LMFDB - Embedded newform 637.2.bb.a.362.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			362.7
Character	$\chi$	$=$	637.362
Dual form			637.2.bb.a.227.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74384 + 1.74384i) q^{2} +(0.146239 + 0.0844309i) q^{3} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(0.107782 + 0.402250i) q^{6} +(-3.63054 + 3.63054i) q^{8} +(-1.48574 - 2.57338i) q^{9} +O(q^{10})$	\(q+(1.74384 + 1.74384i) q^{2} +(0.146239 + 0.0844309i) q^{3} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(0.107782 + 0.402250i) q^{6} +(-3.63054 + 3.63054i) q^{8} +(-1.48574 - 2.57338i) q^{9} +(-3.04263 + 5.26998i) q^{10} +(1.17950 + 4.40195i) q^{11} +(-0.344641 + 0.596935i) q^{12} +(-1.54835 - 3.25617i) q^{13} +(-0.107841 + 0.402470i) q^{15} -4.49827 q^{16} -0.112710 q^{17} +(1.89666 - 7.07845i) q^{18} +(3.32660 + 0.891360i) q^{19} +(-9.72897 + 2.60687i) q^{20} +(-5.61943 + 9.73314i) q^{22} +0.652493i q^{23} +(-0.837454 + 0.224395i) q^{24} +(-0.942740 + 0.544291i) q^{25} +(2.97816 - 8.37828i) q^{26} -1.00836i q^{27} +(-2.82213 - 4.88807i) q^{29} +(-0.889899 + 0.513783i) q^{30} +(-5.34937 - 1.43336i) q^{31} +(-0.583169 - 0.583169i) q^{32} +(-0.199172 + 0.743322i) q^{33} +(-0.196548 - 0.196548i) q^{34} +(10.5044 - 6.06469i) q^{36} +(1.09952 - 1.09952i) q^{37} +(4.24666 + 7.35543i) q^{38} +(0.0484931 - 0.606906i) q^{39} +(-10.9717 - 6.33453i) q^{40} +(10.6793 + 2.86152i) q^{41} +(6.08601 + 3.51376i) q^{43} +(-17.9684 + 4.81463i) q^{44} +(5.18462 - 5.18462i) q^{45} +(-1.13784 + 1.13784i) q^{46} +(5.72325 - 1.53354i) q^{47} +(-0.657821 - 0.379793i) q^{48} +(-2.59314 - 0.694830i) q^{50} +(-0.0164826 - 0.00951622i) q^{51} +(13.2914 - 6.32024i) q^{52} +(-2.41079 - 4.17561i) q^{53} +(1.75841 - 1.75841i) q^{54} +(-9.73846 + 5.62250i) q^{55} +(0.411219 + 0.411219i) q^{57} +(3.60266 - 13.4453i) q^{58} +(-2.79191 - 2.79191i) q^{59} +(-1.64285 - 0.440201i) q^{60} +(-13.2845 + 7.66982i) q^{61} +(-6.82887 - 11.8280i) q^{62} +6.96264i q^{64} +(6.77201 - 5.76988i) q^{65} +(-1.64355 + 0.948907i) q^{66} +(-6.07826 + 1.62866i) q^{67} -0.460075i q^{68} +(-0.0550906 + 0.0954197i) q^{69} +(3.56578 - 0.955449i) q^{71} +(14.7368 + 3.94872i) q^{72} +(0.651157 - 2.43015i) q^{73} +3.83477 q^{74} -0.183820 q^{75} +(-3.63847 + 13.5789i) q^{76} +(1.14291 - 0.973780i) q^{78} +(6.11315 - 10.5883i) q^{79} +(-2.87276 - 10.7213i) q^{80} +(-4.37209 + 7.57269i) q^{81} +(13.6330 + 23.6130i) q^{82} +(3.34105 - 3.34105i) q^{83} +(-0.0719809 - 0.268637i) q^{85} +(4.48558 + 16.7404i) q^{86} -0.953099i q^{87} +(-20.2637 - 11.6992i) q^{88} +(6.14338 + 6.14338i) q^{89} +18.0822 q^{90} -2.66343 q^{92} +(-0.661264 - 0.661264i) q^{93} +(12.6547 + 7.30617i) q^{94} +8.49797i q^{95} +(-0.0360444 - 0.134519i) q^{96} +(-1.04426 - 3.89722i) q^{97} +(9.57547 - 9.57547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.74384	+	1.74384i	1.23308	+	1.23308i	0.962775	+	0.270303i	$0.0871238\pi$
$2$	1.74384	+	1.74384i	1.23308	+	1.23308i	0.270303	+	0.962775i	$0.412876\pi$
$3$	0.146239	+	0.0844309i	0.0844309	+	0.0487462i	0.541621	−	0.840623i	$-0.317811\pi$
$3$	0.146239	+	0.0844309i	0.0844309	+	0.0487462i	−0.457190	+	0.889369i	$0.651144\pi$
$4$			4.08193i			2.04096i
$5$	0.638637	+	2.38343i	0.285607	+	1.06590i	0.948394	+	0.317093i	$0.102707\pi$
$5$	0.638637	+	2.38343i	0.285607	+	1.06590i	−0.662787	+	0.748808i	$0.730627\pi$
$6$	0.107782	+	0.402250i	0.0440020	+	0.164218i
$7$		0			0
$7$		0			0
$8$	−3.63054	+	3.63054i	−1.28359	+	1.28359i
$9$	−1.48574	−	2.57338i	−0.495248	−	0.857794i
$10$	−3.04263	+	5.26998i	−0.962163	+	1.66652i
$11$	1.17950	+	4.40195i	0.355633	+	1.32724i	0.879687	+	0.475554i	$0.157752\pi$
$11$	1.17950	+	4.40195i	0.355633	+	1.32724i	−0.524054	+	0.851685i	$0.675581\pi$
$12$	−0.344641	+	0.596935i	−0.0994892	+	0.172320i
$13$	−1.54835	−	3.25617i	−0.429434	−	0.903098i
$13$	−1.54835	−	3.25617i	−0.429434	−	0.903098i
$14$		0			0
$15$	−0.107841	+	0.402470i	−0.0278445	+	0.103917i
$16$	−4.49827			−1.12457
$17$	−0.112710			−0.0273362			−0.0136681	−	0.999907i	$-0.504351\pi$
$17$	−0.112710			−0.0273362			−0.0136681	+	0.999907i	$0.504351\pi$
$18$	1.89666	−	7.07845i	0.447048	−	1.66841i
$19$	3.32660	+	0.891360i	0.763175	+	0.204492i	0.619354	−	0.785112i	$-0.287395\pi$
$19$	3.32660	+	0.891360i	0.763175	+	0.204492i	0.143820	+	0.989604i	$0.454061\pi$
$20$	−9.72897	+	2.60687i	−2.17546	+	0.582914i
$21$		0			0
$22$	−5.61943	+	9.73314i	−1.19807	+	2.07511i
$23$			0.652493i			0.136054i	0.997683	+	0.0680271i	$0.0216704\pi$
$23$			0.652493i			0.136054i	−0.997683	+	0.0680271i	$0.978330\pi$
$24$	−0.837454	+	0.224395i	−0.170945	+	0.0458045i
$25$	−0.942740	+	0.544291i	−0.188548	+	0.108858i
$26$	2.97816	−	8.37828i	0.584065	−	1.64312i
$27$		−	1.00836i		−	0.194058i
$28$		0			0
$29$	−2.82213	−	4.88807i	−0.524056	−	0.907691i	−0.999608	−	0.0280035i	$-0.991085\pi$
$29$	−2.82213	−	4.88807i	−0.524056	−	0.907691i	0.475552	−	0.879688i	$-0.342248\pi$
$30$	−0.889899	+	0.513783i	−0.162473	+	0.0938036i
$31$	−5.34937	−	1.43336i	−0.960774	−	0.257439i	−0.255846	−	0.966717i	$-0.582354\pi$
$31$	−5.34937	−	1.43336i	−0.960774	−	0.257439i	−0.704928	+	0.709279i	$0.749021\pi$
$32$	−0.583169	−	0.583169i	−0.103091	−	0.103091i
$33$	−0.199172	+	0.743322i	−0.0346715	+	0.129396i
$34$	−0.196548	−	0.196548i	−0.0337077	−	0.0337077i
$35$		0			0
$36$	10.5044	−	6.06469i	1.75073	−	1.01078i
$37$	1.09952	−	1.09952i	0.180760	−	0.180760i	−0.610927	−	0.791687i	$-0.709203\pi$
$37$	1.09952	−	1.09952i	0.180760	−	0.180760i	0.791687	+	0.610927i	$0.209203\pi$
$38$	4.24666	+	7.35543i	0.688899	+	1.19321i
$39$	0.0484931	−	0.606906i	0.00776511	−	0.0971827i
$40$	−10.9717	−	6.33453i	−1.73478	−	1.00158i
$41$	10.6793	+	2.86152i	1.66783	+	0.446894i	0.964525	−	0.263993i	$-0.0850396\pi$
$41$	10.6793	+	2.86152i	1.66783	+	0.446894i	0.703306	+	0.710887i	$0.251706\pi$
$42$		0			0
$43$	6.08601	+	3.51376i	0.928108	+	0.535843i	0.886213	−	0.463279i	$-0.153327\pi$
$43$	6.08601	+	3.51376i	0.928108	+	0.535843i	0.0418951	+	0.999122i	$0.486660\pi$
$44$	−17.9684	+	4.81463i	−2.70885	+	0.725833i
$45$	5.18462	−	5.18462i	0.772877	−	0.772877i
$46$	−1.13784	+	1.13784i	−0.167766	+	0.167766i
$47$	5.72325	−	1.53354i	0.834822	−	0.223690i	0.184006	−	0.982925i	$-0.441093\pi$
$47$	5.72325	−	1.53354i	0.834822	−	0.223690i	0.650816	+	0.759235i	$0.274427\pi$
$48$	−0.657821	−	0.379793i	−0.0949483	−	0.0548184i
$49$		0			0
$50$	−2.59314	−	0.694830i	−0.366725	−	0.0982637i
$51$	−0.0164826	−	0.00951622i	−0.00230802	−	0.00133254i
$52$	13.2914	−	6.32024i	1.84319	−	0.876459i
$53$	−2.41079	−	4.17561i	−0.331147	−	0.573564i	0.651590	−	0.758571i	$-0.274102\pi$
$53$	−2.41079	−	4.17561i	−0.331147	−	0.573564i	−0.982737	+	0.185008i	$0.940769\pi$
$54$	1.75841	−	1.75841i	0.239289	−	0.239289i
$55$	−9.73846	+	5.62250i	−1.31313	+	0.758138i
$56$		0			0
$57$	0.411219	+	0.411219i	0.0544673	+	0.0544673i
$58$	3.60266	−	13.4453i	0.473052	−	1.76546i
$59$	−2.79191	−	2.79191i	−0.363476	−	0.363476i	0.501615	−	0.865091i	$-0.332739\pi$
$59$	−2.79191	−	2.79191i	−0.363476	−	0.363476i	−0.865091	+	0.501615i	$0.832739\pi$
$60$	−1.64285	−	0.440201i	−0.212091	−	0.0568297i
$61$	−13.2845	+	7.66982i	−1.70091	+	0.982020i	−0.756067	+	0.654495i	$0.772881\pi$
$61$	−13.2845	+	7.66982i	−1.70091	+	0.982020i	−0.944842	+	0.327526i	$0.893785\pi$
$62$	−6.82887	−	11.8280i	−0.867268	−	1.50215i
$63$		0			0
$64$			6.96264i			0.870330i
$65$	6.77201	−	5.76988i	0.839964	−	0.715666i
$66$	−1.64355	+	0.948907i	−0.202308	+	0.116802i
$67$	−6.07826	+	1.62866i	−0.742577	+	0.198973i	−0.610223	−	0.792230i	$-0.708920\pi$
$67$	−6.07826	+	1.62866i	−0.742577	+	0.198973i	−0.132354	+	0.991203i	$0.542254\pi$
$68$		−	0.460075i		−	0.0557923i
$69$	−0.0550906	+	0.0954197i	−0.00663213	+	0.0114872i
$70$		0			0
$71$	3.56578	−	0.955449i	0.423181	−	0.113391i	−0.0409427	−	0.999161i	$-0.513036\pi$
$71$	3.56578	−	0.955449i	0.423181	−	0.113391i	0.464123	+	0.885771i	$0.346369\pi$
$72$	14.7368	+	3.94872i	1.73675	+	0.465361i
$73$	0.651157	−	2.43015i	0.0762122	−	0.284428i	−0.917293	−	0.398212i	$-0.869631\pi$
$73$	0.651157	−	2.43015i	0.0762122	−	0.284428i	0.993505	+	0.113785i	$0.0362974\pi$
$74$	3.83477			0.445783
$75$	−0.183820			−0.0212257
$76$	−3.63847	+	13.5789i	−0.417361	+	1.55761i
$77$		0			0
$78$	1.14291	−	0.973780i	0.129409	−	0.110259i
$79$	6.11315	−	10.5883i	0.687783	−	1.19128i	−0.284770	−	0.958596i	$-0.591917\pi$
