LMFDB - Embedded newform 1350.2.q.h.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.1
Root			$0.500000 - 0.410882i$ of defining polynomial
Character	$\chi$	$=$	1350.143
Dual form			1350.2.q.h.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(0.622279 + 2.32238i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(0.622279 + 2.32238i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.991757 - 0.572591i) q^{11} +(0.640322 - 2.38971i) q^{13} +(-1.20215 - 2.08219i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.99855 - 4.99855i) q^{17} -2.78390i q^{19} +(1.10616 + 0.296395i) q^{22} +(-5.95746 - 1.59630i) q^{23} +2.47401i q^{26} +(1.70010 + 1.70010i) q^{28} +(-0.672250 + 1.16437i) q^{29} +(1.25223 + 2.16892i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(6.12195 + 3.53451i) q^{34} +(8.16761 - 8.16761i) q^{37} +(0.720527 + 2.68904i) q^{38} +(1.70826 - 0.986264i) q^{41} +(-8.68498 + 2.32713i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(11.9118 - 3.19175i) q^{47} +(1.05598 - 0.609669i) q^{49} +(-0.640322 - 2.38971i) q^{52} +(1.84828 - 1.84828i) q^{53} +(-2.08219 - 1.20215i) q^{56} +(0.347982 - 1.29869i) q^{58} +(-1.31456 - 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(-1.77092 - 1.77092i) q^{62} -1.00000i q^{64} +(-0.0545285 - 0.0146109i) q^{67} +(-6.82815 - 1.82960i) q^{68} -9.10005i q^{71} +(-7.82779 - 7.82779i) q^{73} +(-5.77537 + 10.0032i) q^{74} +(-1.39195 - 2.41093i) q^{76} +(0.712623 - 2.65955i) q^{77} +(-8.46375 - 4.88655i) q^{79} +(-1.39479 + 1.39479i) q^{82} +(0.724794 + 2.70497i) q^{83} +(7.78674 - 4.49568i) q^{86} +(1.10616 - 0.296395i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(-5.95746 + 1.59630i) q^{92} +(-10.6798 + 6.16599i) q^{94} +(-2.08981 - 7.79929i) q^{97} +(-0.862203 + 0.862203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^16 - 8 * q^22 - 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^38 - 24 * q^41 - 32 * q^46 + 48 * q^47 - 24 * q^56 - 16 * q^58 - 24 * q^61 + 16 * q^67 - 24 * q^68 - 16 * q^73 + 16 * q^76 - 72 * q^77 + 16 * q^82 + 48 * q^83 + 48 * q^86 - 8 * q^88 - 24 * q^92 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.622279	+	2.32238i	0.235199	+	0.877776i	0.978059	+	0.208328i	$0.0668023\pi$
$7$	0.622279	+	2.32238i	0.235199	+	0.877776i	−0.742860	+	0.669447i	$0.766531\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	−0.991757	−	0.572591i	−0.299026	−	0.172643i	0.342979	−	0.939343i	$-0.388564\pi$
$11$	−0.991757	−	0.572591i	−0.299026	−	0.172643i	−0.642005	+	0.766700i	$0.721897\pi$
$12$		0			0
$13$	0.640322	−	2.38971i	0.177593	−	0.662788i	−0.818502	−	0.574504i	$-0.805195\pi$
$13$	0.640322	−	2.38971i	0.177593	−	0.662788i	0.996095	−	0.0882838i	$-0.0281383\pi$
$14$	−1.20215	−	2.08219i	−0.321288	−	0.556487i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.99855	−	4.99855i	−1.21233	−	1.21233i	−0.970259	−	0.242068i	$-0.922174\pi$
$17$	−4.99855	−	4.99855i	−1.21233	−	1.21233i	−0.242068	−	0.970259i	$-0.577826\pi$
$18$		0			0
$19$		−	2.78390i		−	0.638671i	−0.947642	−	0.319336i	$-0.896540\pi$
$19$		−	2.78390i		−	0.638671i	0.947642	−	0.319336i	$-0.103460\pi$
$20$		0			0
$21$		0			0
$22$	1.10616	+	0.296395i	0.235834	+	0.0631917i
$23$	−5.95746	−	1.59630i	−1.24222	−	0.332851i	−0.422891	−	0.906181i	$-0.638985\pi$
$23$	−5.95746	−	1.59630i	−1.24222	−	0.332851i	−0.819325	+	0.573330i	$0.805651\pi$
$24$		0			0
$25$		0			0
$26$			2.47401i			0.485194i
$27$		0			0
$28$	1.70010	+	1.70010i	0.321288	+	0.321288i
$29$	−0.672250	+	1.16437i	−0.124834	+	0.216218i	−0.921668	−	0.387980i	$-0.873173\pi$
$29$	−0.672250	+	1.16437i	−0.124834	+	0.216218i	0.796834	+	0.604198i	$0.206506\pi$
$30$		0			0
$31$	1.25223	+	2.16892i	0.224907	+	0.389550i	0.956292	−	0.292415i	$-0.0944589\pi$
$31$	1.25223	+	2.16892i	0.224907	+	0.389550i	−0.731385	+	0.681965i	$0.761126\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	6.12195	+	3.53451i	1.04991	+	0.606164i
$35$		0			0
$36$		0			0
$37$	8.16761	−	8.16761i	1.34275	−	1.34275i	0.449434	−	0.893314i	$-0.351626\pi$
$37$	8.16761	−	8.16761i	1.34275	−	1.34275i	0.893314	−	0.449434i	$-0.148374\pi$
$38$	0.720527	+	2.68904i	0.116885	+	0.436221i
$39$		0			0
$40$		0			0
$41$	1.70826	−	0.986264i	0.266785	−	0.154029i	−0.360641	−	0.932705i	$-0.617442\pi$
$41$	1.70826	−	0.986264i	0.266785	−	0.154029i	0.627426	+	0.778676i	$0.284109\pi$
$42$		0			0
$43$	−8.68498	+	2.32713i	−1.32445	+	0.354885i	−0.850642	−	0.525745i	$-0.823787\pi$
$43$	−8.68498	+	2.32713i	−1.32445	+	0.354885i	−0.473805	+	0.880630i	$0.657120\pi$
$44$	−1.14518			−0.172643
$45$		0			0
$46$	6.16761			0.909365
$47$	11.9118	−	3.19175i	1.73751	−	0.465565i	0.755621	−	0.655010i	$-0.227335\pi$
$47$	11.9118	−	3.19175i	1.73751	−	0.465565i	0.981891	+	0.189445i	$0.0606688\pi$
$48$		0			0
$49$	1.05598	−	0.609669i	0.150854	−	0.0870956i
$50$		0			0
$51$		0			0
$52$	−0.640322	−	2.38971i	−0.0887967	−	0.331394i
$53$	1.84828	−	1.84828i	0.253881	−	0.253881i	−0.568679	−	0.822560i	$-0.692545\pi$
$53$	1.84828	−	1.84828i	0.253881	−	0.253881i	0.822560	+	0.568679i	$0.192545\pi$
$54$		0			0
$55$		0			0
$56$	−2.08219	−	1.20215i	−0.278244	−	0.160644i
$57$		0			0
$58$	0.347982	−	1.29869i	0.0456923	−	0.170526i
$59$	−1.31456	−	2.27688i	−0.171141	−	0.296424i	0.767678	−	0.640835i	$-0.221412\pi$
$59$	−1.31456	−	2.27688i	−0.171141	−	0.296424i	−0.938819	+	0.344411i	$0.888079\pi$
$60$		0			0
$61$	−3.54275	+	6.13623i	−0.453603	+	0.785664i	−0.998607	−	0.0527700i	$-0.983195\pi$
$61$	−3.54275	+	6.13623i	−0.453603	+	0.785664i	0.545004	+	0.838434i	$0.316528\pi$
$62$	−1.77092	−	1.77092i	−0.224907	−	0.224907i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−0.0545285	−	0.0146109i	−0.00666172	−	0.00178500i	0.255487	−	0.966813i	$-0.417764\pi$
$67$	−0.0545285	−	0.0146109i	−0.00666172	−	0.00178500i	−0.262148	+	0.965028i	$0.584431\pi$
$68$	−6.82815	−	1.82960i	−0.828035	−	0.221871i
$69$		0			0
$70$		0			0
$71$		−	9.10005i		−	1.07998i	−0.841672	−	0.539989i	$-0.818429\pi$
$71$		−	9.10005i		−	1.07998i	0.841672	−	0.539989i	$-0.181571\pi$
$72$		0			0
$73$	−7.82779	−	7.82779i	−0.916174	−	0.916174i	0.0805747	−	0.996749i	$-0.474324\pi$
$73$	−7.82779	−	7.82779i	−0.916174	−	0.916174i	−0.996749	+	0.0805747i	$0.974324\pi$
