LMFDB - Embedded newform 676.2.l.k.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(19,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("676.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.l (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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			319.1
Root			$-1.39427 - 0.236640i$ of defining polynomial
Character	$\chi$	$=$	676.319
Dual form			676.2.l.k.587.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.902074 - 1.08916i) q^{2} +(-0.736159 - 0.425021i) q^{3} +(-0.372527 + 1.96500i) q^{4} +(0.166404 + 0.166404i) q^{5} +(0.201154 + 1.18519i) q^{6} +(-0.684384 + 2.55416i) q^{7} +(2.47624 - 1.36683i) q^{8} +(-1.13871 - 1.97231i) q^{9} +(0.0311314 - 0.331348i) q^{10} +(1.39298 - 0.373247i) q^{11} +(1.10941 - 1.28822i) q^{12} +(3.39924 - 1.55864i) q^{14} +(-0.0517744 - 0.193225i) q^{15} +(-3.72245 - 1.46403i) q^{16} +(1.21178 - 0.699622i) q^{17} +(-1.12095 + 3.01941i) q^{18} +(-5.39188 - 1.44475i) q^{19} +(-0.388973 + 0.264994i) q^{20} +(1.58939 - 1.58939i) q^{21} +(-1.66309 - 1.18047i) q^{22} +(-4.37216 + 7.57279i) q^{23} +(-2.40384 - 0.0462481i) q^{24} -4.94462i q^{25} +4.48604i q^{27} +(-4.76397 - 2.29631i) q^{28} +(-2.11023 + 3.65503i) q^{29} +(-0.163748 + 0.230693i) q^{30} +(-3.88100 + 3.88100i) q^{31} +(1.76336 + 5.37499i) q^{32} +(-1.18409 - 0.317276i) q^{33} +(-1.85511 - 0.688709i) q^{34} +(-0.538906 + 0.311137i) q^{35} +(4.29979 - 1.50283i) q^{36} +(0.133975 + 0.500000i) q^{37} +(3.29032 + 7.17588i) q^{38} +(0.639502 + 0.184609i) q^{40} +(-5.59808 + 1.50000i) q^{41} +(-3.16484 - 0.297348i) q^{42} +(-4.59362 - 7.95638i) q^{43} +(0.214509 + 2.87624i) q^{44} +(0.138714 - 0.517686i) q^{45} +(12.1920 - 2.06925i) q^{46} +(2.80318 + 2.80318i) q^{47} +(2.11807 + 2.65988i) q^{48} +(0.00684229 + 0.00395040i) q^{49} +(-5.38547 + 4.46041i) q^{50} -1.18942 q^{51} -5.94462 q^{53} +(4.88600 - 4.04674i) q^{54} +(0.293906 + 0.169687i) q^{55} +(1.79641 + 7.26015i) q^{56} +(3.35523 + 3.35523i) q^{57} +(5.88449 - 0.998732i) q^{58} +(-2.20512 + 8.22961i) q^{59} +(0.398974 - 0.0297554i) q^{60} +(3.61102 + 6.25448i) q^{61} +(7.72796 + 0.726071i) q^{62} +(5.81691 - 1.55864i) q^{63} +(4.26353 - 6.76922i) q^{64} +(0.722573 + 1.57587i) q^{66} +(0.652790 + 2.43624i) q^{67} +(0.923336 + 2.64178i) q^{68} +(6.43720 - 3.71652i) q^{69} +(0.825010 + 0.306284i) q^{70} +(-10.5002 - 2.81352i) q^{71} +(-5.51555 - 3.32748i) q^{72} +(-5.05407 + 5.05407i) q^{73} +(0.423724 - 0.596956i) q^{74} +(-2.10157 + 3.64002i) q^{75} +(4.84756 - 10.0568i) q^{76} +3.81333i q^{77} +8.51654i q^{79} +(-0.375809 - 0.863050i) q^{80} +(-1.50948 + 2.61449i) q^{81} +(6.68361 + 4.74407i) q^{82} +(6.91195 - 6.91195i) q^{83} +(2.53106 + 3.71523i) q^{84} +(0.318065 + 0.0852251i) q^{85} +(-4.52197 + 12.1804i) q^{86} +(3.10694 - 1.79379i) q^{87} +(2.93918 - 2.82822i) q^{88} +(1.71941 + 6.41693i) q^{89} +(-0.688971 + 0.315910i) q^{90} +(-13.2518 - 11.4124i) q^{92} +(4.50653 - 1.20752i) q^{93} +(0.524430 - 5.58179i) q^{94} +(-0.656818 - 1.13764i) q^{95} +(0.986372 - 4.70632i) q^{96} +(4.00474 - 14.9459i) q^{97} +(-0.00186964 - 0.0110159i) q^{98} +(-2.32236 - 2.32236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 6 q^{4} + 12 q^{5} + 14 q^{6} - 10 q^{8} + 4 q^{9} + 8 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{18} - 2 q^{20} + 28 q^{21} - 10 q^{24} - 12 q^{28} - 8 q^{29} + 42 q^{30} - 28 q^{32} + 20 q^{33}+ \cdots + 2 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 6 * q^4 + 12 * q^5 + 14 * q^6 - 10 * q^8 + 4 * q^9 + 8 * q^14 - 2 * q^16 + 12 * q^17 + 6 * q^18 - 2 * q^20 + 28 * q^21 - 10 * q^24 - 12 * q^28 - 8 * q^29 + 42 * q^30 - 28 * q^32 + 20 * q^33 - 14 * q^34 - 6 * q^36 + 16 * q^37 - 40 * q^40 - 48 * q^41 - 28 * q^42 + 8 * q^44 - 20 * q^45 + 46 * q^46 - 10 * q^48 + 60 * q^49 - 10 * q^50 - 32 * q^53 + 16 * q^54 - 60 * q^56 - 12 * q^57 + 48 * q^58 + 24 * q^60 + 4 * q^61 - 18 * q^62 + 56 * q^66 + 16 * q^68 - 12 * q^69 - 28 * q^70 - 56 * q^72 - 20 * q^73 + 4 * q^74 - 22 * q^76 - 44 * q^80 + 48 * q^81 - 84 * q^84 - 20 * q^85 - 16 * q^86 + 36 * q^88 + 52 * q^89 - 12 * q^92 + 92 * q^93 - 38 * q^94 + 72 * q^96 + 28 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.902074	−	1.08916i	−0.637862	−	0.770150i
$2$	−0.902074	−	1.08916i	−0.637862	−	0.770150i
$3$	−0.736159	−	0.425021i	−0.425021	−	0.245386i	0.272202	−	0.962240i	$-0.412248\pi$
$3$	−0.736159	−	0.425021i	−0.425021	−	0.245386i	−0.697223	+	0.716854i	$0.745581\pi$
$4$	−0.372527	+	1.96500i	−0.186263	+	0.982500i
$5$	0.166404	+	0.166404i	0.0744180	+	0.0744180i	0.743336	−	0.668918i	$-0.233242\pi$
$5$	0.166404	+	0.166404i	0.0744180	+	0.0744180i	−0.668918	+	0.743336i	$0.733242\pi$
$6$	0.201154	+	1.18519i	0.0821208	+	0.483853i
$7$	−0.684384	+	2.55416i	−0.258673	+	0.965381i	0.707337	+	0.706876i	$0.249896\pi$
$7$	−0.684384	+	2.55416i	−0.258673	+	0.965381i	−0.966010	+	0.258504i	$0.916770\pi$
$8$	2.47624	−	1.36683i	0.875483	−	0.483249i
$9$	−1.13871	−	1.97231i	−0.379571	−	0.657437i
$10$	0.0311314	−	0.331348i	0.00984462	−	0.104782i
$11$	1.39298	−	0.373247i	0.419998	−	0.112538i	−0.0426292	−	0.999091i	$-0.513573\pi$
$11$	1.39298	−	0.373247i	0.419998	−	0.112538i	0.462628	+	0.886553i	$0.346907\pi$
$12$	1.10941	−	1.28822i	0.320258	−	0.371877i
$13$		0			0
$13$		0			0
$14$	3.39924	−	1.55864i	0.908486	−	0.416563i
$15$	−0.0517744	−	0.193225i	−0.0133681	−	0.0498904i
$16$	−3.72245	−	1.46403i	−0.930612	−	0.366007i
$17$	1.21178	−	0.699622i	0.293900	−	0.169683i	−0.345799	−	0.938308i	$-0.612392\pi$
$17$	1.21178	−	0.699622i	0.293900	−	0.169683i	0.639699	+	0.768625i	$0.279059\pi$
$18$	−1.12095	+	3.01941i	−0.264211	+	0.711681i
$19$	−5.39188	−	1.44475i	−1.23698	−	0.331449i	−0.419688	−	0.907668i	$-0.637861\pi$
$19$	−5.39188	−	1.44475i	−1.23698	−	0.331449i	−0.817295	+	0.576220i	$0.804527\pi$
$20$	−0.388973	+	0.264994i	−0.0869771	+	0.0592544i
$21$	1.58939	−	1.58939i	0.346833	−	0.346833i
$22$	−1.66309	−	1.18047i	−0.354572	−	0.251678i
$23$	−4.37216	+	7.57279i	−0.911657	+	1.57904i	−0.0999345	+	0.994994i	$0.531863\pi$
$23$	−4.37216	+	7.57279i	−0.911657	+	1.57904i	−0.811723	+	0.584043i	$0.801470\pi$
$24$	−2.40384	−	0.0462481i	−0.490682	−	0.00944036i
$25$		−	4.94462i		−	0.988924i
$26$		0			0
$27$			4.48604i			0.863339i
$28$	−4.76397	−	2.29631i	−0.900305	−	0.433961i
$29$	−2.11023	+	3.65503i	−0.391861	+	0.678723i	−0.992695	−	0.120651i	$-0.961502\pi$
$29$	−2.11023	+	3.65503i	−0.391861	+	0.678723i	0.600834	+	0.799374i	$0.294835\pi$
$30$	−0.163748	+	0.230693i	−0.0298961	+	0.0421187i
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	−0.963773	−	0.266725i	$-0.914058\pi$
$31$	−3.88100	+	3.88100i	−0.697047	+	0.697047i	0.266725	+	0.963773i	$0.414058\pi$
$32$	1.76336	+	5.37499i	0.311722	+	0.950173i
$33$	−1.18409	−	0.317276i	−0.206124	−	0.0552307i
$34$	−1.85511	−	0.688709i	−0.318149	−	0.118113i
$35$	−0.538906	+	0.311137i	−0.0910917	+	0.0525918i
$36$	4.29979	−	1.50283i	0.716632	−	0.250472i
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	0.976064	−	0.217485i	$-0.0697853\pi$
$37$	0.133975	+	0.500000i	0.0220253	+	0.0821995i	−0.954038	+	0.299684i	$0.903119\pi$
$38$	3.29032	+	7.17588i	0.533760	+	1.16408i
$39$		0			0
$40$	0.639502	+	0.184609i	0.101114	+	0.0291893i
$41$	−5.59808	+	1.50000i	−0.874273	+	0.234261i	−0.667934	−	0.744220i	$-0.732821\pi$
$41$	−5.59808	+	1.50000i	−0.874273	+	0.234261i	−0.206338	+	0.978481i	$0.566155\pi$
$42$	−3.16484	−	0.297348i	−0.488345	−	0.0458818i
$43$	−4.59362	−	7.95638i	−0.700520	−	1.21334i	−0.968284	−	0.249852i	$-0.919618\pi$
$43$	−4.59362	−	7.95638i	−0.700520	−	1.21334i	0.267764	−	0.963484i	$-0.413715\pi$
$44$	0.214509	+	2.87624i	0.0323385	+	0.433610i
$45$	0.138714	−	0.517686i	0.0206782	−	0.0771721i
$46$	12.1920	−	2.06925i	1.79761	−	0.305095i
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	0.881350	−	0.472464i	$-0.156635\pi$
$47$	2.80318	+	2.80318i	0.408886	+	0.408886i	−0.472464	+	0.881350i	$0.656635\pi$
$48$	2.11807	+	2.65988i	0.305717	+	0.383920i
$49$	0.00684229	+	0.00395040i	0.000977470	+	0.000564343i
$50$	−5.38547	+	4.46041i	−0.761620	+	0.630797i
$51$	−1.18942			−0.166552
$52$		0			0
$53$	−5.94462			−0.816556			−0.408278	−	0.912858i	$-0.633871\pi$
$53$	−5.94462			−0.816556			−0.408278	+	0.912858i	$0.633871\pi$
$54$	4.88600	−	4.04674i	0.664901	−	0.550691i
$55$	0.293906	+	0.169687i	0.0396303	+	0.0228806i
$56$	1.79641	+	7.26015i	0.240055	+	0.970178i
$57$	3.35523	+	3.35523i	0.444411	+	0.444411i
$58$	5.88449	−	0.998732i	0.772672	−	0.131140i
$59$	−2.20512	+	8.22961i	−0.287082	+	1.07140i	0.660223	+	0.751070i	$0.270462\pi$
$59$	−2.20512	+	8.22961i	−0.287082	+	1.07140i	−0.947305	+	0.320334i	$0.896205\pi$
$60$	0.398974	−	0.0297554i	0.0515073	−	0.00384140i
$61$	3.61102	+	6.25448i	0.462344	+	0.800804i	0.999077	−	0.0429485i	$-0.0136751\pi$
$61$	3.61102	+	6.25448i	0.462344	+	0.800804i	−0.536733	+	0.843752i	$0.680342\pi$
$62$	7.72796	+	0.726071i	0.981452	+	0.0922111i
$63$	5.81691	−	1.55864i	0.732861	−	0.196370i
$64$	4.26353	−	6.76922i	0.532941	−	0.846152i
$65$		0			0
$66$	0.722573	+	1.57587i	0.0889426	+	0.193976i
$67$	0.652790	+	2.43624i	0.0797510	+	0.297635i	0.994269	−	0.106912i	$-0.0340962\pi$
$67$	0.652790	+	2.43624i	0.0797510	+	0.297635i	−0.914518	+	0.404546i	$0.867429\pi$
$68$	0.923336	+	2.64178i	0.111971	+	0.320362i
