LMFDB - Embedded newform 966.2.k.b.229.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.10
Character	$\chi$	$=$	966.229
Dual form			966.2.k.b.367.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.36115 + 2.35758i) q^{5} -1.00000i q^{6} +(2.49823 - 0.871108i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.36115 + 2.35758i) q^{5} -1.00000i q^{6} +(2.49823 - 0.871108i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.36115 + 2.35758i) q^{10} +(2.53196 - 1.46183i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.35874i q^{13} +(0.494715 - 2.59909i) q^{14} +2.72230i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.08913 + 5.35053i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.541689 + 0.938233i) q^{19} +2.72230 q^{20} +(1.72798 - 2.00352i) q^{21} -2.92366i q^{22} +(4.29962 - 2.12444i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.20545 - 2.08790i) q^{25} +(-1.17670 - 0.679369i) q^{26} -1.00000i q^{27} +(-2.00352 - 1.72798i) q^{28} -7.21540 q^{29} +(2.35758 + 1.36115i) q^{30} +(8.29879 - 4.79131i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.46183 - 2.53196i) q^{33} +6.17826 q^{34} +(-1.34676 + 7.07549i) q^{35} -1.00000 q^{36} +(0.810574 + 0.467985i) q^{37} +(0.541689 + 0.938233i) q^{38} +(-0.679369 - 1.17670i) q^{39} +(1.36115 - 2.35758i) q^{40} -3.65266i q^{41} +(-0.871108 - 2.49823i) q^{42} -9.65334i q^{43} +(-2.53196 - 1.46183i) q^{44} +(1.36115 + 2.35758i) q^{45} +(0.309995 - 4.78580i) q^{46} +(6.68553 + 3.85989i) q^{47} +1.00000i q^{48} +(5.48234 - 4.35246i) q^{49} -2.41090 q^{50} +(5.35053 + 3.08913i) q^{51} +(-1.17670 + 0.679369i) q^{52} +(-3.10658 + 1.79359i) q^{53} +(-0.866025 - 0.500000i) q^{54} +7.95907i q^{55} +(-2.49823 + 0.871108i) q^{56} +1.08338i q^{57} +(-3.60770 + 6.24872i) q^{58} +(0.816235 - 0.471253i) q^{59} +(2.35758 - 1.36115i) q^{60} +(2.62356 - 4.54413i) q^{61} -9.58261i q^{62} +(0.494715 - 2.59909i) q^{63} +1.00000 q^{64} +(3.20333 + 1.84944i) q^{65} +(-1.46183 - 2.53196i) q^{66} +(-5.27370 + 3.04477i) q^{67} +(3.08913 - 5.35053i) q^{68} +(2.66136 - 3.98963i) q^{69} +(5.45417 + 4.70407i) q^{70} +9.73354 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-8.70696 + 5.02697i) q^{73} +(0.810574 - 0.467985i) q^{74} +(-2.08790 - 1.20545i) q^{75} +1.08338 q^{76} +(5.05202 - 5.85760i) q^{77} -1.35874 q^{78} +(-8.01433 - 4.62707i) q^{79} +(-1.36115 - 2.35758i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.16330 - 1.82633i) q^{82} -4.05202 q^{83} +(-2.59909 - 0.494715i) q^{84} -16.8190 q^{85} +(-8.36004 - 4.82667i) q^{86} +(-6.24872 + 3.60770i) q^{87} +(-2.53196 + 1.46183i) q^{88} +(-7.90496 + 13.6918i) q^{89} +2.72230 q^{90} +(-1.18361 - 3.39445i) q^{91} +(-3.98963 - 2.66136i) q^{92} +(4.79131 - 8.29879i) q^{93} +(6.68553 - 3.85989i) q^{94} +(-1.47464 - 2.55415i) q^{95} +(0.866025 + 0.500000i) q^{96} +7.72846 q^{97} +(-1.02817 - 6.92408i) q^{98} -2.92366i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.36115	+	2.35758i	−0.608724	+	1.05434i	0.382727	+	0.923861i	$0.374985\pi$
$5$	−1.36115	+	2.35758i	−0.608724	+	1.05434i	−0.991451	+	0.130479i	$0.958348\pi$
$6$		−	1.00000i		−	0.408248i
$7$	2.49823	−	0.871108i	0.944244	−	0.329248i
$7$	2.49823	−	0.871108i	0.944244	−	0.329248i
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.36115	+	2.35758i	0.430433	+	0.745532i
$11$	2.53196	−	1.46183i	0.763415	−	0.440758i	−0.0671052	−	0.997746i	$-0.521376\pi$
$11$	2.53196	−	1.46183i	0.763415	−	0.440758i	0.830521	+	0.556988i	$0.188043\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$		−	1.35874i		−	0.376846i	−0.982088	−	0.188423i	$-0.939662\pi$
$13$		−	1.35874i		−	0.376846i	0.982088	−	0.188423i	$-0.0603376\pi$
$14$	0.494715	−	2.59909i	0.132218	−	0.694635i
$15$			2.72230i			0.702894i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.08913	+	5.35053i	0.749224	+	1.29769i	0.948195	+	0.317688i	$0.102906\pi$
$17$	3.08913	+	5.35053i	0.749224	+	1.29769i	−0.198972	+	0.980005i	$0.563760\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.541689	+	0.938233i	−0.124272	+	0.215245i	−0.921448	−	0.388501i	$-0.872993\pi$
$19$	−0.541689	+	0.938233i	−0.124272	+	0.215245i	0.797176	+	0.603747i	$0.206326\pi$
$20$	2.72230			0.608724
$21$	1.72798	−	2.00352i	0.377076	−	0.437204i
$22$		−	2.92366i		−	0.623326i
$23$	4.29962	−	2.12444i	0.896534	−	0.442976i
$23$	4.29962	−	2.12444i	0.896534	−	0.442976i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−1.20545	−	2.08790i	−0.241090	−	0.417580i
$26$	−1.17670	−	0.679369i	−0.230770	−	0.133235i
$27$		−	1.00000i		−	0.192450i
$28$	−2.00352	−	1.72798i	−0.378629	−	0.326557i
$29$	−7.21540			−1.33987			−0.669933	−	0.742421i	$-0.733677\pi$
$29$	−7.21540			−1.33987			−0.669933	+	0.742421i	$0.733677\pi$
$30$	2.35758	+	1.36115i	0.430433	+	0.248511i
$31$	8.29879	−	4.79131i	1.49051	−	0.860544i	0.490565	−	0.871404i	$-0.336790\pi$
$31$	8.29879	−	4.79131i	1.49051	−	0.860544i	0.999941	+	0.0108603i	$0.00345700\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.46183	−	2.53196i	0.254472	−	0.440758i
$34$	6.17826			1.05956
$35$	−1.34676	+	7.07549i	−0.227644	+	1.19598i
$36$	−1.00000			−0.166667
$37$	0.810574	+	0.467985i	0.133258	+	0.0769363i	0.565147	−	0.824990i	$-0.308820\pi$
$37$	0.810574	+	0.467985i	0.133258	+	0.0769363i	−0.431889	+	0.901927i	$0.642153\pi$
$38$	0.541689	+	0.938233i	0.0878736	+	0.152201i
$39$	−0.679369	−	1.17670i	−0.108786	−	0.188423i
$40$	1.36115	−	2.35758i	0.215216	−	0.372766i
$41$		−	3.65266i		−	0.570450i	−0.958461	−	0.285225i	$-0.907932\pi$
$41$		−	3.65266i		−	0.570450i	0.958461	−	0.285225i	$-0.0920683\pi$
$42$	−0.871108	−	2.49823i	−0.134415	−	0.385486i
$43$		−	9.65334i		−	1.47212i	−0.676916	−	0.736060i	$-0.736684\pi$
$43$		−	9.65334i		−	1.47212i	0.676916	−	0.736060i	$-0.263316\pi$
$44$	−2.53196	−	1.46183i	−0.381708	−	0.220379i
$45$	1.36115	+	2.35758i	0.202908	+	0.351447i
$46$	0.309995	−	4.78580i	0.0457063	−	0.705628i
$47$	6.68553	+	3.85989i	0.975184	+	0.563023i	0.900813	−	0.434208i	$-0.142972\pi$
$47$	6.68553	+	3.85989i	0.975184	+	0.563023i	0.0743715	+	0.997231i	$0.476305\pi$
$48$			1.00000i			0.144338i
$49$	5.48234	−	4.35246i	0.783192	−	0.621780i
$50$	−2.41090			−0.340952
$51$	5.35053	+	3.08913i	0.749224	+	0.432564i
$52$	−1.17670	+	0.679369i	−0.163179	+	0.0942116i
$53$	−3.10658	+	1.79359i	−0.426722	+	0.246368i	−0.697949	−	0.716147i	$-0.745904\pi$
$53$	−3.10658	+	1.79359i	−0.426722	+	0.246368i	0.271227	+	0.962515i	$0.412571\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$			7.95907i			1.07320i
$56$	−2.49823	+	0.871108i	−0.333841	+	0.116407i
$57$			1.08338i			0.143497i
$58$	−3.60770	+	6.24872i	−0.473714	+	0.820497i
$59$	0.816235	−	0.471253i	0.106265	−	0.0613520i	−0.445926	−	0.895070i	$-0.647125\pi$
$59$	0.816235	−	0.471253i	0.106265	−	0.0613520i	0.552190	+	0.833718i	$0.313792\pi$
$60$	2.35758	−	1.36115i	0.304362	−	0.175723i
$61$	2.62356	−	4.54413i	0.335912	−	0.581816i	−0.647748	−	0.761855i	$-0.724289\pi$
$61$	2.62356	−	4.54413i	0.335912	−	0.581816i	0.983660	+	0.180039i	$0.0576222\pi$
$62$		−	9.58261i		−	1.21699i
$63$	0.494715	−	2.59909i	0.0623283	−	0.327454i
$64$	1.00000			0.125000
$65$	3.20333	+	1.84944i	0.397325	+	0.229395i
$66$	−1.46183	−	2.53196i	−0.179939	−	0.311663i
$67$	−5.27370	+	3.04477i	−0.644285	+	0.371978i	−0.786263	−	0.617892i	$-0.787987\pi$
$67$	−5.27370	+	3.04477i	−0.644285	+	0.371978i	0.141978	+	0.989870i	$0.454654\pi$
$68$	3.08913	−	5.35053i	0.374612	−	0.648847i
$69$	2.66136	−	3.98963i	0.320391	−	0.480295i
$70$	5.45417	+	4.70407i	0.651898	+	0.562244i
$71$	9.73354			1.15516			0.577580	−	0.816334i	$-0.303997\pi$
$71$	9.73354			1.15516			0.577580	+	0.816334i	$0.303997\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−8.70696	+	5.02697i	−1.01907	+	0.588362i	−0.913835	−	0.406085i	$-0.866894\pi$
$73$	−8.70696	+	5.02697i	−1.01907	+	0.588362i	−0.105238	+	0.994447i	$0.533560\pi$
$74$	0.810574	−	0.467985i	0.0942274	−	0.0544022i
$75$	−2.08790	−	1.20545i	−0.241090	−	0.139193i
$76$	1.08338			0.124272
$77$	5.05202	−	5.85760i	0.575731	−	0.667536i
$78$	−1.35874			−0.153847
$79$	−8.01433	−	4.62707i	−0.901682	−	0.520586i	−0.0239366	−	0.999713i	$-0.507620\pi$
$79$	−8.01433	−	4.62707i	−0.901682	−	0.520586i	−0.877746	+	0.479127i	$0.840953\pi$
$80$	−1.36115	−	2.35758i	−0.152181	−	0.263585i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.16330	−	1.82633i	−0.349328	−	0.201685i
$83$	−4.05202			−0.444766			−0.222383	−	0.974959i	$-0.571384\pi$
$83$	−4.05202			−0.444766			−0.222383	+	0.974959i	$0.571384\pi$
