LMFDB - Embedded newform 637.2.x.b.80.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.8
Character	$\chi$	$=$	637.80
Dual form			637.2.x.b.215.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.664504 + 2.47996i) q^{2} +2.69629i q^{3} +(-3.97660 + 2.29589i) q^{4} +(0.103104 - 0.384791i) q^{5} +(-6.68671 + 1.79170i) q^{6} +(-4.70528 - 4.70528i) q^{8} -4.27000 q^{9} +O(q^{10})$	\(q+(0.664504 + 2.47996i) q^{2} +2.69629i q^{3} +(-3.97660 + 2.29589i) q^{4} +(0.103104 - 0.384791i) q^{5} +(-6.68671 + 1.79170i) q^{6} +(-4.70528 - 4.70528i) q^{8} -4.27000 q^{9} +1.02278 q^{10} +(2.56721 + 2.56721i) q^{11} +(-6.19040 - 10.7221i) q^{12} +(-3.44571 - 1.06165i) q^{13} +(1.03751 + 0.278000i) q^{15} +(3.95046 - 6.84240i) q^{16} +(-2.04856 - 3.54822i) q^{17} +(-2.83743 - 10.5895i) q^{18} +(0.569532 + 0.569532i) q^{19} +(0.473433 + 1.76688i) q^{20} +(-4.66067 + 8.07252i) q^{22} +(4.41149 + 2.54698i) q^{23} +(12.6868 - 12.6868i) q^{24} +(4.19269 + 2.42065i) q^{25} +(0.343169 - 9.25070i) q^{26} -3.42430i q^{27} +(1.00735 + 1.74478i) q^{29} +2.75772i q^{30} +(-6.06756 + 1.62580i) q^{31} +(6.73893 + 1.80569i) q^{32} +(-6.92197 + 6.92197i) q^{33} +(7.43817 - 7.43817i) q^{34} +(16.9801 - 9.80347i) q^{36} +(-1.73100 + 0.463819i) q^{37} +(-1.03396 + 1.79088i) q^{38} +(2.86252 - 9.29064i) q^{39} +(-2.29568 + 1.32541i) q^{40} +(-0.578490 + 2.15895i) q^{41} +(-2.65096 - 1.53053i) q^{43} +(-16.1028 - 4.31474i) q^{44} +(-0.440256 + 1.64306i) q^{45} +(-3.38495 + 12.6328i) q^{46} +(8.19540 + 2.19595i) q^{47} +(18.4491 + 10.6516i) q^{48} +(-3.21707 + 12.0063i) q^{50} +(9.56703 - 5.52353i) q^{51} +(16.1396 - 3.68921i) q^{52} +(-4.54674 + 7.87518i) q^{53} +(8.49214 - 2.27546i) q^{54} +(1.25253 - 0.723149i) q^{55} +(-1.53563 + 1.53563i) q^{57} +(-3.65761 + 3.65761i) q^{58} +(7.17731 + 1.92316i) q^{59} +(-4.76402 + 1.27652i) q^{60} +2.77536i q^{61} +(-8.06384 - 13.9670i) q^{62} +2.11035i q^{64} +(-0.763781 + 1.21642i) q^{65} +(-21.7659 - 12.5665i) q^{66} +(3.55672 - 3.55672i) q^{67} +(16.2926 + 9.40656i) q^{68} +(-6.86740 + 11.8947i) q^{69} +(-0.582978 - 2.17570i) q^{71} +(20.0916 + 20.0916i) q^{72} +(1.28173 + 4.78349i) q^{73} +(-2.30051 - 3.98460i) q^{74} +(-6.52679 + 11.3047i) q^{75} +(-3.57239 - 0.957219i) q^{76} +(24.9426 + 0.925283i) q^{78} +(1.80984 + 3.13473i) q^{79} +(-2.22558 - 2.22558i) q^{80} -3.57709 q^{81} -5.73853 q^{82} +(-5.36774 - 5.36774i) q^{83} +(-1.57654 + 0.422432i) q^{85} +(2.03409 - 7.59132i) q^{86} +(-4.70444 + 2.71611i) q^{87} -24.1589i q^{88} +(-3.09280 - 11.5425i) q^{89} -4.36728 q^{90} -23.3903 q^{92} +(-4.38363 - 16.3599i) q^{93} +21.7835i q^{94} +(0.277872 - 0.160430i) q^{95} +(-4.86867 + 18.1701i) q^{96} +(7.71975 - 2.06850i) q^{97} +(-10.9620 - 10.9620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.664504	+	2.47996i	0.469875	+	1.75360i	0.640197	+	0.768211i	$0.278853\pi$
$2$	0.664504	+	2.47996i	0.469875	+	1.75360i	−0.170322	+	0.985388i	$0.554481\pi$
$3$			2.69629i			1.55671i	0.627827	+	0.778353i	$0.283945\pi$
$3$			2.69629i			1.55671i	−0.627827	+	0.778353i	$0.716055\pi$
$4$	−3.97660	+	2.29589i	−1.98830	+	1.14795i
$5$	0.103104	−	0.384791i	0.0461097	−	0.172084i	−0.939031	−	0.343832i	$-0.888275\pi$
$5$	0.103104	−	0.384791i	0.0461097	−	0.172084i	0.985141	+	0.171748i	$0.0549416\pi$
$6$	−6.68671	+	1.79170i	−2.72984	+	0.731458i
$7$		0			0
$7$		0			0
$8$	−4.70528	−	4.70528i	−1.66357	−	1.66357i
$9$	−4.27000			−1.42333
$10$	1.02278			0.323432
$11$	2.56721	+	2.56721i	0.774044	+	0.774044i	0.978811	−	0.204767i	$-0.0656435\pi$
$11$	2.56721	+	2.56721i	0.774044	+	0.774044i	−0.204767	+	0.978811i	$0.565644\pi$
$12$	−6.19040	−	10.7221i	−1.78702	−	3.09520i
$13$	−3.44571	−	1.06165i	−0.955667	−	0.294449i
$13$	−3.44571	−	1.06165i	−0.955667	−	0.294449i
$14$		0			0
$15$	1.03751	+	0.278000i	0.267884	+	0.0717792i
$16$	3.95046	−	6.84240i	0.987615	−	1.71060i
$17$	−2.04856	−	3.54822i	−0.496850	−	0.860569i	0.503144	−	0.864203i	$-0.332177\pi$
$17$	−2.04856	−	3.54822i	−0.496850	−	0.860569i	−0.999993	+	0.00363405i	$0.998843\pi$
$18$	−2.83743	−	10.5895i	−0.668790	−	2.49596i
$19$	0.569532	+	0.569532i	0.130660	+	0.130660i	0.769412	−	0.638753i	$-0.220549\pi$
$19$	0.569532	+	0.569532i	0.130660	+	0.130660i	−0.638753	+	0.769412i	$0.720549\pi$
$20$	0.473433	+	1.76688i	0.105863	+	0.395086i
$21$		0			0
$22$	−4.66067	+	8.07252i	−0.993659	+	1.72107i
$23$	4.41149	+	2.54698i	0.919860	+	0.531081i	0.883590	−	0.468261i	$-0.155119\pi$
$23$	4.41149	+	2.54698i	0.919860	+	0.531081i	0.0362693	+	0.999342i	$0.488453\pi$
$24$	12.6868	−	12.6868i	2.58969	−	2.58969i
$25$	4.19269	+	2.42065i	0.838539	+	0.484131i
$26$	0.343169	−	9.25070i	0.0673009	−	1.81421i
$27$		−	3.42430i		−	0.659007i
$28$		0			0
$29$	1.00735	+	1.74478i	0.187060	+	0.323998i	0.944269	−	0.329175i	$-0.106771\pi$
$29$	1.00735	+	1.74478i	0.187060	+	0.323998i	−0.757209	+	0.653173i	$0.773437\pi$
$30$			2.75772i			0.503488i
$31$	−6.06756	+	1.62580i	−1.08977	+	0.292002i	−0.758591	−	0.651567i	$-0.774112\pi$
$31$	−6.06756	+	1.62580i	−1.08977	+	0.292002i	−0.331176	+	0.943569i	$0.607445\pi$
$32$	6.73893	+	1.80569i	1.19129	+	0.319204i
$33$	−6.92197	+	6.92197i	−1.20496	+	1.20496i
$34$	7.43817	−	7.43817i	1.27563	−	1.27563i
$35$		0			0
$36$	16.9801	−	9.80347i	2.83002	−	1.63391i
$37$	−1.73100	+	0.463819i	−0.284574	+	0.0762514i	−0.398283	−	0.917263i	$-0.630394\pi$
$37$	−1.73100	+	0.463819i	−0.284574	+	0.0762514i	0.113708	+	0.993514i	$0.463727\pi$
$38$	−1.03396	+	1.79088i	−0.167731	+	0.290519i
$39$	2.86252	−	9.29064i	0.458371	−	1.48769i
$40$	−2.29568	+	1.32541i	−0.362979	+	0.209566i
$41$	−0.578490	+	2.15895i	−0.0903449	+	0.337172i	−0.996273	−	0.0862606i	$-0.972508\pi$
$41$	−0.578490	+	2.15895i	−0.0903449	+	0.337172i	0.905928	+	0.423432i	$0.139175\pi$
$42$		0			0
$43$	−2.65096	−	1.53053i	−0.404267	−	0.233404i	0.284057	−	0.958808i	$-0.408320\pi$
$43$	−2.65096	−	1.53053i	−0.404267	−	0.233404i	−0.688323	+	0.725404i	$0.741653\pi$
$44$	−16.1028	−	4.31474i	−2.42759	−	0.650472i
$45$	−0.440256	+	1.64306i	−0.0656295	+	0.244933i
$46$	−3.38495	+	12.6328i	−0.499084	+	1.86261i
$47$	8.19540	+	2.19595i	1.19542	+	0.320312i	0.801027	−	0.598629i	$-0.204288\pi$
$47$	8.19540	+	2.19595i	1.19542	+	0.320312i	0.394395	+	0.918941i	$0.370954\pi$
$48$	18.4491	+	10.6516i	2.66290	+	1.53743i
$49$		0			0
$50$	−3.21707	+	12.0063i	−0.454962	+	1.69794i
$51$	9.56703	−	5.52353i	1.33965	−	0.773449i
$52$	16.1396	−	3.68921i	2.23817	−	0.511601i
$53$	−4.54674	+	7.87518i	−0.624542	+	1.08174i	0.364087	+	0.931365i	$0.381381\pi$
$53$	−4.54674	+	7.87518i	−0.624542	+	1.08174i	−0.988629	+	0.150374i	$0.951952\pi$
$54$	8.49214	−	2.27546i	1.15563	−	0.309651i
$55$	1.25253	−	0.723149i	0.168891	−	0.0975094i
$56$		0			0
$57$	−1.53563	+	1.53563i	−0.203399	+	0.203399i
$58$	−3.65761	+	3.65761i	−0.480267	+	0.480267i
$59$	7.17731	+	1.92316i	0.934407	+	0.250374i	0.693733	−	0.720232i	$-0.255965\pi$
$59$	7.17731	+	1.92316i	0.934407	+	0.250374i	0.240674	+	0.970606i	$0.422632\pi$
$60$	−4.76402	+	1.27652i	−0.615032	+	0.164797i
$61$			2.77536i			0.355349i	0.984089	+	0.177674i	$0.0568574\pi$
$61$			2.77536i			0.355349i	−0.984089	+	0.177674i	$0.943143\pi$
$62$	−8.06384	−	13.9670i	−1.02411	−	1.77381i
$63$		0			0
$64$			2.11035i			0.263794i
$65$	−0.763781	+	1.21642i	−0.0947354	+	0.150878i
$66$	−21.7659	−	12.5665i	−2.67920	−	1.54684i
$67$	3.55672	−	3.55672i	0.434523	−	0.434523i	−0.455641	−	0.890164i	$-0.650590\pi$
$67$	3.55672	−	3.55672i	0.434523	−	0.434523i	0.890164	+	0.455641i	$0.150590\pi$
$68$	16.2926	+	9.40656i	1.97577	+	1.14071i
$69$	−6.86740	+	11.8947i	−0.826737	+	1.43195i
$70$		0			0
$71$	−0.582978	−	2.17570i	−0.0691867	−	0.258208i	0.922666	−	0.385601i	$-0.126006\pi$
$71$	−0.582978	−	2.17570i	−0.0691867	−	0.258208i	−0.991852	+	0.127393i	$0.959339\pi$
$72$	20.0916	+	20.0916i	2.36781	+	2.36781i
$73$	1.28173	+	4.78349i	0.150016	+	0.559866i	0.999481	+	0.0322210i	$0.0102580\pi$
$73$	1.28173	+	4.78349i	0.150016	+	0.559866i	−0.849465	+	0.527645i	$0.823075\pi$
$74$	−2.30051	−	3.98460i	−0.267429	−	0.463200i
$75$	−6.52679	+	11.3047i	−0.753649	+	1.30536i
$76$	−3.57239	−	0.957219i	−0.409781	−	0.109801i
$77$		0			0
$78$	24.9426	+	0.925283i	2.82419	+	0.104768i
$79$	1.80984	+	3.13473i	0.203622	+	0.352684i	0.949693	−	0.313183i	$-0.101395\pi$
$79$	1.80984	+	3.13473i	0.203622	+	0.352684i	−0.746071	+	0.665867i	$0.768062\pi$
