LMFDB - Embedded newform 115.3.i.a.14.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,3,Mod(14,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 21]))

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

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

chi := DirichletCharacter("115.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.i (of order $22$, degree $10$, 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:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.19
Character	$\chi$	$=$	115.14
Dual form			115.3.i.a.74.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.761060 + 2.59193i) q^{2} +(-4.31740 + 3.74105i) q^{3} +(-2.77389 + 1.78267i) q^{4} +(-2.01195 - 4.57734i) q^{5} +(-12.9823 - 8.34325i) q^{6} +(-1.74741 + 3.82629i) q^{7} +(1.43453 + 1.24303i) q^{8} +(3.36366 - 23.3948i) q^{9} +O(q^{10})$	\(q+(0.761060 + 2.59193i) q^{2} +(-4.31740 + 3.74105i) q^{3} +(-2.77389 + 1.78267i) q^{4} +(-2.01195 - 4.57734i) q^{5} +(-12.9823 - 8.34325i) q^{6} +(-1.74741 + 3.82629i) q^{7} +(1.43453 + 1.24303i) q^{8} +(3.36366 - 23.3948i) q^{9} +(10.3330 - 8.69847i) q^{10} +(-3.68427 + 12.5475i) q^{11} +(5.30694 - 18.0738i) q^{12} +(-1.43045 + 0.653264i) q^{13} +(-11.2474 - 1.61713i) q^{14} +(25.8104 + 12.2354i) q^{15} +(-7.60913 + 16.6617i) q^{16} +(-15.1946 - 9.76498i) q^{17} +(63.1977 - 9.08646i) q^{18} +(-4.19613 - 6.52930i) q^{19} +(13.7408 + 9.11041i) q^{20} +(-6.77008 - 23.0568i) q^{21} -35.3262 q^{22} +(-21.1967 - 8.92760i) q^{23} -10.8437 q^{24} +(-16.9041 + 18.4188i) q^{25} +(-2.78187 - 3.21045i) q^{26} +(45.2019 + 70.3356i) q^{27} +(-1.97390 - 13.7288i) q^{28} +(33.3387 + 21.4255i) q^{29} +(-12.0701 + 76.2108i) q^{30} +(-18.0482 + 20.8288i) q^{31} +(-41.4616 - 5.96128i) q^{32} +(-31.0343 - 67.9556i) q^{33} +(13.7462 - 46.8152i) q^{34} +(21.0299 + 0.300185i) q^{35} +(32.3748 + 70.8910i) q^{36} +(-3.03247 + 21.0913i) q^{37} +(13.7300 - 15.8453i) q^{38} +(3.73192 - 8.17177i) q^{39} +(2.80356 - 9.06725i) q^{40} +(0.698185 + 4.85598i) q^{41} +(54.6092 - 35.0952i) q^{42} +(38.5890 + 44.5341i) q^{43} +(-12.1483 - 41.3732i) q^{44} +(-113.854 + 31.6725i) q^{45} +(7.00781 - 61.7348i) q^{46} +23.8391i q^{47} +(-29.4804 - 100.401i) q^{48} +(20.5011 + 23.6595i) q^{49} +(-60.6053 - 29.7966i) q^{50} +(102.132 - 14.6844i) q^{51} +(2.80335 - 4.36210i) q^{52} +(7.69912 - 16.8587i) q^{53} +(-147.904 + 170.690i) q^{54} +(64.8467 - 8.38072i) q^{55} +(-7.26290 + 3.31685i) q^{56} +(42.5428 + 12.4917i) q^{57} +(-30.1607 + 102.718i) q^{58} +(-28.8834 - 63.2459i) q^{59} +(-93.4071 + 12.0718i) q^{60} +(47.2335 + 40.9280i) q^{61} +(-67.7226 - 30.9279i) q^{62} +(83.6376 + 53.7506i) q^{63} +(-5.67646 - 39.4806i) q^{64} +(5.86820 + 5.23332i) q^{65} +(152.517 - 132.157i) q^{66} +(14.0314 - 4.11998i) q^{67} +59.5560 q^{68} +(124.913 - 40.7537i) q^{69} +(15.2270 + 54.7367i) q^{70} +(-88.7455 + 26.0580i) q^{71} +(33.9057 - 29.3794i) q^{72} +(46.3853 + 72.1770i) q^{73} +(-56.9751 + 8.19179i) q^{74} +(4.07640 - 142.760i) q^{75} +(23.2792 + 10.6313i) q^{76} +(-41.5724 - 36.0227i) q^{77} +(24.0209 + 3.45369i) q^{78} +(25.4715 - 11.6324i) q^{79} +(91.5753 + 1.30716i) q^{80} +(-254.182 - 74.6345i) q^{81} +(-12.0550 + 5.50535i) q^{82} +(21.4866 - 149.443i) q^{83} +(59.8821 + 51.8881i) q^{84} +(-14.1269 + 89.1976i) q^{85} +(-86.0608 + 133.913i) q^{86} +(-224.090 + 32.2193i) q^{87} +(-20.8821 + 13.4201i) q^{88} +(-69.3682 + 60.1078i) q^{89} +(-168.742 - 270.996i) q^{90} -6.61483i q^{91} +(74.7122 - 13.0225i) q^{92} -157.445i q^{93} +(-61.7895 + 18.1430i) q^{94} +(-21.4444 + 32.3437i) q^{95} +(201.308 - 129.373i) q^{96} +(-16.2748 - 113.194i) q^{97} +(-45.7214 + 71.1439i) q^{98} +(281.153 + 128.398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9}+O(q^{10}) $ 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9	$ 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30} - 152 q^{31} - 264 q^{34} - 13 q^{35} - 62 q^{36} - 118 q^{39} - 11 q^{40} - 80 q^{41} - 242 q^{44} + 226 q^{46} + 90 q^{49} - 211 q^{50} - 22 q^{51} + 658 q^{54} - 565 q^{55} + 770 q^{56} - 172 q^{59} - 891 q^{60} + 286 q^{61} - 474 q^{64} - 242 q^{65} - 44 q^{66} - 288 q^{69} + 790 q^{70} - 210 q^{71} + 506 q^{74} + 804 q^{75} - 2376 q^{76} + 462 q^{79} + 2398 q^{80} - 2408 q^{81} + 1034 q^{84} + 1197 q^{85} - 1518 q^{86} - 22 q^{89} + 154 q^{90} - 210 q^{94} - 338 q^{95} + 2772 q^{96} + 1628 q^{99}+O(q^{100}) $ 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	0.761060	+	2.59193i	0.380530	+	1.29597i	0.897898	+	0.440204i	$0.145094\pi$
$2$	0.761060	+	2.59193i	0.380530	+	1.29597i	−0.517368	+	0.855763i	$0.673088\pi$
$3$	−4.31740	+	3.74105i	−1.43913	+	1.24702i	−0.519366	+	0.854552i	$0.673832\pi$
$3$	−4.31740	+	3.74105i	−1.43913	+	1.24702i	−0.919767	+	0.392464i	$0.871623\pi$
$4$	−2.77389	+	1.78267i	−0.693473	+	0.445668i
$5$	−2.01195	−	4.57734i	−0.402390	−	0.915468i
$5$	−2.01195	−	4.57734i	−0.402390	−	0.915468i
$6$	−12.9823	−	8.34325i	−2.16372	−	1.39054i
$7$	−1.74741	+	3.82629i	−0.249630	+	0.546613i	−0.992417	−	0.122914i	$-0.960776\pi$
$7$	−1.74741	+	3.82629i	−0.249630	+	0.546613i	0.742788	+	0.669527i	$0.233503\pi$
$8$	1.43453	+	1.24303i	0.179316	+	0.155378i
$9$	3.36366	−	23.3948i	0.373740	−	2.59942i
$10$	10.3330	−	8.69847i	1.03330	−	0.869847i
$11$	−3.68427	+	12.5475i	−0.334934	+	1.14068i	0.604115	+	0.796897i	$0.293527\pi$
$11$	−3.68427	+	12.5475i	−0.334934	+	1.14068i	−0.939049	+	0.343783i	$0.888291\pi$
$12$	5.30694	−	18.0738i	0.442245	−	1.50615i
$13$	−1.43045	+	0.653264i	−0.110034	+	0.0502510i	−0.469672	−	0.882841i	$-0.655628\pi$
$13$	−1.43045	+	0.653264i	−0.110034	+	0.0502510i	0.359637	+	0.933092i	$0.382900\pi$
$14$	−11.2474	−	1.61713i	−0.803384	−	0.115509i
$15$	25.8104	+	12.2354i	1.72070	+	0.815694i
$16$	−7.60913	+	16.6617i	−0.475570	+	1.04135i
$17$	−15.1946	−	9.76498i	−0.893801	−	0.574411i	0.0111450	−	0.999938i	$-0.496452\pi$
$17$	−15.1946	−	9.76498i	−0.893801	−	0.574411i	−0.904946	+	0.425527i	$0.860089\pi$
$18$	63.1977	−	9.08646i	3.51098	−	0.504803i
$19$	−4.19613	−	6.52930i	−0.220849	−	0.343647i	0.713095	−	0.701067i	$-0.247293\pi$
$19$	−4.19613	−	6.52930i	−0.220849	−	0.343647i	−0.933944	+	0.357420i	$0.883656\pi$
$20$	13.7408	+	9.11041i	0.687042	+	0.455520i
$21$	−6.77008	−	23.0568i	−0.322385	−	1.09794i
$22$	−35.3262			−1.60574
$23$	−21.1967	−	8.92760i	−0.921594	−	0.388156i
$23$	−21.1967	−	8.92760i	−0.921594	−	0.388156i
$24$	−10.8437			−0.451820
$25$	−16.9041	+	18.4188i	−0.676165	+	0.736750i
$26$	−2.78187	−	3.21045i	−0.106995	−	0.123479i
$27$	45.2019	+	70.3356i	1.67415	+	2.60502i
$28$	−1.97390	−	13.7288i	−0.0704964	−	0.490313i
$29$	33.3387	+	21.4255i	1.14961	+	0.738811i	0.969562	−	0.244847i	$-0.0787377\pi$
$29$	33.3387	+	21.4255i	1.14961	+	0.738811i	0.180050	+	0.983657i	$0.442374\pi$
$30$	−12.0701	+	76.2108i	−0.402336	+	2.54036i
$31$	−18.0482	+	20.8288i	−0.582201	+	0.671896i	−0.968076	−	0.250655i	$-0.919354\pi$
$31$	−18.0482	+	20.8288i	−0.582201	+	0.671896i	0.385876	+	0.922551i	$0.373899\pi$
$32$	−41.4616	−	5.96128i	−1.29567	−	0.186290i
$33$	−31.0343	−	67.9556i	−0.940432	−	2.05926i
$34$	13.7462	−	46.8152i	0.404299	−	1.37692i
$35$	21.0299	+	0.300185i	0.600855	+	0.00857671i
$36$	32.3748	+	70.8910i	0.899301	+	1.96919i
$37$	−3.03247	+	21.0913i	−0.0819587	+	0.570035i	0.906919	+	0.421305i	$0.138428\pi$
$37$	−3.03247	+	21.0913i	−0.0819587	+	0.570035i	−0.988878	+	0.148730i	$0.952481\pi$
$38$	13.7300	−	15.8453i	0.361316	−	0.416981i
$39$	3.73192	−	8.17177i	0.0956903	−	0.209533i
$40$	2.80356	−	9.06725i	0.0700890	−	0.226681i
$41$	0.698185	+	4.85598i	0.0170289	+	0.118439i	0.996563	−	0.0828406i	$-0.0263992\pi$
$41$	0.698185	+	4.85598i	0.0170289	+	0.118439i	−0.979534	+	0.201279i	$0.935490\pi$
$42$	54.6092	−	35.0952i	1.30022	−	0.835599i
$43$	38.5890	+	44.5341i	0.897419	+	1.03568i	0.999165	+	0.0408660i	$0.0130117\pi$
$43$	38.5890	+	44.5341i	0.897419	+	1.03568i	−0.101746	+	0.994810i	$0.532443\pi$
$44$	−12.1483	−	41.3732i	−0.276097	−	0.940301i
$45$	−113.854	+	31.6725i	−2.53008	+	0.703833i
$46$	7.00781	−	61.7348i	0.152344	−	1.34206i
$47$			23.8391i			0.507216i	0.967307	+	0.253608i	$0.0816173\pi$
$47$			23.8391i			0.507216i	−0.967307	+	0.253608i	$0.918383\pi$
$48$	−29.4804	−	100.401i	−0.614176	−	2.09169i
$49$	20.5011	+	23.6595i	0.418390	+	0.482848i
$50$	−60.6053	−	29.7966i	−1.21211	−	0.595932i
$51$	102.132	−	14.6844i	2.00260	−	0.287930i
$52$	2.80335	−	4.36210i	0.0539106	−	0.0838866i
$53$	7.69912	−	16.8587i	0.145266	−	0.318089i	−0.822987	−	0.568060i	$-0.807694\pi$
$53$	7.69912	−	16.8587i	0.145266	−	0.318089i	0.968253	+	0.249971i	$0.0804212\pi$
$54$	−147.904	+	170.690i	−2.73896	+	3.16093i
$55$	64.8467	−	8.38072i	1.17903	−	0.152377i
$56$	−7.26290	+	3.31685i	−0.129695	+	0.0592295i
$57$	42.5428	+	12.4917i	0.746364	+	0.219152i
$58$	−30.1607	+	102.718i	−0.520012	+	1.77100i
$59$	−28.8834	−	63.2459i	−0.489549	−	1.07196i	−0.979726	−	0.200341i	$-0.935795\pi$
$59$	−28.8834	−	63.2459i	−0.489549	−	1.07196i	0.490177	−	0.871623i	$-0.336932\pi$
$60$	−93.4071	+	12.0718i	−1.55679	+	0.201197i
$61$	47.2335	+	40.9280i	0.774319	+	0.670951i	0.949564	−	0.313574i	$-0.101526\pi$
$61$	47.2335	+	40.9280i	0.774319	+	0.670951i	−0.175245	+	0.984525i	$0.556072\pi$
$62$	−67.7226	−	30.9279i	−1.09230	−	0.498836i
$63$	83.6376	+	53.7506i	1.32758	+	0.853184i
$64$	−5.67646	−	39.4806i	−0.0886946	−	0.616885i
$65$	5.86820	+	5.23332i	0.0902800	+	0.0805125i
