LMFDB - Embedded newform 945.2.cs.b.104.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.16
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19076 - 0.797371i) q^{2} +(0.522216 + 1.65145i) q^{3} +(2.63153 + 2.20812i) q^{4} +(2.22823 + 0.187052i) q^{5} +(0.172770 - 4.03433i) q^{6} +(2.63262 - 0.263278i) q^{7} +(-1.67300 - 2.89773i) q^{8} +(-2.45458 + 1.72483i) q^{9} +O(q^{10})$	\(q+(-2.19076 - 0.797371i) q^{2} +(0.522216 + 1.65145i) q^{3} +(2.63153 + 2.20812i) q^{4} +(2.22823 + 0.187052i) q^{5} +(0.172770 - 4.03433i) q^{6} +(2.63262 - 0.263278i) q^{7} +(-1.67300 - 2.89773i) q^{8} +(-2.45458 + 1.72483i) q^{9} +(-4.73236 - 2.18651i) q^{10} +(-3.96348 + 0.698869i) q^{11} +(-2.27237 + 5.49896i) q^{12} +(1.68772 - 0.614279i) q^{13} +(-5.97736 - 1.52239i) q^{14} +(0.854711 + 3.77750i) q^{15} +(0.161544 + 0.916161i) q^{16} +(5.42879 + 3.13432i) q^{17} +(6.75272 - 1.82147i) q^{18} +(7.17570 - 4.14289i) q^{19} +(5.45063 + 5.41243i) q^{20} +(1.80959 + 4.21015i) q^{21} +(9.24029 + 1.62931i) q^{22} +(1.38768 + 1.16440i) q^{23} +(3.91179 - 4.27612i) q^{24} +(4.93002 + 0.833589i) q^{25} -4.18719 q^{26} +(-4.13029 - 3.15289i) q^{27} +(7.50917 + 5.12031i) q^{28} +(1.46750 - 4.03193i) q^{29} +(1.13960 - 8.95710i) q^{30} +(-5.08442 + 6.05938i) q^{31} +(-0.785440 + 4.45445i) q^{32} +(-3.22394 - 6.18054i) q^{33} +(-9.39396 - 11.1953i) q^{34} +(5.91533 - 0.0942090i) q^{35} +(-10.2679 - 0.881063i) q^{36} +(-3.90920 - 2.25698i) q^{37} +(-19.0236 + 3.35438i) q^{38} +(1.89580 + 2.46640i) q^{39} +(-3.18581 - 6.76974i) q^{40} +(-5.58968 + 2.03448i) q^{41} +(-0.607314 - 10.6663i) q^{42} +(9.22292 - 1.62625i) q^{43} +(-11.9732 - 6.91274i) q^{44} +(-5.79200 + 3.38418i) q^{45} +(-2.11161 - 3.65741i) q^{46} +(-2.39686 - 2.85647i) q^{47} +(-1.42863 + 0.745216i) q^{48} +(6.86137 - 1.38622i) q^{49} +(-10.1358 - 5.75725i) q^{50} +(-2.34117 + 10.6022i) q^{51} +(5.79768 + 2.11018i) q^{52} -0.780017 q^{53} +(6.53445 + 10.2006i) q^{54} +(-8.96228 + 0.815865i) q^{55} +(-5.16729 - 7.18815i) q^{56} +(10.5890 + 9.68683i) q^{57} +(-6.42988 + 7.66283i) q^{58} +(0.0111392 - 0.0631733i) q^{59} +(-6.09195 + 11.8279i) q^{60} +(0.356258 + 0.424572i) q^{61} +(15.9703 - 9.22046i) q^{62} +(-6.00787 + 5.18705i) q^{63} +(6.20285 - 10.7437i) q^{64} +(3.87552 - 1.05306i) q^{65} +(2.13470 + 16.1107i) q^{66} +(3.90360 + 10.7250i) q^{67} +(7.36510 + 20.2355i) q^{68} +(-1.19828 + 2.89975i) q^{69} +(-13.0342 - 4.51032i) q^{70} +(-2.16543 - 1.25021i) q^{71} +(9.10460 + 4.22706i) q^{72} +(-3.04424 - 5.27277i) q^{73} +(6.76446 + 8.06157i) q^{74} +(1.19791 + 8.57701i) q^{75} +(28.0311 + 4.94263i) q^{76} +(-10.2503 + 2.88336i) q^{77} +(-2.18662 - 6.91493i) q^{78} +(-3.11986 - 1.13554i) q^{79} +(0.188588 + 2.07163i) q^{80} +(3.04994 - 8.46746i) q^{81} +13.8679 q^{82} +(-0.130659 + 0.358982i) q^{83} +(-4.53453 + 15.0749i) q^{84} +(11.5103 + 7.99944i) q^{85} +(-21.5019 - 3.79137i) q^{86} +(7.42488 + 0.317970i) q^{87} +(8.65605 + 10.3159i) q^{88} +(0.0369063 + 0.0639235i) q^{89} +(15.3873 - 2.79555i) q^{90} +(4.28139 - 2.06150i) q^{91} +(1.08059 + 6.12831i) q^{92} +(-12.6619 - 5.23237i) q^{93} +(2.97328 + 8.16902i) q^{94} +(16.7640 - 7.88909i) q^{95} +(-7.76648 + 1.02907i) q^{96} +(1.33504 + 7.57141i) q^{97} +(-16.1369 - 2.43417i) q^{98} +(8.52326 - 8.55176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.19076	−	0.797371i	−1.54910	−	0.563826i	−0.580893	−	0.813980i	$-0.697297\pi$
$2$	−2.19076	−	0.797371i	−1.54910	−	0.563826i	−0.968206	+	0.250153i	$0.919519\pi$
$3$	0.522216	+	1.65145i	0.301502	+	0.953466i
$3$	0.522216	+	1.65145i	0.301502	+	0.953466i
$4$	2.63153	+	2.20812i	1.31577	+	1.10406i
$5$	2.22823	+	0.187052i	0.996495	+	0.0836521i
$5$	2.22823	+	0.187052i	0.996495	+	0.0836521i
$6$	0.172770	−	4.03433i	0.0705330	−	1.64701i
$7$	2.63262	−	0.263278i	0.995037	−	0.0995099i
$7$	2.63262	−	0.263278i	0.995037	−	0.0995099i
$8$	−1.67300	−	2.89773i	−0.591496	−	1.02450i
$9$	−2.45458	+	1.72483i	−0.818194	+	0.574943i
$10$	−4.73236	−	2.18651i	−1.49650	−	0.691435i
$11$	−3.96348	+	0.698869i	−1.19504	+	0.210717i	−0.735551	−	0.677469i	$-0.763077\pi$
$11$	−3.96348	+	0.698869i	−1.19504	+	0.210717i	−0.459484	+	0.888186i	$0.651966\pi$
$12$	−2.27237	+	5.49896i	−0.655976	+	1.58741i
$13$	1.68772	−	0.614279i	0.468088	−	0.170370i	−0.0971978	−	0.995265i	$-0.530988\pi$
$13$	1.68772	−	0.614279i	0.468088	−	0.170370i	0.565286	+	0.824895i	$0.308766\pi$
$14$	−5.97736	−	1.52239i	−1.59752	−	0.406877i
$15$	0.854711	+	3.77750i	0.220685	+	0.975345i
$16$	0.161544	+	0.916161i	0.0403860	+	0.229040i
$17$	5.42879	+	3.13432i	1.31668	+	0.760183i	0.983192	−	0.182573i	$-0.0584425\pi$
$17$	5.42879	+	3.13432i	1.31668	+	0.760183i	0.333484	+	0.942756i	$0.391776\pi$
$18$	6.75272	−	1.82147i	1.59163	−	0.429325i
$19$	7.17570	−	4.14289i	1.64622	−	0.950444i	0.667662	−	0.744465i	$-0.267295\pi$
$19$	7.17570	−	4.14289i	1.64622	−	0.950444i	0.978556	−	0.205980i	$-0.0660381\pi$
$20$	5.45063	+	5.41243i	1.21880	+	1.21026i
$21$	1.80959	+	4.21015i	0.394884	+	0.918731i
$22$	9.24029	+	1.62931i	1.97004	+	0.347371i
$23$	1.38768	+	1.16440i	0.289351	+	0.242794i	0.775895	−	0.630861i	$-0.217298\pi$
$23$	1.38768	+	1.16440i	0.289351	+	0.242794i	−0.486544	+	0.873656i	$0.661743\pi$
$24$	3.91179	−	4.27612i	0.798490	−	0.872860i
$25$	4.93002	+	0.833589i	0.986005	+	0.166718i
$26$	−4.18719			−0.821175
$27$	−4.13029	−	3.15289i	−0.794875	−	0.606774i
$28$	7.50917	+	5.12031i	1.41910	+	0.967647i
$29$	1.46750	−	4.03193i	0.272508	−	0.748710i	−0.725651	−	0.688063i	$-0.758461\pi$
$29$	1.46750	−	4.03193i	0.272508	−	0.748710i	0.998159	−	0.0606471i	$-0.0193164\pi$
$30$	1.13960	−	8.95710i	0.208061	−	1.63533i
$31$	−5.08442	+	6.05938i	−0.913189	+	1.08830i	0.0825966	+	0.996583i	$0.473679\pi$
$31$	−5.08442	+	6.05938i	−0.913189	+	1.08830i	−0.995785	+	0.0917130i	$0.970766\pi$
$32$	−0.785440	+	4.45445i	−0.138847	+	0.787443i
$33$	−3.22394	−	6.18054i	−0.561216	−	1.07589i
$34$	−9.39396	−	11.1953i	−1.61105	−	1.91998i
$35$	5.91533	−	0.0942090i	0.999873	−	0.0159242i
$36$	−10.2679	−	0.881063i	−1.71132	−	0.146844i
$37$	−3.90920	−	2.25698i	−0.642668	−	0.371045i	0.142973	−	0.989727i	$-0.454334\pi$
$37$	−3.90920	−	2.25698i	−0.642668	−	0.371045i	−0.785642	+	0.618682i	$0.787667\pi$
$38$	−19.0236	+	3.35438i	−3.08604	+	0.544152i
$39$	1.89580	+	2.46640i	0.303572	+	0.394939i
$40$	−3.18581	−	6.76974i	−0.503721	−	1.07039i
$41$	−5.58968	+	2.03448i	−0.872961	+	0.317732i	−0.739366	−	0.673304i	$-0.764875\pi$
$41$	−5.58968	+	2.03448i	−0.872961	+	0.317732i	−0.133596	+	0.991036i	$0.542652\pi$
$42$	−0.607314	−	10.6663i	−0.0937106	−	1.64585i
$43$	9.22292	−	1.62625i	1.40648	−	0.248001i	0.581678	−	0.813419i	$-0.302396\pi$
$43$	9.22292	−	1.62625i	1.40648	−	0.248001i	0.824804	+	0.565418i	$0.191285\pi$
$44$	−11.9732	−	6.91274i	−1.80503	−	1.04213i
$45$	−5.79200	+	3.38418i	−0.863421	+	0.504484i
$46$	−2.11161	−	3.65741i	−0.311340	−	0.539256i
$47$	−2.39686	−	2.85647i	−0.349618	−	0.416659i	0.562363	−	0.826890i	$-0.309892\pi$
$47$	−2.39686	−	2.85647i	−0.349618	−	0.416659i	−0.911981	+	0.410232i	$0.865448\pi$
$48$	−1.42863	+	0.745216i	−0.206206	+	0.107563i
$49$	6.86137	−	1.38622i	0.980196	−	0.198032i
$50$	−10.1358	−	5.75725i	−1.43342	−	0.814198i
$51$	−2.34117	+	10.6022i	−0.327829	+	1.48460i
$52$	5.79768	+	2.11018i	0.803993	+	0.292630i
$53$	−0.780017			−0.107144			−0.0535718	−	0.998564i	$-0.517061\pi$
$53$	−0.780017			−0.107144			−0.0535718	+	0.998564i	$0.517061\pi$
$54$	6.53445	+	10.2006i	0.889225	+	1.38812i
$55$	−8.96228	+	0.815865i	−1.20847	+	0.110011i
$56$	−5.16729	−	7.18815i	−0.690508	−	0.960557i
$57$	10.5890	+	9.68683i	1.40255	+	1.28305i
$58$	−6.42988	+	7.66283i	−0.844285	+	1.00618i
$59$	0.0111392	−	0.0631733i	0.00145019	−	0.00822446i	−0.984074	−	0.177759i	$-0.943115\pi$
$59$	0.0111392	−	0.0631733i	0.00145019	−	0.00822446i	0.985524	+	0.169534i	$0.0542264\pi$
$60$	−6.09195	+	11.8279i	−0.786468	+	1.52697i
$61$	0.356258	+	0.424572i	0.0456142	+	0.0543608i	0.788369	−	0.615202i	$-0.210926\pi$
$61$	0.356258	+	0.424572i	0.0456142	+	0.0543608i	−0.742755	+	0.669563i	$0.766481\pi$
$62$	15.9703	−	9.22046i	2.02823	−	1.17100i
$63$	−6.00787	+	5.18705i	−0.756920	+	0.653507i
$64$	6.20285	−	10.7437i	0.775356	−	1.34296i
$65$	3.87552	−	1.05306i	0.480700	−	0.130617i
$66$	2.13470	+	16.1107i	0.262763	+	1.98309i
$67$	3.90360	+	10.7250i	0.476900	+	1.31027i	0.912111	+	0.409944i	$0.134452\pi$
$67$	3.90360	+	10.7250i	0.476900	+	1.31027i	−0.435210	+	0.900329i	$0.643326\pi$
$68$	7.36510	+	20.2355i	0.893150	+	2.45391i
$69$	−1.19828	+	2.89975i	−0.144256	+	0.349089i
$70$	−13.0342	−	4.51032i	−1.55788	−	0.539086i
$71$	−2.16543	−	1.25021i	−0.256990	−	0.148373i	0.365971	−	0.930626i	$-0.380737\pi$
$71$	−2.16543	−	1.25021i	−0.256990	−	0.148373i	−0.622961	+	0.782253i	$0.714070\pi$
$72$	9.10460	+	4.22706i	1.07299	+	0.498164i
$73$	−3.04424	−	5.27277i	−0.356301	−	0.617131i	0.631039	−	0.775751i	$-0.282629\pi$
$73$	−3.04424	−	5.27277i	−0.356301	−	0.617131i	−0.987340	+	0.158620i	$0.949296\pi$
$74$	6.76446	+	8.06157i	0.786353	+	0.937139i
$75$	1.19791	+	8.57701i	0.138322	+	0.990387i
$76$	28.0311	+	4.94263i	3.21538	+	0.566959i
$77$	−10.2503	+	2.88336i	−1.16814	+	0.328589i
$78$	−2.18662	−	6.91493i	−0.247585	−	0.782962i
$79$	−3.11986	−	1.13554i	−0.351012	−	0.127758i	0.160496	−	0.987036i	$-0.448691\pi$
