.894453i	$0.352435\pi$
$710$			17179.9i			0.908098i
$711$	−2116.42	−	3665.74i	−0.111634	−	0.193356i
$712$	17458.5	−	30238.9i	0.918937	−	1.59165i
$713$	8202.30	+	4735.60i	0.430825	+	0.248737i
$714$	−282.093			−0.0147858
$715$		0			0
$716$	−80831.6			−4.21902
$717$	−2687.90	−	1551.86i	−0.140002	−	0.0808302i
$718$	−21016.6	+	36401.7i	−1.09238	+	1.89206i
$719$	−3608.48	−	6250.08i	−0.187168	−	0.324184i	0.757137	−	0.653256i	$-0.226598\pi$
$719$	−3608.48	−	6250.08i	−0.187168	−	0.324184i	−0.944305	+	0.329072i	$0.893264\pi$
$720$		−	41983.8i		−	2.17312i
$721$	−21198.7	+	12239.1i	−1.09498	+	0.632187i
$722$	−9686.19	+	5592.32i	−0.499283	+	0.288261i
$723$			2781.92i			0.143099i
$724$	−20903.3	−	36205.6i	−1.07302	−	1.85852i
$725$	4596.38	−	7961.17i	0.235456	−	0.407821i
$726$	−10431.7	−	6022.76i	−0.533275	−	0.307886i
$727$	14576.3			0.743612			0.371806	−	0.928310i	$-0.378739\pi$
$727$	14576.3			0.743612			0.371806	+	0.928310i	$0.378739\pi$
$728$		0			0
$729$	−8450.60			−0.429335
$730$	−633.060	−	365.498i	−0.0320967	−	0.0185311i
$731$	264.978	−	458.955i	0.0134070	−	0.0232217i
$732$	−13535.6	−	23444.4i	−0.683457	−	1.18378i
$733$			4019.83i			0.202559i	0.994858	+	0.101279i	$0.0322936\pi$
$733$			4019.83i			0.202559i	−0.994858	+	0.101279i	$0.967706\pi$
$734$	−53193.2	+	30711.1i	−2.67493	+	1.54437i
$735$	1311.25	−	757.053i	0.0658045	−	0.0379923i
$736$		−	22854.5i		−	1.14460i
$737$	266.004	+	460.733i	0.0132950	+	0.0230276i
$738$	−25883.9	+	44832.2i	−1.29105	+	2.23617i
$739$	23537.1	+	13589.2i	1.17162	+	0.676436i	0.954061	−	0.299611i	$-0.0968571\pi$
$739$	23537.1	+	13589.2i	1.17162	+	0.676436i	0.217559	+	0.976047i	$0.430190\pi$
$740$	−42498.7			−2.11120
$741$		0			0
$742$	41181.5			2.03749
$743$	−31054.1	−	17929.1i	−1.53333	−	0.885269i	−0.999205	−	0.0398633i	$-0.987308\pi$
$743$	−31054.1	−	17929.1i	−1.53333	−	0.885269i	−0.534125	−	0.845405i	$-0.679359\pi$
$744$	−16164.9	+	27998.5i	−0.796553	+	1.37967i
$745$	7217.89	+	12501.8i	0.354957	+	0.614804i
$746$		−	56342.8i		−	2.76523i
$747$	−20180.6	+	11651.3i	−0.988445	+	0.570679i
$748$	−96.3500	+	55.6277i	−0.00470976	+	0.00271918i
$749$			1009.70i			0.0492572i
$750$	6679.37	+	11569.0i	0.325195	+	0.563254i
$751$	16784.6	−	29071.7i	0.815549	−	1.41257i	−0.0933834	−	0.995630i	$-0.529768\pi$
$751$	16784.6	−	29071.7i	0.815549	−	1.41257i	0.908933	−	0.416943i	$-0.136898\pi$
$752$	−80939.8	−	46730.6i	−3.92496	−	2.26608i
$753$	−10991.1			−0.531925
$754$		0			0
$755$	12011.3			0.578988
$756$	−23953.9	−	13829.8i	−1.15237	−	0.665322i
$757$	−10675.9	+	18491.2i	−0.512578	+	0.887812i	0.487315	+	0.873226i	$0.337976\pi$
$757$	−10675.9	+	18491.2i	−0.512578	+	0.887812i	−0.999894	+	0.0145856i	$0.995357\pi$