$66$	152.517	−	132.157i	2.31087	−	2.00238i
$67$	14.0314	−	4.11998i	0.209424	−	0.0614923i	−0.175338	−	0.984508i	$-0.556102\pi$
$67$	14.0314	−	4.11998i	0.209424	−	0.0614923i	0.384762	+	0.923016i	$0.374284\pi$
$68$	59.5560			0.875823
$69$	124.913	−	40.7537i	1.81033	−	0.590633i
$70$	15.2270	+	54.7367i	0.217528	+	0.781952i
$71$	−88.7455	+	26.0580i	−1.24994	+	0.367015i	−0.838740	−	0.544532i	$-0.816707\pi$
$71$	−88.7455	+	26.0580i	−1.24994	+	0.367015i	−0.411197	+	0.911547i	$0.634889\pi$
$72$	33.9057	−	29.3794i	0.470912	−	0.408048i
$73$	46.3853	+	72.1770i	0.635416	+	0.988726i	0.998379	+	0.0569225i	$0.0181288\pi$
$73$	46.3853	+	72.1770i	0.635416	+	0.988726i	−0.362963	+	0.931804i	$0.618235\pi$
$74$	−56.9751	+	8.19179i	−0.769934	+	0.110700i
$75$	4.07640	−	142.760i	0.0543520	−	1.90347i
$76$	23.2792	+	10.6313i	0.306305	+	0.139885i
$77$	−41.5724	−	36.0227i	−0.539901	−	0.467827i
$78$	24.0209	+	3.45369i	0.307960	+	0.0442780i
$79$	25.4715	−	11.6324i	0.322423	−	0.147246i	−0.247627	−	0.968855i	$-0.579651\pi$
$79$	25.4715	−	11.6324i	0.322423	−	0.147246i	0.570051	+	0.821610i	$0.306924\pi$
$80$	91.5753	+	1.30716i	1.14469	+	0.0163395i
$81$	−254.182	−	74.6345i	−3.13805	−	0.921413i
$82$	−12.0550	+	5.50535i	−0.147012	+	0.0671384i
$83$	21.4866	−	149.443i	0.258875	−	1.80051i	−0.282005	−	0.959413i	$-0.590999\pi$
$83$	21.4866	−	149.443i	0.258875	−	1.80051i	0.540879	−	0.841100i	$-0.318092\pi$
$84$	59.8821	+	51.8881i	0.712882	+	0.617716i
$85$	−14.1269	+	89.1976i	−0.166199	+	1.04938i
$86$	−86.0608	+	133.913i	−1.00071	+	1.55713i
$87$	−224.090	+	32.2193i	−2.57575	+	0.370337i
$88$	−20.8821	+	13.4201i	−0.237296	+	0.152501i
$89$	−69.3682	+	60.1078i	−0.779417	+	0.675369i	−0.950790	−	0.309837i	$-0.899725\pi$
$89$	−69.3682	+	60.1078i	−0.779417	+	0.675369i	0.171372	+	0.985206i	$0.445180\pi$
$90$	−168.742	−	270.996i	−1.87492	−	3.01107i
$91$		−	6.61483i		−	0.0726904i
$92$	74.7122	−	13.0225i	0.812089	−	0.141549i
$93$		−	157.445i		−	1.69296i
$94$	−61.7895	+	18.1430i	−0.657335	+	0.193011i
$95$	−21.4444	+	32.3437i	−0.225731	+	0.340460i
$96$	201.308	−	129.373i	2.09695	−	1.34763i
$97$	−16.2748	−	113.194i	−0.167782	−	1.16695i	−0.883456	−	0.468513i	$-0.844790\pi$
$97$	−16.2748	−	113.194i	−0.167782	−	1.16695i	0.715675	−	0.698434i	$-0.246119\pi$
$98$	−45.7214	+	71.1439i	−0.466545	+	0.725958i
$99$	281.153	+	128.398i	2.83993	+	1.29695i
$100$	14.0556	−	81.2262i	0.140556	−	0.812262i
$101$	6.52720	−	45.3977i	0.0646257	−	0.449482i	−0.931657	−	0.363339i	$-0.881637\pi$
$101$	6.52720	−	45.3977i	0.0646257	−	0.449482i	0.996283	−	0.0861429i	$-0.0274542\pi$
$102$	115.790	+	253.545i	1.13520	+	2.48573i
$103$	42.7609	+	12.5557i	0.415154	+	0.121900i	0.482638	−	0.875820i	$-0.339679\pi$
$103$	42.7609	+	12.5557i	0.415154	+	0.121900i	−0.0674833	+	0.997720i	$0.521497\pi$
$104$	−2.86405	−	0.840960i	−0.0275389	−	0.00808615i
$105$	−91.9176	+	77.3780i	−0.875406	+	0.736933i
$106$	49.5562	+	7.12510i	0.467511	+	0.0672179i
$107$	8.67750	−	10.0144i	0.0810982	−	0.0935923i	−0.713750	−	0.700400i	$-0.753005\pi$
$107$	8.67750	−	10.0144i	0.0810982	−	0.0935923i	0.794848	+	0.606808i	$0.207550\pi$
$108$	−250.771	−	114.523i	−2.32195	−	1.06040i
$109$	27.4945	−	42.7822i	0.252243	−	0.392498i	−0.691921	−	0.721973i	$-0.743235\pi$
$109$	27.4945	−	42.7822i	0.252243	−	0.392498i	0.944164	+	0.329475i	$0.106872\pi$
$110$	71.0745	+	161.700i	0.646132	+	1.47000i
$111$	−65.8112	−	102.404i	−0.592893	−	0.922560i
$112$	−50.4561	−	58.2295i	−0.450501	−	0.519906i
$113$	−35.1066	+	10.3082i	−0.310678	+	0.0912234i	−0.433355	−	0.901223i	$-0.642670\pi$
$113$	−35.1066	+	10.3082i	−0.310678	+	0.0912234i	0.122677	+	0.992447i	$0.460852\pi$
$114$			119.775i			1.05066i
$115$	1.78191	+	114.986i	0.0154948	+	0.999880i
$116$	−130.673			−1.12649
$117$	10.4714	+	35.6624i	0.0894994	+	0.304807i
$118$	141.947	−	122.998i	1.20294	−	1.04235i
$119$	63.9149	−	41.0756i	0.537100	−	0.345173i
$120$	21.8169	+	49.6352i	0.181808	+	0.413627i
$121$	−42.0739	−	27.0392i	−0.347718	−	0.223465i
$122$	−70.1352	+	153.575i	−0.574879	+	1.25881i
$123$	−21.1808	−	18.3533i	−0.172202	−	0.149214i
$124$	12.9330	−	89.9508i	0.104298	−	0.725410i
$125$	118.319	+	40.3184i	0.946553	+	0.322547i
$126$	−75.6648	+	257.691i	−0.600514	+	2.04516i
$127$	−10.7541	+	36.6253i	−0.0846783	+	0.288388i	−0.990935	−	0.134339i	$-0.957109\pi$
$127$	−10.7541	+	36.6253i	−0.0846783	+	0.288388i	0.906257	+	0.422727i	$0.138927\pi$
$128$	−54.3994	+	24.8434i	−0.424996	+	0.194089i
$129$	−333.208	−	47.9081i	−2.58301	−	0.371381i
$130$	−9.09835	+	19.1929i	−0.0699873	+	0.147637i
$131$	−56.4300	+	123.564i	−0.430763	+	0.943239i	0.562439	+	0.826839i	$0.309863\pi$
$131$	−56.4300	+	123.564i	−0.430763	+	0.943239i	−0.993202	+	0.116401i	$0.962864\pi$
$132$	207.228	+	133.177i	1.56991	+	1.00892i
$133$	32.3153	−	4.64624i	0.242972	−	0.0349342i
$134$	21.3575	+	33.2328i	0.159384	+	0.248006i
$135$	231.006	−	348.416i	1.71116	−	2.58086i
$136$	−9.65899	−	32.8955i	−0.0710220	−	0.241879i
$137$	251.862			1.83841			0.919204	−	0.393781i	$-0.128833\pi$
$137$	251.862			1.83841			0.919204	+	0.393781i	$0.128833\pi$
$138$	200.697	+	292.750i	1.45433	+	2.12138i
$139$	81.0090			0.582798			0.291399	−	0.956602i	$-0.405879\pi$
$139$	81.0090			0.582798			0.291399	+	0.956602i	$0.405879\pi$
$140$	−58.8699	+	36.6568i	−0.420499	+	0.261834i
$141$	−89.1833	−	102.923i	−0.632506	−	0.729951i
$142$	−135.081	−	210.191i	−0.951277	−	1.48022i
$143$	−2.92665	−	20.3553i	−0.0204661	−	0.142345i
$144$	364.202	+	234.058i	2.52918	+	1.62540i
$145$	30.9960	−	195.710i	0.213766	−	1.34972i
$146$	−151.776	+	175.159i	−1.03956	+	1.19972i
$147$	−177.023	−	25.4521i	−1.20424	−	0.173143i
$148$	−29.1871	−	63.9109i	−0.197210	−	0.431830i
$149$	−0.798805	+	2.72048i	−0.00536110	+	0.0182582i	−0.962130	−	0.272591i	$-0.912120\pi$
$149$	−0.798805	+	2.72048i	−0.00536110	+	0.0182582i	0.956769	+	0.290849i	$0.0939377\pi$
$150$	373.127	−	98.0834i	2.48752	−	0.653889i
$151$	57.3421	+	125.562i	0.379749	+	0.831534i	0.998928	+	0.0462843i	$0.0147380\pi$
$151$	57.3421	+	125.562i	0.379749	+	0.831534i	−0.619180	+	0.785249i	$0.712535\pi$
$152$	2.09663	−	14.5824i	0.0137936	−	0.0959367i
$153$	−279.559	+	322.629i	−1.82719	+	2.10868i
$154$	61.7293	−	135.168i	0.400840	−	0.877716i
$155$	131.652	+	40.7065i	0.849371	+	0.262623i
$156$	4.21564	+	29.3204i	0.0270233	+	0.187951i
$157$	−62.0696	+	39.8897i	−0.395348	+	0.254075i	−0.723178	−	0.690662i	$-0.757319\pi$
$157$	−62.0696	+	39.8897i	−0.395348	+	0.254075i	0.327830	+	0.944737i	$0.393683\pi$
$158$	49.5358	+	57.1673i	0.313518	+	0.361819i
$159$	29.8291	+	101.589i	0.187604	+	0.638922i
$160$	56.1318	+	201.778i	0.350824	+	1.26111i
$161$	71.1988	−	65.5044i	0.442228	−	0.406859i
$162$		−	715.623i		−	4.41743i
$163$	89.1172	+	303.505i	0.546731	+	1.86200i	0.505464	+	0.862848i	$0.331321\pi$
$163$	89.1172	+	303.505i	0.546731	+	1.86200i	0.0412678	+	0.999148i	$0.486860\pi$
$164$	−10.5933	−	12.2253i	−0.0645934	−	0.0745448i
$165$	−248.616	+	278.778i	−1.50677	+	1.68956i
$166$	403.698	−	58.0430i	2.43191	−	0.349657i
$167$	30.9273	−	48.1237i	0.185193	−	0.288166i	−0.736226	−	0.676735i	$-0.763394\pi$
$167$	30.9273	−	48.1237i	0.185193	−	0.288166i	0.921420	+	0.388569i	$0.127031\pi$
$168$	18.9483	−	41.4910i	0.112788	−	0.246970i
$169$	−109.052	+	125.853i	−0.645278	+	0.744691i
$170$	−241.946	+	31.2688i	−1.42321	+	0.183934i
$171$	−166.866	+	76.2052i	−0.975825	+	0.445644i
$172$	−186.431	−	54.7412i	−1.08390	−	0.318263i
$173$	8.09916	−	27.5832i	0.0468160	−	0.159441i	−0.932767	−	0.360479i	$-0.882613\pi$
$173$	8.09916	−	27.5832i	0.0468160	−	0.159441i	0.979583	+	0.201038i	$0.0644315\pi$
$174$	−254.057	−	556.307i	−1.46010	−	3.19717i
$175$	−40.9371	−	96.8652i	−0.233926	−	0.553515i
$176$	−181.028	−	156.862i	−1.02857	−	0.891259i
$177$	361.307	+	165.003i	2.04128	+	0.932223i
$178$	−208.589	−	134.052i	−1.17185	−	0.753101i
$179$	−18.8626	−	131.192i	−0.105377	−	0.732916i	−0.972175	−	0.234256i	$-0.924735\pi$
$179$	−18.8626	−	131.192i	−0.105377	−	0.732916i	0.866798	−	0.498660i	$-0.166174\pi$
$180$	259.356	−	290.820i	1.44087	−	1.61566i
$181$	39.5421	−	34.2634i	0.218464	−	0.189301i	−0.538752	−	0.842464i	$-0.681104\pi$
$181$	39.5421	−	34.2634i	0.218464	−	0.189301i	0.757217	+	0.653164i	$0.226559\pi$
$182$	17.1452	−	5.03428i	0.0942043	−	0.0276609i
$183$	−357.039			−1.95103
$184$	−19.3100	−	39.1549i	−0.104946	−	0.212799i
$185$	102.643	−	28.5540i	0.554829	−	0.154346i
$186$	408.088	−	119.825i	2.19402	−	0.644223i
$187$	178.507	−	154.677i	0.954584	−	0.827151i
$188$	−42.4974	−	66.1272i	−0.226050	−	0.351740i
$189$	−348.110	+	50.0507i	−1.84185	+	0.264819i
$190$	−100.153	−	30.9671i	−0.527123	−	0.162985i
$191$	−116.461	−	53.1858i	−0.609742	−	0.278460i	0.0865172	−	0.996250i	$-0.472426\pi$
$191$	−116.461	−	53.1858i	−0.609742	−	0.278460i	−0.696259	+	0.717791i	$0.745154\pi$
$192$	172.206	+	149.218i	0.896908	+	0.777176i
$193$	−75.4867	−	10.8534i	−0.391123	−	0.0562350i	−0.0560519	−	0.998428i	$-0.517851\pi$
$193$	−75.4867	−	10.8534i	−0.391123	−	0.0562350i	−0.335071	+	0.942193i	$0.608760\pi$
$194$	281.005	−	128.331i	1.44848	−	0.661498i
$195$	−44.9134	−	0.641102i	−0.230325	−	0.00328770i
$196$	−99.0451	−	29.0823i	−0.505332	−	0.148379i
$197$	−183.055	+	83.5983i	−0.929212	+	0.424357i	−0.821747	−	0.569852i	$-0.807001\pi$
$197$	−183.055	+	83.5983i	−0.929212	+	0.424357i	−0.107465	+	0.994209i	$0.534273\pi$
$198$	−118.826	+	826.450i	−0.600129	+	4.17399i
