LMFDB - Embedded newform 374.2.g.g.273.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [374,2,Mod(69,374)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(374, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("374.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 374 = 2 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	374.g (of order $5$, degree $4$, 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:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} + 3 x^{17} + 87 x^{16} + 144 x^{15} + 812 x^{14} + 2453 x^{13} + \cdots + 21025 $ x^20 - x^19 + 11x^18 + 3x^17 + 87x^16 + 144x^15 + 812x^14 + 2453x^13 + 7331x^12 + 11173x^11 + 16612x^10 + 24509x^9 + 58717x^8 + 119798x^7 + 196426x^6 + 233079x^5 + 227861x^4 + 175735x^3 + 116835x^2 + 56550x + 21025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			273.2
Root			$1.43989 + 1.04614i$ of defining polynomial
Character	$\chi$	$=$	374.273
Dual form			374.2.g.g.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-1.43989 + 1.04614i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.725811 + 2.23382i) q^{5} +(-0.549988 - 1.69269i) q^{6} +(3.67291 + 2.66852i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.0518163 - 0.159474i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.43989 + 1.04614i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.725811 + 2.23382i) q^{5} +(-0.549988 - 1.69269i) q^{6} +(3.67291 + 2.66852i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.0518163 - 0.159474i) q^{9} -2.34877 q^{10} +(2.96744 - 1.48131i) q^{11} +1.77980 q^{12} +(0.123987 - 0.381594i) q^{13} +(-3.67291 + 2.66852i) q^{14} +(-3.38197 - 2.45714i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.309017 - 0.951057i) q^{17} +(0.135657 + 0.0985604i) q^{18} +(-5.50606 + 4.00039i) q^{19} +(0.725811 - 2.23382i) q^{20} -8.08022 q^{21} +(0.491820 + 3.27996i) q^{22} -3.73562 q^{23} +(-0.549988 + 1.69269i) q^{24} +(-0.418053 + 0.303733i) q^{25} +(0.324603 + 0.235838i) q^{26} +(-1.55774 - 4.79423i) q^{27} +(-1.40293 - 4.31776i) q^{28} +(3.72618 + 2.70723i) q^{29} +(3.38197 - 2.45714i) q^{30} +(-1.02265 + 3.14739i) q^{31} -1.00000 q^{32} +(-2.72313 + 5.23728i) q^{33} +1.00000 q^{34} +(-3.29516 + 10.1414i) q^{35} +(-0.135657 + 0.0985604i) q^{36} +(-5.26411 - 3.82460i) q^{37} +(-2.10313 - 6.47276i) q^{38} +(0.220673 + 0.679160i) q^{39} +(1.90020 + 1.38058i) q^{40} +(9.23827 - 6.71200i) q^{41} +(2.49692 - 7.68474i) q^{42} -6.24378 q^{43} +(-3.27140 - 0.545814i) q^{44} +0.393845 q^{45} +(1.15437 - 3.55279i) q^{46} +(2.52491 - 1.83445i) q^{47} +(-1.43989 - 1.04614i) q^{48} +(4.20611 + 12.9451i) q^{49} +(-0.159682 - 0.491451i) q^{50} +(1.43989 + 1.04614i) q^{51} +(-0.324603 + 0.235838i) q^{52} +(3.98730 - 12.2716i) q^{53} +5.04096 q^{54} +(5.46278 + 5.55357i) q^{55} +4.53996 q^{56} +(3.74314 - 11.5202i) q^{57} +(-3.72618 + 2.70723i) q^{58} +(8.50540 + 6.17954i) q^{59} +(1.29180 + 3.97574i) q^{60} +(-0.842748 - 2.59371i) q^{61} +(-2.67733 - 1.94520i) q^{62} +(0.615876 - 0.447460i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.942403 q^{65} +(-4.13945 - 4.20825i) q^{66} -4.45469 q^{67} +(-0.309017 + 0.951057i) q^{68} +(5.37888 - 3.90798i) q^{69} +(-8.62683 - 6.26776i) q^{70} +(0.973394 + 2.99580i) q^{71} +(-0.0518163 - 0.159474i) q^{72} +(1.12624 + 0.818262i) q^{73} +(5.26411 - 3.82460i) q^{74} +(0.284202 - 0.874683i) q^{75} +6.80587 q^{76} +(14.8521 + 2.47797i) q^{77} -0.714112 q^{78} +(-1.08473 + 3.33846i) q^{79} +(-1.90020 + 1.38058i) q^{80} +(7.66538 + 5.56922i) q^{81} +(3.52871 + 10.8602i) q^{82} +(3.06593 + 9.43596i) q^{83} +(6.53703 + 4.74943i) q^{84} +(1.90020 - 1.38058i) q^{85} +(1.92944 - 5.93819i) q^{86} -8.19741 q^{87} +(1.53002 - 2.94262i) q^{88} -9.88841 q^{89} +(-0.121705 + 0.374569i) q^{90} +(1.47369 - 1.07070i) q^{91} +(3.02218 + 2.19575i) q^{92} +(-1.82011 - 5.60172i) q^{93} +(0.964430 + 2.96821i) q^{94} +(-12.9325 - 9.39601i) q^{95} +(1.43989 - 1.04614i) q^{96} +(-1.65787 + 5.10241i) q^{97} -13.6113 q^{98} +(-0.0824688 - 0.549986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} + q^{6} + 6 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 + q^6 + 6 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} + q^{6} + 6 q^{7} + 5 q^{8} - 6 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 6 q^{14} + 10 q^{15} - 5 q^{16} + 5 q^{17} + 6 q^{18} + 7 q^{19} - 38 q^{21} - 17 q^{22} - 12 q^{23} + q^{24} + 3 q^{25} + 10 q^{26} + 47 q^{27} - 4 q^{28} + 5 q^{29} - 10 q^{30} - 7 q^{31} - 20 q^{32} - 56 q^{33} + 20 q^{34} + 19 q^{35} - 6 q^{36} - 6 q^{37} - 2 q^{38} + 3 q^{39} + 47 q^{41} - 7 q^{42} - 32 q^{43} - 3 q^{44} - 52 q^{45} + 12 q^{46} + 7 q^{47} - q^{48} + 41 q^{49} + 7 q^{50} + q^{51} - 10 q^{52} - 4 q^{53} - 22 q^{54} + 4 q^{56} + 57 q^{57} - 5 q^{58} + 7 q^{59} - 5 q^{60} - 4 q^{61} - 8 q^{62} + 37 q^{63} - 5 q^{64} - 104 q^{65} - 34 q^{66} - 26 q^{67} + 5 q^{68} + 45 q^{69} + 6 q^{70} + 36 q^{71} + 6 q^{72} + 22 q^{73} + 6 q^{74} - 25 q^{75} - 18 q^{76} - 13 q^{77} + 22 q^{78} + 82 q^{79} - 17 q^{81} + 8 q^{82} - 18 q^{83} + 12 q^{84} - 8 q^{86} - 58 q^{87} + 8 q^{88} - 16 q^{89} + 22 q^{90} + 43 q^{91} + 18 q^{92} + 41 q^{93} - 7 q^{94} - 46 q^{95} + q^{96} - 62 q^{97} - 36 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 + q^6 + 6 * q^7 + 5 * q^8 - 6 * q^9 - 3 * q^11 + 4 * q^12 + 10 * q^13 - 6 * q^14 + 10 * q^15 - 5 * q^16 + 5 * q^17 + 6 * q^18 + 7 * q^19 - 38 * q^21 - 17 * q^22 - 12 * q^23 + q^24 + 3 * q^25 + 10 * q^26 + 47 * q^27 - 4 * q^28 + 5 * q^29 - 10 * q^30 - 7 * q^31 - 20 * q^32 - 56 * q^33 + 20 * q^34 + 19 * q^35 - 6 * q^36 - 6 * q^37 - 2 * q^38 + 3 * q^39 + 47 * q^41 - 7 * q^42 - 32 * q^43 - 3 * q^44 - 52 * q^45 + 12 * q^46 + 7 * q^47 - q^48 + 41 * q^49 + 7 * q^50 + q^51 - 10 * q^52 - 4 * q^53 - 22 * q^54 + 4 * q^56 + 57 * q^57 - 5 * q^58 + 7 * q^59 - 5 * q^60 - 4 * q^61 - 8 * q^62 + 37 * q^63 - 5 * q^64 - 104 * q^65 - 34 * q^66 - 26 * q^67 + 5 * q^68 + 45 * q^69 + 6 * q^70 + 36 * q^71 + 6 * q^72 + 22 * q^73 + 6 * q^74 - 25 * q^75 - 18 * q^76 - 13 * q^77 + 22 * q^78 + 82 * q^79 - 17 * q^81 + 8 * q^82 - 18 * q^83 + 12 * q^84 - 8 * q^86 - 58 * q^87 + 8 * q^88 - 16 * q^89 + 22 * q^90 + 43 * q^91 + 18 * q^92 + 41 * q^93 - 7 * q^94 - 46 * q^95 + q^96 - 62 * q^97 - 36 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$.

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−1.43989	+	1.04614i	−0.831319	+	0.603989i	−0.919932	−	0.392077i	$-0.871757\pi$
$3$	−1.43989	+	1.04614i	−0.831319	+	0.603989i	0.0886132	+	0.996066i	$0.471757\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.725811	+	2.23382i	0.324593	+	0.998993i	0.971624	+	0.236530i	$0.0760102\pi$
$5$	0.725811	+	2.23382i	0.324593	+	0.998993i	−0.647031	+	0.762463i	$0.723990\pi$
$6$	−0.549988	−	1.69269i	−0.224532	−	0.691037i
$7$	3.67291	+	2.66852i	1.38823	+	1.00861i	0.996057	+	0.0887144i	$0.0282758\pi$
$7$	3.67291	+	2.66852i	1.38823	+	1.00861i	0.392171	+	0.919892i	$0.371724\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.0518163	−	0.159474i	0.0172721	−	0.0531580i
$10$	−2.34877			−0.742748
$11$	2.96744	−	1.48131i	0.894718	−	0.446632i
$11$	2.96744	−	1.48131i	0.894718	−	0.446632i
$12$	1.77980			0.513783
$13$	0.123987	−	0.381594i	0.0343879	−	0.105835i	−0.932389	−	0.361456i	$-0.882280\pi$
$13$	0.123987	−	0.381594i	0.0343879	−	0.105835i	0.966777	+	0.255621i	$0.0822798\pi$
$14$	−3.67291	+	2.66852i	−0.981626	+	0.713193i
$15$	−3.38197	−	2.45714i	−0.873221	−	0.634432i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	0.135657	+	0.0985604i	0.0319746	+	0.0232309i
$19$	−5.50606	+	4.00039i	−1.26318	+	0.917752i	−0.998909	−	0.0466976i	$-0.985130\pi$
$19$	−5.50606	+	4.00039i	−1.26318	+	0.917752i	−0.264268	+	0.964449i	$0.585130\pi$
$20$	0.725811	−	2.23382i	0.162296	−	0.499497i
$21$	−8.08022			−1.76325
$22$	0.491820	+	3.27996i	0.104856	+	0.699289i
$23$	−3.73562			−0.778932			−0.389466	−	0.921041i	$-0.627340\pi$
$23$	−3.73562			−0.778932			−0.389466	+	0.921041i	$0.627340\pi$
$24$	−0.549988	+	1.69269i	−0.112266	+	0.345519i
$25$	−0.418053	+	0.303733i	−0.0836106	+	0.0607466i
$26$	0.324603	+	0.235838i	0.0636600	+	0.0462517i
$27$	−1.55774	−	4.79423i	−0.299787	−	0.922651i
$28$	−1.40293	−	4.31776i	−0.265128	−	0.815980i
$29$	3.72618	+	2.70723i	0.691934	+	0.502720i	0.877295	−	0.479951i	$-0.159346\pi$
$29$	3.72618	+	2.70723i	0.691934	+	0.502720i	−0.185361	+	0.982670i	$0.559346\pi$
$30$	3.38197	−	2.45714i	0.617460	−	0.448611i
$31$	−1.02265	+	3.14739i	−0.183673	+	0.565289i	−0.999923	−	0.0124108i	$-0.996049\pi$
$31$	−1.02265	+	3.14739i	−0.183673	+	0.565289i	0.816250	+	0.577699i	$0.196049\pi$
$32$	−1.00000			−0.176777
$33$	−2.72313	+	5.23728i	−0.474035	+	0.911693i
$34$	1.00000			0.171499
$35$	−3.29516	+	10.1414i	−0.556983	+	1.71422i
$36$	−0.135657	+	0.0985604i	−0.0226095	+	0.0164267i
$37$	−5.26411	−	3.82460i	−0.865415	−	0.628761i	0.0639380	−	0.997954i	$-0.479634\pi$
$37$	−5.26411	−	3.82460i	−0.865415	−	0.628761i	−0.929353	+	0.369193i	$0.879634\pi$
$38$	−2.10313	−	6.47276i	−0.341172	−	1.05002i
$39$	0.220673	+	0.679160i	0.0353359	+	0.108753i
$40$	1.90020	+	1.38058i	0.300448	+	0.218288i
$41$	9.23827	−	6.71200i	1.44278	−	1.04824i	0.455322	−	0.890327i	$-0.349524\pi$
$41$	9.23827	−	6.71200i	1.44278	−	1.04824i	0.987453	−	0.157911i	$-0.0504759\pi$
$42$	2.49692	−	7.68474i	0.385284	−	1.18578i
$43$	−6.24378			−0.952168			−0.476084	−	0.879400i	$-0.657944\pi$
$43$	−6.24378			−0.952168			−0.476084	+	0.879400i	$0.657944\pi$
$44$	−3.27140	−	0.545814i	−0.493183	−	0.0822846i
