LMFDB - Embedded newform 1183.2.e.l.170.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.10
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.l.508.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438601 + 0.759680i) q^{2} +(0.377512 + 0.653870i) q^{3} +(0.615258 + 1.06566i) q^{4} +(0.132920 - 0.230223i) q^{5} -0.662309 q^{6} +(0.588870 - 2.57939i) q^{7} -2.83382 q^{8} +(1.21497 - 2.10439i) q^{9} +O(q^{10})$	\(q+(-0.438601 + 0.759680i) q^{2} +(0.377512 + 0.653870i) q^{3} +(0.615258 + 1.06566i) q^{4} +(0.132920 - 0.230223i) q^{5} -0.662309 q^{6} +(0.588870 - 2.57939i) q^{7} -2.83382 q^{8} +(1.21497 - 2.10439i) q^{9} +(0.116597 + 0.201953i) q^{10} +(-0.227833 - 0.394618i) q^{11} +(-0.464534 + 0.804597i) q^{12} +(1.70123 + 1.57867i) q^{14} +0.200715 q^{15} +(0.0124011 - 0.0214794i) q^{16} +(1.82851 + 3.16707i) q^{17} +(1.06577 + 1.84598i) q^{18} +(1.77987 - 3.08283i) q^{19} +0.327119 q^{20} +(1.90889 - 0.588705i) q^{21} +0.399712 q^{22} +(1.53976 - 2.66695i) q^{23} +(-1.06980 - 1.85295i) q^{24} +(2.46466 + 4.26892i) q^{25} +4.09973 q^{27} +(3.11105 - 0.959453i) q^{28} -0.612999 q^{29} +(-0.0880338 + 0.152479i) q^{30} +(5.35450 + 9.27426i) q^{31} +(-2.82294 - 4.88947i) q^{32} +(0.172019 - 0.297946i) q^{33} -3.20795 q^{34} +(-0.515563 - 0.478422i) q^{35} +2.99008 q^{36} +(1.09393 - 1.89474i) q^{37} +(1.56131 + 2.70427i) q^{38} +(-0.376670 + 0.652411i) q^{40} +7.13669 q^{41} +(-0.390014 + 1.70835i) q^{42} +6.76740 q^{43} +(0.280352 - 0.485584i) q^{44} +(-0.322986 - 0.559429i) q^{45} +(1.35068 + 2.33945i) q^{46} +(3.73885 - 6.47589i) q^{47} +0.0187263 q^{48} +(-6.30646 - 3.03784i) q^{49} -4.32402 q^{50} +(-1.38057 + 2.39122i) q^{51} +(3.89574 + 6.74762i) q^{53} +(-1.79815 + 3.11448i) q^{54} -0.121134 q^{55} +(-1.66875 + 7.30951i) q^{56} +2.68769 q^{57} +(0.268862 - 0.465683i) q^{58} +(-5.81235 - 10.0673i) q^{59} +(0.123491 + 0.213893i) q^{60} +(0.797373 - 1.38109i) q^{61} -9.39396 q^{62} +(-4.71257 - 4.37309i) q^{63} +5.00218 q^{64} +(0.150896 + 0.261359i) q^{66} +(4.69957 + 8.13989i) q^{67} +(-2.25001 + 3.89713i) q^{68} +2.32511 q^{69} +(0.589574 - 0.181826i) q^{70} -6.89894 q^{71} +(-3.44300 + 5.96345i) q^{72} +(-1.42550 - 2.46904i) q^{73} +(0.959600 + 1.66208i) q^{74} +(-1.86088 + 3.22314i) q^{75} +4.38032 q^{76} +(-1.15204 + 0.355290i) q^{77} +(-4.36724 + 7.56428i) q^{79} +(-0.00329670 - 0.00571006i) q^{80} +(-2.09721 - 3.63248i) q^{81} +(-3.13016 + 5.42160i) q^{82} -7.51728 q^{83} +(1.80182 + 1.67202i) q^{84} +0.972179 q^{85} +(-2.96819 + 5.14106i) q^{86} +(-0.231414 - 0.400822i) q^{87} +(0.645637 + 1.11828i) q^{88} +(-4.21384 + 7.29859i) q^{89} +0.566649 q^{90} +3.78940 q^{92} +(-4.04277 + 7.00228i) q^{93} +(3.27973 + 5.68067i) q^{94} +(-0.473159 - 0.819536i) q^{95} +(2.13139 - 3.69167i) q^{96} -1.61319 q^{97} +(5.07381 - 3.45849i) q^{98} -1.10724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.438601	+	0.759680i	−0.310138	+	0.537175i	−0.978392	−	0.206758i	$-0.933709\pi$
$2$	−0.438601	+	0.759680i	−0.310138	+	0.537175i	0.668254	+	0.743933i	$0.267042\pi$
$3$	0.377512	+	0.653870i	0.217957	+	0.377512i	0.954183	−	0.299223i	$-0.0967276\pi$
$3$	0.377512	+	0.653870i	0.217957	+	0.377512i	−0.736227	+	0.676735i	$0.763394\pi$
$4$	0.615258	+	1.06566i	0.307629	+	0.532829i
$5$	0.132920	−	0.230223i	0.0594434	−	0.102959i	−0.834772	−	0.550595i	$-0.814401\pi$
$5$	0.132920	−	0.230223i	0.0594434	−	0.102959i	0.894216	+	0.447636i	$0.147734\pi$
$6$	−0.662309			−0.270386
$7$	0.588870	−	2.57939i	0.222572	−	0.974916i
$7$	0.588870	−	2.57939i	0.222572	−	0.974916i
$8$	−2.83382			−1.00191
$9$	1.21497	−	2.10439i	0.404990	−	0.701463i
$10$	0.116597	+	0.201953i	0.0368713	+	0.0638630i
$11$	−0.227833	−	0.394618i	−0.0686942	−	0.118982i	0.829633	−	0.558310i	$-0.188550\pi$
$11$	−0.227833	−	0.394618i	−0.0686942	−	0.118982i	−0.898327	+	0.439328i	$0.855217\pi$
$12$	−0.464534	+	0.804597i	−0.134099	+	0.232267i
$13$		0			0
$13$		0			0
$14$	1.70123	+	1.57867i	0.454673	+	0.421919i
$15$	0.200715			0.0518243
$16$	0.0124011	−	0.0214794i	0.00310028	−	0.00536985i
$17$	1.82851	+	3.16707i	0.443479	+	0.768128i	0.997945	−	0.0640782i	$-0.0204107\pi$
$17$	1.82851	+	3.16707i	0.443479	+	0.768128i	−0.554466	+	0.832207i	$0.687077\pi$
$18$	1.06577	+	1.84598i	0.251206	+	0.435101i
$19$	1.77987	−	3.08283i	0.408331	−	0.707250i	−0.586372	−	0.810042i	$-0.699444\pi$
$19$	1.77987	−	3.08283i	0.408331	−	0.707250i	0.994703	+	0.102792i	$0.0327777\pi$
$20$	0.327119			0.0731460
$21$	1.90889	−	0.588705i	0.416553	−	0.128466i
$22$	0.399712			0.0852188
$23$	1.53976	−	2.66695i	0.321063	−	0.556097i	−0.659645	−	0.751577i	$-0.729293\pi$
$23$	1.53976	−	2.66695i	0.321063	−	0.556097i	0.980708	+	0.195481i	$0.0626267\pi$
$24$	−1.06980	−	1.85295i	−0.218372	−	0.378231i
$25$	2.46466	+	4.26892i	0.492933	+	0.853785i
$26$		0			0
$27$	4.09973			0.788994
$28$	3.11105	−	0.959453i	0.587933	−	0.181320i
$29$	−0.612999			−0.113831			−0.0569155	−	0.998379i	$-0.518127\pi$
$29$	−0.612999			−0.113831			−0.0569155	+	0.998379i	$0.518127\pi$
$30$	−0.0880338	+	0.152479i	−0.0160727	+	0.0278387i
$31$	5.35450	+	9.27426i	0.961696	+	1.66571i	0.718242	+	0.695793i	$0.244947\pi$
$31$	5.35450	+	9.27426i	0.961696	+	1.66571i	0.243454	+	0.969913i	$0.421720\pi$
$32$	−2.82294	−	4.88947i	−0.499030	−	0.864345i
$33$	0.172019	−	0.297946i	0.0299447	−	0.0518658i
$34$	−3.20795			−0.550159
$35$	−0.515563	−	0.478422i	−0.0871460	−	0.0808681i
$36$	2.99008			0.498346
$37$	1.09393	−	1.89474i	0.179841	−	0.311494i	−0.761985	−	0.647595i	$-0.775775\pi$
$37$	1.09393	−	1.89474i	0.179841	−	0.311494i	0.941826	+	0.336101i	$0.109108\pi$
$38$	1.56131	+	2.70427i	0.253278	+	0.438690i
$39$		0			0
$40$	−0.376670	+	0.652411i	−0.0595567	+	0.103155i
$41$	7.13669			1.11456			0.557282	−	0.830323i	$-0.311844\pi$
$41$	7.13669			1.11456			0.557282	+	0.830323i	$0.311844\pi$
$42$	−0.390014	+	1.70835i	−0.0601804	+	0.263604i
$43$	6.76740			1.03202			0.516009	−	0.856583i	$-0.327417\pi$
$43$	6.76740			1.03202			0.516009	+	0.856583i	$0.327417\pi$
$44$	0.280352	−	0.485584i	0.0422646	−	0.0732045i
$45$	−0.322986	−	0.559429i	−0.0481480	−	0.0833947i
$46$	1.35068	+	2.33945i	0.199148	+	0.344934i
$47$	3.73885	−	6.47589i	0.545368	−	0.944605i	−0.453216	−	0.891401i	$-0.649723\pi$
$47$	3.73885	−	6.47589i	0.545368	−	0.944605i	0.998584	−	0.0532042i	$-0.0169434\pi$
$48$	0.0187263			0.00270291
$49$	−6.30646	−	3.03784i	−0.900924	−	0.433978i
$50$	−4.32402			−0.611509
$51$	−1.38057	+	2.39122i	−0.193318	+	0.334837i
$52$		0			0
$53$	3.89574	+	6.74762i	0.535121	+	0.926856i	0.999157	+	0.0410404i	$0.0130672\pi$
$53$	3.89574	+	6.74762i	0.535121	+	0.926856i	−0.464037	+	0.885816i	$0.653599\pi$
$54$	−1.79815	+	3.11448i	−0.244697	+	0.423828i
$55$	−0.121134			−0.0163337
$56$	−1.66875	+	7.30951i	−0.222996	+	0.976774i
$57$	2.68769			0.355993
$58$	0.268862	−	0.465683i	0.0353034	−	0.0611472i
$59$	−5.81235	−	10.0673i	−0.756703	−	1.31065i	−0.944523	−	0.328445i	$-0.893475\pi$
$59$	−5.81235	−	10.0673i	−0.756703	−	1.31065i	0.187820	−	0.982204i	$-0.439858\pi$
$60$	0.123491	+	0.213893i	0.0159427	+	0.0276135i
$61$	0.797373	−	1.38109i	0.102093	−	0.176830i	−0.810454	−	0.585803i	$-0.800779\pi$
$61$	0.797373	−	1.38109i	0.102093	−	0.176830i	0.912547	+	0.408972i	$0.134113\pi$
$62$	−9.39396			−1.19303
$63$	−4.71257	−	4.37309i	−0.593728	−	0.550957i
$64$	5.00218			0.625273
$65$		0			0
$66$	0.150896	+	0.261359i	0.0185740	+	0.0321711i
$67$	4.69957	+	8.13989i	0.574144	+	0.994446i	0.996134	+	0.0878457i	$0.0279983\pi$
$67$	4.69957	+	8.13989i	0.574144	+	0.994446i	−0.421990	+	0.906600i	$0.638668\pi$
$68$	−2.25001	+	3.89713i	−0.272854	+	0.472597i
$69$	2.32511			0.279911
$70$	0.589574	−	0.181826i	0.0704676	−	0.0217323i
$71$	−6.89894			−0.818754			−0.409377	−	0.912365i	$-0.634254\pi$
$71$	−6.89894			−0.818754			−0.409377	+	0.912365i	$0.634254\pi$
$72$	−3.44300	+	5.96345i	−0.405762	+	0.702800i
$73$	−1.42550	−	2.46904i	−0.166842	−	0.288979i	0.770466	−	0.637481i	$-0.220024\pi$
$73$	−1.42550	−	2.46904i	−0.166842	−	0.288979i	−0.937308	+	0.348502i	$0.886690\pi$
$74$	0.959600	+	1.66208i	0.111551	+	0.193212i
$75$	−1.86088	+	3.22314i	−0.214876	+	0.372176i
$76$	4.38032			0.502457
$77$	−1.15204	+	0.355290i	−0.131287	+	0.0404891i
$78$		0			0