$80$	−2.22558	−	2.22558i	−0.248828	−	0.248828i
$81$	−3.57709			−0.397454
$82$	−5.73853			−0.633715
$83$	−5.36774	−	5.36774i	−0.589186	−	0.589186i	0.348225	−	0.937411i	$-0.386785\pi$
$83$	−5.36774	−	5.36774i	−0.589186	−	0.589186i	−0.937411	+	0.348225i	$0.886785\pi$
$84$		0			0
$85$	−1.57654	+	0.422432i	−0.170999	+	0.0458191i
$86$	2.03409	−	7.59132i	0.219341	−	0.818593i
$87$	−4.70444	+	2.71611i	−0.504369	+	0.291198i
$88$		−	24.1589i		−	2.57535i
$89$	−3.09280	−	11.5425i	−0.327836	−	1.22350i	−0.911430	−	0.411454i	$-0.865021\pi$
$89$	−3.09280	−	11.5425i	−0.327836	−	1.22350i	0.583595	−	0.812045i	$-0.301646\pi$
$90$	−4.36728			−0.460351
$91$		0			0
$92$	−23.3903			−2.43861
$93$	−4.38363	−	16.3599i	−0.454561	−	1.69645i
$94$			21.7835i			2.24680i
$95$	0.277872	−	0.160430i	0.0285091	−	0.0164597i
$96$	−4.86867	+	18.1701i	−0.496907	+	1.85448i
$97$	7.71975	−	2.06850i	0.783822	−	0.210024i	0.155353	−	0.987859i	$-0.450349\pi$
$97$	7.71975	−	2.06850i	0.783822	−	0.210024i	0.628469	+	0.777835i	$0.283682\pi$
$98$		0			0
$99$	−10.9620	−	10.9620i	−1.10172	−	1.10172i
$100$	−22.2302			−2.22302
$101$	−4.50245			−0.448011			−0.224005	−	0.974588i	$-0.571913\pi$
$101$	−4.50245			−0.448011			−0.224005	+	0.974588i	$0.571913\pi$
$102$	20.0555	+	20.0555i	1.98579	+	1.98579i
$103$	8.05002	+	13.9430i	0.793192	+	1.37385i	0.923981	+	0.382439i	$0.124916\pi$
$103$	8.05002	+	13.9430i	0.793192	+	1.37385i	−0.130788	+	0.991410i	$0.541751\pi$
$104$	11.2177	+	21.2084i	1.09998	+	2.07965i
$105$		0			0
$106$	−22.5515	−	6.04265i	−2.19039	−	0.586914i
$107$	5.40840	−	9.36762i	0.522850	−	0.905602i	−0.476797	−	0.879014i	$-0.658202\pi$
$107$	5.40840	−	9.36762i	0.522850	−	0.905602i	0.999646	−	0.0265887i	$-0.00846443\pi$
$108$	7.86183	+	13.6171i	0.756505	+	1.31030i
$109$	0.863031	+	3.22088i	0.0826634	+	0.308504i	0.994861	−	0.101246i	$-0.0322828\pi$
$109$	0.863031	+	3.22088i	0.0826634	+	0.308504i	−0.912198	+	0.409749i	$0.865616\pi$
$110$	2.62570	+	2.62570i	0.250350	+	0.250350i
$111$	−1.25059	−	4.66728i	−0.118701	−	0.442998i
$112$		0			0
$113$	3.82032	−	6.61699i	0.359386	−	0.622474i	−0.628473	−	0.777832i	$-0.716320\pi$
$113$	3.82032	−	6.61699i	0.359386	−	0.622474i	0.987858	+	0.155357i	$0.0496529\pi$
$114$	−4.82873	−	2.78787i	−0.452252	−	0.261108i
$115$	1.43490	−	1.43490i	0.133805	−	0.133805i
$116$	−8.01166	−	4.62553i	−0.743864	−	0.429470i
$117$	14.7132	+	4.53325i	1.36023	+	0.419099i
$118$			19.0774i			1.75622i
$119$		0			0
$120$	−3.57371	−	6.18984i	−0.326233	−	0.565052i
$121$			2.18118i			0.198289i
$122$	−6.88279	+	1.84424i	−0.623139	+	0.166970i
$123$	−5.82117	−	1.55978i	−0.524877	−	0.140640i
$124$	20.3956	−	20.3956i	1.83158	−	1.83158i
$125$	2.77216	−	2.77216i	0.247950	−	0.247950i
$126$		0			0
$127$	10.8931	−	6.28911i	0.966602	−	0.558068i	0.0684037	−	0.997658i	$-0.478209\pi$
$127$	10.8931	−	6.28911i	0.966602	−	0.558068i	0.898199	+	0.439590i	$0.144876\pi$
$128$	8.24427	−	2.20905i	0.728697	−	0.195254i
$129$	4.12676	−	7.14775i	0.363341	−	0.629325i
$130$	−3.52420	−	1.08584i	−0.309093	−	0.0952341i
$131$	−10.1944	+	5.88576i	−0.890691	+	0.514241i	−0.874169	−	0.485623i	$-0.838593\pi$
$131$	−10.1944	+	5.88576i	−0.890691	+	0.514241i	−0.0165228	+	0.999863i	$0.505260\pi$
$132$	11.6338	−	43.4180i	1.01259	−	3.77905i
$133$		0			0
$134$	11.1840	+	6.45709i	0.966151	+	0.557808i
$135$	−1.31764	−	0.353060i	−0.113404	−	0.0303866i
$136$	−7.05628	+	26.3344i	−0.605071	+	2.25816i
$137$	3.37005	−	12.5772i	0.287923	−	1.07454i	−0.658754	−	0.752358i	$-0.728916\pi$
$137$	3.37005	−	12.5772i	0.287923	−	1.07454i	0.946677	−	0.322184i	$-0.104417\pi$
$138$	−34.0618	−	9.12683i	−2.89953	−	0.776927i
$139$	−7.49780	−	4.32886i	−0.635955	−	0.367169i	0.147099	−	0.989122i	$-0.453006\pi$
$139$	−7.49780	−	4.32886i	−0.635955	−	0.367169i	−0.783055	+	0.621953i	$0.786340\pi$
$140$		0			0
$141$	−5.92093	+	22.0972i	−0.498632	+	1.86092i
$142$	5.00827	−	2.89153i	0.420285	−	0.242652i
$143$	−6.12038	−	11.5714i	−0.511812	−	0.967645i
$144$	−16.8685	+	29.2171i	−1.40571	+	2.43476i
$145$	0.775238	−	0.207724i	0.0643800	−	0.0172506i
$146$	−11.0112	+	6.35730i	−0.911291	+	0.526134i
$147$		0			0
$148$	5.81861	−	5.81861i	0.478287	−	0.478287i
$149$	−13.2090	+	13.2090i	−1.08212	+	1.08212i	−0.0858119	+	0.996311i	$0.527348\pi$
$149$	−13.2090	+	13.2090i	−1.08212	+	1.08212i	−0.996311	+	0.0858119i	$0.972652\pi$
$150$	−32.3724	−	8.67416i	−2.64320	−	0.708242i
$151$	−13.5918	+	3.64190i	−1.10608	+	0.296374i	−0.765238	−	0.643747i	$-0.777379\pi$
$151$	−13.5918	+	3.64190i	−1.10608	+	0.296374i	−0.340842	+	0.940120i	$0.610712\pi$
$152$		−	5.35962i		−	0.434723i
$153$	8.74737	+	15.1509i	0.707183	+	1.22488i
$154$		0			0
$155$			2.50237i			0.200995i
$156$	9.94720	+	43.5172i	0.796413	+	3.48417i
$157$	12.1331	+	7.00506i	0.968328	+	0.559064i	0.898726	−	0.438510i	$-0.144494\pi$
$157$	12.1331	+	7.00506i	0.968328	+	0.559064i	0.0696019	+	0.997575i	$0.477827\pi$
$158$	−6.57136	+	6.57136i	−0.522790	+	0.522790i
$159$	−21.2338	−	12.2593i	−1.68395	−	0.972229i
$160$	1.38963	−	2.40690i	0.109860	−	0.190282i
$161$		0			0
$162$	−2.37699	−	8.87104i	−0.186754	−	0.696975i
$163$	6.70194	+	6.70194i	0.524936	+	0.524936i	0.919058	−	0.394122i	$-0.128951\pi$
$163$	6.70194	+	6.70194i	0.524936	+	0.524936i	−0.394122	+	0.919058i	$0.628951\pi$
$164$	−2.65630	−	9.91345i	−0.207422	−	0.774110i
$165$	1.94982	+	3.37719i	0.151794	+	0.262914i
$166$	9.74492	−	16.8787i	0.756353	−	1.31004i
$167$	9.41229	+	2.52202i	0.728345	+	0.195159i	0.603892	−	0.797066i	$-0.293616\pi$
$167$	9.41229	+	2.52202i	0.728345	+	0.195159i	0.124453	+	0.992226i	$0.460282\pi$
$168$		0			0
$169$	10.7458	+	7.31628i	0.826600	+	0.562790i
$170$	−2.09523	−	3.62905i	−0.160697	−	0.278335i
$171$	−2.43191	−	2.43191i	−0.185972	−	0.185972i
$172$	14.0557			1.07174
$173$	−17.0066			−1.29299			−0.646496	−	0.762918i	$-0.723766\pi$
$173$	−17.0066			−1.29299			−0.646496	+	0.762918i	$0.723766\pi$
$174$	−9.86198	−	9.86198i	−0.747635	−	0.747635i
$175$		0			0
$176$	27.7076	−	7.42423i	2.08854	−	0.559622i
$177$	−5.18539	+	19.3522i	−0.389758	+	1.45460i
$178$	26.5697	−	15.3400i	1.99149	−	1.14978i
$179$			10.8682i			0.812328i	0.913800	+	0.406164i	$0.133134\pi$
$179$			10.8682i			0.812328i	−0.913800	+	0.406164i	$0.866866\pi$
$180$	−2.02156	−	7.54457i	−0.150678	−	0.562339i
$181$	20.7716			1.54394			0.771969	−	0.635661i	$-0.219272\pi$
$181$	20.7716			1.54394			0.771969	+	0.635661i	$0.219272\pi$
$182$		0			0
$183$	−7.48319			−0.553173
$184$	−8.77307	−	32.7415i	−0.646759	−	2.41374i
$185$			0.713894i			0.0524865i
$186$	37.6591	−	21.7425i	2.76130	−	1.59424i
$187$	3.84993	−	14.3681i	0.281535	−	1.05070i
$188$	−37.6315	+	10.0833i	−2.74456	+	0.735402i
$189$		0			0
$190$	0.582507	+	0.582507i	0.0422595	+	0.0422595i
$191$	1.48438			0.107406			0.0537031	−	0.998557i	$-0.482898\pi$
$191$	1.48438			0.107406			0.0537031	+	0.998557i	$0.482898\pi$
$192$	−5.69013			−0.410649
$193$	−5.19197	−	5.19197i	−0.373726	−	0.373726i	0.495106	−	0.868833i	$-0.335129\pi$
$193$	−5.19197	−	5.19197i	−0.373726	−	0.373726i	−0.868833	+	0.495106i	$0.835129\pi$
$194$	10.2596	+	17.7702i	0.736597	+	1.27582i
$195$	−3.27981	−	2.05938i	−0.234872	−	0.147475i
$196$		0			0
$197$	17.4416	+	4.67347i	1.24266	+	0.332971i	0.819499	−	0.573081i	$-0.194252\pi$
$197$	17.4416	+	4.67347i	1.24266	+	0.332971i	0.423166	+	0.906052i	$0.360919\pi$
$198$	19.9011	−	34.4697i	1.41431	−	2.44965i
$199$	−1.63076	−	2.82456i	−0.115602	−	0.200228i	0.802418	−	0.596762i	$-0.203546\pi$
$199$	−1.63076	−	2.82456i	−0.115602	−	0.200228i	−0.918020	+	0.396534i	$0.870213\pi$
$200$	−8.33795	−	31.1177i	−0.589582	−	2.20035i
$201$	9.58998	+	9.58998i	0.676425	+	0.676425i
$202$	−2.99190	−	11.1659i	−0.210509	−	0.785631i
$203$		0			0
$204$	−25.3629	+	43.9298i	−1.77576	+	3.07570i
$205$	0.771100	+	0.445195i	0.0538560	+	0.0310938i
$206$	−29.2290	+	29.2290i	−2.03648	+	2.03648i
$207$	−18.8371	−	10.8756i	−1.30927	−	0.755906i
$208$	−20.8764	+	19.3829i	−1.44752	+	1.34396i
$209$			2.92422i			0.202273i
$210$		0			0
$211$	1.10904	+	1.92091i	0.0763492	+	0.132241i	0.901672	−	0.432420i	$-0.142340\pi$
$211$	1.10904	+	1.92091i	0.0763492	+	0.132241i	−0.825323	+	0.564661i	$0.809007\pi$
$212$		−	41.7553i		−	2.86776i
$213$	5.86633	−	1.57188i	0.401955	−	0.107703i
$214$	26.8253	+	7.18781i	1.83374	+	0.491348i
$215$	−0.862259	+	0.862259i	−0.0588056	+	0.0588056i
