LMFDB - Embedded newform 63.2.f.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
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			43.3
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.2.f.a.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.439693 - 0.761570i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} +(-1.50000 - 0.264490i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})$	\(q+(0.439693 - 0.761570i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} +(-1.50000 - 0.264490i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 + 1.92836i) q^{9} -1.18479 q^{10} +(-0.826352 + 1.43128i) q^{11} +(1.36571 - 1.62760i) q^{12} +(1.68479 + 2.91815i) q^{13} +(0.439693 + 0.761570i) q^{14} +(-1.50000 + 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +0.467911 q^{17} +(0.458111 + 2.59808i) q^{18} -3.22668 q^{19} +(0.826352 - 1.43128i) q^{20} +(1.70574 + 0.300767i) q^{21} +(0.726682 + 1.25865i) q^{22} +(-4.47178 - 7.74535i) q^{23} +(-1.68092 - 4.61830i) q^{24} +(1.59240 - 2.75811i) q^{25} +2.96316 q^{26} +(4.50000 + 2.59808i) q^{27} -1.22668 q^{28} +(-3.13429 + 5.42874i) q^{29} +(0.701867 + 1.92836i) q^{30} +(-4.61721 - 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(2.81908 + 0.497079i) q^{33} +(0.205737 - 0.356347i) q^{34} +1.34730 q^{35} +(-3.45811 - 1.25865i) q^{36} +9.23442 q^{37} +(-1.41875 + 2.45734i) q^{38} +(3.75150 - 4.47086i) q^{39} +(-1.91147 - 3.31077i) q^{40} +(-1.70574 - 2.95442i) q^{41} +(0.979055 - 1.16679i) q^{42} +(2.20574 - 3.82045i) q^{43} -2.02734 q^{44} +(3.79813 + 1.38241i) q^{45} -7.86484 q^{46} +(-4.67752 + 8.10170i) q^{47} +(-0.0714517 - 0.0125989i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.40033 - 2.42544i) q^{50} +(-0.277189 - 0.761570i) q^{51} +(-2.06670 + 3.57964i) q^{52} -0.573978 q^{53} +(3.95723 - 2.28471i) q^{54} +2.22668 q^{55} +(-1.41875 + 2.45734i) q^{56} +(1.91147 + 5.25173i) q^{57} +(2.75624 + 4.77396i) q^{58} +(5.19846 + 9.00400i) q^{59} +(-2.81908 - 0.497079i) q^{60} +(-3.81908 + 6.61484i) q^{61} -8.12061 q^{62} +(-0.520945 - 2.95442i) q^{63} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(1.61809 - 1.92836i) q^{66} +(-0.298133 - 0.516382i) q^{67} +(0.286989 + 0.497079i) q^{68} +(-9.95723 + 11.8666i) q^{69} +(0.592396 - 1.02606i) q^{70} -0.554378 q^{71} +(-6.52094 + 5.47172i) q^{72} +2.04963 q^{73} +(4.06031 - 7.03266i) q^{74} +(-5.43242 - 0.957882i) q^{75} +(-1.97906 - 3.42782i) q^{76} +(-0.826352 - 1.43128i) q^{77} +(-1.75537 - 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} -0.0564370 q^{80} +(1.56283 - 8.86327i) q^{81} -3.00000 q^{82} +(7.52481 - 13.0334i) q^{83} +(0.726682 + 1.99654i) q^{84} +(-0.315207 - 0.545955i) q^{85} +(-1.93969 - 3.35965i) q^{86} +(10.6925 + 1.88538i) q^{87} +(-2.34477 + 4.06126i) q^{88} +9.08647 q^{89} +(2.72281 - 2.28471i) q^{90} -3.36959 q^{91} +(5.48545 - 9.50108i) q^{92} +(-10.2811 + 12.2525i) q^{93} +(4.11334 + 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(6.27719 - 7.48086i) q^{96} +(0.949493 - 1.64457i) q^{97} -0.879385 q^{98} +(-0.860967 - 4.88279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8} - 6 q^{11} + 18 q^{12} + 3 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{17} + 9 q^{18} - 6 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} - 27 q^{24} + 6 q^{25} - 6 q^{26} + 27 q^{27} + 6 q^{28} - 9 q^{29} + 18 q^{30} + 3 q^{31} - 9 q^{34} + 6 q^{35} - 27 q^{36} - 6 q^{37} - 6 q^{38} - 18 q^{39} + 9 q^{40} + 9 q^{42} + 3 q^{43} + 30 q^{44} + 9 q^{45} - 3 q^{47} - 3 q^{49} + 6 q^{50} + 9 q^{51} + 21 q^{52} + 12 q^{53} - 27 q^{54} - 6 q^{56} - 9 q^{57} + 9 q^{58} + 3 q^{59} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} + 36 q^{66} + 12 q^{67} - 6 q^{68} - 9 q^{69} + 18 q^{71} - 36 q^{72} - 42 q^{73} + 30 q^{74} - 9 q^{75} - 15 q^{76} - 6 q^{77} + 54 q^{78} + 21 q^{79} - 30 q^{80} - 18 q^{82} + 18 q^{83} - 9 q^{84} - 9 q^{85} - 6 q^{86} + 9 q^{87} - 27 q^{88} + 24 q^{89} + 27 q^{90} - 6 q^{91} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 27 q^{96} + 3 q^{97} + 6 q^{98} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8 - 6 * q^11 + 18 * q^12 + 3 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^17 + 9 * q^18 - 6 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 - 27 * q^24 + 6 * q^25 - 6 * q^26 + 27 * q^27 + 6 * q^28 - 9 * q^29 + 18 * q^30 + 3 * q^31 - 9 * q^34 + 6 * q^35 - 27 * q^36 - 6 * q^37 - 6 * q^38 - 18 * q^39 + 9 * q^40 + 9 * q^42 + 3 * q^43 + 30 * q^44 + 9 * q^45 - 3 * q^47 - 3 * q^49 + 6 * q^50 + 9 * q^51 + 21 * q^52 + 12 * q^53 - 27 * q^54 - 6 * q^56 - 9 * q^57 + 9 * q^58 + 3 * q^59 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 + 36 * q^66 + 12 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 36 * q^72 - 42 * q^73 + 30 * q^74 - 9 * q^75 - 15 * q^76 - 6 * q^77 + 54 * q^78 + 21 * q^79 - 30 * q^80 - 18 * q^82 + 18 * q^83 - 9 * q^84 - 9 * q^85 - 6 * q^86 + 9 * q^87 - 27 * q^88 + 24 * q^89 + 27 * q^90 - 6 * q^91 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 27 * q^96 + 3 * q^97 + 6 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	−0.667650	−	0.744475i	$-0.732700\pi$
$2$	0.439693	−	0.761570i	0.310910	−	0.538511i	0.978560	+	0.205964i	$0.0660330\pi$
$3$	−0.592396	−	1.62760i	−0.342020	−	0.939693i
$3$	−0.592396	−	1.62760i	−0.342020	−	0.939693i
$4$	0.613341	+	1.06234i	0.306670	+	0.531169i
$5$	−0.673648	−	1.16679i	−0.301265	−	0.521806i	0.675158	−	0.737673i	$-0.264075\pi$
$5$	−0.673648	−	1.16679i	−0.301265	−	0.521806i	−0.976423	+	0.215867i	$0.930742\pi$
$6$	−1.50000	−	0.264490i	−0.612372	−	0.107978i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	2.83750			1.00321
$9$	−2.29813	+	1.92836i	−0.766044	+	0.642788i
$10$	−1.18479			−0.374664
$11$	−0.826352	+	1.43128i	−0.249154	+	0.431548i	−0.963291	−	0.268458i	$-0.913486\pi$
$11$	−0.826352	+	1.43128i	−0.249154	+	0.431548i	0.714137	+	0.700006i	$0.246819\pi$
$12$	1.36571	−	1.62760i	0.394248	−	0.469846i
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	0.999301	−	0.0373813i	$-0.0119016\pi$
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	−0.532024	+	0.846729i	$0.678568\pi$
$14$	0.439693	+	0.761570i	0.117513	+	0.203538i
$15$	−1.50000	+	1.78763i	−0.387298	+	0.461564i
$16$	0.0209445	−	0.0362770i	0.00523613	−	0.00906925i
$17$	0.467911			0.113485			0.0567426	−	0.998389i	$-0.481929\pi$
$17$	0.467911			0.113485			0.0567426	+	0.998389i	$0.481929\pi$
$18$	0.458111	+	2.59808i	0.107978	+	0.612372i
$19$	−3.22668			−0.740252			−0.370126	−	0.928982i	$-0.620685\pi$
$19$	−3.22668			−0.740252			−0.370126	+	0.928982i	$0.620685\pi$
$20$	0.826352	−	1.43128i	0.184778	−	0.320045i
$21$	1.70574	+	0.300767i	0.372222	+	0.0656328i
$22$	0.726682	+	1.25865i	0.154929	+	0.268345i
$23$	−4.47178	−	7.74535i	−0.932431	−	1.61502i	−0.779152	−	0.626835i	$-0.784350\pi$
$23$	−4.47178	−	7.74535i	−0.932431	−	1.61502i	−0.153279	−	0.988183i	$-0.548983\pi$
$24$	−1.68092	−	4.61830i	−0.343117	−	0.942706i
$25$	1.59240	−	2.75811i	0.318479	−	0.551622i
$26$	2.96316			0.581124
$27$	4.50000	+	2.59808i	0.866025	+	0.500000i
$28$	−1.22668			−0.231821
$29$	−3.13429	+	5.42874i	−0.582022	+	1.00809i	0.413217	+	0.910632i	$0.364405\pi$
$29$	−3.13429	+	5.42874i	−0.582022	+	1.00809i	−0.995239	+	0.0974595i	$0.968928\pi$
$30$	0.701867	+	1.92836i	0.128143	+	0.352069i
$31$	−4.61721	−	7.99724i	−0.829276	−	1.43635i	−0.898607	−	0.438754i	$-0.855420\pi$
$31$	−4.61721	−	7.99724i	−0.829276	−	1.43635i	0.0693317	−	0.997594i	$-0.477913\pi$
$32$	2.81908	+	4.88279i	0.498347	+	0.863163i
$33$	2.81908	+	0.497079i	0.490738	+	0.0865304i
$34$	0.205737	−	0.356347i	0.0352836	−	0.0611130i
$35$	1.34730			0.227735
$36$	−3.45811	−	1.25865i	−0.576352	−	0.209775i
$37$	9.23442			1.51813			0.759065	−	0.651015i	$-0.225657\pi$
$37$	9.23442			1.51813			0.759065	+	0.651015i	$0.225657\pi$
$38$	−1.41875	+	2.45734i	−0.230151	+	0.398634i
$39$	3.75150	−	4.47086i	0.600720	−	0.715910i
$40$	−1.91147	−	3.31077i	−0.302231	−	0.523479i
$41$	−1.70574	−	2.95442i	−0.266391	−	0.461403i	0.701536	−	0.712634i	$-0.252498\pi$
$41$	−1.70574	−	2.95442i	−0.266391	−	0.461403i	−0.967927	+	0.251231i	$0.919165\pi$
$42$	0.979055	−	1.16679i	0.151072	−	0.180040i
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	−0.647376	−	0.762171i	$-0.724133\pi$
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	0.983747	+	0.179558i	$0.0574668\pi$
$44$	−2.02734			−0.305633
$45$	3.79813	+	1.38241i	0.566192	+	0.206077i
$46$	−7.86484			−1.15961
$47$	−4.67752	+	8.10170i	−0.682286	+	1.18175i	0.291995	+	0.956420i	$0.405681\pi$
$47$	−4.67752	+	8.10170i	−0.682286	+	1.18175i	−0.974281	+	0.225335i	$0.927652\pi$
$48$	−0.0714517	−	0.0125989i	−0.0103132	−	0.00181849i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−1.40033	−	2.42544i	−0.198037	−	0.343009i
$51$	−0.277189	−	0.761570i	−0.0388142	−	0.106641i
$52$	−2.06670	+	3.57964i	−0.286600	+	0.496406i
$53$	−0.573978			−0.0788419			−0.0394210	−	0.999223i	$-0.512551\pi$
$53$	−0.573978			−0.0788419			−0.0394210	+	0.999223i	$0.512551\pi$
$54$	3.95723	−	2.28471i	0.538511	−	0.310910i
$55$	2.22668			0.300246
$56$	−1.41875	+	2.45734i	−0.189588	+	0.328376i
$57$	1.91147	+	5.25173i	0.253181	+	0.695609i
$58$	2.75624	+	4.77396i	0.361913	+	0.626851i
$59$	5.19846	+	9.00400i	0.676782	+	1.17222i	0.975945	+	0.218019i	$0.0699595\pi$
