LMFDB - Embedded newform 153.4.n.a.13.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$52$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.45
Character	$\chi$	$=$	153.13
Dual form			153.4.n.a.106.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.50903 - 2.02594i) q^{2} +(0.218568 - 5.19155i) q^{3} +(4.20886 - 7.28996i) q^{4} +(-18.5503 + 4.97053i) q^{5} +(-9.75081 - 18.6601i) q^{6} +(-10.4834 - 2.80902i) q^{7} -1.69255i q^{8} +(-26.9045 - 2.26942i) q^{9} +(-55.0234 + 55.0234i) q^{10} +(-22.6073 - 6.05760i) q^{11} +(-36.9263 - 23.4439i) q^{12} +(39.3566 - 68.1676i) q^{13} +(-42.4774 + 11.3818i) q^{14} +(21.7503 + 97.3911i) q^{15} +(30.2419 + 52.3805i) q^{16} +(18.6593 - 67.5635i) q^{17} +(-99.0062 + 46.5433i) q^{18} -33.0912i q^{19} +(-41.8405 + 156.151i) q^{20} +(-16.8745 + 53.8111i) q^{21} +(-91.6019 + 24.5446i) q^{22} +(-36.6429 - 136.753i) q^{23} +(-8.78699 - 0.369939i) q^{24} +(211.153 - 121.909i) q^{25} -318.936i q^{26} +(-17.6623 + 139.180i) q^{27} +(-64.6008 + 64.6008i) q^{28} +(-45.9209 + 171.379i) q^{29} +(273.631 + 297.683i) q^{30} +(69.6906 - 18.6736i) q^{31} +(223.966 + 129.307i) q^{32} +(-36.3896 + 116.043i) q^{33} +(-71.4035 - 274.885i) q^{34} +208.432 q^{35} +(-129.781 + 186.581i) q^{36} +(-203.311 - 203.311i) q^{37} +(-67.0408 - 116.118i) q^{38} +(-345.294 - 219.221i) q^{39} +(8.41289 + 31.3973i) q^{40} +(46.9839 + 175.346i) q^{41} +(49.8050 + 223.012i) q^{42} +(-245.898 + 141.969i) q^{43} +(-139.310 + 139.310i) q^{44} +(510.365 - 91.6310i) q^{45} +(-405.634 - 405.634i) q^{46} +(92.2805 + 159.834i) q^{47} +(278.546 - 145.554i) q^{48} +(-195.036 - 112.604i) q^{49} +(493.961 - 855.566i) q^{50} +(-346.681 - 111.638i) q^{51} +(-331.293 - 573.816i) q^{52} +80.6428i q^{53} +(219.993 + 524.169i) q^{54} +449.480 q^{55} +(-4.75441 + 17.7437i) q^{56} +(-171.795 - 7.23270i) q^{57} +(186.066 + 694.408i) q^{58} +(-207.374 - 119.728i) q^{59} +(801.521 + 251.347i) q^{60} +(131.743 + 35.3005i) q^{61} +(206.715 - 206.715i) q^{62} +(275.675 + 99.3663i) q^{63} +563.999 q^{64} +(-391.246 + 1460.15i) q^{65} +(107.404 + 480.921i) q^{66} +(511.426 - 885.817i) q^{67} +(-414.001 - 420.391i) q^{68} +(-717.970 + 160.344i) q^{69} +(731.394 - 422.270i) q^{70} +(-403.846 - 403.846i) q^{71} +(-3.84112 + 45.5373i) q^{72} +(264.951 + 264.951i) q^{73} +(-1125.32 - 301.529i) q^{74} +(-586.747 - 1122.86i) q^{75} +(-241.234 - 139.276i) q^{76} +(219.985 + 127.008i) q^{77} +(-1655.77 - 69.7094i) q^{78} +(814.697 + 218.298i) q^{79} +(-821.353 - 821.353i) q^{80} +(718.699 + 122.115i) q^{81} +(520.109 + 520.109i) q^{82} +(671.447 - 387.660i) q^{83} +(321.259 + 349.498i) q^{84} +(-10.3091 + 1346.07i) q^{85} +(-575.242 + 996.349i) q^{86} +(879.688 + 275.859i) q^{87} +(-10.2528 + 38.2640i) q^{88} -578.485 q^{89} +(1605.25 - 1355.50i) q^{90} +(-604.074 + 604.074i) q^{91} +(-1151.15 - 308.449i) q^{92} +(-81.7126 - 365.884i) q^{93} +(647.630 + 373.909i) q^{94} +(164.481 + 613.851i) q^{95} +(720.254 - 1134.47i) q^{96} +(-29.6492 + 110.652i) q^{97} -912.515 q^{98} +(594.489 + 214.282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) $ 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.50903	−	2.02594i	1.24063	−	0.716278i	0.271407	−	0.962465i	$-0.412511\pi$
$2$	3.50903	−	2.02594i	1.24063	−	0.716278i	0.969222	+	0.246187i	$0.0791777\pi$
$3$	0.218568	−	5.19155i	0.0420635	−	0.999115i
$3$	0.218568	−	5.19155i	0.0420635	−	0.999115i
$4$	4.20886	−	7.28996i	0.526108	−	0.911245i
$5$	−18.5503	+	4.97053i	−1.65919	+	0.444577i	−0.962164	−	0.272472i	$-0.912159\pi$
$5$	−18.5503	+	4.97053i	−1.65919	+	0.444577i	−0.697022	+	0.717050i	$0.745492\pi$
$6$	−9.75081	−	18.6601i	−0.663459	−	1.26966i
$7$	−10.4834	−	2.80902i	−0.566050	−	0.151673i	−0.0355656	−	0.999367i	$-0.511323\pi$
$7$	−10.4834	−	2.80902i	−0.566050	−	0.151673i	−0.530484	+	0.847695i	$0.677990\pi$
$8$		−	1.69255i		−	0.0748010i
$9$	−26.9045	−	2.26942i	−0.996461	−	0.0840526i
$10$	−55.0234	+	55.0234i	−1.73999	+	1.73999i
$11$	−22.6073	−	6.05760i	−0.619668	−	0.166039i	−0.0646909	−	0.997905i	$-0.520606\pi$
$11$	−22.6073	−	6.05760i	−0.619668	−	0.166039i	−0.554977	+	0.831866i	$0.687273\pi$
$12$	−36.9263	−	23.4439i	−0.888309	−	0.563972i
$13$	39.3566	−	68.1676i	0.839658	−	1.45433i	−0.0505228	−	0.998723i	$-0.516089\pi$
$13$	39.3566	−	68.1676i	0.839658	−	1.45433i	0.890181	−	0.455607i	$-0.150578\pi$
$14$	−42.4774	+	11.3818i	−0.810898	+	0.217279i
$15$	21.7503	+	97.3911i	0.374393	+	1.67642i
$16$	30.2419	+	52.3805i	0.472529	+	0.818445i
$17$	18.6593	−	67.5635i	0.266209	−	0.963915i
$17$	18.6593	−	67.5635i	0.266209	−	0.963915i
$18$	−99.0062	+	46.5433i	−1.29644	+	0.609465i
$19$		−	33.0912i		−	0.399560i	−0.979841	−	0.199780i	$-0.935977\pi$
$19$		−	33.0912i		−	0.399560i	0.979841	−	0.199780i	$-0.0640228\pi$
$20$	−41.8405	+	156.151i	−0.467791	+	1.74582i
$21$	−16.8745	+	53.8111i	−0.175348	+	0.559169i
$22$	−91.6019	+	24.5446i	−0.887708	+	0.237861i
$23$	−36.6429	−	136.753i	−0.332199	−	1.23978i	−0.906875	−	0.421401i	$-0.861539\pi$
$23$	−36.6429	−	136.753i	−0.332199	−	1.23978i	0.574676	−	0.818381i	$-0.305128\pi$
$24$	−8.78699	−	0.369939i	−0.0747348	−	0.00314639i
$25$	211.153	−	121.909i	1.68922	−	0.975273i
$26$		−	318.936i		−	2.40571i
$27$	−17.6623	+	139.180i	−0.125893	+	0.992044i
$28$	−64.6008	+	64.6008i	−0.436014	+	0.436014i
$29$	−45.9209	+	171.379i	−0.294045	+	1.09739i	0.647928	+	0.761702i	$0.275636\pi$
$29$	−45.9209	+	171.379i	−0.294045	+	1.09739i	−0.941973	+	0.335689i	$0.891031\pi$
$30$	273.631	+	297.683i	1.66526	+	1.81164i
$31$	69.6906	−	18.6736i	0.403768	−	0.108189i	−0.0512189	−	0.998687i	$-0.516311\pi$
$31$	69.6906	−	18.6736i	0.403768	−	0.108189i	0.454987	+	0.890498i	$0.349644\pi$
$32$	223.966	+	129.307i	1.23725	+	0.714325i
$33$	−36.3896	+	116.043i	−0.191958	+	0.612135i
$34$	−71.4035	−	274.885i	−0.360164	−	1.38654i
$35$	208.432			1.00661
$36$	−129.781	+	186.581i	−0.600838	+	0.863800i
$37$	−203.311	−	203.311i	−0.903357	−	0.903357i	0.0923681	−	0.995725i	$-0.470556\pi$
$37$	−203.311	−	203.311i	−0.903357	−	0.903357i	−0.995725	+	0.0923681i	$0.970556\pi$
$38$	−67.0408	−	116.118i	−0.286196	−	0.495706i
$39$	−345.294	−	219.221i	−1.41772	−	0.900089i
$40$	8.41289	+	31.3973i	0.0332549	+	0.124109i
$41$	46.9839	+	175.346i	0.178967	+	0.667915i	0.995842	+	0.0910993i	$0.0290381\pi$
$41$	46.9839	+	175.346i	0.178967	+	0.667915i	−0.816875	+	0.576815i	$0.804295\pi$
$42$	49.8050	+	223.012i	0.182978	+	0.819320i
$43$	−245.898	+	141.969i	−0.872072	+	0.503491i	−0.868036	−	0.496501i	$-0.834618\pi$
$43$	−245.898	+	141.969i	−0.872072	+	0.503491i	−0.00403589	+	0.999992i	$0.501285\pi$
$44$	−139.310	+	139.310i	−0.477314	+	0.477314i
$45$	510.365	−	91.6310i	1.69068	−	0.303545i
$46$	−405.634	−	405.634i	−1.30016	−	1.30016i
$47$	92.2805	+	159.834i	0.286393	+	0.496048i	0.972946	−	0.231032i	$-0.0742103\pi$
$47$	92.2805	+	159.834i	0.286393	+	0.496048i	−0.686553	+	0.727080i	$0.740877\pi$
$48$	278.546	−	145.554i	0.837597	−	0.437684i
$49$	−195.036	−	112.604i	−0.568617	−	0.328291i
$50$	493.961	−	855.566i	1.39713	−	2.41991i
$51$	−346.681	−	111.638i	−0.951865	−	0.306519i
$52$	−331.293	−	573.816i	−0.883501	−	1.53027i
$53$			80.6428i			0.209003i	0.994525	+	0.104501i	$0.0333247\pi$
$53$			80.6428i			0.209003i	−0.994525	+	0.104501i	$0.966675\pi$
$54$	219.993	+	524.169i	0.554393	+	1.32093i
$55$	449.480			1.10196
$56$	−4.75441	+	17.7437i	−0.0113453	+	0.0423411i
$57$	−171.795	−	7.23270i	−0.399207	−	0.0168069i
$58$	186.066	+	694.408i	0.421236	+	1.57207i
$59$	−207.374	−	119.728i	−0.457590	−	0.264190i	0.253440	−	0.967351i	$-0.418438\pi$
$59$	−207.374	−	119.728i	−0.457590	−	0.264190i	−0.711031	+	0.703161i	$0.751771\pi$
$60$	801.521	+	251.347i	1.72460	+	0.540812i
$61$	131.743	+	35.3005i	0.276524	+	0.0740945i	0.394416	−	0.918932i	$-0.370947\pi$
$61$	131.743	+	35.3005i	0.276524	+	0.0740945i	−0.117892	+	0.993026i	$0.537614\pi$
$62$	206.715	−	206.715i	0.423433	−	0.423433i
$63$	275.675	+	99.3663i	0.551298	+	0.198714i
$64$	563.999			1.10156
$65$	−391.246	+	1460.15i	−0.746586	+	2.78630i
$66$	107.404	+	480.921i	0.200310	+	0.896928i
$67$	511.426	−	885.817i	0.932547	−	1.61522i	0.153597	−	0.988134i	$-0.450914\pi$
$67$	511.426	−	885.817i	0.932547	−	1.61522i	0.778950	−	0.627086i	$-0.215753\pi$
$68$	−414.001	−	420.391i	−0.738309	−	0.749705i
$69$	−717.970	+	160.344i	−1.25266	+	0.279755i
$70$	731.394	−	422.270i	1.24883	−	0.721014i
$71$	−403.846	−	403.846i	−0.675039	−	0.675039i	0.283834	−	0.958873i	$-0.408393\pi$
$71$	−403.846	−	403.846i	−0.675039	−	0.675039i	−0.958873	+	0.283834i	$0.908393\pi$
$72$	−3.84112	+	45.5373i	−0.00628722	+	0.0745364i
$73$	264.951	+	264.951i	0.424797	+	0.424797i	0.886852	−	0.462054i	$-0.152888\pi$
$73$	264.951	+	264.951i	0.424797	+	0.424797i	−0.462054	+	0.886852i	$0.652888\pi$
$74$	−1125.32	−	301.529i	−1.76779	−	0.473677i
$75$	−586.747	−	1122.86i	−0.903355	−	1.72875i
$76$	−241.234	−	139.276i	−0.364097	−	0.210212i
$77$	219.985	+	127.008i	0.325579	+	0.187973i
$78$	−1655.77	−	69.7094i	−2.40358	−	0.101193i
