LMFDB - Embedded newform 117.3.k.a.29.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.20
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.89941i q^{2} +(-2.99862 - 0.0909164i) q^{3} +0.392234 q^{4} +(5.82785 - 3.36471i) q^{5} +(0.172688 - 5.69562i) q^{6} +(2.17329 + 3.76424i) q^{7} +8.34266i q^{8} +(8.98347 + 0.545248i) q^{9} +(6.39097 + 11.0695i) q^{10} +10.7668i q^{11} +(-1.17616 - 0.0356605i) q^{12} +(-9.80294 - 8.53829i) q^{13} +(-7.14985 + 4.12797i) q^{14} +(-17.7814 + 9.55965i) q^{15} -14.2772 q^{16} +(12.1195 + 6.99720i) q^{17} +(-1.03565 + 17.0633i) q^{18} +(1.12611 - 1.95047i) q^{19} +(2.28588 - 1.31975i) q^{20} +(-6.17463 - 11.4851i) q^{21} -20.4507 q^{22} +(39.1645 + 22.6116i) q^{23} +(0.758485 - 25.0165i) q^{24} +(10.1425 - 17.5674i) q^{25} +(16.2177 - 18.6198i) q^{26} +(-26.8885 - 2.45174i) q^{27} +(0.852437 + 1.47646i) q^{28} -30.1766i q^{29} +(-18.1577 - 33.7742i) q^{30} +(-11.0730 - 19.1790i) q^{31} +6.25233i q^{32} +(0.978883 - 32.2857i) q^{33} +(-13.2906 + 23.0199i) q^{34} +(25.3312 + 14.6250i) q^{35} +(3.52362 + 0.213865i) q^{36} +(-2.46243 - 4.26506i) q^{37} +(3.70475 + 2.13894i) q^{38} +(28.6190 + 26.4943i) q^{39} +(28.0706 + 48.6198i) q^{40} +(-45.8760 - 26.4865i) q^{41} +(21.8150 - 11.7282i) q^{42} +(-19.9603 - 34.5723i) q^{43} +4.22312i q^{44} +(54.1889 - 27.0491i) q^{45} +(-42.9488 + 74.3895i) q^{46} +(-34.4904 - 19.9131i) q^{47} +(42.8120 + 1.29803i) q^{48} +(15.0537 - 26.0737i) q^{49} +(33.3677 + 19.2649i) q^{50} +(-35.7056 - 22.0838i) q^{51} +(-3.84505 - 3.34901i) q^{52} +26.9386i q^{53} +(4.65686 - 51.0723i) q^{54} +(36.2273 + 62.7475i) q^{55} +(-31.4038 + 18.1310i) q^{56} +(-3.55410 + 5.74635i) q^{57} +57.3179 q^{58} -83.3518i q^{59} +(-6.97448 + 3.74962i) q^{60} +(-36.2916 - 62.8589i) q^{61} +(36.4287 - 21.0321i) q^{62} +(17.4712 + 35.0009i) q^{63} -68.9846 q^{64} +(-85.8589 - 16.7758i) q^{65} +(61.3238 + 1.85930i) q^{66} +(-52.6454 + 91.1844i) q^{67} +(4.75368 + 2.74454i) q^{68} +(-115.384 - 71.3644i) q^{69} +(-27.7788 + 48.1143i) q^{70} +(60.2932 + 34.8103i) q^{71} +(-4.54882 + 74.9460i) q^{72} +12.2795 q^{73} +(8.10110 - 4.67717i) q^{74} +(-32.0108 + 51.7559i) q^{75} +(0.441697 - 0.765042i) q^{76} +(-40.5290 + 23.3994i) q^{77} +(-50.3237 + 54.3594i) q^{78} +(35.6253 - 61.7048i) q^{79} +(-83.2055 + 48.0387i) q^{80} +(80.4054 + 9.79644i) q^{81} +(50.3089 - 87.1375i) q^{82} +(46.7575 + 26.9955i) q^{83} +(-2.42190 - 4.50486i) q^{84} +94.1742 q^{85} +(65.6671 - 37.9129i) q^{86} +(-2.74355 + 90.4883i) q^{87} -89.8241 q^{88} +(-26.7527 + 15.4457i) q^{89} +(51.3775 + 102.927i) q^{90} +(10.8356 - 55.4568i) q^{91} +(15.3616 + 8.86905i) q^{92} +(31.4600 + 58.5172i) q^{93} +(37.8231 - 65.5115i) q^{94} -15.1561i q^{95} +(0.568440 - 18.7484i) q^{96} +(75.0256 + 129.948i) q^{97} +(49.5247 + 28.5931i) q^{98} +(-5.87060 + 96.7236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.89941i			0.949706i	0.880065	+	0.474853i	$0.157499\pi$
$2$			1.89941i			0.949706i	−0.880065	+	0.474853i	$0.842501\pi$
$3$	−2.99862	−	0.0909164i	−0.999541	−	0.0303055i
$3$	−2.99862	−	0.0909164i	−0.999541	−	0.0303055i
$4$	0.392234			0.0980585
$5$	5.82785	−	3.36471i	1.16557	−	0.672942i	0.212937	−	0.977066i	$-0.431697\pi$
$5$	5.82785	−	3.36471i	1.16557	−	0.672942i	0.952632	+	0.304124i	$0.0983637\pi$
$6$	0.172688	−	5.69562i	0.0287813	−	0.949270i
$7$	2.17329	+	3.76424i	0.310469	+	0.537749i	0.978464	−	0.206417i	$-0.0661804\pi$
$7$	2.17329	+	3.76424i	0.310469	+	0.537749i	−0.667995	+	0.744166i	$0.732847\pi$
$8$			8.34266i			1.04283i
$9$	8.98347	+	0.545248i	0.998163	+	0.0605831i
$10$	6.39097	+	11.0695i	0.639097	+	1.10695i
$11$			10.7668i			0.978804i	0.872058	+	0.489402i	$0.162785\pi$
$11$			10.7668i			0.978804i	−0.872058	+	0.489402i	$0.837215\pi$
$12$	−1.17616	−	0.0356605i	−0.0980135	−	0.00297171i
$13$	−9.80294	−	8.53829i	−0.754073	−	0.656791i
$13$	−9.80294	−	8.53829i	−0.754073	−	0.656791i
$14$	−7.14985	+	4.12797i	−0.510703	+	0.294855i
$15$	−17.7814	+	9.55965i	−1.18543	+	0.637310i
$16$	−14.2772			−0.892326
$17$	12.1195	+	6.99720i	0.712912	+	0.411600i	0.812138	−	0.583465i	$-0.198303\pi$
$17$	12.1195	+	6.99720i	0.712912	+	0.411600i	−0.0992264	+	0.995065i	$0.531637\pi$
$18$	−1.03565	+	17.0633i	−0.0575362	+	0.947962i
$19$	1.12611	−	1.95047i	0.0592688	−	0.102657i	−0.834869	−	0.550449i	$-0.814456\pi$
$19$	1.12611	−	1.95047i	0.0592688	−	0.102657i	0.894137	+	0.447793i	$0.147790\pi$
$20$	2.28588	−	1.31975i	0.114294	−	0.0659877i
$21$	−6.17463	−	11.4851i	−0.294030	−	0.546911i
$22$	−20.4507			−0.929576
$23$	39.1645	+	22.6116i	1.70280	+	0.983114i	0.942899	+	0.333078i	$0.108087\pi$
$23$	39.1645	+	22.6116i	1.70280	+	0.983114i	0.759904	+	0.650036i	$0.225246\pi$
$24$	0.758485	−	25.0165i	0.0316035	−	1.04235i
$25$	10.1425	−	17.5674i	0.405702	−	0.702696i
$26$	16.2177	−	18.6198i	0.623759	−	0.716147i
$27$	−26.8885	−	2.45174i	−0.995869	−	0.0908051i
$28$	0.852437	+	1.47646i	0.0304442	+	0.0527308i
$29$		−	30.1766i		−	1.04057i	−0.853992	−	0.520287i	$-0.825825\pi$
$29$		−	30.1766i		−	1.04057i	0.853992	−	0.520287i	$-0.174175\pi$
$30$	−18.1577	−	33.7742i	−0.605257	−	1.12581i
$31$	−11.0730	−	19.1790i	−0.357193	−	0.618676i	0.630298	−	0.776353i	$-0.282933\pi$
$31$	−11.0730	−	19.1790i	−0.357193	−	0.618676i	−0.987491	+	0.157677i	$0.949599\pi$
$32$			6.25233i			0.195385i
$33$	0.978883	−	32.2857i	0.0296631	−	0.978354i
$34$	−13.2906	+	23.0199i	−0.390899	+	0.677057i
$35$	25.3312	+	14.6250i	0.723747	+	0.417856i
$36$	3.52362	+	0.213865i	0.0978784	+	0.00594069i
$37$	−2.46243	−	4.26506i	−0.0665522	−	0.115272i	0.830829	−	0.556527i	$-0.187867\pi$
$37$	−2.46243	−	4.26506i	−0.0665522	−	0.115272i	−0.897381	+	0.441256i	$0.854533\pi$
$38$	3.70475	+	2.13894i	0.0974935	+	0.0562879i
$39$	28.6190	+	26.4943i	0.733822	+	0.679342i
$40$	28.0706	+	48.6198i	0.701766	+	1.21549i
$41$	−45.8760	−	26.4865i	−1.11893	−	0.646013i	−0.177801	−	0.984066i	$-0.556898\pi$
$41$	−45.8760	−	26.4865i	−1.11893	−	0.646013i	−0.941127	+	0.338053i	$0.890232\pi$
$42$	21.8150	−	11.7282i	0.519404	−	0.279242i
$43$	−19.9603	−	34.5723i	−0.464194	−	0.804007i	0.534971	−	0.844870i	$-0.320323\pi$
$43$	−19.9603	−	34.5723i	−0.464194	−	0.804007i	−0.999165	+	0.0408632i	$0.986989\pi$
$44$			4.22312i			0.0959801i
$45$	54.1889	−	27.0491i	1.20420	−	0.601092i
$46$	−42.9488	+	74.3895i	−0.933669	+	1.61716i
$47$	−34.4904	−	19.9131i	−0.733839	−	0.423682i	0.0859862	−	0.996296i	$-0.472596\pi$
$47$	−34.4904	−	19.9131i	−0.733839	−	0.423682i	−0.819825	+	0.572614i	$0.805929\pi$
$48$	42.8120	+	1.29803i	0.891916	+	0.0270424i
$49$	15.0537	−	26.0737i	0.307218	−	0.532116i
$50$	33.3677	+	19.2649i	0.667355	+	0.385297i
$51$	−35.7056	−	22.0838i	−0.700111	−	0.433016i
$52$	−3.84505	−	3.34901i	−0.0739432	−	0.0644040i
$53$			26.9386i			0.508275i	0.967168	+	0.254137i	$0.0817915\pi$
$53$			26.9386i			0.508275i	−0.967168	+	0.254137i	$0.918208\pi$
$54$	4.65686	−	51.0723i	0.0862382	−	0.945782i
