LMFDB - Embedded newform 155.2.h.b.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(16,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("155.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	155.101
Dual form			155.2.h.b.66.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.199171 - 0.612984i) q^{2} +(0.903105 + 2.77947i) q^{3} +(1.28195 + 0.931393i) q^{4} -1.00000 q^{5} +1.88364 q^{6} +(-2.42006 - 1.75828i) q^{7} +(1.86913 - 1.35800i) q^{8} +(-4.48281 + 3.25695i) q^{9} +O(q^{10})$	\(q+(0.199171 - 0.612984i) q^{2} +(0.903105 + 2.77947i) q^{3} +(1.28195 + 0.931393i) q^{4} -1.00000 q^{5} +1.88364 q^{6} +(-2.42006 - 1.75828i) q^{7} +(1.86913 - 1.35800i) q^{8} +(-4.48281 + 3.25695i) q^{9} +(-0.199171 + 0.612984i) q^{10} +(1.90509 + 1.38413i) q^{11} +(-1.43104 + 4.40430i) q^{12} +(-1.23340 - 3.79601i) q^{13} +(-1.55980 + 1.13326i) q^{14} +(-0.903105 - 2.77947i) q^{15} +(0.519167 + 1.59783i) q^{16} +(3.75673 - 2.72942i) q^{17} +(1.10362 + 3.39658i) q^{18} +(-0.650565 + 2.00223i) q^{19} +(-1.28195 - 0.931393i) q^{20} +(2.70151 - 8.31440i) q^{21} +(1.22789 - 0.892112i) q^{22} +(5.47953 - 3.98111i) q^{23} +(5.46254 + 3.96877i) q^{24} +1.00000 q^{25} -2.57255 q^{26} +(-6.00797 - 4.36505i) q^{27} +(-1.46476 - 4.50806i) q^{28} +(0.590849 - 1.81845i) q^{29} -1.88364 q^{30} +(-4.67270 + 3.02752i) q^{31} +5.70359 q^{32} +(-2.12665 + 6.54515i) q^{33} +(-0.924864 - 2.84644i) q^{34} +(2.42006 + 1.75828i) q^{35} -8.78026 q^{36} -11.5679 q^{37} +(1.09776 + 0.797573i) q^{38} +(9.43701 - 6.85639i) q^{39} +(-1.86913 + 1.35800i) q^{40} +(0.365283 - 1.12423i) q^{41} +(-4.55853 - 3.31197i) q^{42} +(-2.39794 + 7.38010i) q^{43} +(1.15307 + 3.54877i) q^{44} +(4.48281 - 3.25695i) q^{45} +(-1.34900 - 4.15179i) q^{46} +(-2.02939 - 6.24581i) q^{47} +(-3.97226 + 2.88602i) q^{48} +(0.602037 + 1.85288i) q^{49} +(0.199171 - 0.612984i) q^{50} +(10.9791 + 7.97677i) q^{51} +(1.95442 - 6.01508i) q^{52} +(-9.96708 + 7.24151i) q^{53} +(-3.87232 + 2.81340i) q^{54} +(-1.90509 - 1.38413i) q^{55} -6.91115 q^{56} -6.15268 q^{57} +(-0.997000 - 0.724363i) q^{58} +(-1.83984 - 5.66244i) q^{59} +(1.43104 - 4.40430i) q^{60} +1.16661 q^{61} +(0.925156 + 3.46729i) q^{62} +16.5753 q^{63} +(0.0976541 - 0.300548i) q^{64} +(1.23340 + 3.79601i) q^{65} +(3.58851 + 2.60720i) q^{66} +10.1763 q^{67} +7.35812 q^{68} +(16.0140 + 11.6348i) q^{69} +(1.55980 - 1.13326i) q^{70} +(2.05962 - 1.49640i) q^{71} +(-3.95600 + 12.1753i) q^{72} +(-10.1930 - 7.40561i) q^{73} +(-2.30398 + 7.09091i) q^{74} +(0.903105 + 2.77947i) q^{75} +(-2.69886 + 1.96084i) q^{76} +(-2.17675 - 6.69934i) q^{77} +(-2.32328 - 7.15033i) q^{78} +(9.51120 - 6.91029i) q^{79} +(-0.519167 - 1.59783i) q^{80} +(1.56985 - 4.83151i) q^{81} +(-0.616380 - 0.447826i) q^{82} +(-1.39610 + 4.29676i) q^{83} +(11.2072 - 8.14250i) q^{84} +(-3.75673 + 2.72942i) q^{85} +(4.04629 + 2.93980i) q^{86} +5.58792 q^{87} +5.44050 q^{88} +(0.306544 + 0.222718i) q^{89} +(-1.10362 - 3.39658i) q^{90} +(-3.68954 + 11.3552i) q^{91} +10.7325 q^{92} +(-12.6348 - 10.2535i) q^{93} -4.23278 q^{94} +(0.650565 - 2.00223i) q^{95} +(5.15094 + 15.8530i) q^{96} +(1.11300 + 0.808645i) q^{97} +1.25569 q^{98} -13.0482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} + 18 q^{12} - 5 q^{13} + 6 q^{14} - 24 q^{16} + 7 q^{17} - 18 q^{18} + 2 q^{19} + 6 q^{20} - 10 q^{21} + 28 q^{22} - 15 q^{23} - 32 q^{24} + 24 q^{25} + 22 q^{26} + 9 q^{27} + 38 q^{28} + 15 q^{29} + 16 q^{30} + 6 q^{31} + 74 q^{32} + 5 q^{33} - 20 q^{34} + 9 q^{35} - 58 q^{36} - 56 q^{37} - 21 q^{38} - 10 q^{39} - 11 q^{40} - 24 q^{41} - 38 q^{42} + 21 q^{43} + 41 q^{44} + 6 q^{45} + 48 q^{46} - 8 q^{47} - 26 q^{48} - 23 q^{49} + 2 q^{50} + 26 q^{51} - 27 q^{52} + 26 q^{53} + 11 q^{54} - q^{55} - 48 q^{56} + 62 q^{57} + 52 q^{58} + 10 q^{59} - 18 q^{60} - 40 q^{61} - 28 q^{62} + 26 q^{63} + 9 q^{64} + 5 q^{65} - 2 q^{66} - 26 q^{67} - 8 q^{68} + 64 q^{69} - 6 q^{70} - 7 q^{71} - 127 q^{72} - 51 q^{73} - q^{74} + 43 q^{76} - 39 q^{77} - 31 q^{78} + 31 q^{79} + 24 q^{80} + 34 q^{81} + 58 q^{82} + 6 q^{83} + 113 q^{84} - 7 q^{85} - 22 q^{86} + 4 q^{87} - 28 q^{88} + 13 q^{89} + 18 q^{90} + 54 q^{91} - 2 q^{92} - 72 q^{93} - 10 q^{94} - 2 q^{95} + 101 q^{96} - 39 q^{97} - 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9 - 2 * q^10 + q^11 + 18 * q^12 - 5 * q^13 + 6 * q^14 - 24 * q^16 + 7 * q^17 - 18 * q^18 + 2 * q^19 + 6 * q^20 - 10 * q^21 + 28 * q^22 - 15 * q^23 - 32 * q^24 + 24 * q^25 + 22 * q^26 + 9 * q^27 + 38 * q^28 + 15 * q^29 + 16 * q^30 + 6 * q^31 + 74 * q^32 + 5 * q^33 - 20 * q^34 + 9 * q^35 - 58 * q^36 - 56 * q^37 - 21 * q^38 - 10 * q^39 - 11 * q^40 - 24 * q^41 - 38 * q^42 + 21 * q^43 + 41 * q^44 + 6 * q^45 + 48 * q^46 - 8 * q^47 - 26 * q^48 - 23 * q^49 + 2 * q^50 + 26 * q^51 - 27 * q^52 + 26 * q^53 + 11 * q^54 - q^55 - 48 * q^56 + 62 * q^57 + 52 * q^58 + 10 * q^59 - 18 * q^60 - 40 * q^61 - 28 * q^62 + 26 * q^63 + 9 * q^64 + 5 * q^65 - 2 * q^66 - 26 * q^67 - 8 * q^68 + 64 * q^69 - 6 * q^70 - 7 * q^71 - 127 * q^72 - 51 * q^73 - q^74 + 43 * q^76 - 39 * q^77 - 31 * q^78 + 31 * q^79 + 24 * q^80 + 34 * q^81 + 58 * q^82 + 6 * q^83 + 113 * q^84 - 7 * q^85 - 22 * q^86 + 4 * q^87 - 28 * q^88 + 13 * q^89 + 18 * q^90 + 54 * q^91 - 2 * q^92 - 72 * q^93 - 10 * q^94 - 2 * q^95 + 101 * q^96 - 39 * q^97 - 220 * q^98 - 170 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.199171	−	0.612984i	0.140835	−	0.433445i	−0.855617	−	0.517610i	$-0.826822\pi$
$2$	0.199171	−	0.612984i	0.140835	−	0.433445i	0.996452	+	0.0841641i	$0.0268220\pi$
$3$	0.903105	+	2.77947i	0.521408	+	1.60473i	0.771312	+	0.636458i	$0.219601\pi$
$3$	0.903105	+	2.77947i	0.521408	+	1.60473i	−0.249904	+	0.968271i	$0.580399\pi$
$4$	1.28195	+	0.931393i	0.640977	+	0.465697i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.88364			0.768995
$7$	−2.42006	−	1.75828i	−0.914697	−	0.664566i	0.0275014	−	0.999622i	$-0.491245\pi$
$7$	−2.42006	−	1.75828i	−0.914697	−	0.664566i	−0.942198	+	0.335056i	$0.891245\pi$
$8$	1.86913	−	1.35800i	0.660837	−	0.480126i
$9$	−4.48281	+	3.25695i	−1.49427	+	1.08565i
$10$	−0.199171	+	0.612984i	−0.0629833	+	0.193843i
$11$	1.90509	+	1.38413i	0.574406	+	0.417330i	0.836703	−	0.547657i	$-0.184480\pi$
$11$	1.90509	+	1.38413i	0.574406	+	0.417330i	−0.262297	+	0.964987i	$0.584480\pi$
$12$	−1.43104	+	4.40430i	−0.413107	+	1.27141i
$13$	−1.23340	−	3.79601i	−0.342083	−	1.05282i	−0.963127	−	0.269048i	$-0.913291\pi$
$13$	−1.23340	−	3.79601i	−0.342083	−	1.05282i	0.621044	−	0.783776i	$-0.286709\pi$
$14$	−1.55980	+	1.13326i	−0.416875	+	0.302877i
$15$	−0.903105	−	2.77947i	−0.233181	−	0.717656i
$16$	0.519167	+	1.59783i	0.129792	+	0.399458i
$17$	3.75673	−	2.72942i	0.911141	−	0.661983i	−0.0301623	−	0.999545i	$-0.509602\pi$
$17$	3.75673	−	2.72942i	0.911141	−	0.661983i	0.941303	+	0.337562i	$0.109602\pi$
$18$	1.10362	+	3.39658i	0.260125	+	0.800582i
$19$	−0.650565	+	2.00223i	−0.149250	+	0.459344i	−0.997533	−	0.0701990i	$-0.977637\pi$
$19$	−0.650565	+	2.00223i	−0.149250	+	0.459344i	0.848283	+	0.529543i	$0.177637\pi$
$20$	−1.28195	−	0.931393i	−0.286653	−	0.208266i
$21$	2.70151	−	8.31440i	0.589518	−	1.81435i
$22$	1.22789	−	0.892112i	0.261786	−	0.190199i
$23$	5.47953	−	3.98111i	1.14256	−	0.830119i	0.155087	−	0.987901i	$-0.450434\pi$
$23$	5.47953	−	3.98111i	1.14256	−	0.830119i	0.987474	+	0.157782i	$0.0504343\pi$
$24$	5.46254	+	3.96877i	1.11504	+	0.810122i
$25$	1.00000			0.200000
$26$	−2.57255			−0.504519
$27$	−6.00797	−	4.36505i	−1.15624	−	0.840054i
$28$	−1.46476	−	4.50806i	−0.276813	−	0.851943i
$29$	0.590849	−	1.81845i	0.109718	−	0.337677i	−0.881091	−	0.472947i	$-0.843190\pi$
$29$	0.590849	−	1.81845i	0.109718	−	0.337677i	0.990809	+	0.135270i	$0.0431902\pi$
$30$	−1.88364			−0.343905
$31$	−4.67270	+	3.02752i	−0.839242	+	0.543758i
$31$	−4.67270	+	3.02752i	−0.839242	+	0.543758i
$32$	5.70359			1.00826
$33$	−2.12665	+	6.54515i	−0.370202	+	1.13936i
$34$	−0.924864	−	2.84644i	−0.158613	−	0.488160i
$35$	2.42006	+	1.75828i	0.409065	+	0.297203i
$36$	−8.78026			−1.46338
$37$	−11.5679			−1.90174			−0.950872	−	0.309586i	$-0.899810\pi$
$37$	−11.5679			−1.90174			−0.950872	+	0.309586i	$0.899810\pi$
$38$	1.09776	+	0.797573i	0.178081	+	0.129383i
$39$	9.43701	−	6.85639i	1.51113	−	1.09790i
$40$	−1.86913	+	1.35800i	−0.295535	+	0.214719i
$41$	0.365283	−	1.12423i	0.0570477	−	0.175575i	−0.918472	−	0.395485i	$-0.870576\pi$
$41$	0.365283	−	1.12423i	0.0570477	−	0.175575i	0.975520	+	0.219910i	$0.0705765\pi$
$42$	−4.55853	−	3.31197i	−0.703397	−	0.511048i
$43$	−2.39794	+	7.38010i	−0.365682	+	1.12545i	0.583870	+	0.811847i	$0.301538\pi$
$43$	−2.39794	+	7.38010i	−0.365682	+	1.12545i	−0.949553	+	0.313608i	$0.898462\pi$
$44$	1.15307	+	3.54877i	0.173831	+	0.534998i
$45$	4.48281	−	3.25695i	0.668258	−	0.485518i
$46$	−1.34900	−	4.15179i	−0.198899	−	0.612148i
$47$	−2.02939	−	6.24581i	−0.296017	−	0.911046i	−0.982878	−	0.184257i	$-0.941012\pi$
$47$	−2.02939	−	6.24581i	−0.296017	−	0.911046i	0.686861	−	0.726788i	$-0.258988\pi$
$48$	−3.97226	+	2.88602i	−0.573347	+	0.416561i
$49$	0.602037	+	1.85288i	0.0860052	+	0.264697i
$50$	0.199171	−	0.612984i	0.0281670	−	0.0866891i
$51$	10.9791	+	7.97677i	1.53738	+	1.11697i
$52$	1.95442	−	6.01508i	0.271029	−	0.834142i
$53$	−9.96708	+	7.24151i	−1.36908	+	0.994698i	−0.371276	+	0.928522i	$0.621080\pi$
