LMFDB - Embedded newform 135.3.n.a.74.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(14,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("135.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.n (of order $18$, degree $6$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			74.21
Character	$\chi$	$=$	135.74
Dual form			135.3.n.a.104.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.721015 - 0.262428i) q^{2} +(2.90489 - 0.749413i) q^{3} +(-2.61318 + 2.19272i) q^{4} +(2.96988 + 4.02242i) q^{5} +(1.89780 - 1.30266i) q^{6} +(3.17548 - 3.78438i) q^{7} +(-2.84329 + 4.92472i) q^{8} +(7.87676 - 4.35392i) q^{9} +(3.19692 + 2.12084i) q^{10} +(7.37526 + 1.30046i) q^{11} +(-5.94776 + 8.32797i) q^{12} +(-6.15844 + 16.9202i) q^{13} +(1.29644 - 3.56193i) q^{14} +(11.6416 + 9.45901i) q^{15} +(1.61177 - 9.14083i) q^{16} +(-10.2979 - 17.8366i) q^{17} +(4.53667 - 5.20632i) q^{18} +(13.4766 - 23.3422i) q^{19} +(-16.5809 - 3.99920i) q^{20} +(6.38834 - 13.3730i) q^{21} +(5.65895 - 0.997825i) q^{22} +(-10.0889 + 8.46563i) q^{23} +(-4.56879 + 16.4366i) q^{24} +(-7.35967 + 23.8922i) q^{25} +13.8158i q^{26} +(19.6182 - 18.5506i) q^{27} +16.8522i q^{28} +(-13.1765 - 36.2022i) q^{29} +(10.8761 + 3.76500i) q^{30} +(-34.2162 + 28.7108i) q^{31} +(-5.18655 - 29.4144i) q^{32} +(22.3989 - 1.74943i) q^{33} +(-12.1058 - 10.1580i) q^{34} +(24.6531 + 1.53393i) q^{35} +(-11.0365 + 28.6491i) q^{36} +(-39.3279 + 22.7060i) q^{37} +(3.59121 - 20.3667i) q^{38} +(-5.20939 + 53.7664i) q^{39} +(-28.2535 + 3.18892i) q^{40} +(18.6544 - 51.2525i) q^{41} +(1.09665 - 11.3186i) q^{42} +(27.9365 + 4.92596i) q^{43} +(-22.1245 + 12.7736i) q^{44} +(40.9063 + 18.7530i) q^{45} +(-5.05266 + 8.75146i) q^{46} +(-21.0849 - 17.6923i) q^{47} +(-2.16823 - 27.7610i) q^{48} +(4.27084 + 24.2211i) q^{49} +(0.963538 + 19.1580i) q^{50} +(-43.2813 - 44.0958i) q^{51} +(-21.0081 - 57.7193i) q^{52} -44.0339 q^{53} +(9.27683 - 18.5236i) q^{54} +(16.6726 + 33.5286i) q^{55} +(9.60824 + 26.3984i) q^{56} +(21.6552 - 77.9062i) q^{57} +(-19.0009 - 22.6444i) q^{58} +(-15.0907 + 2.66091i) q^{59} +(-51.1627 + 0.808679i) q^{60} +(-44.3135 - 37.1834i) q^{61} +(-17.1359 + 29.6802i) q^{62} +(8.53555 - 43.6345i) q^{63} +(7.10495 + 12.3061i) q^{64} +(-86.3498 + 25.4790i) q^{65} +(15.6908 - 7.13946i) q^{66} +(-7.91614 + 21.7494i) q^{67} +(66.0210 + 24.0297i) q^{68} +(-22.9630 + 32.1525i) q^{69} +(18.1778 - 5.36368i) q^{70} +(91.6966 - 52.9411i) q^{71} +(-0.954056 + 51.1703i) q^{72} +(67.6524 + 39.0591i) q^{73} +(-22.3973 + 26.6921i) q^{74} +(-3.47394 + 74.9195i) q^{75} +(15.9661 + 90.5481i) q^{76} +(28.3414 - 23.7813i) q^{77} +(10.3538 + 40.1335i) q^{78} +(64.5660 - 23.5001i) q^{79} +(41.5550 - 20.6639i) q^{80} +(43.0867 - 68.5896i) q^{81} -41.8492i q^{82} +(-71.0404 + 25.8566i) q^{83} +(12.6293 + 48.9539i) q^{84} +(41.1625 - 94.3950i) q^{85} +(21.4353 - 3.77963i) q^{86} +(-65.4068 - 95.2888i) q^{87} +(-27.3744 + 32.6235i) q^{88} +(95.3491 + 55.0498i) q^{89} +(34.4153 + 2.78624i) q^{90} +(44.4765 + 77.0355i) q^{91} +(7.80150 - 44.2445i) q^{92} +(-77.8781 + 109.044i) q^{93} +(-19.8455 - 7.22317i) q^{94} +(133.916 - 15.1149i) q^{95} +(-37.1099 - 81.5586i) q^{96} +(86.5584 + 15.2626i) q^{97} +(9.43564 + 16.3430i) q^{98} +(63.7553 - 21.8679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31}+ \cdots + 792 q^{99}+O(q^{100}) $ 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.721015	−	0.262428i	0.360507	−	0.131214i	−0.155415	−	0.987849i	$-0.549672\pi$
$2$	0.721015	−	0.262428i	0.360507	−	0.131214i	0.515922	+	0.856635i	$0.327449\pi$
$3$	2.90489	−	0.749413i	0.968296	−	0.249804i
$3$	2.90489	−	0.749413i	0.968296	−	0.249804i
$4$	−2.61318	+	2.19272i	−0.653296	+	0.548180i
$5$	2.96988	+	4.02242i	0.593975	+	0.804483i
$5$	2.96988	+	4.02242i	0.593975	+	0.804483i
$6$	1.89780	−	1.30266i	0.316300	−	0.217110i
$7$	3.17548	−	3.78438i	0.453639	−	0.540626i	−0.489947	−	0.871752i	$-0.662984\pi$
$7$	3.17548	−	3.78438i	0.453639	−	0.540626i	0.943587	+	0.331126i	$0.107428\pi$
$8$	−2.84329	+	4.92472i	−0.355411	+	0.615590i
$9$	7.87676	−	4.35392i	0.875196	−	0.483769i
$10$	3.19692	+	2.12084i	0.319692	+	0.212084i
$11$	7.37526	+	1.30046i	0.670479	+	0.118223i	0.498517	−	0.866880i	$-0.333878\pi$
$11$	7.37526	+	1.30046i	0.670479	+	0.118223i	0.171962	+	0.985104i	$0.444989\pi$
$12$	−5.94776	+	8.32797i	−0.495646	+	0.693997i
$13$	−6.15844	+	16.9202i	−0.473726	+	1.30155i	0.441011	+	0.897502i	$0.354620\pi$
$13$	−6.15844	+	16.9202i	−0.473726	+	1.30155i	−0.914737	+	0.404050i	$0.867602\pi$
$14$	1.29644	−	3.56193i	0.0926026	−	0.254424i
$15$	11.6416	+	9.45901i	0.776107	+	0.630601i
$16$	1.61177	−	9.14083i	0.100736	−	0.571302i
$17$	−10.2979	−	17.8366i	−0.605761	−	1.04921i	−0.991931	−	0.126781i	$-0.959535\pi$
$17$	−10.2979	−	17.8366i	−0.605761	−	1.04921i	0.386169	−	0.922428i	$-0.373798\pi$
$18$	4.53667	−	5.20632i	0.252037	−	0.289240i
$19$	13.4766	−	23.3422i	0.709297	−	1.22854i	−0.255821	−	0.966724i	$-0.582346\pi$
$19$	13.4766	−	23.3422i	0.709297	−	1.22854i	0.965118	−	0.261815i	$-0.0843209\pi$
$20$	−16.5809	−	3.99920i	−0.829044	−	0.199960i
$21$	6.38834	−	13.3730i	0.304207	−	0.636808i
$22$	5.65895	−	0.997825i	0.257225	−	0.0453557i
$23$	−10.0889	+	8.46563i	−0.438650	+	0.368071i	−0.835204	−	0.549940i	$-0.814650\pi$
$23$	−10.0889	+	8.46563i	−0.438650	+	0.368071i	0.396554	+	0.918011i	$0.370206\pi$
$24$	−4.56879	+	16.4366i	−0.190366	+	0.684857i
$25$	−7.35967	+	23.8922i	−0.294387	+	0.955686i
$26$			13.8158i			0.531378i
$27$	19.6182	−	18.5506i	0.726601	−	0.687059i
$28$			16.8522i			0.601865i
$29$	−13.1765	−	36.2022i	−0.454363	−	1.24835i	−0.929625	−	0.368508i	$-0.879869\pi$
$29$	−13.1765	−	36.2022i	−0.454363	−	1.24835i	0.475262	−	0.879845i	$-0.342353\pi$
$30$	10.8761	+	3.76500i	0.362536	+	0.125500i
$31$	−34.2162	+	28.7108i	−1.10375	+	0.926156i	−0.997672	−	0.0682022i	$-0.978274\pi$
$31$	−34.2162	+	28.7108i	−1.10375	+	0.926156i	−0.106078	+	0.994358i	$0.533829\pi$
$32$	−5.18655	−	29.4144i	−0.162080	−	0.919199i
$33$	22.3989	−	1.74943i	0.678755	−	0.0530131i
$34$	−12.1058	−	10.1580i	−0.356052	−	0.298763i
$35$	24.6531	+	1.53393i	0.704375	+	0.0438266i
$36$	−11.0365	+	28.6491i	−0.306569	+	0.795810i
$37$	−39.3279	+	22.7060i	−1.06292	+	0.613675i	−0.926237	−	0.376941i	$-0.876976\pi$
$37$	−39.3279	+	22.7060i	−1.06292	+	0.613675i	−0.136678	+	0.990615i	$0.543643\pi$
$38$	3.59121	−	20.3667i	0.0945054	−	0.535967i
$39$	−5.20939	+	53.7664i	−0.133574	+	1.37863i
$40$	−28.2535	+	3.18892i	−0.706337	+	0.0797229i
$41$	18.6544	−	51.2525i	0.454985	−	1.25006i	−0.474191	−	0.880422i	$-0.657259\pi$
$41$	18.6544	−	51.2525i	0.454985	−	1.25006i	0.929176	−	0.369638i	$-0.120518\pi$
$42$	1.09665	−	11.3186i	0.0261107	−	0.269490i
$43$	27.9365	+	4.92596i	0.649686	+	0.114557i	0.488772	−	0.872411i	$-0.337445\pi$
$43$	27.9365	+	4.92596i	0.649686	+	0.114557i	0.160913	+	0.986969i	$0.448556\pi$
$44$	−22.1245	+	12.7736i	−0.502829	+	0.290308i
$45$	40.9063	+	18.7530i	0.909029	+	0.416733i
$46$	−5.05266	+	8.75146i	−0.109840	+	0.190249i
$47$	−21.0849	−	17.6923i	−0.448615	−	0.376433i	0.390307	−	0.920685i	$-0.372369\pi$
$47$	−21.0849	−	17.6923i	−0.448615	−	0.376433i	−0.838922	+	0.544252i	$0.816813\pi$
$48$	−2.16823	−	27.7610i	−0.0451714	−	0.578354i
$49$	4.27084	+	24.2211i	0.0871600	+	0.494309i
$50$	0.963538	+	19.1580i	0.0192708	+	0.383160i
$51$	−43.2813	−	44.0958i	−0.848653	−	0.864624i
$52$	−21.0081	−	57.7193i	−0.404002	−	1.10999i
$53$	−44.0339			−0.830828			−0.415414	−	0.909633i	$-0.636363\pi$
$53$	−44.0339			−0.830828			−0.415414	+	0.909633i	$0.636363\pi$
$54$	9.27683	−	18.5236i	0.171793	−	0.343030i
$55$	16.6726	+	33.5286i	0.303139	+	0.609611i
$56$	9.60824	+	26.3984i	0.171576	+	0.471400i
$57$	21.6552	−	77.9062i	0.379916	−	1.36678i
$58$	−19.0009	−	22.6444i	−0.327602	−	0.390421i
$59$	−15.0907	+	2.66091i	−0.255775	+	0.0451001i	−0.300065	−	0.953919i	$-0.597009\pi$
$59$	−15.0907	+	2.66091i	−0.255775	+	0.0451001i	0.0442901	+	0.999019i	$0.485897\pi$
$60$	−51.1627	+	0.808679i	−0.852711	+	0.0134780i
$61$	−44.3135	−	37.1834i	−0.726451	−	0.609564i	0.202711	−	0.979239i	$-0.435025\pi$
$61$	−44.3135	−	37.1834i	−0.726451	−	0.609564i	−0.929161	+	0.369674i	$0.879469\pi$
$62$	−17.1359	+	29.6802i	−0.276385	+	0.478713i
$63$	8.53555	−	43.6345i	0.135485	−	0.692611i
$64$	7.10495	+	12.3061i	0.111015	+	0.192283i
$65$	−86.3498	+	25.4790i	−1.32846	+	0.391985i
$66$	15.6908	−	7.13946i	0.237740	−	0.108174i
$67$	−7.91614	+	21.7494i	−0.118151	+	0.324618i	−0.984645	−	0.174571i	$-0.944146\pi$
$67$	−7.91614	+	21.7494i	−0.118151	+	0.324618i	0.866493	+	0.499189i	$0.166369\pi$
$68$	66.0210	+	24.0297i	0.970897	+	0.353378i
$69$	−22.9630	+	32.1525i	−0.332797	+	0.465978i
$70$	18.1778	−	5.36368i	0.259683	−	0.0766240i
$71$	91.6966	−	52.9411i	1.29150	−	0.745649i	0.312582	−	0.949891i	$-0.398806\pi$
$71$	91.6966	−	52.9411i	1.29150	−	0.745649i	0.978920	+	0.204242i	$0.0654729\pi$
$72$	−0.954056	+	51.1703i	−0.0132508	+	0.710698i
$73$	67.6524	+	39.0591i	0.926745	+	0.535056i	0.885781	−	0.464104i	$-0.153624\pi$
$73$	67.6524	+	39.0591i	0.926745	+	0.535056i	0.0409643	+	0.999161i	$0.486957\pi$
$74$	−22.3973	+	26.6921i	−0.302666	+	0.360703i
$75$	−3.47394	+	74.9195i	−0.0463191	+	0.998927i
$76$	15.9661	+	90.5481i	0.210080	+	1.19142i
