LMFDB - Embedded newform 276.2.c.a.47.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.9
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.469504 - 1.33400i) q^{2} +(1.64481 - 0.542779i) q^{3} +(-1.55913 + 1.25264i) q^{4} -2.34886i q^{5} +(-1.49631 - 1.93934i) q^{6} -0.796368i q^{7} +(2.40305 + 1.49177i) q^{8} +(2.41078 - 1.78553i) q^{9} +O(q^{10})$	\(q+(-0.469504 - 1.33400i) q^{2} +(1.64481 - 0.542779i) q^{3} +(-1.55913 + 1.25264i) q^{4} -2.34886i q^{5} +(-1.49631 - 1.93934i) q^{6} -0.796368i q^{7} +(2.40305 + 1.49177i) q^{8} +(2.41078 - 1.78553i) q^{9} +(-3.13338 + 1.10280i) q^{10} +3.21461 q^{11} +(-1.88456 + 2.90662i) q^{12} -6.69212 q^{13} +(-1.06236 + 0.373898i) q^{14} +(-1.27491 - 3.86342i) q^{15} +(0.861782 - 3.90606i) q^{16} -0.675569i q^{17} +(-3.51378 - 2.37768i) q^{18} +0.720048i q^{19} +(2.94227 + 3.66218i) q^{20} +(-0.432251 - 1.30987i) q^{21} +(-1.50927 - 4.28831i) q^{22} +1.00000 q^{23} +(4.76225 + 1.14935i) q^{24} -0.517128 q^{25} +(3.14198 + 8.92731i) q^{26} +(2.99612 - 4.24538i) q^{27} +(0.997563 + 1.24164i) q^{28} -1.92582i q^{29} +(-4.55524 + 3.51462i) q^{30} +7.61577i q^{31} +(-5.61531 + 0.684292i) q^{32} +(5.28742 - 1.74482i) q^{33} +(-0.901212 + 0.317183i) q^{34} -1.87055 q^{35} +(-1.52210 + 5.80372i) q^{36} +1.89808 q^{37} +(0.960546 - 0.338065i) q^{38} +(-11.0072 + 3.63234i) q^{39} +(3.50395 - 5.64441i) q^{40} -7.63841i q^{41} +(-1.54443 + 1.19162i) q^{42} +11.0728i q^{43} +(-5.01201 + 4.02676i) q^{44} +(-4.19396 - 5.66258i) q^{45} +(-0.469504 - 1.33400i) q^{46} +1.22603 q^{47} +(-0.702661 - 6.89248i) q^{48} +6.36580 q^{49} +(0.242794 + 0.689851i) q^{50} +(-0.366685 - 1.11118i) q^{51} +(10.4339 - 8.38282i) q^{52} +11.3409i q^{53} +(-7.07004 - 2.00362i) q^{54} -7.55067i q^{55} +(1.18800 - 1.91371i) q^{56} +(0.390826 + 1.18434i) q^{57} +(-2.56905 + 0.904180i) q^{58} -0.176969 q^{59} +(6.82722 + 4.42657i) q^{60} +6.71562 q^{61} +(10.1595 - 3.57564i) q^{62} +(-1.42194 - 1.91987i) q^{63} +(3.54926 + 7.16957i) q^{64} +15.7188i q^{65} +(-4.81007 - 6.23424i) q^{66} +9.36728i q^{67} +(0.846246 + 1.05330i) q^{68} +(1.64481 - 0.542779i) q^{69} +(0.878233 + 2.49533i) q^{70} +9.44253 q^{71} +(8.45682 - 0.694391i) q^{72} +0.422106 q^{73} +(-0.891158 - 2.53205i) q^{74} +(-0.850576 + 0.280686i) q^{75} +(-0.901961 - 1.12265i) q^{76} -2.56002i q^{77} +(10.0135 + 12.9783i) q^{78} -10.1253i q^{79} +(-9.17478 - 2.02420i) q^{80} +(2.62375 - 8.60906i) q^{81} +(-10.1897 + 3.58627i) q^{82} +8.44270 q^{83} +(2.31474 + 1.50081i) q^{84} -1.58682 q^{85} +(14.7712 - 5.19874i) q^{86} +(-1.04529 - 3.16760i) q^{87} +(7.72487 + 4.79546i) q^{88} -11.2794i q^{89} +(-5.58482 + 8.25337i) q^{90} +5.32939i q^{91} +(-1.55913 + 1.25264i) q^{92} +(4.13368 + 12.5265i) q^{93} +(-0.575627 - 1.63553i) q^{94} +1.69129 q^{95} +(-8.86469 + 4.17340i) q^{96} -7.27066 q^{97} +(-2.98877 - 8.49200i) q^{98} +(7.74974 - 5.73980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.469504	−	1.33400i	−0.331990	−	0.943283i
$2$	−0.469504	−	1.33400i	−0.331990	−	0.943283i
$3$	1.64481	−	0.542779i	0.949630	−	0.313373i
$3$	1.64481	−	0.542779i	0.949630	−	0.313373i
$4$	−1.55913	+	1.25264i	−0.779566	+	0.626320i
$5$		−	2.34886i		−	1.05044i	−0.850966	−	0.525220i	$-0.823983\pi$
$5$		−	2.34886i		−	1.05044i	0.850966	−	0.525220i	$-0.176017\pi$
$6$	−1.49631	−	1.93934i	−0.610867	−	0.791733i
$7$		−	0.796368i		−	0.300999i	−0.988610	−	0.150499i	$-0.951912\pi$
$7$		−	0.796368i		−	0.300999i	0.988610	−	0.150499i	$-0.0480882\pi$
$8$	2.40305	+	1.49177i	0.849605	+	0.527419i
$9$	2.41078	−	1.78553i	0.803594	−	0.595178i
$10$	−3.13338	+	1.10280i	−0.990863	+	0.348735i
$11$	3.21461			0.969243			0.484621	−	0.874724i	$-0.338957\pi$
$11$	3.21461			0.969243			0.484621	+	0.874724i	$0.338957\pi$
$12$	−1.88456	+	2.90662i	−0.544027	+	0.839068i
$13$	−6.69212			−1.85606			−0.928030	−	0.372505i	$-0.878499\pi$
$13$	−6.69212			−1.85606			−0.928030	+	0.372505i	$0.878499\pi$
$14$	−1.06236	+	0.373898i	−0.283927	+	0.0999285i
$15$	−1.27491	−	3.86342i	−0.329180	−	0.997530i
$16$	0.861782	−	3.90606i	0.215446	−	0.976516i
$17$		−	0.675569i		−	0.163850i	−0.996639	−	0.0819248i	$-0.973893\pi$
$17$		−	0.675569i		−	0.163850i	0.996639	−	0.0819248i	$-0.0261067\pi$
$18$	−3.51378	−	2.37768i	−0.828206	−	0.560424i
$19$			0.720048i			0.165190i	0.996583	+	0.0825951i	$0.0263208\pi$
$19$			0.720048i			0.165190i	−0.996583	+	0.0825951i	$0.973679\pi$
$20$	2.94227	+	3.66218i	0.657912	+	0.818888i
$21$	−0.432251	−	1.30987i	−0.0943250	−	0.285837i
$22$	−1.50927	−	4.28831i	−0.321778	−	0.914270i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	4.76225	+	1.14935i	0.972090	+	0.234610i
$25$	−0.517128			−0.103426
$26$	3.14198	+	8.92731i	0.616193	+	1.75079i
$27$	2.99612	−	4.24538i	0.576604	−	0.817023i
$28$	0.997563	+	1.24164i	0.188522	+	0.234648i
$29$		−	1.92582i		−	0.357616i	−0.983884	−	0.178808i	$-0.942776\pi$
$29$		−	1.92582i		−	0.357616i	0.983884	−	0.178808i	$-0.0572240\pi$
$30$	−4.55524	+	3.51462i	−0.831669	+	0.641680i
$31$			7.61577i			1.36783i	0.729560	+	0.683917i	$0.239725\pi$
$31$			7.61577i			1.36783i	−0.729560	+	0.683917i	$0.760275\pi$
$32$	−5.61531	+	0.684292i	−0.992657	+	0.120967i
$33$	5.28742	−	1.74482i	0.920422	−	0.303735i
$34$	−0.901212	+	0.317183i	−0.154557	+	0.0543964i
$35$	−1.87055			−0.316181
$36$	−1.52210	+	5.80372i	−0.253683	+	0.967287i
$37$	1.89808			0.312043			0.156021	−	0.987754i	$-0.450133\pi$
$37$	1.89808			0.312043			0.156021	+	0.987754i	$0.450133\pi$
$38$	0.960546	−	0.338065i	0.155821	−	0.0548414i
$39$	−11.0072	+	3.63234i	−1.76257	+	0.581640i
$40$	3.50395	−	5.64441i	0.554023	−	0.892460i
$41$		−	7.63841i		−	1.19292i	−0.802643	−	0.596460i	$-0.796574\pi$
$41$		−	7.63841i		−	1.19292i	0.802643	−	0.596460i	$-0.203426\pi$
$42$	−1.54443	+	1.19162i	−0.238311	+	0.183870i
$43$			11.0728i			1.68859i	0.535879	+	0.844295i	$0.319980\pi$
$43$			11.0728i			1.68859i	−0.535879	+	0.844295i	$0.680020\pi$
$44$	−5.01201	+	4.02676i	−0.755588	+	0.607056i
$45$	−4.19396	−	5.66258i	−0.625199	−	0.844128i
$46$	−0.469504	−	1.33400i	−0.0692246	−	0.196688i
$47$	1.22603			0.178835			0.0894175	−	0.995994i	$-0.471499\pi$
$47$	1.22603			0.178835			0.0894175	+	0.995994i	$0.471499\pi$
$48$	−0.702661	−	6.89248i	−0.101420	−	0.994844i
$49$	6.36580			0.909400
$50$	0.242794	+	0.689851i	0.0343362	+	0.0975596i
$51$	−0.366685	−	1.11118i	−0.0513461	−	0.155597i
$52$	10.4339	−	8.38282i	1.44692	−	1.16249i
$53$			11.3409i			1.55780i	0.627151	+	0.778898i	$0.284221\pi$
$53$			11.3409i			1.55780i	−0.627151	+	0.778898i	$0.715779\pi$
$54$	−7.07004	−	2.00362i	−0.962111	−	0.272658i
$55$		−	7.55067i		−	1.01813i
$56$	1.18800	−	1.91371i	0.158753	−	0.255730i
$57$	0.390826	+	1.18434i	0.0517662	+	0.156870i
$58$	−2.56905	+	0.904180i	−0.337333	+	0.118725i
$59$	−0.176969			−0.0230394			−0.0115197	−	0.999934i	$-0.503667\pi$
$59$	−0.176969			−0.0230394			−0.0115197	+	0.999934i	$0.503667\pi$
$60$	6.82722	+	4.42657i	0.881391	+	0.571468i
$61$	6.71562			0.859847			0.429923	−	0.902865i	$-0.358541\pi$
$61$	6.71562			0.859847			0.429923	+	0.902865i	$0.358541\pi$
$62$	10.1595	−	3.57564i	1.29025	−	0.454106i
$63$	−1.42194	−	1.91987i	−0.179148	−	0.241881i
$64$	3.54926	+	7.16957i	0.443658	+	0.896196i
$65$			15.7188i			1.94968i
$66$	−4.81007	−	6.23424i	−0.592078	−	0.767381i
$67$			9.36728i			1.14440i	0.820116	+	0.572198i	$0.193909\pi$
$67$			9.36728i			1.14440i	−0.820116	+	0.572198i	$0.806091\pi$
$68$	0.846246	+	1.05330i	0.102622	+	0.127732i
$69$	1.64481	−	0.542779i	0.198012	−	0.0653429i
$70$	0.878233	+	2.49533i	0.104969	+	0.298249i
$71$	9.44253			1.12062			0.560311	−	0.828282i	$-0.310681\pi$
$71$	9.44253			1.12062			0.560311	+	0.828282i	$0.310681\pi$
$72$	8.45682	−	0.694391i	0.996646	−	0.0818347i
$73$	0.422106			0.0494037			0.0247019	−	0.999695i	$-0.492136\pi$
$73$	0.422106			0.0494037			0.0247019	+	0.999695i	$0.492136\pi$
$74$	−0.891158	−	2.53205i	−0.103595	−	0.294345i
$75$	−0.850576	+	0.280686i	−0.0982161	+	0.0324108i
$76$	−0.901961	−	1.12265i	−0.103462	−	0.128777i
$77$		−	2.56002i		−	0.291741i
$78$	10.0135	+	12.9783i	1.13381	+	1.46950i
$79$		−	10.1253i		−	1.13918i	−0.821928	−	0.569591i	$-0.807101\pi$