$79$	−3.11986	−	1.13554i	−0.351012	−	0.127758i	−0.511508	+	0.859279i	$0.670913\pi$
$80$	0.188588	+	2.07163i	0.0210847	+	0.231616i
$81$	3.04994	−	8.46746i	0.338882	−	0.940829i
$82$	13.8679			1.53145
$83$	−0.130659	+	0.358982i	−0.0143417	+	0.0394034i	−0.946657	−	0.322243i	$-0.895563\pi$
$83$	−0.130659	+	0.358982i	−0.0143417	+	0.0394034i	0.932315	+	0.361647i	$0.117785\pi$
$84$	−4.53453	+	15.0749i	−0.494757	+	1.64481i
$85$	11.5103	+	7.99944i	1.24847	+	0.867661i
$86$	−21.5019	−	3.79137i	−2.31861	−	0.408834i
$87$	7.42488	+	0.317970i	0.796031	+	0.0340900i
$88$	8.65605	+	10.3159i	0.922738	+	1.09968i
$89$	0.0369063	+	0.0639235i	0.00391206	+	0.00677588i	0.867975	−	0.496608i	$-0.165421\pi$
$89$	0.0369063	+	0.0639235i	0.00391206	+	0.00677588i	−0.864063	+	0.503384i	$0.832088\pi$
$90$	15.3873	−	2.79555i	1.62197	−	0.294677i
$91$	4.28139	−	2.06150i	0.448812	−	0.216104i
$92$	1.08059	+	6.12831i	0.112659	+	0.638921i
$93$	−12.6619	−	5.23237i	−1.31298	−	0.542571i
$94$	2.97328	+	8.16902i	0.306670	+	0.842570i
$95$	16.7640	−	7.88909i	1.71995	−	0.809404i
$96$	−7.76648	+	1.02907i	−0.792663	+	0.105029i
$97$	1.33504	+	7.57141i	0.135553	+	0.768760i	0.974473	+	0.224505i	$0.0720765\pi$
$97$	1.33504	+	7.57141i	0.135553	+	0.768760i	−0.838920	+	0.544255i	$0.816812\pi$
$98$	−16.1369	−	2.43417i	−1.63008	−	0.245889i
$99$	8.52326	−	8.55176i	0.856620	−	0.859484i
$100$	11.1328	+	13.0797i	1.11328	+	1.30797i
$101$	3.35643	−	2.81638i	0.333977	−	0.280240i	−0.460341	−	0.887742i	$-0.652273\pi$
$101$	3.35643	−	2.81638i	0.333977	−	0.280240i	0.794318	+	0.607502i	$0.207828\pi$
$102$	13.5828	−	21.3600i	1.34490	−	2.11496i
$103$	−3.17919	+	18.0301i	−0.313255	+	1.77656i	0.268585	+	0.963256i	$0.413444\pi$
$103$	−3.17919	+	18.0301i	−0.313255	+	1.77656i	−0.581840	+	0.813303i	$0.697667\pi$
$104$	−4.60357	−	3.86285i	−0.451417	−	0.378784i
$105$	3.24466	+	9.71968i	0.316646	+	0.948544i
$106$	1.70883	+	0.621963i	0.165976	+	0.0604104i
$107$	−9.15916			−0.885449			−0.442725	−	0.896658i	$-0.645988\pi$
$107$	−9.15916			−0.885449			−0.442725	+	0.896658i	$0.645988\pi$
$108$	−3.90704	−	17.4171i	−0.375955	−	1.67596i
$109$	−5.08910			−0.487448			−0.243724	−	0.969845i	$-0.578369\pi$
$109$	−5.08910			−0.487448			−0.243724	+	0.969845i	$0.578369\pi$
$110$	20.2847	+	5.35890i	1.93407	+	0.510951i
$111$	1.68584	−	7.63448i	0.160013	−	0.724633i
$112$	0.666489	+	2.36937i	0.0629773	+	0.223885i
$113$	0.0955452	−	0.541863i	0.00898813	−	0.0509742i	−0.979984	−	0.199077i	$-0.936206\pi$
$113$	0.0955452	−	0.541863i	0.00898813	−	0.0509742i	0.988972	+	0.148103i	$0.0473167\pi$
$114$	−15.4740	−	29.6649i	−1.44928	−	2.77837i
$115$	2.87427	+	2.85412i	0.268027	+	0.266148i
$116$	12.7647	−	7.36972i	1.18518	−	0.684262i
$117$	−3.08311	+	4.41882i	−0.285034	+	0.408520i
$118$	−0.0747757	+	0.129515i	−0.00688366	+	0.0119228i
$119$	15.1171	+	6.82218i	1.38579	+	0.625388i
$120$	9.51622	−	8.79648i	0.868708	−	0.803005i
$121$	4.88416	−	1.77769i	0.444015	−	0.161608i
$122$	−0.441934	−	1.21420i	−0.0400108	−	0.109929i
$123$	−6.27886	−	8.16865i	−0.566146	−	0.736542i
$124$	−26.7596	+	4.71844i	−2.40308	+	0.423729i
$125$	10.8293	+	2.77960i	0.968602	+	0.248615i
$126$	17.2978	−	6.57308i	1.54101	−	0.585577i
$127$	−4.39516	+	2.53754i	−0.390007	+	0.225171i	−0.682163	−	0.731200i	$-0.738961\pi$
$127$	−4.39516	+	2.53754i	−0.390007	+	0.225171i	0.292156	+	0.956371i	$0.405627\pi$
$128$	−15.2257	+	12.7759i	−1.34578	+	1.12924i
$129$	7.50203	+	14.3819i	0.660517	+	1.26626i
$130$	−9.33002	−	0.783220i	−0.818297	−	0.0686930i
$131$	−10.7179	−	8.99336i	−0.936425	−	0.785754i	0.0405350	−	0.999178i	$-0.487094\pi$
$131$	−10.7179	−	8.99336i	−0.936425	−	0.785754i	−0.976960	+	0.213425i	$0.931538\pi$
$132$	5.16345	−	23.3831i	0.449420	−	2.03524i
$133$	17.8001	−	12.7959i	1.54347	−	1.10954i
$134$		−	26.6086i		−	2.29863i
$135$	−8.61349	−	7.79794i	−0.741331	−	0.671140i
$136$		−	20.9749i		−	1.79858i
$137$	21.2403	+	7.73085i	1.81468	+	0.660491i	0.996312	+	0.0858016i	$0.0273451\pi$
$137$	21.2403	+	7.73085i	1.81468	+	0.660491i	0.818372	+	0.574689i	$0.194877\pi$
$138$	4.93733	−	5.39718i	0.420293	−	0.459438i
$139$	−6.87114	+	8.18871i	−0.582803	+	0.694557i	−0.974206	−	0.225662i	$-0.927545\pi$
$139$	−6.87114	+	8.18871i	−0.582803	+	0.694557i	0.391403	+	0.920219i	$0.371990\pi$
$140$	15.7744	+	12.8138i	1.33318	+	1.08297i
$141$	3.46564	−	5.44999i	0.291859	−	0.458972i
$142$	3.74706	+	4.46557i	0.314446	+	0.374742i
$143$	−6.25994	+	3.61418i	−0.523482	+	0.302233i
$144$	−1.97674	−	1.97016i	−0.164729	−	0.164180i
$145$	4.02411	−	8.70956i	0.334184	−	0.723290i
$146$	2.46483	+	13.9788i	0.203991	+	1.15689i
$147$	5.87240	+	10.6073i	0.484347	+	0.874876i
$148$	−5.30351	−	14.5713i	−0.435946	−	1.19775i
$149$	7.32181	+	20.1165i	0.599826	+	1.64801i	0.751619	+	0.659597i	$0.229273\pi$
$149$	7.32181	+	20.1165i	0.599826	+	1.64801i	−0.151793	+	0.988412i	$0.548505\pi$
$150$	4.21473	−	19.7453i	0.344131	−	1.61220i
$151$	2.53528	+	14.3783i	0.206318	+	1.17009i	0.895352	+	0.445358i	$0.146924\pi$
$151$	2.53528	+	14.3783i	0.206318	+	1.17009i	−0.689034	+	0.724729i	$0.741965\pi$
$152$	−24.0099	−	13.8621i	−1.94746	−	1.12437i
$153$	−18.7316	+	1.67030i	−1.51436	+	0.135036i
$154$	24.7551	+	1.85659i	1.99483	+	0.149608i
$155$	−12.4627	+	12.5506i	−1.00103	+	1.00809i
$156$	−0.457223	+	10.6766i	−0.0366071	+	0.854808i
$157$	2.55864	−	14.5108i	0.204202	−	1.15809i	−0.694489	−	0.719504i	$-0.744369\pi$
$157$	2.55864	−	14.5108i	0.204202	−	1.15809i	0.898691	−	0.438583i	$-0.144520\pi$
$158$	5.92941	+	4.97537i	0.471719	+	0.395819i
$159$	−0.407337	−	1.28816i	−0.0323040	−	0.102158i
$160$	−2.58335	+	9.77863i	−0.204232	+	0.773068i
$161$	3.95979	+	2.70008i	0.312075	+	0.212796i
$162$	−13.4334	+	16.1182i	−1.05543	+	1.26637i
$163$		−	16.5841i		−	1.29897i	−0.760375	−	0.649484i	$-0.774985\pi$
$163$		−	16.5841i		−	1.29897i	0.760375	−	0.649484i	$-0.225015\pi$
$164$	−19.2018	−	6.98888i	−1.49941	−	0.545739i
$165$	−6.02761	−	14.3747i	−0.469249	−	1.11907i
$166$	0.572483	−	0.682259i	0.0444333	−	0.0529536i
$167$	14.7593	+	2.60247i	1.14211	+	0.201385i	0.712529	−	0.701643i	$-0.247550\pi$
$167$	14.7593	+	2.60247i	1.14211	+	0.201385i	0.429582	+	0.903028i	$0.358661\pi$
$168$	9.17243	−	12.2873i	0.707668	−	0.947985i
$169$	−7.48753	+	6.28278i	−0.575964	+	0.483291i
$170$	−18.8378	−	26.7028i	−1.44479	−	2.04801i
$171$	−10.4676	+	22.5459i	−0.800474	+	1.72413i
$172$	27.8613	+	16.0858i	2.12441	+	1.22653i
$173$	−1.73337	+	0.305639i	−0.131785	+	0.0232373i	−0.239152	−	0.970982i	$-0.576869\pi$
$173$	−1.73337	+	0.305639i	−0.131785	+	0.0232373i	0.107366	+	0.994220i	$0.465758\pi$
$174$	−16.0126	−	6.61698i	−1.21391	−	0.501632i
$175$	13.1983	+	0.896553i	0.997701	+	0.0677730i
$176$	−1.28055	−	3.51829i	−0.0965253	−	0.265201i
$177$	0.110145	−	0.0145943i	0.00827897	−	0.00109698i
$178$	−0.0298819	−	0.169469i	−0.00223975	−	0.0127022i
$179$	−15.8550	−	9.15391i	−1.18506	−	0.684195i	−0.227881	−	0.973689i	$-0.573180\pi$
$179$	−15.8550	−	9.15391i	−1.18506	−	0.684195i	−0.957180	+	0.289494i	$0.906513\pi$
$180$	−22.7145	−	3.88384i	−1.69304	−	0.289485i
$181$	13.5703	−	7.83484i	1.00868	−	0.582359i	0.0978717	−	0.995199i	$-0.468797\pi$
$181$	13.5703	−	7.83484i	1.00868	−	0.582359i	0.910803	+	0.412840i	$0.135463\pi$
$182$	−11.0233	+	1.10240i	−0.817099	+	0.0817150i
$183$	−0.515116	+	0.810061i	−0.0380785	+	0.0598814i
$184$	1.05252	−	5.96916i	0.0775931	−	0.440052i
$185$	−8.28843	−	5.76029i	−0.609377	−	0.423505i
$186$	23.5671	+	21.5591i	1.72802	+	1.58079i
$187$	−23.7074	−	8.62879i	−1.73366	−	0.631000i
$188$		−	12.8094i		−	0.934224i
$189$	−11.7036	−	7.21294i	−0.851309	−	0.524664i
$190$	−43.0165	+	3.91593i	−3.12074	+	0.284091i
$191$	4.26549	−	11.7193i	0.308640	−	0.847981i	−0.684283	−	0.729217i	$-0.739884\pi$
$191$	4.26549	−	11.7193i	0.308640	−	0.847981i	0.992922	−	0.118764i	$-0.0378933\pi$
$192$	20.9818	+	4.63320i	1.51423	+	0.334372i
$193$	7.38574	−	8.80199i	0.531637	−	0.633581i	−0.431654	−	0.902039i	$-0.642070\pi$
$193$	7.38574	−	8.80199i	0.531637	−	0.633581i	0.963291	+	0.268459i	$0.0865142\pi$
$194$	3.11246	−	17.6516i	0.223462	−	1.26731i
$195$	3.76295	+	5.85031i	0.269470	+	0.418950i
$196$	21.1168	+	11.5028i	1.50835	+	0.821630i
$197$	8.14640	+	14.1100i	0.580407	+	1.00529i	0.995431	+	0.0954837i	$0.0304398\pi$
$197$	8.14640	+	14.1100i	0.580407	+	1.00529i	−0.415024	+	0.909810i	$0.636227\pi$
$198$	−25.4913	+	11.9386i	−1.81159	+	0.848442i
$199$	−17.0570	−	9.84788i	−1.20914	−	0.698098i	−0.246569	−	0.969125i	$-0.579303\pi$
$199$	−17.0570	−	9.84788i	−1.20914	−	0.698098i	−0.962572	+	0.271027i	$0.912637\pi$
$200$	−5.83243	−	15.6805i	−0.412415	−	1.10878i
$201$	−15.6734	+	12.0474i	−1.10551	+	0.849758i
$202$	−9.59882	+	3.49369i	−0.675371	+	0.245815i
$203$	2.80185	−	11.0009i	0.196652	−	0.772111i
$204$	−29.5717	+	22.7304i	−2.07043	+	1.59145i
$205$	−12.8356	+	3.48772i	−0.896481	+	0.243593i
$206$	21.3415	−	36.9646i	1.48693	−	2.57545i
$207$	−5.41456	−	0.464609i	−0.376338	−	0.0322925i
$208$	0.835419	+	1.44699i	0.0579259	+	0.100331i
$209$	−25.5454	+	21.4352i	−1.76701	+	1.48270i
$210$	0.641921	−	23.8807i	0.0442968	−	1.64792i
$211$	0.890448	−	5.04998i	0.0613010	−	0.347655i	−0.938695	−	0.344749i	$-0.887964\pi$
$211$	0.890448	−	5.04998i	0.0613010	−	0.347655i	0.999996	−	0.00290590i	$-0.000924978\pi$
