LMFDB - Embedded newform 833.2.k.c.120.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(120,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("833.120");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.k (of order $7$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$234$
Relative dimension:	$39$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			120.2
Character	$\chi$	$=$	833.120
Dual form			833.2.k.c.715.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.43956 + 1.17483i) q^{2} +(-0.760566 + 3.33226i) q^{3} +(3.32426 - 4.16849i) q^{4} +(-0.286235 + 1.25408i) q^{5} +(-2.05939 - 9.02278i) q^{6} +(2.05845 - 1.66216i) q^{7} +(-2.00742 + 8.79508i) q^{8} +(-7.82256 - 3.76715i) q^{9} +(-0.775040 - 3.39567i) q^{10} +(-2.85011 + 1.37254i) q^{11} +(11.3621 + 14.2477i) q^{12} +(-2.25954 + 1.08814i) q^{13} +(-3.06897 + 6.47327i) q^{14} +(-3.96120 - 1.90761i) q^{15} +(-3.06268 - 13.4185i) q^{16} +(0.623490 + 0.781831i) q^{17} +23.5094 q^{18} -4.35071 q^{19} +(4.27608 + 5.36203i) q^{20} +(3.97314 + 8.12348i) q^{21} +(5.34052 - 6.69679i) q^{22} +(-2.84940 + 3.57304i) q^{23} +(-27.7807 - 13.3785i) q^{24} +(3.01407 + 1.45150i) q^{25} +(4.23392 - 5.30917i) q^{26} +(12.1095 - 15.1848i) q^{27} +(-0.0858448 - 14.1061i) q^{28} +(-4.93362 - 6.18657i) q^{29} +11.9047 q^{30} +3.83175 q^{31} +(11.9867 + 15.0309i) q^{32} +(-2.40596 - 10.5412i) q^{33} +(-2.43956 - 1.17483i) q^{34} +(1.49527 + 3.05722i) q^{35} +(-41.7075 + 20.0853i) q^{36} +(-4.95930 - 6.21877i) q^{37} +(10.6138 - 5.11135i) q^{38} +(-1.90743 - 8.35698i) q^{39} +(-10.4551 - 5.03491i) q^{40} +(0.0893082 - 0.391285i) q^{41} +(-19.2364 - 15.1500i) q^{42} +(0.690193 + 3.02393i) q^{43} +(-3.75308 + 16.4433i) q^{44} +(6.96337 - 8.73179i) q^{45} +(2.75358 - 12.0642i) q^{46} +(8.00159 - 3.85337i) q^{47} +47.0432 q^{48} +(1.47447 - 6.84295i) q^{49} -9.05827 q^{50} +(-3.07947 + 1.48299i) q^{51} +(-2.97541 + 13.0361i) q^{52} +(2.33215 - 2.92442i) q^{53} +(-11.7023 + 51.2709i) q^{54} +(-0.905469 - 3.96712i) q^{55} +(10.4866 + 21.4409i) q^{56} +(3.30900 - 14.4977i) q^{57} +(19.3041 + 9.29634i) q^{58} +(-0.244683 - 1.07203i) q^{59} +(-21.1199 + 10.1708i) q^{60} +(0.712347 + 0.893256i) q^{61} +(-9.34779 + 4.50166i) q^{62} +(-22.3640 + 5.24782i) q^{63} +(-22.1000 - 10.6428i) q^{64} +(-0.717849 - 3.14510i) q^{65} +(18.2536 + 22.8893i) q^{66} -5.09907 q^{67} +5.33169 q^{68} +(-9.73912 - 12.2125i) q^{69} +(-7.23953 - 5.70160i) q^{70} +(-2.68369 + 3.36524i) q^{71} +(48.8355 - 61.2378i) q^{72} +(7.60567 + 3.66270i) q^{73} +(19.4045 + 9.34473i) q^{74} +(-7.12916 + 8.93969i) q^{75} +(-14.4629 + 18.1359i) q^{76} +(-3.58544 + 7.56264i) q^{77} +(14.4713 + 18.1465i) q^{78} +7.50184 q^{79} +17.7044 q^{80} +(25.1495 + 31.5365i) q^{81} +(0.241821 + 1.05949i) q^{82} +(1.56077 + 0.751627i) q^{83} +(47.0703 + 10.4425i) q^{84} +(-1.15894 + 0.558116i) q^{85} +(-5.23638 - 6.56621i) q^{86} +(24.3676 - 11.7348i) q^{87} +(-6.35023 - 27.8222i) q^{88} +(-0.335516 - 0.161576i) q^{89} +(-6.72920 + 29.4825i) q^{90} +(-2.84251 + 5.99560i) q^{91} +(5.42201 + 23.7554i) q^{92} +(-2.91430 + 12.7684i) q^{93} +(-14.9933 + 18.8010i) q^{94} +(1.24532 - 5.45612i) q^{95} +(-59.2034 + 28.5109i) q^{96} -18.2234 q^{97} +(4.44225 + 18.4261i) q^{98} +27.4657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q + q^{2} - 7 q^{3} - 39 q^{4} + 2 q^{5} + 7 q^{6} - 13 q^{7} - 23 q^{8} - 42 q^{9} + 21 q^{10} - 7 q^{11} + q^{12} - 15 q^{13} - 22 q^{14} + 36 q^{15} - 55 q^{16} - 39 q^{17} + 62 q^{18} - 4 q^{19}+ \cdots + 72 q^{99}+O(q^{100}) $ 234 * q + q^2 - 7 * q^3 - 39 * q^4 + 2 * q^5 + 7 * q^6 - 13 * q^7 - 23 * q^8 - 42 * q^9 + 21 * q^10 - 7 * q^11 + q^12 - 15 * q^13 - 22 * q^14 + 36 * q^15 - 55 * q^16 - 39 * q^17 + 62 * q^18 - 4 * q^19 - 26 * q^20 - 30 * q^21 - 47 * q^22 - 32 * q^23 - 43 * q^24 - 69 * q^25 + 7 * q^26 - 19 * q^27 - 21 * q^28 + 8 * q^29 + 40 * q^30 - 8 * q^31 + 55 * q^32 - 59 * q^33 + q^34 - 20 * q^35 - 109 * q^36 + 22 * q^37 - 71 * q^38 - 41 * q^39 - 32 * q^40 - 9 * q^41 + 104 * q^42 - 15 * q^43 + 40 * q^44 + 102 * q^45 - 2 * q^46 - 21 * q^47 + 32 * q^48 + 35 * q^49 + 102 * q^50 - 21 * q^52 - 42 * q^53 - 59 * q^54 + 39 * q^55 + q^56 - 87 * q^57 - 27 * q^58 + 42 * q^59 + 162 * q^60 + 27 * q^61 - 77 * q^62 - 12 * q^63 - 53 * q^64 - 26 * q^65 - 66 * q^66 + 154 * q^67 + 276 * q^68 - 6 * q^69 - 32 * q^70 - 70 * q^71 + 106 * q^72 - 70 * q^73 - 44 * q^74 - 90 * q^75 - 20 * q^76 + 26 * q^77 - 93 * q^78 + 130 * q^79 - 4 * q^80 + 120 * q^81 - 30 * q^82 - 10 * q^83 - 148 * q^84 - 12 * q^85 - 4 * q^86 - 2 * q^87 - 68 * q^88 - 53 * q^89 + 195 * q^90 + 80 * q^91 + 153 * q^92 - 85 * q^93 + 130 * q^94 - 92 * q^95 - 89 * q^96 - 4 * q^97 + 42 * q^98 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	−2.43956	+	1.17483i	−1.72503	+	0.830731i	−0.737110	+	0.675773i	$0.763810\pi$
$2$	−2.43956	+	1.17483i	−1.72503	+	0.830731i	−0.987921	+	0.154959i	$0.950476\pi$
$3$	−0.760566	+	3.33226i	−0.439113	+	1.92388i	−0.0609457	+	0.998141i	$0.519412\pi$
$3$	−0.760566	+	3.33226i	−0.439113	+	1.92388i	−0.378167	+	0.925737i	$0.623446\pi$
$4$	3.32426	−	4.16849i	1.66213	−	2.08424i
$5$	−0.286235	+	1.25408i	−0.128008	+	0.560840i	0.869725	+	0.493537i	$0.164296\pi$
$5$	−0.286235	+	1.25408i	−0.128008	+	0.560840i	−0.997733	+	0.0673024i	$0.978561\pi$
$6$	−2.05939	−	9.02278i	−0.840743	−	3.68353i
$7$	2.05845	−	1.66216i	0.778023	−	0.628236i
$7$	2.05845	−	1.66216i	0.778023	−	0.628236i
$8$	−2.00742	+	8.79508i	−0.709730	+	3.10953i
$9$	−7.82256	−	3.76715i	−2.60752	−	1.25572i
$10$	−0.775040	−	3.39567i	−0.245089	−	1.07381i
$11$	−2.85011	+	1.37254i	−0.859340	+	0.413836i	−0.811036	−	0.584996i	$-0.801096\pi$
$11$	−2.85011	+	1.37254i	−0.859340	+	0.413836i	−0.0483042	+	0.998833i	$0.515382\pi$
$12$	11.3621	+	14.2477i	3.27997	+	4.11295i
$13$	−2.25954	+	1.08814i	−0.626685	+	0.301795i	−0.720141	−	0.693828i	$-0.755923\pi$
$13$	−2.25954	+	1.08814i	−0.626685	+	0.301795i	0.0934561	+	0.995623i	$0.470209\pi$
$14$	−3.06897	+	6.47327i	−0.820218	+	1.73005i
$15$	−3.96120	−	1.90761i	−1.02278	−	0.492544i
$16$	−3.06268	−	13.4185i	−0.765670	−	3.35462i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$18$	23.5094			5.54121
$19$	−4.35071			−0.998121			−0.499060	−	0.866567i	$-0.666321\pi$
$19$	−4.35071			−0.998121			−0.499060	+	0.866567i	$0.666321\pi$
$20$	4.27608	+	5.36203i	0.956160	+	1.19899i
$21$	3.97314	+	8.12348i	0.867010	+	1.77269i
$22$	5.34052	−	6.69679i	1.13860	−	1.42776i
$23$	−2.84940	+	3.57304i	−0.594142	+	0.745030i	−0.984452	−	0.175653i	$-0.943796\pi$
$23$	−2.84940	+	3.57304i	−0.594142	+	0.745030i	0.390310	+	0.920683i	$0.372368\pi$
$24$	−27.7807	−	13.3785i	−5.67070	−	2.73087i
$25$	3.01407	+	1.45150i	0.602814	+	0.290300i
$26$	4.23392	−	5.30917i	0.830340	−	1.04121i
$27$	12.1095	−	15.1848i	2.33047	−	2.92232i
$28$	−0.0858448	−	14.1061i	−0.0162231	−	2.66580i
$29$	−4.93362	−	6.18657i	−0.916151	−	1.14882i	−0.988467	−	0.151435i	$-0.951611\pi$
$29$	−4.93362	−	6.18657i	−0.916151	−	1.14882i	0.0723164	−	0.997382i	$-0.476961\pi$
$30$	11.9047			2.17349
$31$	3.83175			0.688203			0.344101	−	0.938933i	$-0.388184\pi$
$31$	3.83175			0.688203			0.344101	+	0.938933i	$0.388184\pi$
$32$	11.9867	+	15.0309i	2.11897	+	2.65711i
$33$	−2.40596	−	10.5412i	−0.418824	−	1.83499i
$34$	−2.43956	−	1.17483i	−0.418381	−	0.201482i
$35$	1.49527	+	3.05722i	0.252747	+	0.516765i
$36$	−41.7075	+	20.0853i	−6.95125	+	3.34754i
$37$	−4.95930	−	6.21877i	−0.815305	−	1.02236i	−0.999223	−	0.0394180i	$-0.987450\pi$
$37$	−4.95930	−	6.21877i	−0.815305	−	1.02236i	0.183918	−	0.982942i	$-0.441122\pi$
$38$	10.6138	−	5.11135i	1.72179	−	0.829170i
$39$	−1.90743	−	8.35698i	−0.305433	−	1.33819i
$40$	−10.4551	−	5.03491i	−1.65310	−	0.796089i
$41$	0.0893082	−	0.391285i	0.0139476	−	0.0611084i	−0.967475	−	0.252966i	$-0.918594\pi$
$41$	0.0893082	−	0.391285i	0.0139476	−	0.0611084i	0.981423	+	0.191857i	$0.0614511\pi$
$42$	−19.2364	−	15.1500i	−2.96825	−	2.33769i
$43$	0.690193	+	3.02393i	0.105253	+	0.461145i	0.999897	+	0.0143643i	$0.00457247\pi$
$43$	0.690193	+	3.02393i	0.105253	+	0.461145i	−0.894643	+	0.446781i	$0.852570\pi$
$44$	−3.75308	+	16.4433i	−0.565798	+	2.47892i
$45$	6.96337	−	8.73179i	1.03804	−	1.30166i
$46$	2.75358	−	12.0642i	0.405993	−	1.77877i
$47$	8.00159	−	3.85337i	1.16715	−	0.562071i	0.253010	−	0.967464i	$-0.418579\pi$
$47$	8.00159	−	3.85337i	1.16715	−	0.562071i	0.914143	+	0.405393i	$0.132865\pi$
$48$	47.0432			6.79010
$49$	1.47447	−	6.84295i	0.210639	−	0.977564i
$50$	−9.05827			−1.28103
$51$	−3.07947	+	1.48299i	−0.431212	+	0.207661i
$52$	−2.97541	+	13.0361i	−0.412615	+	1.80779i
$53$	2.33215	−	2.92442i	0.320345	−	0.401700i	−0.595420	−	0.803415i	$-0.703014\pi$
$53$	2.33215	−	2.92442i	0.320345	−	0.401700i	0.915765	+	0.401715i	$0.131586\pi$
$54$	−11.7023	+	51.2709i	−1.59247	+	6.97709i
$55$	−0.905469	−	3.96712i	−0.122093	−	0.534926i
$56$	10.4866	+	21.4409i	1.40133	+	2.86516i
$57$	3.30900	−	14.4977i	0.438288	−	1.92026i
$58$	19.3041	+	9.29634i	2.53475	+	1.22067i
$59$	−0.244683	−	1.07203i	−0.0318550	−	0.139566i	0.956500	−	0.291733i	$-0.0942319\pi$
$59$	−0.244683	−	1.07203i	−0.0318550	−	0.139566i	−0.988355	+	0.152167i	$0.951375\pi$
$60$	−21.1199	+	10.1708i	−2.72657	+	1.31305i