$53$	−9.96708	+	7.24151i	−1.36908	+	0.994698i	−0.997808	+	0.0661756i	$0.978920\pi$
$54$	−3.87232	+	2.81340i	−0.526956	+	0.382856i
$55$	−1.90509	−	1.38413i	−0.256882	−	0.186636i
$56$	−6.91115			−0.923541
$57$	−6.15268			−0.814942
$58$	−0.997000	−	0.724363i	−0.130913	−	0.0951135i
$59$	−1.83984	−	5.66244i	−0.239527	−	0.737187i	−0.996489	−	0.0837283i	$-0.973317\pi$
$59$	−1.83984	−	5.66244i	−0.239527	−	0.737187i	0.756962	−	0.653459i	$-0.226683\pi$
$60$	1.43104	−	4.40430i	0.184747	−	0.568592i
$61$	1.16661			0.149369			0.0746843	−	0.997207i	$-0.476205\pi$
$61$	1.16661			0.149369			0.0746843	+	0.997207i	$0.476205\pi$
$62$	0.925156	+	3.46729i	0.117495	+	0.440346i
$63$	16.5753			2.08829
$64$	0.0976541	−	0.300548i	0.0122068	−	0.0375685i
$65$	1.23340	+	3.79601i	0.152984	+	0.470837i
$66$	3.58851	+	2.60720i	0.441715	+	0.320925i
$67$	10.1763			1.24323			0.621617	−	0.783322i	$-0.286476\pi$
$67$	10.1763			1.24323			0.621617	+	0.783322i	$0.286476\pi$
$68$	7.35812			0.892303
$69$	16.0140	+	11.6348i	1.92786	+	1.40067i
$70$	1.55980	−	1.13326i	0.186432	−	0.135451i
$71$	2.05962	−	1.49640i	0.244431	−	0.177590i	−0.458824	−	0.888527i	$-0.651729\pi$
$71$	2.05962	−	1.49640i	0.244431	−	0.177590i	0.703255	+	0.710937i	$0.251729\pi$
$72$	−3.95600	+	12.1753i	−0.466219	+	1.43488i
$73$	−10.1930	−	7.40561i	−1.19299	−	0.866762i	−0.199417	−	0.979915i	$-0.563905\pi$
$73$	−10.1930	−	7.40561i	−1.19299	−	0.866762i	−0.993578	+	0.113153i	$0.963905\pi$
$74$	−2.30398	+	7.09091i	−0.267832	+	0.824302i
$75$	0.903105	+	2.77947i	0.104282	+	0.320946i
$76$	−2.69886	+	1.96084i	−0.309581	+	0.224924i
$77$	−2.17675	−	6.69934i	−0.248064	−	0.763461i
$78$	−2.32328	−	7.15033i	−0.263060	−	0.809616i
$79$	9.51120	−	6.91029i	1.07009	−	0.777468i	0.0941644	−	0.995557i	$-0.469982\pi$
$79$	9.51120	−	6.91029i	1.07009	−	0.777468i	0.975929	+	0.218088i	$0.0699821\pi$
$80$	−0.519167	−	1.59783i	−0.0580446	−	0.178643i
$81$	1.56985	−	4.83151i	0.174428	−	0.536834i
$82$	−0.616380	−	0.447826i	−0.0680678	−	0.0494541i
$83$	−1.39610	+	4.29676i	−0.153242	+	0.471631i	−0.997979	−	0.0635518i	$-0.979757\pi$
$83$	−1.39610	+	4.29676i	−0.153242	+	0.471631i	0.844736	+	0.535183i	$0.179757\pi$
$84$	11.2072	−	8.14250i	1.22280	−	0.888419i
$85$	−3.75673	+	2.72942i	−0.407475	+	0.296048i
$86$	4.04629	+	2.93980i	0.436322	+	0.317007i
$87$	5.58792			0.599088
$88$	5.44050			0.579959
$89$	0.306544	+	0.222718i	0.0324936	+	0.0236080i	0.603914	−	0.797050i	$-0.293607\pi$
$89$	0.306544	+	0.222718i	0.0324936	+	0.0236080i	−0.571420	+	0.820658i	$0.693607\pi$
$90$	−1.10362	−	3.39658i	−0.116331	−	0.358031i
$91$	−3.68954	+	11.3552i	−0.386769	+	1.19035i
$92$	10.7325			1.11894
$93$	−12.6348	−	10.2535i	−1.31017	−	1.06324i
$94$	−4.23278			−0.436578
$95$	0.650565	−	2.00223i	0.0667466	−	0.205425i
$96$	5.15094	+	15.8530i	0.525715	+	1.61799i
$97$	1.11300	+	0.808645i	0.113008	+	0.0821054i	0.642854	−	0.765989i	$-0.277750\pi$
$97$	1.11300	+	0.808645i	0.113008	+	0.0821054i	−0.529846	+	0.848094i	$0.677750\pi$
$98$	1.25569			0.126844
$99$	−13.0482			−1.31139
$100$	1.28195	+	0.931393i	0.128195	+	0.0931393i
$101$	−11.8181	+	8.58635i	−1.17594	+	0.854374i	−0.991708	−	0.128508i	$-0.958981\pi$
$101$	−11.8181	+	8.58635i	−1.17594	+	0.854374i	−0.184236	+	0.982882i	$0.558981\pi$
$102$	7.07634	−	5.14127i	0.700662	−	0.509061i
$103$	−3.16616	+	9.74445i	−0.311971	+	0.960149i	0.665012	+	0.746833i	$0.268426\pi$
$103$	−3.16616	+	9.74445i	−0.311971	+	0.960149i	−0.976983	+	0.213316i	$0.931574\pi$
$104$	−7.46036	−	5.42027i	−0.731549	−	0.531501i
$105$	−2.70151	+	8.31440i	−0.263641	+	0.811402i
$106$	2.45378	+	7.55196i	0.238332	+	0.733512i
$107$	−8.30568	+	6.03443i	−0.802940	+	0.583370i	−0.911775	−	0.410689i	$-0.865288\pi$
$107$	−8.30568	+	6.03443i	−0.802940	+	0.583370i	0.108835	+	0.994060i	$0.465288\pi$
$108$	−3.63636	−	11.1916i	−0.349909	−	1.07691i
$109$	3.28206	+	10.1012i	0.314365	+	0.967515i	0.976015	+	0.217702i	$0.0698562\pi$
$109$	3.28206	+	10.1012i	0.314365	+	0.967515i	−0.661651	+	0.749812i	$0.730144\pi$
$110$	−1.22789	+	0.892112i	−0.117074	+	0.0850595i
$111$	−10.4470	−	32.1525i	−0.991584	−	3.05178i
$112$	1.55301	−	4.77969i	0.146746	−	0.451638i
$113$	10.1750	+	7.39257i	0.957184	+	0.695435i	0.952495	−	0.304554i	$-0.0985076\pi$
$113$	10.1750	+	7.39257i	0.957184	+	0.695435i	0.00468859	+	0.999989i	$0.498508\pi$
$114$	−1.22543	+	3.77150i	−0.114772	+	0.353233i
$115$	−5.47953	+	3.98111i	−0.510969	+	0.371240i
$116$	2.45113	−	1.78085i	0.227582	−	0.165348i
$117$	17.8925	+	12.9997i	1.65416	+	1.20182i
$118$	−3.83743			−0.353264
$119$	−13.8906			−1.27335
$120$	−5.46254	−	3.96877i	−0.498660	−	0.362298i
$121$	−1.68564	−	5.18785i	−0.153240	−	0.471623i
$122$	0.232354	−	0.715112i	0.0210363	−	0.0647432i
$123$	3.45465			0.311495
$124$	−8.80999	−	0.470988i	−0.791161	−	0.0422960i
$125$	−1.00000			−0.0894427
$126$	3.30131	−	10.1604i	0.294104	−	0.905160i
$127$	1.05534	+	3.24801i	0.0936465	+	0.288214i	0.986899	−	0.161342i	$-0.0515821\pi$
$127$	1.05534	+	3.24801i	0.0936465	+	0.288214i	−0.893252	+	0.449556i	$0.851582\pi$
$128$	9.06382	+	6.58525i	0.801136	+	0.582059i
$129$	−22.6784			−1.99672
$130$	2.57255			0.225628
$131$	4.00837	+	2.91225i	0.350213	+	0.254445i	0.748958	−	0.662617i	$-0.230554\pi$
$131$	4.00837	+	2.91225i	0.350213	+	0.254445i	−0.398745	+	0.917062i	$0.630554\pi$
$132$	−8.82237	+	6.40983i	−0.767889	+	0.557904i
$133$	5.09489	−	3.70165i	0.441783	−	0.320974i
$134$	2.02682	−	6.23792i	0.175091	−	0.538874i
$135$	6.00797	+	4.36505i	0.517084	+	0.375684i
$136$	3.31525	−	10.2033i	0.284280	−	0.874925i
$137$	1.59811	+	4.91847i	0.136536	+	0.420213i	0.995826	−	0.0912751i	$-0.0290943\pi$
$137$	1.59811	+	4.91847i	0.136536	+	0.420213i	−0.859290	+	0.511489i	$0.829094\pi$
$138$	10.3215	−	7.49900i	0.878623	−	0.638357i
$139$	−4.59182	−	14.1322i	−0.389473	−	1.19867i	−0.933183	−	0.359401i	$-0.882981\pi$
$139$	−4.59182	−	14.1322i	−0.389473	−	1.19867i	0.543710	−	0.839273i	$-0.317019\pi$
$140$	1.46476	+	4.50806i	0.123795	+	0.381000i
$141$	15.5273	−	11.2813i	1.30764	−	0.950053i
$142$	−0.507054	−	1.56055i	−0.0425510	−	0.130959i
$143$	2.90443	−	8.93891i	0.242880	−	0.747509i
$144$	−7.53139	−	5.47187i	−0.627616	−	0.455989i
$145$	−0.590849	+	1.81845i	−0.0490674	+	0.151014i
$146$	−6.56966	+	4.77314i	−0.543709	+	0.395028i
$147$	−4.60632	+	3.34669i	−0.379923	+	0.276030i
$148$	−14.8294	−	10.7742i	−1.21897	−	0.885635i
$149$	20.7261			1.69795			0.848975	−	0.528433i	$-0.177220\pi$
$149$	20.7261			1.69795			0.848975	+	0.528433i	$0.177220\pi$
$150$	1.88364			0.153799
$151$	7.06012	+	5.12948i	0.574544	+	0.417431i	0.836753	−	0.547580i	$-0.184451\pi$
$151$	7.06012	+	5.12948i	0.574544	+	0.417431i	−0.262209	+	0.965011i	$0.584451\pi$
$152$	1.50305	+	4.62590i	0.121913	+	0.375210i
$153$	−7.95110	+	24.4710i	−0.642809	+	1.97836i
$154$	−4.54014			−0.365855
$155$	4.67270	−	3.02752i	0.375320	−	0.243176i
$156$	18.4838			1.47989
$157$	−0.452682	+	1.39321i	−0.0361279	+	0.111190i	−0.967494	−	0.252893i	$-0.918618\pi$
$157$	−0.452682	+	1.39321i	−0.0361279	+	0.111190i	0.931366	+	0.364084i	$0.118618\pi$
$158$	−2.34155	−	7.20654i	−0.186284	−	0.573322i
$159$	−29.1289	−	21.1634i	−2.31007	−	1.67837i
$160$	−5.70359			−0.450908
$161$	−20.2607			−1.59677
$162$	−2.64897	−	1.92459i	−0.208123	−	0.151210i
$163$	13.4413	−	9.76565i	1.05280	−	0.764905i	0.0800583	−	0.996790i	$-0.474489\pi$
$163$	13.4413	−	9.76565i	1.05280	−	0.764905i	0.972743	+	0.231885i	$0.0744894\pi$
$164$	1.51537	−	1.10098i	0.118331	−	0.0859724i
$165$	2.12665	−	6.54515i	0.165559	−	0.509539i
$166$	2.35578	+	1.71158i	0.182844	+	0.132844i
$167$	2.88649	−	8.88370i	0.223363	−	0.687441i	−0.775090	−	0.631850i	$-0.782296\pi$
$167$	2.88649	−	8.88370i	0.223363	−	0.687441i	0.998454	−	0.0555910i	$-0.0177043\pi$
$168$	−6.24149	−	19.2093i	−0.481541	−	1.48203i
$169$	−2.37119	+	1.72277i	−0.182399	+	0.132521i
$170$	0.924864	+	2.84644i	0.0709338	+	0.218312i
$171$	−3.60482	−	11.0945i	−0.275667	−	0.848417i
$172$	−9.94782	+	7.22752i	−0.758514	+	0.551093i
$173$	5.56435	+	17.1253i	0.423050	+	1.30201i	0.904849	+	0.425732i	$0.139983\pi$
$173$	5.56435	+	17.1253i	0.423050	+	1.30201i	−0.481800	+	0.876281i	$0.660017\pi$
$174$	1.11295	−	3.42531i	0.0843725	−	0.259672i
$175$	−2.42006	−	1.75828i	−0.182939	−	0.132913i
$176$	−1.22254	+	3.76260i	−0.0921527	+	0.283617i
$177$	14.0770	−	10.2276i	1.05809	−	0.768750i
$178$	0.197577	−	0.143548i	0.0148090	−	0.0107594i
$179$	6.05690	+	4.40059i	0.452714	+	0.328916i	0.790666	−	0.612247i	$-0.209734\pi$
$179$	6.05690	+	4.40059i	0.452714	+	0.328916i	−0.337953	+	0.941163i	$0.609734\pi$
$180$	8.78026			0.654442
$181$	−4.26225			−0.316810			−0.158405	−	0.987374i	$-0.550635\pi$
$181$	−4.26225			−0.316810			−0.158405	+	0.987374i	$0.550635\pi$
$182$	6.22573	+	4.52326i	0.461482	+	0.335286i
$183$	1.05357	+	3.24255i	0.0778820	+	0.239696i
$184$	4.83559	−	14.8824i	0.356484	−	1.09715i
$185$	11.5679			0.850485
$186$	−8.80171	+	5.70277i	−0.645373	+	0.418147i
$187$	10.9348			0.799630
$188$	3.21573	−	9.89700i	0.234531	−	0.721813i
$189$	6.86470	+	21.1274i	0.499333	+	1.53679i
$190$	−1.09776	−	0.797573i	−0.0796402	−	0.0578620i
$191$	−5.21222			−0.377143			−0.188572	−	0.982059i	$-0.560386\pi$
$191$	−5.21222			−0.377143			−0.188572	+	0.982059i	$0.560386\pi$
$192$	0.923557			0.0666520
$193$	−8.06594	−	5.86025i	−0.580599	−	0.421830i	0.258341	−	0.966054i	$-0.416824\pi$