$212$	−2.05264	−	1.72237i	−0.140976	−	0.118293i
$213$	0.933843	−	4.22899i	0.0639859	−	0.289766i
$214$	20.0655	+	7.30325i	1.37165	+	0.499240i
$215$	20.8550	−	1.89850i	1.42230	−	0.129476i
$216$	−2.22622	+	17.2432i	−0.151475	+	1.17325i
$217$	−11.7900	+	17.2906i	−0.800360	+	1.17377i
$218$	11.1490	+	4.05790i	0.755105	+	0.274836i
$219$	7.11798	−	7.78093i	0.480988	−	0.525787i
$220$	−25.3860	−	17.6428i	−1.71153	−	1.18948i
$221$	11.0876	+	1.95505i	0.745834	+	0.131511i
$222$	−9.78078	+	15.3811i	−0.656443	+	1.03231i
$223$	−14.9751	+	12.5656i	−1.00280	+	0.841452i	−0.987370	−	0.158429i	$-0.949357\pi$
$223$	−14.9751	+	12.5656i	−1.00280	+	0.841452i	−0.0154334	+	0.999881i	$0.504913\pi$
$224$	−0.895004	+	11.9337i	−0.0598000	+	0.797351i
$225$	−13.5389	+	6.45733i	−0.902596	+	0.430489i
$226$	−0.641382	+	1.11091i	−0.0426641	+	0.0738964i
$227$	3.63107	−	0.640255i	0.241003	−	0.0424952i	−0.0518421	−	0.998655i	$-0.516509\pi$
$227$	3.63107	−	0.640255i	0.241003	−	0.0424952i	0.292845	+	0.956160i	$0.405398\pi$
$228$	6.47575	+	48.8730i	0.428867	+	3.23670i
$229$	−1.26390	−	3.47255i	−0.0835212	−	0.229473i	0.890901	−	0.454197i	$-0.150074\pi$
$229$	−1.26390	−	3.47255i	−0.0835212	−	0.229473i	−0.974422	+	0.224725i	$0.927852\pi$
$230$	−4.02103	−	8.54454i	−0.265139	−	0.563411i
$231$	−10.1146	−	15.4222i	−0.665493	−	1.01471i
$232$	−14.1386	+	2.49301i	−0.928242	+	0.163674i
$233$	−3.41984	+	5.92333i	−0.224041	+	0.388050i	−0.956031	−	0.293265i	$-0.905258\pi$
$233$	−3.41984	+	5.92333i	−0.224041	+	0.388050i	0.731990	+	0.681315i	$0.238592\pi$
$234$	10.2778	−	7.22218i	0.671880	−	0.472129i
$235$	−4.80645	−	6.81321i	−0.313538	−	0.444445i
$236$	0.168807	−	0.141646i	0.0109884	−	0.00922036i
$237$	0.246042	−	5.74529i	0.0159821	−	0.373197i
$238$	−27.6782	−	26.9997i	−1.79411	−	1.75013i
$239$	4.39459	−	5.23727i	0.284262	−	0.338771i	−0.604952	−	0.796262i	$-0.706808\pi$
$239$	4.39459	−	5.23727i	0.284262	−	0.338771i	0.889214	+	0.457492i	$0.151252\pi$
$240$	−3.32272	+	1.39328i	−0.214481	+	0.0899361i
$241$	4.35662	−	11.9697i	0.280634	−	0.771036i	−0.716653	−	0.697430i	$-0.754327\pi$
$241$	4.35662	−	11.9697i	0.280634	−	0.771036i	0.997287	−	0.0736065i	$-0.0234509\pi$
$242$	−12.1175			−0.778942
$243$	15.5763	+	0.614977i	0.999222	+	0.0394508i
$244$			1.90393i			0.121887i
$245$	15.5480	−	1.80539i	0.993326	−	0.115342i
$246$	7.24202	+	22.9021i	0.461734	+	1.46018i
$247$	9.56566	−	11.3999i	0.608648	−	0.725359i
$248$	26.0647	+	4.59591i	1.65511	+	0.291840i
$249$	−0.661073	−	0.0283104i	−0.0418938	−	0.00179410i
$250$	−21.5080	−	14.7244i	−1.36029	−	0.931252i
$251$	−11.3314	−	19.6266i	−0.715234	−	1.23882i	−0.962869	−	0.269968i	$-0.912987\pi$
$251$	−11.3314	−	19.6266i	−0.715234	−	1.23882i	0.247635	−	0.968853i	$-0.420347\pi$
$252$	−27.2635	+	0.383820i	−1.71744	+	0.0241784i
$253$	−6.31381	−	3.64528i	−0.396946	−	0.229177i
$254$	11.6521	−	2.05458i	0.731117	−	0.128916i
$255$	−7.19981	+	23.1862i	−0.450870	+	1.45197i
$256$	20.2279	−	7.36235i	1.26424	−	0.460147i
$257$	−5.30120	−	14.5649i	−0.330680	−	0.908535i	−0.987935	−	0.154867i	$-0.950505\pi$
$257$	−5.30120	−	14.5649i	−0.330680	−	0.908535i	0.657256	−	0.753668i	$-0.271717\pi$
$258$	−4.96738	−	37.4893i	−0.309256	−	2.33398i
$259$	−10.8856	−	4.91255i	−0.676401	−	0.305251i
$260$	12.5239	+	5.78644i	0.776696	+	0.358860i
$261$	3.35228	+	12.4279i	0.207501	+	0.769266i
$262$	16.3092	+	28.2484i	1.00759	+	1.74519i
$263$	−2.37326	+	1.99140i	−0.146341	+	0.122795i	−0.713019	−	0.701144i	$-0.752673\pi$
$263$	−2.37326	+	1.99140i	−0.146341	+	0.122795i	0.566678	+	0.823939i	$0.308228\pi$
$264$	−12.5158	+	19.6822i	−0.770297	+	1.21135i
$265$	−1.73806	−	0.145904i	−0.106768	−	0.00896278i
$266$	−49.1989	+	13.8393i	−3.01658	+	0.848543i
$267$	−0.0862935	+	0.0943307i	−0.00528108	+	0.00577295i
$268$	−13.4097	+	36.8429i	−0.819129	+	2.25054i
$269$	19.9952			1.21913			0.609566	−	0.792735i	$-0.291344\pi$
$269$	19.9952			1.21913			0.609566	+	0.792735i	$0.291344\pi$
$270$	12.6522	+	23.9515i	0.769989	+	1.45764i
$271$			2.41562i			0.146739i	0.997305	+	0.0733693i	$0.0233752\pi$
$271$			2.41562i			0.146739i	−0.997305	+	0.0733693i	$0.976625\pi$
$272$	−1.99455	+	5.47998i	−0.120937	+	0.332273i
$273$	5.64028	+	5.99396i	0.341365	+	0.362771i
$274$	−40.3681	−	33.8728i	−2.43872	−	2.04633i
$275$	−20.1226	+	0.141526i	−1.21344	+	0.00853435i
$276$	−9.55631	+	4.98484i	−0.575222	+	0.300052i
$277$	−20.2173	−	24.0941i	−1.21474	−	1.44767i	−0.858139	−	0.513417i	$-0.828379\pi$
$277$	−20.2173	−	24.0941i	−1.21474	−	1.44767i	−0.356603	−	0.934256i	$-0.616065\pi$
$278$	21.5824	−	12.4606i	1.29443	−	0.747339i
$279$	2.02874	−	23.6430i	0.121457	−	1.41547i
$280$	−10.1694	−	16.9834i	−0.607735	−	1.01495i
$281$	−15.8370	+	2.79249i	−0.944758	+	0.166586i	−0.624747	−	0.780828i	$-0.714798\pi$
$281$	−15.8370	+	2.79249i	−0.944758	+	0.166586i	−0.320011	+	0.947414i	$0.603687\pi$
$282$	−11.9380	+	9.17622i	−0.710900	+	0.546436i
$283$	−15.0634	+	5.48262i	−0.895424	+	0.325908i	−0.748418	−	0.663228i	$-0.769186\pi$
$283$	−15.0634	+	5.48262i	−0.895424	+	0.325908i	−0.147007	+	0.989136i	$0.546964\pi$
$284$	−2.93779	−	8.07151i	−0.174326	−	0.478956i
$285$	21.7829	+	23.5652i	1.29031	+	1.39588i
$286$	16.5958	−	2.92630i	0.981333	−	0.173035i
$287$	−14.1799	+	6.82765i	−0.837011	+	0.403023i
$288$	−5.75524	−	12.2886i	−0.339131	−	0.724110i
$289$	11.1479	+	19.3087i	0.655757	+	1.13580i
$290$	−15.7606	+	15.8718i	−0.925494	+	0.932026i
$291$	−11.8066	+	6.15867i	−0.692117	+	0.361028i
$292$	3.63189	−	20.5975i	0.212540	−	1.20538i
$293$	8.18877	−	9.75899i	0.478393	−	0.570126i	−0.471833	−	0.881688i	$-0.656408\pi$
$293$	8.18877	−	9.75899i	0.478393	−	0.570126i	0.950226	+	0.311561i	$0.100852\pi$
$294$	−4.40704	−	27.9205i	−0.257024	−	1.62836i
$295$	0.0366373	−	0.138681i	0.00213310	−	0.00807432i
$296$			15.1037i			0.877886i
$297$	18.5738	+	9.60989i	1.07776	+	0.557622i
$298$		−	49.9086i		−	2.89113i
$299$	3.05728	+	1.11276i	0.176807	+	0.0643524i
$300$	−15.7867	+	25.2158i	−0.911446	+	1.45583i
$301$	23.8523	−	6.70949i	1.37482	−	0.386729i
$302$	5.91063	−	33.5209i	0.340119	−	1.92891i
$303$	6.40389	+	4.07222i	0.367894	+	0.233943i
$304$	4.95475	+	5.90484i	0.284174	+	0.338666i
$305$	0.714408	+	1.01268i	0.0409069	+	0.0579860i
$306$	42.3682	+	11.2768i	2.42203	+	0.644650i
$307$	−11.6793	+	20.2292i	−0.666574	+	1.15454i	0.312282	+	0.949989i	$0.398907\pi$
$307$	−11.6793	+	20.2292i	−0.666574	+	1.15454i	−0.978856	+	0.204550i	$0.934427\pi$
$308$	−33.3409	−	15.0463i	−1.89977	−	0.857344i
$309$	−31.4361	+	4.16532i	−1.78834	+	0.236957i
$310$	37.3102	−	17.5580i	2.11908	−	0.997229i
$311$	−25.9494	+	9.44481i	−1.47146	+	0.535566i	−0.948495	−	0.316791i	$-0.897395\pi$
$311$	−25.9494	+	9.44481i	−1.47146	+	0.535566i	−0.522960	+	0.852357i	$0.675172\pi$
$312$	3.97526	−	9.61981i	0.225055	−	0.544615i
$313$	−0.317788	−	1.80226i	−0.0179624	−	0.101870i	0.974508	−	0.224351i	$-0.0720261\pi$
$313$	−0.317788	−	1.80226i	−0.0179624	−	0.101870i	−0.992471	+	0.122481i	$0.960915\pi$
$314$	−17.1758	+	29.7494i	−0.969289	+	1.67886i
$315$	−14.3572	+	10.4342i	−0.808934	+	0.587899i
$316$	−5.70261	−	9.87721i	−0.320797	−	0.555637i
$317$	17.8671	−	14.9923i	1.00352	−	0.842052i	0.0160505	−	0.999871i	$-0.494891\pi$
$317$	17.8671	−	14.9923i	1.00352	−	0.842052i	0.987468	+	0.157819i	$0.0504463\pi$
$318$	−0.134764	+	3.14685i	−0.00755716	+	0.176466i
$319$	−2.99863	+	17.0061i	−0.167891	+	0.952157i
$320$	15.8310	−	22.7791i	0.884980	−	1.27339i
$321$	−4.78306	−	15.1259i	−0.266964	−	0.844246i
$322$	−6.52198	−	9.07264i	−0.363456	−	0.505598i
$323$	51.9405			2.89005
$324$	26.7231	−	15.5478i	1.48462	−	0.863765i
$325$	8.83254	−	1.62155i	0.489941	−	0.0899472i
$326$	−13.2237	+	36.3318i	−0.732392	+	2.01223i
$327$	−2.65761	−	8.40440i	−0.146966	−	0.464764i
$328$	15.2469	+	12.7937i	0.841870	+	0.706413i
$329$	−7.06207	−	6.88895i	−0.389345	−	0.379800i
$330$	1.74306	+	36.2977i	0.0959521	+	1.99812i
$331$	−9.14664	+	7.67494i	−0.502745	+	0.421853i	−0.858568	−	0.512700i	$-0.828645\pi$
$331$	−9.14664	+	7.67494i	−0.502745	+	0.421853i	0.355823	+	0.934554i	$0.384201\pi$
$332$	−1.13651	+	0.656162i	−0.0623739	+	0.0360116i
$333$	13.4883	−	1.20276i	0.739157	−	0.0659110i
$334$	−30.2590	−	17.4700i	−1.65570	−	0.955917i
$335$	6.69198	+	24.6281i	0.365622	+	1.34557i
$336$	−3.56485	+	2.33800i	−0.194479	+	0.127548i
$337$	−11.1284	−	30.5750i	−0.606201	−	1.66552i	−0.738450	−	0.674308i	$-0.764442\pi$
$337$	−11.1284	−	30.5750i	−0.606201	−	1.66552i	0.132249	−	0.991217i	$-0.457780\pi$
$338$	21.4131	−	7.79372i	1.16472	−	0.423922i
$339$	0.944756	−	0.125182i	0.0513121	−	0.00679893i
$340$	12.6261	+	46.4669i	0.684745	+	2.52002i
$341$	15.9173	−	27.5696i	0.861970	−	1.49298i
$342$	40.9093	−	41.0461i	2.21212	−	2.21952i
$343$	17.6984	−	5.45585i	0.955624	−	0.294588i
$344$	−20.1424	−	24.0048i	−1.08601	−	1.29425i
$345$	−3.21245	+	6.23718i	−0.172953	+	0.335798i
$346$	4.04109	+	0.712554i	0.217250	+	0.0383071i
$347$	10.3098	+	8.65097i	0.553461	+	0.464409i	0.876111	−	0.482110i	$-0.160129\pi$
$347$	10.3098	+	8.65097i	0.553461	+	0.464409i	−0.322650	+	0.946518i	$0.604574\pi$
$348$	18.8367	+	17.2318i	1.00975	+	0.923719i
$349$	−4.93555	+	13.5603i	−0.264194	+	0.725867i	0.734680	+	0.678414i	$0.237332\pi$
$349$	−4.93555	+	13.5603i	−0.264194	+	0.725867i	−0.998873	+	0.0474524i	$0.984890\pi$
