LMFDB - Embedded newform 153.4.n.a.106.45

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			106.45
Character	$\chi$	$=$	153.106
Dual form			153.4.n.a.13.45

$q$-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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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	0.969222	−	0.246187i	$-0.0791777\pi$
$2$	3.50903	+	2.02594i	1.24063	+	0.716278i	0.271407	+	0.962465i	$0.412511\pi$
$3$	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	−0.697022	−	0.717050i	$-0.745492\pi$
$5$	−18.5503	−	4.97053i	−1.65919	−	0.444577i	−0.962164	+	0.272472i	$0.912159\pi$
$6$	−9.75081	+	18.6601i	−0.663459	+	1.26966i
$7$	−10.4834	+	2.80902i	−0.566050	+	0.151673i	−0.530484	−	0.847695i	$-0.677990\pi$
$7$	−10.4834	+	2.80902i	−0.566050	+	0.151673i	−0.0355656	+	0.999367i	$0.511323\pi$
$8$			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	−0.554977	−	0.831866i	$-0.687273\pi$
$11$	−22.6073	+	6.05760i	−0.619668	+	0.166039i	−0.0646909	+	0.997905i	$0.520606\pi$
$12$	−36.9263	+	23.4439i	−0.888309	+	0.563972i
$13$	39.3566	+	68.1676i	0.839658	+	1.45433i	0.890181	+	0.455607i	$0.150578\pi$
$13$	39.3566	+	68.1676i	0.839658	+	1.45433i	−0.0505228	+	0.998723i	$0.516089\pi$
$14$	−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	$0.0640228\pi$
$19$			33.0912i			0.399560i	−0.979841	+	0.199780i	$0.935977\pi$
$20$	−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	0.574676	+	0.818381i	$0.305128\pi$
$23$	−36.6429	+	136.753i	−0.332199	+	1.23978i	−0.906875	+	0.421401i	$0.861539\pi$
$24$	−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	−0.941973	−	0.335689i	$-0.891031\pi$
$29$	−45.9209	−	171.379i	−0.294045	−	1.09739i	0.647928	−	0.761702i	$-0.275636\pi$
$30$	273.631	−	297.683i	1.66526	−	1.81164i
$31$	69.6906	+	18.6736i	0.403768	+	0.108189i	0.454987	−	0.890498i	$-0.349644\pi$
$31$	69.6906	+	18.6736i	0.403768	+	0.108189i	−0.0512189	+	0.998687i	$0.516311\pi$
$32$	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	−0.995725	−	0.0923681i	$-0.970556\pi$
$37$	−203.311	+	203.311i	−0.903357	+	0.903357i	0.0923681	+	0.995725i	$0.470556\pi$
$38$	−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	−0.816875	−	0.576815i	$-0.804295\pi$
$41$	46.9839	−	175.346i	0.178967	−	0.667915i	0.995842	−	0.0910993i	$-0.0290381\pi$
$42$	49.8050	−	223.012i	0.182978	−	0.819320i
$43$	−245.898	−	141.969i	−0.872072	−	0.503491i	−0.00403589	−	0.999992i	$-0.501285\pi$
$43$	−245.898	−	141.969i	−0.872072	−	0.503491i	−0.868036	+	0.496501i	$0.834618\pi$
$44$	−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	−0.686553	−	0.727080i	$-0.740877\pi$
$47$	92.2805	−	159.834i	0.286393	−	0.496048i	0.972946	+	0.231032i	$0.0742103\pi$
$48$	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	$-0.966675\pi$
$53$		−	80.6428i		−	0.209003i	0.994525	−	0.104501i	$-0.0333247\pi$
$54$	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	−0.711031	−	0.703161i	$-0.751771\pi$
$59$	−207.374	+	119.728i	−0.457590	+	0.264190i	0.253440	+	0.967351i	$0.418438\pi$
$60$	801.521	−	251.347i	1.72460	−	0.540812i
$61$	131.743	−	35.3005i	0.276524	−	0.0740945i	−0.117892	−	0.993026i	$-0.537614\pi$
$61$	131.743	−	35.3005i	0.276524	−	0.0740945i	0.394416	+	0.918932i	$0.370947\pi$
$62$	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	0.778950	+	0.627086i	$0.215753\pi$
$67$	511.426	+	885.817i	0.932547	+	1.61522i	0.153597	+	0.988134i	$0.450914\pi$
$68$	−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	−0.958873	−	0.283834i	$-0.908393\pi$
$71$	−403.846	+	403.846i	−0.675039	+	0.675039i	0.283834	+	0.958873i	$0.408393\pi$
