LMFDB - Embedded newform 63.2.h.b.25.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,2,Mod(25,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$63 = 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	63.h (of order $3$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9$ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$3$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.3
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	63.25
Dual form			63.2.h.b.58.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-0.495868 q^{2} +(-0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(1.84629 - 3.19787i) q^{5} +(0.109735 + 0.851830i) q^{6} +(0.926641 + 2.47817i) q^{7} +1.86155 q^{8} +(-2.90205 + 0.760316i) q^{9} +(-0.915516 + 1.58572i) q^{10} +(0.446284 + 0.772987i) q^{11} +(0.388182 + 3.01332i) q^{12} +(0.598355 + 1.03638i) q^{13} +(-0.459492 - 1.22885i) q^{14} +(-5.90205 - 2.46398i) q^{15} +2.58515 q^{16} +(-0.124991 + 0.216492i) q^{17} +(1.43904 - 0.377017i) q^{18} +(1.40414 + 2.43204i) q^{19} +(-3.23860 + 5.60943i) q^{20} +(4.05208 - 2.14025i) q^{21} +(-0.221298 - 0.383300i) q^{22} +(-1.23886 + 2.14576i) q^{23} +(-0.411957 - 3.19787i) q^{24} +(-4.31757 - 7.47825i) q^{25} +(-0.296705 - 0.513909i) q^{26} +(1.94833 + 4.81705i) q^{27} +(-1.62544 - 4.34700i) q^{28} +(2.07128 - 3.58755i) q^{29} +(2.92664 + 1.22181i) q^{30} +3.58515 q^{31} -5.00499 q^{32} +(1.22912 - 0.937712i) q^{33} +(0.0619793 - 0.107351i) q^{34} +(9.63571 + 1.61215i) q^{35} +(5.09054 - 1.33368i) q^{36} +(-2.36568 - 4.09747i) q^{37} +(-0.696267 - 1.20597i) q^{38} +(1.64794 - 1.25724i) q^{39} +(3.43695 - 5.95298i) q^{40} +(-2.39093 - 4.14121i) q^{41} +(-2.00930 + 1.06128i) q^{42} +(-4.98928 + 8.64169i) q^{43} +(-0.782834 - 1.35591i) q^{44} +(-2.92664 + 10.6841i) q^{45} +(0.614310 - 1.06402i) q^{46} -10.1731 q^{47} +(-0.572088 - 4.44091i) q^{48} +(-5.28267 + 4.59275i) q^{49} +(2.14095 + 3.70823i) q^{50} +(0.399562 + 0.166808i) q^{51} +(-1.04958 - 1.81793i) q^{52} +(-4.94465 + 8.56438i) q^{53} +(-0.966116 - 2.38862i) q^{54} +3.29588 q^{55} +(1.72499 + 4.61323i) q^{56} +(3.86715 - 2.95031i) q^{57} +(-1.02708 + 1.77895i) q^{58} +1.81237 q^{59} +(10.3529 + 4.32210i) q^{60} +10.8041 q^{61} -1.77776 q^{62} +(-4.57336 - 6.48725i) q^{63} -2.68848 q^{64} +4.41895 q^{65} +(-0.609480 + 0.464982i) q^{66} +1.02937 q^{67} +(0.219249 - 0.379751i) q^{68} +(3.96027 + 1.65332i) q^{69} +(-4.77804 - 0.799412i) q^{70} -4.94533 q^{71} +(-5.40231 + 1.41536i) q^{72} +(-0.915262 + 1.58528i) q^{73} +(1.17306 + 2.03181i) q^{74} +(-11.8911 + 9.07189i) q^{75} +(-2.46302 - 4.26607i) q^{76} +(-1.50205 + 1.82225i) q^{77} +(-0.817161 + 0.623424i) q^{78} -1.79912 q^{79} +(4.77293 - 8.26696i) q^{80} +(7.84384 - 4.41296i) q^{81} +(1.18559 + 2.05350i) q^{82} +(6.16156 - 10.6721i) q^{83} +(-7.10781 + 3.75425i) q^{84} +(0.461541 + 0.799412i) q^{85} +(2.47403 - 4.28514i) q^{86} +(-6.62127 - 2.76423i) q^{87} +(0.830779 + 1.43895i) q^{88} +(-1.20370 - 2.08488i) q^{89} +(1.45123 - 5.29793i) q^{90} +(-2.01387 + 2.44318i) q^{91} +(2.17310 - 3.76392i) q^{92} +(-0.793387 - 6.15877i) q^{93} +5.04450 q^{94} +10.3698 q^{95} +(1.10759 + 8.59784i) q^{96} +(5.52210 - 9.56456i) q^{97} +(2.61951 - 2.27740i) q^{98} +(-1.88286 - 1.90393i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q - 4 q^{2} - q^{3} + 8 q^{4} + 4 q^{5} - 2 q^{6} - 4 q^{7} - 6 q^{8} + 11 q^{9} - 7 q^{10} + 4 q^{11} - 20 q^{12} - 8 q^{13} - 20 q^{14} - 19 q^{15} - 4 q^{16} + 12 q^{17} + 4 q^{18} + q^{19} + 5 q^{20}+ \cdots + 35 q^{99}+O(q^{100})$ 10 * q - 4 * q^2 - q^3 + 8 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 - 6 * q^8 + 11 * q^9 - 7 * q^10 + 4 * q^11 - 20 * q^12 - 8 * q^13 - 20 * q^14 - 19 * q^15 - 4 * q^16 + 12 * q^17 + 4 * q^18 + q^19 + 5 * q^20 + 13 * q^21 - q^22 + 3 * q^23 + 6 * q^24 - q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 + 16 * q^30 + 6 * q^31 + 4 * q^32 + 14 * q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 + 20 * q^38 + 2 * q^39 - 3 * q^40 + 5 * q^41 - 4 * q^42 - 7 * q^43 - 10 * q^44 - 16 * q^45 + 3 * q^46 - 54 * q^47 - 5 * q^48 - 8 * q^49 + 19 * q^50 - 9 * q^51 - 10 * q^52 - 21 * q^53 + q^54 + 4 * q^55 + 18 * q^56 - 4 * q^57 - 10 * q^58 - 60 * q^59 + 10 * q^60 + 28 * q^61 - 12 * q^62 - 59 * q^63 - 50 * q^64 + 22 * q^65 + 19 * q^66 + 4 * q^67 + 27 * q^68 + 15 * q^69 + 40 * q^70 - 6 * q^71 - 36 * q^72 + 15 * q^73 - 36 * q^74 - 14 * q^75 + 5 * q^76 + 11 * q^77 - 20 * q^78 + 8 * q^79 + 20 * q^80 + 23 * q^81 - 5 * q^82 + 9 * q^83 + 35 * q^84 - 6 * q^85 - 8 * q^86 + 2 * q^87 - 18 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 6 * q^93 + 6 * q^94 + 28 * q^95 + 59 * q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$ .

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.495868			−0.350632			−0.175316	−	0.984512i	$-0.556095\pi$
$2$	−0.495868			−0.350632			−0.175316	+	0.984512i	$0.556095\pi$
$3$	−0.221298	−	1.71786i	−0.127767	−	0.991804i
$3$	−0.221298	−	1.71786i	−0.127767	−	0.991804i
$4$	−1.75411			−0.877057
$5$	1.84629	−	3.19787i	0.825686	−	1.43013i	−0.0757082	−	0.997130i	$-0.524122\pi$
$5$	1.84629	−	3.19787i	0.825686	−	1.43013i	0.901394	−	0.433000i	$-0.142545\pi$
$6$	0.109735	+	0.851830i	0.0447990	+	0.347758i
$7$	0.926641	+	2.47817i	0.350238	+	0.936661i
$7$	0.926641	+	2.47817i	0.350238	+	0.936661i
$8$	1.86155			0.658156
$9$	−2.90205	+	0.760316i	−0.967351	+	0.253439i
$10$	−0.915516	+	1.58572i	−0.289512	+	0.501449i
$11$	0.446284	+	0.772987i	0.134560	+	0.233064i	0.925429	−	0.378921i	$-0.123705\pi$
$11$	0.446284	+	0.772987i	0.134560	+	0.233064i	−0.790869	+	0.611985i	$0.790371\pi$
$12$	0.388182	+	3.01332i	0.112059	+	0.869869i
$13$	0.598355	+	1.03638i	0.165954	+	0.287441i	0.936994	−	0.349346i	$-0.113596\pi$
$13$	0.598355	+	1.03638i	0.165954	+	0.287441i	−0.771040	+	0.636787i	$0.780263\pi$
$14$	−0.459492	−	1.22885i	−0.122804	−	0.328423i
$15$	−5.90205	−	2.46398i	−1.52390	−	0.636196i
$16$	2.58515			0.646287
$17$	−0.124991	+	0.216492i	−0.0303149	+	0.0525069i	−0.880785	−	0.473517i	$-0.842984\pi$
$17$	−0.124991	+	0.216492i	−0.0303149	+	0.0525069i	0.850470	+	0.526024i	$0.176318\pi$
$18$	1.43904	−	0.377017i	0.339184	−	0.0888637i
$19$	1.40414	+	2.43204i	0.322131	+	0.557948i	0.980928	−	0.194374i	$-0.0622675\pi$
$19$	1.40414	+	2.43204i	0.322131	+	0.557948i	−0.658796	+	0.752321i	$0.728934\pi$
$20$	−3.23860	+	5.60943i	−0.724174	+	1.25431i
$21$	4.05208	−	2.14025i	0.884236	−	0.467041i
$22$	−0.221298	−	0.383300i	−0.0471809	−	0.0817198i
$23$	−1.23886	+	2.14576i	−0.258320	+	0.447423i	−0.965792	−	0.259318i	$-0.916502\pi$
$23$	−1.23886	+	2.14576i	−0.258320	+	0.447423i	0.707472	+	0.706741i	$0.249835\pi$
$24$	−0.411957	−	3.19787i	−0.0840903	−	0.652762i
$25$	−4.31757	−	7.47825i	−0.863514	−	1.49565i
$26$	−0.296705	−	0.513909i	−0.0581887	−	0.100786i
$27$	1.94833	+	4.81705i	0.374957	+	0.927042i
$28$	−1.62544	−	4.34700i	−0.307178	−	0.821505i
$29$	2.07128	−	3.58755i	0.384626	−	0.666192i	−0.607091	−	0.794632i	$-0.707664\pi$
$29$	2.07128	−	3.58755i	0.384626	−	0.666192i	0.991717	+	0.128440i	$0.0409970\pi$
$30$	2.92664	+	1.22181i	0.534329	+	0.223071i
$31$	3.58515			0.643912			0.321956	−	0.946755i	$-0.395660\pi$
$31$	3.58515			0.643912			0.321956	+	0.946755i	$0.395660\pi$
$32$	−5.00499			−0.884765
$33$	1.22912	−	0.937712i	0.213962	−	0.163235i
$34$	0.0619793	−	0.107351i	0.0106294	−	0.0184106i
$35$	9.63571	+	1.61215i	1.62873	+	0.272502i
$36$	5.09054	−	1.33368i	0.848423	−	0.222280i
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	0.603389	−	0.797447i	$-0.293817\pi$
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	−0.992304	+	0.123826i	$0.960483\pi$
$38$	−0.696267	−	1.20597i	−0.112949	−	0.195634i
$39$	1.64794	−	1.25724i	0.263882	−	0.201319i
$40$	3.43695	−	5.95298i	0.543430	−	0.941249i
$41$	−2.39093	−	4.14121i	−0.373400	−	0.646748i	0.616686	−	0.787209i	$-0.288475\pi$
$41$	−2.39093	−	4.14121i	−0.373400	−	0.646748i	−0.990086	+	0.140461i	$0.955142\pi$
$42$	−2.00930	+	1.06128i	−0.310041	+	0.163759i
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	0.181550	+	0.983382i	$0.441889\pi$
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	−0.782834	−	1.35591i	−0.118017	−	0.204411i
$45$	−2.92664	+	10.6841i	−0.436278	+	1.59270i
$46$	0.614310	−	1.06402i	0.0905751	−	0.156881i
$47$	−10.1731			−1.48389			−0.741947	−	0.670459i	$-0.766097\pi$
$47$	−10.1731			−1.48389			−0.741947	+	0.670459i	$0.766097\pi$
$48$	−0.572088	−	4.44091i	−0.0825738	−	0.640990i
$49$	−5.28267	+	4.59275i	−0.754667	+	0.656108i
$50$	2.14095	+	3.70823i	0.302776	+	0.524423i
$51$	0.399562	+	0.166808i	0.0559498	+	0.0233578i
$52$	−1.04958	−	1.81793i	−0.145551	−	0.252102i
$53$	−4.94465	+	8.56438i	−0.679199	+	1.17641i	0.296023	+	0.955181i	$0.404339\pi$
$53$	−4.94465	+	8.56438i	−0.679199	+	1.17641i	−0.975222	+	0.221227i	$0.928994\pi$
$54$	−0.966116	−	2.38862i	−0.131472	−	0.325051i
$55$	3.29588			0.444416
