LMFDB - Embedded newform 52.2.l.b.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,2,Mod(7,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("52.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	52.l (of order $12$, degree $4$, 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:	$0.415222090511$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.4
Root			$-1.39427 - 0.236640i$ of defining polynomial
Character	$\chi$	$=$	52.7
Dual form			52.2.l.b.15.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.902074 + 1.08916i) q^{2} +(-0.736159 - 0.425021i) q^{3} +(-0.372527 + 1.96500i) q^{4} +(-0.166404 - 0.166404i) q^{5} +(-0.201154 - 1.18519i) q^{6} +(0.684384 - 2.55416i) q^{7} +(-2.47624 + 1.36683i) q^{8} +(-1.13871 - 1.97231i) q^{9} +O(q^{10})$	\(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} +(-0.406663 + 3.58254i) q^{13} +(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} +(-4.26879 + 2.78880i) q^{26} +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} +(1.82203 - 2.46448i) q^{39} +(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} +(-6.88821 - 2.13369i) q^{52} -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} +(0.663819 - 0.528479i) q^{65} +(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} +(4.32781 - 0.238670i) q^{78} +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} +(8.87207 + 3.49052i) q^{91} +(-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}+O(q^{10}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	$ 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 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^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 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}+O(q^{100}) $ 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 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^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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	0.668918	−	0.743336i	$-0.266758\pi$
$5$	−0.166404	−	0.166404i	−0.0744180	−	0.0744180i	−0.743336	+	0.668918i	$0.766758\pi$
$6$	−0.201154	−	1.18519i	−0.0821208	−	0.483853i
$7$	0.684384	−	2.55416i	0.258673	−	0.965381i	−0.707337	−	0.706876i	$-0.750104\pi$
$7$	0.684384	−	2.55416i	0.258673	−	0.965381i	0.966010	−	0.258504i	$-0.0832296\pi$
$8$	−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	−0.462628	−	0.886553i	$-0.653093\pi$
$11$	−1.39298	+	0.373247i	−0.419998	+	0.112538i	0.0426292	+	0.999091i	$0.486427\pi$
$12$	1.10941	−	1.28822i	0.320258	−	0.371877i
$13$	−0.406663	+	3.58254i	−0.112788	+	0.993619i
$13$	−0.406663	+	3.58254i	−0.112788	+	0.993619i
$14$	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	0.817295	−	0.576220i	$-0.195473\pi$
$19$	5.39188	+	1.44475i	1.23698	+	0.331449i	0.419688	+	0.907668i	$0.362139\pi$
$20$	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
$26$	−4.26879	+	2.78880i	−0.837179	+	0.546928i
$27$			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	−0.266725	−	0.963773i	$-0.585942\pi$
$31$	3.88100	−	3.88100i	0.697047	−	0.697047i	0.963773	+	0.266725i	$0.0859416\pi$
$32$	−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	0.954038	−	0.299684i	$-0.0968814\pi$
$37$	−0.133975	−	0.500000i	−0.0220253	−	0.0821995i	−0.976064	+	0.217485i	$0.930215\pi$
$38$	3.29032	+	7.17588i	0.533760	+	1.16408i
$39$	1.82203	−	2.46448i	0.291758	−	0.394633i
$40$	0.639502	+	0.184609i	0.101114	+	0.0291893i
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.206338	−	0.978481i	$-0.433845\pi$
$41$	5.59808	−	1.50000i	0.874273	−	0.234261i	0.667934	+	0.744220i	$0.267179\pi$
$42$	−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	0.472464	−	0.881350i	$-0.343365\pi$
$47$	−2.80318	−	2.80318i	−0.408886	−	0.408886i	−0.881350	+	0.472464i	$0.843365\pi$
$48$	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
$52$	−6.88821	−	2.13369i	−0.955222	−	0.295889i