$79$	−4.36724	+	7.56428i	−0.491353	+	0.851048i	−0.999950	−	0.00995601i	$-0.996831\pi$
$79$	−4.36724	+	7.56428i	−0.491353	+	0.851048i	0.508597	+	0.861004i	$0.330164\pi$
$80$	−0.00329670	−	0.00571006i	−0.000368583	−	0.000638404i
$81$	−2.09721	−	3.63248i	−0.233023	−	0.403608i
$82$	−3.13016	+	5.42160i	−0.345669	+	0.598716i
$83$	−7.51728			−0.825129			−0.412564	−	0.910928i	$-0.635367\pi$
$83$	−7.51728			−0.825129			−0.412564	+	0.910928i	$0.635367\pi$
$84$	1.80182	+	1.67202i	0.196594	+	0.182432i
$85$	0.972179			0.105448
$86$	−2.96819	+	5.14106i	−0.320068	+	0.554374i
$87$	−0.231414	−	0.400822i	−0.0248102	−	0.0429726i
$88$	0.645637	+	1.11828i	0.0688251	+	0.119209i
$89$	−4.21384	+	7.29859i	−0.446666	+	0.773649i	−0.998167	−	0.0605258i	$-0.980722\pi$
$89$	−4.21384	+	7.29859i	−0.446666	+	0.773649i	0.551500	+	0.834175i	$0.314056\pi$
$90$	0.566649			0.0597301
$91$		0			0
$92$	3.78940			0.395072
$93$	−4.04277	+	7.00228i	−0.419216	+	0.726103i
$94$	3.27973	+	5.68067i	0.338279	+	0.585916i
$95$	−0.473159	−	0.819536i	−0.0485451	−	0.0840826i
$96$	2.13139	−	3.69167i	0.217534	−	0.376779i
$97$	−1.61319			−0.163795			−0.0818975	−	0.996641i	$-0.526098\pi$
$97$	−1.61319			−0.163795			−0.0818975	+	0.996641i	$0.526098\pi$
$98$	5.07381	−	3.45849i	0.512533	−	0.349360i
$99$	−1.10724			−0.111282
$100$	−3.03281	+	5.25298i	−0.303281	+	0.525298i
$101$	−3.64884	−	6.31998i	−0.363074	−	0.628862i	0.625391	−	0.780311i	$-0.284939\pi$
$101$	−3.64884	−	6.31998i	−0.363074	−	0.628862i	−0.988465	+	0.151449i	$0.951606\pi$
$102$	−1.21104	−	2.09758i	−0.119911	−	0.207692i
$103$	4.08426	−	7.07415i	0.402434	−	0.697037i	−0.591585	−	0.806243i	$-0.701497\pi$
$103$	4.08426	−	7.07415i	0.402434	−	0.697037i	0.994019	+	0.109206i	$0.0348308\pi$
$104$		0			0
$105$	0.118195	−	0.517721i	0.0115346	−	0.0505244i
$106$	−6.83471			−0.663845
$107$	8.20393	−	14.2096i	0.793104	−	1.37370i	−0.130933	−	0.991391i	$-0.541797\pi$
$107$	8.20393	−	14.2096i	0.793104	−	1.37370i	0.924036	−	0.382304i	$-0.124869\pi$
$108$	2.52239	+	4.36891i	0.242717	+	0.420399i
$109$	2.98395	+	5.16835i	0.285811	+	0.495039i	0.972805	−	0.231624i	$-0.0744038\pi$
$109$	2.98395	+	5.16835i	0.285811	+	0.495039i	−0.686995	+	0.726662i	$0.741071\pi$
$110$	0.0531295	−	0.0920229i	0.00506569	−	0.00877404i
$111$	1.65189			0.156790
$112$	−0.0481010	−	0.0446359i	−0.00454511	−	0.00421769i
$113$	−16.9748			−1.59685			−0.798426	−	0.602093i	$-0.794334\pi$
$113$	−16.9748			−1.59685			−0.798426	+	0.602093i	$0.794334\pi$
$114$	−1.17883	+	2.04179i	−0.110407	+	0.191231i
$115$	−0.409329	−	0.708978i	−0.0381701	−	0.0661126i
$116$	−0.377152	−	0.653247i	−0.0350177	−	0.0606525i
$117$		0			0
$118$	10.1972			0.938730
$119$	9.24586	−	2.85144i	0.847567	−	0.261391i
$120$	−0.568789			−0.0519231
$121$	5.39618	−	9.34647i	0.490562	−	0.849679i
$122$	0.699458	+	1.21150i	0.0633259	+	0.109684i
$123$	2.69419	+	4.66647i	0.242927	+	0.420761i
$124$	−6.58879	+	11.4121i	−0.591691	+	1.02484i
$125$	2.63960			0.236093
$126$	5.38909	−	1.66201i	0.480098	−	0.148063i
$127$	13.3247			1.18238			0.591188	−	0.806534i	$-0.298659\pi$
$127$	13.3247			1.18238			0.591188	+	0.806534i	$0.298659\pi$
$128$	3.45191	−	5.97889i	0.305109	−	0.528464i
$129$	2.55477	+	4.42500i	0.224935	+	0.389599i
$130$		0			0
$131$	−7.63157	+	13.2183i	−0.666773	+	1.15489i	0.312028	+	0.950073i	$0.398992\pi$
$131$	−7.63157	+	13.2183i	−0.666773	+	1.15489i	−0.978801	+	0.204813i	$0.934342\pi$
$132$	0.423345			0.0368474
$133$	−6.90369	−	6.40636i	−0.598626	−	0.555502i
$134$	−8.24495			−0.712255
$135$	0.544934	−	0.943854i	0.0469005	−	0.0812340i
$136$	−5.18167	−	8.97491i	−0.444324	−	0.769592i
$137$	6.80589	+	11.7881i	0.581466	+	1.00713i	0.995306	+	0.0967792i	$0.0308541\pi$
$137$	6.80589	+	11.7881i	0.581466	+	1.00713i	−0.413840	+	0.910350i	$0.635813\pi$
$138$	−1.01980	+	1.76634i	−0.0868110	+	0.150361i
$139$	14.3332			1.21573			0.607863	−	0.794042i	$-0.292027\pi$
$139$	14.3332			1.21573			0.607863	+	0.794042i	$0.292027\pi$
$140$	0.192630	−	0.843766i	0.0162802	−	0.0713112i
$141$	5.64585			0.475466
$142$	3.02589	−	5.24099i	0.253927	−	0.439814i
$143$		0			0
$144$	−0.0301340	−	0.0521936i	−0.00251117	−	0.00434947i
$145$	−0.0814795	+	0.141127i	−0.00676651	+	0.0117199i
$146$	2.50090			0.206976
$147$	−0.394411	−	5.27043i	−0.0325304	−	0.434698i
$148$	2.69220			0.221297
$149$	−9.82794	+	17.0225i	−0.805136	+	1.39454i	0.111063	+	0.993813i	$0.464574\pi$
$149$	−9.82794	+	17.0225i	−0.805136	+	1.39454i	−0.916199	+	0.400723i	$0.868759\pi$
$150$	−1.63237	−	2.82735i	−0.133282	−	0.230852i
$151$	−0.968702	−	1.67784i	−0.0788319	−	0.136541i	0.823914	−	0.566714i	$-0.191786\pi$
$151$	−0.968702	−	1.67784i	−0.0788319	−	0.136541i	−0.902746	+	0.430174i	$0.858452\pi$
$152$	−5.04383	+	8.73617i	−0.409109	+	0.708597i
$153$	8.88634			0.718418
$154$	0.235378	−	1.03101i	0.0189673	−	0.0830812i
$155$	2.84687			0.228666
$156$		0			0
$157$	−12.3707	−	21.4267i	−0.987291	−	1.71004i	−0.631275	−	0.775559i	$-0.717468\pi$
$157$	−12.3707	−	21.4267i	−0.987291	−	1.71004i	−0.356017	−	0.934480i	$-0.615865\pi$
$158$	−3.83096	−	6.63541i	−0.304775	−	0.527885i
$159$	−2.94137	+	5.09461i	−0.233266	+	0.404029i
$160$	−1.50089			−0.118656
$161$	−5.97237	−	5.54213i	−0.470688	−	0.436781i
$162$	3.67936			0.289078
$163$	−3.37117	+	5.83903i	−0.264050	+	0.457348i	−0.967314	−	0.253580i	$-0.918392\pi$
$163$	−3.37117	+	5.83903i	−0.264050	+	0.457348i	0.703264	+	0.710929i	$0.251725\pi$
$164$	4.39090	+	7.60527i	0.342872	+	0.593872i
$165$	−0.0457294	−	0.0792057i	−0.00356003	−	0.00616616i
$166$	3.29709	−	5.71073i	0.255904	−	0.443238i
$167$	2.06354			0.159681			0.0798407	−	0.996808i	$-0.474559\pi$
$167$	2.06354			0.159681			0.0798407	+	0.996808i	$0.474559\pi$
$168$	−5.40944	+	1.66828i	−0.417347	+	0.128711i
$169$		0			0
$170$	−0.426399	+	0.738545i	−0.0327033	+	0.0566438i
$171$	−4.32498	−	7.49109i	−0.330740	−	0.572858i
$172$	4.16369	+	7.21173i	0.317479	+	0.549889i
$173$	6.76136	−	11.7110i	0.514057	−	0.890372i	−0.485810	−	0.874064i	$-0.661475\pi$
$173$	6.76136	−	11.7110i	0.514057	−	0.890372i	0.999867	−	0.0163081i	$-0.00519126\pi$
$174$	0.405995			0.0307784
$175$	12.4626	−	3.84348i	0.942082	−	0.290540i
$176$	−0.0113015			−0.000851886
$177$	4.38846	−	7.60104i	0.329857	−	0.571329i
$178$	−3.69639	−	6.40234i	−0.277057	−	0.479876i
$179$	4.31487	+	7.47357i	0.322508	+	0.558601i	0.981005	−	0.193983i	$-0.0621407\pi$
$179$	4.31487	+	7.47357i	0.322508	+	0.558601i	−0.658497	+	0.752584i	$0.728807\pi$
$180$	0.397440	−	0.688385i	0.0296234	−	0.0513092i
$181$	−23.4579			−1.74361			−0.871806	−	0.489852i	$-0.837051\pi$
$181$	−23.4579			−1.74361			−0.871806	+	0.489852i	$0.837051\pi$
$182$		0			0
$183$	1.20407			0.0890075
$184$	−4.36341	+	7.55764i	−0.321675	+	0.557157i
$185$	−0.290810	−	0.503697i	−0.0213807	−	0.0370325i
$186$	−3.54633	−	6.14242i	−0.260030	−	0.450384i
$187$	0.833190	−	1.44313i	0.0609289	−	0.105532i
$188$	9.20143			0.671084
$189$	2.41421	−	10.5748i	0.175608	−	0.769203i
$190$	0.830114			0.0602228
$191$	−8.58424	+	14.8683i	−0.621134	+	1.07583i	0.368141	+	0.929770i	$0.379994\pi$
$191$	−8.58424	+	14.8683i	−0.621134	+	1.07583i	−0.989275	+	0.146065i	$0.953339\pi$
$192$	1.88838	+	3.27078i	0.136282	+	0.236048i
$193$	8.09474	+	14.0205i	0.582672	+	1.00922i	0.995161	+	0.0982550i	$0.0313261\pi$
$193$	8.09474	+	14.0205i	0.582672	+	1.00922i	−0.412489	+	0.910962i	$0.635341\pi$
$194$	0.707549	−	1.22551i	0.0507990	−	0.0879865i
$195$		0			0
$196$	−0.642799	−	8.58959i	−0.0459142	−	0.613542i
$197$	−14.1272			−1.00652			−0.503262	−	0.864134i	$-0.667867\pi$
$197$	−14.1272			−1.00652			−0.503262	+	0.864134i	$0.667867\pi$
$198$	0.485637	−	0.841149i	0.0345127	−	0.0597778i
$199$	−6.86644	−	11.8930i	−0.486749	−	0.843075i	0.513135	−	0.858308i	$-0.328484\pi$
$199$	−6.86644	−	11.8930i	−0.486749	−	0.843075i	−0.999884	+	0.0152335i	$0.995151\pi$
$200$	−6.98441	−	12.0974i	−0.493872	−	0.855412i
$201$	−3.54829	+	6.14581i	−0.250277	+	0.433492i
$202$	6.40155			0.450412
$203$	−0.360977	+	1.58116i	−0.0253356	+	0.110976i
$204$	−3.39762			−0.237881
$205$	0.948606	−	1.64303i	0.0662535	−	0.114754i
$206$	3.58273	+	6.20547i	0.249620	+	0.432355i
$207$	−3.74153	−	6.48052i	−0.260054	−	0.450427i
$208$		0			0
$209$	−1.62205			−0.112200
$210$	0.341462	+	0.316863i	0.0235631	+	0.0218656i
$211$	18.7380			1.28998			0.644988	−	0.764193i	$-0.276863\pi$
