LMFDB - Embedded newform 490.2.p.a.239.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(29,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 6]))

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

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

chi := DirichletCharacter("490.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.p (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			239.15
Character	$\chi$	$=$	490.239
Dual form			490.2.p.a.449.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(-1.36175 + 2.82770i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.747370 + 2.10747i) q^{5} +(-2.82770 + 1.36175i) q^{6} +(-1.52706 - 2.16058i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-4.27104 - 5.35572i) q^{9} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(-1.36175 + 2.82770i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.747370 + 2.10747i) q^{5} +(-2.82770 + 1.36175i) q^{6} +(-1.52706 - 2.16058i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-4.27104 - 5.35572i) q^{9} +(-1.89830 + 1.18171i) q^{10} +(-0.773489 + 0.969925i) q^{11} +(-3.05982 - 0.698383i) q^{12} +(4.30402 + 3.43234i) q^{13} +(0.153199 - 2.64131i) q^{14} +(-4.94156 - 4.98318i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.89194 - 0.431824i) q^{17} -6.85022i q^{18} +2.48970 q^{19} +(-2.22094 - 0.259676i) q^{20} +(8.18893 - 1.37589i) q^{21} +(-1.20948 + 0.276055i) q^{22} +(-3.40974 + 0.778252i) q^{23} +(-1.95683 - 2.45378i) q^{24} +(-3.88287 - 3.15012i) q^{25} +(1.22499 + 5.36702i) q^{26} +(11.7810 - 2.68893i) q^{27} +(1.76661 - 1.96954i) q^{28} +(-0.423141 + 1.85390i) q^{29} +(-0.756506 - 6.97702i) q^{30} -0.154950 q^{31} +(-0.974928 - 0.222521i) q^{32} +(-1.68936 - 3.50798i) q^{33} +(-1.20994 - 1.51722i) q^{34} +(5.69464 - 1.60347i) q^{35} +(4.27104 - 5.35572i) q^{36} +(5.27825 + 1.20473i) q^{37} +(1.94653 + 1.55230i) q^{38} +(-15.5666 + 7.49648i) q^{39} +(-1.57449 - 1.58776i) q^{40} +(6.23353 + 3.00191i) q^{41} +(7.26021 + 4.03000i) q^{42} +(-0.374898 - 0.778483i) q^{43} +(-1.11772 - 0.538268i) q^{44} +(14.4791 - 4.99840i) q^{45} +(-3.15108 - 1.51748i) q^{46} +(-7.75497 - 6.18438i) q^{47} -3.13851i q^{48} +(-2.33620 + 6.59865i) q^{49} +(-1.07168 - 4.88380i) q^{50} +(3.79742 - 4.76181i) q^{51} +(-2.38855 + 4.95987i) q^{52} +(-10.8465 + 2.47565i) q^{53} +(10.8873 + 5.24303i) q^{54} +(-1.46601 - 2.35500i) q^{55} +(2.60918 - 0.438389i) q^{56} +(-3.39035 + 7.04013i) q^{57} +(-1.48671 + 1.18561i) q^{58} +(-13.2424 + 6.37722i) q^{59} +(3.75864 - 5.92653i) q^{60} +(-2.42207 + 10.6118i) q^{61} +(-0.121145 - 0.0966097i) q^{62} +(-5.04933 + 17.4064i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-10.4503 + 6.50537i) q^{65} +(0.866401 - 3.79595i) q^{66} +10.7671i q^{67} -1.94060i q^{68} +(2.44255 - 10.7015i) q^{69} +(5.45199 + 2.29690i) q^{70} +(-2.64828 - 11.6029i) q^{71} +(6.67847 - 1.52432i) q^{72} +(5.96588 - 4.75763i) q^{73} +(3.37557 + 4.23283i) q^{74} +(14.1951 - 6.68992i) q^{75} +(0.554011 + 2.42728i) q^{76} +(3.27676 + 0.190055i) q^{77} +(-16.8444 - 3.84463i) q^{78} +12.9231 q^{79} +(-0.241040 - 2.22304i) q^{80} +(-3.86628 + 16.9393i) q^{81} +(3.00191 + 6.23353i) q^{82} +(-7.66281 + 6.11089i) q^{83} +(3.16360 + 7.67745i) q^{84} +(2.32404 - 3.66449i) q^{85} +(0.192269 - 0.842387i) q^{86} +(-4.66606 - 3.72106i) q^{87} +(-0.538268 - 1.11772i) q^{88} +(7.92432 + 9.93679i) q^{89} +(14.4367 + 5.11965i) q^{90} +(0.843366 - 14.5405i) q^{91} +(-1.51748 - 3.15108i) q^{92} +(0.211003 - 0.438151i) q^{93} +(-2.20718 - 9.67029i) q^{94} +(-1.86073 + 5.24698i) q^{95} +(1.95683 - 2.45378i) q^{96} -1.61439i q^{97} +(-5.94071 + 3.70243i) q^{98} +8.49825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	$ 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) $ 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$-1$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	−1.36175	+	2.82770i	−0.786205	+	1.63257i	−0.0117595	+	0.999931i	$0.503743\pi$
$3$	−1.36175	+	2.82770i	−0.786205	+	1.63257i	−0.774446	+	0.632641i	$0.781971\pi$
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−0.747370	+	2.10747i	−0.334234	+	0.942490i
$5$	−0.747370	+	2.10747i	−0.334234	+	0.942490i
$6$	−2.82770	+	1.36175i	−1.15440	+	0.555931i
$7$	−1.52706	−	2.16058i	−0.577173	−	0.816622i
$7$	−1.52706	−	2.16058i	−0.577173	−	0.816622i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	−4.27104	−	5.35572i	−1.42368	−	1.78524i
$10$	−1.89830	+	1.18171i	−0.600297	+	0.373689i
$11$	−0.773489	+	0.969925i	−0.233216	+	0.292443i	−0.884644	−	0.466267i	$-0.845599\pi$
$11$	−0.773489	+	0.969925i	−0.233216	+	0.292443i	0.651428	+	0.758710i	$0.274170\pi$
$12$	−3.05982	−	0.698383i	−0.883293	−	0.201606i
$13$	4.30402	+	3.43234i	1.19372	+	0.951960i	0.999579	−	0.0290138i	$-0.00923669\pi$
$13$	4.30402	+	3.43234i	1.19372	+	0.951960i	0.194141	+	0.980974i	$0.437808\pi$
$14$	0.153199	−	2.64131i	0.0409441	−	0.705920i
$15$	−4.94156	−	4.98318i	−1.27591	−	1.28665i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−1.89194	−	0.431824i	−0.458864	−	0.104733i	−0.0131604	−	0.999913i	$-0.504189\pi$
$17$	−1.89194	−	0.431824i	−0.458864	−	0.104733i	−0.445703	+	0.895181i	$0.647046\pi$
$18$		−	6.85022i		−	1.61461i
$19$	2.48970			0.571177			0.285589	−	0.958352i	$-0.407811\pi$
$19$	2.48970			0.571177			0.285589	+	0.958352i	$0.407811\pi$
$20$	−2.22094	−	0.259676i	−0.496617	−	0.0580653i
$21$	8.18893	−	1.37589i	1.78697	−	0.300243i
$22$	−1.20948	+	0.276055i	−0.257861	+	0.0588551i
$23$	−3.40974	+	0.778252i	−0.710981	+	0.162277i	−0.562691	−	0.826667i	$-0.690234\pi$
$23$	−3.40974	+	0.778252i	−0.710981	+	0.162277i	−0.148290	+	0.988944i	$0.547377\pi$
$24$	−1.95683	−	2.45378i	−0.399436	−	0.500876i
$25$	−3.88287	−	3.15012i	−0.776575	−	0.630025i
$26$	1.22499	+	5.36702i	0.240240	+	1.05256i
$27$	11.7810	−	2.68893i	2.26725	−	0.517485i
$28$	1.76661	−	1.96954i	0.333857	−	0.372209i
$29$	−0.423141	+	1.85390i	−0.0785753	+	0.344261i	−0.998900	−	0.0468948i	$-0.985067\pi$
$29$	−0.423141	+	1.85390i	−0.0785753	+	0.344261i	0.920325	+	0.391156i	$0.127925\pi$
$30$	−0.756506	−	6.97702i	−0.138119	−	1.27382i
$31$	−0.154950			−0.0278298			−0.0139149	−	0.999903i	$-0.504429\pi$
$31$	−0.154950			−0.0278298			−0.0139149	+	0.999903i	$0.504429\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	−1.68936	−	3.50798i	−0.294079	−	0.610662i
$34$	−1.20994	−	1.51722i	−0.207504	−	0.260201i
$35$	5.69464	−	1.60347i	0.962569	−	0.271037i
$36$	4.27104	−	5.35572i	0.711841	−	0.892620i
$37$	5.27825	+	1.20473i	0.867739	+	0.198056i	0.633141	−	0.774037i	$-0.281765\pi$
$37$	5.27825	+	1.20473i	0.867739	+	0.198056i	0.234598	+	0.972092i	$0.424623\pi$
$38$	1.94653	+	1.55230i	0.315769	+	0.251817i
$39$	−15.5666	+	7.49648i	−2.49265	+	1.20040i
$40$	−1.57449	−	1.58776i	−0.248949	−	0.251046i
$41$	6.23353	+	3.00191i	0.973514	+	0.468819i	0.851869	−	0.523754i	$-0.175469\pi$
$41$	6.23353	+	3.00191i	0.973514	+	0.468819i	0.121644	+	0.992574i	$0.461183\pi$
$42$	7.26021	+	4.03000i	1.12028	+	0.621842i
$43$	−0.374898	−	0.778483i	−0.0571714	−	0.118718i	0.870426	−	0.492300i	$-0.163844\pi$
$43$	−0.374898	−	0.778483i	−0.0571714	−	0.118718i	−0.927597	+	0.373582i	$0.878129\pi$
$44$	−1.11772	−	0.538268i	−0.168503	−	0.0811469i
$45$	14.4791	−	4.99840i	2.15841	−	0.745117i
$46$	−3.15108	−	1.51748i	−0.464601	−	0.223740i
$47$	−7.75497	−	6.18438i	−1.13118	−	0.902085i	−0.135125	−	0.990829i	$-0.543143\pi$
$47$	−7.75497	−	6.18438i	−1.13118	−	0.902085i	−0.996055	+	0.0887435i	$0.971715\pi$
$48$		−	3.13851i		−	0.453004i
$49$	−2.33620	+	6.59865i	−0.333743	+	0.942664i
$50$	−1.07168	−	4.88380i	−0.151559	−	0.690674i
$51$	3.79742	−	4.76181i	0.531744	−	0.666786i
$52$	−2.38855	+	4.95987i	−0.331232	+	0.687811i
$53$	−10.8465	+	2.47565i	−1.48989	+	0.340057i	−0.888491	−	0.458894i	$-0.848246\pi$
$53$	−10.8465	+	2.47565i	−1.48989	+	0.340057i	−0.601396	+	0.798951i	$0.705389\pi$
$54$	10.8873	+	5.24303i	1.48157	+	0.713486i
$55$	−1.46601	−	2.35500i	−0.197676	−	0.317548i
$56$	2.60918	−	0.438389i	0.348666	−	0.0585823i
$57$	−3.39035	+	7.04013i	−0.449062	+	0.932488i
$58$	−1.48671	+	1.18561i	−0.195215	+	0.155679i
$59$	−13.2424	+	6.37722i	−1.72402	+	0.830243i	−0.735798	+	0.677201i	$0.763193\pi$
$59$	−13.2424	+	6.37722i	−1.72402	+	0.830243i	−0.988220	+	0.153042i	$0.951093\pi$
$60$	3.75864	−	5.92653i	0.485238	−	0.765112i
$61$	−2.42207	+	10.6118i	−0.310114	+	1.35870i	0.544206	+	0.838952i	$0.316831\pi$
$61$	−2.42207	+	10.6118i	−0.310114	+	1.35870i	−0.854320	+	0.519747i	$0.826026\pi$
$62$	−0.121145	−	0.0966097i	−0.0153854	−	0.0122694i
$63$	−5.04933	+	17.4064i	−0.636156	+	2.19300i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−10.4503	+	6.50537i	−1.29619	+	0.806892i
$66$	0.866401	−	3.79595i	0.106647	−	0.467249i
$67$			10.7671i			1.31541i	0.753275	+	0.657705i	$0.228473\pi$
$67$			10.7671i			1.31541i	−0.753275	+	0.657705i	$0.771527\pi$
$68$		−	1.94060i		−	0.235332i
$69$	2.44255	−	10.7015i	0.294048	−	1.28831i
$70$	5.45199	+	2.29690i	0.651638	+	0.274532i
$71$	−2.64828	−	11.6029i	−0.314293	−	1.37701i	−0.847397	−	0.530959i	$-0.821832\pi$
$71$	−2.64828	−	11.6029i	−0.314293	−	1.37701i	0.533104	−	0.846050i	$-0.321025\pi$
$72$	6.67847	−	1.52432i	0.787066	−	0.179643i
$73$	5.96588	−	4.75763i	0.698254	−	0.556839i	−0.208746	−	0.977970i	$-0.566938\pi$
$73$	5.96588	−	4.75763i	0.698254	−	0.556839i	0.907000	+	0.421131i	$0.138367\pi$