$199$	−158.880	−	137.671i	−0.798393	−	0.691812i	0.156854	−	0.987622i	$-0.449865\pi$
$199$	−158.880	−	137.671i	−0.798393	−	0.691812i	−0.955247	+	0.295810i	$0.904410\pi$
$200$	−47.1445	+	5.40998i	−0.235723	+	0.0270499i
$201$	−45.1660	+	70.2797i	−0.224707	+	0.349650i
$202$	122.635	−	17.6323i	0.607105	−	0.0872886i
$203$	−140.237	+	90.1246i	−0.690821	+	0.443963i
$204$	−257.127	+	222.802i	−1.26043	+	1.09217i
$205$	20.8228	−	12.9658i	0.101575	−	0.0632479i
$206$			120.389i			0.584413i
$207$	−280.158	+	465.862i	−1.35342	+	2.25054i
$208$		−	28.8044i		−	0.138483i
$209$	97.3860	−	28.5951i	0.465962	−	0.136819i
$210$	−270.513	−	179.355i	−1.28816	−	0.854072i
$211$	178.127	−	114.475i	0.844202	−	0.542536i	−0.0455596	−	0.998962i	$-0.514507\pi$
$211$	178.127	−	114.475i	0.844202	−	0.542536i	0.889761	+	0.456426i	$0.150871\pi$
$212$	8.69705	+	60.4893i	0.0410238	+	0.285327i
$213$	285.665	−	444.504i	1.34115	−	2.08687i
$214$	32.5607	+	14.8700i	0.152153	+	0.0694858i
$215$	126.209	−	266.235i	0.587017	−	1.23830i
$216$	−22.5855	+	157.086i	−0.104563	+	0.727249i
$217$	−48.1593	−	105.454i	−0.221932	−	0.485964i
$218$	131.814	+	38.7040i	0.604650	+	0.177541i
$219$	−470.282	−	138.087i	−2.14740	−	0.630535i
$220$	−164.938	+	138.848i	−0.749717	+	0.631126i
$221$	28.1142	+	4.04221i	0.127214	+	0.0182906i
$222$	215.339	−	248.514i	0.969994	−	1.11943i
$223$	−254.836	−	116.380i	−1.14276	−	0.521882i	−0.248149	−	0.968722i	$-0.579822\pi$
$223$	−254.836	−	116.380i	−1.14276	−	0.521882i	−0.894614	+	0.446840i	$0.852549\pi$
$224$	95.2599	−	148.227i	0.425267	−	0.661729i
$225$	374.043	+	457.423i	1.66241	+	2.03299i
$226$	−53.4366	−	83.1489i	−0.236445	−	0.367915i
$227$	201.400	+	232.429i	0.887227	+	1.02391i	0.999543	+	0.0302416i	$0.00962766\pi$
$227$	201.400	+	232.429i	0.887227	+	1.02391i	−0.112316	+	0.993673i	$0.535827\pi$
$228$	−140.278	+	41.1892i	−0.615253	+	0.180655i
$229$		−	319.162i		−	1.39372i	−0.717207	−	0.696860i	$-0.754580\pi$
$229$		−	319.162i		−	1.39372i	0.717207	−	0.696860i	$-0.245420\pi$
$230$	−296.680	+	92.1300i	−1.28991	+	0.400565i
$231$	314.247			1.36038
$232$	21.1929	+	72.1765i	0.0913489	+	0.311106i
$233$	3.34851	−	2.90150i	0.0143713	−	0.0124528i	−0.647645	−	0.761942i	$-0.724246\pi$
$233$	3.34851	−	2.90150i	0.0143713	−	0.0124528i	0.662017	+	0.749489i	$0.269701\pi$
$234$	−84.4652	+	54.2825i	−0.360962	+	0.231976i
$235$	109.120	−	47.9631i	0.464340	−	0.204098i
$236$	192.866	+	123.948i	0.817229	+	0.525201i
$237$	−66.4530	+	145.512i	−0.280392	+	0.613974i
$238$	155.108	+	134.402i	0.651715	+	0.564714i
$239$	58.3522	−	405.848i	0.244151	−	1.69811i	−0.386699	−	0.922206i	$-0.626385\pi$
$239$	58.3522	−	405.848i	0.244151	−	1.69811i	0.630851	−	0.775904i	$-0.282706\pi$
$240$	−400.257	+	336.944i	−1.66774	+	1.40393i
$241$	−23.0977	+	78.6634i	−0.0958409	+	0.326404i	−0.993432	−	0.114425i	$-0.963497\pi$
$241$	−23.0977	+	78.6634i	−0.0958409	+	0.326404i	0.897591	+	0.440829i	$0.145316\pi$
$242$	38.0632	−	129.631i	0.157286	−	0.535666i
$243$	692.142	−	316.091i	2.84832	−	1.30078i
$244$	−203.982	−	29.3282i	−0.835991	−	0.120197i
$245$	67.0507	−	141.442i	0.273676	−	0.577316i
$246$	31.4506	−	68.8672i	0.127848	−	0.279948i
$247$	10.2677	+	6.59865i	0.0415696	+	0.0267152i
$248$	−51.7815	+	7.44505i	−0.208796	+	0.0300204i
$249$	466.306	+	725.586i	1.87271	+	2.91400i
$250$	−14.4545	+	337.360i	−0.0578179	+	1.34944i
$251$	67.8710	+	231.147i	0.270402	+	0.920905i	0.976991	+	0.213281i	$0.0684149\pi$
$251$	67.8710	+	231.147i	0.270402	+	0.920905i	−0.706589	+	0.707624i	$0.749767\pi$
$252$	−327.821			−1.30088
$253$	190.113	−	233.073i	0.751436	−	0.921237i
$254$	−103.115			−0.405964
$255$	−272.701	−	437.951i	−1.06942	−	1.71745i
$256$	−210.274	−	242.670i	−0.821384	−	0.947928i
$257$	26.0517	+	40.5372i	0.101368	+	0.157732i	0.888233	−	0.459394i	$-0.151933\pi$
$257$	26.0517	+	40.5372i	0.101368	+	0.157732i	−0.786864	+	0.617126i	$0.788297\pi$
$258$	−129.417	−	900.115i	−0.501616	−	3.48882i
$259$	−75.4025	−	48.4582i	−0.291129	−	0.187097i
$260$	−25.6070	−	4.05558i	−0.0984886	−	0.0155984i
$261$	613.386	−	707.885i	2.35014	−	2.71220i
$262$	−363.217	−	52.2228i	−1.38633	−	0.199323i
$263$	−23.4057	−	51.2512i	−0.0889949	−	0.194872i	0.859901	−	0.510461i	$-0.170525\pi$
$263$	−23.4057	−	51.2512i	−0.0889949	−	0.194872i	−0.948896	+	0.315589i	$0.897798\pi$
$264$	39.9511	−	136.061i	0.151330	−	0.515382i
$265$	−92.6584	−	1.32262i	−0.349654	−	0.00499102i
$266$	36.6367	+	80.2231i	0.137732	+	0.301591i
$267$	74.6237	−	519.019i	0.279489	−	1.94389i
$268$	−31.5770	+	36.4418i	−0.117824	+	0.135977i
$269$	−151.553	+	331.854i	−0.563393	+	1.23366i	0.386849	+	0.922143i	$0.373564\pi$
$269$	−151.553	+	331.854i	−0.563393	+	1.23366i	−0.950241	+	0.311515i	$0.899164\pi$
$270$	1078.88	+	333.586i	3.99586	+	1.23551i
$271$	18.1887	+	126.505i	0.0671171	+	0.466810i	0.995467	+	0.0951032i	$0.0303181\pi$
$271$	18.1887	+	126.505i	0.0671171	+	0.466810i	−0.928350	+	0.371706i	$0.878773\pi$
$272$	278.319	−	178.865i	1.02323	−	0.657590i
$273$	24.7464	+	28.5588i	0.0906461	+	0.104611i
$274$	191.682	+	652.809i	0.699570	+	2.38252i
$275$	−168.830	−	279.964i	−0.613926	−	1.01805i
$276$	−273.845	+	335.725i	−0.992191	+	1.21640i
$277$			311.628i			1.12501i	0.826794	+	0.562505i	$0.190162\pi$
$277$			311.628i			1.12501i	−0.826794	+	0.562505i	$0.809838\pi$
$278$	61.6527	+	209.970i	0.221772	+	0.755287i
$279$	426.577	+	492.296i	1.52895	+	1.76450i
$280$	29.7949	+	26.5714i	0.106411	+	0.0948979i
$281$	−6.79368	+	0.976784i	−0.0241768	+	0.00347610i	−0.154393	−	0.988010i	$-0.549342\pi$
$281$	−6.79368	+	0.976784i	−0.0241768	+	0.00347610i	0.130216	+	0.991486i	$0.458433\pi$
$282$	198.896	−	309.488i	0.705304	−	1.09748i
$283$	−61.9895	+	135.738i	−0.219044	+	0.479640i	−0.986971	−	0.160897i	$-0.948561\pi$
$283$	−61.9895	+	135.738i	−0.219044	+	0.479640i	0.767927	+	0.640538i	$0.221288\pi$
$284$	199.718	−	230.486i	0.703231	−	0.811572i
$285$	−28.4152	−	219.865i	−0.0997023	−	0.771458i
$286$	50.5323	−	23.0773i	0.176686	−	0.0806900i
$287$	−19.8004	−	5.81393i	−0.0689910	−	0.0202576i
$288$	−278.926	+	949.934i	−0.968492	+	3.29838i
$289$	15.4664	+	33.8667i	0.0535169	+	0.117186i
$290$	530.857	−	68.6073i	1.83054	−	0.236577i
$291$	493.728	+	427.818i	1.69666	+	1.47017i
$292$	−257.336	−	117.521i	−0.881287	−	0.402470i
$293$	−407.098	−	261.626i	−1.38941	−	0.892922i	−0.389805	−	0.920897i	$-0.627458\pi$
$293$	−407.098	−	261.626i	−1.38941	−	0.892922i	−0.999609	+	0.0279753i	$0.991094\pi$
$294$	−68.7551	−	478.202i	−0.233861	−	1.62654i
$295$	−231.386	+	259.457i	−0.784359	+	0.879514i
$296$	−30.5673	+	26.4867i	−0.103268	+	0.0894820i
$297$	−1049.07	+	308.035i	−3.53223	+	1.03715i
$298$	−7.65924			−0.0257021
$299$	36.1528	−	1.07654i	0.120912	−	0.00360046i
$300$	243.187	+	403.269i	0.810624	+	1.34423i
$301$	−237.831	+	69.8335i	−0.790136	+	0.232005i
$302$	−281.807	+	244.187i	−0.933134	+	0.808565i
$303$	141.654	+	220.418i	0.467506	+	0.727453i
$304$	140.718	−	20.2322i	0.462888	−	0.0665532i
$305$	92.3103	−	298.549i	0.302657	−	0.978849i
$306$	−1048.99	−	479.059i	−3.42808	−	1.56555i
$307$	198.220	+	171.759i	0.645668	+	0.559475i	0.914940	−	0.403590i	$-0.132238\pi$
$307$	198.220	+	171.759i	0.645668	+	0.559475i	−0.269272	+	0.963064i	$0.586783\pi$
$308$	179.534	+	25.8131i	0.582903	+	0.0838087i
$309$	−231.588	+	105.762i	−0.749474	+	0.342273i
$310$	−5.31305	+	372.215i	−0.0171389	+	1.20069i
$311$	−118.092	−	34.6751i	−0.379718	−	0.111495i	0.0863027	−	0.996269i	$-0.472495\pi$
$311$	−118.092	−	34.6751i	−0.379718	−	0.111495i	−0.466021	+	0.884774i	$0.654313\pi$
$312$	15.5113	−	7.08377i	0.0497157	−	0.0227044i
$313$	−33.0128	+	229.609i	−0.105472	+	0.733575i	0.866619	+	0.498971i	$0.166288\pi$
$313$	−33.0128	+	229.609i	−0.105472	+	0.733575i	−0.972091	+	0.234604i	$0.924621\pi$
$314$	−150.630	−	130.522i	−0.479714	−	0.415675i
$315$	77.7604	−	490.981i	0.246858	−	1.55867i
$316$	−49.9183	+	77.6744i	−0.157969	+	0.245805i
$317$	387.445	−	55.7062i	1.22222	−	0.175729i	0.499159	−	0.866510i	$-0.333642\pi$
$317$	387.445	−	55.7062i	1.22222	−	0.175729i	0.723064	+	0.690781i	$0.242733\pi$
$318$	−240.609	+	154.630i	−0.756633	+	0.486258i
$319$	−391.665	+	339.380i	−1.22779	+	1.06389i
$320$	−169.296	+	105.416i	−0.529049	+	0.329425i
$321$			75.6990i			0.235822i
$322$	223.970	+	134.690i	0.695558	+	0.418291i
$323$			140.185i			0.434010i
$324$	838.122	−	246.095i	2.58679	−	0.759552i
$325$	12.1482	−	37.3899i	0.0373790	−	0.115046i
$326$	−718.842	+	461.972i	−2.20504	+	1.41709i
$327$	41.3458	+	287.566i	0.126440	+	0.879407i
$328$	−5.03455	+	7.83392i	−0.0153493	+	0.0238839i
$329$	−91.2154	−	41.6567i	−0.277251	−	0.126616i
$330$	−911.785	−	432.231i	−2.76299	−	1.30979i
$331$	−35.4214	+	246.361i	−0.107013	+	0.744294i	0.863692	+	0.504020i	$0.168146\pi$
$331$	−35.4214	+	246.361i	−0.107013	+	0.744294i	−0.970705	+	0.240274i	$0.922763\pi$
$332$	206.806	+	452.841i	0.622909	+	1.36398i
$333$	483.227	+	141.888i	1.45113	+	0.426090i
$334$	148.271	+	43.5363i	0.443925	+	0.130348i
$335$	−47.0890	−	55.9372i	−0.140564	−	0.166977i
$336$	435.678	+	62.6411i	1.29666	+	0.186432i
$337$	344.415	−	397.476i	1.02200	−	1.17945i	0.0383700	−	0.999264i	$-0.487783\pi$
$337$	344.415	−	397.476i	1.02200	−	1.17945i	0.983632	−	0.180189i	$-0.0576711\pi$
$338$	−409.197	−	186.874i	−1.21064	−	0.552882i
$339$	113.006	−	175.840i	0.333350	−	0.518703i
$340$	−119.824	−	272.608i	−0.352422	−	0.801789i
$341$	−194.854	−	303.199i	−0.571419	−	0.889146i