$61$	0.712347	+	0.893256i	0.0912068	+	0.114370i	0.825341	−	0.564635i	$-0.190983\pi$
$61$	0.712347	+	0.893256i	0.0912068	+	0.114370i	−0.734134	+	0.679005i	$0.762412\pi$
$62$	−9.34779	+	4.50166i	−1.18717	+	0.571711i
$63$	−22.3640	+	5.24782i	−2.81760	+	0.661163i
$64$	−22.1000	−	10.6428i	−2.76251	−	1.33035i
$65$	−0.717849	−	3.14510i	−0.0890382	−	0.390102i
$66$	18.2536	+	22.8893i	2.24686	+	2.81748i
$67$	−5.09907			−0.622951			−0.311475	−	0.950254i	$-0.600823\pi$
$67$	−5.09907			−0.622951			−0.311475	+	0.950254i	$0.600823\pi$
$68$	5.33169			0.646563
$69$	−9.73912	−	12.2125i	−1.17245	−	1.47021i
$70$	−7.23953	−	5.70160i	−0.865289	−	0.681472i
$71$	−2.68369	+	3.36524i	−0.318495	+	0.399380i	−0.915147	−	0.403120i	$-0.867926\pi$
$71$	−2.68369	+	3.36524i	−0.318495	+	0.399380i	0.596652	+	0.802500i	$0.296497\pi$
$72$	48.8355	−	61.2378i	5.75532	−	7.21694i
$73$	7.60567	+	3.66270i	0.890176	+	0.428686i	0.822331	−	0.569010i	$-0.192673\pi$
$73$	7.60567	+	3.66270i	0.890176	+	0.428686i	0.0678452	+	0.997696i	$0.478388\pi$
$74$	19.4045	+	9.34473i	2.25573	+	1.08630i
$75$	−7.12916	+	8.93969i	−0.823205	+	1.03227i
$76$	−14.4629	+	18.1359i	−1.65900	+	2.08033i
$77$	−3.58544	+	7.56264i	−0.408599	+	0.861843i
$78$	14.4713	+	18.1465i	1.63855	+	2.05468i
$79$	7.50184			0.844023			0.422011	−	0.906591i	$-0.361324\pi$
$79$	7.50184			0.844023			0.422011	+	0.906591i	$0.361324\pi$
$80$	17.7044			1.97942
$81$	25.1495	+	31.5365i	2.79439	+	3.50405i
$82$	0.241821	+	1.05949i	0.0267046	+	0.117001i
$83$	1.56077	+	0.751627i	0.171317	+	0.0825018i	0.517577	−	0.855637i	$-0.326834\pi$
$83$	1.56077	+	0.751627i	0.171317	+	0.0825018i	−0.346260	+	0.938139i	$0.612548\pi$
$84$	47.0703	+	10.4425i	5.13579	+	1.13937i
$85$	−1.15894	+	0.558116i	−0.125705	+	0.0605362i
$86$	−5.23638	−	6.56621i	−0.564653	−	0.708052i
$87$	24.3676	−	11.7348i	2.61248	−	1.25810i
$88$	−6.35023	−	27.8222i	−0.676937	−	2.96586i
$89$	−0.335516	−	0.161576i	−0.0355646	−	0.0171270i	0.416017	−	0.909357i	$-0.363426\pi$
$89$	−0.335516	−	0.161576i	−0.0355646	−	0.0171270i	−0.451582	+	0.892230i	$0.649140\pi$
$90$	−6.72920	+	29.4825i	−0.709320	+	3.10773i
$91$	−2.84251	+	5.99560i	−0.297976	+	0.628510i
$92$	5.42201	+	23.7554i	0.565284	+	2.47667i
$93$	−2.91430	+	12.7684i	−0.302199	+	1.32402i
$94$	−14.9933	+	18.8010i	−1.54644	+	1.93918i
$95$	1.24532	−	5.45612i	0.127767	−	0.559786i
$96$	−59.2034	+	28.5109i	−6.04243	+	2.90988i
$97$	−18.2234			−1.85030			−0.925152	−	0.379596i	$-0.876063\pi$
$97$	−18.2234			−1.85030			−0.925152	+	0.379596i	$0.876063\pi$
$98$	4.44225	+	18.4261i	0.448735	+	1.86131i
$99$	27.4657			2.76041
$100$	16.0701	−	7.73895i	1.60701	−	0.773895i
$101$	1.34380	−	5.88758i	0.133713	−	0.585836i	−0.863027	−	0.505158i	$-0.831434\pi$
$101$	1.34380	−	5.88758i	0.133713	−	0.585836i	0.996740	−	0.0806780i	$-0.0257085\pi$
$102$	5.77028	−	7.23571i	0.571343	−	0.716442i
$103$	2.23912	−	9.81024i	0.220627	−	0.966631i	−0.736380	−	0.676568i	$-0.763466\pi$
$103$	2.23912	−	9.81024i	0.220627	−	0.966631i	0.957007	−	0.290063i	$-0.0936764\pi$
$104$	−5.03441	−	22.0572i	−0.493665	−	2.16289i
$105$	−11.3247	+	2.65740i	−1.10518	+	0.259336i
$106$	−2.25372	+	9.87419i	−0.218901	+	0.959066i
$107$	−8.20122	−	3.94950i	−0.792842	−	0.381812i	−0.00679291	−	0.999977i	$-0.502162\pi$
$107$	−8.20122	−	3.94950i	−0.792842	−	0.381812i	−0.786049	+	0.618165i	$0.787877\pi$
$108$	−23.0426	−	100.956i	−2.21728	−	9.71454i
$109$	−1.50441	+	0.724486i	−0.144096	+	0.0693932i	−0.504542	−	0.863387i	$-0.668339\pi$
$109$	−1.50441	+	0.724486i	−0.144096	+	0.0693932i	0.360446	+	0.932780i	$0.382625\pi$
$110$	6.86965	+	8.61426i	0.654995	+	0.821338i
$111$	24.4944	−	11.7959i	2.32491	−	1.11962i
$112$	−28.6080	−	22.5307i	−2.70320	−	2.12895i
$113$	0.410924	+	0.197891i	0.0386565	+	0.0186160i	0.453112	−	0.891454i	$-0.350314\pi$
$113$	0.410924	+	0.197891i	0.0386565	+	0.0186160i	−0.414456	+	0.910070i	$0.636028\pi$
$114$	8.95981	+	39.2555i	0.839163	+	3.67661i
$115$	−3.66526	−	4.59609i	−0.341788	−	0.428588i
$116$	−42.1892			−3.91717
$117$	21.7746			2.01306
$118$	1.85637	+	2.32781i	0.170893	+	0.214293i
$119$	2.58295	+	0.573027i	0.236779	+	0.0525293i
$120$	24.7294	−	31.0097i	2.25747	−	2.83078i
$121$	−0.619134	+	0.776369i	−0.0562849	+	0.0705790i
$122$	−2.78724	−	1.34226i	−0.252345	−	0.121523i
$123$	1.23594	+	0.595196i	0.111441	+	0.0536670i
$124$	12.7377	−	15.9726i	1.14388	−	1.43438i
$125$	−6.69308	+	8.39285i	−0.598647	+	0.750680i
$126$	48.3930	−	39.0763i	4.31119	−	3.48119i
$127$	6.39986	+	8.02517i	0.567896	+	0.712119i	0.979995	−	0.199020i	$-0.0637759\pi$
$127$	6.39986	+	8.02517i	0.567896	+	0.712119i	−0.412100	+	0.911139i	$0.635204\pi$
$128$	27.9675			2.47200
$129$	−10.6014			−0.933405
$130$	5.44620	+	6.82932i	0.477663	+	0.598971i
$131$	−4.37867	−	19.1842i	−0.382566	−	1.67613i	−0.689410	−	0.724372i	$-0.742130\pi$
$131$	−4.37867	−	19.1842i	−0.382566	−	1.67613i	0.306843	−	0.951760i	$-0.400727\pi$
$132$	−51.9389	−	25.0124i	−4.52070	−	2.17705i
$133$	−8.95573	+	7.23156i	−0.776561	+	0.627056i
$134$	12.4395	−	5.99055i	1.07461	−	0.517505i
$135$	15.5768	+	19.5326i	1.34063	+	1.68110i
$136$	−8.12787	+	3.91418i	−0.696959	+	0.335638i
$137$	−3.02510	−	13.2538i	−0.258452	−	1.13235i	−0.922907	−	0.385023i	$-0.874193\pi$
$137$	−3.02510	−	13.2538i	−0.258452	−	1.13235i	0.664455	−	0.747328i	$-0.268664\pi$
$138$	38.1068	+	18.3513i	3.24386	+	1.56216i
$139$	−1.22908	+	5.38493i	−0.104249	+	0.456744i	0.895679	+	0.444702i	$0.146690\pi$
$139$	−1.22908	+	5.38493i	−0.104249	+	0.456744i	−0.999927	+	0.0120422i	$0.996167\pi$
$140$	17.7147	+	3.92999i	1.49716	+	0.332145i
$141$	6.75466	+	29.5941i	0.568845	+	2.49227i
$142$	2.59344	−	11.3626i	0.217636	−	0.953528i
$143$	4.94643	−	6.20263i	0.413641	−	0.518690i
$144$	−26.5914	+	116.504i	−2.21595	+	9.70870i
$145$	9.17060	−	4.41633i	0.761577	−	0.366756i
$146$	−22.8576			−1.89170
$147$	21.6810	+	10.1178i	1.78822	+	0.834504i
$148$	−42.4089			−3.48599
$149$	−6.18428	+	2.97819i	−0.506636	+	0.243983i	−0.669699	−	0.742633i	$-0.733577\pi$
$149$	−6.18428	+	2.97819i	−0.506636	+	0.243983i	0.163063	+	0.986616i	$0.447863\pi$
$150$	6.88941	−	30.1845i	0.562518	−	2.46455i
$151$	0.842796	−	1.05683i	0.0685857	−	0.0860038i	−0.746355	−	0.665548i	$-0.768198\pi$
$151$	0.842796	−	1.05683i	0.0685857	−	0.0860038i	0.814941	+	0.579544i	$0.196769\pi$
$152$	8.73369	−	38.2648i	0.708396	−	3.10369i
$153$	−1.93201	−	8.46470i	−0.156194	−	0.684330i
$154$	−0.137912	−	22.6618i	−0.0111133	−	1.82614i
$155$	−1.09678	+	4.80531i	−0.0880955	+	0.385971i
$156$	−41.1767	−	19.8297i	−3.29678	−	1.58764i
$157$	−0.734838	−	3.21954i	−0.0586464	−	0.256947i	0.937103	−	0.349054i	$-0.113497\pi$
$157$	−0.734838	−	3.21954i	−0.0586464	−	0.256947i	−0.995749	+	0.0921070i	$0.970640\pi$
$158$	−18.3012	+	8.81339i	−1.45597	+	0.701156i
$159$	7.97117	+	9.99553i	0.632155	+	0.792697i
$160$	−22.2809	+	10.7299i	−1.76146	+	0.848274i
$161$	0.0735823	+	12.0911i	0.00579910	+	0.952911i
$162$	−98.4038	−	47.3888i	−7.73133	−	3.72321i
$163$	−0.147898	−	0.647982i	−0.0115842	−	0.0507539i	0.968805	−	0.247822i	$-0.0797150\pi$
$163$	−0.147898	−	0.647982i	−0.0115842	−	0.0507539i	−0.980390	+	0.197069i	$0.936858\pi$
$164$	−1.33418	−	1.67301i	−0.104182	−	0.130640i
$165$	13.9081			1.08275
$166$	−4.69063			−0.364064
$167$	−4.79139	−	6.00821i	−0.370769	−	0.464929i	0.561088	−	0.827756i	$-0.310383\pi$
$167$	−4.79139	−	6.00821i	−0.370769	−	0.464929i	−0.931856	+	0.362827i	$0.881812\pi$
$168$	−79.4223	+	18.6369i	−6.12757	+	1.43786i
$169$	−4.18388	+	5.24641i	−0.321837	+	0.403570i
$170$	2.17161	−	2.72312i	0.166555	−	0.208854i
$171$	34.0337	+	16.3897i	2.60262	+	1.25336i
$172$	14.8996	+	7.17526i	1.13608	+	0.547109i
$173$	−11.2321	+	14.0846i	−0.853960	+	1.07083i	0.142748	+	0.989759i	$0.454406\pi$
$173$	−11.2321	+	14.0846i	−0.853960	+	1.07083i	−0.996708	+	0.0810728i	$0.974165\pi$
$174$	−45.6598	+	57.2556i	−3.46146	+	4.34053i
$175$	8.61694	−	2.02201i	0.651380	−	0.152850i
$176$	27.1464	+	34.0405i	2.04624	+	2.56590i
$177$	3.75836			0.282496
$178$	1.00834			0.0755780
$179$	−0.960729	−	1.20472i	−0.0718083	−	0.0900447i	0.744630	−	0.667478i	$-0.232626\pi$
$179$	−0.960729	−	1.20472i	−0.0718083	−	0.0900447i	−0.816438	+	0.577433i	$0.804055\pi$
$180$	−13.2503	−	58.0534i	−0.987620	−	4.32705i
$181$	−15.9050	−	7.65947i	−1.18221	−	0.569324i	−0.263657	−	0.964616i	$-0.584929\pi$
$181$	−15.9050	−	7.65947i	−1.18221	−	0.569324i	−0.918555	+	0.395293i	$0.870643\pi$
$182$	−0.109336	−	17.9661i	−0.00810450	−	1.33174i
$183$	−3.51834	+	1.69434i	−0.260083	+	0.125250i
$184$	−25.7052	−	32.2333i	−1.89501	−	2.37627i
$185$	9.21833	−	4.43932i	0.677745	−	0.326385i
$186$	−7.89107	−	34.5730i	−0.578601	−	2.53502i
$187$	−2.85011	−	1.37254i	−0.208421	−	0.100370i
$188$	10.5367	−	46.1641i	0.768465	−	3.36686i
$189$	−0.312713	−	51.3851i	−0.0227465	−	3.73772i
$190$	3.37197	+	14.7736i	0.244629	+	1.07179i
$191$	0.259751	−	1.13804i	0.0187949	−	0.0823459i	−0.964661	−	0.263495i	$-0.915125\pi$
$191$	0.259751	−	1.13804i	0.0187949	−	0.0823459i	0.983456	+	0.181149i	$0.0579818\pi$
$192$	52.2731	−	65.5484i	3.77249	−	4.73055i
$193$	−3.16031	+	13.8462i	−0.227484	+	0.996674i	0.724198	+	0.689592i	$0.242210\pi$
$193$	−3.16031	+	13.8462i	−0.227484	+	0.996674i	−0.951683	+	0.307083i	$0.900647\pi$
$194$	44.4571	−	21.4094i	3.19183	−	1.53711i
$195$	11.0263			0.789606