$69$	6.43720	−	3.71652i	0.774948	−	0.447416i
$70$	0.825010	+	0.306284i	0.0986075	+	0.0366080i
$71$	−10.5002	−	2.81352i	−1.24614	−	0.333903i	−0.425298	−	0.905053i	$-0.639831\pi$
$71$	−10.5002	−	2.81352i	−1.24614	−	0.333903i	−0.820846	+	0.571150i	$0.806498\pi$
$72$	−5.51555	−	3.32748i	−0.650014	−	0.392147i
$73$	−5.05407	+	5.05407i	−0.591534	+	0.591534i	−0.938046	−	0.346512i	$-0.887366\pi$
$73$	−5.05407	+	5.05407i	−0.591534	+	0.591534i	0.346512	+	0.938046i	$0.387366\pi$
$74$	0.423724	−	0.596956i	0.0492569	−	0.0693947i
$75$	−2.10157	+	3.64002i	−0.242668	+	0.420314i
$76$	4.84756	−	10.0568i	0.556053	−	1.15360i
$77$			3.81333i			0.434569i
$78$		0			0
$79$			8.51654i			0.958186i	0.877764	+	0.479093i	$0.159034\pi$
$79$			8.51654i			0.958186i	−0.877764	+	0.479093i	$0.840966\pi$
$80$	−0.375809	−	0.863050i	−0.0420168	−	0.0964919i
$81$	−1.50948	+	2.61449i	−0.167720	+	0.290499i
$82$	6.68361	+	4.74407i	0.738081	+	0.523895i
$83$	6.91195	−	6.91195i	0.758685	−	0.758685i	−0.217398	−	0.976083i	$-0.569757\pi$
$83$	6.91195	−	6.91195i	0.758685	−	0.758685i	0.976083	+	0.217398i	$0.0697570\pi$
$84$	2.53106	+	3.71523i	0.276161	+	0.405365i
$85$	0.318065	+	0.0852251i	0.0344989	+	0.00924396i
$86$	−4.52197	+	12.1804i	−0.487616	+	1.31345i
$87$	3.10694	−	1.79379i	0.333098	−	0.192314i
$88$	2.93918	−	2.82822i	0.313317	−	0.301489i
$89$	1.71941	+	6.41693i	0.182257	+	0.680193i	0.995201	+	0.0978511i	$0.0311969\pi$
$89$	1.71941	+	6.41693i	0.182257	+	0.680193i	−0.812944	+	0.582342i	$0.802136\pi$
$90$	−0.688971	+	0.315910i	−0.0726240	+	0.0332998i
$91$		0			0
$92$	−13.2518	−	11.4124i	−1.38160	−	1.18982i
$93$	4.50653	−	1.20752i	0.467306	−	0.125214i
$94$	0.524430	−	5.58179i	0.0540908	−	0.575717i
$95$	−0.656818	−	1.13764i	−0.0673881	−	0.116720i
$96$	0.986372	−	4.70632i	0.100671	−	0.480336i
$97$	4.00474	−	14.9459i	0.406620	−	1.51753i	−0.394429	−	0.918926i	$-0.629058\pi$
$97$	4.00474	−	14.9459i	0.406620	−	1.51753i	0.801049	−	0.598599i	$-0.204276\pi$
$98$	−0.00186964	−	0.0110159i	−0.000188863	−	0.00111277i
$99$	−2.32236	−	2.32236i	−0.233406	−	0.233406i
$100$	9.71618	+	1.84200i	0.971618	+	0.184200i
$101$	−7.94541	−	4.58728i	−0.790598	−	0.456452i	0.0495752	−	0.998770i	$-0.484213\pi$
$101$	−7.94541	−	4.58728i	−0.790598	−	0.456452i	−0.840173	+	0.542319i	$0.817547\pi$
$102$	1.07294	+	1.29546i	0.106237	+	0.128270i
$103$	−10.9080			−1.07480			−0.537398	−	0.843329i	$-0.680593\pi$
$103$	−10.9080			−1.07480			−0.537398	+	0.843329i	$0.680593\pi$
$104$		0			0
$105$	0.528960			0.0516212
$106$	5.36248	+	6.47462i	0.520850	+	0.628871i
$107$	8.53605	+	4.92829i	0.825211	+	0.476436i	0.852210	−	0.523200i	$-0.175262\pi$
$107$	8.53605	+	4.92829i	0.825211	+	0.476436i	−0.0269990	+	0.999635i	$0.508595\pi$
$108$	−8.81507	−	1.67117i	−0.848230	−	0.160808i
$109$	−0.0243171	−	0.0243171i	−0.00232916	−	0.00232916i	0.705941	−	0.708270i	$-0.250524\pi$
$109$	−0.0243171	−	0.0243171i	−0.00232916	−	0.00232916i	−0.708270	+	0.705941i	$0.750524\pi$
$110$	−0.0803094	−	0.473180i	−0.00765720	−	0.0451160i
$111$	0.113884	−	0.425021i	0.0108094	−	0.0403412i
$112$	6.28695	−	8.50576i	0.594061	−	0.803718i
$113$	−2.27664	−	3.94325i	−0.214168	−	0.370950i	0.738847	−	0.673873i	$-0.235371\pi$
$113$	−2.27664	−	3.94325i	−0.214168	−	0.370950i	−0.953015	+	0.302923i	$0.902037\pi$
$114$	0.627709	−	6.68104i	0.0587903	−	0.625737i
$115$	−1.98769	+	0.532599i	−0.185353	+	0.0496651i
$116$	−6.39602	−	5.50821i	−0.593856	−	0.511424i
$117$		0			0
$118$	10.9525	−	5.02200i	1.00826	−	0.462312i
$119$	0.957620	+	3.57389i	0.0877849	+	0.327618i
$120$	−0.392312	−	0.407704i	−0.0358130	−	0.0372181i
$121$	−7.72521	+	4.46015i	−0.702292	+	0.405468i
$122$	3.55470	−	9.57497i	0.321827	−	0.866877i
$123$	4.75860	+	1.27506i	0.429069	+	0.114969i
$124$	−6.18038	−	9.07193i	−0.555015	−	0.814683i
$125$	1.65482	−	1.65482i	0.148012	−	0.148012i
$126$	−6.94488	−	4.92952i	−0.618699	−	0.439157i
$127$	2.67207	−	4.62816i	0.237108	−	0.410683i	−0.722775	−	0.691083i	$-0.757134\pi$
$127$	2.67207	−	4.62816i	0.237108	−	0.410683i	0.959883	+	0.280400i	$0.0904672\pi$
$128$	−11.2188	+	1.46268i	−0.991608	+	0.129284i
$129$			7.80954i			0.687592i
$130$		0			0
$131$		−	11.2254i		−	0.980764i	−0.871508	−	0.490382i	$-0.836857\pi$
$131$		−	11.2254i		−	0.980764i	0.871508	−	0.490382i	$-0.163143\pi$
$132$	1.06455	−	2.20854i	0.0926574	−	0.192229i
$133$	7.38024	−	12.7830i	0.639948	−	1.10842i
$134$	2.06459	−	2.90866i	0.178353	−	0.251270i
$135$	−0.746494	+	0.746494i	−0.0642480	+	0.0642480i
$136$	2.04439	−	3.38873i	0.175305	−	0.290582i
$137$	−4.64424	−	1.24442i	−0.396784	−	0.106318i	0.0549089	−	0.998491i	$-0.482513\pi$
$137$	−4.64424	−	1.24442i	−0.396784	−	0.106318i	−0.451693	+	0.892173i	$0.649180\pi$
$138$	−9.85470	−	3.65855i	−0.838888	−	0.311436i
$139$	−6.01080	+	3.47034i	−0.509830	+	0.294350i	−0.732764	−	0.680483i	$-0.761770\pi$
$139$	−6.01080	+	3.47034i	−0.509830	+	0.294350i	0.222934	+	0.974834i	$0.428437\pi$
$140$	−0.410628	−	1.17486i	−0.0347044	−	0.0992935i
$141$	−0.872175	−	3.25500i	−0.0734504	−	0.274121i
$142$	6.40759	+	13.9744i	0.537713	+	1.17270i
$143$		0			0
$144$	1.35128	+	9.00893i	0.112607	+	0.750744i
$145$	−0.959363	+	0.257060i	−0.0796707	+	0.0213477i
$146$	10.0638	+	0.945533i	0.832887	+	0.0782529i
$147$	−0.00335801	−	0.00581624i	−0.000276964	−	0.000479715i
$148$	−1.03241	+	0.0769967i	−0.0848635	+	0.00632909i
$149$	−3.92298	+	14.6408i	−0.321383	+	1.19942i	0.596515	+	0.802602i	$0.296552\pi$
$149$	−3.92298	+	14.6408i	−0.321383	+	1.19942i	−0.917898	+	0.396817i	$0.870115\pi$
$150$	5.86033	−	0.994631i	0.478494	−	0.0812113i
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	0.726401	−	0.687272i	$-0.241192\pi$
$151$	0.480824	+	0.480824i	0.0391289	+	0.0391289i	−0.687272	+	0.726401i	$0.741192\pi$
$152$	−15.3263	+	3.79226i	−1.24313	+	0.307593i
$153$	−2.75974	−	1.59334i	−0.223112	−	0.128814i
$154$	4.15331	−	3.43990i	0.334683	−	0.277195i
$155$	−1.29162			−0.103746
$156$		0			0
$157$	5.90408			0.471197			0.235598	−	0.971851i	$-0.424295\pi$
$157$	5.90408			0.471197			0.235598	+	0.971851i	$0.424295\pi$
$158$	9.27585	−	7.68255i	0.737947	−	0.611191i
$159$	4.37618	+	2.52659i	0.347054	+	0.200372i
$160$	−0.600989	+	1.18785i	−0.0475123	+	0.0939078i
$161$	−16.3499	−	16.3499i	−1.28855	−	1.28855i
$162$	4.20925	−	0.714406i	0.330710	−	0.0561290i
$163$	4.07194	−	15.1967i	0.318939	−	1.19030i	−0.601327	−	0.799003i	$-0.705361\pi$
$163$	4.07194	−	15.1967i	0.318939	−	1.19030i	0.920266	−	0.391294i	$-0.127972\pi$
$164$	−0.862067	−	11.5590i	−0.0673161	−	0.902607i
$165$	−0.144241	−	0.249833i	−0.0112292	−	0.0194495i
$166$	−13.7633	−	1.29311i	−1.06824	−	0.100365i
$167$	−5.41542	+	1.45106i	−0.419058	+	0.112286i	−0.462185	−	0.886783i	$-0.652935\pi$
$167$	−5.41542	+	1.45106i	−0.419058	+	0.112286i	0.0431274	+	0.999070i	$0.486268\pi$
$168$	1.76327	−	6.10813i	0.136040	−	0.471253i
$169$		0			0
$170$	−0.194094	−	0.423302i	−0.0148863	−	0.0324658i
$171$	3.29032	+	12.2796i	0.251617	+	0.939046i
$172$	17.3455	−	6.06249i	1.32258	−	0.462261i
$173$	1.87129	−	1.08039i	0.142272	−	0.0821405i	−0.427175	−	0.904169i	$-0.640491\pi$
$173$	1.87129	−	1.08039i	0.142272	−	0.0821405i	0.569446	+	0.822029i	$0.307158\pi$
$174$	−4.75640	−	1.76581i	−0.360582	−	0.133866i
$175$	12.6293	+	3.38402i	0.954688	+	0.255808i
$176$	−5.73173	−	0.649967i	−0.432045	−	0.0489931i
$177$	5.12108	−	5.12108i	0.384924	−	0.384924i
$178$	5.43801	−	7.66125i	0.407596	−	0.574235i
$179$	5.06638	−	8.77523i	0.378679	−	0.655892i	−0.612191	−	0.790710i	$-0.709712\pi$
$179$	5.06638	−	8.77523i	0.378679	−	0.655892i	0.990870	+	0.134818i	$0.0430450\pi$
$180$	0.965579	+	0.465424i	0.0719700	+	0.0346907i
$181$		−	13.8528i		−	1.02967i	−0.857289	−	0.514836i	$-0.827853\pi$
$181$		−	13.8528i		−	1.02967i	0.857289	−	0.514836i	$-0.172147\pi$
$182$		0			0
$183$		−	6.13905i		−	0.453812i
$184$	−0.475750	+	24.7281i	−0.0350727	+	1.82298i
$185$	−0.0609080	+	0.105496i	−0.00447805	+	0.00775620i
$186$	−5.38041	−	3.81905i	−0.394511	−	0.280026i
$187$	1.42685	−	1.42685i	0.104342	−	0.104342i
$188$	−6.55252	+	4.46400i	−0.477891	+	0.325570i
$189$	−11.4580	−	3.07017i	−0.833450	−	0.223322i
$190$	−0.646573	+	1.74162i	−0.0469073	+	0.126350i
$191$	−3.35193	+	1.93524i	−0.242537	+	0.140029i	−0.616342	−	0.787478i	$-0.711386\pi$
$191$	−3.35193	+	1.93524i	−0.242537	+	0.140029i	0.373805	+	0.927507i	$0.378053\pi$
$192$	−6.01570	+	3.17113i	−0.434146	+	0.228856i
$193$	−2.12861	−	7.94409i	−0.153221	−	0.571828i	−0.999251	−	0.0386934i	$-0.987680\pi$
$193$	−2.12861	−	7.94409i	−0.153221	−	0.571828i	0.846030	−	0.533135i	$-0.178986\pi$
$194$	−19.8910	+	9.12050i	−1.42809	+	0.654814i
$195$		0			0
$196$	−0.0103115	+	0.0119735i	−0.000736533	+	0.000855248i
$197$	11.9588	−	3.20436i	0.852032	−	0.228301i	0.193730	−	0.981055i	$-0.437942\pi$
$197$	11.9588	−	3.20436i	0.852032	−	0.228301i	0.658302	+	0.752754i	$0.271275\pi$
$198$	−0.434476	+	4.62436i	−0.0308768	+	0.328639i
$199$	1.21698	+	2.10788i	0.0862696	+	0.149423i	0.905932	−	0.423424i	$-0.139172\pi$
$199$	1.21698	+	2.10788i	0.0862696	+	0.149423i	−0.819662	+	0.572848i	$0.805839\pi$
$200$	−6.75848	−	12.2441i	−0.477896	−	0.865786i
$201$	0.554899	−	2.07091i	0.0391396	−	0.146071i
$202$	2.17107	+	12.7919i	0.152756	+	0.900032i
$203$	−7.89132	−	7.89132i	−0.553862	−	0.553862i
$204$	0.443089	−	2.33720i	0.0310225	−	0.163637i
$205$	−1.18115	−	0.681935i	−0.0824949	−	0.0476284i