$211$	18.7380			1.28998			0.644988	+	0.764193i	$0.276863\pi$
$212$	−4.79376	+	8.30304i	−0.329237	+	0.570255i
$213$	−2.60443	−	4.51101i	−0.178453	−	0.309089i
$214$	7.19651	+	12.4647i	0.491943	+	0.852071i
$215$	0.899519	−	1.55801i	0.0613467	−	0.106256i
$216$	−11.6179			−0.790497
$217$	27.0750	−	8.34998i	1.83797	−	0.566834i
$218$	−5.23506			−0.354563
$219$	1.07629	−	1.86418i	0.0727287	−	0.125970i
$220$	−0.0745285	−	0.129087i	−0.00502471	−	0.00870305i
$221$		0			0
$222$	−0.724520	+	1.25491i	−0.0486266	+	0.0842238i
$223$	−3.78482			−0.253450			−0.126725	−	0.991938i	$-0.540447\pi$
$223$	−3.78482			−0.253450			−0.126725	+	0.991938i	$0.540447\pi$
$224$	−14.2742	+	4.40219i	−0.953734	+	0.294133i
$225$	11.9780			0.798531
$226$	7.44516	−	12.8954i	0.495245	−	0.857789i
$227$	−4.50190	−	7.79752i	−0.298802	−	0.517540i	0.677060	−	0.735927i	$-0.263254\pi$
$227$	−4.50190	−	7.79752i	−0.298802	−	0.517540i	−0.975862	+	0.218388i	$0.929920\pi$
$228$	1.65362	+	2.86416i	0.109514	+	0.189684i
$229$	−0.541984	+	0.938743i	−0.0358153	+	0.0620339i	−0.883377	−	0.468662i	$-0.844736\pi$
$229$	−0.541984	+	0.938743i	−0.0358153	+	0.0620339i	0.847562	+	0.530696i	$0.178069\pi$
$230$	0.718129			0.0473520
$231$	−0.667221	−	0.619156i	−0.0438999	−	0.0407375i
$232$	1.73713			0.114048
$233$	7.05354	−	12.2171i	0.462093	−	0.800369i	−0.536972	−	0.843600i	$-0.680432\pi$
$233$	7.05354	−	12.2171i	0.462093	−	0.800369i	0.999065	+	0.0432314i	$0.0137653\pi$
$234$		0			0
$235$	−0.993933	−	1.72154i	−0.0648371	−	0.112301i
$236$	7.15218	−	12.3879i	0.465567	−	0.806387i
$237$	−6.59474			−0.428375
$238$	−1.88906	+	8.27454i	−0.122450	+	0.536359i
$239$	−18.9679			−1.22693			−0.613467	−	0.789721i	$-0.710225\pi$
$239$	−18.9679			−1.22693			−0.613467	+	0.789721i	$0.710225\pi$
$240$	0.00248909	−	0.00431123i	0.000160670	−	0.000278289i
$241$	−12.5569	−	21.7492i	−0.808862	−	1.40099i	−0.913653	−	0.406495i	$-0.866751\pi$
$241$	−12.5569	−	21.7492i	−0.808862	−	1.40099i	0.104791	−	0.994494i	$-0.466583\pi$
$242$	4.73355	+	8.19875i	0.304284	+	0.527035i
$243$	7.73304	−	13.3940i	0.496075	−	0.859227i
$244$	1.96236			0.125627
$245$	−1.53763	+	1.04811i	−0.0982359	+	0.0669611i
$246$	−4.72670			−0.301363
$247$		0			0
$248$	−15.1737	−	26.2816i	−0.963528	−	1.66888i
$249$	−2.83786	−	4.91532i	−0.179842	−	0.311496i
$250$	−1.15773	+	2.00525i	−0.0732215	+	0.126823i
$251$	−21.2412			−1.34073			−0.670367	−	0.742030i	$-0.733863\pi$
$251$	−21.2412			−1.34073			−0.670367	+	0.742030i	$0.733863\pi$
$252$	1.76077	−	7.71256i	0.110918	−	0.485846i
$253$	−1.40323			−0.0882206
$254$	−5.84423	+	10.1225i	−0.366700	+	0.635142i
$255$	0.367009	+	0.635678i	0.0229830	+	0.0398077i
$256$	8.03021	+	13.9087i	0.501888	+	0.869296i
$257$	−12.6609	+	21.9292i	−0.789762	+	1.36791i	0.136350	+	0.990661i	$0.456463\pi$
$257$	−12.6609	+	21.9292i	−0.789762	+	1.36791i	−0.926112	+	0.377248i	$0.876870\pi$
$258$	−4.48211			−0.279044
$259$	−4.24309	−	3.93743i	−0.263653	−	0.244660i
$260$		0			0
$261$	−0.744775	+	1.28999i	−0.0461004	+	0.0798483i
$262$	−6.69444	−	11.5951i	−0.413584	−	0.716348i
$263$	−5.20946	−	9.02305i	−0.321229	−	0.556385i	0.659513	−	0.751693i	$-0.270763\pi$
$263$	−5.20946	−	9.02305i	−0.321229	−	0.556385i	−0.980742	+	0.195308i	$0.937429\pi$
$264$	−0.487471	+	0.844325i	−0.0300018	+	0.0519646i
$265$	2.07128			0.127238
$266$	7.89475	−	2.43476i	0.484058	−	0.149285i
$267$	−6.36310			−0.389416
$268$	−5.78289	+	10.0163i	−0.353246	+	0.611840i
$269$	−14.7653	−	25.5742i	−0.900254	−	1.55929i	−0.827164	−	0.561960i	$-0.810047\pi$
$269$	−14.7653	−	25.5742i	−0.900254	−	1.55929i	−0.0730895	−	0.997325i	$-0.523286\pi$
$270$	0.478018	+	0.827952i	0.0290913	+	0.0503875i
$271$	−12.7161	+	22.0249i	−0.772446	+	1.33791i	0.163774	+	0.986498i	$0.447633\pi$
$271$	−12.7161	+	22.0249i	−0.772446	+	1.33791i	−0.936219	+	0.351417i	$0.885700\pi$
$272$	0.0907024			0.00549964
$273$		0			0
$274$	−11.9403			−0.721339
$275$	1.12306	−	1.94520i	0.0677233	−	0.117300i
$276$	1.43054	+	2.47778i	0.0861086	+	0.149145i
$277$	−5.70379	−	9.87926i	−0.342708	−	0.593587i	0.642227	−	0.766515i	$-0.278011\pi$
$277$	−5.70379	−	9.87926i	−0.342708	−	0.593587i	−0.984935	+	0.172927i	$0.944677\pi$
$278$	−6.28656	+	10.8886i	−0.377043	+	0.653058i
$279$	26.0222			1.55791
$280$	1.46101	+	1.35576i	0.0873121	+	0.0810222i
$281$	11.9773			0.714507			0.357253	−	0.934008i	$-0.383713\pi$
$281$	11.9773			0.714507			0.357253	+	0.934008i	$0.383713\pi$
$282$	−2.47628	+	4.28904i	−0.147460	+	0.255408i
$283$	−1.16453	−	2.01702i	−0.0692239	−	0.119899i	0.829336	−	0.558750i	$-0.188719\pi$
$283$	−1.16453	−	2.01702i	−0.0692239	−	0.119899i	−0.898560	+	0.438851i	$0.855386\pi$
$284$	−4.24463	−	7.35191i	−0.251872	−	0.436256i
$285$	0.357247	−	0.618769i	0.0211615	−	0.0366527i
$286$		0			0
$287$	4.20258	−	18.4083i	0.248071	−	1.08661i
$288$	−13.7191			−0.808408
$289$	1.81309	−	3.14037i	0.106653	−	0.184728i
$290$	−0.0714741	−	0.123797i	−0.00419710	−	0.00726960i
$291$	−0.609000	−	1.05482i	−0.0357002	−	0.0618345i
$292$	1.75410	−	3.03819i	0.102651	−	0.177797i
$293$	29.8421			1.74339			0.871696	−	0.490047i	$-0.163021\pi$
$293$	29.8421			1.74339			0.871696	+	0.490047i	$0.163021\pi$
$294$	4.17683	+	2.01199i	0.243598	+	0.117342i
$295$	−3.09030			−0.179924
$296$	−3.10000	+	5.36936i	−0.180184	+	0.312088i
$297$	−0.934054	−	1.61783i	−0.0541993	−	0.0938760i
$298$	−8.62110	−	14.9322i	−0.499407	−	0.864998i
$299$		0			0
$300$	−4.57968			−0.264408
$301$	3.98512	−	17.4557i	0.229698	−	1.00613i
$302$	1.69950			0.0977950
$303$	2.75496	−	4.77174i	0.158269	−	0.274129i
$304$	−0.0441448	−	0.0764611i	−0.00253188	−	0.00438535i
$305$	−0.211973	−	0.367148i	−0.0121375	−	0.0210228i
$306$	−3.89756	+	6.75078i	−0.222809	+	0.385916i
$307$	13.3825			0.763780			0.381890	−	0.924208i	$-0.375273\pi$
$307$	13.3825			0.763780			0.381890	+	0.924208i	$0.375273\pi$
$308$	−1.08742	−	1.00908i	−0.0619614	−	0.0574978i
$309$	6.16743			0.350853
$310$	−1.24864	+	2.16271i	−0.0709180	+	0.122834i
$311$	10.1372	+	17.5581i	0.574828	+	0.995631i	0.996060	+	0.0886781i	$0.0282642\pi$
$311$	10.1372	+	17.5581i	0.574828	+	0.995631i	−0.421233	+	0.906953i	$0.638402\pi$
$312$		0			0
$313$	−0.592866	+	1.02687i	−0.0335107	+	0.0580423i	−0.882294	−	0.470698i	$-0.844002\pi$
$313$	−0.592866	+	1.02687i	−0.0335107	+	0.0580423i	0.848784	+	0.528740i	$0.177335\pi$
$314$	21.7033			1.22479
$315$	−1.63318	+	0.503676i	−0.0920192	+	0.0283789i
$316$	−10.7479			−0.604617
$317$	−1.90664	+	3.30239i	−0.107087	+	0.185481i	−0.914589	−	0.404384i	$-0.867486\pi$
$317$	−1.90664	+	3.30239i	−0.107087	+	0.185481i	0.807502	+	0.589865i	$0.200819\pi$
$318$	−2.58018	−	4.46901i	−0.144689	−	0.250609i
$319$	0.139661	+	0.241901i	0.00781954	+	0.0135438i
$320$	0.664888	−	1.15162i	0.0371684	−	0.0643775i
$321$	12.3883			0.691448
$322$	6.82973	−	2.10630i	0.380606	−	0.117380i
$323$	13.0181			0.724344
$324$	2.58065	−	4.46982i	0.143369	−	0.248323i
$325$		0			0
$326$	−2.95720	−	5.12202i	−0.163784	−	0.283682i
$327$	−2.25295	+	3.90223i	−0.124589	+	0.215794i
$328$	−20.2241			−1.11669
$329$	−14.5021	−	13.4574i	−0.799527	−	0.741931i
$330$	0.0802280			0.00441641
$331$	−4.89113	+	8.47168i	−0.268841	+	0.465646i	−0.968563	−	0.248769i	$-0.919974\pi$
$331$	−4.89113	+	8.47168i	−0.268841	+	0.465646i	0.699722	+	0.714415i	$0.253307\pi$
$332$	−4.62506	−	8.01085i	−0.253833	−	0.439652i
$333$	−2.65819	−	4.60411i	−0.145668	−	0.252304i
$334$	−0.905071	+	1.56763i	−0.0495233	+	0.0857769i
$335$	2.49866			0.136516
$336$	0.0110273	−	0.0483023i	0.000601591	−	0.00263511i
$337$	−7.21841			−0.393212			−0.196606	−	0.980483i	$-0.562992\pi$
$337$	−7.21841			−0.393212			−0.196606	+	0.980483i	$0.562992\pi$
$338$		0			0
$339$	−6.40818	−	11.0993i	−0.348044	−	0.602831i
$340$	0.598141	+	1.03601i	0.0324387	+	0.0561855i
$341$	2.43986	−	4.22596i	0.132126	−	0.228849i
$342$	7.58777			0.410300
$343$	−11.5495	+	14.4779i	−0.623612	+	0.781734i
$344$	−19.1776			−1.03399
$345$	0.309053	−	0.535296i	0.0166389	−	0.0288193i
$346$	5.93109	+	10.2729i	0.318857	+	0.552277i
$347$	−7.43940	−	12.8854i	−0.399368	−	0.691725i	0.594280	−	0.804258i	$-0.297437\pi$
$347$	−7.43940	−	12.8854i	−0.399368	−	0.691725i	−0.993648	+	0.112533i	$0.964104\pi$
$348$	0.284759	−	0.493217i	0.0152647	−	0.0264392i