$56$	1.72499	+	4.61323i	0.230511	+	0.616469i
$57$	3.86715	−	2.95031i	0.512217	−	0.390778i
$58$	−1.02708	+	1.77895i	−0.134862	+	0.233588i
$59$	1.81237			0.235951			0.117975	−	0.993017i	$-0.462360\pi$
$59$	1.81237			0.235951			0.117975	+	0.993017i	$0.462360\pi$
$60$	10.3529	+	4.32210i	1.33655	+	0.557980i
$61$	10.8041			1.38332			0.691662	−	0.722221i	$-0.256879\pi$
$61$	10.8041			1.38332			0.691662	+	0.722221i	$0.256879\pi$
$62$	−1.77776			−0.225776
$63$	−4.57336	−	6.48725i	−0.576189	−	0.817316i
$64$	−2.68848			−0.336060
$65$	4.41895			0.548103
$66$	−0.609480	+	0.464982i	−0.0750219	+	0.0572353i
$67$	1.02937			0.125757			0.0628787	−	0.998021i	$-0.479972\pi$
$67$	1.02937			0.125757			0.0628787	+	0.998021i	$0.479972\pi$
$68$	0.219249	−	0.379751i	0.0265879	−	0.0460516i
$69$	3.96027	+	1.65332i	0.476761	+	0.199037i
$70$	−4.77804	−	0.799412i	−0.571086	−	0.0955480i
$71$	−4.94533			−0.586903			−0.293451	−	0.955974i	$-0.594804\pi$
$71$	−4.94533			−0.586903			−0.293451	+	0.955974i	$0.594804\pi$
$72$	−5.40231	+	1.41536i	−0.636668	+	0.166802i
$73$	−0.915262	+	1.58528i	−0.107123	+	0.185543i	−0.914604	−	0.404351i	$-0.867497\pi$
$73$	−0.915262	+	1.58528i	−0.107123	+	0.185543i	0.807480	+	0.589894i	$0.200831\pi$
$74$	1.17306	+	2.03181i	0.136366	+	0.236193i
$75$	−11.8911	+	9.07189i	−1.37306	+	1.04753i
$76$	−2.46302	−	4.26607i	−0.282527	−	0.489352i
$77$	−1.50205	+	1.82225i	−0.171174	+	0.207665i
$78$	−0.817161	+	0.623424i	−0.0925253	+	0.0705889i
$79$	−1.79912			−0.202417			−0.101209	−	0.994865i	$-0.532271\pi$
$79$	−1.79912			−0.202417			−0.101209	+	0.994865i	$0.532271\pi$
$80$	4.77293	−	8.26696i	0.533630	−	0.924274i
$81$	7.84384	−	4.41296i	0.871538	−	0.490329i
$82$	1.18559	+	2.05350i	0.130926	+	0.226771i
$83$	6.16156	−	10.6721i	0.676319	−	1.17142i	−0.299763	−	0.954014i	$-0.596908\pi$
$83$	6.16156	−	10.6721i	0.676319	−	1.17142i	0.976082	−	0.217405i	$-0.0697591\pi$
$84$	−7.10781	+	3.75425i	−0.775525	+	0.409622i
$85$	0.461541	+	0.799412i	0.0500611	+	0.0867084i
$86$	2.47403	−	4.28514i	0.266781	−	0.462079i
$87$	−6.62127	−	2.76423i	−0.709875	−	0.296357i
$88$	0.830779	+	1.43895i	0.0885613	+	0.153393i
$89$	−1.20370	−	2.08488i	−0.127592	−	0.220997i	0.795151	−	0.606412i	$-0.207392\pi$
$89$	−1.20370	−	2.08488i	−0.127592	−	0.220997i	−0.922743	+	0.385415i	$0.874058\pi$
$90$	1.45123	−	5.29793i	0.152973	−	0.558451i
$91$	−2.01387	+	2.44318i	−0.211111	+	0.256115i
$92$	2.17310	−	3.76392i	0.226561	−	0.392416i
$93$	−0.793387	−	6.15877i	−0.0822704	−	0.638634i
$94$	5.04450			0.520300
$95$	10.3698			1.06392
$96$	1.10759	+	8.59784i	0.113043	+	0.877513i
$97$	5.52210	−	9.56456i	0.560684	−	0.971134i	−0.436752	−	0.899582i	$-0.643871\pi$
$97$	5.52210	−	9.56456i	0.560684	−	0.971134i	0.997437	−	0.0715522i	$-0.0227952\pi$
$98$	2.61951	−	2.27740i	0.264610	−	0.230052i
$99$	−1.88286	−	1.90393i	−0.189234	−	0.191352i
$100$	7.57351	+	13.1177i	0.757351	+	1.31177i
$101$	1.29982	+	2.25136i	0.129337	+	0.224018i	0.923420	−	0.383791i	$-0.125382\pi$
$101$	1.29982	+	2.25136i	0.129337	+	0.224018i	−0.794083	+	0.607810i	$0.792048\pi$
$102$	−0.198130	−	0.0827148i	−0.0196178	−	0.00818999i
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	−0.999695	−	0.0247032i	$-0.992136\pi$
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	0.521241	+	0.853409i	$0.325469\pi$
$104$	1.11387	+	1.92927i	0.109224	+	0.189181i
$105$	0.637069	−	16.9095i	0.0621716	−	1.65020i
$106$	2.45189	−	4.24680i	0.238149	−	0.412486i
$107$	−5.45025	−	9.44012i	−0.526896	−	0.912610i	−0.999509	−	0.0313403i	$-0.990022\pi$
$107$	−5.45025	−	9.44012i	−0.526896	−	0.912610i	0.472613	−	0.881270i	$-0.343311\pi$
$108$	−3.41760	−	8.44966i	−0.328859	−	0.813069i
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	−0.912353	−	0.409404i	$-0.865737\pi$
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	0.810731	+	0.585419i	$0.199070\pi$
$110$	−1.63432			−0.155826
$111$	−6.51535	+	4.97066i	−0.618410	+	0.471794i
$112$	2.39550	+	6.40644i	0.226354	+	0.605352i
$113$	7.91318	+	13.7060i	0.744409	+	1.28935i	0.950470	+	0.310816i	$0.100602\pi$
$113$	7.91318	+	13.7060i	0.744409	+	1.28935i	−0.206061	+	0.978539i	$0.566065\pi$
$114$	−1.91760	+	1.46297i	−0.179600	+	0.137019i
$115$	4.57458	+	7.92341i	0.426582	+	0.738861i
$116$	−3.63325	+	6.29298i	−0.337339	+	0.584289i
$117$	−2.52444	−	2.55270i	−0.233384	−	0.235997i
$118$	−0.898698			−0.0827318
$119$	−0.652326	−	0.109140i	−0.0597986	−	0.0100049i
$120$	−10.9869	−	4.58681i	−1.00297	−	0.418716i
$121$	5.10166	−	8.83634i	0.463787	−	0.803303i
$122$	−5.35741			−0.485038
$123$	−6.58489	+	5.02371i	−0.593740	+	0.452973i
$124$	−6.28876			−0.564747
$125$	−13.4230			−1.20059
$126$	2.26778	+	3.21682i	0.202030	+	0.286577i
$127$	−1.26946			−0.112647			−0.0563233	−	0.998413i	$-0.517938\pi$
$127$	−1.26946			−0.112647			−0.0563233	+	0.998413i	$0.517938\pi$
$128$	11.3431			1.00260
$129$	15.9493	+	6.65848i	1.40426	+	0.586246i
$130$	−2.19122			−0.192182
$131$	7.51444	−	13.0154i	0.656540	−	1.13716i	−0.324965	−	0.945726i	$-0.605353\pi$
$131$	7.51444	−	13.0154i	0.656540	−	1.13716i	0.981505	−	0.191435i	$-0.0613140\pi$
$132$	−2.15601	+	1.64485i	−0.187657	+	0.143166i
$133$	−4.72587	+	5.73332i	−0.409785	+	0.497142i
$134$	−0.510432			−0.0440946
$135$	19.0015	+	2.66316i	1.63539	+	0.229209i
$136$	−0.232677	+	0.403009i	−0.0199519	+	0.0345577i
$137$	0.244246	+	0.423047i	0.0208674	+	0.0361433i	0.876271	−	0.481819i	$-0.160024\pi$
$137$	0.244246	+	0.423047i	0.0208674	+	0.0361433i	−0.855403	+	0.517963i	$0.826691\pi$
$138$	−1.96377	−	0.819831i	−0.167167	−	0.0697887i
$139$	−4.93487	−	8.54745i	−0.418570	−	0.724985i	0.577226	−	0.816585i	$-0.304135\pi$
$139$	−4.93487	−	8.54745i	−0.418570	−	0.724985i	−0.995796	+	0.0915997i	$0.970802\pi$
$140$	−16.9021	−	2.82789i	−1.42849	−	0.239000i
$141$	2.25128	+	17.4759i	0.189592	+	1.47173i
$142$	2.45223			0.205787
$143$	−0.534073	+	0.925042i	−0.0446614	+	0.0773559i
$144$	−7.50224	+	1.96553i	−0.625187	+	0.163794i
$145$	−7.64835	−	13.2473i	−0.635161	−	1.10013i
$146$	0.453849	−	0.786090i	0.0375609	−	0.0650573i
$147$	9.05873	+	8.05850i	0.747152	+	0.664654i
$148$	4.14967	+	7.18744i	0.341101	+	0.590804i
$149$	−10.5120	+	18.2073i	−0.861175	+	1.49160i	0.00962096	+	0.999954i	$0.496938\pi$
$149$	−10.5120	+	18.2073i	−0.861175	+	1.49160i	−0.870796	+	0.491645i	$0.836396\pi$
$150$	5.89641	−	4.49846i	0.481440	−	0.367298i
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	0.833930	−	0.551870i	$-0.186086\pi$
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	−0.894898	+	0.446270i	$0.852752\pi$
$152$	2.61387	+	4.52735i	0.212013	+	0.367217i
$153$	0.198130	−	0.723303i	0.0160179	−	0.0584756i
$154$	0.744818	−	0.903596i	0.0600192	−	0.0728139i
$155$	6.61922	−	11.4648i	0.531669	−	0.920877i
$156$	−2.89068	+	2.20534i	−0.231439	+	0.176568i
$157$	−16.6796			−1.33118			−0.665590	−	0.746317i	$-0.731820\pi$
$157$	−16.6796			−1.33118			−0.665590	+	0.746317i	$0.731820\pi$
$158$	0.892128			0.0709739
$159$	15.8066	+	6.59890i	1.25355	+	0.523327i
$160$	−9.24065	+	16.0053i	−0.730538	+	1.26533i
$161$	−6.46555	−	1.08175i	−0.509557	−	0.0852537i
$162$	−3.88951	+	2.18825i	−0.305589	+	0.171925i
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	0.704983	−	0.709224i	$-0.250954\pi$
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	−0.966698	+	0.255921i	$0.917621\pi$
$164$	4.19396	+	7.26416i	0.327494	+	0.567236i
$165$	−0.729372	−	5.66184i	−0.0567815	−	0.440774i
$166$	−3.05532	+	5.29197i	−0.237139	+	0.410737i
$167$	8.81549	+	15.2689i	0.682163	+	1.18154i	0.974319	+	0.225170i	$0.0722939\pi$
$167$	8.81549	+	15.2689i	0.682163	+	1.18154i	−0.292156	+	0.956371i	$0.594373\pi$
$168$	7.54313	−	3.98418i	0.581965	−	0.307386i
$169$	5.78394	−	10.0181i	0.444919	−	0.770622i
$170$	−0.228863	−	0.396403i	−0.0175530	−	0.0304027i
$171$	−5.92400	−	5.99031i	−0.453020	−	0.458091i
$172$	8.75178	−	15.1585i	0.667317	−	1.15583i
$173$	−3.88685			−0.295511			−0.147756	−	0.989024i	$-0.547205\pi$
$173$	−3.88685			−0.295511			−0.147756	+	0.989024i	$0.547205\pi$
$174$	3.28328	+	1.37070i	0.248905	+	0.103912i
$175$	14.5316	−	17.6293i	1.09848	−	1.33265i
$176$	1.15371	+	1.99829i	0.0869642	+	0.150626i
$177$	−0.401075	−	3.11339i	−0.0301466	−	0.234017i
$178$	0.596879	+	1.03382i	0.0447380	+	0.0774884i
$179$	3.66758	−	6.35244i	0.274128	−	0.474804i	−0.695787	−	0.718248i	$-0.744944\pi$
$179$	3.66758	−	6.35244i	0.274128	−	0.474804i	0.969915	+	0.243445i	$0.0782775\pi$
$180$	5.13366	−	18.7412i	0.382641	−	1.39689i
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$	0.998615	−	1.21150i	0.0740223	−	0.0898021i
$183$	−2.39093	−	18.5599i	−0.176743	−	1.37199i
$184$	−2.30619	+	3.99444i	−0.170015	+	0.294474i
$185$	−17.4709			−1.28449
$186$	0.393415	+	3.05394i	0.0288466	+	0.223925i
$187$	−0.223127			−0.0163167
$188$	17.8447			1.30146
$189$	−10.1321	+	9.29198i	−0.737000	+	0.675892i
$190$	−5.14204			−0.373043
$191$	−23.8459			−1.72543			−0.862715	−	0.505690i	$-0.831238\pi$
