LMFDB - Embedded newform 605.2.s.b.416.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(16,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("605.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.s (of order $55$, degree $40$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$880$
Relative dimension:	$22$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			416.19
Character	$\chi$	$=$	605.416
Dual form			605.2.s.b.16.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13889 - 0.245415i) q^{2} +(-1.59867 + 1.16150i) q^{3} +(2.56661 - 0.596840i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-3.13432 + 2.87666i) q^{6} +(-2.87657 + 2.95992i) q^{7} +(1.28779 - 0.459482i) q^{8} +(0.279601 - 0.860523i) q^{9} +O(q^{10})$	\(q+(2.13889 - 0.245415i) q^{2} +(-1.59867 + 1.16150i) q^{3} +(2.56661 - 0.596840i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-3.13432 + 2.87666i) q^{6} +(-2.87657 + 2.95992i) q^{7} +(1.28779 - 0.459482i) q^{8} +(0.279601 - 0.860523i) q^{9} +(-1.40987 - 1.62707i) q^{10} +(-3.08684 - 1.21301i) q^{11} +(-3.40992 + 3.93526i) q^{12} +(2.25345 + 3.73693i) q^{13} +(-5.42626 + 7.03690i) q^{14} +(1.86114 + 0.664053i) q^{15} +(-2.08778 + 1.02649i) q^{16} +(0.584647 + 0.478064i) q^{17} +(0.386851 - 1.90919i) q^{18} +(-0.538414 + 0.0307876i) q^{19} +(-1.94138 - 1.78178i) q^{20} +(1.16073 - 8.07304i) q^{21} +(-6.90012 - 1.83695i) q^{22} +(0.613360 + 4.26602i) q^{23} +(-1.52506 + 2.23032i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(5.73699 + 7.43986i) q^{26} +(-1.27940 - 3.93759i) q^{27} +(-5.61643 + 9.31380i) q^{28} +(0.886648 + 2.27734i) q^{29} +(4.14375 + 0.963587i) q^{30} +(4.74950 - 2.00716i) q^{31} +(-6.51411 + 4.18637i) q^{32} +(6.34374 - 1.64616i) q^{33} +(1.36782 + 0.879046i) q^{34} +(4.06699 + 0.703820i) q^{35} +(0.204032 - 2.37551i) q^{36} +(-0.267728 - 3.11710i) q^{37} +(-1.14405 + 0.197986i) q^{38} +(-7.94295 - 3.35672i) q^{39} +(-1.10617 - 0.803682i) q^{40} +(-8.80037 - 4.96980i) q^{41} +(0.501427 - 17.5522i) q^{42} +(6.67512 + 1.95999i) q^{43} +(-8.64670 - 1.27098i) q^{44} +(-0.868157 + 0.254914i) q^{45} +(2.35886 + 8.97402i) q^{46} +(0.180915 + 0.892852i) q^{47} +(2.14539 - 4.06596i) q^{48} +(-0.286581 - 10.0316i) q^{49} +(-0.547313 + 2.08220i) q^{50} +(-1.48993 - 0.0851970i) q^{51} +(8.01408 + 8.24629i) q^{52} +(6.87964 + 3.38249i) q^{53} +(-3.70284 - 8.10809i) q^{54} +(0.741040 + 3.23278i) q^{55} +(-2.34438 + 5.13348i) q^{56} +(0.824984 - 0.674586i) q^{57} +(2.45534 + 4.65338i) q^{58} +(-9.92069 + 5.60247i) q^{59} +(5.17315 + 0.593564i) q^{60} +(13.9880 + 1.60497i) q^{61} +(9.66609 - 5.45869i) q^{62} +(1.74279 + 3.30295i) q^{63} +(-9.30355 + 7.60748i) q^{64} +(1.81278 - 3.96944i) q^{65} +(13.1646 - 5.07781i) q^{66} +(4.83403 + 10.5851i) q^{67} +(1.78589 + 0.878063i) q^{68} +(-5.93553 - 6.10751i) q^{69} +(8.87158 + 0.507295i) q^{70} +(-2.37963 + 9.05307i) q^{71} +(-0.0353281 - 1.23664i) q^{72} +(7.30935 - 13.8528i) q^{73} +(-1.33762 - 6.60143i) q^{74} +(-0.502350 - 1.91114i) q^{75} +(-1.36352 + 0.400367i) q^{76} +(12.4699 - 5.64749i) q^{77} +(-17.8129 - 5.23034i) q^{78} +(0.135550 - 4.74486i) q^{79} +(2.02577 + 1.14400i) q^{80} +(8.81484 + 6.40436i) q^{81} +(-20.0427 - 8.47013i) q^{82} +(-8.48854 + 1.46900i) q^{83} +(-1.83917 - 21.4131i) q^{84} +(0.0646280 - 0.752450i) q^{85} +(14.7584 + 2.55404i) q^{86} +(-4.06257 - 2.61086i) q^{87} +(-4.53256 - 0.143755i) q^{88} +(-10.7477 + 6.90714i) q^{89} +(-1.79433 + 0.758292i) q^{90} +(-17.5432 - 4.07949i) q^{91} +(4.12039 + 10.5831i) q^{92} +(-5.26156 + 8.72531i) q^{93} +(0.606078 + 1.86532i) q^{94} +(0.329319 + 0.427068i) q^{95} +(5.55143 - 14.2587i) q^{96} +(-2.95333 + 4.31910i) q^{97} +(-3.07488 - 21.3863i) q^{98} +(-1.90691 + 2.31714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) $ 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{53}{55}\right)$

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 $

$2$	2.13889	−	0.245415i	1.51243	−	0.173535i	0.682284	−	0.731087i	$-0.260987\pi$
$2$	2.13889	−	0.245415i	1.51243	−	0.173535i	0.830142	+	0.557553i	$0.188259\pi$
$3$	−1.59867	+	1.16150i	−0.922990	+	0.670591i	−0.944266	−	0.329182i	$-0.893227\pi$
$3$	−1.59867	+	1.16150i	−0.922990	+	0.670591i	0.0212767	+	0.999774i	$0.493227\pi$
$4$	2.56661	−	0.596840i	1.28331	−	0.298420i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$6$	−3.13432	+	2.87666i	−1.27958	+	1.17439i
$7$	−2.87657	+	2.95992i	−1.08724	+	1.11874i	−0.0948644	+	0.995490i	$0.530242\pi$
$7$	−2.87657	+	2.95992i	−1.08724	+	1.11874i	−0.992375	+	0.123253i	$0.960667\pi$
$8$	1.28779	−	0.459482i	0.455302	−	0.162452i
$9$	0.279601	−	0.860523i	0.0932003	−	0.286841i
$10$	−1.40987	−	1.62707i	−0.445839	−	0.514526i
$11$	−3.08684	−	1.21301i	−0.930718	−	0.365737i
$11$	−3.08684	−	1.21301i	−0.930718	−	0.365737i
$12$	−3.40992	+	3.93526i	−0.984360	+	1.13601i
$13$	2.25345	+	3.73693i	0.624995	+	1.03644i	0.994247	+	0.107108i	$0.0341592\pi$
$13$	2.25345	+	3.73693i	0.624995	+	1.03644i	−0.369253	+	0.929329i	$0.620386\pi$
$14$	−5.42626	+	7.03690i	−1.45023	+	1.88069i
$15$	1.86114	+	0.664053i	0.480544	+	0.171458i
$16$	−2.08778	+	1.02649i	−0.521944	+	0.256622i
$17$	0.584647	+	0.478064i	0.141798	+	0.115948i	0.701251	−	0.712914i	$-0.252625\pi$
$17$	0.584647	+	0.478064i	0.141798	+	0.115948i	−0.559453	+	0.828862i	$0.688989\pi$
$18$	0.386851	−	1.90919i	0.0911817	−	0.449999i
$19$	−0.538414	+	0.0307876i	−0.123521	+	0.00706317i	−0.118740	−	0.992925i	$-0.537885\pi$
$19$	−0.538414	+	0.0307876i	−0.123521	+	0.00706317i	−0.00478087	+	0.999989i	$0.501522\pi$
$20$	−1.94138	−	1.78178i	−0.434106	−	0.398419i
$21$	1.16073	−	8.07304i	0.253292	−	1.76168i
$22$	−6.90012	−	1.83695i	−1.47111	−	0.391638i
$23$	0.613360	+	4.26602i	0.127895	+	0.889526i	0.948217	+	0.317624i	$0.102885\pi$
$23$	0.613360	+	4.26602i	0.127895	+	0.889526i	−0.820322	+	0.571902i	$0.806206\pi$
$24$	−1.52506	+	2.23032i	−0.311301	+	0.455263i
$25$	−0.362808	+	0.931864i	−0.0725615	+	0.186373i
$26$	5.73699	+	7.43986i	1.12512	+	1.45908i
$27$	−1.27940	−	3.93759i	−0.246220	−	0.757789i
$28$	−5.61643	+	9.31380i	−1.06141	+	1.76014i
$29$	0.886648	+	2.27734i	0.164646	+	0.422891i	0.989881	−	0.141899i	$-0.0453209\pi$
$29$	0.886648	+	2.27734i	0.164646	+	0.422891i	−0.825235	+	0.564790i	$0.808957\pi$
$30$	4.14375	+	0.963587i	0.756541	+	0.175926i
$31$	4.74950	−	2.00716i	0.853036	−	0.360496i	0.0814936	−	0.996674i	$-0.474031\pi$
$31$	4.74950	−	2.00716i	0.853036	−	0.360496i	0.771543	+	0.636178i	$0.219486\pi$
$32$	−6.51411	+	4.18637i	−1.15154	+	0.740052i
$33$	6.34374	−	1.64616i	1.10430	−	0.286560i
$34$	1.36782	+	0.879046i	0.234580	+	0.150755i
$35$	4.06699	+	0.703820i	0.687446	+	0.118967i
$36$	0.204032	−	2.37551i	0.0340054	−	0.395918i
$37$	−0.267728	−	3.11710i	−0.0440142	−	0.512448i	−0.984829	−	0.173527i	$-0.944484\pi$
$37$	−0.267728	−	3.11710i	−0.0440142	−	0.512448i	0.940815	−	0.338921i	$-0.110062\pi$
$38$	−1.14405	+	0.197986i	−0.185590	+	0.0321176i
$39$	−7.94295	−	3.35672i	−1.27189	−	0.537505i
$40$	−1.10617	−	0.803682i	−0.174901	−	0.127073i
$41$	−8.80037	−	4.96980i	−1.37439	−	0.776152i	−0.385203	−	0.922832i	$-0.625869\pi$
$41$	−8.80037	−	4.96980i	−1.37439	−	0.776152i	−0.989184	+	0.146679i	$0.953141\pi$
$42$	0.501427	−	17.5522i	0.0773718	−	2.70837i
$43$	6.67512	+	1.95999i	1.01795	+	0.298896i	0.747801	−	0.663923i	$-0.231110\pi$
$43$	6.67512	+	1.95999i	1.01795	+	0.298896i	0.270146	+	0.962819i	$0.412928\pi$
$44$	−8.64670	−	1.27098i	−1.30354	−	0.191607i
$45$	−0.868157	+	0.254914i	−0.129417	+	0.0380003i
$46$	2.35886	+	8.97402i	0.347795	+	1.32315i
$47$	0.180915	+	0.892852i	0.0263892	+	0.130236i	0.991112	−	0.133034i	$-0.0424719\pi$
$47$	0.180915	+	0.892852i	0.0263892	+	0.130236i	−0.964722	+	0.263270i	$0.915199\pi$
$48$	2.14539	−	4.06596i	0.309660	−	0.586871i
$49$	−0.286581	−	10.0316i	−0.0409401	−	1.43309i
$50$	−0.547313	+	2.08220i	−0.0774018	+	0.294467i
$51$	−1.48993	−	0.0851970i	−0.208631	−	0.0119300i
$52$	8.01408	+	8.24629i	1.11135	+	1.14355i
$53$	6.87964	+	3.38249i	0.944992	+	0.464621i	0.847606	−	0.530626i	$-0.178043\pi$
$53$	6.87964	+	3.38249i	0.944992	+	0.464621i	0.0973855	+	0.995247i	$0.468952\pi$
$54$	−3.70284	−	8.10809i	−0.503893	−	1.10337i
$55$	0.741040	+	3.23278i	0.0999218	+	0.435908i
$56$	−2.34438	+	5.13348i	−0.313281	+	0.685990i
$57$	0.824984	−	0.674586i	0.109272	−	0.0893511i
$58$	2.45534	+	4.65338i	0.322402	+	0.611019i
$59$	−9.92069	+	5.60247i	−1.29156	+	0.729379i	−0.975634	−	0.219403i	$-0.929589\pi$
$59$	−9.92069	+	5.60247i	−1.29156	+	0.729379i	−0.315929	+	0.948783i	$0.602316\pi$
$60$	5.17315	+	0.593564i	0.667851	+	0.0766288i
$61$	13.9880	+	1.60497i	1.79098	+	0.205495i	0.944854	−	0.327492i	$-0.106204\pi$
$61$	13.9880	+	1.60497i	1.79098	+	0.205495i	0.846123	+	0.532988i	$0.178931\pi$
$62$	9.66609	−	5.45869i	1.22760	−	0.693255i
$63$	1.74279	+	3.30295i	0.219570	+	0.416132i
$64$	−9.30355	+	7.60748i	−1.16294	+	0.950934i
$65$	1.81278	−	3.96944i	0.224848	−	0.492349i
$66$	13.1646	−	5.07781i	1.62045	−	0.625036i
$67$	4.83403	+	10.5851i	0.590571	+	1.29317i	0.935097	+	0.354393i	$0.115313\pi$
$67$	4.83403	+	10.5851i	0.590571	+	1.29317i	−0.344526	+	0.938777i	$0.611960\pi$
$68$	1.78589	+	0.878063i	0.216571	+	0.106481i
$69$	−5.93553	−	6.10751i	−0.714554	−	0.735258i
$70$	8.87158	+	0.507295i	1.06036	+	0.0606334i
$71$	−2.37963	+	9.05307i	−0.282411	+	1.07440i	0.663026	+	0.748596i	$0.269272\pi$
$71$	−2.37963	+	9.05307i	−0.282411	+	1.07440i	−0.945437	+	0.325805i	$0.894365\pi$