$45$	0.393845			0.0587109
$46$	1.15437	−	3.55279i	0.170203	−	0.523830i
$47$	2.52491	−	1.83445i	0.368296	−	0.267583i	−0.388208	−	0.921572i	$-0.626906\pi$
$47$	2.52491	−	1.83445i	0.368296	−	0.267583i	0.756504	+	0.653989i	$0.226906\pi$
$48$	−1.43989	−	1.04614i	−0.207830	−	0.150997i
$49$	4.20611	+	12.9451i	0.600873	+	1.84930i
$50$	−0.159682	−	0.491451i	−0.0225824	−	0.0695016i
$51$	1.43989	+	1.04614i	0.201624	+	0.146489i
$52$	−0.324603	+	0.235838i	−0.0450144	+	0.0327049i
$53$	3.98730	−	12.2716i	0.547697	−	1.68564i	−0.166791	−	0.985992i	$-0.553341\pi$
$53$	3.98730	−	12.2716i	0.547697	−	1.68564i	0.714489	−	0.699647i	$-0.246659\pi$
$54$	5.04096			0.685987
$55$	5.46278	+	5.55357i	0.736601	+	0.748844i
$56$	4.53996			0.606678
$57$	3.74314	−	11.5202i	0.495791	−	1.52589i
$58$	−3.72618	+	2.70723i	−0.489271	+	0.355476i
$59$	8.50540	+	6.17954i	1.10731	+	0.804507i	0.982238	−	0.187641i	$-0.0600841\pi$
$59$	8.50540	+	6.17954i	1.10731	+	0.804507i	0.125071	+	0.992148i	$0.460084\pi$
$60$	1.29180	+	3.97574i	0.166770	+	0.513266i
$61$	−0.842748	−	2.59371i	−0.107903	−	0.332091i	0.882498	−	0.470316i	$-0.155860\pi$
$61$	−0.842748	−	2.59371i	−0.107903	−	0.332091i	−0.990401	+	0.138226i	$0.955860\pi$
$62$	−2.67733	−	1.94520i	−0.340022	−	0.247040i
$63$	0.615876	−	0.447460i	0.0775931	−	0.0563747i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.942403			0.116891
$66$	−4.13945	−	4.20825i	−0.509532	−	0.518000i
$67$	−4.45469			−0.544227			−0.272114	−	0.962265i	$-0.587723\pi$
$67$	−4.45469			−0.544227			−0.272114	+	0.962265i	$0.587723\pi$
$68$	−0.309017	+	0.951057i	−0.0374738	+	0.115333i
$69$	5.37888	−	3.90798i	0.647541	−	0.470466i
$70$	−8.62683	−	6.26776i	−1.03110	−	0.749140i
$71$	0.973394	+	2.99580i	0.115521	+	0.355536i	0.992055	−	0.125803i	$-0.0401507\pi$
$71$	0.973394	+	2.99580i	0.115521	+	0.355536i	−0.876535	+	0.481339i	$0.840151\pi$
$72$	−0.0518163	−	0.159474i	−0.00610660	−	0.0187942i
$73$	1.12624	+	0.818262i	0.131816	+	0.0957703i	0.651740	−	0.758443i	$-0.274039\pi$
$73$	1.12624	+	0.818262i	0.131816	+	0.0957703i	−0.519923	+	0.854213i	$0.674039\pi$
$74$	5.26411	−	3.82460i	0.611941	−	0.444601i
$75$	0.284202	−	0.874683i	0.0328168	−	0.101000i
$76$	6.80587			0.780686
$77$	14.8521	+	2.47797i	1.69255	+	0.282391i
$78$	−0.714112			−0.0808572
$79$	−1.08473	+	3.33846i	−0.122042	+	0.375606i	−0.993351	−	0.115129i	$-0.963272\pi$
$79$	−1.08473	+	3.33846i	−0.122042	+	0.375606i	0.871309	+	0.490735i	$0.163272\pi$
$80$	−1.90020	+	1.38058i	−0.212449	+	0.154353i
$81$	7.66538	+	5.56922i	0.851708	+	0.618802i
$82$	3.52871	+	10.8602i	0.389680	+	1.19931i
$83$	3.06593	+	9.43596i	0.336529	+	1.03573i	0.965964	+	0.258677i	$0.0832866\pi$
$83$	3.06593	+	9.43596i	0.336529	+	1.03573i	−0.629434	+	0.777054i	$0.716713\pi$
$84$	6.53703	+	4.74943i	0.713249	+	0.518205i
$85$	1.90020	−	1.38058i	0.206105	−	0.149744i
$86$	1.92944	−	5.93819i	0.208056	−	0.640332i
$87$	−8.19741			−0.878855
$88$	1.53002	−	2.94262i	0.163101	−	0.313685i
$89$	−9.88841			−1.04817			−0.524085	−	0.851666i	$-0.675592\pi$
$89$	−9.88841			−1.04817			−0.524085	+	0.851666i	$0.675592\pi$
$90$	−0.121705	+	0.374569i	−0.0128288	+	0.0394830i
$91$	1.47369	−	1.07070i	0.154484	−	0.112239i
$92$	3.02218	+	2.19575i	0.315084	+	0.228922i
$93$	−1.82011	−	5.60172i	−0.188737	−	0.580872i
$94$	0.964430	+	2.96821i	0.0994734	+	0.306148i
$95$	−12.9325	−	9.39601i	−1.32685	−	0.964010i
$96$	1.43989	−	1.04614i	0.146958	−	0.106771i
$97$	−1.65787	+	5.10241i	−0.168331	+	0.518071i	−0.999266	−	0.0382987i	$-0.987806\pi$
$97$	−1.65787	+	5.10241i	−0.168331	+	0.518071i	0.830935	+	0.556370i	$0.187806\pi$
$98$	−13.6113			−1.37494
$99$	−0.0824688	−	0.549986i	−0.00828842	−	0.0552757i
$100$	0.516742			0.0516742
$101$	3.40553	−	10.4811i	0.338862	−	1.04291i	−0.625926	−	0.779883i	$-0.715279\pi$
$101$	3.40553	−	10.4811i	0.338862	−	1.04291i	0.964788	−	0.263029i	$-0.0847214\pi$
$102$	−1.43989	+	1.04614i	−0.142570	+	0.103583i
$103$	15.3267	+	11.1355i	1.51018	+	1.09721i	0.966095	+	0.258186i	$0.0831247\pi$
$103$	15.3267	+	11.1355i	1.51018	+	1.09721i	0.544089	+	0.839027i	$0.316875\pi$
$104$	−0.123987	−	0.381594i	−0.0121580	−	0.0374184i
$105$	−5.86471	−	18.0497i	−0.572337	−	1.76147i
$106$	10.4389	+	7.58429i	1.01391	+	0.736651i
$107$	−9.83396	+	7.14479i	−0.950685	+	0.690713i	−0.950969	−	0.309287i	$-0.899910\pi$
$107$	−9.83396	+	7.14479i	−0.950685	+	0.690713i	0.000284112		1.00000i	$0.499910\pi$
$108$	−1.55774	+	4.79423i	−0.149894	+	0.461325i
$109$	−0.568643			−0.0544661			−0.0272330	−	0.999629i	$-0.508670\pi$
$109$	−0.568643			−0.0544661			−0.0272330	+	0.999629i	$0.508670\pi$
$110$	−6.96985	+	3.47926i	−0.664550	+	0.331735i
$111$	11.5808			1.09920
$112$	−1.40293	+	4.31776i	−0.132564	+	0.407990i
$113$	14.8315	−	10.7757i	1.39523	−	1.01370i	0.399964	−	0.916531i	$-0.369023\pi$
$113$	14.8315	−	10.7757i	1.39523	−	1.01370i	0.995268	−	0.0971642i	$-0.0309772\pi$
$114$	9.79968	+	7.11988i	0.917824	+	0.666838i
$115$	−2.71136	−	8.34470i	−0.252835	−	0.778148i
$116$	−1.42327	−	4.38039i	−0.132148	−	0.406709i
$117$	−0.0544298	−	0.0395456i	−0.00503204	−	0.00365599i
$118$	−8.50540	+	6.17954i	−0.782986	+	0.568872i
$119$	1.40293	−	4.31776i	0.128606	−	0.395808i
$120$	−4.18034			−0.381611
$121$	6.61144	−	8.79141i	0.601040	−	0.799219i
$122$	2.72719			0.246908
$123$	−6.28038	+	19.3290i	−0.566283	+	1.74284i
$124$	2.67733	−	1.94520i	0.240432	−	0.174684i
$125$	8.51908	+	6.18947i	0.761970	+	0.553603i
$126$	0.235244	+	0.724006i	0.0209572	+	0.0644996i
$127$	−5.34695	−	16.4562i	−0.474465	−	1.46025i	−0.846677	−	0.532106i	$-0.821401\pi$
$127$	−5.34695	−	16.4562i	−0.474465	−	1.46025i	0.372212	−	0.928148i	$-0.378599\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	8.99034	−	6.53187i	0.791555	−	0.575099i
$130$	−0.291219	+	0.896279i	−0.0255416	+	0.0786088i
$131$	−6.34476			−0.554344			−0.277172	−	0.960820i	$-0.589397\pi$
$131$	−6.34476			−0.554344			−0.277172	+	0.960820i	$0.589397\pi$
$132$	5.28145	−	2.63643i	0.459691	−	0.229472i
$133$	−30.8984			−2.67923
$134$	1.37658	−	4.23667i	0.118918	−	0.365992i
$135$	9.57882	−	6.95942i	0.824413	−	0.598971i
$136$	−0.809017	−	0.587785i	−0.0693726	−	0.0504022i
$137$	4.93333	+	15.1832i	0.421483	+	1.29719i	0.906322	+	0.422587i	$0.138878\pi$
$137$	4.93333	+	15.1832i	0.421483	+	1.29719i	−0.484839	+	0.874603i	$0.661122\pi$
$138$	2.05455	+	6.32325i	0.174895	+	0.538271i
$139$	−1.86062	−	1.35182i	−0.157816	−	0.114660i	0.506075	−	0.862490i	$-0.331096\pi$
$139$	−1.86062	−	1.35182i	−0.157816	−	0.114660i	−0.663891	+	0.747830i	$0.731096\pi$
$140$	8.62683	−	6.26776i	0.729100	−	0.529722i
$141$	−1.71649	+	5.28282i	−0.144555	+	0.444893i
$142$	−3.14997			−0.264339
$143$	−0.197334	−	1.31602i	−0.0165019	−	0.110051i
$144$	0.167681			0.0139734
$145$	−3.34295	+	10.2885i	−0.277617	+	0.854417i
$146$	−1.12624	+	0.818262i	−0.0932083	+	0.0677198i
$147$	−19.5987	−	14.2393i	−1.61647	−	1.17443i
$148$	2.01071	+	6.18833i	0.165279	+	0.508678i
$149$	−3.65355	−	11.2445i	−0.299310	−	0.921182i	−0.981739	−	0.190230i	$-0.939077\pi$
$149$	−3.65355	−	11.2445i	−0.299310	−	0.921182i	0.682429	−	0.730952i	$-0.260923\pi$
$150$	0.744050	+	0.540584i	0.0607514	+	0.0441385i
$151$	6.71569	−	4.87923i	0.546515	−	0.397066i	−0.279984	−	0.960005i	$-0.590329\pi$
$151$	6.71569	−	4.87923i	0.546515	−	0.397066i	0.826499	+	0.562938i	$0.190329\pi$
$152$	−2.10313	+	6.47276i	−0.170586	+	0.525010i
$153$	−0.167681			−0.0135562
$154$	−6.94623	+	13.3594i	−0.559743	+	1.07653i
$155$	−7.77295			−0.624339
$156$	0.220673	−	0.679160i	0.0176679	−	0.0543764i
$157$	−6.75615	+	4.90863i	−0.539200	+	0.391752i	−0.823788	−	0.566898i	$-0.808143\pi$
$157$	−6.75615	+	4.90863i	−0.539200	+	0.391752i	0.284588	+	0.958650i	$0.408143\pi$
$158$	−2.83986	−	2.06328i	−0.225927	−	0.164146i
$159$	7.09658	+	21.8410i	0.562796	+	1.73211i
$160$	−0.725811	−	2.23382i	−0.0573804	−	0.176599i
$161$	−13.7206	−	9.96860i	−1.08133	−	0.785636i
$162$	−7.66538	+	5.56922i	−0.602249	+	0.437559i
$163$	2.17999	−	6.70932i	0.170750	−	0.525514i	−0.828664	−	0.559746i	$-0.810899\pi$
$163$	2.17999	−	6.70932i	0.170750	−	0.525514i	0.999414	+	0.0342321i	$0.0108986\pi$
$164$	−11.4191			−0.891684
$165$	−13.6756	−	2.28169i	−1.06464	−	0.177629i
$166$	−9.92155			−0.770062
$167$	3.78564	−	11.6510i	0.292942	−	0.901582i	−0.690963	−	0.722890i	$-0.742813\pi$
$167$	3.78564	−	11.6510i	0.292942	−	0.901582i	0.983905	−	0.178692i	$-0.0571866\pi$
$168$	−6.53703	+	4.74943i	−0.504343	+	0.366427i
$169$	10.3870	+	7.54658i	0.798998	+	0.580506i
$170$	0.725811	+	2.23382i	0.0556672	+	0.171326i
$171$	0.352654	+	1.08536i	0.0269682	+	0.0829995i
$172$	5.05133	+	3.67000i	0.385160	+	0.279835i
$173$	1.16162	−	0.843970i	0.0883167	−	0.0641658i	−0.542751	−	0.839894i	$-0.682617\pi$
$173$	1.16162	−	0.843970i	0.0883167	−	0.0641658i	0.631067	+	0.775728i	$0.282617\pi$
$174$	2.53314	−	7.79620i	0.192037	−	0.591029i
$175$	−2.34599			−0.177340
$176$	2.32580	+	2.36446i	0.175314	+	0.178228i
$177$	−18.7115			−1.40644
$178$	3.05569	−	9.40443i	0.229033	−	0.704892i
$179$	11.6805	−	8.48637i	0.873041	−	0.634301i	−0.0583603	−	0.998296i	$-0.518587\pi$
$179$	11.6805	−	8.48637i	0.873041	−	0.634301i	0.931401	+	0.363994i	$0.118587\pi$
$180$	−0.318627	−	0.231496i	−0.0237491	−	0.0172547i
$181$	3.01943	+	9.29286i	0.224433	+	0.690733i	0.998349	+	0.0574447i	$0.0182953\pi$
$181$	3.01943	+	9.29286i	0.224433	+	0.690733i	−0.773916	+	0.633288i	$0.781705\pi$
$182$	0.562898	+	1.73242i	0.0417248	+	0.128416i
$183$	3.92684	+	2.85302i	0.290281	+	0.210901i
$184$	−3.02218	+	2.19575i	−0.222798	+	0.161872i
