LMFDB - Embedded newform 441.2.g.c.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not 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			67.3
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.c.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.439693 - 0.761570i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} +1.34730 q^{5} +(-1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(0.439693 - 0.761570i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} +1.34730 q^{5} +(-1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +(0.592396 - 1.02606i) q^{10} +1.65270 q^{11} +(0.726682 - 1.99654i) q^{12} +(1.68479 - 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(-0.233956 + 0.405223i) q^{17} +(2.02094 + 1.69577i) q^{18} +(1.61334 + 2.79439i) q^{19} +(0.826352 + 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +8.94356 q^{23} +(-3.15910 - 3.76487i) q^{24} -3.18479 q^{25} +(-1.48158 - 2.56617i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(-2.02094 + 0.356347i) q^{30} +(-4.61721 - 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(-1.84002 - 2.19285i) q^{33} +(0.205737 + 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} +2.83750 q^{38} +(-5.74763 + 1.01346i) q^{39} +3.82295 q^{40} +(-1.70574 + 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(-0.701867 + 3.98048i) q^{45} +(3.93242 - 6.81115i) q^{46} +(-4.67752 + 8.10170i) q^{47} +(-0.0714517 + 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(0.798133 - 0.140732i) q^{51} +4.13341 q^{52} +(0.286989 - 0.497079i) q^{53} -4.56942i q^{54} +2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} -5.51249 q^{58} +(5.19846 + 9.00400i) q^{59} +(0.979055 - 2.68993i) q^{60} +(-3.81908 + 6.61484i) q^{61} -8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(-2.47906 + 0.437124i) q^{66} +(-0.298133 - 0.516382i) q^{67} -0.573978 q^{68} +(-9.95723 - 11.8666i) q^{69} -0.554378 q^{71} +(-1.47818 + 8.38316i) q^{72} +(-1.02481 + 1.77503i) q^{73} -8.12061 q^{74} +(3.54576 + 4.22567i) q^{75} +(-1.97906 + 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +(0.0282185 - 0.0488759i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(1.50000 + 2.59808i) q^{82} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +3.87939 q^{86} +(-3.71348 + 10.2027i) q^{87} +4.68954 q^{88} +(-4.54323 - 7.86911i) q^{89} +(2.72281 + 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-5.47044 + 15.0299i) q^{93} +(4.11334 + 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(3.34002 - 9.17664i) 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} + 6 q^{5} - 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8} + 12 q^{11} - 9 q^{12} + 3 q^{13} - 9 q^{15} - 3 q^{16} - 6 q^{17} + 9 q^{18} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 24 q^{23} + 18 q^{24} - 12 q^{25} + 3 q^{26} + 27 q^{27} - 9 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{33} - 9 q^{34} - 27 q^{36} + 3 q^{37} + 12 q^{38} - 18 q^{39} - 18 q^{40} + 3 q^{43} - 15 q^{44} - 18 q^{45} - 3 q^{47} + 6 q^{50} - 9 q^{51} - 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} + 3 q^{59} + 9 q^{60} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} - 18 q^{66} + 12 q^{67} + 12 q^{68} - 9 q^{69} + 18 q^{71} + 45 q^{72} + 21 q^{73} - 60 q^{74} - 9 q^{75} - 15 q^{76} + 54 q^{78} + 21 q^{79} + 15 q^{80} + 9 q^{82} + 18 q^{83} - 9 q^{85} + 12 q^{86} + 36 q^{87} + 54 q^{88} - 12 q^{89} + 27 q^{90} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8 + 12 * q^11 - 9 * q^12 + 3 * q^13 - 9 * q^15 - 3 * q^16 - 6 * q^17 + 9 * q^18 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 24 * q^23 + 18 * q^24 - 12 * q^25 + 3 * q^26 + 27 * q^27 - 9 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^33 - 9 * q^34 - 27 * q^36 + 3 * q^37 + 12 * q^38 - 18 * q^39 - 18 * q^40 + 3 * q^43 - 15 * q^44 - 18 * q^45 - 3 * q^47 + 6 * q^50 - 9 * q^51 - 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 + 3 * q^59 + 9 * q^60 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 - 18 * q^66 + 12 * q^67 + 12 * q^68 - 9 * q^69 + 18 * q^71 + 45 * q^72 + 21 * q^73 - 60 * q^74 - 9 * q^75 - 15 * q^76 + 54 * q^78 + 21 * q^79 + 15 * q^80 + 9 * q^82 + 18 * q^83 - 9 * q^85 + 12 * q^86 + 36 * q^87 + 54 * q^88 - 12 * q^89 + 27 * q^90 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.439693	−	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	$0.0660330\pi$
$3$	−1.11334	−	1.32683i	−0.642788	−	0.766044i
$3$	−1.11334	−	1.32683i	−0.642788	−	0.766044i
$4$	0.613341	+	1.06234i	0.306670	+	0.531169i
$5$	1.34730			0.602529			0.301265	−	0.953541i	$-0.402591\pi$
$5$	1.34730			0.602529			0.301265	+	0.953541i	$0.402591\pi$
$6$	−1.50000	+	0.264490i	−0.612372	+	0.107978i
$7$		0			0
$7$		0			0
$8$	2.83750			1.00321
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$	0.592396	−	1.02606i	0.187332	−	0.324469i
$11$	1.65270			0.498309			0.249154	−	0.968464i	$-0.419847\pi$
$11$	1.65270			0.498309			0.249154	+	0.968464i	$0.419847\pi$
$12$	0.726682	−	1.99654i	0.209775	−	0.576352i
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	−0.532024	−	0.846729i	$-0.678568\pi$
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	0.999301	+	0.0373813i	$0.0119016\pi$
$14$		0			0
$15$	−1.50000	−	1.78763i	−0.387298	−	0.461564i
$16$	0.0209445	−	0.0362770i	0.00523613	−	0.00906925i
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	−0.893001	−	0.450054i	$-0.851405\pi$
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	0.836259	+	0.548335i	$0.184738\pi$
$18$	2.02094	+	1.69577i	0.476341	+	0.399698i
$19$	1.61334	+	2.79439i	0.370126	+	0.641077i	0.989585	−	0.143953i	$-0.0459813\pi$
$19$	1.61334	+	2.79439i	0.370126	+	0.641077i	−0.619459	+	0.785029i	$0.712648\pi$
$20$	0.826352	+	1.43128i	0.184778	+	0.320045i
$21$		0			0
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	8.94356			1.86486			0.932431	−	0.361348i	$-0.117683\pi$
$23$	8.94356			1.86486			0.932431	+	0.361348i	$0.117683\pi$
$24$	−3.15910	−	3.76487i	−0.644849	−	0.768501i
$25$	−3.18479			−0.636959
$26$	−1.48158	−	2.56617i	−0.290562	−	0.503268i
$27$	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	$-0.364405\pi$
$30$	−2.02094	+	0.356347i	−0.368972	+	0.0650598i
$31$	−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
$33$	−1.84002	−	2.19285i	−0.320307	−	0.381727i
$34$	0.205737	+	0.356347i	0.0352836	+	0.0611130i
$35$		0			0
$36$	−3.45811	+	1.25865i	−0.576352	+	0.209775i
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	−0.943328	−	0.331862i	$-0.892323\pi$
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	0.184263	−	0.982877i	$-0.441010\pi$
$38$	2.83750			0.460303
$39$	−5.74763	+	1.01346i	−0.920357	+	0.162284i
$40$	3.82295			0.604461
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	−0.967927	−	0.251231i	$-0.919165\pi$
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	0.701536	+	0.712634i	$0.252498\pi$
$42$		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	$0.724133\pi$
$44$	1.01367	+	1.75573i	0.152817	+	0.264686i
$45$	−0.701867	+	3.98048i	−0.104628	+	0.593375i
$46$	3.93242	−	6.81115i	0.579803	−	1.00425i
$47$	−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			0
$50$	−1.40033	+	2.42544i	−0.198037	+	0.343009i
$51$	0.798133	−	0.140732i	0.111761	−	0.0197065i