$350$	−28.1995	−	12.4881i	−1.50733	−	0.667517i
$351$	−8.90751	−	2.78403i	−0.475448	−	0.148601i
$352$		−	18.2041i		−	0.970280i
$353$	0.0746404	−	0.205073i	0.00397271	−	0.0109149i	−0.937690	−	0.347472i	$-0.887040\pi$
$353$	0.0746404	−	0.205073i	0.00397271	−	0.0109149i	0.941663	+	0.336557i	$0.109262\pi$
$354$	−0.252937	−	0.0558534i	−0.0134435	−	0.00296858i
$355$	−4.59123	−	3.19081i	−0.243677	−	0.169351i
$356$	−0.0440306	+	0.249710i	−0.00233362	+	0.0132346i
$357$	−3.37208	+	28.5279i	−0.178469	+	1.50986i
$358$	27.4355	+	32.6963i	1.45001	+	1.72805i
$359$	5.28674	−	3.05230i	0.279024	−	0.161094i	−0.353958	−	0.935261i	$-0.615164\pi$
$359$	5.28674	−	3.05230i	0.279024	−	0.161094i	0.632981	+	0.774167i	$0.281831\pi$
$360$	19.4965	+	11.1219i	1.02755	+	0.586176i
$361$	24.8271	−	43.0018i	1.30669	−	2.26325i
$362$	−35.9766	+	6.34364i	−1.89089	+	0.333414i
$363$	5.48636	+	7.13762i	0.287959	+	0.374628i
$364$	15.8186	+	4.02890i	0.829122	+	0.211172i
$365$	−5.79698	−	12.3184i	−0.303428	−	0.644774i
$366$	1.77441	−	1.36391i	0.0927500	−	0.0712926i
$367$	−2.73875	−	15.5322i	−0.142962	−	0.810776i	−0.968981	−	0.247134i	$-0.920511\pi$
$367$	−2.73875	−	15.5322i	−0.142962	−	0.810776i	0.826020	−	0.563641i	$-0.190600\pi$
$368$	−0.842608	+	1.45944i	−0.0439240	+	0.0760785i
$369$	10.2112	−	14.6350i	0.531574	−	0.761869i
$370$	13.5648	+	19.2283i	0.705203	+	0.999634i
$371$	−2.05349	+	0.205362i	−0.106612	+	0.0106618i
$372$	−21.7666	−	41.7282i	−1.12854	−	2.16350i
$373$	−3.50789	−	0.618535i	−0.181632	−	0.0320266i	0.0820925	−	0.996625i	$-0.473840\pi$
$373$	−3.50789	−	0.618535i	−0.181632	−	0.0320266i	−0.263724	+	0.964598i	$0.584951\pi$
$374$	45.0569	+	37.8072i	2.32983	+	1.95496i
$375$	1.06487	+	19.3356i	0.0549895	+	0.998487i
$376$	−4.26731	+	11.7243i	−0.220070	+	0.604636i
$377$		−	7.70621i		−	0.396890i
$378$	19.8883	+	25.1339i	1.02294	+	1.29275i
$379$	4.28040			0.219869			0.109935	−	0.993939i	$-0.464936\pi$
$379$	4.28040			0.219869			0.109935	+	0.993939i	$0.464936\pi$
$380$	61.5351	+	16.2566i	3.15669	+	0.833945i
$381$	−6.48585	−	5.93324i	−0.332280	−	0.303969i
$382$	−18.6893	+	22.2730i	−0.956228	+	1.13959i
$383$	−4.92741	−	0.868836i	−0.251779	−	0.0443955i	0.0463340	−	0.998926i	$-0.485246\pi$
$383$	−4.92741	−	0.868836i	−0.251779	−	0.0443955i	−0.298113	+	0.954531i	$0.596357\pi$
$384$	−29.0499	−	18.4728i	−1.48245	−	0.942684i
$385$	−23.3795	+	4.50744i	−1.19153	+	0.229720i
$386$	−23.1988	+	13.3938i	−1.18079	+	0.681729i
$387$	−19.8334	+	19.8997i	−1.00819	+	1.01156i
$388$	−13.2053	+	22.8723i	−0.670400	+	1.16117i
$389$	24.9489	−	4.39916i	1.26496	−	0.223046i	0.499377	−	0.866385i	$-0.333562\pi$
$389$	24.9489	−	4.39916i	1.26496	−	0.223046i	0.765582	+	0.643338i	$0.222451\pi$
$390$	−3.57883	−	15.8171i	−0.181221	−	0.800929i
$391$	3.88382	+	10.6707i	0.196413	+	0.539641i
$392$	−15.4960	−	17.5632i	−0.782666	−	0.887077i
$393$	9.25505	−	22.3965i	0.466856	−	1.12975i
$394$	−6.59591	−	37.4072i	−0.332297	−	1.88455i
$395$	−6.73936	−	3.11381i	−0.339094	−	0.156673i
$396$	41.3125	−	3.68386i	2.07603	−	0.185121i
$397$	5.19532	+	8.99855i	0.260746	+	0.451624i	0.966440	−	0.256892i	$-0.0826983\pi$
$397$	5.19532	+	8.99855i	0.260746	+	0.451624i	−0.705695	+	0.708516i	$0.749365\pi$
$398$	29.5154	+	35.1751i	1.47947	+	1.76317i
$399$	30.4273	+	22.7139i	1.52327	+	1.13712i
$400$	0.0327138	+	4.65136i	0.00163569	+	0.232568i
$401$	13.1051	−	15.6180i	0.654437	−	0.779928i	−0.332139	−	0.943230i	$-0.607770\pi$
$401$	13.1051	−	15.6180i	0.654437	−	0.779928i	0.986576	+	0.163303i	$0.0522147\pi$
$402$	43.9428	−	13.8954i	2.19167	−	0.693041i
$403$	−4.85892	+	13.3498i	−0.242040	+	0.664999i
$404$	15.0514			0.748837
$405$	8.37981	−	18.2970i	0.416396	−	0.909183i
$406$	−14.9100	+	21.8662i	−0.739969	+	1.08520i
$407$	17.0714	+	6.21347i	0.846197	+	0.307990i
$408$	34.6390	−	10.9534i	1.71489	−	0.542275i
$409$	−2.69260	+	3.20891i	−0.133140	+	0.158671i	−0.828495	−	0.559996i	$-0.810803\pi$
$409$	−2.69260	+	3.20891i	−0.133140	+	0.158671i	0.695355	+	0.718666i	$0.255247\pi$
$410$	30.9008	+	2.59401i	1.52608	+	0.128109i
$411$	−1.67508	+	39.1145i	−0.0826255	+	1.92938i
$412$	−48.1787	+	40.4267i	−2.37360	+	1.99168i
$413$	0.0126930	−	0.169244i	0.000624581	−	0.00832795i
$414$	11.4915	+	5.33526i	0.564778	+	0.262214i
$415$	−0.358286	+	0.775455i	−0.0175876	+	0.0380656i
$416$	1.41067	+	8.00033i	0.0691640	+	0.392249i
$417$	−17.1115	−	7.07108i	−0.837952	−	0.346272i
$418$	73.0556	−	26.5901i	3.57327	−	1.30056i
$419$	−11.5666	+	4.20990i	−0.565065	+	0.205667i	−0.608727	−	0.793379i	$-0.708320\pi$
$419$	−11.5666	+	4.20990i	−0.565065	+	0.205667i	0.0436622	+	0.999046i	$0.486097\pi$
$420$	−12.9238	+	32.7422i	−0.630615	+	1.59766i
$421$	1.29171	+	7.32568i	0.0629543	+	0.357032i	0.999970	+	0.00774437i	$0.00246513\pi$
$421$	1.29171	+	7.32568i	0.0629543	+	0.357032i	−0.937016	+	0.349287i	$0.886424\pi$
$422$	−5.97747	+	10.3533i	−0.290978	+	0.503990i
$423$	10.8102	+	2.87726i	0.525610	+	0.139897i
$424$	1.30497	+	2.26028i	0.0633750	+	0.109769i
$425$	24.1514	+	19.9776i	1.17151	+	0.969057i
$426$	−5.41790	+	8.52007i	−0.262498	+	0.412799i
$427$	1.04967	+	1.02394i	0.0507972	+	0.0495520i
$428$	−24.1026	−	20.2245i	−1.16504	−	0.977588i
$429$	−9.23768	−	8.45060i	−0.445999	−	0.407999i
$430$	−47.2020	−	12.4700i	−2.27628	−	0.601357i
$431$		−	25.0387i		−	1.20607i	−0.797714	−	0.603036i	$-0.793957\pi$
$431$		−	25.0387i		−	1.20607i	0.797714	−	0.603036i	$-0.206043\pi$
$432$	2.22133	−	4.29334i	0.106874	−	0.206563i
$433$	−6.58137			−0.316280			−0.158140	−	0.987417i	$-0.550550\pi$
$433$	−6.58137			−0.316280			−0.158140	+	0.987417i	$0.550550\pi$
$434$	39.6162	−	28.4786i	1.90164	−	1.36702i
$435$	16.4849	+	2.09735i	0.790389	+	0.100560i
$436$	−13.3921	−	11.2373i	−0.641367	−	0.538170i
$437$	14.7816	+	2.60639i	0.707097	+	0.124680i
$438$	−21.7980	+	11.3705i	−1.04155	+	0.543302i
$439$	−17.0671	−	20.3397i	−0.814567	−	0.970763i	0.185362	−	0.982670i	$-0.440654\pi$
$439$	−17.0671	−	20.3397i	−0.814567	−	0.970763i	−0.999929	+	0.0119075i	$0.996210\pi$
$440$	17.3581	+	24.6053i	0.827514	+	1.17301i
$441$	−14.4508	+	15.2373i	−0.688133	+	0.725585i
$442$	−22.7314	−	13.1240i	−1.08122	−	0.624243i
$443$	−6.67948	−	37.8812i	−0.317352	−	1.79979i	−0.558720	−	0.829356i	$-0.688707\pi$
$443$	−6.67948	−	37.8812i	−0.317352	−	1.79979i	0.241369	−	0.970434i	$-0.422404\pi$
$444$	21.2942	−	16.3678i	1.01058	−	0.776783i
$445$	0.0702786	+	0.149340i	0.00333153	+	0.00707938i
$446$	42.8261	−	15.5874i	2.02788	−	0.738086i
$447$	−29.3979	+	22.5968i	−1.39047	+	1.06879i
$448$	13.5012	−	29.9170i	0.637871	−	1.41345i
$449$	−10.4343	−	6.02427i	−0.492427	−	0.284303i	0.233154	−	0.972440i	$-0.425095\pi$
$449$	−10.4343	−	6.02427i	−0.492427	−	0.284303i	−0.725581	+	0.688137i	$0.758429\pi$
$450$	34.8094	−	3.35090i	1.64093	−	0.157963i
$451$	20.7328	−	11.9701i	0.976268	−	0.563649i
$452$	1.44793	−	1.21496i	0.0681048	−	0.0571467i
$453$	−22.4210	+	11.6954i	−1.05343	+	0.549500i
$454$	−8.46531	−	1.49266i	−0.397297	−	0.0700542i
$455$	9.92553	−	3.79266i	0.465316	−	0.177803i
$456$	10.3543	−	46.8903i	0.484884	−	2.19584i
$457$	5.37460	−	14.7666i	0.251413	−	0.690752i	−0.748214	−	0.663457i	$-0.769088\pi$
$457$	5.37460	−	14.7666i	0.251413	−	0.690752i	0.999627	−	0.0272949i	$-0.00868933\pi$
$458$			8.61532i			0.402567i
$459$	−12.5404	−	30.0620i	−0.585333	−	1.40317i
$460$	1.26149	+	13.8574i	0.0588171	+	0.646106i
$461$	−3.47757	−	1.26573i	−0.161967	−	0.0589510i	0.259764	−	0.965672i	$-0.416355\pi$
$461$	−3.47757	−	1.26573i	−0.161967	−	0.0589510i	−0.421731	+	0.906721i	$0.638577\pi$
$462$	9.86145	+	41.8514i	0.458796	+	1.94710i
$463$	−11.5151	+	13.7231i	−0.535150	+	0.637767i	−0.964093	−	0.265565i	$-0.914442\pi$
$463$	−11.5151	+	13.7231i	−0.535150	+	0.637767i	0.428943	+	0.903331i	$0.358886\pi$
$464$	3.93096	+	0.693134i	0.182490	+	0.0321779i
$465$	−27.2350	−	14.0274i	−1.26299	−	0.650503i
$466$	12.2151	−	10.2497i	0.565855	−	0.474808i
$467$	−9.58631	+	5.53466i	−0.443601	+	0.256113i	−0.705124	−	0.709084i	$-0.749109\pi$
$467$	−9.58631	+	5.53466i	−0.443601	+	0.256113i	0.261523	+	0.965197i	$0.415775\pi$
$468$	−17.8706	+	4.82039i	−0.826068	+	0.222822i
$469$	13.1004	+	27.2072i	0.604919	+	1.25631i
$470$	5.09712	+	18.7586i	0.235113	+	0.865270i
$471$	25.3000	−	3.35229i	1.16576	−	0.154465i
$472$	−0.201695	+	0.0734109i	−0.00928375	+	0.00337901i
$473$	−35.4184	+	12.8912i	−1.62854	+	0.592739i
$474$	−5.12014	+	12.3904i	−0.235176	+	0.569108i
$475$	38.8298	−	14.4430i	1.78163	−	0.662689i
$476$	24.7171	+	51.3332i	1.13291	+	2.35285i
$477$	1.91462	−	1.34540i	0.0876642	−	0.0616014i
$478$	−13.8035	+	7.96947i	−0.631359	+	0.364515i
$479$	10.6442	−	8.93150i	0.486344	−	0.408091i	−0.366370	−	0.930469i	$-0.619400\pi$
$479$	10.6442	−	8.93150i	0.486344	−	0.408091i	0.852714	+	0.522378i	$0.174955\pi$
$480$	−17.4980	+	0.840272i	−0.798670	+	0.0383530i
$481$	−7.98404	−	1.40780i	−0.364041	−	0.0641902i
$482$	−19.0886	+	22.7489i	−0.869461	+	1.03618i
$483$	−2.39118	+	7.94943i	−0.108802	+	0.361711i
$484$	16.7782	+	6.10676i	0.762644	+	0.277580i
$485$	1.55854	+	17.1206i	0.0707697	+	0.777405i
$486$	−33.6336	−	13.7674i	−1.52565	−	0.624500i
$487$			10.4617i			0.474067i	0.971501	+	0.237034i	$0.0761751\pi$
$487$			10.4617i			0.474067i	−0.971501	+	0.237034i	$0.923825\pi$