$79$	6.11315	−	10.5883i	0.687783	−	1.19128i	0.972553	−	0.232680i	$-0.0747493\pi$
$80$	−2.87276	−	10.7213i	−0.321185	−	1.19868i
$81$	−4.37209	+	7.57269i	−0.485788	+	0.841410i
$82$	13.6330	+	23.6130i	1.50551	+	2.60762i
$83$	3.34105	−	3.34105i	0.366728	−	0.366728i	−0.499554	−	0.866283i	$-0.666503\pi$
$83$	3.34105	−	3.34105i	0.366728	−	0.366728i	0.866283	+	0.499554i	$0.166503\pi$
$84$		0			0
$85$	−0.0719809	−	0.268637i	−0.00780743	−	0.0291377i
$86$	4.48558	+	16.7404i	0.483693	+	1.80517i
$87$		−	0.953099i		−	0.102183i
$88$	−20.2637	−	11.6992i	−2.16011	−	1.24714i
$89$	6.14338	+	6.14338i	0.651197	+	0.651197i	0.953281	−	0.302084i	$-0.0976824\pi$
$89$	6.14338	+	6.14338i	0.651197	+	0.651197i	−0.302084	+	0.953281i	$0.597682\pi$
$90$	18.0822			1.90604
$91$		0			0
$92$	−2.66343			−0.277682
$93$	−0.661264	−	0.661264i	−0.0685699	−	0.0685699i
$94$	12.6547	+	7.30617i	1.30523	+	0.753574i
$95$			8.49797i			0.871873i
$96$	−0.0360444	−	0.134519i	−0.00367876	−	0.0137293i
$97$	−1.04426	−	3.89722i	−0.106028	−	0.395703i	0.892431	−	0.451183i	$-0.148998\pi$
$97$	−1.04426	−	3.89722i	−0.106028	−	0.395703i	−0.998460	+	0.0554799i	$0.982331\pi$
$98$		0			0
$99$	9.57547	−	9.57547i	0.962371	−	0.962371i
$100$	−2.22176	−	3.84820i	−0.222176	−	0.384820i
$101$	−2.26018	+	3.91475i	−0.224897	+	0.389532i	−0.956288	−	0.292425i	$-0.905538\pi$
$101$	−2.26018	+	3.91475i	−0.224897	+	0.389532i	0.731392	+	0.681957i	$0.238871\pi$
$102$	−0.0121482	−	0.0453376i	−0.00120285	−	0.00448910i
$103$	6.72989	−	11.6565i	0.663115	−	1.14855i	−0.316677	−	0.948533i	$-0.602567\pi$
$103$	6.72989	−	11.6565i	0.663115	−	1.14855i	0.979793	−	0.200016i	$-0.0640994\pi$
$104$	17.4430	+	6.20031i	1.71042	+	0.607990i
$105$		0			0
$106$	3.07755	−	11.4856i	0.298919	−	1.11558i
$107$	8.25997			0.798521			0.399261	−	0.916837i	$-0.369267\pi$
$107$	8.25997			0.798521			0.399261	+	0.916837i	$0.369267\pi$
$108$	4.11603			0.396066
$109$	3.48535	−	13.0075i	0.333836	−	1.24589i	−0.571289	−	0.820749i	$-0.693557\pi$
$109$	3.48535	−	13.0075i	0.333836	−	1.24589i	0.905125	−	0.425145i	$-0.139777\pi$
$110$	−26.7870	−	7.17755i	−2.55404	−	0.684353i
$111$	0.253626	−	0.0679589i	0.0240731	−	0.00645037i
$112$		0			0
$113$	1.14314	−	1.97997i	0.107537	−	0.186260i	−0.807235	−	0.590231i	$-0.799037\pi$
$113$	1.14314	−	1.97997i	0.107537	−	0.186260i	0.914772	+	0.403970i	$0.132370\pi$
$114$			1.43420i			0.134325i
$115$	−1.55517	+	0.416707i	−0.145020	+	0.0388581i
$116$	19.9527	−	11.5197i	1.85256	−	1.06958i
$117$	−6.07892	+	8.82231i	−0.561996	+	0.815623i
$118$		−	9.73726i		−	0.896388i
$119$		0			0
$120$	−1.06966	−	1.85270i	−0.0976461	−	0.169128i
$121$	−8.45969	+	4.88420i	−0.769063	+	0.444018i
$122$	−36.5409	−	9.79112i	−3.30826	−	0.886446i
$123$	1.32013	+	1.32013i	0.119032	+	0.119032i
$124$	5.85086	−	21.8357i	0.525423	−	1.96091i
$125$	6.82460	+	6.82460i	0.610411	+	0.610411i
$126$		0			0
$127$	−4.38857	+	2.53374i	−0.389422	+	0.224833i	−0.681910	−	0.731436i	$-0.738850\pi$
$127$	−4.38857	+	2.53374i	−0.389422	+	0.224833i	0.292488	+	0.956269i	$0.405517\pi$
$128$	−13.3080	+	13.3080i	−1.17628	+	1.17628i
$129$	0.593340	+	1.02769i	0.0522406	+	0.0904834i
$130$	21.8710	+	1.74754i	1.91821	+	0.153269i
$131$	4.92213	+	2.84179i	0.430048	+	0.248288i	0.699367	−	0.714763i	$-0.253465\pi$
$131$	4.92213	+	2.84179i	0.430048	+	0.248288i	−0.269319	+	0.963051i	$0.586799\pi$
$132$	−3.03418	−	0.813007i	−0.264092	−	0.0707632i
$133$		0			0
$134$	−13.4396	−	7.75936i	−1.16100	−	0.670306i
$135$	2.40334	−	0.643974i	0.206847	−	0.0554244i
$136$	0.409199	−	0.409199i	0.0350885	−	0.0350885i
$137$	−6.04202	+	6.04202i	−0.516205	+	0.516205i	−0.916421	−	0.400216i	$-0.868935\pi$
$137$	−6.04202	+	6.04202i	−0.516205	+	0.516205i	0.400216	+	0.916421i	$0.368935\pi$
$138$	−0.262465	+	0.0703274i	−0.0223425	+	0.00598666i
$139$	−9.91348	−	5.72355i	−0.840850	−	0.485465i	0.0167030	−	0.999860i	$-0.494683\pi$
$139$	−9.91348	−	5.72355i	−0.840850	−	0.485465i	−0.857553	+	0.514395i	$0.828016\pi$
$140$		0			0
$141$	0.966439	+	0.258957i	0.0813888	+	0.0218081i
$142$	7.88429	+	4.55200i	0.661635	+	0.381995i
$143$	12.5072	−	10.6564i	1.04591	−	0.891133i
$144$	6.68327	+	11.5758i	0.556939	+	0.964647i
$145$	9.84803	−	9.84803i	0.817835	−	0.817835i
$146$	5.37330	−	3.10227i	0.444697	−	0.256746i
$147$		0			0
$148$	4.48817	+	4.48817i	0.368925	+	0.368925i
$149$	−1.97417	+	7.36771i	−0.161730	+	0.603586i	0.836704	+	0.547655i	$0.184479\pi$
$149$	−1.97417	+	7.36771i	−0.161730	+	0.603586i	−0.998435	+	0.0559311i	$0.982187\pi$
$150$	−0.320552	−	0.320552i	−0.0261730	−	0.0261730i
$151$	6.37363	+	1.70781i	0.518679	+	0.138980i	0.508656	−	0.860970i	$-0.330143\pi$
$151$	6.37363	+	1.70781i	0.518679	+	0.138980i	0.0100235	+	0.999950i	$0.496809\pi$
$152$	−15.3135	+	8.84123i	−1.24209	+	0.717119i
$153$	0.167458	+	0.290046i	0.0135382	+	0.0234489i
$154$		0			0
$155$		−	13.6652i		−	1.09762i
$156$	2.47734	+	0.197945i	0.198346	+	0.0158483i
$157$	−8.20626	+	4.73788i	−0.654931	+	0.378124i	−0.790343	−	0.612665i	$-0.790097\pi$
$157$	−8.20626	+	4.73788i	−0.654931	+	0.378124i	0.135412	+	0.990789i	$0.456764\pi$
$158$	29.1246	−	7.80390i	2.31703	−	0.620845i
$159$		−	0.814180i		−	0.0645687i
$160$	1.01751	−	1.76238i	0.0804411	−	0.139328i
$161$		0			0
$162$	−20.8297	+	5.58131i	−1.63654	+	0.438509i
$163$	−17.8485	−	4.78249i	−1.39800	−	0.374594i	−0.520376	−	0.853937i	$-0.674208\pi$
$163$	−17.8485	−	4.78249i	−1.39800	−	0.374594i	−0.877627	+	0.479344i	$0.840875\pi$
$164$	−11.6805	+	43.5922i	−0.912094	+	3.40398i
$165$	−1.89885			−0.147825
$166$	11.6525			0.904409
$167$	4.24807	−	15.8540i	0.328725	−	1.22682i	−0.581788	−	0.813341i	$-0.697647\pi$
$167$	4.24807	−	15.8540i	0.328725	−	1.22682i	0.910513	−	0.413480i	$-0.135687\pi$
$168$		0			0
$169$	−8.20525	+	10.0833i	−0.631173	+	0.775642i
$170$	0.342935	−	0.593981i	0.0263019	−	0.0455563i
$171$	−2.64866	−	9.88495i	−0.202548	−	0.755921i
$172$	−14.3429	+	24.8426i	−1.09364	+	1.89423i
$173$	−9.11872	−	15.7941i	−0.693283	−	1.20080i	−0.970756	−	0.240068i	$-0.922830\pi$
$173$	−9.11872	−	15.7941i	−0.693283	−	1.20080i	0.277473	−	0.960733i	$-0.410503\pi$
$174$	1.66205	−	1.66205i	0.125999	−	0.125999i
$175$		0			0
$176$	−5.30571	−	19.8012i	−0.399933	−	1.49257i
$177$	−0.172561	−	0.644008i	−0.0129705	−	0.0484066i
$178$			21.4261i			1.60595i
$179$	−20.4226	−	11.7910i	−1.52645	−	0.881299i	−0.999507	−	0.0314008i	$-0.990003\pi$
$179$	−20.4226	−	11.7910i	−1.52645	−	0.881299i	−0.526947	−	0.849898i	$-0.676663\pi$
$180$	21.1632	+	21.1632i	1.57741	+	1.57741i
$181$	−4.65138			−0.345735			−0.172867	−	0.984945i	$-0.555303\pi$
$181$	−4.65138			−0.345735			−0.172867	+	0.984945i	$0.555303\pi$
$182$		0			0
$183$	−2.59028			−0.191479
$184$	−2.36890	−	2.36890i	−0.174638	−	0.174638i
$185$	3.32282	+	1.91843i	0.244299	+	0.141046i
$186$		−	2.30627i		−	0.169104i
$187$	−0.132942	−	0.496145i	−0.00972165	−	0.0362817i
$188$	6.25980	+	23.3619i	0.456543	+	1.70384i
$189$		0			0
$190$	−14.8191	+	14.8191i	−1.07509	+	1.07509i
$191$	−3.84978	−	6.66801i	−0.278560	−	0.482480i	0.692467	−	0.721450i	$-0.256524\pi$
$191$	−3.84978	−	6.66801i	−0.278560	−	0.482480i	−0.971027	+	0.238969i	$0.923190\pi$
$192$	−0.587862	+	1.01821i	−0.0424253	+	0.0734827i
$193$	0.0645055	+	0.240738i	0.00464321	+	0.0173287i	0.968209	−	0.250144i	$-0.0804781\pi$
$193$	0.0645055	+	0.240738i	0.00464321	+	0.0173287i	−0.963565	+	0.267473i	$0.913811\pi$
$194$	4.97510	−	8.61713i	0.357192	−	0.618674i
$195$	1.47748	−	0.272013i	0.105805	−	0.0194792i
$196$		0			0
$197$	−1.72653	+	6.44350i	−0.123010	+	0.459081i	−0.999761	−	0.0218645i	$-0.993040\pi$
$197$	−1.72653	+	6.44350i	−0.123010	+	0.459081i	0.876751	+	0.480945i	$0.159706\pi$
$198$	33.3961			2.37336
$199$	5.38835			0.381970			0.190985	−	0.981593i	$-0.438832\pi$
$199$	5.38835			0.381970			0.190985	+	0.981593i	$0.438832\pi$
$200$	1.44658	−	5.39873i	0.102289	−	0.381748i
$201$	−1.02639	−	0.275019i	−0.0723956	−	0.0193984i
$202$	−10.7681	+	2.88530i	−0.757639	+	0.203009i
$203$		0			0
$204$	0.0388445	−	0.0672807i	0.00271966	−	0.00471059i
$205$			27.2809i			1.90538i
$206$	32.0628	−	8.59121i	2.23392	−	0.598578i
$207$	1.67912	−	0.969438i	0.116707	−	0.0673806i
$208$	6.96488	+	14.6471i	0.482928	+	1.01560i
$209$			15.6949i			1.08564i
$210$		0			0
$211$	−1.44964	−	2.51085i	−0.0997974	−	0.172854i	0.811803	−	0.583931i	$-0.198486\pi$
$211$	−1.44964	−	2.51085i	−0.0997974	−	0.172854i	−0.911601	+	0.411077i	$0.865153\pi$
$212$	17.0445	−	9.84066i	1.17062	−	0.675859i
$213$	0.602125	+	0.161339i	0.0412569	+	0.0110548i