$79$		−	10.1253i		−	1.13918i	0.821928	−	0.569591i	$-0.192899\pi$
$80$	−9.17478	−	2.02420i	−1.02577	−	0.226313i
$81$	2.62375	−	8.60906i	0.291527	−	0.956562i
$82$	−10.1897	+	3.58627i	−1.12526	+	0.396037i
$83$	8.44270			0.926706			0.463353	−	0.886174i	$-0.346646\pi$
$83$	8.44270			0.926706			0.463353	+	0.886174i	$0.346646\pi$
$84$	2.31474	+	1.50081i	0.252558	+	0.163751i
$85$	−1.58682			−0.172114
$86$	14.7712	−	5.19874i	1.59282	−	0.560594i
$87$	−1.04529	−	3.16760i	−0.112067	−	0.339602i
$88$	7.72487	+	4.79546i	0.823473	+	0.511197i
$89$		−	11.2794i		−	1.19562i	−0.801640	−	0.597808i	$-0.796039\pi$
$89$		−	11.2794i		−	1.19562i	0.801640	−	0.597808i	$-0.203961\pi$
$90$	−5.58482	+	8.25337i	−0.588692	+	0.869981i
$91$			5.32939i			0.558672i
$92$	−1.55913	+	1.25264i	−0.162551	+	0.130597i
$93$	4.13368	+	12.5265i	0.428643	+	1.29894i
$94$	−0.575627	−	1.63553i	−0.0593714	−	0.168692i
$95$	1.69129			0.173523
$96$	−8.86469	+	4.17340i	−0.904749	+	0.425946i
$97$	−7.27066			−0.738224			−0.369112	−	0.929385i	$-0.620338\pi$
$97$	−7.27066			−0.738224			−0.369112	+	0.929385i	$0.620338\pi$
$98$	−2.98877	−	8.49200i	−0.301911	−	0.857821i
$99$	7.74974	−	5.73980i	0.778878	−	0.576871i
$100$	0.806271	−	0.647776i	0.0806271	−	0.0647776i
$101$			7.25596i			0.721995i	0.932567	+	0.360997i	$0.117564\pi$
$101$			7.25596i			0.721995i	−0.932567	+	0.360997i	$0.882436\pi$
$102$	−1.31016	+	1.01086i	−0.129725	+	0.100090i
$103$			11.6113i			1.14410i	0.820219	+	0.572050i	$0.193852\pi$
$103$			11.6113i			1.14410i	−0.820219	+	0.572050i	$0.806148\pi$
$104$	−16.0815	−	9.98308i	−1.57692	−	0.978922i
$105$	−3.07670	+	1.01530i	−0.300255	+	0.0990828i
$106$	15.1288	−	5.32461i	1.46944	−	0.517172i
$107$	−19.9682			−1.93040			−0.965198	−	0.261521i	$-0.915776\pi$
$107$	−19.9682			−1.93040			−0.965198	+	0.261521i	$0.915776\pi$
$108$	0.646582	+	10.3722i	0.0622174	+	0.998063i
$109$	−14.8640			−1.42371			−0.711855	−	0.702327i	$-0.752145\pi$
$109$	−14.8640			−1.42371			−0.711855	+	0.702327i	$0.752145\pi$
$110$	−10.0726	+	3.54507i	−0.960386	+	0.338009i
$111$	3.12198	−	1.03024i	0.296325	−	0.0977859i
$112$	−3.11066	−	0.686296i	−0.293930	−	0.0648489i
$113$			11.7321i			1.10367i	0.833954	+	0.551834i	$0.186072\pi$
$113$			11.7321i			1.10367i	−0.833954	+	0.551834i	$0.813928\pi$
$114$	1.39642	−	1.07742i	0.130787	−	0.100909i
$115$		−	2.34886i		−	0.219032i
$116$	2.41236	+	3.00261i	0.223982	+	0.278785i
$117$	−16.1332	+	11.9490i	−1.49152	+	1.10469i
$118$	0.0830878	+	0.236077i	0.00764885	+	0.0217327i
$119$	−0.538002			−0.0493185
$120$	2.69965	−	11.1858i	0.246443	−	1.02112i
$121$	−0.666258			−0.0605689
$122$	−3.15301	−	8.95866i	−0.285460	−	0.811079i
$123$	−4.14597	−	12.5637i	−0.373829	−	1.13283i
$124$	−9.53983	−	11.8740i	−0.856702	−	1.06632i
$125$		−	10.5296i		−	0.941798i
$126$	−1.89351	+	2.79826i	−0.168687	+	0.249289i
$127$		−	10.7727i		−	0.955926i	−0.878380	−	0.477963i	$-0.841375\pi$
$127$		−	10.7727i		−	0.955926i	0.878380	−	0.477963i	$-0.158625\pi$
$128$	7.89784	−	8.10087i	0.698077	−	0.716023i
$129$	6.01009	+	18.2127i	0.529159	+	1.60354i
$130$	20.9690	−	7.38006i	1.83910	−	0.647274i
$131$	−5.76563			−0.503745			−0.251873	−	0.967760i	$-0.581046\pi$
$131$	−5.76563			−0.503745			−0.251873	+	0.967760i	$0.581046\pi$
$132$	−6.05815	+	9.34365i	−0.527294	+	0.813260i
$133$	0.573423			0.0497221
$134$	12.4960	−	4.39798i	1.07949	−	0.379927i
$135$	−9.97179	−	7.03747i	−0.858235	−	0.605689i
$136$	1.00779	−	1.62342i	0.0864175	−	0.139208i
$137$			14.4134i			1.23142i	0.787971	+	0.615712i	$0.211132\pi$
$137$			14.4134i			1.23142i	−0.787971	+	0.615712i	$0.788868\pi$
$138$	−1.49631	−	1.93934i	−0.127375	−	0.165088i
$139$		−	11.6755i		−	0.990301i	−0.868807	−	0.495150i	$-0.835113\pi$
$139$		−	11.6755i		−	0.990301i	0.868807	−	0.495150i	$-0.164887\pi$
$140$	2.91644	−	2.34313i	0.246484	−	0.198031i
$141$	2.01659	−	0.665464i	0.169827	−	0.0560421i
$142$	−4.43331	−	12.5964i	−0.372035	−	1.05706i
$143$	−21.5126			−1.79897
$144$	−4.89683	−	10.9554i	−0.408069	−	0.912951i
$145$	−4.52347			−0.375654
$146$	−0.198180	−	0.563091i	−0.0164015	−	0.0466017i
$147$	10.4705	−	3.45522i	0.863593	−	0.284982i
$148$	−2.95936	+	2.37762i	−0.243258	+	0.195439i
$149$		−	15.0305i		−	1.23135i	−0.788000	−	0.615675i	$-0.788883\pi$
$149$		−	15.0305i		−	1.23135i	0.788000	−	0.615675i	$-0.211117\pi$
$150$	0.773785	+	1.00289i	0.0631793	+	0.0818855i
$151$			0.656832i			0.0534523i	0.999643	+	0.0267261i	$0.00850821\pi$
$151$			0.656832i			0.0534523i	−0.999643	+	0.0267261i	$0.991492\pi$
$152$	−1.07414	+	1.73031i	−0.0871245	+	0.140346i
$153$	−1.20625	−	1.62865i	−0.0975196	−	0.131669i
$154$	−3.41507	+	1.20194i	−0.275194	+	0.0968549i
$155$	17.8884			1.43683
$156$	12.6117	−	19.4514i	1.00975	−	1.55736i
$157$	−13.6112			−1.08629			−0.543146	−	0.839638i	$-0.682767\pi$
$157$	−13.6112			−1.08629			−0.543146	+	0.839638i	$0.682767\pi$
$158$	−13.5072	+	4.75386i	−1.07457	+	0.378197i
$159$	6.15561	+	18.6536i	0.488172	+	1.47933i
$160$	1.60730	+	13.1896i	0.127069	+	1.04273i
$161$		−	0.796368i		−	0.0627626i
$162$	−12.7164	+	0.541903i	−0.999093	+	0.0425759i
$163$			3.07465i			0.240825i	0.992724	+	0.120413i	$0.0384218\pi$
$163$			3.07465i			0.240825i	−0.992724	+	0.120413i	$0.961578\pi$
$164$	9.56818	+	11.9093i	0.747150	+	0.929959i
$165$	−4.09834	−	12.4194i	−0.319055	−	0.966848i
$166$	−3.96388	−	11.2626i	−0.307657	−	0.874146i
$167$	−4.30533			−0.333157			−0.166578	−	0.986028i	$-0.553272\pi$
$167$	−4.30533			−0.333157			−0.166578	+	0.986028i	$0.553272\pi$
$168$	0.915303	−	3.79250i	0.0706172	−	0.292598i
$169$	31.7845			2.44496
$170$	0.745017	+	2.11682i	0.0571402	+	0.162353i
$171$	1.28567	+	1.73588i	0.0983175	+	0.132746i
$172$	−13.8703	−	17.2640i	−1.05760	−	1.31637i
$173$		−	5.68962i		−	0.432574i	−0.976330	−	0.216287i	$-0.930605\pi$
$173$		−	5.68962i		−	0.432574i	0.976330	−	0.216287i	$-0.0693947\pi$
$174$	−3.73482	+	2.88163i	−0.283136	+	0.218456i
$175$			0.411824i			0.0311310i
$176$	2.77030	−	12.5565i	0.208819	−	0.946481i
$177$	−0.291080	+	0.0960551i	−0.0218789	+	0.00721994i
$178$	−15.0468	+	5.29573i	−1.12780	+	0.396932i
$179$	−21.1309			−1.57939			−0.789697	−	0.613497i	$-0.789762\pi$
$179$	−21.1309			−1.57939			−0.789697	+	0.613497i	$0.789762\pi$
$180$	13.6321	+	3.57519i	1.01608	+	0.266479i
$181$	−12.7953			−0.951067			−0.475533	−	0.879698i	$-0.657745\pi$
$181$	−12.7953			−0.951067			−0.475533	+	0.879698i	$0.657745\pi$
$182$	7.10942	−	2.50217i	0.526986	−	0.185473i
$183$	11.0459	−	3.64509i	0.816536	−	0.269453i
$184$	2.40305	+	1.49177i	0.177155	+	0.109975i
$185$		−	4.45832i		−	0.327782i
$186$	14.7696	−	11.3956i	1.08296	−	0.835564i
$187$		−	2.17169i		−	0.158810i
$188$	−1.91154	+	1.53578i	−0.139414	+	0.112008i
$189$	−3.38088	−	2.38602i	−0.245923	−	0.173557i
$190$	−0.794067	−	2.25619i	−0.0576077	−	0.163681i
$191$	−8.07378			−0.584198			−0.292099	−	0.956388i	$-0.594354\pi$
$191$	−8.07378			−0.584198			−0.292099	+	0.956388i	$0.594354\pi$
$192$	9.72934	+	9.86610i	0.702155	+	0.712024i
$193$	5.34117			0.384466			0.192233	−	0.981349i	$-0.438427\pi$
$193$	5.34117			0.384466			0.192233	+	0.981349i	$0.438427\pi$
$194$	3.41361	+	9.69909i	0.245083	+	0.696354i
$195$	8.53185	+	25.8544i	0.610978	+	1.85148i
$196$	−9.92512	+	7.97406i	−0.708937	+	0.569576i
$197$			1.19189i			0.0849186i	0.999098	+	0.0424593i	$0.0135193\pi$
$197$			1.19189i			0.0849186i	−0.999098	+	0.0424593i	$0.986481\pi$
$198$	−11.2954	−	7.64332i	−0.802732	−	0.543187i
$199$			24.2553i			1.71941i	0.510788	+	0.859707i	$0.329354\pi$
$199$			24.2553i			1.71941i	−0.510788	+	0.859707i	$0.670646\pi$
$200$	−1.24268	−	0.771435i	−0.0878709	−	0.0545487i
$201$	5.08436	+	15.4074i	0.358623	+	1.08675i
$202$	9.67948	−	3.40670i	0.681046	−	0.239695i
$203$	−1.53366			−0.107642
$204$	1.96362	+	1.27315i	0.137481	+	0.0891386i
$205$	−17.9415			−1.25309
$206$	15.4896	−	5.45158i	1.07921	−	0.379829i
$207$	2.41078	−	1.78553i	0.167561	−	0.124103i
$208$	−5.76715	+	26.1398i	−0.399880	+	1.81247i
$209$			2.31467i			0.160109i
$210$	2.79893	+	3.62764i	0.193145	+	0.250331i
$211$			18.3549i			1.26361i	0.775129	+	0.631803i	$0.217685\pi$
$211$			18.3549i			1.26361i	−0.775129	+	0.631803i	$0.782315\pi$