$74$	3.37557	+	4.23283i	0.392402	+	0.492056i
$75$	14.1951	−	6.68992i	1.63911	−	0.772485i
$76$	0.554011	+	2.42728i	0.0635494	+	0.278428i
$77$	3.27676	+	0.190055i	0.373421	+	0.0216588i
$78$	−16.8444	−	3.84463i	−1.90726	−	0.435319i
$79$	12.9231			1.45396			0.726982	−	0.686657i	$-0.240923\pi$
$79$	12.9231			1.45396			0.726982	+	0.686657i	$0.240923\pi$
$80$	−0.241040	−	2.22304i	−0.0269491	−	0.248543i
$81$	−3.86628	+	16.9393i	−0.429586	+	1.88214i
$82$	3.00191	+	6.23353i	0.331505	+	0.688378i
$83$	−7.66281	+	6.11089i	−0.841103	+	0.670757i	−0.946157	−	0.323709i	$-0.895070\pi$
$83$	−7.66281	+	6.11089i	−0.841103	+	0.670757i	0.105054	+	0.994467i	$0.466499\pi$
$84$	3.16360	+	7.67745i	0.345177	+	0.837678i
$85$	2.32404	−	3.66449i	0.252077	−	0.397469i
$86$	0.192269	−	0.842387i	0.0207329	−	0.0908370i
$87$	−4.66606	−	3.72106i	−0.500254	−	0.398939i
$88$	−0.538268	−	1.11772i	−0.0573795	−	0.119150i
$89$	7.92432	+	9.93679i	0.839977	+	1.05330i	0.997831	+	0.0658349i	$0.0209711\pi$
$89$	7.92432	+	9.93679i	0.839977	+	1.05330i	−0.157854	+	0.987462i	$0.550457\pi$
$90$	14.4367	+	5.11965i	1.52176	+	0.539659i
$91$	0.843366	−	14.5405i	0.0884088	−	1.52426i
$92$	−1.51748	−	3.15108i	−0.158208	−	0.328523i
$93$	0.211003	−	0.438151i	0.0218799	−	0.0454342i
$94$	−2.20718	−	9.67029i	−0.227653	−	0.997415i
$95$	−1.86073	+	5.24698i	−0.190907	+	0.538329i
$96$	1.95683	−	2.45378i	0.199718	−	0.250438i
$97$		−	1.61439i		−	0.163917i	−0.996636	−	0.0819584i	$-0.973883\pi$
$97$		−	1.61439i		−	0.163917i	0.996636	−	0.0819584i	$-0.0261175\pi$
$98$	−5.94071	+	3.70243i	−0.600102	+	0.374002i
$99$	8.49825			0.854106
$100$	2.20712	−	4.48649i	0.220712	−	0.448649i
$101$	16.4881	+	7.94026i	1.64063	+	0.790085i	0.999748	+	0.0224455i	$0.00714522\pi$
$101$	16.4881	+	7.94026i	1.64063	+	0.790085i	0.640881	+	0.767640i	$0.278569\pi$
$102$	5.93788	−	1.35528i	0.587937	−	0.134193i
$103$	−5.58338	+	11.5940i	−0.550146	+	1.14239i	0.421691	+	0.906739i	$0.361437\pi$
$103$	−5.58338	+	11.5940i	−0.550146	+	1.14239i	−0.971838	+	0.235651i	$0.924278\pi$
$104$	−4.95987	+	2.38855i	−0.486356	+	0.234217i
$105$	−3.22052	+	18.2862i	−0.314290	+	1.78455i
$106$	−10.0237	−	4.82717i	−0.973589	−	0.468856i
$107$	0.113059	−	0.0901614i	0.0109298	−	0.00871623i	−0.618010	−	0.786170i	$-0.712061\pi$
$107$	0.113059	−	0.0901614i	0.0109298	−	0.00871623i	0.628939	+	0.777454i	$0.283489\pi$
$108$	5.24303	+	10.8873i	0.504511	+	1.04763i
$109$	3.52479	−	4.41995i	0.337614	−	0.423354i	−0.583824	−	0.811880i	$-0.698444\pi$
$109$	3.52479	−	4.41995i	0.337614	−	0.423354i	0.921438	+	0.388526i	$0.127016\pi$
$110$	0.322149	−	2.75525i	0.0307157	−	0.262703i
$111$	−10.5942	+	13.2848i	−1.00556	+	1.26093i
$112$	2.31327	+	1.28405i	0.218583	+	0.121331i
$113$	14.0800	−	11.2284i	1.32453	−	1.05628i	0.330894	−	0.943668i	$-0.392650\pi$
$113$	14.0800	−	11.2284i	1.32453	−	1.05628i	0.993639	−	0.112612i	$-0.0359216\pi$
$114$	−7.04013	+	3.39035i	−0.659368	+	0.317535i
$115$	0.908198	−	7.76758i	0.0846899	−	0.724331i
$116$	−1.90158			−0.176557
$117$		−	37.7108i		−	3.48636i
$118$	−14.3295	−	3.27061i	−1.31914	−	0.301084i
$119$	1.95611	+	4.74711i	0.179317	+	0.435167i
$120$	6.63375	−	2.29007i	0.605576	−	0.209054i
$121$	2.10526	+	9.22375i	0.191387	+	0.838523i
$122$	−8.50999	+	6.78649i	−0.770458	+	0.614420i
$123$	−16.9770	+	13.5387i	−1.53076	+	1.22074i
$124$	−0.0344796	−	0.151065i	−0.00309636	−	0.0135660i
$125$	9.54074	−	5.82874i	0.853350	−	0.521338i
$126$	−14.8004	+	10.4607i	−1.31853	+	0.931911i
$127$	3.89563	+	0.889152i	0.345681	+	0.0788995i	0.391837	−	0.920035i	$-0.371840\pi$
$127$	3.89563	+	0.889152i	0.345681	+	0.0788995i	−0.0461555	+	0.998934i	$0.514697\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.71183			0.238763
$130$	−12.2264	−	1.42953i	−1.07232	−	0.125378i
$131$	−1.03126	+	0.496628i	−0.0901014	+	0.0433906i	−0.478392	−	0.878147i	$-0.658780\pi$
$131$	−1.03126	+	0.496628i	−0.0901014	+	0.0433906i	0.388290	+	0.921537i	$0.373066\pi$
$132$	3.04412	−	2.42760i	0.264956	−	0.211296i
$133$	−3.80192	−	5.37920i	−0.329668	−	0.466436i
$134$	−6.71318	+	8.41806i	−0.579930	+	0.727210i
$135$	−3.13791	+	26.8377i	−0.270068	+	2.30982i
$136$	1.20994	−	1.51722i	0.103752	−	0.130101i
$137$	0.498275	+	1.03468i	0.0425705	+	0.0883986i	0.921169	−	0.389162i	$-0.127235\pi$
$137$	0.498275	+	1.03468i	0.0425705	+	0.0883986i	−0.878599	+	0.477561i	$0.841521\pi$
$138$	8.58194	−	6.84387i	0.730543	−	0.582589i
$139$	2.37498	+	1.14373i	0.201443	+	0.0970100i	0.531886	−	0.846816i	$-0.321484\pi$
$139$	2.37498	+	1.14373i	0.201443	+	0.0970100i	−0.330442	+	0.943826i	$0.607198\pi$
$140$	2.83045	+	5.19505i	0.239216	+	0.439062i
$141$	28.0479	−	13.5071i	2.36206	−	1.13751i
$142$	5.16377	−	10.7227i	0.433334	−	0.899827i
$143$	−6.65822	+	1.51970i	−0.556789	+	0.127083i
$144$	6.17184	+	2.97220i	0.514320	+	0.247683i
$145$	−3.59080	−	2.27731i	−0.298200	−	0.189120i
$146$	7.63065			0.631517
$147$	−15.4777	−	15.5918i	−1.27658	−	1.28599i
$148$			5.41399i			0.445027i
$149$	3.57680	−	4.48517i	0.293023	−	0.367439i	−0.613428	−	0.789751i	$-0.710210\pi$
$149$	3.57680	−	4.48517i	0.293023	−	0.367439i	0.906451	+	0.422312i	$0.138781\pi$
$150$	15.2693	+	3.62010i	1.24673	+	0.295580i
$151$	−1.61069	−	7.05688i	−0.131076	−	0.574281i	−0.997222	−	0.0744895i	$-0.976267\pi$
$151$	−1.61069	−	7.05688i	−0.131076	−	0.574281i	0.866146	−	0.499791i	$-0.166590\pi$
$152$	−1.08024	+	2.24315i	−0.0876192	+	0.181943i
$153$	5.76785	+	11.9771i	0.466303	+	0.968288i
$154$	2.44338	+	2.19162i	0.196893	+	0.176606i
$155$	0.115805	−	0.326553i	0.00930168	−	0.0262293i
$156$	−10.7724	−	13.5082i	−0.862484	−	1.08152i
$157$	3.10930	+	6.45653i	0.248149	+	0.515287i	0.987420	−	0.158122i	$-0.0505438\pi$
$157$	3.10930	+	6.45653i	0.248149	+	0.515287i	−0.739270	+	0.673409i	$0.764829\pi$
$158$	10.1037	+	8.05743i	0.803807	+	0.641014i
$159$	7.76985	−	34.0419i	0.616189	−	2.69970i
$160$	1.19759	−	1.88833i	0.0946777	−	0.149285i
$161$	6.88834	+	6.17859i	0.542878	+	0.486941i
$162$	−13.5842	+	10.8331i	−1.06728	+	0.851126i
$163$	−6.41353	−	13.3178i	−0.502346	−	1.04313i	−0.985825	−	0.167777i	$-0.946341\pi$
$163$	−6.41353	−	13.3178i	−0.502346	−	1.04313i	0.483479	−	0.875356i	$-0.339373\pi$
$164$	−1.53955	+	6.74523i	−0.120219	+	0.526714i
$165$	8.65555	−	0.938507i	0.673834	−	0.0730627i
$166$	−9.80111			−0.760713
$167$	18.0628	+	4.12271i	1.39774	+	0.319025i	0.854019	−	0.520242i	$-0.174158\pi$
$167$	18.0628	+	4.12271i	1.39774	+	0.319025i	0.543720	+	0.839267i	$0.317015\pi$
$168$	−2.31341	+	7.97494i	−0.178483	+	0.615280i
$169$	3.85084	+	16.8716i	0.296219	+	1.29782i
$170$	4.10178	−	1.41600i	0.314592	−	0.108602i
$171$	−10.6336	−	13.3342i	−0.813174	−	1.01969i
$172$	0.675542	−	0.538727i	0.0515096	−	0.0410776i
$173$	−15.0853	+	3.44311i	−1.14691	+	0.261775i	−0.753411	−	0.657550i	$-0.771593\pi$
$173$	−15.0853	+	3.44311i	−1.14691	+	0.261775i	−0.393500	+	0.919325i	$0.628736\pi$
$174$	−1.32803	−	5.81848i	−0.100678	−	0.441098i
$175$	−0.876727	+	13.1997i	−0.0662743	+	0.997801i
$176$	0.276055	−	1.20948i	0.0208084	−	0.0911677i
$177$		−	46.1297i		−	3.46732i
$178$			12.7096i			0.952627i
$179$	−0.902765	+	3.95527i	−0.0674758	+	0.295631i	−0.997395	−	0.0721331i	$-0.977019\pi$
$179$	−0.902765	+	3.95527i	−0.0674758	+	0.295631i	0.929919	+	0.367764i	$0.119877\pi$
$180$	8.09498	+	13.0038i	0.603364	+	0.969247i
$181$	−15.8540	−	19.8803i	−1.17842	−	1.47769i	−0.844881	−	0.534954i	$-0.820329\pi$
$181$	−15.8540	−	19.8803i	−1.17842	−	1.47769i	−0.333538	−	0.942737i	$-0.608242\pi$
$182$	9.72525	−	10.8424i	0.720884	−	0.803694i
$183$	−26.7086	−	21.2994i	−1.97436	−	1.57450i
$184$	0.778252	−	3.40974i	0.0573735	−	0.251370i
$185$	−6.48373	+	10.2234i	−0.476693	+	0.751638i
$186$	0.438151	−	0.211003i	0.0321268	−	0.0154715i
$187$	1.88223	−	1.50103i	0.137643	−	0.109766i
$188$	4.30369	−	8.93669i	0.313878	−	0.651775i
$189$	−23.7999	−	21.3476i	−1.73119	−	1.55281i
$190$	−4.72622	+	2.94211i	−0.342876	+	0.213443i
$191$	8.15435	+	3.92693i	0.590028	+	0.284143i	0.704978	−	0.709229i	$-0.250957\pi$
$191$	8.15435	+	3.92693i	0.590028	+	0.284143i	−0.114950	+	0.993371i	$0.536671\pi$
$192$	3.05982	−	0.698383i	0.220823	−	0.0504015i
$193$	4.36493	−	9.06387i	0.314194	−	0.652432i	−0.682741	−	0.730661i	$-0.739212\pi$
$193$	4.36493	−	9.06387i	0.314194	−	0.652432i	0.996935	+	0.0782290i	$0.0249265\pi$
$194$	1.00656	−	1.26218i	0.0722666	−	0.0906195i
$195$	−4.16460	−	38.4088i	−0.298233	−	2.75051i
$196$	−6.95306	−	0.809292i	−0.496647	−	0.0578066i
$197$			22.0030i			1.56765i	0.620981	+	0.783826i	$0.286735\pi$
$197$			22.0030i			1.56765i	−0.620981	+	0.783826i	$0.713265\pi$
$198$	6.64420	+	5.29857i	0.472183	+	0.376553i
$199$	3.95806	+	1.90610i	0.280579	+	0.135120i	0.568881	−	0.822420i	$-0.307376\pi$
$199$	3.95806	+	1.90610i	0.280579	+	0.135120i	−0.288302	+	0.957540i	$0.593091\pi$
$200$	4.52288	−	2.13156i	0.319816	−	0.150724i
$201$	−30.4461	−	14.6621i	−2.14750	−	1.03418i
$202$	7.94026	+	16.4881i	0.558675	+	1.16010i
$203$	4.65166	−	1.91678i	0.326483	−	0.134532i
$204$	5.48742	+	2.64260i	0.384197	+	0.185019i
$205$	−10.9852	+	10.8934i	−0.767239	+	0.760831i
$206$	−11.5940	+	5.58338i	−0.807792	+	0.389012i
$207$	18.7313	+	14.9377i	1.30191	+	1.03824i
$208$	−5.36702	−	1.22499i	−0.372136	−	0.0849376i
$209$	−1.92576	+	2.41483i	−0.133208	+	0.167037i
$210$	−13.9192	+	12.2888i	−0.960514	+	0.848007i