$59$	5.19846	+	9.00400i	0.676782	+	1.17222i	−0.299162	+	0.954202i	$0.596707\pi$
$60$	−2.81908	−	0.497079i	−0.363941	−	0.0641727i
$61$	−3.81908	+	6.61484i	−0.488983	+	0.846943i	−0.999920	−	0.0126752i	$-0.995965\pi$
$61$	−3.81908	+	6.61484i	−0.488983	+	0.846943i	0.510937	+	0.859618i	$0.329299\pi$
$62$	−8.12061			−1.03132
$63$	−0.520945	−	2.95442i	−0.0656328	−	0.372222i
$64$	5.04189			0.630236
$65$	2.26991	−	3.93161i	0.281548	−	0.487656i
$66$	1.61809	−	1.92836i	0.199173	−	0.237365i
$67$	−0.298133	−	0.516382i	−0.0364228	−	0.0630861i	0.847239	−	0.531211i	$-0.178263\pi$
$67$	−0.298133	−	0.516382i	−0.0364228	−	0.0630861i	−0.883662	+	0.468125i	$0.844930\pi$
$68$	0.286989	+	0.497079i	0.0348025	+	0.0602797i
$69$	−9.95723	+	11.8666i	−1.19871	+	1.42857i
$70$	0.592396	−	1.02606i	0.0708049	−	0.122638i
$71$	−0.554378			−0.0657925			−0.0328963	−	0.999459i	$-0.510473\pi$
$71$	−0.554378			−0.0657925			−0.0328963	+	0.999459i	$0.510473\pi$
$72$	−6.52094	+	5.47172i	−0.768501	+	0.644849i
$73$	2.04963			0.239891			0.119946	−	0.992780i	$-0.461728\pi$
$73$	2.04963			0.239891			0.119946	+	0.992780i	$0.461728\pi$
$74$	4.06031	−	7.03266i	0.472001	−	0.817530i
$75$	−5.43242	−	0.957882i	−0.627282	−	0.110607i
$76$	−1.97906	−	3.42782i	−0.227013	−	0.393198i
$77$	−0.826352	−	1.43128i	−0.0941715	−	0.163110i
$78$	−1.75537	−	4.82283i	−0.198756	−	0.546078i
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	−0.790461	−	0.612512i	$-0.790159\pi$
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	0.925682	+	0.378303i	$0.123492\pi$
$80$	−0.0564370			−0.00630985
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$	−3.00000			−0.331295
$83$	7.52481	−	13.0334i	0.825956	−	1.43060i	−0.0752309	−	0.997166i	$-0.523969\pi$
$83$	7.52481	−	13.0334i	0.825956	−	1.43060i	0.901187	−	0.433431i	$-0.142697\pi$
$84$	0.726682	+	1.99654i	0.0792875	+	0.217841i
$85$	−0.315207	−	0.545955i	−0.0341891	−	0.0592172i
$86$	−1.93969	−	3.35965i	−0.209162	−	0.362280i
$87$	10.6925	+	1.88538i	1.14636	+	0.202134i
$88$	−2.34477	+	4.06126i	−0.249953	+	0.432932i
$89$	9.08647			0.963164			0.481582	−	0.876401i	$-0.340062\pi$
$89$	9.08647			0.963164			0.481582	+	0.876401i	$0.340062\pi$
$90$	2.72281	−	2.28471i	0.287010	−	0.240830i
$91$	−3.36959			−0.353228
$92$	5.48545	−	9.50108i	0.571898	−	0.990556i
$93$	−10.2811	+	12.2525i	−1.06610	+	1.27052i
$94$	4.11334	+	7.12452i	0.424259	+	0.734838i
$95$	2.17365	+	3.76487i	0.223012	+	0.386267i
$96$	6.27719	−	7.48086i	0.640663	−	0.763512i
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	−0.813788	−	0.581161i	$-0.802598\pi$
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	0.910195	+	0.414181i	$0.135932\pi$
$98$	−0.879385			−0.0888313
$99$	−0.860967	−	4.88279i	−0.0865304	−	0.490738i
$100$	3.90673			0.390673
$101$	0.854570	−	1.48016i	0.0850329	−	0.147281i	−0.820372	−	0.571830i	$-0.806234\pi$
$101$	0.854570	−	1.48016i	0.0850329	−	0.147281i	0.905405	+	0.424548i	$0.139567\pi$
$102$	−0.701867	−	0.123758i	−0.0694952	−	0.0122539i
$103$	1.81908	+	3.15074i	0.179239	+	0.310451i	0.941620	−	0.336677i	$-0.109303\pi$
$103$	1.81908	+	3.15074i	0.179239	+	0.310451i	−0.762381	+	0.647128i	$0.775970\pi$
$104$	4.78059	+	8.28023i	0.468776	+	0.811943i
$105$	−0.798133	−	2.19285i	−0.0778898	−	0.214001i
$106$	−0.252374	+	0.437124i	−0.0245127	+	0.0424573i
$107$	7.12836			0.689124			0.344562	−	0.938764i	$-0.388027\pi$
$107$	7.12836			0.689124			0.344562	+	0.938764i	$0.388027\pi$
$108$			6.37402i			0.613341i
$109$	0.403733			0.0386706			0.0193353	−	0.999813i	$-0.493845\pi$
$109$	0.403733			0.0386706			0.0193353	+	0.999813i	$0.493845\pi$
$110$	0.979055	−	1.69577i	0.0933493	−	0.161686i
$111$	−5.47044	−	15.0299i	−0.519231	−	1.42658i
$112$	0.0209445	+	0.0362770i	0.00197907	+	0.00342785i
$113$	−7.18479	−	12.4444i	−0.675888	−	1.17067i	−0.976208	−	0.216835i	$-0.930427\pi$
$113$	−7.18479	−	12.4444i	−0.675888	−	1.17067i	0.300320	−	0.953839i	$-0.402907\pi$
$114$	4.84002	+	0.853427i	0.453310	+	0.0799307i
$115$	−6.02481	+	10.4353i	−0.561817	+	0.973095i
$116$	−7.68954			−0.713956
$117$	−9.49912	−	3.45740i	−0.878194	−	0.319637i
$118$	9.14290			0.841672
$119$	−0.233956	+	0.405223i	−0.0214467	+	0.0371467i
$120$	−4.25624	+	5.07239i	−0.388540	+	0.463044i
$121$	4.13429	+	7.16079i	0.375844	+	0.650981i
$122$	3.35844	+	5.81699i	0.304059	+	0.526646i
$123$	−3.79813	+	4.52644i	−0.342466	+	0.408135i
$124$	5.66385	−	9.81007i	0.508629	−	0.880971i
$125$	−11.0273			−0.986315
$126$	−2.47906	−	0.902302i	−0.220852	−	0.0803835i
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	−3.42127	+	5.92582i	−0.302401	+	0.523774i
$129$	−7.52481	−	1.32683i	−0.662523	−	0.116821i
$130$	−1.99613	−	3.45740i	−0.175072	−	0.303234i
$131$	3.58260	+	6.20524i	0.313013	+	0.542154i	0.979013	−	0.203797i	$-0.0653284\pi$
$131$	3.58260	+	6.20524i	0.313013	+	0.542154i	−0.666000	+	0.745952i	$0.731995\pi$
$132$	1.20099	+	3.29969i	0.104533	+	0.287201i
$133$	1.61334	−	2.79439i	0.139894	−	0.242304i
$134$	−0.524348			−0.0452968
$135$		−	7.00076i		−	0.602529i
$136$	1.32770			0.113849
$137$	−1.28446	+	2.22475i	−0.109739	+	0.190074i	−0.915665	−	0.401943i	$-0.868335\pi$
$137$	−1.28446	+	2.22475i	−0.109739	+	0.190074i	0.805925	+	0.592017i	$0.201668\pi$
$138$	4.65910	+	12.8008i	0.396609	+	1.08967i
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	0.966272	−	0.257523i	$-0.0829064\pi$
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	−0.706158	+	0.708055i	$0.749573\pi$
$140$	0.826352	+	1.43128i	0.0698395	+	0.120966i
$141$	15.9572	+	2.81369i	1.34384	+	0.236956i
$142$	−0.243756	+	0.422197i	−0.0204555	+	0.0354300i
$143$	−5.56893			−0.465697
$144$	0.0218219	+	0.123758i	0.00181849	+	0.0103132i
$145$	8.44562			0.701371
$146$	0.901207	−	1.56094i	0.0745844	−	0.129184i
$147$	−1.11334	+	1.32683i	−0.0918268	+	0.109435i
$148$	5.66385	+	9.81007i	0.465565	+	0.806383i
$149$	−0.215537	−	0.373321i	−0.0176575	−	0.0305837i	0.857062	−	0.515214i	$-0.172288\pi$
$149$	−0.215537	−	0.373321i	−0.0176575	−	0.0305837i	−0.874719	+	0.484630i	$0.838954\pi$
$150$	−3.11809	+	3.71599i	−0.254591	+	0.303410i
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	−0.811375	−	0.584526i	$-0.801280\pi$
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	0.911902	+	0.410408i	$0.134614\pi$
$152$	−9.15570			−0.742625
$153$	−1.07532	+	0.902302i	−0.0869346	+	0.0729468i
$154$	−1.45336			−0.117115
$155$	−6.22075	+	10.7747i	−0.499663	+	0.865441i
$156$	7.05051	+	1.24319i	0.564492	+	0.0995352i
$157$	−5.06670	−	8.77579i	−0.404367	−	0.700384i	0.589881	−	0.807491i	$-0.299175\pi$
$157$	−5.06670	−	8.77579i	−0.404367	−	0.700384i	−0.994248	+	0.107106i	$0.965841\pi$
$158$	−1.05690	−	1.83061i	−0.0840828	−	0.145636i
$159$	0.340022	+	0.934204i	0.0269655	+	0.0740872i
$160$	3.79813	−	6.57856i	0.300269	−	0.520081i
$161$	8.94356			0.704852
$162$	−6.06283	−	5.08732i	−0.476341	−	0.399698i
$163$	−2.59627			−0.203355			−0.101678	−	0.994817i	$-0.532421\pi$
$163$	−2.59627			−0.203355			−0.101678	+	0.994817i	$0.532421\pi$
$164$	2.09240	−	3.62414i	0.163389	−	0.282998i
$165$	−1.31908	−	3.62414i	−0.102690	−	0.282139i
$166$	−6.61721	−	11.4613i	−0.513595	−	0.889573i
$167$	11.5915	+	20.0771i	0.896979	+	1.55361i	0.831337	+	0.555769i	$0.187576\pi$
$167$	11.5915	+	20.0771i	0.896979	+	1.55361i	0.0656422	+	0.997843i	$0.479090\pi$
$168$	4.84002	+	0.853427i	0.373416	+	0.0658433i
$169$	0.822948	−	1.42539i	0.0633037	−	0.109645i
$170$	−0.554378			−0.0425188
$171$	7.41534	−	6.22221i	0.567066	−	0.475825i
$172$	5.41147			0.412621
$173$	2.37598	−	4.11532i	0.180643	−	0.312882i	−0.761457	−	0.648215i	$-0.775516\pi$
$173$	2.37598	−	4.11532i	0.180643	−	0.312882i	0.942100	+	0.335333i	$0.108849\pi$
$174$	6.13728	−	7.31412i	0.465266	−	0.554482i
$175$	1.59240	+	2.75811i	0.120374	+	0.208494i
$176$	0.0346151	+	0.0599551i	0.00260921	+	0.00451929i
$177$	11.5753	−	13.7949i	0.870054	−	1.03689i
$178$	3.99525	−	6.91998i	0.299457	−	0.518674i
$179$	−8.53209			−0.637718			−0.318859	−	0.947802i	$-0.603300\pi$
$179$	−8.53209			−0.637718			−0.318859	+	0.947802i	$0.603300\pi$
$180$	0.860967	+	4.88279i	0.0641727	+	0.363941i
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$	−1.48158	+	2.56617i	−0.109822	+	0.190218i
$183$	13.0287	+	2.29731i	0.963108	+	0.169822i
$184$	−12.6887	−	21.9774i	−0.935421	−	1.62020i
$185$	−6.22075	−	10.7747i	−0.457359	−	0.792169i
$186$	4.81062	+	13.2171i	0.352732	+	0.969123i
$187$	−0.386659	+	0.669713i	−0.0282753	+	0.0489743i
$188$	−11.4757			−0.836948
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$	3.82295			0.277346
$191$	−6.45471	+	11.1799i	−0.467046	+	0.808948i	−0.999291	−	0.0376425i	$-0.988015\pi$
$191$	−6.45471	+	11.1799i	−0.467046	+	0.808948i	0.532245	+	0.846590i	$0.321349\pi$
$192$	−2.98680	−	8.20616i	−0.215553	−	0.592228i
$193$	0.319078	+	0.552659i	0.0229677	+	0.0397813i	0.877281	−	0.479977i	$-0.159355\pi$
$193$	0.319078	+	0.552659i	0.0229677	+	0.0397813i	−0.854313	+	0.519759i	$0.826022\pi$
$194$	−0.834970	−	1.44621i	−0.0599473	−	0.103832i
$195$	−7.74376	−	1.36543i	−0.554542	−	0.0977807i
$196$	0.613341	−	1.06234i	0.0438101	−	0.0758812i
$197$	11.4456			0.815467			0.407733	−	0.913101i	$-0.366319\pi$
$197$	11.4456			0.815467			0.407733	+	0.913101i	$0.366319\pi$
$198$	−4.09714	−	1.49124i	−0.291171	−	0.105978i
$199$	−3.63816			−0.257902			−0.128951	−	0.991651i	$-0.541161\pi$
$199$	−3.63816			−0.257902			−0.128951	+	0.991651i	$0.541161\pi$