$72$	−0.0353281	−	1.23664i	−0.00416345	−	0.145740i
$73$	7.30935	−	13.8528i	0.855495	−	1.62134i	0.0741467	−	0.997247i	$-0.476377\pi$
$73$	7.30935	−	13.8528i	0.855495	−	1.62134i	0.781348	−	0.624096i	$-0.214532\pi$
$74$	−1.33762	−	6.60143i	−0.155496	−	0.767401i
$75$	−0.502350	−	1.91114i	−0.0580064	−	0.220679i
$76$	−1.36352	+	0.400367i	−0.156407	+	0.0459252i
$77$	12.4699	−	5.64749i	1.42108	−	0.643591i
$78$	−17.8129	−	5.23034i	−2.01691	−	0.592219i
$79$	0.135550	−	4.74486i	0.0152505	−	0.533838i	−0.955671	−	0.294438i	$-0.904867\pi$
$79$	0.135550	−	4.74486i	0.0152505	−	0.533838i	0.970921	−	0.239400i	$-0.0769507\pi$
$80$	2.02577	+	1.14400i	0.226488	+	0.127904i
$81$	8.81484	+	6.40436i	0.979427	+	0.711595i
$82$	−20.0427	−	8.47013i	−2.21335	−	0.935369i
$83$	−8.48854	+	1.46900i	−0.931738	+	0.161244i	−0.616129	−	0.787646i	$-0.711300\pi$
$83$	−8.48854	+	1.46900i	−0.931738	+	0.161244i	−0.315609	+	0.948889i	$0.602209\pi$
$84$	−1.83917	−	21.4131i	−0.200670	−	2.33636i
$85$	0.0646280	−	0.752450i	0.00700989	−	0.0816146i
$86$	14.7584	+	2.55404i	1.59144	+	0.275409i
$87$	−4.06257	−	2.61086i	−0.435554	−	0.279913i
$88$	−4.53256	−	0.143755i	−0.483173	−	0.0153243i
$89$	−10.7477	+	6.90714i	−1.13926	+	0.732155i	−0.967472	−	0.252979i	$-0.918590\pi$
$89$	−10.7477	+	6.90714i	−1.13926	+	0.732155i	−0.171784	+	0.985135i	$0.554953\pi$
$90$	−1.79433	+	0.758292i	−0.189139	+	0.0799310i
$91$	−17.5432	−	4.07949i	−1.83903	−	0.427647i
$92$	4.12039	+	10.5831i	0.429580	+	1.10337i
$93$	−5.26156	+	8.72531i	−0.545598	+	0.904773i
$94$	0.606078	+	1.86532i	0.0625121	+	0.192393i
$95$	0.329319	+	0.427068i	0.0337874	+	0.0438162i
$96$	5.55143	−	14.2587i	0.566590	−	1.45528i
$97$	−2.95333	+	4.31910i	−0.299865	+	0.438538i	−0.945750	−	0.324897i	$-0.894670\pi$
$97$	−2.95333	+	4.31910i	−0.299865	+	0.438538i	0.645885	+	0.763435i	$0.276489\pi$
$98$	−3.07488	−	21.3863i	−0.310610	−	2.16034i
$99$	−1.90691	+	2.31714i	−0.191652	+	0.232881i
$100$	−0.375013	+	2.60827i	−0.0375013	+	0.260827i
$101$	−0.959820	−	0.880914i	−0.0955056	−	0.0876543i	0.627000	−	0.779019i	$-0.284282\pi$
$101$	−0.959820	−	0.880914i	−0.0955056	−	0.0876543i	−0.722506	+	0.691365i	$0.757010\pi$
$102$	−3.20770	+	0.183423i	−0.317610	+	0.0181616i
$103$	0.752112	−	3.71182i	0.0741078	−	0.365737i	−0.925817	−	0.377971i	$-0.876622\pi$
$103$	0.752112	−	3.71182i	0.0741078	−	0.365737i	0.999925	+	0.0122347i	$0.00389452\pi$
$104$	4.61902	+	3.77696i	0.452932	+	0.370361i
$105$	−7.31923	+	3.59862i	−0.714284	+	0.351190i
$106$	15.5449	+	5.54642i	1.50986	+	0.538716i
$107$	−5.48663	+	7.11519i	−0.530413	+	0.687852i	−0.978526	−	0.206125i	$-0.933914\pi$
$107$	−5.48663	+	7.11519i	−0.530413	+	0.687852i	0.448113	+	0.893977i	$0.352096\pi$
$108$	−5.63383	−	9.34265i	−0.542115	−	0.898997i
$109$	5.97083	−	6.89071i	0.571902	−	0.660010i	−0.393942	−	0.919135i	$-0.628889\pi$
$109$	5.97083	−	6.89071i	0.571902	−	0.660010i	0.965844	+	0.259125i	$0.0834342\pi$
$110$	2.37838	+	6.73271i	0.226769	+	0.641938i
$111$	4.04851	+	4.67223i	0.384268	+	0.443468i
$112$	2.96730	−	9.13240i	0.280383	−	0.862931i
$113$	9.00582	−	3.21327i	0.847197	−	0.302279i	0.123455	−	0.992350i	$-0.460603\pi$
$113$	9.00582	−	3.21327i	0.847197	−	0.302279i	0.723742	+	0.690071i	$0.242421\pi$
$114$	1.59900	−	1.64533i	0.149760	−	0.154099i
$115$	3.17527	−	2.91424i	0.296095	−	0.271754i
$116$	3.63488	+	5.31585i	0.337491	+	0.493564i
$117$	3.84578	−	0.894298i	0.355543	−	0.0826779i
$118$	−19.8444	+	14.4178i	−1.82682	+	1.32726i
$119$	−3.09681	+	0.355325i	−0.283884	+	0.0325726i
$120$	2.70188			0.246646
$121$	8.05720	+	7.48876i	0.732473	+	0.680796i
$122$	30.3127			2.74438
$123$	19.8413	−	2.27657i	1.78903	−	0.205272i
$124$	10.9922	−	7.98628i	0.987127	−	0.717190i
$125$	0.974012	−	0.226497i	0.0871183	−	0.0202585i
$126$	4.53823	+	6.63694i	0.404297	+	0.591266i
$127$	−9.37051	+	8.60018i	−0.831498	+	0.763142i	−0.973975	−	0.226656i	$-0.927221\pi$
$127$	−9.37051	+	8.60018i	−0.831498	+	0.763142i	0.142477	+	0.989798i	$0.454493\pi$
$128$	−7.23906	+	7.44882i	−0.639848	+	0.658388i
$129$	−12.9478	+	4.61977i	−1.13999	+	0.406748i
$130$	2.90319	−	8.93510i	0.254627	−	0.783660i
$131$	3.16710	+	3.65503i	0.276711	+	0.319342i	0.877045	−	0.480408i	$-0.159511\pi$
$131$	3.16710	+	3.65503i	0.276711	+	0.319342i	−0.600334	+	0.799749i	$0.704966\pi$
$132$	15.2994	−	8.01125i	1.33164	−	0.697290i
$133$	1.45766	−	1.68222i	0.126395	−	0.145867i
$134$	12.9372	+	21.4540i	1.11760	+	1.85334i
$135$	−2.52822	+	3.27865i	−0.217594	+	0.282181i
$136$	0.972564	+	0.347010i	0.0833967	+	0.0297559i
$137$	3.92109	−	1.92787i	0.335001	−	0.164709i	−0.265967	−	0.963982i	$-0.585691\pi$
$137$	3.92109	−	1.92787i	0.335001	−	0.164709i	0.600968	+	0.799273i	$0.294782\pi$
$138$	−14.1943	−	11.6066i	−1.20830	−	0.988024i
$139$	3.10166	−	15.3073i	0.263079	−	1.29835i	−0.602719	−	0.797953i	$-0.705916\pi$
$139$	3.10166	−	15.3073i	0.263079	−	1.29835i	0.865798	−	0.500393i	$-0.166811\pi$
$140$	10.8584	−	0.620908i	0.917705	−	0.0524763i
$141$	−1.32627	−	1.21724i	−0.111692	−	0.102510i
$142$	−2.86802	+	19.9475i	−0.240679	+	1.67396i
$143$	−2.42311	−	14.2688i	−0.202631	−	1.19321i
$144$	0.299575	+	2.08359i	0.0249645	+	0.173632i
$145$	1.37941	−	2.01733i	0.114554	−	0.167530i
$146$	12.2342	−	31.4234i	1.01251	−	2.60062i
$147$	12.1099	+	15.7044i	0.998806	+	1.29527i
$148$	−2.54756	−	7.84059i	−0.209408	−	0.644492i
$149$	−3.01439	+	4.99880i	−0.246948	+	0.409518i	−0.954983	−	0.296660i	$-0.904127\pi$
$149$	−3.01439	+	4.99880i	−0.246948	+	0.409518i	0.708035	+	0.706177i	$0.249582\pi$
$150$	−1.54350	−	3.96444i	−0.126026	−	0.323695i
$151$	14.4741	+	3.36581i	1.17789	+	0.273906i	0.769345	−	0.638834i	$-0.220583\pi$
$151$	14.4741	+	3.36581i	1.17789	+	0.273906i	0.408542	+	0.912739i	$0.366037\pi$
$152$	−0.679218	+	0.287040i	−0.0550918	+	0.0232820i
$153$	0.574853	−	0.369436i	0.0464741	−	0.0298671i
$154$	25.2859	−	15.1397i	2.03759	−	1.21999i
$155$	−4.33768	−	2.78766i	−0.348411	−	0.223910i
$156$	−22.3899	−	3.87472i	−1.79262	−	0.310226i
$157$	−0.243839	+	2.83896i	−0.0194605	+	0.226574i	0.980140	+	0.198307i	$0.0635443\pi$
$157$	−0.243839	+	2.83896i	−0.0194605	+	0.226574i	−0.999600	+	0.0282670i	$0.991001\pi$
$158$	−0.874534	−	10.1820i	−0.0695742	−	0.810037i
$159$	−14.9270	+	2.58322i	−1.18379	+	0.204863i
$160$	7.13257	+	3.01425i	0.563880	+	0.238297i
$161$	−14.3914	−	10.4560i	−1.13420	−	0.824047i
$162$	20.4257	+	11.5349i	1.60480	+	0.906271i
$163$	−0.558628	+	19.5545i	−0.0437551	+	1.53163i	0.620549	+	0.784167i	$0.286910\pi$
$163$	−0.558628	+	19.5545i	−0.0437551	+	1.53163i	−0.664305	+	0.747462i	$0.731272\pi$
$164$	−25.5533	−	7.50313i	−1.99538	−	0.585896i
$165$	−4.93954	−	4.30741i	−0.384543	−	0.335332i
$166$	−17.7956	+	5.22525i	−1.38120	+	0.405558i
$167$	−3.71845	−	14.1465i	−0.287743	−	1.09469i	−0.941235	−	0.337753i	$-0.890333\pi$
$167$	−3.71845	−	14.1465i	−0.287743	−	1.09469i	0.653492	−	0.756933i	$-0.273303\pi$
$168$	−2.21465	−	10.9297i	−0.170864	−	0.843245i
$169$	−2.81992	+	5.34434i	−0.216917	+	0.411103i
$170$	−0.0464302	−	1.62527i	−0.00356104	−	0.124653i
$171$	−0.124048	+	0.471926i	−0.00948616	+	0.0360891i
$172$	18.3022	+	1.04656i	1.39553	+	0.0797995i
$173$	17.6663	+	18.1782i	1.34314	+	1.38206i	0.863288	+	0.504711i	$0.168401\pi$
$173$	17.6663	+	18.1782i	1.34314	+	1.38206i	0.479853	+	0.877349i	$0.340690\pi$
$174$	−9.33016	−	4.58733i	−0.707317	−	0.347765i
$175$	−1.71460	−	3.75445i	−0.129612	−	0.283810i
$176$	7.68978	−	0.636116i	0.579639	−	0.0479491i
$177$	9.35260	−	20.4793i	0.702984	−	1.53932i
$178$	−21.2931	+	17.4113i	−1.59599	+	1.30503i
$179$	4.19016	+	7.94123i	0.313187	+	0.593555i	0.989747	−	0.142832i	$-0.0456209\pi$
$179$	4.19016	+	7.94123i	0.313187	+	0.593555i	−0.676560	+	0.736388i	$0.736530\pi$
$180$	−2.07608	+	1.17241i	−0.154742	+	0.0873866i
$181$	−11.5331	−	1.32330i	−0.857248	−	0.0983601i	−0.325788	−	0.945443i	$-0.605629\pi$
$181$	−11.5331	−	1.32330i	−0.857248	−	0.0983601i	−0.531461	+	0.847083i	$0.678357\pi$
$182$	−38.5242	−	4.42024i	−2.85560	−	0.327650i
$183$	−24.2263	+	13.6812i	−1.79086	+	1.01134i
$184$	2.75004	+	5.21190i	0.202735	+	0.384226i
$185$	−2.42196	+	1.98043i	−0.178066	+	0.145604i
$186$	−9.11258	+	19.9538i	−0.668167	+	1.46308i
$187$	−1.22482	−	2.18489i	−0.0895675	−	0.159775i
$188$	0.997228	+	2.18363i	0.0727304	+	0.159257i
$189$	15.3352	+	7.53981i	1.11547	+	0.548441i
$190$	0.809186	+	0.832633i	0.0587045	+	0.0604055i
$191$	4.07546	+	0.233043i	0.294890	+	0.0168624i	0.203908	−	0.978990i	$-0.434636\pi$
$191$	4.07546	+	0.233043i	0.294890	+	0.0168624i	0.0909823	+	0.995853i	$0.470999\pi$
$192$	6.03719	−	22.9679i	0.435697	−	1.65756i
$193$	0.0396518	+	1.38799i	0.00285420	+	0.0999099i	0.999770	+	0.0214346i	$0.00682336\pi$
$193$	0.0396518	+	1.38799i	0.00285420	+	0.0999099i	−0.996916	+	0.0784753i	$0.974995\pi$
$194$	−5.25687	+	9.96289i	−0.377422	+	0.715294i
$195$	1.71247	+	8.45136i	0.122632	+	0.605214i
$196$	−6.72282	−	25.5763i	−0.480202	−	1.82688i
$197$	−10.3896	+	3.05065i	−0.740226	+	0.217350i	−0.630042	−	0.776561i	$-0.716962\pi$
$197$	−10.3896	+	3.05065i	−0.740226	+	0.217350i	−0.110184	+	0.993911i	$0.535144\pi$
$198$	−3.51001	+	5.42410i	−0.249446	+	0.385474i
$199$	−7.76656	−	2.28047i	−0.550557	−	0.161658i	−0.00538965	−	0.999985i	$-0.501716\pi$
$199$	−7.76656	−	2.28047i	−0.550557	−	0.161658i	−0.545167	+	0.838327i	$0.683534\pi$
$200$	−0.0390449	+	1.36675i	−0.00276089	+	0.0966437i
$201$	−20.0225	−	11.3072i	−1.41228	−	0.797551i