$349$	6.61098			0.353878			0.176939	−	0.984222i	$-0.443380\pi$
$349$	6.61098			0.353878			0.176939	+	0.984222i	$0.443380\pi$
$350$	−2.54629	+	11.1533i	−0.136105	+	0.596170i
$351$		0			0
$352$	−1.28632	+	2.22797i	−0.0685609	+	0.118751i
$353$	−17.6694	−	30.6043i	−0.940447	−	1.62890i	−0.764620	−	0.644482i	$-0.777073\pi$
$353$	−17.6694	−	30.6043i	−0.940447	−	1.62890i	−0.175827	−	0.984421i	$-0.556260\pi$
$354$	3.84957	+	6.66765i	0.204602	+	0.354382i
$355$	−0.917004	+	1.58830i	−0.0486695	+	0.0842981i
$356$	−10.3704			−0.549630
$357$	5.35489	+	4.96914i	0.283411	+	0.262995i
$358$	−7.57003			−0.400088
$359$	7.01289	−	12.1467i	0.370126	−	0.641077i	−0.619458	−	0.785029i	$-0.712648\pi$
$359$	7.01289	−	12.1467i	0.370126	−	0.641077i	0.989585	+	0.143952i	$0.0459811\pi$
$360$	0.915284	+	1.58532i	0.0482397	+	0.0835536i
$361$	3.16411	+	5.48040i	0.166532	+	0.288442i
$362$	10.2887	−	17.8205i	0.540760	−	0.936624i
$363$	8.14849			0.427685
$364$		0			0
$365$	−0.757907			−0.0396707
$366$	−0.528107	+	0.914708i	−0.0276046	+	0.0478126i
$367$	12.6850	+	21.9711i	0.662152	+	1.14688i	0.980049	+	0.198756i	$0.0636902\pi$
$367$	12.6850	+	21.9711i	0.662152	+	1.14688i	−0.317897	+	0.948125i	$0.602977\pi$
$368$	−0.0381896	−	0.0661463i	−0.00199077	−	0.00344811i
$369$	8.67086	−	15.0184i	0.451387	−	0.781826i
$370$	0.510198			0.0265239
$371$	19.6988	−	6.07515i	1.02271	−	0.315406i
$372$	−9.94938			−0.515851
$373$	−9.10799	+	15.7755i	−0.471594	+	0.816825i	−0.999472	−	0.0324955i	$-0.989655\pi$
$373$	−9.10799	+	15.7755i	−0.471594	+	0.816825i	0.527878	+	0.849320i	$0.322988\pi$
$374$	0.730877	+	1.26592i	0.0377927	+	0.0654590i
$375$	0.996481	+	1.72596i	0.0514581	+	0.0891280i
$376$	−10.5952	+	18.3515i	−0.546407	+	0.946405i
$377$		0			0
$378$	6.97458	+	6.47215i	0.358734	+	0.332891i
$379$	7.24143			0.371968			0.185984	−	0.982553i	$-0.440453\pi$
$379$	7.24143			0.371968			0.185984	+	0.982553i	$0.440453\pi$
$380$	0.582230	−	1.00845i	0.0298678	−	0.0517325i
$381$	5.03023	+	8.71261i	0.257707	+	0.446361i
$382$	−7.53012	−	13.0425i	−0.385274	−	0.667315i
$383$	0.183588	−	0.317984i	0.00938091	−	0.0162482i	−0.861297	−	0.508102i	$-0.830347\pi$
$383$	0.183588	−	0.317984i	0.00938091	−	0.0162482i	0.870678	+	0.491854i	$0.163681\pi$
$384$	5.21255			0.266002
$385$	−0.0713320	+	0.312451i	−0.00363542	+	0.0159240i
$386$	−14.2015			−0.722835
$387$	8.22218	−	14.2412i	0.417957	−	0.723923i
$388$	−0.992529	−	1.71911i	−0.0503880	−	0.0872746i
$389$	−5.57799	−	9.66137i	−0.282815	−	0.489851i	0.689262	−	0.724513i	$-0.257935\pi$
$389$	−5.57799	−	9.66137i	−0.282815	−	0.489851i	−0.972077	+	0.234662i	$0.924602\pi$
$390$		0			0
$391$	11.2619			0.569538
$392$	17.8714	+	8.60870i	0.902640	+	0.434805i
$393$	−11.5240			−0.581311
$394$	6.19622	−	10.7322i	0.312161	−	0.540679i
$395$	1.16098	+	2.01088i	0.0584154	+	0.101178i
$396$	−0.681238	−	1.17994i	−0.0342335	−	0.0592942i
$397$	−1.58938	+	2.75289i	−0.0797686	+	0.138163i	−0.903150	−	0.429325i	$-0.858751\pi$
$397$	−1.58938	+	2.75289i	−0.0797686	+	0.138163i	0.823381	+	0.567488i	$0.192085\pi$
$398$	12.0465			0.603838
$399$	1.58270	−	6.93259i	0.0792341	−	0.347064i
$400$	0.122258			0.00611292
$401$	−4.04618	+	7.00819i	−0.202057	+	0.349972i	−0.949191	−	0.314701i	$-0.898096\pi$
$401$	−4.04618	+	7.00819i	−0.202057	+	0.349972i	0.747134	+	0.664673i	$0.231429\pi$
$402$	−3.11257	−	5.39112i	−0.155241	−	0.268885i
$403$		0			0
$404$	4.48996	−	7.77683i	0.223384	−	0.386912i
$405$	−1.11504			−0.0554068
$406$	−1.04285	−	0.967726i	−0.0517559	−	0.0480275i
$407$	−0.996934			−0.0494162
$408$	3.91228	−	6.77627i	0.193687	−	0.335475i
$409$	−1.56514	−	2.71091i	−0.0773913	−	0.134046i	0.824732	−	0.565523i	$-0.191326\pi$
$409$	−1.56514	−	2.71091i	−0.0773913	−	0.134046i	−0.902124	+	0.431478i	$0.857992\pi$
$410$	0.832120	+	1.44127i	0.0410955	+	0.0711794i
$411$	−5.13861	+	8.90033i	−0.253469	+	0.439021i
$412$	10.0515			0.495202
$413$	−29.3901	+	9.06397i	−1.44619	+	0.446009i
$414$	6.56416			0.322611
$415$	−0.999193	+	1.73065i	−0.0490485	+	0.0849544i
$416$		0			0
$417$	5.41095	+	9.37205i	0.264976	+	0.458951i
$418$	0.711435	−	1.23224i	0.0347974	−	0.0602709i
$419$	11.4655			0.560128			0.280064	−	0.959981i	$-0.409644\pi$
$419$	11.4655			0.560128			0.280064	+	0.959981i	$0.409644\pi$
$420$	0.624433	−	0.192576i	0.0304692	−	0.00939677i
$421$	22.1642			1.08022			0.540108	−	0.841596i	$-0.318383\pi$
$421$	22.1642			1.08022			0.540108	+	0.841596i	$0.318383\pi$
$422$	−8.21850	+	14.2349i	−0.400070	+	0.692942i
$423$	−9.08519	−	15.7360i	−0.441737	−	0.765111i
$424$	−11.0398	−	19.1215i	−0.536141	−	0.928623i
$425$	−9.01333	+	15.6116i	−0.437211	+	0.757272i
$426$	4.56923			0.221380
$427$	−3.09282	−	2.87001i	−0.149672	−	0.138890i
$428$	20.1901			0.975926
$429$		0			0
$430$	0.789061	+	1.36669i	0.0380519	+	0.0659078i
$431$	10.6568	+	18.4581i	0.513319	+	0.889094i	0.999881	+	0.0154479i	$0.00491741\pi$
$431$	10.6568	+	18.4581i	0.513319	+	0.889094i	−0.486562	+	0.873646i	$0.661749\pi$
$432$	0.0508413	−	0.0880597i	0.00244610	−	0.00423678i
$433$	0.0447167			0.00214895			0.00107447	−	0.999999i	$-0.499658\pi$
$433$	0.0447167			0.00214895			0.00107447	+	0.999999i	$0.499658\pi$
$434$	−5.53182	+	24.2306i	−0.265536	+	1.16311i
$435$	−0.123038			−0.00589922
$436$	−3.67180	+	6.35974i	−0.175847	+	0.304576i
$437$	−5.48116	−	9.49365i	−0.262199	−	0.454143i
$438$	0.944121	+	1.63527i	0.0451119	+	0.0781360i
$439$	1.66462	−	2.88321i	0.0794481	−	0.137608i	−0.823564	−	0.567224i	$-0.808018\pi$
$439$	1.66462	−	2.88321i	0.0794481	−	0.137608i	0.903012	+	0.429615i	$0.141351\pi$
$440$	0.343271			0.0163648
$441$	−14.0550	+	9.58037i	−0.669284	+	0.456208i
$442$		0			0
$443$	−15.2276	+	26.3750i	−0.723485	+	1.25311i	0.236109	+	0.971727i	$0.424128\pi$
$443$	−15.2276	+	26.3750i	−0.723485	+	1.25311i	−0.959594	+	0.281387i	$0.909206\pi$
$444$	1.01634	+	1.76035i	0.0482332	+	0.0835424i
$445$	1.12020	+	1.94025i	0.0531028	+	0.0919767i
$446$	1.66003	−	2.87525i	0.0786046	−	0.136147i
$447$	−14.8407			−0.701939
$448$	2.94563	−	12.9026i	0.139168	−	0.609589i
$449$	−6.77363			−0.319667			−0.159834	−	0.987144i	$-0.551096\pi$
$449$	−6.77363			−0.319667			−0.159834	+	0.987144i	$0.551096\pi$
$450$	−5.25356	+	9.09942i	−0.247655	+	0.428951i
$451$	−1.62597	−	2.81627i	−0.0765641	−	0.132613i
$452$	−10.4439	−	18.0893i	−0.491238	−	0.850849i
$453$	0.731393	−	1.26681i	0.0343638	−	0.0595199i
$454$	7.89816			0.370679
$455$		0			0
$456$	−7.61643			−0.356672
$457$	−16.0851	+	27.8602i	−0.752430	+	1.30325i	0.194212	+	0.980960i	$0.437785\pi$
$457$	−16.0851	+	27.8602i	−0.752430	+	1.30325i	−0.946642	+	0.322287i	$0.895548\pi$
$458$	−0.475430	−	0.823468i	−0.0222154	−	0.0384781i
$459$	7.49641	+	12.9842i	0.349902	+	0.606049i
$460$	0.503685	−	0.872409i	0.0234845	−	0.0406763i
$461$	−24.4018			−1.13651			−0.568253	−	0.822854i	$-0.692380\pi$
$461$	−24.4018			−1.13651			−0.568253	+	0.822854i	$0.692380\pi$
$462$	0.763004	−	0.235312i	0.0354982	−	0.0109477i
$463$	−23.4370			−1.08921			−0.544604	−	0.838693i	$-0.683320\pi$
$463$	−23.4370			−1.08921			−0.544604	+	0.838693i	$0.683320\pi$
$464$	−0.00760188	+	0.0131668i	−0.000352908	+	0.000611255i
$465$	1.07473	+	1.86148i	0.0498392	+	0.0863241i
$466$	6.18739	+	10.7169i	0.286625	+	0.496450i
$467$	13.9375	−	24.1405i	0.644952	−	1.11709i	−0.339360	−	0.940656i	$-0.610211\pi$
$467$	13.9375	−	24.1405i	0.644952	−	1.11709i	0.984313	−	0.176433i	$-0.0564560\pi$
$468$		0			0
$469$	23.7634	−	7.32867i	1.09729	−	0.338406i
$470$	1.74376			0.0804338
$471$	9.34019	−	16.1777i	0.430373	−	0.745428i
$472$	16.4711	+	28.5288i	0.758145	+	1.31315i
$473$	−1.54184	−	2.67054i	−0.0708937	−	0.122792i
$474$	2.89246	−	5.00989i	0.132855	−	0.230112i
$475$	17.5472			0.805119
$476$	8.72725	+	8.09855i	0.400013	+	0.371196i
$477$	18.9328			0.866874
$478$	8.31936	−	14.4096i	0.380519	−	0.659078i
$479$	−1.03601	−	1.79442i	−0.0473365	−	0.0819892i	0.841386	−	0.540434i	$-0.181740\pi$
$479$	−1.03601	−	1.79442i	−0.0473365	−	0.0819892i	−0.888723	+	0.458445i	$0.848407\pi$
$480$	−0.566605	−	0.981389i	−0.0258619	−	0.0447941i
$481$		0			0
$482$	22.0299			1.00343
$483$	1.36919	−	5.99737i	0.0623003	−	0.272890i
$484$	13.2802			0.603644
$485$	−0.214425	+	0.371395i	−0.00973653	+	0.0168642i
$486$	6.78345	+	11.7493i	0.307703	+	0.532958i
