LMFDB - Embedded newform 418.2.m.b.189.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, degree $4$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.9
Character	$\chi$	$=$	418.189
Dual form			418.2.m.b.303.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(1.24511 + 1.71374i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.810373 - 2.49407i) q^{5} +(-2.01463 + 0.654592i) q^{6} +(2.23258 - 3.07288i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.459575 + 1.41443i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(1.24511 + 1.71374i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.810373 - 2.49407i) q^{5} +(-2.01463 + 0.654592i) q^{6} +(2.23258 - 3.07288i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.459575 + 1.41443i) q^{9} +2.62242 q^{10} +(3.29414 - 0.385561i) q^{11} -2.11830i q^{12} +(0.226957 - 0.698503i) q^{13} +(2.23258 + 3.07288i) q^{14} +(3.26520 - 4.49416i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.93721 + 0.954357i) q^{17} +(-1.20318 - 0.874163i) q^{18} +(3.63898 + 2.39954i) q^{19} +(-0.810373 + 2.49407i) q^{20} +8.04594 q^{21} +(-0.651254 + 3.25206i) q^{22} -1.91948 q^{23} +(2.01463 + 0.654592i) q^{24} +(-1.51860 + 1.10333i) q^{25} +(0.594182 + 0.431698i) q^{26} +(3.04770 - 0.990257i) q^{27} +(-3.61239 + 1.17374i) q^{28} +(-4.18847 - 3.04310i) q^{29} +(3.26520 + 4.49416i) q^{30} +(-1.73117 - 0.562491i) q^{31} -1.00000 q^{32} +(4.76231 + 5.16524i) q^{33} -3.08836i q^{34} +(-9.47322 - 3.07803i) q^{35} +(1.20318 - 0.874163i) q^{36} +(-3.05990 + 4.21160i) q^{37} +(-3.40661 + 2.71938i) q^{38} +(1.47964 - 0.480765i) q^{39} +(-2.12158 - 1.54142i) q^{40} +(-7.29522 + 5.30029i) q^{41} +(-2.48633 + 7.65215i) q^{42} +7.16858i q^{43} +(-2.89164 - 1.62432i) q^{44} +3.90011 q^{45} +(0.593153 - 1.82554i) q^{46} +(1.67274 - 1.21531i) q^{47} +(-1.24511 + 1.71374i) q^{48} +(-2.29508 - 7.06353i) q^{49} +(-0.580055 - 1.78523i) q^{50} +(-5.29267 - 3.84535i) q^{51} +(-0.594182 + 0.431698i) q^{52} +(10.8413 + 3.52257i) q^{53} +3.20454i q^{54} +(-3.63110 - 7.90337i) q^{55} -3.79829i q^{56} +(0.418719 + 9.22398i) q^{57} +(4.18847 - 3.04310i) q^{58} +(-1.48002 + 2.03708i) q^{59} +(-5.28320 + 1.71662i) q^{60} +(12.2970 - 3.99554i) q^{61} +(1.06992 - 1.47262i) q^{62} +(3.32033 + 4.57004i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.92604 q^{65} +(-6.38408 + 2.93308i) q^{66} -11.2953i q^{67} +(2.93721 + 0.954357i) q^{68} +(-2.38997 - 3.28951i) q^{69} +(5.85477 - 8.05840i) q^{70} +(5.05547 - 1.64262i) q^{71} +(0.459575 + 1.41443i) q^{72} +(-1.28522 + 1.76895i) q^{73} +(-3.05990 - 4.21160i) q^{74} +(-3.78165 - 1.22873i) q^{75} +(-1.53358 - 4.08021i) q^{76} +(6.16964 - 10.9833i) q^{77} +1.55579i q^{78} +(-2.63258 + 8.10225i) q^{79} +(2.12158 - 1.54142i) q^{80} +(9.10131 + 6.61249i) q^{81} +(-2.78653 - 8.57605i) q^{82} +(-12.5898 + 4.09066i) q^{83} +(-6.50931 - 4.72929i) q^{84} +(4.76047 + 6.55222i) q^{85} +(-6.81773 - 2.21521i) q^{86} -10.9670i q^{87} +(2.43839 - 2.24817i) q^{88} +16.5351i q^{89} +(-1.20520 + 3.70922i) q^{90} +(-1.63972 - 2.25688i) q^{91} +(1.55290 + 1.12824i) q^{92} +(-1.19153 - 3.66714i) q^{93} +(0.638929 + 1.96642i) q^{94} +(3.03570 - 11.0204i) q^{95} +(-1.24511 - 1.71374i) q^{96} +(11.6797 + 3.79496i) q^{97} +7.42703 q^{98} +(-0.968555 + 4.83651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	1.24511	+	1.71374i	0.718864	+	0.989431i	0.999561	+	0.0296345i	$0.00943434\pi$
$3$	1.24511	+	1.71374i	0.718864	+	0.989431i	−0.280697	+	0.959796i	$0.590566\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.810373	−	2.49407i	−0.362410	−	1.11538i	−0.951587	−	0.307379i	$-0.900548\pi$
$5$	−0.810373	−	2.49407i	−0.362410	−	1.11538i	0.589177	−	0.808004i	$-0.299452\pi$
$6$	−2.01463	+	0.654592i	−0.822468	+	0.267236i
$7$	2.23258	−	3.07288i	0.843836	−	1.16144i	−0.141351	−	0.989960i	$-0.545145\pi$
$7$	2.23258	−	3.07288i	0.843836	−	1.16144i	0.985187	−	0.171481i	$-0.0548554\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.459575	+	1.41443i	−0.153192	+	0.471475i
$10$	2.62242			0.829283
$11$	3.29414	−	0.385561i	0.993220	−	0.116251i
$11$	3.29414	−	0.385561i	0.993220	−	0.116251i
$12$		−	2.11830i		−	0.611502i
$13$	0.226957	−	0.698503i	0.0629466	−	0.193730i	−0.914638	−	0.404275i	$-0.867524\pi$
$13$	0.226957	−	0.698503i	0.0629466	−	0.193730i	0.977584	+	0.210545i	$0.0675239\pi$
$14$	2.23258	+	3.07288i	0.596682	+	0.821263i
$15$	3.26520	−	4.49416i	0.843071	−	1.16039i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.93721	+	0.954357i	−0.712378	+	0.231466i	−0.642715	−	0.766105i	$-0.722192\pi$
$17$	−2.93721	+	0.954357i	−0.712378	+	0.231466i	−0.0696624	+	0.997571i	$0.522192\pi$
$18$	−1.20318	−	0.874163i	−0.283593	−	0.206042i
$19$	3.63898	+	2.39954i	0.834840	+	0.550493i
$19$	3.63898	+	2.39954i	0.834840	+	0.550493i
$20$	−0.810373	+	2.49407i	−0.181205	+	0.557691i
$21$	8.04594			1.75577
$22$	−0.651254	+	3.25206i	−0.138848	+	0.693341i
$23$	−1.91948			−0.400240			−0.200120	−	0.979771i	$-0.564133\pi$
$23$	−1.91948			−0.400240			−0.200120	+	0.979771i	$0.564133\pi$
$24$	2.01463	+	0.654592i	0.411234	+	0.133618i
$25$	−1.51860	+	1.10333i	−0.303721	+	0.220666i
$26$	0.594182	+	0.431698i	0.116529	+	0.0846630i
$27$	3.04770	−	0.990257i	0.586530	−	0.190575i
$28$	−3.61239	+	1.17374i	−0.682678	+	0.221815i
$29$	−4.18847	−	3.04310i	−0.777779	−	0.565090i	0.126532	−	0.991962i	$-0.459615\pi$
$29$	−4.18847	−	3.04310i	−0.777779	−	0.565090i	−0.904312	+	0.426873i	$0.859615\pi$
$30$	3.26520	+	4.49416i	0.596141	+	0.820518i
$31$	−1.73117	−	0.562491i	−0.310927	−	0.101026i	0.149397	−	0.988777i	$-0.452267\pi$
$31$	−1.73117	−	0.562491i	−0.310927	−	0.101026i	−0.460324	+	0.887751i	$0.652267\pi$
$32$	−1.00000			−0.176777
$33$	4.76231	+	5.16524i	0.829012	+	0.899154i
$34$		−	3.08836i		−	0.529650i
$35$	−9.47322	−	3.07803i	−1.60127	−	0.520283i
$36$	1.20318	−	0.874163i	0.200530	−	0.145694i
$37$	−3.05990	+	4.21160i	−0.503045	+	0.692382i	−0.982727	−	0.185060i	$-0.940752\pi$
$37$	−3.05990	+	4.21160i	−0.503045	+	0.692382i	0.479682	+	0.877442i	$0.340752\pi$
$38$	−3.40661	+	2.71938i	−0.552625	+	0.441141i
$39$	1.47964	−	0.480765i	0.236932	−	0.0769840i
$40$	−2.12158	−	1.54142i	−0.335452	−	0.243720i
$41$	−7.29522	+	5.30029i	−1.13932	+	0.827766i	−0.987025	−	0.160569i	$-0.948667\pi$
$41$	−7.29522	+	5.30029i	−1.13932	+	0.827766i	−0.152297	+	0.988335i	$0.548667\pi$
$42$	−2.48633	+	7.65215i	−0.383650	+	1.18075i
$43$			7.16858i			1.09320i	0.837394	+	0.546599i	$0.184078\pi$
$43$			7.16858i			1.09320i	−0.837394	+	0.546599i	$0.815922\pi$
$44$	−2.89164	−	1.62432i	−0.435931	−	0.244875i
$45$	3.90011			0.581393
$46$	0.593153	−	1.82554i	0.0874557	−	0.269161i
$47$	1.67274	−	1.21531i	0.243994	−	0.177272i	−0.459067	−	0.888402i	$-0.651816\pi$
$47$	1.67274	−	1.21531i	0.243994	−	0.177272i	0.703061	+	0.711130i	$0.251816\pi$
$48$	−1.24511	+	1.71374i	−0.179716	+	0.247358i
$49$	−2.29508	−	7.06353i	−0.327869	−	1.00908i
$50$	−0.580055	−	1.78523i	−0.0820321	−	0.252469i
$51$	−5.29267	−	3.84535i	−0.741122	−	0.538456i
$52$	−0.594182	+	0.431698i	−0.0823982	+	0.0598658i
$53$	10.8413	+	3.52257i	1.48917	+	0.483862i	0.936839	−	0.349761i	$-0.113737\pi$
$53$	10.8413	+	3.52257i	1.48917	+	0.483862i	0.552334	+	0.833623i	$0.313737\pi$
$54$			3.20454i			0.436083i
$55$	−3.63110	−	7.90337i	−0.489617	−	1.06569i
$56$		−	3.79829i		−	0.507568i
$57$	0.418719	+	9.22398i	0.0554607	+	1.22175i
$58$	4.18847	−	3.04310i	0.549973	−	0.399579i
$59$	−1.48002	+	2.03708i	−0.192682	+	0.265205i	−0.894417	−	0.447234i	$-0.852409\pi$
$59$	−1.48002	+	2.03708i	−0.192682	+	0.265205i	0.701735	+	0.712438i	$0.252409\pi$
$60$	−5.28320	+	1.71662i	−0.682059	+	0.221614i
$61$	12.2970	−	3.99554i	1.57447	−	0.511577i	0.613847	−	0.789425i	$-0.289621\pi$
$61$	12.2970	−	3.99554i	1.57447	−	0.511577i	0.960625	+	0.277848i	$0.0896211\pi$
$62$	1.06992	−	1.47262i	0.135880	−	0.187023i
$63$	3.32033	+	4.57004i	0.418322	+	0.575771i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−1.92604			−0.238895
$66$	−6.38408	+	2.93308i	−0.785825	+	0.361037i
$67$		−	11.2953i		−	1.37994i	−0.723839	−	0.689969i	$-0.757624\pi$
$67$		−	11.2953i		−	1.37994i	0.723839	−	0.689969i	$-0.242376\pi$
$68$	2.93721	+	0.954357i	0.356189	+	0.115733i
$69$	−2.38997	−	3.28951i	−0.287718	−	0.396010i
$70$	5.85477	−	8.05840i	0.699779	−	0.963163i
$71$	5.05547	−	1.64262i	0.599974	−	0.194943i	0.00674493	−	0.999977i	$-0.497853\pi$
$71$	5.05547	−	1.64262i	0.599974	−	0.194943i	0.593229	+	0.805034i	$0.297853\pi$
$72$	0.459575	+	1.41443i	0.0541614	+	0.166692i
$73$	−1.28522	+	1.76895i	−0.150424	+	0.207040i	−0.877578	−	0.479433i	$-0.840842\pi$
$73$	−1.28522	+	1.76895i	−0.150424	+	0.207040i	0.727155	+	0.686474i	$0.240842\pi$
$74$	−3.05990	−	4.21160i	−0.355707	−	0.489588i
$75$	−3.78165	−	1.22873i	−0.436667	−	0.141882i
$76$	−1.53358	−	4.08021i	−0.175914	−	0.468032i
$77$	6.16964	−	10.9833i	0.703096	−	1.25166i