$74$	−5.77537	+	10.0032i	−0.671374	+	1.16285i
$75$		0			0
$76$	−1.39195	−	2.41093i	−0.159668	−	0.276553i
$77$	0.712623	−	2.65955i	0.0812109	−	0.303083i
$78$		0			0
$79$	−8.46375	−	4.88655i	−0.952246	−	0.549779i	−0.0584679	−	0.998289i	$-0.518622\pi$
$79$	−8.46375	−	4.88655i	−0.952246	−	0.549779i	−0.893778	+	0.448510i	$0.851955\pi$
$80$		0			0
$81$		0			0
$82$	−1.39479	+	1.39479i	−0.154029	+	0.154029i
$83$	0.724794	+	2.70497i	0.0795565	+	0.296909i	0.994228	−	0.107290i	$-0.0342172\pi$
$83$	0.724794	+	2.70497i	0.0795565	+	0.296909i	−0.914671	+	0.404198i	$0.867551\pi$
$84$		0			0
$85$		0			0
$86$	7.78674	−	4.49568i	0.839666	−	0.484781i
$87$		0			0
$88$	1.10616	−	0.296395i	0.117917	−	0.0315958i
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$		0			0
$91$	5.94827			0.623549
$92$	−5.95746	+	1.59630i	−0.621108	+	0.166425i
$93$		0			0
$94$	−10.6798	+	6.16599i	−1.10154	+	0.635974i
$95$		0			0
$96$		0			0
$97$	−2.08981	−	7.79929i	−0.212188	−	0.791898i	−0.987137	−	0.159874i	$-0.948891\pi$
$97$	−2.08981	−	7.79929i	−0.212188	−	0.791898i	0.774949	−	0.632024i	$-0.217775\pi$
$98$	−0.862203	+	0.862203i	−0.0870956	+	0.0870956i
$99$		0			0
$100$		0			0
$101$	0.631074	+	0.364351i	0.0627942	+	0.0362543i	0.531068	−	0.847329i	$-0.321791\pi$
$101$	0.631074	+	0.364351i	0.0627942	+	0.0362543i	−0.468274	+	0.883583i	$0.655124\pi$
$102$		0			0
$103$	−0.353393	+	1.31888i	−0.0348209	+	0.129953i	−0.981148	−	0.193256i	$-0.938095\pi$
$103$	−0.353393	+	1.31888i	−0.0348209	+	0.129953i	0.946327	+	0.323209i	$0.104762\pi$
$104$	1.23701	+	2.14256i	0.121299	+	0.210095i
$105$		0			0
$106$	−1.30693	+	2.26367i	−0.126940	+	0.219867i
$107$	−0.399208	−	0.399208i	−0.0385929	−	0.0385929i	0.687547	−	0.726140i	$-0.258688\pi$
$107$	−0.399208	−	0.399208i	−0.0385929	−	0.0385929i	−0.726140	+	0.687547i	$0.758688\pi$
$108$		0			0
$109$		−	13.5974i		−	1.30239i	−0.758909	−	0.651196i	$-0.774268\pi$
$109$		−	13.5974i		−	1.30239i	0.758909	−	0.651196i	$-0.225732\pi$
$110$		0			0
$111$		0			0
$112$	2.32238	+	0.622279i	0.219444	+	0.0587998i
$113$	4.94392	+	1.32472i	0.465084	+	0.124619i	0.483749	−	0.875207i	$-0.339275\pi$
$113$	4.94392	+	1.32472i	0.465084	+	0.124619i	−0.0186645	+	0.999826i	$0.505941\pi$
$114$		0			0
$115$		0			0
$116$			1.34450i			0.124834i
$117$		0			0
$118$	1.85906	+	1.85906i	0.171141	+	0.171141i
$119$	8.49803	−	14.7190i	0.779013	−	1.34929i
$120$		0			0
$121$	−4.84428	−	8.39054i	−0.440389	−	0.762776i
$122$	1.83386	−	6.84408i	0.166030	−	0.619633i
$123$		0			0
$124$	2.16892	+	1.25223i	0.194775	+	0.112453i
$125$		0			0
$126$		0			0
$127$	4.88817	−	4.88817i	0.433755	−	0.433755i	−0.456149	−	0.889904i	$-0.650772\pi$
$127$	4.88817	−	4.88817i	0.433755	−	0.433755i	0.889904	+	0.456149i	$0.150772\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$		0			0
$131$	−4.98351	+	2.87723i	−0.435412	+	0.251385i	−0.701649	−	0.712522i	$-0.747553\pi$
$131$	−4.98351	+	2.87723i	−0.435412	+	0.251385i	0.266238	+	0.963907i	$0.414219\pi$
$132$		0			0
$133$	6.46527	−	1.73236i	0.560610	−	0.150215i
$134$	0.0564521			0.00487672
$135$		0			0
$136$	7.06902			0.606164
$137$	−10.0458	+	2.69177i	−0.858272	+	0.229973i	−0.661010	−	0.750377i	$-0.729872\pi$
$137$	−10.0458	+	2.69177i	−0.858272	+	0.229973i	−0.197262	+	0.980351i	$0.563205\pi$
$138$		0			0
$139$	−2.19537	+	1.26750i	−0.186209	+	0.107508i	−0.590207	−	0.807252i	$-0.700954\pi$
$139$	−2.19537	+	1.26750i	−0.186209	+	0.107508i	0.403998	+	0.914760i	$0.367620\pi$
$140$		0			0
$141$		0			0
$142$	2.35527	+	8.78997i	0.197650	+	0.737638i
$143$	−2.00337	+	2.00337i	−0.167531	+	0.167531i
$144$		0			0
$145$		0			0
$146$	9.58705	+	5.53509i	0.793430	+	0.458087i
$147$		0			0
$148$	2.98955	−	11.1572i	0.245740	−	0.917114i
$149$	−6.49294	−	11.2461i	−0.531922	−	0.921316i	−0.999306	−	0.0372613i	$-0.988137\pi$
$149$	−6.49294	−	11.2461i	−0.531922	−	0.921316i	0.467384	−	0.884055i	$-0.345197\pi$
$150$		0			0
$151$	1.58502	−	2.74534i	0.128987	−	0.223412i	−0.794297	−	0.607529i	$-0.792161\pi$
$151$	1.58502	−	2.74534i	0.128987	−	0.223412i	0.923284	+	0.384117i	$0.125494\pi$
$152$	1.96852	+	1.96852i	0.159668	+	0.159668i
$153$		0			0
$154$			2.75336i			0.221872i
$155$		0			0
$156$		0			0
$157$	−10.3186	−	2.76487i	−0.823515	−	0.220660i	−0.177633	−	0.984097i	$-0.556844\pi$
$157$	−10.3186	−	2.76487i	−0.823515	−	0.220660i	−0.645883	+	0.763437i	$0.723511\pi$
$158$	9.44008	+	2.52946i	0.751013	+	0.201233i
$159$		0			0
$160$		0			0
$161$		−	14.8288i		−	1.16867i
$162$		0			0
$163$	15.7354	+	15.7354i	1.23249	+	1.23249i	0.963003	+	0.269490i	$0.0868552\pi$
$163$	15.7354	+	15.7354i	1.23249	+	1.23249i	0.269490	+	0.963003i	$0.413145\pi$
$164$	0.986264	−	1.70826i	0.0770143	−	0.133393i
$165$		0			0
$166$	−1.40019	−	2.42521i	−0.108676	−	0.188233i
$167$	−1.05230	+	3.92724i	−0.0814295	+	0.303899i	−0.994614	−	0.103647i	$-0.966949\pi$
$167$	−1.05230	+	3.92724i	−0.0814295	+	0.303899i	0.913185	+	0.407546i	$0.133615\pi$
$168$		0			0
$169$	5.95761	+	3.43963i	0.458277	+	0.264587i
$170$		0			0
$171$		0			0
$172$	−6.35785	+	6.35785i	−0.484781	+	0.484781i
$173$	−1.44105	−	5.37809i	−0.109561	−	0.408889i	0.889261	−	0.457400i	$-0.151219\pi$
$173$	−1.44105	−	5.37809i	−0.109561	−	0.408889i	−0.998823	+	0.0485110i	$0.984552\pi$
$174$		0			0
$175$		0			0
$176$	−0.991757	+	0.572591i	−0.0747565	+	0.0431607i
$177$		0			0
$178$	−4.71209	+	1.26260i	−0.353186	+	0.0946359i
$179$	0.310192			0.0231848			0.0115924	−	0.999933i	$-0.496310\pi$
$179$	0.310192			0.0231848			0.0115924	+	0.999933i	$0.496310\pi$
$180$		0			0
$181$	3.07416			0.228501			0.114250	−	0.993452i	$-0.463553\pi$
$181$	3.07416			0.228501			0.114250	+	0.993452i	$0.463553\pi$
$182$	−5.74559	+	1.53953i	−0.425892	+	0.114117i
$183$		0			0
$184$	5.34131	−	3.08381i	0.393767	−	0.227341i
$185$		0			0
$186$		0			0
$187$	2.09522	+	7.81948i	0.153218	+	0.571817i
$188$	8.72003	−	8.72003i	0.635974	−	0.635974i
$189$		0			0
$190$		0			0
$191$	12.3541	+	7.13262i	0.893909	+	0.516098i	0.875219	−	0.483727i	$-0.160717\pi$
$191$	12.3541	+	7.13262i	0.893909	+	0.516098i	0.0186896	+	0.999825i	$0.494051\pi$
$192$		0			0
$193$	2.48506	−	9.27437i	0.178879	−	0.667584i	−0.816980	−	0.576666i	$-0.804353\pi$
$193$	2.48506	−	9.27437i	0.178879	−	0.667584i	0.995858	−	0.0909176i	$-0.0289800\pi$