$211$	0.921619	+	1.15567i	0.0634469	+	0.0795598i	0.812542	−	0.582902i	$-0.198083\pi$
$211$	0.921619	+	1.15567i	0.0634469	+	0.0795598i	−0.749095	+	0.662462i	$0.769512\pi$
$212$	−4.82717	−	10.0237i	−0.331531	−	0.688431i
$213$	36.4157	+	8.31165i	2.49516	+	0.569505i
$214$	0.144608			0.00988518
$215$	1.92082	−	0.208271i	0.130999	−	0.0142040i
$216$	−2.68893	+	11.7810i	−0.182959	+	0.801594i
$217$	0.236617	+	0.334782i	0.0160626	+	0.0227265i
$218$	5.51159	−	1.25798i	0.373292	−	0.0852014i
$219$	5.32912	+	23.3484i	0.360109	+	1.57774i
$220$	1.96974	−	1.95329i	0.132800	−	0.131691i
$221$	−6.66079	−	8.35237i	−0.448053	−	0.561841i
$222$	−16.5658	+	3.78104i	−1.11182	+	0.253767i
$223$	27.7752	−	6.33952i	1.85997	−	0.424525i	0.863199	−	0.504863i	$-0.168457\pi$
$223$	27.7752	−	6.33952i	1.85997	−	0.424525i	0.996768	+	0.0803379i	$0.0255999\pi$
$224$	1.00800	+	2.44621i	0.0673495	+	0.163444i
$225$	−0.287254	+	34.2499i	−0.0191503	+	2.28333i
$226$	18.0090			1.19794
$227$			9.38202i			0.622706i	0.950294	+	0.311353i	$0.100782\pi$
$227$			9.38202i			0.622706i	−0.950294	+	0.311353i	$0.899218\pi$
$228$	−7.61804	−	1.73877i	−0.504517	−	0.115153i
$229$	0.141788	−	0.0682816i	0.00936963	−	0.00451218i	−0.429193	−	0.903213i	$-0.641202\pi$
$229$	0.141788	−	0.0682816i	0.00936963	−	0.00451218i	0.438563	+	0.898701i	$0.355488\pi$
$230$	5.55307	−	5.50669i	0.366158	−	0.363100i
$231$	−4.99954	+	9.00688i	−0.328945	+	0.592609i
$232$	−1.48671	−	1.18561i	−0.0976075	−	0.0778394i
$233$	9.77527	+	2.23114i	0.640399	+	0.146167i	0.530377	−	0.847762i	$-0.322051\pi$
$233$	9.77527	+	2.23114i	0.640399	+	0.146167i	0.110023	+	0.993929i	$0.464908\pi$
$234$	23.5123	−	29.4835i	1.53705	−	1.92740i
$235$	18.8293	−	11.7214i	1.22829	−	0.764617i
$236$	−9.16405	−	11.4913i	−0.596529	−	0.748023i
$237$	−17.5980	+	36.5426i	−1.14311	+	2.37370i
$238$	−1.43042	+	4.93106i	−0.0927207	+	0.319633i
$239$	−8.73838	+	4.20818i	−0.565239	+	0.272205i	−0.694604	−	0.719392i	$-0.744420\pi$
$239$	−8.73838	+	4.20818i	−0.565239	+	0.272205i	0.129365	+	0.991597i	$0.458706\pi$
$240$	6.61431	+	2.34563i	0.426952	+	0.151410i
$241$	−2.19273	−	9.60698i	−0.141246	−	0.618840i	−0.995147	−	0.0984037i	$-0.968626\pi$
$241$	−2.19273	−	9.60698i	−0.141246	−	0.618840i	0.853900	−	0.520437i	$-0.174231\pi$
$242$	−4.10496	+	8.52403i	−0.263877	+	0.547945i
$243$	−14.2914	−	11.3970i	−0.916792	−	0.731117i
$244$	−10.8847			−0.696820
$245$	−12.1605	−	9.85512i	−0.776903	−	0.629620i
$246$	−21.7144			−1.38446
$247$	10.7157	+	8.54551i	0.681826	+	0.543738i
$248$	0.0672302	−	0.139605i	0.00426913	−	0.00886493i
$249$	−6.84493	−	29.9896i	−0.433780	−	1.90051i
$250$	11.0934	+	1.39146i	0.701609	+	0.0880040i
$251$	0.713022	−	0.343373i	0.0450056	−	0.0216735i	−0.411246	−	0.911525i	$-0.634906\pi$
$251$	0.713022	−	0.343373i	0.0450056	−	0.0216735i	0.456251	+	0.889851i	$0.349192\pi$
$252$	−18.0936	−	1.04945i	−1.13979	−	0.0661089i
$253$	1.88255	−	3.90917i	0.118355	−	0.245767i
$254$	2.49135	+	3.12405i	0.156321	+	0.196020i
$255$	7.19730	+	11.5618i	0.450712	+	0.724027i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−4.72307	−	1.07801i	−0.294617	−	0.0672444i	0.0726577	−	0.997357i	$-0.476852\pi$
$257$	−4.72307	−	1.07801i	−0.294617	−	0.0672444i	−0.367275	+	0.930113i	$0.619709\pi$
$258$	2.12019	+	1.69080i	0.131998	+	0.105265i
$259$	−5.45727	−	13.2438i	−0.339098	−	0.822927i
$260$	−8.66766	−	8.74067i	−0.537546	−	0.542073i
$261$	11.7362	−	5.65187i	0.726455	−	0.349842i
$262$	−1.11591	−	0.254700i	−0.0689413	−	0.0157354i
$263$		−	2.18906i		−	0.134983i	−0.997720	−	0.0674915i	$-0.978500\pi$
$263$		−	2.18906i		−	0.134983i	0.997720	−	0.0674915i	$-0.0214996\pi$
$264$	3.89357			0.239633
$265$	2.88902	−	24.7090i	0.177471	−	1.51786i
$266$	0.381420	−	6.57609i	0.0233863	−	0.403206i
$267$	−38.8891	+	8.87619i	−2.37998	+	0.543214i
$268$	−10.4971	+	2.39591i	−0.641215	+	0.146353i
$269$	14.6693	+	18.3947i	0.894402	+	1.12155i	0.991990	+	0.126318i	$0.0403160\pi$
$269$	14.6693	+	18.3947i	0.894402	+	1.12155i	−0.0975875	+	0.995227i	$0.531113\pi$
$270$	−19.1864	+	19.0261i	−1.16764	+	1.15789i
$271$	6.32972	+	27.7323i	0.384503	+	1.68462i	0.683169	+	0.730260i	$0.260601\pi$
$271$	6.32972	+	27.7323i	0.384503	+	1.68462i	−0.298666	+	0.954358i	$0.596542\pi$
$272$	1.89194	−	0.431824i	0.114716	−	0.0261832i
$273$	39.9678	+	22.1853i	2.41896	+	1.34272i
$274$	−0.255545	+	1.11961i	−0.0154380	+	0.0676384i
$275$	6.05874	−	1.32951i	0.365356	−	0.0801724i
$276$	10.9767			0.660721
$277$	13.2014	+	3.01314i	0.793196	+	0.181042i	0.599875	−	0.800094i	$-0.295217\pi$
$277$	13.2014	+	3.01314i	0.793196	+	0.181042i	0.193321	+	0.981136i	$0.438074\pi$
$278$	1.14373	+	2.37498i	0.0685965	+	0.142442i
$279$	0.661798	+	0.829868i	0.0396208	+	0.0496829i
$280$	−1.02613	+	5.82641i	−0.0613230	+	0.348195i
$281$	−11.6578	+	14.6184i	−0.695444	+	0.872059i	−0.996674	−	0.0814922i	$-0.974031\pi$
$281$	−11.6578	+	14.6184i	−0.695444	+	0.872059i	0.301230	+	0.953552i	$0.402603\pi$
$282$	30.3503	+	6.92725i	1.80733	+	0.412512i
$283$	−8.98425	−	7.16470i	−0.534058	−	0.425897i	0.318968	−	0.947766i	$-0.396664\pi$
$283$	−8.98425	−	7.16470i	−0.534058	−	0.425897i	−0.853026	+	0.521868i	$0.825235\pi$
$284$	10.7227	−	5.16377i	0.636274	−	0.306413i
$285$	−12.3030	−	12.4066i	−0.728768	−	0.734906i
$286$	−6.15312	−	2.96319i	−0.363842	−	0.175217i
$287$	−3.03308	−	18.0521i	−0.179037	−	1.06558i
$288$	2.97220	+	6.17184i	0.175139	+	0.363679i
$289$	−11.9235	−	5.74205i	−0.701382	−	0.337768i
$290$	−1.38752	−	4.01930i	−0.0814782	−	0.236021i
$291$	4.56502	+	2.19840i	0.267606	+	0.128872i
$292$	5.96588	+	4.75763i	0.349127	+	0.278419i
$293$		−	7.65083i		−	0.446966i	−0.974708	−	0.223483i	$-0.928257\pi$
$293$		−	7.65083i		−	0.446966i	0.974708	−	0.223483i	$-0.0717428\pi$
$294$	−2.37962	−	21.8403i	−0.138782	−	1.27375i
$295$	−3.54281	−	32.6742i	−0.206270	−	1.90236i
$296$	−3.37557	+	4.23283i	−0.196201	+	0.246028i
$297$	−6.50440	+	13.5065i	−0.377424	+	0.783728i
$298$	5.59291	−	1.27655i	0.323989	−	0.0739483i
$299$	−17.3468	−	8.35379i	−1.00319	−	0.483112i
$300$	9.68089	+	12.3505i	0.558927	+	0.713059i
$301$	−1.10948	+	1.99878i	−0.0639496	+	0.115208i
$302$	3.14061	−	6.52154i	0.180722	−	0.375272i
$303$	−44.9053	+	35.8108i	−2.57974	+	2.05728i
$304$	−2.24315	+	1.08024i	−0.128653	+	0.0619561i
$305$	−20.5538	−	13.0354i	−1.17691	−	0.746403i
$306$	−2.95809	+	12.9602i	−0.169103	+	0.740887i
$307$	9.32891	+	7.43956i	0.532429	+	0.424598i	0.852447	−	0.522813i	$-0.175118\pi$
$307$	9.32891	+	7.43956i	0.532429	+	0.424598i	−0.320018	+	0.947411i	$0.603689\pi$
$308$	0.543857	+	3.23690i	0.0309891	+	0.184439i
$309$	−25.1812	−	31.5762i	−1.43251	−	1.79631i
$310$	0.294142	−	0.183106i	0.0167062	−	0.0103997i
$311$	1.07993	−	4.73148i	0.0612371	−	0.268297i	−0.935036	−	0.354553i	$-0.884633\pi$
$311$	1.07993	−	4.73148i	0.0612371	−	0.268297i	0.996273	+	0.0862556i	$0.0274902\pi$
$312$		−	17.2776i		−	0.978153i
$313$		−	3.39428i		−	0.191856i	−0.995388	−	0.0959280i	$-0.969418\pi$
$313$		−	3.39428i		−	0.191856i	0.995388	−	0.0959280i	$-0.0305819\pi$
$314$	−1.59463	+	6.98653i	−0.0899902	+	0.394273i
$315$	−32.9098	−	23.6504i	−1.85426	−	1.33255i
$316$	2.87566	+	12.5991i	0.161769	+	0.708755i
$317$	23.4002	−	5.34094i	1.31429	−	0.299977i	0.492769	−	0.870160i	$-0.335985\pi$
$317$	23.4002	−	5.34094i	1.31429	−	0.299977i	0.821518	+	0.570183i	$0.193128\pi$
$318$	27.2995	−	21.7706i	1.53088	−	1.22084i
$319$	−1.47085	−	1.84439i	−0.0823518	−	0.103266i
$320$	2.11367	−	0.729669i	0.118158	−	0.0407898i
$321$	0.100992	+	0.442473i	0.00563680	+	0.0246964i
$322$	1.53324	+	9.12543i	0.0854440	+	0.508540i
$323$	−4.71038	−	1.07511i	−0.262093	−	0.0598209i
$324$	−17.3749			−0.965272
$325$	−5.89967	−	26.8855i	−0.327255	−	1.49134i
$326$	3.28923	−	14.4111i	0.182174	−	0.798155i
$327$	7.69840	+	15.9859i	0.425723	+	0.884022i
$328$	−5.40925	+	4.31374i	−0.298676	+	0.238186i
$329$	−1.51958	+	26.1991i	−0.0837769	+	1.44440i
$330$	7.35233	+	4.66290i	0.404733	+	0.256684i
$331$	3.98276	−	17.4496i	0.218912	−	0.959116i	−0.739372	−	0.673298i	$-0.764877\pi$
$331$	3.98276	−	17.4496i	0.218912	−	0.959116i	0.958284	−	0.285819i	$-0.0922655\pi$
$332$	−7.66281	−	6.11089i	−0.420552	−	0.335379i
$333$	−16.0915	−	33.4143i	−0.881806	−	1.83109i
$334$	11.5516	+	14.4852i	0.632074	+	0.792596i
$335$	−22.6914	−	8.04701i	−1.23976	−	0.439655i
$336$	−6.78099	+	4.79267i	−0.369933	+	0.261462i
$337$	−7.03143	−	14.6009i	−0.383026	−	0.795362i	−0.999965	−	0.00835117i	$-0.997342\pi$
$337$	−7.03143	−	14.6009i	−0.383026	−	0.795362i	0.616939	−	0.787011i	$-0.288373\pi$
$338$	−7.50859	+	15.5917i	−0.408413	+	0.848079i
$339$	12.5772	+	55.1042i	0.683098	+	2.99285i
$340$	4.08976	+	1.45035i	0.221798	+	0.0786561i
$341$	0.119852	−	0.150290i	0.00649035	−	0.00813865i
$342$		−	17.0550i		−	0.922230i
$343$	17.8244	−	5.02895i	0.962428	−	0.271538i
$344$	0.864051			0.0465865
$345$	20.7276	+	13.1456i	1.11594	+	0.707735i
$346$	−13.9409	−	6.71357i	−0.749466	−	0.360924i
$347$	−2.70790	+	0.618060i	−0.145367	+	0.0331792i	−0.294585	−	0.955625i	$-0.595182\pi$
$347$	−2.70790	+	0.618060i	−0.145367	+	0.0331792i	0.149218	+	0.988804i	$0.452324\pi$
$348$	2.58947	−	5.37709i	0.138810	−	0.288242i
$349$	−3.07603	+	1.48134i	−0.164656	+	0.0792943i	−0.514397	−	0.857552i	$-0.671984\pi$
$349$	−3.07603	+	1.48134i	−0.164656	+	0.0792943i	0.349740	+	0.936847i	$0.386270\pi$
$350$	−8.91531	+	9.77329i	−0.476544	+	0.522404i
$351$	59.9349	+	28.8631i	3.19909	+	1.54060i