$185$	4.72271	−	14.5350i	0.347220	−	1.06863i
$186$	5.89000			0.431876
$187$	−2.32580	−	2.36446i	−0.170079	−	0.172906i
$188$	−3.12096			−0.227619
$189$	7.07208	−	21.7656i	0.514418	−	1.58322i
$190$	12.9325	−	9.39601i	0.938222	−	0.681658i
$191$	−1.25527	−	0.912010i	−0.0908284	−	0.0659907i	0.541444	−	0.840737i	$-0.317878\pi$
$191$	−1.25527	−	0.912010i	−0.0908284	−	0.0659907i	−0.632273	+	0.774746i	$0.717878\pi$
$192$	0.549988	+	1.69269i	0.0396920	+	0.122159i
$193$	1.84495	+	5.67818i	0.132802	+	0.408724i	0.995242	−	0.0974365i	$-0.0310643\pi$
$193$	1.84495	+	5.67818i	0.132802	+	0.408724i	−0.862439	+	0.506161i	$0.831064\pi$
$194$	−4.34037	−	3.15346i	−0.311620	−	0.226405i
$195$	−1.35695	+	0.985885i	−0.0971735	+	0.0706007i
$196$	4.20611	−	12.9451i	0.300436	−	0.924648i
$197$	−4.12660			−0.294008			−0.147004	−	0.989136i	$-0.546963\pi$
$197$	−4.12660			−0.294008			−0.147004	+	0.989136i	$0.546963\pi$
$198$	0.548552	+	0.0915226i	0.0389839	+	0.00650423i
$199$	−2.45497			−0.174028			−0.0870142	−	0.996207i	$-0.527733\pi$
$199$	−2.45497			−0.174028			−0.0870142	+	0.996207i	$0.527733\pi$
$200$	−0.159682	+	0.491451i	−0.0112912	+	0.0347508i
$201$	6.41426	−	4.66023i	0.452427	−	0.328707i
$202$	8.91578	+	6.47769i	0.627312	+	0.455769i
$203$	6.46161	+	19.8868i	0.453516	+	1.39578i
$204$	−0.549988	−	1.69269i	−0.0385069	−	0.118512i
$205$	21.6986	+	15.7650i	1.51550	+	1.10107i
$206$	−15.3267	+	11.1355i	−1.06786	+	0.775847i
$207$	−0.193566	+	0.595735i	−0.0134538	+	0.0414065i
$208$	0.401232			0.0278204
$209$	−10.4131	+	20.0271i	−0.720290	+	1.38530i
$210$	18.9786			1.30965
$211$	−1.66265	+	5.11712i	−0.114462	+	0.352277i	−0.991834	−	0.127532i	$-0.959294\pi$
$211$	−1.66265	+	5.11712i	−0.114462	+	0.352277i	0.877373	+	0.479810i	$0.159294\pi$
$212$	−10.4389	+	7.58429i	−0.716945	+	0.520891i
$213$	−4.53560	−	3.29531i	−0.310774	−	0.225791i
$214$	−3.75624	−	11.5605i	−0.256771	−	0.790260i
$215$	−4.53181	−	13.9475i	−0.309067	−	0.951210i
$216$	−4.07822	−	2.96300i	−0.277488	−	0.201607i
$217$	−12.1550	+	8.83112i	−0.825134	+	0.599495i
$218$	0.175720	−	0.540811i	0.0119013	−	0.0366284i
$219$	−2.47767			−0.167426
$220$	−1.15517	−	7.70388i	−0.0778818	−	0.519395i
$221$	−0.401232			−0.0269898
$222$	−3.57866	+	11.0140i	−0.240184	+	0.739210i
$223$	7.01729	−	5.09836i	0.469913	−	0.341412i	−0.327495	−	0.944853i	$-0.606204\pi$
$223$	7.01729	−	5.09836i	0.469913	−	0.341412i	0.797407	+	0.603441i	$0.206204\pi$
$224$	−3.67291	−	2.66852i	−0.245406	−	0.178298i
$225$	0.0267756	+	0.0824069i	0.00178504	+	0.00549379i
$226$	5.66514	+	17.4355i	0.376839	+	1.15979i
$227$	−22.6098	−	16.4270i	−1.50067	−	1.09030i	−0.970115	−	0.242646i	$-0.921985\pi$
$227$	−22.6098	−	16.4270i	−1.50067	−	1.09030i	−0.530552	−	0.847652i	$-0.678015\pi$
$228$	−9.79968	+	7.11988i	−0.648999	+	0.471526i
$229$	−6.75050	+	20.7759i	−0.446086	+	1.37291i	0.435203	+	0.900333i	$0.356677\pi$
$229$	−6.75050	+	20.7759i	−0.446086	+	1.37291i	−0.881288	+	0.472579i	$0.843323\pi$
$230$	8.77414			0.578550
$231$	−23.9776	+	11.9693i	−1.57761	+	0.787523i
$232$	4.60581			0.302386
$233$	−0.0211658	+	0.0651416i	−0.00138662	+	0.00426757i	−0.951747	−	0.306882i	$-0.900714\pi$
$233$	−0.0211658	+	0.0651416i	−0.00138662	+	0.00426757i	0.950361	+	0.311150i	$0.100714\pi$
$234$	0.0544298	−	0.0395456i	0.00355819	−	0.00258517i
$235$	5.93045	+	4.30872i	0.386860	+	0.281070i
$236$	−3.24877	−	9.99870i	−0.211477	−	0.650860i
$237$	−1.93060	−	5.94178i	−0.125406	−	0.385960i
$238$	3.67291	+	2.66852i	0.238079	+	0.172975i
$239$	5.95847	−	4.32908i	0.385421	−	0.280025i	−0.378155	−	0.925742i	$-0.623441\pi$
$239$	5.95847	−	4.32908i	0.385421	−	0.280025i	0.763577	+	0.645717i	$0.223441\pi$
$240$	1.29180	−	3.97574i	0.0833852	−	0.256633i
$241$	23.8852			1.53858			0.769291	−	0.638899i	$-0.220610\pi$
$241$	23.8852			1.53858			0.769291	+	0.638899i	$0.220610\pi$
$242$	6.31808	+	9.00455i	0.406142	+	0.578834i
$243$	−1.74059			−0.111659
$244$	−0.842748	+	2.59371i	−0.0539514	+	0.166045i
$245$	−25.8641	+	18.7914i	−1.65240	+	1.20054i
$246$	−16.4423	−	11.9460i	−1.04832	−	0.761649i
$247$	0.843842	+	2.59708i	0.0536924	+	0.165248i
$248$	1.02265	+	3.14739i	0.0649383	+	0.199860i
$249$	−14.2859	−	10.3793i	−0.905333	−	0.657763i
$250$	−8.51908	+	6.18947i	−0.538794	+	0.391457i
$251$	−4.08246	+	12.5645i	−0.257683	+	0.793066i	0.735606	+	0.677409i	$0.236897\pi$
$251$	−4.08246	+	12.5645i	−0.257683	+	0.793066i	−0.993289	+	0.115657i	$0.963103\pi$
$252$	−0.761265			−0.0479552
$253$	−11.0853	+	5.53362i	−0.696924	+	0.347896i
$254$	17.3031			1.08569
$255$	−1.29180	+	3.97574i	−0.0808955	+	0.248971i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	12.7256	+	9.24568i	0.793800	+	0.576730i	0.909089	−	0.416602i	$-0.136779\pi$
$257$	12.7256	+	9.24568i	0.793800	+	0.576730i	−0.115289	+	0.993332i	$0.536779\pi$
$258$	3.43400	+	10.5688i	0.213792	+	0.657983i
$259$	−9.12855	−	28.0948i	−0.567221	−	1.74573i
$260$	−0.762420	−	0.553931i	−0.0472833	−	0.0343533i
$261$	0.624809	−	0.453950i	0.0386747	−	0.0280988i
$262$	1.96064	−	6.03422i	0.121129	−	0.372795i
$263$	−29.4792			−1.81777			−0.908883	−	0.417051i	$-0.863064\pi$
$263$	−29.4792			−1.81777			−0.908883	+	0.417051i	$0.863064\pi$
$264$	0.875340	+	5.83766i	0.0538734	+	0.359283i
$265$	30.3066			1.86172
$266$	9.54812	−	29.3861i	0.585433	−	1.80178i
$267$	14.2382	−	10.3446i	0.871363	−	0.633082i
$268$	3.60392	+	2.61840i	0.220145	+	0.159944i
$269$	−0.606177	−	1.86562i	−0.0369593	−	0.113749i	0.930875	−	0.365338i	$-0.119047\pi$
$269$	−0.606177	−	1.86562i	−0.0369593	−	0.113749i	−0.967834	+	0.251590i	$0.919047\pi$
$270$	3.65878	+	11.2606i	0.222666	+	0.685297i
$271$	16.4509	+	11.9523i	0.999321	+	0.726049i	0.961943	−	0.273252i	$-0.0880992\pi$
$271$	16.4509	+	11.9523i	0.999321	+	0.726049i	0.0373788	+	0.999301i	$0.488099\pi$
$272$	0.809017	−	0.587785i	0.0490539	−	0.0356397i
$273$	−1.00185	+	3.08336i	−0.0606344	+	0.186614i
$274$	−15.9646			−0.964456
$275$	−0.790625	+	1.52058i	−0.0476765	+	0.0916942i
$276$	−6.64866			−0.400202
$277$	4.39059	−	13.5129i	0.263805	−	0.811909i	−0.728161	−	0.685406i	$-0.759625\pi$
$277$	4.39059	−	13.5129i	0.263805	−	0.811909i	0.991966	−	0.126503i	$-0.0403753\pi$
$278$	1.86062	−	1.35182i	0.111592	−	0.0810767i
$279$	0.448938	+	0.326172i	0.0268772	+	0.0195274i
$280$	3.29516	+	10.1414i	0.196923	+	0.606067i
$281$	−2.66298	−	8.19580i	−0.158860	−	0.488921i	0.839672	−	0.543094i	$-0.182747\pi$
$281$	−2.66298	−	8.19580i	−0.158860	−	0.488921i	−0.998532	+	0.0541739i	$0.982747\pi$
$282$	−4.49383	−	3.26496i	−0.267604	−	0.194425i
$283$	−15.3586	+	11.1586i	−0.912972	+	0.663313i	−0.941765	−	0.336273i	$-0.890834\pi$
$283$	−15.3586	+	11.1586i	−0.912972	+	0.663313i	0.0287931	+	0.999585i	$0.490834\pi$
$284$	0.973394	−	2.99580i	0.0577603	−	0.177768i
$285$	28.4509			1.68528
$286$	1.31259	+	0.218998i	0.0776152	+	0.0129496i
$287$	51.8424			3.06016
$288$	−0.0518163	+	0.159474i	−0.00305330	+	0.00939710i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−8.75195	−	6.35867i	−0.513932	−	0.373394i
$291$	−2.95068	−	9.08126i	−0.172972	−	0.532353i
$292$	−0.430186	−	1.32398i	−0.0251747	−	0.0774798i
$293$	−0.786980	−	0.571774i	−0.0459759	−	0.0334034i	0.564560	−	0.825392i	$-0.309046\pi$
$293$	−0.786980	−	0.571774i	−0.0459759	−	0.0334034i	−0.610536	+	0.791989i	$0.709046\pi$
$294$	19.5987	−	14.2393i	1.14302	−	0.830451i
$295$	−7.63064	+	23.4847i	−0.444273	+	1.36733i
$296$	−6.50680			−0.378200
$297$	−11.7243	−	11.9191i	−0.680310	−	0.691617i
$298$	11.8231			0.684895
$299$	−0.463171	+	1.42549i	−0.0267858	+	0.0824384i
$300$	−0.744050	+	0.540584i	−0.0429577	+	0.0312106i
$301$	−22.9328	−	16.6617i	−1.32183	−	0.960363i
$302$	2.56517	+	7.89477i	0.147609	+	0.454293i
$303$	6.06115	+	18.6543i	0.348204	+	1.07166i
$304$	−5.50606	−	4.00039i	−0.315794	−	0.229438i
$305$	5.18220	−	3.76509i	0.296732	−	0.215588i
$306$	0.0518163	−	0.159474i	0.00296214	−	0.00911652i
$307$	28.8312			1.64548			0.822741	−	0.568416i	$-0.192444\pi$
$307$	28.8312			1.64548			0.822741	+	0.568416i	$0.192444\pi$
$308$	−10.5590	−	10.7345i	−0.601657	−	0.611657i
$309$	−33.7180			−1.91815
$310$	2.40197	−	7.39252i	0.136423	−	0.419867i
$311$	6.86551	−	4.98809i	0.389308	−	0.282848i	−0.375864	−	0.926675i	$-0.622654\pi$
$311$	6.86551	−	4.98809i	0.389308	−	0.282848i	0.765172	+	0.643826i	$0.222654\pi$
$312$	0.577728	+	0.419744i	0.0327074	+	0.0237633i
$313$	−0.918124	−	2.82569i	−0.0518954	−	0.159718i	0.921750	−	0.387785i	$-0.126760\pi$
$313$	−0.918124	−	2.82569i	−0.0518954	−	0.159718i	−0.973645	+	0.228067i	$0.926760\pi$
$314$	−2.58062	−	7.94233i	−0.145633	−	0.448212i
$315$	1.44655	+	1.05098i	0.0815041	+	0.0592162i
$316$	2.83986	−	2.06328i	0.159755	−	0.116069i
$317$	4.41382	−	13.5844i	0.247905	−	0.762973i	−0.747240	−	0.664554i	$-0.768621\pi$
$317$	4.41382	−	13.5844i	0.247905	−	0.762973i	0.995145	−	0.0984191i	$-0.0313786\pi$
$318$	−22.9650			−1.28781
$319$	15.0675	+	2.51392i	0.843616	+	0.140752i
$320$	2.34877			0.131300
$321$	6.68534	−	20.5754i	0.373140	−	1.14841i
$322$	13.7206	−	9.96860i	0.764619	−	0.555528i
$323$	5.50606	+	4.00039i	0.306365	+	0.222587i
$324$	−2.92791	−	9.01119i	−0.162662	−	0.500622i
$325$	0.0640695	+	0.197186i	0.00355394	+	0.0109379i
$326$	5.70729	+	4.14659i	0.316097	+	0.229658i
$327$	0.818781	−	0.594879i	0.0452787	−	0.0328969i
$328$	3.52871	−	10.8602i	0.194840	−	0.599656i
$329$	14.1690			0.781165
$330$	6.39601	−	12.3012i	0.352089	−	0.677158i
$331$	28.2359			1.55199			0.775993	−	0.630742i	$-0.217249\pi$
$331$	28.2359			1.55199			0.775993	+	0.630742i	$0.217249\pi$
$332$	3.06593	−	9.43596i	0.168265	−	0.517865i