$72$	−3.84112	−	45.5373i	−0.00628722	−	0.0745364i
$73$	264.951	−	264.951i	0.424797	−	0.424797i	−0.462054	−	0.886852i	$-0.652888\pi$
$73$	264.951	−	264.951i	0.424797	−	0.424797i	0.886852	+	0.462054i	$0.152888\pi$
$74$	−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	0.373191	−	0.927755i	$-0.378264\pi$
$79$	814.697	−	218.298i	1.16026	−	0.310891i	0.787070	+	0.616864i	$0.211597\pi$
$80$	−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	0.873275	−	0.487227i	$-0.161992\pi$
$83$	671.447	+	387.660i	0.887962	+	0.512665i	0.0146869	+	0.999892i	$0.495325\pi$
$84$	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	0.948671	−	0.316266i	$-0.102429\pi$
$97$	−29.6492	−	110.652i	−0.0310352	−	0.115825i	−0.979706	+	0.200441i	$0.935763\pi$
$98$	−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	0.0150754	−	0.999886i	$-0.495201\pi$
$101$	886.599	−	1535.64i	0.873465	−	1.51289i	0.858389	−	0.512999i	$-0.171465\pi$
$102$	−1442.69	−	310.614i	−1.40046	−	0.301523i
$103$	907.231	+	1571.37i	0.867884	+	1.50322i	0.864154	+	0.503227i	$0.167854\pi$
$103$	907.231	+	1571.37i	0.867884	+	1.50322i	0.00372989	+	0.999993i	$0.498813\pi$
$104$	−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	−0.832124	−	0.554590i	$-0.812875\pi$
$107$	−307.180	+	307.180i	−0.277535	+	0.277535i	0.554590	+	0.832124i	$0.312875\pi$
$108$	940.278	−	714.546i	0.837762	−	0.636641i
$109$	648.241	+	648.241i	0.569636	+	0.569636i	0.932026	−	0.362391i	$-0.118039\pi$
$109$	648.241	+	648.241i	0.569636	+	0.569636i	−0.362391	+	0.932026i	$0.618039\pi$
$110$	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	0.479946	+	0.877298i	$0.340656\pi$
$113$	−449.670	+	1678.19i	−0.374349	+	1.39709i	−0.854294	+	0.519790i	$0.826010\pi$
$114$	−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	$0.0324957\pi$
$127$			291.714i			0.203822i	−0.994794	+	0.101911i	$0.967504\pi$
$128$	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	−0.148360	−	0.988933i	$-0.547399\pi$
$131$	−1156.47	−	309.876i	−0.771309	−	0.206672i	−0.622950	+	0.782262i	$0.714066\pi$
$132$	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	0.483220	+	0.875499i	$0.339467\pi$
$137$	−828.381	+	1434.80i	−0.516594	+	0.894767i	−0.999814	+	0.0192685i	$0.993866\pi$
$138$	−2194.53	−	2017.21i	−1.35370	−	1.24432i
$139$	−442.311	−	118.517i	−0.269902	−	0.0723200i	0.121330	−	0.992612i	$-0.461284\pi$
$139$	−442.311	−	118.517i	−0.269902	−	0.0723200i	−0.391232	+	0.920292i	$0.627951\pi$
$140$	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	−0.985030	−	0.172382i	$-0.944854\pi$
$149$	−1167.29	−	2021.81i	−0.641802	−	1.11163i	0.343228	−	0.939252i	$-0.388480\pi$
$150$	−4333.75	+	2751.43i	−2.35900	+	1.49769i
$151$	−2058.80	−	1188.65i	−1.10955	−	0.640601i	−0.170839	−	0.985299i	$-0.554648\pi$
$151$	−2058.80	−	1188.65i	−1.10955	−	0.640601i	−0.938713	+	0.344698i	$0.887981\pi$
$152$	−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	0.532883	−	0.846189i	$-0.321109\pi$
$157$	−917.464	−	1589.10i	−0.466380	−	0.807794i	−0.999263	+	0.0383955i	$0.987775\pi$
$158$	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	0.993676	−	0.112282i	$-0.0358160\pi$
$163$	1834.22	+	1834.22i	0.881394	+	0.881394i	−0.112282	+	0.993676i	$0.535816\pi$
$164$	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	−0.0972294	−	0.995262i	$-0.530998\pi$
$167$	−1465.50	−	392.679i	−0.679064	−	0.181955i	−0.581834	+	0.813307i	$0.697665\pi$
$168$	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	0.981034	+	0.193838i	$0.0620936\pi$
$173$	519.607	+	1939.20i	0.228353	+	0.852223i	−0.752681	+	0.658385i	$0.771240\pi$