$758$	−19078.5	−	33044.9i	−0.914197	−	1.58344i
$759$		−	150.834i		−	0.00721333i
$760$	−46093.7	+	26612.2i	−2.19999	+	1.27017i
$761$	−33574.1	+	19384.0i	−1.59929	+	0.923350i	−0.607665	+	0.794194i	$0.707893\pi$
$761$	−33574.1	+	19384.0i	−1.59929	+	0.923350i	−0.991624	+	0.129156i	$0.958773\pi$
$762$		−	3845.01i		−	0.182795i
$763$	2480.16	+	4295.76i	0.117677	+	0.203823i
$764$	26376.0	−	45684.6i	1.24902	−	2.16336i
$765$	333.513	+	192.554i	0.0157623	+	0.00910039i
$766$	−28935.0			−1.36484
$767$		0			0
$768$	13259.0			0.622972
$769$	952.253	+	549.784i	0.0446543	+	0.0257812i	0.522161	−	0.852847i	$-0.325126\pi$
$769$	952.253	+	549.784i	0.0446543	+	0.0257812i	−0.477507	+	0.878628i	$0.658459\pi$
$770$	−789.103	+	1366.77i	−0.0369316	+	0.0639673i
$771$	1659.06	+	2873.58i	0.0774964	+	0.134228i
$772$		−	25847.2i		−	1.20500i
$773$	14332.0	−	8274.61i	0.666866	−	0.385015i	−0.128022	−	0.991771i	$-0.540863\pi$
$773$	14332.0	−	8274.61i	0.666866	−	0.385015i	0.794888	+	0.606756i	$0.207529\pi$
$774$	29192.8	−	16854.5i	1.35570	−	0.782716i
$775$			17311.3i			0.802373i
$776$	−38269.9	−	66285.4i	−1.77037	−	3.06638i
$777$	−3231.65	+	5597.38i	−0.149208	+	0.258436i
$778$	−1062.91	−	613.674i	−0.0489812	−	0.0282793i
$779$	37226.3			1.71216
$780$		0			0
$781$	1030.45			0.0472118
$782$	348.217	+	201.043i	0.0159235	+	0.00919346i
$783$	−6011.33	+	10411.9i	−0.274365	+	0.475213i
$784$	−13196.3	−	22856.7i	−0.601145	−	1.04121i
$785$			17744.3i			0.806779i
$786$	13733.3	−	7928.93i	0.623220	−	0.359816i
$787$	34239.5	−	19768.2i	1.55083	−	0.895374i	0.552760	−	0.833340i	$-0.313575\pi$
$787$	34239.5	−	19768.2i	1.55083	−	0.895374i	0.998074	−	0.0620340i	$-0.0197587\pi$
$788$			8584.64i			0.388090i
$789$	277.468	+	480.588i	0.0125198	+	0.0216849i
$790$	−3660.70	+	6340.51i	−0.164863	+	0.285551i
$791$	−6362.54	−	3673.42i	−0.286000	−	0.165122i
$792$	−4439.43			−0.199177
$793$		0			0
$794$	−68852.3			−3.07743
$795$	5646.69	+	3260.12i	0.251909	+	0.145439i
$796$	40381.4	−	69942.7i	1.79809	−	3.11439i
$797$	3955.06	+	6850.37i	0.175779	+	0.304458i	0.940430	−	0.339986i	$-0.110422\pi$
$797$	3955.06	+	6850.37i	0.175779	+	0.304458i	−0.764652	+	0.644444i	$0.777089\pi$
$798$			12903.0i			0.572381i
$799$	742.442	−	428.649i	0.0328732	−	0.0189794i
$800$	36176.5	−	20886.5i	1.59879	−	0.923062i
$801$			11555.9i			0.509748i
$802$	27936.6	+	48387.6i	1.23002	+	2.13046i
$803$	−21.9226	+	37.9710i	−0.000963426	+	0.00166870i
$804$	6600.58	+	3810.85i	0.289533	+	0.167162i
$805$	4155.25			0.181930
$806$		0			0
$807$	−9688.62			−0.422621
$808$	24897.0	+	14374.3i	1.08400	+	0.625849i
