LMFDB - Embedded newform 630.2.cd.a.527.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.43
Character	$\chi$	$=$	630.527
Dual form			630.2.cd.a.263.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.47129 + 0.913950i) q^{3} -1.00000i q^{4} +(-1.83586 - 1.27656i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.96337 + 1.77346i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.32939 + 2.68937i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.47129 + 0.913950i) q^{3} -1.00000i q^{4} +(-1.83586 - 1.27656i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.96337 + 1.77346i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.32939 + 2.68937i) q^{9} +(-2.20082 + 0.395490i) q^{10} +(3.93553 + 2.27218i) q^{11} +(0.913950 - 1.47129i) q^{12} +(-1.13198 - 4.22459i) q^{13} +(2.64234 - 0.134290i) q^{14} +(-1.53438 - 3.55608i) q^{15} -1.00000 q^{16} +(1.13496 + 0.304112i) q^{17} +(2.84169 + 0.961652i) q^{18} +(5.35282 + 3.09045i) q^{19} +(-1.27656 + 1.83586i) q^{20} +(1.26784 + 4.40370i) q^{21} +(4.38951 - 1.17617i) q^{22} +(1.94889 - 7.27337i) q^{23} +(-0.394099 - 1.68662i) q^{24} +(1.74080 + 4.68718i) q^{25} +(-3.78767 - 2.18681i) q^{26} +(-0.502033 + 5.17184i) q^{27} +(1.77346 - 1.96337i) q^{28} +(-3.13342 - 5.42724i) q^{29} +(-3.59950 - 1.42956i) q^{30} -0.358961 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.71365 + 6.93992i) q^{33} +(1.01758 - 0.587499i) q^{34} +(-1.34057 - 5.76219i) q^{35} +(2.68937 - 1.32939i) q^{36} +(-9.20775 + 2.46721i) q^{37} +(5.97029 - 1.59973i) q^{38} +(2.19560 - 7.25017i) q^{39} +(0.395490 + 2.20082i) q^{40} +(-8.04851 - 4.64681i) q^{41} +(4.01038 + 2.21739i) q^{42} +(8.19545 + 2.19596i) q^{43} +(2.27218 - 3.93553i) q^{44} +(0.992558 - 6.63437i) q^{45} +(-3.76497 - 6.52113i) q^{46} +(-2.15351 + 2.15351i) q^{47} +(-1.47129 - 0.913950i) q^{48} +(0.709677 + 6.96393i) q^{49} +(4.54527 + 2.08340i) q^{50} +(1.39191 + 1.48474i) q^{51} +(-4.22459 + 1.13198i) q^{52} +(0.0189078 - 0.0705647i) q^{53} +(3.30205 + 4.01204i) q^{54} +(-4.32453 - 9.19535i) q^{55} +(-0.134290 - 2.64234i) q^{56} +(5.05103 + 9.43915i) q^{57} +(-6.05330 - 1.62198i) q^{58} -8.50788 q^{59} +(-3.55608 + 1.53438i) q^{60} -5.89163 q^{61} +(-0.253824 + 0.253824i) q^{62} +(-2.15940 + 7.63786i) q^{63} +1.00000i q^{64} +(-3.31478 + 9.20082i) q^{65} +(7.53321 + 2.28131i) q^{66} +(6.76808 + 6.76808i) q^{67} +(0.304112 - 1.13496i) q^{68} +(9.51489 - 8.92005i) q^{69} +(-5.02241 - 3.12656i) q^{70} +13.2021i q^{71} +(0.961652 - 2.84169i) q^{72} +(-9.16835 - 2.45665i) q^{73} +(-4.76628 + 8.25544i) q^{74} +(-1.72262 + 8.48720i) q^{75} +(3.09045 - 5.35282i) q^{76} +(3.69730 + 11.4406i) q^{77} +(-3.57412 - 6.67917i) q^{78} +5.26884i q^{79} +(1.83586 + 1.27656i) q^{80} +(-5.46544 + 7.15045i) q^{81} +(-8.97694 + 2.40536i) q^{82} +(0.957089 - 3.57191i) q^{83} +(4.40370 - 1.26784i) q^{84} +(-1.69542 - 2.00715i) q^{85} +(7.34784 - 4.24228i) q^{86} +(0.350059 - 10.8488i) q^{87} +(-1.17617 - 4.38951i) q^{88} +(2.74487 - 4.75426i) q^{89} +(-3.98936 - 5.39305i) q^{90} +(5.26966 - 10.3020i) q^{91} +(-7.27337 - 1.94889i) q^{92} +(-0.528136 - 0.328073i) q^{93} +3.04553i q^{94} +(-5.88191 - 12.5068i) q^{95} +(-1.68662 + 0.394099i) q^{96} +(0.903546 - 3.37208i) q^{97} +(5.42606 + 4.42243i) q^{98} +(-0.878880 + 13.6047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.47129	+	0.913950i	0.849450	+	0.527669i
$3$	1.47129	+	0.913950i	0.849450	+	0.527669i
$4$		−	1.00000i		−	0.500000i
$5$	−1.83586	−	1.27656i	−0.821024	−	0.570894i
$5$	−1.83586	−	1.27656i	−0.821024	−	0.570894i
$6$	1.68662	−	0.394099i	0.688560	−	0.160890i
$7$	1.96337	+	1.77346i	0.742086	+	0.670305i
$7$	1.96337	+	1.77346i	0.742086	+	0.670305i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.32939	+	2.68937i	0.443130	+	0.896457i
$10$	−2.20082	+	0.395490i	−0.695959	+	0.125065i
$11$	3.93553	+	2.27218i	1.18661	+	0.685088i	0.957534	−	0.288321i	$-0.0930971\pi$
$11$	3.93553	+	2.27218i	1.18661	+	0.685088i	0.229073	+	0.973409i	$0.426430\pi$
$12$	0.913950	−	1.47129i	0.263835	−	0.424725i
$13$	−1.13198	−	4.22459i	−0.313954	−	1.17169i	−0.924960	−	0.380065i	$-0.875901\pi$
$13$	−1.13198	−	4.22459i	−0.313954	−	1.17169i	0.611006	−	0.791626i	$-0.290765\pi$
$14$	2.64234	−	0.134290i	0.706195	−	0.0358904i
$15$	−1.53438	−	3.55608i	−0.396175	−	0.918175i
$16$	−1.00000			−0.250000
$17$	1.13496	+	0.304112i	0.275269	+	0.0737580i	0.393812	−	0.919191i	$-0.371156\pi$
$17$	1.13496	+	0.304112i	0.275269	+	0.0737580i	−0.118544	+	0.992949i	$0.537823\pi$
$18$	2.84169	+	0.961652i	0.669794	+	0.226664i
$19$	5.35282	+	3.09045i	1.22802	+	0.708998i	0.966615	−	0.256232i	$-0.0824810\pi$
$19$	5.35282	+	3.09045i	1.22802	+	0.708998i	0.261405	+	0.965229i	$0.415814\pi$
$20$	−1.27656	+	1.83586i	−0.285447	+	0.410512i
$21$	1.26784	+	4.40370i	0.276665	+	0.960966i
$22$	4.38951	−	1.17617i	0.935848	−	0.250760i
$23$	1.94889	−	7.27337i	0.406373	−	1.51660i	−0.395138	−	0.918622i	$-0.629303\pi$
$23$	1.94889	−	7.27337i	0.406373	−	1.51660i	0.801510	−	0.597981i	$-0.204030\pi$
$24$	−0.394099	−	1.68662i	−0.0804451	−	0.344280i
$25$	1.74080	+	4.68718i	0.348160	+	0.937435i
$26$	−3.78767	−	2.18681i	−0.742823	−	0.428869i
$27$	−0.502033	+	5.17184i	−0.0966163	+	0.995322i
$28$	1.77346	−	1.96337i	0.335152	−	0.371043i
$29$	−3.13342	−	5.42724i	−0.581861	−	1.00781i	−0.995259	−	0.0972625i	$-0.968991\pi$
$29$	−3.13342	−	5.42724i	−0.581861	−	1.00781i	0.413398	−	0.910551i	$-0.364342\pi$
$30$	−3.59950	−	1.42956i	−0.657175	−	0.261000i
$31$	−0.358961			−0.0644714			−0.0322357	−	0.999480i	$-0.510263\pi$
$31$	−0.358961			−0.0644714			−0.0322357	+	0.999480i	$0.510263\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.71365	+	6.93992i	0.646463	+	1.20808i
$34$	1.01758	−	0.587499i	0.174513	−	0.100755i
$35$	−1.34057	−	5.76219i	−0.226597	−	0.973989i
$36$	2.68937	−	1.32939i	0.448229	−	0.221565i
$37$	−9.20775	+	2.46721i	−1.51374	+	0.405607i	−0.917677	−	0.397328i	$-0.869938\pi$
$37$	−9.20775	+	2.46721i	−1.51374	+	0.405607i	−0.596068	+	0.802934i	$0.703271\pi$
$38$	5.97029	−	1.59973i	0.968509	−	0.259511i
$39$	2.19560	−	7.25017i	0.351578	−	1.16096i
$40$	0.395490	+	2.20082i	0.0625324	+	0.347979i
$41$	−8.04851	−	4.64681i	−1.25697	−	0.725709i	−0.284482	−	0.958681i	$-0.591822\pi$
$41$	−8.04851	−	4.64681i	−1.25697	−	0.725709i	−0.972483	+	0.232972i	$0.925155\pi$
$42$	4.01038	+	2.21739i	0.618816	+	0.342151i
$43$	8.19545	+	2.19596i	1.24979	+	0.334881i	0.822257	−	0.569116i	$-0.192715\pi$
$43$	8.19545	+	2.19596i	1.24979	+	0.334881i	0.427537	+	0.903998i	$0.359381\pi$
$44$	2.27218	−	3.93553i	0.342544	−	0.593304i
$45$	0.992558	−	6.63437i	0.147962	−	0.988993i
$46$	−3.76497	−	6.52113i	−0.555115	−	0.961488i
$47$	−2.15351	+	2.15351i	−0.314122	+	0.314122i	−0.846504	−	0.532382i	$-0.821297\pi$
$47$	−2.15351	+	2.15351i	−0.314122	+	0.314122i	0.532382	+	0.846504i	$0.321297\pi$
$48$	−1.47129	−	0.913950i	−0.212362	−	0.131917i
$49$	0.709677	+	6.96393i	0.101382	+	0.994848i
$50$	4.54527	+	2.08340i	0.642798	+	0.294638i
$51$	1.39191	+	1.48474i	0.194907	+	0.207905i
$52$	−4.22459	+	1.13198i	−0.585846	+	0.156977i
$53$	0.0189078	−	0.0705647i	0.00259718	−	0.00969281i	−0.964615	−	0.263662i	$-0.915070\pi$
$53$	0.0189078	−	0.0705647i	0.00259718	−	0.00969281i	0.967212	+	0.253969i	$0.0817362\pi$
$54$	3.30205	+	4.01204i	0.449353	+	0.545969i
$55$	−4.32453	−	9.19535i	−0.583120	−	1.23990i
$56$	−0.134290	−	2.64234i	−0.0179452	−	0.353098i
$57$	5.05103	+	9.43915i	0.669025	+	1.25025i
$58$	−6.05330	−	1.62198i	−0.794837	−	0.212976i
$59$	−8.50788			−1.10763			−0.553816	−	0.832639i	$-0.686829\pi$
$59$	−8.50788			−1.10763			−0.553816	+	0.832639i	$0.686829\pi$
$60$	−3.55608	+	1.53438i	−0.459087	+	0.198088i
$61$	−5.89163			−0.754346			−0.377173	−	0.926143i	$-0.623104\pi$
$61$	−5.89163			−0.754346			−0.377173	+	0.926143i	$0.623104\pi$
$62$	−0.253824	+	0.253824i	−0.0322357	+	0.0322357i
$63$	−2.15940	+	7.63786i	−0.272059	+	0.962280i
$64$			1.00000i			0.125000i
$65$	−3.31478	+	9.20082i	−0.411148	+	1.14122i
$66$	7.53321	+	2.28131i	0.927274	+	0.280810i
$67$	6.76808	+	6.76808i	0.826853	+	0.826853i	0.987080	−	0.160227i	$-0.0512226\pi$
$67$	6.76808	+	6.76808i	0.826853	+	0.826853i	−0.160227	+	0.987080i	$0.551223\pi$
$68$	0.304112	−	1.13496i	0.0368790	−	0.137634i
$69$	9.51489	−	8.92005i	1.14546	−	1.07385i
$70$	−5.02241	−	3.12656i	−0.600293	−	0.373696i
$71$			13.2021i			1.56680i	0.621520	+	0.783398i	$0.286515\pi$
$71$			13.2021i			1.56680i	−0.621520	+	0.783398i	$0.713485\pi$
$72$	0.961652	−	2.84169i	0.113332	−	0.334897i
$73$	−9.16835	−	2.45665i	−1.07307	−	0.287529i	−0.321319	−	0.946971i	$-0.604126\pi$
$73$	−9.16835	−	2.45665i	−1.07307	−	0.287529i	−0.751756	+	0.659442i	$0.770793\pi$
$74$	−4.76628	+	8.25544i	−0.554069	+	0.959675i
$75$	−1.72262	+	8.48720i	−0.198911	+	0.980017i
$76$	3.09045	−	5.35282i	0.354499	−	0.614010i
$77$	3.69730	+	11.4406i	0.421346	+	1.30378i
$78$	−3.57412	−	6.67917i	−0.404690	−	0.756267i
$79$			5.26884i			0.592791i	0.955065	+	0.296395i	$0.0957846\pi$
$79$			5.26884i			0.592791i	−0.955065	+	0.296395i	$0.904215\pi$
$80$	1.83586	+	1.27656i	0.205256	+	0.142724i
$81$	−5.46544	+	7.15045i	−0.607271	+	0.794494i
$82$	−8.97694	+	2.40536i	−0.991338	+	0.265628i