$174$	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	$-0.893087\pi$
$179$		−	1578.67i		−	0.659194i	0.944122	−	0.329597i	$-0.106913\pi$
$180$	1480.07	+	4106.20i	0.612876	+	1.70032i
$181$	−815.347	−	815.347i	−0.334830	−	0.334830i	0.519587	−	0.854417i	$-0.326086\pi$
$181$	−815.347	−	815.347i	−0.334830	−	0.334830i	−0.854417	+	0.519587i	$0.826086\pi$
$182$	−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	−0.825811	−	0.563947i	$-0.809282\pi$
$191$	199.260	−	345.128i	0.0754866	−	0.130747i	0.901298	+	0.433200i	$0.142616\pi$
$192$	123.272	+	2928.03i	0.0463355	+	1.10059i
$193$	−1066.40	+	3979.87i	−0.397728	+	1.48434i	0.419357	+	0.907821i	$0.362256\pi$
$193$	−1066.40	+	3979.87i	−0.397728	+	1.48434i	−0.817084	+	0.576518i	$0.804411\pi$
$194$	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	0.842126	−	0.539280i	$-0.181304\pi$
$197$	837.378	+	837.378i	0.302846	+	0.302846i	−0.539280	+	0.842126i	$0.681304\pi$
$198$	2520.20	+	452.477i	0.904560	+	0.162405i
$199$	3089.11	−	3089.11i	1.10041	−	1.10041i	0.106047	−	0.994361i	$-0.466181\pi$
$199$	3089.11	−	3089.11i	1.10041	−	1.10041i	0.994361	−	0.106047i	$-0.0338193\pi$
$200$	−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	−0.662578	−	0.748993i	$-0.730538\pi$
$211$	875.741	−	3268.31i	0.285728	−	1.06635i	0.948306	−	0.317357i	$-0.102795\pi$
$212$	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	0.912902	−	0.408180i	$-0.133836\pi$
$223$	3382.91	+	1953.12i	1.01586	+	0.586506i	0.102957	+	0.994686i	$0.467170\pi$
$224$	−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	−0.203439	−	0.979088i	$-0.565212\pi$
$227$	375.944	−	100.734i	0.109922	−	0.0294535i	0.313361	+	0.949634i	$0.398545\pi$
$228$	−775.787	−	1221.94i	−0.225341	−	0.354933i
$229$	3331.70	−	1923.56i	0.961420	−	0.555076i	0.0648103	−	0.997898i	$-0.479356\pi$
$229$	3331.70	−	1923.56i	0.961420	−	0.555076i	0.896610	+	0.442821i	$0.146022\pi$
$230$	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	−0.216326	−	0.976321i	$-0.569408\pi$
$233$	2702.99	−	2702.99i	0.759995	−	0.759995i	0.976321	+	0.216326i	$0.0694075\pi$
$234$	−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	0.998551	−	0.0538214i	$-0.0171402\pi$
$239$	1672.53	+	2896.90i	0.452665	+	0.784038i	−0.545886	+	0.837859i	$0.683807\pi$
$240$	−4443.62	−	4084.58i	−1.19514	−	1.09858i
$241$	1100.72	+	4107.96i	0.294207	+	1.09800i	0.941845	+	0.336048i	$0.109090\pi$
$241$	1100.72	+	4107.96i	0.294207	+	1.09800i	−0.647638	+	0.761948i	$0.724243\pi$
$242$	−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	−0.112404	−	0.993663i	$-0.535855\pi$
$257$	2850.77	−	1645.90i	0.691932	−	0.399487i	0.804335	+	0.594176i	$0.202522\pi$
$258$	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	0.838587	−	0.544768i	$-0.183382\pi$
$263$	3352.82	+	1935.75i	0.786097	+	0.453854i	−0.0524895	+	0.998621i	$0.516716\pi$
$264$	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	−0.853306	−	0.521410i	$-0.825406\pi$
$269$	−1464.30	+	1464.30i	−0.331896	+	0.331896i	0.521410	+	0.853306i	$0.325406\pi$
$270$	−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	0.927425	−	0.374010i	$-0.122017\pi$
$277$	−289.306	−	1079.71i	−0.0627536	−	0.234199i	−0.990178	+	0.139810i	$0.955351\pi$
$278$	−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	0.199260	−	0.979947i	$-0.436146\pi$
$281$	−2589.64	−	1495.13i	−0.549769	−	0.317410i	−0.749029	+	0.662537i	$0.769480\pi$
$282$	2082.72	+	3280.48i	0.439802	+	0.692730i
$283$	−918.834	+	3429.14i	−0.193000	+	0.720286i	0.799775	+	0.600299i	$0.204952\pi$
$283$	−918.834	+	3429.14i	−0.193000	+	0.720286i	−0.992775	+	0.119987i	$0.961715\pi$