$809$	2861.50	−	4956.27i	0.124357	−	0.215393i	−0.797124	−	0.603815i	$-0.793646\pi$
$809$	2861.50	−	4956.27i	0.124357	−	0.215393i	0.921482	+	0.388422i	$0.126980\pi$
$810$	10662.6	+	18468.2i	0.462526	+	0.801119i
$811$		−	7697.61i		−	0.333292i	−0.986017	−	0.166646i	$-0.946706\pi$
$811$		−	7697.61i		−	0.333292i	0.986017	−	0.166646i	$-0.0532937\pi$
$812$	39161.4	−	22609.8i	1.69248	−	0.977154i
$813$	−6219.10	+	3590.60i	−0.268282	+	0.154893i
$814$			3499.03i			0.150665i
$815$	1216.11	+	2106.37i	0.0522682	+	0.0905312i
$816$	−389.269	+	674.234i	−0.0166999	+	0.0289251i
$817$	−20992.7	−	12120.1i	−0.898948	−	0.519008i
$818$	−62603.0			−2.67587
$819$		0			0
$820$	65231.5			2.77803
$821$	16482.5	+	9516.19i	0.700662	+	0.404528i	0.807594	−	0.589739i	$-0.200769\pi$
$821$	16482.5	+	9516.19i	0.700662	+	0.404528i	−0.106932	+	0.994266i	$0.534103\pi$
$822$	9794.04	−	16963.8i	0.415579	−	0.719805i
$823$	651.994	+	1129.29i	0.0276149	+	0.0478305i	0.879503	−	0.475894i	$-0.157875\pi$
$823$	651.994	+	1129.29i	0.0276149	+	0.0478305i	−0.851888	+	0.523725i	$0.824542\pi$
$824$			119098.i			5.03517i
$825$	238.756	−	137.846i	0.0100756	−	0.00581717i
$826$	8499.36	−	4907.11i	0.358027	−	0.206707i
$827$		−	26093.6i		−	1.09717i	−0.836093	−	0.548587i	$-0.815166\pi$
$827$		−	26093.6i		−	1.09717i	0.836093	−	0.548587i	$-0.184834\pi$
$828$	9316.03	+	16135.8i	0.391008	+	0.677245i
$829$	−13739.8	+	23798.0i	−0.575635	+	0.997030i	0.420337	+	0.907368i	$0.361912\pi$
$829$	−13739.8	+	23798.0i	−0.575635	+	0.997030i	−0.995972	+	0.0896616i	$0.971421\pi$
$830$	34905.7	+	20152.8i	1.45975	+	0.842788i
$831$	−57.7989			−0.00241278
$832$		0			0
$833$	242.094			0.0100697
$834$	−10155.9	−	5863.49i	−0.421665	−	0.243449i
$835$	2857.00	−	4948.46i	0.118408	−	0.205088i
$836$	2544.42	+	4407.06i	0.105264	+	0.182322i
$837$		−	22640.4i		−	0.934965i
$838$	19618.7	−	11326.9i	0.808732	−	0.466921i
$839$	−8642.58	+	4989.79i	−0.355632	+	0.205324i	−0.667163	−	0.744912i	$-0.732491\pi$
$839$	−8642.58	+	4989.79i	−0.355632	+	0.205324i	0.311531	+	0.950236i	$0.399158\pi$
$840$			14183.9i			0.582609i
$841$	2366.77	+	4099.37i	0.0970426	+	0.168083i
$842$	−5291.87	+	9165.78i	−0.216591	+	0.375147i
$843$	−6115.33	−	3530.69i	−0.249850	−	0.144251i
$844$	52643.3			2.14699
$845$		0			0
$846$	54530.4			2.21607
$847$	−17237.0	−	9951.79i	−0.699257	−	0.403716i
$848$	56827.7	−	98428.4i	2.30126	−	3.98590i
$849$	524.209	+	907.956i	0.0211906	+	0.0367032i
$850$			734.925i			0.0296561i
$851$	7978.33	−	4606.29i	0.321379	−	0.185548i
$852$	12784.7	−	7381.25i	0.514081	−	0.296805i
$853$		−	21573.0i		−	0.865940i	−0.901408	−	0.432970i	$-0.857466\pi$
$853$		−	21573.0i		−	0.865940i	0.901408	−	0.432970i	$-0.142534\pi$
