LMFDB - Embedded newform 145.4.c.b.86.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [145,4,Mod(86,145)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(145, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("145.86");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	145.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.55527695083$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 95 x^{14} + 3576 x^{12} + 68256 x^{10} + 700479 x^{8} + 3754089 x^{6} + 9373424 x^{4} + \cdots + 2560000 $ x^16 + 95x^14 + 3576x^12 + 68256x^10 + 700479x^8 + 3754089x^6 + 9373424x^4 + 8978880*x^2 + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			86.8
Root			$-0.702546i$ of defining polynomial
Character	$\chi$	$=$	145.86
Dual form			145.4.c.b.86.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.702546i q^{2} -0.260656i q^{3} +7.50643 q^{4} -5.00000 q^{5} -0.183122 q^{6} +0.749935 q^{7} -10.8940i q^{8} +26.9321 q^{9} +O(q^{10})$	\(q-0.702546i q^{2} -0.260656i q^{3} +7.50643 q^{4} -5.00000 q^{5} -0.183122 q^{6} +0.749935 q^{7} -10.8940i q^{8} +26.9321 q^{9} +3.51273i q^{10} -20.4233i q^{11} -1.95659i q^{12} +28.8903 q^{13} -0.526863i q^{14} +1.30328i q^{15} +52.3979 q^{16} +85.6406i q^{17} -18.9210i q^{18} -157.803i q^{19} -37.5321 q^{20} -0.195475i q^{21} -14.3483 q^{22} +67.9963 q^{23} -2.83958 q^{24} +25.0000 q^{25} -20.2967i q^{26} -14.0577i q^{27} +5.62933 q^{28} +(121.277 + 98.3910i) q^{29} +0.915612 q^{30} -184.356i q^{31} -123.964i q^{32} -5.32344 q^{33} +60.1664 q^{34} -3.74967 q^{35} +202.164 q^{36} -286.331i q^{37} -110.864 q^{38} -7.53041i q^{39} +54.4699i q^{40} +108.517i q^{41} -0.137330 q^{42} +352.237i q^{43} -153.306i q^{44} -134.660 q^{45} -47.7705i q^{46} +508.650i q^{47} -13.6578i q^{48} -342.438 q^{49} -17.5636i q^{50} +22.3227 q^{51} +216.863 q^{52} -667.231 q^{53} -9.87617 q^{54} +102.116i q^{55} -8.16977i q^{56} -41.1323 q^{57} +(69.1241 - 85.2029i) q^{58} -367.954 q^{59} +9.78297i q^{60} +513.500i q^{61} -129.519 q^{62} +20.1973 q^{63} +332.093 q^{64} -144.451 q^{65} +3.73996i q^{66} +94.0371 q^{67} +642.855i q^{68} -17.7236i q^{69} +2.63432i q^{70} -38.3555 q^{71} -293.397i q^{72} +721.153i q^{73} -201.161 q^{74} -6.51639i q^{75} -1184.54i q^{76} -15.3161i q^{77} -5.29046 q^{78} +365.512i q^{79} -261.990 q^{80} +723.501 q^{81} +76.2383 q^{82} -1030.81 q^{83} -1.46732i q^{84} -428.203i q^{85} +247.463 q^{86} +(25.6462 - 31.6117i) q^{87} -222.490 q^{88} +796.188i q^{89} +94.6050i q^{90} +21.6658 q^{91} +510.410 q^{92} -48.0535 q^{93} +357.350 q^{94} +789.016i q^{95} -32.3118 q^{96} -1026.88i q^{97} +240.578i q^{98} -550.040i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9}+O(q^{10}) $ 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9	$ 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9} - 14 q^{13} + 210 q^{16} + 310 q^{20} + 88 q^{22} + 42 q^{23} + 62 q^{24} + 400 q^{25} - 346 q^{28} + 28 q^{29} - 250 q^{30} - 460 q^{33} - 626 q^{34} - 190 q^{35} - 12 q^{36} - 292 q^{38} + 584 q^{42} + 630 q^{45} + 1894 q^{49} - 320 q^{51} - 294 q^{52} + 614 q^{53} + 1840 q^{54} - 1360 q^{57} - 644 q^{58} - 2086 q^{59} - 30 q^{62} - 1456 q^{63} - 894 q^{64} + 70 q^{65} - 1604 q^{67} + 792 q^{71} + 1720 q^{74} + 4894 q^{78} - 1050 q^{80} - 192 q^{81} + 1276 q^{82} + 4400 q^{83} - 2042 q^{86} - 2046 q^{87} - 9264 q^{88} + 212 q^{91} - 2030 q^{92} - 1816 q^{93} + 4304 q^{94} + 2234 q^{96}+O(q^{100}) $ 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9 - 14 * q^13 + 210 * q^16 + 310 * q^20 + 88 * q^22 + 42 * q^23 + 62 * q^24 + 400 * q^25 - 346 * q^28 + 28 * q^29 - 250 * q^30 - 460 * q^33 - 626 * q^34 - 190 * q^35 - 12 * q^36 - 292 * q^38 + 584 * q^42 + 630 * q^45 + 1894 * q^49 - 320 * q^51 - 294 * q^52 + 614 * q^53 + 1840 * q^54 - 1360 * q^57 - 644 * q^58 - 2086 * q^59 - 30 * q^62 - 1456 * q^63 - 894 * q^64 + 70 * q^65 - 1604 * q^67 + 792 * q^71 + 1720 * q^74 + 4894 * q^78 - 1050 * q^80 - 192 * q^81 + 1276 * q^82 + 4400 * q^83 - 2042 * q^86 - 2046 * q^87 - 9264 * q^88 + 212 * q^91 - 2030 * q^92 - 1816 * q^93 + 4304 * q^94 + 2234 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/145\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	0.702546i		−	0.248387i	−0.992258	−	0.124194i	$-0.960366\pi$
$2$		−	0.702546i		−	0.248387i	0.992258	−	0.124194i	$-0.0396344\pi$
$3$		−	0.260656i		−	0.0501632i	−0.999685	−	0.0250816i	$-0.992015\pi$
$3$		−	0.260656i		−	0.0501632i	0.999685	−	0.0250816i	$-0.00798456\pi$
$4$	7.50643			0.938304
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−0.183122			−0.0124599
$7$	0.749935			0.0404927			0.0202463	−	0.999795i	$-0.493555\pi$
$7$	0.749935			0.0404927			0.0202463	+	0.999795i	$0.493555\pi$
$8$		−	10.8940i		−	0.481450i
$9$	26.9321			0.997484
$10$			3.51273i			0.111082i
$11$		−	20.4233i		−	0.559804i	−0.960029	−	0.279902i	$-0.909698\pi$
$11$		−	20.4233i		−	0.559804i	0.960029	−	0.279902i	$-0.0903020\pi$
$12$		−	1.95659i		−	0.0470683i
$13$	28.8903			0.616363			0.308181	−	0.951328i	$-0.400280\pi$
$13$	28.8903			0.616363			0.308181	+	0.951328i	$0.400280\pi$
$14$		−	0.526863i		−	0.0100579i
$15$			1.30328i			0.0224337i
$16$	52.3979			0.818718
$17$			85.6406i			1.22182i	0.791701	+	0.610908i	$0.209196\pi$
$17$			85.6406i			1.22182i	−0.791701	+	0.610908i	$0.790804\pi$
$18$		−	18.9210i		−	0.247762i
$19$		−	157.803i		−	1.90540i	−0.303919	−	0.952698i	$-0.598295\pi$
$19$		−	157.803i		−	1.90540i	0.303919	−	0.952698i	$-0.401705\pi$
$20$	−37.5321			−0.419622
$21$		−	0.195475i		−	0.00203124i
$22$	−14.3483			−0.139048
$23$	67.9963			0.616444			0.308222	−	0.951314i	$-0.400266\pi$
$23$	67.9963			0.616444			0.308222	+	0.951314i	$0.400266\pi$
$24$	−2.83958			−0.0241511
$25$	25.0000			0.200000
$26$		−	20.2967i		−	0.153097i
$27$		−	14.0577i		−	0.100200i
$28$	5.62933			0.0379944
$29$	121.277	+	98.3910i	0.776574	+	0.630026i
$29$	121.277	+	98.3910i	0.776574	+	0.630026i
$30$	0.915612			0.00557224
$31$		−	184.356i		−	1.06811i	−0.845450	−	0.534054i	$-0.820668\pi$
$31$		−	184.356i		−	1.06811i	0.845450	−	0.534054i	$-0.179332\pi$
$32$		−	123.964i		−	0.684809i
$33$	−5.32344			−0.0280816
$34$	60.1664			0.303484
$35$	−3.74967			−0.0181089
$36$	202.164			0.935943
$37$		−	286.331i		−	1.27223i	−0.771593	−	0.636116i	$-0.780540\pi$
$37$		−	286.331i		−	1.27223i	0.771593	−	0.636116i	$-0.219460\pi$
$38$	−110.864			−0.473276
$39$		−	7.53041i		−	0.0309187i
$40$			54.4699i			0.215311i
$41$			108.517i			0.413355i	0.978409	+	0.206677i	$0.0662650\pi$
$41$			108.517i			0.413355i	−0.978409	+	0.206677i	$0.933735\pi$
$42$	−0.137330			−0.000504535
$43$			352.237i			1.24920i	0.780944	+	0.624600i	$0.214738\pi$
$43$			352.237i			1.24920i	−0.780944	+	0.624600i	$0.785262\pi$
$44$		−	153.306i		−	0.525266i
$45$	−134.660			−0.446088
$46$		−	47.7705i		−	0.153117i
$47$			508.650i			1.57860i	0.614008	+	0.789300i	$0.289556\pi$
