LMFDB - Embedded newform 357.2.i.f.256.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(205,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("357.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.i (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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5743021975227.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 2x^{8} + 10x^{7} - 8x^{6} - 12x^{5} - 24x^{4} + 90x^{3} + 54x^{2} - 324x + 243 $ x^10 - 4x^9 + 2x^8 + 10x^7 - 8x^6 - 12x^5 - 24x^4 + 90x^3 + 54x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.3
Root			$1.70973 + 0.277167i$ of defining polynomial
Character	$\chi$	$=$	357.256
Dual form			357.2.i.f.205.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.614831 + 1.06492i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.243965 - 0.422560i) q^{4} +(1.20973 + 2.09531i) q^{5} +1.22966 q^{6} +(-1.25146 - 2.33106i) q^{7} +3.05931 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.614831 + 1.06492i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.243965 - 0.422560i) q^{4} +(1.20973 + 2.09531i) q^{5} +1.22966 q^{6} +(-1.25146 - 2.33106i) q^{7} +3.05931 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.48756 + 2.57653i) q^{10} +(-1.73939 + 3.01271i) q^{11} +(-0.243965 - 0.422560i) q^{12} +5.95098 q^{13} +(1.71296 - 2.76591i) q^{14} +2.41946 q^{15} +(1.39303 + 2.41280i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.614831 - 1.06492i) q^{18} +(-3.59032 - 6.21862i) q^{19} +1.18053 q^{20} +(-2.64449 - 0.0817379i) q^{21} -4.27772 q^{22} +(1.40510 + 2.43371i) q^{23} +(1.52966 - 2.64944i) q^{24} +(-0.426896 + 0.739405i) q^{25} +(3.65885 + 6.33731i) q^{26} -1.00000 q^{27} +(-1.29033 - 0.0398824i) q^{28} -3.43234 q^{29} +(1.48756 + 2.57653i) q^{30} +(-3.13700 + 5.43344i) q^{31} +(1.34636 - 2.33196i) q^{32} +(1.73939 + 3.01271i) q^{33} -1.22966 q^{34} +(3.37038 - 5.44215i) q^{35} -0.487931 q^{36} +(3.78575 + 6.55711i) q^{37} +(4.41488 - 7.64680i) q^{38} +(2.97549 - 5.15370i) q^{39} +(3.70095 + 6.41023i) q^{40} -2.69271 q^{41} +(-1.53887 - 2.86642i) q^{42} -9.25568 q^{43} +(0.848700 + 1.46999i) q^{44} +(1.20973 - 2.09531i) q^{45} +(-1.72780 + 2.99264i) q^{46} +(-4.20515 - 7.28354i) q^{47} +2.78606 q^{48} +(-3.86771 + 5.83445i) q^{49} -1.04987 q^{50} +(0.500000 + 0.866025i) q^{51} +(1.45183 - 2.51465i) q^{52} +(-1.52217 + 2.63647i) q^{53} +(-0.614831 - 1.06492i) q^{54} -8.41676 q^{55} +(-3.82860 - 7.13146i) q^{56} -7.18064 q^{57} +(-2.11031 - 3.65517i) q^{58} +(-0.655564 + 1.13547i) q^{59} +(0.590264 - 1.02237i) q^{60} +(-4.96119 - 8.59303i) q^{61} -7.71489 q^{62} +(-1.39303 + 2.24933i) q^{63} +8.88325 q^{64} +(7.19908 + 12.4692i) q^{65} +(-2.13886 + 3.70461i) q^{66} +(-6.89069 + 11.9350i) q^{67} +(0.243965 + 0.422560i) q^{68} +2.81020 q^{69} +(7.86767 + 0.243180i) q^{70} +1.20552 q^{71} +(-1.52966 - 2.64944i) q^{72} +(6.15427 - 10.6595i) q^{73} +(-4.65519 + 8.06303i) q^{74} +(0.426896 + 0.739405i) q^{75} -3.50366 q^{76} +(9.19958 + 0.284348i) q^{77} +7.31770 q^{78} +(0.160141 + 0.277373i) q^{79} +(-3.37038 + 5.83768i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.65556 - 2.86752i) q^{82} -11.1337 q^{83} +(-0.679703 + 1.09751i) q^{84} -2.41946 q^{85} +(-5.69068 - 9.85655i) q^{86} +(-1.71617 + 2.97250i) q^{87} +(-5.32133 + 9.21682i) q^{88} +(-5.84964 - 10.1319i) q^{89} +2.97512 q^{90} +(-7.44740 - 13.8721i) q^{91} +1.37118 q^{92} +(3.13700 + 5.43344i) q^{93} +(5.17092 - 8.95629i) q^{94} +(8.68664 - 15.0457i) q^{95} +(-1.34636 - 2.33196i) q^{96} +8.62561 q^{97} +(-8.59121 - 0.531595i) q^{98} +3.47878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9} - 13 q^{10} + 11 q^{11} + 8 q^{12} + 14 q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} - 5 q^{17} + 2 q^{18} - 9 q^{19} + 24 q^{20} - 7 q^{21} + 10 q^{22} + 23 q^{23} - 14 q^{25} - 18 q^{26} - 10 q^{27} + 7 q^{28} - 36 q^{29} + 13 q^{30} - 9 q^{31} - 3 q^{32} - 11 q^{33} - 4 q^{34} - 5 q^{35} + 16 q^{36} + 7 q^{39} - 31 q^{40} + 6 q^{41} - 3 q^{42} + 24 q^{43} + 33 q^{44} - q^{45} - 13 q^{46} - 11 q^{47} + 4 q^{48} + 3 q^{49} + 48 q^{50} + 5 q^{51} - 5 q^{52} + 3 q^{53} - 2 q^{54} - 20 q^{55} - 27 q^{56} - 18 q^{57} + 34 q^{58} + 14 q^{59} + 12 q^{60} - 29 q^{61} - 10 q^{62} - 2 q^{63} + 8 q^{65} + 5 q^{66} - 16 q^{67} - 8 q^{68} + 46 q^{69} + 18 q^{70} - 38 q^{71} - 11 q^{73} - 45 q^{74} + 14 q^{75} + 18 q^{76} + 21 q^{77} - 36 q^{78} - q^{79} + 5 q^{80} - 5 q^{81} + 4 q^{82} + 10 q^{83} - 28 q^{84} + 2 q^{85} + 3 q^{86} - 18 q^{87} - 37 q^{88} - 8 q^{89} + 26 q^{90} - 33 q^{91} - 96 q^{92} + 9 q^{93} + 18 q^{94} + 21 q^{95} + 3 q^{96} + 38 q^{97} - 17 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9 - 13 * q^10 + 11 * q^11 + 8 * q^12 + 14 * q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 - 5 * q^17 + 2 * q^18 - 9 * q^19 + 24 * q^20 - 7 * q^21 + 10 * q^22 + 23 * q^23 - 14 * q^25 - 18 * q^26 - 10 * q^27 + 7 * q^28 - 36 * q^29 + 13 * q^30 - 9 * q^31 - 3 * q^32 - 11 * q^33 - 4 * q^34 - 5 * q^35 + 16 * q^36 + 7 * q^39 - 31 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 + 33 * q^44 - q^45 - 13 * q^46 - 11 * q^47 + 4 * q^48 + 3 * q^49 + 48 * q^50 + 5 * q^51 - 5 * q^52 + 3 * q^53 - 2 * q^54 - 20 * q^55 - 27 * q^56 - 18 * q^57 + 34 * q^58 + 14 * q^59 + 12 * q^60 - 29 * q^61 - 10 * q^62 - 2 * q^63 + 8 * q^65 + 5 * q^66 - 16 * q^67 - 8 * q^68 + 46 * q^69 + 18 * q^70 - 38 * q^71 - 11 * q^73 - 45 * q^74 + 14 * q^75 + 18 * q^76 + 21 * q^77 - 36 * q^78 - q^79 + 5 * q^80 - 5 * q^81 + 4 * q^82 + 10 * q^83 - 28 * q^84 + 2 * q^85 + 3 * q^86 - 18 * q^87 - 37 * q^88 - 8 * q^89 + 26 * q^90 - 33 * q^91 - 96 * q^92 + 9 * q^93 + 18 * q^94 + 21 * q^95 + 3 * q^96 + 38 * q^97 - 17 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.614831	+	1.06492i	0.434751	+	0.753011i	0.997275	−	0.0737696i	$-0.0235030\pi$
$2$	0.614831	+	1.06492i	0.434751	+	0.753011i	−0.562524	+	0.826781i	$0.690170\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.243965	−	0.422560i	0.121983	−	0.211280i
$5$	1.20973	+	2.09531i	0.541008	+	0.937053i	0.998846	+	0.0480178i	$0.0152904\pi$
$5$	1.20973	+	2.09531i	0.541008	+	0.937053i	−0.457839	+	0.889035i	$0.651376\pi$
$6$	1.22966			0.502008
$7$	−1.25146	−	2.33106i	−0.473006	−	0.881059i
$7$	−1.25146	−	2.33106i	−0.473006	−	0.881059i
$8$	3.05931			1.08163
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.48756	+	2.57653i	−0.470408	+	0.814770i
$11$	−1.73939	+	3.01271i	−0.524445	+	0.908366i	0.475150	+	0.879905i	$0.342394\pi$
$11$	−1.73939	+	3.01271i	−0.524445	+	0.908366i	−0.999595	+	0.0284607i	$0.990939\pi$
$12$	−0.243965	−	0.422560i	−0.0704267	−	0.121983i
$13$	5.95098			1.65051			0.825253	−	0.564764i	$-0.191033\pi$
$13$	5.95098			1.65051			0.825253	+	0.564764i	$0.191033\pi$
$14$	1.71296	−	2.76591i	0.457807	−	0.739221i
$15$	2.41946			0.624702
$16$	1.39303	+	2.41280i	0.348258	+	0.603200i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$	0.614831	−	1.06492i	0.144917	−	0.251004i
$19$	−3.59032	−	6.21862i	−0.823676	−	1.42665i	−0.902927	−	0.429794i	$-0.858586\pi$
$19$	−3.59032	−	6.21862i	−0.823676	−	1.42665i	0.0792505	−	0.996855i	$-0.474747\pi$
$20$	1.18053			0.263974
$21$	−2.64449	−	0.0817379i	−0.577075	−	0.0178367i
$22$	−4.27772			−0.912013
$23$	1.40510	+	2.43371i	0.292984	+	0.507463i	0.974514	−	0.224327i	$-0.0720185\pi$
$23$	1.40510	+	2.43371i	0.292984	+	0.507463i	−0.681530	+	0.731790i	$0.738685\pi$
$24$	1.52966	−	2.64944i	0.312240	−	0.540816i
$25$	−0.426896	+	0.739405i	−0.0853791	+	0.147881i
$26$	3.65885	+	6.33731i	0.717559	+	1.24285i
$27$	−1.00000			−0.192450
$28$	−1.29033	−	0.0398824i	−0.243849	−	0.00753707i
$29$	−3.43234			−0.637370			−0.318685	−	0.947861i	$-0.603241\pi$
$29$	−3.43234			−0.637370			−0.318685	+	0.947861i	$0.603241\pi$
$30$	1.48756	+	2.57653i	0.271590	+	0.470408i
$31$	−3.13700	+	5.43344i	−0.563421	+	0.975874i	0.433773	+	0.901022i	$0.357182\pi$
$31$	−3.13700	+	5.43344i	−0.563421	+	0.975874i	−0.997195	+	0.0748522i	$0.976152\pi$
$32$	1.34636	−	2.33196i	0.238004	−	0.412236i
$33$	1.73939	+	3.01271i	0.302789	+	0.524445i
$34$	−1.22966			−0.210885
$35$	3.37038	−	5.44215i	0.569699	−	0.919892i
$36$	−0.487931			−0.0813218
$37$	3.78575	+	6.55711i	0.622373	+	1.07798i	0.989043	+	0.147631i	$0.0471648\pi$
$37$	3.78575	+	6.55711i	0.622373	+	1.07798i	−0.366669	+	0.930351i	$0.619502\pi$
$38$	4.41488	−	7.64680i	0.716189	−	1.24048i
$39$	2.97549	−	5.15370i	0.476460	−	0.825253i
$40$	3.70095	+	6.41023i	0.585171	+	1.01355i
$41$	−2.69271			−0.420531			−0.210266	−	0.977644i	$-0.567433\pi$
$41$	−2.69271			−0.420531			−0.210266	+	0.977644i	$0.567433\pi$
$42$	−1.53887	−	2.86642i	−0.237453	−	0.442298i
$43$	−9.25568			−1.41148			−0.705739	−	0.708472i	$-0.749385\pi$
$43$	−9.25568			−1.41148			−0.705739	+	0.708472i	$0.749385\pi$
$44$	0.848700	+	1.46999i	0.127946	+	0.221610i
$45$	1.20973	−	2.09531i	0.180336	−	0.312351i
$46$	−1.72780	+	2.99264i	−0.254750	+	0.441240i
$47$	−4.20515	−	7.28354i	−0.613385	−	1.06241i	−0.990666	−	0.136314i	$-0.956474\pi$
$47$	−4.20515	−	7.28354i	−0.613385	−	1.06241i	0.377281	−	0.926099i	$-0.376859\pi$