$55$	36.2273	+	62.7475i	0.658678	+	1.14086i
$56$	−31.4038	+	18.1310i	−0.560782	+	0.323768i
$57$	−3.55410	+	5.74635i	−0.0623526	+	0.100813i
$58$	57.3179			0.988239
$59$		−	83.3518i		−	1.41274i	−0.707842	−	0.706371i	$-0.750331\pi$
$59$		−	83.3518i		−	1.41274i	0.707842	−	0.706371i	$-0.249669\pi$
$60$	−6.97448	+	3.74962i	−0.116241	+	0.0624936i
$61$	−36.2916	−	62.8589i	−0.594944	−	1.03047i	−0.993555	−	0.113353i	$-0.963841\pi$
$61$	−36.2916	−	62.8589i	−0.594944	−	1.03047i	0.398611	−	0.917120i	$-0.369492\pi$
$62$	36.4287	−	21.0321i	0.587560	−	0.339228i
$63$	17.4712	+	35.0009i	0.277321	+	0.555570i
$64$	−68.9846			−1.07788
$65$	−85.8589	−	16.7758i	−1.32091	−	0.258089i
$66$	61.3238	+	1.85930i	0.929149	+	0.0281712i
$67$	−52.6454	+	91.1844i	−0.785752	+	1.36096i	0.142797	+	0.989752i	$0.454390\pi$
$67$	−52.6454	+	91.1844i	−0.785752	+	1.36096i	−0.928549	+	0.371210i	$0.878943\pi$
$68$	4.75368	+	2.74454i	0.0699071	+	0.0403609i
$69$	−115.384	−	71.3644i	−1.67223	−	1.03427i
$70$	−27.7788	+	48.1143i	−0.396840	+	0.687347i
$71$	60.2932	+	34.8103i	0.849200	+	0.490286i	0.860381	−	0.509652i	$-0.170226\pi$
$71$	60.2932	+	34.8103i	0.849200	+	0.490286i	−0.0111809	+	0.999937i	$0.503559\pi$
$72$	−4.54882	+	74.9460i	−0.0631781	+	1.04092i
$73$	12.2795			0.168213			0.0841064	−	0.996457i	$-0.473196\pi$
$73$	12.2795			0.168213			0.0841064	+	0.996457i	$0.473196\pi$
$74$	8.10110	−	4.67717i	0.109474	−	0.0632050i
$75$	−32.0108	+	51.7559i	−0.426811	+	0.690078i
$76$	0.441697	−	0.765042i	0.00581181	−	0.0100663i
$77$	−40.5290	+	23.3994i	−0.526351	+	0.303889i
$78$	−50.3237	+	54.3594i	−0.645175	+	0.696915i
$79$	35.6253	−	61.7048i	0.450953	−	0.781074i	−0.547492	−	0.836811i	$-0.684417\pi$
$79$	35.6253	−	61.7048i	0.450953	−	0.781074i	0.998445	+	0.0557370i	$0.0177508\pi$
$80$	−83.2055	+	48.0387i	−1.04007	+	0.600484i
$81$	80.4054	+	9.79644i	0.992659	+	0.120944i
$82$	50.3089	−	87.1375i	0.613523	−	1.06265i
$83$	46.7575	+	26.9955i	0.563344	+	0.325247i	0.754486	−	0.656316i	$-0.227886\pi$
$83$	46.7575	+	26.9955i	0.563344	+	0.325247i	−0.191143	+	0.981562i	$0.561219\pi$
$84$	−2.42190	−	4.50486i	−0.0288321	−	0.0536292i
$85$	94.1742			1.10793
$86$	65.6671	−	37.9129i	0.763571	−	0.440848i
$87$	−2.74355	+	90.4883i	−0.0315351	+	1.04010i
$88$	−89.8241			−1.02073
$89$	−26.7527	+	15.4457i	−0.300592	+	0.173547i	−0.642709	−	0.766110i	$-0.722190\pi$
$89$	−26.7527	+	15.4457i	−0.300592	+	0.173547i	0.342117	+	0.939657i	$0.388856\pi$
$90$	51.3775	+	102.927i	0.570861	+	1.14363i
$91$	10.8356	−	55.4568i	0.119072	−	0.609415i
$92$	15.3616	+	8.86905i	0.166974	+	0.0964027i
$93$	31.4600	+	58.5172i	0.338279	+	0.629217i
$94$	37.8231	−	65.5115i	0.402373	−	0.696931i
$95$		−	15.1561i		−	0.159538i
$96$	0.568440	−	18.7484i	0.00592125	−	0.195296i
$97$	75.0256	+	129.948i	0.773460	+	1.33967i	0.935656	+	0.352914i	$0.114809\pi$
$97$	75.0256	+	129.948i	0.773460	+	1.33967i	−0.162196	+	0.986759i	$0.551858\pi$
$98$	49.5247	+	28.5931i	0.505354	+	0.291766i
$99$	−5.87060	+	96.7236i	−0.0592990	+	0.977006i
$100$	3.97825	−	6.89053i	0.0397825	−	0.0689053i
$101$		−	13.7627i		−	0.136265i	−0.997676	−	0.0681324i	$-0.978296\pi$
$101$		−	13.7627i		−	0.136265i	0.997676	−	0.0681324i	$-0.0217040\pi$
$102$	41.9463	−	67.8197i	0.411238	−	0.664899i
$103$	−22.7960	−	39.4838i	−0.221320	−	0.383338i	0.733889	−	0.679270i	$-0.237703\pi$
$103$	−22.7960	−	39.4838i	−0.221320	−	0.383338i	−0.955209	+	0.295932i	$0.904370\pi$
$104$	71.2320	−	81.7826i	0.684923	−	0.786372i
$105$	−74.6289	−	46.1577i	−0.710752	−	0.439597i
$106$	−51.1674			−0.482712
$107$	−159.973	+	92.3602i	−1.49507	+	0.863179i	−0.999984	−	0.00566409i	$-0.998197\pi$
$107$	−159.973	+	92.3602i	−1.49507	+	0.863179i	−0.495087	+	0.868844i	$0.664864\pi$
$108$	−10.5466	−	0.961655i	−0.0976534	−	0.00890421i
$109$	−10.4891			−0.0962307			−0.0481153	−	0.998842i	$-0.515322\pi$
$109$	−10.4891			−0.0962307			−0.0481153	+	0.998842i	$0.515322\pi$
$110$	−119.183	+	68.8106i	−1.08349	+	0.625551i
$111$	6.99614	+	13.0132i	0.0630283	+	0.117236i
$112$	−31.0285	−	53.7429i	−0.277040	−	0.479847i
$113$		−	132.144i		−	1.16942i	−0.811243	−	0.584709i	$-0.801209\pi$
$113$		−	132.144i		−	1.16942i	0.811243	−	0.584709i	$-0.198791\pi$
$114$	−10.9147	−	6.75070i	−0.0957429	−	0.0592166i
$115$	304.326			2.64631
$116$		−	11.8363i		−	0.102037i
$117$	−83.4089	−	82.0485i	−0.712897	−	0.701269i
$118$	158.319			1.34169
$119$			60.8276i			0.511157i
$120$	−79.7529	−	148.344i	−0.664607	−	1.23620i
$121$	5.07507			0.0419427
$122$	119.395	−	68.9327i	0.978647	−	0.565022i
$123$	135.157	+	83.5940i	1.09884	+	0.679626i
$124$	−4.34320	−	7.52264i	−0.0350258	−	0.0606664i
$125$			31.7286i			0.253829i
$126$	−66.4812	+	33.1850i	−0.527628	+	0.263373i
$127$	−80.9910	−	140.281i	−0.637725	−	1.10457i	−0.985931	−	0.167154i	$-0.946542\pi$
$127$	−80.9910	−	140.281i	−0.637725	−	1.10457i	0.348206	−	0.937418i	$-0.386791\pi$
$128$		−	106.021i		−	0.828288i
$129$	56.7103	+	105.484i	0.439615	+	0.817706i
$130$	31.8641	−	163.081i	0.245108	−	1.25447i
$131$	−172.357	+	99.5104i	−1.31570	+	0.759622i	−0.983034	−	0.183422i	$-0.941283\pi$
$131$	−172.357	+	99.5104i	−1.31570	+	0.759622i	−0.332669	+	0.943044i	$0.607949\pi$
$132$	0.383951	−	12.6635i	0.00290872	−	0.0959360i
$133$	9.78941			0.0736046
$134$	−173.197	−	99.9952i	−1.29251	−	0.746233i
$135$	−164.951	+	76.1835i	−1.22186	+	0.564322i
$136$	−58.3753	+	101.109i	−0.429230	+	0.743448i
$137$	−61.2087	+	35.3389i	−0.446779	+	0.257948i	−0.706469	−	0.707744i	$-0.749713\pi$
$137$	−61.2087	+	35.3389i	−0.446779	+	0.257948i	0.259690	+	0.965692i	$0.416380\pi$
$138$	135.550	−	219.161i	0.982249	−	1.58812i
$139$	19.0314			0.136917			0.0684583	−	0.997654i	$-0.478192\pi$
$139$	19.0314			0.136917			0.0684583	+	0.997654i	$0.478192\pi$
$140$	9.93574	+	5.73640i	0.0709696	+	0.0409743i
$141$	101.613	+	62.8475i	0.720662	+	0.445727i
$142$	−66.1191	+	114.522i	−0.465627	+	0.806490i
$143$	91.9304	−	105.547i	0.642870	−	0.738089i
$144$	−128.259	−	7.78463i	−0.890687	−	0.0540599i
$145$	−101.536	−	175.865i	−0.700246	−	1.21286i
$146$			23.3239i			0.159753i
$147$	−47.5108	+	76.8165i	−0.323202	+	0.522562i
$148$	−0.965850	−	1.67290i	−0.00652601	−	0.0113034i
$149$		−	17.4914i		−	0.117392i	−0.998276	−	0.0586958i	$-0.981306\pi$
$149$		−	17.4914i		−	0.117392i	0.998276	−	0.0586958i	$-0.0186942\pi$
$150$	−98.3057	−	60.8017i	−0.655372	−	0.405345i
$151$	89.5177	−	155.049i	0.592832	−	1.02682i	−0.401016	−	0.916071i	$-0.631343\pi$
$151$	89.5177	−	155.049i	0.592832	−	1.02682i	0.993849	−	0.110745i	$-0.0353237\pi$
$152$	16.2721	+	9.39473i	0.107054	+	0.0618074i
$153$	105.060	+	69.4672i	0.686666	+	0.454034i
$154$	−44.4452	−	76.9813i	−0.288605	−	0.499878i
$155$	−129.063	−	74.5147i	−0.832666	−	0.480740i
$156$	11.2254	+	10.3920i	0.0719575	+	0.0666153i
$157$	−70.7984	−	122.627i	−0.450946	−	0.781061i	0.547500	−	0.836806i	$-0.315580\pi$
$157$	−70.7984	−	122.627i	−0.450946	−	0.781061i	−0.998445	+	0.0557455i	$0.982246\pi$