$79$	814.697	+	218.298i	1.16026	+	0.310891i	0.787070	−	0.616864i	$-0.211597\pi$
$79$	814.697	+	218.298i	1.16026	+	0.310891i	0.373191	+	0.927755i	$0.378264\pi$
$80$	−821.353	−	821.353i	−1.14788	−	1.14788i
$81$	718.699	+	122.115i	0.985870	+	0.167510i
$82$	520.109	+	520.109i	0.700444	+	0.700444i
$83$	671.447	−	387.660i	0.887962	−	0.512665i	0.0146869	−	0.999892i	$-0.495325\pi$
$83$	671.447	−	387.660i	0.887962	−	0.512665i	0.873275	+	0.487227i	$0.161992\pi$
$84$	321.259	+	349.498i	0.417288	+	0.453968i
$85$	−10.3091	+	1346.07i	−0.0131550	+	1.71767i
$86$	−575.242	+	996.349i	−0.721279	+	1.24929i
$87$	879.688	+	275.859i	1.08405	+	0.339945i
$88$	−10.2528	+	38.2640i	−0.0124199	+	0.0463518i
$89$	−578.485			−0.688981			−0.344490	−	0.938790i	$-0.611948\pi$
$89$	−578.485			−0.688981			−0.344490	+	0.938790i	$0.611948\pi$
$90$	1605.25	−	1355.50i	1.88009	−	1.58759i
$91$	−604.074	+	604.074i	−0.695870	+	0.695870i
$92$	−1151.15	−	308.449i	−1.30452	−	0.349544i
$93$	−81.7126	−	365.884i	−0.0911097	−	0.407961i
$94$	647.630	+	373.909i	0.710616	+	0.410274i
$95$	164.481	+	613.851i	0.177636	+	0.662945i
$96$	720.254	−	1134.47i	0.765736	−	1.20610i
$97$	−29.6492	+	110.652i	−0.0310352	+	0.115825i	−0.979706	−	0.200441i	$-0.935763\pi$
$97$	−29.6492	+	110.652i	−0.0310352	+	0.115825i	0.948671	+	0.316266i	$0.102429\pi$
$98$	−912.515			−0.940591
$99$	594.489	+	214.282i	0.603519	+	0.217537i
$100$		−	2052.39i		−	2.05239i
$101$	886.599	+	1535.64i	0.873465	+	1.51289i	0.858389	+	0.512999i	$0.171465\pi$
$101$	886.599	+	1535.64i	0.873465	+	1.51289i	0.0150754	+	0.999886i	$0.495201\pi$
$102$	−1442.69	+	310.614i	−1.40046	+	0.301523i
$103$	907.231	−	1571.37i	0.867884	−	1.50322i	0.00372989	−	0.999993i	$-0.498813\pi$
$103$	907.231	−	1571.37i	0.867884	−	1.50322i	0.864154	−	0.503227i	$-0.167854\pi$
$104$	−115.377	−	66.6132i	−0.108785	−	0.0628073i
$105$	45.5566	−	1082.09i	0.0423416	−	1.00572i
$106$	163.377	+	282.978i	0.149704	+	0.259295i
$107$	−307.180	−	307.180i	−0.277535	−	0.277535i	0.554590	−	0.832124i	$-0.312875\pi$
$107$	−307.180	−	307.180i	−0.277535	−	0.277535i	−0.832124	+	0.554590i	$0.812875\pi$
$108$	940.278	+	714.546i	0.837762	+	0.636641i
$109$	648.241	−	648.241i	0.569636	−	0.569636i	−0.362391	−	0.932026i	$-0.618039\pi$
$109$	648.241	−	648.241i	0.569636	−	0.569636i	0.932026	+	0.362391i	$0.118039\pi$
$110$	1577.24	−	910.619i	1.36713	−	0.789310i
$111$	−1099.94	+	1011.07i	−0.940556	+	0.864559i
$112$	−169.900	−	634.075i	−0.143340	−	0.534950i
$113$	−449.670	−	1678.19i	−0.374349	−	1.39709i	−0.854294	−	0.519790i	$-0.826010\pi$
$113$	−449.670	−	1678.19i	−0.374349	−	1.39709i	0.479946	−	0.877298i	$-0.340656\pi$
$114$	−617.486	+	322.666i	−0.507306	+	0.265092i
$115$	1359.47	+	2354.67i	1.10236	+	1.90934i
$116$	1056.07	+	1056.07i	0.845293	+	0.845293i
$117$	−1213.57	+	1744.70i	−0.958927	+	1.37861i
$118$	−970.243			−0.756933
$119$	−385.400	+	655.881i	−0.296887	+	0.505248i
$120$	164.840	−	36.8135i	0.125398	−	0.0280050i
$121$	−678.286	−	391.609i	−0.509607	−	0.294221i
$122$	533.807	−	143.033i	0.396136	−	0.106144i
$123$	920.589	−	205.594i	0.674851	−	0.150714i
$124$	157.189	−	586.636i	0.113838	−	0.424851i
$125$	−1613.52	+	1613.52i	−1.15454	+	1.15454i
$126$	1168.66	−	209.822i	0.826291	−	0.148353i
$127$		−	291.714i		−	0.203822i	−0.994794	−	0.101911i	$-0.967504\pi$
$127$		−	291.714i		−	0.203822i	0.994794	−	0.101911i	$-0.0324957\pi$
$128$	187.366	−	108.176i	0.129383	−	0.0746991i
$129$	683.296	+	1307.62i	0.466363	+	0.892479i
$130$	1585.28	+	5916.35i	1.06953	+	3.99153i
$131$	−1156.47	+	309.876i	−0.771309	+	0.206672i	−0.622950	−	0.782262i	$-0.714066\pi$
$131$	−1156.47	+	309.876i	−0.771309	+	0.206672i	−0.148360	+	0.988933i	$0.547399\pi$
$132$	692.789	+	753.686i	0.456814	+	0.496969i
$133$	−92.9538	+	346.908i	−0.0606024	+	0.226171i
$134$		−	4144.48i		−	2.67185i
$135$	−364.158	−	2669.61i	−0.232161	−	1.70195i
$136$	−114.355	−	31.5819i	−0.0721019	−	0.0199127i
$137$	−828.381	−	1434.80i	−0.516594	−	0.894767i	−0.999814	−	0.0192685i	$-0.993866\pi$
$137$	−828.381	−	1434.80i	−0.516594	−	0.894767i	0.483220	−	0.875499i	$-0.339467\pi$
$138$	−2194.53	+	2017.21i	−1.35370	+	1.24432i
$139$	−442.311	+	118.517i	−0.269902	+	0.0723200i	−0.391232	−	0.920292i	$-0.627951\pi$
$139$	−442.311	+	118.517i	−0.269902	+	0.0723200i	0.121330	+	0.992612i	$0.461284\pi$
$140$	877.261	−	1519.46i	0.529586	−	0.917270i
$141$	849.959	−	444.144i	0.507656	−	0.265274i
$142$	−2235.28	−	598.941i	−1.32099	−	0.353958i
$143$	−1302.68	+	1302.68i	−0.761785	+	0.761785i
$144$	−694.768	−	1477.90i	−0.402065	−	0.855266i
$145$		−	3407.38i		−	1.95150i
$146$	1466.50	+	392.947i	0.831289	+	0.222743i
$147$	−627.218	+	987.927i	−0.351919	+	0.554305i
$148$	−2337.84	+	626.423i	−1.29844	+	0.347917i
$149$	−1167.29	+	2021.81i	−0.641802	+	1.11163i	0.343228	+	0.939252i	$0.388480\pi$
$149$	−1167.29	+	2021.81i	−0.641802	+	1.11163i	−0.985030	+	0.172382i	$0.944854\pi$
$150$	−4333.75	−	2751.43i	−2.35900	−	1.49769i
$151$	−2058.80	+	1188.65i	−1.10955	+	0.640601i	−0.938713	−	0.344698i	$-0.887981\pi$
$151$	−2058.80	+	1188.65i	−1.10955	+	0.640601i	−0.170839	+	0.985299i	$0.554648\pi$
$152$	−56.0087			−0.0298875
$153$	−655.349	+	1775.41i	−0.346286	+	0.938129i
$154$	1029.24			0.538564
$155$	−1199.96	+	692.799i	−0.621828	+	0.359012i
$156$	−3051.41	+	1594.51i	−1.56608	+	0.818350i
$157$	−917.464	+	1589.10i	−0.466380	+	0.807794i	−0.999263	−	0.0383955i	$-0.987775\pi$
$157$	−917.464	+	1589.10i	−0.466380	+	0.807794i	0.532883	+	0.846189i	$0.321109\pi$
$158$	3301.06	−	884.515i	1.66214	−	0.445369i
$159$	418.662	+	17.6260i	0.208818	+	0.00879139i
$160$	−4797.34	−	1285.44i	−2.37040	−	0.635145i
$161$			1536.57i			0.752164i
$162$	2769.34	−	1027.54i	1.34308	−	0.498339i
$163$	1834.22	−	1834.22i	0.881394	−	0.881394i	−0.112282	−	0.993676i	$-0.535816\pi$
$163$	1834.22	−	1834.22i	0.881394	−	0.881394i	0.993676	+	0.112282i	$0.0358160\pi$
$164$	1476.02	+	395.497i	0.702790	+	0.188312i
$165$	98.2421	−	2333.50i	0.0463523	−	1.10099i
$166$	1570.75	−	2720.62i	0.734421	−	1.27206i
$167$	−1465.50	+	392.679i	−0.679064	+	0.181955i	−0.581834	−	0.813307i	$-0.697665\pi$
$167$	−1465.50	+	392.679i	−0.679064	+	0.181955i	−0.0972294	+	0.995262i	$0.530998\pi$
$168$	91.0783	+	28.5610i	0.0418264	+	0.0131162i
$169$	−1999.38	−	3463.03i	−0.910051	−	1.57625i
$170$	2690.88	+	4744.28i	1.21400	+	2.14041i
$171$	−75.0979	+	890.301i	−0.0335841	+	0.398146i
$172$			2390.12i			1.05956i
$173$	519.607	−	1939.20i	0.228353	−	0.852223i	−0.752681	−	0.658385i	$-0.771240\pi$
$173$	519.607	−	1939.20i	0.228353	−	0.852223i	0.981034	−	0.193838i	$-0.0620936\pi$
$174$	3645.72	−	814.196i	1.58840	−	0.354736i
$175$	−2556.04	+	684.890i	−1.10411	+	0.295845i
$176$	−366.386	−	1367.37i	−0.156917	−	0.585622i
$177$	−666.898	+	1050.43i	−0.283204	+	0.446073i
$178$	−2029.92	+	1171.98i	−0.854770	+	0.493502i
$179$			1578.67i			0.659194i	0.944122	+	0.329597i	$0.106913\pi$
$179$			1578.67i			0.659194i	−0.944122	+	0.329597i	$0.893087\pi$
$180$	1480.07	−	4106.20i	0.612876	−	1.70032i
$181$	−815.347	+	815.347i	−0.334830	+	0.334830i	−0.854417	−	0.519587i	$-0.826086\pi$
$181$	−815.347	+	815.347i	−0.334830	+	0.334830i	0.519587	+	0.854417i	$0.326086\pi$
$182$	−895.897	+	3343.53i	−0.364881	+	1.36175i
$183$	212.059	−	676.236i	0.0856605	−	0.273163i
$184$	−231.462	+	62.0201i	−0.0927370	+	0.0248488i
$185$	4782.05	+	2760.92i	1.90045	+	1.09722i
$186$	−1027.99	−	1118.35i	−0.405247	−	0.440869i
$187$	−831.109	+	1414.40i	−0.325009	+	0.553106i
$188$	1553.58			0.602695
$189$	576.119	−	1409.46i	0.221728	−	0.542452i
$190$	1820.79	+	1820.79i	0.695233	+	0.695233i
$191$	199.260	+	345.128i	0.0754866	+	0.130747i	0.901298	−	0.433200i	$-0.142616\pi$
$191$	199.260	+	345.128i	0.0754866	+	0.130747i	−0.825811	+	0.563947i	$0.809282\pi$
$192$	123.272	−	2928.03i	0.0463355	−	1.10059i
$193$	−1066.40	−	3979.87i	−0.397728	−	1.48434i	−0.817084	−	0.576518i	$-0.804411\pi$
$193$	−1066.40	−	3979.87i	−0.397728	−	1.48434i	0.419357	−	0.907821i	$-0.362256\pi$
$194$	120.135	+	448.349i	0.0444597	+	0.165926i
$195$	7494.93	+	2350.32i	2.75243	+	0.863127i
$196$	−1641.76	+	947.869i	−0.598308	+	0.345433i
$197$	837.378	−	837.378i	0.302846	−	0.302846i	−0.539280	−	0.842126i	$-0.681304\pi$
$197$	837.378	−	837.378i	0.302846	−	0.302846i	0.842126	+	0.539280i	$0.181304\pi$
$198$	2520.20	−	452.477i	0.904560	−	0.162405i
$199$	3089.11	+	3089.11i	1.10041	+	1.10041i	0.994361	+	0.106047i	$0.0338193\pi$
$199$	3089.11	+	3089.11i	1.10041	+	1.10041i	0.106047	+	0.994361i	$0.466181\pi$
$200$	−206.338	−	357.388i	−0.0729515	−	0.126356i
$201$	−4486.98	−	2848.71i	−1.57456	−	0.999664i
$202$	6222.21	+	3592.39i	2.16729	+	1.25129i
$203$	962.814	−	1667.64i	0.332888	−	0.576579i
$204$	−2272.97	+	2057.42i	−0.780097	+	0.706120i
$205$	−1743.13	−	3019.19i	−0.593880	−	1.02863i
$206$		−	7351.98i		−	2.48658i
$207$	675.506	+	3762.42i	0.226816	+	1.26332i
$208$	4760.87			1.58705
$209$	−200.453	+	748.102i	−0.0663428	+	0.247595i
$210$	−2032.38	−	3889.37i	−0.667846	−	1.27806i