$333$	−0.882691	+	0.641313i	−0.0483712	+	0.0351437i
$334$	9.91094	+	7.20072i	0.542302	+	0.394006i
$335$	−3.23327	−	9.95097i	−0.176652	−	0.543680i
$336$	−2.49692	−	7.68474i	−0.136218	−	0.419237i
$337$	−23.3488	−	16.9639i	−1.27189	−	0.924081i	−0.272613	−	0.962124i	$-0.587888\pi$
$337$	−23.3488	−	16.9639i	−1.27189	−	0.924081i	−0.999276	+	0.0380427i	$0.987888\pi$
$338$	−10.3870	+	7.54658i	−0.564977	+	0.410480i
$339$	−10.0828	+	31.0317i	−0.547622	+	1.68541i
$340$	−2.34877			−0.127380
$341$	1.62761	+	10.8546i	0.0881401	+	0.587808i
$342$	−1.14121			−0.0617098
$343$	−9.27510	+	28.5458i	−0.500808	+	1.54133i
$344$	−5.05133	+	3.67000i	−0.272349	+	0.197873i
$345$	12.6338	+	9.17897i	0.680179	+	0.494179i
$346$	0.443701	+	1.36557i	0.0238535	+	0.0734136i
$347$	−3.68413	−	11.3386i	−0.197774	−	0.608687i	−0.999933	−	0.0115758i	$-0.996315\pi$
$347$	−3.68413	−	11.3386i	−0.197774	−	0.608687i	0.802159	−	0.597111i	$-0.203685\pi$
$348$	6.63185	+	4.81832i	0.355504	+	0.258289i
$349$	−10.3610	+	7.52773i	−0.554613	+	0.402950i	−0.829484	−	0.558531i	$-0.811365\pi$
$349$	−10.3610	+	7.52773i	−0.554613	+	0.402950i	0.274870	+	0.961481i	$0.411365\pi$
$350$	0.724950	−	2.23117i	0.0387502	−	0.119261i
$351$	−2.02259			−0.107958
$352$	−2.96744	+	1.48131i	−0.158165	+	0.0789541i
$353$	27.6343			1.47082			0.735412	−	0.677620i	$-0.236989\pi$
$353$	27.6343			1.47082			0.735412	+	0.677620i	$0.236989\pi$
$354$	5.78216	−	17.7957i	0.307318	−	0.945829i
$355$	−5.98557	+	4.34877i	−0.317681	+	0.230809i
$356$	7.99989	+	5.81226i	0.423993	+	0.308049i
$357$	2.49692	+	7.68474i	0.132151	+	0.406720i
$358$	4.46155	+	13.7312i	0.235800	+	0.725719i
$359$	28.3608	+	20.6053i	1.49683	+	1.08751i	0.971624	+	0.236530i	$0.0760103\pi$
$359$	28.3608	+	20.6053i	1.49683	+	1.08751i	0.525202	+	0.850977i	$0.323990\pi$
$360$	0.318627	−	0.231496i	0.0167931	−	0.0122009i
$361$	8.44228	−	25.9827i	0.444331	−	1.36751i
$362$	−9.77109			−0.513557
$363$	−0.322686	+	19.5751i	−0.0169366	+	1.02743i
$364$	−1.82158			−0.0954766
$365$	−1.01041	+	3.10972i	−0.0528872	+	0.162770i
$366$	−3.92684	+	2.85302i	−0.205259	+	0.149130i
$367$	−14.1219	−	10.2601i	−0.737156	−	0.535575i	0.154663	−	0.987967i	$-0.450571\pi$
$367$	−14.1219	−	10.2601i	−0.737156	−	0.535575i	−0.891819	+	0.452392i	$0.850571\pi$
$368$	−1.15437	−	3.55279i	−0.0601758	−	0.185202i
$369$	−0.591697	−	1.82106i	−0.0308025	−	0.0948003i
$370$	12.3642	+	8.98312i	0.642785	+	0.467010i
$371$	47.3921	−	34.4324i	2.46048	−	1.78764i
$372$	−1.82011	+	5.60172i	−0.0943683	+	0.290436i
$373$	−31.0299			−1.60667			−0.803333	−	0.595530i	$-0.796942\pi$
$373$	−31.0299			−1.60667			−0.803333	+	0.595530i	$0.796942\pi$
$374$	2.96744	−	1.48131i	0.153443	−	0.0765967i
$375$	−18.7416			−0.967810
$376$	0.964430	−	2.96821i	0.0497367	−	0.153074i
$377$	1.49506	−	1.08623i	0.0769996	−	0.0559435i
$378$	18.5150	+	13.4519i	0.952307	+	0.691891i
$379$	−8.99054	−	27.6700i	−0.461813	−	1.42131i	−0.862947	−	0.505295i	$-0.831384\pi$
$379$	−8.99054	−	27.6700i	−0.461813	−	1.42131i	0.401134	−	0.916019i	$-0.368616\pi$
$380$	4.93977	+	15.2031i	0.253405	+	0.779900i
$381$	24.9145	+	18.1015i	1.27641	+	0.927365i
$382$	1.25527	−	0.912010i	0.0642254	−	0.0466625i
$383$	−2.87596	+	8.85129i	−0.146955	+	0.452280i	−0.997257	−	0.0740145i	$-0.976419\pi$
$383$	−2.87596	+	8.85129i	−0.146955	+	0.452280i	0.850303	+	0.526294i	$0.176419\pi$
$384$	−1.77980			−0.0908249
$385$	5.24444	+	34.9753i	0.267282	+	1.78251i
$386$	−5.97039			−0.303885
$387$	−0.323529	+	0.995721i	−0.0164459	+	0.0506154i
$388$	4.34037	−	3.15346i	0.220349	−	0.160093i
$389$	0.585979	+	0.425739i	0.0297103	+	0.0215858i	0.602541	−	0.798088i	$-0.294155\pi$
$389$	0.585979	+	0.425739i	0.0297103	+	0.0215858i	−0.572831	+	0.819673i	$0.694155\pi$
$390$	−0.518310	−	1.59519i	−0.0262457	−	0.0807758i
$391$	1.15437	+	3.55279i	0.0583791	+	0.179672i
$392$	11.0117	+	8.00049i	0.556177	+	0.404086i
$393$	9.13573	−	6.63750i	0.460837	−	0.334817i
$394$	1.27519	−	3.92463i	0.0642431	−	0.197720i
$395$	−8.24481			−0.414842
$396$	−0.256555	+	0.493422i	−0.0128924	+	0.0247954i
$397$	12.4930			0.627005			0.313503	−	0.949587i	$-0.398498\pi$
$397$	12.4930			0.627005			0.313503	+	0.949587i	$0.398498\pi$
$398$	0.758628	−	2.33482i	0.0380266	−	0.117034i
$399$	44.4902	−	32.3240i	2.22729	−	1.61822i
$400$	−0.418053	−	0.303733i	−0.0209026	−	0.0151867i
$401$	−3.30470	−	10.1708i	−0.165029	−	0.507906i	0.834010	−	0.551750i	$-0.186040\pi$
$401$	−3.30470	−	10.1708i	−0.165029	−	0.507906i	−0.999038	+	0.0438437i	$0.986040\pi$
$402$	2.45003	+	7.54041i	0.122196	+	0.376081i
$403$	1.07423	+	0.780475i	0.0535113	+	0.0388782i
$404$	−8.91578	+	6.47769i	−0.443577	+	0.322277i
$405$	−6.87701	+	21.1653i	−0.341721	+	1.05171i
$406$	−20.9102			−1.03776
$407$	−21.2864	−	3.55150i	−1.05513	−	0.176041i
$408$	1.77980			0.0881131
$409$	4.77865	−	14.7072i	0.236289	−	0.727223i	−0.760659	−	0.649152i	$-0.775124\pi$
$409$	4.77865	−	14.7072i	0.236289	−	0.727223i	0.996948	−	0.0780709i	$-0.0248760\pi$
$410$	−21.6986	+	15.7650i	−1.07162	+	0.778576i
$411$	−22.9872	−	16.7012i	−1.13388	−	0.823809i
$412$	−5.85428	−	18.0176i	−0.288420	−	0.887664i
$413$	14.7493	+	45.3937i	0.725766	+	2.23368i
$414$	−0.506763	−	0.368185i	−0.0249060	−	0.0180953i
$415$	−18.8529	+	13.6974i	−0.925454	+	0.672381i
$416$	−0.123987	+	0.381594i	−0.00607898	+	0.0187092i
$417$	4.09327			0.200448
$418$	−15.8291	−	16.0922i	−0.774226	−	0.787094i
$419$	−3.05415			−0.149205			−0.0746026	−	0.997213i	$-0.523769\pi$
$419$	−3.05415			−0.149205			−0.0746026	+	0.997213i	$0.523769\pi$
$420$	−5.86471	+	18.0497i	−0.286169	+	0.880736i
$421$	−9.47163	+	6.88154i	−0.461619	+	0.335386i	−0.794166	−	0.607701i	$-0.792092\pi$
$421$	−9.47163	+	6.88154i	−0.461619	+	0.335386i	0.332547	+	0.943087i	$0.392092\pi$
$422$	−4.35288	−	3.16256i	−0.211895	−	0.153951i
$423$	−0.161717	−	0.497712i	−0.00786293	−	0.0241996i
$424$	−3.98730	−	12.2716i	−0.193640	−	0.595963i
$425$	0.418053	+	0.303733i	0.0202785	+	0.0147332i
$426$	4.53560	−	3.29531i	0.219750	−	0.159658i
$427$	3.82604	−	11.7753i	0.185155	−	0.569849i
$428$	12.1554			0.587555
$429$	1.66088	+	1.68849i	0.0801881	+	0.0815208i
$430$	14.6652			0.707221
$431$	−7.52434	+	23.1575i	−0.362435	+	1.11546i	0.589137	+	0.808033i	$0.299468\pi$
$431$	−7.52434	+	23.1575i	−0.362435	+	1.11546i	−0.951572	+	0.307426i	$0.900532\pi$
$432$	4.07822	−	2.96300i	0.196213	−	0.142557i
$433$	−22.9848	−	16.6994i	−1.10458	−	0.802522i	−0.122776	−	0.992434i	$-0.539180\pi$
$433$	−22.9848	−	16.6994i	−1.10458	−	0.802522i	−0.981801	+	0.189912i	$0.939180\pi$
$434$	−4.64279	−	14.2890i	−0.222861	−	0.685896i
$435$	−5.94977	−	18.3115i	−0.285270	−	0.877970i
$436$	0.460042	+	0.334240i	0.0220320	+	0.0160072i
$437$	20.5686	−	14.9439i	0.983928	−	0.714866i
$438$	0.765644	−	2.35641i	0.0365839	−	0.112594i
$439$	7.35267			0.350924			0.175462	−	0.984486i	$-0.443858\pi$
$439$	7.35267			0.350924			0.175462	+	0.984486i	$0.443858\pi$
$440$	7.68379	+	1.28199i	0.366310	+	0.0611167i
$441$	2.28235			0.108683
$442$	0.123987	−	0.381594i	0.00589748	−	0.0181506i
$443$	6.30251	−	4.57904i	0.299441	−	0.217557i	−0.427911	−	0.903821i	$-0.640750\pi$
$443$	6.30251	−	4.57904i	0.299441	−	0.217557i	0.727353	+	0.686264i	$0.240750\pi$
$444$	−9.36906	−	6.80702i	−0.444636	−	0.323047i
$445$	−7.17712	−	22.0889i	−0.340228	−	1.04711i
$446$	2.68037	+	8.24932i	0.126919	+	0.390617i
$447$	17.0240	+	12.3686i	0.805206	+	0.585016i
$448$	3.67291	−	2.66852i	0.173529	−	0.126076i
$449$	10.1929	−	31.3705i	0.481033	−	1.48047i	−0.356612	−	0.934253i	$-0.616068\pi$
$449$	10.1929	−	31.3705i	0.481033	−	1.48047i	0.837645	−	0.546215i	$-0.183932\pi$
$450$	−0.0866477			−0.00408461
$451$	17.4715	−	33.6022i	0.822700	−	1.58227i
$452$	−18.3328			−0.862301
$453$	−4.56548	+	14.0511i	−0.214505	+	0.660178i
$454$	22.6098	−	16.4270i	1.06113	−	0.770957i
$455$	3.46136	+	2.51482i	0.162271	+	0.117897i
$456$	−3.74314	−	11.5202i	−0.175289	−	0.539483i
$457$	1.58769	+	4.88640i	0.0742689	+	0.228576i	0.981299	−	0.192490i	$-0.0616562\pi$
$457$	1.58769	+	4.88640i	0.0742689	+	0.228576i	−0.907030	+	0.421066i	$0.861656\pi$
$458$	−17.6731	−	12.8402i	−0.825807	−	0.599984i
$459$	−4.07822	+	2.96300i	−0.190355	+	0.138301i
$460$	−2.71136	+	8.34470i	−0.126418	+	0.389074i
$461$	−38.2472			−1.78135			−0.890676	−	0.454639i	$-0.849768\pi$
$461$	−38.2472			−1.78135			−0.890676	+	0.454639i	$0.849768\pi$
$462$	−3.97401	−	26.5028i	−0.184888	−	1.23302i
$463$	−37.0096			−1.71998			−0.859992	−	0.510308i	$-0.829531\pi$
$463$	−37.0096			−1.71998			−0.859992	+	0.510308i	$0.829531\pi$
$464$	−1.42327	+	4.38039i	−0.0660738	+	0.203354i
$465$	11.1922	−	8.13159i	0.519025	−	0.377093i
$466$	−0.0554128	−	0.0402597i	−0.00256695	−	0.00186500i
$467$	3.88637	+	11.9610i	0.179840	+	0.553490i	0.999821	−	0.0189001i	$-0.00601646\pi$
$467$	3.88637	+	11.9610i	0.179840	+	0.553490i	−0.819982	+	0.572390i	$0.806016\pi$
$468$	0.0207903	+	0.0639861i	0.000961033	+	0.00295776i
$469$	−16.3617	−	11.8875i	−0.755512	−	0.548912i
$470$	−5.93045	+	4.30872i	−0.273551	+	0.198746i
$471$	4.59298	−	14.1358i	0.211634	−	0.651341i
$472$	10.5133			0.483912
$473$	−18.5281	+	9.24898i	−0.851922	+	0.425269i
$474$	6.24756			0.286960
$475$	1.08677	−	3.34475i	0.0498646	−	0.153467i
$476$	−3.67291	+	2.66852i	−0.168347	+	0.122312i
$477$	−1.75040	−	1.27174i	−0.0801454	−	0.0582290i
$478$	2.27593	+	7.00460i	0.104099	+	0.320383i
$479$	−0.813592	−	2.50398i	−0.0371740	−	0.114410i	0.930748	−	0.365662i	$-0.119158\pi$
$479$	−0.813592	−	2.50398i	−0.0371740	−	0.114410i	−0.967922	+	0.251253i	$0.919158\pi$