$214$	14.4040	+	14.4040i	0.984639	+	0.984639i
$215$	−4.48804	+	16.7496i	−0.306081	+	1.14231i
$216$	3.66087	+	3.66087i	0.249091	+	0.249091i
$217$		0			0
$218$	28.7608	−	16.6051i	1.94793	−	1.12464i
$219$	0.300404	−	0.300404i	0.0202994	−	0.0202994i
$220$	−22.9506	−	39.7517i	−1.54733	−	2.68006i
$221$	0.174514	+	0.367003i	0.0117391	+	0.0246873i
$222$	0.560791	+	0.323773i	0.0376379	+	0.0217302i
$223$	18.1024	+	4.85053i	1.21223	+	0.324816i	0.807636	−	0.589681i	$-0.200747\pi$
$223$	18.1024	+	4.85053i	1.21223	+	0.324816i	0.404593	+	0.914497i	$0.367413\pi$
$224$		0			0
$225$	2.80134	+	1.61735i	0.186756	+	0.107824i
$226$	5.44619	−	1.45930i	0.362275	−	0.0970714i
$227$	−4.51374	+	4.51374i	−0.299587	+	0.299587i	−0.840852	−	0.541265i	$-0.817946\pi$
$227$	−4.51374	+	4.51374i	−0.299587	+	0.299587i	0.541265	+	0.840852i	$0.317946\pi$
$228$	−1.67857	+	1.67857i	−0.111166	+	0.111166i
$229$	−16.7169	+	4.47928i	−1.10468	+	0.295999i	−0.764671	−	0.644421i	$-0.777098\pi$
$229$	−16.7169	+	4.47928i	−1.10468	+	0.295999i	−0.340014	+	0.940420i	$0.610432\pi$
$230$	−3.43863	−	1.98529i	−0.226737	−	0.130906i
$231$		0			0
$232$	27.9921	+	7.50047i	1.83777	+	0.492430i
$233$	1.08707	+	0.627620i	0.0712163	+	0.0411167i	0.535185	−	0.844735i	$-0.320242\pi$
$233$	1.08707	+	0.627620i	0.0712163	+	0.0411167i	−0.463969	+	0.885851i	$0.653575\pi$
$234$	−25.9853	+	4.78403i	−1.69871	+	0.312742i
$235$	7.31017	+	12.6616i	0.476863	+	0.825950i
$236$	11.3964	−	11.3964i	0.741840	−	0.741840i
$237$	1.78796	−	1.03228i	0.116140	−	0.0670536i
$238$		0			0
$239$	−8.59429	−	8.59429i	−0.555918	−	0.555918i	0.372225	−	0.928143i	$-0.378595\pi$
$239$	−8.59429	−	8.59429i	−0.555918	−	0.555918i	−0.928143	+	0.372225i	$0.878595\pi$
$240$	0.485100	−	1.81042i	0.0313131	−	0.116862i
$241$	1.71820	+	1.71820i	0.110679	+	0.110679i	0.760277	−	0.649599i	$-0.225063\pi$
$241$	1.71820	+	1.71820i	0.110679	+	0.110679i	−0.649599	+	0.760277i	$0.725063\pi$
$242$	−23.2696	−	6.23506i	−1.49582	−	0.400805i
$243$	−3.89852	+	2.25081i	−0.250090	+	0.144390i
$244$	−31.3077	−	54.2264i	−2.00427	−	3.47149i
$245$		0			0
$246$			4.60418i			0.293552i
$247$	−2.24831	−	12.2121i	−0.143057	−	0.777037i
$248$	24.6249	−	14.2172i	1.56368	−	0.902794i
$249$	0.770679	−	0.206503i	0.0488398	−	0.0130866i
$250$			23.8020i			1.50537i
$251$	−7.94802	+	13.7664i	−0.501675	+	0.868926i	0.498323	+	0.866991i	$0.333949\pi$
$251$	−7.94802	+	13.7664i	−0.501675	+	0.868926i	−0.999998	+	0.00193499i	$0.999384\pi$
$252$		0			0
$253$	−2.87225	+	0.769616i	−0.180577	+	0.0483853i
$254$	−12.0714	−	3.23451i	−0.757425	−	0.202951i
$255$	0.0121548	−	0.0453624i	0.000761165	−	0.00284071i
$256$	−32.4888			−2.03055
$257$	−14.1941			−0.885401			−0.442701	−	0.896670i	$-0.645980\pi$
$257$	−14.1941			−0.885401			−0.442701	+	0.896670i	$0.645980\pi$
$258$	−0.757443	+	2.82682i	−0.0471564	+	0.175990i
$259$		0			0
$260$	23.5522	+	27.6428i	1.46065	+	1.71434i
$261$	−8.38591	+	14.5248i	−0.519075	+	0.899064i
$262$	3.62776	+	13.5390i	0.224124	+	0.836442i
$263$	9.46835	−	16.3997i	0.583843	−	1.01125i	−0.411175	−	0.911556i	$-0.634882\pi$
$263$	9.46835	−	16.3997i	0.583843	−	1.01125i	0.995019	−	0.0996901i	$-0.0317851\pi$
$264$	−1.97555	−	3.42176i	−0.121587	−	0.210595i
$265$	8.41264	−	8.41264i	0.516784	−	0.516784i
$266$		0			0
$267$	0.379708	+	1.41709i	0.0232378	+	0.0867245i
$268$	−6.64809	−	24.8110i	−0.406096	−	1.51557i
$269$		−	24.2202i		−	1.47673i	−0.674400	−	0.738366i	$-0.735598\pi$
$269$		−	24.2202i		−	1.47673i	0.674400	−	0.738366i	$-0.264402\pi$
$270$	5.31402	+	3.06805i	0.323401	+	0.186716i
$271$	−11.1386	−	11.1386i	−0.676624	−	0.676624i	0.282610	−	0.959235i	$-0.408800\pi$
$271$	−11.1386	−	11.1386i	−0.676624	−	0.676624i	−0.959235	+	0.282610i	$0.908800\pi$
$272$	0.507001			0.0307414
$273$		0			0
$274$	−21.0726			−1.27304
$275$	−3.50791	−	3.50791i	−0.211535	−	0.211535i
$276$	−0.389496	−	0.224876i	−0.0234449	−	0.0135359i
$277$			0.746768i			0.0448689i	0.999748	+	0.0224345i	$0.00714171\pi$
$277$			0.746768i			0.0448689i	−0.999748	+	0.0224345i	$0.992858\pi$
$278$	−7.30655	−	27.2684i	−0.438218	−	1.63545i
$279$	4.25920	+	15.8956i	0.254992	+	0.951643i
$280$		0			0
$281$	−0.536856	+	0.536856i	−0.0320261	+	0.0320261i	−0.722939	−	0.690912i	$-0.757209\pi$
$281$	−0.536856	+	0.536856i	−0.0320261	+	0.0320261i	0.690912	+	0.722939i	$0.257209\pi$
$282$	1.23373	+	2.13689i	0.0734677	+	0.127250i
$283$	−9.63432	+	16.6871i	−0.572701	+	0.991947i	0.423587	+	0.905856i	$0.360771\pi$
$283$	−9.63432	+	16.6871i	−0.572701	+	0.991947i	−0.996287	+	0.0860911i	$0.972562\pi$
$284$	3.90007	+	14.5553i	0.231427	+	0.863696i
$285$	−0.717491	+	1.24273i	−0.0425005	+	0.0736130i
$286$	40.3935	+	3.22753i	2.38852	+	0.190848i
$287$		0			0
$288$	−0.634278	+	2.36716i	−0.0373752	+	0.139486i
$289$	−16.9873			−0.999253
$290$	34.3467			2.01691
$291$	0.176335	−	0.658092i	0.0103370	−	0.0385780i
$292$	9.91970	+	2.65798i	0.580507	+	0.155546i
$293$	−14.0543	+	3.76584i	−0.821062	+	0.220003i	−0.644811	−	0.764342i	$-0.723064\pi$
$293$	−14.0543	+	3.76584i	−0.821062	+	0.220003i	−0.176251	+	0.984345i	$0.556397\pi$
$294$		0			0
$295$	4.87129	−	8.43733i	0.283618	−	0.491240i
$296$			7.98371i			0.464044i
$297$	4.43873	−	1.18936i	0.257562	−	0.0690134i
$298$	−16.2907	+	9.40544i	−0.943695	+	0.544843i
$299$	2.12463	−	1.01029i	0.122870	−	0.0584263i
$300$		−	0.750340i		−	0.0433209i
$301$		0			0
$302$	8.13643	+	14.0927i	0.468199	+	0.810944i
$303$	−0.661052	+	0.381659i	−0.0379764	+	0.0219257i
$304$	−14.9639	−	4.00958i	−0.858241	−	0.229965i
$305$	−26.7645	−	26.7645i	−1.53253	−	1.53253i
$306$	−0.213773	+	0.797813i	−0.0122206	+	0.0456079i
$307$	−9.47209	−	9.47209i	−0.540601	−	0.540601i	0.383104	−	0.923705i	$-0.374855\pi$
$307$	−9.47209	−	9.47209i	−0.540601	−	0.540601i	−0.923705	+	0.383104i	$0.874855\pi$
$308$		0			0
$309$	1.96834	−	1.13642i	0.111975	−	0.0646487i
$310$	23.8299	−	23.8299i	1.35345	−	1.35345i
$311$	4.14087	+	7.17220i	0.234807	+	0.406698i	0.959217	−	0.282672i	$-0.0912207\pi$
$311$	4.14087	+	7.17220i	0.234807	+	0.406698i	−0.724409	+	0.689370i	$0.757887\pi$
$312$	2.02734	+	2.37945i	0.114775	+	0.134710i
$313$	4.98156	+	2.87611i	0.281574	+	0.162567i	0.634136	−	0.773222i	$-0.281356\pi$
$313$	4.98156	+	2.87611i	0.281574	+	0.162567i	−0.352562	+	0.935789i	$0.614689\pi$
$314$	−22.5725	−	6.04827i	−1.27384	−	0.341324i
$315$		0			0
$316$	43.2206	+	24.9534i	2.43135	+	1.40374i
$317$	9.94515	−	2.66479i	0.558575	−	0.149670i	0.0315235	−	0.999503i	$-0.489964\pi$
$317$	9.94515	−	2.66479i	0.558575	−	0.149670i	0.527052	+	0.849833i	$0.323297\pi$
$318$	1.41980	−	1.41980i	0.0796182	−	0.0796182i
$319$	18.1883	−	18.1883i	1.01835	−	1.01835i
$320$	−16.5949	+	4.44660i	−0.927685	+	0.248573i
$321$	1.20793	+	0.697397i	0.0674199	+	0.0389249i
$322$		0			0
$323$	−0.374942	−	0.100465i	−0.0208623	−	0.00559004i
$324$	−30.9111	−	17.8466i	−1.71729	−	0.991475i
$325$	3.23199	+	2.22697i	0.179279	+	0.123530i
$326$	−22.7850	−	39.4647i	−1.26194	−	2.18575i
$327$	1.60793	−	1.60793i	0.0889186	−	0.0889186i
$328$	−49.1605	+	28.3829i	−2.71444	+	1.56718i
$329$		0			0
$330$	−3.31129	−	3.31129i	−0.182280	−	0.182280i
$331$	−4.48552	+	16.7402i	−0.246547	+	0.920125i	0.726053	+	0.687639i	$0.241353\pi$
$331$	−4.48552	+	16.7402i	−0.246547	+	0.920125i	−0.972600	+	0.232486i	$0.925314\pi$
$332$	13.6379	+	13.6379i	0.748479	+	0.748479i
$333$	−4.46309	−	1.19588i	−0.244576	−	0.0655340i
$334$	35.0547	−	20.2389i	1.91811	−	1.10742i
$335$	−7.76360	−	13.4470i	−0.424171	−	0.734686i
$336$		0			0
$337$			12.1069i			0.659506i	0.944067	+	0.329753i	$0.106965\pi$
$337$			12.1069i			0.659506i	−0.944067	+	0.329753i	$0.893035\pi$
$338$	−31.8923	+	3.27510i	−1.73471	+	0.178142i
$339$	0.334342	−	0.193032i	0.0181589	−	0.0104841i
$340$	1.09655	−	0.293821i	0.0594690	−	0.0159347i
$341$		−	25.2383i		−	1.36673i
$342$	12.6189	−	21.8566i	0.682351	−	1.18187i
$343$		0			0
$344$	−34.8523	+	9.33865i	−1.87911	+	0.503506i
$345$	−0.262609	−	0.0703659i	−0.0141384	−	0.00378837i
$346$	11.6407	−	43.4438i	0.625810	−	2.33555i
$347$	−2.86789			−0.153957			−0.0769783	−	0.997033i	$-0.524527\pi$
$347$	−2.86789			−0.153957			−0.0769783	+	0.997033i	$0.524527\pi$
$348$	3.89048			0.208552
$349$	−3.12009	+	11.6443i	−0.167014	+	0.623306i	0.830760	+	0.556630i	$0.187906\pi$
$349$	−3.12009	+	11.6443i	−0.167014	+	0.623306i	−0.997775	+	0.0666760i	$0.978761\pi$
$350$		0			0
$351$	−3.28338	+	1.56128i	−0.175254	+	0.0833352i