$78$			1.55579i			0.176158i
$79$	−2.63258	+	8.10225i	−0.296188	+	0.911574i	0.686631	+	0.727006i	$0.259089\pi$
$79$	−2.63258	+	8.10225i	−0.296188	+	0.911574i	−0.982820	+	0.184568i	$0.940911\pi$
$80$	2.12158	−	1.54142i	0.237200	−	0.172336i
$81$	9.10131	+	6.61249i	1.01126	+	0.734721i
$82$	−2.78653	−	8.57605i	−0.307720	−	0.947066i
$83$	−12.5898	+	4.09066i	−1.38191	+	0.449009i	−0.903296	−	0.429019i	$-0.858859\pi$
$83$	−12.5898	+	4.09066i	−1.38191	+	0.449009i	−0.478611	+	0.878027i	$0.658859\pi$
$84$	−6.50931	−	4.72929i	−0.710223	−	0.516008i
$85$	4.76047	+	6.55222i	0.516345	+	0.710688i
$86$	−6.81773	−	2.21521i	−0.735175	−	0.238873i
$87$		−	10.9670i		−	1.17578i
$88$	2.43839	−	2.24817i	0.259933	−	0.239656i
$89$			16.5351i			1.75272i	0.481660	+	0.876358i	$0.340034\pi$
$89$			16.5351i			1.75272i	−0.481660	+	0.876358i	$0.659966\pi$
$90$	−1.20520	+	3.70922i	−0.127039	+	0.390986i
$91$	−1.63972	−	2.25688i	−0.171889	−	0.236585i
$92$	1.55290	+	1.12824i	0.161901	+	0.117628i
$93$	−1.19153	−	3.66714i	−0.123556	−	0.380265i
$94$	0.638929	+	1.96642i	0.0659005	+	0.202821i
$95$	3.03570	−	11.0204i	0.311457	−	1.13067i
$96$	−1.24511	−	1.71374i	−0.127078	−	0.174908i
$97$	11.6797	+	3.79496i	1.18589	+	0.385319i	0.834552	−	0.550929i	$-0.185726\pi$
$97$	11.6797	+	3.79496i	1.18589	+	0.385319i	0.351339	+	0.936248i	$0.385726\pi$
$98$	7.42703			0.750244
$99$	−0.968555	+	4.83651i	−0.0973434	+	0.486087i
$100$	1.87710			0.187710
$101$	−9.91295	−	3.22091i	−0.986375	−	0.320493i	−0.228967	−	0.973434i	$-0.573535\pi$
$101$	−9.91295	−	3.22091i	−0.986375	−	0.320493i	−0.757408	+	0.652941i	$0.773535\pi$
$102$	5.29267	−	3.84535i	0.524052	−	0.380746i
$103$	1.31878	−	1.81515i	0.129943	−	0.178852i	−0.739088	−	0.673609i	$-0.764743\pi$
$103$	1.31878	−	1.81515i	0.129943	−	0.178852i	0.869031	+	0.494758i	$0.164743\pi$
$104$	−0.226957	−	0.698503i	−0.0222550	−	0.0684938i
$105$	−6.52021	−	20.0672i	−0.636308	−	1.95835i
$106$	−6.70032	+	9.22220i	−0.650793	+	0.895739i
$107$	−5.96578	+	4.33439i	−0.576734	+	0.419022i	−0.837545	−	0.546368i	$-0.816010\pi$
$107$	−5.96578	+	4.33439i	−0.576734	+	0.419022i	0.260811	+	0.965390i	$0.416010\pi$
$108$	−3.04770	−	0.990257i	−0.293265	−	0.0952875i
$109$	−11.5907			−1.11019			−0.555094	−	0.831788i	$-0.687318\pi$
$109$	−11.5907			−1.11019			−0.555094	+	0.831788i	$0.687318\pi$
$110$	8.63862	−	1.01110i	0.823660	−	0.0964050i
$111$	−11.0275			−1.04669
$112$	3.61239	+	1.17374i	0.341339	+	0.110908i
$113$	−8.44789	−	11.6275i	−0.794711	−	1.09383i	−0.993505	−	0.113784i	$-0.963703\pi$
$113$	−8.44789	−	11.6275i	−0.794711	−	1.09383i	0.198795	−	0.980041i	$-0.436297\pi$
$114$	−8.90192	−	2.45214i	−0.833741	−	0.229664i
$115$	1.55550	+	4.78733i	0.145051	+	0.446421i
$116$	1.59985	+	4.92384i	0.148543	+	0.457167i
$117$	0.883676	+	0.642028i	0.0816959	+	0.0593556i
$118$	−1.48002	−	2.03708i	−0.136247	−	0.187528i
$119$	−3.62493	+	11.1564i	−0.332297	+	1.02270i
$120$		−	5.55509i		−	0.507108i
$121$	10.7027	−	2.54018i	0.972971	−	0.230926i
$122$			12.9299i			1.17061i
$123$	−18.1667	−	5.90271i	−1.63803	−	0.532230i
$124$	1.06992	+	1.47262i	0.0960818	+	0.132245i
$125$	−6.62550	−	4.81371i	−0.592603	−	0.430551i
$126$	−5.37240	+	1.74560i	−0.478612	+	0.155510i
$127$	−2.38988	−	7.35529i	−0.212067	−	0.652676i	−0.999349	−	0.0360823i	$-0.988512\pi$
$127$	−2.38988	−	7.35529i	−0.212067	−	0.652676i	0.787282	−	0.616594i	$-0.211488\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−12.2851	+	8.92566i	−1.08164	+	0.785861i
$130$	0.595178	−	1.83177i	0.0522005	−	0.160657i
$131$			7.33564i			0.640918i	0.947262	+	0.320459i	$0.103837\pi$
$131$			7.33564i			0.640918i	−0.947262	+	0.320459i	$0.896163\pi$
$132$	−0.816736	−	6.97799i	−0.0710878	−	0.607356i
$133$	15.4978	−	5.82499i	1.34383	−	0.505091i
$134$	10.7425	+	3.49043i	0.928006	+	0.301528i
$135$	−4.93954	−	6.79870i	−0.425128	−	0.585139i
$136$	−1.81529	+	2.49854i	−0.155660	+	0.214248i
$137$	−4.50176	−	13.8550i	−0.384611	−	1.18371i	−0.936762	−	0.349967i	$-0.886193\pi$
$137$	−4.50176	−	13.8550i	−0.384611	−	1.18371i	0.552151	−	0.833744i	$-0.313807\pi$
$138$	3.86705	−	1.25648i	0.329185	−	0.106959i
$139$	−3.10068	+	4.26772i	−0.262996	+	0.361983i	−0.920010	−	0.391896i	$-0.871819\pi$
$139$	−3.10068	+	4.26772i	−0.262996	+	0.361983i	0.657013	+	0.753879i	$0.271819\pi$
$140$	5.85477	+	8.05840i	0.494818	+	0.681059i
$141$	4.16548	+	1.35345i	0.350796	+	0.113981i
$142$			5.31563i			0.446078i
$143$	0.478313	−	2.38847i	0.0399985	−	0.199734i
$144$	−1.48722			−0.123935
$145$	−4.19549	+	12.9124i	−0.348416	+	1.07232i
$146$	−1.28522	−	1.76895i	−0.106366	−	0.146400i
$147$	9.24746	−	12.7280i	0.762718	−	1.04979i
$148$	4.95103	−	1.60869i	0.406972	−	0.132233i
$149$	−18.7327	+	6.08661i	−1.53464	+	0.498635i	−0.949891	−	0.312580i	$-0.898807\pi$
$149$	−18.7327	+	6.08661i	−1.53464	+	0.498635i	−0.584748	+	0.811215i	$0.698807\pi$
$150$	2.33719	−	3.21686i	0.190831	−	0.262656i
$151$	−2.92755	+	2.12699i	−0.238240	+	0.173092i	−0.700499	−	0.713653i	$-0.747039\pi$
$151$	−2.92755	+	2.12699i	−0.238240	+	0.173092i	0.462259	+	0.886745i	$0.347039\pi$
$152$	4.35441	−	0.197667i	0.353190	−	0.0160329i
$153$		−	4.59306i		−	0.371327i
$154$	8.53921	+	9.26171i	0.688109	+	0.746330i
$155$			4.77349i			0.383416i
$156$	−1.47964	−	0.480765i	−0.118466	−	0.0384920i
$157$	4.55308	−	3.30800i	0.363375	−	0.264007i	−0.391083	−	0.920355i	$-0.627900\pi$
$157$	4.55308	−	3.30800i	0.363375	−	0.264007i	0.754458	+	0.656348i	$0.227900\pi$
$158$	−6.89219	−	5.00747i	−0.548313	−	0.398373i
$159$	7.46187	+	22.9653i	0.591765	+	1.82126i
$160$	0.810373	+	2.49407i	0.0640656	+	0.197174i
$161$	−4.28541	+	5.89835i	−0.337737	+	0.464855i
$162$	−9.10131	+	6.61249i	−0.715066	+	0.519526i
$163$	−2.51310	+	7.73453i	−0.196841	+	0.605815i	0.803109	+	0.595832i	$0.203178\pi$
$163$	−2.51310	+	7.73453i	−0.196841	+	0.605815i	−0.999950	+	0.00998284i	$0.996822\pi$
$164$	9.01739			0.704140
$165$	9.02324	−	16.0633i	0.702458	−	1.25053i
$166$		−	13.2377i		−	1.02744i
$167$	−7.08015	+	21.7904i	−0.547878	+	1.68620i	0.166169	+	0.986097i	$0.446860\pi$
$167$	−7.08015	+	21.7904i	−0.547878	+	1.68620i	−0.714047	+	0.700098i	$0.753140\pi$
$168$	6.50931	−	4.72929i	0.502204	−	0.364872i
$169$	10.0808	+	7.32415i	0.775448	+	0.563396i
$170$	−7.70260	+	2.50273i	−0.590762	+	0.191950i
$171$	−5.06636	+	4.04430i	−0.387434	+	0.309275i
$172$	4.21359	−	5.79951i	0.321283	−	0.442208i
$173$	10.5220	−	7.64471i	0.799975	−	0.581216i	−0.110932	−	0.993828i	$-0.535383\pi$
$173$	10.5220	−	7.64471i	0.799975	−	0.581216i	0.910907	+	0.412612i	$0.135383\pi$
$174$	10.4302	+	3.38898i	0.790711	+	0.256918i
$175$			7.12977i			0.538960i
$176$	1.38464	+	3.01377i	0.104371	+	0.227171i
$177$	−5.33381			−0.400914
$178$	−15.7258	−	5.10962i	−1.17870	−	0.382983i
$179$	−12.2509	−	16.8619i	−0.915674	−	1.26032i	−0.965191	−	0.261544i	$-0.915768\pi$
$179$	−12.2509	−	16.8619i	−0.915674	−	1.26032i	0.0495170	−	0.998773i	$-0.484232\pi$
$180$	−3.15525	−	2.29242i	−0.235179	−	0.170867i
$181$	6.50507	−	2.11363i	0.483518	−	0.157105i	−0.0571072	−	0.998368i	$-0.518188\pi$
$181$	6.50507	−	2.11363i	0.483518	−	0.157105i	0.540625	+	0.841263i	$0.318188\pi$
$182$	2.65312	−	0.862050i	0.196662	−	0.0638994i
$183$	22.1585	+	16.0991i	1.63800	+	1.19008i
$184$	−1.55290	+	1.12824i	−0.114481	+	0.0831753i
$185$	12.9837	+	4.21865i	0.954579	+	0.310162i
$186$	3.85586			0.282726
$187$	−9.30761	+	4.27626i	−0.680640	+	0.312711i
$188$	−2.06762			−0.150796
$189$	3.76129	−	11.5761i	0.273593	−	0.842034i
$190$	9.54294	+	6.29262i	0.692318	+	0.456515i
$191$	16.0727	+	11.6775i	1.16298	+	0.844955i	0.990152	−	0.139997i	$-0.0447093\pi$
$191$	16.0727	+	11.6775i	1.16298	+	0.844955i	0.172829	+	0.984952i	$0.444709\pi$
$192$	2.01463	−	0.654592i	0.145393	−	0.0472411i
$193$	0.424933	+	1.30781i	0.0305873	+	0.0941381i	0.965185	−	0.261569i	$-0.0842400\pi$
$193$	0.424933	+	1.30781i	0.0305873	+	0.0941381i	−0.934597	+	0.355707i	$0.884240\pi$
$194$	−7.21844	+	9.93533i	−0.518254	+	0.713315i
$195$	−2.39812	−	3.30073i	−0.171733	−	0.236370i
$196$	−2.29508	+	7.06353i	−0.163934	+	0.504538i
$197$		−	7.21258i		−	0.513875i	−0.966428	−	0.256938i	$-0.917287\pi$
$197$		−	7.21258i		−	0.513875i	0.966428	−	0.256938i	$-0.0827135\pi$
$198$	−4.30049	−	2.41571i	−0.305623	−	0.171677i
$199$	3.60236			0.255365			0.127682	−	0.991815i	$-0.459246\pi$
$199$	3.60236			0.255365			0.127682	+	0.991815i	$0.459246\pi$
$200$	−0.580055	+	1.78523i	−0.0410161	+	0.126234i
$201$	19.3572	−	14.0638i	1.36535	−	0.991987i
$202$	6.12654	−	8.43246i	0.431062	−	0.593306i
$203$	−18.7022	+	6.07671i	−1.31264	+	0.426501i
$204$	2.02162	+	6.22190i	0.141542	+	0.435620i
$205$	19.1311	+	13.8996i	1.33618	+	0.970790i
$206$	1.31878	+	1.81515i	0.0918838	+	0.126467i
$207$	0.882147	−	2.71497i	0.0613134	−	0.188703i
$208$	0.734449			0.0509249
$209$	12.9125	+	6.50138i	0.893175	+	0.449710i
$210$	21.0999			1.45603
$211$	−0.103130	+	0.317403i	−0.00709980	+	0.0218509i	−0.954544	−	0.298071i	$-0.903657\pi$