$480$	3.38197	+	2.45714i	0.154365	+	0.112153i
$481$	−2.11213	+	1.53455i	−0.0963048	+	0.0699695i
$482$	−7.38094	+	22.7162i	−0.336192	+	1.03469i
$483$	30.1847			1.37345
$484$	−10.5162	+	3.22629i	−0.478010	+	0.146650i
$485$	−12.6011			−0.572189
$486$	0.537871	−	1.65540i	0.0243983	−	0.0750903i
$487$	−14.0754	+	10.2264i	−0.637817	+	0.463401i	−0.859100	−	0.511808i	$-0.828976\pi$
$487$	−14.0754	+	10.2264i	−0.637817	+	0.463401i	0.221282	+	0.975210i	$0.428976\pi$
$488$	−2.20634	−	1.60300i	−0.0998764	−	0.0725645i
$489$	3.87994	+	11.9412i	0.175457	+	0.540001i
$490$	−9.87920	−	30.4051i	−0.446297	−	1.37356i
$491$	−14.6623	−	10.6528i	−0.661698	−	0.480752i	0.205538	−	0.978649i	$-0.434106\pi$
$491$	−14.6623	−	10.6528i	−0.661698	−	0.480752i	−0.867236	+	0.497897i	$0.834106\pi$
$492$	16.4423	−	11.9460i	0.741274	−	0.538567i
$493$	1.42327	−	4.38039i	0.0641010	−	0.197283i
$494$	−2.73073			−0.122861
$495$	1.16871	−	0.583406i	0.0525297	−	0.0262222i
$496$	−3.30937			−0.148595
$497$	−4.41917	+	13.6008i	−0.198227	+	0.610080i
$498$	14.2859	−	10.3793i	0.640167	−	0.465109i
$499$	−1.44446	−	1.04946i	−0.0646627	−	0.0469802i	0.554984	−	0.831861i	$-0.312724\pi$
$499$	−1.44446	−	1.04946i	−0.0646627	−	0.0469802i	−0.619647	+	0.784881i	$0.712724\pi$
$500$	−3.25400	−	10.0148i	−0.145523	−	0.447875i
$501$	6.73768	+	20.7364i	0.301017	+	0.926435i
$502$	−10.6880	−	7.76531i	−0.477030	−	0.346583i
$503$	−25.0067	+	18.1684i	−1.11499	+	0.810089i	−0.983442	−	0.181221i	$-0.941995\pi$
$503$	−25.0067	+	18.1684i	−1.11499	+	0.810089i	−0.131549	+	0.991310i	$0.541995\pi$
$504$	0.235244	−	0.724006i	0.0104786	−	0.0322498i
$505$	25.8847			1.15185
$506$	−1.83725	−	12.2527i	−0.0816759	−	0.544698i
$507$	−22.8508			−1.01484
$508$	−5.34695	+	16.4562i	−0.237233	+	0.730127i
$509$	−8.53883	+	6.20382i	−0.378477	+	0.274980i	−0.760717	−	0.649083i	$-0.775153\pi$
$509$	−8.53883	+	6.20382i	−0.378477	+	0.274980i	0.382240	+	0.924063i	$0.375153\pi$
$510$	−3.38197	−	2.45714i	−0.149756	−	0.108804i
$511$	1.95303	+	6.01080i	0.0863968	+	0.265902i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	27.7558	+	20.1658i	1.22545	+	0.890341i
$514$	−12.7256	+	9.24568i	−0.561301	+	0.407809i
$515$	−13.7504	+	42.3193i	−0.605914	+	1.86481i
$516$	−11.1127			−0.489208
$517$	4.77513	−	9.18382i	0.210010	−	0.403904i
$518$	29.5406			1.29794
$519$	−0.789698	+	2.43044i	−0.0346639	+	0.106685i
$520$	0.762420	−	0.553931i	0.0334343	−	0.0242915i
$521$	9.97310	+	7.24588i	0.436929	+	0.317448i	0.784414	−	0.620238i	$-0.212964\pi$
$521$	9.97310	+	7.24588i	0.436929	+	0.317448i	−0.347484	+	0.937686i	$0.612964\pi$
$522$	0.238656	+	0.734507i	0.0104457	+	0.0321485i
$523$	−11.1222	−	34.2306i	−0.486339	−	1.49680i	−0.830032	−	0.557716i	$-0.811678\pi$
$523$	−11.1222	−	34.2306i	−0.486339	−	1.49680i	0.343692	−	0.939082i	$-0.388322\pi$
$524$	5.13302	+	3.72935i	0.224237	+	0.162918i
$525$	3.37796	−	2.45423i	0.147426	−	0.107111i
$526$	9.10958	−	28.0364i	0.397196	−	1.22245i
$527$	3.30937			0.144158
$528$	−5.82244	−	0.971439i	−0.253389	−	0.0422764i
$529$	−9.04511			−0.393265
$530$	−9.36526	+	28.8233i	−0.406801	+	1.25200i
$531$	1.42619	−	1.03619i	0.0618915	−	0.0449668i
$532$	24.9973	+	18.1616i	1.08377	+	0.787405i
$533$	−1.41583	−	4.35747i	−0.0613264	−	0.188743i
$534$	5.43850	+	16.7380i	0.235347	+	0.724324i
$535$	−23.0977	−	16.7815i	−0.998603	−	0.725527i
$536$	−3.60392	+	2.61840i	−0.155666	+	0.113098i
$537$	−7.94066	+	24.4388i	−0.342665	+	1.05461i
$538$	1.96163			0.0845718
$539$	31.6571	+	32.1832i	1.36357	+	1.38623i
$540$	−11.8401			−0.509515
$541$	−3.47724	+	10.7018i	−0.149498	+	0.460108i	−0.997562	−	0.0697859i	$-0.977768\pi$
$541$	−3.47724	+	10.7018i	−0.149498	+	0.460108i	0.848064	+	0.529894i	$0.177768\pi$
$542$	−16.4509	+	11.9523i	−0.706627	+	0.513394i
$543$	−14.0693	−	10.2219i	−0.603770	−	0.438665i
$544$	0.309017	+	0.951057i	0.0132490	+	0.0407762i
$545$	−0.412727	−	1.27024i	−0.0176793	−	0.0544113i
$546$	−2.62286	−	1.90562i	−0.112248	−	0.0815531i
$547$	−28.1946	+	20.4846i	−1.20551	+	0.875857i	−0.994816	−	0.101694i	$-0.967574\pi$
$547$	−28.1946	+	20.4846i	−1.20551	+	0.875857i	−0.210698	+	0.977551i	$0.567574\pi$
$548$	4.93333	−	15.1832i	0.210741	−	0.648595i
$549$	−0.457298			−0.0195170
$550$	−1.20184	−	1.22181i	−0.0512465	−	0.0520983i
$551$	−31.3465			−1.33541
$552$	2.05455	−	6.32325i	0.0874474	−	0.269135i
$553$	−12.8929	+	9.36721i	−0.548260	+	0.398334i
$554$	11.4947	+	8.35141i	0.488364	+	0.354817i
$555$	8.40547	+	25.8694i	0.356792	+	1.09809i
$556$	0.710693	+	2.18729i	0.0301401	+	0.0927617i
$557$	21.2689	+	15.4528i	0.901193	+	0.654755i	0.938772	−	0.344539i	$-0.111965\pi$
$557$	21.2689	+	15.4528i	0.901193	+	0.654755i	−0.0375794	+	0.999294i	$0.511965\pi$
$558$	−0.448938	+	0.326172i	−0.0190050	+	0.0138080i
$559$	−0.774151	+	2.38259i	−0.0327431	+	0.100773i
$560$	−10.6633			−0.450609
$561$	5.82244	+	0.971439i	0.245824	+	0.0410142i
$562$	8.61758			0.363510
$563$	−9.79205	+	30.1368i	−0.412686	+	1.27012i	0.501619	+	0.865089i	$0.332738\pi$
$563$	−9.79205	+	30.1368i	−0.412686	+	1.27012i	−0.914305	+	0.405027i	$0.867262\pi$
$564$	4.49383	−	3.26496i	0.189224	−	0.137480i
$565$	34.8359	+	25.3098i	1.46556	+	1.06479i
$566$	−5.86645	−	18.0551i	−0.246585	−	0.758911i
$567$	13.2926	+	40.9105i	0.558237	+	1.71808i
$568$	2.54838	+	1.85151i	0.106928	+	0.0776874i
$569$	−14.1314	+	10.2671i	−0.592419	+	0.430418i	−0.843180	−	0.537631i	$-0.819319\pi$
$569$	−14.1314	+	10.2671i	−0.592419	+	0.430418i	0.250761	+	0.968049i	$0.419319\pi$
$570$	−8.79180	+	27.0584i	−0.368248	+	1.13335i
$571$	11.0988			0.464469			0.232235	−	0.972660i	$-0.425396\pi$
$571$	11.0988			0.464469			0.232235	+	0.972660i	$0.425396\pi$
$572$	−0.613892	+	1.18067i	−0.0256681	+	0.0493665i
$573$	2.76154			0.115365
$574$	−16.0202	+	49.3051i	−0.668670	+	2.05795i
$575$	1.56169	−	1.13463i	0.0651269	−	0.0473175i
$576$	−0.135657	−	0.0985604i	−0.00565236	−	0.00410668i
$577$	0.618424	+	1.90331i	0.0257453	+	0.0792360i	0.963104	−	0.269131i	$-0.0867364\pi$
$577$	0.618424	+	1.90331i	0.0257453	+	0.0792360i	−0.937358	+	0.348367i	$0.886736\pi$
$578$	−0.309017	−	0.951057i	−0.0128534	−	0.0395587i
$579$	−8.59668	−	6.24586i	−0.357266	−	0.259569i
$580$	8.75195	−	6.35867i	0.363405	−	0.264029i
$581$	−13.9192	+	42.8389i	−0.577466	+	1.77726i
$582$	9.54860			0.395802
$583$	−6.34603	−	42.3218i	−0.262826	−	1.75279i
$584$	1.39211			0.0576059
$585$	0.0488318	−	0.150289i	0.00201895	−	0.00621368i
$586$	0.786980	−	0.571774i	0.0325098	−	0.0236198i
$587$	3.96760	+	2.88263i	0.163760	+	0.118979i	0.666647	−	0.745373i	$-0.267729\pi$
$587$	3.96760	+	2.88263i	0.163760	+	0.118979i	−0.502887	+	0.864352i	$0.667729\pi$
$588$	7.48602	+	23.0396i	0.308718	+	0.950138i
$589$	−6.96002	−	21.4207i	−0.286783	−	0.882626i
$590$	−19.9773	−	14.5143i	−0.822451	−	0.597546i
$591$	5.94184	−	4.31700i	0.244415	−	0.177578i
$592$	2.01071	−	6.18833i	0.0826397	−	0.254339i
$593$	5.84556			0.240048			0.120024	−	0.992771i	$-0.461703\pi$
$593$	5.84556			0.240048			0.120024	+	0.992771i	$0.461703\pi$
$594$	14.9588	−	7.46722i	0.613765	−	0.306384i
$595$	10.6633			0.437155
$596$	−3.65355	+	11.2445i	−0.149655	+	0.460591i
$597$	3.53488	−	2.56824i	0.144673	−	0.105111i
$598$	−1.21260	−	0.881003i	−0.0495868	−	0.0360269i
$599$	−3.66683	−	11.2853i	−0.149823	−	0.461106i	0.847777	−	0.530353i	$-0.177941\pi$
$599$	−3.66683	−	11.2853i	−0.149823	−	0.461106i	−0.997600	+	0.0692464i	$0.977941\pi$
$600$	−0.284202	−	0.874683i	−0.0116025	−	0.0357088i
$601$	−21.3833	−	15.5359i	−0.872244	−	0.633722i	0.0589443	−	0.998261i	$-0.481227\pi$
$601$	−21.3833	−	15.5359i	−0.872244	−	0.633722i	−0.931188	+	0.364539i	$0.881227\pi$
$602$	22.9328	−	16.6617i	0.934672	−	0.679079i
$603$	−0.230826	+	0.710408i	−0.00939994	+	0.0289301i
$604$	−8.30105			−0.337765
$605$	24.4371	+	8.38784i	0.993508	+	0.341014i
$606$	−19.6143			−0.796776
$607$	11.4701	−	35.3012i	0.465555	−	1.43283i	−0.392727	−	0.919655i	$-0.628468\pi$
$607$	11.4701	−	35.3012i	0.465555	−	1.43283i	0.858283	−	0.513177i	$-0.171532\pi$
$608$	5.50606	−	4.00039i	0.223300	−	0.162237i
$609$	−30.1083	−	21.8750i	−1.22005	−	0.886419i
$610$	1.97942	+	6.09204i	0.0801446	+	0.246660i
$611$	−0.386960	−	1.19094i	−0.0156547	−	0.0481803i
$612$	0.135657	+	0.0985604i	0.00548360	+	0.00398407i
$613$	−16.3568	+	11.8839i	−0.660644	+	0.479986i	−0.866880	−	0.498516i	$-0.833878\pi$
$613$	−16.3568	+	11.8839i	−0.660644	+	0.479986i	0.206237	+	0.978502i	$0.433878\pi$
$614$	−8.90932	+	27.4201i	−0.359551	+	1.10658i
$615$	−47.7359			−1.92490
$616$	13.4721	−	6.72509i	0.542806	−	0.270962i
$617$	1.81082			0.0729007			0.0364503	−	0.999335i	$-0.488395\pi$
$617$	1.81082			0.0729007			0.0364503	+	0.999335i	$0.488395\pi$
$618$	10.4194	−	32.0677i	0.419131	−	1.28995i
$619$	19.7583	−	14.3552i	0.794151	−	0.576985i	−0.115041	−	0.993361i	$-0.536700\pi$
$619$	19.7583	−	14.3552i	0.794151	−	0.576985i	0.909192	+	0.416376i	$0.136700\pi$
$620$	6.28845	+	4.56883i	0.252550	+	0.183489i
$621$	5.81914	+	17.9095i	0.233514	+	0.718682i
$622$	2.62239	+	8.07090i	0.105148	+	0.323613i
$623$	−36.3192	−	26.3874i	−1.45510	−	1.05719i
$624$	−0.577728	+	0.419744i	−0.0231276	+	0.0168032i
$625$	−8.44132	+	25.9797i	−0.337653	+	1.03919i
$626$	2.97111			0.118749
$627$	−5.95744	−	39.7303i	−0.237917	−	1.58668i
$628$	8.35107			0.333244
$629$	−2.01071	+	6.18833i	−0.0801723	+	0.246745i
$630$	−1.44655	+	1.05098i	−0.0576321	+	0.0418722i
$631$	9.83482	+	7.14542i	0.391518	+	0.284455i	0.766077	−	0.642748i	$-0.222206\pi$
$631$	9.83482	+	7.14542i	0.391518	+	0.284455i	−0.374559	+	0.927203i	$0.622206\pi$
