LMFDB - Embedded newform 64.2.i.a.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	64.29
Dual form			64.2.i.a.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28112 + 0.598933i) q^{2} +(-1.22190 - 0.243052i) q^{3} +(1.28256 + 1.53462i) q^{4} +(0.884671 - 1.32400i) q^{5} +(-1.41984 - 1.04322i) q^{6} +(-2.40727 + 0.997123i) q^{7} +(0.723982 + 2.73420i) q^{8} +(-1.33766 - 0.554078i) q^{9} +O(q^{10})$	\(q+(1.28112 + 0.598933i) q^{2} +(-1.22190 - 0.243052i) q^{3} +(1.28256 + 1.53462i) q^{4} +(0.884671 - 1.32400i) q^{5} +(-1.41984 - 1.04322i) q^{6} +(-2.40727 + 0.997123i) q^{7} +(0.723982 + 2.73420i) q^{8} +(-1.33766 - 0.554078i) q^{9} +(1.92636 - 1.16635i) q^{10} +(-0.432397 - 2.17381i) q^{11} +(-1.19417 - 2.18688i) q^{12} +(-2.18211 - 3.26576i) q^{13} +(-3.68122 - 0.164355i) q^{14} +(-1.40279 + 1.40279i) q^{15} +(-0.710093 + 3.93647i) q^{16} +(4.38547 + 4.38547i) q^{17} +(-1.38185 - 1.51101i) q^{18} +(2.64242 - 1.76561i) q^{19} +(3.16648 - 0.340480i) q^{20} +(3.18380 - 0.633298i) q^{21} +(0.748011 - 3.04389i) q^{22} +(-2.12144 + 5.12160i) q^{23} +(-0.220084 - 3.51690i) q^{24} +(0.943074 + 2.27678i) q^{25} +(-0.839581 - 5.49078i) q^{26} +(4.60747 + 3.07861i) q^{27} +(-4.61766 - 2.41536i) q^{28} +(-0.836699 + 4.20637i) q^{29} +(-2.63732 + 0.956967i) q^{30} -8.37185i q^{31} +(-3.26740 + 4.61780i) q^{32} +2.76128i q^{33} +(2.99173 + 8.24494i) q^{34} +(-0.809445 + 4.06936i) q^{35} +(-0.865331 - 2.76343i) q^{36} +(-5.42017 - 3.62164i) q^{37} +(4.44275 - 0.679329i) q^{38} +(1.87258 + 4.52081i) q^{39} +(4.26058 + 1.46031i) q^{40} +(3.00227 - 7.24812i) q^{41} +(4.45815 + 1.09555i) q^{42} +(8.60595 - 1.71183i) q^{43} +(2.78138 - 3.45159i) q^{44} +(-1.91699 + 1.28089i) q^{45} +(-5.78532 + 5.29081i) q^{46} +(0.0771294 + 0.0771294i) q^{47} +(1.82443 - 4.63740i) q^{48} +(-0.149067 + 0.149067i) q^{49} +(-0.155446 + 3.48168i) q^{50} +(-4.29273 - 6.42453i) q^{51} +(2.21300 - 7.53722i) q^{52} +(0.846775 + 4.25703i) q^{53} +(4.05885 + 6.70365i) q^{54} +(-3.26066 - 1.35061i) q^{55} +(-4.46915 - 5.86005i) q^{56} +(-3.65792 + 1.51516i) q^{57} +(-3.59125 + 4.88776i) q^{58} +(-0.657977 + 0.984732i) q^{59} +(-3.95189 - 0.353584i) q^{60} +(-9.90754 - 1.97073i) q^{61} +(5.01418 - 10.7254i) q^{62} +3.77259 q^{63} +(-6.95170 + 3.95902i) q^{64} -6.25433 q^{65} +(-1.65382 + 3.53754i) q^{66} +(-9.06082 - 1.80231i) q^{67} +(-1.10540 + 12.3546i) q^{68} +(3.83701 - 5.74249i) q^{69} +(-3.47427 + 4.72855i) q^{70} +(9.94840 - 4.12076i) q^{71} +(0.546516 - 4.05858i) q^{72} +(-10.8278 - 4.48502i) q^{73} +(-4.77479 - 7.88609i) q^{74} +(-0.598970 - 3.01123i) q^{75} +(6.09858 + 1.79060i) q^{76} +(3.20845 + 4.80178i) q^{77} +(-0.308656 + 6.91327i) q^{78} +(-0.842912 + 0.842912i) q^{79} +(4.58370 + 4.42264i) q^{80} +(-1.81022 - 1.81022i) q^{81} +(8.18742 - 7.48758i) q^{82} +(0.766957 - 0.512464i) q^{83} +(5.05528 + 4.07368i) q^{84} +(9.68608 - 1.92668i) q^{85} +(12.0506 + 2.96132i) q^{86} +(2.04473 - 4.93642i) q^{87} +(5.63057 - 2.75606i) q^{88} +(2.03287 + 4.90777i) q^{89} +(-3.22307 + 0.492832i) q^{90} +(8.50928 + 5.68572i) q^{91} +(-10.5806 + 3.31316i) q^{92} +(-2.03480 + 10.2296i) q^{93} +(0.0526169 + 0.145008i) q^{94} -5.06055i q^{95} +(5.11482 - 4.84837i) q^{96} +5.90730i q^{97} +(-0.280255 + 0.101692i) q^{98} +(-0.626056 + 3.14740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	1.28112	+	0.598933i	0.905891	+	0.423510i
$2$	1.28112	+	0.598933i	0.905891	+	0.423510i
$3$	−1.22190	−	0.243052i	−0.705467	−	0.140326i	−0.170697	−	0.985324i	$-0.554602\pi$
$3$	−1.22190	−	0.243052i	−0.705467	−	0.140326i	−0.534770	+	0.844997i	$0.679602\pi$
$4$	1.28256	+	1.53462i	0.641279	+	0.767308i
$5$	0.884671	−	1.32400i	0.395637	−	0.592113i	−0.579158	−	0.815215i	$-0.696619\pi$
$5$	0.884671	−	1.32400i	0.395637	−	0.592113i	0.974795	+	0.223103i	$0.0716186\pi$
$6$	−1.41984	−	1.04322i	−0.579647	−	0.425893i
$7$	−2.40727	+	0.997123i	−0.909861	+	0.376877i	−0.788004	−	0.615671i	$-0.788885\pi$
$7$	−2.40727	+	0.997123i	−0.909861	+	0.376877i	−0.121858	+	0.992548i	$0.538885\pi$
$8$	0.723982	+	2.73420i	0.255966	+	0.966686i
$9$	−1.33766	−	0.554078i	−0.445887	−	0.184693i
$10$	1.92636	−	1.16635i	0.609170	−	0.368834i
$11$	−0.432397	−	2.17381i	−0.130373	−	0.655427i	−0.989602	−	0.143836i	$-0.954056\pi$
$11$	−0.432397	−	2.17381i	−0.130373	−	0.655427i	0.859229	−	0.511591i	$-0.170944\pi$
$12$	−1.19417	−	2.18688i	−0.344728	−	0.631299i
$13$	−2.18211	−	3.26576i	−0.605208	−	0.905758i	0.394707	−	0.918807i	$-0.370846\pi$
$13$	−2.18211	−	3.26576i	−0.605208	−	0.905758i	−0.999915	+	0.0130490i	$0.995846\pi$
$14$	−3.68122	−	0.164355i	−0.983847	−	0.0439257i
$15$	−1.40279	+	1.40279i	−0.362198	+	0.362198i
$16$	−0.710093	+	3.93647i	−0.177523	+	0.984117i
$17$	4.38547	+	4.38547i	1.06363	+	1.06363i	0.997833	+	0.0658001i	$0.0209600\pi$
$17$	4.38547	+	4.38547i	1.06363	+	1.06363i	0.0658001	+	0.997833i	$0.479040\pi$
$18$	−1.38185	−	1.51101i	−0.325706	−	0.356149i
$19$	2.64242	−	1.76561i	0.606212	−	0.405058i	−0.214234	−	0.976782i	$-0.568725\pi$
$19$	2.64242	−	1.76561i	0.606212	−	0.405058i	0.820446	+	0.571724i	$0.193725\pi$
$20$	3.16648	−	0.340480i	0.708046	−	0.0761337i
$21$	3.18380	−	0.633298i	0.694763	−	0.138197i
$22$	0.748011	−	3.04389i	0.159477	−	0.648960i
$23$	−2.12144	+	5.12160i	−0.442350	+	1.06793i	0.532772	+	0.846259i	$0.321150\pi$
$23$	−2.12144	+	5.12160i	−0.442350	+	1.06793i	−0.975122	+	0.221669i	$0.928850\pi$
$24$	−0.220084	−	3.51690i	−0.0449246	−	0.717884i
$25$	0.943074	+	2.27678i	0.188615	+	0.455356i
$26$	−0.839581	−	5.49078i	−0.164655	−	1.07683i
$27$	4.60747	+	3.07861i	0.886708	+	0.592479i
$28$	−4.61766	−	2.41536i	−0.872655	−	0.456461i
$29$	−0.836699	+	4.20637i	−0.155371	+	0.781104i	0.821986	+	0.569508i	$0.192866\pi$
$29$	−0.836699	+	4.20637i	−0.155371	+	0.781104i	−0.977357	+	0.211596i	$0.932134\pi$
$30$	−2.63732	+	0.956967i	−0.481506	+	0.174717i
$31$		−	8.37185i		−	1.50363i	−0.659375	−	0.751815i	$-0.729179\pi$
$31$		−	8.37185i		−	1.50363i	0.659375	−	0.751815i	$-0.270821\pi$
$32$	−3.26740	+	4.61780i	−0.577600	+	0.816320i
$33$			2.76128i			0.480677i
$34$	2.99173	+	8.24494i	0.513077	+	1.41400i
$35$	−0.809445	+	4.06936i	−0.136821	+	0.687847i
$36$	−0.865331	−	2.76343i	−0.144222	−	0.460572i
$37$	−5.42017	−	3.62164i	−0.891070	−	0.595394i	0.0235436	−	0.999723i	$-0.492505\pi$
$37$	−5.42017	−	3.62164i	−0.891070	−	0.595394i	−0.914614	+	0.404329i	$0.867505\pi$
$38$	4.44275	−	0.679329i	0.720708	−	0.110202i
$39$	1.87258	+	4.52081i	0.299853	+	0.723909i
$40$	4.26058	+	1.46031i	0.673656	+	0.230896i
$41$	3.00227	−	7.24812i	0.468876	−	1.13197i	−0.495779	−	0.868449i	$-0.665117\pi$
$41$	3.00227	−	7.24812i	0.468876	−	1.13197i	0.964655	−	0.263517i	$-0.0848825\pi$
$42$	4.45815	+	1.09555i	0.687908	+	0.169048i
$43$	8.60595	−	1.71183i	1.31239	−	0.261052i	0.511203	−	0.859460i	$-0.329200\pi$
$43$	8.60595	−	1.71183i	1.31239	−	0.261052i	0.801191	+	0.598408i	$0.204200\pi$
$44$	2.78138	−	3.45159i	0.419309	−	0.520347i
$45$	−1.91699	+	1.28089i	−0.285768	+	0.190944i
$46$	−5.78532	+	5.29081i	−0.852999	+	0.780087i
$47$	0.0771294	+	0.0771294i	0.0112505	+	0.0112505i	0.712710	−	0.701459i	$-0.247468\pi$
$47$	0.0771294	+	0.0771294i	0.0112505	+	0.0112505i	−0.701459	+	0.712710i	$0.747468\pi$
$48$	1.82443	−	4.63740i	0.263334	−	0.669351i
$49$	−0.149067	+	0.149067i	−0.0212953	+	0.0212953i
$50$	−0.155446	+	3.48168i	−0.0219834	+	0.492384i
$51$	−4.29273	−	6.42453i	−0.601103	−	0.899614i
$52$	2.21300	−	7.53722i	0.306888	−	1.04522i
$53$	0.846775	+	4.25703i	0.116314	+	0.584748i	0.994350	+	0.106153i	$0.0338535\pi$
$53$	0.846775	+	4.25703i	0.116314	+	0.584748i	−0.878036	+	0.478594i	$0.841147\pi$
$54$	4.05885	+	6.70365i	0.552340	+	0.912251i
$55$	−3.26066	−	1.35061i	−0.439667	−	0.182116i
$56$	−4.46915	−	5.86005i	−0.597215	−	0.783082i
$57$	−3.65792	+	1.51516i	−0.484503	+	0.200688i
$58$	−3.59125	+	4.88776i	−0.471555	+	0.641794i
$59$	−0.657977	+	0.984732i	−0.0856613	+	0.128201i	−0.871826	−	0.489816i	$-0.837064\pi$
$59$	−0.657977	+	0.984732i	−0.0856613	+	0.128201i	0.786164	+	0.618017i	$0.212064\pi$
$60$	−3.95189	−	0.353584i	−0.510187	−	0.0456475i
$61$	−9.90754	−	1.97073i	−1.26853	−	0.252327i	−0.485460	−	0.874259i	$-0.661348\pi$
$61$	−9.90754	−	1.97073i	−1.26853	−	0.252327i	−0.783071	+	0.621932i	$0.786348\pi$
$62$	5.01418	−	10.7254i	0.636802	−	1.36212i
$63$	3.77259			0.475302
$64$	−6.95170	+	3.95902i	−0.868962	+	0.494878i
$65$	−6.25433			−0.775754
$66$	−1.65382	+	3.53754i	−0.203571	+	0.435441i
$67$	−9.06082	−	1.80231i	−1.10696	−	0.220187i	−0.392420	−	0.919786i	$-0.628362\pi$
$67$	−9.06082	−	1.80231i	−1.10696	−	0.220187i	−0.714536	+	0.699599i	$0.753362\pi$
$68$	−1.10540	+	12.3546i	−0.134049	+	1.49822i
$69$	3.83701	−	5.74249i	0.461922	−	0.691315i
$70$	−3.47427	+	4.72855i	−0.415255	+	0.565169i
$71$	9.94840	−	4.12076i	1.18066	−	0.489044i	0.295956	−	0.955202i	$-0.404362\pi$
$71$	9.94840	−	4.12076i	1.18066	−	0.489044i	0.884702	+	0.466157i	$0.154362\pi$
$72$	0.546516	−	4.05858i	0.0644075	−	0.478308i
$73$	−10.8278	−	4.48502i	−1.26730	−	0.524931i	−0.355155	−	0.934807i	$-0.615572\pi$
$73$	−10.8278	−	4.48502i	−1.26730	−	0.524931i	−0.912141	+	0.409876i	$0.865572\pi$
$74$	−4.77479	−	7.88609i	−0.555058	−	0.916739i
$75$	−0.598970	−	3.01123i	−0.0691631	−	0.347706i
$76$	6.09858	+	1.79060i	0.699555	+	0.205396i
