LMFDB - Embedded newform 441.2.f.c.148.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, 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("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.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:	$3.52140272914$
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:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.3
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.c.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.439693 + 0.761570i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})$	\(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} +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} +(-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} +(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} +(-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} +(-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} +(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} +(-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} +(1.91147 - 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} +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} -0.554378 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} +(-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} +(-0.315207 + 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} +(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} +(-0.860967 + 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} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} - 18 q^{12} - 3 q^{13} - 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} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 9 q^{34} - 27 q^{36} - 6 q^{37} + 6 q^{38} - 18 q^{39} - 9 q^{40} + 3 q^{43} + 30 q^{44} - 9 q^{45} + 3 q^{47} + 6 q^{50} + 9 q^{51} - 21 q^{52} + 12 q^{53} + 27 q^{54} - 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} + 54 q^{78} + 21 q^{79} + 30 q^{80} + 18 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} - 9 q^{87} - 27 q^{88} - 24 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 - 18 * q^12 - 3 * q^13 - 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 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 9 * q^34 - 27 * q^36 - 6 * q^37 + 6 * q^38 - 18 * q^39 - 9 * q^40 + 3 * q^43 + 30 * q^44 - 9 * q^45 + 3 * q^47 + 6 * q^50 + 9 * q^51 - 21 * q^52 + 12 * q^53 + 27 * q^54 - 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 + 54 * q^78 + 21 * q^79 + 30 * q^80 + 18 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 - 9 * q^87 - 27 * q^88 - 24 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 27 * q^96 - 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.439693	+	0.761570i	0.310910	+	0.538511i	0.978560	−	0.205964i	$-0.0660330\pi$
$2$	0.439693	+	0.761570i	0.310910	+	0.538511i	−0.667650	+	0.744475i	$0.732700\pi$
$3$	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	$-0.735925\pi$
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	0.976423	+	0.215867i	$0.0692579\pi$
$6$	1.50000	−	0.264490i	0.612372	−	0.107978i
$7$		0			0
$7$		0			0
$8$	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	0.714137	−	0.700006i	$-0.246819\pi$
$11$	−0.826352	−	1.43128i	−0.249154	−	0.431548i	−0.963291	+	0.268458i	$0.913486\pi$
$12$	−1.36571	−	1.62760i	−0.394248	−	0.469846i
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	−0.999301	−	0.0373813i	$-0.988098\pi$
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	0.532024	+	0.846729i	$0.321432\pi$
$14$		0			0
$15$	−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	$-0.518071\pi$
$17$	−0.467911			−0.113485			−0.0567426	+	0.998389i	$0.518071\pi$
$18$	0.458111	−	2.59808i	0.107978	−	0.612372i
$19$	3.22668			0.740252			0.370126	−	0.928982i	$-0.379315\pi$
$19$	3.22668			0.740252			0.370126	+	0.928982i	$0.379315\pi$
$20$	−0.826352	−	1.43128i	−0.184778	−	0.320045i
$21$		0			0
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.153279	+	0.988183i	$0.548983\pi$
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.779152	+	0.626835i	$0.784350\pi$
$24$	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
$28$		0			0
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	−0.995239	−	0.0974595i	$-0.968928\pi$
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	0.413217	−	0.910632i	$-0.364405\pi$
$30$	0.701867	−	1.92836i	0.128143	−	0.352069i
$31$	4.61721	−	7.99724i	0.829276	−	1.43635i	−0.0693317	−	0.997594i	$-0.522087\pi$
$31$	4.61721	−	7.99724i	0.829276	−	1.43635i	0.898607	−	0.438754i	$-0.144580\pi$
$32$	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
$35$		0			0
$36$	−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	$-0.747502\pi$
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	0.967927	+	0.251231i	$0.0808353\pi$
$42$		0			0
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	0.983747	−	0.179558i	$-0.0574668\pi$
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	−0.647376	+	0.762171i	$0.724133\pi$
$44$	−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	0.974281	+	0.225335i	$0.0723475\pi$