$211$	−0.103130	+	0.317403i	−0.00709980	+	0.0218509i	0.947444	+	0.319922i	$0.103657\pi$
$212$	−6.70032	−	9.22220i	−0.460180	−	0.633383i
$213$	9.10964	+	6.61854i	0.624182	+	0.453495i
$214$	−2.27873	−	7.01319i	−0.155770	−	0.479412i
$215$	17.8790	−	5.80923i	1.21934	−	0.396186i
$216$	1.88358	−	2.59253i	0.128161	−	0.176399i
$217$	−5.59344	+	4.06388i	−0.379708	+	0.275874i
$218$	3.58172	−	11.0234i	0.242585	−	0.746600i
$219$	−4.63177			−0.312986
$220$	−1.70786	+	8.52826i	−0.115144	+	0.574975i
$221$			2.26825i			0.152579i
$222$	3.40769	−	10.4878i	0.228709	−	0.703894i
$223$	−7.73233	−	10.6426i	−0.517795	−	0.712684i	0.467414	−	0.884038i	$-0.345186\pi$
$223$	−7.73233	−	10.6426i	−0.517795	−	0.712684i	−0.985209	+	0.171355i	$0.945186\pi$
$224$	−2.23258	+	3.07288i	−0.149171	+	0.205316i
$225$	−0.862666	−	2.65501i	−0.0575111	−	0.177001i
$226$	13.6690	−	4.44132i	0.909247	−	0.295432i
$227$	1.67334	+	1.21575i	0.111064	+	0.0806924i	0.641931	−	0.766763i	$-0.278134\pi$
$227$	1.67334	+	1.21575i	0.111064	+	0.0806924i	−0.530867	+	0.847455i	$0.678134\pi$
$228$	5.08297	−	7.70847i	0.336628	−	0.510506i
$229$	−3.07428	+	9.46166i	−0.203154	+	0.625244i	0.796630	+	0.604467i	$0.206614\pi$
$229$	−3.07428	+	9.46166i	−0.203154	+	0.625244i	−0.999784	+	0.0207769i	$0.993386\pi$
$230$	−5.03370			−0.331912
$231$	26.5044	−	3.10220i	1.74386	−	0.204110i
$232$	−5.17723			−0.339902
$233$	2.28040	+	0.740947i	0.149394	+	0.0485410i	0.382759	−	0.923848i	$-0.374974\pi$
$233$	2.28040	+	0.740947i	0.149394	+	0.0485410i	−0.233365	+	0.972389i	$0.574974\pi$
$234$	−0.883676	+	0.642028i	−0.0577677	+	0.0419707i
$235$	−4.38662	−	3.18707i	−0.286152	−	0.207901i
$236$	2.39473	−	0.778093i	0.155883	−	0.0506496i
$237$	−17.1630	+	5.57661i	−1.11486	+	0.362240i
$238$	−9.49018	−	6.89502i	−0.615157	−	0.446938i
$239$	−6.60002	−	9.08415i	−0.426920	−	0.587605i	0.540323	−	0.841458i	$-0.318302\pi$
$239$	−6.60002	−	9.08415i	−0.426920	−	0.587605i	−0.967243	+	0.253853i	$0.918302\pi$
$240$	5.28320	+	1.71662i	0.341029	+	0.110807i
$241$	10.1120			0.651371			0.325685	−	0.945478i	$-0.394405\pi$
$241$	10.1120			0.651371			0.325685	+	0.945478i	$0.394405\pi$
$242$	−0.891453	+	10.9638i	−0.0573047	+	0.704781i
$243$			14.2170i			0.912019i
$244$	−12.2970	−	3.99554i	−0.787236	−	0.255789i
$245$	−15.7571	+	11.4482i	−1.00668	+	0.731398i
$246$	11.2276	−	15.4535i	0.715847	−	0.985279i
$247$	2.50198	−	1.99724i	0.159197	−	0.127082i
$248$	−1.73117	+	0.562491i	−0.109929	+	0.0357182i
$249$	−22.6860	−	16.4823i	−1.43767	−	1.04452i
$250$	6.62550	−	4.81371i	0.419033	−	0.304446i
$251$	−1.07867	+	3.31980i	−0.0680849	+	0.209544i	−0.979310	−	0.202364i	$-0.935137\pi$
$251$	−1.07867	+	3.31980i	−0.0680849	+	0.209544i	0.911225	+	0.411908i	$0.135137\pi$
$252$		−	5.64888i		−	0.355846i
$253$	−6.32305	+	0.740079i	−0.397527	+	0.0465284i
$254$	7.73381			0.485262
$255$	−5.30154	+	16.3165i	−0.331995	+	1.02178i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−8.66668	+	11.9287i	−0.540613	+	0.744090i	−0.988701	−	0.149900i	$-0.952105\pi$
$257$	−8.66668	+	11.9287i	−0.540613	+	0.744090i	0.448089	+	0.893989i	$0.352105\pi$
$258$	−4.69250	−	14.4420i	−0.292142	−	0.899121i
$259$	6.11026	+	18.8055i	0.379673	+	1.16851i
$260$	1.55820	+	1.13210i	0.0966352	+	0.0702096i
$261$	6.22916	−	4.52575i	0.385575	−	0.280137i
$262$	−6.97661	−	2.26684i	−0.431016	−	0.140046i
$263$			15.9539i			0.983762i	0.870662	+	0.491881i	$0.163690\pi$
$263$			15.9539i			0.983762i	−0.870662	+	0.491881i	$0.836310\pi$
$264$	6.88885	+	1.37955i	0.423979	+	0.0849057i
$265$		−	29.8937i		−	1.83635i
$266$	0.750798	+	16.5393i	0.0460344	+	1.01409i
$267$	−28.3369	+	20.5880i	−1.73419	+	1.25996i
$268$	−6.63920	+	9.13808i	−0.405554	+	0.558197i
$269$	5.87773	−	1.90979i	0.358371	−	0.116442i	−0.124297	−	0.992245i	$-0.539668\pi$
$269$	5.87773	−	1.90979i	0.358371	−	0.116442i	0.482668	+	0.875803i	$0.339668\pi$
$270$	7.99235	−	2.59687i	0.486399	−	0.158041i
$271$	−4.95718	+	6.82298i	−0.301127	+	0.414466i	−0.932589	−	0.360941i	$-0.882456\pi$
$271$	−4.95718	+	6.82298i	−0.301127	+	0.414466i	0.631461	+	0.775408i	$0.282456\pi$
$272$	−1.81529	−	2.49854i	−0.110068	−	0.151496i
$273$	1.82609	−	5.62011i	0.110520	−	0.340145i
$274$	14.5680			0.880085
$275$	−4.57709	+	4.22004i	−0.276009	+	0.254478i
$276$			4.06605i			0.244748i
$277$	25.1604	+	8.17510i	1.51174	+	0.491194i	0.943416	−	0.331610i	$-0.107592\pi$
$277$	25.1604	+	8.17510i	1.51174	+	0.491194i	0.568324	+	0.822805i	$0.307592\pi$
$278$	−3.10068	−	4.26772i	−0.185966	−	0.255961i
$279$	1.59120	−	2.19010i	0.0952629	−	0.131118i
$280$	−9.47322	+	3.07803i	−0.566133	+	0.183948i
$281$	10.0413	+	30.9041i	0.599017	+	1.84358i	0.533620	+	0.845724i	$0.320831\pi$
$281$	10.0413	+	30.9041i	0.599017	+	1.84358i	0.0653966	+	0.997859i	$0.479169\pi$
$282$	−2.57441	+	3.54337i	−0.153304	+	0.211004i
$283$	−18.9708	−	26.1110i	−1.12769	−	1.55214i	−0.792375	−	0.610034i	$-0.791156\pi$
$283$	−18.9708	−	26.1110i	−1.12769	−	1.55214i	−0.335320	−	0.942104i	$-0.608844\pi$
$284$	−5.05547	−	1.64262i	−0.299987	−	0.0974716i
$285$	22.6659	−	8.51918i	1.34261	−	0.504633i
$286$	2.12376	+	1.19298i	0.125581	+	0.0705424i
$287$			34.2507i			2.02175i
$288$	0.459575	−	1.41443i	0.0270807	−	0.0833458i
$289$	−6.03689	+	4.38606i	−0.355111	+	0.258003i
$290$	−10.9839	−	7.98029i	−0.644999	−	0.468619i
$291$	8.03888	+	24.7411i	0.471247	+	1.45035i
$292$	2.07953	−	0.675680i	0.121695	−	0.0395412i
$293$	−4.98671	−	3.62306i	−0.291327	−	0.211661i	0.432516	−	0.901626i	$-0.357626\pi$
$293$	−4.98671	−	3.62306i	−0.291327	−	0.211661i	−0.723843	+	0.689965i	$0.757626\pi$
$294$	9.24746	+	12.7280i	0.539323	+	0.742314i
$295$	6.27998	+	2.04049i	0.365635	+	0.118802i
$296$			5.20582i			0.302582i
$297$	9.65773	−	4.43712i	0.560398	−	0.257468i
$298$		−	19.6967i		−	1.14100i
$299$	−0.435641	+	1.34077i	−0.0251938	+	0.0775385i
$300$	2.33719	+	3.21686i	0.134938	+	0.185726i
$301$	22.0282	+	16.0044i	1.26969	+	0.922481i
$302$	−1.11822	−	3.44154i	−0.0643465	−	0.198038i
$303$	−6.82287	−	20.9986i	−0.391964	−	1.20634i
$304$	−1.15760	+	4.20238i	−0.0663927	+	0.241023i
$305$	−19.9303	−	27.4318i	−1.14121	−	1.57074i
$306$	4.36826	+	1.41933i	0.249717	+	0.0811379i
$307$	31.5559			1.80099			0.900494	−	0.434868i	$-0.143205\pi$
$307$	31.5559			1.80099			0.900494	+	0.434868i	$0.143205\pi$
$308$	−11.4472	+	5.25925i	−0.652263	+	0.299674i
$309$	4.75272			0.270373
$310$	−4.53986	−	1.47509i	−0.257846	−	0.0837794i
$311$	1.37720	−	1.00059i	0.0780937	−	0.0567384i	−0.548053	−	0.836443i	$-0.684631\pi$
$311$	1.37720	−	1.00059i	0.0780937	−	0.0567384i	0.626147	+	0.779705i	$0.284631\pi$
$312$	0.914469	−	1.25866i	0.0517716	−	0.0712575i
$313$	1.05364	+	3.24277i	0.0595552	+	0.183292i	0.976408	−	0.215933i	$-0.0692792\pi$
$313$	1.05364	+	3.24277i	0.0595552	+	0.183292i	−0.916853	+	0.399225i	$0.869279\pi$
$314$	1.73912	+	5.35246i	0.0981443	+	0.302057i
$315$	8.70730	−	11.9846i	0.490601	−	0.675254i
$316$	6.89219	−	5.00747i	0.387716	−	0.281692i
$317$	−22.3997	−	7.27811i	−1.25809	−	0.408780i	−0.397279	−	0.917698i	$-0.630046\pi$
$317$	−22.3997	−	7.27811i	−1.25809	−	0.408780i	−0.860815	+	0.508918i	$0.830046\pi$
$318$	−24.1471			−1.35410
$319$	−14.9707	−	8.40948i	−0.838198	−	0.470841i
$320$	−2.62242			−0.146598
$321$	−14.8561	−	4.82703i	−0.829186	−	0.269419i
$322$	−4.28541	−	5.89835i	−0.238816	−	0.328702i
$323$	−12.9785	−	3.57508i	−0.722141	−	0.198923i
$324$	−3.47639	−	10.6992i	−0.193133	−	0.594402i
$325$	0.426021	+	1.31116i	0.0236314	+	0.0727299i
$326$	−6.57938	−	4.78020i	−0.364398	−	0.264751i
$327$	−14.4317	−	19.8635i	−0.798074	−	1.09845i
$328$	−2.78653	+	8.57605i	−0.153860	+	0.473533i
$329$		−	7.85341i		−	0.432973i
$330$	12.4888	+	13.5455i	0.687485	+	0.745653i
$331$		−	30.6577i		−	1.68510i	−0.538619	−	0.842550i	$-0.681054\pi$
$331$		−	30.6577i		−	1.68510i	0.538619	−	0.842550i	$-0.318946\pi$
$332$	12.5898	+	4.09066i	0.690953	+	0.224504i
$333$	−4.55074	−	6.26355i	−0.249379	−	0.343240i
$334$	−18.5361	−	13.4672i	−1.01425	−	0.736894i
$335$	−28.1712	+	9.15339i	−1.53916	+	0.500103i
$336$	2.48633	+	7.65215i	0.135641	+	0.417459i
$337$	−24.4146	−	17.7383i	−1.32995	−	0.966265i	−0.999750	−	0.0223541i	$-0.992884\pi$
$337$	−24.4146	−	17.7383i	−1.32995	−	0.966265i	−0.330200	−	0.943911i	$-0.607116\pi$
$338$	−10.0808	+	7.32415i	−0.548325	+	0.398381i
$339$	9.40807	−	28.9551i	0.510976	−	1.57262i
$340$		−	8.09899i		−	0.439230i
$341$	−5.91958	−	1.18545i	−0.320563	−	0.0641958i
$342$	−2.28076	−	6.06815i	−0.123330	−	0.328128i
$343$	−1.54261	−	0.501226i	−0.0832933	−	0.0270636i
$344$	4.21359	+	5.79951i	0.227181	+	0.312688i
$345$	−6.26750	+	8.62648i	−0.337431	+	0.464434i
$346$	4.01906	+	12.3694i	0.216066	+	0.664983i
$347$	17.3025	−	5.62193i	0.928848	−	0.301801i	0.194757	−	0.980852i	$-0.437608\pi$
$347$	17.3025	−	5.62193i	0.928848	−	0.301801i	0.734092	+	0.679050i	$0.237608\pi$
$348$	−6.44622	+	8.87245i	−0.345553	+	0.475613i