$47$			508.650i			1.57860i	−0.614008	+	0.789300i	$0.710444\pi$
$48$		−	13.6578i		−	0.0410695i
$49$	−342.438			−0.998360
$50$		−	17.5636i		−	0.0496775i
$51$	22.3227			0.0612902
$52$	216.863			0.578336
$53$	−667.231			−1.72927			−0.864634	−	0.502402i	$-0.832450\pi$
$53$	−667.231			−1.72927			−0.864634	+	0.502402i	$0.832450\pi$
$54$	−9.87617			−0.0248885
$55$			102.116i			0.250352i
$56$		−	8.16977i		−	0.0194952i
$57$	−41.1323			−0.0955808
$58$	69.1241	−	85.2029i	0.156490	−	0.192891i
$59$	−367.954			−0.811924			−0.405962	−	0.913890i	$-0.633064\pi$
$59$	−367.954			−0.811924			−0.405962	+	0.913890i	$0.633064\pi$
$60$			9.78297i			0.0210496i
$61$			513.500i			1.07782i	0.842364	+	0.538909i	$0.181163\pi$
$61$			513.500i			1.07782i	−0.842364	+	0.538909i	$0.818837\pi$
$62$	−129.519			−0.265305
$63$	20.1973			0.0403908
$64$	332.093			0.648620
$65$	−144.451			−0.275646
$66$			3.73996i			0.00697510i
$67$	94.0371			0.171469			0.0857347	−	0.996318i	$-0.472676\pi$
$67$	94.0371			0.171469			0.0857347	+	0.996318i	$0.472676\pi$
$68$			642.855i			1.14644i
$69$		−	17.7236i		−	0.0309228i
$70$			2.63432i			0.00449802i
$71$	−38.3555			−0.0641121			−0.0320560	−	0.999486i	$-0.510206\pi$
$71$	−38.3555			−0.0641121			−0.0320560	+	0.999486i	$0.510206\pi$
$72$		−	293.397i		−	0.480239i
$73$			721.153i			1.15623i	0.815956	+	0.578114i	$0.196211\pi$
$73$			721.153i			1.15623i	−0.815956	+	0.578114i	$0.803789\pi$
$74$	−201.161			−0.316006
$75$		−	6.51639i		−	0.0100326i
$76$		−	1184.54i		−	1.78784i
$77$		−	15.3161i		−	0.0226680i
$78$	−5.29046			−0.00767982
$79$			365.512i			0.520548i	0.965535	+	0.260274i	$0.0838129\pi$
$79$			365.512i			0.520548i	−0.965535	+	0.260274i	$0.916187\pi$
$80$	−261.990			−0.366142
$81$	723.501			0.992457
$82$	76.2383			0.102672
$83$	−1030.81			−1.36321			−0.681605	−	0.731720i	$-0.738718\pi$
$83$	−1030.81			−1.36321			−0.681605	+	0.731720i	$0.738718\pi$
$84$		−	1.46732i		−	0.00190592i
$85$		−	428.203i		−	0.546413i
$86$	247.463			0.310286
$87$	25.6462	−	31.6117i	0.0316041	−	0.0389555i
$88$	−222.490			−0.269518
$89$			796.188i			0.948267i	0.880453	+	0.474133i	$0.157239\pi$
$89$			796.188i			0.948267i	−0.880453	+	0.474133i	$0.842761\pi$
$90$			94.6050i			0.110803i
$91$	21.6658			0.0249582
$92$	510.410			0.578412
$93$	−48.0535			−0.0535797
$94$	357.350			0.392104
$95$			789.016i			0.852119i
$96$	−32.3118			−0.0343522
$97$		−	1026.88i		−	1.07489i	−0.843300	−	0.537444i	$-0.819390\pi$
$97$		−	1026.88i		−	1.07489i	0.843300	−	0.537444i	$-0.180610\pi$
$98$			240.578i			0.247980i
$99$		−	550.040i		−	0.558395i
$100$	187.661			0.187661
$101$		−	1592.50i		−	1.56891i	−0.620185	−	0.784456i	$-0.712942\pi$
$101$		−	1592.50i		−	1.56891i	0.620185	−	0.784456i	$-0.287058\pi$
$102$		−	15.6827i		−	0.0152237i
$103$	−1192.20			−1.14049			−0.570245	−	0.821474i	$-0.693152\pi$
$103$	−1192.20			−1.14049			−0.570245	+	0.821474i	$0.693152\pi$
$104$		−	314.730i		−	0.296748i
$105$			0.977374i			0.000908399i
$106$			468.760i			0.429528i
$107$	1074.70			0.970983			0.485492	−	0.874241i	$-0.338641\pi$
$107$	1074.70			0.970983			0.485492	+	0.874241i	$0.338641\pi$
$108$		−	105.523i		−	0.0940182i
$109$	−1132.08			−0.994807			−0.497403	−	0.867519i	$-0.665713\pi$
$109$	−1132.08			−0.994807			−0.497403	+	0.867519i	$0.665713\pi$
$110$	71.7413			0.0621842
$111$	−74.6339			−0.0638192
$112$	39.2950			0.0331521
$113$			1750.93i			1.45764i	0.684704	+	0.728822i	$0.259932\pi$
$113$			1750.93i			1.45764i	−0.684704	+	0.728822i	$0.740068\pi$
$114$			28.8973i			0.0237411i
$115$	−339.982			−0.275682
$116$	910.361	+	738.565i	0.728663	+	0.591155i
$117$	778.074			0.614812
$118$			258.504i			0.201672i
$119$			64.2248i			0.0494746i
$120$	14.1979			0.0108007
$121$	913.891			0.686620
$122$	360.757			0.267717
$123$	28.2856			0.0207352
$124$		−	1383.86i		−	1.00221i
$125$	−125.000			−0.0894427
$126$		−	14.1895i		−	0.0100326i
$127$		−	1306.97i		−	0.913187i	−0.889675	−	0.456594i	$-0.849069\pi$
$127$		−	1306.97i		−	0.913187i	0.889675	−	0.456594i	$-0.150931\pi$
$128$		−	1225.02i		−	0.845918i
$129$	91.8126			0.0626639
$130$			101.484i			0.0684669i
$131$		−	1486.65i		−	0.991520i	−0.868460	−	0.495760i	$-0.834890\pi$
$131$		−	1486.65i		−	0.991520i	0.868460	−	0.495760i	$-0.165110\pi$
$132$	−39.9600			−0.0263490
$133$		−	118.342i		−	0.0771546i
$134$		−	66.0653i		−	0.0425908i
$135$			70.2885i			0.0448109i
$136$	932.966			0.588244
$137$		−	1086.03i		−	0.677270i	−0.940918	−	0.338635i	$-0.890035\pi$
$137$		−	1086.03i		−	0.677270i	0.940918	−	0.338635i	$-0.109965\pi$
$138$	−12.4517			−0.00768084
$139$	2548.45			1.55509			0.777543	−	0.628829i	$-0.216466\pi$
$139$	2548.45			1.55509			0.777543	+	0.628829i	$0.216466\pi$
$140$	−28.1467			−0.0169916
$141$	132.582			0.0791876
$142$			26.9465i			0.0159246i
$143$		−	590.033i		−	0.345042i
$144$	1411.18			0.816657
$145$	−606.387	−	491.955i	−0.347295	−	0.281756i
$146$	506.643			0.287192
$147$			89.2583i			0.0500810i
$148$		−	2149.33i		−	1.19374i
$149$	909.758			0.500203			0.250101	−	0.968220i	$-0.419536\pi$
$149$	909.758			0.500203			0.250101	+	0.968220i	$0.419536\pi$
$150$	−4.57806			−0.00249198
$151$	1531.36			0.825299			0.412649	−	0.910890i	$-0.364603\pi$
$151$	1531.36			0.825299			0.412649	+	0.910890i	$0.364603\pi$
$152$	−1719.10			−0.917353
$153$			2306.48i			1.21874i
$154$	−10.7603			−0.00563043
$155$			921.781i			0.477673i
$156$		−	56.5265i		−	0.0290112i
$157$			2764.09i			1.40509i	0.711641	+	0.702543i	$0.247952\pi$
$157$			2764.09i			1.40509i	−0.711641	+	0.702543i	$0.752048\pi$
$158$	256.789			0.129298
$159$			173.918i			0.0867456i
$160$			619.819i			0.306256i
$161$	50.9928			0.0249615
$162$		−	508.293i		−	0.246514i
$163$			761.250i			0.365802i	0.983131	+	0.182901i	$0.0585488\pi$
$163$			761.250i			0.365802i	−0.983131	+	0.182901i	$0.941451\pi$
$164$			814.577i			0.387852i
$165$	26.6172			0.0125585
$166$			724.193i			0.338604i
$167$	−2607.55			−1.20825			−0.604126	−	0.796889i	$-0.706478\pi$
$167$	−2607.55			−1.20825			−0.604126	+	0.796889i	$0.706478\pi$
$168$	−2.12950			−0.000977942
$169$	−1362.35			−0.620097
$170$	−300.832			−0.135722
$171$		−	4249.96i		−	1.90060i
$172$			2644.04i			1.17213i
$173$	−3985.94			−1.75171			−0.875854	−	0.482576i	$-0.839701\pi$
$173$	−3985.94			−1.75171			−0.875854	+	0.482576i	$0.839701\pi$
$174$	−22.2086	−	18.0176i	−0.00967604	−	0.00785006i
$175$	18.7484			0.00809853
$176$		−	1070.14i		−	0.458321i
$177$			95.9093i			0.0407287i
$178$	559.358			0.235537
$179$	1515.40			0.632772			0.316386	−	0.948631i	$-0.397531\pi$
$179$	1515.40			0.632772			0.316386	+	0.948631i	$0.397531\pi$
$180$	−1010.82			−0.418566
$181$	−2305.13			−0.946624			−0.473312	−	0.880895i	$-0.656942\pi$
$181$	−2305.13			−0.946624			−0.473312	+	0.880895i	$0.656942\pi$
$182$		−	15.2212i		−	0.00619930i
$183$	133.847			0.0540668