$77$	28.3414	−	23.7813i	0.368070	−	0.308848i
$78$	10.3538	+	40.1335i	0.132741	+	0.514532i
$79$	64.5660	−	23.5001i	0.817291	−	0.297470i	0.100659	−	0.994921i	$-0.467905\pi$
$79$	64.5660	−	23.5001i	0.817291	−	0.297470i	0.716632	+	0.697451i	$0.245683\pi$
$80$	41.5550	−	20.6639i	0.519437	−	0.258299i
$81$	43.0867	−	68.5896i	0.531935	−	0.846785i
$82$		−	41.8492i		−	0.510356i
$83$	−71.0404	+	25.8566i	−0.855908	+	0.311525i	−0.732447	−	0.680824i	$-0.761622\pi$
$83$	−71.0404	+	25.8566i	−0.855908	+	0.311525i	−0.123461	+	0.992349i	$0.539399\pi$
$84$	12.6293	+	48.9539i	0.150349	+	0.582784i
$85$	41.1625	−	94.3950i	0.484264	−	1.11053i
$86$	21.4353	−	3.77963i	0.249248	−	0.0439491i
$87$	−65.4068	−	95.2888i	−0.751802	−	1.09527i
$88$	−27.3744	+	32.6235i	−0.311073	+	0.370722i
$89$	95.3491	+	55.0498i	1.07134	+	0.618538i	0.928547	−	0.371215i	$-0.121059\pi$
$89$	95.3491	+	55.0498i	1.07134	+	0.618538i	0.142792	+	0.989753i	$0.454392\pi$
$90$	34.4153	+	2.78624i	0.382393	+	0.0309582i
$91$	44.4765	+	77.0355i	0.488752	+	0.846544i
$92$	7.80150	−	44.2445i	0.0847989	−	0.480919i
$93$	−77.8781	+	109.044i	−0.837399	+	1.17251i
$94$	−19.8455	−	7.22317i	−0.211122	−	0.0768422i
$95$	133.916	−	15.1149i	1.40964	−	0.159104i
$96$	−37.1099	−	81.5586i	−0.386561	−	0.849569i
$97$	86.5584	+	15.2626i	0.892355	+	0.157346i	0.600981	−	0.799263i	$-0.294777\pi$
$97$	86.5584	+	15.2626i	0.892355	+	0.157346i	0.291373	+	0.956609i	$0.405888\pi$
$98$	9.43564	+	16.3430i	0.0962820	+	0.166765i
$99$	63.7553	−	21.8679i	0.643993	−	0.220888i
$100$	−33.1567	−	78.5723i	−0.331567	−	0.785723i
$101$	−55.4210	+	66.0482i	−0.548723	+	0.653942i	−0.967120	−	0.254322i	$-0.918148\pi$
$101$	−55.4210	+	66.0482i	−0.548723	+	0.653942i	0.418397	+	0.908264i	$0.362592\pi$
$102$	−42.7784	−	20.4355i	−0.419396	−	0.200348i
$103$	64.4706	−	11.3679i	0.625928	−	0.110368i	0.148318	−	0.988940i	$-0.452614\pi$
$103$	64.4706	−	11.3679i	0.625928	−	0.110368i	0.477611	+	0.878572i	$0.341503\pi$
$104$	−65.8169	−	78.4375i	−0.632854	−	0.754207i
$105$	72.7642	−	14.0195i	0.692992	−	0.133519i
$106$	−31.7491	+	11.5557i	−0.299519	+	0.109016i
$107$	−17.0726			−0.159557			−0.0797785	−	0.996813i	$-0.525421\pi$
$107$	−17.0726			−0.159557			−0.0797785	+	0.996813i	$0.525421\pi$
$108$	−10.5897	+	91.4935i	−0.0980531	+	0.847162i
$109$	72.2226			0.662592			0.331296	−	0.943527i	$-0.392514\pi$
$109$	72.2226			0.662592			0.331296	+	0.943527i	$0.392514\pi$
$110$	20.8200	+	19.7992i	0.189273	+	0.179993i
$111$	−97.2270	+	95.4311i	−0.875919	+	0.859740i
$112$	−29.4743	−	35.1261i	−0.263163	−	0.313625i
$113$	−3.89736	−	22.1030i	−0.0344899	−	0.195602i	0.962694	−	0.270591i	$-0.0872190\pi$
$113$	−3.89736	−	22.1030i	−0.0344899	−	0.195602i	−0.997184	+	0.0749887i	$0.976108\pi$
$114$	−4.83104	−	61.8544i	−0.0423776	−	0.542583i
$115$	−64.0152	−	15.4401i	−0.556654	−	0.134261i
$116$	113.814	+	65.7106i	0.981156	+	0.566471i
$117$	25.1606	+	160.089i	0.215047	+	1.36829i
$118$	−10.1824	+	5.87878i	−0.0862911	+	0.0498202i
$119$	−100.201	−	17.6682i	−0.842027	−	0.148472i
$120$	−79.6834	+	30.4370i	−0.664028	+	0.253641i
$121$	−60.9995	−	22.2020i	−0.504128	−	0.183488i
$122$	−41.7086	−	15.1807i	−0.341874	−	0.124432i
$123$	15.7796	−	162.863i	0.128290	−	1.32409i
$124$	26.4585	−	150.053i	0.213375	−	1.21011i
$125$	−117.962	+	41.3531i	−0.943692	+	0.330825i
$126$	−5.29664	−	33.7010i	−0.0420369	−	0.267469i
$127$	−47.3382	−	27.3308i	−0.372742	−	0.215203i	0.301914	−	0.953335i	$-0.402375\pi$
$127$	−47.3382	−	27.3308i	−0.372742	−	0.215203i	−0.674656	+	0.738133i	$0.735708\pi$
$128$	99.8735	+	83.8039i	0.780262	+	0.654718i
$129$	84.8440	−	6.62660i	0.657705	−	0.0513690i
$130$	−55.5730	+	41.0313i	−0.427485	+	0.315625i
$131$	26.7119	+	31.8340i	0.203908	+	0.243008i	0.858301	−	0.513147i	$-0.171520\pi$
$131$	26.7119	+	31.8340i	0.203908	+	0.243008i	−0.654393	+	0.756154i	$0.727076\pi$
$132$	−54.6964	+	53.6862i	−0.414367	+	0.406713i
$133$	−45.5412	−	125.124i	−0.342415	−	0.940778i
$134$			17.7591i			0.132530i
$135$	132.882	+	23.8197i	0.984311	+	0.176442i
$136$	117.120			0.861177
$137$	134.025	−	48.7812i	0.978286	−	0.356067i	0.197112	−	0.980381i	$-0.436844\pi$
$137$	134.025	−	48.7812i	0.978286	−	0.356067i	0.781173	+	0.624314i	$0.214621\pi$
$138$	−8.11896	+	29.2086i	−0.0588330	+	0.211656i
$139$	−143.525	+	120.432i	−1.03256	+	0.866418i	−0.991153	−	0.132724i	$-0.957628\pi$
$139$	−143.525	+	120.432i	−1.03256	+	0.866418i	−0.0414040	+	0.999142i	$0.513183\pi$
$140$	−67.7867	+	50.0490i	−0.484191	+	0.357493i
$141$	−74.5082	−	35.5930i	−0.528427	−	0.252433i
$142$	52.2214	−	62.2350i	0.367756	−	0.438275i
$143$	−67.4241	+	116.782i	−0.471497	+	0.816657i
$144$	−27.1029	−	79.0177i	−0.188215	−	0.548734i
$145$	106.488	−	160.518i	0.734398	−	1.10702i
$146$	59.0285	+	10.4083i	0.404305	+	0.0712899i
$147$	30.5579	+	67.1591i	0.207877	+	0.456865i
$148$	52.9831	−	145.570i	0.357994	−	0.983581i
$149$	7.98047	−	21.9262i	0.0535602	−	0.147155i	−0.910028	−	0.414548i	$-0.863940\pi$
$149$	7.98047	−	21.9262i	0.0535602	−	0.147155i	0.963588	+	0.267392i	$0.0861620\pi$
$150$	17.1562	+	54.9297i	0.114375	+	0.366198i
$151$	−40.1381	+	227.635i	−0.265815	+	1.50751i	0.500888	+	0.865512i	$0.333007\pi$
$151$	−40.1381	+	227.635i	−0.265815	+	1.50751i	−0.766703	+	0.642002i	$0.778104\pi$
$152$	76.6360	+	132.737i	0.504184	+	0.873272i
$153$	−158.773	−	95.6579i	−1.03773	−	0.625215i
$154$	14.1937	−	24.5842i	0.0921669	−	0.159638i
$155$	−217.105	−	52.3643i	−1.40068	−	0.337834i
$156$	−104.282	−	151.924i	−0.668473	−	0.973874i
$157$	8.04210	−	1.41804i	0.0512236	−	0.00903209i	−0.147978	−	0.988991i	$-0.547276\pi$
$157$	8.04210	−	1.41804i	0.0512236	−	0.00903209i	0.199201	+	0.979959i	$0.436165\pi$
$158$	40.3860	−	33.8878i	0.255607	−	0.214480i
$159$	−127.914	+	32.9995i	−0.804488	+	0.207544i
$160$	102.913	−	108.220i	0.643209	−	0.676372i
$161$			65.0629i			0.404117i
$162$	13.0663	−	60.7613i	0.0806564	−	0.375069i
$163$			43.1204i			0.264542i	0.991214	+	0.132271i	$0.0422269\pi$
$163$			43.1204i			0.264542i	−0.991214	+	0.132271i	$0.957773\pi$
$164$	63.6351	+	174.836i	0.388019	+	1.06607i
$165$	73.5589	+	84.9021i	0.445812	+	0.514558i
$166$	−44.4356	+	37.2859i	−0.267685	+	0.224614i
$167$	27.8841	+	158.139i	0.166971	+	0.946937i	0.947009	+	0.321206i	$0.104088\pi$
$167$	27.8841	+	158.139i	0.166971	+	0.946937i	−0.780039	+	0.625731i	$0.784801\pi$
$168$	47.6942	+	69.4839i	0.283894	+	0.413595i
$169$	−118.904	−	99.7725i	−0.703575	−	0.590370i
$170$	4.90686	−	78.8623i	0.0288639	−	0.463896i
$171$	4.52204	−	242.538i	0.0264447	−	1.41835i
$172$	−83.8044	+	48.3845i	−0.487235	+	0.281305i
$173$	19.1710	−	108.724i	0.110815	−	0.628462i	−0.877923	−	0.478802i	$-0.841071\pi$
$173$	19.1710	−	108.724i	0.110815	−	0.628462i	0.988738	−	0.149660i	$-0.0478178\pi$
$174$	−72.1657	−	51.5400i	−0.414745	−	0.296207i
$175$	67.0467	+	103.721i	0.383124	+	0.592690i
$176$	23.7745	−	65.3200i	0.135083	−	0.371136i
$177$	−41.8428	+	19.0388i	−0.236400	+	0.107564i
$178$	83.1947	+	14.6695i	0.467386	+	0.0824128i
$179$	−173.652	+	100.258i	−0.970122	+	0.560100i	−0.899273	−	0.437387i	$-0.855904\pi$
$179$	−173.652	+	100.258i	−0.970122	+	0.560100i	−0.0708485	+	0.997487i	$0.522571\pi$
$180$	−148.016	+	40.6911i	−0.822310	+	0.226062i
$181$	−45.7267	+	79.2010i	−0.252634	+	0.437575i	−0.964250	−	0.264994i	$-0.914630\pi$
$181$	−45.7267	+	79.2010i	−0.252634	+	0.437575i	0.711616	+	0.702568i	$0.247963\pi$
$182$	52.2844	+	43.8718i	0.287277	+	0.241054i
$183$	−156.591	−	74.8046i	−0.855691	−	0.408769i
$184$	−13.0051	−	73.7555i	−0.0706798	−	0.400845i
$185$	−208.132	−	90.7592i	−1.12504	−	0.490590i
$186$	−27.5351	+	99.0596i	−0.148038	+	0.532578i
$187$	−52.7543	−	144.941i	−0.282109	−	0.775088i
$188$	93.8932			0.499432
$189$	−7.90541	−	133.150i	−0.0418276	−	0.704497i
$190$	92.5890	−	46.0414i	0.487310	−	0.242323i
$191$	−74.8263	−	205.584i	−0.391761	−	1.07635i	−0.966197	−	0.257804i	$-0.917001\pi$
$191$	−74.8263	−	205.584i	−0.391761	−	1.07635i	0.574436	−	0.818549i	$-0.305221\pi$
$192$	29.8615	+	30.4234i	0.155529	+	0.158455i
$193$	−124.937	−	148.894i	−0.647341	−	0.771471i	0.338170	−	0.941085i	$-0.390192\pi$
$193$	−124.937	−	148.894i	−0.647341	−	0.771471i	−0.985510	+	0.169614i	$0.945748\pi$
$194$	66.4152	−	11.7108i	0.342346	−	0.0603649i
$195$	−231.742	+	138.725i	−1.18842	+	0.711412i
$196$	−64.2707	−	53.9295i	−0.327912	−	0.275151i
$197$	−55.9942	+	96.9847i	−0.284234	+	0.492308i	−0.972423	−	0.233223i	$-0.925073\pi$
$197$	−55.9942	+	96.9847i	−0.284234	+	0.492308i	0.688189	+	0.725532i	$0.258406\pi$
$198$	40.2297	−	32.4983i	0.203180	−	0.164133i
$199$	11.4037	+	19.7519i	0.0573053	+	0.0992556i	0.893255	−	0.449551i	$-0.148416\pi$
$199$	11.4037	+	19.7519i	0.0573053	+	0.0992556i	−0.835950	+	0.548806i	$0.815083\pi$
$200$	−96.7365	−	104.177i	−0.483683	−	0.520883i
$201$	−6.69622	+	69.1121i	−0.0333145	+	0.343841i
$202$	−22.6265	+	62.1657i	−0.112012	+	0.307751i
$203$	−178.845	−	65.0942i	−0.881009	−	0.320661i
$204$	209.792	+	20.3266i	1.02839	+	0.0996401i
$205$	261.560	−	77.1778i	1.27590	−	0.376477i
$206$	43.5010	−	25.1153i	0.211170	−	0.121919i
$207$	−42.6095	+	110.608i	−0.205843	+	0.534339i
$208$	144.738	+	83.5647i	0.695857	+	0.401753i
$209$	129.749	−	154.629i	0.620811	−	0.739853i
$210$	48.7849	−	29.2036i	0.232309	−	0.139065i