$193$	−8.06594	−	5.86025i	−0.580599	−	0.421830i	−0.838940	+	0.544224i	$0.816824\pi$
$194$	0.717364	−	0.521196i	0.0515038	−	0.0374197i
$195$	−9.43701	+	6.85639i	−0.675798	+	0.490996i
$196$	−0.953976	+	2.93604i	−0.0681411	+	0.209717i
$197$	−12.3014	−	8.93747i	−0.876437	−	0.636769i	0.0558697	−	0.998438i	$-0.482207\pi$
$197$	−12.3014	−	8.93747i	−0.876437	−	0.636769i	−0.932306	+	0.361670i	$0.882207\pi$
$198$	−2.59882	+	7.99833i	−0.184690	+	0.568417i
$199$	4.70746	+	14.4881i	0.333703	+	1.02703i	0.967357	+	0.253416i	$0.0815542\pi$
$199$	4.70746	+	14.4881i	0.333703	+	1.02703i	−0.633654	+	0.773616i	$0.718446\pi$
$200$	1.86913	−	1.35800i	0.132167	−	0.0960252i
$201$	9.19027	+	28.2847i	0.648232	+	1.99505i
$202$	2.90948	+	8.95446i	0.204710	+	0.630033i
$203$	−4.62723	+	3.36188i	−0.324768	+	0.235957i
$204$	6.64515	+	20.4517i	0.465254	+	1.43190i
$205$	−0.365283	+	1.12423i	−0.0255125	+	0.0785194i
$206$	5.34259	+	3.88162i	0.372236	+	0.270445i
$207$	−11.5974	+	35.6931i	−0.806075	+	2.48084i
$208$	5.42504	−	3.94152i	0.376159	−	0.273296i
$209$	−4.01073	+	2.91397i	−0.277428	+	0.201563i
$210$	4.55853	+	3.31197i	0.314569	+	0.228548i
$211$	2.78487			0.191719			0.0958593	−	0.995395i	$-0.469440\pi$
$211$	2.78487			0.191719			0.0958593	+	0.995395i	$0.469440\pi$
$212$	−19.5220			−1.34078
$213$	6.01925	+	4.37324i	0.412432	+	0.299649i
$214$	2.04476	+	6.29313i	0.139777	+	0.430190i
$215$	2.39794	−	7.38010i	0.163538	−	0.503319i
$216$	−17.1574			−1.16741
$217$	16.6314	+	0.889128i	1.12902	+	0.0603579i
$218$	6.84554			0.463638
$219$	11.3784	−	35.0191i	0.768880	−	2.36637i
$220$	−1.15307	−	3.54877i	−0.0777397	−	0.239258i
$221$	−14.9945	−	10.8941i	−1.00864	−	0.732817i
$222$	−21.7897			−1.46243
$223$	−20.0460			−1.34238			−0.671191	−	0.741284i	$-0.734217\pi$
$223$	−20.0460			−1.34238			−0.671191	+	0.741284i	$0.734217\pi$
$224$	−13.8030	−	10.0285i	−0.922254	−	0.670057i
$225$	−4.48281	+	3.25695i	−0.298854	+	0.217130i
$226$	6.55809	−	4.76473i	0.436238	−	0.316945i
$227$	2.93415	−	9.03038i	0.194746	−	0.599368i	−0.805233	−	0.592958i	$-0.797960\pi$
$227$	2.93415	−	9.03038i	0.194746	−	0.599368i	0.999979	−	0.00640929i	$-0.00204015\pi$
$228$	−7.88745	−	5.73057i	−0.522359	−	0.379516i
$229$	−6.74257	+	20.7515i	−0.445562	+	1.37130i	0.436305	+	0.899799i	$0.356287\pi$
$229$	−6.74257	+	20.7515i	−0.445562	+	1.37130i	−0.881867	+	0.471499i	$0.843713\pi$
$230$	1.34900	+	4.15179i	0.0889502	+	0.273761i
$231$	16.6548	−	12.1004i	1.09581	−	0.796149i
$232$	−1.36508	−	4.20129i	−0.0896219	−	0.275828i
$233$	−0.199891	−	0.615201i	−0.0130953	−	0.0403031i	0.944295	−	0.329099i	$-0.106745\pi$
$233$	−0.199891	−	0.615201i	−0.0130953	−	0.0403031i	−0.957391	+	0.288796i	$0.906745\pi$
$234$	11.5323	−	8.37868i	0.753887	−	0.547731i
$235$	2.02939	+	6.24581i	0.132383	+	0.407432i
$236$	2.91537	−	8.97260i	0.189775	−	0.584066i
$237$	27.7966	+	20.1954i	1.80558	+	1.31183i
$238$	−2.76660	+	8.51472i	−0.179332	+	0.551927i
$239$	20.0913	−	14.5972i	1.29960	−	0.944215i	0.299648	−	0.954050i	$-0.403131\pi$
$239$	20.0913	−	14.5972i	1.29960	−	0.944215i	0.999952	+	0.00983498i	$0.00313062\pi$
$240$	3.97226	−	2.88602i	0.256409	−	0.186292i
$241$	−13.9007	−	10.0995i	−0.895425	−	0.650564i	0.0418621	−	0.999123i	$-0.486671\pi$
$241$	−13.9007	−	10.0995i	−0.895425	−	0.650564i	−0.937287	+	0.348559i	$0.886671\pi$
$242$	−3.51580			−0.226004
$243$	−7.43201			−0.476764
$244$	1.49553	+	1.08657i	0.0957418	+	0.0695605i
$245$	−0.602037	−	1.85288i	−0.0384627	−	0.118376i
$246$	0.688064	−	2.11764i	0.0438694	−	0.135016i
$247$	8.40290			0.534664
$248$	−4.62251	+	12.0044i	−0.293530	+	0.762277i
$249$	−13.2035			−0.836741
$250$	−0.199171	+	0.612984i	−0.0125967	+	0.0387685i
$251$	−3.93134	−	12.0994i	−0.248144	−	0.763709i	−0.995103	−	0.0988395i	$-0.968487\pi$
$251$	−3.93134	−	12.0994i	−0.248144	−	0.763709i	0.746959	−	0.664870i	$-0.231513\pi$
$252$	21.2488	+	15.4381i	1.33855	+	0.972510i
$253$	15.9493			1.00273
$254$	2.20117			0.138114
$255$	−10.9791	−	7.97677i	−0.687536	−	0.499524i
$256$	6.35323	−	4.61589i	0.397077	−	0.288493i
$257$	−4.04725	+	2.94050i	−0.252461	+	0.183423i	−0.706817	−	0.707397i	$-0.749869\pi$
$257$	−4.04725	+	2.94050i	−0.252461	+	0.183423i	0.454356	+	0.890820i	$0.349869\pi$
$258$	−4.51687	+	13.9015i	−0.281208	+	0.865469i
$259$	27.9949	+	20.3395i	1.73952	+	1.26383i
$260$	−1.95442	+	6.01508i	−0.121208	+	0.373040i
$261$	3.27393	+	10.0761i	0.202651	+	0.623696i
$262$	2.58352	−	1.87703i	0.159610	−	0.115964i
$263$	4.13401	+	12.7232i	0.254914	+	0.784544i	0.993847	+	0.110765i	$0.0353301\pi$
$263$	4.13401	+	12.7232i	0.254914	+	0.784544i	−0.738933	+	0.673779i	$0.764670\pi$
$264$	4.91334	+	15.1217i	0.302395	+	0.930677i
$265$	9.96708	−	7.24151i	0.612273	−	0.444842i
$266$	−1.25430	−	3.86035i	−0.0769063	−	0.236693i
$267$	−0.342195	+	1.05317i	−0.0209420	+	0.0644529i
$268$	13.0455	+	9.47814i	0.796883	+	0.578970i
$269$	4.79980	−	14.7723i	0.292649	−	0.900681i	−0.691352	−	0.722518i	$-0.742985\pi$
$269$	4.79980	−	14.7723i	0.292649	−	0.900681i	0.984001	−	0.178163i	$-0.0570154\pi$
$270$	3.87232	−	2.81340i	0.235662	−	0.171218i
$271$	4.15506	−	3.01883i	0.252402	−	0.183381i	−0.454389	−	0.890804i	$-0.650142\pi$
$271$	4.15506	−	3.01883i	0.252402	−	0.183381i	0.706791	+	0.707423i	$0.250142\pi$
$272$	6.31153	+	4.58559i	0.382693	+	0.278043i
$273$	−34.8936			−2.11185
$274$	3.33324			0.201369
$275$	1.90509	+	1.38413i	0.114881	+	0.0834660i
$276$	9.69255	+	29.8306i	0.583423	+	1.79559i
$277$	3.67497	−	11.3104i	0.220808	−	0.679576i	−0.777882	−	0.628410i	$-0.783706\pi$
$277$	3.67497	−	11.3104i	0.220808	−	0.679576i	0.998690	−	0.0511665i	$-0.0162939\pi$
$278$	−9.57735			−0.574411
$279$	11.0864	−	28.7905i	0.663723	−	1.72365i
$280$	6.91115			0.413020
$281$	−3.02062	+	9.29652i	−0.180195	+	0.554584i	−0.999833	−	0.0182990i	$-0.994175\pi$
$281$	−3.02062	+	9.29652i	−0.180195	+	0.554584i	0.819637	+	0.572883i	$0.194175\pi$
$282$	−3.82265	−	11.7649i	−0.227635	−	0.700589i
$283$	14.0273	+	10.1914i	0.833834	+	0.605816i	0.920642	−	0.390409i	$-0.127666\pi$
$283$	14.0273	+	10.1914i	0.833834	+	0.605816i	−0.0868072	+	0.996225i	$0.527666\pi$
$284$	4.03407			0.239378
$285$	6.15268			0.364453
$286$	−4.90094	−	3.56074i	−0.289798	−	0.210551i
$287$	−2.86071	+	2.07843i	−0.168862	+	0.122686i
$288$	−25.5681	+	18.5763i	−1.50661	+	1.09462i
$289$	1.40998	−	4.33946i	0.0829397	−	0.255262i
$290$	0.997000	+	0.724363i	0.0585459	+	0.0425361i
$291$	−1.24245	+	3.82385i	−0.0728334	+	0.224158i
$292$	−6.16935	−	18.9873i	−0.361034	−	1.11115i
$293$	21.2879	−	15.4666i	1.24365	−	0.903566i	0.245815	−	0.969317i	$-0.420944\pi$
$293$	21.2879	−	15.4666i	1.24365	−	0.903566i	0.997836	+	0.0657510i	$0.0209443\pi$
$294$	1.13402	+	3.49016i	0.0661376	+	0.203551i
$295$	1.83984	+	5.66244i	0.107120	+	0.329680i
$296$	−21.6218	+	15.7092i	−1.25674	+	0.913076i
$297$	−5.40394	−	16.6316i	−0.313568	−	0.965063i
$298$	4.12804	−	12.7048i	0.239131	−	0.735969i
$299$	−21.8708	−	15.8900i	−1.26482	−	0.918945i
$300$	−1.43104	+	4.40430i	−0.0826213	+	0.254282i
$301$	18.7794	−	13.6440i	1.08243	−	0.786430i
$302$	4.55046	−	3.30610i	0.261849	−	0.190245i
$303$	−34.5385	−	25.0937i	−1.98418	−	1.44159i
$304$	−3.53698			−0.202860
$305$	−1.16661			−0.0667997
$306$	13.4167	+	9.74781i	0.766982	+	0.557245i
$307$	4.76158	+	14.6546i	0.271758	+	0.836384i	0.990059	+	0.140652i	$0.0449199\pi$
$307$	4.76158	+	14.6546i	0.271758	+	0.836384i	−0.718301	+	0.695732i	$0.755080\pi$
$308$	3.44924	−	10.6157i	0.196538	−	0.604883i
$309$	−29.9438			−1.70344
$310$	−0.925156	−	3.46729i	−0.0525453	−	0.196929i
$311$	−6.37511			−0.361500			−0.180750	−	0.983529i	$-0.557852\pi$
$311$	−6.37511			−0.361500			−0.180750	+	0.983529i	$0.557852\pi$
$312$	8.32800	−	25.6309i	0.471480	−	1.45107i
$313$	−6.26503	−	19.2818i	−0.354120	−	1.08987i	−0.956518	−	0.291674i	$-0.905788\pi$
$313$	−6.26503	−	19.2818i	−0.354120	−	1.08987i	0.602398	−	0.798196i	$-0.294212\pi$
$314$	0.763856	+	0.554974i	0.0431069	+	0.0313190i
$315$	−16.5753			−0.933912
$316$	18.6291			1.04797
$317$	−25.1584	−	18.2786i	−1.41303	−	1.02663i	−0.992873	−	0.119181i	$-0.961973\pi$
$317$	−25.1584	−	18.2786i	−1.41303	−	1.02663i	−0.420162	−	0.907449i	$-0.638027\pi$
$318$	−18.7744	+	13.6404i	−1.05282	+	0.764917i
$319$	3.64258	−	2.64649i	0.203945	−	0.148175i
$320$	−0.0976541	+	0.300548i	−0.00545903	+	0.0168012i
$321$	−24.2734	−	17.6357i	−1.35481	−	0.984327i
$322$	−4.03534	+	12.4195i	−0.224880	+	0.692111i
$323$	3.02095	+	9.29752i	0.168090	+	0.517328i
$324$	6.51251	−	4.73162i	0.361806	−	0.262868i
$325$	−1.23340	−	3.79601i	−0.0684166	−	0.210565i
$326$	−3.30909	−	10.1843i	−0.183273	−	0.564057i
$327$	−25.1118	+	18.2448i	−1.38869	+	1.00894i
$328$	−0.843940	−	2.59738i	−0.0465988	−	0.143416i
$329$	−6.07063	+	18.6835i	−0.334685	+	1.03005i
$330$	−3.58851	−	2.60720i	−0.197541	−	0.143522i
$331$	−7.31287	+	22.5067i	−0.401951	+	1.23708i	0.521463	+	0.853274i	$0.325387\pi$
$331$	−7.31287	+	22.5067i	−0.401951	+	1.23708i	−0.923414	+	0.383805i	$0.874613\pi$
$332$	−5.79171	+	4.20793i	−0.317862	+	0.230940i
$333$	51.8565	−	37.6759i	2.84172	−	2.06463i
$334$	−4.87067	−	3.53875i	−0.266511	−	0.193632i
$335$	−10.1763			−0.555991
$336$	14.6875			0.801271
$337$	−4.47023	−	3.24781i	−0.243509	−	0.176920i	0.459336	−	0.888262i	$-0.348087\pi$
$337$	−4.47023	−	3.24781i	−0.243509	−	0.176920i	−0.702845	+	0.711343i	$0.748087\pi$
$338$	0.583760	+	1.79663i	0.0317523	+	0.0977236i