$194$	4.03721	+	6.99265i	0.289855	+	0.502043i
$195$		0			0
$196$	0.609669	−	1.05598i	0.0435478	−	0.0754270i
$197$	4.62495	+	4.62495i	0.329514	+	0.329514i	0.852402	−	0.522887i	$-0.175145\pi$
$197$	4.62495	+	4.62495i	0.329514	+	0.329514i	−0.522887	+	0.852402i	$0.675145\pi$
$198$		0			0
$199$		−	4.07227i		−	0.288675i	−0.989528	−	0.144338i	$-0.953895\pi$
$199$		−	4.07227i		−	0.288675i	0.989528	−	0.144338i	$-0.0461051\pi$
$200$		0			0
$201$		0			0
$202$	−0.703872	−	0.188602i	−0.0495243	−	0.0132700i
$203$	−3.12243	−	0.836654i	−0.219152	−	0.0587216i
$204$		0			0
$205$		0			0
$206$		−	1.36541i		−	0.0951324i
$207$		0			0
$208$	−1.74939	−	1.74939i	−0.121299	−	0.121299i
$209$	−1.59404	+	2.76096i	−0.110262	+	0.190979i
$210$		0			0
$211$	−7.58800	−	13.1428i	−0.522379	−	0.904788i	−0.999661	−	0.0260371i	$-0.991711\pi$
$211$	−7.58800	−	13.1428i	−0.522379	−	0.904788i	0.477282	−	0.878750i	$-0.341622\pi$
$212$	0.676517	−	2.52480i	0.0464634	−	0.173404i
$213$		0			0
$214$	0.488928	+	0.282283i	0.0334224	+	0.0192964i
$215$		0			0
$216$		0			0
$217$	−4.25782	+	4.25782i	−0.289040	+	0.289040i
$218$	3.51926	+	13.1341i	0.238354	+	0.889551i
$219$		0			0
$220$		0			0
$221$	−15.1458	+	8.74443i	−1.01882	+	0.588214i
$222$		0			0
$223$	−8.21978	+	2.20248i	−0.550437	+	0.147489i	−0.523309	−	0.852143i	$-0.675303\pi$
$223$	−8.21978	+	2.20248i	−0.550437	+	0.147489i	−0.0271279	+	0.999632i	$0.508636\pi$
$224$	−2.40430			−0.160644
$225$		0			0
$226$	−5.11832			−0.340465
$227$	19.6687	−	5.27021i	1.30546	−	0.349796i	0.461946	−	0.886908i	$-0.347151\pi$
$227$	19.6687	−	5.27021i	1.30546	−	0.349796i	0.843511	+	0.537112i	$0.180485\pi$
$228$		0			0
$229$	−12.2032	+	7.04551i	−0.806409	+	0.465580i	−0.845707	−	0.533647i	$-0.820821\pi$
$229$	−12.2032	+	7.04551i	−0.806409	+	0.465580i	0.0392983	+	0.999228i	$0.487488\pi$
$230$		0			0
$231$		0			0
$232$	−0.347982	−	1.29869i	−0.0228461	−	0.0852630i
$233$	0.643009	−	0.643009i	0.0421249	−	0.0421249i	−0.685731	−	0.727855i	$-0.740517\pi$
$233$	0.643009	−	0.643009i	0.0421249	−	0.0421249i	0.727855	+	0.685731i	$0.240517\pi$
$234$		0			0
$235$		0			0
$236$	−2.27688	−	1.31456i	−0.148212	−	0.0855703i
$237$		0			0
$238$	−4.39890	+	16.4169i	−0.285139	+	1.06415i
$239$	5.34131	+	9.25142i	0.345501	+	0.598425i	0.985445	−	0.169997i	$-0.0543758\pi$
$239$	5.34131	+	9.25142i	0.345501	+	0.598425i	−0.639944	+	0.768422i	$0.721042\pi$
$240$		0			0
$241$	−10.5666	+	18.3019i	−0.680654	+	1.17893i	0.294127	+	0.955766i	$0.404971\pi$
$241$	−10.5666	+	18.3019i	−0.680654	+	1.17893i	−0.974782	+	0.223161i	$0.928362\pi$
$242$	6.85084	+	6.85084i	0.440389	+	0.440389i
$243$		0			0
$244$			7.08551i			0.453603i
$245$		0			0
$246$		0			0
$247$	−6.65274	−	1.78260i	−0.423303	−	0.113424i
$248$	−2.41912	−	0.648201i	−0.153614	−	0.0411608i
$249$		0			0
$250$		0			0
$251$			24.6952i			1.55874i	0.626561	+	0.779372i	$0.284462\pi$
$251$			24.6952i			1.55874i	−0.626561	+	0.779372i	$0.715538\pi$
$252$		0			0
$253$	4.99433	+	4.99433i	0.313991	+	0.313991i
$254$	−3.45646	+	5.98676i	−0.216877	+	0.375643i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.36020	+	5.07632i	−0.0848467	+	0.316652i	−0.995285	−	0.0969925i	$-0.969078\pi$
$257$	−1.36020	+	5.07632i	−0.0848467	+	0.316652i	0.910438	+	0.413645i	$0.135744\pi$
$258$		0			0
$259$	24.0508	+	13.8857i	1.49444	+	0.862818i
$260$		0			0
$261$		0			0
$262$	4.06902	−	4.06902i	0.251385	−	0.251385i
$263$	−3.86551	−	14.4263i	−0.238358	−	0.889563i	−0.976606	−	0.215034i	$-0.931014\pi$
$263$	−3.86551	−	14.4263i	−0.238358	−	0.889563i	0.738249	−	0.674529i	$-0.235653\pi$
$264$		0			0
$265$		0			0
$266$	−5.79660	+	3.34667i	−0.355413	+	0.205198i
$267$		0			0
$268$	−0.0545285	+	0.0146109i	−0.00333086	+	0.000892501i
$269$	−20.0071			−1.21985			−0.609927	−	0.792457i	$-0.708801\pi$
$269$	−20.0071			−1.21985			−0.609927	+	0.792457i	$0.708801\pi$
$270$		0			0
$271$	−3.02714			−0.183886			−0.0919428	−	0.995764i	$-0.529308\pi$
$271$	−3.02714			−0.183886			−0.0919428	+	0.995764i	$0.529308\pi$
$272$	−6.82815	+	1.82960i	−0.414018	+	0.110936i
$273$		0			0
$274$	9.00683	−	5.20010i	0.544123	−	0.314149i
$275$		0			0
$276$		0			0
$277$	0.723941	+	2.70178i	0.0434974	+	0.162334i	0.984258	−	0.176736i	$-0.0565540\pi$
$277$	0.723941	+	2.70178i	0.0434974	+	0.162334i	−0.940761	+	0.339071i	$0.889887\pi$
$278$	1.79251	−	1.79251i	0.107508	−	0.107508i
$279$		0			0
$280$		0			0
$281$	−13.0998	−	7.56319i	−0.781470	−	0.451182i	0.0554808	−	0.998460i	$-0.482331\pi$
$281$	−13.0998	−	7.56319i	−0.781470	−	0.451182i	−0.836951	+	0.547278i	$0.815664\pi$
$282$		0			0
$283$	6.22154	−	23.2191i	0.369832	−	1.38023i	−0.490918	−	0.871206i	$-0.663339\pi$
$283$	6.22154	−	23.2191i	0.369832	−	1.38023i	0.860750	−	0.509027i	$-0.169995\pi$
$284$	−4.55002	−	7.88087i	−0.269994	−	0.467644i
$285$		0			0
$286$	1.41660	−	2.45362i	0.0837653	−	0.145086i
$287$	3.35349	+	3.35349i	0.197950	+	0.197950i
$288$		0			0
$289$			32.9711i			1.93948i
$290$		0			0
$291$		0			0
$292$	−10.6930	−	2.86517i	−0.625758	−	0.167671i
$293$	14.5851	+	3.90805i	0.852068	+	0.228311i	0.658318	−	0.752740i	$-0.271268\pi$
$293$	14.5851	+	3.90805i	0.852068	+	0.228311i	0.193750	+	0.981051i	$0.437935\pi$
$294$		0			0
$295$		0			0
$296$			11.5507i			0.671374i
$297$		0			0
$298$	9.18240	+	9.18240i	0.531922	+	0.531922i
$299$	−7.62938	+	13.2145i	−0.441219	+	0.764213i
$300$		0			0
$301$	−10.8090	−	18.7217i	−0.623018	−	1.07910i
$302$	−0.820468	+	3.06203i	−0.0472126	+	0.176200i
$303$		0			0
$304$	−2.41093	−	1.39195i	−0.138276	−	0.0798339i
$305$		0			0
$306$		0			0
$307$	−8.29531	+	8.29531i	−0.473438	+	0.473438i	−0.903025	−	0.429587i	$-0.858659\pi$
$307$	−8.29531	+	8.29531i	−0.473438	+	0.473438i	0.429587	+	0.903025i	$0.358659\pi$
$308$	−0.712623	−	2.65955i	−0.0406055	−	0.151542i
$309$		0			0
$310$		0			0
$311$	−10.8857	+	6.28488i	−0.617274	+	0.356383i	−0.775807	−	0.630971i	$-0.782657\pi$
$311$	−10.8857	+	6.28488i	−0.617274	+	0.356383i	0.158533	+	0.987354i	$0.449324\pi$
$312$		0			0
$313$	−11.5304	+	3.08956i	−0.651737	+	0.174632i	−0.569514	−	0.821982i	$-0.692869\pi$
$313$	−11.5304	+	3.08956i	−0.651737	+	0.174632i	−0.0822229	+	0.996614i	$0.526202\pi$
$314$	10.6826			0.602855