$488$	0.634272	−	1.74265i	0.0287122	−	0.0788860i
$489$	27.3878	−	8.66049i	1.23852	−	0.391641i
$490$	−35.5015	−	8.44234i	−1.60379	−	0.381386i
$491$	−19.3878	−	3.41859i	−0.874959	−	0.154279i	−0.281906	−	0.959442i	$-0.590967\pi$
$491$	−19.3878	−	3.41859i	−0.874959	−	0.154279i	−0.593053	+	0.805163i	$0.702078\pi$
$492$	1.51431	−	35.3605i	0.0682704	−	1.59417i
$493$	20.6041	−	17.2889i	0.927962	−	0.778652i
$494$	−30.0460	+	17.3471i	−1.35183	+	0.780481i
$495$	20.5914	−	17.4610i	0.925515	−	0.784814i
$496$	−6.37272	−	3.67929i	−0.286144	−	0.165205i
$497$	−6.02992	−	2.72123i	−0.270479	−	0.122064i
$498$	1.42568	+	0.589142i	0.0638861	+	0.0264001i
$499$	16.1483	−	5.87751i	0.722899	−	0.263114i	0.0457428	−	0.998953i	$-0.485435\pi$
$499$	16.1483	−	5.87751i	0.722899	−	0.263114i	0.677156	+	0.735840i	$0.263212\pi$
$500$	22.3600	+	31.2270i	0.999969	+	1.39651i
$501$	3.40971	+	25.7333i	0.152334	+	1.14968i
$502$	9.17474	+	52.0325i	0.409489	+	2.32233i
$503$	−30.9495	−	17.8687i	−1.37997	−	0.796725i	−0.387813	−	0.921738i	$-0.626770\pi$
$503$	−30.9495	−	17.8687i	−1.37997	−	0.796725i	−0.992155	+	0.125013i	$0.960103\pi$
$504$	25.0819	+	8.73120i	1.11723	+	0.388919i
$505$	8.00571	−	5.64772i	0.356249	−	0.251320i
$506$	10.9254	+	13.0204i	0.485692	+	0.578826i
$507$	−14.2858	−	9.08432i	−0.634455	−	0.403449i
$508$	−17.1692	−	3.02739i	−0.761759	−	0.134319i
$509$	−8.34618	−	7.00328i	−0.369938	−	0.310415i	0.438799	−	0.898585i	$-0.355404\pi$
$509$	−8.34618	−	7.00328i	−0.369938	−	0.310415i	−0.808737	+	0.588170i	$0.799848\pi$
$510$	34.2610	−	45.0544i	1.51710	−	1.99504i
$511$	−9.40252	−	13.0797i	−0.415943	−	0.578613i
$512$	−10.4334			−0.461096
$513$	−42.6998	−	5.51283i	−1.88524	−	0.243397i
$514$			36.1352i			1.59386i
$515$	−10.4565	+	39.5806i	−0.460770	+	1.74413i
$516$	−12.0152	+	54.4119i	−0.528940	+	2.39535i
$517$	11.4962	+	9.64647i	0.505603	+	0.424251i
$518$	19.9307	+	19.4421i	0.875704	+	0.854237i
$519$	−1.40994	−	2.70296i	−0.0618895	−	0.118647i
$520$	−9.53526	−	9.46843i	−0.418149	−	0.415218i
$521$	−2.11784	−	3.66820i	−0.0927841	−	0.160707i	0.815898	−	0.578197i	$-0.196243\pi$
$521$	−2.11784	−	3.66820i	−0.0927841	−	0.160707i	−0.908682	+	0.417490i	$0.862910\pi$
$522$	2.56559	−	29.8995i	0.112293	−	1.30866i
$523$	−3.72530	+	6.45241i	−0.162896	+	0.282144i	−0.935906	−	0.352249i	$-0.885417\pi$
$523$	−3.72530	+	6.45241i	−0.162896	+	0.282144i	0.773010	+	0.634394i	$0.218750\pi$
$524$	−8.34602	−	47.3326i	−0.364597	−	2.06773i
$525$	5.41177	+	22.2646i	0.236189	+	0.971707i
$526$	6.78712	−	2.47031i	0.295932	−	0.107711i
$527$	−46.5943	+	16.9589i	−2.02968	+	0.738742i
$528$	5.14156	−	3.95208i	0.223758	−	0.171992i
$529$	−3.42408	−	19.4189i	−0.148873	−	0.844302i
$530$	3.69133	+	1.70552i	0.160341	+	0.0740829i
$531$	0.0816211	+	0.174277i	0.00354205	+	0.00756298i
$532$	75.0964	+	5.63210i	3.25584	+	0.244182i
$533$	−8.18406	+	6.86724i	−0.354491	+	0.297453i
$534$	0.264265	−	0.137848i	0.0114359	−	0.00596526i
$535$	−20.4087	−	1.71324i	−0.882346	−	0.0740697i
$536$	24.5475	−	29.2546i	1.06029	−	1.26361i
$537$	6.83748	−	30.9641i	0.295059	−	1.33620i
$538$	−43.8047	−	15.9436i	−1.88856	−	0.687378i
$539$	−26.2261	+	10.2895i	−1.12964	+	0.443199i
$540$	−5.44790	−	39.5401i	−0.234440	−	1.70153i
$541$	−17.3135			−0.744364			−0.372182	−	0.928160i	$-0.621390\pi$
$541$	−17.3135			−0.744364			−0.372182	+	0.928160i	$0.621390\pi$
$542$	1.92615	−	5.29204i	0.0827350	−	0.227313i
$543$	20.0255	+	18.3193i	0.859376	+	0.786155i
$544$	−18.2256	+	21.7205i	−0.781418	+	0.931258i
$545$	−11.3397	−	0.951925i	−0.485739	−	0.0407760i
$546$	−7.57708	−	17.6287i	−0.324269	−	0.754439i
$547$	29.4741	+	35.1258i	1.26022	+	1.50187i	0.781502	+	0.623902i	$0.214454\pi$
$547$	29.4741	+	35.1258i	1.26022	+	1.50187i	0.478717	+	0.877969i	$0.341102\pi$
$548$	38.8240	+	67.2451i	1.65848	+	2.87257i
$549$	−1.60678	−	0.427662i	−0.0685756	−	0.0182522i
$550$	44.1967	+	15.7351i	1.88455	+	0.670949i
$551$	−6.17349	−	35.0116i	−0.262999	−	1.49154i
$552$	10.4074	−	1.37900i	0.442969	−	0.0586941i
$553$	−8.51236	−	2.16804i	−0.361983	−	0.0921945i
$554$	25.0794	+	68.9050i	1.06552	+	2.92749i
$555$	5.18449	−	16.6960i	0.220069	−	0.708708i
$556$	−36.1632	+	6.37655i	−1.53366	+	0.270426i
$557$	−16.0203	+	27.7481i	−0.678804	+	1.17572i	0.296537	+	0.955021i	$0.404168\pi$
$557$	−16.0203	+	27.7481i	−0.678804	+	1.17572i	−0.975341	+	0.220702i	$0.929165\pi$
$558$	−23.2967	+	50.1784i	−0.986228	+	2.12422i
$559$	14.5667	−	8.41009i	0.616106	−	0.355709i
$560$	1.04190	+	5.40418i	0.0440281	+	0.228368i
$561$	1.86964	−	43.6577i	0.0789363	−	1.84323i
$562$	36.9217	+	6.51030i	1.55745	+	0.274620i
$563$	14.1782	−	16.8969i	0.597540	−	0.712121i	−0.379496	−	0.925193i	$-0.623903\pi$
$563$	14.1782	−	16.8969i	0.597540	−	0.712121i	0.977036	+	0.213073i	$0.0683471\pi$
$564$	21.1542	−	6.68929i	0.890751	−	0.281670i
$565$	0.314253	−	1.18952i	0.0132207	−	0.0500437i
$566$	37.3719			1.57086
$567$	5.80002	−	23.0946i	0.243578	−	0.969881i
$568$			8.36645i			0.351048i
$569$	12.1217	−	33.3041i	0.508168	−	1.39618i	−0.374957	−	0.927042i	$-0.622343\pi$
$569$	12.1217	−	33.3041i	0.508168	−	1.39618i	0.883125	−	0.469137i	$-0.155435\pi$
$570$	−28.9309	−	68.9947i	−1.21178	−	2.88987i
$571$	−18.7477	−	15.7312i	−0.784567	−	0.658330i	0.159827	−	0.987145i	$-0.448906\pi$
$571$	−18.7477	−	15.7312i	−0.784567	−	0.658330i	−0.944394	+	0.328815i	$0.893351\pi$
$572$	−24.4537	−	4.31185i	−1.02246	−	0.180288i
$573$	21.5814	+	0.924223i	0.901577	+	0.0386100i
$574$	36.5088	−	3.65111i	1.52385	−	0.152394i
$575$	5.87066	+	6.89728i	0.244823	+	0.287636i
$576$	3.30555	+	37.0700i	0.137731	+	1.54458i
$577$	2.88192	−	4.99164i	0.119976	−	0.207805i	−0.799782	−	0.600291i	$-0.795052\pi$
$577$	2.88192	−	4.99164i	0.119976	−	0.207805i	0.919758	+	0.392486i	$0.128385\pi$
$578$	−9.02611	−	51.1896i	−0.375437	−	2.12921i
$579$	18.3930	+	7.60066i	0.764387	+	0.315873i
$580$	29.8213	−	14.0338i	1.23826	−	0.582721i
$581$	−0.249463	+	0.979462i	−0.0103494	+	0.0406349i
$582$	30.7762	−	4.07789i	1.27571	−	0.169034i
$583$	3.09159	−	0.545130i	0.128040	−	0.0225770i
$584$	−10.1860	+	17.6427i	−0.421501	+	0.730061i
$585$	−7.69643	+	9.26945i	−0.318208	+	0.383244i
$586$	−25.7211	+	14.8501i	−1.06253	+	0.613452i
$587$	2.87749	+	3.42926i	0.118767	+	0.141541i	0.822152	−	0.569268i	$-0.192773\pi$
$587$	2.87749	+	3.42926i	0.118767	+	0.141541i	−0.703385	+	0.710809i	$0.748329\pi$
$588$	−7.96878	+	40.8804i	−0.328627	+	1.68588i
$589$	−11.3809	+	64.5445i	−0.468943	+	2.65951i
$590$	−0.190844	+	0.274603i	−0.00785690	+	0.0113052i
$591$	−19.0478	+	20.8218i	−0.783520	+	0.856496i
$592$	1.43625	−	3.94606i	0.0590294	−	0.162182i
$593$		−	27.0328i		−	1.11010i	−0.831815	−	0.555052i	$-0.812698\pi$
$593$		−	27.0328i		−	1.11010i	0.831815	−	0.555052i	$-0.187302\pi$
$594$	−33.0280	−	35.8631i	−1.35516	−	1.47148i
$595$	32.4084	+	18.0291i	1.32861	+	0.739120i
$596$	−25.1520	+	69.1047i	−1.03027	+	2.83064i
$597$	7.35584	−	33.3116i	0.301055	−	1.36335i
$598$	−5.81047	−	4.87556i	−0.237608	−	0.199377i
$599$	35.9561	+	6.34004i	1.46913	+	0.259047i	0.850225	−	0.526420i	$-0.176466\pi$
$599$	35.9561	+	6.34004i	1.46913	+	0.259047i	0.618903	+	0.785467i	$0.287577\pi$
$600$	22.8497	−	17.8206i	0.932836	−	0.727522i
$601$	8.30518	+	9.89773i	0.338775	+	0.403737i	0.908355	−	0.418199i	$-0.137339\pi$
$601$	8.30518	+	9.89773i	0.338775	+	0.403737i	−0.569580	+	0.821936i	$0.692894\pi$
$602$	−57.6045	−	4.32024i	−2.34779	−	0.176080i
$603$	−28.0806	−	19.5925i	−1.14353	−	0.797867i
$604$	−25.0772	+	43.4350i	−1.02038	+	1.76735i
$605$	11.2156	−	3.04751i	0.455978	−	0.123899i
$606$	−10.7823	−	14.0275i	−0.438001	−	0.569829i
$607$	−24.4687	+	8.90588i	−0.993155	+	0.361479i	−0.786941	−	0.617028i	$-0.788336\pi$
$607$	−24.4687	+	8.90588i	−0.993155	+	0.361479i	−0.206214	+	0.978507i	$0.566114\pi$
$608$	12.8182	+	35.2178i	0.519848	+	1.42827i
$609$	19.6306	−	1.11772i	0.795472	−	0.0452921i
$610$	−0.757612	−	2.78819i	−0.0306748	−	0.112891i
$611$	−5.79989	−	3.34857i	−0.234639	−	0.135469i
$612$	−52.9809	−	36.9660i	−2.14163	−	1.49426i
$613$	20.4123	−	11.7851i	0.824445	−	0.475994i	−0.0275016	−	0.999622i	$-0.508755\pi$
$613$	20.4123	−	11.7851i	0.824445	−	0.475994i	0.851947	+	0.523628i	$0.175422\pi$
$614$	41.7167	−	35.0045i	1.68355	−	1.41267i
$615$	−12.4628	−	19.3761i	−0.502548	−	0.781320i
$616$	25.5040	+	24.8788i	1.02759	+	1.00240i
$617$	−0.517692	−	0.434396i	−0.0208415	−	0.0174881i	0.632307	−	0.774718i	$-0.282108\pi$
$617$	−0.517692	−	0.434396i	−0.0208415	−	0.0174881i	−0.653149	+	0.757230i	$0.726552\pi$
$618$	72.1901	+	15.9410i	2.90391	+	0.641240i
$619$	15.0010	−	41.2150i	0.602942	−	1.65657i	−0.142339	−	0.989818i	$-0.545462\pi$
$619$	15.0010	−	41.2150i	0.602942	−	1.65657i	0.745281	−	0.666751i	$-0.232316\pi$
$620$	−60.5092	+	5.50835i	−2.43011	+	0.221221i
$621$	−2.06029	−	9.18451i	−0.0826767	−	0.368562i
$622$	64.3799			2.58140
$623$	0.113990	+	0.158570i	0.00456690	+	0.00635296i
$624$	−1.95336	+	2.13529i	−0.0781970	+	0.0854801i
$625$	23.6103	+	8.21922i	0.944410	+	0.328769i
$626$	−0.740876	+	4.20172i	−0.0296114	+	0.167934i
$627$	−48.7393	−	30.9932i	−1.94646	−	1.23775i
$628$	38.7747	−	32.5358i	1.54728	−	1.29832i
$629$	−14.1482	−	24.5053i	−0.564124	−	0.977091i
$630$	39.7730	−	11.4108i	1.58459	−	0.454616i
$631$	23.1714	−	40.1341i	0.922440	−	1.59771i	0.126814	−	0.991927i	$-0.459525\pi$