$48$	2.78606			0.402133
$49$	−3.86771	+	5.83445i	−0.552530	+	0.833493i
$50$	−1.04987			−0.148475
$51$	0.500000	+	0.866025i	0.0700140	+	0.121268i
$52$	1.45183	−	2.51465i	0.201333	−	0.348719i
$53$	−1.52217	+	2.63647i	−0.209086	+	0.362147i	−0.951427	−	0.307875i	$-0.900382\pi$
$53$	−1.52217	+	2.63647i	−0.209086	+	0.362147i	0.742341	+	0.670022i	$0.233715\pi$
$54$	−0.614831	−	1.06492i	−0.0836679	−	0.144917i
$55$	−8.41676			−1.13492
$56$	−3.82860	−	7.13146i	−0.511618	−	0.952981i
$57$	−7.18064			−0.951099
$58$	−2.11031	−	3.65517i	−0.277097	−	0.479947i
$59$	−0.655564	+	1.13547i	−0.0853471	+	0.147826i	−0.905539	−	0.424263i	$-0.860533\pi$
$59$	−0.655564	+	1.13547i	−0.0853471	+	0.147826i	0.820192	+	0.572088i	$0.193867\pi$
$60$	0.590264	−	1.02237i	0.0762028	−	0.131987i
$61$	−4.96119	−	8.59303i	−0.635215	−	1.10022i	−0.986470	−	0.163945i	$-0.947578\pi$
$61$	−4.96119	−	8.59303i	−0.635215	−	1.10022i	0.351255	−	0.936280i	$-0.385755\pi$
$62$	−7.71489			−0.979792
$63$	−1.39303	+	2.24933i	−0.175505	+	0.283388i
$64$	8.88325			1.11041
$65$	7.19908	+	12.4692i	0.892936	+	1.54661i
$66$	−2.13886	+	3.70461i	−0.263275	+	0.456006i
$67$	−6.89069	+	11.9350i	−0.841831	+	1.45809i	0.0465133	+	0.998918i	$0.485189\pi$
$67$	−6.89069	+	11.9350i	−0.841831	+	1.45809i	−0.888345	+	0.459177i	$0.848144\pi$
$68$	0.243965	+	0.422560i	0.0295851	+	0.0512430i
$69$	2.81020			0.338308
$70$	7.86767	+	0.243180i	0.940366	+	0.0290656i
$71$	1.20552			0.143069			0.0715347	−	0.997438i	$-0.477210\pi$
$71$	1.20552			0.143069			0.0715347	+	0.997438i	$0.477210\pi$
$72$	−1.52966	−	2.64944i	−0.180272	−	0.312240i
$73$	6.15427	−	10.6595i	0.720303	−	1.24760i	−0.240575	−	0.970630i	$-0.577336\pi$
$73$	6.15427	−	10.6595i	0.720303	−	1.24760i	0.960878	−	0.276971i	$-0.0893305\pi$
$74$	−4.65519	+	8.06303i	−0.541155	+	0.937308i
$75$	0.426896	+	0.739405i	0.0492936	+	0.0853791i
$76$	−3.50366			−0.401897
$77$	9.19958	+	0.284348i	1.04839	+	0.0324044i
$78$	7.31770			0.828566
$79$	0.160141	+	0.277373i	0.0180173	+	0.0312069i	0.874893	−	0.484315i	$-0.160931\pi$
$79$	0.160141	+	0.277373i	0.0180173	+	0.0312069i	−0.856876	+	0.515522i	$0.827598\pi$
$80$	−3.37038	+	5.83768i	−0.376820	+	0.652672i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.65556	−	2.86752i	−0.182826	−	0.316665i
$83$	−11.1337			−1.22209			−0.611043	−	0.791598i	$-0.709250\pi$
$83$	−11.1337			−1.22209			−0.611043	+	0.791598i	$0.709250\pi$
$84$	−0.679703	+	1.09751i	−0.0741616	+	0.119749i
$85$	−2.41946			−0.262427
$86$	−5.69068	−	9.85655i	−0.613642	−	1.06286i
$87$	−1.71617	+	2.97250i	−0.183993	+	0.318685i
$88$	−5.32133	+	9.21682i	−0.567256	+	0.982516i
$89$	−5.84964	−	10.1319i	−0.620061	−	1.07398i	−0.989474	−	0.144711i	$-0.953775\pi$
$89$	−5.84964	−	10.1319i	−0.620061	−	1.07398i	0.369413	−	0.929265i	$-0.379559\pi$
$90$	2.97512			0.313605
$91$	−7.44740	−	13.8721i	−0.780699	−	1.45419i
$92$	1.37118			0.142956
$93$	3.13700	+	5.43344i	0.325291	+	0.563421i
$94$	5.17092	−	8.95629i	0.533339	−	0.923771i
$95$	8.68664	−	15.0457i	0.891231	−	1.54366i
$96$	−1.34636	−	2.33196i	−0.137412	−	0.238004i
$97$	8.62561			0.875798			0.437899	−	0.899024i	$-0.355723\pi$
$97$	8.62561			0.875798			0.437899	+	0.899024i	$0.355723\pi$
$98$	−8.59121	−	0.531595i	−0.867843	−	0.0536992i
$99$	3.47878			0.349630
$100$	0.208295	+	0.360778i	0.0208295	+	0.0360778i
$101$	3.86581	−	6.69577i	0.384662	−	0.666254i	−0.607060	−	0.794656i	$-0.707651\pi$
$101$	3.86581	−	6.69577i	0.384662	−	0.666254i	0.991722	+	0.128401i	$0.0409846\pi$
$102$	−0.614831	+	1.06492i	−0.0608774	+	0.105443i
$103$	−3.74620	−	6.48861i	−0.369124	−	0.639341i	0.620305	−	0.784361i	$-0.287009\pi$
$103$	−3.74620	−	6.48861i	−0.369124	−	0.639341i	−0.989429	+	0.145019i	$0.953676\pi$
$104$	18.2059			1.78524
$105$	−3.02785	−	5.63992i	−0.295488	−	0.550399i
$106$	−3.74350			−0.363601
$107$	−0.554167	−	0.959845i	−0.0535733	−	0.0927917i	0.837995	−	0.545678i	$-0.183728\pi$
$107$	−0.554167	−	0.959845i	−0.0535733	−	0.0927917i	−0.891568	+	0.452886i	$0.850394\pi$
$108$	−0.243965	+	0.422560i	−0.0234756	+	0.0406609i
$109$	−3.13835	+	5.43578i	−0.300599	+	0.520653i	−0.976272	−	0.216549i	$-0.930520\pi$
$109$	−3.13835	+	5.43578i	−0.300599	+	0.520653i	0.675673	+	0.737202i	$0.263853\pi$
$110$	−5.17489	−	8.96317i	−0.493406	−	0.854604i
$111$	7.57150			0.718655
$112$	3.88107	−	6.26676i	0.366727	−	0.592153i
$113$	1.61373			0.151807			0.0759033	−	0.997115i	$-0.475816\pi$
$113$	1.61373			0.151807			0.0759033	+	0.997115i	$0.475816\pi$
$114$	−4.41488	−	7.64680i	−0.413492	−	0.716189i
$115$	−3.39959	+	5.88826i	−0.317013	+	0.549083i
$116$	−0.837372	+	1.45037i	−0.0777481	+	0.134664i
$117$	−2.97549	−	5.15370i	−0.275084	−	0.476460i
$118$	−1.61224			−0.148419
$119$	2.64449	+	0.0817379i	0.242420	+	0.00749290i
$120$	7.40189			0.675697
$121$	−0.550939	−	0.954254i	−0.0500854	−	0.0867504i
$122$	6.10059	−	10.5665i	0.552321	−	0.956648i
$123$	−1.34636	+	2.33196i	−0.121397	+	0.210266i
$124$	1.53064	+	2.65114i	0.137455	+	0.238079i
$125$	10.0316			0.897253
$126$	−3.25183	−	0.100510i	−0.289696	−	0.00895414i
$127$	14.7866			1.31210			0.656048	−	0.754719i	$-0.272227\pi$
$127$	14.7866			1.31210			0.656048	+	0.754719i	$0.272227\pi$
$128$	2.76899	+	4.79603i	0.244746	+	0.423913i
$129$	−4.62784	+	8.01566i	−0.407459	+	0.705739i
$130$	−8.85244	+	15.3329i	−0.776410	+	1.34478i
$131$	10.6629	+	18.4688i	0.931626	+	1.61362i	0.780543	+	0.625102i	$0.214943\pi$
$131$	10.6629	+	18.4688i	0.931626	+	1.61362i	0.151083	+	0.988521i	$0.451724\pi$
$132$	1.69740			0.147740
$133$	−10.0029	+	16.1516i	−0.867358	+	1.40052i
$134$	−16.9464			−1.46395
$135$	−1.20973	−	2.09531i	−0.104117	−	0.180336i
$136$	−1.52966	+	2.64944i	−0.131167	+	0.227188i
$137$	−1.00478	+	1.74033i	−0.0858439	+	0.148686i	−0.905751	−	0.423811i	$-0.860692\pi$
$137$	−1.00478	+	1.74033i	−0.0858439	+	0.148686i	0.819907	+	0.572497i	$0.194025\pi$
$138$	1.72780	+	2.99264i	0.147080	+	0.254750i
$139$	8.53092			0.723583			0.361792	−	0.932259i	$-0.382165\pi$
$139$	8.53092			0.723583			0.361792	+	0.932259i	$0.382165\pi$
$140$	−1.47738	−	2.75189i	−0.124862	−	0.232577i
$141$	−8.41031			−0.708276
$142$	0.741193	+	1.28378i	0.0621996	+	0.107733i
$143$	−10.3511	+	17.9286i	−0.865599	+	1.49926i
$144$	1.39303	−	2.41280i	0.116086	−	0.201067i
$145$	−4.15221	−	7.19184i	−0.344822	−	0.597249i
$146$	15.1354			1.25261
$147$	3.11893	+	6.26676i	0.257245	+	0.516874i
$148$	3.69437			0.303675
$149$	5.38306	+	9.32374i	0.440998	+	0.763831i	0.997764	−	0.0668388i	$-0.0212913\pi$
$149$	5.38306	+	9.32374i	0.440998	+	0.763831i	−0.556766	+	0.830669i	$0.687958\pi$
$150$	−0.524937	+	0.909218i	−0.0428610	+	0.0742373i
$151$	1.42882	−	2.47478i	0.116275	−	0.201395i	−0.802013	−	0.597306i	$-0.796238\pi$
$151$	1.42882	−	2.47478i	0.116275	−	0.201395i	0.918289	+	0.395911i	$0.129571\pi$
$152$	−10.9839	−	19.0247i	−0.890914	−	1.54311i
$153$	1.00000			0.0808452
$154$	5.35338	+	9.97163i	0.431388	+	0.803537i
$155$	−15.1797			−1.21926
$156$	−1.45183	−	2.51465i	−0.116240	−	0.201333i
$157$	−2.45011	+	4.24372i	−0.195540	+	0.338686i	−0.947077	−	0.321005i	$-0.895979\pi$
$157$	−2.45011	+	4.24372i	−0.195540	+	0.338686i	0.751537	+	0.659691i	$0.229313\pi$
$158$	−0.196920	+	0.341075i	−0.0156661	+	0.0271345i
$159$	1.52217	+	2.63647i	0.120716	+	0.209086i
$160$	6.51491			0.515049
$161$	3.91470	−	6.32106i	0.308521	−	0.498169i
$162$	−1.22966			−0.0966114
$163$	−4.15235	−	7.19208i	−0.325237	−	0.563327i	0.656323	−	0.754480i	$-0.272111\pi$
$163$	−4.15235	−	7.19208i	−0.325237	−	0.563327i	−0.981560	+	0.191153i	$0.938777\pi$
$164$	−0.656928	+	1.13783i	−0.0512975	+	0.0888499i
$165$	−4.20838	+	7.28913i	−0.327622	+	0.567458i
$166$	−6.84536	−	11.8565i	−0.531303	−	0.920244i
$167$	−10.2826			−0.795694			−0.397847	−	0.917452i	$-0.630243\pi$
$167$	−10.2826			−0.795694			−0.397847	+	0.917452i	$0.630243\pi$
$168$	−8.09032	−	0.250062i	−0.624182	−	0.0192927i
$169$	22.4142			1.72417
$170$	−1.48756	−	2.57653i	−0.114091	−	0.197611i
$171$	−3.59032	+	6.21862i	−0.274559	+	0.475550i
$172$	−2.25807	+	3.91108i	−0.172176	+	0.298217i
$173$	10.3904	+	17.9968i	0.789971	+	1.36827i	0.925984	+	0.377563i	$0.123238\pi$
$173$	10.3904	+	17.9968i	0.789971	+	1.36827i	−0.136013	+	0.990707i	$0.543429\pi$
$174$	−4.22062			−0.319964
$175$	2.25784	+	0.0697871i	0.170677	+	0.00527541i
$176$	−9.69209			−0.730568
$177$	0.655564	+	1.13547i	0.0492752	+	0.0853471i
$178$	7.19308	−	12.4588i	0.539144	−	0.933825i
$179$	4.50806	−	7.80819i	0.336948	−	0.583612i	−0.646909	−	0.762567i	$-0.723939\pi$
$179$	4.50806	−	7.80819i	0.336948	−	0.583612i	0.983857	+	0.178956i	$0.0572719\pi$
$180$	−0.590264	−	1.02237i	−0.0439957	−	0.0762028i
$181$	−0.663030			−0.0492826			−0.0246413	−	0.999696i	$-0.507844\pi$
$181$	−0.663030			−0.0492826			−0.0246413	+	0.999696i	$0.507844\pi$
$182$	10.1938	−	16.4599i	0.755613	−	1.22009i
$183$	−9.92238			−0.733483
$184$	4.29864	+	7.44547i	0.316900	+	0.548887i
$185$	−9.15947	+	15.8647i	−0.673418	+	1.16639i
$186$	−3.85745	+	6.68129i	−0.282842	+	0.489896i
$187$	−1.73939	−	3.01271i	−0.127197	−	0.220311i
$188$	−4.10365			−0.299289