$284$	−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	0.950931	−	0.309402i	$-0.100129\pi$
$293$	1040.76	+	1802.66i	0.207516	+	0.359428i	−0.743416	+	0.668830i	$0.766796\pi$
$294$	−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	0.410257	−	0.911970i	$-0.365439\pi$
$311$	1697.82	+	454.931i	0.309565	+	0.0829478i	−0.100692	+	0.994918i	$0.532106\pi$
$312$	−371.044	−	584.428i	−0.0673276	−	0.106047i
$313$	−2201.28	+	589.831i	−0.397520	+	0.106515i	−0.452040	−	0.891998i	$-0.649304\pi$
$313$	−2201.28	+	589.831i	−0.397520	+	0.106515i	0.0545204	+	0.998513i	$0.482637\pi$
$314$		−	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	0.119235	−	0.992866i	$-0.461956\pi$
$317$	4057.66	−	1087.25i	0.718929	−	0.192637i	0.599694	+	0.800229i	$0.295289\pi$
$318$	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	0.433762	−	0.901027i	$-0.357186\pi$
$331$	−780.873	−	450.837i	−0.129670	−	0.0748648i	−0.563432	+	0.826163i	$0.690519\pi$
$332$			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	−0.625526	−	0.780204i	$-0.715115\pi$
$337$	−9634.53	−	2581.57i	−1.55735	−	0.417290i	−0.931823	+	0.362913i	$0.881782\pi$
$338$	−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	−0.772816	−	0.634630i	$-0.781152\pi$
$347$	1381.83	−	5157.08i	0.213777	−	0.797828i	0.986593	−	0.163198i	$-0.0521809\pi$
$348$	5713.48	+	5251.84i	0.880100	+	0.808988i
$349$	5823.80	+	3362.37i	0.893241	+	0.515713i	0.875001	−	0.484121i	$-0.160861\pi$
$349$	5823.80	+	3362.37i	0.893241	+	0.515713i	0.0182395	+	0.999834i	$0.494194\pi$
$350$	−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	0.459550	+	0.888152i	$0.348011\pi$
$353$	−3577.36	+	6196.17i	−0.539387	+	0.934246i	−0.998937	+	0.0460941i	$0.985323\pi$
$354$	−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	$-0.915986\pi$
$359$		−	3549.12i		−	0.521770i	0.965370	−	0.260885i	$-0.0840144\pi$
$360$	−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	−0.0614086	−	0.998113i	$-0.519559\pi$
$367$	2703.07	−	724.286i	0.384466	−	0.103017i	0.445875	+	0.895095i	$0.352893\pi$
$368$	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	0.580538	−	0.814233i	$-0.302842\pi$
$373$	−2988.71	−	5176.60i	−0.414878	−	0.718590i	−0.995416	+	0.0956435i	$0.969509\pi$
$374$	−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	−0.558840	−	0.829275i	$-0.688754\pi$
$379$	1995.36	−	1995.36i	0.270435	−	0.270435i	0.829275	+	0.558840i	$0.188754\pi$
$380$	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	0.283618	−	0.958937i	$-0.408465\pi$
$383$	9413.48	−	5434.87i	1.25589	−	0.725089i	0.972273	+	0.233848i	$0.0751319\pi$
$384$	−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	0.142352	−	0.989816i	$-0.454534\pi$
$389$	−4938.48	−	2851.23i	−0.643678	−	0.371628i	−0.786030	+	0.618188i	$0.787867\pi$
$390$	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	0.478866	−	0.877888i	$-0.341048\pi$
$397$	−3156.33	−	3156.33i	−0.399022	−	0.399022i	−0.877888	+	0.478866i	$0.841048\pi$
$398$	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	0.793186	+	0.608980i	$0.208421\pi$
$401$	−1591.74	+	5940.44i	−0.198223	+	0.739779i	−0.991409	+	0.130799i	$0.958246\pi$
$402$	−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	0.932073	−	0.362272i	$-0.117999\pi$
$409$	1259.75	+	2181.95i	0.152300	+	0.263791i	−0.779773	+	0.626063i	$0.784665\pi$
$410$	−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	0.755357	+	0.655314i	$0.227464\pi$
$419$	−1942.27	+	7248.65i	−0.226458	+	0.845154i	−0.981815	+	0.189840i	$0.939203\pi$
$420$	−7696.62	+	4886.45i	−0.894182	+	0.567701i