$631$	23.1714	−	40.1341i	0.922440	−	1.59771i	0.795627	−	0.605787i	$-0.207142\pi$
$632$	1.92906	+	10.9403i	0.0767340	+	0.435180i
$633$	8.80481	−	1.16665i	0.349960	−	0.0463702i
$634$	−51.0970	+	18.5978i	−2.02932	+	0.738613i
$635$	−10.2681	+	4.83211i	−0.407476	+	0.191757i
$636$	1.77249	−	4.28928i	0.0702837	−	0.170081i
$637$	10.7285	−	6.55435i	0.425080	−	0.259693i
$638$	20.1294	−	34.8652i	0.796931	−	1.38032i
$639$	7.47164	−	0.666250i	0.295573	−	0.0263564i
$640$	−36.3162	+	25.6196i	−1.43552	+	1.01271i
$641$	−8.30443	−	9.89684i	−0.328005	−	0.390902i	0.576688	−	0.816964i	$-0.304345\pi$
$641$	−8.30443	−	9.89684i	−0.328005	−	0.390902i	−0.904694	+	0.426063i	$0.859900\pi$
$642$	−1.58243	+	36.9511i	−0.0624534	+	1.45834i
$643$	−0.826073	+	4.68489i	−0.0325771	+	0.184754i	−0.996754	−	0.0805055i	$-0.974347\pi$
$643$	−0.826073	+	4.68489i	−0.0325771	+	0.184754i	0.964177	+	0.265260i	$0.0854577\pi$
$644$	4.45823	+	15.8490i	0.175679	+	0.624539i
$645$	14.0261	+	33.4496i	0.552276	+	1.31708i
$646$	−113.789	−	41.4158i	−4.47697	−	1.62948i
$647$			13.1376i			0.516491i	0.966079	+	0.258246i	$0.0831444\pi$
$647$			13.1376i			0.516491i	−0.966079	+	0.258246i	$0.916856\pi$
$648$	−29.6389	+	5.32821i	−1.16433	+	0.209312i
$649$			0.258171i			0.0101341i
$650$	−20.6429	−	3.49039i	−0.809682	−	0.136904i
$651$	−34.7116	−	10.4412i	−1.36046	−	0.409224i
$652$	36.6196	−	43.6416i	1.43414	−	1.70914i
$653$	3.80446	−	21.5761i	0.148880	−	0.844340i	−0.815290	−	0.579053i	$-0.803422\pi$
$653$	3.80446	−	21.5761i	0.148880	−	0.844340i	0.964170	−	0.265287i	$-0.0854666\pi$
$654$	−0.879244	+	20.5311i	−0.0343811	+	0.802830i
$655$	−22.1997	−	22.0441i	−0.867413	−	0.861333i
$656$	−2.76689	−	4.79239i	−0.108029	−	0.187111i
$657$	16.5669	+	7.69166i	0.646338	+	0.300080i
$658$	9.97824	+	20.7231i	0.388992	+	0.807871i
$659$	−0.327122	+	0.0576805i	−0.0127429	+	0.00224691i	−0.180016	−	0.983664i	$-0.557615\pi$
$659$	−0.327122	+	0.0576805i	−0.0127429	+	0.00224691i	0.167273	+	0.985911i	$0.446504\pi$
$660$	15.8792	−	51.1371i	0.618097	−	1.99051i
$661$	4.35079	+	11.9537i	0.169226	+	0.464945i	0.995096	−	0.0989162i	$-0.0315376\pi$
$661$	4.35079	+	11.9537i	0.169226	+	0.464945i	−0.825870	+	0.563861i	$0.809315\pi$
$662$	26.1579	−	9.52068i	1.01665	−	0.370032i
$663$	2.56147	+	19.3316i	0.0994791	+	0.750777i
$664$	1.25882	−	0.221965i	0.0488519	−	0.00861390i
$665$	42.0563	−	25.1826i	1.63087	−	0.976539i
$666$	−30.5087	−	8.12025i	−1.18219	−	0.314653i
$667$	6.73120	−	3.88626i	0.260633	−	0.150477i
$668$	33.0931	+	39.4388i	1.28041	+	1.52593i
$669$	−28.5716	−	18.1686i	−1.10464	−	0.702440i
$670$	4.97718	−	59.2901i	0.192285	−	2.29058i
$671$	−1.70874	−	1.43381i	−0.0659653	−	0.0553514i
$672$	−20.1752	+	4.75389i	−0.778277	+	0.183385i
$673$	−13.8266	+	37.9881i	−0.532974	+	1.46434i	0.322540	+	0.946556i	$0.395463\pi$
$673$	−13.8266	+	37.9881i	−0.532974	+	1.46434i	−0.855514	+	0.517779i	$0.826759\pi$
$674$			75.8558i			2.92186i
$675$	−17.7342	−	18.9868i	−0.682590	−	0.730801i
$676$	−33.5768			−1.29141
$677$	−0.515901	+	1.41743i	−0.0198277	+	0.0544761i	−0.949212	−	0.314638i	$-0.898117\pi$
$677$	−0.515901	+	1.41743i	−0.0198277	+	0.0544761i	0.929384	+	0.369114i	$0.120339\pi$
$678$	−2.16955	−	0.479078i	−0.0833210	−	0.0183989i
$679$	5.50805	+	19.5811i	0.211380	+	0.751456i
$680$	3.92339	−	46.7369i	0.150455	−	1.79228i
$681$	2.95355	+	5.66218i	0.113180	+	0.216975i
$682$	−56.8541	+	47.7063i	−2.17706	+	1.82677i
$683$	−15.3025	−	26.5047i	−0.585533	−	1.01417i	−0.994809	−	0.101762i	$-0.967552\pi$
$683$	−15.3025	−	26.5047i	−0.585533	−	1.01417i	0.409275	−	0.912411i	$-0.365781\pi$
$684$	−77.3297	+	36.2167i	−2.95677	+	1.38478i
$685$	45.8823	+	21.1992i	1.75307	+	0.809978i
$686$	−43.1233	−	2.15975i	−1.64645	−	0.0824597i
$687$	5.07471	−	3.90070i	0.193612	−	0.148821i
$688$	2.97981	+	8.18697i	0.113604	+	0.312125i
$689$	−1.31645	+	0.479148i	−0.0501527	+	0.0182541i
$690$	12.0111	−	11.1026i	0.457253	−	0.422670i
$691$	−2.84281	+	0.501264i	−0.108146	+	0.0190690i	−0.227459	−	0.973788i	$-0.573042\pi$
$691$	−2.84281	+	0.501264i	−0.108146	+	0.0190690i	0.119313	+	0.992857i	$0.461931\pi$
$692$	−5.23629	−	3.02317i	−0.199054	−	0.114924i
$693$	20.1870	−	24.7575i	0.766841	−	0.940460i
$694$	−15.6883	−	27.1729i	−0.595520	−	1.03147i
$695$	−16.8422	+	16.9611i	−0.638861	+	0.643370i
$696$	−11.5005	−	22.0472i	−0.435924	−	0.835699i
$697$	−36.7219	−	6.47506i	−1.39094	−	0.245261i
$698$	21.6252	−	25.7719i	0.818525	−	0.975480i
$699$	−11.5680	−	2.55443i	−0.437541	−	0.0966176i
$700$	32.7521	+	31.5028i	1.23791	+	1.19069i
$701$			12.2223i			0.461630i	0.972998	+	0.230815i	$0.0741393\pi$
$701$			12.2223i			0.461630i	−0.972998	+	0.230815i	$0.925861\pi$
$702$	17.2943	+	13.2017i	0.652731	+	0.498267i
$703$	−37.4016			−1.41063
$704$	−17.0765	+	46.9173i	−0.643594	+	1.76826i
$705$	8.74167	−	11.4956i	0.329230	−	0.432949i
$706$	−0.327038	+	0.389749i	−0.0123082	+	0.0146684i
$707$	8.09471	−	8.29813i	0.304433	−	0.312083i
$708$	0.322075	+	0.204807i	0.0121043	+	0.00769711i
$709$	−22.1990	+	18.6272i	−0.833700	+	0.699557i	−0.956137	−	0.292919i	$-0.905373\pi$
$709$	−22.1990	+	18.6272i	−0.833700	+	0.699557i	0.122437	+	0.992476i	$0.460929\pi$
$710$	7.51402	+	10.6512i	0.281996	+	0.399733i
$711$	9.61655	−	2.59396i	0.360649	−	0.0972810i
$712$	0.123489	−	0.213889i	0.00462793	−	0.00801581i
$713$	−14.1111	+	2.48817i	−0.528464	+	0.0931825i
$714$	30.1347	−	59.8089i	1.12776	−	2.23829i
$715$	−14.6246	+	6.88229i	−0.546930	+	0.257383i
$716$	−21.5101	−	59.0985i	−0.803871	−	2.20862i
$717$	10.9440	+	4.52247i	0.408712	+	0.168895i
$718$	−14.0158	+	2.47136i	−0.523065	+	0.0922304i
$719$	−14.7019	+	25.4645i	−0.548290	+	0.949666i	0.450102	+	0.892977i	$0.351388\pi$
$719$	−14.7019	+	25.4645i	−0.548290	+	0.949666i	−0.998392	+	0.0566886i	$0.981946\pi$
$720$	−4.03612	−	4.75971i	−0.150417	−	0.177384i
$721$	−3.62267	+	48.3034i	−0.134915	+	1.79891i
$722$	−88.6785	+	74.4101i	−3.30027	+	2.76926i
$723$	22.0425	+	0.943968i	0.819768	+	0.0351065i
$724$	53.0110	+	9.34727i	1.97014	+	0.347388i
$725$	10.5958	−	18.6542i	0.393518	−	0.692800i
$726$	−6.32795	−	20.0115i	−0.234852	−	0.742695i
$727$	42.2703	+	15.3851i	1.56772	+	0.570604i	0.972489	−	0.232951i	$-0.0748380\pi$
$727$	42.2703	+	15.3851i	1.56772	+	0.570604i	0.595232	+	0.803554i	$0.297060\pi$
$728$	−13.1365	−	8.95740i	−0.486869	−	0.331983i
$729$	7.11860	+	26.0447i	0.263652	+	0.964618i
$730$	2.87746	+	31.6089i	0.106500	+	1.16990i
$731$	55.1665	+	20.0790i	2.04041	+	0.742648i
$732$	−3.14425	+	0.994264i	−0.116215	+	0.0367491i
$733$	−10.1269	−	8.49751i	−0.374047	−	0.313863i	0.436313	−	0.899795i	$-0.356284\pi$
$733$	−10.1269	−	8.49751i	−0.374047	−	0.313863i	−0.810360	+	0.585932i	$0.800728\pi$
$734$	−6.38500	+	36.2112i	−0.235675	+	1.33658i
$735$	11.1009	+	24.7340i	0.409464	+	0.912326i
$736$	−6.27670	+	5.26678i	−0.231362	+	0.194136i
$737$	−22.9673	−	39.7804i	−0.846010	−	1.46533i
$738$	−34.0398	+	23.9197i	−1.25302	+	0.880496i
$739$	−8.53512	+	14.7833i	−0.313969	+	0.543811i	−0.979218	−	0.202811i	$-0.934992\pi$
$739$	−8.53512	+	14.7833i	−0.313969	+	0.543811i	0.665248	+	0.746622i	$0.268326\pi$
$740$	−9.09186	−	33.4602i	−0.334223	−	1.23002i
$741$	23.8217	+	9.84400i	0.875113	+	0.361628i
$742$	4.66245	+	1.18749i	0.171164	+	0.0435943i
$743$	−22.4023	+	8.15376i	−0.821860	+	0.299133i	−0.718514	−	0.695513i	$-0.755177\pi$
$743$	−22.4023	+	8.15376i	−0.821860	+	0.299133i	−0.103346	+	0.994645i	$0.532955\pi$
$744$	6.02148	+	45.4446i	0.220758	+	1.66608i
$745$	12.5519	+	46.1938i	0.459865	+	1.69241i
$746$	7.19173	+	4.15215i	0.263308	+	0.152021i
$747$	−0.298470	−	1.10651i	−0.0109204	−	0.0404852i
$748$	−43.3334	−	75.0557i	−1.58443	−	2.74431i
$749$	−24.1126	+	2.41141i	−0.881055	+	0.0881109i
$750$	13.0848	−	43.2087i	0.477789	−	1.57776i
$751$	−0.385591	+	2.18679i	−0.0140704	+	0.0797973i	−0.991034	−	0.133607i	$-0.957344\pi$
$751$	−0.385591	+	2.18679i	−0.0140704	+	0.0797973i	0.976964	+	0.213404i	$0.0684551\pi$
$752$	2.22979	−	2.65736i	0.0813120	−	0.0969038i
$753$	26.4950	−	28.9627i	0.965530	−	1.05546i
$754$	−6.14470	+	16.8824i	−0.223777	+	0.614822i
$755$	2.95970	+	32.5123i	0.107715	+	1.18324i
$756$	−14.8713	−	44.8239i	−0.540864	−	1.63023i
$757$			3.36025i			0.122131i	0.998134	+	0.0610653i	$0.0194498\pi$
$757$			3.36025i			0.122131i	−0.998134	+	0.0610653i	$0.980550\pi$
$758$	−9.37731	−	3.41306i	−0.340599	−	0.123968i
$759$	2.72283	−	12.3306i	0.0988324	−	0.447571i
$760$	−50.9067	−	35.3792i	−1.84658	−	1.28334i
$761$	1.47788	−	8.38148i	0.0535732	−	0.303828i	−0.946234	−	0.323484i	$-0.895146\pi$
$761$	1.47788	−	8.38148i	0.0535732	−	0.303828i	0.999807	+	0.0196555i	$0.00625693\pi$
$762$	9.47794	+	18.1699i	0.343349	+	0.658226i
$763$	−13.3977	+	1.33985i	−0.485028	+	0.0485058i
$764$	37.1024	−	21.4211i	1.34232	−	0.774988i
$765$	−42.0507	+	0.218052i	−1.52035	+	0.00788368i
$766$	10.1020	+	5.83239i	0.365000	+	0.210733i
$767$	−0.0200063	−	0.113461i	−0.000722384	−	0.00409684i
$768$	22.7219	+	29.5606i	0.819906	+	1.06668i
$769$	−2.30802	−	6.34122i	−0.0832292	−	0.228670i	0.891096	−	0.453814i	$-0.149937\pi$
$769$	−2.30802	−	6.34122i	−0.0832292	−	0.228670i	−0.974326	+	0.225144i	$0.927715\pi$
$770$	54.8129	+	8.76740i	1.97532	+	0.315955i
$771$	21.2849	−	16.3607i	0.766556	−	0.589216i
$772$	38.8716	−	6.85412i	1.39902	−	0.246685i