$206$	9.83981	+	11.8805i	0.685572	+	0.827755i
$207$	19.9145			1.38416
$208$		0			0
$209$	−8.05002			−0.556831
$210$	−0.477161	−	0.576121i	−0.0329272	−	0.0397561i
$211$	−3.62910	−	2.09526i	−0.249838	−	0.144244i	0.369852	−	0.929091i	$-0.379408\pi$
$211$	−3.62910	−	2.09526i	−0.249838	−	0.144244i	−0.619690	+	0.784847i	$0.712742\pi$
$212$	2.21453	−	11.6812i	0.152094	−	0.802266i
$213$	6.53401	+	6.53401i	0.447703	+	0.447703i
$214$	−2.33246	−	13.7428i	−0.159444	−	0.939437i
$215$	0.559576	−	2.08837i	0.0381628	−	0.142425i
$216$	6.13167	+	11.1085i	0.417207	+	0.755838i
$217$	−7.25658	−	12.5688i	−0.492609	−	0.853223i
$218$	−0.00454933	+	0.0484210i	−0.000308120	+	0.00327948i
$219$	5.86868	−	1.57251i	0.396569	−	0.106260i
$220$	−0.442923	+	0.514313i	−0.0298618	+	0.0346750i
$221$		0			0
$222$	−0.565647	+	0.259363i	−0.0379637	+	0.0174073i
$223$	−4.87316	−	18.1869i	−0.326331	−	1.21788i	−0.912967	−	0.408033i	$-0.866215\pi$
$223$	−4.87316	−	18.1869i	−0.326331	−	1.21788i	0.586636	−	0.809850i	$-0.300452\pi$
$224$	−14.9354	+	0.825347i	−0.997913	+	0.0551458i
$225$	−9.75232	+	5.63051i	−0.650155	+	0.375367i
$226$	−2.24113	+	6.03672i	−0.149078	+	0.401557i
$227$	7.18635	+	1.92558i	0.476974	+	0.127805i	0.489293	−	0.872119i	$-0.337255\pi$
$227$	7.18635	+	1.92558i	0.476974	+	0.127805i	−0.0123190	+	0.999924i	$0.503921\pi$
$228$	−7.84294	+	5.34312i	−0.519412	+	0.353857i
$229$	3.17720	−	3.17720i	0.209955	−	0.209955i	−0.594293	−	0.804248i	$-0.702568\pi$
$229$	3.17720	−	3.17720i	0.209955	−	0.209955i	0.804248	+	0.594293i	$0.202568\pi$
$230$	2.37312	+	1.68446i	0.156479	+	0.111070i
$231$	1.62075	−	2.80721i	0.106637	−	0.184701i
$232$	−0.229622	+	11.9351i	−0.0150754	+	0.783577i
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$		0			0
$235$			0.932921i			0.0608571i
$236$	−15.3497	−	7.39881i	−0.999182	−	0.481621i
$237$	3.61971	−	6.26953i	0.235126	−	0.407250i
$238$	3.02868	−	4.26691i	0.196320	−	0.276583i
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	−0.487300	−	0.873235i	$-0.662018\pi$
$239$	5.96641	−	5.96641i	0.385935	−	0.385935i	0.873235	+	0.487300i	$0.162018\pi$
$240$	−0.0901592	+	0.795068i	−0.00581975	+	0.0513215i
$241$	14.9406	+	4.00333i	0.962410	+	0.257877i	0.705620	−	0.708590i	$-0.250668\pi$
$241$	14.9406	+	4.00333i	0.962410	+	0.257877i	0.256790	+	0.966467i	$0.417335\pi$
$242$	11.8265	+	4.39058i	0.760237	+	0.282237i
$243$	13.8775	−	8.01218i	0.890242	−	0.513982i
$244$	−13.6352	+	4.76570i	−0.872907	+	0.305093i
$245$	0.000481222		0.00179594i	3.07441e−5		0.000114739i
$246$	−2.90387	−	6.33307i	−0.185144	−	0.403782i
$247$		0			0
$248$	−4.30560	+	14.9150i	−0.273406	+	0.947101i
$249$	−8.02602	+	2.15056i	−0.508628	+	0.136287i
$250$	−3.29513	−	0.309590i	−0.208403	−	0.0195802i
$251$	13.7387	+	23.7962i	0.867182	+	1.50200i	0.864865	+	0.502005i	$0.167404\pi$
$251$	13.7387	+	23.7962i	0.867182	+	1.50200i	0.00231697	+	0.999997i	$0.499262\pi$
$252$	0.895766	+	12.0109i	0.0564279	+	0.756613i
$253$	−3.26379	+	12.1806i	−0.205193	+	0.765789i
$254$	−7.45120	+	1.26464i	−0.467530	+	0.0793504i
$255$	−0.197923	−	0.197923i	−0.0123944	−	0.0123944i
$256$	11.7132	+	10.8995i	0.732077	+	0.681222i
$257$	24.1060	+	13.9176i	1.50369	+	0.868157i	0.999991	+	0.00427985i	$0.00136232\pi$
$257$	24.1060	+	13.9176i	1.50369	+	0.868157i	0.503702	+	0.863878i	$0.331971\pi$
$258$	8.50582	−	7.04478i	0.529549	−	0.438589i
$259$	−1.36877			−0.0850511
$260$		0			0
$261$	9.61181			0.594956
$262$	−12.2262	+	10.1261i	−0.755335	+	0.625592i
$263$	−20.6166	−	11.9030i	−1.27128	−	0.733972i	−0.296048	−	0.955173i	$-0.595669\pi$
$263$	−20.6166	−	11.9030i	−1.27128	−	0.733972i	−0.975228	+	0.221201i	$0.929002\pi$
$264$	−3.36575	+	0.832803i	−0.207148	+	0.0512555i
$265$	−0.989207	−	0.989207i	−0.0607665	−	0.0607665i
$266$	−20.5802	+	3.49292i	−1.26185	+	0.214165i
$267$	1.46157	−	5.45466i	0.0894468	−	0.333820i
$268$	−5.03040	+	0.375166i	−0.307281	+	0.0229169i
$269$	10.3559	+	17.9370i	0.631412	+	1.09364i	0.987263	+	0.159095i	$0.0508576\pi$
$269$	10.3559	+	17.9370i	0.631412	+	1.09364i	−0.355851	+	0.934543i	$0.615809\pi$
$270$	1.48644	+	0.139657i	0.0904620	+	0.00849924i
$271$	−13.3489	+	3.57684i	−0.810890	+	0.217277i	−0.640360	−	0.768075i	$-0.721215\pi$
$271$	−13.3489	+	3.57684i	−0.810890	+	0.217277i	−0.170530	+	0.985352i	$0.554548\pi$
$272$	−5.53506	+	0.830223i	−0.335612	+	0.0503397i
$273$		0			0
$274$	2.83408	+	6.18087i	0.171213	+	0.373400i
$275$	−1.84556	−	6.88774i	−0.111292	−	0.415346i
$276$	4.90493	+	14.0336i	0.295242	+	0.844723i
$277$	11.0276	−	6.36681i	0.662587	−	0.382545i	−0.130675	−	0.991425i	$-0.541714\pi$
$277$	11.0276	−	6.36681i	0.662587	−	0.382545i	0.793262	+	0.608880i	$0.208381\pi$
$278$	9.20193	+	3.41621i	0.551895	+	0.204891i
$279$	12.0739	+	3.23518i	0.722844	+	0.193685i
$280$	−0.909186	+	1.50705i	−0.0543343	+	0.0900632i
$281$	−15.4454	+	15.4454i	−0.921396	+	0.921396i	−0.997128	−	0.0757324i	$-0.975871\pi$
$281$	−15.4454	+	15.4454i	−0.921396	+	0.921396i	0.0757324	+	0.997128i	$0.475871\pi$
$282$	−2.75844	+	3.88619i	−0.164263	+	0.231419i
$283$	10.3449	−	17.9178i	0.614939	−	1.06511i	−0.375456	−	0.926840i	$-0.622514\pi$
$283$	10.3449	−	17.9178i	0.614939	−	1.06511i	0.990395	−	0.138265i	$-0.0441527\pi$
$284$	9.44017	−	19.5848i	0.560171	−	1.16214i
$285$			1.11665i			0.0661445i
$286$		0			0
$287$		−	15.3249i		−	0.904603i
$288$	8.59319	−	9.59848i	0.506358	−	0.565596i
$289$	−7.52106	+	13.0269i	−0.442415	+	0.766286i
$290$	1.14539	+	0.813009i	0.0672599	+	0.0477415i
$291$	−9.30045	+	9.30045i	−0.545202	+	0.545202i
$292$	−8.04846	−	11.8140i	−0.471001	−	0.691363i
$293$	22.2734	+	5.96815i	1.30123	+	0.348663i	0.841914	−	0.539611i	$-0.181429\pi$
$293$	22.2734	+	5.96815i	1.30123	+	0.348663i	0.459314	+	0.888274i	$0.348095\pi$
$294$	−0.00330563	+	0.00890407i	−0.000192788	+	0.000519296i
$295$	−1.73638	+	1.00250i	−0.101096	+	0.0583677i
$296$	1.01517	+	1.05500i	0.0590056	+	0.0613206i
$297$	1.67440	+	6.24895i	0.0971586	+	0.362601i
$298$	19.4849	−	8.93431i	1.12873	−	0.517551i
$299$		0			0
$300$	−6.36976	−	5.48559i	−0.367758	−	0.316711i
$301$	23.4656	−	6.28760i	1.35254	−	0.362411i
$302$	0.0899543	−	0.957432i	0.00517629	−	0.0550940i
$303$	3.89939	+	6.75394i	0.224014	+	0.388004i
$304$	17.9559	+	13.2719i	1.02984	+	0.761195i
$305$	−0.439881	+	1.64166i	−0.0251875	+	0.0940010i
$306$	0.754095	+	4.44310i	0.0431087	+	0.253995i
$307$	16.3164	+	16.3164i	0.931228	+	0.931228i	0.997783	−	0.0665547i	$-0.0212007\pi$
$307$	16.3164	+	16.3164i	0.931228	+	0.931228i	−0.0665547	+	0.997783i	$0.521201\pi$
$308$	−7.49318	−	1.42057i	−0.426964	−	0.0809442i
$309$	8.03001	+	4.63613i	0.456811	+	0.263740i
$310$	1.16514	+	1.40678i	0.0661755	+	0.0798999i
$311$	8.54527			0.484558			0.242279	−	0.970207i	$-0.422105\pi$
$311$	8.54527			0.484558			0.242279	+	0.970207i	$0.422105\pi$
$312$		0			0
$313$	5.88378			0.332571			0.166285	−	0.986078i	$-0.446823\pi$
$313$	5.88378			0.332571			0.166285	+	0.986078i	$0.446823\pi$
$314$	−5.32591	−	6.43047i	−0.300559	−	0.362892i
$315$	1.22732	+	0.708592i	0.0691515	+	0.0399247i
$316$	−16.7350	−	3.17264i	−0.941417	−	0.178475i
$317$	16.5045	+	16.5045i	0.926984	+	0.926984i	0.997510	−	0.0705258i	$-0.0224677\pi$
$317$	16.5045	+	16.5045i	0.926984	+	0.926984i	−0.0705258	+	0.997510i	$0.522468\pi$
$318$	−1.19578	−	7.04552i	−0.0670563	−	0.395093i
$319$	−1.57528	+	5.87902i	−0.0881986	+	0.329162i
$320$	1.83589	−	0.416956i	0.102629	−	0.0233086i
$321$	−4.18926	−	7.25601i	−0.233822	−	0.404991i
$322$	−3.05879	+	32.5564i	−0.170460	+	1.81430i
$323$	−7.54456	+	2.02156i	−0.419790	+	0.112483i
$324$	−4.57516	−	3.94009i	−0.254175	−	0.218894i
$325$		0			0
$326$	−20.2248	+	9.27355i	−1.12015	+	0.513614i
$327$	0.00756596	+	0.0282365i	0.000418399	+	0.00156148i
$328$	−11.8119	+	11.3660i	−0.652205	+	0.627582i
$329$	−9.07823	+	5.24132i	−0.500499	+	0.288963i
$330$	−0.141991	+	0.382469i	−0.00781636	+	0.0210542i
$331$	13.8768	+	3.71829i	0.762740	+	0.204375i	0.619162	−	0.785264i	$-0.287473\pi$
$331$	13.8768	+	3.71829i	0.762740	+	0.204375i	0.143578	+	0.989639i	$0.454139\pi$
$332$	11.0071	+	16.1569i	0.604093	+	0.886723i
$333$	0.833596	−	0.833596i	0.0456808	−	0.0456808i
$334$	6.46554	+	4.58929i	0.353779	+	0.251115i
$335$	−0.296774	+	0.514027i	−0.0162145	+	0.0280843i
$336$	−8.24332	+	3.58950i	−0.449710	+	0.195823i
$337$		−	14.3427i		−	0.781297i	−0.920540	−	0.390649i	$-0.872251\pi$
$337$		−	14.3427i		−	0.781297i	0.920540	−	0.390649i	$-0.127749\pi$
$338$		0			0
$339$			3.87048i			0.210216i
$340$	−0.285955	+	0.593248i	−0.0155081	+	0.0321734i
$341$	−3.95757	+	6.85471i	−0.214314	+	0.371203i
$342$	10.4063	−	14.6608i	0.562710	−	0.792765i
$343$	−13.1032	+	13.1032i	−0.707505	+	0.707505i
$344$	−22.2499	−	13.4232i	−1.19964	−	0.723730i
$345$	1.68962	+	0.452732i	0.0909659	+	0.0243743i
$346$	−2.86476	−	1.06354i	−0.154010	−	0.0571762i
$347$	0.407300	−	0.235155i	0.0218650	−	0.0126238i	−0.489028	−	0.872268i	$-0.662648\pi$
$347$	0.407300	−	0.235155i	0.0218650	−	0.0126238i	0.510893	+	0.859645i	$0.329315\pi$
$348$	2.36738	+	6.77336i	0.126905	+	0.363090i
$349$	−7.32017	−	27.3192i	−0.391840	−	1.46237i	−0.827097	−	0.562059i	$-0.810009\pi$
$349$	−7.32017	−	27.3192i	−0.391840	−	1.46237i	0.435257	−	0.900306i	$-0.356657\pi$
$350$	−7.70686	−	16.8080i	−0.411949	−	0.898423i
$351$		0			0
$352$	4.46252	+	6.82907i	0.237853	+	0.363991i