$191$	−23.8459			−1.72543			−0.862715	+	0.505690i	$0.831238\pi$
$192$	0.594956	+	4.61842i	0.0429373	+	0.333306i
$193$	5.93456			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$193$	5.93456			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$194$	−2.73823	+	4.74276i	−0.196594	+	0.340510i
$195$	−0.977905	−	7.59112i	−0.0700293	−	0.543611i
$196$	9.26641	−	8.05622i	0.661887	−	0.575444i
$197$	−15.4682			−1.10206			−0.551032	−	0.834484i	$-0.685766\pi$
$197$	−15.4682			−1.10206			−0.551032	+	0.834484i	$0.685766\pi$
$198$	0.933648	+	0.944100i	0.0663515	+	0.0670942i
$199$	7.74818	−	13.4202i	0.549254	−	0.951336i	−0.449072	−	0.893496i	$-0.648245\pi$
$199$	7.74818	−	13.4202i	0.549254	−	0.951336i	0.998326	−	0.0578402i	$-0.0184214\pi$
$200$	−8.03736	−	13.9211i	−0.568327	−	0.984371i
$201$	−0.227798	−	1.76831i	−0.0160676	−	0.124727i
$202$	−0.644540	−	1.11638i	−0.0453497	−	0.0785480i
$203$	10.8099	+	1.80860i	0.758707	+	0.126939i
$204$	−0.700877	−	0.292600i	−0.0490712	−	0.0204861i
$205$	−17.6574			−1.23325
$206$	2.40783	−	4.17048i	0.167761	−	0.290571i
$207$	1.96377	−	7.16905i	0.136492	−	0.498283i
$208$	1.54684	+	2.67920i	0.107254	+	0.185769i
$209$	−1.25329	+	2.17076i	−0.0866918	+	0.150155i
$210$	−0.315902	+	8.38490i	−0.0217993	+	0.578613i
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	0.891372	−	0.453273i	$-0.149744\pi$
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	−0.838232	+	0.545314i	$0.816410\pi$
$212$	8.67347	−	15.0229i	0.595697	−	1.03178i
$213$	1.09439	+	8.49536i	0.0749866	+	0.582093i
$214$	2.70261	+	4.68105i	0.184746	+	0.319990i
$215$	18.4233	+	31.9101i	1.25646	+	2.17625i
$216$	3.62691	+	8.96717i	0.246780	+	0.610138i
$217$	3.32215	+	8.88461i	0.225522	+	0.603127i
$218$	0.526098	−	0.911229i	0.0356319	−	0.0617162i
$219$	2.92583	+	1.22147i	0.197709	+	0.0825392i
$220$	−5.78135			−0.389779
$221$	−0.299157			−0.0201235
$222$	3.23075	−	2.46479i	0.216834	−	0.165426i
$223$	−2.72171	+	4.71414i	−0.182259	+	0.315682i	−0.942649	−	0.333784i	$-0.891674\pi$
$223$	−2.72171	+	4.71414i	−0.182259	+	0.315682i	0.760390	+	0.649466i	$0.225008\pi$
$224$	−4.63783	−	12.4032i	−0.309878	−	0.828725i
$225$	18.2157	+	18.4196i	1.21438	+	1.22797i
$226$	−3.92389	−	6.79638i	−0.261014	−	0.452089i
$227$	8.03818	+	13.9225i	0.533513	+	0.924072i	0.999234	+	0.0391399i	$0.0124618\pi$
$227$	8.03818	+	13.9225i	0.533513	+	0.924072i	−0.465721	+	0.884932i	$0.654205\pi$
$228$	−6.78343	+	5.17518i	−0.449244	+	0.342735i
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	−0.653021	−	0.757340i	$-0.726499\pi$
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	0.982386	+	0.186863i	$0.0598319\pi$
$230$	−2.26839	−	3.92897i	−0.149573	−	0.259068i
$231$	3.46276	+	2.17704i	0.227833	+	0.143239i
$232$	3.85578	−	6.67840i	0.253144	−	0.438458i
$233$	8.27045	+	14.3248i	0.541815	+	0.938451i	0.998800	+	0.0489765i	$0.0155959\pi$
$233$	8.27045	+	14.3248i	0.541815	+	0.938451i	−0.456985	+	0.889474i	$0.651071\pi$
$234$	1.25179	+	1.26580i	0.0818320	+	0.0827480i
$235$	−18.7824	+	32.5321i	−1.22523	+	2.12216i
$236$	−3.17911			−0.206942
$237$	0.398143	+	3.09063i	0.0258621	+	0.200758i
$238$	0.323468	+	0.0541192i	0.0209673	+	0.00350803i
$239$	−11.0119	−	19.0732i	−0.712303	−	1.23375i	−0.963990	−	0.265937i	$-0.914319\pi$
$239$	−11.0119	−	19.0732i	−0.712303	−	1.23375i	0.251687	−	0.967809i	$-0.419015\pi$
$240$	−15.2577	−	6.36974i	−0.984879	−	0.411165i
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	−0.998984	−	0.0450623i	$-0.985651\pi$
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	0.460467	−	0.887677i	$-0.347682\pi$
$242$	−2.52975	+	4.38166i	−0.162619	+	0.281664i
$243$	−9.31665	−	12.4980i	−0.597664	−	0.801747i
$244$	−18.9516			−1.21325
$245$	4.93368	+	25.3728i	0.315201	+	1.62101i
$246$	3.26524	−	2.49110i	0.208184	−	0.158827i
$247$	−1.68035	+	2.91045i	−0.106918	+	0.185187i
$248$	6.67392			0.423794
$249$	−19.6967	−	8.22294i	−1.24823	−	0.521108i
$250$	6.65606			0.420966
$251$	−8.53099			−0.538471			−0.269236	−	0.963074i	$-0.586771\pi$
$251$	−8.53099			−0.538471			−0.269236	+	0.963074i	$0.586771\pi$
$252$	8.02220	+	11.3794i	0.505351	+	0.716833i
$253$	−2.21153			−0.139038
$254$	0.629487			0.0394975
$255$	1.27114	−	0.969769i	0.0796017	−	0.0607293i
$256$	−0.247722			−0.0154826
$257$	8.55986	−	14.8261i	0.533950	−	0.924828i	−0.465264	−	0.885172i	$-0.654041\pi$
$257$	8.55986	−	14.8261i	0.533950	−	0.924828i	0.999213	−	0.0396557i	$-0.0126261\pi$
$258$	−7.90875	−	3.30173i	−0.492377	−	0.205557i
$259$	7.96211	−	9.65945i	0.494741	−	0.600209i
$260$	−7.75135			−0.480718
$261$	−3.28328	+	11.9861i	−0.203230	+	0.741921i
$262$	−3.72617	+	6.45392i	−0.230204	+	0.398725i
$263$	−10.2763	−	17.7991i	−0.633666	−	1.09754i	−0.986796	−	0.161967i	$-0.948216\pi$
$263$	−10.2763	−	17.7991i	−0.633666	−	1.09754i	0.353130	−	0.935574i	$-0.385117\pi$
$264$	2.28806	−	1.74559i	0.140820	−	0.107434i
$265$	18.2585	+	31.6246i	1.12161	+	1.94269i
$266$	2.34341	−	2.84297i	0.143684	−	0.174314i
$267$	−3.31514	+	2.52917i	−0.202883	+	0.154783i
$268$	−1.80563			−0.110297
$269$	9.92267	−	17.1866i	0.604996	−	1.04788i	−0.387057	−	0.922056i	$-0.626508\pi$
$269$	9.92267	−	17.1866i	0.604996	−	1.04788i	0.992052	−	0.125827i	$-0.0401585\pi$
$270$	−9.42223	−	1.32058i	−0.573419	−	0.0803679i
$271$	5.32056	+	9.21548i	0.323201	+	0.559801i	0.981147	−	0.193265i	$-0.0619077\pi$
$271$	5.32056	+	9.21548i	0.323201	+	0.559801i	−0.657946	+	0.753065i	$0.728574\pi$
$272$	−0.323121	+	0.559663i	−0.0195921	+	0.0339345i
$273$	4.64270	+	2.91887i	0.280989	+	0.176658i
$274$	−0.121114	−	0.209776i	−0.00731676	−	0.0126730i
$275$	3.85373	−	6.67485i	0.232388	−	0.402509i
$276$	−6.94677	−	2.90012i	−0.418146	−	0.174567i
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	0.949024	+	0.315205i	$0.102073\pi$
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	−0.201536	+	0.979481i	$0.564593\pi$
$278$	2.44705	+	4.23841i	0.146764	+	0.254203i
$279$	−10.4043	+	2.72585i	−0.622889	+	0.163192i
$280$	17.9373	+	3.00109i	1.07196	+	0.179349i
$281$	−6.83733	+	11.8426i	−0.407881	+	0.706470i	−0.994652	−	0.103282i	$-0.967065\pi$
$281$	−6.83733	+	11.8426i	−0.407881	+	0.706470i	0.586771	+	0.809753i	$0.300399\pi$
$282$	−1.11634	−	8.66572i	−0.0664770	−	0.516036i
$283$	6.32179			0.375791			0.187896	−	0.982189i	$-0.439833\pi$
$283$	6.32179			0.375791			0.187896	+	0.982189i	$0.439833\pi$
$284$	8.67468			0.514747
$285$	−2.29481	−	17.8138i	−0.135933	−	1.05520i
$286$	0.264830	−	0.458699i	0.0156597	−	0.0271234i
$287$	8.04710	−	9.76255i	0.475005	−	0.576265i
$288$	14.5247	−	3.80537i	0.855878	−	0.224234i
$289$	8.46875	+	14.6683i	0.498162	+	0.862842i
$290$	3.79257	+	6.56893i	0.222708	+	0.385741i
$291$	−17.6526	−	7.36955i	−1.03481	−	0.432011i
$292$	1.60547	−	2.78076i	0.0939533	−	0.162732i
$293$	−1.31508	−	2.27778i	−0.0768277	−	0.133069i	0.825052	−	0.565057i	$-0.191146\pi$
$293$	−1.31508	−	2.27778i	−0.0768277	−	0.133069i	−0.901880	+	0.431987i	$0.857812\pi$
$294$	−4.49194	−	3.99595i	−0.261975	−	0.233049i
$295$	3.34616	−	5.79573i	0.194821	−	0.337440i
$296$	−4.40382	−	7.62764i	−0.255967	−	0.443348i
$297$	−2.85401	+	3.65581i	−0.165606	+	0.212132i
$298$	5.21256	−	9.02841i	0.301955	−	0.523002i
$299$	−2.96511			−0.171477
$300$	20.8583	−	15.9131i	1.20426	−	0.918745i
$301$	−26.0389	−	4.35655i	−1.50086	−	0.251108i
$302$	0.371500	+	0.643457i	0.0213774	+	0.0370268i
$303$	3.57986	−	2.73113i	0.205657	−	0.156899i
$304$	3.62990	+	6.28717i	0.208189	+	0.360594i
$305$	19.9475	−	34.5501i	1.14219	−	1.97833i
$306$	−0.0982463	+	0.358663i	−0.00561637	+	0.0205034i
$307$	−2.79496			−0.159517			−0.0797583	−	0.996814i	$-0.525415\pi$
$307$	−2.79496			−0.159517			−0.0797583	+	0.996814i	$0.525415\pi$
$308$	2.63477	−	3.19644i	0.150130	−	0.182134i
$309$	15.5225	+	6.48030i	0.883045	+	0.368652i
$310$	−3.28226	+	5.68504i	−0.186420	+	0.322889i
$311$	−15.1003			−0.856258			−0.428129	−	0.903718i	$-0.640827\pi$
$311$	−15.1003			−0.856258			−0.428129	+	0.903718i	$0.640827\pi$
$312$	3.06772	−	2.34041i	0.173675	−	0.132499i
$313$	−25.4785			−1.44013			−0.720064	−	0.693908i	$-0.755888\pi$
$313$	−25.4785			−1.44013			−0.720064	+	0.693908i	$0.755888\pi$
$314$	8.27090			0.466754
$315$	−29.1891	+	2.64766i	−1.64462	+	0.149178i
$316$	3.15587			0.177531
$317$	32.5209			1.82656			0.913278	−	0.407337i	$-0.133543\pi$
$317$	32.5209			1.82656			0.913278	+	0.407337i	$0.133543\pi$
$318$	−7.83799	−	3.27219i	−0.439533	−	0.183495i
$319$	3.69751			0.207021
$320$	−4.96372	+	8.59741i	−0.277480	+	0.480610i
$321$	−15.0106	+	11.4518i	−0.837811	+	0.639179i
$322$	3.20606	+	0.536405i	0.178667	+	0.0298927i
$323$	−0.702021			−0.0390615
$324$	−13.7590	+	7.74084i	−0.764388	+	0.430046i
$325$	5.16688	−	8.94931i	0.286607	−	0.496418i
$326$	1.65687	+	2.86978i	0.0917654	+	0.158942i
$327$	3.39159	+	1.41591i	0.187556	+	0.0783003i
$328$	−4.45083	−	7.70906i	−0.245756	−	0.425661i
$329$	−9.42678	−	25.2106i	−0.519715	−	1.38991i