$196$	−23.6232	−	28.8940i	−1.68737	−	2.06386i
$197$	10.0563			0.716481			0.358241	−	0.933629i	$-0.383377\pi$
$197$	10.0563			0.716481			0.358241	+	0.933629i	$0.383377\pi$
$198$	−67.0043	+	32.2676i	−4.76179	+	2.29316i
$199$	1.52816	−	6.69529i	0.108328	−	0.474616i	−0.891441	−	0.453136i	$-0.850305\pi$
$199$	1.52816	−	6.69529i	0.108328	−	0.474616i	0.999769	−	0.0214799i	$-0.00683779\pi$
$200$	−18.8165	+	23.5952i	−1.33053	+	1.66843i
$201$	3.87818	−	16.9914i	0.273546	−	1.19848i
$202$	3.63862	+	15.9418i	0.256013	+	1.12166i
$203$	−20.4387	−	4.53431i	−1.43451	−	0.318247i
$204$	−4.05510	+	17.7666i	−0.283914	+	1.24391i
$205$	0.465138	+	0.223999i	0.0324866	+	0.0156447i
$206$	6.06289	+	26.5633i	0.422422	+	1.85075i
$207$	35.7498	−	17.2162i	2.48478	−	1.19661i
$208$	21.5214	+	26.9870i	1.49224	+	1.87121i
$209$	12.4000	−	5.97152i	0.857725	−	0.413059i
$210$	24.5053	−	19.7875i	1.69103	−	1.36547i
$211$	−15.3898	−	7.41134i	−1.05948	−	0.510218i	−0.178777	−	0.983890i	$-0.557214\pi$
$211$	−15.3898	−	7.41134i	−1.05948	−	0.510218i	−0.880701	+	0.473672i	$0.842928\pi$
$212$	−4.43775	−	19.4431i	−0.304786	−	1.33535i
$213$	−9.17272	−	11.5022i	−0.628504	−	0.788119i
$214$	24.6474			1.68486
$215$	−3.98980			−0.272102
$216$	109.243	+	136.986i	7.43303	+	9.32073i
$217$	7.88749	−	6.36897i	0.535437	−	0.432354i
$218$	2.81895	−	3.53486i	0.190924	−	0.239411i
$219$	−17.9896	+	22.5583i	−1.21563	+	1.52435i
$220$	−19.5469	−	9.41329i	−1.31785	−	0.634644i
$221$	−2.25954	−	1.08814i	−0.151993	−	0.0731961i
$222$	−45.8975	+	57.5536i	−3.08044	+	3.86274i
$223$	7.21338	−	9.04529i	0.483043	−	0.605717i	−0.479268	−	0.877669i	$-0.659098\pi$
$223$	7.21338	−	9.04529i	0.483043	−	0.605717i	0.962311	+	0.271952i	$0.0876691\pi$
$224$	49.6578	+	11.0166i	3.31790	+	0.736076i
$225$	−18.1097	−	22.7089i	−1.20731	−	1.51392i
$226$	−1.23496			−0.0821486
$227$	3.48794			0.231503			0.115751	−	0.993278i	$-0.463072\pi$
$227$	3.48794			0.231503			0.115751	+	0.993278i	$0.463072\pi$
$228$	−49.4334	−	61.9875i	−3.27380	−	4.10522i
$229$	−4.32878	−	18.9656i	−0.286054	−	1.25328i	−0.889890	−	0.456175i	$-0.849219\pi$
$229$	−4.32878	−	18.9656i	−0.286054	−	1.25328i	0.603836	−	0.797108i	$-0.293638\pi$
$230$	14.3413	+	6.90639i	0.945636	+	0.455394i
$231$	−22.4737	−	17.6995i	−1.47866	−	1.16454i
$232$	64.3152	−	30.9726i	4.22250	−	2.03345i
$233$	2.65827	+	3.33337i	0.174149	+	0.218376i	0.861244	−	0.508191i	$-0.169686\pi$
$233$	2.65827	+	3.33337i	0.174149	+	0.218376i	−0.687095	+	0.726568i	$0.741114\pi$
$234$	−53.1205	+	25.5815i	−3.47259	+	1.67231i
$235$	2.54208	+	11.1376i	0.165827	+	0.726535i
$236$	−5.28212	−	2.54373i	−0.343836	−	0.165583i
$237$	−5.70564	+	24.9980i	−0.370621	+	1.62380i
$238$	−6.97448	+	1.63660i	−0.452089	+	0.106085i
$239$	1.48281	+	6.49663i	0.0959152	+	0.420232i	0.999974	−	0.00717553i	$-0.00228406\pi$
$239$	1.48281	+	6.49663i	0.0959152	+	0.420232i	−0.904059	+	0.427408i	$0.859427\pi$
$240$	−13.4654	+	58.9957i	−0.869187	+	3.80816i
$241$	−13.6327	+	17.0948i	−0.878158	+	1.10118i	0.116001	+	0.993249i	$0.462992\pi$
$241$	−13.6327	+	17.0948i	−0.878158	+	1.10118i	−0.994159	+	0.107926i	$0.965579\pi$
$242$	0.598313	−	2.62138i	0.0384610	−	0.168509i
$243$	−71.7192	+	34.5382i	−4.60079	+	2.21562i
$244$	6.09155			0.389971
$245$	8.15953	+	3.80779i	0.521293	+	0.243271i
$246$	−3.71440			−0.236821
$247$	9.83061	−	4.73417i	0.625507	−	0.301228i
$248$	−7.69193	+	33.7005i	−0.488438	+	2.13999i
$249$	−3.69168	+	4.62922i	−0.233951	+	0.293365i
$250$	6.46799	−	28.3381i	0.409072	−	1.79226i
$251$	−0.143016	−	0.626596i	−0.00902711	−	0.0395504i	0.970214	−	0.242250i	$-0.0778855\pi$
$251$	−0.143016	−	0.626596i	−0.00902711	−	0.0395504i	−0.979241	+	0.202700i	$0.935028\pi$
$252$	−52.4681	+	110.669i	−3.30518	+	6.97149i
$253$	3.21697	−	14.0945i	0.202249	−	0.886112i
$254$	−25.0411	−	12.0591i	−1.57122	−	0.756658i
$255$	−0.978336	−	4.28637i	−0.0612658	−	0.268423i
$256$	−24.0284	+	11.5715i	−1.50177	+	0.723217i
$257$	−13.4893	−	16.9151i	−0.841441	−	1.05513i	−0.997725	−	0.0674214i	$-0.978523\pi$
$257$	−13.4893	−	16.9151i	−0.841441	−	1.05513i	0.156284	−	0.987712i	$-0.450049\pi$
$258$	25.8629	−	12.4549i	1.61015	−	0.775409i
$259$	−20.5451	−	4.55792i	−1.27661	−	0.283215i
$260$	−15.4966	−	7.46278i	−0.961060	−	0.462822i
$261$	15.2879	+	66.9805i	0.946294	+	4.14599i
$262$	33.2202	+	41.6569i	2.05235	+	2.57357i
$263$	10.1917			0.628447			0.314224	−	0.949349i	$-0.398256\pi$
$263$	10.1917			0.628447			0.314224	+	0.949349i	$0.398256\pi$
$264$	97.5404			6.00320
$265$	2.99991	+	3.76176i	0.184283	+	0.231083i
$266$	13.3522	−	28.1633i	0.818677	−	1.72680i
$267$	0.793594	−	0.995135i	0.0485671	−	0.0609013i
$268$	−16.9506	+	21.2554i	−1.03542	+	1.29838i
$269$	6.96330	+	3.35335i	0.424560	+	0.204457i	0.633948	−	0.773375i	$-0.281433\pi$
$269$	6.96330	+	3.35335i	0.424560	+	0.204457i	−0.209389	+	0.977832i	$0.567147\pi$
$270$	−60.9480	−	29.3510i	−3.70918	−	1.78625i
$271$	3.54128	−	4.44062i	0.215117	−	0.269749i	−0.662551	−	0.749017i	$-0.730526\pi$
$271$	3.54128	−	4.44062i	0.215117	−	0.269749i	0.877669	+	0.479268i	$0.159098\pi$
$272$	8.58144	−	10.7608i	0.520326	−	0.652469i
$273$	−17.8170	−	14.0320i	−1.07833	−	0.849256i
$274$	22.9509	+	28.7796i	1.38652	+	1.73864i
$275$	−10.5827			−0.638159
$276$	−83.2828			−5.01304
$277$	15.9764	+	20.0337i	0.959927	+	1.20371i	0.978993	+	0.203892i	$0.0653590\pi$
$277$	15.9764	+	20.0337i	0.959927	+	1.20371i	−0.0190669	+	0.999818i	$0.506070\pi$
$278$	−3.32798	−	14.5808i	−0.199599	−	0.874500i
$279$	−29.9741	−	14.4348i	−1.79450	−	0.864187i
$280$	−29.8902	+	7.01388i	−1.78628	+	0.419159i
$281$	−12.9744	+	6.24813i	−0.773986	+	0.372732i	−0.778813	−	0.627256i	$-0.784178\pi$
$281$	−12.9744	+	6.24813i	−0.773986	+	0.372732i	0.00482665	+	0.999988i	$0.498464\pi$
$282$	−51.2465	−	64.2611i	−3.05168	−	3.82669i
$283$	29.0227	−	13.9766i	1.72522	−	0.830824i	0.737359	−	0.675501i	$-0.236072\pi$
$283$	29.0227	−	13.9766i	1.72522	−	0.830824i	0.987864	−	0.155323i	$-0.0496418\pi$
$284$	5.10668	+	22.3738i	0.303026	+	1.32764i
$285$	17.2340	+	8.29947i	1.02086	+	0.491618i
$286$	−4.78009	+	20.9429i	−0.282652	+	1.23838i
$287$	−0.466540	−	0.953887i	−0.0275390	−	0.0563061i
$288$	−37.1434	−	162.736i	−2.18869	−	9.58930i
$289$	−0.222521	+	0.974928i	−0.0130895	+	0.0573487i
$290$	−17.1838	+	21.5478i	−1.00907	+	1.26533i
$291$	13.8601	−	60.7250i	0.812492	−	3.55976i
$292$	40.5511	−	19.5284i	2.37307	−	1.14281i
$293$	−5.08785			−0.297235			−0.148618	−	0.988895i	$-0.547482\pi$
$293$	−5.08785			−0.297235			−0.148618	+	0.988895i	$0.547482\pi$
$294$	−64.7789	+	0.788475i	−3.77798	+	0.0459848i
$295$	1.41444			0.0823518
$296$	64.6500	−	31.1338i	3.75770	−	1.80961i
$297$	−13.6716	+	59.8991i	−0.793306	+	3.47570i
$298$	11.5881	−	14.5310i	0.671278	−	0.841757i
$299$	2.55039	−	11.1740i	0.147493	−	0.646208i
$300$	13.5658	+	59.4356i	0.783221	+	3.43152i
$301$	6.44698	+	5.07742i	0.371598	+	0.292657i
$302$	−0.814453	+	3.56835i	−0.0468665	+	0.205335i
$303$	18.5969	+	8.95577i	1.06836	+	0.514496i
$304$	13.3248	+	58.3799i	0.764231	+	3.34832i
$305$	−1.32411	+	0.637657i	−0.0758182	+	0.0365121i
$306$	14.6579	+	18.3804i	0.837934	+	1.05074i
$307$	8.86819	−	4.27069i	0.506134	−	0.243741i	−0.163349	−	0.986568i	$-0.552230\pi$
$307$	8.86819	−	4.27069i	0.506134	−	0.243741i	0.669484	+	0.742827i	$0.266515\pi$
$308$	19.6058	+	40.0860i	1.11715	+	2.28411i
$309$	30.9872	+	14.9227i	1.76280	+	0.848920i
$310$	−2.96976	−	13.0114i	−0.168671	−	0.738996i
$311$	−10.8832	−	13.6471i	−0.617129	−	0.773855i	0.370808	−	0.928709i	$-0.379081\pi$
$311$	−10.8832	−	13.6471i	−0.617129	−	0.773855i	−0.987937	+	0.154854i	$0.950509\pi$
$312$	77.3293			4.37791
$313$	−2.90606			−0.164260			−0.0821301	−	0.996622i	$-0.526172\pi$
$313$	−2.90606			−0.164260			−0.0821301	+	0.996622i	$0.526172\pi$
$314$	5.57509	+	6.99095i	0.314621	+	0.394522i
$315$	−0.179820	−	29.5482i	−0.0101317	−	1.66485i
$316$	24.9380	−	31.2713i	1.40287	−	1.75915i
$317$	−3.00778	+	3.77164i	−0.168934	+	0.211837i	−0.859091	−	0.511823i	$-0.828970\pi$
$317$	−3.00778	+	3.77164i	−0.168934	+	0.211837i	0.690157	+	0.723660i	$0.257542\pi$
$318$	−31.1892	−	15.0199i	−1.74900	−	0.842276i
$319$	22.5527	+	10.8608i	1.26271	+	0.608088i
$320$	19.6727	−	24.6688i	1.09974	−	1.37903i
$321$	19.3983	−	24.3247i	1.08271	−	1.35767i
$322$	−14.3845	−	29.4105i	−0.801617	−	1.63898i
$323$	−2.71262	−	3.40152i	−0.150934	−	0.189266i
$324$	215.063			11.9479
$325$	−8.38985			−0.465385
$326$	1.12208	+	1.40704i	0.0621460	+	0.0779286i
$327$	−1.26997	−	5.56410i	−0.0702295	−	0.307695i
$328$	3.26210	+	1.57095i	0.180119	+	0.0867410i
$329$	10.0660	−	21.2319i	0.554958	−	1.17055i
$330$	−33.9297	+	16.3397i	−1.86777	+	0.899471i
$331$	−21.6108	−	27.0990i	−1.18784	−	1.48950i	−0.831845	−	0.555009i	$-0.812715\pi$
$331$	−21.6108	−	27.0990i	−1.18784	−	1.48950i	−0.355991	−	0.934489i	$-0.615857\pi$
$332$	8.32155	−	4.00745i	0.456704	−	0.219937i
$333$	15.3674	+	67.3291i	0.842130	+	3.68961i
$334$	18.7475	+	9.02833i	1.02582	+	0.494008i
$335$	1.45953	−	6.39462i	0.0797427	−	0.349376i
$336$	96.8363	−	78.1931i	5.28285	−	4.26579i
$337$	−5.82939	−	25.5402i	−0.317547	−	1.39126i	−0.841840	−	0.539727i	$-0.818528\pi$
$337$	−5.82939	−	25.5402i	−0.317547	−	1.39126i	0.524293	−	0.851538i	$-0.324330\pi$
$338$	4.04317	−	17.7143i	0.219920	−	0.963531i