$184$		−	740.750i		−	0.296787i
$185$			1431.66i			0.568960i
$186$			33.7598i			0.0133085i
$187$	1749.06			0.683978
$188$			3818.14i			1.48121i
$189$		−	10.5424i		−	0.00405737i
$190$	554.319			0.211656
$191$			4595.21i			1.74083i	0.492321	+	0.870414i	$0.336149\pi$
$191$			4595.21i			1.74083i	−0.492321	+	0.870414i	$0.663851\pi$
$192$		−	86.5620i		−	0.0325368i
$193$		−	3552.85i		−	1.32508i	−0.749029	−	0.662538i	$-0.769480\pi$
$193$		−	3552.85i		−	1.32508i	0.749029	−	0.662538i	$-0.230520\pi$
$194$	−721.431			−0.266988
$195$			37.6521i			0.0138273i
$196$	−2570.48			−0.936765
$197$	838.413			0.303221			0.151610	−	0.988440i	$-0.451554\pi$
$197$	838.413			0.303221			0.151610	+	0.988440i	$0.451554\pi$
$198$	−386.428			−0.138698
$199$	−378.636			−0.134878			−0.0674391	−	0.997723i	$-0.521483\pi$
$199$	−378.636			−0.134878			−0.0674391	+	0.997723i	$0.521483\pi$
$200$		−	272.349i		−	0.0962900i
$201$		−	24.5113i		−	0.00860146i
$202$	−1118.81			−0.389698
$203$	90.9502	+	73.7868i	0.0314456	+	0.0255114i
$204$	167.564			0.0575089
$205$		−	542.586i		−	0.184858i
$206$			837.572i			0.283283i
$207$	1831.28			0.614893
$208$	1513.79			0.504627
$209$	−3222.85			−1.06665
$210$	0.686650			0.000225635
$211$		−	1823.72i		−	0.595024i	−0.954718	−	0.297512i	$-0.903843\pi$
$211$		−	1823.72i		−	0.595024i	0.954718	−	0.297512i	$-0.0961568\pi$
$212$	−5008.52			−1.62258
$213$			9.99757i			0.00321607i
$214$		−	755.026i		−	0.241180i
$215$		−	1761.19i		−	0.558660i
$216$	−153.144			−0.0482414
$217$		−	138.255i		−	0.0432506i
$218$			795.340i			0.247097i
$219$	187.973			0.0580001
$220$			766.529i			0.234906i
$221$			2474.18i			0.753083i
$222$			52.4337i			0.0158519i
$223$	3024.91			0.908354			0.454177	−	0.890911i	$-0.349933\pi$
$223$	3024.91			0.908354			0.454177	+	0.890911i	$0.349933\pi$
$224$		−	92.9647i		−	0.0277298i
$225$	673.301			0.199497
$226$	1230.11			0.362060
$227$	3464.13			1.01288			0.506438	−	0.862277i	$-0.330962\pi$
$227$	3464.13			1.01288			0.506438	+	0.862277i	$0.330962\pi$
$228$	−308.757			−0.0896838
$229$			4857.40i			1.40169i	0.713316	+	0.700843i	$0.247192\pi$
$229$			4857.40i			1.40169i	−0.713316	+	0.700843i	$0.752808\pi$
$230$			238.853i			0.0684760i
$231$	−3.99223			−0.00113710
$232$	1071.87	−	1321.19i	0.303326	−	0.373882i
$233$	−1518.33			−0.426907			−0.213453	−	0.976953i	$-0.568471\pi$
$233$	−1518.33			−0.426907			−0.213453	+	0.976953i	$0.568471\pi$
$234$		−	546.633i		−	0.152712i
$235$		−	2543.25i		−	0.705971i
$236$	−2762.02			−0.761832
$237$	95.2728			0.0261124
$238$	45.1209			0.0122889
$239$	−2424.17			−0.656096			−0.328048	−	0.944661i	$-0.606391\pi$
$239$	−2424.17			−0.656096			−0.328048	+	0.944661i	$0.606391\pi$
$240$			68.2891i			0.0183668i
$241$	−4370.91			−1.16828			−0.584139	−	0.811654i	$-0.698568\pi$
$241$	−4370.91			−1.16828			−0.584139	+	0.811654i	$0.698568\pi$
$242$		−	642.050i		−	0.170548i
$243$		−	568.143i		−	0.149985i
$244$			3854.55i			1.01132i
$245$	1712.19			0.446480
$246$		−	19.8719i		−	0.00515036i
$247$		−	4558.97i		−	1.17442i
$248$	−2008.37			−0.514241
$249$			268.687i			0.0683830i
$250$			87.8182i			0.0222164i
$251$			1066.96i			0.268310i	0.990960	+	0.134155i	$0.0428320\pi$
$251$			1066.96i			0.268310i	−0.990960	+	0.134155i	$0.957168\pi$
$252$	151.610			0.0378988
$253$		−	1388.71i		−	0.345088i
$254$	−918.205			−0.226824
$255$	−111.613			−0.0274098
$256$	1796.11			0.438504
$257$	−1243.55			−0.301830			−0.150915	−	0.988547i	$-0.548222\pi$
$257$	−1243.55			−0.301830			−0.150915	+	0.988547i	$0.548222\pi$
$258$		−	64.5025i		−	0.0155649i
$259$		−	214.730i		−	0.0515161i
$260$	−1084.31			−0.258640
$261$	3266.25	+	2649.87i	0.774620	+	0.628440i
$262$	−1044.44			−0.246281
$263$		−	1285.68i		−	0.301440i	−0.988576	−	0.150720i	$-0.951841\pi$
$263$		−	1285.68i		−	0.301440i	0.988576	−	0.150720i	$-0.0481592\pi$
$264$			57.9934i			0.0135199i
$265$	3336.15			0.773352
$266$	−83.1407			−0.0191642
$267$	207.531			0.0475681
$268$	705.883			0.160890
$269$			1663.13i			0.376961i	0.982077	+	0.188481i	$0.0603563\pi$
$269$			1663.13i			0.376961i	−0.982077	+	0.188481i	$0.939644\pi$
$270$	49.3809			0.0111305
$271$			2409.91i			0.540190i	0.962834	+	0.270095i	$0.0870551\pi$
$271$			2409.91i			0.540190i	−0.962834	+	0.270095i	$0.912945\pi$
$272$			4487.39i			1.00032i
$273$		−	5.64732i		−	0.00125198i
$274$	−762.987			−0.168225
$275$		−	510.581i		−	0.111961i
$276$		−	133.041i		−	0.0290150i
$277$	4668.95			1.01274			0.506372	−	0.862315i	$-0.330986\pi$
$277$	4668.95			1.01274			0.506372	+	0.862315i	$0.330986\pi$
$278$		−	1790.40i		−	0.386264i
$279$		−	4965.09i		−	1.06542i
$280$			40.8488i			0.00871852i
$281$	−482.466			−0.102425			−0.0512126	−	0.998688i	$-0.516309\pi$
$281$	−482.466			−0.102425			−0.0512126	+	0.998688i	$0.516309\pi$
$282$		−	93.1452i		−	0.0196692i
$283$	7419.37			1.55843			0.779215	−	0.626756i	$-0.215618\pi$
$283$	7419.37			1.55843			0.779215	+	0.626756i	$0.215618\pi$
$284$	−287.913			−0.0601566
$285$	205.661			0.0427450
$286$	−414.525			−0.0857042
$287$			81.3808i			0.0167378i
$288$		−	3338.60i		−	0.683086i
$289$	−2421.30			−0.492836
$290$	−345.621	+	426.015i	−0.0699846	+	0.0862636i
$291$	−267.663			−0.0539198
$292$			5413.29i			1.08489i
$293$		−	283.298i		−	0.0564861i	−0.999601	−	0.0282431i	$-0.991009\pi$
$293$		−	283.298i		−	0.0564861i	0.999601	−	0.0282431i	$-0.00899124\pi$
$294$	62.7080			0.0124395
$295$	1839.77			0.363104
$296$	−3119.29			−0.612516
$297$	−287.104			−0.0560925
$298$		−	639.146i		−	0.124244i
$299$	1964.43			0.379953
$300$		−	48.9148i		−	0.00941366i
$301$			264.155i			0.0505835i
$302$		−	1075.85i		−	0.204994i
$303$	−415.095			−0.0787016
$304$		−	8268.56i		−	1.55998i
$305$		−	2567.50i		−	0.482015i
$306$	1620.40			0.302720
$307$		−	6778.63i		−	1.26018i	−0.776520	−	0.630092i	$-0.783017\pi$
$307$		−	6778.63i		−	1.26018i	0.776520	−	0.630092i	$-0.216983\pi$
$308$		−	114.969i		−	0.0212694i
$309$			310.753i			0.0572107i
$310$	647.593			0.118648
$311$		−	3553.89i		−	0.647982i	−0.946060	−	0.323991i	$-0.894975\pi$
$311$		−	3553.89i		−	0.647982i	0.946060	−	0.323991i	$-0.105025\pi$
$312$	−82.0361			−0.0148858
$313$	8669.94			1.56567			0.782833	−	0.622231i	$-0.213774\pi$
$313$	8669.94			1.56567			0.782833	+	0.622231i	$0.213774\pi$
$314$	1941.90			0.349006
$315$	−100.986			−0.0180633
$316$			2743.69i			0.488432i
$317$			2287.04i			0.405215i	0.979260	+	0.202608i	$0.0649416\pi$
$317$			2287.04i			0.405215i	−0.979260	+	0.202608i	$0.935058\pi$
$318$	122.185			0.0215465
$319$	2009.46	−	2476.88i	0.352691	−	0.434729i
$320$	−1660.47			−0.290072
$321$		−	280.127i		−	0.0487076i
$322$		−	35.8248i		−	0.00620012i
$323$	13514.3			2.32804
$324$	5430.91			0.931226
$325$	722.257			0.123273
$326$	534.813			0.0908605
$327$			295.084i			0.0499027i
$328$	1182.18			0.199010
$329$			381.454i			0.0639217i
$330$		−	18.6998i		−	0.00311936i