$342$	−324.514	−	374.509i	−0.948871	−	1.09506i
$343$	−324.117	+	95.1695i	−0.944949	+	0.277462i
$344$			111.853i			0.325153i
$345$	−437.862	−	489.775i	−1.26917	−	1.41964i
$346$	77.6578			0.224445
$347$	0.0135617	+	0.0461869i	3.90827e−5	+	0.000133104i	0.959513	−	0.281666i	$-0.0908870\pi$
$347$	0.0135617	+	0.0461869i	3.90827e−5	+	0.000133104i	−0.959473	+	0.281799i	$0.909069\pi$
$348$	564.166	−	488.853i	1.62117	−	1.40475i
$349$	37.0395	−	23.8039i	0.106130	−	0.0682059i	−0.486499	−	0.873681i	$-0.661726\pi$
$349$	37.0395	−	23.8039i	0.106130	−	0.0682059i	0.592629	+	0.805475i	$0.298090\pi$
$350$	219.912	−	179.826i	0.628321	−	0.513790i
$351$	−110.607	−	71.0826i	−0.315119	−	0.202514i
$352$	227.555	−	498.276i	0.646463	−	1.41556i
$353$	64.4951	+	55.8853i	0.182706	+	0.158315i	0.741412	−	0.671050i	$-0.234157\pi$
$353$	64.4951	+	55.8853i	0.182706	+	0.158315i	−0.558706	+	0.829366i	$0.688702\pi$
$354$	−152.701	+	1062.06i	−0.431360	+	3.00017i
$355$	297.828	+	353.791i	0.838952	+	0.996595i
$356$	85.2672	−	290.393i	0.239515	−	0.815712i
$357$	−122.280	+	416.448i	−0.342522	+	1.16652i
$358$	325.685	−	148.736i	0.909736	−	0.415462i
$359$	558.467	+	80.2955i	1.55562	+	0.223664i	0.865827	−	0.500343i	$-0.166793\pi$
$359$	558.467	+	80.2955i	1.55562	+	0.223664i	0.689792	+	0.724007i	$0.257702\pi$
$360$	−202.696	−	96.0879i	−0.563045	−	0.266911i
$361$	124.941	−	273.582i	0.346096	−	0.757844i
$362$	118.902	+	76.4139i	0.328460	+	0.211088i
$363$	282.805	−	40.6612i	0.779077	−	0.112014i
$364$	11.7921	+	18.3488i	0.0323958	+	0.0504088i
$365$	237.054	−	357.538i	0.649463	−	0.979556i
$366$	−271.729	−	925.422i	−0.742428	−	2.52848i
$367$	−37.2451			−0.101485			−0.0507427	−	0.998712i	$-0.516159\pi$
$367$	−37.2451			−0.101485			−0.0507427	+	0.998712i	$0.516159\pi$
$368$	310.037	−	285.240i	0.842491	−	0.775109i
$369$	115.953			0.314236
$370$	152.128	+	244.313i	0.411156	+	0.660306i
$371$	51.0528	+	58.9181i	0.137609	+	0.158809i
$372$	280.673	+	436.736i	0.754499	+	1.17402i
$373$	−8.34457	−	58.0377i	−0.0223715	−	0.155597i	0.975574	−	0.219673i	$-0.0704991\pi$
$373$	−8.34457	−	58.0377i	−0.0223715	−	0.155597i	−0.997945	+	0.0640760i	$0.979590\pi$
$374$	536.768	+	344.960i	1.43521	+	0.922353i
$375$	−661.664	+	268.567i	−1.76444	+	0.716179i
$376$	−29.6327	+	34.1980i	−0.0788104	+	0.0909521i
$377$	−61.6858	−	8.86908i	−0.163623	−	0.0235254i
$378$	−394.661	−	864.188i	−1.04408	−	2.28621i
$379$	19.9535	−	67.9552i	0.0526477	−	0.179301i	−0.928972	−	0.370151i	$-0.879306\pi$
$379$	19.9535	−	67.9552i	0.0526477	−	0.179301i	0.981619	+	0.190849i	$0.0611242\pi$
$380$	1.82633	−	127.946i	0.00480613	−	0.336701i
$381$	−90.5869	−	198.358i	−0.237761	−	0.520624i
$382$	49.2205	−	342.336i	0.128849	−	0.896167i
$383$	13.4185	−	15.4857i	0.0350351	−	0.0404327i	−0.737962	−	0.674843i	$-0.764211\pi$
$383$	13.4185	−	15.4857i	0.0350351	−	0.0404327i	0.772997	+	0.634410i	$0.218757\pi$
$384$	141.924	−	310.770i	0.369593	−	0.809296i
$385$	−81.2466	+	262.767i	−0.211030	+	0.682511i
$386$	−29.3188	−	203.917i	−0.0759554	−	0.528281i
$387$	1171.67	−	752.984i	3.02756	−	1.94570i
$388$	246.932	+	284.975i	0.636423	+	0.734471i
$389$	−49.9897	−	170.249i	−0.128508	−	0.437659i	0.869952	−	0.493137i	$-0.164150\pi$
$389$	−49.9897	−	170.249i	−0.128508	−	0.437659i	−0.998460	+	0.0554780i	$0.982332\pi$
$390$	−32.5201	−	116.901i	−0.0833850	−	0.299745i
$391$	234.897	+	342.636i	0.600760	+	0.876308i
$392$			59.4238i			0.151591i
$393$	−218.630	−	744.584i	−0.556309	−	1.89462i
$394$	−355.997	−	410.842i	−0.903546	−	1.04275i
$395$	−104.493	−	93.1877i	−0.264539	−	0.235918i
$396$	−1008.78	+	145.041i	−2.54743	+	0.366265i
$397$	−158.134	+	246.062i	−0.398323	+	0.619803i	−0.981254	−	0.192719i	$-0.938270\pi$
$397$	−158.134	+	246.062i	−0.398323	+	0.619803i	0.582931	+	0.812522i	$0.301906\pi$
$398$	235.915	−	516.583i	0.592752	−	1.29795i
$399$	−122.136	+	140.953i	−0.306106	+	0.353265i
$400$	−178.262	−	421.801i	−0.445654	−	1.05450i
$401$	−149.708	+	68.3695i	−0.373337	+	0.170498i	−0.593243	−	0.805024i	$-0.702152\pi$
$401$	−149.708	+	68.3695i	−0.373337	+	0.170498i	0.219905	+	0.975521i	$0.429425\pi$
$402$	−216.534	−	63.5802i	−0.538643	−	0.158160i
$403$	12.2104	−	41.5847i	0.0302987	−	0.103188i
$404$	62.8234	+	137.564i	0.155503	+	0.340505i
$405$	169.773	+	1313.64i	0.419193	+	3.24355i
$406$	−340.325	−	294.894i	−0.838240	−	0.726339i
$407$	−253.470	−	115.756i	−0.622777	−	0.284413i
$408$	164.765	+	105.888i	0.403837	+	0.259530i
$409$	−27.1893	−	189.106i	−0.0664776	−	0.462362i	−0.995685	−	0.0928021i	$-0.970418\pi$
$409$	−27.1893	−	189.106i	−0.0664776	−	0.462362i	0.929207	−	0.369560i	$-0.120491\pi$
$410$	49.4539	+	44.1035i	0.120619	+	0.107570i
$411$	−1087.39	+	942.228i	−2.64571	+	2.29252i
$412$	−140.997	+	41.4004i	−0.342226	+	0.100486i
$413$	292.468			0.708155
$414$	−1420.70	−	371.601i	−3.43164	−	0.897588i
$415$	−727.280	+	202.319i	−1.75248	+	0.487516i
$416$	63.2029	−	18.5581i	0.151930	−	0.0446107i
$417$	−349.748	+	303.058i	−0.838724	+	0.726759i
$418$	148.233	+	230.655i	0.354625	+	0.551807i
$419$	172.292	−	24.7719i	0.411199	−	0.0591214i	0.0663884	−	0.997794i	$-0.478852\pi$
$419$	172.292	−	24.7719i	0.411199	−	0.0591214i	0.344810	+	0.938672i	$0.387943\pi$
$420$	117.030	−	378.497i	0.278643	−	0.901184i
$421$	486.593	+	222.220i	1.15580	+	0.527838i	0.898708	−	0.438548i	$-0.144507\pi$
$421$	486.593	+	222.220i	1.15580	+	0.527838i	0.257096	+	0.966386i	$0.417234\pi$
$422$	432.277	+	374.570i	1.02435	+	0.887606i
$423$	557.712	+	80.1869i	1.31847	+	0.189567i
$424$	32.0005	−	14.6141i	0.0754728	−	0.0344673i
$425$	436.710	−	114.797i	1.02755	−	0.270111i
$426$	1369.53	+	402.131i	3.21487	+	0.943971i
$427$	−239.139	+	109.211i	−0.560044	+	0.255763i
$428$	−6.21812	+	43.2479i	−0.0145283	+	0.101047i
$429$	88.7858	+	76.9333i	0.206960	+	0.179332i
$430$	786.117	+	124.503i	1.82818	+	0.289542i
$431$	175.615	−	273.262i	0.407459	−	0.634018i	−0.575509	−	0.817795i	$-0.695196\pi$
$431$	175.615	−	273.262i	0.407459	−	0.634018i	0.982968	+	0.183777i	$0.0588324\pi$
$432$	−1515.85	+	217.947i	−3.50892	+	0.504507i
$433$	−356.956	+	229.402i	−0.824379	+	0.529796i	−0.883487	−	0.468455i	$-0.844811\pi$
$433$	−356.956	+	229.402i	−0.824379	+	0.529796i	0.0591082	+	0.998252i	$0.481174\pi$
$434$	236.678	−	205.083i	0.545341	−	0.472540i
$435$	598.338	+	960.915i	1.37549	+	2.20900i
$436$			167.687i			0.384603i
$437$	30.6529	+	175.861i	0.0701438	+	0.402427i
$438$		−	1324.03i		−	3.02290i
$439$	−67.4574	+	19.8073i	−0.153662	+	0.0451191i	−0.357659	−	0.933852i	$-0.616425\pi$
$439$	−67.4574	+	19.8073i	−0.153662	+	0.0451191i	0.203997	+	0.978971i	$0.434607\pi$
$440$	103.442	+	68.5839i	0.235096	+	0.155872i
$441$	622.469	−	400.037i	1.41149	−	0.907113i
$442$	10.9195	+	75.9465i	0.0247047	+	0.171825i
$443$	−375.550	+	584.368i	−0.847744	+	1.31911i	0.0983270	+	0.995154i	$0.468651\pi$
$443$	−375.550	+	584.368i	−0.847744	+	1.31911i	−0.946071	+	0.323961i	$0.894985\pi$
$444$	365.106	+	166.738i	0.822311	+	0.375537i
$445$	414.699	+	196.588i	0.931909	+	0.441770i
$446$	107.703	−	749.090i	0.241486	−	1.67957i
$447$	−6.72868	−	14.7338i	−0.0150530	−	0.0329614i
$448$	160.983	+	47.2690i	0.359338	+	0.105511i
$449$	285.282	+	83.7664i	0.635372	+	0.186562i	0.583528	−	0.812093i	$-0.301672\pi$
$449$	285.282	+	83.7664i	0.635372	+	0.186562i	0.0518442	+	0.998655i	$0.483490\pi$
$450$	−900.941	+	1317.62i	−2.00209	+	2.92805i
$451$	−63.5027	−	9.13031i	−0.140804	−	0.0202446i
$452$	79.0058	−	91.1776i	0.174792	−	0.201720i
$453$	−717.300	−	327.580i	−1.58344	−	0.723135i
$454$	−449.161	+	698.909i	−0.989342	+	1.53945i
$455$	−30.2783	+	13.3087i	−0.0665458	+	0.0292499i
$456$	45.5014	+	70.8016i	0.0997838	+	0.155267i
$457$	−243.433	−	280.937i	−0.532677	−	0.614741i	0.424082	−	0.905624i	$-0.360597\pi$
$457$	−243.433	−	280.937i	−0.532677	−	0.614741i	−0.956759	+	0.290882i	$0.906051\pi$
$458$	827.247	−	242.902i	1.80622	−	0.530353i
$459$		−	1510.12i		−	3.29002i
$460$	−209.926	−	315.783i	−0.456360	−	0.686484i
$461$	827.548			1.79511			0.897557	−	0.440897i	$-0.145340\pi$
$461$	827.548			1.79511			0.897557	+	0.440897i	$0.145340\pi$
$462$	239.161	+	814.508i	0.517665	+	1.76300i
$463$	367.281	−	318.251i	0.793264	−	0.687367i	−0.160795	−	0.986988i	$-0.551406\pi$
$463$	367.281	−	318.251i	0.793264	−	0.687367i	0.954058	+	0.299621i	$0.0968602\pi$
$464$	−610.663	+	392.449i	−1.31608	+	0.845796i
$465$	−720.681	+	316.772i	−1.54985	+	0.681230i
$466$	10.0689	+	6.47090i	0.0216071	+	0.0138861i
$467$	−246.854	+	540.536i	−0.528596	+	1.15746i	0.437485	+	0.899226i	$0.355869\pi$
$467$	−246.854	+	540.536i	−0.528596	+	1.15746i	−0.966081	+	0.258238i	$0.916858\pi$
$468$	−92.6210	−	80.2565i	−0.197908	−	0.171488i
$469$	−8.75429	+	60.8874i	−0.0186659	+	0.129824i
$470$	207.364	+	246.329i	0.441200	+	0.524104i
$471$	118.750	−	404.425i	0.252123	−	0.858653i
$472$	37.1822	−	126.631i	0.0787759	−	0.268286i
$473$	−700.963	+	320.119i	−1.48195	+	0.676785i
$474$	−427.732	−	61.4985i	−0.902387	−	0.129744i
$475$	191.193	+	33.0847i	0.402512	+	0.0696519i
$476$	−104.069	+	227.878i	−0.218632	+	0.478736i
$477$	−368.509	−	236.826i	−0.772556	−	0.496491i
$478$	1096.34	−	157.630i	2.29360	−	0.329770i
$479$	−111.945	−	174.190i	−0.233706	−	0.363654i	0.704515	−	0.709689i	$-0.251164\pi$
$479$	−111.945	−	174.190i	−0.233706	−	0.363654i	−0.938222	+	0.346034i	$0.887528\pi$
$480$	−997.203	−	661.163i	−2.07751	−	1.37742i
$481$	−9.44039	−	32.1510i	−0.0196266	−	0.0668420i