$487$	−3.00981	−	5.21314i	−0.136388	−	0.236230i	0.789739	−	0.613443i	$-0.210216\pi$
$487$	−3.00981	−	5.21314i	−0.136388	−	0.236230i	−0.926127	+	0.377213i	$0.876883\pi$
$488$	−2.25961	+	3.91376i	−0.102288	+	0.177167i
$489$	−5.09062			−0.230206
$490$	−0.121817	−	1.62781i	−0.00550312	−	0.0735370i
$491$	2.01551			0.0909588			0.0454794	−	0.998965i	$-0.485518\pi$
$491$	2.01551			0.0909588			0.0454794	+	0.998965i	$0.485518\pi$
$492$	−3.31524	+	5.74216i	−0.149462	+	0.258876i
$493$	−1.12088	−	1.94141i	−0.0504817	−	0.0874369i
$494$		0			0
$495$	−0.147174	+	0.254913i	−0.00661497	+	0.0114575i
$496$	0.265607			0.0119261
$497$	−4.06258	+	17.7950i	−0.182232	+	0.798217i
$498$	4.97876			0.223104
$499$	3.75587	−	6.50536i	0.168136	−	0.291220i	−0.769629	−	0.638492i	$-0.779559\pi$
$499$	3.75587	−	6.50536i	0.168136	−	0.291220i	0.937764	+	0.347272i	$0.112892\pi$
$500$	1.62404	+	2.81291i	0.0726291	+	0.125797i
$501$	0.779011	+	1.34929i	0.0348036	+	0.0602816i
$502$	9.31643	−	16.1365i	0.415813	−	0.720209i
$503$	−15.1154			−0.673962			−0.336981	−	0.941511i	$-0.609406\pi$
$503$	−15.1154			−0.673962			−0.336981	+	0.941511i	$0.609406\pi$
$504$	13.3546	+	12.3925i	0.594860	+	0.552007i
$505$	−1.94001			−0.0863293
$506$	0.615461	−	1.06601i	0.0273606	−	0.0473899i
$507$		0			0
$508$	8.19812	+	14.1996i	0.363733	+	0.630004i
$509$	−18.3350	+	31.7571i	−0.812683	+	1.40761i	0.0982965	+	0.995157i	$0.468661\pi$
$509$	−18.3350	+	31.7571i	−0.812683	+	1.40761i	−0.910980	+	0.412451i	$0.864673\pi$
$510$	−0.643883			−0.0285116
$511$	−7.20804	+	2.22297i	−0.318865	+	0.0983385i
$512$	−0.280601			−0.0124009
$513$	7.29700	−	12.6388i	0.322170	−	0.558016i
$514$	−11.1061	−	19.2364i	−0.489871	−	0.848481i
$515$	−1.08576	−	1.88059i	−0.0478441	−	0.0828685i
$516$	−3.14369	+	5.44502i	−0.138393	+	0.239704i
$517$	−3.40734			−0.149855
$518$	4.85221	−	1.49643i	0.213194	−	0.0657495i
$519$	10.2100			0.448168
$520$		0			0
$521$	15.9042	+	27.5468i	0.696774	+	1.20685i	0.969579	+	0.244778i	$0.0787152\pi$
$521$	15.9042	+	27.5468i	0.696774	+	1.20685i	−0.272805	+	0.962069i	$0.587951\pi$
$522$	−0.653319	−	1.13158i	−0.0285950	−	0.0495280i
$523$	19.7798	−	34.2596i	0.864909	−	1.49807i	−0.00222791	−	0.999998i	$-0.500709\pi$
$523$	19.7798	−	34.2596i	0.864909	−	1.49807i	0.867137	−	0.498069i	$-0.165957\pi$
$524$	−18.7815			−0.820475
$525$	7.21790	+	6.69794i	0.315015	+	0.292322i
$526$	9.13951			0.398501
$527$	−19.5815	+	33.9162i	−0.852984	+	1.47741i
$528$	−0.00426647	−	0.00738974i	−0.000185674	−	0.000321597i
$529$	6.75826	+	11.7057i	0.293838	+	0.508942i
$530$	−0.908466	+	1.57351i	−0.0394612	+	0.0683488i
$531$	−28.2473			−1.22583
$532$	2.57944	−	11.2985i	0.111833	−	0.489854i
$533$		0			0
$534$	2.79087	−	4.83392i	0.120773	−	0.209184i
$535$	−2.18092	−	3.77747i	−0.0942896	−	0.163314i
$536$	−13.3177	−	23.0670i	−0.575238	−	0.996341i
$537$	−3.25783	+	5.64272i	−0.140586	+	0.243501i
$538$	25.9043			1.11681
$539$	0.238032	+	3.18077i	0.0102527	+	0.137005i
$540$	1.34110			0.0577118
$541$	−11.1142	+	19.2503i	−0.477836	+	0.827637i	−0.999677	−	0.0254061i	$-0.991912\pi$
$541$	−11.1142	+	19.2503i	−0.477836	+	0.827637i	0.521841	+	0.853043i	$0.325245\pi$
$542$	−11.1546	−	19.3203i	−0.479129	−	0.829877i
$543$	−8.85563	−	15.3384i	−0.380032	−	0.658234i
$544$	10.3236	−	17.8809i	0.442619	−	0.766638i
$545$	1.58650			0.0679582
$546$		0			0
$547$	−14.1989			−0.607100			−0.303550	−	0.952816i	$-0.598172\pi$
$547$	−14.1989			−0.607100			−0.303550	+	0.952816i	$0.598172\pi$
$548$	−8.37475	+	14.5055i	−0.357751	+	0.619644i
$549$	−1.93757	−	3.35596i	−0.0826934	−	0.143229i
$550$	0.985155	+	1.70634i	0.0420071	+	0.0727585i
$551$	−1.09106	+	1.88977i	−0.0464807	+	0.0805070i
$552$	−6.58895			−0.280444
$553$	16.9395	+	15.7192i	0.720340	+	0.668448i
$554$	10.0068			0.425147
$555$	0.219568	−	0.380303i	0.00932015	−	0.0161430i
$556$	8.81861	+	15.2743i	0.373992	+	0.647774i
$557$	−13.3089	−	23.0518i	−0.563918	−	0.976734i	−0.997149	−	0.0754517i	$-0.975960\pi$
$557$	−13.3089	−	23.0518i	−0.563918	−	0.976734i	0.433232	−	0.901283i	$-0.357373\pi$
$558$	−11.4134	+	19.7685i	−0.483167	+	0.836869i
$559$		0			0
$560$	−0.0166698	+	0.00514099i	−0.000704426	+	0.000217247i
$561$	1.25816			0.0531194
$562$	−5.25327	+	9.09893i	−0.221596	+	0.383815i
$563$	10.4757	+	18.1444i	0.441498	+	0.764697i	0.997801	−	0.0662828i	$-0.0211140\pi$
$563$	10.4757	+	18.1444i	0.441498	+	0.764697i	−0.556303	+	0.830979i	$0.687781\pi$
$564$	3.47365	+	6.01654i	0.146267	+	0.253342i
$565$	−2.25628	+	3.90799i	−0.0949223	+	0.164410i
$566$	2.04305			0.0858759
$567$	−10.6045	+	3.27046i	−0.445349	+	0.137346i
$568$	19.5503			0.820314
$569$	0.562573	−	0.974405i	0.0235843	−	0.0408492i	−0.853992	−	0.520286i	$-0.825826\pi$
$569$	0.562573	−	0.974405i	0.0235843	−	0.0408492i	0.877577	+	0.479436i	$0.159159\pi$
$570$	0.313378	+	0.542786i	0.0131259	+	0.0227348i
$571$	20.8144	+	36.0516i	0.871055	+	1.50871i	0.860906	+	0.508764i	$0.169897\pi$
$571$	20.8144	+	36.0516i	0.871055	+	1.50871i	0.0101493	+	0.999948i	$0.496769\pi$
$572$		0			0
$573$	−12.9626			−0.541521
$574$	12.1411	+	11.2665i	0.506762	+	0.470255i
$575$	15.1800			0.633049
$576$	6.07750	−	10.5265i	0.253229	−	0.438606i
$577$	14.7123	+	25.4825i	0.612481	+	1.06085i	0.990821	+	0.135182i	$0.0431619\pi$
$577$	14.7123	+	25.4825i	0.612481	+	1.06085i	−0.378339	+	0.925667i	$0.623505\pi$
$578$	1.59045	+	2.75474i	0.0661541	+	0.114582i
$579$	−6.11172	+	10.5858i	−0.253994	+	0.439931i
$580$	−0.200524			−0.00832629
$581$	−4.42670	+	19.3900i	−0.183650	+	0.804431i
$582$	1.06843			0.0442879
$583$	1.77516	−	3.07466i	0.0735194	−	0.127339i
$584$	4.03961	+	6.99680i	0.167160	+	0.289530i
$585$		0			0
$586$	−13.0888	+	22.6704i	−0.540692	+	0.936506i
$587$	36.0961			1.48985			0.744923	−	0.667150i	$-0.232486\pi$
$587$	36.0961			1.48985			0.744923	+	0.667150i	$0.232486\pi$
$588$	5.37381	−	3.66298i	0.221612	−	0.151059i
$589$	38.1213			1.57076
$590$	1.35541	−	2.34764i	0.0558013	−	0.0966507i
$591$	−5.33320	−	9.23736i	−0.219378	−	0.379974i
$592$	−0.0271320	−	0.0469939i	−0.00111512	−	0.00193144i
$593$	−2.03883	+	3.53135i	−0.0837246	+	0.145015i	−0.904847	−	0.425737i	$-0.860015\pi$
$593$	−2.03883	+	3.53135i	−0.0837246	+	0.145015i	0.821122	+	0.570752i	$0.193348\pi$
$594$	1.63871			0.0672371
$595$	0.572487	−	2.50763i	0.0234697	−	0.102803i
$596$	−24.1869			−0.990732
$597$	5.18433	−	8.97952i	0.212180	−	0.367507i
$598$		0			0
$599$	12.6996	+	21.9964i	0.518894	+	0.898750i	0.999759	+	0.0219556i	$0.00698924\pi$
$599$	12.6996	+	21.9964i	0.518894	+	0.898750i	−0.480865	+	0.876794i	$0.659677\pi$
$600$	5.27339	−	9.13379i	0.215285	−	0.372885i
$601$	−43.4761			−1.77343			−0.886713	−	0.462321i	$-0.847017\pi$
$601$	−43.4761			−1.77343			−0.886713	+	0.462321i	$0.847017\pi$
$602$	11.5129	+	10.6835i	0.469230	+	0.435428i
$603$	22.8393			0.930089
$604$	1.19200	−	2.06461i	0.0485019	−	0.0840078i
$605$	−1.43452	−	2.48466i	−0.0583214	−	0.101016i
$606$	2.41666	+	4.18578i	0.0981702	+	0.170036i
$607$	9.11698	−	15.7911i	0.370047	−	0.640940i	−0.619526	−	0.784976i	$-0.712675\pi$
$607$	9.11698	−	15.7911i	0.370047	−	0.640940i	0.989572	+	0.144037i	$0.0460083\pi$
$608$	−20.0979			−0.815077
$609$	−1.17015	+	0.360876i	−0.0474167	+	0.0146234i
$610$	0.371886			0.0150572
$611$		0			0
$612$	5.46739	+	9.46980i	0.221006	+	0.382794i
$613$	16.1136	+	27.9096i	0.650823	+	1.12726i	0.982924	+	0.184014i	$0.0589093\pi$
$613$	16.1136	+	27.9096i	0.650823	+	1.12726i	−0.332101	+	0.943244i	$0.607757\pi$
$614$	−5.86959	+	10.1664i	−0.236877	+	0.410283i
$615$	1.43244			0.0577615
$616$	3.26466	−	1.00683i	0.131537	−	0.0405663i
$617$	−37.0753			−1.49260			−0.746298	−	0.665612i	$-0.768170\pi$
$617$	−37.0753			−1.49260			−0.746298	+	0.665612i	$0.768170\pi$
$618$	−2.70504	+	4.68527i	−0.108813	+	0.188469i
$619$	−16.9264	−	29.3173i	−0.680328	−	1.17836i	−0.974881	−	0.222728i	$-0.928504\pi$
$619$	−16.9264	−	29.3173i	−0.680328	−	1.17836i	0.294553	−	0.955635i	$-0.404829\pi$
$620$	1.75156	+	3.03379i	0.0703442	+	0.121840i
$621$	6.31261	−	10.9338i	0.253317	−	0.438757i
$622$	−17.7848			−0.713104
$623$	16.3445	+	15.1670i	0.654828	+	0.607655i
$624$		0			0
$625$	−11.9725	+	20.7369i	−0.478899	+	0.829477i
$626$	−0.520063	−	0.900776i	−0.0207859	−	0.0360023i
$627$	−0.612345	−	1.06061i	−0.0244547	−	0.0423568i
$628$	15.2224	−	26.3659i	0.607439	−	1.05211i