$216$	−16.1123	+	16.1123i	−1.09630	+	1.09630i
$217$		0			0
$218$	−7.41417	+	4.28057i	−0.502151	+	0.289917i
$219$	−12.8977	+	3.45593i	−0.871546	+	0.233530i
$220$	−3.32055	+	5.75136i	−0.223871	+	0.387756i
$221$	3.29178	+	14.4010i	0.221429	+	0.968714i
$222$	10.7437	−	6.20285i	0.721067	−	0.416308i
$223$	−1.40793	+	5.25448i	−0.0942823	+	0.351866i	−0.996910	−	0.0785566i	$-0.974969\pi$
$223$	−1.40793	+	5.25448i	−0.0942823	+	0.351866i	0.902627	+	0.430423i	$0.141636\pi$
$224$		0			0
$225$	−17.9028	−	10.3362i	−1.19352	−	0.689080i
$226$	18.9485	+	5.07724i	1.26044	+	0.337733i
$227$	−0.0897430	+	0.334926i	−0.00595646	+	0.0222298i	−0.968840	−	0.247687i	$-0.920330\pi$
$227$	−0.0897430	+	0.334926i	−0.00595646	+	0.0222298i	0.962884	+	0.269917i	$0.0869962\pi$
$228$	2.58094	−	9.63221i	0.170927	−	0.637909i
$229$	25.6082	+	6.86169i	1.69224	+	0.453433i	0.970965	−	0.239220i	$-0.0768919\pi$
$229$	25.6082	+	6.86169i	1.69224	+	0.453433i	0.721270	+	0.692654i	$0.243559\pi$
$230$	4.51199	+	2.60500i	0.297512	+	0.171768i
$231$		0			0
$232$	3.46982	−	12.9496i	0.227805	−	0.850180i
$233$	−18.9024	+	10.9133i	−1.23833	+	0.714953i	−0.968754	−	0.248025i	$-0.920218\pi$
$233$	−18.9024	+	10.9133i	−1.23833	+	0.714953i	−0.269581	+	0.962978i	$0.586885\pi$
$234$	−1.46533	+	39.5005i	−0.0957916	+	2.58223i
$235$	1.68996	−	2.92710i	0.110241	−	0.190943i
$236$	−32.9567	+	8.83072i	−2.14530	+	0.574831i
$237$	−8.45215	+	4.87985i	−0.549026	+	0.316980i
$238$		0			0
$239$	2.02192	−	2.02192i	0.130787	−	0.130787i	−0.638683	−	0.769470i	$-0.720520\pi$
$239$	2.02192	−	2.02192i	0.130787	−	0.130787i	0.769470	+	0.638683i	$0.220520\pi$
$240$	6.00082	−	6.00082i	0.387352	−	0.387352i
$241$	29.1475	+	7.81005i	1.87756	+	0.503090i	0.999708	+	0.0241515i	$0.00768840\pi$
$241$	29.1475	+	7.81005i	1.87756	+	0.503090i	0.877849	+	0.478938i	$0.158978\pi$
$242$	−5.40925	+	1.44940i	−0.347720	+	0.0931712i
$243$		−	19.9178i		−	1.27773i
$244$	−6.37193	−	11.0365i	−0.407921	−	0.706540i
$245$		0			0
$246$		−	15.4728i		−	0.986508i
$247$	−1.35780	−	2.56709i	−0.0863946	−	0.163340i
$248$	36.1994	+	20.8997i	2.29867	+	1.32714i
$249$	14.4730	−	14.4730i	0.917190	−	0.917190i
$250$	8.71697	+	5.03275i	0.551310	+	0.318299i
$251$	−8.33953	+	14.4445i	−0.526386	+	0.911728i	0.473141	+	0.880987i	$0.343120\pi$
$251$	−8.33953	+	14.4445i	−0.526386	+	0.911728i	−0.999527	+	0.0307412i	$0.990213\pi$
$252$		0			0
$253$	4.78661	+	17.8639i	0.300932	+	1.12309i
$254$	22.8352	+	22.8352i	1.43281	+	1.43281i
$255$	−1.13900	−	4.25081i	−0.0713269	−	0.266196i
$256$	13.0671	+	22.6328i	0.816691	+	1.41455i
$257$	−6.10569	+	10.5754i	−0.380863	+	0.659674i	−0.991186	−	0.132479i	$-0.957706\pi$
$257$	−6.10569	+	10.5754i	−0.380863	+	0.659674i	0.610323	+	0.792153i	$0.291040\pi$
$258$	20.4684	+	5.48450i	1.27431	+	0.341450i
$259$		0			0
$260$	0.244494	−	6.59076i	0.0151629	−	0.408742i
$261$	−4.30139	−	7.45022i	−0.266249	−	0.461157i
$262$	−21.3707	−	21.3707i	−1.32029	−	1.32029i
$263$	14.6063			0.900662			0.450331	−	0.892862i	$-0.351306\pi$
$263$	14.6063			0.900662			0.450331	+	0.892862i	$0.351306\pi$
$264$	65.1396			4.00906
$265$	2.56151	+	2.56151i	0.157352	+	0.157352i
$266$		0			0
$267$	31.1219	−	8.33909i	1.90463	−	0.510344i
$268$	−5.97782	+	22.3095i	−0.365154	+	1.36277i
$269$	4.31634	−	2.49204i	0.263172	−	0.151942i	−0.362609	−	0.931941i	$-0.618114\pi$
$269$	4.31634	−	2.49204i	0.263172	−	0.151942i	0.625781	+	0.779999i	$0.284781\pi$
$270$		−	3.50231i		−	0.213144i
$271$	6.85721	+	25.5915i	0.416546	+	1.55457i	0.781719	+	0.623631i	$0.214343\pi$
$271$	6.85721	+	25.5915i	0.416546	+	1.55457i	−0.365173	+	0.930940i	$0.618990\pi$
$272$	−32.3711			−1.96278
$273$		0			0
$274$	33.4304			2.01960
$275$	4.54921	+	16.9779i	0.274328	+	1.02380i
$276$		−	63.0672i		−	3.79620i
$277$	−17.6881	+	10.2122i	−1.06277	+	0.613592i	−0.926198	−	0.377038i	$-0.876943\pi$
$277$	−17.6881	+	10.2122i	−1.06277	+	0.613592i	−0.136574	+	0.990630i	$0.543609\pi$
$278$	5.75309	−	21.4708i	0.345047	−	1.28773i
$279$	25.9085	−	6.94216i	1.55110	−	0.415617i
$280$		0			0
$281$	−3.86728	−	3.86728i	−0.230703	−	0.230703i	0.582283	−	0.812986i	$-0.302159\pi$
$281$	−3.86728	−	3.86728i	−0.230703	−	0.230703i	−0.812986	+	0.582283i	$0.802159\pi$
$282$	−58.7347			−3.49760
$283$	−25.0379			−1.48835			−0.744174	−	0.667986i	$-0.767157\pi$
$283$	−25.0379			−1.48835			−0.744174	+	0.667986i	$0.767157\pi$
$284$	7.31345	+	7.31345i	0.433973	+	0.433973i
$285$	0.432565	+	0.749225i	0.0256230	+	0.0443803i
$286$	24.6295	−	22.8675i	1.45637	−	1.35219i
$287$		0			0
$288$	−28.7753	−	7.71031i	−1.69560	−	0.454334i
$289$	0.106779	−	0.184946i	0.00628111	−	0.0108792i
$290$	1.03030	+	1.78453i	0.0605012	+	0.104791i
$291$	5.57729	+	20.8147i	0.326946	+	1.22018i
$292$	−16.0793	−	16.0793i	−0.940972	−	0.940972i
$293$	4.77690	+	17.8276i	0.279069	+	1.04150i	0.953065	+	0.302766i	$0.0979100\pi$
$293$	4.77690	+	17.8276i	0.279069	+	1.04150i	−0.673996	+	0.738735i	$0.735423\pi$
$294$		0			0
$295$	1.48003	−	2.56348i	0.0861704	−	0.149251i
$296$	10.3272	+	5.96243i	0.600258	+	0.346559i
$297$	8.79091	−	8.79091i	0.510101	−	0.510101i
$298$	−41.5353	−	23.9804i	−2.40607	−	1.38915i
$299$	−12.4967	−	13.4596i	−0.722703	−	0.778389i
$300$		−	59.9393i		−	3.46059i
$301$		0			0
$302$	−18.0636	−	31.2870i	−1.03944	−	1.80036i
$303$		−	12.1399i		−	0.697421i
$304$	6.14688	−	1.64705i	0.352548	−	0.0944649i
$305$	1.06793	+	0.286152i	0.0611497	+	0.0163850i
$306$	−31.7610	+	31.7610i	−1.81565	+	1.81565i
$307$	14.6697	−	14.6697i	0.837243	−	0.837243i	−0.151252	−	0.988495i	$-0.548330\pi$
$307$	14.6697	−	14.6697i	0.837243	−	0.837243i	0.988495	+	0.151252i	$0.0483305\pi$
$308$		0			0
$309$	−37.5946	+	21.7052i	−2.13868	+	1.23477i
$310$	−6.20579	+	1.66284i	−0.352465	+	0.0944427i
$311$	2.93074	−	5.07620i	0.166187	−	0.287845i	−0.770889	−	0.636969i	$-0.780188\pi$
$311$	2.93074	−	5.07620i	0.166187	−	0.287845i	0.937076	+	0.349125i	$0.113521\pi$
$312$	−57.1840	+	30.2461i	−3.23741	+	1.71235i
$313$	17.6735	−	10.2038i	0.998967	−	0.576754i	0.0910244	−	0.995849i	$-0.470986\pi$
$313$	17.6735	−	10.2038i	0.998967	−	0.576754i	0.907942	+	0.419095i	$0.137653\pi$
$314$	−9.30978	+	34.7446i	−0.525381	+	1.96075i
$315$		0			0
$316$	−14.3940	−	8.31037i	−0.809725	−	0.467495i
$317$	7.40911	+	1.98526i	0.416137	+	0.111504i	0.460812	−	0.887498i	$-0.347558\pi$
$317$	7.40911	+	1.98526i	0.416137	+	0.111504i	−0.0446745	+	0.999002i	$0.514225\pi$
$318$	16.2928	−	60.8054i	0.913653	−	3.40980i
$319$	−1.89314	+	7.06531i	−0.105996	+	0.395582i
$320$	0.812043	+	0.217586i	0.0453946	+	0.0121634i
$321$	25.2579	+	14.5826i	1.40976	+	0.813923i
$322$		0			0
$323$	0.854101	−	3.18755i	0.0475234	−	0.177360i
$324$	14.2246	−	8.21260i	0.790258	−	0.456256i
$325$	−11.8769	−	12.7920i	−0.658812	−	0.709575i
$326$	−12.1671	+	21.0740i	−0.673873	+	1.16718i
$327$	−8.68443	+	2.32699i	−0.480250	+	0.128683i
$328$	12.8804	−	7.43652i	0.711203	−	0.410613i
$329$		0			0
$330$	−7.07965	+	7.07965i	−0.389722	+	0.389722i
$331$	17.8253	−	17.8253i	0.979770	−	0.979770i	−0.0200296	−	0.999799i	$-0.506376\pi$
$331$	17.8253	−	17.8253i	0.979770	−	0.979770i	0.999799	+	0.0200296i	$0.00637603\pi$
$332$	33.6691	+	9.02162i	1.84783	+	0.495126i
$333$	7.39136	−	1.98051i	0.405044	−	0.108531i
$334$			25.0180i			1.36893i
$335$	−1.00188	−	1.73531i	−0.0547386	−	0.0948100i
$336$		0			0
$337$		−	30.1306i		−	1.64132i	−0.571417	−	0.820660i	$-0.693606\pi$
$337$		−	30.1306i		−	1.64132i	0.571417	−	0.820660i	$-0.306394\pi$
$338$	−11.0035	+	31.5109i	−0.598510	+	1.71397i
$339$	17.8414	+	10.3007i	0.969010	+	0.559458i
$340$	5.29940	−	5.29940i	0.287400	−	0.287400i
$341$	−19.7505	−	11.4030i	−1.06955	−	0.617505i
$342$	4.41503	−	7.64705i	0.238737	−	0.413505i
$343$		0			0
$344$	5.27192	+	19.6751i	0.284243	+	1.06081i
$345$	3.86890	+	3.86890i	0.208295	+	0.208295i
$346$	−11.3010	−	42.1759i	−0.607545	−	2.26739i
$347$	−17.2300	−	29.8433i	−0.924957	−	1.60207i	−0.791631	−	0.611000i	$-0.790768\pi$
$347$	−17.2300	−	29.8433i	−0.924957	−	1.60207i	−0.133326	−	0.991072i	$-0.542566\pi$
$348$	12.4718	−	21.6018i	0.668559	−	1.15798i
$349$	−3.97028	−	1.06383i	−0.212524	−	0.0569457i	0.150986	−	0.988536i	$-0.451755\pi$
$349$	−3.97028	−	1.06383i	−0.212524	−	0.0569457i	−0.363510	+	0.931590i	$0.618422\pi$
$350$		0			0
$351$	−3.63541	+	11.7991i	−0.194044	+	0.629791i
$352$	12.6647	+	21.9359i	0.675030	+	1.16919i