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	−0.291995	+	0.956420i	$0.594319\pi$
$48$	0.0714517	−	0.0125989i	0.0103132	−	0.00181849i
$49$		0			0
$50$	−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
$56$		0			0
$57$	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	0.299162	+	0.954202i	$0.403293\pi$
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	−0.975945	+	0.218019i	$0.930041\pi$
$60$	−2.81908	+	0.497079i	−0.363941	+	0.0641727i
$61$	3.81908	+	6.61484i	0.488983	+	0.846943i	0.999920	−	0.0126752i	$-0.00403474\pi$
$61$	3.81908	+	6.61484i	0.488983	+	0.846943i	−0.510937	+	0.859618i	$0.670701\pi$
$62$	8.12061			1.03132
$63$		0			0
$64$	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	−0.883662	−	0.468125i	$-0.844930\pi$
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	0.847239	+	0.531211i	$0.178263\pi$
$68$	−0.286989	+	0.497079i	−0.0348025	+	0.0602797i
$69$	9.95723	+	11.8666i	1.19871	+	1.42857i
$70$		0			0
$71$	−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	$-0.538272\pi$
$73$	−2.04963			−0.239891			−0.119946	+	0.992780i	$0.538272\pi$
$74$	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			0
$78$	−1.75537	+	4.82283i	−0.198756	+	0.546078i
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	0.925682	−	0.378303i	$-0.123492\pi$
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	−0.790461	+	0.612512i	$0.790159\pi$
$80$	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	−0.901187	−	0.433431i	$-0.857303\pi$
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	0.0752309	−	0.997166i	$-0.476031\pi$
$84$		0			0
$85$	−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	$-0.659938\pi$
$89$	−9.08647			−0.963164			−0.481582	+	0.876401i	$0.659938\pi$
$90$	−2.72281	−	2.28471i	−0.287010	−	0.240830i
$91$		0			0
$92$	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	$-0.197402\pi$
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	−0.910195	+	0.414181i	$0.864068\pi$
$98$		0			0
$99$	−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	$-0.193766\pi$
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	−0.905405	+	0.424548i	$0.860433\pi$
$102$	−0.701867	+	0.123758i	−0.0694952	+	0.0122539i
$103$	−1.81908	+	3.15074i	−0.179239	+	0.310451i	−0.941620	−	0.336677i	$-0.890697\pi$
$103$	−1.81908	+	3.15074i	−0.179239	+	0.310451i	0.762381	+	0.647128i	$0.224030\pi$
$104$	−4.78059	+	8.28023i	−0.468776	+	0.811943i
$105$		0			0
$106$	−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			0
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	0.300320	+	0.953839i	$0.402907\pi$
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	−0.976208	+	0.216835i	$0.930427\pi$
$114$	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			0
$120$	−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
$126$		0			0
$127$	−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	$-0.934672\pi$
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	0.666000	+	0.745952i	$0.268005\pi$
$132$	−1.20099	+	3.29969i	−0.104533	+	0.287201i
$133$		0			0
$134$	−0.524348			−0.0452968
$135$			7.00076i			0.602529i
$136$	−1.32770			−0.113849
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	0.805925	−	0.592017i	$-0.201668\pi$
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	−0.915665	+	0.401943i	$0.868335\pi$
$138$	−4.65910	+	12.8008i	−0.396609	+	1.08967i
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	−0.966272	−	0.257523i	$-0.917094\pi$
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	0.706158	+	0.708055i	$0.250427\pi$
$140$		0			0
$141$	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
$147$		0			0
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	−0.874719	−	0.484630i	$-0.838954\pi$
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	0.857062	+	0.515214i	$0.172288\pi$
$150$	3.11809	+	3.71599i	0.254591	+	0.303410i
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	0.911902	−	0.410408i	$-0.134614\pi$
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	−0.811375	+	0.584526i	$0.801280\pi$
$152$	9.15570			0.742625
$153$	1.07532	+	0.902302i	0.0869346	+	0.0729468i
$154$		0			0
$155$	−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	$-0.700825\pi$
$157$	5.06670	−	8.77579i	0.404367	−	0.700384i	0.994248	+	0.107106i	$0.0341585\pi$
$158$	−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
$161$		0			0
$162$	−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	−0.0656422	+	0.997843i	$0.520910\pi$
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.831337	+	0.555769i	$0.812424\pi$
$168$		0			0
$169$	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	$-0.224484\pi$
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	−0.942100	+	0.335333i	$0.891151\pi$
$174$	−6.13728	−	7.31412i	−0.465266	−	0.554482i
$175$		0			0
$176$	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	$-0.278722\pi$
$181$	17.2344			1.28102			0.640512	+	0.767948i	$0.278722\pi$
$182$		0			0
$183$	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
$189$		0			0
$190$	3.82295			0.277346