$330$	0.361672	+	2.80753i	0.0199094	+	0.154549i
$331$	18.0948			0.994582			0.497291	−	0.867584i	$-0.334328\pi$
$331$	18.0948			0.994582			0.497291	+	0.867584i	$0.334328\pi$
$332$	−10.8081	+	18.7201i	−0.593170	+	1.02740i
$333$	9.98070	+	10.0924i	0.546939	+	0.553062i
$334$	−4.37132	−	7.57135i	−0.239188	−	0.414286i
$335$	1.90051	−	3.29179i	0.103836	−	0.179850i
$336$	10.4752	−	5.53286i	0.571470	−	0.301842i
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	−0.974557	−	0.224139i	$-0.928043\pi$
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	0.293168	−	0.956061i	$-0.405290\pi$
$338$	−2.86807	+	4.96765i	−0.156003	+	0.270204i
$339$	21.7938	−	16.6268i	1.18368	−	0.903045i
$340$	−0.809596	−	1.40226i	−0.0439065	−	0.0760483i
$341$	1.59999	+	2.77127i	0.0866446	+	0.150073i
$342$	2.93752	+	2.97041i	0.158843	+	0.160621i
$343$	−16.2768	−	8.83553i	−0.878863	−	0.477074i
$344$	−9.28778	+	16.0869i	−0.500764	+	0.867348i
$345$	12.5989	−	9.61190i	0.678303	−	0.517488i
$346$	1.92736			0.103616
$347$	10.7489			0.577030			0.288515	−	0.957475i	$-0.406838\pi$
$347$	10.7489			0.577030			0.288515	+	0.957475i	$0.406838\pi$
$348$	11.6145	+	4.84878i	0.622601	+	0.259922i
$349$	−1.64301	+	2.84577i	−0.0879482	+	0.152331i	−0.906644	−	0.421897i	$-0.861364\pi$
$349$	−1.64301	+	2.84577i	−0.0879482	+	0.152331i	0.818695	+	0.574228i	$0.194698\pi$
$350$	−7.20574	+	8.74183i	−0.385163	+	0.467270i
$351$	−3.82651	+	4.90153i	−0.204244	+	0.261624i
$352$	−2.23365	−	3.86879i	−0.119054	−	0.206207i
$353$	−8.40960	−	14.5658i	−0.447598	−	0.775262i	0.550631	−	0.834748i	$-0.314387\pi$
$353$	−8.40960	−	14.5658i	−0.447598	−	0.775262i	−0.998229	+	0.0594866i	$0.981054\pi$
$354$	0.198880	+	1.54383i	0.0105704	+	0.0820538i
$355$	−9.13051	+	15.8145i	−0.484597	+	0.839347i
$356$	2.11144	+	3.65711i	0.111906	+	0.193827i
$357$	−0.0431288	+	1.14475i	−0.00228262	+	0.0605868i
$358$	−1.81864	+	3.14997i	−0.0961180	+	0.166481i
$359$	11.8921	+	20.5978i	0.627642	+	1.08711i	0.988024	+	0.154303i	$0.0493131\pi$
$359$	11.8921	+	20.5978i	0.627642	+	1.08711i	−0.360382	+	0.932805i	$0.617354\pi$
$360$	−5.44808	+	19.8890i	−0.287139	+	1.04824i
$361$	5.55680	−	9.62466i	0.292463	−	0.506561i
$362$	−5.58177			−0.293371
$363$	−16.3085	−	6.80845i	−0.855976	−	0.357351i
$364$	3.53256	−	4.28562i	0.185157	−	0.224628i
$365$	3.37968	+	5.85377i	0.176900	+	0.306401i
$366$	1.18559	+	9.20326i	0.0619716	+	0.481062i
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	0.874889	−	0.484323i	$-0.160934\pi$
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	−0.856881	+	0.515515i	$0.827601\pi$
$368$	−3.20263	+	5.54712i	−0.166949	+	0.289164i
$369$	10.0872	+	10.2002i	0.525121	+	0.530999i
$370$	8.66327			0.450382
$371$	−25.8059	−	4.31757i	−1.33978	−	0.224157i
$372$	1.39169	+	10.8032i	0.0721558	+	0.560119i
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	−0.813239	−	0.581929i	$-0.802298\pi$
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	0.910585	+	0.413321i	$0.135631\pi$
$374$	0.110642			0.00572114
$375$	2.97050	+	23.0589i	0.153396	+	1.19075i
$376$	−18.9376			−0.976634
$377$	4.95744			0.255321
$378$	5.02418	−	4.60760i	0.258416	−	0.236989i
$379$	32.8735			1.68860			0.844300	−	0.535872i	$-0.180017\pi$
$379$	32.8735			1.68860			0.844300	+	0.535872i	$0.180017\pi$
$380$	−18.1898			−0.933116
$381$	0.280930	+	2.18075i	0.0143925	+	0.111723i
$382$	11.8244			0.604991
$383$	0.536335	−	0.928960i	0.0274055	−	0.0474676i	−0.851997	−	0.523546i	$-0.824609\pi$
$383$	0.536335	−	0.928960i	0.0274055	−	0.0474676i	0.879403	+	0.476078i	$0.157942\pi$
$384$	−2.51021	−	19.4858i	−0.128099	−	0.994381i
$385$	3.05410	+	8.16775i	0.155651	+	0.416267i
$386$	−2.94276			−0.149782
$387$	7.90875	−	28.8721i	0.402024	−	1.46765i
$388$	−9.68640	+	16.7773i	−0.491752	+	0.851740i
$389$	11.8718	+	20.5626i	0.601925	+	1.04256i	0.992529	+	0.122006i	$0.0389326\pi$
$389$	11.8718	+	20.5626i	0.601925	+	1.04256i	−0.390605	+	0.920559i	$0.627734\pi$
$390$	0.484912	+	3.76419i	0.0245545	+	0.190607i
$391$	−0.309693	−	0.536405i	−0.0156619	−	0.0271271i
$392$	−9.83394	+	8.54962i	−0.496689	+	0.431821i
$393$	−24.0215	−	10.0284i	−1.21172	−	0.505868i
$394$	7.67019			0.386419
$395$	−3.32170	+	5.75336i	−0.167133	+	0.289483i
$396$	3.30274	+	3.33972i	0.165969	+	0.167827i
$397$	−0.0160489	−	0.0277975i	−0.000805471	−	0.00139512i	0.865622	−	0.500697i	$-0.166923\pi$
$397$	−0.0160489	−	0.0277975i	−0.000805471	−	0.00139512i	−0.866428	+	0.499302i	$0.833590\pi$
$398$	−3.84208	+	6.65467i	−0.192586	+	0.333569i
$399$	10.8948	+	6.84959i	0.545424	+	0.342909i
$400$	−11.1616	−	19.3324i	−0.558078	−	0.966619i
$401$	−12.2628	+	21.2398i	−0.612374	+	1.06066i	0.378465	+	0.925616i	$0.376452\pi$
$401$	−12.2628	+	21.2398i	−0.612374	+	1.06066i	−0.990839	+	0.135048i	$0.956881\pi$
$402$	0.112958	+	0.876848i	0.00563381	+	0.0437332i
$403$	2.14519	+	3.71558i	0.106860	+	0.185086i
$404$	−2.28004	−	3.94914i	−0.113436	−	0.196477i
$405$	0.369938	−	33.2312i	0.0183824	−	1.65127i
$406$	−5.36029	−	0.896827i	−0.266027	−	0.0445088i
$407$	2.11153	−	3.65728i	0.104665	−	0.181284i
$408$	0.743802	+	0.310521i	0.0368237	+	0.0153731i
$409$	26.7897			1.32467			0.662333	−	0.749210i	$-0.269567\pi$
$409$	26.7897			1.32467			0.662333	+	0.749210i	$0.269567\pi$
$410$	8.75574			0.432415
$411$	0.672682	−	0.513199i	0.0331810	−	0.0253143i
$412$	8.51759	−	14.7529i	0.419631	−	0.726823i
$413$	1.67942	+	4.49137i	0.0826388	+	0.221006i
$414$	−0.973773	+	3.55490i	−0.0478583	+	0.174714i
$415$	−22.7520	−	39.4077i	−1.11685	−	1.93445i
$416$	−2.99476	−	5.18708i	−0.146830	−	0.254317i
$417$	−13.5912	+	10.3689i	−0.665564	+	0.507769i
$418$	0.621466	−	1.07641i	0.0303969	−	0.0526490i
$419$	−10.5262	−	18.2320i	−0.514240	−	0.890689i	−0.999864	−	0.0165215i	$-0.994741\pi$
$419$	−10.5262	−	18.2320i	−0.514240	−	0.890689i	0.485624	−	0.874168i	$-0.338593\pi$
$420$	−1.11749	+	29.6612i	−0.0545280	+	1.44732i
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	−0.988431	−	0.151672i	$-0.951534\pi$
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	0.625568	+	0.780170i	$0.284867\pi$
$422$	−0.382760	−	0.662959i	−0.0186325	−	0.0322724i
$423$	29.5228	−	7.73475i	1.43545	−	0.376076i
$424$	−9.20469	+	15.9430i	−0.447019	+	0.774260i
$425$	2.15864			0.104709
$426$	−0.542675	−	4.21258i	−0.0262927	−	0.204100i
$427$	10.0115	+	26.7744i	0.484492	+	1.29571i
$428$	9.56037	+	16.5590i	0.462118	+	0.800412i
$429$	1.70728	+	0.712750i	0.0824281	+	0.0344119i
$430$	−9.13554	−	15.8232i	−0.440555	−	0.763064i
$431$	−7.95192	+	13.7731i	−0.383031	+	0.663428i	−0.991494	−	0.130154i	$-0.958453\pi$
$431$	−7.95192	+	13.7731i	−0.383031	+	0.663428i	0.608463	+	0.793582i	$0.291786\pi$
$432$	5.03673	+	12.4528i	0.242330	+	0.599135i
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$	−1.64735	−	4.40560i	−0.0790752	−	0.211475i
$435$	−21.0644	+	16.0704i	−1.00996	+	0.770515i
$436$	1.86105	−	3.22344i	0.0891282	−	0.154375i
$437$	−6.95811			−0.332851
$438$	−1.45083	−	0.605687i	−0.0693231	−	0.0289409i
$439$	−15.5447			−0.741909			−0.370954	−	0.928651i	$-0.620969\pi$
$439$	−15.5447			−0.741909			−0.370954	+	0.928651i	$0.620969\pi$
$440$	6.13543			0.292495
$441$	11.8387	−	17.3449i	0.563745	−	0.825949i
$442$	0.148343			0.00705594
$443$	1.79005			0.0850480			0.0425240	−	0.999095i	$-0.486460\pi$
$443$	1.79005			0.0850480			0.0425240	+	0.999095i	$0.486460\pi$
$444$	11.4287	−	8.71910i	0.542381	−	0.413790i
$445$	−8.88955			−0.421405
$446$	1.34961	−	2.33759i	0.0639058	−	0.110688i
$447$	33.6038	+	14.0288i	1.58940	+	0.663540i
$448$	−2.49126	−	6.66252i	−0.117701	−	0.314774i
$449$	13.5666			0.640250			0.320125	−	0.947375i	$-0.396275\pi$
$449$	13.5666			0.640250			0.320125	+	0.947375i	$0.396275\pi$
$450$	−9.03257	−	9.13368i	−0.425799	−	0.430566i
$451$	2.13407	−	3.69631i	0.100489	−	0.174053i
$452$	−13.8806	−	24.0419i	−0.652890	−	1.13084i
$453$	−2.06336	+	1.57417i	−0.0969450	+	0.0739608i
$454$	−3.98588	−	6.90375i	−0.187067	−	0.324009i
$455$	4.09478	+	10.9509i	0.191966	+	0.513387i
$456$	7.19889	−	5.49214i	0.337119	−	0.257193i
$457$	2.56917			0.120181			0.0600905	−	0.998193i	$-0.480861\pi$
$457$	2.56917			0.120181			0.0600905	+	0.998193i	$0.480861\pi$
$458$	−2.47151	+	4.28078i	−0.115486	+	0.200028i
$459$	−1.28638	−	0.180293i	−0.0600429	−	0.00841535i
$460$	−8.02434	−	13.8986i	−0.374137	−	0.648024i
$461$	18.0934	−	31.3388i	0.842695	−	1.45959i	−0.0449122	−	0.998991i	$-0.514301\pi$
$461$	18.0934	−	31.3388i	0.842695	−	1.45959i	0.887608	−	0.460600i	$-0.152366\pi$
$462$	−1.71707	−	1.07953i	−0.0798855	−	0.0502241i
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	0.991166	−	0.132626i	$-0.0423409\pi$
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	−0.610440	+	0.792062i	$0.709008\pi$
$464$	5.35455	−	9.27436i	0.248579	−	0.430551i
$465$	−21.1597	−	8.83372i	−0.981259	−	0.409654i
$466$	−4.10105	−	7.10323i	−0.189978	−	0.329051i
$467$	−4.35022	−	7.53480i	−0.201304	−	0.348669i	0.747645	−	0.664099i	$-0.231185\pi$