$339$	−11.3583	+	34.9574i	−0.616901	+	1.89862i
$340$	−7.35812			−0.399050
$341$	−13.0924	−	0.699928i	−0.708992	−	0.0379032i
$342$	−7.51873			−0.406566
$343$	−4.66976	+	14.3720i	−0.252143	+	0.776017i
$344$	5.54013	+	17.0508i	0.298704	+	0.919316i
$345$	−16.0140	−	11.6348i	−0.862163	−	0.626398i
$346$	11.6058			0.623932
$347$	−7.48412			−0.401769			−0.200884	−	0.979615i	$-0.564382\pi$
$347$	−7.48412			−0.401769			−0.200884	+	0.979615i	$0.564382\pi$
$348$	7.16345	+	5.20455i	0.384001	+	0.278993i
$349$	21.0182	−	15.2706i	1.12508	−	0.817417i	0.140107	−	0.990136i	$-0.455255\pi$
$349$	21.0182	−	15.2706i	1.12508	−	0.817417i	0.984971	+	0.172719i	$0.0552552\pi$
$350$	−1.55980	+	1.13326i	−0.0833749	+	0.0605754i
$351$	−9.15954	+	28.1902i	−0.488900	+	1.50468i
$352$	10.8658	+	7.89449i	0.579151	+	0.420778i
$353$	6.65122	−	20.4704i	0.354009	−	1.08953i	−0.602573	−	0.798064i	$-0.705858\pi$
$353$	6.65122	−	20.4704i	0.354009	−	1.08953i	0.956582	−	0.291464i	$-0.0941423\pi$
$354$	−3.46560	−	10.6660i	−0.184195	−	0.566893i
$355$	−2.05962	+	1.49640i	−0.109313	+	0.0794206i
$356$	0.185538	+	0.571027i	0.00983349	+	0.0302644i
$357$	−12.5447	−	38.6085i	−0.663934	−	2.04338i
$358$	3.90385	−	2.83631i	0.206325	−	0.149904i
$359$	2.57270	+	7.91795i	0.135782	+	0.417893i	0.995711	−	0.0925204i	$-0.0294923\pi$
$359$	2.57270	+	7.91795i	0.135782	+	0.417893i	−0.859929	+	0.510414i	$0.829492\pi$
$360$	3.95600	−	12.1753i	0.208500	−	0.641696i
$361$	11.7856	+	8.56275i	0.620296	+	0.450671i
$362$	−0.848915	+	2.61269i	−0.0446180	+	0.137320i
$363$	12.8972	−	9.37035i	0.676926	−	0.491816i
$364$	−15.3060	+	11.1205i	−0.802252	+	0.582870i
$365$	10.1930	+	7.40561i	0.533524	+	0.387628i
$366$	2.19747			0.114864
$367$	27.9972			1.46144			0.730721	−	0.682677i	$-0.239184\pi$
$367$	27.9972			1.46144			0.730721	+	0.682677i	$0.239184\pi$
$368$	9.20593	+	6.68850i	0.479892	+	0.348662i
$369$	2.02406	+	6.22941i	0.105368	+	0.324290i
$370$	2.30398	−	7.09091i	0.119778	−	0.368639i
$371$	36.8535			1.91334
$372$	−6.64725	−	24.9125i	−0.344644	−	1.29165i
$373$	−4.65517			−0.241036			−0.120518	−	0.992711i	$-0.538456\pi$
$373$	−4.65517			−0.241036			−0.120518	+	0.992711i	$0.538456\pi$
$374$	2.17789	−	6.70285i	0.112616	−	0.346596i
$375$	−0.903105	−	2.77947i	−0.0466361	−	0.143531i
$376$	−12.2750	−	8.91832i	−0.633035	−	0.459927i
$377$	−7.63159			−0.393047
$378$	14.3180			0.736438
$379$	−0.793051	−	0.576185i	−0.0407363	−	0.0295966i	0.567231	−	0.823559i	$-0.308015\pi$
$379$	−0.793051	−	0.576185i	−0.0407363	−	0.0295966i	−0.607967	+	0.793962i	$0.708015\pi$
$380$	2.69886	−	1.96084i	0.138449	−	0.100589i
$381$	−8.07467	+	5.86659i	−0.413678	+	0.300555i
$382$	−1.03812	+	3.19501i	−0.0531150	+	0.163471i
$383$	8.90331	+	6.46863i	0.454938	+	0.330532i	0.791542	−	0.611114i	$-0.209278\pi$
$383$	8.90331	+	6.46863i	0.454938	+	0.330532i	−0.336604	+	0.941646i	$0.609278\pi$
$384$	−10.1179	+	31.1398i	−0.516329	+	1.58910i
$385$	2.17675	+	6.69934i	0.110937	+	0.341430i
$386$	−5.19874	+	3.77711i	−0.264609	+	0.192250i
$387$	−13.2871	−	40.8936i	−0.675423	−	2.07874i
$388$	0.673652	+	2.07329i	0.0341995	+	0.105255i
$389$	2.39564	−	1.74054i	0.121464	−	0.0882488i	−0.525395	−	0.850859i	$-0.676082\pi$
$389$	2.39564	−	1.74054i	0.121464	−	0.0882488i	0.646859	+	0.762610i	$0.276082\pi$
$390$	2.32328	+	7.15033i	0.117644	+	0.362071i
$391$	9.71897	−	29.9119i	0.491509	−	1.51271i
$392$	3.64150	+	2.64570i	0.183923	+	0.133628i
$393$	−4.47454	+	13.7712i	−0.225711	+	0.694666i
$394$	−7.92861	+	5.76047i	−0.399437	+	0.290208i
$395$	−9.51120	+	6.91029i	−0.478560	+	0.347694i
$396$	−16.7272	−	12.1530i	−0.840571	−	0.610711i
$397$	−13.9836			−0.701816			−0.350908	−	0.936410i	$-0.614127\pi$
$397$	−13.9836			−0.701816			−0.350908	+	0.936410i	$0.614127\pi$
$398$	9.81855			0.492160
$399$	14.8899	+	10.8181i	0.745425	+	0.541583i
$400$	0.519167	+	1.59783i	0.0259583	+	0.0798916i
$401$	9.88764	−	30.4310i	0.493765	−	1.51965i	−0.325107	−	0.945677i	$-0.605400\pi$
$401$	9.88764	−	30.4310i	0.493765	−	1.51965i	0.818872	−	0.573976i	$-0.194600\pi$
$402$	19.1685			0.956040
$403$	17.2558	+	14.0035i	0.859572	+	0.697563i
$404$	−23.1475			−1.15163
$405$	−1.56985	+	4.83151i	−0.0780066	+	0.240080i
$406$	1.13917	+	3.50600i	0.0565361	+	0.174000i
$407$	−22.0378	−	16.0114i	−1.09237	−	0.793655i
$408$	31.3538			1.55224
$409$	−19.4362			−0.961059			−0.480529	−	0.876979i	$-0.659555\pi$
$409$	−19.4362			−0.961059			−0.480529	+	0.876979i	$0.659555\pi$
$410$	0.616380	+	0.447826i	0.0304408	+	0.0221166i
$411$	−12.2275	+	8.88379i	−0.603138	+	0.438205i
$412$	−13.1348	+	9.54298i	−0.647105	+	0.470149i
$413$	−5.50362	+	16.9384i	−0.270815	+	0.833484i
$414$	19.5695	+	14.2181i	0.961787	+	0.698779i
$415$	1.39610	−	4.29676i	0.0685320	−	0.210920i
$416$	−7.03479	−	21.6509i	−0.344909	−	1.06152i
$417$	35.1330	−	25.5256i	1.72047	−	1.25000i
$418$	0.987396	+	3.03889i	0.0482951	+	0.148637i
$419$	6.70813	+	20.6455i	0.327714	+	1.00860i	0.970201	+	0.242302i	$0.0779026\pi$
$419$	6.70813	+	20.6455i	0.327714	+	1.00860i	−0.642487	+	0.766297i	$0.722097\pi$
$420$	−11.2072	+	8.14250i	−0.546855	+	0.397313i
$421$	8.31701	+	25.5971i	0.405346	+	1.24753i	0.920606	+	0.390493i	$0.127696\pi$
$421$	8.31701	+	25.5971i	0.405346	+	1.24753i	−0.515259	+	0.857034i	$0.672304\pi$
$422$	0.554665	−	1.70708i	0.0270007	−	0.0830995i
$423$	29.4397	+	21.3892i	1.43141	+	1.03998i
$424$	−8.79578	+	27.0706i	−0.427161	+	1.31467i
$425$	3.75673	−	2.72942i	0.182228	−	0.132397i
$426$	3.87958	−	2.81868i	0.187966	−	0.136566i
$427$	−2.82326	−	2.05122i	−0.136627	−	0.0992654i
$428$	−16.2679			−0.786340
$429$	27.4684			1.32619
$430$	−4.04629	−	2.93980i	−0.195129	−	0.141770i
$431$	−4.68655	−	14.4237i	−0.225743	−	0.694765i	−0.998215	−	0.0597170i	$-0.980980\pi$
$431$	−4.68655	−	14.4237i	−0.225743	−	0.694765i	0.772472	−	0.635048i	$-0.219020\pi$
$432$	3.85547	−	11.8659i	0.185496	−	0.570899i
$433$	−16.5276			−0.794267			−0.397133	−	0.917761i	$-0.629995\pi$
$433$	−16.5276			−0.794267			−0.397133	+	0.917761i	$0.629995\pi$
$434$	3.85752	−	10.0177i	0.185167	−	0.480866i
$435$	−5.58792			−0.267920
$436$	−5.20069	+	16.0061i	−0.249068	+	0.766553i
$437$	4.40632	+	13.5613i	0.210783	+	0.648724i
$438$	−19.1999	−	13.9495i	−0.917407	−	0.666535i
$439$	2.10624			0.100525			0.0502626	−	0.998736i	$-0.483994\pi$
$439$	2.10624			0.100525			0.0502626	+	0.998736i	$0.483994\pi$
$440$	−5.44050			−0.259366
$441$	−8.73355	−	6.34530i	−0.415883	−	0.302157i
$442$	−9.66438	+	7.02158i	−0.459688	+	0.333983i
$443$	23.4641	−	17.0477i	1.11481	−	0.809960i	0.131400	−	0.991329i	$-0.458053\pi$
$443$	23.4641	−	17.0477i	1.11481	−	0.809960i	0.983415	+	0.181369i	$0.0580529\pi$
$444$	16.5541	−	50.9483i	0.785622	−	2.41790i
$445$	−0.306544	−	0.222718i	−0.0145316	−	0.0105578i
$446$	−3.99259	+	12.2879i	−0.189054	+	0.581850i
$447$	18.7179	+	57.6077i	0.885325	+	2.72475i
$448$	−0.764776	+	0.555642i	−0.0361323	+	0.0262516i
$449$	6.35280	+	19.5519i	0.299807	+	0.922712i	0.981564	+	0.191133i	$0.0612162\pi$
$449$	6.35280	+	19.5519i	0.299807	+	0.922712i	−0.681757	+	0.731579i	$0.738784\pi$
$450$	1.10362	+	3.39658i	0.0520250	+	0.160116i
$451$	2.25197	−	1.63615i	0.106041	−	0.0770434i
$452$	6.15848	+	18.9539i	0.289671	+	0.891514i
$453$	−7.88120	+	24.2558i	−0.370291	+	1.13964i
$454$	−4.95109	−	3.59718i	−0.232366	−	0.168824i
$455$	3.68954	−	11.3552i	0.172968	−	0.532341i
$456$	−11.5001	+	8.35535i	−0.538544	+	0.391275i
$457$	0.809993	−	0.588494i	0.0378899	−	0.0275286i	−0.568679	−	0.822559i	$-0.692545\pi$
$457$	0.809993	−	0.588494i	0.0378899	−	0.0275286i	0.606569	+	0.795031i	$0.292545\pi$
$458$	11.3774	+	8.26618i	0.531632	+	0.386253i
$459$	−34.4844			−1.60959
$460$	−10.7325			−0.500404
$461$	−1.13947	−	0.827872i	−0.0530703	−	0.0385578i	0.560934	−	0.827861i	$-0.310442\pi$
$461$	−1.13947	−	0.827872i	−0.0530703	−	0.0385578i	−0.614004	+	0.789303i	$0.710442\pi$
$462$	−4.10022	−	12.6192i	−0.190760	−	0.587098i
$463$	−10.5615	+	32.5049i	−0.490834	+	1.51063i	0.332517	+	0.943097i	$0.392102\pi$
$463$	−10.5615	+	32.5049i	−0.490834	+	1.51063i	−0.823350	+	0.567534i	$0.807898\pi$
$464$	3.21232			0.149128
$465$	12.6348	+	10.2535i	0.585926	+	0.475493i
$466$	−0.416921			−0.0193135
$467$	−6.40563	+	19.7145i	−0.296417	+	0.912278i	0.686324	+	0.727295i	$0.259223\pi$
$467$	−6.40563	+	19.7145i	−0.296417	+	0.912278i	−0.982742	+	0.184983i	$0.940777\pi$
$468$	10.8295	+	33.3299i	0.500596	+	1.54068i
$469$	−24.6273	−	17.8928i	−1.13718	−	0.826211i
$470$	4.23278			0.195244
$471$	−4.28121			−0.197268
$472$	−11.1285	−	8.08533i	−0.512231	−	0.372157i
$473$	−14.7833	+	10.7407i	−0.679736	+	0.493857i
$474$	17.9157	−	13.0165i	0.822896	−	0.597869i
$475$	−0.650565	+	2.00223i	−0.0298500	+	0.0918688i
$476$	−17.8071	−	12.9376i	−0.816187	−	0.592994i
$477$	21.0953	−	64.9246i	0.965887	−	2.97269i
$478$	−4.94626	−	15.2230i	−0.226236	−	0.696284i
$479$	5.34644	−	3.88441i	0.244285	−	0.177483i	−0.458905	−	0.888485i	$-0.651758\pi$
$479$	5.34644	−	3.88441i	0.244285	−	0.177483i	0.703190	+	0.711002i	$0.251758\pi$
$480$	−5.15094	−	15.8530i	−0.235107	−	0.723585i
$481$	14.2678	+	43.9117i	0.650554	+	2.00220i
$482$	−8.95944	+	6.50941i	−0.408091	+	0.296496i
$483$	−18.2975	−	56.3140i	−0.832566	−	2.56238i
$484$	2.67103	−	8.22057i	0.121410	−	0.373662i
$485$	−1.11300	−	0.808645i	−0.0505389	−	0.0367187i
$486$	−1.48024	+	4.55571i	−0.0671450	+	0.206651i