$352$	0.969925	−	0.773489i	0.0516972	−	0.0412271i
$353$	−14.0919	−	29.2622i	−0.750038	−	1.55747i	−0.828137	−	0.560525i	$-0.810599\pi$
$353$	−14.0919	−	29.2622i	−0.750038	−	1.55747i	0.0780990	−	0.996946i	$-0.475115\pi$
$354$	28.7614	−	36.0657i	1.52865	−	1.91687i
$355$	26.4320	+	3.09047i	1.40286	+	0.164025i
$356$	−7.92432	+	9.93679i	−0.419988	+	0.526649i
$357$	−16.0871	−	0.933070i	−0.851421	−	0.0493833i
$358$	−3.17188	+	2.52949i	−0.167639	+	0.133688i
$359$	13.1655	−	6.34017i	0.694848	−	0.334621i	−0.0529036	−	0.998600i	$-0.516848\pi$
$359$	13.1655	−	6.34017i	0.694848	−	0.334621i	0.747752	+	0.663978i	$0.231133\pi$
$360$	−1.77884	+	15.2139i	−0.0937529	+	0.801844i
$361$	−12.8014			−0.673757
$362$		−	25.4279i		−	1.33646i
$363$	−28.9488	−	6.60738i	−1.51942	−	0.346797i
$364$	14.3636	−	2.41335i	0.752860	−	0.126494i
$365$	5.56785	+	16.1286i	0.291435	+	0.844212i
$366$	−7.60168	−	33.3051i	−0.397346	−	1.74089i
$367$	12.6070	−	10.0538i	0.658081	−	0.524802i	−0.236543	−	0.971621i	$-0.576015\pi$
$367$	12.6070	−	10.0538i	0.658081	−	0.524802i	0.894624	+	0.446819i	$0.147443\pi$
$368$	2.73440	−	2.18061i	0.142541	−	0.113672i
$369$	−10.5463	−	46.2063i	−0.549018	−	2.40541i
$370$	−11.4434	+	3.95042i	−0.594912	+	0.205373i
$371$	21.9121	+	19.6544i	1.13762	+	1.02040i
$372$	0.474118	+	0.108214i	0.0245819	+	0.00561066i
$373$		−	23.1425i		−	1.19827i	−0.800648	−	0.599136i	$-0.795511\pi$
$373$		−	23.1425i		−	1.19827i	0.800648	−	0.599136i	$-0.204489\pi$
$374$	2.40747			0.124487
$375$	3.48983	+	34.9156i	0.180214	+	1.80303i
$376$	8.93669	−	4.30369i	0.460875	−	0.221946i
$377$	−8.18443	+	6.52686i	−0.421519	+	0.336151i
$378$	−5.29748	−	31.5292i	−0.272473	−	1.62169i
$379$	−9.02790	+	11.3206i	−0.463732	+	0.581502i	−0.957624	−	0.288022i	$-0.907002\pi$
$379$	−9.02790	+	11.3206i	−0.463732	+	0.581502i	0.493892	+	0.869523i	$0.335574\pi$
$380$	−5.52948	−	0.646516i	−0.283656	−	0.0331656i
$381$	−7.81911	+	9.80486i	−0.400585	+	0.502318i
$382$	3.92693	+	8.15435i	0.200919	+	0.417213i
$383$	11.5283	−	9.19354i	0.589070	−	0.469768i	−0.283019	−	0.959114i	$-0.591336\pi$
$383$	11.5283	−	9.19354i	0.589070	−	0.469768i	0.872090	+	0.489346i	$0.162765\pi$
$384$	2.82770	+	1.36175i	0.144300	+	0.0694914i
$385$	−2.84949	+	6.76364i	−0.145223	+	0.344707i
$386$	9.06387	−	4.36493i	0.461339	−	0.222169i
$387$	−2.56813	+	5.33278i	−0.130546	+	0.271081i
$388$	1.57392	−	0.359236i	0.0799035	−	0.0182375i
$389$	8.65997	+	4.17042i	0.439078	+	0.211449i	0.640345	−	0.768088i	$-0.278792\pi$
$389$	8.65997	+	4.17042i	0.439078	+	0.211449i	−0.201267	+	0.979536i	$0.564506\pi$
$390$	20.6915	−	32.6258i	1.04775	−	1.65207i
$391$	6.78711			0.343239
$392$	−4.93154	−	4.96789i	−0.249080	−	0.250916i
$393$		−	3.59237i		−	0.181211i
$394$	−13.7187	+	17.2027i	−0.691137	+	0.866658i
$395$	−9.65835	+	27.2351i	−0.485964	+	1.37035i
$396$	1.89104	+	8.28518i	0.0950283	+	0.416346i
$397$	0.308237	−	0.640061i	0.0154700	−	0.0321237i	−0.893091	−	0.449877i	$-0.851468\pi$
$397$	0.308237	−	0.640061i	0.0154700	−	0.0321237i	0.908561	+	0.417753i	$0.137182\pi$
$398$	1.90610	+	3.95806i	0.0955442	+	0.198400i
$399$	20.3880	−	3.42555i	1.02068	−	0.171492i
$400$	4.86514	+	1.15345i	0.243257	+	0.0576724i
$401$	11.6348	+	14.5896i	0.581013	+	0.728568i	0.982285	−	0.187391i	$-0.0600033\pi$
$401$	11.6348	+	14.5896i	0.581013	+	0.728568i	−0.401272	+	0.915959i	$0.631432\pi$
$402$	−14.6621	−	30.4461i	−0.731278	−	1.51851i
$403$	−0.666907	−	0.531841i	−0.0332210	−	0.0264929i
$404$	−4.07223	+	17.8416i	−0.202601	+	0.887653i
$405$	−32.8095	−	20.8080i	−1.63032	−	1.03396i
$406$	4.83191	+	1.40166i	0.239804	+	0.0695634i
$407$	−5.25116	+	4.18766i	−0.260290	+	0.207575i
$408$	2.64260	+	5.48742i	0.130828	+	0.271668i
$409$	−5.42419	+	23.7649i	−0.268209	+	1.17510i	0.643886	+	0.765121i	$0.277321\pi$
$409$	−5.42419	+	23.7649i	−0.268209	+	1.17510i	−0.912095	+	0.409979i	$0.865536\pi$
$410$	−15.3805	+	1.66768i	−0.759590	+	0.0823610i
$411$	−3.60429			−0.177786
$412$	−12.5457	−	2.86348i	−0.618084	−	0.141074i
$413$	34.0004	+	18.8729i	1.67305	+	0.928677i
$414$	5.33120	+	23.3575i	0.262014	+	1.14796i
$415$	−7.15157	−	20.7163i	−0.351057	−	1.01692i
$416$	−3.43234	−	4.30402i	−0.168284	−	0.211022i
$417$	−6.46825	+	5.15826i	−0.316752	+	0.252601i
$418$	−3.01124	+	0.687295i	−0.147284	+	0.0336167i
$419$	1.01486	+	4.44641i	0.0495793	+	0.217221i	0.993649	−	0.112525i	$-0.0358939\pi$
$419$	1.01486	+	4.44641i	0.0495793	+	0.217221i	−0.944070	+	0.329746i	$0.893037\pi$
$420$	−18.5444	+	0.929298i	−0.904873	+	0.0453451i
$421$	2.75390	−	12.0656i	0.134217	−	0.588042i	−0.862427	−	0.506181i	$-0.831057\pi$
$421$	2.75390	−	12.0656i	0.134217	−	0.588042i	0.996644	−	0.0818607i	$-0.0260863\pi$
$422$			1.47816i			0.0719558i
$423$			67.9472i			3.30371i
$424$	2.47565	−	10.8465i	0.120228	−	0.526755i
$425$	5.98588	+	7.63658i	0.290358	+	0.370428i
$426$	23.2887	+	29.2031i	1.12834	+	1.41490i
$427$	26.6262	−	10.9717i	1.28853	−	0.530958i
$428$	0.113059	+	0.0901614i	0.00546490	+	0.00435812i
$429$	4.76958	−	20.8969i	0.230277	−	1.00891i
$430$	1.63161	+	1.03478i	0.0786833	+	0.0499014i
$431$	20.3003	−	9.77612i	0.977832	−	0.470899i	0.124473	−	0.992223i	$-0.460276\pi$
$431$	20.3003	−	9.77612i	0.977832	−	0.470899i	0.853359	+	0.521324i	$0.174562\pi$
$432$	−9.44761	+	7.53422i	−0.454549	+	0.362490i
$433$	5.93170	−	12.3173i	0.285060	−	0.591932i	−0.708440	−	0.705771i	$-0.750601\pi$
$433$	5.93170	−	12.3173i	0.285060	−	0.591932i	0.993499	+	0.113839i	$0.0363149\pi$
$434$	−0.0237381	+	0.409271i	−0.00113947	+	0.0196456i
$435$	11.3293	−	7.05258i	0.543199	−	0.338145i
$436$	5.09347	+	2.45289i	0.243933	+	0.117472i
$437$	−8.48925	+	1.93762i	−0.406096	+	0.0926888i
$438$	−10.3910	+	21.5772i	−0.496502	+	1.03100i
$439$	−14.3723	+	18.0222i	−0.685950	+	0.860154i	−0.995887	−	0.0906027i	$-0.971121\pi$
$439$	−14.3723	+	18.0222i	−0.685950	+	0.860154i	0.309937	+	0.950757i	$0.399692\pi$
$440$	2.75786	−	0.299030i	0.131476	−	0.0142557i
$441$	45.3185	−	15.6711i	2.15803	−	0.746242i
$442$		−	10.6831i		−	0.508142i
$443$	2.59097	+	2.06623i	0.123100	+	0.0981694i	0.683105	−	0.730320i	$-0.260629\pi$
$443$	2.59097	+	2.06623i	0.123100	+	0.0981694i	−0.560004	+	0.828490i	$0.689201\pi$
$444$	−15.3091	−	7.37248i	−0.726538	−	0.349882i
$445$	−26.8639	+	9.27383i	−1.27347	+	0.439622i
$446$	25.6682	+	12.3611i	1.21542	+	0.585317i
$447$	7.81199	+	16.2218i	0.369495	+	0.767264i
$448$	−0.737105	+	2.54100i	−0.0348249	+	0.120051i
$449$	−21.4806	−	10.3445i	−1.01373	−	0.488188i	−0.148156	−	0.988964i	$-0.547334\pi$
$449$	−21.4806	−	10.3445i	−1.01373	−	0.488188i	−0.865577	+	0.500776i	$0.833048\pi$
$450$	−21.5791	+	26.5986i	−1.01725	+	1.25387i
$451$	−7.73319	+	3.72411i	−0.364142	+	0.175361i
$452$	14.0800	+	11.2284i	0.662266	+	0.528140i
$453$	22.1481	+	5.05515i	1.04061	+	0.237512i
$454$	−5.84959	+	7.33516i	−0.274535	+	0.344256i
$455$	30.0135	+	12.6445i	1.40705	+	0.592785i
$456$	−4.87192	−	6.10919i	−0.228149	−	0.286089i
$457$	6.76512	+	14.0479i	0.316459	+	0.657134i	0.997151	−	0.0754363i	$-0.0240350\pi$
$457$	6.76512	+	14.0479i	0.316459	+	0.657134i	−0.680692	+	0.732570i	$0.738321\pi$
$458$	0.153427	+	0.0350188i	0.00716919	+	0.00163632i
$459$	−23.4501			−1.09456
$460$	7.77493	−	0.843022i	0.362508	−	0.0393061i
$461$	0.618388	−	2.70933i	0.0288012	−	0.126186i	−0.958484	−	0.285148i	$-0.907957\pi$
$461$	0.618388	−	2.70933i	0.0288012	−	0.126186i	0.987285	+	0.158961i	$0.0508145\pi$
$462$	−9.52449	+	3.92470i	−0.443119	+	0.182594i
$463$	−8.95702	+	2.04438i	−0.416268	+	0.0950105i	−0.425525	−	0.904947i	$-0.639911\pi$
$463$	−8.95702	+	2.04438i	−0.416268	+	0.0950105i	0.00925686	+	0.999957i	$0.497053\pi$
$464$	−0.423141	−	1.85390i	−0.0196438	−	0.0860652i
$465$	0.765695	+	0.772143i	0.0355082	+	0.0358073i
$466$	6.25152	+	7.83916i	0.289596	+	0.363142i
$467$	−26.6968	+	6.09336i	−1.23538	+	0.281967i	−0.789850	−	0.613300i	$-0.789842\pi$
$467$	−26.6968	+	6.09336i	−1.23538	+	0.281967i	−0.445529	+	0.895267i	$0.646984\pi$
$468$	36.7653	−	8.39144i	1.69948	−	0.387895i
$469$	23.2632	−	16.4420i	1.07419	−	0.759219i
$470$	22.0295	+	2.57572i	1.01614	+	0.118809i
$471$	−22.4912			−1.03634
$472$		−	14.6980i		−	0.676530i
$473$	1.04505	+	0.238526i	0.0480514	+	0.0109674i
$474$	−36.5426	+	17.5980i	−1.67846	+	0.808303i
$475$	−9.66721	−	7.84288i	−0.443562	−	0.359856i
$476$	−4.19282	+	2.96340i	−0.192177	+	0.135827i
$477$	59.5850	+	47.5174i	2.72821	+	2.17567i
$478$	−9.45570	−	2.15820i	−0.432494	−	0.0987138i
$479$	1.38976	−	1.74271i	0.0634998	−	0.0796263i	−0.749067	−	0.662494i	$-0.769498\pi$
$479$	1.38976	−	1.74271i	0.0634998	−	0.0796263i	0.812567	+	0.582868i	$0.198069\pi$
$480$	3.70880	+	5.95784i	0.169283	+	0.271937i
$481$	18.5826	+	23.3019i	0.847296	+	1.06248i
$482$	4.27551	−	8.87819i	0.194744	−	0.404390i
$483$	−26.8514	+	11.0645i	−1.22178	+	0.503451i
$484$	−8.52403	+	4.10496i	−0.387456	+	0.186589i
$485$	3.40229	+	1.20655i	0.154490	+	0.0547866i
$486$	−4.06754	−	17.8211i	−0.184507	−	0.808379i
$487$	8.50561	−	17.6621i	0.385426	−	0.800345i	−0.614509	−	0.788910i	$-0.710646\pi$
$487$	8.50561	−	17.6621i	0.385426	−	0.800345i	0.999935	−	0.0114352i	$-0.00364001\pi$
$488$	−8.50999	−	6.78649i	−0.385229	−	0.307210i
$489$	46.3924			2.09794
$490$	−3.36286	−	15.2870i	−0.151919	−	0.690594i
$491$	9.62915			0.434557			0.217279	−	0.976110i	$-0.430282\pi$
$491$	9.62915			0.434557			0.217279	+	0.976110i	$0.430282\pi$