$53$	−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	$-0.729538\pi$
$59$	2.20512	−	8.22961i	0.287082	−	1.07140i	0.947305	−	0.320334i	$-0.103795\pi$
$60$	−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
$65$	0.663819	−	0.528479i	0.0823366	−	0.0655497i
$66$	0.722573	+	1.57587i	0.0889426	+	0.193976i
$67$	−0.652790	−	2.43624i	−0.0797510	−	0.297635i	0.914518	−	0.404546i	$-0.132571\pi$
$67$	−0.652790	−	2.43624i	−0.0797510	−	0.297635i	−0.994269	+	0.106912i	$0.965904\pi$
$68$	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	0.820846	−	0.571150i	$-0.193502\pi$
$71$	10.5002	+	2.81352i	1.24614	+	0.333903i	0.425298	+	0.905053i	$0.360169\pi$
$72$	5.51555	+	3.32748i	0.650014	+	0.392147i
$73$	5.05407	−	5.05407i	0.591534	−	0.591534i	−0.346512	−	0.938046i	$-0.612634\pi$
$73$	5.05407	−	5.05407i	0.591534	−	0.591534i	0.938046	+	0.346512i	$0.112634\pi$
$74$	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
$78$	4.32781	−	0.238670i	0.490028	−	0.0270240i
$79$			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	−0.976083	−	0.217398i	$-0.930243\pi$
$83$	−6.91195	+	6.91195i	−0.758685	+	0.758685i	0.217398	+	0.976083i	$0.430243\pi$
$84$	−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	$-0.968803\pi$
$89$	−1.71941	−	6.41693i	−0.182257	−	0.680193i	0.812944	−	0.582342i	$-0.197864\pi$
$90$	−0.688971	+	0.315910i	−0.0726240	+	0.0332998i
$91$	8.87207	+	3.49052i	0.930045	+	0.365906i
$92$	−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	$0.370942\pi$
$97$	−4.00474	+	14.9459i	−0.406620	+	1.51753i	−0.801049	+	0.598599i	$0.795724\pi$
$98$	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	$0.680593\pi$
$104$	−3.88975	−	9.42708i	−0.381421	−	0.924401i
$105$	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	0.708270	−	0.705941i	$-0.249476\pi$
$109$	0.0243171	+	0.0243171i	0.00232916	+	0.00232916i	−0.705941	+	0.708270i	$0.749476\pi$
$110$	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
$117$	7.52896	−	3.27743i	0.696053	−	0.302998i
$118$	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
$130$	1.17441	+	0.246277i	0.103003	+	0.0215999i
$131$		−	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	0.451693	−	0.892173i	$-0.350820\pi$
$137$	4.64424	+	1.24442i	0.396784	+	0.106318i	−0.0549089	+	0.998491i	$0.517487\pi$
$138$	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
$143$	−0.770702	−	5.14219i	−0.0644494	−	0.430011i
$144$	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	$-0.703448\pi$
$149$	3.92298	−	14.6408i	0.321383	−	1.19942i	0.917898	−	0.396817i	$-0.129885\pi$
$150$	−5.86033	+	0.994631i	−0.478494	+	0.0812113i
$151$	−0.480824	−	0.480824i	−0.0391289	−	0.0391289i	0.687272	−	0.726401i	$-0.258808\pi$
$151$	−0.480824	−	0.480824i	−0.0391289	−	0.0391289i	−0.726401	+	0.687272i	$0.758808\pi$
$152$	−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
$156$	4.16395	+	4.49837i	0.333383	+	0.360158i
$157$	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	$0.294639\pi$
$163$	−4.07194	+	15.1967i	−0.318939	+	1.19030i	−0.920266	+	0.391294i	$0.872028\pi$
$164$	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	−0.0431274	−	0.999070i	$-0.513732\pi$
$167$	5.41542	−	1.45106i	0.419058	−	0.112286i	0.462185	+	0.886783i	$0.347065\pi$
$168$	1.76327	−	6.10813i	0.136040	−	0.471253i
$169$	−12.6693	−	2.91377i	−0.974558	−	0.224137i
$170$	−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	$-0.172147\pi$
$182$	4.20153	+	12.8118i	0.311438	+	0.949672i
$183$		−	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	$0.0123196\pi$
$193$	2.12861	+	7.94409i	0.153221	+	0.571828i	−0.846030	+	0.533135i	$0.821014\pi$
$194$	−19.8910	+	9.12050i	−1.42809	+	0.654814i
$195$	−0.713291	+	0.106907i	−0.0510798	+	0.00765576i
$196$	−0.0103115	+	0.0119735i	−0.000736533	+	0.000855248i
$197$	−11.9588	+	3.20436i	−0.852032	+	0.228301i	−0.658302	−	0.752754i	$-0.728725\pi$