$482$	−221.469			−0.459479
$483$	−62.3386	+	549.167i	−0.129065	+	1.13699i
$484$	164.911			0.340724
$485$	−485.383	+	302.236i	−1.00079	+	0.623166i
$486$	1346.05	+	1553.42i	2.76965	+	3.19634i
$487$	−331.773	−	516.249i	−0.681259	−	1.06006i	−0.993910	−	0.110191i	$-0.964854\pi$
$487$	−331.773	−	516.249i	−0.681259	−	1.06006i	0.312652	−	0.949868i	$-0.398783\pi$
$488$	16.8832	+	117.425i	0.0345967	+	0.240625i
$489$	−1520.18	−	976.962i	−3.10876	−	1.99788i
$490$	417.639	+	66.1446i	0.852324	+	0.134989i
$491$	214.219	−	247.221i	0.436290	−	0.503506i	−0.494440	−	0.869212i	$-0.664627\pi$
$491$	214.219	−	247.221i	0.436290	−	0.503506i	0.930731	+	0.365706i	$0.119172\pi$
$492$	91.4712	+	13.1516i	0.185917	+	0.0267308i
$493$	−297.349	−	651.105i	−0.603143	−	1.32070i
$494$	−9.28892	+	31.6351i	−0.0188035	+	0.0640388i
$495$	22.0574	−	1545.27i	0.0445604	−	3.12175i
$496$	−209.711	−	459.202i	−0.422804	−	0.925811i
$497$	55.3690	−	385.100i	0.111407	−	0.774849i
$498$	−1525.78	+	1760.85i	−3.06382	+	3.53584i
$499$	−53.0112	+	116.078i	−0.106235	+	0.232622i	−0.955283	−	0.295694i	$-0.904449\pi$
$499$	−53.0112	+	116.078i	−0.106235	+	0.232622i	0.849048	+	0.528316i	$0.177176\pi$
$500$	−400.079	+	99.0856i	−0.800158	+	0.198171i
$501$	46.5079	+	323.470i	0.0928302	+	0.645648i
$502$	−547.464	+	351.834i	−1.09057	+	0.700865i
$503$	366.923	+	423.451i	0.729469	+	0.841852i	0.992412	−	0.122960i	$-0.0392386\pi$
$503$	366.923	+	423.451i	0.729469	+	0.841852i	−0.262943	+	0.964811i	$0.584693\pi$
$504$	53.1672	+	181.071i	0.105490	+	0.359267i
$505$	−220.933	+	61.4605i	−0.437491	+	0.121704i
$506$	748.797	+	315.378i	1.47984	+	0.623277i
$507$		−	951.325i		−	1.87638i
$508$	−35.4600	−	120.766i	−0.0698031	−	0.237728i
$509$	334.272	+	385.770i	0.656723	+	0.757899i	0.982238	−	0.187638i	$-0.0600832\pi$
$509$	334.272	+	385.770i	0.656723	+	0.757899i	−0.325515	+	0.945537i	$0.605538\pi$
$510$	927.598	−	1040.13i	1.81882	−	2.03947i
$511$	−357.224	+	51.3611i	−0.699069	+	0.100511i
$512$	339.622	−	528.463i	0.663325	−	1.03215i
$513$	269.569	−	590.274i	0.525476	−	1.15063i
$514$	−85.2429	+	98.3755i	−0.165842	+	0.191392i
$515$	−28.5609	−	220.993i	−0.0554580	−	0.429112i
$516$	1009.69	−	461.109i	1.95676	−	0.893623i
$517$	−299.121	−	87.8299i	−0.578571	−	0.169884i
$518$	68.2147	−	232.318i	0.131689	−	0.448490i
$519$	68.2228	+	149.387i	0.131450	+	0.287836i
$520$	1.91295	+	14.8017i	0.00367876	+	0.0284648i
$521$	51.3392	+	44.4856i	0.0985396	+	0.0853851i	0.702737	−	0.711449i	$-0.251961\pi$
$521$	51.3392	+	44.4856i	0.0985396	+	0.0853851i	−0.604198	+	0.796834i	$0.706506\pi$
$522$	2301.61	+	1051.11i	4.40922	+	2.01362i
$523$	442.501	+	284.378i	0.846081	+	0.543744i	0.890350	−	0.455276i	$-0.150459\pi$
$523$	442.501	+	284.378i	0.846081	+	0.543744i	−0.0442689	+	0.999020i	$0.514096\pi$
$524$	−63.7442	−	443.350i	−0.121649	−	0.846089i
$525$	539.119	+	265.058i	1.02689	+	0.504872i
$526$	115.027	−	99.6712i	0.218682	−	0.189489i
$527$	477.628	−	140.244i	0.906316	−	0.266118i
$528$	1368.40			2.59166
$529$	369.596	+	378.470i	0.698669	+	0.715445i
$530$	−67.0905	−	241.171i	−0.126586	−	0.455039i
$531$	−1576.78	+	462.984i	−2.96945	+	0.871909i
$532$	−81.3566	+	70.4959i	−0.152926	+	0.132511i
$533$	−4.17095	−	6.49013i	−0.00782543	−	0.0121766i
$534$	1402.06	−	201.585i	2.62557	−	0.377500i
$535$	−63.2979	−	19.5715i	−0.118314	−	0.0365822i
$536$	25.2497	+	11.5312i	0.0471077	+	0.0215133i
$537$	572.233	+	495.842i	1.06561	+	0.923357i
$538$	−975.484	−	140.253i	−1.81317	−	0.260694i
$539$	−372.400	+	170.069i	−0.690908	+	0.315527i
$540$	−19.6738	+	1378.28i	−0.0364329	+	2.55237i
$541$	16.8225	+	4.93953i	0.0310952	+	0.00913038i	0.297243	−	0.954802i	$-0.403933\pi$
$541$	16.8225	+	4.93953i	0.0310952	+	0.00913038i	−0.266148	+	0.963932i	$0.585751\pi$
$542$	−314.051	+	143.422i	−0.579430	+	0.264617i
$543$	−42.5379	+	295.858i	−0.0783386	+	0.544857i
$544$	571.781	+	495.451i	1.05107	+	0.910756i
$545$	−251.146	−	39.7759i	−0.460819	−	0.0729834i
$546$	−55.1891	+	85.8760i	−0.101079	+	0.157282i
$547$	−636.898	+	91.5721i	−1.16435	+	0.167408i	−0.697270	−	0.716809i	$-0.745602\pi$
$547$	−636.898	+	91.5721i	−1.16435	+	0.167408i	−0.467077	+	0.884216i	$0.654693\pi$
$548$	−698.638	+	448.987i	−1.27489	+	0.819320i
$549$	1116.38	−	967.349i	2.03348	−	1.76202i
$550$	597.159	−	650.665i	1.08574	−	1.18303i
$551$		−	307.583i		−	0.558226i
$552$	229.849	+	96.8079i	0.416394	+	0.175377i
$553$			117.788i			0.212998i
$554$	−807.719	+	237.168i	−1.45798	+	0.428100i
$555$	−336.330	+	507.272i	−0.606001	+	0.914004i
$556$	−224.710	+	144.412i	−0.404155	+	0.259735i
$557$	−127.879	−	889.419i	−0.229586	−	1.59680i	−0.699858	−	0.714282i	$-0.746754\pi$
$557$	−127.879	−	889.419i	−0.229586	−	1.59680i	0.470273	−	0.882521i	$-0.344155\pi$
$558$	−951.347	+	1480.32i	−1.70492	+	2.65291i
$559$	−84.2921	−	38.4949i	−0.150791	−	0.0688638i
$560$	−165.021	+	348.110i	−0.294680	+	0.621624i
$561$	−192.031	+	1335.61i	−0.342302	+	2.38076i
$562$	−7.70216	−	16.8654i	−0.0137049	−	0.0300096i
$563$	−481.572	−	141.402i	−0.855367	−	0.251158i	−0.175487	−	0.984482i	$-0.556150\pi$
$563$	−481.572	−	141.402i	−0.855367	−	0.251158i	−0.679880	+	0.733323i	$0.737968\pi$
$564$	430.863	+	126.513i	0.763942	+	0.224314i
$565$	117.817	+	139.955i	0.208526	+	0.247709i
$566$	−399.002	−	57.3678i	−0.704951	−	0.101357i
$567$	729.732	−	842.156i	1.28701	−	1.48528i
$568$	−159.699	−	72.9321i	−0.281160	−	0.128402i
$569$	−597.900	+	930.350i	−1.05079	+	1.63506i	−0.327026	+	0.945015i	$0.606046\pi$
$569$	−597.900	+	930.350i	−1.05079	+	1.63506i	−0.723765	+	0.690047i	$0.757590\pi$
$570$	548.251	−	240.981i	0.961844	−	0.422774i
$571$	425.679	+	662.370i	0.745498	+	1.16002i	0.982091	+	0.188408i	$0.0603328\pi$
$571$	425.679	+	662.370i	0.745498	+	1.16002i	−0.236593	+	0.971609i	$0.576031\pi$
$572$	44.4051	+	51.2462i	0.0776313	+	0.0895913i
$573$	701.778	−	206.061i	1.22474	−	0.359617i
$574$		−	55.7461i		−	0.0971186i
$575$	522.746	−	239.503i	0.909124	−	0.416527i
$576$	−942.735			−1.63669
$577$	−26.5043	−	90.2652i	−0.0459346	−	0.156439i	0.933332	−	0.359014i	$-0.116887\pi$
$577$	−26.5043	−	90.2652i	−0.0459346	−	0.156439i	−0.979267	+	0.202575i	$0.935069\pi$
$578$	−76.0093	+	65.8624i	−0.131504	+	0.113949i
$579$	366.509	−	235.541i	0.633004	−	0.406807i
$580$	262.907	+	598.134i	0.453288	+	1.03127i
$581$	534.265	+	343.351i	0.919561	+	0.590966i
$582$	−733.119	+	1605.31i	−1.25965	+	2.75826i
$583$	183.169	+	158.717i	0.314183	+	0.272241i
$584$	−23.1768	+	161.198i	−0.0396864	+	0.276025i
$585$	142.171	−	119.682i	0.243027	−	0.204585i
$586$	368.291	−	1254.28i	0.628483	−	2.14042i
$587$	−143.186	+	487.646i	−0.243928	+	0.830742i	0.742960	+	0.669336i	$0.233421\pi$
$587$	−143.186	+	487.646i	−0.243928	+	0.830742i	−0.986888	+	0.161407i	$0.948397\pi$
$588$	536.415	−	244.973i	0.912271	−	0.416620i
$589$	211.730	+	30.4422i	0.359473	+	0.0516845i
$590$	−848.593	−	402.275i	−1.43829	−	0.681822i
$591$	477.575	−	1045.74i	0.808080	−	1.76945i
$592$	−328.342	−	211.012i	−0.554631	−	0.356440i
$593$	213.194	−	30.6526i	0.359517	−	0.0516908i	0.0398103	−	0.999207i	$-0.487325\pi$
$593$	213.194	−	30.6526i	0.359517	−	0.0516908i	0.319707	+	0.947516i	$0.396416\pi$
$594$	−1596.81	−	2484.69i	−2.68824	−	4.18298i
$595$	−316.610	−	209.918i	−0.532118	−	0.352804i
$596$	−2.63392	−	8.97032i	−0.00441934	−	0.0150509i
$597$	1200.98			2.01169
$598$	30.3048	+	92.8863i	0.0506769	+	0.155328i
$599$	−1185.33			−1.97885			−0.989426	−	0.145037i	$-0.953670\pi$
$599$	−1185.33			−1.97885			−0.989426	+	0.145037i	$0.953670\pi$
$600$	183.303	−	199.727i	0.305505	−	0.332878i
$601$	−486.386	−	561.319i	−0.809294	−	0.933975i	0.189558	−	0.981869i	$-0.439294\pi$
$601$	−486.386	−	561.319i	−0.809294	−	0.933975i	−0.998852	+	0.0478944i	$0.984749\pi$
$602$	−362.008	−	563.295i	−0.601342	−	0.935706i
$603$	−49.1894	−	342.120i	−0.0815744	−	0.567362i
$604$	−382.896	−	246.072i	−0.633934	−	0.407404i
$605$	−39.1174	+	246.988i	−0.0646568	+	0.408245i
$606$	−463.502	+	534.910i	−0.764855	+	0.882690i
$607$	−537.668	−	77.3050i	−0.885779	−	0.127356i	−0.315616	−	0.948887i	$-0.602211\pi$
$607$	−537.668	−	77.3050i	−0.885779	−	0.127356i	−0.570163	+	0.821531i	$0.693120\pi$
$608$	135.055	+	295.729i	0.222130	+	0.486397i
$609$	268.297	−	913.736i	0.440553	−	1.50039i
$610$	844.072	+	12.0484i	1.38373	+	0.0197515i
$611$	−15.5732	−	34.1006i	−0.0254881	−	0.0558112i
$612$	200.326	−	1393.30i	0.327331	−	2.27663i
$613$	272.183	−	314.116i	0.444018	−	0.512425i	−0.488985	−	0.872292i	$-0.662633\pi$
$613$	272.183	−	314.116i	0.444018	−	0.512425i	0.933003	+	0.359868i	$0.117178\pi$
$614$	−294.330	+	644.492i	−0.479364	+	1.04966i
$615$	−41.3945	+	133.878i	−0.0673081	+	0.217687i
$616$	−14.8597	−	103.351i	−0.0241228	−	0.167778i
$617$	−286.975	+	184.427i	−0.465113	+	0.298910i	−0.752129	−	0.659016i	$-0.770973\pi$
$617$	−286.975	+	184.427i	−0.465113	+	0.298910i	0.287016	+	0.957926i	$0.407337\pi$
$618$	−450.381	−	519.768i	−0.728772	−	0.841048i
$619$	−211.814	−	721.373i	−0.342188	−	1.16538i	−0.933391	−	0.358862i	$-0.883165\pi$
$619$	−211.814	−	721.373i	−0.342188	−	1.16538i	0.591203	−	0.806523i	$-0.298653\pi$
$620$	−437.756	+	121.778i	−0.706058	+	0.196416i
$621$	−330.202	−	1894.42i	−0.531726	−	3.05060i
$622$		−	332.478i		−	0.534530i
$623$	−108.776	−	370.456i	−0.174600	−	0.594632i
$624$	107.759	+	124.360i	0.172690	+	0.199295i
$625$	−53.5012	−	622.706i	−0.0856020	−	0.996329i