$212$	−14.2061	−	17.6820i	−0.975679	−	1.21440i
$213$	15.5312	−	5.12521i	1.06418	−	0.351173i
$214$	9.37514	+	26.6376i	0.640871	+	1.82091i
$215$	26.0085			1.77376
$216$	13.5329	−	5.73232i	0.920800	−	0.390035i
$217$	6.06496			0.411716
$218$	6.97869	+	19.8286i	0.472657	+	1.34296i
$219$	0.694283	−	0.229110i	0.0469153	−	0.0154818i
$220$	9.45827	+	11.7725i	0.637677	+	0.793701i
$221$			4.52099i			0.304115i
$222$	−2.84012	−	3.68103i	−0.190617	−	0.247055i
$223$		−	26.3795i		−	1.76650i	−0.468899	−	0.883252i	$-0.655349\pi$
$223$		−	26.3795i		−	1.76650i	0.468899	−	0.883252i	$-0.344651\pi$
$224$	0.544948	+	4.47186i	0.0364109	+	0.298788i
$225$	−1.24668	+	0.923349i	−0.0831122	+	0.0615566i
$226$	15.6507	−	5.50829i	1.04107	−	0.366406i
$227$	6.18899			0.410778			0.205389	−	0.978680i	$-0.434154\pi$
$227$	6.18899			0.410778			0.205389	+	0.978680i	$0.434154\pi$
$228$	−2.09290	−	1.35698i	−0.138606	−	0.0898679i
$229$	5.28251			0.349078			0.174539	−	0.984650i	$-0.444156\pi$
$229$	5.28251			0.349078			0.174539	+	0.984650i	$0.444156\pi$
$230$	−3.13338	+	1.10280i	−0.206609	+	0.0727164i
$231$	−1.38952	−	4.21073i	−0.0914238	−	0.277046i
$232$	2.87287	−	4.62783i	0.188613	−	0.303832i
$233$			10.0481i			0.658272i	0.944283	+	0.329136i	$0.106757\pi$
$233$			10.0481i			0.658272i	−0.944283	+	0.329136i	$0.893243\pi$
$234$	23.5146	+	15.9117i	1.53720	+	1.04018i
$235$		−	2.87977i		−	0.187856i
$236$	0.275918	−	0.221679i	0.0179607	−	0.0144301i
$237$	−5.49579	−	16.6541i	−0.356990	−	1.08180i
$238$	0.252594	+	0.717696i	0.0163732	+	0.0465214i
$239$	−13.7376			−0.888613			−0.444307	−	0.895875i	$-0.646550\pi$
$239$	−13.7376			−0.888613			−0.444307	+	0.895875i	$0.646550\pi$
$240$	−16.1894	+	1.65045i	−1.04502	+	0.106536i
$241$	−14.6530			−0.943881			−0.471940	−	0.881631i	$-0.656446\pi$
$241$	−14.6530			−0.943881			−0.471940	+	0.881631i	$0.656446\pi$
$242$	0.312811	+	0.888791i	0.0201082	+	0.0571336i
$243$	−0.357257	−	15.5844i	−0.0229180	−	0.999737i
$244$	−10.4705	+	8.41226i	−0.670307	+	0.538540i
$245$		−	14.9523i		−	0.955270i
$246$	−14.8135	+	11.4294i	−0.944474	+	0.728715i
$247$		−	4.81864i		−	0.306603i
$248$	−11.3610	+	18.3011i	−0.721422	+	1.16212i
$249$	13.8866	−	4.58252i	0.880028	−	0.290405i
$250$	−14.0466	+	4.94370i	−0.888382	+	0.312667i
$251$	−0.497047			−0.0313734			−0.0156867	−	0.999877i	$-0.504993\pi$
$251$	−0.497047			−0.0313734			−0.0156867	+	0.999877i	$0.504993\pi$
$252$	4.62190	+	1.21215i	0.291152	+	0.0763582i
$253$	3.21461			0.202101
$254$	−14.3709	+	5.05785i	−0.901709	+	0.317358i
$255$	−2.61001	+	0.861290i	−0.163445	+	0.0539361i
$256$	−14.5147	−	6.73235i	−0.907166	−	0.420772i
$257$		−	15.6813i		−	0.978170i	−0.872236	−	0.489085i	$-0.837331\pi$
$257$		−	15.6813i		−	0.978170i	0.872236	−	0.489085i	$-0.162669\pi$
$258$	21.4740	−	16.5684i	1.33691	−	1.03150i
$259$		−	1.51157i		−	0.0939245i
$260$	−19.6900	−	24.5077i	−1.22112	−	1.51990i
$261$	−3.43861	−	4.64273i	−0.212845	−	0.287378i
$262$	2.70699	+	7.69137i	0.167238	+	0.475174i
$263$	27.6024			1.70204			0.851018	−	0.525136i	$-0.175985\pi$
$263$	27.6024			1.70204			0.851018	+	0.525136i	$0.175985\pi$
$264$	15.3088	+	3.69471i	0.942191	+	0.227394i
$265$	26.6382			1.63637
$266$	−0.269224	−	0.764948i	−0.0165072	−	0.0469020i
$267$	−6.12222	−	18.5525i	−0.374674	−	1.13539i
$268$	−11.7338	−	14.6048i	−0.716758	−	0.892131i
$269$		−	26.6429i		−	1.62444i	−0.583348	−	0.812222i	$-0.698258\pi$
$269$		−	26.6429i		−	1.62444i	0.583348	−	0.812222i	$-0.301742\pi$
$270$	−4.70621	+	16.6065i	−0.286411	+	1.01064i
$271$			3.04363i			0.184888i	0.995718	+	0.0924438i	$0.0294678\pi$
$271$			3.04363i			0.184888i	−0.995718	+	0.0924438i	$0.970532\pi$
$272$	−2.63882	−	0.582194i	−0.160002	−	0.0353007i
$273$	2.89268	+	8.76582i	0.175073	+	0.530531i
$274$	19.2276	−	6.76717i	1.16158	−	0.408820i
$275$	−1.66237			−0.100244
$276$	−1.88456	+	2.90662i	−0.113437	+	0.174958i
$277$	0.169013			0.0101550			0.00507749	−	0.999987i	$-0.498384\pi$
$277$	0.169013			0.0101550			0.00507749	+	0.999987i	$0.498384\pi$
$278$	−15.5751	+	5.48168i	−0.934134	+	0.328770i
$279$	13.5982	+	18.3600i	0.814104	+	1.09918i
$280$	−4.49503	−	2.79043i	−0.268629	−	0.166760i
$281$			4.21550i			0.251476i	0.992064	+	0.125738i	$0.0401298\pi$
$281$			4.21550i			0.251476i	−0.992064	+	0.125738i	$0.959870\pi$
$282$	−1.83453	−	2.37769i	−0.109244	−	0.141590i
$283$			3.01367i			0.179144i	0.995980	+	0.0895719i	$0.0285499\pi$
$283$			3.01367i			0.179144i	−0.995980	+	0.0895719i	$0.971450\pi$
$284$	−14.7222	+	11.8281i	−0.873599	+	0.701869i
$285$	2.78184	−	0.917995i	0.164782	−	0.0543773i
$286$	10.1002	+	28.6979i	0.597240	+	1.69694i
$287$	−6.08298			−0.359067
$288$	−12.3155	+	11.6760i	−0.725696	+	0.688015i
$289$	16.5436			0.973153
$290$	2.12379	+	6.03433i	0.124713	+	0.354348i
$291$	−11.9588	+	3.94636i	−0.701039	+	0.231340i
$292$	−0.658118	+	0.528747i	−0.0385135	+	0.0309426i
$293$			9.32392i			0.544709i	0.962197	+	0.272355i	$0.0878023\pi$
$293$			9.32392i			0.544709i	−0.962197	+	0.272355i	$0.912198\pi$
$294$	−9.52522	−	12.3455i	−0.555522	−	0.720002i
$295$			0.415675i			0.0242015i
$296$	4.56118	+	2.83150i	0.265113	+	0.164577i
$297$	9.63138	−	13.6473i	0.558870	−	0.791894i
$298$	−20.0508	+	7.05690i	−1.16151	+	0.408795i
$299$	−6.69212			−0.387015
$300$	0.974561	−	1.50309i	0.0562663	−	0.0867811i
$301$	8.81804			0.508263
$302$	0.876217	−	0.308386i	0.0504206	−	0.0177456i
$303$	3.93838	+	11.9347i	0.226254	+	0.685628i
$304$	2.81255	+	0.620524i	0.161311	+	0.0355895i
$305$		−	15.7740i		−	0.903218i
$306$	−1.60629	+	2.37380i	−0.0918253	+	0.135701i
$307$		−	4.19690i		−	0.239529i	−0.992802	−	0.119765i	$-0.961786\pi$
$307$		−	4.19690i		−	0.239529i	0.992802	−	0.119765i	$-0.0382140\pi$
$308$	3.20678	+	3.99140i	0.182723	+	0.227431i
$309$	6.30239	+	19.0984i	0.358530	+	1.08647i
$310$	−8.39866	−	23.8631i	−0.477012	−	1.35534i
$311$	−1.57780			−0.0894688			−0.0447344	−	0.998999i	$-0.514244\pi$
$311$	−1.57780			−0.0894688			−0.0447344	+	0.998999i	$0.514244\pi$
$312$	−31.8695	−	7.69157i	−1.80426	−	0.435449i
$313$	7.02504			0.397079			0.198539	−	0.980093i	$-0.436380\pi$
$313$	7.02504			0.397079			0.198539	+	0.980093i	$0.436380\pi$
$314$	6.39052	+	18.1574i	0.360638	+	1.02468i
$315$	−4.50950	+	3.33994i	−0.254082	+	0.188184i
$316$	12.6833	+	15.7866i	0.713493	+	0.888068i
$317$			0.0798294i			0.00448367i	0.999997	+	0.00224183i	$0.000713598\pi$
$317$			0.0798294i			0.00448367i	−0.999997	+	0.00224183i	$0.999286\pi$
$318$	21.9939	−	16.9696i	1.23336	−	0.951606i
$319$		−	6.19076i		−	0.346616i
$320$	16.8403	−	8.33671i	0.941401	−	0.466036i
$321$	−32.8438	+	10.8383i	−1.83316	+	0.604935i
$322$	−1.06236	+	0.373898i	−0.0592029	+	0.0208365i
$323$	0.486442			0.0270664
$324$	6.69330	+	16.7093i	0.371850	+	0.928293i
$325$	3.46068			0.191964
$326$	4.10160	−	1.44356i	0.227166	−	0.0799515i
$327$	−24.4484	+	8.06784i	−1.35200	+	0.446153i
$328$	11.3947	−	18.3555i	0.629169	−	1.01351i
$329$		−	0.976372i		−	0.0538291i
$330$	−14.6433	+	11.2982i	−0.806089	+	0.621943i
$331$		−	29.4692i		−	1.61977i	−0.586588	−	0.809886i	$-0.699529\pi$
$331$		−	29.4692i		−	1.61977i	0.586588	−	0.809886i	$-0.300471\pi$
$332$	−13.1633	+	10.5757i	−0.722429	+	0.580415i
$333$	4.57586	−	3.38909i	0.250756	−	0.185721i
$334$	2.02137	+	5.74333i	0.110605	+	0.314261i
$335$	22.0024			1.20212
$336$	−5.48895	+	0.559577i	−0.299447	+	0.0305274i
$337$	−12.3468			−0.672575			−0.336287	−	0.941759i	$-0.609171\pi$
$337$	−12.3468			−0.672575			−0.336287	+	0.941759i	$0.609171\pi$
$338$	−14.9229	−	42.4006i	−0.811701	−	2.30629i
$339$	6.36796	+	19.2971i	0.345860	+	1.04808i
$340$	2.47405	−	1.98771i	0.134174	−	0.107799i
$341$			24.4818i			1.32576i
$342$	1.71204	−	2.53009i	0.0925766	−	0.136812i
$343$		−	10.6441i		−	0.574727i
$344$	−16.5181	+	26.6085i	−0.890595	+	1.43463i
$345$	−1.27491	−	3.86342i	−0.0686388	−	0.207999i
$346$	−7.58998	+	2.67130i	−0.408040	+	0.143610i
$347$	−17.0322			−0.914339			−0.457169	−	0.889380i	$-0.651137\pi$
$347$	−17.0322			−0.914339			−0.457169	+	0.889380i	$0.651137\pi$
$348$	5.59762	+	3.62933i	0.300064	+	0.194553i
$349$	18.1974			0.974082			0.487041	−	0.873379i	$-0.338076\pi$