$487$	−15.8604	+	11.5233i	−0.718704	+	0.522169i	−0.885970	−	0.463743i	$-0.846506\pi$
$487$	−15.8604	+	11.5233i	−0.718704	+	0.522169i	0.167266	+	0.985912i	$0.446506\pi$
$488$	2.18054	−	1.58425i	0.0987083	−	0.0717158i
$489$	39.2822	+	28.5402i	1.77640	+	1.29063i
$490$	−1.25569			−0.0567265
$491$	−8.10375			−0.365717			−0.182859	−	0.983139i	$-0.558535\pi$
$491$	−8.10375			−0.365717			−0.182859	+	0.983139i	$0.558535\pi$
$492$	4.42869	+	3.21763i	0.199661	+	0.145062i
$493$	−2.74365	−	8.44409i	−0.123568	−	0.380303i
$494$	1.67361	−	5.15085i	0.0752994	−	0.231748i
$495$	13.0482			0.586472
$496$	−7.26337	−	5.89440i	−0.326135	−	0.264666i
$497$	−7.61548			−0.341601
$498$	−2.62976	+	8.09357i	−0.117842	+	0.362682i
$499$	−1.66326	−	5.11900i	−0.0744579	−	0.229158i	0.906900	−	0.421345i	$-0.138442\pi$
$499$	−1.66326	−	5.11900i	−0.0744579	−	0.229158i	−0.981358	+	0.192187i	$0.938442\pi$
$500$	−1.28195	−	0.931393i	−0.0573307	−	0.0416532i
$501$	27.2988			1.21962
$502$	−8.19977			−0.365974
$503$	17.4863	+	12.7045i	0.779674	+	0.566466i	0.904881	−	0.425664i	$-0.139960\pi$
$503$	17.4863	+	12.7045i	0.779674	+	0.566466i	−0.125207	+	0.992131i	$0.539960\pi$
$504$	30.9814	−	22.5093i	1.38002	−	1.00264i
$505$	11.8181	−	8.58635i	0.525898	−	0.382088i
$506$	3.17664	−	9.77670i	0.141219	−	0.434627i
$507$	−6.92982	−	5.03481i	−0.307764	−	0.223604i
$508$	−1.67228	+	5.14674i	−0.0741953	+	0.228350i
$509$	8.67739	+	26.7063i	0.384619	+	1.18373i	0.936757	+	0.349981i	$0.113812\pi$
$509$	8.67739	+	26.7063i	0.384619	+	1.18373i	−0.552138	+	0.833753i	$0.686188\pi$
$510$	−7.07634	+	5.14127i	−0.313346	+	0.227659i
$511$	11.6464	+	35.8441i	0.515208	+	1.58565i
$512$	5.36005	+	16.4965i	0.236883	+	0.729051i
$513$	12.6484	−	9.18962i	0.558442	−	0.405732i
$514$	0.996387	+	3.06656i	0.0439487	+	0.135260i
$515$	3.16616	−	9.74445i	0.139518	−	0.429392i
$516$	−29.0726	−	21.1225i	−1.27985	−	0.929865i
$517$	4.77884	−	14.7078i	0.210173	−	0.646846i
$518$	18.0436	−	13.1094i	0.792788	−	0.575994i
$519$	−42.5741	+	30.9319i	−1.86880	+	1.35776i
$520$	7.46036	+	5.42027i	0.327159	+	0.237695i
$521$	15.0815			0.660732			0.330366	−	0.943853i	$-0.392828\pi$
$521$	15.0815			0.660732			0.330366	+	0.943853i	$0.392828\pi$
$522$	6.82858			0.298879
$523$	−21.6669	−	15.7419i	−0.947429	−	0.688347i	0.00276855	−	0.999996i	$-0.499119\pi$
$523$	−21.6669	−	15.7419i	−0.947429	−	0.688347i	−0.950197	+	0.311649i	$0.899119\pi$
$524$	2.42609	+	7.46674i	0.105984	+	0.326186i
$525$	2.70151	−	8.31440i	0.117904	−	0.362870i
$526$	8.62248			0.375958
$527$	−9.29070	+	24.1273i	−0.404709	+	1.05100i
$528$	−11.5621			−0.503177
$529$	7.06860	−	21.7549i	0.307331	−	0.945866i
$530$	−2.45378	−	7.55196i	−0.106585	−	0.328036i
$531$	26.6900	+	19.3914i	1.15825	+	0.841514i
$532$	9.97910			0.432649
$533$	−4.71811			−0.204364
$534$	0.577421	+	0.419521i	0.0249874	+	0.0181544i
$535$	8.30568	−	6.03443i	0.359086	−	0.260891i
$536$	19.0208	−	13.8194i	0.821574	−	0.596909i
$537$	−6.76131	+	20.8092i	−0.291772	+	0.897982i
$538$	−8.09919	−	5.88441i	−0.349181	−	0.253695i
$539$	−1.41769	+	4.36319i	−0.0610641	+	0.187936i
$540$	3.63636	+	11.1916i	0.156484	+	0.481609i
$541$	−2.95260	+	2.14519i	−0.126942	+	0.0922288i	−0.649445	−	0.760409i	$-0.724999\pi$
$541$	−2.95260	+	2.14519i	−0.126942	+	0.0922288i	0.522503	+	0.852638i	$0.324999\pi$
$542$	−1.02293	−	3.14825i	−0.0439386	−	0.135229i
$543$	−3.84926	−	11.8468i	−0.165187	−	0.508395i
$544$	21.4268	−	15.5675i	0.918668	−	0.667452i
$545$	−3.28206	−	10.1012i	−0.140588	−	0.432686i
$546$	−6.94978	+	21.3892i	−0.297423	+	0.915374i
$547$	−7.91720	−	5.75218i	−0.338515	−	0.245946i	0.405520	−	0.914086i	$-0.367090\pi$
$547$	−7.91720	−	5.75218i	−0.338515	−	0.245946i	−0.744035	+	0.668141i	$0.767090\pi$
$548$	−2.53233	+	7.79372i	−0.108176	+	0.332931i
$549$	−5.22968	+	3.79958i	−0.223197	+	0.162162i
$550$	1.22789	−	0.892112i	0.0523572	−	0.0380398i
$551$	3.25657	+	2.36604i	0.138735	+	0.100797i
$552$	45.7323			1.94650
$553$	−35.1679			−1.49549
$554$	−6.20116	−	4.50540i	−0.263462	−	0.191416i
$555$	10.4470	+	32.1525i	0.443450	+	1.36480i
$556$	7.27611	−	22.3935i	0.308576	−	0.949698i
$557$	−34.7028			−1.47041			−0.735203	−	0.677847i	$-0.762913\pi$
$557$	−34.7028			−1.47041			−0.735203	+	0.677847i	$0.762913\pi$
$558$	−15.4401	−	12.5300i	−0.653631	−	0.530437i
$559$	30.9725			1.31000
$560$	−1.55301	+	4.77969i	−0.0656269	+	0.201979i
$561$	9.87525	+	30.3929i	0.416933	+	1.28319i
$562$	5.09700	+	3.70319i	0.215004	+	0.156210i
$563$	23.4166			0.986892			0.493446	−	0.869777i	$-0.335737\pi$
$563$	23.4166			0.986892			0.493446	+	0.869777i	$0.335737\pi$
$564$	30.4126			1.28060
$565$	−10.1750	−	7.39257i	−0.428065	−	0.311008i
$566$	9.04099	−	6.56867i	0.380021	−	0.276102i
$567$	−12.2943	+	8.93231i	−0.516311	+	0.375122i
$568$	1.81758	−	5.59392i	0.0762638	−	0.234716i
$569$	−24.8737	−	18.0718i	−1.04276	−	0.757611i	−0.0719388	−	0.997409i	$-0.522919\pi$
$569$	−24.8737	−	18.0718i	−1.04276	−	0.757611i	−0.970823	+	0.239798i	$0.922919\pi$
$570$	1.22543	−	3.77150i	0.0513278	−	0.157971i
$571$	−13.6101	−	41.8875i	−0.569563	−	1.75294i	−0.653987	−	0.756505i	$-0.726905\pi$
$571$	−13.6101	−	41.8875i	−0.569563	−	1.75294i	0.0844241	−	0.996430i	$-0.473095\pi$
$572$	12.0490	−	8.75410i	0.503793	−	0.366027i
$573$	−4.70719	−	14.4872i	−0.196645	−	0.605213i
$574$	0.704274	+	2.16753i	0.0293958	+	0.0904711i
$575$	5.47953	−	3.98111i	0.228512	−	0.166024i
$576$	0.541107	+	1.66536i	0.0225461	+	0.0693898i
$577$	−0.538808	+	1.65828i	−0.0224309	+	0.0690351i	−0.961645	−	0.274296i	$-0.911555\pi$
$577$	−0.538808	+	1.65828i	−0.0224309	+	0.0690351i	0.939214	+	0.343331i	$0.111555\pi$
$578$	−2.37919	−	1.72859i	−0.0989615	−	0.0718997i
$579$	9.00400	−	27.7115i	0.374194	−	1.15165i
$580$	−2.45113	+	1.78085i	−0.101778	+	0.0739458i
$581$	10.9335	−	7.94369i	0.453600	−	0.329560i
$582$	2.09650	+	1.52320i	0.0869029	+	0.0631386i
$583$	−29.0113			−1.20153
$584$	−29.1088			−1.20453
$585$	−17.8925	−	12.9997i	−0.739764	−	0.537470i
$586$	−5.24083	−	16.1296i	−0.216497	−	0.666309i
$587$	1.76569	−	5.43425i	0.0728780	−	0.224295i	−0.907982	−	0.419009i	$-0.862378\pi$
$587$	1.76569	−	5.43425i	0.0728780	−	0.224295i	0.980860	+	0.194713i	$0.0623777\pi$
$588$	−9.02217			−0.372068
$589$	−3.02190	−	11.3254i	−0.124515	−	0.466657i
$590$	3.83743			0.157985
$591$	13.7320	−	42.2628i	0.564860	−	1.73846i
$592$	−6.00565	−	18.4835i	−0.246831	−	0.759666i
$593$	−20.2764	−	14.7317i	−0.832652	−	0.604957i	0.0876560	−	0.996151i	$-0.472062\pi$
$593$	−20.2764	−	14.7317i	−0.832652	−	0.604957i	−0.920309	+	0.391193i	$0.872062\pi$
$594$	−11.2712			−0.462464
$595$	13.8906			0.569459
$596$	26.5699	+	19.3042i	1.08835	+	0.790730i
$597$	−36.0179	+	26.1685i	−1.47411	+	1.07101i
$598$	−14.0964	+	10.2416i	−0.576443	+	0.418811i
$599$	6.26818	−	19.2915i	0.256111	−	0.788228i	−0.737498	−	0.675349i	$-0.763993\pi$
$599$	6.26818	−	19.2915i	0.256111	−	0.788228i	0.993609	−	0.112879i	$-0.0360072\pi$
$600$	5.46254	+	3.96877i	0.223007	+	0.162024i
$601$	1.39916	−	4.30616i	0.0570728	−	0.175652i	−0.918456	−	0.395523i	$-0.870564\pi$
$601$	1.39916	−	4.30616i	0.0570728	−	0.175652i	0.975529	+	0.219871i	$0.0705635\pi$
$602$	−4.62328	−	14.2290i	−0.188431	−	0.579930i
$603$	−45.6184	+	33.1437i	−1.85773	+	1.34972i
$604$	4.27318	+	13.1515i	0.173873	+	0.535127i
$605$	1.68564	+	5.18785i	0.0685308	+	0.210916i
$606$	−22.2611	+	16.1736i	−0.904295	+	0.657009i
$607$	13.0329	+	40.1110i	0.528987	+	1.62805i	0.756294	+	0.654232i	$0.227008\pi$
$607$	13.0329	+	40.1110i	0.528987	+	1.62805i	−0.227307	+	0.973823i	$0.572992\pi$
$608$	−3.71056	+	11.4199i	−0.150483	+	0.463139i
$609$	−13.5231	−	9.82511i	−0.547984	−	0.398134i
$610$	−0.232354	+	0.715112i	−0.00940773	+	0.0289540i
$611$	−21.2061	+	15.4071i	−0.857908	+	0.623306i
$612$	−32.9850	+	23.9650i	−1.33334	+	0.968729i
$613$	15.4350	+	11.2142i	0.623413	+	0.452936i	0.854112	−	0.520089i	$-0.174101\pi$
$613$	15.4350	+	11.2142i	0.623413	+	0.452936i	−0.230699	+	0.973025i	$0.574101\pi$
$614$	9.93143			0.400800
$615$	−3.45465			−0.139305
$616$	−13.1663	−	9.56591i	−0.530487	−	0.385421i
$617$	−3.13305	−	9.64253i	−0.126132	−	0.388194i	0.867974	−	0.496610i	$-0.165422\pi$
$617$	−3.13305	−	9.64253i	−0.126132	−	0.388194i	−0.994106	+	0.108416i	$0.965422\pi$
$618$	−5.96393	+	18.3551i	−0.239904	+	0.738350i
$619$	18.6209			0.748437			0.374218	−	0.927341i	$-0.377911\pi$
$619$	18.6209			0.748437			0.374218	+	0.927341i	$0.377911\pi$
$620$	8.80999	+	0.470988i	0.353818	+	0.0189153i
$621$	−50.2986			−2.01841
$622$	−1.26974	+	3.90785i	−0.0509118	+	0.156690i
$623$	−0.350257	−	1.07798i	−0.0140327	−	0.0431884i
$624$	15.8547	+	11.5191i	0.634697	+	0.461135i
$625$	1.00000			0.0400000
$626$	−13.0672			−0.522272
$627$	−11.7214	−	8.51609i	−0.468107	−	0.340100i
$628$	−1.87794	+	1.36441i	−0.0749382	+	0.0544458i
$629$	−43.4573	+	31.5736i	−1.73276	+	1.25892i
$630$	−3.30131	+	10.1604i	−0.131527	+	0.404800i
$631$	−9.22332	−	6.70114i	−0.367175	−	0.266768i	0.388864	−	0.921295i	$-0.372868\pi$
$631$	−9.22332	−	6.70114i	−0.367175	−	0.266768i	−0.756038	+	0.654527i	$0.772868\pi$
$632$	8.39347	−	25.8324i	0.333874	−	1.02756i
$633$	2.51503	+	7.74047i	0.0999636	+	0.307656i
$634$	−16.2153	+	11.7811i	−0.643993	+	0.467888i
$635$	−1.05534	−	3.24801i	−0.0418800	−	0.128893i
$636$	−17.6304	−	54.2609i	−0.699092	−	2.15159i
$637$	6.29099	−	4.57067i	0.249258	−	0.181097i
$638$	−0.896762	−	2.75995i	−0.0355032	−	0.109267i