$189$	1.25146	+	2.33106i	0.0910301	+	0.169560i
$190$	21.3633			1.54985
$191$	11.9237	+	20.6524i	0.862768	+	1.49436i	0.869247	+	0.494378i	$0.164604\pi$
$191$	11.9237	+	20.6524i	0.862768	+	1.49436i	−0.00647909	+	0.999979i	$0.502062\pi$
$192$	4.44163	−	7.69312i	0.320547	−	0.555203i
$193$	−5.67228	+	9.82468i	−0.408300	+	0.707196i	−0.994699	−	0.102826i	$-0.967212\pi$
$193$	−5.67228	+	9.82468i	−0.408300	+	0.707196i	0.586400	+	0.810022i	$0.300545\pi$
$194$	5.30329	+	9.18558i	0.380754	+	0.659486i
$195$	14.3982			1.03107
$196$	1.52182	+	3.05774i	0.108701	+	0.218410i
$197$	−17.4455			−1.24294			−0.621470	−	0.783438i	$-0.713464\pi$
$197$	−17.4455			−1.24294			−0.621470	+	0.783438i	$0.713464\pi$
$198$	2.13886	+	3.70461i	0.152002	+	0.263275i
$199$	5.82748	−	10.0935i	0.413099	−	0.715508i	−0.582128	−	0.813097i	$-0.697780\pi$
$199$	5.82748	−	10.0935i	0.413099	−	0.715508i	0.995227	+	0.0975890i	$0.0311131\pi$
$200$	−1.30601	+	2.26207i	−0.0923487	+	0.159953i
$201$	6.89069	+	11.9350i	0.486032	+	0.841831i
$202$	9.50727			0.668930
$203$	4.29543	+	8.00101i	0.301480	+	0.561561i
$204$	0.487931			0.0341620
$205$	−3.25746	−	5.64208i	−0.227511	−	0.394060i
$206$	4.60656	−	7.97880i	0.320954	−	0.555909i
$207$	1.40510	−	2.43371i	0.0976613	−	0.169154i
$208$	8.28990	+	14.3585i	0.574801	+	0.995585i
$209$	24.9798			1.72789
$210$	4.14444	−	6.69201i	0.285993	−	0.461793i
$211$	−0.420088			−0.0289200			−0.0144600	−	0.999895i	$-0.504603\pi$
$211$	−0.420088			−0.0289200			−0.0144600	+	0.999895i	$0.504603\pi$
$212$	0.742711	+	1.28641i	0.0510096	+	0.0883512i
$213$	0.602762	−	1.04401i	0.0413006	−	0.0715347i
$214$	0.681438	−	1.18029i	0.0465821	−	0.0806826i
$215$	−11.1969	−	19.3936i	−0.763621	−	1.32263i
$216$	−3.05931			−0.208160
$217$	16.5915	+	0.512823i	1.12630	+	0.0348127i
$218$	−7.71821			−0.522743
$219$	−6.15427	−	10.6595i	−0.415867	−	0.720303i
$220$	−2.05340	+	3.55659i	−0.138440	+	0.239785i
$221$	−2.97549	+	5.15370i	−0.200153	+	0.346675i
$222$	4.65519	+	8.06303i	0.312436	+	0.541155i
$223$	17.3626			1.16269			0.581344	−	0.813658i	$-0.302527\pi$
$223$	17.3626			1.16269			0.581344	+	0.813658i	$0.302527\pi$
$224$	−7.12085	−	0.220097i	−0.475782	−	0.0147058i
$225$	0.853791			0.0569194
$226$	0.992169	+	1.71849i	0.0659981	+	0.114312i
$227$	−1.80891	+	3.13312i	−0.120061	+	0.207953i	−0.919792	−	0.392407i	$-0.871643\pi$
$227$	−1.80891	+	3.13312i	−0.120061	+	0.207953i	0.799730	+	0.600360i	$0.204976\pi$
$228$	−1.75183	+	3.03425i	−0.116018	+	0.200948i
$229$	−6.96285	−	12.0600i	−0.460118	−	0.796948i	0.538848	−	0.842403i	$-0.318860\pi$
$229$	−6.96285	−	12.0600i	−0.460118	−	0.796948i	−0.998966	+	0.0454549i	$0.985526\pi$
$230$	−8.36069			−0.551287
$231$	4.84604	−	7.82490i	0.318846	−	0.514840i
$232$	−10.5006			−0.689399
$233$	−11.5325	−	19.9749i	−0.755520	−	1.30860i	−0.945115	−	0.326737i	$-0.894051\pi$
$233$	−11.5325	−	19.9749i	−0.755520	−	1.30860i	0.189595	−	0.981862i	$-0.439283\pi$
$234$	3.65885	−	6.33731i	0.239186	−	0.414283i
$235$	10.1742	−	17.6222i	0.663692	−	1.14955i
$236$	0.319870	+	0.554030i	0.0208217	+	0.0360643i
$237$	0.320283			0.0208046
$238$	1.53887	+	2.86642i	0.0997501	+	0.185802i
$239$	25.0229			1.61860			0.809299	−	0.587397i	$-0.199847\pi$
$239$	25.0229			1.61860			0.809299	+	0.587397i	$0.199847\pi$
$240$	3.37038	+	5.83768i	0.217557	+	0.376820i
$241$	8.42784	−	14.5974i	0.542885	−	0.940304i	−0.455852	−	0.890056i	$-0.650665\pi$
$241$	8.42784	−	14.5974i	0.542885	−	0.940304i	0.998737	−	0.0502483i	$-0.0160013\pi$
$242$	0.677469	−	1.17341i	0.0435494	−	0.0754297i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.84143			−0.309941
$245$	−16.9039	−	1.04596i	−1.07995	−	0.0668237i
$246$	−3.31113			−0.211110
$247$	−21.3659	−	37.0069i	−1.35948	−	2.35469i
$248$	−9.59706	+	16.6226i	−0.609414	+	1.05554i
$249$	−5.56686	+	9.64209i	−0.352786	+	0.611043i
$250$	6.16773	+	10.6828i	0.390082	+	0.675641i
$251$	14.0767			0.888511			0.444256	−	0.895900i	$-0.353468\pi$
$251$	14.0767			0.888511			0.444256	+	0.895900i	$0.353468\pi$
$252$	0.610624	+	1.13740i	0.0384657	+	0.0716493i
$253$	−9.77606			−0.614616
$254$	9.09125	+	15.7465i	0.570436	+	0.988023i
$255$	−1.20973	+	2.09531i	−0.0757563	+	0.131214i
$256$	5.47833	−	9.48875i	0.342396	−	0.593047i
$257$	2.53152	+	4.38472i	0.157912	+	0.273511i	0.934116	−	0.356971i	$-0.116190\pi$
$257$	2.53152	+	4.38472i	0.157912	+	0.273511i	−0.776204	+	0.630482i	$0.782857\pi$
$258$	−11.3814			−0.708573
$259$	10.5473	−	17.0308i	0.655379	−	1.05824i
$260$	7.02531			0.435691
$261$	1.71617	+	2.97250i	0.106228	+	0.183993i
$262$	−13.1118	+	22.7103i	−0.810051	+	1.40305i
$263$	12.6438	−	21.8996i	0.779648	−	1.35039i	−0.152497	−	0.988304i	$-0.548731\pi$
$263$	12.6438	−	21.8996i	0.779648	−	1.35039i	0.932145	−	0.362086i	$-0.117935\pi$
$264$	5.32133	+	9.21682i	0.327505	+	0.567256i
$265$	−7.36564			−0.452468
$266$	−23.3502	−	0.721727i	−1.43169	−	0.0442519i
$267$	−11.6993			−0.715984
$268$	3.36218	+	5.82346i	0.205378	+	0.355725i
$269$	−14.2206	+	24.6307i	−0.867043	+	1.50176i	−0.00203901	+	0.999998i	$0.500649\pi$
$269$	−14.2206	+	24.6307i	−0.867043	+	1.50176i	−0.865004	+	0.501765i	$0.832684\pi$
$270$	1.48756	−	2.57653i	0.0905300	−	0.156803i
$271$	−0.253873	−	0.439721i	−0.0154217	−	0.0267112i	0.858212	−	0.513296i	$-0.171576\pi$
$271$	−0.253873	−	0.439721i	−0.0154217	−	0.0267112i	−0.873633	+	0.486585i	$0.838242\pi$
$272$	−2.78606			−0.168930
$273$	−15.7373	−	0.486421i	−0.952465	−	0.0294395i
$274$	−2.47107			−0.149283
$275$	−1.48507	−	2.57222i	−0.0895533	−	0.155111i
$276$	0.685592	−	1.18748i	0.0412678	−	0.0714779i
$277$	5.57603	−	9.65797i	0.335031	−	0.580291i	−0.648459	−	0.761249i	$-0.724586\pi$
$277$	5.57603	−	9.65797i	0.335031	−	0.580291i	0.983491	+	0.180958i	$0.0579197\pi$
$278$	5.24508	+	9.08474i	0.314579	+	0.544867i
$279$	6.27399			0.375614
$280$	10.3111	−	16.6493i	0.616204	−	0.994984i
$281$	9.49919			0.566674			0.283337	−	0.959020i	$-0.408558\pi$
$281$	9.49919			0.566674			0.283337	+	0.959020i	$0.408558\pi$
$282$	−5.17092	−	8.95629i	−0.307924	−	0.533339i
$283$	−2.48470	+	4.30363i	−0.147700	+	0.255824i	−0.930377	−	0.366604i	$-0.880520\pi$
$283$	−2.48470	+	4.30363i	−0.147700	+	0.255824i	0.782677	+	0.622428i	$0.213854\pi$
$284$	0.294106	−	0.509406i	0.0174520	−	0.0302277i
$285$	−8.68664	−	15.0457i	−0.514552	−	0.891231i
$286$	−25.4566			−1.50528
$287$	3.36981	+	6.27688i	0.198914	+	0.370513i
$288$	−2.69271			−0.158670
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	5.10581	−	8.84353i	0.299824	−	0.519310i
$291$	4.31281	−	7.47000i	0.252821	−	0.437899i
$292$	−3.00286	−	5.20110i	−0.175729	−	0.304371i
$293$	−9.41812			−0.550213			−0.275106	−	0.961414i	$-0.588713\pi$
$293$	−9.41812			−0.550213			−0.275106	+	0.961414i	$0.588713\pi$
$294$	−4.75598	+	7.17440i	−0.277374	+	0.418420i
$295$	−3.17222			−0.184694
$296$	11.5818	+	20.0603i	0.673178	+	1.16598i
$297$	1.73939	−	3.01271i	0.100930	−	0.174815i
$298$	−6.61935	+	11.4651i	−0.383449	+	0.664153i
$299$	8.36173	+	14.4829i	0.483571	+	0.837570i
$300$	0.416591			0.0240519
$301$	11.5831	+	21.5756i	0.667638	+	1.24360i
$302$	3.51392			0.202203
$303$	−3.86581	−	6.69577i	−0.222085	−	0.384662i
$304$	10.0029	−	17.3255i	0.573703	−	0.993683i
$305$	12.0034	−	20.7905i	0.687313	−	1.19046i
$306$	0.614831	+	1.06492i	0.0351476	+	0.0608774i
$307$	23.4105			1.33611			0.668055	−	0.744112i	$-0.267127\pi$
$307$	23.4105			1.33611			0.668055	+	0.744112i	$0.267127\pi$
$308$	2.36453	−	3.81801i	0.134732	−	0.217551i
$309$	−7.49240			−0.426228
$310$	−9.33294	−	16.1651i	−0.530075	−	0.918118i
$311$	−7.06635	+	12.2393i	−0.400696	+	0.694026i	−0.993810	−	0.111093i	$-0.964565\pi$
$311$	−7.06635	+	12.2393i	−0.400696	+	0.694026i	0.593114	+	0.805118i	$0.297898\pi$
$312$	9.10296	−	15.7668i	0.515354	−	0.892619i
$313$	−1.27634	−	2.21068i	−0.0721428	−	0.124955i	0.827697	−	0.561175i	$-0.189650\pi$
$313$	−1.27634	−	2.21068i	−0.0721428	−	0.124955i	−0.899840	+	0.436220i	$0.856317\pi$
$314$	−6.02562			−0.340045
$315$	−6.39824	−	0.197762i	−0.360500	−	0.0111426i
$316$	0.156276			0.00879120
$317$	−14.9745	−	25.9366i	−0.841051	−	1.45674i	−0.889007	−	0.457894i	$-0.848604\pi$
$317$	−14.9745	−	25.9366i	−0.841051	−	1.45674i	0.0479552	−	0.998849i	$-0.484730\pi$
$318$	−1.87175	+	3.24197i	−0.104962	+	0.181800i
$319$	5.97017	−	10.3406i	0.334266	−	0.578965i
$320$	10.7463	+	18.6132i	0.600739	+	1.04051i
$321$	−1.10833			−0.0618611
$322$	9.13829	+	0.282453i	0.509257	+	0.0157405i
$323$	7.18064			0.399542
$324$	0.243965	+	0.422560i	0.0135536	+	0.0234756i
$325$	−2.54045	+	4.40018i	−0.140919	+	0.244078i
$326$	5.10599	−	8.84383i	0.282795	−	0.489815i
$327$	3.13835	+	5.43578i	0.173551	+	0.300599i
$328$	−8.23786			−0.454859
$329$	−11.7158	+	18.9175i	−0.645914	+	1.04296i
$330$	−10.3498			−0.569736
$331$	0.0724924	+	0.125561i	0.00398454	+	0.00690143i	0.868011	−	0.496545i	$-0.165398\pi$
$331$	0.0724924	+	0.125561i	0.00398454	+	0.00690143i	−0.864026	+	0.503447i	$0.832065\pi$
$332$	−2.71624	+	4.70467i	−0.149073	+	0.258202i
$333$	3.78575	−	6.55711i	0.207458	−	0.359327i
$334$	−6.32208	−	10.9502i	−0.345929	−	0.599167i