$467$	−4.35022	−	7.53480i	−0.201304	−	0.348669i	−0.948949	+	0.315430i	$0.897851\pi$
$468$	4.42815	+	4.47772i	0.204692	+	0.206983i
$469$	0.953856	+	2.55095i	0.0440450	+	0.117792i
$470$	9.31361	−	16.1316i	0.429605	−	0.744097i
$471$	3.69117	+	28.6532i	0.170080	+	1.32027i
$472$	3.37381			0.155292
$473$	−8.90655			−0.409524
$474$	−0.197426	−	1.53255i	−0.00906809	−	0.0703922i
$475$	12.1249	−	21.0010i	0.556330	−	0.963591i
$476$	1.14425	+	0.191445i	0.0524468	+	0.00877485i
$477$	7.83799	−	28.6138i	0.358877	−	1.31014i
$478$	5.46047	+	9.45782i	0.249756	+	0.432591i
$479$	8.88370	+	15.3870i	0.405907	+	0.703051i	0.994427	−	0.105432i	$-0.0336224\pi$
$479$	8.88370	+	15.3870i	0.405907	+	0.703051i	−0.588520	+	0.808483i	$0.700289\pi$
$480$	29.5397	+	12.3322i	1.34830	+	0.562884i
$481$	2.83103	−	4.90349i	0.129084	−	0.223580i
$482$	4.14548	+	7.18018i	0.188821	+	0.327048i
$483$	−0.427472	+	11.3463i	−0.0194507	+	0.516273i
$484$	−8.94890	+	15.4999i	−0.406768	+	0.704543i
$485$	−20.3908	−	35.3179i	−0.925898	−	1.60370i
$486$	4.61983	+	6.19736i	0.209560	+	0.281118i
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	−0.613316	−	0.789837i	$-0.710165\pi$
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	0.990677	+	0.136229i	$0.0434983\pi$
$488$	20.1123			0.910443
$489$	−9.20245	+	7.02068i	−0.416149	+	0.317486i
$490$	−2.44645	−	12.5816i	−0.110519	−	0.568378i
$491$	−3.21021	−	5.56025i	−0.144875	−	0.250930i	0.784451	−	0.620190i	$-0.212945\pi$
$491$	−3.21021	−	5.56025i	−0.144875	−	0.250930i	−0.929326	+	0.369260i	$0.879611\pi$
$492$	11.5507	−	8.81217i	0.520744	−	0.397283i
$493$	0.517784	+	0.896827i	0.0233198	+	0.0403911i
$494$	0.833230	−	1.44320i	0.0374888	−	0.0649325i
$495$	−9.56482	+	2.50591i	−0.429907	+	0.112632i
$496$	9.26814			0.416152
$497$	−4.58255	−	12.2554i	−0.205555	−	0.549729i
$498$	9.76698	+	4.07750i	0.437669	+	0.182717i
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	−0.963382	−	0.268134i	$-0.913593\pi$
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	0.713902	+	0.700246i	$0.246926\pi$
$500$	23.5456			1.05299
$501$	24.2789	−	18.5227i	1.08470	−	0.827533i
$502$	4.23025			0.188805
$503$	−17.7223			−0.790200			−0.395100	−	0.918638i	$-0.629290\pi$
$503$	−17.7223			−0.790200			−0.395100	+	0.918638i	$0.629290\pi$
$504$	−8.51352	−	12.0763i	−0.379222	−	0.537922i
$505$	9.59939			0.427167
$506$	1.09663			0.0487511
$507$	−18.4896	−	7.71899i	−0.821151	−	0.342812i
$508$	2.22678			0.0987976
$509$	−15.5411	+	26.9180i	−0.688848	+	1.19312i	0.283362	+	0.959013i	$0.408550\pi$
$509$	−15.5411	+	26.9180i	−0.688848	+	1.19312i	−0.972211	+	0.234107i	$0.924783\pi$
$510$	−0.630316	+	0.480878i	−0.0279109	+	0.0212936i
$511$	−4.77672	−	0.799190i	−0.211310	−	0.0353541i
$512$	−22.5634			−0.997169
$513$	−8.97952	+	11.5022i	−0.396456	+	0.507835i
$514$	−4.24456	+	7.35180i	−0.187220	+	0.324274i
$515$	17.9303	+	31.0563i	0.790105	+	1.36850i
$516$	−27.9769	−	11.6797i	−1.23161	−	0.514172i
$517$	−4.54008	−	7.86365i	−0.199672	−	0.345843i
$518$	−3.94816	+	4.78981i	−0.173472	+	0.210452i
$519$	0.860152	+	6.67704i	0.0377565	+	0.293089i
$520$	8.22608			0.360737
$521$	−2.37986	+	4.12203i	−0.104263	+	0.180590i	−0.913437	−	0.406980i	$-0.866582\pi$
$521$	−2.37986	+	4.12203i	−0.104263	+	0.180590i	0.809174	+	0.587570i	$0.199915\pi$
$522$	1.62807	−	5.94353i	0.0712588	−	0.260141i
$523$	20.1258	+	34.8588i	0.880038	+	1.52427i	0.851298	+	0.524683i	$0.175816\pi$
$523$	20.1258	+	34.8588i	0.880038	+	1.52427i	0.0287402	+	0.999587i	$0.490850\pi$
$524$	−13.1812	+	22.8305i	−0.575823	+	0.997355i
$525$	−33.5005	−	21.0618i	−1.46208	−	0.919211i
$526$	5.09571	+	8.82602i	0.222183	+	0.384833i
$527$	−0.448113	+	0.776154i	−0.0195201	+	0.0338098i
$528$	3.17745	−	2.42412i	0.138281	−	0.105496i
$529$	8.43046	+	14.6020i	0.366542	+	0.634869i
$530$	−9.05381	−	15.6817i	−0.393272	−	0.681168i
$531$	−5.25960	+	1.37798i	−0.228247	+	0.0597991i
$532$	8.28972	−	10.0569i	0.359405	−	0.436022i
$533$	2.86125	−	4.95583i	0.123935	−	0.214661i
$534$	1.64387	−	1.25413i	0.0711373	−	0.0542717i
$535$	−40.2510			−1.74020
$536$	1.91622			0.0827680
$537$	−11.7242	−	4.89459i	−0.505937	−	0.211217i
$538$	−4.92033	+	8.52227i	−0.212131	+	0.367421i
$539$	−5.90771	−	2.03376i	−0.254463	−	0.0876003i
$540$	−33.3308	−	4.67150i	−1.43433	−	0.201029i
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	0.999775	+	0.0212301i	$0.00675826\pi$
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	−0.481502	+	0.876445i	$0.659908\pi$
$542$	−2.63830	−	4.56966i	−0.113325	−	0.196284i
$543$	−2.49105	−	19.3371i	−0.106901	−	0.829836i
$544$	0.625580	−	1.08354i	0.0268215	−	0.0464563i
$545$	3.91769	+	6.78564i	0.167815	+	0.290665i
$546$	−2.30217	−	1.44737i	−0.0985237	−	0.0619419i
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	−0.967336	−	0.253499i	$-0.918419\pi$
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	0.703204	+	0.710988i	$0.251752\pi$
$548$	−0.428436	−	0.742073i	−0.0183019	−	0.0316998i
$549$	−31.3541	+	8.21454i	−1.33816	+	0.350588i
$550$	−1.91094	+	3.30985i	−0.0814828	+	0.141132i
$551$	11.6334			0.495600
$552$	7.37223	+	3.07774i	0.313783	+	0.130997i
$553$	−1.66714	−	4.45854i	−0.0708941	−	0.189596i
$554$	−6.16893	−	10.6849i	−0.262093	−	0.453958i
$555$	3.86628	+	30.0125i	0.164114	+	1.27396i
$556$	8.65633	+	14.9932i	0.367110	+	0.635853i
$557$	4.03845	−	6.99479i	0.171114	−	0.296379i	−0.767695	−	0.640815i	$-0.778597\pi$
$557$	4.03845	−	6.99479i	0.171114	−	0.296379i	0.938810	+	0.344436i	$0.111930\pi$
$558$	5.15916	−	1.35166i	0.218405	−	0.0572204i
$559$	−11.9415			−0.505070
$560$	24.9097	+	4.16764i	1.05263	+	0.176115i
$561$	0.0493776	+	0.383300i	0.00208472	+	0.0161829i
$562$	3.39041	−	5.87237i	0.143016	−	0.247711i
$563$	45.2127			1.90549			0.952744	−	0.303774i	$-0.0982467\pi$
$563$	45.2127			1.90549			0.952744	+	0.303774i	$0.0982467\pi$
$564$	−3.94900	−	30.6547i	−0.166283	−	1.29079i
$565$	58.4401			2.45859
$566$	−3.13477			−0.131764
$567$	18.2045	+	15.3491i	0.764517	+	0.644604i
$568$	−9.20596			−0.386274
$569$	22.4299			0.940309			0.470155	−	0.882584i	$-0.344198\pi$
$569$	22.4299			0.940309			0.470155	+	0.882584i	$0.344198\pi$
$570$	1.13792	+	8.83329i	0.0476624	+	0.369986i
$571$	−21.8269			−0.913426			−0.456713	−	0.889614i	$-0.650973\pi$
$571$	−21.8269			−0.913426			−0.456713	+	0.889614i	$0.650973\pi$
$572$	0.936826	−	1.62263i	0.0391706	−	0.0678455i
$573$	5.27706	+	40.9638i	0.220452	+	1.71129i
$574$	−3.99030	+	4.84094i	−0.166552	+	0.202057i
$575$	21.3954			0.892251
$576$	7.80212	−	2.04410i	0.325088	−	0.0851707i
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	0.307465	+	0.951559i	$0.400519\pi$
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	−0.977807	+	0.209508i	$0.932814\pi$
$578$	−4.19939	−	7.27355i	−0.174671	−	0.302540i
$579$	−1.31331	−	10.1947i	−0.0545791	−	0.423678i
$580$	13.4161	+	23.2373i	0.557072	+	0.964878i
$581$	32.1569	+	5.38016i	1.33409	+	0.223207i
$582$	8.75335	+	3.65433i	0.362838	+	0.151477i
$583$	−8.82687			−0.365571
$584$	−1.70380	+	2.95107i	−0.0705039	+	0.122116i
$585$	−12.8240	+	3.35980i	−0.530209	+	0.138911i
$586$	0.652105	+	1.12948i	0.0269382	+	0.0466584i
$587$	−9.72304	+	16.8408i	−0.401313	+	0.695094i	−0.993885	−	0.110424i	$-0.964779\pi$
$587$	−9.72304	+	16.8408i	−0.401313	+	0.695094i	0.592572	+	0.805518i	$0.298113\pi$
$588$	−15.8901	−	14.1355i	−0.655295	−	0.582939i
$589$	5.03404	+	8.71921i	0.207424	+	0.359269i
$590$	−1.65926	+	2.87392i	−0.0683105	+	0.118317i
$591$	3.42309	+	26.5721i	0.140807	+	1.09303i
$592$	−6.11563	−	10.5926i	−0.251351	−	0.435352i
$593$	−14.4202	−	24.9766i	−0.592168	−	1.02566i	−0.993940	−	0.109925i	$-0.964939\pi$
$593$	−14.4202	−	24.9766i	−0.592168	−	1.02566i	0.401772	−	0.915740i	$-0.368394\pi$
$594$	1.41521	−	1.81280i	0.0580669	−	0.0743801i
$595$	−1.55340	+	1.88455i	−0.0636831	+	0.0772589i
$596$	18.4392	−	31.9377i	0.755300	−	1.30822i
$597$	−24.7687	−	10.3404i	−1.01372	−	0.423204i
$598$	1.47030			0.0601252
$599$	−46.9989			−1.92032			−0.960161	−	0.279447i	$-0.909849\pi$
$599$	−46.9989			−1.92032			−0.960161	+	0.279447i	$0.909849\pi$
$600$	−22.1358	+	16.8877i	−0.903690	+	0.689439i
$601$	−7.80843	+	13.5246i	−0.318512	+	0.551680i	−0.980178	−	0.198119i	$-0.936517\pi$
$601$	−7.80843	+	13.5246i	−0.318512	+	0.551680i	0.661665	+	0.749799i	$0.269850\pi$
$602$	12.9119	+	2.16028i	0.526248	+	0.0880463i
$603$	−2.98729	+	0.782646i	−0.121652	+	0.0318718i
$604$	1.31417	+	2.27620i	0.0534727	+	0.0926174i
$605$	−18.8383	−	32.6289i	−0.765885	−	1.32655i
$606$	−1.77514	+	1.35428i	−0.0721100	+	0.0550138i
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	−0.413802	−	0.910367i	$-0.635800\pi$
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	0.995302	−	0.0968200i	$-0.0308671\pi$
$608$	−7.02769	−	12.1723i	−0.285010	−	0.493652i
$609$	0.714701	−	18.9701i	0.0289611	−	0.768707i
$610$	−9.89134	+	17.1323i	−0.400489	+	0.693667i
$611$	−6.08711	−	10.5432i	−0.246258	−	0.426531i