$52$	4.13341			0.573201
$53$	0.286989	−	0.497079i	0.0394210	−	0.0682791i	−0.845642	−	0.533751i	$-0.820782\pi$
$53$	0.286989	−	0.497079i	0.0394210	−	0.0682791i	0.885063	+	0.465472i	$0.154115\pi$
$54$		−	4.56942i		−	0.621819i
$55$	2.22668			0.300246
$56$		0			0
$57$	1.91147	−	5.25173i	0.253181	−	0.695609i
$58$	−5.51249			−0.723825
$59$	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	$0.596707\pi$
$60$	0.979055	−	2.68993i	0.126396	−	0.347269i
$61$	−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			0
$64$	5.04189			0.630236
$65$	2.26991	−	3.93161i	0.281548	−	0.487656i
$66$	−2.47906	+	0.437124i	−0.305151	+	0.0538063i
$67$	−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	$0.844930\pi$
$68$	−0.573978			−0.0696051
$69$	−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	$0.510473\pi$
$72$	−1.47818	+	8.38316i	−0.174205	+	0.987965i
$73$	−1.02481	+	1.77503i	−0.119946	+	0.207752i	−0.919746	−	0.392514i	$-0.871605\pi$
$73$	−1.02481	+	1.77503i	−0.119946	+	0.207752i	0.799800	+	0.600266i	$0.204939\pi$
$74$	−8.12061			−0.944002
$75$	3.54576	+	4.22567i	0.409429	+	0.487939i
$76$	−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	−0.790461	−	0.612512i	$-0.790159\pi$
$79$	1.20187	−	2.08169i	0.135221	−	0.234209i	0.925682	+	0.378303i	$0.123492\pi$
$80$	0.0282185	−	0.0488759i	0.00315492	−	0.00546449i
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	0.901187	+	0.433431i	$0.142697\pi$
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	−0.0752309	+	0.997166i	$0.523969\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$	3.87939			0.418325
$87$	−3.71348	+	10.2027i	−0.398127	+	1.09384i
$88$	4.68954			0.499907
$89$	−4.54323	−	7.86911i	−0.481582	−	0.834124i	0.518195	−	0.855263i	$-0.326604\pi$
$89$	−4.54323	−	7.86911i	−0.481582	−	0.834124i	−0.999777	+	0.0211385i	$0.993271\pi$
$90$	2.72281	+	2.28471i	0.287010	+	0.240830i
$91$		0			0
$92$	5.48545	+	9.50108i	0.571898	+	0.990556i
$93$	−5.47044	+	15.0299i	−0.567258	+	1.55853i
$94$	4.11334	+	7.12452i	0.424259	+	0.734838i
$95$	2.17365	+	3.76487i	0.223012	+	0.386267i
$96$	3.34002	−	9.17664i	0.340890	−	0.936587i
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	0.910195	−	0.414181i	$-0.135932\pi$
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	−0.813788	+	0.581161i	$0.802598\pi$
$98$		0			0
$99$	−0.860967	+	4.88279i	−0.0865304	+	0.490738i
$100$	−1.95336	−	3.38332i	−0.195336	−	0.338332i
$101$	−1.70914			−0.170066			−0.0850329	−	0.996378i	$-0.527100\pi$
$101$	−1.70914			−0.170066			−0.0850329	+	0.996378i	$0.527100\pi$
$102$	0.243756	−	0.669713i	0.0241354	−	0.0663115i
$103$	−3.63816			−0.358478			−0.179239	−	0.983806i	$-0.557364\pi$
$103$	−3.63816			−0.358478			−0.179239	+	0.983806i	$0.557364\pi$
$104$	4.78059	−	8.28023i	0.468776	−	0.811943i
$105$		0			0
$106$	−0.252374	−	0.437124i	−0.0245127	−	0.0424573i
$107$	−3.56418	−	6.17334i	−0.344562	−	0.596799i	0.640712	−	0.767781i	$-0.278639\pi$
$107$	−3.56418	−	6.17334i	−0.344562	−	0.596799i	−0.985274	+	0.170982i	$0.945306\pi$
$108$	5.52007	+	3.18701i	0.531169	+	0.306670i
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	−0.875531	−	0.483162i	$-0.839488\pi$
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	0.856196	+	0.516651i	$0.172822\pi$
$110$	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	$0.930427\pi$
$114$	−3.15910	−	3.76487i	−0.295877	−	0.352612i
$115$	12.0496			1.12363
$116$	3.84477	−	6.65934i	0.356978	−	0.618304i
$117$	7.74376	+	6.49778i	0.715910	+	0.600720i
$118$	9.14290			0.841672
$119$		0			0
$120$	−4.25624	−	5.07239i	−0.388540	−	0.463044i
$121$	−8.26857			−0.751688
$122$	3.35844	+	5.81699i	0.304059	+	0.526646i
$123$	5.81908	−	1.02606i	0.524689	−	0.0925168i
$124$	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
$129$	2.61334	−	7.18009i	0.230092	−	0.632172i
$130$	−1.99613	−	3.45740i	−0.175072	−	0.303234i
$131$	−7.16519			−0.626026			−0.313013	−	0.949749i	$-0.601338\pi$
$131$	−7.16519			−0.626026			−0.313013	+	0.949749i	$0.601338\pi$
$132$	1.20099	−	3.29969i	0.104533	−	0.287201i
$133$		0			0
$134$	−0.524348			−0.0452968
$135$	6.06283	−	3.50038i	0.521806	−	0.301265i
$136$	−0.663848	+	1.14982i	−0.0569245	+	0.0985961i
$137$	2.56893			0.219478			0.109739	−	0.993960i	$-0.464998\pi$
$137$	2.56893			0.219478			0.109739	+	0.993960i	$0.464998\pi$
$138$	−13.4153	+	2.36549i	−1.14199	+	0.201364i
$139$	3.06670	−	5.31169i	0.260114	−	0.450531i	−0.706158	−	0.708055i	$-0.749573\pi$
$139$	3.06670	−	5.31169i	0.260114	−	0.450531i	0.966272	+	0.257523i	$0.0829064\pi$
$140$		0			0
$141$	15.9572	−	2.81369i	1.34384	−	0.236956i
$142$	−0.243756	+	0.422197i	−0.0204555	+	0.0354300i
$143$	2.78446	−	4.82283i	0.232848	−	0.403305i
$144$	0.0962667	+	0.0807773i	0.00802222	+	0.00673144i
$145$	−4.22281	−	7.31412i	−0.350685	−	0.607405i
$146$	0.901207	+	1.56094i	0.0745844	+	0.129184i
$147$		0			0
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	0.431074			0.0353150			0.0176575	−	0.999844i	$-0.494379\pi$
$149$	0.431074			0.0353150			0.0176575	+	0.999844i	$0.494379\pi$
$150$	4.77719	−	0.842347i	0.390056	−	0.0687774i
$151$	−2.47060			−0.201055			−0.100527	−	0.994934i	$-0.532053\pi$
$151$	−2.47060			−0.201055			−0.100527	+	0.994934i	$0.532053\pi$
$152$	4.57785	+	7.92907i	0.371313	+	0.643132i
$153$	−1.07532	−	0.902302i	−0.0869346	−	0.0729468i
$154$		0			0
$155$	−6.22075	−	10.7747i	−0.499663	−	0.865441i
$156$	−4.60189	−	5.48432i	−0.368446	−	0.439097i
$157$	−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
$159$	−0.979055	+	0.172634i	−0.0776441	+	0.0136908i
$160$	3.79813	+	6.57856i	0.300269	+	0.520081i
$161$		0			0
$162$	−6.06283	+	5.08732i	−0.476341	+	0.399698i
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	0.912376	−	0.409353i	$-0.134246\pi$
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	−0.810698	+	0.585464i	$0.800912\pi$
$164$	−4.18479			−0.326777
$165$	−2.47906	−	2.95442i	−0.192994	−	0.230002i
$166$	13.2344			1.02719
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.0656422	−	0.997843i	$-0.479090\pi$
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.831337	−	0.555769i	$-0.187576\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$	0.277189	+	0.480105i	0.0212594	+	0.0368224i
$171$	−9.09627	+	3.31077i	−0.695609	+	0.253181i
$172$	−2.70574	+	4.68647i	−0.206311	+	0.357340i
$173$	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
$175$		0			0
$176$	0.0346151	−	0.0599551i	0.00260921	−	0.00451929i
$177$	6.15910	−	16.9220i	0.462946	−	1.27193i
$178$	−7.99050			−0.598914
$179$	4.26604	−	7.38901i	0.318859	−	0.552280i	−0.661391	−	0.750041i	$-0.730034\pi$
$179$	4.26604	−	7.38901i	0.318859	−	0.552280i	0.980250	+	0.197761i	$0.0633670\pi$
$180$	−4.65910	+	1.69577i	−0.347269	+	0.126396i
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$		0			0
$183$	13.0287	−	2.29731i	0.963108	−	0.169822i
$184$	25.3773			1.87084
$185$	−6.22075	−	10.7747i	−0.457359	−	0.792169i
$186$	9.04101	+	10.7747i	0.662919	+	0.790036i
$187$	−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	−0.999291	−	0.0376425i	$-0.988015\pi$
$191$	−6.45471	+	11.1799i	−0.467046	+	0.808948i	0.532245	+	0.846590i	$0.321349\pi$
$192$	−5.61334	−	6.68972i	−0.405108	−	0.482789i
$193$	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	$0.826022\pi$