$77$	3.20845	+	4.80178i	0.365636	+	0.547214i
$78$	−0.308656	+	6.91327i	−0.0349484	+	0.782774i
$79$	−0.842912	+	0.842912i	−0.0948351	+	0.0948351i	−0.752933	−	0.658098i	$-0.771361\pi$
$79$	−0.842912	+	0.842912i	−0.0948351	+	0.0948351i	0.658098	+	0.752933i	$0.271361\pi$
$80$	4.58370	+	4.42264i	0.512473	+	0.494467i
$81$	−1.81022	−	1.81022i	−0.201136	−	0.201136i
$82$	8.18742	−	7.48758i	0.904149	−	0.826865i
$83$	0.766957	−	0.512464i	0.0841845	−	0.0562503i	−0.512766	−	0.858529i	$-0.671379\pi$
$83$	0.766957	−	0.512464i	0.0841845	−	0.0562503i	0.596950	+	0.802278i	$0.296379\pi$
$84$	5.05528	+	4.07368i	0.551576	+	0.444474i
$85$	9.68608	−	1.92668i	1.05060	−	0.208978i
$86$	12.0506	+	2.96132i	1.29944	+	0.319328i
$87$	2.04473	−	4.93642i	0.219218	−	0.529240i
$88$	5.63057	−	2.75606i	0.600221	−	0.293797i
$89$	2.03287	+	4.90777i	0.215483	+	0.520223i	0.994249	−	0.107092i	$-0.0341539\pi$
$89$	2.03287	+	4.90777i	0.215483	+	0.520223i	−0.778766	+	0.627315i	$0.784154\pi$
$90$	−3.22307	+	0.492832i	−0.339742	+	0.0519491i
$91$	8.50928	+	5.68572i	0.892015	+	0.596025i
$92$	−10.5806	+	3.31316i	−1.10310	+	0.345421i
$93$	−2.03480	+	10.2296i	−0.210998	+	1.06076i
$94$	0.0526169	+	0.145008i	0.00542702	+	0.0149564i
$95$		−	5.06055i		−	0.519202i
$96$	5.11482	−	4.84837i	0.522029	−	0.494834i
$97$			5.90730i			0.599796i	0.953971	+	0.299898i	$0.0969526\pi$
$97$			5.90730i			0.599796i	−0.953971	+	0.299898i	$0.903047\pi$
$98$	−0.280255	+	0.101692i	−0.0283100	+	0.0102725i
$99$	−0.626056	+	3.14740i	−0.0629210	+	0.316325i
$100$	−2.28444	+	4.36736i	−0.228444	+	0.436736i
$101$	−0.429855	−	0.287220i	−0.0427722	−	0.0285794i	0.534000	−	0.845484i	$-0.320688\pi$
$101$	−0.429855	−	0.287220i	−0.0427722	−	0.0285794i	−0.576773	+	0.816905i	$0.695688\pi$
$102$	−1.65166	−	10.8017i	−0.163538	−	1.06953i
$103$	3.33979	+	8.06296i	0.329079	+	0.794467i	0.998661	+	0.0517290i	$0.0164732\pi$
$103$	3.33979	+	8.06296i	0.329079	+	0.794467i	−0.669582	+	0.742738i	$0.733527\pi$
$104$	7.34943	−	8.33067i	0.720671	−	0.816890i
$105$	1.97813	−	4.77563i	0.193046	−	0.466054i
$106$	−1.46485	+	5.96094i	−0.142279	+	0.578978i
$107$	−18.7622	+	3.73203i	−1.81381	+	0.360789i	−0.981188	−	0.193054i	$-0.938161\pi$
$107$	−18.7622	+	3.73203i	−1.81381	+	0.360789i	−0.832621	+	0.553843i	$0.813161\pi$
$108$	1.18486	+	11.0192i	0.114013	+	1.06032i
$109$	10.6124	−	7.09099i	1.01648	−	0.679193i	0.0685465	−	0.997648i	$-0.478164\pi$
$109$	10.6124	−	7.09099i	1.01648	−	0.679193i	0.947938	+	0.318455i	$0.103164\pi$
$110$	−3.36838	−	3.68321i	−0.321163	−	0.351181i
$111$	5.74268	+	5.74268i	0.545071	+	0.545071i
$112$	−2.21576	−	10.1842i	−0.209369	−	0.962314i
$113$	11.6172	−	11.6172i	1.09285	−	1.09285i	0.0976320	−	0.995223i	$-0.468873\pi$
$113$	11.6172	−	11.6172i	1.09285	−	1.09285i	0.995223	−	0.0976320i	$-0.0311268\pi$
$114$	−5.59372	−	0.249743i	−0.523900	−	0.0233905i
$115$	4.90425	+	7.33973i	0.457323	+	0.684433i
$116$	−7.52828	+	4.11090i	−0.698983	+	0.381688i
$117$	1.10944	+	5.57754i	0.102568	+	0.515643i
$118$	−1.43274	+	0.867479i	−0.131894	+	0.0798579i
$119$	−14.9299	−	6.18415i	−1.36862	−	0.566900i
$120$	−4.85109	−	2.81990i	−0.442842	−	0.257421i
$121$	5.62421	−	2.32962i	0.511292	−	0.211784i
$122$	−11.5125	−	8.45871i	−1.04229	−	0.765816i
$123$	−5.43016	+	8.12680i	−0.489621	+	0.732769i
$124$	12.8476	−	10.7374i	1.15375	−	0.964245i
$125$	11.6576	+	2.31885i	1.04269	+	0.207404i
$126$	4.83316	+	2.25953i	0.430572	+	0.201295i
$127$	2.24655			0.199349			0.0996747	−	0.995020i	$-0.468220\pi$
$127$	2.24655			0.199349			0.0996747	+	0.995020i	$0.468220\pi$
$128$	−11.2772	+	0.908394i	−0.996771	+	0.0802915i
$129$	−10.9317			−0.962484
$130$	−8.01257	−	3.74592i	−0.702749	−	0.328539i
$131$	−5.29169	−	1.05258i	−0.462338	−	0.0919646i	−0.0415748	−	0.999135i	$-0.513237\pi$
$131$	−5.29169	−	1.05258i	−0.462338	−	0.0919646i	−0.420763	+	0.907171i	$0.638237\pi$
$132$	−4.23750	+	3.54150i	−0.368827	+	0.308248i
$133$	−4.60048	+	6.88510i	−0.398912	+	0.597014i
$134$	−10.5286	−	7.73581i	−0.909530	−	0.668272i
$135$	8.15219	−	3.37675i	0.701629	−	0.290624i
$136$	−8.81575	+	15.1658i	−0.755945	+	1.30045i
$137$	6.00408	+	2.48697i	0.512963	+	0.212476i	0.624123	−	0.781326i	$-0.285457\pi$
$137$	6.00408	+	2.48697i	0.512963	+	0.212476i	−0.111160	+	0.993803i	$0.535457\pi$
$138$	8.35506	−	5.05873i	0.711230	−	0.430628i
$139$	−0.350641	−	1.76279i	−0.0297410	−	0.149518i	0.963061	−	0.269282i	$-0.0867863\pi$
$139$	−0.350641	−	1.76279i	−0.0297410	−	0.149518i	−0.992802	+	0.119764i	$0.961786\pi$
$140$	−7.28306	+	3.97700i	−0.615531	+	0.336117i
$141$	−0.0754983	−	0.112991i	−0.00635811	−	0.00951558i
$142$	15.2132	+	0.679222i	1.27666	+	0.0569991i
$143$	−6.15559	+	6.15559i	−0.514756	+	0.514756i
$144$	3.13097	−	4.87221i	0.260914	−	0.406018i
$145$	4.82905	+	4.82905i	0.401031	+	0.401031i
$146$	−11.1855	−	12.2310i	−0.925719	−	1.01224i
$147$	0.218377	−	0.145915i	0.0180114	−	0.0120349i
$148$	−1.39385	−	12.9628i	−0.114574	−	1.06554i
$149$	−3.29611	+	0.655636i	−0.270028	+	0.0537118i	−0.328247	−	0.944592i	$-0.606458\pi$
$149$	−3.29611	+	0.655636i	−0.270028	+	0.0537118i	0.0582192	+	0.998304i	$0.481458\pi$
$150$	1.03617	−	4.21650i	0.0846029	−	0.344276i
$151$	−1.32342	+	3.19501i	−0.107698	+	0.260007i	−0.968536	−	0.248873i	$-0.919940\pi$
$151$	−1.32342	+	3.19501i	−0.107698	+	0.260007i	0.860838	+	0.508879i	$0.169940\pi$
$152$	6.74059	+	5.94663i	0.546734	+	0.482335i
$153$	−3.43638	−	8.29617i	−0.277815	−	0.670705i
$154$	1.23447	+	8.07332i	0.0994765	+	0.650567i
$155$	−11.0844	−	7.40634i	−0.890318	−	0.594891i
$156$	−4.53602	+	8.67189i	−0.363172	+	0.694307i
$157$	−0.605421	+	3.04366i	−0.0483178	+	0.242910i	−0.997395	−	0.0721336i	$-0.977019\pi$
$157$	−0.605421	+	3.04366i	−0.0483178	+	0.242910i	0.949077	+	0.315044i	$0.102019\pi$
$158$	−1.58472	+	0.575027i	−0.126074	+	0.0457467i
$159$		−	5.40749i		−	0.428842i
$160$	3.22342	+	8.41129i	0.254833	+	0.664971i
$161$		−	14.4444i		−	1.13838i
$162$	−1.23491	−	3.40332i	−0.0970241	−	0.267390i
$163$	0.0943209	−	0.474183i	0.00738778	−	0.0371409i	−0.976916	−	0.213626i	$-0.931473\pi$
$163$	0.0943209	−	0.474183i	0.00738778	−	0.0371409i	0.984303	+	0.176485i	$0.0564727\pi$
$164$	14.9737	−	4.68880i	1.16925	−	0.366133i
$165$	3.65594	+	2.44282i	0.284615	+	0.190174i
$166$	1.28950	−	0.197174i	0.100085	−	0.0153037i
$167$	−3.40598	−	8.22277i	−0.263563	−	0.636297i	0.735591	−	0.677426i	$-0.236905\pi$
$167$	−3.40598	−	8.22277i	−0.263563	−	0.636297i	−0.999154	+	0.0411288i	$0.986905\pi$
$168$	4.03658	+	8.24666i	0.311429	+	0.636244i
$169$	−0.928687	+	2.24205i	−0.0714375	+	0.172465i
$170$	13.5630	+	3.33300i	1.04024	+	0.255629i
$171$	−4.51294	+	0.897680i	−0.345113	+	0.0686473i
$172$	13.6646	+	11.0113i	1.04192	+	0.839604i
$173$	10.7422	−	7.17768i	0.816711	−	0.545709i	−0.0755956	−	0.997139i	$-0.524086\pi$
$173$	10.7422	−	7.17768i	0.816711	−	0.545709i	0.892307	+	0.451430i	$0.149086\pi$
$174$	5.57615	−	5.09951i	0.422727	−	0.386593i
$175$	−4.54046	−	4.54046i	−0.343227	−	0.343227i
$176$	8.86416	−	0.158511i	0.668161	−	0.0119482i
$177$	1.04333	−	1.04333i	0.0784212	−	0.0784212i
$178$	−0.335076	+	7.50502i	−0.0251150	+	0.562525i
$179$	8.89422	+	13.3111i	0.664785	+	0.994921i	0.998632	+	0.0522939i	$0.0166533\pi$
$179$	8.89422	+	13.3111i	0.664785	+	0.994921i	−0.333847	+	0.942627i	$0.608347\pi$
$180$	−4.42433	−	1.29903i	−0.329770	−	0.0968238i
$181$	−0.271646	−	1.36566i	−0.0201913	−	0.101508i	0.969376	−	0.245583i	$-0.0789794\pi$
$181$	−0.271646	−	1.36566i	−0.0201913	−	0.101508i	−0.989567	+	0.144075i	$0.953979\pi$
$182$	7.49608	+	12.3806i	0.555646	+	0.917712i
$183$	11.6271	+	4.81610i	0.859499	+	0.356016i
$184$	−15.5394	−	2.09249i	−1.14558	−	0.154260i
$185$	−9.59013	+	3.97236i	−0.705081	+	0.292054i
$186$	−8.73368	+	11.8867i	−0.640385	+	0.871574i
$187$	7.63690	−	11.4294i	0.558465	−	0.835803i
$188$	−0.0194411	+	0.217287i	−0.00141789	+	0.0158473i
$189$	−14.1612	−	2.81683i	−1.03007	−	0.204894i
$190$	3.03093	−	6.48319i	0.219887	−	0.470340i
$191$	−3.56574			−0.258008			−0.129004	−	0.991644i	$-0.541178\pi$
$191$	−3.56574			−0.258008			−0.129004	+	0.991644i	$0.541178\pi$
$192$	9.45656	−	3.14793i	0.682469	−	0.227182i
$193$	−3.86751			−0.278389			−0.139195	−	0.990265i	$-0.544451\pi$
$193$	−3.86751			−0.278389			−0.139195	+	0.990265i	$0.544451\pi$
$194$	−3.53808	+	7.56799i	−0.254019	+	0.543350i
$195$	7.64219	+	1.52013i	0.547269	+	0.108859i
$196$	−0.419948	−	0.0375737i	−0.0299963	−	0.00268384i
$197$	−10.0325	+	15.0147i	−0.714788	+	1.06976i	0.279196	+	0.960234i	$0.409932\pi$
$197$	−10.0325	+	15.0147i	−0.714788	+	1.06976i	−0.993984	+	0.109522i	$0.965068\pi$
$198$	−2.68714	+	3.65724i	−0.190967	+	0.259909i
$199$	−12.9440	+	5.36160i	−0.917579	+	0.380074i	−0.790953	−	0.611877i	$-0.790415\pi$
$199$	−12.9440	+	5.36160i	−0.917579	+	0.380074i	−0.126626	+	0.991951i	$0.540415\pi$
$200$	−5.54241	+	4.22690i	−0.391907	+	0.298887i
$201$	10.6334	+	4.40450i	0.750022	+	0.310669i
$202$	−0.378672	−	0.625419i	−0.0266433	−	0.0440043i
$203$	−2.18011	−	10.9602i	−0.153014	−	0.769252i
$204$	4.35351	−	14.8275i	0.304806	−	1.03813i
$205$	−6.94051	−	10.3872i	−0.484747	−	0.725474i
$206$	−0.550495	+	12.3300i	−0.0383548	+	0.859069i
$207$	5.67553	−	5.67553i	0.394477	−	0.394477i
$208$	14.4050	−	6.27081i	0.998810	−	0.434802i
$209$	−4.98066	−	4.98066i	−0.344519	−	0.344519i
$210$	5.39451	−	4.93340i	0.372257	−	0.340437i