$629$	8.00106			0.319023
$630$	0.333682	−	1.46161i	0.0132942	−	0.0582318i
$631$	−33.2239			−1.32262			−0.661311	−	0.750111i	$-0.730000\pi$
$631$	−33.2239			−1.32262			−0.661311	+	0.750111i	$0.730000\pi$
$632$	12.3760	−	21.4358i	0.492289	−	0.852670i
$633$	7.07381	+	12.2522i	0.281159	+	0.486981i
$634$	−1.67251	−	2.89687i	−0.0664238	−	0.115049i
$635$	1.77111	−	3.06766i	0.0702844	−	0.121736i
$636$	−7.23881			−0.287038
$637$		0			0
$638$	−0.245023			−0.00970055
$639$	−8.38201	+	14.5181i	−0.331587	+	0.574326i
$640$	−0.917653	−	1.58942i	−0.0362734	−	0.0628274i
$641$	5.91885	+	10.2517i	0.233780	+	0.404919i	0.958918	−	0.283685i	$-0.0915570\pi$
$641$	5.91885	+	10.2517i	0.233780	+	0.404919i	−0.725137	+	0.688604i	$0.758224\pi$
$642$	−5.43353	+	9.41116i	−0.214444	+	0.371429i
$643$	40.1562			1.58360			0.791802	−	0.610778i	$-0.209143\pi$
$643$	40.1562			1.58360			0.791802	+	0.610778i	$0.209143\pi$
$644$	2.23146	−	9.77433i	0.0879320	−	0.385163i
$645$	1.35832			0.0534837
$646$	−5.70974	+	9.88956i	−0.224647	+	0.389100i
$647$	−1.58849	−	2.75135i	−0.0624501	−	0.108167i	0.833110	−	0.553107i	$-0.186558\pi$
$647$	−1.58849	−	2.75135i	−0.0624501	−	0.108167i	−0.895560	+	0.444941i	$0.853225\pi$
$648$	5.94311	+	10.2938i	0.233468	+	0.404378i
$649$	−2.64849	+	4.58732i	−0.103962	+	0.180068i
$650$		0			0
$651$	15.6809	+	14.5513i	0.614584	+	0.570310i
$652$	−8.29654			−0.324918
$653$	−15.3388	+	26.5675i	−0.600253	+	1.03967i	0.392530	+	0.919739i	$0.371600\pi$
$653$	−15.3388	+	26.5675i	−0.600253	+	1.03967i	−0.992782	+	0.119929i	$0.961733\pi$
$654$	−1.97630	−	3.42305i	−0.0772793	−	0.133852i
$655$	2.02877	+	3.51393i	0.0792706	+	0.137301i
$656$	0.0885030	−	0.153292i	0.00345546	−	0.00598504i
$657$	−6.92775			−0.270277
$658$	16.5840	−	5.11453i	0.646510	−	0.199385i
$659$	−8.19638			−0.319286			−0.159643	−	0.987175i	$-0.551034\pi$
$659$	−8.19638			−0.319286			−0.159643	+	0.987175i	$0.551034\pi$
$660$	0.0562708	−	0.0974638i	0.00219034	−	0.00379377i
$661$	−15.4002	−	26.6740i	−0.599000	−	1.03750i	−0.992969	−	0.118374i	$-0.962232\pi$
$661$	−15.4002	−	26.6740i	−0.599000	−	1.03750i	0.393969	−	0.919124i	$-0.371102\pi$
$662$	−4.29051	−	7.43139i	−0.166755	−	0.288829i
$663$		0			0
$664$	21.3026			0.826701
$665$	−2.39253	+	0.737861i	−0.0927783	+	0.0286130i
$666$	4.66354			0.180708
$667$	−0.943873	+	1.63484i	−0.0365469	+	0.0633011i
$668$	1.26961	+	2.19903i	0.0491226	+	0.0850829i
$669$	−1.42881	−	2.47478i	−0.0552412	−	0.0956805i
$670$	−1.09591	+	1.89818i	−0.0423389	+	0.0733331i
$671$	−0.726671			−0.0280528
$672$	−8.26713	−	7.67158i	−0.318911	−	0.295938i
$673$	−29.7292			−1.14598			−0.572988	−	0.819564i	$-0.694216\pi$
$673$	−29.7292			−1.14598			−0.572988	+	0.819564i	$0.694216\pi$
$674$	3.16600	−	5.48368i	0.121950	−	0.211223i
$675$	10.1045	+	17.5015i	0.388921	+	0.673631i
$676$		0			0
$677$	13.9033	−	24.0813i	0.534349	−	0.925519i	−0.464846	−	0.885392i	$-0.653890\pi$
$677$	13.9033	−	24.0813i	0.534349	−	0.925519i	0.999195	−	0.0401277i	$-0.0127765\pi$
$678$	11.2425			0.431767
$679$	−0.949961	+	4.16105i	−0.0364561	+	0.159686i
$680$	−2.75498			−0.105649
$681$	3.39904	−	5.88731i	0.130252	−	0.225602i
$682$	2.14025	+	3.70703i	0.0819545	+	0.141949i
$683$	−6.91159	−	11.9712i	−0.264465	−	0.458066i	0.702959	−	0.711231i	$-0.251862\pi$
$683$	−6.91159	−	11.9712i	−0.264465	−	0.458066i	−0.967423	+	0.253165i	$0.918529\pi$
$684$	5.32195	−	9.21790i	0.203490	−	0.352455i
$685$	3.61854			0.138257
$686$	−5.93297	−	15.1239i	−0.226522	−	0.577434i
$687$	−0.818421			−0.0312247
$688$	0.0839234	−	0.145360i	0.00319955	−	0.00554178i
$689$		0			0
$690$	0.271102	+	0.469563i	0.0103207	+	0.0178760i
$691$	1.02093	−	1.76831i	0.0388381	−	0.0672696i	−0.845953	−	0.533258i	$-0.820968\pi$
$691$	1.02093	−	1.76831i	0.0388381	−	0.0672696i	0.884791	+	0.465988i	$0.154301\pi$
$692$	16.6399			0.632555
$693$	−0.652020	+	2.85600i	−0.0247682	+	0.108491i
$694$	13.0517			0.495437
$695$	1.90516	−	3.29984i	0.0722669	−	0.125170i
$696$	0.655786	+	1.13586i	0.0248575	+	0.0430545i
$697$	13.0495	+	22.6024i	0.494286	+	0.856128i
$698$	−2.89959	+	5.02223i	−0.109751	+	0.190094i
$699$	10.6512			0.402865
$700$	11.7635	+	10.9161i	0.444619	+	0.412590i
$701$	−27.0161			−1.02039			−0.510193	−	0.860060i	$-0.670426\pi$
$701$	−27.0161			−1.02039			−0.510193	+	0.860060i	$0.670426\pi$
$702$		0			0
$703$	−3.89412	−	6.74481i	−0.146869	−	0.254385i
$704$	−1.13966	−	1.97395i	−0.0429527	−	0.0743962i
$705$	0.750443	−	1.29981i	0.0282633	−	0.0489535i
$706$	30.9993			1.16667
$707$	−18.4504	+	5.69013i	−0.693898	+	0.213999i
$708$	10.8001			0.405894
$709$	1.41915	−	2.45804i	0.0532973	−	0.0923136i	−0.838146	−	0.545446i	$-0.816360\pi$
$709$	1.41915	−	2.45804i	0.0532973	−	0.0923136i	0.891443	+	0.453133i	$0.149694\pi$
$710$	−0.804399	−	1.39326i	−0.0301885	−	0.0522881i
$711$	10.6121	+	18.3808i	0.397986	+	0.689332i
$712$	11.9413	−	20.6829i	0.447518	−	0.775123i
$713$	32.9786			1.23506
$714$	−6.12362	+	1.88854i	−0.229171	+	0.0706767i
$715$		0			0
$716$	−5.30951	+	9.19634i	−0.198426	+	0.343683i
$717$	−7.16062	−	12.4026i	−0.267418	−	0.463182i
$718$	6.15173	+	10.6551i	0.229580	+	0.397645i
$719$	−19.6194	+	33.9819i	−0.731682	+	1.26731i	0.224482	+	0.974478i	$0.427931\pi$
$719$	−19.6194	+	33.9819i	−0.731682	+	1.26731i	−0.956164	+	0.292832i	$0.905402\pi$
$720$	−0.0160216			−0.000597089
$721$	−15.8419	−	14.7006i	−0.589982	−	0.547481i
$722$	−5.55113			−0.206592
$723$	9.48076	−	16.4212i	0.352593	−	0.610710i
$724$	−14.4326	−	24.9981i	−0.536385	−	0.929046i
$725$	−1.51084	−	2.61685i	−0.0561111	−	0.0971873i
$726$	−3.57394	+	6.19025i	−0.132641	+	0.229742i
$727$	12.9172			0.479074			0.239537	−	0.970887i	$-0.423004\pi$
$727$	12.9172			0.479074			0.239537	+	0.970887i	$0.423004\pi$
$728$		0			0
$729$	−0.906005			−0.0335558
$730$	0.332419	−	0.575767i	0.0123034	−	0.0213101i
$731$	12.3743	+	21.4328i	0.457679	+	0.792723i
$732$	0.740813	+	1.28313i	0.0273813	+	0.0474257i
$733$	3.60982	−	6.25239i	0.133332	−	0.230937i	−0.791627	−	0.611004i	$-0.790766\pi$
$733$	3.60982	−	6.25239i	0.133332	−	0.230937i	0.924959	+	0.380067i	$0.124099\pi$
$734$	−22.2547			−0.821434
$735$	−1.26580	−	0.609740i	−0.0466898	−	0.0224906i
$736$	−17.3866			−0.640879
$737$	2.14143	−	3.70907i	0.0788807	−	0.136625i
$738$	7.60611	+	13.1742i	0.279985	+	0.484948i
$739$	−12.2015	−	21.1336i	−0.448838	−	0.777411i	0.549472	−	0.835512i	$-0.314829\pi$
$739$	−12.2015	−	21.1336i	−0.448838	−	0.777411i	−0.998311	+	0.0581011i	$0.981495\pi$
$740$	0.357846	−	0.619807i	0.0131547	−	0.0227845i
$741$		0			0
$742$	−4.02475	+	17.6293i	−0.147753	+	0.647194i
$743$	43.6054			1.59973			0.799864	−	0.600182i	$-0.204905\pi$
$743$	43.6054			1.59973			0.799864	+	0.600182i	$0.204905\pi$
$744$	11.4565	−	19.8432i	0.420015	−	0.727487i
$745$	2.61265	+	4.52524i	0.0957201	+	0.165792i
$746$	−7.98956	−	13.8383i	−0.292518	−	0.506657i
$747$	−9.13327	+	15.8193i	−0.334169	+	0.578797i
$748$	2.05051			0.0749739
$749$	−31.8210	−	29.5287i	−1.16272	−	1.07896i
$750$	−1.74823			−0.0638364
$751$	−0.263524	+	0.456437i	−0.00961612	+	0.0166556i	−0.870793	−	0.491649i	$-0.836394\pi$
$751$	−0.263524	+	0.456437i	−0.00961612	+	0.0166556i	0.861177	+	0.508305i	$0.169728\pi$
$752$	−0.0927320	−	0.160617i	−0.00338159	−	0.00585708i
$753$	−8.01881	−	13.8890i	−0.292222	−	0.506143i
$754$		0			0
$755$	−0.515038			−0.0187441
$756$	12.7545	−	3.93350i	0.463875	−	0.143060i
$757$	−17.4591			−0.634563			−0.317282	−	0.948331i	$-0.602770\pi$
$757$	−17.4591			−0.634563			−0.317282	+	0.948331i	$0.602770\pi$
$758$	−3.17610	+	5.50117i	−0.115361	+	0.199812i
$759$	−0.529738	−	0.917533i	−0.0192283	−	0.0333043i
$760$	1.34085	+	2.32242i	0.0486376	+	0.0842429i
$761$	18.1656	−	31.4637i	0.658501	−	1.14056i	−0.322503	−	0.946569i	$-0.604524\pi$
$761$	18.1656	−	31.4637i	0.658501	−	1.14056i	0.981004	−	0.193989i	$-0.0621425\pi$
$762$	−8.82507			−0.319698
$763$	15.0883	−	4.65327i	0.546235	−	0.168460i
$764$	−21.1261			−0.764314
$765$	1.18117	−	2.04584i	0.0427052	−	0.0739676i
$766$	0.161044	+	0.278936i	0.00581875	+	0.0100784i
$767$		0			0
$768$	−6.06300	+	10.5014i	−0.218780	+	0.378938i
$769$	−30.7750			−1.10977			−0.554887	−	0.831926i	$-0.687239\pi$
$769$	−30.7750			−1.10977			−0.554887	+	0.831926i	$0.687239\pi$
$770$	−0.206076	−	0.191231i	−0.00742647	−	0.00689148i