$194$	1.66994			0.119895
$195$	−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	$0.366319\pi$
$198$	3.34002	+	2.80261i	0.237365	+	0.199173i
$199$	1.81908	−	3.15074i	0.128951	−	0.223350i	−0.794319	−	0.607500i	$-0.792172\pi$
$199$	1.81908	−	3.15074i	0.128951	−	0.223350i	0.923270	+	0.384151i	$0.125506\pi$
$200$	−9.03684			−0.639001
$201$	−0.353226	+	0.970481i	−0.0249147	+	0.0684524i
$202$	−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
$206$	−1.59967	+	2.77071i	−0.111454	+	0.193045i
$207$	−4.65910	+	26.4231i	−0.323830	+	1.83653i
$208$	−0.0705744	−	0.122238i	−0.00489345	−	0.00847571i
$209$	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	$0.230902\pi$
$212$	0.704088			0.0483570
$213$	0.617211	+	0.735564i	0.0422906	+	0.0504000i
$214$	−6.26857			−0.428511
$215$	2.97178	+	5.14728i	0.202674	+	0.351041i
$216$	12.7687	−	7.37203i	0.868802	−	0.501603i
$217$		0			0
$218$	0.177519	+	0.307471i	0.0120231	+	0.0208246i
$219$	3.49613	−	0.616462i	0.236247	−	0.0416566i
$220$	1.36571	+	2.36549i	0.0920765	+	0.159481i
$221$	0.788333	+	1.36543i	0.0530290	+	0.0918490i
$222$	9.04101	+	10.7747i	0.606793	+	0.723148i
$223$	−3.54189	−	6.13473i	−0.237182	−	0.410812i	0.722722	−	0.691139i	$-0.242891\pi$
$223$	−3.54189	−	6.13473i	−0.237182	−	0.410812i	−0.959905	+	0.280327i	$0.909557\pi$
$224$		0			0
$225$	1.65910	−	9.40923i	0.110607	−	0.627282i
$226$	6.31820	+	10.9434i	0.420280	+	0.727947i
$227$	−11.9436			−0.792722			−0.396361	−	0.918095i	$-0.629727\pi$
$227$	−11.9436			−0.792722			−0.396361	+	0.918095i	$0.629727\pi$
$228$	6.75150	−	1.19047i	0.447129	−	0.0788409i
$229$	−17.5526			−1.15991			−0.579955	−	0.814649i	$-0.696930\pi$
$229$	−17.5526			−1.15991			−0.579955	+	0.814649i	$0.696930\pi$
$230$	5.29813	−	9.17664i	0.349349	−	0.605089i
$231$		0			0
$232$	−8.89352	−	15.4040i	−0.583888	−	1.01132i
$233$	−8.12701	−	14.0764i	−0.532418	−	0.922175i	−0.999284	−	0.0378470i	$-0.987950\pi$
$233$	−8.12701	−	14.0764i	−0.532418	−	0.922175i	0.466865	−	0.884328i	$-0.345383\pi$
$234$	8.35339	−	3.04038i	0.546078	−	0.198756i
$235$	−6.30200	+	10.9154i	−0.411097	+	0.712042i
$236$	−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	$0.00426745\pi$
$240$	−0.0962667	+	0.0169744i	−0.00621399	+	0.00109569i
$241$	−15.6382			−1.00734			−0.503671	−	0.863896i	$-0.668018\pi$
$241$	−15.6382			−1.00734			−0.503671	+	0.863896i	$0.668018\pi$
$242$	−3.63563	+	6.29710i	−0.233707	+	0.404793i
$243$	5.33157	+	14.6484i	0.342020	+	0.939693i
$244$	−9.36959			−0.599826
$245$		0			0
$246$	1.77719	−	4.88279i	0.113309	−	0.311315i
$247$	10.8726			0.691806
$248$	−13.1013	−	22.6922i	−0.831935	−	1.44095i
$249$	8.91534	−	24.4947i	0.564987	−	1.55229i
$250$	−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	$0.294494\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	−9.13310	+	15.8190i	−0.573062	+	0.992572i
$255$	1.07532	−	0.189608i	0.0673393	−	0.0118737i
$256$	8.05051	+	13.9439i	0.503157	+	0.871493i
$257$	26.5817			1.65812			0.829061	−	0.559158i	$-0.188876\pi$
$257$	26.5817			1.65812			0.829061	+	0.559158i	$0.188876\pi$
$258$	−4.31908	−	5.14728i	−0.268894	−	0.320455i
$259$		0			0
$260$	5.56893			0.345370
$261$	17.6716	−	6.43193i	1.09384	−	0.398127i
$262$	−3.15048	+	5.45680i	−0.194637	+	0.337122i
$263$	−0.734118			−0.0452676			−0.0226338	−	0.999744i	$-0.507205\pi$
$263$	−0.734118			−0.0452676			−0.0226338	+	0.999744i	$0.507205\pi$
$264$	−5.22106	−	6.22221i	−0.321334	−	0.382951i
$265$	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
$269$	10.4251	−	18.0569i	0.635632	−	1.10095i	−0.350749	−	0.936470i	$-0.614073\pi$
$269$	10.4251	−	18.0569i	0.635632	−	1.10095i	0.986381	−	0.164478i	$-0.0525939\pi$
$270$		−	6.15636i		−	0.374664i
$271$	−3.47906	−	6.02590i	−0.211338	−	0.366047i	0.740796	−	0.671730i	$-0.234449\pi$
$271$	−3.47906	−	6.02590i	−0.211338	−	0.366047i	−0.952133	+	0.305683i	$0.901115\pi$
$272$	0.00980018	+	0.0169744i	0.000594223	+	0.00102922i
$273$		0			0
$274$	1.12954	−	1.95642i	0.0682379	−	0.118191i
$275$	−5.26352			−0.317402
$276$	6.49912	−	17.8562i	0.391201	−	1.07482i
$277$	17.8726			1.07386			0.536930	−	0.843627i	$-0.319584\pi$
$277$	17.8726			1.07386			0.536930	+	0.843627i	$0.319584\pi$
$278$	−2.69681	−	4.67102i	−0.161744	−	0.280149i
$279$	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	$-0.398433\pi$
$282$	4.87346	−	13.3897i	0.290210	−	0.797346i
$283$	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
$285$	2.57532	−	7.07564i	0.152549	−	0.419125i
$286$	−2.44862	−	4.24113i	−0.144790	−	0.250783i
$287$		0			0
$288$	−15.8944	+	5.78509i	−0.936587	+	0.340890i
$289$	8.39053	+	14.5328i	0.493561	+	0.854872i
$290$	−7.42696			−0.436126
$291$	1.12495	−	3.09078i	0.0659459	−	0.181185i
$292$	−2.51424			−0.147135
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	−0.991406	−	0.130822i	$-0.958238\pi$
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	0.608998	+	0.793171i	$0.291572\pi$
$294$		0			0
$295$	7.00387	+	12.1311i	0.407781	+	0.706298i
$296$	−13.1013	−	22.6922i	−0.761499	−	1.31895i
$297$	7.43717	−	4.29385i	0.431548	−	0.249154i
$298$	0.189540	−	0.328293i	0.0109798	−	0.0190175i
$299$	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
$303$	1.90286	+	2.26774i	0.109316	+	0.130278i
$304$	0.135163			0.00775211
$305$	−5.14543	+	8.91215i	−0.294626	+	0.510308i
$306$	−1.15998	+	0.422197i	−0.0663115	+	0.0241354i
$307$	6.31046			0.360157			0.180078	−	0.983652i	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$		0			0
$309$	4.05051	+	4.82721i	0.230425	+	0.274610i
$310$	−10.9409			−0.621400
$311$	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	$0.746297\pi$
$312$	−16.3089	+	2.87569i	−0.923308	+	0.162804i
$313$	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
$315$		0			0
$316$	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	$0.239501\pi$
$318$	−0.299011	+	0.821525i	−0.0167677	+	0.0460688i
$319$	−5.18004	−	8.97210i	−0.290027	−	0.502341i
$320$	6.79292			0.379736
$321$	−4.22281	+	11.6021i	−0.235694	+	0.647565i
$322$		0			0
$323$	−1.50980			−0.0840075
$324$	−1.91710	−	10.8724i	−0.106506	−	0.604023i
$325$	−5.36571	+	9.29369i	−0.297636	+	0.515521i
$326$	2.28312			0.126450
$327$	0.688663	−	0.121430i	0.0380831	−	0.00671509i
$328$	−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	0.353378	+	0.935481i	$0.385033\pi$
$331$	−11.5248	+	19.9616i	−0.633461	+	1.09719i	−0.986839	+	0.161706i	$0.948300\pi$
$332$	−9.23055	+	15.9878i	−0.506592	+	0.877444i
$333$	26.0326	−	9.47508i	1.42658	−	0.519231i
$334$	−10.1934	−	17.6555i	−0.557759	−	0.966066i
$335$	−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	$0.876489\pi$
$338$	1.44738			0.0787269
$339$	24.5107	−	4.32190i	1.33124	−	0.234734i
$340$	−0.773318			−0.0419391
$341$	−7.63088	−	13.2171i	−0.413235	−	0.715745i
$342$	−1.47818	+	8.38316i	−0.0799307	+	0.453310i
$343$		0			0
$344$	6.25877	+	10.8405i	0.337450	+	0.584481i
$345$	−13.4153	−	15.9878i	−0.722258	−	0.860753i
$346$	−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	$0.946301\pi$
$348$	−13.1163	+	2.31276i	−0.703109	+	0.123977i
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	0.845785	−	0.533524i	$-0.179132\pi$
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	−0.884938	+	0.465710i	$0.845799\pi$
$350$		0			0
$351$		−	17.5089i		−	0.934555i