$315$		0			0
$316$	−9.77309			−0.549779
$317$	−1.87547	+	0.502531i	−0.105337	+	0.0282249i	−0.311102	−	0.950376i	$-0.600698\pi$
$317$	−1.87547	+	0.502531i	−0.105337	+	0.0282249i	0.205766	+	0.978601i	$0.434032\pi$
$318$		0			0
$319$	1.33342	−	0.769849i	0.0746570	−	0.0431033i
$320$		0			0
$321$		0			0
$322$	3.83797	+	14.3235i	0.213882	+	0.798218i
$323$	−13.9155	+	13.9155i	−0.774279	+	0.774279i
$324$		0			0
$325$		0			0
$326$	−19.2719	−	11.1266i	−1.06737	−	0.616247i
$327$		0			0
$328$	−0.510528	+	1.90532i	−0.0281892	+	0.105203i
$329$	14.8249	+	25.6775i	0.817323	+	1.41565i
$330$		0			0
$331$	−10.9811	+	19.0198i	−0.603575	+	1.04542i	0.388700	+	0.921364i	$0.372924\pi$
$331$	−10.9811	+	19.0198i	−0.603575	+	1.04542i	−0.992275	+	0.124058i	$0.960409\pi$
$332$	1.98017	+	1.98017i	0.108676	+	0.108676i
$333$		0			0
$334$		−	4.06578i		−	0.222470i
$335$		0			0
$336$		0			0
$337$	25.8842	+	6.93565i	1.41000	+	0.377809i	0.881926	−	0.471388i	$-0.156247\pi$
$337$	25.8842	+	6.93565i	1.41000	+	0.377809i	0.528076	+	0.849197i	$0.322914\pi$
$338$	−6.64485	−	1.78048i	−0.361432	−	0.0968454i
$339$		0			0
$340$		0			0
$341$		−	2.86806i		−	0.155314i
$342$		0			0
$343$	13.9737	+	13.9737i	0.754508	+	0.754508i
$344$	4.49568	−	7.78674i	0.242391	−	0.419833i
$345$		0			0
$346$	2.78390	+	4.82186i	0.149664	+	0.259225i
$347$	−7.78712	+	29.0619i	−0.418035	+	1.56013i	0.360644	+	0.932704i	$0.382557\pi$
$347$	−7.78712	+	29.0619i	−0.418035	+	1.56013i	−0.778679	+	0.627423i	$0.784110\pi$
$348$		0			0
$349$	−22.2846	−	12.8660i	−1.19287	−	0.688702i	−0.233911	−	0.972258i	$-0.575152\pi$
$349$	−22.2846	−	12.8660i	−1.19287	−	0.688702i	−0.958956	+	0.283556i	$0.908486\pi$
$350$		0			0
$351$		0			0
$352$	0.809767	−	0.809767i	0.0431607	−	0.0431607i
$353$	−4.03627	−	15.0636i	−0.214829	−	0.801752i	−0.986227	−	0.165399i	$-0.947109\pi$
$353$	−4.03627	−	15.0636i	−0.214829	−	0.801752i	0.771398	−	0.636353i	$-0.219558\pi$
$354$		0			0
$355$		0			0
$356$	4.22474	−	2.43916i	0.223911	−	0.129275i
$357$		0			0
$358$	−0.299622	+	0.0802835i	−0.0158355	+	0.00424312i
$359$	22.9830			1.21300			0.606498	−	0.795085i	$-0.292574\pi$
$359$	22.9830			1.21300			0.606498	+	0.795085i	$0.292574\pi$
$360$		0			0
$361$	11.2499			0.592099
$362$	−2.96941	+	0.795652i	−0.156069	+	0.0418185i
$363$		0			0
$364$	5.15136	−	2.97414i	0.270004	−	0.155887i
$365$		0			0
$366$		0			0
$367$	0.901720	+	3.36526i	0.0470694	+	0.175665i	0.985459	−	0.169914i	$-0.0543490\pi$
$367$	0.901720	+	3.36526i	0.0470694	+	0.175665i	−0.938389	+	0.345580i	$0.887682\pi$
$368$	−4.36116	+	4.36116i	−0.227341	+	0.227341i
$369$		0			0
$370$		0			0
$371$	5.44254	+	3.14225i	0.282563	+	0.163138i
$372$		0			0
$373$	−5.91894	+	22.0898i	−0.306471	+	1.14377i	0.625200	+	0.780464i	$0.285017\pi$
$373$	−5.91894	+	22.0898i	−0.306471	+	1.14377i	−0.931671	+	0.363302i	$0.881649\pi$
$374$	−4.04766	−	7.01076i	−0.209300	−	0.362518i
$375$		0			0
$376$	−6.16599	+	10.6798i	−0.317987	+	0.550769i
$377$	2.35206	+	2.35206i	0.121137	+	0.121137i
$378$		0			0
$379$		−	36.3113i		−	1.86519i	−0.360927	−	0.932594i	$-0.617540\pi$
$379$		−	36.3113i		−	1.86519i	0.360927	−	0.932594i	$-0.382460\pi$
$380$		0			0
$381$		0			0
$382$	−13.7792	−	3.69212i	−0.705003	−	0.188905i
$383$	16.0342	+	4.29635i	0.819308	+	0.219533i	0.644044	−	0.764988i	$-0.277255\pi$
$383$	16.0342	+	4.29635i	0.819308	+	0.219533i	0.175264	+	0.984521i	$0.443922\pi$
$384$		0			0
$385$		0			0
$386$			9.60153i			0.488705i
$387$		0			0
$388$	−5.70947	−	5.70947i	−0.289855	−	0.289855i
$389$	11.7878	−	20.4171i	0.597667	−	1.03519i	−0.395497	−	0.918467i	$-0.629428\pi$
$389$	11.7878	−	20.4171i	0.597667	−	1.03519i	0.993164	−	0.116723i	$-0.0372390\pi$
$390$		0			0
$391$	21.7995	+	37.7578i	1.10245	+	1.90950i
$392$	−0.315588	+	1.17779i	−0.0159396	+	0.0594874i
$393$		0			0
$394$	−5.66439	−	3.27034i	−0.285368	−	0.164757i
$395$		0			0
$396$		0			0
$397$	−27.6509	+	27.6509i	−1.38776	+	1.38776i	−0.557748	+	0.830011i	$0.688334\pi$
$397$	−27.6509	+	27.6509i	−1.38776	+	1.38776i	−0.830011	+	0.557748i	$0.811666\pi$
$398$	1.05398	+	3.93351i	0.0528312	+	0.197169i
$399$		0			0
$400$		0			0
$401$	26.4658	−	15.2801i	1.32164	−	0.763050i	0.337651	−	0.941272i	$-0.390368\pi$
$401$	26.4658	−	15.2801i	1.32164	−	0.763050i	0.983990	+	0.178222i	$0.0570344\pi$
$402$		0			0
$403$	5.98494	−	1.60366i	0.298131	−	0.0798840i
$404$	0.728702			0.0362543
$405$		0			0
$406$	3.23258			0.160430
$407$	−12.7770	+	3.42359i	−0.633332	+	0.169701i
$408$		0			0
$409$	−2.43668	+	1.40682i	−0.120486	+	0.0695626i	−0.559032	−	0.829146i	$-0.688827\pi$
$409$	−2.43668	+	1.40682i	−0.120486	+	0.0695626i	0.438546	+	0.898709i	$0.355494\pi$
$410$		0			0
$411$		0			0
$412$	0.353393	+	1.31888i	0.0174104	+	0.0649766i
$413$	4.46974	−	4.46974i	0.219942	−	0.219942i
$414$		0			0
$415$		0			0
$416$	2.14256	+	1.23701i	0.105048	+	0.0606493i
$417$		0			0
$418$	0.825136	−	3.07945i	0.0403587	−	0.150621i
$419$	2.23812	+	3.87654i	0.109339	+	0.189381i	0.915503	−	0.402311i	$-0.131793\pi$
$419$	2.23812	+	3.87654i	0.109339	+	0.189381i	−0.806163	+	0.591693i	$0.798460\pi$
$420$		0			0
$421$	2.85177	−	4.93941i	0.138987	−	0.240732i	−0.788127	−	0.615513i	$-0.788949\pi$
$421$	2.85177	−	4.93941i	0.138987	−	0.240732i	0.927113	+	0.374781i	$0.122282\pi$
$422$	10.7310	+	10.7310i	0.522379	+	0.522379i
$423$		0			0
$424$			2.61386i			0.126940i
$425$		0			0
$426$		0			0
$427$	−16.4552	−	4.40916i	−0.796324	−	0.213374i
$428$	−0.545328	−	0.146120i	−0.0263594	−	0.00706299i
$429$		0			0
$430$		0			0
$431$			28.4120i			1.36856i	0.729221	+	0.684278i	$0.239883\pi$
$431$			28.4120i			1.36856i	−0.729221	+	0.684278i	$0.760117\pi$
$432$		0			0
$433$	−20.2290	−	20.2290i	−0.972142	−	0.972142i	0.0274806	−	0.999622i	$-0.491252\pi$
$433$	−20.2290	−	20.2290i	−0.972142	−	0.972142i	−0.999622	+	0.0274806i	$0.991252\pi$
$434$	3.01073	−	5.21475i	0.144520	−	0.250316i
$435$		0			0
$436$	−6.79869	−	11.7757i	−0.325598	−	0.563952i
$437$	−4.44393	+	16.5850i	−0.212582	+	0.793368i
$438$		0			0
$439$	12.4785	+	7.20447i	0.595567	+	0.343851i	0.767296	−	0.641293i	$-0.221602\pi$
$439$	12.4785	+	7.20447i	0.595567	+	0.343851i	−0.171729	+	0.985144i	$0.554935\pi$
$440$		0			0
$441$		0			0
$442$	12.3665	−	12.3665i	0.588214	−	0.588214i