$349$	−3.59202	−	4.94399i	−0.192276	−	0.264646i	0.701984	−	0.712193i	$-0.252298\pi$
$349$	−3.59202	−	4.94399i	−0.192276	−	0.264646i	−0.894260	+	0.447547i	$0.852298\pi$
$350$	−6.78081	−	2.20322i	−0.362450	−	0.117767i
$351$		−	2.35357i		−	0.125624i
$352$	−3.29414	+	0.385561i	−0.175578	+	0.0205505i
$353$	23.1595			1.23266			0.616328	−	0.787490i	$-0.288620\pi$
$353$	23.1595			1.23266			0.616328	+	0.787490i	$0.288620\pi$
$354$	1.64824	−	5.07276i	0.0876029	−	0.269614i
$355$	−8.19363	−	11.2776i	−0.434873	−	0.598551i
$356$	9.71908	−	13.3772i	0.515110	−	0.708989i
$357$	−23.6326	+	7.67870i	−1.25077	+	0.406400i
$358$	19.8224	−	6.44067i	1.04764	−	0.340400i
$359$	21.0952	−	29.0350i	1.11336	−	1.53241i	0.296992	−	0.954880i	$-0.404017\pi$
$359$	21.0952	−	29.0350i	1.11336	−	1.53241i	0.816369	−	0.577530i	$-0.195983\pi$
$360$	3.15525	−	2.29242i	0.166296	−	0.120821i
$361$	7.48437	+	17.4638i	0.393914	+	0.919147i
$362$			6.83984i			0.359494i
$363$	17.6792	+	15.1789i	0.927919	+	0.796684i
$364$			2.78965i			0.146218i
$365$	5.45340	+	1.77192i	0.285444	+	0.0927464i
$366$	−22.1585	+	16.0991i	−1.15824	+	0.841512i
$367$	−2.45924	−	1.78674i	−0.128371	−	0.0932673i	0.521747	−	0.853100i	$-0.325281\pi$
$367$	−2.45924	−	1.78674i	−0.128371	−	0.0932673i	−0.650118	+	0.759833i	$0.725281\pi$
$368$	−0.593153	−	1.82554i	−0.0309203	−	0.0951628i
$369$	−4.14416	−	12.7544i	−0.215737	−	0.663969i
$370$	−8.02436	+	11.0446i	−0.417167	+	0.574180i
$371$	35.0286	−	25.4498i	1.81860	−	1.32129i
$372$	−1.19153	+	3.66714i	−0.0617778	+	0.190133i
$373$	−29.8208			−1.54406			−0.772031	−	0.635585i	$-0.780759\pi$
$373$	−29.8208			−1.54406			−0.772031	+	0.635585i	$0.780759\pi$
$374$	−1.19075	−	10.1735i	−0.0615724	−	0.526059i
$375$		−	17.3480i		−	0.895847i
$376$	0.638929	−	1.96642i	0.0329502	−	0.101410i
$377$	−3.07622	+	2.23500i	−0.158433	+	0.115109i
$378$	9.84718	+	7.15439i	0.506484	+	0.367982i
$379$	−28.9054	+	9.39195i	−1.48477	+	0.482432i	−0.935535	−	0.353234i	$-0.885082\pi$
$379$	−28.9054	+	9.39195i	−1.48477	+	0.482432i	−0.549238	+	0.835666i	$0.685082\pi$
$380$	−8.93357	+	7.13135i	−0.458282	+	0.365831i
$381$	9.62943	−	13.2538i	0.493330	−	0.679011i
$382$	−16.0727	+	11.6775i	−0.822352	+	0.597473i
$383$	−14.4138	−	4.68333i	−0.736512	−	0.239307i	−0.0833445	−	0.996521i	$-0.526560\pi$
$383$	−14.4138	−	4.68333i	−0.736512	−	0.239307i	−0.653167	+	0.757214i	$0.726560\pi$
$384$			2.11830i			0.108099i
$385$	−32.3928	−	6.48696i	−1.65089	−	0.330606i
$386$	−1.37511			−0.0699913
$387$	−10.1394	−	3.29450i	−0.515416	−	0.167469i
$388$	−7.21844	−	9.93533i	−0.366461	−	0.504390i
$389$	19.5556	+	14.2080i	0.991509	+	0.720373i	0.960251	−	0.279138i	$-0.0900487\pi$
$389$	19.5556	+	14.2080i	0.991509	+	0.720373i	0.0312579	+	0.999511i	$0.490049\pi$
$390$	3.88024	−	1.26077i	0.196484	−	0.0638415i
$391$	5.63793	−	1.83187i	0.285122	−	0.0926418i
$392$	−6.00860	−	4.36550i	−0.303480	−	0.220491i
$393$	−12.5714	+	9.13366i	−0.634144	+	0.460732i
$394$	6.85957	+	2.22881i	0.345580	+	0.112286i
$395$	22.3410			1.12410
$396$	3.62640	−	3.34351i	0.182234	−	0.168018i
$397$	25.5483			1.28223			0.641115	−	0.767445i	$-0.278472\pi$
$397$	25.5483			1.28223			0.641115	+	0.767445i	$0.278472\pi$
$398$	−1.11319	+	3.42605i	−0.0557993	+	0.171732i
$399$	29.2790	+	19.3066i	1.46579	+	0.966539i
$400$	−1.51860	−	1.10333i	−0.0759302	−	0.0551665i
$401$	16.4245	−	5.33665i	0.820202	−	0.266500i	0.131289	−	0.991344i	$-0.458088\pi$
$401$	16.4245	−	5.33665i	0.820202	−	0.266500i	0.688913	+	0.724844i	$0.258088\pi$
$402$	7.39380	+	22.7558i	0.368769	+	1.13496i
$403$	−0.785803	+	1.08156i	−0.0391436	+	0.0538766i
$404$	6.12654	+	8.43246i	0.304807	+	0.419530i
$405$	9.11656	−	28.0579i	0.453006	−	1.39421i
$406$		−	19.6646i		−	0.975940i
$407$	−8.45591	+	15.0534i	−0.419144	+	0.746167i
$408$	−6.54210			−0.323882
$409$	−10.4735	+	32.2341i	−0.517880	+	1.59387i	0.260099	+	0.965582i	$0.416245\pi$
$409$	−10.4735	+	32.2341i	−0.517880	+	1.59387i	−0.777980	+	0.628290i	$0.783755\pi$
$410$	−19.1311	+	13.8996i	−0.944820	+	0.686452i
$411$	18.1387	−	24.9658i	0.894718	−	1.23147i
$412$	−2.13383	+	0.693324i	−0.105126	+	0.0341576i
$413$	2.95543	+	9.09587i	0.145427	+	0.447579i
$414$	2.30949	+	1.67794i	0.113505	+	0.0824664i
$415$	20.4048	+	28.0848i	1.00163	+	1.37863i
$416$	−0.226957	+	0.698503i	−0.0111275	+	0.0342469i
$417$	−11.1745			−0.547216
$418$	−10.1734	+	10.2715i	−0.497595	+	0.502393i
$419$	−26.6533			−1.30210			−0.651050	−	0.759035i	$-0.725671\pi$
$419$	−26.6533			−1.30210			−0.651050	+	0.759035i	$0.725671\pi$
$420$	−6.52021	+	20.0672i	−0.318154	+	0.979177i
$421$	14.2829	+	19.6587i	0.696107	+	0.958108i	0.999985	+	0.00539777i	$0.00171817\pi$
$421$	14.2829	+	19.6587i	0.696107	+	0.958108i	−0.303879	+	0.952711i	$0.598282\pi$
$422$	−0.269999	−	0.196166i	−0.0131434	−	0.00954920i
$423$	0.950224	+	2.92449i	0.0462015	+	0.142194i
$424$	10.8413	−	3.52257i	0.526502	−	0.171071i
$425$	3.40748	−	4.69000i	0.165287	−	0.227498i
$426$	−9.10964	+	6.61854i	−0.441363	+	0.320669i
$427$	15.1763	−	46.7077i	0.734430	−	2.26034i
$428$	7.37411			0.356441
$429$	4.68878	−	2.15420i	0.226376	−	0.104006i
$430$			18.7991i			0.906571i
$431$	5.85662	−	18.0248i	0.282103	−	0.868225i	−0.705148	−	0.709060i	$-0.749120\pi$
$431$	5.85662	−	18.0248i	0.282103	−	0.868225i	0.987252	−	0.159165i	$-0.0508803\pi$
$432$	1.88358	+	2.59253i	0.0906238	+	0.124733i
$433$	1.30649	−	1.79823i	0.0627860	−	0.0864175i	−0.776469	−	0.630155i	$-0.782991\pi$
$433$	1.30649	−	1.79823i	0.0627860	−	0.0864175i	0.839255	+	0.543738i	$0.182991\pi$
$434$	−2.13651	−	6.57549i	−0.102556	−	0.315634i
$435$	−27.3524	+	8.88733i	−1.31145	+	0.426115i
$436$	9.37707	+	6.81284i	0.449080	+	0.326276i
$437$	−6.98497	−	4.60589i	−0.334136	−	0.220330i
$438$	1.43130	−	4.40508i	0.0683900	−	0.210483i
$439$	−24.8868			−1.18778			−0.593891	−	0.804545i	$-0.702409\pi$
$439$	−24.8868			−1.18778			−0.593891	+	0.804545i	$0.702409\pi$
$440$	−7.58310	−	4.25965i	−0.361510	−	0.203071i
$441$	11.0456			0.525981
$442$	−2.15723	−	0.700927i	−0.102609	−	0.0333397i
$443$	29.3763	−	21.3431i	1.39571	−	1.01404i	0.400496	−	0.916298i	$-0.368838\pi$
$443$	29.3763	−	21.3431i	1.39571	−	1.01404i	0.995212	−	0.0977426i	$-0.0311622\pi$
$444$	8.92144	+	6.48181i	0.423393	+	0.307613i
$445$	41.2397	−	13.3996i	1.95495	−	0.635201i
$446$	12.5112	−	4.06513i	0.592421	−	0.192489i
$447$	−33.7551	−	24.5245i	−1.59656	−	1.15997i
$448$	−2.23258	−	3.07288i	−0.105480	−	0.145180i
$449$	25.7478	+	8.36597i	1.21511	+	0.394815i	0.845300	−	0.534291i	$-0.179421\pi$
$449$	25.7478	+	8.36597i	1.21511	+	0.394815i	0.369814	+	0.929106i	$0.379421\pi$
$450$	2.79165			0.131600
$451$	−21.9879	+	20.2726i	−1.03537	+	0.954601i
$452$			14.3724i			0.676021i
$453$	−7.29022	−	2.36874i	−0.342524	−	0.111293i
$454$	−1.67334	+	1.21575i	−0.0785338	+	0.0570581i
$455$	−4.30003	+	5.91848i	−0.201589	+	0.277463i
$456$	5.76047	+	7.21624i	0.269759	+	0.337931i
$457$	−5.50815	+	1.78971i	−0.257660	+	0.0837189i	−0.434999	−	0.900431i	$-0.643251\pi$
$457$	−5.50815	+	1.78971i	−0.257660	+	0.0837189i	0.177339	+	0.984150i	$0.443251\pi$
$458$	−8.04857	−	5.84763i	−0.376085	−	0.273242i
$459$	−8.00667	+	5.81718i	−0.373719	+	0.271523i
$460$	1.55550	−	4.78733i	0.0725255	−	0.223211i
$461$			25.3943i			1.18273i	0.806404	+	0.591365i	$0.201411\pi$
$461$			25.3943i			1.18273i	−0.806404	+	0.591365i	$0.798589\pi$
$462$	−5.23995	+	26.1659i	−0.243785	+	1.21735i
$463$	−29.3453			−1.36379			−0.681895	−	0.731450i	$-0.738844\pi$
$463$	−29.3453			−1.36379			−0.681895	+	0.731450i	$0.738844\pi$
$464$	1.59985	−	4.92384i	0.0742713	−	0.228584i
$465$	−8.18054	+	5.94351i	−0.379363	+	0.275624i
$466$	−1.40936	+	1.93982i	−0.0652876	+	0.0898606i
$467$	4.64539	+	14.2970i	0.214963	+	0.661588i	0.999156	+	0.0410712i	$0.0130770\pi$
$467$	4.64539	+	14.2970i	0.214963	+	0.661588i	−0.784193	+	0.620517i	$0.786923\pi$
$468$	−0.337534	−	1.03882i	−0.0156025	−	0.0480197i
$469$	−34.7091	−	25.2176i	−1.60272	−	1.16444i
$470$	4.38662	−	3.18707i	0.202340	−	0.147008i
$471$	11.3381	+	3.68399i	0.522434	+	0.169749i
$472$			2.51796i			0.115899i
$473$	2.76393	+	23.6143i	0.127086	+	1.08579i
$474$		−	18.0463i		−	0.828893i
$475$	−8.17366	+	0.371041i	−0.375033	+	0.0170245i
$476$	9.49018	−	6.89502i	0.434982	−	0.316033i
$477$	−9.96482	+	13.7154i	−0.456258	+	0.627985i
$478$	10.6791	−	3.46983i	0.488449	−	0.158707i
$479$	10.7653	−	3.49787i	0.491880	−	0.159822i	−0.0525657	−	0.998617i	$-0.516740\pi$
$479$	10.7653	−	3.49787i	0.491880	−	0.159822i	0.544446	+	0.838796i	$0.316740\pi$
$480$	−3.26520	+	4.49416i	−0.149035	+	0.205129i
$481$	2.24734	+	3.09320i	0.102470	+	0.141038i
$482$	−3.12478	+	9.61708i	−0.142330	+	0.438046i
$483$	−15.4441			−0.702729
$484$	−10.1517	−	4.23583i	−0.461443	−	0.192538i
$485$		−	32.2053i		−	1.46237i
$486$	−13.5211	−	4.39328i	−0.613331	−	0.199283i
$487$	−2.25751	−	3.10719i	−0.102298	−	0.140800i	0.754799	−	0.655956i	$-0.227734\pi$