$352$	4.65910	+	8.06980i	0.248331	+	0.430122i
$353$	14.3327			0.762855			0.381428	−	0.924399i	$-0.375433\pi$
$353$	14.3327			0.762855			0.381428	+	0.924399i	$0.375433\pi$
$354$	−10.1792	−	12.1311i	−0.541017	−	0.644759i
$355$	−0.746911			−0.0396419
$356$	5.57310	−	9.65289i	0.295374	−	0.511602i
$357$		0			0
$358$	−3.75150	−	6.49778i	−0.198273	−	0.343418i
$359$	10.4684	+	18.1318i	0.552500	+	0.956958i	0.998093	+	0.0617224i	$0.0196594\pi$
$359$	10.4684	+	18.1318i	0.552500	+	0.956958i	−0.445593	+	0.895235i	$0.647007\pi$
$360$	−1.99154	+	11.2946i	−0.104964	+	0.595278i
$361$	4.29426	−	7.43788i	0.226014	−	0.391467i
$362$	−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
$366$	3.97906	−	10.9324i	0.207989	−	0.571444i
$367$	−12.0574			−0.629390			−0.314695	−	0.949193i	$-0.601902\pi$
$367$	−12.0574			−0.629390			−0.314695	+	0.949193i	$0.601902\pi$
$368$	0.187319	−	0.324446i	0.00976466	−	0.0169129i
$369$	−7.84002	−	6.57856i	−0.408135	−	0.342466i
$370$	−10.9409			−0.568789
$371$		0			0
$372$	−19.3221	+	3.40700i	−1.00180	+	0.176645i
$373$	−0.781059			−0.0404417			−0.0202209	−	0.999796i	$-0.506437\pi$
$373$	−0.781059			−0.0404417			−0.0202209	+	0.999796i	$0.506437\pi$
$374$	0.340022	+	0.588936i	0.0175821	+	0.0304532i
$375$	12.2772	+	14.6314i	0.633991	+	0.755561i
$376$	−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
$381$	23.1258	+	27.5603i	1.18477	+	1.41196i
$382$	5.67617	+	9.83142i	0.290418	+	0.503019i
$383$	7.73236			0.395105			0.197553	−	0.980292i	$-0.436701\pi$
$383$	7.73236			0.395105			0.197553	+	0.980292i	$0.436701\pi$
$384$	11.6716	−	2.05802i	0.595613	−	0.105023i
$385$		0			0
$386$	0.561185			0.0285636
$387$	−12.4363	+	4.52644i	−0.632172	+	0.230092i
$388$	−1.16473	+	2.01736i	−0.0591300	+	0.102416i
$389$	5.39961			0.273771			0.136886	−	0.990587i	$-0.456291\pi$
$389$	5.39961			0.273771			0.136886	+	0.990587i	$0.456291\pi$
$390$	−2.36500	+	6.49778i	−0.119756	+	0.329028i
$391$	−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
$395$	1.61927	−	2.80466i	0.0814743	−	0.141118i
$396$	−5.71523	+	2.08017i	−0.287201	+	0.104533i
$397$	14.6172	+	25.3178i	0.733617	+	1.27066i	0.955328	+	0.295549i	$0.0955026\pi$
$397$	14.6172	+	25.3178i	0.733617	+	1.27066i	−0.221711	+	0.975112i	$0.571164\pi$
$398$	−1.59967	−	2.77071i	−0.0801842	−	0.138883i
$399$		0			0
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	−27.3979			−1.36818			−0.684092	−	0.729396i	$-0.739801\pi$
$401$	−27.3979			−1.36818			−0.684092	+	0.729396i	$0.739801\pi$
$402$	0.583778	+	0.695720i	0.0291162	+	0.0346993i
$403$	−31.1162			−1.55001
$404$	−1.04829	−	1.81568i	−0.0521542	−	0.0903337i
$405$	−11.3944	−	4.14722i	−0.566192	−	0.206077i
$406$		0			0
$407$	−7.63088	−	13.2171i	−0.378249	−	0.655146i
$408$	2.26470	−	0.399328i	0.112119	−	0.0197697i
$409$	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
$411$	−2.86009	−	3.40852i	−0.141078	−	0.168130i
$412$	−2.23143	−	3.86495i	−0.109935	−	0.190412i
$413$		0			0
$414$	18.0744	+	15.1663i	0.888310	+	0.745381i
$415$	10.1382	+	17.5598i	0.497662	+	0.861977i
$416$	18.9982			0.931466
$417$	−10.4620	+	1.84473i	−0.512325	+	0.0903368i
$418$	4.68954			0.229373
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	−0.868158	−	0.496287i	$-0.834696\pi$
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	0.863877	+	0.503704i	$0.168030\pi$
$420$		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	$0.627694\pi$
$422$	2.56031	+	4.43458i	0.124634	+	0.215872i
$423$	−21.4991	−	18.0399i	−1.04532	−	0.877130i
$424$	0.814330	−	1.41046i	0.0395474	−	0.0684980i
$425$	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
$429$	−9.49912	+	1.67495i	−0.458622	+	0.0808674i
$430$	5.22668			0.252053
$431$	14.6596	−	25.3911i	0.706126	−	1.22305i	−0.260157	−	0.965566i	$-0.583774\pi$
$431$	14.6596	−	25.3911i	0.706126	−	1.22305i	0.966283	−	0.257481i	$-0.0828924\pi$
$432$		−	0.217662i		−	0.0104723i
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$		0			0
$435$	−5.00316	+	13.7461i	−0.239883	+	0.659073i
$436$	−0.495252			−0.0237183
$437$	14.4290	+	24.9918i	0.690233	+	1.19552i
$438$	1.06774	−	2.93360i	0.0510188	−	0.140173i
$439$	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
$441$		0			0
$442$	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	$0.0200583\pi$
$444$	−19.3221	+	3.40700i	−0.916985	+	0.161689i
$445$	−6.12108	−	10.6020i	−0.290167	−	0.502584i
$446$	−6.22937			−0.294969
$447$	−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	$0.449616\pi$
$450$	−6.43629	−	5.40069i	−0.303410	−	0.254591i
$451$	−2.81908	+	4.88279i	−0.132745	+	0.229921i
$452$	−17.6269			−0.829100
$453$	2.75062	+	3.27806i	0.129235	+	0.154017i
$454$	−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	−0.544236	−	0.838932i	$-0.683180\pi$
$457$	9.71436	−	16.8258i	0.454418	−	0.787076i	0.998655	+	0.0518563i	$0.0165138\pi$
$458$	−7.71776	+	13.3676i	−0.360627	+	0.624625i
$459$			2.43134i			0.113485i
$460$	7.39053	+	12.8008i	0.344585	+	0.596839i
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	0.877052	−	0.480395i	$-0.159507\pi$
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	−0.854560	+	0.519352i	$0.826173\pi$
$462$		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	$0.163371\pi$
$464$	−0.262585			−0.0121902
$465$	−7.37030	+	20.2497i	−0.341789	+	0.939059i
$466$	−14.2935			−0.662136
$467$	17.1074	+	29.6309i	0.791637	+	1.37115i	0.924953	+	0.380081i	$0.124104\pi$
$467$	17.1074	+	29.6309i	0.791637	+	1.37115i	−0.133317	+	0.991074i	$0.542563\pi$
$468$	−2.15328	+	12.2118i	−0.0995352	+	0.564492i
$469$		0			0
$470$	5.54189	+	9.59883i	0.255628	+	0.442761i
$471$	−6.00299	+	16.4931i	−0.276603	+	0.759961i
$472$	14.7506	+	25.5488i	0.678952	+	1.17598i
$473$	3.64543	+	6.31407i	0.167617	+	0.290321i
$474$	−1.25221	+	3.44042i	−0.0575160	+	0.158024i
$475$	−5.13816	−	8.89955i	−0.235755	−	0.408339i
$476$		0			0
$477$	1.31908	+	1.10684i	0.0603964	+	0.0506786i
$478$	−6.63903	−	11.4991i	−0.303662	−	0.525959i
$479$	−21.7929			−0.995744			−0.497872	−	0.867251i	$-0.665885\pi$
$479$	−21.7929			−0.995744			−0.497872	+	0.867251i	$0.665885\pi$
$480$	4.50000	−	12.3636i	0.205396	−	0.564321i
$481$	−31.1162			−1.41878
$482$	−6.87598	+	11.9095i	−0.313192	+	0.542465i
$483$		0			0
$484$	−5.07145	−	8.78401i	−0.230521	−	0.399273i
$485$	1.27925	+	2.21572i	0.0580877	+	0.100611i
$486$	13.5000	+	2.38041i	0.612372	+	0.107978i
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	−0.997642	−	0.0686297i	$-0.978137\pi$
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	0.558256	+	0.829669i	$0.311471\pi$
$488$	−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	$0.965709\pi$
$492$	4.65910	+	5.55250i	0.210048	+	0.250326i
$493$	2.93313			0.132102
$494$	4.78059	−	8.28023i	0.215089	−	0.372545i
$495$	−1.15998	+	6.57856i	−0.0521371	+	0.295684i
$496$	−0.386821			−0.0173688
$497$		0			0
$498$	−14.7344	−	17.5598i	−0.660265	−	0.786873i
$499$	−14.3013			−0.640214			−0.320107	−	0.947381i	$-0.603719\pi$
$499$	−14.3013			−0.640214			−0.320107	+	0.947381i	$0.603719\pi$
$500$	−6.76352	−	11.7148i	−0.302474	−	0.523900i
$501$	−39.5442	+	6.97270i	−1.76670	+	0.311517i
$502$	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	$0.363092\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	6.49912	−	11.2568i	0.288921	−	0.500426i