$158$	117.203	+	67.6671i	0.741790	+	0.428273i
$159$	2.44916	−	80.7786i	0.0154035	−	0.508041i
$160$	21.0373	+	36.4376i	0.131483	+	0.227735i
$161$			196.566i			1.22091i
$162$	−18.6075	+	152.723i	−0.114861	+	0.942735i
$163$	20.6255	−	35.7244i	0.126537	−	0.219168i	−0.795796	−	0.605565i	$-0.792947\pi$
$163$	20.6255	−	35.7244i	0.126537	−	0.219168i	0.922333	+	0.386397i	$0.126280\pi$
$164$	−17.9941	−	10.3889i	−0.109720	−	0.0633471i
$165$	−102.927	−	191.450i	−0.623801	−	1.16030i
$166$	−51.2755	+	88.8118i	−0.308889	+	0.535011i
$167$	−24.7775	−	14.3053i	−0.148369	−	0.0856606i	0.423978	−	0.905673i	$-0.360633\pi$
$167$	−24.7775	−	14.3053i	−0.148369	−	0.0856606i	−0.572346	+	0.820012i	$0.693967\pi$
$168$	95.8165	−	51.5129i	0.570336	−	0.306624i
$169$	23.1954	+	167.401i	0.137251	+	0.990536i
$170$			178.876i			1.05221i
$171$	11.1798	−	16.9080i	0.0653792	−	0.0988773i
$172$	−7.82912	−	13.5604i	−0.0455182	−	0.0788398i
$173$	92.6345	−	53.4825i	0.535459	−	0.309148i	−0.207777	−	0.978176i	$-0.566623\pi$
$173$	92.6345	−	53.4825i	0.535459	−	0.309148i	0.743237	+	0.669029i	$0.233290\pi$
$174$	−171.875	−	5.21114i	−0.987785	−	0.0299491i
$175$	88.1706			0.503832
$176$		−	153.721i		−	0.873412i
$177$	−7.57805	+	249.940i	−0.0428138	+	1.41209i
$178$	−29.3377	−	50.8144i	−0.164819	−	0.285474i
$179$	275.120	−	158.840i	1.53698	−	0.887376i	0.537967	−	0.842966i	$-0.319192\pi$
$179$	275.120	−	158.840i	1.53698	−	0.887376i	0.999013	−	0.0444106i	$-0.0141410\pi$
$180$	21.2547	−	10.6096i	0.118082	−	0.0589422i
$181$	246.323			1.36090			0.680451	−	0.732794i	$-0.261784\pi$
$181$	246.323			1.36090			0.680451	+	0.732794i	$0.261784\pi$
$182$	105.335	+	20.5812i	0.578765	+	0.113084i
$183$	103.110	+	191.789i	0.563442	+	1.04803i
$184$	−188.641	+	326.736i	−1.02522	+	1.77574i
$185$	−28.7014	−	16.5707i	−0.155142	−	0.0895715i
$186$	−111.148	+	59.7555i	−0.597571	+	0.321266i
$187$	−75.3377	+	130.489i	−0.402876	+	0.697801i
$188$	−13.5283	−	7.81058i	−0.0719591	−	0.0415456i
$189$	−49.2074	−	106.543i	−0.260356	−	0.563719i
$190$	28.7877			0.151514
$191$	−14.1190	+	8.15160i	−0.0739214	+	0.0426785i	−0.536505	−	0.843897i	$-0.680256\pi$
$191$	−14.1190	+	8.15160i	−0.0739214	+	0.0426785i	0.462584	+	0.886576i	$0.346922\pi$
$192$	206.859	+	6.27184i	1.07739	+	0.0326658i
$193$	−78.3005	+	135.621i	−0.405702	+	0.702697i	−0.994403	−	0.105654i	$-0.966306\pi$
$193$	−78.3005	+	135.621i	−0.405702	+	0.702697i	0.588701	+	0.808351i	$0.299640\pi$
$194$	−246.825	+	142.505i	−1.27229	+	0.734560i
$195$	255.933	+	58.1102i	1.31248	+	0.298001i
$196$	5.90456	−	10.2270i	0.0301253	−	0.0521785i
$197$	224.786	−	129.780i	1.14104	−	0.658782i	0.194356	−	0.980931i	$-0.437738\pi$
$197$	224.786	−	129.780i	1.14104	−	0.658782i	0.946689	+	0.322149i	$0.104405\pi$
$198$	−183.718	−	11.1507i	−0.927869	−	0.0563166i
$199$	−136.220	+	235.939i	−0.684521	+	1.18563i	0.289066	+	0.957309i	$0.406655\pi$
$199$	−136.220	+	235.939i	−0.684521	+	1.18563i	−0.973587	+	0.228316i	$0.926678\pi$
$200$	146.559	+	84.6158i	0.732794	+	0.423079i
$201$	166.154	−	268.641i	0.826635	−	1.33652i
$202$	26.1411			0.129412
$203$	113.592	−	65.5825i	0.559567	−	0.323066i
$204$	−14.0050	−	8.66202i	−0.0686518	−	0.0424609i
$205$	−356.478			−1.73892
$206$	74.9961	−	43.2990i	0.364059	−	0.210189i
$207$	339.504	+	224.485i	1.64012	+	1.08447i
$208$	139.959	+	121.903i	0.672879	+	0.586072i
$209$	21.0004	+	12.1246i	0.100481	+	0.0580125i
$210$	87.6725	−	141.751i	0.417488	−	0.675005i
$211$	−136.308	+	236.093i	−0.646011	+	1.11892i	0.338056	+	0.941126i	$0.390231\pi$
$211$	−136.308	+	236.093i	−0.646011	+	1.11892i	−0.984067	+	0.177798i	$0.943103\pi$
$212$			10.5662i			0.0498407i
$213$	−177.632	−	109.865i	−0.833951	−	0.515796i
$214$	−175.430	−	303.854i	−0.819767	−	1.41988i
$215$	−232.652	−	134.321i	−1.08210	−	0.624751i
$216$	20.4540	−	224.321i	0.0946945	−	1.03852i
$217$	48.1295	−	83.3627i	0.221795	−	0.384160i
$218$		−	19.9232i		−	0.0913909i
$219$	−36.8217	−	1.11641i	−0.168136	−	0.00509777i
$220$	14.2096	+	24.6117i	0.0645890	+	0.111871i
$221$	−59.0627	−	172.073i	−0.267252	−	0.778610i
$222$	−24.7174	+	13.2885i	−0.111340	+	0.0598583i
$223$	197.694			0.886518			0.443259	−	0.896393i	$-0.353822\pi$
$223$	197.694			0.886518			0.443259	+	0.896393i	$0.353822\pi$
$224$	−23.5353	+	13.5881i	−0.105068	+	0.0606612i
$225$	100.694	−	152.286i	0.447528	−	0.676827i
$226$	250.996			1.11060
$227$	−237.667	+	137.217i	−1.04699	+	0.604480i	−0.921805	−	0.387654i	$-0.873286\pi$
$227$	−237.667	+	137.217i	−1.04699	+	0.604480i	−0.125184	+	0.992133i	$0.539952\pi$
$228$	−1.39404	+	2.25391i	−0.00611420	+	0.00988559i
$229$	−48.5933	−	84.1661i	−0.212198	−	0.367538i	0.740204	−	0.672382i	$-0.234729\pi$
$229$	−48.5933	−	84.1661i	−0.212198	−	0.367538i	−0.952402	+	0.304845i	$0.901395\pi$
$230$			578.041i			2.51322i
$231$	123.659	−	66.4813i	0.535318	−	0.287798i
$232$	251.754			1.08514
$233$			121.511i			0.521507i	0.965405	+	0.260754i	$0.0839710\pi$
$233$			121.511i			0.521507i	−0.965405	+	0.260754i	$0.916029\pi$
$234$	155.844	−	158.428i	0.665999	−	0.677043i
$235$	−268.007			−1.14045
$236$		−	32.6934i		−	0.138531i
$237$	−112.437	+	181.791i	−0.474417	+	0.767049i
$238$	−115.537			−0.485449
$239$	−259.747	+	149.965i	−1.08681	+	0.627467i	−0.932724	−	0.360591i	$-0.882575\pi$
$239$	−259.747	+	149.965i	−1.08681	+	0.627467i	−0.154081	+	0.988058i	$0.549242\pi$
$240$	253.869	−	136.485i	1.05779	−	0.568688i
$241$	187.966	+	325.566i	0.779940	+	1.35090i	0.931976	+	0.362521i	$0.118084\pi$
$241$	187.966	+	325.566i	0.779940	+	1.35090i	−0.152035	+	0.988375i	$0.548583\pi$
$242$			9.63964i			0.0398332i
$243$	−240.215	−	36.6860i	−0.988538	−	0.150971i
$244$	−14.2348	−	24.6554i	−0.0583393	−	0.101047i
$245$		−	202.605i		−	0.826958i
$246$	−158.780	+	256.719i	−0.645445	+	1.04357i
$247$	−27.6929	+	9.50536i	−0.112117	+	0.0384833i
$248$	160.004	−	92.3781i	0.645176	−	0.372492i
$249$	−137.754	−	85.2002i	−0.553228	−	0.342170i
$250$	−60.2657			−0.241063
$251$	3.31004	+	1.91105i	0.0131874	+	0.00761375i	0.506579	−	0.862193i	$-0.330910\pi$
$251$	3.31004	+	1.91105i	0.0131874	+	0.00761375i	−0.493392	+	0.869807i	$0.664243\pi$
$252$	6.85280	+	13.7286i	0.0271936	+	0.0544784i
$253$	−243.456	+	421.678i	−0.962276	+	1.66671i
$254$	266.451	−	153.835i	1.04902	−	0.605651i
$255$	−282.393	−	8.56198i	−1.10742	−	0.0335764i
$256$	−74.5611			−0.291254
$257$	224.378	+	129.545i	0.873066	+	0.504065i	0.868366	−	0.495924i	$-0.165171\pi$
$257$	224.378	+	129.545i	0.873066	+	0.504065i	0.00470007	+	0.999989i	$0.498504\pi$
$258$	−200.358	+	107.716i	−0.776580	+	0.417505i
$259$	10.7031	−	18.5384i	0.0413248	−	0.0715767i
$260$	−33.6768	−	6.58003i	−0.129526	−	0.0253078i
$261$	16.4538	−	271.091i	0.0630412	−	1.03866i
$262$	−189.011	−	327.377i	−0.721417	−	1.24953i
$263$			202.869i			0.771365i	0.922632	+	0.385683i	$0.126034\pi$
$263$			202.869i			0.771365i	−0.922632	+	0.385683i	$0.873966\pi$