$211$	875.741	+	3268.31i	0.285728	+	1.06635i	0.948306	+	0.317357i	$0.102795\pi$
$211$	875.741	+	3268.31i	0.285728	+	1.06635i	−0.662578	+	0.748993i	$0.730538\pi$
$212$	587.883	+	339.414i	0.190453	+	0.109958i
$213$	−2184.86	+	2008.32i	−0.702836	+	0.646047i
$214$	−1700.23	−	455.575i	−0.543109	−	0.145526i
$215$	3855.81	−	3855.81i	1.22309	−	1.22309i
$216$	235.570	+	29.8944i	0.0742059	+	0.00941692i
$217$	−783.049			−0.244962
$218$	961.401	−	3588.00i	0.298689	−	1.11472i
$219$	1433.42	−	1317.60i	0.442290	−	0.406553i
$220$	1891.80	−	3276.69i	0.579750	−	1.00416i
$221$	−3871.28	−	3931.03i	−1.17833	−	1.19651i
$222$	−1811.37	+	5776.27i	−0.547617	+	1.74630i
$223$	3382.91	−	1953.12i	1.01586	−	0.586506i	0.102957	−	0.994686i	$-0.467170\pi$
$223$	3382.91	−	1953.12i	1.01586	−	0.586506i	0.912902	+	0.408180i	$0.133836\pi$
$224$	−1984.69	−	1984.69i	−0.592000	−	0.592000i
$225$	−5957.62	+	2800.71i	−1.76522	+	0.829839i
$226$	−4977.82	−	4977.82i	−1.46513	−	1.46513i
$227$	375.944	+	100.734i	0.109922	+	0.0294535i	0.313361	−	0.949634i	$-0.398545\pi$
$227$	375.944	+	100.734i	0.109922	+	0.0294535i	−0.203439	+	0.979088i	$0.565212\pi$
$228$	−775.787	+	1221.94i	−0.225341	+	0.354933i
$229$	3331.70	+	1923.56i	0.961420	+	0.555076i	0.896610	−	0.442821i	$-0.146022\pi$
$229$	3331.70	+	1923.56i	0.961420	+	0.555076i	0.0648103	+	0.997898i	$0.479356\pi$
$230$	9540.84	+	5508.41i	2.73524	+	1.57919i
$231$	707.452	−	1114.30i	0.201502	−	0.317384i
$232$	290.069	+	77.7237i	0.0820860	+	0.0219949i
$233$	2702.99	+	2702.99i	0.759995	+	0.759995i	0.976321	−	0.216326i	$-0.0694075\pi$
$233$	2702.99	+	2702.99i	0.759995	+	0.759995i	−0.216326	+	0.976321i	$0.569408\pi$
$234$	−723.800	+	8580.81i	−0.202206	+	2.39720i
$235$	−2506.29	−	2506.29i	−0.695711	−	0.695711i
$236$	−1745.62	+	1007.83i	−0.481484	+	0.277985i
$237$	1311.37	−	4181.83i	0.359421	−	1.14616i
$238$	−23.6064	+	3082.30i	−0.00642930	+	0.839479i
$239$	1672.53	−	2896.90i	0.452665	−	0.784038i	−0.545886	−	0.837859i	$-0.683807\pi$
$239$	1672.53	−	2896.90i	0.452665	−	0.784038i	0.998551	+	0.0538214i	$0.0171402\pi$
$240$	−4443.62	+	4084.58i	−1.19514	+	1.09858i
$241$	1100.72	−	4107.96i	0.294207	−	1.09800i	−0.647638	−	0.761948i	$-0.724243\pi$
$241$	1100.72	−	4107.96i	0.294207	−	1.09800i	0.941845	−	0.336048i	$-0.109090\pi$
$242$	−3173.50			−0.842977
$243$	791.051	−	3704.48i	0.208831	−	0.977952i
$244$	811.828	−	811.828i	0.213000	−	0.213000i
$245$	4177.67	+	1119.40i	1.08939	+	0.291902i
$246$	2813.85	−	2586.49i	0.729287	−	0.670361i
$247$	−2255.75	−	1302.36i	−0.581093	−	0.335494i
$248$	−31.6060	−	117.955i	−0.00809267	−	0.0302023i
$249$	−1865.80	−	3570.58i	−0.474861	−	0.908741i
$250$	−2393.00	+	8930.79i	−0.605386	+	2.25933i
$251$	−980.160			−0.246483			−0.123241	−	0.992377i	$-0.539329\pi$
$251$	−980.160			−0.246483			−0.123241	+	0.992377i	$0.539329\pi$
$252$	1884.65	−	1591.44i	0.471119	−	0.397823i
$253$			3313.58i			0.823411i
$254$	−590.994	−	1023.63i	−0.145993	−	0.252868i
$255$	6985.93	+	347.728i	1.71559	+	0.0853944i
$256$	−1817.68	+	3148.32i	−0.443770	+	0.768632i
$257$	2850.77	+	1645.90i	0.691932	+	0.399487i	0.804335	−	0.594176i	$-0.202522\pi$
$257$	2850.77	+	1645.90i	0.691932	+	0.399487i	−0.112404	+	0.993663i	$0.535855\pi$
$258$	5046.87	+	3204.17i	1.21785	+	0.773190i
$259$	1560.29	+	2702.50i	0.374331	+	0.648360i
$260$	8997.74	+	8997.74i	2.14621	+	2.14621i
$261$	1624.41	−	4506.65i	0.385243	−	1.06879i
$262$	−3430.31	+	3430.31i	−0.808875	+	0.808875i
$263$	3352.82	−	1935.75i	0.786097	−	0.453854i	−0.0524895	−	0.998621i	$-0.516716\pi$
$263$	3352.82	−	1935.75i	0.786097	−	0.453854i	0.838587	+	0.544768i	$0.183382\pi$
$264$	196.409	+	61.5913i	0.0457883	+	0.0143587i
$265$	−400.837	−	1495.95i	−0.0929179	−	0.346774i
$266$	376.638	+	1405.63i	0.0868163	+	0.324003i
$267$	−126.439	+	3003.24i	−0.0289809	+	0.688371i
$268$	−4305.04	−	7456.56i	−0.981241	−	1.69956i
$269$	−1464.30	−	1464.30i	−0.331896	−	0.331896i	0.521410	−	0.853306i	$-0.325406\pi$
$269$	−1464.30	−	1464.30i	−0.331896	−	0.331896i	−0.853306	+	0.521410i	$0.825406\pi$
$270$	−6686.32	−	8629.99i	−1.50710	−	1.94520i
$271$	4854.01			1.08804			0.544022	−	0.839071i	$-0.316901\pi$
$271$	4854.01			1.08804			0.544022	+	0.839071i	$0.316901\pi$
$272$	4103.30	−	1065.86i	0.914703	−	0.237601i
$273$	3004.05	+	3268.12i	0.665984	+	0.724525i
$274$	−5813.63	−	3356.50i	−1.28180	−	0.740050i
$275$	−5512.06	+	1476.95i	−1.20869	+	0.323868i
$276$	−1852.94	+	5908.83i	−0.404108	+	1.28866i
$277$	−289.306	+	1079.71i	−0.0627536	+	0.234199i	−0.990178	−	0.139810i	$-0.955351\pi$
$277$	−289.306	+	1079.71i	−0.0627536	+	0.234199i	0.927425	+	0.374010i	$0.122017\pi$
$278$	−1311.98	+	1311.98i	−0.283047	+	0.283047i
$279$	−1917.37	+	344.244i	−0.411433	+	0.0738687i
$280$		−	352.782i		−	0.0752957i
$281$	−2589.64	+	1495.13i	−0.549769	+	0.317410i	−0.749029	−	0.662537i	$-0.769480\pi$
$281$	−2589.64	+	1495.13i	−0.549769	+	0.317410i	0.199260	+	0.979947i	$0.436146\pi$
$282$	2082.72	−	3280.48i	0.439802	−	0.692730i
$283$	−918.834	−	3429.14i	−0.193000	−	0.720286i	−0.992775	−	0.119987i	$-0.961715\pi$
$283$	−918.834	−	3429.14i	−0.193000	−	0.720286i	0.799775	−	0.600299i	$-0.204952\pi$
$284$	−4643.76	+	1244.29i	−0.970269	+	0.259983i
$285$	3222.79	−	719.743i	0.669830	−	0.149593i
$286$	−1931.99	+	7210.27i	−0.399443	+	1.49074i
$287$		−	1970.20i		−	0.405217i
$288$	−5732.22	−	3987.20i	−1.17283	−	0.815791i
$289$	−4216.66	−	2521.38i	−0.858266	−	0.513206i
$290$	−6903.15	−	11956.6i	−1.39782	−	2.42109i
$291$	567.976	+	178.110i	0.114417	+	0.0358798i
$292$	3046.63	−	816.341i	0.610583	−	0.163605i
$293$	1040.76	−	1802.66i	0.207516	−	0.359428i	−0.743416	−	0.668830i	$-0.766796\pi$
$293$	1040.76	−	1802.66i	0.207516	−	0.359428i	0.950931	+	0.309402i	$0.100129\pi$
$294$	−199.447	+	4737.37i	−0.0395646	+	0.939759i
$295$	4441.96	+	1190.22i	0.876680	+	0.234906i
$296$	−344.116	+	344.116i	−0.0675720	+	0.0675720i
$297$	1242.39	−	3039.48i	0.242730	−	0.593834i
$298$			9459.47i			1.83883i
$299$	−10764.3	−	2884.28i	−2.08199	−	0.557866i
$300$	−10655.1	−	448.589i	−2.05058	−	0.0863309i
$301$	2976.64	−	797.588i	0.570002	−	0.152732i
$302$	−4816.25	+	8341.99i	−0.917696	+	1.58950i
$303$	8166.11	−	4267.19i	1.54829	−	0.809054i
$304$	1733.33	−	1000.74i	0.327018	−	0.188804i
$305$	−2619.33			−0.491746
$306$	1297.24	+	7557.68i	0.242348	+	1.41191i
$307$	−6502.82			−1.20891			−0.604455	−	0.796639i	$-0.706609\pi$
$307$	−6502.82			−1.20891			−0.604455	+	0.796639i	$0.706609\pi$
$308$	1851.77	−	1069.12i	0.342579	−	0.197788i
$309$	−7959.56	−	5053.39i	−1.46538	−	0.930347i
$310$	−2807.14	+	4862.10i	−0.514305	+	0.890803i
$311$	1697.82	−	454.931i	0.309565	−	0.0829478i	−0.100692	−	0.994918i	$-0.532106\pi$
$311$	1697.82	−	454.931i	0.309565	−	0.0829478i	0.410257	+	0.911970i	$0.365439\pi$
$312$	−371.044	+	584.428i	−0.0673276	+	0.106047i
$313$	−2201.28	−	589.831i	−0.397520	−	0.106515i	0.0545204	−	0.998513i	$-0.482637\pi$
$313$	−2201.28	−	589.831i	−0.397520	−	0.106515i	−0.452040	+	0.891998i	$0.649304\pi$
$314$			7434.91i			1.33623i
$315$	−5607.75	−	473.019i	−1.00305	−	0.0846083i
$316$	5020.33	−	5020.33i	0.893720	−	0.893720i
$317$	4057.66	+	1087.25i	0.718929	+	0.192637i	0.599694	−	0.800229i	$-0.295289\pi$
$317$	4057.66	+	1087.25i	0.718929	+	0.192637i	0.119235	+	0.992866i	$0.461956\pi$
$318$	1504.81	−	786.333i	0.265363	−	0.138665i
$319$	2076.29	−	3596.24i	0.364420	−	0.631194i
$320$	−10462.3	+	2803.37i	−1.82770	+	0.489729i
$321$	−1661.88	+	1527.60i	−0.288963	+	0.265615i
$322$	3112.99	+	5391.86i	0.538758	+	0.933157i
$323$	−2235.76	−	617.460i	−0.385142	−	0.106367i
$324$	3915.12	−	4725.33i	0.671317	−	0.810241i
$325$		−	19191.7i		−	3.27558i
$326$	2720.32	−	10152.4i	0.462161	−	1.72481i
$327$	−3223.70	−	3507.07i	−0.545170	−	0.593092i
$328$	296.783	−	79.5228i	0.0499607	−	0.0133869i
$329$	−518.435	−	1934.82i	−0.0868761	−	0.324226i
$330$	−4382.79	−	8387.35i	−0.731105	−	1.39912i
$331$	−780.873	+	450.837i	−0.129670	+	0.0748648i	−0.563432	−	0.826163i	$-0.690519\pi$
$331$	−780.873	+	450.837i	−0.129670	+	0.0748648i	0.433762	+	0.901027i	$0.357186\pi$
$332$		−	6526.43i		−	1.07887i
$333$	5008.59	+	5931.38i	0.824231	+	0.976090i
$334$	−4346.93	+	4346.93i	−0.712136	+	0.712136i
$335$	−5084.12	+	18974.2i	−0.829179	+	3.09454i
$336$	−3328.97	+	743.455i	−0.540506	+	0.120711i
$337$	−9634.53	+	2581.57i	−1.55735	+	0.417290i	−0.931823	−	0.362913i	$-0.881782\pi$
$337$	−9634.53	+	2581.57i	−1.55735	+	0.417290i	−0.625526	+	0.780204i	$0.715115\pi$
$338$	−14031.8	−	8101.25i	−2.25807	−	1.30370i
$339$	−8810.70	+	1967.69i	−1.41160	+	0.315251i
$340$	9769.39	+	5740.56i	1.55829	+	0.915664i
$341$	−1688.63			−0.268166
$342$	1540.18	+	3276.24i	0.243518	+	0.518008i
$343$	4360.64	+	4360.64i	0.686450	+	0.686450i
$344$	240.291	+	416.196i	0.0376617	+	0.0652319i
$345$	12521.5	−	6543.10i	1.95402	−	1.02107i
$346$	−2105.38	−	7857.40i	−0.327128	−	1.22086i
$347$	1381.83	+	5157.08i	0.213777	+	0.797828i	0.986593	+	0.163198i	$0.0521809\pi$
$347$	1381.83	+	5157.08i	0.213777	+	0.797828i	−0.772816	+	0.634630i	$0.781152\pi$