$191$	−6.45471	−	11.1799i	−0.467046	−	0.808948i	0.532245	−	0.846590i	$-0.321349\pi$
$191$	−6.45471	−	11.1799i	−0.467046	−	0.808948i	−0.999291	+	0.0376425i	$0.988015\pi$
$192$	2.98680	−	8.20616i	0.215553	−	0.592228i
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	−0.854313	−	0.519759i	$-0.826022\pi$
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	0.877281	+	0.479977i	$0.159355\pi$
$194$	0.834970	−	1.44621i	0.0599473	−	0.103832i
$195$	7.74376	−	1.36543i	0.554542	−	0.0977807i
$196$		0			0
$197$	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	$-0.458839\pi$
$199$	3.63816			0.257902			0.128951	+	0.991651i	$0.458839\pi$
$200$	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
$203$		0			0
$204$	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
$210$		0			0
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	−0.948668	−	0.316273i	$-0.897569\pi$
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	0.748234	+	0.663435i	$0.230902\pi$
$212$	−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
$217$		0			0
$218$	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	$-0.0904428\pi$
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	−0.722722	+	0.691139i	$0.757109\pi$
$224$		0			0
$225$	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	$-0.296394\pi$
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	−0.993274	+	0.115789i	$0.963060\pi$
$228$	−4.40673	−	5.25173i	−0.291843	−	0.347804i
$229$	−8.77631	+	15.2010i	−0.579955	+	1.00451i	0.415529	+	0.909580i	$0.363597\pi$
$229$	−8.77631	+	15.2010i	−0.579955	+	1.00451i	−0.995484	+	0.0949315i	$0.969737\pi$
$230$	−5.29813	+	9.17664i	−0.349349	+	0.605089i
$231$		0			0
$232$	−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			0
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	−0.511565	−	0.859244i	$-0.670934\pi$
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	0.999910	+	0.0134062i	$0.00426745\pi$
$240$	0.0334331	−	0.0918566i	0.00215809	−	0.00592932i
$241$	−7.81908	−	13.5430i	−0.503671	−	0.872384i	−0.999991	−	0.00424420i	$-0.998649\pi$
$241$	−7.81908	−	13.5430i	−0.503671	−	0.872384i	0.496320	−	0.868140i	$-0.334684\pi$
$242$	7.27126			0.467414
$243$	15.3516	+	2.70691i	0.984808	+	0.173648i
$244$	9.36959			0.599826
$245$		0			0
$246$	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	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	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	−0.0697146	−	0.997567i	$-0.522209\pi$
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	0.898776	−	0.438409i	$-0.144458\pi$
$258$	4.31908	+	5.14728i	0.268894	+	0.320455i
$259$		0			0
$260$	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	0.877120	−	0.480270i	$-0.159461\pi$
$263$	0.367059	+	0.635765i	0.0226338	+	0.0392029i	−0.854487	+	0.519473i	$0.826128\pi$
$264$	−7.99912	+	1.41046i	−0.492312	+	0.0868079i
$265$	−0.386659	+	0.669713i	−0.0237523	+	0.0411402i
$266$		0			0
$267$	−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	$-0.280739\pi$
$269$	20.8503			1.27126			0.635632	+	0.771992i	$0.280739\pi$
$270$	−5.33157	+	3.07818i	−0.324469	+	0.187332i
$271$	−6.95811			−0.422675			−0.211338	−	0.977413i	$-0.567782\pi$
$271$	−6.95811			−0.422675			−0.211338	+	0.977413i	$0.567782\pi$
$272$	−0.00980018	−	0.0169744i	−0.000594223	−	0.00102922i
$273$		0			0
$274$	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	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$	−5.39363			−0.323488
$279$	−26.0326	+	9.47508i	−1.55853	+	0.567258i
$280$		0			0
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	−0.979159	−	0.203095i	$-0.934900\pi$
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	0.313694	−	0.949524i	$-0.398433\pi$
$282$	9.15910	+	10.9154i	0.545416	+	0.650002i
$283$	−9.29726	+	16.1033i	−0.552665	+	0.957243i	0.445417	+	0.895323i	$0.353056\pi$
$283$	−9.29726	+	16.1033i	−0.552665	+	0.957243i	−0.998081	+	0.0619196i	$0.980278\pi$
$284$	−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
$287$		0			0
$288$	−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	$-0.708428\pi$
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	0.991406	+	0.130822i	$0.0417618\pi$
$294$		0			0
$295$	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
$301$		0			0
$302$	−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	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$	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	$-0.920370\pi$
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	0.698833	+	0.715285i	$0.253703\pi$
$312$	10.6449	+	12.6860i	0.602646	+	0.718206i
$313$	−8.81433	−	15.2669i	−0.498215	−	0.862934i	0.501782	−	0.864994i	$-0.332678\pi$
$313$	−8.81433	−	15.2669i	−0.498215	−	0.862934i	−0.999998	+	0.00205946i	$0.999344\pi$
$314$	8.91117			0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	−4.03849	−	6.99486i	−0.226824	−	0.392871i	0.730041	−	0.683403i	$-0.239501\pi$
$317$	−4.03849	−	6.99486i	−0.226824	−	0.392871i	−0.956865	+	0.290533i	$0.906168\pi$
$318$	−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