$353$	−34.7270	+	9.30507i	−1.84833	+	0.495259i	−0.999445	−	0.0333153i	$-0.989393\pi$
$353$	−34.7270	+	9.30507i	−1.84833	+	0.495259i	−0.848887	+	0.528574i	$0.822727\pi$
$354$	−10.1972	−	0.958070i	−0.541978	−	0.0509208i
$355$	−1.27909	−	2.21545i	−0.0678872	−	0.117584i
$356$	−13.2498	+	0.988165i	−0.702238	+	0.0523726i
$357$	0.814018	−	3.03796i	0.0430824	−	0.160786i
$358$	−14.1279	+	2.39782i	−0.746681	+	0.126729i
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	0.326733	−	0.945117i	$-0.394052\pi$
$359$	−11.7167	−	11.7167i	−0.618383	−	0.618383i	−0.945117	+	0.326733i	$0.894052\pi$
$360$	−0.364103	−	1.47151i	−0.0191899	−	0.0775556i
$361$	10.5306	+	6.07986i	0.554244	+	0.319993i
$362$	−15.0879	+	12.4963i	−0.793002	+	0.656789i
$363$	7.58264			0.397985
$364$		0			0
$365$	−1.68203			−0.0880416
$366$	−6.68639	+	5.53787i	−0.349503	+	0.289469i
$367$	−8.79501	−	5.07780i	−0.459096	−	0.265059i	0.252568	−	0.967579i	$-0.418725\pi$
$367$	−8.79501	−	5.07780i	−0.459096	−	0.265059i	−0.711664	+	0.702520i	$0.752058\pi$
$368$	27.3619	−	21.7884i	1.42634	−	1.13580i
$369$	9.33307	+	9.33307i	0.485860	+	0.485860i
$370$	0.169845	−	0.0288266i	0.00882982	−	0.00149862i
$371$	4.06840	−	15.1835i	0.211221	−	0.788288i
$372$	0.693977	+	9.30517i	0.0359810	+	0.482451i
$373$	7.50790	+	13.0041i	0.388744	+	0.673325i	0.992281	−	0.124010i	$-0.0395756\pi$
$373$	7.50790	+	13.0041i	0.388744	+	0.673325i	−0.603537	+	0.797335i	$0.706242\pi$
$374$	−2.84119	−	0.266940i	−0.146914	−	0.0138032i
$375$	−1.92155	+	0.514877i	−0.0992283	+	0.0265881i
$376$	10.7728	+	3.10987i	0.555567	+	0.160379i
$377$		0			0
$378$	6.99210	+	15.2491i	0.359635	+	0.784331i
$379$	−8.63337	−	32.2202i	−0.443467	−	1.65504i	−0.719953	−	0.694022i	$-0.755837\pi$
$379$	−8.63337	−	32.2202i	−0.443467	−	1.65504i	0.276487	−	0.961018i	$-0.410830\pi$
$380$	2.48015	−	0.866845i	0.127229	−	0.0444682i
$381$	−3.93413	+	2.27137i	−0.201552	+	0.116366i
$382$	5.13147	+	1.90505i	0.262549	+	0.0974711i
$383$	−20.2216	−	5.41837i	−1.03328	−	0.276866i	−0.297953	−	0.954581i	$-0.596304\pi$
$383$	−20.2216	−	5.41837i	−1.03328	−	0.276866i	−0.735325	+	0.677715i	$0.762970\pi$
$384$	8.88046	+	3.69145i	0.453179	+	0.188378i
$385$	−0.634552	+	0.634552i	−0.0323398	+	0.0323398i
$386$	−6.73220	+	9.48455i	−0.342660	+	0.482751i
$387$	−10.4616	+	18.1201i	−0.531794	+	0.921095i
$388$	27.8768	+	13.4371i	1.41523	+	0.682163i
$389$			9.60410i			0.486947i	0.969908	+	0.243474i	$0.0782870\pi$
$389$			9.60410i			0.486947i	−0.969908	+	0.243474i	$0.921713\pi$
$390$		0			0
$391$			12.2354i			0.618772i
$392$	0.0223427		0.000429857i	0.00112848		2.17111e-5i
$393$	−4.77101	+	8.26364i	−0.240666	+	0.416846i
$394$	−14.2778	−	10.1345i	−0.719305	−	0.510568i
$395$	−1.41718	+	1.41718i	−0.0713063	+	0.0713063i
$396$	5.42858	−	3.69830i	0.272796	−	0.185846i
$397$	−2.49473	−	0.668462i	−0.125207	−	0.0335492i	0.195671	−	0.980670i	$-0.437311\pi$
$397$	−2.49473	−	0.668462i	−0.125207	−	0.0335492i	−0.320878	+	0.947120i	$0.603978\pi$
$398$	1.19800	−	3.22694i	0.0600503	−	0.161752i
$399$	−10.8661	+	6.27352i	−0.543983	+	0.314069i
$400$	−7.23907	+	18.4061i	−0.361953	+	0.920304i
$401$	7.00137	+	26.1295i	0.349632	+	1.30484i	0.887107	+	0.461563i	$0.152711\pi$
$401$	7.00137	+	26.1295i	0.349632	+	1.30484i	−0.537476	+	0.843279i	$0.680622\pi$
$402$	−2.75611	+	1.26374i	−0.137462	+	0.0630298i
$403$		0			0
$404$	11.9739	−	13.9038i	0.595723	−	0.691742i
$405$	−0.686244	+	0.183879i	−0.0340998	+	0.00913700i
$406$	−1.47634	+	15.7134i	−0.0732693	+	0.779845i
$407$	0.373247	+	0.646483i	0.0185012	+	0.0320450i
$408$	−2.94528	+	1.62574i	−0.145813	+	0.0804859i
$409$	−1.24095	+	4.63129i	−0.0613611	+	0.229003i	−0.989796	−	0.142493i	$-0.954488\pi$
$409$	−1.24095	+	4.63129i	−0.0613611	+	0.229003i	0.928435	+	0.371496i	$0.121155\pi$
$410$	0.322746	+	1.90161i	0.0159393	+	0.0939139i
$411$	2.88999	+	2.88999i	0.142553	+	0.142553i
$412$	4.06352	−	21.4342i	0.200195	−	1.05599i
$413$	−19.5106	−	11.2644i	−0.960053	−	0.554287i
$414$	−17.9644	−	21.6901i	−0.882901	−	1.06601i
$415$	2.30035			0.112920
$416$		0			0
$417$	5.89987			0.288918
$418$	7.26171	+	8.76774i	0.355182	+	0.428844i
$419$	−4.85410	−	2.80251i	−0.237138	−	0.136912i	0.376723	−	0.926326i	$-0.377051\pi$
$419$	−4.85410	−	2.80251i	−0.237138	−	0.136912i	−0.613861	+	0.789414i	$0.710384\pi$
$420$	−0.197052	+	1.03941i	−0.00961514	+	0.0507178i
$421$	−3.55354	−	3.55354i	−0.173189	−	0.173189i	0.615190	−	0.788379i	$-0.289079\pi$
$421$	−3.55354	−	3.55354i	−0.173189	−	0.173189i	−0.788379	+	0.615190i	$0.789079\pi$
$422$	0.991646	+	5.84274i	0.0482726	+	0.284420i
$423$	2.33672	−	8.72077i	0.113615	−	0.424018i
$424$	−14.7203	+	8.12531i	−0.714881	+	0.394600i
$425$	−3.45936	−	5.99179i	−0.167804	−	0.290645i
$426$	1.22241	−	13.0107i	0.0592257	−	0.630371i
$427$	−18.4462	+	4.94266i	−0.892676	+	0.239192i
$428$	−12.8640	+	14.9374i	−0.621805	+	0.722027i
$429$		0			0
$430$	−2.77934	+	1.27439i	−0.134032	+	0.0614567i
$431$	0.894922	+	3.33989i	0.0431069	+	0.160877i	0.984124	−	0.177482i	$-0.0567950\pi$
$431$	0.894922	+	3.33989i	0.0431069	+	0.160877i	−0.941017	+	0.338359i	$0.890128\pi$
$432$	6.56769	−	16.6990i	0.315988	−	0.803433i
$433$	−4.73943	+	2.73631i	−0.227762	+	0.131499i	−0.609539	−	0.792756i	$-0.708646\pi$
$433$	−4.73943	+	2.73631i	−0.227762	+	0.131499i	0.381777	+	0.924254i	$0.375312\pi$
$434$	−7.14339	+	19.2415i	−0.342894	+	0.923622i
$435$	0.815499	+	0.218512i	0.0391002	+	0.0104769i
$436$	0.0568419	−	0.0387243i	0.00272223	−	0.00185456i
$437$	34.5150	−	34.5150i	1.65107	−	1.65107i
$438$	−7.00669	−	4.97340i	−0.334793	−	0.237638i
$439$	15.2532	−	26.4193i	0.727994	−	1.26092i	−0.229736	−	0.973253i	$-0.573786\pi$
$439$	15.2532	−	26.4193i	0.727994	−	1.26092i	0.957730	−	0.287669i	$-0.0928804\pi$
$440$	0.959717	+	0.0184642i	0.0457527	+	0.000880248i
$441$		−	0.0179935i		−	0.000856833i
$442$		0			0
$443$		−	12.8994i		−	0.612869i	−0.951892	−	0.306434i	$-0.900864\pi$
$443$		−	12.8994i		−	0.612869i	0.951892	−	0.306434i	$-0.0991360\pi$
$444$	0.792742	+	0.382114i	0.0376219	+	0.0181343i
$445$	−0.781685	+	1.35392i	−0.0370554	+	0.0641819i
$446$	−15.4124	+	21.7135i	−0.729799	+	1.02817i
$447$	9.11058	−	9.11058i	0.430916	−	0.430916i
$448$	14.3718	+	15.5225i	0.679002	+	0.733368i
$449$	−9.53370	−	2.55455i	−0.449923	−	0.120557i	0.0267403	−	0.999642i	$-0.491487\pi$
$449$	−9.53370	−	2.55455i	−0.449923	−	0.120557i	−0.476663	+	0.879086i	$0.658154\pi$
$450$	14.9298	+	5.54268i	0.703798	+	0.261284i
$451$	−7.23812	+	4.17893i	−0.340830	+	0.196778i
$452$	8.59660	−	3.00463i	0.404350	−	0.141326i
$453$	−0.149602	−	0.558323i	−0.00702893	−	0.0262323i
$454$	−4.38536	−	9.56407i	−0.205815	−	0.448864i
$455$		0			0
$456$	12.8944	+	3.72231i	0.603836	+	0.174313i
$457$	−10.0284	+	2.68710i	−0.469108	+	0.125697i	−0.485626	−	0.874166i	$-0.661408\pi$
$457$	−10.0284	+	2.68710i	−0.469108	+	0.125697i	0.0165184	+	0.999864i	$0.494742\pi$
$458$	−6.32653	−	0.594401i	−0.295619	−	0.0277746i
$459$	3.13853	+	5.43609i	0.146494	+	0.253735i
$460$	−0.306091	−	4.10421i	−0.0142715	−	0.191360i
$461$	−7.43710	+	27.7556i	−0.346380	+	1.29271i	0.544611	+	0.838689i	$0.316677\pi$
$461$	−7.43710	+	27.7556i	−0.346380	+	1.29271i	−0.890991	+	0.454021i	$0.849989\pi$
$462$	−4.51953	+	0.767066i	−0.210267	+	0.0356872i
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	0.830612	−	0.556852i	$-0.187991\pi$
$463$	5.89061	+	5.89061i	0.273760	+	0.273760i	−0.556852	+	0.830612i	$0.687991\pi$
$464$	13.2063	−	10.5162i	0.613088	−	0.488204i
$465$	0.950841	+	0.548968i	0.0440942	+	0.0254578i
$466$	14.5081	−	12.0161i	0.672076	−	0.556634i
$467$	3.30334			0.152860			0.0764301	−	0.997075i	$-0.475648\pi$
$467$	3.30334			0.152860			0.0764301	+	0.997075i	$0.475648\pi$
$468$		0			0
$469$	−6.66931			−0.307960
$470$	1.01610	−	0.841563i	0.0468691	−	0.0388184i
$471$	−4.34634	−	2.50936i	−0.200269	−	0.115625i
$472$	5.78811	+	23.3925i	0.266420	+	1.07673i
$473$	−9.36849	−	9.36849i	−0.430764	−	0.430764i
$474$	−10.0937	+	1.71314i	−0.463621	+	0.0786870i
$475$	−7.14374	+	26.6608i	−0.327777	+	1.22328i
$476$	−7.37943	+	0.550355i	−0.338235	+	0.0252255i
$477$	6.76922	+	11.7246i	0.309941	+	0.536834i
$478$	−11.8805	−	1.11622i	−0.543402	−	0.0510546i
$479$	26.8650	−	7.19847i	1.22750	−	0.328906i	0.413892	−	0.910326i	$-0.364169\pi$
$479$	26.8650	−	7.19847i	1.22750	−	0.328906i	0.813604	+	0.581420i	$0.197503\pi$
$480$	0.947285	−	0.619013i	0.0432374	−	0.0282539i
$481$		0			0
$482$	−9.11729	−	19.8840i	−0.415281	−	0.905691i
$483$	5.08705	+	18.9851i	0.231469	+	0.863854i
$484$	−5.88635	−	16.8416i	−0.267561	−	0.765525i
$485$	3.15346	−	1.82065i	0.143191	−	0.0826714i
$486$	−21.2451	−	7.88721i	−0.963695	−	0.357771i
$487$	9.96577	+	2.67032i	0.451592	+	0.121004i	0.477444	−	0.878662i	$-0.341563\pi$
$487$	9.96577	+	2.67032i	0.451592	+	0.121004i	−0.0258522	+	0.999666i	$0.508230\pi$
$488$	17.4906	+	10.5519i	0.791762	+	0.477663i
$489$	−9.45652	+	9.45652i	−0.427638	+	0.427638i
$490$	0.00152197	−	0.00214420i	6.87555e−5	−	9.68651e-5i
$491$	−6.81243	+	11.7995i	−0.307441	+	0.532503i	−0.977802	−	0.209532i	$-0.932806\pi$
$491$	−6.81243	+	11.7995i	−0.307441	+	0.532503i	0.670361	+	0.742035i	$0.266139\pi$
$492$	−4.27821	+	8.87566i	−0.192877	+	0.400146i
$493$			5.90546i			0.265969i
$494$		0			0
$495$		−	0.772899i		−	0.0347392i
$496$	20.1287	−	8.76491i	0.903805	−	0.393556i
$497$	14.3723	−	24.8936i	0.644688	−	1.11663i