$339$	−0.971957	+	1.21880i	−0.0527895	+	0.0661959i
$340$	−1.52612	+	6.68635i	−0.0827652	+	0.362618i
$341$	−10.9209	+	5.25923i	−0.591400	+	0.284803i
$342$	−102.282			−5.53080
$343$	−8.33892	−	16.5367i	−0.450259	−	0.892898i
$344$	−27.9812			−1.50865
$345$	18.1030	−	8.71796i	0.974635	−	0.469359i
$346$	10.8544	−	47.5561i	0.583534	−	2.55663i
$347$	−18.2174	+	22.8439i	−0.977962	+	1.22633i	−0.00391151	+	0.999992i	$0.501245\pi$
$347$	−18.2174	+	22.8439i	−0.977962	+	1.22633i	−0.974050	+	0.226333i	$0.927326\pi$
$348$	32.0877	−	140.585i	1.72008	−	7.53616i
$349$	4.69818	+	20.5841i	0.251488	+	1.10184i	0.930089	+	0.367333i	$0.119729\pi$
$349$	4.69818	+	20.5841i	0.251488	+	1.10184i	−0.678602	+	0.734506i	$0.737414\pi$
$350$	−18.6460	+	15.0563i	−0.996673	+	0.804792i
$351$	−10.8387	+	47.4876i	−0.578528	+	2.53470i
$352$	−54.7940	−	26.3874i	−2.92053	−	1.40645i
$353$	−4.93750	−	21.6326i	−0.262796	−	1.15139i	−0.918203	−	0.396110i	$-0.870360\pi$
$353$	−4.93750	−	21.6326i	−0.262796	−	1.15139i	0.655407	−	0.755276i	$-0.272497\pi$
$354$	−9.16876	+	4.41544i	−0.487314	+	0.234678i
$355$	−3.45210	−	4.32880i	−0.183218	−	0.229749i
$356$	−1.78887	+	0.861473i	−0.0948098	+	0.0456580i
$357$	−3.87398	+	8.17123i	−0.205033	+	0.432467i
$358$	3.75910	+	1.81029i	0.198674	+	0.0956766i
$359$	−5.89359	−	25.8215i	−0.311052	−	1.36281i	−0.852788	−	0.522258i	$-0.825090\pi$
$359$	−5.89359	−	25.8215i	−0.311052	−	1.36281i	0.541736	−	0.840549i	$-0.317767\pi$
$360$	62.8184	+	78.7718i	3.31082	+	4.15164i
$361$	−0.0713432			−0.00375491
$362$	47.7999			2.51231
$363$	−2.11617	−	2.65359i	−0.111070	−	0.139277i
$364$	15.5433	+	31.7799i	0.814692	+	1.66572i
$365$	−6.77030	+	8.48969i	−0.354374	+	0.444371i
$366$	6.59265	−	8.26692i	0.344603	−	0.432119i
$367$	−11.3284	−	5.45545i	−0.591335	−	0.284772i	0.114187	−	0.993459i	$-0.463574\pi$
$367$	−11.3284	−	5.45545i	−0.591335	−	0.284772i	−0.705523	+	0.708687i	$0.749288\pi$
$368$	56.6716	+	27.2916i	2.95421	+	1.42267i
$369$	−2.17265	+	2.72441i	−0.113103	+	0.141827i
$370$	−17.2733	+	21.6600i	−0.897994	+	1.12605i
$371$	−0.0602249	−	9.89619i	−0.00312672	−	0.513784i
$372$	43.5369	+	54.5935i	2.25728	+	2.83054i
$373$	20.2699			1.04954			0.524768	−	0.851245i	$-0.324152\pi$
$373$	20.2699			1.04954			0.524768	+	0.851245i	$0.324152\pi$
$374$	8.56552			0.442913
$375$	−22.8766	−	28.6864i	−1.18134	−	1.48136i
$376$	17.8281	+	78.1100i	0.919413	+	4.02821i
$377$	17.8796	+	8.61035i	0.920845	+	0.443456i
$378$	61.1317	+	124.990i	3.14428	+	6.42878i
$379$	27.5161	−	13.2511i	1.41341	−	0.680662i	0.437577	−	0.899181i	$-0.355837\pi$
$379$	27.5161	−	13.2511i	1.41341	−	0.680662i	0.975833	+	0.218519i	$0.0701226\pi$
$380$	−18.6040	−	23.3286i	−0.954364	−	1.19673i
$381$	−31.6094	+	15.2223i	−1.61940	+	0.779862i
$382$	0.703330	+	3.08149i	0.0359855	+	0.157663i
$383$	2.05349	+	0.988906i	0.104928	+	0.0505308i	0.485612	−	0.874175i	$-0.338597\pi$
$383$	2.05349	+	0.988906i	0.104928	+	0.0505308i	−0.380683	+	0.924705i	$0.624311\pi$
$384$	−21.2711	+	93.1949i	−1.08549	+	4.75583i
$385$	−8.45784	−	6.66111i	−0.431052	−	0.339481i
$386$	−8.55722	−	37.4916i	−0.435551	−	1.90827i
$387$	5.99252	−	26.2549i	0.304617	−	1.33461i
$388$	−60.5792	+	75.9639i	−3.07544	+	3.85648i
$389$	−7.06825	+	30.9680i	−0.358375	+	1.57014i	0.398868	+	0.917008i	$0.369403\pi$
$389$	−7.06825	+	30.9680i	−0.358375	+	1.57014i	−0.757243	+	0.653134i	$0.773454\pi$
$390$	−26.8992	+	12.9540i	−1.36210	+	0.655951i
$391$	−4.57009			−0.231119
$392$	57.2244	+	26.7047i	2.89027	+	1.34879i
$393$	67.2569			3.39266
$394$	−24.5330	+	11.8145i	−1.23595	+	0.595204i
$395$	−2.14729	+	9.40787i	−0.108042	+	0.473361i
$396$	91.3030	−	114.490i	4.58815	−	5.75336i
$397$	−5.82547	+	25.5231i	−0.292372	+	1.28097i	0.588842	+	0.808248i	$0.299584\pi$
$397$	−5.82547	+	25.5231i	−0.292372	+	1.28097i	−0.881214	+	0.472717i	$0.843273\pi$
$398$	4.13780	+	18.1289i	0.207409	+	0.908719i
$399$	−17.2860	−	35.3429i	−0.865381	−	1.76936i
$400$	10.2458	−	44.8897i	0.512289	−	2.24449i
$401$	−9.37312	−	4.51386i	−0.468071	−	0.225411i	0.184954	−	0.982747i	$-0.440786\pi$
$401$	−9.37312	−	4.51386i	−0.468071	−	0.225411i	−0.653026	+	0.757336i	$0.726501\pi$
$402$	10.5010	+	46.0078i	0.523741	+	2.29466i
$403$	−8.65801	+	4.16948i	−0.431286	+	0.207696i
$404$	−20.0751	−	25.1734i	−0.998775	−	1.25242i
$405$	−46.7478	+	22.5125i	−2.32292	+	1.11866i
$406$	55.1885	−	12.9503i	2.73896	−	0.642711i
$407$	22.6701	+	10.9173i	1.12371	+	0.541152i
$408$	−6.86126	−	30.0611i	−0.339683	−	1.48825i
$409$	−9.57801	−	12.0104i	−0.473602	−	0.593878i	0.486447	−	0.873710i	$-0.338293\pi$
$409$	−9.57801	−	12.0104i	−0.473602	−	0.593878i	−0.960049	+	0.279832i	$0.909721\pi$
$410$	−1.39789			−0.0690370
$411$	46.4659			2.29200
$412$	−33.4504	−	41.9455i	−1.64798	−	2.06651i
$413$	−2.28554	−	1.80002i	−0.112464	−	0.0885730i
$414$	−66.9877	+	83.9999i	−3.29227	+	4.12837i
$415$	−1.38934	+	1.74218i	−0.0682002	+	0.0855204i
$416$	−43.4402	−	20.9197i	−2.12983	−	1.02567i
$417$	−17.0092	−	8.19119i	−0.832943	−	0.401124i
$418$	−23.2350	+	29.1358i	−1.13646	+	1.42508i
$419$	−7.90278	+	9.90978i	−0.386076	+	0.484124i	−0.936453	−	0.350792i	$-0.885912\pi$
$419$	−7.90278	+	9.90978i	−0.386076	+	0.484124i	0.550377	+	0.834916i	$0.314484\pi$
$420$	−26.5689	+	56.0407i	−1.29643	+	2.73451i
$421$	−12.0326	−	15.0885i	−0.586435	−	0.735367i	0.396760	−	0.917922i	$-0.370134\pi$
$421$	−12.0326	−	15.0885i	−0.586435	−	0.735367i	−0.983196	+	0.182556i	$0.941563\pi$
$422$	46.2515			2.25149
$423$	−77.1091			−3.74917
$424$	21.0389	+	26.3820i	1.02174	+	1.28122i
$425$	0.744413	+	3.26149i	0.0361094	+	0.158205i
$426$	35.8906	+	17.2840i	1.73890	+	0.837412i
$427$	2.95107	+	0.654693i	0.142812	+	0.0316828i
$428$	−43.7264	+	21.0575i	−2.11359	+	1.01785i
$429$	16.9067	+	21.2003i	0.816261	+	1.02356i
$430$	9.73335	−	4.68734i	0.469384	−	0.226043i
$431$	−5.21801	−	22.8616i	−0.251343	−	1.10120i	−0.930235	−	0.366965i	$-0.880397\pi$
$431$	−5.21801	−	22.8616i	−0.251343	−	1.10120i	0.678892	−	0.734238i	$-0.262460\pi$
$432$	−240.845	−	115.985i	−11.5876	−	5.58032i
$433$	2.89219	−	12.6715i	0.138990	−	0.608953i	−0.856668	−	0.515867i	$-0.827470\pi$
$433$	2.89219	−	12.6715i	0.138990	−	0.608953i	0.995658	−	0.0930860i	$-0.0296732\pi$
$434$	−11.7595	+	24.8040i	−0.564476	+	1.19063i
$435$	7.74149	+	33.9177i	0.371176	+	1.62623i
$436$	−1.98104	+	8.67949i	−0.0948745	+	0.415672i
$437$	12.3969	−	15.5452i	0.593025	−	0.743630i
$438$	17.3847	−	76.1672i	0.830671	−	3.63941i
$439$	−24.9038	+	11.9930i	−1.18859	+	0.572396i	−0.920404	−	0.390970i	$-0.872140\pi$
$439$	−24.9038	+	11.9930i	−1.18859	+	0.572396i	−0.268190	+	0.963366i	$0.586425\pi$
$440$	36.7088			1.75002
$441$	−37.3125	+	47.9748i	−1.77679	+	2.28451i
$442$	6.79068			0.323000
$443$	2.02533	−	0.975349i	0.0962265	−	0.0463403i	−0.385151	−	0.922853i	$-0.625851\pi$
$443$	2.02533	−	0.975349i	0.0962265	−	0.0463403i	0.481378	+	0.876513i	$0.340136\pi$
$444$	32.2547	−	141.317i	1.53074	−	6.70661i
$445$	0.298665	−	0.374514i	0.0141581	−	0.0177536i
$446$	−6.97079	+	30.5410i	−0.330077	+	1.44616i
$447$	−5.22055	−	22.8727i	−0.246923	−	1.08184i
$448$	−63.1820	+	14.8260i	−2.98507	+	0.700461i
$449$	9.07667	−	39.7675i	0.428354	−	1.87674i	−0.0502907	−	0.998735i	$-0.516015\pi$
$449$	9.07667	−	39.7675i	0.428354	−	1.87674i	0.478645	−	0.878008i	$-0.341128\pi$
$450$	70.8589	+	34.1238i	3.34032	+	1.60861i
$451$	0.282516	+	1.23778i	0.0133032	+	0.0582850i
$452$	2.19092	−	1.05509i	0.103052	−	0.0496274i
$453$	2.88063	+	3.61220i	0.135344	+	0.169716i
$454$	−8.50905	+	4.09774i	−0.399349	+	0.192317i
$455$	−6.70531	−	5.28087i	−0.314350	−	0.247571i
$456$	120.866	+	58.2058i	5.66005	+	2.72574i
$457$	3.30497	+	14.4800i	0.154600	+	0.677347i	0.991513	+	0.130010i	$0.0415011\pi$
$457$	3.30497	+	14.4800i	0.154600	+	0.677347i	−0.836913	+	0.547337i	$0.815642\pi$
$458$	32.8417	+	41.1822i	1.53459	+	1.92432i
$459$	19.4221			0.906546
$460$	−31.3430			−1.46138
$461$	23.1054	+	28.9732i	1.07612	+	1.34942i	0.933067	+	0.359702i	$0.117122\pi$
$461$	23.1054	+	28.9732i	1.07612	+	1.34942i	0.143056	+	0.989715i	$0.454307\pi$
$462$	75.6199	+	16.7762i	3.51815	+	0.780501i
$463$	−2.00496	+	2.51414i	−0.0931785	+	0.116842i	−0.826235	−	0.563326i	$-0.809522\pi$
$463$	−2.00496	+	2.51414i	−0.0931785	+	0.116842i	0.733056	+	0.680168i	$0.238093\pi$
$464$	−67.9042	+	85.1492i	−3.15238	+	3.95295i
$465$	−15.1783	−	7.30950i	−0.703878	−	0.338970i
$466$	−10.4012	−	5.00894i	−0.481825	−	0.232035i
$467$	−7.19261	+	9.01924i	−0.332834	+	0.417361i	−0.919884	−	0.392190i	$-0.871718\pi$
$467$	−7.19261	+	9.01924i	−0.332834	+	0.417361i	0.587050	+	0.809551i	$0.300289\pi$
$468$	72.3843	−	90.7671i	3.34597	−	4.19571i
$469$	−10.4962	+	8.47546i	−0.484670	+	0.391360i
$470$	−19.2863	−	24.1843i	−0.889612	−	1.11554i
$471$	11.2872			0.520087
$472$	9.91974			0.456593
$473$	−6.11759	−	7.67122i	−0.281287	−	0.352723i
$474$	−15.4492	−	67.6874i	−0.709606	−	3.10899i
$475$	−13.1133	−	6.31505i	−0.601681	−	0.289754i
$476$	10.9750	−	8.86211i	0.503041	−	0.406194i
$477$	−29.2601	+	14.0909i	−1.33973	+	0.645179i
$478$	−11.2499	−	14.1069i	−0.514557	−	0.645234i
$479$	−9.64516	+	4.64487i	−0.440699	+	0.212229i	−0.641057	−	0.767493i	$-0.721504\pi$
$479$	−9.64516	+	4.64487i	−0.440699	+	0.212229i	0.200358	+	0.979723i	$0.435789\pi$