$200$	4.51842	−	7.82613i	0.319500	−	0.553391i
$201$	−0.663848	+	0.791143i	−0.0468242	+	0.0558029i
$202$	−0.751497	−	1.30163i	−0.0528751	−	0.0915824i
$203$	−3.13429	−	5.42874i	−0.219984	−	0.381023i
$204$	0.639033	−	0.761570i	0.0447413	−	0.0533206i
$205$	−2.29813	+	3.98048i	−0.160509	+	0.278009i
$206$	3.19934			0.222909
$207$	25.2126	+	9.17664i	1.75240	+	0.637820i
$208$	0.141149			0.00978691
$209$	2.66637	−	4.61830i	0.184437	−	0.319454i
$210$	−2.02094	−	0.356347i	−0.139458	−	0.0245903i
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	0.748234	−	0.663435i	$-0.230902\pi$
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	−0.948668	+	0.316273i	$0.897569\pi$
$212$	−0.352044	−	0.609758i	−0.0241785	−	0.0418784i
$213$	0.328411	+	0.902302i	0.0225024	+	0.0618247i
$214$	3.13429	−	5.42874i	0.214255	−	0.371101i
$215$	−5.94356			−0.405348
$216$	12.7687	+	7.37203i	0.868802	+	0.501603i
$217$	9.23442			0.626873
$218$	0.177519	−	0.307471i	0.0120231	−	0.0208246i
$219$	−1.21419	−	3.33597i	−0.0820476	−	0.225424i
$220$	1.36571	+	2.36549i	0.0920765	+	0.159481i
$221$	0.788333	+	1.36543i	0.0530290	+	0.0918490i
$222$	−13.8516	−	2.44242i	−0.929661	−	0.163924i
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	−0.959905	−	0.280327i	$-0.909557\pi$
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	0.722722	+	0.691139i	$0.242891\pi$
$224$	−5.63816			−0.376715
$225$	1.65910	+	9.40923i	0.110607	+	0.627282i
$226$	−12.6364			−0.840561
$227$	5.97178	−	10.3434i	0.396361	−	0.686517i	−0.596913	−	0.802306i	$-0.703606\pi$
$227$	5.97178	−	10.3434i	0.396361	−	0.686517i	0.993274	+	0.115789i	$0.0369395\pi$
$228$	−4.40673	+	5.25173i	−0.291843	+	0.347804i
$229$	8.77631	+	15.2010i	0.579955	+	1.00451i	0.995484	+	0.0949315i	$0.0302632\pi$
$229$	8.77631	+	15.2010i	0.579955	+	1.00451i	−0.415529	+	0.909580i	$0.636403\pi$
$230$	5.29813	+	9.17664i	0.349349	+	0.605089i
$231$	−1.84002	+	2.19285i	−0.121065	+	0.144279i
$232$	−8.89352	+	15.4040i	−0.583888	+	1.01132i
$233$	16.2540			1.06484			0.532418	−	0.846481i	$-0.321283\pi$
$233$	16.2540			1.06484			0.532418	+	0.846481i	$0.321283\pi$
$234$	−6.80974	+	5.71405i	−0.445167	+	0.373539i
$235$	12.6040			0.822195
$236$	−6.37686	+	11.0450i	−0.415098	+	0.718971i
$237$	−4.10014	−	0.722965i	−0.266333	−	0.0469616i
$238$	0.205737	+	0.356347i	0.0133360	+	0.0230985i
$239$	7.54963	+	13.0763i	0.488345	+	0.845838i	0.999910	−	0.0134062i	$-0.00426745\pi$
$239$	7.54963	+	13.0763i	0.488345	+	0.845838i	−0.511565	+	0.859244i	$0.670934\pi$
$240$	0.0334331	+	0.0918566i	0.00215809	+	0.00592932i
$241$	7.81908	−	13.5430i	0.503671	−	0.872384i	−0.496320	−	0.868140i	$-0.665316\pi$
$241$	7.81908	−	13.5430i	0.503671	−	0.872384i	0.999991	−	0.00424420i	$-0.00135097\pi$
$242$	7.27126			0.467414
$243$	−15.3516	+	2.70691i	−0.984808	+	0.173648i
$244$	−9.36959			−0.599826
$245$	−0.673648	+	1.16679i	−0.0430378	+	0.0745437i
$246$	1.77719	+	4.88279i	0.113309	+	0.311315i
$247$	−5.43629	−	9.41593i	−0.345903	−	0.599121i
$248$	−13.1013	−	22.6922i	−0.831935	−	1.44095i
$249$	−25.6707	−	4.52644i	−1.62682	−	0.286851i
$250$	−4.84864	+	8.39809i	−0.306655	+	0.531142i
$251$	19.0651			1.20338			0.601690	−	0.798730i	$-0.294494\pi$
$251$	19.0651			1.20338			0.601690	+	0.798730i	$0.294494\pi$
$252$	2.81908	−	2.36549i	0.177585	−	0.149012i
$253$	14.7811			0.929277
$254$	−9.13310	+	15.8190i	−0.573062	+	0.992572i
$255$	−0.701867	+	0.836452i	−0.0439526	+	0.0523807i
$256$	8.05051	+	13.9439i	0.503157	+	0.871493i
$257$	−13.2909	−	23.0204i	−0.829061	−	1.43598i	−0.898776	−	0.438409i	$-0.855542\pi$
$257$	−13.2909	−	23.0204i	−0.829061	−	1.43598i	0.0697146	−	0.997567i	$-0.477791\pi$
$258$	−4.31908	+	5.14728i	−0.268894	+	0.320455i
$259$	−4.61721	+	7.99724i	−0.286900	+	0.496925i
$260$	5.56893			0.345370
$261$	−3.26558	−	18.5200i	−0.202134	−	1.14636i
$262$	6.30096			0.389275
$263$	0.367059	−	0.635765i	0.0226338	−	0.0392029i	−0.854487	−	0.519473i	$-0.826128\pi$
$263$	0.367059	−	0.635765i	0.0226338	−	0.0392029i	0.877120	+	0.480270i	$0.159461\pi$
$264$	7.99912	+	1.41046i	0.492312	+	0.0868079i
$265$	0.386659	+	0.669713i	0.0237523	+	0.0411402i
$266$	−1.41875	−	2.45734i	−0.0869890	−	0.150669i
$267$	−5.38279	−	14.7891i	−0.329421	−	0.905078i
$268$	0.365715	−	0.633436i	0.0223396	−	0.0386933i
$269$	−20.8503			−1.27126			−0.635632	−	0.771992i	$-0.719261\pi$
$269$	−20.8503			−1.27126			−0.635632	+	0.771992i	$0.719261\pi$
$270$	−5.33157	−	3.07818i	−0.324469	−	0.187332i
$271$	6.95811			0.422675			0.211338	−	0.977413i	$-0.432218\pi$
$271$	6.95811			0.422675			0.211338	+	0.977413i	$0.432218\pi$
$272$	0.00980018	−	0.0169744i	0.000594223	−	0.00102922i
$273$	1.99613	+	5.48432i	0.120811	+	0.331926i
$274$	1.12954	+	1.95642i	0.0682379	+	0.118191i
$275$	2.63176	+	4.55834i	0.158701	+	0.274878i
$276$	−18.7135	−	3.29969i	−1.12642	−	0.198618i
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	0.462138	+	0.886808i	$0.347083\pi$
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	−0.999067	+	0.0431811i	$0.986251\pi$
$278$	5.39363			0.323488
$279$	26.0326	+	9.47508i	1.55853	+	0.567258i
$280$	3.82295			0.228465
$281$	−11.1552	+	19.3214i	−0.665465	+	1.15262i	0.313694	+	0.949524i	$0.398433\pi$
$281$	−11.1552	+	19.3214i	−0.665465	+	1.15262i	−0.979159	+	0.203095i	$0.934900\pi$
$282$	9.15910	−	10.9154i	0.545416	−	0.650002i
$283$	9.29726	+	16.1033i	0.552665	+	0.957243i	0.998081	+	0.0619196i	$0.0197222\pi$
$283$	9.29726	+	16.1033i	0.552665	+	0.957243i	−0.445417	+	0.895323i	$0.646944\pi$
$284$	−0.340022	−	0.588936i	−0.0201766	−	0.0349469i
$285$	4.84002	−	5.76811i	0.286698	−	0.341674i
$286$	−2.44862	+	4.24113i	−0.144790	+	0.250783i
$287$	3.41147			0.201373
$288$	−15.8944	−	5.78509i	−0.936587	−	0.340890i
$289$	−16.7811			−0.987121
$290$	3.71348	−	6.43193i	0.218063	−	0.377696i
$291$	−3.23917	−	0.571153i	−0.189884	−	0.0334816i
$292$	1.25712	+	2.17740i	0.0735675	+	0.127423i
$293$	−6.54576	−	11.3376i	−0.382407	−	0.662349i	0.608998	−	0.793171i	$-0.291572\pi$
$293$	−6.54576	−	11.3376i	−0.382407	−	0.662349i	−0.991406	+	0.130822i	$0.958238\pi$
$294$	0.520945	+	1.43128i	0.0303821	+	0.0834741i
$295$	7.00387	−	12.1311i	0.407781	−	0.706298i
$296$	26.2026			1.52300
$297$	−7.43717	+	4.29385i	−0.431548	+	0.249154i
$298$	−0.379081			−0.0219595
$299$	15.0680	−	26.0986i	0.871408	−	1.50932i
$300$	−2.31433	−	6.35857i	−0.133618	−	0.367112i
$301$	2.20574	+	3.82045i	0.127137	+	0.220207i
$302$	−1.08630	−	1.88153i	−0.0625098	−	0.108270i
$303$	−2.91534	−	0.514054i	−0.167482	−	0.0295316i
$304$	−0.0675813	+	0.117054i	−0.00387606	+	0.00671353i
$305$	10.2909			0.589253
$306$	0.214355	+	1.21567i	0.0122539	+	0.0694952i
$307$	6.31046			0.360157			0.180078	−	0.983652i	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$	1.01367	−	1.75573i	0.0577592	−	0.100042i
$309$	4.05051	−	4.82721i	0.230425	−	0.274610i
$310$	5.47044	+	9.47508i	0.310700	+	0.538148i
$311$	4.76217	+	8.24833i	0.270038	+	0.467720i	0.968871	−	0.247565i	$-0.0796304\pi$
$311$	4.76217	+	8.24833i	0.270038	+	0.467720i	−0.698833	+	0.715285i	$0.746297\pi$
$312$	10.6449	−	12.6860i	0.602646	−	0.718206i
$313$	8.81433	−	15.2669i	0.498215	−	0.862934i	−0.501782	−	0.864994i	$-0.667322\pi$
$313$	8.81433	−	15.2669i	0.498215	−	0.862934i	0.999998	+	0.00205946i	$0.000655547\pi$
$314$	−8.91117			−0.502886
$315$	−3.09627	+	2.59808i	−0.174455	+	0.146385i
$316$	2.94862			0.165873
$317$	−4.03849	+	6.99486i	−0.226824	+	0.392871i	−0.956865	−	0.290533i	$-0.906168\pi$
$317$	−4.03849	+	6.99486i	−0.226824	+	0.392871i	0.730041	+	0.683403i	$0.239501\pi$
$318$	0.860967	+	0.151812i	0.0482806	+	0.00851318i
$319$	−5.18004	−	8.97210i	−0.290027	−	0.502341i
$320$	−3.39646	−	5.88284i	−0.189868	−	0.328861i
$321$	−4.22281	−	11.6021i	−0.235694	−	0.647565i
$322$	3.93242	−	6.81115i	0.219145	−	0.379570i
$323$	−1.50980			−0.0840075
$324$	10.3743	−	3.77595i	0.576352	−	0.209775i
$325$	10.7314			0.595273
$326$	−1.14156	+	1.97724i	−0.0632251	+	0.109509i
$327$	−0.239170	−	0.657115i	−0.0132261	−	0.0363385i
$328$	−4.84002	−	8.38316i	−0.267246	−	0.462883i
$329$	−4.67752	−	8.10170i	−0.257880	−	0.446661i
$330$	−3.34002	−	0.588936i	−0.183862	−	0.0324199i
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	0.353378	+	0.935481i	$0.385033\pi$
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	−0.986839	+	0.161706i	$0.948300\pi$
$332$	18.4611			1.01318
$333$	−21.2219	+	17.8073i	−1.16295	+	0.975835i
$334$	20.3868			1.11552
$335$	−0.401674	+	0.695720i	−0.0219458	+	0.0380112i
$336$	0.0466368	−	0.0555796i	0.00254425	−	0.00303211i
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	−0.925659	−	0.378359i	$-0.876489\pi$
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	0.135161	−	0.990824i	$-0.456845\pi$
$338$	−0.723689	−	1.25347i	−0.0393635	−	0.0681795i
$339$	−15.9982	+	19.0660i	−0.868905	+	1.03552i
$340$	0.386659	−	0.669713i	0.0209695	−	0.0363203i
$341$	15.2618			0.826471
$342$	−1.47818	−	8.38316i	−0.0799307	−	0.453310i
$343$	1.00000			0.0539949
$344$	6.25877	−	10.8405i	0.337450	−	0.584481i
$345$	20.5535	+	3.62414i	1.10656	+	0.195117i
$346$	−2.08940	−	3.61895i	−0.112327	−	0.194556i
$347$	−6.47313	−	11.2118i	−0.347496	−	0.601880i	0.638308	−	0.769781i	$-0.279635\pi$
$347$	−6.47313	−	11.2118i	−0.347496	−	0.601880i	−0.985804	+	0.167901i	$0.946301\pi$
$348$	4.55525	+	12.5155i	0.244187	+	0.670899i
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	−0.884938	−	0.465710i	$-0.845799\pi$