$612$	−0.347543	+	1.26876i	−0.0140486	+	0.0512865i
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	−0.401220	−	0.915982i	$-0.631414\pi$
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	0.993873	−	0.110524i	$-0.0352529\pi$
$614$	1.38593			0.0559316
$615$	3.90755	+	30.3328i	0.157568	+	1.22314i
$616$	−2.79613	+	3.39220i	−0.112659	+	0.136676i
$617$	2.06401	+	3.57497i	0.0830938	+	0.143923i	0.904577	−	0.426310i	$-0.140187\pi$
$617$	2.06401	+	3.57497i	0.0830938	+	0.143923i	−0.821484	+	0.570232i	$0.806853\pi$
$618$	−7.69712	−	3.21338i	−0.309624	−	0.129261i
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	0.542315	−	0.840175i	$-0.317548\pi$
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	−0.998771	+	0.0495708i	$0.984215\pi$
$620$	−11.6109	+	20.1106i	−0.466304	+	0.807662i
$621$	−12.7500	−	1.78698i	−0.511639	−	0.0717090i
$622$	7.48774			0.300231
$623$	4.05128	−	4.91492i	0.162311	−	0.196912i
$624$	4.26017	−	3.25014i	0.170543	−	0.130110i
$625$	−3.19498	+	5.53387i	−0.127799	+	0.221355i
$626$	12.6340			0.504955
$627$	4.00640	+	1.67258i	0.160000	+	0.0667965i
$628$	29.2580			1.16752
$629$	1.18276			0.0471597
$630$	14.4740	−	1.31289i	0.576656	−	0.0523067i
$631$	−38.6411			−1.53828			−0.769138	−	0.639082i	$-0.779314\pi$
$631$	−38.6411			−1.53828			−0.769138	+	0.639082i	$0.779314\pi$
$632$	−3.34915			−0.133222
$633$	2.12590	−	1.62188i	0.0844968	−	0.0644639i
$634$	−16.1261			−0.640449
$635$	−2.34380	+	4.05958i	−0.0930107	+	0.161099i
$636$	−27.7266	−	11.5752i	−1.09943	−	0.458988i
$637$	−7.92076	−	2.72677i	−0.313832	−	0.108038i
$638$	−1.83348			−0.0725881
$639$	14.3516	−	3.76002i	0.567741	−	0.148744i
$640$	20.9427	−	36.2737i	0.827831	−	1.43385i
$641$	14.2363	+	24.6580i	0.562301	+	0.973933i	0.997295	+	0.0735002i	$0.0234169\pi$
$641$	14.2363	+	24.6580i	0.562301	+	0.973933i	−0.434995	+	0.900433i	$0.643250\pi$
$642$	7.44329	−	5.67860i	0.293763	−	0.224116i
$643$	−8.52125	−	14.7592i	−0.336045	−	0.582048i	0.647640	−	0.761947i	$-0.275756\pi$
$643$	−8.52125	−	14.7592i	−0.336045	−	0.582048i	−0.983685	+	0.179899i	$0.942423\pi$
$644$	11.3413	+	1.89751i	0.446911	+	0.0747724i
$645$	50.7400	−	38.7103i	1.99788	−	1.52422i
$646$	0.348110			0.0136962
$647$	1.68809	−	2.92386i	0.0663657	−	0.114949i	−0.830933	−	0.556372i	$-0.812193\pi$
$647$	1.68809	−	2.92386i	0.0663657	−	0.114949i	0.897299	+	0.441423i	$0.145526\pi$
$648$	14.6017	−	8.21493i	0.573608	−	0.322713i
$649$	0.808833	+	1.40094i	0.0317495	+	0.0549917i
$650$	−2.56209	+	4.43768i	−0.100494	+	0.174060i
$651$	14.5273	−	7.67312i	0.569370	−	0.300733i
$652$	5.86110	+	10.1517i	0.229538	+	0.397572i
$653$	9.17255	−	15.8873i	0.358950	−	0.621719i	−0.628836	−	0.777538i	$-0.716468\pi$
$653$	9.17255	−	15.8873i	0.358950	−	0.621719i	0.987786	+	0.155819i	$0.0498017\pi$
$654$	−1.68178	−	0.702107i	−0.0657629	−	0.0274546i
$655$	−27.7477	−	48.0604i	−1.08419	−	1.87787i
$656$	−6.18090	−	10.7056i	−0.241324	−	0.417985i
$657$	1.45083	−	5.29646i	0.0566021	−	0.206635i
$658$	4.67444	+	12.5011i	0.182229	+	0.487345i
$659$	−13.9248	+	24.1184i	−0.542432	+	0.939519i	0.456332	+	0.889810i	$0.349163\pi$
$659$	−13.9248	+	24.1184i	−0.542432	+	0.939519i	−0.998764	+	0.0497098i	$0.984170\pi$
$660$	1.27940	+	9.93152i	0.0498007	+	0.386584i
$661$	39.0141			1.51747			0.758737	−	0.651397i	$-0.225817\pi$
$661$	39.0141			1.51747			0.758737	+	0.651397i	$0.225817\pi$
$662$	−8.97265			−0.348732
$663$	0.0662030	+	0.513909i	0.00257111	+	0.0199586i
$664$	11.4700	−	19.8667i	0.445123	−	0.770976i
$665$	9.60906	+	25.6981i	0.372624	+	0.996529i
$666$	−4.94911	−	5.00452i	−0.191774	−	0.193921i
$667$	5.13203	+	8.88894i	0.198713	+	0.344181i
$668$	−15.4634	−	26.7834i	−0.598296	−	1.03628i
$669$	8.70051	+	3.63227i	0.336381	+	0.140432i
$670$	−0.942405	+	1.63229i	−0.0364083	+	0.0630610i
$671$	4.82170	+	8.35143i	0.186140	+	0.322404i
$672$	−20.2806	+	10.7119i	−0.782341	+	0.413221i
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.201014	−	0.979588i	$-0.435576\pi$
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.747841	−	0.663878i	$-0.231090\pi$
$674$	6.20264	+	10.7433i	0.238917	+	0.413816i
$675$	27.6111	−	35.3681i	1.06275	−	1.36132i
$676$	−10.1457	+	17.5729i	−0.390219	+	0.675879i
$677$	−23.3915			−0.899010			−0.449505	−	0.893278i	$-0.648400\pi$
$677$	−23.3915			−0.899010			−0.449505	+	0.893278i	$0.648400\pi$
$678$	−10.8069	+	8.24471i	−0.415035	+	0.316636i
$679$	28.8196	+	4.82180i	1.10600	+	0.185044i
$680$	0.859180	+	1.48814i	0.0329480	+	0.0570677i
$681$	22.1381	−	16.8895i	0.848333	−	0.647206i
$682$	−0.793387	−	1.37419i	−0.0303803	−	0.0526203i
$683$	−15.1632	+	26.2634i	−0.580204	+	1.00494i	0.415251	+	0.909707i	$0.363694\pi$
$683$	−15.1632	+	26.2634i	−0.580204	+	1.00494i	−0.995455	+	0.0952356i	$0.969640\pi$
$684$	10.3914	+	10.5077i	0.397324	+	0.401772i
$685$	1.80380			0.0689196
$686$	8.07114	+	4.38126i	0.308157	+	0.167277i
$687$	−15.9330	−	6.65169i	−0.607884	−	0.253778i
$688$	−12.8980	+	22.3401i	−0.491733	+	0.851707i
$689$	−11.8346			−0.450863
$690$	−6.24741	+	4.76624i	−0.237835	+	0.181448i
$691$	−4.11330			−0.156477			−0.0782387	−	0.996935i	$-0.524930\pi$
$691$	−4.11330			−0.156477			−0.0782387	+	0.996935i	$0.524930\pi$
$692$	6.81797			0.259180
$693$	2.97354	−	6.43030i	0.112955	−	0.244267i
$694$	−5.33003			−0.202325
$695$	−36.4448			−1.38243
$696$	−12.3258	−	5.14575i	−0.467208	−	0.195049i
$697$	1.19538			0.0452784
$698$	0.814716	−	1.41113i	0.0308375	−	0.0534120i
$699$	22.7778	−	17.3775i	0.861534	−	0.657277i
$700$	−25.4900	+	30.9239i	−0.963432	+	1.16881i
$701$	29.1835			1.10225			0.551123	−	0.834424i	$-0.314200\pi$
$701$	29.1835			1.10225			0.551123	+	0.834424i	$0.314200\pi$
$702$	1.89745	−	2.43051i	0.0716145	−	0.0917338i
$703$	6.64347	−	11.5068i	0.250563	−	0.433988i
$704$	−1.19983	−	2.07816i	−0.0452202	−	0.0783236i
$705$	60.0420	+	25.0662i	2.26131	+	0.944047i
$706$	4.17005	+	7.22274i	0.156942	+	0.271831i
$707$	−4.37478	+	5.30738i	−0.164531	+	0.199605i
$708$	0.703531	+	5.46125i	0.0264403	+	0.205246i
$709$	−42.4617			−1.59468			−0.797342	−	0.603528i	$-0.793761\pi$
$709$	−42.4617			−1.59468			−0.797342	+	0.603528i	$0.793761\pi$
$710$	4.52753	−	7.84192i	0.169915	−	0.294302i
$711$	5.22115	−	1.36790i	0.195809	−	0.0513004i
$712$	−2.24075	−	3.88109i	−0.0839757	−	0.145450i
$713$	−4.44149	+	7.69288i	−0.166335	+	0.288101i
$714$	0.0213862	−	0.567647i	0.000800358	−	0.0212437i
$715$	1.97211	+	3.41579i	0.0737526	+	0.127743i
$716$	−6.43336	+	11.1429i	−0.240426	+	0.416430i
$717$	−30.3282	+	23.1378i	−1.13263	+	0.864097i
$718$	−5.89692	−	10.2138i	−0.220071	−	0.381175i
$719$	−5.57126	−	9.64970i	−0.207773	−	0.359873i	0.743240	−	0.669025i	$-0.233288\pi$
$719$	−5.57126	−	9.64970i	−0.207773	−	0.359873i	−0.951013	+	0.309152i	$0.899955\pi$
$720$	−7.56580	+	27.6201i	−0.281961	+	1.02934i
$721$	−25.3421	−	4.23997i	−0.943789	−	0.157905i
$722$	−2.75544	+	4.77256i	−0.102547	+	0.177616i
$723$	−23.0245	+	17.5657i	−0.856290	+	0.653277i
$724$	−19.7453			−0.733828
$725$	−35.7715			−1.32852
$726$	8.08689	+	3.37609i	0.300132	+	0.125299i
$727$	−14.3410	+	24.8393i	−0.531878	+	0.921239i	0.467430	+	0.884030i	$0.345180\pi$
$727$	−14.3410	+	24.8393i	−0.531878	+	0.921239i	−0.999308	+	0.0372089i	$0.988153\pi$
$728$	−3.74892	+	4.54810i	−0.138944	+	0.168564i
$729$	−19.4080	+	18.7704i	−0.718815	+	0.695202i
$730$	−1.67588	−	2.90270i	−0.0620269	−	0.107434i
$731$	−1.24724	−	2.16028i	−0.0461307	−	0.0799007i
$732$	4.19396	+	32.5562i	0.155013	+	1.20331i
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	−0.536419	−	0.843952i	$-0.680223\pi$
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	0.999093	+	0.0425768i	$0.0135567\pi$
$734$	−0.171071	−	0.296303i	−0.00631433	−	0.0109367i
$735$	42.4950	−	14.0903i	1.56745	−	0.519729i
$736$	6.20047	−	10.7395i	0.228552	−	0.395864i
$737$	0.459391	+	0.795689i	0.0169219	+	0.0293096i
$738$	−5.00194	−	5.05793i	−0.184124	−	0.186185i
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	−0.493776	−	0.869589i	$-0.664384\pi$
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	0.999974	−	0.00717223i	$-0.00228301\pi$
$740$	30.6460			1.12657
$741$	5.37158	+	2.24252i	0.197330	+	0.0823809i
$742$	12.7963	+	2.14095i	0.469768	+	0.0785967i
$743$	−7.00608	−	12.1349i	−0.257028	−	0.445186i	0.708416	−	0.705795i	$-0.249410\pi$
$743$	−7.00608	−	12.1349i	−0.257028	−	0.445186i	−0.965444	+	0.260609i	$0.916077\pi$
$744$	−1.47693	−	11.4648i	−0.0541467	−	0.420321i
$745$	38.8163	+	67.2318i	1.42212	+	2.46318i
$746$	−0.932261	+	1.61472i	−0.0341325	+	0.0591192i
$747$	−9.76698	+	35.6558i	−0.357355	+	1.30458i
$748$	0.391390			0.0143106
$749$	18.3438	−	22.2543i	0.670268	−	0.813153i
$750$	−1.47297	−	11.4342i	−0.0537854	−	0.417516i
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.215692	−	0.976461i	$-0.430799\pi$
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.737795	−	0.675025i	$-0.235867\pi$
$752$	−26.2989			−0.959021
$753$	1.88789	+	14.6550i	0.0687986	+	0.534058i