$348$	5713.48	−	5251.84i	0.880100	−	0.808988i
$349$	5823.80	−	3362.37i	0.893241	−	0.515713i	0.0182395	−	0.999834i	$-0.494194\pi$
$349$	5823.80	−	3362.37i	0.893241	−	0.515713i	0.875001	+	0.484121i	$0.160861\pi$
$350$	−7581.69	+	7581.69i	−1.15788	+	1.15788i
$351$	8792.43	+	6681.64i	1.33705	+	1.01607i
$352$	−4279.96	−	4279.96i	−0.648076	−	0.648076i
$353$	−3577.36	−	6196.17i	−0.539387	−	0.934246i	−0.998937	−	0.0460941i	$-0.985323\pi$
$353$	−3577.36	−	6196.17i	−0.539387	−	0.934246i	0.459550	−	0.888152i	$-0.348011\pi$
$354$	−212.065	+	5037.07i	−0.0318393	+	0.756264i
$355$	9498.79	+	5484.13i	1.42012	+	0.819908i
$356$	−2434.76	+	4217.13i	−0.362478	+	0.627830i
$357$	3320.80	+	2144.18i	0.492312	+	0.317877i
$358$	3198.30	+	5539.62i	0.472166	+	0.817815i
$359$			3549.12i			0.521770i	0.965370	+	0.260885i	$0.0840144\pi$
$359$			3549.12i			0.521770i	−0.965370	+	0.260885i	$0.915986\pi$
$360$	−155.090	−	863.820i	−0.0227055	−	0.126465i
$361$	5763.97			0.840351
$362$	−1209.23	+	4512.92i	−0.175569	+	0.655232i
$363$	−2181.31	+	3435.77i	−0.315397	+	0.496780i
$364$	1861.21	+	6946.14i	0.268006	+	1.00021i
$365$	−6231.86	−	3597.97i	−0.893673	−	0.515962i
$366$	−625.891	−	2802.55i	−0.0893876	−	0.400251i
$367$	2703.07	+	724.286i	0.384466	+	0.103017i	0.445875	−	0.895095i	$-0.352893\pi$
$367$	2703.07	+	724.286i	0.384466	+	0.103017i	−0.0614086	+	0.998113i	$0.519559\pi$
$368$	6055.04	−	6055.04i	0.857719	−	0.857719i
$369$	−866.142	−	4824.22i	−0.122194	−	0.680594i
$370$	22373.8			3.14367
$371$	226.527	−	845.410i	0.0317000	−	0.118306i
$372$	−3011.20	−	944.274i	−0.419686	−	0.131608i
$373$	−2988.71	+	5176.60i	−0.414878	+	0.718590i	−0.995416	−	0.0956435i	$-0.969509\pi$
$373$	−2988.71	+	5176.60i	−0.414878	+	0.718590i	0.580538	+	0.814233i	$0.302842\pi$
$374$	−50.9067	+	6646.93i	−0.00703829	+	0.918996i
$375$	8024.02	+	8729.35i	1.10496	+	1.20208i
$376$	270.529	−	156.190i	0.0371049	−	0.0214225i
$377$	9875.22	+	9875.22i	1.34907	+	1.34907i
$378$	−833.869	−	6113.03i	−0.113465	−	0.831800i
$379$	1995.36	+	1995.36i	0.270435	+	0.270435i	0.829275	−	0.558840i	$-0.188754\pi$
$379$	1995.36	+	1995.36i	0.270435	+	0.270435i	−0.558840	+	0.829275i	$0.688754\pi$
$380$	5167.23	+	1384.55i	0.697561	+	0.186911i
$381$	−1514.45	−	63.7594i	−0.203642	−	0.00857347i
$382$	1398.42	+	807.377i	0.187302	+	0.108139i
$383$	9413.48	+	5434.87i	1.25589	+	0.725089i	0.972273	−	0.233848i	$-0.0751319\pi$
$383$	9413.48	+	5434.87i	1.25589	+	0.725089i	0.283618	+	0.958937i	$0.408465\pi$
$384$	−520.648	−	996.365i	−0.0691907	−	0.132410i
$385$	−4712.07	−	1262.60i	−0.623765	−	0.167137i
$386$	−11805.0	−	11805.0i	−1.55663	−	1.55663i
$387$	6937.94	−	3261.56i	0.911306	−	0.428410i
$388$	681.861	+	681.861i	0.0892171	+	0.0892171i
$389$	−4938.48	+	2851.23i	−0.643678	+	0.371628i	−0.786030	−	0.618188i	$-0.787867\pi$
$389$	−4938.48	+	2851.23i	−0.643678	+	0.371628i	0.142352	+	0.989816i	$0.454534\pi$
$390$	31061.5	−	6936.95i	4.03298	−	0.900682i
$391$	−9923.25	−	75.9990i	−1.28348	−	0.00982975i
$392$	−190.588	+	330.109i	−0.0245565	+	0.0425332i
$393$	1355.97	+	6071.62i	0.174045	+	0.779320i
$394$	1241.91	−	4634.86i	0.158798	−	0.592642i
$395$	−16197.9			−2.06330
$396$	4064.22	−	3431.92i	0.515745	−	0.435506i
$397$	−3156.33	+	3156.33i	−0.399022	+	0.399022i	−0.877888	−	0.478866i	$-0.841048\pi$
$397$	−3156.33	+	3156.33i	−0.399022	+	0.399022i	0.478866	+	0.877888i	$0.341048\pi$
$398$	17098.1	+	4581.43i	2.15340	+	0.577001i
$399$	1780.68	+	558.398i	0.223422	+	0.0700623i
$400$	12771.3	+	7373.52i	1.59641	+	0.921690i
$401$	−1591.74	−	5940.44i	−0.198223	−	0.739779i	−0.991409	−	0.130799i	$-0.958246\pi$
$401$	−1591.74	−	5940.44i	−0.198223	−	0.739779i	0.793186	−	0.608980i	$-0.208421\pi$
$402$	−21516.3	−	905.851i	−2.66949	−	0.112387i
$403$	1469.85	−	5485.57i	0.181684	−	0.678054i
$404$	14926.3			1.83815
$405$	−13939.0	+	1307.05i	−1.71021	+	0.160365i
$406$		−	7802.41i		−	0.953762i
$407$	3364.74	+	5827.89i	0.409788	+	0.709774i
$408$	−188.954	+	586.777i	−0.0229279	+	0.0712005i
$409$	1259.75	−	2181.95i	0.152300	−	0.263791i	−0.779773	−	0.626063i	$-0.784665\pi$
$409$	1259.75	−	2181.95i	0.152300	−	0.263791i	0.932073	+	0.362272i	$0.117999\pi$
$410$	−12233.4	−	7062.94i	−1.47357	−	0.850765i
$411$	−7629.89	+	3986.98i	−0.915705	+	0.478500i
$412$	−7636.81	−	13227.3i	−0.913201	−	1.58171i
$413$	1837.67	+	1837.67i	0.218949	+	0.218949i
$414$	9992.82	+	11833.9i	1.18628	+	1.40484i
$415$	−10528.6	+	10528.6i	−1.24538	+	1.24538i
$416$	17629.0	−	10178.1i	2.07773	−	1.19958i
$417$	518.612	+	2322.19i	0.0609030	+	0.272705i
$418$	812.212	+	3031.22i	0.0950397	+	0.354693i
$419$	−1942.27	−	7248.65i	−0.226458	−	0.845154i	−0.981815	−	0.189840i	$-0.939203\pi$
$419$	−1942.27	−	7248.65i	−0.226458	−	0.845154i	0.755357	−	0.655314i	$-0.227464\pi$
$420$	−7696.62	−	4886.45i	−0.894182	−	0.567701i
$421$	−2277.77	−	3945.22i	−0.263686	−	0.456718i	0.703532	−	0.710663i	$-0.251605\pi$
$421$	−2277.77	−	3945.22i	−0.263686	−	0.456718i	−0.967219	+	0.253945i	$0.918272\pi$
$422$	9694.40	+	9694.40i	1.11828	+	1.11828i
$423$	−2120.02	−	4509.68i	−0.243686	−	0.518365i
$424$	136.492			0.0156336
$425$	−4296.64	−	16541.0i	−0.490395	−	1.88789i
$426$	−3597.99	+	11473.7i	−0.409210	+	1.30493i
$427$	−1281.96	−	740.138i	−0.145288	−	0.0838824i
$428$	−3532.21	+	946.452i	−0.398915	+	0.106889i
$429$	6478.19	+	7047.64i	0.729067	+	0.793154i
$430$	5718.52	−	21341.8i	0.641329	−	2.39347i
$431$	2678.92	−	2678.92i	0.299395	−	0.299395i	−0.541382	−	0.840777i	$-0.682099\pi$
$431$	2678.92	−	2678.92i	0.299395	−	0.299395i	0.840777	+	0.541382i	$0.182099\pi$
$432$	−7824.45	+	3283.90i	−0.871421	+	0.365733i
$433$			1482.15i			0.164498i	0.996612	+	0.0822491i	$0.0262103\pi$
$433$			1482.15i			0.164498i	−0.996612	+	0.0822491i	$0.973790\pi$
$434$	−2747.74	+	1586.41i	−0.303907	+	0.175461i
$435$	−17689.6	−	744.746i	−1.94977	−	0.0820870i
$436$	−1997.30	−	7454.01i	−0.219388	−	0.818767i
$437$	−4525.33	+	1212.56i	−0.495368	+	0.132733i
$438$	2360.53	−	7527.51i	0.257513	−	0.821184i
$439$	1365.13	−	5094.75i	0.148415	−	0.553893i	−0.851164	−	0.524899i	$-0.824103\pi$
$439$	1365.13	−	5094.75i	0.148415	−	0.553893i	0.999580	−	0.0289938i	$-0.00923030\pi$
$440$		−	760.769i		−	0.0824278i
$441$	4991.79	+	3472.17i	0.539012	+	0.374923i
$442$	−21548.5	−	5951.14i	−2.31890	−	0.640422i
$443$	−3515.90	−	6089.72i	−0.377078	−	0.653118i	0.613558	−	0.789650i	$-0.289738\pi$
$443$	−3515.90	−	6089.72i	−0.377078	−	0.653118i	−0.990636	+	0.136531i	$0.956405\pi$
$444$	2741.13	+	12274.0i	0.292992	+	1.31193i
$445$	10731.0	−	2875.38i	1.14315	−	0.306305i
$446$	7913.82	−	13707.1i	0.840203	−	1.45527i
$447$	10241.2	+	6501.98i	1.08365	+	0.687993i
$448$	−5912.63	−	1584.28i	−0.623539	−	0.167077i
$449$	−766.789	+	766.789i	−0.0805947	+	0.0805947i	−0.746255	−	0.665660i	$-0.768150\pi$
$449$	−766.789	+	766.789i	−0.0805947	+	0.0805947i	0.665660	+	0.746255i	$0.268150\pi$
$450$	−15231.4	+	21897.5i	−1.59559	+	2.29391i
$451$		−	4248.71i		−	0.443601i
$452$	−14126.5	−	3785.20i	−1.47004	−	0.393895i
$453$	5720.93	+	10948.2i	0.593362	+	1.13552i
$454$	1523.28	−	408.161i	0.157469	−	0.0421937i
$455$	8203.17	−	14208.3i	0.845210	−	1.46395i
$456$	−12.2417	+	290.772i	−0.00125717	+	0.0298611i
$457$	−5488.29	+	3168.67i	−0.561776	+	0.324341i	−0.753858	−	0.657038i	$-0.771809\pi$
$457$	−5488.29	+	3168.67i	−0.561776	+	0.324341i	0.192082	+	0.981379i	$0.438476\pi$
$458$	15588.1			1.59035
$459$	9073.92	+	3790.33i	0.922732	+	0.385441i
$460$	22887.3			2.31984
$461$	−11211.4	+	6472.91i	−1.13268	+	0.653956i	−0.944609	−	0.328199i	$-0.893558\pi$
$461$	−11211.4	+	6472.91i	−1.13268	+	0.653956i	−0.188076	+	0.982154i	$0.560225\pi$
$462$	224.960	−	5343.38i	0.0226539	−	0.538087i
$463$	4385.38	−	7595.70i	0.440185	−	0.762423i	−0.557518	−	0.830165i	$-0.688246\pi$
$463$	4385.38	−	7595.70i	0.440185	−	0.762423i	0.997703	+	0.0677418i	$0.0215794\pi$
$464$	−10365.7	+	2777.47i	−1.03710	+	0.277890i
$465$	3334.43	+	6381.09i	0.332538	+	0.636379i
$466$	14961.0	+	4008.78i	1.48724	+	0.398505i
$467$		−	11548.7i		−	1.14435i	−0.820131	−	0.572175i	$-0.806100\pi$
$467$		−	11548.7i		−	1.14435i	0.820131	−	0.572175i	$-0.193900\pi$
$468$	7611.02	+	16190.0i	0.751751	+	1.59911i
$469$	−7849.76	+	7849.76i	−0.772853	+	0.772853i
$470$	−13872.2	−	3717.05i	−1.36144	−	0.364797i
$471$	8049.34	+	5110.39i	0.787461	+	0.499946i
$472$	−202.645	+	350.992i	−0.0197617	+	0.0342282i
$473$	6419.07	−	1719.99i	0.623994	−	0.167199i
$474$	−3870.50	−	17330.9i	−0.375059	−	1.67940i
$475$	−4034.12	−	6987.31i	−0.389681	−	0.674947i
$476$	3159.25	+	5570.06i	0.304210	+	0.536352i
$477$	183.012	−	2169.65i	0.0175672	−	0.208263i
$478$		−	13553.8i		−	1.29693i
$479$	2903.12	−	10834.6i	0.276925	−	1.03350i	−0.677615	−	0.735416i	$-0.736987\pi$
$479$	2903.12	−	10834.6i	0.276925	−	1.03350i	0.954540	−	0.298082i	$-0.0963467\pi$
$480$	−7722.00	+	24624.7i	−0.734290	+	2.34158i
$481$	−21860.9	+	5857.61i	−2.07229	+	0.555268i
$482$	−4460.00	−	16645.0i	−0.421468	−	1.57294i
$483$	7977.17	+	335.845i	0.751498	+	0.0316386i