$353$	7.69746	+	7.69746i	0.409694	+	0.409694i	0.881632	−	0.471938i	$-0.156445\pi$
$353$	7.69746	+	7.69746i	0.409694	+	0.409694i	−0.471938	+	0.881632i	$0.656445\pi$
$354$	−51.4383			−2.73392
$355$	−0.897298			−0.0476236
$356$	38.7991	+	38.7991i	2.05635	+	2.05635i
$357$		0			0
$358$	−26.9528	+	7.22197i	−1.42450	+	0.381693i
$359$	7.96687	−	29.7328i	0.420475	−	1.56923i	−0.353135	−	0.935572i	$-0.614884\pi$
$359$	7.96687	−	29.7328i	0.420475	−	1.56923i	0.773610	−	0.633662i	$-0.218449\pi$
$360$	9.80258	−	5.65952i	0.516641	−	0.298283i
$361$		−	18.3513i		−	0.965856i
$362$	13.8028	+	51.5127i	0.725458	+	2.70745i
$363$	−5.88111			−0.308678
$364$		0			0
$365$	1.97280			0.103261
$366$	−4.97261	−	18.5580i	−0.259923	−	0.970044i
$367$		−	24.9379i		−	1.30175i	−0.759187	−	0.650873i	$-0.774403\pi$
$367$		−	24.9379i		−	1.30175i	0.759187	−	0.650873i	$-0.225597\pi$
$368$	34.8548	−	20.1235i	1.81693	−	1.04901i
$369$	2.47015	−	9.21873i	0.128591	−	0.479908i
$370$	−1.77043	+	0.474385i	−0.0920403	+	0.0246621i
$371$		0			0
$372$	54.9926	+	54.9926i	2.85123	+	2.85123i
$373$	18.1892			0.941803			0.470902	−	0.882186i	$-0.343929\pi$
$373$	18.1892			0.941803			0.470902	+	0.882186i	$0.343929\pi$
$374$	38.1907			1.97480
$375$	7.47456	+	7.47456i	0.385985	+	0.385985i
$376$	−28.2291	−	48.8942i	−1.45580	−	2.52153i
$377$	−1.61868	−	7.08146i	−0.0833665	−	0.364714i
$378$		0			0
$379$	−0.810924	−	0.217286i	−0.0416544	−	0.0111613i	0.237932	−	0.971282i	$-0.423531\pi$
$379$	−0.810924	−	0.217286i	−0.0416544	−	0.0111613i	−0.279586	+	0.960121i	$0.590197\pi$
$380$	−0.736658	+	1.27593i	−0.0377898	+	0.0654538i
$381$	16.9573	+	29.3709i	0.868748	+	1.50472i
$382$	0.986379	+	3.68122i	0.0504676	+	0.188347i
$383$	4.10501	+	4.10501i	0.209756	+	0.209756i	0.804164	−	0.594408i	$-0.202613\pi$
$383$	4.10501	+	4.10501i	0.209756	+	0.209756i	−0.594408	+	0.804164i	$0.702613\pi$
$384$	5.95624	+	22.2290i	0.303953	+	1.13437i
$385$		0			0
$386$	9.42582	−	16.3260i	0.479761	−	0.830971i
$387$	11.3196	+	6.53537i	0.575407	+	0.332211i
$388$	−25.9493	+	25.9493i	−1.31738	+	1.31738i
$389$	7.55715	+	4.36312i	0.383163	+	0.221219i	0.679193	−	0.733959i	$-0.262330\pi$
$389$	7.55715	+	4.36312i	0.383163	+	0.221219i	−0.296031	+	0.955178i	$0.595663\pi$
$390$	2.92773	−	9.50229i	0.148252	−	0.481167i
$391$		−	20.8706i		−	1.05547i
$392$		0			0
$393$	−15.8697	−	27.4872i	−0.800522	−	1.38654i
$394$			46.3601i			2.33559i
$395$	1.39282	−	0.373204i	0.0700802	−	0.0187779i
$396$	68.7592	+	18.4240i	3.45528	+	0.925839i
$397$	−0.150383	+	0.150383i	−0.00754752	+	0.00754752i	−0.710870	−	0.703323i	$-0.751699\pi$
$397$	−0.150383	+	0.150383i	−0.00754752	+	0.00754752i	0.703323	+	0.710870i	$0.251699\pi$
$398$	5.92117	−	5.92117i	0.296801	−	0.296801i
$399$		0			0
$400$	33.1261	−	19.1254i	1.65631	−	0.956269i
$401$	6.77934	−	1.81652i	0.338544	−	0.0907126i	−0.0855419	−	0.996335i	$-0.527262\pi$
$401$	6.77934	−	1.81652i	0.338544	−	0.0907126i	0.424086	+	0.905622i	$0.360595\pi$
$402$	−17.4102	+	30.1554i	−0.868342	+	1.50401i
$403$	22.6331	+	0.839608i	1.12743	+	0.0418238i
$404$	17.9045	−	10.3371i	0.890781	−	0.514292i
$405$	−0.368813	+	1.37643i	−0.0183265	+	0.0683953i
$406$		0			0
$407$	−5.63456	−	3.25312i	−0.279295	−	0.161251i
$408$	−71.0053	−	19.0258i	−3.51529	−	0.941918i
$409$	−2.77106	+	10.3417i	−0.137020	+	0.511366i	0.862961	+	0.505270i	$0.168607\pi$
$409$	−2.77106	+	10.3417i	−0.137020	+	0.511366i	−0.999981	+	0.00609589i	$0.998060\pi$
$410$	−0.591668	+	2.20813i	−0.0292204	+	0.109052i
$411$	33.9118	+	9.08664i	1.67275	+	0.448211i
$412$	−64.0235	−	36.9640i	−3.15421	−	1.82108i
$413$		0			0
$414$	14.4538	−	53.9421i	0.710363	−	2.65111i
$415$	−2.61890	+	1.51202i	−0.128557	+	0.0742222i
$416$	−21.3034	−	13.3763i	−1.04448	−	0.655826i
$417$	11.6719	−	20.2163i	0.571574	−	0.989996i
$418$	−7.25197	+	1.94316i	−0.354705	+	0.0950430i
$419$	0.903448	−	0.521606i	0.0441363	−	0.0254821i	−0.477769	−	0.878485i	$-0.658555\pi$
$419$	0.903448	−	0.521606i	0.0441363	−	0.0254821i	0.521906	+	0.853003i	$0.325221\pi$
$420$		0			0
$421$	−22.9876	+	22.9876i	−1.12035	+	1.12035i	−0.128658	+	0.991689i	$0.541067\pi$
$421$	−22.9876	+	22.9876i	−1.12035	+	1.12035i	−0.991689	+	0.128658i	$0.958933\pi$
$422$	−4.02682	+	4.02682i	−0.196022	+	0.196022i
$423$	−34.9944	−	9.37671i	−1.70148	−	0.455911i
$424$	58.4486	−	15.6613i	2.83851	−	0.760578i
$425$		−	19.8354i		−	0.962160i
$426$	7.79641	+	13.5038i	0.377737	+	0.654260i
$427$		0			0
$428$			49.6684i			2.40081i
$429$	31.1998	−	16.5024i	1.50634	−	0.796741i
$430$	−2.71134	−	1.56540i	−0.130753	−	0.0754901i
$431$	−5.78670	+	5.78670i	−0.278735	+	0.278735i	−0.832604	−	0.553869i	$-0.813151\pi$
$431$	−5.78670	+	5.78670i	−0.278735	+	0.278735i	0.553869	+	0.832604i	$0.313151\pi$
$432$	−23.4304	−	13.5276i	−1.12730	−	0.650845i
$433$	9.95068	−	17.2351i	0.478199	−	0.828266i	−0.521488	−	0.853258i	$-0.674623\pi$
$433$	9.95068	−	17.2351i	0.478199	−	0.828266i	0.999688	+	0.0249929i	$0.00795632\pi$
$434$		0			0
$435$	0.560086	+	2.09027i	0.0268541	+	0.100221i
$436$	−10.8267	−	10.8267i	−0.518506	−	0.518506i
$437$	1.06190	+	3.96307i	0.0507977	+	0.189579i
$438$	−17.1412	−	29.6894i	−0.819036	−	1.41861i
$439$	−3.63272	+	6.29205i	−0.173380	+	0.300303i	−0.939599	−	0.342276i	$-0.888802\pi$
$439$	−3.63272	+	6.29205i	−0.173380	+	0.300303i	0.766219	+	0.642579i	$0.222136\pi$
$440$	−9.29613	−	2.49089i	−0.443176	−	0.118749i
$441$		0			0
$442$	−33.5265	+	17.7330i	−1.59469	+	0.843473i
$443$	−13.2808	−	23.0031i	−0.630992	−	1.09291i	−0.987349	−	0.158561i	$-0.949315\pi$
$443$	−13.2808	−	23.0031i	−0.630992	−	1.09291i	0.356357	−	0.934350i	$-0.384019\pi$
$444$	15.6887	+	15.6887i	0.744552	+	0.744552i
$445$	−4.76032			−0.225661
$446$	−13.9665			−0.661333
$447$	−35.6153	−	35.6153i	−1.68455	−	1.68455i
$448$		0			0
$449$	19.1518	−	5.13170i	0.903828	−	0.242180i	0.223168	−	0.974780i	$-0.428360\pi$
$449$	19.1518	−	5.13170i	0.903828	−	0.242180i	0.680659	+	0.732600i	$0.261693\pi$
$450$	13.7369	−	51.2668i	0.647563	−	2.41674i
$451$	−7.02760	+	4.05739i	−0.330917	+	0.191055i
$452$			35.0842i			1.65022i
$453$	−9.81963	−	36.6474i	−0.461366	−	1.72184i
$454$	−0.890238			−0.0417809
$455$		0			0
$456$	14.4511			0.676735
$457$	−6.49628	−	24.2444i	−0.303883	−	1.13411i	−0.933903	−	0.357528i	$-0.883620\pi$
$457$	−6.49628	−	24.2444i	−0.303883	−	1.13411i	0.630019	−	0.776579i	$-0.283047\pi$
$458$			68.0670i			3.18056i
$459$	−12.1502	+	7.01490i	−0.567121	+	0.327427i
$460$	−2.41165	+	9.00038i	−0.112444	+	0.419645i
$461$	−32.6719	+	8.75440i	−1.52168	+	0.407733i	−0.920295	−	0.391226i	$-0.872051\pi$
$461$	−32.6719	+	8.75440i	−1.52168	+	0.407733i	−0.601386	+	0.798959i	$0.705385\pi$
$462$		0			0
$463$	13.6651	+	13.6651i	0.635073	+	0.635073i	0.949336	−	0.314263i	$-0.101757\pi$
$463$	13.6651	+	13.6651i	0.635073	+	0.635073i	−0.314263	+	0.949336i	$0.601757\pi$
$464$	15.9180			0.738974
$465$	−6.74712			−0.312890
$466$	−39.6252	−	39.6252i	−1.83560	−	1.83560i
$467$	−7.57629	−	13.1225i	−0.350589	−	0.607238i	0.635764	−	0.771884i	$-0.280685\pi$
$467$	−7.57629	−	13.1225i	−0.350589	−	0.607238i	−0.986353	+	0.164646i	$0.947352\pi$
$468$	−68.9163	+	15.7529i	−3.18566	+	0.728180i
$469$		0			0
$470$	8.38209	+	2.24597i	0.386637	+	0.103599i
$471$	−18.8877	+	32.7145i	−0.870299	+	1.50740i
$472$	−24.7223	−	42.8203i	−1.13794	−	1.97096i
$473$	−2.87637	−	10.7348i	−0.132256	−	0.493585i
$474$	−17.7183	−	17.7183i	−0.813830	−	0.813830i
$475$	1.00923	+	3.76652i	0.0463069	+	0.172820i
$476$		0			0
$477$	19.4146	−	33.6270i	0.888932	−	1.53968i
$478$	6.35787	+	3.67072i	0.290802	+	0.167895i
$479$	17.7763	−	17.7763i	0.812220	−	0.812220i	−0.172746	−	0.984966i	$-0.555264\pi$
$479$	17.7763	−	17.7763i	0.812220	−	0.812220i	0.984966	+	0.172746i	$0.0552641\pi$
$480$	6.48972	+	3.74684i	0.296214	+	0.171019i
$481$	6.45692	+	0.239529i	0.294410	+	0.0109216i
$482$			77.4746i			3.52887i
$483$		0			0
$484$	−5.00776	−	8.67369i	−0.227625	−	0.394259i
$485$		−	3.18376i		−	0.144567i
$486$	49.3954	−	13.2354i	2.24062	−	0.600372i
$487$	24.9540	+	6.68642i	1.13078	+	0.302990i	0.775237	−	0.631671i	$-0.217631\pi$
$487$	24.9540	+	6.68642i	1.13078	+	0.302990i	0.355539	+	0.934661i	$0.384297\pi$
$488$	13.0589	−	13.0589i	0.591147	−	0.591147i
$489$	−18.0704	+	18.0704i	−0.817172	+	0.817172i
$490$		0			0
$491$	−31.2520	+	18.0433i	−1.41038	+	0.814284i	−0.995424	−	0.0955563i	$-0.969537\pi$