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	0.845785	+	0.533524i	$0.179132\pi$
$350$	2.80066			0.149702
$351$			17.5089i			0.934555i
$352$	−9.31820			−0.496662
$353$	−7.16637	+	12.4125i	−0.381428	+	0.660652i	−0.991267	−	0.131873i	$-0.957901\pi$
$353$	−7.16637	+	12.4125i	−0.381428	+	0.660652i	0.609839	+	0.792525i	$0.291234\pi$
$354$	−5.41622	−	14.8809i	−0.287869	−	0.790913i
$355$	0.373455	+	0.646844i	0.0198210	+	0.0343309i
$356$	5.57310	+	9.65289i	0.295374	+	0.511602i
$357$	0.798133	+	0.140732i	0.0422417	+	0.00744835i
$358$	−3.75150	+	6.49778i	−0.198273	+	0.343418i
$359$	−20.9368			−1.10500			−0.552500	−	0.833513i	$-0.686326\pi$
$359$	−20.9368			−1.10500			−0.552500	+	0.833513i	$0.686326\pi$
$360$	10.7772	+	3.92258i	0.568008	+	0.206738i
$361$	−8.58853			−0.452028
$362$	−7.57785	+	13.1252i	−0.398283	+	0.689846i
$363$	9.20574	−	10.9710i	0.483176	−	0.575827i
$364$	−2.06670	−	3.57964i	−0.108325	−	0.187624i
$365$	−1.38073	−	2.39149i	−0.0722707	−	0.125176i
$366$	7.47818	−	8.91215i	0.390891	−	0.465845i
$367$	6.02869	−	10.4420i	0.314695	−	0.545067i	−0.664678	−	0.747130i	$-0.731431\pi$
$367$	6.02869	−	10.4420i	0.314695	−	0.545067i	0.979373	+	0.202063i	$0.0647645\pi$
$368$	−0.374638			−0.0195293
$369$	9.61721	+	3.50038i	0.500652	+	0.182222i
$370$	−10.9409			−0.568789
$371$	0.286989	−	0.497079i	0.0148997	−	0.0258071i
$372$	−19.3221	−	3.40700i	−1.00180	−	0.176645i
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	0.875959	−	0.482386i	$-0.160230\pi$
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	−0.855738	+	0.517410i	$0.826896\pi$
$374$	0.340022	+	0.588936i	0.0175821	+	0.0304532i
$375$	6.53256	+	17.9480i	0.337340	+	0.926833i
$376$	−13.2724	+	22.9885i	−0.684474	+	1.18554i
$377$	−21.1225			−1.08786
$378$			4.56942i			0.235026i
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	−2.66637	+	4.61830i	−0.136782	+	0.236914i
$381$	12.3050	+	33.8077i	0.630404	+	1.73202i
$382$	5.67617	+	9.83142i	0.290418	+	0.503019i
$383$	−3.86618	−	6.69642i	−0.197553	−	0.342171i	0.750182	−	0.661232i	$-0.229966\pi$
$383$	−3.86618	−	6.69642i	−0.197553	−	0.342171i	−0.947734	+	0.319061i	$0.896633\pi$
$384$	11.6716	+	2.05802i	0.595613	+	0.105023i
$385$	−1.11334	+	1.92836i	−0.0567411	+	0.0982785i
$386$	0.561185			0.0285636
$387$	2.29813	+	13.0334i	0.116821	+	0.662523i
$388$	2.32945			0.118260
$389$	−2.69981	+	4.67620i	−0.136886	+	0.237093i	−0.926316	−	0.376747i	$-0.877043\pi$
$389$	−2.69981	+	4.67620i	−0.136886	+	0.237093i	0.789431	+	0.613840i	$0.210376\pi$
$390$	−4.44475	+	5.29704i	−0.225068	+	0.268226i
$391$	−2.09240	−	3.62414i	−0.105817	−	0.183280i
$392$	−1.41875	−	2.45734i	−0.0716576	−	0.124115i
$393$	7.97730	−	9.50698i	0.402402	−	0.479564i
$394$	5.03256	−	8.71664i	0.253536	−	0.439138i
$395$	−3.23854			−0.162949
$396$	4.65910	−	3.90945i	0.234129	−	0.196457i
$397$	−29.2344			−1.46723			−0.733617	−	0.679563i	$-0.762169\pi$
$397$	−29.2344			−1.46723			−0.733617	+	0.679563i	$0.762169\pi$
$398$	−1.59967	+	2.77071i	−0.0801842	+	0.138883i
$399$	−5.50387	−	0.970481i	−0.275538	−	0.0485848i
$400$	−0.0667040	−	0.115535i	−0.00333520	−	0.00577674i
$401$	13.6989	+	23.7272i	0.684092	+	1.18488i	0.973721	+	0.227743i	$0.0731346\pi$
$401$	13.6989	+	23.7272i	0.684092	+	1.18488i	−0.289629	+	0.957139i	$0.593532\pi$
$402$	0.310622	+	0.853427i	0.0154924	+	0.0425650i
$403$	15.5581	−	26.9474i	0.775003	−	1.34235i
$404$	2.09657			0.104308
$405$	−11.3944	+	4.14722i	−0.566192	+	0.206077i
$406$	−5.51249			−0.273580
$407$	−7.63088	+	13.2171i	−0.378249	+	0.655146i
$408$	−0.786522	−	2.16095i	−0.0389386	−	0.106983i
$409$	4.51249	+	7.81586i	0.223128	+	0.386469i	0.955756	−	0.294160i	$-0.0950398\pi$
$409$	4.51249	+	7.81586i	0.223128	+	0.386469i	−0.732628	+	0.680629i	$0.761706\pi$
$410$	2.02094	+	3.50038i	0.0998073	+	0.172871i
$411$	4.38191	+	0.772649i	0.216144	+	0.0381120i
$412$	−2.23143	+	3.86495i	−0.109935	+	0.190412i
$413$	−10.3969			−0.511599
$414$	18.0744	−	15.1663i	0.888310	−	0.745381i
$415$	−20.2763			−0.995325
$416$	−9.49912	+	16.4530i	−0.465733	+	0.806673i
$417$	6.82857	−	8.13798i	0.334397	−	0.398518i
$418$	−2.34477	−	4.06126i	−0.114686	−	0.198643i
$419$	−0.0876485	−	0.151812i	−0.00428191	−	0.00741649i	0.863877	−	0.503704i	$-0.168030\pi$
$419$	−0.0876485	−	0.151812i	−0.00428191	−	0.00741649i	−0.868158	+	0.496287i	$0.834696\pi$
$420$	1.84002	−	2.19285i	0.0897839	−	0.107000i
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	−0.390490	−	0.920607i	$-0.627694\pi$
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	0.992514	−	0.122130i	$-0.0389724\pi$
$422$	−5.12061			−0.249268
$423$	−4.87346	−	27.6387i	−0.236956	−	1.34384i
$424$	−1.62866			−0.0790947
$425$	0.745100	−	1.29055i	0.0361427	−	0.0626009i
$426$	0.831566	+	0.146628i	0.0402895	+	0.00710413i
$427$	−3.81908	−	6.61484i	−0.184818	−	0.320114i
$428$	4.37211	+	7.57272i	0.211334	+	0.366041i
$429$	3.29901	+	9.06396i	0.159278	+	0.437612i
$430$	−2.61334	+	4.52644i	−0.126026	+	0.218284i
$431$	−29.3191			−1.41225			−0.706126	−	0.708086i	$-0.749559\pi$
$431$	−29.3191			−1.41225			−0.706126	+	0.708086i	$0.749559\pi$
$432$	0.188501	−	0.108831i	0.00906925	−	0.00523613i
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$	4.06031	−	7.03266i	0.194901	−	0.337578i
$435$	−5.00316	−	13.7461i	−0.239883	−	0.659073i
$436$	0.247626	+	0.428901i	0.0118591	+	0.0205406i
$437$	14.4290	+	24.9918i	0.690233	+	1.19552i
$438$	−3.07444	−	0.542108i	−0.146903	−	0.0259029i
$439$	10.9650	−	18.9919i	0.523330	−	0.906434i	−0.476302	−	0.879282i	$-0.658023\pi$
$439$	10.9650	−	18.9919i	0.523330	−	0.906434i	0.999631	−	0.0271516i	$-0.00864370\pi$
$440$	6.31820			0.301208
$441$	2.81908	+	1.02606i	0.134242	+	0.0488600i
$442$	1.38650			0.0659489
$443$	9.35504	−	16.2034i	0.444471	−	0.769847i	−0.553544	−	0.832820i	$-0.686725\pi$
$443$	9.35504	−	16.2034i	0.444471	−	0.769847i	0.998015	+	0.0629732i	$0.0200583\pi$
$444$	12.6116	−	15.0299i	0.598519	−	0.713288i
$445$	−6.12108	−	10.6020i	−0.290167	−	0.502584i
$446$	3.11468	+	5.39479i	0.147485	+	0.255451i
$447$	−0.479933	+	0.571962i	−0.0227000	+	0.0270529i
$448$	−2.52094	+	4.36640i	−0.119103	+	0.206293i
$449$	6.68004			0.315251			0.157625	−	0.987499i	$-0.449616\pi$
$449$	6.68004			0.315251			0.157625	+	0.987499i	$0.449616\pi$
$450$	7.89528	+	2.87365i	0.372187	+	0.135465i
$451$	5.63816			0.265490
$452$	8.81345	−	15.2653i	0.414550	−	0.718022i
$453$	−4.21419	−	0.743076i	−0.198000	−	0.0349128i
$454$	−5.25150	−	9.09586i	−0.246465	−	0.426890i
$455$	2.26991	+	3.93161i	0.106415	+	0.184317i
$456$	5.42380	+	14.9018i	0.253993	+	0.697839i
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	−0.544236	−	0.838932i	$-0.683180\pi$
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	0.998655	+	0.0518563i	$0.0165138\pi$
$458$	15.4355			0.721254
$459$	2.10560	+	1.21567i	0.0982810	+	0.0567426i
$460$	−14.7811			−0.689170
$461$	0.482926	−	0.836452i	0.0224921	−	0.0389575i	−0.854560	−	0.519352i	$-0.826173\pi$
$461$	0.482926	−	0.836452i	0.0224921	−	0.0389575i	0.877052	+	0.480395i	$0.159507\pi$
$462$	0.860967	+	2.36549i	0.0400558	+	0.110052i
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	0.871156	−	0.491006i	$-0.163371\pi$
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	−0.860802	+	0.508941i	$0.830037\pi$
$464$	0.131292	+	0.227405i	0.00609509	+	0.0105570i
$465$	21.2219	+	3.74200i	0.984144	+	0.173531i
$466$	7.14677	−	12.3786i	0.331068	−	0.573426i
$467$	−34.2148			−1.58327			−0.791637	−	0.610992i	$-0.790771\pi$
$467$	−34.2148			−1.58327			−0.791637	+	0.610992i	$0.790771\pi$
$468$	−2.15328	−	12.2118i	−0.0995352	−	0.564492i
$469$	0.596267			0.0275330
$470$	5.54189	−	9.59883i	0.255628	−	0.442761i
$471$	−11.2819	+	13.4453i	−0.519844	+	0.619526i
$472$	14.7506	+	25.5488i	0.678952	+	1.17598i
$473$	3.64543	+	6.31407i	0.167617	+	0.290321i
$474$	−2.35339	+	2.80466i	−0.108095	+	0.128822i
$475$	−5.13816	+	8.89955i	−0.235755	+	0.408339i
$476$	−0.573978			−0.0263082
$477$	1.31908	−	1.10684i	0.0603964	−	0.0506786i
$478$	13.2781			0.607325
$479$	10.8965	−	18.8732i	0.497872	−	0.862339i	−0.502125	−	0.864795i	$-0.667448\pi$
$479$	10.8965	−	18.8732i	0.497872	−	0.862339i	0.999997	+	0.00245553i	$0.000781622\pi$
$480$	−12.9572	−	2.28471i	−0.591414	−	0.104282i
$481$	15.5581	+	26.9474i	0.709388	+	1.22870i
$482$	−6.87598	−	11.9095i	−0.313192	−	0.542465i
$483$	−5.29813	−	14.5565i	−0.241073	−	0.662344i
$484$	−5.07145	+	8.78401i	−0.230521	+	0.399273i
$485$	−2.55850			−0.116175
$486$	−4.68850	+	12.8816i	−0.212675	+	0.584319i
$487$	19.3928			0.878772			0.439386	−	0.898298i	$-0.355196\pi$
$487$	19.3928			0.878772			0.439386	+	0.898298i	$0.355196\pi$
$488$	−10.8366	+	18.7696i	−0.490551	+	0.849659i
$489$	1.53802	+	4.22567i	0.0695516	+	0.191091i
$490$	0.592396	+	1.02606i	0.0267617	+	0.0463527i
$491$	−13.0783	−	22.6523i	−0.590216	−	1.02228i	−0.994203	−	0.107519i	$-0.965709\pi$
$491$	−13.0783	−	22.6523i	−0.590216	−	1.02228i	0.403987	−	0.914765i	$-0.367624\pi$
$492$	−7.13816	−	1.25865i	−0.321813	−	0.0567443i
$493$	−1.46657	+	2.54017i	−0.0660509	+	0.114403i
$494$	−9.56118			−0.430178
$495$	−5.11721	+	4.29385i	−0.230002	+	0.192994i
$496$	−0.386821			−0.0173688
$497$	0.277189	−	0.480105i	0.0124336	−	0.0215357i
$498$	−14.7344	+	17.5598i	−0.660265	+	0.786873i
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	0.980510	−	0.196470i	$-0.0629479\pi$