$443$	6.94511	+	25.9195i	0.329972	+	1.23147i	0.909218	+	0.416320i	$0.136680\pi$
$443$	6.94511	+	25.9195i	0.329972	+	1.23147i	−0.579246	+	0.815153i	$0.696653\pi$
$444$		0			0
$445$		0			0
$446$	7.36965	−	4.25487i	0.348963	−	0.201474i
$447$		0			0
$448$	2.32238	−	0.622279i	0.109722	−	0.0293999i
$449$	1.72288			0.0813077			0.0406538	−	0.999173i	$-0.487056\pi$
$449$	1.72288			0.0813077			0.0406538	+	0.999173i	$0.487056\pi$
$450$		0			0
$451$	−2.25891			−0.106368
$452$	4.94392	−	1.32472i	0.232542	−	0.0623095i
$453$		0			0
$454$	−17.6345	+	10.1813i	−0.827626	+	0.477830i
$455$		0			0
$456$		0			0
$457$	3.30155	+	12.3215i	0.154440	+	0.576377i	0.999153	+	0.0411576i	$0.0131046\pi$
$457$	3.30155	+	12.3215i	0.154440	+	0.576377i	−0.844713	+	0.535220i	$0.820229\pi$
$458$	9.96386	−	9.96386i	0.465580	−	0.465580i
$459$		0			0
$460$		0			0
$461$	−8.72418	−	5.03691i	−0.406326	−	0.234592i	0.282884	−	0.959154i	$-0.408709\pi$
$461$	−8.72418	−	5.03691i	−0.406326	−	0.234592i	−0.689210	+	0.724562i	$0.742042\pi$
$462$		0			0
$463$	−9.90706	+	36.9737i	−0.460420	+	1.71831i	0.211224	+	0.977438i	$0.432255\pi$
$463$	−9.90706	+	36.9737i	−0.460420	+	1.71831i	−0.671644	+	0.740874i	$0.734412\pi$
$464$	0.672250	+	1.16437i	0.0312084	+	0.0540546i
$465$		0			0
$466$	−0.454676	+	0.787522i	−0.0210625	+	0.0364813i
$467$	−14.5094	−	14.5094i	−0.671413	−	0.671413i	0.286629	−	0.958042i	$-0.407465\pi$
$467$	−14.5094	−	14.5094i	−0.671413	−	0.671413i	−0.958042	+	0.286629i	$0.907465\pi$
$468$		0			0
$469$		−	0.135728i		−	0.00626733i
$470$		0			0
$471$		0			0
$472$	2.53953	+	0.680464i	0.116891	+	0.0313209i
$473$	9.94589	+	2.66499i	0.457313	+	0.122537i
$474$		0			0
$475$		0			0
$476$		−	16.9961i		−	0.779013i
$477$		0			0
$478$	−7.55375	−	7.55375i	−0.345501	−	0.345501i
$479$	−2.27813	+	3.94584i	−0.104091	+	0.180290i	−0.913366	−	0.407139i	$-0.866527\pi$
$479$	−2.27813	+	3.94584i	−0.104091	+	0.180290i	0.809276	+	0.587429i	$0.199860\pi$
$480$		0			0
$481$	−14.2884	−	24.7482i	−0.651493	−	1.12842i
$482$	5.46967	−	20.4131i	0.249137	−	0.929791i
$483$		0			0
$484$	−8.39054	−	4.84428i	−0.381388	−	0.220194i
$485$		0			0
$486$		0			0
$487$	18.4889	−	18.4889i	0.837814	−	0.837814i	−0.150757	−	0.988571i	$-0.548171\pi$
$487$	18.4889	−	18.4889i	0.837814	−	0.837814i	0.988571	+	0.150757i	$0.0481710\pi$
$488$	−1.83386	−	6.84408i	−0.0830151	−	0.309817i
$489$		0			0
$490$		0			0
$491$	0.730071	−	0.421507i	0.0329476	−	0.0190223i	−0.483436	−	0.875380i	$-0.660611\pi$
$491$	0.730071	−	0.421507i	0.0329476	−	0.0190223i	0.516383	+	0.856358i	$0.327278\pi$
$492$		0			0
$493$	9.18045	−	2.45989i	0.413467	−	0.110788i
$494$	6.88742			0.309880
$495$		0			0
$496$	2.50446			0.112453
$497$	21.1337	−	5.66277i	0.947978	−	0.254010i
$498$		0			0
$499$	−8.45869	+	4.88363i	−0.378663	+	0.218621i	−0.677236	−	0.735765i	$-0.736823\pi$
$499$	−8.45869	+	4.88363i	−0.378663	+	0.218621i	0.298573	+	0.954387i	$0.403489\pi$
$500$		0			0
$501$		0			0
$502$	−6.39158	−	23.8537i	−0.285270	−	1.06464i
$503$	22.3161	−	22.3161i	0.995025	−	0.995025i	−0.00496279	−	0.999988i	$-0.501580\pi$
$503$	22.3161	−	22.3161i	0.995025	−	0.995025i	0.999988	+	0.00496279i	$0.00157971\pi$
$504$		0			0
$505$		0			0
$506$	−6.11678	−	3.53152i	−0.271924	−	0.156995i
$507$		0			0
$508$	1.78919	−	6.67736i	0.0793826	−	0.296260i
$509$	−3.83647	−	6.64497i	−0.170049	−	0.294533i	0.768388	−	0.639984i	$-0.221059\pi$
$509$	−3.83647	−	6.64497i	−0.170049	−	0.294533i	−0.938437	+	0.345451i	$0.887726\pi$
$510$		0			0
$511$	13.3080	−	23.0501i	0.588712	−	1.01968i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	5.25539i		−	0.231805i
$515$		0			0
$516$		0			0
$517$	−13.6412	−	3.65514i	−0.599938	−	0.160753i
$518$	−26.8252	−	7.18779i	−1.17863	−	0.315813i
$519$		0			0
$520$		0			0
$521$		−	23.2333i		−	1.01787i	−0.860805	−	0.508934i	$-0.830040\pi$
$521$		−	23.2333i		−	1.01787i	0.860805	−	0.508934i	$-0.169960\pi$
$522$		0			0
$523$	3.86103	+	3.86103i	0.168831	+	0.168831i	0.786465	−	0.617634i	$-0.211909\pi$
$523$	3.86103	+	3.86103i	0.168831	+	0.168831i	−0.617634	+	0.786465i	$0.711909\pi$
$524$	−2.87723	+	4.98351i	−0.125693	+	0.217706i
$525$		0			0
$526$	7.46760	+	12.9343i	0.325603	+	0.563960i
$527$	4.58215	−	17.1008i	0.199602	−	0.744923i
$528$		0			0
$529$	13.0246	+	7.51973i	0.566285	+	0.326945i
$530$		0			0
$531$		0			0
$532$	4.73291	−	4.73291i	0.205198	−	0.205198i
$533$	−1.26305	−	4.71378i	−0.0547089	−	0.204176i
$534$		0			0
$535$		0			0
$536$	0.0488889	−	0.0282260i	0.00211168	−	0.00121918i
$537$		0			0
$538$	19.3254	−	5.17822i	0.833176	−	0.223249i
$539$	−1.39637			−0.0601457
$540$		0			0
$541$	−21.3692			−0.918732			−0.459366	−	0.888247i	$-0.651923\pi$
$541$	−21.3692			−0.918732			−0.459366	+	0.888247i	$0.651923\pi$
$542$	2.92399	−	0.783481i	0.125596	−	0.0336534i
$543$		0			0
$544$	6.12195	−	3.53451i	0.262477	−	0.151541i
$545$		0			0
$546$		0			0
$547$	−7.10984	−	26.5343i	−0.303995	−	1.13452i	−0.933807	−	0.357777i	$-0.883535\pi$
$547$	−7.10984	−	26.5343i	−0.303995	−	1.13452i	0.629812	−	0.776747i	$-0.283132\pi$
$548$	−7.35405	+	7.35405i	−0.314149	+	0.314149i
$549$		0			0
$550$		0			0
$551$	3.24150	+	1.87148i	0.138092	+	0.0797277i
$552$		0			0
$553$	6.08159	−	22.6968i	0.258615	−	0.965166i
$554$	−1.39855	−	2.42235i	−0.0594185	−	0.102916i
$555$		0			0
$556$	−1.26750	+	2.19537i	−0.0537539	+	0.0931045i
$557$	−13.7347	−	13.7347i	−0.581958	−	0.581958i	0.353483	−	0.935441i	$-0.384997\pi$
$557$	−13.7347	−	13.7347i	−0.581958	−	0.581958i	−0.935441	+	0.353483i	$0.884997\pi$
$558$		0			0
$559$			22.2447i			0.940852i
$560$		0			0
$561$		0			0
$562$	14.6110	+	3.91500i	0.616326	+	0.165144i
$563$	−14.3759	−	3.85201i	−0.605872	−	0.162343i	−0.0571749	−	0.998364i	$-0.518209\pi$
$563$	−14.3759	−	3.85201i	−0.605872	−	0.162343i	−0.548697	+	0.836021i	$0.684876\pi$
$564$		0			0
$565$		0			0
$566$			24.0382i			1.01040i
$567$		0			0
$568$	6.43471	+	6.43471i	0.269994	+	0.269994i
$569$	−14.7082	+	25.4753i	−0.616599	+	1.06798i	0.373503	+	0.927629i	$0.378157\pi$
$569$	−14.7082	+	25.4753i	−0.616599	+	1.06798i	−0.990102	+	0.140351i	$0.955177\pi$
$570$		0			0
$571$	15.2909	+	26.4847i	0.639906	+	1.10835i	0.985453	+	0.169948i	$0.0543599\pi$