$487$	−2.25751	−	3.10719i	−0.102298	−	0.140800i	−0.857097	+	0.515155i	$0.827734\pi$
$488$	7.59998	−	10.4605i	0.344035	−	0.473523i
$489$	−16.3841	+	5.32351i	−0.740914	+	0.240738i
$490$	−6.01867	−	18.5236i	−0.271896	−	0.836809i
$491$	6.36047	−	8.75444i	0.287044	−	0.395082i	−0.641007	−	0.767535i	$-0.721483\pi$
$491$	6.36047	−	8.75444i	0.287044	−	0.395082i	0.928051	+	0.372453i	$0.121483\pi$
$492$	11.2276	+	15.4535i	0.506181	+	0.696698i
$493$	15.2066	+	4.94093i	0.684871	+	0.222528i
$494$	1.12634	+	2.99671i	0.0506763	+	0.134828i
$495$	12.8475	−	1.50373i	0.577452	−	0.0675876i
$496$		−	1.82026i		−	0.0817320i
$497$	6.23916	−	19.2021i	0.279864	−	0.861334i
$498$	22.6860	−	16.4823i	1.01658	−	0.738591i
$499$	−2.47214	−	1.79611i	−0.110668	−	0.0804051i	0.531075	−	0.847325i	$-0.321788\pi$
$499$	−2.47214	−	1.79611i	−0.110668	−	0.0804051i	−0.641743	+	0.766920i	$0.721788\pi$
$500$	2.53072	+	7.78874i	0.113177	+	0.348323i
$501$	−46.1588	+	14.9979i	−2.06222	+	0.670057i
$502$	−2.82399	−	2.05175i	−0.126041	−	0.0915740i
$503$	3.44805	+	4.74583i	0.153741	+	0.211606i	0.878939	−	0.476934i	$-0.158252\pi$
$503$	3.44805	+	4.74583i	0.153741	+	0.211606i	−0.725198	+	0.688540i	$0.758252\pi$
$504$	5.37240	+	1.74560i	0.239306	+	0.0777552i
$505$			27.3337i			1.21634i
$506$	1.25007	−	6.24227i	0.0555725	−	0.277503i
$507$			26.3953i			1.17226i
$508$	−2.38988	+	7.35529i	−0.106034	+	0.326338i
$509$	−8.13460	−	11.1963i	−0.360560	−	0.496268i	0.589745	−	0.807590i	$-0.299228\pi$
$509$	−8.13460	−	11.1963i	−0.360560	−	0.496268i	−0.950305	+	0.311322i	$0.899228\pi$
$510$	−13.8796	−	10.0841i	−0.614599	−	0.446532i
$511$	2.56643	+	7.89866i	0.113532	+	0.349416i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	13.4667	+	3.70956i	0.594569	+	0.163781i
$514$	−8.66668	−	11.9287i	−0.382271	−	0.526151i
$515$	−5.59581	−	1.81819i	−0.246581	−	0.0801189i
$516$	15.1852			0.668493
$517$	5.04165	−	4.64836i	0.221731	−	0.204434i
$518$	−19.7732			−0.868786
$519$	26.2021	+	8.51359i	1.15015	+	0.373705i
$520$	−1.55820	+	1.13210i	−0.0683314	+	0.0496457i
$521$	14.9981	−	20.6432i	0.657081	−	0.904394i	−0.342300	−	0.939591i	$-0.611206\pi$
$521$	14.9981	−	20.6432i	0.657081	−	0.904394i	0.999380	+	0.0351967i	$0.0112058\pi$
$522$	2.37933	+	7.32281i	0.104140	+	0.320511i
$523$	−10.7982	−	33.2334i	−0.472172	−	1.45320i	−0.849734	−	0.527211i	$-0.823238\pi$
$523$	−10.7982	−	33.2334i	−0.472172	−	1.45320i	0.377563	−	0.925984i	$-0.376762\pi$
$524$	4.31178	−	5.93466i	0.188361	−	0.259257i
$525$	−12.2186	+	8.87733i	−0.533263	+	0.387438i
$526$	−15.1731	−	4.93004i	−0.661578	−	0.214960i
$527$	5.62162			0.244882
$528$	−3.44080	+	6.12538i	−0.149742	+	0.266573i
$529$	−19.3156			−0.839808
$530$	28.4306	+	9.23766i	1.23495	+	0.401258i
$531$	−2.20111	−	3.02957i	−0.0955201	−	0.131472i
$532$	−15.9619	−	4.39689i	−0.692034	−	0.190629i
$533$	2.04656	+	6.29867i	0.0886465	+	0.272826i
$534$	−10.8237	−	33.3120i	−0.468389	−	1.44155i
$535$	15.6448	+	11.3666i	0.676383	+	0.491421i
$536$	−6.63920	−	9.13808i	−0.286770	−	0.394705i
$537$	13.6433	−	41.9898i	0.588752	−	1.81199i
$538$			6.18021i			0.266448i
$539$	−10.2837	−	22.3833i	−0.442952	−	0.964119i
$540$			8.40365i			0.361636i
$541$	−0.322589	−	0.104816i	−0.0138692	−	0.00450638i	0.302074	−	0.953284i	$-0.402321\pi$
$541$	−0.322589	−	0.104816i	−0.0138692	−	0.00450638i	−0.315943	+	0.948778i	$0.602321\pi$
$542$	−4.95718	−	6.82298i	−0.212929	−	0.293072i
$543$	11.7217	+	8.51634i	0.503028	+	0.365471i
$544$	2.93721	−	0.954357i	0.125932	−	0.0409177i
$545$	9.39279	+	28.9080i	0.402343	+	1.23828i
$546$	4.78075	+	3.47342i	0.204597	+	0.148649i
$547$	16.1475	−	11.7318i	0.690417	−	0.501617i	−0.186380	−	0.982478i	$-0.559676\pi$
$547$	16.1475	−	11.7318i	0.690417	−	0.501617i	0.876797	+	0.480860i	$0.159676\pi$
$548$	−4.50176	+	13.8550i	−0.192306	+	0.591856i
$549$			19.2295i			0.820694i
$550$	−2.59909	−	5.65713i	−0.110826	−	0.241221i
$551$	−7.93970	−	21.1242i	−0.338243	−	0.899921i
$552$	−3.86705	−	1.25648i	−0.164592	−	0.0534793i
$553$	19.0198	+	26.1785i	0.808805	+	1.11322i
$554$	−15.5500	+	21.4027i	−0.660655	+	0.909313i
$555$	8.93640	+	27.5034i	0.379329	+	1.16745i
$556$	5.01701	−	1.63012i	0.212768	−	0.0691327i
$557$	−3.46066	+	4.76319i	−0.146633	+	0.201823i	−0.876015	−	0.482283i	$-0.839808\pi$
$557$	−3.46066	+	4.76319i	−0.146633	+	0.201823i	0.729382	+	0.684106i	$0.239808\pi$
$558$	1.59120	+	2.19010i	0.0673610	+	0.0927145i
$559$	5.00728	+	1.62696i	0.211785	+	0.0688132i
$560$		−	9.96073i		−	0.420918i
$561$	−18.9174	−	10.6265i	−0.798693	−	0.448649i
$562$	−32.4945			−1.37070
$563$	10.3207	−	31.7638i	0.434965	−	1.33869i	−0.458157	−	0.888871i	$-0.651490\pi$
$563$	10.3207	−	31.7638i	0.434965	−	1.33869i	0.893122	−	0.449814i	$-0.148510\pi$
$564$	−2.57441	−	3.54337i	−0.108402	−	0.149203i
$565$	−22.1539	+	30.4923i	−0.932023	+	1.28282i
$566$	30.6953	−	9.97352i	1.29022	−	0.419218i
$567$	40.6388	−	13.2044i	1.70667	−	0.554531i
$568$	3.12445	−	4.30044i	0.131099	−	0.180442i
$569$	16.4240	−	11.9328i	0.688531	−	0.500247i	−0.187646	−	0.982237i	$-0.560086\pi$
$569$	16.4240	−	11.9328i	0.688531	−	0.500247i	0.876177	+	0.481990i	$0.160086\pi$
$570$	1.09806	+	24.1892i	0.0459926	+	1.01317i
$571$		−	6.93476i		−	0.290211i	−0.989416	−	0.145105i	$-0.953648\pi$
$571$		−	6.93476i		−	0.290211i	0.989416	−	0.145105i	$-0.0463521\pi$
$572$	−1.79087	+	1.65117i	−0.0748801	+	0.0690388i
$573$			42.0843i			1.75810i
$574$	−32.5743	−	10.5840i	−1.35963	−	0.441770i
$575$	2.91494	−	2.11783i	0.121561	−	0.0883194i
$576$	1.20318	+	0.874163i	0.0501326	+	0.0364235i
$577$	−5.17643	−	15.9314i	−0.215498	−	0.663234i	−0.999118	−	0.0419935i	$-0.986629\pi$
$577$	−5.17643	−	15.9314i	−0.215498	−	0.663234i	0.783620	−	0.621240i	$-0.213371\pi$
$578$	−2.30589	−	7.09679i	−0.0959123	−	0.295188i
$579$	−1.71216	+	2.35659i	−0.0711550	+	0.0979365i
$580$	10.9839	−	7.98029i	0.456083	−	0.331364i
$581$	−15.5375	+	47.8196i	−0.644606	+	1.98389i
$582$	−26.0143			−1.07833
$583$	37.0710	+	7.42381i	1.53533	+	0.307463i
$584$			2.18655i			0.0904799i
$585$	0.885157	−	2.72423i	0.0365968	−	0.112633i
$586$	4.98671	−	3.62306i	0.205999	−	0.149667i
$587$	−12.2882	−	8.92790i	−0.507188	−	0.368494i	0.304568	−	0.952491i	$-0.401488\pi$
$587$	−12.2882	−	8.92790i	−0.507188	−	0.368494i	−0.811756	+	0.583997i	$0.801488\pi$
$588$	−14.9627	+	4.86168i	−0.617052	+	0.200492i
$589$	−4.94997	−	6.20091i	−0.203960	−	0.255504i
$590$	−3.88124	+	5.34207i	−0.159788	+	0.219930i
$591$	12.3605	−	8.98044i	0.508444	−	0.369406i
$592$	−4.95103	−	1.60869i	−0.203486	−	0.0661166i
$593$		−	25.4323i		−	1.04438i	−0.852829	−	0.522190i	$-0.825115\pi$
$593$		−	25.4323i		−	1.04438i	0.852829	−	0.522190i	$-0.174885\pi$
$594$	1.23555	+	10.5562i	0.0506951	+	0.433126i
$595$	30.7624			1.26113
$596$	18.7327	+	6.08661i	0.767320	+	0.249317i
$597$	4.48533	+	6.17353i	0.183572	+	0.252666i
$598$	−1.14052	−	0.828639i	−0.0466395	−	0.0338856i
$599$	38.4405	−	12.4901i	1.57064	−	0.510331i	0.611013	−	0.791620i	$-0.290762\pi$
$599$	38.4405	−	12.4901i	1.57064	−	0.510331i	0.959623	+	0.281290i	$0.0907622\pi$
$600$	−3.78165	+	1.22873i	−0.154385	+	0.0501628i
$601$	31.1093	+	22.6022i	1.26898	+	0.921965i	0.999161	−	0.0409479i	$-0.0130378\pi$
$601$	31.1093	+	22.6022i	1.26898	+	0.921965i	0.269814	+	0.962912i	$0.413038\pi$
$602$	−22.0282	+	16.0044i	−0.897804	+	0.652293i
$603$	15.9763	+	5.19103i	0.650607	+	0.211395i
$604$	3.61864			0.147241
$605$	−15.0086	−	24.6348i	−0.610185	−	1.00155i
$606$	22.0793			0.896910
$607$	−10.4161	+	32.0575i	−0.422777	+	1.30118i	0.482329	+	0.875990i	$0.339791\pi$
$607$	−10.4161	+	32.0575i	−0.422777	+	1.30118i	−0.905106	+	0.425185i	$0.860209\pi$
$608$	−3.63898	−	2.39954i	−0.147580	−	0.0973144i
$609$	−33.7002	−	24.4846i	−1.36560	−	0.992167i
$610$	32.2480	−	10.4780i	1.30568	−	0.424242i
$611$	−0.469261	−	1.44424i	−0.0189843	−	0.0584275i
$612$	−2.69973	+	3.71586i	−0.109130	+	0.150205i
$613$	−11.4168	−	15.7139i	−0.461122	−	0.634680i	0.513619	−	0.858018i	$-0.328304\pi$
$613$	−11.4168	−	15.7139i	−0.461122	−	0.634680i	−0.974741	+	0.223338i	$0.928304\pi$
$614$	−9.75130	+	30.0114i	−0.393530	+	1.21116i
$615$			50.0924i			2.01992i
$616$	−1.46448	−	12.5121i	−0.0590054	−	0.504127i
$617$	−23.7779			−0.957263			−0.478631	−	0.878016i	$-0.658867\pi$
$617$	−23.7779			−0.957263			−0.478631	+	0.878016i	$0.658867\pi$
$618$	−1.46867	+	4.52011i	−0.0590786	+	0.181825i
$619$	−5.92009	+	4.30120i	−0.237949	+	0.172880i	−0.700369	−	0.713781i	$-0.746981\pi$
$619$	−5.92009	+	4.30120i	−0.237949	+	0.172880i	0.462420	+	0.886661i	$0.346981\pi$
$620$	2.80579	−	3.86183i	0.112683	−	0.155095i
$621$	−5.85001	+	1.90078i	−0.234753	+	0.0762758i
$622$	0.526042	+	1.61899i	0.0210924	+	0.0649157i
$623$	50.8104	+	36.9159i	2.03568	+	1.47901i
$624$	0.914469	+	1.25866i	0.0366081	+	0.0503867i
$625$	−9.53688	+	29.3515i	−0.381475	+	1.17406i
$626$	−3.40965			−0.136277
$627$	4.93573	+	30.2236i	0.197114	+	1.20701i