$754$	−2.45824			−0.0895237
$755$	−5.53289			−0.201363
$756$	17.7728	−	16.2992i	0.646392	−	0.592796i
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$	−16.3009			−0.592077
$759$	0.489408	+	3.79909i	0.0177644	+	0.137898i
$760$	19.3038			0.700223
$761$	8.62550	−	14.9398i	0.312674	−	0.541568i	−0.666266	−	0.745714i	$-0.732109\pi$
$761$	8.62550	−	14.9398i	0.312674	−	0.541568i	0.978940	+	0.204146i	$0.0654419\pi$
$762$	−0.139304	−	1.08137i	−0.00504646	−	0.0391738i
$763$	−5.53713	−	0.926414i	−0.200457	−	0.0335384i
$764$	41.8285			1.51330
$765$	−1.94722	−	1.96902i	−0.0704020	−	0.0711901i
$766$	−0.265952	+	0.460642i	−0.00960922	+	0.0166437i
$767$	1.08444	+	1.87831i	0.0391570	+	0.0678218i
$768$	0.0548204	+	0.425550i	0.00197816	+	0.0153557i
$769$	−10.6727	−	18.4856i	−0.384867	−	0.666609i	0.606884	−	0.794790i	$-0.292419\pi$
$769$	−10.6727	−	18.4856i	−0.384867	−	0.666609i	−0.991751	+	0.128182i	$0.959086\pi$
$770$	−1.51443	−	4.05013i	−0.0545763	−	0.145957i
$771$	−27.3634	−	11.4236i	−0.985469	−	0.411411i
$772$	−10.4099			−0.374660
$773$	−6.57357	+	11.3858i	−0.236435	+	0.409517i	−0.959689	−	0.281065i	$-0.909312\pi$
$773$	−6.57357	+	11.3858i	−0.236435	+	0.409517i	0.723254	+	0.690582i	$0.242646\pi$
$774$	−3.92170	+	14.3168i	−0.140963	+	0.514605i
$775$	−15.4791	−	26.8106i	−0.556027	−	0.963066i
$776$	10.2796	−	17.8049i	0.369018	−	0.639158i
$777$	−18.3555	−	11.5401i	−0.658501	−	0.414000i
$778$	−5.88685	−	10.1963i	−0.211054	−	0.365556i
$779$	6.71439	−	11.6297i	0.240568	−	0.416676i
$780$	1.71536	+	13.3157i	0.0614197	+	0.476778i
$781$	−2.20702	−	3.82268i	−0.0789735	−	0.136786i
$782$	0.153567	+	0.265986i	0.00549155	+	0.00951164i
$783$	21.3170	+	2.98769i	0.761807	+	0.106771i
$784$	−13.6565	+	11.8729i	−0.487732	+	0.424034i
$785$	−30.7954	+	53.3393i	−1.09914	+	1.90376i
$786$	11.9115	+	4.97279i	0.424869	+	0.177373i
$787$	−28.1301			−1.00273			−0.501364	−	0.865236i	$-0.667168\pi$
$787$	−28.1301			−1.00273			−0.501364	+	0.865236i	$0.667168\pi$
$788$	27.1330			0.966573
$789$	−28.3022	+	21.5922i	−1.00758	+	0.768701i
$790$	1.64713	−	2.85291i	0.0586021	−	0.101502i
$791$	−26.6332	+	32.3108i	−0.946968	+	1.14884i
$792$	−3.50502	−	3.54426i	−0.124546	−	0.125940i
$793$	6.46470	+	11.1972i	0.229568	+	0.397624i
$794$	0.00795814	+	0.0137839i	0.000282424	+	0.000489172i
$795$	50.2860	−	38.3639i	1.78346	−	1.36063i
$796$	−13.5912	+	23.5406i	−0.481727	+	0.834376i
$797$	12.8683	+	22.2885i	0.455817	+	0.789499i	0.998735	−	0.0502873i	$-0.0160137\pi$
$797$	12.8683	+	22.2885i	0.455817	+	0.789499i	−0.542917	+	0.839786i	$0.682680\pi$
$798$	−5.40241	−	3.39650i	−0.191243	−	0.120235i
$799$	1.27155	−	2.20238i	0.0449841	−	0.0779147i
$800$	21.6094	+	37.4285i	0.764007	+	1.32330i
$801$	5.07838	+	5.13523i	0.179436	+	0.181444i
$802$	6.08073	−	10.5321i	0.214718	−	0.371902i
$803$	−1.63387			−0.0576580
$804$	0.399583	+	3.10181i	0.0140922	+	0.109393i
$805$	−15.3966	+	18.6788i	−0.542658	+	0.658340i
$806$	−1.06373	−	1.84244i	−0.0374684	−	0.0648972i
$807$	−31.7199	−	13.2423i	−1.11659	−	0.466153i
$808$	2.41968	+	4.19100i	0.0851240	+	0.147439i
$809$	15.9353	−	27.6007i	0.560254	−	0.970388i	−0.437220	−	0.899355i	$-0.644037\pi$
$809$	15.9353	−	27.6007i	0.560254	−	0.970388i	0.997474	−	0.0710338i	$-0.0226298\pi$
$810$	−0.183441	+	16.4783i	−0.00644544	+	0.578988i
$811$	43.3860			1.52349			0.761744	−	0.647878i	$-0.224343\pi$
$811$	43.3860			1.52349			0.761744	+	0.647878i	$0.224343\pi$
$812$	−18.9618	−	3.17249i	−0.665429	−	0.111333i
$813$	14.6534	−	11.1793i	0.513918	−	0.392076i
$814$	−1.04704	+	1.81353i	−0.0366987	+	0.0635641i
$815$	−24.6764			−0.864375
$816$	1.03293	+	0.431223i	0.0361596	+	0.0150958i
$817$	−28.0226			−0.980385
$818$	−13.2842			−0.464470
$819$	3.98677	−	8.62143i	0.139309	−	0.301257i
$820$	30.9731			1.08163
$821$	−16.3935			−0.572139			−0.286069	−	0.958209i	$-0.592349\pi$
$821$	−16.3935			−0.572139			−0.286069	+	0.958209i	$0.592349\pi$
$822$	−0.333562	+	0.254479i	−0.0116343	+	0.00887598i
$823$	−26.3780			−0.919478			−0.459739	−	0.888054i	$-0.652057\pi$
$823$	−26.3780			−0.919478			−0.459739	+	0.888054i	$0.652057\pi$
$824$	−9.03925	+	15.6564i	−0.314897	+	0.545418i
$825$	−12.3193	−	5.14301i	−0.428901	−	0.179057i
$826$	−0.832771	−	2.22713i	−0.0289758	−	0.0774917i
$827$	36.7225			1.27697			0.638484	−	0.769635i	$-0.279562\pi$
$827$	36.7225			1.27697			0.638484	+	0.769635i	$0.279562\pi$
$828$	−3.44468	+	12.5753i	−0.119711	+	0.437023i
$829$	12.1579	−	21.0581i	0.422261	−	0.731377i	−0.573899	−	0.818926i	$-0.694570\pi$
$829$	12.1579	−	21.0581i	0.422261	−	0.731377i	0.996160	+	0.0875485i	$0.0279033\pi$
$830$	11.2820	+	19.5410i	0.391604	+	0.678279i
$831$	34.2630	−	26.1398i	1.18857	−	0.906779i
$832$	−1.60867	−	2.78629i	−0.0557705	−	0.0965974i
$833$	−0.334004	−	1.71771i	−0.0115725	−	0.0595151i
$834$	6.73944	−	5.14162i	0.233368	−	0.178040i
$835$	65.1038			2.25301
$836$	2.19841	−	3.80776i	0.0760337	−	0.131694i
$837$	6.98506	+	17.2698i	0.241439	+	0.596933i
$838$	5.21962	+	9.04065i	0.180309	+	0.312304i
$839$	−12.8405	+	22.2404i	−0.443303	+	0.767824i	−0.997932	−	0.0642741i	$-0.979527\pi$
$839$	−12.8405	+	22.2404i	−0.443303	+	0.767824i	0.554629	+	0.832098i	$0.312860\pi$
$840$	1.18593	−	31.4779i	0.0409186	−	1.08609i
$841$	5.91963	+	10.2531i	0.204125	+	0.353555i
$842$	3.69190	−	6.39456i	0.127231	−	0.220371i
$843$	21.8570	+	9.12480i	0.752794	+	0.314275i
$844$	−1.35400	−	2.34519i	−0.0466065	−	0.0807249i
$845$	−21.3577	−	36.9926i	−0.734726	−	1.27258i
$846$	−14.6394	+	3.83542i	−0.503313	+	0.131864i
$847$	26.6254	+	4.45468i	0.914859	+	0.153065i
$848$	−12.7826	+	22.1402i	−0.438958	+	0.760297i
$849$	−1.39900	−	10.8599i	−0.0480135	−	0.372711i
$850$	−1.07040			−0.0367144
$851$	11.7230			0.401858
$852$	−1.91969	−	14.9018i	−0.0657675	−	0.510529i
$853$	14.4872	−	25.0925i	0.496031	−	0.859150i	−0.503959	−	0.863728i	$-0.668124\pi$
$853$	14.4872	−	25.0925i	0.496031	−	0.859150i	0.999990	+	0.00457743i	$0.00145705\pi$
$854$	−4.96440	−	13.2766i	−0.169878	−	0.454316i
$855$	−30.0937	+	7.88431i	−1.02918	+	0.269638i
$856$	−10.1459	−	17.5732i	−0.346780	−	0.600640i
$857$	12.6934	+	21.9856i	0.433598	+	0.751015i	0.997180	−	0.0750458i	$-0.0239103\pi$
$857$	12.6934	+	21.9856i	0.433598	+	0.751015i	−0.563582	+	0.826060i	$0.690577\pi$
$858$	−0.846585	−	0.353430i	−0.0289019	−	0.0120659i
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	−0.810721	−	0.585433i	$-0.800925\pi$
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	0.912360	+	0.409388i	$0.134258\pi$
$860$	−32.3166	−	55.9740i	−1.10199	−	1.90870i
$861$	−18.5515	−	11.6633i	−0.632232	−	0.397485i
$862$	3.94310	−	6.82966i	0.134303	−	0.232619i
$863$	8.19545	+	14.1949i	0.278977	+	0.483201i	0.971131	−	0.238548i	$-0.0766715\pi$
$863$	8.19545	+	14.1949i	0.278977	+	0.483201i	−0.692154	+	0.721750i	$0.743338\pi$
$864$	−9.75138	−	24.1093i	−0.331749	−	0.820214i
$865$	−7.17624	+	12.4296i	−0.244000	+	0.422620i
$866$	8.11528			0.275768
$867$	23.3239	−	17.7942i	0.792122	−	0.604322i
$868$	−5.82743	−	15.5846i	−0.197796	−	0.528977i
$869$	−0.802920	−	1.39070i	−0.0272372	−	0.0471762i
$870$	10.4452	−	7.96879i	0.354125	−	0.270167i
$871$	0.615929	+	1.06682i	0.0208700	+	0.0361478i
$872$	−1.97503	+	3.42086i	−0.0668830	+	0.115845i
$873$	−8.75335	+	31.9554i	−0.296256	+	1.08153i
$874$	3.45030			0.116708
$875$	−12.4384	−	33.2646i	−0.420493	−	1.12455i
$876$	−5.13224	−	2.14260i	−0.173402	−	0.0723916i
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	0.398295	+	0.917257i	$0.369602\pi$
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	−0.993516	+	0.113695i	$0.963731\pi$
$878$	7.70813			0.260137
$879$	−3.62188	+	2.76318i	−0.122163	+	0.0931998i
$880$	8.52033			0.287220
$881$	26.2582			0.884661			0.442331	−	0.896852i	$-0.354152\pi$
$881$	26.2582			0.884661			0.442331	+	0.896852i	$0.354152\pi$
$882$	−5.87041	+	8.60080i	−0.197667	+	0.289604i
$883$	10.0087			0.336821			0.168410	−	0.985717i	$-0.446137\pi$
$883$	10.0087			0.336821			0.168410	+	0.985717i	$0.446137\pi$
$884$	0.524756			0.0176495
$885$	−10.6967	−	4.46564i	−0.359566	−	0.150111i
$886$	−0.887631			−0.0298205
$887$	7.95282	−	13.7747i	0.267030	−	0.462509i	−0.701064	−	0.713099i	$-0.747291\pi$
$887$	7.95282	−	13.7747i	0.267030	−	0.462509i	0.968093	+	0.250590i	$0.0806245\pi$
$888$	−12.1286	+	9.25311i	−0.407010	+	0.310514i
$889$	−1.17634	−	3.14595i	−0.0394531	−	0.105512i
$890$	4.40804			0.147758
$891$	6.91174	+	4.09375i	0.231552	+	0.137146i
$892$	4.77419	−	8.26914i	0.159852	−	0.276871i
$893$	−14.2844	−	24.7413i	−0.478009	−	0.827935i
$894$	−16.6630	−	6.95645i	−0.557295	−	0.232658i
$895$	−13.5428	−	23.4569i	−0.452687	−	0.784077i
$896$	10.5110	+	28.1102i	0.351148	+	0.939095i
$897$	0.656173	+	5.09363i	0.0219090	+	0.170071i
$898$	−6.72727			−0.224492
$899$	7.42583	−	12.8619i	0.247665	−	0.428969i
$900$	−31.9524	−	32.3100i	−1.06508	−	1.07700i
$901$	−1.23608	−	2.14095i	−0.0411797	−	0.0713253i
$902$	−1.05822	+	1.83288i	−0.0352348	+	0.0610284i