$335$	−33.3435			−1.82175
$336$	−3.48664	−	6.49449i	−0.190212	−	0.354303i
$337$	−3.92618			−0.213873			−0.106936	−	0.994266i	$-0.534104\pi$
$337$	−3.92618			−0.213873			−0.106936	+	0.994266i	$0.534104\pi$
$338$	13.7809	+	23.8693i	0.749584	+	1.29832i
$339$	0.806863	−	1.39753i	0.0438228	−	0.0759033i
$340$	−0.590264	+	1.02237i	−0.0320116	+	0.0554457i
$341$	−10.9129	−	18.9017i	−0.590967	−	1.02358i
$342$	−8.82977			−0.477459
$343$	18.4407	+	1.71431i	0.995707	+	0.0925641i
$344$	−28.3160			−1.52670
$345$	3.39959	+	5.88826i	0.183028	+	0.317013i
$346$	−12.7767	+	22.1300i	−0.686882	+	1.18971i
$347$	8.80544	−	15.2515i	0.472701	−	0.818742i	−0.526811	−	0.849982i	$-0.676612\pi$
$347$	8.80544	−	15.2515i	0.472701	−	0.818742i	0.999512	+	0.0312405i	$0.00994579\pi$
$348$	0.837372	+	1.45037i	0.0448879	+	0.0777481i
$349$	14.3609			0.768722			0.384361	−	0.923183i	$-0.374422\pi$
$349$	14.3609			0.768722			0.384361	+	0.923183i	$0.374422\pi$
$350$	1.31387	+	2.44732i	0.0702295	+	0.130815i
$351$	−5.95098			−0.317640
$352$	4.68367	+	8.11236i	0.249641	+	0.432390i
$353$	−7.56531	+	13.1035i	−0.402661	+	0.697429i	−0.994046	−	0.108960i	$-0.965248\pi$
$353$	−7.56531	+	13.1035i	−0.402661	+	0.697429i	0.591385	+	0.806389i	$0.298581\pi$
$354$	−0.806122	+	1.39624i	−0.0428449	+	0.0742095i
$355$	1.45836	+	2.52595i	0.0774016	+	0.134064i
$356$	−5.70844			−0.302547
$357$	1.39303	−	2.24933i	0.0737270	−	0.119047i
$358$	11.0868			0.585955
$359$	−14.3131	−	24.7910i	−0.755415	−	1.30842i	−0.945168	−	0.326585i	$-0.894102\pi$
$359$	−14.3131	−	24.7910i	−0.755415	−	1.30842i	0.189753	−	0.981832i	$-0.439231\pi$
$360$	3.70095	−	6.41023i	0.195057	−	0.337849i
$361$	−16.2808	+	28.1992i	−0.856885	+	1.48417i
$362$	−0.407652	−	0.706073i	−0.0214257	−	0.0371104i
$363$	−1.10188			−0.0578336
$364$	−7.67871	−	0.237340i	−0.402474	−	0.0124400i
$365$	29.7800			1.55876
$366$	−6.10059	−	10.5665i	−0.318883	−	0.552321i
$367$	14.5151	−	25.1409i	0.757684	−	1.31235i	−0.186345	−	0.982484i	$-0.559664\pi$
$367$	14.5151	−	25.1409i	0.757684	−	1.31235i	0.944029	−	0.329862i	$-0.107002\pi$
$368$	−3.91470	+	6.78046i	−0.204068	+	0.353456i
$369$	1.34636	+	2.33196i	0.0700885	+	0.121397i
$370$	−22.5261			−1.17108
$371$	8.05070	+	0.248837i	0.417971	+	0.0129190i
$372$	3.06127			0.158720
$373$	−3.53968	−	6.13091i	−0.183278	−	0.317446i	0.759717	−	0.650254i	$-0.225337\pi$
$373$	−3.53968	−	6.13091i	−0.183278	−	0.317446i	−0.942995	+	0.332807i	$0.892004\pi$
$374$	2.13886	−	3.70461i	0.110598	−	0.191561i
$375$	5.01580	−	8.68761i	0.259015	−	0.448626i
$376$	−12.8649	−	22.2826i	−0.663456	−	1.14914i
$377$	−20.4258			−1.05198
$378$	−1.71296	+	2.76591i	−0.0881051	+	0.142263i
$379$	−2.83980			−0.145871			−0.0729355	−	0.997337i	$-0.523237\pi$
$379$	−2.83980			−0.145871			−0.0729355	+	0.997337i	$0.523237\pi$
$380$	−4.23848	−	7.34126i	−0.217429	−	0.376599i
$381$	7.39329	−	12.8056i	0.378770	−	0.656048i
$382$	−14.6621	+	25.3955i	−0.750179	+	1.29935i
$383$	−12.4287	−	21.5271i	−0.635077	−	1.09999i	−0.986499	−	0.163769i	$-0.947635\pi$
$383$	−12.4287	−	21.5271i	−0.635077	−	1.09999i	0.351422	−	0.936217i	$-0.385698\pi$
$384$	5.53798			0.282609
$385$	10.5332	+	19.6200i	0.536822	+	0.999928i
$386$	−13.9500			−0.710036
$387$	4.62784	+	8.01566i	0.235246	+	0.407459i
$388$	2.10435	−	3.64484i	0.106832	−	0.185039i
$389$	−6.32118	+	10.9486i	−0.320496	+	0.555116i	−0.980591	−	0.196067i	$-0.937183\pi$
$389$	−6.32118	+	10.9486i	−0.320496	+	0.555116i	0.660094	+	0.751183i	$0.270516\pi$
$390$	8.85244	+	15.3329i	0.448261	+	0.776410i
$391$	−2.81020			−0.142118
$392$	−11.8325	+	17.8494i	−0.597634	+	0.901532i
$393$	21.3259			1.07575
$394$	−10.7260	−	18.5780i	−0.540369	−	0.935947i
$395$	−0.387456	+	0.671093i	−0.0194950	+	0.0337663i
$396$	0.848700	−	1.46999i	0.0426488	−	0.0738699i
$397$	−12.6621	−	21.9314i	−0.635491	−	1.10070i	−0.986411	−	0.164298i	$-0.947464\pi$
$397$	−12.6621	−	21.9314i	−0.635491	−	1.10070i	0.350919	−	0.936406i	$-0.385869\pi$
$398$	14.3317			0.718381
$399$	8.98627	+	16.7385i	0.449876	+	0.837975i
$400$	−2.37872			−0.118936
$401$	−0.0257489	−	0.0445985i	−0.00128584	−	0.00222714i	0.865382	−	0.501113i	$-0.167076\pi$
$401$	−0.0257489	−	0.0445985i	−0.00128584	−	0.00222714i	−0.866668	+	0.498886i	$0.833743\pi$
$402$	−8.47322	+	14.6760i	−0.422606	+	0.731975i
$403$	−18.6682	+	32.3343i	−0.929930	+	1.61069i
$404$	−1.88625	−	3.26707i	−0.0938442	−	0.162543i
$405$	−2.41946			−0.120224
$406$	−5.87946	+	9.49355i	−0.291793	+	0.471157i
$407$	−26.3395			−1.30560
$408$	1.52966	+	2.64944i	0.0757293	+	0.131167i
$409$	−9.43476	+	16.3415i	−0.466519	+	0.808035i	−0.999269	−	0.0382383i	$-0.987825\pi$
$409$	−9.43476	+	16.3415i	−0.466519	+	0.808035i	0.532750	+	0.846273i	$0.321159\pi$
$410$	4.00557	−	6.93785i	0.197821	−	0.342636i
$411$	1.00478	+	1.74033i	0.0495620	+	0.0858439i
$412$	−3.65577			−0.180107
$413$	3.46726	+	0.107169i	0.170613	+	0.00527343i
$414$	3.45560			0.169833
$415$	−13.4688	−	23.3287i	−0.661158	−	1.14516i
$416$	8.01214	−	13.8774i	0.392828	−	0.680397i
$417$	4.26546	−	7.38800i	0.208881	−	0.361792i
$418$	15.3584	+	26.6015i	0.751203	+	1.30112i
$419$	20.3934			0.996281			0.498140	−	0.867096i	$-0.334016\pi$
$419$	20.3934			0.996281			0.498140	+	0.867096i	$0.334016\pi$
$420$	−3.12190	−	0.0964940i	−0.152333	−	0.00470842i
$421$	1.70878			0.0832808			0.0416404	−	0.999133i	$-0.486742\pi$
$421$	1.70878			0.0832808			0.0416404	+	0.999133i	$0.486742\pi$
$422$	−0.258283	−	0.447359i	−0.0125730	−	0.0217771i
$423$	−4.20515	+	7.28354i	−0.204462	+	0.354138i
$424$	−4.65678	+	8.06578i	−0.226153	+	0.391709i
$425$	−0.426896	−	0.739405i	−0.0207075	−	0.0358664i
$426$	1.48239			0.0718219
$427$	−13.8222	+	22.3186i	−0.668902	+	1.08008i
$428$	−0.540790			−0.0261401
$429$	10.3511	+	17.9286i	0.499754	+	0.865599i
$430$	13.7684	−	23.8475i	0.663970	−	1.15003i
$431$	−18.0203	+	31.2120i	−0.868006	+	1.50343i	−0.00397534	+	0.999992i	$0.501265\pi$
$431$	−18.0203	+	31.2120i	−0.868006	+	1.50343i	−0.864031	+	0.503439i	$0.832068\pi$
$432$	−1.39303	−	2.41280i	−0.0670222	−	0.116086i
$433$	−23.2422			−1.11695			−0.558474	−	0.829522i	$-0.688613\pi$
$433$	−23.2422			−1.11695			−0.558474	+	0.829522i	$0.688613\pi$
$434$	9.65486	+	17.9839i	0.463448	+	0.863255i
$435$	−8.30442			−0.398166
$436$	1.53130	+	2.65228i	0.0733357	+	0.127021i
$437$	10.0895	−	17.4756i	0.482648	−	0.835970i
$438$	7.56768	−	13.1076i	0.361598	−	0.626305i
$439$	−11.6986	−	20.2625i	−0.558342	−	0.967076i	−0.997635	−	0.0687325i	$-0.978105\pi$
$439$	−11.6986	−	20.2625i	−0.558342	−	0.967076i	0.439294	−	0.898344i	$-0.355229\pi$
$440$	−25.7495			−1.22756
$441$	6.98664	+	0.432310i	0.332697	+	0.0205862i
$442$	−7.31770			−0.348067
$443$	2.92828	+	5.07193i	0.139127	+	0.240974i	0.927166	−	0.374650i	$-0.122237\pi$
$443$	2.92828	+	5.07193i	0.139127	+	0.240974i	−0.788040	+	0.615625i	$0.788904\pi$
$444$	1.84718	−	3.19941i	0.0876634	−	0.151837i
$445$	14.1530	−	24.5137i	0.670916	−	1.16206i
$446$	10.6751	+	18.4898i	0.505480	+	0.875518i
$447$	10.7661			0.509220
$448$	−11.1170	−	20.7074i	−0.525229	−	0.978334i
$449$	9.53965			0.450204			0.225102	−	0.974335i	$-0.427728\pi$
$449$	9.53965			0.450204			0.225102	+	0.974335i	$0.427728\pi$
$450$	0.524937	+	0.909218i	0.0247458	+	0.0428610i
$451$	4.68367	−	8.11236i	0.220545	−	0.381996i
$452$	0.393693	−	0.681897i	0.0185178	−	0.0320737i
$453$	−1.42882	−	2.47478i	−0.0671316	−	0.116275i
$454$	−4.44869			−0.208788
$455$	20.0571	−	32.3862i	0.940291	−	1.51829i
$456$	−21.9678			−1.02874
$457$	18.3090	+	31.7121i	0.856458	+	1.48343i	0.875286	+	0.483606i	$0.160673\pi$
$457$	18.3090	+	31.7121i	0.856458	+	1.48343i	−0.0188274	+	0.999823i	$0.505993\pi$
$458$	8.56196	−	14.8297i	0.400074	−	0.692948i
$459$	0.500000	−	0.866025i	0.0233380	−	0.0404226i
$460$	1.65876	+	2.87306i	0.0773402	+	0.133957i
$461$	20.5184			0.955638			0.477819	−	0.878458i	$-0.341427\pi$
$461$	20.5184			0.955638			0.477819	+	0.878458i	$0.341427\pi$
$462$	11.3124	+	0.349652i	0.526299	+	0.0162673i
$463$	−32.4080			−1.50613			−0.753063	−	0.657948i	$-0.771425\pi$
$463$	−32.4080			−1.50613			−0.753063	+	0.657948i	$0.771425\pi$
$464$	−4.78136	−	8.28156i	−0.221969	−	0.384462i
$465$	−7.58984	+	13.1460i	−0.351970	+	0.609631i
$466$	14.1811	−	24.5624i	0.656927	−	1.13783i
$467$	9.71084	+	16.8197i	0.449364	+	0.778321i	0.998345	−	0.0575137i	$-0.0183173\pi$
$467$	9.71084	+	16.8197i	0.449364	+	0.778321i	−0.548981	+	0.835835i	$0.684984\pi$
$468$	−2.90367			−0.134222
$469$	36.4447	+	1.12646i	1.68286	+	0.0520151i
$470$	25.0217			1.15416
$471$	2.45011	+	4.24372i	0.112895	+	0.195540i
$472$	−2.00558	+	3.47376i	−0.0923141	+	0.159893i
$473$	16.0992	−	27.8847i	0.740243	−	1.28214i
$474$	0.196920	+	0.341075i	0.00904482	+	0.0156661i
$475$	6.13077			0.281299
$476$	0.679703	−	1.09751i	0.0311541	−	0.0503045i
$477$	3.04433			0.139390
$478$	15.3849	+	26.6474i	0.703688	+	1.21882i
$479$	0.0989067	−	0.171311i	0.00451916	−	0.00782742i	−0.863757	−	0.503909i	$-0.831895\pi$
$479$	0.0989067	−	0.171311i	0.00451916	−	0.00782742i	0.868276	+	0.496081i	$0.165228\pi$
$480$	3.25746	−	5.64208i	0.148682	−	0.257525i