$492$	−16.9770	−	13.5387i	−0.765381	−	0.610371i
$493$	1.60112	−	3.32476i	0.0721107	−	0.149739i
$494$	3.04986	+	13.3623i	0.137220	+	0.601198i
$495$	−6.35134	+	17.9098i	−0.285472	+	0.804987i
$496$	0.139605	−	0.0672302i	0.00626845	−	0.00301873i
$497$	−21.0249	+	23.4401i	−0.943094	+	1.05143i
$498$	13.3466	−	27.7146i	0.598077	−	1.24192i
$499$	16.0838	+	20.1685i	0.720010	+	0.902865i	0.998339	−	0.0576215i	$-0.0183517\pi$
$499$	16.0838	+	20.1685i	0.720010	+	0.902865i	−0.278328	+	0.960486i	$0.589780\pi$
$500$	7.80562	+	8.00452i	0.349078	+	0.357973i
$501$	−36.2547	+	45.4620i	−1.61974	+	2.03109i
$502$	0.771553	+	0.176102i	0.0344361	+	0.00785981i
$503$	−5.83060	−	4.64975i	−0.259973	−	0.207322i	0.484825	−	0.874611i	$-0.338883\pi$
$503$	−5.83060	−	4.64975i	−0.259973	−	0.207322i	−0.744799	+	0.667289i	$0.767455\pi$
$504$	−13.4918	−	12.1017i	−0.600973	−	0.539050i
$505$	−29.0566	+	28.8139i	−1.29300	+	1.28220i
$506$	3.90917	−	1.88255i	0.173784	−	0.0836898i
$507$	−52.9518	−	12.0859i	−2.35167	−	0.536753i
$508$			3.99581i			0.177286i
$509$	−20.0981			−0.890831			−0.445416	−	0.895324i	$-0.646944\pi$
$509$	−20.0981			−0.890831			−0.445416	+	0.895324i	$0.646944\pi$
$510$	−1.58158	+	13.5268i	−0.0700334	+	0.598977i
$511$	−19.3895	−	5.62459i	−0.857740	−	0.248817i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	29.3312	−	6.69464i	1.29500	−	0.295576i
$514$	−3.02052	−	3.78761i	−0.133229	−	0.167064i
$515$	−20.2612	−	20.4318i	−0.892814	−	0.900334i
$516$	0.603439	+	2.64384i	0.0265649	+	0.116389i
$517$	11.9968	−	2.73819i	0.527618	−	0.120425i
$518$	3.99068	−	13.7569i	0.175340	−	0.604445i
$519$	10.8062	−	47.3452i	0.474341	−	2.07822i
$520$	−1.32694	−	12.2379i	−0.0581901	−	0.536669i
$521$	−21.9874			−0.963286			−0.481643	−	0.876367i	$-0.659960\pi$
$521$	−21.9874			−0.963286			−0.481643	+	0.876367i	$0.659960\pi$
$522$	12.6996	+	2.89861i	0.555848	+	0.126869i
$523$	7.08195	+	14.7058i	0.309672	+	0.643041i	0.996483	−	0.0837955i	$-0.0267043\pi$
$523$	7.08195	+	14.7058i	0.309672	+	0.643041i	−0.686811	+	0.726836i	$0.740990\pi$
$524$	−0.713653	−	0.894892i	−0.0311761	−	0.0390935i
$525$	−36.1308	−	20.4537i	−1.57688	−	0.892674i
$526$	1.36485	−	1.71147i	0.0595105	−	0.0746238i
$527$	0.293156	+	0.0669111i	0.0127701	+	0.00291469i
$528$	3.04412	+	2.42760i	0.132478	+	0.105648i
$529$	−9.70160	+	4.67204i	−0.421809	+	0.203132i
$530$	17.6645	−	17.5170i	0.767299	−	0.760890i
$531$	90.7136	+	43.6854i	3.93664	+	1.89578i
$532$	4.39833	−	4.90358i	0.190692	−	0.212597i
$533$	16.5256	+	34.3159i	0.715805	+	1.48638i
$534$	−35.9390	−	17.3073i	−1.55523	−	0.748960i
$535$	0.105516	+	0.305652i	0.00456185	+	0.0132145i
$536$	−9.70082	−	4.67167i	−0.419012	−	0.201785i
$537$	−9.95497	−	7.93882i	−0.429589	−	0.342585i
$538$			23.5277i			1.01435i
$539$	−4.59316	−	7.36992i	−0.197842	−	0.317445i
$540$	−26.8631	+	2.91272i	−1.15600	+	0.125343i
$541$	14.3069	−	17.9403i	0.615103	−	0.771315i	−0.372543	−	0.928015i	$-0.621514\pi$
$541$	14.3069	−	17.9403i	0.615103	−	0.771315i	0.987646	+	0.156700i	$0.0500855\pi$
$542$	−12.3420	+	25.6285i	−0.530136	+	1.10084i
$543$	77.8046	−	17.7584i	3.33891	−	0.762085i
$544$	1.74842	+	0.841994i	0.0749628	+	0.0361002i
$545$	6.68059	+	10.7317i	0.286165	+	0.459697i
$546$	17.4158	+	42.2647i	0.745326	+	1.80876i
$547$	−9.44930	+	19.6217i	−0.404023	+	0.838962i	0.595347	+	0.803469i	$0.297015\pi$
$547$	−9.44930	+	19.6217i	−0.404023	+	0.838962i	−0.999370	+	0.0354934i	$0.988700\pi$
$548$	−0.897861	+	0.716021i	−0.0383547	+	0.0305869i
$549$	67.1785	−	32.3515i	2.86711	−	1.38073i
$550$	5.56585	+	2.73811i	0.237329	+	0.116754i
$551$	−1.05350	+	4.61567i	−0.0448804	+	0.196634i
$552$	8.58194	+	6.84387i	0.365272	+	0.291294i
$553$	−19.7343	−	27.9214i	−0.839188	−	1.18734i
$554$	8.44262	+	10.5867i	0.358693	+	0.449786i
$555$	−20.0794	−	32.2557i	−0.852324	−	1.36918i
$556$	−0.586572	+	2.56994i	−0.0248762	+	0.108990i
$557$			12.5607i			0.532213i	0.963944	+	0.266107i	$0.0857373\pi$
$557$			12.5607i			0.532213i	−0.963944	+	0.266107i	$0.914263\pi$
$558$			1.06144i			0.0449344i
$559$	1.05845	−	4.63738i	0.0447678	−	0.196140i
$560$	−4.43497	+	3.91549i	−0.187412	+	0.165460i
$561$	1.68134	+	7.36641i	0.0709861	+	0.311010i
$562$	−18.2288	+	4.16061i	−0.768936	+	0.175505i
$563$	12.3653	−	9.86099i	0.521135	−	0.415591i	−0.327276	−	0.944929i	$-0.606131\pi$
$563$	12.3653	−	9.86099i	0.521135	−	0.415591i	0.848411	+	0.529337i	$0.177559\pi$
$564$	19.4097	+	24.3390i	0.817297	+	1.02486i
$565$	13.1406	+	38.0649i	0.552829	+	1.60140i
$566$	−2.55705	−	11.2032i	−0.107481	−	0.470905i
$567$	42.5026	−	17.5138i	1.78494	−	0.735511i
$568$	11.6029	+	2.64828i	0.486846	+	0.111119i
$569$	13.7721			0.577357			0.288678	−	0.957426i	$-0.406784\pi$
$569$	13.7721			0.577357			0.288678	+	0.957426i	$0.406784\pi$
$570$	−1.88348	−	17.3707i	−0.0788902	−	0.727579i
$571$	2.84731	−	12.4749i	0.119156	−	0.522058i	−0.879756	−	0.475426i	$-0.842294\pi$
$571$	2.84731	−	12.4749i	0.119156	−	0.522058i	0.998912	−	0.0466323i	$-0.0148489\pi$
$572$	−2.96319	−	6.15312i	−0.123897	−	0.257275i
$573$	−22.2083	+	17.7105i	−0.927766	+	0.739869i
$574$	8.88395	−	16.0048i	0.370809	−	0.668028i
$575$	15.6912	+	7.71927i	0.654368	+	0.321916i
$576$	−1.52432	+	6.67847i	−0.0635133	+	0.278270i
$577$	−16.2917	−	12.9922i	−0.678231	−	0.540871i	0.222671	−	0.974894i	$-0.428522\pi$
$577$	−16.2917	−	12.9922i	−0.678231	−	0.540871i	−0.900902	+	0.434023i	$0.857094\pi$
$578$	−5.74205	−	11.9235i	−0.238838	−	0.495952i
$579$	19.6859	+	24.6854i	0.818120	+	1.02589i
$580$	1.42118	−	4.00752i	0.0590114	−	0.166403i
$581$	24.9046	+	7.22444i	1.03322	+	0.299720i
$582$	2.19840	+	4.56502i	0.0911264	+	0.189226i
$583$	5.98849	−	12.4352i	0.248018	−	0.515014i
$584$	1.69798	+	7.43934i	0.0702629	+	0.307842i
$585$	79.4744	+	28.1839i	3.28586	+	1.16526i
$586$	4.77022	−	5.98166i	0.197056	−	0.247100i
$587$		−	34.0164i		−	1.40401i	−0.712173	−	0.702004i	$-0.752289\pi$
$587$		−	34.0164i		−	1.40401i	0.712173	−	0.702004i	$-0.247711\pi$
$588$	11.7567	−	18.5591i	0.484840	−	0.765364i
$589$	−0.385779			−0.0158958
$590$	17.6021	−	27.7546i	0.724669	−	1.14264i
$591$	−62.2179	−	29.9626i	−2.55930	−	1.23250i
$592$	−5.27825	+	1.20473i	−0.216935	+	0.0495139i
$593$	−15.1375	+	31.4333i	−0.621622	+	1.29081i	0.317835	+	0.948146i	$0.397044\pi$
$593$	−15.1375	+	31.4333i	−0.621622	+	1.29081i	−0.939457	+	0.342666i	$0.888670\pi$
$594$	−13.5065	+	6.50440i	−0.554179	+	0.266879i
$595$	−11.4663	+	0.574603i	−0.470074	+	0.0235564i
$596$	5.16863	+	2.48908i	0.211715	+	0.101957i
$597$	−10.7798	+	8.59656i	−0.441186	+	0.351834i
$598$	−8.35379	−	17.3468i	−0.341612	−	0.709365i
$599$	5.02366	−	6.29947i	0.205261	−	0.257389i	−0.668536	−	0.743680i	$-0.733079\pi$
$599$	5.02366	−	6.29947i	0.205261	−	0.257389i	0.873797	+	0.486290i	$0.161650\pi$
$600$	−0.131609	+	15.6920i	−0.00537291	+	0.640622i
$601$	−13.2798	+	16.6523i	−0.541693	+	0.679262i	−0.975056	−	0.221958i	$-0.928755\pi$
$601$	−13.2798	+	16.6523i	−0.541693	+	0.679262i	0.433363	+	0.901219i	$0.357327\pi$
$602$	−2.11365	+	0.870959i	−0.0861460	+	0.0354976i
$603$	57.6656	−	45.9868i	2.34832	−	1.87273i
$604$	6.52154	−	3.14061i	0.265358	−	0.127789i
$605$	−21.0122	−	2.45678i	−0.854268	−	0.0998824i
$606$	−57.4360			−2.33318
$607$			5.03903i			0.204528i	0.994757	+	0.102264i	$0.0326087\pi$
$607$			5.03903i			0.204528i	−0.994757	+	0.102264i	$0.967391\pi$
$608$	−2.42728	−	0.554011i	−0.0984393	−	0.0224681i
$609$	−0.914308	+	15.7637i	−0.0370496	+	0.638776i
$610$	−7.94222	−	23.0066i	−0.321571	−	0.931509i
$611$	−12.1506	−	53.2354i	−0.491562	−	2.15367i
$612$	−10.3933	+	8.28838i	−0.420124	+	0.335038i
$613$	27.3018	−	21.7725i	1.10271	−	0.879381i	0.109301	−	0.994009i	$-0.465139\pi$
$613$	27.3018	−	21.7725i	1.10271	−	0.879381i	0.993409	+	0.114627i	$0.0365674\pi$
$614$	2.65515	+	11.6330i	0.107153	+	0.469468i
$615$	−15.8443	−	45.8969i	−0.638904	−	1.85074i
$616$	−1.59297	+	2.86980i	−0.0641825	+	0.115627i
$617$	14.5380	+	3.31821i	0.585279	+	0.133586i	0.504900	−	0.863178i	$-0.331530\pi$
$617$	14.5380	+	3.31821i	0.585279	+	0.133586i	0.0803798	+	0.996764i	$0.474387\pi$
$618$		−	40.3875i		−	1.62462i
$619$	−37.6604			−1.51370			−0.756850	−	0.653589i	$-0.773262\pi$
$619$	−37.6604			−1.51370			−0.756850	+	0.653589i	$0.773262\pi$
$620$	0.344134	+	0.0402367i	0.0138208	+	0.00161595i
$621$	−38.0775	+	18.3371i	−1.52800	+	0.735844i
$622$	3.79435	−	3.02589i	0.152140	−	0.121327i
$623$	9.36833	−	32.2952i	0.375334	−	1.29388i
$624$	10.7724	−	13.5082i	0.431242	−	0.540760i
$625$	5.15343	+	24.4631i	0.206137	+	0.978523i
$626$	2.11630	−	2.65376i	0.0845843	−	0.106065i
$627$	−4.20600	−	8.73384i	−0.167971	−	0.348796i
$628$	−5.60277	+	4.46806i	−0.223575	+	0.178295i
$629$	−9.46592	−	4.55855i	−0.377431	−	0.181761i
$630$	−10.9842	−	39.0095i	−0.437619	−	1.55418i
$631$	0.536973	−	0.258593i	0.0213766	−	0.0102944i	−0.423165	−	0.906053i	$-0.639081\pi$
$631$	0.536973	−	0.258593i	0.0213766	−	0.0102944i	0.444541	+	0.895758i	$0.353367\pi$
$632$	−5.60713	+	11.6433i	−0.223040	+	0.463146i
$633$	−4.52291	+	1.03232i	−0.179769	+	0.0410312i
$634$	21.6250	+	10.4141i	0.858840	+	0.413596i
$635$	−4.78534	+	7.54540i	−0.189900	+	0.299430i
$636$	34.9174			1.38456
$637$	−32.7039	+	20.3821i	−1.29577	+	0.807567i
$638$		−	2.35906i		−	0.0933961i
$639$	−50.8309	+	63.7399i	−2.01084	+	2.52151i
$640$	2.10747	+	0.747370i	0.0833051	+	0.0295424i
$641$	−0.447891	−	1.96234i	−0.0176906	−	0.0775077i	0.965312	−	0.261099i	$-0.0840849\pi$