$322$		0			0
$323$	−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
$329$		0			0
$330$	−3.34002	+	0.588936i	−0.183862	+	0.0324199i
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	−0.986839	−	0.161706i	$-0.948300\pi$
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	0.353378	−	0.935481i	$-0.385033\pi$
$332$	−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			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$	−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
$343$		0			0
$344$	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	−0.985804	−	0.167901i	$-0.946301\pi$
$347$	−6.47313	+	11.2118i	−0.347496	+	0.601880i	0.638308	+	0.769781i	$0.279635\pi$
$348$	−4.55525	+	12.5155i	−0.244187	+	0.670899i
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	0.884938	−	0.465710i	$-0.154201\pi$
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	−0.845785	+	0.533524i	$0.820868\pi$
$350$		0			0
$351$		−	17.5089i		−	0.934555i
$352$	−9.31820			−0.496662
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	0.991267	−	0.131873i	$-0.0420992\pi$
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	−0.609839	+	0.792525i	$0.708766\pi$
$354$	−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			0
$358$	−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
$364$		0			0
$365$	−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	$-0.268569\pi$
$367$	−6.02869	−	10.4420i	−0.314695	−	0.545067i	−0.979373	+	0.202063i	$0.935236\pi$
$368$	−0.374638			−0.0195293
$369$	−9.61721	+	3.50038i	−0.500652	+	0.182222i
$370$	10.9409			0.568789
$371$		0			0
$372$	−19.3221	+	3.40700i	−1.00180	+	0.176645i
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$	−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
$378$		0			0
$379$	−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	$-0.770034\pi$
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	0.947734	+	0.319061i	$0.103367\pi$
$384$	−11.6716	+	2.05802i	−0.595613	+	0.105023i
$385$		0			0
$386$	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	0.789431	−	0.613840i	$-0.210376\pi$
$389$	−2.69981	−	4.67620i	−0.136886	−	0.237093i	−0.926316	+	0.376747i	$0.877043\pi$
$390$	4.44475	+	5.29704i	0.225068	+	0.268226i
$391$	2.09240	−	3.62414i	0.105817	−	0.183280i
$392$		0			0
$393$	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	$-0.237831\pi$
$397$	29.2344			1.46723			0.733617	+	0.679563i	$0.237831\pi$
$398$	1.59967	+	2.77071i	0.0801842	+	0.138883i
$399$		0			0
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	−0.289629	−	0.957139i	$-0.593532\pi$
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	0.973721	−	0.227743i	$-0.0731346\pi$
$402$	−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
$406$		0			0
$407$	−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	$-0.904960\pi$
$409$	−4.51249	+	7.81586i	−0.223128	+	0.386469i	0.732628	+	0.680629i	$0.238294\pi$
$410$	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
$413$		0			0
$414$	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	$-0.831970\pi$
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	0.868158	+	0.496287i	$0.165304\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$	−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
$427$		0			0
$428$	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	$-0.656572\pi$
$433$	−19.6554			−0.944578			−0.472289	+	0.881444i	$0.656572\pi$
$434$		0			0
$435$	−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	−0.999631	−	0.0271516i	$-0.991356\pi$
$439$	−10.9650	−	18.9919i	−0.523330	−	0.906434i	0.476302	−	0.879282i	$-0.341977\pi$
$440$	−6.31820			−0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	9.35504	+	16.2034i	0.444471	+	0.769847i	0.998015	−	0.0629732i	$-0.0200583\pi$
$443$	9.35504	+	16.2034i	0.444471	+	0.769847i	−0.553544	+	0.832820i	$0.686725\pi$
$444$	−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
$448$		0			0
$449$	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
$455$		0			0
$456$	5.42380	−	14.9018i	0.253993	−	0.697839i
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	0.998655	−	0.0518563i	$-0.0165138\pi$
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	−0.544236	+	0.838932i	$0.683180\pi$
$458$	−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	$-0.173827\pi$
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	−0.877052	+	0.480395i	$0.840493\pi$
$462$		0			0
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	−0.860802	−	0.508941i	$-0.830037\pi$
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	0.871156	+	0.491006i	$0.163371\pi$
$464$	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	$-0.209229\pi$
$467$	34.2148			1.58327			0.791637	+	0.610992i	$0.209229\pi$
$468$	2.15328	−	12.2118i	0.0995352	−	0.564492i
$469$		0			0
$470$	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			0
$477$	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	$-0.332552\pi$
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	−0.999997	+	0.00245553i	$0.999218\pi$