$484$	−5709.63	+	3296.45i	−0.536216	+	0.309584i
$485$		−	2200.00i		−	0.205973i
$486$	−4729.22	−	14601.7i	−0.441403	−	1.36286i
$487$	−6611.29	+	6611.29i	−0.615167	+	0.615167i	−0.944288	−	0.329121i	$-0.893248\pi$
$487$	−6611.29	+	6611.29i	−0.615167	+	0.615167i	0.329121	+	0.944288i	$0.393248\pi$
$488$	59.7480	−	222.983i	0.00554234	−	0.0206843i
$489$	−9121.55	−	9923.36i	−0.843540	−	0.917689i
$490$	16927.4	−	4535.68i	1.56062	−	0.418166i
$491$	9935.94	+	5736.52i	0.913244	+	0.527261i	0.881473	−	0.472234i	$-0.156552\pi$
$491$	9935.94	+	5736.52i	0.913244	+	0.527261i	0.0317703	+	0.999495i	$0.489886\pi$
$492$	2375.86	−	7576.38i	0.217707	−	0.694247i
$493$	10722.1	+	6300.40i	0.979514	+	0.575570i
$494$	−10554.0			−0.961228
$495$	−12093.0	−	1020.06i	−1.09806	−	0.0926226i
$496$	3085.70	+	3085.70i	0.279339	+	0.279339i
$497$	3099.27	+	5368.09i	0.279721	+	0.484491i
$498$	−13780.9	−	8749.28i	−1.24004	−	0.787279i
$499$	299.350	+	1117.19i	0.0268552	+	0.100225i	0.978053	−	0.208358i	$-0.0668119\pi$
$499$	299.350	+	1117.19i	0.0268552	+	0.100225i	−0.951197	+	0.308583i	$0.900145\pi$
$500$	4971.42	+	18553.6i	0.444657	+	1.65948i
$501$	1718.30	+	7694.04i	0.153230	+	0.686116i
$502$	−3439.41	+	1985.74i	−0.305794	+	0.176550i
$503$	12435.0	−	12435.0i	1.10228	−	1.10228i	0.108145	−	0.994135i	$-0.465509\pi$
$503$	12435.0	−	12435.0i	1.10228	−	1.10228i	0.994135	−	0.108145i	$-0.0344912\pi$
$504$	168.183	−	466.595i	0.0148640	−	0.0412377i
$505$	−24079.6	−	24079.6i	−2.12183	−	2.12183i
$506$	6713.11	+	11627.4i	0.589791	+	1.02155i
$507$	−18415.5	+	9622.99i	−1.61314	+	0.842943i
$508$	−2126.58	−	1227.78i	−0.185732	−	0.107232i
$509$	5172.82	−	8959.59i	0.450454	−	0.780210i	−0.547960	−	0.836505i	$-0.684595\pi$
$509$	5172.82	−	8959.59i	0.450454	−	0.780210i	0.998414	+	0.0562947i	$0.0179286\pi$
$510$	25218.3	−	12932.9i	2.18958	−	1.12290i
$511$	−2033.34	−	3521.84i	−0.176026	−	0.304887i
$512$			16460.9i			1.42085i
$513$	4605.63	+	584.466i	0.396381	+	0.0503018i
$514$	13337.9			1.14457
$515$	−9018.83	+	33658.7i	−0.771684	+	2.87996i
$516$	12408.4	+	522.404i	1.05862	+	0.0445689i
$517$	−1118.00	−	4172.42i	−0.0951052	−	0.354937i
$518$	10950.2	+	6322.10i	0.928811	+	0.536249i
$519$	−9953.89	−	3121.42i	−0.841864	−	0.263998i
$520$	2471.38	+	662.205i	0.208418	+	0.0558454i
$521$	12624.5	−	12624.5i	1.06160	−	1.06160i	0.0636210	−	0.997974i	$-0.479735\pi$
$521$	12624.5	−	12624.5i	1.06160	−	1.06160i	0.997974	−	0.0636210i	$-0.0202649\pi$
$522$	−3430.10	−	19104.9i	−0.287608	−	1.60192i
$523$	−9432.32			−0.788617			−0.394308	−	0.918978i	$-0.629016\pi$
$523$	−9432.32			−0.788617			−0.394308	+	0.918978i	$0.629016\pi$
$524$	−2608.45	+	9734.87i	−0.217463	+	0.811583i
$525$	2996.97	+	13419.5i	0.249140	+	1.11557i
$526$	7843.43	−	13585.2i	0.650170	−	1.12613i
$527$	38.7298	−	5056.98i	0.00320132	−	0.417999i
$528$	−7178.86	+	1603.25i	−0.591704	+	0.132145i
$529$	−6821.76	+	3938.55i	−0.560678	+	0.323707i
$530$	−4437.25	−	4437.25i	−0.363663	−	0.363663i
$531$	5307.58	+	3691.83i	0.433765	+	0.301717i
$532$	2137.72	+	2137.72i	0.174214	+	0.174214i
$533$	13802.1	+	3698.25i	1.12164	+	0.300542i
$534$	5640.70	+	10794.6i	0.457110	+	0.874772i
$535$	7225.11	+	4171.42i	0.583867	+	0.337096i
$536$	−1499.29	−	865.617i	−0.120820	−	0.0697555i
$537$	8195.77	+	345.048i	0.658610	+	0.0277280i
$538$	−8104.87	−	2171.69i	−0.649490	−	0.174030i
$539$	3727.11	+	3727.11i	0.297844	+	0.297844i
$540$	−20994.1	−	8581.34i	−1.67304	−	0.683856i
$541$	16598.2	+	16598.2i	1.31906	+	1.31906i	0.914522	+	0.404536i	$0.132567\pi$
$541$	16598.2	+	16598.2i	1.31906	+	1.31906i	0.404536	+	0.914522i	$0.367433\pi$
$542$	17032.9	−	9833.92i	1.34986	−	0.779342i
$543$	4054.71	+	4411.13i	0.320450	+	0.348618i
$544$	12915.5	−	12719.1i	1.01791	−	1.00244i
$545$	−8802.95	+	15247.2i	−0.691884	+	1.19838i
$546$	17162.3	+	5381.89i	1.34520	+	0.421838i
$547$	−5312.13	+	19825.1i	−0.415229	+	1.54966i	0.369147	+	0.929371i	$0.379650\pi$
$547$	−5312.13	+	19825.1i	−0.415229	+	1.54966i	−0.784376	+	0.620286i	$0.787017\pi$
$548$	−13946.2			−1.08714
$549$	−3464.37	−	1248.72i	−0.269318	−	0.0970749i
$550$	−16349.8	+	16349.8i	−1.26756	+	1.26756i
$551$	5671.15	+	1519.58i	0.438474	+	0.117489i
$552$	271.390	+	1215.20i	0.0209260	+	0.0937001i
$553$	−7927.59	−	4577.00i	−0.609612	−	0.351960i
$554$	1172.23	+	4374.84i	0.0898980	+	0.335504i
$555$	15378.6	−	24222.8i	1.17619	−	1.85261i
$556$	−997.643	+	3723.25i	−0.0760962	+	0.283995i
$557$	−25659.8			−1.95196			−0.975978	−	0.217870i	$-0.930089\pi$
$557$	−25659.8			−1.95196			−0.975978	+	0.217870i	$0.930089\pi$
$558$	−6030.68	+	5092.43i	−0.457525	+	0.386344i
$559$			22349.7i			1.69104i
$560$	6303.37	+	10917.8i	0.475654	+	0.823856i
$561$	7161.25	+	4623.89i	0.538945	+	0.347987i
$562$	−6058.09	+	10492.9i	−0.454707	+	0.787575i
$563$	21741.1	+	12552.2i	1.62749	+	0.939631i	0.984839	+	0.173472i	$0.0554985\pi$
$563$	21741.1	+	12552.2i	1.62749	+	0.939631i	0.642650	+	0.766160i	$0.277835\pi$
$564$	339.564	−	8065.51i	0.0253515	−	0.602161i
$565$	16683.0	+	28895.8i	1.24223	+	2.15160i
$566$	−10171.4	−	10171.4i	−0.755366	−	0.755366i
$567$	−7191.39	−	3299.02i	−0.532645	−	0.244349i
$568$	−683.532	+	683.532i	−0.0504936	+	0.0504936i
$569$	−14567.9	+	8410.79i	−1.07332	+	0.619681i	−0.929086	−	0.369863i	$-0.879405\pi$
$569$	−14567.9	+	8410.79i	−1.07332	+	0.619681i	−0.144233	+	0.989544i	$0.546071\pi$
$570$	9850.71	−	9054.78i	0.723861	−	0.665373i
$571$	693.512	+	2588.22i	0.0508276	+	0.189691i	0.986672	−	0.162723i	$-0.0520276\pi$
$571$	693.512	+	2588.22i	0.0508276	+	0.189691i	−0.935844	+	0.352414i	$0.885361\pi$
$572$	4013.68	+	14979.2i	0.293392	+	1.09495i
$573$	1835.30	−	959.035i	0.133806	−	0.0699201i
$574$	−3991.51	−	6913.50i	−0.290248	−	0.502725i
$575$	−24408.7	−	24408.7i	−1.77028	−	1.77028i
$576$	−15174.1	−	1279.95i	−1.09766	−	0.0925891i
$577$	−19947.1			−1.43918			−0.719592	−	0.694397i	$-0.755671\pi$
$577$	−19947.1			−1.43918			−0.719592	+	0.694397i	$0.755671\pi$
$578$	−19904.5	−	304.903i	−1.43239	−	0.0219417i
$579$	−20894.8	+	4666.42i	−1.49976	+	0.334939i
$580$	−24839.7	−	14341.2i	−1.77830	−	1.02670i
$581$	−8127.98	+	2177.89i	−0.580388	+	0.155515i
$582$	2353.89	−	525.691i	0.167649	−	0.0374409i
$583$	488.502	−	1823.11i	0.0347027	−	0.129512i
$584$	448.444	−	448.444i	0.0317753	−	0.0317753i
$585$	13840.0	−	38396.6i	0.978140	−	2.71368i
$586$		−	8434.10i		−	0.594556i
$587$	1601.49	−	924.619i	0.112607	−	0.0650138i	−0.442639	−	0.896700i	$-0.645958\pi$
$587$	1601.49	−	924.619i	0.112607	−	0.0650138i	0.555246	+	0.831686i	$0.312624\pi$
$588$	4562.07	+	8730.44i	0.319961	+	0.612308i
$589$	−617.931	−	2306.15i	−0.0432282	−	0.161330i
$590$	17998.3	−	4822.62i	1.25589	−	0.336516i
$591$	−4164.27	−	4530.32i	−0.289840	−	0.315317i
$592$	4501.03	−	16798.1i	0.312485	−	1.16621i
$593$			9095.95i			0.629892i	0.949110	+	0.314946i	$0.101986\pi$
$593$			9095.95i			0.629892i	−0.949110	+	0.314946i	$0.898014\pi$
$594$	−1798.22	−	13182.7i	−0.124212	−	0.910590i
$595$	3889.20	−	14082.4i	0.267969	−	0.970289i
$596$	9825.96	+	17019.1i	0.675314	+	1.16968i
$597$	16712.5	−	15362.1i	1.14572	−	1.05315i
$598$	−43615.5	+	11686.7i	−2.98256	+	0.799174i
$599$	12365.2	−	21417.1i	0.843450	−	1.46090i	−0.0435111	−	0.999053i	$-0.513854\pi$
$599$	12365.2	−	21417.1i	0.843450	−	1.46090i	0.886961	−	0.461845i	$-0.152812\pi$
$600$	−1900.50	+	993.101i	−0.129312	+	0.0675719i
$601$	21485.3	+	5756.97i	1.45824	+	0.390735i	0.898882	−	0.438191i	$-0.144381\pi$
$601$	21485.3	+	5756.97i	1.45824	+	0.390735i	0.559359	+	0.828925i	$0.311047\pi$
$602$	8829.25	−	8829.25i	0.597763	−	0.597763i
$603$	−15769.9	+	22671.8i	−1.06501	+	1.53112i
$604$			20011.4i			1.34810i
$605$	14528.9	+	3893.00i	0.976336	+	0.261608i
$606$	20010.1	−	31517.7i	1.34134	−	2.11274i
$607$	3332.81	−	893.024i	0.222858	−	0.0597146i	−0.145662	−	0.989334i	$-0.546531\pi$
$607$	3332.81	−	893.024i	0.222858	−	0.0597146i	0.368520	+	0.929620i	$0.379865\pi$
$608$	4278.91	−	7411.30i	0.285416	−	0.494355i
$609$	−8447.22	−	5363.00i	−0.562067	−	0.356847i
$610$	−9191.32	+	5306.61i	−0.610075	+	0.352227i
$611$	14527.4			0.961890
$612$	10184.4	+	12249.9i	0.672681	+	0.809108i
$613$	11641.2			0.767023			0.383511	−	0.923536i	$-0.374715\pi$
$613$	11641.2			0.767023			0.383511	+	0.923536i	$0.374715\pi$
$614$	−22818.6	+	13174.3i	−1.49981	+	0.865915i
$615$	−16055.3	+	8389.64i	−1.05270	+	0.550086i
$616$	214.968	−	372.336i	0.0140606	−	0.0243537i
$617$	8136.85	−	2180.26i	0.530920	−	0.142259i	0.0166067	−	0.999862i	$-0.494714\pi$
$617$	8136.85	−	2180.26i	0.530920	−	0.142259i	0.514313	+	0.857603i	$0.328047\pi$
$618$	−38168.2	−	1606.91i	−2.48438	−	0.104594i
$619$	15817.2	+	4238.19i	1.02705	+	0.275198i	0.732738	−	0.680511i	$-0.238242\pi$
$619$	15817.2	+	4238.19i	1.02705	+	0.275198i	0.294314	+	0.955709i	$0.404909\pi$
$620$			11663.6i			0.755516i
$621$	19680.5	−	2684.58i	1.27174	−	0.173476i
$622$	5036.06	−	5036.06i	0.324642	−	0.324642i
$623$	6064.48	+	1624.97i	0.389997	+	0.104500i
$624$	1040.58	−	24716.3i	0.0667570	−	1.58565i