$641$	−0.447891	−	1.96234i	−0.0176906	−	0.0775077i	−0.983003	+	0.183591i	$0.941228\pi$
$642$	−0.196919	+	0.408907i	−0.00777178	+	0.0161383i
$643$	−3.39946	−	7.05906i	−0.134062	−	0.278382i	0.823121	−	0.567866i	$-0.192231\pi$
$643$	−3.39946	−	7.05906i	−0.134062	−	0.278382i	−0.957183	+	0.289484i	$0.906516\pi$
$644$	−4.49088	+	8.09050i	−0.176965	+	0.318811i
$645$	−2.02674	+	5.71511i	−0.0798029	+	0.225032i
$646$	−3.01240	−	3.77743i	−0.118521	−	0.148621i
$647$	16.7220	+	34.7237i	0.657411	+	1.36513i	0.916797	+	0.399354i	$0.130766\pi$
$647$	16.7220	+	34.7237i	0.657411	+	1.36513i	−0.259386	+	0.965774i	$0.583520\pi$
$648$	−13.5842	−	10.8331i	−0.533639	−	0.425563i
$649$	4.05745	−	17.7769i	0.159269	−	0.697803i
$650$	12.1503	−	24.6983i	0.476575	−	0.968749i
$651$	−1.26887	+	0.213194i	−0.0497311	+	0.00835572i
$652$	11.5568	−	9.21623i	0.452598	−	0.360935i
$653$	11.4841	+	23.8470i	0.449408	+	0.933205i	0.995435	+	0.0954381i	$0.0304252\pi$
$653$	11.4841	+	23.8470i	0.449408	+	0.933205i	−0.546027	+	0.837767i	$0.683861\pi$
$654$	−3.94819	+	17.2982i	−0.154386	+	0.676411i
$655$	−0.275897	−	2.54451i	−0.0107802	−	0.0994223i
$656$	−6.91869			−0.270130
$657$	−50.9611	−	11.6315i	−1.98818	−	0.453790i
$658$	−17.5229	+	19.5359i	−0.683115	+	0.761587i
$659$	−6.39318	−	28.0103i	−0.249043	−	1.09113i	−0.932509	−	0.361146i	$-0.882386\pi$
$659$	−6.39318	−	28.0103i	−0.249043	−	1.09113i	0.683467	−	0.729982i	$-0.260472\pi$
$660$	2.84102	+	8.22970i	0.110586	+	0.320341i
$661$	−24.7666	−	31.0563i	−0.963309	−	1.20795i	−0.978116	−	0.208061i	$-0.933285\pi$
$661$	−24.7666	−	31.0563i	−0.963309	−	1.20795i	0.0148070	−	0.999890i	$-0.495287\pi$
$662$	13.9935	−	11.1594i	0.543872	−	0.433724i
$663$	32.6883	−	7.46089i	1.26951	−	0.289757i
$664$	−2.18095	−	9.55537i	−0.0846373	−	0.370820i
$665$	14.1780	−	3.99217i	0.549798	−	0.154810i
$666$	8.25264	−	36.1572i	0.319783	−	1.40106i
$667$		−	6.65064i		−	0.257514i
$668$			18.5273i			0.716842i
$669$	−19.8966	+	87.1727i	−0.769247	+	3.37029i
$670$	−12.7236	−	20.4392i	−0.491555	−	0.789637i
$671$	−8.41918	−	10.5573i	−0.325019	−	0.407561i
$672$	−8.28978	−	0.480815i	−0.319785	−	0.0185479i
$673$	−19.9613	−	15.9186i	−0.769452	−	0.613618i	0.158052	−	0.987431i	$-0.449479\pi$
$673$	−19.9613	−	15.9186i	−0.769452	−	0.613618i	−0.927504	+	0.373813i	$0.878050\pi$
$674$	3.60613	−	15.7995i	0.138903	−	0.608573i
$675$	−54.2145	−	26.6708i	−2.08672	−	1.02656i
$676$	−15.5917	+	7.50859i	−0.599682	+	0.288792i
$677$	9.22898	−	7.35987i	0.354698	−	0.282863i	−0.429888	−	0.902882i	$-0.641447\pi$
$677$	9.22898	−	7.35987i	0.354698	−	0.282863i	0.784586	+	0.620020i	$0.212875\pi$
$678$	−24.5237	+	50.9239i	−0.941825	+	1.95572i
$679$	−3.48802	+	2.46527i	−0.133858	+	0.0946083i
$680$	2.29322	+	3.68385i	0.0879411	+	0.141269i
$681$	−26.5295	−	12.7759i	−1.01661	−	0.489575i
$682$	0.187408	−	0.0427747i	0.00717623	−	0.00163793i
$683$	2.83068	−	5.87796i	0.108313	−	0.224914i	−0.839767	−	0.542948i	$-0.817308\pi$
$683$	2.83068	−	5.87796i	0.108313	−	0.224914i	0.948079	+	0.318034i	$0.103022\pi$
$684$	10.6336	−	13.3342i	0.406587	−	0.509844i
$685$	−2.55295	+	0.276812i	−0.0975434	+	0.0105765i
$686$	17.0712	+	7.18155i	0.651781	+	0.274193i
$687$			0.493916i			0.0188441i
$688$	0.675542	+	0.538727i	0.0257548	+	0.0205388i
$689$	−55.1810	−	26.5738i	−2.10223	−	1.01238i
$690$	8.00937	+	23.2011i	0.304912	+	0.883251i
$691$	−11.2382	−	5.41205i	−0.427522	−	0.205884i	0.207734	−	0.978185i	$-0.433391\pi$
$691$	−11.2382	−	5.41205i	−0.427522	−	0.205884i	−0.635256	+	0.772301i	$0.719105\pi$
$692$	−6.71357	−	13.9409i	−0.255212	−	0.529952i
$693$	−12.9773	−	18.3611i	−0.492967	−	0.697482i
$694$	−2.50247	−	1.20513i	−0.0949926	−	0.0457460i
$695$	−4.18537	+	4.15042i	−0.158760	+	0.157434i
$696$	5.37709	−	2.58947i	0.203818	−	0.0981536i
$697$	−10.4972	−	8.37123i	−0.397609	−	0.317083i
$698$	−3.32854	−	0.759717i	−0.125987	−	0.0287557i
$699$	−19.6204	+	24.6033i	−0.742113	+	0.930581i
$700$	−13.0638	+	2.08246i	−0.493766	+	0.0787095i
$701$	−6.09461	−	7.64239i	−0.230190	−	0.288649i	0.653300	−	0.757099i	$-0.273384\pi$
$701$	−6.09461	−	7.64239i	−0.230190	−	0.288649i	−0.883490	+	0.468450i	$0.844813\pi$
$702$	28.8631	+	59.9349i	1.08937	+	2.26210i
$703$	13.1413	+	2.99941i	0.495633	+	0.113125i
$704$	1.24058			0.0467561
$705$	7.50377	+	69.2049i	0.282608	+	2.60641i
$706$	7.22717	−	31.6643i	0.271998	−	1.19170i
$707$	−8.02272	−	47.7491i	−0.301725	−	1.79579i
$708$	44.9732	−	10.2648i	1.69019	−	0.385776i
$709$	2.33043	+	10.2103i	0.0875212	+	0.383455i	0.999650	−	0.0264479i	$-0.00841962\pi$
$709$	2.33043	+	10.2103i	0.0875212	+	0.383455i	−0.912129	+	0.409903i	$0.865562\pi$
$710$	18.7385	+	18.8963i	0.703243	+	0.709166i
$711$	−55.1952	−	69.2126i	−2.06998	−	2.59567i
$712$	−12.3910	+	2.82816i	−0.464371	+	0.105990i
$713$	0.528340	−	0.120590i	0.0197865	−	0.00451613i
$714$	−11.9957	−	10.7597i	−0.448926	−	0.402670i
$715$	1.77344	−	15.1678i	0.0663230	−	0.567243i
$716$	−4.05699			−0.151617
$717$		−	30.4400i		−	1.13680i
$718$	14.2462	+	3.25161i	0.531664	+	0.121349i
$719$	35.3876	−	17.0418i	1.31974	−	0.635551i	0.364447	−	0.931224i	$-0.381258\pi$
$719$	35.3876	−	17.0418i	1.31974	−	0.635551i	0.955289	+	0.295673i	$0.0955438\pi$
$720$	−10.8765	+	10.7856i	−0.405342	+	0.401957i
$721$	33.5759	−	5.64136i	1.25043	−	0.210095i
$722$	−10.0085	−	7.98153i	−0.372478	−	0.297042i
$723$	30.1516	+	6.88190i	1.12135	+	0.255941i
$724$	15.8540	−	19.8803i	0.589210	−	0.738845i
$725$	7.48302	−	5.86552i	0.277913	−	0.217840i
$726$	−18.5135	−	23.2151i	−0.687099	−	0.861595i
$727$	−18.4308	+	38.2719i	−0.683559	+	1.41943i	0.213245	+	0.976999i	$0.431597\pi$
$727$	−18.4308	+	38.2719i	−0.683559	+	1.41943i	−0.896805	+	0.442427i	$0.854118\pi$
$728$	12.7347	+	7.06875i	0.471978	+	0.261985i
$729$	4.72577	−	2.27581i	0.175028	−	0.0842892i
$730$	−5.70292	+	16.0814i	−0.211075	+	0.595199i
$731$	0.373118	+	1.63474i	0.0138003	+	0.0604629i
$732$	14.8222	−	30.7786i	0.547844	−	1.13761i
$733$	5.85818	+	4.67175i	0.216377	+	0.172555i	0.725680	−	0.688032i	$-0.241525\pi$
$733$	5.85818	+	4.67175i	0.216377	+	0.172555i	−0.509303	+	0.860587i	$0.670097\pi$
$734$	16.1250			0.595184
$735$	44.4267	−	20.9659i	1.63871	−	0.773339i
$736$	3.49743			0.128917
$737$	−10.4433	−	8.32824i	−0.384683	−	0.306775i
$738$	20.5637	−	42.7011i	0.756962	−	1.57185i
$739$	−3.83780	−	16.8145i	−0.141176	−	0.618531i	−0.995163	−	0.0982371i	$-0.968680\pi$
$739$	−3.83780	−	16.8145i	−0.141176	−	0.618531i	0.853987	−	0.520294i	$-0.174177\pi$
$740$	−11.4098	−	4.04625i	−0.419434	−	0.148743i
$741$	−38.7562	+	18.6640i	−1.42375	+	0.685640i
$742$	4.87729	+	29.0284i	0.179051	+	1.06567i
$743$	−8.68262	+	18.0297i	−0.318535	+	0.661444i	−0.997341	−	0.0728733i	$-0.976783\pi$
$743$	−8.68262	+	18.0297i	−0.318535	+	0.661444i	0.678807	+	0.734317i	$0.262497\pi$
$744$	0.303210	+	0.380214i	0.0111162	+	0.0139393i
$745$	6.77917	+	10.8901i	0.248370	+	0.398982i
$746$	14.4291	−	18.0935i	0.528286	−	0.662450i
$747$	65.4564	+	14.9400i	2.39493	+	0.546626i
$748$	1.88223	+	1.50103i	0.0688213	+	0.0548832i
$749$	−0.367448	−	0.106591i	−0.0134263	−	0.00389475i
$750$	−19.0411	+	29.4740i	−0.695281	+	1.07624i
$751$	−21.2883	+	10.2519i	−0.776820	+	0.374097i	−0.779904	−	0.625899i	$-0.784732\pi$
$751$	−21.2883	+	10.2519i	−0.776820	+	0.374097i	0.00308472	+	0.999995i	$0.499018\pi$
$752$	9.67029	+	2.20718i	0.352639	+	0.0804876i
$753$			2.48380i			0.0905146i
$754$	−10.4683			−0.381232
$755$	16.0759	+	1.87963i	0.585064	+	0.0684066i
$756$	15.5164	−	27.9534i	0.564326	−	1.01666i
$757$	23.2511	−	5.30692i	0.845077	−	0.192883i	0.222003	−	0.975046i	$-0.428741\pi$
$757$	23.2511	−	5.30692i	0.845077	−	0.192883i	0.623074	+	0.782163i	$0.285883\pi$
$758$	−14.1166	+	3.22202i	−0.512738	+	0.117029i
$759$	8.49037	+	10.6466i	0.308181	+	0.386447i
$760$	−3.92003	−	3.95304i	−0.142194	−	0.143392i
$761$	−6.43747	−	28.2044i	−0.233358	−	1.02241i	−0.946832	−	0.321727i	$-0.895737\pi$
$761$	−6.43747	−	28.2044i	−0.233358	−	1.02241i	0.713474	−	0.700681i	$-0.247121\pi$
$762$	−12.2265	+	2.79061i	−0.442918	+	0.101093i
$763$	−14.9322	−	0.866083i	−0.540582	−	0.0313543i
$764$	−2.01396	+	8.82373i	−0.0728625	+	0.319231i
$765$	−29.5520	+	3.20428i	−1.06846	+	0.115851i
$766$	14.7453			0.532769
$767$	−78.8844	−	18.0049i	−2.84835	−	0.650118i
$768$	1.36175	+	2.82770i	0.0491378	+	0.102036i
$769$	23.0950	+	28.9602i	0.832826	+	1.04433i	0.998310	+	0.0581179i	$0.0185099\pi$
$769$	23.0950	+	28.9602i	0.832826	+	1.04433i	−0.165484	+	0.986212i	$0.552919\pi$
$770$	−6.44488	+	3.51140i	−0.232257	+	0.126542i
$771$	9.47991	−	11.8874i	0.341411	−	0.428115i
$772$	9.80791	+	2.23859i	0.352994	+	0.0805686i
$773$	12.4845	+	9.95604i	0.449036	+	0.358094i	0.821746	−	0.569854i	$-0.193000\pi$
$773$	12.4845	+	9.95604i	0.449036	+	0.358094i	−0.372711	+	0.927948i	$0.621572\pi$
$774$	−5.33278	+	2.56813i	−0.191683	+	0.0923096i
$775$	0.601651	+	0.488112i	0.0216119	+	0.0175335i
$776$	1.45452	+	0.700459i	0.0522142	+	0.0251450i
$777$	44.8807	+	2.60313i	1.61009	+	0.0933867i
$778$	4.17042	+	8.65997i	0.149517	+	0.310475i
$779$	15.5196	+	7.47386i	0.556049	+	0.267779i
$780$	36.5191	−	12.6070i	1.30759	−	0.451401i
$781$	13.3023	+	6.40607i	0.475995	+	0.229227i
$782$	5.30638	+	4.23170i	0.189756	+	0.151325i
$783$			22.9786i			0.821187i
$784$	−0.758200	−	6.95882i	−0.0270786	−	0.248529i
$785$	−15.9307	+	1.72734i	−0.568593	+	0.0616515i