$211$	15.7003	−	10.4906i	1.08085	−	0.722204i	0.118215	−	0.992988i	$-0.462283\pi$
$211$	15.7003	−	10.4906i	1.08085	−	0.722204i	0.962640	+	0.270784i	$0.0872829\pi$
$212$	−5.44686	+	6.75936i	−0.374092	+	0.464234i
$213$	−13.1576	+	2.61720i	−0.901541	+	0.179328i
$214$	−26.2719	−	6.45611i	−1.79591	−	0.441330i
$215$	5.34696	−	12.9087i	0.364660	−	0.880367i
$216$	−5.08182	+	14.8266i	−0.345774	+	1.00882i
$217$	8.34776	+	20.1533i	0.566683	+	1.36809i
$218$	17.8428	−	2.72830i	1.20847	−	0.184784i
$219$	12.1404	+	8.11198i	0.820374	+	0.548157i
$220$	−2.10931	−	6.73609i	−0.142210	−	0.454147i
$221$	4.75231	−	23.8915i	0.319675	−	1.60711i
$222$	3.91760	+	10.7966i	0.262932	+	0.724619i
$223$			25.9711i			1.73915i	0.493797	+	0.869577i	$0.335609\pi$
$223$			25.9711i			1.73915i	−0.493797	+	0.869577i	$0.664391\pi$
$224$	3.26099	−	14.3743i	0.217884	−	0.960422i
$225$		−	3.56810i		−	0.237873i
$226$	21.8410	−	7.92515i	1.45284	−	0.527173i
$227$	−0.214031	+	1.07600i	−0.0142057	+	0.0714169i	−0.987238	−	0.159253i	$-0.949092\pi$
$227$	−0.214031	+	1.07600i	−0.0142057	+	0.0714169i	0.973032	+	0.230669i	$0.0740916\pi$
$228$	−7.01668	−	3.67022i	−0.464691	−	0.243066i
$229$	−13.0798	−	8.73965i	−0.864338	−	0.577532i	0.0424596	−	0.999098i	$-0.486481\pi$
$229$	−13.0798	−	8.73965i	−0.864338	−	0.577532i	−0.906798	+	0.421566i	$0.861481\pi$
$230$	1.88694	+	12.3404i	0.124421	+	0.813703i
$231$	−2.75333	−	6.64714i	−0.181156	−	0.437349i
$232$	−12.1068	+	0.757634i	−0.794851	+	0.0497411i
$233$	−7.41658	+	17.9052i	−0.485876	+	1.17301i	0.470900	+	0.882186i	$0.343929\pi$
$233$	−7.41658	+	17.9052i	−0.485876	+	1.17301i	−0.956777	+	0.290823i	$0.906071\pi$
$234$	−1.91924	+	7.81000i	−0.125465	+	0.510555i
$235$	0.170354	−	0.0338855i	0.0111127	−	0.00221044i
$236$	−2.35508	+	0.253233i	−0.153303	+	0.0164841i
$237$	1.23483	−	0.825087i	0.0802108	−	0.0535952i
$238$	−15.4231	−	16.8646i	−0.999731	−	1.09317i
$239$	7.81165	+	7.81165i	0.505293	+	0.505293i	0.913078	−	0.407785i	$-0.133699\pi$
$239$	7.81165	+	7.81165i	0.505293	+	0.505293i	−0.407785	+	0.913078i	$0.633699\pi$
$240$	−4.52591	−	6.51813i	−0.292146	−	0.420743i
$241$	−6.52981	+	6.52981i	−0.420622	+	0.420622i	−0.885418	−	0.464796i	$-0.846128\pi$
$241$	−6.52981	+	6.52981i	−0.420622	+	0.420622i	0.464796	+	0.885418i	$0.346128\pi$
$242$	8.60060	+	0.383990i	0.552867	+	0.0246838i
$243$	−7.46390	−	11.1705i	−0.478809	−	0.716589i
$244$	−9.68268	−	17.7319i	−0.619870	−	1.13517i
$245$	0.0654901	+	0.329241i	0.00418401	+	0.0210344i
$246$	−11.8241	+	7.15914i	−0.753878	+	0.456450i
$247$	−11.5321	−	4.77675i	−0.733769	−	0.303937i
$248$	22.8903	−	6.06107i	1.45354	−	0.384878i
$249$	−1.06170	+	0.439772i	−0.0672828	+	0.0278694i
$250$	13.5460	+	9.95287i	0.856726	+	0.629475i
$251$	−4.91732	+	7.35930i	−0.310379	+	0.464515i	−0.953562	−	0.301198i	$-0.902614\pi$
$251$	−4.91732	+	7.35930i	−0.310379	+	0.464515i	0.643183	+	0.765713i	$0.277614\pi$
$252$	4.83856	+	5.78948i	0.304801	+	0.364703i
$253$	12.0507	+	2.39703i	0.757619	+	0.150700i
$254$	2.87811	+	1.34554i	0.180589	+	0.0844265i
$255$	−12.3038			−0.770491
$256$	−14.9915	−	5.59052i	−0.936971	−	0.349407i
$257$	4.85309			0.302727			0.151364	−	0.988478i	$-0.451634\pi$
$257$	4.85309			0.302727			0.151364	+	0.988478i	$0.451634\pi$
$258$	−14.0049	−	6.54737i	−0.871906	−	0.407621i
$259$	16.6590	+	3.31368i	1.03514	+	0.205902i
$260$	−8.02153	−	9.59799i	−0.497474	−	0.595242i
$261$	3.44988	−	5.16310i	0.213542	−	0.319588i
$262$	−6.14889	−	4.51786i	−0.379880	−	0.279115i
$263$	15.7364	−	6.51821i	0.970346	−	0.401930i	0.159505	−	0.987197i	$-0.449010\pi$
$263$	15.7364	−	6.51821i	0.970346	−	0.401930i	0.810841	+	0.585267i	$0.199010\pi$
$264$	−7.54989	+	1.99912i	−0.464664	+	0.123037i
$265$	6.38544	+	2.64493i	0.392254	+	0.162477i
$266$	−10.0175	+	6.06529i	−0.614212	+	0.371887i
$267$	−1.29113	−	6.49093i	−0.0790156	−	0.397238i
$268$	−8.85517	−	16.2164i	−0.540915	−	0.990577i
$269$	1.78214	+	2.66716i	0.108659	+	0.162620i	0.881814	−	0.471598i	$-0.156322\pi$
$269$	1.78214	+	2.66716i	0.108659	+	0.162620i	−0.773155	+	0.634217i	$0.781322\pi$
$270$	12.4664	+	0.556587i	0.758682	+	0.0338728i
$271$	−4.32788	+	4.32788i	−0.262900	+	0.262900i	−0.826231	−	0.563331i	$-0.809520\pi$
$271$	−4.32788	+	4.32788i	−0.262900	+	0.262900i	0.563331	+	0.826231i	$0.309520\pi$
$272$	−20.3774	+	14.1492i	−1.23556	+	0.857919i
$273$	−9.01561	−	9.01561i	−0.545649	−	0.545649i
$274$	6.20244	+	6.78216i	0.374703	+	0.409725i
$275$	4.54150	−	3.03453i	0.273863	−	0.182989i
$276$	13.7337	−	1.47674i	0.826672	−	0.0888891i
$277$	3.82789	−	0.761415i	0.229996	−	0.0457490i	−0.0787468	−	0.996895i	$-0.525092\pi$
$277$	3.82789	−	0.761415i	0.229996	−	0.0457490i	0.308742	+	0.951146i	$0.400092\pi$
$278$	0.606580	−	2.46836i	0.0363802	−	0.148043i
$279$	−4.63866	+	11.1987i	−0.277709	+	0.670449i
$280$	−11.7125	+	0.732956i	−0.699953	+	0.0438025i
$281$	2.18086	+	5.26507i	0.130099	+	0.314088i	0.975484	−	0.220070i	$-0.0706287\pi$
$281$	2.18086	+	5.26507i	0.130099	+	0.314088i	−0.845385	+	0.534158i	$0.820629\pi$
$282$	−0.0290485	−	0.189974i	−0.00172981	−	0.0113128i
$283$	−18.8263	−	12.5793i	−1.11911	−	0.747764i	−0.148615	−	0.988895i	$-0.547482\pi$
$283$	−18.8263	−	12.5793i	−1.11911	−	0.747764i	−0.970492	+	0.241131i	$0.922482\pi$
$284$	19.0832	+	9.98186i	1.13238	+	0.592314i
$285$	−1.22998	+	6.18351i	−0.0728576	+	0.366280i
$286$	−11.5729	+	4.19928i	−0.684317	+	0.248309i
$287$			20.4418i			1.20664i
$288$	6.92929	−	4.36666i	0.408313	−	0.257308i
$289$			21.4647i			1.26263i
$290$	3.29433	+	9.07889i	0.193450	+	0.533131i
$291$	1.43578	−	7.21816i	0.0841670	−	0.423136i
$292$	−7.00448	−	22.3688i	−0.409906	−	1.30903i
$293$	−5.52242	−	3.68996i	−0.322623	−	0.215570i	0.383703	−	0.923457i	$-0.374649\pi$
$293$	−5.52242	−	3.68996i	−0.322623	−	0.215570i	−0.706326	+	0.707887i	$0.749649\pi$
$294$	0.367161	−	0.0561417i	0.0214133	−	0.00327425i
$295$	0.721696	+	1.74233i	0.0420187	+	0.101442i
$296$	5.97818	−	17.4418i	0.347475	−	1.01379i
$297$	4.70005	−	11.3469i	0.272725	−	0.658415i
$298$	−4.61540	−	1.13420i	−0.267363	−	0.0657023i
$299$	21.3551	−	4.24780i	1.23500	−	0.245657i
$300$	3.85286	−	4.78126i	0.222445	−	0.276046i
$301$	−19.0099	+	12.7020i	−1.09571	+	0.732132i
$302$	−3.60906	+	3.30057i	−0.207678	+	0.189926i
$303$	0.455432	+	0.455432i	0.0261639	+	0.0261639i
$304$	5.07389	+	11.6555i	0.291008	+	0.668491i
$305$	−11.3742	+	11.3742i	−0.651283	+	0.651283i
$306$	0.566417	−	12.6866i	0.0323799	−	0.725244i
$307$	1.13328	+	1.69608i	0.0646798	+	0.0968002i	0.862400	−	0.506228i	$-0.168961\pi$
$307$	1.13328	+	1.69608i	0.0646798	+	0.0968002i	−0.797720	+	0.603028i	$0.793961\pi$
$308$	−3.25387	+	11.0823i	−0.185407	+	0.631472i
$309$	−2.12118	−	10.6639i	−0.120670	−	0.606649i
$310$	−9.76454	−	16.1272i	−0.554589	−	0.915965i
$311$	24.3362	+	10.0804i	1.37998	+	0.571607i	0.944476	−	0.328580i	$-0.106570\pi$
$311$	24.3362	+	10.0804i	1.37998	+	0.571607i	0.435505	+	0.900186i	$0.356570\pi$
$312$	−11.0051	+	8.39300i	−0.623040	+	0.475160i
$313$	10.8933	−	4.51214i	0.615725	−	0.255041i	−0.0529494	−	0.998597i	$-0.516862\pi$
$313$	10.8933	−	4.51214i	0.615725	−	0.255041i	0.668674	+	0.743556i	$0.266862\pi$
$314$	−2.59857	+	3.53669i	−0.146646	+	0.199587i
$315$	3.33750	−	4.99493i	0.188047	−	0.281432i
$316$	−2.37463	−	0.212463i	−0.133583	−	0.0119520i
$317$	13.7108	+	2.72726i	0.770078	+	0.153178i	0.564467	−	0.825456i	$-0.309082\pi$
$317$	13.7108	+	2.72726i	0.770078	+	0.153178i	0.205611	+	0.978634i	$0.434082\pi$
$318$	3.23873	−	6.92767i	0.181619	−	0.388484i
$319$	9.50562			0.532213
$320$	−0.908205	+	12.7065i	−0.0507702	+	0.710316i
$321$	23.8327			1.33021
$322$	8.65123	−	18.5051i	0.482114	−	1.03125i
$323$	19.3313	+	3.84523i	1.07562	+	0.213954i
$324$	0.456282	−	5.09970i	0.0253490	−	0.283317i
$325$	5.37753	−	8.04804i	0.298292	−	0.446425i
$326$	0.404841	−	0.550996i	0.0224221	−	0.0305168i
$327$	−14.6908	+	6.08514i	−0.812405	+	0.336509i
$328$	21.9914	+	2.96130i	1.21427	+	0.163510i
$329$	−0.262578	−	0.108764i	−0.0144764	−	0.00599633i
$330$	3.22063	+	5.31923i	0.177290	+	0.292814i
$331$	6.48019	+	32.5781i	0.356184	+	1.79066i	0.578501	+	0.815682i	$0.303638\pi$
$331$	6.48019	+	32.5781i	0.356184	+	1.79066i	−0.222318	+	0.974974i	$0.571362\pi$
$332$	1.77010	+	0.519720i	0.0971470	+	0.0285233i
$333$	5.24368	+	7.84772i	0.287352	+	0.430052i
$334$	0.561406	−	12.5743i	0.0307188	−	0.688038i
$335$	−10.4021	+	10.4021i	−0.568328	+	0.568328i
$336$	0.232159	+	12.9826i	0.0126653	+	0.708261i
$337$	4.67117	+	4.67117i	0.254455	+	0.254455i	0.822794	−	0.568339i	$-0.192414\pi$
$337$	4.67117	+	4.67117i	0.254455	+	0.254455i	−0.568339	+	0.822794i	$0.692414\pi$
$338$	−2.53260	+	2.31612i	−0.137755	+	0.125980i
$339$	−17.0187	+	11.3715i	−0.924329	+	0.617617i
$340$	15.3797	+	12.3933i	0.834080	+	0.672123i
$341$	−18.1988	+	3.61996i	−0.985520	+	0.196032i
$342$	−6.31929	−	1.55291i	−0.341708	−	0.0839719i
$343$	7.19006	−	17.3584i	0.388227	−	0.937263i
$344$	10.9110	+	22.2910i	0.588284	+	1.20185i
$345$	−4.20859	−	10.1604i	−0.226583	−	0.547019i
$346$	18.0610	−	2.76166i	0.970965	−	0.148468i
$347$	−11.6056	−	7.75460i	−0.623020	−	0.416289i	0.203596	−	0.979055i	$-0.434737\pi$
$347$	−11.6056	−	7.75460i	−0.623020	−	0.416289i	−0.826616	+	0.562766i	$0.809737\pi$
$348$	10.1980	−	3.19337i	0.546670	−	0.171182i
$349$	3.22983	−	16.2374i	0.172889	−	0.869170i	−0.792803	−	0.609478i	$-0.791379\pi$