$491$	−31.2520	+	18.0433i	−1.41038	+	0.814284i	−0.414958	+	0.909841i	$0.636204\pi$
$492$	26.7296	−	7.16217i	1.20506	−	0.322895i
$493$	4.12724	−	7.14859i	0.185882	−	0.321956i
$494$	5.46402	−	5.07313i	0.245838	−	0.228251i
$495$	−5.34831	+	3.08785i	−0.240389	+	0.138789i
$496$	−12.8453	+	47.9393i	−0.576771	+	2.15254i
$497$		0			0
$498$	45.5099	+	26.2752i	2.03935	+	1.17742i
$499$	−27.2810	−	7.30993i	−1.22127	−	0.327237i	−0.410093	−	0.912044i	$-0.634504\pi$
$499$	−27.2810	−	7.30993i	−1.22127	−	0.327237i	−0.811173	+	0.584806i	$0.801171\pi$
$500$	−4.65920	+	17.3884i	−0.208366	+	0.777632i
$501$	−6.80010	+	25.3783i	−0.303806	+	1.13382i
$502$	−41.3635	−	11.0833i	−1.84614	−	0.494672i
$503$	−23.3796	−	13.4982i	−1.04244	−	0.601855i	−0.121920	−	0.992540i	$-0.538905\pi$
$503$	−23.3796	−	13.4982i	−1.04244	−	0.601855i	−0.920525	+	0.390685i	$0.872238\pi$
$504$		0			0
$505$	−0.464223	+	1.73250i	−0.0206576	+	0.0770954i
$506$	−41.1210	+	23.7412i	−1.82805	+	1.05543i
$507$	−19.7268	+	28.9738i	−0.876099	+	1.28677i
$508$	−28.8782	+	50.0186i	−1.28126	+	2.21922i
$509$	−4.85539	+	1.30100i	−0.215212	+	0.0576658i	−0.364814	−	0.931081i	$-0.618867\pi$
$509$	−4.85539	+	1.30100i	−0.215212	+	0.0576658i	0.149602	+	0.988746i	$0.452201\pi$
$510$	9.78497	−	5.64936i	0.433286	−	0.250158i
$511$		0			0
$512$	−35.3750	+	35.3750i	−1.56337	+	1.56337i
$513$	1.95025	−	1.95025i	0.0861057	−	0.0861057i
$514$	−30.2838	−	8.11452i	−1.33576	−	0.357916i
$515$	6.19515	−	1.65999i	0.272991	−	0.0731477i
$516$			37.8984i			1.66838i
$517$	15.4019	+	26.6768i	0.677373	+	1.17325i
$518$		0			0
$519$		−	45.8549i		−	2.01281i
$520$	9.31738	−	2.12977i	0.408594	−	0.0933967i
$521$	−24.7411	−	14.2843i	−1.08393	−	0.625806i	−0.151975	−	0.988384i	$-0.548563\pi$
$521$	−24.7411	−	14.2843i	−1.08393	−	0.625806i	−0.931953	+	0.362578i	$0.881897\pi$
$522$	15.6180	−	15.6180i	0.683581	−	0.683581i
$523$	15.9700	+	9.22026i	0.698318	+	0.403174i	0.806720	−	0.590933i	$-0.201240\pi$
$523$	15.9700	+	9.22026i	0.698318	+	0.403174i	−0.108403	+	0.994107i	$0.534574\pi$
$524$	27.0261	−	46.8106i	1.18064	−	2.04493i
$525$		0			0
$526$	9.70594	+	36.2230i	0.423199	+	1.57940i
$527$	18.1985	+	18.1985i	0.792738	+	0.792738i
$528$	20.0179	+	74.7078i	0.871167	+	3.25124i
$529$	1.47417	+	2.55334i	0.0640944	+	0.111015i
$530$	−4.65031	+	8.05458i	−0.201997	+	0.349868i
$531$	−30.6472	−	8.21188i	−1.32997	−	0.356365i
$532$		0			0
$533$	4.28536	−	6.82496i	0.185620	−	0.295622i
$534$	41.3613	+	71.6398i	1.78988	+	3.10016i
$535$	−3.04695	−	3.04695i	−0.131731	−	0.131731i
$536$	−33.4708			−1.44572
$537$	−29.3039			−1.26456
$538$	9.04840	+	9.04840i	0.390104	+	0.390104i
$539$		0			0
$540$	6.05032	−	1.62118i	0.260364	−	0.0697644i
$541$	−1.71180	+	6.38853i	−0.0735961	+	0.274665i	−0.992911	−	0.118858i	$-0.962077\pi$
$541$	−1.71180	+	6.38853i	−0.0735961	+	0.274665i	0.919315	+	0.393522i	$0.128743\pi$
$542$	−58.9092	+	34.0113i	−2.53037	+	1.46091i
$543$			56.0062i			2.40346i
$544$	−7.39814	−	27.6103i	−0.317193	−	1.18378i
$545$	1.32835			0.0569001
$546$		0			0
$547$	33.8006			1.44521			0.722605	−	0.691261i	$-0.242944\pi$
$547$	33.8006			1.44521			0.722605	+	0.691261i	$0.242944\pi$
$548$	15.4745	+	57.7518i	0.661040	+	2.46703i
$549$		−	11.8508i		−	0.505780i
$550$	−39.0816	+	22.5637i	−1.66644	+	0.962121i
$551$	−0.419991	+	1.56743i	−0.0178922	+	0.0667747i
$552$	88.2808	−	23.6548i	3.75748	−	1.00681i
$553$		0			0
$554$	−37.0797	−	37.0797i	−1.57536	−	1.57536i
$555$	−1.92487			−0.0817061
$556$	39.7544			1.68596
$557$	17.5294	+	17.5294i	0.742746	+	0.742746i	0.973106	−	0.230359i	$-0.0739901\pi$
$557$	17.5294	+	17.5294i	0.742746	+	0.742746i	−0.230359	+	0.973106i	$0.573990\pi$
$558$	34.4326	+	59.6391i	1.45765	+	2.52472i
$559$	7.50953	+	8.08815i	0.317619	+	0.342092i
$560$		0			0
$561$	38.7407	+	10.3805i	1.63563	+	0.438267i
$562$	7.02090	−	12.1606i	0.296159	−	0.512962i
$563$	−2.10194	−	3.64067i	−0.0885863	−	0.153436i	0.818327	−	0.574752i	$-0.194902\pi$
$563$	−2.10194	−	3.64067i	−0.0885863	−	0.153436i	−0.906914	+	0.421316i	$0.861568\pi$
$564$	−27.1876	−	101.466i	−1.14481	−	4.27247i
$565$	−2.15227	−	2.15227i	−0.0905465	−	0.0905465i
$566$	−16.6378	−	62.0931i	−0.699338	−	2.60997i
$567$		0			0
$568$	−7.49422	+	12.9804i	−0.314450	+	0.544644i
$569$	0.733859	+	0.423694i	0.0307650	+	0.0177622i	0.515304	−	0.857008i	$-0.327679\pi$
$569$	0.733859	+	0.423694i	0.0307650	+	0.0177622i	−0.484539	+	0.874770i	$0.661012\pi$
$570$	−1.57061	+	1.57061i	−0.0657856	+	0.0657856i
$571$	−15.4798	−	8.93729i	−0.647811	−	0.374014i	0.139806	−	0.990179i	$-0.455352\pi$
$571$	−15.4798	−	8.93729i	−0.647811	−	0.374014i	−0.787617	+	0.616165i	$0.788685\pi$
$572$	50.9049	+	31.9629i	2.12844	+	1.33644i
$573$			4.00234i			0.167200i
$574$		0			0
$575$	12.3307	+	21.3574i	0.514225	+	0.890664i
$576$		−	9.01120i		−	0.375467i
$577$	−8.25729	+	2.21253i	−0.343755	+	0.0921090i	−0.426566	−	0.904456i	$-0.640277\pi$
$577$	−8.25729	+	2.21253i	−0.343755	+	0.0921090i	0.0828109	+	0.996565i	$0.473610\pi$
$578$	0.529615	+	0.141910i	0.0220291	+	0.00590268i
$579$	13.9991	−	13.9991i	0.581782	−	0.581782i
$580$	−2.60590	+	2.60590i	−0.108204	+	0.108204i
$581$		0			0
$582$	−47.9136	+	27.6629i	−1.98608	+	1.14667i
$583$	−31.8897	+	8.54482i	−1.32074	+	0.353890i
$584$	16.4768	−	28.5386i	0.681813	−	1.18094i
$585$	3.26135	−	5.19410i	0.134840	−	0.214749i
$586$	−41.0376	+	23.6931i	−1.69525	+	0.978751i
$587$	10.7910	−	40.2727i	0.445394	−	1.66223i	−0.269502	−	0.963000i	$-0.586859\pi$
$587$	10.7910	−	40.2727i	0.445394	−	1.66223i	0.714895	−	0.699231i	$-0.246474\pi$
$588$		0			0
$589$	−4.38162	−	2.52973i	−0.180541	−	0.104236i
$590$	7.34082	+	1.96697i	0.302217	+	0.0809787i
$591$	−12.6011	+	47.0278i	−0.518338	+	1.93446i
$592$	−3.66460	+	13.6765i	−0.150614	+	0.562100i
$593$	−8.88654	−	2.38114i	−0.364926	−	0.0977817i	0.0716962	−	0.997427i	$-0.477159\pi$
$593$	−8.88654	−	2.38114i	−0.364926	−	0.0977817i	−0.436623	+	0.899645i	$0.643825\pi$
$594$	27.6427	+	15.9595i	1.13420	+	0.654828i
$595$		0			0
$596$	22.2005	−	82.8534i	0.909368	−	3.39381i
$597$	7.61585	−	4.39702i	0.311696	−	0.179958i
$598$	25.0752	−	39.9353i	1.02540	−	1.63308i
$599$	20.7873	−	36.0046i	0.849345	−	1.47111i	−0.0324484	−	0.999473i	$-0.510330\pi$
$599$	20.7873	−	36.0046i	0.849345	−	1.47111i	0.881794	−	0.471636i	$-0.156336\pi$
$600$	83.9023	−	22.4816i	3.42530	−	0.917806i
$601$	−22.6812	+	13.0950i	−0.925184	+	0.534155i	−0.885285	−	0.465049i	$-0.846037\pi$
$601$	−22.6812	+	13.0950i	−0.925184	+	0.534155i	−0.0398987	+	0.999204i	$0.512704\pi$
$602$		0			0
$603$	−15.1872	+	15.1872i	−0.618472	+	0.618472i
$604$	45.6876	−	45.6876i	1.85900	−	1.85900i
$605$	0.839298	+	0.224889i	0.0341223	+	0.00914305i
$606$	30.1066	−	8.06704i	1.22300	−	0.327701i
$607$		−	19.1314i		−	0.776519i	−0.921550	−	0.388260i	$-0.873076\pi$
$607$		−	19.1314i		−	0.776519i	0.921550	−	0.388260i	$-0.126924\pi$
$608$	2.80964	+	4.86644i	0.113946	+	0.197360i
$609$		0			0
$610$			2.83859i			0.114931i
$611$	−25.9076	−	16.2673i	−1.04811	−	0.658103i
$612$	−69.5696	−	40.1660i	−2.81219	−	1.62362i
$613$	7.89553	−	7.89553i	0.318897	−	0.318897i	−0.529446	−	0.848344i	$-0.677600\pi$
$613$	7.89553	−	7.89553i	0.318897	−	0.318897i	0.848344	+	0.529446i	$0.177600\pi$
$614$	46.1284	+	26.6322i	1.86159	+	1.07479i
$615$	−1.20038	+	2.07911i	−0.0484039	+	0.0838379i
$616$		0			0
$617$	−2.84075	−	10.6018i	−0.114364	−	0.426814i	0.884874	−	0.465830i	$-0.154244\pi$
$617$	−2.84075	−	10.6018i	−0.114364	−	0.426814i	−0.999239	+	0.0390163i	$0.987578\pi$
$618$	−78.8099	−	78.8099i	−3.17020	−	3.17020i
$619$	6.88065	+	25.6790i	0.276557	+	1.03212i	0.954791	+	0.297278i	$0.0960789\pi$
$619$	6.88065	+	25.6790i	0.276557	+	1.03212i	−0.678234	+	0.734846i	$0.737254\pi$
$620$	−5.74517	−	9.95093i	−0.230732	−	0.399639i
$621$	8.72161	−	15.1063i	0.349986	−	0.606194i
$622$	14.5363	+	3.89498i	0.582851	+	0.156175i
$623$		0			0
$624$	−52.2620	−	56.2888i	−2.09215	−	2.25336i
$625$	11.3224	+	19.6109i	0.452895	+	0.784438i
$626$	37.0492	+	37.0492i	1.48078	+	1.48078i
$627$	−7.88457			−0.314879
$628$	−64.3314			−2.56710
$629$	5.19179	+	5.19179i	0.207010	+	0.207010i
$630$		0			0
$631$	−34.9180	+	9.35626i	−1.39007	+	0.372467i	−0.874767	−	0.484544i	$-0.838986\pi$
$631$	−34.9180	+	9.35626i	−1.39007	+	0.372467i	−0.515298	+	0.857011i	$0.672319\pi$
$632$	6.23399	−	23.2656i	0.247975	−	0.925454i