$352$	1.87924	−	3.25493i	0.100164	−	0.173488i
$353$	−7.89564	−	29.4669i	−0.420242	−	1.56837i	−0.774098	−	0.633066i	$-0.781796\pi$
$353$	−7.89564	−	29.4669i	−0.420242	−	1.56837i	0.353856	−	0.935300i	$-0.384870\pi$
$354$	0.822126	−	1.42396i	0.0436955	−	0.0756828i
$355$	4.55449	+	7.88860i	0.241727	+	0.418683i
$356$	−25.0768	+	25.0768i	−1.32907	+	1.32907i
$357$		0			0
$358$	−15.0521	−	56.1751i	−0.795527	−	2.96895i
$359$	−4.63302	−	17.2907i	−0.244521	−	0.912566i	−0.973623	−	0.228161i	$-0.926729\pi$
$359$	−4.63302	−	17.2907i	−0.244521	−	0.912566i	0.729102	−	0.684405i	$-0.239938\pi$
$360$			37.6459i			1.98411i
$361$	−6.18273	−	3.56960i	−0.325407	−	0.187874i
$362$	−8.11125	−	8.11125i	−0.426318	−	0.426318i
$363$	−1.64951			−0.0865769
$364$		0			0
$365$	6.20794			0.324939
$366$	−4.51702	−	4.51702i	−0.236109	−	0.236109i
$367$	6.26259	+	3.61571i	0.326905	+	0.188738i	0.654466	−	0.756091i	$-0.272893\pi$
$367$	6.26259	+	3.61571i	0.326905	+	0.188738i	−0.327561	+	0.944830i	$0.606227\pi$
$368$		−	2.93509i		−	0.153002i
$369$	−8.50296	−	31.7335i	−0.442646	−	1.65198i
$370$	2.44903	+	9.13989i	0.127319	+	0.475160i
$371$		0			0
$372$	2.69923	−	2.69923i	0.139949	−	0.139949i
$373$	12.2087	+	21.1462i	0.632145	+	1.09491i	0.987112	+	0.160029i	$0.0511586\pi$
$373$	12.2087	+	21.1462i	0.632145	+	1.09491i	−0.354967	+	0.934879i	$0.615508\pi$
$374$	0.633367	−	1.09702i	0.0327506	−	0.0567257i
$375$	0.421813	+	1.57423i	0.0217823	+	0.0812927i
$376$	−15.2109	+	26.3461i	−0.784443	+	1.35869i
$377$	−11.5467	+	16.7577i	−0.594687	+	0.863067i
$378$		0			0
$379$	−2.27080	+	8.47475i	−0.116643	+	0.435319i	−0.999405	−	0.0345031i	$-0.989015\pi$
$379$	−2.27080	+	8.47475i	−0.116643	+	0.435319i	0.882761	+	0.469822i	$0.155682\pi$
$380$	−34.6881			−1.77946
$381$	−0.855704			−0.0438390
$382$	4.91454	−	18.3413i	0.251449	−	0.938422i
$383$	16.9913	+	4.55280i	0.868213	+	0.232637i	0.665315	−	0.746563i	$-0.268297\pi$
$383$	16.9913	+	4.55280i	0.868213	+	0.232637i	0.202898	+	0.979200i	$0.434964\pi$
$384$	−3.06976	+	0.822539i	−0.156653	+	0.0419750i
$385$		0			0
$386$	−0.307320	+	0.532294i	−0.0156422	+	0.0270931i
$387$		−	20.8822i		−	1.06150i
$388$	15.9082	−	4.26258i	0.807615	−	0.216400i
$389$	8.77740	−	5.06764i	0.445032	−	0.256939i	−0.260698	−	0.965420i	$-0.583953\pi$
$389$	8.77740	−	5.06764i	0.445032	−	0.256939i	0.705730	+	0.708481i	$0.250619\pi$
$390$	3.05084	+	2.10215i	0.154485	+	0.106446i
$391$		−	0.0735427i		−	0.00371921i
$392$		0			0
$393$	0.479870	+	0.831159i	0.0242062	+	0.0419264i
$394$	−14.2472	+	8.22563i	−0.717764	+	0.414401i
$395$	29.1405	+	7.80817i	1.46622	+	0.392872i
$396$	39.0864	+	39.0864i	1.96416	+	1.96416i
$397$	−2.18723	+	8.16286i	−0.109774	+	0.409682i	−0.998843	−	0.0480910i	$-0.984686\pi$
$397$	−2.18723	+	8.16286i	−0.109774	+	0.409682i	0.889069	+	0.457773i	$0.151353\pi$
$398$	9.39641	+	9.39641i	0.470999	+	0.470999i
$399$		0			0
$400$	4.24070	−	2.44837i	0.212035	−	0.122419i
$401$	6.65097	−	6.65097i	0.332134	−	0.332134i	−0.521263	−	0.853396i	$-0.674539\pi$
$401$	6.65097	−	6.65097i	0.332134	−	0.332134i	0.853396	+	0.521263i	$0.174539\pi$
$402$	−1.31026	−	2.26944i	−0.0653498	−	0.113189i
$403$	3.61542	+	19.6378i	0.180097	+	0.978227i
$404$	−15.9797	−	9.22590i	−0.795021	−	0.459006i
$405$	−20.8411	−	5.58436i	−1.03560	−	0.277489i
$406$		0			0
$407$	6.13693	+	3.54316i	0.304196	+	0.175628i
$408$	0.0943896	−	0.0252916i	0.00467298	−	0.00125212i
$409$	−17.9666	+	17.9666i	−0.888390	+	0.888390i	−0.994368	−	0.105979i	$-0.966203\pi$
$409$	−17.9666	+	17.9666i	−0.888390	+	0.888390i	0.105979	+	0.994368i	$0.466203\pi$
$410$	−47.5734	+	47.5734i	−2.34948	+	2.34948i
$411$	−1.39371	+	0.373444i	−0.0687467	+	0.0184206i
$412$	47.5810	+	27.4709i	2.34415	+	1.35339i
$413$		0			0
$414$	4.61864	+	1.23756i	0.226994	+	0.0608228i
$415$	10.0969	+	5.82944i	0.495636	+	0.286156i
$416$	−0.995948	+	2.80184i	−0.0488304	+	0.137372i
$417$	−0.966489	−	1.67401i	−0.0473292	−	0.0819765i
$418$	−27.3693	+	27.3693i	−1.33868	+	1.33868i
$419$	17.4075	−	10.0503i	0.850414	−	0.490987i	−0.0103762	−	0.999946i	$-0.503303\pi$
$419$	17.4075	−	10.0503i	0.850414	−	0.490987i	0.860791	+	0.508959i	$0.169970\pi$
$420$		0			0
$421$	−2.51951	−	2.51951i	−0.122793	−	0.122793i	0.643040	−	0.765833i	$-0.277673\pi$
$421$	−2.51951	−	2.51951i	−0.122793	−	0.122793i	−0.765833	+	0.643040i	$0.777673\pi$
$422$	1.85058	−	6.90645i	0.0900847	−	0.336201i
$423$	−12.4497	−	12.4497i	−0.605324	−	0.605324i
$424$	23.9122	+	6.40724i	1.16128	+	0.311163i
$425$	0.106256	−	0.0613472i	0.00515419	−	0.00297578i
$426$	0.768658	+	1.33135i	0.0372416	+	0.0645044i
$427$		0			0
$428$			33.7166i			1.62975i
$429$	2.72877	−	0.502381i	0.131746	−	0.0242552i
$430$	−37.0349	+	21.3821i	−1.78598	+	1.03114i
$431$	23.1558	−	6.20458i	1.11538	−	0.298864i	0.346365	−	0.938100i	$-0.387416\pi$
$431$	23.1558	−	6.20458i	1.11538	−	0.298864i	0.769011	+	0.639236i	$0.220749\pi$
$432$			4.53586i			0.218232i
$433$	11.7141	−	20.2893i	0.562941	−	0.975043i	−0.434296	−	0.900770i	$-0.643003\pi$
$433$	11.7141	−	20.2893i	0.562941	−	0.975043i	0.997238	−	0.0742732i	$-0.0236637\pi$
$434$		0			0
$435$	2.27164	−	0.608684i	0.108917	−	0.0291842i
$436$	53.0957	+	14.2269i	2.54282	+	0.681347i
$437$	−0.581607	+	2.17059i	−0.0278220	+	0.103833i
$438$	1.04771			0.0500616
$439$	33.7642			1.61148			0.805738	−	0.592272i	$-0.201769\pi$
$439$	33.7642			1.61148			0.805738	+	0.592272i	$0.201769\pi$
$440$	14.9431	−	55.7686i	0.712386	−	2.65866i
$441$		0			0
$442$	−0.335669	+	0.944318i	−0.0159661	+	0.0449166i
$443$	−15.5134	+	26.8699i	−0.737062	+	1.27663i	0.216750	+	0.976227i	$0.430454\pi$
$443$	−15.5134	+	26.8699i	−0.737062	+	1.27663i	−0.953813	+	0.300402i	$0.902879\pi$
$444$	0.277403	+	1.03528i	0.0131650	+	0.0491324i
$445$	−10.7189	+	18.5657i	−0.508125	+	0.880098i
$446$	23.1091	+	40.0262i	1.09425	+	1.89530i
$447$	−0.910762	+	0.910762i	−0.0430776	+	0.0430776i
$448$		0			0
$449$	−0.388197	−	1.44877i	−0.0183202	−	0.0683718i	0.956161	−	0.292843i	$-0.0946013\pi$
$449$	−0.388197	−	1.44877i	−0.0183202	−	0.0683718i	−0.974481	+	0.224471i	$0.927935\pi$
$450$	2.06468	+	7.70548i	0.0973298	+	0.363240i
$451$			50.3851i			2.37254i
$452$	8.08210	+	4.66620i	0.380150	+	0.219480i
$453$	0.787880	+	0.787880i	0.0370178	+	0.0370178i
$454$	−15.7424			−0.738829
$455$		0			0
$456$	−2.98589			−0.139827
$457$	21.6961	+	21.6961i	1.01490	+	1.01490i	0.999887	+	0.0150158i	$0.00477986\pi$
$457$	21.6961	+	21.6961i	1.01490	+	1.01490i	0.0150158	+	0.999887i	$0.495220\pi$
$458$	−36.9627	−	21.3404i	−1.72715	−	0.997172i
$459$			0.113652i			0.00530482i
$460$	−1.70097	−	6.34809i	−0.0793080	−	0.295981i
$461$	−6.69670	−	24.9924i	−0.311896	−	1.16401i	−0.926845	−	0.375445i	$-0.877490\pi$
$461$	−6.69670	−	24.9924i	−0.311896	−	1.16401i	0.614948	−	0.788568i	$-0.289177\pi$
$462$		0			0
$463$	−26.5381	+	26.5381i	−1.23333	+	1.23333i	−0.270652	+	0.962677i	$0.587239\pi$
$463$	−26.5381	+	26.5381i	−1.23333	+	1.23333i	−0.962677	+	0.270652i	$0.912761\pi$
$464$	12.6947	+	21.9878i	0.589336	+	1.02076i
$465$	1.15377	−	1.99838i	0.0535047	−	0.0926728i
$466$	0.801205	+	2.99014i	0.0371151	+	0.138515i
$467$	−4.11119	+	7.12080i	−0.190243	+	0.329511i	−0.945331	−	0.326113i	$-0.894261\pi$
$467$	−4.11119	+	7.12080i	−0.190243	+	0.329511i	0.755087	+	0.655624i	$0.227594\pi$
$468$	−36.0120	−	24.8137i	−1.66466	−	1.14701i
$469$		0			0
$470$	−9.33199	+	34.8274i	−0.430452	+	1.60647i
$471$	−1.60010			−0.0737285
$472$	20.2723			0.933106
$473$	−8.28895	+	30.9348i	−0.381127	+	1.42238i
$474$	4.91803	+	1.31778i	0.225892	+	0.0605277i
$475$	−3.62128	+	0.970319i	−0.166156	+	0.0445213i
$476$		0			0
$477$	−7.16362	+	12.4078i	−0.328000	+	0.568112i
$478$		−	29.9740i		−	1.37098i
$479$	−20.9972	+	5.62619i	−0.959388	+	0.257067i	−0.704342	−	0.709861i	$-0.748758\pi$
$479$	−20.9972	+	5.62619i	−0.959388	+	0.257067i	−0.255047	+	0.966929i	$0.582091\pi$
$480$	0.297598	−	0.171818i	0.0135834	−	0.00784239i
$481$	−5.28267	−	1.87779i	−0.240869	−	0.0856196i
$482$			5.99250i			0.272951i
$483$		0			0
$484$	−19.9370	−	34.5318i	−0.906225	−	1.56963i
$485$	8.62185	−	4.97782i	0.391498	−	0.226031i
$486$	−10.7234	−	2.87333i	−0.486425	−	0.130337i
$487$	12.7599	+	12.7599i	0.578206	+	0.578206i	0.934409	−	0.356202i	$-0.115929\pi$
$487$	12.7599	+	12.7599i	0.578206	+	0.578206i	−0.356202	+	0.934409i	$0.615929\pi$
$488$	20.3844	−	76.0755i	0.922758	−	3.44378i
$489$	−2.20635	−	2.20635i	−0.0997746	−	0.0997746i
$490$		0			0