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	−0.660403	+	0.750911i	$0.729615\pi$
$500$	−6.76352	−	11.7148i	−0.302474	−	0.523900i
$501$	25.8106	−	30.7599i	1.15313	−	1.37425i
$502$	8.38279	−	14.5194i	0.374142	−	0.648033i
$503$	18.7033			0.833937			0.416969	−	0.908921i	$-0.363092\pi$
$503$	18.7033			0.833937			0.416969	+	0.908921i	$0.363092\pi$
$504$	−1.47818	−	8.38316i	−0.0658433	−	0.373416i
$505$	−2.30272			−0.102470
$506$	6.49912	−	11.2568i	0.288921	−	0.500426i
$507$	−2.80747	−	0.495032i	−0.124684	−	0.0219851i
$508$	−12.7400	−	22.0664i	−0.565248	−	0.979039i
$509$	12.8045	+	22.1781i	0.567551	+	0.983027i	0.996807	+	0.0798442i	$0.0254423\pi$
$509$	12.8045	+	22.1781i	0.567551	+	0.983027i	−0.429257	+	0.903183i	$0.641224\pi$
$510$	0.328411	+	0.902302i	0.0145423	+	0.0399546i
$511$	−1.02481	+	1.77503i	−0.0453351	+	0.0785228i
$512$	0.473897			0.0209435
$513$	−14.5201	−	8.38316i	−0.641077	−	0.370126i
$514$	−23.3756			−1.03105
$515$	2.45084	−	4.24497i	0.107997	−	0.187056i
$516$	−3.20574	−	8.80769i	−0.141125	−	0.387737i
$517$	−7.73055	−	13.3897i	−0.339989	−	0.588879i
$518$	4.06031	+	7.03266i	0.178400	+	0.308997i
$519$	−8.10560	−	1.42924i	−0.355796	−	0.0627365i
$520$	6.44087	−	11.1559i	0.282451	−	0.489220i
$521$	−21.2121			−0.929320			−0.464660	−	0.885489i	$-0.653824\pi$
$521$	−21.2121			−0.929320			−0.464660	+	0.885489i	$0.653824\pi$
$522$	−15.5401	−	5.65615i	−0.680173	−	0.247563i
$523$	20.8057			0.909770			0.454885	−	0.890550i	$-0.349680\pi$
$523$	20.8057			0.909770			0.454885	+	0.890550i	$0.349680\pi$
$524$	−4.39470	+	7.61185i	−0.191984	+	0.332525i
$525$	3.54576	−	4.22567i	0.154750	−	0.184423i
$526$	−0.322786	−	0.559082i	−0.0140741	−	0.0243771i
$527$	−2.16044	−	3.74200i	−0.0941104	−	0.163004i
$528$	0.0770768	−	0.0918566i	0.00335434	−	0.00399754i
$529$	−28.4937	+	49.3525i	−1.23885	+	2.14576i
$530$	0.680045			0.0295393
$531$	−29.3097	−	10.6679i	−1.27193	−	0.462946i
$532$	3.95811			0.171606
$533$	5.74763	−	9.95518i	0.248957	−	0.431207i
$534$	−13.6297	−	2.40328i	−0.589815	−	0.104000i
$535$	−4.80200	−	8.31731i	−0.207609	−	0.359589i
$536$	−0.845952	−	1.46523i	−0.0365396	−	0.0632884i
$537$	5.05438	+	13.8868i	0.218112	+	0.599259i
$538$	−9.16772	+	15.8790i	−0.395248	+	0.684590i
$539$	1.65270			0.0711870
$540$	7.43717	−	4.29385i	0.320045	−	0.184778i
$541$	26.7297			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$541$	26.7297			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$542$	3.05943	−	5.29909i	0.131414	−	0.227615i
$543$	10.2096	+	28.0507i	0.438136	+	1.20377i
$544$	1.31908	+	2.28471i	0.0565550	+	0.0979561i
$545$	−0.271974	−	0.471073i	−0.0116501	−	0.0201786i
$546$	5.05438	+	0.891223i	0.216307	+	0.0381408i
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	0.142523	+	0.989792i	$0.454479\pi$
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	−0.928446	+	0.371467i	$0.878855\pi$
$548$	−3.15125			−0.134615
$549$	−3.97906	−	22.5663i	−0.169822	−	0.963108i
$550$	4.62866			0.197367
$551$	10.1133	−	17.5168i	0.430843	−	0.746242i
$552$	−28.2536	+	33.6713i	−1.20255	+	1.43315i
$553$	1.20187	+	2.08169i	0.0511086	+	0.0885226i
$554$	7.85844	+	13.6112i	0.333873	+	0.578285i
$555$	−13.8516	+	16.5077i	−0.587969	+	0.700714i
$556$	−3.76187	+	6.51575i	−0.159539	+	0.276329i
$557$	32.3387			1.37024			0.685118	−	0.728432i	$-0.259751\pi$
$557$	32.3387			1.37024			0.685118	+	0.728432i	$0.259751\pi$
$558$	18.6623	−	15.6595i	0.790036	−	0.662919i
$559$	14.8648			0.628716
$560$	0.0282185	−	0.0488759i	0.00119245	−	0.00206538i
$561$	1.31908	+	0.232589i	0.0556915	+	0.00981992i
$562$	9.80974	+	16.9910i	0.413799	+	0.716721i
$563$	8.87093	+	15.3649i	0.373865	+	0.647553i	0.990156	−	0.139965i	$-0.0446990\pi$
$563$	8.87093	+	15.3649i	0.373865	+	0.647553i	−0.616291	+	0.787518i	$0.711366\pi$
$564$	6.79813	+	18.6777i	0.286253	+	0.786474i
$565$	−9.68004	+	16.7663i	−0.407243	+	0.705365i
$566$	16.3517			0.687315
$567$	6.89440	+	5.78509i	0.289538	+	0.242951i
$568$	−1.57304			−0.0660035
$569$	13.3007	−	23.0374i	0.557593	−	0.965779i	−0.440104	−	0.897947i	$-0.645058\pi$
$569$	13.3007	−	23.0374i	0.557593	−	0.965779i	0.997697	−	0.0678320i	$-0.0216082\pi$
$570$	−2.26470	−	6.22221i	−0.0948579	−	0.260620i
$571$	5.00862	+	8.67518i	0.209604	+	0.363045i	0.951590	−	0.307371i	$-0.0994491\pi$
$571$	5.00862	+	8.67518i	0.209604	+	0.363045i	−0.741986	+	0.670416i	$0.766116\pi$
$572$	−3.41565	−	5.91608i	−0.142815	−	0.247364i
$573$	22.0201	+	3.88273i	0.919902	+	0.162203i
$574$	1.50000	−	2.59808i	0.0626088	−	0.108442i
$575$	−28.4834			−1.18784
$576$	−11.5869	+	9.72259i	−0.482789	+	0.405108i
$577$	−32.9145			−1.37025			−0.685124	−	0.728427i	$-0.740252\pi$
$577$	−32.9145			−1.37025			−0.685124	+	0.728427i	$0.740252\pi$
$578$	−7.37851	+	12.7800i	−0.306905	+	0.531576i
$579$	0.710485	−	0.846723i	0.0295267	−	0.0351886i
$580$	5.18004	+	8.97210i	0.215090	+	0.372546i
$581$	7.52481	+	13.0334i	0.312182	+	0.540715i
$582$	−1.85921	+	2.21572i	−0.0770668	+	0.0918447i
$583$	0.474308	−	0.821525i	0.0196438	−	0.0340241i
$584$	5.81582			0.240660
$585$	2.36500	+	13.4126i	0.0977807	+	0.554542i
$586$	−11.5125			−0.475577
$587$	7.53643	−	13.0535i	0.311062	−	0.538774i	−0.667531	−	0.744582i	$-0.732649\pi$
$587$	7.53643	−	13.0535i	0.311062	−	0.538774i	0.978592	+	0.205808i	$0.0659821\pi$
$588$	−2.09240	−	0.368946i	−0.0862890	−	0.0152151i
$589$	14.8983	+	25.8046i	0.613873	+	1.06326i
$590$	−6.15910	−	10.6679i	−0.253566	−	0.439189i
$591$	−6.78034	−	18.6288i	−0.278906	−	0.766288i
$592$	0.193411	−	0.334997i	0.00794913	−	0.0137683i
$593$	41.0009			1.68371			0.841853	−	0.539706i	$-0.181465\pi$
$593$	41.0009			1.68371			0.841853	+	0.539706i	$0.181465\pi$
$594$			7.55190i			0.309858i
$595$	0.630415			0.0258445
$596$	0.264396	−	0.457947i	0.0108301	−	0.0187582i
$597$	2.15523	+	5.92145i	0.0882077	+	0.242349i
$598$	−13.2506	−	22.9507i	−0.541858	−	0.938526i
$599$	−3.03684	−	5.25996i	−0.124082	−	0.214916i	0.797292	−	0.603594i	$-0.206265\pi$
$599$	−3.03684	−	5.25996i	−0.124082	−	0.214916i	−0.921374	+	0.388678i	$0.872932\pi$
$600$	−15.4145	−	2.71799i	−0.629293	−	0.110961i
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	−0.685110	−	0.728440i	$-0.740246\pi$
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	0.973402	+	0.229102i	$0.0735791\pi$
$602$	3.87939			0.158112
$603$	1.68092	+	0.611806i	0.0684524	+	0.0249147i
$604$	3.03064			0.123315
$605$	5.57011	−	9.64771i	0.226457	−	0.392235i
$606$	−1.67334	+	1.99421i	−0.0679749	+	0.0810094i
$607$	−23.0449	−	39.9149i	−0.935363	−	1.62010i	−0.773986	−	0.633203i	$-0.781740\pi$
$607$	−23.0449	−	39.9149i	−0.935363	−	1.62010i	−0.161377	−	0.986893i	$-0.551594\pi$
$608$	−9.09627	−	15.7552i	−0.368902	−	0.638958i
$609$	−6.97906	+	8.31731i	−0.282806	+	0.337035i
$610$	4.52481	−	7.83721i	0.183204	−	0.317319i
$611$	−31.5226			−1.27527
$612$	−1.61809	−	0.588936i	−0.0654074	−	0.0238063i
$613$	−26.4938			−1.07008			−0.535038	−	0.844828i	$-0.679703\pi$
$613$	−26.4938			−1.07008			−0.535038	+	0.844828i	$0.679703\pi$
$614$	2.77466	−	4.80586i	0.111976	−	0.193949i
$615$	7.84002	+	1.38241i	0.316140	+	0.0557440i
$616$	−2.34477	−	4.06126i	−0.0944735	−	0.163633i
$617$	1.12495	+	1.94847i	0.0452889	+	0.0784426i	0.887781	−	0.460266i	$-0.152246\pi$
$617$	1.12495	+	1.94847i	0.0452889	+	0.0784426i	−0.842492	+	0.538708i	$0.818913\pi$
$618$	−1.89528	−	5.20723i	−0.0762392	−	0.209466i
$619$	−3.09539	+	5.36137i	−0.124414	+	0.215492i	−0.921504	−	0.388369i	$-0.873038\pi$
$619$	−3.09539	+	5.36137i	−0.124414	+	0.215492i	0.797090	+	0.603861i	$0.206372\pi$
$620$	−15.2618			−0.612927
$621$		−	46.4721i		−	1.86486i
$622$	8.37557			0.335830
$623$	−4.54323	+	7.86911i	−0.182021	+	0.315269i
$624$	−0.0836160	−	0.229733i	−0.00334732	−	0.00919668i
$625$	−0.533433	−	0.923933i	−0.0213373	−	0.0369573i
$626$	−7.75119	−	13.4255i	−0.309800	−	0.536589i
$627$	−9.09627	−	1.60392i	−0.363270	−	0.0640543i
$628$	6.21523	−	10.7651i	0.248015	−	0.429574i
$629$	4.32089			0.172285
$630$	0.617211	+	3.50038i	0.0245903	+	0.139458i
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	3.41029	−	5.90680i	0.135654	−	0.234960i
$633$	−6.48293	+	7.72605i	−0.257673	+	0.307083i
$634$	3.55138	+	6.15118i	0.141043	+	0.244295i
$635$	13.9927	+	24.2361i	0.555284	+	0.961781i
$636$	−0.783890	+	0.934204i	−0.0310833	+	0.0370436i
$637$	1.68479	−	2.91815i	0.0667539	−	0.115621i
$638$	−9.11051			−0.360689
$639$	1.27403	−	1.06904i	0.0504000	−	0.0422906i
$640$	9.21894			0.364411
$641$	−2.44444	+	4.23389i	−0.0965496	+	0.167229i	−0.910254	−	0.414050i	$-0.864114\pi$
$641$	−2.44444	+	4.23389i	−0.0965496	+	0.167229i	0.813705	+	0.581278i	$0.197447\pi$
$642$	−10.6925	−	1.88538i	−0.422001	−	0.0744101i
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	0.922218	+	0.386671i	$0.126375\pi$
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	−0.126242	+	0.992000i	$0.540291\pi$
$644$	5.48545	+	9.50108i	0.216157	+	0.374395i
$645$	3.52094	+	9.67372i	0.138637	+	0.380902i
$646$	−0.663848	+	1.14982i	−0.0261188	+	0.0452390i
$647$	−2.28075			−0.0896657			−0.0448329	−	0.998995i	$-0.514276\pi$
$647$	−2.28075			−0.0896657			−0.0448329	+	0.998995i	$0.514276\pi$
$648$	4.43453	−	25.1495i	0.174205	−	0.987965i
$649$	−17.1830			−0.674493
$650$	4.71853	−	8.17273i	0.185076	−	0.320561i
$651$	−5.47044	−	15.0299i	−0.214403	−	0.589068i