$264$	269.349	+	8.16649i	1.02026	+	0.0309337i
$265$	90.6404	+	156.994i	0.342039	+	0.592430i
$266$			18.5941i			0.0699027i
$267$	81.6255	−	43.8835i	0.305714	−	0.164358i
$268$	−20.6493	+	35.7656i	−0.0770496	+	0.133454i
$269$	182.658	+	105.458i	0.679027	+	0.392036i	0.799488	−	0.600682i	$-0.205104\pi$
$269$	182.658	+	105.458i	0.679027	+	0.392036i	−0.120462	+	0.992718i	$0.538437\pi$
$270$	−144.704	−	313.310i	−0.535940	−	1.16041i
$271$	54.5228	+	94.4363i	0.201191	+	0.348474i	0.948913	−	0.315539i	$-0.102185\pi$
$271$	54.5228	+	94.4363i	0.201191	+	0.348474i	−0.747721	+	0.664013i	$0.768852\pi$
$272$	−173.033	−	99.9005i	−0.636150	−	0.367281i
$273$	−37.5337	+	165.309i	−0.137486	+	0.605527i
$274$	−67.1231	−	116.261i	−0.244975	−	0.424309i
$275$	189.145	+	109.203i	0.687802	+	0.397103i
$276$	−45.2574	−	27.9915i	−0.163976	−	0.101419i
$277$	−152.861	−	264.763i	−0.551844	−	0.955822i	−0.998142	−	0.0609373i	$-0.980591\pi$
$277$	−152.861	−	264.763i	−0.551844	−	0.955822i	0.446298	−	0.894885i	$-0.352742\pi$
$278$			36.1485i			0.130031i
$279$	−89.0164	−	178.331i	−0.319055	−	0.639179i
$280$	−122.011	+	211.329i	−0.435754	+	0.754748i
$281$	176.239	+	101.751i	0.627184	+	0.362105i	0.779661	−	0.626202i	$-0.215392\pi$
$281$	176.239	+	101.751i	0.627184	+	0.362105i	−0.152477	+	0.988307i	$0.548725\pi$
$282$	−119.373	+	193.006i	−0.423309	+	0.684417i
$283$	−41.0373	+	71.0787i	−0.145008	+	0.251161i	−0.929376	−	0.369135i	$-0.879654\pi$
$283$	−41.0373	+	71.0787i	−0.145008	+	0.251161i	0.784368	+	0.620296i	$0.212987\pi$
$284$	23.6490	+	13.6538i	0.0832713	+	0.0480767i
$285$	−1.37794	+	45.4474i	−0.00483487	+	0.159464i
$286$	200.477	+	174.614i	0.700968	+	0.610537i
$287$		−	230.251i		−	0.802269i
$288$	−3.40907	+	56.1676i	−0.0118371	+	0.195026i
$289$	−46.5785	−	80.6763i	−0.161171	−	0.279157i
$290$	334.040	−	192.858i	1.15186	−	0.665028i
$291$	−213.159	−	396.487i	−0.732506	−	1.36250i
$292$	4.81645			0.0164947
$293$		−	76.2493i		−	0.260237i	−0.991498	−	0.130118i	$-0.958464\pi$
$293$		−	76.2493i		−	0.260237i	0.991498	−	0.130118i	$-0.0415357\pi$
$294$	−145.906	−	90.2425i	−0.496280	−	0.306947i
$295$	−280.454	−	485.761i	−0.950693	−	1.64665i
$296$	35.5819	−	20.5432i	0.120209	−	0.0694028i
$297$	26.3975	−	289.504i	0.0888804	−	0.974760i
$298$	33.2233			0.111488
$299$	−190.863	−	556.058i	−0.638337	−	1.85973i
$300$	−12.5557	+	20.3004i	−0.0418524	+	0.0676680i
$301$	86.7590	−	150.271i	0.288236	−	0.499239i
$302$	294.502	+	170.031i	0.975173	+	0.563016i
$303$	−1.25126	+	41.2693i	−0.00412957	+	0.136202i
$304$	−16.0777	+	27.8473i	−0.0528871	+	0.0916031i
$305$	−423.004	−	244.221i	−1.38690	−	0.800726i
$306$	−131.947	+	199.552i	−0.431199	+	0.652131i
$307$	165.711			0.539777			0.269888	−	0.962892i	$-0.413013\pi$
$307$	165.711			0.539777			0.269888	+	0.962892i	$0.413013\pi$
$308$	−15.8969	+	9.17805i	−0.0516132	+	0.0297989i
$309$	64.7669	+	120.470i	0.209601	+	0.389869i
$310$	141.534	−	245.144i	0.456562	−	0.790788i
$311$	−82.1589	+	47.4344i	−0.264176	+	0.152522i	−0.626238	−	0.779632i	$-0.715406\pi$
$311$	−82.1589	+	47.4344i	−0.264176	+	0.152522i	0.362062	+	0.932154i	$0.382073\pi$
$312$	−221.033	+	238.759i	−0.708440	+	0.765253i
$313$	226.404	−	392.144i	0.723337	−	1.25286i	−0.236318	−	0.971676i	$-0.575941\pi$
$313$	226.404	−	392.144i	0.723337	−	1.25286i	0.959655	−	0.281180i	$-0.0907258\pi$
$314$	232.918	−	134.475i	0.741778	−	0.428266i
$315$	219.587	+	145.195i	0.697103	+	0.460935i
$316$	13.9735	−	24.2027i	0.0442198	−	0.0765909i
$317$	387.765	+	223.876i	1.22323	+	0.706234i	0.965606	−	0.260011i	$-0.0837262\pi$
$317$	387.765	+	223.876i	1.22323	+	0.706234i	0.257627	+	0.966245i	$0.417059\pi$
$318$	153.432	+	4.65196i	0.482490	+	0.0146288i
$319$	324.907			1.01852
$320$	−402.032	+	232.113i	−1.25635	+	0.725354i
$321$	488.094	−	262.409i	1.52054	−	0.817474i
$322$	−373.360			−1.15950
$323$	27.2957	−	15.7592i	0.0845068	−	0.0487900i
$324$	31.5377	+	3.84250i	0.0973387	+	0.0118596i
$325$	−249.422	+	85.6123i	−0.767453	+	0.263422i
$326$	67.8554	+	39.1764i	0.208146	+	0.120173i
$327$	31.4530	+	0.953636i	0.0961865	+	0.00291632i
$328$	220.968	−	382.728i	0.673684	−	1.16685i
$329$		−	173.107i		−	0.526161i
$330$	363.642	−	195.501i	1.10195	−	0.592428i
$331$	−26.4122	−	45.7473i	−0.0797952	−	0.138209i	0.823366	−	0.567510i	$-0.192093\pi$
$331$	−26.4122	−	45.7473i	−0.0797952	−	0.138209i	−0.903161	+	0.429301i	$0.858760\pi$
$332$	18.3399	+	10.5885i	0.0552406	+	0.0318932i
$333$	−19.7957	−	39.6576i	−0.0594464	−	0.119092i
$334$	27.1717	−	47.0628i	0.0813524	−	0.140906i
$335$			708.545i			2.11506i
$336$	88.1565	+	163.976i	0.262371	+	0.488023i
$337$	−321.124	−	556.204i	−0.952891	−	1.65046i	−0.739121	−	0.673572i	$-0.764759\pi$
$337$	−321.124	−	556.204i	−0.952891	−	1.65046i	−0.213770	−	0.976884i	$-0.568574\pi$
$338$	−317.963	+	44.0576i	−0.940718	+	0.130348i
$339$	−12.0141	+	396.250i	−0.0354398	+	1.16888i
$340$	36.9383			0.108642
$341$	206.497	−	119.221i	0.605563	−	0.349622i
$342$	32.1153	+	21.2351i	0.0939043	+	0.0620910i
$343$	343.846			1.00247
$344$	288.425	−	166.522i	0.838445	−	0.484077i
$345$	−912.559	−	27.6682i	−2.64510	−	0.0801978i
$346$	101.585	+	175.951i	0.293599	+	0.508529i
$347$		−	285.274i		−	0.822117i	−0.911609	−	0.411058i	$-0.865159\pi$
$347$		−	285.274i		−	0.822117i	0.911609	−	0.411058i	$-0.134841\pi$
$348$	−1.07611	+	35.4926i	−0.00309228	+	0.101990i
$349$	−232.958			−0.667502			−0.333751	−	0.942661i	$-0.608314\pi$
$349$	−232.958			−0.667502			−0.333751	+	0.942661i	$0.608314\pi$
$350$			167.472i			0.478492i
$351$	242.652	+	253.616i	0.691317	+	0.722551i
$352$	−67.3179			−0.191244
$353$			211.272i			0.598506i	0.954174	+	0.299253i	$0.0967374\pi$
$353$			211.272i			0.598506i	−0.954174	+	0.299253i	$0.903263\pi$
$354$	−474.740	−	14.3938i	−1.34107	−	0.0406605i
$355$	468.506			1.31974
$356$	−10.4933	+	6.05832i	−0.0294756	+	0.0170178i
$357$	5.53023	−	182.399i	0.0154908	−	0.510922i
$358$	301.703	+	522.565i	0.842747	+	1.45968i
$359$			124.143i			0.345801i	0.984939	+	0.172901i	$0.0553139\pi$
$359$			124.143i			0.345801i	−0.984939	+	0.172901i	$0.944686\pi$
$360$	225.662	+	452.080i	0.626838	+	1.25578i
$361$	177.964	+	308.242i	0.492974	+	0.853857i
$362$			467.869i			1.29246i
$363$	−15.2182	−	0.461407i	−0.0419234	−	0.00127109i
$364$	4.25008	−	21.7520i	0.0116760	−	0.0597583i
$365$	71.5633	−	41.3171i	0.196064	−	0.113197i
$366$	−364.287	+	195.848i	−0.995320	+	0.535104i
$367$	−10.8912			−0.0296764			−0.0148382	−	0.999890i	$-0.504723\pi$
$367$	−10.8912			−0.0296764			−0.0148382	+	0.999890i	$0.504723\pi$
$368$	−559.160	−	322.831i	−1.51946	−	0.877258i
$369$	−397.684	−	262.955i	−1.07774	−	0.712615i
$370$	31.4747	−	54.5157i	0.0850666	−	0.147340i
$371$	−101.403	+	58.5452i	−0.273324	+	0.157804i
$372$	12.3397	+	22.9524i	0.0331712	+	0.0617001i
$373$	−241.181			−0.646597			−0.323299	−	0.946297i	$-0.604792\pi$
$373$	−241.181			−0.646597			−0.323299	+	0.946297i	$0.604792\pi$