$632$	1.08473	+	3.33846i	0.0431483	+	0.132797i
$633$	−2.95919	−	9.10744i	−0.117617	−	0.361988i
$634$	11.5555	+	8.39559i	0.458929	+	0.333432i
$635$	32.8793	−	23.8882i	1.30478	−	0.947976i
$636$	7.09658	−	21.8410i	0.281398	−	0.866054i
$637$	5.46127			0.216383
$638$	−7.04698	+	13.5532i	−0.278993	+	0.536575i
$639$	0.528190			0.0208949
$640$	−0.725811	+	2.23382i	−0.0286902	+	0.0882994i
$641$	−12.9072	+	9.37762i	−0.509803	+	0.370394i	−0.812749	−	0.582614i	$-0.802030\pi$
$641$	−12.9072	+	9.37762i	−0.509803	+	0.370394i	0.302946	+	0.953008i	$0.402030\pi$
$642$	17.5025	+	12.7163i	0.690767	+	0.501872i
$643$	2.22104	+	6.83565i	0.0875892	+	0.269572i	0.985252	−	0.171112i	$-0.0547360\pi$
$643$	2.22104	+	6.83565i	0.0875892	+	0.269572i	−0.897662	+	0.440684i	$0.854736\pi$
$644$	5.24080	+	16.1295i	0.206517	+	0.635593i
$645$	21.1163	+	15.3419i	0.831453	+	0.604086i
$646$	−5.50606	+	4.00039i	−0.216633	+	0.157393i
$647$	10.8303	−	33.3322i	0.425783	−	1.31042i	−0.476460	−	0.879196i	$-0.658080\pi$
$647$	10.8303	−	33.3322i	0.425783	−	1.31042i	0.902243	−	0.431228i	$-0.141920\pi$
$648$	9.47493			0.372210
$649$	34.3931	+	5.73828i	1.35005	+	0.225247i
$650$	−0.207333			−0.00813228
$651$	8.26323	−	25.4316i	0.323862	−	0.996744i
$652$	−5.70729	+	4.14659i	−0.223515	+	0.162393i
$653$	−38.5687	−	28.0218i	−1.50931	−	1.09658i	−0.966483	−	0.256732i	$-0.917354\pi$
$653$	−38.5687	−	28.0218i	−1.50931	−	1.09658i	−0.542826	−	0.839845i	$-0.682646\pi$
$654$	0.312747	+	0.962535i	0.0122294	+	0.0376381i
$655$	−4.60510	−	14.1730i	−0.179936	−	0.553786i
$656$	9.23827	+	6.71200i	0.360694	+	0.262059i
$657$	0.188849	−	0.137207i	0.00736770	−	0.00535295i
$658$	−4.37848	+	13.4756i	−0.170691	+	0.525332i
$659$	21.6584			0.843693			0.421846	−	0.906667i	$-0.361382\pi$
$659$	21.6584			0.843693			0.421846	+	0.906667i	$0.361382\pi$
$660$	9.72265	+	9.88424i	0.378453	+	0.384744i
$661$	5.96122			0.231865			0.115932	−	0.993257i	$-0.463014\pi$
$661$	5.96122			0.231865			0.115932	+	0.993257i	$0.463014\pi$
$662$	−8.72537	+	26.8539i	−0.339121	+	1.04371i
$663$	0.577728	−	0.419744i	0.0224371	−	0.0163015i
$664$	8.02671	+	5.83174i	0.311497	+	0.226316i
$665$	−22.4264	−	69.0213i	−0.869658	−	2.67653i
$666$	−0.337158	−	1.03767i	−0.0130646	−	0.0402087i
$667$	−13.9196	−	10.1132i	−0.538969	−	0.391584i
$668$	−9.91094	+	7.20072i	−0.383466	+	0.278604i
$669$	−4.77051	+	14.6821i	−0.184439	+	0.567644i
$670$	10.4631			0.404224
$671$	−6.34290	−	6.44832i	−0.244865	−	0.248935i
$672$	8.08022			0.311701
$673$	11.5802	−	35.6403i	0.446386	−	1.37383i	−0.434571	−	0.900637i	$-0.643100\pi$
$673$	11.5802	−	35.6403i	0.446386	−	1.37383i	0.880957	−	0.473196i	$-0.156900\pi$
$674$	23.3488	−	16.9639i	0.899361	−	0.653424i
$675$	2.10739	+	1.53111i	0.0811133	+	0.0589323i
$676$	−3.96747	−	12.2106i	−0.152595	−	0.469640i
$677$	−12.9043	−	39.7153i	−0.495952	−	1.52638i	−0.815468	−	0.578802i	$-0.803520\pi$
$677$	−12.9043	−	39.7153i	−0.495952	−	1.52638i	0.319516	−	0.947581i	$-0.396480\pi$
$678$	−26.3971	−	19.1786i	−1.01377	−	0.736550i
$679$	−19.7051	+	14.3166i	−0.756212	+	0.549420i
$680$	0.725811	−	2.23382i	0.0278336	−	0.0856630i
$681$	49.7405			1.90606
$682$	−10.8263	−	1.80630i	−0.414559	−	0.0691667i
$683$	43.1623			1.65156			0.825779	−	0.563993i	$-0.190736\pi$
$683$	43.1623			1.65156			0.825779	+	0.563993i	$0.190736\pi$
$684$	0.352654	−	1.08536i	0.0134841	−	0.0414997i
$685$	−30.3359	+	22.0403i	−1.15907	+	0.842117i
$686$	−24.2825	−	17.6423i	−0.927111	−	0.673585i
$687$	−12.0145	−	36.9769i	−0.458383	−	1.41076i
$688$	−1.92944	−	5.93819i	−0.0735590	−	0.226391i
$689$	−4.18841	−	3.04306i	−0.159566	−	0.115931i
$690$	−12.6338	+	9.17897i	−0.480959	+	0.349437i
$691$	6.33013	−	19.4821i	0.240809	−	0.741135i	−0.755488	−	0.655162i	$-0.772600\pi$
$691$	6.33013	−	19.4821i	0.240809	−	0.741135i	0.996297	−	0.0859727i	$-0.0273998\pi$
$692$	−1.43585			−0.0545827
$693$	1.16475	−	2.24012i	0.0442452	−	0.0850950i
$694$	11.9221			0.452556
$695$	1.66926	−	5.13745i	0.0633185	−	0.194874i
$696$	−6.63185	+	4.81832i	−0.251379	+	0.182638i
$697$	−9.23827	−	6.71200i	−0.349924	−	0.254235i
$698$	−3.95756	−	12.1801i	−0.149796	−	0.461024i
$699$	−0.0376708	−	0.115939i	−0.00142484	−	0.00438521i
$700$	1.89794	+	1.37894i	0.0717355	+	0.0521189i
$701$	−4.18998	+	3.04420i	−0.158253	+	0.114978i	−0.664094	−	0.747649i	$-0.731182\pi$
$701$	−4.18998	+	3.04420i	−0.158253	+	0.114978i	0.505840	+	0.862627i	$0.331182\pi$
$702$	0.625015	−	1.92360i	0.0235897	−	0.0726016i
$703$	44.2844			1.67022
$704$	−0.491820	−	3.27996i	−0.0185361	−	0.123618i
$705$	−13.0467			−0.491367
$706$	−8.53946	+	26.2818i	−0.321387	+	0.989127i
$707$	40.4773	−	29.4085i	1.52231	−	1.10602i
$708$	15.1379	+	10.9983i	0.568917	+	0.413342i
$709$	−1.56541	−	4.81785i	−0.0587904	−	0.180938i	0.917349	−	0.398085i	$-0.130325\pi$
$709$	−1.56541	−	4.81785i	−0.0587904	−	0.180938i	−0.976139	+	0.217147i	$0.930325\pi$
$710$	−2.28628	−	7.03645i	−0.0858027	−	0.264073i
$711$	0.476191	+	0.345973i	0.0178585	+	0.0129750i
$712$	−7.99989	+	5.81226i	−0.299809	+	0.217824i
$713$	3.82024	−	11.7575i	0.143069	−	0.440321i
$714$	−8.08022			−0.302394
$715$	2.79653	−	1.39599i	0.104584	−	0.0522071i
$716$	−14.4379			−0.539569
$717$	−4.05070	+	12.4668i	−0.151276	+	0.465580i
$718$	−28.3608	+	20.6053i	−1.05842	+	0.768984i
$719$	8.12604	+	5.90392i	0.303050	+	0.220179i	0.728909	−	0.684611i	$-0.240028\pi$
$719$	8.12604	+	5.90392i	0.303050	+	0.220179i	−0.425858	+	0.904790i	$0.640028\pi$
$720$	0.121705	+	0.374569i	0.00453567	+	0.0139593i
$721$	26.5782	+	81.7993i	0.989824	+	3.04636i
$722$	22.1022	+	16.0582i	0.822558	+	0.597623i
$723$	−34.3920	+	24.9873i	−1.27905	+	0.929286i
$724$	3.01943	−	9.29286i	0.112216	−	0.345367i
$725$	−2.38001			−0.0883915
$726$	−18.5173	−	6.35594i	−0.687243	−	0.235891i
$727$	−43.5582			−1.61549			−0.807743	−	0.589535i	$-0.799311\pi$
$727$	−43.5582			−1.61549			−0.807743	+	0.589535i	$0.799311\pi$
$728$	0.562898	−	1.73242i	0.0208624	−	0.0642079i
$729$	−20.4899	+	14.8868i	−0.758884	+	0.551362i
$730$	−2.64529	−	1.92191i	−0.0979064	−	0.0711332i
$731$	1.92944	+	5.93819i	0.0713627	+	0.219632i
$732$	−1.49992	−	4.61628i	−0.0554387	−	0.170623i
$733$	39.8178	+	28.9293i	1.47070	+	1.06853i	0.980409	+	0.196973i	$0.0631112\pi$
$733$	39.8178	+	28.9293i	1.47070	+	1.06853i	0.490296	+	0.871556i	$0.336889\pi$
$734$	14.1219	−	10.2601i	0.521248	−	0.378709i
$735$	17.5830	−	54.1149i	0.648558	−	1.99606i
$736$	3.73562			0.137697
$737$	−13.2191	+	6.59879i	−0.486930	+	0.243069i
$738$	1.91477			0.0704837
$739$	−3.50153	+	10.7766i	−0.128806	+	0.396424i	−0.994575	−	0.104019i	$-0.966830\pi$
$739$	−3.50153	+	10.7766i	−0.128806	+	0.396424i	0.865769	+	0.500443i	$0.166830\pi$
$740$	−12.3642	+	8.98312i	−0.454517	+	0.330226i
$741$	−3.93194	−	2.85672i	−0.144443	−	0.104944i
$742$	18.1022	+	55.7128i	0.664552	+	2.04528i
$743$	−9.44217	−	29.0600i	−0.346400	−	1.06611i	−0.960830	−	0.277138i	$-0.910614\pi$
$743$	−9.44217	−	29.0600i	−0.346400	−	1.06611i	0.614431	−	0.788971i	$-0.289386\pi$
$744$	−4.76511	−	3.46206i	−0.174697	−	0.126925i
$745$	22.4663	−	16.3227i	0.823101	−	0.598018i
$746$	9.58876	−	29.5112i	0.351069	−	1.08048i
$747$	1.66366			0.0608700
$748$	0.491820	+	3.27996i	0.0179827	+	0.119927i
$749$	−55.1852			−2.01642
$750$	5.79146	−	17.8243i	0.211474	−	0.650851i
$751$	−23.7516	+	17.2566i	−0.866708	+	0.629701i	−0.929702	−	0.368313i	$-0.879935\pi$
$751$	−23.7516	+	17.2566i	−0.866708	+	0.629701i	0.0629933	+	0.998014i	$0.479935\pi$
$752$	2.52491	+	1.83445i	0.0920740	+	0.0668957i
$753$	−7.26596	−	22.3623i	−0.264786	−	0.814928i
$754$	0.571063	+	1.75755i	0.0207969	+	0.0640062i
$755$	15.7736	+	11.4602i	0.574062	+	0.417080i
$756$	−18.5150	+	13.4519i	−0.673383	+	0.489241i
$757$	−4.19579	+	12.9133i	−0.152498	+	0.469342i	−0.997899	−	0.0647912i	$-0.979362\pi$
$757$	−4.19579	+	12.9133i	−0.152498	+	0.469342i	0.845400	+	0.534133i	$0.179362\pi$
$758$	29.0940			1.05674
$759$	10.1726	−	19.5645i	0.369241	−	0.710147i
$760$	−15.9854			−0.579853
$761$	−2.67123	+	8.22120i	−0.0968320	+	0.298018i	−0.987727	−	0.156191i	$-0.950078\pi$
$761$	−2.67123	+	8.22120i	−0.0968320	+	0.298018i	0.890895	+	0.454210i	$0.150078\pi$
$762$	−24.9145	+	18.1015i	−0.902557	+	0.655746i
$763$	−2.08857	−	1.51744i	−0.0756114	−	0.0549349i
$764$	0.479472	+	1.47566i	0.0173467	+	0.0533876i
$765$	−0.121705	−	0.374569i	−0.00440024	−	0.0135426i
$766$	−7.52935	−	5.47040i	−0.272047	−	0.197653i
$767$	3.41264	−	2.47943i	0.123223	−	0.0895269i
$768$	0.549988	−	1.69269i	0.0198460	−	0.0610796i
$769$	4.03103			0.145363			0.0726813	−	0.997355i	$-0.476844\pi$
$769$	4.03103			0.145363			0.0726813	+	0.997355i	$0.476844\pi$
$770$	−34.8841	−	5.82020i	−1.25714	−	0.209746i
$771$	−27.9957			−1.00824
$772$	1.84495	−	5.67818i	0.0664012	−	0.204362i
$773$	−3.17057	+	2.30355i	−0.114037	+	0.0828530i	−0.643342	−	0.765579i	$-0.722453\pi$
$773$	−3.17057	+	2.30355i	−0.114037	+	0.0828530i	0.529305	+	0.848432i	$0.322453\pi$
$774$	−0.847011	−	0.615390i	−0.0304452	−	0.0221197i
$775$	−0.528446	−	1.62639i	−0.0189823	−	0.0584216i
$776$	1.65787	+	5.10241i	0.0595142	+	0.183166i
$777$	42.5352	+	30.9036i	1.52594	+	1.10866i
$778$	−0.585979	+	0.425739i	−0.0210084	+	0.0152635i
$779$	−24.0159	+	73.9133i	−0.860459	+	2.64822i
$780$	1.67729			0.0600565
$781$	7.32620	+	7.44796i	0.262152	+	0.266509i
$782$	−3.73562			−0.133586
$783$	7.17466	−	22.0813i	0.256401	−	0.789122i
$784$	−11.0117	+	8.00049i	−0.393276	+	0.285732i
$785$	−15.8687	−	11.5293i	−0.566378	−	0.411497i
$786$	3.48954	+	10.7397i	0.124468	+	0.383072i
$787$	−4.55979	−	14.0336i	−0.162539	−	0.500244i	0.836307	−	0.548261i	$-0.184710\pi$