$331$		−	480.145i		−	0.0797315i	−0.999205	−	0.0398658i	$-0.987307\pi$
$331$		−	480.145i		−	0.0797315i	0.999205	−	0.0398658i	$-0.0126930\pi$
$332$	−7737.72			−1.27910
$333$		−	7711.49i		−	1.26903i
$334$			1831.92i			0.300114i
$335$	−470.185			−0.0766835
$336$		−	10.2425i		−	0.00166301i
$337$		−	371.348i		−	0.0600256i	−0.999550	−	0.0300128i	$-0.990445\pi$
$337$		−	371.348i		−	0.0600256i	0.999550	−	0.0300128i	$-0.00955480\pi$
$338$			957.115i			0.154024i
$339$	456.390			0.0731201
$340$		−	3214.27i		−	0.512701i
$341$	−3765.15			−0.597931
$342$	−2985.79			−0.472085
$343$	−514.034			−0.0809190
$344$	3837.26			0.601428
$345$			88.6182i			0.0138291i
$346$			2800.30i			0.435102i
$347$	−329.969			−0.0510480			−0.0255240	−	0.999674i	$-0.508125\pi$
$347$	−329.969			−0.0510480			−0.0255240	+	0.999674i	$0.508125\pi$
$348$	192.511	−	237.291i	0.0296543	−	0.0365521i
$349$	−9179.88			−1.40799			−0.703993	−	0.710206i	$-0.748602\pi$
$349$	−9179.88			−1.40799			−0.703993	+	0.710206i	$0.748602\pi$
$350$		−	13.1716i		−	0.00201157i
$351$		−	406.131i		−	0.0617597i
$352$	−2531.74			−0.383359
$353$	469.239			0.0707509			0.0353755	−	0.999374i	$-0.488737\pi$
$353$	469.239			0.0707509			0.0353755	+	0.999374i	$0.488737\pi$
$354$	67.3806			0.0101165
$355$	191.777			0.0286718
$356$			5976.53i			0.889762i
$357$	16.7406			0.00248181
$358$		−	1064.64i		−	0.157172i
$359$			1666.06i			0.244933i	0.992473	+	0.122467i	$0.0390805\pi$
$359$			1666.06i			0.244933i	−0.992473	+	0.122467i	$0.960920\pi$
$360$			1466.99i			0.214769i
$361$	−18042.8			−2.63053
$362$			1619.46i			0.235129i
$363$		−	238.211i		−	0.0344430i
$364$	162.633			0.0234184
$365$		−	3605.77i		−	0.517081i
$366$		−	94.0334i		−	0.0134295i
$367$			1626.59i			0.231354i	0.993287	+	0.115677i	$0.0369038\pi$
$367$			1626.59i			0.231354i	−0.993287	+	0.115677i	$0.963096\pi$
$368$	3562.87			0.504694
$369$			2922.59i			0.412315i
$370$	1005.80			0.141322
$371$	−500.380			−0.0700227
$372$	−360.710			−0.0502741
$373$	−3223.36			−0.447452			−0.223726	−	0.974652i	$-0.571822\pi$
$373$	−3223.36			−0.447452			−0.223726	+	0.974652i	$0.571822\pi$
$374$		−	1228.79i		−	0.169891i
$375$			32.5820i			0.00448673i
$376$	5541.22			0.760017
$377$	3503.74	+	2842.54i	0.478652	+	0.388324i
$378$	−7.40649			−0.00100780
$379$			8682.97i			1.17682i	0.808563	+	0.588409i	$0.200246\pi$
$379$			8682.97i			1.17682i	−0.808563	+	0.588409i	$0.799754\pi$
$380$			5922.69i			0.799546i
$381$	−340.669			−0.0458084
$382$	3228.35			0.432400
$383$	−9051.26			−1.20757			−0.603783	−	0.797149i	$-0.706341\pi$
$383$	−9051.26			−1.20757			−0.603783	+	0.797149i	$0.706341\pi$
$384$	−319.308			−0.0424340
$385$			76.5805i			0.0101374i
$386$	−2496.04			−0.329132
$387$			9486.47i			1.24606i
$388$		−	7708.22i		−	1.00857i
$389$		−	7273.00i		−	0.947959i	−0.880536	−	0.473979i	$-0.842817\pi$
$389$		−	7273.00i		−	0.947959i	0.880536	−	0.473979i	$-0.157183\pi$
$390$	26.4523			0.00343452
$391$			5823.24i			0.753182i
$392$			3730.51i			0.480661i
$393$	−387.503			−0.0497378
$394$		−	589.023i		−	0.0753161i
$395$		−	1827.56i		−	0.232796i
$396$		−	4128.84i		−	0.523944i
$397$	−153.154			−0.0193617			−0.00968084	−	0.999953i	$-0.503082\pi$
$397$	−153.154			−0.0193617			−0.00968084	+	0.999953i	$0.503082\pi$
$398$			266.009i			0.0335020i
$399$	−30.8465			−0.00387032
$400$	1309.95			0.163744
$401$	7559.20			0.941368			0.470684	−	0.882302i	$-0.344007\pi$
$401$	7559.20			0.941368			0.470684	+	0.882302i	$0.344007\pi$
$402$	−17.2203			−0.00213649
$403$		−	5326.10i		−	0.658342i
$404$		−	11954.0i		−	1.47212i
$405$	−3617.51			−0.443840
$406$	51.8386	−	63.8966i	0.00633671	−	0.00781068i
$407$	−5847.82			−0.712200
$408$		−	243.183i		−	0.0295082i
$409$			5240.16i			0.633518i	0.948506	+	0.316759i	$0.102595\pi$
$409$			5240.16i			0.633518i	−0.948506	+	0.316759i	$0.897405\pi$
$410$	−381.191			−0.0459163
$411$	−283.080			−0.0339740
$412$	−8949.13			−1.07013
$413$	−275.942			−0.0328770
$414$		−	1286.56i		−	0.152732i
$415$	5154.06			0.609646
$416$		−	3581.34i		−	0.422091i
$417$		−	664.269i		−	0.0780081i
$418$			2264.20i			0.264942i
$419$	−11062.2			−1.28980			−0.644899	−	0.764268i	$-0.723101\pi$
$419$	−11062.2			−1.28980			−0.644899	+	0.764268i	$0.723101\pi$
$420$			7.33659i			0.000852354i
$421$			9553.19i			1.10592i	0.833206	+	0.552962i	$0.186503\pi$
$421$			9553.19i			1.10592i	−0.833206	+	0.552962i	$0.813497\pi$
$422$	−1281.25			−0.147796
$423$			13699.0i			1.57463i
$424$			7268.80i			0.832556i
$425$			2141.01i			0.244363i
$426$	7.02375			0.000798830
$427$			385.092i			0.0436438i
$428$	8067.16			0.911077
$429$	−153.795			−0.0173084
$430$	−1237.31			−0.138764
$431$	9579.11			1.07056			0.535278	−	0.844676i	$-0.320207\pi$
$431$	9579.11			1.07056			0.535278	+	0.844676i	$0.320207\pi$
$432$		−	736.594i		−	0.0820357i
$433$			11966.1i			1.32807i	0.747702	+	0.664035i	$0.231157\pi$
$433$			11966.1i			1.32807i	−0.747702	+	0.664035i	$0.768843\pi$
$434$	−97.1306			−0.0107429
$435$	−128.231	+	158.058i	−0.0141338	+	0.0174214i
$436$	−8497.91			−0.933431
$437$		−	10730.0i		−	1.17457i
$438$		−	132.059i		−	0.0144065i
$439$	2419.37			0.263030			0.131515	−	0.991314i	$-0.458016\pi$
$439$	2419.37			0.263030			0.131515	+	0.991314i	$0.458016\pi$
$440$	1112.45			0.120532
$441$	−9222.55			−0.995848
$442$	1738.22			0.187056
$443$		−	16518.9i		−	1.77164i	−0.464033	−	0.885818i	$-0.653598\pi$
$443$		−	16518.9i		−	1.77164i	0.464033	−	0.885818i	$-0.346402\pi$
$444$	−560.234			−0.0598818
$445$		−	3980.94i		−	0.424078i
$446$		−	2125.14i		−	0.225624i
$447$		−	237.133i		−	0.0250918i
$448$	249.048			0.0262643
$449$			10498.5i			1.10346i	0.834022	+	0.551732i	$0.186033\pi$
$449$			10498.5i			1.10346i	−0.834022	+	0.551732i	$0.813967\pi$
$450$		−	473.025i		−	0.0495525i
$451$	2216.27			0.231398
$452$			13143.2i			1.36771i
$453$		−	399.157i		−	0.0413996i
$454$		−	2433.71i		−	0.251585i
$455$	−108.329			−0.0111616
$456$			448.094i			0.0460174i
$457$	56.5857			0.00579205			0.00289603	−	0.999996i	$-0.499078\pi$
$457$	56.5857			0.00579205			0.00289603	+	0.999996i	$0.499078\pi$
$458$	3412.54			0.348161
$459$	1203.91			0.122426
$460$	−2552.05			−0.258674
$461$			16324.7i			1.64928i	0.565658	+	0.824640i	$0.308622\pi$
$461$			16324.7i			1.64928i	−0.565658	+	0.824640i	$0.691378\pi$
$462$			2.80472i			0.000282441i
$463$	−18047.4			−1.81152			−0.905761	−	0.423790i	$-0.860700\pi$
$463$	−18047.4			−1.81152			−0.905761	+	0.423790i	$0.860700\pi$
$464$	6354.69	+	5155.48i	0.635795	+	0.515813i
$465$	240.268			0.0239616
$466$			1066.70i			0.106038i
$467$		−	14536.6i		−	1.44042i	−0.693757	−	0.720209i	$-0.744046\pi$
$467$		−	14536.6i		−	1.44042i	0.693757	−	0.720209i	$-0.255954\pi$
$468$	5840.56			0.576880
$469$	70.5217			0.00694326
$470$	−1786.75			−0.175354
$471$	720.476			0.0704836
$472$			4008.48i			0.390901i