$633$	−5.17933	+	2.99029i	−0.205860	+	0.118853i
$634$			19.6935i			0.782130i
$635$	−1.29687	−	4.83998i	−0.0514647	−	0.192069i
$636$	112.584			4.46427
$637$		0			0
$638$	−18.7797			−0.743496
$639$	2.48932	+	9.29025i	0.0984758	+	0.367517i
$640$		−	3.40008i		−	0.134400i
$641$	−21.5157	+	12.4221i	−0.849819	+	0.490643i	−0.860590	−	0.509299i	$-0.829905\pi$
$641$	−21.5157	+	12.4221i	−0.849819	+	0.490643i	0.0107708	+	0.999942i	$0.496571\pi$
$642$	−19.3804	+	72.3288i	−0.764885	+	2.85459i
$643$	28.7931	−	7.71509i	1.13549	−	0.304253i	0.358353	−	0.933586i	$-0.383338\pi$
$643$	28.7931	−	7.71509i	1.13549	−	0.304253i	0.777136	+	0.629333i	$0.216672\pi$
$644$		0			0
$645$	−2.32490	−	2.32490i	−0.0915430	−	0.0915430i
$646$	8.47255			0.333348
$647$	−13.7535			−0.540705			−0.270352	−	0.962761i	$-0.587140\pi$
$647$	−13.7535			−0.540705			−0.270352	+	0.962761i	$0.587140\pi$
$648$	16.8312	+	16.8312i	0.661192	+	0.661192i
$649$	13.4886	+	23.3629i	0.529472	+	0.917072i
$650$	23.8315	−	37.9547i	0.934750	−	1.48870i
$651$		0			0
$652$	−42.0379	−	11.2640i	−1.64633	−	0.441133i
$653$	−0.855193	+	1.48124i	−0.0334663	+	0.0579653i	−0.882273	−	0.470737i	$-0.843988\pi$
$653$	−0.855193	+	1.48124i	−0.0334663	+	0.0579653i	0.848807	+	0.528703i	$0.177321\pi$
$654$	−11.5417	−	19.9908i	−0.451315	−	0.781701i
$655$	1.21369	+	4.52957i	0.0474230	+	0.176985i
$656$	12.4871	+	12.4871i	0.487540	+	0.487540i
$657$	−5.47300	−	20.4255i	−0.213522	−	0.796876i
$658$		0			0
$659$	−4.73353	+	8.19872i	−0.184392	+	0.319377i	−0.943372	−	0.331738i	$-0.892365\pi$
$659$	−4.73353	+	8.19872i	−0.184392	+	0.319377i	0.758979	+	0.651115i	$0.225698\pi$
$660$	−15.5073	−	8.95317i	−0.603623	−	0.348502i
$661$	6.24335	−	6.24335i	0.242838	−	0.242838i	−0.575185	−	0.818023i	$-0.695070\pi$
$661$	6.24335	−	6.24335i	0.242838	−	0.242838i	0.818023	+	0.575185i	$0.195070\pi$
$662$	56.0512	+	32.3612i	2.17849	+	1.25775i
$663$	−38.8293	+	8.87561i	−1.50800	+	0.344700i
$664$			50.5135i			1.96030i
$665$		0			0
$666$	9.82318	+	17.0143i	0.380641	+	0.659289i
$667$			10.2628i			0.397377i
$668$	−43.2192	+	11.5806i	−1.67220	+	0.448065i
$669$	−14.1676	−	3.79621i	−0.547752	−	0.146770i
$670$	3.63775	−	3.63775i	0.140538	−	0.140538i
$671$	−7.12495	+	7.12495i	−0.275056	+	0.275056i
$672$		0			0
$673$	15.2065	−	8.77951i	0.586169	−	0.338425i	−0.177412	−	0.984137i	$-0.556773\pi$
$673$	15.2065	−	8.77951i	0.586169	−	0.338425i	0.763581	+	0.645712i	$0.223439\pi$
$674$	74.7228	−	20.0219i	2.87822	−	0.771216i
$675$	8.28904	−	14.3570i	0.319045	−	0.552603i
$676$	−59.5291	−	4.42273i	−2.28958	−	0.170105i
$677$	20.3504	−	11.7493i	0.782131	−	0.451564i	−0.0550539	−	0.998483i	$-0.517533\pi$
$677$	20.3504	−	11.7493i	0.782131	−	0.451564i	0.837185	+	0.546920i	$0.184200\pi$
$678$	−13.6897	+	51.0908i	−0.525751	+	1.96213i
$679$		0			0
$680$	9.40571	+	5.43039i	0.360692	+	0.208246i
$681$	−0.903058	−	0.241974i	−0.0346053	−	0.00927245i
$682$	15.1546	−	56.5579i	0.580301	−	2.16571i
$683$	9.01937	−	33.6607i	0.345117	−	1.28799i	−0.547359	−	0.836898i	$-0.684367\pi$
$683$	9.01937	−	33.6607i	0.345117	−	1.28799i	0.892476	−	0.451095i	$-0.148966\pi$
$684$	15.2541	+	4.08733i	0.583256	+	0.156283i
$685$	−4.49212	−	2.59353i	−0.171635	−	0.0990936i
$686$		0			0
$687$	−18.5011	+	69.0472i	−0.705862	+	2.63431i
$688$	−20.9450	+	12.0926i	−0.798520	+	0.461026i
$689$	24.0274	−	22.3085i	0.915371	−	0.849886i
$690$	−7.02384	+	12.1656i	−0.267393	+	0.463138i
$691$	44.9582	−	12.0465i	1.71029	−	0.458271i	0.734795	−	0.678290i	$-0.237279\pi$
$691$	44.9582	−	12.0465i	1.71029	−	0.458271i	0.975496	+	0.220019i	$0.0706119\pi$
$692$	67.6287	−	39.0454i	2.57086	−	1.48428i
$693$		0			0
$694$	62.5609	−	62.5609i	2.37478	−	2.37478i
$695$	−2.43876	+	2.43876i	−0.0925075	+	0.0925075i
$696$	34.9158	+	9.35566i	1.32348	+	0.354625i
$697$	8.84550	−	2.37014i	0.335047	−	0.0897756i
$698$		−	10.5531i		−	0.399440i
$699$	−29.4254	−	50.9663i	−1.11297	−	1.92772i
$700$		0			0
$701$			7.19399i			0.271713i	0.990729	+	0.135857i	$0.0433787\pi$
$701$			7.19399i			0.271713i	−0.990729	+	0.135857i	$0.956621\pi$
$702$	−31.6772	−	1.17511i	−1.19558	−	0.0443518i
$703$	−1.25002	−	0.721699i	−0.0471454	−	0.0272194i
$704$	−5.41772	+	5.41772i	−0.204188	+	0.204188i
$705$	7.89233	+	4.55664i	0.297242	+	0.171613i
$706$	−13.9744	+	24.2044i	−0.525934	+	0.910945i
$707$		0			0
$708$	−23.8102	−	88.8609i	−0.894843	−	3.33960i
$709$	0.110125	+	0.110125i	0.00413582	+	0.00413582i	0.709172	−	0.705036i	$-0.249069\pi$
$709$	0.110125	+	0.110125i	0.00413582	+	0.00413582i	−0.705036	+	0.709172i	$0.749069\pi$
$710$	−0.596258	−	2.22527i	−0.0223772	−	0.0835127i
$711$	−7.72800	−	13.3853i	−0.289823	−	0.501988i
$712$	−39.7581	+	68.8630i	−1.49000	+	2.58075i
$713$	−30.9079	−	8.28174i	−1.15751	−	0.310154i
$714$		0			0
$715$	−5.08359	+	1.16201i	−0.190115	+	0.0434567i
$716$	−24.9522	−	43.2186i	−0.932509	−	1.61515i
$717$	5.45170	+	5.45170i	0.203597	+	0.203597i
$718$	79.0302			2.94938
$719$	12.9627			0.483429			0.241714	−	0.970347i	$-0.422290\pi$
$719$	12.9627			0.483429			0.241714	+	0.970347i	$0.422290\pi$
$720$	9.50324	+	9.50324i	0.354165	+	0.354165i
$721$		0			0
$722$	45.5105	−	12.1945i	1.69372	−	0.453832i
$723$	−21.0582	+	78.5903i	−0.783163	+	2.92280i
$724$	−82.6002	+	47.6893i	−3.06981	+	1.77236i
$725$			9.75378i			0.362246i
$726$	−3.90802	−	14.5849i	−0.145040	−	0.541297i
$727$	−49.4330			−1.83337			−0.916684	−	0.399614i	$-0.869144\pi$
$727$	−49.4330			−1.83337			−0.916684	+	0.399614i	$0.869144\pi$
$728$		0			0
$729$	42.9729			1.59159
$730$	1.31093	+	4.89246i	0.0485198	+	0.181078i
$731$			12.5415i			0.463866i
$732$	29.7577	−	17.1806i	1.09988	−	0.635013i
$733$	−8.85517	+	33.0480i	−0.327073	+	1.22065i	0.585138	+	0.810934i	$0.301040\pi$
$733$	−8.85517	+	33.0480i	−0.327073	+	1.22065i	−0.912211	+	0.409720i	$0.865626\pi$
$734$	61.8450	−	16.5713i	2.28274	−	0.611658i
$735$		0			0
$736$	25.1297	+	25.1297i	0.926292	+	0.926292i
$737$	18.2618			0.672680
$738$	24.5036			0.901988
$739$	3.02262	+	3.02262i	0.111189	+	0.111189i	0.760512	−	0.649323i	$-0.224948\pi$
$739$	3.02262	+	3.02262i	0.111189	+	0.111189i	−0.649323	+	0.760512i	$0.724948\pi$
$740$	−1.63902	−	2.83887i	−0.0602517	−	0.104359i
$741$	6.92162	−	3.66102i	0.254272	−	0.134491i
$742$		0			0
$743$	23.2815	+	6.23826i	0.854115	+	0.228859i	0.659206	−	0.751962i	$-0.270892\pi$
$743$	23.2815	+	6.23826i	0.854115	+	0.228859i	0.194909	+	0.980821i	$0.437559\pi$
$744$	−56.3519	+	97.6043i	−2.06596	+	3.57835i
$745$	3.72080	+	6.44461i	0.136319	+	0.236112i
$746$	12.0868	+	45.1087i	0.442530	+	1.65155i
$747$	22.9203	+	22.9203i	0.838609	+	0.838609i
$748$	17.6780	+	65.9754i	0.646373	+	2.41230i
$749$		0			0
$750$	−13.5698	+	23.5035i	−0.495498	+	0.858227i
$751$	11.3539	+	6.55518i	0.414310	+	0.239202i	0.692640	−	0.721283i	$-0.256447\pi$
$751$	11.3539	+	6.55518i	0.414310	+	0.239202i	−0.278330	+	0.960486i	$0.589781\pi$
$752$	47.4012	−	47.4012i	1.72854	−	1.72854i
$753$	−38.9466	−	22.4858i	−1.41929	−	0.819429i
$754$	16.4861	−	8.71994i	0.600390	−	0.317561i
$755$			5.60548i			0.204004i
$756$		0			0
$757$	7.95111	+	13.7717i	0.288988	+	0.500542i	0.973568	−	0.228395i	$-0.0733479\pi$
$757$	7.95111	+	13.7717i	0.288988	+	0.500542i	−0.684580	+	0.728937i	$0.740015\pi$
$758$		−	2.15545i		−	0.0782895i
$759$	−48.1663	+	12.9061i	−1.74832	+	0.468462i
$760$	−2.06233	−	0.552600i	−0.0748087	−	0.0200449i
$761$	27.9954	−	27.9954i	1.01483	−	1.01483i	0.0149439	−	0.999888i	$-0.495243\pi$
$761$	27.9954	−	27.9954i	1.01483	−	1.01483i	0.999888	−	0.0149439i	$-0.00475696\pi$
$762$	−61.5705	+	61.5705i	−2.23047	+	2.23047i
$763$		0			0
$764$	−5.90280	+	3.40799i	−0.213556	+	0.123297i
$765$	6.73181	−	1.80378i	0.243389	−	0.0652160i
$766$	−7.45248	+	12.9081i	−0.269269	+	0.466388i
$767$	−22.6892	−	14.2464i	−0.819260	−	0.514409i
$768$	−61.0247	+	35.2326i	−2.20204	+	1.27135i
$769$	−1.28737	+	4.80452i	−0.0464236	+	0.173255i	−0.985245	−	0.171148i	$-0.945252\pi$
$769$	−1.28737	+	4.80452i	−0.0464236	+	0.173255i	0.938822	+	0.344404i	$0.111919\pi$
$770$		0			0
$771$	−28.5143	−	16.4627i	−1.02692	−	0.592891i
$772$	32.5666	+	8.72620i	1.17210	+	0.314063i
$773$	8.58704	−	32.0473i	0.308855	−	1.15266i	−0.620722	−	0.784031i	$-0.713160\pi$
$773$	8.58704	−	32.0473i	0.308855	−	1.15266i	0.929576	−	0.368630i	$-0.120173\pi$
$774$	−8.68556	+	32.4149i	−0.312196	+	1.16513i