$507$	0.975023	−	2.67885i	0.0433023	−	0.118972i
$508$	−12.7400	−	22.0664i	−0.565248	−	0.979039i
$509$	−25.6091			−1.13510			−0.567551	−	0.823338i	$-0.692109\pi$
$509$	−25.6091			−1.13510			−0.567551	+	0.823338i	$0.692109\pi$
$510$	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
$514$	11.6878	−	20.2438i	0.515526	−	0.892917i
$515$	−4.90167			−0.215994
$516$	9.23055	−	1.62760i	0.406352	−	0.0716509i
$517$	−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
$521$	10.6061	−	18.3702i	0.464660	−	0.804815i	−0.534526	−	0.845152i	$-0.679510\pi$
$521$	10.6061	−	18.3702i	0.464660	−	0.804815i	0.999186	+	0.0403370i	$0.0128431\pi$
$522$	2.87170	−	16.2862i	0.125691	−	0.712829i
$523$	−10.4029	−	18.0183i	−0.454885	−	0.787884i	0.543796	−	0.839217i	$-0.316986\pi$
$523$	−10.4029	−	18.0183i	−0.454885	−	0.787884i	−0.998682	+	0.0513330i	$0.983653\pi$
$524$	−4.39470	−	7.61185i	−0.191984	−	0.332525i
$525$		0			0
$526$	−0.322786	+	0.559082i	−0.0140741	+	0.0243771i
$527$	4.32089			0.188221
$528$	−0.118089	+	0.0208222i	−0.00513914	+	0.000906170i
$529$	56.9873			2.47771
$530$	−0.340022	−	0.588936i	−0.0147696	−	0.0255817i
$531$	−29.3097	+	10.6679i	−1.27193	+	0.462946i
$532$		0			0
$533$	5.74763	+	9.95518i	0.248957	+	0.431207i
$534$	8.89615	+	10.6020i	0.384974	+	0.458794i
$535$	−4.80200	−	8.31731i	−0.207609	−	0.359589i
$536$	−0.845952	−	1.46523i	−0.0365396	−	0.0632884i
$537$	−14.5535	+	2.56617i	−0.628030	+	0.110739i
$538$	−9.16772	−	15.8790i	−0.395248	−	0.684590i
$539$		0			0
$540$	7.43717	+	4.29385i	0.320045	+	0.184778i
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	−0.996085	−	0.0884001i	$-0.971825\pi$
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	0.421486	−	0.906835i	$-0.361509\pi$
$542$	−6.11886			−0.262828
$543$	19.1878	+	22.8671i	0.823427	+	0.981322i
$544$	−2.63816			−0.113110
$545$	−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	$-0.454479\pi$
$548$	1.57563	+	2.72907i	0.0673074	+	0.116580i
$549$	−17.5535	−	14.7291i	−0.749165	−	0.628624i
$550$	−2.31433	+	4.00854i	−0.0986834	+	0.170925i
$551$	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
$555$	−7.37030	+	20.2497i	−0.312852	+	0.859553i
$556$	7.52374			0.319078
$557$	−16.1694	+	28.0062i	−0.685118	+	1.18666i	0.288282	+	0.957546i	$0.406916\pi$
$557$	−16.1694	+	28.0062i	−0.685118	+	1.18666i	−0.973400	+	0.229114i	$0.926417\pi$
$558$	4.23039	−	23.9917i	0.179087	−	1.01565i
$559$	14.8648			0.628716
$560$		0			0
$561$	1.31908	−	0.232589i	0.0556915	−	0.00981992i
$562$	−19.6195			−0.827598
$563$	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	$0.711366\pi$
$564$	12.7763	+	15.2262i	0.537980	+	0.641139i
$565$	−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	−0.440104	−	0.897947i	$-0.645058\pi$
$569$	13.3007	−	23.0374i	0.557593	−	0.965779i	0.997697	−	0.0678320i	$-0.0216082\pi$
$570$	−4.25624	−	5.07239i	−0.178274	−	0.212459i
$571$	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	$0.766116\pi$
$572$	6.83130			0.285631
$573$	22.0201	−	3.88273i	0.919902	−	0.162203i
$574$		0			0
$575$	−28.4834			−1.18784
$576$	−2.62654	+	14.8959i	−0.109439	+	0.620661i
$577$	16.4572	−	28.5048i	0.685124	−	1.18667i	−0.288274	−	0.957548i	$-0.593082\pi$
$577$	16.4572	−	28.5048i	0.685124	−	1.18667i	0.973398	−	0.229121i	$-0.0735852\pi$
$578$	14.7570			0.613811
$579$	0.378041	−	1.03866i	0.0157109	−	0.0431652i
$580$	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
$584$	−2.90791	+	5.03665i	−0.120330	+	0.208418i
$585$	10.4331	+	8.75444i	0.431357	+	0.361951i
$586$	5.75624	+	9.97011i	0.237788	+	0.411861i
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	0.978592	−	0.205808i	$-0.0659821\pi$
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	−0.667531	+	0.744582i	$0.732649\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$	12.3182			0.507132
$591$	−12.7429	−	15.1864i	−0.524172	−	0.624684i
$592$	−0.386821			−0.0158983
$593$	−20.5005	−	35.5079i	−0.841853	−	1.45813i	−0.888326	−	0.459213i	$-0.848131\pi$
$593$	−20.5005	−	35.5079i	−0.841853	−	1.45813i	0.0464729	−	0.998920i	$-0.485202\pi$
$594$		−	7.55190i		−	0.309858i
$595$		0			0
$596$	0.264396	+	0.457947i	0.0108301	+	0.0187582i
$597$	−6.20574	+	1.09424i	−0.253984	+	0.0447842i
$598$	−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	$0.872932\pi$
$600$	10.0611	+	11.9903i	0.410742	+	0.489503i
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	0.973402	−	0.229102i	$-0.0735791\pi$
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	−0.685110	+	0.728440i	$0.740246\pi$
$602$		0			0
$603$	1.68092	−	0.611806i	0.0684524	−	0.0249147i
$604$	−1.51532	−	2.62461i	−0.0616575	−	0.106794i
$605$	−11.1402			−0.452914
$606$	2.56371	−	0.452051i	0.104144	−	0.0183633i
$607$	46.0898			1.87073			0.935363	−	0.353689i	$-0.115073\pi$
$607$	46.0898			1.87073			0.935363	+	0.353689i	$0.115073\pi$
$608$	−9.09627	+	15.7552i	−0.368902	+	0.638958i
$609$		0			0
$610$	4.52481	+	7.83721i	0.183204	+	0.317319i
$611$	15.7613	+	27.2994i	0.637634	+	1.10441i
$612$	0.299011	−	1.69577i	0.0120868	−	0.0685476i
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	−0.464124	−	0.885770i	$-0.653631\pi$
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	0.999162	−	0.0409421i	$-0.0130359\pi$
$614$	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	$0.152246\pi$
$618$	5.45723	−	0.962258i	0.219522	−	0.0387077i
$619$	6.19078			0.248828			0.124414	−	0.992230i	$-0.460295\pi$
$619$	6.19078			0.248828			0.124414	+	0.992230i	$0.460295\pi$
$620$	7.63088	−	13.2171i	0.306464	−	0.530811i
$621$	40.2460	−	23.2361i	1.61502	−	0.932431i
$622$	8.37557			0.335830
$623$		0			0
$624$	−0.0836160	+	0.229733i	−0.00334732	+	0.00919668i
$625$	1.06687			0.0426746
$626$	−7.75119	−	13.4255i	−0.309800	−	0.536589i
$627$	3.15910	−	8.67956i	0.126162	−	0.346628i
$628$	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
$633$	9.93242	−	1.75135i	0.394778	−	0.0696100i
$634$	3.55138	+	6.15118i	0.141043	+	0.244295i
$635$	−27.9855			−1.11057
$636$	−0.783890	−	0.934204i	−0.0310833	−	0.0370436i
$637$		0			0
$638$	−9.11051			−0.360689
$639$	0.288800	−	1.63787i	0.0114248	−	0.0647930i
$640$	−4.60947	+	7.98384i	−0.182205	+	0.315589i
$641$	4.88888			0.193099			0.0965496	−	0.995328i	$-0.469219\pi$
$641$	4.88888			0.193099			0.0965496	+	0.995328i	$0.469219\pi$
$642$	6.97906	+	8.31731i	0.275441	+	0.328258i
$643$	20.1839	−	34.9596i	0.795976	−	1.37867i	−0.126242	−	0.992000i	$-0.540291\pi$
$643$	20.1839	−	34.9596i	0.795976	−	1.37867i	0.922218	−	0.386671i	$-0.126375\pi$
$644$		0			0
$645$	3.52094	−	9.67372i	0.138637	−	0.380902i
$646$	−0.663848	+	1.14982i	−0.0261188	+	0.0452390i
$647$	1.14038	−	1.97519i	0.0448329	−	0.0776528i	−0.842738	−	0.538324i	$-0.819058\pi$
$647$	1.14038	−	1.97519i	0.0448329	−	0.0776528i	0.887571	+	0.460671i	$0.152391\pi$
$648$	−23.9974	−	8.73433i	−0.942706	−	0.343117i
$649$	8.59152	+	14.8809i	0.337247	+	0.584128i
$650$	4.71853	+	8.17273i	0.185076	+	0.320561i
$651$		0			0
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	23.4793			0.918815			0.459407	−	0.888226i	$-0.348062\pi$
$653$	23.4793			0.918815			0.459407	+	0.888226i	$0.348062\pi$
$654$	0.210323	−	0.577857i	0.00822427	−	0.0225960i
$655$	−9.65364			−0.377199
$656$	0.0714517	+	0.123758i	0.00278972	+	0.00483194i
$657$	−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	$0.449472\pi$