$786$	2.23980	−	2.80863i	0.0798912	−	0.100180i
$787$	18.5303	−	38.4786i	0.660535	−	1.37162i	−0.254038	−	0.967194i	$-0.581759\pi$
$787$	18.5303	−	38.4786i	0.660535	−	1.37162i	0.914573	−	0.404421i	$-0.132527\pi$
$788$	−21.4514	+	4.89614i	−0.764174	+	0.174418i
$789$	6.18999	+	2.98094i	0.220369	+	0.106124i
$790$	−24.5320	+	15.2714i	−0.872809	+	0.543331i
$791$	−45.7608	−	13.2745i	−1.62707	−	0.471987i
$792$	−3.68725	+	7.65666i	−0.131021	+	0.272068i
$793$	−46.8479	+	37.3599i	−1.66362	+	1.32669i
$794$	0.640061	−	0.308237i	0.0227149	−	0.0109389i
$795$	65.9355	+	41.8167i	2.33849	+	1.48309i
$796$	−0.977560	+	4.28297i	−0.0346487	+	0.151806i
$797$	−21.9587	−	17.5114i	−0.777815	−	0.620287i	0.151972	−	0.988385i	$-0.451438\pi$
$797$	−21.9587	−	17.5114i	−0.777815	−	0.620287i	−0.929787	+	0.368098i	$0.880009\pi$
$798$	18.0758	+	10.0335i	0.639876	+	0.355182i
$799$	12.0014	+	15.0493i	0.424579	+	0.532406i
$800$	3.08455	+	3.93517i	0.109055	+	0.139129i
$801$	19.3735	−	84.8809i	0.684530	−	2.99912i
$802$			18.6607i			0.658934i
$803$			9.46644i			0.334063i
$804$	7.51957	−	32.9454i	0.265195	−	1.16189i
$805$	−18.1693	+	9.89930i	−0.640385	+	0.348904i
$806$	−0.189812	−	0.831620i	−0.00668583	−	0.0292926i
$807$	−71.9905	+	16.4314i	−2.53419	+	0.578411i
$808$	−14.3079	+	11.4101i	−0.503349	+	0.401407i
$809$	−6.95994	−	8.72749i	−0.244699	−	0.306842i	0.644281	−	0.764789i	$-0.277157\pi$
$809$	−6.95994	−	8.72749i	−0.244699	−	0.306842i	−0.888980	+	0.457946i	$0.848585\pi$
$810$	−12.6779	−	36.7247i	−0.445457	−	1.29037i
$811$	−5.00582	−	21.9319i	−0.175778	−	0.770134i	−0.983550	−	0.180639i	$-0.942184\pi$
$811$	−5.00582	−	21.9319i	−0.175778	−	0.770134i	0.807771	−	0.589496i	$-0.200674\pi$
$812$	2.90382	+	4.10851i	0.101904	+	0.144180i
$813$	−87.0380	−	19.8659i	−3.05256	−	0.696726i
$814$	−6.71649			−0.235413
$815$	32.8602	−	3.56298i	1.15104	−	0.124806i
$816$	−1.35528	+	5.93788i	−0.0474444	+	0.207867i
$817$	−0.933384	−	1.93819i	−0.0326550	−	0.0678088i
$818$	−19.0580	+	15.1982i	−0.666347	+	0.531394i
$819$	−81.4771	+	57.5865i	−2.84704	+	2.01223i
$820$	−13.0648	−	8.28575i	−0.456241	−	0.289351i
$821$	−3.48433	+	15.2658i	−0.121604	+	0.532781i	0.877026	+	0.480444i	$0.159524\pi$
$821$	−3.48433	+	15.2658i	−0.121604	+	0.532781i	−0.998629	+	0.0523377i	$0.983333\pi$
$822$	−2.81794	−	2.24724i	−0.0982871	−	0.0783813i
$823$	6.22234	+	12.9208i	0.216897	+	0.450391i	0.980820	−	0.194916i	$-0.0624435\pi$
$823$	6.22234	+	12.9208i	0.216897	+	0.450391i	−0.763923	+	0.645308i	$0.776729\pi$
$824$	−8.02330	−	10.0609i	−0.279505	−	0.350488i
$825$	−4.49103	+	18.9427i	−0.156358	+	0.659502i
$826$	14.8155	+	35.9544i	0.515497	+	1.25101i
$827$	−14.8613	−	30.8598i	−0.516778	−	1.07310i	−0.982170	−	0.187996i	$-0.939801\pi$
$827$	−14.8613	−	30.8598i	−0.516778	−	1.07310i	0.465392	−	0.885105i	$-0.345913\pi$
$828$	−10.3951	+	21.5856i	−0.361254	+	0.750151i
$829$	8.76798	+	38.4150i	0.304524	+	1.33421i	0.863217	+	0.504834i	$0.168446\pi$
$829$	8.76798	+	38.4150i	0.304524	+	1.33421i	−0.558692	+	0.829375i	$0.688697\pi$
$830$	7.32506	−	20.6556i	0.254256	−	0.716965i
$831$	−26.4972	+	33.2265i	−0.919179	+	1.15261i
$832$		−	5.50505i		−	0.190853i
$833$	7.26942	−	11.4754i	0.251870	−	0.397601i
$834$	−8.27320			−0.286478
$835$	−22.1881	+	34.9856i	−0.767850	+	1.21073i
$836$	−2.78280	−	1.34013i	−0.0962452	−	0.0463493i
$837$	−1.82546	+	0.416650i	−0.0630972	+	0.0144015i
$838$	−1.97884	+	4.10910i	−0.0683578	+	0.141947i
$839$	−16.1364	+	7.77090i	−0.557092	+	0.268281i	−0.691173	−	0.722689i	$-0.742906\pi$
$839$	−16.1364	+	7.77090i	−0.557092	+	0.268281i	0.134081	+	0.990970i	$0.457192\pi$
$840$	−15.0780	−	10.8357i	−0.520240	−	0.373866i
$841$	22.8702	+	11.0137i	0.788627	+	0.379783i
$842$	9.67587	−	7.71625i	0.333453	−	0.265920i
$843$	−25.4614	−	52.8712i	−0.876938	−	1.82098i
$844$	−0.921619	+	1.15567i	−0.0317234	+	0.0397799i
$845$	−38.4345	−	4.49383i	−1.32219	−	0.154592i
$846$	−42.3644	+	53.1233i	−1.45652	+	1.82642i
$847$	16.7138	−	18.6338i	0.574293	−	0.640264i
$848$	8.69825	−	6.93662i	0.298699	−	0.238205i
$849$	32.4939	−	15.6482i	1.11519	−	0.537046i
$850$	−0.0813762	+	9.70265i	−0.00279118	+	0.332798i
$851$	−18.9351			−0.649085
$852$			37.3522i			1.27967i
$853$	−32.7423	−	7.47322i	−1.12108	−	0.255878i	−0.378474	−	0.925612i	$-0.623551\pi$
$853$	−32.7423	−	7.47322i	−1.12108	−	0.255878i	−0.742601	+	0.669734i	$0.766408\pi$
$854$	27.6580	+	8.02315i	0.946436	+	0.274547i
$855$	36.0486	−	12.4445i	1.23284	−	0.425594i
$856$	0.0321782	+	0.140982i	0.00109983	+	0.00481867i
$857$	−5.12860	+	4.08992i	−0.175190	+	0.139709i	−0.707159	−	0.707054i	$-0.750024\pi$
$857$	−5.12860	+	4.08992i	−0.175190	+	0.139709i	0.531969	+	0.846764i	$0.321452\pi$
$858$	16.7580	−	13.3641i	0.572108	−	0.456241i
$859$	5.89035	+	25.8073i	0.200976	+	0.880534i	0.970344	+	0.241728i	$0.0777142\pi$
$859$	5.89035	+	25.8073i	0.200976	+	0.880534i	−0.769368	+	0.638806i	$0.779429\pi$
$860$	0.630472	+	1.82632i	0.0214989	+	0.0622768i
$861$	55.1762	+	16.0058i	1.88040	+	0.545475i
$862$	21.9667	+	5.01377i	0.748190	+	0.170770i
$863$			50.9696i			1.73502i	0.497416	+	0.867512i	$0.334282\pi$
$863$			50.9696i			1.73502i	−0.497416	+	0.867512i	$0.665718\pi$
$864$	−12.0840			−0.411104
$865$	4.01802	−	34.3650i	0.136617	−	1.16845i
$866$	12.3173	−	5.93170i	0.418559	−	0.201568i
$867$	32.4736	−	25.8968i	1.10286	−	0.879501i
$868$	−0.273736	+	0.305181i	−0.00929119	+	0.0103585i
$869$	−9.99588	+	12.5344i	−0.339087	+	0.425202i
$870$	13.2548	+	1.54977i	0.449380	+	0.0525423i
$871$	−36.9564	+	46.3418i	−1.25222	+	1.57023i
$872$	2.45289	+	5.09347i	0.0830652	+	0.172487i
$873$	−8.64624	+	6.89515i	−0.292631	+	0.233365i
$874$	−7.84525	−	3.77807i	−0.265370	−	0.127795i
$875$	−27.1627	−	11.7127i	−0.918267	−	0.395962i
$876$	−21.5772	+	10.3910i	−0.729025	+	0.351080i
$877$	−0.340084	+	0.706191i	−0.0114838	+	0.0238464i	−0.906632	−	0.421923i	$-0.861355\pi$
$877$	−0.340084	+	0.706191i	−0.0114838	+	0.0238464i	0.895148	+	0.445769i	$0.147070\pi$
$878$	−22.4734	+	5.12940i	−0.758439	+	0.173109i
$879$	21.6342	+	10.4185i	0.729705	+	0.351407i
$880$	2.34262	+	1.48571i	0.0789698	+	0.0500831i
$881$	−4.04222			−0.136186			−0.0680929	−	0.997679i	$-0.521691\pi$
$881$	−4.04222			−0.136186			−0.0680929	+	0.997679i	$0.521691\pi$
$882$	45.2022	+	16.0035i	1.52204	+	0.538866i
$883$			57.4759i			1.93422i	0.254364	+	0.967109i	$0.418134\pi$
$883$			57.4759i			1.93422i	−0.254364	+	0.967109i	$0.581866\pi$
$884$	6.66079	−	8.35237i	0.224027	−	0.280921i
$885$	97.2171	+	34.4760i	3.26792	+	1.15890i
$886$	0.737428	+	3.23088i	0.0247744	+	0.108544i
$887$	−4.70200	+	9.76379i	−0.157878	+	0.327836i	−0.964871	−	0.262724i	$-0.915379\pi$
$887$	−4.70200	+	9.76379i	−0.157878	+	0.327836i	0.806993	+	0.590560i	$0.201093\pi$
$888$	−7.37248	−	15.3091i	−0.247404	−	0.513740i
$889$	−4.02776	−	9.77460i	−0.135087	−	0.327830i
$890$	−26.7852	−	9.49880i	−0.897841	−	0.318401i
$891$	−13.4393	−	16.8523i	−0.450233	−	0.564575i
$892$	12.3611	+	25.6682i	0.413882	+	0.859434i
$893$	−19.3076	−	15.3973i	−0.646104	−	0.515251i
$894$	−4.00645	+	17.5534i	−0.133996	+	0.587073i
$895$	−7.66092	−	4.85860i	−0.256076	−	0.162405i
$896$	−2.16058	+	1.52706i	−0.0721799	+	0.0510153i
$897$	47.2440	−	37.6758i	1.57743	−	1.25796i
$898$	−10.3445	−	21.4806i	−0.345201	−	0.716817i
$899$	0.0655657	−	0.287262i	0.00218674	−	0.00958072i
$900$	−33.4551	+	7.34127i	−1.11517	+	0.244709i
$901$	21.5901			0.719270
$902$	−8.36800	−	1.90994i	−0.278624	−	0.0635941i
$903$	−4.14112	−	5.85912i	−0.137808	−	0.194979i
$904$	4.00737	+	17.5574i	0.133283	+	0.583952i
$905$	53.7460	−	18.5539i	1.78658	−	0.616753i
$906$	14.1642	+	17.7614i	0.470574	+	0.590082i
$907$	−7.07747	+	5.64409i	−0.235003	+	0.187409i	−0.733910	−	0.679247i	$-0.762307\pi$
$907$	−7.07747	+	5.64409i	−0.235003	+	0.187409i	0.498906	+	0.866656i	$0.333735\pi$
$908$	−9.14679	+	2.08770i	−0.303547	+	0.0692826i
$909$	−27.8957	−	122.219i	−0.925241	−	4.05375i
$910$	15.5817	+	28.5990i	0.516530	+	0.948048i
$911$	7.41012	−	32.4658i	0.245508	−	1.07564i	−0.690408	−	0.723420i	$-0.742569\pi$
$911$	7.41012	−	32.4658i	0.245508	−	1.07564i	0.935917	−	0.352222i	$-0.114574\pi$
$912$		−	7.81395i		−	0.258746i
$913$		−	12.1591i		−	0.402406i
$914$	−3.46955	+	15.2011i	−0.114762	+	0.502807i
$915$	64.8492	−	40.3692i	2.14385	−	1.33456i
$916$	0.0981205	+	0.123039i	0.00324199	+	0.00406533i
$917$	2.64779	+	1.46974i	0.0874378	+	0.0485350i
$918$	−18.3340	−	14.6209i	−0.605113	−	0.482561i
$919$	11.6171	−	50.8979i	0.383213	−	1.67897i	−0.304129	−	0.952631i	$-0.598365\pi$
$919$	11.6171	−	50.8979i	0.383213	−	1.67897i	0.687342	−	0.726334i	$-0.258778\pi$
$920$	6.60430	+	4.18849i	0.217737	+	0.138090i
$921$	−33.7404	+	16.2485i	−1.11179	+	0.535408i
$922$	2.17272	−	1.73268i	0.0715546	−	0.0570629i
$923$	28.4268	−	59.0288i	0.935679	−	1.94296i
$924$	−9.89356	−	2.86997i	−0.325474	−	0.0944151i
$925$	−16.6997	−	21.3049i	−0.549084	−	0.700502i
$926$	−8.27753	−	3.98625i	−0.272017	−	0.130996i
$927$	85.9411	−	19.6155i	2.82268	−	0.644257i
$928$	0.825064	−	1.71326i	0.0270841	−	0.0562406i
$929$	12.8480	−	16.1109i	0.421530	−	0.528582i	−0.525041	−	0.851077i	$-0.675950\pi$
$929$	12.8480	−	16.1109i	0.421530	−	0.528582i	0.946571	+	0.322495i	$0.104522\pi$
$930$	0.117221	+	1.08109i	0.00384381	+	0.0354503i
$931$	−5.81645	+	16.4287i	−0.190627	+	0.538428i
$932$			10.0267i			0.328434i
$933$	11.9086	+	9.49679i	0.389870	+	0.310911i