$480$	−18.8087	−	82.4064i	−0.858497	−	3.76132i
$481$	17.9727	+	8.65517i	0.819482	+	0.394642i
$482$	13.1742	−	57.7200i	0.600069	−	2.62908i
$483$	−40.3466	−	8.95087i	−1.83583	−	0.407279i
$484$	1.17812	+	5.16170i	0.0535511	+	0.234623i
$485$	5.21616	−	22.8535i	0.236854	−	1.03772i
$486$	134.387	−	168.516i	6.09592	−	7.64404i
$487$	−6.69871	+	29.3490i	−0.303548	+	1.32993i	0.561182	+	0.827692i	$0.310347\pi$
$487$	−6.69871	+	29.3490i	−0.303548	+	1.32993i	−0.864730	+	0.502237i	$0.832510\pi$
$488$	−9.28623	+	4.47201i	−0.420368	+	0.202439i
$489$	2.27173			0.102731
$490$	−24.3792	+	0.296738i	−1.10134	+	0.0134053i
$491$	20.3456			0.918185			0.459093	−	0.888388i	$-0.348175\pi$
$491$	20.3456			0.918185			0.459093	+	0.888388i	$0.348175\pi$
$492$	6.58963	−	3.17340i	0.297084	−	0.143068i
$493$	1.76079	−	7.71452i	0.0793020	−	0.347445i
$494$	−18.4205	+	23.0986i	−0.828779	+	1.03926i
$495$	−7.86163	+	34.4441i	−0.353354	+	1.54815i
$496$	−11.7354	−	51.4163i	−0.526936	−	2.30866i
$497$	0.0693029	+	11.3879i	0.00310866	+	0.510817i
$498$	3.56753	−	15.6304i	0.159865	−	0.700414i
$499$	−33.4958	−	16.1307i	−1.49948	−	0.722111i	−0.509128	−	0.860691i	$-0.670032\pi$
$499$	−33.4958	−	16.1307i	−1.49948	−	0.722111i	−0.990351	+	0.138580i	$0.955746\pi$
$500$	12.7360	+	55.8000i	0.569571	+	2.49545i
$501$	23.6650	−	11.3965i	1.05728	−	0.509157i
$502$	1.08504	+	1.36060i	0.0484278	+	0.0607265i
$503$	12.4756	−	6.00795i	0.556261	−	0.267881i	−0.134562	−	0.990905i	$-0.542963\pi$
$503$	12.4756	−	6.00795i	0.556261	−	0.267881i	0.690823	+	0.723024i	$0.257248\pi$
$504$	−1.26112	−	207.227i	−0.0561746	−	9.23064i
$505$	6.99882	+	3.37046i	0.311444	+	0.149983i
$506$	8.71062	+	38.1637i	0.387234	+	1.69658i
$507$	−14.3003	−	17.9320i	−0.635098	−	0.796387i
$508$	54.7276			2.42814
$509$	−2.03117			−0.0900300			−0.0450150	−	0.998986i	$-0.514334\pi$
$509$	−2.03117			−0.0900300			−0.0450150	+	0.998986i	$0.514334\pi$
$510$	7.42247	+	9.30748i	0.328673	+	0.412142i
$511$	21.7439	−	5.10232i	0.961893	−	0.225713i
$512$	10.1493	−	12.7269i	0.448541	−	0.562453i
$513$	−52.6848	+	66.0647i	−2.32609	+	2.91683i
$514$	52.7804	+	25.4177i	2.32804	+	1.12113i
$515$	11.6619	+	5.61606i	0.513883	+	0.247473i
$516$	−35.2419	+	44.1920i	−1.55144	+	1.94544i
$517$	−17.5165	+	21.9650i	−0.770376	+	0.966020i
$518$	55.4758	−	13.0177i	2.43747	−	0.571964i
$519$	−38.3907	−	48.1404i	−1.68517	−	2.11313i
$520$	29.1024			1.27623
$521$	1.29663			0.0568066			0.0284033	−	0.999597i	$-0.490958\pi$
$521$	1.29663			0.0568066			0.0284033	+	0.999597i	$0.490958\pi$
$522$	−115.986	−	145.442i	−5.07659	−	6.36584i
$523$	3.82163	+	16.7437i	0.167108	+	0.732149i	0.987144	+	0.159836i	$0.0510966\pi$
$523$	3.82163	+	16.7437i	0.167108	+	0.732149i	−0.820035	+	0.572313i	$0.806046\pi$
$524$	−94.5249	−	45.5208i	−4.12934	−	1.98859i
$525$	0.184102	+	30.2517i	0.00803486	+	1.32029i
$526$	−24.8633	+	11.9735i	−1.08409	+	0.522071i
$527$	2.38906	+	2.99578i	0.104069	+	0.130498i
$528$	−134.078	+	64.5687i	−5.83500	+	2.80999i
$529$	0.470476	+	2.06129i	0.0204555	+	0.0896213i
$530$	−11.7379	−	5.65267i	−0.509861	−	0.245536i
$531$	−2.12443	+	9.30775i	−0.0921925	+	0.403922i
$532$	0.373486	+	61.3714i	0.0161927	+	2.66079i
$533$	0.223977	+	0.981305i	0.00970150	+	0.0425050i
$534$	−0.766906	+	3.36003i	−0.0331872	+	0.145403i
$535$	7.30044	−	9.15447i	0.315626	−	0.395782i
$536$	10.2360	−	44.8467i	0.442127	−	1.93708i
$537$	4.74512	−	2.28513i	0.204767	−	0.0986106i
$538$	−20.9270			−0.902227
$539$	5.18982	+	21.5269i	0.223541	+	0.927230i
$540$	133.203			5.73213
$541$	−34.5087	+	16.6185i	−1.48365	+	0.714487i	−0.988060	−	0.154071i	$-0.950761\pi$
$541$	−34.5087	+	16.6185i	−1.48365	+	0.714487i	−0.495587	+	0.868558i	$0.665047\pi$
$542$	−3.42219	+	14.9936i	−0.146996	+	0.644029i
$543$	37.6201	−	47.1741i	1.61443	−	2.02444i
$544$	−4.27801	+	18.7432i	−0.183418	+	0.803608i
$545$	−0.477946	−	2.09402i	−0.0204730	−	0.0896979i
$546$	59.9508	+	13.3001i	2.56566	+	0.569190i
$547$	−2.27177	+	9.95326i	−0.0971337	+	0.425571i	−0.999990	−	0.00437094i	$-0.998609\pi$
$547$	−2.27177	+	9.95326i	−0.0971337	+	0.425571i	0.902857	+	0.429942i	$0.141466\pi$
$548$	−65.3046	−	31.4490i	−2.78967	−	1.34344i
$549$	−2.20736	−	9.67106i	−0.0942077	−	0.412751i
$550$	25.8171	−	12.4328i	1.10084	−	0.530138i
$551$	21.4648	+	26.9159i	0.914429	+	1.14666i
$552$	126.960	−	61.1408i	5.40378	−	2.60232i
$553$	15.4422	−	12.4692i	0.656669	−	0.530246i
$554$	−62.5116	−	30.1040i	−2.65586	−	1.27900i
$555$	7.78179	+	34.0942i	0.330318	+	1.44722i
$556$	18.3613	+	23.0243i	0.778691	+	0.976447i
$557$	−39.9773			−1.69389			−0.846946	−	0.531679i	$-0.821561\pi$
$557$	−39.9773			−1.69389			−0.846946	+	0.531679i	$0.821561\pi$
$558$	90.0821			3.81348
$559$	−4.84998	−	6.08168i	−0.205132	−	0.257228i
$560$	36.4438	−	29.4276i	1.54003	−	1.24354i
$561$	6.74135	−	8.45338i	0.284620	−	0.356902i
$562$	24.3113	−	30.4854i	1.02551	−	1.28595i
$563$	−42.3637	−	20.4013i	−1.78542	−	0.859811i	−0.951328	−	0.308180i	$-0.900280\pi$
$563$	−42.3637	−	20.4013i	−1.78542	−	0.859811i	−0.834088	−	0.551631i	$-0.814006\pi$
$564$	145.817	+	70.2217i	6.13999	+	2.95686i
$565$	−0.365791	+	0.458687i	−0.0153889	+	0.0192971i
$566$	−54.3826	+	68.1937i	−2.28587	+	2.86639i
$567$	104.188	+	23.1140i	4.37547	+	0.970696i
$568$	−24.2102	−	30.3587i	−1.01584	−	1.27382i
$569$	−27.4044			−1.14885			−0.574427	−	0.818556i	$-0.694775\pi$
$569$	−27.4044			−1.14885			−0.574427	+	0.818556i	$0.694775\pi$
$570$	−51.7940			−2.16941
$571$	−25.1410	−	31.5259i	−1.05212	−	1.31932i	−0.945716	−	0.324994i	$-0.894638\pi$
$571$	−25.1410	−	31.5259i	−1.05212	−	1.31932i	−0.106404	−	0.994323i	$-0.533934\pi$
$572$	−9.41236	−	41.2383i	−0.393551	−	1.72426i
$573$	3.59469	+	1.73111i	0.150170	+	0.0723183i
$574$	2.25881	+	1.77896i	0.0942809	+	0.0742524i
$575$	−13.7746	+	6.63348i	−0.574439	+	0.276635i
$576$	132.786	+	166.508i	5.53274	+	6.93784i
$577$	−13.3439	+	6.42606i	−0.555512	+	0.267521i	−0.690507	−	0.723326i	$-0.742612\pi$
$577$	−13.3439	+	6.42606i	−0.555512	+	0.267521i	0.134995	+	0.990846i	$0.456898\pi$
$578$	−0.602522	−	2.63982i	−0.0250616	−	0.109802i
$579$	−43.7356	−	21.0620i	−1.81759	−	0.875305i
$580$	12.0760	−	52.9085i	0.501430	−	2.19691i
$581$	4.46210	−	1.04705i	0.185119	−	0.0434391i
$582$	37.5291	+	164.426i	1.55563	+	6.81566i
$583$	−2.63299	+	11.5359i	−0.109047	+	0.477768i
$584$	−47.4815	+	59.5399i	−1.96480	+	2.46378i
$585$	−6.23264	+	27.3070i	−0.257688	+	1.12900i
$586$	12.4121	−	5.97737i	0.512740	−	0.246923i
$587$	0.00360154			0.000148651			7.43257e−5	−	1.00000i	$-0.499976\pi$
$587$	0.00360154			0.000148651			7.43257e−5		1.00000i	$0.499976\pi$
$588$	114.249	−	56.7428i	4.71156	−	2.34003i
$589$	−16.6708			−0.686909
$590$	−3.45061	+	1.66173i	−0.142059	+	0.0684122i
$591$	−7.64847	+	33.5101i	−0.314616	+	1.37842i
$592$	−68.2577	+	85.5925i	−2.80537	+	3.51783i
$593$	−3.27399	+	14.3443i	−0.134447	+	0.589050i	0.862152	+	0.506649i	$0.169116\pi$
$593$	−3.27399	+	14.3443i	−0.134447	+	0.589050i	−0.996599	+	0.0824009i	$0.973741\pi$
$594$	−37.0187	−	162.189i	−1.51890	−	6.65472i
$595$	−1.45795	+	3.07520i	−0.0597701	+	0.126071i
$596$	−8.14358	+	35.6794i	−0.333574	+	1.46148i
$597$	21.1481	+	10.1844i	0.865536	+	0.416820i
$598$	6.90571	+	30.2559i	0.282396	+	1.23726i
$599$	−6.75880	+	3.25486i	−0.276157	+	0.132990i	−0.566837	−	0.823830i	$-0.691833\pi$
$599$	−6.75880	+	3.25486i	−0.276157	+	0.132990i	0.290680	+	0.956820i	$0.406119\pi$
$600$	−64.3140	−	80.6472i	−2.62561	−	3.29241i
$601$	−19.6625	+	9.46894i	−0.802048	+	0.386246i	−0.789558	−	0.613676i	$-0.789690\pi$
$601$	−19.6625	+	9.46894i	−0.802048	+	0.386246i	−0.0124903	+	0.999922i	$0.503976\pi$
$602$	−21.6929	−	4.81256i	−0.884137	−	0.196145i
$603$	39.8878	+	19.2089i	1.62436	+	0.782249i
$604$	−1.60372	−	7.02636i	−0.0652545	−	0.285899i
$605$	−0.796408	−	0.998665i	−0.0323786	−	0.0406015i
$606$	−55.8897			−2.27036
$607$	19.7470			0.801506			0.400753	−	0.916186i	$-0.368749\pi$
$607$	19.7470			0.801506			0.400753	+	0.916186i	$0.368749\pi$
$608$	−52.1508	−	65.3950i	−2.11499	−	2.65212i
$609$	30.6545	−	64.6583i	1.24218	−	2.62009i
$610$	2.48111	−	3.11121i	0.100457	−	0.125969i
$611$	−13.8870	+	17.4137i	−0.561806	+	0.704483i
$612$	−41.7075	−	20.0853i	−1.68592	−	0.811899i
$613$	−42.1871	−	20.3162i	−1.70392	−	0.820565i	−0.993111	−	0.117181i	$-0.962614\pi$
$613$	−42.1871	−	20.3162i	−1.70392	−	0.820565i	−0.710810	−	0.703384i	$-0.751672\pi$
$614$	−16.6172	+	20.8373i	−0.670614	+	0.840923i
$615$	−1.10019	+	1.37959i	−0.0443639	+	0.0556305i
$616$	−59.3165	−	46.7156i	−2.38993	−	1.88223i
$617$	6.55882	+	8.22450i	0.264048	+	0.331106i	0.896127	−	0.443798i	$-0.146369\pi$
$617$	6.55882	+	8.22450i	0.264048	+	0.331106i	−0.632078	+	0.774904i	$0.717798\pi$
$618$	−93.1268			−3.74611
$619$	17.5201			0.704191			0.352096	−	0.935964i	$-0.385469\pi$
$619$	17.5201			0.704191			0.352096	+	0.935964i	$0.385469\pi$
$620$	16.3849	+	20.5460i	0.658032	+	0.825146i
$621$	19.7511	+	86.5353i	0.792585	+	3.47254i
$622$	42.5832	+	20.5070i	1.70743	+	0.822256i
$623$	−0.959208	+	0.225083i	−0.0384299	+	0.00901776i
$624$	−106.296	+	51.1895i	−4.25525	+	2.04922i
$625$	1.81952	+	2.28160i	0.0727806	+	0.0912640i
$626$	7.08951	−	3.41413i	0.283354	−	0.136456i
$627$	10.4676	+	45.8617i	0.418037	+	1.83154i
$628$	−15.8634	−	7.63940i	−0.633018	−	0.304845i