$202$	−2.26914	−	1.64863i	−0.159656	−	0.115997i
$203$	−9.29123	−	3.92650i	−0.652116	−	0.275587i
$204$	−3.87491	+	0.670579i	−0.271298	+	0.0469499i
$205$	0.864881	+	10.0696i	0.0604059	+	0.703294i
$206$	0.697751	−	8.12377i	0.0486146	−	0.566010i
$207$	3.84250	+	0.664971i	0.267072	+	0.0462187i
$208$	−8.54062	−	5.48872i	−0.592185	−	0.380574i
$209$	1.69935	+	0.558067i	0.117546	+	0.0386023i
$210$	−14.7719	+	9.49332i	−1.01936	+	0.655102i
$211$	−21.8517	+	9.23460i	−1.50433	+	0.635736i	−0.976869	−	0.213841i	$-0.931403\pi$
$211$	−21.8517	+	9.23460i	−1.50433	+	0.635736i	−0.527464	+	0.849577i	$0.676857\pi$
$212$	19.6762	+	4.57550i	1.35137	+	0.314247i
$213$	−6.71088	−	17.2368i	−0.459822	−	1.18104i
$214$	−9.98915	+	16.5651i	−0.682844	+	1.13237i
$215$	−2.14981	−	6.61643i	−0.146616	−	0.451237i
$216$	−3.45685	−	4.48292i	−0.235209	−	0.305024i
$217$	−7.72124	+	19.8319i	−0.524152	+	1.34627i
$218$	11.0799	−	16.2038i	0.750425	−	1.09746i
$219$	4.40475	+	30.6357i	0.297646	+	2.07017i
$220$	3.83141	+	7.85500i	0.258314	+	0.529584i
$221$	−0.469016	+	3.26208i	−0.0315494	+	0.219431i
$222$	9.80596	+	8.99983i	0.658133	+	0.604029i
$223$	0.797394	−	0.0455966i	0.0533974	−	0.00305338i	−0.0303697	−	0.999539i	$-0.509668\pi$
$223$	0.797394	−	0.0455966i	0.0533974	−	0.00305338i	0.0837671	+	0.996485i	$0.473305\pi$
$224$	6.34698	−	31.3236i	0.424076	−	2.09290i
$225$	0.700449	+	0.572755i	0.0466966	+	0.0381836i
$226$	18.4739	−	9.08301i	1.22887	−	0.604193i
$227$	−25.8403	−	9.21979i	−1.71508	−	0.611939i	−0.718573	−	0.695452i	$-0.755204\pi$
$227$	−25.8403	−	9.21979i	−1.71508	−	0.611939i	−0.996507	+	0.0835123i	$0.973386\pi$
$228$	1.71479	−	2.22378i	0.113565	−	0.147274i
$229$	13.2145	+	21.9138i	0.873240	+	1.44811i	0.893874	+	0.448318i	$0.147977\pi$
$229$	13.2145	+	21.9138i	0.873240	+	1.44811i	−0.0206344	+	0.999787i	$0.506569\pi$
$230$	6.07636	−	7.01250i	0.400664	−	0.462390i
$231$	−13.3757	+	23.5122i	−0.880055	+	1.54699i
$232$	2.18821	+	2.52533i	0.143663	+	0.165796i
$233$	−0.746415	+	2.29723i	−0.0488993	+	0.150496i	−0.972525	−	0.232800i	$-0.925211\pi$
$233$	−0.746415	+	2.29723i	−0.0488993	+	0.150496i	0.923625	+	0.383296i	$0.125211\pi$
$234$	8.00624	−	2.85662i	0.523384	−	0.186743i
$235$	0.634908	−	0.653305i	0.0414168	−	0.0426169i
$236$	−22.1188	+	20.3004i	−1.43981	+	1.32144i
$237$	5.29445	+	7.74288i	0.343911	+	0.502954i
$238$	−6.53653	+	1.52001i	−0.423701	+	0.0985273i
$239$	−14.2209	+	10.3321i	−0.919876	+	0.668329i	−0.943493	−	0.331392i	$-0.892482\pi$
$239$	−14.2209	+	10.3321i	−0.919876	+	0.668329i	0.0236172	+	0.999721i	$0.492482\pi$
$240$	−4.56729	+	0.524047i	−0.294817	+	0.0338271i
$241$	−12.6456			−0.814574			−0.407287	−	0.913300i	$-0.633525\pi$
$241$	−12.6456			−0.814574			−0.407287	+	0.913300i	$0.633525\pi$
$242$	19.0713	+	14.0403i	1.22595	+	0.902544i
$243$	−9.10996			−0.584405
$244$	36.8596	−	4.22925i	2.35969	−	0.270750i
$245$	−8.11908	+	5.89886i	−0.518709	+	0.376864i
$246$	41.8796	−	9.73869i	2.67015	−	0.620916i
$247$	−1.32834	−	1.94264i	−0.0845203	−	0.123607i
$248$	5.19411	−	4.76711i	0.329826	−	0.302712i
$249$	11.8641	−	12.2079i	0.751856	−	0.773641i
$250$	2.02772	−	0.723490i	0.128244	−	0.0457575i
$251$	1.17493	−	3.61605i	0.0741607	−	0.228243i	−0.907104	−	0.420906i	$-0.861712\pi$
$251$	1.17493	−	3.61605i	0.0741607	−	0.228243i	0.981265	+	0.192663i	$0.0617123\pi$
$252$	6.44438	+	7.43722i	0.405958	+	0.468501i
$253$	3.28138	−	13.9125i	0.206299	−	0.874674i
$254$	−17.9319	+	20.6945i	−1.12515	+	1.29849i
$255$	0.770651	+	1.27798i	0.0482600	+	0.0800302i
$256$	1.02188	−	1.32520i	0.0638675	−	0.0828249i
$257$	−7.53788	−	2.68951i	−0.470200	−	0.167767i	0.0903116	−	0.995914i	$-0.471214\pi$
$257$	−7.53788	−	2.68951i	−0.470200	−	0.167767i	−0.560512	+	0.828147i	$0.689396\pi$
$258$	−26.5602	+	13.0588i	−1.65357	+	0.813004i
$259$	9.99648	+	8.17408i	0.621151	+	0.507913i
$260$	2.28359	−	11.2700i	0.141622	−	0.698933i
$261$	2.20761	−	0.126236i	0.136648	−	0.00781379i
$262$	7.67109	+	7.04047i	0.473922	+	0.434961i
$263$	−1.14225	+	7.94449i	−0.0704339	+	0.489879i	0.923820	+	0.382828i	$0.125050\pi$
$263$	−1.14225	+	7.94449i	−0.0704339	+	0.489879i	−0.994254	+	0.107051i	$0.965859\pi$
$264$	7.41302	−	5.03475i	0.456240	−	0.309867i
$265$	−1.09102	−	7.58818i	−0.0670205	−	0.466138i
$266$	2.70493	−	3.95583i	0.165850	−	0.242547i
$267$	9.15937	−	23.5257i	0.560544	−	1.43975i
$268$	18.7247	+	24.2826i	1.14379	+	1.48329i
$269$	−1.42408	−	4.38286i	−0.0868275	−	0.267228i	0.898210	−	0.439566i	$-0.144868\pi$
$269$	−1.42408	−	4.38286i	−0.0868275	−	0.267228i	−0.985038	+	0.172338i	$0.944868\pi$
$270$	−4.60296	+	7.63315i	−0.280127	+	0.464539i
$271$	−7.27582	−	18.6878i	−0.441974	−	1.13520i	−0.960040	−	0.279862i	$-0.909711\pi$
$271$	−7.27582	−	18.6878i	−0.441974	−	1.13520i	0.518066	−	0.855341i	$-0.326652\pi$
$272$	−1.71134	−	0.397955i	−0.103765	−	0.0241296i
$273$	32.7840	−	13.8546i	1.98418	−	0.838521i
$274$	7.91366	−	5.08580i	0.478082	−	0.307244i
$275$	2.25029	−	2.43643i	0.135698	−	0.146922i
$276$	−18.8794	−	12.1331i	−1.13641	−	0.730324i
$277$	−15.6855	−	2.71447i	−0.942447	−	0.163097i	−0.321465	−	0.946921i	$-0.604175\pi$
$277$	−15.6855	−	2.71447i	−0.942447	−	0.163097i	−0.620982	+	0.783825i	$0.713266\pi$
$278$	2.87747	−	33.5018i	0.172579	−	2.00931i
$279$	−0.399240	−	4.64826i	−0.0239018	−	0.278284i
$280$	5.56081	−	0.962336i	0.332322	−	0.0575106i
$281$	8.03264	+	3.39462i	0.479187	+	0.202506i	0.615465	−	0.788164i	$-0.288968\pi$
$281$	8.03264	+	3.39462i	0.479187	+	0.202506i	−0.136277	+	0.990671i	$0.543514\pi$
$282$	−3.13548	−	2.27806i	−0.186715	−	0.135656i
$283$	18.8733	+	10.6582i	1.12190	+	0.633566i	0.937048	−	0.349201i	$-0.113547\pi$
$283$	18.8733	+	10.6582i	1.12190	+	0.633566i	0.184851	+	0.982766i	$0.440820\pi$
$284$	−0.704364	+	24.6560i	−0.0417963	+	1.46306i
$285$	−1.02251	−	0.300236i	−0.0605682	−	0.0177844i
$286$	−8.68454	−	29.9247i	−0.513528	−	1.76949i
$287$	40.0250	−	11.7524i	2.36260	−	0.693723i
$288$	1.78111	+	6.77606i	0.104953	+	0.399283i
$289$	−3.26277	−	16.1024i	−0.191928	−	0.947200i
$290$	2.45534	−	4.65338i	0.144182	−	0.273256i
$291$	−0.295249	−	10.3351i	−0.0173078	−	0.605853i
$292$	10.4924	−	39.9172i	0.614020	−	2.33597i
$293$	15.5255	+	0.887779i	0.907008	+	0.0518646i	0.504363	−	0.863492i	$-0.331727\pi$
$293$	15.5255	+	0.887779i	0.907008	+	0.0518646i	0.402645	+	0.915356i	$0.368091\pi$
$294$	29.7558	+	30.6180i	1.73540	+	1.78568i
$295$	10.2243	+	5.02697i	0.595284	+	0.292682i
$296$	−1.77703	−	3.89115i	−0.103288	−	0.226168i
$297$	−0.827036	+	13.7066i	−0.0479895	+	0.795340i
$298$	−5.22067	+	11.4317i	−0.302425	+	0.662219i
$299$	−14.5596	+	11.9053i	−0.842004	+	0.688504i
$300$	−2.42998	−	4.60533i	−0.140295	−	0.265889i
$301$	−25.0028	+	14.1198i	−1.44114	+	0.813849i
$302$	31.7846	+	3.64694i	1.82900	+	0.209858i
$303$	2.55761	+	0.293458i	0.146931	+	0.0168587i
$304$	1.09248	−	0.616954i	0.0626583	−	0.0353848i
$305$	−6.57056	−	12.4526i	−0.376229	−	0.713034i
$306$	1.13888	−	0.931261i	0.0651057	−	0.0532366i
$307$	−3.05405	+	6.68744i	−0.174304	+	0.381673i	−0.976540	−	0.215334i	$-0.930916\pi$
$307$	−3.05405	+	6.68744i	−0.174304	+	0.381673i	0.802236	+	0.597006i	$0.203643\pi$
$308$	28.6348	−	21.9374i	1.63162	−	1.25000i
$309$	3.10890	+	6.80754i	0.176859	+	0.387267i
$310$	−9.96196	−	4.89797i	−0.565801	−	0.278186i
$311$	12.2056	+	12.5593i	0.692119	+	0.712173i	0.968539	−	0.248864i	$-0.0800571\pi$
$311$	12.2056	+	12.5593i	0.692119	+	0.712173i	−0.276420	+	0.961037i	$0.589148\pi$
$312$	−11.7712	−	0.673101i	−0.666413	−	0.0381069i
$313$	3.99222	−	15.1880i	0.225654	−	0.858476i	−0.753850	−	0.657047i	$-0.771805\pi$
$313$	3.99222	−	15.1880i	0.225654	−	0.858476i	0.979503	−	0.201429i	$-0.0645584\pi$
$314$	0.175180	+	6.13208i	0.00988595	+	0.346053i
$315$	1.74279	−	3.30295i	0.0981949	−	0.186100i
$316$	−2.48402	−	12.2591i	−0.139737	−	0.689629i
$317$	−1.94797	−	7.41084i	−0.109409	−	0.416234i	0.889785	−	0.456380i	$-0.150854\pi$
$317$	−1.94797	−	7.41084i	−0.109409	−	0.416234i	−0.999194	+	0.0401455i	$0.987218\pi$
$318$	−31.2933	+	9.18854i	−1.75484	+	0.515268i
$319$	0.0254946	−	8.10530i	0.00142742	−	0.453809i
$320$	11.5311	+	3.38583i	0.644607	+	0.189274i
$321$	0.507006	−	17.7475i	0.0282983	−	0.990570i
$322$	−33.3478	−	18.8323i	−1.85840	−	1.04949i
$323$	−0.329501	−	0.239396i	−0.0183339	−	0.0133204i
$324$	26.4466	+	11.1764i	1.46926	+	0.620914i
$325$	−4.29988	+	0.744123i	−0.238514	+	0.0412765i
$326$	3.60413	+	41.9622i	0.199614	+	2.32407i
$327$	−1.54182	+	17.9510i	−0.0852627	+	0.992695i
$328$	−13.6166	−	2.35644i	−0.751849	−	0.130113i
$329$	−3.16318	−	2.03285i	−0.174392	−	0.112075i
$330$	−11.6223	−	8.00086i	−0.639784	−	0.440433i
$331$	7.04173	−	4.52544i	0.387048	−	0.248741i	−0.332617	−	0.943062i	$-0.607932\pi$
$331$	7.04173	−	4.52544i	0.387048	−	0.248741i	0.719665	+	0.694321i	$0.244295\pi$
$332$	−20.9100	+	8.83664i	−1.14759	+	0.484974i
$333$	−2.75719	−	0.641157i	−0.151093	−	0.0351352i
$334$	−11.4251	−	29.3452i	−0.625155	−	1.60570i
$335$	6.00913	−	9.96502i	0.328314	−	0.544447i
$336$	5.86356	+	18.0462i	0.319883	+	0.984499i
$337$	9.77952	+	12.6823i	0.532724	+	0.690849i	0.978957	−	0.204068i	$-0.0654164\pi$
$337$	9.77952	+	12.6823i	0.532724	+	0.690849i	−0.446232	+	0.894917i	$0.647235\pi$
$338$	−4.71992	+	12.1230i	−0.256730	+	0.659405i
$339$	−10.6651	+	15.5972i	−0.579248	+	0.847123i
$340$	−0.283217	−	1.96982i	−0.0153596	−	0.106828i
$341$	−17.0957	+	0.434572i	−0.925783	+	0.0235334i
$342$	−0.149507	+	1.03984i	−0.00808440	+	0.0562283i