$626$	−620.256	+	89.1793i	−0.990824	+	0.142459i
$627$	−313.479	+	487.782i	−0.499966	+	0.777962i
$628$	101.064	−	221.300i	0.160930	−	0.352388i
$629$	252.033	−	290.862i	0.400689	−	0.462420i
$630$	1331.77	−	172.117i	2.11392	−	0.273201i
$631$	−404.407	+	184.687i	−0.640899	+	0.292689i	−0.709233	−	0.704974i	$-0.750959\pi$
$631$	−404.407	+	184.687i	−0.640899	+	0.292689i	0.0683345	+	0.997662i	$0.478231\pi$
$632$	50.9990	+	14.9747i	0.0806946	+	0.0236941i
$633$	−340.787	+	1160.61i	−0.538368	+	1.83351i
$634$	439.256	+	961.836i	0.692832	+	1.51709i
$635$	189.283	−	24.4627i	0.298084	−	0.0385240i
$636$	−263.842	−	228.620i	−0.414846	−	0.359466i
$637$	−44.7817	−	20.4511i	−0.0703009	−	0.0321054i
$638$	−1177.73	−	756.882i	−1.84597	−	1.18634i
$639$	311.112	+	2163.83i	0.486874	+	3.38628i
$640$	223.166	+	199.021i	0.348696	+	0.310971i
$641$	21.6911	−	18.7955i	0.0338395	−	0.0293221i	−0.637777	−	0.770221i	$-0.720146\pi$
$641$	21.6911	−	18.7955i	0.0338395	−	0.0293221i	0.671616	+	0.740899i	$0.265600\pi$
$642$	−196.207	+	57.6115i	−0.305618	+	0.0897376i
$643$	−763.762			−1.18781			−0.593905	−	0.804535i	$-0.702415\pi$
$643$	−763.762			−1.18781			−0.593905	+	0.804535i	$0.702415\pi$
$644$	−80.7249	+	308.626i	−0.125349	+	0.479233i
$645$	451.106	+	1621.60i	0.699389	+	2.51410i
$646$	−363.351	+	106.689i	−0.562463	+	0.165154i
$647$	−283.185	+	245.381i	−0.437689	+	0.379260i	−0.845649	−	0.533740i	$-0.820786\pi$
$647$	−283.185	+	245.381i	−0.437689	+	0.379260i	0.407959	+	0.913000i	$0.366241\pi$
$648$	−271.859	−	423.020i	−0.419535	−	0.652809i
$649$	899.991	−	129.399i	1.38674	−	0.199382i
$650$	106.158	+	3.03124i	0.163319	+	0.00466345i
$651$	602.432	+	275.121i	0.925394	+	0.422613i
$652$	−788.252	−	683.024i	−1.20898	−	1.04758i
$653$	774.914	+	111.416i	1.18670	+	0.170621i	0.707260	−	0.706954i	$-0.249931\pi$
$653$	774.914	+	111.416i	1.18670	+	0.170621i	0.479439	+	0.877575i	$0.340840\pi$
$654$	−713.886	+	326.021i	−1.09157	+	0.498503i
$655$	679.131	+	9.69402i	1.03684	+	0.0148000i
$656$	−86.2213	−	25.3169i	−0.131435	−	0.0385928i
$657$	1844.59	−	842.397i	2.80760	−	1.28219i
$658$	38.5509	−	268.128i	0.0585880	−	0.407489i
$659$	−668.540	−	579.293i	−1.01448	−	0.879049i	−0.0217890	−	0.999763i	$-0.506936\pi$
$659$	−668.540	−	579.293i	−1.01448	−	0.879049i	−0.992687	+	0.120714i	$0.961482\pi$
$660$	192.666	−	1216.50i	0.291919	−	1.84318i
$661$	−446.291	+	694.443i	−0.675176	+	1.05059i	0.319505	+	0.947585i	$0.396483\pi$
$661$	−446.291	+	694.443i	−0.675176	+	1.05059i	−0.994680	+	0.103009i	$0.967153\pi$
$662$	−665.510	+	95.6859i	−1.00530	+	0.144541i
$663$	−136.502	+	87.7247i	−0.205886	+	0.132315i
$664$	216.585	−	187.672i	0.326181	−	0.282638i
$665$	−86.2843	−	138.570i	−0.129751	−	0.208376i
$666$			1360.48i			2.04276i
$667$	−515.391	−	751.784i	−0.772701	−	1.12711i
$668$			188.623i			0.282370i
$669$	1535.61	−	450.896i	2.29538	−	0.673985i
$670$	109.148	−	164.623i	0.162907	−	0.245706i
$671$	−687.565	+	441.871i	−1.02469	+	0.658526i
$672$	143.250	+	996.328i	0.213170	+	1.48263i
$673$	493.134	−	767.331i	0.732739	−	1.14016i	−0.252269	−	0.967657i	$-0.581177\pi$
$673$	493.134	−	767.331i	0.732739	−	1.14016i	0.985008	−	0.172508i	$-0.0551869\pi$
$674$	1292.35	+	590.197i	1.91743	+	0.875663i
$675$	−2059.59	−	356.398i	−3.05125	−	0.527997i
$676$	78.1444	−	543.506i	0.115598	−	0.804003i
$677$	100.707	+	220.518i	0.148755	+	0.325728i	0.969311	−	0.245838i	$-0.0790633\pi$
$677$	100.707	+	220.518i	0.148755	+	0.325728i	−0.820556	+	0.571566i	$0.806336\pi$
$678$	541.771	+	159.078i	0.799072	+	0.234629i
$679$	461.551	+	135.524i	0.679751	+	0.199593i
$680$	−131.141	+	110.397i	−0.192854	+	0.162348i
$681$	−1739.05	−	250.038i	−2.55367	−	0.367163i
$682$	637.575	−	735.801i	0.934861	−	1.07889i
$683$	522.736	+	238.726i	0.765353	+	0.349525i	0.759542	−	0.650458i	$-0.225423\pi$
$683$	522.736	+	238.726i	0.765353	+	0.349525i	0.00581096	+	0.999983i	$0.498150\pi$
$684$	327.020	−	508.852i	0.478099	−	0.743936i
$685$	−506.733	−	1152.86i	−0.739757	−	1.68300i
$686$	−493.346	−	767.661i	−0.719163	−	1.11904i
$687$	1194.00	+	1377.95i	1.73799	+	2.00575i
$688$	−1035.64	+	304.092i	−1.50529	+	0.441993i
$689$			29.1451i			0.0423005i
$690$	936.225	−	1507.66i	1.35685	−	2.18501i
$691$	433.136			0.626825			0.313413	−	0.949617i	$-0.398528\pi$
$691$	433.136			0.626825			0.313413	+	0.949617i	$0.398528\pi$
$692$	26.7056	+	90.9510i	0.0385919	+	0.131432i
$693$	−982.579	+	851.410i	−1.41786	+	1.22859i
$694$	−0.109392	+	0.0703021i	−0.000157626	+	0.000101300i
$695$	−162.986	−	370.806i	−0.234512	−	0.533533i
$696$	−361.514	−	232.331i	−0.519417	−	0.333809i
$697$	36.8099	−	80.6025i	0.0528120	−	0.115642i
$698$	89.8874	+	77.8879i	0.128778	+	0.111587i
$699$	−3.60220	+	25.0539i	−0.00515337	+	0.0358425i
$700$	286.234	+	195.716i	0.408906	+	0.279594i
$701$	−170.509	+	580.702i	−0.243237	+	0.828391i	0.743869	+	0.668325i	$0.232989\pi$
$701$	−170.509	+	580.702i	−0.243237	+	0.828391i	−0.987106	+	0.160065i	$0.948830\pi$
$702$	100.063	−	340.783i	0.142540	−	0.485446i
$703$	150.436	−	68.7019i	0.213992	−	0.0977267i
$704$	516.296	+	74.2322i	0.733375	+	0.105443i
$705$	−291.682	+	615.299i	−0.413733	+	0.872764i
$706$	−95.7664	+	209.699i	−0.135646	+	0.297024i
$707$	162.299	+	104.303i	0.229560	+	0.147529i
$708$	−1296.37	+	186.390i	−1.83104	+	0.263263i
$709$	−211.650	−	329.334i	−0.298519	−	0.464505i	0.659298	−	0.751881i	$-0.270853\pi$
$709$	−211.650	−	329.334i	−0.298519	−	0.464505i	−0.957818	+	0.287376i	$0.907217\pi$
$710$	−690.338	+	1041.21i	−0.972307	+	1.46649i
$711$	−186.461	−	635.027i	−0.262251	−	0.893146i
$712$	−174.226			−0.244700
$713$	568.513	−	280.373i	0.797353	−	0.393230i
$714$	−1172.47			−1.64211
$715$	−87.2850	+	54.3502i	−0.122077	+	0.0760142i
$716$	286.195	+	330.287i	0.399714	+	0.461294i
$717$	1266.37	+	1970.51i	1.76620	+	2.74827i
$718$	216.907	+	1508.62i	0.302099	+	2.10114i
$719$	213.298	+	137.078i	0.296659	+	0.190651i	0.680500	−	0.732748i	$-0.261763\pi$
$719$	213.298	+	137.078i	0.296659	+	0.190651i	−0.383841	+	0.923399i	$0.625399\pi$
$720$	338.609	−	2137.99i	0.470291	−	2.96943i
$721$	−122.763	+	141.676i	−0.170267	+	0.196499i
$722$	804.193	+	115.625i	1.11384	+	0.160146i
$723$	−194.562	−	426.031i	−0.269103	−	0.589254i
$724$	−48.6050	+	165.534i	−0.0671340	+	0.228637i
$725$	−958.193	+	251.879i	−1.32165	+	0.347419i
$726$	320.623	+	702.066i	0.441629	+	0.967033i
$727$	−8.47120	+	58.9185i	−0.0116523	+	0.0810433i	−0.994818	−	0.101674i	$-0.967580\pi$
$727$	−8.47120	+	58.9185i	−0.0116523	+	0.0810433i	0.983166	+	0.182717i	$0.0584893\pi$
$728$	8.22241	−	9.48917i	0.0112945	−	0.0130346i
$729$	−815.305	+	1785.27i	−1.11839	+	2.44893i
$730$	1107.13	+	342.320i	1.51661	+	0.468931i
$731$	−151.470	−	1053.50i	−0.207210	−	1.44118i
$732$	990.389	−	636.484i	1.35299	−	0.869514i
$733$	20.5336	+	23.6971i	0.0280131	+	0.0323289i	0.769583	−	0.638546i	$-0.220464\pi$
$733$	20.5336	+	23.6971i	0.0280131	+	0.0323289i	−0.741570	+	0.670875i	$0.765919\pi$
$734$	−28.3458	−	96.5368i	−0.0386182	−	0.131522i
$735$	239.658	+	861.503i	0.326066	+	1.17211i
$736$	825.627	+	496.511i	1.12178	+	0.674608i
$737$			191.238i			0.259481i
$738$	88.2474	+	300.543i	0.119576	+	0.407240i
$739$	−36.3534	−	41.9541i	−0.0491927	−	0.0567714i	0.730620	−	0.682784i	$-0.239231\pi$
$739$	−36.3534	−	41.9541i	−0.0491927	−	0.0567714i	−0.779813	+	0.626013i	$0.784686\pi$
$740$	−233.819	+	262.185i	−0.315972	+	0.354304i
$741$	−69.0156	+	9.92294i	−0.0931384	+	0.0133913i
$742$	−113.858	+	177.166i	−0.153447	+	0.238768i
$743$	−137.190	+	300.404i	−0.184643	+	0.404312i	−0.979206	−	0.202870i	$-0.934973\pi$
$743$	−137.190	+	300.404i	−0.184643	+	0.404312i	0.794562	+	0.607182i	$0.207700\pi$
$744$	195.709	−	225.860i	0.263050	−	0.303576i
$745$	14.0597	−	1.81706i	0.0188721	−	0.00243901i
$746$	144.079	−	65.7988i	0.193136	−	0.0882021i
$747$	−3423.91	−	1005.35i	−4.58354	−	1.34585i
$748$	−219.421	+	747.278i	−0.293343	+	0.999035i
$749$	23.1548	+	50.7018i	0.0309142	+	0.0676927i
$750$	−1199.67	−	1510.59i	−1.59957	−	2.01412i
$751$	418.702	+	362.807i	0.557526	+	0.483099i	0.887447	−	0.460909i	$-0.152477\pi$
$751$	418.702	+	362.807i	0.557526	+	0.483099i	−0.329921	+	0.944008i	$0.607022\pi$
$752$	−397.200	−	181.395i	−0.528191	−	0.241217i
$753$	−1157.76	−	744.046i	−1.53753	−	0.988109i
$754$	−23.9586	−	166.635i	−0.0317753	−	0.221002i
$755$	459.369	−	515.098i	0.608436	−	0.682249i
$756$	876.397	−	759.402i	1.15926	−	1.00450i
$757$	630.285	−	185.068i	0.832609	−	0.244476i	0.162472	−	0.986713i	$-0.448053\pi$
$757$	630.285	−	185.068i	0.832609	−	0.244476i	0.670137	+	0.742237i	$0.266235\pi$
$758$	191.321			0.252403
$759$	51.1425	+	1717.49i	0.0673815	+	2.26283i
$760$	−70.9669	+	19.7420i	−0.0933775	+	0.0259763i
$761$	841.715	−	247.150i	1.10606	−	0.324770i	0.322805	−	0.946465i	$-0.395374\pi$
$761$	841.715	−	247.150i	1.10606	−	0.324770i	0.783259	+	0.621696i	$0.213556\pi$
$762$	445.188	−	385.757i	0.584236	−	0.506243i
$763$	115.653	+	179.960i	0.151577	+	0.235858i
$764$	417.862	−	60.0795i	0.546940	−	0.0786381i
$765$	2039.24	+	630.527i	2.66568	+	0.824218i
$766$	50.3502	+	22.9942i	0.0657313	+	0.0300185i
$767$	82.6324	+	71.6014i	0.107735	+	0.0933526i
$768$	1815.68	+	261.055i	2.36416	+	0.339915i
$769$	469.114	−	214.237i	0.610032	−	0.278592i	−0.0863488	−	0.996265i	$-0.527520\pi$
$769$	469.114	−	214.237i	0.610032	−	0.278592i	0.696380	+	0.717673i	$0.254793\pi$
$770$	−742.908	−	10.6044i	−0.964815	−	0.0137719i