$480$	−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
$483$		0			0
$484$	−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			0
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	0.403987	+	0.914765i	$0.367624\pi$
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	−0.994203	+	0.107519i	$0.965709\pi$
$492$	−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			0
$498$	−14.7344	−	17.5598i	−0.660265	−	0.786873i
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	−0.660403	−	0.750911i	$-0.729615\pi$
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	0.980510	+	0.196470i	$0.0629479\pi$
$500$	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	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−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	0.429257	+	0.903183i	$0.358776\pi$
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	−0.996807	+	0.0798442i	$0.974558\pi$
$510$	−0.328411	+	0.902302i	−0.0145423	+	0.0399546i
$511$		0			0
$512$	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
$518$		0			0
$519$	−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	$-0.346176\pi$
$521$	21.2121			0.929320			0.464660	+	0.885489i	$0.346176\pi$
$522$	−15.5401	+	5.65615i	−0.680173	+	0.247563i
$523$	−20.8057			−0.909770			−0.454885	−	0.890550i	$-0.650320\pi$
$523$	−20.8057			−0.909770			−0.454885	+	0.890550i	$0.650320\pi$
$524$	4.39470	+	7.61185i	0.191984	+	0.332525i
$525$		0			0
$526$	−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
$532$		0			0
$533$	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
$539$		0			0
$540$	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
$546$		0			0
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	−0.928446	−	0.371467i	$-0.878855\pi$
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	0.142523	−	0.989792i	$-0.454479\pi$
$548$	−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
$553$		0			0
$554$	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			0
$561$	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	$-0.955301\pi$
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	0.616291	+	0.787518i	$0.288634\pi$
$564$	6.79813	−	18.6777i	0.286253	−	0.786474i
$565$	9.68004	+	16.7663i	0.407243	+	0.705365i
$566$	−16.3517			−0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	13.3007	+	23.0374i	0.557593	+	0.965779i	0.997697	+	0.0678320i	$0.0216082\pi$
$569$	13.3007	+	23.0374i	0.557593	+	0.965779i	−0.440104	+	0.897947i	$0.645058\pi$
$570$	2.26470	−	6.22221i	0.0948579	−	0.260620i
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	−0.741986	−	0.670416i	$-0.766116\pi$
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	0.951590	+	0.307371i	$0.0994491\pi$
$572$	3.41565	−	5.91608i	0.142815	−	0.247364i
$573$	−22.0201	+	3.88273i	−0.919902	+	0.162203i
$574$		0			0
$575$	−28.4834			−1.18784
$576$	−11.5869	−	9.72259i	−0.482789	−	0.405108i
$577$	32.9145			1.37025			0.685124	−	0.728427i	$-0.259748\pi$
$577$	32.9145			1.37025			0.685124	+	0.728427i	$0.259748\pi$
$578$	−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
$581$		0			0
$582$	−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	$-0.267351\pi$
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	−0.978592	+	0.205808i	$0.934018\pi$
$588$		0			0
$589$	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	$-0.818535\pi$
$593$	−41.0009			−1.68371			−0.841853	+	0.539706i	$0.818535\pi$
$594$			7.55190i			0.309858i
$595$		0			0
$596$	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	−0.921374	−	0.388678i	$-0.872932\pi$
$599$	−3.03684	+	5.25996i	−0.124082	+	0.214916i	0.797292	+	0.603594i	$0.206265\pi$
$600$	15.4145	−	2.71799i	0.629293	−	0.110961i
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	0.685110	−	0.728440i	$-0.259754\pi$
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	−0.973402	+	0.229102i	$0.926421\pi$
$602$		0			0
$603$	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	0.161377	−	0.986893i	$-0.448406\pi$
$607$	23.0449	−	39.9149i	0.935363	−	1.62010i	0.773986	−	0.633203i	$-0.218260\pi$
$608$	9.09627	−	15.7552i	0.368902	−	0.638958i
$609$		0			0
$610$	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
$616$		0			0
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	−0.842492	−	0.538708i	$-0.818913\pi$
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	0.887781	+	0.460266i	$0.152246\pi$
$618$	−1.89528	+	5.20723i	−0.0762392	+	0.209466i
$619$	3.09539	+	5.36137i	0.124414	+	0.215492i	0.921504	−	0.388369i	$-0.126962\pi$
$619$	3.09539	+	5.36137i	0.124414	+	0.215492i	−0.797090	+	0.603861i	$0.793628\pi$
$620$	−15.2618			−0.612927
$621$		−	46.4721i		−	1.86486i
$622$	−8.37557			−0.335830
$623$		0			0
$624$	−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			0
$631$	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
$637$		0			0
$638$	−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	0.813705	−	0.581278i	$-0.197447\pi$
$641$	−2.44444	−	4.23389i	−0.0965496	−	0.167229i	−0.910254	+	0.414050i	$0.864114\pi$
$642$	10.6925	−	1.88538i	0.422001	−	0.0744101i