$854$	−30700.7	−	53175.2i	−1.23016	−	2.13070i
$855$	8807.45	−	15254.9i	0.352290	−	0.610185i
$856$	4254.50	+	2456.34i	0.169878	+	0.0980794i
$857$	38422.7			1.53150			0.765749	−	0.643139i	$-0.222368\pi$
$857$	38422.7			1.53150			0.765749	+	0.643139i	$0.222368\pi$
$858$		0			0
$859$	38359.4			1.52364			0.761820	−	0.647788i	$-0.224306\pi$
$859$	38359.4			1.52364			0.761820	+	0.647788i	$0.224306\pi$
$860$	−36785.3	−	21238.0i	−1.45857	−	0.842105i
$861$	4960.27	−	8591.45i	0.196336	−	0.340065i
$862$	−3141.86	−	5441.85i	−0.124144	−	0.215023i
$863$		−	961.590i		−	0.0379292i	−0.999820	−	0.0189646i	$-0.993963\pi$
$863$		−	961.590i		−	0.0379292i	0.999820	−	0.0189646i	$-0.00603698\pi$
$864$	−47313.1	+	27316.2i	−1.86299	+	1.07560i
$865$	−10075.9	+	5817.33i	−0.396059	+	0.228665i
$866$			60508.5i			2.37432i
$867$	4111.30	+	7120.98i	0.161046	+	0.278940i
$868$	−42577.5	+	73746.4i	−1.66495	+	2.88377i
$869$	380.305	+	219.569i	0.0148457	+	0.00857119i
$870$	9827.71			0.382978
$871$		0			0
$872$	24134.3			0.937261
$873$	21937.5	+	12665.6i	0.850483	+	0.491026i
$874$	9195.74	−	15927.5i	0.355893	−	0.616425i
$875$	11036.8	+	19116.2i	0.426412	+	0.738567i
$876$			628.137i			0.0242269i
$877$	8592.14	−	4960.67i	0.330828	−	0.191003i	−0.325381	−	0.945583i	$-0.605492\pi$
$877$	8592.14	−	4960.67i	0.330828	−	0.191003i	0.656209	+	0.754580i	$0.272159\pi$
$878$	−15727.7	+	9080.40i	−0.604539	+	0.349031i
$879$		−	1488.34i		−	0.0571110i
$880$	2177.82	+	3772.09i	0.0834253	+	0.144497i
$881$	−1503.44	+	2604.03i	−0.0574939	+	0.0995824i	−0.893340	−	0.449382i	$-0.851644\pi$
$881$	−1503.44	+	2604.03i	−0.0574939	+	0.0995824i	0.835846	+	0.548964i	$0.184978\pi$
$882$	13335.9	+	7699.46i	0.509117	+	0.293939i
$883$	−6550.51			−0.249651			−0.124826	−	0.992179i	$-0.539837\pi$
$883$	−6550.51			−0.249651			−0.124826	+	0.992179i	$0.539837\pi$
$884$		0			0
$885$	1553.88			0.0590204
$886$	−57921.0	−	33440.7i	−2.19627	−	1.26802i
$887$	−10864.7	+	18818.3i	−0.411276	+	0.712352i	−0.995030	−	0.0995795i	$-0.968250\pi$
$887$	−10864.7	+	18818.3i	−0.411276	+	0.712352i	0.583753	+	0.811931i	$0.301584\pi$
$888$	15723.5	+	27234.0i	0.594198	+	1.02918i
$889$		−	6353.36i		−	0.239690i
$890$	17310.0	−	9993.95i	0.651948	−	0.376402i
$891$	1107.72	−	639.545i	0.0416500	−	0.0240466i
$892$			98969.8i			3.71497i
$893$	−19606.5	−	33959.4i	−0.734721	−	1.27257i
$894$	8513.63	−	14746.0i	0.318499	−	0.551657i
$895$	−25138.7	−	14513.8i	−0.938876	−	0.542061i
$896$	58610.6			2.18531
$897$		0			0
$898$	−77189.4			−2.86842
$899$	32055.1	+	18507.0i	1.18921	+	0.686589i
$900$	−17027.7	+	29492.8i	−0.630654	+	1.09233i
$901$	521.267	+	902.861i	0.0192741	+	0.0333837i