$628$	−5.62791			−0.224578
$629$	4.96821	−	15.2906i	0.198095	−	0.609675i
$630$	8.70730	+	11.9846i	0.346907	+	0.477477i
$631$	0.256588	+	0.186422i	0.0102146	+	0.00742134i	0.592881	−	0.805290i	$-0.297991\pi$
$631$	0.256588	+	0.186422i	0.0102146	+	0.00742134i	−0.582666	+	0.812712i	$0.697991\pi$
$632$	2.63258	+	8.10225i	0.104718	+	0.322290i
$633$	−0.672356	+	0.218462i	−0.0267238	+	0.00868308i
$634$	13.8438	−	19.0544i	0.549807	−	0.756745i
$635$	−16.4079	+	11.9210i	−0.651128	+	0.473072i
$636$	7.46187	−	22.9653i	0.295882	−	0.910632i
$637$	−5.45478			−0.216126
$638$	12.6241	−	11.6393i	0.499793	−	0.460805i
$639$			7.90549i			0.312736i
$640$	0.810373	−	2.49407i	0.0320328	−	0.0985868i
$641$	−4.38312	−	6.03285i	−0.173123	−	0.238283i	0.713635	−	0.700518i	$-0.247048\pi$
$641$	−4.38312	−	6.03285i	−0.173123	−	0.238283i	−0.886758	+	0.462235i	$0.847048\pi$
$642$	9.18156	−	12.6373i	0.362367	−	0.498756i
$643$	−0.964890	−	2.96962i	−0.0380515	−	0.117111i	0.930226	−	0.366986i	$-0.119610\pi$
$643$	−0.964890	−	2.96962i	−0.0380515	−	0.117111i	−0.968278	+	0.249875i	$0.919610\pi$
$644$	6.93393	−	2.25297i	0.273235	−	0.0887795i
$645$	32.2168	+	23.4069i	1.26853	+	0.921644i
$646$	7.41067	−	11.2385i	0.291569	−	0.442173i
$647$	−13.1437	+	40.4521i	−0.516732	+	1.59034i	0.263376	+	0.964693i	$0.415164\pi$
$647$	−13.1437	+	40.4521i	−0.516732	+	1.59034i	−0.780108	+	0.625644i	$0.784836\pi$
$648$	11.2498			0.441935
$649$	−4.08998	+	7.28104i	−0.160546	+	0.285806i
$650$	−1.37863			−0.0540744
$651$	−13.9289	−	4.52577i	−0.545916	−	0.177379i
$652$	6.57938	−	4.78020i	0.257669	−	0.187207i
$653$	−16.4231	−	11.9321i	−0.642685	−	0.466938i	0.218086	−	0.975929i	$-0.430019\pi$
$653$	−16.4231	−	11.9321i	−0.642685	−	0.466938i	−0.860772	+	0.508991i	$0.830019\pi$
$654$	23.3509	−	7.58718i	0.913094	−	0.296682i
$655$	18.2956	−	5.94460i	0.714868	−	0.232275i
$656$	−7.29522	−	5.30029i	−0.284831	−	0.206941i
$657$	−1.91140	−	2.63081i	−0.0745707	−	0.102638i
$658$	7.46904	+	2.42684i	0.291174	+	0.0946080i
$659$	10.5410			0.410619			0.205309	−	0.978697i	$-0.434180\pi$
$659$	10.5410			0.410619			0.205309	+	0.978697i	$0.434180\pi$
$660$	−16.7417	+	7.69177i	−0.651671	+	0.299402i
$661$			6.75071i			0.262572i	0.991345	+	0.131286i	$0.0419106\pi$
$661$			6.75071i			0.262572i	−0.991345	+	0.131286i	$0.958089\pi$
$662$	29.1572	+	9.47375i	1.13323	+	0.368208i
$663$	−3.88719	+	2.82421i	−0.150966	+	0.109683i
$664$	−7.78090	+	10.7095i	−0.301958	+	0.415609i
$665$	−27.0870	−	33.9323i	−1.05039	−	1.31584i
$666$	7.36324	−	2.39246i	0.285320	−	0.0927061i
$667$	8.03970	+	5.84119i	0.311299	+	0.226172i
$668$	18.5361	−	13.4672i	0.717182	−	0.521063i
$669$	8.61118	−	26.5025i	0.332927	−	1.02464i
$670$		−	29.6210i		−	1.14436i
$671$	38.9676	−	17.9031i	1.50433	−	0.691143i
$672$	−8.04594			−0.310379
$673$	6.53571	−	20.1149i	0.251933	−	0.775371i	−0.742485	−	0.669862i	$-0.766353\pi$
$673$	6.53571	−	20.1149i	0.251933	−	0.775371i	0.994418	−	0.105508i	$-0.0336470\pi$
$674$	24.4146	−	17.7383i	0.940417	−	0.683253i
$675$	−3.53566	+	4.86642i	−0.136088	+	0.187309i
$676$	−3.85053	−	11.8507i	−0.148097	−	0.455797i
$677$	−7.71735	−	23.7516i	−0.296602	−	0.912847i	−0.982679	−	0.185318i	$-0.940669\pi$
$677$	−7.71735	−	23.7516i	−0.296602	−	0.912847i	0.686077	−	0.727529i	$-0.259331\pi$
$678$	24.6306	+	17.8952i	0.945934	+	0.687261i
$679$	37.7373	−	27.4177i	1.44822	−	1.05220i
$680$	7.70260	+	2.50273i	0.295381	+	0.0959752i
$681$			4.38142i			0.167897i
$682$	2.95668	−	5.26353i	0.113217	−	0.201551i
$683$		−	43.3170i		−	1.65748i	−0.559635	−	0.828739i	$-0.689059\pi$
$683$		−	43.3170i		−	1.65748i	0.559635	−	0.828739i	$-0.310941\pi$
$684$	6.47595	−	0.293974i	0.247614	−	0.0112404i
$685$	−30.9072	+	22.4554i	−1.18090	+	0.857977i
$686$	0.953388	−	1.31223i	0.0364005	−	0.0501010i
$687$	−20.0427	+	6.51226i	−0.764676	+	0.248458i
$688$	−6.81773	+	2.21521i	−0.259923	+	0.0844543i
$689$	4.92104	−	6.77324i	0.187477	−	0.258040i
$690$	−6.26750	−	8.62648i	−0.238600	−	0.328404i
$691$	4.04336	−	12.4442i	0.153817	−	0.473399i	−0.844222	−	0.535993i	$-0.819937\pi$
$691$	4.04336	−	12.4442i	0.153817	−	0.473399i	0.998039	+	0.0625940i	$0.0199373\pi$
$692$	−13.0059			−0.494412
$693$	12.6996	+	13.7742i	0.482420	+	0.523237i
$694$			18.1930i			0.690595i
$695$	13.1567	+	4.27487i	0.499062	+	0.162155i
$696$	−6.44622	−	8.87245i	−0.244343	−	0.336310i
$697$	16.3692	−	22.5303i	0.620028	−	0.853396i
$698$	5.81201	−	1.88844i	0.219988	−	0.0714784i
$699$	1.56955	+	4.83058i	0.0593659	+	0.182709i
$700$	4.19077	−	5.76810i	0.158396	−	0.218014i
$701$	−14.1266	−	19.4436i	−0.533555	−	0.734376i	0.454112	−	0.890945i	$-0.349957\pi$
$701$	−14.1266	−	19.4436i	−0.533555	−	0.734376i	−0.987667	+	0.156569i	$0.949957\pi$
$702$	2.23838	+	0.727294i	0.0844822	+	0.0274499i
$703$	−21.2408	+	7.98354i	−0.801114	+	0.301105i
$704$	0.651254	−	3.25206i	0.0245451	−	0.122566i
$705$		−	11.4858i		−	0.432580i
$706$	−7.15668	+	22.0260i	−0.269345	+	0.828959i
$707$	−32.0290	+	23.2704i	−1.20457	+	0.875173i
$708$	4.31515	+	3.13514i	0.162173	+	0.117826i
$709$	−1.16097	−	3.57309i	−0.0436010	−	0.134190i	0.926886	−	0.375342i	$-0.122475\pi$
$709$	−1.16097	−	3.57309i	−0.0436010	−	0.134190i	−0.970487	+	0.241152i	$0.922475\pi$
$710$	13.2576	−	4.30765i	0.497548	−	0.161663i
$711$	−10.2502	−	7.44718i	−0.384411	−	0.279291i
$712$	9.71908	+	13.3772i	0.364238	+	0.501331i
$713$	3.32295	+	1.07969i	0.124446	+	0.0404348i
$714$		−	24.8488i		−	0.929943i
$715$	−6.34463	+	0.742605i	−0.237276	+	0.0277719i
$716$			20.8425i			0.778919i
$717$	7.35017	−	22.6215i	0.274497	−	0.844815i
$718$	21.0952	+	29.0350i	0.787265	+	1.08358i
$719$	30.8714	+	22.4294i	1.15131	+	0.836475i	0.988654	−	0.150208i	$-0.0479945\pi$
$719$	30.8714	+	22.4294i	1.15131	+	0.836475i	0.162654	+	0.986683i	$0.447994\pi$
$720$	1.20520	+	3.70922i	0.0449151	+	0.138235i
$721$	−2.63345	−	8.10492i	−0.0980747	−	0.301843i
$722$	−18.9219	+	1.72145i	−0.704199	+	0.0640657i
$723$	12.5905	+	17.3294i	0.468247	+	0.644487i
$724$	−6.50507	−	2.11363i	−0.241759	−	0.0785523i
$725$	9.71817			0.360924
$726$	−19.8991	+	12.1234i	−0.738526	+	0.449942i
$727$	−14.2835			−0.529747			−0.264873	−	0.964283i	$-0.585330\pi$
$727$	−14.2835			−0.529747			−0.264873	+	0.964283i	$0.585330\pi$
$728$	−2.65312	−	0.862050i	−0.0983311	−	0.0319497i
$729$	2.93968	−	2.13580i	0.108877	−	0.0791038i
$730$	−3.37039	+	4.63894i	−0.124744	+	0.171695i
$731$	−6.84139	−	21.0556i	−0.253038	−	0.778771i
$732$	−8.46378	−	26.0488i	−0.312830	−	0.962793i
$733$	21.6103	−	29.7441i	0.798196	−	1.09862i	−0.194843	−	0.980834i	$-0.562420\pi$
$733$	21.6103	−	29.7441i	0.798196	−	1.09862i	0.993039	−	0.117788i	$-0.0375803\pi$
$734$	2.45924	−	1.78674i	0.0907723	−	0.0659499i
$735$	−39.2385	−	12.7494i	−1.44734	−	0.470268i
$736$	1.91948			0.0707532
$737$	−4.35502	−	37.2082i	−0.160419	−	1.37058i
$738$	13.4108			0.493658
$739$	3.79021	+	1.23152i	0.139425	+	0.0453020i	0.377898	−	0.925847i	$-0.376647\pi$
$739$	3.79021	+	1.23152i	0.139425	+	0.0453020i	−0.238473	+	0.971149i	$0.576647\pi$
$740$	−8.02436	−	11.0446i	−0.294981	−	0.406007i
$741$	6.53801	+	1.80097i	0.240180	+	0.0661604i
$742$	13.3797	+	41.1786i	0.491186	+	1.51171i
$743$	−7.81395	−	24.0489i	−0.286666	−	0.882267i	−0.985894	−	0.167369i	$-0.946473\pi$
$743$	−7.81395	−	24.0489i	−0.286666	−	0.882267i	0.699228	−	0.714898i	$-0.253527\pi$
$744$	−3.11946	−	2.26642i	−0.114365	−	0.0830910i
$745$	30.3609	+	41.7882i	1.11234	+	1.53100i
$746$	9.21513	−	28.3613i	0.337390	−	1.03838i
$747$		−	19.6873i		−	0.720319i
$748$	10.0435	+	2.01131i	0.367228	+	0.0735407i
$749$			28.0090i			1.02343i
$750$	16.4989	+	5.36083i	0.602456	+	0.195750i
$751$	6.20169	+	8.53589i	0.226303	+	0.311479i	0.907037	−	0.421052i	$-0.138339\pi$
$751$	6.20169	+	8.53589i	0.226303	+	0.311479i	−0.680734	+	0.732531i	$0.738339\pi$
$752$	1.67274	+	1.21531i	0.0609984	+	0.0443180i
$753$	−7.03234	+	2.28495i	−0.256273	+	0.0832681i
$754$	−1.17501	−	3.61631i	−0.0427914	−	0.131698i
$755$	7.67726	+	5.57785i	0.279404	+	0.202999i
$756$	−9.84718	+	7.15439i	−0.358138	+	0.260203i
$757$	−7.66568	+	23.5925i	−0.278614	+	0.857486i	0.709626	+	0.704578i	$0.248864\pi$
$757$	−7.66568	+	23.5925i	−0.278614	+	0.857486i	−0.988240	+	0.152908i	$0.951136\pi$
$758$		−	30.3930i		−	1.10392i
$759$	−9.14119	−	9.91461i	−0.331804	−	0.359878i
$760$	−4.02170	−	10.7000i	−0.145882	−	0.388131i
$761$	25.9330	+	8.42613i	0.940069	+	0.305447i	0.738674	−	0.674063i	$-0.235452\pi$
$761$	25.9330	+	8.42613i	0.940069	+	0.305447i	0.201395	+	0.979510i	$0.435452\pi$
$762$	9.62943	+	13.2538i	0.348837	+	0.480133i
$763$	−25.8772	+	35.6169i	−0.936817	+	1.28942i
$764$	−6.13923	−	18.8946i	−0.222110	−	0.683583i
$765$	−11.4554	+	3.72209i	−0.414172	+	0.134573i
$766$	8.90823	−	12.2611i	0.321867	−	0.443013i
$767$	1.08700	+	1.49613i	0.0392493	+	0.0540221i
$768$	−2.01463	−	0.654592i	−0.0726966	−	0.0236206i
$769$			45.5111i			1.64117i	0.571523	+	0.820586i	$0.306353\pi$