$421$	−2277.77	+	3945.22i	−0.263686	+	0.456718i	−0.967219	−	0.253945i	$-0.918272\pi$
$421$	−2277.77	+	3945.22i	−0.263686	+	0.456718i	0.703532	+	0.710663i	$0.251605\pi$
$422$	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	0.840777	−	0.541382i	$-0.182099\pi$
$431$	2678.92	+	2678.92i	0.299395	+	0.299395i	−0.541382	+	0.840777i	$0.682099\pi$
$432$	−7824.45	−	3283.90i	−0.871421	−	0.365733i
$433$		−	1482.15i		−	0.164498i	−0.996612	−	0.0822491i	$-0.973790\pi$
$433$		−	1482.15i		−	0.164498i	0.996612	−	0.0822491i	$-0.0262103\pi$
$434$	−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	0.999580	+	0.0289938i	$0.00923030\pi$
$439$	1365.13	+	5094.75i	0.148415	+	0.553893i	−0.851164	+	0.524899i	$0.824103\pi$
$440$			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	−0.990636	−	0.136531i	$-0.956405\pi$
$443$	−3515.90	+	6089.72i	−0.377078	+	0.653118i	0.613558	+	0.789650i	$0.289738\pi$
$444$	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	0.665660	−	0.746255i	$-0.268150\pi$
$449$	−766.789	−	766.789i	−0.0805947	−	0.0805947i	−0.746255	+	0.665660i	$0.768150\pi$
$450$	−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	0.192082	−	0.981379i	$-0.438476\pi$
$457$	−5488.29	−	3168.67i	−0.561776	−	0.324341i	−0.753858	+	0.657038i	$0.771809\pi$
$458$	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	−0.188076	−	0.982154i	$-0.560225\pi$
$461$	−11211.4	−	6472.91i	−1.13268	−	0.653956i	−0.944609	+	0.328199i	$0.893558\pi$
$462$	224.960	+	5343.38i	0.0226539	+	0.538087i
$463$	4385.38	+	7595.70i	0.440185	+	0.762423i	0.997703	−	0.0677418i	$-0.0215794\pi$
$463$	4385.38	+	7595.70i	0.440185	+	0.762423i	−0.557518	+	0.830165i	$0.688246\pi$
$464$	−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	$0.193900\pi$
$467$			11548.7i			1.14435i	−0.820131	+	0.572175i	$0.806100\pi$
$468$	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	0.954540	+	0.298082i	$0.0963467\pi$
$479$	2903.12	+	10834.6i	0.276925	+	1.03350i	−0.677615	+	0.735416i	$0.736987\pi$
$480$	−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	0.329121	−	0.944288i	$-0.393248\pi$
$487$	−6611.29	−	6611.29i	−0.615167	−	0.615167i	−0.944288	+	0.329121i	$0.893248\pi$
$488$	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	0.0317703	−	0.999495i	$-0.489886\pi$
$491$	9935.94	−	5736.52i	0.913244	−	0.527261i	0.881473	+	0.472234i	$0.156552\pi$
$492$	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	−0.951197	−	0.308583i	$-0.900145\pi$
$499$	299.350	−	1117.19i	0.0268552	−	0.100225i	0.978053	+	0.208358i	$0.0668119\pi$
$500$	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	0.994135	+	0.108145i	$0.0344912\pi$
$503$	12435.0	+	12435.0i	1.10228	+	1.10228i	0.108145	+	0.994135i	$0.465509\pi$
$504$	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	0.998414	−	0.0562947i	$-0.0179286\pi$
$509$	5172.82	+	8959.59i	0.450454	+	0.780210i	−0.547960	+	0.836505i	$0.684595\pi$
$510$	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	0.997974	+	0.0636210i	$0.0202649\pi$
$521$	12624.5	+	12624.5i	1.06160	+	1.06160i	0.0636210	+	0.997974i	$0.479735\pi$
$522$	−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	0.404536	−	0.914522i	$-0.367433\pi$
$541$	16598.2	−	16598.2i	1.31906	−	1.31906i	0.914522	−	0.404536i	$-0.132567\pi$
$542$	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	−0.784376	−	0.620286i	$-0.787017\pi$
$547$	−5312.13	−	19825.1i	−0.415229	−	1.54966i	0.369147	−	0.929371i	$-0.379650\pi$
$548$	−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	0.642650	−	0.766160i	$-0.277835\pi$