$934$	−24.6715	−	11.8812i	−0.807277	−	0.388764i
$935$	1.75666	+	5.08858i	0.0574488	+	0.166414i
$936$	33.9763	+	16.3621i	1.11055	+	0.534812i
$937$	1.64871	+	3.42357i	0.0538609	+	0.111843i	0.926162	−	0.377126i	$-0.123087\pi$
$937$	1.64871	+	3.42357i	0.0538609	+	0.111843i	−0.872301	+	0.488969i	$0.837373\pi$
$938$	28.4393	+	1.64951i	0.928575	+	0.0538583i
$939$	9.59800	+	4.62215i	0.313219	+	0.150838i
$940$	15.6174	+	15.7489i	0.509383	+	0.513673i
$941$	35.9697	−	17.3221i	1.17258	−	0.564684i	0.256838	−	0.966454i	$-0.417319\pi$
$941$	35.9697	−	17.3221i	1.17258	−	0.564684i	0.915741	+	0.401770i	$0.131605\pi$
$942$	−17.5843	−	14.0230i	−0.572928	−	0.456895i
$943$	−23.5910	−	5.38449i	−0.768228	−	0.175343i
$944$	9.16405	−	11.4913i	0.298264	−	0.374012i
$945$	62.7768	−	34.2030i	2.04213	−	1.11262i
$946$	0.668334	+	0.838064i	0.0217294	+	0.0272478i
$947$	15.7444	+	32.6935i	0.511623	+	1.06240i	0.983530	+	0.180747i	$0.0578515\pi$
$947$	15.7444	+	32.6935i	0.511623	+	1.06240i	−0.471907	+	0.881648i	$0.656434\pi$
$948$	−39.5424	−	9.02528i	−1.28428	−	0.293128i
$949$	42.0071			1.36361
$950$	−2.66817	−	12.1592i	−0.0865670	−	0.394497i
$951$	−16.7626	+	73.4417i	−0.543564	+	2.38151i
$952$	−5.12573	−	0.297297i	−0.166126	−	0.00963546i
$953$	42.4940	−	9.69898i	1.37652	−	0.314181i	0.530657	−	0.847587i	$-0.321945\pi$
$953$	42.4940	−	9.69898i	1.37652	−	0.314181i	0.845859	+	0.533406i	$0.179088\pi$
$954$	16.9588	+	74.3012i	0.549061	+	2.40559i
$955$	−14.3702	+	14.2502i	−0.465009	+	0.461125i
$956$	−6.04715	−	7.58288i	−0.195579	−	0.245248i
$957$	7.21830	−	1.64753i	0.233334	−	0.0532570i
$958$	2.17312	−	0.496000i	0.0702103	−	0.0160250i
$959$	1.47461	−	2.65658i	0.0476177	−	0.0857853i
$960$	−0.814994	+	6.97043i	−0.0263038	+	0.224970i
$961$	−30.9760			−0.999226
$962$			29.8043i			0.960928i
$963$	−0.965759	−	0.220428i	−0.0311211	−	0.00710320i
$964$	8.87819	−	4.27551i	0.285947	−	0.137705i
$965$	15.8396	+	15.9730i	0.509896	+	0.514190i
$966$	−27.8918	−	8.09099i	−0.897405	−	0.260323i
$967$	−6.69504	−	5.33912i	−0.215298	−	0.171694i	0.509902	−	0.860232i	$-0.329681\pi$
$967$	−6.69504	−	5.33912i	−0.215298	−	0.171694i	−0.725200	+	0.688538i	$0.758253\pi$
$968$	−9.22375	−	2.10526i	−0.296463	−	0.0676657i
$969$	9.45444	−	11.8555i	0.303720	−	0.380853i
$970$	1.90774	+	3.06461i	0.0612540	+	0.0983987i
$971$	5.27635	+	6.61633i	0.169326	+	0.212328i	0.859253	−	0.511551i	$-0.170929\pi$
$971$	5.27635	+	6.61633i	0.169326	+	0.212328i	−0.689927	+	0.723879i	$0.742357\pi$
$972$	7.93112	−	16.4691i	0.254391	−	0.528248i
$973$	−1.15561	−	6.87788i	−0.0370471	−	0.220495i
$974$	17.6621	−	8.50561i	0.565930	−	0.272537i
$975$	84.0580	+	19.9288i	2.69201	+	0.638234i
$976$	−2.42207	−	10.6118i	−0.0775286	−	0.339675i
$977$	−4.08562	+	8.48387i	−0.130710	+	0.271423i	−0.956044	−	0.293222i	$-0.905273\pi$
$977$	−4.08562	+	8.48387i	−0.130710	+	0.271423i	0.825334	+	0.564645i	$0.190987\pi$
$978$	36.2710	+	28.9252i	1.15982	+	0.924925i
$979$	−15.7673			−0.503926
$980$	6.90207	−	14.0485i	0.220479	−	0.448764i
$981$	−38.7266			−1.23644
$982$	7.52837	+	6.00368i	0.240240	+	0.191585i
$983$	2.09369	−	4.34759i	0.0667783	−	0.138667i	−0.864908	−	0.501930i	$-0.832623\pi$
$983$	2.09369	−	4.34759i	0.0667783	−	0.138667i	0.931686	+	0.363264i	$0.118338\pi$
$984$	−4.83190	−	21.1699i	−0.154035	−	0.674873i
$985$	−46.3708	−	16.4444i	−1.47750	−	0.523963i
$986$	3.32476	−	1.60112i	0.105882	−	0.0509900i
$987$	−72.0139	−	39.9735i	−2.29223	−	1.27237i
$988$	−5.94678	+	12.3486i	−0.189192	+	0.392862i
$989$	1.88416	+	2.36266i	0.0599129	+	0.0751283i
$990$	−16.1323	+	10.0425i	−0.512717	+	0.319171i
$991$	28.7642	−	36.0692i	0.913726	−	1.14578i	−0.0751709	−	0.997171i	$-0.523950\pi$
$991$	28.7642	−	36.0692i	0.913726	−	1.14578i	0.988897	−	0.148605i	$-0.0474783\pi$
$992$	0.151065	+	0.0344796i	0.00479632	+	0.00109473i
$993$	43.9187	+	35.0240i	1.39372	+	1.11145i
$994$	−31.0526	+	5.21739i	−0.984927	+	0.165486i
$995$	−6.97519	+	6.91694i	−0.221128	+	0.219282i
$996$	27.7146	−	13.3466i	0.878169	−	0.422904i
$997$	50.3681	+	11.4962i	1.59517	+	0.364088i	0.925554	−	0.378616i	$-0.123600\pi$
$997$	50.3681	+	11.4962i	1.59517	+	0.364088i	0.669620	+	0.742704i	$0.266457\pi$
$998$			25.7964i			0.816572i
$999$	65.4224			2.06987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.p.a.239.15	yes	168
5.4	even	2	inner	490.2.p.a.239.14	✓	168
49.8	even	7	inner	490.2.p.a.449.14	yes	168
245.204	even	14	inner	490.2.p.a.449.15	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.p.a.239.14	✓	168	5.4	even	2	inner
490.2.p.a.239.15	yes	168	1.1	even	1	trivial
490.2.p.a.449.14	yes	168	49.8	even	7	inner
490.2.p.a.449.15	yes	168	245.204	even	14	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.36175 + 2.82770i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.747370 + 2.10747i) q^{5} +(-2.82770 + 1.36175i) q^{6} +(-1.52706 - 2.16058i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-4.27104 - 5.35572i) q^{9} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(-1.36175 + 2.82770i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.747370 + 2.10747i) q^{5} +(-2.82770 + 1.36175i) q^{6} +(-1.52706 - 2.16058i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-4.27104 - 5.35572i) q^{9} +(-1.89830 + 1.18171i) q^{10} +(-0.773489 + 0.969925i) q^{11} +(-3.05982 - 0.698383i) q^{12} +(4.30402 + 3.43234i) q^{13} +(0.153199 - 2.64131i) q^{14} +(-4.94156 - 4.98318i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-1.89194 - 0.431824i) q^{17} -6.85022i q^{18} +2.48970 q^{19} +(-2.22094 - 0.259676i) q^{20} +(8.18893 - 1.37589i) q^{21} +(-1.20948 + 0.276055i) q^{22} +(-3.40974 + 0.778252i) q^{23} +(-1.95683 - 2.45378i) q^{24} +(-3.88287 - 3.15012i) q^{25} +(1.22499 + 5.36702i) q^{26} +(11.7810 - 2.68893i) q^{27} +(1.76661 - 1.96954i) q^{28} +(-0.423141 + 1.85390i) q^{29} +(-0.756506 - 6.97702i) q^{30} -0.154950 q^{31} +(-0.974928 - 0.222521i) q^{32} +(-1.68936 - 3.50798i) q^{33} +(-1.20994 - 1.51722i) q^{34} +(5.69464 - 1.60347i) q^{35} +(4.27104 - 5.35572i) q^{36} +(5.27825 + 1.20473i) q^{37} +(1.94653 + 1.55230i) q^{38} +(-15.5666 + 7.49648i) q^{39} +(-1.57449 - 1.58776i) q^{40} +(6.23353 + 3.00191i) q^{41} +(7.26021 + 4.03000i) q^{42} +(-0.374898 - 0.778483i) q^{43} +(-1.11772 - 0.538268i) q^{44} +(14.4791 - 4.99840i) q^{45} +(-3.15108 - 1.51748i) q^{46} +(-7.75497 - 6.18438i) q^{47} -3.13851i q^{48} +(-2.33620 + 6.59865i) q^{49} +(-1.07168 - 4.88380i) q^{50} +(3.79742 - 4.76181i) q^{51} +(-2.38855 + 4.95987i) q^{52} +(-10.8465 + 2.47565i) q^{53} +(10.8873 + 5.24303i) q^{54} +(-1.46601 - 2.35500i) q^{55} +(2.60918 - 0.438389i) q^{56} +(-3.39035 + 7.04013i) q^{57} +(-1.48671 + 1.18561i) q^{58} +(-13.2424 + 6.37722i) q^{59} +(3.75864 - 5.92653i) q^{60} +(-2.42207 + 10.6118i) q^{61} +(-0.121145 - 0.0966097i) q^{62} +(-5.04933 + 17.4064i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-10.4503 + 6.50537i) q^{65} +(0.866401 - 3.79595i) q^{66} +10.7671i q^{67} -1.94060i q^{68} +(2.44255 - 10.7015i) q^{69} +(5.45199 + 2.29690i) q^{70} +(-2.64828 - 11.6029i) q^{71} +(6.67847 - 1.52432i) q^{72} +(5.96588 - 4.75763i) q^{73} +(3.37557 + 4.23283i) q^{74} +(14.1951 - 6.68992i) q^{75} +(0.554011 + 2.42728i) q^{76} +(3.27676 + 0.190055i) q^{77} +(-16.8444 - 3.84463i) q^{78} +12.9231 q^{79} +(-0.241040 - 2.22304i) q^{80} +(-3.86628 + 16.9393i) q^{81} +(3.00191 + 6.23353i) q^{82} +(-7.66281 + 6.11089i) q^{83} +(3.16360 + 7.67745i) q^{84} +(2.32404 - 3.66449i) q^{85} +(0.192269 - 0.842387i) q^{86} +(-4.66606 - 3.72106i) q^{87} +(-0.538268 - 1.11772i) q^{88} +(7.92432 + 9.93679i) q^{89} +(14.4367 + 5.11965i) q^{90} +(0.843366 - 14.5405i) q^{91} +(-1.51748 - 3.15108i) q^{92} +(0.211003 - 0.438151i) q^{93} +(-2.20718 - 9.67029i) q^{94} +(-1.86073 + 5.24698i) q^{95} +(1.95683 - 2.45378i) q^{96} -1.61439i q^{97} +(-5.94071 + 3.70243i) q^{98} +8.49825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9}+O(q^{10}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9	\( 168 q + 28 q^{4} - 4 q^{5} + 14 q^{6} + 18 q^{9} - 4 q^{10} - 24 q^{11} + 4 q^{14} - 2 q^{15} - 28 q^{16} + 44 q^{19} - 10 q^{20} + 22 q^{26} - 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 4 q^{35} - 18 q^{36} - 80 q^{39} - 10 q^{40} + 52 q^{41} - 18 q^{44} - 72 q^{45} + 26 q^{46} - 52 q^{49} - 8 q^{50} + 64 q^{51} - 42 q^{54} - 60 q^{55} + 10 q^{56} - 58 q^{59} + 2 q^{60} + 32 q^{61} + 28 q^{64} + 4 q^{65} + 48 q^{66} - 48 q^{69} + 18 q^{70} - 68 q^{71} - 10 q^{74} - 16 q^{76} - 4 q^{80} + 34 q^{81} + 84 q^{84} - 48 q^{85} - 64 q^{86} + 100 q^{89} + 54 q^{90} + 78 q^{91} - 86 q^{94} - 64 q^{95} - 212 q^{99}+O(q^{100}) \) 168 * q + 28 * q^4 - 4 * q^5 + 14 * q^6 + 18 * q^9 - 4 * q^10 - 24 * q^11 + 4 * q^14 - 2 * q^15 - 28 * q^16 + 44 * q^19 - 10 * q^20 + 22 * q^26 - 2 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 - 4 * q^35 - 18 * q^36 - 80 * q^39 - 10 * q^40 + 52 * q^41 - 18 * q^44 - 72 * q^45 + 26 * q^46 - 52 * q^49 - 8 * q^50 + 64 * q^51 - 42 * q^54 - 60 * q^55 + 10 * q^56 - 58 * q^59 + 2 * q^60 + 32 * q^61 + 28 * q^64 + 4 * q^65 + 48 * q^66 - 48 * q^69 + 18 * q^70 - 68 * q^71 - 10 * q^74 - 16 * q^76 - 4 * q^80 + 34 * q^81 + 84 * q^84 - 48 * q^85 - 64 * q^86 + 100 * q^89 + 54 * q^90 + 78 * q^91 - 86 * q^94 - 64 * q^95 - 212 * q^99

Introduction

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