$211$	22.0191	+	124.877i	0.104356	+	0.591833i	0.991476	+	0.130293i	$0.0415918\pi$
$211$	22.0191	+	124.877i	0.104356	+	0.591833i	−0.887119	+	0.461540i	$0.847297\pi$
$212$	115.069	−	96.5540i	0.542777	−	0.455444i
$213$	226.694	−	222.507i	1.06429	−	1.04463i
$214$	−12.3096	+	4.48033i	−0.0575215	+	0.0209361i
$215$	63.1537	+	127.002i	0.293738	+	0.590705i
$216$	35.5762	+	149.359i	0.164705	+	0.691477i
$217$			220.658i			1.01686i
$218$	52.0735	−	18.9532i	0.238869	−	0.0869413i
$219$	225.794	+	62.7628i	1.03102	+	0.286588i
$220$	−117.088	−	51.0579i	−0.532216	−	0.232081i
$221$	365.217	−	64.3976i	1.65256	−	0.291392i
$222$	−45.0583	+	94.3223i	−0.202965	+	0.424875i
$223$	−265.212	+	316.068i	−1.18929	+	1.41734i	−0.303773	+	0.952744i	$0.598246\pi$
$223$	−265.212	+	316.068i	−1.18929	+	1.41734i	−0.885521	+	0.464600i	$0.846198\pi$
$224$	−127.785	−	73.7767i	−0.570469	−	0.329360i
$225$	46.0542	+	220.236i	0.204685	+	0.978828i
$226$	−8.61051	−	14.9138i	−0.0380996	−	0.0659904i
$227$	−18.5556	+	105.234i	−0.0817428	+	0.463586i	0.916269	+	0.400563i	$0.131185\pi$
$227$	−18.5556	+	105.234i	−0.0817428	+	0.463586i	−0.998012	+	0.0630234i	$0.979926\pi$
$228$	114.238	+	251.067i	0.501042	+	1.10117i
$229$	130.547	+	47.5153i	0.570076	+	0.207491i	0.610944	−	0.791674i	$-0.290790\pi$
$229$	130.547	+	47.5153i	0.570076	+	0.207491i	−0.0408682	+	0.999165i	$0.513012\pi$
$230$	−50.2078	+	5.66686i	−0.218295	+	0.0246385i
$231$	64.5067	−	90.3213i	0.279250	−	0.391001i
$232$	215.750	+	38.0426i	0.929959	+	0.163977i
$233$	−53.0900	−	91.9546i	−0.227854	−	0.394655i	0.729318	−	0.684175i	$-0.239838\pi$
$233$	−53.0900	−	91.9546i	−0.227854	−	0.394655i	−0.957172	+	0.289520i	$0.906504\pi$
$234$	60.1531	+	108.824i	0.257064	+	0.465060i
$235$	8.54639	−	137.356i	0.0363676	−	0.584495i
$236$	33.6003	−	40.0433i	0.142374	−	0.169675i
$237$	169.946	−	116.652i	0.717071	−	0.492202i
$238$	−76.8832	+	13.5566i	−0.323039	+	0.0569604i
$239$	162.764	+	193.975i	0.681023	+	0.811611i	0.990239	−	0.139381i	$-0.0445112\pi$
$239$	162.764	+	193.975i	0.681023	+	0.811611i	−0.309216	+	0.950992i	$0.600067\pi$
$240$	105.227	−	91.1682i	0.438445	−	0.379867i
$241$	3.56022	−	1.29581i	0.0147727	−	0.00537682i	−0.334623	−	0.942352i	$-0.608609\pi$
$241$	3.56022	−	1.29581i	0.0147727	−	0.00537682i	0.349396	+	0.936975i	$0.386387\pi$
$242$	−49.8079			−0.205818
$243$	73.7602	−	231.535i	0.303540	−	0.952819i
$244$	197.332			0.808739
$245$	−84.7436	+	89.1129i	−0.345892	+	0.363726i
$246$	−31.3623	−	121.567i	−0.127489	−	0.494176i
$247$	311.960	+	371.779i	1.26299	+	1.50518i
$248$	−44.1062	−	250.138i	−0.177847	−	1.00862i
$249$	−186.987	+	128.349i	−0.750952	+	0.515458i
$250$	−74.1998	+	60.7726i	−0.296799	+	0.243090i
$251$	155.039	+	89.5116i	0.617684	+	0.356620i	0.775967	−	0.630774i	$-0.217262\pi$
$251$	155.039	+	89.5116i	0.617684	+	0.356620i	−0.158283	+	0.987394i	$0.550596\pi$
$252$	73.3733	+	132.741i	0.291164	+	0.526750i
$253$	−85.4179	+	49.3160i	−0.337620	+	0.194925i
$254$	−41.3039	−	7.28299i	−0.162614	−	0.0286732i
$255$	48.8316	−	305.055i	0.191496	−	1.19629i
$256$	40.5910	+	14.7739i	0.158558	+	0.0577106i
$257$	−151.112	−	55.0003i	−0.587985	−	0.214009i	0.0308578	−	0.999524i	$-0.490176\pi$
$257$	−151.112	−	55.0003i	−0.587985	−	0.214009i	−0.618843	+	0.785515i	$0.712398\pi$
$258$	59.4347	−	27.0433i	0.230367	−	0.104819i
$259$	−38.9566	+	220.934i	−0.150412	+	0.853027i
$260$	169.779	−	255.922i	0.652998	−	0.984317i
$261$	−261.410	−	227.787i	−1.00157	−	0.872746i
$262$	27.6138	+	15.9428i	0.105396	+	0.0608505i
$263$	131.661	+	110.477i	0.500613	+	0.420064i	0.857811	−	0.513965i	$-0.171824\pi$
$263$	131.661	+	110.477i	0.500613	+	0.420064i	−0.357199	+	0.934028i	$0.616268\pi$
$264$	−55.0711	+	115.282i	−0.208603	+	0.436676i
$265$	−130.775	−	177.123i	−0.493491	−	0.668387i
$266$	−65.6718	−	78.2646i	−0.246886	−	0.294228i
$267$	318.234	+	88.4578i	1.19189	+	0.331303i
$268$	−27.0041	−	74.1931i	−0.100761	−	0.276840i
$269$		−	352.895i		−	1.31188i	−0.754814	−	0.655939i	$-0.772273\pi$
$269$		−	352.895i		−	1.31188i	0.754814	−	0.655939i	$-0.227727\pi$
$270$	102.061	−	17.6976i	0.378003	−	0.0655466i
$271$	−477.336			−1.76139			−0.880693	−	0.473687i	$-0.842923\pi$
$271$	−477.336			−1.76139			−0.880693	+	0.473687i	$0.842923\pi$
$272$	−179.639	+	65.3832i	−0.660437	+	0.240379i
$273$	186.931	+	190.448i	0.684727	+	0.697613i
$274$	83.8325	−	70.3438i	0.305958	−	0.256729i
$275$	−85.3503	+	166.640i	−0.310365	+	0.605964i
$276$	−10.4949	−	134.372i	−0.0380250	−	0.486855i
$277$	−293.699	+	350.017i	−1.06028	+	1.26360i	−0.0969521	+	0.995289i	$0.530909\pi$
$277$	−293.699	+	350.017i	−1.06028	+	1.26360i	−0.963333	+	0.268309i	$0.913535\pi$
$278$	−71.8792	+	124.498i	−0.258558	+	0.447836i
$279$	−144.508	+	375.123i	−0.517951	+	1.34453i
$280$	−77.6502	+	117.048i	−0.277322	+	0.418030i
$281$	409.029	+	72.1229i	1.45562	+	0.256665i	0.844791	−	0.535097i	$-0.179725\pi$
$281$	409.029	+	72.1229i	1.45562	+	0.256665i	0.610830	+	0.791762i	$0.290836\pi$
$282$	−63.0621	−	6.11004i	−0.223624	−	0.0216668i
$283$	71.4696	−	196.361i	0.252543	−	0.693856i	−0.747034	−	0.664785i	$-0.768523\pi$
$283$	71.4696	−	196.361i	0.252543	−	0.693856i	0.999577	−	0.0290706i	$-0.00925476\pi$
$284$	−123.535	+	339.410i	−0.434983	+	1.19511i
$285$	377.684	−	144.266i	1.32521	−	0.506195i
$286$	−17.9669	+	101.895i	−0.0628214	+	0.356278i
$287$	−134.723	−	233.346i	−0.469416	−	0.813053i
$288$	−168.921	−	209.108i	−0.586532	−	0.726070i
$289$	−67.5952	+	117.078i	−0.233893	+	0.405115i
$290$	34.6549	−	143.681i	0.119500	−	0.495451i
$291$	262.881	−	20.5319i	0.903369	−	0.0705562i
$292$	−262.434	+	46.2742i	−0.898746	+	0.158473i
$293$	115.593	−	96.9943i	0.394516	−	0.331038i	−0.423853	−	0.905731i	$-0.639323\pi$
$293$	115.593	−	96.9943i	0.394516	−	0.331038i	0.818369	+	0.574692i	$0.194878\pi$
$294$	39.6571	+	40.4034i	0.134888	+	0.137427i
$295$	−55.5209	−	52.7987i	−0.188207	−	0.178979i
$296$		−	258.238i		−	0.872427i
$297$	168.814	−	111.303i	0.568397	−	0.374757i
$298$		−	17.9034i		−	0.0600784i
$299$	−81.1078	−	222.842i	−0.271263	−	0.745290i
$300$	−155.200	−	203.396i	−0.517332	−	0.677986i
$301$	107.353	−	90.0802i	0.356656	−	0.299270i
$302$	30.7975	+	174.661i	0.101978	+	0.578348i
$303$	−111.494	+	233.396i	−0.367969	+	0.770283i
$304$	−191.646	−	160.810i	−0.630415	−	0.528981i
$305$	17.9617	−	288.677i	0.0588907	−	0.946483i
$306$	−139.581	−	27.3042i	−0.456148	−	0.0892293i
$307$	302.653	−	174.737i	0.985842	−	0.569176i	0.0818129	−	0.996648i	$-0.473929\pi$
$307$	302.653	−	174.737i	0.985842	−	0.569176i	0.904029	+	0.427472i	$0.140596\pi$
$308$	−21.9156	+	124.290i	−0.0711546	+	0.403538i
$309$	178.761	−	81.3376i	0.578514	−	0.263229i
$310$	−170.278	+	19.2189i	−0.549283	+	0.0619965i
$311$	−7.30453	+	20.0690i	−0.0234872	+	0.0645306i	−0.950882	−	0.309553i	$-0.899821\pi$
$311$	−7.30453	+	20.0690i	−0.0234872	+	0.0645306i	0.927395	+	0.374084i	$0.122043\pi$
$312$	−249.973	−	178.528i	−0.801195	−	0.572206i
$313$	−383.992	−	67.7082i	−1.22681	−	0.216320i	−0.477557	−	0.878601i	$-0.658477\pi$
$313$	−383.992	−	67.7082i	−1.22681	−	0.216320i	−0.749256	+	0.662281i	$0.769589\pi$
$314$	5.42634	−	3.13290i	0.0172813	−	0.00997738i
$315$	200.866	−	95.2554i	0.637668	−	0.302398i
$316$	−117.194	+	202.985i	−0.370866	+	0.642359i
$317$	−209.280	−	175.607i	−0.660190	−	0.553965i	0.249954	−	0.968258i	$-0.419585\pi$
$317$	−209.280	−	175.607i	−0.660190	−	0.553965i	−0.910144	+	0.414293i	$0.864029\pi$
$318$	−83.5675	+	57.3612i	−0.262791	+	0.180381i
$319$	−50.1009	−	284.136i	−0.157056	−	0.890710i
$320$	−28.3996	+	65.1268i	−0.0887487	+	0.203521i
$321$	−49.5940	+	12.7944i	−0.154499	+	0.0398580i
$322$	17.0743	+	46.9113i	0.0530258	+	0.145687i
$323$	−555.127			−1.71866
$324$	37.8044	+	273.714i	0.116680	+	0.844798i
$325$	−358.935	−	271.665i	−1.10442	−	0.835893i
$326$	11.3160	+	31.0904i	0.0347116	+	0.0953693i
$327$	209.799	−	54.1245i	0.641586	−	0.165518i
$328$	199.364	+	237.593i	0.607818	+	0.724369i
$329$	−133.909	+	23.6118i	−0.407019	+	0.0717684i
$330$	75.3177	+	41.9118i	0.228236	+	0.127005i
$331$	231.258	+	194.049i	0.698665	+	0.586249i	0.921393	−	0.388631i	$-0.127052\pi$
$331$	231.258	+	194.049i	0.698665	+	0.586249i	−0.222729	+	0.974880i	$0.571496\pi$
$332$	128.945	−	223.340i	0.388389	−	0.672710i
$333$	−210.916	+	350.080i	−0.633382	+	1.05129i
$334$	61.6048	+	106.703i	0.184445	+	0.319469i
$335$	−110.995	+	32.7510i	−0.331329	+	0.0977643i
$336$	−111.943	−	79.9489i	−0.333165	−	0.237943i
$337$	52.9227	−	145.404i	0.157041	−	0.431466i	−0.836073	−	0.548618i	$-0.815154\pi$
$337$	52.9227	−	145.404i	0.157041	−	0.431466i	0.993114	+	0.117152i	$0.0373764\pi$
$338$	−111.915	−	40.7336i	−0.331109	−	0.120514i
$339$	−27.8857	−	61.2861i	−0.0822587	−	0.180785i
$340$	99.4169	+	336.929i	0.292403	+	0.990968i
$341$	−289.691	+	167.253i	−0.849534	+	0.490478i
$342$	−60.3881	−	176.060i	−0.176573	−	0.514795i
$343$	314.861	+	181.785i	0.917962	+	0.529986i
$344$	−103.690	+	123.573i	−0.301426	+	0.359225i
$345$	−197.528	+	3.12214i	−0.572545	+	0.00904968i
$346$	−14.7096	−	83.4225i	−0.0425134	−	0.241106i
$347$	−164.299	+	137.863i	−0.473483	+	0.397300i	−0.848063	−	0.529895i	$-0.822231\pi$
$347$	−164.299	+	137.863i	−0.473483	+	0.397300i	0.374580	+	0.927195i	$0.377787\pi$
$348$	379.862	+	105.588i	1.09156	+	0.303415i