$84$	−2.59909	−	0.494715i	−0.283584	−	0.0539779i
$85$	−16.8190			−1.82428
$86$	−8.36004	−	4.82667i	−0.901486	−	0.520473i
$87$	−6.24872	+	3.60770i	−0.669933	+	0.386786i
$88$	−2.53196	+	1.46183i	−0.269908	+	0.155832i
$89$	−7.90496	+	13.6918i	−0.837925	+	1.45133i	0.0537022	+	0.998557i	$0.482898\pi$
$89$	−7.90496	+	13.6918i	−0.837925	+	1.45133i	−0.891627	+	0.452771i	$0.850436\pi$
$90$	2.72230			0.286955
$91$	−1.18361	−	3.39445i	−0.124076	−	0.355835i
$92$	−3.98963	−	2.66136i	−0.415948	−	0.277466i
$93$	4.79131	−	8.29879i	0.496835	−	0.860544i
$94$	6.68553	−	3.85989i	0.689559	−	0.398117i
$95$	−1.47464	−	2.55415i	−0.151295	−	0.262050i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	7.72846			0.784706			0.392353	−	0.919815i	$-0.371661\pi$
$97$	7.72846			0.784706			0.392353	+	0.919815i	$0.371661\pi$
$98$	−1.02817	−	6.92408i	−0.103861	−	0.699438i
$99$		−	2.92366i		−	0.293839i
$100$	−1.20545	+	2.08790i	−0.120545	+	0.208790i
$101$	−12.1987	+	7.04294i	−1.21382	+	0.700799i	−0.963589	−	0.267387i	$-0.913840\pi$
$101$	−12.1987	+	7.04294i	−1.21382	+	0.700799i	−0.250231	+	0.968186i	$0.580506\pi$
$102$	5.35053	−	3.08913i	0.529781	−	0.305869i
$103$	−4.60109	+	7.96932i	−0.453359	+	0.785240i	−0.998592	−	0.0530440i	$-0.983108\pi$
$103$	−4.60109	+	7.96932i	−0.453359	+	0.785240i	0.545234	+	0.838284i	$0.316441\pi$
$104$			1.35874i			0.133235i
$105$	2.37141	+	6.80093i	0.231426	+	0.663703i
$106$			3.58717i			0.348417i
$107$	6.18869	+	3.57304i	0.598283	+	0.345419i	0.768366	−	0.640011i	$-0.221070\pi$
$107$	6.18869	+	3.57304i	0.598283	+	0.345419i	−0.170083	+	0.985430i	$0.554403\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−12.0283	+	6.94453i	−1.15210	+	0.665166i	−0.949398	−	0.314075i	$-0.898306\pi$
$109$	−12.0283	+	6.94453i	−1.15210	+	0.665166i	−0.202703	+	0.979240i	$0.564972\pi$
$110$	6.89275	+	3.97953i	0.657198	+	0.379434i
$111$	0.935971			0.0888384
$112$	−0.494715	+	2.59909i	−0.0467462	+	0.245591i
$113$			4.83911i			0.455225i	0.973752	+	0.227613i	$0.0730920\pi$
$113$			4.83911i			0.455225i	−0.973752	+	0.227613i	$0.926908\pi$
$114$	0.938233	+	0.541689i	0.0878736	+	0.0507338i
$115$	−0.843899	+	13.0284i	−0.0786940	+	1.21490i
$116$	3.60770	+	6.24872i	0.334967	+	0.580179i
$117$	−1.17670	−	0.679369i	−0.108786	−	0.0628077i
$118$		−	0.942507i		−	0.0867648i
$119$	12.3782	+	10.6759i	1.13471	+	0.978658i
$120$		−	2.72230i		−	0.248511i
$121$	−1.22611	+	2.12368i	−0.111465	+	0.193062i
$122$	−2.62356	−	4.54413i	−0.237526	−	0.411406i
$123$	−1.82633	−	3.16330i	−0.164675	−	0.285225i
$124$	−8.29879	−	4.79131i	−0.745253	−	0.430272i
$125$	−7.04830			−0.630419
$126$	−2.00352	−	1.72798i	−0.178488	−	0.153941i
$127$	−17.4300			−1.54667			−0.773333	−	0.634000i	$-0.781412\pi$
$127$	−17.4300			−1.54667			−0.773333	+	0.634000i	$0.781412\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.82667	−	8.36004i	−0.424964	−	0.736060i
$130$	3.20333	−	1.84944i	0.280951	−	0.162207i
$131$	16.5091	+	9.53156i	1.44241	+	0.832776i	0.998010	−	0.0630526i	$-0.0200836\pi$
$131$	16.5091	+	9.53156i	1.44241	+	0.832776i	0.444400	+	0.895828i	$0.353417\pi$
$132$	−2.92366			−0.254472
$133$	−0.535964	+	2.81579i	−0.0464739	+	0.244160i
$134$			6.08954i			0.526056i
$135$	2.35758	+	1.36115i	0.202908	+	0.117149i
$136$	−3.08913	−	5.35053i	−0.264891	−	0.458804i
$137$	−4.38654	+	2.53257i	−0.374767	+	0.216372i	−0.675539	−	0.737324i	$-0.736089\pi$
$137$	−4.38654	+	2.53257i	−0.374767	+	0.216372i	0.300772	+	0.953696i	$0.402756\pi$
$138$	−2.12444	−	4.29962i	−0.180844	−	0.366008i
$139$		−	11.6813i		−	0.990791i	−0.868668	−	0.495396i	$-0.835023\pi$
$139$		−	11.6813i		−	0.990791i	0.868668	−	0.495396i	$-0.164977\pi$
$140$	6.80093	−	2.37141i	0.574784	−	0.200421i
$141$	7.71978			0.650123
$142$	4.86677	−	8.42950i	0.408410	−	0.707388i
$143$	−1.98624	−	3.44028i	−0.166098	−	0.287690i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	9.82123	−	17.0109i	0.815609	−	1.41268i
$146$			10.0539i			0.832070i
$147$	2.57162	−	6.51051i	0.212103	−	0.536978i
$148$		−	0.935971i		−	0.0769363i
$149$	−2.43807	−	1.40762i	−0.199734	−	0.115317i	0.396797	−	0.917906i	$-0.370122\pi$
$149$	−2.43807	−	1.40762i	−0.199734	−	0.115317i	−0.596532	+	0.802590i	$0.703455\pi$
$150$	−2.08790	+	1.20545i	−0.170476	+	0.0984245i
$151$	−4.20972	−	7.29145i	−0.342582	−	0.593370i	0.642329	−	0.766429i	$-0.277968\pi$
$151$	−4.20972	−	7.29145i	−0.342582	−	0.593370i	−0.984911	+	0.173059i	$0.944635\pi$
$152$	0.541689	−	0.938233i	0.0439368	−	0.0761007i
$153$	6.17826			0.499482
$154$	−2.54682	−	7.30398i	−0.205229	−	0.588572i
$155$			26.0867i			2.09534i
$156$	−0.679369	+	1.17670i	−0.0543931	+	0.0942116i
$157$	−2.85671	−	4.94796i	−0.227990	−	0.394890i	0.729222	−	0.684277i	$-0.239882\pi$
$157$	−2.85671	−	4.94796i	−0.227990	−	0.394890i	−0.957212	+	0.289387i	$0.906549\pi$
$158$	−8.01433	+	4.62707i	−0.637586	+	0.368110i
$159$	−1.79359	+	3.10658i	−0.142241	+	0.246368i
$160$	−2.72230			−0.215216
$161$	8.89085	−	9.05278i	0.700697	−	0.713459i
$162$	−1.00000			−0.0785674
$163$	−4.54820	+	7.87772i	−0.356243	+	0.617031i	−0.987330	−	0.158681i	$-0.949276\pi$
$163$	−4.54820	+	7.87772i	−0.356243	+	0.617031i	0.631087	+	0.775712i	$0.282609\pi$
$164$	−3.16330	+	1.82633i	−0.247012	+	0.142612i
$165$	3.97953	+	6.89275i	0.309806	+	0.536600i
$166$	−2.02601	+	3.50915i	−0.157249	+	0.272363i
$167$		−	2.39661i		−	0.185455i	−0.995692	−	0.0927276i	$-0.970441\pi$
$167$		−	2.39661i		−	0.185455i	0.995692	−	0.0927276i	$-0.0295586\pi$
$168$	−1.72798	+	2.00352i	−0.133317	+	0.154575i
$169$	11.1538			0.857987
$170$	−8.40952	+	14.5657i	−0.644981	+	1.11714i
$171$	0.541689	+	0.938233i	0.0414240	+	0.0717485i
$172$	−8.36004	+	4.82667i	−0.637447	+	0.368030i
$173$	13.2333	+	7.64025i	1.00611	+	0.580878i	0.910050	−	0.414498i	$-0.136043\pi$
$173$	13.2333	+	7.64025i	1.00611	+	0.580878i	0.0960593	+	0.995376i	$0.469376\pi$
$174$			7.21540i			0.546998i
$175$	−4.83028	−	4.16598i	−0.365135	−	0.314919i
$176$			2.92366i			0.220379i
$177$	0.471253	−	0.816235i	0.0354216	−	0.0613520i
$178$	7.90496	+	13.6918i	0.592502	+	1.02624i
$179$	−7.69546	−	13.3289i	−0.575186	−	0.996251i	−0.996021	−	0.0891143i	$-0.971596\pi$
$179$	−7.69546	−	13.3289i	−0.575186	−	0.996251i	0.420835	−	0.907137i	$-0.361737\pi$
$180$	1.36115	−	2.35758i	0.101454	−	0.175723i
$181$	−7.81291			−0.580729			−0.290364	−	0.956916i	$-0.593776\pi$
$181$	−7.81291			−0.580729			−0.290364	+	0.956916i	$0.593776\pi$
$182$	−3.53148	−	0.672189i	−0.261771	−	0.0498260i
$183$		−	5.24711i		−	0.387878i
$184$	−4.29962	+	2.12444i	−0.316972	+	0.156616i
$185$	−2.20662	+	1.27399i	−0.162234	+	0.0936660i
$186$	−4.79131	−	8.29879i	−0.351316	−	0.608497i
$187$	15.6431	+	9.03156i	1.14394	+	0.660453i
$188$		−	7.71978i		−	0.563023i
$189$	−0.871108	−	2.49823i	−0.0633638	−	0.181720i
$190$	−2.94928			−0.213963
$191$	0.0160412	+	0.00926140i	0.00116070	+	0.000670131i	0.500580	−	0.865690i	$-0.333120\pi$
$191$	0.0160412	+	0.00926140i	0.00116070	+	0.000670131i	−0.499420	+	0.866360i	$0.666453\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	1.45973	+	2.52833i	0.105074	+	0.181993i	0.913768	−	0.406236i	$-0.133159\pi$
$193$	1.45973	+	2.52833i	0.105074	+	0.181993i	−0.808695	+	0.588229i	$0.799825\pi$
$194$	3.86423	−	6.69304i	0.277436	−	0.480532i
$195$	3.69889			0.264883
$196$	−6.51051	−	2.57162i	−0.465037	−	0.183687i
$197$	−4.02713			−0.286921			−0.143460	−	0.989656i	$-0.545823\pi$
$197$	−4.02713			−0.286921			−0.143460	+	0.989656i	$0.545823\pi$
$198$	−2.53196	−	1.46183i	−0.179939	−	0.103888i
$199$	−2.91462	−	5.04827i	−0.206612	−	0.357863i	0.744033	−	0.668143i	$-0.232910\pi$
$199$	−2.91462	−	5.04827i	−0.206612	−	0.357863i	−0.950645	+	0.310280i	$0.899577\pi$
$200$	1.20545	+	2.08790i	0.0852381	+	0.147637i
$201$	−3.04477	+	5.27370i	−0.214762	+	0.371978i
$202$			14.0859i			0.991080i
$203$	−18.0258	+	6.28539i	−1.26516	+	0.441148i
$204$		−	6.17826i		−	0.432564i
$205$	8.61143	+	4.97181i	0.601449	+	0.347247i
$206$	4.60109	+	7.96932i	0.320573	+	0.555249i
$207$	0.309995	−	4.78580i	0.0215462	−	0.332636i
$208$	1.17670	+	0.679369i	0.0815896	+	0.0471058i
$209$			3.16743i			0.219096i
$210$	7.07549	+	1.34676i	0.488255	+	0.0929354i
$211$	13.6220			0.937778			0.468889	−	0.883257i	$-0.344654\pi$
$211$	13.6220			0.937778			0.468889	+	0.883257i	$0.344654\pi$
$212$	3.10658	+	1.79359i	0.213361	+	0.123184i
$213$	8.42950	−	4.86677i	0.577580	−	0.333466i
$214$	6.18869	−	3.57304i	0.423050	−	0.244248i
$215$	22.7585	+	13.1396i	1.55212	+	0.896115i