$481$	22.5289	+	39.0212i	1.02723	+	1.77922i
$482$	20.7268			0.944079
$483$	−3.51685	−	6.55076i	−0.160022	−	0.298070i
$484$	−0.537640			−0.0244382
$485$	10.4347	+	18.0734i	0.473814	+	0.820669i
$486$	−0.614831	+	1.06492i	−0.0278893	+	0.0483057i
$487$	−16.6137	+	28.7758i	−0.752840	+	1.30396i	0.193601	+	0.981080i	$0.437983\pi$
$487$	−16.6137	+	28.7758i	−0.752840	+	1.30396i	−0.946441	+	0.322876i	$0.895350\pi$
$488$	−15.1778	−	26.2888i	−0.687068	−	1.19004i
$489$	−8.30470			−0.375552
$490$	−9.27918	−	18.6444i	−0.419191	−	0.842267i
$491$	23.6344			1.06661			0.533303	−	0.845924i	$-0.320951\pi$
$491$	23.6344			1.06661			0.533303	+	0.845924i	$0.320951\pi$
$492$	0.656928	+	1.13783i	0.0296166	+	0.0512975i
$493$	1.71617	−	2.97250i	0.0772925	−	0.133874i
$494$	26.2729	−	45.5060i	1.18207	−	2.04741i
$495$	4.20838	+	7.28913i	0.189153	+	0.327622i
$496$	−17.4797			−0.784863
$497$	−1.50866	−	2.81015i	−0.0676727	−	0.126053i
$498$	−13.6907			−0.613496
$499$	5.38419	+	9.32568i	0.241029	+	0.417475i	0.961008	−	0.276521i	$-0.0891817\pi$
$499$	5.38419	+	9.32568i	0.241029	+	0.417475i	−0.719978	+	0.693996i	$0.755848\pi$
$500$	2.44736	−	4.23895i	0.109449	−	0.189572i
$501$	−5.14132	+	8.90502i	−0.229697	+	0.397847i
$502$	8.65477	+	14.9905i	0.386281	+	0.669059i
$503$	−34.0342			−1.51751			−0.758755	−	0.651376i	$-0.774192\pi$
$503$	−34.0342			−1.51751			−0.758755	+	0.651376i	$0.774192\pi$
$504$	−4.26172	+	6.88139i	−0.189832	+	0.306522i
$505$	18.7063			0.832421
$506$	−6.01063	−	10.4107i	−0.267205	−	0.462812i
$507$	11.2071	−	19.4112i	0.497724	−	0.862084i
$508$	3.60741	−	6.24822i	0.160053	−	0.277220i
$509$	−21.6184	−	37.4441i	−0.958218	−	1.65968i	−0.726827	−	0.686821i	$-0.759006\pi$
$509$	−21.6184	−	37.4441i	−0.958218	−	1.65968i	−0.231391	−	0.972861i	$-0.574328\pi$
$510$	−2.97512			−0.131741
$511$	−32.5498	−	1.00607i	−1.43992	−	0.0445061i
$512$	24.5489			1.08492
$513$	3.59032	+	6.21862i	0.158517	+	0.274559i
$514$	−3.11291	+	5.39173i	−0.137305	+	0.237819i
$515$	9.06378	−	15.6989i	0.399398	−	0.691778i
$516$	2.25807	+	3.91108i	0.0994058	+	0.172176i
$517$	29.2576			1.28675
$518$	24.6212	+	0.761011i	1.08179	+	0.0334369i
$519$	20.7809			0.912180
$520$	22.0243	+	38.1471i	0.965828	+	1.67286i
$521$	−4.28457	+	7.42109i	−0.187710	+	0.325124i	−0.944486	−	0.328550i	$-0.893440\pi$
$521$	−4.28457	+	7.42109i	−0.187710	+	0.325124i	0.756776	+	0.653674i	$0.226773\pi$
$522$	−2.11031	+	3.65517i	−0.0923658	+	0.159982i
$523$	6.07868	+	10.5286i	0.265802	+	0.460383i	0.967773	−	0.251822i	$-0.0810299\pi$
$523$	6.07868	+	10.5286i	0.265802	+	0.460383i	−0.701971	+	0.712205i	$0.747697\pi$
$524$	10.4056			0.454569
$525$	1.18936	−	1.92045i	0.0519078	−	0.0838155i
$526$	31.0951			1.35581
$527$	−3.13700	−	5.43344i	−0.136650	−	0.236684i
$528$	−4.84604	+	8.39359i	−0.210897	+	0.365284i
$529$	7.55138	−	13.0794i	0.328321	−	0.568669i
$530$	−4.52862	−	7.84381i	−0.196711	−	0.340713i
$531$	1.31113			0.0568981
$532$	4.38467	+	8.16724i	0.190100	+	0.354095i
$533$	−16.0243			−0.694089
$534$	−7.19308	−	12.4588i	−0.311275	−	0.539144i
$535$	1.34078	−	2.32231i	0.0579672	−	0.100402i
$536$	−21.0808	+	36.5130i	−0.910551	+	1.57712i
$537$	−4.50806	−	7.80819i	−0.194537	−	0.336948i
$538$	−34.9730			−1.50779
$539$	−10.8500	−	21.8007i	−0.467345	−	0.939021i
$540$	−1.18053			−0.0508019
$541$	−18.8910	−	32.7202i	−0.812188	−	1.40675i	−0.911330	−	0.411677i	$-0.864943\pi$
$541$	−18.8910	−	32.7202i	−0.812188	−	1.40675i	0.0991420	−	0.995073i	$-0.468390\pi$
$542$	0.312178	−	0.540709i	0.0134092	−	0.0232254i
$543$	−0.331515	+	0.574201i	−0.0142267	+	0.0246413i
$544$	1.34636	+	2.33196i	0.0577246	+	0.0999819i
$545$	−15.1862			−0.650506
$546$	−9.15778	−	17.0580i	−0.391917	−	0.730016i
$547$	28.0254			1.19828			0.599140	−	0.800644i	$-0.295509\pi$
$547$	28.0254			1.19828			0.599140	+	0.800644i	$0.295509\pi$
$548$	0.490261	+	0.849158i	0.0209429	+	0.0362742i
$549$	−4.96119	+	8.59303i	−0.211738	+	0.366742i
$550$	1.82614	−	3.16297i	0.0778668	−	0.134869i
$551$	12.3232	+	21.3444i	0.524986	+	0.909303i
$552$	8.59729			0.365925
$553$	0.446164	−	0.720420i	0.0189728	−	0.0306354i
$554$	13.7133			0.582621
$555$	9.15947	+	15.8647i	0.388798	+	0.673418i
$556$	2.08125	−	3.60483i	0.0882646	−	0.152879i
$557$	−12.1886	+	21.1113i	−0.516448	+	0.894515i	0.483369	+	0.875417i	$0.339413\pi$
$557$	−12.1886	+	21.1113i	−0.516448	+	0.894515i	−0.999818	+	0.0190983i	$0.993920\pi$
$558$	3.85745	+	6.68129i	0.163299	+	0.282842i
$559$	−55.0804			−2.32965
$560$	17.8259	+	0.550976i	0.753281	+	0.0232830i
$561$	−3.47878			−0.146874
$562$	5.84040	+	10.1159i	0.246362	+	0.426712i
$563$	16.1493	−	27.9713i	0.680610	−	1.17885i	−0.294185	−	0.955748i	$-0.595048\pi$
$563$	16.1493	−	27.9713i	0.680610	−	1.17885i	0.974795	−	0.223102i	$-0.0716184\pi$
$564$	−2.05182	+	3.55386i	−0.0863973	+	0.149645i
$565$	1.95217	+	3.38126i	0.0821286	+	0.142251i
$566$	−6.11069			−0.256852
$567$	2.64449	+	0.0817379i	0.111058	+	0.00343267i
$568$	3.68808			0.154748
$569$	3.38585	+	5.86446i	0.141942	+	0.245851i	0.928228	−	0.372012i	$-0.121332\pi$
$569$	3.38585	+	5.86446i	0.141942	+	0.245851i	−0.786286	+	0.617863i	$0.787999\pi$
$570$	10.6816	−	18.5011i	0.447405	−	0.774927i
$571$	−1.36611	+	2.36616i	−0.0571697	+	0.0990209i	−0.893194	−	0.449672i	$-0.851541\pi$
$571$	−1.36611	+	2.36616i	−0.0571697	+	0.0990209i	0.836024	+	0.548693i	$0.184874\pi$
$572$	5.05060	+	8.74790i	0.211176	+	0.365768i
$573$	23.8474			0.996238
$574$	−4.61250	+	7.44780i	−0.192522	+	0.310865i
$575$	−2.39932			−0.100059
$576$	−4.44163	−	7.69312i	−0.185068	−	0.320547i
$577$	−17.0087	+	29.4599i	−0.708082	+	1.22643i	0.257486	+	0.966282i	$0.417106\pi$
$577$	−17.0087	+	29.4599i	−0.708082	+	1.22643i	−0.965568	+	0.260151i	$0.916228\pi$
$578$	0.614831	−	1.06492i	0.0255736	−	0.0442948i
$579$	5.67228	+	9.82468i	0.235732	+	0.408300i
$580$	−4.05198			−0.168249
$581$	13.9334	+	25.9534i	0.578054	+	1.07673i
$582$	10.6066			0.439657
$583$	−5.29527	−	9.17168i	−0.219308	−	0.379852i
$584$	18.8279	−	32.6108i	0.779102	−	1.34944i
$585$	7.19908	−	12.4692i	0.297645	−	0.515537i
$586$	−5.79056	−	10.0295i	−0.239206	−	0.414316i
$587$	10.2949			0.424917			0.212458	−	0.977170i	$-0.431853\pi$
$587$	10.2949			0.424917			0.212458	+	0.977170i	$0.431853\pi$
$588$	3.40899	+	0.210937i	0.140585	+	0.00869890i
$589$	45.0513			1.85631
$590$	−1.95038	−	3.37816i	−0.0802959	−	0.139077i
$591$	−8.72274	+	15.1082i	−0.358806	+	0.621470i
$592$	−10.5473	+	18.2685i	−0.433493	+	0.750831i
$593$	11.0092	+	19.0685i	0.452095	+	0.783051i	0.998516	−	0.0544594i	$-0.0173435\pi$
$593$	11.0092	+	19.0685i	0.452095	+	0.783051i	−0.546421	+	0.837511i	$0.684010\pi$
$594$	4.27772			0.175517
$595$	3.02785	+	5.63992i	0.124130	+	0.231214i
$596$	5.25312			0.215176
$597$	−5.82748	−	10.0935i	−0.238503	−	0.413099i
$598$	−10.2821	+	17.8091i	−0.420466	+	0.728269i
$599$	18.9896	−	32.8910i	0.775894	−	1.34389i	−0.158396	−	0.987376i	$-0.550632\pi$
$599$	18.9896	−	32.8910i	0.775894	−	1.34389i	0.934290	−	0.356513i	$-0.116034\pi$
$600$	1.30601	+	2.26207i	0.0533175	+	0.0923487i
$601$	−11.4958			−0.468923			−0.234461	−	0.972125i	$-0.575333\pi$
$601$	−11.4958			−0.468923			−0.234461	+	0.972125i	$0.575333\pi$
$602$	−15.8546	+	25.6004i	−0.646185	+	1.04339i
$603$	13.7814			0.561221
$604$	−0.697163	−	1.20752i	−0.0283672	−	0.0491334i
$605$	1.33298	−	2.30878i	0.0541932	−	0.0938653i
$606$	4.75364	−	8.23354i	0.193103	−	0.334465i
$607$	3.57892	+	6.19887i	0.145264	+	0.251604i	0.929471	−	0.368894i	$-0.120264\pi$
$607$	3.57892	+	6.19887i	0.145264	+	0.251604i	−0.784208	+	0.620499i	$0.786930\pi$
$608$	−19.3354			−0.784154
$609$	9.07679	+	0.280552i	0.367810	+	0.0113686i
$610$	29.5203			1.19524
$611$	−25.0248	−	43.3442i	−1.01239	−	1.75352i
$612$	0.243965	−	0.422560i	0.00986171	−	0.0170810i
$613$	2.52527	−	4.37389i	0.101995	−	0.176660i	−0.810512	−	0.585722i	$-0.800811\pi$
$613$	2.52527	−	4.37389i	0.101995	−	0.176660i	0.912506	+	0.409063i	$0.134144\pi$
$614$	14.3935	+	24.9303i	0.580875	+	1.00611i
$615$	−6.51491			−0.262707
$616$	28.1444	+	0.869909i	1.13397	+	0.0350496i
$617$	−5.41515			−0.218006			−0.109003	−	0.994041i	$-0.534766\pi$
$617$	−5.41515			−0.218006			−0.109003	+	0.994041i	$0.534766\pi$
$618$	−4.60656	−	7.97880i	−0.185303	−	0.320954i
$619$	3.08185	−	5.33792i	0.123870	−	0.214549i	−0.797421	−	0.603424i	$-0.793803\pi$
$619$	3.08185	−	5.33792i	0.123870	−	0.214549i	0.921291	+	0.388875i	$0.127136\pi$
$620$	−3.70332	+	6.41433i	−0.148729	+	0.257606i
$621$	−1.40510	−	2.43371i	−0.0563847	−	0.0976613i
$622$	−17.3785			−0.696812
$623$	−16.2975	+	26.3155i	−0.652944	+	1.05431i
$624$	16.5798			0.663723
$625$	14.2700	+	24.7164i	0.570800	+	0.988654i
$626$	1.56946	−	2.71839i	0.0627284	−	0.108649i
$627$	12.4899	−	21.6332i	0.498799	−	0.863946i
$628$	1.19548	+	2.07064i	0.0477050	+	0.0826275i
$629$	−7.57150			−0.301895
$630$	−3.72323	−	6.93519i	−0.148337	−	0.276305i
$631$	−0.737721			−0.0293682			−0.0146841	−	0.999892i	$-0.504674\pi$
$631$	−0.737721			−0.0293682			−0.0146841	+	0.999892i	$0.504674\pi$
$632$	0.489923	+	0.848571i	0.0194881	+	0.0337543i
$633$	−0.210044	+	0.363807i	−0.00834849	+	0.0144600i