$349$	3.22983	−	16.2374i	0.172889	−	0.869170i	0.965692	−	0.259692i	$-0.0836210\pi$
$350$	−3.09746	−	8.53633i	−0.165566	−	0.456286i
$351$		−	21.7647i		−	1.16172i
$352$	11.4510	+	5.10597i	0.610342	+	0.272149i
$353$		−	29.4440i		−	1.56715i	−0.621299	−	0.783573i	$-0.713395\pi$
$353$		−	29.4440i		−	1.56715i	0.621299	−	0.783573i	$-0.286605\pi$
$354$	1.96151	−	0.711747i	0.104253	−	0.0378289i
$355$	3.34516	−	16.8172i	0.177542	−	0.892566i
$356$	−4.92428	+	9.41417i	−0.260986	+	0.498950i
$357$	16.7398	+	11.1852i	0.885964	+	0.591982i
$358$	3.42211	+	22.3803i	0.180864	+	1.18283i
$359$	−6.81567	−	16.4545i	−0.359717	−	0.868435i	−0.995339	−	0.0964342i	$-0.969256\pi$
$359$	−6.81567	−	16.4545i	−0.359717	−	0.868435i	0.635622	−	0.772001i	$-0.280744\pi$
$360$	−4.89008	−	4.31409i	−0.257730	−	0.227373i
$361$	−3.40598	+	8.22277i	−0.179262	+	0.432777i
$362$	0.469925	−	1.91227i	0.0246987	−	0.100507i
$363$	−7.43847	+	1.47960i	−0.390418	+	0.0776590i
$364$	2.18824	+	20.3507i	0.114695	+	1.06667i
$365$	−15.5172	+	10.3683i	−0.812208	+	0.542700i
$366$	12.0112	+	13.1339i	0.627836	+	0.686518i
$367$	−21.7396	−	21.7396i	−1.13480	−	1.13480i	−0.989369	−	0.145427i	$-0.953545\pi$
$367$	−21.7396	−	21.7396i	−1.13480	−	1.13480i	−0.145427	−	0.989369i	$-0.546455\pi$
$368$	−18.6546	−	11.9878i	−0.972438	−	0.624906i
$369$	−8.03204	+	8.03204i	−0.418131	+	0.418131i
$370$	−14.6653	−	0.654762i	−0.762414	−	0.0340394i
$371$	−6.28319	−	9.40346i	−0.326207	−	0.488203i
$372$	−18.3083	+	9.99743i	−0.949239	+	0.518343i
$373$	−2.98424	−	15.0028i	−0.154518	−	0.776816i	−0.977858	−	0.209268i	$-0.932892\pi$
$373$	−2.98424	−	15.0028i	−0.154518	−	0.776816i	0.823340	−	0.567548i	$-0.192108\pi$
$374$	16.6293	−	10.0685i	0.859880	−	0.520631i
$375$	−13.6809	−	5.66682i	−0.706479	−	0.292633i
$376$	−0.155047	+	0.266728i	−0.00799593	+	0.0137554i
$377$	15.5628	−	6.44631i	0.801523	−	0.332002i
$378$	−16.4551	−	12.0903i	−0.846359	−	0.621858i
$379$	−9.23758	+	13.8250i	−0.474503	+	0.710143i	−0.989093	−	0.147293i	$-0.952944\pi$
$379$	−9.23758	+	13.8250i	−0.474503	+	0.710143i	0.514590	+	0.857436i	$0.327944\pi$
$380$	7.76601	−	6.49045i	0.398388	−	0.332953i
$381$	−2.74508	−	0.546029i	−0.140634	−	0.0279739i
$382$	−4.56816	−	2.13564i	−0.233727	−	0.109269i
$383$	−10.4632			−0.534645			−0.267322	−	0.963607i	$-0.586139\pi$
$383$	−10.4632			−0.534645			−0.267322	+	0.963607i	$0.586139\pi$
$384$	14.0004	+	1.63097i	0.714456	+	0.0832301i
$385$	9.19599			0.468671
$386$	−4.95476	−	2.31638i	−0.252190	−	0.117901i
$387$	−12.4603	−	2.47851i	−0.633394	−	0.125990i
$388$	−9.06544	+	7.57645i	−0.460228	+	0.384636i
$389$	5.64815	−	8.45306i	0.286373	−	0.428587i	−0.660194	−	0.751095i	$-0.729526\pi$
$389$	5.64815	−	8.45306i	0.286373	−	0.428587i	0.946567	+	0.322508i	$0.104526\pi$
$390$	8.88014	+	6.52463i	0.449663	+	0.330388i
$391$	−31.7641	+	13.1571i	−1.60638	+	0.665385i
$392$	−0.515502	−	0.299658i	−0.0260368	−	0.0151350i
$393$	6.21011	+	2.57231i	0.313259	+	0.129756i
$394$	−21.8457	+	13.2269i	−1.10057	+	0.666363i
$395$	0.370319	+	1.86172i	0.0186328	+	0.0936733i
$396$	−5.63300	+	3.07596i	−0.283069	+	0.154573i
$397$	−1.45561	−	2.17847i	−0.0730549	−	0.109334i	0.793143	−	0.609035i	$-0.208443\pi$
$397$	−1.45561	−	2.17847i	−0.0730549	−	0.109334i	−0.866198	+	0.499701i	$0.833443\pi$
$398$	−19.7942	−	0.883749i	−0.992192	−	0.0442983i
$399$	7.29478	−	7.29478i	0.365196	−	0.365196i
$400$	−9.63214	+	2.09565i	−0.481607	+	0.104783i
$401$	−14.8490	−	14.8490i	−0.741524	−	0.741524i	0.231347	−	0.972871i	$-0.425687\pi$
$401$	−14.8490	−	14.8490i	−0.741524	−	0.741524i	−0.972871	+	0.231347i	$0.925687\pi$
$402$	10.9847	+	12.0114i	0.547867	+	0.599075i
$403$	−27.3404	+	18.2683i	−1.36192	+	0.910009i
$404$	−0.110541	−	1.02804i	−0.00549964	−	0.0511468i
$405$	−3.99819	+	0.795289i	−0.198671	+	0.0395182i
$406$	3.77141	−	15.3471i	0.187172	−	0.761661i
$407$	−5.52908	+	13.3484i	−0.274066	+	0.661655i
$408$	14.4581	−	16.3884i	0.715782	−	0.811348i
$409$	−8.95302	−	21.6145i	−0.442698	−	1.06877i	−0.974998	−	0.222212i	$-0.928672\pi$
$409$	−8.95302	−	21.6145i	−0.442698	−	1.06877i	0.532300	−	0.846556i	$-0.321328\pi$
$410$	−2.67041	−	17.4642i	−0.131882	−	0.862496i
$411$	−6.73195	−	4.49814i	−0.332062	−	0.221877i
$412$	−8.09008	+	15.4665i	−0.398570	+	0.761980i
$413$	0.602027	−	3.02660i	0.0296238	−	0.148929i
$414$	10.6703	−	3.87179i	0.524418	−	0.190288i
$415$		−	1.46882i		−	0.0721014i
$416$	22.2104	+	0.593981i	1.08896	+	0.0291223i
$417$			2.23918i			0.109653i
$418$	−3.39776	−	9.36393i	−0.166190	−	0.458005i
$419$	−2.28680	+	11.4965i	−0.111718	+	0.561643i	0.883864	+	0.467744i	$0.154933\pi$
$419$	−2.28680	+	11.4965i	−0.111718	+	0.561643i	−0.995582	+	0.0938989i	$0.970067\pi$
$420$	9.86582	−	3.08935i	0.481403	−	0.150745i
$421$	27.2435	+	18.2035i	1.32777	+	0.887185i	0.998374	−	0.0570087i	$-0.0181563\pi$
$421$	27.2435	+	18.2035i	1.32777	+	0.887185i	0.329392	+	0.944193i	$0.393156\pi$
$422$	26.3972	−	4.03634i	1.28500	−	0.196486i
$423$	−0.0604374	−	0.145909i	−0.00293856	−	0.00709432i
$424$	−11.0265	+	5.39726i	−0.535495	+	0.262114i
$425$	−5.84894	+	14.1206i	−0.283715	+	0.684949i
$426$	−18.4240	−	4.52754i	−0.892645	−	0.219360i
$427$	25.8152	−	5.13496i	1.24928	−	0.248498i
$428$	−29.7908	−	24.0062i	−1.43999	−	1.16038i
$429$	9.01767	−	6.02541i	0.435377	−	0.290910i
$430$	14.5816	−	13.3352i	0.703186	−	0.643080i
$431$	11.1659	+	11.1659i	0.537842	+	0.537842i	0.922895	−	0.385053i	$-0.125817\pi$
$431$	11.1659	+	11.1659i	0.537842	+	0.537842i	−0.385053	+	0.922895i	$0.625817\pi$
$432$	−15.3906	+	15.9510i	−0.740480	+	0.767445i
$433$	15.3110	−	15.3110i	0.735802	−	0.735802i	−0.235961	−	0.971763i	$-0.575824\pi$
$433$	15.3110	−	15.3110i	0.735802	−	0.735802i	0.971763	+	0.235961i	$0.0758237\pi$
$434$	−1.37596	+	30.8186i	−0.0660480	+	1.47934i
$435$	−4.72693	−	7.07435i	−0.226639	−	0.339189i
$436$	24.4930	+	7.19138i	1.17300	+	0.344405i
$437$	3.43701	+	17.2790i	0.164415	+	0.826568i
$438$	10.6949	+	17.6638i	0.511020	+	0.844007i
$439$	37.8088	+	15.6609i	1.80452	+	0.747455i	0.984565	+	0.175021i	$0.0559995\pi$
$439$	37.8088	+	15.6609i	1.80452	+	0.747455i	0.819951	+	0.572434i	$0.194001\pi$
$440$	1.33218	−	9.89310i	0.0635090	−	0.471635i
$441$	0.281996	−	0.116807i	0.0134284	−	0.00556222i
$442$	20.3977	−	27.7616i	0.970219	−	1.32049i
$443$	18.8638	−	28.2317i	0.896247	−	1.34133i	−0.0433550	−	0.999060i	$-0.513805\pi$
$443$	18.8638	−	28.2317i	0.896247	−	1.34133i	0.939602	−	0.342269i	$-0.111195\pi$
$444$	−1.44749	+	16.1781i	−0.0686950	+	0.767780i
$445$	8.29633	+	1.65024i	0.393284	+	0.0782290i
$446$	−15.5550	+	33.2722i	−0.736549	+	1.57549i
$447$	4.18688			0.198033
$448$	12.7870	−	16.4621i	0.604127	−	0.777762i
$449$	−2.12507			−0.100288			−0.0501442	−	0.998742i	$-0.515968\pi$
$449$	−2.12507			−0.100288			−0.0501442	+	0.998742i	$0.515968\pi$
$450$	2.13705	−	4.57118i	0.100742	−	0.215487i
$451$	−17.0542	−	3.39229i	−0.803050	−	0.159737i
$452$	32.7277	+	2.92822i	1.53938	+	0.137732i
$453$	2.39365	−	3.58234i	0.112463	−	0.168313i
$454$	−0.918655	+	1.25031i	−0.0431146	+	0.0586797i
$455$	15.0558	−	6.23633i	0.705828	−	0.292364i
$456$	−6.79101	−	8.90453i	−0.318018	−	0.416993i
$457$	−32.1519	−	13.3177i	−1.50400	−	0.622978i	−0.529691	−	0.848190i	$-0.677692\pi$
$457$	−32.1519	−	13.3177i	−1.50400	−	0.622978i	−0.974310	+	0.225213i	$0.927692\pi$
$458$	−11.5224	−	19.0305i	−0.538406	−	0.889237i
$459$	6.70476	+	33.7071i	0.312951	+	1.57331i
$460$	−4.97368	+	16.9398i	−0.231899	+	0.789820i
$461$	7.57489	+	11.3366i	0.352798	+	0.528000i	0.964844	−	0.262822i	$-0.0846534\pi$
$461$	7.57489	+	11.3366i	0.352798	+	0.528000i	−0.612046	+	0.790822i	$0.709653\pi$
$462$	0.453830	−	10.1649i	0.0211141	−	0.472913i
$463$	16.2876	−	16.2876i	0.756949	−	0.756949i	−0.218817	−	0.975766i	$-0.570220\pi$
$463$	16.2876	−	16.2876i	0.756949	−	0.756949i	0.975766	+	0.218817i	$0.0702197\pi$
$464$	−15.9641	−	6.28055i	−0.741115	−	0.291567i
$465$	11.7439	+	11.7439i	0.544611	+	0.544611i
$466$	−20.2256	+	18.4968i	−0.936932	+	0.856846i
$467$	−13.6451	+	9.11734i	−0.631418	+	0.421900i	−0.829672	−	0.558250i	$-0.811473\pi$
$467$	−13.6451	+	9.11734i	−0.631418	+	0.421900i	0.198254	+	0.980151i	$0.436473\pi$
$468$	−7.13646	+	8.85608i	−0.329883	+	0.409372i
$469$	23.6089	−	4.69611i	1.09016	−	0.216846i
$470$	0.238539	+	0.0586191i	0.0110030	+	0.00270390i
$471$	1.47953	−	3.57191i	0.0681733	−	0.164585i
$472$	−3.16882	−	1.08611i	−0.145857	−	0.0499924i
$473$	−7.44237	−	17.9675i	−0.342201	−	0.826145i
$474$	2.07614	−	0.317458i	0.0953604	−	0.0145813i
$475$	6.51190	+	4.35111i	0.298786	+	0.199643i
$476$	−9.65810	−	30.8431i	−0.442678	−	1.41369i
$477$	1.22602	−	6.16364i	0.0561358	−	0.282214i
$478$	5.32903	+	14.6863i	0.243744	+	0.671738i
$479$		−	4.14550i		−	0.189413i	−0.995505	−	0.0947064i	$-0.969809\pi$
$479$		−	4.14550i		−	0.189413i	0.995505	−	0.0947064i	$-0.0301912\pi$
$480$	−1.89433	−	11.0612i	−0.0864638	−	0.504875i
$481$			25.6038i			1.16743i
$482$	−12.2764	+	4.45457i	−0.559175	+	0.202900i
$483$	−3.51074	+	17.6497i	−0.159744	+	0.803088i
$484$	10.7884	+	5.64312i	0.490384	+	0.256506i
$485$	7.82129	+	5.22602i	0.355146	+	0.237301i
$486$	−2.87178	−	18.7812i	−0.130267	−	0.851932i
$487$	0.228313	+	0.551195i	0.0103458	+	0.0249770i	0.928968	−	0.370160i	$-0.120697\pi$
$487$	0.228313	+	0.551195i	0.0103458	+	0.0249770i	−0.918622	+	0.395137i	$0.870697\pi$