$216$			1.00000i			0.0680414i
$217$	16.5586	−	19.1989i	1.12407	−	1.30331i
$218$			13.8891i			0.940686i
$219$	−5.02697	+	8.70696i	−0.339691	+	0.588362i
$220$	6.89275	−	3.97953i	0.464709	−	0.268300i
$221$	7.26997	−	4.19732i	0.489031	−	0.282342i
$222$	0.467985	−	0.810574i	0.0314091	−	0.0544022i
$223$			21.7372i			1.45563i	0.685771	+	0.727817i	$0.259465\pi$
$223$			21.7372i			1.45563i	−0.685771	+	0.727817i	$0.740535\pi$
$224$	2.00352	+	1.72798i	0.133866	+	0.115456i
$225$	−2.41090			−0.160727
$226$	4.19079	+	2.41956i	0.278767	+	0.160946i
$227$	2.00900	+	3.47969i	0.133342	+	0.230955i	0.924963	−	0.380058i	$-0.124096\pi$
$227$	2.00900	+	3.47969i	0.133342	+	0.230955i	−0.791621	+	0.611013i	$0.790762\pi$
$228$	0.938233	−	0.541689i	0.0621360	−	0.0358742i
$229$	12.1490	−	21.0427i	0.802829	−	1.39054i	−0.114918	−	0.993375i	$-0.536660\pi$
$229$	12.1490	−	21.0427i	0.802829	−	1.39054i	0.917747	−	0.397166i	$-0.130006\pi$
$230$	10.8610	+	7.24502i	0.716150	+	0.477723i
$231$	1.44638	−	7.59885i	0.0951647	−	0.499967i
$232$	7.21540			0.473714
$233$	7.84129	−	13.5815i	0.513700	−	0.889755i	−0.486174	−	0.873862i	$-0.661608\pi$
$233$	7.84129	−	13.5815i	0.513700	−	0.889755i	0.999874	−	0.0158924i	$-0.00505893\pi$
$234$	−1.17670	+	0.679369i	−0.0769234	+	0.0444118i
$235$	−18.2000	+	10.5078i	−1.18724	+	0.685451i
$236$	−0.816235	−	0.471253i	−0.0531324	−	0.0306760i
$237$	−9.25415			−0.601121
$238$	15.4347	−	5.38193i	1.00048	−	0.348859i
$239$	−29.6717			−1.91931			−0.959653	−	0.281187i	$-0.909272\pi$
$239$	−29.6717			−1.91931			−0.959653	+	0.281187i	$0.909272\pi$
$240$	−2.35758	−	1.36115i	−0.152181	−	0.0878617i
$241$	5.83374	+	10.1043i	0.375784	+	0.650877i	0.990444	−	0.137915i	$-0.0440400\pi$
$241$	5.83374	+	10.1043i	0.375784	+	0.650877i	−0.614660	+	0.788792i	$0.710707\pi$
$242$	1.22611	+	2.12368i	0.0788173	+	0.136516i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−5.24711			−0.335912
$245$	2.79899	+	18.8494i	0.178821	+	1.20424i
$246$	−3.65266			−0.232885
$247$	1.27481	+	0.736014i	0.0811144	+	0.0468314i
$248$	−8.29879	+	4.79131i	−0.526974	+	0.304248i
$249$	−3.50915	+	2.02601i	−0.222383	+	0.128393i
$250$	−3.52415	+	6.10401i	−0.222887	+	0.386051i
$251$	−26.9984			−1.70412			−0.852062	−	0.523440i	$-0.824648\pi$
$251$	−26.9984			−1.70412			−0.852062	+	0.523440i	$0.824648\pi$
$252$	−2.49823	+	0.871108i	−0.157374	+	0.0548746i
$253$	7.78092	−	11.6643i	0.489182	−	0.733329i
$254$	−8.71502	+	15.0949i	−0.546829	+	0.947136i
$255$	−14.5657	+	8.40952i	−0.912141	+	0.526625i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.68924	−	3.86203i	−0.417263	−	0.240907i	0.276642	−	0.960973i	$-0.410778\pi$
$257$	−6.68924	−	3.86203i	−0.417263	−	0.240907i	−0.693906	+	0.720066i	$0.744112\pi$
$258$	−9.65334			−0.600991
$259$	2.43267	+	0.463039i	0.151159	+	0.0287718i
$260$		−	3.69889i		−	0.229395i
$261$	−3.60770	+	6.24872i	−0.223311	+	0.386786i
$262$	16.5091	−	9.53156i	1.01994	−	0.588861i
$263$	−9.20999	+	5.31739i	−0.567913	+	0.327884i	−0.756315	−	0.654207i	$-0.773002\pi$
$263$	−9.20999	+	5.31739i	−0.567913	+	0.327884i	0.188403	+	0.982092i	$0.439669\pi$
$264$	−1.46183	+	2.53196i	−0.0899694	+	0.155832i
$265$		−	9.76535i		−	0.599881i
$266$	2.17057	+	1.87206i	0.133086	+	0.114783i
$267$			15.8099i			0.967552i
$268$	5.27370	+	3.04477i	0.322142	+	0.185989i
$269$	24.8393	−	14.3410i	1.51448	−	0.874383i	0.514621	−	0.857418i	$-0.327933\pi$
$269$	24.8393	−	14.3410i	1.51448	−	0.874383i	0.999856	−	0.0169655i	$-0.00540053\pi$
$270$	2.35758	−	1.36115i	0.143478	−	0.0828368i
$271$	−5.32212	−	3.07273i	−0.323296	−	0.186655i	0.329565	−	0.944133i	$-0.393098\pi$
$271$	−5.32212	−	3.07273i	−0.323296	−	0.186655i	−0.652861	+	0.757478i	$0.726431\pi$
$272$	−6.17826			−0.374612
$273$	−2.72226	−	2.34787i	−0.164759	−	0.142100i
$274$			5.06514i			0.305996i
$275$	−6.10430	−	3.52432i	−0.368103	−	0.212525i
$276$	−4.78580	−	0.309995i	−0.288071	−	0.0186595i
$277$	−14.3064	−	24.7795i	−0.859591	−	1.48886i	−0.872319	−	0.488936i	$-0.837385\pi$
$277$	−14.3064	−	24.7795i	−0.859591	−	1.48886i	0.0127284	−	0.999919i	$-0.495948\pi$
$278$	−10.1163	−	5.84063i	−0.606733	−	0.350298i
$279$		−	9.58261i		−	0.573696i
$280$	1.34676	−	7.07549i	0.0804844	−	0.422841i
$281$			27.4967i			1.64032i	0.572136	+	0.820159i	$0.306115\pi$
$281$			27.4967i			1.64032i	−0.572136	+	0.820159i	$0.693885\pi$
$282$	3.85989	−	6.68553i	0.229853	−	0.398117i
$283$	1.90989	+	3.30802i	0.113531	+	0.196641i	0.917192	−	0.398446i	$-0.130451\pi$
$283$	1.90989	+	3.30802i	0.113531	+	0.196641i	−0.803661	+	0.595088i	$0.797117\pi$
$284$	−4.86677	−	8.42950i	−0.288790	−	0.500199i
$285$	−2.55415	−	1.47464i	−0.151295	−	0.0873500i
$286$	−3.97249			−0.234898
$287$	−3.18186	−	9.12520i	−0.187819	−	0.538644i
$288$	1.00000			0.0589256
$289$	−10.5854	+	18.3345i	−0.622672	+	1.07850i
$290$	−9.82123	−	17.0109i	−0.576723	−	0.998913i
$291$	6.69304	−	3.86423i	0.392353	−	0.226525i
$292$	8.70696	+	5.02697i	0.509537	+	0.294181i
$293$	−28.0385			−1.63802			−0.819012	−	0.573776i	$-0.805478\pi$
$293$	−28.0385			−1.63802			−0.819012	+	0.573776i	$0.805478\pi$
$294$	−4.35246	−	5.48234i	−0.253841	−	0.319737i
$295$			2.56578i			0.149386i
$296$	−0.810574	−	0.467985i	−0.0471137	−	0.0272011i
$297$	−1.46183	−	2.53196i	−0.0848239	−	0.146919i
$298$	−2.43807	+	1.40762i	−0.141233	+	0.0815412i
$299$	−2.88656	−	5.84207i	−0.166934	−	0.337855i
$300$			2.41090i			0.139193i
$301$	−8.40910	−	24.1163i	−0.484692	−	1.39004i
$302$	−8.41944			−0.484485
$303$	−7.04294	+	12.1987i	−0.404607	+	0.700799i
$304$	−0.541689	−	0.938233i	−0.0310680	−	0.0538113i
$305$	7.14210	+	12.3705i	0.408955	+	0.708331i
$306$	3.08913	−	5.35053i	0.176594	−	0.305869i
$307$		−	1.38597i		−	0.0791014i	−0.999218	−	0.0395507i	$-0.987407\pi$
$307$		−	1.38597i		−	0.0791014i	0.999218	−	0.0395507i	$-0.0125927\pi$
$308$	−7.59885	−	1.44638i	−0.432984	−	0.0824151i
$309$			9.20218i			0.523493i
$310$	22.5918	+	13.0434i	1.28313	+	0.740813i
$311$	−14.6219	+	8.44198i	−0.829134	+	0.478701i	−0.853556	−	0.521001i	$-0.825559\pi$
$311$	−14.6219	+	8.44198i	−0.829134	+	0.478701i	0.0244217	+	0.999702i	$0.492226\pi$
$312$	0.679369	+	1.17670i	0.0384617	+	0.0666177i
$313$	14.6230	−	25.3279i	0.826543	−	1.43162i	−0.0741906	−	0.997244i	$-0.523637\pi$
$313$	14.6230	−	25.3279i	0.826543	−	1.43162i	0.900734	−	0.434371i	$-0.143029\pi$
$314$	−5.71341			−0.322427
$315$	5.45417	+	4.70407i	0.307308	+	0.265045i
$316$			9.25415i			0.520586i
$317$	5.03623	−	8.72300i	0.282863	−	0.489933i	−0.689226	−	0.724546i	$-0.742049\pi$
$317$	5.03623	−	8.72300i	0.282863	−	0.489933i	0.972089	+	0.234614i	$0.0753826\pi$
$318$	1.79359	+	3.10658i	0.100579	+	0.174209i
$319$	−18.2691	+	10.5477i	−1.02287	+	0.590557i
$320$	−1.36115	+	2.35758i	−0.0760905	+	0.131793i
$321$	7.14608			0.398855
$322$	−3.39451	−	12.2261i	−0.189169	−	0.681333i
$323$	−6.69339			−0.372430
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.83691	+	1.63789i	−0.157363	+	0.0908538i
$326$	4.54820	+	7.87772i	0.251902	+	0.436307i
$327$	−6.94453	+	12.0283i	−0.384034	+	0.665166i
$328$			3.65266i			0.201685i
$329$	20.0644	+	3.81909i	1.10619	+	0.210553i
$330$	7.95907			0.438132
$331$	−3.03257	+	5.25256i	−0.166685	+	0.288707i	−0.937252	−	0.348652i	$-0.886640\pi$
$331$	−3.03257	+	5.25256i	−0.166685	+	0.288707i	0.770567	+	0.637358i	$0.219973\pi$
$332$	2.02601	+	3.50915i	0.111192	+	0.192590i
$333$	0.810574	−	0.467985i	0.0444192	−	0.0256454i
$334$	−2.07552	−	1.19830i	−0.113568	−	0.0655683i
$335$		−	16.5775i		−	0.905728i
$336$	0.871108	+	2.49823i	0.0475228	+	0.136290i
$337$			22.7775i			1.24077i	0.784297	+	0.620385i	$0.213024\pi$
$337$			22.7775i			1.24077i	−0.784297	+	0.620385i	$0.786976\pi$
$338$	5.57691	−	9.65950i	0.303344	−	0.525407i
$339$	2.41956	+	4.19079i	0.131412	+	0.227613i
$340$	8.40952	+	14.5657i	0.456070	+	0.789937i
$341$	14.0081	−	24.2628i	0.758584	−	1.31391i
$342$	1.08338			0.0585824
$343$	9.90471	−	15.6492i	0.534804	−	0.844976i
$344$			9.65334i			0.520473i
$345$	5.78335	+	11.7049i	0.311365	+	0.630168i
$346$	13.2333	−	7.64025i	0.711427	−	0.410742i
$347$	−2.21821	−	3.84206i	−0.119080	−	0.206252i	0.800323	−	0.599569i	$-0.204661\pi$
$347$	−2.21821	−	3.84206i	−0.119080	−	0.206252i	−0.919403	+	0.393316i	$0.871328\pi$
$348$	6.24872	+	3.60770i	0.334967	+	0.193393i
$349$			14.8181i			0.793197i	0.917992	+	0.396599i	$0.129810\pi$
$349$			14.8181i			0.793197i	−0.917992	+	0.396599i	$0.870190\pi$
$350$	−6.02299	+	2.10015i	−0.321942	+	0.112258i
$351$	−1.35874			−0.0725241