$473$	7193.83			0.699308
$474$		−	66.9334i		−	0.00648598i
$475$		−	3945.08i		−	0.381079i
$476$			482.099i			0.0464222i
$477$	−17969.9			−1.72492
$478$			1703.09i			0.162966i
$479$		−	6578.64i		−	0.627528i	−0.949501	−	0.313764i	$-0.898410\pi$
$479$		−	6578.64i		−	0.627528i	0.949501	−	0.313764i	$-0.101590\pi$
$480$	161.559			0.0153628
$481$		−	8272.19i		−	0.784157i
$482$			3070.76i			0.290186i
$483$		−	13.2916i		−	0.00125215i
$484$	6860.06			0.644258
$485$			5134.41i			0.480704i
$486$	−399.146			−0.0372544
$487$	14087.6			1.31082			0.655409	−	0.755274i	$-0.272496\pi$
$487$	14087.6			1.31082			0.655409	+	0.755274i	$0.272496\pi$
$488$	5594.05			0.518916
$489$	198.424			0.0183498
$490$		−	1202.89i		−	0.110900i
$491$		−	9408.56i		−	0.864771i	−0.901689	−	0.432385i	$-0.857672\pi$
$491$		−	9408.56i		−	0.864771i	0.901689	−	0.432385i	$-0.142328\pi$
$492$	212.324			0.0194559
$493$	−8426.26	+	10386.3i	−0.769776	+	0.948832i
$494$	−3202.89			−0.291710
$495$			2750.20i			0.249722i
$496$		−	9659.89i		−	0.874479i
$497$	−28.7641			−0.00259607
$498$	188.765			0.0169855
$499$	−13042.9			−1.17010			−0.585052	−	0.810996i	$-0.698926\pi$
$499$	−13042.9			−1.17010			−0.585052	+	0.810996i	$0.698926\pi$
$500$	−938.304			−0.0839244
$501$			679.672i			0.0606098i
$502$	749.587			0.0666448
$503$			1051.24i			0.0931861i	0.998914	+	0.0465930i	$0.0148364\pi$
$503$			1051.24i			0.0931861i	−0.998914	+	0.0465930i	$0.985164\pi$
$504$		−	220.029i		−	0.0194461i
$505$			7962.52i			0.701638i
$506$	−975.630			−0.0857155
$507$			355.105i			0.0311060i
$508$		−	9810.67i		−	0.856847i
$509$	15303.4			1.33264			0.666319	−	0.745667i	$-0.267869\pi$
$509$	15303.4			1.33264			0.666319	+	0.745667i	$0.267869\pi$
$510$			78.4135i			0.00680826i
$511$			540.818i			0.0468187i
$512$		−	11062.0i		−	0.954837i
$513$	−2218.35			−0.190921
$514$			873.648i			0.0749708i
$515$	5960.98			0.510043
$516$	689.185			0.0587978
$517$	10388.3			0.883706
$518$	−150.858			−0.0127959
$519$			1038.96i			0.0878713i
$520$			1573.65i			0.132710i
$521$	1164.47			0.0979197			0.0489598	−	0.998801i	$-0.484409\pi$
$521$	1164.47			0.0979197			0.0489598	+	0.998801i	$0.484409\pi$
$522$	1861.66	−	2294.69i	0.156097	−	0.192406i
$523$	−23530.9			−1.96737			−0.983683	−	0.179908i	$-0.942420\pi$
$523$	−23530.9			−1.96737			−0.983683	+	0.179908i	$0.942420\pi$
$524$		−	11159.4i		−	0.930347i
$525$		−	4.88687i		−	0.000406248i
$526$	−903.252			−0.0748739
$527$	15788.4			1.30503
$528$	−278.937			−0.0229909
$529$	−7543.50			−0.619996
$530$		−	2343.80i		−	0.192091i
$531$	−9909.76			−0.809881
$532$		−	888.326i		−	0.0723944i
$533$			3135.09i			0.254776i
$534$		−	145.800i		−	0.0118153i
$535$	−5373.50			−0.434237
$536$		−	1024.44i		−	0.0825540i
$537$		−	394.997i		−	0.0317419i
$538$	1168.42			0.0936324
$539$			6993.69i			0.558886i
$540$			527.616i			0.0420462i
$541$		−	8712.72i		−	0.692401i	−0.938160	−	0.346201i	$-0.887472\pi$
$541$		−	8712.72i		−	0.692401i	0.938160	−	0.346201i	$-0.112528\pi$
$542$	1693.07			0.134176
$543$			600.845i			0.0474857i
$544$	10616.3			0.836711
$545$	5660.42			0.444891
$546$	−3.96750			−0.000310977
$547$	20255.7			1.58331			0.791656	−	0.610967i	$-0.209219\pi$
$547$	20255.7			1.58331			0.791656	+	0.610967i	$0.209219\pi$
$548$		−	8152.22i		−	0.635485i
$549$			13829.6i			1.07511i
$550$	−358.707			−0.0278096
$551$	15526.4	−	19138.0i	1.20045	−	1.47968i
$552$	−193.081			−0.0148878
$553$			274.110i			0.0210784i
$554$		−	3280.15i		−	0.251553i
$555$	373.169			0.0285408
$556$	19129.8			1.45914
$557$	−7354.79			−0.559484			−0.279742	−	0.960075i	$-0.590249\pi$
$557$	−7354.79			−0.559484			−0.279742	+	0.960075i	$0.590249\pi$
$558$	−3488.20			−0.264637
$559$			10176.2i			0.769961i
$560$	−196.475			−0.0148261
$561$		−	455.902i		−	0.0343105i
$562$			338.954i			0.0254411i
$563$			8899.97i			0.666233i	0.942886	+	0.333116i	$0.108100\pi$
$563$			8899.97i			0.666233i	−0.942886	+	0.333116i	$0.891900\pi$
$564$	995.221			0.0743020
$565$		−	8754.65i		−	0.651878i
$566$		−	5212.45i		−	0.387094i
$567$	542.579			0.0401873
$568$			417.843i			0.0308668i
$569$		−	22986.8i		−	1.69360i	−0.531913	−	0.846799i	$-0.678527\pi$
$569$		−	22986.8i		−	1.69360i	0.531913	−	0.846799i	$-0.321473\pi$
$570$		−	144.487i		−	0.0106173i
$571$	15897.1			1.16510			0.582551	−	0.812794i	$-0.302055\pi$
$571$	15897.1			1.16510			0.582551	+	0.812794i	$0.302055\pi$
$572$		−	4429.04i		−	0.323755i
$573$	1197.77			0.0873255
$574$	57.1737			0.00415747
$575$	1699.91			0.123289
$576$	8943.96			0.646988
$577$		−	9121.19i		−	0.658094i	−0.944314	−	0.329047i	$-0.893273\pi$
$577$		−	9121.19i		−	0.658094i	0.944314	−	0.329047i	$-0.106727\pi$
$578$			1701.08i			0.122414i
$579$	−926.070			−0.0664700
$580$	−4551.80	−	3692.82i	−0.325868	−	0.264373i
$581$	−773.042			−0.0552000
$582$			188.045i			0.0133930i
$583$			13627.0i			0.968051i
$584$	7856.22			0.556666
$585$	−3890.37			−0.274952
$586$	−199.030			−0.0140304
$587$	13244.0			0.931243			0.465622	−	0.884984i	$-0.345831\pi$
$587$	13244.0			0.931243			0.465622	+	0.884984i	$0.345831\pi$
$588$			670.011i			0.0469911i
$589$	−29092.0			−2.03517
$590$		−	1292.52i		−	0.0901903i
$591$		−	218.537i		−	0.0152105i
$592$		−	15003.2i		−	1.04160i
$593$	−9343.12			−0.647008			−0.323504	−	0.946227i	$-0.604861\pi$
$593$	−9343.12			−0.647008			−0.323504	+	0.946227i	$0.604861\pi$
$594$			201.704i			0.0139327i
$595$		−	321.124i		−	0.0221257i
$596$	6829.03			0.469342
$597$			98.6935i			0.00676592i
$598$		−	1380.10i		−	0.0943756i
$599$			9177.01i			0.625981i	0.949756	+	0.312991i	$0.101331\pi$
$599$			9177.01i			0.625981i	−0.949756	+	0.312991i	$0.898669\pi$
$600$	−70.9894			−0.00483022
$601$		−	957.868i		−	0.0650121i	−0.999472	−	0.0325060i	$-0.989651\pi$
$601$		−	957.868i		−	0.0650121i	0.999472	−	0.0325060i	$-0.0103488\pi$
$602$	185.581			0.0125643
$603$	2532.61			0.171038
$604$	11495.0			0.774381
$605$	−4569.45			−0.307066
$606$			291.623i			0.0195485i
$607$		−	27135.2i		−	1.81447i	−0.420626	−	0.907234i	$-0.638189\pi$
$607$		−	27135.2i		−	1.81447i	0.420626	−	0.907234i	$-0.361811\pi$
$608$	−19561.9			−1.30483
$609$	19.2330	−	23.7067i	0.00127973	−	0.00157741i
$610$	−1803.79			−0.119726
$611$			14695.0i			0.972990i
$612$			17313.4i			1.14355i
$613$	12116.5			0.798338			0.399169	−	0.916877i	$-0.369299\pi$
$613$	12116.5			0.798338			0.399169	+	0.916877i	$0.369299\pi$
$614$	−4762.29			−0.313014
$615$	−141.428			−0.00927306
$616$	−166.853			−0.0109135
$617$			7220.67i			0.471140i	0.971857	+	0.235570i	$0.0756957\pi$
$617$			7220.67i			0.471140i	−0.971857	+	0.235570i	$0.924304\pi$
$618$	218.318			0.0142104
$619$		−	1237.39i		−	0.0803472i	−0.999193	−	0.0401736i	$-0.987209\pi$
$619$		−	1237.39i		−	0.0803472i	0.999193	−	0.0401736i	$-0.0127911\pi$
$620$			6919.29i			0.448202i
$621$		−	955.872i		−	0.0617678i
$622$	−2496.77			−0.160951