$773$	16.2025	+	9.35452i	0.582763	+	0.336459i	0.762231	−	0.647305i	$-0.224104\pi$
$773$	16.2025	+	9.35452i	0.582763	+	0.336459i	−0.179467	+	0.983764i	$0.557437\pi$
$774$	59.3176	−	27.7809i	2.13213	−	0.998563i
$775$	−30.1173	+	25.6346i	−1.08185	+	0.920820i
$776$	19.7063	−	16.5356i	0.707417	−	0.593593i
$777$	2.42818	−	20.5425i	0.0871106	−	0.736959i
$778$	−58.1648	−	10.2560i	−2.08531	−	0.367696i
$779$	−31.6812	+	37.7562i	−1.13510	+	1.35276i
$780$	−3.01587	+	23.7043i	−0.107985	+	0.848750i
$781$	9.45640	+	3.44185i	0.338377	+	0.123159i
$782$		−	26.4738i		−	0.946701i
$783$	−18.7734	+	12.0262i	−0.670907	+	0.429780i
$784$	2.37842	+	6.06218i	0.0849434	+	0.216507i
$785$	8.41552	−	31.8548i	0.300363	−	1.13695i
$786$	−38.1339	+	41.6856i	−1.36019	+	1.48688i
$787$	17.4095	+	14.6083i	0.620580	+	0.520729i	0.897986	−	0.440024i	$-0.145030\pi$
$787$	17.4095	+	14.6083i	0.620580	+	0.520729i	−0.277406	+	0.960753i	$0.589475\pi$
$788$	−9.71897	+	55.1190i	−0.346224	+	1.96353i
$789$	−4.52805	−	2.87938i	−0.161203	−	0.102509i
$790$	12.2814	+	12.1954i	0.436954	+	0.433892i
$791$	0.108873	−	1.45168i	0.00387108	−	0.0516156i
$792$	−39.0401	−	10.3910i	−1.38723	−	0.369227i
$793$	0.862068	+	0.497715i	0.0306129	+	0.0176744i
$794$	−4.20650	−	23.8562i	−0.149283	−	0.846626i
$795$	−0.666689	−	2.94651i	−0.0236450	−	0.104502i
$796$	−23.1408	−	63.5789i	−0.820205	−	2.25350i
$797$	−14.8351	−	40.7592i	−0.525488	−	1.44377i	−0.864331	−	0.502923i	$-0.832258\pi$
$797$	−14.8351	−	40.7592i	−0.525488	−	1.44377i	0.338843	−	0.940843i	$-0.389964\pi$
$798$	−48.5474	−	74.0224i	−1.71856	−	2.62036i
$799$	−4.05899	−	23.0197i	−0.143597	−	0.814379i
$800$	−7.58542	+	21.3058i	−0.268185	+	0.753274i
$801$	−0.200846	−	0.0932485i	−0.00709656	−	0.00329477i
$802$	−41.1634	+	23.7657i	−1.45353	+	0.839197i
$803$	15.7508	+	18.7710i	0.555832	+	0.662415i
$804$	−67.8470	−	2.90554i	−2.39278	−	0.102471i
$805$	8.31828	+	6.75708i	0.293181	+	0.238156i
$806$	21.2894	−	25.3717i	0.749888	−	0.893682i
$807$	10.4418	+	33.0212i	0.367570	+	1.16240i
$808$	−13.7764	−	5.01421i	−0.484653	−	0.176399i
$809$		−	30.0405i		−	1.05617i	−0.849192	−	0.528084i	$-0.822911\pi$
$809$		−	30.0405i		−	1.05617i	0.849192	−	0.528084i	$-0.177089\pi$
$810$	−32.9476	+	33.4024i	−1.15766	+	1.17364i
$811$			37.2637i			1.30851i	0.756276	+	0.654253i	$0.227017\pi$
$811$			37.2637i			1.30851i	−0.756276	+	0.654253i	$0.772983\pi$
$812$	31.6644	−	22.7624i	1.11120	−	0.798802i
$813$	−3.98928	+	1.26148i	−0.139910	+	0.0442419i
$814$	−32.4448	−	27.2244i	−1.13719	−	0.954216i
$815$	3.10209	−	36.9532i	0.108661	−	1.29441i
$816$	−10.0915	−	0.432168i	−0.353273	−	0.0151289i
$817$	59.4435	−	49.8790i	2.07967	−	1.74505i
$818$	8.45753	−	4.88295i	0.295710	−	0.170728i
$819$	−6.95328	+	12.4448i	−0.242967	+	0.434856i
$820$	−41.4787	−	19.1646i	−1.44850	−	0.669255i
$821$	12.0567	−	2.12592i	0.420782	−	0.0741952i	0.0407516	−	0.999169i	$-0.487025\pi$
$821$	12.0567	−	2.12592i	0.420782	−	0.0741952i	0.380030	+	0.924974i	$0.375914\pi$
$822$	34.8585	−	84.3548i	1.21583	−	2.94221i
$823$	6.01195	+	16.5177i	0.209563	+	0.575771i	0.999290	−	0.0376889i	$-0.0119996\pi$
$823$	6.01195	+	16.5177i	0.209563	+	0.575771i	−0.789726	+	0.613460i	$0.789777\pi$
$824$	57.5651	−	20.9520i	2.00538	−	0.729897i
$825$	−10.7421	−	33.1576i	−0.373991	−	1.15440i
$826$	−0.162757	+	0.360651i	−0.00566305	+	0.0125487i
$827$	3.40354	−	5.89511i	0.118353	−	0.204993i	−0.800762	−	0.598982i	$-0.795572\pi$
$827$	3.40354	−	5.89511i	0.118353	−	0.204993i	0.919115	+	0.393989i	$0.128905\pi$
$828$	−13.2227	−	13.1786i	−0.459520	−	0.457989i
$829$	−2.61158	+	1.50780i	−0.0907039	+	0.0523679i	−0.544666	−	0.838653i	$-0.683344\pi$
$829$	−2.61158	+	1.50780i	−0.0907039	+	0.0523679i	0.453962	+	0.891021i	$0.350010\pi$
$830$	1.40324	−	1.41315i	0.0487073	−	0.0490510i
$831$	29.2324	−	45.9703i	1.01406	−	1.59469i
$832$	3.86906	−	21.9425i	0.134136	−	0.760720i
$833$	41.5938	+	13.9802i	1.44114	+	0.484384i
$834$	31.8488	+	29.1352i	1.10283	+	1.00887i
$835$	32.4004	+	8.55965i	1.12126	+	0.296219i
$836$	−114.555			−3.96196
$837$	40.1047	−	8.99638i	1.38622	−	0.310960i
$838$	28.6965			0.991303
$839$	−32.4526	−	11.8118i	−1.12039	−	0.407788i	−0.285594	−	0.958351i	$-0.592191\pi$
$839$	−32.4526	−	11.8118i	−1.12039	−	0.407788i	−0.834794	+	0.550563i	$0.814413\pi$
$840$	22.7367	−	25.6632i	0.784489	−	0.885465i
$841$	8.11242	+	6.80713i	0.279739	+	0.234729i
$842$	3.01145	−	17.0788i	0.103781	−	0.588573i
$843$	−12.8820	−	24.6958i	−0.443680	−	0.850568i
$844$	13.4942	−	11.3230i	0.464489	−	0.389753i
$845$	−17.8591	+	12.5989i	−0.614373	+	0.433416i
$846$	−21.3883	−	14.9231i	−0.735345	−	0.513068i
$847$	12.3901	−	5.96588i	0.425729	−	0.204990i
$848$	−0.126007	−	0.714621i	−0.00432710	−	0.0245402i
$849$	−16.9206	−	22.0133i	−0.580714	−	0.755494i
$850$	−36.9802	−	63.0237i	−1.26841	−	2.16170i
$851$	−2.79669	−	7.68383i	−0.0958692	−	0.263398i
$852$	11.7955	−	9.06668i	0.404109	−	0.310619i
$853$	−9.74714	−	55.2788i	−0.333736	−	1.89271i	−0.439374	−	0.898304i	$-0.644800\pi$
$853$	−9.74714	−	55.2788i	−0.333736	−	1.89271i	0.105638	−	0.994405i	$-0.466311\pi$
$854$	−1.48312	−	3.08018i	−0.0507512	−	0.105402i
$855$	−27.5414	+	48.2795i	−0.941895	+	1.65112i
$856$	15.3233	+	26.5407i	0.523740	+	0.907144i
$857$	15.1123	+	18.0101i	0.516225	+	0.615213i	0.959684	−	0.281082i	$-0.0906933\pi$
$857$	15.1123	+	18.0101i	0.516225	+	0.615213i	−0.443459	+	0.896295i	$0.646249\pi$
$858$	13.4992	+	25.8791i	0.460857	+	0.883497i
$859$	−35.4854	−	6.25704i	−1.21075	−	0.213487i	−0.468409	−	0.883512i	$-0.655172\pi$
$859$	−35.4854	−	6.25704i	−1.21075	−	0.213487i	−0.742339	+	0.670025i	$0.766284\pi$
$860$	59.0726	+	41.0543i	2.01436	+	1.39994i
$861$	−18.6805	−	19.8518i	−0.636629	−	0.676549i
$862$	−19.9651	+	54.8537i	−0.680015	+	1.86833i
$863$	15.2105			0.517771			0.258886	−	0.965908i	$-0.416645\pi$
$863$	15.2105			0.517771			0.258886	+	0.965908i	$0.416645\pi$
$864$	17.2885	−	15.9218i	0.588166	−	0.541670i
$865$	−3.91951	+	0.356805i	−0.133267	+	0.0121318i
$866$	14.4182	+	5.24779i	0.489950	+	0.178327i
$867$	−26.0657	+	28.4935i	−0.885239	+	0.967689i
$868$	−69.2056	+	19.4671i	−2.34899	+	0.660756i
$869$	13.1591	+	2.32030i	0.446392	+	0.0787109i
$870$	−34.4420	−	17.7393i	−1.16769	−	0.601420i
$871$	13.1763	+	15.7030i	0.446463	+	0.532074i
$872$	8.51409	+	14.7468i	0.288323	+	0.499391i
$873$	−16.3364	−	16.2819i	−0.552902	−	0.551059i
$874$	−30.3045	−	17.4963i	−1.02507	−	0.591822i
$875$	29.2412	+	4.46650i	0.988534	+	0.150995i
$876$	35.9124	−	4.75844i	1.21337	−	0.160773i
$877$	10.5294	+	28.9294i	0.355554	+	0.976877i	0.980554	+	0.196252i	$0.0628770\pi$
$877$	10.5294	+	28.9294i	0.355554	+	0.976877i	−0.624999	+	0.780625i	$0.714901\pi$
$878$	21.1715	+	58.1682i	0.714504	+	1.96308i
$879$	20.3928	+	8.42705i	0.687832	+	0.284237i
$880$	−2.19527	−	8.07909i	−0.0740024	−	0.272346i
$881$	−20.6688	+	35.7993i	−0.696348	+	1.20611i	0.273376	+	0.961907i	$0.411860\pi$
$881$	−20.6688	+	35.7993i	−0.696348	+	1.20611i	−0.969724	+	0.244203i	$0.921474\pi$
$882$	43.8079	−	21.8586i	1.47509	−	0.736016i
$883$	−16.8453	+	9.72565i	−0.566890	+	0.327294i	−0.755906	−	0.654680i	$-0.772803\pi$
$883$	−16.8453	+	9.72565i	−0.566890	+	0.327294i	0.189016	+	0.981974i	$0.439470\pi$
$884$	24.8604	+	29.6275i	0.836147	+	0.996481i
$885$	0.248157	−	0.0119168i	0.00834172	−	0.000400578i
$886$	−15.5722	+	88.3145i	−0.523160	+	2.96698i
$887$	−15.1598	+	18.0668i	−0.509018	+	0.606624i	−0.957948	−	0.286943i	$-0.907361\pi$
$887$	−15.1598	+	18.0668i	−0.509018	+	0.606624i	0.448930	+	0.893567i	$0.351805\pi$
$888$	−24.9431	+	7.88741i	−0.837034	+	0.264684i
$889$	−10.9027	+	7.83754i	−0.365664	+	0.262863i
$890$	−0.0348844	−	0.383205i	−0.00116933	−	0.0128451i
$891$	−6.17073	+	35.6921i	−0.206727	+	1.19573i
$892$	−67.1535			−2.24847
$893$	−29.0332	−	10.5672i	−0.971559	−	0.353619i
$894$	82.4216	−	26.0631i	2.75659	−	0.871680i
$895$	−33.6164	−	23.3627i	−1.12367	−	0.780930i
$896$	−36.7199	+	37.6427i	−1.22673	+	1.25755i
$897$	−0.241106	+	5.63004i	−0.00805030	+	0.187982i
$898$	18.0555	+	21.5178i	0.602521	+	0.718057i
$899$	16.9696	+	29.3921i	0.565967	+	0.980283i
$900$	−49.8867	−	12.9029i	−1.66289	−	0.430096i
$901$	−4.23455	−	2.44482i	−0.141073	−	0.0814488i
$902$	−54.9651	+	9.69182i	−1.83014	+	0.322702i
$903$	23.5364	+	35.8871i	0.783244	+	1.19425i
$904$	−1.73002	+	0.629676i	−0.0575396	+	0.0209427i
$905$	31.7034	−	14.9195i	1.05386	−	0.495940i
$906$	58.4447	−	7.74401i	1.94169	−	0.257277i
$907$	−31.1907	+	5.49976i	−1.03567	+	0.182616i	−0.665539	−	0.746363i	$-0.731798\pi$
$907$	−31.1907	+	5.49976i	−1.03567	+	0.182616i	−0.370131	+	0.928980i	$0.620687\pi$
$908$	10.9690	+	6.33297i	0.364020	+	0.210167i
$909$	−3.38086	+	12.7023i	−0.112136	+	0.421308i
$910$	−24.7686	+	0.394471i	−0.821071	+	0.0130766i
$911$	8.22757	+	9.80524i	0.272592	+	0.324862i	0.884921	−	0.465740i	$-0.154212\pi$
$911$	8.22757	+	9.80524i	0.272592	+	0.324862i	−0.612330	+	0.790603i	$0.709767\pi$
$912$	−7.16410	+	11.2661i	−0.237227	+	0.373058i
$913$	0.266982	−	1.51413i	0.00883583	−	0.0501105i
$914$	−23.5489	+	28.0645i	−0.778928	+	0.928291i
$915$	−1.29932	+	1.70865i	−0.0429542	+	0.0564862i
$916$	4.34179	−	11.9290i	0.143457	−	0.394144i
$917$	−30.5838	−	20.8543i	−1.00997	−	0.688670i
$918$	3.50231	+	75.8579i	0.115593	+	2.50368i