$343$	9.23122	+	8.47234i	0.498439	+	0.457463i
$344$	9.49673	−	0.543043i	0.512029	−	0.0292789i
$345$	−1.69131	+	8.34696i	−0.0910572	+	0.449385i
$346$	42.2474	+	34.5456i	2.27124	+	1.85718i
$347$	23.3558	−	11.4833i	1.25381	−	0.616455i	0.311194	−	0.950346i	$-0.399271\pi$
$347$	23.3558	−	11.4833i	1.25381	−	0.616455i	0.942611	+	0.333892i	$0.108362\pi$
$348$	−11.9853	−	4.27635i	−0.642480	−	0.229236i
$349$	7.24353	−	9.39358i	0.387737	−	0.502827i	−0.557064	−	0.830469i	$-0.688072\pi$
$349$	7.24353	−	9.39358i	0.387737	−	0.502827i	0.944802	+	0.327643i	$0.106254\pi$
$350$	−4.58874	−	7.60958i	−0.245279	−	0.406749i
$351$	11.8314	−	13.6542i	0.631514	−	0.728806i
$352$	25.1862	−	5.02096i	1.34243	−	0.267618i
$353$	22.6005	+	26.0824i	1.20291	+	1.38823i	0.900390	+	0.435083i	$0.143281\pi$
$353$	22.6005	+	26.0824i	1.20291	+	1.38823i	0.302515	+	0.953145i	$0.402174\pi$
$354$	14.9783	−	46.0984i	0.796086	−	2.45010i
$355$	8.81622	−	3.14562i	0.467916	−	0.166952i
$356$	−23.4628	+	24.1426i	−1.24352	+	1.27956i
$357$	4.53804	−	4.16498i	0.240179	−	0.220434i
$358$	10.9112	+	15.9571i	0.576675	+	0.843360i
$359$	17.5251	−	4.07529i	0.924941	−	0.215086i	0.263133	−	0.964759i	$-0.415244\pi$
$359$	17.5251	−	4.07529i	0.924941	−	0.215086i	0.661808	+	0.749674i	$0.269790\pi$
$360$	−1.00087	+	0.727178i	−0.0527507	+	0.0383256i
$361$	−18.5872	+	2.13268i	−0.978274	+	0.112247i
$362$	−24.9928			−1.31359
$363$	−21.5789	−	2.61359i	−1.13260	−	0.137178i
$364$	−47.4614			−2.48765
$365$	−15.5608	+	1.78543i	−0.814488	+	0.0934538i
$366$	−48.4598	+	35.2081i	−2.53303	+	1.84036i
$367$	28.6764	−	6.66842i	1.49690	−	0.348089i	0.603503	−	0.797361i	$-0.293771\pi$
$367$	28.6764	−	6.66842i	1.49690	−	0.348089i	0.893395	+	0.449272i	$0.148317\pi$
$368$	−5.65958	−	8.27687i	−0.295026	−	0.431462i
$369$	−6.73722	+	6.18337i	−0.350726	+	0.321893i
$370$	−4.69428	+	4.83031i	−0.244044	+	0.251116i
$371$	−29.8016	+	10.6332i	−1.54722	+	0.552049i
$372$	−8.29676	+	25.5348i	−0.430167	+	1.32392i
$373$	−8.62971	−	9.95922i	−0.446830	−	0.515669i	0.486993	−	0.873406i	$-0.338094\pi$
$373$	−8.62971	−	9.95922i	−0.446830	−	0.515669i	−0.933822	+	0.357737i	$0.883548\pi$
$374$	−3.15596	−	4.37266i	−0.163191	−	0.226105i
$375$	−1.29404	+	1.49341i	−0.0668241	+	0.0771191i
$376$	0.643230	+	1.06668i	0.0331721	+	0.0550097i
$377$	−6.51223	+	8.44520i	−0.335397	+	0.434950i
$378$	34.6507	+	12.3634i	1.78224	+	0.635902i
$379$	−5.07683	+	2.49611i	−0.260779	+	0.128216i	−0.566928	−	0.823767i	$-0.691868\pi$
$379$	−5.07683	+	2.49611i	−0.260779	+	0.128216i	0.306149	+	0.951983i	$0.400959\pi$
$380$	1.10012	+	0.899567i	0.0564352	+	0.0461468i
$381$	4.99122	−	24.6326i	0.255708	−	1.26197i
$382$	8.77417	−	0.501725i	0.448926	−	0.0256705i
$383$	−0.570139	−	0.523269i	−0.0291327	−	0.0267378i	0.661476	−	0.749966i	$-0.269930\pi$
$383$	−0.570139	−	0.523269i	−0.0291327	−	0.0267378i	−0.690609	+	0.723228i	$0.742657\pi$
$384$	2.92104	−	20.3163i	0.149064	−	1.03676i
$385$	−11.7004	−	7.10588i	−0.596308	−	0.362149i
$386$	0.425445	+	2.95904i	0.0216546	+	0.150611i
$387$	3.55299	−	5.19608i	0.180609	−	0.264132i
$388$	−5.00223	+	12.8481i	−0.253950	+	0.652264i
$389$	−8.65474	−	11.2237i	−0.438813	−	0.569062i	0.519614	−	0.854401i	$-0.326076\pi$
$389$	−8.65474	−	11.2237i	−0.438813	−	0.569062i	−0.958427	+	0.285339i	$0.907894\pi$
$390$	5.73687	+	17.6563i	0.290498	+	0.894061i
$391$	−1.68083	+	2.78734i	−0.0850031	+	0.140962i
$392$	−4.97842	−	12.7870i	−0.251448	−	0.645839i
$393$	−9.30845	−	2.16459i	−0.469549	−	0.109189i
$394$	−21.4735	+	9.07477i	−1.08182	+	0.457180i
$395$	−3.99326	+	2.56631i	−0.200923	+	0.129125i
$396$	−3.51133	+	7.08532i	−0.176451	+	0.356051i
$397$	5.76120	+	3.70250i	0.289146	+	0.185823i	0.677170	−	0.735826i	$-0.263206\pi$
$397$	5.76120	+	3.70250i	0.289146	+	0.185823i	−0.388024	+	0.921649i	$0.626842\pi$
$398$	−17.1715	−	2.97164i	−0.860729	−	0.148955i
$399$	−0.376403	+	4.38238i	−0.0188437	+	0.219393i
$400$	−0.199088	−	2.31794i	−0.00995441	−	0.115897i
$401$	21.9306	−	3.79524i	1.09516	−	0.189525i	0.405813	−	0.913956i	$-0.366988\pi$
$401$	21.9306	−	3.79524i	1.09516	−	0.189525i	0.689347	+	0.724431i	$0.257897\pi$
$402$	−45.6010	−	19.2711i	−2.27437	−	0.961157i
$403$	18.2034	+	13.2255i	0.906775	+	0.658810i
$404$	−2.98925	−	1.68811i	−0.148721	−	0.0839864i
$405$	0.311139	−	10.8913i	0.0154606	−	0.541193i
$406$	−20.8366	−	6.11817i	−1.03410	−	0.303639i
$407$	−2.95464	+	9.94675i	−0.146456	+	0.493042i
$408$	−1.95786	+	0.574879i	−0.0969283	+	0.0284607i
$409$	−5.59742	−	21.2948i	−0.276775	−	1.05296i	−0.949677	−	0.313229i	$-0.898589\pi$
$409$	−5.59742	−	21.2948i	−0.276775	−	1.05296i	0.672903	−	0.739731i	$-0.265047\pi$
$410$	4.32113	+	21.3256i	0.213405	+	1.05320i
$411$	−4.02929	+	7.63635i	−0.198750	+	0.376673i
$412$	−0.284983	−	9.97569i	−0.0140401	−	0.491467i
$413$	11.9547	−	45.4803i	0.588251	−	2.23794i
$414$	8.38189	+	0.479294i	0.411948	+	0.0235560i
$415$	6.00391	+	6.17788i	0.294721	+	0.303260i
$416$	−30.3234	−	14.9090i	−1.48673	−	0.730974i
$417$	12.8209	+	28.0738i	0.627840	+	1.37478i
$418$	3.77168	+	0.776599i	0.184479	+	0.0379847i
$419$	10.7511	−	23.5417i	0.525227	−	1.15009i	−0.442195	−	0.896919i	$-0.645800\pi$
$419$	10.7511	−	23.5417i	0.525227	−	1.15009i	0.967422	−	0.253168i	$-0.0814726\pi$
$420$	−16.6378	+	13.6047i	−0.811842	+	0.663840i
$421$	−6.00175	−	11.3746i	−0.292508	−	0.554363i	0.693622	−	0.720339i	$-0.256014\pi$
$421$	−6.00175	−	11.3746i	−0.292508	−	0.554363i	−0.986130	+	0.165975i	$0.946923\pi$
$422$	−44.4721	+	25.1146i	−2.16487	+	1.22256i
$423$	0.818904	+	0.0939605i	0.0398165	+	0.00456851i
$424$	10.4137	+	1.19486i	0.505735	+	0.0580277i
$425$	−0.657605	+	0.371367i	−0.0318985	+	0.0180139i
$426$	−18.5840	−	35.2206i	−0.900399	−	1.70645i
$427$	−44.9879	+	36.7864i	−2.17712	+	1.78022i
$428$	−9.83542	+	21.5366i	−0.475413	+	1.04101i
$429$	20.4469	+	19.9966i	0.987185	+	0.965443i
$430$	−6.22198	−	13.6242i	−0.300051	−	0.657019i
$431$	−24.3817	−	11.9877i	−1.17443	−	0.577426i	−0.253565	−	0.967318i	$-0.581603\pi$
$431$	−24.3817	−	11.9877i	−1.17443	−	0.577426i	−0.920860	+	0.389892i	$0.872512\pi$
$432$	6.71299	+	6.90750i	0.322979	+	0.332337i
$433$	31.2610	+	1.78757i	1.50231	+	0.0859050i	0.788759	−	0.614702i	$-0.210724\pi$
$433$	31.2610	+	1.78757i	1.50231	+	0.0859050i	0.713547	+	0.700607i	$0.247087\pi$
$434$	−11.6479	+	44.3131i	−0.559116	+	2.12710i
$435$	0.137903	+	4.82722i	0.00661193	+	0.231448i
$436$	11.2122	−	21.2494i	0.536965	−	1.01766i
$437$	−0.461583	−	2.27800i	−0.0220805	−	0.108972i
$438$	16.9398	+	64.4455i	0.809413	+	3.07933i
$439$	35.0792	−	10.3002i	1.67424	−	0.491601i	0.699441	−	0.714691i	$-0.253432\pi$
$439$	35.0792	−	10.3002i	1.67424	−	0.491601i	0.974798	+	0.223090i	$0.0716143\pi$
$440$	2.43971	+	3.82264i	0.116309	+	0.182237i
$441$	−8.71259	−	2.55825i	−0.414885	−	0.121821i
$442$	−0.202612	+	7.09234i	−0.00963726	+	0.337348i
$443$	3.16311	+	1.78629i	0.150284	+	0.0848693i	0.565041	−	0.825063i	$-0.308861\pi$
$443$	3.16311	+	1.78629i	0.150284	+	0.0848693i	−0.414757	+	0.909932i	$0.636133\pi$
$444$	13.1795	+	9.57548i	0.625472	+	0.454432i
$445$	11.7681	+	4.97325i	0.557863	+	0.235755i
$446$	1.69435	−	0.293219i	0.0802298	−	0.0138843i
$447$	−0.987101	−	11.4926i	−0.0466883	−	0.543582i
$448$	4.24478	−	49.4211i	0.200547	−	2.33493i
$449$	−6.20420	−	1.07368i	−0.292794	−	0.0506700i	0.0222325	−	0.999753i	$-0.492923\pi$
$449$	−6.20420	−	1.07368i	−0.292794	−	0.0506700i	−0.315027	+	0.949083i	$0.602013\pi$
$450$	1.63875	+	1.05316i	0.0772514	+	0.0496464i
$451$	21.1369	+	26.0160i	0.995300	+	1.22504i
$452$	21.1966	−	13.6222i	0.997006	−	0.640737i
$453$	−27.0486	+	11.4309i	−1.27086	+	0.537068i
$454$	−57.5323	−	13.3786i	−2.70012	−	0.627887i
$455$	6.53463	+	16.7841i	0.306348	+	0.786849i
$456$	0.752445	−	1.24779i	0.0352365	−	0.0584331i
$457$	12.0703	+	37.1487i	0.564627	+	1.73774i	0.669058	+	0.743210i	$0.266698\pi$
$457$	12.0703	+	37.1487i	0.564627	+	1.73774i	−0.104431	+	0.994532i	$0.533302\pi$
$458$	33.6424	+	43.6283i	1.57201	+	2.03861i
$459$	1.13442	−	2.91373i	0.0529502	−	0.136001i
$460$	6.41035	−	9.37484i	0.298884	−	0.437104i
$461$	−4.85544	−	33.7703i	−0.226140	−	1.57284i	−0.714143	−	0.699999i	$-0.753184\pi$
$461$	−4.85544	−	33.7703i	−0.226140	−	1.57284i	0.488003	−	0.872842i	$-0.337726\pi$
$462$	−22.8389	+	53.5727i	−1.06256	+	2.49243i
$463$	2.48188	−	17.2619i	0.115343	−	0.802226i	−0.847235	−	0.531219i	$-0.821734\pi$
$463$	2.48188	−	17.2619i	0.115343	−	0.802226i	0.962577	−	0.271007i	$-0.0873568\pi$
$464$	−4.18878	−	3.84443i	−0.194459	−	0.178473i
$465$	10.1724	−	0.581676i	0.471731	−	0.0269746i
$466$	−1.03273	+	5.09671i	−0.0478401	+	0.236100i
$467$	3.60513	+	2.94790i	0.166826	+	0.136413i	0.712740	−	0.701428i	$-0.247454\pi$
$467$	3.60513	+	2.94790i	0.166826	+	0.136413i	−0.545914	+	0.837841i	$0.683818\pi$
$468$	9.33687	−	4.59063i	0.431597	−	0.212202i
$469$	−45.2363	−	16.1403i	−2.08882	−	0.745289i
$470$	1.19767	−	1.55316i	0.0552443	−	0.0716421i
$471$	−2.90764	−	4.82177i	−0.133977	−	0.222176i
$472$	−10.2015	+	11.7732i	−0.469563	+	0.541905i
$473$	−18.2276	−	14.1472i	−0.838104	−	0.650489i
$474$	13.2245	+	15.2619i	0.607420	+	0.701000i
$475$	0.166651	−	0.512899i	0.00764647	−	0.0235334i
$476$	−7.73622	+	2.76028i	−0.354589	+	0.126517i
$477$	4.83427	−	4.97435i	0.221346	−	0.227760i
$478$	−27.8814	+	25.5893i	−1.27527	+	1.17043i
$479$	−3.02927	−	4.43016i	−0.138411	−	0.202419i	0.750038	−	0.661394i	$-0.230035\pi$
$479$	−3.02927	−	4.43016i	−0.138411	−	0.202419i	−0.888449	+	0.458975i	$0.848217\pi$