$625$	6672.54	−	11557.2i	0.427043	−	0.739660i
$626$	−8919.32	+	2389.92i	−0.569469	+	0.152589i
$627$	3840.00	+	1204.18i	0.244585	+	0.0766988i
$628$	7722.96	+	13376.6i	0.490732	+	0.849973i
$629$	−17530.1	+	9942.78i	−1.11124	+	0.630278i
$630$	−20636.1	+	9701.12i	−1.30502	+	0.613495i
$631$			1025.21i			0.0646800i	0.999477	+	0.0323400i	$0.0102959\pi$
$631$			1025.21i			0.0646800i	−0.999477	+	0.0323400i	$0.989704\pi$
$632$	369.480	−	1378.92i	0.0232550	−	0.0867887i
$633$	17159.0	−	3832.11i	1.07742	−	0.240620i
$634$	16441.1	−	4405.39i	1.02991	−	0.275963i
$635$	1449.97	+	5411.36i	0.0906147	+	0.338178i
$636$	1890.58	−	2977.84i	0.117872	−	0.185659i
$637$	−15351.9	+	8863.42i	−0.954888	+	0.551305i
$638$		−	16825.8i		−	1.04410i
$639$	9948.77	+	11781.8i	0.615911	+	0.729389i
$640$	−2938.00	+	2938.00i	−0.181460	+	0.181460i
$641$	6180.61	−	23066.4i	0.380842	−	1.42132i	−0.463777	−	0.885952i	$-0.653506\pi$
$641$	6180.61	−	23066.4i	0.380842	−	1.42132i	0.844618	−	0.535369i	$-0.179827\pi$
$642$	−2736.76	+	8727.27i	−0.168242	+	0.536507i
$643$	−4151.13	+	1112.29i	−0.254595	+	0.0682184i	−0.383859	−	0.923392i	$-0.625405\pi$
$643$	−4151.13	+	1112.29i	−0.254595	+	0.0682184i	0.129264	+	0.991610i	$0.458738\pi$
$644$	11201.5	+	6467.19i	0.685406	+	0.395719i
$645$	−19174.9	−	20860.4i	−1.17056	−	1.27345i
$646$	−9096.28	+	2362.83i	−0.554007	+	0.143907i
$647$	4503.53			0.273651			0.136825	−	0.990595i	$-0.456310\pi$
$647$	4503.53			0.273651			0.136825	+	0.990595i	$0.456310\pi$
$648$	206.686	−	1216.44i	0.0125299	−	0.0737441i
$649$	3962.90	+	3962.90i	0.239688	+	0.239688i
$650$	−38881.3	−	67344.3i	−2.34623	−	4.06379i
$651$	−171.150	+	4065.24i	−0.0103040	+	0.244745i
$652$	−5651.42	−	21091.4i	−0.339458	−	1.26687i
$653$	3352.08	+	12510.1i	0.200884	+	0.749708i	0.990665	+	0.136319i	$0.0435273\pi$
$653$	3352.08	+	12510.1i	0.200884	+	0.749708i	−0.789781	+	0.613388i	$0.789806\pi$
$654$	−18417.1	−	5775.39i	−1.10117	−	0.345314i
$655$	19912.6	−	11496.6i	1.18786	−	0.685814i
$656$	−7763.84	+	7763.84i	−0.462084	+	0.462084i
$657$	−6527.08	−	7729.65i	−0.387589	−	0.458999i
$658$	−5739.04	−	5739.04i	−0.340017	−	0.340017i
$659$	1192.13	+	2064.82i	0.0704684	+	0.122055i	0.899107	−	0.437730i	$-0.144217\pi$
$659$	1192.13	+	2064.82i	0.0704684	+	0.122055i	−0.828638	+	0.559784i	$0.810884\pi$
$660$	−16597.6	−	10537.6i	−0.978881	−	0.621475i
$661$	−27831.4	−	16068.5i	−1.63770	−	0.945524i	−0.981624	−	0.190825i	$-0.938884\pi$
$661$	−27831.4	−	16068.5i	−1.63770	−	0.945524i	−0.656071	−	0.754699i	$-0.727783\pi$
$662$	−1826.74	+	3164.00i	−0.107248	+	0.185759i
$663$	−21254.3	+	19238.7i	−1.24502	+	1.12695i
$664$	−656.136	−	1136.46i	−0.0383479	−	0.0664205i
$665$		−	6897.27i		−	0.402202i
$666$	29591.9	+	10666.3i	1.72172	+	0.620587i
$667$	25119.3			1.45821
$668$	−3305.46	+	12336.1i	−0.191455	+	0.714521i
$669$	−9400.35	−	17989.5i	−0.543257	−	1.03963i
$670$	20600.2	+	76881.1i	1.18785	+	4.43310i
$671$	−2764.52	−	1596.09i	−0.159051	−	0.0918279i
$672$	−10737.4	+	9869.86i	−0.616378	+	0.566574i
$673$	2179.07	+	583.880i	0.124810	+	0.0334426i	0.320683	−	0.947187i	$-0.396088\pi$
$673$	2179.07	+	583.880i	0.124810	+	0.0334426i	−0.195874	+	0.980629i	$0.562754\pi$
$674$	−28577.8	+	28577.8i	−1.63320	+	1.63320i
$675$	13237.9	+	31541.4i	0.754853	+	1.79856i
$676$	−33660.5			−1.91514
$677$	−7571.49	+	28257.2i	−0.429831	+	1.60415i	0.323309	+	0.946293i	$0.395205\pi$
$677$	−7571.49	+	28257.2i	−0.429831	+	1.60415i	−0.753141	+	0.657859i	$0.771462\pi$
$678$	−26930.6	+	24754.6i	−1.52546	+	1.40221i
$679$	621.648	−	1076.73i	0.0351350	−	0.0608556i
$680$	2278.29	+	17.4487i	0.128483	+	0.000984011i
$681$	605.134	−	1929.71i	0.0340511	−	0.108586i
$682$	−5925.46	+	3421.06i	−0.332694	+	0.192081i
$683$	−8323.07	−	8323.07i	−0.466286	−	0.466286i	0.434423	−	0.900709i	$-0.356952\pi$
$683$	−8323.07	−	8323.07i	−0.466286	−	0.466286i	−0.900709	+	0.434423i	$0.856952\pi$
$684$	6174.19	+	4294.61i	0.345140	+	0.240071i
$685$	22498.4	+	22498.4i	1.25492	+	1.25492i
$686$	24136.0	+	6467.23i	1.34332	+	0.359941i
$687$	10714.5	−	16876.3i	0.595026	−	0.937221i
$688$	−14872.8	−	8586.84i	−0.824159	−	0.475829i
$689$	5497.23	+	3173.83i	0.303959	+	0.175491i
$690$	30682.5	−	48327.8i	1.69285	−	2.66639i
$691$	−9451.27	−	2532.46i	−0.520323	−	0.139420i	−0.0109072	−	0.999941i	$-0.503472\pi$
$691$	−9451.27	−	2532.46i	−0.520323	−	0.139420i	−0.509416	+	0.860520i	$0.670139\pi$
$692$	−11949.7	−	11949.7i	−0.656446	−	0.656446i
$693$	−5630.34	−	3916.33i	−0.308627	−	0.214674i
$694$	15296.8	+	15296.8i	0.836685	+	0.836685i
$695$	7615.90	−	4397.04i	0.415666	−	0.239985i
$696$	466.907	−	1488.92i	0.0254282	−	0.0810881i
$697$	12723.7	+	97.4467i	0.691456	+	0.00529564i
$698$	13623.9	−	23597.3i	0.738787	−	1.27962i
$699$	14623.5	−	13441.9i	0.791290	−	0.727354i
$700$	−5765.21	+	21516.1i	−0.311292	+	1.16176i
$701$	−27774.2			−1.49646			−0.748229	−	0.663440i	$-0.769096\pi$
$701$	−27774.2			−1.49646			−0.748229	+	0.663440i	$0.769096\pi$
$702$	44389.5	+	5633.14i	2.38657	+	0.302862i
$703$	−6727.83	+	6727.83i	−0.360946	+	0.360946i
$704$	−12750.5	−	3416.48i	−0.682602	−	0.182903i
$705$	−13559.3	+	12463.7i	−0.724360	+	0.665832i
$706$	−25106.1	−	14495.0i	−1.33836	−	0.772702i
$707$	−4980.94	−	18589.1i	−0.264961	−	0.988849i
$708$	4850.68	+	9282.75i	0.257486	+	0.492750i
$709$	339.873	−	1268.42i	0.0180031	−	0.0671885i	−0.956340	−	0.292257i	$-0.905594\pi$
$709$	339.873	−	1268.42i	0.0180031	−	0.0671885i	0.974343	+	0.225068i	$0.0722605\pi$
$710$	44442.0			2.34913
$711$	−21423.6	−	7722.07i	−1.13002	−	0.407314i
$712$			979.117i			0.0515365i
$713$	−5107.33	−	8846.16i	−0.268262	−	0.464644i
$714$	15996.8	+	796.247i	0.838465	+	0.0417350i
$715$	17690.0	−	30640.0i	0.925270	−	1.60262i
$716$	11508.5	+	6644.42i	0.600687	+	0.346807i
$717$	−14673.9	−	9316.19i	−0.764304	−	0.485243i
$718$	7190.31	+	12454.0i	0.373732	+	0.647324i
$719$	7702.43	+	7702.43i	0.399516	+	0.399516i	0.878062	−	0.478546i	$-0.158836\pi$
$719$	7702.43	+	7702.43i	0.399516	+	0.399516i	−0.478546	+	0.878062i	$0.658836\pi$
$720$	20234.1	+	23962.1i	1.04733	+	1.24030i
$721$	−13924.9	+	13924.9i	−0.719263	+	0.719263i
$722$	20225.9	−	11677.5i	1.04256	−	0.601925i
$723$	−21086.1	−	6612.34i	−1.08465	−	0.340132i
$724$	2512.17	+	9375.53i	0.128956	+	0.481269i
$725$	11196.4	+	41785.4i	0.573548	+	2.14051i
$726$	−693.627	+	16475.4i	−0.0354586	+	0.842231i
$727$	4670.70	+	8089.89i	0.238276	+	0.412706i	0.960220	−	0.279246i	$-0.0900844\pi$
$727$	4670.70	+	8089.89i	0.238276	+	0.412706i	−0.721944	+	0.691952i	$0.756751\pi$
$728$	1022.43	+	1022.43i	0.0520518	+	0.0520518i
$729$	−19059.1	−	4916.47i	−0.968302	−	0.249782i
$730$	−29157.1			−1.47829
$731$	5003.65	+	19262.8i	0.253169	+	0.974638i
$732$	−4037.21	−	4392.09i	−0.203852	−	0.221771i
$733$	−25145.3	−	14517.6i	−1.26707	−	0.731543i	−0.292638	−	0.956223i	$-0.594533\pi$
$733$	−25145.3	−	14517.6i	−1.26707	−	0.731543i	−0.974433	+	0.224680i	$0.927866\pi$
$734$	10952.5	−	2934.72i	0.550769	−	0.147578i
$735$	6724.54	−	21443.9i	0.337467	−	1.07615i
$736$	9476.33	−	35366.1i	0.474595	−	1.77121i
$737$	−16927.9	+	16927.9i	−0.846060	+	0.846060i
$738$	−12812.9	−	15173.6i	−0.639091	−	0.756840i
$739$		−	7244.88i		−	0.360632i	−0.983609	−	0.180316i	$-0.942288\pi$
$739$		−	7244.88i		−	0.360632i	0.983609	−	0.180316i	$-0.0577121\pi$
$740$	40253.9	−	23240.6i	1.99968	−	1.15452i
$741$	−7254.30	+	11426.2i	−0.359640	+	0.566466i
$742$	−917.860	−	3425.50i	−0.0454120	−	0.169480i
$743$	−4897.55	+	1312.29i	−0.241822	+	0.0647959i	−0.377694	−	0.925930i	$-0.623283\pi$
$743$	−4897.55	+	1312.29i	−0.241822	+	0.0647959i	0.135872	+	0.990726i	$0.456616\pi$
$744$	−619.279	+	138.303i	−0.0305159	+	0.00681510i
$745$	11604.1	−	43307.2i	0.570661	−	2.12974i
$746$			24219.8i			1.18867i
$747$	−18944.7	+	8905.99i	−0.927911	+	0.436216i
$748$	6812.86	+	12011.7i	0.333025	+	0.587156i
$749$	2357.41	+	4083.16i	0.115004	+	0.199193i
$750$	45841.6	+	14375.4i	2.23187	+	0.699885i
$751$	28855.0	−	7731.67i	1.40204	−	0.375676i	0.522964	−	0.852355i	$-0.324826\pi$
$751$	28855.0	−	7731.67i	1.40204	−	0.375676i	0.879077	+	0.476679i	$0.158160\pi$
$752$	−5581.47	+	9667.39i	−0.270658	+	0.468794i
$753$	−214.232	+	5088.55i	−0.0103679	+	0.246264i
$754$	54659.1	+	14645.9i	2.64001	+	0.707388i
$755$	32283.0	−	32283.0i	1.55616	−	1.55616i
$756$	−7850.13	−	10132.1i	−0.377654	−	0.487436i
$757$			38831.9i			1.86443i	0.361910	+	0.932213i	$0.382125\pi$
$757$			38831.9i			1.86443i	−0.361910	+	0.932213i	$0.617875\pi$
$758$	11044.3	+	2959.30i	0.529216	+	0.141803i
$759$	17202.6	+	724.244i	0.822682	+	0.0346355i
$760$	1038.98	−	278.393i	0.0495890	−	0.0132873i
$761$	14054.9	−	24343.8i	0.669500	−	1.15961i	−0.308544	−	0.951210i	$-0.599842\pi$
$761$	14054.9	−	24343.8i	0.669500	−	1.15961i	0.978044	−	0.208398i	$-0.0668250\pi$
$762$	−5443.41	+	2844.44i	−0.258785	+	0.135227i
$763$	−8616.69	+	4974.85i	−0.408840	+	0.236044i
$764$	3354.63			0.158856
$765$	3332.15	−	36191.8i	0.157483	−	1.71048i
$766$	44042.9			2.07746
$767$	−16323.1	+	9424.14i	−0.768439	+	0.443658i