$771$	−264.127	−	77.5548i	−0.342577	−	0.100590i
$772$	228.740	−	104.462i	0.296295	−	0.135314i
$773$	−57.4861	+	399.825i	−0.0743675	+	0.517238i	0.918255	+	0.395990i	$0.129599\pi$
$773$	−57.4861	+	399.825i	−0.0743675	+	0.517238i	−0.992622	+	0.121247i	$0.961311\pi$
$774$	2843.39	+	2463.82i	3.67364	+	3.18322i
$775$	−78.5505	−	684.518i	−0.101355	−	0.883249i
$776$	117.356	−	182.610i	0.151232	−	0.235322i
$777$	506.827	−	72.8707i	0.652287	−	0.0937847i
$778$	403.230	−	259.140i	0.518290	−	0.333085i
$779$	28.7765	−	24.9350i	0.0369403	−	0.0320090i
$780$	125.728	−	78.2876i	0.161190	−	0.100369i
$781$		−	1209.54i		−	1.54870i
$782$	−709.320	+	869.604i	−0.907059	+	1.11203i
$783$			3313.37i			4.23164i
$784$	−550.203	+	161.554i	−0.701790	+	0.206064i
$785$	307.470	+	203.858i	0.391681	+	0.259692i
$786$	1763.52	−	1133.35i	2.24367	−	1.44192i
$787$	113.997	+	792.864i	0.144850	+	1.00745i	0.924485	+	0.381218i	$0.124495\pi$
$787$	113.997	+	792.864i	0.144850	+	1.00745i	−0.779636	+	0.626233i	$0.784596\pi$
$788$	358.746	−	558.220i	0.455261	−	0.708400i
$789$	292.785	+	133.710i	0.371083	+	0.169468i
$790$	162.011	−	341.760i	0.205077	−	0.432608i
$791$	21.9033	−	152.341i	0.0276907	−	0.192593i
$792$	243.720	+	533.673i	0.307728	+	0.673829i
$793$	−94.3018	−	27.6895i	−0.118918	−	0.0349174i
$794$	−758.126	−	222.606i	−0.954818	−	0.280360i
$795$	404.991	−	340.929i	0.509423	−	0.428842i
$796$	686.138	+	98.6518i	0.861983	+	0.123934i
$797$	916.340	−	1057.51i	1.14974	−	1.32687i	0.212910	−	0.977072i	$-0.431706\pi$
$797$	916.340	−	1057.51i	1.14974	−	1.32687i	0.936826	−	0.349795i	$-0.113749\pi$
$798$	−458.294	−	209.296i	−0.574303	−	0.262275i
$799$	232.789	−	362.226i	0.291350	−	0.453350i
$800$	810.671	−	662.901i	1.01334	−	0.828626i
$801$	1172.88	+	1825.04i	1.46427	+	2.27845i
$802$	−291.146	−	336.001i	−0.363025	−	0.418954i
$803$	−1076.54	+	316.100i	−1.34064	+	0.393648i
$804$		−	275.464i		−	0.342618i
$805$	−443.084	−	194.110i	−0.550415	−	0.241130i
$806$	117.078			0.145258
$807$	−587.168	−	1999.71i	−0.727594	−	2.47796i
$808$	65.7940	−	57.0108i	0.0814282	−	0.0705580i
$809$	−1019.62	+	655.268i	−1.26034	+	0.809972i	−0.988331	−	0.152322i	$-0.951325\pi$
$809$	−1019.62	+	655.268i	−1.26034	+	0.809972i	−0.272011	+	0.962294i	$0.587689\pi$
$810$	−3275.65	+	1439.80i	−4.04402	+	1.77753i
$811$	−566.258	−	363.912i	−0.698222	−	0.448720i	0.142778	−	0.989755i	$-0.454396\pi$
$811$	−566.258	−	363.912i	−0.698222	−	0.448720i	−0.841000	+	0.541035i	$0.818033\pi$
$812$	228.339	−	499.992i	0.281205	−	0.615753i
$813$	−551.791	−	478.129i	−0.678709	−	0.588105i
$814$	107.126	−	745.076i	0.131604	−	0.915326i
$815$	1209.95	−	1018.56i	1.48460	−	1.24976i
$816$	−532.472	+	1813.43i	−0.652539	+	2.22234i
$817$	128.852	−	438.830i	0.157714	−	0.537123i
$818$	469.457	−	214.394i	0.573909	−	0.262095i
$819$	−154.753	−	22.2501i	−0.188953	−	0.0271673i
$820$	−34.6464	+	73.0860i	−0.0422516	+	0.0891293i
$821$	−207.427	+	454.202i	−0.252652	+	0.553230i	−0.992879	−	0.119126i	$-0.961991\pi$
$821$	−207.427	+	454.202i	−0.252652	+	0.553230i	0.740227	+	0.672357i	$0.234718\pi$
$822$	−3269.76	−	2101.35i	−3.97781	−	2.55638i
$823$	64.9007	−	9.33131i	0.0788587	−	0.0113382i	−0.102773	−	0.994705i	$-0.532771\pi$
$823$	64.9007	−	9.33131i	0.0788587	−	0.0113382i	0.181631	+	0.983367i	$0.441862\pi$
$824$	45.7347	+	71.1646i	0.0555033	+	0.0863648i
$825$	1776.26	+	577.117i	2.15305	+	0.699535i
$826$	222.586	+	758.058i	0.269474	+	0.917746i
$827$	−120.332			−0.145504			−0.0727518	−	0.997350i	$-0.523178\pi$
$827$	−120.332			−0.145504			−0.0727518	+	0.997350i	$0.523178\pi$
$828$	−53.3517	−	1791.68i	−0.0644344	−	2.16387i
$829$	13.6715			0.0164916			0.00824580	−	0.999966i	$-0.497375\pi$
$829$	13.6715			0.0164916			0.00824580	+	0.999966i	$0.497375\pi$
$830$	−1077.90	−	1731.08i	−1.29868	−	2.08564i
$831$	−1165.81	−	1345.42i	−1.40291	−	1.61904i
$832$	33.9111	+	52.7667i	0.0407586	+	0.0634216i
$833$	−80.4714	−	559.691i	−0.0966043	−	0.671898i
$834$	−1051.69	−	675.878i	−1.26102	−	0.810405i
$835$	−282.503	−	44.7421i	−0.338327	−	0.0535834i
$836$	−219.163	+	252.927i	−0.262156	+	0.302544i
$837$	−2280.82	−	327.932i	−2.72499	−	0.391795i
$838$	195.332	+	427.717i	0.233093	+	0.510402i
$839$	−138.947	+	473.212i	−0.165611	+	0.564019i	0.834308	+	0.551298i	$0.185867\pi$
$839$	−138.947	+	473.212i	−0.165611	+	0.564019i	−0.999919	+	0.0127205i	$0.995951\pi$
$840$	−228.042	−	3.25510i	−0.271478	−	0.00387512i
$841$	303.055	+	663.598i	0.360351	+	0.789059i
$842$	−205.652	+	1430.34i	−0.244242	+	1.69874i
$843$	25.6768	−	29.6326i	0.0304589	−	0.0351514i
$844$	−290.033	+	635.083i	−0.343640	+	0.752468i
$845$	795.478	+	245.959i	0.941394	+	0.291076i
$846$	216.613	+	1506.58i	0.256044	+	1.78083i
$847$	176.980	−	113.738i	0.208949	−	0.134284i
$848$	222.311	+	256.560i	0.262159	+	0.302547i
$849$	−240.169	−	817.942i	−0.282885	−	0.963418i
$850$	629.910	+	1044.56i	0.741071	+	1.22889i
$851$	252.573	−	419.992i	0.296795	−	0.493528i
$852$			1742.25i			2.04490i
$853$	295.369	+	1005.93i	0.346271	+	1.17929i	0.930067	+	0.367389i	$0.119748\pi$
$853$	295.369	+	1005.93i	0.346271	+	1.17929i	−0.583797	+	0.811900i	$0.698434\pi$
$854$	−465.066	−	536.715i	−0.544574	−	0.628472i
$855$	684.543	+	610.482i	0.800635	+	0.714014i
$856$	24.8963	−	3.57955i	0.0290845	−	0.00418171i
$857$	−689.740	+	1073.26i	−0.804831	+	1.25234i	0.159384	+	0.987217i	$0.449049\pi$
$857$	−689.740	+	1073.26i	−0.804831	+	1.25234i	−0.964214	+	0.265124i	$0.914587\pi$
$858$	−131.835	+	288.678i	−0.153654	+	0.336454i
$859$	115.990	−	133.860i	0.135029	−	0.155832i	−0.684208	−	0.729287i	$-0.739852\pi$
$859$	115.990	−	133.860i	0.135029	−	0.155832i	0.819237	+	0.573455i	$0.194397\pi$
$860$	124.521	+	963.497i	0.144792	+	1.12035i
$861$	107.236	−	48.9732i	0.124549	−	0.0568795i
$862$	841.930	+	247.213i	0.976717	+	0.286790i
$863$	472.882	−	1610.49i	0.547951	−	1.86615i	0.0503765	−	0.998730i	$-0.483958\pi$
$863$	472.882	−	1610.49i	0.547951	−	1.86615i	0.497575	−	0.867421i	$-0.334224\pi$
$864$	−1454.85	−	3185.69i	−1.68386	−	3.68714i
$865$	−142.553	+	18.4234i	−0.164801	+	0.0212987i
$866$	−866.259	−	750.618i	−1.00030	−	0.866764i
$867$	−193.471	−	88.3554i	−0.223150	−	0.101909i
$868$	321.579	+	206.666i	0.370482	+	0.238095i
$869$	52.1139	+	362.460i	0.0599699	+	0.417100i
$870$	−2035.26	+	2282.17i	−2.33938	+	2.62318i
$871$	−17.3797	+	15.0596i	−0.0199538	+	0.0172900i
$872$	92.6212	−	27.1960i	0.106217	−	0.0311881i
$873$	−2702.89			−3.09609
$874$	−432.490	+	213.291i	−0.494840	+	0.244040i
$875$	−361.022	+	382.271i	−0.412596	+	0.436881i
$876$	1550.67	−	455.319i	1.77018	−	0.519771i
$877$	−338.330	+	293.165i	−0.385781	+	0.334281i	−0.826062	−	0.563579i	$-0.809424\pi$
$877$	−338.330	+	293.165i	−0.385781	+	0.334281i	0.440281	+	0.897860i	$0.354879\pi$
$878$	−102.678	−	159.771i	−0.116946	−	0.181971i
$879$	2736.36	−	393.429i	3.11304	−	0.447587i
$880$	−353.790	+	1144.22i	−0.402034	+	1.30025i
$881$	720.028	+	328.826i	0.817285	+	0.373241i	0.779779	−	0.626055i	$-0.215331\pi$
$881$	720.028	+	328.826i	0.817285	+	0.373241i	0.0375058	+	0.999296i	$0.488059\pi$
$882$	1510.61	+	1308.95i	1.71270	+	1.48407i
$883$	438.749	+	63.0825i	0.496884	+	0.0714411i	0.386201	−	0.922415i	$-0.373787\pi$
$883$	438.749	+	63.0825i	0.496884	+	0.0714411i	0.110683	+	0.993856i	$0.464696\pi$
$884$	−85.1917	+	38.9058i	−0.0963707	+	0.0440110i
$885$	28.3457	−	1985.80i	0.0320290	−	2.24385i
$886$	−1800.46	−	528.663i	−2.03212	−	0.596685i
$887$	881.420	−	402.531i	0.993709	−	0.453812i	0.148884	−	0.988855i	$-0.452432\pi$
$887$	881.420	−	402.531i	0.993709	−	0.453812i	0.844825	+	0.535043i	$0.179705\pi$
$888$	32.8831	−	228.707i	0.0370305	−	0.257553i
$889$	−121.347	−	105.148i	−0.136498	−	0.118276i
$890$	−193.931	+	1224.49i	−0.217900	+	1.37583i
$891$	1872.95	−	2914.37i	2.10208	−	3.27090i
$892$	914.355	−	131.464i	1.02506	−	0.147382i
$893$	155.653	−	100.032i	0.174303	−	0.112018i
$894$	33.0680	−	28.6536i	0.0369888	−	0.0320510i
$895$	−562.560	+	350.292i	−0.628559	+	0.391388i
$896$		−	251.560i		−	0.280758i
$897$	−152.059	+	139.897i	−0.169519	+	0.155961i
$898$			803.183i			0.894414i
$899$	−1047.97	+	307.712i	−1.16571	+	0.342283i
$900$	−1852.99	−	602.046i	−2.05888	−	0.668940i
$901$	−281.610	+	180.980i	−0.312553	+	0.200866i
$902$	−24.6642	−	171.543i	−0.0273439	−	0.190181i
$903$	765.561	−	1191.24i	0.847798	−	1.31920i
$904$	−63.1750	−	28.8511i	−0.0698838	−	0.0319149i
$905$	−236.392	−	112.061i	−0.261207	−	0.123825i
$906$	303.157	−	2108.50i	0.334610	−	2.32727i
$907$	−26.0820	−	57.1116i	−0.0287564	−	0.0629676i	0.894709	−	0.446650i	$-0.147383\pi$
$907$	−26.0820	−	57.1116i	−0.0287564	−	0.0629676i	−0.923465	+	0.383682i	$0.874656\pi$
$908$	−973.007	−	285.701i	−1.07159	−	0.314648i
$909$	−1040.11	−	305.405i	−1.14424	−	0.335979i
$910$	−57.5389	−	68.3507i	−0.0632295	−	0.0751106i
$911$	1608.55	+	231.275i	1.76570	+	0.253869i	0.947201	−	0.320641i	$-0.103898\pi$
$911$	1608.55	+	231.275i	1.76570	+	0.253869i	0.818497	+	0.574510i	$0.194807\pi$
$912$	−531.846	+	613.783i	−0.583164	+	0.673007i
$913$	1795.97	+	820.190i	1.96710	+	0.898347i
$914$	542.902	−	844.772i	0.593985	−	0.924259i
$915$	718.345	+	1634.29i	0.785077	+	1.78611i
$916$	568.961	+	885.321i	0.621137	+	0.966508i
$917$	−374.187	−	431.835i	−0.408056	−	0.470921i
$918$	3914.12	−	1149.29i	4.26375	−	1.25195i
$919$			1554.72i			1.69176i	0.533375	+	0.845879i	$0.320923\pi$
$919$			1554.72i			1.69176i	−0.533375	+	0.845879i	$0.679077\pi$