$902$		−	5370.68i		−	0.198253i
$903$	−5594.39	+	3229.92i	−0.206168	+	0.119031i
$904$	−30956.9	+	17872.9i	−1.13895	+	0.657572i
$905$		−	15013.3i		−	0.551447i
$906$	−7083.77	−	12269.5i	−0.259760	−	0.449918i
$907$	−8920.92	+	15451.5i	−0.326587	+	0.565665i	−0.981832	−	0.189751i	$-0.939232\pi$
$907$	−8920.92	+	15451.5i	−0.326587	+	0.565665i	0.655245	+	0.755416i	$0.272565\pi$
$908$	−29533.6	−	17051.3i	−1.07941	−	0.623200i
$909$	−9514.49			−0.347168
$910$		0			0
$911$	30706.4			1.11674			0.558370	−	0.829592i	$-0.311427\pi$
$911$	30706.4			1.11674			0.558370	+	0.829592i	$0.311427\pi$
$912$	30839.6	+	17805.2i	1.11974	+	0.646480i
$913$	1208.77	−	2093.65i	0.0438164	−	0.0758922i
$914$	−41489.8	−	71862.4i	−1.50149	−	2.60065i
$915$		−	9721.64i		−	0.351243i
$916$	−6569.21	+	3792.74i	−0.236957	+	0.136807i
$917$	22692.5	−	13101.5i	0.817198	−	0.471810i
$918$		−	961.164i		−	0.0345568i
$919$	−24930.7	−	43181.3i	−0.894873	−	1.54997i	−0.833962	−	0.551822i	$-0.813933\pi$
$919$	−24930.7	−	43181.3i	−0.894873	−	1.54997i	−0.0609114	−	0.998143i	$-0.519401\pi$
$920$	10108.7	−	17508.7i	0.362253	−	0.627440i
$921$	6481.42	+	3742.05i	0.231889	+	0.133881i
$922$	−38555.1			−1.37716
$923$		0			0
$924$	1356.14			0.0482832
$925$	14582.6	+	8419.29i	0.518351	+	0.299270i
$926$	−35634.8	+	61721.2i	−1.26461	+	2.19037i
$927$	−19708.1	−	34135.3i	−0.698271	−	1.20944i
$928$		−	89316.7i		−	3.15945i
$929$	2955.69	−	1706.47i	0.104384	−	0.0602663i	−0.446899	−	0.894584i	$-0.647472\pi$
$929$	2955.69	−	1706.47i	0.104384	−	0.0602663i	0.551283	+	0.834318i	$0.314138\pi$
$930$	−16027.5	+	9253.49i	−0.565121	+	0.326273i
$931$		−	11073.4i		−	0.389814i
$932$	71087.5	+	123127.i	2.49844	+	4.32743i
$933$	−2280.47	+	3949.88i	−0.0800205	+	0.138600i
$934$	59561.4	+	34387.8i	2.08663	+	1.20471i
$935$	−39.9533			−0.00139745
$936$		0			0
$937$	−12818.0			−0.446900			−0.223450	−	0.974715i	$-0.571732\pi$
$937$	−12818.0			−0.446900			−0.223450	+	0.974715i	$0.571732\pi$
$938$	14971.1	+	8643.54i	0.521133	+	0.300876i
$939$	2105.37	−	3646.61i	0.0731695	−	0.126733i
$940$	−34356.3	−	59506.9i	−1.19211	−	2.06479i
$941$			23306.2i			0.807396i	0.914892	+	0.403698i	$0.132275\pi$
$941$			23306.2i			0.807396i	−0.914892	+	0.403698i	$0.867725\pi$
$942$	18125.7	−	10464.9i	0.626928	−	0.361957i
$943$	−12246.0	+	7070.21i	−0.422888	+	0.244155i
$944$		−	27085.9i		−	0.933868i
$945$	−4966.45	−	8602.14i	−0.170962	−	0.296114i
$946$	−1748.58	+	3028.63i	−0.0600965	+	0.104090i
$947$	6065.26	+	3501.78i	0.208125	+	0.120161i	0.600440	−	0.799670i	$-0.294992\pi$
$947$	6065.26	+	3501.78i	0.208125	+	0.120161i	−0.392315	+	0.919831i	$0.628326\pi$
$948$	6291.20			0.215537