$349$	370.917	−	135.003i	1.06280	−	0.386827i	0.249320	−	0.968421i	$-0.419793\pi$
$349$	370.917	−	135.003i	1.06280	−	0.386827i	0.813479	+	0.581594i	$0.197571\pi$
$350$	75.5608	+	57.1893i	0.215888	+	0.163398i
$351$	193.062	+	446.187i	0.550033	+	1.27119i
$352$		−	223.684i		−	0.635465i
$353$	628.739	−	228.842i	1.78113	−	0.648278i	0.781425	−	0.623999i	$-0.214493\pi$
$353$	628.739	−	228.842i	1.78113	−	0.648278i	0.999705	−	0.0242794i	$-0.00772913\pi$
$354$	−25.1730	+	24.7080i	−0.0711101	+	0.0697966i
$355$	485.279	+	211.614i	1.36698	+	0.596095i
$356$	−369.874	+	65.2187i	−1.03897	+	0.183199i
$357$	−304.314	+	23.7680i	−0.852421	+	0.0665770i
$358$	−98.8950	+	117.858i	−0.276243	+	0.329214i
$359$	−212.551	−	122.716i	−0.592064	−	0.341828i	0.173849	−	0.984772i	$-0.444380\pi$
$359$	−212.551	−	122.716i	−0.592064	−	0.341828i	−0.765913	+	0.642944i	$0.777713\pi$
$360$	−208.662	+	148.132i	−0.579616	+	0.411477i
$361$	−182.740	−	316.515i	−0.506205	−	0.876773i
$362$	−12.1851	+	69.1050i	−0.0336604	+	0.190898i
$363$	−193.835	−	18.7805i	−0.533981	−	0.0517370i
$364$	−285.143	−	103.783i	−0.783359	−	0.285119i
$365$	43.8071	+	388.127i	0.120020	+	1.06336i
$366$	−132.536	−	12.8413i	−0.362119	−	0.0350854i
$367$	458.235	+	80.7991i	1.24860	+	0.220161i	0.758596	−	0.651561i	$-0.225886\pi$
$367$	458.235	+	80.7991i	1.24860	+	0.220161i	0.490000	+	0.871723i	$0.336997\pi$
$368$	61.1218	+	105.866i	0.166092	+	0.287679i
$369$	−76.2132	−	484.923i	−0.206540	−	1.31415i
$370$	−173.884	−	10.8191i	−0.469956	−	0.0292409i
$371$	−139.828	+	166.641i	−0.376896	+	0.449167i
$372$	−35.5930	−	455.717i	−0.0956802	−	1.22504i
$373$	516.884	−	91.1405i	1.38575	−	0.244345i	0.569473	−	0.822010i	$-0.307147\pi$
$373$	516.884	−	91.1405i	1.38575	−	0.244345i	0.816274	+	0.577665i	$0.196036\pi$
$374$	−76.0733	−	90.6606i	−0.203405	−	0.242408i
$375$	−311.675	+	208.528i	−0.831132	+	0.556075i
$376$	147.080	−	53.5328i	0.391171	−	0.142375i
$377$	693.694			1.84004
$378$	−40.6422	−	93.9284i	−0.107519	−	0.248488i
$379$	−368.487			−0.972262			−0.486131	−	0.873886i	$-0.661592\pi$
$379$	−368.487			−0.972262			−0.486131	+	0.873886i	$0.661592\pi$
$380$	−316.805	+	333.139i	−0.833697	+	0.876681i
$381$	−157.994	−	43.9169i	−0.414683	−	0.115267i
$382$	−107.902	−	128.592i	−0.282465	−	0.336629i
$383$	−102.899	−	583.571i	−0.268667	−	1.52368i	−0.758387	−	0.651805i	$-0.774012\pi$
$383$	−102.899	−	583.571i	−0.268667	−	1.52368i	0.489720	−	0.871880i	$-0.337099\pi$
$384$	352.925	+	168.594i	0.919076	+	0.439048i
$385$	179.829	+	43.3735i	0.467087	+	0.112659i
$386$	−129.155	−	74.5677i	−0.334599	−	0.193181i
$387$	241.496	−	82.8327i	0.624021	−	0.214038i
$388$	−259.660	+	149.915i	−0.669226	+	0.386378i
$389$	319.283	+	56.2982i	0.820778	+	0.144725i	0.568241	−	0.822862i	$-0.307624\pi$
$389$	319.283	+	56.2982i	0.820778	+	0.144725i	0.252537	+	0.967587i	$0.418735\pi$
$390$	−130.684	+	160.839i	−0.335087	+	0.412407i
$391$	254.893	+	92.7735i	0.651901	+	0.237272i
$392$	−131.426	−	47.8350i	−0.335269	−	0.122028i
$393$	101.452	+	72.4560i	0.258147	+	0.184366i
$394$	−14.9211	+	84.6218i	−0.0378708	+	0.214776i
$395$	286.280	+	189.919i	0.724760	+	0.480808i
$396$	−118.654	+	196.943i	−0.299631	+	0.497330i
$397$	−652.770	−	376.877i	−1.64426	−	0.949313i	−0.979296	−	0.202436i	$-0.935114\pi$
$397$	−652.770	−	376.877i	−1.64426	−	0.949313i	−0.664962	−	0.746877i	$-0.731552\pi$
$398$	13.4057	+	11.2487i	0.0336827	+	0.0282631i
$399$	−226.061	−	329.341i	−0.566570	−	0.825415i
$400$	206.532	+	105.782i	0.516330	+	0.264456i
$401$	197.570	+	235.455i	0.492693	+	0.587168i	0.953900	−	0.300124i	$-0.0970280\pi$
$401$	197.570	+	235.455i	0.492693	+	0.587168i	−0.461207	+	0.887292i	$0.652584\pi$
$402$	13.3089	+	51.5881i	0.0331066	+	0.128329i
$403$	−275.073	−	755.758i	−0.682564	−	1.87533i
$404$		−	294.119i		−	0.728017i
$405$	403.858	−	30.3899i	0.997181	−	0.0750368i
$406$	−146.032			−0.359685
$407$	−319.582	+	116.318i	−0.785213	+	0.285794i
$408$	340.221	−	87.7713i	0.833874	−	0.215126i
$409$	379.249	−	318.228i	0.927260	−	0.778064i	−0.0480632	−	0.998844i	$-0.515305\pi$
$409$	379.249	−	318.228i	0.927260	−	0.778064i	0.975324	+	0.220781i	$0.0708605\pi$
$410$	168.335	−	124.287i	0.410573	−	0.303139i
$411$	352.771	−	242.144i	0.858323	−	0.589158i
$412$	−143.547	+	171.073i	−0.348415	+	0.415225i
$413$	−37.8504	+	65.5588i	−0.0916475	+	0.158738i
$414$	−1.69540	+	90.9321i	−0.00409518	+	0.219643i
$415$	−314.987	−	208.963i	−0.759005	−	0.503526i
$416$	529.637	+	93.3893i	1.27317	+	0.224494i
$417$	−326.672	+	457.402i	−0.783386	+	1.09689i
$418$	52.9722	−	145.540i	0.126728	−	0.348182i
$419$	94.5066	−	259.655i	0.225553	−	0.619701i	−0.774362	−	0.632743i	$-0.781929\pi$
$419$	94.5066	−	259.655i	0.225553	−	0.619701i	0.999915	+	0.0130416i	$0.00415138\pi$
$420$	−159.405	+	196.187i	−0.379537	+	0.467112i
$421$	−74.2093	+	420.862i	−0.176269	+	0.999672i	0.760400	+	0.649455i	$0.225003\pi$
$421$	−74.2093	+	420.862i	−0.176269	+	0.999672i	−0.936669	+	0.350217i	$0.886108\pi$
$422$	48.6473	+	84.2595i	0.115278	+	0.199667i
$423$	−243.112	−	47.5563i	−0.574733	−	0.112426i
$424$	125.201	−	216.854i	0.295285	−	0.511449i
$425$	501.943	−	114.769i	1.18104	−	0.270044i
$426$	105.058	−	219.921i	0.246614	−	0.516247i
$427$	−281.433	+	49.6242i	−0.659093	+	0.116216i
$428$	44.6139	−	37.4355i	0.104238	−	0.0874661i
$429$	−108.342	+	389.767i	−0.252545	+	0.908548i
$430$	78.8635	+	74.9968i	0.183403	+	0.174411i
$431$			243.191i			0.564247i	0.959378	+	0.282124i	$0.0910389\pi$
$431$			243.191i			0.564247i	−0.959378	+	0.282124i	$0.908961\pi$
$432$	−137.948	−	209.226i	−0.319323	−	0.484320i
$433$			279.518i			0.645539i	0.946478	+	0.322769i	$0.104614\pi$
$433$			279.518i			0.645539i	−0.946478	+	0.322769i	$0.895386\pi$
$434$	57.9068	+	159.098i	0.133426	+	0.366584i
$435$	189.041	−	546.089i	0.434577	−	1.25538i
$436$	−188.731	+	158.364i	−0.432869	+	0.363220i
$437$	61.6416	+	349.587i	0.141056	+	0.799970i
$438$	179.272	−	14.0017i	0.409296	−	0.0319674i
$439$	420.534	+	352.870i	0.957937	+	0.803805i	0.980616	−	0.195938i	$-0.0627752\pi$
$439$	420.534	+	352.870i	0.957937	+	0.803805i	−0.0226791	+	0.999743i	$0.507220\pi$
$440$	−212.524	−	13.2234i	−0.483009	−	0.0300531i
$441$	139.097	+	172.189i	0.315413	+	0.390452i
$442$	246.427	−	142.275i	0.557527	−	0.321888i
$443$	−117.125	+	664.248i	−0.264390	+	1.49943i	0.506376	+	0.862313i	$0.330985\pi$
$443$	−117.125	+	664.248i	−0.264390	+	1.49943i	−0.770766	+	0.637119i	$0.780126\pi$
$444$	44.8181	−	462.571i	0.100942	−	1.04183i
$445$	61.7417	+	547.025i	0.138745	+	1.22927i
$446$	−108.277	+	297.489i	−0.242774	+	0.667015i
$447$	6.75063	−	69.6737i	0.0151021	−	0.155870i
$448$	69.1328	+	12.1900i	0.154314	+	0.0272098i
$449$	−277.596	+	160.270i	−0.618255	+	0.356950i	−0.776189	−	0.630500i	$-0.782850\pi$
$449$	−277.596	+	160.270i	−0.618255	+	0.356950i	0.157934	+	0.987450i	$0.449517\pi$
$450$	91.0019	+	146.708i	0.202226	+	0.326017i
$451$	204.233	−	353.741i	0.452844	−	0.784349i
$452$	58.6503	+	49.2135i	0.129757	+	0.108879i
$453$	53.9955	+	691.333i	0.119195	+	1.52612i
$454$	14.2375	+	80.7448i	0.0313601	+	0.177852i
$455$	−177.779	+	407.689i	−0.390724	+	0.896019i
$456$	322.094	+	328.155i	0.706347	+	0.719639i
$457$	−187.236	−	514.427i	−0.409707	−	1.12566i	−0.957345	−	0.288946i	$-0.906695\pi$
$457$	−187.236	−	514.427i	−0.409707	−	1.12566i	0.547638	−	0.836715i	$-0.315527\pi$
$458$	106.596			0.232742
$459$	−532.906	−	158.889i	−1.16102	−	0.346163i
$460$	201.139	−	100.020i	0.437259	−	0.217434i
$461$	−147.291	−	404.678i	−0.319503	−	0.877826i	−0.990641	−	0.136494i	$-0.956417\pi$
$461$	−147.291	−	404.678i	−0.319503	−	0.877826i	0.671138	−	0.741332i	$-0.265806\pi$
$462$	22.8074	−	82.0513i	0.0493667	−	0.177600i
$463$	−198.499	−	236.562i	−0.428724	−	0.510933i	0.507830	−	0.861457i	$-0.330448\pi$
$463$	−198.499	−	236.562i	−0.428724	−	0.510933i	−0.936554	+	0.350524i	$0.886003\pi$
$464$	−352.156	+	62.0946i	−0.758957	+	0.133825i
$465$	−669.908	+	10.5886i	−1.44066	+	0.0227712i
$466$	−62.4101	−	52.3683i	−0.133927	−	0.112378i
$467$	372.274	−	644.797i	0.797161	−	1.38072i	−0.124298	−	0.992245i	$-0.539668\pi$
$467$	372.274	−	644.797i	0.797161	−	1.38072i	0.921458	−	0.388478i	$-0.126999\pi$
$468$	−416.781	−	363.173i	−0.890557	−	0.776011i
$469$	57.1706	+	99.0224i	0.121899	+	0.211135i
$470$	−29.8841	−	101.279i	−0.0635831	−	0.215487i
$471$	22.2987	−	10.1461i	0.0473433	−	0.0215416i
$472$	29.8031	−	81.8834i	0.0631422	−	0.173482i
$473$	199.633	+	72.6605i	0.422057	+	0.153616i
$474$	91.9207	−	128.706i	0.193926	−	0.271532i
$475$	458.513	+	493.777i	0.965290	+	1.03953i
$476$	300.586	−	173.543i	0.631483	−	0.364587i
$477$	−346.844	+	191.720i	−0.727137	+	0.401929i
$478$	168.260	+	97.1449i	0.352008	+	0.203232i
$479$	419.779	−	500.273i	0.876365	−	1.04441i	−0.122286	−	0.992495i	$-0.539023\pi$
$479$	419.779	−	500.273i	0.876365	−	1.04441i	0.998651	−	0.0519167i	$-0.0165330\pi$
$480$	217.851	−	391.490i	0.453857	−	0.815605i
$481$	−141.990	−	805.268i	−0.295198	−	1.67415i
$482$	2.22691	−	1.86860i	0.00462015	−	0.00387677i
$483$	48.7589	+	189.000i	0.100950	+	0.391305i
$484$	208.086	−	75.7370i	0.429929	−	0.156481i
$485$	195.675	+	393.502i	0.403454	+	0.811344i
$486$	−7.57902	−	186.297i	−0.0155947	−	0.383327i
$487$		−	645.774i		−	1.32603i	−0.748608	−	0.663013i	$-0.769278\pi$