$920$	−140.375	+	167.166i	−0.152581	+	0.181702i
$921$	−1498.35			−1.62688
$922$	629.814	+	2144.95i	0.683095	+	2.32641i
$923$	109.923	−	95.2489i	0.119093	−	0.103195i
$924$	−871.688	+	560.200i	−0.943385	+	0.606277i
$925$	−337.214	−	412.384i	−0.364556	−	0.445821i
$926$	1104.41	+	709.760i	1.19267	+	0.766480i
$927$	437.572	−	958.150i	0.472030	−	1.03360i
$928$	−1254.55	−	1087.08i	−1.35189	−	1.17142i
$929$	−140.048	+	974.055i	−0.150751	+	1.04850i	0.764213	+	0.644964i	$0.223127\pi$
$929$	−140.048	+	974.055i	−0.150751	+	1.04850i	−0.914965	+	0.403534i	$0.867782\pi$
$930$	−1369.53	−	1626.88i	−1.47262	−	1.74933i
$931$	68.4550	−	233.136i	0.0735285	−	0.250415i
$932$	−4.11598	+	14.0178i	−0.00441629	+	0.0150405i
$933$	639.573	−	292.083i	0.685502	−	0.313058i
$934$	−1588.90	−	228.450i	−1.70118	−	0.244593i
$935$	−1067.16	−	505.885i	−1.14135	−	0.541054i
$936$	−29.3078	+	64.1751i	−0.0313117	+	0.0685631i
$937$	674.632	+	433.560i	0.719991	+	0.462710i	0.848634	−	0.528981i	$-0.177426\pi$
$937$	674.632	+	433.560i	0.719991	+	0.462710i	−0.128643	+	0.991691i	$0.541062\pi$
$938$	−164.479	+	23.6485i	−0.175350	+	0.0252116i
$939$	−716.448	−	1114.82i	−0.762991	−	1.18724i
$940$	−217.184	+	327.570i	−0.231047	+	0.348478i
$941$	477.785	+	1627.19i	0.507741	+	1.72921i	0.669907	+	0.742445i	$0.266334\pi$
$941$	477.785	+	1627.19i	0.507741	+	1.72921i	−0.162165	+	0.986764i	$0.551848\pi$
$942$	1138.62			1.20873
$943$	28.5531	−	109.164i	0.0302790	−	0.115762i
$944$	1273.56			1.34911
$945$	929.480	+	1492.72i	0.983577	+	1.57960i
$946$	−1363.20	−	1573.22i	−1.44102	−	1.66302i
$947$	765.682	+	1191.42i	0.808535	+	1.25810i	0.962838	+	0.270081i	$0.0870504\pi$
$947$	765.682	+	1191.42i	0.808535	+	1.25810i	−0.154303	+	0.988024i	$0.549313\pi$
$948$	−75.0663	−	522.098i	−0.0791839	−	0.550736i
$949$	−113.502	−	72.9436i	−0.119602	−	0.0768636i
$950$	59.7565	+	520.740i	0.0629016	+	0.548147i
$951$	−1464.35	+	1689.96i	−1.53981	+	1.77703i
$952$	142.746	+	20.5238i	0.149943	+	0.0215586i
$953$	−227.785	−	498.779i	−0.239018	−	0.523377i	0.751668	−	0.659542i	$-0.229250\pi$
$953$	−227.785	−	498.779i	−0.239018	−	0.523377i	−0.990686	+	0.136165i	$0.956522\pi$
$954$	333.381	−	1135.39i	0.349456	−	1.19014i
$955$	−9.13672	+	640.088i	−0.00956724	+	0.670249i
$956$	561.632	+	1229.80i	0.587481	+	1.28640i
$957$	421.339	−	2930.48i	0.440271	−	3.06215i
$958$	366.293	−	422.724i	0.382352	−	0.441257i
$959$	−440.106	+	963.697i	−0.458921	+	1.00490i
$960$	336.550	−	1088.47i	0.350573	−	1.13382i
$961$	28.6657	+	199.374i	0.0298290	+	0.207465i
$962$	76.1486	−	48.9377i	0.0791565	−	0.0508708i
$963$	−205.096	−	236.693i	−0.212976	−	0.245788i
$964$	−76.1606	−	259.379i	−0.0790048	−	0.269066i
$965$	102.196	+	367.365i	0.105903	+	0.380689i
$966$	−1470.85	+	256.372i	−1.52262	+	0.265395i
$967$		−	1204.90i		−	1.24602i	−0.782215	−	0.623008i	$-0.785910\pi$
$967$		−	1204.90i		−	1.24602i	0.782215	−	0.623008i	$-0.214090\pi$
$968$	−26.7457	−	91.0876i	−0.0276299	−	0.0940988i
$969$	−524.440	−	605.236i	−0.541218	−	0.624598i
$970$	−1152.78	−	1028.06i	−1.18843	−	1.05986i
$971$	907.760	−	130.516i	0.934872	−	0.134414i	0.341990	−	0.939704i	$-0.388899\pi$
$971$	907.760	−	130.516i	0.934872	−	0.134414i	0.592882	+	0.805289i	$0.297990\pi$
$972$	−1356.44	+	2110.66i	−1.39552	+	2.17147i
$973$	−141.556	+	309.964i	−0.145484	+	0.318565i
$974$	1085.58	−	1252.83i	1.11456	−	1.28627i
$975$	87.4290	+	206.874i	0.0896708	+	0.212179i
$976$	−1041.33	+	475.561i	−1.06694	+	0.487256i
$977$	614.440	+	180.416i	0.628905	+	0.184663i	0.580626	−	0.814171i	$-0.302808\pi$
$977$	614.440	+	180.416i	0.628905	+	0.184663i	0.0482796	+	0.998834i	$0.484626\pi$
$978$	1375.27	−	4683.74i	1.40621	−	4.78910i
$979$	−498.631	−	1091.85i	−0.509327	−	1.11527i
$980$	66.1542	+	511.875i	0.0675043	+	0.522322i
$981$	−908.400	−	787.133i	−0.925994	−	0.802378i
$982$	803.815	+	367.090i	0.818549	+	0.373819i
$983$	−156.906	−	100.837i	−0.159620	−	0.102581i	0.458392	−	0.888750i	$-0.348425\pi$
$983$	−156.906	−	100.837i	−0.159620	−	0.102581i	−0.618012	+	0.786169i	$0.712062\pi$
$984$	−7.57089	−	52.6567i	−0.00769399	−	0.0535129i
$985$	750.955	+	669.709i	0.762391	+	0.679907i
$986$	1461.32	−	1266.24i	1.48207	−	1.28422i
$987$	549.653	−	161.393i	0.556893	−	0.163518i
$988$	−40.2447			−0.0407335
$989$	−420.375	−	1288.48i	−0.425051	−	1.30281i
$990$	4022.01	−	1118.87i	4.06264	−	1.13017i
$991$	−420.780	+	123.552i	−0.424601	+	0.124674i	−0.487050	−	0.873374i	$-0.661927\pi$
$991$	−420.780	+	123.552i	−0.424601	+	0.124674i	0.0624490	+	0.998048i	$0.480109\pi$
$992$	872.474	−	756.003i	0.879510	−	0.762100i
$993$	−768.721	−	1196.15i	−0.774140	−	1.20459i
$994$	1040.29	−	149.572i	1.04657	−	0.150474i
$995$	−310.506	+	1004.24i	−0.312066	+	1.00928i
$996$	−2586.96	−	1181.43i	−2.59735	−	1.18617i
$997$	−144.590	−	125.288i	−0.145025	−	0.125665i	0.579327	−	0.815095i	$-0.303315\pi$
$997$	−144.590	−	125.288i	−0.145025	−	0.125665i	−0.724352	+	0.689430i	$0.757861\pi$
$998$	−341.212	−	49.0589i	−0.341896	−	0.0491572i
$999$	−1620.54	+	740.077i	−1.62216	+	0.740818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.i.a.14.19	yes	220
5.4	even	2	inner	115.3.i.a.14.4	✓	220
23.5	odd	22	inner	115.3.i.a.74.4	yes	220
115.74	odd	22	inner	115.3.i.a.74.19	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.i.a.14.4	✓	220	5.4	even	2	inner
115.3.i.a.14.19	yes	220	1.1	even	1	trivial
115.3.i.a.74.4	yes	220	23.5	odd	22	inner
115.3.i.a.74.19	yes	220	115.74	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.761060 + 2.59193i) q^{2} +(-4.31740 + 3.74105i) q^{3} +(-2.77389 + 1.78267i) q^{4} +(-2.01195 - 4.57734i) q^{5} +(-12.9823 - 8.34325i) q^{6} +(-1.74741 + 3.82629i) q^{7} +(1.43453 + 1.24303i) q^{8} +(3.36366 - 23.3948i) q^{9} +O(q^{10})\)	\(q+(0.761060 + 2.59193i) q^{2} +(-4.31740 + 3.74105i) q^{3} +(-2.77389 + 1.78267i) q^{4} +(-2.01195 - 4.57734i) q^{5} +(-12.9823 - 8.34325i) q^{6} +(-1.74741 + 3.82629i) q^{7} +(1.43453 + 1.24303i) q^{8} +(3.36366 - 23.3948i) q^{9} +(10.3330 - 8.69847i) q^{10} +(-3.68427 + 12.5475i) q^{11} +(5.30694 - 18.0738i) q^{12} +(-1.43045 + 0.653264i) q^{13} +(-11.2474 - 1.61713i) q^{14} +(25.8104 + 12.2354i) q^{15} +(-7.60913 + 16.6617i) q^{16} +(-15.1946 - 9.76498i) q^{17} +(63.1977 - 9.08646i) q^{18} +(-4.19613 - 6.52930i) q^{19} +(13.7408 + 9.11041i) q^{20} +(-6.77008 - 23.0568i) q^{21} -35.3262 q^{22} +(-21.1967 - 8.92760i) q^{23} -10.8437 q^{24} +(-16.9041 + 18.4188i) q^{25} +(-2.78187 - 3.21045i) q^{26} +(45.2019 + 70.3356i) q^{27} +(-1.97390 - 13.7288i) q^{28} +(33.3387 + 21.4255i) q^{29} +(-12.0701 + 76.2108i) q^{30} +(-18.0482 + 20.8288i) q^{31} +(-41.4616 - 5.96128i) q^{32} +(-31.0343 - 67.9556i) q^{33} +(13.7462 - 46.8152i) q^{34} +(21.0299 + 0.300185i) q^{35} +(32.3748 + 70.8910i) q^{36} +(-3.03247 + 21.0913i) q^{37} +(13.7300 - 15.8453i) q^{38} +(3.73192 - 8.17177i) q^{39} +(2.80356 - 9.06725i) q^{40} +(0.698185 + 4.85598i) q^{41} +(54.6092 - 35.0952i) q^{42} +(38.5890 + 44.5341i) q^{43} +(-12.1483 - 41.3732i) q^{44} +(-113.854 + 31.6725i) q^{45} +(7.00781 - 61.7348i) q^{46} +23.8391i q^{47} +(-29.4804 - 100.401i) q^{48} +(20.5011 + 23.6595i) q^{49} +(-60.6053 - 29.7966i) q^{50} +(102.132 - 14.6844i) q^{51} +(2.80335 - 4.36210i) q^{52} +(7.69912 - 16.8587i) q^{53} +(-147.904 + 170.690i) q^{54} +(64.8467 - 8.38072i) q^{55} +(-7.26290 + 3.31685i) q^{56} +(42.5428 + 12.4917i) q^{57} +(-30.1607 + 102.718i) q^{58} +(-28.8834 - 63.2459i) q^{59} +(-93.4071 + 12.0718i) q^{60} +(47.2335 + 40.9280i) q^{61} +(-67.7226 - 30.9279i) q^{62} +(83.6376 + 53.7506i) q^{63} +(-5.67646 - 39.4806i) q^{64} +(5.86820 + 5.23332i) q^{65} +(152.517 - 132.157i) q^{66} +(14.0314 - 4.11998i) q^{67} +59.5560 q^{68} +(124.913 - 40.7537i) q^{69} +(15.2270 + 54.7367i) q^{70} +(-88.7455 + 26.0580i) q^{71} +(33.9057 - 29.3794i) q^{72} +(46.3853 + 72.1770i) q^{73} +(-56.9751 + 8.19179i) q^{74} +(4.07640 - 142.760i) q^{75} +(23.2792 + 10.6313i) q^{76} +(-41.5724 - 36.0227i) q^{77} +(24.0209 + 3.45369i) q^{78} +(25.4715 - 11.6324i) q^{79} +(91.5753 + 1.30716i) q^{80} +(-254.182 - 74.6345i) q^{81} +(-12.0550 + 5.50535i) q^{82} +(21.4866 - 149.443i) q^{83} +(59.8821 + 51.8881i) q^{84} +(-14.1269 + 89.1976i) q^{85} +(-86.0608 + 133.913i) q^{86} +(-224.090 + 32.2193i) q^{87} +(-20.8821 + 13.4201i) q^{88} +(-69.3682 + 60.1078i) q^{89} +(-168.742 - 270.996i) q^{90} -6.61483i q^{91} +(74.7122 - 13.0225i) q^{92} -157.445i q^{93} +(-61.7895 + 18.1430i) q^{94} +(-21.4444 + 32.3437i) q^{95} +(201.308 - 129.373i) q^{96} +(-16.2748 - 113.194i) q^{97} +(-45.7214 + 71.1439i) q^{98} +(281.153 + 128.398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9}+O(q^{10}) \) 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9	\( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30} - 152 q^{31} - 264 q^{34} - 13 q^{35} - 62 q^{36} - 118 q^{39} - 11 q^{40} - 80 q^{41} - 242 q^{44} + 226 q^{46} + 90 q^{49} - 211 q^{50} - 22 q^{51} + 658 q^{54} - 565 q^{55} + 770 q^{56} - 172 q^{59} - 891 q^{60} + 286 q^{61} - 474 q^{64} - 242 q^{65} - 44 q^{66} - 288 q^{69} + 790 q^{70} - 210 q^{71} + 506 q^{74} + 804 q^{75} - 2376 q^{76} + 462 q^{79} + 2398 q^{80} - 2408 q^{81} + 1034 q^{84} + 1197 q^{85} - 1518 q^{86} - 22 q^{89} + 154 q^{90} - 210 q^{94} - 338 q^{95} + 2772 q^{96} + 1628 q^{99}+O(q^{100}) \) 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

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