$660$	1.61809	−	4.44566i	0.0629840	−	0.173047i
$661$	−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
$663$	0.934011	−	2.56617i	0.0362740	−	0.0996620i
$664$	21.3516	+	36.9821i	0.828604	+	1.43518i
$665$		0			0
$666$	4.23039	−	23.9917i	0.163924	−	0.929661i
$667$	−28.0317	−	48.5523i	−1.08539	−	1.87995i
$668$	28.4382			1.10031
$669$	−4.19640	+	11.5295i	−0.162242	+	0.445757i
$670$	−0.706452			−0.0272926
$671$	−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	$-0.336003\pi$
$674$	12.7613	+	22.1032i	0.491547	+	0.851384i
$675$	−14.3316	+	8.27433i	−0.551622	+	0.318479i
$676$	−1.00950	+	1.74850i	−0.0388267	+	0.0672499i
$677$	−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			0
$680$	−0.894400	+	1.54915i	−0.0342987	+	0.0594070i
$681$	13.2973	+	15.8471i	0.509552	+	0.607260i
$682$	−13.4210			−0.513915
$683$	−17.5321	+	30.3665i	−0.670847	+	1.16194i	0.306818	+	0.951768i	$0.400736\pi$
$683$	−17.5321	+	30.3665i	−0.670847	+	1.16194i	−0.977664	+	0.210172i	$0.932597\pi$
$684$	−9.09627	−	7.63267i	−0.347804	−	0.291843i
$685$	3.46110			0.132242
$686$		0			0
$687$	19.5421	+	23.2893i	0.745576	+	0.888543i
$688$	0.184793			0.00704515
$689$	−0.967034	−	1.67495i	−0.0368411	−	0.0638106i
$690$	−18.0744	+	3.18701i	−0.688082	+	0.121327i
$691$	−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
$693$		0			0
$694$	−11.3847			−0.432159
$695$	4.13176	−	7.15642i	0.156727	−	0.271458i
$696$	−10.5370	+	28.9501i	−0.399403	+	1.09735i
$697$	−0.798133	−	1.38241i	−0.0302315	−	0.0523624i
$698$	−1.28642			−0.0486916
$699$	−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
$703$	14.8983	−	25.8046i	0.561899	−	0.973237i
$704$	8.33275			0.314052
$705$	21.4991	−	3.79088i	0.809704	−	0.142773i
$706$	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	−0.938785	−	0.344504i	$-0.888047\pi$
$709$	−4.55438	+	7.88841i	−0.171043	+	0.296256i	0.767742	+	0.640760i	$0.221380\pi$
$710$	−0.328411	+	0.568825i	−0.0123251	+	0.0213476i
$711$	5.52410	+	4.63527i	0.207170	+	0.173836i
$712$	−12.8914	−	22.3286i	−0.483126	−	0.836799i
$713$	−41.2943	−	71.5239i	−1.54648	−	2.67859i
$714$		0			0
$715$	3.75150	−	6.49778i	0.140298	−	0.243003i
$716$	10.4662			0.391139
$717$	−25.7554	+	4.54137i	−0.961852	+	0.169600i
$718$	18.4115			0.687110
$719$	12.9768	+	22.4765i	0.483954	+	0.838233i	0.999830	−	0.0184300i	$-0.00586678\pi$
$719$	12.9768	+	22.4765i	0.483954	+	0.838233i	−0.515876	+	0.856663i	$0.672533\pi$
$720$	0.129700	+	0.108831i	0.00483362	+	0.00405589i
$721$		0			0
$722$	−3.77631	−	6.54076i	−0.140540	−	0.243422i
$723$	17.4106	+	20.7491i	0.647507	+	0.771669i
$724$	−10.5706	−	18.3088i	−0.392852	−	0.680440i
$725$	9.98205	+	17.2894i	0.370724	+	0.642113i
$726$	12.4029	−	2.18696i	0.460313	−	0.0811656i
$727$	5.08007	+	8.79894i	0.188409	+	0.326335i	0.944720	−	0.327878i	$-0.106333\pi$
$727$	5.08007	+	8.79894i	0.188409	+	0.326335i	−0.756311	+	0.654213i	$0.773000\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	1.21419	+	2.10304i	0.0449393	+	0.0778372i
$731$	−2.06418			−0.0763464
$732$	10.4315	+	12.4318i	0.385561	+	0.459494i
$733$	40.6614			1.50186			0.750931	−	0.660381i	$-0.229605\pi$
$733$	40.6614			1.50186			0.750931	+	0.660381i	$0.229605\pi$
$734$	−5.30154	+	9.18253i	−0.195683	+	0.338933i
$735$		0			0
$736$	25.2126	+	43.6695i	0.929349	+	1.60968i
$737$	−0.492726	−	0.853427i	−0.0181498	−	0.0314364i
$738$	−8.45723	+	3.07818i	−0.311315	+	0.113309i
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	−0.532791	−	0.846247i	$-0.678857\pi$
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	0.999267	+	0.0382877i	$0.0121903\pi$
$740$	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	$0.0316023\pi$
$744$	−15.5223	+	42.6473i	−0.569077	+	1.56353i
$745$	0.580785			0.0212783
$746$	−0.343426	+	0.594831i	−0.0125737	+	0.0217783i
$747$	−42.4261	+	15.4418i	−1.55229	+	0.564987i
$748$	−0.948615			−0.0346848
$749$		0			0
$750$	16.5410	−	2.91663i	0.603992	−	0.106500i
$751$	24.2172			0.883698			0.441849	−	0.897090i	$-0.354323\pi$
$751$	24.2172			0.883698			0.441849	+	0.897090i	$0.354323\pi$
$752$	0.195937	+	0.339373i	0.00714508	+	0.0123756i
$753$	−21.2260	−	25.2961i	−0.773517	−	0.921842i
$754$	−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
$759$	−16.4564	−	19.6119i	−0.597328	−	0.711868i
$760$	6.16772	+	10.6828i	0.223727	+	0.387506i
$761$	−18.2722			−0.662366			−0.331183	−	0.943566i	$-0.607448\pi$
$761$	−18.2722			−0.662366			−0.331183	+	0.943566i	$0.607448\pi$
$762$	31.1573	−	5.49388i	1.12871	−	0.199022i
$763$		0			0
$764$	−15.8357			−0.572917
$765$	−1.44878	−	1.21567i	−0.0523807	−	0.0439526i
$766$	3.39986	−	5.88874i	0.122842	−	0.212769i
$767$	35.0333			1.26498
$768$	9.53818	−	26.2059i	0.344179	−	0.945625i
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	−0.983310	−	0.181936i	$-0.941764\pi$
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	0.649217	+	0.760604i	$0.275097\pi$
$770$		0			0
$771$	−29.5945	−	35.2694i	−1.06582	−	1.27020i
$772$	−0.391407	+	0.677937i	−0.0140870	+	0.0243995i
$773$	1.48040	−	2.56413i	0.0532463	−	0.0922253i	−0.838174	−	0.545403i	$-0.816376\pi$
$773$	1.48040	−	2.56413i	0.0532463	−	0.0922253i	0.891420	+	0.453178i	$0.149710\pi$
$774$	−2.02094	+	11.4613i	−0.0726414	+	0.411970i
$775$	14.7049	+	25.4696i	0.528214	+	0.914894i
$776$	2.69418	+	4.66646i	0.0967155	+	0.167516i
$777$		0			0
$778$	2.37417	−	4.11218i	0.0851181	−	0.147429i
$779$	−11.0077			−0.394393
$780$	−6.20011	−	7.38901i	−0.222000	−	0.264569i
$781$	−0.916222			−0.0327850
$782$	1.84002	+	3.18701i	0.0657991	+	0.113967i
$783$	−28.2086	−	16.2862i	−1.00809	−	0.582022i
$784$		0			0
$785$	−6.82635	−	11.8236i	−0.243643	−	0.422002i
$786$	10.7478	−	1.89513i	0.383361	−	0.0675969i
$787$	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
$789$	0.817323	+	0.974048i	0.0290975	+	0.0346770i
$790$	−1.42396	−	2.46638i	−0.0506623	−	0.0877497i
$791$		0			0
$792$	−2.44299	+	13.8549i	−0.0868079	+	0.492312i
$793$	12.8687	+	22.2893i	0.456981	+	0.791515i
$794$	25.7083			0.912354
$795$	−1.31908	+	0.232589i	−0.0467829	+	0.00824908i
$796$	4.46286			0.158182
$797$	−24.6755	+	42.7391i	−0.874050	+	1.51390i	−0.0162779	+	0.999868i	$0.505182\pi$
$797$	−24.6755	+	42.7391i	−0.874050	+	1.51390i	−0.857772	+	0.514031i	$0.828152\pi$
$798$		0			0
$799$	−2.18866	−	3.79088i	−0.0774293	−	0.134112i
$800$	−8.97818	−	15.5507i	−0.317427	−	0.549799i
$801$	25.6155	−	9.32326i	0.905078	−	0.329421i
$802$	−12.0466	+	20.8654i	−0.425382	+	0.736782i
$803$	−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
$807$	−35.5651	+	6.27109i	−1.25195	+	0.220753i
$808$	−4.84968			−0.170611
$809$	−9.91400	+	17.1716i	−0.348558	+	0.603720i	−0.985993	−	0.166784i	$-0.946662\pi$
$809$	−9.91400	+	17.1716i	−0.348558	+	0.603720i	0.637436	+	0.770503i	$0.279995\pi$
$810$	−8.16843	+	6.85413i	−0.287010	+	0.240830i
$811$	−23.8557			−0.837686			−0.418843	−	0.908059i	$-0.637564\pi$
$811$	−23.8557			−0.837686			−0.418843	+	0.908059i	$0.637564\pi$
$812$		0			0
$813$	−4.12196	+	11.3250i	−0.144563	+	0.397185i
$814$	−13.4210			−0.470405
$815$	1.74897	+	3.02931i	0.0612638	+	0.106112i
$816$	0.0116112	−	0.0319015i	0.000406473	−	0.00111677i
$817$	−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	0.0478469	−	0.998855i	$-0.484764\pi$