$349$	18.1974			0.974082			0.487041	+	0.873379i	$0.338076\pi$
$350$	0.549375	−	0.193353i	0.0293653	−	0.0103352i
$351$	−20.0504	+	28.4106i	−1.07021	+	1.51644i
$352$	−18.0511	+	2.19974i	−0.962125	+	0.117246i
$353$		−	9.37154i		−	0.498797i	−0.968401	−	0.249398i	$-0.919767\pi$
$353$		−	9.37154i		−	0.498797i	0.968401	−	0.249398i	$-0.0802329\pi$
$354$	0.264801	+	0.343204i	0.0140740	+	0.0182411i
$355$		−	22.1792i		−	1.17715i
$356$	14.1290	+	17.5861i	0.748838	+	0.932061i
$357$	−0.884909	+	0.292016i	−0.0468344	+	0.0154551i
$358$	9.92103	+	28.1886i	0.524343	+	1.48982i
$359$	34.0837			1.79887			0.899434	−	0.437057i	$-0.143979\pi$
$359$	34.0837			1.79887			0.899434	+	0.437057i	$0.143979\pi$
$360$	−1.63102	−	19.8639i	−0.0859625	−	1.04692i
$361$	18.4815			0.972712
$362$	6.00745	+	17.0690i	0.315744	+	0.897125i
$363$	−1.09587	+	0.361631i	−0.0575180	+	0.0189807i
$364$	−6.67581	−	8.30922i	−0.349908	−	0.435521i
$365$		−	0.991466i		−	0.0518957i
$366$	−10.0487	−	13.0239i	−0.525252	−	0.680769i
$367$			31.6260i			1.65086i	0.564502	+	0.825432i	$0.309068\pi$
$367$			31.6260i			1.65086i	−0.564502	+	0.825432i	$0.690932\pi$
$368$	0.861782	−	3.90606i	0.0449235	−	0.203618i
$369$	−13.6386	−	18.4145i	−0.709999	−	0.958623i
$370$	−5.94742	+	2.09320i	−0.309192	+	0.108820i
$371$	9.03155			0.468895
$372$	−22.1361	−	14.3524i	−1.14770	−	0.744138i
$373$	−10.5471			−0.546110			−0.273055	−	0.961998i	$-0.588034\pi$
$373$	−10.5471			−0.546110			−0.273055	+	0.961998i	$0.588034\pi$
$374$	−2.89705	+	1.01962i	−0.149803	+	0.0527233i
$375$	−5.71525	−	17.3192i	−0.295134	−	0.894360i
$376$	2.94621	+	1.82895i	0.151939	+	0.0943211i
$377$			12.8878i			0.663756i
$378$	−1.59562	+	5.63036i	−0.0820697	+	0.289594i
$379$			11.3796i			0.584531i	0.956337	+	0.292265i	$0.0944091\pi$
$379$			11.3796i			0.584531i	−0.956337	+	0.292265i	$0.905591\pi$
$380$	−2.63694	+	2.11858i	−0.135272	+	0.108681i
$381$	−5.84721	−	17.7191i	−0.299562	−	0.907776i
$382$	3.79068	+	10.7705i	0.193948	+	0.551065i
$383$	15.0762			0.770360			0.385180	−	0.922842i	$-0.374139\pi$
$383$	15.0762			0.770360			0.385180	+	0.922842i	$0.374139\pi$
$384$	8.59345	−	17.6112i	0.438532	−	0.898715i
$385$	−6.01311			−0.306456
$386$	−2.50770	−	7.12514i	−0.127639	−	0.362660i
$387$	19.7709	+	26.6942i	1.00501	+	1.35694i
$388$	11.3359	−	9.10753i	0.575494	−	0.462365i
$389$		−	9.20298i		−	0.466610i	−0.972404	−	0.233305i	$-0.925046\pi$
$389$		−	9.20298i		−	0.466610i	0.972404	−	0.233305i	$-0.0749540\pi$
$390$	30.4842	−	23.5203i	1.54363	−	1.19100i
$391$		−	0.675569i		−	0.0341650i
$392$	15.2973	+	9.49629i	0.772631	+	0.479635i
$393$	−9.48335	+	3.12946i	−0.478372	+	0.157860i
$394$	1.58998	−	0.559597i	0.0801023	−	0.0281921i
$395$	−23.7828			−1.19664
$396$	−4.89295	+	18.6567i	−0.245880	+	0.937536i
$397$	−28.5280			−1.43178			−0.715890	−	0.698214i	$-0.753979\pi$
$397$	−28.5280			−1.43178			−0.715890	+	0.698214i	$0.753979\pi$
$398$	32.3567	−	11.3880i	1.62189	−	0.570827i
$399$	0.943170	−	0.311242i	0.0472176	−	0.0155816i
$400$	−0.445652	+	2.01993i	−0.0222826	+	0.100997i
$401$			5.92896i			0.296078i	0.988982	+	0.148039i	$0.0472961\pi$
$401$			5.92896i			0.296078i	−0.988982	+	0.148039i	$0.952704\pi$
$402$	18.1664	−	14.0164i	0.906056	−	0.699073i
$403$		−	50.9657i		−	2.53878i
$404$	−9.08911	−	11.3130i	−0.452200	−	0.562843i
$405$	−20.2215	−	6.16281i	−1.00481	−	0.306232i
$406$	0.720060	+	2.04591i	0.0357360	+	0.101537i
$407$	6.10160			0.302445
$408$	0.776464	−	3.21723i	0.0384407	−	0.159277i
$409$	1.37988			0.0682306			0.0341153	−	0.999418i	$-0.489139\pi$
$409$	1.37988			0.0682306			0.0341153	+	0.999418i	$0.489139\pi$
$410$	8.42362	+	23.9341i	0.416013	+	1.18202i
$411$	7.82331	+	23.7073i	0.385895	+	1.16940i
$412$	−14.5448	−	18.1036i	−0.716573	−	0.891901i
$413$			0.140933i			0.00693484i
$414$	−3.51378	−	2.37768i	−0.172693	−	0.116856i
$415$		−	19.8307i		−	0.973450i
$416$	37.5783	−	4.57937i	1.84243	−	0.224522i
$417$	−6.33720	−	19.2039i	−0.310334	−	0.940419i
$418$	3.08778	−	1.08675i	0.151028	−	0.0531547i
$419$	15.3755			0.751144			0.375572	−	0.926793i	$-0.377446\pi$
$419$	15.3755			0.751144			0.375572	+	0.926793i	$0.377446\pi$
$420$	3.52518	−	5.43698i	0.172011	−	0.265298i
$421$	25.5241			1.24397			0.621984	−	0.783030i	$-0.286327\pi$
$421$	25.5241			1.24397			0.621984	+	0.783030i	$0.286327\pi$
$422$	24.4855	−	8.61772i	1.19194	−	0.419504i
$423$	2.95569	−	2.18912i	0.143711	−	0.106439i
$424$	−16.9180	+	27.2528i	−0.821612	+	1.32351i
$425$			0.349356i			0.0169463i
$426$	−14.1290	−	18.3123i	−0.684552	−	0.887234i
$427$		−	5.34810i		−	0.258813i
$428$	31.1330	−	25.0129i	1.50487	−	1.20905i
$429$	−35.3841	+	11.6766i	−1.70836	+	0.563750i
$430$	−12.2111	−	34.6954i	−0.588871	−	1.67316i
$431$	17.1182			0.824556			0.412278	−	0.911058i	$-0.364733\pi$
$431$	17.1182			0.824556			0.412278	+	0.911058i	$0.364733\pi$
$432$	−14.0007	−	15.3616i	−0.673609	−	0.739087i
$433$	−31.8725			−1.53169			−0.765846	−	0.643024i	$-0.777680\pi$
$433$	−31.8725			−1.53169			−0.765846	+	0.643024i	$0.777680\pi$
$434$	−2.84752	−	8.09068i	−0.136685	−	0.388365i
$435$	−7.44024	+	2.45524i	−0.356732	+	0.117720i
$436$	23.1749	−	18.6192i	1.10988	−	0.891698i
$437$			0.720048i			0.0344445i
$438$	−0.631602	−	0.818608i	−0.0301791	−	0.0391146i
$439$			9.98392i			0.476507i	0.971203	+	0.238253i	$0.0765748\pi$
$439$			9.98392i			0.476507i	−0.971203	+	0.238253i	$0.923425\pi$
$440$	11.2638	−	18.1446i	0.536982	−	0.865010i
$441$	15.3466	−	11.3663i	0.730788	−	0.541254i
$442$	6.03102	−	2.12262i	0.286866	−	0.100963i
$443$	−39.5217			−1.87773			−0.938866	−	0.344284i	$-0.888122\pi$
$443$	−39.5217			−1.87773			−0.938866	+	0.344284i	$0.888122\pi$
$444$	−3.57706	+	5.51700i	−0.169760	+	0.261825i
$445$	−26.4937			−1.25592
$446$	−35.1904	+	12.3853i	−1.66631	+	0.586461i
$447$	−8.15826	−	24.7223i	−0.385872	−	1.16933i
$448$	5.70962	−	2.82652i	0.269754	−	0.133540i
$449$		−	22.2438i		−	1.04975i	−0.851180	−	0.524875i	$-0.824112\pi$
$449$		−	22.2438i		−	1.04975i	0.851180	−	0.524875i	$-0.175888\pi$
$450$	1.81707	+	1.22956i	0.0856577	+	0.0579622i
$451$		−	24.5545i		−	1.15623i
$452$	−14.6962	−	18.2920i	−0.691249	−	0.860381i
$453$	0.356515	+	1.08036i	0.0167505	+	0.0507599i
$454$	−2.90576	−	8.25614i	−0.136374	−	0.387480i
$455$	12.5180			0.586852
$456$	−0.827585	+	3.42904i	−0.0387552	+	0.160580i
$457$	12.2420			0.572657			0.286329	−	0.958131i	$-0.407565\pi$
$457$	12.2420			0.572657			0.286329	+	0.958131i	$0.407565\pi$
$458$	−2.48016	−	7.04689i	−0.115890	−	0.329280i
$459$	−2.86805	−	2.02409i	−0.133869	−	0.0944764i
$460$	2.94227	+	3.66218i	0.137184	+	0.170750i
$461$			25.1325i			1.17054i	0.810840	+	0.585268i	$0.199011\pi$
$461$			25.1325i			1.17054i	−0.810840	+	0.585268i	$0.800989\pi$
$462$	−4.96475	+	3.83058i	−0.230981	+	0.178215i
$463$			22.2615i			1.03458i	0.855810	+	0.517290i	$0.173059\pi$
$463$			22.2615i			1.03458i	−0.855810	+	0.517290i	$0.826941\pi$
$464$	−7.52237	−	1.65964i	−0.349217	−	0.0770467i
$465$	29.4229	−	9.70942i	1.36445	−	0.450264i
$466$	13.4042	−	4.71762i	0.620937	−	0.218539i
$467$	−10.3712			−0.479921			−0.239960	−	0.970783i	$-0.577134\pi$
$467$	−10.3712			−0.479921			−0.239960	+	0.970783i	$0.577134\pi$
$468$	10.1861	−	38.8392i	0.470850	−	1.79534i
$469$	7.45980			0.344462
$470$	−3.84163	+	1.35206i	−0.177201	+	0.0623661i
$471$	−22.3878	+	7.38787i	−1.03158	+	0.340415i
$472$	−0.425265	−	0.263997i	−0.0195744	−	0.0121514i
$473$			35.5949i			1.63665i
$474$	−19.6364	+	15.1506i	−0.901929	+	0.695889i
$475$		−	0.372357i		−	0.0170849i
$476$	0.838816	−	0.673923i	0.0384471	−	0.0308892i
$477$	20.2496	+	27.3405i	0.927165	+	1.25184i
$478$	6.44988	+	18.3260i	0.295010	+	0.838214i
$479$	−14.8914			−0.680407			−0.340203	−	0.940352i	$-0.610496\pi$
$479$	−14.8914			−0.680407			−0.340203	+	0.940352i	$0.610496\pi$
$480$	9.80272	+	20.8219i	0.447431	+	0.950385i
$481$	−12.7022			−0.579170
$482$	6.87963	+	19.5471i	0.313359	+	0.890347i
$483$	−0.432251	−	1.30987i	−0.0196681	−	0.0596012i
$484$	1.03878	−	0.834582i	0.0472174	−	0.0379355i
$485$			17.0777i			0.775460i
$486$	−20.6219	+	7.79351i	−0.935427	+	0.353521i
$487$		−	13.0830i		−	0.592848i	−0.955056	−	0.296424i	$-0.904206\pi$