$197$	−11.9588	+	3.20436i	−0.852032	+	0.228301i	−0.193730	+	0.981055i	$0.562058\pi$
$198$	−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
$208$	6.75873	−	12.7405i	0.468634	−	0.883393i
$209$	−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
$221$	2.01364	+	4.62577i	0.135452	+	0.311163i
$222$	−0.565647	+	0.259363i	−0.0379637	+	0.0174073i
$223$	4.87316	+	18.1869i	0.326331	+	1.21788i	0.912967	+	0.408033i	$0.133785\pi$
$223$	4.87316	+	18.1869i	0.326331	+	1.21788i	−0.586636	+	0.809850i	$0.699548\pi$
$224$	−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	0.0123190	−	0.999924i	$-0.496079\pi$
$227$	−7.18635	−	1.92558i	−0.476974	−	0.127805i	−0.489293	+	0.872119i	$0.662745\pi$
$228$	7.84294	−	5.34312i	0.519412	−	0.353857i
$229$	−3.17720	+	3.17720i	−0.209955	+	0.209955i	−0.804248	−	0.594293i	$-0.797432\pi$
$229$	−3.17720	+	3.17720i	−0.209955	+	0.209955i	0.594293	+	0.804248i	$0.297432\pi$
$230$	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	$0.856279\pi$
$234$	10.3613	+	5.24374i	0.677340	+	0.342794i
$235$			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	−0.873235	−	0.487300i	$-0.837982\pi$
$239$	−5.96641	+	5.96641i	−0.385935	+	0.385935i	0.487300	+	0.873235i	$0.337982\pi$
$240$	0.0901592	−	0.795068i	0.00581975	−	0.0513215i
$241$	−14.9406	−	4.00333i	−0.962410	−	0.257877i	−0.256790	−	0.966467i	$-0.582665\pi$
$241$	−14.9406	−	4.00333i	−0.962410	−	0.257877i	−0.705620	+	0.708590i	$0.749332\pi$
$242$	−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
$247$	−7.36856	+	18.7291i	−0.468851	+	1.19171i
$248$	−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
$260$	0.791170	+	1.50128i	0.0490663	+	0.0931053i
$261$	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	0.170530	−	0.985352i	$-0.445452\pi$
$271$	13.3489	−	3.57684i	0.810890	−	0.217277i	0.640360	+	0.768075i	$0.278785\pi$
$272$	−5.53506	+	0.830223i	−0.335612	+	0.0503397i
$273$	−5.04770	−	6.34039i	−0.305501	−	0.383738i
$274$	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	−0.0757324	−	0.997128i	$-0.524129\pi$
$281$	15.4454	−	15.4454i	0.921396	−	0.921396i	0.997128	+	0.0757324i	$0.0241295\pi$
$282$	−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
$286$	4.90542	−	5.47805i	0.290064	−	0.323924i
$287$		−	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	−0.459314	−	0.888274i	$-0.651905\pi$
$293$	−22.2734	−	5.96815i	−1.30123	−	0.348663i	−0.841914	+	0.539611i	$0.818571\pi$
$294$	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
$299$	−25.3519	−	18.7430i	−1.46614	−	1.08394i
$300$	−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	0.0665547	−	0.997783i	$-0.478799\pi$
$307$	−16.3164	−	16.3164i	−0.931228	−	0.931228i	−0.997783	+	0.0665547i	$0.978799\pi$
$308$	−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	$0.422105\pi$
$312$	−1.14324	+	8.59305i	−0.0647231	+	0.486486i
$313$	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	0.0705258	−	0.997510i	$-0.477532\pi$
$317$	−16.5045	−	16.5045i	−0.926984	−	0.926984i	−0.997510	+	0.0705258i	$0.977532\pi$
$318$	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
$325$	17.7143	+	2.01079i	0.982614	+	0.111539i
$326$	−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	−0.143578	−	0.989639i	$-0.545861\pi$
$331$	−13.8768	−	3.71829i	−0.762740	−	0.204375i	−0.619162	+	0.785264i	$0.712527\pi$
$332$	−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	$-0.127749\pi$
$338$	−8.25504	−	16.4272i	−0.449015	−	0.893524i
$339$			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	$0.189991\pi$
$349$	7.32017	+	27.3192i	0.391840	+	1.46237i	−0.435257	+	0.900306i	$0.643343\pi$
$350$	−7.70686	−	16.8080i	−0.411949	−	0.898423i
$351$	−16.0714	−	1.82431i	−0.857830	−	0.0973742i
$352$	4.46252	+	6.82907i	0.237853	+	0.363991i
$353$	34.7270	−	9.30507i	1.84833	−	0.495259i	0.848887	−	0.528574i	$-0.177273\pi$
$353$	34.7270	−	9.30507i	1.84833	−	0.495259i	0.999445	+	0.0333153i	$0.0106066\pi$