$623$			597.089i			0.0383979i
$624$		−	394.578i		−	0.0253137i
$625$	625.000			0.0400000
$626$		−	6091.02i		−	0.388892i
$627$			840.055i			0.0535065i
$628$			20748.5i			1.31840i
$629$	24521.6			1.55443
$630$			70.9476i			0.00448670i
$631$	−15074.3			−0.951026			−0.475513	−	0.879709i	$-0.657737\pi$
$631$	−15074.3			−0.951026			−0.475513	+	0.879709i	$0.657737\pi$
$632$	3981.88			0.250618
$633$	−475.363			−0.0298483
$634$	1606.75			0.100650
$635$			6534.85i			0.408390i
$636$			1305.50i			0.0813938i
$637$	−9893.11			−0.615352
$638$	−1740.12	−	1411.74i	−0.107981	−	0.0876039i
$639$	−1032.99			−0.0639507
$640$			6125.10i			0.378306i
$641$		−	7258.04i		−	0.447232i	−0.974677	−	0.223616i	$-0.928214\pi$
$641$		−	7258.04i		−	0.447232i	0.974677	−	0.223616i	$-0.0717861\pi$
$642$	−196.802			−0.0120984
$643$	−10177.0			−0.624173			−0.312086	−	0.950054i	$-0.601028\pi$
$643$	−10177.0			−0.624173			−0.312086	+	0.950054i	$0.601028\pi$
$644$	382.774			0.0234214
$645$	−459.063			−0.0280242
$646$		−	9494.44i		−	0.578257i
$647$	−9522.88			−0.578645			−0.289322	−	0.957232i	$-0.593430\pi$
$647$	−9522.88			−0.578645			−0.289322	+	0.957232i	$0.593430\pi$
$648$		−	7881.80i		−	0.477819i
$649$			7514.82i			0.454518i
$650$		−	507.418i		−	0.0306193i
$651$	−36.0370			−0.00216959
$652$			5714.27i			0.343233i
$653$			5253.00i			0.314802i	0.987535	+	0.157401i	$0.0503115\pi$
$653$			5253.00i			0.314802i	−0.987535	+	0.157401i	$0.949688\pi$
$654$	207.310			0.0123952
$655$			7433.24i			0.443421i
$656$			5686.08i			0.338421i
$657$			19422.1i			1.15332i
$658$	267.989			0.0158773
$659$		−	9643.61i		−	0.570048i	−0.958520	−	0.285024i	$-0.907998\pi$
$659$		−	9643.61i		−	0.570048i	0.958520	−	0.285024i	$-0.0920016\pi$
$660$	199.800			0.0117836
$661$	2006.02			0.118041			0.0590204	−	0.998257i	$-0.481202\pi$
$661$	2006.02			0.118041			0.0590204	+	0.998257i	$0.481202\pi$
$662$	−337.323			−0.0198043
$663$	644.909			0.0377770
$664$			11229.6i			0.656317i
$665$			591.710i			0.0345046i
$666$	−5417.68			−0.315211
$667$	8246.42	+	6690.23i	0.478715	+	0.388376i
$668$	−19573.4			−1.13371
$669$		−	788.460i		−	0.0455659i
$670$			330.327i			0.0190472i
$671$	10487.3			0.603367
$672$	−24.2318			−0.00139101
$673$	−2029.01			−0.116215			−0.0581075	−	0.998310i	$-0.518507\pi$
$673$	−2029.01			−0.116215			−0.0581075	+	0.998310i	$0.518507\pi$
$674$	−260.889			−0.0149096
$675$		−	351.442i		−	0.0200400i
$676$	−10226.4			−0.581839
$677$		−	6459.49i		−	0.366703i	−0.983047	−	0.183352i	$-0.941305\pi$
$677$		−	6459.49i		−	0.366703i	0.983047	−	0.183352i	$-0.0586947\pi$
$678$		−	320.635i		−	0.0181621i
$679$		−	770.094i		−	0.0435251i
$680$	−4664.83			−0.263071
$681$		−	902.946i		−	0.0508091i
$682$			2645.19i			0.148519i
$683$	20758.5			1.16296			0.581481	−	0.813560i	$-0.302474\pi$
$683$	20758.5			1.16296			0.581481	+	0.813560i	$0.302474\pi$
$684$		−	31902.1i		−	1.78334i
$685$			5430.16i			0.302884i
$686$			361.132i			0.0200992i
$687$	1266.11			0.0703130
$688$			18456.5i			1.02274i
$689$	−19276.5			−1.06586
$690$	62.2583			0.00343498
$691$	19700.4			1.08457			0.542286	−	0.840194i	$-0.317559\pi$
$691$	19700.4			1.08457			0.542286	+	0.840194i	$0.317559\pi$
$692$	−29920.2			−1.64363
$693$		−	412.494i		−	0.0226109i
$694$			231.818i			0.0126797i
$695$	−12742.3			−0.695456
$696$	−344.376	−	279.389i	−0.0187551	−	0.0152158i
$697$	−9293.47			−0.505044
$698$			6449.28i			0.349726i
$699$			395.762i			0.0214150i
$700$	140.733			0.00759889
$701$	21184.3			1.14140			0.570699	−	0.821159i	$-0.306672\pi$
$701$	21184.3			1.14140			0.570699	+	0.821159i	$0.306672\pi$
$702$	−285.325			−0.0153403
$703$	−45184.0			−2.42411
$704$		−	6782.42i		−	0.363100i
$705$	−662.912			−0.0354138
$706$		−	329.662i		−	0.0175736i
$707$		−	1194.27i		−	0.0635294i
$708$			719.936i			0.0382159i
$709$	−3620.22			−0.191763			−0.0958817	−	0.995393i	$-0.530567\pi$
$709$	−3620.22			−0.191763			−0.0958817	+	0.995393i	$0.530567\pi$
$710$		−	134.732i		−	0.00712171i
$711$			9843.99i			0.519238i
$712$	8673.65			0.456543
$713$		−	12535.6i		−	0.658429i
$714$		−	11.7610i		−	0.000616449i
$715$			2950.17i			0.154308i
$716$	11375.2			0.593732
$717$			631.875i			0.0329119i
$718$	1170.48			0.0608383
$719$	18796.0			0.974927			0.487463	−	0.873143i	$-0.337922\pi$
$719$	18796.0			0.974927			0.487463	+	0.873143i	$0.337922\pi$
$720$	−7055.92			−0.365220
$721$	−894.069			−0.0461815
$722$			12675.9i			0.653391i
$723$			1139.30i			0.0586046i
$724$	−17303.3			−0.888220
$725$	3031.94	+	2459.77i	0.155315	+	0.126005i
$726$	−167.354			−0.00855522
$727$		−	6712.96i		−	0.342462i	−0.985231	−	0.171231i	$-0.945226\pi$
$727$		−	6712.96i		−	0.342462i	0.985231	−	0.171231i	$-0.0547745\pi$
$728$		−	236.027i		−	0.0120161i
$729$	19386.4			0.984934
$730$	−2533.21			−0.128436
$731$	−30165.8			−1.52629
$732$	1004.71			0.0507311
$733$			23783.9i			1.19847i	0.800574	+	0.599234i	$0.204528\pi$
$733$			23783.9i			1.19847i	−0.800574	+	0.599234i	$0.795472\pi$
$734$	1142.75			0.0574655
$735$		−	446.292i		−	0.0223969i
$736$		−	8429.08i		−	0.422147i
$737$		−	1920.54i		−	0.0959893i
$738$	2053.25			0.102414
$739$		−	15926.7i		−	0.792792i	−0.918080	−	0.396396i	$-0.870261\pi$
$739$		−	15926.7i		−	0.792792i	0.918080	−	0.396396i	$-0.129739\pi$
$740$			10746.6i			0.533857i
$741$	−1188.32			−0.0589124
$742$			351.540i			0.0173928i
$743$			18447.5i			0.910867i	0.890270	+	0.455434i	$0.150516\pi$
$743$			18447.5i			0.910867i	−0.890270	+	0.455434i	$0.849484\pi$
$744$			523.494i			0.0257960i
$745$	−4548.79			−0.223698
$746$			2264.56i			0.111141i
$747$	−27761.9			−1.35978
$748$	13129.2			0.641779
$749$	805.955			0.0393177
$750$	22.8903			0.00111445
$751$		−	25690.4i		−	1.24828i	−0.781314	−	0.624138i	$-0.785450\pi$
$751$		−	25690.4i		−	1.24828i	0.781314	−	0.624138i	$-0.214550\pi$
$752$			26652.2i			1.29243i
$753$	278.109			0.0134593
$754$	1997.01	−	2461.53i	0.0964549	−	0.118891i
$755$	−7656.79			−0.369085
$756$		−	79.1355i		−	0.00380705i
$757$			5216.53i			0.250460i	0.992128	+	0.125230i	$0.0399669\pi$
$757$			5216.53i			0.250460i	−0.992128	+	0.125230i	$0.960033\pi$
$758$	6100.18			0.292307
$759$	−361.974			−0.0173107
$760$	8595.52			0.410253
$761$	22366.9			1.06544			0.532719	−	0.846292i	$-0.321170\pi$
$761$	22366.9			1.06544			0.532719	+	0.846292i	$0.321170\pi$
$762$			239.335i			0.0113782i
$763$	−848.989			−0.0402824
$764$			34493.7i			1.63343i
$765$		−	11532.4i		−	0.545038i
$766$			6358.92i			0.299944i
$767$	−10630.3			−0.500440
$768$		−	468.167i		−	0.0219968i
$769$			2100.89i			0.0985178i	0.998786	+	0.0492589i	$0.0156859\pi$
$769$			2100.89i			0.0985178i	−0.998786	+	0.0492589i	$0.984314\pi$
$770$	53.8013			0.00251801
$771$			324.138i			0.0151408i
$772$		−	26669.2i		−	1.24332i
$773$		−	29744.0i		−	1.38398i	−0.721907	−	0.691990i	$-0.756734\pi$
$773$		−	29744.0i		−	1.38398i	0.721907	−	0.691990i	$-0.243266\pi$