$498$	9.58236	+	6.80163i	0.429396	+	0.304788i
$499$	−11.2288	+	11.2288i	−0.502670	+	0.502670i	−0.912267	−	0.409597i	$-0.865669\pi$
$499$	−11.2288	+	11.2288i	−0.502670	+	0.502670i	0.409597	+	0.912267i	$0.365669\pi$
$500$	2.63526	+	3.86819i	0.117852	+	0.172991i
$501$	4.60334	+	1.23346i	0.205662	+	0.0551070i
$502$	13.5244	−	36.4296i	0.603625	−	1.62593i
$503$	19.7978	−	11.4303i	0.882739	−	0.509650i	0.0111787	−	0.999938i	$-0.496442\pi$
$503$	19.7978	−	11.4303i	0.882739	−	0.509650i	0.871561	+	0.490288i	$0.163108\pi$
$504$	12.2737	−	11.8103i	0.546712	−	0.526073i
$505$	−0.558805	−	2.08549i	−0.0248665	−	0.0928030i
$506$	16.2108	−	7.43304i	0.720657	−	0.330439i
$507$		0			0
$508$	8.09892	+	6.97473i	0.359331	+	0.309454i
$509$	9.52759	−	2.55291i	0.422303	−	0.113156i	−0.0414078	−	0.999142i	$-0.513184\pi$
$509$	9.52759	−	2.55291i	0.422303	−	0.113156i	0.463711	+	0.885987i	$0.346518\pi$
$510$	−0.0370282	+	0.394111i	−0.00163964	+	0.0174515i
$511$	−9.44995	−	16.3678i	−0.418041	−	0.724069i
$512$	1.30512	−	22.5897i	0.0576787	−	0.998335i
$513$	6.48121	−	24.1882i	0.286152	−	1.06794i
$514$	−6.58693	−	38.8100i	−0.290537	−	1.71183i
$515$	−1.81513	−	1.81513i	−0.0799842	−	0.0799842i
$516$	−15.3457	−	2.90926i	−0.675559	−	0.128073i
$517$	4.95105	+	2.85849i	0.217747	+	0.125716i
$518$	1.23473	+	1.49080i	0.0542509	+	0.0655022i
$519$	−1.83676			−0.0806246
$520$		0			0
$521$	15.9204			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$521$	15.9204			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$522$	−8.67056	−	10.4688i	−0.379500	−	0.458206i
$523$	1.86869	+	1.07889i	0.0817122	+	0.0471766i	0.540299	−	0.841473i	$-0.318311\pi$
$523$	1.86869	+	1.07889i	0.0817122	+	0.0471766i	−0.458587	+	0.888649i	$0.651644\pi$
$524$	22.0578	+	4.18174i	0.963600	+	0.182680i
$525$	−7.85891	−	7.85891i	−0.342991	−	0.342991i
$526$	5.63346	+	33.1922i	0.245631	+	1.44725i
$527$	−1.98769	+	7.41814i	−0.0865849	+	0.323139i
$528$	3.94321	+	2.91459i	0.171606	+	0.126841i
$529$	−26.7315	−	46.3003i	−1.16224	−	2.01306i
$530$	−0.185064	+	1.96974i	−0.00803869	+	0.0855600i
$531$	18.7423	−	5.02200i	0.813348	−	0.217936i
$532$	22.3692	+	19.2642i	0.969826	+	0.835207i
$533$		0			0
$534$	−7.25943	+	3.32863i	−0.314146	+	0.144044i
$535$	0.600345	+	2.24052i	0.0259552	+	0.0968660i
$536$	4.94641	+	5.14047i	0.213652	+	0.222034i
$537$	−7.45933	+	4.30664i	−0.321894	+	0.185845i
$538$	10.1944	−	27.4597i	0.439512	−	1.18387i
$539$	0.0110056	+	0.00294895i	0.000474046	+	0.000127020i
$540$	−1.18877	−	1.74495i	−0.0511566	−	0.0750907i
$541$	−8.15947	+	8.15947i	−0.350803	+	0.350803i	−0.860408	−	0.509605i	$-0.829791\pi$
$541$	−8.15947	+	8.15947i	−0.350803	+	0.350803i	0.509605	+	0.860408i	$0.329791\pi$
$542$	15.9375	+	11.3125i	0.684572	+	0.485914i
$543$	−5.88774	+	10.1979i	−0.252667	+	0.437632i
$544$	5.89727	+	5.27962i	0.252843	+	0.226362i
$545$		−	0.00809292i		−	0.000346663i
$546$		0			0
$547$			8.11076i			0.346791i	0.984852	+	0.173396i	$0.0554739\pi$
$547$			8.11076i			0.346791i	−0.984852	+	0.173396i	$0.944526\pi$
$548$	4.17539	−	8.66235i	0.178364	−	0.370037i
$549$	8.22384	−	14.2441i	0.350985	−	0.607924i
$550$	−5.83700	+	8.22336i	−0.248890	+	0.350645i
$551$	16.6588	−	16.6588i	0.709687	−	0.709687i
$552$	10.8602	−	18.0016i	0.462240	−	0.766198i
$553$	−21.7526	−	5.82859i	−0.925014	−	0.247857i
$554$	−16.8822	−	6.26750i	−0.717256	−	0.266281i
$555$	0.0896759	−	0.0517744i	0.00380653	−	0.00219770i
$556$	−4.58003	−	13.1040i	−0.194237	−	0.555734i
$557$	0.887873	+	3.31359i	0.0376204	+	0.140401i	0.982182	−	0.187934i	$-0.0601791\pi$
$557$	0.887873	+	3.31359i	0.0376204	+	0.140401i	−0.944561	+	0.328335i	$0.893512\pi$
$558$	−7.36789	−	16.0687i	−0.311908	−	0.680243i
$559$		0			0
$560$	2.46156	−	0.369219i	0.104020	−	0.0156023i
$561$	−1.65683	+	0.443946i	−0.0699514	+	0.0187434i
$562$	30.7554	+	2.88958i	1.29734	+	0.121890i
$563$	−3.12130	−	5.40625i	−0.131547	−	0.227846i	0.792726	−	0.609578i	$-0.208661\pi$
$563$	−3.12130	−	5.40625i	−0.131547	−	0.227846i	−0.924273	+	0.381732i	$0.875328\pi$
$564$	6.72099	−	0.501249i	0.283005	−	0.0211064i
$565$	0.277331	−	1.03501i	0.0116674	−	0.0435434i
$566$	−28.8472	+	4.89602i	−1.21254	+	0.205795i
$567$	−5.64476	−	5.64476i	−0.237058	−	0.237058i
$568$	−29.8466	+	7.38508i	−1.25234	+	0.309871i
$569$	−27.8969	−	16.1063i	−1.16950	−	0.675211i	−0.215937	−	0.976407i	$-0.569281\pi$
$569$	−27.8969	−	16.1063i	−1.16950	−	0.675211i	−0.953562	+	0.301197i	$0.902614\pi$
$570$	1.21620	−	1.00730i	0.0509412	−	0.0421911i
$571$	−41.4189			−1.73333			−0.866663	−	0.498894i	$-0.833740\pi$
$571$	−41.4189			−1.73333			−0.866663	+	0.498894i	$0.833740\pi$
$572$		0			0
$573$	3.29007			0.137445
$574$	−16.6913	+	13.8242i	−0.696680	+	0.577012i
$575$	37.4446	+	21.6186i	1.56155	+	0.901560i
$576$	−18.2059	−	0.700797i	−0.758581	−	0.0291999i
$577$	−12.3408	−	12.3408i	−0.513753	−	0.513753i	0.401921	−	0.915674i	$-0.368343\pi$
$577$	−12.3408	−	12.3408i	−0.513753	−	0.513753i	−0.915674	+	0.401921i	$0.868343\pi$
$578$	20.9728	−	3.55957i	0.872355	−	0.148058i
$579$	−1.80941	+	6.75282i	−0.0751966	+	0.280638i
$580$	−0.147736	−	1.98091i	−0.00613439	−	0.0822528i
$581$	12.9238	+	22.3846i	0.536168	+	0.928671i
$582$	18.5193	+	1.73996i	0.767651	+	0.0721237i
$583$	−8.28072	+	2.21881i	−0.342952	+	0.0918938i
$584$	−5.60701	+	19.4231i	−0.232020	+	0.803736i
$585$		0			0
$586$	−13.5920	−	29.6430i	−0.561481	−	1.22454i
$587$	5.98011	+	22.3181i	0.246825	+	0.921165i	0.972457	+	0.233082i	$0.0748810\pi$
$587$	5.98011	+	22.3181i	0.246825	+	0.921165i	−0.725632	+	0.688083i	$0.758452\pi$
$588$	0.0126799	−	0.00443178i	0.000522908	−	0.000182764i
$589$	26.5330	−	15.3188i	1.09327	−	0.631200i
$590$	2.65822	+	0.986862i	0.109437	+	0.0406285i
$591$	−10.1655	−	2.72384i	−0.418154	−	0.112044i
$592$	0.233301	−	2.05737i	0.00958862	−	0.0845572i
$593$	−11.0244	+	11.0244i	−0.452717	+	0.452717i	−0.896255	−	0.443538i	$-0.853723\pi$
$593$	−11.0244	+	11.0244i	−0.452717	+	0.452717i	0.443538	+	0.896255i	$0.353723\pi$
$594$	5.29565	−	7.46070i	0.217283	−	0.306116i
$595$	−0.435357	+	0.754060i	−0.0178479	+	0.0309134i
$596$	−27.3077	−	13.1627i	−1.11857	−	0.539167i
$597$		−	2.06898i		−	0.0846775i
$598$		0			0
$599$			10.6090i			0.433471i	0.976230	+	0.216735i	$0.0695409\pi$
$599$			10.6090i			0.433471i	−0.976230	+	0.216735i	$0.930459\pi$
$600$	−0.228679	+	11.8861i	−0.00933579	+	0.485247i
$601$	−14.1251	+	24.4655i	−0.576177	+	0.997967i	0.419736	+	0.907646i	$0.362123\pi$
$601$	−14.1251	+	24.4655i	−0.576177	+	0.997967i	−0.995913	+	0.0903210i	$0.971211\pi$
$602$	−28.0159	−	19.8859i	−1.14184	−	0.810488i
$603$	4.06169	−	4.06169i	0.165405	−	0.165405i
$604$	−1.12394	+	0.765700i	−0.0457324	+	0.0311559i
$605$	−2.02769	−	0.543318i	−0.0824373	−	0.0220890i
$606$	3.83856	−	10.3396i	0.155931	−	0.420017i
$607$	−8.89476	+	5.13539i	−0.361027	+	0.208439i	−0.669531	−	0.742784i	$-0.733505\pi$
$607$	−8.89476	+	5.13539i	−0.361027	+	0.208439i	0.308504	+	0.951223i	$0.400172\pi$
$608$	−1.74233	−	31.5290i	−0.0706606	−	1.27867i
$609$	2.45528	+	9.16324i	0.0994931	+	0.371313i
$610$	2.18483	−	1.00180i	0.0884610	−	0.0405615i
$611$		0			0
$612$	4.15898	−	4.82933i	0.168117	−	0.195214i
$613$	34.2262	−	9.17089i	1.38238	−	0.370409i	0.510397	−	0.859939i	$-0.329498\pi$
$613$	34.2262	−	9.17089i	1.38238	−	0.370409i	0.871986	+	0.489530i	$0.162832\pi$
$614$	3.05254	−	32.4898i	0.123190	−	1.31118i
$615$	0.579674	+	1.00403i	0.0233747	+	0.0404862i
$616$	5.21218	+	9.44271i	0.210005	+	0.380458i
$617$	10.8473	−	40.4828i	0.436697	−	1.62978i	−0.300275	−	0.953853i	$-0.597078\pi$
$617$	10.8473	−	40.4828i	0.436697	−	1.62978i	0.736972	−	0.675923i	$-0.236255\pi$
$618$	−2.19419	−	12.9281i	−0.0882632	−	0.520043i
$619$	−12.0880	−	12.0880i	−0.485858	−	0.485858i	0.421138	−	0.906996i	$-0.361631\pi$
$619$	−12.0880	−	12.0880i	−0.485858	−	0.485858i	−0.906996	+	0.421138i	$0.861631\pi$
$620$	0.481165	−	2.53804i	0.0193240	−	0.101930i
$621$	−33.9719	−	19.6137i	−1.36324	−	0.787069i
$622$	−7.70846	−	9.30714i	−0.309081	−	0.373182i
$623$	−17.5666			−0.703790
$624$		0			0
$625$	−24.1724			−0.966894
$626$	−5.30760	−	6.40836i	−0.212134	−	0.256129i
$627$	5.92609	+	3.42143i	0.236665	+	0.136639i
$628$	−2.19943	+	11.6015i	−0.0877667	+	0.462951i
$629$	0.512159	+	0.512159i	0.0204211	+	0.0204211i
$630$	−0.335363	−	1.97594i	−0.0133612	−	0.0787235i
$631$	3.12081	−	11.6470i	0.124237	−	0.463660i	−0.875574	−	0.483084i	$-0.839517\pi$
$631$	3.12081	−	11.6470i	0.124237	−	0.463660i	0.999811	+	0.0194238i	$0.00618318\pi$
$632$	11.6407	+	21.0890i	0.463042	+	0.838875i
$633$	1.78106	+	3.08489i	0.0707909	+	0.122613i
$634$	3.08772	−	32.8642i	0.122629	−	1.30521i
$635$	1.21479	−	0.325501i	0.0482073	−	0.0129171i
$636$	−6.59499	+	7.65798i	−0.261509	+	0.303659i
$637$		0			0
$638$	7.82419	−	3.58758i	0.309763	−	0.142034i
$639$	6.40759	+	23.9134i	0.253480	+	0.946001i
$640$	−2.11024	−	1.62345i	−0.0834146	−	0.0641724i
$641$	−1.81632	+	1.04865i	−0.0717404	+	0.0414193i	−0.535441	−	0.844573i	$-0.679855\pi$
$641$	−1.81632	+	1.04865i	−0.0717404	+	0.0414193i	0.463701	+	0.885992i	$0.346521\pi$
$642$	−4.12391	+	11.1082i	−0.162758	+	0.438406i
$643$	−40.9391	−	10.9696i	−1.61448	−	0.432599i	−0.665108	−	0.746747i	$-0.731614\pi$
$643$	−40.9391	−	10.9696i	−1.61448	−	0.432599i	−0.949374	+	0.314148i	$0.898281\pi$
$644$	38.2183	−	26.0367i	1.50601	−	1.02599i