$354$	−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	0.945117	−	0.326733i	$-0.105948\pi$
$359$	11.7167	+	11.7167i	0.618383	+	0.618383i	−0.326733	+	0.945117i	$0.605948\pi$
$360$	−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
$364$	−10.1639	+	16.1333i	−0.532736	+	0.845615i
$365$	−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
$377$	−12.2362	−	9.04638i	−0.630195	−	0.465912i
$378$	6.99210	+	15.2491i	0.359635	+	0.784331i
$379$	8.63337	+	32.2202i	0.443467	+	1.65504i	0.719953	+	0.694022i	$0.244163\pi$
$379$	8.63337	+	32.2202i	0.443467	+	1.65504i	−0.276487	+	0.961018i	$0.589170\pi$
$380$	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	0.735325	−	0.677715i	$-0.237030\pi$
$383$	20.2216	+	5.41837i	1.03328	+	0.276866i	0.297953	+	0.954581i	$0.403696\pi$
$384$	−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	$0.921713\pi$
$390$	−0.759879	−	0.680448i	−0.0384780	−	0.0344558i
$391$			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	0.320878	−	0.947120i	$-0.396022\pi$
$397$	2.49473	+	0.668462i	0.125207	+	0.0335492i	−0.195671	+	0.980670i	$0.562689\pi$
$398$	−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	$-0.847289\pi$
$401$	−7.00137	−	26.1295i	−0.349632	−	1.30484i	0.537476	−	0.843279i	$-0.319378\pi$
$402$	−2.75611	+	1.26374i	−0.137462	+	0.0630298i
$403$	12.3256	+	15.4821i	0.613981	+	0.771218i
$404$	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	−0.928435	−	0.371496i	$-0.878845\pi$
$409$	1.24095	−	4.63129i	0.0613611	−	0.229003i	0.989796	+	0.142493i	$0.0455118\pi$
$410$	−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
$416$	19.9732	−	4.13152i	0.979269	−	0.202564i
$417$	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	0.788379	−	0.615190i	$-0.210921\pi$
$421$	3.55354	+	3.55354i	0.173189	+	0.173189i	−0.615190	+	0.788379i	$0.710921\pi$
$422$	−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
$429$	−1.61818	+	4.11303i	−0.0781265	+	0.198579i
$430$	−2.77934	+	1.27439i	−0.134032	+	0.0614567i
$431$	−0.894922	−	3.33989i	−0.0431069	−	0.160877i	0.941017	−	0.338359i	$-0.109872\pi$
$431$	−0.894922	−	3.33989i	−0.0431069	−	0.160877i	−0.984124	+	0.177482i	$0.943205\pi$
$432$	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
$442$	−3.22174	+	6.36595i	−0.153242	+	0.302797i
$443$		−	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	0.476663	−	0.879086i	$-0.341846\pi$
$449$	9.53370	+	2.55455i	0.449923	+	0.120557i	−0.0267403	+	0.999642i	$0.508513\pi$
$450$	−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
$455$	−0.895510	−	2.05718i	−0.0419822	−	0.0964421i
$456$	12.8944	+	3.72231i	0.603836	+	0.174313i
$457$	10.0284	−	2.68710i	0.469108	−	0.125697i	−0.0165184	−	0.999864i	$-0.505258\pi$
$457$	10.0284	−	2.68710i	0.469108	−	0.125697i	0.485626	+	0.874166i	$0.338592\pi$
$458$	−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	$-0.683323\pi$
$461$	7.43710	−	27.7556i	0.346380	−	1.29271i	0.890991	−	0.454021i	$-0.150011\pi$
$462$	4.51953	−	0.767066i	0.210267	−	0.0356872i
$463$	−5.89061	−	5.89061i	−0.273760	−	0.273760i	0.556852	−	0.830612i	$-0.312009\pi$
$463$	−5.89061	−	5.89061i	−0.273760	−	0.273760i	−0.830612	+	0.556852i	$0.812009\pi$
$464$	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	$0.475648\pi$
$468$	3.63541	+	16.0153i	0.168047	+	0.740309i
$469$	−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	−0.813604	−	0.581420i	$-0.802497\pi$
$479$	−26.8650	+	7.19847i	−1.22750	+	0.328906i	−0.413892	+	0.910326i	$0.635831\pi$
$480$	0.947285	−	0.619013i	0.0432374	−	0.0282539i
$481$	1.84575	−	0.276639i	0.0841592	−	0.0126136i
$482$	−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	0.0258522	−	0.999666i	$-0.491770\pi$
$487$	−9.96577	−	2.67032i	−0.451592	−	0.121004i	−0.477444	+	0.878662i	$0.658437\pi$
$488$	−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
$494$	−27.0460	+	8.86954i	−1.21686	+	0.399059i