$352$	2.53196	+	1.46183i	0.134954	+	0.0779158i
$353$	−21.4311	+	12.3733i	−1.14066	+	0.658562i	−0.946595	−	0.322426i	$-0.895502\pi$
$353$	−21.4311	+	12.3733i	−1.14066	+	0.658562i	−0.194068	+	0.980988i	$0.562168\pi$
$354$	−0.471253	−	0.816235i	−0.0250468	−	0.0433824i
$355$	−13.2488	+	22.9476i	−0.703173	+	1.21793i
$356$	15.8099			0.837925
$357$	16.0578	+	3.05648i	0.849870	+	0.161766i
$358$	−15.3909			−0.813436
$359$	−14.3556	−	8.28820i	−0.757659	−	0.437434i	0.0707959	−	0.997491i	$-0.477446\pi$
$359$	−14.3556	−	8.28820i	−0.757659	−	0.437434i	−0.828454	+	0.560056i	$0.810779\pi$
$360$	−1.36115	−	2.35758i	−0.0717388	−	0.124255i
$361$	8.91315	+	15.4380i	0.469113	+	0.812527i
$362$	−3.90645	+	6.76617i	−0.205319	+	0.355622i
$363$			2.45222i			0.128708i
$364$	−2.34787	+	2.72226i	−0.123062	+	0.142685i
$365$		−	27.3698i		−	1.43260i
$366$	−4.54413	−	2.62356i	−0.237526	−	0.137135i
$367$	−3.82750	−	6.62942i	−0.199794	−	0.346053i	0.748668	−	0.662945i	$-0.230694\pi$
$367$	−3.82750	−	6.62942i	−0.199794	−	0.346053i	−0.948461	+	0.316893i	$0.897361\pi$
$368$	−0.309995	+	4.78580i	−0.0161596	+	0.249477i
$369$	−3.16330	−	1.82633i	−0.164675	−	0.0950750i
$370$			2.54799i			0.132464i
$371$	−6.19856	+	7.18697i	−0.321813	+	0.373129i
$372$	−9.58261			−0.496835
$373$	−23.5985	−	13.6246i	−1.22188	−	0.705455i	−0.256565	−	0.966527i	$-0.582591\pi$
$373$	−23.5985	−	13.6246i	−1.22188	−	0.705455i	−0.965319	+	0.261072i	$0.915924\pi$
$374$	15.6431	−	9.03156i	0.808886	−	0.467011i
$375$	−6.10401	+	3.52415i	−0.315210	+	0.181986i
$376$	−6.68553	−	3.85989i	−0.344780	−	0.199059i
$377$			9.80385i			0.504924i
$378$	−2.59909	−	0.494715i	−0.133683	−	0.0254454i
$379$		−	11.8932i		−	0.610910i	−0.952206	−	0.305455i	$-0.901191\pi$
$379$		−	11.8932i		−	0.610910i	0.952206	−	0.305455i	$-0.0988086\pi$
$380$	−1.47464	+	2.55415i	−0.0756473	+	0.131025i
$381$	−15.0949	+	8.71502i	−0.773333	+	0.446484i
$382$	0.0160412	−	0.00926140i	0.000820740	−	0.000473854i
$383$	13.4113	−	23.2290i	0.685284	−	1.18695i	−0.288064	−	0.957611i	$-0.593012\pi$
$383$	13.4113	−	23.2290i	0.685284	−	1.18695i	0.973348	−	0.229335i	$-0.0736551\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	6.93320	+	19.8836i	0.353349	+	1.01336i
$386$	2.91946			0.148597
$387$	−8.36004	−	4.82667i	−0.424964	−	0.245353i
$388$	−3.86423	−	6.69304i	−0.196177	−	0.339788i
$389$	28.6634	−	16.5488i	1.45329	−	0.839060i	0.454627	−	0.890682i	$-0.349772\pi$
$389$	28.6634	−	16.5488i	1.45329	−	0.839060i	0.998667	+	0.0516221i	$0.0164391\pi$
$390$	1.84944	−	3.20333i	0.0936503	−	0.162207i
$391$	24.6489	+	16.4426i	1.24655	+	0.831538i
$392$	−5.48234	+	4.35246i	−0.276900	+	0.219833i
$393$	19.0631			0.961607
$394$	−2.01356	+	3.48759i	−0.101442	+	0.175702i
$395$	21.8174	−	12.5963i	1.09775	−	0.633787i
$396$	−2.53196	+	1.46183i	−0.127236	+	0.0734597i
$397$	5.07145	+	2.92800i	0.254529	+	0.146952i	0.621836	−	0.783147i	$-0.286387\pi$
$397$	5.07145	+	2.92800i	0.254529	+	0.146952i	−0.367307	+	0.930100i	$0.619720\pi$
$398$	−5.82924			−0.292194
$399$	0.943739	+	2.70653i	0.0472460	+	0.135496i
$400$	2.41090			0.120545
$401$	4.52889	+	2.61476i	0.226162	+	0.130575i	0.608800	−	0.793323i	$-0.291651\pi$
$401$	4.52889	+	2.61476i	0.226162	+	0.130575i	−0.382638	+	0.923898i	$0.624984\pi$
$402$	3.04477	+	5.27370i	0.151859	+	0.263028i
$403$	−6.51014	−	11.2759i	−0.324293	−	0.561692i
$404$	12.1987	+	7.04294i	0.606910	+	0.350400i
$405$	2.72230			0.135272
$406$	−3.56957	+	18.7535i	−0.177155	+	0.930719i
$407$	2.73646			0.135641
$408$	−5.35053	−	3.08913i	−0.264891	−	0.152935i
$409$	−2.58935	+	1.49496i	−0.128035	+	0.0739212i	−0.562650	−	0.826695i	$-0.690218\pi$
$409$	−2.58935	+	1.49496i	−0.128035	+	0.0739212i	0.434614	+	0.900617i	$0.356885\pi$
$410$	8.61143	−	4.97181i	0.425288	−	0.245540i
$411$	−2.53257	+	4.38654i	−0.124922	+	0.216372i
$412$	9.20218			0.453359
$413$	1.62863	−	1.88833i	0.0801398	−	0.0929186i
$414$	−3.98963	−	2.66136i	−0.196080	−	0.130799i
$415$	5.51539	−	9.55294i	0.270740	−	0.468935i
$416$	1.17670	−	0.679369i	0.0576926	−	0.0333088i
$417$	−5.84063	−	10.1163i	−0.286017	−	0.495396i
$418$	2.74307	+	1.58371i	0.134168	+	0.0774620i
$419$	12.0724			0.589776			0.294888	−	0.955532i	$-0.404718\pi$
$419$	12.0724			0.589776			0.294888	+	0.955532i	$0.404718\pi$
$420$	4.70407	−	5.45417i	0.229535	−	0.266136i
$421$		−	1.81297i		−	0.0883586i	−0.999024	−	0.0441793i	$-0.985933\pi$
$421$		−	1.81297i		−	0.0883586i	0.999024	−	0.0441793i	$-0.0140673\pi$
$422$	6.81101	−	11.7970i	0.331555	−	0.574269i
$423$	6.68553	−	3.85989i	0.325061	−	0.187674i
$424$	3.10658	−	1.79359i	0.150869	−	0.0871043i
$425$	7.44757	−	12.8996i	0.361260	−	0.625721i
$426$		−	9.73354i		−	0.471592i
$427$	2.59583	−	13.6377i	0.125621	−	0.659975i
$428$		−	7.14608i		−	0.345419i
$429$	−3.44028	−	1.98624i	−0.166098	−	0.0958968i
$430$	22.7585	−	13.1396i	1.09751	−	0.633649i
$431$	−14.3961	+	8.31161i	−0.693437	+	0.400356i	−0.804898	−	0.593413i	$-0.797780\pi$
$431$	−14.3961	+	8.31161i	−0.693437	+	0.400356i	0.111461	+	0.993769i	$0.464447\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	7.39176			0.355225			0.177613	−	0.984100i	$-0.443163\pi$
$433$	7.39176			0.355225			0.177613	+	0.984100i	$0.443163\pi$
$434$	−8.34749	−	23.9396i	−0.400692	−	1.14914i
$435$		−	19.6425i		−	0.941784i
$436$	12.0283	+	6.94453i	0.576050	+	0.332583i
$437$	−0.335842	+	5.18483i	−0.0160655	+	0.248024i
$438$	5.02697	+	8.70696i	0.240198	+	0.416035i
$439$	14.1011	+	8.14128i	0.673010	+	0.388562i	0.797216	−	0.603694i	$-0.206305\pi$
$439$	14.1011	+	8.14128i	0.673010	+	0.388562i	−0.124206	+	0.992256i	$0.539639\pi$
$440$		−	7.95907i		−	0.379434i
$441$	−1.02817	−	6.92408i	−0.0489605	−	0.329718i
$442$		−	8.39464i		−	0.399292i
$443$	−12.5407	+	21.7211i	−0.595825	+	1.03200i	0.397605	+	0.917557i	$0.369841\pi$
$443$	−12.5407	+	21.7211i	−0.595825	+	1.03200i	−0.993430	+	0.114442i	$0.963492\pi$
$444$	−0.467985	−	0.810574i	−0.0222096	−	0.0384682i
$445$	−21.5197	−	37.2731i	−1.02013	−	1.76692i
$446$	18.8250	+	10.8686i	0.891390	+	0.514644i
$447$	−2.81524			−0.133156
$448$	2.49823	−	0.871108i	0.118030	−	0.0411560i
$449$	−6.11865			−0.288757			−0.144378	−	0.989523i	$-0.546118\pi$
$449$	−6.11865			−0.288757			−0.144378	+	0.989523i	$0.546118\pi$
$450$	−1.20545	+	2.08790i	−0.0568254	+	0.0984245i
$451$	−5.33957	−	9.24840i	−0.251430	−	0.435490i
$452$	4.19079	−	2.41956i	0.197118	−	0.113806i
$453$	−7.29145	−	4.20972i	−0.342582	−	0.197790i
$454$	4.01800			0.188574
$455$	9.61374	+	1.82990i	0.450699	+	0.0857869i
$456$		−	1.08338i		−	0.0507338i
$457$	30.5252	+	17.6237i	1.42791	+	0.824403i	0.996956	−	0.0779720i	$-0.0248445\pi$
$457$	30.5252	+	17.6237i	1.42791	+	0.824403i	0.430952	+	0.902375i	$0.358178\pi$
$458$	−12.1490	−	21.0427i	−0.567686	−	0.983261i
$459$	5.35053	−	3.08913i	0.249741	−	0.144188i
$460$	11.7049	−	5.78335i	0.545741	−	0.269650i
$461$		−	7.10680i		−	0.330997i	−0.986210	−	0.165498i	$-0.947077\pi$
$461$		−	7.10680i		−	0.330997i	0.986210	−	0.165498i	$-0.0529232\pi$
$462$	−5.85760	−	5.05202i	−0.272520	−	0.235041i
$463$	0.974965			0.0453105			0.0226552	−	0.999743i	$-0.492788\pi$
$463$	0.974965			0.0453105			0.0226552	+	0.999743i	$0.492788\pi$
$464$	3.60770	−	6.24872i	0.167483	−	0.290090i
$465$	13.0434	+	22.5918i	0.604871	+	1.04767i
$466$	−7.84129	−	13.5815i	−0.363241	−	0.629152i
$467$	17.6399	−	30.5532i	0.816277	−	1.41383i	−0.0921296	−	0.995747i	$-0.529367\pi$
$467$	17.6399	−	30.5532i	0.816277	−	1.41383i	0.908407	−	0.418087i	$-0.137299\pi$
$468$			1.35874i			0.0628077i
$469$	−10.5226	+	12.2005i	−0.485889	+	0.563367i
$470$			21.0155i			0.969374i
$471$	−4.94796	−	2.85671i	−0.227990	−	0.131630i
$472$	−0.816235	+	0.471253i	−0.0375703	+	0.0216912i
$473$	−14.1115	−	24.4419i	−0.648849	−	1.12384i
$474$	−4.62707	+	8.01433i	−0.212529	+	0.368110i
$475$	2.61191			0.119843
$476$	3.05648	−	16.0578i	0.140093	−	0.736009i
$477$			3.58717i			0.164245i
$478$	−14.8359	+	25.6965i	−0.678577	+	1.17533i
$479$	−14.2528	−	24.6865i	−0.651225	−	1.12795i	−0.982826	−	0.184535i	$-0.940922\pi$
$479$	−14.2528	−	24.6865i	−0.651225	−	1.12795i	0.331601	−	0.943420i	$-0.392411\pi$
$480$	−2.35758	+	1.36115i	−0.107608	+	0.0621276i
$481$	0.635870	−	1.10136i	0.0289932	−	0.0502176i
$482$	11.6675			0.531439
$483$	3.17331	−	12.2854i	0.144391	−	0.559003i
$484$	2.45222			0.111465
$485$	−10.5196	+	18.2204i	−0.477669	+	0.827348i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−18.1711	−	31.4733i	−0.823411	−	1.42619i	−0.903128	−	0.429372i	$-0.858735\pi$