$83$	0.957089	−	3.57191i	0.105054	−	0.392068i	−0.893297	−	0.449467i	$-0.851614\pi$
$83$	0.957089	−	3.57191i	0.105054	−	0.392068i	0.998351	+	0.0573990i	$0.0182807\pi$
$84$	4.40370	−	1.26784i	0.480483	−	0.138333i
$85$	−1.69542	−	2.00715i	−0.183894	−	0.217706i
$86$	7.34784	−	4.24228i	0.792338	−	0.457457i
$87$	0.350059	−	10.8488i	0.0375302	−	1.16312i
$88$	−1.17617	−	4.38951i	−0.125380	−	0.467924i
$89$	2.74487	−	4.75426i	0.290956	−	0.503951i	−0.683080	−	0.730344i	$-0.739360\pi$
$89$	2.74487	−	4.75426i	0.290956	−	0.503951i	0.974036	+	0.226393i	$0.0726933\pi$
$90$	−3.98936	−	5.39305i	−0.420516	−	0.568477i
$91$	5.26966	−	10.3020i	0.552410	−	1.07994i
$92$	−7.27337	−	1.94889i	−0.758301	−	0.203186i
$93$	−0.528136	−	0.328073i	−0.0547652	−	0.0340196i
$94$			3.04553i			0.314122i
$95$	−5.88191	−	12.5068i	−0.603471	−	1.28317i
$96$	−1.68662	+	0.394099i	−0.172140	+	0.0402226i
$97$	0.903546	−	3.37208i	0.0917412	−	0.342383i	−0.904764	−	0.425913i	$-0.859953\pi$
$97$	0.903546	−	3.37208i	0.0917412	−	0.342383i	0.996505	+	0.0835303i	$0.0266195\pi$
$98$	5.42606	+	4.42243i	0.548115	+	0.446733i
$99$	−0.878880	+	13.6047i	−0.0883308	+	1.36733i
$100$	4.68718	−	1.74080i	0.468718	−	0.174080i
$101$	−8.23544	−	4.75473i	−0.819457	−	0.473114i	0.0307724	−	0.999526i	$-0.490203\pi$
$101$	−8.23544	−	4.75473i	−0.819457	−	0.473114i	−0.850229	+	0.526413i	$0.823537\pi$
$102$	2.03410	+	0.0656341i	0.201406	+	0.00649875i
$103$	−2.97201	−	0.796349i	−0.292841	−	0.0784666i	0.109408	−	0.993997i	$-0.465105\pi$
$103$	−2.97201	−	0.796349i	−0.292841	−	0.0784666i	−0.402249	+	0.915530i	$0.631771\pi$
$104$	−2.18681	+	3.78767i	−0.214434	+	0.371411i
$105$	3.29400	−	9.70307i	0.321461	−	0.946923i
$106$	−0.0365270	−	0.0632666i	−0.00354782	−	0.00614500i
$107$	−3.52788	−	13.1662i	−0.341053	−	1.27283i	−0.897156	−	0.441713i	$-0.854371\pi$
$107$	−3.52788	−	13.1662i	−0.341053	−	1.27283i	0.556104	−	0.831113i	$-0.312296\pi$
$108$	5.17184	+	0.502033i	0.497661	+	0.0483081i
$109$	−0.421534	+	0.243373i	−0.0403756	+	0.0233109i	−0.520052	−	0.854135i	$-0.674087\pi$
$109$	−0.421534	+	0.243373i	−0.0403756	+	0.0233109i	0.479676	+	0.877446i	$0.340754\pi$
$110$	−9.56000	−	3.44419i	−0.911510	−	0.328390i
$111$	−15.8022	−	4.78544i	−1.49988	−	0.454214i
$112$	−1.96337	−	1.77346i	−0.185521	−	0.167576i
$113$	2.84653	−	0.762725i	0.267779	−	0.0717511i	−0.122431	−	0.992477i	$-0.539069\pi$
$113$	2.84653	−	0.762725i	0.267779	−	0.0717511i	0.390210	+	0.920726i	$0.372402\pi$
$114$	10.2461	+	3.10287i	0.959636	+	0.290611i
$115$	−12.8628	+	10.8651i	−1.19946	+	1.01317i
$116$	−5.42724	+	3.13342i	−0.503907	+	0.290931i
$117$	9.85667	−	8.66044i	0.911249	−	0.800658i
$118$	−6.01598	+	6.01598i	−0.553816	+	0.553816i
$119$	1.68902	+	2.60990i	0.154833	+	0.239249i
$120$	−1.42956	+	3.59950i	−0.130500	+	0.328588i
$121$	4.82560	+	8.35819i	0.438691	+	0.759835i
$122$	−4.16601	+	4.16601i	−0.377173	+	0.377173i
$123$	−7.59474	−	14.1927i	−0.684795	−	1.27972i
$124$			0.358961i			0.0322357i
$125$	2.78758	−	10.8273i	0.249329	−	0.968419i
$126$	3.87386	+	6.92771i	0.345111	+	0.617170i
$127$	8.13579	+	8.13579i	0.721935	+	0.721935i	0.968999	−	0.247064i	$-0.0794659\pi$
$127$	8.13579	+	8.13579i	0.721935	+	0.721935i	−0.247064	+	0.968999i	$0.579466\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	10.0509	+	10.7211i	0.884931	+	0.943943i
$130$	4.16206	+	8.84987i	0.365036	+	0.776185i
$131$	−8.06148	+	4.65430i	−0.704335	+	0.406648i	−0.808960	−	0.587864i	$-0.799969\pi$
$131$	−8.06148	+	4.65430i	−0.704335	+	0.406648i	0.104625	+	0.994512i	$0.466636\pi$
$132$	6.93992	−	3.71365i	0.604042	−	0.323232i
$133$	5.02879	+	15.5607i	0.436051	+	1.34928i
$134$	9.57152			0.826853
$135$	7.52382	−	8.85393i	0.647547	−	0.762025i
$136$	−0.587499	−	1.01758i	−0.0503777	−	0.0872567i
$137$	−4.81689	−	17.9769i	−0.411535	−	1.53587i	−0.791676	−	0.610941i	$-0.790791\pi$
$137$	−4.81689	−	17.9769i	−0.411535	−	1.53587i	0.380141	−	0.924929i	$-0.375876\pi$
$138$	0.420615	−	13.0355i	0.0358051	−	1.10965i
$139$	−14.1952	−	8.19559i	−1.20402	−	0.695141i	−0.242573	−	0.970133i	$-0.577991\pi$
$139$	−14.1952	−	8.19559i	−1.20402	−	0.695141i	−0.961446	+	0.274992i	$0.911325\pi$
$140$	−5.76219	+	1.34057i	−0.486994	+	0.113298i
$141$	−5.13665	+	1.20024i	−0.432584	+	0.101078i
$142$	9.33527	+	9.33527i	0.783398	+	0.783398i
$143$	5.14411	−	19.1981i	0.430172	−	1.60542i
$144$	−1.32939	−	2.68937i	−0.110783	−	0.224114i
$145$	−1.17565	+	13.9637i	−0.0976327	+	1.15962i
$146$	−8.22012	+	4.74589i	−0.680302	+	0.392772i
$147$	−5.32055	+	10.8946i	−0.438831	+	0.898570i
$148$	2.46721	+	9.20775i	0.202803	+	0.756872i
$149$	2.24301	+	3.88501i	0.183754	+	0.318272i	0.943156	−	0.332350i	$-0.107842\pi$
$149$	2.24301	+	3.88501i	0.183754	+	0.318272i	−0.759402	+	0.650622i	$0.774508\pi$
$150$	4.78328	+	7.21944i	0.390553	+	0.589464i
$151$	0.594012	−	1.02886i	0.0483400	−	0.0837273i	−0.840843	−	0.541279i	$-0.817940\pi$
$151$	0.594012	−	1.02886i	0.0483400	−	0.0837273i	0.889183	+	0.457552i	$0.151274\pi$
$152$	−1.59973	−	5.97029i	−0.129756	−	0.484254i
$153$	0.690937	+	3.45662i	0.0558589	+	0.279451i
$154$	10.7041	+	5.47537i	0.862565	+	0.441218i
$155$	0.659005	+	0.458235i	0.0529325	+	0.0368063i
$156$	−7.25017	−	2.19560i	−0.580479	−	0.175789i
$157$	3.09903	+	3.09903i	0.247329	+	0.247329i	0.819874	−	0.572545i	$-0.194044\pi$
$157$	3.09903	+	3.09903i	0.247329	+	0.247329i	−0.572545	+	0.819874i	$0.694044\pi$
$158$	3.72563	+	3.72563i	0.296395	+	0.296395i
$159$	0.0923115	−	0.0865405i	0.00732077	−	0.00686310i
$160$	2.20082	−	0.395490i	0.173990	−	0.0312662i
$161$	16.7254	−	10.8241i	1.31815	−	0.853056i
$162$	1.19148	+	8.92078i	0.0936115	+	0.700883i
$163$	−4.60602	−	17.1899i	−0.360771	−	1.34642i	−0.873064	−	0.487606i	$-0.837870\pi$
$163$	−4.60602	−	17.1899i	−0.360771	−	1.34642i	0.512293	−	0.858811i	$-0.328796\pi$
$164$	−4.64681	+	8.04851i	−0.362855	+	0.628483i
$165$	2.04144	−	17.4814i	0.158926	−	1.36093i
$166$	−1.84895	−	3.20248i	−0.143507	−	0.248561i
$167$	3.33901	+	12.4613i	0.258380	+	0.964287i	0.966179	+	0.257873i	$0.0830217\pi$
$167$	3.33901	+	12.4613i	0.258380	+	0.964287i	−0.707799	+	0.706414i	$0.750312\pi$
$168$	2.21739	−	4.01038i	0.171075	−	0.309408i
$169$	−5.30750	+	3.06428i	−0.408269	+	0.235714i
$170$	−2.61811	−	0.220429i	−0.200800	−	0.0169061i
$171$	−1.19539	+	18.5041i	−0.0914135	+	1.41505i
$172$	2.19596	−	8.19545i	0.167441	−	0.624897i
$173$	−10.8173	−	10.8173i	−0.822426	−	0.822426i	0.164029	−	0.986456i	$-0.447551\pi$
$173$	−10.8173	−	10.8173i	−0.822426	−	0.822426i	−0.986456	+	0.164029i	$0.947551\pi$
$174$	−7.42375	−	7.91881i	−0.562793	−	0.600324i
$175$	−4.89468	+	12.2899i	−0.370003	+	0.929031i
$176$	−3.93553	−	2.27218i	−0.296652	−	0.171272i
$177$	−12.5176	−	7.77578i	−0.940877	−	0.584463i
$178$	−1.42085	−	5.30269i	−0.106497	−	0.397453i
$179$	5.38279	+	9.32327i	0.402329	+	0.696854i	0.994007	−	0.109321i	$-0.0348675\pi$
$179$	5.38279	+	9.32327i	0.402329	+	0.696854i	−0.591678	+	0.806175i	$0.701534\pi$
$180$	−6.63437	−	0.992558i	−0.494497	−	0.0739809i
$181$	0.210492			0.0156458			0.00782288	−	0.999969i	$-0.497510\pi$
$181$	0.210492			0.0156458			0.00782288	+	0.999969i	$0.497510\pi$
$182$	−3.55839	−	11.0108i	−0.263765	−	0.816175i
$183$	−8.66830	−	5.38466i	−0.640779	−	0.398045i
$184$	−6.52113	+	3.76497i	−0.480744	+	0.277558i
$185$	20.0537	+	7.22476i	1.47438	+	0.531175i
$186$	−0.605431	+	0.141466i	−0.0443924	+	0.0103728i
$187$	3.77568	+	3.77568i	0.276105	+	0.276105i
$188$	2.15351	+	2.15351i	0.157061	+	0.157061i
$189$	−10.1577	+	9.26393i	−0.738867	+	0.673852i
$190$	−13.0028	−	4.68452i	−0.943322	−	0.339851i
$191$			21.6280i			1.56495i	0.622685	+	0.782473i	$0.286042\pi$
$191$			21.6280i			1.56495i	−0.622685	+	0.782473i	$0.713958\pi$
$192$	−0.913950	+	1.47129i	−0.0659587	+	0.106181i
$193$	−15.2559	+	15.2559i	−1.09815	+	1.09815i	−0.103520	+	0.994627i	$0.533011\pi$
$193$	−15.2559	+	15.2559i	−1.09815	+	1.09815i	−0.994627	+	0.103520i	$0.966989\pi$
$194$	−1.74552	−	3.02332i	−0.125321	−	0.217062i
$195$	−13.2861	+	10.5075i	−0.951437	+	0.752460i
$196$	6.96393	−	0.709677i	0.497424	−	0.0506912i
$197$	3.69607	−	3.69607i	0.263334	−	0.263334i	−0.563073	−	0.826407i	$-0.690381\pi$
$197$	3.69607	−	3.69607i	0.263334	−	0.263334i	0.826407	+	0.563073i	$0.190381\pi$
$198$	8.99853	+	10.2415i	0.639498	+	0.727828i
$199$	−3.82151	+	2.20635i	−0.270900	+	0.156404i	−0.629296	−	0.777165i	$-0.716657\pi$
$199$	−3.82151	+	2.20635i	−0.270900	+	0.156404i	0.358397	+	0.933569i	$0.383323\pi$
$200$	2.08340	−	4.54527i	0.147319	−	0.321399i
$201$	3.77213	+	16.1435i	0.266065	+	1.13868i
$202$	−9.18544	+	2.46123i	−0.646285	+	0.173172i
$203$	3.47292	−	16.2127i	0.243751	−	1.13791i
$204$	1.48474	−	1.39191i	0.103952	−	0.0974535i
$205$	8.84405	+	18.8053i	0.617695	+	1.31342i
$206$	−2.66463	+	1.53843i	−0.185654	+	0.107187i
$207$	22.1516	−	4.42785i	1.53965	−	0.307757i
$208$	1.13198	+	4.22459i	0.0784885	+	0.292923i
$209$	14.0441	+	24.3251i	0.971452	+	1.68260i
$210$	−4.53190	−	9.19032i	−0.312731	−	0.634192i
$211$	7.09284	−	12.2852i	0.488291	−	0.845745i	−0.511618	−	0.859213i	$-0.670954\pi$
$211$	7.09284	−	12.2852i	0.488291	−	0.845745i	0.999909	+	0.0134680i	$0.00428714\pi$
$212$	−0.0705647	−	0.0189078i	−0.00484641	−	0.00129859i