$488$	−1.78451	−	28.5160i	−0.0807808	−	1.29086i
$489$	−0.230502	+	0.556482i	−0.0104237	+	0.0251650i
$490$	−0.113293	+	0.461023i	−0.00511804	+	0.0208269i
$491$	−31.2490	+	6.21581i	−1.41025	+	0.280516i	−0.840726	−	0.541461i	$-0.817871\pi$
$491$	−31.2490	+	6.21581i	−1.41025	+	0.280516i	−0.569521	+	0.821977i	$0.692871\pi$
$492$	−19.4360	+	2.08989i	−0.876243	+	0.0942193i
$493$	−22.1162	+	14.7776i	−0.996065	+	0.665550i
$494$	−11.9131	−	13.0266i	−0.535995	−	0.586093i
$495$	3.61331	+	3.61331i	0.162406	+	0.162406i
$496$	32.9555	+	5.94480i	1.47975	+	0.266929i
$497$	−19.8395	+	19.8395i	−0.889925	+	0.889925i
$498$	−1.62357	−	0.0724874i	−0.0727539	−	0.00324824i
$499$	4.65337	+	6.96426i	0.208313	+	0.311763i	0.920884	−	0.389838i	$-0.127469\pi$
$499$	4.65337	+	6.96426i	0.208313	+	0.311763i	−0.712570	+	0.701601i	$0.752469\pi$
$500$	11.3930	+	20.8640i	0.509512	+	0.933068i
$501$	2.16323	+	10.8753i	0.0966459	+	0.485871i
$502$	−10.7074	+	6.48302i	−0.477896	+	0.289351i
$503$	16.9351	+	7.01476i	0.755100	+	0.312772i	0.726820	−	0.686828i	$-0.240997\pi$
$503$	16.9351	+	7.01476i	0.755100	+	0.312772i	0.0282792	+	0.999600i	$0.490997\pi$
$504$	2.73129	+	10.3150i	0.121661	+	0.459467i
$505$	−0.760560	+	0.315034i	−0.0338445	+	0.0140188i
$506$	14.0027	+	10.2884i	0.622498	+	0.457377i
$507$	1.67970	−	2.51385i	0.0745982	−	0.111644i
$508$	2.88133	+	3.44760i	0.127839	+	0.152962i
$509$	−13.8146	−	2.74790i	−0.612322	−	0.121798i	−0.120819	−	0.992675i	$-0.538552\pi$
$509$	−13.8146	−	2.74790i	−0.612322	−	0.121798i	−0.491503	+	0.870876i	$0.663552\pi$
$510$	−15.7626	−	7.36913i	−0.697981	−	0.326311i
$511$	30.5375			1.35090
$512$	−15.8577	−	16.1411i	−0.700817	−	0.713342i
$513$	17.6105			0.777521
$514$	6.21741	+	2.90668i	0.274238	+	0.128208i
$515$	13.6300	+	2.71118i	0.600610	+	0.119469i
$516$	−14.0205	−	16.7760i	−0.617220	−	0.738521i
$517$	0.134314	−	0.201015i	0.00590712	−	0.00884062i
$518$	19.3576	+	14.2229i	0.850523	+	0.624917i
$519$	−14.8704	+	6.15954i	−0.652740	+	0.270374i
$520$	−4.52802	−	17.1006i	−0.198567	−	0.749910i
$521$	1.55454	+	0.643912i	0.0681057	+	0.0282103i	0.416476	−	0.909147i	$-0.363265\pi$
$521$	1.55454	+	0.643912i	0.0681057	+	0.0282103i	−0.348371	+	0.937357i	$0.613265\pi$
$522$	7.51208	−	4.54833i	0.328795	−	0.199075i
$523$	−5.90096	−	29.6661i	−0.258031	−	1.29721i	−0.864714	−	0.502265i	$-0.832500\pi$
$523$	−5.90096	−	29.6661i	−0.258031	−	1.29721i	0.606683	−	0.794944i	$-0.292500\pi$
$524$	−5.17159	−	9.47072i	−0.225922	−	0.413730i
$525$	4.44444	+	6.65158i	0.193971	+	0.290299i
$526$	24.0642	+	1.07439i	1.04925	+	0.0468458i
$527$	36.7145	−	36.7145i	1.59931	−	1.59931i
$528$	−10.8697	−	1.96077i	−0.473042	−	0.0853314i
$529$	−5.46686	−	5.46686i	−0.237690	−	0.237690i
$530$	6.59640	+	7.21294i	0.286529	+	0.313310i
$531$	1.42577	−	0.952668i	0.0618731	−	0.0413423i
$532$	−16.4664	+	1.77057i	−0.713907	+	0.0767640i
$533$	−30.2219	+	6.01150i	−1.30905	+	0.260387i
$534$	2.23354	−	9.08898i	0.0966548	−	0.393319i
$535$	−11.6571	+	28.1428i	−0.503982	+	1.21672i
$536$	−1.63200	−	26.0789i	−0.0704916	−	1.12644i
$537$	−7.63259	−	18.4267i	−0.329371	−	0.795171i
$538$	0.685690	+	4.48435i	0.0295622	+	0.193334i
$539$	0.388500	+	0.259587i	0.0167339	+	0.0111812i
$540$	15.6377	+	8.17961i	0.672938	+	0.351994i
$541$	−5.86328	+	29.4767i	−0.252082	+	1.26730i	0.622575	+	0.782560i	$0.286087\pi$
$541$	−5.86328	+	29.4767i	−0.252082	+	1.26730i	−0.874657	+	0.484742i	$0.838913\pi$
$542$	−8.13667	+	2.95244i	−0.349500	+	0.126818i
$543$			1.73473i			0.0744442i
$544$	−34.5803	+	5.92216i	−1.48262	+	0.253910i
$545$		−	20.3241i		−	0.870587i
$546$	−6.15036	−	16.9499i	−0.263211	−	0.725387i
$547$	8.35722	−	42.0146i	0.357329	−	1.79641i	−0.215243	−	0.976560i	$-0.569054\pi$
$547$	8.35722	−	42.0146i	0.357329	−	1.79641i	0.572572	−	0.819854i	$-0.305946\pi$
$548$	3.88403	+	12.4036i	0.165917	+	0.529857i
$549$	12.1610	+	8.12572i	0.519019	+	0.346797i
$550$	7.63571	−	1.16756i	0.325588	−	0.0497848i
$551$	5.21589	+	12.5923i	0.222204	+	0.536449i
$552$	18.4790	+	6.33369i	0.786521	+	0.269580i
$553$	1.18863	−	2.86960i	0.0505456	−	0.122028i
$554$	5.36004	+	1.31719i	0.227726	+	0.0559618i
$555$	12.6837	−	2.52295i	0.538394	−	0.107093i
$556$	2.25549	−	2.79898i	0.0956540	−	0.118703i
$557$	−6.44120	+	4.30387i	−0.272923	+	0.182361i	−0.684498	−	0.729015i	$-0.739979\pi$
$557$	−6.44120	+	4.30387i	−0.272923	+	0.182361i	0.411576	+	0.911376i	$0.364979\pi$
$558$	−12.6500	+	11.5687i	−0.535516	+	0.489741i
$559$	−24.3695	−	24.3695i	−1.03072	−	1.03072i
$560$	−15.4441	−	6.07598i	−0.652632	−	0.256757i
$561$	−12.1095	+	12.1095i	−0.511264	+	0.511264i
$562$	−0.359470	+	8.05140i	−0.0151633	+	0.339628i
$563$	−1.09582	−	1.64001i	−0.0461832	−	0.0691181i	0.807659	−	0.589649i	$-0.200734\pi$
$563$	−1.09582	−	1.64001i	−0.0461832	−	0.0691181i	−0.853843	+	0.520531i	$0.825734\pi$
$564$	0.0765672	−	0.260779i	0.00322406	−	0.0109808i
$565$	−5.10382	−	25.6586i	−0.214719	−	1.07947i
$566$	−16.5846	−	27.3914i	−0.697105	−	1.15135i
$567$	6.16269	+	2.55267i	0.258809	+	0.107202i
$568$	18.4695	+	24.2176i	0.774961	+	1.01615i
$569$	−35.9156	+	14.8767i	−1.50566	+	0.623664i	−0.974657	−	0.223706i	$-0.928184\pi$
$569$	−35.9156	+	14.8767i	−1.50566	+	0.623664i	−0.531002	+	0.847370i	$0.678184\pi$
$570$	−5.27927	+	7.18517i	−0.221124	+	0.300954i
$571$	−7.30296	+	10.9297i	−0.305619	+	0.457392i	−0.952209	−	0.305446i	$-0.901194\pi$
$571$	−7.30296	+	10.9297i	−0.305619	+	0.457392i	0.646590	+	0.762838i	$0.276194\pi$
$572$	−17.3414	−	1.55157i	−0.725079	−	0.0648744i
$573$	4.35700	+	0.866660i	0.182016	+	0.0362053i
$574$	−12.2433	+	26.1885i	−0.511024	+	1.09308i
$575$	−13.6614			−0.569722
$576$	11.4926	−	1.44405i	0.478859	−	0.0601689i
$577$	3.92683			0.163476			0.0817381	−	0.996654i	$-0.473953\pi$
$577$	3.92683			0.163476			0.0817381	+	0.996654i	$0.473953\pi$
$578$	−12.8559	+	27.4990i	−0.534736	+	1.14381i
$579$	4.72573	+	0.940005i	0.196394	+	0.0390653i
$580$	−1.21720	+	13.6043i	−0.0505416	+	0.564886i
$581$	−1.33528	+	1.99839i	−0.0553968	+	0.0829072i
$582$	6.16261	−	8.38742i	0.255448	−	0.347670i
$583$	8.88781	−	3.68145i	0.368095	−	0.152470i
$584$	4.42381	−	32.8524i	0.183058	−	1.35944i
$585$	8.36617	+	3.46538i	0.345899	+	0.143276i
$586$	−4.86486	−	8.03486i	−0.200966	−	0.331917i
$587$	7.25567	+	36.4767i	0.299473	+	1.50555i	0.778439	+	0.627721i	$0.216012\pi$
$587$	7.25567	+	36.4767i	0.299473	+	1.50555i	−0.478965	+	0.877834i	$0.658988\pi$
$588$	0.504004	+	0.147981i	0.0207848	+	0.00610262i
$589$	−14.7814	−	22.1219i	−0.609057	−	0.911518i
$590$	−0.118957	+	2.66439i	−0.00489737	+	0.109691i
$591$	15.9082	−	15.9082i	0.654374	−	0.654374i
$592$	18.1053	−	18.7646i	0.744123	−	0.771221i
$593$	6.42206	+	6.42206i	0.263723	+	0.263723i	0.826565	−	0.562842i	$-0.190292\pi$
$593$	6.42206	+	6.42206i	0.263723	+	0.263723i	−0.562842	+	0.826565i	$0.690292\pi$
$594$	12.8174	−	11.7218i	0.525904	−	0.480951i
$595$	−21.3958	+	14.2962i	−0.877144	+	0.586089i
$596$	−5.23360	−	4.21737i	−0.214376	−	0.172750i
$597$	17.1195	−	3.40529i	0.700656	−	0.139369i
$598$	29.9027	+	7.34834i	1.22281	+	0.300496i
$599$	12.0671	−	29.1324i	0.493046	−	1.19032i	−0.460116	−	0.887859i	$-0.652192\pi$
$599$	12.0671	−	29.1324i	0.493046	−	1.19032i	0.953162	−	0.302460i	$-0.0978079\pi$
$600$	7.79965	−	3.81778i	0.318419	−	0.155860i
$601$	−13.5123	−	32.6215i	−0.551177	−	1.33066i	−0.916596	−	0.399815i	$-0.869074\pi$
$601$	−13.5123	−	32.6215i	−0.551177	−	1.33066i	0.365419	−	0.930843i	$-0.380926\pi$
$602$	−31.9617	+	4.88718i	−1.30266	+	0.199187i
$603$	11.1217	+	7.43128i	0.452910	+	0.302625i
$604$	−6.60048	+	2.06685i	−0.268570	+	0.0840989i
$605$	1.89114	−	9.50742i	0.0768859	−	0.386532i
$606$	0.310692	+	0.856239i	0.0126210	+	0.0347823i
$607$			12.7147i			0.516076i	0.966135	+	0.258038i	$0.0830759\pi$
$607$			12.7147i			0.516076i	−0.966135	+	0.258038i	$0.916924\pi$
$608$	−0.480607	+	17.9711i	−0.0194912	+	0.728825i
$609$			13.9221i			0.564154i
$610$	−21.3841	+	7.75936i	−0.865817	+	0.314167i
$611$	0.0835811	−	0.420191i	0.00338133	−	0.0169991i
$612$	8.32407	−	15.9138i	0.336481	−	0.643279i
$613$	−0.425673	−	0.284426i	−0.0171928	−	0.0114878i	0.546944	−	0.837169i	$-0.315791\pi$
$613$	−0.425673	−	0.284426i	−0.0171928	−	0.0114878i	−0.564137	+	0.825681i	$0.690791\pi$
$614$	0.436038	+	2.85164i	0.0175971	+	0.115083i
$615$	5.95602	+	14.3791i	0.240170	+	0.579821i
$616$	−10.8062	+	12.2489i	−0.435393	+	0.493524i
$617$	4.10135	−	9.90154i	0.165114	−	0.398621i	−0.819567	−	0.572983i	$-0.805786\pi$
$617$	4.10135	−	9.90154i	0.165114	−	0.398621i	0.984682	+	0.174362i	$0.0557862\pi$
$618$	3.66947	−	14.9322i	0.147608	−	0.600663i
$619$	27.4882	−	5.46774i	1.10484	−	0.219767i	0.391220	−	0.920297i	$-0.372053\pi$
$619$	27.4882	−	5.46774i	1.10484	−	0.219767i	0.713623	+	0.700530i	$0.247053\pi$
$620$	−2.85045	−	26.5093i	−0.114477	−	1.06464i
$621$	−25.5419	+	17.0665i	−1.02496	+	0.684857i
$622$	25.1402	+	27.4900i	1.00803	+	1.10225i
$623$	−9.78730	−	9.78730i	−0.392120	−	0.392120i
$624$	−19.1257	+	4.16116i	−0.765642	+	0.166580i
$625$	4.67046	−	4.67046i	0.186818	−	0.186818i
$626$	16.6581	+	0.743734i	0.665792	+	0.0297256i
$627$	4.87533	+	7.29645i	0.194702	+	0.291392i
$628$	−5.44733	+	2.97457i	−0.217372	+	0.118698i
$629$	−7.88739	−	39.6526i	−0.314491	−	1.58105i
$630$	7.26738	−	4.40018i	0.289539	−	0.175307i