$495$		−	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	−0.409597	−	0.912267i	$-0.634331\pi$
$499$	11.2288	−	11.2288i	0.502670	−	0.502670i	0.912267	+	0.409597i	$0.134331\pi$
$500$	−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
$507$	8.08816	+	7.52970i	0.359208	+	0.334406i
$508$	8.09892	+	6.97473i	0.359331	+	0.309454i
$509$	−9.52759	+	2.55291i	−0.422303	+	0.113156i	−0.463711	−	0.885987i	$-0.653482\pi$
$509$	−9.52759	+	2.55291i	−0.422303	+	0.113156i	0.0414078	+	0.999142i	$0.486816\pi$
$510$	−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
$520$	−0.921433	+	2.21597i	−0.0404075	+	0.0971768i
$521$	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
$533$	3.09729	+	20.6654i	0.134158	+	0.895116i
$534$	−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	−0.509605	−	0.860408i	$-0.670209\pi$
$541$	8.15947	−	8.15947i	0.350803	−	0.350803i	0.860408	+	0.509605i	$0.170209\pi$
$542$	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
$546$	2.35228	−	11.2172i	0.100668	−	0.480054i
$547$			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	0.944561	−	0.328335i	$-0.106488\pi$
$557$	−0.887873	−	3.31359i	−0.0376204	−	0.140401i	−0.982182	+	0.187934i	$0.939821\pi$
$558$	−7.36789	−	16.0687i	−0.311908	−	0.680243i
$559$	30.3721	−	13.2213i	1.28460	−	0.559200i
$560$	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	$0.833740\pi$
$572$	10.3915	+	0.401172i	0.434491	+	0.0167738i
$573$	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	0.915674	−	0.401921i	$-0.131657\pi$
$577$	12.3408	+	12.3408i	0.513753	+	0.513753i	−0.401921	+	0.915674i	$0.631657\pi$
$578$	−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
$585$	−1.79822	−	0.707471i	−0.0743474	−	0.0292503i
$586$	−13.5920	−	29.6430i	−0.561481	−	1.22454i
$587$	−5.98011	−	22.3181i	−0.246825	−	0.921165i	−0.972457	−	0.233082i	$-0.925119\pi$
$587$	−5.98011	−	22.3181i	−0.246825	−	0.921165i	0.725632	−	0.688083i	$-0.241548\pi$
$588$	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	−0.443538	−	0.896255i	$-0.646277\pi$
$593$	11.0244	−	11.0244i	0.452717	−	0.452717i	0.896255	+	0.443538i	$0.146277\pi$
$594$	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
$598$	−2.45517	−	44.5198i	−0.100400	−	1.82055i
$599$			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
$611$	11.1825	−	8.90258i	0.452395	−	0.360160i
$612$	4.15898	−	4.82933i	0.168117	−	0.195214i
$613$	−34.2262	+	9.17089i	−1.38238	+	0.370409i	−0.871986	−	0.489530i	$-0.837168\pi$
$613$	−34.2262	+	9.17089i	−1.38238	+	0.370409i	−0.510397	+	0.859939i	$0.670502\pi$
$614$	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	$0.402922\pi$
$617$	−10.8473	+	40.4828i	−0.436697	+	1.62978i	−0.736972	+	0.675923i	$0.763745\pi$
$618$	2.19419	+	12.9281i	0.0882632	+	0.520043i
$619$	12.0880	+	12.0880i	0.485858	+	0.485858i	0.906996	−	0.421138i	$-0.138369\pi$
$619$	12.0880	+	12.0880i	0.485858	+	0.485858i	−0.421138	+	0.906996i	$0.638369\pi$
$620$	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
$624$	−10.3905	+	6.50640i	−0.415952	+	0.260465i
$625$	−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	−0.999811	−	0.0194238i	$-0.993817\pi$
$631$	−3.12081	+	11.6470i	−0.124237	+	0.463660i	0.875574	+	0.483084i	$0.160483\pi$
$632$	−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
$637$	−0.0169350	+	0.0229063i	−0.000670988	+	0.000907582i
$638$	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	0.949374	−	0.314148i	$-0.101719\pi$
$643$	40.9391	+	10.9696i	1.61448	+	0.432599i	0.665108	+	0.746747i	$0.268386\pi$
$644$	−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
$650$	13.7896	+	21.1076i	0.540871	+	0.827907i
$651$			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	0.894264	−	0.447540i	$-0.147700\pi$
$661$	−2.67284	−	9.97516i	−0.103961	−	0.387989i	−0.998225	+	0.0595512i	$0.981033\pi$
$662$	−8.46813	−	18.4682i	−0.329123	−	0.717788i
$663$	0.483691	−	4.26114i	0.0187850	−	0.165489i