$374$	−247.852	−	143.097i	−0.662706	−	0.382613i
$375$	2.88465	−	95.1421i	0.00769241	−	0.253712i
$376$	166.128	−	287.742i	0.441829	−	0.765271i
$377$	−257.657	+	295.820i	−0.683440	+	0.784668i
$378$	202.369	−	93.4651i	0.535368	−	0.247262i
$379$	−206.602	−	357.845i	−0.545124	−	0.944182i	−0.998599	−	0.0529130i	$-0.983149\pi$
$379$	−206.602	−	357.845i	−0.545124	−	0.944182i	0.453476	−	0.891269i	$-0.350184\pi$
$380$		−	5.94473i		−	0.0156440i
$381$	230.108	+	428.012i	0.603957	+	1.12339i
$382$	−15.4833	−	26.8178i	−0.0405321	−	0.0702036i
$383$			651.689i			1.70154i	0.525540	+	0.850769i	$0.323863\pi$
$383$			651.689i			1.70154i	−0.525540	+	0.850769i	$0.676137\pi$
$384$	−9.63904	+	317.917i	−0.0251017	+	0.827908i
$385$	−157.465	+	272.737i	−0.408999	+	0.708407i
$386$	−257.599	−	148.725i	−0.667356	−	0.385298i
$387$	−160.463	−	321.463i	−0.414632	−	0.830653i
$388$	29.4276	+	50.9701i	0.0758444	+	0.131366i
$389$	53.1062	+	30.6609i	0.136520	+	0.0788197i	0.566704	−	0.823921i	$-0.308218\pi$
$389$	53.1062	+	30.6609i	0.136520	+	0.0788197i	−0.430185	+	0.902741i	$0.641552\pi$
$390$	−110.375	+	486.123i	−0.283013	+	1.24647i
$391$	316.436	+	548.083i	0.809299	+	1.40175i
$392$	217.524	+	125.588i	0.554908	+	0.320376i
$393$	525.881	−	282.724i	1.33812	−	0.719400i
$394$	246.506	+	426.961i	0.625650	+	1.08366i
$395$		−	479.475i		−	1.21386i
$396$	−2.30265	+	37.9383i	−0.00581477	+	0.0958038i
$397$	166.978	−	289.214i	0.420599	−	0.728499i	−0.575399	−	0.817873i	$-0.695153\pi$
$397$	166.978	−	289.214i	0.420599	−	0.728499i	0.995998	+	0.0893738i	$0.0284866\pi$
$398$	−448.146	−	258.737i	−1.12600	−	0.650094i
$399$	−29.3547	−	0.890018i	−0.0735707	−	0.00223062i
$400$	−144.807	+	250.814i	−0.362018	+	0.627034i
$401$	−503.053	−	290.438i	−1.25450	−	0.724284i	−0.282497	−	0.959268i	$-0.591163\pi$
$401$	−503.053	−	290.438i	−1.25450	−	0.724284i	−0.971999	+	0.234985i	$0.924496\pi$
$402$	510.261	+	315.594i	1.26930	+	0.785061i
$403$	−55.2076	+	282.554i	−0.136992	+	0.701128i
$404$		−	5.39822i		−	0.0133619i
$405$	501.553	−	213.449i	1.23840	−	0.527034i
$406$	124.568	+	215.758i	0.306818	+	0.531424i
$407$	45.9212	−	26.5126i	0.112829	−	0.0651416i
$408$	184.238	−	297.880i	0.451563	−	0.730098i
$409$	44.3794			0.108507			0.0542535	−	0.998527i	$-0.482722\pi$
$409$	44.3794			0.108507			0.0542535	+	0.998527i	$0.482722\pi$
$410$		−	677.099i		−	1.65146i
$411$	186.755	−	100.403i	0.454391	−	0.244290i
$412$	−8.94137	−	15.4869i	−0.0217023	−	0.0375896i
$413$	313.756	−	181.147i	0.759700	−	0.438613i
$414$	−426.390	+	644.858i	−1.02993	+	1.55763i
$415$	363.328			0.875488
$416$	53.3842	−	61.2913i	0.128327	−	0.147335i
$417$	−57.0680	−	1.73027i	−0.136854	−	0.00414932i
$418$	−23.0296	+	39.8885i	−0.0550948	+	0.0954270i
$419$	−228.253	−	131.782i	−0.544756	−	0.314515i	0.202248	−	0.979334i	$-0.435175\pi$
$419$	−228.253	−	131.782i	−0.544756	−	0.314515i	−0.747004	+	0.664819i	$0.768509\pi$
$420$	−29.2720	−	18.1046i	−0.0696952	−	0.0431063i
$421$	−220.575	+	382.047i	−0.523931	+	0.907475i	0.475681	+	0.879618i	$0.342202\pi$
$421$	−220.575	+	382.047i	−0.523931	+	0.907475i	−0.999612	+	0.0278569i	$0.991132\pi$
$422$	−448.438	−	258.906i	−1.06265	−	0.613521i
$423$	−298.986	−	197.694i	−0.706823	−	0.467362i
$424$	−224.739			−0.530046
$425$	245.845	−	141.939i	0.578459	−	0.333974i
$426$	208.678	−	337.396i	0.489855	−	0.792009i
$427$	157.744	−	273.221i	0.369424	−	0.639861i
$428$	−62.7467	+	36.2268i	−0.146604	+	0.0846421i
$429$	−285.260	+	308.137i	−0.664943	+	0.718268i
$430$	255.132	−	441.901i	0.593330	−	1.02768i
$431$	−682.231	+	393.886i	−1.58290	+	0.913889i	−0.588469	+	0.808520i	$0.700269\pi$
$431$	−682.231	+	393.886i	−1.58290	+	0.913889i	−0.994433	+	0.105369i	$0.966398\pi$
$432$	383.892	+	35.0040i	0.888640	+	0.0810278i
$433$	−315.221	+	545.978i	−0.727993	+	1.26092i	0.229738	+	0.973253i	$0.426213\pi$
$433$	−315.221	+	545.978i	−0.727993	+	1.26092i	−0.957730	+	0.287668i	$0.907120\pi$
$434$	158.340	+	91.4177i	0.364839	+	0.210640i
$435$	288.478	+	536.584i	0.663168	+	1.23353i
$436$	−4.11420			−0.00943624
$437$	88.2067	−	50.9262i	0.201846	−	0.116536i
$438$	2.12053	−	69.9395i	0.00484138	−	0.159679i
$439$	−91.3244			−0.208028			−0.104014	−	0.994576i	$-0.533169\pi$
$439$	−91.3244			−0.208028			−0.104014	+	0.994576i	$0.533169\pi$
$440$	−523.481	+	302.232i	−1.18973	+	0.686891i
$441$	149.451	−	226.024i	0.338890	−	0.512527i
$442$	326.837	−	112.184i	0.739451	−	0.253811i
$443$	−122.310	−	70.6155i	−0.276094	−	0.159403i	0.355560	−	0.934653i	$-0.384290\pi$
$443$	−122.310	−	70.6155i	−0.276094	−	0.159403i	−0.631654	+	0.775251i	$0.717624\pi$
$444$	2.74412	+	5.10421i	0.00618046	+	0.0114960i
$445$	−103.940	+	180.030i	−0.233574	+	0.404562i
$446$			375.502i			0.841932i
$447$	−1.59025	+	52.4500i	−0.00355761	+	0.117338i
$448$	−149.923	−	259.675i	−0.334650	−	0.579631i
$449$	356.884	+	206.047i	0.794841	+	0.458902i	0.841664	−	0.540001i	$-0.181576\pi$
$449$	356.884	+	206.047i	0.794841	+	0.458902i	−0.0468227	+	0.998903i	$0.514910\pi$
$450$	289.254	+	191.259i	0.642786	+	0.425020i
$451$	285.177	−	493.940i	0.632320	−	1.09521i
$452$		−	51.8314i		−	0.114671i
$453$	−282.526	+	456.795i	−0.623678	+	1.00838i
$454$	−260.631	−	451.427i	−0.574078	−	0.994332i
$455$	−123.448	−	359.652i	−0.271314	−	0.790444i
$456$	−47.9399	−	29.6506i	−0.105131	−	0.0650233i
$457$	−511.496			−1.11925			−0.559624	−	0.828747i	$-0.689054\pi$
$457$	−511.496			−1.11925			−0.559624	+	0.828747i	$0.689054\pi$
$458$	159.866	−	92.2987i	0.349053	−	0.201526i
$459$	−308.719	−	217.858i	−0.672591	−	0.474635i
$460$	119.367			0.259494
$461$	204.728	−	118.200i	0.444096	−	0.256399i	−0.261238	−	0.965274i	$-0.584131\pi$
$461$	204.728	−	118.200i	0.444096	−	0.256399i	0.705333	+	0.708876i	$0.250797\pi$
$462$	126.275	+	234.879i	0.273323	+	0.508395i
$463$	119.938	+	207.738i	0.259044	+	0.448678i	0.965986	−	0.258594i	$-0.0832591\pi$
$463$	119.938	+	207.738i	0.259044	+	0.448678i	−0.706942	+	0.707272i	$0.749926\pi$
$464$			430.838i			0.928531i
$465$	380.237	+	235.175i	0.817715	+	0.505754i
$466$	−230.800			−0.495279
$467$		−	667.629i		−	1.42961i	−0.699322	−	0.714807i	$-0.746515\pi$
$467$		−	667.629i		−	1.42961i	0.699322	−	0.714807i	$-0.253485\pi$
$468$	−32.7158	−	32.1822i	−0.0699056	−	0.0687654i
$469$	−457.654			−0.975807
$470$		−	509.055i		−	1.08310i
$471$	201.149	+	374.147i	0.427068	+	0.794368i
$472$	695.376			1.47325
$473$	372.235	−	214.910i	0.786966	−	0.454355i
$474$	−345.295	−	213.564i	−0.728471	−	0.450556i
$475$	−22.8432	−	39.5655i	−0.0480909	−	0.0832959i
$476$			23.8587i			0.0501233i
$477$	−14.6882	+	242.002i	−0.0307929	+	0.507341i
$478$	−284.845	−	493.366i	−0.595910	−	1.03215i
$479$		−	122.851i		−	0.256473i	−0.991744	−	0.128237i	$-0.959068\pi$
$479$		−	122.851i		−	0.256473i	0.991744	−	0.128237i	$-0.0409317\pi$
$480$	−59.7701	−	111.175i	−0.124521	−	0.231615i
$481$	−12.2772	+	62.8351i	−0.0255243	+	0.130634i