$629$	1.76996	−	7.75468i	0.0705727	−	0.309199i
$630$	35.1529	+	71.8735i	1.40052	+	2.86351i
$631$	2.29323	+	10.0473i	0.0912921	+	0.399977i	0.999842	−	0.0178004i	$-0.00566635\pi$
$631$	2.29323	+	10.0473i	0.0912921	+	0.399977i	−0.908549	+	0.417777i	$0.862809\pi$
$632$	−15.0593	+	65.9792i	−0.599028	+	2.62451i
$633$	36.4014	−	45.6460i	1.44683	−	1.81426i
$634$	2.90663	−	12.7348i	0.115437	−	0.505763i
$635$	−11.8960	+	5.72883i	−0.472080	+	0.227342i
$636$	68.1644			2.70290
$637$	4.11445	+	17.0664i	0.163020	+	0.676194i
$638$	−67.7783			−2.68337
$639$	33.6707	−	16.2149i	1.33199	−	0.641453i
$640$	−8.00527	+	35.0734i	−0.316436	+	1.38640i
$641$	9.81458	−	12.3071i	0.387653	−	0.486101i	−0.549266	−	0.835647i	$-0.685093\pi$
$641$	9.81458	−	12.3071i	0.387653	−	0.486101i	0.936919	+	0.349546i	$0.113664\pi$
$642$	−18.7459	+	82.1314i	−0.739843	+	3.24147i
$643$	8.66433	+	37.9609i	0.341688	+	1.49703i	0.795510	+	0.605940i	$0.207203\pi$
$643$	8.66433	+	37.9609i	0.341688	+	1.49703i	−0.453823	+	0.891092i	$0.649940\pi$
$644$	50.6461	+	39.8872i	1.99574	+	1.57177i
$645$	3.03450	−	13.2950i	0.119483	−	0.523491i
$646$	10.6138	+	5.11135i	0.417595	+	0.201103i
$647$	−1.40126	−	6.13931i	−0.0550891	−	0.241361i	0.939885	−	0.341490i	$-0.110932\pi$
$647$	−1.40126	−	6.13931i	−0.0550891	−	0.241361i	−0.994974	+	0.100129i	$0.968074\pi$
$648$	−327.851	+	157.885i	−12.8792	+	6.20230i
$649$	2.16877	+	2.71955i	0.0851318	+	0.106752i
$650$	20.4676	−	9.85666i	0.802804	−	0.386610i
$651$	15.2241	+	31.1271i	0.596679	+	1.21997i
$652$	−3.19275	−	1.53755i	−0.125038	−	0.0602151i
$653$	−2.92933	−	12.8342i	−0.114634	−	0.502243i	−0.999348	−	0.0361089i	$-0.988504\pi$
$653$	−2.92933	−	12.8342i	−0.114634	−	0.502243i	0.884714	−	0.466134i	$-0.154353\pi$
$654$	9.63505	+	12.0820i	0.376760	+	0.472442i
$655$	25.3118			0.989013
$656$	−5.52397			−0.215675
$657$	−45.6979	−	57.3033i	−1.78284	−	2.23562i
$658$	0.387184	+	63.6224i	0.0150940	+	2.48026i
$659$	16.1996	−	20.3137i	0.631049	−	0.791310i	−0.358803	−	0.933413i	$-0.616815\pi$
$659$	16.1996	−	20.3137i	0.631049	−	0.791310i	0.989852	+	0.142103i	$0.0453865\pi$
$660$	46.2342	−	57.9758i	1.79966	−	2.25671i
$661$	1.75392	+	0.844644i	0.0682196	+	0.0328528i	0.467682	−	0.883897i	$-0.345089\pi$
$661$	1.75392	+	0.844644i	0.0682196	+	0.0328528i	−0.399463	+	0.916749i	$0.630803\pi$
$662$	84.5576	+	40.7208i	3.28643	+	1.58266i
$663$	5.34449	−	6.70178i	0.207563	−	0.260275i
$664$	−9.74374	+	12.2183i	−0.378130	+	0.474161i
$665$	−6.50548	−	13.3011i	−0.252272	−	0.515794i
$666$	−116.590	−	146.199i	−4.51778	−	5.66511i
$667$	36.1627			1.40023
$668$	−40.9729			−1.58529
$669$	24.6550	+	30.9163i	0.953216	+	1.19529i
$670$	3.95199	+	17.3148i	0.152679	+	0.668928i
$671$	−3.25630	−	1.56815i	−0.125708	−	0.0605378i
$672$	−74.4781	+	157.094i	−2.87305	+	6.06002i
$673$	32.9233	−	15.8550i	1.26910	−	0.611166i	0.326533	−	0.945186i	$-0.394120\pi$
$673$	32.9233	−	15.8550i	1.26910	−	0.611166i	0.942566	+	0.334020i	$0.108405\pi$
$674$	44.2266	+	55.4584i	1.70355	+	2.13618i
$675$	58.5396	−	28.1912i	2.25319	−	1.08508i
$676$	7.96133	+	34.8809i	0.306205	+	1.34157i
$677$	19.5059	+	9.39356i	0.749674	+	0.361024i	0.769388	−	0.638782i	$-0.220561\pi$
$677$	19.5059	+	9.39356i	0.749674	+	0.361024i	−0.0197143	+	0.999806i	$0.506276\pi$
$678$	0.939271	−	4.11521i	0.0360725	−	0.158044i
$679$	−37.5120	+	30.2901i	−1.43958	+	1.16243i
$680$	−2.58220	−	11.3133i	−0.0990227	−	0.433847i
$681$	−2.65281	+	11.6227i	−0.101656	+	0.445383i
$682$	20.4635	−	25.6604i	0.783589	−	0.982589i
$683$	−11.0609	+	48.4609i	−0.423233	+	1.85430i	0.0898357	+	0.995957i	$0.471366\pi$
$683$	−11.0609	+	48.4609i	−0.423233	+	1.85430i	−0.513069	+	0.858348i	$0.671491\pi$
$684$	181.457	−	87.3851i	6.93818	−	3.34125i
$685$	17.4872			0.668151
$686$	39.7711	+	30.5455i	1.51847	+	1.16623i
$687$	66.4906			2.53677
$688$	38.4627	−	18.5227i	1.46638	−	0.706170i
$689$	−2.08741	+	9.14556i	−0.0795242	+	0.348418i
$690$	−33.9213	+	42.5360i	−1.29136	+	1.61932i
$691$	1.46023	−	6.39770i	0.0555499	−	0.243380i	−0.939529	−	0.342471i	$-0.888736\pi$
$691$	1.46023	−	6.39770i	0.0555499	−	0.243380i	0.995078	+	0.0990907i	$0.0315934\pi$
$692$	21.3731	+	93.6416i	0.812483	+	3.55972i
$693$	56.5369	−	45.6523i	2.14766	−	1.73419i
$694$	17.6048	−	77.1315i	0.668268	−	2.92787i
$695$	−6.40131	−	3.08271i	−0.242816	−	0.116934i
$696$	54.2926	+	237.871i	2.05795	+	9.01649i
$697$	0.361602	−	0.174138i	0.0136966	−	0.00659595i
$698$	−35.6443	−	44.6965i	−1.34916	−	1.69179i
$699$	−13.1294	+	6.32280i	−0.496601	+	0.239150i
$700$	20.2162	−	42.6413i	0.764101	−	1.61169i
$701$	−31.9981	−	15.4095i	−1.20855	−	0.582008i	−0.282450	−	0.959282i	$-0.591147\pi$
$701$	−31.9981	−	15.4095i	−1.20855	−	0.582008i	−0.926102	+	0.377274i	$0.876861\pi$
$702$	−29.3481	−	128.583i	−1.10767	−	4.85304i
$703$	21.5765	+	27.0561i	0.813772	+	1.02044i
$704$	77.5952			2.92448
$705$	−39.0467			−1.47058
$706$	37.4600	+	46.9733i	1.40982	+	1.76786i
$707$	−7.01992	−	14.3529i	−0.264011	−	0.539797i
$708$	12.4938	−	15.6667i	0.469544	−	0.588790i
$709$	−9.87107	+	12.3779i	−0.370716	+	0.464863i	−0.931840	−	0.362868i	$-0.881797\pi$
$709$	−9.87107	+	12.3779i	−0.370716	+	0.464863i	0.561125	+	0.827731i	$0.310369\pi$
$710$	13.5072	+	6.50473i	0.506917	+	0.244118i
$711$	−58.6836	−	28.2605i	−2.20081	−	1.05985i
$712$	2.09459	−	2.62654i	0.0784982	−	0.0984336i
$713$	−10.9182	+	13.6910i	−0.408890	+	0.512732i
$714$	−0.149010	−	24.4855i	−0.00557658	−	0.916347i
$715$	6.36273	+	7.97861i	0.237952	+	0.298383i
$716$	−8.21555			−0.307030
$717$	−22.7762			−0.850593
$718$	44.7137	+	56.0692i	1.66870	+	2.09248i
$719$	−6.78553	−	29.7293i	−0.253058	−	1.10872i	−0.928508	−	0.371312i	$-0.878908\pi$
$719$	−6.78553	−	29.7293i	−0.253058	−	1.10872i	0.675450	−	0.737405i	$-0.263949\pi$
$720$	−138.494	−	66.6952i	−5.16137	−	2.48558i
$721$	−11.6970	−	23.9157i	−0.435620	−	0.890667i
$722$	0.174046	−	0.0838162i	0.00647733	−	0.00311932i
$723$	−46.5958	−	58.4293i	−1.73292	−	2.17301i
$724$	−84.8008	+	40.8379i	−3.15160	+	1.51773i
$725$	−5.89048	−	25.8079i	−0.218767	−	0.958481i
$726$	8.28005	+	3.98746i	0.307301	+	0.147989i
$727$	9.48607	−	41.5612i	0.351819	−	1.54142i	−0.421159	−	0.906987i	$-0.638377\pi$
$727$	9.48607	−	41.5612i	0.351819	−	1.54142i	0.772978	−	0.634433i	$-0.218766\pi$
$728$	−47.0256	−	37.0358i	−1.74289	−	1.37264i
$729$	−33.6156	−	147.279i	−1.24502	−	5.45479i
$730$	6.54262	−	28.6651i	0.242153	−	1.06094i
$731$	−1.93388	+	2.42500i	−0.0715270	+	0.0896920i
$732$	−4.63302	+	20.2986i	−0.171241	+	0.750258i
$733$	12.6809	−	6.10681i	0.468380	−	0.225560i	−0.184780	−	0.982780i	$-0.559157\pi$
$733$	12.6809	−	6.10681i	0.468380	−	0.225560i	0.653160	+	0.757220i	$0.273443\pi$
$734$	34.0455			1.25664
$735$	−18.8944	+	24.2936i	−0.696930	+	0.896082i
$736$	−87.8610			−3.23860
$737$	14.5329	−	6.99868i	0.535327	−	0.257800i
$738$	2.09958	−	9.19887i	0.0772867	−	0.338615i
$739$	−13.5987	+	17.0522i	−0.500235	+	0.627274i	−0.966282	−	0.257485i	$-0.917106\pi$
$739$	−13.5987	+	17.0522i	−0.500235	+	0.627274i	0.466048	+	0.884760i	$0.345678\pi$
$740$	12.1389	−	53.1839i	0.446234	−	1.95508i
$741$	8.29865	+	36.3588i	0.304859	+	1.33567i
$742$	11.7733	+	24.0716i	0.432210	+	0.883697i
$743$	−6.01440	+	26.3508i	−0.220647	+	0.966717i	0.736346	+	0.676605i	$0.236550\pi$
$743$	−6.01440	+	26.3508i	−0.220647	+	0.966717i	−0.956993	+	0.290112i	$0.906308\pi$
$744$	−106.449	−	51.2629i	−3.90259	−	1.87939i
$745$	−1.96472	−	8.60802i	−0.0719819	−	0.315373i
$746$	−49.4497	+	23.8137i	−1.81048	+	0.871882i
$747$	−9.37773	−	11.7593i	−0.343113	−	0.430250i
$748$	−15.1959	+	7.31796i	−0.555617	+	0.267571i
$749$	−23.4465	+	5.50184i	−0.856717	+	0.201033i
$750$	89.5105	+	43.1060i	3.26846	+	1.57401i
$751$	−3.33510	−	14.6120i	−0.121699	−	0.533200i	−0.998618	−	0.0525604i	$-0.983262\pi$
$751$	−3.33510	−	14.6120i	−0.121699	−	0.533200i	0.876918	−	0.480639i	$-0.159595\pi$
$752$	−76.2126	−	95.5676i	−2.77919	−	3.48499i
$753$	2.19675			0.0800540
$754$	−53.7341			−1.95688
$755$	1.08411	+	1.35943i	0.0394548	+	0.0494748i
$756$	−215.238	−	169.514i	−7.82812	−	6.16516i
$757$	30.4642	−	38.2008i	1.10724	−	1.38843i	0.194003	−	0.981001i	$-0.437853\pi$
$757$	30.4642	−	38.2008i	1.10724	−	1.38843i	0.913236	−	0.407432i	$-0.133576\pi$
$758$	−51.5596	+	64.6537i	−1.87273	+	2.34833i
$759$	44.5196	+	21.4395i	1.61596	+	0.778206i
$760$	45.4871	+	21.9054i	1.64999	+	0.794593i
$761$	5.70326	−	7.15166i	0.206743	−	0.259247i	−0.667640	−	0.744485i	$-0.732695\pi$
$761$	5.70326	−	7.15166i	0.206743	−	0.259247i	0.874383	+	0.485237i	$0.161267\pi$
$762$	59.2295	−	74.2715i	2.14566	−	2.69057i
$763$	−1.89255	+	3.99189i	−0.0685150	+	0.144516i
$764$	−3.88044	−	4.86592i	−0.140389	−	0.176043i
$765$	11.1684			0.403794
$766$	−6.17140			−0.222982
$767$	1.71939	+	2.15604i	0.0620834	+	0.0778501i
$768$	−20.2839	−	88.8696i	−0.731932	−	3.20681i
$769$	19.5580	+	9.41862i	0.705279	+	0.339644i	0.751908	−	0.659268i	$-0.229134\pi$
$769$	19.5580	+	9.41862i	0.705279	+	0.339644i	−0.0466295	+	0.998912i	$0.514848\pi$
$770$	28.4591	+	6.31364i	1.02560	+	0.227528i
$771$	66.6249	−	32.0848i	2.39944	−	1.15551i
$772$	47.2122	+	59.2022i	1.69920	+	2.13073i
$773$	7.75999	−	3.73701i	0.279107	−	0.134411i	−0.289094	−	0.957301i	$-0.593354\pi$
$773$	7.75999	−	3.73701i	0.279107	−	0.134411i	0.568201	+	0.822890i	$0.307640\pi$