$563$	21741.1	−	12552.2i	1.62749	−	0.939631i	0.984839	−	0.173472i	$-0.0554985\pi$
$564$	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	−0.144233	−	0.989544i	$-0.546071\pi$
$569$	−14567.9	−	8410.79i	−1.07332	−	0.619681i	−0.929086	+	0.369863i	$0.879405\pi$
$570$	9850.71	+	9054.78i	0.723861	+	0.665373i
$571$	693.512	−	2588.22i	0.0508276	−	0.189691i	−0.935844	−	0.352414i	$-0.885361\pi$
$571$	693.512	−	2588.22i	0.0508276	−	0.189691i	0.986672	+	0.162723i	$0.0520276\pi$
$572$	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	0.555246	−	0.831686i	$-0.312624\pi$
$587$	1601.49	+	924.619i	0.112607	+	0.0650138i	−0.442639	+	0.896700i	$0.645958\pi$
$588$	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	$-0.898014\pi$
$593$		−	9095.95i		−	0.629892i	0.949110	−	0.314946i	$-0.101986\pi$
$594$	−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	0.886961	+	0.461845i	$0.152812\pi$
$599$	12365.2	+	21417.1i	0.843450	+	1.46090i	−0.0435111	+	0.999053i	$0.513854\pi$
$600$	−1900.50	−	993.101i	−0.129312	−	0.0675719i
$601$	21485.3	−	5756.97i	1.45824	−	0.390735i	0.559359	−	0.828925i	$-0.311047\pi$
$601$	21485.3	−	5756.97i	1.45824	−	0.390735i	0.898882	+	0.438191i	$0.144381\pi$
$602$	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	0.368520	−	0.929620i	$-0.379865\pi$
$607$	3332.81	+	893.024i	0.222858	+	0.0597146i	−0.145662	+	0.989334i	$0.546531\pi$
$608$	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	0.514313	−	0.857603i	$-0.328047\pi$
$617$	8136.85	+	2180.26i	0.530920	+	0.142259i	0.0166067	+	0.999862i	$0.494714\pi$
$618$	−38168.2	+	1606.91i	−2.48438	+	0.104594i
$619$	15817.2	−	4238.19i	1.02705	−	0.275198i	0.294314	−	0.955709i	$-0.404909\pi$
$619$	15817.2	−	4238.19i	1.02705	−	0.275198i	0.732738	+	0.680511i	$0.238242\pi$
$620$		−	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	$-0.989704\pi$
$631$		−	1025.21i		−	0.0646800i	0.999477	−	0.0323400i	$-0.0102959\pi$
$632$	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	0.844618	+	0.535369i	$0.179827\pi$
$641$	6180.61	+	23066.4i	0.380842	+	1.42132i	−0.463777	+	0.885952i	$0.653506\pi$
$642$	−2736.76	−	8727.27i	−0.168242	−	0.536507i
$643$	−4151.13	−	1112.29i	−0.254595	−	0.0682184i	0.129264	−	0.991610i	$-0.458738\pi$
$643$	−4151.13	−	1112.29i	−0.254595	−	0.0682184i	−0.383859	+	0.923392i	$0.625405\pi$
$644$	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	−0.789781	−	0.613388i	$-0.789806\pi$
$653$	3352.08	−	12510.1i	0.200884	−	0.749708i	0.990665	−	0.136319i	$-0.0435273\pi$
$654$	−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	−0.828638	−	0.559784i	$-0.810884\pi$
$659$	1192.13	−	2064.82i	0.0704684	−	0.122055i	0.899107	+	0.437730i	$0.144217\pi$
$660$	−16597.6	+	10537.6i	−0.978881	+	0.621475i
$661$	−27831.4	+	16068.5i	−1.63770	+	0.945524i	−0.656071	+	0.754699i	$0.727783\pi$
$661$	−27831.4	+	16068.5i	−1.63770	+	0.945524i	−0.981624	+	0.190825i	$0.938884\pi$
$662$	−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	−0.195874	−	0.980629i	$-0.562754\pi$
$673$	2179.07	−	583.880i	0.124810	−	0.0334426i	0.320683	+	0.947187i	$0.396088\pi$
$674$	−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	−0.753141	−	0.657859i	$-0.771462\pi$
$677$	−7571.49	−	28257.2i	−0.429831	−	1.60415i	0.323309	−	0.946293i	$-0.395205\pi$
$678$	−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	−0.900709	−	0.434423i	$-0.856952\pi$
$683$	−8323.07	+	8323.07i	−0.466286	+	0.466286i	0.434423	+	0.900709i	$0.356952\pi$
$684$	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	−0.509416	−	0.860520i	$-0.670139\pi$
$691$	−9451.27	+	2532.46i	−0.520323	+	0.139420i	−0.0109072	+	0.999941i	$0.503472\pi$