$482$	−618.384	+	357.024i	−1.28295	+	0.740714i
$483$	17.8711	−	589.427i	0.0370002	−	1.22035i
$484$	1.99061			0.00411284
$485$	874.476	+	504.879i	1.80304	+	1.04099i
$486$	69.6818	−	456.267i	0.143378	−	0.938821i
$487$	346.529	−	600.205i	0.711558	−	1.23245i	−0.252715	−	0.967541i	$-0.581323\pi$
$487$	346.529	−	600.205i	0.711558	−	1.23245i	0.964272	−	0.264913i	$-0.0853432\pi$
$488$	524.410	−	302.768i	1.07461	−	0.620427i
$489$	−65.0961	+	105.249i	−0.133121	+	0.215233i
$490$	384.830			0.785367
$491$	329.459	+	190.213i	0.670997	+	0.387400i	0.796454	−	0.604699i	$-0.206707\pi$
$491$	329.459	+	190.213i	0.670997	+	0.387400i	−0.125458	+	0.992099i	$0.540040\pi$
$492$	53.0131	+	32.7884i	0.107750	+	0.0666431i
$493$	211.152	−	365.726i	0.428300	−	0.741837i
$494$	−18.0546	−	52.6002i	−0.0365478	−	0.106478i
$495$	291.234	+	583.443i	0.588351	+	1.17867i
$496$	158.091	+	273.822i	0.318732	+	0.552061i
$497$			302.611i			0.608875i
$498$	161.830	−	261.651i	0.324960	−	0.525404i
$499$	−215.620	−	373.465i	−0.432104	−	0.748426i	0.564950	−	0.825125i	$-0.308895\pi$
$499$	−215.620	−	373.465i	−0.432104	−	0.748426i	−0.997054	+	0.0766989i	$0.975562\pi$
$500$			12.4450i			0.0248901i
$501$	72.9979	+	45.1489i	0.145704	+	0.0901176i
$502$	−3.62987	+	6.28712i	−0.00723082	+	0.0125241i
$503$	162.685	+	93.9264i	0.323430	+	0.186732i	0.652920	−	0.757426i	$-0.273544\pi$
$503$	162.685	+	93.9264i	0.323430	+	0.186732i	−0.329490	+	0.944159i	$0.606877\pi$
$504$	−292.001	+	145.756i	−0.579367	+	0.289199i
$505$	−46.3077	−	80.2072i	−0.0916983	−	0.158826i
$506$	−800.940	−	462.423i	−1.58288	−	0.913879i
$507$	−54.3347	−	504.080i	−0.107169	−	0.994241i
$508$	−31.7674	−	55.0228i	−0.0625343	−	0.108313i
$509$	540.974	+	312.331i	1.06282	+	0.613618i	0.926210	−	0.377008i	$-0.123047\pi$
$509$	540.974	+	312.331i	1.06282	+	0.613618i	0.136607	+	0.990625i	$0.456380\pi$
$510$	16.2627	−	536.380i	0.0318877	−	1.05173i
$511$	26.6869	+	46.2231i	0.0522249	+	0.0904562i
$512$		−	565.706i		−	1.10489i
$513$	−35.0613	+	49.6843i	−0.0683456	+	0.0968505i
$514$	−246.059	+	426.186i	−0.478713	+	0.829156i
$515$	−265.703	−	153.404i	−0.515929	−	0.297872i
$516$	22.2437	+	41.3744i	0.0431080	+	0.0801830i
$517$	214.401	−	371.353i	0.414702	−	0.718284i
$518$	35.2120	+	20.3297i	0.0679769	+	0.0392465i
$519$	−282.638	+	151.952i	−0.544582	+	0.292778i
$520$	139.955	−	716.292i	0.269143	−	1.37748i
$521$		−	7.80764i		−	0.0149859i	−0.999972	−	0.00749293i	$-0.997615\pi$
$521$		−	7.80764i		−	0.0149859i	0.999972	−	0.00749293i	$-0.00238510\pi$
$522$	514.913	+	31.2525i	0.986424	+	0.0598706i
$523$	−153.833	−	266.447i	−0.294136	−	0.509458i	0.680648	−	0.732611i	$-0.261698\pi$
$523$	−153.833	−	266.447i	−0.294136	−	0.509458i	−0.974784	+	0.223153i	$0.928365\pi$
$524$	−67.6043	+	39.0314i	−0.129016	+	0.0744874i
$525$	−264.390	−	8.01616i	−0.503601	−	0.0152689i
$526$	−385.332			−0.732570
$527$		−	309.919i		−	0.588082i
$528$	−13.9757	+	460.950i	−0.0264692	+	0.873011i
$529$	758.070	+	1313.02i	1.43303	+	2.48207i
$530$	−298.196	+	172.164i	−0.562634	+	0.324837i
$531$	45.4474	−	748.788i	0.0855883	−	1.41015i
$532$	3.83974			0.00721755
$533$	223.571	+	651.349i	0.419457	+	1.22204i
$534$	83.3529	+	155.041i	0.156092	+	0.290338i
$535$	−621.531	+	1076.52i	−1.16174	+	2.01219i
$536$	−760.721	−	439.202i	−1.41926	−	0.819408i
$537$	−839.421	+	451.289i	−1.56317	+	0.840390i
$538$	−200.308	+	346.943i	−0.372319	+	0.644876i
$539$	280.731	+	162.080i	0.520838	+	0.300706i
$540$	−64.6995	+	29.8818i	−0.119814	+	0.0553366i
$541$	−104.066			−0.192359			−0.0961795	−	0.995364i	$-0.530662\pi$
$541$	−104.066			−0.192359			−0.0961795	+	0.995364i	$0.530662\pi$
$542$	−179.373	+	103.561i	−0.330947	+	0.191073i
$543$	−738.630	−	22.3948i	−1.36028	−	0.0412428i
$544$	−43.7488	+	75.7751i	−0.0804206	+	0.139293i
$545$	−61.1291	+	35.2929i	−0.112164	+	0.0647577i
$546$	−313.989	−	71.2920i	−0.575072	−	0.130571i
$547$	266.804	−	462.117i	0.487758	−	0.844822i	−0.512143	−	0.858900i	$-0.671148\pi$
$547$	266.804	−	462.117i	0.487758	−	0.844822i	0.999901	+	0.0140786i	$0.00448151\pi$
$548$	−24.0081	+	13.8611i	−0.0438105	+	0.0252940i
$549$	−291.751	−	584.479i	−0.531422	−	1.06462i
$550$	−207.422	+	359.265i	−0.377131	+	0.653209i
$551$	−58.8588	−	33.9821i	−0.106822	−	0.0616735i
$552$	595.369	−	962.607i	1.07857	−	1.74385i
$553$	309.696			0.560029
$554$	502.893	−	290.346i	0.907750	−	0.524090i
$555$	84.5580	+	52.2988i	0.152357	+	0.0942321i
$556$	7.46477			0.0134258
$557$	−385.575	+	222.612i	−0.692235	+	0.399662i	−0.804449	−	0.594022i	$-0.797539\pi$
$557$	−385.575	+	222.612i	−0.692235	+	0.399662i	0.112214	+	0.993684i	$0.464206\pi$
$558$	338.724	−	169.079i	0.607033	−	0.303009i
$559$	−99.5183	+	509.337i	−0.178029	+	0.911158i
$560$	−361.658	−	208.804i	−0.645819	−	0.372864i
$561$	237.773	−	384.437i	0.423838	−	0.685271i
$562$	−193.268	+	334.750i	−0.343893	+	0.595640i
$563$		−	42.9231i		−	0.0762400i	−0.999273	−	0.0381200i	$-0.987863\pi$
$563$		−	42.9231i		−	0.0762400i	0.999273	−	0.0381200i	$-0.0121369\pi$
$564$	39.8562	+	24.6509i	0.0706670	+	0.0437073i
$565$	−444.627	−	770.116i	−0.786950	−	1.36304i
$566$	−135.008	−	77.9467i	−0.238529	−	0.137715i
$567$	137.868	+	323.956i	0.243153	+	0.571351i
$568$	−290.410	+	503.006i	−0.511286	+	0.885573i
$569$			416.946i			0.732769i	0.930464	+	0.366385i	$0.119405\pi$
$569$			416.946i			0.732769i	−0.930464	+	0.366385i	$0.880595\pi$
$570$	−86.3233	−	2.61727i	−0.151444	−	0.00459170i
$571$	−337.496	−	584.561i	−0.591062	−	1.02375i	−0.994090	−	0.108561i	$-0.965376\pi$
$571$	−337.496	−	584.561i	−0.591062	−	1.02375i	0.403028	−	0.915188i	$-0.367958\pi$
$572$	36.0582	−	41.3990i	0.0630389	−	0.0723759i
$573$	43.0786	−	23.1599i	0.0751809	−	0.0404187i
$574$	437.342			0.761920
$575$	794.455	−	458.679i	1.38166	−	0.797702i
$576$	−619.721	−	37.6137i	−1.07590	−	0.0653016i
$577$	−1085.40			−1.88111			−0.940554	−	0.339645i	$-0.889693\pi$
$577$	−1085.40			−1.88111			−0.940554	+	0.339645i	$0.889693\pi$
$578$	153.237	−	88.4717i	0.265117	−	0.153065i
$579$	247.124	−	399.556i	0.426812	−	0.690079i
$580$	−39.8257	−	68.9802i	−0.0686651	−	0.118931i
$581$			234.675i			0.403916i
$582$	753.092	−	404.877i	1.29397	−	0.695665i
$583$	−290.043			−0.497501
$584$			102.444i			0.175418i
$585$	−762.164	−	197.519i	−1.30284	−	0.337639i
$586$	144.829			0.247148
$587$			872.015i			1.48555i	0.669543	+	0.742773i	$0.266490\pi$
$587$			872.015i			1.48555i	−0.669543	+	0.742773i	$0.733510\pi$
$588$	−18.6353	+	30.1301i	−0.0316927	+	0.0512416i
$589$	−49.8774			−0.0846815
$590$	922.661	−	532.699i	1.56383	−	0.902879i
$591$	−685.847	+	368.725i	−1.16049	+	0.623900i
$592$	35.1567	+	60.8931i	0.0593863	+	0.102860i
$593$			533.078i			0.898951i	0.893293	+	0.449475i	$0.148389\pi$
$593$			533.078i			0.898951i	−0.893293	+	0.449475i	$0.851611\pi$
$594$	549.887	+	50.1397i	0.925736	+	0.0844103i
$595$	204.667	+	354.494i	0.343979	+	0.595789i
$596$		−	6.86071i		−	0.0115113i