$487$		−	645.774i		−	1.32603i	0.748608	−	0.663013i	$-0.230722\pi$
$488$	309.114	−	112.508i	0.633430	−	0.230550i
$489$	32.3149	+	125.260i	0.0660837	+	0.256155i
$490$	−37.7157	+	86.4908i	−0.0769708	+	0.176512i
$491$	−293.377	+	51.7303i	−0.597509	+	0.105357i	−0.464219	−	0.885720i	$-0.653665\pi$
$491$	−293.377	+	51.7303i	−0.597509	+	0.105357i	−0.133289	+	0.991077i	$0.542554\pi$
$492$	315.877	+	460.190i	0.642027	+	0.935346i
$493$	−510.032	+	607.832i	−1.03455	+	1.23293i
$494$	322.492	+	186.191i	0.652819	+	0.376905i
$495$	277.307	+	191.505i	0.560217	+	0.386879i
$496$	207.292	+	359.040i	0.417927	+	0.723871i
$497$	90.8310	−	515.128i	0.182759	−	1.03648i
$498$	−101.138	+	141.612i	−0.203088	+	0.284362i
$499$	24.0172	+	8.74156i	0.0481307	+	0.0175182i	0.365973	−	0.930625i	$-0.380736\pi$
$499$	24.0172	+	8.74156i	0.0481307	+	0.0175182i	−0.317843	+	0.948143i	$0.602958\pi$
$500$	217.579	−	366.720i	0.435159	−	0.733440i
$501$	199.511	+	438.478i	0.398226	+	0.875206i
$502$	135.275	+	23.8527i	0.269473	+	0.0475154i
$503$	186.800	+	323.547i	0.371372	+	0.643234i	0.989777	−	0.142625i	$-0.0455543\pi$
$503$	186.800	+	323.547i	0.371372	+	0.643234i	−0.618405	+	0.785859i	$0.712221\pi$
$504$	190.618	+	166.101i	0.378211	+	0.329564i
$505$	−430.267	−	26.7714i	−0.852013	−	0.0530127i
$506$	−48.6456	+	57.9736i	−0.0961376	+	0.114572i
$507$	−420.174	−	200.720i	−0.828746	−	0.395897i
$508$	183.632	−	32.3793i	0.361481	−	0.0637388i
$509$	472.660	+	563.294i	0.928605	+	1.10667i	0.994062	+	0.108813i	$0.0347051\pi$
$509$	472.660	+	563.294i	0.928605	+	1.10667i	−0.0654568	+	0.997855i	$0.520850\pi$
$510$	−44.8466	−	232.764i	−0.0879344	−	0.456399i
$511$	362.643	−	131.991i	0.709674	−	0.258300i
$512$	−488.359			−0.953826
$513$	−168.625	−	707.933i	−0.328703	−	1.37999i
$514$	−123.388			−0.240054
$515$	237.196	+	225.566i	0.460575	+	0.437993i
$516$	−207.183	+	203.356i	−0.401517	+	0.394100i
$517$	−132.499	−	157.906i	−0.256284	−	0.305427i
$518$	29.8909	+	169.520i	0.0577045	+	0.327259i
$519$	−25.7896	−	330.198i	−0.0496909	−	0.636220i
$520$	120.040	−	497.692i	0.230847	−	0.957101i
$521$	−817.489	−	471.978i	−1.56908	−	0.905907i	−0.996277	−	0.0862122i	$-0.972524\pi$
$521$	−817.489	−	471.978i	−1.56908	−	0.905907i	−0.572800	−	0.819695i	$-0.694143\pi$
$522$	−248.258	−	95.6362i	−0.475590	−	0.183211i
$523$	433.608	−	250.343i	0.829077	−	0.478668i	−0.0244592	−	0.999701i	$-0.507786\pi$
$523$	433.608	−	250.343i	0.829077	−	0.478668i	0.853537	+	0.521033i	$0.174453\pi$
$524$	−139.606	−	24.6163i	−0.266424	−	0.0469777i
$525$	272.493	+	251.052i	0.519034	+	0.478194i
$526$	123.922	+	45.1038i	0.235593	+	0.0857487i
$527$	864.459	+	314.637i	1.64034	+	0.597035i
$528$	20.1107	−	207.564i	0.0380885	−	0.393114i
$529$	−61.7400	+	350.145i	−0.116711	+	0.661899i
$530$	−140.773	−	93.3889i	−0.265609	−	0.176205i
$531$	−107.281	+	86.6633i	−0.202035	+	0.163208i
$532$	393.369	+	227.112i	0.739415	+	0.426901i
$533$	752.319	+	631.270i	1.41148	+	1.18437i
$534$	252.665	−	19.7340i	0.473155	−	0.0369550i
$535$	−50.7035	−	68.6731i	−0.0947729	−	0.128361i
$536$	−84.6019	−	100.825i	−0.157839	−	0.188106i
$537$	−429.305	+	421.375i	−0.799450	+	0.784684i
$538$	−92.6095	−	254.443i	−0.172137	−	0.472942i
$539$			184.191i			0.341728i
$540$	−399.475	+	229.128i	−0.739769	+	0.424311i
$541$	788.754			1.45796			0.728978	−	0.684538i	$-0.239996\pi$
$541$	788.754			1.45796			0.728978	+	0.684538i	$0.239996\pi$
$542$	−344.166	+	125.266i	−0.634993	+	0.231118i
$543$	−73.4768	+	264.338i	−0.135316	+	0.486811i
$544$	−471.240	+	395.418i	−0.866251	+	0.726871i
$545$	214.492	+	290.509i	0.393564	+	0.533045i
$546$	184.759	+	88.2602i	0.338386	+	0.161649i
$547$	161.404	−	192.354i	0.295071	−	0.351652i	−0.598058	−	0.801453i	$-0.704061\pi$
$547$	161.404	−	192.354i	0.295071	−	0.351652i	0.893129	+	0.449801i	$0.148505\pi$
$548$	−243.269	+	421.354i	−0.443921	+	0.768894i
$549$	−510.940	−	99.9475i	−0.930675	−	0.182054i
$550$	−17.8078	+	142.548i	−0.0323778	+	0.259178i
$551$	−1022.62	−	180.315i	−1.85593	−	0.327250i
$552$	−93.0516	−	204.505i	−0.168572	−	0.370481i
$553$	116.094	−	318.967i	0.209936	−	0.576793i
$554$	−119.907	+	329.442i	−0.216439	+	0.594660i
$555$	−672.616	−	107.669i	−1.21192	−	0.193998i
$556$	110.984	−	629.423i	0.199612	−	1.13206i
$557$	−250.586	−	434.027i	−0.449884	−	0.779223i	0.548494	−	0.836155i	$-0.315202\pi$
$557$	−250.586	−	434.027i	−0.449884	−	0.779223i	−0.998378	+	0.0569320i	$0.981868\pi$
$558$	−5.74989	+	308.392i	−0.0103045	+	0.552674i
$559$	−255.393	+	442.354i	−0.456875	+	0.791331i
$560$	53.7567	−	222.878i	0.0959941	−	0.397996i
$561$	−261.866	−	381.504i	−0.466785	−	0.680042i
$562$	313.843	−	55.3390i	0.558440	−	0.0984680i
$563$	73.5000	−	61.6738i	0.130551	−	0.109545i	−0.575174	−	0.818031i	$-0.695066\pi$
$563$	73.5000	−	61.6738i	0.130551	−	0.109545i	0.705725	+	0.708486i	$0.250621\pi$
$564$	272.749	−	70.3647i	0.483598	−	0.124760i
$565$	77.3329	−	81.3201i	0.136872	−	0.143929i
$566$		−	160.335i		−	0.283277i
$567$	−122.749	−	380.861i	−0.216488	−	0.671713i
$568$			602.107i			1.06005i
$569$	65.3089	+	179.435i	0.114778	+	0.315351i	0.983759	−	0.179496i	$-0.0574465\pi$
$569$	65.3089	+	179.435i	0.114778	+	0.315351i	−0.868980	+	0.494846i	$0.835224\pi$
$570$	234.457	−	203.132i	0.411327	−	0.356373i
$571$	490.869	−	411.888i	0.859666	−	0.721345i	−0.102230	−	0.994761i	$-0.532598\pi$
$571$	490.869	−	411.888i	0.859666	−	0.721345i	0.961896	+	0.273415i	$0.0881534\pi$
$572$	−79.8788	−	453.015i	−0.139648	−	0.791984i
$573$	−371.429	−	541.122i	−0.648218	−	0.944366i
$574$	−158.373	−	132.891i	−0.275912	−	0.231518i
$575$	−128.011	−	303.351i	−0.222628	−	0.527567i
$576$	109.544	+	65.9981i	0.190181	+	0.114580i
$577$	−101.569	+	58.6408i	−0.176029	+	0.101630i	−0.585426	−	0.810726i	$-0.699073\pi$
$577$	−101.569	+	58.6408i	−0.176029	+	0.101630i	0.409397	+	0.912357i	$0.365739\pi$
$578$	−18.0125	+	102.154i	−0.0311635	+	0.176737i
$579$	−474.510	−	338.891i	−0.819534	−	0.585304i
$580$	73.6984	+	652.960i	0.127066	+	1.12579i
$581$	−127.736	+	350.951i	−0.219855	+	0.604046i
$582$	184.153	−	83.7909i	0.316413	−	0.143971i
$583$	−324.761	−	57.2642i	−0.557052	−	0.0982233i
$584$	−384.710	+	222.113i	−0.658751	+	0.380330i
$585$	−569.223	+	576.652i	−0.973031	+	0.985730i
$586$	57.8904	−	100.269i	0.0987891	−	0.171108i
$587$	−177.386	−	148.845i	−0.302191	−	0.253569i	0.479064	−	0.877780i	$-0.340976\pi$
$587$	−177.386	−	148.845i	−0.302191	−	0.253569i	−0.781256	+	0.624211i	$0.785420\pi$
$588$	−227.115	−	108.494i	−0.386250	−	0.184514i
$589$	209.055	+	1185.61i	0.354932	+	2.01292i
$590$	−53.8872	−	23.4984i	−0.0913343	−	0.0398278i
$591$	−89.9752	+	323.693i	−0.152242	+	0.547703i
$592$	144.164	+	396.086i	0.243520	+	0.669065i
$593$	−557.117			−0.939489			−0.469745	−	0.882802i	$-0.655654\pi$
$593$	−557.117			−0.939489			−0.469745	+	0.882802i	$0.655654\pi$
$594$	92.5083	−	124.553i	0.155738	−	0.209684i
$595$	−226.517	−	455.523i	−0.380700	−	0.765586i
$596$	27.2235	+	74.7960i	0.0456771	+	0.125497i
$597$	47.9289	+	48.8309i	0.0802829	+	0.0817938i
$598$	−116.960	−	139.387i	−0.195585	−	0.233089i
$599$	459.818	−	81.0783i	0.767642	−	0.135356i	0.223904	−	0.974611i	$-0.428120\pi$
$599$	459.818	−	81.0783i	0.767642	−	0.135356i	0.543738	+	0.839255i	$0.317009\pi$
$600$	−359.080	−	230.126i	−0.598467	−	0.383543i
$601$	−568.779	−	477.262i	−0.946387	−	0.794113i	0.0322984	−	0.999478i	$-0.489717\pi$
$601$	−568.779	−	477.262i	−0.946387	−	0.794113i	−0.978685	+	0.205365i	$0.934162\pi$
$602$	53.7638	−	93.1216i	0.0893086	−	0.154687i
$603$	32.3417	+	205.781i	0.0536347	+	0.341262i
$604$	−394.251	−	682.863i	−0.652734	−	1.13057i
$605$	−91.8552	−	311.302i	−0.151827	−	0.514550i
$606$	−19.1396	+	197.541i	−0.0315835	+	0.325975i
$607$	−61.7933	+	169.776i	−0.101801	+	0.279696i	−0.980129	−	0.198363i	$-0.936437\pi$
$607$	−61.7933	+	169.776i	−0.101801	+	0.279696i	0.878327	+	0.478060i	$0.158660\pi$
$608$	−756.495	−	275.342i	−1.24423	−	0.452864i
$609$	−568.307	−	55.0628i	−0.933181	−	0.0904151i
$610$	−62.8064	−	212.854i	−0.102961	−	0.348941i
$611$	429.208	−	247.803i	0.702467	−	0.405570i
$612$	624.655	−	98.1743i	1.02068	−	0.160416i
$613$	−259.241	−	149.673i	−0.422905	−	0.244164i	0.273414	−	0.961896i	$-0.411847\pi$
$613$	−259.241	−	149.673i	−0.422905	−	0.244164i	−0.696319	+	0.717732i	$0.745180\pi$
$614$	172.362	−	205.413i	0.280719	−	0.334548i
$615$	701.965	−	420.209i	1.14141	−	0.683267i
$616$	36.5333	+	207.190i	0.0593072	+	0.336348i
$617$	−422.548	+	354.560i	−0.684842	+	0.574651i	−0.917417	−	0.397928i	$-0.869729\pi$
$617$	−422.548	+	354.560i	−0.684842	+	0.574651i	0.232575	+	0.972579i	$0.425285\pi$
$618$	107.544	−	105.557i	0.174019	−	0.170805i
$619$	−872.582	+	317.594i	−1.40966	+	0.513076i	−0.931031	−	0.364940i	$-0.881090\pi$
$619$	−872.582	+	317.594i	−1.40966	+	0.513076i	−0.478633	+	0.878015i	$0.658867\pi$
$620$	682.155	−	339.213i	1.10025	−	0.547118i
$621$	−40.8847	+	353.237i	−0.0658369	+	0.568819i
$622$			16.3870i			0.0263456i
$623$	511.109	−	186.028i	0.820399	−	0.298601i
$624$	483.073	+	134.277i	0.774156	+	0.215188i
$625$	−516.671	−	351.677i	−0.826673	−	0.562683i
$626$	−294.632	+	51.9516i	−0.470659	+	0.0829899i
$627$	261.027	−	546.417i	0.416310	−	0.871479i
$628$	−17.9061	+	21.3397i	−0.0285129	+	0.0339804i