$664$	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
$676$	10.4452	−	23.8096i	0.401738	−	0.915754i
$677$	−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	−0.986404	−	0.164342i	$-0.947450\pi$
$683$	−1.30625	+	4.87499i	−0.0499823	+	0.186536i	0.936421	+	0.350878i	$0.114117\pi$
$684$	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
$689$	2.41746	−	21.2969i	0.0920977	−	0.811346i
$690$	−1.03106	−	2.24866i	−0.0392519	−	0.0856049i
$691$	2.89268	+	10.7956i	0.110043	+	0.410685i	0.998868	−	0.0475604i	$-0.0151447\pi$
$691$	2.89268	+	10.7956i	0.110043	+	0.410685i	−0.888826	+	0.458246i	$0.848478\pi$
$692$	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	$-0.171346\pi$
$702$	−12.5107	−	19.1500i	−0.472184	−	0.722769i
$703$		−	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	0.926024	−	0.377465i	$-0.123204\pi$
$709$	40.9857	+	10.9821i	1.53925	+	0.412441i	0.613228	+	0.789906i	$0.289871\pi$
$710$	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
$715$	−0.727432	+	0.983927i	−0.0272044	+	0.0367968i
$716$	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	$0.703267\pi$
$728$	−26.7403	+	3.48329i	−0.991062	+	0.129099i
$729$	−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	0.257054	−	0.966397i	$-0.417248\pi$
$733$	−19.2047	−	19.2047i	−0.709343	−	0.709343i	−0.966397	+	0.257054i	$0.917248\pi$
$734$	−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	−0.646743	−	0.762708i	$-0.723869\pi$
$739$	−22.4404	+	6.01290i	−0.825485	+	0.221188i	−0.178742	+	0.983896i	$0.557203\pi$
$740$	−0.184609	−	0.158984i	−0.00678637	−	0.00584438i
$741$	13.3847	−	10.6558i	0.491700	−	0.391451i
$742$	−20.2072	+	9.26549i	−0.741830	+	0.340147i
$743$	−9.98778	−	37.2749i	−0.366416	−	1.36748i	−0.865491	−	0.500925i	$-0.832993\pi$
$743$	−9.98778	−	37.2749i	−0.366416	−	1.36748i	0.499075	−	0.866559i	$-0.333673\pi$
$744$	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
$754$	−1.18500	−	21.4876i	−0.0431551	−	0.782532i
$755$			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	0.407875	−	0.913038i	$-0.366270\pi$
$761$	8.40241	+	2.25142i	0.304587	+	0.0816138i	−0.103288	+	0.994651i	$0.532936\pi$
$762$	−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
$767$	28.5862	+	11.2466i	1.03219	+	0.406092i
$768$	−3.99026	−	13.0022i	−0.143986	−	0.469175i
$769$	−9.35018	+	2.50537i	−0.337176	+	0.0903461i	−0.423434	−	0.905927i	$-0.639176\pi$
$769$	−9.35018	+	2.50537i	−0.337176	+	0.0903461i	0.0862584	+	0.996273i	$0.472509\pi$
$770$	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	$0.195551\pi$
$773$	−4.96928	+	18.5456i	−0.178732	+	0.667039i	−0.995886	+	0.0906182i	$0.971116\pi$
$774$	−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
$780$	0.0556480	−	1.44144i	0.00199252	−	0.0516119i
$781$	−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	$-0.737799\pi$
$787$	7.73737	−	28.8763i	0.275808	−	1.02933i	0.955298	−	0.295644i	$-0.0955341\pi$
$788$	−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
$793$	−23.8754	+	10.3932i	−0.847841	+	0.369073i
$794$	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
$806$	−5.74385	+	27.3905i	−0.202319	+	0.964789i
$807$		−	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	−0.778502	−	0.627643i	$-0.784020\pi$
$811$	−4.29617	+	4.29617i	−0.150859	+	0.150859i	0.627643	+	0.778502i	$0.284020\pi$
$812$	−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
$819$	−3.21836	−	21.4732i	−0.112459	−	0.750333i
$820$	1.78001	−	2.06691i	0.0621607	−	0.0721798i
$821$	18.2378	−	4.88681i	0.636505	−	0.170551i	0.0738852	−	0.997267i	$-0.476460\pi$
$821$	18.2378	−	4.88681i	0.636505	−	0.170551i	0.562620	+	0.826716i	$0.309793\pi$
$822$	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	0.344723	−	0.938705i	$-0.387973\pi$
$827$	−17.0815	−	17.0815i	−0.593982	−	0.593982i	−0.938705	+	0.344723i	$0.887973\pi$
$828$	−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