$639$	−4.35917	+	13.4161i	−0.172446	+	0.530734i
$640$	−9.06382	−	6.58525i	−0.358279	−	0.260305i
$641$	0.456684	−	1.40553i	0.0180379	−	0.0555150i	−0.941632	−	0.336643i	$-0.890708\pi$
$641$	0.456684	−	1.40553i	0.0180379	−	0.0555150i	0.959670	+	0.281128i	$0.0907085\pi$
$642$	−15.6449	+	11.3667i	−0.617457	+	0.448609i
$643$	−12.7582	+	9.26940i	−0.503135	+	0.365549i	−0.810213	−	0.586135i	$-0.800649\pi$
$643$	−12.7582	+	9.26940i	−0.503135	+	0.365549i	0.307078	+	0.951684i	$0.400649\pi$
$644$	−25.9732	−	18.8707i	−1.02349	−	0.743609i
$645$	22.6784			0.892960
$646$	6.30092			0.247906
$647$	13.6869	+	9.94414i	0.538089	+	0.390945i	0.823375	−	0.567498i	$-0.192089\pi$
$647$	13.6869	+	9.94414i	0.538089	+	0.390945i	−0.285286	+	0.958443i	$0.592089\pi$
$648$	−3.62694	−	11.1626i	−0.142480	−	0.438507i
$649$	4.33249	−	13.3340i	0.170065	−	0.523406i
$650$	−2.57255			−0.100904
$651$	12.5486	+	47.0296i	0.491819	+	1.84323i
$652$	26.3267			1.03103
$653$	3.52786	−	10.8576i	0.138056	−	0.424892i	−0.857997	−	0.513655i	$-0.828291\pi$
$653$	3.52786	−	10.8576i	0.138056	−	0.424892i	0.996053	+	0.0887626i	$0.0282912\pi$
$654$	6.18224	+	19.0270i	0.241745	+	0.744014i
$655$	−4.00837	−	2.91225i	−0.156620	−	0.113791i
$656$	1.98597			0.0775390
$657$	69.8128			2.72366
$658$	10.2436	+	7.44240i	0.399337	+	0.290135i
$659$	22.8827	−	16.6253i	0.891385	−	0.647629i	−0.0448538	−	0.998994i	$-0.514282\pi$
$659$	22.8827	−	16.6253i	0.891385	−	0.647629i	0.936239	+	0.351364i	$0.114282\pi$
$660$	8.82237	−	6.40983i	0.343410	−	0.249502i
$661$	7.51580	−	23.1313i	0.292331	−	0.899702i	−0.691774	−	0.722114i	$-0.743171\pi$
$661$	7.51580	−	23.1313i	0.292331	−	0.899702i	0.984105	−	0.177588i	$-0.0568293\pi$
$662$	12.3397	+	8.96535i	0.479598	+	0.348448i
$663$	16.7383	−	51.5152i	0.650062	−	2.00068i
$664$	3.22551	+	9.92711i	0.125174	+	0.385246i
$665$	−5.09489	+	3.70165i	−0.197571	+	0.143544i
$666$	−12.7665	−	39.2912i	−0.494691	−	1.52250i
$667$	−4.00186	−	12.3165i	−0.154953	−	0.476896i
$668$	11.9746	−	8.70003i	0.463310	−	0.336614i
$669$	−18.1037	−	55.7174i	−0.699929	−	2.15416i
$670$	−2.02682	+	6.23792i	−0.0783030	+	0.240992i
$671$	2.22249	+	1.61473i	0.0857982	+	0.0623360i
$672$	15.4083	−	47.4219i	0.594388	−	1.82934i
$673$	2.01633	−	1.46495i	0.0777240	−	0.0564698i	−0.548245	−	0.836318i	$-0.684704\pi$
$673$	2.01633	−	1.46495i	0.0777240	−	0.0564698i	0.625969	+	0.779848i	$0.284704\pi$
$674$	−2.88120	+	2.09331i	−0.110980	+	0.0806314i
$675$	−6.00797	−	4.36505i	−0.231247	−	0.168011i
$676$	−4.64433			−0.178628
$677$	21.8810			0.840954			0.420477	−	0.907303i	$-0.361863\pi$
$677$	21.8810			0.840954			0.420477	+	0.907303i	$0.361863\pi$
$678$	19.1661	+	13.9250i	0.736069	+	0.534785i
$679$	−1.27172	−	3.91394i	−0.0488040	−	0.150203i
$680$	−3.31525	+	10.2033i	−0.127134	+	0.391278i
$681$	27.7495			1.06336
$682$	−3.03666	+	7.88602i	−0.116280	+	0.301971i
$683$	11.8465			0.453294			0.226647	−	0.973977i	$-0.427224\pi$
$683$	11.8465			0.453294			0.226647	+	0.973977i	$0.427224\pi$
$684$	5.71213	−	17.5801i	0.218409	−	0.672193i
$685$	−1.59811	−	4.91847i	−0.0610606	−	0.187925i
$686$	7.87976	+	5.72498i	0.300851	+	0.218581i
$687$	−63.7674			−2.43288
$688$	−13.0371			−0.497034
$689$	39.7822	+	28.9035i	1.51558	+	1.10113i
$690$	−10.3215	+	7.49900i	−0.392932	+	0.285482i
$691$	−17.2968	+	12.5669i	−0.658002	+	0.478066i	−0.865988	−	0.500066i	$-0.833309\pi$
$691$	−17.2968	+	12.5669i	−0.658002	+	0.478066i	0.207986	+	0.978132i	$0.433309\pi$
$692$	−8.81717	+	27.1364i	−0.335178	+	1.03157i
$693$	31.5774	+	22.9423i	1.19953	+	0.871507i
$694$	−1.49062	+	4.58765i	−0.0565831	+	0.174145i
$695$	4.59182	+	14.1322i	0.174178	+	0.536063i
$696$	10.4445	−	7.58840i	0.395899	−	0.287638i
$697$	−1.69622	−	5.22043i	−0.0642489	−	0.197738i
$698$	−5.17444	−	15.9253i	−0.195855	−	0.602781i
$699$	1.52941	−	1.11118i	0.0578476	−	0.0420287i
$700$	−1.46476	−	4.50806i	−0.0553626	−	0.170389i
$701$	−3.19701	+	9.83939i	−0.120750	+	0.371629i	−0.993103	−	0.117247i	$-0.962593\pi$
$701$	−3.19701	+	9.83939i	−0.120750	+	0.371629i	0.872353	+	0.488876i	$0.162593\pi$
$702$	15.4558	+	11.2293i	0.583342	+	0.423823i
$703$	7.52564	−	23.1615i	0.283835	−	0.873554i
$704$	0.602037	−	0.437405i	0.0226901	−	0.0164853i
$705$	−15.5273	+	11.2813i	−0.584792	+	0.424876i
$706$	−11.2233	−	8.15419i	−0.422394	−	0.306887i
$707$	43.6977			1.64342
$708$	27.5720			1.03622
$709$	−25.0928	−	18.2310i	−0.942382	−	0.684680i	0.00661112	−	0.999978i	$-0.497896\pi$
$709$	−25.0928	−	18.2310i	−0.942382	−	0.684680i	−0.948993	+	0.315298i	$0.897896\pi$
$710$	0.507054	+	1.56055i	0.0190294	+	0.0585664i
$711$	−20.1304	+	61.9550i	−0.754949	+	2.32350i
$712$	0.875422			0.0328078
$713$	−13.5513	+	35.1919i	−0.507501	+	1.31795i
$714$	−26.1650			−0.979199
$715$	−2.90443	+	8.93891i	−0.108619	+	0.334296i
$716$	3.66597	+	11.2827i	0.137004	+	0.421655i
$717$	58.7171	+	42.6605i	2.19283	+	1.59318i
$718$	5.36598			0.200257
$719$	−6.74458			−0.251530			−0.125765	−	0.992060i	$-0.540139\pi$
$719$	−6.74458			−0.251530			−0.125765	+	0.992060i	$0.540139\pi$
$720$	7.53139	+	5.47187i	0.280678	+	0.203925i
$721$	24.7958	−	18.0152i	0.923442	−	0.670920i
$722$	7.59618	−	5.51895i	0.282701	−	0.205394i
$723$	15.5174	−	47.7575i	0.577097	−	1.77612i
$724$	−5.46400	−	3.96983i	−0.203068	−	0.147538i
$725$	0.590849	−	1.81845i	0.0219436	−	0.0675354i
$726$	−3.17514	−	9.77207i	−0.117840	−	0.362676i
$727$	−33.2568	+	24.1625i	−1.23343	+	0.896137i	−0.997142	−	0.0755467i	$-0.975930\pi$
$727$	−33.2568	+	24.1625i	−1.23343	+	0.896137i	−0.236285	+	0.971684i	$0.575930\pi$
$728$	8.52419	+	26.2348i	0.315928	+	0.972325i
$729$	−11.4214	−	35.1516i	−0.423016	−	1.30191i
$730$	6.56966	−	4.77314i	0.243154	−	0.176662i
$731$	11.1350	+	34.2700i	0.411843	+	1.26752i
$732$	−1.66946	+	5.13808i	−0.0617052	+	0.189909i
$733$	9.98768	+	7.25648i	0.368904	+	0.268024i	0.756756	−	0.653697i	$-0.226783\pi$
$733$	9.98768	+	7.25648i	0.368904	+	0.268024i	−0.387853	+	0.921721i	$0.626783\pi$
$734$	5.57622	−	17.1618i	0.205822	−	0.633455i
$735$	4.60632	−	3.34669i	0.169907	−	0.123444i
$736$	31.2530	−	22.7066i	1.15200	−	0.836977i
$737$	19.3868	+	14.0853i	0.714120	+	0.518839i
$738$	4.22166			0.155402
$739$	−12.4607			−0.458373			−0.229186	−	0.973383i	$-0.573607\pi$
$739$	−12.4607			−0.458373			−0.229186	+	0.973383i	$0.573607\pi$
$740$	14.8294	+	10.7742i	0.545141	+	0.396068i
$741$	7.58870	+	23.3556i	0.278778	+	0.857990i
$742$	7.34014	−	22.5906i	0.269465	−	0.829329i
$743$	−3.43119			−0.125878			−0.0629391	−	0.998017i	$-0.520047\pi$
$743$	−3.43119			−0.125878			−0.0629391	+	0.998017i	$0.520047\pi$
$744$	−37.5404	−	2.00693i	−1.37630	−	0.0735778i
$745$	−20.7261			−0.759347
$746$	−0.927174	+	2.85355i	−0.0339463	+	0.104476i
$747$	−7.73588	−	23.8086i	−0.283041	−	0.871111i
$748$	14.0179	+	10.1846i	0.512544	+	0.372385i
$749$	30.7104			1.12214
$750$	−1.88364			−0.0687810
$751$	−17.0563	−	12.3921i	−0.622392	−	0.452194i	0.231364	−	0.972867i	$-0.425681\pi$
$751$	−17.0563	−	12.3921i	−0.622392	−	0.452194i	−0.853756	+	0.520673i	$0.825681\pi$
$752$	8.92617	−	6.48524i	0.325504	−	0.236492i
$753$	30.0796	−	21.8541i	1.09616	−	0.796408i
$754$	−1.51999	+	4.67805i	−0.0553548	+	0.170364i
$755$	−7.06012	−	5.12948i	−0.256944	−	0.186681i
$756$	−10.8777	+	33.4780i	−0.395617	+	1.21758i
$757$	12.4506	+	38.3190i	0.452525	+	1.39273i	0.874016	+	0.485897i	$0.161507\pi$
$757$	12.4506	+	38.3190i	0.452525	+	1.39273i	−0.421491	+	0.906832i	$0.638493\pi$
$758$	−0.511145	+	0.371369i	−0.0185656	+	0.0134887i
$759$	14.4039	+	44.3308i	0.522830	+	1.60910i
$760$	−1.50305	−	4.62590i	−0.0545212	−	0.167799i
$761$	27.6988	−	20.1243i	1.00408	−	0.729506i	0.0411200	−	0.999154i	$-0.486907\pi$
$761$	27.6988	−	20.1243i	1.00408	−	0.729506i	0.962959	+	0.269648i	$0.0869074\pi$
$762$	1.98789	+	6.11810i	0.0720137	+	0.221635i
$763$	9.81783	−	30.2162i	0.355429	−	1.09390i
$764$	−6.68183	−	4.85463i	−0.241740	−	0.175634i
$765$	7.95110	−	24.4710i	0.287473	−	0.884750i
$766$	5.73845	−	4.16923i	0.207339	−	0.150640i
$767$	−19.2254	+	13.9681i	−0.694190	+	0.504358i
$768$	18.5674	+	13.4900i	0.669992	+	0.486778i
$769$	−29.8891			−1.07783			−0.538915	−	0.842360i	$-0.681166\pi$
$769$	−29.8891			−1.07783			−0.538915	+	0.842360i	$0.681166\pi$
$770$	4.54014			0.163615
$771$	−11.8281	−	8.59364i	−0.425980	−	0.309492i
$772$	−4.88196	−	15.0251i	−0.175706	−	0.540766i
$773$	4.76094	−	14.6527i	0.171239	−	0.527019i	−0.828203	−	0.560429i	$-0.810636\pi$
$773$	4.76094	−	14.6527i	0.171239	−	0.527019i	0.999442	+	0.0334092i	$0.0106365\pi$
$774$	−27.7135			−0.996142
$775$	−4.67270	+	3.02752i	−0.167848	+	0.108752i
$776$	3.17849			0.114101
$777$	−31.2507	+	96.1797i	−1.12111	+	3.45043i
$778$	−0.589780	−	1.81516i	−0.0211446	−	0.0650765i
$779$	2.01332	+	1.46277i	0.0721348	+	0.0524090i
$780$	−18.4838			−0.661826
$781$	5.99496			0.214516
$782$	−16.3998	−	11.9152i	−0.586456	−	0.426085i
$783$	−11.4874	+	8.34610i	−0.410527	+	0.298265i
$784$	−2.64803	+	1.92391i	−0.0945725	+	0.0687109i
$785$	0.452682	−	1.39321i	0.0161569	−	0.0497258i
$786$	7.55035	+	5.48565i	0.269312	+	0.195667i
$787$	−0.163564	+	0.503398i	−0.00583042	+	0.0179442i	−0.953929	−	0.300031i	$-0.903003\pi$
$787$	−0.163564	+	0.503398i	−0.00583042	+	0.0179442i	0.948099	+	0.317975i	$0.103003\pi$
$788$	−7.44548	−	22.9148i	−0.265234	−	0.816307i
$789$	−31.6302	+	22.9807i	−1.12607	+	0.818135i
$790$	2.34155	+	7.20654i	0.0833085	+	0.256397i