$629$	809.992	+	467.649i	1.28775	+	0.743481i
$630$	119.829	−	121.393i	0.190205	−	0.192688i
$631$	−144.104	−	249.596i	−0.228374	−	0.395556i	0.728952	−	0.684565i	$-0.240008\pi$
$631$	−144.104	−	249.596i	−0.228374	−	0.395556i	−0.957326	+	0.289009i	$0.906674\pi$
$632$	−67.8483	+	384.787i	−0.107355	+	0.608840i
$633$	157.547	+	346.252i	0.248890	+	0.547001i
$634$	−196.978	−	71.6942i	−0.310691	−	0.113082i
$635$	−30.6531	−	271.583i	−0.0482726	−	0.427690i
$636$	261.903	−	366.713i	0.411797	−	0.576592i
$637$	−436.127	−	76.9010i	−0.684659	−	0.120724i
$638$	−110.689	−	191.719i	−0.173493	−	0.300499i
$639$	491.771	−	816.244i	0.769595	−	1.27738i
$640$	−40.4819	+	650.620i	−0.0632530	+	1.01659i
$641$	−589.951	+	703.077i	−0.920361	+	1.09684i	0.0746633	+	0.997209i	$0.476212\pi$
$641$	−589.951	+	703.077i	−0.920361	+	1.09684i	−0.995024	+	0.0996345i	$0.968233\pi$
$642$	−32.4004	+	22.2398i	−0.0504679	+	0.0346415i
$643$	814.024	−	143.534i	1.26598	−	0.223226i	0.499962	−	0.866048i	$-0.333347\pi$
$643$	814.024	−	143.534i	1.26598	−	0.223226i	0.766016	+	0.642822i	$0.222236\pi$
$644$	−142.665	−	170.021i	−0.221529	−	0.264008i
$645$	278.631	+	321.598i	0.431986	+	0.498601i
$646$	−400.255	+	145.681i	−0.619589	+	0.225512i
$647$	166.913			0.257979			0.128990	−	0.991646i	$-0.458827\pi$
$647$	166.913			0.257979			0.128990	+	0.991646i	$0.458827\pi$
$648$	215.277	+	407.210i	0.332217	+	0.628410i
$649$	−114.759			−0.176824
$650$	−330.090	−	101.680i	−0.507831	−	0.156431i
$651$	165.364	+	640.987i	0.254015	+	0.984619i
$652$	−94.5510	−	112.681i	−0.145017	−	0.172824i
$653$	−206.391	−	1170.50i	−0.316067	−	1.79250i	−0.566175	−	0.824285i	$-0.691577\pi$
$653$	−206.391	−	1170.50i	−0.316067	−	1.79250i	0.250109	−	0.968218i	$-0.419534\pi$
$654$	137.064	−	94.0815i	0.209578	−	0.143856i
$655$	−48.7186	+	201.989i	−0.0743795	+	0.308381i
$656$	−438.423	−	253.124i	−0.668328	−	0.385859i
$657$	702.942	+	13.1062i	1.06993	+	0.0199485i
$658$	−90.3541	+	52.1660i	−0.137316	+	0.0792796i
$659$	190.385	+	33.5700i	0.288900	+	0.0509408i	0.316220	−	0.948686i	$-0.397586\pi$
$659$	190.385	+	33.5700i	0.288900	+	0.0509408i	−0.0273202	+	0.999627i	$0.508697\pi$
$660$	−378.390	−	60.5707i	−0.573318	−	0.0917737i
$661$	−714.570	−	260.082i	−1.08104	−	0.393468i	−0.260747	−	0.965407i	$-0.583969\pi$
$661$	−714.570	−	260.082i	−1.08104	−	0.393468i	−0.820296	+	0.571940i	$0.806191\pi$
$662$	217.664	+	79.2233i	0.328798	+	0.119673i
$663$	1012.65	−	460.766i	1.52738	−	0.694971i
$664$	74.6518	−	423.371i	0.112427	−	0.637608i
$665$	368.047	−	554.787i	0.553454	−	0.834267i
$666$	−60.2030	+	307.763i	−0.0903949	+	0.462107i
$667$	439.412	+	253.695i	0.658789	+	0.380352i
$668$	−419.620	−	352.103i	−0.628174	−	0.527100i
$669$	−533.547	+	1116.90i	−0.797530	+	1.66950i
$670$	−71.4343	+	52.7422i	−0.106618	+	0.0787197i
$671$	−278.468	−	331.865i	−0.415005	−	0.494583i
$672$	−426.491	−	118.549i	−0.634659	−	0.176413i
$673$	259.131	+	711.958i	0.385039	+	1.05789i	0.969206	+	0.246253i	$0.0791993\pi$
$673$	259.131	+	711.958i	0.385039	+	1.05789i	−0.584166	+	0.811634i	$0.698578\pi$
$674$		−	118.727i		−	0.176153i
$675$	298.830	+	605.248i	0.442712	+	0.896664i
$676$	529.492			0.783272
$677$	−185.869	+	67.6509i	−0.274549	+	0.0999275i	−0.475625	−	0.879648i	$-0.657778\pi$
$677$	−185.869	+	67.6509i	−0.274549	+	0.0999275i	0.201077	+	0.979575i	$0.435556\pi$
$678$	−36.1892	−	36.8702i	−0.0533764	−	0.0543808i
$679$	332.624	−	279.104i	0.489873	−	0.411052i
$680$	347.832	+	471.106i	0.511518	+	0.692802i
$681$	24.9618	+	319.599i	0.0366546	+	0.469309i
$682$	−164.979	+	196.615i	−0.241905	+	0.288292i
$683$	−521.767	+	903.727i	−0.763934	+	1.32317i	0.176874	+	0.984233i	$0.443401\pi$
$683$	−521.767	+	903.727i	−0.763934	+	1.32317i	−0.940808	+	0.338939i	$0.889932\pi$
$684$	520.000	+	643.711i	0.760234	+	0.941098i
$685$	594.256	+	394.231i	0.867527	+	0.575520i
$686$	274.725	+	48.4414i	0.400474	+	0.0706143i
$687$	414.834	+	40.1930i	0.603834	+	0.0585050i
$688$	90.0546	−	247.423i	0.130893	−	0.359627i
$689$	271.180	−	745.061i	0.393585	−	1.08137i
$690$	−141.601	+	54.0880i	−0.205219	+	0.0783884i
$691$	120.650	−	684.241i	0.174602	−	0.990219i	−0.764000	−	0.645217i	$-0.776767\pi$
$691$	120.650	−	684.241i	0.174602	−	0.990219i	0.938602	−	0.345002i	$-0.112122\pi$
$692$	188.304	+	326.152i	0.272116	+	0.471318i
$693$	119.697	−	310.716i	0.172723	−	0.448363i
$694$	−82.2826	+	142.518i	−0.118563	+	0.205357i
$695$	−910.681	−	219.651i	−1.31033	−	0.316044i
$696$	655.241	−	51.1765i	0.941438	−	0.0735295i
$697$	−1106.27	+	195.065i	−1.58719	+	0.279864i
$698$	232.008	−	194.678i	0.332390	−	0.278908i
$699$	−223.133	−	227.332i	−0.319217	−	0.325224i
$700$	−402.636	−	124.027i	−0.575194	−	0.177181i
$701$			1192.44i			1.70105i	0.525936	+	0.850524i	$0.323715\pi$
$701$			1192.44i			1.70105i	−0.525936	+	0.850524i	$0.676285\pi$
$702$	256.292	+	271.042i	0.365088	+	0.386100i
$703$			1224.00i			1.74111i
$704$	36.3973	+	100.001i	0.0517007	+	0.142046i
$705$	−78.1103	−	405.410i	−0.110795	−	0.575049i
$706$	393.275	−	329.997i	0.557047	−	0.467418i
$707$	73.9636	+	419.469i	0.104616	+	0.593308i
$708$	67.5962	−	141.502i	0.0954748	−	0.199861i
$709$	−128.669	−	107.966i	−0.181479	−	0.152279i	0.547523	−	0.836791i	$-0.315571\pi$
$709$	−128.669	−	107.966i	−0.181479	−	0.152279i	−0.729002	+	0.684512i	$0.760015\pi$
$710$	405.426	+	25.2259i	0.571023	+	0.0355294i
$711$	406.253	−	466.220i	0.571383	−	0.655725i
$712$	−542.210	+	313.045i	−0.761531	+	0.439670i
$713$	102.150	−	579.324i	0.143269	−	0.812516i
$714$	−213.178	+	96.9976i	−0.298568	+	0.135851i
$715$	−669.987	+	75.6201i	−0.937044	+	0.105762i
$716$	233.946	−	642.763i	0.326741	−	0.897713i
$717$	618.180	+	441.498i	0.862176	+	0.615758i
$718$	−185.457	−	32.7010i	−0.258296	−	0.0455446i
$719$	35.4071	−	20.4423i	0.0492449	−	0.0284315i	−0.475175	−	0.879891i	$-0.657615\pi$
$719$	35.4071	−	20.4423i	0.0492449	−	0.0284315i	0.524420	+	0.851460i	$0.324282\pi$
$720$	237.350	−	343.692i	0.329652	−	0.477350i
$721$	161.704	−	280.080i	0.224278	−	0.388461i
$722$	−214.821	−	180.256i	−0.297535	−	0.249662i
$723$	9.37095	−	6.43227i	0.0129612	−	0.00889664i
$724$	−54.1734	−	307.233i	−0.0748252	−	0.424355i
$725$	961.924	−	48.3794i	1.32679	−	0.0667302i
$726$	−144.687	+	37.3267i	−0.199293	+	0.0514142i
$727$	315.233	+	866.096i	0.433608	+	1.19133i	0.943582	+	0.331139i	$0.107433\pi$
$727$	315.233	+	866.096i	0.433608	+	1.19133i	−0.509974	+	0.860190i	$0.670345\pi$
$728$	−505.837			−0.694832
$729$	40.7500	−	727.860i	0.0558985	−	0.998436i
$730$	133.441	+	268.349i	0.182796	+	0.367601i
$731$	−199.826	−	549.018i	−0.273360	−	0.751051i
$732$	573.228	−	147.883i	0.783099	−	0.202026i
$733$	−238.564	−	284.310i	−0.325463	−	0.387871i	0.578358	−	0.815783i	$-0.303694\pi$
$733$	−238.564	−	284.310i	−0.325463	−	0.387871i	−0.903820	+	0.427912i	$0.859249\pi$
$734$	351.598	−	61.9962i	0.479016	−	0.0844635i
$735$	−179.389	+	322.371i	−0.244066	+	0.438600i
$736$	301.338	+	252.853i	0.409427	+	0.343550i
$737$	−86.6678	+	150.113i	−0.117595	+	0.203681i
$738$	−182.208	−	329.636i	−0.246895	−	0.446661i
$739$	254.858	+	441.428i	0.344869	+	0.597331i	0.985330	−	0.170660i	$-0.0545899\pi$
$739$	254.858	+	441.428i	0.344869	+	0.597331i	−0.640461	+	0.767991i	$0.721257\pi$
$740$	742.896	−	219.205i	1.00391	−	0.296222i
$741$	1184.82	+	846.190i	1.59895	+	1.14196i
$742$	−57.0871	+	156.846i	−0.0769368	+	0.211382i
$743$	−585.060	−	212.945i	−0.787430	−	0.286601i	−0.0831627	−	0.996536i	$-0.526502\pi$
$743$	−585.060	−	212.945i	−0.787430	−	0.286601i	−0.704267	+	0.709935i	$0.748724\pi$
$744$	−315.580	−	693.571i	−0.424167	−	0.932219i
$745$	111.897	−	33.0172i	0.150198	−	0.0443184i
$746$	348.763	−	201.358i	0.467510	−	0.269917i
$747$	−446.990	+	512.970i	−0.598381	+	0.686707i
$748$	455.673	+	263.083i	0.609188	+	0.351715i
$749$	−54.2136	+	64.6093i	−0.0723814	+	0.0862607i
$750$	−169.998	+	232.144i	−0.226664	+	0.309525i
$751$	68.2732	+	387.196i	0.0909097	+	0.515575i	0.995924	+	0.0901939i	$0.0287487\pi$
$751$	68.2732	+	387.196i	0.0909097	+	0.515575i	−0.905015	+	0.425381i	$0.860140\pi$
$752$	−195.707	+	164.218i	−0.260248	+	0.218374i
$753$	517.451	+	143.833i	0.687186	+	0.191014i
$754$	500.164	−	182.045i	0.663347	−	0.241439i
$755$	−1034.85	+	514.594i	−1.37066	+	0.681582i
$756$	312.619	+	330.611i	0.413517	+	0.437316i
$757$			480.153i			0.634283i	0.948378	+	0.317142i	$0.102723\pi$
$757$			480.153i			0.634283i	−0.948378	+	0.317142i	$0.897277\pi$
$758$	−265.685	+	96.7013i	−0.350508	+	0.127574i
$759$	−211.171	+	207.271i	−0.278223	+	0.273084i
$760$	−306.326	+	702.475i	−0.403060	+	0.924310i
$761$	−13.3027	+	2.34562i	−0.0174805	+	0.00308229i	−0.182382	−	0.983228i	$-0.558381\pi$
$761$	−13.3027	+	2.34562i	−0.0174805	+	0.00308229i	0.164901	+	0.986310i	$0.447270\pi$
$762$	−125.441	+	9.79739i	−0.164621	+	0.0128575i
$763$	229.341	−	273.318i	0.300578	−	0.358215i
$764$	646.322	+	373.154i	0.845972	+	0.488422i
$765$	−86.7616	−	922.745i	−0.113414	−	1.20620i
$766$	−227.337	−	393.760i	−0.296785	−	0.514047i
$767$	47.9125	−	271.725i	0.0624673	−	0.354270i
$768$	128.984	+	12.4972i	0.167948	+	0.0162723i
$769$	−54.1363	−	19.7040i	−0.0703983	−	0.0256229i	0.306581	−	0.951845i	$-0.400815\pi$
$769$	−54.1363	−	19.7040i	−0.0703983	−	0.0256229i	−0.376979	+	0.926222i	$0.623037\pi$