$491$	5.63350	−	3.25250i	0.254236	−	0.146783i	−0.367466	−	0.930037i	$-0.619775\pi$
$491$	5.63350	−	3.25250i	0.254236	−	0.146783i	0.621703	+	0.783253i	$0.286441\pi$
$492$	−5.38867	+	5.38867i	−0.242940	+	0.242940i
$493$	0.318082	+	0.550935i	0.0143257	+	0.0248129i
$494$	17.3752	−	25.2166i	0.781748	−	1.13455i
$495$	28.9377	+	16.7072i	1.30065	+	0.750932i
$496$	24.0629	+	6.44763i	1.08046	+	0.289507i
$497$		0			0
$498$	1.70405	+	0.983831i	0.0763601	+	0.0440865i
$499$	19.4522	−	5.21221i	0.870802	−	0.233331i	0.204367	−	0.978894i	$-0.434486\pi$
$499$	19.4522	−	5.21221i	0.870802	−	0.233331i	0.666434	+	0.745564i	$0.267820\pi$
$500$	−27.8575	+	27.8575i	−1.24583	+	1.24583i
$501$	1.95980	−	1.95980i	0.0875574	−	0.0875574i
$502$	−37.8664	+	10.1463i	−1.69006	+	0.452850i
$503$	17.1138	+	9.88067i	0.763068	+	0.440557i	0.830396	−	0.557173i	$-0.188114\pi$
$503$	17.1138	+	9.88067i	0.763068	+	0.440557i	−0.0673282	+	0.997731i	$0.521447\pi$
$504$		0			0
$505$	−10.7740	−	2.88687i	−0.479435	−	0.128464i
$506$	−6.35081	−	3.66664i	−0.282328	−	0.163002i
$507$	−2.05127	+	0.781798i	−0.0911001	+	0.0347209i
$508$	−10.3425	−	17.9138i	−0.458876	−	0.794796i
$509$	−21.0947	+	21.0947i	−0.935004	+	0.935004i	−0.998013	−	0.0630085i	$-0.979930\pi$
$509$	−21.0947	+	21.0947i	−0.935004	+	0.935004i	0.0630085	+	0.998013i	$0.479930\pi$
$510$	0.100301	−	0.0579086i	0.00444139	−	0.00256424i
$511$		0			0
$512$	−30.0390	−	30.0390i	−1.32755	−	1.32755i
$513$	0.898808	−	3.35440i	0.0396833	−	0.148100i
$514$	−24.7521	−	24.7521i	−1.09177	−	1.09177i
$515$	32.0804	+	8.59591i	1.41363	+	0.378781i
$516$	−4.19497	+	2.42197i	−0.184673	+	0.106621i
$517$	13.5012	+	23.3847i	0.593780	+	1.02846i
$518$		0			0
$519$		−	3.07961i		−	0.135180i
$520$	−3.63825	+	45.5338i	−0.159548	+	1.99679i
$521$	−6.67564	+	3.85418i	−0.292465	+	0.168855i	−0.639053	−	0.769163i	$-0.720674\pi$
$521$	−6.67564	+	3.85418i	−0.292465	+	0.168855i	0.346588	+	0.938018i	$0.387340\pi$
$522$	−39.9525	+	10.7053i	−1.74868	+	0.468556i
$523$		−	0.0152739i		−	0.000667882i	−1.00000		0.000333941i	$-0.999894\pi$
$523$		−	0.0152739i		−	0.000667882i	1.00000		0.000333941i	$-0.000106297\pi$
$524$	−11.6000	+	20.0918i	−0.506748	+	0.877713i
$525$		0			0
$526$	45.1096	−	12.0871i	1.96687	−	0.527021i
$527$	0.602928	+	0.161554i	0.0262640	+	0.00703741i
$528$	0.895931	−	3.34366i	0.0389904	−	0.145514i
$529$	22.5743			0.981489
$530$	29.3405			1.27447
$531$	−3.03659	+	11.3327i	−0.131777	+	0.491798i
$532$		0			0
$533$	−7.21772	−	39.2043i	−0.312634	−	1.69813i
$534$	−1.80902	+	3.13332i	−0.0782841	+	0.135592i
$535$	5.27513	+	19.6870i	0.228064	+	0.851145i
$536$	16.1544	−	27.9803i	0.697764	−	1.20856i
$537$	−1.99105	−	3.44859i	−0.0859199	−	0.148818i
$538$	42.2361	−	42.2361i	1.82093	−	1.82093i
$539$		0			0
$540$	2.62865	+	9.81027i	0.113119	+	0.422167i
$541$	−12.0108	−	44.8251i	−0.516386	−	1.92718i	−0.325325	−	0.945602i	$-0.605474\pi$
$541$	−12.0108	−	44.8251i	−0.516386	−	1.92718i	−0.191061	−	0.981578i	$-0.561193\pi$
$542$		−	38.8479i		−	1.66866i
$543$	−0.680212	−	0.392720i	−0.0291907	−	0.0168532i
$544$	0.0657291	+	0.0657291i	0.00281811	+	0.00281811i
$545$	33.2283			1.42334
$546$		0			0
$547$	22.9225			0.980097			0.490049	−	0.871695i	$-0.336979\pi$
$547$	22.9225			0.980097			0.490049	+	0.871695i	$0.336979\pi$
$548$	−24.6631	−	24.6631i	−1.05355	−	1.05355i
$549$	39.4748	+	22.7908i	1.68474	+	0.972686i
$550$		−	12.2344i		−	0.521678i
$551$	−5.03106	−	18.7762i	−0.214330	−	0.799892i
$552$	−0.146416	−	0.546434i	−0.00623190	−	0.0232578i
$553$		0			0
$554$	−1.30224	+	1.30224i	−0.0553269	+	0.0553269i
$555$	0.323950	+	0.561098i	0.0137509	+	0.0238173i
$556$	23.3631	−	40.4661i	0.990816	−	1.71614i
$557$	−4.20224	−	15.6830i	−0.178055	−	0.664509i	−0.996011	−	0.0892288i	$-0.971560\pi$
$557$	−4.20224	−	15.6830i	−0.178055	−	0.664509i	0.817957	−	0.575280i	$-0.195107\pi$
$558$	−20.2919	+	35.1466i	−0.859025	+	1.48787i
$559$	2.01814	−	25.2576i	0.0853581	−	1.06828i
$560$		0			0
$561$	0.0224488	−	0.0837799i	0.000947788	−	0.00353719i
$562$	−1.87238			−0.0789814
$563$	−10.5234			−0.443507			−0.221753	−	0.975103i	$-0.571178\pi$
$563$	−10.5234			−0.443507			−0.221753	+	0.975103i	$0.571178\pi$
$564$	−1.05704	+	3.94493i	−0.0445095	+	0.166112i
$565$	5.44917	+	1.46010i	0.229248	+	0.0614269i
$566$	−45.9003	+	12.2989i	−1.92933	+	0.516963i
$567$		0			0
$568$	−9.47692	+	16.4145i	−0.397643	+	0.688737i
$569$			35.6613i			1.49500i	0.664262	+	0.747500i	$0.268746\pi$
$569$			35.6613i			1.49500i	−0.664262	+	0.747500i	$0.731254\pi$
$570$	−3.41830	+	0.915932i	−0.143177	+	0.0383642i
$571$	9.54352	−	5.50995i	0.399384	−	0.230584i	−0.286834	−	0.957980i	$-0.592603\pi$
$571$	9.54352	−	5.50995i	0.399384	−	0.230584i	0.686218	+	0.727396i	$0.259270\pi$
$572$	43.4986	+	51.0535i	1.81877	+	2.13466i
$573$		−	1.30016i		−	0.0543150i
$574$		0			0
$575$	−0.355147	−	0.615132i	−0.0148106	−	0.0256528i
$576$	17.9175	−	10.3447i	0.746564	−	0.431029i
$577$	26.6870	+	7.15076i	1.11099	+	0.297690i	0.767234	−	0.641367i	$-0.221633\pi$
$577$	26.6870	+	7.15076i	1.11099	+	0.297690i	0.343760	+	0.939057i	$0.388299\pi$
$578$	−29.6231	−	29.6231i	−1.23216	−	1.23216i
$579$	−0.0108925	+	0.0406514i	−0.000452677	+	0.00168942i
$580$	40.1989	+	40.1989i	1.66917	+	1.66917i
$581$		0			0
$582$	1.45510	−	0.840105i	0.0603160	−	0.0348235i
$583$	15.5373	−	15.5373i	0.643489	−	0.643489i
$584$	6.45871	+	11.1868i	0.267263	+	0.462914i
$585$	−24.9096	−	8.85440i	−1.02988	−	0.366084i
$586$	−31.0754	−	17.9414i	−1.28371	−	0.741153i
$587$	7.45089	+	1.99646i	0.307531	+	0.0824027i	0.409284	−	0.912407i	$-0.365778\pi$
$587$	7.45089	+	1.99646i	0.307531	+	0.0824027i	−0.101753	+	0.994810i	$0.532445\pi$
$588$		0			0
$589$	−16.5176	−	9.53642i	−0.680594	−	0.392941i
$590$	23.2081	−	6.21858i	0.955460	−	0.256015i
$591$	−0.796517	+	0.796517i	−0.0327643	+	0.0327643i
$592$	−4.94594	+	4.94594i	−0.203277	+	0.203277i
$593$	−9.89297	+	2.65081i	−0.406256	+	0.108856i	−0.456159	−	0.889898i	$-0.650775\pi$
$593$	−9.89297	+	2.65081i	−0.406256	+	0.108856i	0.0499035	+	0.998754i	$0.484109\pi$
$594$	9.81446	+	5.66638i	0.402692	+	0.232495i
$595$		0			0
$596$	−30.0744	−	8.05842i	−1.23190	−	0.330086i
$597$	0.787985	+	0.454944i	0.0322501	+	0.0186196i
$598$	5.46677	+	1.94323i	0.223553	+	0.0794646i
$599$	19.8784	+	34.4305i	0.812211	+	1.40679i	0.911313	+	0.411714i	$0.135070\pi$
$599$	19.8784	+	34.4305i	0.812211	+	1.40679i	−0.0991022	+	0.995077i	$0.531597\pi$
$600$	0.667366	−	0.667366i	0.0272451	−	0.0272451i
$601$	−5.65826	+	3.26680i	−0.230805	+	0.133255i	−0.610943	−	0.791674i	$-0.709210\pi$
$601$	−5.65826	+	3.26680i	−0.230805	+	0.133255i	0.380138	+	0.924930i	$0.375876\pi$
$602$		0			0
$603$	13.2219	+	13.2219i	0.538437	+	0.538437i
$604$	−6.97116	+	26.0167i	−0.283652	+	1.05860i
$605$	−17.0438	−	17.0438i	−0.692930	−	0.692930i
$606$	−1.81832	−	0.487216i	−0.0738640	−	0.0197918i
$607$	−5.87637	+	3.39272i	−0.238514	+	0.137706i	−0.614494	−	0.788922i	$-0.710640\pi$
$607$	−5.87637	+	3.39272i	−0.238514	+	0.137706i	0.375979	+	0.926628i	$0.377306\pi$
$608$	−1.42016	−	2.45979i	−0.0575950	−	0.0997575i
$609$		0			0
$610$		−	93.3456i		−	3.77945i
$611$	−13.8550	−	16.2614i	−0.560515	−	0.657866i
$612$	−1.18395	+	0.683553i	−0.0478583	+	0.0276310i
$613$	19.0899	−	5.11512i	0.771034	−	0.206598i	0.148206	−	0.988957i	$-0.452650\pi$
$613$	19.0899	−	5.11512i	0.771034	−	0.206598i	0.622828	+	0.782359i	$0.285984\pi$
$614$		−	33.0355i		−	1.33321i
$615$	−2.30335	+	3.98952i	−0.0928800	+	0.160873i
$616$		0			0
$617$	−2.05438	+	0.550470i	−0.0827063	+	0.0221611i	−0.299935	−	0.953960i	$-0.596965\pi$
$617$	−2.05438	+	0.550470i	−0.0827063	+	0.0221611i	0.217229	+	0.976121i	$0.430298\pi$
$618$	5.41419	+	1.45073i	0.217791	+	0.0583568i
$619$	7.70516	−	28.7560i	0.309696	−	1.15580i	−0.619130	−	0.785288i	$-0.712515\pi$
$619$	7.70516	−	28.7560i	0.309696	−	1.15580i	0.928827	−	0.370514i	$-0.120819\pi$
$620$	55.7804			2.24020
$621$	0.657946			0.0264024
$622$	−5.28614	+	19.7281i	−0.211955	+	0.791027i
$623$		0			0
$624$	−0.218135	+	2.73003i	−0.00873239	+	0.109288i
$625$	−14.6290	+	25.3381i	−0.585158	+	1.01352i
$626$	3.67157	+	13.7025i	0.146745	+	0.547661i
$627$	−1.32513	+	2.29520i	−0.0529208	+	0.0916615i
$628$	−19.3397	−	33.4973i	−0.771738	−	1.33669i
$629$	−0.123927	+	0.123927i	−0.00494130	+	0.00494130i
$630$		0			0
$631$	6.04595	+	22.5638i	0.240686	+	0.898251i	0.975503	+	0.219986i	$0.0706011\pi$
$631$	6.04595	+	22.5638i	0.240686	+	0.898251i	−0.734817	+	0.678265i	$0.762732\pi$