$634$	18.4136	−	31.8932i	0.731296	−	1.26664i
$635$	17.8878	+	30.9825i	0.709855	+	1.22950i
$636$	1.48542			0.0589008
$637$	−23.0167	+	34.7207i	−0.911954	+	1.37568i
$638$	14.6826			0.581289
$639$	−0.602762	−	1.04401i	−0.0238449	−	0.0413006i
$640$	−6.69946	+	11.6038i	−0.264819	+	0.458681i
$641$	2.78130	−	4.81736i	0.109855	−	0.190274i	−0.805856	−	0.592111i	$-0.798295\pi$
$641$	2.78130	−	4.81736i	0.109855	−	0.190274i	0.915711	+	0.401837i	$0.131628\pi$
$642$	−0.681438	−	1.18029i	−0.0268942	−	0.0465821i
$643$	−14.0644			−0.554646			−0.277323	−	0.960777i	$-0.589447\pi$
$643$	−14.0644			−0.554646			−0.277323	+	0.960777i	$0.589447\pi$
$644$	−1.71598	−	3.19631i	−0.0676190	−	0.125952i
$645$	−22.3938			−0.881754
$646$	4.41488	+	7.64680i	0.173701	+	0.300859i
$647$	−0.684284	+	1.18521i	−0.0269020	+	0.0465956i	−0.879163	−	0.476521i	$-0.841898\pi$
$647$	−0.684284	+	1.18521i	−0.0269020	+	0.0465956i	0.852261	+	0.523117i	$0.175231\pi$
$648$	−1.52966	+	2.64944i	−0.0600906	+	0.104080i
$649$	−2.28056	−	3.95004i	−0.0895198	−	0.155053i
$650$	−6.24778			−0.245058
$651$	8.73987	−	14.1123i	0.342542	−	0.553103i
$652$	−4.05212			−0.158693
$653$	3.41501	+	5.91497i	0.133640	+	0.231471i	0.925077	−	0.379780i	$-0.124000\pi$
$653$	3.41501	+	5.91497i	0.133640	+	0.231471i	−0.791437	+	0.611250i	$0.790667\pi$
$654$	−3.85911	+	6.68417i	−0.150903	+	0.261372i
$655$	−25.7986	+	44.6844i	−1.00803	+	1.74597i
$656$	−3.75103	−	6.49698i	−0.146453	−	0.253664i
$657$	−12.3085			−0.480202
$658$	−27.3489	−	0.845320i	−1.06617	−	0.0329540i
$659$	8.51125			0.331551			0.165776	−	0.986163i	$-0.446987\pi$
$659$	8.51125			0.331551			0.165776	+	0.986163i	$0.446987\pi$
$660$	2.05340	+	3.55659i	0.0799284	+	0.138440i
$661$	−4.25089	+	7.36275i	−0.165340	+	0.286378i	−0.936776	−	0.349929i	$-0.886206\pi$
$661$	−4.25089	+	7.36275i	−0.165340	+	0.286378i	0.771436	+	0.636307i	$0.219539\pi$
$662$	−0.0891412	+	0.154397i	−0.00346457	+	0.00600081i
$663$	2.97549	+	5.15370i	0.115558	+	0.200153i
$664$	−34.0616			−1.32185
$665$	−45.9435	−	1.42006i	−1.78161	−	0.0550674i
$666$	9.31039			0.360770
$667$	−4.82279	−	8.35331i	−0.186739	−	0.323441i
$668$	−2.50861	+	4.34503i	−0.0970609	+	0.168114i
$669$	8.68132	−	15.0365i	0.335639	−	0.581344i
$670$	−20.5006	−	35.5081i	−0.792008	−	1.37180i
$671$	34.5177			1.33254
$672$	−3.75103	+	6.05679i	−0.144699	+	0.233646i
$673$	−39.3500			−1.51683			−0.758416	−	0.651771i	$-0.774026\pi$
$673$	−39.3500			−1.51683			−0.758416	+	0.651771i	$0.774026\pi$
$674$	−2.41394	−	4.18106i	−0.0929814	−	0.161049i
$675$	0.426896	−	0.739405i	0.0164312	−	0.0284597i
$676$	5.46828	−	9.47134i	0.210318	−	0.364282i
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$	1.98434			0.0762081
$679$	−10.7946	−	20.1068i	−0.414258	−	0.771630i
$680$	−7.40189			−0.283850
$681$	1.80891	+	3.13312i	0.0693175	+	0.120061i
$682$	13.4192	−	23.2427i	0.513847	−	0.890010i
$683$	−18.2574	+	31.6227i	−0.698598	+	1.21001i	0.270354	+	0.962761i	$0.412859\pi$
$683$	−18.2574	+	31.6227i	−0.698598	+	1.21001i	−0.968953	+	0.247247i	$0.920474\pi$
$684$	1.75183	+	3.03425i	0.0669828	+	0.116018i
$685$	−4.86204			−0.185769
$686$	9.51234	+	20.6919i	0.363183	+	0.790021i
$687$	−13.9257			−0.531299
$688$	−12.8935	−	22.3321i	−0.491558	−	0.851404i
$689$	−9.05838	+	15.6896i	−0.345097	+	0.597725i
$690$	−4.18034	+	7.24057i	−0.159143	+	0.275644i
$691$	14.8824	+	25.7771i	0.566153	+	0.980606i	0.996941	+	0.0781528i	$0.0249022\pi$
$691$	14.8824	+	25.7771i	0.566153	+	0.980606i	−0.430788	+	0.902453i	$0.641764\pi$
$692$	10.1396			0.385451
$693$	−4.35354	−	8.10924i	−0.165377	−	0.308045i
$694$	21.6554			0.822029
$695$	10.3201	+	17.8750i	0.391464	+	0.678036i
$696$	−5.25031	+	9.09380i	−0.199012	+	0.344700i
$697$	1.34636	−	2.33196i	0.0509969	−	0.0883292i
$698$	8.82954	+	15.2932i	0.334203	+	0.578856i
$699$	−23.0650			−0.872400
$700$	0.580324	−	0.937048i	0.0219342	−	0.0354171i
$701$	−13.1980			−0.498480			−0.249240	−	0.968442i	$-0.580181\pi$
$701$	−13.1980			−0.498480			−0.249240	+	0.968442i	$0.580181\pi$
$702$	−3.65885	−	6.33731i	−0.138094	−	0.239186i
$703$	27.1841	−	47.0843i	1.02527	−	1.77582i
$704$	−15.4514	+	26.7626i	−0.582347	+	1.00866i
$705$	−10.1742	−	17.6222i	−0.383183	−	0.663692i
$706$	−18.6056			−0.700230
$707$	−20.4462	−	0.631966i	−0.768957	−	0.0237675i
$708$	0.639739			0.0240429
$709$	11.2092	+	19.4150i	0.420972	+	0.729145i	0.996035	−	0.0889642i	$-0.0283557\pi$
$709$	11.2092	+	19.4150i	0.420972	+	0.729145i	−0.575063	+	0.818109i	$0.695022\pi$
$710$	−1.79329	+	3.10607i	−0.0673009	+	0.116569i
$711$	0.160141	−	0.277373i	0.00600577	−	0.0104023i
$712$	−17.8959	−	30.9966i	−0.670677	−	1.16165i
$713$	−17.6312			−0.660293
$714$	3.25183	+	0.100510i	0.121697	+	0.00376149i
$715$	−50.0880			−1.87318
$716$	−2.19962	−	3.80986i	−0.0822037	−	0.142381i
$717$	12.5115	−	21.6705i	0.467249	−	0.809299i
$718$	17.6002	−	30.4845i	0.656835	−	1.13767i
$719$	5.91816	+	10.2505i	0.220710	+	0.382281i	0.955024	−	0.296529i	$-0.0958292\pi$
$719$	5.91816	+	10.2505i	0.220710	+	0.382281i	−0.734314	+	0.678810i	$0.762496\pi$
$720$	6.74077			0.251214
$721$	−10.4371	+	16.8528i	−0.388700	+	0.627633i
$722$	−40.0398			−1.49013
$723$	−8.42784	−	14.5974i	−0.313435	−	0.542885i
$724$	−0.161756	+	0.280170i	−0.00601163	+	0.0104124i
$725$	1.46525	−	2.53789i	0.0544181	−	0.0942549i
$726$	−0.677469	−	1.17341i	−0.0251432	−	0.0435494i
$727$	−8.90070			−0.330109			−0.165054	−	0.986284i	$-0.552780\pi$
$727$	−8.90070			−0.330109			−0.165054	+	0.986284i	$0.552780\pi$
$728$	−22.7839	−	42.4392i	−0.844429	−	1.57290i
$729$	1.00000			0.0370370
$730$	18.3097	+	31.7133i	0.677672	+	1.17376i
$731$	4.62784	−	8.01566i	0.171167	−	0.296470i
$732$	−2.42072	+	4.19280i	−0.0894722	+	0.154970i
$733$	−1.88327	−	3.26191i	−0.0695600	−	0.120481i	0.829148	−	0.559030i	$-0.188826\pi$
$733$	−1.88327	−	3.26191i	−0.0695600	−	0.120481i	−0.898708	+	0.438548i	$0.855493\pi$
$734$	35.6974			1.31762
$735$	−9.35777	+	14.1162i	−0.345167	+	0.520685i
$736$	7.56707			0.278926
$737$	−23.9712	−	41.5193i	−0.882989	−	1.52938i
$738$	−1.65556	+	2.86752i	−0.0609421	+	0.105555i
$739$	4.19320	−	7.26283i	0.154249	−	0.267168i	−0.778536	−	0.627600i	$-0.784037\pi$
$739$	4.19320	−	7.26283i	0.154249	−	0.267168i	0.932785	+	0.360432i	$0.117371\pi$
$740$	4.46919	+	7.74086i	0.164291	+	0.284560i
$741$	−42.7319			−1.56979
$742$	4.68483	+	8.72633i	0.171985	+	0.320354i
$743$	−20.0289			−0.734788			−0.367394	−	0.930065i	$-0.619750\pi$
$743$	−20.0289			−0.734788			−0.367394	+	0.930065i	$0.619750\pi$
$744$	9.59706	+	16.6226i	0.351845	+	0.609414i
$745$	−13.0241	+	22.5584i	−0.477167	+	0.826477i
$746$	4.35261	−	7.53895i	0.159360	−	0.276020i
$747$	5.56686	+	9.64209i	0.203681	+	0.352786i
$748$	−1.69740			−0.0620631
$749$	−1.54394	+	2.49300i	−0.0564145	+	0.0910923i
$750$	12.3355			0.450428
$751$	−18.6141	−	32.2406i	−0.679238	−	1.17647i	−0.975211	−	0.221278i	$-0.928977\pi$
$751$	−18.6141	−	32.2406i	−0.679238	−	1.17647i	0.295973	−	0.955196i	$-0.404356\pi$
$752$	11.7158	−	20.2924i	0.427232	−	0.739987i
$753$	7.03833	−	12.1907i	0.256491	−	0.444256i
$754$	−12.5584	−	21.7518i	−0.457351	−	0.792155i
$755$	6.91393			0.251624
$756$	1.29033	+	0.0398824i	0.0469287	+	0.00145051i
$757$	29.9226			1.08756			0.543778	−	0.839229i	$-0.316993\pi$
$757$	29.9226			1.08756			0.543778	+	0.839229i	$0.316993\pi$
$758$	−1.74600	−	3.02416i	−0.0634176	−	0.109842i
$759$	−4.88803	+	8.46632i	−0.177424	+	0.307308i
$760$	26.5752	−	46.0295i	0.963983	−	1.66967i
$761$	7.08165	+	12.2658i	0.256710	+	0.444634i	0.965358	−	0.260927i	$-0.0840283\pi$
$761$	7.08165	+	12.2658i	0.256710	+	0.444634i	−0.708649	+	0.705561i	$0.750695\pi$
$762$	18.1825			0.658682
$763$	16.5986	+	0.513044i	0.600911	+	0.0185734i
$764$	11.6359			0.420971
$765$	1.20973	+	2.09531i	0.0437379	+	0.0757563i
$766$	15.2831	−	26.4711i	0.552201	−	0.956441i
$767$	−3.90125	+	6.75716i	−0.140866	+	0.243987i
$768$	−5.47833	−	9.48875i	−0.197682	−	0.342396i
$769$	15.2864			0.551240			0.275620	−	0.961267i	$-0.411117\pi$
$769$	15.2864			0.551240			0.275620	+	0.961267i	$0.411117\pi$
$770$	−14.4176	+	23.2800i	−0.519573	+	0.838953i
$771$	5.06304			0.182341
$772$	2.76768	+	4.79376i	0.0996110	+	0.172531i
$773$	−7.93843	+	13.7498i	−0.285525	+	0.494545i	−0.972736	−	0.231913i	$-0.925501\pi$
$773$	−7.93843	+	13.7498i	−0.285525	+	0.494545i	0.687211	+	0.726458i	$0.258835\pi$
$774$	−5.69068	+	9.85655i	−0.204547	+	0.354286i
$775$	−2.67834	−	4.63902i	−0.0962088	−	0.166639i
$776$	26.3885			0.947290
$777$	−9.47541	−	17.6496i	−0.339928	−	0.633177i
$778$	−15.5458			−0.557345
$779$	9.66771	+	16.7450i	0.346381	+	0.599950i
$780$	3.51265	−	6.08409i	0.125773	−	0.217845i
$781$	−2.09687	+	3.63189i	−0.0750320	+	0.129959i
$782$	−1.72780	−	2.99264i	−0.0617860	−	0.107016i
$783$	3.43234			0.122662
$784$	−19.4652	−	1.20444i	−0.695186	−	0.0430158i
$785$	−11.8559			−0.423155
$786$	13.1118	+	22.7103i	0.467683	+	0.810051i
$787$	−18.3681	+	31.8145i	−0.654751	+	1.13406i	0.327205	+	0.944954i	$0.393893\pi$
$787$	−18.3681	+	31.8145i	−0.654751	+	1.13406i	−0.981956	+	0.189109i	$0.939440\pi$