$487$	−18.1711	−	31.4733i	−0.823411	−	1.42619i	0.0797171	−	0.996818i	$-0.474598\pi$
$488$	−2.62356	+	4.54413i	−0.118763	+	0.205703i
$489$			9.09641i			0.411354i
$490$	17.7235	+	7.00070i	0.800668	+	0.316260i
$491$	−21.9356			−0.989938			−0.494969	−	0.868910i	$-0.664821\pi$
$491$	−21.9356			−0.989938			−0.494969	+	0.868910i	$0.664821\pi$
$492$	−1.82633	+	3.16330i	−0.0823374	+	0.142612i
$493$	−22.2893	−	38.6062i	−1.00386	−	1.73874i
$494$	1.27481	−	0.736014i	0.0573566	−	0.0331148i
$495$	6.89275	+	3.97953i	0.309806	+	0.178867i
$496$			9.58261i			0.430272i
$497$	24.3167	−	8.47897i	1.09075	−	0.380334i
$498$			4.05202i			0.181575i
$499$	−13.0071	+	22.5289i	−0.582277	+	1.00853i	0.412932	+	0.910762i	$0.364505\pi$
$499$	−13.0071	+	22.5289i	−0.582277	+	1.00853i	−0.995209	+	0.0977711i	$0.968829\pi$
$500$	3.52415	+	6.10401i	0.157605	+	0.272980i
$501$	−1.19830	−	2.07552i	−0.0535363	−	0.0927276i
$502$	−13.4992	+	23.3813i	−0.602499	+	1.04356i
$503$	−2.17490			−0.0969742			−0.0484871	−	0.998824i	$-0.515440\pi$
$503$	−2.17490			−0.0969742			−0.0484871	+	0.998824i	$0.515440\pi$
$504$	−0.494715	+	2.59909i	−0.0220364	+	0.115773i
$505$		−	38.3460i		−	1.70637i
$506$	−6.21113	−	12.5706i	−0.276118	−	0.558833i
$507$	9.65950	−	5.57691i	0.428993	−	0.247679i
$508$	8.71502	+	15.0949i	0.386666	+	0.669726i
$509$	1.03627	+	0.598293i	0.0459320	+	0.0265189i	0.522790	−	0.852461i	$-0.324891\pi$
$509$	1.03627	+	0.598293i	0.0459320	+	0.0265189i	−0.476858	+	0.878980i	$0.658224\pi$
$510$			16.8190i			0.744760i
$511$	−17.3730	+	20.1432i	−0.768536	+	0.891085i
$512$	−1.00000			−0.0441942
$513$	0.938233	+	0.541689i	0.0414240	+	0.0239162i
$514$	−6.68924	+	3.86203i	−0.295050	+	0.170347i
$515$	−12.5255	−	21.6948i	−0.551941	−	0.955989i
$516$	−4.82667	+	8.36004i	−0.212482	+	0.368030i
$517$	22.5700			0.992628
$518$	1.61734	−	1.87523i	0.0710618	−	0.0823931i
$519$	15.2805			0.670740
$520$	−3.20333	−	1.84944i	−0.140475	−	0.0811035i
$521$	21.2845	+	36.8658i	0.932489	+	1.61512i	0.779052	+	0.626960i	$0.215701\pi$
$521$	21.2845	+	36.8658i	0.932489	+	1.61512i	0.153437	+	0.988158i	$0.450966\pi$
$522$	3.60770	+	6.24872i	0.157905	+	0.273499i
$523$	2.83056	−	4.90267i	0.123772	−	0.214379i	−0.797480	−	0.603345i	$-0.793834\pi$
$523$	2.83056	−	4.90267i	0.123772	−	0.214379i	0.921252	+	0.388966i	$0.127168\pi$
$524$		−	19.0631i		−	0.832776i
$525$	−6.26613	−	1.19271i	−0.273477	−	0.0520540i
$526$			10.6348i			0.463699i
$527$	51.2720	+	29.6019i	2.23344	+	1.28948i
$528$	1.46183	+	2.53196i	0.0636180	+	0.110190i
$529$	13.9735	−	18.2686i	0.607545	−	0.794285i
$530$	−8.45704	−	4.88267i	−0.367350	−	0.212090i
$531$		−	0.942507i		−	0.0409013i
$532$	2.70653	−	0.943739i	0.117343	−	0.0409163i
$533$	−4.96301			−0.214972
$534$	13.6918	+	7.90496i	0.592502	+	0.342081i
$535$	−16.8474	+	9.72688i	−0.728379	+	0.420530i
$536$	5.27370	−	3.04477i	0.227789	−	0.131514i
$537$	−13.3289	−	7.69546i	−0.575186	−	0.332084i
$538$		−	28.6819i		−	1.23656i
$539$	7.51853	−	19.0345i	0.323846	−	0.819875i
$540$		−	2.72230i		−	0.117149i
$541$	15.8800	−	27.5050i	0.682735	−	1.18253i	−0.291408	−	0.956599i	$-0.594124\pi$
$541$	15.8800	−	27.5050i	0.682735	−	1.18253i	0.974143	−	0.225933i	$-0.0725430\pi$
$542$	−5.32212	+	3.07273i	−0.228605	+	0.131985i
$543$	−6.76617	+	3.90645i	−0.290364	+	0.167642i
$544$	−3.08913	+	5.35053i	−0.132445	+	0.229402i
$545$		−	37.8102i		−	1.61961i
$546$	−3.39445	+	1.18361i	−0.145269	+	0.0506538i
$547$	6.43908			0.275315			0.137658	−	0.990480i	$-0.456043\pi$
$547$	6.43908			0.275315			0.137658	+	0.990480i	$0.456043\pi$
$548$	4.38654	+	2.53257i	0.187384	+	0.108186i
$549$	−2.62356	−	4.54413i	−0.111971	−	0.193939i
$550$	−6.10430	+	3.52432i	−0.260288	+	0.150278i
$551$	3.90850	−	6.76973i	0.166508	−	0.288400i
$552$	−2.66136	+	3.98963i	−0.113275	+	0.169810i
$553$	−24.0523	−	4.57817i	−1.02281	−	0.194684i
$554$	−28.6129			−1.21565
$555$	−1.27399	+	2.20662i	−0.0540781	+	0.0936660i
$556$	−10.1163	+	5.84063i	−0.429025	+	0.247698i
$557$	4.47332	−	2.58267i	0.189540	−	0.109431i	−0.402227	−	0.915540i	$-0.631764\pi$
$557$	4.47332	−	2.58267i	0.189540	−	0.109431i	0.591767	+	0.806109i	$0.298430\pi$
$558$	−8.29879	−	4.79131i	−0.351316	−	0.202832i
$559$	−13.1164			−0.554763
$560$	−5.45417	−	4.70407i	−0.230481	−	0.198783i
$561$	18.0631			0.762625
$562$	23.8129	+	13.7484i	1.00449	+	0.579940i
$563$	15.1048	+	26.1622i	0.636591	+	1.10261i	0.986176	+	0.165703i	$0.0529892\pi$
$563$	15.1048	+	26.1622i	0.636591	+	1.10261i	−0.349585	+	0.936905i	$0.613677\pi$
$564$	−3.85989	−	6.68553i	−0.162531	−	0.281511i
$565$	−11.4086	−	6.58675i	−0.479963	−	0.277107i
$566$	3.81977			0.160557
$567$	−2.00352	−	1.72798i	−0.0841399	−	0.0725683i
$568$	−9.73354			−0.408410
$569$	−11.5178	−	6.64981i	−0.482852	−	0.278775i	0.238752	−	0.971080i	$-0.423262\pi$
$569$	−11.5178	−	6.64981i	−0.482852	−	0.278775i	−0.721604	+	0.692306i	$0.756595\pi$
$570$	−2.55415	+	1.47464i	−0.106981	+	0.0617658i
$571$	−9.96129	+	5.75115i	−0.416867	+	0.240678i	−0.693736	−	0.720229i	$-0.744037\pi$
$571$	−9.96129	+	5.75115i	−0.416867	+	0.240678i	0.276869	+	0.960908i	$0.410703\pi$
$572$	−1.98624	+	3.44028i	−0.0830490	+	0.143845i
$573$	0.0185228			0.000773801
$574$	−9.49359	−	1.80703i	−0.396255	−	0.0754239i
$575$	−9.61859	−	6.41628i	−0.401123	−	0.267577i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	8.80249	−	5.08212i	0.366452	−	0.211571i	−0.305455	−	0.952206i	$-0.598809\pi$
$577$	8.80249	−	5.08212i	0.366452	−	0.211571i	0.671907	+	0.740635i	$0.265475\pi$
$578$	10.5854	+	18.3345i	0.440296	+	0.762614i
$579$	2.52833	+	1.45973i	0.105074	+	0.0606643i
$580$	−19.6425			−0.815609
$581$	−10.1229	+	3.52974i	−0.419968	+	0.146438i
$582$		−	7.72846i		−	0.320355i
$583$	−5.24383	+	9.08259i	−0.217177	+	0.376162i
$584$	8.70696	−	5.02697i	0.360297	−	0.208017i
$585$	3.20333	−	1.84944i	0.132442	−	0.0764651i
$586$	−14.0192	+	24.2820i	−0.579129	+	1.00308i
$587$		−	41.6586i		−	1.71944i	−0.510769	−	0.859718i	$-0.670639\pi$
$587$		−	41.6586i		−	1.71944i	0.510769	−	0.859718i	$-0.329361\pi$
$588$	−6.92408	+	1.02817i	−0.285544	+	0.0424011i
$589$			10.3816i			0.427766i
$590$	2.22203	+	1.28289i	0.0914797	+	0.0528158i
$591$	−3.48759	+	2.01356i	−0.143460	+	0.0828269i
$592$	−0.810574	+	0.467985i	−0.0333144	+	0.0192341i
$593$	−10.7189	−	6.18856i	−0.440172	−	0.254134i	0.263498	−	0.964660i	$-0.415124\pi$
$593$	−10.7189	−	6.18856i	−0.440172	−	0.254134i	−0.703671	+	0.710526i	$0.748457\pi$
$594$	−2.92366			−0.119959
$595$	−42.0179	+	14.6512i	−1.72257	+	0.600641i
$596$			2.81524i			0.115317i
$597$	−5.04827	−	2.91462i	−0.206612	−	0.119288i
$598$	−6.50266	−	0.421202i	−0.265913	−	0.0172243i
$599$	17.3090	+	29.9801i	0.707227	+	1.22495i	0.965882	+	0.258984i	$0.0833876\pi$
$599$	17.3090	+	29.9801i	0.707227	+	1.22495i	−0.258654	+	0.965970i	$0.583279\pi$
$600$	2.08790	+	1.20545i	0.0852381	+	0.0492122i
$601$		−	3.90464i		−	0.159273i	−0.996824	−	0.0796367i	$-0.974624\pi$
$601$		−	3.90464i		−	0.159273i	0.996824	−	0.0796367i	$-0.0253760\pi$
$602$	−25.0899	−	4.77565i	−1.02259	−	0.194641i
$603$			6.08954i			0.247985i
$604$	−4.20972	+	7.29145i	−0.171291	+	0.296685i
$605$	−3.33783	−	5.78130i	−0.135702	−	0.235043i
$606$	7.04294	+	12.1987i	0.286100	+	0.495540i
$607$	29.9151	+	17.2715i	1.21421	+	0.701027i	0.963675	−	0.267079i	$-0.0860584\pi$
$607$	29.9151	+	17.2715i	1.21421	+	0.701027i	0.250540	+	0.968106i	$0.419392\pi$
$608$	−1.08338			−0.0439368
$609$	−12.4681	+	14.4562i	−0.505232	+	0.585794i
$610$	14.2842			0.578350
$611$	5.24458	−	9.08389i	0.212173	−	0.367495i
$612$	−3.08913	−	5.35053i	−0.124871	−	0.216282i
$613$	31.4497	−	18.1575i	1.27024	−	0.733374i	0.295208	−	0.955433i	$-0.404611\pi$
$613$	31.4497	−	18.1575i	1.27024	−	0.733374i	0.975033	+	0.222059i	$0.0712778\pi$
$614$	−1.20028	−	0.692984i	−0.0484395	−	0.0279666i
$615$	9.94363			0.400966
$616$	−5.05202	+	5.85760i	−0.203552	+	0.236010i
$617$		−	33.0304i		−	1.32975i	−0.746953	−	0.664877i	$-0.768484\pi$
$617$		−	33.0304i		−	1.32975i	0.746953	−	0.664877i	$-0.231516\pi$
$618$	7.96932	+	4.60109i	0.320573	+	0.185083i
$619$	2.98293	+	5.16659i	0.119894	+	0.207663i	0.919726	−	0.392562i	$-0.128411\pi$
$619$	2.98293	+	5.16659i	0.119894	+	0.207663i	−0.799831	+	0.600225i	$0.795078\pi$
$620$	22.5918	−	13.0434i	0.907307	−	0.523834i
$621$	−2.12444	−	4.29962i	−0.0852507	−	0.172538i
$622$			16.8840i			0.676985i
$623$	−7.82141	+	41.0914i	−0.313358	+	1.64629i
$624$	1.35874			0.0543931
$625$	15.6210	−	27.0564i	0.624841	−	1.08226i
$626$	−14.6230	−	25.3279i	−0.584454	−	1.01230i