$571$	15.2909	+	26.4847i	0.639906	+	1.10835i	−0.345548	+	0.938401i	$0.612307\pi$
$572$	−0.733286	+	2.73666i	−0.0306602	+	0.114426i
$573$		0			0
$574$	−4.10717	−	2.37128i	−0.171430	−	0.0989751i
$575$		0			0
$576$		0			0
$577$	2.75877	−	2.75877i	0.114849	−	0.114849i	−0.647347	−	0.762196i	$-0.724121\pi$
$577$	2.75877	−	2.75877i	0.114849	−	0.114849i	0.762196	+	0.647347i	$0.224121\pi$
$578$	−8.53354	−	31.8476i	−0.354949	−	1.32469i
$579$		0			0
$580$		0			0
$581$	−5.83093	+	3.36649i	−0.241908	+	0.139665i
$582$		0			0
$583$	−2.89135	+	0.774736i	−0.119748	+	0.0320863i
$584$	11.0702			0.458087
$585$		0			0
$586$	−15.0996			−0.623757
$587$	−15.5484	+	4.16617i	−0.641750	+	0.171956i	−0.564996	−	0.825094i	$-0.691122\pi$
$587$	−15.5484	+	4.16617i	−0.641750	+	0.171956i	−0.0767539	+	0.997050i	$0.524456\pi$
$588$		0			0
$589$	6.03808	−	3.48608i	0.248795	−	0.143642i
$590$		0			0
$591$		0			0
$592$	−2.98955	−	11.1572i	−0.122870	−	0.458557i
$593$	−31.4829	+	31.4829i	−1.29285	+	1.29285i	−0.359830	+	0.933018i	$0.617165\pi$
$593$	−31.4829	+	31.4829i	−1.29285	+	1.29285i	−0.933018	+	0.359830i	$0.882835\pi$
$594$		0			0
$595$		0			0
$596$	−11.2461	−	6.49294i	−0.460658	−	0.265961i
$597$		0			0
$598$	3.94926	−	14.7388i	0.161497	−	0.602716i
$599$	0.0708577	+	0.122729i	0.00289517	+	0.00501457i	0.867469	−	0.497491i	$-0.165745\pi$
$599$	0.0708577	+	0.122729i	0.00289517	+	0.00501457i	−0.864574	+	0.502505i	$0.832412\pi$
$600$		0			0
$601$	21.9425	−	38.0055i	0.895052	−	1.55028i	0.0613115	−	0.998119i	$-0.480472\pi$
$601$	21.9425	−	38.0055i	0.895052	−	1.55028i	0.833740	−	0.552157i	$-0.186195\pi$
$602$	15.2862	+	15.2862i	0.623018	+	0.623018i
$603$		0			0
$604$		−	3.17004i		−	0.128987i
$605$		0			0
$606$		0			0
$607$	32.2841	+	8.65049i	1.31037	+	0.351113i	0.845362	−	0.534194i	$-0.179385\pi$
$607$	32.2841	+	8.65049i	1.31037	+	0.351113i	0.465008	+	0.885306i	$0.346051\pi$
$608$	2.68904	+	0.720527i	0.109055	+	0.0292212i
$609$		0			0
$610$		0			0
$611$		−	30.5095i		−	1.23428i
$612$		0			0
$613$	−6.75021	−	6.75021i	−0.272638	−	0.272638i	0.557523	−	0.830161i	$-0.311752\pi$
$613$	−6.75021	−	6.75021i	−0.272638	−	0.272638i	−0.830161	+	0.557523i	$0.811752\pi$
$614$	5.86567	−	10.1596i	0.236719	−	0.410010i
$615$		0			0
$616$	1.37668	+	2.38448i	0.0554681	+	0.0960736i
$617$	8.53953	−	31.8700i	0.343789	−	1.28304i	−0.550232	−	0.835012i	$-0.685461\pi$
$617$	8.53953	−	31.8700i	0.343789	−	1.28304i	0.894021	−	0.448025i	$-0.147872\pi$
$618$		0			0
$619$	13.2360	+	7.64183i	0.532001	+	0.307151i	0.741831	−	0.670587i	$-0.233958\pi$
$619$	13.2360	+	7.64183i	0.532001	+	0.307151i	−0.209830	+	0.977738i	$0.567291\pi$
$620$		0			0
$621$		0			0
$622$	8.88817	−	8.88817i	0.356383	−	0.356383i
$623$	3.03567	+	11.3293i	0.121622	+	0.453898i
$624$		0			0
$625$		0			0
$626$	10.3379	−	5.96858i	0.413185	−	0.238552i
$627$		0			0
$628$	−10.3186	+	2.76487i	−0.411758	+	0.110330i
$629$	−81.6525			−3.25570
$630$		0			0
$631$	10.8347			0.431321			0.215660	−	0.976468i	$-0.430810\pi$
$631$	10.8347			0.431321			0.215660	+	0.976468i	$0.430810\pi$
$632$	9.44008	−	2.52946i	0.375506	−	0.100617i
$633$		0			0
$634$	1.68150	−	0.970815i	0.0667809	−	0.0385560i
$635$		0			0
$636$		0			0
$637$	−0.780770	−	2.91387i	−0.0309352	−	0.115452i
$638$	−1.08873	+	1.08873i	−0.0431033	+	0.0431033i
$639$		0			0
$640$		0			0
$641$	23.0771	+	13.3236i	0.911491	+	0.526250i	0.880911	−	0.473283i	$-0.156931\pi$
$641$	23.0771	+	13.3236i	0.911491	+	0.526250i	0.0305804	+	0.999532i	$0.490264\pi$
$642$		0			0
$643$	3.67008	−	13.6969i	0.144734	−	0.540153i	−0.855033	−	0.518573i	$-0.826463\pi$
$643$	3.67008	−	13.6969i	0.144734	−	0.540153i	0.999767	−	0.0215806i	$-0.00686984\pi$
$644$	−7.41440	−	12.8421i	−0.292168	−	0.506050i
$645$		0			0
$646$	9.83974	−	17.0429i	0.387139	−	0.670545i
$647$	−22.3507	−	22.3507i	−0.878698	−	0.878698i	0.114702	−	0.993400i	$-0.463409\pi$
$647$	−22.3507	−	22.3507i	−0.878698	−	0.878698i	−0.993400	+	0.114702i	$0.963409\pi$
$648$		0			0
$649$			3.01081i			0.118185i
$650$		0			0
$651$		0			0
$652$	21.4950	+	5.75956i	0.841809	+	0.225562i
$653$	24.6425	+	6.60293i	0.964334	+	0.258393i	0.706434	−	0.707779i	$-0.250303\pi$
$653$	24.6425	+	6.60293i	0.964334	+	0.258393i	0.257900	+	0.966172i	$0.416969\pi$
$654$		0			0
$655$		0			0
$656$		−	1.97253i		−	0.0770143i
$657$		0			0
$658$	−20.9656	−	20.9656i	−0.817323	−	0.817323i
$659$	10.2346	−	17.7269i	0.398684	−	0.690540i	−0.594880	−	0.803814i	$-0.702800\pi$
$659$	10.2346	−	17.7269i	0.398684	−	0.690540i	0.993564	+	0.113274i	$0.0361338\pi$
$660$		0			0
$661$	−0.883223	−	1.52979i	−0.0343534	−	0.0595018i	0.848338	−	0.529456i	$-0.177604\pi$
$661$	−0.883223	−	1.52979i	−0.0343534	−	0.0595018i	−0.882691	+	0.469954i	$0.844271\pi$
$662$	5.68423	−	21.2138i	0.220924	−	0.824499i
$663$		0			0
$664$	−2.42521	−	1.40019i	−0.0941163	−	0.0543381i
$665$		0			0
$666$		0			0
$667$	5.86358	−	5.86358i	0.227039	−	0.227039i
$668$	1.05230	+	3.92724i	0.0407148	+	0.151950i
$669$		0			0
$670$		0			0
$671$	7.02711	−	4.05710i	0.271278	−	0.156623i
$672$		0			0
$673$	13.4819	−	3.61246i	0.519688	−	0.139250i	0.0105656	−	0.999944i	$-0.496637\pi$
$673$	13.4819	−	3.61246i	0.519688	−	0.139250i	0.509122	+	0.860694i	$0.329970\pi$
$674$	−26.7973			−1.03219
$675$		0			0
$676$	6.87925			0.264587
$677$	−1.70954	+	0.458071i	−0.0657031	+	0.0176051i	−0.291521	−	0.956564i	$-0.594161\pi$
$677$	−1.70954	+	0.458071i	−0.0657031	+	0.0176051i	0.225818	+	0.974170i	$0.427495\pi$
$678$		0			0
$679$	16.8124	−	9.70666i	0.645202	−	0.372508i
$680$		0			0
$681$		0			0
$682$	0.742309	+	2.77034i	0.0284245	+	0.106082i
$683$	−22.8964	+	22.8964i	−0.876105	+	0.876105i	−0.993129	−	0.117024i	$-0.962665\pi$
$683$	−22.8964	+	22.8964i	−0.876105	+	0.876105i	0.117024	+	0.993129i	$0.462665\pi$
$684$		0			0
$685$		0			0
$686$	−17.1142	−	9.88088i	−0.653423	−	0.377254i
$687$		0			0
$688$	−2.32713	+	8.68498i	−0.0887211	+	0.331112i
$689$	−3.23336	−	5.60035i	−0.123181	−	0.213356i
$690$		0			0
$691$	11.3908	−	19.7295i	0.433327	−	0.750545i	−0.563830	−	0.825891i	$-0.690673\pi$
$691$	11.3908	−	19.7295i	0.433327	−	0.750545i	0.997157	+	0.0753461i	$0.0240062\pi$
$692$	−3.93703	−	3.93703i	−0.149664	−	0.149664i
$693$		0			0
$694$		−	30.0871i		−	1.14209i
$695$		0			0
$696$		0			0