$788$	−4.25609	+	7.37177i	−0.151617	+	0.262608i
$789$	−12.6438	−	21.8996i	−0.450130	−	0.779648i
$790$	−0.952879			−0.0339019
$791$	−2.01951	−	3.76170i	−0.0718055	−	0.133751i
$792$	10.6427			0.378171
$793$	−29.5239	−	51.1370i	−1.04843	−	1.81593i
$794$	15.5701	−	26.9682i	0.552561	−	0.957064i
$795$	−3.68282	+	6.37883i	−0.130616	+	0.226234i
$796$	−2.84340	−	4.92492i	−0.100782	−	0.174559i
$797$	23.1262			0.819172			0.409586	−	0.912272i	$-0.365673\pi$
$797$	23.1262			0.819172			0.409586	+	0.912272i	$0.365673\pi$
$798$	−12.3001	+	19.8610i	−0.435420	+	0.703072i
$799$	8.41031			0.297535
$800$	1.14951	+	1.99100i	0.0406412	+	0.0703926i
$801$	−5.84964	+	10.1319i	−0.206687	+	0.357992i
$802$	0.0316625	−	0.0548410i	0.00111804	−	0.00193650i
$803$	21.4093	+	37.0820i	0.755519	+	1.30860i
$804$	6.72435			0.237150
$805$	17.9803	+	0.555750i	0.633723	+	0.0195876i
$806$	−45.9112			−1.61715
$807$	14.2206	+	24.6307i	0.500588	+	0.867043i
$808$	11.8267	−	20.4845i	0.416063	−	0.720641i
$809$	27.2634	−	47.2216i	0.958530	−	1.66022i	0.232454	−	0.972607i	$-0.425324\pi$
$809$	27.2634	−	47.2216i	0.958530	−	1.66022i	0.726075	−	0.687615i	$-0.241342\pi$
$810$	−1.48756	−	2.57653i	−0.0522675	−	0.0905300i
$811$	18.5864			0.652656			0.326328	−	0.945257i	$-0.394189\pi$
$811$	18.5864			0.652656			0.326328	+	0.945257i	$0.394189\pi$
$812$	4.42884	+	0.136890i	0.155422	+	0.00480390i
$813$	−0.507746			−0.0178074
$814$	−16.1944	−	28.0495i	−0.567612	−	0.983134i
$815$	10.0465	−	17.4010i	0.351912	−	0.609529i
$816$	−1.39303	+	2.41280i	−0.0487658	+	0.0844649i
$817$	33.2309	+	57.5576i	1.16260	+	2.01368i
$818$	−23.2031			−0.811279
$819$	−8.28990	+	13.3857i	−0.289673	+	0.467734i
$820$	−3.17883			−0.111009
$821$	−9.83537	−	17.0354i	−0.343257	−	0.594538i	0.641779	−	0.766890i	$-0.278197\pi$
$821$	−9.83537	−	17.0354i	−0.343257	−	0.594538i	−0.985035	+	0.172352i	$0.944863\pi$
$822$	−1.23554	+	2.14001i	−0.0430943	+	0.0746415i
$823$	0.584220	−	1.01190i	0.0203646	−	0.0352726i	−0.855663	−	0.517533i	$-0.826851\pi$
$823$	0.584220	−	1.01190i	0.0203646	−	0.0352726i	0.876028	+	0.482260i	$0.160184\pi$
$824$	−11.4608	−	19.8507i	−0.399256	−	0.691532i
$825$	−2.97015			−0.103407
$826$	2.01765	+	3.75824i	0.0702032	+	0.130766i
$827$	−19.4510			−0.676377			−0.338189	−	0.941078i	$-0.609814\pi$
$827$	−19.4510			−0.676377			−0.338189	+	0.941078i	$0.609814\pi$
$828$	−0.685592	−	1.18748i	−0.0238260	−	0.0412678i
$829$	11.5690	−	20.0382i	0.401809	−	0.695954i	−0.592135	−	0.805839i	$-0.701715\pi$
$829$	11.5690	−	20.0382i	0.401809	−	0.695954i	0.993944	+	0.109884i	$0.0350481\pi$
$830$	16.5621	−	28.6864i	0.574878	−	0.995719i
$831$	−5.57603	−	9.65797i	−0.193430	−	0.335031i
$832$	52.8641			1.83273
$833$	−3.11893	−	6.26676i	−0.108064	−	0.217130i
$834$	10.4902			0.363244
$835$	−12.4392	−	21.5454i	−0.430477	−	0.745608i
$836$	6.09422	−	10.5555i	0.210773	−	0.365069i
$837$	3.13700	−	5.43344i	0.108430	−	0.187807i
$838$	12.5385	+	21.7173i	0.433134	+	0.750211i
$839$	−13.5536			−0.467922			−0.233961	−	0.972246i	$-0.575169\pi$
$839$	−13.5536			−0.467922			−0.233961	+	0.972246i	$0.575169\pi$
$840$	−9.26315	−	17.2543i	−0.319609	−	0.595329i
$841$	−17.2190			−0.593760
$842$	1.05061	+	1.81971i	0.0362065	+	0.0627114i
$843$	4.74959	−	8.22654i	0.163585	−	0.283337i
$844$	−0.102487	+	0.177512i	−0.00352774	+	0.00611023i
$845$	27.1151	+	46.9647i	0.932788	+	1.61564i
$846$	−10.3418			−0.355560
$847$	−1.53495	+	2.47848i	−0.0527415	+	0.0851617i
$848$	−8.48170			−0.291263
$849$	2.48470	+	4.30363i	0.0852748	+	0.147700i
$850$	0.524937	−	0.909218i	0.0180052	−	0.0311859i
$851$	−10.6387	+	18.4268i	−0.364691	+	0.631663i
$852$	−0.294106	−	0.509406i	−0.0100759	−	0.0174520i
$853$	−25.8370			−0.884641			−0.442320	−	0.896857i	$-0.645845\pi$
$853$	−25.8370			−0.884641			−0.442320	+	0.896857i	$0.645845\pi$
$854$	−32.2659	−	0.997298i	−1.10411	−	0.0341268i
$855$	−17.3733			−0.594154
$856$	−1.69537	−	2.93647i	−0.0579466	−	0.100366i
$857$	−1.30113	+	2.25362i	−0.0444458	+	0.0769823i	−0.887392	−	0.461015i	$-0.847486\pi$
$857$	−1.30113	+	2.25362i	−0.0444458	+	0.0769823i	0.842947	+	0.537997i	$0.180819\pi$
$858$	−12.7283	+	22.0461i	−0.434537	+	0.752641i
$859$	−3.01764	−	5.22671i	−0.102961	−	0.178333i	0.809943	−	0.586509i	$-0.199498\pi$
$859$	−3.01764	−	5.22671i	−0.102961	−	0.178333i	−0.912903	+	0.408176i	$0.866165\pi$
$860$	−10.9266			−0.372594
$861$	7.12085	+	0.220097i	0.242678	+	0.00750087i
$862$	−44.3177			−1.50947
$863$	20.0175	+	34.6713i	0.681403	+	1.18023i	0.974553	+	0.224158i	$0.0719633\pi$
$863$	20.0175	+	34.6713i	0.681403	+	1.18023i	−0.293149	+	0.956067i	$0.594703\pi$
$864$	−1.34636	+	2.33196i	−0.0458040	+	0.0793348i
$865$	−25.1393	+	43.5425i	−0.854761	+	1.48049i
$866$	−14.2900	−	24.7510i	−0.485594	−	0.841074i
$867$	−1.00000			−0.0339618
$868$	4.26445	−	6.88580i	0.144745	−	0.233719i
$869$	−1.11419			−0.0377964
$870$	−5.10581	−	8.84353i	−0.173103	−	0.299824i
$871$	−41.0063	+	71.0251i	−1.38945	+	2.40659i
$872$	−9.60119	+	16.6297i	−0.325137	+	0.563154i
$873$	−4.31281	−	7.47000i	−0.145966	−	0.252821i
$874$	24.8134			0.839327
$875$	−12.5541	−	23.3843i	−0.424406	−	0.790533i
$876$	−6.00571			−0.202914
$877$	20.4122	+	35.3549i	0.689270	+	1.19385i	0.972074	+	0.234673i	$0.0754020\pi$
$877$	20.4122	+	35.3549i	0.689270	+	1.19385i	−0.282804	+	0.959178i	$0.591265\pi$
$878$	14.3853	−	24.9160i	0.485479	−	0.840875i
$879$	−4.70906	+	8.15633i	−0.158833	+	0.275106i
$880$	−11.7248	−	20.3080i	−0.395243	−	0.684581i
$881$	−9.86270			−0.332283			−0.166141	−	0.986102i	$-0.553131\pi$
$881$	−9.86270			−0.332283			−0.166141	+	0.986102i	$0.553131\pi$
$882$	3.83523	+	7.70600i	0.129139	+	0.259475i
$883$	−15.2724			−0.513957			−0.256979	−	0.966417i	$-0.582727\pi$
$883$	−15.2724			−0.513957			−0.256979	+	0.966417i	$0.582727\pi$
$884$	1.45183	+	2.51465i	0.0488304	+	0.0845768i
$885$	−1.58611	+	2.74722i	−0.0533165	+	0.0923469i
$886$	−3.60079	+	6.23676i	−0.120971	+	0.209528i
$887$	4.59318	+	7.95562i	0.154224	+	0.267124i	0.932776	−	0.360456i	$-0.117379\pi$
$887$	4.59318	+	7.95562i	0.154224	+	0.267124i	−0.778552	+	0.627580i	$0.784046\pi$
$888$	23.1636			0.777319
$889$	−18.5048	−	34.4684i	−0.620630	−	1.15603i
$890$	34.8068			1.16673
$891$	−1.73939	−	3.01271i	−0.0582717	−	0.100930i
$892$	4.23588	−	7.33677i	0.141828	−	0.245653i
$893$	−30.1957	+	52.3005i	−1.01046	+	1.75017i
$894$	6.61935	+	11.4651i	0.221384	+	0.383449i
$895$	21.8142			0.729167
$896$	7.71457	−	12.4567i	0.257726	−	0.416149i
$897$	16.7235			0.558380
$898$	5.86527	+	10.1590i	0.195727	+	0.339009i
$899$	10.7672	−	18.6494i	0.359108	−	0.621993i
$900$	0.208295	−	0.360778i	0.00694318	−	0.0120259i
$901$	−1.52217	−	2.63647i	−0.0507107	−	0.0878335i
$902$	11.5187			0.383530
$903$	24.4765	+	0.756540i	0.814528	+	0.0251761i
$904$	4.93690			0.164199
$905$	−0.802088	−	1.38926i	−0.0266623	−	0.0461805i
$906$	1.75696	−	3.04315i	0.0583711	−	0.101102i
$907$	5.76286	−	9.98157i	0.191353	−	0.331433i	−0.754346	−	0.656477i	$-0.772046\pi$
$907$	5.76286	−	9.98157i	0.191353	−	0.331433i	0.945699	+	0.325044i	$0.105379\pi$
$908$	0.882622	+	1.52875i	0.0292908	+	0.0507332i
$909$	−7.73161			−0.256441
$910$	46.8204	+	1.44716i	1.55208	+	0.0479729i
$911$	47.5409			1.57510			0.787550	−	0.616251i	$-0.211349\pi$
$911$	47.5409			1.57510			0.787550	+	0.616251i	$0.211349\pi$
$912$	−10.0029	−	17.3255i	−0.331228	−	0.573703i
$913$	19.3659	−	33.5427i	0.640917	−	1.11010i
$914$	−22.5139	+	38.9952i	−0.744693	+	1.28985i
$915$	−12.0034	−	20.7905i	−0.396820	−	0.687313i
$916$	−6.79478			−0.224506
$917$	29.7076	−	47.9689i	0.981032	−	1.58407i
$918$	1.22966			0.0405849
$919$	6.85200	+	11.8680i	0.226027	+	0.391490i	0.956627	−	0.291316i	$-0.0940930\pi$
$919$	6.85200	+	11.8680i	0.226027	+	0.391490i	−0.730600	+	0.682805i	$0.760760\pi$
$920$	−10.4004	+	18.0140i	−0.342891	+	0.593905i
$921$	11.7053	−	20.2741i	0.385702	−	0.668055i
$922$	12.6154	+	21.8504i	0.415465	+	0.719606i
$923$	7.17405			0.236137
$924$	−2.12422	−	3.95675i	−0.0698819	−	0.130167i
$925$	−6.46448			−0.212551
$926$	−19.9254	−	34.5119i	−0.654790	−	1.13413i
$927$	−3.74620	+	6.48861i	−0.123041	+	0.213114i
$928$	−4.62116	+	8.00408i	−0.151697	+	0.262747i
$929$	−23.1821	−	40.1525i	−0.760579	−	1.31736i	−0.942553	−	0.334058i	$-0.891582\pi$
$929$	−23.1821	−	40.1525i	−0.760579	−	1.31736i	0.181974	−	0.983303i	$-0.441751\pi$
$930$	−18.6659			−0.612078
$931$	50.1686	+	3.10426i	1.64421	+	0.101738i
$932$	−11.2541			−0.368642
$933$	7.06635	+	12.2393i	0.231342	+	0.400696i
$934$	−11.9411	+	20.6825i	−0.390723	+	0.676752i
$935$	4.20838	−	7.28913i	0.137629	−	0.238380i
$936$	−9.10296	−	15.7668i	−0.297540	−	0.515354i
$937$	21.0492			0.687646			0.343823	−	0.939034i	$-0.388278\pi$
$937$	21.0492			0.687646			0.343823	+	0.939034i	$0.388278\pi$
$938$	21.2077	+	39.5032i	0.692457	+	1.28983i
$939$	−2.55267			−0.0833034
$940$	−4.96430	−	8.59843i	−0.161918	−	0.280450i
$941$	−20.8369	+	36.0905i	−0.679263	+	1.17652i	0.295940	+	0.955206i	$0.404367\pi$
$941$	−20.8369	+	36.0905i	−0.679263	+	1.17652i	−0.975203	+	0.221311i	$0.928966\pi$
$942$	−3.01281	+	5.21834i	−0.0981627	+	0.170023i