$627$	1.58371	+	2.74307i	0.0632474	+	0.109548i
$628$	−2.85671	+	4.94796i	−0.113995	+	0.197445i
$629$			5.78267i			0.230570i
$630$	6.80093	−	2.37141i	0.270956	−	0.0944794i
$631$		−	26.9670i		−	1.07354i	−0.843729	−	0.536769i	$-0.819645\pi$
$631$		−	26.9670i		−	1.07354i	0.843729	−	0.536769i	$-0.180355\pi$
$632$	8.01433	+	4.62707i	0.318793	+	0.184055i
$633$	11.7970	−	6.81101i	0.468889	−	0.270713i
$634$	−5.03623	−	8.72300i	−0.200014	−	0.346435i
$635$	23.7249	−	41.0927i	0.941493	−	1.63071i
$636$	3.58717			0.142241
$637$	−5.91386	−	7.44907i	−0.234316	−	0.295143i
$638$			21.0954i			0.835174i
$639$	4.86677	−	8.42950i	0.192527	−	0.333466i
$640$	1.36115	+	2.35758i	0.0538041	+	0.0931914i
$641$	−18.6560	+	10.7710i	−0.736866	+	0.425430i	−0.820929	−	0.571030i	$-0.806544\pi$
$641$	−18.6560	+	10.7710i	−0.736866	+	0.425430i	0.0840625	+	0.996460i	$0.473210\pi$
$642$	3.57304	−	6.18869i	0.141017	−	0.244248i
$643$	−27.1326			−1.07001			−0.535003	−	0.844850i	$-0.679689\pi$
$643$	−27.1326			−1.07001			−0.535003	+	0.844850i	$0.679689\pi$
$644$	−12.2854	−	3.17331i	−0.484111	−	0.125046i
$645$	26.2792			1.03474
$646$	−3.34669	+	5.79664i	−0.131674	+	0.228066i
$647$	−19.6045	+	11.3186i	−0.770731	+	0.444982i	−0.833135	−	0.553069i	$-0.813457\pi$
$647$	−19.6045	+	11.3186i	−0.770731	+	0.444982i	0.0624042	+	0.998051i	$0.480123\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	1.37778	−	2.38639i	0.0540828	−	0.0936741i
$650$			3.27578i			0.128487i
$651$	4.74067	−	24.9061i	0.185801	−	0.976145i
$652$	9.09641			0.356243
$653$	2.55612	−	4.42733i	0.100029	−	0.173255i	−0.811668	−	0.584120i	$-0.801440\pi$
$653$	2.55612	−	4.42733i	0.100029	−	0.173255i	0.911696	+	0.410865i	$0.134773\pi$
$654$	6.94453	+	12.0283i	0.271553	+	0.470343i
$655$	−44.9428	+	25.9477i	−1.75606	+	1.01386i
$656$	3.16330	+	1.82633i	0.123506	+	0.0713062i
$657$			10.0539i			0.392241i
$658$	13.3396	−	15.4667i	0.520033	−	0.602956i
$659$			18.0627i			0.703624i	0.936071	+	0.351812i	$0.114434\pi$
$659$			18.0627i			0.703624i	−0.936071	+	0.351812i	$0.885566\pi$
$660$	3.97953	−	6.89275i	0.154903	−	0.268300i
$661$	17.8473	+	30.9124i	0.694179	+	1.20235i	0.970457	+	0.241275i	$0.0775657\pi$
$661$	17.8473	+	30.9124i	0.694179	+	1.20235i	−0.276278	+	0.961078i	$0.589101\pi$
$662$	3.03257	+	5.25256i	0.117864	+	0.204146i
$663$	4.19732	−	7.26997i	0.163010	−	0.282342i
$664$	4.05202			0.157249
$665$	−5.90893	−	5.09629i	−0.229138	−	0.197626i
$666$		−	0.935971i		−	0.0362681i
$667$	−31.0235	+	15.3287i	−1.20124	+	0.593529i
$668$	−2.07552	+	1.19830i	−0.0803045	+	0.0463638i
$669$	10.8686	+	18.8250i	0.420205	+	0.727817i
$670$	−14.3566	−	8.28877i	−0.554643	−	0.320223i
$671$		−	15.3408i		−	0.592224i
$672$	2.59909	+	0.494715i	0.100262	+	0.0190841i
$673$	22.8131			0.879382			0.439691	−	0.898149i	$-0.355088\pi$
$673$	22.8131			0.879382			0.439691	+	0.898149i	$0.355088\pi$
$674$	19.7259	+	11.3888i	0.759813	+	0.438679i
$675$	−2.08790	+	1.20545i	−0.0803633	+	0.0463978i
$676$	−5.57691	−	9.65950i	−0.214497	−	0.371519i
$677$	−7.16903	+	12.4171i	−0.275528	+	0.477229i	−0.970268	−	0.242032i	$-0.922186\pi$
$677$	−7.16903	+	12.4171i	−0.275528	+	0.477229i	0.694740	+	0.719261i	$0.255519\pi$
$678$	4.83911			0.185845
$679$	19.3075	−	6.73232i	0.740954	−	0.258363i
$680$	16.8190			0.644981
$681$	3.47969	+	2.00900i	0.133342	+	0.0769850i
$682$	−14.0081	−	24.2628i	−0.536400	−	0.929071i
$683$	−7.60788	−	13.1772i	−0.291107	−	0.504213i	0.682964	−	0.730452i	$-0.260690\pi$
$683$	−7.60788	−	13.1772i	−0.291107	−	0.504213i	−0.974072	+	0.226239i	$0.927357\pi$
$684$	0.541689	−	0.938233i	0.0207120	−	0.0358742i
$685$		−	13.7888i		−	0.526843i
$686$	−8.60023	−	16.4023i	−0.328358	−	0.626243i
$687$		−	24.2980i		−	0.927027i
$688$	8.36004	+	4.82667i	0.318723	+	0.184015i
$689$	2.43702	+	4.22103i	0.0928429	+	0.160809i
$690$	13.0284	+	0.843899i	0.495982	+	0.0321267i
$691$	30.7150	+	17.7333i	1.16845	+	0.674608i	0.953316	−	0.301976i	$-0.0976462\pi$
$691$	30.7150	+	17.7333i	1.16845	+	0.674608i	0.215139	+	0.976583i	$0.430980\pi$
$692$		−	15.2805i		−	0.580878i
$693$	−2.54682	−	7.30398i	−0.0967458	−	0.277455i
$694$	−4.43642			−0.168404
$695$	27.5395	+	15.8999i	1.04463	+	0.603118i
$696$	6.24872	−	3.60770i	0.236857	−	0.136750i
$697$	19.5437	−	11.2835i	0.740269	−	0.427395i
$698$	12.8329	+	7.40907i	0.485732	+	0.280438i
$699$		−	15.6826i		−	0.593170i
$700$	−1.19271	+	6.26613i	−0.0450801	+	0.236838i
$701$		−	19.8211i		−	0.748634i	−0.927301	−	0.374317i	$-0.877877\pi$
$701$		−	19.8211i		−	0.748634i	0.927301	−	0.374317i	$-0.122123\pi$
$702$	−0.679369	+	1.17670i	−0.0256411	+	0.0444118i
$703$	−0.878158	+	0.507005i	−0.0331204	+	0.0191221i
$704$	2.53196	−	1.46183i	0.0954269	−	0.0550948i
$705$	−10.5078	+	18.2000i	−0.395745	+	0.685451i
$706$			24.7465i			0.931347i
$707$	−24.3401	+	28.2213i	−0.915405	+	1.06137i
$708$	−0.942507			−0.0354216
$709$	−29.9958	−	17.3181i	−1.12652	−	0.650394i	−0.183459	−	0.983027i	$-0.558730\pi$
$709$	−29.9958	−	17.3181i	−1.12652	−	0.650394i	−0.943056	+	0.332633i	$0.892063\pi$
$710$	13.2488	+	22.9476i	0.497218	+	0.861208i
$711$	−8.01433	+	4.62707i	−0.300561	+	0.173529i
$712$	7.90496	−	13.6918i	0.296251	−	0.513122i
$713$	25.5028	−	38.2311i	0.955089	−	1.43176i
$714$	10.6759	−	12.3782i	0.399536	−	0.463244i
$715$	10.8143			0.404432
$716$	−7.69546	+	13.3289i	−0.287593	+	0.498126i
$717$	−25.6965	+	14.8359i	−0.959653	+	0.554056i
$718$	−14.3556	+	8.28820i	−0.535745	+	0.309313i
$719$	−10.4461	−	6.03108i	−0.389575	−	0.224921i	0.292401	−	0.956296i	$-0.405546\pi$
$719$	−10.4461	−	6.03108i	−0.389575	−	0.224921i	−0.681976	+	0.731375i	$0.738879\pi$
$720$	−2.72230			−0.101454
$721$	−4.55246	+	23.9173i	−0.169542	+	0.890725i
$722$	17.8263			0.663426
$723$	10.1043	+	5.83374i	0.375784	+	0.216959i
$724$	3.90645	+	6.76617i	0.145182	+	0.251463i
$725$	8.69780	+	15.0650i	0.323028	+	0.559501i
$726$	2.12368	+	1.22611i	0.0788173	+	0.0455052i
$727$	24.6195			0.913086			0.456543	−	0.889701i	$-0.349087\pi$
$727$	24.6195			0.913086			0.456543	+	0.889701i	$0.349087\pi$
$728$	1.18361	+	3.39445i	0.0438674	+	0.125807i
$729$	−1.00000			−0.0370370
$730$	−23.7029	−	13.6849i	−0.877285	−	0.506501i
$731$	51.6504	−	29.8204i	1.91036	−	1.10295i
$732$	−4.54413	+	2.62356i	−0.167956	+	0.0969694i
$733$	−22.4207	+	38.8338i	−0.828129	+	1.43436i	0.0713761	+	0.997449i	$0.477261\pi$
$733$	−22.4207	+	38.8338i	−0.828129	+	1.43436i	−0.899505	+	0.436911i	$0.856072\pi$
$734$	−7.65499			−0.282551
$735$	11.8487	+	14.9246i	0.437046	+	0.550501i
$736$	3.98963	+	2.66136i	0.147060	+	0.0980992i
$737$	−8.90187	+	15.4185i	−0.327905	+	0.567947i
$738$	−3.16330	+	1.82633i	−0.116443	+	0.0672282i
$739$	15.3901	+	26.6564i	0.566133	+	0.980571i	0.996943	+	0.0781287i	$0.0248945\pi$
$739$	15.3901	+	26.6564i	0.566133	+	0.980571i	−0.430810	+	0.902443i	$0.641772\pi$
$740$	2.20662	+	1.27399i	0.0811171	+	0.0468330i
$741$	1.47203			0.0540763
$742$	3.12481	+	8.96160i	0.114716	+	0.328991i
$743$		−	38.0164i		−	1.39468i	−0.716738	−	0.697342i	$-0.754366\pi$
$743$		−	38.0164i		−	1.39468i	0.716738	−	0.697342i	$-0.245634\pi$
$744$	−4.79131	+	8.29879i	−0.175658	+	0.304248i
$745$	6.63714	−	3.83196i	0.243166	−	0.140392i
$746$	−23.5985	+	13.6246i	−0.864003	+	0.498832i
$747$	−2.02601	+	3.50915i	−0.0741277	+	0.128393i
$748$		−	18.0631i		−	0.660453i
$749$	18.5733	+	3.53528i	0.678654	+	0.129176i
$750$			7.04830i			0.257368i
$751$	18.8265	+	10.8695i	0.686988	+	0.396633i	0.802483	−	0.596675i	$-0.203512\pi$
$751$	18.8265	+	10.8695i	0.686988	+	0.396633i	−0.115495	+	0.993308i	$0.536845\pi$
$752$	−6.68553	+	3.85989i	−0.243796	+	0.140756i
$753$	−23.3813	+	13.4992i	−0.852062	+	0.491938i
$754$	8.49038	+	4.90192i	0.309201	+	0.178518i
$755$	22.9202			0.834152
$756$	−1.72798	+	2.00352i	−0.0628460	+	0.0728673i
$757$			11.3510i			0.412558i	0.978493	+	0.206279i	$0.0661354\pi$
$757$			11.3510i			0.412558i	−0.978493	+	0.206279i	$0.933865\pi$
$758$	−10.2998	−	5.94658i	−0.374105	−	0.215989i
$759$	0.906320	−	13.9921i	0.0328973	−	0.507879i
$760$	1.47464	+	2.55415i	0.0534907	+	0.0926487i
$761$	−9.35589	−	5.40163i	−0.339151	−	0.195809i	0.320746	−	0.947165i	$-0.396067\pi$
$761$	−9.35589	−	5.40163i	−0.339151	−	0.195809i	−0.659896	+	0.751357i	$0.729400\pi$
$762$			17.4300i			0.631424i
$763$	−24.0000	+	27.8270i	−0.868859	+	1.00741i
$764$		−	0.0185228i		−	0.000670131i
$765$	−8.40952	+	14.5657i	−0.304047	+	0.526625i
$766$	−13.4113	−	23.2290i	−0.484569	−	0.839298i