$487$		−	13.0830i		−	0.592848i	0.955056	−	0.296424i	$-0.0957942\pi$
$488$	16.1379	+	10.0181i	0.730530	+	0.453500i
$489$	1.66885	+	5.05721i	0.0754682	+	0.228695i
$490$	−19.9465	+	7.02019i	−0.901090	+	0.317140i
$491$	−33.1384			−1.49552			−0.747758	−	0.663972i	$-0.768870\pi$
$491$	−33.1384			−1.49552			−0.747758	+	0.663972i	$0.768870\pi$
$492$	22.2019	+	14.3951i	1.00094	+	0.648980i
$493$	−1.30102			−0.0585952
$494$	−6.42809	+	2.26237i	−0.289213	+	0.101789i
$495$	−13.4820	−	18.2030i	−0.605969	−	0.818165i
$496$	29.7477	+	6.56314i	1.33571	+	0.294694i
$497$		−	7.51973i		−	0.337306i
$498$	−12.6329	−	16.3733i	−0.566094	−	0.733704i
$499$			41.0462i			1.83748i	0.394865	+	0.918739i	$0.370791\pi$
$499$			41.0462i			1.83748i	−0.394865	+	0.918739i	$0.629209\pi$
$500$	13.1898	+	16.4171i	0.589867	+	0.734194i
$501$	−7.08144	+	2.33684i	−0.316376	+	0.104402i
$502$	0.233366	+	0.663063i	0.0104156	+	0.0295940i
$503$	−15.3234			−0.683239			−0.341619	−	0.939838i	$-0.610975\pi$
$503$	−15.3234			−0.683239			−0.341619	+	0.939838i	$0.610975\pi$
$504$	−0.552991	−	6.73474i	−0.0246322	−	0.299989i
$505$	17.0432			0.758413
$506$	−1.50927	−	4.28831i	−0.0670954	−	0.190638i
$507$	52.2793	−	17.2519i	2.32181	−	0.766185i
$508$	13.4944	+	16.7961i	0.598716	+	0.745207i
$509$			15.9280i			0.705996i	0.935624	+	0.352998i	$0.114838\pi$
$509$			15.9280i			0.705996i	−0.935624	+	0.352998i	$0.885162\pi$
$510$	2.37437	+	3.07738i	0.105139	+	0.136269i
$511$		−	0.336151i		−	0.0148705i
$512$	−2.16629	+	22.5235i	−0.0957374	+	0.995407i
$513$	3.05687	+	2.15735i	0.134964	+	0.0952494i
$514$	−20.9188	+	7.36241i	−0.922691	+	0.324742i
$515$	27.2734			1.20181
$516$	−32.1844	−	20.8675i	−1.41684	−	0.918638i
$517$	3.94122			0.173335
$518$	−2.01644	+	0.709689i	−0.0885974	+	0.0311820i
$519$	−3.08821	−	9.35834i	−0.135557	−	0.410785i
$520$	−23.4488	+	37.7731i	−1.02830	+	1.65646i
$521$		−	8.57243i		−	0.375565i	−0.982211	−	0.187783i	$-0.939870\pi$
$521$		−	8.57243i		−	0.375565i	0.982211	−	0.187783i	$-0.0601300\pi$
$522$	−4.57898	+	6.76690i	−0.200416	+	0.296179i
$523$		−	18.2693i		−	0.798860i	−0.916764	−	0.399430i	$-0.869208\pi$
$523$		−	18.2693i		−	0.798860i	0.916764	−	0.399430i	$-0.130792\pi$
$524$	8.98937	−	7.22226i	0.392703	−	0.315506i
$525$	0.223529	+	0.677371i	0.00975562	+	0.0295629i
$526$	−12.9594	−	36.8217i	−0.565059	−	1.60550i
$527$	5.14498			0.224119
$528$	−2.25879	−	22.1567i	−0.0983010	−	0.964245i
$529$	1.00000			0.0434783
$530$	−12.5068	−	35.5355i	−0.543259	−	1.54356i
$531$	−0.426634	+	0.315984i	−0.0185143	+	0.0137125i
$532$	−0.894042	+	0.718293i	−0.0387616	+	0.0311419i
$533$			51.1172i			2.21413i
$534$	−21.8746	+	16.8775i	−0.946608	+	0.730362i
$535$			46.9024i			2.02777i
$536$	−13.9738	+	22.5100i	−0.603576	+	0.972284i
$537$	−34.7562	+	11.4694i	−1.49984	+	0.494940i
$538$	−35.5417	+	12.5089i	−1.53231	+	0.539299i
$539$	20.4636			0.881429
$540$	24.3627	−	1.51873i	1.04841	−	0.0653557i
$541$	−7.80032			−0.335362			−0.167681	−	0.985841i	$-0.553628\pi$
$541$	−7.80032			−0.335362			−0.167681	+	0.985841i	$0.553628\pi$
$542$	4.06022	−	1.42900i	0.174401	−	0.0613807i
$543$	−21.0458	+	6.94501i	−0.903162	+	0.298039i
$544$	0.462287	+	3.79353i	0.0198204	+	0.162646i
$545$			34.9133i			1.49552i
$546$	10.3355	−	7.97443i	0.442319	−	0.341274i
$547$			8.69373i			0.371717i	0.982577	+	0.185859i	$0.0595066\pi$
$547$			8.69373i			0.371717i	−0.982577	+	0.185859i	$0.940493\pi$
$548$	−18.0549	−	22.4725i	−0.771266	−	0.959976i
$549$	16.1899	−	11.9910i	0.690968	−	0.511761i
$550$	0.780488	+	2.21760i	0.0332801	+	0.0945589i
$551$	1.38668			0.0590746
$552$	4.76225	+	1.14935i	0.202695	+	0.0489195i
$553$	−8.06345			−0.342893
$554$	−0.0793521	−	0.225463i	−0.00337135	−	0.00957902i
$555$	−2.41988	−	7.33308i	−0.102718	−	0.311272i
$556$	14.6252	+	18.2036i	0.620246	+	0.772005i
$557$		−	15.8975i		−	0.673598i	−0.941577	−	0.336799i	$-0.890656\pi$
$557$		−	15.8975i		−	0.673598i	0.941577	−	0.336799i	$-0.109344\pi$
$558$	18.1079	−	26.7602i	0.766567	−	1.13285i
$559$		−	74.1007i		−	3.13412i
$560$	−1.61201	+	7.30650i	−0.0681199	+	0.308756i
$561$	−1.17875	−	3.57202i	−0.0497668	−	0.150811i
$562$	5.62349	−	1.97919i	0.237213	−	0.0834873i
$563$	−22.2168			−0.936325			−0.468162	−	0.883642i	$-0.655084\pi$
$563$	−22.2168			−0.936325			−0.468162	+	0.883642i	$0.655084\pi$
$564$	−2.31053	+	3.56360i	−0.0972911	+	0.150055i
$565$	27.5571			1.15934
$566$	4.02024	−	1.41493i	0.168983	−	0.0594739i
$567$	−6.85598	−	2.08947i	−0.287924	−	0.0877494i
$568$	22.6908	+	14.0861i	0.952087	+	0.591038i
$569$		−	2.61033i		−	0.109431i	−0.998502	−	0.0547155i	$-0.982575\pi$
$569$		−	2.61033i		−	0.109431i	0.998502	−	0.0547155i	$-0.0174252\pi$
$570$	−2.53070	−	3.27999i	−0.105999	−	0.137384i
$571$			17.4391i			0.729802i	0.931046	+	0.364901i	$0.118897\pi$
$571$			17.4391i			0.729802i	−0.931046	+	0.364901i	$0.881103\pi$
$572$	33.5409	−	26.9475i	1.40242	−	1.12673i
$573$	−13.2798	+	4.38228i	−0.554772	+	0.183072i
$574$	2.85599	+	8.11472i	0.119207	+	0.338702i
$575$	−0.517128			−0.0215657
$576$	21.3580	+	10.9470i	0.889917	+	0.456123i
$577$	31.5241			1.31237			0.656184	−	0.754601i	$-0.272170\pi$
$577$	31.5241			1.31237			0.656184	+	0.754601i	$0.272170\pi$
$578$	−7.76729	−	22.0692i	−0.323077	−	0.917959i
$579$	8.78520	−	2.89907i	0.365100	−	0.120481i
$580$	7.05269	−	5.66629i	0.292847	−	0.235280i
$581$		−	6.72349i		−	0.278937i
$582$	10.8792	+	14.1003i	0.450957	+	0.584476i
$583$			36.4567i			1.50988i
$584$	1.01434	+	0.629684i	0.0419737	+	0.0260565i
$585$	28.0665	+	37.8947i	1.16041	+	1.56675i
$586$	12.4381	−	4.37762i	0.513815	−	0.180838i
$587$	1.18762			0.0490183			0.0245092	−	0.999700i	$-0.492198\pi$
$587$	1.18762			0.0490183			0.0245092	+	0.999700i	$0.492198\pi$
$588$	−11.9968	+	18.5029i	−0.494738	+	0.763048i
$589$	−5.48372			−0.225953
$590$	0.554512	−	0.195161i	0.0228289	−	0.00803466i
$591$	0.646932	+	1.96043i	0.0266112	+	0.0806412i
$592$	1.63573	−	7.41403i	0.0672283	−	0.304715i
$593$			1.62727i			0.0668238i	0.999442	+	0.0334119i	$0.0106373\pi$
$593$			1.62727i			0.0668238i	−0.999442	+	0.0334119i	$0.989363\pi$
$594$	−22.7275	−	6.44086i	−0.932519	−	0.264272i
$595$			1.26369i			0.0518062i
$596$	18.8279	+	23.4346i	0.771220	+	0.959918i
$597$	13.1653	+	39.8953i	0.538818	+	1.63281i
$598$	3.14198	+	8.92731i	0.128485	+	0.365065i
$599$	6.10795			0.249564			0.124782	−	0.992184i	$-0.460177\pi$
$599$	6.10795			0.249564			0.124782	+	0.992184i	$0.460177\pi$
$600$	−2.46269	−	0.594360i	−0.100539	−	0.0242646i
$601$	−31.6552			−1.29124			−0.645621	−	0.763658i	$-0.723401\pi$
$601$	−31.6552			−1.29124			−0.645621	+	0.763658i	$0.723401\pi$
$602$	−4.14011	−	11.7633i	−0.168738	−	0.479436i
$603$	16.7256	+	22.5825i	0.681118	+	0.919629i
$604$	−0.822775	−	1.02409i	−0.0334782	−	0.0416696i
$605$			1.56494i			0.0636240i
$606$	14.0718	−	10.8572i	0.571627	−	0.441043i
$607$		−	16.3567i		−	0.663898i	−0.943297	−	0.331949i	$-0.892294\pi$
$607$		−	16.3567i		−	0.663898i	0.943297	−	0.331949i	$-0.107706\pi$
$608$	−0.492723	−	4.04329i	−0.0199826	−	0.163977i
$609$	−2.52258	+	0.832438i	−0.102220	+	0.0337321i
$610$	−21.0426	+	7.40597i	−0.851990	+	0.299859i
$611$	−8.20475			−0.331929
$612$	3.92082	+	1.02828i	0.158490	+	0.0415658i
$613$	35.0612			1.41611			0.708054	−	0.706158i	$-0.249573\pi$
$613$	35.0612			1.41611			0.708054	+	0.706158i	$0.249573\pi$
$614$	−5.59867	+	1.97046i	−0.225944	+	0.0795213i
$615$	−29.5104	+	9.73828i	−1.18997	+	0.392685i
$616$	3.81895	−	6.15183i	0.153870	−	0.247864i
$617$		−	30.9142i		−	1.24456i	−0.782795	−	0.622279i	$-0.786207\pi$
$617$		−	30.9142i		−	1.24456i	0.782795	−	0.622279i	$-0.213793\pi$
$618$	22.5184	−	17.3742i	0.905822	−	0.698893i
$619$			31.1753i			1.25304i	0.779405	+	0.626520i	$0.215521\pi$
$619$			31.1753i			1.25304i	−0.779405	+	0.626520i	$0.784479\pi$
$620$	−27.8903	+	22.4077i	−1.12010	+	0.899915i
$621$	2.99612	−	4.24538i	0.120230	−	0.170361i
$622$	0.740784	+	2.10479i	0.0297027	+	0.0843944i
$623$	−8.98256			−0.359879
$624$	4.70229	+	46.1253i	0.188242	+	1.84649i
$625$	−27.3182			−1.09273
$626$	−3.29829	−	9.37143i	−0.131826	−	0.374558i
$627$	1.25636	+	3.80719i	0.0501740	+	0.152045i