$631$	−39.9593	−	16.5517i	−1.59075	−	0.658911i	−0.600683	−	0.799487i	$-0.705105\pi$
$631$	−39.9593	−	16.5517i	−1.59075	−	0.658911i	−0.990070	+	0.140576i	$0.955105\pi$
$632$	−2.91494	−	1.69444i	−0.115950	−	0.0674011i
$633$	−21.7341	+	9.00254i	−0.863852	+	0.357819i
$634$	15.9318	+	11.7058i	0.632735	+	0.464898i
$635$	1.98746	−	2.97445i	0.0788700	−	0.118037i
$636$	8.29842	−	6.93542i	0.329054	−	0.275007i
$637$	0.812099	+	0.161536i	0.0321765	+	0.00640031i
$638$	12.1779	+	5.69324i	0.482127	+	0.225397i
$639$	−15.5908			−0.616763
$640$	−8.77388	+	15.7347i	−0.346818	+	0.621967i
$641$	5.29159			0.209005			0.104503	−	0.994525i	$-0.466675\pi$
$641$	5.29159			0.209005			0.104503	+	0.994525i	$0.466675\pi$
$642$	30.5326	+	14.2742i	1.20503	+	0.563358i
$643$	−20.3921	−	4.05624i	−0.804185	−	0.159962i	−0.224151	−	0.974554i	$-0.571961\pi$
$643$	−20.3921	−	4.05624i	−0.804185	−	0.159962i	−0.580034	+	0.814592i	$0.696961\pi$
$644$	22.1666	−	18.5258i	0.873487	−	0.730018i
$645$	−9.67097	+	14.4736i	−0.380794	+	0.569899i
$646$	22.4627	+	16.5044i	0.883783	+	0.649355i
$647$	−10.8250	+	4.48386i	−0.425575	+	0.176279i	−0.585182	−	0.810902i	$-0.698977\pi$
$647$	−10.8250	+	4.48386i	−0.425575	+	0.176279i	0.159608	+	0.987181i	$0.448977\pi$
$648$	3.63894	−	6.26007i	0.142951	−	0.245919i
$649$	2.42512	+	1.00452i	0.0951944	+	0.0394308i
$650$	11.7095	−	7.08975i	0.459285	−	0.278083i
$651$	−5.30188	−	26.6543i	−0.207797	−	1.04467i
$652$	0.848661	−	0.463421i	0.0332361	−	0.0181490i
$653$	20.9476	+	31.3503i	0.819744	+	1.22683i	0.971175	+	0.238366i	$0.0766117\pi$
$653$	20.9476	+	31.3503i	0.819744	+	1.22683i	−0.151431	+	0.988468i	$0.548388\pi$
$654$	−22.4654	−	1.00301i	−0.878466	−	0.0392208i
$655$	−6.07503	+	6.07503i	−0.237371	+	0.237371i
$656$	26.4001	+	16.9652i	1.03075	+	0.662378i
$657$	11.9989	+	11.9989i	0.468120	+	0.468120i
$658$	−0.271253	−	0.296607i	−0.0105746	−	0.0115629i
$659$	29.0678	−	19.4225i	1.13232	−	0.756594i	0.159283	−	0.987233i	$-0.449082\pi$
$659$	29.0678	−	19.4225i	1.13232	−	0.756594i	0.973039	+	0.230639i	$0.0740817\pi$
$660$	0.940162	+	8.74353i	0.0365957	+	0.340342i
$661$	43.2043	−	8.59387i	1.68045	−	0.334263i	0.739592	−	0.673056i	$-0.235019\pi$
$661$	43.2043	−	8.59387i	1.68045	−	0.334263i	0.940861	+	0.338793i	$0.110019\pi$
$662$	−11.2102	+	45.6178i	−0.435697	+	1.77299i
$663$	−11.6137	+	28.0380i	−0.451040	+	1.08891i
$664$	1.95644	+	1.72600i	0.0759247	+	0.0669818i
$665$	5.04599	+	12.1821i	0.195675	+	0.472402i
$666$	2.01754	+	13.1945i	0.0781781	+	0.511277i
$667$	−19.7684	−	13.2088i	−0.765434	−	0.511447i
$668$	8.25043	−	15.7731i	0.319219	−	0.610278i
$669$	6.31233	−	31.7342i	0.244049	−	1.22692i
$670$	−19.5566	+	7.09622i	−0.755536	+	0.274151i
$671$			22.3892i			0.864326i
$672$	−7.47831	+	16.7714i	−0.288482	+	0.646971i
$673$			6.94905i			0.267866i	0.990990	+	0.133933i	$0.0427607\pi$
$673$			6.94905i			0.267866i	−0.990990	+	0.133933i	$0.957239\pi$
$674$	3.18663	+	8.78207i	0.122744	+	0.338273i
$675$	−2.66414	+	13.3936i	−0.102543	+	0.515518i
$676$	−4.63178	+	1.45038i	−0.178145	+	0.0557838i
$677$	−27.1193	−	18.1206i	−1.04228	−	0.696430i	−0.0882375	−	0.996099i	$-0.528123\pi$
$677$	−27.1193	−	18.1206i	−1.04228	−	0.696430i	−0.954043	+	0.299670i	$0.903123\pi$
$678$	−28.6139	+	4.37527i	−1.09891	+	0.168031i
$679$	−5.89030	−	14.2204i	−0.226049	−	0.545731i
$680$	12.2805	+	25.0888i	0.470935	+	0.962111i
$681$	0.523050	−	1.26275i	0.0200433	−	0.0483889i
$682$	−25.4830	−	6.26224i	−0.975795	−	0.239794i
$683$	−11.0672	+	2.20141i	−0.423476	+	0.0842347i	−0.402228	−	0.915540i	$-0.631764\pi$
$683$	−11.0672	+	2.20141i	−0.423476	+	0.0842347i	−0.0212483	+	0.999774i	$0.506764\pi$
$684$	−7.16570	−	5.77431i	−0.273987	−	0.220786i
$685$	8.60439	−	5.74927i	0.328757	−	0.219668i
$686$	19.6079	−	17.9318i	0.748632	−	0.684640i
$687$	13.8581	+	13.8581i	0.528719	+	0.528719i
$688$	0.627535	+	35.0926i	0.0239245	+	1.33789i
$689$	12.0547	−	12.0547i	0.459246	−	0.459246i
$690$	0.693699	−	15.5374i	0.0264087	−	0.591500i
$691$	−7.02304	−	10.5107i	−0.267169	−	0.399846i	0.673492	−	0.739194i	$-0.264794\pi$
$691$	−7.02304	−	10.5107i	−0.267169	−	0.399846i	−0.940661	+	0.339348i	$0.889794\pi$
$692$	24.7924	+	7.27930i	0.942466	+	0.276717i
$693$	−1.63126	−	8.20088i	−0.0619663	−	0.311526i
$694$	−10.2237	−	16.8856i	−0.388086	−	0.640968i
$695$	−2.64414	−	1.09524i	−0.100298	−	0.0415448i
$696$	14.9775	+	2.01683i	0.567722	+	0.0764477i
$697$	44.9528	−	18.6200i	1.70271	−	0.705284i
$698$	13.8630	−	18.8677i	0.524720	−	0.714154i
$699$	13.4143	−	20.0758i	0.507374	−	0.759338i
$700$	1.14446	−	12.7913i	0.0432566	−	0.483464i
$701$	−31.1018	−	6.18654i	−1.17470	−	0.233662i	−0.431111	−	0.902299i	$-0.641878\pi$
$701$	−31.1018	−	6.18654i	−1.17470	−	0.233662i	−0.743589	+	0.668637i	$0.766878\pi$
$702$	13.0356	−	27.8833i	0.491998	−	1.05239i
$703$	−20.7167			−0.781347
$704$	11.6120	+	13.3998i	0.437645	+	0.505023i
$705$	−0.216392			−0.00814980
$706$	17.6350	−	37.7214i	0.663702	−	1.41966i
$707$	1.32117	+	0.262797i	0.0496877	+	0.00988349i
$708$	2.93923	+	0.262979i	0.110463	+	0.00988337i
$709$	−9.97024	+	14.9215i	−0.374440	+	0.560389i	−0.970056	−	0.242880i	$-0.921908\pi$
$709$	−9.97024	+	14.9215i	−0.374440	+	0.560389i	0.595616	+	0.803269i	$0.296908\pi$
$710$	14.3580	−	19.5414i	0.538845	−	0.733377i
$711$	1.59457	−	0.660493i	0.0598011	−	0.0247704i
$712$	−11.9471	+	9.11140i	−0.447736	+	0.341464i
$713$	42.8773	+	17.7604i	1.60577	+	0.665131i
$714$	14.7466	+	24.3556i	0.551877	+	0.911486i
$715$	2.70435	+	13.5957i	0.101137	+	0.508450i
$716$	−9.02014	+	30.7215i	−0.337099	+	1.14812i
$717$	−7.64645	−	11.4437i	−0.285562	−	0.427374i
$718$	1.12342	−	25.1624i	0.0419258	−	0.939052i
$719$	−30.0253	+	30.0253i	−1.11975	+	1.11975i	−0.127978	+	0.991777i	$0.540849\pi$
$719$	−30.0253	+	30.0253i	−1.11975	+	1.11975i	−0.991777	+	0.127978i	$0.959151\pi$
$720$	−3.68095	−	8.45572i	−0.137181	−	0.315126i
$721$	−16.0795	−	16.0795i	−0.598833	−	0.598833i
$722$	−9.28838	+	8.49443i	−0.345678	+	0.316130i
$723$	9.56589	−	6.39172i	0.355759	−	0.237711i
$724$	1.74736	−	2.16840i	0.0649400	−	0.0805881i
$725$	−10.3661	+	2.06194i	−0.384986	+	0.0765784i
$726$	−10.4158	−	2.55959i	−0.386566	−	0.0949954i
$727$	14.5339	−	35.0878i	0.539031	−	1.30134i	−0.386369	−	0.922344i	$-0.626271\pi$
$727$	14.5339	−	35.0878i	0.539031	−	1.30134i	0.925400	−	0.378992i	$-0.123729\pi$
$728$	−9.38533	+	27.3824i	−0.347843	+	1.01486i
$729$	9.34421	+	22.5589i	0.346082	+	0.835515i
$730$	−26.0894	+	3.98926i	−0.965611	+	0.147649i
$731$	45.2483	+	30.2340i	1.67357	+	1.11824i
$732$	7.52155	+	24.0200i	0.278004	+	0.887806i
$733$	−7.98081	+	40.1222i	−0.294778	+	1.48195i	0.495182	+	0.868789i	$0.335101\pi$
$733$	−7.98081	+	40.1222i	−0.294778	+	1.48195i	−0.789960	+	0.613159i	$0.789899\pi$
$734$	−14.8305	−	40.8716i	−0.547404	−	1.50860i
$735$		−	0.418219i		−	0.0154262i
$736$	−16.7190	−	26.5307i	−0.616269	−	0.977935i
$737$			20.4758i			0.754235i
$738$	−15.1007	+	5.47938i	−0.555864	+	0.201699i
$739$	2.49769	−	12.5568i	0.0918791	−	0.461908i	−0.907266	−	0.420558i	$-0.861834\pi$
$739$	2.49769	−	12.5568i	0.0918791	−	0.461908i	0.999145	−	0.0413495i	$-0.0131657\pi$
$740$	−18.3959	−	9.62239i	−0.676248	−	0.353726i
$741$	12.9301	+	8.63963i	0.475000	+	0.317385i
$742$	−2.41750	−	15.8102i	−0.0887492	−	0.580411i
$743$	0.0423479	+	0.102237i	0.00155359	+	0.00375071i	0.924654	−	0.380807i	$-0.124354\pi$
$743$	0.0423479	+	0.102237i	0.00155359	+	0.00375071i	−0.923101	+	0.384558i	$0.874354\pi$
$744$	−29.4430	+	1.84251i	−1.07943	+	0.0675499i
$745$	−2.04791	+	4.94408i	−0.0750294	+	0.181137i
$746$	5.16250	−	21.0078i	0.189012	−	0.769151i
$747$	−1.30987	+	0.260550i	−0.0479258	+	0.00953303i
$748$	27.3345	−	2.93919i	0.999450	−	0.107467i
$749$	41.4443	−	27.6922i	1.51434	−	1.01185i
$750$	−14.1329	−	15.4538i	−0.516060	−	0.564295i
$751$	1.45742	+	1.45742i	0.0531820	+	0.0531820i	0.733198	−	0.680016i	$-0.238027\pi$
$751$	1.45742	+	1.45742i	0.0531820	+	0.0531820i	−0.680016	+	0.733198i	$0.738027\pi$
$752$	−0.358386	+	0.248848i	−0.0130690	+	0.00907456i
$753$	7.79719	−	7.79719i	0.284146	−	0.284146i
$754$	23.7987	+	1.06254i	0.866699	+	0.0386954i
$755$	3.05942	+	4.57875i	0.111344	+	0.166638i
$756$	−13.8397	−	25.3447i	−0.503347	−	0.921777i
$757$	6.72211	+	33.7943i	0.244319	+	1.22828i	0.886865	+	0.462028i	$0.152878\pi$
$757$	6.72211	+	33.7943i	0.244319	+	1.22828i	−0.642546	+	0.766247i	$0.722122\pi$
$758$	−20.1147	+	12.1789i	−0.730601	+	0.442356i
$759$	−14.1422	−	5.85788i	−0.513328	−	0.212628i
$760$	13.8366	−	3.66375i	0.501905	−	0.132898i
$761$	20.6469	−	8.55221i	0.748448	−	0.310018i	0.0243401	−	0.999704i	$-0.492252\pi$
$761$	20.6469	−	8.55221i	0.748448	−	0.310018i	0.724108	+	0.689686i	$0.242252\pi$
$762$	−3.18975	−	2.34365i	−0.115552	−	0.0849014i
$763$	−18.4763	+	27.6518i	−0.668888	+	1.00106i
$764$	−4.57327	−	5.47204i	−0.165455	−	0.197972i
$765$	−14.0242	−	2.78959i	−0.507047	−	0.100858i
$766$	−13.4047	−	6.26676i	−0.484330	−	0.226427i
$767$	4.65167			0.167962
$768$	16.9594	+	10.4748i	0.611971	+	0.377977i
$769$	−23.8846			−0.861299			−0.430650	−	0.902519i	$-0.641716\pi$
$769$	−23.8846			−0.861299			−0.430650	+	0.902519i	$0.641716\pi$
$770$	11.7812	+	5.50779i	0.424565	+	0.198487i
$771$	−5.93001	−	1.17955i	−0.213564	−	0.0424805i
$772$	−4.96030	−	5.93514i	−0.178525	−	0.213610i
$773$	11.9528	−	17.8887i	0.429914	−	0.643412i	−0.551755	−	0.834006i	$-0.686042\pi$