$774$	6664.68			0.309505
$775$		−	4608.91i		−	0.213622i
$776$	−11186.8			−0.517505
$777$	−55.9706			−0.00258421
$778$	−5109.62			−0.235461
$779$	17124.4			0.787604
$780$			282.633i			0.0129742i
$781$			783.343i			0.0358902i
$782$	4091.09			0.187081
$783$	1383.15	−	1704.88i	0.0631287	−	0.0778129i
$784$	−17943.0			−0.817375
$785$		−	13820.5i		−	0.628373i
$786$			272.239i			0.0123542i
$787$	15934.9			0.721751			0.360875	−	0.932614i	$-0.382478\pi$
$787$	15934.9			0.721751			0.360875	+	0.932614i	$0.382478\pi$
$788$	6293.49			0.284513
$789$	−335.121			−0.0151212
$790$	−1283.94			−0.0578236
$791$			1313.08i			0.0590239i
$792$	−5992.12			−0.268839
$793$			14835.1i			0.664327i
$794$			107.598i			0.00480919i
$795$		−	869.588i		−	0.0387938i
$796$	−2842.20			−0.126557
$797$		−	6928.06i		−	0.307910i	−0.988078	−	0.153955i	$-0.950799\pi$
$797$		−	6928.06i		−	0.307910i	0.988078	−	0.153955i	$-0.0492011\pi$
$798$			21.6711i			0.000961339i
$799$	−43561.0			−1.92876
$800$		−	3099.09i		−	0.136962i
$801$			21443.0i			0.945881i
$802$		−	5310.68i		−	0.233824i
$803$	14728.3			0.647261
$804$		−	183.992i		−	0.00807078i
$805$	−254.964			−0.0111631
$806$	−3741.83			−0.163524
$807$	433.503			0.0189096
$808$	−17348.7			−0.755353
$809$		−	43601.8i		−	1.89488i	−0.319933	−	0.947440i	$-0.603660\pi$
$809$		−	43601.8i		−	1.89488i	0.319933	−	0.947440i	$-0.396340\pi$
$810$			2541.46i			0.110244i
$811$	18082.8			0.782950			0.391475	−	0.920189i	$-0.371965\pi$
$811$	18082.8			0.782950			0.391475	+	0.920189i	$0.371965\pi$
$812$	682.711	+	553.876i	0.0295055	+	0.0239375i
$813$	628.156			0.0270977
$814$			4108.36i			0.176902i
$815$		−	3806.25i		−	0.163592i
$816$	1169.66			0.0501794
$817$	55584.1			2.38022
$818$	3681.45			0.157358
$819$	583.505			0.0248954
$820$		−	4072.88i		−	0.173453i
$821$	−18056.9			−0.767590			−0.383795	−	0.923418i	$-0.625383\pi$
$821$	−18056.9			−0.767590			−0.383795	+	0.923418i	$0.625383\pi$
$822$			198.877i			0.00843872i
$823$			24106.9i			1.02104i	0.859866	+	0.510519i	$0.170547\pi$
$823$			24106.9i			1.02104i	−0.859866	+	0.510519i	$0.829453\pi$
$824$			12987.7i			0.549089i
$825$	−133.086			−0.00561631
$826$			193.861i			0.00816623i
$827$		−	4471.24i		−	0.188005i	−0.995572	−	0.0940026i	$-0.970034\pi$
$827$		−	4471.24i		−	0.188005i	0.995572	−	0.0940026i	$-0.0299662\pi$
$828$	13746.4			0.576956
$829$			25414.5i			1.06475i	0.846508	+	0.532377i	$0.178701\pi$
$829$			25414.5i			1.06475i	−0.846508	+	0.532377i	$0.821299\pi$
$830$		−	3620.96i		−	0.151428i
$831$		−	1216.99i		−	0.0508025i
$832$	9594.26			0.399785
$833$		−	29326.5i		−	1.21981i
$834$	−466.679			−0.0193762
$835$	13037.7			0.540346
$836$	−24192.1			−1.00084
$837$	−2591.62			−0.107025
$838$			7771.72i			0.320369i
$839$			2810.55i			0.115651i	0.998327	+	0.0578254i	$0.0184167\pi$
$839$			2810.55i			0.115651i	−0.998327	+	0.0578254i	$0.981583\pi$
$840$	10.6475			0.000437349
$841$	5027.44	+	23865.2i	0.206135	+	0.978523i
$842$	6711.55			0.274698
$843$			125.757i			0.00513798i
$844$		−	13689.6i		−	0.558313i
$845$	6811.76			0.277316
$846$	9624.16			0.391117
$847$	685.358			0.0278031
$848$	−34961.5			−1.41578
$849$		−	1933.90i		−	0.0781759i
$850$	1504.16			0.0606968
$851$		−	19469.5i		−	0.784260i
$852$			75.0461i			0.00301765i
$853$		−	28705.4i		−	1.15223i	−0.817368	−	0.576116i	$-0.804568\pi$
$853$		−	28705.4i		−	1.15223i	0.817368	−	0.576116i	$-0.195432\pi$
$854$	270.544			0.0108406
$855$			21249.8i			0.849975i
$856$		−	11707.8i		−	0.467480i
$857$	878.580			0.0350195			0.0175098	−	0.999847i	$-0.494426\pi$
$857$	878.580			0.0350195			0.0175098	+	0.999847i	$0.494426\pi$
$858$			108.048i			0.00429920i
$859$			32796.6i			1.30269i	0.758784	+	0.651343i	$0.225794\pi$
$859$			32796.6i			1.30269i	−0.758784	+	0.651343i	$0.774206\pi$
$860$		−	13220.2i		−	0.524192i
$861$	21.2124			0.000839624
$862$		−	6729.76i		−	0.265912i
$863$	−11086.6			−0.437303			−0.218652	−	0.975803i	$-0.570166\pi$
$863$	−11086.6			−0.437303			−0.218652	+	0.975803i	$0.570166\pi$
$864$	−1742.64			−0.0686180
$865$	19929.7			0.783388
$866$	8406.73			0.329876
$867$			631.127i			0.0247222i
$868$		−	1037.80i		−	0.0405822i
$869$	7464.94			0.291405
$870$	111.043	+	90.0880i	0.00432726	+	0.00351065i
$871$	2716.76			0.105687
$872$			12332.9i			0.478950i
$873$		−	27656.0i		−	1.07218i
$874$	−7538.34			−0.291748
$875$	−93.7419			−0.00362177
$876$	1411.00			0.0544217
$877$	27008.6			1.03993			0.519964	−	0.854188i	$-0.325945\pi$
$877$	27008.6			1.03993			0.519964	+	0.854188i	$0.325945\pi$
$878$		−	1699.71i		−	0.0653332i
$879$	−73.8432			−0.00283353
$880$			5350.68i			0.204968i
$881$			2049.80i			0.0783876i	0.999232	+	0.0391938i	$0.0124790\pi$
$881$			2049.80i			0.0783876i	−0.999232	+	0.0391938i	$0.987521\pi$
$882$			6479.26i			0.247356i
$883$	−4525.79			−0.172486			−0.0862429	−	0.996274i	$-0.527486\pi$
$883$	−4525.79			−0.172486			−0.0862429	+	0.996274i	$0.527486\pi$
$884$			18572.2i			0.706620i
$885$		−	479.546i		−	0.0182144i
$886$	−11605.3			−0.440052
$887$		−	19358.9i		−	0.732816i	−0.930454	−	0.366408i	$-0.880587\pi$
$887$		−	19358.9i		−	0.732816i	0.930454	−	0.366408i	$-0.119413\pi$
$888$			813.060i			0.0307258i
$889$		−	980.142i		−	0.0369774i
$890$	−2796.79			−0.105336
$891$		−	14776.3i		−	0.555581i
$892$	22706.3			0.852312
$893$	80266.5			3.00786
$894$	−166.597			−0.00623248
$895$	−7576.99			−0.282984
$896$		−	918.685i		−	0.0342535i
$897$		−	512.040i		−	0.0190597i
$898$	7375.68			0.274086
$899$	18139.0	−	22358.3i	0.672936	−	0.829466i
$900$	5054.09			0.187189
$901$		−	57142.0i		−	2.11285i
$902$		−	1557.03i		−	0.0574762i
$903$	68.8534			0.00253743
$904$	19074.6			0.701783
$905$	11525.6			0.423343
$906$	−280.426			−0.0102831
$907$		−	46378.0i		−	1.69786i	−0.528507	−	0.848929i	$-0.677248\pi$
$907$		−	46378.0i		−	1.69786i	0.528507	−	0.848929i	$-0.322752\pi$
$908$	26003.3			0.950385
$909$		−	42889.4i		−	1.56496i
$910$			76.1061i			0.00277241i
$911$			19248.7i			0.700040i	0.936742	+	0.350020i	$0.113825\pi$
$911$			19248.7i			0.700040i	−0.936742	+	0.350020i	$0.886175\pi$
$912$	−2155.25			−0.0782537
$913$			21052.6i			0.763130i
$914$		−	39.7540i		−	0.00143867i
$915$	−669.233			−0.0241794
$916$			36461.7i			1.31521i
$917$		−	1114.89i		−	0.0401493i
$918$		−	845.801i		−	0.0304091i
$919$	4695.28			0.168534			0.0842672	−	0.996443i	$-0.473145\pi$
$919$	4695.28			0.168534			0.0842672	+	0.996443i	$0.473145\pi$
$920$			3703.75i			0.132727i
$921$	−1766.89			−0.0632149
$922$	11468.9			0.409660
$923$	−1108.10			−0.0395163
$924$	−29.9674			−0.00106694
$925$		−	7158.28i		−	0.254446i
$926$			12679.1i			0.449959i
$927$	−32108.3			−1.13762
$928$	12196.9	−	15034.0i	0.431447	−	0.531805i
$929$	3528.94			0.124629			0.0623147	−	0.998057i	$-0.480152\pi$
$929$	3528.94			0.124629			0.0623147	+	0.998057i	$0.480152\pi$
$930$		−	168.799i		−	0.00595176i