$597$	429.922	−	695.109i	0.720138	−	1.16434i
$598$	1056.18	−	362.527i	1.76619	−	0.606232i
$599$	−137.101	+	79.1555i	−0.228884	+	0.132146i	−0.610057	−	0.792358i	$-0.708853\pi$
$599$	−137.101	+	79.1555i	−0.228884	+	0.132146i	0.381173	+	0.924504i	$0.375520\pi$
$600$	−431.782	−	267.055i	−0.719636	−	0.445092i
$601$	874.328			1.45479			0.727394	−	0.686220i	$-0.240731\pi$
$601$	874.328			1.45479			0.727394	+	0.686220i	$0.240731\pi$
$602$	285.427	+	164.791i	0.474131	+	0.273739i
$603$	−522.656	+	790.448i	−0.866760	+	1.31086i
$604$	35.1119	−	60.8156i	0.0581323	−	0.100688i
$605$	29.5767	−	17.0761i	0.0488871	−	0.0282250i
$606$	−78.3874	−	2.37666i	−0.129352	−	0.00392188i
$607$	−851.480			−1.40277			−0.701384	−	0.712784i	$-0.747434\pi$
$607$	−851.480			−1.40277			−0.701384	+	0.712784i	$0.747434\pi$
$608$	12.1950	+	7.04079i	0.0200576	+	0.0115803i
$609$	−346.583	+	186.330i	−0.569101	+	0.305960i
$610$	463.877	−	803.458i	0.760454	−	1.31714i
$611$	168.084	+	489.696i	0.275097	+	0.801466i
$612$	41.2081	+	27.2474i	0.0673335	+	0.0445219i
$613$	215.476	+	373.215i	0.351511	+	0.608834i	0.986514	−	0.163675i	$-0.0523348\pi$
$613$	215.476	+	373.215i	0.351511	+	0.608834i	−0.635004	+	0.772509i	$0.719001\pi$
$614$			314.754i			0.512629i
$615$	1068.94	+	32.4097i	1.73812	+	0.0526987i
$616$	−195.214	−	338.120i	−0.316905	−	0.548896i
$617$			735.561i			1.19216i	0.802926	+	0.596079i	$0.203275\pi$
$617$			735.561i			1.19216i	−0.802926	+	0.596079i	$0.796725\pi$
$618$	−228.821	+	123.019i	−0.370261	+	0.199060i
$619$	201.576	−	349.140i	0.325648	−	0.564039i	−0.655995	−	0.754765i	$-0.727751\pi$
$619$	201.576	−	349.140i	0.325648	−	0.564039i	0.981643	+	0.190726i	$0.0610841\pi$
$620$	−50.6230	−	29.2272i	−0.0816500	−	0.0471406i
$621$	−997.634	−	704.012i	−1.60650	−	1.13368i
$622$	−90.0975	−	156.054i	−0.144851	−	0.250890i
$623$	−116.283	−	67.1358i	−0.186649	−	0.107762i
$624$	−408.600	−	378.265i	−0.654808	−	0.606195i
$625$	360.321	+	624.095i	0.576514	+	0.998551i
$626$	744.843	+	430.035i	1.18984	+	0.686957i
$627$	−61.8701	−	38.2664i	−0.0986764	−	0.0610310i
$628$	−27.7696	−	48.0983i	−0.0442190	−	0.0765896i
$629$		−	68.9205i		−	0.109572i
$630$	−275.784	+	417.087i	−0.437753	+	0.662043i
$631$	362.274	−	627.478i	0.574127	−	0.994418i	−0.422008	−	0.906592i	$-0.638675\pi$
$631$	362.274	−	627.478i	0.574127	−	0.994418i	0.996136	−	0.0878260i	$-0.0279919\pi$
$632$	514.782	+	297.210i	0.814529	+	0.470269i
$633$	430.202	−	695.561i	0.679624	−	1.09883i
$634$	−425.233	+	736.525i	−0.670714	+	1.16171i
$635$	−944.007	−	545.023i	−1.48662	−	0.858303i
$636$	0.960643	−	31.6841i	0.00151045	−	0.0498178i
$637$	−370.195	+	127.067i	−0.581154	+	0.199477i
$638$			617.133i			0.967293i
$639$	522.662	+	345.592i	0.817937	+	0.540832i
$640$	−356.730	−	617.874i	−0.557390	−	0.965428i
$641$	−36.6359	+	21.1518i	−0.0571544	+	0.0329981i	−0.528305	−	0.849055i	$-0.677172\pi$
$641$	−36.6359	+	21.1518i	−0.0571544	+	0.0329981i	0.471151	+	0.882053i	$0.343839\pi$
$642$	498.423	+	927.092i	0.776360	+	1.44407i
$643$	−388.142			−0.603642			−0.301821	−	0.953365i	$-0.597595\pi$
$643$	−388.142			−0.603642			−0.301821	+	0.953365i	$0.597595\pi$
$644$			77.0999i			0.119720i
$645$	685.422	+	423.931i	1.06267	+	0.657258i
$646$	29.9332	+	51.8458i	0.0463362	+	0.0802566i
$647$	94.1041	−	54.3311i	0.145447	−	0.0839738i	−0.425511	−	0.904953i	$-0.639905\pi$
$647$	94.1041	−	54.3311i	0.145447	−	0.0839738i	0.570957	+	0.820980i	$0.306572\pi$
$648$	−81.7284	+	670.795i	−0.126124	+	1.03518i
$649$	897.435			1.38280
$650$	−162.613	−	473.756i	−0.250174	−	0.728855i
$651$	−151.901	+	245.597i	−0.233335	+	0.377262i
$652$	8.09003	−	14.0123i	0.0124080	−	0.0214913i
$653$	847.926	+	489.550i	1.29851	+	0.749694i	0.980147	−	0.198275i	$-0.0635338\pi$
$653$	847.926	+	489.550i	1.29851	+	0.749694i	0.318362	+	0.947969i	$0.396867\pi$
$654$	−1.81135	+	59.7422i	−0.00276964	+	0.0913489i
$655$	−669.648	+	1159.86i	−1.02236	+	1.77078i
$656$	654.982	+	378.154i	0.998448	+	0.576455i
$657$	110.313	+	6.69539i	0.167904	+	0.0101909i
$658$	328.802			0.499698
$659$	123.321	−	71.1993i	0.187133	−	0.108041i	−0.403507	−	0.914977i	$-0.632209\pi$
$659$	123.321	−	71.1993i	0.187133	−	0.108041i	0.590640	+	0.806935i	$0.298875\pi$
$660$	−40.3716	−	75.0931i	−0.0611690	−	0.113777i
$661$	−532.421	+	922.180i	−0.805478	+	1.39513i	0.110490	+	0.993877i	$0.464758\pi$
$661$	−532.421	+	922.180i	−0.805478	+	1.39513i	−0.915968	+	0.401252i	$0.868575\pi$
$662$	86.8929	−	50.1677i	0.131258	−	0.0757820i
$663$	161.462	+	521.351i	0.243533	+	0.786352i
$664$	−225.214	+	390.082i	−0.339178	+	0.587473i
$665$	57.0512	−	32.9385i	0.0857912	−	0.0495316i
$666$	75.3262	−	37.6001i	0.113102	−	0.0564566i
$667$	682.343	−	1181.85i	1.02300	−	1.77189i
$668$	−9.71859	−	5.61103i	−0.0145488	−	0.00839975i
$669$	−592.808	−	17.9736i	−0.886111	−	0.0268664i
$670$	−1345.82			−2.00869
$671$	676.792	−	390.746i	1.00863	−	0.582334i
$672$	71.8088	−	38.6058i	0.106858	−	0.0574492i
$673$	−417.411			−0.620224			−0.310112	−	0.950700i	$-0.600367\pi$
$673$	−417.411			−0.620224			−0.310112	+	0.950700i	$0.600367\pi$
$674$	1056.46	−	609.948i	1.56745	−	0.904967i
$675$	−315.788	+	447.493i	−0.467834	+	0.662953i
$676$	9.09802	+	65.6602i	0.0134586	+	0.0971305i
$677$	−406.765	−	234.846i	−0.600835	−	0.346892i	0.168535	−	0.985696i	$-0.446096\pi$
$677$	−406.765	−	234.846i	−0.600835	−	0.346892i	−0.769370	+	0.638803i	$0.779430\pi$
$678$	−752.643	−	22.8197i	−1.11009	−	0.0336574i
$679$	−326.104	+	564.829i	−0.480271	+	0.831855i
$680$			785.663i			1.15539i
$681$	725.148	−	389.854i	1.06483	−	0.572473i
$682$	226.450	+	392.223i	0.332038	+	0.575106i
$683$	328.925	+	189.905i	0.481589	+	0.278046i	0.721078	−	0.692853i	$-0.243647\pi$
$683$	328.925	+	189.905i	0.481589	+	0.278046i	−0.239489	+	0.970899i	$0.576980\pi$
$684$	4.38511	−	6.63190i	0.00641098	−	0.00969576i
$685$	−237.810	+	411.899i	−0.347168	+	0.601313i
$686$			653.104i			0.952047i
$687$	138.061	+	256.800i	0.200962	+	0.373800i
$688$	284.978	+	493.596i	0.414212	+	0.717437i
$689$	230.009	−	264.077i	0.333830	−	0.383276i
$690$	52.5534	−	1733.33i	0.0761644	−	2.51207i
$691$	78.7758			0.114003			0.0570013	−	0.998374i	$-0.481846\pi$
$691$	78.7758			0.114003			0.0570013	+	0.998374i	$0.481846\pi$
$692$	36.3344	−	20.9777i	0.0525064	−	0.0303146i
$693$	−376.849	+	188.110i	−0.543794	+	0.271443i
$694$	541.854			0.780769
$695$	110.912	−	64.0352i	0.159586	−	0.0921369i
$696$	−754.914	−	22.8885i	−1.08465	−	0.0328858i
$697$	−370.663	−	642.007i	−0.531798	−	0.921101i
$698$		−	442.484i		−	0.633931i
$699$	11.0474	−	364.366i	0.0158045	−	0.521268i
$700$	34.5835			0.0494050
$701$			1265.05i			1.80464i	0.431067	+	0.902320i	$0.358137\pi$
$701$			1265.05i			1.80464i	−0.431067	+	0.902320i	$0.641863\pi$
$702$	−481.720	+	460.897i	−0.686211	+	0.656548i
$703$	−11.0918			−0.0157779
$704$		−	742.747i		−	1.05504i
$705$	803.650	+	24.3662i	1.13993	+	0.0345620i
$706$	−401.293			−0.568404