$770$	141.041	−	15.9191i	0.183171	−	0.0206741i
$771$	−480.182	−	46.5245i	−0.622804	−	0.0603430i
$772$	652.966	+	115.135i	0.845810	+	0.149139i
$773$	163.063	+	282.433i	0.210948	+	0.365372i	0.952011	−	0.306062i	$-0.0990116\pi$
$773$	163.063	+	282.433i	0.210948	+	0.365372i	−0.741064	+	0.671435i	$0.765678\pi$
$774$	152.385	−	123.099i	0.196879	−	0.159043i
$775$	−434.143	−	1028.80i	−0.560185	−	1.32749i
$776$	−321.274	+	382.880i	−0.414013	+	0.493402i
$777$	52.4061	+	670.983i	0.0674467	+	0.863557i
$778$	244.982	−	43.1969i	0.314887	−	0.0555230i
$779$	−944.949	−	1126.15i	−1.21303	−	1.44563i
$780$	301.399	−	870.661i	0.386409	−	1.11623i
$781$	745.135	−	271.207i	0.954078	−	0.347256i
$782$	208.128			0.266148
$783$	−930.073	−	465.791i	−1.18783	−	0.594880i
$784$	228.285			0.291180
$785$	29.5880	+	28.1373i	0.0376917	+	0.0358437i
$786$	92.1627	+	25.6180i	0.117255	+	0.0325929i
$787$	745.755	+	888.757i	0.947593	+	1.12930i	0.991480	+	0.130260i	$0.0415814\pi$
$787$	745.755	+	888.757i	0.947593	+	1.12930i	−0.0438871	+	0.999036i	$0.513974\pi$
$788$	−66.3375	−	376.219i	−0.0841846	−	0.477435i
$789$	465.254	+	222.254i	0.589675	+	0.281691i
$790$	256.252	+	61.8064i	0.324370	+	0.0782360i
$791$	−96.0224	−	55.4385i	−0.121394	−	0.0700866i
$792$	−73.5812	+	376.154i	−0.0929056	+	0.474942i
$793$	902.052	−	520.800i	1.13752	−	0.656746i
$794$	−569.560	−	100.429i	−0.717330	−	0.126485i
$795$	−512.625	−	416.517i	−0.644812	−	0.523921i
$796$	−73.1104	−	26.6100i	−0.0918473	−	0.0334297i
$797$	−438.957	−	159.767i	−0.550762	−	0.200461i	0.0516233	−	0.998667i	$-0.483560\pi$
$797$	−438.957	−	159.767i	−0.550762	−	0.200461i	−0.602385	+	0.798206i	$0.705783\pi$
$798$	−249.422	−	178.135i	−0.312559	−	0.223226i
$799$	−98.4393	+	558.277i	−0.123203	+	0.698720i
$800$	740.944	+	92.5623i	0.926180	+	0.115703i
$801$	990.725	+	18.4718i	1.23686	+	0.0230609i
$802$	204.241	+	117.918i	0.254664	+	0.147030i
$803$	448.159	+	376.050i	0.558106	+	0.468307i
$804$	−134.045	−	195.286i	−0.166723	−	0.242892i
$805$	−261.710	+	193.229i	−0.325105	+	0.240036i
$806$	−396.664	−	472.726i	−0.492139	−	0.586508i
$807$	−264.464	−	1025.12i	−0.327713	−	1.27029i
$808$	−167.691	−	460.727i	−0.207538	−	0.570206i
$809$		−	1348.17i		−	1.66646i	−0.552923	−	0.833232i	$-0.686488\pi$
$809$		−	1348.17i		−	1.66646i	0.552923	−	0.833232i	$-0.313512\pi$
$810$	283.212	−	127.895i	0.349645	−	0.157895i
$811$	−802.634			−0.989685			−0.494842	−	0.868983i	$-0.664774\pi$
$811$	−802.634			−0.989685			−0.494842	+	0.868983i	$0.664774\pi$
$812$	610.088	−	222.054i	0.751340	−	0.273465i
$813$	−1386.61	+	357.722i	−1.70554	+	0.440002i
$814$	−199.898	+	167.734i	−0.245575	+	0.206062i
$815$	−173.448	+	128.062i	−0.212820	+	0.157131i
$816$	−472.832	+	324.555i	−0.579451	+	0.397738i
$817$	491.473	−	585.715i	0.601558	−	0.716909i
$818$	189.932	−	328.973i	0.232191	−	0.402167i
$819$	685.737	+	413.143i	0.837286	+	0.504448i
$820$	−514.275	+	775.208i	−0.627164	+	0.945376i
$821$	151.564	+	26.7248i	0.184609	+	0.0325515i	0.265188	−	0.964197i	$-0.414566\pi$
$821$	151.564	+	26.7248i	0.184609	+	0.0325515i	−0.0805793	+	0.996748i	$0.525677\pi$
$822$	190.808	−	267.166i	0.232126	−	0.325020i
$823$	−22.3175	+	61.3168i	−0.0271172	+	0.0745040i	−0.952513	−	0.304499i	$-0.901511\pi$
$823$	−22.3175	+	61.3168i	−0.0271172	+	0.0745040i	0.925395	+	0.379003i	$0.123733\pi$
$824$	−127.325	+	349.822i	−0.154520	+	0.424541i
$825$	−123.051	+	548.033i	−0.149153	+	0.664283i
$826$	−10.0862	+	57.2019i	−0.0122109	+	0.0692517i
$827$	535.860	+	928.136i	0.647956	+	1.12229i	0.983610	+	0.180307i	$0.0577092\pi$
$827$	535.860	+	928.136i	0.647956	+	1.12229i	−0.335654	+	0.941985i	$0.608957\pi$
$828$	−131.187	−	382.471i	−0.158438	−	0.461921i
$829$	377.159	−	653.259i	0.454957	−	0.788009i	−0.543729	−	0.839261i	$-0.682988\pi$
$829$	377.159	−	653.259i	0.454957	−	0.788009i	0.998686	+	0.0512524i	$0.0163213\pi$
$830$	−281.948	−	68.0041i	−0.339696	−	0.0819326i
$831$	−590.856	+	1236.86i	−0.711018	+	1.48840i
$832$	−251.977	+	44.4304i	−0.302857	+	0.0534019i
$833$	388.041	−	325.605i	0.465835	−	0.390882i
$834$	−115.500	+	415.521i	−0.138490	+	0.498227i
$835$	−553.287	+	581.813i	−0.662619	+	0.696783i
$836$			688.579i			0.823660i
$837$	−138.659	+	1197.99i	−0.165662	+	1.43129i
$838$		−	212.016i		−	0.253002i
$839$	88.8598	+	244.140i	0.105912	+	0.290990i	0.981316	−	0.192401i	$-0.0616274\pi$
$839$	88.8598	+	244.140i	0.105912	+	0.290990i	−0.875405	+	0.483390i	$0.839405\pi$
$840$	−137.848	+	398.205i	−0.164104	+	0.474053i
$841$	−492.736	+	413.455i	−0.585893	+	0.491623i
$842$	56.9399	+	322.922i	0.0676246	+	0.383518i
$843$	1242.23	−	97.0228i	1.47359	−	0.115092i
$844$	−331.360	−	278.044i	−0.392607	−	0.329436i
$845$	48.1957	−	774.594i	0.0570363	−	0.916680i
$846$	−187.767	+	29.5106i	−0.221947	+	0.0348825i
$847$	−277.723	+	160.344i	−0.327890	+	0.189308i
$848$	−70.9727	+	402.506i	−0.0836942	+	0.474653i
$849$	60.4558	−	623.968i	0.0712082	−	0.734944i
$850$	331.790	−	214.474i	0.390341	−	0.252322i
$851$	204.557	−	562.015i	0.240372	−	0.660417i
$852$	−104.498	+	1078.53i	−0.122650	+	1.26588i
$853$	−287.962	−	50.7754i	−0.337587	−	0.0595257i	0.00228492	−	0.999997i	$-0.499273\pi$
$853$	−287.962	−	50.7754i	−0.337587	−	0.0595257i	−0.339872	+	0.940472i	$0.610384\pi$
$854$	−189.894	+	109.636i	−0.222359	+	0.128379i
$855$	989.017	−	702.117i	1.15674	−	0.821189i
$856$	48.5423	−	84.0778i	0.0567083	−	0.0982217i
$857$	−554.776	−	465.512i	−0.647346	−	0.543188i	0.258918	−	0.965899i	$-0.416634\pi$
$857$	−554.776	−	465.512i	−0.647346	−	0.543188i	−0.906264	+	0.422711i	$0.861078\pi$
$858$	24.1698	+	309.460i	0.0281700	+	0.360675i
$859$	−57.6146	−	326.749i	−0.0670717	−	0.380383i	−0.999804	−	0.0198122i	$-0.993693\pi$
$859$	−57.6146	−	326.749i	−0.0670717	−	0.380383i	0.932732	−	0.360570i	$-0.117418\pi$
$860$	−443.512	−	193.400i	−0.515711	−	0.224884i
$861$	−566.227	−	576.882i	−0.657638	−	0.670014i
$862$	63.8200	+	175.344i	0.0740371	+	0.203415i
$863$	−238.506			−0.276369			−0.138184	−	0.990407i	$-0.544127\pi$
$863$	−238.506			−0.276369			−0.138184	+	0.990407i	$0.544127\pi$
$864$	−647.405	−	480.844i	−0.749312	−	0.556533i
$865$	494.268	−	245.783i	0.571408	−	0.284142i
$866$	73.3533	+	201.537i	0.0847036	+	0.232721i
$867$	−108.617	+	390.756i	−0.125279	+	0.450699i
$868$	−483.841	−	576.620i	−0.557421	−	0.664308i
$869$	506.752	−	89.3541i	0.583144	−	0.102824i
$870$	−7.00758	−	443.348i	−0.00805469	−	0.509595i
$871$	−319.253	−	267.885i	−0.366536	−	0.307560i
$872$	−205.350	+	355.676i	−0.235493	+	0.407885i
$873$	748.252	−	256.649i	0.857104	−	0.293985i
$874$	136.186	+	235.881i	0.155819	+	0.269886i
$875$	−218.088	+	577.728i	−0.249243	+	0.660260i
$876$	−727.663	+	331.093i	−0.830665	+	0.377960i
$877$	−31.9931	+	87.9005i	−0.0364802	+	0.100229i	−0.956595	−	0.291419i	$-0.905873\pi$
$877$	−31.9931	+	87.9005i	−0.0364802	+	0.100229i	0.920115	+	0.391648i	$0.128095\pi$
$878$	395.814	+	144.065i	0.450814	+	0.164083i
$879$	263.097	−	368.385i	0.299314	−	0.419095i
$880$	333.352	−	98.3612i	0.378809	−	0.111774i
$881$	−1228.28	+	709.150i	−1.39419	+	0.804937i	−0.993776	−	0.111396i	$-0.964468\pi$
$881$	−1228.28	+	709.150i	−1.39419	+	0.804937i	−0.400416	+	0.916333i	$0.631135\pi$
$882$	145.478	+	87.6479i	0.164942	+	0.0993741i
$883$	47.9457	+	27.6814i	0.0542986	+	0.0313493i	0.526904	−	0.849925i	$-0.323353\pi$
$883$	47.9457	+	27.6814i	0.0542986	+	0.0313493i	−0.472605	+	0.881274i	$0.656686\pi$
$884$	−813.173	+	969.102i	−0.919879	+	1.09627i
$885$	−200.850	−	111.766i	−0.226949	−	0.126290i
$886$	89.8685	+	509.669i	0.101432	+	0.575248i
$887$	500.234	−	419.746i	0.563962	−	0.473220i	−0.315674	−	0.948868i	$-0.602231\pi$
$887$	500.234	−	419.746i	0.563962	−	0.473220i	0.879636	+	0.475647i	$0.157786\pi$
$888$	−193.527	−	750.154i	−0.217936	−	0.844768i
$889$	−253.752	+	92.3580i	−0.285435	+	0.103890i
$890$	188.071	+	378.210i	0.211316	+	0.424955i
$891$	406.974	−	449.834i	0.456761	−	0.504864i
$892$		−	1407.48i		−	1.57789i
$893$	−697.133	+	253.736i	−0.780664	+	0.284138i
$894$	−13.4170	−	52.0073i	−0.0150079	−	0.0581737i
$895$	−919.004	−	400.746i	−1.02682	−	0.447761i
$896$	634.292	−	111.843i	0.707915	−	0.124825i
$897$	−402.610	−	586.547i	−0.448840	−	0.653899i
$898$	−158.092	+	188.406i	−0.176049	+	0.209807i
$899$	1490.25	+	860.394i	1.65767	+	0.957057i
$900$	−603.265	−	474.534i	−0.670295	−	0.527260i
$901$	453.458	+	785.413i	0.503283	+	0.871712i
$902$	54.4231	−	308.649i	0.0603361	−	0.342183i
$903$	244.342	−	342.125i	0.270590	−	0.378876i
$904$	119.933	+	43.6519i	0.132669	+	0.0482875i
$905$	−454.382	+	51.2853i	−0.502080	+	0.0566688i
$906$	220.357	+	484.291i	0.243219	+	0.534538i
$907$	−105.493	−	18.6012i	−0.116309	−	0.0205085i	0.115190	−	0.993343i	$-0.463252\pi$
$907$	−105.493	−	18.6012i	−0.116309	−	0.0205085i	−0.231500	+	0.972835i	$0.574363\pi$
$908$	−182.260	−	315.683i	−0.200727	−	0.347669i
$909$	−148.969	+	761.544i	−0.163883	+	0.837782i
$910$	−21.1925	+	340.604i	−0.0232885	+	0.374290i
$911$	427.389	−	509.342i	0.469142	−	0.559102i	−0.478644	−	0.878009i	$-0.658871\pi$
$911$	427.389	−	509.342i	0.469142	−	0.559102i	0.947786	+	0.318907i	$0.103316\pi$
$912$	−677.224	−	323.514i	−0.742570	−	0.354730i
$913$	−557.567	+	98.3141i	−0.610698	+	0.107682i
$914$	−270.000	−	321.774i	−0.295405	−	0.352050i