$771$	−19.1185			−0.688536
$772$	−9.96070	+	17.2524i	−0.358493	+	0.620929i
$773$	−14.8361	−	25.6968i	−0.533616	−	0.924250i	−0.999229	−	0.0392613i	$-0.987500\pi$
$773$	−14.8361	−	25.6968i	−0.533616	−	0.924250i	0.465613	−	0.884988i	$-0.345834\pi$
$774$	7.21252	+	12.4925i	0.259249	+	0.449032i
$775$	−26.3941	+	45.7159i	−0.948103	+	1.64216i
$776$	4.57149			0.164107
$777$	0.972747	−	4.26086i	0.0348971	−	0.152857i
$778$	9.78606			0.350847
$779$	12.7024	−	22.0012i	0.455111	−	0.788275i
$780$		0			0
$781$	1.57181	+	2.72245i	0.0562437	+	0.0974169i
$782$	−4.93948	+	8.55543i	−0.176636	+	0.305942i
$783$	−2.51313			−0.0898120
$784$	−0.143458	+	0.0977863i	−0.00512351	+	0.00349237i
$785$	−6.57724			−0.234752
$786$	5.05446	−	8.75458i	0.180287	−	0.312265i
$787$	13.7877	+	23.8810i	0.491479	+	0.851267i	0.999952	−	0.00981100i	$-0.00312299\pi$
$787$	13.7877	+	23.8810i	0.491479	+	0.851267i	−0.508473	+	0.861078i	$0.669790\pi$
$788$	−8.69188	−	15.0548i	−0.309635	−	0.536304i
$789$	3.93327	−	6.81262i	0.140028	−	0.242536i
$790$	−2.03684			−0.0724674
$791$	−9.99593	+	43.7845i	−0.355414	+	1.55680i
$792$	3.13772			0.111494
$793$		0			0
$794$	−1.39421	−	2.41484i	−0.0494786	−	0.0856994i
$795$	0.781932	+	1.35435i	0.0277323	+	0.0480337i
$796$	8.44926	−	14.6346i	0.299476	−	0.518708i
$797$	−15.4319			−0.546627			−0.273314	−	0.961925i	$-0.588120\pi$
$797$	−15.4319			−0.546627			−0.273314	+	0.961925i	$0.588120\pi$
$798$	4.57238	+	4.24299i	0.161860	+	0.150200i
$799$	27.3461			0.967437
$800$	13.9152	−	24.1018i	0.491976	−	0.852128i
$801$	10.2394	+	17.7351i	0.361791	+	0.626640i
$802$	−3.54932	−	6.14761i	−0.125331	−	0.217080i
$803$	−0.649552	+	1.12506i	−0.0229222	+	0.0397024i
$804$	−8.73244			−0.307969
$805$	−2.06977	+	0.638321i	−0.0729498	+	0.0224979i
$806$		0			0
$807$	11.1481	−	19.3091i	0.392432	−	0.679713i
$808$	10.3402	+	17.9097i	0.363765	+	0.630060i
$809$	−3.22756	−	5.59030i	−0.113475	−	0.196545i	0.803694	−	0.595043i	$-0.202865\pi$
$809$	−3.22756	−	5.59030i	−0.113475	−	0.196545i	−0.917169	+	0.398498i	$0.869532\pi$
$810$	0.489059	−	0.847074i	0.0171838	−	0.0297632i
$811$	−21.6726			−0.761027			−0.380513	−	0.924775i	$-0.624253\pi$
$811$	−21.6726			−0.761027			−0.380513	+	0.924775i	$0.624253\pi$
$812$	−1.90707	+	0.588144i	−0.0669250	+	0.0206398i
$813$	−19.2019			−0.673438
$814$	0.437257	−	0.757351i	0.0153258	−	0.0265451i
$815$	0.896188	+	1.55224i	0.0313921	+	0.0543727i
$816$	0.0342412	+	0.0593075i	0.00119868	+	0.00207618i
$817$	12.0451	−	20.8627i	0.421405	−	0.729894i
$818$	2.74589			0.0960079
$819$		0			0
$820$	2.33455			0.0815259
$821$	12.3934	−	21.4661i	0.432534	−	0.749171i	−0.564557	−	0.825394i	$-0.690953\pi$
$821$	12.3934	−	21.4661i	0.432534	−	0.749171i	0.997091	+	0.0762232i	$0.0242862\pi$
$822$	−4.50760	−	7.80739i	−0.157221	−	0.272314i
$823$	6.05646	+	10.4901i	0.211115	+	0.365662i	0.952064	−	0.305900i	$-0.0989572\pi$
$823$	6.05646	+	10.4901i	0.211115	+	0.365662i	−0.740949	+	0.671561i	$0.765624\pi$
$824$	−11.5741	+	20.0469i	−0.403201	+	0.698365i
$825$	1.69588			0.0590430
$826$	6.00483	−	26.3026i	0.208935	−	0.915183i
$827$	44.8946			1.56114			0.780569	−	0.625069i	$-0.214929\pi$
$827$	44.8946			1.56114			0.780569	+	0.625069i	$0.214929\pi$
$828$	4.60401	−	7.97438i	0.160000	−	0.277129i
$829$	0.870804	+	1.50828i	0.0302443	+	0.0523846i	0.880751	−	0.473579i	$-0.157038\pi$
$829$	0.870804	+	1.50828i	0.0302443	+	0.0523846i	−0.850507	+	0.525964i	$0.823705\pi$
$830$	−0.876495	−	1.51813i	−0.0304236	−	0.0526952i
$831$	4.30650	−	7.45908i	0.149391	−	0.258752i
$832$		0			0
$833$	−1.91036	−	25.5278i	−0.0661901	−	0.884485i
$834$	−9.49301			−0.328716
$835$	0.274285	−	0.475075i	0.00949201	−	0.0164406i
$836$	−0.997981	−	1.72855i	−0.0345159	−	0.0597833i
$837$	21.9520	+	38.0220i	0.758772	+	1.31423i
$838$	−5.02880	+	8.71014i	−0.173717	+	0.300887i
$839$	−6.96538			−0.240472			−0.120236	−	0.992745i	$-0.538365\pi$
$839$	−6.96538			−0.240472			−0.120236	+	0.992745i	$0.538365\pi$
$840$	−0.334943	+	1.46713i	−0.0115566	+	0.0506207i
$841$	−28.6242			−0.987042
$842$	−9.72125	+	16.8377i	−0.335016	+	0.580265i
$843$	4.52158	+	7.83160i	0.155731	+	0.269735i
$844$	11.5287	+	19.9683i	0.396833	+	0.687336i
$845$		0			0
$846$	15.9391			0.547998
$847$	−20.9305	−	19.4227i	−0.719180	−	0.667372i
$848$	0.193246			0.00663610
$849$	0.879245	−	1.52290i	0.0301756	−	0.0522657i
$850$	−7.90652	−	13.6945i	−0.271191	−	0.469717i
$851$	−3.36879	−	5.83491i	−0.115481	−	0.200018i
$852$	3.20479	−	5.55087i	0.109794	−	0.190170i
$853$	10.5953			0.362774			0.181387	−	0.983412i	$-0.441941\pi$
$853$	10.5953			0.362774			0.181387	+	0.983412i	$0.441941\pi$
$854$	3.53681	−	1.09076i	0.121027	−	0.0373250i
$855$	−2.29950			−0.0786412
$856$	−23.2484	+	40.2675i	−0.794615	+	1.37631i
$857$	9.22951	+	15.9860i	0.315274	+	0.546071i	0.979496	−	0.201465i	$-0.0645702\pi$
$857$	9.22951	+	15.9860i	0.315274	+	0.546071i	−0.664222	+	0.747536i	$0.731237\pi$
$858$		0			0
$859$	19.4883	−	33.7547i	0.664932	−	1.15170i	−0.314371	−	0.949300i	$-0.601794\pi$
$859$	19.4883	−	33.7547i	0.664932	−	1.15170i	0.979304	−	0.202396i	$-0.0648729\pi$
$860$	2.21374			0.0754880
$861$	13.6231	−	4.20140i	0.464276	−	0.143183i
$862$	−18.6963			−0.636799
$863$	−2.08142	+	3.60512i	−0.0708524	+	0.122720i	−0.899275	−	0.437383i	$-0.855905\pi$
$863$	−2.08142	+	3.60512i	−0.0708524	+	0.122720i	0.828423	+	0.560103i	$0.189239\pi$
$864$	−11.5733	−	20.0455i	−0.393731	−	0.681963i
$865$	−1.79743	−	3.11325i	−0.0611146	−	0.105854i
$866$	−0.0196128	+	0.0339704i	−0.000666470	+	0.00115436i
$867$	2.73786			0.0929825
$868$	25.5563	+	23.7153i	0.867438	+	0.804949i
$869$	3.98001			0.135012
$870$	0.0539646	−	0.0934695i	0.00182957	−	0.00316891i
$871$		0			0
$872$	−8.45597	−	14.6462i	−0.286355	−	0.495982i
$873$	−1.95998	+	3.39479i	−0.0663353	+	0.114896i
$874$	9.61618			0.325272
$875$	1.55438	−	6.80856i	0.0525477	−	0.230171i
$876$	2.64877			0.0894937
$877$	−1.78666	+	3.09459i	−0.0603312	+	0.104497i	−0.894613	−	0.446841i	$-0.852549\pi$
$877$	−1.78666	+	3.09459i	−0.0603312	+	0.104497i	0.834282	+	0.551338i	$0.185882\pi$
$878$	1.46021	+	2.52916i	0.0492798	+	0.0853551i
$879$	11.2657	+	19.5128i	0.379984	+	0.658151i
$880$	−0.00150220	+	0.00260188i	−5.06390e−5	+	8.77093e-5i
$881$	−21.4938			−0.724144			−0.362072	−	0.932150i	$-0.617931\pi$
$881$	−21.4938			−0.724144			−0.362072	+	0.932150i	$0.617931\pi$
$882$	−1.11348	−	14.8792i	−0.0374929	−	0.501010i
$883$	7.48321			0.251830			0.125915	−	0.992041i	$-0.459813\pi$
$883$	7.48321			0.251830			0.125915	+	0.992041i	$0.459813\pi$
$884$		0			0
$885$	−1.16662	−	2.02065i	−0.0392156	−	0.0679235i
$886$	−13.3577	−	23.1362i	−0.448761	−	0.777276i
$887$	−14.7435	+	25.5365i	−0.495038	+	0.857431i	−0.999984	−	0.00572046i	$-0.998179\pi$
$887$	−14.7435	+	25.5365i	−0.495038	+	0.857431i	0.504946	+	0.863151i	$0.331512\pi$
$888$	−4.68115			−0.157089
$889$	7.84651	−	34.3695i	0.263163	−	1.15272i
$890$	−1.96529			−0.0658767
$891$	−0.955628	+	1.65520i	−0.0320147	+	0.0554511i
$892$	−2.32864	−	4.03332i	−0.0779686	−	0.135046i
$893$	−13.3094	−	23.0525i	−0.445381	−	0.771422i
$894$	6.50913	−	11.2741i	0.217698	−	0.377064i
$895$	2.29412			0.0766840
$896$	−13.3891	−	12.4246i	−0.447300	−	0.415077i
$897$		0			0
$898$	2.97092	−	5.14579i	0.0991410	−	0.171717i
$899$	−3.28230	−	5.68511i	−0.109471	−	0.189609i
$900$	7.36954	+	12.7644i	0.245651	+	0.425480i
$901$	−14.2468	+	24.6762i	−0.474630	+	0.822083i
$902$	2.85262			0.0949818
$903$	12.9182	−	3.98400i	0.429891	−	0.132579i
$904$	48.1034			1.59990
$905$	−3.11801	+	5.40055i	−0.103646	+	0.179521i
$906$	0.641580	+	1.11125i	0.0213151	+	0.0369188i
$907$	12.3821	+	21.4464i	0.411140	+	0.712115i	0.995015	−	0.0997287i	$-0.0317975\pi$
$907$	12.3821	+	21.4464i	0.411140	+	0.712115i	−0.583875	+	0.811844i	$0.698464\pi$
$908$	5.53966	−	9.59497i	0.183840	−	0.318420i
$909$	−17.7329			−0.588164
$910$		0			0
$911$	−5.42252			−0.179656			−0.0898281	−	0.995957i	$-0.528632\pi$
$911$	−5.42252			−0.179656			−0.0898281	+	0.995957i	$0.528632\pi$
$912$	0.0333304	−	0.0577300i	0.00110368	−	0.00191163i
$913$	1.71268	+	2.96646i	0.0566816	+	0.0981754i
$914$	−14.1099	−	24.4391i	−0.466714	−	0.808373i
$915$	0.160044	−	0.277205i	0.00529091	−	0.00916412i
$916$	−1.33384			−0.0440713