$692$	−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	0.974343	−	0.225068i	$-0.0722605\pi$
$709$	339.873	+	1268.42i	0.0180031	+	0.0671885i	−0.956340	+	0.292257i	$0.905594\pi$
$710$	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	−0.478546	−	0.878062i	$-0.658836\pi$
$719$	7702.43	−	7702.43i	0.399516	−	0.399516i	0.878062	+	0.478546i	$0.158836\pi$
$720$	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	−0.721944	−	0.691952i	$-0.756751\pi$
$727$	4670.70	−	8089.89i	0.238276	−	0.412706i	0.960220	+	0.279246i	$0.0900844\pi$
$728$	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	−0.974433	−	0.224680i	$-0.927866\pi$
$733$	−25145.3	+	14517.6i	−1.26707	+	0.731543i	−0.292638	+	0.956223i	$0.594533\pi$
$734$	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	$0.0577121\pi$
$739$			7244.88i			0.360632i	−0.983609	+	0.180316i	$0.942288\pi$
$740$	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	0.135872	−	0.990726i	$-0.456616\pi$
$743$	−4897.55	−	1312.29i	−0.241822	−	0.0647959i	−0.377694	+	0.925930i	$0.623283\pi$
$744$	−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	0.879077	−	0.476679i	$-0.158160\pi$
$751$	28855.0	+	7731.67i	1.40204	+	0.375676i	0.522964	+	0.852355i	$0.324826\pi$
$752$	−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	$-0.617875\pi$
$757$		−	38831.9i		−	1.86443i	0.361910	−	0.932213i	$-0.382125\pi$
$758$	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	0.978044	+	0.208398i	$0.0668250\pi$
$761$	14054.9	+	24343.8i	0.669500	+	1.15961i	−0.308544	+	0.951210i	$0.599842\pi$
$762$	−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	0.678763	−	0.734358i	$-0.262517\pi$
$769$	−6324.81	−	10954.9i	−0.296591	−	0.513711i	−0.975354	+	0.220647i	$0.929183\pi$
$770$	−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	$0.219641\pi$
$773$			27361.2i			1.27311i	−0.771231	+	0.636555i	$0.780359\pi$
$774$	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	0.295364	−	0.955385i	$-0.404559\pi$
$787$	1621.97	+	434.605i	0.0734650	+	0.0196849i	−0.221899	+	0.975070i	$0.571226\pi$
$788$	−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	−0.969517	−	0.245025i	$-0.921204\pi$
$797$	−27947.1	+	16135.2i	−1.24208	+	0.717114i	−0.272560	+	0.962139i	$0.587870\pi$
$798$	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	0.629300	−	0.777163i	$-0.283342\pi$
$809$	−3402.38	−	3402.38i	−0.147863	−	0.147863i	−0.777163	+	0.629300i	$0.783342\pi$
$810$	−46264.5	−	32826.1i	−2.00687	−	1.42394i
$811$	−1228.19	+	1228.19i	−0.0531782	+	0.0531782i	−0.733196	−	0.680018i	$-0.761972\pi$
$811$	−1228.19	+	1228.19i	−0.0531782	+	0.0531782i	0.680018	+	0.733196i	$0.261972\pi$
$812$	−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	0.737448	+	0.675404i	$0.236031\pi$
$821$	10268.3	+	38322.0i	0.436501	+	1.62904i	−0.300947	+	0.953641i	$0.597303\pi$
$822$	−18696.1	−	29448.1i	−0.793312	−	1.24954i
$823$	7271.10	−	27136.1i	0.307964	−	1.14934i	−0.622399	−	0.782700i	$-0.713842\pi$
$823$	7271.10	−	27136.1i	0.307964	−	1.14934i	0.930363	−	0.366639i	$-0.119492\pi$
$824$	−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	0.504311	−	0.863522i	$-0.331746\pi$
$827$	−8542.95	−	8542.95i	−0.359211	−	0.359211i	−0.863522	+	0.504311i	$0.831746\pi$
$828$	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	0.129228	−	0.991615i	$-0.458750\pi$
$839$	17909.4	−	4798.81i	0.736950	−	0.197465i	0.607722	+	0.794150i	$0.292083\pi$
$840$	−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	−0.893443	−	0.449177i	$-0.851717\pi$
$853$	−8577.18	−	32010.5i	−0.344287	−	1.28490i	0.549155	−	0.835720i	$-0.314950\pi$