$769$			45.5111i			1.64117i	−0.571523	+	0.820586i	$0.693647\pi$
$770$	16.1794	−	28.8028i	0.583065	−	1.03798i
$771$	−31.2336			−1.12485
$772$	0.424933	−	1.30781i	0.0152937	−	0.0470691i
$773$	10.0813	+	13.8757i	0.362599	+	0.499075i	0.950871	−	0.309589i	$-0.100191\pi$
$773$	10.0813	+	13.8757i	0.362599	+	0.499075i	−0.588272	+	0.808663i	$0.700191\pi$
$774$	6.26651	−	8.62512i	0.225245	−	0.310023i
$775$	3.24957	−	1.05585i	0.116728	−	0.0379273i
$776$	11.6797	−	3.79496i	0.419276	−	0.136231i
$777$	−24.6198	+	33.8863i	−0.883231	+	1.21566i
$778$	−19.5556	+	14.2080i	−0.701103	+	0.509381i
$779$	−39.2655	+	1.78244i	−1.40683	+	0.0638626i
$780$			4.07993i			0.146085i
$781$	16.0201	−	7.36021i	0.573243	−	0.263369i
$782$			5.92807i			0.211987i
$783$	−15.7786	−	5.12679i	−0.563883	−	0.183217i
$784$	6.00860	−	4.36550i	0.214593	−	0.155911i
$785$	−11.9401	−	8.67498i	−0.426160	−	0.309623i
$786$	−4.80185	−	14.7786i	−0.171276	−	0.527134i
$787$	3.54643	+	10.9148i	0.126417	+	0.389070i	0.994157	−	0.107948i	$-0.0344281\pi$
$787$	3.54643	+	10.9148i	0.126417	+	0.389070i	−0.867740	+	0.497018i	$0.834428\pi$
$788$	−4.23945	+	5.83510i	−0.151024	+	0.207867i
$789$	−27.3410	+	19.8644i	−0.973365	+	0.707191i
$790$	−6.90374	+	21.2475i	−0.245624	+	0.755953i
$791$	−54.5906			−1.94102
$792$	2.05925	+	4.48212i	0.0731723	+	0.159265i
$793$		−	9.49632i		−	0.337224i
$794$	−7.89485	+	24.2978i	−0.280178	+	0.862298i
$795$	51.2301	−	37.2209i	1.81695	−	1.32009i
$796$	−2.91437	−	2.11742i	−0.103297	−	0.0750498i
$797$	−12.7150	+	4.13136i	−0.450389	+	0.146340i	−0.525424	−	0.850841i	$-0.676093\pi$
$797$	−12.7150	+	4.13136i	−0.450389	+	0.146340i	0.0750348	+	0.997181i	$0.476093\pi$
$798$	−27.4094	+	21.8800i	−0.970282	+	0.774542i
$799$	−3.75333	+	5.16602i	−0.132783	+	0.182761i
$800$	1.51860	−	1.10333i	0.0536907	−	0.0390086i
$801$	−23.3877	−	7.59911i	−0.826362	−	0.268501i
$802$			17.2698i			0.609817i
$803$	−3.55165	+	6.32271i	−0.125335	+	0.223123i
$804$	−23.9269			−0.843835
$805$	18.1837	+	5.90824i	0.640891	+	0.208238i
$806$	−0.785803	−	1.08156i	−0.0276787	−	0.0380965i
$807$	10.5913	+	7.69503i	0.372831	+	0.270878i
$808$	−9.91295	+	3.22091i	−0.348736	+	0.113311i
$809$	−9.13979	+	2.96970i	−0.321338	+	0.104409i	−0.465244	−	0.885182i	$-0.654034\pi$
$809$	−9.13979	+	2.96970i	−0.321338	+	0.104409i	0.143906	+	0.989591i	$0.454034\pi$
$810$	23.8675	+	17.3407i	0.838617	+	0.609291i
$811$	−11.5083	+	8.36126i	−0.404110	+	0.293603i	−0.771213	−	0.636577i	$-0.780350\pi$
$811$	−11.5083	+	8.36126i	−0.404110	+	0.293603i	0.367103	+	0.930180i	$0.380350\pi$
$812$	18.7022	+	6.07671i	0.656318	+	0.213251i
$813$	−17.8651			−0.626556
$814$	−11.7036	−	12.6938i	−0.410210	−	0.444917i
$815$	21.3270			0.747053
$816$	2.02162	−	6.22190i	0.0707708	−	0.217810i
$817$	−17.2013	+	26.0863i	−0.601799	+	0.912646i
$818$	−27.4199	−	19.9217i	−0.958715	−	0.696547i
$819$	3.94576	−	1.28205i	0.137876	−	0.0447986i
$820$	−7.30745	−	22.4900i	−0.255187	−	0.785385i
$821$	−1.93014	+	2.65661i	−0.0673624	+	0.0927163i	−0.841369	−	0.540461i	$-0.818250\pi$
$821$	−1.93014	+	2.65661i	−0.0673624	+	0.0927163i	0.774007	+	0.633178i	$0.218250\pi$
$822$	18.1387	+	24.9658i	0.632661	+	0.870783i
$823$	9.63189	−	29.6439i	0.335747	−	1.03332i	−0.630606	−	0.776103i	$-0.717194\pi$
$823$	9.63189	−	29.6439i	0.335747	−	1.03332i	0.966353	−	0.257219i	$-0.0828062\pi$
$824$		−	2.24364i		−	0.0781610i
$825$	−12.9310	−	2.58956i	−0.450201	−	0.0901568i
$826$	−9.56396			−0.332773
$827$	5.93031	−	18.2516i	0.206217	−	0.634671i	−0.793444	−	0.608643i	$-0.791714\pi$
$827$	5.93031	−	18.2516i	0.206217	−	0.634671i	0.999661	−	0.0260279i	$-0.00828586\pi$
$828$	−2.30949	+	1.67794i	−0.0802603	+	0.0583126i
$829$	6.76137	−	9.30623i	0.234832	−	0.323219i	−0.675295	−	0.737548i	$-0.735984\pi$
$829$	6.76137	−	9.30623i	0.234832	−	0.323219i	0.910127	+	0.414329i	$0.135984\pi$
$830$	−33.0157	+	10.7274i	−1.14599	+	0.372355i
$831$	17.3174	+	53.2974i	0.600733	+	1.84886i
$832$	−0.594182	−	0.431698i	−0.0205996	−	0.0149665i
$833$	13.4823	+	18.5567i	0.467132	+	0.642953i
$834$	3.45310	−	10.6275i	0.119571	−	0.368002i
$835$	60.0845			2.07931
$836$	−6.62500	−	12.8495i	−0.229130	−	0.444409i
$837$	−5.83309			−0.201621
$838$	8.23633	−	25.3488i	0.284519	−	0.875660i
$839$	−8.07069	−	11.1083i	−0.278631	−	0.383503i	0.646649	−	0.762788i	$-0.276170\pi$
$839$	−8.07069	−	11.1083i	−0.278631	−	0.383503i	−0.925280	+	0.379285i	$0.876170\pi$
$840$	−17.0701	−	12.4022i	−0.588976	−	0.427916i
$841$	−0.678682	−	2.08877i	−0.0234028	−	0.0720265i
$842$	−23.1102	+	7.50897i	−0.796431	+	0.258776i
$843$	−40.4592	+	55.6873i	−1.39349	+	1.91797i
$844$	0.269999	−	0.196166i	0.00929375	−	0.00675231i
$845$	10.0977	−	31.0776i	0.347372	−	1.06910i
$846$	−3.07499			−0.105720
$847$	16.0889	−	38.5593i	0.552822	−	1.32491i
$848$			11.3993i			0.391452i
$849$	21.1270	−	65.0221i	0.725075	−	2.23155i
$850$	3.40748	+	4.69000i	0.116876	+	0.160866i
$851$	5.87344	−	8.08410i	0.201339	−	0.277119i
$852$	−3.47957	−	10.7090i	−0.119208	−	0.366885i
$853$	−44.2669	+	14.3832i	−1.51567	+	0.492471i	−0.944542	−	0.328390i	$-0.893494\pi$
$853$	−44.2669	+	14.3832i	−1.51567	+	0.492471i	−0.571128	+	0.820861i	$0.693494\pi$
$854$	39.7319	+	28.8669i	1.35960	+	0.987806i
$855$	14.1924	+	9.35848i	0.485370	+	0.320053i
$856$	−2.27873	+	7.01319i	−0.0778852	+	0.239706i
$857$	16.5609			0.565709			0.282854	−	0.959163i	$-0.408719\pi$
$857$	16.5609			0.565709			0.282854	+	0.959163i	$0.408719\pi$
$858$	0.599851	+	5.12498i	0.0204786	+	0.174964i
$859$	12.1926			0.416008			0.208004	−	0.978128i	$-0.433303\pi$
$859$	12.1926			0.416008			0.208004	+	0.978128i	$0.433303\pi$
$860$	−17.8790	−	5.80923i	−0.609668	−	0.198093i
$861$	−58.6969	+	42.6458i	−2.00039	+	1.45337i
$862$	15.3328	+	11.1400i	0.522238	+	0.379428i
$863$	−23.2208	+	7.54491i	−0.790446	+	0.256832i	−0.676294	−	0.736632i	$-0.736415\pi$
$863$	−23.2208	+	7.54491i	−0.790446	+	0.256832i	−0.114152	+	0.993463i	$0.536415\pi$
$864$	−3.04770	+	0.990257i	−0.103685	+	0.0336892i
$865$	−27.5932	−	20.0476i	−0.938197	−	0.681640i
$866$	1.30649	+	1.79823i	0.0443964	+	0.0611064i
$867$	−15.0332	−	4.88457i	−0.510553	−	0.165889i
$868$	6.91388			0.234672
$869$	−5.54817	+	27.7049i	−0.188209	+	0.939826i
$870$		−	28.7600i		−	0.975055i
$871$	−7.88979	−	2.56355i	−0.267335	−	0.0868625i
$872$	−9.37707	+	6.81284i	−0.317548	+	0.230712i
$873$	−10.7354	+	14.7760i	−0.363337	+	0.500091i
$874$	6.53894	−	5.21980i	0.221183	−	0.176562i
$875$	−29.5839	+	9.61240i	−1.00012	+	0.324959i
$876$	3.74718	+	2.72249i	0.126606	+	0.0919843i
$877$	−46.3064	+	33.6436i	−1.56366	+	1.13606i	−0.630726	+	0.776005i	$0.717243\pi$
$877$	−46.3064	+	33.6436i	−1.56366	+	1.13606i	−0.932930	+	0.360057i	$0.882757\pi$
$878$	7.69045	−	23.6688i	0.259540	−	0.798782i
$879$		−	13.0570i		−	0.440403i
$880$	6.39448	−	5.89565i	0.215558	−	0.198742i
$881$	3.54233			0.119344			0.0596721	−	0.998218i	$-0.480995\pi$
$881$	3.54233			0.119344			0.0596721	+	0.998218i	$0.480995\pi$
$882$	−3.41328	+	10.5050i	−0.114931	+	0.353721i
$883$	22.9925	−	16.7050i	0.773758	−	0.562168i	−0.129341	−	0.991600i	$-0.541286\pi$
$883$	22.9925	−	16.7050i	0.773758	−	0.562168i	0.903099	+	0.429432i	$0.141286\pi$
$884$	1.33324	−	1.83505i	0.0448418	−	0.0617194i
$885$	4.32238	+	13.3029i	0.145295	+	0.447173i
$886$	11.2207	+	34.5339i	0.376968	+	1.16019i
$887$	−1.15172	−	0.836771i	−0.0386709	−	0.0280960i	0.568282	−	0.822834i	$-0.307608\pi$
$887$	−1.15172	−	0.836771i	−0.0386709	−	0.0280960i	−0.606953	+	0.794738i	$0.707608\pi$
$888$	−8.92144	+	6.48181i	−0.299384	+	0.217515i
$889$	−27.9375	−	9.07746i	−0.936995	−	0.304448i
$890$			43.3620i			1.45350i
$891$	32.5305	+	18.2733i	1.08981	+	0.612180i
$892$			13.1550i			0.440463i
$893$	9.00326	−	0.408700i	0.301283	−	0.0136766i
$894$	33.7551	−	24.5245i	1.12894	−	0.820222i
$895$	−32.1270	+	44.2190i	−1.07389	+	1.47808i
$896$	3.61239	−	1.17374i	0.120682	−	0.0392118i
$897$	−2.84015	+	0.922821i	−0.0948298	+	0.0308121i
$898$	−15.9130	+	21.9024i	−0.531024	+	0.730892i
$899$	5.53923	+	7.62410i	0.184744	+	0.254278i
$900$	−0.862666	+	2.65501i	−0.0287555	+	0.0885005i
$901$	−35.2051			−1.17285
$902$	−12.4858	−	27.1763i	−0.415731	−	0.904872i
$903$			57.6780i			1.91940i
$904$	−13.6690	−	4.44132i	−0.454623	−	0.147716i
$905$	−10.5431	−	14.5113i	−0.350463	−	0.482372i
$906$	4.50560	−	6.20143i	0.149689	−	0.206029i
$907$	0.914664	−	0.297192i	0.0303709	−	0.00986811i	−0.293792	−	0.955869i	$-0.594917\pi$
$907$	0.914664	−	0.297192i	0.0303709	−	0.00986811i	0.324163	+	0.946001i	$0.394917\pi$
$908$	−0.639159	−	1.96713i	−0.0212112	−	0.0652815i
$909$	9.11148	−	12.5409i	0.302209	−	0.415955i
$910$	−4.30003	−	5.91848i	−0.142545	−	0.196196i
$911$	−51.9706	−	16.8863i	−1.72186	−	0.559467i	−0.729628	−	0.683845i	$-0.760307\pi$
$911$	−51.9706	−	16.8863i	−1.72186	−	0.559467i	−0.992235	+	0.124378i	$0.960307\pi$
$912$	−8.64313	+	3.24859i	−0.286203	+	0.107572i