$767$	−0.640310	−	1.10905i	−0.0231203	−	0.0400455i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−12.8572			−0.463641			−0.231821	−	0.972759i	$-0.574468\pi$
$769$	−12.8572			−0.463641			−0.231821	+	0.972759i	$0.574468\pi$
$770$	20.6863	+	3.93747i	0.745483	+	0.141897i
$771$	−7.72407			−0.278176
$772$	1.45973	−	2.52833i	0.0525368	−	0.0909965i
$773$	9.37276	+	16.2341i	0.337115	+	0.583900i	0.983889	−	0.178782i	$-0.0572157\pi$
$773$	9.37276	+	16.2341i	0.337115	+	0.583900i	−0.646774	+	0.762682i	$0.723882\pi$
$774$	−8.36004	+	4.82667i	−0.300495	+	0.173491i
$775$	−20.0075	−	11.5514i	−0.718692	−	0.414937i
$776$	−7.72846			−0.277436
$777$	2.33827	−	0.815331i	0.0838851	−	0.0292498i
$778$		−	33.0977i		−	1.18661i
$779$	3.42705	+	1.97861i	0.122787	+	0.0708909i
$780$	−1.84944	−	3.20333i	−0.0662208	−	0.114698i
$781$	24.6450	−	14.2288i	0.881866	−	0.509146i
$782$	26.5642	−	13.1253i	0.949933	−	0.469360i
$783$			7.21540i			0.257857i
$784$	1.02817	+	6.92408i	0.0367204	+	0.247289i
$785$	15.5536			0.555132
$786$	9.53156	−	16.5091i	0.339979	−	0.588861i
$787$	16.9471	+	29.3532i	0.604099	+	1.04633i	0.992193	+	0.124711i	$0.0398002\pi$
$787$	16.9471	+	29.3532i	0.604099	+	1.04633i	−0.388094	+	0.921620i	$0.626866\pi$
$788$	2.01356	+	3.48759i	0.0717302	+	0.124240i
$789$	−5.31739	+	9.20999i	−0.189304	+	0.327884i
$790$		−	25.1925i		−	0.896310i
$791$	4.21539	+	12.0892i	0.149882	+	0.429844i
$792$			2.92366i			0.103888i
$793$	−6.17429	−	3.56473i	−0.219255	−	0.126587i
$794$	5.07145	−	2.92800i	0.179979	−	0.103911i
$795$	−4.88267	−	8.45704i	−0.173171	−	0.299940i
$796$	−2.91462	+	5.04827i	−0.103306	+	0.178931i
$797$	−39.3239			−1.39293			−0.696463	−	0.717593i	$-0.745244\pi$
$797$	−39.3239			−1.39293			−0.696463	+	0.717593i	$0.745244\pi$
$798$	2.81579	+	0.535964i	0.0996780	+	0.0189729i
$799$			47.6948i			1.68732i
$800$	1.20545	−	2.08790i	0.0426191	−	0.0738184i
$801$	7.90496	+	13.6918i	0.279308	+	0.483776i
$802$	4.52889	−	2.61476i	0.159921	−	0.0923303i
$803$	−14.6971	+	25.4562i	−0.518651	+	0.898329i
$804$	6.08954			0.214762
$805$	9.24086	+	33.2830i	0.325698	+	1.17307i
$806$	−13.0203			−0.458619
$807$	14.3410	−	24.8393i	0.504826	−	0.874383i
$808$	12.1987	−	7.04294i	0.429150	−	0.247770i
$809$	−4.02489	−	6.97131i	−0.141508	−	0.245098i	0.786557	−	0.617518i	$-0.211862\pi$
$809$	−4.02489	−	6.97131i	−0.141508	−	0.245098i	−0.928065	+	0.372419i	$0.878528\pi$
$810$	1.36115	−	2.35758i	0.0478259	−	0.0828368i
$811$			20.1857i			0.708814i	0.935091	+	0.354407i	$0.115317\pi$
$811$			20.1857i			0.708814i	−0.935091	+	0.354407i	$0.884683\pi$
$812$	14.4562	+	12.4681i	0.507313	+	0.437543i
$813$	−6.14546			−0.215531
$814$	1.36823	−	2.36984i	0.0479564	−	0.0830629i
$815$	−12.3816	−	21.4455i	−0.433707	−	0.751203i
$816$	−5.35053	+	3.08913i	−0.187306	+	0.108141i
$817$	9.05708	+	5.22911i	0.316867	+	0.182943i
$818$			2.98993i			0.104540i
$819$	−3.53148	−	0.672189i	−0.123400	−	0.0234882i
$820$		−	9.94363i		−	0.347247i
$821$	−8.77417	+	15.1973i	−0.306221	+	0.530389i	−0.977532	−	0.210786i	$-0.932398\pi$
$821$	−8.77417	+	15.1973i	−0.306221	+	0.530389i	0.671312	+	0.741175i	$0.265731\pi$
$822$	2.53257	+	4.38654i	0.0883335	+	0.152998i
$823$	11.0651	+	19.1653i	0.385705	+	0.668060i	0.991867	−	0.127281i	$-0.0406250\pi$
$823$	11.0651	+	19.1653i	0.385705	+	0.668060i	−0.606162	+	0.795341i	$0.707292\pi$
$824$	4.60109	−	7.96932i	0.160286	−	0.277624i
$825$	−7.04864			−0.245402
$826$	−0.821025	−	2.35460i	−0.0285671	−	0.0819271i
$827$		−	17.5340i		−	0.609717i	−0.952398	−	0.304859i	$-0.901391\pi$
$827$		−	17.5340i		−	0.609717i	0.952398	−	0.304859i	$-0.0986092\pi$
$828$	−4.29962	+	2.12444i	−0.149422	+	0.0738293i
$829$	−45.3809	+	26.2007i	−1.57614	+	0.909987i	−0.580753	+	0.814080i	$0.697242\pi$
$829$	−45.3809	+	26.2007i	−1.57614	+	0.909987i	−0.995390	+	0.0959066i	$0.969425\pi$
$830$	−5.51539	−	9.55294i	−0.191442	−	0.331587i
$831$	−24.7795	−	14.3064i	−0.859591	−	0.496285i
$832$		−	1.35874i		−	0.0471058i
$833$	40.2236	+	15.8881i	1.39367	+	0.550490i
$834$	−11.6813			−0.404489
$835$	5.65019	+	3.26214i	0.195533	+	0.112891i
$836$	2.74307	−	1.58371i	0.0948712	−	0.0547739i
$837$	−4.79131	−	8.29879i	−0.165612	−	0.286848i
$838$	6.03621	−	10.4550i	0.208517	−	0.361163i
$839$	11.0854			0.382712			0.191356	−	0.981521i	$-0.438712\pi$
$839$	11.0854			0.382712			0.191356	+	0.981521i	$0.438712\pi$
$840$	−2.37141	−	6.80093i	−0.0818216	−	0.234654i
$841$	23.0620			0.795243
$842$	−1.57007	−	0.906483i	−0.0541084	−	0.0312395i
$843$	13.7484	+	23.8129i	0.473519	+	0.820159i
$844$	−6.81101	−	11.7970i	−0.234444	−	0.406070i
$845$	−15.1820	+	26.2960i	−0.522277	+	0.904611i
$846$		−	7.71978i		−	0.265412i
$847$	−1.21315	+	6.37353i	−0.0416843	+	0.218997i
$848$		−	3.58717i		−	0.123184i
$849$	3.30802	+	1.90989i	0.113531	+	0.0655472i
$850$	−7.44757	−	12.8996i	−0.255450	−	0.442452i
$851$	4.47937	+	0.290146i	0.153551	+	0.00994609i
$852$	−8.42950	−	4.86677i	−0.288790	−	0.166733i
$853$			1.57346i			0.0538743i	0.999637	+	0.0269372i	$0.00857541\pi$
$853$			1.57346i			0.0538743i	−0.999637	+	0.0269372i	$0.991425\pi$
$854$	−10.5127	−	9.06690i	−0.359737	−	0.310263i
$855$	−2.94928			−0.100863
$856$	−6.18869	−	3.57304i	−0.211525	−	0.122124i
$857$	21.9829	−	12.6919i	0.750923	−	0.433546i	−0.0751044	−	0.997176i	$-0.523929\pi$
$857$	21.9829	−	12.6919i	0.750923	−	0.433546i	0.826027	+	0.563630i	$0.190596\pi$
$858$	−3.44028	+	1.98624i	−0.117449	+	0.0678093i
$859$	43.1483	+	24.9117i	1.47220	+	0.849976i	0.999512	−	0.0312526i	$-0.00994962\pi$
$859$	43.1483	+	24.9117i	1.47220	+	0.849976i	0.472690	+	0.881229i	$0.343283\pi$
$860$		−	26.2792i		−	0.896115i
$861$	−7.31817	−	6.31173i	−0.249403	−	0.215103i
$862$			16.6232i			0.566189i
$863$	−17.8424	+	30.9040i	−0.607363	+	1.05198i	0.384310	+	0.923204i	$0.374439\pi$
$863$	−17.8424	+	30.9040i	−0.607363	+	1.05198i	−0.991673	+	0.128780i	$0.958894\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−36.0250	+	20.7990i	−1.22489	+	0.707188i
$866$	3.69588	−	6.40145i	0.125591	−	0.217530i
$867$			21.1708i			0.719000i
$868$	−24.9061	−	4.74067i	−0.845367	−	0.160909i
$869$	−27.0560			−0.917811
$870$	−17.0109	−	9.82123i	−0.576723	−	0.332971i
$871$	4.13705	+	7.16558i	0.140179	+	0.242796i
$872$	12.0283	−	6.94453i	0.407329	−	0.235172i
$873$	3.86423	−	6.69304i	0.130784	−	0.226525i
$874$	4.32228	+	2.88326i	0.146203	+	0.0975279i
$875$	−17.6083	+	6.13983i	−0.595269	+	0.207564i
$876$	10.0539			0.339691
$877$	−20.8594	+	36.1296i	−0.704372	+	1.22001i	0.262545	+	0.964920i	$0.415438\pi$
$877$	−20.8594	+	36.1296i	−0.704372	+	1.22001i	−0.966918	+	0.255089i	$0.917895\pi$
$878$	14.1011	−	8.14128i	0.475890	−	0.274755i
$879$	−24.2820	+	14.0192i	−0.819012	+	0.472857i
$880$	−6.89275	−	3.97953i	−0.232355	−	0.134150i
$881$	−46.1248			−1.55399			−0.776993	−	0.629510i	$-0.783256\pi$
$881$	−46.1248			−1.55399			−0.776993	+	0.629510i	$0.783256\pi$
$882$	−6.51051	−	2.57162i	−0.219220	−	0.0865908i
$883$	38.7832			1.30516			0.652579	−	0.757721i	$-0.273687\pi$
$883$	38.7832			1.30516			0.652579	+	0.757721i	$0.273687\pi$
$884$	−7.26997	−	4.19732i	−0.244516	−	0.141171i
$885$	1.28289	+	2.22203i	0.0431239	+	0.0746928i
$886$	12.5407	+	21.7211i	0.421312	+	0.729733i
$887$	14.2120	+	8.20531i	0.477193	+	0.275507i	0.719246	−	0.694756i	$-0.244488\pi$
$887$	14.2120	+	8.20531i	0.477193	+	0.275507i	−0.242053	+	0.970263i	$0.577821\pi$
$888$	−0.935971			−0.0314091
$889$	−43.5443	+	15.1834i	−1.46043	+	0.509236i
$890$	−43.0393			−1.44268
$891$	−2.53196	−	1.46183i	−0.0848239	−	0.0489731i
$892$	18.8250	−	10.8686i	0.630308	−	0.363908i
$893$	−7.24295	+	4.18172i	−0.242376	+	0.139936i
$894$	−1.40762	+	2.43807i	−0.0470778	+	0.0815412i
$895$	41.8987			1.40052
$896$	0.494715	−	2.59909i	0.0165273	−	0.0868294i
$897$	−5.42086	−	3.61610i	−0.180997	−	0.120738i
$898$	−3.05932	+	5.29891i	−0.102091	+	0.176827i
$899$	−59.8791	+	34.5712i	−1.99708	+	1.15301i
$900$	1.20545	+	2.08790i	0.0401816	+	0.0695966i
$901$	−19.1933	−	11.0812i	−0.639420	−	0.369169i
$902$	−10.6791			−0.355576
$903$	−19.3406	−	16.6808i	−0.643616	−	0.555101i
$904$		−	4.83911i		−	0.160946i
$905$	10.6345	−	18.4195i	0.353503	−	0.612286i
$906$	−7.29145	+	4.20972i	−0.242242	+	0.139859i
$907$	−12.0751	+	6.97158i	−0.400948	+	0.231488i	−0.686893	−	0.726759i	$-0.741026\pi$
$907$	−12.0751	+	6.97158i	−0.400948	+	0.231488i	0.285945	+	0.958246i	$0.407693\pi$
$908$	2.00900	−	3.47969i	0.0666710	−	0.115478i
$909$			14.0859i			0.467199i
$910$	6.39161	−	7.41079i	0.211880	−	0.245665i
$911$		−	23.8823i		−	0.791254i	−0.918411	−	0.395627i	$-0.870527\pi$