$480$	−14.9036	+	3.46569i	−0.680255	+	0.158187i
$481$	11.0451	−	8.02470i	0.503611	−	0.365895i
$482$	−27.0476	+	3.10342i	−1.23198	+	0.141357i
$483$	35.1517			1.59946
$484$	25.1493	+	14.4119i	1.14315	+	0.655085i
$485$	5.23228			0.237586
$486$	−19.4852	+	2.23572i	−0.883868	+	0.101414i
$487$	18.1115	−	13.1588i	0.820712	−	0.596282i	−0.0962041	−	0.995362i	$-0.530670\pi$
$487$	18.1115	−	13.1588i	0.820712	−	0.596282i	0.916916	+	0.399079i	$0.130670\pi$
$488$	18.7510	−	4.36036i	0.848819	−	0.197384i
$489$	−21.8195	−	31.9100i	−0.986712	−	1.44302i
$490$	−15.9182	+	14.6096i	−0.719110	+	0.659993i
$491$	23.0822	−	23.7510i	1.04168	−	1.07187i	0.0443404	−	0.999016i	$-0.485881\pi$
$491$	23.0822	−	23.7510i	1.04168	−	1.07187i	0.997343	−	0.0728502i	$-0.0232095\pi$
$492$	49.5661	−	17.6851i	2.23461	−	0.797307i
$493$	−0.570336	+	1.75531i	−0.0256866	+	0.0790553i
$494$	−3.31793	−	3.82910i	−0.149281	−	0.172279i
$495$	2.98908	+	0.266206i	0.134349	+	0.0119651i
$496$	−7.85557	+	9.06581i	−0.352726	+	0.407067i
$497$	−19.9511	−	33.0853i	−0.894931	−	1.48408i
$498$	22.3800	−	29.0229i	1.00287	−	1.30055i
$499$	19.6314	+	7.00445i	0.878820	+	0.313562i	0.736645	−	0.676279i	$-0.236409\pi$
$499$	19.6314	+	7.00445i	0.878820	+	0.313562i	0.142175	+	0.989842i	$0.454591\pi$
$500$	2.36473	−	1.16266i	0.105754	−	0.0519956i
$501$	22.3757	+	18.2965i	0.999671	+	0.817427i
$502$	1.62561	−	8.02270i	0.0725545	−	0.358070i
$503$	−28.1513	+	1.60975i	−1.25520	+	0.0717751i	−0.672000	−	0.740551i	$-0.734564\pi$
$503$	−28.1513	+	1.60975i	−1.25520	+	0.0717751i	−0.583203	+	0.812326i	$0.698201\pi$
$504$	3.76199	+	3.45272i	0.167572	+	0.153796i
$505$	−0.185406	+	1.28953i	−0.00825048	+	0.0573833i
$506$	3.60418	−	30.5627i	0.160225	−	1.35868i
$507$	−1.69934	−	11.8191i	−0.0754701	−	0.524906i
$508$	−18.9175	+	27.6660i	−0.839329	+	1.22748i
$509$	−1.85478	+	4.76396i	−0.0822116	+	0.211159i	−0.966969	−	0.254892i	$-0.917960\pi$
$509$	−1.85478	+	4.76396i	−0.0822116	+	0.211159i	0.884758	+	0.466051i	$0.154324\pi$
$510$	1.96197	+	2.54433i	0.0868777	+	0.112665i
$511$	19.9772	+	61.4834i	0.883738	+	2.71987i
$512$	12.5881	−	20.8750i	0.556319	−	0.922552i
$513$	0.810076	+	2.08066i	0.0357657	+	0.0918635i
$514$	−16.7828	−	3.90266i	−0.740256	−	0.172139i
$515$	−3.48853	+	1.47426i	−0.153723	+	0.0649639i
$516$	−30.4747	+	19.5849i	−1.34158	+	0.862178i
$517$	0.524583	−	2.97555i	0.0230712	−	0.130864i
$518$	23.3875	+	15.0302i	1.02759	+	0.660389i
$519$	−49.3563	−	8.54145i	−2.16650	−	0.374928i
$520$	0.510595	−	5.94475i	0.0223911	−	0.260695i
$521$	1.45182	+	16.9032i	0.0636052	+	0.740542i	0.956776	+	0.290825i	$0.0939298\pi$
$521$	1.45182	+	16.9032i	0.0636052	+	0.740542i	−0.893171	+	0.449717i	$0.851525\pi$
$522$	4.69086	−	0.811785i	0.205313	−	0.0355309i
$523$	20.3021	+	8.57976i	0.887751	+	0.375167i	0.784967	−	0.619537i	$-0.212680\pi$
$523$	20.3021	+	8.57976i	0.887751	+	0.375167i	0.102783	+	0.994704i	$0.467225\pi$
$524$	10.3102	+	7.49079i	0.450403	+	0.327237i
$525$	7.10185	+	4.01060i	0.309950	+	0.175037i
$526$	−0.493443	+	17.2727i	−0.0215151	+	0.753128i
$527$	3.73633	+	1.09709i	0.162757	+	0.0477899i
$528$	−11.5545	+	9.94860i	−0.502847	+	0.432957i
$529$	4.24566	−	1.24664i	0.184594	−	0.0542016i
$530$	−4.19582	−	15.9626i	−0.182255	−	0.693369i
$531$	2.04722	+	10.1034i	0.0888419	+	0.438452i
$532$	2.73722	−	5.18760i	0.118673	−	0.224911i
$533$	−1.25942	−	44.0856i	−0.0545517	−	1.90956i
$534$	13.8174	−	52.5667i	0.597936	−	2.27478i
$535$	8.97028	+	0.512939i	0.387819	+	0.0221763i
$536$	11.0889	+	11.4102i	0.478966	+	0.492844i
$537$	−15.9224	−	7.82851i	−0.687102	−	0.337825i
$538$	−4.12157	−	9.02497i	−0.177693	−	0.389094i
$539$	−11.2839	+	31.3137i	−0.486031	+	1.34878i
$540$	−4.53212	+	9.92396i	−0.195031	+	0.427059i
$541$	−19.1344	+	15.6461i	−0.822653	+	0.672680i	−0.947591	−	0.319485i	$-0.896490\pi$
$541$	−19.1344	+	15.6461i	−0.822653	+	0.672680i	0.124939	+	0.992164i	$0.460127\pi$
$542$	−20.1485	−	38.1856i	−0.865451	−	1.64021i
$543$	19.9746	−	11.2802i	0.857191	−	0.484078i
$544$	−5.80981	−	0.666613i	−0.249094	−	0.0285808i
$545$	−9.05828	−	1.03934i	−0.388014	−	0.0445205i
$546$	66.7214	−	37.6793i	2.85541	−	1.61252i
$547$	−3.72981	−	7.06878i	−0.159475	−	0.302239i	0.791689	−	0.610924i	$-0.209202\pi$
$547$	−3.72981	−	7.06878i	−0.159475	−	0.302239i	−0.951164	+	0.308685i	$0.900111\pi$
$548$	8.91328	−	7.28835i	0.380756	−	0.311343i
$549$	5.29217	−	11.5882i	0.225864	−	0.494573i
$550$	4.21520	−	5.76351i	0.179737	−	0.245757i
$551$	−0.547498	−	1.19885i	−0.0233242	−	0.0510728i
$552$	−10.4500	−	5.13792i	−0.444782	−	0.218684i
$553$	13.6545	+	14.0501i	0.580647	+	0.597472i
$554$	−34.2157	−	1.95652i	−1.45368	−	0.0831247i
$555$	1.57164	−	5.97914i	0.0667124	−	0.253800i
$556$	−1.17525	−	41.1390i	−0.0498416	−	1.74468i
$557$	−6.45529	+	12.2341i	−0.273519	+	0.518377i	−0.982362	−	0.186990i	$-0.940127\pi$
$557$	−6.45529	+	12.2341i	−0.273519	+	0.518377i	0.708843	+	0.705367i	$0.249218\pi$
$558$	−1.99468	−	9.84416i	−0.0844417	−	0.416736i
$559$	7.71771	+	29.3612i	0.326424	+	1.24185i
$560$	−9.21341	+	2.70530i	−0.389338	+	0.114320i
$561$	4.49582	+	2.07029i	0.189814	+	0.0874076i
$562$	18.0141	+	5.28940i	0.759877	+	0.223120i
$563$	0.0174821	−	0.611952i	0.000736781	−	0.0257907i	−0.999141	−	0.0414490i	$-0.986803\pi$
$563$	0.0174821	−	0.611952i	0.000736781	−	0.0257907i	0.999877	+	0.0156583i	$0.00498440\pi$
$564$	−4.13051	−	2.33261i	−0.173926	−	0.0982205i
$565$	−7.73574	−	5.62034i	−0.325445	−	0.236450i
$566$	42.9836	+	18.1650i	1.80673	+	0.763533i
$567$	−44.3128	+	7.66864i	−1.86096	+	0.322053i
$568$	1.09526	+	12.7518i	0.0459559	+	0.535055i
$569$	0.659398	−	7.67723i	0.0276434	−	0.321846i	−0.969428	−	0.245374i	$-0.921089\pi$
$569$	0.659398	−	7.67723i	0.0276434	−	0.321846i	0.997072	−	0.0764716i	$-0.0243655\pi$
$570$	−2.26072	−	0.391233i	−0.0946911	−	0.0163869i
$571$	26.7264	+	17.1760i	1.11847	+	0.718795i	0.963122	−	0.269066i	$-0.0867148\pi$
$571$	26.7264	+	17.1760i	1.11847	+	0.718795i	0.155345	+	0.987860i	$0.450351\pi$
$572$	−14.7353	−	35.1762i	−0.616116	−	1.47079i
$573$	−6.78598	+	4.36108i	−0.283488	+	0.182187i
$574$	82.7251	−	34.9599i	3.45288	−	1.45920i
$575$	−4.19788	−	0.976175i	−0.175064	−	0.0407093i
$576$	3.94513	+	10.1330i	0.164380	+	0.422207i
$577$	6.20292	−	10.2864i	0.258231	−	0.428228i	−0.700034	−	0.714110i	$-0.746832\pi$
$577$	6.20292	−	10.2864i	0.258231	−	0.428228i	0.958265	+	0.285881i	$0.0922863\pi$
$578$	−10.9305	−	33.6406i	−0.454648	−	1.39926i
$579$	−1.67554	−	2.17288i	−0.0696331	−	0.0903018i
$580$	2.33640	−	6.00099i	0.0970137	−	0.249178i
$581$	20.0697	−	29.3510i	0.832632	−	1.21769i
$582$	−3.16789	−	22.0332i	−0.131313	−	0.913304i
$583$	−17.1334	−	18.7863i	−0.709592	−	0.778050i
$584$	3.04781	−	21.1979i	0.126119	−	0.877177i
$585$	−2.90894	−	2.66980i	−0.120270	−	0.110383i
$586$	33.4252	−	1.91132i	1.38078	−	0.0789560i
$587$	3.37007	−	16.6319i	0.139097	−	0.686473i	−0.848466	−	0.529250i	$-0.822473\pi$
$587$	3.37007	−	16.6319i	0.139097	−	0.686473i	0.987563	−	0.157223i	$-0.0502541\pi$
$588$	40.4543	+	33.0794i	1.66831	+	1.36417i
$589$	−2.49541	+	1.22691i	−0.102821	+	0.0505539i
$590$	23.1025	+	8.24295i	0.951114	+	0.339357i
$591$	13.0661	−	16.9444i	0.537468	−	0.697000i
$592$	3.75862	+	6.23298i	0.154479	+	0.256174i
$593$	21.8879	−	25.2600i	0.898829	−	1.03730i	−0.100274	−	0.994960i	$-0.531972\pi$
$593$	21.8879	−	25.2600i	0.898829	−	1.03730i	0.999103	−	0.0423445i	$-0.0134827\pi$
$594$	1.59487	+	29.5200i	0.0654385	+	1.21122i
$595$	2.04128	+	2.35576i	0.0836844	+	0.0965769i
$596$	−4.75327	+	14.6291i	−0.194702	+	0.599230i
$597$	15.0649	−	5.37514i	0.616565	−	0.219990i
$598$	−28.2197	+	29.0374i	−1.15399	+	1.18743i
$599$	32.8100	−	30.1127i	1.34058	−	1.23037i	0.389651	−	0.920963i	$-0.372596\pi$
$599$	32.8100	−	30.1127i	1.34058	−	1.23037i	0.950929	−	0.309410i	$-0.100132\pi$
$600$	−1.52506	−	2.23032i	−0.0622601	−	0.0910525i
$601$	23.6322	−	5.49544i	0.963978	−	0.224164i	0.285168	−	0.958477i	$-0.407950\pi$
$601$	23.6322	−	5.49544i	0.963978	−	0.224164i	0.678810	+	0.734314i	$0.262496\pi$
$602$	−50.0132	+	36.3367i	−2.03839	+	1.48097i
$603$	10.4603	−	1.20021i	0.425976	−	0.0488762i
$604$	39.1583			1.59333
$605$	1.63393	−	10.8780i	0.0664286	−	0.442252i
$606$	5.54247			0.225148
$607$	28.1665	−	3.23181i	1.14324	−	0.131175i	0.478389	−	0.878148i	$-0.341221\pi$
$607$	28.1665	−	3.23181i	1.14324	−	0.131175i	0.664854	+	0.746973i	$0.268494\pi$
$608$	3.37840	−	2.45455i	0.137012	−	0.0995453i
$609$	19.4142	−	4.51458i	0.786702	−	0.182940i
$610$	−17.1098	−	25.0223i	−0.692755	−	1.01312i
$611$	−2.92884	+	2.68806i	−0.118488	+	0.108747i
$612$	1.25493	−	1.29129i	0.0507275	−	0.0521974i
$613$	−31.4809	+	11.2323i	−1.27150	+	0.453670i	−0.883692	−	0.468070i	$-0.844950\pi$
$613$	−31.4809	+	11.2323i	−1.27150	+	0.453670i	−0.387809	+	0.921740i	$0.626768\pi$
$614$	−4.89109	+	15.0532i	−0.197388	+	0.607499i
$615$	−13.0785	−	15.0934i	−0.527377	−	0.608625i
$616$	13.4637	−	13.0025i	0.542468	−	0.523885i
$617$	10.0458	−	11.5935i	0.404430	−	0.466737i	−0.516601	−	0.856226i	$-0.672803\pi$
$617$	10.0458	−	11.5935i	0.404430	−	0.466737i	0.921031	+	0.389489i	$0.127348\pi$
$618$	8.32027	+	13.7976i	0.334690	+	0.555022i
$619$	−23.6677	+	30.6928i	−0.951285	+	1.23365i	0.0209831	+	0.999780i	$0.493320\pi$
$619$	−23.6677	+	30.6928i	−0.951285	+	1.23365i	−0.972268	+	0.233869i	$0.924861\pi$
$620$	−12.7969	−	4.56593i	−0.513936	−	0.183372i
$621$	16.0131	−	7.87310i	0.642582	−	0.315937i