$632$	16.2472	+	60.6352i	0.646277	+	2.41194i
$633$		−	0.489578i		−	0.0194590i
$634$	21.9897	+	12.6957i	0.873321	+	0.504212i
$635$	−8.84168	−	8.84168i	−0.350872	−	0.350872i
$636$	3.32342			0.131782
$637$		0			0
$638$	63.4349			2.51141
$639$	−7.75657	−	7.75657i	−0.306845	−	0.306845i
$640$	−40.2177	−	23.2197i	−1.58975	−	0.917840i
$641$		−	25.5854i		−	1.01056i	−0.862955	−	0.505280i	$-0.831389\pi$
$641$		−	25.5854i		−	1.01056i	0.862955	−	0.505280i	$-0.168611\pi$
$642$	0.890280	+	3.32257i	0.0351366	+	0.131131i
$643$	7.72960	+	28.8473i	0.304826	+	1.13763i	0.933095	+	0.359630i	$0.117097\pi$
$643$	7.72960	+	28.8473i	0.304826	+	1.13763i	−0.628269	+	0.777996i	$0.716236\pi$
$644$		0			0
$645$	−2.07051	+	2.07051i	−0.0815261	+	0.0815261i
$646$	−0.478642	−	0.829032i	−0.0188319	−	0.0326178i
$647$	−1.41318	+	2.44770i	−0.0555577	+	0.0962288i	−0.892467	−	0.451113i	$-0.851027\pi$
$647$	−1.41318	+	2.44770i	−0.0555577	+	0.0962288i	0.836909	+	0.547342i	$0.184360\pi$
$648$	−11.6199	−	43.3660i	−0.456472	−	1.70358i
$649$	8.99679	−	15.5829i	0.353155	−	0.611683i
$650$	1.75260	+	9.51953i	0.0687425	+	0.373387i
$651$		0			0
$652$	19.5218	−	72.8563i	0.764532	−	2.85327i
$653$	26.1013			1.02142			0.510711	−	0.859753i	$-0.329382\pi$
$653$	26.1013			1.02142			0.510711	+	0.859753i	$0.329382\pi$
$654$	5.60793			0.219287
$655$	−3.62975	+	13.5464i	−0.141826	+	0.529302i
$656$	−48.0385	−	12.8719i	−1.87559	−	0.502562i
$657$	−7.22116	+	1.93490i	−0.281724	+	0.0754878i
$658$		0			0
$659$	−9.04837	+	15.6722i	−0.352475	+	0.610504i	−0.986682	−	0.162659i	$-0.947993\pi$
$659$	−9.04837	+	15.6722i	−0.352475	+	0.610504i	0.634208	+	0.773163i	$0.281326\pi$
$660$		−	7.75097i		−	0.301706i
$661$	1.36965	−	0.366997i	0.0532733	−	0.0142745i	−0.232084	−	0.972696i	$-0.574554\pi$
$661$	1.36965	−	0.366997i	0.0532733	−	0.0142745i	0.285357	+	0.958421i	$0.407888\pi$
$662$	−37.0142	+	21.3702i	−1.43860	+	0.830574i
$663$	−0.00546567	+	0.0684044i	−0.000212269	+	0.00265661i
$664$			24.2596i			0.941457i
$665$		0			0
$666$	−5.69748	−	9.86833i	−0.220773	−	0.382390i
$667$	3.18943	−	1.84142i	0.123495	−	0.0713000i
$668$	64.7149	+	17.3403i	2.50389	+	0.670917i
$669$	2.23774	+	2.23774i	0.0865160	+	0.0865160i
$670$	9.91083	−	36.9877i	0.382889	−	1.42896i
$671$	−49.4313	−	49.4313i	−1.90827	−	1.90827i
$672$		0			0
$673$	−3.78674	+	2.18627i	−0.145968	+	0.0842747i	−0.571205	−	0.820807i	$-0.693524\pi$
$673$	−3.78674	+	2.18627i	−0.145968	+	0.0842747i	0.425237	+	0.905082i	$0.360191\pi$
$674$	−21.1125	+	21.1125i	−0.813222	+	0.813222i
$675$	0.548839	+	0.950618i	0.0211248	+	0.0365893i
$676$	−41.1595	−	33.4932i	−1.58306	−	1.28820i
$677$	40.1930	+	23.2054i	1.54474	+	0.891857i	0.998530	+	0.0542097i	$0.0172639\pi$
$677$	40.1930	+	23.2054i	1.54474	+	0.891857i	0.546212	+	0.837647i	$0.316069\pi$
$678$	0.919654	+	0.246420i	0.0353191	+	0.00946372i
$679$		0			0
$680$	1.23662	+	0.713966i	0.0474224	+	0.0273793i
$681$	−1.04118	+	0.278984i	−0.0398982	+	0.0106907i
$682$	44.0115	−	44.0115i	1.68529	−	1.68529i
$683$	2.74654	−	2.74654i	0.105094	−	0.105094i	−0.652605	−	0.757698i	$-0.726324\pi$
$683$	2.74654	−	2.74654i	0.105094	−	0.105094i	0.757698	+	0.652605i	$0.226324\pi$
$684$	40.3496	−	10.8116i	1.54281	−	0.413394i
$685$	−18.2594	−	10.5421i	−0.697655	−	0.402791i
$686$		0			0
$687$	−2.82285	−	0.756380i	−0.107698	−	0.0288577i
$688$	−27.3765	−	15.8058i	−1.04372	−	0.602592i
$689$	−9.86374	+	14.3152i	−0.375779	+	0.545366i
$690$	−0.335240	−	0.580653i	−0.0127624	−	0.0221051i
$691$	30.7245	−	30.7245i	1.16882	−	1.16882i	0.186329	−	0.982487i	$-0.440341\pi$
$691$	30.7245	−	30.7245i	1.16882	−	1.16882i	0.982487	−	0.186329i	$-0.0596590\pi$
$692$	64.4703	−	37.2219i	2.45079	−	1.41497i
$693$		0			0
$694$	−5.00114	−	5.00114i	−0.189841	−	0.189841i
$695$	7.31054	−	27.2833i	0.277305	−	1.03492i
$696$	3.46026	+	3.46026i	0.131161	+	0.131161i
$697$	−1.20367	−	0.322522i	−0.0455922	−	0.0122164i
$698$	−25.7467	+	14.8649i	−0.974527	+	0.562644i
$699$	0.105981	+	0.183564i	0.00400857	+	0.00694305i
$700$		0			0
$701$			33.2095i			1.25430i	0.778897	+	0.627152i	$0.215780\pi$
$701$			33.2095i			1.25430i	−0.778897	+	0.627152i	$0.784220\pi$
$702$	−8.44829	−	3.00304i	−0.318860	−	0.113343i
$703$	4.63774	−	2.67760i	0.174916	−	0.100988i
$704$	−30.6492	+	8.21243i	−1.15514	+	0.309518i
$705$			2.46882i			0.0929810i
$706$	37.6168	−	65.1542i	1.41573	−	2.45211i
$707$		0			0
$708$	2.62879	−	0.704383i	0.0987961	−	0.0264723i
$709$	−21.4384	−	5.74441i	−0.805138	−	0.215736i	−0.167299	−	0.985906i	$-0.553505\pi$
$709$	−21.4384	−	5.74441i	−0.805138	−	0.215736i	−0.637838	+	0.770170i	$0.720171\pi$
$710$	−5.81415	+	21.6987i	−0.218201	+	0.814338i
$711$	−36.3303			−1.36249
$712$	−44.6075			−1.67174
$713$	0.935257	−	3.49043i	0.0350256	−	0.130717i
$714$		0			0
$715$	33.3863	+	23.0045i	1.24858	+	0.860319i
$716$	48.1299	−	83.3634i	1.79870	−	3.11544i
$717$	−0.531193	−	1.98244i	−0.0198378	−	0.0740356i
$718$	22.0728	−	38.2313i	0.823751	−	1.42678i
$719$	14.2145	+	24.6202i	0.530111	+	0.918180i	0.999383	+	0.0351257i	$0.0111832\pi$
$719$	14.2145	+	24.6202i	0.530111	+	0.918180i	−0.469272	+	0.883054i	$0.655484\pi$
$720$	−23.3218	+	23.3218i	−0.869153	+	0.869153i
$721$		0			0
$722$	−4.55687	−	17.0065i	−0.169589	−	0.632915i
$723$	0.106198	+	0.396335i	0.00394953	+	0.0147399i
$724$		−	18.9866i		−	0.705632i
$725$	5.32106	+	3.07212i	0.197619	+	0.114096i
$726$	−2.87648	−	2.87648i	−0.106756	−	0.106756i
$727$	0.462661			0.0171591			0.00857957	−	0.999963i	$-0.497269\pi$
$727$	0.462661			0.0171591			0.00857957	+	0.999963i	$0.497269\pi$
$728$		0			0
$729$	25.4724			0.943422
$730$	10.8256	+	10.8256i	0.400675	+	0.400675i
$731$	−0.685955	−	0.396036i	−0.0253710	−	0.0146479i
$732$		−	10.5733i		−	0.390802i
$733$	9.38272	+	35.0168i	0.346559	+	1.29337i	0.890781	+	0.454433i	$0.150158\pi$
$733$	9.38272	+	35.0168i	0.346559	+	1.29337i	−0.544222	+	0.838941i	$0.683175\pi$
$734$	4.61573	+	17.2261i	0.170370	+	0.635828i
$735$		0			0
$736$	0.380514	−	0.380514i	0.0140259	−	0.0140259i
$737$	−14.3386	−	24.8352i	−0.528169	−	0.914816i
$738$	40.5102	−	70.1657i	1.49120	−	2.58284i
$739$	−0.379862	−	1.41767i	−0.0139735	−	0.0521497i	0.958587	−	0.284800i	$-0.0919270\pi$
$739$	−0.379862	−	1.41767i	−0.0139735	−	0.0521497i	−0.972561	+	0.232650i	$0.925260\pi$
$740$	−7.83091	+	13.5635i	−0.287870	+	0.498605i
$741$	0.702289	−	1.97571i	0.0257992	−	0.0725794i
$742$		0			0
$743$	0.513502	−	1.91642i	0.0188386	−	0.0703065i	−0.955867	−	0.293801i	$-0.905080\pi$
$743$	0.513502	−	1.91642i	0.0188386	−	0.0703065i	0.974705	+	0.223494i	$0.0717464\pi$
$744$	4.80149			0.176031
$745$	−18.8212			−0.689555
$746$	−15.5854	+	58.1655i	−0.570622	+	2.12959i
$747$	−13.5618	−	3.63386i	−0.496199	−	0.132956i
$748$	2.02523	−	0.542658i	0.0740496	−	0.0198415i
$749$		0			0
$750$	−2.00962	+	3.48077i	−0.0733810	+	0.127100i
$751$		−	18.1843i		−	0.663555i	−0.943358	−	0.331778i	$-0.892352\pi$
$751$		−	18.1843i		−	0.663555i	0.943358	−	0.331778i	$-0.107648\pi$
$752$	−25.7447	+	6.89828i	−0.938814	+	0.251554i
$753$	−2.32462	+	1.34212i	−0.0847137	+	0.0489095i
$754$	−49.3583	+	9.08713i	−1.79752	+	0.330934i
$755$			16.2818i			0.592554i
$756$		0			0
$757$	2.77153	+	4.80044i	0.100733	+	0.174475i	0.911987	−	0.410219i	$-0.134548\pi$
$757$	2.77153	+	4.80044i	0.100733	+	0.174475i	−0.811254	+	0.584694i	$0.801215\pi$
$758$	−18.7385	+	10.8187i	−0.680612	+	0.392952i
$759$	−0.485013	−	0.129959i	−0.0176048	−	0.00471720i
$760$	−30.8522	−	30.8522i	−1.11913	−	1.11913i
$761$	−11.4195	+	42.6182i	−0.413957	+	1.54491i	0.372960	+	0.927848i	$0.378343\pi$
$761$	−11.4195	+	42.6182i	−0.413957	+	1.54491i	−0.786916	+	0.617060i	$0.788324\pi$
$762$	−1.49221	−	1.49221i	−0.0540569	−	0.0540569i
$763$		0			0
$764$	27.2183	−	15.7145i	0.984725	−	0.568531i
$765$	−0.584359	+	0.584359i	−0.0211276	+	0.0211276i
$766$	21.6907	+	37.5693i	0.783715	+	1.35743i
$767$	−4.76808	+	13.4138i	−0.172165	+	0.484343i
$768$	−4.75111	−	2.74306i	−0.171441	−	0.0989815i
$769$	−27.2136	−	7.29187i	−0.981348	−	0.262951i	−0.267736	−	0.963492i	$-0.586275\pi$
$769$	−27.2136	−	7.29187i	−0.981348	−	0.262951i	−0.713612	+	0.700541i	$0.752942\pi$
$770$		0			0
$771$	−2.07572	−	1.19842i	−0.0747552	−	0.0431599i
$772$	−0.982674	+	0.263307i	−0.0353672	+	0.00947661i
$773$	−14.6663	+	14.6663i	−0.527511	+	0.527511i	−0.919829	−	0.392319i	$-0.871673\pi$
$773$	−14.6663	+	14.6663i	−0.527511	+	0.527511i	0.392319	+	0.919829i	$0.371673\pi$
$774$	36.4151	−	36.4151i	1.30891	−	1.30891i