$821$	25.4714	−	44.1177i	0.888957	−	1.53972i	0.841110	−	0.540864i	$-0.181903\pi$
$822$	−3.85339	+	0.679456i	−0.134402	+	0.0236988i
$823$	−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	$0.909594\pi$
$824$	−10.3233			−0.359628
$825$	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	$0.283189\pi$
$828$	−30.9278	+	11.2568i	−1.07482	+	0.391201i
$829$	−12.6630	+	21.9329i	−0.439803	+	0.761761i	−0.997674	−	0.0681664i	$-0.978285\pi$
$829$	−12.6630	+	21.9329i	−0.439803	+	0.761761i	0.557871	+	0.829928i	$0.311618\pi$
$830$	17.8307			0.618912
$831$	−19.8983	−	23.7138i	−0.690263	−	0.822624i
$832$	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
$836$	−3.27079	+	5.66518i	−0.113123	+	0.195934i
$837$	−41.5549	−	23.9917i	−1.43635	−	0.829276i
$838$	0.0770768	+	0.133501i	0.00266257	+	0.00461171i
$839$	−4.35710	−	7.54671i	−0.150424	−	0.260541i	0.780960	−	0.624582i	$-0.214730\pi$
$839$	−4.35710	−	7.54671i	−0.150424	−	0.260541i	−0.931383	+	0.364040i	$0.881397\pi$
$840$		0			0
$841$	−5.14749	+	8.91571i	−0.177500	+	0.307438i
$842$	21.7252			0.748701
$843$	−13.2166	+	36.3124i	−0.455205	+	1.25067i
$844$	−7.14290			−0.245869
$845$	1.10876	+	1.92042i	0.0381423	+	0.0660645i
$846$	−23.1917	+	8.44107i	−0.797346	+	0.290210i
$847$		0			0
$848$	−0.0120217	−	0.0208222i	−0.000412827	−	0.000715037i
$849$	11.0153	−	30.2643i	0.378045	−	1.03867i
$850$	−0.655230	−	1.13489i	−0.0224742	−	0.0389265i
$851$	−41.2943	−	71.5239i	−1.41555	−	2.45181i
$852$	−0.402856	+	1.10684i	−0.0138016	+	0.0379196i
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	0.950170	−	0.311733i	$-0.100909\pi$
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	−0.745053	+	0.667005i	$0.767576\pi$
$854$		0			0
$855$	−12.2554	+	4.46059i	−0.419125	+	0.152549i
$856$	−10.1133	−	17.5168i	−0.345667	−	0.598713i
$857$	6.50030			0.222046			0.111023	−	0.993818i	$-0.464587\pi$
$857$	6.50030			0.222046			0.111023	+	0.993818i	$0.464587\pi$
$858$	−2.90110	+	7.97071i	−0.0990420	+	0.272116i
$859$	−53.5526			−1.82719			−0.913596	−	0.406623i	$-0.866706\pi$
$859$	−53.5526			−1.82719			−0.913596	+	0.406623i	$0.866706\pi$
$860$	−3.64543	+	6.31407i	−0.124308	+	0.215308i
$861$		0			0
$862$	−12.8914	−	22.3286i	−0.439083	−	0.760514i
$863$	−1.84982	−	3.20399i	−0.0629687	−	0.109065i	0.832822	−	0.553540i	$-0.186723\pi$
$863$	−1.84982	−	3.20399i	−0.0629687	−	0.109065i	−0.895791	+	0.444475i	$0.853390\pi$
$864$	25.3717	+	14.6484i	0.863163	+	0.498347i
$865$	3.20115	−	5.54456i	0.108842	−	0.188521i
$866$	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
$870$	8.26873	+	9.85429i	0.280336	+	0.334092i
$871$	−2.00917			−0.0680782
$872$	−0.572796	+	0.992112i	−0.0193973	+	0.0335971i
$873$	−5.35339	+	1.94847i	−0.181185	+	0.0659459i
$874$	25.3773			0.858401
$875$		0			0
$876$	2.79921	+	3.33597i	0.0945765	+	0.112712i
$877$	−11.7888			−0.398079			−0.199040	−	0.979991i	$-0.563782\pi$
$877$	−11.7888			−0.398079			−0.199040	+	0.979991i	$0.563782\pi$
$878$	−9.64244	−	16.7012i	−0.325416	−	0.563638i
$879$	22.3307	−	3.93750i	0.753195	−	0.132809i
$880$	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	$0.186271\pi$
$882$		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
$885$	8.29813	−	22.7989i	0.278939	−	0.766378i
$886$	−8.22668	−	14.2490i	−0.276381	−	0.478706i
$887$	11.8848			0.399051			0.199526	−	0.979893i	$-0.436060\pi$
$887$	11.8848			0.399051			0.199526	+	0.979893i	$0.436060\pi$
$888$	−15.5223	+	42.6473i	−0.520896	+	1.43115i
$889$		0			0
$890$	−10.7656			−0.360863
$891$	−13.9773	−	5.08732i	−0.468257	−	0.170432i
$892$	4.34477	−	7.52536i	0.145474	−	0.251968i
$893$	−30.1857			−1.01013
$894$	−0.646612	+	0.114015i	−0.0216259	+	0.00381324i
$895$	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
$899$	−28.9433	+	50.1313i	−0.965314	+	1.67197i
$900$	11.0134	−	4.00854i	0.367112	−	0.133618i
$901$	0.134285	+	0.232589i	0.00447369	+	0.00774866i
$902$	2.47906	+	4.29385i	0.0825435	+	0.142970i
$903$		0			0
$904$	−20.3868	+	35.3110i	−0.678056	+	1.17443i
$905$	−23.2199			−0.771855
$906$	3.70590	−	0.653450i	0.123120	−	0.0217094i
$907$	−26.0215			−0.864029			−0.432014	−	0.901867i	$-0.642197\pi$
$907$	−26.0215			−0.864029			−0.432014	+	0.901867i	$0.642197\pi$
$908$	−7.32547	−	12.6881i	−0.243104	−	0.421069i
$909$	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	$0.812053\pi$
$912$	−0.150482	−	0.179338i	−0.00498296	−	0.00593846i
$913$	12.4363	+	21.5403i	0.411581	+	0.712879i
$914$	−8.54266	−	14.7963i	−0.282566	−	0.489419i
$915$	17.5535	−	3.09516i	0.580301	−	0.102323i
$916$	−10.7657	−	18.6468i	−0.355710	−	0.616108i
$917$		0			0
$918$	1.85163	+	1.06904i	0.0611130	+	0.0352836i
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	0.546167	−	0.837677i	$-0.316087\pi$
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	−0.998532	+	0.0541559i	$0.982753\pi$
$920$	34.1908			1.12724
$921$	−7.02569	−	8.37289i	−0.231504	−	0.275896i
$922$	0.849356			0.0279720
$923$	−0.934011	+	1.61775i	−0.0307434	+	0.0532491i
$924$		0			0
$925$	14.7049	+	25.4696i	0.483493	+	0.837434i
$926$	−0.195937	−	0.339373i	−0.00643889	−	0.0111525i
$927$	1.89528	−	10.7487i	0.0622491	−	0.353032i
$928$	17.6716	−	30.6081i	0.580098	−	1.00476i
$929$	−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
$931$		0			0
$932$	9.96926	−	17.2673i	0.326554	−	0.565608i
$933$	5.64219	−	15.5018i	0.184717	−	0.507506i
$934$	30.0880			0.984510
$935$	−0.520945	+	0.902302i	−0.0170367	+	0.0295084i
$936$	21.9729	+	18.4374i	0.718206	+	0.602646i
$937$	−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			0
$939$	−30.0699	+	5.30213i	−0.981293	+	0.173028i
$940$	−15.4611			−0.504286
$941$	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	$0.801427\pi$
$942$	9.92117	+	11.8236i	0.323249	+	0.385233i
$943$	−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	−0.907684	−	0.419654i	$-0.862151\pi$
$947$	−2.78224	+	4.81898i	−0.0904107	+	0.156596i	0.817273	+	0.576250i	$0.195485\pi$
$948$	−3.28281	−	3.91231i	−0.106621	−	0.127066i
$949$	3.45320	+	5.98112i	0.112096	+	0.194155i
$950$	−9.03684			−0.293194
$951$	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	$0.545108\pi$
$954$	1.42292	−	0.517902i	0.0460688	−	0.0167677i
$955$	−8.69640	+	15.0626i	−0.281409	+	0.487415i
$956$	18.5220			0.599044
$957$	−6.13728	+	16.8620i	−0.198390	+	0.545072i
$958$	−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
$962$	−13.6816	+	23.6971i	−0.441111	+	0.764027i
$963$	20.0954	−	7.31412i	0.647565	−	0.235694i
$964$	−9.59152	−	16.6130i	−0.308922	−	0.535069i
$965$	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	$-0.212557\pi$
$968$	−23.4620			−0.754098
$969$	1.68092	+	2.00324i	0.0539990	+	0.0643535i
$970$	2.24990			0.0722401
$971$	15.3596	+	26.6036i	0.492914	+	0.853752i	0.999967	−	0.00816326i	$-0.00259847\pi$
$971$	15.3596	+	26.6036i	0.492914	+	0.853752i	−0.507053	+	0.861915i	$0.669265\pi$
$972$	−12.2914	+	14.6484i	−0.394248	+	0.469846i
$973$		0			0
$974$	8.52687	+	14.7690i	0.273219	+	0.473229i
$975$	18.3050	−	3.22766i	0.586229	−	0.103368i
$976$	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	$0.886019\pi$
$978$	−2.54189	−	3.02931i	−0.0812806	−	0.0968665i
$979$	−7.50862	−	13.0053i	−0.239976	−	0.415651i
$980$		0			0
$981$	−0.927833	−	0.778544i	−0.0296234	−	0.0248570i
$982$	11.5009	+	19.9201i	0.367008	+	0.635676i