$791$	−11.6259	−	35.7809i	−0.413371	−	1.27222i
$792$	−24.3887	+	17.7195i	−0.866616	+	0.629633i
$793$	−1.43889	−	4.42845i	−0.0510965	−	0.157259i
$794$	−2.78512	+	8.57172i	−0.0988402	+	0.304199i
$795$	29.1289	+	21.1634i	1.03310	+	0.750588i
$796$	−7.45935	+	22.9575i	−0.264390	+	0.813708i
$797$	32.9292	−	23.9245i	1.16641	−	0.847448i	0.175837	−	0.984419i	$-0.443737\pi$
$797$	32.9292	−	23.9245i	1.16641	−	0.847448i	0.990575	+	0.136971i	$0.0437368\pi$
$798$	9.59696	−	6.97260i	0.339729	−	0.246827i
$799$	−24.6713	−	17.9248i	−0.872809	−	0.634133i
$800$	5.70359			0.201652
$801$	−2.09956			−0.0741843
$802$	−16.6844	−	12.1219i	−0.589147	−	0.428041i
$803$	−9.16816	−	28.2167i	−0.323537	−	0.995745i
$804$	−14.5627	+	44.8195i	−0.513588	+	1.58066i
$805$	20.2607			0.714095
$806$	12.0208	−	7.78844i	0.423413	−	0.274336i
$807$	45.3938			1.59794
$808$	−10.4293	+	32.0980i	−0.366900	+	1.12920i
$809$	−6.11645	−	18.8245i	−0.215043	−	0.661834i	−0.999151	−	0.0412094i	$-0.986879\pi$
$809$	−6.11645	−	18.8245i	−0.215043	−	0.661834i	0.784107	−	0.620625i	$-0.213121\pi$
$810$	2.64897	+	1.92459i	0.0930753	+	0.0676232i
$811$	−28.3575			−0.995765			−0.497882	−	0.867245i	$-0.665889\pi$
$811$	−28.3575			−0.995765			−0.497882	+	0.867245i	$0.665889\pi$
$812$	−9.06311			−0.318053
$813$	12.1432	+	8.82256i	0.425881	+	0.309421i
$814$	−14.2040	+	10.3198i	−0.497850	+	0.361709i
$815$	−13.4413	+	9.76565i	−0.470827	+	0.342076i
$816$	−7.04555	+	21.6840i	−0.246644	+	0.759091i
$817$	−13.2167	−	9.60247i	−0.462393	−	0.335948i
$818$	−3.87112	+	11.9141i	−0.135351	+	0.416566i
$819$	−20.4439	−	62.9200i	−0.714369	−	2.19860i
$820$	−1.51537	+	1.10098i	−0.0529191	+	0.0384480i
$821$	−4.05632	−	12.4841i	−0.141567	−	0.435697i	0.854987	−	0.518650i	$-0.173565\pi$
$821$	−4.05632	−	12.4841i	−0.141567	−	0.435697i	−0.996554	+	0.0829523i	$0.973565\pi$
$822$	3.01027	+	9.26465i	0.104995	+	0.323142i
$823$	24.5890	−	17.8649i	0.857118	−	0.622732i	−0.0699816	−	0.997548i	$-0.522294\pi$
$823$	24.5890	−	17.8649i	0.857118	−	0.622732i	0.927099	+	0.374816i	$0.122294\pi$
$824$	7.31501	+	22.5133i	0.254830	+	0.784287i
$825$	−2.12665	+	6.54515i	−0.0740404	+	0.227873i
$826$	9.28682	+	6.74727i	0.323130	+	0.234767i
$827$	−2.23939	+	6.89214i	−0.0778712	+	0.239663i	−0.982413	−	0.186723i	$-0.940213\pi$
$827$	−2.23939	+	6.89214i	−0.0778712	+	0.239663i	0.904541	+	0.426386i	$0.140213\pi$
$828$	−48.1117	+	34.9552i	−1.67200	+	1.21478i
$829$	24.0117	−	17.4455i	0.833962	−	0.605909i	−0.0867155	−	0.996233i	$-0.527637\pi$
$829$	24.0117	−	17.4455i	0.833962	−	0.605909i	0.920677	+	0.390324i	$0.127637\pi$
$830$	−2.35578	−	1.71158i	−0.0817705	−	0.0594097i
$831$	34.7558			1.20567
$832$	−1.26133			−0.0437288
$833$	7.31898	+	5.31755i	0.253588	+	0.184242i
$834$	−8.64935	−	26.6200i	−0.299502	−	0.921774i
$835$	−2.88649	+	8.88370i	−0.0998911	+	0.307433i
$836$	−7.85562			−0.271692
$837$	41.2887	+	2.20732i	1.42715	+	0.0762963i
$838$	13.9914			0.483326
$839$	−8.28514	+	25.4990i	−0.286035	+	0.880325i	0.700052	+	0.714092i	$0.253160\pi$
$839$	−8.28514	+	25.4990i	−0.286035	+	0.880325i	−0.986087	+	0.166233i	$0.946840\pi$
$840$	6.24149	+	19.2093i	0.215352	+	0.662785i
$841$	20.5038	+	14.8969i	0.707029	+	0.513687i
$842$	17.3471			0.597822
$843$	−28.5673			−0.983911
$844$	3.57008	+	2.59381i	0.122887	+	0.0892827i
$845$	2.37119	−	1.72277i	0.0815714	−	0.0592651i
$846$	18.9748	−	13.7860i	0.652366	−	0.473971i
$847$	−5.04234	+	15.5187i	−0.173257	+	0.533230i
$848$	−16.7453	−	12.1662i	−0.575036	−	0.417788i
$849$	−15.6586	+	48.1923i	−0.537403	+	1.65395i
$850$	−0.924864	−	2.84644i	−0.0317226	−	0.0976320i
$851$	−63.3864	+	46.0529i	−2.17286	+	1.57867i
$852$	3.64319	+	11.2126i	0.124813	+	0.384136i
$853$	1.56005	+	4.80135i	0.0534152	+	0.164395i	0.974205	−	0.225663i	$-0.0724549\pi$
$853$	1.56005	+	4.80135i	0.0534152	+	0.164395i	−0.920790	+	0.390058i	$0.872455\pi$
$854$	−1.81967	+	1.32207i	−0.0622680	+	0.0452403i
$855$	3.60482	+	11.0945i	0.123282	+	0.379424i
$856$	−7.32962	+	22.5583i	−0.250521	+	0.771025i
$857$	−29.1182	−	21.1556i	−0.994660	−	0.722663i	−0.0337236	−	0.999431i	$-0.510737\pi$
$857$	−29.1182	−	21.1556i	−0.994660	−	0.722663i	−0.960937	+	0.276768i	$0.910737\pi$
$858$	5.47091	−	16.8377i	0.186774	−	0.574831i
$859$	5.35453	−	3.89029i	0.182694	−	0.132735i	−0.492679	−	0.870211i	$-0.663982\pi$
$859$	5.35453	−	3.89029i	0.182694	−	0.132735i	0.675374	+	0.737476i	$0.263982\pi$
$860$	9.94782	−	7.22752i	0.339218	−	0.246456i
$861$	−8.36045	−	6.07422i	−0.284923	−	0.207009i
$862$	−9.77493			−0.332935
$863$	−28.7811			−0.979721			−0.489861	−	0.871801i	$-0.662952\pi$
$863$	−28.7811			−0.979721			−0.489861	+	0.871801i	$0.662952\pi$
$864$	−34.2670	−	24.8964i	−1.16579	−	0.846994i
$865$	−5.56435	−	17.1253i	−0.189194	−	0.582278i
$866$	−3.29182	+	10.1312i	−0.111861	+	0.344271i
$867$	13.3348			0.452872
$868$	20.4926	+	16.6302i	0.695564	+	0.564467i
$869$	27.6844			0.939129
$870$	−1.11295	+	3.42531i	−0.0377325	+	0.116129i
$871$	−12.5514	−	38.6293i	−0.425289	−	1.30891i
$872$	19.8520	+	14.4233i	0.672273	+	0.488435i
$873$	−7.62310			−0.258003
$874$	9.19046			0.310872
$875$	2.42006	+	1.75828i	0.0818130	+	0.0594406i
$876$	47.2031	−	34.2950i	1.59484	−	1.15872i
$877$	23.5374	−	17.1009i	0.794801	−	0.577456i	−0.114584	−	0.993414i	$-0.536553\pi$
$877$	23.5374	−	17.1009i	0.794801	−	0.577456i	0.909384	+	0.415957i	$0.136553\pi$
$878$	0.419500	−	1.29109i	0.0141575	−	0.0435722i
$879$	62.2140	+	45.2011i	2.09843	+	1.52460i
$880$	1.22254	−	3.76260i	0.0412119	−	0.126837i
$881$	−5.21121	−	16.0385i	−0.175570	−	0.540349i	0.824089	−	0.566460i	$-0.191688\pi$
$881$	−5.21121	−	16.0385i	−0.175570	−	0.540349i	−0.999659	+	0.0261113i	$0.991688\pi$
$882$	−5.62904	+	4.08973i	−0.189540	+	0.137709i
$883$	−4.74308	−	14.5977i	−0.159617	−	0.491251i	0.838982	−	0.544159i	$-0.183151\pi$
$883$	−4.74308	−	14.5977i	−0.159617	−	0.491251i	−0.998599	+	0.0529076i	$0.983151\pi$
$884$	−9.07549	−	27.9315i	−0.305242	−	0.939437i
$885$	−14.0770	+	10.2276i	−0.473194	+	0.343796i
$886$	−5.77660	−	17.7786i	−0.194069	−	0.597282i
$887$	7.10402	−	21.8639i	0.238530	−	0.734119i	−0.758104	−	0.652134i	$-0.773874\pi$
$887$	7.10402	−	21.8639i	0.238530	−	0.734119i	0.996634	−	0.0819852i	$-0.0261260\pi$
$888$	−63.1899	−	45.9102i	−2.12051	−	1.54064i
$889$	3.15691	−	9.71597i	0.105879	−	0.325863i
$890$	−0.197577	+	0.143548i	−0.00662280	+	0.00481174i
$891$	9.67813	−	7.03157i	0.324230	−	0.235567i
$892$	−25.6981	−	18.6708i	−0.860436	−	0.625143i
$893$	13.8258			0.462664
$894$	39.0407			1.30571
$895$	−6.05690	−	4.40059i	−0.202460	−	0.147096i
$896$	−10.3563	−	31.8734i	−0.345980	−	1.06482i
$897$	24.4143	−	75.1395i	0.815170	−	2.50884i
$898$	13.2503			0.442169
$899$	2.74452	+	10.2859i	0.0915348	+	0.343053i
$900$	−8.78026			−0.292675
$901$	−17.6785	+	54.4088i	−0.588956	+	1.81262i
$902$	−0.554409	−	1.70630i	−0.0184598	−	0.0568135i
$903$	54.8830	+	39.8749i	1.82639	+	1.32695i
$904$	29.0575			0.966438
$905$	4.26225			0.141682
$906$	13.2988	+	9.66211i	0.441821	+	0.321002i
$907$	−23.7817	+	17.2784i	−0.789657	+	0.573720i	−0.907862	−	0.419270i	$-0.862286\pi$
$907$	−23.7817	+	17.2784i	−0.789657	+	0.573720i	0.118204	+	0.992989i	$0.462286\pi$
$908$	12.1723	−	8.84368i	0.403951	−	0.293488i
$909$	25.0129	−	76.9819i	0.829627	−	2.55333i
$910$	−6.22573	−	4.52326i	−0.206381	−	0.149945i
$911$	1.10899	−	3.41313i	0.0367426	−	0.113082i	−0.931003	−	0.365012i	$-0.881065\pi$
$911$	1.10899	−	3.41313i	0.0367426	−	0.113082i	0.967746	+	0.251929i	$0.0810650\pi$
$912$	−3.19427	−	9.83095i	−0.105773	−	0.325535i
$913$	−8.60696	+	6.25332i	−0.284849	+	0.206955i
$914$	−0.199411	−	0.613724i	−0.00659593	−	0.0203002i
$915$	−1.05357	−	3.24255i	−0.0348299	−	0.107195i
$916$	−27.9715	+	20.3225i	−0.924203	+	0.671473i
$917$	−4.57996	−	14.0957i	−0.151243	−	0.465480i
$918$	−6.86828	+	21.1384i	−0.226687	+	0.697671i
$919$	−26.8678	−	19.5206i	−0.886286	−	0.643924i	0.0486213	−	0.998817i	$-0.484517\pi$
$919$	−26.8678	−	19.5206i	−0.886286	−	0.643924i	−0.934907	+	0.354893i	$0.884517\pi$
$920$	−4.83559	+	14.8824i	−0.159425	+	0.490659i
$921$	−36.4319	+	26.4693i	−1.20047	+	0.872195i
$922$	−0.734421	+	0.533588i	−0.0241869	+	0.0175728i
$923$	−8.22067	−	5.97266i	−0.270587	−	0.196593i
$924$	32.6209			1.07315
$925$	−11.5679			−0.380349
$926$	17.8215	+	12.9481i	0.585650	+	0.425499i
$927$	−17.5439	−	53.9946i	−0.576217	−	1.77341i
$928$	3.36996	−	10.3717i	0.110624	−	0.340467i
$929$	−31.7551			−1.04185			−0.520926	−	0.853602i	$-0.674413\pi$
$929$	−31.7551			−1.04185			−0.520926	+	0.853602i	$0.674413\pi$
$930$	8.80171	−	5.70277i	0.288619	−	0.187001i
$931$	−4.10156			−0.134423
$932$	0.316743	−	0.974835i	0.0103753	−	0.0319318i
$933$	−5.75740	−	17.7194i	−0.188489	−	0.580109i
$934$	10.8089	+	7.85310i	0.353677	+	0.256961i
$935$	−10.9348			−0.357605
$936$	51.0970			1.67016
$937$	1.67858	+	1.21956i	0.0548367	+	0.0398412i	0.614866	−	0.788632i	$-0.289210\pi$
$937$	1.67858	+	1.21956i	0.0548367	+	0.0398412i	−0.560029	+	0.828473i	$0.689210\pi$
$938$	−15.8730	+	11.5324i	−0.518272	+	0.376547i
$939$	47.9351	−	34.8269i	1.56430	−	1.13653i
$940$	−3.21573	+	9.89700i	−0.104886	+	0.322805i
$941$	11.5141	+	8.36548i	0.375349	+	0.272707i	0.759425	−	0.650594i	$-0.225480\pi$
$941$	11.5141	+	8.36548i	0.375349	+	0.272707i	−0.384077	+	0.923301i	$0.625480\pi$
$942$	−0.852692	+	2.62432i	−0.0277822	+	0.0855048i