$213$	−12.0660	+	19.4241i	−0.826750	+	1.33091i
$214$	−11.8045	−	6.81534i	−0.806940	−	0.465887i
$215$	−12.2425	−	14.4935i	−0.834929	−	0.988446i
$216$	4.01204	−	3.30205i	0.272984	−	0.224676i
$217$	−0.704776	−	0.636604i	−0.0478433	−	0.0432155i
$218$	−0.125979	+	0.470160i	−0.00853238	+	0.0318433i
$219$	−11.2440	−	11.9939i	−0.759802	−	0.810470i
$220$	−9.19535	+	4.32453i	−0.619950	+	0.291560i
$221$		−	5.13900i		−	0.345687i
$222$	−14.5576	+	7.79001i	−0.977045	+	0.522831i
$223$	−2.29046	−	0.613728i	−0.153381	−	0.0410982i	0.181312	−	0.983426i	$-0.441966\pi$
$223$	−2.29046	−	0.613728i	−0.153381	−	0.0410982i	−0.334692	+	0.942327i	$0.608632\pi$
$224$	−2.64234	+	0.134290i	−0.176549	+	0.00897260i
$225$	−10.2914	+	10.9127i	−0.686090	+	0.727516i
$226$	1.47347	−	2.55213i	0.0980139	−	0.169765i
$227$	−0.142382	−	0.531375i	−0.00945019	−	0.0352686i	0.961040	−	0.276410i	$-0.0891448\pi$
$227$	−0.142382	−	0.531375i	−0.00945019	−	0.0352686i	−0.970490	+	0.241142i	$0.922478\pi$
$228$	9.43915	−	5.05103i	0.625123	−	0.334513i
$229$	17.0459	−	9.84143i	1.12642	−	0.650340i	0.183389	−	0.983040i	$-0.441293\pi$
$229$	17.0459	−	9.84143i	1.12642	−	0.650340i	0.943033	+	0.332700i	$0.107960\pi$
$230$	−1.41261	+	16.7781i	−0.0931449	+	1.10632i
$231$	−5.01638	+	20.2117i	−0.330054	+	1.32983i
$232$	−1.62198	+	6.05330i	−0.106488	+	0.397419i
$233$	5.84244	−	1.56548i	0.382751	−	0.102558i	−0.0623128	−	0.998057i	$-0.519848\pi$
$233$	5.84244	−	1.56548i	0.382751	−	0.102558i	0.445064	+	0.895499i	$0.353181\pi$
$234$	0.845859	−	13.0936i	0.0552956	−	0.855954i
$235$	6.70264	−	1.20447i	0.437232	−	0.0785713i
$236$			8.50788i			0.553816i
$237$	−4.81546	+	7.75199i	−0.312798	+	0.503546i
$238$	3.03979	+	0.651154i	0.197041	+	0.0422081i
$239$	−10.1819	+	17.6355i	−0.658610	+	1.14075i	0.322365	+	0.946615i	$0.395522\pi$
$239$	−10.1819	+	17.6355i	−0.658610	+	1.14075i	−0.980976	+	0.194131i	$0.937811\pi$
$240$	1.53438	+	3.55608i	0.0990438	+	0.229544i
$241$	4.74276	−	8.21469i	0.305508	−	0.529155i	−0.671866	−	0.740672i	$-0.734507\pi$
$241$	4.74276	−	8.21469i	0.305508	−	0.529155i	0.977374	+	0.211517i	$0.0678405\pi$
$242$	9.32235	+	2.49792i	0.599263	+	0.160572i
$243$	−14.5764	+	5.52525i	−0.935077	+	0.354445i
$244$			5.89163i			0.377173i
$245$	7.58699	−	13.6908i	0.484715	−	0.874672i
$246$	−15.4061	−	4.66549i	−0.982255	−	0.297461i
$247$	6.99663	−	26.1118i	0.445185	−	1.66145i
$248$	0.253824	+	0.253824i	0.0161178	+	0.0161178i
$249$	4.67270	−	4.38058i	0.296120	−	0.277608i
$250$	−5.68491	−	9.62714i	−0.359545	−	0.608874i
$251$		−	12.4751i		−	0.787419i	−0.919235	−	0.393710i	$-0.871192\pi$
$251$		−	12.4751i		−	0.787419i	0.919235	−	0.393710i	$-0.128808\pi$
$252$	7.63786	+	2.15940i	0.481140	+	0.136030i
$253$	24.1963	−	24.1963i	1.52121	−	1.52121i
$254$	11.5057			0.721935
$255$	−0.660017	−	4.50263i	−0.0413319	−	0.281966i
$256$	1.00000			0.0625000
$257$	10.5768	+	2.83403i	0.659760	+	0.176782i	0.573138	−	0.819459i	$-0.305726\pi$
$257$	10.5768	+	2.83403i	0.659760	+	0.176782i	0.0866223	+	0.996241i	$0.472393\pi$
$258$	14.6880	+	0.473938i	0.914437	+	0.0295061i
$259$	−22.4538	−	11.4855i	−1.39521	−	0.713676i
$260$	9.20082	+	3.31478i	0.570611	+	0.205574i
$261$	10.4303	−	15.6418i	0.645621	−	0.968206i
$262$	−2.40924	+	8.99141i	−0.148843	+	0.555491i
$263$	8.25180	−	2.21106i	0.508828	−	0.136340i	0.00473372	−	0.999989i	$-0.498493\pi$
$263$	8.25180	−	2.21106i	0.508828	−	0.136340i	0.504094	+	0.863649i	$0.331827\pi$
$264$	2.28131	−	7.53321i	0.140405	−	0.463637i
$265$	−0.124792	+	0.105410i	−0.00766592	+	0.00647531i
$266$	14.5590	+	7.44719i	0.892668	+	0.456617i
$267$	8.38366	−	4.48622i	0.513072	−	0.274552i
$268$	6.76808	−	6.76808i	0.413427	−	0.413427i
$269$	1.89941	+	3.28987i	0.115809	+	0.200587i	0.918103	−	0.396342i	$-0.129721\pi$
$269$	1.89941	+	3.28987i	0.115809	+	0.200587i	−0.802294	+	0.596929i	$0.796387\pi$
$270$	−0.940530	−	11.5808i	−0.0572388	−	0.704786i
$271$	−9.26483	+	16.0472i	−0.562798	+	0.974795i	0.434452	+	0.900695i	$0.356942\pi$
$271$	−9.26483	+	16.0472i	−0.562798	+	0.974795i	−0.997251	+	0.0741005i	$0.976391\pi$
$272$	−1.13496	−	0.304112i	−0.0688172	−	0.0184395i
$273$	17.1687	−	10.3410i	1.03910	−	0.625865i
$274$	−16.1176	−	9.30553i	−0.973702	−	0.562167i
$275$	−3.79913	+	22.4019i	−0.229096	+	1.35089i
$276$	−8.92005	−	9.51489i	−0.536924	−	0.572729i
$277$	19.1569	−	5.13308i	1.15103	−	0.308417i	0.367651	−	0.929964i	$-0.380162\pi$
$277$	19.1569	−	5.13308i	1.15103	−	0.308417i	0.783377	+	0.621547i	$0.213496\pi$
$278$	−15.8327	+	4.24235i	−0.949580	+	0.254439i
$279$	−0.477200	−	0.965381i	−0.0285692	−	0.0577958i
$280$	−3.12656	+	5.02241i	−0.186848	+	0.300146i
$281$	10.0568	−	5.80629i	0.599938	−	0.346374i	−0.169079	−	0.985602i	$-0.554079\pi$
$281$	10.0568	−	5.80629i	0.599938	−	0.346374i	0.769017	+	0.639228i	$0.220746\pi$
$282$	−2.78346	+	4.48085i	−0.165753	+	0.266831i
$283$	18.3438	−	18.3438i	1.09042	−	1.09042i	0.0949410	−	0.995483i	$-0.469734\pi$
$283$	18.3438	−	18.3438i	1.09042	−	1.09042i	0.995483	−	0.0949410i	$-0.0302663\pi$
$284$	13.2021			0.783398
$285$	2.77662	−	23.7769i	0.164473	−	1.40842i
$286$	−9.93766	−	17.2125i	−0.587626	−	1.01780i
$287$	−7.56130	−	23.3971i	−0.446330	−	1.38109i
$288$	−2.84169	−	0.961652i	−0.167448	−	0.0566659i
$289$	−13.5268	−	7.80969i	−0.795693	−	0.459393i
$290$	9.04249	+	10.7051i	0.530993	+	0.628626i
$291$	4.41129	−	4.13551i	0.258595	−	0.242428i
$292$	−2.45665	+	9.16835i	−0.143765	+	0.536537i
$293$	6.70156	−	1.79568i	0.391510	−	0.104905i	−0.0576935	−	0.998334i	$-0.518375\pi$
$293$	6.70156	−	1.79568i	0.391510	−	0.104905i	0.449203	+	0.893430i	$0.351708\pi$
$294$	3.94143	+	11.4658i	0.229869	+	0.668700i
$295$	15.6193	+	10.8608i	0.909392	+	0.632340i
$296$	8.25544	+	4.76628i	0.479838	+	0.277034i
$297$	−13.7271	+	19.2132i	−0.796529	+	1.11487i
$298$	4.33316	+	1.16107i	0.251013	+	0.0672588i
$299$	−32.9331			−1.90457
$300$	8.48720	+	1.72262i	0.490009	+	0.0994557i
$301$	12.1963	+	18.8458i	0.702982	+	1.08625i
$302$	−0.307483	−	1.14754i	−0.0176937	−	0.0660337i
$303$	−7.77113	−	14.5224i	−0.446440	−	0.834288i
$304$	−5.35282	−	3.09045i	−0.307005	−	0.177249i
$305$	10.8162	+	7.52101i	0.619336	+	0.430652i
$306$	2.93276	+	1.95563i	0.167655	+	0.111796i
$307$	6.86513	+	6.86513i	0.391814	+	0.391814i	0.875333	−	0.483520i	$-0.160642\pi$
$307$	6.86513	+	6.86513i	0.391814	+	0.391814i	−0.483520	+	0.875333i	$0.660642\pi$
$308$	11.4406	−	3.69730i	0.651891	−	0.210673i
$309$	−3.64487	−	3.88793i	−0.207349	−	0.221177i
$310$	0.790008	−	0.141966i	0.0448694	−	0.00806310i
$311$		−	0.941850i		−	0.0534074i	−0.999643	−	0.0267037i	$-0.991499\pi$
$311$		−	0.941850i		−	0.0534074i	0.999643	−	0.0267037i	$-0.00850106\pi$
$312$	−6.67917	+	3.57412i	−0.378134	+	0.202345i
$313$	−11.8339	+	11.8339i	−0.668890	+	0.668890i	−0.957459	−	0.288569i	$-0.906820\pi$
$313$	−11.8339	+	11.8339i	−0.668890	+	0.668890i	0.288569	+	0.957459i	$0.406820\pi$
$314$	4.38268			0.247329
$315$	13.7145	−	11.2655i	0.772727	−	0.634738i
$316$	5.26884			0.296395
$317$	8.55250	−	8.55250i	0.480356	−	0.480356i	−0.424889	−	0.905245i	$-0.639687\pi$
$317$	8.55250	−	8.55250i	0.480356	−	0.480356i	0.905245	+	0.424889i	$0.139687\pi$
$318$	0.00408071	−	0.126467i	0.000228835	−	0.00709194i
$319$		−	28.4788i		−	1.59450i
$320$	1.27656	−	1.83586i	0.0713618	−	0.102628i
$321$	6.84273	−	22.5956i	0.381924	−	1.26117i
$322$	4.17291	−	19.4804i	0.232547	−	1.08560i
$323$	5.13540	+	5.13540i	0.285741	+	0.285741i
$324$	7.15045	+	5.46544i	0.397247	+	0.303636i
$325$	17.8309	−	12.6599i	0.989079	−	0.702247i
$326$	−15.4120	−	8.89815i	−0.853594	−	0.492823i
$327$	−0.842629	−	0.0271891i	−0.0465975	−	0.00150356i
$328$	2.40536	+	8.97694i	0.132814	+	0.495669i
$329$	−8.04732	+	0.408982i	−0.443663	+	0.0225479i
$330$	−10.9177	−	13.8048i	−0.601001	−	0.759927i
$331$	−18.1440			−0.997285			−0.498643	−	0.866808i	$-0.666168\pi$
$331$	−18.1440			−0.997285			−0.498643	+	0.866808i	$0.666168\pi$
$332$	−3.57191	−	0.957089i	−0.196034	−	0.0525271i
$333$	−18.8759	−	21.4832i	−1.03439	−	1.17727i
$334$	11.1725	+	6.45046i	0.611334	+	0.352954i
$335$	−3.78544	−	21.0651i	−0.206821	−	1.15091i
$336$	−1.26784	−	4.40370i	−0.0691663	−	0.240242i
$337$	11.2533	−	3.01532i	0.613007	−	0.164255i	0.0610603	−	0.998134i	$-0.480552\pi$
$337$	11.2533	−	3.01532i	0.613007	−	0.164255i	0.551947	+	0.833879i	$0.313885\pi$
$338$	−1.58619	+	5.91974i	−0.0862774	+	0.321992i
$339$	4.88516	+	1.47940i	0.265326	+	0.0803497i
$340$	−2.00715	+	1.69542i	−0.108853	+	0.0919470i
$341$	−1.41270	−	0.815625i	−0.0765022	−	0.0441686i
$342$	12.2391	+	13.9297i	0.661816	+	0.753230i
$343$	−10.9569	+	14.9314i	−0.591617	+	0.806219i
$344$	−4.24228	−	7.34784i	−0.228728	−	0.396169i
$345$	−28.8550	+	4.22970i	−1.55350	+	0.227719i
$346$	−15.2980			−0.822426
$347$	5.91862	−	5.91862i	0.317728	−	0.317728i	−0.530166	−	0.847894i	$-0.677870\pi$
$347$	5.91862	−	5.91862i	0.317728	−	0.317728i	0.847894	+	0.530166i	$0.177870\pi$
$348$	−10.8488	−	0.350059i	−0.581559	−	0.0187651i
$349$	13.2937	−	7.67509i	0.711593	−	0.410838i	−0.100058	−	0.994982i	$-0.531903\pi$
$349$	13.2937	−	7.67509i	0.711593	−	0.410838i	0.811651	+	0.584143i	$0.198569\pi$
$350$	5.22923	+	12.1513i	0.279514	+	0.649517i
$351$	22.4172	−	3.73352i	1.19654	−	0.199281i