$919$	45.4832			1.50035			0.750176	−	0.661238i	$-0.229969\pi$
$919$	45.4832			1.50035			0.750176	+	0.661238i	$0.229969\pi$
$920$	3.46181	−	13.1038i	0.114132	−	0.432019i
$921$	−39.5066	−	8.72382i	−1.30179	−	0.287460i
$922$	6.60925	+	5.54582i	0.217664	+	0.182642i
$923$	−4.42262	−	0.779827i	−0.145572	−	0.0256683i
$924$	7.43712	−	62.9183i	0.244663	−	2.06986i
$925$	−17.3911	−	14.3856i	−0.571814	−	0.472996i
$926$	36.1691	−	20.8822i	1.18859	−	0.686233i
$927$	−23.2952	−	49.7399i	−0.765116	−	1.63367i
$928$	16.8074	+	9.70375i	0.551729	+	0.318541i
$929$	6.88550	+	39.0496i	0.225906	+	1.28118i	0.860946	+	0.508697i	$0.169873\pi$
$929$	6.88550	+	39.0496i	0.225906	+	1.28118i	−0.635040	+	0.772479i	$0.719016\pi$
$930$	48.4802	+	52.4469i	1.58973	+	1.71980i
$931$	43.4921	−	38.3730i	1.42540	−	1.25763i
$932$	−22.0788	+	8.03603i	−0.723215	+	0.263229i
$933$	−29.1488	−	37.9219i	−0.954290	−	1.24151i
$934$	25.4145	−	4.48125i	0.831586	−	0.146631i
$935$	−51.2116	−	23.6615i	−1.67480	−	0.773812i
$936$	17.9626	+	1.54132i	0.587126	+	0.0503796i
$937$	−14.8009	−	25.6358i	−0.483523	−	0.837486i	0.516298	−	0.856409i	$-0.327310\pi$
$937$	−14.8009	−	25.6358i	−0.483523	−	0.837486i	−0.999821	+	0.0189228i	$0.993976\pi$
$938$	−7.00547	−	70.0503i	−0.228737	−	2.28722i
$939$	2.81040	−	1.46598i	0.0917138	−	0.0478405i
$940$	2.39603	−	28.5424i	0.0781498	−	0.930950i
$941$	8.57363	+	7.19413i	0.279492	+	0.234522i	0.771748	−	0.635929i	$-0.219383\pi$
$941$	8.57363	+	7.19413i	0.279492	+	0.234522i	−0.492255	+	0.870451i	$0.663827\pi$
$942$	−58.0992	−	12.8294i	−1.89298	−	0.418006i
$943$	−10.1256	−	3.68543i	−0.329736	−	0.120014i
$944$	0.0596763			0.00194230
$945$	−24.7291	−	18.2613i	−0.804436	−	0.594039i
$946$	87.8721			2.85697
$947$	14.0251	+	5.10471i	0.455753	+	0.165881i	0.559688	−	0.828703i	$-0.310921\pi$
$947$	14.0251	+	5.10471i	0.455753	+	0.165881i	−0.103934	+	0.994584i	$0.533143\pi$
$948$	13.3337	−	14.5756i	0.433060	−	0.473394i
$949$	−8.37676	−	7.02894i	−0.271921	−	0.228169i
$950$	−96.5831	+	0.679287i	−3.13357	+	0.0220390i
$951$	34.0896	+	21.6775i	1.10543	+	0.702941i
$952$	−5.52223	−	55.2189i	−0.178977	−	1.78965i
$953$	−15.7502	−	27.2801i	−0.510199	−	0.883690i	−0.999930	−	0.0118165i	$-0.996239\pi$
$953$	−15.7502	−	27.2801i	−0.510199	−	0.883690i	0.489732	−	0.871873i	$-0.337095\pi$
$954$	−5.26724	+	1.42078i	−0.170533	+	0.0459994i
$955$	11.6966	−	25.3155i	0.378494	−	0.819191i
$956$	23.1290	−	4.07827i	0.748045	−	0.131901i
$957$	−29.6506	+	3.92875i	−0.958468	+	0.126998i
$958$	−30.4405	+	11.0794i	−0.983487	+	0.357960i
$959$	57.9531	+	14.7603i	1.87140	+	0.476634i
$960$	45.8857	+	14.2485i	1.48096	+	0.459869i
$961$	−5.48162	−	31.0878i	−0.176826	−	1.00283i
$962$	16.3685	+	9.45039i	0.527743	+	0.304693i
$963$	22.4819	−	15.7980i	0.724469	−	0.509083i
$964$	37.8951	−	21.8787i	1.22052	−	0.704666i
$965$	18.1036	−	18.2313i	0.582774	−	0.586888i
$966$	11.5771	−	15.5086i	0.372488	−	0.498981i
$967$	53.0440	+	9.35309i	1.70578	+	0.300775i	0.939708	−	0.341979i	$-0.111097\pi$
$967$	53.0440	+	9.35309i	1.70578	+	0.300775i	0.766073	+	0.642754i	$0.222208\pi$
$968$	−13.3225	−	11.1789i	−0.428201	−	0.359303i
$969$	27.1242	+	85.7772i	0.871354	+	2.75556i
$970$	10.2371	−	38.7498i	0.328692	−	1.24418i
$971$	22.9650			0.736980			0.368490	−	0.929632i	$-0.379875\pi$
$971$	22.9650			0.736980			0.368490	+	0.929632i	$0.379875\pi$
$972$	39.6316	+	36.0127i	1.27119	+	1.15511i
$973$	−15.9332	+	23.3668i	−0.510795	+	0.749104i
$974$	8.34189	−	22.9192i	0.267291	−	0.734377i
$975$	7.29040	+	13.7397i	0.233480	+	0.440023i
$976$	−0.331425	+	0.394977i	−0.0106086	+	0.0126429i
$977$	2.38116	−	13.5042i	0.0761802	−	0.432039i	−0.922733	−	0.385439i	$-0.874050\pi$
$977$	2.38116	−	13.5042i	0.0761802	−	0.432039i	0.998914	−	0.0466004i	$-0.0148388\pi$
$978$	−66.9058	−	2.86524i	−2.13941	−	0.0916201i
$979$	−0.190951	−	0.227567i	−0.00610284	−	0.00727308i
$980$	44.9016	+	29.5809i	1.43433	+	0.944926i
$981$	12.4916	−	8.77783i	0.398826	−	0.280254i
$982$	39.7481	+	22.9486i	1.26841	+	0.732318i
$983$	−30.5911	+	5.39404i	−0.975705	+	0.172043i	−0.638697	−	0.769458i	$-0.720526\pi$
$983$	−30.5911	+	5.39404i	−0.975705	+	0.172043i	−0.337009	+	0.941502i	$0.609415\pi$
$984$	−13.1660	+	31.8606i	−0.419715	+	1.01568i
$985$	15.5128	+	32.9641i	0.494278	+	1.05032i
$986$	−58.9242	+	21.4467i	−1.87653	+	0.683001i
$987$	7.68884	−	15.2602i	0.244739	−	0.485737i
$988$	50.3446	−	8.87712i	1.60168	−	0.282419i
$989$	14.6921	+	8.48246i	0.467180	+	0.269727i
$990$	−59.0337	+	21.8338i	−1.87621	+	0.693925i
$991$	−15.5983	−	27.0171i	−0.495497	−	0.858226i	0.504489	−	0.863418i	$-0.331681\pi$
$991$	−15.5983	−	27.0171i	−0.495497	−	0.858226i	−0.999987	+	0.00519174i	$0.998347\pi$
$992$	−22.9977	−	27.4076i	−0.730177	−	0.870191i
$993$	−17.4513	−	11.0973i	−0.553801	−	0.352161i
$994$	11.0403	+	10.7696i	0.350176	+	0.341592i
$995$	−36.1649	−	25.1339i	−1.14651	−	0.796798i
$996$	−1.67712	−	1.53423i	−0.0531416	−	0.0486138i
$997$	13.4893	+	4.90969i	0.427209	+	0.155491i	0.546671	−	0.837347i	$-0.315895\pi$
$997$	13.4893	+	4.90969i	0.427209	+	0.155491i	−0.119462	+	0.992839i	$0.538117\pi$
$998$	−40.0636			−1.26819
$999$	9.03013	+	21.6472i	0.285701	+	0.684888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.16	yes	816
5.4	even	2	inner	945.2.cs.b.104.121	yes	816
7.6	odd	2	inner	945.2.cs.b.104.15	✓	816
27.20	odd	18	inner	945.2.cs.b.209.122	yes	816
35.34	odd	2	inner	945.2.cs.b.104.122	yes	816
135.74	odd	18	inner	945.2.cs.b.209.15	yes	816
189.20	even	18	inner	945.2.cs.b.209.121	yes	816
945.209	even	18	inner	945.2.cs.b.209.16	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.15	✓	816	7.6	odd	2	inner
945.2.cs.b.104.16	yes	816	1.1	even	1	trivial
945.2.cs.b.104.121	yes	816	5.4	even	2	inner
945.2.cs.b.104.122	yes	816	35.34	odd	2	inner
945.2.cs.b.209.15	yes	816	135.74	odd	18	inner
945.2.cs.b.209.16	yes	816	945.209	even	18	inner
945.2.cs.b.209.121	yes	816	189.20	even	18	inner
945.2.cs.b.209.122	yes	816	27.20	odd	18	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19076 - 0.797371i) q^{2} +(0.522216 + 1.65145i) q^{3} +(2.63153 + 2.20812i) q^{4} +(2.22823 + 0.187052i) q^{5} +(0.172770 - 4.03433i) q^{6} +(2.63262 - 0.263278i) q^{7} +(-1.67300 - 2.89773i) q^{8} +(-2.45458 + 1.72483i) q^{9} +O(q^{10})\)	\(q+(-2.19076 - 0.797371i) q^{2} +(0.522216 + 1.65145i) q^{3} +(2.63153 + 2.20812i) q^{4} +(2.22823 + 0.187052i) q^{5} +(0.172770 - 4.03433i) q^{6} +(2.63262 - 0.263278i) q^{7} +(-1.67300 - 2.89773i) q^{8} +(-2.45458 + 1.72483i) q^{9} +(-4.73236 - 2.18651i) q^{10} +(-3.96348 + 0.698869i) q^{11} +(-2.27237 + 5.49896i) q^{12} +(1.68772 - 0.614279i) q^{13} +(-5.97736 - 1.52239i) q^{14} +(0.854711 + 3.77750i) q^{15} +(0.161544 + 0.916161i) q^{16} +(5.42879 + 3.13432i) q^{17} +(6.75272 - 1.82147i) q^{18} +(7.17570 - 4.14289i) q^{19} +(5.45063 + 5.41243i) q^{20} +(1.80959 + 4.21015i) q^{21} +(9.24029 + 1.62931i) q^{22} +(1.38768 + 1.16440i) q^{23} +(3.91179 - 4.27612i) q^{24} +(4.93002 + 0.833589i) q^{25} -4.18719 q^{26} +(-4.13029 - 3.15289i) q^{27} +(7.50917 + 5.12031i) q^{28} +(1.46750 - 4.03193i) q^{29} +(1.13960 - 8.95710i) q^{30} +(-5.08442 + 6.05938i) q^{31} +(-0.785440 + 4.45445i) q^{32} +(-3.22394 - 6.18054i) q^{33} +(-9.39396 - 11.1953i) q^{34} +(5.91533 - 0.0942090i) q^{35} +(-10.2679 - 0.881063i) q^{36} +(-3.90920 - 2.25698i) q^{37} +(-19.0236 + 3.35438i) q^{38} +(1.89580 + 2.46640i) q^{39} +(-3.18581 - 6.76974i) q^{40} +(-5.58968 + 2.03448i) q^{41} +(-0.607314 - 10.6663i) q^{42} +(9.22292 - 1.62625i) q^{43} +(-11.9732 - 6.91274i) q^{44} +(-5.79200 + 3.38418i) q^{45} +(-2.11161 - 3.65741i) q^{46} +(-2.39686 - 2.85647i) q^{47} +(-1.42863 + 0.745216i) q^{48} +(6.86137 - 1.38622i) q^{49} +(-10.1358 - 5.75725i) q^{50} +(-2.34117 + 10.6022i) q^{51} +(5.79768 + 2.11018i) q^{52} -0.780017 q^{53} +(6.53445 + 10.2006i) q^{54} +(-8.96228 + 0.815865i) q^{55} +(-5.16729 - 7.18815i) q^{56} +(10.5890 + 9.68683i) q^{57} +(-6.42988 + 7.66283i) q^{58} +(0.0111392 - 0.0631733i) q^{59} +(-6.09195 + 11.8279i) q^{60} +(0.356258 + 0.424572i) q^{61} +(15.9703 - 9.22046i) q^{62} +(-6.00787 + 5.18705i) q^{63} +(6.20285 - 10.7437i) q^{64} +(3.87552 - 1.05306i) q^{65} +(2.13470 + 16.1107i) q^{66} +(3.90360 + 10.7250i) q^{67} +(7.36510 + 20.2355i) q^{68} +(-1.19828 + 2.89975i) q^{69} +(-13.0342 - 4.51032i) q^{70} +(-2.16543 - 1.25021i) q^{71} +(9.10460 + 4.22706i) q^{72} +(-3.04424 - 5.27277i) q^{73} +(6.76446 + 8.06157i) q^{74} +(1.19791 + 8.57701i) q^{75} +(28.0311 + 4.94263i) q^{76} +(-10.2503 + 2.88336i) q^{77} +(-2.18662 - 6.91493i) q^{78} +(-3.11986 - 1.13554i) q^{79} +(0.188588 + 2.07163i) q^{80} +(3.04994 - 8.46746i) q^{81} +13.8679 q^{82} +(-0.130659 + 0.358982i) q^{83} +(-4.53453 + 15.0749i) q^{84} +(11.5103 + 7.99944i) q^{85} +(-21.5019 - 3.79137i) q^{86} +(7.42488 + 0.317970i) q^{87} +(8.65605 + 10.3159i) q^{88} +(0.0369063 + 0.0639235i) q^{89} +(15.3873 - 2.79555i) q^{90} +(4.28139 - 2.06150i) q^{91} +(1.08059 + 6.12831i) q^{92} +(-12.6619 - 5.23237i) q^{93} +(2.97328 + 8.16902i) q^{94} +(16.7640 - 7.88909i) q^{95} +(-7.76648 + 1.02907i) q^{96} +(1.33504 + 7.57141i) q^{97} +(-16.1369 - 2.43417i) q^{98} +(8.52326 - 8.55176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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