$775$	5.82323	−	1.56033i	0.209177	−	0.0560487i
$776$	17.9402	+	10.3578i	0.644017	+	0.371823i
$777$		0			0
$778$	24.1435	+	6.46922i	0.865585	+	0.231933i
$779$	32.9752	+	19.0383i	1.18146	+	0.682116i
$780$	1.11034	+	6.03098i	0.0397564	+	0.215944i
$781$	8.41168	+	14.5695i	0.300994	+	0.521336i
$782$	0.128246	−	0.128246i	0.00458608	−	0.00458608i
$783$	−4.92891	+	2.84571i	−0.176145	+	0.101697i
$784$		0			0
$785$	−16.5332	−	16.5332i	−0.590096	−	0.590096i
$786$	−0.612591	+	2.28622i	−0.0218504	+	0.0815467i
$787$	−32.1068	−	32.1068i	−1.14448	−	1.14448i	−0.987620	−	0.156863i	$-0.949862\pi$
$787$	−32.1068	−	32.1068i	−1.14448	−	1.14448i	−0.156863	−	0.987620i	$-0.550138\pi$
$788$	−26.3019	−	7.04758i	−0.936967	−	0.251060i
$789$	2.76928	−	1.59884i	0.0985888	−	0.0569203i
$790$	37.2001	+	64.4324i	1.32352	+	2.29240i
$791$		0			0
$792$			69.5282i			2.47058i
$793$	45.5433	+	31.3811i	1.61729	+	1.11438i
$794$	−18.0489	+	10.4205i	−0.640530	+	0.369810i
$795$	1.94054	−	0.519966i	0.0688238	−	0.0184413i
$796$			21.9949i			0.779587i
$797$	15.9452	−	27.6179i	0.564809	−	0.978277i	−0.432259	−	0.901750i	$-0.642283\pi$
$797$	15.9452	−	27.6179i	0.564809	−	0.978277i	0.997067	−	0.0765277i	$-0.0243834\pi$
$798$		0			0
$799$	−0.645069	+	0.172846i	−0.0228209	+	0.00611484i
$800$	0.867191	+	0.232363i	0.0306598	+	0.00821528i
$801$	6.68178	−	24.9367i	0.236089	−	0.881096i
$802$	23.1964			0.819094
$803$	11.4655			0.404607
$804$	1.12261	−	4.18963i	0.0395913	−	0.147757i
$805$		0			0
$806$	−27.9403	+	40.5497i	−0.984157	+	1.42830i
$807$	2.04494	−	3.54193i	0.0719851	−	0.124682i
$808$	−6.00697	−	22.4183i	−0.211325	−	0.788674i
$809$	−14.6403	+	25.3577i	−0.514726	+	0.891531i	0.485128	+	0.874443i	$0.338773\pi$
$809$	−14.6403	+	25.3577i	−0.514726	+	0.891531i	−0.999854	+	0.0170879i	$0.994560\pi$
$810$	−26.6053	−	46.0817i	−0.934815	−	1.61915i
$811$	−35.8857	+	35.8857i	−1.26012	+	1.26012i	−0.309082	+	0.951035i	$0.600022\pi$
$811$	−35.8857	+	35.8857i	−1.26012	+	1.26012i	−0.951035	+	0.309082i	$0.899978\pi$
$812$		0			0
$813$	−0.688454	−	2.56935i	−0.0241451	−	0.0901109i
$814$	4.52311	+	16.8805i	0.158535	+	0.591660i
$815$		−	45.5949i		−	1.59712i
$816$	0.0741431	+	0.0428065i	0.00259553	+	0.00149853i
$817$	17.1137	+	17.1137i	0.598732	+	0.598732i
$818$	−62.6615			−2.19091
$819$		0			0
$820$	−111.359			−3.88881
$821$	−6.93408	−	6.93408i	−0.242001	−	0.242001i	0.575677	−	0.817678i	$-0.304739\pi$
$821$	−6.93408	−	6.93408i	−0.242001	−	0.242001i	−0.817678	+	0.575677i	$0.804739\pi$
$822$	−3.08163	−	1.77918i	−0.107484	−	0.0620559i
$823$		−	27.5693i		−	0.961006i	−0.876993	−	0.480503i	$-0.840454\pi$
$823$		−	27.5693i		−	0.961006i	0.876993	−	0.480503i	$-0.159546\pi$
$824$	17.8863	+	66.7525i	0.623098	+	2.32543i
$825$	−0.216816	−	0.809167i	−0.00754855	−	0.0281716i
$826$		0			0
$827$	18.9789	−	18.9789i	0.659961	−	0.659961i	−0.295410	−	0.955371i	$-0.595456\pi$
$827$	18.9789	−	18.9789i	0.659961	−	0.659961i	0.955371	+	0.295410i	$0.0954562\pi$
$828$	3.95717	+	6.85402i	0.137521	+	0.238194i
$829$	−14.8153	+	25.6608i	−0.514556	+	0.891238i	0.485301	+	0.874347i	$0.338710\pi$
$829$	−14.8153	+	25.6608i	−0.514556	+	0.891238i	−0.999857	+	0.0168908i	$0.994623\pi$
$830$	7.44172	+	27.7729i	0.258306	+	0.964011i
$831$	−0.0630503	+	0.109206i	−0.00218719	+	0.00378832i
$832$	22.6715	−	10.7806i	0.785993	−	0.373749i
$833$		0			0
$834$	1.23380	−	4.60459i	0.0427229	−	0.159444i
$835$	40.4999			1.40156
$836$	−64.0654			−2.21575
$837$	−1.44534	+	5.39406i	−0.0499581	+	0.186446i
$838$	47.8819	+	12.8299i	1.65405	+	0.443202i
$839$	51.8608	−	13.8961i	1.79043	−	0.479745i	0.798014	−	0.602638i	$-0.205884\pi$
$839$	51.8608	−	13.8961i	1.79043	−	0.479745i	0.992420	+	0.122893i	$0.0392172\pi$
$840$		0			0
$841$	−1.42879	+	2.47474i	−0.0492686	+	0.0853357i
$842$		−	8.78721i		−	0.302827i
$843$	−0.123836	+	0.0331818i	−0.00426515	+	0.00114284i
$844$	10.2491	−	5.91733i	0.352789	−	0.203683i
$845$	−29.2731	−	13.1170i	−1.00703	−	0.451239i
$846$		−	43.4204i		−	1.49282i
$847$		0			0
$848$	10.8444	+	18.7830i	0.372397	+	0.645011i
$849$	−2.81782	+	1.62687i	−0.0967073	+	0.0558340i
$850$	0.292273	+	0.0783144i	0.0100249	+	0.00268616i
$851$	0.717431	+	0.717431i	0.0245932	+	0.0245932i
$852$	−0.658573	+	2.45783i	−0.0225623	+	0.0842038i
$853$	36.2761	+	36.2761i	1.24207	+	1.24207i	0.959140	+	0.282930i	$0.0913066\pi$
$853$	36.2761	+	36.2761i	1.24207	+	1.24207i	0.282930	+	0.959140i	$0.408693\pi$
$854$		0			0
$855$	21.8685	−	12.6258i	0.747887	−	0.431793i
$856$	−29.9881	+	29.9881i	−1.02497	+	1.02497i
$857$	23.1941	+	40.1733i	0.792295	+	1.37230i	0.924543	+	0.381079i	$0.124447\pi$
$857$	23.1941	+	40.1733i	0.792295	+	1.37230i	−0.132247	+	0.991217i	$0.542219\pi$
$858$	5.63459	+	3.88245i	0.192362	+	0.132545i
$859$	6.53039	+	3.77032i	0.222814	+	0.128642i	0.607253	−	0.794509i	$-0.292272\pi$
$859$	6.53039	+	3.77032i	0.222814	+	0.128642i	−0.384439	+	0.923151i	$0.625605\pi$
$860$	−68.3705	−	18.3198i	−2.33142	−	0.624701i
$861$		0			0
$862$	51.1997	+	29.5601i	1.74387	+	1.00682i
$863$	18.4118	−	4.93343i	0.626745	−	0.167936i	0.0685528	−	0.997647i	$-0.478162\pi$
$863$	18.4118	−	4.93343i	0.626745	−	0.167936i	0.558192	+	0.829712i	$0.311495\pi$
$864$	−0.588042	+	0.588042i	−0.0200056	+	0.0200056i
$865$	31.8205	−	31.8205i	1.08193	−	1.08193i
$866$	55.8087	−	14.9539i	1.89646	−	0.508154i
$867$	−2.48420	−	1.43425i	−0.0843678	−	0.0487098i
$868$		0			0
$869$	53.8196	+	14.4209i	1.82570	+	0.489196i
$870$	5.02281	+	2.89992i	0.170289	+	0.0983166i
$871$	14.7144	+	17.2701i	0.498580	+	0.585174i
$872$	34.5705	+	59.8779i	1.17071	+	2.02772i
$873$	−8.47755	+	8.47755i	−0.286921	+	0.286921i
$874$	−4.79937	+	2.77092i	−0.162341	+	0.0937277i
$875$		0			0
$876$	1.22623	+	1.22623i	0.0414304	+	0.0414304i
$877$	−4.25400	+	15.8761i	−0.143647	+	0.536099i	0.856165	+	0.516703i	$0.172841\pi$
$877$	−4.25400	+	15.8761i	−0.143647	+	0.536099i	−0.999812	+	0.0193959i	$0.993826\pi$
$878$	58.8792	+	58.8792i	1.98708	+	1.98708i
$879$	−2.37324	−	0.635907i	−0.0800473	−	0.0214486i
$880$	43.8062	−	25.2915i	1.47671	−	0.852578i
$881$	−6.33542	−	10.9733i	−0.213446	−	0.369699i	0.739345	−	0.673327i	$-0.235135\pi$
$881$	−6.33542	−	10.9733i	−0.213446	−	0.369699i	−0.952791	+	0.303628i	$0.901802\pi$
$882$		0			0
$883$		−	48.6526i		−	1.63729i	−0.574300	−	0.818645i	$-0.694726\pi$
$883$		−	48.6526i		−	1.63729i	0.574300	−	0.818645i	$-0.305274\pi$
$884$	−1.49808	+	0.712355i	−0.0503859	+	0.0239591i
$885$	1.42474	−	0.822575i	0.0478922	−	0.0276506i
$886$	−73.9095	+	19.8040i	−2.48304	+	0.665328i
$887$		−	11.4213i		−	0.383489i	−0.981445	−	0.191744i	$-0.938586\pi$
$887$		−	11.4213i		−	0.383489i	0.981445	−	0.191744i	$-0.0614144\pi$
$888$	−0.674072	+	1.16753i	−0.0226204	+	0.0391796i
$889$		0			0
$890$	−51.0675	+	13.6835i	−1.71179	+	0.458672i
$891$	−38.4915	−	10.3138i	−1.28951	−	0.345524i
$892$	−19.7995	+	73.8928i	−0.662937	+	2.47411i
$893$	20.4059			0.682858
$894$	−3.17644			−0.106236
$895$	15.0603	−	56.2059i	0.503411	−	1.87875i
$896$		0			0
$897$	0.396002	+	0.0316414i	0.0132221	+	0.00105648i
$898$	1.84947	−	3.20337i	0.0617176	−	0.106898i
$899$	8.09024	+	30.1932i	0.269824	+	1.00700i
$900$	−6.60192	+	11.4349i	−0.220064	+	0.381162i
$901$	0.271720	+	0.470633i	0.00905232	+	0.0156791i
$902$	−87.8633	+	87.8633i	−2.92553	+	2.92553i
$903$		0			0
$904$	3.03816	+	11.3386i	0.101048	+	0.377115i
$905$	−2.97055	−	11.0862i	−0.0987443	−	0.368519i
$906$			2.74786i			0.0912917i
$907$	23.0490	+	13.3073i	0.765328	+	0.441862i	0.831205	−	0.555965i	$-0.187651\pi$
$907$	23.0490	+	13.3073i	0.765328	+	0.441862i	−0.0658773	+	0.997828i	$0.520985\pi$
$908$	−18.4247	−	18.4247i	−0.611447	−	0.611447i
$909$	13.4322			0.445518
$910$		0			0
$911$	−57.5752			−1.90755			−0.953775	−	0.300520i	$-0.902840\pi$
$911$	−57.5752			−1.90755			−0.953775	+	0.300520i	$0.902840\pi$
$912$	−1.84977	−	1.84977i	−0.0612522	−	0.0612522i
$913$	18.6479	+	10.7664i	0.617157	+	0.356316i
$914$			75.6690i			2.50291i
$915$	−1.65425	−	6.17374i	−0.0546878	−	0.204098i
$916$	−18.2841	−	68.2372i	−0.604124	−	2.25462i
$917$		0			0
$918$	−0.198190	+	0.198190i	−0.00654126	+	0.00654126i
$919$	−18.1716	−	31.4741i	−0.599424	−	1.03823i	−0.992906	−	0.118901i	$-0.962063\pi$
$919$	−18.1716	−	31.4741i	−0.599424	−	1.03823i	0.393482	−	0.919332i	$-0.371270\pi$
$920$	4.13324	−	7.15898i	0.136269	−	0.236024i
$921$	−0.585448	−	2.18492i	−0.0192912	−	0.0719956i
$922$	31.9047	−	55.2606i	1.05073	−	1.81991i