$352$	−4.38951	+	1.17617i	−0.233962	+	0.0626899i
$353$	16.2841	−	4.36332i	0.866717	−	0.232236i	0.202049	−	0.979375i	$-0.435240\pi$
$353$	16.2841	−	4.36332i	0.866717	−	0.232236i	0.664668	+	0.747139i	$0.268573\pi$
$354$	−14.3496	+	3.35295i	−0.762670	+	0.178207i
$355$	16.8532	−	24.2372i	0.894475	−	1.28638i
$356$	−4.75426	−	2.74487i	−0.251975	−	0.145478i
$357$	0.0997304	+	5.38360i	0.00527829	+	0.284930i
$358$	10.3988	+	2.78634i	0.549591	+	0.147263i
$359$	−14.1397	+	24.4907i	−0.746264	+	1.29257i	0.203337	+	0.979109i	$0.434821\pi$
$359$	−14.1397	+	24.4907i	−0.746264	+	1.29257i	−0.949602	+	0.313459i	$0.898512\pi$
$360$	−5.39305	+	3.98936i	−0.284239	+	0.210258i
$361$	9.60175	+	16.6307i	0.505355	+	0.875301i
$362$	0.148840	−	0.148840i	0.00782288	−	0.00782288i
$363$	−0.539106	+	16.7077i	−0.0282957	+	0.876926i
$364$	−10.3020	−	5.26966i	−0.539970	−	0.276205i
$365$	13.6958	+	16.2140i	0.716871	+	0.848680i
$366$	−9.93694	+	2.32189i	−0.519412	+	0.121367i
$367$	18.9891	−	5.08813i	0.991225	−	0.265598i	0.273460	−	0.961883i	$-0.411832\pi$
$367$	18.9891	−	5.08813i	0.991225	−	0.265598i	0.717765	+	0.696285i	$0.245165\pi$
$368$	−1.94889	+	7.27337i	−0.101593	+	0.379151i
$369$	1.79739	−	27.8229i	0.0935682	−	1.44840i
$370$	19.2888	−	9.07144i	1.00278	−	0.471602i
$371$	0.162267	−	0.105013i	0.00842447	−	0.00545199i
$372$	−0.328073	+	0.528136i	−0.0170098	+	0.0273826i
$373$	−5.20254	−	1.39402i	−0.269377	−	0.0721794i	0.121602	−	0.992579i	$-0.461197\pi$
$373$	−5.20254	−	1.39402i	−0.269377	−	0.0721794i	−0.390979	+	0.920400i	$0.627864\pi$
$374$	5.33962			0.276105
$375$	13.9969	−	13.3823i	0.722797	−	0.691060i
$376$	3.04553			0.157061
$377$	−19.3809	+	19.3809i	−0.998169	+	0.998169i
$378$	−0.632018	+	13.7332i	−0.0325075	+	0.706359i
$379$			19.4353i			0.998326i	0.866508	+	0.499163i	$0.166359\pi$
$379$			19.4353i			0.998326i	−0.866508	+	0.499163i	$0.833641\pi$
$380$	−12.5068	+	5.88191i	−0.641587	+	0.301736i
$381$	4.53440	+	19.4058i	0.232305	+	0.994190i
$382$	15.2933	+	15.2933i	0.782473	+	0.782473i
$383$	−3.72445	+	13.8998i	−0.190311	+	0.710249i	0.803121	+	0.595817i	$0.203171\pi$
$383$	−3.72445	+	13.8998i	−0.190311	+	0.710249i	−0.993431	+	0.114432i	$0.963495\pi$
$384$	0.394099	+	1.68662i	0.0201113	+	0.0860700i
$385$	7.81691	−	25.7233i	0.398386	−	1.31098i
$386$			21.5752i			1.09815i
$387$	4.98919	+	24.9599i	0.253615	+	1.26878i
$388$	−3.37208	−	0.903546i	−0.171191	−	0.0458706i
$389$	−3.14536	+	5.44791i	−0.159476	+	0.276220i	−0.934680	−	0.355491i	$-0.884314\pi$
$389$	−3.14536	+	5.44791i	−0.159476	+	0.276220i	0.775204	+	0.631711i	$0.217647\pi$
$390$	−1.96474	+	16.8246i	−0.0994887	+	0.851948i
$391$	4.42384	−	7.66232i	0.223723	−	0.387500i
$392$	4.42243	−	5.42606i	0.223366	−	0.274058i
$393$	−16.1146	−	0.519968i	−0.812872	−	0.0262289i
$394$		−	5.22703i		−	0.263334i
$395$	6.72598	−	9.67288i	0.338421	−	0.486695i
$396$	13.6047	+	0.878880i	0.683663	+	0.0441654i
$397$	−14.9394	+	4.00301i	−0.749788	+	0.200905i	−0.613424	−	0.789754i	$-0.710208\pi$
$397$	−14.9394	+	4.00301i	−0.749788	+	0.200905i	−0.136364	+	0.990659i	$0.543542\pi$
$398$	−1.14209	+	4.26234i	−0.0572478	+	0.213652i
$399$	−6.82291	+	27.4904i	−0.341572	+	1.37624i
$400$	−1.74080	−	4.68718i	−0.0870400	−	0.234359i
$401$	−5.27255	+	3.04411i	−0.263299	+	0.152015i	−0.625838	−	0.779953i	$-0.715243\pi$
$401$	−5.27255	+	3.04411i	−0.263299	+	0.152015i	0.362540	+	0.931968i	$0.381910\pi$
$402$	14.0825	+	8.74789i	0.702370	+	0.436305i
$403$	0.406336	+	1.51647i	0.0202410	+	0.0755406i
$404$	−4.75473	+	8.23544i	−0.236557	+	0.409728i
$405$	19.1618	−	6.15031i	0.952156	−	0.305611i
$406$	−9.00838	−	13.9198i	−0.447078	−	0.690830i
$407$	−41.8433	−	11.2119i	−2.07410	−	0.555752i
$408$	0.0656341	−	2.03410i	0.00324937	−	0.100703i
$409$			1.69471i			0.0837981i	0.999122	+	0.0418991i	$0.0133408\pi$
$409$			1.69471i			0.0837981i	−0.999122	+	0.0418991i	$0.986659\pi$
$410$	19.5510	+	7.04366i	0.965557	+	0.347862i
$411$	9.34294	−	30.8516i	0.460853	−	1.52180i
$412$	−0.796349	+	2.97201i	−0.0392333	+	0.146421i
$413$	−16.7042	−	15.0884i	−0.821958	−	0.742451i
$414$	12.5326	−	18.7945i	0.615944	−	0.923701i
$415$	−6.31683	+	5.33576i	−0.310081	+	0.261922i
$416$	3.78767	+	2.18681i	0.185706	+	0.107217i
$417$	−13.3949	−	25.0318i	−0.655949	−	1.22581i
$418$	27.1311	+	7.26977i	1.32703	+	0.355576i
$419$	−2.28863	+	3.96402i	−0.111807	+	0.193655i	−0.916499	−	0.400037i	$-0.868997\pi$
$419$	−2.28863	+	3.96402i	−0.111807	+	0.193655i	0.804692	+	0.593693i	$0.202330\pi$
$420$	−9.70307	−	3.29400i	−0.473461	−	0.160731i
$421$	5.63946	+	9.76784i	0.274851	+	0.476055i	0.970097	−	0.242716i	$-0.0780383\pi$
$421$	5.63946	+	9.76784i	0.274851	+	0.476055i	−0.695247	+	0.718771i	$0.744705\pi$
$422$	−3.67152	−	13.7023i	−0.178727	−	0.667018i
$423$	−8.65446	−	2.92874i	−0.420794	−	0.142400i
$424$	−0.0632666	+	0.0365270i	−0.00307250	+	0.00177391i
$425$	0.550315	+	5.84916i	0.0266942	+	0.283726i
$426$	5.20292	+	22.2669i	0.252082	+	1.07883i
$427$	−11.5675	−	10.4486i	−0.559790	−	0.505642i
$428$	−13.1662	+	3.52788i	−0.636413	+	0.170526i
$429$	25.1146	−	23.5445i	1.21254	−	1.13674i
$430$	−18.9052	−	1.59169i	−0.911688	−	0.0767583i
$431$	−1.92684	+	1.11246i	−0.0928126	+	0.0535854i	−0.545688	−	0.837988i	$-0.683732\pi$
$431$	−1.92684	+	1.11246i	−0.0928126	+	0.0535854i	0.452875	+	0.891574i	$0.350398\pi$
$432$	0.502033	−	5.17184i	0.0241541	−	0.248830i
$433$	21.7168	−	21.7168i	1.04364	−	1.04364i	0.0446415	−	0.999003i	$-0.485785\pi$
$433$	21.7168	−	21.7168i	1.04364	−	1.04364i	0.999003	−	0.0446415i	$-0.0142146\pi$
$434$	−0.948498	+	0.0482048i	−0.0455294	+	0.00231390i
$435$	−14.4918	+	19.4701i	−0.694830	+	0.933521i
$436$	0.243373	+	0.421534i	0.0116554	+	0.0201878i
$437$	32.9101	−	32.9101i	1.57430	−	1.57430i
$438$	−16.4317	−	0.530200i	−0.785136	−	0.0253339i
$439$			14.3639i			0.685553i	0.939417	+	0.342776i	$0.111367\pi$
$439$			14.3639i			0.685553i	−0.939417	+	0.342776i	$0.888633\pi$
$440$	−3.44419	+	9.56000i	−0.164195	+	0.455755i
$441$	−17.7852	+	11.1664i	−0.846913	+	0.531732i
$442$	−3.63382	−	3.63382i	−0.172843	−	0.172843i
$443$	6.74697	+	6.74697i	0.320558	+	0.320558i	0.848981	−	0.528423i	$-0.177216\pi$
$443$	6.74697	+	6.74697i	0.320558	+	0.320558i	−0.528423	+	0.848981i	$0.677216\pi$
$444$	−4.78544	+	15.8022i	−0.227107	+	0.749938i
$445$	−11.1083	+	5.22419i	−0.526584	+	0.247650i
$446$	−2.05357	+	1.18563i	−0.0972395	+	0.0561412i
$447$	−0.250584	+	7.76597i	−0.0118522	+	0.367318i
$448$	−1.77346	+	1.96337i	−0.0837881	+	0.0927607i
$449$	40.8669			1.92863			0.964313	−	0.264764i	$-0.0852941\pi$
$449$	40.8669			1.92863			0.964313	+	0.264764i	$0.0852941\pi$
$450$	0.439388	+	14.9936i	0.0207129	+	0.706803i
$451$	−21.1168	−	36.5753i	−0.994350	−	1.72226i
$452$	−0.762725	−	2.84653i	−0.0358756	−	0.133889i
$453$	1.81429	−	0.970853i	0.0852427	−	0.0456146i
$454$	−0.476418	−	0.275060i	−0.0223594	−	0.0129092i
$455$	−22.8254	+	12.1860i	−1.07007	+	0.571289i
$456$	3.10287	−	10.2461i	0.145305	−	0.479818i
$457$	−16.4449	−	16.4449i	−0.769259	−	0.769259i	0.208717	−	0.977976i	$-0.433071\pi$
$457$	−16.4449	−	16.4449i	−0.769259	−	0.769259i	−0.977976	+	0.208717i	$0.933071\pi$
$458$	5.09430	−	19.0122i	0.238041	−	0.888381i
$459$	−2.14261	+	5.71717i	−0.100008	+	0.266855i
$460$	10.8651	+	12.8628i	0.506586	+	0.599731i
$461$	−15.9837	+	9.22818i	−0.744434	+	0.429799i	−0.823679	−	0.567056i	$-0.808082\pi$
$461$	−15.9837	+	9.22818i	−0.744434	+	0.429799i	0.0792453	+	0.996855i	$0.474749\pi$
$462$	10.7447	+	17.8389i	0.499888	+	0.829942i
$463$	−4.81433	−	17.9673i	−0.223741	−	0.835012i	−0.982905	−	0.184113i	$-0.941059\pi$
$463$	−4.81433	−	17.9673i	−0.223741	−	0.835012i	0.759164	−	0.650899i	$-0.225608\pi$
$464$	3.13342	+	5.42724i	0.145465	+	0.251953i
$465$	0.550783	+	1.27649i	0.0255420	+	0.0591960i
$466$	3.02427	−	5.23819i	0.140097	−	0.242654i
$467$	−0.760775	−	2.83925i	−0.0352045	−	0.131385i	0.946087	−	0.323912i	$-0.104998\pi$
$467$	−0.760775	−	2.83925i	−0.0352045	−	0.131385i	−0.981292	+	0.192527i	$0.938332\pi$
$468$	−8.66044	−	9.85667i	−0.400329	−	0.455625i
$469$	1.28535	+	25.2912i	0.0593521	+	1.16784i
$470$	3.88779	−	5.59118i	0.179330	−	0.257902i
$471$	1.72721	+	7.39192i	0.0795857	+	0.340602i
$472$	6.01598	+	6.01598i	0.276908	+	0.276908i
$473$	27.2638	+	27.2638i	1.25359	+	1.25359i
$474$	2.07644	+	8.88653i	0.0953743	+	0.408172i
$475$	−5.16730	+	30.4694i	−0.237092	+	1.39803i
$476$	2.60990	−	1.68902i	0.119624	−	0.0774163i
$477$	0.214911	−	0.0429581i	0.00984008	−	0.00196691i
$478$	5.27052	+	19.6699i	0.241068	+	0.899679i
$479$	−0.117676	+	0.203821i	−0.00537676	+	0.00931282i	−0.868701	−	0.495336i	$-0.835045\pi$
$479$	−0.117676	+	0.203821i	−0.00537676	+	0.00931282i	0.863325	+	0.504649i	$0.168378\pi$
$480$	3.59950	+	1.42956i	0.164294	+	0.0652500i
$481$	20.8459	+	36.1062i	0.950492	+	1.64630i
$482$	−2.45503	−	9.16230i	−0.111824	−	0.417331i
$483$	34.5006	−	0.639120i	1.56983	−	0.0290810i
$484$	8.35819	−	4.82560i	0.379918	−	0.219346i
$485$	−5.96344	+	5.03726i	−0.270786	+	0.228730i
$486$	−6.40014	+	14.2140i	−0.290316	+	0.644761i
$487$	3.92751	−	14.6577i	0.177973	−	0.664202i	−0.818054	−	0.575142i	$-0.804947\pi$
$487$	3.92751	−	14.6577i	0.177973	−	0.664202i	0.996026	−	0.0890606i	$-0.0283865\pi$
$488$	4.16601	+	4.16601i	0.188587	+	0.188587i