$645$	−1.29954	+	1.29954i	−0.0511692	+	0.0511692i
$646$	9.00754	+	6.39362i	0.354397	+	0.251553i
$647$	−21.5400	+	37.3083i	−0.846824	+	1.46674i	0.0372042	+	0.999308i	$0.488155\pi$
$647$	−21.5400	+	37.3083i	−0.846824	+	1.46674i	−0.884028	+	0.467434i	$0.845179\pi$
$648$	−0.164252	+	8.53732i	−0.00645242	+	0.335377i
$649$			12.2867i			0.482296i
$650$		0			0
$651$			12.3368i			0.483518i
$652$	28.3446	+	13.6625i	1.11006	+	0.535066i
$653$	5.56059	−	9.63123i	0.217603	−	0.376899i	−0.736472	−	0.676468i	$-0.763510\pi$
$653$	5.56059	−	9.63123i	0.217603	−	0.376899i	0.954075	+	0.299569i	$0.0968429\pi$
$654$	0.0239290	−	0.0337120i	0.000935697	−	0.00131824i
$655$	1.86794	−	1.86794i	0.0729865	−	0.0729865i
$656$	23.0346	+	2.61208i	0.899350	+	0.101984i
$657$	15.7233	+	4.21305i	0.613425	+	0.164367i
$658$	13.8978	+	5.15956i	0.541795	+	0.201141i
$659$	−13.2010	+	7.62162i	−0.514239	+	0.296896i	−0.734575	−	0.678528i	$-0.762618\pi$
$659$	−13.2010	+	7.62162i	−0.514239	+	0.296896i	0.220335	+	0.975424i	$0.429285\pi$
$660$	0.544655	−	0.190364i	0.0212007	−	0.00740992i
$661$	2.67284	+	9.97516i	0.103961	+	0.387989i	0.998225	−	0.0595512i	$-0.0189669\pi$
$661$	2.67284	+	9.97516i	0.103961	+	0.387989i	−0.894264	+	0.447540i	$0.852300\pi$
$662$	−8.46813	−	18.4682i	−0.329123	−	0.717788i
$663$		0			0
$664$	7.66815	−	26.5631i	0.297582	−	1.03085i
$665$	3.35523	−	0.899032i	0.130110	−	0.0348630i
$666$	−1.65988	−	0.155952i	−0.0643191	−	0.00604302i
$667$	−18.4525	−	31.9607i	−0.714485	−	1.23753i
$668$	−0.833940	−	11.1819i	−0.0322661	−	0.432639i
$669$	−4.14239	+	15.4596i	−0.160154	+	0.597704i
$670$	0.827568	−	0.140457i	0.0319717	−	0.00542633i
$671$	7.36454	+	7.36454i	0.284305	+	0.284305i
$672$	11.3456	+	5.74028i	0.437666	+	0.221436i
$673$	25.8030	+	14.8974i	0.994631	+	0.574251i	0.906655	−	0.421872i	$-0.138627\pi$
$673$	25.8030	+	14.8974i	0.994631	+	0.574251i	0.0879759	+	0.996123i	$0.471960\pi$
$674$	−15.6215	+	12.9382i	−0.601716	+	0.498360i
$675$	22.1818			0.853776
$676$		0			0
$677$	−29.1021			−1.11849			−0.559243	−	0.829004i	$-0.688908\pi$
$677$	−29.1021			−1.11849			−0.559243	+	0.829004i	$0.688908\pi$
$678$	4.21556	−	3.49146i	0.161898	−	0.134089i
$679$	35.4334	+	20.4575i	1.35981	+	0.785085i
$680$	0.904093	−	0.223704i	0.0346704	−	0.00857864i
$681$	−4.47188	−	4.47188i	−0.171363	−	0.171363i
$682$	11.0359	−	1.87304i	0.422585	−	0.0717223i
$683$	1.30625	−	4.87499i	0.0499823	−	0.186536i	−0.936421	−	0.350878i	$-0.885883\pi$
$683$	1.30625	−	4.87499i	0.0499823	−	0.186536i	0.986404	+	0.164342i	$0.0525499\pi$
$684$	−25.3552	+	1.89098i	−0.969480	+	0.0723035i
$685$	−0.565743	−	0.979896i	−0.0216159	−	0.0374399i
$686$	26.0915	+	2.45139i	0.996176	+	0.0935945i
$687$	−3.68930	+	0.988544i	−0.140755	+	0.0377153i
$688$	5.45113	+	36.3424i	0.207822	+	1.38554i
$689$		0			0
$690$	−1.03106	−	2.24866i	−0.0392519	−	0.0856049i
$691$	−2.89268	−	10.7956i	−0.110043	−	0.410685i	0.888826	−	0.458246i	$-0.151522\pi$
$691$	−2.89268	−	10.7956i	−0.110043	−	0.410685i	−0.998868	+	0.0475604i	$0.984855\pi$
$692$	1.42586	+	4.07956i	0.0542031	+	0.155082i
$693$	7.52106	−	4.34229i	0.285701	−	0.164950i
$694$	−0.623535	−	0.231487i	−0.0236691	−	0.00878711i
$695$	−1.57770	−	0.422743i	−0.0598455	−	0.0160355i
$696$	5.24170	−	8.68852i	0.198686	−	0.329337i
$697$	−5.73421	+	5.73421i	−0.217199	+	0.217199i
$698$	−23.1516	+	32.6168i	−0.876302	+	1.23456i
$699$	5.66150	−	9.80601i	0.214138	−	0.370897i
$700$	−11.3544	+	23.5560i	−0.429155	+	0.890333i
$701$		−	27.1476i		−	1.02535i	−0.858582	−	0.512676i	$-0.828654\pi$
$701$		−	27.1476i		−	1.02535i	0.858582	−	0.512676i	$-0.171346\pi$
$702$		0			0
$703$		−	2.88950i		−	0.108980i
$704$	3.41241	−	11.0207i	0.128610	−	0.415359i
$705$	0.396511	−	0.686778i	0.0149335	−	0.0258656i
$706$	41.4610	+	29.4293i	1.56041	+	1.10759i
$707$	17.1544	−	17.1544i	0.645156	−	0.645156i
$708$	8.15518	+	11.9707i	0.306490	+	0.449885i
$709$	−40.9857	−	10.9821i	−1.53925	−	0.412441i	−0.613228	−	0.789906i	$-0.710129\pi$
$709$	−40.9857	−	10.9821i	−1.53925	−	0.412441i	−0.926024	+	0.377465i	$0.876796\pi$
$710$	−1.25914	+	3.39163i	−0.0472547	+	0.127286i
$711$	16.7973	−	9.69790i	0.629946	−	0.363700i
$712$	13.0286	+	13.5397i	0.488266	+	0.507422i
$713$	−12.4217	−	46.3583i	−0.465195	−	1.73613i
$714$	−4.04312	+	1.85387i	−0.151310	+	0.0693792i
$715$		0			0
$716$	15.3560	+	13.2245i	0.573880	+	0.494221i
$717$	−6.92808	+	1.85637i	−0.258734	+	0.0693275i
$718$	−2.19200	+	23.3306i	−0.0818047	+	0.870692i
$719$	−8.21566	−	14.2299i	−0.306392	−	0.530687i	0.671178	−	0.741296i	$-0.265789\pi$
$719$	−8.21566	−	14.2299i	−0.306392	−	0.530687i	−0.977570	+	0.210609i	$0.932455\pi$
$720$	−1.27426	+	1.72398i	−0.0474889	+	0.0642489i
$721$	7.46526	−	27.8607i	0.278021	−	1.03759i
$722$	−2.87748	−	16.9540i	−0.107089	−	0.630963i
$723$	−9.29717	−	9.29717i	−0.345765	−	0.345765i
$724$	27.2208	+	5.16054i	1.01165	+	0.191790i
$725$	18.0728	+	10.4343i	0.671205	+	0.387520i
$726$	−6.84010	−	8.25869i	−0.253860	−	0.306509i
$727$	−32.1429			−1.19211			−0.596057	−	0.802942i	$-0.703267\pi$
$727$	−32.1429			−1.19211			−0.596057	+	0.802942i	$0.703267\pi$
$728$		0			0
$729$	−4.56452			−0.169056
$730$	1.51732	+	1.83200i	0.0561584	+	0.0678052i
$731$	−11.1329	−	6.42759i	−0.411765	−	0.237733i
$732$	12.0632	+	2.28696i	0.445870	+	0.0845284i
$733$	19.2047	+	19.2047i	0.709343	+	0.709343i	0.966397	−	0.257054i	$-0.0827518\pi$
$733$	19.2047	+	19.2047i	0.709343	+	0.709343i	−0.257054	+	0.966397i	$0.582752\pi$
$734$	2.40322	+	14.1597i	0.0887045	+	0.522644i
$735$	0.000409059	−	0.00152663i	1.50884e−5	−	5.63106e-5i
$736$	−48.4134	−	10.1467i	−1.78454	−	0.374013i
$737$	1.81864	+	3.14998i	0.0669905	+	0.116031i
$738$	1.74606	−	18.5843i	0.0642735	−	0.684097i
$739$	22.4404	−	6.01290i	0.825485	−	0.221188i	0.178742	−	0.983896i	$-0.442797\pi$
$739$	22.4404	−	6.01290i	0.825485	−	0.221188i	0.646743	+	0.762708i	$0.276131\pi$
$740$	−0.184609	−	0.158984i	−0.00678637	−	0.00584438i
$741$		0			0
$742$	−20.2072	+	9.26549i	−0.741830	+	0.340147i
$743$	9.98778	+	37.2749i	0.366416	+	1.36748i	0.865491	+	0.500925i	$0.167007\pi$
$743$	9.98778	+	37.2749i	0.366416	+	1.36748i	−0.499075	+	0.866559i	$0.666327\pi$
$744$	9.50878	−	9.14980i	0.348609	−	0.335448i
$745$	−3.08908	+	1.78348i	−0.113175	+	0.0653417i
$746$	7.39079	−	19.9079i	0.270596	−	0.728880i
$747$	−21.5032	−	5.76177i	−0.786762	−	0.210812i
$748$	2.27222	+	3.33530i	0.0830806	+	0.121951i
$749$	−18.4296	+	18.4296i	−0.673402	+	0.673402i
$750$	2.29416	+	1.62841i	0.0837708	+	0.0594611i
$751$	−0.646973	+	1.12059i	−0.0236084	+	0.0408909i	−0.877588	−	0.479415i	$-0.840849\pi$
$751$	−0.646973	+	1.12059i	−0.0236084	+	0.0408909i	0.853980	+	0.520306i	$0.174182\pi$
$752$	−6.33076	−	14.5387i	−0.230859	−	0.530170i
$753$		−	23.3570i		−	0.851178i
$754$		0			0
$755$			0.160022i			0.00582380i
$756$	10.3013	−	21.3713i	0.374655	−	0.777268i
$757$	11.2800	−	19.5376i	0.409979	−	0.710104i	−0.584908	−	0.811100i	$-0.698869\pi$
$757$	11.2800	−	19.5376i	0.409979	−	0.710104i	0.994887	+	0.100995i	$0.0322027\pi$
$758$	−27.3049	+	38.4681i	−0.991759	+	1.39722i
$759$	7.57969	−	7.57969i	0.275125	−	0.275125i
$760$	−3.18141	−	1.91931i	−0.115402	−	0.0696208i
$761$	−8.40241	−	2.25142i	−0.304587	−	0.0816138i	0.103288	−	0.994651i	$-0.467064\pi$
$761$	−8.40241	−	2.25142i	−0.304587	−	0.0816138i	−0.407875	+	0.913038i	$0.633730\pi$
$762$	6.02276	+	2.23594i	0.218182	+	0.0809997i
$763$	0.0787520	−	0.0454675i	0.00285101	−	0.00164603i
$764$	−2.55406	−	7.30748i	−0.0924027	−	0.264375i
$765$	−0.194094	−	0.724369i	−0.00701748	−	0.0261896i
$766$	12.3399	+	26.9123i	0.445860	+	0.972381i
$767$		0			0
$768$	−3.99026	−	13.0022i	−0.143986	−	0.469175i
$769$	9.35018	−	2.50537i	0.337176	−	0.0903461i	−0.0862584	−	0.996273i	$-0.527491\pi$
$769$	9.35018	−	2.50537i	0.337176	−	0.0903461i	0.423434	+	0.905927i	$0.360824\pi$
$770$	1.26354	+	0.118714i	0.0455348	+	0.00427816i
$771$	−11.8306	−	20.4912i	−0.426068	−	0.737971i
$772$	16.4031	−	1.22334i	0.590361	−	0.0440289i
$773$	4.96928	−	18.5456i	0.178732	−	0.667039i	−0.817153	−	0.576420i	$-0.804449\pi$
$773$	4.96928	−	18.5456i	0.178732	−	0.667039i	0.995886	−	0.0906182i	$-0.0288843\pi$
$774$	29.1728	−	4.95128i	1.04859	−	0.177970i
$775$	19.1900	+	19.1900i	0.689327	+	0.689327i
$776$	−10.5119	−	42.4834i	−0.377354	−	1.52507i
$777$	1.00763	+	0.581756i	0.0361486	+	0.0208704i
$778$	10.4604	−	8.66361i	0.375023	−	0.310605i
$779$	32.3513			1.15911
$780$		0			0
$781$	−15.6767			−0.560955
$782$	13.3263	−	11.0372i	0.476547	−	0.394691i
$783$	−16.3966	−	9.46660i	−0.585968	−	0.338309i
$784$	−0.0196866	−	0.0247225i	−0.000703092	−	0.000882945i
$785$	0.982461	+	0.982461i	0.0350655	+	0.0350655i
$786$	13.3042	−	2.25803i	0.474545	−	0.0805411i
$787$	−7.73737	+	28.8763i	−0.275808	+	1.02933i	0.679491	+	0.733684i	$0.262201\pi$
$787$	−7.73737	+	28.8763i	−0.275808	+	1.02933i	−0.955298	+	0.295644i	$0.904466\pi$
$788$	1.84158	+	24.6928i	0.0656037	+	0.879645i
$789$	10.1181	+	17.5250i	0.360213	+	0.623907i
$790$	2.82194	+	0.265132i	0.100400	+	0.00943298i
$791$	11.6298	−	3.11619i	0.413508	−	0.110799i
$792$	−8.92500	−	2.57644i	−0.317136	−	0.0915498i
$793$		0			0
$794$	1.52237	+	3.32016i	0.0540270	+	0.117828i
$795$	0.307779	+	1.14865i	0.0109158	+	0.0407383i
$796$	−4.59533	+	1.60613i	−0.162877	+	0.0569278i
$797$	32.2562	−	18.6231i	1.14257	−	0.659665i	0.195507	−	0.980702i	$-0.437365\pi$