$774$	16.2260	+	71.0907i	0.583231	+	2.55530i
$775$	11.5492	+	5.56178i	0.414858	+	0.199785i
$776$	36.5820	−	160.276i	1.31322	−	5.75358i
$777$	30.8140	−	64.9948i	1.10545	−	2.33168i
$778$	−19.1388	−	83.8525i	−0.686159	−	3.00626i
$779$	−0.388554	+	1.70237i	−0.0139214	+	0.0609936i
$780$	36.6541	−	45.9628i	1.31243	−	1.64573i
$781$	3.02988	−	13.2748i	0.108418	−	0.475009i
$782$	11.1490	−	5.36908i	0.398688	−	0.191998i
$783$	−153.686			−5.49227
$784$	−96.3378	+	1.17260i	−3.44064	+	0.0418787i
$785$	4.24788			0.151613
$786$	−164.077	+	79.0156i	−5.85245	+	2.81839i
$787$	1.79365	−	7.85850i	0.0639367	−	0.280125i	−0.932846	−	0.360275i	$-0.882683\pi$
$787$	1.79365	−	7.85850i	0.0639367	−	0.280125i	0.996783	+	0.0801500i	$0.0255399\pi$
$788$	33.4297	−	41.9195i	1.19088	−	1.49332i
$789$	−7.75145	+	33.9613i	−0.275959	+	1.20906i
$790$	−5.81423	−	25.4738i	−0.206861	−	0.906317i
$791$	1.17479	−	0.275671i	0.0417709	−	0.00980175i
$792$	−55.1352	+	241.563i	−1.95914	+	8.58357i
$793$	−2.58157	−	1.24322i	−0.0916741	−	0.0441479i
$794$	−15.7737	−	69.1090i	−0.559787	−	2.45259i
$795$	−14.8168	+	7.13538i	−0.525497	+	0.253066i
$796$	−22.8292	−	28.6269i	−0.809160	−	1.01466i
$797$	26.7974	−	12.9050i	0.949213	−	0.457117i	0.105803	−	0.994387i	$-0.466259\pi$
$797$	26.7974	−	12.9050i	0.949213	−	0.457117i	0.843410	+	0.537270i	$0.180544\pi$
$798$	83.6921	+	65.9130i	2.96267	+	2.33330i
$799$	8.00159	+	3.85337i	0.283076	+	0.136322i
$800$	14.3115	+	62.7028i	0.505988	+	2.21688i
$801$	2.01591	+	2.52787i	0.0712287	+	0.0893180i
$802$	28.1693			0.994694
$803$	−26.7042			−0.942370
$804$	−57.9364	−	72.6499i	−2.04326	−	2.56217i
$805$	−15.1842	−	3.36861i	−0.535173	−	0.118728i
$806$	16.2233	−	20.3434i	0.571442	−	0.716566i
$807$	−16.4702	+	20.6530i	−0.579780	+	0.727021i
$808$	49.0841	+	23.6377i	1.72677	+	0.831570i
$809$	−12.6049	−	6.07021i	−0.443165	−	0.213417i	0.198975	−	0.980005i	$-0.436239\pi$
$809$	−12.6049	−	6.07021i	−0.443165	−	0.213417i	−0.642140	+	0.766588i	$0.721953\pi$
$810$	87.5957	−	109.841i	3.07780	−	3.85944i
$811$	−7.31827	+	9.17682i	−0.256979	+	0.322242i	−0.893539	−	0.448986i	$-0.851785\pi$
$811$	−7.31827	+	9.17682i	−0.256979	+	0.322242i	0.636560	+	0.771227i	$0.280357\pi$
$812$	−86.8446	+	70.1251i	−3.04765	+	2.46091i
$813$	12.1039	+	15.1778i	0.424503	+	0.532310i
$814$	−68.1311			−2.38799
$815$	0.854952			0.0299477
$816$	29.3309	+	36.7798i	1.02679	+	1.28755i
$817$	−3.00283	−	13.1562i	−0.105056	−	0.460279i
$818$	37.4764	+	18.0477i	1.31033	+	0.631022i
$819$	44.8220	−	36.1928i	1.56621	−	1.26468i
$820$	2.47997	−	1.19429i	0.0866044	−	0.0417065i
$821$	12.4967	+	15.6703i	0.436136	+	0.546898i	0.950520	−	0.310662i	$-0.100551\pi$
$821$	12.4967	+	15.6703i	0.436136	+	0.546898i	−0.514384	+	0.857560i	$0.671979\pi$
$822$	−113.357	+	54.5896i	−3.95376	+	1.90403i
$823$	−7.79714	−	34.1615i	−0.271791	−	1.19080i	−0.907897	−	0.419193i	$-0.862313\pi$
$823$	−7.79714	−	34.1615i	−0.271791	−	1.19080i	0.636106	−	0.771602i	$-0.280544\pi$
$824$	81.7869	+	39.3865i	2.84918	+	1.37209i
$825$	8.04881	−	35.2641i	0.280224	−	1.22774i
$826$	7.69044	+	1.70612i	0.267585	+	0.0593636i
$827$	7.45662	+	32.6696i	0.259292	+	1.13603i	0.922011	+	0.387164i	$0.126545\pi$
$827$	7.45662	+	32.6696i	0.259292	+	1.13603i	−0.662719	+	0.748868i	$0.730598\pi$
$828$	47.0760	−	206.253i	1.63600	−	7.16780i
$829$	13.9855	−	17.5373i	0.485737	−	0.609095i	−0.477209	−	0.878790i	$-0.658351\pi$
$829$	13.9855	−	17.5373i	0.485737	−	0.609095i	0.962946	+	0.269695i	$0.0869229\pi$
$830$	1.34262	−	5.88241i	0.0466031	−	0.204181i
$831$	−78.9086	+	38.0004i	−2.73731	+	1.31822i
$832$	61.5169			2.13271
$833$	6.26935	−	3.11372i	0.217220	−	0.107884i
$834$	51.1182			1.77008
$835$	8.90621	−	4.28900i	0.308212	−	0.148427i
$836$	16.3285	−	71.5400i	0.564735	−	2.47426i
$837$	46.4005	−	58.1844i	1.60384	−	2.01115i
$838$	7.63702	−	33.4600i	0.263816	−	1.15585i
$839$	7.58515	+	33.2327i	0.261868	+	1.14732i	0.919223	+	0.393738i	$0.128818\pi$
$839$	7.58515	+	33.2327i	0.261868	+	1.14732i	−0.657354	+	0.753582i	$0.728324\pi$
$840$	−0.638606	−	104.936i	−0.0220340	−	3.62064i
$841$	−7.47988	+	32.7715i	−0.257927	+	1.13005i
$842$	47.0808	+	22.6729i	1.62251	+	0.781360i
$843$	−10.9525	−	47.9860i	−0.377224	−	1.65273i
$844$	−82.0538	+	39.5150i	−2.82441	+	1.36016i
$845$	−5.38183	−	6.74860i	−0.185141	−	0.232159i
$846$	188.113	−	90.5902i	6.46744	−	3.11456i
$847$	0.0159884	+	2.62722i	0.000549367	+	0.0902723i
$848$	−46.3839	−	22.3373i	−1.59283	−	0.767067i
$849$	24.5000	+	107.341i	0.840836	+	3.68394i
$850$	−5.64774	−	7.08204i	−0.193716	−	0.242912i
$851$	36.3510			1.24609
$852$	−78.4393			−2.68729
$853$	−8.93109	−	11.1992i	−0.305795	−	0.383455i	0.605061	−	0.796179i	$-0.293149\pi$
$853$	−8.93109	−	11.1992i	−0.305795	−	0.383455i	−0.910856	+	0.412724i	$0.864577\pi$
$854$	−7.96846	+	1.86984i	−0.272675	+	0.0639846i
$855$	−30.2956	+	37.9895i	−1.03609	+	1.29921i
$856$	51.1994	−	64.2020i	1.74996	−	2.19438i
$857$	−47.8589	−	23.0476i	−1.63483	−	0.787291i	−0.999892	−	0.0147268i	$-0.995312\pi$
$857$	−47.8589	−	23.0476i	−1.63483	−	0.787291i	−0.634936	−	0.772565i	$-0.718974\pi$
$858$	−66.1516	−	31.8569i	−2.25838	−	1.08758i
$859$	27.9800	−	35.0858i	0.954665	−	1.19711i	−0.0256498	−	0.999671i	$-0.508165\pi$
$859$	27.9800	−	35.0858i	0.954665	−	1.19711i	0.980315	−	0.197441i	$-0.0632631\pi$
$860$	−13.2631	+	16.6314i	−0.452268	+	0.567126i
$861$	3.53343	−	0.829137i	0.120419	−	0.0282569i
$862$	39.5882	+	49.6420i	1.34838	+	1.69081i
$863$	−20.2768			−0.690231			−0.345116	−	0.938560i	$-0.612160\pi$
$863$	−20.2768			−0.690231			−0.345116	+	0.938560i	$0.612160\pi$
$864$	373.394			12.7031
$865$	−14.4481	−	18.1174i	−0.491251	−	0.616010i
$866$	7.83120	+	34.3107i	0.266115	+	1.16593i
$867$	−3.07947	−	1.48299i	−0.104584	−	0.0503651i
$868$	−0.328936	−	54.0510i	−0.0111648	−	1.83461i
$869$	−21.3811	+	10.2966i	−0.725303	+	0.349287i
$870$	−58.7334	−	73.6494i	−1.99125	−	2.49695i
$871$	11.5216	−	5.54850i	0.390394	−	0.188004i
$872$	−3.35193	−	14.6858i	−0.113511	−	0.497322i
$873$	142.554	+	68.6501i	4.82471	+	2.32346i
$874$	−11.9800	+	52.4879i	−0.405230	+	1.77543i
$875$	0.172840	+	28.4013i	0.00584307	+	0.960138i
$876$	34.2318	+	149.979i	1.15658	+	5.06733i
$877$	−0.543271	+	2.38023i	−0.0183450	+	0.0803745i	−0.983272	−	0.182145i	$-0.941696\pi$
$877$	−0.543271	+	2.38023i	−0.0183450	+	0.0803745i	0.964927	+	0.262519i	$0.0845533\pi$
$878$	46.6646	−	58.5155i	1.57485	−	1.97480i
$879$	3.86964	−	16.9540i	0.130520	−	0.571845i
$880$	−50.4596	+	24.3001i	−1.70099	+	0.819155i
$881$	−16.5908			−0.558959			−0.279479	−	0.960152i	$-0.590162\pi$
$881$	−16.5908			−0.558959			−0.279479	+	0.960152i	$0.590162\pi$
$882$	34.6639	−	160.873i	1.16719	−	5.41689i
$883$	57.2785			1.92757			0.963787	−	0.266672i	$-0.0859242\pi$
$883$	57.2785			1.92757			0.963787	+	0.266672i	$0.0859242\pi$
$884$	−12.0472	+	5.80162i	−0.405191	+	0.195130i
$885$	−1.07577	+	4.71327i	−0.0361617	+	0.158435i
$886$	−3.79506	+	4.75885i	−0.127497	+	0.159877i
$887$	8.37009	−	36.6718i	0.281040	−	1.23132i	−0.615422	−	0.788198i	$-0.711014\pi$
$887$	8.37009	−	36.6718i	0.281040	−	1.23132i	0.896462	−	0.443120i	$-0.146128\pi$
$888$	54.5752	+	239.109i	1.83142	+	8.02399i
$889$	26.5129	+	5.88188i	0.889214	+	0.197272i
$890$	−0.288621	+	1.26453i	−0.00967459	+	0.0423871i
$891$	−114.964	−	55.3637i	−3.85143	−	1.85475i
$892$	−13.7260	−	60.1377i	−0.459582	−	2.01356i
$893$	−34.8126	+	16.7649i	−1.16496	+	0.561015i
$894$	39.6074	+	49.6661i	1.32467	+	1.66108i
$895$	1.78580	−	0.859996i	0.0596927	−	0.0287465i
$896$	57.5699	−	46.4864i	1.92327	−	1.55300i
$897$	35.2948	+	16.9971i	1.17846	+	0.567516i
$898$	24.5770	+	107.679i	0.820144	+	3.59329i
$899$	−18.9044	−	23.7054i	−0.630497	−	0.790619i
$900$	−154.863			−5.16210
$901$	3.74048			0.124613
$902$	−2.14340	−	2.68774i	−0.0713675	−	0.0894920i
$903$	−21.8226	+	17.6213i	−0.726211	+	0.586399i
$904$	−2.56536	+	3.21686i	−0.0853226	+	0.106991i
$905$	14.1581	−	17.7537i	0.470632	−	0.590154i
$906$	−11.2712	−	5.42793i	−0.374461	−	0.180331i
$907$	4.62559	+	2.22756i	0.153590	+	0.0739651i	0.509100	−	0.860708i	$-0.329978\pi$
$907$	4.62559	+	2.22756i	0.153590	+	0.0739651i	−0.355510	+	0.934673i	$0.615693\pi$
$908$	11.5948	−	14.5394i	0.384787	−	0.482508i
$909$	−32.6913	+	40.9936i	−1.08430	+	1.35967i
$910$	22.5622	+	5.00541i	0.747928	+	0.165928i
$911$	27.4489	+	34.4198i	0.909421	+	1.14038i	0.989636	+	0.143600i	$0.0458680\pi$
$911$	27.4489	+	34.4198i	0.909421	+	1.14038i	−0.0802148	+	0.996778i	$0.525561\pi$
$912$	−204.671			−6.77734
$913$	−5.48000			−0.181362
$914$	−25.0743	−	31.4421i	−0.829383	−	1.04001i
$915$	−1.11776	−	4.89725i	−0.0369522	−	0.161898i
$916$	−93.4479	−	45.0021i	−3.08760	−	1.48691i
$917$	−40.9004	−	32.2118i	−1.35065	−	1.06373i
$918$	−47.3814	+	22.8177i	−1.56382	+	0.753096i
$919$	12.5699	+	15.7621i	0.414641	+	0.519944i	0.944664	−	0.328040i	$-0.106388\pi$
$919$	12.5699	+	15.7621i	0.414641	+	0.519944i	−0.530023	+	0.847983i	$0.677817\pi$
$920$	47.7807	−	23.0100i	1.57528	−	0.758617i
$921$	7.48621	+	32.7992i	0.246679	+	1.08077i
$922$	−90.4056	−	43.5370i	−2.97735	−	1.43382i
$923$	2.40206	−	10.5241i	0.0790649	−	0.346406i
$924$	−148.488	+	34.8435i	−4.88491	+	1.14627i
$925$	−5.92114	−	25.9422i	−0.194686	−	0.852975i