$622$	29.1888	+	23.8676i	1.17036	+	0.957003i
$623$	10.4720	−	51.6812i	0.419550	−	2.07056i
$624$	20.0287	−	1.14528i	0.801791	−	0.0458481i
$625$	−0.736741	−	0.676175i	−0.0294696	−	0.0270470i
$626$	4.81157	−	33.4652i	0.192309	−	1.33754i
$627$	−3.36488	+	1.08163i	−0.134380	+	0.0431960i
$628$	1.06857	+	7.43205i	0.0426405	+	0.296571i
$629$	1.33365	−	1.95039i	0.0531759	−	0.0777673i
$630$	2.91704	−	7.49236i	0.116218	−	0.298503i
$631$	−15.2369	−	19.7596i	−0.606573	−	0.786617i	0.384040	−	0.923316i	$-0.374532\pi$
$631$	−15.2369	−	19.7596i	−0.606573	−	0.786617i	−0.990613	+	0.136699i	$0.956351\pi$
$632$	−2.00562	−	6.17266i	−0.0797792	−	0.245535i
$633$	24.2076	−	40.1437i	0.962164	−	1.59557i
$634$	−5.98523	−	15.3729i	−0.237704	−	0.610537i
$635$	12.3883	+	2.88078i	0.491616	+	0.114320i
$636$	−36.7700	+	15.5392i	−1.45803	+	0.616167i
$637$	36.8417	−	23.6767i	1.45972	−	0.938107i
$638$	−1.93463	−	17.3426i	−0.0765928	−	0.686601i
$639$	7.12503	+	4.57898i	0.281862	+	0.181142i
$640$	10.2348	+	1.77121i	0.404567	+	0.0700131i
$641$	−1.70811	+	19.8872i	−0.0674664	+	0.785497i	0.881923	+	0.471394i	$0.156249\pi$
$641$	−1.70811	+	19.8872i	−0.0674664	+	0.785497i	−0.949389	+	0.314103i	$0.898296\pi$
$642$	−3.27108	−	38.0845i	−0.129099	−	1.50307i
$643$	−45.1820	+	7.81906i	−1.78180	+	0.308353i	−0.963754	−	0.266792i	$-0.914036\pi$
$643$	−45.1820	+	7.81906i	−1.78180	+	0.308353i	−0.818051	+	0.575146i	$0.804945\pi$
$644$	−43.1777	−	18.2471i	−1.70144	−	0.719035i
$645$	11.1218	+	8.08046i	0.437920	+	0.318168i
$646$	−0.763519	−	0.431179i	−0.0300402	−	0.0169645i
$647$	0.216291	−	7.57119i	0.00850329	−	0.297654i	−0.984199	−	0.177065i	$-0.943340\pi$
$647$	0.216291	−	7.57119i	0.00850329	−	0.297654i	0.992702	−	0.120589i	$-0.0384784\pi$
$648$	14.2943	+	4.19720i	0.561535	+	0.164882i
$649$	37.4195	−	5.26003i	1.46884	−	0.206474i
$650$	−9.01436	+	2.64686i	−0.353572	+	0.103818i
$651$	−10.6910	−	40.6727i	−0.419012	−	1.59409i
$652$	10.2371	+	50.5223i	0.400917	+	1.97861i
$653$	−11.7321	+	22.2347i	−0.459111	+	0.870112i	0.540476	+	0.841360i	$0.318244\pi$
$653$	−11.7321	+	22.2347i	−0.459111	+	0.870112i	−0.999587	+	0.0287522i	$0.990847\pi$
$654$	1.10768	+	38.7738i	0.0433136	+	1.51617i
$655$	1.22948	−	4.67741i	0.0480396	−	0.182762i
$656$	23.4747	+	1.34233i	0.916531	+	0.0524091i
$657$	−9.87692	−	10.1631i	−0.385335	−	0.396501i
$658$	−7.26460	−	3.57176i	−0.283204	−	0.139242i
$659$	−14.4209	−	31.5773i	−0.561757	−	1.23008i	−0.951071	−	0.308972i	$-0.900015\pi$
$659$	−14.4209	−	31.5773i	−0.561757	−	1.23008i	0.389314	−	0.921105i	$-0.372712\pi$
$660$	−15.2487	−	8.10734i	−0.593555	−	0.315578i
$661$	−14.2291	+	31.1573i	−0.553446	+	1.21188i	0.401707	+	0.915768i	$0.368417\pi$
$661$	−14.2291	+	31.1573i	−0.553446	+	1.21188i	−0.955154	+	0.296110i	$0.904310\pi$
$662$	13.9509	−	11.4076i	0.542217	−	0.443368i
$663$	−3.03910	−	5.75973i	−0.118029	−	0.223689i
$664$	−10.2565	+	5.79209i	−0.398028	+	0.224777i
$665$	−2.21139	−	0.253734i	−0.0857541	−	0.00983937i
$666$	−6.05469	−	0.694711i	−0.234614	−	0.0269195i
$667$	−9.17132	+	5.17928i	−0.355115	+	0.200543i
$668$	−17.9870	−	34.0892i	−0.695938	−	1.31895i
$669$	−1.22181	+	0.999065i	−0.0472377	+	0.0386261i
$670$	10.4073	−	22.7888i	0.402070	−	0.880410i
$671$	−41.2318	−	21.9219i	−1.59174	−	0.846285i
$672$	26.2356	+	57.4479i	1.01206	+	2.21610i
$673$	7.45244	+	3.66412i	0.287270	+	0.141241i	0.579168	−	0.815208i	$-0.303378\pi$
$673$	7.45244	+	3.66412i	0.287270	+	0.141241i	−0.291898	+	0.956450i	$0.594287\pi$
$674$	24.0298	+	24.7261i	0.925592	+	0.952412i
$675$	4.13347	+	0.236360i	0.159097	+	0.00909752i
$676$	−4.04792	+	15.3999i	−0.155689	+	0.592303i
$677$	1.36167	+	47.6645i	0.0523331	+	1.83190i	0.426445	+	0.904514i	$0.359766\pi$
$677$	1.36167	+	47.6645i	0.0523331	+	1.83190i	−0.374112	+	0.927384i	$0.622052\pi$
$678$	−18.9837	+	35.9781i	−0.729064	+	1.38173i
$679$	−4.28874	−	21.1658i	−0.164587	−	0.812268i
$680$	−0.262510	−	0.998692i	−0.0100668	−	0.0382981i
$681$	52.0187	−	15.2741i	1.99336	−	0.585304i
$682$	−36.4592	+	5.12504i	−1.39609	+	0.196248i
$683$	−3.36062	−	0.986768i	−0.128591	−	0.0377576i	0.216804	−	0.976215i	$-0.430437\pi$
$683$	−3.36062	−	0.986768i	−0.128591	−	0.0377576i	−0.345395	+	0.938458i	$0.612255\pi$
$684$	−0.0367177	+	1.28529i	−0.00140394	+	0.0491442i
$685$	−3.80463	−	2.14857i	−0.145368	−	0.0820928i
$686$	21.8238	+	15.8559i	0.833238	+	0.605383i
$687$	−46.5784	−	19.6842i	−1.77708	−	0.750999i
$688$	−15.9481	+	2.75992i	−0.608014	+	0.105221i
$689$	2.86280	+	33.3310i	0.109064	+	1.26981i
$690$	−1.56907	+	18.2683i	−0.0597334	+	0.695463i
$691$	29.9161	+	5.17719i	1.13806	+	0.196950i	0.708245	−	0.705966i	$-0.249487\pi$
$691$	29.9161	+	5.17719i	1.13806	+	0.196950i	0.429817	+	0.902916i	$0.358578\pi$
$692$	56.1919	+	36.1123i	2.13609	+	1.37278i
$693$	−1.37319	−	12.3097i	−0.0521632	−	0.467607i
$694$	47.1374	−	30.2934i	1.78931	−	1.14992i
$695$	−14.3864	+	6.07976i	−0.545709	+	0.230618i
$696$	−6.43138	−	1.49555i	−0.243781	−	0.0566888i
$697$	−2.76923	−	7.11272i	−0.104892	−	0.269414i
$698$	13.1878	−	21.8695i	0.499166	−	0.827774i
$699$	−1.47496	−	4.53946i	−0.0557881	−	0.171698i
$700$	−6.64151	−	8.61287i	−0.251026	−	0.325536i
$701$	4.19809	−	10.7827i	0.158560	−	0.407257i	−0.830064	−	0.557668i	$-0.811696\pi$
$701$	4.19809	−	10.7827i	0.158560	−	0.407257i	0.988624	+	0.150411i	$0.0480597\pi$
$702$	21.9552	−	32.1084i	0.828645	−	1.21185i
$703$	0.240116	+	1.67005i	0.00905616	+	0.0629870i
$704$	37.9466	−	12.1978i	1.43016	−	0.459720i
$705$	−0.256193	+	1.78186i	−0.00964877	+	0.0671087i
$706$	54.7412	+	50.2410i	2.06021	+	1.89084i
$707$	5.36842	−	0.306977i	0.201900	−	0.0115451i
$708$	11.7816	−	58.1445i	0.442780	−	2.18520i
$709$	25.0316	+	20.4683i	0.940083	+	0.768702i	0.973012	−	0.230755i	$-0.0741197\pi$
$709$	25.0316	+	20.4683i	0.940083	+	0.768702i	−0.0329286	+	0.999458i	$0.510483\pi$
$710$	18.0850	−	8.89178i	0.678717	−	0.333703i
$711$	−4.04516	−	1.44331i	−0.151705	−	0.0541284i
$712$	−10.6671	+	13.8333i	−0.399766	+	0.518426i
$713$	11.4757	+	19.0303i	0.429769	+	0.712692i
$714$	8.68424	−	10.0222i	0.325000	−	0.375070i
$715$	−10.4108	+	10.0541i	−0.389341	+	0.376003i
$716$	15.4941	+	17.8812i	0.579043	+	0.668252i
$717$	10.7338	−	33.0352i	0.400860	−	1.23372i
$718$	36.4842	−	13.0176i	1.36158	−	0.485811i
$719$	9.67212	−	9.95237i	0.360709	−	0.371161i	−0.512349	−	0.858777i	$-0.671224\pi$
$719$	9.67212	−	9.95237i	0.360709	−	0.371161i	0.873058	+	0.487617i	$0.162134\pi$
$720$	1.55085	−	1.42336i	0.0577967	−	0.0530454i
$721$	8.82318	+	12.9035i	0.328592	+	0.480551i
$722$	−39.2327	+	9.12316i	−1.46009	+	0.339529i
$723$	20.2161	−	14.6878i	0.751843	−	0.546246i
$724$	−30.3908	+	3.48702i	−1.12946	+	0.129594i
$725$	−2.44385			−0.0907623
$726$	−46.7965	−	0.294392i	−1.73678	−	0.0109259i
$727$	−17.5182			−0.649713			−0.324856	−	0.945763i	$-0.605316\pi$
$727$	−17.5182			−0.649713			−0.324856	+	0.945763i	$0.605316\pi$
$728$	−24.4664	+	2.80726i	−0.906785	+	0.104044i
$729$	−11.8807	+	8.63187i	−0.440028	+	0.319699i
$730$	−32.8447	+	7.63770i	−1.21564	+	0.282684i
$731$	2.96559	+	4.33704i	0.109686	+	0.160411i
$732$	−54.0139	+	49.5735i	−1.99641	+	1.83229i
$733$	−23.4714	+	24.1515i	−0.866935	+	0.892055i	−0.995017	−	0.0997090i	$-0.968209\pi$
$733$	−23.4714	+	24.1515i	−0.866935	+	0.892055i	0.128082	+	0.991764i	$0.459118\pi$
$734$	59.6993	−	21.3007i	2.20354	−	0.786222i
$735$	6.12818	−	18.8606i	0.226041	−	0.695683i
$736$	−21.8546	−	25.2216i	−0.805571	−	0.929679i
$737$	−2.08210	−	38.5381i	−0.0766950	−	1.41957i
$738$	−12.8927	+	14.8790i	−0.474587	+	0.547703i
$739$	18.7663	+	31.1204i	0.690328	+	1.14478i	0.982112	+	0.188296i	$0.0602966\pi$
$739$	18.7663	+	31.1204i	0.690328	+	1.14478i	−0.291784	+	0.956484i	$0.594249\pi$
$740$	−5.03423	+	6.52850i	−0.185062	+	0.239993i
$741$	4.37994	+	1.56276i	0.160901	+	0.0574094i
$742$	−61.1330	+	30.0571i	−2.24426	+	1.10343i
$743$	−25.1597	−	20.5730i	−0.923021	−	0.754750i	0.0467148	−	0.998908i	$-0.485125\pi$
$743$	−25.1597	−	20.5730i	−0.923021	−	0.754750i	−0.969735	+	0.244158i	$0.921488\pi$
$744$	−2.76665	+	13.6540i	−0.101430	+	0.500578i
$745$	5.82782	−	0.333247i	0.213515	−	0.0122092i
$746$	−20.9022	−	19.1838i	−0.765283	−	0.702370i
$747$	−1.10929	+	7.71532i	−0.0405870	+	0.282289i
$748$	−4.44766	−	4.87675i	−0.162623	−	0.178312i
$749$	−5.27771	−	36.7073i	−0.192843	−	1.34126i
$750$	−2.40132	+	3.51181i	−0.0876836	+	0.128233i
$751$	−5.97597	+	15.3492i	−0.218066	+	0.560099i	−0.997820	−	0.0659869i	$-0.978980\pi$
$751$	−5.97597	+	15.3492i	−0.218066	+	0.560099i	0.779754	+	0.626086i	$0.215344\pi$
$752$	−1.29421	−	1.67837i	−0.0471951	−	0.0612037i
$753$	2.32172	+	7.14553i	0.0846084	+	0.260398i
$754$	−11.8564	+	19.6616i	−0.431784	+	0.716033i
$755$	−5.39143	−	13.8478i	−0.196214	−	0.503973i
$756$	43.8595	+	10.1991i	1.59516	+	0.370938i
$757$	−27.5405	+	11.6387i	−1.00098	+	0.423016i	−0.827284	−	0.561784i	$-0.810115\pi$
$757$	−27.5405	+	11.6387i	−1.00098	+	0.423016i	−0.173692	+	0.984800i	$0.555570\pi$
$758$	−10.2462	+	6.58484i	−0.372159	+	0.239172i
$759$	10.9136	+	26.0528i	0.396137	+	0.945657i
$760$	0.620323	+	0.398657i	0.0225015	+	0.0144608i
$761$	−24.4267	−	4.22720i	−0.885467	−	0.153236i	−0.290393	−	0.956907i	$-0.593786\pi$
$761$	−24.4267	−	4.22720i	−0.885467	−	0.153236i	−0.595073	+	0.803671i	$0.702877\pi$
$762$	4.63046	−	53.9115i	0.167744	−	1.95301i
$763$	3.22043	+	37.4947i	0.116587	+	1.35740i
$764$	10.5992	−	1.83427i	0.383466	−	0.0663614i
$765$	−0.629431	−	0.266000i	−0.0227571	−	0.00961724i