$628$	21.2216	−	17.0499i	0.846836	−	0.680367i
$629$		−	1.28229i		−	0.0511281i
$630$	6.57272	+	4.44758i	0.261863	+	0.177196i
$631$		−	29.0712i		−	1.15731i	−0.815574	−	0.578653i	$-0.803578\pi$
$631$		−	29.0712i		−	1.15731i	0.815574	−	0.578653i	$-0.196422\pi$
$632$	15.1046	−	24.3315i	0.600827	−	0.967856i
$633$	9.96266	+	30.1903i	0.395980	+	1.19996i
$634$	0.106493	−	0.0374802i	0.00422937	−	0.00148853i
$635$	−25.3036			−1.00414
$636$	−32.9637	−	21.3727i	−1.30710	−	0.847483i
$637$	−42.6007			−1.68790
$638$	−8.25850	+	2.90659i	−0.326957	+	0.115073i
$639$	22.7639	−	16.8600i	0.900526	−	0.666969i
$640$	−19.0278	−	18.5509i	−0.752139	−	0.733289i
$641$			1.69974i			0.0671358i	0.999436	+	0.0335679i	$0.0106870\pi$
$641$			1.69974i			0.0671358i	−0.999436	+	0.0335679i	$0.989313\pi$
$642$	29.8786	+	38.7251i	1.17922	+	1.52836i
$643$			8.93016i			0.352171i	0.984375	+	0.176086i	$0.0563436\pi$
$643$			8.93016i			0.352171i	−0.984375	+	0.176086i	$0.943656\pi$
$644$	0.997563	+	1.24164i	0.0393095	+	0.0489276i
$645$	42.7789	−	14.1168i	1.68442	−	0.555850i
$646$	−0.228387	−	0.648916i	−0.00898575	−	0.0255312i
$647$	23.1977			0.911997			0.455999	−	0.889981i	$-0.349282\pi$
$647$	23.1977			0.911997			0.455999	+	0.889981i	$0.349282\pi$
$648$	19.1477	−	16.7740i	0.752193	−	0.658943i
$649$	−0.568887			−0.0223308
$650$	−1.62481	−	4.61656i	−0.0637301	−	0.181077i
$651$	9.97569	−	3.29193i	0.390978	−	0.129021i
$652$	−3.85143	−	4.79379i	−0.150834	−	0.187739i
$653$		−	18.6140i		−	0.728422i	−0.931317	−	0.364211i	$-0.881339\pi$
$653$		−	18.6140i		−	0.728422i	0.931317	−	0.364211i	$-0.118661\pi$
$654$	22.2411	+	28.8263i	0.869697	+	1.12720i
$655$			13.5426i			0.529154i
$656$	−29.8361	−	6.58265i	−1.16490	−	0.257009i
$657$	1.01761	−	0.753684i	0.0397006	−	0.0294040i
$658$	−1.30248	+	0.458411i	−0.0507761	+	0.0178707i
$659$	9.00688			0.350858			0.175429	−	0.984492i	$-0.443869\pi$
$659$	9.00688			0.350858			0.175429	+	0.984492i	$0.443869\pi$
$660$	21.9469	+	14.2297i	0.854282	+	0.553891i
$661$	7.53200			0.292961			0.146480	−	0.989214i	$-0.453205\pi$
$661$	7.53200			0.292961			0.146480	+	0.989214i	$0.453205\pi$
$662$	−39.3120	+	13.8359i	−1.52790	+	0.537747i
$663$	2.45390	+	7.43616i	0.0953015	+	0.288797i
$664$	20.2882	+	12.5945i	0.787334	+	0.488763i
$665$		−	1.34689i		−	0.0522301i
$666$	−6.66944	−	4.51303i	−0.258436	−	0.174876i
$667$		−	1.92582i		−	0.0745680i
$668$	6.71258	−	5.39304i	0.259718	−	0.208663i
$669$	−14.3182	−	43.3892i	−0.553575	−	1.67752i
$670$	−10.3302	−	29.3513i	−0.399091	−	1.13394i
$671$	21.5881			0.833400
$672$	3.32356	+	7.05955i	0.128209	+	0.272328i
$673$	−18.3835			−0.708633			−0.354316	−	0.935126i	$-0.615286\pi$
$673$	−18.3835			−0.708633			−0.354316	+	0.935126i	$0.615286\pi$
$674$	5.79689	+	16.4707i	0.223288	+	0.634428i
$675$	−1.54938	+	2.19540i	−0.0596357	+	0.0845011i
$676$	−49.5562	+	39.8145i	−1.90601	+	1.53133i
$677$		−	39.7266i		−	1.52682i	−0.645915	−	0.763409i	$-0.723524\pi$
$677$		−	39.7266i		−	1.52682i	0.645915	−	0.763409i	$-0.276476\pi$
$678$	22.7526	−	17.5550i	0.873810	−	0.674194i
$679$			5.79012i			0.222204i
$680$	−3.81319	−	2.36716i	−0.146229	−	0.0907764i
$681$	10.1797	−	3.35925i	0.390087	−	0.128727i
$682$	32.6588	−	11.4943i	1.25057	−	0.440139i
$683$	−1.64291			−0.0628641			−0.0314320	−	0.999506i	$-0.510007\pi$
$683$	−1.64291			−0.0628641			−0.0314320	+	0.999506i	$0.510007\pi$
$684$	−4.17896	−	1.09598i	−0.159786	−	0.0419059i
$685$	33.8551			1.29354
$686$	−14.1993	+	4.99745i	−0.542130	+	0.190803i
$687$	8.68871	−	2.86723i	0.331495	−	0.109392i
$688$	43.2512	+	9.54237i	1.64893	+	0.363799i
$689$		−	75.8948i		−	2.89136i
$690$	−4.55524	+	3.51462i	−0.173415	+	0.133799i
$691$		−	43.5396i		−	1.65632i	−0.560489	−	0.828162i	$-0.689387\pi$
$691$		−	43.5396i		−	1.65632i	0.560489	−	0.828162i	$-0.310613\pi$
$692$	7.12706	+	8.87087i	0.270930	+	0.337220i
$693$	−4.57099	−	6.17164i	−0.173638	−	0.234441i
$694$	7.99671	+	22.7211i	0.303551	+	0.862480i
$695$	−27.4240			−1.04025
$696$	2.21344	−	9.17123i	0.0839000	−	0.347634i
$697$	−5.16028			−0.195459
$698$	−8.54373	−	24.2753i	−0.323385	−	0.918835i
$699$	5.45388	+	16.5272i	0.206285	+	0.625115i
$700$	−0.515868	−	0.642088i	−0.0194980	−	0.0242686i
$701$			40.8332i			1.54225i	0.636684	+	0.771125i	$0.280305\pi$
$701$			40.8332i			1.54225i	−0.636684	+	0.771125i	$0.719695\pi$
$702$	47.3136	+	13.4084i	1.78574	+	0.506069i
$703$			1.36671i			0.0515464i
$704$	11.4095	+	23.0474i	0.430012	+	0.868632i
$705$	−1.56308	−	4.73667i	−0.0588689	−	0.178393i
$706$	−12.5017	+	4.39998i	−0.470507	+	0.165595i
$707$	5.77841			0.217320
$708$	0.333510	−	0.514381i	0.0125341	−	0.0193316i
$709$	6.73893			0.253086			0.126543	−	0.991961i	$-0.459612\pi$
$709$	6.73893			0.253086			0.126543	+	0.991961i	$0.459612\pi$
$710$	−29.5871	+	10.4132i	−1.11038	+	0.390801i
$711$	−18.0790	−	24.4098i	−0.678016	−	0.915441i
$712$	16.8263	−	27.1049i	0.630591	−	1.01580i
$713$			7.61577i			0.285213i
$714$	0.805019	+	1.04337i	0.0301271	+	0.0390471i
$715$			50.5300i			1.88971i
$716$	32.9458	−	26.4694i	1.23124	−	0.989207i
$717$	−22.5958	+	7.45649i	−0.843854	+	0.278468i
$718$	−16.0024	−	45.4678i	−0.597205	−	1.69684i
$719$	−16.1780			−0.603339			−0.301670	−	0.953413i	$-0.597544\pi$
$719$	−16.1780			−0.603339			−0.301670	+	0.953413i	$0.597544\pi$
$720$	−25.7327	+	11.5020i	−0.959001	+	0.428653i
$721$	9.24690			0.344373
$722$	−8.67716	−	24.6544i	−0.322930	−	0.917543i
$723$	−24.1013	+	7.95332i	−0.896337	+	0.295787i
$724$	19.9495	−	16.0279i	0.741419	−	0.595673i
$725$			0.995895i			0.0369866i
$726$	0.996930	+	1.29210i	0.0369996	+	0.0479544i
$727$			17.7372i			0.657836i	0.944358	+	0.328918i	$0.106684\pi$
$727$			17.7372i			0.657836i	−0.944358	+	0.328918i	$0.893316\pi$
$728$	−7.95021	+	12.8068i	−0.294654	+	0.474650i
$729$	−9.04648	−	25.4394i	−0.335055	−	0.942199i
$730$	−1.32262	+	0.465497i	−0.0489523	+	0.0172288i
$731$	7.48046			0.276675
$732$	−12.6560	+	19.5197i	−0.467780	+	0.721470i
$733$	−21.9273			−0.809903			−0.404951	−	0.914338i	$-0.632712\pi$
$733$	−21.9273			−0.809903			−0.404951	+	0.914338i	$0.632712\pi$
$734$	42.1892	−	14.8485i	1.55723	−	0.548070i
$735$	−8.11581	−	24.5937i	−0.299356	−	0.907153i
$736$	−5.61531	+	0.684292i	−0.206983	+	0.0252233i
$737$			30.1122i			1.10920i
$738$	−18.1617	+	26.8397i	−0.668541	+	0.987983i
$739$			21.5215i			0.791682i	0.918319	+	0.395841i	$0.129547\pi$
$739$			21.5215i			0.791682i	−0.918319	+	0.395841i	$0.870453\pi$
$740$	5.58468	+	6.95111i	0.205297	+	0.255528i
$741$	−2.61546	−	7.92574i	−0.0960812	−	0.291159i
$742$	−4.24035	−	12.0481i	−0.155668	−	0.442300i
$743$	−6.40397			−0.234939			−0.117469	−	0.993076i	$-0.537478\pi$
$743$	−6.40397			−0.234939			−0.117469	+	0.993076i	$0.537478\pi$
$744$	−8.75317	+	36.2682i	−0.320907	+	1.32966i
$745$	−35.3046			−1.29346
$746$	4.95192	+	14.0699i	0.181303	+	0.515136i
$747$	20.3535	−	15.0747i	0.744696	−	0.551555i
$748$	2.72035	+	3.38596i	0.0994660	+	0.123803i
$749$			15.9020i			0.581047i
$750$	−20.4205	+	15.7556i	−0.745653	+	0.575314i
$751$			49.9030i			1.82099i	0.413525	+	0.910493i	$0.364297\pi$
$751$			49.9030i			1.82099i	−0.413525	+	0.910493i	$0.635703\pi$
$752$	1.05657	−	4.78896i	0.0385292	−	0.174635i
$753$	−0.817547	+	0.269787i	−0.0297931	+	0.00983158i
$754$	17.1924	−	6.05088i	0.626110	−	0.220360i
$755$	1.54281			0.0561484
$756$	8.26006	−	0.514917i	0.300416	−	0.0187274i
$757$	29.0398			1.05547			0.527735	−	0.849409i	$-0.323041\pi$
$757$	29.0398			1.05547			0.527735	+	0.849409i	$0.323041\pi$
$758$	15.1804	−	5.34277i	0.551378	−	0.194058i
$759$	5.28742	−	1.74482i	0.191921	−	0.0633331i
$760$	4.06424	+	2.52301i	0.147426	+	0.0915191i
$761$		−	26.7922i		−	0.971216i	−0.874177	−	0.485608i	$-0.838598\pi$
$761$		−	26.7922i		−	0.971216i	0.874177	−	0.485608i	$-0.161402\pi$
$762$	−20.8920	+	16.1194i	−0.756838	+	0.583944i
$763$			11.8372i			0.428535i
$764$	12.5881	−	10.1136i	0.455421	−	0.365895i
$765$	−3.82547	+	2.83331i	−0.138310	+	0.102439i
$766$	−7.07836	−	20.1118i	−0.255751	−	0.726667i
$767$	1.18430			0.0427625
$768$	−27.5280	−	3.19518i	−0.993331	−	0.115296i
$769$	−35.3787			−1.27579			−0.637894	−	0.770124i	$-0.720194\pi$