$652$	−1.59240	−	2.75811i	−0.0623631	−	0.108016i
$653$	−11.7396	−	20.3336i	−0.459407	−	0.795717i	0.539522	−	0.841971i	$-0.318605\pi$
$653$	−11.7396	−	20.3336i	−0.459407	−	0.795717i	−0.998930	+	0.0462542i	$0.985272\pi$
$654$	−0.605600	−	0.106784i	−0.0236808	−	0.00417557i
$655$	4.82682	−	8.36030i	0.188599	−	0.326664i
$656$	−0.142903			−0.00557944
$657$	−4.71032	+	3.95243i	−0.183767	+	0.154199i
$658$	−8.22668			−0.320709
$659$	23.9812	−	41.5366i	0.934174	−	1.61804i	0.158073	−	0.987427i	$-0.449472\pi$
$659$	23.9812	−	41.5366i	0.934174	−	1.61804i	0.776101	−	0.630609i	$-0.217195\pi$
$660$	3.04101	−	3.62414i	0.118371	−	0.141069i
$661$	−14.6545	−	25.3824i	−0.569995	−	0.987260i	−0.996566	−	0.0828055i	$-0.973612\pi$
$661$	−14.6545	−	25.3824i	−0.569995	−	0.987260i	0.426571	−	0.904454i	$-0.359721\pi$
$662$	10.1348	+	17.5539i	0.393898	+	0.682252i
$663$	1.75537	−	2.09196i	0.0681728	−	0.0812452i
$664$	21.3516	−	36.9821i	0.828604	−	1.43518i
$665$	−4.34730			−0.168581
$666$	4.23039	+	23.9917i	0.163924	+	0.929661i
$667$	56.0634			2.17078
$668$	−14.2191	+	24.6282i	−0.550154	+	0.952894i
$669$	12.0831	+	2.13057i	0.467158	+	0.0823726i
$670$	0.353226	+	0.611806i	0.0136463	+	0.0236361i
$671$	−6.31180	−	10.9324i	−0.243664	−	0.422039i
$672$	3.34002	+	9.17664i	0.128844	+	0.353996i
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	0.492719	+	0.870189i	$0.336003\pi$
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	−0.999965	+	0.00838731i	$0.997330\pi$
$674$	−25.5226			−0.983094
$675$	14.3316	−	8.27433i	0.551622	−	0.318479i
$676$	2.01899			0.0776535
$677$	−17.9454	+	31.0823i	−0.689697	+	1.19459i	0.282239	+	0.959344i	$0.408923\pi$
$677$	−17.9454	+	31.0823i	−0.689697	+	1.19459i	−0.971936	+	0.235246i	$0.924411\pi$
$678$	7.48576	+	20.5669i	0.287489	+	0.789869i
$679$	0.949493	+	1.64457i	0.0364382	+	0.0631128i
$680$	−0.894400	−	1.54915i	−0.0342987	−	0.0594070i
$681$	−20.3726	−	3.59224i	−0.780679	−	0.137655i
$682$	6.71048	−	11.6229i	0.256958	−	0.445064i
$683$	35.0642			1.34169			0.670847	−	0.741596i	$-0.265931\pi$
$683$	35.0642			1.34169			0.670847	+	0.741596i	$0.265931\pi$
$684$	11.1582	+	4.06126i	0.426645	+	0.155286i
$685$	3.46110			0.132242
$686$	0.439693	−	0.761570i	0.0167875	−	0.0290769i
$687$	19.5421	−	23.2893i	0.745576	−	0.888543i
$688$	−0.0923963	−	0.160035i	−0.00352257	−	0.00610128i
$689$	−0.967034	−	1.67495i	−0.0368411	−	0.0638106i
$690$	11.7973	−	14.0594i	0.449114	−	0.535233i
$691$	−1.03343	+	1.78996i	−0.0393136	+	0.0680932i	−0.885013	−	0.465567i	$-0.845850\pi$
$691$	−1.03343	+	1.78996i	−0.0393136	+	0.0680932i	0.845699	+	0.533660i	$0.179184\pi$
$692$	5.82915			0.221591
$693$	4.65910	+	1.69577i	0.176985	+	0.0644171i
$694$	−11.3847			−0.432159
$695$	4.13176	−	7.15642i	0.156727	−	0.271458i
$696$	30.3400	+	5.34976i	1.15004	+	0.202782i
$697$	−0.798133	−	1.38241i	−0.0302315	−	0.0523624i
$698$	0.643208	+	1.11407i	0.0243458	+	0.0421681i
$699$	−9.62882	−	26.4550i	−0.364196	−	1.00062i
$700$	−1.95336	+	3.38332i	−0.0738302	+	0.127878i
$701$	−7.36009			−0.277987			−0.138993	−	0.990293i	$-0.544387\pi$
$701$	−7.36009			−0.277987			−0.138993	+	0.990293i	$0.544387\pi$
$702$	13.3342	+	7.69852i	0.503268	+	0.290562i
$703$	−29.7965			−1.12380
$704$	−4.16637	+	7.21637i	−0.157026	+	0.271977i
$705$	−7.46657	−	20.5142i	−0.281207	−	0.772610i
$706$	6.30200	+	10.9154i	0.237179	+	0.410806i
$707$	0.854570	+	1.48016i	0.0321394	+	0.0556671i
$708$	21.7545	+	3.83590i	0.817584	+	0.144162i
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	−0.938785	−	0.344504i	$-0.888047\pi$
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	0.767742	+	0.640760i	$0.221380\pi$
$710$	0.656822			0.0246501
$711$	1.25221	+	7.10165i	0.0469616	+	0.266333i
$712$	25.7828			0.966252
$713$	−41.2943	+	71.5239i	−1.54648	+	2.67859i
$714$	0.458111	−	0.545955i	0.0171444	−	0.0204319i
$715$	3.75150	+	6.49778i	0.140298	+	0.243003i
$716$	−5.23308	−	9.06396i	−0.195569	−	0.338736i
$717$	16.8106	−	20.0341i	0.627804	−	0.748188i
$718$	−9.20574	+	15.9448i	−0.343555	+	0.595055i
$719$	−25.9537			−0.967908			−0.483954	−	0.875093i	$-0.660800\pi$
$719$	−25.9537			−0.967908			−0.483954	+	0.875093i	$0.660800\pi$
$720$	0.129700	−	0.108831i	0.00483362	−	0.00405589i
$721$	−3.63816			−0.135492
$722$	−3.77631	+	6.54076i	−0.140540	+	0.243422i
$723$	−26.6746	−	4.70345i	−0.992038	−	0.174923i
$724$	−10.5706	−	18.3088i	−0.392852	−	0.680440i
$725$	9.98205	+	17.2894i	0.370724	+	0.642113i
$726$	−4.30747	−	11.8347i	−0.159865	−	0.439226i
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	−0.756311	−	0.654213i	$-0.773000\pi$
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	0.944720	+	0.327878i	$0.106333\pi$
$728$	−9.56118			−0.354361
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	−2.42839			−0.0898786
$731$	1.03209	−	1.78763i	0.0381732	−	0.0661179i
$732$	5.55051	+	15.2499i	0.205153	+	0.563652i
$733$	−20.3307	−	35.2138i	−0.750931	−	1.30065i	−0.947372	−	0.320135i	$-0.896272\pi$
$733$	−20.3307	−	35.2138i	−0.750931	−	1.30065i	0.196441	−	0.980516i	$-0.437062\pi$
$734$	−5.30154	−	9.18253i	−0.195683	−	0.338933i
$735$	2.29813	+	0.405223i	0.0847679	+	0.0149469i
$736$	25.2126	−	43.6695i	0.929349	−	1.60968i
$737$	0.985452			0.0362996
$738$	6.89440	−	5.78509i	0.253786	−	0.212952i
$739$	−25.3618			−0.932951			−0.466475	−	0.884534i	$-0.654476\pi$
$739$	−25.3618			−0.932951			−0.466475	+	0.884534i	$0.654476\pi$
$740$	7.63088	−	13.2171i	0.280517	−	0.485869i
$741$	−12.1049	+	14.4260i	−0.444684	+	0.529954i
$742$	−0.252374	−	0.437124i	−0.00926494	−	0.0160473i
$743$	11.2221	+	19.4372i	0.411699	+	0.713083i	0.995076	−	0.0991184i	$-0.0316023\pi$
$743$	11.2221	+	19.4372i	0.411699	+	0.713083i	−0.583377	+	0.812202i	$0.698269\pi$
$744$	−29.1725	+	34.7664i	−1.06951	+	1.27460i
$745$	−0.290393	+	0.502975i	−0.0106392	+	0.0184276i
$746$	0.686852			0.0251474
$747$	7.84002	+	44.4630i	0.286851	+	1.62682i
$748$	−0.948615			−0.0346848
$749$	−3.56418	+	6.17334i	−0.130232	+	0.225569i
$750$	16.5410	+	2.91663i	0.603992	+	0.106500i
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	0.555978	−	0.831197i	$-0.312344\pi$
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	−0.997827	+	0.0658924i	$0.979011\pi$
$752$	0.195937	+	0.339373i	0.00714508	+	0.0123756i
$753$	−11.2941	−	31.0303i	−0.411580	−	1.13081i
$754$	−9.28740	+	16.0862i	−0.338227	+	0.585827i
$755$	−3.32863			−0.121141
$756$	−5.52007	−	3.18701i	−0.200763	−	0.115911i
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	−3.04442	+	5.27308i	−0.110578	+	0.191527i
$759$	−8.75624	−	24.0576i	−0.317832	−	0.873235i
$760$	6.16772	+	10.6828i	0.223727	+	0.387506i
$761$	9.13610	+	15.8242i	0.331183	+	0.573626i	0.982744	−	0.184970i	$-0.0592188\pi$
$761$	9.13610	+	15.8242i	0.331183	+	0.573626i	−0.651561	+	0.758596i	$0.725886\pi$
$762$	31.1573	+	5.49388i	1.12871	+	0.199022i
$763$	−0.201867	+	0.349643i	−0.00730806	+	0.0126579i
$764$	−15.8357			−0.572917
$765$	1.77719	+	0.646844i	0.0642544	+	0.0233867i
$766$	−6.79973			−0.245684
$767$	−17.5167	+	30.3398i	−0.632490	+	1.09550i
$768$	17.9259	−	21.3633i	0.646846	−	0.770881i
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	0.649217	−	0.760604i	$-0.275097\pi$
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	−0.983310	+	0.181936i	$0.941764\pi$
$770$	0.979055	+	1.69577i	0.0352827	+	0.0611114i
$771$	−29.5945	+	35.2694i	−1.06582	+	1.27020i
$772$	−0.391407	+	0.677937i	−0.0140870	+	0.0243995i
$773$	−2.96080			−0.106493			−0.0532463	−	0.998581i	$-0.516957\pi$
$773$	−2.96080			−0.106493			−0.0532463	+	0.998581i	$0.516957\pi$
$774$	10.9363	+	3.98048i	0.393097	+	0.143076i
$775$	−29.4097			−1.05643
$776$	2.69418	−	4.66646i	0.0967155	−	0.167516i
$777$	15.7515	+	2.77741i	0.565082	+	0.0996392i
$778$	2.37417	+	4.11218i	0.0851181	+	0.147429i
$779$	5.50387	+	9.53298i	0.197197	+	0.341555i
$780$	−3.29901	−	9.06396i	−0.118124	−	0.324542i
$781$	0.458111	−	0.793471i	0.0163925	−	0.0283926i
$782$	−3.68004			−0.131598
$783$	−28.2086	+	16.2862i	−1.00809	+	0.582022i
$784$	−0.0418891			−0.00149604
$785$	−6.82635	+	11.8236i	−0.243643	+	0.422002i
$786$	−3.73267	−	10.2554i	−0.133140	−	0.365799i
$787$	16.7010	+	28.9270i	0.595326	+	1.03113i	0.993501	+	0.113825i	$0.0363104\pi$
$787$	16.7010	+	28.9270i	0.595326	+	1.03113i	−0.398175	+	0.917310i	$0.630356\pi$
$788$	7.02007	+	12.1591i	0.250080	+	0.433150i
$789$	−1.25221	−	0.220799i	−0.0445799	−	0.00786064i
$790$	−1.42396	+	2.46638i	−0.0506623	+	0.0877497i
$791$	14.3696			0.510924
$792$	−2.44299	−	13.8549i	−0.0868079	−	0.492312i
$793$	−25.7374			−0.913962
$794$	−12.8542	+	22.2641i	−0.456177	+	0.790122i
$795$	0.860967	−	1.02606i	0.0305354	−	0.0363906i
$796$	−2.23143	−	3.86495i	−0.0790909	−	0.136989i
$797$	−24.6755	−	42.7391i	−0.874050	−	1.51390i	−0.857772	−	0.514031i	$-0.828152\pi$
$797$	−24.6755	−	42.7391i	−0.874050	−	1.51390i	−0.0162779	−	0.999868i	$-0.505182\pi$
$798$	−3.15910	+	3.76487i	−0.111831	+	0.133275i
$799$	−2.18866	+	3.79088i	−0.0774293	+	0.134112i
$800$	17.9564			0.634853
$801$	−20.8819	+	17.5220i	−0.737826	+	0.619110i
$802$	24.0933			0.850763
$803$	−1.69372	+	2.93360i	−0.0597699	+	0.103525i
$804$	−1.24763	−	0.219990i	−0.0440004	−	0.00775845i
$805$	−6.02481	−	10.4353i	−0.212347	−	0.367795i
$806$	−13.6816	−	23.6971i	−0.481912	−	0.834696i
$807$	12.3516	+	33.9358i	0.434798	+	1.19460i
$808$	2.42484	−	4.19995i	0.0853056	−	0.147754i