$949$		0			0
$950$	33615.6			1.14804
$951$	4452.38	+	2570.58i	0.151817	+	0.0876518i
$952$	−1133.95	+	1964.06i	−0.0386046	+	0.0668651i
$953$	−6192.33	−	10725.4i	−0.210482	−	0.364566i	0.741383	−	0.671082i	$-0.234170\pi$
$953$	−6192.33	−	10725.4i	−0.210482	−	0.364566i	−0.951865	+	0.306516i	$0.900837\pi$
$954$			66312.7i			2.25048i
$955$	16405.9	−	9471.97i	0.555899	−	0.320949i
$956$	−34446.5	+	19887.7i	−1.16536	+	0.672818i
$957$		−	589.467i		−	0.0199109i
$958$	428.887	+	742.855i	0.0144642	+	0.0250528i
$959$	16183.3	−	28030.3i	0.544929	−	0.943844i
$960$	18536.4	+	10702.0i	0.623189	+	0.359798i
$961$	−39911.6			−1.33972
$962$		0			0
$963$	−1625.87			−0.0544061
$964$	30875.1	+	17825.7i	1.03155	+	0.595568i
$965$	4641.04	−	8038.51i	0.154819	−	0.268154i
$966$	−2450.60	−	4244.56i	−0.0816218	−	0.141373i
$967$		−	53796.7i		−	1.78902i	−0.447045	−	0.894511i	$-0.647524\pi$
$967$		−	53796.7i		−	1.78902i	0.447045	−	0.894511i	$-0.352476\pi$
$968$	−83866.4	+	48420.3i	−2.78468	+	1.60773i
$969$	−282.884	+	163.323i	−0.00937828	+	0.00541455i
$970$		−	43814.6i		−	1.45031i
$971$	24286.6	+	42065.6i	0.802671	+	1.39027i	0.917852	+	0.396922i	$0.129922\pi$
$971$	24286.6	+	42065.6i	0.802671	+	1.39027i	−0.115181	+	0.993344i	$0.536745\pi$
$972$	34014.5	−	58914.8i	1.12244	−	1.94413i
$973$	−16781.2	−	9688.63i	−0.552909	−	0.319222i
$974$	−69523.2			−2.28713
$975$		0			0
$976$	−169460.			−5.55766
$977$	1053.63	+	608.315i	0.0345022	+	0.0199199i	0.517152	−	0.855894i	$-0.326992\pi$
$977$	1053.63	+	608.315i	0.0345022	+	0.0199199i	−0.482650	+	0.875814i	$0.660326\pi$
$978$	1434.43	−	2484.50i	0.0468997	−	0.0812327i
$979$	−599.438	−	1038.26i	−0.0195691	−	0.0338947i
$980$		−	19403.9i		−	0.632484i
$981$	−6917.27	+	3993.69i	−0.225129	+	0.129978i
$982$	66917.8	−	38635.0i	2.17457	−	1.25549i
$983$			10230.5i			0.331944i	0.986130	+	0.165972i	$0.0530761\pi$
$983$			10230.5i			0.331944i	−0.986130	+	0.165972i	$0.946924\pi$
$984$	−24134.1	−	41801.5i	−0.781878	−	1.35425i
$985$	−1541.43	+	2669.83i	−0.0498619	+	0.0863634i
$986$	1360.85	+	785.688i	0.0439537	+	0.0253767i
$987$	−10450.0			−0.337007
$988$		0			0
$989$	9207.66			0.296043
$990$	−2200.84	−	1270.66i	−0.0706540	−	0.0407921i
$991$	816.414	−	1414.07i	0.0261698	−	0.0453274i	−0.852644	−	0.522492i	$-0.825002\pi$
$991$	816.414	−	1414.07i	0.0261698	−	0.0453274i	0.878814	+	0.477165i	$0.158336\pi$
$992$	84098.0	+	145662.i	2.69165	+	4.66207i
$993$		−	15811.4i		−	0.505298i
$994$	28997.5	−	16741.7i	0.925298	−	0.534221i
$995$	25117.3	−	14501.5i	0.800275	−	0.462039i
$996$		−	34634.2i		−	1.10184i
$997$	−30543.6	−	52903.0i	−0.970236	−	1.68050i	−0.694837	−	0.719168i	$-0.744523\pi$