$832$	22.5172	+	18.0271i	0.780644	+	0.624976i
$833$	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	$-0.674570\pi$
$839$	10.3356	−	38.5731i	0.356825	−	1.33169i	0.878172	−	0.478345i	$-0.158763\pi$
$840$	−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
$845$	1.62335	+	2.59307i	0.0558449	+	0.0892045i
$846$	−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	−0.813621	−	0.581395i	$-0.802507\pi$
$853$	−6.78242	+	6.78242i	−0.232226	+	0.232226i	0.581395	+	0.813621i	$0.302507\pi$
$854$	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	$0.855001\pi$
$858$	−5.93945	+	1.94780i	−0.202770	+	0.0664969i
$859$			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	$-0.429347\pi$
$863$	35.1233	−	35.1233i	1.19561	−	1.19561i	0.975467	−	0.220144i	$-0.0706527\pi$
$864$	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
$871$	8.99342	−	1.34792i	0.304730	−	0.0456725i
$872$	−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	$-0.700922\pi$
$877$	9.61256	−	35.8746i	0.324593	−	1.21140i	0.914720	−	0.404088i	$-0.132411\pi$
$878$	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	$0.587671\pi$
$884$	−9.83976	+	2.23358i	−0.330947	+	0.0751234i
$885$	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
$897$	10.6968	+	24.5729i	0.357157	+	0.820466i
$898$	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
$910$	1.43278	−	2.83108i	0.0474961	−	0.0938494i
$911$			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
$923$	−14.3496	+	36.4733i	−0.472323	+	1.20053i
$924$	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	−0.988894	−	0.148623i	$-0.952516\pi$
$929$	−1.77316	+	6.61751i	−0.0581754	+	0.217113i	0.930719	+	0.365736i	$0.119183\pi$
$930$	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
$936$	−14.1638	+	18.4065i	−0.462959	+	0.601636i
$937$	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	0.286606	−	0.958048i	$-0.407473\pi$
$941$	−20.5970	−	20.5970i	−0.671442	−	0.671442i	−0.958048	+	0.286606i	$0.907473\pi$
$942$	−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	0.232896	−	0.972502i	$-0.425180\pi$
$947$	28.3374	−	7.59297i	0.920841	−	0.246739i	0.687945	+	0.725763i	$0.258513\pi$
$948$	10.9712	+	9.44830i	0.356327	+	0.306867i
$949$	16.0511	+	20.1617i	0.521041	+	0.654477i
$950$	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
$962$	1.96631	+	1.76077i	0.0633964	+	0.0567695i
$963$		−	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	−0.465478	−	0.885059i	$-0.654118\pi$
$967$	13.0476	−	13.0476i	0.419581	−	0.419581i	0.885059	+	0.465478i	$0.154118\pi$
$968$	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
$975$	−12.1859	−	9.00923i	−0.390262	−	0.288526i
$976$	−4.28511	−	28.5686i	−0.137163	−	0.914459i
$977$	0.239374	−	0.0641402i	0.00765826	−	0.00205203i	−0.254988	−	0.966944i	$-0.582071\pi$
$977$	0.239374	−	0.0641402i	0.00765826	−	0.00205203i	0.262646	+	0.964892i	$0.415405\pi$
$978$	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	0.828903	−	0.559393i	$-0.188966\pi$
$983$	8.44991	+	8.44991i	0.269510	+	0.269510i	−0.559393	+	0.828903i	$0.688966\pi$
$984$	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
$988$	−34.0578	−	21.4563i	−1.08352	−	0.682617i
$989$	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	52.2.l.b.7.4	yes	16
3.2	odd	2		468.2.cb.f.163.1		16
4.3	odd	2	inner	52.2.l.b.7.3	✓	16
8.3	odd	2		832.2.bu.n.319.2		16
8.5	even	2		832.2.bu.n.319.3		16
12.11	even	2		468.2.cb.f.163.2		16
13.2	odd	12	inner	52.2.l.b.15.3	yes	16
13.3	even	3		676.2.l.m.427.1		16
13.4	even	6		676.2.f.i.99.3		16
13.5	odd	4		676.2.l.m.19.3		16
13.6	odd	12		676.2.f.h.239.1		16
13.7	odd	12		676.2.f.i.239.8		16
13.8	odd	4		676.2.l.i.19.2		16
13.9	even	3		676.2.f.h.99.6		16
13.10	even	6		676.2.l.i.427.4		16
13.11	odd	12		676.2.l.k.587.2		16
13.12	even	2		676.2.l.k.319.1		16
39.2	even	12		468.2.cb.f.379.2		16
52.3	odd	6		676.2.l.m.427.3		16