$773$	11.9528	−	17.8887i	0.429914	−	0.643412i	0.981669	+	0.190595i	$0.0610416\pi$
$774$	−14.4788	−	10.6382i	−0.520428	−	0.382382i
$775$	19.0609	−	7.89528i	0.684687	−	0.283607i
$776$	−16.1517	+	4.27678i	−0.579814	+	0.153527i
$777$	−19.5503	−	8.09801i	−0.701364	−	0.290515i
$778$	12.2988	−	7.44655i	0.440933	−	0.266972i
$779$	−4.86408	−	24.4534i	−0.174274	−	0.876133i
$780$	7.46874	+	13.6775i	0.267424	+	0.489732i
$781$	−13.2594	−	19.8441i	−0.474459	−	0.710077i
$782$	−48.5741	−	2.16868i	−1.73700	−	0.0775519i
$783$	−16.8048	+	16.8048i	−0.600556	+	0.600556i
$784$	−0.480947	−	0.692650i	−0.0171767	−	0.0247375i
$785$	3.49421	+	3.49421i	0.124714	+	0.124714i
$786$	6.41528	+	7.01490i	0.228826	+	0.250213i
$787$	−16.2057	+	10.8283i	−0.577672	+	0.385988i	−0.809808	−	0.586695i	$-0.800429\pi$
$787$	−16.2057	+	10.8283i	−0.577672	+	0.385988i	0.232136	+	0.972683i	$0.425429\pi$
$788$	−35.9092	+	3.86119i	−1.27921	+	0.137549i
$789$	−20.8126	+	4.13988i	−0.740948	+	0.147384i
$790$	−0.640622	+	2.60689i	−0.0227923	+	0.0927490i
$791$	−16.3819	+	39.5495i	−0.582474	+	1.40622i
$792$	−9.05887	+	0.566896i	−0.321893	+	0.0201438i
$793$	15.1834	+	36.6560i	0.539179	+	1.30169i
$794$	−0.560055	−	3.66271i	−0.0198756	−	0.129985i
$795$	−7.15954	−	4.78385i	−0.253923	−	0.169666i
$796$	−24.8295	−	12.9876i	−0.880057	−	0.460333i
$797$	0.0842043	−	0.423324i	0.00298267	−	0.0149949i	−0.979265	−	0.202582i	$-0.935067\pi$
$797$	0.0842043	−	0.423324i	0.00298267	−	0.0149949i	0.982248	+	0.187587i	$0.0600667\pi$
$798$	13.7146	−	4.97643i	0.485492	−	0.176164i
$799$			0.676497i			0.0239328i
$800$	−13.5951	−	3.08422i	−0.480660	−	0.109044i
$801$		−	7.69131i		−	0.271759i
$802$	−10.1299	−	27.9170i	−0.357697	−	0.985783i
$803$	−5.06765	+	25.4768i	−0.178834	+	0.899057i
$804$	6.87873	+	21.9672i	0.242594	+	0.774724i
$805$	−19.1244	−	12.7785i	−0.674048	−	0.450384i
$806$	−45.9680	+	7.02885i	−1.61915	+	0.247581i
$807$	−1.52935	−	3.69217i	−0.0538355	−	0.129971i
$808$	0.474109	−	1.38325i	0.0166791	−	0.0486626i
$809$	−8.87822	+	21.4339i	−0.312142	+	0.753576i	0.687484	+	0.726200i	$0.258715\pi$
$809$	−8.87822	+	21.4339i	−0.312142	+	0.753576i	−0.999625	+	0.0273765i	$0.991285\pi$
$810$	−5.59850	−	1.37578i	−0.196711	−	0.0483401i
$811$	−0.570557	+	0.113491i	−0.0200350	+	0.00398520i	−0.205098	−	0.978742i	$-0.565751\pi$
$811$	−0.570557	+	0.113491i	−0.0200350	+	0.00398520i	0.185063	+	0.982727i	$0.440751\pi$
$812$	14.0235	−	17.4027i	0.492129	−	0.610713i
$813$	6.34016	−	4.23636i	0.222359	−	0.148576i
$814$	−15.0782	+	13.7894i	−0.528492	+	0.483318i
$815$	−0.544377	−	0.544377i	−0.0190687	−	0.0190687i
$816$	28.3382	−	12.3362i	0.992034	−	0.431853i
$817$	19.7181	−	19.7181i	0.689849	−	0.689849i
$818$	1.47572	−	33.0531i	0.0515973	−	1.15567i
$819$	−8.23221	−	12.3204i	−0.287657	−	0.430509i
$820$	7.03878	−	23.9732i	0.245805	−	0.837181i
$821$	0.267849	+	1.34657i	0.00934799	+	0.0469955i	0.985178	−	0.171537i	$-0.0548732\pi$
$821$	0.267849	+	1.34657i	0.00934799	+	0.0469955i	−0.975830	+	0.218532i	$0.929873\pi$
$822$	−5.93037	−	9.79467i	−0.206845	−	0.341628i
$823$	32.6695	+	13.5321i	1.13879	+	0.471701i	0.870759	−	0.491710i	$-0.163628\pi$
$823$	32.6695	+	13.5321i	1.13879	+	0.471701i	0.268028	+	0.963411i	$0.413628\pi$
$824$	−19.6278	+	14.9691i	−0.683767	+	0.521473i
$825$	−6.28683	+	2.60409i	−0.218879	+	0.0906628i
$826$	2.58400	−	3.51687i	0.0899089	−	0.122368i
$827$	16.7811	−	25.1146i	0.583534	−	0.873321i	−0.415813	−	0.909450i	$-0.636503\pi$
$827$	16.7811	−	25.1146i	0.583534	−	0.873321i	0.999347	+	0.0361292i	$0.0115028\pi$
$828$	15.9890	+	1.43057i	0.555655	+	0.0497156i
$829$	43.8051	+	8.71338i	1.52142	+	0.302628i	0.883851	−	0.467769i	$-0.154942\pi$
$829$	43.8051	+	8.71338i	1.52142	+	0.302628i	0.637564	+	0.770397i	$0.279942\pi$
$830$	0.879724	−	1.88174i	0.0305357	−	0.0653160i
$831$	−4.86238			−0.168674
$832$	28.0986	+	14.0635i	0.974143	+	0.487566i
$833$	−1.30746			−0.0453008
$834$	−1.34112	+	2.86867i	−0.0464393	+	0.0993340i
$835$	−13.9002	−	2.76491i	−0.481035	−	0.0956838i
$836$	1.25542	−	14.0314i	0.0434196	−	0.485286i
$837$	25.7737	−	38.5730i	0.890869	−	1.33328i
$838$	−9.81534	+	13.3589i	−0.339065	+	0.461474i
$839$	−22.5256	+	9.33043i	−0.777672	+	0.322122i	−0.735976	−	0.677008i	$-0.763276\pi$
$839$	−22.5256	+	9.33043i	−0.777672	+	0.322122i	−0.0416962	+	0.999130i	$0.513276\pi$
$840$	14.4897	+	1.95113i	0.499941	+	0.0673205i
$841$	9.79901	+	4.05888i	0.337897	+	0.139961i
$842$	23.9996	+	39.6380i	0.827080	+	1.36601i
$843$	−1.38512	−	6.96348i	−0.0477061	−	0.239835i
$844$	36.2356	+	10.6391i	1.24728	+	0.366214i
$845$	2.14690	+	3.21306i	0.0738556	+	0.110533i
$846$	0.00996185	−	0.223125i	0.000342495	−	0.00767120i
$847$	−11.2160	+	11.2160i	−0.385388	+	0.385388i
$848$	−17.3589	+	0.310417i	−0.596108	+	0.0106598i
$849$	19.9465	+	19.9465i	0.684563	+	0.684563i
$850$	−15.9505	+	14.5871i	−0.547098	+	0.500333i
$851$	30.0472	−	20.0769i	1.03000	−	0.688226i
$852$	−20.8917	−	16.8351i	−0.715739	−	0.576761i
$853$	−30.2500	+	6.01711i	−1.03574	+	0.206022i	−0.683548	−	0.729905i	$-0.739564\pi$
$853$	−30.2500	+	6.01711i	−1.03574	+	0.206022i	−0.352193	+	0.935927i	$0.614564\pi$
$854$	36.1479	+	8.88305i	1.23696	+	0.303972i
$855$	−2.80394	+	6.76931i	−0.0958927	+	0.231505i
$856$	−23.7876	−	48.5977i	−0.813044	−	1.66103i
$857$	9.31614	+	22.4912i	0.318233	+	0.768283i	0.999348	+	0.0361064i	$0.0114955\pi$
$857$	9.31614	+	22.4912i	0.318233	+	0.768283i	−0.681115	+	0.732177i	$0.738504\pi$
$858$	15.1616	−	2.31832i	0.517608	−	0.0791461i
$859$	0.219064	+	0.146374i	0.00747437	+	0.00499421i	0.559302	−	0.828964i	$-0.311069\pi$
$859$	0.219064	+	0.146374i	0.00747437	+	0.00499421i	−0.551827	+	0.833958i	$0.686069\pi$
$860$	26.6677	−	8.35063i	0.909361	−	0.284754i
$861$	4.96842	−	24.9779i	0.169323	−	0.851245i
$862$	7.61726	+	20.9925i	0.259445	+	0.715008i
$863$		−	24.2153i		−	0.824299i	−0.911116	−	0.412150i	$-0.864778\pi$
$863$		−	24.2153i		−	0.824299i	0.911116	−	0.412150i	$-0.135222\pi$
$864$	−29.2709	+	11.2173i	−0.995815	+	0.381621i
$865$		−	20.5725i		−	0.699487i
$866$	28.7856	−	10.4450i	0.978176	−	0.354937i
$867$	5.21704	−	26.2278i	0.177180	−	0.890744i
$868$	−20.2211	+	38.6584i	−0.686348	+	1.31215i
$869$	2.19680	+	1.46786i	0.0745214	+	0.0497936i
$870$	−1.81872	−	11.8942i	−0.0616603	−	0.403252i
$871$	13.8858	+	33.5233i	0.470502	+	1.13589i
$872$	27.0714	+	23.8827i	0.916752	+	0.808770i
$873$	3.27310	−	7.90197i	0.110778	−	0.267441i
$874$	−5.94575	+	24.1951i	−0.201118	+	0.818413i
$875$	−30.3752	+	6.04200i	−1.02687	+	0.204257i
$876$	3.12203	+	29.0350i	0.105484	+	0.981001i
$877$	17.9632	−	12.0027i	0.606576	−	0.405301i	−0.214004	−	0.976833i	$-0.568651\pi$
$877$	17.9632	−	12.0027i	0.606576	−	0.405301i	0.820580	+	0.571532i	$0.193651\pi$
$878$	39.0579	+	42.7085i	1.31814	+	1.44134i
$879$	5.85102	+	5.85102i	0.197350	+	0.197350i
$880$	7.63199	−	11.8764i	0.257274	−	0.400354i
$881$	−15.8713	+	15.8713i	−0.534718	+	0.534718i	−0.921973	−	0.387255i	$-0.873423\pi$
$881$	−15.8713	+	15.8713i	−0.534718	+	0.534718i	0.387255	+	0.921973i	$0.373423\pi$
$882$	0.431232	+	0.0192532i	0.0145203	+	0.000648288i
$883$	16.2902	+	24.3799i	0.548207	+	0.820450i	0.997330	−	0.0730197i	$-0.0232636\pi$
$883$	16.2902	+	24.3799i	0.548207	+	0.820450i	−0.449123	+	0.893470i	$0.648264\pi$
$884$	42.7593	−	23.3492i	1.43815	−	0.785319i
$885$	−0.458367	−	2.30437i	−0.0154078	−	0.0774605i
$886$	41.0758	−	24.8701i	1.37997	−	0.835529i
$887$	−34.2563	−	14.1894i	−1.15021	−	0.476435i	−0.275609	−	0.961270i	$-0.588880\pi$
$887$	−34.2563	−	14.1894i	−1.15021	−	0.476435i	−0.874606	+	0.484835i	$0.838880\pi$
$888$	−11.5440	+	19.8592i	−0.387393	+	0.666433i
$889$	−5.40805	+	2.24009i	−0.181380	+	0.0751302i
$890$	9.64024	+	7.08312i	0.323142	+	0.237427i
$891$	−3.15233	+	4.71780i	−0.105607	+	0.158052i
$892$	−39.8557	+	33.3095i	−1.33447	+	1.11528i
$893$	0.339988	+	0.0676279i	0.0113773	+	0.00226308i
$894$	5.36392	+	2.50766i	0.179396	+	0.0838688i
$895$	25.4925			0.852119
$896$	26.2414	−	13.4315i	0.876664	−	0.448714i
$897$	−27.1264			−0.905723
$898$	−2.72248	−	1.27278i	−0.0908503	−	0.0424731i
$899$	35.2151	+	7.00472i	1.17449	+	0.233621i
$900$	5.47566	−	4.57629i	0.182522	−	0.152543i
$901$	−14.9556	+	22.3826i	−0.498242	+	0.745672i
$902$	−19.8168	−	14.5603i	−0.659826	−	0.484803i
$903$	26.3155	−	10.9003i	0.875727	−	0.362738i
$904$	40.1744	+	23.3531i	1.33618	+	0.776713i
$905$	−2.04845	−	0.848496i	−0.0680928	−	0.0282050i
$906$	5.21214	−	3.15579i	0.173162	−	0.104844i
$907$	−0.117687	−	0.591654i	−0.00390775	−	0.0196456i	0.978782	−	0.204903i	$-0.0656880\pi$
$907$	−0.117687	−	0.591654i	−0.00390775	−	0.0196456i	−0.982690	+	0.185258i	$0.940688\pi$
$908$	−1.92576	+	1.05158i	−0.0639086	+	0.0348980i
$909$	0.415858	+	0.622376i	0.0137931	+	0.0206429i
$910$	23.0235	+	1.02793i	0.763223	+	0.0340755i
$911$	−25.7854	+	25.7854i	−0.854308	+	0.854308i	−0.990660	−	0.136352i	$-0.956462\pi$
$911$	−25.7854	+	25.7854i	−0.854308	+	0.854308i	0.136352	+	0.990660i	$0.456462\pi$
$912$	−3.36691	−	15.4752i	−0.111490	−	0.512434i
$913$	−1.44563	−	1.44563i	−0.0478433	−	0.0478433i
$914$	−33.2141	−	36.3185i	−1.09862	−	1.20131i
$915$	16.6627	−	11.1336i	0.550851	−	0.368067i
$916$	−3.36360	−	31.2816i	−0.111136	−	1.03357i
$917$	13.7881	−	2.74262i	0.455322	−	0.0905693i
$918$	−11.5987	+	47.1987i	−0.382813	+	1.55779i