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	0.126242	+	0.992000i	$0.459709\pi$
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	−0.922218	+	0.386671i	$0.873625\pi$
$644$		0			0
$645$	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	$-0.485724\pi$
$647$	2.28075			0.0896657			0.0448329	+	0.998995i	$0.485724\pi$
$648$	4.43453	+	25.1495i	0.174205	+	0.987965i
$649$	17.1830			0.674493
$650$	−4.71853	−	8.17273i	−0.185076	−	0.320561i
$651$		0			0
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	−0.998930	−	0.0462542i	$-0.985272\pi$
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	0.539522	+	0.841971i	$0.318605\pi$
$654$	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
$658$		0			0
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.776101	+	0.630609i	$0.217195\pi$
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.158073	+	0.987427i	$0.449472\pi$
$660$	3.04101	+	3.62414i	0.118371	+	0.141069i
$661$	14.6545	−	25.3824i	0.569995	−	0.987260i	−0.426571	−	0.904454i	$-0.640279\pi$
$661$	14.6545	−	25.3824i	0.569995	−	0.987260i	0.996566	−	0.0828055i	$-0.0263880\pi$
$662$	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
$665$		0			0
$666$	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
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$	−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	0.971936	+	0.235246i	$0.0755895\pi$
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	−0.282239	+	0.959344i	$0.591077\pi$
$678$	−7.48576	+	20.5669i	−0.287489	+	0.789869i
$679$		0			0
$680$	−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			0
$687$	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	$-0.154150\pi$
$691$	1.03343	+	1.78996i	0.0393136	+	0.0680932i	−0.845699	+	0.533660i	$0.820816\pi$
$692$	−5.82915			−0.221591
$693$		0			0
$694$	−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
$700$		0			0
$701$	−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			0
$708$	21.7545	−	3.83590i	0.817584	−	0.144162i
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	0.767742	−	0.640760i	$-0.221380\pi$
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	−0.938785	+	0.344504i	$0.888047\pi$
$710$	−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			0
$715$	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	$-0.339200\pi$
$719$	25.9537			0.967908			0.483954	+	0.875093i	$0.339200\pi$
$720$	−0.129700	−	0.108831i	−0.00483362	−	0.00405589i
$721$		0			0
$722$	−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	$-0.227000\pi$
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	−0.944720	+	0.327878i	$0.893667\pi$
$728$		0			0
$729$	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	−0.196441	−	0.980516i	$-0.562938\pi$
$733$	20.3307	−	35.2138i	0.750931	−	1.30065i	0.947372	−	0.320135i	$-0.103728\pi$
$734$	5.30154	−	9.18253i	0.195683	−	0.338933i
$735$		0			0
$736$	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			0
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	−0.583377	−	0.812202i	$-0.698269\pi$
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	0.995076	+	0.0991184i	$0.0316023\pi$
$744$	−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
$749$		0			0
$750$	16.5410	−	2.91663i	0.603992	−	0.106500i
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	−0.997827	−	0.0658924i	$-0.979011\pi$
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	0.555978	+	0.831197i	$0.312344\pi$
$752$	−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
$756$		0			0
$757$	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	$-0.940781\pi$
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	0.651561	+	0.758596i	$0.274114\pi$
$762$	−31.1573	+	5.49388i	−1.12871	+	0.199022i
$763$		0			0
$764$	−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	$-0.724903\pi$
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	0.983310	+	0.181936i	$0.0582365\pi$
$770$		0			0
$771$	−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	$-0.483043\pi$
$773$	2.96080			0.106493			0.0532463	+	0.998581i	$0.483043\pi$
$774$	10.9363	−	3.98048i	0.393097	−	0.143076i
$775$	29.4097			1.05643
$776$	−2.69418	−	4.66646i	−0.0967155	−	0.167516i
$777$		0			0
$778$	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			0
$785$	−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	0.398175	+	0.917310i	$0.369644\pi$
$787$	−16.7010	+	28.9270i	−0.595326	+	1.03113i	−0.993501	+	0.113825i	$0.963690\pi$
$788$	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
$791$		0			0
$792$	−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	0.0162779	−	0.999868i	$-0.494818\pi$
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.857772	−	0.514031i	$-0.171848\pi$
$798$		0			0
$799$	−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
$805$		0			0
$806$	−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	$-0.362436\pi$
$811$	23.8557			0.837686			0.418843	+	0.908059i	$0.362436\pi$
$812$		0			0
$813$	−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
$819$		0			0
$820$	−5.63816			−0.196893