$697$	−13.4687	−	3.60893i	−0.510164	−	0.136698i
$698$	24.8552	+	6.65994i	0.940784	+	0.252082i
$699$		0			0
$700$		0			0
$701$		−	26.0321i		−	0.983220i	−0.870816	−	0.491610i	$-0.836409\pi$
$701$		−	26.0321i		−	0.983220i	0.870816	−	0.491610i	$-0.163591\pi$
$702$		0			0
$703$	−22.7379	−	22.7379i	−0.857574	−	0.857574i
$704$	−0.572591	+	0.991757i	−0.0215804	+	0.0373783i
$705$		0			0
$706$	7.79747	+	13.5056i	0.293462	+	0.508291i
$707$	−0.453456	+	1.69232i	−0.0170540	+	0.0636462i
$708$		0			0
$709$	−2.58254	−	1.49103i	−0.0969892	−	0.0559968i	0.450721	−	0.892665i	$-0.351167\pi$
$709$	−2.58254	−	1.49103i	−0.0969892	−	0.0559968i	−0.547710	+	0.836668i	$0.684500\pi$
$710$		0			0
$711$		0			0
$712$	−3.44949	+	3.44949i	−0.129275	+	0.129275i
$713$	−3.99786	−	14.9202i	−0.149721	−	0.558766i
$714$		0			0
$715$		0			0
$716$	0.268634	−	0.155096i	0.0100393	−	0.00579621i
$717$		0			0
$718$	−22.1999	+	5.94843i	−0.828491	+	0.221994i
$719$	7.38853			0.275546			0.137773	−	0.990464i	$-0.456006\pi$
$719$	7.38853			0.275546			0.137773	+	0.990464i	$0.456006\pi$
$720$		0			0
$721$	−3.28285			−0.122260
$722$	−10.8665	+	2.91168i	−0.404411	+	0.108362i
$723$		0			0
$724$	2.66230	−	1.53708i	0.0989437	−	0.0571252i
$725$		0			0
$726$		0			0
$727$	5.57881	+	20.8204i	0.206906	+	0.772185i	0.988860	+	0.148849i	$0.0475567\pi$
$727$	5.57881	+	20.8204i	0.206906	+	0.772185i	−0.781954	+	0.623337i	$0.785777\pi$
$728$	−4.20607	+	4.20607i	−0.155887	+	0.155887i
$729$		0			0
$730$		0			0
$731$	55.0446	+	31.7800i	2.03590	+	1.17543i
$732$		0			0
$733$	1.74734	−	6.52116i	0.0645395	−	0.240865i	−0.926119	−	0.377232i	$-0.876876\pi$
$733$	1.74734	−	6.52116i	0.0645395	−	0.240865i	0.990658	+	0.136367i	$0.0435427\pi$
$734$	−1.74199	−	3.01721i	−0.0642980	−	0.111367i
$735$		0			0
$736$	3.08381	−	5.34131i	0.113671	−	0.196883i
$737$	0.0457130	+	0.0457130i	0.00168386	+	0.00168386i
$738$		0			0
$739$			12.8637i			0.473200i	0.971607	+	0.236600i	$0.0760331\pi$
$739$			12.8637i			0.473200i	−0.971607	+	0.236600i	$0.923967\pi$
$740$		0			0
$741$		0			0
$742$	−6.07037	−	1.62655i	−0.222850	−	0.0597125i
$743$	−32.7401	−	8.77270i	−1.20112	−	0.321839i	−0.397848	−	0.917452i	$-0.630243\pi$
$743$	−32.7401	−	8.77270i	−1.20112	−	0.321839i	−0.803272	+	0.595613i	$0.796909\pi$
$744$		0			0
$745$		0			0
$746$		−	22.8690i		−	0.837295i
$747$		0			0
$748$	5.72426	+	5.72426i	0.209300	+	0.209300i
$749$	0.678692	−	1.17553i	0.0247989	−	0.0429529i
$750$		0			0
$751$	6.70415	+	11.6119i	0.244638	+	0.423725i	0.962030	−	0.272945i	$-0.0879975\pi$
$751$	6.70415	+	11.6119i	0.244638	+	0.423725i	−0.717392	+	0.696670i	$0.754664\pi$
$752$	3.19175	−	11.9118i	0.116391	−	0.434378i
$753$		0			0
$754$	−2.88067	−	1.66316i	−0.104908	−	0.0605686i
$755$		0			0
$756$		0			0
$757$	1.11492	−	1.11492i	0.0405223	−	0.0405223i	−0.686555	−	0.727078i	$-0.740878\pi$
$757$	1.11492	−	1.11492i	0.0405223	−	0.0405223i	0.727078	+	0.686555i	$0.240878\pi$
$758$	9.39806	+	35.0741i	0.341353	+	1.27395i
$759$		0			0
$760$		0			0
$761$	29.7531	−	17.1780i	1.07855	−	0.622702i	0.148046	−	0.988981i	$-0.452702\pi$
$761$	29.7531	−	17.1780i	1.07855	−	0.622702i	0.930505	+	0.366279i	$0.119368\pi$
$762$		0			0
$763$	31.5782	−	8.46136i	1.14321	−	0.306322i
$764$	14.2652			0.516098
$765$		0			0
$766$	−16.5998			−0.599775
$767$	−6.28282	+	1.68348i	−0.226860	+	0.0607869i
$768$		0			0
$769$	14.4890	−	8.36522i	0.522486	−	0.301658i	−0.215465	−	0.976512i	$-0.569127\pi$
$769$	14.4890	−	8.36522i	0.522486	−	0.301658i	0.737951	+	0.674854i	$0.235793\pi$
$770$		0			0
$771$		0			0
$772$	−2.48506	−	9.27437i	−0.0894393	−	0.333792i
$773$	5.20827	−	5.20827i	0.187328	−	0.187328i	−0.607212	−	0.794540i	$-0.707712\pi$
$773$	5.20827	−	5.20827i	0.187328	−	0.187328i	0.794540	+	0.607212i	$0.207712\pi$
$774$		0			0
$775$		0			0
$776$	6.99265	+	4.03721i	0.251022	+	0.144927i
$777$		0			0
$778$	−6.10184	+	22.7724i	−0.218761	+	0.816429i
$779$	−2.74567	−	4.75563i	−0.0983737	−	0.170388i
$780$		0			0
$781$	−5.21061	+	9.02504i	−0.186450	+	0.322941i
$782$	−30.8291	−	30.8291i	−1.10245	−	1.10245i
$783$		0			0
$784$		−	1.21934i		−	0.0435478i
$785$		0			0
$786$		0			0
$787$	44.6815	+	11.9724i	1.59272	+	0.426769i	0.942834	−	0.333262i	$-0.108149\pi$
$787$	44.6815	+	11.9724i	1.59272	+	0.426769i	0.649888	+	0.760030i	$0.274816\pi$
$788$	6.31780	+	1.69285i	0.225062	+	0.0603053i
$789$		0			0
$790$		0			0
$791$			12.3060i			0.437550i
$792$		0			0
$793$	12.3953	+	12.3953i	0.440171	+	0.440171i
$794$	19.5521	−	33.8653i	0.693879	−	1.20183i
$795$		0			0
$796$	−2.03613	−	3.52669i	−0.0721688	−	0.125000i
$797$	13.3339	−	49.7628i	0.472311	−	1.76269i	−0.159123	−	0.987259i	$-0.550866\pi$
$797$	13.3339	−	49.7628i	0.472311	−	1.76269i	0.631434	−	0.775430i	$-0.282467\pi$
$798$		0			0
$799$	−75.4958	−	43.5875i	−2.67085	−	1.54202i
$800$		0			0
$801$		0			0
$802$	−21.6093	+	21.6093i	−0.763050	+	0.763050i
$803$	3.28114	+	12.2454i	0.115789	+	0.432131i
$804$		0			0
$805$		0			0
$806$	−5.36595	+	3.09803i	−0.189008	+	0.109124i
$807$		0			0
$808$	−0.703872	+	0.188602i	−0.0247621	+	0.00663499i
$809$	18.0260			0.633762			0.316881	−	0.948465i	$-0.397364\pi$
$809$	18.0260			0.633762			0.316881	+	0.948465i	$0.397364\pi$
$810$		0			0
$811$	46.7969			1.64326			0.821630	−	0.570021i	$-0.193065\pi$
$811$	46.7969			1.64326			0.821630	+	0.570021i	$0.193065\pi$
$812$	−3.12243	+	0.836654i	−0.109576	+	0.0293608i
$813$		0			0
$814$	11.4555	−	6.61386i	0.401517	−	0.231816i
$815$		0			0
$816$		0			0
$817$	6.47852	+	24.1782i	0.226655	+	0.845886i
$818$	1.98954	−	1.98954i	0.0695626	−	0.0695626i
$819$		0			0
$820$		0			0
$821$	−5.91006	−	3.41218i	−0.206263	−	0.119086i	0.393311	−	0.919406i	$-0.371330\pi$
$821$	−5.91006	−	3.41218i	−0.206263	−	0.119086i	−0.599573	+	0.800320i	$0.704663\pi$
$822$		0			0
$823$	−5.27529	+	19.6876i	−0.183885	+	0.686268i	0.810982	+	0.585072i	$0.198934\pi$
$823$	−5.27529	+	19.6876i	−0.183885	+	0.686268i	−0.994866	+	0.101196i	$0.967733\pi$
$824$	−0.682703	−	1.18248i	−0.0237831	−	0.0411935i
$825$		0			0
$826$	−3.16059	+	5.47430i	−0.109971	+	0.190475i
$827$	29.8425	+	29.8425i	1.03773	+	1.03773i	0.999260	+	0.0384654i	$0.0122469\pi$
$827$	29.8425	+	29.8425i	1.03773	+	1.03773i	0.0384654	+	0.999260i	$0.487753\pi$
$828$		0			0