$917$	29.6010	+	27.4686i	0.977512	+	0.907093i
$918$	−13.1517			−0.434072
$919$	−6.93023	+	12.0035i	−0.228607	+	0.395959i	−0.957396	−	0.288780i	$-0.906750\pi$
$919$	−6.93023	+	12.0035i	−0.228607	+	0.395959i	0.728788	+	0.684739i	$0.240084\pi$
$920$	1.15996	+	2.00912i	0.0382429	+	0.0662386i
$921$	5.05206	+	8.75042i	0.166471	+	0.288336i
$922$	10.7027	−	18.5376i	0.352474	−	0.610502i
$923$		0			0
$924$	0.249295	−	1.09197i	0.00820120	−	0.0359232i
$925$	10.7847			0.354599
$926$	10.2795	−	17.8046i	0.337805	−	0.585096i
$927$	−9.92451	−	17.1898i	−0.325964	−	0.564586i
$928$	1.73046	+	2.99724i	0.0568051	+	0.0983893i
$929$	−6.77516	+	11.7349i	−0.222286	+	0.385010i	−0.955502	−	0.294986i	$-0.904685\pi$
$929$	−6.77516	+	11.7349i	−0.222286	+	0.385010i	0.733216	+	0.679996i	$0.238018\pi$
$930$	−1.88551			−0.0618282
$931$	−20.5899	+	14.0348i	−0.674805	+	0.459971i
$932$	17.3590			0.568613
$933$	−7.65382	+	13.2568i	−0.250575	+	0.434008i
$934$	12.2260	+	21.1761i	0.400048	+	0.692904i
$935$	−0.221494	−	0.383640i	−0.00724364	−	0.0125464i
$936$		0			0
$937$	−9.85431			−0.321926			−0.160963	−	0.986960i	$-0.551460\pi$
$937$	−9.85431			−0.321926			−0.160963	+	0.986960i	$0.551460\pi$
$938$	−4.85520	+	21.2669i	−0.158528	+	0.694389i
$939$	−0.895255			−0.0292155
$940$	1.22305	−	2.11838i	0.0398915	−	0.0690941i
$941$	−19.3083	−	33.4430i	−0.629433	−	1.09021i	−0.987666	−	0.156578i	$-0.949954\pi$
$941$	−19.3083	−	33.4430i	−0.629433	−	1.09021i	0.358232	−	0.933632i	$-0.383380\pi$
$942$	8.19324	+	14.1911i	0.266950	+	0.462371i
$943$	10.9888	−	19.0332i	0.357845	−	0.619806i
$944$	−0.288319			−0.00938398
$945$	−2.11367	−	1.96140i	−0.0687577	−	0.0638045i
$946$	2.70501			0.0879473
$947$	17.3511	−	30.0531i	0.563837	−	0.976594i	−0.433320	−	0.901240i	$-0.642658\pi$
$947$	17.3511	−	30.0531i	0.563837	−	0.976594i	0.997157	−	0.0753537i	$-0.0240086\pi$
$948$	−4.05746	−	7.02773i	−0.131780	−	0.228250i
$949$		0			0
$950$	−7.69621	+	13.3302i	−0.249698	+	0.432489i
$951$	−2.87911			−0.0933617
$952$	−26.2011	+	8.08047i	−0.849182	+	0.261889i
$953$	−8.61339			−0.279015			−0.139508	−	0.990221i	$-0.544552\pi$
$953$	−8.61339			−0.279015			−0.139508	+	0.990221i	$0.544552\pi$
$954$	−8.30396	+	14.3829i	−0.268851	+	0.465663i
$955$	2.28203	+	3.95258i	0.0738446	+	0.127903i
$956$	−11.6702	−	20.2133i	−0.377440	−	0.653745i
$957$	−0.105448	+	0.182641i	−0.00340864	+	0.00590394i
$958$	1.81758			0.0587234
$959$	34.4140	−	10.6133i	1.11128	−	0.342722i
$960$	1.00401			0.0324044
$961$	−41.8412	+	72.4712i	−1.34972	+	2.33778i
$962$		0			0
$963$	−19.9350	−	34.5285i	−0.642398	−	1.11267i
$964$	15.4515	−	26.7627i	0.497658	−	0.861969i
$965$	4.30379			0.138544
$966$	3.95555	+	3.67060i	0.127268	+	0.118100i
$967$	−12.9432			−0.416225			−0.208113	−	0.978105i	$-0.566732\pi$
$967$	−12.9432			−0.416225			−0.208113	+	0.978105i	$0.566732\pi$
$968$	−15.2918	+	26.4862i	−0.491497	+	0.851298i
$969$	4.91447	+	8.51212i	0.157876	+	0.273449i
$970$	−0.188094	−	0.325789i	−0.00603934	−	0.0104604i
$971$	−15.8916	+	27.5251i	−0.509987	+	0.883323i	0.489946	+	0.871753i	$0.337016\pi$
$971$	−15.8916	+	27.5251i	−0.509987	+	0.883323i	−0.999933	+	0.0115705i	$0.996317\pi$
$972$	19.0313			0.610428
$973$	8.44039	−	36.9709i	0.270586	−	1.18523i
$974$	5.28043			0.169196
$975$		0			0
$976$	−0.0197766	−	0.0342541i	−0.000633035	−	0.00109645i
$977$	−9.35550	−	16.2042i	−0.299309	−	0.518418i	0.676669	−	0.736287i	$-0.263423\pi$
$977$	−9.35550	−	16.2042i	−0.299309	−	0.518418i	−0.975978	+	0.217869i	$0.930089\pi$
$978$	2.23275	−	3.86724i	0.0713956	−	0.123661i
$979$	3.84021			0.122734
$980$	−2.06296	−	0.993736i	−0.0658990	−	0.0317437i
$981$	14.5016			0.463002
$982$	−0.884006	+	1.53114i	−0.0282098	+	0.0488608i
$983$	−3.16234	−	5.47733i	−0.100863	−	0.174700i	0.811177	−	0.584800i	$-0.198827\pi$
$983$	−3.16234	−	5.47733i	−0.100863	−	0.174700i	−0.912040	+	0.410100i	$0.865494\pi$
$984$	−7.63483	−	13.2239i	−0.243390	−	0.421563i
$985$	−1.87778	+	3.25242i	−0.0598312	+	0.103631i
$986$	1.96647			0.0626252
$987$	3.32467	−	14.5628i	0.105825	−	0.463540i
$988$		0			0
$989$	10.4202	−	18.0483i	0.331343	−	0.573902i
$990$	−0.129101	−	0.223610i	−0.00410311	−	0.00710680i
$991$	−7.79742	−	13.5055i	−0.247693	−	0.429017i	0.715192	−	0.698928i	$-0.246339\pi$
$991$	−7.79742	−	13.5055i	−0.247693	−	0.429017i	−0.962885	+	0.269911i	$0.913006\pi$
$992$	30.2308	−	52.3613i	0.959830	−	1.66247i
$993$	−7.38584			−0.234382
$994$	−11.7367	−	10.8912i	−0.372265	−	0.345448i
$995$	−3.65074			−0.115736
$996$	3.49203	−	6.04838i	0.110649	−	0.191650i
$997$	−15.5517	−	26.9364i	−0.492528	−	0.853083i	0.507435	−	0.861690i	$-0.330594\pi$
$997$	−15.5517	−	26.9364i	−0.492528	−	0.853083i	−0.999963	+	0.00860678i	$0.997260\pi$
$998$	3.29466	+	5.70652i	0.104291	+	0.180637i
$999$	4.48483	−	7.76795i	0.141894	−	0.245767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.l.170.10	yes	48
7.2	even	3		8281.2.a.cu.1.15		24
7.4	even	3	inner	1183.2.e.l.508.10	yes	48
7.5	odd	6		8281.2.a.ct.1.15		24
13.12	even	2		1183.2.e.k.170.15	✓	48
91.12	odd	6		8281.2.a.cw.1.10		24
91.25	even	6		1183.2.e.k.508.15	yes	48
91.51	even	6		8281.2.a.cv.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.15	✓	48	13.12	even	2
1183.2.e.k.508.15	yes	48	91.25	even	6
1183.2.e.l.170.10	yes	48	1.1	even	1	trivial
1183.2.e.l.508.10	yes	48	7.4	even	3	inner
8281.2.a.ct.1.15		24	7.5	odd	6
8281.2.a.cu.1.15		24	7.2	even	3
8281.2.a.cv.1.10		24	91.51	even	6
8281.2.a.cw.1.10		24	91.12	odd	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.438601 + 0.759680i) q^{2} +(0.377512 + 0.653870i) q^{3} +(0.615258 + 1.06566i) q^{4} +(0.132920 - 0.230223i) q^{5} -0.662309 q^{6} +(0.588870 - 2.57939i) q^{7} -2.83382 q^{8} +(1.21497 - 2.10439i) q^{9} +O(q^{10})\)	\(q+(-0.438601 + 0.759680i) q^{2} +(0.377512 + 0.653870i) q^{3} +(0.615258 + 1.06566i) q^{4} +(0.132920 - 0.230223i) q^{5} -0.662309 q^{6} +(0.588870 - 2.57939i) q^{7} -2.83382 q^{8} +(1.21497 - 2.10439i) q^{9} +(0.116597 + 0.201953i) q^{10} +(-0.227833 - 0.394618i) q^{11} +(-0.464534 + 0.804597i) q^{12} +(1.70123 + 1.57867i) q^{14} +0.200715 q^{15} +(0.0124011 - 0.0214794i) q^{16} +(1.82851 + 3.16707i) q^{17} +(1.06577 + 1.84598i) q^{18} +(1.77987 - 3.08283i) q^{19} +0.327119 q^{20} +(1.90889 - 0.588705i) q^{21} +0.399712 q^{22} +(1.53976 - 2.66695i) q^{23} +(-1.06980 - 1.85295i) q^{24} +(2.46466 + 4.26892i) q^{25} +4.09973 q^{27} +(3.11105 - 0.959453i) q^{28} -0.612999 q^{29} +(-0.0880338 + 0.152479i) q^{30} +(5.35450 + 9.27426i) q^{31} +(-2.82294 - 4.88947i) q^{32} +(0.172019 - 0.297946i) q^{33} -3.20795 q^{34} +(-0.515563 - 0.478422i) q^{35} +2.99008 q^{36} +(1.09393 - 1.89474i) q^{37} +(1.56131 + 2.70427i) q^{38} +(-0.376670 + 0.652411i) q^{40} +7.13669 q^{41} +(-0.390014 + 1.70835i) q^{42} +6.76740 q^{43} +(0.280352 - 0.485584i) q^{44} +(-0.322986 - 0.559429i) q^{45} +(1.35068 + 2.33945i) q^{46} +(3.73885 - 6.47589i) q^{47} +0.0187263 q^{48} +(-6.30646 - 3.03784i) q^{49} -4.32402 q^{50} +(-1.38057 + 2.39122i) q^{51} +(3.89574 + 6.74762i) q^{53} +(-1.79815 + 3.11448i) q^{54} -0.121134 q^{55} +(-1.66875 + 7.30951i) q^{56} +2.68769 q^{57} +(0.268862 - 0.465683i) q^{58} +(-5.81235 - 10.0673i) q^{59} +(0.123491 + 0.213893i) q^{60} +(0.797373 - 1.38109i) q^{61} -9.39396 q^{62} +(-4.71257 - 4.37309i) q^{63} +5.00218 q^{64} +(0.150896 + 0.261359i) q^{66} +(4.69957 + 8.13989i) q^{67} +(-2.25001 + 3.89713i) q^{68} +2.32511 q^{69} +(0.589574 - 0.181826i) q^{70} -6.89894 q^{71} +(-3.44300 + 5.96345i) q^{72} +(-1.42550 - 2.46904i) q^{73} +(0.959600 + 1.66208i) q^{74} +(-1.86088 + 3.22314i) q^{75} +4.38032 q^{76} +(-1.15204 + 0.355290i) q^{77} +(-4.36724 + 7.56428i) q^{79} +(-0.00329670 - 0.00571006i) q^{80} +(-2.09721 - 3.63248i) q^{81} +(-3.13016 + 5.42160i) q^{82} -7.51728 q^{83} +(1.80182 + 1.67202i) q^{84} +0.972179 q^{85} +(-2.96819 + 5.14106i) q^{86} +(-0.231414 - 0.400822i) q^{87} +(0.645637 + 1.11828i) q^{88} +(-4.21384 + 7.29859i) q^{89} +0.566649 q^{90} +3.78940 q^{92} +(-4.04277 + 7.00228i) q^{93} +(3.27973 + 5.68067i) q^{94} +(-0.473159 - 0.819536i) q^{95} +(2.13139 - 3.69167i) q^{96} -1.61319 q^{97} +(5.07381 - 3.45849i) q^{98} -1.10724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Introduction

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