$766$	−1.34788	−	0.979295i	−0.0487010	−	0.0353834i
$767$	−43.2918	−	24.4480i	−1.56318	−	0.882766i
$768$	−0.0944294	+	3.30546i	−0.00340743	+	0.119276i
$769$	−27.4153	−	8.04985i	−0.988620	−	0.290285i	−0.252842	−	0.967508i	$-0.581365\pi$
$769$	−27.4153	−	8.04985i	−0.988620	−	0.290285i	−0.735778	+	0.677222i	$0.763183\pi$
$770$	−26.7698	−	12.3273i	−0.964717	−	0.444244i
$771$	15.1744	−	4.45561i	0.546493	−	0.160465i
$772$	0.930180	+	3.53877i	0.0334779	+	0.127363i
$773$	8.25748	+	40.7523i	0.297001	+	1.46576i	0.799231	+	0.601023i	$0.205240\pi$
$773$	8.25748	+	40.7523i	0.297001	+	1.46576i	−0.502231	+	0.864734i	$0.667487\pi$
$774$	6.32427	−	11.9858i	0.227321	−	0.430821i
$775$	0.147241	+	5.15410i	0.00528905	+	0.185141i
$776$	−1.81871	+	6.91909i	−0.0652879	+	0.248381i
$777$	−25.4752	−	1.45673i	−0.913918	−	0.0522597i
$778$	−21.2660	−	21.8822i	−0.762423	−	0.784515i
$779$	4.89126	+	2.40487i	0.175247	+	0.0861633i
$780$	9.43934	+	20.6693i	0.337983	+	0.740079i
$781$	18.3270	−	25.0589i	0.655793	−	0.896677i
$782$	−2.91106	+	6.37432i	−0.104099	+	0.227945i
$783$	7.83283	−	6.40487i	0.279923	−	0.228892i
$784$	10.8957	+	20.6496i	0.389132	+	0.737487i
$785$	2.48112	−	1.40115i	0.0885549	−	0.0500093i
$786$	−20.4410	−	2.34539i	−0.729106	−	0.0836571i
$787$	−32.4795	−	3.72668i	−1.15777	−	0.132842i	−0.486245	−	0.873823i	$-0.661634\pi$
$787$	−32.4795	−	3.72668i	−1.15777	−	0.132842i	−0.671526	+	0.740981i	$0.734361\pi$
$788$	−24.8452	+	14.0307i	−0.885074	+	0.499824i
$789$	−7.40145	−	14.0273i	−0.263499	−	0.499385i
$790$	−7.91134	+	6.46907i	−0.281473	+	0.230159i
$791$	−16.3948	+	35.8997i	−0.582933	+	1.27645i
$792$	−1.39101	+	3.86018i	−0.0494275	+	0.137166i
$793$	25.5236	+	55.8888i	0.906368	+	1.98467i
$794$	13.2312	+	6.50536i	0.469559	+	0.230867i
$795$	10.5578	+	10.8637i	0.374447	+	0.385297i
$796$	−21.2948	−	1.21768i	−0.754774	−	0.0431596i
$797$	−12.0772	+	45.9466i	−0.427798	+	1.62751i	0.308763	+	0.951139i	$0.400085\pi$
$797$	−12.0772	+	45.9466i	−0.427798	+	1.62751i	−0.736560	+	0.676372i	$0.763551\pi$
$798$	0.270416	+	9.46581i	0.00957264	+	0.335086i
$799$	−0.321069	+	0.608492i	−0.0113586	+	0.0215269i
$800$	−1.53775	−	7.58911i	−0.0543678	−	0.268316i
$801$	2.93868	+	11.1799i	0.103833	+	0.395022i
$802$	45.9757	−	13.4997i	1.62346	−	0.476691i
$803$	−39.3664	+	33.8950i	−1.38921	+	1.19613i
$804$	−58.1386	−	17.0710i	−2.05039	−	0.602049i
$805$	−0.507977	+	17.7815i	−0.0179038	+	0.626716i
$806$	42.1808	+	23.8206i	1.48576	+	0.839045i
$807$	7.36730	+	5.35266i	0.259341	+	0.188422i
$808$	−1.64081	−	0.693412i	−0.0577235	−	0.0243941i
$809$	−46.5264	+	8.05171i	−1.63578	+	0.283083i	−0.912990	−	0.407983i	$-0.866232\pi$
$809$	−46.5264	+	8.05171i	−1.63578	+	0.283083i	−0.722792	+	0.691066i	$0.757141\pi$
$810$	−2.00740	−	23.3717i	−0.0705327	−	0.821197i
$811$	0.138453	−	1.61198i	0.00486174	−	0.0566042i	−0.993499	−	0.113843i	$-0.963684\pi$
$811$	0.138453	−	1.61198i	0.00486174	−	0.0566042i	0.998361	+	0.0572384i	$0.0182295\pi$
$812$	−26.1905	−	4.53244i	−0.919105	−	0.159057i
$813$	33.3374	+	21.4247i	1.16919	+	0.751396i
$814$	−3.87859	+	22.0001i	−0.135944	+	0.771105i
$815$	16.4570	−	10.5763i	0.576465	−	0.370471i
$816$	3.19808	−	1.35152i	0.111955	−	0.0473127i
$817$	−3.65432	−	0.849777i	−0.127849	−	0.0297299i
$818$	−17.1984	−	44.1736i	−0.601326	−	1.54449i
$819$	−8.41559	+	13.9557i	−0.294065	+	0.487651i
$820$	8.22977	+	25.3286i	0.287396	+	0.884514i
$821$	6.66868	+	8.64810i	0.232739	+	0.301821i	0.893759	−	0.448547i	$-0.148058\pi$
$821$	6.66868	+	8.64810i	0.232739	+	0.301821i	−0.661021	+	0.750368i	$0.729876\pi$
$822$	−6.74414	+	17.3222i	−0.235229	+	0.604181i
$823$	−15.4190	+	22.5495i	−0.537472	+	0.786027i	−0.994645	−	0.103350i	$-0.967044\pi$
$823$	−15.4190	+	22.5495i	−0.537472	+	0.786027i	0.457173	+	0.889378i	$0.348862\pi$
$824$	−0.736954	−	5.12563i	−0.0256730	−	0.178560i
$825$	−0.767558	+	6.50874i	−0.0267230	+	0.226605i
$826$	14.4082	−	100.211i	0.501326	−	3.48680i
$827$	27.9613	+	25.6627i	0.972311	+	0.892379i	0.994218	−	0.107381i	$-0.0342466\pi$
$827$	27.9613	+	25.6627i	0.972311	+	0.892379i	−0.0219073	+	0.999760i	$0.506974\pi$
$828$	10.2591	−	0.586636i	0.356528	−	0.0203870i
$829$	7.87301	−	38.8548i	0.273441	−	1.34948i	−0.574113	−	0.818776i	$-0.694653\pi$
$829$	7.87301	−	38.8548i	0.273441	−	1.34948i	0.847554	−	0.530709i	$-0.178074\pi$
$830$	14.3579	+	11.7404i	0.498369	+	0.407514i
$831$	28.2286	−	13.8791i	0.979241	−	0.481460i
$832$	−49.3937	−	17.6236i	−1.71242	−	0.610989i
$833$	4.62822	−	6.00198i	0.160358	−	0.207956i
$834$	34.3122	+	56.9004i	1.18813	+	1.97030i
$835$	−9.57865	+	11.0544i	−0.331483	+	0.382552i
$836$	4.69464	+	0.418102i	0.162367	+	0.0144604i
$837$	−13.9799	−	16.1336i	−0.483215	−	0.557660i
$838$	17.2180	−	52.9917i	0.594787	−	1.83057i
$839$	17.1410	−	6.11591i	0.591775	−	0.211145i	−0.0231481	−	0.999732i	$-0.507369\pi$
$839$	17.1410	−	6.11591i	0.591775	−	0.211145i	0.614923	+	0.788587i	$0.289187\pi$
$840$	−7.77212	+	7.99733i	−0.268164	+	0.275934i
$841$	16.9654	−	15.5707i	0.585013	−	0.536920i
$842$	−15.6286	−	22.8561i	−0.538597	−	0.787673i
$843$	−16.7844	+	3.90303i	−0.578084	+	0.134428i
$844$	−50.5732	+	36.7436i	−1.74080	+	1.26477i
$845$	6.00329	−	0.688813i	0.206519	−	0.0236959i
$846$	1.77461			0.0610122
$847$	−45.3432	+	2.30674i	−1.55801	+	0.0792604i
$848$	−17.8352			−0.612465
$849$	−42.5515	+	4.88233i	−1.46036	+	0.167561i
$850$	−1.31541	+	0.955700i	−0.0451181	+	0.0327802i
$851$	13.1334	−	3.05404i	0.450206	−	0.104691i
$852$	−27.5118	−	40.2347i	−0.942539	−	1.37842i
$853$	5.48860	−	5.03739i	0.187926	−	0.172477i	−0.576690	−	0.816963i	$-0.695656\pi$
$853$	5.48860	−	5.03739i	0.187926	−	0.172477i	0.764616	+	0.644486i	$0.222929\pi$
$854$	−87.1964	+	89.7230i	−2.98380	+	3.07026i
$855$	0.459580	−	0.163978i	0.0157173	−	0.00560792i
$856$	−3.79632	+	11.6839i	−0.129756	+	0.399347i
$857$	−28.1129	−	32.4440i	−0.960318	−	1.10827i	−0.994060	−	0.108836i	$-0.965288\pi$
$857$	−28.1129	−	32.4440i	−0.960318	−	1.10827i	0.0337413	−	0.999431i	$-0.489258\pi$
$858$	48.6412	+	37.7525i	1.66058	+	1.28885i
$859$	34.6744	−	40.0164i	1.18308	−	1.36534i	0.267321	−	0.963607i	$-0.413861\pi$
$859$	34.6744	−	40.0164i	1.18308	−	1.36534i	0.915756	−	0.401736i	$-0.131593\pi$
$860$	−9.46667	−	15.6987i	−0.322811	−	0.535322i
$861$	−50.3362	+	65.2772i	−1.71545	+	2.22464i
$862$	−55.0918	−	19.6567i	−1.87643	−	0.669510i
$863$	−18.4700	+	9.08110i	−0.628727	+	0.309124i	−0.727627	−	0.685973i	$-0.759377\pi$
$863$	−18.4700	+	9.08110i	−0.628727	+	0.309124i	0.0988998	+	0.995097i	$0.468468\pi$
$864$	24.8183	+	20.2938i	0.844337	+	0.690411i
$865$	5.03395	−	24.8435i	0.171160	−	0.844706i
$866$	67.3026	−	3.84850i	2.28703	−	0.130777i
$867$	23.9190	+	21.9527i	0.812332	+	0.745551i
$868$	−7.98099	+	55.5090i	−0.270892	+	1.88410i
$869$	−6.17399	+	14.4822i	−0.209438	+	0.491275i
$870$	1.47963	+	10.2911i	0.0501642	+	0.348900i
$871$	−28.6623	+	41.9173i	−0.971186	+	1.42031i
$872$	4.52302	−	11.6173i	0.153169	−	0.393410i
$873$	2.89093	+	3.74903i	0.0978433	+	0.126885i
$874$	−1.54633	−	4.75912i	−0.0523054	−	0.160980i
$875$	−2.13140	+	3.53453i	−0.0720544	+	0.119489i
$876$	29.5899	+	76.0010i	0.999750	+	2.56784i
$877$	−29.1312	−	6.77418i	−0.983692	−	0.228748i	−0.296348	−	0.955080i	$-0.595769\pi$
$877$	−29.1312	−	6.77418i	−0.983692	−	0.228748i	−0.687344	+	0.726332i	$0.741223\pi$
$878$	72.5028	−	30.6400i	2.44685	−	1.03405i
$879$	−25.8512	+	16.6136i	−0.871939	+	0.560361i
$880$	−4.86554	−	5.98865i	−0.164017	−	0.201877i
$881$	16.9070	+	10.8655i	0.569612	+	0.366067i	0.793521	−	0.608543i	$-0.208246\pi$
$881$	16.9070	+	10.8655i	0.569612	+	0.366067i	−0.223909	+	0.974610i	$0.571882\pi$
$882$	−19.2631	−	3.33362i	−0.648623	−	0.112249i
$883$	−0.458184	+	5.33454i	−0.0154191	+	0.179522i	0.984571	+	0.174988i	$0.0559886\pi$
$883$	−0.458184	+	5.33454i	−0.0154191	+	0.179522i	−0.999990	+	0.00453378i	$0.998557\pi$
$884$	0.743156	+	8.65241i	0.0249951	+	0.291012i
$885$	−22.1841	+	3.83911i	−0.745711	+	0.129050i
$886$	7.20394	+	3.04441i	0.242021	+	0.102279i
$887$	−26.8974	−	19.5421i	−0.903128	−	0.656161i	0.0361397	−	0.999347i	$-0.488494\pi$
$887$	−26.8974	−	19.5421i	−0.903128	−	0.656161i	−0.939267	+	0.343186i	$0.888494\pi$
$888$	7.36043	+	4.15663i	0.247000	+	0.139487i
$889$	1.49909	−	52.4749i	0.0502778	−	1.75995i
$890$	26.3913	+	7.74918i	0.884637	+	0.259753i
$891$	−19.4415	−	30.4618i	−0.651314	−	1.02051i
$892$	2.01939	−	0.592945i	0.0676140	−	0.0198533i
$893$	−0.124896	−	0.475154i	−0.00417949	−	0.0159004i
$894$	−4.93176	−	24.3392i	−0.164943	−	0.814025i
$895$	4.19016	−	7.94123i	0.140062	−	0.265446i
$896$	−1.22424	−	42.8540i	−0.0408990	−	1.43165i
$897$	9.44792	−	35.9436i	0.315457	−	1.20012i
$898$	−13.5336	−	0.773880i	−0.451622	−	0.0258247i
$899$	8.78211	+	9.03658i	0.292900	+	0.301387i
$900$	2.13962	+	1.05198i	0.0713208	+	0.0350661i
$901$	2.40512	+	5.26648i	0.0801261	+	0.175452i
$902$	51.5944	+	50.4580i	1.71790	+	1.68007i
$903$	23.5711	−	51.6135i	0.784397	−	1.71759i
$904$	10.1212	−	8.27603i	0.336625	−	0.275257i
$905$	5.41743	+	10.2672i	0.180082	+	0.341292i
$906$	−55.0489	+	31.0875i	−1.82888	+	1.03281i
$907$	41.0041	+	4.70478i	1.36152	+	0.156220i	0.763783	−	0.645473i	$-0.223340\pi$
$907$	41.0041	+	4.70478i	1.36152	+	0.156220i	0.597736	+	0.801693i	$0.296067\pi$
$908$	−71.8247	−	8.24111i	−2.38359	−	0.273491i
$909$	−1.02641	+	0.579643i	−0.0340440	+	0.0192255i
$910$	18.0959	+	34.2956i	0.599874	+	1.13689i
$911$	8.25161	−	6.74731i	0.273388	−	0.223548i	−0.486372	−	0.873752i	$-0.661680\pi$