$797$	32.2562	−	18.6231i	1.14257	−	0.659665i	0.947067	+	0.321037i	$0.104031\pi$
$798$	16.6348	+	6.17567i	0.588867	+	0.218616i
$799$	5.35801	+	1.43567i	0.189553	+	0.0507905i
$800$	26.5773	−	8.71916i	0.939649	−	0.308269i
$801$	10.6983	−	10.6983i	0.378004	−	0.378004i
$802$	22.1433	−	31.1963i	0.781908	−	1.10158i
$803$	−5.15378	+	8.92661i	−0.181873	+	0.315013i
$804$	3.86263	+	1.86185i	0.136224	+	0.0656623i
$805$		−	5.44136i		−	0.191783i
$806$		0			0
$807$		−	17.6060i		−	0.619759i
$808$	−25.9448	−	0.499159i	−0.912735	−	0.0175603i
$809$	−20.9090	+	36.2154i	−0.735121	+	1.27327i	0.219550	+	0.975601i	$0.429541\pi$
$809$	−20.9090	+	36.2154i	−0.735121	+	1.27327i	−0.954670	+	0.297665i	$0.903792\pi$
$810$	0.819316	+	0.581556i	0.0287878	+	0.0204338i
$811$	4.29617	−	4.29617i	0.150859	−	0.150859i	−0.627643	−	0.778502i	$-0.715980\pi$
$811$	4.29617	−	4.29617i	0.150859	−	0.150859i	0.778502	+	0.627643i	$0.215980\pi$
$812$	18.4462	−	12.5667i	0.647333	−	0.441005i
$813$	11.3472	+	3.04046i	0.397962	+	0.106634i
$814$	0.367425	−	0.989700i	0.0128782	−	0.0346890i
$815$	3.20637	−	1.85120i	0.112314	−	0.0648447i
$816$	4.42754	+	1.74134i	0.154995	+	0.0609591i
$817$	13.2733	+	49.5365i	0.464373	+	1.73306i
$818$	6.16364	−	2.82618i	0.215506	−	0.0988149i
$819$		0			0
$820$	1.78001	−	2.06691i	0.0621607	−	0.0721798i
$821$	−18.2378	+	4.88681i	−0.636505	+	0.170551i	−0.562620	−	0.826716i	$-0.690207\pi$
$821$	−18.2378	+	4.88681i	−0.636505	+	0.170551i	−0.0738852	+	0.997267i	$0.523540\pi$
$822$	0.540670	−	5.75464i	0.0188580	−	0.200716i
$823$	6.80437	+	11.7855i	0.237185	+	0.410817i	0.959906	−	0.280324i	$-0.0904418\pi$
$823$	6.80437	+	11.7855i	0.237185	+	0.410817i	−0.722720	+	0.691141i	$0.757108\pi$
$824$	−27.0108	+	14.9094i	−0.940966	+	0.519394i
$825$	−1.56881	+	5.85487i	−0.0546189	+	0.203841i
$826$	5.33123	+	31.4114i	0.185497	+	1.09294i
$827$	17.0815	+	17.0815i	0.593982	+	0.593982i	0.938705	−	0.344723i	$-0.112027\pi$
$827$	17.0815	+	17.0815i	0.593982	+	0.593982i	−0.344723	+	0.938705i	$0.612027\pi$
$828$	−7.41869	+	39.1320i	−0.257817	+	1.35993i
$829$	−23.8014	−	13.7417i	−0.826657	−	0.477270i	0.0260500	−	0.999661i	$-0.491707\pi$
$829$	−23.8014	−	13.7417i	−0.826657	−	0.477270i	−0.852707	+	0.522390i	$0.825040\pi$
$830$	−2.07508	−	2.50544i	−0.0720272	−	0.0869651i
$831$	−10.8241			−0.375485
$832$		0			0
$833$	0.0110551			0.000383038
$834$	−5.32212	−	6.42589i	−0.184290	−	0.222510i
$835$	−1.14261	−	0.659685i	−0.0395416	−	0.0228294i
$836$	2.99885	−	15.8183i	0.103717	−	0.547087i
$837$	−17.4103	−	17.4103i	−0.601788	−	0.601788i
$838$	1.32637	+	7.81495i	0.0458188	+	0.269963i
$839$	−10.3356	+	38.5731i	−0.356825	+	1.33169i	0.521347	+	0.853345i	$0.325430\pi$
$839$	−10.3356	+	38.5731i	−0.356825	+	1.33169i	−0.878172	+	0.478345i	$0.841237\pi$
$840$	1.30983	−	0.723001i	0.0451935	−	0.0249459i
$841$	5.59382	+	9.68878i	0.192890	+	0.334096i
$842$	−0.664809	+	7.07592i	−0.0229108	+	0.243852i
$843$	17.9349	−	4.80564i	0.617711	−	0.165515i
$844$	5.46913	−	6.35064i	0.188255	−	0.218598i
$845$		0			0
$846$	−11.6062	+	5.32172i	−0.399029	+	0.182964i
$847$	−6.10491	−	22.7839i	−0.209767	−	0.782862i
$848$	22.1285	+	8.70310i	0.759897	+	0.298866i
$849$	−15.2309	+	8.79359i	−0.522725	+	0.301795i
$850$	−3.40540	+	9.17283i	−0.116804	+	0.314625i
$851$	−4.37216	−	1.17152i	−0.149876	−	0.0401590i
$852$	−15.2734	+	10.4052i	−0.523258	+	0.356477i
$853$	6.78242	−	6.78242i	0.232226	−	0.232226i	−0.581395	−	0.813621i	$-0.697493\pi$
$853$	6.78242	−	6.78242i	0.232226	−	0.232226i	0.813621	+	0.581395i	$0.197493\pi$
$854$	22.0232	+	15.6322i	0.753618	+	0.534923i
$855$	−1.49586	+	2.59090i	−0.0511572	+	0.0886068i
$856$	27.8735	+	0.536265i	0.952696	+	0.0183292i
$857$			25.7579i			0.879872i	0.898029	+	0.439936i	$0.144999\pi$
$857$			25.7579i			0.879872i	−0.898029	+	0.439936i	$0.855001\pi$
$858$		0			0
$859$			51.8251i			1.76825i	0.467252	+	0.884124i	$0.345244\pi$
$859$			51.8251i			1.76825i	−0.467252	+	0.884124i	$0.654756\pi$
$860$	3.89518	+	1.87754i	0.132825	+	0.0640236i
$861$	−6.51343	+	11.2816i	−0.221977	+	0.384476i
$862$	2.83038	−	3.98754i	0.0964032	−	0.135816i
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.220144	+	0.975467i	$0.570653\pi$
$863$	−35.1233	+	35.1233i	−1.19561	+	1.19561i	−0.975467	+	0.220144i	$0.929347\pi$
$864$	−24.1124	+	7.91052i	−0.820321	+	0.269121i
$865$	0.491171	+	0.131609i	0.0167003	+	0.00447483i
$866$	7.25558	+	2.69363i	0.246555	+	0.0915332i
$867$	11.0734	−	6.39322i	0.376072	−	0.217125i
$868$	27.4009	−	9.57698i	0.930047	−	0.325064i
$869$	3.17877	+	11.8633i	0.107833	+	0.402436i
$870$	−0.497646	−	1.08532i	−0.0168718	−	0.0367958i
$871$		0			0
$872$	−0.0934525	−	0.0269775i	−0.00316470	−	0.000913575i
$873$	−34.0382	+	9.12050i	−1.15202	+	0.308682i
$874$	−68.7272	−	6.45718i	−2.32473	−	0.218417i
$875$	3.09414	+	5.35921i	0.104601	+	0.181174i
$876$	0.903738	+	12.1178i	0.0305345	+	0.409421i
$877$	−9.61256	+	35.8746i	−0.324593	+	1.21140i	0.590127	+	0.807310i	$0.299078\pi$
$877$	−9.61256	+	35.8746i	−0.324593	+	1.21140i	−0.914720	+	0.404088i	$0.867589\pi$
$878$	−42.5342	+	7.21902i	−1.43546	+	0.243630i
$879$	−13.8602	−	13.8602i	−0.467493	−	0.467493i
$880$	−0.845624	−	1.06194i	−0.0285060	−	0.0357979i
$881$	−1.73014	−	0.998897i	−0.0582899	−	0.0336537i	0.470572	−	0.882362i	$-0.344048\pi$
$881$	−1.73014	−	0.998897i	−0.0582899	−	0.0336537i	−0.528862	+	0.848708i	$0.677381\pi$
$882$	−0.0195977	+	0.0162314i	−0.000659890	+	0.000546541i
$883$	−16.1625			−0.543913			−0.271956	−	0.962310i	$-0.587671\pi$
$883$	−16.1625			−0.543913			−0.271956	+	0.962310i	$0.587671\pi$
$884$		0			0
$885$	1.70433			0.0572906
$886$	−14.0495	+	11.6362i	−0.472001	+	0.390926i
$887$	15.2472	+	8.80298i	0.511951	+	0.295575i	0.733635	−	0.679543i	$-0.237822\pi$
$887$	15.2472	+	8.80298i	0.511951	+	0.295575i	−0.221684	+	0.975119i	$0.571155\pi$
$888$	−0.298929	−	1.20812i	−0.0100314	−	0.0405417i
$889$	9.99232	+	9.99232i	0.335132	+	0.335132i
$890$	2.17977	−	0.369956i	0.0730659	−	0.0124009i
$891$	−1.12682	+	4.20534i	−0.0377498	+	0.140884i
$892$	37.5526	−	2.80066i	1.25735	−	0.0937730i
$893$	−11.0645	−	19.1644i	−0.370261	−	0.641311i
$894$	−18.1413	−	1.70444i	−0.606735	−	0.0570050i
$895$	2.30330	−	0.617167i	0.0769908	−	0.0206296i
$896$	3.94203	−	29.6555i	0.131694	−	0.990721i
$897$		0			0
$898$	5.81779	+	12.6881i	0.194142	+	0.423407i
$899$	−5.99536	−	22.3750i	−0.199956	−	0.746247i
$900$	−7.43094	−	21.2608i	−0.247698	−	0.708694i
$901$	−7.20357	+	4.15898i	−0.239986	+	0.138556i
$902$	11.0808	+	4.11375i	0.368951	+	0.136973i
$903$	−19.9468	−	5.34473i	−0.663788	−	0.177861i
$904$	−11.0273	−	6.65265i	−0.366762	−	0.221264i
$905$	2.30516	−	2.30516i	0.0766261	−	0.0766261i
$906$	−0.473150	+	0.666589i	−0.0157193	+	0.0221459i
$907$	−14.7054	+	25.4704i	−0.488283	+	0.845731i	−0.999909	−	0.0134769i	$-0.995710\pi$
$907$	−14.7054	+	25.4704i	−0.488283	+	0.845731i	0.511626	+	0.859208i	$0.329043\pi$
$908$	−6.46086	+	13.4038i	−0.214411	+	0.444822i
$909$			20.8944i			0.693024i
$910$		0			0
$911$			20.5091i			0.679495i	0.940517	+	0.339748i	$0.110342\pi$
$911$			20.5091i			0.679495i	−0.940517	+	0.339748i	$0.889658\pi$
$912$	−7.57752	−	17.4018i	−0.250917	−	0.576232i
$913$	7.04832	−	12.2080i	0.233265	−	0.404027i
$914$	11.9730	+	8.49853i	0.396032	+	0.281106i
$915$	1.02156	−	1.02156i	0.0337718	−	0.0337718i
$916$	5.05960	+	7.42678i	0.167174	+	0.245388i
$917$	28.6713	+	7.68245i	0.946810	+	0.253697i
$918$	3.08958	−	8.32211i	0.101971	−	0.274671i
$919$	−42.4137	+	24.4876i	−1.39910	+	0.807770i	−0.994298	−	0.106635i	$-0.965992\pi$
$919$	−42.4137	+	24.4876i	−1.39910	+	0.807770i	−0.404800	+	0.914405i	$0.632659\pi$
$920$	−4.19401	+	4.03568i	−0.138272	+	0.133052i
$921$	−5.07665	−	18.9463i	−0.167281	−	0.624302i
$922$	36.9391	−	16.9375i	1.21652	−	0.557806i
$923$		0			0
$924$	4.91240	+	4.23053i	0.161606	+	0.139174i
$925$	2.47231	−	0.662453i	0.0812890	−	0.0217813i
$926$	1.10204	−	11.7296i	0.0362152	−	0.385457i
$927$	12.4211	+	21.5139i	0.407962	+	0.706610i
$928$	−23.3669	−	4.89734i	−0.767056	−	0.160763i
$929$	1.77316	−	6.61751i	0.0581754	−	0.217113i	−0.930719	−	0.365736i	$-0.880817\pi$
$929$	1.77316	−	6.61751i	0.0581754	−	0.217113i	0.988894	+	0.148623i	$0.0474840\pi$
$930$	−0.259816	−	1.53082i	−0.00851969	−	0.0501977i
$931$	−0.0311855	−	0.0311855i	−0.00102206	−	0.00102206i
$932$	−26.1748	−	4.96224i	−0.857384	−	0.162544i
$933$	−6.29067	−	3.63192i	−0.205947	−	0.118904i
$934$	−2.97985	−	3.59785i	−0.0975038	−	0.117725i
$935$	0.474867			0.0155298
$936$		0			0
$937$	11.1107			0.362970			0.181485	−	0.983394i	$-0.441910\pi$
$937$	11.1107			0.362970			0.181485	+	0.983394i	$0.441910\pi$
$938$	6.01621	+	7.26393i	0.196436	+	0.237176i
$939$	−4.33139	−	2.50073i	−0.141350	−	0.0816083i
$940$	−1.83319	−	0.347538i	−0.0597921	−	0.0113354i
$941$	20.5970	+	20.5970i	0.671442	+	0.671442i	0.958048	−	0.286606i	$-0.0925272\pi$
$941$	20.5970	+	20.5970i	0.671442	+	0.671442i	−0.286606	+	0.958048i	$0.592527\pi$
$942$	1.18763	+	6.99747i	0.0386951	+	0.227990i
$943$	13.1165	−	48.9513i	0.427131	−	1.59407i
$944$	20.2568	−	27.4059i	0.659304	−	0.891988i
$945$	−1.39577	−	2.41755i	−0.0454045	−	0.0786430i
$946$	−1.75269	+	18.6548i	−0.0569849	+	0.606521i
$947$	−28.3374	+	7.59297i	−0.920841	+	0.246739i	−0.687945	−	0.725763i	$-0.741487\pi$
$947$	−28.3374	+	7.59297i	−0.920841	+	0.246739i	−0.232896	+	0.972502i	$0.574820\pi$