$919$	13.0040	−	31.3945i	0.428964	−	1.03561i	−0.550653	−	0.834734i	$-0.685621\pi$
$919$	13.0040	−	31.3945i	0.428964	−	1.03561i	0.979617	−	0.200876i	$-0.0643788\pi$
$920$	−16.5177	+	18.7230i	−0.544572	+	0.617280i
$921$	−0.972528	−	2.34789i	−0.0320459	−	0.0773656i
$922$	2.91449	+	19.0605i	0.0959837	+	0.627724i
$923$	−35.1659	−	23.4971i	−1.15750	−	0.773417i
$924$	6.66949	−	12.7506i	0.219410	−	0.419465i
$925$	3.13407	−	15.7560i	0.103047	−	0.518055i
$926$	30.6216	−	11.1112i	1.00629	−	0.365138i
$927$		−	12.6360i		−	0.415021i
$928$	−16.6904	−	17.6076i	−0.547888	−	0.577998i
$929$			9.78678i			0.321094i	0.987028	+	0.160547i	$0.0513258\pi$
$929$			9.78678i			0.321094i	−0.987028	+	0.160547i	$0.948674\pi$
$930$	8.01159	+	22.0792i	0.262710	+	0.724007i
$931$	−0.130704	+	0.657092i	−0.00428364	+	0.0215353i
$932$	−36.9898	+	11.5829i	−1.21164	+	0.379409i
$933$	−27.2865	−	18.2323i	−0.893320	−	0.596897i
$934$	−22.9417	+	3.50796i	−0.750675	+	0.114784i
$935$	−8.37646	−	20.2226i	−0.273940	−	0.661349i
$936$	−14.4469	+	7.07147i	−0.472211	+	0.231138i
$937$	9.02858	−	21.7969i	0.294951	−	0.712075i	−0.705045	−	0.709163i	$-0.749073\pi$
$937$	9.02858	−	21.7969i	0.294951	−	0.712075i	0.999996	−	0.00291192i	$-0.000926893\pi$
$938$	33.0586	+	8.12388i	1.07940	+	0.265254i
$939$	−14.4072	+	2.86578i	−0.470162	+	0.0935211i
$940$	0.270490	+	0.217968i	0.00882240	+	0.00710932i
$941$	6.14014	−	4.10271i	0.200163	−	0.133745i	−0.451450	−	0.892297i	$-0.649093\pi$
$941$	6.14014	−	4.10271i	0.200163	−	0.133745i	0.651612	+	0.758552i	$0.274093\pi$
$942$	4.03480	−	3.68992i	0.131461	−	0.120224i
$943$	30.7529	+	30.7529i	1.00145	+	1.00145i
$944$	−3.40914	−	3.28935i	−0.110958	−	0.107059i
$945$	−16.2575	+	16.2575i	−0.528855	+	0.528855i
$946$	1.22672	−	27.4760i	0.0398841	−	0.893323i
$947$	10.3655	+	15.5130i	0.336832	+	0.504105i	0.960762	−	0.277376i	$-0.0894647\pi$
$947$	10.3655	+	15.5130i	0.336832	+	0.504105i	−0.623929	+	0.781481i	$0.714465\pi$
$948$	2.84993	+	0.836769i	0.0925615	+	0.0271770i
$949$	8.98044	+	45.1477i	0.291517	+	1.46556i
$950$	5.73652	+	9.47450i	0.186117	+	0.307393i
$951$	−16.0905	−	6.66490i	−0.521770	−	0.216124i
$952$	6.09975	−	45.2984i	0.197694	−	1.46813i
$953$	−1.50663	+	0.624068i	−0.0488047	+	0.0202156i	−0.406952	−	0.913449i	$-0.633408\pi$
$953$	−1.50663	+	0.624068i	−0.0488047	+	0.0202156i	0.358148	+	0.933665i	$0.383408\pi$
$954$	5.26230	−	7.16208i	0.170373	−	0.231881i
$955$	−3.15451	+	4.72105i	−0.102077	+	0.152770i
$956$	−1.96899	+	22.0068i	−0.0636818	+	0.711749i
$957$	−11.6150	−	2.31036i	−0.375459	−	0.0746833i
$958$	2.48288	−	5.31090i	0.0802182	−	0.171587i
$959$	−16.9332			−0.546802
$960$	4.19808	−	15.3054i	0.135493	−	0.493980i
$961$	−39.0879			−1.26090
$962$	−15.3350	+	32.8016i	−0.494419	+	1.05757i
$963$	27.1653	+	5.40351i	0.875389	+	0.174126i
$964$	−18.3956	−	1.64589i	−0.592482	−	0.0530107i
$965$	−3.42147	+	5.12059i	−0.110141	+	0.164838i
$966$	−15.0687	+	20.5087i	−0.484827	+	0.659858i
$967$	6.20220	−	2.56904i	0.199449	−	0.0826147i	−0.280723	−	0.959789i	$-0.590574\pi$
$967$	6.20220	−	2.56904i	0.199449	−	0.0826147i	0.480172	+	0.877174i	$0.340574\pi$
$968$	10.4415	+	13.6911i	0.335602	+	0.440049i
$969$	−22.6864	−	9.39700i	−0.728791	−	0.301875i
$970$	6.89000	+	11.3796i	0.221225	+	0.365377i
$971$	−4.68288	−	23.5424i	−0.150281	−	0.755512i	−0.980259	−	0.197716i	$-0.936647\pi$
$971$	−4.68288	−	23.5424i	−0.150281	−	0.755512i	0.829979	−	0.557795i	$-0.188353\pi$
$972$	7.56957	−	25.7810i	0.242794	−	0.826927i
$973$	2.60180	+	3.89387i	0.0834100	+	0.124832i
$974$	−0.0376326	+	0.842894i	−0.00120583	+	0.0270081i
$975$	−8.52692	+	8.52692i	−0.273080	+	0.273080i
$976$	14.7930	−	37.6013i	0.473513	−	1.20359i
$977$	−24.0769	−	24.0769i	−0.770289	−	0.770289i	0.207868	−	0.978157i	$-0.433348\pi$
$977$	−24.0769	−	24.0769i	−0.770289	−	0.770289i	−0.978157	+	0.207868i	$0.933348\pi$
$978$	−0.628598	+	0.574867i	−0.0201003	+	0.0183822i
$979$	9.78954	−	6.54116i	0.312875	−	0.209057i
$980$	−0.421264	+	0.522773i	−0.0134568	+	0.0166994i
$981$	−18.1248	+	3.60524i	−0.578679	+	0.115106i
$982$	−43.7567	−	10.7528i	−1.39633	−	0.343137i
$983$	18.5278	−	44.7301i	0.590946	−	1.42667i	−0.291644	−	0.956527i	$-0.594202\pi$
$983$	18.5278	−	44.7301i	0.590946	−	1.42667i	0.882590	−	0.470143i	$-0.155798\pi$
$984$	−26.1516	−	8.96347i	−0.833684	−	0.285745i
$985$	11.0041	+	26.5662i	0.350619	+	0.846470i
$986$	−37.1844	+	5.68578i	−1.18419	+	0.181072i
$987$	0.294411	+	0.196719i	0.00937120	+	0.00626163i
$988$	−7.46009	−	23.8238i	−0.237337	−	0.757935i
$989$	−9.48967	+	47.7078i	−0.301754	+	1.51702i
$990$	2.46497	+	6.79324i	0.0783418	+	0.215903i
$991$		−	23.7163i		−	0.753372i	−0.926341	−	0.376686i	$-0.877064\pi$
$991$		−	23.7163i		−	0.753372i	0.926341	−	0.376686i	$-0.122936\pi$
$992$	38.6596	+	27.3542i	1.22744	+	0.868496i
$993$		−	41.3824i		−	1.31323i
$994$	−37.2995	+	13.5344i	−1.18307	+	0.429284i
$995$	−4.35244	+	21.8812i	−0.137982	+	0.693681i
$996$	−2.03658	−	1.06528i	−0.0645315	−	0.0337545i
$997$	−42.3286	−	28.2831i	−1.34056	−	0.895734i	−0.341535	−	0.939869i	$-0.610947\pi$
$997$	−42.3286	−	28.2831i	−1.34056	−	0.895734i	−0.999026	+	0.0441354i	$0.985947\pi$
$998$	1.79042	+	11.7091i	0.0566746	+	0.370646i
$999$	−13.8236	−	33.3732i	−0.437360	−	1.05588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.29.7	✓	56
3.2	odd	2		576.2.bd.a.541.1		56
4.3	odd	2		256.2.i.a.209.5		56
8.3	odd	2		512.2.i.a.161.3		56
8.5	even	2		512.2.i.b.161.5		56
64.11	odd	16		256.2.i.a.49.5		56
64.21	even	16		512.2.i.b.353.5		56
64.43	odd	16		512.2.i.a.353.3		56
64.53	even	16	inner	64.2.i.a.53.7	yes	56
192.53	odd	16		576.2.bd.a.181.1		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.7	✓	56	1.1	even	1	trivial
64.2.i.a.53.7	yes	56	64.53	even	16	inner
256.2.i.a.49.5		56	64.11	odd	16
256.2.i.a.209.5		56	4.3	odd	2
512.2.i.a.161.3		56	8.3	odd	2
512.2.i.a.353.3		56	64.43	odd	16
512.2.i.b.161.5		56	8.5	even	2
512.2.i.b.353.5		56	64.21	even	16
576.2.bd.a.181.1		56	192.53	odd	16
576.2.bd.a.541.1		56	3.2	odd	2

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28112 + 0.598933i) q^{2} +(-1.22190 - 0.243052i) q^{3} +(1.28256 + 1.53462i) q^{4} +(0.884671 - 1.32400i) q^{5} +(-1.41984 - 1.04322i) q^{6} +(-2.40727 + 0.997123i) q^{7} +(0.723982 + 2.73420i) q^{8} +(-1.33766 - 0.554078i) q^{9} +O(q^{10})\)	\(q+(1.28112 + 0.598933i) q^{2} +(-1.22190 - 0.243052i) q^{3} +(1.28256 + 1.53462i) q^{4} +(0.884671 - 1.32400i) q^{5} +(-1.41984 - 1.04322i) q^{6} +(-2.40727 + 0.997123i) q^{7} +(0.723982 + 2.73420i) q^{8} +(-1.33766 - 0.554078i) q^{9} +(1.92636 - 1.16635i) q^{10} +(-0.432397 - 2.17381i) q^{11} +(-1.19417 - 2.18688i) q^{12} +(-2.18211 - 3.26576i) q^{13} +(-3.68122 - 0.164355i) q^{14} +(-1.40279 + 1.40279i) q^{15} +(-0.710093 + 3.93647i) q^{16} +(4.38547 + 4.38547i) q^{17} +(-1.38185 - 1.51101i) q^{18} +(2.64242 - 1.76561i) q^{19} +(3.16648 - 0.340480i) q^{20} +(3.18380 - 0.633298i) q^{21} +(0.748011 - 3.04389i) q^{22} +(-2.12144 + 5.12160i) q^{23} +(-0.220084 - 3.51690i) q^{24} +(0.943074 + 2.27678i) q^{25} +(-0.839581 - 5.49078i) q^{26} +(4.60747 + 3.07861i) q^{27} +(-4.61766 - 2.41536i) q^{28} +(-0.836699 + 4.20637i) q^{29} +(-2.63732 + 0.956967i) q^{30} -8.37185i q^{31} +(-3.26740 + 4.61780i) q^{32} +2.76128i q^{33} +(2.99173 + 8.24494i) q^{34} +(-0.809445 + 4.06936i) q^{35} +(-0.865331 - 2.76343i) q^{36} +(-5.42017 - 3.62164i) q^{37} +(4.44275 - 0.679329i) q^{38} +(1.87258 + 4.52081i) q^{39} +(4.26058 + 1.46031i) q^{40} +(3.00227 - 7.24812i) q^{41} +(4.45815 + 1.09555i) q^{42} +(8.60595 - 1.71183i) q^{43} +(2.78138 - 3.45159i) q^{44} +(-1.91699 + 1.28089i) q^{45} +(-5.78532 + 5.29081i) q^{46} +(0.0771294 + 0.0771294i) q^{47} +(1.82443 - 4.63740i) q^{48} +(-0.149067 + 0.149067i) q^{49} +(-0.155446 + 3.48168i) q^{50} +(-4.29273 - 6.42453i) q^{51} +(2.21300 - 7.53722i) q^{52} +(0.846775 + 4.25703i) q^{53} +(4.05885 + 6.70365i) q^{54} +(-3.26066 - 1.35061i) q^{55} +(-4.46915 - 5.86005i) q^{56} +(-3.65792 + 1.51516i) q^{57} +(-3.59125 + 4.88776i) q^{58} +(-0.657977 + 0.984732i) q^{59} +(-3.95189 - 0.353584i) q^{60} +(-9.90754 - 1.97073i) q^{61} +(5.01418 - 10.7254i) q^{62} +3.77259 q^{63} +(-6.95170 + 3.95902i) q^{64} -6.25433 q^{65} +(-1.65382 + 3.53754i) q^{66} +(-9.06082 - 1.80231i) q^{67} +(-1.10540 + 12.3546i) q^{68} +(3.83701 - 5.74249i) q^{69} +(-3.47427 + 4.72855i) q^{70} +(9.94840 - 4.12076i) q^{71} +(0.546516 - 4.05858i) q^{72} +(-10.8278 - 4.48502i) q^{73} +(-4.77479 - 7.88609i) q^{74} +(-0.598970 - 3.01123i) q^{75} +(6.09858 + 1.79060i) q^{76} +(3.20845 + 4.80178i) q^{77} +(-0.308656 + 6.91327i) q^{78} +(-0.842912 + 0.842912i) q^{79} +(4.58370 + 4.42264i) q^{80} +(-1.81022 - 1.81022i) q^{81} +(8.18742 - 7.48758i) q^{82} +(0.766957 - 0.512464i) q^{83} +(5.05528 + 4.07368i) q^{84} +(9.68608 - 1.92668i) q^{85} +(12.0506 + 2.96132i) q^{86} +(2.04473 - 4.93642i) q^{87} +(5.63057 - 2.75606i) q^{88} +(2.03287 + 4.90777i) q^{89} +(-3.22307 + 0.492832i) q^{90} +(8.50928 + 5.68572i) q^{91} +(-10.5806 + 3.31316i) q^{92} +(-2.03480 + 10.2296i) q^{93} +(0.0526169 + 0.145008i) q^{94} -5.06055i q^{95} +(5.11482 - 4.84837i) q^{96} +5.90730i q^{97} +(-0.280255 + 0.101692i) q^{98} +(-0.626056 + 3.14740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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