$809$	19.8280			0.697115			0.348558	−	0.937287i	$-0.386672\pi$
$809$	19.8280			0.697115			0.348558	+	0.937287i	$0.386672\pi$
$810$	−1.85163	+	10.5011i	−0.0650598	+	0.368972i
$811$	−23.8557			−0.837686			−0.418843	−	0.908059i	$-0.637564\pi$
$811$	−23.8557			−0.837686			−0.418843	+	0.908059i	$0.637564\pi$
$812$	3.84477	−	6.65934i	0.134925	−	0.233697i
$813$	−4.12196	−	11.3250i	−0.144563	−	0.397185i
$814$	6.71048	+	11.6229i	0.235202	+	0.407382i
$815$	1.74897	+	3.02931i	0.0612638	+	0.106112i
$816$	−0.0334331	−	0.00589515i	−0.00117039	−	0.000206372i
$817$	−7.11721	+	12.3274i	−0.249000	+	0.431280i
$818$	7.93643			0.277491
$819$	7.74376	−	6.49778i	0.270589	−	0.227051i
$820$	−5.63816			−0.196893
$821$	25.4714	−	44.1177i	0.888957	−	1.53972i	0.0478469	−	0.998855i	$-0.484764\pi$
$821$	25.4714	−	44.1177i	0.888957	−	1.53972i	0.841110	−	0.540864i	$-0.181903\pi$
$822$	2.51512	−	2.99740i	0.0877249	−	0.104546i
$823$	−6.80747	−	11.7909i	−0.237293	−	0.411004i	0.722643	−	0.691221i	$-0.242927\pi$
$823$	−6.80747	−	11.7909i	−0.237293	−	0.411004i	−0.959937	+	0.280217i	$0.909594\pi$
$824$	5.16163	+	8.94020i	0.179814	+	0.311447i
$825$	5.86009	−	6.98378i	0.204022	−	0.243144i
$826$	−4.57145	+	7.91799i	−0.159061	+	0.275502i
$827$	36.2158			1.25935			0.629673	−	0.776861i	$-0.283189\pi$
$827$	36.2158			1.25935			0.629673	+	0.776861i	$0.283189\pi$
$828$	5.71523	+	32.4127i	0.198618	+	1.12642i
$829$	25.3259			0.879606			0.439803	−	0.898094i	$-0.355048\pi$
$829$	25.3259			0.879606			0.439803	+	0.898094i	$0.355048\pi$
$830$	−8.91534	+	15.4418i	−0.309456	+	0.535994i
$831$	30.4859	+	5.37549i	1.05754	+	0.186474i
$832$	8.49454	+	14.7130i	0.294495	+	0.510080i
$833$	−0.233956	−	0.405223i	−0.00810608	−	0.0140401i
$834$	−3.19517	−	8.77864i	−0.110640	−	0.303980i
$835$	15.6172	−	27.0498i	0.540456	−	0.936097i
$836$	6.54158			0.226245
$837$		−	47.9835i		−	1.65855i
$838$	−0.154154			−0.00532515
$839$	−4.35710	+	7.54671i	−0.150424	+	0.260541i	−0.931383	−	0.364040i	$-0.881397\pi$
$839$	−4.35710	+	7.54671i	−0.150424	+	0.260541i	0.780960	+	0.624582i	$0.214730\pi$
$840$	−2.26470	−	6.22221i	−0.0781396	−	0.214687i
$841$	−5.14749	−	8.91571i	−0.177500	−	0.307438i
$842$	−10.8626	−	18.8146i	−0.374350	−	0.648394i
$843$	38.0558	+	6.71026i	1.31071	+	0.231114i
$844$	3.57145	−	6.18594i	0.122934	−	0.212929i
$845$	−2.21751			−0.0762847
$846$	−23.1917	−	8.44107i	−0.797346	−	0.290210i
$847$	−8.26857			−0.284111
$848$	−0.0120217	+	0.0208222i	−0.000412827	+	0.000715037i
$849$	20.7020	−	24.6717i	0.710492	−	0.846731i
$850$	−0.655230	−	1.13489i	−0.0224742	−	0.0389265i
$851$	−41.2943	−	71.5239i	−1.41555	−	2.45181i
$852$	−0.757122	+	0.902302i	−0.0259386	+	0.0309124i
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	−0.745053	−	0.667005i	$-0.767576\pi$
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	0.950170	+	0.311733i	$0.100909\pi$
$854$	−6.71688			−0.229847
$855$	−12.2554	−	4.46059i	−0.419125	−	0.152549i
$856$	20.2267			0.691334
$857$	−3.25015	+	5.62943i	−0.111023	+	0.192298i	−0.916183	−	0.400760i	$-0.868746\pi$
$857$	−3.25015	+	5.62943i	−0.111023	+	0.192298i	0.805160	+	0.593058i	$0.202079\pi$
$858$	8.35339	+	1.47293i	0.285180	+	0.0502849i
$859$	26.7763	+	46.3779i	0.913596	+	1.58239i	0.808944	+	0.587886i	$0.200040\pi$
$859$	26.7763	+	46.3779i	0.913596	+	1.58239i	0.104652	+	0.994509i	$0.466627\pi$
$860$	−3.64543	−	6.31407i	−0.124308	−	0.215308i
$861$	−2.02094	−	5.55250i	−0.0688736	−	0.189229i
$862$	−12.8914	+	22.3286i	−0.439083	+	0.760514i
$863$	3.69965			0.125937			0.0629687	−	0.998016i	$-0.479943\pi$
$863$	3.69965			0.125937			0.0629687	+	0.998016i	$0.479943\pi$
$864$			29.2967i			0.996695i
$865$	−6.40230			−0.217685
$866$	8.64233	−	14.9690i	0.293678	−	0.508666i
$867$	9.94104	+	27.3128i	0.337615	+	0.927590i
$868$	5.66385	+	9.81007i	0.192244	+	0.332976i
$869$	1.98633	+	3.44042i	0.0673816	+	0.116708i
$870$	−12.6684	−	2.23379i	−0.429500	−	0.0757325i
$871$	1.00459	−	1.73999i	0.0340391	−	0.0589574i
$872$	1.14559			0.0387946
$873$	0.989266	+	5.61041i	0.0334816	+	0.189884i
$874$	25.3773			0.858401
$875$	5.51367	−	9.54996i	0.186396	−	0.322847i
$876$	2.79921	−	3.33597i	0.0945765	−	0.112712i
$877$	5.89440	+	10.2094i	0.199040	+	0.344747i	0.948217	−	0.317622i	$-0.102884\pi$
$877$	5.89440	+	10.2094i	0.199040	+	0.344747i	−0.749178	+	0.662369i	$0.769551\pi$
$878$	−9.64244	−	16.7012i	−0.325416	−	0.563638i
$879$	−14.5753	+	17.3702i	−0.491613	+	0.585882i
$880$	0.0466368	−	0.0807773i	0.00157213	−	0.00272300i
$881$	49.4858			1.66722			0.833609	−	0.552355i	$-0.186271\pi$
$881$	49.4858			1.66722			0.833609	+	0.552355i	$0.186271\pi$
$882$	2.02094	−	1.69577i	0.0680487	−	0.0570997i
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	−0.967034	+	1.67495i	−0.0325249	+	0.0563347i
$885$	−23.8935	−	4.21307i	−0.803172	−	0.141621i
$886$	−8.22668	−	14.2490i	−0.276381	−	0.478706i
$887$	−5.94238	−	10.2925i	−0.199526	−	0.345589i	0.748849	−	0.662741i	$-0.230607\pi$
$887$	−5.94238	−	10.2925i	−0.199526	−	0.345589i	−0.948375	+	0.317152i	$0.897273\pi$
$888$	−15.5223	−	42.6473i	−0.520896	−	1.43115i
$889$	10.3858	−	17.9887i	0.348328	−	0.603322i
$890$	−10.7656			−0.360863
$891$	11.3944	+	9.56104i	0.381727	+	0.320307i
$892$	−8.68954			−0.290947
$893$	15.0929	−	26.1416i	0.505063	−	0.874795i
$894$	0.224566	+	0.616990i	0.00751061	+	0.0206352i
$895$	5.74763	+	9.95518i	0.192122	+	0.332765i
$896$	−3.42127	−	5.92582i	−0.114297	−	0.197968i
$897$	−51.4043	−	9.06396i	−1.71634	−	0.302637i
$898$	2.93717	−	5.08732i	0.0980145	−	0.169766i
$899$	57.8866			1.93063
$900$	−8.97818	+	7.53359i	−0.299273	+	0.251120i
$901$	−0.268571			−0.00894739
$902$	2.47906	−	4.29385i	0.0825435	−	0.142970i
$903$	4.91147	−	5.85327i	0.163444	−	0.194785i
$904$	−20.3868	−	35.3110i	−0.678056	−	1.17443i
$905$	11.6099	+	20.1090i	0.385927	+	0.668446i
$906$	−2.41885	+	2.88268i	−0.0803610	+	0.0957706i
$907$	13.0107	−	22.5353i	0.432014	−	0.748271i	−0.565032	−	0.825069i	$-0.691136\pi$
$907$	13.0107	−	22.5353i	0.432014	−	0.748271i	0.997047	+	0.0767980i	$0.0244697\pi$
$908$	14.6509			0.486209
$909$	0.890367	+	5.04952i	0.0295316	+	0.167482i
$910$	3.99226			0.132342
$911$	2.01636	−	3.49244i	0.0668050	−	0.115710i	−0.830688	−	0.556738i	$-0.812053\pi$
$911$	2.01636	−	3.49244i	0.0668050	−	0.115710i	0.897493	+	0.441028i	$0.145386\pi$
$912$	0.230552	+	0.0406525i	0.00763434	+	0.00134614i
$913$	12.4363	+	21.5403i	0.411581	+	0.712879i
$914$	−8.54266	−	14.7963i	−0.282566	−	0.489419i
$915$	−6.09627	−	16.7494i	−0.201536	−	0.553717i
$916$	−10.7657	+	18.6468i	−0.355710	+	0.616108i
$917$	−7.16519			−0.236615
$918$	1.85163	−	1.06904i	0.0611130	−	0.0352836i
$919$	27.4270			0.904732			0.452366	−	0.891832i	$-0.350580\pi$
$919$	27.4270			0.904732			0.452366	+	0.891832i	$0.350580\pi$
$920$	−17.0954	+	29.6101i	−0.563618	+	0.976216i
$921$	−3.73829	−	10.2709i	−0.123181	−	0.338437i
$922$	−0.424678	−	0.735564i	−0.0139860	−	0.0242245i
$923$	−0.934011	−	1.61775i	−0.0307434	−	0.0532491i
$924$	−3.45811	−	0.609758i	−0.113763	−	0.0200596i
$925$	14.7049	−	25.4696i	0.483493	−	0.837434i
$926$	0.391874			0.0128778
$927$	−10.2562	−	3.73297i	−0.336859	−	0.122607i
$928$	−35.3432			−1.16020
$929$	−3.83837	+	6.64826i	−0.125933	+	0.218122i	−0.922097	−	0.386958i	$-0.873526\pi$
$929$	−3.83837	+	6.64826i	−0.125933	+	0.218122i	0.796164	+	0.605081i	$0.206859\pi$
$930$	12.1809	−	14.5167i	0.399428	−	0.476020i
$931$	1.61334	+	2.79439i	0.0528751	+	0.0915824i
$932$	9.96926	+	17.2673i	0.326554	+	0.565608i
$933$	10.6038	−	12.6372i	0.347154	−	0.413722i
$934$	−15.0440	+	26.0570i	−0.492255	+	0.852610i
$935$	1.04189			0.0340734
$936$	−26.9537	−	9.81035i	−0.881010	−	0.320661i
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$	0.262174	−	0.454099i	0.00856029	−	0.0148269i
$939$	−30.0699	−	5.30213i	−0.981293	−	0.173028i
$940$	7.73055	+	13.3897i	0.252143	+	0.436724i
$941$	3.06964	+	5.31677i	0.100067	+	0.173322i	0.911712	−	0.410829i	$-0.134761\pi$
$941$	3.06964	+	5.31677i	0.100067	+	0.173322i	−0.811645	+	0.584151i	$0.801427\pi$
$942$	5.27894	+	14.5038i	0.171997	+	0.472559i
$943$	−15.2554	+	26.4231i	−0.496783	+	0.860454i
$944$	0.435518			0.0141749
$945$	6.06283	+	3.50038i	0.197224	+	0.113867i
$946$	6.41147			0.208455
$947$	−2.78224	+	4.81898i	−0.0904107	+	0.156596i	−0.907684	−	0.419654i	$-0.862151\pi$
$947$	−2.78224	+	4.81898i	−0.0904107	+	0.156596i	0.817273	+	0.576250i	$0.195485\pi$
$948$	−1.74675	−	4.79915i	−0.0567318	−	0.155869i
$949$	3.45320	+	5.98112i	0.112096	+	0.194155i
$950$	4.51842	+	7.82613i	0.146597	+	0.253913i
$951$	13.7772	+	2.42929i	0.446756	+	0.0787751i
$952$	−0.663848	+	1.14982i	−0.0215154	+	0.0372658i
$953$	−8.72018			−0.282474			−0.141237	−	0.989976i	$-0.545108\pi$
$953$	−8.72018			−0.282474			−0.141237	+	0.989976i	$0.545108\pi$
$954$	−0.262946	−	1.49124i	−0.00851318	−	0.0482806i
$955$	17.3928			0.562818
$956$	−9.26099	+	16.0405i	−0.299522	+	0.518787i
$957$	−11.5343	+	13.7461i	−0.372851	+	0.444347i
$958$	−9.58219	−	16.5968i	−0.309586	−	0.536219i
$959$	−1.28446	−	2.22475i	−0.0414775	−	0.0718411i
$960$	−7.56283	+	9.01303i	−0.244089	+	0.290894i
$961$	−27.1373	+	47.0031i	−0.875396	+	1.51623i
$962$	27.3631			0.882222
$963$	−16.3819	+	13.7461i	−0.527900	+	0.442960i
$964$	19.1830			0.617844
$965$	0.429892	−	0.744596i	0.0138387	−	0.0239694i
$966$	−13.4153	−	2.36549i	−0.431632	−	0.0761083i
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.785206	+	0.619235i	$0.212557\pi$