$821$	25.4714	+	44.1177i	0.888957	+	1.53972i	0.841110	+	0.540864i	$0.181903\pi$
$821$	25.4714	+	44.1177i	0.888957	+	1.53972i	0.0478469	+	0.998855i	$0.484764\pi$
$822$	−2.51512	−	2.99740i	−0.0877249	−	0.104546i
$823$	−6.80747	+	11.7909i	−0.237293	+	0.411004i	−0.959937	−	0.280217i	$-0.909594\pi$
$823$	−6.80747	+	11.7909i	−0.237293	+	0.411004i	0.722643	+	0.691221i	$0.242927\pi$
$824$	−5.16163	+	8.94020i	−0.179814	+	0.311447i
$825$	−5.86009	−	6.98378i	−0.204022	−	0.243144i
$826$		0			0
$827$	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	$-0.644952\pi$
$829$	−25.3259			−0.879606			−0.439803	+	0.898094i	$0.644952\pi$
$830$	−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			0
$834$	−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	$-0.118603\pi$
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	−0.780960	+	0.624582i	$0.785270\pi$
$840$		0			0
$841$	−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
$847$		0			0
$848$	−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	$-0.232424\pi$
$853$	−5.99067	−	10.3761i	−0.205117	−	0.355272i	−0.950170	+	0.311733i	$0.899091\pi$
$854$		0			0
$855$	−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	$-0.131254\pi$
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	−0.805160	+	0.593058i	$0.797921\pi$
$858$	8.35339	−	1.47293i	0.285180	−	0.0502849i
$859$	−26.7763	+	46.3779i	−0.913596	+	1.58239i	−0.104652	+	0.994509i	$0.533373\pi$
$859$	−26.7763	+	46.3779i	−0.913596	+	1.58239i	−0.808944	+	0.587886i	$0.799960\pi$
$860$	3.64543	−	6.31407i	0.124308	−	0.215308i
$861$		0			0
$862$	−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
$868$		0			0
$869$	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
$875$		0			0
$876$	2.79921	+	3.33597i	0.0945765	+	0.112712i
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	−0.749178	−	0.662369i	$-0.769551\pi$
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	0.948217	+	0.317622i	$0.102884\pi$
$878$	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	$-0.813729\pi$
$881$	−49.4858			−1.66722			−0.833609	+	0.552355i	$0.813729\pi$
$882$		0			0
$883$	−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	$-0.769393\pi$
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	0.948375	+	0.317152i	$0.102727\pi$
$888$	15.5223	−	42.6473i	0.520896	−	1.43115i
$889$		0			0
$890$	−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
$896$		0			0
$897$	−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
$903$		0			0
$904$	−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	0.997047	−	0.0767980i	$-0.0244697\pi$
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	−0.565032	+	0.825069i	$0.691136\pi$
$908$	−14.6509			−0.486209
$909$	−0.890367	+	5.04952i	−0.0295316	+	0.167482i
$910$		0			0
$911$	2.01636	+	3.49244i	0.0668050	+	0.115710i	0.897493	−	0.441028i	$-0.145386\pi$
$911$	2.01636	+	3.49244i	0.0668050	+	0.115710i	−0.830688	+	0.556738i	$0.812053\pi$
$912$	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
$917$		0			0
$918$	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
$924$		0			0
$925$	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	$-0.126474\pi$
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	−0.796164	+	0.605081i	$0.793141\pi$
$930$	−12.1809	−	14.5167i	−0.399428	−	0.476020i
$931$		0			0
$932$	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	$-0.489471\pi$
$937$	2.02465			0.0661425			0.0330713	+	0.999453i	$0.489471\pi$
$938$		0			0
$939$	−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	$-0.865239\pi$
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	0.811645	+	0.584151i	$0.198573\pi$
$942$	5.27894	−	14.5038i	0.171997	−	0.472559i
$943$	15.2554	+	26.4231i	0.496783	+	0.860454i
$944$	−0.435518			−0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	−2.78224	−	4.81898i	−0.0904107	−	0.156596i	0.817273	−	0.576250i	$-0.195485\pi$
$947$	−2.78224	−	4.81898i	−0.0904107	−	0.156596i	−0.907684	+	0.419654i	$0.862151\pi$
$948$	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			0
$953$	−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
$959$		0			0
$960$	−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
$966$		0			0
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.143670	−	0.989626i	$-0.454110\pi$
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.785206	−	0.619235i	$-0.212557\pi$
$968$	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	$-0.335932\pi$
$971$	30.7192			0.985828			0.492914	+	0.870078i	$0.335932\pi$
$972$	12.2914	−	14.6484i	0.394248	−	0.469846i
$973$		0			0
$974$	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	−0.936571	−	0.350477i	$-0.886019\pi$
$977$	−5.15002	+	8.92009i	−0.164764	+	0.285379i	0.771808	+	0.635856i	$0.219353\pi$
$978$	−3.89440	+	0.686688i	−0.124529	+	0.0219579i
$979$	7.50862	+	13.0053i	0.239976	+	0.415651i
$980$		0			0
$981$	−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	$-0.0965755\pi$
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	−0.735903	+	0.677087i	$0.763242\pi$
$984$	−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