$943$	−2.47409	−	7.61447i	−0.0805675	−	0.247961i
$944$	8.09244	−	5.87950i	0.263387	−	0.191362i
$945$	−6.86470	−	21.1274i	−0.223309	−	0.687273i
$946$	3.63948	+	11.2012i	0.118330	+	0.364181i
$947$	4.49212	−	3.26372i	0.145974	−	0.106057i	−0.512401	−	0.858746i	$-0.671244\pi$
$947$	4.49212	−	3.26372i	0.145974	−	0.106057i	0.658376	+	0.752690i	$0.271244\pi$
$948$	16.8240	+	51.7791i	0.546419	+	1.68171i
$949$	−15.5398	+	47.8266i	−0.504443	+	1.55252i
$950$	1.09776	+	0.797573i	0.0356162	+	0.0258767i
$951$	28.0843	−	86.4345i	0.910695	−	2.80283i
$952$	−25.9633	+	18.8635i	−0.841476	+	0.611368i
$953$	−24.7277	+	17.9657i	−0.801009	+	0.581967i	−0.911210	−	0.411942i	$-0.864851\pi$
$953$	−24.7277	+	17.9657i	−0.801009	+	0.581967i	0.110201	+	0.993909i	$0.464851\pi$
$954$	−35.5962	−	25.8622i	−1.15247	−	0.837319i
$955$	5.21222			0.168664
$956$	39.3519			1.27273
$957$	10.6455	+	7.73439i	0.344119	+	0.250017i
$958$	−1.31623	−	4.05094i	−0.0425255	−	0.130880i
$959$	4.78052	−	14.7129i	0.154371	−	0.475105i
$960$	−0.923557			−0.0298077
$961$	12.6683	−	28.2934i	0.408654	−	0.912689i
$962$	29.7589			0.959465
$963$	17.5789	−	54.1024i	0.566473	−	1.74343i
$964$	−8.41350	−	25.8941i	−0.270981	−	0.833993i
$965$	8.06594	+	5.86025i	0.259652	+	0.188648i
$966$	−38.1639			−1.22790
$967$	43.7449			1.40674			0.703370	−	0.710824i	$-0.251678\pi$
$967$	43.7449			1.40674			0.703370	+	0.710824i	$0.251678\pi$
$968$	−10.1958	−	7.40767i	−0.327705	−	0.238091i
$969$	−23.1140	+	16.7933i	−0.742527	+	0.539478i
$970$	−0.717364	+	0.521196i	−0.0230332	+	0.0167346i
$971$	−6.57403	+	20.2328i	−0.210971	+	0.649301i	0.788445	+	0.615106i	$0.210887\pi$
$971$	−6.57403	+	20.2328i	−0.210971	+	0.649301i	−0.999415	+	0.0341951i	$0.989113\pi$
$972$	−9.52749	−	6.92213i	−0.305594	−	0.222027i
$973$	−13.7358	+	42.2744i	−0.440349	+	1.35525i
$974$	3.90465	+	12.0173i	0.125113	+	0.385059i
$975$	9.43701	−	6.85639i	0.302226	−	0.219580i
$976$	0.605664	+	1.86404i	0.0193868	+	0.0596665i
$977$	0.584362	+	1.79848i	0.0186954	+	0.0575385i	0.959969	−	0.280106i	$-0.0903697\pi$
$977$	0.584362	+	1.79848i	0.0186954	+	0.0575385i	−0.941274	+	0.337645i	$0.890370\pi$
$978$	25.3186	−	18.3950i	0.809599	−	0.588208i
$979$	0.275725	+	0.848593i	0.00881220	+	0.0271212i
$980$	0.953976	−	2.93604i	0.0304736	−	0.0937882i
$981$	−47.6118	−	34.5920i	−1.52013	−	1.10444i
$982$	−1.61403	+	4.96747i	−0.0515058	+	0.158518i
$983$	−26.4673	+	19.2296i	−0.844176	+	0.613330i	−0.923534	−	0.383516i	$-0.874713\pi$
$983$	−26.4673	+	19.2296i	−0.844176	+	0.613330i	0.0793582	+	0.996846i	$0.474713\pi$
$984$	6.45718	−	4.69141i	0.205847	−	0.149557i
$985$	12.3014	+	8.93747i	0.391954	+	0.284772i
$986$	−5.72255			−0.182243
$987$	−57.4126			−1.82746
$988$	10.7721	+	7.82641i	0.342707	+	0.248991i
$989$	16.2414	+	49.9859i	0.516447	+	1.58946i
$990$	2.59882	−	7.99833i	0.0825958	−	0.254204i
$991$	−55.8805			−1.77510			−0.887551	−	0.460709i	$-0.847595\pi$
$991$	−55.8805			−1.77510			−0.887551	+	0.460709i	$0.847595\pi$
$992$	−26.6512	+	17.2677i	−0.846175	+	0.548250i
$993$	−69.1610			−2.19476
$994$	−1.51678	+	4.66817i	−0.0481094	+	0.148065i
$995$	−4.70746	−	14.4881i	−0.149237	−	0.459303i
$996$	−16.9263	−	12.2977i	−0.536331	−	0.389668i
$997$	10.8645			0.344081			0.172040	−	0.985090i	$-0.444964\pi$
$997$	10.8645			0.344081			0.172040	+	0.985090i	$0.444964\pi$
$998$	−3.46914			−0.109814
$999$	69.4993	+	50.4942i	2.19886	+	1.59757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.h.b.101.3	yes	24
5.2	odd	4		775.2.bf.c.349.7		48
5.3	odd	4		775.2.bf.c.349.6		48
5.4	even	2		775.2.k.d.101.4		24
31.2	even	5		4805.2.a.u.1.7		12
31.4	even	5	inner	155.2.h.b.66.3	✓	24
31.29	odd	10		4805.2.a.v.1.7		12
155.4	even	10		775.2.k.d.376.4		24
155.97	odd	20		775.2.bf.c.624.6		48
155.128	odd	20		775.2.bf.c.624.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.h.b.66.3	✓	24	31.4	even	5	inner
155.2.h.b.101.3	yes	24	1.1	even	1	trivial
775.2.k.d.101.4		24	5.4	even	2
775.2.k.d.376.4		24	155.4	even	10
775.2.bf.c.349.6		48	5.3	odd	4
775.2.bf.c.349.7		48	5.2	odd	4
775.2.bf.c.624.6		48	155.97	odd	20
775.2.bf.c.624.7		48	155.128	odd	20
4805.2.a.u.1.7		12	31.2	even	5
4805.2.a.v.1.7		12	31.29	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.199171 - 0.612984i) q^{2} +(0.903105 + 2.77947i) q^{3} +(1.28195 + 0.931393i) q^{4} -1.00000 q^{5} +1.88364 q^{6} +(-2.42006 - 1.75828i) q^{7} +(1.86913 - 1.35800i) q^{8} +(-4.48281 + 3.25695i) q^{9} +O(q^{10})\)	\(q+(0.199171 - 0.612984i) q^{2} +(0.903105 + 2.77947i) q^{3} +(1.28195 + 0.931393i) q^{4} -1.00000 q^{5} +1.88364 q^{6} +(-2.42006 - 1.75828i) q^{7} +(1.86913 - 1.35800i) q^{8} +(-4.48281 + 3.25695i) q^{9} +(-0.199171 + 0.612984i) q^{10} +(1.90509 + 1.38413i) q^{11} +(-1.43104 + 4.40430i) q^{12} +(-1.23340 - 3.79601i) q^{13} +(-1.55980 + 1.13326i) q^{14} +(-0.903105 - 2.77947i) q^{15} +(0.519167 + 1.59783i) q^{16} +(3.75673 - 2.72942i) q^{17} +(1.10362 + 3.39658i) q^{18} +(-0.650565 + 2.00223i) q^{19} +(-1.28195 - 0.931393i) q^{20} +(2.70151 - 8.31440i) q^{21} +(1.22789 - 0.892112i) q^{22} +(5.47953 - 3.98111i) q^{23} +(5.46254 + 3.96877i) q^{24} +1.00000 q^{25} -2.57255 q^{26} +(-6.00797 - 4.36505i) q^{27} +(-1.46476 - 4.50806i) q^{28} +(0.590849 - 1.81845i) q^{29} -1.88364 q^{30} +(-4.67270 + 3.02752i) q^{31} +5.70359 q^{32} +(-2.12665 + 6.54515i) q^{33} +(-0.924864 - 2.84644i) q^{34} +(2.42006 + 1.75828i) q^{35} -8.78026 q^{36} -11.5679 q^{37} +(1.09776 + 0.797573i) q^{38} +(9.43701 - 6.85639i) q^{39} +(-1.86913 + 1.35800i) q^{40} +(0.365283 - 1.12423i) q^{41} +(-4.55853 - 3.31197i) q^{42} +(-2.39794 + 7.38010i) q^{43} +(1.15307 + 3.54877i) q^{44} +(4.48281 - 3.25695i) q^{45} +(-1.34900 - 4.15179i) q^{46} +(-2.02939 - 6.24581i) q^{47} +(-3.97226 + 2.88602i) q^{48} +(0.602037 + 1.85288i) q^{49} +(0.199171 - 0.612984i) q^{50} +(10.9791 + 7.97677i) q^{51} +(1.95442 - 6.01508i) q^{52} +(-9.96708 + 7.24151i) q^{53} +(-3.87232 + 2.81340i) q^{54} +(-1.90509 - 1.38413i) q^{55} -6.91115 q^{56} -6.15268 q^{57} +(-0.997000 - 0.724363i) q^{58} +(-1.83984 - 5.66244i) q^{59} +(1.43104 - 4.40430i) q^{60} +1.16661 q^{61} +(0.925156 + 3.46729i) q^{62} +16.5753 q^{63} +(0.0976541 - 0.300548i) q^{64} +(1.23340 + 3.79601i) q^{65} +(3.58851 + 2.60720i) q^{66} +10.1763 q^{67} +7.35812 q^{68} +(16.0140 + 11.6348i) q^{69} +(1.55980 - 1.13326i) q^{70} +(2.05962 - 1.49640i) q^{71} +(-3.95600 + 12.1753i) q^{72} +(-10.1930 - 7.40561i) q^{73} +(-2.30398 + 7.09091i) q^{74} +(0.903105 + 2.77947i) q^{75} +(-2.69886 + 1.96084i) q^{76} +(-2.17675 - 6.69934i) q^{77} +(-2.32328 - 7.15033i) q^{78} +(9.51120 - 6.91029i) q^{79} +(-0.519167 - 1.59783i) q^{80} +(1.56985 - 4.83151i) q^{81} +(-0.616380 - 0.447826i) q^{82} +(-1.39610 + 4.29676i) q^{83} +(11.2072 - 8.14250i) q^{84} +(-3.75673 + 2.72942i) q^{85} +(4.04629 + 2.93980i) q^{86} +5.58792 q^{87} +5.44050 q^{88} +(0.306544 + 0.222718i) q^{89} +(-1.10362 - 3.39658i) q^{90} +(-3.68954 + 11.3552i) q^{91} +10.7325 q^{92} +(-12.6348 - 10.2535i) q^{93} -4.23278 q^{94} +(0.650565 - 2.00223i) q^{95} +(5.15094 + 15.8530i) q^{96} +(1.11300 + 0.808645i) q^{97} +1.25569 q^{98} -13.0482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} + 18 q^{12} - 5 q^{13} + 6 q^{14} - 24 q^{16} + 7 q^{17} - 18 q^{18} + 2 q^{19} + 6 q^{20} - 10 q^{21} + 28 q^{22} - 15 q^{23} - 32 q^{24} + 24 q^{25} + 22 q^{26} + 9 q^{27} + 38 q^{28} + 15 q^{29} + 16 q^{30} + 6 q^{31} + 74 q^{32} + 5 q^{33} - 20 q^{34} + 9 q^{35} - 58 q^{36} - 56 q^{37} - 21 q^{38} - 10 q^{39} - 11 q^{40} - 24 q^{41} - 38 q^{42} + 21 q^{43} + 41 q^{44} + 6 q^{45} + 48 q^{46} - 8 q^{47} - 26 q^{48} - 23 q^{49} + 2 q^{50} + 26 q^{51} - 27 q^{52} + 26 q^{53} + 11 q^{54} - q^{55} - 48 q^{56} + 62 q^{57} + 52 q^{58} + 10 q^{59} - 18 q^{60} - 40 q^{61} - 28 q^{62} + 26 q^{63} + 9 q^{64} + 5 q^{65} - 2 q^{66} - 26 q^{67} - 8 q^{68} + 64 q^{69} - 6 q^{70} - 7 q^{71} - 127 q^{72} - 51 q^{73} - q^{74} + 43 q^{76} - 39 q^{77} - 31 q^{78} + 31 q^{79} + 24 q^{80} + 34 q^{81} + 58 q^{82} + 6 q^{83} + 113 q^{84} - 7 q^{85} - 22 q^{86} + 4 q^{87} - 28 q^{88} + 13 q^{89} + 18 q^{90} + 54 q^{91} - 2 q^{92} - 72 q^{93} - 10 q^{94} - 2 q^{95} + 101 q^{96} - 39 q^{97} - 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9 - 2 * q^10 + q^11 + 18 * q^12 - 5 * q^13 + 6 * q^14 - 24 * q^16 + 7 * q^17 - 18 * q^18 + 2 * q^19 + 6 * q^20 - 10 * q^21 + 28 * q^22 - 15 * q^23 - 32 * q^24 + 24 * q^25 + 22 * q^26 + 9 * q^27 + 38 * q^28 + 15 * q^29 + 16 * q^30 + 6 * q^31 + 74 * q^32 + 5 * q^33 - 20 * q^34 + 9 * q^35 - 58 * q^36 - 56 * q^37 - 21 * q^38 - 10 * q^39 - 11 * q^40 - 24 * q^41 - 38 * q^42 + 21 * q^43 + 41 * q^44 + 6 * q^45 + 48 * q^46 - 8 * q^47 - 26 * q^48 - 23 * q^49 + 2 * q^50 + 26 * q^51 - 27 * q^52 + 26 * q^53 + 11 * q^54 - q^55 - 48 * q^56 + 62 * q^57 + 52 * q^58 + 10 * q^59 - 18 * q^60 - 40 * q^61 - 28 * q^62 + 26 * q^63 + 9 * q^64 + 5 * q^65 - 2 * q^66 - 26 * q^67 - 8 * q^68 + 64 * q^69 - 6 * q^70 - 7 * q^71 - 127 * q^72 - 51 * q^73 - q^74 + 43 * q^76 - 39 * q^77 - 31 * q^78 + 31 * q^79 + 24 * q^80 + 34 * q^81 + 58 * q^82 + 6 * q^83 + 113 * q^84 - 7 * q^85 - 22 * q^86 + 4 * q^87 - 28 * q^88 + 13 * q^89 + 18 * q^90 + 54 * q^91 - 2 * q^92 - 72 * q^93 - 10 * q^94 - 2 * q^95 + 101 * q^96 - 39 * q^97 - 220 * q^98 - 170 * q^99

Introduction

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