$787$	−4.55979	−	14.0336i	−0.162539	−	0.500244i	−0.998847	+	0.0480170i	$0.984710\pi$
$788$	3.33849	+	2.42556i	0.118929	+	0.0864068i
$789$	42.4467	−	30.8394i	1.51114	−	1.09791i
$790$	2.54779	−	7.84128i	0.0906462	−	0.278980i
$791$	83.2301			2.95932
$792$	−0.389992	−	0.396474i	−0.0138578	−	0.0140881i
$793$	−1.09423			−0.0388574
$794$	−3.86055	+	11.8815i	−0.137006	+	0.421660i
$795$	−43.6381	+	31.7049i	−1.54768	+	1.12446i
$796$	1.98611	+	1.44300i	0.0703960	+	0.0511457i
$797$	6.20210	+	19.0881i	0.219690	+	0.676135i	0.998787	+	0.0492326i	$0.0156775\pi$
$797$	6.20210	+	19.0881i	0.219690	+	0.676135i	−0.779098	+	0.626902i	$0.784322\pi$
$798$	16.9937	+	52.3013i	0.601571	+	1.85145i
$799$	−2.52491	−	1.83445i	−0.0893249	−	0.0648984i
$800$	0.418053	−	0.303733i	0.0147804	−	0.0107386i
$801$	−0.512380	+	1.57694i	−0.0181041	+	0.0557186i
$802$	10.6942			0.377626
$803$	4.55415	+	0.759833i	0.160713	+	0.0268139i
$804$	−7.92846			−0.279615
$805$	12.3095	−	37.8846i	0.433852	−	1.33526i
$806$	−1.07423	+	0.780475i	−0.0378382	+	0.0274910i
$807$	2.82452	+	2.05214i	0.0994280	+	0.0722386i
$808$	−3.40553	−	10.4811i	−0.119806	−	0.368725i
$809$	1.83612	+	5.65100i	0.0645546	+	0.198679i	0.978132	−	0.207987i	$-0.0666913\pi$
$809$	1.83612	+	5.65100i	0.0645546	+	0.198679i	−0.913577	+	0.406666i	$0.866691\pi$
$810$	−18.0042	−	13.0808i	−0.632605	−	0.459614i
$811$	37.0203	−	26.8968i	1.29996	−	0.944475i	0.300003	−	0.953938i	$-0.403012\pi$
$811$	37.0203	−	26.8968i	1.29996	−	0.944475i	0.999955	+	0.00946343i	$0.00301235\pi$
$812$	6.46161	−	19.8868i	0.226758	−	0.697889i
$813$	−36.1912			−1.26928
$814$	9.95553	−	19.1471i	0.348941	−	0.671104i
$815$	16.5696			0.580409
$816$	−0.549988	+	1.69269i	−0.0192534	+	0.0592559i
$817$	34.3786	−	24.9775i	1.20276	−	0.873854i
$818$	12.5107	+	9.08953i	0.437425	+	0.317808i
$819$	−0.0943873	−	0.290494i	−0.00329816	−	0.0101507i
$820$	−8.28813	−	25.5083i	−0.289434	−	0.890787i
$821$	−27.9388	−	20.2987i	−0.975070	−	0.708430i	−0.0184686	−	0.999829i	$-0.505879\pi$
$821$	−27.9388	−	20.2987i	−0.975070	−	0.708430i	−0.956601	+	0.291400i	$0.905879\pi$
$822$	22.9872	−	16.7012i	0.801771	−	0.582521i
$823$	13.7392	−	42.2848i	0.478917	−	1.47396i	−0.361684	−	0.932301i	$-0.617798\pi$
$823$	13.7392	−	42.2848i	0.478917	−	1.47396i	0.840601	−	0.541655i	$-0.182202\pi$
$824$	18.9448			0.659975
$825$	−0.452324	−	3.01656i	−0.0157479	−	0.105023i
$826$	−47.7298			−1.66073
$827$	6.65340	−	20.4771i	0.231361	−	0.712057i	−0.766222	−	0.642576i	$-0.777866\pi$
$827$	6.65340	−	20.4771i	0.231361	−	0.712057i	0.997583	−	0.0694809i	$-0.0221343\pi$
$828$	0.506763	−	0.368185i	0.0176112	−	0.0127953i
$829$	−36.1355	−	26.2540i	−1.25504	−	0.911839i	−0.256536	−	0.966535i	$-0.582581\pi$
$829$	−36.1355	−	26.2540i	−1.25504	−	0.911839i	−0.998503	+	0.0546957i	$0.982581\pi$
$830$	−7.20118	−	22.1629i	−0.249956	−	0.769287i
$831$	7.81437	+	24.0502i	0.271078	+	0.834291i
$832$	−0.324603	−	0.235838i	−0.0112536	−	0.00817622i
$833$	11.0117	−	8.00049i	0.381534	−	0.277201i
$834$	−1.26489	+	3.89293i	−0.0437995	+	0.134801i
$835$	28.7739			0.995761
$836$	20.1960	−	10.0816i	0.698494	−	0.348679i
$837$	16.6824			0.576627
$838$	0.943785	−	2.90467i	0.0326025	−	0.100340i
$839$	3.19161	−	2.31884i	0.110187	−	0.0800552i	−0.531327	−	0.847167i	$-0.678307\pi$
$839$	3.19161	−	2.31884i	0.110187	−	0.0800552i	0.641514	+	0.767111i	$0.278307\pi$
$840$	−15.3540	−	11.1553i	−0.529764	−	0.384896i
$841$	−2.40616	−	7.40541i	−0.0829712	−	0.255359i
$842$	−3.61784	−	11.1346i	−0.124679	−	0.383722i
$843$	12.4083	+	9.01518i	0.427366	+	0.310499i
$844$	4.35288	−	3.16256i	0.149832	−	0.108860i
$845$	−9.31870	+	28.6800i	−0.320573	+	0.986622i
$846$	0.523326			0.0179923
$847$	47.7433	−	14.6473i	1.64048	−	0.503285i
$848$	12.9032			0.443097
$849$	10.4411	−	32.1344i	0.358337	−	1.10285i
$850$	−0.418053	+	0.303733i	−0.0143391	+	0.0104180i
$851$	19.6647	+	14.2873i	0.674099	+	0.489761i
$852$	1.73244	+	5.33192i	0.0593526	+	0.182668i
$853$	−4.30049	−	13.2355i	−0.147246	−	0.453176i	0.850047	−	0.526707i	$-0.176573\pi$
$853$	−4.30049	−	13.2355i	−0.147246	−	0.453176i	−0.997293	+	0.0735304i	$0.976573\pi$
$854$	10.0167	+	7.27757i	0.342765	+	0.249033i
$855$	−2.16853	+	1.57553i	−0.0741623	+	0.0538820i
$856$	−3.75624	+	11.5605i	−0.128386	+	0.395130i
$857$	−29.0885			−0.993645			−0.496822	−	0.867852i	$-0.665500\pi$
$857$	−29.0885			−0.993645			−0.496822	+	0.867852i	$0.665500\pi$
$858$	−2.11909	+	1.05782i	−0.0723444	+	0.0361134i
$859$	1.76082			0.0600785			0.0300392	−	0.999549i	$-0.490437\pi$
$859$	1.76082			0.0600785			0.0300392	+	0.999549i	$0.490437\pi$
$860$	−4.53181	+	13.9475i	−0.154533	+	0.475605i
$861$	−74.6472	+	54.2344i	−2.54397	+	1.84830i
$862$	−19.6990	−	14.3121i	−0.670950	−	0.487474i
$863$	−9.48475	−	29.1911i	−0.322865	−	0.993675i	−0.972395	−	0.233340i	$-0.925035\pi$
$863$	−9.48475	−	29.1911i	−0.322865	−	0.993675i	0.649531	−	0.760335i	$-0.274965\pi$
$864$	1.55774	+	4.79423i	0.0529954	+	0.163103i
$865$	2.72839	+	1.98229i	0.0927682	+	0.0674000i
$866$	22.9848	−	16.6994i	0.781054	−	0.567469i
$867$	0.549988	−	1.69269i	0.0186786	−	0.0574867i
$868$	15.0244			0.509961
$869$	1.72642	+	11.5135i	0.0585646	+	0.390569i
$870$	19.2539			0.652767
$871$	−0.552326	+	1.69989i	−0.0187149	+	0.0575984i
$872$	−0.460042	+	0.334240i	−0.0155790	+	0.0113188i
$873$	0.727797	+	0.528775i	0.0246322	+	0.0178963i
$874$	7.85650	+	24.1798i	0.265750	+	0.817894i
$875$	14.7730	+	45.4667i	0.499420	+	1.53706i
$876$	2.00448	+	1.45634i	0.0677251	+	0.0492052i
$877$	22.7182	−	16.5058i	0.767140	−	0.557360i	−0.133952	−	0.990988i	$-0.542767\pi$
$877$	22.7182	−	16.5058i	0.767140	−	0.557360i	0.901092	+	0.433628i	$0.142767\pi$
$878$	−2.27210	+	6.99281i	−0.0766797	+	0.235996i
$879$	1.73132			0.0583959
$880$	−3.59367	+	6.91156i	−0.121143	+	0.232989i
$881$	29.0569			0.978951			0.489476	−	0.872017i	$-0.337188\pi$
$881$	29.0569			0.978951			0.489476	+	0.872017i	$0.337188\pi$
$882$	−0.705284	+	2.17064i	−0.0237482	+	0.0730893i
$883$	−15.0095	+	10.9050i	−0.505110	+	0.366984i	−0.810966	−	0.585094i	$-0.801058\pi$
$883$	−15.0095	+	10.9050i	−0.505110	+	0.366984i	0.305855	+	0.952078i	$0.401058\pi$
$884$	0.324603	+	0.235838i	0.0109176	+	0.00793209i
$885$	−13.5810	−	41.7980i	−0.456520	−	1.40502i
$886$	2.40734	+	7.40904i	0.0808763	+	0.248912i
$887$	16.4611	+	11.9597i	0.552710	+	0.401567i	0.828784	−	0.559569i	$-0.189033\pi$
$887$	16.4611	+	11.9597i	0.552710	+	0.401567i	−0.276074	+	0.961136i	$0.589033\pi$
$888$	9.36906	−	6.80702i	0.314405	−	0.228429i
$889$	24.2750	−	74.7107i	0.814156	−	2.50571i
$890$	23.2256			0.778525
$891$	30.9963	+	5.17155i	1.03842	+	0.173253i
$892$	−8.67385			−0.290422
$893$	−6.56378	+	20.2012i	−0.219649	+	0.676009i
$894$	−17.0240	+	12.3686i	−0.569366	+	0.413669i
$895$	27.4348	+	19.9326i	0.917046	+	0.666273i
$896$	1.40293	+	4.31776i	0.0468684	+	0.144246i
$897$	−0.824350	−	2.53709i	−0.0275242	−	0.0847109i
$898$	26.6854	+	19.3881i	0.890503	+	0.646988i
$899$	−12.3313	+	8.95920i	−0.411271	+	0.298806i
$900$	0.0267756	−	0.0824069i	0.000892521	−	0.00274690i
$901$	−12.9032			−0.429867
$902$	26.5586	+	27.0000i	0.884305	+	0.899003i
$903$	50.4511			1.67891
$904$	5.66514	−	17.4355i	0.188420	−	0.579896i
$905$	−18.5670	+	13.4897i	−0.617189	+	0.448414i
$906$	−11.9526	−	8.68405i	−0.397098	−	0.288508i
$907$	2.92406	+	8.99934i	0.0970919	+	0.298818i	0.987793	−	0.155771i	$-0.0497861\pi$
$907$	2.92406	+	8.99934i	0.0970919	+	0.298818i	−0.890701	+	0.454589i	$0.849786\pi$
$908$	8.63619	+	26.5794i	0.286602	+	0.882070i
$909$	−1.49501	−	1.08619i	−0.0495862	−	0.0360265i
$910$	−3.46136	+	2.51482i	−0.114743	+	0.0833656i
$911$	1.17298	−	3.61005i	0.0388625	−	0.119606i	−0.929743	−	0.368209i	$-0.879971\pi$
$911$	1.17298	−	3.61005i	0.0388625	−	0.119606i	0.968606	+	0.248602i	$0.0799712\pi$
$912$	12.1131			0.401104
$913$	23.0756	+	23.4591i	0.763689	+	0.776382i
$914$	−5.13787			−0.169946
$915$	−3.52298	+	10.8426i	−0.116466	+	0.358445i
$916$	17.6731	−	12.8402i	0.583934	−	0.424253i
$917$	−23.3037	−	16.9311i	−0.769556	−	0.559115i
$918$	−1.55774	−	4.79423i	−0.0514131	−	0.158233i
$919$	−9.86037	−	30.3471i	−0.325264	−	1.00106i	−0.971321	−	0.237770i	$-0.923583\pi$
$919$	−9.86037	−	30.3471i	−0.325264	−	1.00106i	0.646058	−	0.763289i	$-0.276417\pi$
$920$	−7.09843	−	5.15731i	−0.234028	−	0.170031i
$921$	−41.5136	+	30.1614i	−1.36792	+	0.993853i
$922$	11.8190	−	36.3753i	0.389240	−	1.19796i
$923$	1.26387			0.0416007
$924$	26.4337	+	4.41029i	0.869603	+	0.145088i
$925$	3.36233			0.110553
$926$	11.4366	−	35.1983i	0.375830	−	1.15669i
$927$	2.57000	−	1.86721i	0.0844097	−	0.0613272i
$928$	−3.72618	−	2.70723i	−0.122318	−	0.0888691i
$929$	6.36908	+	19.6020i	0.208963	+	0.643121i	0.999527	+	0.0307424i	$0.00978715\pi$
$929$	6.36908	+	19.6020i	0.208963	+	0.643121i	−0.790565	+	0.612379i	$0.790213\pi$
$930$	4.27503	+	13.1572i	0.140184	+	0.431441i
$931$	−74.9444	−	54.4503i	−2.45620	−	1.78454i
$932$	0.0554128	−	0.0402597i	0.00181511	−	0.00131875i
$933$	−4.66733	+	14.3646i	−0.152802	+	0.470275i
$934$	−12.5766			−0.411517
$935$	3.59367	−	6.91156i	0.117526	−	0.226032i
$936$	−0.0672789			−0.00219908
$937$	−9.74471	+	29.9911i	−0.318346	+	0.979768i	0.656010	+	0.754753i	$0.272243\pi$
$937$	−9.74471	+	29.9911i	−0.318346	+	0.979768i	−0.974355	+	0.225015i	$0.927757\pi$
$938$	16.3617	−	11.8875i	0.534228	−	0.388139i
$939$	4.27806	+	3.10819i	0.139609	+	0.101432i
$940$	−2.26523	−	6.97166i	−0.0738836	−	0.227390i
$941$	−6.84607	−	21.0700i	−0.223175	−	0.686863i	−0.998472	−	0.0552657i	$-0.982399\pi$