$913$	−39.8952	+	18.3293i	−1.32034	+	0.606612i
$914$		−	5.79161i		−	0.191570i
$915$	22.1956	−	68.3110i	0.733764	−	2.25829i
$916$	8.04857	−	5.84763i	0.265932	−	0.193211i
$917$	22.5416	+	16.3774i	0.744388	+	0.540830i
$918$	−3.05827	−	9.41240i	−0.100938	−	0.310655i
$919$	29.0664	−	9.44424i	0.958812	−	0.311537i	0.212521	−	0.977157i	$-0.431833\pi$
$919$	29.0664	−	9.44424i	0.958812	−	0.311537i	0.746291	+	0.665620i	$0.231833\pi$
$920$	4.07235	+	2.95873i	0.134261	+	0.0975466i
$921$	39.2905	+	54.0787i	1.29467	+	1.78195i
$922$	−24.1514	−	7.84727i	−0.795384	−	0.258436i
$923$		−	3.90406i		−	0.128504i
$924$	−23.2660	−	13.0692i	−0.765394	−	0.429945i
$925$		−	9.77183i		−	0.321296i
$926$	9.06819	−	27.9090i	0.297999	−	0.917147i
$927$	1.96131	+	2.69951i	0.0644179	+	0.0886636i
$928$	4.18847	+	3.04310i	0.137493	+	0.0998947i
$929$	5.18722	+	15.9646i	0.170187	+	0.523783i	0.999381	−	0.0351786i	$-0.0112000\pi$
$929$	5.18722	+	15.9646i	0.170187	+	0.523783i	−0.829194	+	0.558961i	$0.811200\pi$
$930$	−3.12469	−	9.61680i	−0.102463	−	0.315347i
$931$	8.59750	−	31.2112i	0.281772	−	1.02291i
$932$	−1.40936	−	1.93982i	−0.0461653	−	0.0635411i
$933$	3.42952	+	1.11432i	0.112277	+	0.0364811i
$934$	−15.0328			−0.491888
$935$	18.2079	+	19.7485i	0.595463	+	0.645844i
$936$	1.09228			0.0357024
$937$	32.7496	+	10.6410i	1.06988	+	0.347626i	0.790442	−	0.612537i	$-0.209851\pi$
$937$	32.7496	+	10.6410i	1.06988	+	0.347626i	0.279441	+	0.960163i	$0.409851\pi$
$938$	34.7091	−	25.2176i	1.13329	−	0.823385i
$939$	−4.24538	+	5.84327i	−0.138543	+	0.190688i
$940$	1.67554	+	5.15678i	0.0546501	+	0.168196i
$941$	−2.98705	−	9.19320i	−0.0973751	−	0.299690i	0.890490	−	0.455002i	$-0.150362\pi$
$941$	−2.98705	−	9.19320i	−0.0973751	−	0.299690i	−0.987865	+	0.155312i	$0.950362\pi$
$942$	−7.00736	+	9.64481i	−0.228312	+	0.314245i
$943$	14.0031	−	10.1738i	0.456003	−	0.331305i
$944$	−2.39473	−	0.778093i	−0.0779417	−	0.0253248i
$945$	−31.9195			−1.03834
$946$	−23.3126	−	4.66857i	−0.757959	−	0.151788i
$947$	−47.0485			−1.52887			−0.764435	−	0.644700i	$-0.776982\pi$
$947$	−47.0485			−1.52887			−0.764435	+	0.644700i	$0.776982\pi$
$948$	17.1630	+	5.57661i	0.557429	+	0.181120i
$949$	0.943929	+	1.29921i	0.0306412	+	0.0421740i
$950$	2.17292	−	7.88827i	0.0704988	−	0.255929i
$951$	−15.4173	−	47.4495i	−0.499939	−	1.53865i
$952$	3.62493	+	11.1564i	0.117485	+	0.361580i
$953$	1.07429	+	0.780520i	0.0347998	+	0.0252835i	0.605049	−	0.796188i	$-0.293153\pi$
$953$	1.07429	+	0.780520i	0.0347998	+	0.0252835i	−0.570249	+	0.821472i	$0.693153\pi$
$954$	−9.96482	−	13.7154i	−0.322623	−	0.444052i
$955$	16.0997	−	49.5496i	0.520972	−	1.60339i
$956$			11.2286i			0.363160i
$957$	−4.22843	−	36.1267i	−0.136686	−	1.16781i
$958$			11.3193i			0.365711i
$959$	−52.6253	−	17.0990i	−1.69936	−	0.552156i
$960$	−3.26520	−	4.49416i	−0.105384	−	0.145048i
$961$	−22.3990	−	16.2738i	−0.722548	−	0.524962i
$962$	−3.63628	+	1.18150i	−0.117238	+	0.0380930i
$963$	−3.38895	−	10.4301i	−0.109208	−	0.336106i
$964$	−8.18078	−	5.94368i	−0.263485	−	0.191433i
$965$	2.91741	−	2.11963i	0.0939149	−	0.0682331i
$966$	4.77248	−	14.6882i	0.153552	−	0.472584i
$967$		−	39.9865i		−	1.28588i	−0.765917	−	0.642940i	$-0.777715\pi$
$967$		−	39.9865i		−	1.28588i	0.765917	−	0.642940i	$-0.222285\pi$
$968$	7.16557	−	8.34593i	0.230310	−	0.268248i
$969$	−10.0328	−	26.6931i	−0.322301	−	0.857507i
$970$	30.6290	+	9.95198i	0.983439	+	0.319539i
$971$	−15.2654	−	21.0111i	−0.489891	−	0.674277i	0.490477	−	0.871454i	$-0.336823\pi$
$971$	−15.2654	−	21.0111i	−0.489891	−	0.674277i	−0.980368	+	0.197177i	$0.936823\pi$
$972$	8.35652	−	11.5018i	0.268036	−	0.368919i
$973$	6.19169	+	19.0561i	0.198496	+	0.610909i
$974$	3.65273	−	1.18684i	0.117041	−	0.0380289i
$975$	−1.71655	+	2.36262i	−0.0549735	+	0.0756645i
$976$	7.59998	+	10.4605i	0.243269	+	0.334832i
$977$	10.8541	+	3.52671i	0.347253	+	0.112829i	0.477450	−	0.878659i	$-0.341561\pi$
$977$	10.8541	+	3.52671i	0.347253	+	0.112829i	−0.130197	+	0.991488i	$0.541561\pi$
$978$		−	17.2273i		−	0.550867i
$979$	6.37529	+	54.4689i	0.203755	+	1.74083i
$980$	19.4768			0.622164
$981$	5.32679	−	16.3942i	0.170071	−	0.523426i
$982$	6.36047	+	8.75444i	0.202971	+	0.279365i
$983$	33.6713	−	46.3445i	1.07395	−	1.47816i	0.207931	−	0.978143i	$-0.433327\pi$
$983$	33.6713	−	46.3445i	1.07395	−	1.47816i	0.866015	−	0.500017i	$-0.166673\pi$
$984$	−18.1667	+	5.90271i	−0.579133	+	0.188172i
$985$	−17.9887	+	5.84488i	−0.573167	+	0.186233i
$986$	−9.39820	+	12.9355i	−0.299300	+	0.411951i
$987$	13.4587	−	9.77835i	0.428397	−	0.311248i
$988$	−3.19810	+	0.145177i	−0.101745	+	0.00461868i
$989$		−	13.7600i		−	0.437542i
$990$	−2.53996	+	12.6834i	−0.0807252	+	0.403104i
$991$		−	31.1452i		−	0.989359i	−0.869076	−	0.494679i	$-0.835285\pi$
$991$		−	31.1452i		−	0.989359i	0.869076	−	0.494679i	$-0.164715\pi$
$992$	1.73117	+	0.562491i	0.0549647	+	0.0178591i
$993$	52.5394	−	38.1721i	1.66729	−	1.21136i
$994$	16.3343	+	11.8676i	0.518093	+	0.376417i
$995$	−2.91926	−	8.98455i	−0.0925467	−	0.284829i
$996$	8.66527	+	26.6690i	0.274570	+	0.845038i
$997$	34.5922	−	47.6121i	1.09555	−	1.50789i	0.254386	−	0.967103i	$-0.418127\pi$
$997$	34.5922	−	47.6121i	1.09555	−	1.50789i	0.841160	−	0.540787i	$-0.181873\pi$
$998$	2.47214	−	1.79611i	0.0782542	−	0.0568550i
$999$	−5.15510	+	15.8658i	−0.163100	+	0.501971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.189.9	yes	40
11.6	odd	10		418.2.m.a.303.2	yes	40
19.18	odd	2		418.2.m.a.189.2	✓	40
209.94	even	10	inner	418.2.m.b.303.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.189.2	✓	40	19.18	odd	2
418.2.m.a.303.2	yes	40	11.6	odd	10
418.2.m.b.189.9	yes	40	1.1	even	1	trivial
418.2.m.b.303.9	yes	40	209.94	even	10	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.24511 + 1.71374i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.810373 - 2.49407i) q^{5} +(-2.01463 + 0.654592i) q^{6} +(2.23258 - 3.07288i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.459575 + 1.41443i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.24511 + 1.71374i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.810373 - 2.49407i) q^{5} +(-2.01463 + 0.654592i) q^{6} +(2.23258 - 3.07288i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.459575 + 1.41443i) q^{9} +2.62242 q^{10} +(3.29414 - 0.385561i) q^{11} -2.11830i q^{12} +(0.226957 - 0.698503i) q^{13} +(2.23258 + 3.07288i) q^{14} +(3.26520 - 4.49416i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.93721 + 0.954357i) q^{17} +(-1.20318 - 0.874163i) q^{18} +(3.63898 + 2.39954i) q^{19} +(-0.810373 + 2.49407i) q^{20} +8.04594 q^{21} +(-0.651254 + 3.25206i) q^{22} -1.91948 q^{23} +(2.01463 + 0.654592i) q^{24} +(-1.51860 + 1.10333i) q^{25} +(0.594182 + 0.431698i) q^{26} +(3.04770 - 0.990257i) q^{27} +(-3.61239 + 1.17374i) q^{28} +(-4.18847 - 3.04310i) q^{29} +(3.26520 + 4.49416i) q^{30} +(-1.73117 - 0.562491i) q^{31} -1.00000 q^{32} +(4.76231 + 5.16524i) q^{33} -3.08836i q^{34} +(-9.47322 - 3.07803i) q^{35} +(1.20318 - 0.874163i) q^{36} +(-3.05990 + 4.21160i) q^{37} +(-3.40661 + 2.71938i) q^{38} +(1.47964 - 0.480765i) q^{39} +(-2.12158 - 1.54142i) q^{40} +(-7.29522 + 5.30029i) q^{41} +(-2.48633 + 7.65215i) q^{42} +7.16858i q^{43} +(-2.89164 - 1.62432i) q^{44} +3.90011 q^{45} +(0.593153 - 1.82554i) q^{46} +(1.67274 - 1.21531i) q^{47} +(-1.24511 + 1.71374i) q^{48} +(-2.29508 - 7.06353i) q^{49} +(-0.580055 - 1.78523i) q^{50} +(-5.29267 - 3.84535i) q^{51} +(-0.594182 + 0.431698i) q^{52} +(10.8413 + 3.52257i) q^{53} +3.20454i q^{54} +(-3.63110 - 7.90337i) q^{55} -3.79829i q^{56} +(0.418719 + 9.22398i) q^{57} +(4.18847 - 3.04310i) q^{58} +(-1.48002 + 2.03708i) q^{59} +(-5.28320 + 1.71662i) q^{60} +(12.2970 - 3.99554i) q^{61} +(1.06992 - 1.47262i) q^{62} +(3.32033 + 4.57004i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.92604 q^{65} +(-6.38408 + 2.93308i) q^{66} -11.2953i q^{67} +(2.93721 + 0.954357i) q^{68} +(-2.38997 - 3.28951i) q^{69} +(5.85477 - 8.05840i) q^{70} +(5.05547 - 1.64262i) q^{71} +(0.459575 + 1.41443i) q^{72} +(-1.28522 + 1.76895i) q^{73} +(-3.05990 - 4.21160i) q^{74} +(-3.78165 - 1.22873i) q^{75} +(-1.53358 - 4.08021i) q^{76} +(6.16964 - 10.9833i) q^{77} +1.55579i q^{78} +(-2.63258 + 8.10225i) q^{79} +(2.12158 - 1.54142i) q^{80} +(9.10131 + 6.61249i) q^{81} +(-2.78653 - 8.57605i) q^{82} +(-12.5898 + 4.09066i) q^{83} +(-6.50931 - 4.72929i) q^{84} +(4.76047 + 6.55222i) q^{85} +(-6.81773 - 2.21521i) q^{86} -10.9670i q^{87} +(2.43839 - 2.24817i) q^{88} +16.5351i q^{89} +(-1.20520 + 3.70922i) q^{90} +(-1.63972 - 2.25688i) q^{91} +(1.55290 + 1.12824i) q^{92} +(-1.19153 - 3.66714i) q^{93} +(0.638929 + 1.96642i) q^{94} +(3.03570 - 11.0204i) q^{95} +(-1.24511 - 1.71374i) q^{96} +(11.6797 + 3.79496i) q^{97} +7.42703 q^{98} +(-0.968555 + 4.83651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

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