$926$	1.93754	−	8.48890i	0.0636714	−	0.278963i
$927$	−54.4723	+	68.3061i	−1.78910	+	2.24347i
$928$	33.8516	−	148.313i	1.11123	−	4.86863i
$929$	−23.6794	+	11.4034i	−0.776897	+	0.374134i	−0.779934	−	0.625861i	$-0.784748\pi$
$929$	−23.6794	+	11.4034i	−0.776897	+	0.374134i	0.00303717	+	0.999995i	$0.499033\pi$
$930$	45.6159			1.49580
$931$	−6.41499	+	29.7717i	−0.210243	+	0.975727i
$932$	22.7319			0.744608
$933$	53.7530	−	25.8861i	1.75979	−	0.847472i
$934$	6.95072	−	30.4531i	0.227435	−	0.996456i
$935$	2.53707	−	3.18138i	0.0829710	−	0.104042i
$936$	−43.7107	+	191.509i	−1.42873	+	6.25967i
$937$	−1.61749	−	7.08667i	−0.0528410	−	0.231512i	0.941611	−	0.336703i	$-0.109312\pi$
$937$	−1.61749	−	7.08667i	−0.0528410	−	0.231512i	−0.994452	+	0.105191i	$0.966455\pi$
$938$	15.6489	−	33.0077i	0.510955	−	1.07774i
$939$	2.21025	−	9.68373i	0.0721287	−	0.316017i
$940$	54.8773	+	26.4275i	1.78990	+	0.861971i
$941$	−7.73657	−	33.8961i	−0.252205	−	1.10498i	−0.929370	−	0.369150i	$-0.879649\pi$
$941$	−7.73657	−	33.8961i	−0.252205	−	1.10498i	0.677165	−	0.735831i	$-0.263208\pi$
$942$	−27.5358	+	13.2606i	−0.897166	+	0.432052i
$943$	1.14360	+	1.43403i	0.0372408	+	0.0466985i
$944$	−13.6356	+	6.56655i	−0.443800	+	0.213723i
$945$	64.5303	+	14.3160i	2.09917	+	0.465701i
$946$	23.9366	+	11.5273i	0.778247	+	0.374784i
$947$	−4.89695	−	21.4550i	−0.159130	−	0.697192i	−0.990040	−	0.140786i	$-0.955037\pi$
$947$	−4.89695	−	21.4550i	−0.159130	−	0.697192i	0.830910	−	0.556406i	$-0.187820\pi$
$948$	85.2370	+	106.884i	2.76837	+	3.47142i
$949$	−21.1709			−0.687235
$950$	39.4099			1.27863
$951$	−10.2805	−	12.8913i	−0.333367	−	0.418029i
$952$	−10.2249	+	21.5670i	−0.331390	+	0.698989i
$953$	−5.73143	+	7.18698i	−0.185659	+	0.232809i	−0.865947	−	0.500136i	$-0.833283\pi$
$953$	−5.73143	+	7.18698i	−0.185659	+	0.232809i	0.680288	+	0.732945i	$0.261855\pi$
$954$	54.8274	−	68.7514i	1.77510	−	2.22591i
$955$	1.35284	+	0.651495i	0.0437770	+	0.0210819i
$956$	32.0104	+	15.4154i	1.03529	+	0.498569i
$957$	−53.3437	+	66.8909i	−1.72436	+	2.16228i
$958$	18.0730	−	22.6629i	0.583914	−	0.732204i
$959$	−28.2570	−	22.2542i	−0.912465	−	0.718626i
$960$	67.2403	+	84.3167i	2.17017	+	2.72131i
$961$	−16.3177			−0.526377
$962$	−54.0138			−1.74147
$963$	49.2762	+	61.7904i	1.58790	+	1.99117i
$964$	25.9411	+	113.655i	0.835506	+	3.66059i
$965$	−16.4596	−	7.92655i	−0.529855	−	0.255165i
$966$	108.944	−	25.5642i	3.50521	−	0.822515i
$967$	−16.9278	+	8.15200i	−0.544362	+	0.262151i	−0.685792	−	0.727797i	$-0.740544\pi$
$967$	−16.9278	+	8.15200i	−0.544362	+	0.262151i	0.141431	+	0.989948i	$0.454830\pi$
$968$	−5.58537	−	7.00383i	−0.179520	−	0.225112i
$969$	13.3979	−	6.45207i	0.430401	−	0.207270i
$970$	14.1239	+	61.8807i	0.453490	+	1.98687i
$971$	33.0547	+	15.9183i	1.06077	+	0.510842i	0.881123	−	0.472888i	$-0.156788\pi$
$971$	33.0547	+	15.9183i	1.06077	+	0.510842i	0.179652	+	0.983730i	$0.442503\pi$
$972$	−94.4413	+	413.774i	−3.02921	+	13.2718i
$973$	6.42061	+	13.1276i	0.205835	+	0.420850i
$974$	−18.1382	−	79.4685i	−0.581185	−	2.54634i
$975$	6.38103	−	27.9571i	0.204357	−	0.895345i
$976$	9.80444	−	12.2944i	0.313832	−	0.393534i
$977$	−9.56984	+	41.9282i	−0.306166	+	1.34140i	0.554479	+	0.832198i	$0.312918\pi$
$977$	−9.56984	+	41.9282i	−0.306166	+	1.34140i	−0.860645	+	0.509205i	$0.829940\pi$
$978$	−5.54202	+	2.66890i	−0.177214	+	0.0853419i
$979$	1.17803			0.0376499
$980$	42.9971	−	21.3548i	1.37349	−	0.682155i
$981$	14.4976			0.462872
$982$	−49.6344	+	23.9027i	−1.58390	+	0.762765i
$983$	5.83715	−	25.5742i	0.186176	−	0.815691i	−0.792432	−	0.609960i	$-0.791186\pi$
$983$	5.83715	−	25.5742i	0.186176	−	0.815691i	0.978609	−	0.205731i	$-0.0659572\pi$
$984$	−7.71583	+	9.67535i	−0.245972	+	0.308439i
$985$	−2.87846	+	12.6114i	−0.0917154	+	0.401831i
$986$	4.76771	+	20.8887i	0.151835	+	0.665231i
$987$	63.0942	+	49.6908i	2.00831	+	1.58168i
$988$	12.9451	−	56.7164i	0.411840	−	1.80439i
$989$	−12.7713	−	6.15031i	−0.406102	−	0.195569i
$990$	−21.2870	−	93.2646i	−0.676546	−	2.96414i
$991$	12.2277	−	5.88857i	0.388427	−	0.187057i	−0.229470	−	0.973316i	$-0.573699\pi$
$991$	12.2277	−	5.88857i	0.388427	−	0.187057i	0.617897	+	0.786259i	$0.287985\pi$
$992$	45.9302	+	57.5946i	1.45828	+	1.82863i
$993$	106.737	−	51.4020i	3.38721	−	1.63119i
$994$	−13.5479	−	27.7001i	−0.429714	−	0.878593i
$995$	7.95899	+	3.83285i	0.252317	+	0.121509i
$996$	7.02475	+	30.7775i	0.222588	+	0.975221i
$997$	28.3457	+	35.5444i	0.897718	+	1.12570i	0.991500	+	0.130110i	$0.0415330\pi$
$997$	28.3457	+	35.5444i	0.897718	+	1.12570i	−0.0937818	+	0.995593i	$0.529896\pi$
$998$	100.666			3.18653
$999$	−154.486			−4.88771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.k.c.120.2	✓	234
49.29	even	7	inner	833.2.k.c.715.2	yes	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.k.c.120.2	✓	234	1.1	even	1	trivial
833.2.k.c.715.2	yes	234	49.29	even	7	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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43956 + 1.17483i) q^{2} +(-0.760566 + 3.33226i) q^{3} +(3.32426 - 4.16849i) q^{4} +(-0.286235 + 1.25408i) q^{5} +(-2.05939 - 9.02278i) q^{6} +(2.05845 - 1.66216i) q^{7} +(-2.00742 + 8.79508i) q^{8} +(-7.82256 - 3.76715i) q^{9} +(-0.775040 - 3.39567i) q^{10} +(-2.85011 + 1.37254i) q^{11} +(11.3621 + 14.2477i) q^{12} +(-2.25954 + 1.08814i) q^{13} +(-3.06897 + 6.47327i) q^{14} +(-3.96120 - 1.90761i) q^{15} +(-3.06268 - 13.4185i) q^{16} +(0.623490 + 0.781831i) q^{17} +23.5094 q^{18} -4.35071 q^{19} +(4.27608 + 5.36203i) q^{20} +(3.97314 + 8.12348i) q^{21} +(5.34052 - 6.69679i) q^{22} +(-2.84940 + 3.57304i) q^{23} +(-27.7807 - 13.3785i) q^{24} +(3.01407 + 1.45150i) q^{25} +(4.23392 - 5.30917i) q^{26} +(12.1095 - 15.1848i) q^{27} +(-0.0858448 - 14.1061i) q^{28} +(-4.93362 - 6.18657i) q^{29} +11.9047 q^{30} +3.83175 q^{31} +(11.9867 + 15.0309i) q^{32} +(-2.40596 - 10.5412i) q^{33} +(-2.43956 - 1.17483i) q^{34} +(1.49527 + 3.05722i) q^{35} +(-41.7075 + 20.0853i) q^{36} +(-4.95930 - 6.21877i) q^{37} +(10.6138 - 5.11135i) q^{38} +(-1.90743 - 8.35698i) q^{39} +(-10.4551 - 5.03491i) q^{40} +(0.0893082 - 0.391285i) q^{41} +(-19.2364 - 15.1500i) q^{42} +(0.690193 + 3.02393i) q^{43} +(-3.75308 + 16.4433i) q^{44} +(6.96337 - 8.73179i) q^{45} +(2.75358 - 12.0642i) q^{46} +(8.00159 - 3.85337i) q^{47} +47.0432 q^{48} +(1.47447 - 6.84295i) q^{49} -9.05827 q^{50} +(-3.07947 + 1.48299i) q^{51} +(-2.97541 + 13.0361i) q^{52} +(2.33215 - 2.92442i) q^{53} +(-11.7023 + 51.2709i) q^{54} +(-0.905469 - 3.96712i) q^{55} +(10.4866 + 21.4409i) q^{56} +(3.30900 - 14.4977i) q^{57} +(19.3041 + 9.29634i) q^{58} +(-0.244683 - 1.07203i) q^{59} +(-21.1199 + 10.1708i) q^{60} +(0.712347 + 0.893256i) q^{61} +(-9.34779 + 4.50166i) q^{62} +(-22.3640 + 5.24782i) q^{63} +(-22.1000 - 10.6428i) q^{64} +(-0.717849 - 3.14510i) q^{65} +(18.2536 + 22.8893i) q^{66} -5.09907 q^{67} +5.33169 q^{68} +(-9.73912 - 12.2125i) q^{69} +(-7.23953 - 5.70160i) q^{70} +(-2.68369 + 3.36524i) q^{71} +(48.8355 - 61.2378i) q^{72} +(7.60567 + 3.66270i) q^{73} +(19.4045 + 9.34473i) q^{74} +(-7.12916 + 8.93969i) q^{75} +(-14.4629 + 18.1359i) q^{76} +(-3.58544 + 7.56264i) q^{77} +(14.4713 + 18.1465i) q^{78} +7.50184 q^{79} +17.7044 q^{80} +(25.1495 + 31.5365i) q^{81} +(0.241821 + 1.05949i) q^{82} +(1.56077 + 0.751627i) q^{83} +(47.0703 + 10.4425i) q^{84} +(-1.15894 + 0.558116i) q^{85} +(-5.23638 - 6.56621i) q^{86} +(24.3676 - 11.7348i) q^{87} +(-6.35023 - 27.8222i) q^{88} +(-0.335516 - 0.161576i) q^{89} +(-6.72920 + 29.4825i) q^{90} +(-2.84251 + 5.99560i) q^{91} +(5.42201 + 23.7554i) q^{92} +(-2.91430 + 12.7684i) q^{93} +(-14.9933 + 18.8010i) q^{94} +(1.24532 - 5.45612i) q^{95} +(-59.2034 + 28.5109i) q^{96} -18.2234 q^{97} +(4.44225 + 18.4261i) q^{98} +27.4657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q + q^{2} - 7 q^{3} - 39 q^{4} + 2 q^{5} + 7 q^{6} - 13 q^{7} - 23 q^{8} - 42 q^{9} + 21 q^{10} - 7 q^{11} + q^{12} - 15 q^{13} - 22 q^{14} + 36 q^{15} - 55 q^{16} - 39 q^{17} + 62 q^{18} - 4 q^{19}+ \cdots + 72 q^{99}+O(q^{100}) \) 234 * q + q^2 - 7 * q^3 - 39 * q^4 + 2 * q^5 + 7 * q^6 - 13 * q^7 - 23 * q^8 - 42 * q^9 + 21 * q^10 - 7 * q^11 + q^12 - 15 * q^13 - 22 * q^14 + 36 * q^15 - 55 * q^16 - 39 * q^17 + 62 * q^18 - 4 * q^19 - 26 * q^20 - 30 * q^21 - 47 * q^22 - 32 * q^23 - 43 * q^24 - 69 * q^25 + 7 * q^26 - 19 * q^27 - 21 * q^28 + 8 * q^29 + 40 * q^30 - 8 * q^31 + 55 * q^32 - 59 * q^33 + q^34 - 20 * q^35 - 109 * q^36 + 22 * q^37 - 71 * q^38 - 41 * q^39 - 32 * q^40 - 9 * q^41 + 104 * q^42 - 15 * q^43 + 40 * q^44 + 102 * q^45 - 2 * q^46 - 21 * q^47 + 32 * q^48 + 35 * q^49 + 102 * q^50 - 21 * q^52 - 42 * q^53 - 59 * q^54 + 39 * q^55 + q^56 - 87 * q^57 - 27 * q^58 + 42 * q^59 + 162 * q^60 + 27 * q^61 - 77 * q^62 - 12 * q^63 - 53 * q^64 - 26 * q^65 - 66 * q^66 + 154 * q^67 + 276 * q^68 - 6 * q^69 - 32 * q^70 - 70 * q^71 + 106 * q^72 - 70 * q^73 - 44 * q^74 - 90 * q^75 - 20 * q^76 + 26 * q^77 - 93 * q^78 + 130 * q^79 - 4 * q^80 + 120 * q^81 - 30 * q^82 - 10 * q^83 - 148 * q^84 - 12 * q^85 - 4 * q^86 - 2 * q^87 - 68 * q^88 - 53 * q^89 + 195 * q^90 + 80 * q^91 + 153 * q^92 - 85 * q^93 + 130 * q^94 - 92 * q^95 - 89 * q^96 - 4 * q^97 + 42 * q^98 + 72 * q^99

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