$943$	−3.78353	−	6.55327i	−0.123209	−	0.213404i
$944$	−3.65288			−0.118891
$945$	−3.37038	+	5.44215i	−0.109639	+	0.177033i
$946$	39.5932			1.28729
$947$	−1.31068	−	2.27017i	−0.0425915	−	0.0737706i	0.843944	−	0.536432i	$-0.180228\pi$
$947$	−1.31068	−	2.27017i	−0.0425915	−	0.0737706i	−0.886535	+	0.462661i	$0.846895\pi$
$948$	0.0781379	−	0.135339i	0.00253780	−	0.00439560i
$949$	36.6240	−	63.4345i	1.18886	−	2.05917i
$950$	3.76939	+	6.52877i	0.122295	+	0.211821i
$951$	−29.9490			−0.971163
$952$	8.09032	+	0.250062i	0.262209	+	0.00810455i
$953$	7.65023			0.247815			0.123908	−	0.992294i	$-0.460457\pi$
$953$	7.65023			0.247815			0.123908	+	0.992294i	$0.460457\pi$
$954$	1.87175	+	3.24197i	0.0606001	+	0.104962i
$955$	−28.8489	+	49.9677i	−0.933528	+	1.61692i
$956$	6.10472	−	10.5737i	0.197441	−	0.341978i
$957$	−5.97017	−	10.3406i	−0.192988	−	0.334266i
$958$	0.243244			0.00785885
$959$	5.31424	+	0.164257i	0.171606	+	0.00530413i
$960$	21.4927			0.693673
$961$	−4.18150	−	7.24256i	−0.134887	−	0.233631i
$962$	−27.7030	+	47.9829i	−0.893179	+	1.54703i
$963$	−0.554167	+	0.959845i	−0.0178578	+	0.0309306i
$964$	−4.11220	−	7.12254i	−0.132445	−	0.229401i
$965$	−27.4477			−0.883574
$966$	4.81376	−	7.77277i	0.154880	−	0.250085i
$967$	−17.0958			−0.549764			−0.274882	−	0.961478i	$-0.588639\pi$
$967$	−17.0958			−0.549764			−0.274882	+	0.961478i	$0.588639\pi$
$968$	−1.68550	−	2.91936i	−0.0541739	−	0.0938319i
$969$	3.59032	−	6.21862i	0.115338	−	0.199771i
$970$	−12.8311	+	22.2241i	−0.411982	+	0.713574i
$971$	25.0769	+	43.4345i	0.804757	+	1.39388i	0.916455	+	0.400138i	$0.131038\pi$
$971$	25.0769	+	43.4345i	0.804757	+	1.39388i	−0.111697	+	0.993742i	$0.535629\pi$
$972$	0.487931			0.0156504
$973$	−10.6761	−	19.8861i	−0.342260	−	0.637520i
$974$	−40.8585			−1.30919
$975$	2.54045	+	4.40018i	0.0813594	+	0.140919i
$976$	13.8222	−	23.9407i	0.442437	−	0.766324i
$977$	−16.4457	+	28.4848i	−0.526145	+	0.911310i	0.473391	+	0.880853i	$0.343030\pi$
$977$	−16.4457	+	28.4848i	−0.526145	+	0.911310i	−0.999536	+	0.0304578i	$0.990303\pi$
$978$	−5.10599	−	8.84383i	−0.163272	−	0.282795i
$979$	40.6992			1.30075
$980$	−4.56594	+	6.88774i	−0.145854	+	0.220021i
$981$	6.27669			0.200399
$982$	14.5312	+	25.1687i	0.463708	+	0.803166i
$983$	2.44724	−	4.23874i	0.0780548	−	0.135195i	−0.824356	−	0.566072i	$-0.808462\pi$
$983$	2.44724	−	4.23874i	0.0780548	−	0.135195i	0.902411	+	0.430877i	$0.141796\pi$
$984$	−4.11893	+	7.13419i	−0.131307	+	0.227430i
$985$	−21.1043	−	36.5538i	−0.672440	−	1.16470i
$986$	4.22062			0.134412
$987$	10.5251	+	19.6050i	0.335019	+	0.624033i
$988$	−20.8502			−0.663333
$989$	−13.0052	−	22.5256i	−0.413540	−	0.716273i
$990$	−5.17489	+	8.96317i	−0.164469	+	0.284868i
$991$	8.68162	−	15.0370i	0.275781	−	0.477666i	−0.694551	−	0.719443i	$-0.744397\pi$
$991$	8.68162	−	15.0370i	0.275781	−	0.477666i	0.970332	+	0.241777i	$0.0777303\pi$
$992$	8.44703	+	14.6307i	0.268193	+	0.464525i
$993$	0.144985			0.00460095
$994$	2.06501	−	3.33437i	0.0654982	−	0.105760i
$995$	28.1987			0.893959
$996$	2.71624	+	4.70467i	0.0860675	+	0.149073i
$997$	20.4074	−	35.3466i	0.646309	−	1.11944i	−0.337689	−	0.941258i	$-0.609645\pi$
$997$	20.4074	−	35.3466i	0.646309	−	1.11944i	0.983998	−	0.178181i	$-0.0570214\pi$
$998$	−6.62073	+	11.4674i	−0.209576	+	0.362996i
$999$	−3.78575	−	6.55711i	−0.119776	−	0.207458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.i.f.256.3	yes	10
3.2	odd	2		1071.2.i.g.613.3		10
7.2	even	3	inner	357.2.i.f.205.3	✓	10
7.3	odd	6		2499.2.a.bb.1.3		5
7.4	even	3		2499.2.a.ba.1.3		5
21.2	odd	6		1071.2.i.g.919.3		10
21.11	odd	6		7497.2.a.bv.1.3		5
21.17	even	6		7497.2.a.bw.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.3	✓	10	7.2	even	3	inner
357.2.i.f.256.3	yes	10	1.1	even	1	trivial
1071.2.i.g.613.3		10	3.2	odd	2
1071.2.i.g.919.3		10	21.2	odd	6
2499.2.a.ba.1.3		5	7.4	even	3
2499.2.a.bb.1.3		5	7.3	odd	6
7497.2.a.bv.1.3		5	21.11	odd	6
7497.2.a.bw.1.3		5	21.17	even	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.614831 + 1.06492i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.243965 - 0.422560i) q^{4} +(1.20973 + 2.09531i) q^{5} +1.22966 q^{6} +(-1.25146 - 2.33106i) q^{7} +3.05931 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.614831 + 1.06492i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.243965 - 0.422560i) q^{4} +(1.20973 + 2.09531i) q^{5} +1.22966 q^{6} +(-1.25146 - 2.33106i) q^{7} +3.05931 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.48756 + 2.57653i) q^{10} +(-1.73939 + 3.01271i) q^{11} +(-0.243965 - 0.422560i) q^{12} +5.95098 q^{13} +(1.71296 - 2.76591i) q^{14} +2.41946 q^{15} +(1.39303 + 2.41280i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.614831 - 1.06492i) q^{18} +(-3.59032 - 6.21862i) q^{19} +1.18053 q^{20} +(-2.64449 - 0.0817379i) q^{21} -4.27772 q^{22} +(1.40510 + 2.43371i) q^{23} +(1.52966 - 2.64944i) q^{24} +(-0.426896 + 0.739405i) q^{25} +(3.65885 + 6.33731i) q^{26} -1.00000 q^{27} +(-1.29033 - 0.0398824i) q^{28} -3.43234 q^{29} +(1.48756 + 2.57653i) q^{30} +(-3.13700 + 5.43344i) q^{31} +(1.34636 - 2.33196i) q^{32} +(1.73939 + 3.01271i) q^{33} -1.22966 q^{34} +(3.37038 - 5.44215i) q^{35} -0.487931 q^{36} +(3.78575 + 6.55711i) q^{37} +(4.41488 - 7.64680i) q^{38} +(2.97549 - 5.15370i) q^{39} +(3.70095 + 6.41023i) q^{40} -2.69271 q^{41} +(-1.53887 - 2.86642i) q^{42} -9.25568 q^{43} +(0.848700 + 1.46999i) q^{44} +(1.20973 - 2.09531i) q^{45} +(-1.72780 + 2.99264i) q^{46} +(-4.20515 - 7.28354i) q^{47} +2.78606 q^{48} +(-3.86771 + 5.83445i) q^{49} -1.04987 q^{50} +(0.500000 + 0.866025i) q^{51} +(1.45183 - 2.51465i) q^{52} +(-1.52217 + 2.63647i) q^{53} +(-0.614831 - 1.06492i) q^{54} -8.41676 q^{55} +(-3.82860 - 7.13146i) q^{56} -7.18064 q^{57} +(-2.11031 - 3.65517i) q^{58} +(-0.655564 + 1.13547i) q^{59} +(0.590264 - 1.02237i) q^{60} +(-4.96119 - 8.59303i) q^{61} -7.71489 q^{62} +(-1.39303 + 2.24933i) q^{63} +8.88325 q^{64} +(7.19908 + 12.4692i) q^{65} +(-2.13886 + 3.70461i) q^{66} +(-6.89069 + 11.9350i) q^{67} +(0.243965 + 0.422560i) q^{68} +2.81020 q^{69} +(7.86767 + 0.243180i) q^{70} +1.20552 q^{71} +(-1.52966 - 2.64944i) q^{72} +(6.15427 - 10.6595i) q^{73} +(-4.65519 + 8.06303i) q^{74} +(0.426896 + 0.739405i) q^{75} -3.50366 q^{76} +(9.19958 + 0.284348i) q^{77} +7.31770 q^{78} +(0.160141 + 0.277373i) q^{79} +(-3.37038 + 5.83768i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.65556 - 2.86752i) q^{82} -11.1337 q^{83} +(-0.679703 + 1.09751i) q^{84} -2.41946 q^{85} +(-5.69068 - 9.85655i) q^{86} +(-1.71617 + 2.97250i) q^{87} +(-5.32133 + 9.21682i) q^{88} +(-5.84964 - 10.1319i) q^{89} +2.97512 q^{90} +(-7.44740 - 13.8721i) q^{91} +1.37118 q^{92} +(3.13700 + 5.43344i) q^{93} +(5.17092 - 8.95629i) q^{94} +(8.68664 - 15.0457i) q^{95} +(-1.34636 - 2.33196i) q^{96} +8.62561 q^{97} +(-8.59121 - 0.531595i) q^{98} +3.47878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 8 q^{4} - q^{5} + 4 q^{6} - 5 q^{7} - 5 q^{9} - 13 q^{10} + 11 q^{11} + 8 q^{12} + 14 q^{13} + 3 q^{14} - 2 q^{15} + 2 q^{16} - 5 q^{17} + 2 q^{18} - 9 q^{19} + 24 q^{20} - 7 q^{21} + 10 q^{22} + 23 q^{23} - 14 q^{25} - 18 q^{26} - 10 q^{27} + 7 q^{28} - 36 q^{29} + 13 q^{30} - 9 q^{31} - 3 q^{32} - 11 q^{33} - 4 q^{34} - 5 q^{35} + 16 q^{36} + 7 q^{39} - 31 q^{40} + 6 q^{41} - 3 q^{42} + 24 q^{43} + 33 q^{44} - q^{45} - 13 q^{46} - 11 q^{47} + 4 q^{48} + 3 q^{49} + 48 q^{50} + 5 q^{51} - 5 q^{52} + 3 q^{53} - 2 q^{54} - 20 q^{55} - 27 q^{56} - 18 q^{57} + 34 q^{58} + 14 q^{59} + 12 q^{60} - 29 q^{61} - 10 q^{62} - 2 q^{63} + 8 q^{65} + 5 q^{66} - 16 q^{67} - 8 q^{68} + 46 q^{69} + 18 q^{70} - 38 q^{71} - 11 q^{73} - 45 q^{74} + 14 q^{75} + 18 q^{76} + 21 q^{77} - 36 q^{78} - q^{79} + 5 q^{80} - 5 q^{81} + 4 q^{82} + 10 q^{83} - 28 q^{84} + 2 q^{85} + 3 q^{86} - 18 q^{87} - 37 q^{88} - 8 q^{89} + 26 q^{90} - 33 q^{91} - 96 q^{92} + 9 q^{93} + 18 q^{94} + 21 q^{95} + 3 q^{96} + 38 q^{97} - 17 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 - q^5 + 4 * q^6 - 5 * q^7 - 5 * q^9 - 13 * q^10 + 11 * q^11 + 8 * q^12 + 14 * q^13 + 3 * q^14 - 2 * q^15 + 2 * q^16 - 5 * q^17 + 2 * q^18 - 9 * q^19 + 24 * q^20 - 7 * q^21 + 10 * q^22 + 23 * q^23 - 14 * q^25 - 18 * q^26 - 10 * q^27 + 7 * q^28 - 36 * q^29 + 13 * q^30 - 9 * q^31 - 3 * q^32 - 11 * q^33 - 4 * q^34 - 5 * q^35 + 16 * q^36 + 7 * q^39 - 31 * q^40 + 6 * q^41 - 3 * q^42 + 24 * q^43 + 33 * q^44 - q^45 - 13 * q^46 - 11 * q^47 + 4 * q^48 + 3 * q^49 + 48 * q^50 + 5 * q^51 - 5 * q^52 + 3 * q^53 - 2 * q^54 - 20 * q^55 - 27 * q^56 - 18 * q^57 + 34 * q^58 + 14 * q^59 + 12 * q^60 - 29 * q^61 - 10 * q^62 - 2 * q^63 + 8 * q^65 + 5 * q^66 - 16 * q^67 - 8 * q^68 + 46 * q^69 + 18 * q^70 - 38 * q^71 - 11 * q^73 - 45 * q^74 + 14 * q^75 + 18 * q^76 + 21 * q^77 - 36 * q^78 - q^79 + 5 * q^80 - 5 * q^81 + 4 * q^82 + 10 * q^83 - 28 * q^84 + 2 * q^85 + 3 * q^86 - 18 * q^87 - 37 * q^88 - 8 * q^89 + 26 * q^90 - 33 * q^91 - 96 * q^92 + 9 * q^93 + 18 * q^94 + 21 * q^95 + 3 * q^96 + 38 * q^97 - 17 * q^98 - 22 * q^99

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