$983$	13.6963			0.436846			0.218423	−	0.975854i	$-0.429909\pi$
$983$	13.6963			0.436846			0.218423	+	0.975854i	$0.429909\pi$
$984$	16.5116	−	2.91144i	0.526371	−	0.0928134i
$985$	15.4206			0.491343
$986$	1.28968	−	2.23379i	0.0410717	−	0.0711383i
$987$		0			0
$988$	6.66860	+	11.5503i	0.212156	+	0.367465i
$989$	19.7271	+	34.1684i	0.627287	+	1.08649i
$990$	4.50000	+	3.77595i	0.143019	+	0.120008i
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.122922	+	0.992416i	$0.539227\pi$
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.797997	+	0.602662i	$0.794107\pi$
$992$	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
$996$	31.4898	−	5.55250i	0.997792	−	0.175938i
$997$	16.2175			0.513614			0.256807	−	0.966463i	$-0.417330\pi$
$997$	16.2175			0.513614			0.256807	+	0.966463i	$0.417330\pi$
$998$	−6.28817	+	10.8914i	−0.199049	+	0.344762i
$999$	−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.g.c.67.3		6
3.2	odd	2		1323.2.g.d.361.1		6
7.2	even	3		441.2.h.d.373.1		6
7.3	odd	6		441.2.f.c.148.3		6
7.4	even	3		63.2.f.a.22.3	✓	6
7.5	odd	6		441.2.h.e.373.1		6
7.6	odd	2		441.2.g.b.67.3		6
9.2	odd	6		1323.2.h.c.802.3		6
9.7	even	3		441.2.h.d.214.1		6
21.2	odd	6		1323.2.h.c.226.3		6
21.5	even	6		1323.2.h.b.226.3		6
21.11	odd	6		189.2.f.b.64.1		6
21.17	even	6		1323.2.f.d.442.1		6
21.20	even	2		1323.2.g.e.361.1		6
28.11	odd	6		1008.2.r.h.337.2		6
63.2	odd	6		1323.2.g.d.667.1		6
63.4	even	3		567.2.a.h.1.1		3
63.11	odd	6		189.2.f.b.127.1		6
63.16	even	3	inner	441.2.g.c.79.3		6
63.20	even	6		1323.2.h.b.802.3		6
63.25	even	3		63.2.f.a.43.3	yes	6
63.31	odd	6		3969.2.a.q.1.1		3
63.32	odd	6		567.2.a.c.1.3		3
63.34	odd	6		441.2.h.e.214.1		6
63.38	even	6		1323.2.f.d.883.1		6
63.47	even	6		1323.2.g.e.667.1		6
63.52	odd	6		441.2.f.c.295.3		6
63.59	even	6		3969.2.a.l.1.3		3
63.61	odd	6		441.2.g.b.79.3		6
84.11	even	6		3024.2.r.k.1009.2		6
252.11	even	6		3024.2.r.k.2017.2		6
252.67	odd	6		9072.2.a.ca.1.2		3
252.95	even	6		9072.2.a.bs.1.2		3
252.151	odd	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	7.4	even	3
63.2.f.a.43.3	yes	6	63.25	even	3
189.2.f.b.64.1		6	21.11	odd	6
189.2.f.b.127.1		6	63.11	odd	6
441.2.f.c.148.3		6	7.3	odd	6
441.2.f.c.295.3		6	63.52	odd	6
441.2.g.b.67.3		6	7.6	odd	2
441.2.g.b.79.3		6	63.61	odd	6
441.2.g.c.67.3		6	1.1	even	1	trivial
441.2.g.c.79.3		6	63.16	even	3	inner
441.2.h.d.214.1		6	9.7	even	3
441.2.h.d.373.1		6	7.2	even	3
441.2.h.e.214.1		6	63.34	odd	6
441.2.h.e.373.1		6	7.5	odd	6
567.2.a.c.1.3		3	63.32	odd	6
567.2.a.h.1.1		3	63.4	even	3
1008.2.r.h.337.2		6	28.11	odd	6
1008.2.r.h.673.2		6	252.151	odd	6
1323.2.f.d.442.1		6	21.17	even	6
1323.2.f.d.883.1		6	63.38	even	6
1323.2.g.d.361.1		6	3.2	odd	2
1323.2.g.d.667.1		6	63.2	odd	6
1323.2.g.e.361.1		6	21.20	even	2
1323.2.g.e.667.1		6	63.47	even	6
1323.2.h.b.226.3		6	21.5	even	6
1323.2.h.b.802.3		6	63.20	even	6
1323.2.h.c.226.3		6	21.2	odd	6
1323.2.h.c.802.3		6	9.2	odd	6
3024.2.r.k.1009.2		6	84.11	even	6
3024.2.r.k.2017.2		6	252.11	even	6
3969.2.a.l.1.3		3	63.59	even	6
3969.2.a.q.1.1		3	63.31	odd	6
9072.2.a.bs.1.2		3	252.95	even	6
9072.2.a.ca.1.2		3	252.67	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 - 0.761570i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} +1.34730 q^{5} +(-1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(0.439693 - 0.761570i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} +1.34730 q^{5} +(-1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +(0.592396 - 1.02606i) q^{10} +1.65270 q^{11} +(0.726682 - 1.99654i) q^{12} +(1.68479 - 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(-0.233956 + 0.405223i) q^{17} +(2.02094 + 1.69577i) q^{18} +(1.61334 + 2.79439i) q^{19} +(0.826352 + 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +8.94356 q^{23} +(-3.15910 - 3.76487i) q^{24} -3.18479 q^{25} +(-1.48158 - 2.56617i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(-2.02094 + 0.356347i) q^{30} +(-4.61721 - 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(-1.84002 - 2.19285i) q^{33} +(0.205737 + 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} +2.83750 q^{38} +(-5.74763 + 1.01346i) q^{39} +3.82295 q^{40} +(-1.70574 + 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(-0.701867 + 3.98048i) q^{45} +(3.93242 - 6.81115i) q^{46} +(-4.67752 + 8.10170i) q^{47} +(-0.0714517 + 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(0.798133 - 0.140732i) q^{51} +4.13341 q^{52} +(0.286989 - 0.497079i) q^{53} -4.56942i q^{54} +2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} -5.51249 q^{58} +(5.19846 + 9.00400i) q^{59} +(0.979055 - 2.68993i) q^{60} +(-3.81908 + 6.61484i) q^{61} -8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(-2.47906 + 0.437124i) q^{66} +(-0.298133 - 0.516382i) q^{67} -0.573978 q^{68} +(-9.95723 - 11.8666i) q^{69} -0.554378 q^{71} +(-1.47818 + 8.38316i) q^{72} +(-1.02481 + 1.77503i) q^{73} -8.12061 q^{74} +(3.54576 + 4.22567i) q^{75} +(-1.97906 + 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +(0.0282185 - 0.0488759i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(1.50000 + 2.59808i) q^{82} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +3.87939 q^{86} +(-3.71348 + 10.2027i) q^{87} +4.68954 q^{88} +(-4.54323 - 7.86911i) q^{89} +(2.72281 + 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-5.47044 + 15.0299i) q^{93} +(4.11334 + 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(3.34002 - 9.17664i) q^{96} +(0.949493 + 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8} + 12 q^{11} - 9 q^{12} + 3 q^{13} - 9 q^{15} - 3 q^{16} - 6 q^{17} + 9 q^{18} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 24 q^{23} + 18 q^{24} - 12 q^{25} + 3 q^{26} + 27 q^{27} - 9 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{33} - 9 q^{34} - 27 q^{36} + 3 q^{37} + 12 q^{38} - 18 q^{39} - 18 q^{40} + 3 q^{43} - 15 q^{44} - 18 q^{45} - 3 q^{47} + 6 q^{50} - 9 q^{51} - 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} + 3 q^{59} + 9 q^{60} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} - 18 q^{66} + 12 q^{67} + 12 q^{68} - 9 q^{69} + 18 q^{71} + 45 q^{72} + 21 q^{73} - 60 q^{74} - 9 q^{75} - 15 q^{76} + 54 q^{78} + 21 q^{79} + 15 q^{80} + 9 q^{82} + 18 q^{83} - 9 q^{85} + 12 q^{86} + 36 q^{87} + 54 q^{88} - 12 q^{89} + 27 q^{90} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8 + 12 * q^11 - 9 * q^12 + 3 * q^13 - 9 * q^15 - 3 * q^16 - 6 * q^17 + 9 * q^18 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 24 * q^23 + 18 * q^24 - 12 * q^25 + 3 * q^26 + 27 * q^27 - 9 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^33 - 9 * q^34 - 27 * q^36 + 3 * q^37 + 12 * q^38 - 18 * q^39 - 18 * q^40 + 3 * q^43 - 15 * q^44 - 18 * q^45 - 3 * q^47 + 6 * q^50 - 9 * q^51 - 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 + 3 * q^59 + 9 * q^60 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 - 18 * q^66 + 12 * q^67 + 12 * q^68 - 9 * q^69 + 18 * q^71 + 45 * q^72 + 21 * q^73 - 60 * q^74 - 9 * q^75 - 15 * q^76 + 54 * q^78 + 21 * q^79 + 15 * q^80 + 9 * q^82 + 18 * q^83 - 9 * q^85 + 12 * q^86 + 36 * q^87 + 54 * q^88 - 12 * q^89 + 27 * q^90 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 3 * q^97 + 18 * q^99

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