$769$	−35.3787			−1.27579			−0.637894	+	0.770124i	$0.720194\pi$
$770$	2.82318	+	8.02151i	0.101740	+	0.289075i
$771$	−8.51145	−	25.7926i	−0.306532	−	0.928899i
$772$	−8.32759	+	6.69057i	−0.299717	+	0.240799i
$773$		−	42.2942i		−	1.52122i	−0.649211	−	0.760608i	$-0.724901\pi$
$773$		−	42.2942i		−	1.52122i	0.649211	−	0.760608i	$-0.275099\pi$
$774$	26.3276	−	38.9075i	0.946326	−	1.39850i
$775$		−	3.93833i		−	0.141469i
$776$	−17.4717	−	10.8461i	−0.627199	−	0.389354i
$777$	−0.820449	−	2.48624i	−0.0294334	−	0.0891935i
$778$	−12.2768	+	4.32084i	−0.440145	+	0.154910i
$779$	5.50002			0.197059
$780$	−45.6886	−	29.6231i	−1.63591	−	1.06068i
$781$	30.3541			1.08616
$782$	−0.901212	+	0.317183i	−0.0322273	+	0.0113424i
$783$	−8.17583	−	5.76999i	−0.292180	−	0.206203i
$784$	5.48593	−	24.8652i	0.195926	−	0.888043i
$785$			31.9708i			1.14109i
$786$	8.62718	+	11.1815i	0.307721	+	0.398832i
$787$			1.09045i			0.0388705i	0.999811	+	0.0194352i	$0.00618682\pi$
$787$			1.09045i			0.0388705i	−0.999811	+	0.0194352i	$0.993813\pi$
$788$	−1.49301	−	1.85831i	−0.0531862	−	0.0661996i
$789$	45.4006	−	14.9820i	1.61631	−	0.533373i
$790$	11.1661	+	31.7264i	0.397273	+	1.12877i
$791$	9.34310			0.332202
$792$	27.1854	−	2.23220i	0.965992	−	0.0793177i
$793$	−44.9417			−1.59593
$794$	13.3940	+	38.0565i	0.475336	+	1.35057i
$795$	43.8147	−	14.4587i	1.55395	−	0.512796i
$796$	−30.3832	−	37.8172i	−1.07690	−	1.34040i
$797$		−	17.1558i		−	0.607688i	−0.952722	−	0.303844i	$-0.901730\pi$
$797$		−	17.1558i		−	0.607688i	0.952722	−	0.303844i	$-0.0982702\pi$
$798$	−0.858020	−	1.11206i	−0.0303736	−	0.0393666i
$799$		−	0.828269i		−	0.0293021i
$800$	2.90384	−	0.353867i	0.102666	−	0.0125111i
$801$	−20.1398	−	27.1922i	−0.711603	−	0.960789i
$802$	7.90926	−	2.78367i	0.279286	−	0.0982949i
$803$	1.35691			0.0478842
$804$	−27.2271	−	17.6532i	−0.960225	−	0.622582i
$805$	−1.87055			−0.0659284
$806$	−67.9884	+	23.9286i	−2.39479	+	0.842849i
$807$	−14.4612	−	43.8224i	−0.509058	−	1.54262i
$808$	−10.8242	+	17.4364i	−0.380794	+	0.613411i
$809$			41.0217i			1.44225i	0.692806	+	0.721124i	$0.256374\pi$
$809$			41.0217i			1.44225i	−0.692806	+	0.721124i	$0.743626\pi$
$810$	1.27285	+	29.8690i	0.0447235	+	1.04949i
$811$			0.995583i			0.0349596i	0.999847	+	0.0174798i	$0.00556428\pi$
$811$			0.995583i			0.0349596i	−0.999847	+	0.0174798i	$0.994436\pi$
$812$	2.39118	−	1.92113i	0.0839139	−	0.0674183i
$813$	1.65202	+	5.00619i	0.0579388	+	0.175575i
$814$	−2.86473	−	8.13956i	−0.100409	−	0.285291i
$815$	7.22192			0.252973
$816$	−4.65635	+	0.474697i	−0.163005	+	0.0166177i
$817$	−7.97296			−0.278939
$818$	−0.647859	−	1.84076i	−0.0226519	−	0.0643608i
$819$	9.51580	+	12.8480i	0.332509	+	0.448945i
$820$	27.9732	−	22.4743i	0.976867	−	0.784836i
$821$			1.60669i			0.0560738i	0.999607	+	0.0280369i	$0.00892559\pi$
$821$			1.60669i			0.0560738i	−0.999607	+	0.0280369i	$0.991074\pi$
$822$	27.9526	−	21.5670i	0.974959	−	0.752236i
$823$			19.6188i			0.683869i	0.939724	+	0.341934i	$0.111082\pi$
$823$			19.6188i			0.683869i	−0.939724	+	0.341934i	$0.888918\pi$
$824$	−17.3214	+	27.9026i	−0.603420	+	0.972033i
$825$	−2.73427	+	0.902297i	−0.0951952	+	0.0314140i
$826$	0.188005	−	0.0661684i	0.00654151	−	0.00230229i
$827$	22.2783			0.774694			0.387347	−	0.921934i	$-0.373392\pi$
$827$	22.2783			0.774694			0.387347	+	0.921934i	$0.373392\pi$
$828$	−1.52210	+	5.80372i	−0.0528965	+	0.201693i
$829$	37.8163			1.31341			0.656707	−	0.754146i	$-0.271949\pi$
$829$	37.8163			1.31341			0.656707	+	0.754146i	$0.271949\pi$
$830$	−26.4542	+	9.31059i	−0.918239	+	0.323175i
$831$	0.277993	−	0.0917364i	0.00964347	−	0.00318230i
$832$	−23.7521	−	47.9796i	−0.823455	−	1.66339i
$833$		−	4.30054i		−	0.149005i
$834$	−22.6427	+	17.4702i	−0.784054	+	0.604942i
$835$			10.1126i			0.349961i
$836$	−2.89946	−	3.60888i	−0.100280	−	0.124816i
$837$	32.3318	+	22.8178i	1.11755	+	0.788699i
$838$	−7.21888	−	20.5110i	−0.249372	−	0.708541i
$839$	−9.88894			−0.341404			−0.170702	−	0.985323i	$-0.554604\pi$
$839$	−9.88894			−0.341404			−0.170702	+	0.985323i	$0.554604\pi$
$840$	−8.90804	−	2.14992i	−0.307357	−	0.0741792i
$841$	25.2912			0.872111
$842$	−11.9837	−	34.0492i	−0.412985	−	1.17341i
$843$	2.28808	+	6.93368i	0.0788057	+	0.238809i
$844$	−22.9921	−	28.6178i	−0.791422	−	0.985064i
$845$		−	74.6572i		−	2.56828i
$846$	−4.30800	−	2.91511i	−0.148112	−	0.100223i
$847$			0.530586i			0.0182312i
$848$	44.2984	+	9.77341i	1.52121	+	0.335620i
$849$	1.63575	+	4.95690i	0.0561389	+	0.170120i
$850$	0.466042	−	0.164024i	0.0159851	−	0.00562598i
$851$	1.89808			0.0650654
$852$	−17.7951	+	27.4458i	−0.609649	+	0.940278i
$853$	18.9941			0.650345			0.325173	−	0.945655i	$-0.394578\pi$
$853$	18.9941			0.650345			0.325173	+	0.945655i	$0.394578\pi$
$854$	−7.13439	+	2.51096i	−0.244134	+	0.0859232i
$855$	4.07733	−	3.01985i	0.139442	−	0.103277i
$856$	−47.9844	−	29.7879i	−1.64007	−	1.01813i
$857$		−	31.1980i		−	1.06570i	−0.846208	−	0.532852i	$-0.821120\pi$
$857$		−	31.1980i		−	1.06570i	0.846208	−	0.532852i	$-0.178880\pi$
$858$	32.1895	+	41.7203i	1.09893	+	1.42431i
$859$		−	30.5041i		−	1.04079i	−0.853927	−	0.520393i	$-0.825786\pi$
$859$		−	30.5041i		−	1.04079i	0.853927	−	0.520393i	$-0.174214\pi$
$860$	−40.5506	+	32.5793i	−1.38277	+	1.11094i
$861$	−10.0053	+	3.30171i	−0.340981	+	0.112522i
$862$	−8.03708	−	22.8358i	−0.273744	−	0.777789i
$863$	36.1335			1.23000			0.614999	−	0.788528i	$-0.289157\pi$
$863$	36.1335			1.23000			0.614999	+	0.788528i	$0.289157\pi$
$864$	−13.9191	+	25.8894i	−0.473537	+	0.880774i
$865$	−13.3641			−0.454393
$866$	14.9643	+	42.5180i	0.508506	+	1.44482i
$867$	27.2110	−	8.97952i	0.924136	−	0.304960i
$868$	−9.45607	+	7.59721i	−0.320960	+	0.257866i
$869$		−	32.5489i		−	1.10414i
$870$	6.76853	+	8.77256i	0.229475	+	0.297418i
$871$		−	62.6869i		−	2.12407i
$872$	−35.7188	−	22.1736i	−1.20959	−	0.750892i
$873$	−17.5280	+	12.9820i	−0.593232	+	0.439374i
$874$	0.960546	−	0.338065i	0.0324910	−	0.0114352i
$875$	−8.38545			−0.283480
$876$	−0.795486	+	1.22690i	−0.0268770	+	0.0414531i
$877$	−29.8694			−1.00862			−0.504308	−	0.863524i	$-0.668252\pi$
$877$	−29.8694			−1.00862			−0.504308	+	0.863524i	$0.668252\pi$
$878$	13.3186	−	4.68749i	0.449481	−	0.158195i
$879$	5.06082	+	15.3360i	0.170697	+	0.517272i
$880$	−29.4934	−	6.50703i	−0.994222	−	0.219352i
$881$			18.4324i			0.621003i	0.950573	+	0.310501i	$0.100497\pi$
$881$			18.4324i			0.621003i	−0.950573	+	0.310501i	$0.899503\pi$
$882$	−22.3680	−	15.1358i	−0.753170	−	0.509649i
$883$		−	30.3693i		−	1.02201i	−0.859579	−	0.511003i	$-0.829274\pi$
$883$		−	30.3693i		−	1.02201i	0.859579	−	0.511003i	$-0.170726\pi$
$884$	−5.66318	−	7.04882i	−0.190473	−	0.237078i
$885$	0.225620	+	0.683706i	0.00758412	+	0.0229825i
$886$	18.5556	+	52.7221i	0.623387	+	1.77123i
$887$	−26.0710			−0.875377			−0.437688	−	0.899127i	$-0.644203\pi$
$887$	−26.0710			−0.875377			−0.437688	+	0.899127i	$0.644203\pi$
$888$	9.03914	+	2.18156i	0.303334	+	0.0732082i
$889$	−8.57907			−0.287733
$890$	12.4389	+	35.3427i	0.416953	+	1.18469i
$891$	8.43433	−	27.6748i	0.282561	−	0.927141i
$892$	33.0441	+	41.1291i	1.10640	+	1.37711i
$893$			0.882801i			0.0295418i
$894$	−29.1494	+	22.4904i	−0.974901	+	0.752191i
$895$			49.6334i			1.65906i
$896$	−6.45127	−	6.28959i	−0.215522	−	0.210120i
$897$	−11.0072	+	3.63234i	−0.367521	+	0.121280i
$898$	−29.6733	+	10.4436i	−0.990211	+	0.348506i
$899$	14.6666			0.489159
$900$	0.787119	−	3.00127i	0.0262373	−	0.100042i
$901$	7.66158			0.255244
$902$	−32.7558	+	11.5285i	−1.09065	+	0.383856i
$903$	14.5040	−	4.78624i	0.482662	−	0.159276i
$904$	−17.5016	+	28.1929i	−0.582095	+	0.937681i
$905$			30.0543i			0.999039i
$906$	1.27382	−	0.982827i	0.0423199	−	0.0326522i
$907$			1.21466i			0.0403321i	0.999797	+	0.0201661i	$0.00641949\pi$
$907$			1.21466i			0.0403321i	−0.999797	+	0.0201661i	$0.993581\pi$
$908$	−9.64946	+	7.75259i	−0.320228	+	0.257279i
$909$	12.9558	+	17.4925i	0.429715	+	0.580191i
$910$	−5.87724	−	16.6990i	−0.194829	−	0.553567i
$911$	−27.8311			−0.922085			−0.461042	−	0.887378i	$-0.652524\pi$
$911$	−27.8311			−0.922085			−0.461042	+	0.887378i	$0.652524\pi$
$912$	4.96291	−	0.505950i	0.164338	−	0.0167537i
$913$	27.1400			0.898203