$997$	−30543.6	−	52903.0i	−0.970236	−	1.68050i	−0.275399	−	0.961330i	$-0.588810\pi$
$998$	−1030.83	+	1785.44i	−0.0326956	+	0.0566305i
$999$	−19071.8	−	11011.1i	−0.604008	−	0.348724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.h.147.1		36
13.2	odd	12		169.4.c.k.146.1		18
13.3	even	3	inner	169.4.e.h.23.18		36
13.4	even	6		169.4.b.g.168.1		18
13.5	odd	4		169.4.c.k.22.1		18
13.6	odd	12		169.4.a.l.1.9	yes	9
13.7	odd	12		169.4.a.k.1.1	✓	9
13.8	odd	4		169.4.c.l.22.9		18
13.9	even	3		169.4.b.g.168.18		18
13.10	even	6	inner	169.4.e.h.23.1		36
13.11	odd	12		169.4.c.l.146.9		18
13.12	even	2	inner	169.4.e.h.147.18		36
39.20	even	12		1521.4.a.bh.1.9		9
39.32	even	12		1521.4.a.bg.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.4.a.k.1.1	✓	9	13.7	odd	12
169.4.a.l.1.9	yes	9	13.6	odd	12
169.4.b.g.168.1		18	13.4	even	6
169.4.b.g.168.18		18	13.9	even	3
169.4.c.k.22.1		18	13.5	odd	4
169.4.c.k.146.1		18	13.2	odd	12
169.4.c.l.22.9		18	13.8	odd	4
169.4.c.l.146.9		18	13.11	odd	12
169.4.e.h.23.1		36	13.10	even	6	inner
169.4.e.h.23.18		36	13.3	even	3	inner
169.4.e.h.147.1		36	1.1	even	1	trivial
169.4.e.h.147.18		36	13.12	even	2	inner
1521.4.a.bg.1.1		9	39.32	even	12
1521.4.a.bh.1.9		9	39.20	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.70109 - 2.71418i) q^{2} +(-0.837548 + 1.45068i) q^{3} +(10.7335 + 18.5910i) q^{4} +7.70909i q^{5} +(7.87478 - 4.54651i) q^{6} +(13.0120 - 7.51249i) q^{7} -73.1038i q^{8} +(12.0970 + 20.9527i) q^{9} +O(q^{10})\)	\(q+(-4.70109 - 2.71418i) q^{2} +(-0.837548 + 1.45068i) q^{3} +(10.7335 + 18.5910i) q^{4} +7.70909i q^{5} +(7.87478 - 4.54651i) q^{6} +(13.0120 - 7.51249i) q^{7} -73.1038i q^{8} +(12.0970 + 20.9527i) q^{9} +(20.9238 - 36.2412i) q^{10} +(-2.17375 - 1.25501i) q^{11} -35.9593 q^{12} -81.5609 q^{14} +(-11.1834 - 6.45673i) q^{15} +(-112.549 + 194.940i) q^{16} +(-1.03238 - 1.78814i) q^{17} -131.334i q^{18} +(-81.7897 + 47.2213i) q^{19} +(-143.320 + 82.7456i) q^{20} +25.1683i q^{21} +(6.81266 + 11.7999i) q^{22} +(17.9370 - 31.0678i) q^{23} +(106.050 + 61.2279i) q^{24} +65.5699 q^{25} -85.7549 q^{27} +(279.329 + 161.271i) q^{28} +(70.0990 - 121.415i) q^{29} +(35.0494 + 60.7074i) q^{30} +264.013i q^{31} +(551.724 - 318.538i) q^{32} +(3.64124 - 2.10227i) q^{33} +11.2083i q^{34} +(57.9145 + 100.311i) q^{35} +(-259.687 + 449.791i) q^{36} +(222.398 + 128.402i) q^{37} +512.668 q^{38} +563.564 q^{40} +(-341.360 - 197.084i) q^{41} +(68.3111 - 118.318i) q^{42} +(128.333 + 222.280i) q^{43} -53.8828i q^{44} +(-161.526 + 93.2571i) q^{45} +(-168.647 + 97.3685i) q^{46} +415.204i q^{47} +(-188.530 - 326.543i) q^{48} +(-58.6251 + 101.542i) q^{49} +(-308.250 - 177.968i) q^{50} +3.45868 q^{51} -504.917 q^{53} +(403.142 + 232.754i) q^{54} +(9.67502 - 16.7576i) q^{55} +(-549.191 - 951.227i) q^{56} -158.200i q^{57} +(-659.083 + 380.522i) q^{58} +(-104.209 + 60.1650i) q^{59} -277.214i q^{60} +(376.415 + 651.969i) q^{61} +(716.577 - 1241.15i) q^{62} +(314.813 + 181.758i) q^{63} -1657.50 q^{64} -22.8237 q^{66} +(-183.557 - 105.977i) q^{67} +(22.1622 - 38.3860i) q^{68} +(30.0462 + 52.0416i) q^{69} -628.760i q^{70} +(-355.532 + 205.267i) q^{71} +(1531.72 - 884.339i) q^{72} -17.4680i q^{73} +(-697.010 - 1207.26i) q^{74} +(-54.9179 + 95.1206i) q^{75} +(-1755.78 - 1013.70i) q^{76} -37.7131 q^{77} -174.953 q^{79} +(-1502.81 - 867.647i) q^{80} +(-254.796 + 441.319i) q^{81} +(1069.84 + 1853.02i) q^{82} +963.151i q^{83} +(-467.903 + 270.144i) q^{84} +(13.7849 - 7.95873i) q^{85} -1393.28i q^{86} +(117.422 + 203.382i) q^{87} +(-91.7463 + 158.909i) q^{88} +(413.644 + 238.817i) q^{89} +1012.47 q^{90} +770.109 q^{92} +(-382.997 - 221.123i) q^{93} +(1126.94 - 1951.91i) q^{94} +(-364.033 - 630.525i) q^{95} +1067.16i q^{96} +(906.730 - 523.501i) q^{97} +(551.204 - 318.238i) q^{98} -60.7278i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9}+O(q^{10}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9	\( 36 q - 2 q^{3} + 74 q^{4} - 132 q^{9} - 294 q^{10} - 156 q^{12} - 588 q^{14} - 538 q^{16} - 110 q^{17} - 680 q^{22} - 408 q^{23} - 1228 q^{25} - 2672 q^{27} - 560 q^{29} + 1042 q^{30} - 40 q^{35} - 1818 q^{36} + 2956 q^{38} + 52 q^{40} + 8 q^{42} - 1066 q^{43} + 264 q^{48} + 806 q^{49} - 1880 q^{51} - 1112 q^{53} + 500 q^{55} + 500 q^{56} + 272 q^{61} + 4070 q^{62} - 1136 q^{64} + 13116 q^{66} + 3072 q^{68} - 4100 q^{69} + 3980 q^{74} + 4786 q^{75} + 2872 q^{77} + 1648 q^{79} + 1670 q^{81} + 5514 q^{82} + 1572 q^{87} - 1272 q^{88} + 5120 q^{90} + 16040 q^{92} + 5062 q^{94} - 3228 q^{95}+O(q^{100}) \) 36 * q - 2 * q^3 + 74 * q^4 - 132 * q^9 - 294 * q^10 - 156 * q^12 - 588 * q^14 - 538 * q^16 - 110 * q^17 - 680 * q^22 - 408 * q^23 - 1228 * q^25 - 2672 * q^27 - 560 * q^29 + 1042 * q^30 - 40 * q^35 - 1818 * q^36 + 2956 * q^38 + 52 * q^40 + 8 * q^42 - 1066 * q^43 + 264 * q^48 + 806 * q^49 - 1880 * q^51 - 1112 * q^53 + 500 * q^55 + 500 * q^56 + 272 * q^61 + 4070 * q^62 - 1136 * q^64 + 13116 * q^66 + 3072 * q^68 - 4100 * q^69 + 3980 * q^74 + 4786 * q^75 + 2872 * q^77 + 1648 * q^79 + 1670 * q^81 + 5514 * q^82 + 1572 * q^87 - 1272 * q^88 + 5120 * q^90 + 16040 * q^92 + 5062 * q^94 - 3228 * q^95

Introduction

L-functions

Modular forms

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Database

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