$768$	15947.4	+	10124.7i	0.749286	+	0.475709i
$769$	−6324.81	+	10954.9i	−0.296591	+	0.513711i	−0.975354	−	0.220647i	$-0.929183\pi$
$769$	−6324.81	+	10954.9i	−0.296591	+	0.513711i	0.678763	+	0.734358i	$0.262517\pi$
$770$	−19092.8	+	5115.89i	−0.893578	+	0.239433i
$771$	9167.84	−	14440.2i	0.428238	−	0.674515i
$772$	−33501.5	−	8976.69i	−1.56184	−	0.418495i
$773$		−	27361.2i		−	1.27311i	−0.771231	−	0.636555i	$-0.780359\pi$
$773$		−	27361.2i		−	1.27311i	0.771231	−	0.636555i	$-0.219641\pi$
$774$	17737.7	−	25500.8i	0.823733	−	1.18425i
$775$	12438.9	−	12438.9i	0.576540	−	0.576540i
$776$	187.285	+	50.1828i	0.00866383	+	0.00232147i
$777$	14371.2	−	7509.64i	0.663531	−	0.346727i
$778$	−11552.8	+	20010.1i	−0.532377	+	0.922105i
$779$	5802.43	−	1554.76i	0.266872	−	0.0715082i
$780$	48678.8	−	44745.6i	2.23459	−	2.05404i
$781$	6683.52	+	11576.2i	0.306217	+	0.530383i
$782$	−34974.9	+	19837.2i	−1.59936	+	0.907132i
$783$	−23041.5	−	9418.22i	−1.05164	−	0.429859i
$784$		−	13621.4i		−	0.620509i
$785$	9120.56	−	34038.4i	0.414684	−	1.54762i
$786$	17058.9	+	18558.4i	0.774135	+	0.842183i
$787$	1621.97	−	434.605i	0.0734650	−	0.0196849i	−0.221899	−	0.975070i	$-0.571226\pi$
$787$	1621.97	−	434.605i	0.0734650	−	0.0196849i	0.295364	+	0.955385i	$0.404559\pi$
$788$	−2580.05	−	9628.86i	−0.116637	−	0.435297i
$789$	−9316.73	−	17829.4i	−0.420386	−	0.804492i
$790$	−56838.9	+	32816.0i	−2.55980	+	1.47790i
$791$			18856.3i			0.847600i
$792$	362.683	−	1006.20i	0.0162720	−	0.0451438i
$793$	7591.31	−	7591.31i	0.339944	−	0.339944i
$794$	−4681.13	+	17470.2i	−0.209228	+	0.780849i
$795$	−7853.89	+	1754.00i	−0.350376	+	0.0782491i
$796$	35521.1	−	9517.85i	1.58167	−	0.423808i
$797$	−27947.1	−	16135.2i	−1.24208	−	0.717114i	−0.272560	−	0.962139i	$-0.587870\pi$
$797$	−27947.1	−	16135.2i	−1.24208	−	0.717114i	−0.969517	+	0.245025i	$0.921204\pi$
$798$	7379.73	−	1648.11i	0.327368	−	0.0731107i
$799$	12520.9	−	3252.39i	0.554389	−	0.144007i
$800$	63054.6			2.78665
$801$	15563.8	+	1312.82i	0.686543	+	0.0579106i
$802$	−17620.4	−	17620.4i	−0.775809	−	0.775809i
$803$	−4384.85	−	7594.79i	−0.192700	−	0.333766i
$804$	−39652.1	+	20720.1i	−1.73933	+	0.908883i
$805$	−7637.54	−	28503.7i	−0.334395	−	1.24798i
$806$	−5955.67	−	22226.9i	−0.260272	−	0.971350i
$807$	−7922.05	+	7281.95i	−0.345563	+	0.317642i
$808$	2599.15	−	1500.62i	0.113165	−	0.0653361i
$809$	−3402.38	+	3402.38i	−0.147863	+	0.147863i	−0.777163	−	0.629300i	$-0.783342\pi$
$809$	−3402.38	+	3402.38i	−0.147863	+	0.147863i	0.629300	+	0.777163i	$0.283342\pi$
$810$	−46264.5	+	32826.1i	−2.00687	+	1.42394i
$811$	−1228.19	−	1228.19i	−0.0531782	−	0.0531782i	0.680018	−	0.733196i	$-0.261972\pi$
$811$	−1228.19	−	1228.19i	−0.0531782	−	0.0531782i	−0.733196	+	0.680018i	$0.761972\pi$
$812$	−8104.70	−	14037.8i	−0.350270	−	0.606686i
$813$	1060.93	−	25199.8i	0.0457669	−	1.08708i
$814$	23613.9	+	13633.5i	1.01679	+	0.587044i
$815$	−24908.2	+	43142.3i	−1.07055	+	1.85425i
$816$	−4636.63	−	21535.5i	−0.198915	−	0.923888i
$817$	4697.94	+	8137.07i	0.201175	+	0.348446i
$818$		−	10208.7i		−	0.436356i
$819$	17623.2	−	14881.4i	0.751898	−	0.634918i
$820$	−29346.3			−1.24978
$821$	10268.3	−	38322.0i	0.436501	−	1.62904i	−0.300947	−	0.953641i	$-0.597303\pi$
$821$	10268.3	−	38322.0i	0.436501	−	1.62904i	0.737448	−	0.675404i	$-0.236031\pi$
$822$	−18696.1	+	29448.1i	−0.793312	+	1.24954i
$823$	7271.10	+	27136.1i	0.307964	+	1.14934i	0.930363	+	0.366639i	$0.119492\pi$
$823$	7271.10	+	27136.1i	0.307964	+	1.14934i	−0.622399	+	0.782700i	$0.713842\pi$
$824$	−2659.63	−	1535.54i	−0.112442	−	0.0649187i
$825$	6462.92	+	28939.0i	0.272739	+	1.22124i
$826$	10171.4	+	2725.43i	0.428462	+	0.114806i
$827$	−8542.95	+	8542.95i	−0.359211	+	0.359211i	−0.863522	−	0.504311i	$-0.831746\pi$
$827$	−8542.95	+	8542.95i	−0.359211	+	0.359211i	0.504311	+	0.863522i	$0.331746\pi$
$828$	30271.0	+	10911.1i	1.27052	+	0.457955i
$829$	3416.00			0.143115			0.0715576	−	0.997436i	$-0.477203\pi$
$829$	3416.00			0.143115			0.0715576	+	0.997436i	$0.477203\pi$
$830$	−15614.9	+	58275.7i	−0.653015	+	2.43708i
$831$	5542.12	+	1737.94i	0.231353	+	0.0725493i
$832$	22197.1	−	38446.5i	0.924935	−	1.60203i
$833$	−11247.2	+	11076.2i	−0.467816	+	0.460705i
$834$	6524.44	+	7097.95i	0.270891	+	0.294702i
$835$	25233.5	−	14568.6i	1.04580	−	0.603793i
$836$	4609.95	+	4609.95i	0.190716	+	0.190716i
$837$	1368.09	+	10029.4i	0.0564970	+	0.414176i
$838$	−21500.8	−	21500.8i	−0.886316	−	0.886316i
$839$	17909.4	+	4798.81i	0.736950	+	0.197465i	0.607722	−	0.794150i	$-0.292083\pi$
$839$	17909.4	+	4798.81i	0.736950	+	0.197465i	0.129228	+	0.991615i	$0.458750\pi$
$840$	−1831.49	−	77.1071i	−0.0752290	−	0.00316720i
$841$	−6140.63	−	3545.29i	−0.251779	−	0.145364i
$842$	−15985.6	−	9229.27i	−0.654274	−	0.377745i
$843$	7196.04	+	13771.1i	0.294003	+	0.562634i
$844$	27511.7	+	7371.75i	1.12203	+	0.300647i
$845$	54302.2	+	54302.2i	2.21071	+	2.21071i
$846$	−16575.6	−	11529.6i	−0.673617	−	0.468552i
$847$	6010.71	+	6010.71i	0.243837	+	0.243837i
$848$	−4224.11	+	2438.79i	−0.171057	+	0.0987599i
$849$	−18003.4	+	4020.68i	−0.727767	+	0.162531i
$850$	−48588.1	−	49338.0i	−1.96065	−	1.99092i
$851$	−20353.5	+	35253.4i	−0.819872	+	1.42006i
$852$	5444.83	+	24380.3i	0.218940	+	0.980346i
$853$	−8577.18	+	32010.5i	−0.344287	+	1.28490i	0.549155	+	0.835720i	$0.314950\pi$
$853$	−8577.18	+	32010.5i	−0.344287	+	1.28490i	−0.893443	+	0.449177i	$0.851717\pi$
$854$	−5997.89			−0.240332
$855$	−3032.18	−	16888.6i	−0.121285	−	0.675530i
$856$	−519.919	+	519.919i	−0.0207599	+	0.0207599i
$857$	10603.9	+	2841.31i	0.422664	+	0.113253i	0.463881	−	0.885898i	$-0.346457\pi$
$857$	10603.9	+	2841.31i	0.422664	+	0.113253i	−0.0412164	+	0.999150i	$0.513123\pi$
$858$	37010.2	+	11606.0i	1.47262	+	0.461796i
$859$	42208.1	+	24368.9i	1.67651	+	0.967934i	0.963858	+	0.266416i	$0.0858396\pi$
$859$	42208.1	+	24368.9i	1.67651	+	0.967934i	0.712652	+	0.701517i	$0.247494\pi$
$860$	−11880.1	−	44337.3i	−0.471057	−	1.75801i
$861$	−10228.4	−	430.624i	−0.404859	−	0.0170449i
$862$	3973.08	−	14827.7i	0.156988	−	0.585887i
$863$	−22647.9			−0.893329			−0.446665	−	0.894701i	$-0.647388\pi$
$863$	−22647.9			−0.893329			−0.446665	+	0.894701i	$0.647388\pi$
$864$	−21952.6	+	28887.7i	−0.864402	+	1.13747i
$865$			38555.4i			1.51552i
$866$	3002.75	+	5200.92i	0.117826	+	0.204081i
$867$	−14011.5	+	21339.9i	−0.548853	+	0.835919i
$868$	−3295.74	+	5708.39i	−0.128876	+	0.223221i
$869$	−17095.7	−	9870.22i	−0.667356	−	0.385298i
$870$	−63582.2	+	33224.7i	−2.47774	+	1.29474i
$871$	−40256.0	−	69725.4i	−1.56604	−	2.71246i
$872$	−1097.18	−	1097.18i	−0.0426093	−	0.0426093i
$873$	1048.81	−	2909.75i	0.0406608	−	0.112807i
$874$	−13422.9	+	13422.9i	−0.519494	+	0.519494i
$875$	21447.6	−	12382.8i	0.828641	−	0.478416i
$876$	−3572.18	−	15995.2i	−0.137777	−	0.616925i
$877$	2547.10	+	9505.92i	0.0980725	+	0.366011i	0.997467	−	0.0711256i	$-0.0226591\pi$
$877$	2547.10	+	9505.92i	0.0980725	+	0.366011i	−0.899395	+	0.437137i	$0.855992\pi$
$878$	−5531.35	−	20643.3i	−0.212613	−	0.793482i
$879$	−9131.11	−	5797.19i	−0.350381	−	0.222451i
$880$	13593.1	+	23544.0i	0.520709	+	0.901894i
$881$	13446.5	+	13446.5i	0.514218	+	0.514218i	0.915816	−	0.401598i	$-0.131545\pi$
$881$	13446.5	+	13446.5i	0.514218	+	0.514218i	−0.401598	+	0.915816i	$0.631545\pi$
$882$	24550.7	+	2070.88i	0.937263	+	0.0790591i
$883$	−26753.0			−1.01960			−0.509801	−	0.860292i	$-0.670281\pi$
$883$	−26753.0			−1.01960			−0.509801	+	0.860292i	$0.670281\pi$
$884$	−44950.7	+	11676.3i	−1.71024	+	0.444249i
$885$	7149.96	−	22800.5i	0.271574	−	0.866023i
$886$	−24674.8	−	14246.0i	−0.935628	−	0.540185i
$887$	46359.2	−	12421.9i	1.75489	−	0.470222i	0.769232	−	0.638970i	$-0.220639\pi$
$887$	46359.2	−	12421.9i	1.75489	−	0.470222i	0.985659	+	0.168748i	$0.0539724\pi$
$888$	1711.28	+	1861.71i	0.0646699	+	0.0703546i
$889$	−819.428	+	3058.15i	−0.0309142	+	0.115373i
$890$	31830.2	−	31830.2i	1.19882	−	1.19882i
$891$	−15508.1	−	7114.27i	−0.583099	−	0.267494i
$892$		−	32881.7i		−	1.23426i
$893$	5289.12	−	3053.67i	0.198201	−	0.114431i
$894$	49109.4	+	2067.54i	1.83721	+	0.0773478i
$895$	−7846.85	−	29284.8i	−0.293063	−	1.09373i
$896$	−2268.10	+	607.735i	−0.0845668	+	0.0226596i
$897$	−17326.6	+	55252.9i	−0.644948	+	2.05668i
$898$	−1137.22	+	4244.15i	−0.0422600	+	0.157716i
$899$			12801.0i			0.474904i
$900$	−4657.74	+	55218.6i	−0.172509	+	2.04513i
$901$	5448.51	+	1504.74i	0.201461	+	0.0556384i
$902$	−8607.63	−	14908.8i	−0.317741	−	0.550344i
$903$	−3490.12	−	15627.7i	−0.128620	−	0.575922i
$904$	−2840.43	+	761.091i	−0.104504	+	0.0280017i
$905$	11072.2	−	19177.6i	0.406688	−	0.704404i
$906$	42255.2	+	26827.1i	1.54949	+	0.983743i
$907$	−5260.90	−	1409.65i	−0.192597	−	0.0516062i	0.161231	−	0.986917i	$-0.448454\pi$
$907$	−5260.90	−	1409.65i	−0.192597	−	0.0516062i	−0.353828	+	0.935310i	$0.615120\pi$
$908$	2316.64	−	2316.64i	0.0846700	−	0.0846700i
$909$	−20368.5	−	43327.5i	−0.743212	−	1.58095i
$910$		−	66476.5i		−	2.42162i
$911$	−42941.7	−	11506.2i	−1.56171	−	0.418460i	−0.628508	−	0.777803i	$-0.716334\pi$