$489$	8.93392	−	29.5010i	0.404006	−	1.33408i
$490$	−4.31603	−	15.0457i	−0.194979	−	0.679694i
$491$	−2.37876	−	1.37337i	−0.107352	−	0.0619795i	0.445363	−	0.895350i	$-0.353075\pi$
$491$	−2.37876	−	1.37337i	−0.107352	−	0.0619795i	−0.552715	+	0.833371i	$0.686408\pi$
$492$	−14.1927	+	7.59474i	−0.639858	+	0.342397i
$493$	−1.90582	−	7.11262i	−0.0858338	−	0.320336i
$494$	−13.5165	−	23.4112i	−0.608134	−	1.05332i
$495$	18.9807	−	23.8545i	0.853120	−	1.07218i
$496$	0.358961			0.0161178
$497$	−23.4133	+	25.9206i	−1.05023	+	1.16270i
$498$	0.206561	−	6.40163i	0.00925622	−	0.286864i
$499$	30.0413	−	17.3443i	1.34483	−	0.776439i	0.357320	−	0.933982i	$-0.383691\pi$
$499$	30.0413	−	17.3443i	1.34483	−	0.776439i	0.987512	+	0.157543i	$0.0503572\pi$
$500$	−10.8273	−	2.78758i	−0.484209	−	0.124664i
$501$	−6.47640	+	21.3859i	−0.289344	+	0.955453i
$502$	−8.82121	−	8.82121i	−0.393710	−	0.393710i
$503$	23.1452	+	23.1452i	1.03199	+	1.03199i	0.999471	+	0.0325210i	$0.0103536\pi$
$503$	23.1452	+	23.1452i	1.03199	+	1.03199i	0.0325210	+	0.999471i	$0.489646\pi$
$504$	6.92771	−	3.87386i	0.308585	−	0.172555i
$505$	9.04946	+	19.2421i	0.402696	+	0.856260i
$506$		−	34.2188i		−	1.52121i
$507$	−10.6095	−	0.342335i	−0.471183	−	0.0152036i
$508$	8.13579	−	8.13579i	0.360967	−	0.360967i
$509$	18.7316	+	32.4440i	0.830262	+	1.43806i	0.897830	+	0.440341i	$0.145143\pi$
$509$	18.7316	+	32.4440i	0.830262	+	1.43806i	−0.0675684	+	0.997715i	$0.521524\pi$
$510$	−3.65055	−	2.71714i	−0.161649	−	0.120317i
$511$	−13.6441	−	21.0830i	−0.603581	−	0.932659i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.6706	+	26.1324i	−0.824327	+	1.15377i
$514$	9.48286	−	5.47493i	0.418271	−	0.241489i
$515$	4.43963	+	5.25594i	0.195633	+	0.231604i
$516$	10.7211	−	10.0509i	0.471972	−	0.442466i
$517$	−13.3684	+	3.58205i	−0.587941	+	0.157538i
$518$	−23.9987	+	7.75571i	−1.05444	+	0.340766i
$519$	−6.02893	−	25.8019i	−0.264641	−	1.13258i
$520$	8.84987	−	4.16206i	0.388092	−	0.182518i
$521$	−28.8826	+	16.6754i	−1.26537	+	0.730562i	−0.974109	−	0.226081i	$-0.927409\pi$
$521$	−28.8826	+	16.6754i	−1.26537	+	0.730562i	−0.291263	+	0.956643i	$0.594075\pi$
$522$	−3.68510	−	18.4358i	−0.161292	−	0.806914i
$523$	10.4614	+	39.0426i	0.457447	+	1.70722i	0.680793	+	0.732476i	$0.261635\pi$
$523$	10.4614	+	39.0426i	0.457447	+	1.70722i	−0.223346	+	0.974739i	$0.571698\pi$
$524$	4.65430	+	8.06148i	0.203324	+	0.352167i
$525$	−18.4339	+	13.6085i	−0.804520	+	0.593926i
$526$	4.27144	−	7.39836i	0.186244	−	0.322584i
$527$	−0.407407	−	0.109164i	−0.0177469	−	0.00475528i
$528$	−3.71365	−	6.93992i	−0.161616	−	0.302021i
$529$	−29.1852	−	16.8501i	−1.26892	−	0.732612i
$530$	−0.0137049	+	0.162778i	−0.000595301	+	0.00707061i
$531$	−11.3103	−	22.8809i	−0.490825	−	0.992944i
$532$	15.5607	−	5.02879i	0.674642	−	0.218026i
$533$	−10.5202	+	39.2618i	−0.455679	+	1.70062i
$534$	2.75591	−	9.10038i	0.119260	−	0.393812i
$535$	−10.3307	+	28.6749i	−0.446637	+	1.23973i
$536$		−	9.57152i		−	0.413427i
$537$	−0.601354	+	18.6368i	−0.0259503	+	0.804239i
$538$	3.66937	+	0.983206i	0.158198	+	0.0423890i
$539$	−13.0304	+	29.0193i	−0.561257	+	1.24995i
$540$	−8.85393	−	7.52382i	−0.381013	−	0.323774i
$541$	15.8159	−	27.3939i	0.679977	−	1.17776i	−0.295010	−	0.955494i	$-0.595323\pi$
$541$	15.8159	−	27.3939i	0.679977	−	1.17776i	0.974987	−	0.222261i	$-0.0713438\pi$
$542$	4.79583	+	17.8983i	0.205998	+	0.768797i
$543$	0.309695	+	0.192379i	0.0132903	+	0.00825579i
$544$	−1.01758	+	0.587499i	−0.0436283	+	0.0251888i
$545$	1.08456	+	0.0913130i	0.0464574	+	0.00391142i
$546$	4.82791	−	19.4523i	0.206615	−	0.832481i
$547$	5.47211	−	20.4222i	0.233971	−	0.873190i	−0.744640	−	0.667467i	$-0.767379\pi$
$547$	5.47211	−	20.4222i	0.233971	−	0.873190i	0.978610	−	0.205723i	$-0.0659547\pi$
$548$	−17.9769	+	4.81689i	−0.767935	+	0.205768i
$549$	−7.83228	−	15.8448i	−0.334274	−	0.676239i
$550$	13.1542	+	18.5270i	0.560896	+	0.789992i
$551$		−	38.7347i		−	1.65015i
$552$	−13.0355	−	0.420615i	−0.554826	−	0.0179025i
$553$	−9.34408	+	10.3447i	−0.397351	+	0.439902i
$554$	9.91635	−	17.1756i	0.421305	−	0.729722i
$555$	22.9018	+	28.9578i	0.972126	+	1.22919i
$556$	−8.19559	+	14.1952i	−0.347570	+	0.602010i
$557$	1.68142	+	0.450534i	0.0712439	+	0.0190898i	0.294265	−	0.955724i	$-0.404925\pi$
$557$	1.68142	+	0.450534i	0.0712439	+	0.0190898i	−0.223021	+	0.974814i	$0.571592\pi$
$558$	−1.02006	−	0.345196i	−0.0431825	−	0.0146133i
$559$		−	37.1082i		−	1.56951i
$560$	1.34057	+	5.76219i	0.0566492	+	0.243497i
$561$	2.10434	+	9.00590i	0.0888452	+	0.380230i
$562$	3.00556	−	11.2169i	0.126782	−	0.473156i
$563$	9.75124	+	9.75124i	0.410966	+	0.410966i	0.882075	−	0.471109i	$-0.156146\pi$
$563$	9.75124	+	9.75124i	0.410966	+	0.410966i	−0.471109	+	0.882075i	$0.656146\pi$
$564$	1.20024	+	5.13665i	0.0505392	+	0.216292i
$565$	−6.19950	−	2.23350i	−0.260815	−	0.0939640i
$566$		−	25.9420i		−	1.09042i
$567$	−23.4117	+	4.34626i	−0.983201	+	0.182526i
$568$	9.33527	−	9.33527i	0.391699	−	0.391699i
$569$	−16.6912			−0.699731			−0.349866	−	0.936800i	$-0.613773\pi$
$569$	−16.6912			−0.699731			−0.349866	+	0.936800i	$0.613773\pi$
$570$	−14.8495	−	18.7762i	−0.621976	−	0.786449i
$571$	20.3215			0.850428			0.425214	−	0.905093i	$-0.360199\pi$
$571$	20.3215			0.850428			0.425214	+	0.905093i	$0.360199\pi$
$572$	−19.1981	−	5.14411i	−0.802712	−	0.215086i
$573$	−19.7669	+	31.8210i	−0.825774	+	1.32934i
$574$	−21.8909	−	11.1976i	−0.913709	−	0.467380i
$575$	37.4842	−	3.52668i	1.56320	−	0.147073i
$576$	−2.68937	+	1.32939i	−0.112057	+	0.0553913i
$577$	−5.50888	+	20.5594i	−0.229338	+	0.855900i	0.751282	+	0.659981i	$0.229436\pi$
$577$	−5.50888	+	20.5594i	−0.229338	+	0.855900i	−0.980620	+	0.195919i	$0.937231\pi$
$578$	−15.0872	+	4.04259i	−0.627543	+	0.168150i
$579$	−36.3891	+	8.50275i	−1.51228	+	0.353362i
$580$	13.9637	+	1.17565i	0.579810	+	0.0488163i
$581$	8.21376	−	5.31563i	0.340764	−	0.220529i
$582$	0.195005	−	6.04350i	0.00808323	−	0.250511i
$583$	0.234748	−	0.234748i	0.00972226	−	0.00972226i
$584$	4.74589	+	8.22012i	0.196386	+	0.340151i
$585$	−29.1511	+	3.31679i	−1.20525	+	0.137133i
$586$	3.46898	−	6.00846i	0.143302	−	0.248207i
$587$	−2.96086	−	0.793359i	−0.122208	−	0.0327455i	0.197197	−	0.980364i	$-0.436816\pi$
$587$	−2.96086	−	0.793359i	−0.122208	−	0.0327455i	−0.319405	+	0.947618i	$0.603483\pi$
$588$	10.8946	+	5.32055i	0.449285	+	0.219416i
$589$	−1.92145	−	1.10935i	−0.0791721	−	0.0457101i
$590$	18.7243	−	3.36478i	0.770866	−	0.138526i
$591$	8.81601	−	2.05997i	0.362642	−	0.0847357i
$592$	9.20775	−	2.46721i	0.378436	−	0.101402i
$593$	−23.6708	+	6.34257i	−0.972042	+	0.260458i	−0.709690	−	0.704514i	$-0.751165\pi$
$593$	−23.6708	+	6.34257i	−0.972042	+	0.260458i	−0.262352	+	0.964972i	$0.584498\pi$
$594$	3.87927	+	23.2924i	0.159168	+	0.955697i
$595$	0.230863	−	6.94755i	0.00946444	−	0.284822i
$596$	3.88501	−	2.24301i	0.159136	−	0.0918772i
$597$	−7.63904	−	0.246488i	−0.312645	−	0.0100881i
$598$	−23.2873	+	23.2873i	−0.952287	+	0.952287i
$599$	−29.8865			−1.22113			−0.610565	−	0.791966i	$-0.709058\pi$
$599$	−29.8865			−1.22113			−0.610565	+	0.791966i	$0.709058\pi$
$600$	7.21944	−	4.78328i	0.294732	−	0.195277i
$601$	0.0345488	+	0.0598402i	0.00140927	+	0.00244093i	0.866729	−	0.498779i	$-0.166218\pi$
$601$	0.0345488	+	0.0598402i	0.00140927	+	0.00244093i	−0.865320	+	0.501220i	$0.832885\pi$
$602$	21.9501	+	4.70192i	0.894618	+	0.191636i
$603$	−9.20447	+	27.1993i	−0.374835	+	1.10764i
$604$	−1.02886	−	0.594012i	−0.0418637	−	0.0241700i
$605$	1.81056	−	21.5047i	0.0736096	−	0.874289i
$606$	−15.7639	−	4.77385i	−0.640364	−	0.193924i
$607$	9.76233	−	36.4335i	0.396241	−	1.47879i	−0.423416	−	0.905935i	$-0.639169\pi$
$607$	9.76233	−	36.4335i	0.396241	−	1.47879i	0.819657	−	0.572855i	$-0.194164\pi$
$608$	−5.97029	+	1.59973i	−0.242127	+	0.0648778i
$609$	19.9273	−	20.6795i	0.807494	−	0.837976i
$610$	12.9664	−	2.33008i	0.524994	−	0.0943422i
$611$	11.5354	+	6.65999i	0.466674	+	0.269434i
$612$	3.45662	−	0.690937i	0.139725	−	0.0279295i
$613$	−36.4169	−	9.75789i	−1.47087	−	0.394117i	−0.567638	−	0.823278i	$-0.692143\pi$
$613$	−36.4169	−	9.75789i	−1.47087	−	0.394117i	−0.903228	+	0.429161i	$0.858809\pi$
$614$	9.70876			0.391814
$615$	−4.17493	+	35.7511i	−0.168350	+	1.44162i
$616$	5.47537	−	10.7041i	0.220609	−	0.431282i
$617$	5.39816	+	20.1462i	0.217322	+	0.811056i	0.985336	+	0.170624i	$0.0545782\pi$
$617$	5.39816	+	20.1462i	0.217322	+	0.811056i	−0.768014	+	0.640433i	$0.778755\pi$
$618$	−5.32650	−	0.171870i	−0.214263	−	0.00691361i
$619$	27.1475	+	15.6736i	1.09115	+	0.629977i	0.933883	−	0.357579i	$-0.116398\pi$
$619$	27.1475	+	15.6736i	1.09115	+	0.629977i	0.157269	+	0.987556i	$0.449731\pi$
$620$	0.458235	−	0.659005i	0.0184032	−	0.0264663i
$621$	36.6383	+	13.7308i	1.47025	+	0.551000i
$622$	−0.665989	−	0.665989i	−0.0267037	−	0.0267037i
$623$	13.8207	−	4.46647i	0.553715	−	0.178945i
$624$	−2.19560	+	7.25017i	−0.0878944	+	0.290239i
$625$	−18.9392	+	16.3189i	−0.757569	+	0.652755i
$626$			16.7356i			0.668890i
$627$	−1.56898	+	48.6249i	−0.0626589	+	1.94189i
$628$	3.09903	−	3.09903i	0.123665	−	0.123665i
$629$	−11.2007			−0.446603
$630$	1.73175	−	17.6636i	0.0689946	−	0.703733i
$631$	1.35271			0.0538504			0.0269252	−	0.999637i	$-0.491428\pi$