52.7	even	12		676.2.f.i.239.3		16
52.11	even	12		676.2.l.k.587.1		16
52.15	even	12	inner	52.2.l.b.15.4	yes	16
52.19	even	12		676.2.f.h.239.6		16
52.23	odd	6		676.2.l.i.427.2		16
52.31	even	4		676.2.l.m.19.1		16
52.35	odd	6		676.2.f.h.99.1		16
52.43	odd	6		676.2.f.i.99.8		16
52.47	even	4		676.2.l.i.19.4		16
52.51	odd	2		676.2.l.k.319.2		16
104.67	even	12		832.2.bu.n.639.3		16
104.93	odd	12		832.2.bu.n.639.2		16
156.119	odd	12		468.2.cb.f.379.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.3	✓	16	4.3	odd	2	inner
52.2.l.b.7.4	yes	16	1.1	even	1	trivial
52.2.l.b.15.3	yes	16	13.2	odd	12	inner
52.2.l.b.15.4	yes	16	52.15	even	12	inner
468.2.cb.f.163.1		16	3.2	odd	2
468.2.cb.f.163.2		16	12.11	even	2
468.2.cb.f.379.1		16	156.119	odd	12
468.2.cb.f.379.2		16	39.2	even	12
676.2.f.h.99.1		16	52.35	odd	6
676.2.f.h.99.6		16	13.9	even	3
676.2.f.h.239.1		16	13.6	odd	12
676.2.f.h.239.6		16	52.19	even	12
676.2.f.i.99.3		16	13.4	even	6
676.2.f.i.99.8		16	52.43	odd	6
676.2.f.i.239.3		16	52.7	even	12
676.2.f.i.239.8		16	13.7	odd	12
676.2.l.i.19.2		16	13.8	odd	4
676.2.l.i.19.4		16	52.47	even	4
676.2.l.i.427.2		16	52.23	odd	6
676.2.l.i.427.4		16	13.10	even	6
676.2.l.k.319.1		16	13.12	even	2
676.2.l.k.319.2		16	52.51	odd	2
676.2.l.k.587.1		16	52.11	even	12
676.2.l.k.587.2		16	13.11	odd	12
676.2.l.m.19.1		16	52.31	even	4
676.2.l.m.19.3		16	13.5	odd	4
676.2.l.m.427.1		16	13.3	even	3
676.2.l.m.427.3		16	52.3	odd	6
832.2.bu.n.319.2		16	8.3	odd	2
832.2.bu.n.319.3		16	8.5	even	2
832.2.bu.n.639.2		16	104.93	odd	12
832.2.bu.n.639.3		16	104.67	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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.902074 + 1.08916i) q^{2} +(-0.736159 - 0.425021i) q^{3} +(-0.372527 + 1.96500i) q^{4} +(-0.166404 - 0.166404i) q^{5} +(-0.201154 - 1.18519i) q^{6} +(0.684384 - 2.55416i) q^{7} +(-2.47624 + 1.36683i) q^{8} +(-1.13871 - 1.97231i) q^{9} +O(q^{10})\)	\(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} +(-0.406663 + 3.58254i) q^{13} +(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} +(-4.26879 + 2.78880i) q^{26} +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} +(1.82203 - 2.46448i) q^{39} +(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} +(-6.88821 - 2.13369i) q^{52} -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} +(0.663819 - 0.528479i) q^{65} +(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} +(4.32781 - 0.238670i) q^{78} +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} +(8.87207 + 3.49052i) q^{91} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9	\( 16 q - 2 q^{2} - 6 q^{4} - 12 q^{5} - 14 q^{6} + 10 q^{8} + 4 q^{9} - 12 q^{13} + 8 q^{14} - 2 q^{16} + 12 q^{17} - 6 q^{18} + 2 q^{20} - 28 q^{21} + 10 q^{24} + 16 q^{26} + 12 q^{28} - 8 q^{29} + 42 q^{30} + 28 q^{32} - 20 q^{33} + 14 q^{34} - 6 q^{36} - 16 q^{37} - 40 q^{40} + 48 q^{41} - 28 q^{42} - 8 q^{44} + 20 q^{45} - 46 q^{46} - 10 q^{48} + 60 q^{49} + 10 q^{50} - 32 q^{52} - 32 q^{53} - 16 q^{54} - 60 q^{56} + 12 q^{57} - 48 q^{58} - 24 q^{60} + 4 q^{61} - 18 q^{62} - 8 q^{65} + 56 q^{66} + 16 q^{68} - 12 q^{69} + 28 q^{70} + 56 q^{72} + 20 q^{73} + 4 q^{74} + 22 q^{76} + 68 q^{78} + 44 q^{80} + 48 q^{81} + 84 q^{84} + 20 q^{85} + 16 q^{86} + 36 q^{88} - 52 q^{89} - 12 q^{92} - 92 q^{93} - 38 q^{94} - 72 q^{96} - 28 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 6 * q^4 - 12 * q^5 - 14 * q^6 + 10 * q^8 + 4 * q^9 - 12 * q^13 + 8 * q^14 - 2 * q^16 + 12 * q^17 - 6 * q^18 + 2 * q^20 - 28 * q^21 + 10 * q^24 + 16 * q^26 + 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^52 - 32 * q^53 - 16 * q^54 - 60 * q^56 + 12 * q^57 - 48 * q^58 - 24 * q^60 + 4 * q^61 - 18 * q^62 - 8 * q^65 + 56 * q^66 + 16 * q^68 - 12 * q^69 + 28 * q^70 + 56 * q^72 + 20 * q^73 + 4 * q^74 + 22 * q^76 + 68 * q^78 + 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more