$987$		0			0
$988$	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			0
$995$	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	$-0.0839962\pi$
$997$	8.10876	+	14.0448i	0.256807	+	0.444803i	−0.708578	+	0.705633i	$0.750663\pi$
$998$	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	441.2.f.c.148.3		6
3.2	odd	2		1323.2.f.d.442.1		6
7.2	even	3		441.2.g.b.67.3		6
7.3	odd	6		441.2.h.d.373.1		6
7.4	even	3		441.2.h.e.373.1		6
7.5	odd	6		441.2.g.c.67.3		6
7.6	odd	2		63.2.f.a.22.3	✓	6
9.2	odd	6		1323.2.f.d.883.1		6
9.4	even	3		3969.2.a.q.1.1		3
9.5	odd	6		3969.2.a.l.1.3		3
9.7	even	3	inner	441.2.f.c.295.3		6
21.2	odd	6		1323.2.g.e.361.1		6
21.5	even	6		1323.2.g.d.361.1		6
21.11	odd	6		1323.2.h.b.226.3		6
21.17	even	6		1323.2.h.c.226.3		6
21.20	even	2		189.2.f.b.64.1		6
28.27	even	2		1008.2.r.h.337.2		6
63.2	odd	6		1323.2.h.b.802.3		6
63.11	odd	6		1323.2.g.e.667.1		6
63.13	odd	6		567.2.a.h.1.1		3
63.16	even	3		441.2.h.e.214.1		6
63.20	even	6		189.2.f.b.127.1		6
63.25	even	3		441.2.g.b.79.3		6
63.34	odd	6		63.2.f.a.43.3	yes	6
63.38	even	6		1323.2.g.d.667.1		6
63.41	even	6		567.2.a.c.1.3		3
63.47	even	6		1323.2.h.c.802.3		6
63.52	odd	6		441.2.g.c.79.3		6
63.61	odd	6		441.2.h.d.214.1		6
84.83	odd	2		3024.2.r.k.1009.2		6
252.83	odd	6		3024.2.r.k.2017.2		6
252.139	even	6		9072.2.a.ca.1.2		3
252.167	odd	6		9072.2.a.bs.1.2		3
252.223	even	6		1008.2.r.h.673.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	7.6	odd	2
63.2.f.a.43.3	yes	6	63.34	odd	6
189.2.f.b.64.1		6	21.20	even	2
189.2.f.b.127.1		6	63.20	even	6
441.2.f.c.148.3		6	1.1	even	1	trivial
441.2.f.c.295.3		6	9.7	even	3	inner
441.2.g.b.67.3		6	7.2	even	3
441.2.g.b.79.3		6	63.25	even	3
441.2.g.c.67.3		6	7.5	odd	6
441.2.g.c.79.3		6	63.52	odd	6
441.2.h.d.214.1		6	63.61	odd	6
441.2.h.d.373.1		6	7.3	odd	6
441.2.h.e.214.1		6	63.16	even	3
441.2.h.e.373.1		6	7.4	even	3
567.2.a.c.1.3		3	63.41	even	6
567.2.a.h.1.1		3	63.13	odd	6
1008.2.r.h.337.2		6	28.27	even	2
1008.2.r.h.673.2		6	252.223	even	6
1323.2.f.d.442.1		6	3.2	odd	2
1323.2.f.d.883.1		6	9.2	odd	6
1323.2.g.d.361.1		6	21.5	even	6
1323.2.g.d.667.1		6	63.38	even	6
1323.2.g.e.361.1		6	21.2	odd	6
1323.2.g.e.667.1		6	63.11	odd	6
1323.2.h.b.226.3		6	21.11	odd	6
1323.2.h.b.802.3		6	63.2	odd	6
1323.2.h.c.226.3		6	21.17	even	6
1323.2.h.c.802.3		6	63.47	even	6
3024.2.r.k.1009.2		6	84.83	odd	2
3024.2.r.k.2017.2		6	252.83	odd	6
3969.2.a.l.1.3		3	9.5	odd	6
3969.2.a.q.1.1		3	9.4	even	3
9072.2.a.bs.1.2		3	252.167	odd	6
9072.2.a.ca.1.2		3	252.139	even	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 + 0.761570i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\)	\(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} +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} +(-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} +(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} +(-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} +(-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} +(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} +(-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} +(1.91147 - 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} +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} -0.554378 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} +(-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} +(-0.315207 + 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} +(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} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} - 18 q^{12} - 3 q^{13} - 9 q^{15} - 3 q^{16} - 12 q^{17} + 9 q^{18} + 6 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} + 27 q^{24} + 6 q^{25} + 6 q^{26} - 27 q^{27} - 9 q^{29} + 18 q^{30} - 3 q^{31} + 9 q^{34} - 27 q^{36} - 6 q^{37} + 6 q^{38} - 18 q^{39} - 9 q^{40} + 3 q^{43} + 30 q^{44} - 9 q^{45} + 3 q^{47} + 6 q^{50} + 9 q^{51} - 21 q^{52} + 12 q^{53} + 27 q^{54} - 9 q^{57} + 9 q^{58} - 3 q^{59} + 6 q^{61} + 60 q^{62} + 24 q^{64} - 15 q^{65} - 36 q^{66} + 12 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 36 q^{72} + 42 q^{73} + 30 q^{74} + 9 q^{75} + 15 q^{76} + 54 q^{78} + 21 q^{79} + 30 q^{80} + 18 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} - 9 q^{87} - 27 q^{88} - 24 q^{89} - 27 q^{90} - 3 q^{92} - 27 q^{93} - 18 q^{94} + 12 q^{95} - 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 - 18 * q^12 - 3 * q^13 - 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 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 9 * q^34 - 27 * q^36 - 6 * q^37 + 6 * q^38 - 18 * q^39 - 9 * q^40 + 3 * q^43 + 30 * q^44 - 9 * q^45 + 3 * q^47 + 6 * q^50 + 9 * q^51 - 21 * q^52 + 12 * q^53 + 27 * q^54 - 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 + 54 * q^78 + 21 * q^79 + 30 * q^80 + 18 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 - 9 * q^87 - 27 * q^88 - 24 * q^89 - 27 * q^90 - 3 * q^92 - 27 * q^93 - 18 * q^94 + 12 * q^95 - 27 * q^96 - 3 * q^97 + 18 * q^99

Introduction

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