$854$	−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	−0.0412164	−	0.999150i	$-0.513123\pi$
$857$	10603.9	−	2841.31i	0.422664	−	0.113253i	0.463881	+	0.885898i	$0.346457\pi$
$858$	37010.2	−	11606.0i	1.47262	−	0.461796i
$859$	42208.1	−	24368.9i	1.67651	−	0.967934i	0.712652	−	0.701517i	$-0.247494\pi$
$859$	42208.1	−	24368.9i	1.67651	−	0.967934i	0.963858	−	0.266416i	$-0.0858396\pi$
$860$	−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	−0.899395	−	0.437137i	$-0.855992\pi$
$877$	2547.10	−	9505.92i	0.0980725	−	0.366011i	0.997467	+	0.0711256i	$0.0226591\pi$
$878$	−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	−0.401598	−	0.915816i	$-0.631545\pi$
$881$	13446.5	−	13446.5i	0.514218	−	0.514218i	0.915816	+	0.401598i	$0.131545\pi$
$882$	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	0.985659	−	0.168748i	$-0.0539724\pi$
$887$	46359.2	+	12421.9i	1.75489	+	0.470222i	0.769232	+	0.638970i	$0.220639\pi$
$888$	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	−0.353828	−	0.935310i	$-0.615120\pi$
$907$	−5260.90	+	1409.65i	−0.192597	+	0.0516062i	0.161231	+	0.986917i	$0.448454\pi$
$908$	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	−0.933205	−	0.359343i	$-0.883001\pi$
$911$	−42941.7	+	11506.2i	−1.56171	+	0.418460i	−0.628508	+	0.777803i	$0.716334\pi$
$912$	−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	0.337818	−	0.941211i	$-0.390311\pi$
$929$	31174.8	−	8353.27i	1.10098	−	0.295007i	0.763165	+	0.646204i	$0.223644\pi$
$930$	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	$0.00935180\pi$
$937$			1685.09i			0.0587506i	−0.999568	+	0.0293753i	$0.990648\pi$
$938$	−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	−0.868397	−	0.495869i	$-0.834850\pi$
$941$	3798.49	−	14176.2i	0.131591	−	0.491105i	0.999989	+	0.00476375i	$0.00151635\pi$
$942$	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	0.953780	+	0.300506i	$0.0971555\pi$
$947$	8102.61	+	30239.3i	0.278035	+	1.03764i	−0.675745	+	0.737136i	$0.736178\pi$
$948$	−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	0.472833	−	0.881152i	$-0.343231\pi$
$967$	44274.2	−	25561.7i	1.47235	−	0.850061i	0.999517	+	0.0310909i	$0.00989815\pi$
$968$	−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	$0.318378\pi$
$971$			50928.1i			1.68317i	−0.540122	+	0.841587i	$0.681622\pi$
$972$	−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	−0.558313	−	0.829631i	$-0.688551\pi$
$977$	−3633.66	+	2097.89i	−0.118988	+	0.0686976i	0.439325	+	0.898328i	$0.355218\pi$
$978$	−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	0.929995	+	0.367573i	$0.119811\pi$
$983$	9504.29	+	35470.5i	0.308382	+	1.15090i	−0.621613	+	0.783325i	$0.713522\pi$
$984$	−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	−0.577043	−	0.816714i	$-0.695794\pi$
$991$	7476.97	−	7476.97i	0.239671	−	0.239671i	0.816714	+	0.577043i	$0.195794\pi$
$992$	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	0.250822	−	0.968033i	$-0.419299\pi$
$997$	29971.3	−	8030.79i	0.952057	−	0.255103i	0.701235	+	0.712930i	$0.252632\pi$
$998$	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.106.45	yes	208
9.4	even	3	inner	153.4.n.a.4.8	✓	208
17.13	even	4	inner	153.4.n.a.115.8	yes	208
153.13	even	12	inner	153.4.n.a.13.45	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.n.a.4.8	✓	208	9.4	even	3	inner
153.4.n.a.13.45	yes	208	153.13	even	12	inner
153.4.n.a.106.45	yes	208	1.1	even	1	trivial
153.4.n.a.115.8	yes	208	17.13	even	4	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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