$923$	−8.63217	−	10.1314i	−0.284131	−	0.333480i
$924$		0			0
$925$	−0.438103	+	1.63502i	−0.0144047	+	0.0537592i
$926$	−92.5561			−3.04158
$927$	−39.9955			−1.31363
$928$	−1.20479	+	4.49635i	−0.0395492	+	0.147600i
$929$	−49.1711	−	13.1754i	−1.61325	−	0.432269i	−0.664242	−	0.747518i	$-0.731246\pi$
$929$	−49.1711	−	13.1754i	−1.61325	−	0.432269i	−0.949009	+	0.315248i	$0.897912\pi$
$930$	5.49683	−	1.47287i	0.180248	−	0.0482974i
$931$		0			0
$932$	−2.56190	+	4.43734i	−0.0839177	+	0.145350i
$933$			1.39847i			0.0457839i
$934$	−19.5867	+	5.24825i	−0.640898	+	0.171728i
$935$	1.09762	−	0.633713i	0.0358961	−	0.0207246i
$936$	−9.96000	−	54.0995i	−0.325553	−	1.76830i
$937$			55.7488i			1.82123i	0.413251	+	0.910617i	$0.364393\pi$
$937$			55.7488i			1.82123i	−0.413251	+	0.910617i	$0.635607\pi$
$938$		0			0
$939$	0.485664	+	0.841195i	0.0158491	+	0.0274514i
$940$	−51.6836	+	29.8396i	−1.68573	+	0.973259i
$941$	−7.44082	−	1.99376i	−0.242564	−	0.0649948i	0.135489	−	0.990779i	$-0.456740\pi$
$941$	−7.44082	−	1.99376i	−0.242564	−	0.0649948i	−0.378053	+	0.925784i	$0.623406\pi$
$942$	−2.79030	−	2.79030i	−0.0909130	−	0.0909130i
$943$	−1.86712	+	6.96819i	−0.0608018	+	0.226916i
$944$	12.5588	+	12.5588i	0.408753	+	0.408753i
$945$		0			0
$946$	−68.3998	+	39.4906i	−2.22387	+	1.28395i
$947$	−27.7853	+	27.7853i	−0.902900	+	0.902900i	−0.995686	−	0.0927863i	$-0.970423\pi$
$947$	−27.7853	+	27.7853i	−0.902900	+	0.902900i	0.0927863	+	0.995686i	$0.470423\pi$
$948$	4.21368	+	7.29831i	0.136854	+	0.237038i
$949$	−8.92120	+	1.64244i	−0.289594	+	0.0533159i
$950$	−8.00700	−	4.62284i	−0.259781	−	0.149985i
$951$	1.67936	+	0.449982i	0.0544568	+	0.0145917i
$952$		0			0
$953$	−34.9303	−	20.1670i	−1.13150	−	0.653275i	−0.187192	−	0.982323i	$-0.559939\pi$
$953$	−34.9303	−	20.1670i	−1.13150	−	0.653275i	−0.944313	+	0.329049i	$0.893272\pi$
$954$	−34.1293	+	9.14491i	−1.10498	+	0.296077i
$955$	13.4341	−	13.4341i	0.434717	−	0.434717i
$956$	35.0812	−	35.0812i	1.13461	−	1.13461i
$957$	4.19549	−	1.12418i	0.135621	−	0.0363396i
$958$	−46.4269	−	26.8046i	−1.49999	−	0.866017i
$959$		0			0
$960$	−2.80225	−	0.750861i	−0.0904423	−	0.0242339i
$961$	−0.285588	−	0.164884i	−0.00921252	−	0.00531885i
$962$	−5.93755	−	12.4867i	−0.191434	−	0.402586i
$963$	−12.2722	−	21.2561i	−0.395466	−	0.684967i
$964$	−7.01355	+	7.01355i	−0.225891	+	0.225891i
$965$	−0.532585	+	0.307488i	−0.0171445	+	0.00989840i
$966$		0			0
$967$	−1.13971	−	1.13971i	−0.0366507	−	0.0366507i	0.688544	−	0.725195i	$-0.258250\pi$
$967$	−1.13971	−	1.13971i	−0.0366507	−	0.0366507i	−0.725195	+	0.688544i	$0.758250\pi$
$968$	12.9809	−	48.4455i	0.417223	−	1.55710i
$969$	−0.0463486	−	0.0463486i	−0.00148893	−	0.00148893i
$970$	23.7156	+	6.35457i	0.761462	+	0.204033i
$971$	22.6332	−	13.0673i	0.726333	−	0.419348i	−0.0907462	−	0.995874i	$-0.528925\pi$
$971$	22.6332	−	13.0673i	0.726333	−	0.419348i	0.817079	+	0.576526i	$0.195592\pi$
$972$	−9.18765	−	15.9135i	−0.294694	−	0.510425i
$973$		0			0
$974$			44.5023i			1.42595i
$975$	0.284617	+	0.598549i	0.00911504	+	0.0191689i
$976$	59.7574	−	34.5009i	1.91279	−	1.10435i
$977$	15.3729	−	4.11917i	0.491824	−	0.131784i	−0.00437887	−	0.999990i	$-0.501394\pi$
$977$	15.3729	−	4.11917i	0.491824	−	0.131784i	0.496203	+	0.868207i	$0.334727\pi$
$978$		−	7.69503i		−	0.246060i
$979$	−19.7967	+	34.2890i	−0.632707	+	1.09588i
$980$		0			0
$981$	−38.6516	+	10.3567i	−1.23405	+	0.330663i
$982$	15.4957	+	4.15207i	0.494489	+	0.132498i
$983$	−2.03290	+	7.58689i	−0.0648395	+	0.241984i	−0.990738	−	0.135788i	$-0.956643\pi$
$983$	−2.03290	+	7.58689i	−0.0648395	+	0.241984i	0.925898	+	0.377773i	$0.123310\pi$
$984$	−9.58556			−0.305577
$985$	−16.4603			−0.524467
$986$	−0.406056	+	1.51542i	−0.0129315	+	0.0482609i
$987$		0			0
$988$	49.8489	−	9.17745i	1.58590	−	0.291974i
$989$	−2.29270	+	3.97108i	−0.0729038	+	0.126273i
$990$	21.3280	+	79.5972i	0.677848	+	2.52976i
$991$	−2.27497	+	3.94037i	−0.0722669	+	0.125170i	−0.899894	−	0.436108i	$-0.856357\pi$
$991$	−2.27497	+	3.94037i	−0.0722669	+	0.125170i	0.827628	+	0.561278i	$0.189690\pi$
$992$	2.28370	+	3.95548i	0.0725074	+	0.125586i
$993$	−2.06935	+	2.06935i	−0.0656688	+	0.0656688i
$994$		0			0
$995$	3.44120	+	12.8428i	0.109094	+	0.407143i
$996$	0.842930	+	3.14586i	0.0267093	+	0.0996803i
$997$		−	20.0987i		−	0.636534i	−0.948001	−	0.318267i	$-0.896899\pi$
$997$		−	20.0987i		−	0.636534i	0.948001	−	0.318267i	$-0.103101\pi$
$998$	43.0108	+	24.8323i	1.36148	+	0.786052i
$999$	−1.10871	−	1.10871i	−0.0350780	−	0.0350780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.362.7		28
7.2	even	3		637.2.bd.a.440.7		28
7.3	odd	6		637.2.x.a.570.1		28
7.4	even	3		91.2.w.a.24.1	yes	28
7.5	odd	6		637.2.bd.b.440.7		28
7.6	odd	2		91.2.ba.a.89.7	yes	28
13.6	odd	12		637.2.x.a.19.1		28
21.11	odd	6		819.2.gh.b.388.7		28
21.20	even	2		819.2.et.b.271.1		28
91.6	even	12		91.2.w.a.19.1	✓	28
91.19	even	12		637.2.bd.a.97.7		28
91.32	odd	12		91.2.ba.a.45.7	yes	28
91.45	even	12	inner	637.2.bb.a.227.7		28
91.58	odd	12		637.2.bd.b.97.7		28
273.32	even	12		819.2.et.b.136.1		28
273.188	odd	12		819.2.gh.b.19.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.1	✓	28	91.6	even	12
91.2.w.a.24.1	yes	28	7.4	even	3
91.2.ba.a.45.7	yes	28	91.32	odd	12
91.2.ba.a.89.7	yes	28	7.6	odd	2
637.2.x.a.19.1		28	13.6	odd	12
637.2.x.a.570.1		28	7.3	odd	6
637.2.bb.a.227.7		28	91.45	even	12	inner
637.2.bb.a.362.7		28	1.1	even	1	trivial
637.2.bd.a.97.7		28	91.19	even	12
637.2.bd.a.440.7		28	7.2	even	3
637.2.bd.b.97.7		28	91.58	odd	12
637.2.bd.b.440.7		28	7.5	odd	6
819.2.et.b.136.1		28	273.32	even	12
819.2.et.b.271.1		28	21.20	even	2
819.2.gh.b.19.7		28	273.188	odd	12
819.2.gh.b.388.7		28	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.74384 + 1.74384i) q^{2} +(0.146239 + 0.0844309i) q^{3} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(0.107782 + 0.402250i) q^{6} +(-3.63054 + 3.63054i) q^{8} +(-1.48574 - 2.57338i) q^{9} +O(q^{10})\)	\(q+(1.74384 + 1.74384i) q^{2} +(0.146239 + 0.0844309i) q^{3} +4.08193i q^{4} +(0.638637 + 2.38343i) q^{5} +(0.107782 + 0.402250i) q^{6} +(-3.63054 + 3.63054i) q^{8} +(-1.48574 - 2.57338i) q^{9} +(-3.04263 + 5.26998i) q^{10} +(1.17950 + 4.40195i) q^{11} +(-0.344641 + 0.596935i) q^{12} +(-1.54835 - 3.25617i) q^{13} +(-0.107841 + 0.402470i) q^{15} -4.49827 q^{16} -0.112710 q^{17} +(1.89666 - 7.07845i) q^{18} +(3.32660 + 0.891360i) q^{19} +(-9.72897 + 2.60687i) q^{20} +(-5.61943 + 9.73314i) q^{22} +0.652493i q^{23} +(-0.837454 + 0.224395i) q^{24} +(-0.942740 + 0.544291i) q^{25} +(2.97816 - 8.37828i) q^{26} -1.00836i q^{27} +(-2.82213 - 4.88807i) q^{29} +(-0.889899 + 0.513783i) q^{30} +(-5.34937 - 1.43336i) q^{31} +(-0.583169 - 0.583169i) q^{32} +(-0.199172 + 0.743322i) q^{33} +(-0.196548 - 0.196548i) q^{34} +(10.5044 - 6.06469i) q^{36} +(1.09952 - 1.09952i) q^{37} +(4.24666 + 7.35543i) q^{38} +(0.0484931 - 0.606906i) q^{39} +(-10.9717 - 6.33453i) q^{40} +(10.6793 + 2.86152i) q^{41} +(6.08601 + 3.51376i) q^{43} +(-17.9684 + 4.81463i) q^{44} +(5.18462 - 5.18462i) q^{45} +(-1.13784 + 1.13784i) q^{46} +(5.72325 - 1.53354i) q^{47} +(-0.657821 - 0.379793i) q^{48} +(-2.59314 - 0.694830i) q^{50} +(-0.0164826 - 0.00951622i) q^{51} +(13.2914 - 6.32024i) q^{52} +(-2.41079 - 4.17561i) q^{53} +(1.75841 - 1.75841i) q^{54} +(-9.73846 + 5.62250i) q^{55} +(0.411219 + 0.411219i) q^{57} +(3.60266 - 13.4453i) q^{58} +(-2.79191 - 2.79191i) q^{59} +(-1.64285 - 0.440201i) q^{60} +(-13.2845 + 7.66982i) q^{61} +(-6.82887 - 11.8280i) q^{62} +6.96264i q^{64} +(6.77201 - 5.76988i) q^{65} +(-1.64355 + 0.948907i) q^{66} +(-6.07826 + 1.62866i) q^{67} -0.460075i q^{68} +(-0.0550906 + 0.0954197i) q^{69} +(3.56578 - 0.955449i) q^{71} +(14.7368 + 3.94872i) q^{72} +(0.651157 - 2.43015i) q^{73} +3.83477 q^{74} -0.183820 q^{75} +(-3.63847 + 13.5789i) q^{76} +(1.14291 - 0.973780i) q^{78} +(6.11315 - 10.5883i) q^{79} +(-2.87276 - 10.7213i) q^{80} +(-4.37209 + 7.57269i) q^{81} +(13.6330 + 23.6130i) q^{82} +(3.34105 - 3.34105i) q^{83} +(-0.0719809 - 0.268637i) q^{85} +(4.48558 + 16.7404i) q^{86} -0.953099i q^{87} +(-20.2637 - 11.6992i) q^{88} +(6.14338 + 6.14338i) q^{89} +18.0822 q^{90} -2.66343 q^{92} +(-0.661264 - 0.661264i) q^{93} +(12.6547 + 7.30617i) q^{94} +8.49797i q^{95} +(-0.0360444 - 0.134519i) q^{96} +(-1.04426 - 3.89722i) q^{97} +(9.57547 - 9.57547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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