$707$	51.8063	−	29.9104i	0.0732762	−	0.0423061i
$708$	−2.97237	+	98.0351i	−0.00419826	+	0.138468i
$709$	465.030	+	805.455i	0.655895	+	1.13604i	0.981669	+	0.190596i	$0.0610420\pi$
$709$	465.030	+	805.455i	0.655895	+	1.13604i	−0.325773	+	0.945448i	$0.605625\pi$
$710$			889.886i			1.25336i
$711$	353.683	−	534.899i	0.497445	−	0.752319i
$712$	−128.858	−	223.189i	−0.180981	−	0.313467i
$713$		−	1001.51i		−	1.40464i
$714$	346.451	+	10.5042i	0.485226	+	0.0147118i
$715$	180.622	−	924.430i	0.252618	−	1.29291i
$716$	107.911	−	62.3026i	0.150714	−	0.0870148i
$717$	792.516	−	426.072i	1.10532	−	0.594243i
$718$	−235.798			−0.328410
$719$	−663.267	−	382.937i	−0.922485	−	0.532597i	−0.0380580	−	0.999276i	$-0.512117\pi$
$719$	−663.267	−	382.937i	−0.922485	−	0.532597i	−0.884427	+	0.466679i	$0.845451\pi$
$720$	−773.667	+	386.186i	−1.07454	+	0.536370i
$721$	99.0844	−	171.619i	0.137426	−	0.238030i
$722$	−585.479	+	338.027i	−0.810913	+	0.468181i
$723$	−534.039	−	993.339i	−0.738643	−	1.37391i
$724$	96.6163			0.133448
$725$	−530.125	−	306.068i	−0.731207	−	0.422163i
$726$	0.876402	−	28.9056i	0.00120717	−	0.0398149i
$727$	33.7945	−	58.5338i	0.0464849	−	0.0805141i	−0.841847	−	0.539717i	$-0.818531\pi$
$727$	33.7945	−	58.5338i	0.0464849	−	0.0805141i	0.888332	+	0.459202i	$0.151865\pi$
$728$	462.657	+	90.3975i	0.635518	+	0.124172i
$729$	716.978	+	131.847i	0.983509	+	0.180860i
$730$	78.4781	+	135.928i	0.107504	+	0.186203i
$731$		−	558.666i		−	0.764248i
$732$	40.4432	+	75.2264i	0.0552503	+	0.102768i
$733$	−299.220	−	518.265i	−0.408213	−	0.707046i	0.586476	−	0.809966i	$-0.300515\pi$
$733$	−299.220	−	518.265i	−0.408213	−	0.707046i	−0.994690	+	0.102920i	$0.967181\pi$
$734$		−	20.6869i		−	0.0281838i
$735$	−18.4201	+	607.535i	−0.0250614	+	0.826578i
$736$	−141.375	+	244.869i	−0.192086	+	0.332703i
$737$	−981.769	−	566.824i	−1.33211	−	0.769097i
$738$	499.460	−	755.366i	0.676775	−	1.02353i
$739$	625.661	+	1083.68i	0.846632	+	1.46641i	0.884196	+	0.467115i	$0.154707\pi$
$739$	625.661	+	1083.68i	0.846632	+	1.46641i	−0.0375643	+	0.999294i	$0.511960\pi$
$740$	−11.2576	−	6.49961i	−0.0152130	−	0.00878325i
$741$	83.9046	−	25.9853i	0.113232	−	0.0350678i
$742$	−111.201	−	192.607i	−0.149867	−	0.259578i
$743$	−984.439	−	568.366i	−1.32495	−	0.764961i	−0.340437	−	0.940267i	$-0.610575\pi$
$743$	−984.439	−	568.366i	−1.32495	−	0.764961i	−0.984514	+	0.175306i	$0.943908\pi$
$744$	−488.189	+	262.460i	−0.656168	+	0.352769i
$745$	−58.8534	−	101.937i	−0.0789978	−	0.136828i
$746$		−	458.102i		−	0.614077i
$747$	405.325	+	268.007i	0.542604	+	0.358778i
$748$	−29.5500	+	51.1821i	−0.0395054	+	0.0684253i
$749$	−695.332	−	401.450i	−0.928347	−	0.535982i
$750$	180.714	+	5.47915i	0.240952	+	0.00730553i
$751$	253.160	−	438.486i	0.337097	−	0.583870i	−0.646788	−	0.762670i	$-0.723888\pi$
$751$	253.160	−	438.486i	0.337097	−	0.583870i	0.983885	+	0.178800i	$0.0572215\pi$
$752$	492.427	+	284.303i	0.654823	+	0.378062i
$753$	−9.75180	−	6.03145i	−0.0129506	−	0.00800990i
$754$	−561.884	−	489.396i	−0.745204	−	0.649067i
$755$		−	1204.80i		−	1.59577i
$756$	−19.3008	−	41.7898i	−0.0255302	−	0.0552775i
$757$	−164.329	−	284.626i	−0.217079	−	0.375993i	0.736834	−	0.676073i	$-0.236320\pi$
$757$	−164.329	−	284.626i	−0.217079	−	0.375993i	−0.953914	+	0.300081i	$0.902986\pi$
$758$	679.695	−	392.422i	0.896695	−	0.517707i
$759$	768.369	−	1242.32i	1.01234	−	1.63678i
$760$	126.442			0.166371
$761$		−	701.867i		−	0.922295i	−0.887323	−	0.461148i	$-0.847438\pi$
$761$		−	701.867i		−	0.922295i	0.887323	−	0.461148i	$-0.152562\pi$
$762$	−812.971	+	437.069i	−1.06689	+	0.573582i
$763$	−22.7959	−	39.4837i	−0.0298767	−	0.0517479i
$764$	−5.53795	+	3.19734i	−0.00724862	+	0.00418499i
$765$	846.011	+	51.3483i	1.10590	+	0.0671219i
$766$	−1237.83			−1.61596
$767$	−711.681	+	817.093i	−0.927876	+	1.06531i
$768$	223.581	+	6.77883i	0.291121	+	0.00882661i
$769$	431.615	−	747.579i	0.561268	−	0.972144i	−0.436118	−	0.899889i	$-0.643647\pi$
$769$	431.615	−	747.579i	0.561268	−	0.972144i	0.997386	−	0.0722550i	$-0.0230195\pi$

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.89941i q^{2} +(-2.99862 - 0.0909164i) q^{3} +0.392234 q^{4} +(5.82785 - 3.36471i) q^{5} +(0.172688 - 5.69562i) q^{6} +(2.17329 + 3.76424i) q^{7} +8.34266i q^{8} +(8.98347 + 0.545248i) q^{9} +(6.39097 + 11.0695i) q^{10} +10.7668i q^{11} +(-1.17616 - 0.0356605i) q^{12} +(-9.80294 - 8.53829i) q^{13} +(-7.14985 + 4.12797i) q^{14} +(-17.7814 + 9.55965i) q^{15} -14.2772 q^{16} +(12.1195 + 6.99720i) q^{17} +(-1.03565 + 17.0633i) q^{18} +(1.12611 - 1.95047i) q^{19} +(2.28588 - 1.31975i) q^{20} +(-6.17463 - 11.4851i) q^{21} -20.4507 q^{22} +(39.1645 + 22.6116i) q^{23} +(0.758485 - 25.0165i) q^{24} +(10.1425 - 17.5674i) q^{25} +(16.2177 - 18.6198i) q^{26} +(-26.8885 - 2.45174i) q^{27} +(0.852437 + 1.47646i) q^{28} -30.1766i q^{29} +(-18.1577 - 33.7742i) q^{30} +(-11.0730 - 19.1790i) q^{31} +6.25233i q^{32} +(0.978883 - 32.2857i) q^{33} +(-13.2906 + 23.0199i) q^{34} +(25.3312 + 14.6250i) q^{35} +(3.52362 + 0.213865i) q^{36} +(-2.46243 - 4.26506i) q^{37} +(3.70475 + 2.13894i) q^{38} +(28.6190 + 26.4943i) q^{39} +(28.0706 + 48.6198i) q^{40} +(-45.8760 - 26.4865i) q^{41} +(21.8150 - 11.7282i) q^{42} +(-19.9603 - 34.5723i) q^{43} +4.22312i q^{44} +(54.1889 - 27.0491i) q^{45} +(-42.9488 + 74.3895i) q^{46} +(-34.4904 - 19.9131i) q^{47} +(42.8120 + 1.29803i) q^{48} +(15.0537 - 26.0737i) q^{49} +(33.3677 + 19.2649i) q^{50} +(-35.7056 - 22.0838i) q^{51} +(-3.84505 - 3.34901i) q^{52} +26.9386i q^{53} +(4.65686 - 51.0723i) q^{54} +(36.2273 + 62.7475i) q^{55} +(-31.4038 + 18.1310i) q^{56} +(-3.55410 + 5.74635i) q^{57} +57.3179 q^{58} -83.3518i q^{59} +(-6.97448 + 3.74962i) q^{60} +(-36.2916 - 62.8589i) q^{61} +(36.4287 - 21.0321i) q^{62} +(17.4712 + 35.0009i) q^{63} -68.9846 q^{64} +(-85.8589 - 16.7758i) q^{65} +(61.3238 + 1.85930i) q^{66} +(-52.6454 + 91.1844i) q^{67} +(4.75368 + 2.74454i) q^{68} +(-115.384 - 71.3644i) q^{69} +(-27.7788 + 48.1143i) q^{70} +(60.2932 + 34.8103i) q^{71} +(-4.54882 + 74.9460i) q^{72} +12.2795 q^{73} +(8.10110 - 4.67717i) q^{74} +(-32.0108 + 51.7559i) q^{75} +(0.441697 - 0.765042i) q^{76} +(-40.5290 + 23.3994i) q^{77} +(-50.3237 + 54.3594i) q^{78} +(35.6253 - 61.7048i) q^{79} +(-83.2055 + 48.0387i) q^{80} +(80.4054 + 9.79644i) q^{81} +(50.3089 - 87.1375i) q^{82} +(46.7575 + 26.9955i) q^{83} +(-2.42190 - 4.50486i) q^{84} +94.1742 q^{85} +(65.6671 - 37.9129i) q^{86} +(-2.74355 + 90.4883i) q^{87} -89.8241 q^{88} +(-26.7527 + 15.4457i) q^{89} +(51.3775 + 102.927i) q^{90} +(10.8356 - 55.4568i) q^{91} +(15.3616 + 8.86905i) q^{92} +(31.4600 + 58.5172i) q^{93} +(37.8231 - 65.5115i) q^{94} -15.1561i q^{95} +(0.568440 - 18.7484i) q^{96} +(75.0256 + 129.948i) q^{97} +(49.5247 + 28.5931i) q^{98} +(-5.87060 + 96.7236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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