$903$	−1.72157	+	45.6951i	−0.0572903	+	1.52064i
$904$	14.7307	+	25.5144i	0.489937	+	0.848597i
$905$	20.7829	−	35.9970i	0.690846	−	1.19658i
$906$	1.02315	−	0.780579i	0.0339920	−	0.0259330i
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	0.972311	−	0.233691i	$-0.0750804\pi$
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$908$	−14.0999	−	24.4217i	−0.467922	−	0.810464i
$909$	−5.48390	−	5.54528i	−0.181889	−	0.183925i
$910$	−2.03047	−	5.43021i	−0.0673095	−	0.180010i
$911$	14.9435	−	25.8829i	0.495099	−	0.857537i	−0.504885	−	0.863187i	$-0.668465\pi$
$911$	14.9435	−	25.8829i	0.495099	−	0.857537i	0.999984	+	0.00564955i	$0.00179832\pi$
$912$	9.99717	−	7.62699i	0.331039	−	0.252555i
$913$	10.9992			0.364021
$914$	−1.27397			−0.0421393
$915$	−63.7664	−	26.6211i	−2.10805	−	0.880065i
$916$	−8.74286	+	15.1431i	−0.288872	+	0.500341i
$917$	39.2176	+	6.56148i	1.29508	+	0.216679i
$918$	0.637873	+	0.0894015i	0.0210530	+	0.00295069i
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	0.992473	−	0.122462i	$-0.0390791\pi$
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	−0.602292	+	0.798276i	$0.705746\pi$
$920$	8.51579	+	14.7498i	0.280757	+	0.486286i
$921$	0.618519	+	4.80133i	0.0203809	+	0.158209i
$922$	−8.97196	+	15.5399i	−0.295476	+	0.511779i
$923$	−2.95907	−	5.12525i	−0.0973989	−	0.168700i
$924$	−6.07408	−	3.81878i	−0.199823	−	0.125629i
$925$	−20.4280	+	35.3823i	−0.671667	+	1.16336i
$926$	−4.06227	−	7.03606i	−0.133495	−	0.231219i
$927$	7.69712	−	28.0995i	0.252807	−	0.922909i
$928$	−10.3667	+	17.9557i	−0.340304	+	0.589423i
$929$	12.6176			0.413970			0.206985	−	0.978344i	$-0.433635\pi$
$929$	12.6176			0.413970			0.206985	+	0.978344i	$0.433635\pi$
$930$	10.4924	+	4.38036i	0.344061	+	0.143638i
$931$	−18.5873	−	6.39880i	−0.609176	−	0.209712i
$932$	−14.5073	−	25.1274i	−0.475203	−	0.823075i
$933$	3.34166	+	25.9401i	0.109401	+	0.849240i
$934$	2.15714	+	3.73627i	0.0705836	+	0.122254i
$935$	−0.411957	+	0.713530i	−0.0134724	+	0.0233349i
$936$	−4.69936	−	4.75196i	−0.153603	−	0.155323i
$937$	−26.3440			−0.860622			−0.430311	−	0.902681i	$-0.641596\pi$
$937$	−26.3440			−0.860622			−0.430311	+	0.902681i	$0.641596\pi$
$938$	−0.472987	−	1.26494i	−0.0154436	−	0.0413017i
$939$	5.63834	+	43.7683i	0.184000	+	1.42833i
$940$	32.9465	−	57.0651i	1.07460	−	1.86126i
$941$	50.9397			1.66059			0.830294	−	0.557326i	$-0.188173\pi$
$941$	50.9397			1.66059			0.830294	+	0.557326i	$0.188173\pi$
$942$	−1.83034	−	14.2082i	−0.0596356	−	0.462929i
$943$	11.8481			0.385827
$944$	4.68525			0.152492
$945$	11.0078	+	49.5567i	0.358083	+	1.61208i
$946$	4.41648			0.143592
$947$	27.6798			0.899474			0.449737	−	0.893161i	$-0.351518\pi$
$947$	27.6798			0.899474			0.449737	+	0.893161i	$0.351518\pi$
$948$	−0.698388	−	5.42133i	−0.0226826	−	0.176076i
$949$	−2.19061			−0.0711102
$950$	−6.01236	+	10.4137i	−0.195067	+	0.337866i
$951$	−7.19682	−	55.8662i	−0.233373	−	1.81159i
$952$	−1.21433	−	0.203170i	−0.0393568	−	0.00658477i
$953$	−27.4017			−0.887628			−0.443814	−	0.896119i	$-0.646375\pi$
$953$	−27.4017			−0.887628			−0.443814	+	0.896119i	$0.646375\pi$
$954$	−3.88661	+	14.1887i	−0.125834	+	0.459375i
$955$	−44.0265	+	76.2561i	−1.42466	+	2.46759i
$956$	19.3162	+	33.4567i	0.624731	+	1.08207i
$957$	−0.818252	−	6.35179i	−0.0264503	−	0.205324i
$958$	−4.40515	−	7.62994i	−0.142324	−	0.246512i
$959$	−0.822054	+	0.997297i	−0.0265455	+	0.0322044i
$960$	15.8676	+	6.62436i	0.512123	+	0.213800i
$961$	−18.1467			−0.585378
$962$	−1.40382	+	2.43149i	−0.0452610	+	0.0783943i
$963$	22.9944	+	23.2518i	0.740984	+	0.749279i
$964$	14.6645	+	25.3996i	0.472310	+	0.818066i
$965$	10.9569	−	18.9779i	0.352715	−	0.610921i
$966$	0.211970	−	5.62626i	0.00682002	−	0.181022i
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	0.974362	−	0.224986i	$-0.0722338\pi$
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	−0.682025	+	0.731329i	$0.738900\pi$
$968$	9.49698	−	16.4492i	0.305244	−	0.528699i
$969$	0.155356	+	1.20597i	0.00499075	+	0.0387413i
$970$	10.1111	+	17.5130i	0.324649	+	0.562309i
$971$	19.7416	+	34.1935i	0.633538	+	1.09732i	0.986823	+	0.161804i	$0.0517313\pi$
$971$	19.7416	+	34.1935i	0.633538	+	1.09732i	−0.353285	+	0.935516i	$0.614935\pi$
$972$	16.3425	+	21.9229i	0.524185	+	0.703178i
$973$	16.6092	−	20.1499i	0.532466	−	0.645975i
$974$	−4.12941	+	7.15234i	−0.132315	+	0.229176i
$975$	−16.5170	−	6.89549i	−0.528968	−	0.220833i
$976$	27.9302			0.894024
$977$	11.9156			0.381215			0.190608	−	0.981666i	$-0.438954\pi$
$977$	11.9156			0.381215			0.190608	+	0.981666i	$0.438954\pi$
$978$	4.56320	−	3.48133i	0.145915	−	0.111321i
$979$	1.07439	−	1.86090i	0.0343376	−	0.0594745i
$980$	−8.65423	−	44.5069i	−0.276449	−	1.42172i
$981$	1.68178	−	6.13961i	0.0536952	−	0.196023i
$982$	1.59184	+	2.75715i	0.0507977	+	0.0879842i
$983$	9.23896	+	16.0024i	0.294677	+	0.510396i	0.974910	−	0.222601i	$-0.0714546\pi$
$983$	9.23896	+	16.0024i	0.294677	+	0.510396i	−0.680233	+	0.732996i	$0.738121\pi$
$984$	−12.2581	+	9.35187i	−0.390773	+	0.298127i
$985$	−28.5588	+	49.4653i	−0.909959	+	1.57609i
$986$	−0.256752	−	0.444708i	−0.00817666	−	0.0141624i
$987$	−41.2220	+	21.7729i	−1.31211	+	0.693039i
$988$	2.94752	−	5.10525i	0.0937731	−	0.162420i
$989$	−12.3620	−	21.4117i	−0.393090	−	0.680851i
$990$	4.74289	−	1.24260i	0.150739	−	0.0394925i
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	−0.949066	−	0.315079i	$-0.897969\pi$
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	0.747399	+	0.664376i	$0.231302\pi$
$992$	−17.9436			−0.569710
$993$	−4.00435	−	31.0843i	−0.127074	−	0.986430i
$994$	2.27234	+	6.07706i	0.0720743	+	0.192752i
$995$	−28.6108	−	49.5553i	−0.907023	−	1.57101i
$996$	34.5503	+	14.4240i	1.09477	+	0.457041i
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	−0.979464	−	0.201617i	$-0.935380\pi$
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	0.315127	−	0.949050i	$-0.397953\pi$
$998$	2.76345	−	4.78644i	0.0874755	−	0.151512i
$999$	15.1286	−	19.3788i	0.478648	−	0.613119i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.h.b.25.3	yes	10
3.2	odd	2		189.2.h.b.46.3		10
4.3	odd	2		1008.2.q.i.529.3		10
7.2	even	3		63.2.g.b.16.3	yes	10
7.3	odd	6		441.2.f.f.295.3		10
7.4	even	3		441.2.f.e.295.3		10
7.5	odd	6		441.2.g.f.79.3		10
7.6	odd	2		441.2.h.f.214.3		10
9.2	odd	6		567.2.e.e.487.3		10
9.4	even	3		63.2.g.b.4.3	✓	10
9.5	odd	6		189.2.g.b.172.3		10
9.7	even	3		567.2.e.f.487.3		10
12.11	even	2		3024.2.q.i.2881.1		10
21.2	odd	6		189.2.g.b.100.3		10
21.5	even	6		1323.2.g.f.667.3		10
21.11	odd	6		1323.2.f.e.883.3		10
21.17	even	6		1323.2.f.f.883.3		10
21.20	even	2		1323.2.h.f.802.3		10
28.23	odd	6		1008.2.t.i.961.1		10
36.23	even	6		3024.2.t.i.1873.5		10
36.31	odd	6		1008.2.t.i.193.1		10
63.2	odd	6		567.2.e.e.163.3		10
63.4	even	3		441.2.f.e.148.3		10
63.5	even	6		1323.2.h.f.226.3		10
63.11	odd	6		3969.2.a.bc.1.3		5
63.13	odd	6		441.2.g.f.67.3		10
63.16	even	3		567.2.e.f.163.3		10
63.23	odd	6		189.2.h.b.37.3		10
63.25	even	3		3969.2.a.z.1.3		5
63.31	odd	6		441.2.f.f.148.3		10
63.32	odd	6		1323.2.f.e.442.3		10
63.38	even	6		3969.2.a.bb.1.3		5
63.40	odd	6		441.2.h.f.373.3		10
63.41	even	6		1323.2.g.f.361.3		10
63.52	odd	6		3969.2.a.ba.1.3		5
63.58	even	3	inner	63.2.h.b.58.3	yes	10
63.59	even	6		1323.2.f.f.442.3		10
84.23	even	6		3024.2.t.i.289.5		10
252.23	even	6		3024.2.q.i.2305.1		10
252.247	odd	6		1008.2.q.i.625.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	9.4	even	3
63.2.g.b.16.3	yes	10	7.2	even	3
63.2.h.b.25.3	yes	10	1.1	even	1	trivial
63.2.h.b.58.3	yes	10	63.58	even	3	inner
189.2.g.b.100.3		10	21.2	odd	6
189.2.g.b.172.3		10	9.5	odd	6
189.2.h.b.37.3		10	63.23	odd	6
189.2.h.b.46.3		10	3.2	odd	2
441.2.f.e.148.3		10	63.4	even	3
441.2.f.e.295.3		10	7.4	even	3
441.2.f.f.148.3		10	63.31	odd	6
441.2.f.f.295.3		10	7.3	odd	6
441.2.g.f.67.3		10	63.13	odd	6
441.2.g.f.79.3		10	7.5	odd	6
441.2.h.f.214.3		10	7.6	odd	2
441.2.h.f.373.3		10	63.40	odd	6
567.2.e.e.163.3		10	63.2	odd	6
567.2.e.e.487.3		10	9.2	odd	6
567.2.e.f.163.3		10	63.16	even	3
567.2.e.f.487.3		10	9.7	even	3
1008.2.q.i.529.3		10	4.3	odd	2
1008.2.q.i.625.3		10	252.247	odd	6
1008.2.t.i.193.1		10	36.31	odd	6
1008.2.t.i.961.1		10	28.23	odd	6
1323.2.f.e.442.3		10	63.32	odd	6
1323.2.f.e.883.3		10	21.11	odd	6
1323.2.f.f.442.3		10	63.59	even	6
1323.2.f.f.883.3		10	21.17	even	6
1323.2.g.f.361.3		10	63.41	even	6
1323.2.g.f.667.3		10	21.5	even	6
1323.2.h.f.226.3		10	63.5	even	6
1323.2.h.f.802.3		10	21.20	even	2
3024.2.q.i.2305.1		10	252.23	even	6
3024.2.q.i.2881.1		10	12.11	even	2
3024.2.t.i.289.5		10	84.23	even	6
3024.2.t.i.1873.5		10	36.23	even	6
3969.2.a.z.1.3		5	63.25	even	3
3969.2.a.ba.1.3		5	63.52	odd	6
3969.2.a.bb.1.3		5	63.38	even	6
3969.2.a.bc.1.3		5	63.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	63.2.h.b.25.3

Level	$63$
Weight	$2$
Character	63.25
Analytic conductor	$0.503$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$