$941$	−6.84607	−	21.0700i	−0.223175	−	0.686863i	0.775296	−	0.631598i	$-0.217601\pi$
$942$	12.0246	+	8.73638i	0.391782	+	0.284646i
$943$	−34.5107	+	25.0735i	−1.12382	+	0.816506i
$944$	−3.24877	+	9.99870i	−0.105739	+	0.325430i
$945$	53.7535			1.74860
$946$	−3.07082	−	20.4793i	−0.0998408	−	0.665841i
$947$	−24.1814			−0.785789			−0.392894	−	0.919584i	$-0.628526\pi$
$947$	−24.1814			−0.785789			−0.392894	+	0.919584i	$0.628526\pi$
$948$	−1.93060	+	5.94178i	−0.0627030	+	0.192980i
$949$	0.451884	−	0.328313i	0.0146688	−	0.0106575i
$950$	2.84521	+	2.06717i	0.0923108	+	0.0670677i
$951$	7.85572	+	24.1774i	0.254739	+	0.784006i
$952$	−1.40293	−	4.31776i	−0.0454691	−	0.139939i
$953$	−4.93264	−	3.58377i	−0.159784	−	0.116090i	0.505020	−	0.863107i	$-0.331485\pi$
$953$	−4.93264	−	3.58377i	−0.159784	−	0.116090i	−0.664804	+	0.747018i	$0.731485\pi$
$954$	1.75040	−	1.27174i	0.0566713	−	0.0411741i
$955$	1.12617	−	3.46600i	0.0364420	−	0.112157i
$956$	−7.36507			−0.238203
$957$	−24.3254	+	12.1429i	−0.786327	+	0.392525i
$958$	2.63284			0.0850632
$959$	−22.3971	+	68.9313i	−0.723241	+	2.22591i
$960$	−3.38197	+	2.45714i	−0.109153	+	0.0793040i
$961$	16.2193	+	11.7840i	0.523202	+	0.380128i
$962$	−0.806761	−	2.48296i	−0.0260110	−	0.0800537i
$963$	0.629849	+	1.93848i	0.0202966	+	0.0624666i
$964$	−19.3235	−	14.0394i	−0.622369	−	0.452178i
$965$	−11.3449	+	8.24257i	−0.365206	+	0.265338i
$966$	−9.32757	+	28.7073i	−0.300110	+	0.923643i
$967$	−42.8736			−1.37872			−0.689361	−	0.724418i	$-0.742108\pi$
$967$	−42.8736			−1.37872			−0.689361	+	0.724418i	$0.742108\pi$
$968$	0.181305	−	10.9985i	0.00582737	−	0.353505i
$969$	−12.1131			−0.389128
$970$	3.89397	−	11.9844i	0.125028	−	0.384796i
$971$	35.3472	−	25.6812i	1.13435	−	0.824151i	0.148024	−	0.988984i	$-0.452709\pi$
$971$	35.3472	−	25.6812i	1.13435	−	0.824151i	0.986321	+	0.164833i	$0.0527086\pi$
$972$	1.40816	+	1.02309i	0.0451669	+	0.0328157i
$973$	−3.22652	−	9.93020i	−0.103437	−	0.318348i
$974$	−5.37633	−	16.5466i	−0.172269	−	0.530188i
$975$	−0.298536	−	0.216899i	−0.00956081	−	0.00694634i
$976$	2.20634	−	1.60300i	0.0706233	−	0.0513108i
$977$	11.8104	−	36.3488i	0.377849	−	1.16290i	−0.563687	−	0.825989i	$-0.690617\pi$
$977$	11.8104	−	36.3488i	0.377849	−	1.16290i	0.941536	−	0.336912i	$-0.109383\pi$
$978$	−12.5558			−0.401489
$979$	−29.3433	+	14.6478i	−0.937815	+	0.468146i
$980$	31.9698			1.02124
$981$	−0.0294649	+	0.0906837i	−0.000940743	+	0.00289531i
$982$	14.6623	−	10.6528i	0.467891	−	0.339943i
$983$	38.8579	+	28.2319i	1.23937	+	0.900458i	0.997557	−	0.0698635i	$-0.0222564\pi$
$983$	38.8579	+	28.2319i	1.23937	+	0.900458i	0.241818	+	0.970322i	$0.422256\pi$
$984$	6.28038	+	19.3290i	0.200211	+	0.616187i
$985$	−2.99513	−	9.21807i	−0.0954329	−	0.293712i
$986$	3.72618	+	2.70723i	0.118666	+	0.0862157i
$987$	−20.4018	+	14.8228i	−0.649397	+	0.471815i
$988$	0.843842	−	2.59708i	0.0268462	−	0.0826241i
$989$	23.3244			0.741674
$990$	0.193701	+	1.29179i	0.00615621	+	0.0410559i
$991$	33.9815			1.07946			0.539729	−	0.841839i	$-0.318527\pi$
$991$	33.9815			1.07946			0.539729	+	0.841839i	$0.318527\pi$
$992$	1.02265	−	3.14739i	0.0324692	−	0.0999298i
$993$	−40.6565	+	29.5387i	−1.29020	+	0.937382i
$994$	−11.5695	−	8.40576i	−0.366964	−	0.266615i
$995$	−1.78185	−	5.48396i	−0.0564883	−	0.173853i
$996$	5.45673	+	16.7941i	0.172903	+	0.532141i
$997$	12.5398	+	9.11070i	0.397139	+	0.288539i	0.768375	−	0.640000i	$-0.221066\pi$
$997$	12.5398	+	9.11070i	0.397139	+	0.288539i	−0.371235	+	0.928539i	$0.621066\pi$
$998$	1.44446	−	1.04946i	0.0457235	−	0.0332200i
$999$	−10.1359	+	31.1951i	−0.320686	+	0.986970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.g.273.2	yes	20
11.4	even	5		4114.2.a.bk.1.8		10
11.5	even	5	inner	374.2.g.g.137.2	✓	20
11.7	odd	10		4114.2.a.bl.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.g.137.2	✓	20	11.5	even	5	inner
374.2.g.g.273.2	yes	20	1.1	even	1	trivial
4114.2.a.bk.1.8		10	11.4	even	5
4114.2.a.bl.1.8		10	11.7	odd	10

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:	\( N \)	\(=\)	\( 374 = 2 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	374.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.43989 + 1.04614i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.725811 + 2.23382i) q^{5} +(-0.549988 - 1.69269i) q^{6} +(3.67291 + 2.66852i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.0518163 - 0.159474i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.43989 + 1.04614i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.725811 + 2.23382i) q^{5} +(-0.549988 - 1.69269i) q^{6} +(3.67291 + 2.66852i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.0518163 - 0.159474i) q^{9} -2.34877 q^{10} +(2.96744 - 1.48131i) q^{11} +1.77980 q^{12} +(0.123987 - 0.381594i) q^{13} +(-3.67291 + 2.66852i) q^{14} +(-3.38197 - 2.45714i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.309017 - 0.951057i) q^{17} +(0.135657 + 0.0985604i) q^{18} +(-5.50606 + 4.00039i) q^{19} +(0.725811 - 2.23382i) q^{20} -8.08022 q^{21} +(0.491820 + 3.27996i) q^{22} -3.73562 q^{23} +(-0.549988 + 1.69269i) q^{24} +(-0.418053 + 0.303733i) q^{25} +(0.324603 + 0.235838i) q^{26} +(-1.55774 - 4.79423i) q^{27} +(-1.40293 - 4.31776i) q^{28} +(3.72618 + 2.70723i) q^{29} +(3.38197 - 2.45714i) q^{30} +(-1.02265 + 3.14739i) q^{31} -1.00000 q^{32} +(-2.72313 + 5.23728i) q^{33} +1.00000 q^{34} +(-3.29516 + 10.1414i) q^{35} +(-0.135657 + 0.0985604i) q^{36} +(-5.26411 - 3.82460i) q^{37} +(-2.10313 - 6.47276i) q^{38} +(0.220673 + 0.679160i) q^{39} +(1.90020 + 1.38058i) q^{40} +(9.23827 - 6.71200i) q^{41} +(2.49692 - 7.68474i) q^{42} -6.24378 q^{43} +(-3.27140 - 0.545814i) q^{44} +0.393845 q^{45} +(1.15437 - 3.55279i) q^{46} +(2.52491 - 1.83445i) q^{47} +(-1.43989 - 1.04614i) q^{48} +(4.20611 + 12.9451i) q^{49} +(-0.159682 - 0.491451i) q^{50} +(1.43989 + 1.04614i) q^{51} +(-0.324603 + 0.235838i) q^{52} +(3.98730 - 12.2716i) q^{53} +5.04096 q^{54} +(5.46278 + 5.55357i) q^{55} +4.53996 q^{56} +(3.74314 - 11.5202i) q^{57} +(-3.72618 + 2.70723i) q^{58} +(8.50540 + 6.17954i) q^{59} +(1.29180 + 3.97574i) q^{60} +(-0.842748 - 2.59371i) q^{61} +(-2.67733 - 1.94520i) q^{62} +(0.615876 - 0.447460i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.942403 q^{65} +(-4.13945 - 4.20825i) q^{66} -4.45469 q^{67} +(-0.309017 + 0.951057i) q^{68} +(5.37888 - 3.90798i) q^{69} +(-8.62683 - 6.26776i) q^{70} +(0.973394 + 2.99580i) q^{71} +(-0.0518163 - 0.159474i) q^{72} +(1.12624 + 0.818262i) q^{73} +(5.26411 - 3.82460i) q^{74} +(0.284202 - 0.874683i) q^{75} +6.80587 q^{76} +(14.8521 + 2.47797i) q^{77} -0.714112 q^{78} +(-1.08473 + 3.33846i) q^{79} +(-1.90020 + 1.38058i) q^{80} +(7.66538 + 5.56922i) q^{81} +(3.52871 + 10.8602i) q^{82} +(3.06593 + 9.43596i) q^{83} +(6.53703 + 4.74943i) q^{84} +(1.90020 - 1.38058i) q^{85} +(1.92944 - 5.93819i) q^{86} -8.19741 q^{87} +(1.53002 - 2.94262i) q^{88} -9.88841 q^{89} +(-0.121705 + 0.374569i) q^{90} +(1.47369 - 1.07070i) q^{91} +(3.02218 + 2.19575i) q^{92} +(-1.82011 - 5.60172i) q^{93} +(0.964430 + 2.96821i) q^{94} +(-12.9325 - 9.39601i) q^{95} +(1.43989 - 1.04614i) q^{96} +(-1.65787 + 5.10241i) q^{97} -13.6113 q^{98} +(-0.0824688 - 0.549986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} + q^{6} + 6 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 + q^6 + 6 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} + q^{6} + 6 q^{7} + 5 q^{8} - 6 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 6 q^{14} + 10 q^{15} - 5 q^{16} + 5 q^{17} + 6 q^{18} + 7 q^{19} - 38 q^{21} - 17 q^{22} - 12 q^{23} + q^{24} + 3 q^{25} + 10 q^{26} + 47 q^{27} - 4 q^{28} + 5 q^{29} - 10 q^{30} - 7 q^{31} - 20 q^{32} - 56 q^{33} + 20 q^{34} + 19 q^{35} - 6 q^{36} - 6 q^{37} - 2 q^{38} + 3 q^{39} + 47 q^{41} - 7 q^{42} - 32 q^{43} - 3 q^{44} - 52 q^{45} + 12 q^{46} + 7 q^{47} - q^{48} + 41 q^{49} + 7 q^{50} + q^{51} - 10 q^{52} - 4 q^{53} - 22 q^{54} + 4 q^{56} + 57 q^{57} - 5 q^{58} + 7 q^{59} - 5 q^{60} - 4 q^{61} - 8 q^{62} + 37 q^{63} - 5 q^{64} - 104 q^{65} - 34 q^{66} - 26 q^{67} + 5 q^{68} + 45 q^{69} + 6 q^{70} + 36 q^{71} + 6 q^{72} + 22 q^{73} + 6 q^{74} - 25 q^{75} - 18 q^{76} - 13 q^{77} + 22 q^{78} + 82 q^{79} - 17 q^{81} + 8 q^{82} - 18 q^{83} + 12 q^{84} - 8 q^{86} - 58 q^{87} + 8 q^{88} - 16 q^{89} + 22 q^{90} + 43 q^{91} + 18 q^{92} + 41 q^{93} - 7 q^{94} - 46 q^{95} + q^{96} - 62 q^{97} - 36 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 + q^6 + 6 * q^7 + 5 * q^8 - 6 * q^9 - 3 * q^11 + 4 * q^12 + 10 * q^13 - 6 * q^14 + 10 * q^15 - 5 * q^16 + 5 * q^17 + 6 * q^18 + 7 * q^19 - 38 * q^21 - 17 * q^22 - 12 * q^23 + q^24 + 3 * q^25 + 10 * q^26 + 47 * q^27 - 4 * q^28 + 5 * q^29 - 10 * q^30 - 7 * q^31 - 20 * q^32 - 56 * q^33 + 20 * q^34 + 19 * q^35 - 6 * q^36 - 6 * q^37 - 2 * q^38 + 3 * q^39 + 47 * q^41 - 7 * q^42 - 32 * q^43 - 3 * q^44 - 52 * q^45 + 12 * q^46 + 7 * q^47 - q^48 + 41 * q^49 + 7 * q^50 + q^51 - 10 * q^52 - 4 * q^53 - 22 * q^54 + 4 * q^56 + 57 * q^57 - 5 * q^58 + 7 * q^59 - 5 * q^60 - 4 * q^61 - 8 * q^62 + 37 * q^63 - 5 * q^64 - 104 * q^65 - 34 * q^66 - 26 * q^67 + 5 * q^68 + 45 * q^69 + 6 * q^70 + 36 * q^71 + 6 * q^72 + 22 * q^73 + 6 * q^74 - 25 * q^75 - 18 * q^76 - 13 * q^77 + 22 * q^78 + 82 * q^79 - 17 * q^81 + 8 * q^82 - 18 * q^83 + 12 * q^84 - 8 * q^86 - 58 * q^87 + 8 * q^88 - 16 * q^89 + 22 * q^90 + 43 * q^91 + 18 * q^92 + 41 * q^93 - 7 * q^94 - 46 * q^95 + q^96 - 62 * q^97 - 36 * q^98 + 3 * q^99

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