$915$	−164.162	−	852.037i	−0.179412	−	0.931188i
$916$	−445.332	+	162.088i	−0.486170	+	0.176952i
$917$	205.295			0.223877
$918$	−425.930	+	25.2884i	−0.463976	+	0.0275473i
$919$	836.732			0.910481			0.455241	−	0.890368i	$-0.349553\pi$
$919$	836.732			0.910481			0.455241	+	0.890368i	$0.349553\pi$
$920$	258.052	−	271.356i	0.280491	−	0.294953i
$921$	748.224	−	734.404i	0.812404	−	0.797398i
$922$	−212.398	−	253.125i	−0.230366	−	0.274540i
$923$	331.064	+	1877.56i	0.358683	+	2.03419i
$924$	29.4818	+	377.471i	0.0319067	+	0.408519i
$925$	−253.054	−	1106.74i	−0.273572	−	1.19647i
$926$	−205.201	−	118.473i	−0.221600	−	0.127941i
$927$	458.325	−	370.242i	0.494417	−	0.399398i
$928$	−996.525	+	575.344i	−1.07384	+	0.619983i
$929$	−973.810	−	171.709i	−1.04823	−	0.184832i	−0.377104	−	0.926171i	$-0.623080\pi$
$929$	−973.810	−	171.709i	−1.04823	−	0.184832i	−0.671131	+	0.741339i	$0.734191\pi$
$930$	−480.235	+	183.437i	−0.516381	+	0.197244i
$931$	622.932	+	226.729i	0.669100	+	0.243533i
$932$	340.365	+	123.883i	0.365198	+	0.132921i
$933$	−6.17886	+	63.7724i	−0.00662257	+	0.0683520i
$934$	99.2022	−	562.603i	0.106212	−	0.602359i
$935$	426.341	−	642.658i	0.455979	−	0.687335i
$936$	−859.934	−	331.272i	−0.918733	−	0.353923i
$937$	−469.038	−	270.799i	−0.500575	−	0.289007i	0.228376	−	0.973573i	$-0.426658\pi$
$937$	−469.038	−	270.799i	−0.500575	−	0.289007i	−0.728951	+	0.684566i	$0.759992\pi$
$938$	67.2071	+	56.3934i	0.0716493	+	0.0601209i
$939$	−1166.20	+	91.0839i	−1.24196	+	0.0970010i
$940$	278.851	+	377.677i	0.296650	+	0.401784i
$941$	166.260	+	198.142i	0.176685	+	0.210565i	0.847118	−	0.531406i	$-0.178336\pi$
$941$	166.260	+	198.142i	0.176685	+	0.210565i	−0.670433	+	0.741970i	$0.733891\pi$
$942$	13.4151	−	13.1673i	0.0142411	−	0.0139780i
$943$	245.682	+	675.004i	0.260532	+	0.715805i
$944$			142.231i			0.150668i
$945$	512.106	−	427.238i	0.541912	−	0.452103i
$946$	163.006			0.172311
$947$	366.881	−	133.534i	0.387414	−	0.141007i	−0.140967	−	0.990014i	$-0.545021\pi$
$947$	366.881	−	133.534i	0.387414	−	0.141007i	0.528382	+	0.849007i	$0.322799\pi$
$948$	−188.315	+	677.477i	−0.198644	+	0.714638i
$949$	−1077.52	+	904.146i	−1.13543	+	0.952736i
$950$	460.175	+	235.694i	0.484395	+	0.248099i
$951$	−739.538	−	353.281i	−0.777642	−	0.371484i
$952$	371.912	−	443.227i	0.390664	−	0.465575i
$953$	−232.132	+	402.064i	−0.243580	+	0.421893i	−0.961732	−	0.273994i	$-0.911655\pi$
$953$	−232.132	+	402.064i	−0.243580	+	0.421893i	0.718151	+	0.695887i	$0.244989\pi$
$954$	−199.767	+	229.255i	−0.209399	+	0.240309i
$955$	604.718	−	911.540i	0.633212	−	0.954492i
$956$	−850.667	−	149.995i	−0.889819	−	0.156899i
$957$	−358.473	−	787.839i	−0.374580	−	0.823238i
$958$	171.381	−	470.866i	0.178895	−	0.491509i
$959$	240.987	−	662.106i	0.251290	−	0.690413i
$960$	−33.6908	+	210.469i	−0.0350946	+	0.219239i
$961$	179.563	−	1018.35i	0.186850	−	1.05968i
$962$	−313.702	−	543.347i	−0.326093	−	0.564810i
$963$	−134.477	+	74.3328i	−0.139644	+	0.0771888i
$964$	−6.46215	+	11.1928i	−0.00670348	+	0.0116108i
$965$	227.866	−	944.744i	0.236131	−	0.979009i
$966$	84.7549	+	123.476i	0.0877380	+	0.127822i
$967$	641.635	−	113.138i	0.663532	−	0.116999i	0.168268	−	0.985741i	$-0.446183\pi$
$967$	641.635	−	113.138i	0.663532	−	0.116999i	0.495264	+	0.868743i	$0.335071\pi$
$968$	282.778	−	237.279i	0.292126	−	0.245123i
$969$	−1612.58	+	416.019i	−1.66417	+	0.429328i
$970$	244.351	+	232.370i	0.251908	+	0.239557i
$971$			40.3111i			0.0415150i	0.999785	+	0.0207575i	$0.00660779\pi$
$971$			40.3111i			0.0415150i	−0.999785	+	0.0207575i	$0.993392\pi$
$972$	314.943	+	766.779i	0.324015	+	0.788867i
$973$			925.585i			0.951269i
$974$	−169.469	−	465.613i	−0.173993	−	0.478042i
$975$	−1246.26	−	520.167i	−1.27821	−	0.533504i
$976$	−411.311	+	345.131i	−0.421425	+	0.353617i
$977$	−86.1735	−	488.714i	−0.0882021	−	0.500219i	−0.996620	−	0.0821549i	$-0.973820\pi$
$977$	−86.1735	−	488.714i	−0.0882021	−	0.500219i	0.908417	−	0.418064i	$-0.137291\pi$
$978$	56.1712	+	81.8338i	0.0574348	+	0.0836747i
$979$	631.635	+	530.005i	0.645184	+	0.541374i
$980$	26.0510	−	418.688i	0.0265826	−	0.427232i
$981$	568.880	−	314.451i	0.579898	−	0.320542i
$982$	−197.954	+	114.289i	−0.201582	+	0.116383i
$983$	330.085	−	1872.00i	0.335793	−	1.90438i	−0.0834645	−	0.996511i	$-0.526599\pi$
$983$	330.085	−	1872.00i	0.335793	−	1.90438i	0.419258	−	0.907867i	$-0.362290\pi$
$984$	757.186	+	540.775i	0.769498	+	0.549568i
$985$	−556.409	+	62.8008i	−0.564882	+	0.0637572i
$986$	−208.228	+	572.102i	−0.211185	+	0.580226i
$987$	−371.297	+	168.943i	−0.376187	+	0.171168i
$988$	−1630.42	−	287.486i	−1.65022	−	0.290978i
$989$	−323.551	+	186.802i	−0.327150	+	0.188880i
$990$	250.199	+	65.3050i	0.252726	+	0.0659646i
$991$	200.715	−	347.649i	0.202538	−	0.350806i	−0.746808	−	0.665040i	$-0.768414\pi$
$991$	200.715	−	347.649i	0.202538	−	0.350806i	0.949345	+	0.314234i	$0.101748\pi$
$992$	1021.98	+	857.539i	1.03022	+	0.864455i
$993$	817.201	+	390.382i	0.822962	+	0.393134i
$994$	−69.6935	−	395.252i	−0.0701142	−	0.397638i
$995$	−45.5825	+	104.531i	−0.0458116	+	0.105057i
$996$	207.198	−	745.410i	0.208030	−	0.748404i
$997$	−463.244	−	1272.75i	−0.464638	−	1.27658i	−0.921961	−	0.387282i	$-0.873414\pi$
$997$	−463.244	−	1272.75i	−0.464638	−	1.27658i	0.457323	−	0.889300i	$-0.348808\pi$
$998$	19.6108			0.0196501
$999$	−350.334	+	1175.01i	−0.350685	+	1.17618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.n.a.74.21	yes	204
3.2	odd	2		405.3.n.a.224.14		204
5.4	even	2	inner	135.3.n.a.74.14	✓	204
15.14	odd	2		405.3.n.a.224.21		204
27.4	even	9		405.3.n.a.179.21		204
27.23	odd	18	inner	135.3.n.a.104.14	yes	204
135.4	even	18		405.3.n.a.179.14		204
135.104	odd	18	inner	135.3.n.a.104.21	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.14	✓	204	5.4	even	2	inner
135.3.n.a.74.21	yes	204	1.1	even	1	trivial
135.3.n.a.104.14	yes	204	27.23	odd	18	inner
135.3.n.a.104.21	yes	204	135.104	odd	18	inner
405.3.n.a.179.14		204	135.4	even	18
405.3.n.a.179.21		204	27.4	even	9
405.3.n.a.224.14		204	3.2	odd	2
405.3.n.a.224.21		204	15.14	odd	2

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.n (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.721015 - 0.262428i) q^{2} +(2.90489 - 0.749413i) q^{3} +(-2.61318 + 2.19272i) q^{4} +(2.96988 + 4.02242i) q^{5} +(1.89780 - 1.30266i) q^{6} +(3.17548 - 3.78438i) q^{7} +(-2.84329 + 4.92472i) q^{8} +(7.87676 - 4.35392i) q^{9} +(3.19692 + 2.12084i) q^{10} +(7.37526 + 1.30046i) q^{11} +(-5.94776 + 8.32797i) q^{12} +(-6.15844 + 16.9202i) q^{13} +(1.29644 - 3.56193i) q^{14} +(11.6416 + 9.45901i) q^{15} +(1.61177 - 9.14083i) q^{16} +(-10.2979 - 17.8366i) q^{17} +(4.53667 - 5.20632i) q^{18} +(13.4766 - 23.3422i) q^{19} +(-16.5809 - 3.99920i) q^{20} +(6.38834 - 13.3730i) q^{21} +(5.65895 - 0.997825i) q^{22} +(-10.0889 + 8.46563i) q^{23} +(-4.56879 + 16.4366i) q^{24} +(-7.35967 + 23.8922i) q^{25} +13.8158i q^{26} +(19.6182 - 18.5506i) q^{27} +16.8522i q^{28} +(-13.1765 - 36.2022i) q^{29} +(10.8761 + 3.76500i) q^{30} +(-34.2162 + 28.7108i) q^{31} +(-5.18655 - 29.4144i) q^{32} +(22.3989 - 1.74943i) q^{33} +(-12.1058 - 10.1580i) q^{34} +(24.6531 + 1.53393i) q^{35} +(-11.0365 + 28.6491i) q^{36} +(-39.3279 + 22.7060i) q^{37} +(3.59121 - 20.3667i) q^{38} +(-5.20939 + 53.7664i) q^{39} +(-28.2535 + 3.18892i) q^{40} +(18.6544 - 51.2525i) q^{41} +(1.09665 - 11.3186i) q^{42} +(27.9365 + 4.92596i) q^{43} +(-22.1245 + 12.7736i) q^{44} +(40.9063 + 18.7530i) q^{45} +(-5.05266 + 8.75146i) q^{46} +(-21.0849 - 17.6923i) q^{47} +(-2.16823 - 27.7610i) q^{48} +(4.27084 + 24.2211i) q^{49} +(0.963538 + 19.1580i) q^{50} +(-43.2813 - 44.0958i) q^{51} +(-21.0081 - 57.7193i) q^{52} -44.0339 q^{53} +(9.27683 - 18.5236i) q^{54} +(16.6726 + 33.5286i) q^{55} +(9.60824 + 26.3984i) q^{56} +(21.6552 - 77.9062i) q^{57} +(-19.0009 - 22.6444i) q^{58} +(-15.0907 + 2.66091i) q^{59} +(-51.1627 + 0.808679i) q^{60} +(-44.3135 - 37.1834i) q^{61} +(-17.1359 + 29.6802i) q^{62} +(8.53555 - 43.6345i) q^{63} +(7.10495 + 12.3061i) q^{64} +(-86.3498 + 25.4790i) q^{65} +(15.6908 - 7.13946i) q^{66} +(-7.91614 + 21.7494i) q^{67} +(66.0210 + 24.0297i) q^{68} +(-22.9630 + 32.1525i) q^{69} +(18.1778 - 5.36368i) q^{70} +(91.6966 - 52.9411i) q^{71} +(-0.954056 + 51.1703i) q^{72} +(67.6524 + 39.0591i) q^{73} +(-22.3973 + 26.6921i) q^{74} +(-3.47394 + 74.9195i) q^{75} +(15.9661 + 90.5481i) q^{76} +(28.3414 - 23.7813i) q^{77} +(10.3538 + 40.1335i) q^{78} +(64.5660 - 23.5001i) q^{79} +(41.5550 - 20.6639i) q^{80} +(43.0867 - 68.5896i) q^{81} -41.8492i q^{82} +(-71.0404 + 25.8566i) q^{83} +(12.6293 + 48.9539i) q^{84} +(41.1625 - 94.3950i) q^{85} +(21.4353 - 3.77963i) q^{86} +(-65.4068 - 95.2888i) q^{87} +(-27.3744 + 32.6235i) q^{88} +(95.3491 + 55.0498i) q^{89} +(34.4153 + 2.78624i) q^{90} +(44.4765 + 77.0355i) q^{91} +(7.80150 - 44.2445i) q^{92} +(-77.8781 + 109.044i) q^{93} +(-19.8455 - 7.22317i) q^{94} +(133.916 - 15.1149i) q^{95} +(-37.1099 - 81.5586i) q^{96} +(86.5584 + 15.2626i) q^{97} +(9.43564 + 16.3430i) q^{98} +(63.7553 - 21.8679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31}+ \cdots + 792 q^{99}+O(q^{100}) \) 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Introduction

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