$914$	−5.74768	−	16.3309i	−0.190116	−	0.540178i
$915$	−8.56180	−	25.9452i	−0.283044	−	0.857723i
$916$	−8.23613	+	6.61709i	−0.272129	+	0.218635i
$917$			4.59156i			0.151627i
$918$	−1.35358	+	4.77631i	−0.0446749	+	0.157642i
$919$		−	33.8802i		−	1.11760i	−0.829301	−	0.558802i	$-0.811261\pi$
$919$		−	33.8802i		−	1.11760i	0.829301	−	0.558802i	$-0.188739\pi$
$920$	3.50395	−	5.64441i	0.115522	−	0.186091i
$921$	−2.27799	−	6.90308i	−0.0750622	−	0.227464i
$922$	33.5268	−	11.7998i	1.10415	−	0.388606i
$923$	−63.1906			−2.07994
$924$	7.44098	+	4.82451i	0.244790	+	0.158715i
$925$	−0.981552			−0.0322732
$926$	29.6970	−	10.4519i	0.975902	−	0.343470i
$927$	20.7324	+	27.9924i	0.680942	+	0.919392i
$928$	1.31782	+	10.8141i	0.0432597	+	0.354989i
$929$		−	38.5389i		−	1.26442i	−0.774798	−	0.632209i	$-0.782148\pi$
$929$		−	38.5389i		−	1.26442i	0.774798	−	0.632209i	$-0.217852\pi$
$930$	−26.7666	−	34.6917i	−0.877711	−	1.13758i
$931$			4.58368i			0.150224i
$932$	−12.5866	−	15.6663i	−0.412289	−	0.513166i
$933$	−2.59518	+	0.856396i	−0.0849623	+	0.0280372i
$934$	4.86931	+	13.8352i	0.159329	+	0.452701i
$935$	−5.10100			−0.166821
$936$	−56.5941	+	4.64695i	−1.84983	+	0.151890i
$937$	31.1633			1.01806			0.509031	−	0.860748i	$-0.330004\pi$
$937$	31.1633			1.01806			0.509031	+	0.860748i	$0.330004\pi$
$938$	−3.50241	−	9.95140i	−0.114358	−	0.324925i
$939$	11.5548	−	3.81304i	0.377078	−	0.124434i
$940$	3.60732	+	4.48994i	0.117658	+	0.146446i
$941$			39.0601i			1.27332i	0.771143	+	0.636662i	$0.219685\pi$
$941$			39.0601i			1.27332i	−0.771143	+	0.636662i	$0.780315\pi$
$942$	20.3666	+	26.3968i	0.663580	+	0.860053i
$943$		−	7.63841i		−	0.248741i
$944$	−0.152509	+	0.691253i	−0.00496374	+	0.0224984i
$945$	−5.60441	+	7.94121i	−0.182312	+	0.258328i
$946$	47.4837	−	16.7119i	1.54383	−	0.543352i
$947$	−51.7977			−1.68320			−0.841599	−	0.540103i	$-0.818385\pi$
$947$	−51.7977			−1.68320			−0.841599	+	0.540103i	$0.818385\pi$
$948$	29.4303	+	19.0817i	0.955852	+	0.619746i
$949$	−2.82478			−0.0916963
$950$	−0.496725	+	0.174823i	−0.0161159	+	0.00567201i
$951$	0.0433297	+	0.131304i	0.00140506	+	0.00425782i
$952$	−1.29284	−	0.802573i	−0.0419013	−	0.0260116i
$953$		−	33.0339i		−	1.07007i	−0.844829	−	0.535036i	$-0.820298\pi$
$953$		−	33.0339i		−	1.07007i	0.844829	−	0.535036i	$-0.179702\pi$
$954$	26.9651	−	39.8495i	0.873026	−	1.29018i
$955$			18.9642i			0.613666i
$956$	21.4188	−	17.2083i	0.692733	−	0.556557i
$957$	−3.36021	−	10.1826i	−0.108620	−	0.329157i
$958$	6.99159	+	19.8652i	0.225888	+	0.641816i
$959$	11.4784			0.370657
$960$	23.1741	−	22.8528i	0.747939	−	0.737572i
$961$	−27.0000			−0.870968
$962$	5.96373	+	16.9448i	0.192278	+	0.546321i
$963$	−48.1389	+	35.6538i	−1.55125	+	1.14893i
$964$	22.8459	−	18.3549i	0.735817	−	0.591172i
$965$		−	12.5456i		−	0.403859i
$966$	−1.54443	+	1.19162i	−0.0496912	+	0.0383396i
$967$			1.66263i			0.0534665i	0.999643	+	0.0267332i	$0.00851047\pi$
$967$			1.66263i			0.0534665i	−0.999643	+	0.0267332i	$0.991490\pi$
$968$	−1.60105	−	0.993902i	−0.0514597	−	0.0319452i
$969$	0.800104	−	0.264030i	0.0257030	−	0.00848188i
$970$	22.7818	−	8.01807i	0.731479	−	0.257445i
$971$	48.4858			1.55598			0.777991	−	0.628275i	$-0.216239\pi$
$971$	48.4858			1.55598			0.777991	+	0.628275i	$0.216239\pi$
$972$	20.0786	+	23.8506i	0.644022	+	0.765007i
$973$	−9.29797			−0.298079
$974$	−17.4528	+	6.14254i	−0.559224	+	0.196820i
$975$	5.69216	−	1.87838i	0.182295	−	0.0601564i
$976$	5.78740	−	26.2316i	0.185250	−	0.839654i
$977$		−	39.7689i		−	1.27232i	−0.771557	−	0.636160i	$-0.780522\pi$
$977$		−	39.7689i		−	1.27232i	0.771557	−	0.636160i	$-0.219478\pi$
$978$	5.96280	−	4.60064i	0.190669	−	0.147112i
$979$		−	36.2589i		−	1.15884i
$980$	18.7299	+	23.3127i	0.598305	+	0.744696i
$981$	−35.8338	+	26.5401i	−1.14408	+	0.847360i
$982$	15.5586	+	44.2068i	0.496496	+	1.41069i
$983$	−11.2968			−0.360313			−0.180156	−	0.983638i	$-0.557660\pi$
$983$	−11.2968			−0.360313			−0.180156	+	0.983638i	$0.557660\pi$
$984$	8.77919	−	36.3760i	0.279870	−	1.15962i
$985$	2.79958			0.0892019
$986$	0.610836	+	1.73557i	0.0194530	+	0.0552719i
$987$	−0.529954	−	1.60594i	−0.0168686	−	0.0511178i
$988$	6.03603	+	7.51290i	0.192032	+	0.239017i
$989$			11.0728i			0.352095i
$990$	−17.9531	+	26.5314i	−0.570586	+	0.843223i
$991$			9.26312i			0.294253i	0.989118	+	0.147126i	$0.0470024\pi$
$991$			9.26312i			0.294253i	−0.989118	+	0.147126i	$0.952998\pi$
$992$	−5.21141	−	42.7650i	−0.165463	−	1.35779i
$993$	−15.9952	−	48.4711i	−0.507593	−	1.53818i
$994$	−10.0313	+	3.53055i	−0.318175	+	0.111982i
$995$	56.9722			1.80614
$996$	−15.9108	+	24.5397i	−0.504153	+	0.777569i
$997$	−6.05016			−0.191610			−0.0958052	−	0.995400i	$-0.530543\pi$
$997$	−6.05016			−0.191610			−0.0958052	+	0.995400i	$0.530543\pi$
$998$	54.7557	−	19.2713i	1.73326	−	0.610024i
$999$	5.68689	−	8.05808i	0.179925	−	0.254946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.a.47.9	✓	22
3.2	odd	2		276.2.c.b.47.14	yes	22
4.3	odd	2		276.2.c.b.47.13	yes	22
12.11	even	2	inner	276.2.c.a.47.10	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.9	✓	22	1.1	even	1	trivial
276.2.c.a.47.10	yes	22	12.11	even	2	inner
276.2.c.b.47.13	yes	22	4.3	odd	2
276.2.c.b.47.14	yes	22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.469504 - 1.33400i) q^{2} +(1.64481 - 0.542779i) q^{3} +(-1.55913 + 1.25264i) q^{4} -2.34886i q^{5} +(-1.49631 - 1.93934i) q^{6} -0.796368i q^{7} +(2.40305 + 1.49177i) q^{8} +(2.41078 - 1.78553i) q^{9} +O(q^{10})\)	\(q+(-0.469504 - 1.33400i) q^{2} +(1.64481 - 0.542779i) q^{3} +(-1.55913 + 1.25264i) q^{4} -2.34886i q^{5} +(-1.49631 - 1.93934i) q^{6} -0.796368i q^{7} +(2.40305 + 1.49177i) q^{8} +(2.41078 - 1.78553i) q^{9} +(-3.13338 + 1.10280i) q^{10} +3.21461 q^{11} +(-1.88456 + 2.90662i) q^{12} -6.69212 q^{13} +(-1.06236 + 0.373898i) q^{14} +(-1.27491 - 3.86342i) q^{15} +(0.861782 - 3.90606i) q^{16} -0.675569i q^{17} +(-3.51378 - 2.37768i) q^{18} +0.720048i q^{19} +(2.94227 + 3.66218i) q^{20} +(-0.432251 - 1.30987i) q^{21} +(-1.50927 - 4.28831i) q^{22} +1.00000 q^{23} +(4.76225 + 1.14935i) q^{24} -0.517128 q^{25} +(3.14198 + 8.92731i) q^{26} +(2.99612 - 4.24538i) q^{27} +(0.997563 + 1.24164i) q^{28} -1.92582i q^{29} +(-4.55524 + 3.51462i) q^{30} +7.61577i q^{31} +(-5.61531 + 0.684292i) q^{32} +(5.28742 - 1.74482i) q^{33} +(-0.901212 + 0.317183i) q^{34} -1.87055 q^{35} +(-1.52210 + 5.80372i) q^{36} +1.89808 q^{37} +(0.960546 - 0.338065i) q^{38} +(-11.0072 + 3.63234i) q^{39} +(3.50395 - 5.64441i) q^{40} -7.63841i q^{41} +(-1.54443 + 1.19162i) q^{42} +11.0728i q^{43} +(-5.01201 + 4.02676i) q^{44} +(-4.19396 - 5.66258i) q^{45} +(-0.469504 - 1.33400i) q^{46} +1.22603 q^{47} +(-0.702661 - 6.89248i) q^{48} +6.36580 q^{49} +(0.242794 + 0.689851i) q^{50} +(-0.366685 - 1.11118i) q^{51} +(10.4339 - 8.38282i) q^{52} +11.3409i q^{53} +(-7.07004 - 2.00362i) q^{54} -7.55067i q^{55} +(1.18800 - 1.91371i) q^{56} +(0.390826 + 1.18434i) q^{57} +(-2.56905 + 0.904180i) q^{58} -0.176969 q^{59} +(6.82722 + 4.42657i) q^{60} +6.71562 q^{61} +(10.1595 - 3.57564i) q^{62} +(-1.42194 - 1.91987i) q^{63} +(3.54926 + 7.16957i) q^{64} +15.7188i q^{65} +(-4.81007 - 6.23424i) q^{66} +9.36728i q^{67} +(0.846246 + 1.05330i) q^{68} +(1.64481 - 0.542779i) q^{69} +(0.878233 + 2.49533i) q^{70} +9.44253 q^{71} +(8.45682 - 0.694391i) q^{72} +0.422106 q^{73} +(-0.891158 - 2.53205i) q^{74} +(-0.850576 + 0.280686i) q^{75} +(-0.901961 - 1.12265i) q^{76} -2.56002i q^{77} +(10.0135 + 12.9783i) q^{78} -10.1253i q^{79} +(-9.17478 - 2.02420i) q^{80} +(2.62375 - 8.60906i) q^{81} +(-10.1897 + 3.58627i) q^{82} +8.44270 q^{83} +(2.31474 + 1.50081i) q^{84} -1.58682 q^{85} +(14.7712 - 5.19874i) q^{86} +(-1.04529 - 3.16760i) q^{87} +(7.72487 + 4.79546i) q^{88} -11.2794i q^{89} +(-5.58482 + 8.25337i) q^{90} +5.32939i q^{91} +(-1.55913 + 1.25264i) q^{92} +(4.13368 + 12.5265i) q^{93} +(-0.575627 - 1.63553i) q^{94} +1.69129 q^{95} +(-8.86469 + 4.17340i) q^{96} -7.27066 q^{97} +(-2.98877 - 8.49200i) q^{98} +(7.74974 - 5.73980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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