$631$	1.35271			0.0538504			0.0269252	+	0.999637i	$0.491428\pi$
$632$	3.72563	−	3.72563i	0.148198	−	0.148198i
$633$	21.6636	−	11.5925i	0.861052	−	0.460762i
$634$		−	12.0951i		−	0.480356i
$635$	−4.55041	−	25.3220i	−0.180577	−	1.00487i
$636$	−0.0865405	−	0.0923115i	−0.00343155	−	0.00366039i
$637$	28.6165	−	10.8811i	1.13383	−	0.431125i
$638$	−20.1375	−	20.1375i	−0.797252	−	0.797252i
$639$	−35.5052	+	17.5507i	−1.40457	+	0.694295i
$640$	−0.395490	−	2.20082i	−0.0156331	−	0.0869949i
$641$	−26.0320	−	15.0296i	−1.02820	−	0.593632i	−0.111732	−	0.993738i	$-0.535640\pi$
$641$	−26.0320	−	15.0296i	−1.02820	−	0.593632i	−0.916469	+	0.400107i	$0.868973\pi$
$642$	−11.1390	−	20.8161i	−0.439621	−	0.821545i
$643$	9.85511	+	36.7798i	0.388648	+	1.45045i	0.832336	+	0.554272i	$0.187003\pi$
$643$	9.85511	+	36.7798i	0.388648	+	1.45045i	−0.443688	+	0.896181i	$0.646330\pi$
$644$	−10.8241	−	16.7254i	−0.426528	−	0.659075i
$645$	−4.76592	−	32.5131i	−0.187658	−	1.28020i
$646$	7.26255			0.285741
$647$	−28.5483	−	7.64948i	−1.12235	−	0.300732i	−0.350515	−	0.936557i	$-0.613993\pi$
$647$	−28.5483	−	7.64948i	−1.12235	−	0.300732i	−0.771833	+	0.635825i	$0.780660\pi$
$648$	8.92078	−	1.19148i	0.350441	−	0.0468057i
$649$	−33.4830	−	19.3314i	−1.31432	−	0.758825i
$650$	3.65640	−	21.5603i	0.143416	−	0.845663i
$651$	−0.455105	−	1.58076i	−0.0178370	−	0.0619548i
$652$	−17.1899	+	4.60602i	−0.673208	+	0.180386i
$653$	7.13480	−	26.6274i	0.279206	−	1.04201i	−0.673764	−	0.738947i	$-0.735323\pi$
$653$	7.13480	−	26.6274i	0.279206	−	1.04201i	0.952970	−	0.303065i	$-0.0980099\pi$
$654$	−0.615055	+	0.576603i	−0.0240505	+	0.0225470i
$655$	20.7413	+	1.74628i	0.810428	+	0.0682329i
$656$	8.04851	+	4.64681i	0.314241	+	0.181427i
$657$	−5.58147	−	27.9230i	−0.217754	−	1.08938i
$658$	−5.40112	+	5.97951i	−0.210558	+	0.233106i
$659$	16.0689	+	27.8321i	0.625954	+	1.08418i	0.988356	+	0.152162i	$0.0486234\pi$
$659$	16.0689	+	27.8321i	0.625954	+	1.08418i	−0.362402	+	0.932022i	$0.618043\pi$
$660$	−17.4814	−	2.04144i	−0.680464	−	0.0794631i
$661$	7.17196			0.278957			0.139479	−	0.990225i	$-0.455457\pi$
$661$	7.17196			0.278957			0.139479	+	0.990225i	$0.455457\pi$
$662$	−12.8298	+	12.8298i	−0.498643	+	0.498643i
$663$	4.69679	−	7.56096i	0.182408	−	0.293643i
$664$	−3.20248	+	1.84895i	−0.124280	+	0.0717534i
$665$	10.6320	−	34.9869i	0.412290	−	1.35673i
$666$	−28.5382	−	1.84360i	−1.10583	−	0.0714380i
$667$	−45.5810	+	12.2134i	−1.76490	+	0.472905i
$668$	12.4613	−	3.33901i	0.482144	−	0.129190i
$669$	−2.80902	−	2.99634i	−0.108603	−	0.115845i
$670$	−17.5720	−	12.2186i	−0.678866	−	0.472046i
$671$	−23.1867	−	13.3868i	−0.895113	−	0.516794i
$672$	−4.01038	−	2.21739i	−0.154704	−	0.0855376i
$673$	−43.9221	−	11.7689i	−1.69307	−	0.453658i	−0.721894	−	0.692004i	$-0.756728\pi$
$673$	−43.9221	−	11.7689i	−1.69307	−	0.453658i	−0.971180	+	0.238346i	$0.923395\pi$
$674$	5.82514	−	10.0894i	0.224376	−	0.388631i
$675$	−25.1153	+	6.65003i	−0.966687	+	0.255960i
$676$	3.06428	+	5.30750i	0.117857	+	0.204134i
$677$	7.30344	−	7.30344i	0.280694	−	0.280694i	−0.552692	−	0.833386i	$-0.686399\pi$
$677$	7.30344	−	7.30344i	0.280694	−	0.280694i	0.833386	+	0.552692i	$0.186399\pi$
$678$	4.50042	−	2.40824i	0.172838	−	0.0924879i
$679$	7.75425	−	5.01825i	0.297581	−	0.192583i
$680$	−0.220429	+	2.61811i	−0.00845306	+	0.100400i
$681$	0.276166	−	0.911937i	0.0105827	−	0.0349455i
$682$	−1.57567	+	0.422199i	−0.0603354	+	0.0161668i
$683$	−0.809428	+	3.02083i	−0.0309719	+	0.115589i	−0.979681	−	0.200561i	$-0.935724\pi$
$683$	−0.809428	+	3.02083i	−0.0309719	+	0.115589i	0.948709	+	0.316150i	$0.102390\pi$
$684$	18.5041	+	1.19539i	0.707523	+	0.0457068i
$685$	−14.1054	+	39.1522i	−0.538939	+	1.49593i
$686$	2.81039	+	18.3058i	0.107301	+	0.698918i
$687$	34.0740	+	1.09946i	1.30000	+	0.0419471i
$688$	−8.19545	−	2.19596i	−0.312449	−	0.0837204i
$689$	−0.319511			−0.0121724
$690$	−17.4127	+	23.3944i	−0.662891	+	0.890610i
$691$	30.8285			1.17277			0.586386	−	0.810032i	$-0.300550\pi$
$691$	30.8285			1.17277			0.586386	+	0.810032i	$0.300550\pi$
$692$	−10.8173	+	10.8173i	−0.411213	+	0.411213i
$693$	−25.8530	+	25.1525i	−0.982074	+	0.955464i
$694$		−	8.37019i		−	0.317728i
$695$	15.5983	+	33.1670i	0.591677	+	1.25809i
$696$	−7.91881	+	7.42375i	−0.300162	+	0.281397i
$697$	−7.72160	−	7.72160i	−0.292476	−	0.292476i
$698$	3.97292	−	14.8271i	0.150377	−	0.561216i
$699$	10.0267	+	3.03643i	0.379244	+	0.114848i
$700$	12.2899	+	4.89468i	0.464515	+	0.185001i
$701$			40.5025i			1.52976i	0.644174	+	0.764879i	$0.277201\pi$
$701$			40.5025i			1.52976i	−0.644174	+	0.764879i	$0.722799\pi$
$702$	13.2114	−	18.4914i	0.498631	−	0.697912i
$703$	−56.9122	−	15.2496i	−2.14648	−	0.575148i
$704$	−2.27218	+	3.93553i	−0.0856360	+	0.148326i
$705$	10.9624	+	4.35375i	0.412866	+	0.163972i
$706$	8.42929	−	14.6000i	0.317240	−	0.549477i
$707$	−7.73692	−	23.9405i	−0.290977	−	0.900377i
$708$	−7.77578	+	12.5176i	−0.292232	+	0.470439i
$709$		−	13.4311i		−	0.504416i	−0.967673	−	0.252208i	$-0.918843\pi$
$709$		−	13.4311i		−	0.504416i	0.967673	−	0.252208i	$-0.0811567\pi$
$710$	−5.22128	−	29.0553i	−0.195951	−	1.09043i
$711$	−14.1699	+	7.00434i	−0.531412	+	0.262683i
$712$	−5.30269	+	1.42085i	−0.198727	+	0.0532487i
$713$	−0.699578	+	2.61086i	−0.0261994	+	0.0977775i
$714$	3.87730	+	3.73626i	0.145104	+	0.139826i
$715$	−33.9513	+	28.6783i	−1.26971	+	1.07251i
$716$	9.32327	−	5.38279i	0.348427	−	0.201164i
$717$	−31.0985	+	16.6412i	−1.16139	+	0.621479i
$718$	7.31924	+	27.3158i	0.273152	+	1.01942i
$719$	2.12346	−	3.67795i	0.0791919	−	0.137164i	−0.823710	−	0.567012i	$-0.808099\pi$
$719$	2.12346	−	3.67795i	0.0791919	−	0.137164i	0.902901	+	0.429848i	$0.141433\pi$
$720$	−0.992558	+	6.63437i	−0.0369905	+	0.247248i
$721$	−4.42288	−	6.83428i	−0.164717	−	0.254522i
$722$	18.5492	+	4.97023i	0.690328	+	0.184973i
$723$	14.4858	−	7.75156i	0.538732	−	0.288284i
$724$		−	0.210492i		−	0.00782288i
$725$	19.9838	−	24.1346i	0.742179	−	0.896337i
$726$	11.4329	+	12.1953i	0.424315	+	0.452611i
$727$	−3.48815	+	13.0179i	−0.129368	+	0.482809i	−0.999958	−	0.00920135i	$-0.997071\pi$
$727$	−3.48815	+	13.0179i	−0.129368	+	0.482809i	0.870589	+	0.492010i	$0.163738\pi$
$728$	−11.0108	+	3.55839i	−0.408088	+	0.131883i
$729$	−26.4959	−	5.19287i	−0.981331	−	0.192329i
$730$	21.1494	+	1.78065i	0.782775	+	0.0659048i
$731$	8.63370	+	4.98467i	0.319329	+	0.184365i
$732$	−5.38466	+	8.66830i	−0.199023	+	0.320390i
$733$	23.7963	+	6.37620i	0.878937	+	0.235510i	0.669948	−	0.742408i	$-0.266316\pi$
$733$	23.7963	+	6.37620i	0.878937	+	0.235510i	0.208989	+	0.977918i	$0.432983\pi$
$734$	9.82951	−	17.0252i	0.362814	−	0.628412i
$735$	23.6754	−	13.2090i	0.873279	−	0.487221i
$736$	3.76497	+	6.52113i	0.138779	+	0.240372i
$737$	11.2577	+	42.0143i	0.414683	+	1.54762i
$738$	−18.4028	−	20.9447i	−0.677416	−	0.770984i
$739$	21.0639	−	12.1612i	0.774847	−	0.447358i	−0.0597540	−	0.998213i	$-0.519032\pi$
$739$	21.0639	−	12.1612i	0.774847	−	0.447358i	0.834601	+	0.550855i	$0.185698\pi$
$740$	7.22476	−	20.0537i	0.265587	−	0.737189i
$741$	34.1589	−	32.0234i	1.25486	−	1.17641i
$742$	0.0404847	−	0.188995i	0.00148624	−	0.00693823i
$743$	−19.6154	+	5.25592i	−0.719618	+	0.192821i	−0.600001	−	0.799999i	$-0.704833\pi$
$743$	−19.6154	+	5.25592i	−0.719618	+	0.192821i	−0.119617	+	0.992820i	$0.538167\pi$
$744$	0.141466	+	0.605431i	0.00518641	+	0.0221962i
$745$	0.841573	−	9.99568i	0.0308328	−	0.366213i
$746$	−4.66447	+	2.69303i	−0.170778	+	0.0985990i
$747$	10.8785	−	2.17449i	0.398025	−	0.0795603i
$748$	3.77568	−	3.77568i	0.138053	−	0.138053i
$749$	16.4232	−	32.1068i	0.600091	−	1.17316i
$750$	0.434573	−	19.3600i	0.0158684	−	0.706929i
$751$	−15.8277	−	27.4144i	−0.577562	−	1.00037i	−0.995758	−	0.0920100i	$-0.970671\pi$
$751$	−15.8277	−	27.4144i	−0.577562	−	1.00037i	0.418196	−	0.908357i	$-0.362663\pi$
$752$	2.15351	−	2.15351i	0.0785305	−	0.0785305i
$753$	11.4016	−	18.3545i	0.415497	−	0.668873i
$754$			27.4088i			0.998169i
$755$	−2.40392	+	1.13055i	−0.0874877	+	0.0411451i
$756$	9.26393	+	10.1577i	0.336926	+	0.369433i
$757$	−4.79302	−	4.79302i	−0.174205	−	0.174205i	0.614619	−	0.788824i	$-0.289310\pi$
$757$	−4.79302	−	4.79302i	−0.174205	−	0.174205i	−0.788824	+	0.614619i	$0.789310\pi$
$758$	13.7429	+	13.7429i	0.499163	+	0.499163i
$759$	57.7141	−	13.4856i	2.09489	−	0.489496i
$760$	−4.68452	+	13.0028i	−0.169926	+	0.471661i
$761$	9.12740	−	5.26971i	0.330868	−	0.191027i	−0.325358	−	0.945591i	$-0.605485\pi$
$761$	9.12740	−	5.26971i	0.330868	−	0.191027i	0.656226	+	0.754564i	$0.272152\pi$
$762$	16.9283	+	10.5157i	0.613247	+	0.380943i
$763$	−1.25924	−	0.269742i	−0.0455876	−	0.00976531i
$764$	21.6280			0.782473
$765$	3.14411	−	7.22790i	0.113675	−	0.261325i
$766$	7.19509	+	12.4623i	0.259969	+	0.450280i
$767$	9.63072	+	35.9423i	0.347745	+	1.29780i
$768$	1.47129	+	0.913950i	0.0530906	+	0.0329793i
$769$	−15.0585	−	8.69401i	−0.543022	−	0.313514i	0.203281	−	0.979121i	$-0.434840\pi$
$769$	−15.0585	−	8.69401i	−0.543022	−	0.313514i	−0.746303	+	0.665607i	$0.768173\pi$
$770$	−12.6617	−	23.7165i	−0.456297	−	0.854684i
$771$	12.9713	+	13.8363i	0.467150	+	0.498303i
$772$	15.2559	+	15.2559i	0.549074	+	0.549074i
$773$	8.00635	−	29.8801i	0.287968	−	1.07471i	−0.658674	−	0.752428i	$-0.728882\pi$