$775$	−29.3749	−	7.87099i	−1.05518	−	0.282734i
$776$	−46.0565	−	26.5907i	−1.65333	−	0.954551i
$777$		0			0
$778$	−5.79862	+	21.6408i	−0.207891	+	0.775859i
$779$	−1.55906	+	0.900125i	−0.0558592	+	0.0322503i
$780$	17.7706	+	0.659228i	0.636291	+	0.0236041i
$781$	4.08887	−	7.08212i	0.146311	−	0.253418i
$782$	51.7582	−	13.8686i	1.85087	−	0.495939i
$783$	5.97466	−	3.44947i	0.213517	−	0.123274i
$784$		0			0
$785$	3.94646	−	3.94646i	0.140855	−	0.140855i
$786$	57.6217	−	57.6217i	2.05530	−	2.05530i
$787$	12.2216	+	3.27477i	0.435653	+	0.116733i	0.469978	−	0.882678i	$-0.344262\pi$
$787$	12.2216	+	3.27477i	0.435653	+	0.116733i	−0.0343257	+	0.999411i	$0.510928\pi$
$788$	−80.0882	+	21.4596i	−2.85302	+	0.764466i
$789$			39.3828i			1.40207i
$790$	1.85106	+	3.20614i	0.0658579	+	0.114069i
$791$		0			0
$792$			103.159i			3.66558i
$793$	2.94646	−	9.56308i	0.104632	−	0.339595i
$794$	−0.472875	−	0.273015i	−0.0167817	−	0.00968893i
$795$	−6.90658	+	6.90658i	−0.244951	+	0.244951i
$796$	12.9698	+	7.48811i	0.459702	+	0.265409i
$797$	3.71613	−	6.43653i	0.131632	−	0.227994i	−0.792674	−	0.609646i	$-0.791312\pi$
$797$	3.71613	−	6.43653i	0.131632	−	0.227994i	0.924306	+	0.381652i	$0.124645\pi$
$798$		0			0
$799$	−8.99708	−	33.5776i	−0.318294	−	1.18789i
$800$	23.8833	+	23.8833i	0.844403	+	0.844403i
$801$	13.2062	+	49.2864i	0.466620	+	1.74145i
$802$	9.00980	+	15.6054i	0.318147	+	0.551047i
$803$	−8.98977	+	15.5707i	−0.317242	+	0.549479i
$804$	−60.1531	−	16.1180i	−2.12144	−	0.568437i
$805$		0			0
$806$	12.9576	+	56.6871i	0.456411	+	1.99672i
$807$	6.71927	+	11.6381i	0.236530	+	0.409681i
$808$	21.1853	+	21.1853i	0.745297	+	0.745297i
$809$	−53.8245			−1.89237			−0.946185	−	0.323626i	$-0.895098\pi$
$809$	−53.8245			−1.89237			−0.946185	+	0.323626i	$0.895098\pi$
$810$	−3.65857			−0.128549
$811$	19.2534	+	19.2534i	0.676078	+	0.676078i	0.959110	−	0.283032i	$-0.0913404\pi$
$811$	19.2534	+	19.2534i	0.676078	+	0.676078i	−0.283032	+	0.959110i	$0.591340\pi$
$812$		0			0
$813$	−69.0021	+	18.4891i	−2.42001	+	0.648440i
$814$	4.32342	−	16.1352i	0.151536	−	0.565539i
$815$	3.26984	−	1.88784i	0.114538	−	0.0661283i
$816$		−	87.2819i		−	3.05548i
$817$	−0.638119	−	2.38149i	−0.0223249	−	0.0833178i
$818$	−27.4885			−0.961113
$819$		0			0
$820$	−4.08848			−0.142776
$821$	−2.43089	−	9.07220i	−0.0848386	−	0.316622i	0.910445	−	0.413630i	$-0.135739\pi$
$821$	−2.43089	−	9.07220i	−0.0848386	−	0.316622i	−0.995284	+	0.0970082i	$0.969073\pi$
$822$			90.1382i			3.14393i
$823$	37.1775	−	21.4644i	1.29592	−	0.748202i	0.316227	−	0.948684i	$-0.397584\pi$
$823$	37.1775	−	21.4644i	1.29592	−	0.748202i	0.979698	+	0.200481i	$0.0642505\pi$
$824$	27.7283	−	103.484i	0.965963	−	3.60502i
$825$	−45.7774	+	12.2660i	−1.59376	+	0.427048i
$826$		0			0
$827$	−2.53773	−	2.53773i	−0.0882457	−	0.0882457i	0.661606	−	0.749852i	$-0.269875\pi$
$827$	−2.53773	−	2.53773i	−0.0882457	−	0.0882457i	−0.749852	+	0.661606i	$0.769875\pi$
$828$	99.8768			3.47096
$829$	−50.7495			−1.76260			−0.881301	−	0.472556i	$-0.843331\pi$
$829$	−50.7495			−1.76260			−0.881301	+	0.472556i	$0.843331\pi$
$830$	−5.49002	−	5.49002i	−0.190561	−	0.190561i
$831$	−27.5351	−	47.6922i	−0.955182	−	1.65442i
$832$	2.24046	−	7.27165i	0.0776738	−	0.252099i
$833$		0			0
$834$	57.8917	+	15.5120i	2.00462	+	0.537138i
$835$	1.94090	−	3.36173i	0.0671675	−	0.116338i
$836$	−6.71370	−	11.6285i	−0.232198	−	0.402179i
$837$	5.56722	+	20.7772i	0.192431	+	0.718164i
$838$	1.89391	+	1.89391i	0.0654240	+	0.0654240i
$839$	3.51172	+	13.1059i	0.121238	+	0.452466i	0.999678	−	0.0253868i	$-0.00808173\pi$
$839$	3.51172	+	13.1059i	0.121238	+	0.452466i	−0.878440	+	0.477853i	$0.841415\pi$
$840$		0			0
$841$	12.4705	−	21.5995i	0.430017	−	0.744811i
$842$	−72.2838	−	41.7331i	−2.49106	−	1.43822i
$843$	10.4273	−	10.4273i	0.359137	−	0.359137i
$844$	−8.82039	−	5.09245i	−0.303610	−	0.175290i
$845$	3.92317	−	3.38054i	0.134961	−	0.116294i
$846$		−	93.0156i		−	3.19794i
$847$		0			0
$848$	35.9234	+	62.2212i	1.23361	+	2.13668i
$849$		−	67.5095i		−	2.31692i
$850$	49.1912	−	13.1807i	1.68724	−	0.452095i
$851$	−8.81761	−	2.36267i	−0.302264	−	0.0809914i
$852$	−19.7192	+	19.7192i	−0.675569	+	0.675569i
$853$	35.8111	−	35.8111i	1.22615	−	1.22615i	0.260737	−	0.965410i	$-0.416034\pi$
$853$	35.8111	−	35.8111i	1.22615	−	1.22615i	0.965410	−	0.260737i	$-0.0839656\pi$
$854$		0			0
$855$	−1.18651	+	0.685035i	−0.0405780	+	0.0234277i
$856$	−69.5253	+	18.6293i	−2.37633	+	0.636735i
$857$	−15.4326	+	26.7300i	−0.527167	+	0.913081i	0.472331	+	0.881421i	$0.343413\pi$
$857$	−15.4326	+	26.7300i	−0.527167	+	0.913081i	−0.999499	+	0.0316597i	$0.989921\pi$
$858$	61.6576	+	66.4084i	2.10496	+	2.26715i
$859$	−28.1342	+	16.2433i	−0.959928	+	0.554215i	−0.896151	−	0.443750i	$-0.853648\pi$
$859$	−28.1342	+	16.2433i	−0.959928	+	0.554215i	−0.0637770	+	0.997964i	$0.520315\pi$
$860$	1.44921	−	5.40851i	0.0494175	−	0.184429i
$861$		0			0
$862$	−18.1961	−	10.5055i	−0.619761	−	0.357819i
$863$	7.31448	+	1.95991i	0.248988	+	0.0667161i	0.381154	−	0.924511i	$-0.375527\pi$
$863$	7.31448	+	1.95991i	0.248988	+	0.0667161i	−0.132166	+	0.991228i	$0.542193\pi$
$864$	6.18323	−	23.0761i	0.210358	−	0.785066i
$865$	−1.75346	+	6.54400i	−0.0596194	+	0.222503i
$866$	49.3547	+	13.2245i	1.67714	+	0.449388i
$867$	0.498670	+	0.287907i	0.0169357	+	0.00977784i
$868$		0			0
$869$	−3.40128	+	12.6938i	−0.115381	+	0.430606i
$870$	−4.81161	+	2.77799i	−0.163129	+	0.0941826i
$871$	−16.0314	+	8.47943i	−0.543204	+	0.287315i
$872$	11.0943	−	19.2159i	0.375701	−	0.650733i
$873$	−32.9634	+	8.83250i	−1.11564	+	0.298935i
$874$	−9.12264	+	5.26696i	−0.308578	+	0.178158i
$875$		0			0
$876$	43.3546	−	43.3546i	1.46482	−	1.46482i
$877$	−13.5466	+	13.5466i	−0.457437	+	0.457437i	−0.897813	−	0.440376i	$-0.854845\pi$
$877$	−13.5466	+	13.5466i	−0.457437	+	0.457437i	0.440376	+	0.897813i	$0.354845\pi$
$878$	−18.0180	−	4.82791i	−0.608078	−	0.162934i
$879$	−48.0685	+	12.8799i	−1.62131	+	0.434429i
$880$		−	11.4271i		−	0.385207i
$881$	3.37117	+	5.83904i	0.113578	+	0.196722i	0.917210	−	0.398403i	$-0.130436\pi$
$881$	3.37117	+	5.83904i	0.113578	+	0.196722i	−0.803633	+	0.595126i	$0.797102\pi$
$882$		0			0
$883$		−	41.6349i		−	1.40112i	−0.713591	−	0.700562i	$-0.752933\pi$
$883$		−	41.6349i		−	1.40112i	0.713591	−	0.700562i	$-0.247067\pi$
$884$	−46.1532	−	49.7094i	−1.55230	−	1.67191i
$885$	6.91189	+	3.99058i	0.232341	+	0.134142i
$886$	48.2217	−	48.2217i	1.62004	−	1.62004i
$887$	−16.4801	−	9.51479i	−0.553348	−	0.319475i	0.197123	−	0.980379i	$-0.436840\pi$
$887$	−16.4801	−	9.51479i	−0.553348	−	0.319475i	−0.750471	+	0.660903i	$0.770173\pi$
$888$	−16.0765	+	27.8452i	−0.539491	+	0.934425i
$889$		0			0
$890$	−3.16325	−	11.8054i	−0.106032	−	0.395718i
$891$	−9.18315	−	9.18315i	−0.307647	−	0.307647i
$892$	−6.46493	−	24.1275i	−0.216462	−	0.807847i
$893$	3.41688	+	5.91821i	0.114342	+	0.198045i
$894$	64.6582	−	111.991i	2.16249	−	3.74555i
$895$	4.18199	+	1.12056i	0.139788	+	0.0374562i
$896$		0			0
$897$	36.2910	−	33.6948i	1.21172	−	1.12504i
$898$	25.4529	+	44.0856i	0.849373	+	1.47116i
$899$	−8.94882	−	8.94882i	−0.298460	−	0.298460i
$900$	94.9232			3.16411
$901$	37.2571			1.24121
$902$	−14.7320	−	14.7320i	−0.490523	−	0.490523i
$903$		0			0
$904$	−49.1105	+	13.1591i	−1.63339	+	0.437666i
$905$	2.14164	−	7.99270i	0.0711905	−	0.265686i
$906$	84.3589	−	48.7047i	2.80264	−	1.61810i
$907$		−	5.52339i		−	0.183401i	−0.995787	−	0.0917006i	$-0.970770\pi$
$907$		−	5.52339i		−	0.183401i	0.995787	−	0.0917006i	$-0.0292303\pi$
$908$	−0.412081	−	1.53791i	−0.0136754	−	0.0510372i
$909$	19.2255			0.637669
$910$		0			0
$911$	−23.9393			−0.793146			−0.396573	−	0.918003i	$-0.629801\pi$
$911$	−23.9393			−0.793146			−0.396573	+	0.918003i	$0.629801\pi$
$912$	4.44094	+	16.5738i	0.147054	+	0.548814i
$913$		−	27.5603i		−	0.912113i
$914$	55.8085	−	32.2211i	1.84598	−	1.06578i
$915$	−0.771550	+	2.87946i	−0.0255066	+	0.0951921i
$916$	−117.587	+	31.5074i	−3.88519	+	1.04103i
$917$		0			0
$918$	−25.4705	−	25.4705i	−0.840652	−	0.840652i
$919$	−43.5665			−1.43712			−0.718562	−	0.695462i	$-0.755200\pi$
$919$	−43.5665			−1.43712			−0.718562	+	0.695462i	$0.755200\pi$
$920$	−13.5032			−0.445187
$921$	39.5538	+	39.5538i	1.30334	+	1.30334i
$922$	−43.4212	−	75.2077i	−1.43000	−	2.47683i
$923$	−0.301066	+	8.11575i	−0.00990971	+	0.267133i
$924$		0			0