$911$		−	23.8823i		−	0.791254i	0.918411	−	0.395627i	$-0.129473\pi$
$912$	−0.938233	−	0.541689i	−0.0310680	−	0.0179371i
$913$	−10.2596	+	5.92336i	−0.339542	+	0.196034i
$914$	30.5252	−	17.6237i	1.00968	−	0.582941i
$915$	12.3705	+	7.14210i	0.408955	+	0.236110i
$916$	−24.2980			−0.802829
$917$	49.5467	+	9.43081i	1.63618	+	0.311433i
$918$		−	6.17826i		−	0.203913i
$919$	−44.4534	−	25.6652i	−1.46638	−	0.846616i	−0.467089	−	0.884210i	$-0.654697\pi$
$919$	−44.4534	−	25.6652i	−1.46638	−	0.846616i	−0.999293	+	0.0375939i	$0.988031\pi$
$920$	0.843899	−	13.0284i	0.0278225	−	0.429533i
$921$	−0.692984	−	1.20028i	−0.0228346	−	0.0395507i
$922$	−6.15467	−	3.55340i	−0.202693	−	0.117025i
$923$		−	13.2253i		−	0.435317i
$924$	−7.30398	+	2.54682i	−0.240283	+	0.0837843i
$925$		−	2.25653i		−	0.0741942i
$926$	0.487482	−	0.844344i	0.0160197	−	0.0277469i
$927$	4.60109	+	7.96932i	0.151120	+	0.261747i
$928$	−3.60770	−	6.24872i	−0.118429	−	0.205124i
$929$	32.2706	+	18.6315i	1.05877	+	0.611278i	0.925090	−	0.379747i	$-0.123989\pi$
$929$	32.2706	+	18.6315i	1.05877	+	0.611278i	0.133675	+	0.991025i	$0.457322\pi$
$930$	26.0867			0.855417
$931$	1.11390	+	7.50139i	0.0365065	+	0.245848i
$932$	−15.6826			−0.513700
$933$	−8.44198	+	14.6219i	−0.276378	+	0.478701i
$934$	−17.6399	−	30.5532i	−0.577195	−	0.999732i
$935$	−42.5852	+	24.5866i	−1.39268	+	0.804067i
$936$	1.17670	+	0.679369i	0.0384617	+	0.0222059i
$937$	15.9550			0.521228			0.260614	−	0.965443i	$-0.416075\pi$
$937$	15.9550			0.521228			0.260614	+	0.965443i	$0.416075\pi$
$938$	5.30465	+	15.2131i	0.173203	+	0.496725i
$939$		−	29.2461i		−	0.954410i
$940$	18.2000	+	10.5078i	0.593618	+	0.342726i
$941$	−12.6669	−	21.9398i	−0.412930	−	0.715216i	0.582278	−	0.812989i	$-0.302161\pi$
$941$	−12.6669	−	21.9398i	−0.412930	−	0.715216i	−0.995209	+	0.0977732i	$0.968828\pi$
$942$	−4.94796	+	2.85671i	−0.161213	+	0.0930765i
$943$	−7.75985	−	15.7051i	−0.252696	−	0.511427i
$944$			0.942507i			0.0306760i
$945$	7.07549	+	1.34676i	0.230166	+	0.0438102i
$946$	−28.2231			−0.917611
$947$	28.3879	−	49.1693i	0.922482	−	1.59779i	0.126921	−	0.991913i	$-0.459490\pi$
$947$	28.3879	−	49.1693i	0.922482	−	1.59779i	0.795561	−	0.605874i	$-0.207176\pi$
$948$	4.62707	+	8.01433i	0.150280	+	0.260293i
$949$	6.83034	+	11.8305i	0.221722	+	0.384034i
$950$	1.30596	−	2.26198i	0.0423708	−	0.0733884i
$951$		−	10.0725i		−	0.326622i
$952$	−12.3782	−	10.6759i	−0.401181	−	0.346008i
$953$			48.9113i			1.58439i	0.610267	+	0.792196i	$0.291062\pi$
$953$			48.9113i			1.58439i	−0.610267	+	0.792196i	$0.708938\pi$
$954$	3.10658	+	1.79359i	0.100579	+	0.0580695i
$955$	−0.0436689	+	0.0252123i	−0.00141309	+	0.000815850i
$956$	14.8359	+	25.6965i	0.479826	+	0.831084i
$957$	−10.5477	+	18.2691i	−0.340958	+	0.590557i
$958$	−28.5055			−0.920971
$959$	−8.75246	+	10.1481i	−0.282632	+	0.327699i
$960$			2.72230i			0.0878617i
$961$	30.4133	−	52.6773i	0.981073	−	1.69927i
$962$	−0.635870	−	1.10136i	−0.0205013	−	0.0355092i
$963$	6.18869	−	3.57304i	0.199428	−	0.115140i
$964$	5.83374	−	10.1043i	0.187892	−	0.325439i
$965$	−7.94764			−0.255844
$966$	−9.05278	−	8.89085i	−0.291268	−	0.286058i
$967$	44.1770			1.42064			0.710319	−	0.703880i	$-0.248551\pi$
$967$	44.1770			1.42064			0.710319	+	0.703880i	$0.248551\pi$
$968$	1.22611	−	2.12368i	0.0394087	−	0.0682578i
$969$	−5.79664	+	3.34669i	−0.186215	+	0.107511i
$970$	10.5196	+	18.2204i	0.337763	+	0.585023i
$971$	−21.4210	+	37.1022i	−0.687431	+	1.19067i	0.285235	+	0.958458i	$0.407928\pi$
$971$	−21.4210	+	37.1022i	−0.687431	+	1.19067i	−0.972666	+	0.232208i	$0.925405\pi$
$972$			1.00000i			0.0320750i
$973$	−10.1756	−	29.1825i	−0.326216	−	0.935548i
$974$	−36.3422			−1.16448
$975$	−1.63789	+	2.83691i	−0.0524545	+	0.0908538i
$976$	2.62356	+	4.54413i	0.0839780	+	0.145454i
$977$	19.2776	−	11.1299i	0.616745	−	0.356078i	−0.158855	−	0.987302i	$-0.550780\pi$
$977$	19.2776	−	11.1299i	0.616745	−	0.356078i	0.775601	+	0.631224i	$0.217447\pi$
$978$	7.87772	+	4.54820i	0.251902	+	0.145436i
$979$			46.2228i			1.47729i
$980$	14.9246	−	11.8487i	0.476748	−	0.378493i
$981$			13.8891i			0.443444i
$982$	−10.9678	+	18.9968i	−0.349996	+	0.606211i
$983$	−8.83987	−	15.3111i	−0.281948	−	0.488349i	0.689916	−	0.723889i	$-0.257647\pi$
$983$	−8.83987	−	15.3111i	−0.281948	−	0.488349i	−0.971865	+	0.235540i	$0.924314\pi$
$984$	1.82633	+	3.16330i	0.0582213	+	0.100842i
$985$	5.48152	−	9.49427i	0.174656	−	0.302512i
$986$	−44.5786			−1.41967
$987$	19.2858	−	6.72476i	0.613874	−	0.214052i
$988$		−	1.47203i		−	0.0468314i
$989$	−20.5079	−	41.5057i	−0.652114	−	1.31981i
$990$	6.89275	−	3.97953i	0.219066	−	0.126478i
$991$	−20.7863	−	36.0029i	−0.660298	−	1.14367i	−0.980537	−	0.196333i	$-0.937097\pi$
$991$	−20.7863	−	36.0029i	−0.660298	−	1.14367i	0.320240	−	0.947337i	$-0.396237\pi$
$992$	8.29879	+	4.79131i	0.263487	+	0.152124i
$993$			6.06513i			0.192471i
$994$	4.81533	−	25.2983i	0.152733	−	0.802414i
$995$	15.8689			0.503079
$996$	3.50915	+	2.02601i	0.111192	+	0.0641965i
$997$	−47.9577	+	27.6884i	−1.51884	+	0.876901i	−0.519083	+	0.854724i	$0.673726\pi$
$997$	−47.9577	+	27.6884i	−1.51884	+	0.876901i	−0.999754	+	0.0221768i	$0.992940\pi$
$998$	13.0071	+	22.5289i	0.411732	+	0.713140i
$999$	0.467985	−	0.810574i	0.0148064	−	0.0256454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.229.10	✓	32
7.3	odd	6	inner	966.2.k.b.367.15	yes	32
23.22	odd	2	inner	966.2.k.b.229.15	yes	32
161.45	even	6	inner	966.2.k.b.367.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.10	✓	32	1.1	even	1	trivial
966.2.k.b.229.15	yes	32	23.22	odd	2	inner
966.2.k.b.367.10	yes	32	161.45	even	6	inner
966.2.k.b.367.15	yes	32	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.36115 + 2.35758i) q^{5} -1.00000i q^{6} +(2.49823 - 0.871108i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.36115 + 2.35758i) q^{5} -1.00000i q^{6} +(2.49823 - 0.871108i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.36115 + 2.35758i) q^{10} +(2.53196 - 1.46183i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.35874i q^{13} +(0.494715 - 2.59909i) q^{14} +2.72230i q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.08913 + 5.35053i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.541689 + 0.938233i) q^{19} +2.72230 q^{20} +(1.72798 - 2.00352i) q^{21} -2.92366i q^{22} +(4.29962 - 2.12444i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.20545 - 2.08790i) q^{25} +(-1.17670 - 0.679369i) q^{26} -1.00000i q^{27} +(-2.00352 - 1.72798i) q^{28} -7.21540 q^{29} +(2.35758 + 1.36115i) q^{30} +(8.29879 - 4.79131i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.46183 - 2.53196i) q^{33} +6.17826 q^{34} +(-1.34676 + 7.07549i) q^{35} -1.00000 q^{36} +(0.810574 + 0.467985i) q^{37} +(0.541689 + 0.938233i) q^{38} +(-0.679369 - 1.17670i) q^{39} +(1.36115 - 2.35758i) q^{40} -3.65266i q^{41} +(-0.871108 - 2.49823i) q^{42} -9.65334i q^{43} +(-2.53196 - 1.46183i) q^{44} +(1.36115 + 2.35758i) q^{45} +(0.309995 - 4.78580i) q^{46} +(6.68553 + 3.85989i) q^{47} +1.00000i q^{48} +(5.48234 - 4.35246i) q^{49} -2.41090 q^{50} +(5.35053 + 3.08913i) q^{51} +(-1.17670 + 0.679369i) q^{52} +(-3.10658 + 1.79359i) q^{53} +(-0.866025 - 0.500000i) q^{54} +7.95907i q^{55} +(-2.49823 + 0.871108i) q^{56} +1.08338i q^{57} +(-3.60770 + 6.24872i) q^{58} +(0.816235 - 0.471253i) q^{59} +(2.35758 - 1.36115i) q^{60} +(2.62356 - 4.54413i) q^{61} -9.58261i q^{62} +(0.494715 - 2.59909i) q^{63} +1.00000 q^{64} +(3.20333 + 1.84944i) q^{65} +(-1.46183 - 2.53196i) q^{66} +(-5.27370 + 3.04477i) q^{67} +(3.08913 - 5.35053i) q^{68} +(2.66136 - 3.98963i) q^{69} +(5.45417 + 4.70407i) q^{70} +9.73354 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-8.70696 + 5.02697i) q^{73} +(0.810574 - 0.467985i) q^{74} +(-2.08790 - 1.20545i) q^{75} +1.08338 q^{76} +(5.05202 - 5.85760i) q^{77} -1.35874 q^{78} +(-8.01433 - 4.62707i) q^{79} +(-1.36115 - 2.35758i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.16330 - 1.82633i) q^{82} -4.05202 q^{83} +(-2.59909 - 0.494715i) q^{84} -16.8190 q^{85} +(-8.36004 - 4.82667i) q^{86} +(-6.24872 + 3.60770i) q^{87} +(-2.53196 + 1.46183i) q^{88} +(-7.90496 + 13.6918i) q^{89} +2.72230 q^{90} +(-1.18361 - 3.39445i) q^{91} +(-3.98963 - 2.66136i) q^{92} +(4.79131 - 8.29879i) q^{93} +(6.68553 - 3.85989i) q^{94} +(-1.47464 - 2.55415i) q^{95} +(0.866025 + 0.500000i) q^{96} +7.72846 q^{97} +(-1.02817 - 6.92408i) q^{98} -2.92366i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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