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.143670	+	0.989626i	$0.454110\pi$
$968$	11.7310	+	20.3187i	0.377049	+	0.653068i
$969$	0.894400	+	2.45734i	0.0287323	+	0.0789413i
$970$	−1.12495	+	1.94847i	−0.0361200	+	0.0625617i
$971$	−30.7192			−0.985828			−0.492914	−	0.870078i	$-0.664068\pi$
$971$	−30.7192			−0.985828			−0.492914	+	0.870078i	$0.664068\pi$
$972$	−12.2914	−	14.6484i	−0.394248	−	0.469846i
$973$	−6.13341			−0.196628
$974$	8.52687	−	14.7690i	0.273219	−	0.473229i
$975$	−6.35726	−	17.4664i	−0.203595	−	0.559373i
$976$	0.159978	+	0.277089i	0.00512076	+	0.00886941i
$977$	−5.15002	−	8.92009i	−0.164764	−	0.285379i	0.771808	−	0.635856i	$-0.219353\pi$
$977$	−5.15002	−	8.92009i	−0.164764	−	0.285379i	−0.936571	+	0.350477i	$0.886019\pi$
$978$	3.89440	+	0.686688i	0.124529	+	0.0219579i
$979$	−7.50862	+	13.0053i	−0.239976	+	0.415651i
$980$	−1.65270			−0.0527937
$981$	−0.927833	+	0.778544i	−0.0296234	+	0.0248570i
$982$	−23.0018			−0.734015
$983$	−6.84817	+	11.8614i	−0.218423	+	0.378319i	−0.954326	−	0.298767i	$-0.903425\pi$
$983$	−6.84817	+	11.8614i	−0.218423	+	0.378319i	0.735903	+	0.677087i	$0.236758\pi$
$984$	−10.7772	+	12.8438i	−0.343564	+	0.409444i
$985$	−7.71032	−	13.3547i	−0.245671	−	0.425515i
$986$	1.28968	+	2.23379i	0.0410717	+	0.0711383i
$987$	−10.4153	+	12.4125i	−0.331524	+	0.395095i
$988$	6.66860	−	11.5503i	0.212156	−	0.367465i
$989$	−39.4543			−1.25457
$990$	1.02007	+	5.78509i	0.0324199	+	0.183862i
$991$	57.9813			1.84184			0.920919	−	0.389754i	$-0.127440\pi$
$991$	57.9813			1.84184			0.920919	+	0.389754i	$0.127440\pi$
$992$	26.0326	−	45.0897i	0.826534	−	1.43160i
$993$	39.3166	+	6.93258i	1.24767	+	0.219999i
$994$	−0.243756	−	0.422197i	−0.00773146	−	0.0133913i
$995$	2.45084	+	4.24497i	0.0776968	+	0.134575i
$996$	−10.9363	−	30.0472i	−0.346530	−	0.952082i
$997$	−8.10876	+	14.0448i	−0.256807	+	0.444803i	−0.965385	−	0.260830i	$-0.916004\pi$
$997$	−8.10876	+	14.0448i	−0.256807	+	0.444803i	0.708578	+	0.705633i	$0.249337\pi$
$998$	12.5763			0.398097
$999$	41.5549	+	23.9917i	1.31474	+	0.759065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.f.a.43.3	yes	6
3.2	odd	2		189.2.f.b.127.1		6
4.3	odd	2		1008.2.r.h.673.2		6
7.2	even	3		441.2.h.d.214.1		6
7.3	odd	6		441.2.g.b.79.3		6
7.4	even	3		441.2.g.c.79.3		6
7.5	odd	6		441.2.h.e.214.1		6
7.6	odd	2		441.2.f.c.295.3		6
9.2	odd	6		567.2.a.c.1.3		3
9.4	even	3	inner	63.2.f.a.22.3	✓	6
9.5	odd	6		189.2.f.b.64.1		6
9.7	even	3		567.2.a.h.1.1		3
12.11	even	2		3024.2.r.k.2017.2		6
21.2	odd	6		1323.2.h.c.802.3		6
21.5	even	6		1323.2.h.b.802.3		6
21.11	odd	6		1323.2.g.d.667.1		6
21.17	even	6		1323.2.g.e.667.1		6
21.20	even	2		1323.2.f.d.883.1		6
36.7	odd	6		9072.2.a.ca.1.2		3
36.11	even	6		9072.2.a.bs.1.2		3
36.23	even	6		3024.2.r.k.1009.2		6
36.31	odd	6		1008.2.r.h.337.2		6
63.4	even	3		441.2.h.d.373.1		6
63.5	even	6		1323.2.g.e.361.1		6
63.13	odd	6		441.2.f.c.148.3		6
63.20	even	6		3969.2.a.l.1.3		3
63.23	odd	6		1323.2.g.d.361.1		6
63.31	odd	6		441.2.h.e.373.1		6
63.32	odd	6		1323.2.h.c.226.3		6
63.34	odd	6		3969.2.a.q.1.1		3
63.40	odd	6		441.2.g.b.67.3		6
63.41	even	6		1323.2.f.d.442.1		6
63.58	even	3		441.2.g.c.67.3		6
63.59	even	6		1323.2.h.b.226.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	9.4	even	3	inner
63.2.f.a.43.3	yes	6	1.1	even	1	trivial
189.2.f.b.64.1		6	9.5	odd	6
189.2.f.b.127.1		6	3.2	odd	2
441.2.f.c.148.3		6	63.13	odd	6
441.2.f.c.295.3		6	7.6	odd	2
441.2.g.b.67.3		6	63.40	odd	6
441.2.g.b.79.3		6	7.3	odd	6
441.2.g.c.67.3		6	63.58	even	3
441.2.g.c.79.3		6	7.4	even	3
441.2.h.d.214.1		6	7.2	even	3
441.2.h.d.373.1		6	63.4	even	3
441.2.h.e.214.1		6	7.5	odd	6
441.2.h.e.373.1		6	63.31	odd	6
567.2.a.c.1.3		3	9.2	odd	6
567.2.a.h.1.1		3	9.7	even	3
1008.2.r.h.337.2		6	36.31	odd	6
1008.2.r.h.673.2		6	4.3	odd	2
1323.2.f.d.442.1		6	63.41	even	6
1323.2.f.d.883.1		6	21.20	even	2
1323.2.g.d.361.1		6	63.23	odd	6
1323.2.g.d.667.1		6	21.11	odd	6
1323.2.g.e.361.1		6	63.5	even	6
1323.2.g.e.667.1		6	21.17	even	6
1323.2.h.b.226.3		6	63.59	even	6
1323.2.h.b.802.3		6	21.5	even	6
1323.2.h.c.226.3		6	63.32	odd	6
1323.2.h.c.802.3		6	21.2	odd	6
3024.2.r.k.1009.2		6	36.23	even	6
3024.2.r.k.2017.2		6	12.11	even	2
3969.2.a.l.1.3		3	63.20	even	6
3969.2.a.q.1.1		3	63.34	odd	6
9072.2.a.bs.1.2		3	36.11	even	6
9072.2.a.ca.1.2		3	36.7	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.439693 - 0.761570i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} +(-1.50000 - 0.264490i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\)	\(q+(0.439693 - 0.761570i) q^{2} +(-0.592396 - 1.62760i) q^{3} +(0.613341 + 1.06234i) q^{4} +(-0.673648 - 1.16679i) q^{5} +(-1.50000 - 0.264490i) q^{6} +(-0.500000 + 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 + 1.92836i) q^{9} -1.18479 q^{10} +(-0.826352 + 1.43128i) q^{11} +(1.36571 - 1.62760i) q^{12} +(1.68479 + 2.91815i) q^{13} +(0.439693 + 0.761570i) q^{14} +(-1.50000 + 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +0.467911 q^{17} +(0.458111 + 2.59808i) q^{18} -3.22668 q^{19} +(0.826352 - 1.43128i) q^{20} +(1.70574 + 0.300767i) q^{21} +(0.726682 + 1.25865i) q^{22} +(-4.47178 - 7.74535i) q^{23} +(-1.68092 - 4.61830i) q^{24} +(1.59240 - 2.75811i) q^{25} +2.96316 q^{26} +(4.50000 + 2.59808i) q^{27} -1.22668 q^{28} +(-3.13429 + 5.42874i) q^{29} +(0.701867 + 1.92836i) q^{30} +(-4.61721 - 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(2.81908 + 0.497079i) q^{33} +(0.205737 - 0.356347i) q^{34} +1.34730 q^{35} +(-3.45811 - 1.25865i) q^{36} +9.23442 q^{37} +(-1.41875 + 2.45734i) q^{38} +(3.75150 - 4.47086i) q^{39} +(-1.91147 - 3.31077i) q^{40} +(-1.70574 - 2.95442i) q^{41} +(0.979055 - 1.16679i) q^{42} +(2.20574 - 3.82045i) q^{43} -2.02734 q^{44} +(3.79813 + 1.38241i) q^{45} -7.86484 q^{46} +(-4.67752 + 8.10170i) q^{47} +(-0.0714517 - 0.0125989i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.40033 - 2.42544i) q^{50} +(-0.277189 - 0.761570i) q^{51} +(-2.06670 + 3.57964i) q^{52} -0.573978 q^{53} +(3.95723 - 2.28471i) q^{54} +2.22668 q^{55} +(-1.41875 + 2.45734i) q^{56} +(1.91147 + 5.25173i) q^{57} +(2.75624 + 4.77396i) q^{58} +(5.19846 + 9.00400i) q^{59} +(-2.81908 - 0.497079i) q^{60} +(-3.81908 + 6.61484i) q^{61} -8.12061 q^{62} +(-0.520945 - 2.95442i) q^{63} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(1.61809 - 1.92836i) q^{66} +(-0.298133 - 0.516382i) q^{67} +(0.286989 + 0.497079i) q^{68} +(-9.95723 + 11.8666i) q^{69} +(0.592396 - 1.02606i) q^{70} -0.554378 q^{71} +(-6.52094 + 5.47172i) q^{72} +2.04963 q^{73} +(4.06031 - 7.03266i) q^{74} +(-5.43242 - 0.957882i) q^{75} +(-1.97906 - 3.42782i) q^{76} +(-0.826352 - 1.43128i) q^{77} +(-1.75537 - 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} -0.0564370 q^{80} +(1.56283 - 8.86327i) q^{81} -3.00000 q^{82} +(7.52481 - 13.0334i) q^{83} +(0.726682 + 1.99654i) q^{84} +(-0.315207 - 0.545955i) q^{85} +(-1.93969 - 3.35965i) q^{86} +(10.6925 + 1.88538i) q^{87} +(-2.34477 + 4.06126i) q^{88} +9.08647 q^{89} +(2.72281 - 2.28471i) q^{90} -3.36959 q^{91} +(5.48545 - 9.50108i) q^{92} +(-10.2811 + 12.2525i) q^{93} +(4.11334 + 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(6.27719 - 7.48086i) q^{96} +(0.949493 - 1.64457i) q^{97} -0.879385 q^{98} +(-0.860967 - 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8} - 6 q^{11} + 18 q^{12} + 3 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{17} + 9 q^{18} - 6 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} - 27 q^{24} + 6 q^{25} - 6 q^{26} + 27 q^{27} + 6 q^{28} - 9 q^{29} + 18 q^{30} + 3 q^{31} - 9 q^{34} + 6 q^{35} - 27 q^{36} - 6 q^{37} - 6 q^{38} - 18 q^{39} + 9 q^{40} + 9 q^{42} + 3 q^{43} + 30 q^{44} + 9 q^{45} - 3 q^{47} - 3 q^{49} + 6 q^{50} + 9 q^{51} + 21 q^{52} + 12 q^{53} - 27 q^{54} - 6 q^{56} - 9 q^{57} + 9 q^{58} + 3 q^{59} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} + 36 q^{66} + 12 q^{67} - 6 q^{68} - 9 q^{69} + 18 q^{71} - 36 q^{72} - 42 q^{73} + 30 q^{74} - 9 q^{75} - 15 q^{76} - 6 q^{77} + 54 q^{78} + 21 q^{79} - 30 q^{80} - 18 q^{82} + 18 q^{83} - 9 q^{84} - 9 q^{85} - 6 q^{86} + 9 q^{87} - 27 q^{88} + 24 q^{89} + 27 q^{90} - 6 q^{91} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 27 q^{96} + 3 q^{97} + 6 q^{98} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8 - 6 * q^11 + 18 * q^12 + 3 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^17 + 9 * q^18 - 6 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 - 27 * q^24 + 6 * q^25 - 6 * q^26 + 27 * q^27 + 6 * q^28 - 9 * q^29 + 18 * q^30 + 3 * q^31 - 9 * q^34 + 6 * q^35 - 27 * q^36 - 6 * q^37 - 6 * q^38 - 18 * q^39 + 9 * q^40 + 9 * q^42 + 3 * q^43 + 30 * q^44 + 9 * q^45 - 3 * q^47 - 3 * q^49 + 6 * q^50 + 9 * q^51 + 21 * q^52 + 12 * q^53 - 27 * q^54 - 6 * q^56 - 9 * q^57 + 9 * q^58 + 3 * q^59 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 + 36 * q^66 + 12 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 36 * q^72 - 42 * q^73 + 30 * q^74 - 9 * q^75 - 15 * q^76 - 6 * q^77 + 54 * q^78 + 21 * q^79 - 30 * q^80 - 18 * q^82 + 18 * q^83 - 9 * q^84 - 9 * q^85 - 6 * q^86 + 9 * q^87 - 27 * q^88 + 24 * q^89 + 27 * q^90 - 6 * q^91 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 27 * q^96 + 3 * q^97 + 6 * q^98 + 18 * q^99

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