$925$	−8.38029	−	2.24549i	−0.275542	−	0.0738313i
$926$	−24.8085	+	42.9696i	−0.815258	+	1.41207i
$927$	−34.3736	−	59.5369i	−1.12898	−	1.95545i
$928$	3.63793	+	13.5769i	0.119421	+	0.445684i
$929$	−23.8005	−	23.8005i	−0.780868	−	0.780868i	0.199110	−	0.979977i	$-0.436195\pi$
$929$	−23.8005	−	23.8005i	−0.780868	−	0.780868i	−0.979977	+	0.199110i	$0.936195\pi$
$930$	−4.48349	−	16.7326i	−0.147020	−	0.548684i
$931$		0			0
$932$	50.1114	−	86.7955i	1.64145	−	2.84308i
$933$	13.6869	+	7.90215i	0.448090	+	0.258705i
$934$	27.5089	−	27.5089i	0.900119	−	0.900119i
$935$	−5.13178	−	2.96283i	−0.167827	−	0.0968950i
$936$	−47.8994	−	90.5599i	−1.56564	−	2.96004i
$937$			9.65419i			0.315389i	0.987488	+	0.157694i	$0.0504061\pi$
$937$			9.65419i			0.315389i	−0.987488	+	0.157694i	$0.949594\pi$
$938$		0			0
$939$	27.5125	+	47.6530i	0.897836	+	1.55510i
$940$			15.5199i			0.506203i
$941$	11.8762	−	3.18222i	0.387154	−	0.103737i	−0.0599916	−	0.998199i	$-0.519107\pi$
$941$	11.8762	−	3.18222i	0.387154	−	0.103737i	0.447145	+	0.894461i	$0.352441\pi$
$942$	−93.6816	−	25.1019i	−3.05231	−	0.817864i
$943$	−8.05080	+	8.05080i	−0.262170	+	0.262170i
$944$	41.5127	−	41.5127i	1.35112	−	1.35112i
$945$		0			0
$946$	24.7105	−	14.2666i	0.803407	−	0.463847i
$947$	26.7529	−	7.16842i	0.869353	−	0.232942i	0.203545	−	0.979066i	$-0.434754\pi$
$947$	26.7529	−	7.16842i	0.869353	−	0.232942i	0.665808	+	0.746123i	$0.268087\pi$
$948$	22.4072	−	38.8104i	0.727753	−	1.26050i
$949$	0.661923	−	17.8433i	0.0214869	−	0.579217i
$950$	−8.67018	+	5.00573i	−0.281298	+	0.162407i
$951$	−5.35286	+	19.9771i	−0.173578	+	0.647803i
$952$		0			0
$953$	−19.2186	−	11.0958i	−0.622550	−	0.359430i	0.155311	−	0.987866i	$-0.450362\pi$
$953$	−19.2186	−	11.0958i	−0.622550	−	0.359430i	−0.777861	+	0.628436i	$0.783695\pi$
$954$	96.2949	+	25.8021i	3.11766	+	0.835375i
$955$	0.153046	−	0.571177i	0.00495247	−	0.0184829i
$956$	−3.39826	+	12.6825i	−0.109908	+	0.410181i
$957$	−19.0502	−	5.10447i	−0.615804	−	0.165004i
$958$	55.8970	+	32.2722i	1.80595	+	1.04267i
$959$		0			0
$960$	−0.586677	+	2.18951i	−0.0189349	+	0.0706661i
$961$	7.32532	−	4.22927i	0.236301	−	0.136428i
$962$	3.69663	+	16.1721i	0.119184	+	0.521409i
$963$	−23.0939	+	39.9998i	−0.744190	+	1.28897i
$964$	−133.839	+	35.8621i	−4.31067	+	1.15504i
$965$	−2.53314	+	1.46251i	−0.0815446	+	0.0470798i
$966$		0			0
$967$	−14.2351	+	14.2351i	−0.457769	+	0.457769i	−0.897923	−	0.440153i	$-0.854924\pi$
$967$	−14.2351	+	14.2351i	−0.457769	+	0.457769i	0.440153	+	0.897923i	$0.354924\pi$
$968$	10.2631	−	10.2631i	0.329868	−	0.329868i
$969$	8.59457	+	2.30291i	0.276097	+	0.0739800i
$970$	7.89561	−	2.11562i	0.253513	−	0.0679285i
$971$			45.6667i			1.46552i	0.680490	+	0.732758i	$0.261767\pi$
$971$			45.6667i			1.46552i	−0.680490	+	0.732758i	$0.738233\pi$
$972$	45.7291	+	79.2051i	1.46676	+	2.54050i
$973$		0			0
$974$			66.3283i			2.12529i
$975$	34.4911	−	32.0236i	1.10460	−	1.02558i
$976$	18.9901	+	10.9640i	0.607859	+	0.350948i
$977$	23.9587	−	23.9587i	0.766508	−	0.766508i	−0.210982	−	0.977490i	$-0.567666\pi$
$977$	23.9587	−	23.9587i	0.766508	−	0.766508i	0.977490	+	0.210982i	$0.0676663\pi$
$978$	−56.8218	−	32.8061i	−1.81696	−	1.04902i
$979$	21.6921	−	37.5719i	0.693283	−	1.20080i
$980$		0			0
$981$	−3.68514	−	13.7531i	−0.117658	−	0.439104i
$982$	−65.5139	−	65.5139i	−2.09063	−	2.09063i
$983$	−9.21537	−	34.3922i	−0.293925	−	1.09694i	−0.942068	−	0.335423i	$-0.891121\pi$
$983$	−9.21537	−	34.3922i	−0.293925	−	1.09694i	0.648143	−	0.761519i	$-0.275546\pi$
$984$	20.0511	+	34.7294i	0.639204	+	1.10713i
$985$	3.59662	−	6.22952i	0.114598	−	0.198489i
$986$	20.4708	+	5.48514i	0.651923	+	0.174682i
$987$		0			0
$988$	11.2932	+	7.09093i	0.359284	+	0.225592i
$989$	−7.79644	−	13.5038i	−0.247912	−	0.429397i
$990$	−11.2117	−	11.2117i	−0.356332	−	0.356332i
$991$	49.6294			1.57653			0.788265	−	0.615336i	$-0.210980\pi$
$991$	49.6294			1.57653			0.788265	+	0.615336i	$0.210980\pi$
$992$	−43.8246			−1.39143
$993$	48.0624	+	48.0624i	1.52521	+	1.52521i
$994$		0			0
$995$	−1.25500	+	0.336278i	−0.0397863	+	0.0106607i
$996$	−24.3249	+	90.7819i	−0.770765	+	2.87654i
$997$	6.36471	−	3.67467i	0.201572	−	0.116378i	−0.395816	−	0.918330i	$-0.629538\pi$
$997$	6.36471	−	3.67467i	0.201572	−	0.116378i	0.597389	+	0.801952i	$0.296205\pi$
$998$		−	72.5134i		−	2.29537i
$999$	1.58826	+	5.92745i	0.0502502	+	0.187536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.80.8		32
7.2	even	3		637.2.bb.b.509.7		32
7.3	odd	6		91.2.bc.a.41.1	yes	32
7.4	even	3		91.2.bc.a.41.2	yes	32
7.5	odd	6		637.2.bb.b.509.8		32
7.6	odd	2	inner	637.2.x.b.80.7		32
13.7	odd	12		637.2.bb.b.423.8		32
21.11	odd	6		819.2.fm.g.496.7		32
21.17	even	6		819.2.fm.g.496.8		32
91.20	even	12		637.2.bb.b.423.7		32
91.33	even	12	inner	637.2.x.b.215.7		32
91.46	odd	12		91.2.bc.a.20.1	✓	32
91.59	even	12		91.2.bc.a.20.2	yes	32
91.72	odd	12	inner	637.2.x.b.215.8		32
273.59	odd	12		819.2.fm.g.748.7		32
273.137	even	12		819.2.fm.g.748.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.1	✓	32	91.46	odd	12
91.2.bc.a.20.2	yes	32	91.59	even	12
91.2.bc.a.41.1	yes	32	7.3	odd	6
91.2.bc.a.41.2	yes	32	7.4	even	3
637.2.x.b.80.7		32	7.6	odd	2	inner
637.2.x.b.80.8		32	1.1	even	1	trivial
637.2.x.b.215.7		32	91.33	even	12	inner
637.2.x.b.215.8		32	91.72	odd	12	inner
637.2.bb.b.423.7		32	91.20	even	12
637.2.bb.b.423.8		32	13.7	odd	12
637.2.bb.b.509.7		32	7.2	even	3
637.2.bb.b.509.8		32	7.5	odd	6
819.2.fm.g.496.7		32	21.11	odd	6
819.2.fm.g.496.8		32	21.17	even	6
819.2.fm.g.748.7		32	273.59	odd	12
819.2.fm.g.748.8		32	273.137	even	12

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.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.664504 + 2.47996i) q^{2} +2.69629i q^{3} +(-3.97660 + 2.29589i) q^{4} +(0.103104 - 0.384791i) q^{5} +(-6.68671 + 1.79170i) q^{6} +(-4.70528 - 4.70528i) q^{8} -4.27000 q^{9} +O(q^{10})\)	\(q+(0.664504 + 2.47996i) q^{2} +2.69629i q^{3} +(-3.97660 + 2.29589i) q^{4} +(0.103104 - 0.384791i) q^{5} +(-6.68671 + 1.79170i) q^{6} +(-4.70528 - 4.70528i) q^{8} -4.27000 q^{9} +1.02278 q^{10} +(2.56721 + 2.56721i) q^{11} +(-6.19040 - 10.7221i) q^{12} +(-3.44571 - 1.06165i) q^{13} +(1.03751 + 0.278000i) q^{15} +(3.95046 - 6.84240i) q^{16} +(-2.04856 - 3.54822i) q^{17} +(-2.83743 - 10.5895i) q^{18} +(0.569532 + 0.569532i) q^{19} +(0.473433 + 1.76688i) q^{20} +(-4.66067 + 8.07252i) q^{22} +(4.41149 + 2.54698i) q^{23} +(12.6868 - 12.6868i) q^{24} +(4.19269 + 2.42065i) q^{25} +(0.343169 - 9.25070i) q^{26} -3.42430i q^{27} +(1.00735 + 1.74478i) q^{29} +2.75772i q^{30} +(-6.06756 + 1.62580i) q^{31} +(6.73893 + 1.80569i) q^{32} +(-6.92197 + 6.92197i) q^{33} +(7.43817 - 7.43817i) q^{34} +(16.9801 - 9.80347i) q^{36} +(-1.73100 + 0.463819i) q^{37} +(-1.03396 + 1.79088i) q^{38} +(2.86252 - 9.29064i) q^{39} +(-2.29568 + 1.32541i) q^{40} +(-0.578490 + 2.15895i) q^{41} +(-2.65096 - 1.53053i) q^{43} +(-16.1028 - 4.31474i) q^{44} +(-0.440256 + 1.64306i) q^{45} +(-3.38495 + 12.6328i) q^{46} +(8.19540 + 2.19595i) q^{47} +(18.4491 + 10.6516i) q^{48} +(-3.21707 + 12.0063i) q^{50} +(9.56703 - 5.52353i) q^{51} +(16.1396 - 3.68921i) q^{52} +(-4.54674 + 7.87518i) q^{53} +(8.49214 - 2.27546i) q^{54} +(1.25253 - 0.723149i) q^{55} +(-1.53563 + 1.53563i) q^{57} +(-3.65761 + 3.65761i) q^{58} +(7.17731 + 1.92316i) q^{59} +(-4.76402 + 1.27652i) q^{60} +2.77536i q^{61} +(-8.06384 - 13.9670i) q^{62} +2.11035i q^{64} +(-0.763781 + 1.21642i) q^{65} +(-21.7659 - 12.5665i) q^{66} +(3.55672 - 3.55672i) q^{67} +(16.2926 + 9.40656i) q^{68} +(-6.86740 + 11.8947i) q^{69} +(-0.582978 - 2.17570i) q^{71} +(20.0916 + 20.0916i) q^{72} +(1.28173 + 4.78349i) q^{73} +(-2.30051 - 3.98460i) q^{74} +(-6.52679 + 11.3047i) q^{75} +(-3.57239 - 0.957219i) q^{76} +(24.9426 + 0.925283i) q^{78} +(1.80984 + 3.13473i) q^{79} +(-2.22558 - 2.22558i) q^{80} -3.57709 q^{81} -5.73853 q^{82} +(-5.36774 - 5.36774i) q^{83} +(-1.57654 + 0.422432i) q^{85} +(2.03409 - 7.59132i) q^{86} +(-4.70444 + 2.71611i) q^{87} -24.1589i q^{88} +(-3.09280 - 11.5425i) q^{89} -4.36728 q^{90} -23.3903 q^{92} +(-4.38363 - 16.3599i) q^{93} +21.7835i q^{94} +(0.277872 - 0.160430i) q^{95} +(-4.86867 + 18.1701i) q^{96} +(7.71975 - 2.06850i) q^{97} +(-10.9620 - 10.9620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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