$948$	10.9712	+	9.44830i	0.356327	+	0.306867i
$949$		0			0
$950$	35.4820	−	16.2694i	1.15119	−	0.527848i
$951$	−5.13516	−	19.1647i	−0.166519	−	0.621457i
$952$	7.25621	+	7.54089i	0.235175	+	0.244402i
$953$	−11.3638	+	6.56091i	−0.368110	+	0.212529i	−0.672633	−	0.739977i	$-0.734837\pi$
$953$	−11.3638	+	6.56091i	−0.368110	+	0.212529i	0.304522	+	0.952505i	$0.401503\pi$
$954$	6.66363	−	17.9492i	0.215743	−	0.581128i
$955$	−0.879806	−	0.235743i	−0.0284699	−	0.00762847i
$956$	9.50135	+	13.9466i	0.307296	+	0.451067i
$957$	3.65836	−	3.65836i	0.118258	−	0.118258i
$958$	−32.0745	−	22.7667i	−1.03628	−	0.735559i
$959$	6.35689	−	11.0105i	0.205275	−	0.355546i
$960$	−1.52872	−	0.473347i	−0.0493393	−	0.0152772i
$961$			0.875747i			0.0282499i
$962$		0			0
$963$		−	22.4477i		−	0.723365i
$964$	−13.4323	+	27.8670i	−0.432626	+	0.897535i
$965$	0.967718	−	1.67614i	0.0311519	−	0.0539568i
$966$	16.0889	−	22.6666i	0.517652	−	0.729286i
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	−0.885059	−	0.465478i	$-0.845882\pi$
$967$	−13.0476	+	13.0476i	−0.419581	+	0.419581i	0.465478	+	0.885059i	$0.345882\pi$
$968$	−13.0332	+	21.6035i	−0.418902	+	0.694362i
$969$	6.41320	+	1.71841i	0.206022	+	0.0552033i
$970$	−4.82762	−	1.79225i	−0.155006	−	0.0575457i
$971$	38.3512	−	22.1421i	1.23075	−	0.710573i	0.263562	−	0.964642i	$-0.415103\pi$
$971$	38.3512	−	22.1421i	1.23075	−	0.710573i	0.967186	+	0.254070i	$0.0817692\pi$
$972$	10.5742	+	30.2540i	0.339167	+	0.970399i
$973$	−4.75009	−	17.7276i	−0.152281	−	0.568320i
$974$	−6.08146	−	13.2631i	−0.194862	−	0.424978i
$975$		0			0
$976$	−4.28511	−	28.5686i	−0.137163	−	0.914459i
$977$	−0.239374	+	0.0641402i	−0.00765826	+	0.00205203i	−0.262646	−	0.964892i	$-0.584595\pi$
$977$	−0.239374	+	0.0641402i	−0.00765826	+	0.00205203i	0.254988	+	0.966944i	$0.417929\pi$
$978$	18.8301	+	1.76916i	0.602120	+	0.0565715i
$979$	4.79020	+	8.29687i	0.153095	+	0.265169i
$980$	−0.00370830		0.000276564i	−0.000118457		8.83450e-6i
$981$	−0.0202707	+	0.0756511i	−0.000647192	+	0.00241535i
$982$	18.9968	−	3.22419i	0.606212	−	0.102888i
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	0.559393	−	0.828903i	$-0.311034\pi$
$983$	−8.44991	−	8.44991i	−0.269510	−	0.269510i	−0.828903	+	0.559393i	$0.811034\pi$
$984$	13.5262	−	3.34686i	0.431201	−	0.106694i
$985$	2.52321	+	1.45678i	0.0803963	+	0.0464168i
$986$	6.43198	−	5.32716i	0.204836	−	0.169651i
$987$	8.91069			0.283630
$988$		0			0
$989$	80.3360			2.55454
$990$	−0.841809	+	0.697212i	−0.0267544	+	0.0221588i
$991$	−36.2254	−	20.9147i	−1.15074	−	0.664379i	−0.201671	−	0.979453i	$-0.564637\pi$
$991$	−36.2254	−	20.9147i	−1.15074	−	0.664379i	−0.949067	+	0.315074i	$0.897971\pi$
$992$	−27.7039	−	14.0167i	−0.879601	−	0.445031i
$993$	−8.63520	−	8.63520i	−0.274030	−	0.274030i
$994$	−40.0780	+	6.80214i	−1.27120	+	0.215751i
$995$	−0.148248	+	0.553269i	−0.00469978	+	0.0175398i
$996$	−1.23595	−	16.5723i	−0.0391627	−	0.525112i
$997$	−6.38088	−	11.0520i	−0.202085	−	0.350021i	0.747115	−	0.664694i	$-0.231438\pi$
$997$	−6.38088	−	11.0520i	−0.202085	−	0.350021i	−0.949200	+	0.314674i	$0.898105\pi$
$998$	22.3591	+	2.10072i	0.707765	+	0.0664972i
$999$	−2.24302	+	0.601015i	−0.0709660	+	0.0190153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.l.k.319.1		16
4.3	odd	2	inner	676.2.l.k.319.2		16
13.2	odd	12	inner	676.2.l.k.587.2		16
13.3	even	3		676.2.l.i.427.4		16
13.4	even	6		676.2.f.h.99.6		16
13.5	odd	4		676.2.l.i.19.2		16
13.6	odd	12		676.2.f.i.239.8		16
13.7	odd	12		676.2.f.h.239.1		16
13.8	odd	4		676.2.l.m.19.3		16
13.9	even	3		676.2.f.i.99.3		16
13.10	even	6		676.2.l.m.427.1		16
13.11	odd	12		52.2.l.b.15.3	yes	16
13.12	even	2		52.2.l.b.7.4	yes	16
39.11	even	12		468.2.cb.f.379.2		16
39.38	odd	2		468.2.cb.f.163.1		16
52.3	odd	6		676.2.l.i.427.2		16
52.7	even	12		676.2.f.h.239.6		16
52.11	even	12		52.2.l.b.15.4	yes	16
52.15	even	12	inner	676.2.l.k.587.1		16
52.19	even	12		676.2.f.i.239.3		16
52.23	odd	6		676.2.l.m.427.3		16
52.31	even	4		676.2.l.i.19.4		16
52.35	odd	6		676.2.f.i.99.8		16
52.43	odd	6		676.2.f.h.99.1		16
52.47	even	4		676.2.l.m.19.1		16
52.51	odd	2		52.2.l.b.7.3	✓	16
104.11	even	12		832.2.bu.n.639.3		16
104.37	odd	12		832.2.bu.n.639.2		16
104.51	odd	2		832.2.bu.n.319.2		16
104.77	even	2		832.2.bu.n.319.3		16
156.11	odd	12		468.2.cb.f.379.1		16
156.155	even	2		468.2.cb.f.163.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.3	✓	16	52.51	odd	2
52.2.l.b.7.4	yes	16	13.12	even	2
52.2.l.b.15.3	yes	16	13.11	odd	12
52.2.l.b.15.4	yes	16	52.11	even	12
468.2.cb.f.163.1		16	39.38	odd	2
468.2.cb.f.163.2		16	156.155	even	2
468.2.cb.f.379.1		16	156.11	odd	12
468.2.cb.f.379.2		16	39.11	even	12
676.2.f.h.99.1		16	52.43	odd	6
676.2.f.h.99.6		16	13.4	even	6
676.2.f.h.239.1		16	13.7	odd	12
676.2.f.h.239.6		16	52.7	even	12
676.2.f.i.99.3		16	13.9	even	3
676.2.f.i.99.8		16	52.35	odd	6
676.2.f.i.239.3		16	52.19	even	12
676.2.f.i.239.8		16	13.6	odd	12
676.2.l.i.19.2		16	13.5	odd	4
676.2.l.i.19.4		16	52.31	even	4
676.2.l.i.427.2		16	52.3	odd	6
676.2.l.i.427.4		16	13.3	even	3
676.2.l.k.319.1		16	1.1	even	1	trivial
676.2.l.k.319.2		16	4.3	odd	2	inner
676.2.l.k.587.1		16	52.15	even	12	inner
676.2.l.k.587.2		16	13.2	odd	12	inner
676.2.l.m.19.1		16	52.47	even	4
676.2.l.m.19.3		16	13.8	odd	4
676.2.l.m.427.1		16	13.10	even	6
676.2.l.m.427.3		16	52.23	odd	6
832.2.bu.n.319.2		16	104.51	odd	2
832.2.bu.n.319.3		16	104.77	even	2
832.2.bu.n.639.2		16	104.37	odd	12
832.2.bu.n.639.3		16	104.11	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.902074 - 1.08916i) q^{2} +(-0.736159 - 0.425021i) q^{3} +(-0.372527 + 1.96500i) q^{4} +(0.166404 + 0.166404i) q^{5} +(0.201154 + 1.18519i) q^{6} +(-0.684384 + 2.55416i) q^{7} +(2.47624 - 1.36683i) q^{8} +(-1.13871 - 1.97231i) q^{9} +(0.0311314 - 0.331348i) q^{10} +(1.39298 - 0.373247i) q^{11} +(1.10941 - 1.28822i) q^{12} +(3.39924 - 1.55864i) q^{14} +(-0.0517744 - 0.193225i) q^{15} +(-3.72245 - 1.46403i) q^{16} +(1.21178 - 0.699622i) q^{17} +(-1.12095 + 3.01941i) q^{18} +(-5.39188 - 1.44475i) q^{19} +(-0.388973 + 0.264994i) q^{20} +(1.58939 - 1.58939i) q^{21} +(-1.66309 - 1.18047i) q^{22} +(-4.37216 + 7.57279i) q^{23} +(-2.40384 - 0.0462481i) q^{24} -4.94462i q^{25} +4.48604i q^{27} +(-4.76397 - 2.29631i) q^{28} +(-2.11023 + 3.65503i) q^{29} +(-0.163748 + 0.230693i) q^{30} +(-3.88100 + 3.88100i) q^{31} +(1.76336 + 5.37499i) q^{32} +(-1.18409 - 0.317276i) q^{33} +(-1.85511 - 0.688709i) q^{34} +(-0.538906 + 0.311137i) q^{35} +(4.29979 - 1.50283i) q^{36} +(0.133975 + 0.500000i) q^{37} +(3.29032 + 7.17588i) q^{38} +(0.639502 + 0.184609i) q^{40} +(-5.59808 + 1.50000i) q^{41} +(-3.16484 - 0.297348i) q^{42} +(-4.59362 - 7.95638i) q^{43} +(0.214509 + 2.87624i) q^{44} +(0.138714 - 0.517686i) q^{45} +(12.1920 - 2.06925i) q^{46} +(2.80318 + 2.80318i) q^{47} +(2.11807 + 2.65988i) q^{48} +(0.00684229 + 0.00395040i) q^{49} +(-5.38547 + 4.46041i) q^{50} -1.18942 q^{51} -5.94462 q^{53} +(4.88600 - 4.04674i) q^{54} +(0.293906 + 0.169687i) q^{55} +(1.79641 + 7.26015i) q^{56} +(3.35523 + 3.35523i) q^{57} +(5.88449 - 0.998732i) q^{58} +(-2.20512 + 8.22961i) q^{59} +(0.398974 - 0.0297554i) q^{60} +(3.61102 + 6.25448i) q^{61} +(7.72796 + 0.726071i) q^{62} +(5.81691 - 1.55864i) q^{63} +(4.26353 - 6.76922i) q^{64} +(0.722573 + 1.57587i) q^{66} +(0.652790 + 2.43624i) q^{67} +(0.923336 + 2.64178i) q^{68} +(6.43720 - 3.71652i) q^{69} +(0.825010 + 0.306284i) q^{70} +(-10.5002 - 2.81352i) q^{71} +(-5.51555 - 3.32748i) q^{72} +(-5.05407 + 5.05407i) q^{73} +(0.423724 - 0.596956i) q^{74} +(-2.10157 + 3.64002i) q^{75} +(4.84756 - 10.0568i) q^{76} +3.81333i q^{77} +8.51654i q^{79} +(-0.375809 - 0.863050i) q^{80} +(-1.50948 + 2.61449i) q^{81} +(6.68361 + 4.74407i) q^{82} +(6.91195 - 6.91195i) q^{83} +(2.53106 + 3.71523i) q^{84} +(0.318065 + 0.0852251i) q^{85} +(-4.52197 + 12.1804i) q^{86} +(3.10694 - 1.79379i) q^{87} +(2.93918 - 2.82822i) q^{88} +(1.71941 + 6.41693i) q^{89} +(-0.688971 + 0.315910i) q^{90} +(-13.2518 - 11.4124i) q^{92} +(4.50653 - 1.20752i) q^{93} +(0.524430 - 5.58179i) q^{94} +(-0.656818 - 1.13764i) q^{95} +(0.986372 - 4.70632i) q^{96} +(4.00474 - 14.9459i) q^{97} +(-0.00186964 - 0.0110159i) q^{98} +(-2.32236 - 2.32236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 6 q^{4} + 12 q^{5} + 14 q^{6} - 10 q^{8} + 4 q^{9} + 8 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{18} - 2 q^{20} + 28 q^{21} - 10 q^{24} - 12 q^{28} - 8 q^{29} + 42 q^{30} - 28 q^{32} + 20 q^{33}+ \cdots + 2 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 6 * q^4 + 12 * q^5 + 14 * q^6 - 10 * q^8 + 4 * q^9 + 8 * q^14 - 2 * q^16 + 12 * q^17 + 6 * q^18 - 2 * q^20 + 28 * q^21 - 10 * q^24 - 12 * q^28 - 8 * q^29 + 42 * q^30 - 28 * q^32 + 20 * q^33 - 14 * q^34 - 6 * q^36 + 16 * q^37 - 40 * q^40 - 48 * q^41 - 28 * q^42 + 8 * q^44 - 20 * q^45 + 46 * q^46 - 10 * q^48 + 60 * q^49 - 10 * q^50 - 32 * q^53 + 16 * q^54 - 60 * q^56 - 12 * q^57 + 48 * q^58 + 24 * q^60 + 4 * q^61 - 18 * q^62 + 56 * q^66 + 16 * q^68 - 12 * q^69 - 28 * q^70 - 56 * q^72 - 20 * q^73 + 4 * q^74 - 22 * q^76 - 44 * q^80 + 48 * q^81 - 84 * q^84 - 20 * q^85 - 16 * q^86 + 36 * q^88 + 52 * q^89 - 12 * q^92 + 92 * q^93 - 38 * q^94 + 72 * q^96 + 28 * q^97 + 2 * q^98

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