$911$	8.25161	−	6.74731i	0.273388	−	0.223548i	0.759760	+	0.650203i	$0.225316\pi$
$912$	−1.02993	+	2.25522i	−0.0341042	+	0.0746779i
$913$	27.9847	+	5.76213i	0.926158	+	0.190699i
$914$	34.9340	+	76.4948i	1.15551	+	2.53022i
$915$	24.9678	+	12.2758i	0.825410	+	0.405827i
$916$	46.9955	+	48.3573i	1.55278	+	1.59777i
$917$	−19.9290	−	1.13958i	−0.658112	−	0.0376322i
$918$	1.71133	−	6.51057i	0.0564823	−	0.214881i
$919$	0.0767848	+	2.68782i	0.00253290	+	0.0886629i	0.999875	+	0.0158035i	$0.00503062\pi$
$919$	0.0767848	+	2.68782i	0.00253290	+	0.0886629i	−0.997342	+	0.0728594i	$0.976788\pi$
$920$	2.75004	−	5.21190i	0.0906661	−	0.171831i
$921$	−2.88504	−	14.2383i	−0.0950655	−	0.469167i
$922$	−18.6730	−	71.0395i	−0.614963	−	2.33956i
$923$	−39.1930	+	11.5081i	−1.29005	+	0.378794i
$924$	−20.2971	+	68.3299i	−0.667727	+	2.24789i
$925$	3.00184	+	0.881421i	0.0987000	+	0.0289809i
$926$	1.07216	−	37.5304i	0.0352332	−	1.23332i
$927$	−2.98382	−	1.68504i	−0.0980014	−	0.0553439i
$928$	−15.3095	−	11.1230i	−0.502559	−	0.365130i
$929$	−14.0220	−	5.92575i	−0.460047	−	0.194418i	0.146914	−	0.989149i	$-0.453066\pi$
$929$	−14.0220	−	5.92575i	−0.460047	−	0.194418i	−0.606961	+	0.794732i	$0.707612\pi$
$930$	21.6148	−	3.74059i	0.708778	−	0.122659i
$931$	0.463150	+	5.39236i	0.0151791	+	0.176727i
$932$	−0.544679	+	6.34158i	−0.0178416	+	0.207725i
$933$	−34.1004	−	5.90130i	−1.11640	−	0.193200i
$934$	8.43445	+	5.42049i	0.275984	+	0.177364i
$935$	−1.11223	+	2.24430i	−0.0363737	+	0.0733965i
$936$	4.54164	−	2.91874i	0.148448	−	0.0954018i
$937$	−40.3517	+	17.0528i	−1.31823	+	0.557089i	−0.931042	−	0.364911i	$-0.881099\pi$
$937$	−40.3517	+	17.0528i	−1.31823	+	0.557089i	−0.387189	+	0.922000i	$0.626554\pi$
$938$	−100.717	−	23.4206i	−3.28851	−	0.764711i
$939$	11.2586	+	28.9175i	0.367410	+	0.943686i
$940$	1.23964	−	2.05572i	0.0404327	−	0.0670501i
$941$	−7.99145	−	24.5952i	−0.260514	−	0.801779i	−0.992693	−	0.120667i	$-0.961497\pi$
$941$	−7.99145	−	24.5952i	−0.260514	−	0.801779i	0.732179	−	0.681112i	$-0.238503\pi$
$942$	−7.40246	−	9.59968i	−0.241185	−	0.312774i
$943$	15.8034	−	40.5908i	0.514631	−	1.32182i
$944$	14.9613	−	21.8802i	0.486948	−	0.712139i
$945$	−2.43195	−	16.9146i	−0.0791113	−	0.550231i
$946$	−42.4587	−	25.7860i	−1.38045	−	0.838376i
$947$	2.26637	−	15.7630i	0.0736471	−	0.512227i	−0.919290	−	0.393582i	$-0.871236\pi$
$947$	2.26637	−	15.7630i	0.0736471	−	0.512227i	0.992937	−	0.118645i	$-0.0378551\pi$
$948$	18.2100	+	16.7130i	0.591435	+	0.542814i
$949$	68.2380	−	3.90199i	2.21510	−	0.126664i
$950$	0.230575	−	1.13793i	0.00748085	−	0.0369195i
$951$	11.7218	+	9.58489i	0.380106	+	0.310811i
$952$	−3.82477	+	1.88051i	−0.123961	+	0.0609477i
$953$	27.3879	+	9.77197i	0.887180	+	0.316545i	0.740034	−	0.672570i	$-0.234809\pi$
$953$	27.3879	+	9.77197i	0.887180	+	0.316545i	0.147146	+	0.989115i	$0.452991\pi$
$954$	9.11921	−	11.8260i	0.295245	−	0.382881i
$955$	−2.10800	−	3.49572i	−0.0682132	−	0.113119i
$956$	−30.3330	+	35.0061i	−0.981039	+	1.13218i
$957$	9.37353	+	12.9873i	0.303003	+	0.419819i
$958$	−7.56651	−	8.73222i	−0.244463	−	0.282125i
$959$	−5.57293	+	17.1517i	−0.179959	+	0.553858i
$960$	−22.3670	+	7.98052i	−0.721891	+	0.257570i
$961$	−3.07595	+	3.16508i	−0.0992243	+	0.102099i
$962$	21.6548	−	19.8746i	0.698179	−	0.640783i
$963$	4.58872	+	6.71079i	0.147869	+	0.216252i
$964$	−32.4563	+	7.54739i	−1.04535	+	0.243085i
$965$	1.12337	−	0.816174i	0.0361625	−	0.0262736i
$966$	75.1856	−	8.62675i	2.41906	−	0.277561i
$967$	21.4895			0.691057			0.345528	−	0.938408i	$-0.387700\pi$
$967$	21.4895			0.691057			0.345528	+	0.938408i	$0.387700\pi$
$968$	13.8169	+	5.94180i	0.444093	+	0.190977i
$969$	0.804820			0.0258545
$970$	11.1913	−	1.28408i	0.359331	−	0.0412294i
$971$	−6.89025	+	5.00606i	−0.221119	+	0.160652i	−0.692830	−	0.721101i	$-0.743636\pi$
$971$	−6.89025	+	5.00606i	−0.221119	+	0.160652i	0.471711	+	0.881753i	$0.343636\pi$
$972$	−23.3817	+	5.43719i	−0.749969	+	0.174398i
$973$	36.3861	+	53.2130i	1.16649	+	1.70593i
$974$	35.5093	−	32.5901i	1.13779	−	1.04425i
$975$	6.00977	−	6.18390i	0.192467	−	0.198043i
$976$	−30.8512	+	11.0077i	−0.987524	+	0.352348i
$977$	−10.6996	+	32.9300i	−0.342311	+	1.05352i	0.620697	+	0.784051i	$0.286850\pi$
$977$	−10.6996	+	32.9300i	−0.342311	+	1.05352i	−0.963008	+	0.269474i	$0.913150\pi$
$978$	−54.5008	−	62.8972i	−1.74274	−	2.01123i
$979$	41.5550	−	8.28414i	1.32810	−	0.264762i
$980$	−17.3178	+	19.9859i	−0.553198	+	0.638425i
$981$	−4.26016	−	7.06469i	−0.136017	−	0.225558i
$982$	43.5414	−	56.4655i	1.38946	−	1.80189i
$983$	37.4963	+	13.3786i	1.19595	+	0.426712i	0.857604	−	0.514311i	$-0.171952\pi$
$983$	37.4963	+	13.3786i	1.19595	+	0.426712i	0.338342	+	0.941023i	$0.390134\pi$
$984$	24.5053	−	12.0485i	0.781201	−	0.384091i
$985$	8.38254	+	6.85437i	0.267090	+	0.218398i
$986$	−0.789107	+	3.89440i	−0.0251303	+	0.124023i
$987$	7.41802	−	0.424178i	0.236118	−	0.0135017i
$988$	−4.56878	−	4.19319i	−0.145352	−	0.133403i
$989$	−4.26710	+	29.6784i	−0.135686	+	0.943717i
$990$	6.45865	−	0.164179i	0.205269	−	0.00521794i
$991$	3.67164	+	25.5368i	0.116633	+	0.811204i	0.961220	+	0.275784i	$0.0889374\pi$
$991$	3.67164	+	25.5368i	0.116633	+	0.811204i	−0.844586	+	0.535420i	$0.820153\pi$
$992$	−22.5361	+	32.9580i	−0.715522	+	1.04642i
$993$	−6.00107	+	15.4136i	−0.190438	+	0.489136i
$994$	−50.7930	−	65.8695i	−1.61106	−	2.08925i
$995$	2.50132	+	7.69827i	0.0792972	+	0.244052i
$996$	23.1644	−	38.4138i	0.733991	−	1.21719i
$997$	−14.5793	−	37.4468i	−0.461733	−	1.18595i	−0.949720	−	0.313100i	$-0.898632\pi$
$997$	−14.5793	−	37.4468i	−0.461733	−	1.18595i	0.487987	−	0.872851i	$-0.337731\pi$
$998$	43.7084	+	10.1639i	1.38356	+	0.321734i
$999$	−11.9313	+	5.04221i	−0.377490	+	0.159529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.s.b.416.19	yes	880
121.16	even	55	inner	605.2.s.b.16.19	✓	880

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.s.b.16.19	✓	880	121.16	even	55	inner
605.2.s.b.416.19	yes	880	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13889 - 0.245415i) q^{2} +(-1.59867 + 1.16150i) q^{3} +(2.56661 - 0.596840i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-3.13432 + 2.87666i) q^{6} +(-2.87657 + 2.95992i) q^{7} +(1.28779 - 0.459482i) q^{8} +(0.279601 - 0.860523i) q^{9} +O(q^{10})\)	\(q+(2.13889 - 0.245415i) q^{2} +(-1.59867 + 1.16150i) q^{3} +(2.56661 - 0.596840i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(-3.13432 + 2.87666i) q^{6} +(-2.87657 + 2.95992i) q^{7} +(1.28779 - 0.459482i) q^{8} +(0.279601 - 0.860523i) q^{9} +(-1.40987 - 1.62707i) q^{10} +(-3.08684 - 1.21301i) q^{11} +(-3.40992 + 3.93526i) q^{12} +(2.25345 + 3.73693i) q^{13} +(-5.42626 + 7.03690i) q^{14} +(1.86114 + 0.664053i) q^{15} +(-2.08778 + 1.02649i) q^{16} +(0.584647 + 0.478064i) q^{17} +(0.386851 - 1.90919i) q^{18} +(-0.538414 + 0.0307876i) q^{19} +(-1.94138 - 1.78178i) q^{20} +(1.16073 - 8.07304i) q^{21} +(-6.90012 - 1.83695i) q^{22} +(0.613360 + 4.26602i) q^{23} +(-1.52506 + 2.23032i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(5.73699 + 7.43986i) q^{26} +(-1.27940 - 3.93759i) q^{27} +(-5.61643 + 9.31380i) q^{28} +(0.886648 + 2.27734i) q^{29} +(4.14375 + 0.963587i) q^{30} +(4.74950 - 2.00716i) q^{31} +(-6.51411 + 4.18637i) q^{32} +(6.34374 - 1.64616i) q^{33} +(1.36782 + 0.879046i) q^{34} +(4.06699 + 0.703820i) q^{35} +(0.204032 - 2.37551i) q^{36} +(-0.267728 - 3.11710i) q^{37} +(-1.14405 + 0.197986i) q^{38} +(-7.94295 - 3.35672i) q^{39} +(-1.10617 - 0.803682i) q^{40} +(-8.80037 - 4.96980i) q^{41} +(0.501427 - 17.5522i) q^{42} +(6.67512 + 1.95999i) q^{43} +(-8.64670 - 1.27098i) q^{44} +(-0.868157 + 0.254914i) q^{45} +(2.35886 + 8.97402i) q^{46} +(0.180915 + 0.892852i) q^{47} +(2.14539 - 4.06596i) q^{48} +(-0.286581 - 10.0316i) q^{49} +(-0.547313 + 2.08220i) q^{50} +(-1.48993 - 0.0851970i) q^{51} +(8.01408 + 8.24629i) q^{52} +(6.87964 + 3.38249i) q^{53} +(-3.70284 - 8.10809i) q^{54} +(0.741040 + 3.23278i) q^{55} +(-2.34438 + 5.13348i) q^{56} +(0.824984 - 0.674586i) q^{57} +(2.45534 + 4.65338i) q^{58} +(-9.92069 + 5.60247i) q^{59} +(5.17315 + 0.593564i) q^{60} +(13.9880 + 1.60497i) q^{61} +(9.66609 - 5.45869i) q^{62} +(1.74279 + 3.30295i) q^{63} +(-9.30355 + 7.60748i) q^{64} +(1.81278 - 3.96944i) q^{65} +(13.1646 - 5.07781i) q^{66} +(4.83403 + 10.5851i) q^{67} +(1.78589 + 0.878063i) q^{68} +(-5.93553 - 6.10751i) q^{69} +(8.87158 + 0.507295i) q^{70} +(-2.37963 + 9.05307i) q^{71} +(-0.0353281 - 1.23664i) q^{72} +(7.30935 - 13.8528i) q^{73} +(-1.33762 - 6.60143i) q^{74} +(-0.502350 - 1.91114i) q^{75} +(-1.36352 + 0.400367i) q^{76} +(12.4699 - 5.64749i) q^{77} +(-17.8129 - 5.23034i) q^{78} +(0.135550 - 4.74486i) q^{79} +(2.02577 + 1.14400i) q^{80} +(8.81484 + 6.40436i) q^{81} +(-20.0427 - 8.47013i) q^{82} +(-8.48854 + 1.46900i) q^{83} +(-1.83917 - 21.4131i) q^{84} +(0.0646280 - 0.752450i) q^{85} +(14.7584 + 2.55404i) q^{86} +(-4.06257 - 2.61086i) q^{87} +(-4.53256 - 0.143755i) q^{88} +(-10.7477 + 6.90714i) q^{89} +(-1.79433 + 0.758292i) q^{90} +(-17.5432 - 4.07949i) q^{91} +(4.12039 + 10.5831i) q^{92} +(-5.26156 + 8.72531i) q^{93} +(0.606078 + 1.86532i) q^{94} +(0.329319 + 0.427068i) q^{95} +(5.55143 - 14.2587i) q^{96} +(-2.95333 + 4.31910i) q^{97} +(-3.07488 - 21.3863i) q^{98} +(-1.90691 + 2.31714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Introduction

L-functions

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