$773$	8.00635	−	29.8801i	0.287968	−	1.07471i	0.946643	−	0.322285i	$-0.104451\pi$
$774$	21.1772	+	14.1214i	0.761199	+	0.507584i
$775$	−0.624880	−	1.68252i	−0.0224464	−	0.0604377i
$776$	−3.02332	+	1.74552i	−0.108531	+	0.0626604i
$777$	−22.5388	−	37.4201i	−0.808575	−	1.34244i
$778$	1.62816	+	6.07636i	0.0583722	+	0.217848i
$779$	−28.7214	−	49.7470i	−1.02905	−	1.78237i
$780$	10.5075	+	13.2861i	0.376230	+	0.475719i
$781$	−29.9975	+	51.9571i	−1.07339	+	1.85917i
$782$	−2.28995	−	8.54620i	−0.0818884	−	0.305612i
$783$	29.6419	−	13.4809i	1.05932	−	0.481768i
$784$	−0.709677	−	6.96393i	−0.0253456	−	0.248712i
$785$	−1.73331	−	9.64548i	−0.0618644	−	0.344262i
$786$	−11.7624	+	11.0270i	−0.419551	+	0.393322i
$787$	−4.78870	−	4.78870i	−0.170699	−	0.170699i	0.616588	−	0.787286i	$-0.288515\pi$
$787$	−4.78870	−	4.78870i	−0.170699	−	0.170699i	−0.787286	+	0.616588i	$0.788515\pi$
$788$	−3.69607	−	3.69607i	−0.131667	−	0.131667i
$789$	14.1616	+	4.28862i	0.504166	+	0.152679i
$790$	−2.08377	−	11.5957i	−0.0741373	−	0.412558i
$791$	6.94146	+	3.55069i	0.246810	+	0.126248i
$792$	10.2415	−	8.99853i	0.363914	−	0.319749i
$793$	6.66919	+	24.8898i	0.236830	+	0.883861i
$794$	−7.73321	+	13.3943i	−0.274441	+	0.475347i
$795$	−0.279945	+	0.0410357i	−0.00992864	+	0.00145539i
$796$	2.20635	+	3.82151i	0.0782020	+	0.135450i
$797$	−2.62468	−	9.79545i	−0.0929710	−	0.346973i	0.903733	−	0.428097i	$-0.140816\pi$
$797$	−2.62468	−	9.79545i	−0.0929710	−	0.346973i	−0.996704	+	0.0811240i	$0.974149\pi$
$798$	14.6141	+	24.2632i	0.517334	+	0.858907i
$799$	−3.09906	+	1.78925i	−0.109637	+	0.0632989i
$800$	−4.54527	−	2.08340i	−0.160699	−	0.0736594i
$801$	16.4350	+	1.06172i	0.580702	+	0.0375140i
$802$	−1.57575	+	5.88077i	−0.0556415	+	0.207657i
$803$	−30.5004	−	30.5004i	−1.07633	−	1.07633i
$804$	16.1435	−	3.77213i	0.569338	−	0.133033i
$805$	−44.5232	−	1.47948i	−1.56924	−	0.0521447i
$806$	1.35963	+	0.784981i	0.0478908	+	0.0276498i
$807$	−0.212198	+	6.57632i	−0.00746971	+	0.231497i
$808$	2.46123	+	9.18544i	0.0865858	+	0.323143i
$809$	1.25982	+	2.18207i	0.0442929	+	0.0767175i	0.887322	−	0.461151i	$-0.152563\pi$
$809$	1.25982	+	2.18207i	0.0442929	+	0.0767175i	−0.843029	+	0.537868i	$0.819230\pi$
$810$	9.20050	−	17.8983i	0.323273	−	0.628884i
$811$	−6.87827			−0.241529			−0.120764	−	0.992681i	$-0.538535\pi$
$811$	−6.87827			−0.241529			−0.120764	+	0.992681i	$0.538535\pi$
$812$	−16.2127	−	3.47292i	−0.568954	−	0.121876i
$813$	−28.2976	+	15.1424i	−0.992439	+	0.531068i
$814$	−37.5157	+	21.6597i	−1.31492	+	0.759172i
$815$	−13.4879	+	37.4382i	−0.472459	+	1.31140i
$816$	−1.39191	−	1.48474i	−0.0487268	−	0.0519761i
$817$	37.0822	+	37.0822i	1.29734	+	1.29734i
$818$	1.19834	+	1.19834i	0.0418991	+	0.0418991i
$819$	34.7113	+	0.476720i	1.21291	+	0.0166579i
$820$	18.8053	−	8.84405i	0.656709	−	0.308848i
$821$			14.9316i			0.521116i	0.965458	+	0.260558i	$0.0839065\pi$
$821$			14.9316i			0.521116i	−0.965458	+	0.260558i	$0.916093\pi$
$822$	−15.2089	−	28.4219i	−0.530473	−	0.991326i
$823$	19.0072	−	19.0072i	0.662550	−	0.662550i	−0.293431	−	0.955980i	$-0.594797\pi$
$823$	19.0072	−	19.0072i	0.662550	−	0.662550i	0.955980	+	0.293431i	$0.0947969\pi$
$824$	1.53843	+	2.66463i	0.0535937	+	0.0928269i
$825$	−26.0639	+	29.4875i	−0.907428	+	1.02662i
$826$	−22.4807	+	1.14252i	−0.782204	+	0.0397533i
$827$	−5.42032	+	5.42032i	−0.188483	+	0.188483i	−0.795040	−	0.606557i	$-0.792550\pi$
$827$	−5.42032	+	5.42032i	−0.188483	+	0.188483i	0.606557	+	0.795040i	$0.292550\pi$
$828$	−4.42785	−	22.1516i	−0.153878	−	0.769823i
$829$	−12.1226	+	6.99901i	−0.421037	+	0.243086i	−0.695521	−	0.718506i	$-0.744826\pi$
$829$	−12.1226	+	6.99901i	−0.421037	+	0.243086i	0.274484	+	0.961592i	$0.411493\pi$
$830$	−0.693724	+	8.23962i	−0.0240795	+	0.286002i
$831$	32.8768	+	9.95621i	1.14048	+	0.345377i
$832$	4.22459	−	1.13198i	0.146461	−	0.0392442i
$833$	−1.31236	+	8.11962i	−0.0454706	+	0.281328i
$834$	−27.1717	−	8.22854i	−0.940880	−	0.284931i
$835$	9.77766	−	27.1398i	0.338370	−	0.939210i
$836$	24.3251	−	14.0441i	0.841302	−	0.485726i
$837$	0.180210	−	1.85649i	0.00622898	−	0.0641698i
$838$	1.18468	+	4.42129i	0.0409241	+	0.152731i
$839$	16.7773	+	29.0592i	0.579217	+	1.00323i	0.995569	+	0.0940302i	$0.0299750\pi$
$839$	16.7773	+	29.0592i	0.579217	+	1.00323i	−0.416352	+	0.909203i	$0.636692\pi$
$840$	−9.19032	+	4.53190i	−0.317096	+	0.156365i
$841$	−5.13662	+	8.89689i	−0.177125	+	0.306789i
$842$	10.8946	+	2.91920i	0.375453	+	0.100602i
$843$	20.1031	+	0.648666i	0.692388	+	0.0223412i
$844$	−12.2852	−	7.09284i	−0.422872	−	0.244145i
$845$	13.6556	+	1.14971i	0.469766	+	0.0395514i
$846$	−8.19055	+	4.04869i	−0.281597	+	0.139197i
$847$	−5.34845	+	24.9683i	−0.183775	+	0.857920i
$848$	−0.0189078	+	0.0705647i	−0.000649295	+	0.00242320i
$849$	43.7543	−	10.2237i	1.50164	−	0.350877i
$850$	4.52511	+	3.74685i	0.155210	+	0.128516i
$851$			71.7797i			2.46058i
$852$	19.4241	+	12.0660i	0.665457	+	0.413375i
$853$	−5.70488	−	1.52862i	−0.195331	−	0.0523389i	0.159827	−	0.987145i	$-0.448906\pi$
$853$	−5.70488	−	1.52862i	−0.195331	−	0.0523389i	−0.355158	+	0.934806i	$0.615573\pi$
$854$	−15.5677	+	0.791184i	−0.532716	+	0.0270738i
$855$	25.8162	−	32.4451i	0.882894	−	1.10960i
$856$	−6.81534	+	11.8045i	−0.232943	+	0.403470i
$857$	0.183061	+	0.683192i	0.00625324	+	0.0233374i	0.968982	−	0.247131i	$-0.0794880\pi$
$857$	0.183061	+	0.683192i	0.00625324	+	0.0233374i	−0.962729	+	0.270469i	$0.912821\pi$
$858$	1.11021	−	34.4071i	0.0379020	−	1.17464i
$859$	−33.5325	+	19.3600i	−1.14411	+	0.660555i	−0.947446	−	0.319915i	$-0.896346\pi$
$859$	−33.5325	+	19.3600i	−1.14411	+	0.660555i	−0.196668	+	0.980470i	$0.563012\pi$
$860$	−14.4935	+	12.2425i	−0.494223	+	0.417465i
$861$	10.2589	−	41.3346i	0.349624	−	1.40868i
$862$	−0.575852	+	2.14911i	−0.0196136	+	0.0731990i
$863$	−4.74346	+	1.27101i	−0.161469	+	0.0432655i	−0.338648	−	0.940913i	$-0.609970\pi$
$863$	−4.74346	+	1.27101i	−0.161469	+	0.0432655i	0.177179	+	0.984179i	$0.443303\pi$
$864$	−3.30205	−	4.01204i	−0.112338	−	0.136492i
$865$	6.05021	+	33.6681i	0.205713	+	1.14475i
$866$		−	30.7122i		−	1.04364i
$867$	−12.7642	−	23.8531i	−0.433493	−	0.810094i
$868$	−0.636604	+	0.704776i	−0.0216077	+	0.0239216i
$869$	−11.9718	+	20.7357i	−0.406114	+	0.703410i
$870$	3.52019	+	24.0147i	0.119346	+	0.814175i
$871$	20.9311	−	36.2537i	0.709223	−	1.22841i
$872$	0.470160	+	0.125979i	0.0159216	+	0.00426619i
$873$	10.2699	−	2.05284i	0.347585	−	0.0694781i
$874$		−	46.5419i		−	1.57430i
$875$	24.6748	−	16.3143i	0.834159	−	0.551524i
$876$	−11.9939	+	11.2440i	−0.405235	+	0.379901i
$877$	−0.474735	+	1.77174i	−0.0160307	+	0.0598273i	−0.973478	−	0.228781i	$-0.926526\pi$
$877$	−0.474735	+	1.77174i	−0.0160307	+	0.0598273i	0.957447	+	0.288609i	$0.0931926\pi$
$878$	10.1568	+	10.1568i	0.342776	+	0.342776i
$879$	11.5011	+	3.48293i	0.387923	+	0.117476i
$880$	4.32453	+	9.19535i	0.145780	+	0.309975i
$881$			9.87338i			0.332643i	0.986072	+	0.166321i	$0.0531889\pi$
$881$			9.87338i			0.332643i	−0.986072	+	0.166321i	$0.946811\pi$
$882$	−4.68020	+	20.4718i	−0.157590	+	0.689322i
$883$	20.1725	−	20.1725i	0.678857	−	0.678857i	−0.280884	−	0.959742i	$-0.590628\pi$
$883$	20.1725	−	20.1725i	0.678857	−	0.678857i	0.959742	+	0.280884i	$0.0906277\pi$
$884$	−5.13900			−0.172843
$885$	13.0543	+	30.2547i	0.438816	+	1.01700i
$886$	9.54166			0.320558
$887$	12.0064	+	3.21711i	0.403136	+	0.108020i	0.454689	−	0.890650i	$-0.349750\pi$
$887$	12.0064	+	3.21711i	0.403136	+	0.108020i	−0.0515529	+	0.998670i	$0.516417\pi$
$888$	7.79001	+	14.5576i	0.261415	+	0.488523i
$889$	1.54510	+	30.4021i	0.0518210	+	1.01965i
$890$	−4.16070	+	11.5488i	−0.139467	+	0.387117i
$891$	−37.7565	+	15.7223i	−1.26489	+	0.526718i
$892$	−0.613728	+	2.29046i	−0.0205491	+	0.0766904i
$893$	−18.1827	+	4.87203i	−0.608460	+	0.163036i
$894$	5.31418	+	5.66856i	0.177733	+	0.189585i
$895$	2.01961	−	23.9877i	0.0675082	−	0.801821i
$896$	0.134290	+	2.64234i	0.00448630	+	0.0882744i
$897$	−48.4542	−	30.0993i	−1.61784	−	1.00498i
$898$	28.8972	−	28.8972i	0.964313	−	0.964313i
$899$	1.12478	+	1.94817i	0.0375134	+	0.0649751i
$900$	10.9127	+	10.2914i	0.363758	+	0.343045i
$901$	0.0429192	−	0.0743382i	0.00142985	−	0.00247656i
$902$	−40.7945	−	10.9308i	−1.35831	−	0.363957i
$903$	0.720144	+	38.8744i	0.0239649	+	1.29366i
$904$	−2.55213	−	1.47347i	−0.0848825	−	0.0490069i
$905$	−0.386435	−	0.268705i	−0.0128455	−	0.00893207i
$906$	0.596400	−	1.96939i	0.0198141	−	0.0654287i
$907$	−32.2171	+	8.63256i	−1.06975	+	0.286639i	−0.750391	−	0.660994i	$-0.770135\pi$
$907$	−32.2171	+	8.63256i	−1.06975	+	0.286639i	−0.319361	+	0.947633i	$0.603468\pi$
$908$	−0.531375	+	0.142382i	−0.0176343	+	0.00472510i
$909$	1.83913	−	28.4690i	0.0610002	−	0.944259i
$910$	−7.52321	+	24.7568i	−0.249392	+	0.820681i
$911$	−18.7417	+	10.8205i	−0.620941	+	0.358501i	−0.777235	−	0.629210i	$-0.783379\pi$
$911$	−18.7417	+	10.8205i	−0.620941	+	0.358501i	0.156294	+	0.987711i	$0.450045\pi$
$912$	−5.05103	−	9.43915i	−0.167256	−	0.312562i
$913$	11.8827	−	11.8827i	0.393259	−	0.393259i
$914$	−23.2566			−0.769259
$915$	9.04000	+	20.9511i	0.298853	+	0.692622i
$916$	−9.84143	−	17.0459i	−0.325170	−	0.563211i
$917$	−24.0819	−	5.15858i	−0.795255	−	0.170351i