$931$			54037.7i			1.90227i
$932$	−11397.3			−0.400568
$933$	−926.341			−0.0325049
$934$	−10212.6			−0.357781
$935$	−8745.29			−0.305884
$936$		−	8476.32i		−	0.296001i
$937$	−23907.6			−0.833541			−0.416770	−	0.909012i	$-0.636838\pi$
$937$	−23907.6			−0.833541			−0.416770	+	0.909012i	$0.636838\pi$
$938$		−	49.5447i		−	0.00172462i
$939$		−	2259.87i		−	0.0785389i
$940$		−	19090.7i		−	0.662415i
$941$	4265.50			0.147770			0.0738848	−	0.997267i	$-0.476460\pi$
$941$	4265.50			0.147770			0.0738848	+	0.997267i	$0.476460\pi$
$942$		−	506.167i		−	0.0175072i
$943$			7378.77i			0.254810i
$944$	−19280.0			−0.664737
$945$			52.7118i			0.00181451i
$946$		−	5053.99i		−	0.173699i
$947$		−	8485.96i		−	0.291190i	−0.989344	−	0.145595i	$-0.953490\pi$
$947$		−	8485.96i		−	0.291190i	0.989344	−	0.145595i	$-0.0465096\pi$
$948$	715.158			0.0245013
$949$			20834.3i			0.712656i
$950$	−2771.60			−0.0946553
$951$	596.131			0.0203269
$952$	699.664			0.0238196
$953$	−9378.00			−0.318765			−0.159383	−	0.987217i	$-0.550950\pi$
$953$	−9378.00			−0.318765			−0.159383	+	0.987217i	$0.550950\pi$
$954$			12624.7i			0.428447i
$955$		−	22976.1i		−	0.778522i
$956$	−18196.9			−0.615617
$957$	−645.613	−	523.778i	−0.0218074	−	0.0176921i
$958$	−4621.79			−0.155870
$959$		−	814.453i		−	0.0274245i
$960$			432.810i			0.0145509i
$961$	−4196.23			−0.140856
$962$	−5811.59			−0.194775
$963$	28943.9			0.968540
$964$	−32809.9			−1.09620
$965$			17764.2i			0.592592i
$966$	−9.33793			−0.000311018
$967$			17477.3i			0.581213i	0.956843	+	0.290607i	$0.0938571\pi$
$967$			17477.3i			0.581213i	−0.956843	+	0.290607i	$0.906143\pi$
$968$		−	9955.90i		−	0.330573i
$969$		−	3522.59i		−	0.116782i
$970$	3607.16			0.119401
$971$		−	14368.0i		−	0.474863i	−0.971404	−	0.237432i	$-0.923694\pi$
$971$		−	14368.0i		−	0.474863i	0.971404	−	0.237432i	$-0.0763055\pi$
$972$		−	4264.72i		−	0.140732i
$973$	1911.17			0.0629696
$974$		−	9897.15i		−	0.325591i
$975$		−	188.260i		−	0.00618375i
$976$			26906.3i			0.882429i
$977$	−22544.5			−0.738242			−0.369121	−	0.929381i	$-0.620341\pi$
$977$	−22544.5			−0.738242			−0.369121	+	0.929381i	$0.620341\pi$
$978$		−	139.402i		−	0.00455786i
$979$	16260.7			0.530843
$980$	12852.4			0.418934
$981$	−30489.3			−0.992304
$982$	−6609.94			−0.214798
$983$			32899.0i			1.06746i	0.845654	+	0.533732i	$0.179211\pi$
$983$			32899.0i			1.06746i	−0.845654	+	0.533732i	$0.820789\pi$
$984$		−	308.143i		−	0.00998296i
$985$	−4192.06			−0.135604
$986$	7296.83	+	5919.83i	0.235678	+	0.191203i
$987$	99.4282			0.00320652
$988$		−	34221.6i		−	1.10196i
$989$			23950.8i			0.770063i
$990$	1932.14			0.0620278
$991$	23125.7			0.741284			0.370642	−	0.928776i	$-0.379138\pi$
$991$	23125.7			0.741284			0.370642	+	0.928776i	$0.379138\pi$
$992$	−22853.5			−0.731451
$993$	−125.152			−0.00399959
$994$			20.2081i			0.000644831i
$995$	1893.18			0.0603194
$996$			2016.88i			0.0641640i
$997$		−	8970.92i		−	0.284967i	−0.989797	−	0.142483i	$-0.954491\pi$
$997$		−	8970.92i		−	0.284967i	0.989797	−	0.142483i	$-0.0455088\pi$
$998$			9163.25i			0.290639i
$999$	−4025.16			−0.127478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.4.c.b.86.8	✓	16
29.28	even	2	inner	145.4.c.b.86.9	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.4.c.b.86.8	✓	16	1.1	even	1	trivial
145.4.c.b.86.9	yes	16	29.28	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	145.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.702546i q^{2} -0.260656i q^{3} +7.50643 q^{4} -5.00000 q^{5} -0.183122 q^{6} +0.749935 q^{7} -10.8940i q^{8} +26.9321 q^{9} +O(q^{10})\)	\(q-0.702546i q^{2} -0.260656i q^{3} +7.50643 q^{4} -5.00000 q^{5} -0.183122 q^{6} +0.749935 q^{7} -10.8940i q^{8} +26.9321 q^{9} +3.51273i q^{10} -20.4233i q^{11} -1.95659i q^{12} +28.8903 q^{13} -0.526863i q^{14} +1.30328i q^{15} +52.3979 q^{16} +85.6406i q^{17} -18.9210i q^{18} -157.803i q^{19} -37.5321 q^{20} -0.195475i q^{21} -14.3483 q^{22} +67.9963 q^{23} -2.83958 q^{24} +25.0000 q^{25} -20.2967i q^{26} -14.0577i q^{27} +5.62933 q^{28} +(121.277 + 98.3910i) q^{29} +0.915612 q^{30} -184.356i q^{31} -123.964i q^{32} -5.32344 q^{33} +60.1664 q^{34} -3.74967 q^{35} +202.164 q^{36} -286.331i q^{37} -110.864 q^{38} -7.53041i q^{39} +54.4699i q^{40} +108.517i q^{41} -0.137330 q^{42} +352.237i q^{43} -153.306i q^{44} -134.660 q^{45} -47.7705i q^{46} +508.650i q^{47} -13.6578i q^{48} -342.438 q^{49} -17.5636i q^{50} +22.3227 q^{51} +216.863 q^{52} -667.231 q^{53} -9.87617 q^{54} +102.116i q^{55} -8.16977i q^{56} -41.1323 q^{57} +(69.1241 - 85.2029i) q^{58} -367.954 q^{59} +9.78297i q^{60} +513.500i q^{61} -129.519 q^{62} +20.1973 q^{63} +332.093 q^{64} -144.451 q^{65} +3.73996i q^{66} +94.0371 q^{67} +642.855i q^{68} -17.7236i q^{69} +2.63432i q^{70} -38.3555 q^{71} -293.397i q^{72} +721.153i q^{73} -201.161 q^{74} -6.51639i q^{75} -1184.54i q^{76} -15.3161i q^{77} -5.29046 q^{78} +365.512i q^{79} -261.990 q^{80} +723.501 q^{81} +76.2383 q^{82} -1030.81 q^{83} -1.46732i q^{84} -428.203i q^{85} +247.463 q^{86} +(25.6462 - 31.6117i) q^{87} -222.490 q^{88} +796.188i q^{89} +94.6050i q^{90} +21.6658 q^{91} +510.410 q^{92} -48.0535 q^{93} +357.350 q^{94} +789.016i q^{95} -32.3118 q^{96} -1026.88i q^{97} +240.578i q^{98} -550.040i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9}+O(q^{10}) \) 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9	\( 16 q - 62 q^{4} - 80 q^{5} + 50 q^{6} + 38 q^{7} - 126 q^{9} - 14 q^{13} + 210 q^{16} + 310 q^{20} + 88 q^{22} + 42 q^{23} + 62 q^{24} + 400 q^{25} - 346 q^{28} + 28 q^{29} - 250 q^{30} - 460 q^{33} - 626 q^{34} - 190 q^{35} - 12 q^{36} - 292 q^{38} + 584 q^{42} + 630 q^{45} + 1894 q^{49} - 320 q^{51} - 294 q^{52} + 614 q^{53} + 1840 q^{54} - 1360 q^{57} - 644 q^{58} - 2086 q^{59} - 30 q^{62} - 1456 q^{63} - 894 q^{64} + 70 q^{65} - 1604 q^{67} + 792 q^{71} + 1720 q^{74} + 4894 q^{78} - 1050 q^{80} - 192 q^{81} + 1276 q^{82} + 4400 q^{83} - 2042 q^{86} - 2046 q^{87} - 9264 q^{88} + 212 q^{91} - 2030 q^{92} - 1816 q^{93} + 4304 q^{94} + 2234 q^{96}+O(q^{100}) \) 16 * q - 62 * q^4 - 80 * q^5 + 50 * q^6 + 38 * q^7 - 126 * q^9 - 14 * q^13 + 210 * q^16 + 310 * q^20 + 88 * q^22 + 42 * q^23 + 62 * q^24 + 400 * q^25 - 346 * q^28 + 28 * q^29 - 250 * q^30 - 460 * q^33 - 626 * q^34 - 190 * q^35 - 12 * q^36 - 292 * q^38 + 584 * q^42 + 630 * q^45 + 1894 * q^49 - 320 * q^51 - 294 * q^52 + 614 * q^53 + 1840 * q^54 - 1360 * q^57 - 644 * q^58 - 2086 * q^59 - 30 * q^62 - 1456 * q^63 - 894 * q^64 + 70 * q^65 - 1604 * q^67 + 792 * q^71 + 1720 * q^74 + 4894 * q^78 - 1050 * q^80 - 192 * q^81 + 1276 * q^82 + 4400 * q^83 - 2042 * q^86 - 2046 * q^87 - 9264 * q^88 + 212 * q^91 - 2030 * q^92 - 1816 * q^93 + 4304 * q^94 + 2234 * q^96

Introduction

L-functions

Modular forms

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