$911$	−42941.7	−	11506.2i	−1.56171	−	0.418460i	−0.933205	+	0.359343i	$0.883001\pi$
$912$	−4816.55	−	9217.42i	−0.174881	−	0.334670i
$913$	−17527.9	+	4696.58i	−0.635364	+	0.170245i
$914$	−12839.1	+	22237.9i	−0.464637	+	0.804775i
$915$	−572.503	+	13598.4i	−0.0206846	+	0.491311i
$916$	28045.4	−	16192.0i	1.01162	−	0.584060i
$917$	12994.2			0.467946
$918$	39519.6	−	5082.83i	1.42085	−	0.182743i
$919$	−33199.4			−1.19167			−0.595836	−	0.803106i	$-0.703179\pi$
$919$	−33199.4			−1.19167			−0.595836	+	0.803106i	$0.703179\pi$
$920$	3985.41	−	2300.98i	0.142821	−	0.0824575i
$921$	−1421.31	+	33759.7i	−0.0508510	+	1.20784i
$922$	−26227.5	+	45427.3i	−0.936828	+	1.62263i
$923$	−43423.3	+	11635.2i	−1.54853	+	0.414928i
$924$	−5145.66	−	9847.24i	−0.183203	−	0.350596i
$925$	−67715.3	−	18144.3i	−2.40699	−	0.644951i
$926$		−	35538.0i		−	1.26118i
$927$	−27974.6	+	40218.0i	−0.991163	+	1.42495i
$928$	−32445.2	+	32445.2i	−1.14770	+	1.14770i
$929$	31174.8	+	8353.27i	1.10098	+	0.295007i	0.763165	−	0.646204i	$-0.223644\pi$
$929$	31174.8	+	8353.27i	1.10098	+	0.295007i	0.337818	+	0.941211i	$0.390311\pi$
$930$	24628.3	+	15636.1i	0.868381	+	0.551320i
$931$	−3726.20	+	6453.97i	−0.131172	+	0.227197i
$932$	31081.2	−	8328.18i	1.09238	−	0.292702i
$933$	−1990.71	−	8913.78i	−0.0698530	−	0.312780i
$934$	−23397.0	−	40524.9i	−0.819673	−	1.41972i
$935$	8386.99	−	30368.4i	0.293352	−	1.06220i
$936$	2952.99	+	2054.03i	0.103121	+	0.0717287i
$937$		−	1685.09i		−	0.0587506i	−0.999568	−	0.0293753i	$-0.990648\pi$
$937$		−	1685.09i		−	0.0587506i	0.999568	−	0.0293753i	$-0.00935180\pi$
$938$	−11641.9	+	43448.2i	−0.405247	+	1.51240i
$939$	−3543.27	+	11299.1i	−0.123142	+	0.392688i
$940$	−28819.4	+	7722.12i	−0.999983	+	0.267945i
$941$	3798.49	+	14176.2i	0.131591	+	0.491105i	0.999989	−	0.00476375i	$-0.00151635\pi$
$941$	3798.49	+	14176.2i	0.131591	+	0.491105i	−0.868397	+	0.495869i	$0.834850\pi$
$942$	38598.7	+	1625.04i	1.33505	+	0.0562065i
$943$	22257.5	−	12850.4i	0.768616	−	0.443760i
$944$		−	14483.1i		−	0.499350i
$945$	−3681.38	+	29009.5i	−0.126725	+	0.998604i
$946$	19040.1	−	19040.1i	0.654385	−	0.654385i
$947$	8102.61	−	30239.3i	0.278035	−	1.03764i	−0.675745	−	0.737136i	$-0.736178\pi$
$947$	8102.61	−	30239.3i	0.278035	−	1.03764i	0.953780	−	0.300506i	$-0.0971555\pi$
$948$	−24966.0	−	27160.6i	−0.855336	−	0.930522i
$949$	28488.7	−	7633.52i	0.974480	−	0.261111i
$950$	−28311.7	−	16345.8i	−0.966898	−	0.558239i
$951$	6531.37	−	20827.9i	0.222707	−	0.710190i
$952$	1110.11	+	652.311i	0.0377931	+	0.0222075i
$953$	−30887.6			−1.04989			−0.524946	−	0.851135i	$-0.675915\pi$
$953$	−30887.6			−1.04989			−0.524946	+	0.851135i	$0.675915\pi$
$954$	−3753.39	−	7984.14i	−0.127380	−	0.270960i
$955$	−5411.79	−	5411.79i	−0.183373	−	0.183373i
$956$	−14078.9	−	24385.3i	−0.476301	−	0.824977i
$957$	−18216.3	−	11565.2i	−0.615307	−	0.390648i
$958$	−11763.1	−	43900.5i	−0.396710	−	1.48054i
$959$	4653.87	+	17368.5i	0.156706	+	0.584836i
$960$	12267.1	+	54928.5i	0.412417	+	1.84668i
$961$	−21291.7	+	12292.8i	−0.714702	+	0.412633i
$962$	−64843.4	+	64843.4i	−2.17322	+	2.17322i
$963$	7567.39	+	8961.63i	0.253225	+	0.299880i
$964$	−25314.1	−	25314.1i	−0.845759	−	0.845759i
$965$	39564.1	+	68527.1i	1.31981	+	2.28597i
$966$	28672.5	−	14982.8i	0.954993	−	0.499030i
$967$	44274.2	+	25561.7i	1.47235	+	0.850061i	0.999517	−	0.0310909i	$-0.00989815\pi$
$967$	44274.2	+	25561.7i	1.47235	+	0.850061i	0.472833	+	0.881152i	$0.343231\pi$
$968$	−662.819	+	1148.04i	−0.0220081	+	0.0381191i
$969$	−3694.24	+	11472.1i	−0.122473	+	0.380327i
$970$	−4457.06	−	7719.86i	−0.147534	−	0.255536i
$971$		−	50928.1i		−	1.68317i	−0.540122	−	0.841587i	$-0.681622\pi$
$971$		−	50928.1i		−	1.68317i	0.540122	−	0.841587i	$-0.318378\pi$
$972$	−23676.1	−	21358.4i	−0.781286	−	0.704804i
$973$	4969.84			0.163747
$974$	−9805.15	+	36593.3i	−0.322564	+	1.20382i
$975$	−99634.8	−	4194.70i	−3.27268	−	0.137783i
$976$	2135.11	+	7968.32i	0.0700236	+	0.261332i
$977$	−3633.66	−	2097.89i	−0.118988	−	0.0686976i	0.439325	−	0.898328i	$-0.355218\pi$
$977$	−3633.66	−	2097.89i	−0.118988	−	0.0686976i	−0.558313	+	0.829631i	$0.688551\pi$
$978$	−52111.9	−	16341.6i	−1.70384	−	0.534303i
$979$	13078.0	+	3504.23i	0.426939	+	0.114398i
$980$	25743.6	−	25743.6i	0.839132	−	0.839132i
$981$	−18911.7	+	15969.5i	−0.615499	+	0.519740i
$982$	46487.3			1.51066
$983$	9504.29	−	35470.5i	0.308382	−	1.15090i	−0.621613	−	0.783325i	$-0.713522\pi$
$983$	9504.29	−	35470.5i	0.308382	−	1.15090i	0.929995	−	0.367573i	$-0.119811\pi$
$984$	−347.980	−	1558.15i	−0.0112736	−	0.0504796i
$985$	−11371.4	+	19695.8i	−0.367840	+	0.637117i
$986$	50388.5	+	385.909i	1.62748	+	0.0124644i
$987$	−10158.1	+	2268.59i	−0.327593	+	0.0731611i
$988$	−18988.3	+	10962.9i	−0.611435	+	0.353012i
$989$	28425.1	+	28425.1i	0.913920	+	0.913920i
$990$	−44501.3	+	20920.3i	−1.42863	+	0.671607i
$991$	7476.97	+	7476.97i	0.239671	+	0.239671i	0.816714	−	0.577043i	$-0.195794\pi$
$991$	7476.97	+	7476.97i	0.239671	+	0.239671i	−0.577043	+	0.816714i	$0.695794\pi$
$992$	18022.9	+	4829.23i	0.576843	+	0.154565i
$993$	2169.87	+	4152.48i	0.0693442	+	0.132704i
$994$	21750.9	+	12557.9i	0.694060	+	0.400716i
$995$	−72658.3	−	41949.3i	−2.31500	−	1.33656i
$996$	−33882.3	−	1426.47i	−1.07791	−	0.0453810i
$997$	29971.3	+	8030.79i	0.952057	+	0.255103i	0.701235	−	0.712930i	$-0.252632\pi$
$997$	29971.3	+	8030.79i	0.952057	+	0.255103i	0.250822	+	0.968033i	$0.419299\pi$
$998$	3313.78	+	3313.78i	0.105106	+	0.105106i
$999$	31887.8	−	24705.9i	1.00990	−	0.782443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.n.a.13.45	yes	208
9.7	even	3	inner	153.4.n.a.115.8	yes	208
17.4	even	4	inner	153.4.n.a.4.8	✓	208
153.106	even	12	inner	153.4.n.a.106.45	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.n.a.4.8	✓	208	17.4	even	4	inner
153.4.n.a.13.45	yes	208	1.1	even	1	trivial
153.4.n.a.106.45	yes	208	153.106	even	12	inner
153.4.n.a.115.8	yes	208	9.7	even	3	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.50903 - 2.02594i) q^{2} +(0.218568 - 5.19155i) q^{3} +(4.20886 - 7.28996i) q^{4} +(-18.5503 + 4.97053i) q^{5} +(-9.75081 - 18.6601i) q^{6} +(-10.4834 - 2.80902i) q^{7} -1.69255i q^{8} +(-26.9045 - 2.26942i) q^{9} +(-55.0234 + 55.0234i) q^{10} +(-22.6073 - 6.05760i) q^{11} +(-36.9263 - 23.4439i) q^{12} +(39.3566 - 68.1676i) q^{13} +(-42.4774 + 11.3818i) q^{14} +(21.7503 + 97.3911i) q^{15} +(30.2419 + 52.3805i) q^{16} +(18.6593 - 67.5635i) q^{17} +(-99.0062 + 46.5433i) q^{18} -33.0912i q^{19} +(-41.8405 + 156.151i) q^{20} +(-16.8745 + 53.8111i) q^{21} +(-91.6019 + 24.5446i) q^{22} +(-36.6429 - 136.753i) q^{23} +(-8.78699 - 0.369939i) q^{24} +(211.153 - 121.909i) q^{25} -318.936i q^{26} +(-17.6623 + 139.180i) q^{27} +(-64.6008 + 64.6008i) q^{28} +(-45.9209 + 171.379i) q^{29} +(273.631 + 297.683i) q^{30} +(69.6906 - 18.6736i) q^{31} +(223.966 + 129.307i) q^{32} +(-36.3896 + 116.043i) q^{33} +(-71.4035 - 274.885i) q^{34} +208.432 q^{35} +(-129.781 + 186.581i) q^{36} +(-203.311 - 203.311i) q^{37} +(-67.0408 - 116.118i) q^{38} +(-345.294 - 219.221i) q^{39} +(8.41289 + 31.3973i) q^{40} +(46.9839 + 175.346i) q^{41} +(49.8050 + 223.012i) q^{42} +(-245.898 + 141.969i) q^{43} +(-139.310 + 139.310i) q^{44} +(510.365 - 91.6310i) q^{45} +(-405.634 - 405.634i) q^{46} +(92.2805 + 159.834i) q^{47} +(278.546 - 145.554i) q^{48} +(-195.036 - 112.604i) q^{49} +(493.961 - 855.566i) q^{50} +(-346.681 - 111.638i) q^{51} +(-331.293 - 573.816i) q^{52} +80.6428i q^{53} +(219.993 + 524.169i) q^{54} +449.480 q^{55} +(-4.75441 + 17.7437i) q^{56} +(-171.795 - 7.23270i) q^{57} +(186.066 + 694.408i) q^{58} +(-207.374 - 119.728i) q^{59} +(801.521 + 251.347i) q^{60} +(131.743 + 35.3005i) q^{61} +(206.715 - 206.715i) q^{62} +(275.675 + 99.3663i) q^{63} +563.999 q^{64} +(-391.246 + 1460.15i) q^{65} +(107.404 + 480.921i) q^{66} +(511.426 - 885.817i) q^{67} +(-414.001 - 420.391i) q^{68} +(-717.970 + 160.344i) q^{69} +(731.394 - 422.270i) q^{70} +(-403.846 - 403.846i) q^{71} +(-3.84112 + 45.5373i) q^{72} +(264.951 + 264.951i) q^{73} +(-1125.32 - 301.529i) q^{74} +(-586.747 - 1122.86i) q^{75} +(-241.234 - 139.276i) q^{76} +(219.985 + 127.008i) q^{77} +(-1655.77 - 69.7094i) q^{78} +(814.697 + 218.298i) q^{79} +(-821.353 - 821.353i) q^{80} +(718.699 + 122.115i) q^{81} +(520.109 + 520.109i) q^{82} +(671.447 - 387.660i) q^{83} +(321.259 + 349.498i) q^{84} +(-10.3091 + 1346.07i) q^{85} +(-575.242 + 996.349i) q^{86} +(879.688 + 275.859i) q^{87} +(-10.2528 + 38.2640i) q^{88} -578.485 q^{89} +(1605.25 - 1355.50i) q^{90} +(-604.074 + 604.074i) q^{91} +(-1151.15 - 308.449i) q^{92} +(-81.7126 - 365.884i) q^{93} +(647.630 + 373.909i) q^{94} +(164.481 + 613.851i) q^{95} +(720.254 - 1134.47i) q^{96} +(-29.6492 + 110.652i) q^{97} -912.515 q^{98} +(594.489 + 214.282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) \) 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

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