$918$	2.52760	+	5.55770i	0.0834231	+	0.183432i
$919$	21.8011	+	12.5868i	0.719150	+	0.415202i	0.814440	−	0.580248i	$-0.197044\pi$
$919$	21.8011	+	12.5868i	0.719150	+	0.415202i	−0.0952895	+	0.995450i	$0.530378\pi$
$920$	16.7781	+	1.41261i	0.553158	+	0.0465724i
$921$	3.82621	+	16.3750i	0.126078	+	0.539574i
$922$	−4.77686	+	17.8275i	−0.157317	+	0.587117i
$923$	55.7733	−	14.9444i	1.83580	−	0.491902i
$924$	20.2117	+	5.01638i	0.664915	+	0.165027i
$925$	−27.5931	−	38.8634i	−0.907255	−	1.27782i
$926$	−16.1091	−	9.30057i	−0.529377	−	0.305636i
$927$	−1.80929	−	9.05151i	−0.0594248	−	0.297290i
$928$	6.05330	+	1.62198i	0.198709	+	0.0532440i
$929$	33.2557			1.09108			0.545541	−	0.838084i	$-0.316324\pi$
$929$	33.2557			1.09108			0.545541	+	0.838084i	$0.316324\pi$
$930$	1.29208	+	0.513155i	0.0423690	+	0.0168270i
$931$	−17.7229	+	39.4699i	−0.580845	+	1.29357i
$932$	−1.56548	−	5.84244i	−0.0512789	−	0.191376i
$933$	0.860804	−	1.38573i	0.0281815	−	0.0453669i
$934$	−2.54560	−	1.46970i	−0.0832947	−	0.0480902i
$935$	−2.11176	−	11.7515i	−0.0690621	−	0.384316i
$936$	−13.0936	−	0.845859i	−0.427977	−	0.0276478i
$937$	6.44273	+	6.44273i	0.210475	+	0.210475i	0.804469	−	0.593994i	$-0.202450\pi$
$937$	6.44273	+	6.44273i	0.210475	+	0.210475i	−0.593994	+	0.804469i	$0.702450\pi$
$938$	18.7925	+	16.9747i	0.613596	+	0.554244i
$939$	−28.2266	+	6.59549i	−0.921141	+	0.215236i
$940$	−1.20447	−	6.70264i	−0.0392856	−	0.218616i
$941$		−	46.7275i		−	1.52327i	−0.648005	−	0.761636i	$-0.724396\pi$
$941$		−	46.7275i		−	1.52327i	0.648005	−	0.761636i	$-0.275604\pi$
$942$	6.44820	+	4.00555i	0.210094	+	0.130508i
$943$	−49.4837	+	49.4837i	−1.61141	+	1.61141i
$944$	8.50788			0.276908
$945$	30.4742	−	4.04038i	0.991325	−	0.131434i
$946$	38.5569			1.25359
$947$	20.1451	−	20.1451i	0.654627	−	0.654627i	−0.299477	−	0.954104i	$-0.596812\pi$
$947$	20.1451	−	20.1451i	0.654627	−	0.654627i	0.954104	+	0.299477i	$0.0968120\pi$
$948$	7.75199	+	4.81546i	0.251773	+	0.156399i
$949$			41.5134i			1.34758i
$950$	17.8913	+	25.1990i	0.580471	+	0.817563i
$951$	20.3998	−	4.76665i	0.661508	−	0.154569i
$952$	0.651154	−	3.03979i	0.0211040	−	0.0985203i
$953$	10.3138	+	10.3138i	0.334098	+	0.334098i	0.854140	−	0.520042i	$-0.174084\pi$
$953$	10.3138	+	10.3138i	0.334098	+	0.334098i	−0.520042	+	0.854140i	$0.674084\pi$
$954$	0.121589	−	0.182341i	0.00393658	−	0.00590350i
$955$	27.6094	−	39.7060i	0.893418	−	1.28486i
$956$	17.6355	+	10.1819i	0.570373	+	0.329305i
$957$	26.0282	−	41.9005i	0.841371	−	1.35445i
$958$	0.0609136	+	0.227333i	0.00196803	+	0.00734479i
$959$	22.4239	−	43.8379i	0.724107	−	1.41560i
$960$	3.55608	−	1.53438i	0.114772	−	0.0495219i
$961$	−30.8711			−0.995843
$962$	40.2712	+	10.7906i	1.29840	+	0.347904i
$963$	30.7189	−	26.9908i	0.989904	−	0.869767i
$964$	−8.21469	−	4.74276i	−0.264577	−	0.152754i
$965$	47.4830	−	8.53276i	1.52853	−	0.274679i
$966$	23.9437	−	24.8476i	0.770376	−	0.799457i
$967$	45.7943	−	12.2705i	1.47265	−	0.394594i	0.568808	−	0.822470i	$-0.307405\pi$
$967$	45.7943	−	12.2705i	1.47265	−	0.394594i	0.903837	+	0.427876i	$0.140738\pi$
$968$	2.49792	−	9.32235i	0.0802861	−	0.299632i
$969$	2.86216	+	12.2492i	0.0919459	+	0.393500i
$970$	−0.654915	+	7.77867i	−0.0210281	+	0.249758i
$971$	−29.2801	−	16.9049i	−0.939642	−	0.542503i	−0.0497939	−	0.998760i	$-0.515856\pi$
$971$	−29.2801	−	16.9049i	−0.939642	−	0.542503i	−0.889848	+	0.456257i	$0.849190\pi$
$972$	5.52525	+	14.5764i	0.177222	+	0.467538i
$973$	−13.3359	−	41.2656i	−0.427529	−	1.32291i
$974$	−7.58737	−	13.1417i	−0.243115	−	0.421087i
$975$	37.8049	−	2.32993i	1.21073	−	0.0746175i
$976$	5.89163			0.188587
$977$	−37.6141	+	37.6141i	−1.20338	+	1.20338i	−0.230250	+	0.973131i	$0.573954\pi$
$977$	−37.6141	+	37.6141i	−1.20338	+	1.20338i	−0.973131	+	0.230250i	$0.926046\pi$
$978$	−14.5431	−	27.1776i	−0.465038	−	0.869044i
$979$	21.6051	−	12.4737i	0.690501	−	0.398661i
$980$	−13.6908	−	7.58699i	−0.437336	−	0.242358i
$981$	−1.21490	−	0.810124i	−0.0387889	−	0.0258653i
$982$	−2.65316	+	0.710911i	−0.0846656	+	0.0226861i
$983$	−52.2246	+	13.9935i	−1.66571	+	0.446324i	−0.963948	−	0.266091i	$-0.914268\pi$
$983$	−52.2246	+	13.9935i	−1.66571	+	0.446324i	−0.701758	+	0.712416i	$0.747601\pi$
$984$	−4.66549	+	15.4061i	−0.148730	+	0.491128i
$985$	−11.5037	+	2.06724i	−0.366539	+	0.0658677i
$986$	−6.37700	−	3.68176i	−0.203085	−	0.117251i
$987$	−12.2137	−	6.75312i	−0.388767	−	0.214954i
$988$	−26.1118	−	6.99663i	−0.830727	−	0.222593i
$989$	31.9441	−	55.3289i	1.01576	−	1.75936i
$990$	−3.44628	−	30.2891i	−0.109530	−	0.962650i
$991$	7.91050	+	13.7014i	0.251285	+	0.435239i	0.963880	−	0.266337i	$-0.0858134\pi$
$991$	7.91050	+	13.7014i	0.251285	+	0.435239i	−0.712595	+	0.701576i	$0.752480\pi$
$992$	0.253824	−	0.253824i	0.00805892	−	0.00805892i
$993$	−26.6951	−	16.5827i	−0.847144	−	0.526237i
$994$	1.77290	+	34.8843i	0.0562329	+	1.10646i
$995$	9.83230	+	0.827818i	0.311705	+	0.0262436i
$996$	−4.38058	−	4.67270i	−0.138804	−	0.148060i
$997$	47.5545	−	12.7422i	1.50607	−	0.403549i	0.590940	−	0.806715i	$-0.298757\pi$
$997$	47.5545	−	12.7422i	1.50607	−	0.403549i	0.915127	+	0.403166i	$0.132090\pi$
$998$	8.97809	−	33.5067i	0.284196	−	1.06064i
$999$	−8.13742	−	48.8596i	−0.257457	−	1.54585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.527.43	yes	192
5.3	odd	4	inner	630.2.cd.a.23.7	yes	192
7.4	even	3		630.2.bt.a.347.38	yes	192
9.2	odd	6		630.2.bt.a.317.47	✓	192
35.18	odd	12		630.2.bt.a.473.47	yes	192
45.38	even	12		630.2.bt.a.443.38	yes	192
63.11	odd	6	inner	630.2.cd.a.137.7	yes	192
315.263	even	12	inner	630.2.cd.a.263.43	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.47	✓	192	9.2	odd	6
630.2.bt.a.347.38	yes	192	7.4	even	3
630.2.bt.a.443.38	yes	192	45.38	even	12
630.2.bt.a.473.47	yes	192	35.18	odd	12
630.2.cd.a.23.7	yes	192	5.3	odd	4	inner
630.2.cd.a.137.7	yes	192	63.11	odd	6	inner
630.2.cd.a.263.43	yes	192	315.263	even	12	inner
630.2.cd.a.527.43	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.47129 + 0.913950i) q^{3} -1.00000i q^{4} +(-1.83586 - 1.27656i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.96337 + 1.77346i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.32939 + 2.68937i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.47129 + 0.913950i) q^{3} -1.00000i q^{4} +(-1.83586 - 1.27656i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.96337 + 1.77346i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.32939 + 2.68937i) q^{9} +(-2.20082 + 0.395490i) q^{10} +(3.93553 + 2.27218i) q^{11} +(0.913950 - 1.47129i) q^{12} +(-1.13198 - 4.22459i) q^{13} +(2.64234 - 0.134290i) q^{14} +(-1.53438 - 3.55608i) q^{15} -1.00000 q^{16} +(1.13496 + 0.304112i) q^{17} +(2.84169 + 0.961652i) q^{18} +(5.35282 + 3.09045i) q^{19} +(-1.27656 + 1.83586i) q^{20} +(1.26784 + 4.40370i) q^{21} +(4.38951 - 1.17617i) q^{22} +(1.94889 - 7.27337i) q^{23} +(-0.394099 - 1.68662i) q^{24} +(1.74080 + 4.68718i) q^{25} +(-3.78767 - 2.18681i) q^{26} +(-0.502033 + 5.17184i) q^{27} +(1.77346 - 1.96337i) q^{28} +(-3.13342 - 5.42724i) q^{29} +(-3.59950 - 1.42956i) q^{30} -0.358961 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.71365 + 6.93992i) q^{33} +(1.01758 - 0.587499i) q^{34} +(-1.34057 - 5.76219i) q^{35} +(2.68937 - 1.32939i) q^{36} +(-9.20775 + 2.46721i) q^{37} +(5.97029 - 1.59973i) q^{38} +(2.19560 - 7.25017i) q^{39} +(0.395490 + 2.20082i) q^{40} +(-8.04851 - 4.64681i) q^{41} +(4.01038 + 2.21739i) q^{42} +(8.19545 + 2.19596i) q^{43} +(2.27218 - 3.93553i) q^{44} +(0.992558 - 6.63437i) q^{45} +(-3.76497 - 6.52113i) q^{46} +(-2.15351 + 2.15351i) q^{47} +(-1.47129 - 0.913950i) q^{48} +(0.709677 + 6.96393i) q^{49} +(4.54527 + 2.08340i) q^{50} +(1.39191 + 1.48474i) q^{51} +(-4.22459 + 1.13198i) q^{52} +(0.0189078 - 0.0705647i) q^{53} +(3.30205 + 4.01204i) q^{54} +(-4.32453 - 9.19535i) q^{55} +(-0.134290 - 2.64234i) q^{56} +(5.05103 + 9.43915i) q^{57} +(-6.05330 - 1.62198i) q^{58} -8.50788 q^{59} +(-3.55608 + 1.53438i) q^{60} -5.89163 q^{61} +(-0.253824 + 0.253824i) q^{62} +(-2.15940 + 7.63786i) q^{63} +1.00000i q^{64} +(-3.31478 + 9.20082i) q^{65} +(7.53321 + 2.28131i) q^{66} +(6.76808 + 6.76808i) q^{67} +(0.304112 - 1.13496i) q^{68} +(9.51489 - 8.92005i) q^{69} +(-5.02241 - 3.12656i) q^{70} +13.2021i q^{71} +(0.961652 - 2.84169i) q^{72} +(-9.16835 - 2.45665i) q^{73} +(-4.76628 + 8.25544i) q^{74} +(-1.72262 + 8.48720i) q^{75} +(3.09045 - 5.35282i) q^{76} +(3.69730 + 11.4406i) q^{77} +(-3.57412 - 6.67917i) q^{78} +5.26884i q^{79} +(1.83586 + 1.27656i) q^{80} +(-5.46544 + 7.15045i) q^{81} +(-8.97694 + 2.40536i) q^{82} +(0.957089 - 3.57191i) q^{83} +(4.40370 - 1.26784i) q^{84} +(-1.69542 - 2.00715i) q^{85} +(7.34784 - 4.24228i) q^{86} +(0.350059 - 10.8488i) q^{87} +(-1.17617 - 4.38951i) q^{88} +(2.74487 - 4.75426i) q^{89} +(-3.98936 - 5.39305i) q^{90} +(5.26966 - 10.3020i) q^{91} +(-7.27337 - 1.94889i) q^{92} +(-0.528136 - 0.328073i) q^{93} +3.04553i q^{94} +(-5.88191 - 12.5068i) q^{95} +(-1.68662 + 0.394099i) q^{96} +(0.903546 - 3.37208i) q^{97} +(5.42606 + 4.42243i) q^{98} +(-0.878880 + 13.6047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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