$829$			20.4152i			0.709050i	0.935047	+	0.354525i	$0.115357\pi$
$829$			20.4152i			0.709050i	−0.935047	+	0.354525i	$0.884643\pi$
$830$		0			0
$831$		0			0
$832$	−2.38971	−	0.640322i	−0.0828484	−	0.0221992i
$833$	−8.32583	−	2.23090i	−0.288473	−	0.0772961i
$834$		0			0
$835$		0			0
$836$			3.18808i			0.110262i
$837$		0			0
$838$	−3.16518	−	3.16518i	−0.109339	−	0.109339i
$839$	−9.70261	+	16.8054i	−0.334971	+	0.580187i	−0.983479	−	0.181021i	$-0.942060\pi$
$839$	−9.70261	+	16.8054i	−0.334971	+	0.580187i	0.648508	+	0.761208i	$0.275393\pi$
$840$		0			0
$841$	13.5962	+	23.5492i	0.468833	+	0.812043i
$842$	−1.47618	+	5.50919i	−0.0508726	+	0.189859i
$843$		0			0
$844$	−13.1428	−	7.58800i	−0.452394	−	0.261190i
$845$		0			0
$846$		0			0
$847$	16.4715	−	16.4715i	0.565967	−	0.565967i
$848$	−0.676517	−	2.52480i	−0.0232317	−	0.0867018i
$849$		0			0
$850$		0			0
$851$	−61.6961	+	35.6203i	−2.11492	+	1.22105i
$852$		0			0
$853$	0.496213	−	0.132960i	0.0169900	−	0.00455246i	−0.250314	−	0.968165i	$-0.580534\pi$
$853$	0.496213	−	0.132960i	0.0169900	−	0.00455246i	0.267304	+	0.963612i	$0.413867\pi$
$854$	17.0357			0.582949
$855$		0			0
$856$	0.564565			0.0192964
$857$	−43.0427	+	11.5332i	−1.47031	+	0.393968i	−0.903037	−	0.429562i	$-0.858668\pi$
$857$	−43.0427	+	11.5332i	−1.47031	+	0.393968i	−0.567272	+	0.823530i	$0.692001\pi$
$858$		0			0
$859$	25.5432	−	14.7474i	0.871522	−	0.503174i	0.00366859	−	0.999993i	$-0.498832\pi$
$859$	25.5432	−	14.7474i	0.871522	−	0.503174i	0.867854	+	0.496820i	$0.165499\pi$
$860$		0			0
$861$		0			0
$862$	−7.35356	−	27.4438i	−0.250463	−	0.934741i
$863$	−6.17951	+	6.17951i	−0.210353	+	0.210353i	−0.804417	−	0.594064i	$-0.797522\pi$
$863$	−6.17951	+	6.17951i	−0.210353	+	0.210353i	0.594064	+	0.804417i	$0.297522\pi$
$864$		0			0
$865$		0			0
$866$	24.7753	+	14.3040i	0.841899	+	0.486071i
$867$		0			0
$868$	−1.55847	+	5.81629i	−0.0528979	+	0.197418i
$869$	5.59599	+	9.69254i	0.189831	+	0.328797i
$870$		0			0
$871$	−0.0698316	+	0.120952i	−0.00236615	+	0.00409830i
$872$	9.61480	+	9.61480i	0.325598	+	0.325598i
$873$		0			0
$874$		−	17.1700i		−	0.580785i
$875$		0			0
$876$		0			0
$877$	−20.0896	−	5.38298i	−0.678376	−	0.181770i	−0.0968513	−	0.995299i	$-0.530877\pi$
$877$	−20.0896	−	5.38298i	−0.678376	−	0.181770i	−0.581525	+	0.813528i	$0.697544\pi$
$878$	−13.9180	−	3.72931i	−0.469709	−	0.125858i
$879$		0			0
$880$		0			0
$881$			28.3087i			0.953745i	0.878972	+	0.476873i	$0.158230\pi$
$881$			28.3087i			0.953745i	−0.878972	+	0.476873i	$0.841770\pi$
$882$		0			0
$883$	−15.1647	−	15.1647i	−0.510333	−	0.510333i	0.404295	−	0.914629i	$-0.367517\pi$
$883$	−15.1647	−	15.1647i	−0.510333	−	0.510333i	−0.914629	+	0.404295i	$0.867517\pi$
$884$	−8.74443	+	15.1458i	−0.294107	+	0.509408i
$885$		0			0
$886$	−13.4169	−	23.2388i	−0.450750	−	0.780723i
$887$	−12.4339	+	46.4040i	−0.417490	+	1.55809i	0.362306	+	0.932059i	$0.381989\pi$
$887$	−12.4339	+	46.4040i	−0.417490	+	1.55809i	−0.779796	+	0.626034i	$0.784677\pi$
$888$		0			0
$889$	14.3940	+	8.31036i	0.482758	+	0.278721i
$890$		0			0
$891$		0			0
$892$	−6.01730	+	6.01730i	−0.201474	+	0.201474i
$893$	−8.88553	−	33.1613i	−0.297343	−	1.10970i
$894$		0			0
$895$		0			0
$896$	−2.08219	+	1.20215i	−0.0695609	+	0.0401610i
$897$		0			0
$898$	−1.66417	+	0.445914i	−0.0555342	+	0.0148803i
$899$	−3.36724			−0.112304
$900$		0			0
$901$	−18.4774			−0.615573
$902$	2.18194	−	0.584648i	0.0726505	−	0.0194666i
$903$		0			0
$904$	−4.43259	+	2.55916i	−0.147426	+	0.0851164i
$905$		0			0
$906$		0			0
$907$	−9.66001	−	36.0516i	−0.320755	−	1.19707i	−0.918511	−	0.395396i	$-0.870607\pi$
$907$	−9.66001	−	36.0516i	−0.320755	−	1.19707i	0.597755	−	0.801679i	$-0.296059\pi$
$908$	14.3985	−	14.3985i	0.477830	−	0.477830i
$909$		0			0
$910$		0			0
$911$	−46.5957	−	26.9020i	−1.54378	−	0.891304i	−0.998595	−	0.0529906i	$-0.983125\pi$
$911$	−46.5957	−	26.9020i	−1.54378	−	0.891304i	−0.545189	−	0.838313i	$-0.683542\pi$
$912$		0			0
$913$	0.830022	−	3.09768i	0.0274697	−	0.102518i
$914$	−6.37810	−	11.0472i	−0.210969	−	0.365409i
$915$		0			0
$916$	−7.04551	+	12.2032i	−0.232790	+	0.403204i
$917$	−9.78315	−	9.78315i	−0.323068	−	0.323068i
$918$		0			0
$919$			23.1668i			0.764203i	0.924120	+	0.382101i	$0.124799\pi$
$919$			23.1668i			0.764203i	−0.924120	+	0.382101i	$0.875201\pi$
$920$		0			0
$921$		0			0
$922$	9.73056	+	2.60729i	0.320459	+	0.0858667i
$923$	−21.7465	−	5.82696i	−0.715795	−	0.191797i
$924$		0			0
$925$		0			0
$926$		−	38.2779i		−	1.25789i
$927$		0			0
$928$	−0.950705	−	0.950705i	−0.0312084	−	0.0312084i
$929$	6.78350	−	11.7494i	0.222559	−	0.385484i	−0.733025	−	0.680202i	$-0.761892\pi$
$929$	6.78350	−	11.7494i	0.222559	−	0.385484i	0.955584	+	0.294717i	$0.0952255\pi$
$930$		0			0
$931$	−1.69726	−	2.93974i	−0.0556255	−	0.0963462i
$932$	0.235358	−	0.878367i	0.00770940	−	0.0287719i
$933$		0			0
$934$	17.7703	+	10.2597i	0.581461	+	0.335706i
$935$		0			0
$936$		0			0
$937$	6.94086	−	6.94086i	0.226748	−	0.226748i	−0.584585	−	0.811333i	$-0.698742\pi$
$937$	6.94086	−	6.94086i	0.226748	−	0.226748i	0.811333	+	0.584585i	$0.198742\pi$
$938$	0.0351289	+	0.131103i	0.00114700	+	0.00428066i
$939$		0			0
$940$		0			0
$941$	14.5976	−	8.42791i	0.475867	−	0.274742i	−0.242825	−	0.970070i	$-0.578074\pi$
$941$	14.5976	−	8.42791i	0.475867	−	0.274742i	0.718693	+	0.695328i	$0.244741\pi$
$942$		0			0
$943$	−11.7513	+	3.14874i	−0.382673	+	0.102537i
$944$	−2.62911			−0.0855703
$945$		0			0
$946$	−10.2967			−0.334776
$947$	37.0498	−	9.92745i	1.20396	−	0.322599i	0.399568	−	0.916704i	$-0.369160\pi$
$947$	37.0498	−	9.92745i	1.20396	−	0.322599i	0.804388	+	0.594105i	$0.202494\pi$
$948$		0			0
$949$	−23.7185	+	13.6939i	−0.769935	+	0.444522i
$950$		0			0
$951$		0			0
$952$	4.39890	+	16.4169i	0.142569	+	0.532076i
$953$	18.8861	−	18.8861i	0.611780	−	0.611780i	−0.331630	−	0.943410i	$-0.607598\pi$
$953$	18.8861	−	18.8861i	0.611780	−	0.611780i	0.943410	+	0.331630i	$0.107598\pi$
$954$		0			0
$955$		0			0
$956$	9.25142	+	5.34131i	0.299212	+	0.172750i
$957$		0			0
$958$	1.17925	−	4.40102i	0.0380998	−	0.142190i
$959$	−12.5026	−	21.6551i	−0.403730	−	0.699281i
$960$		0			0
$961$	12.3638	−	21.4148i	0.398834	−	0.690800i
$962$	20.2068	+	20.2068i	0.651493	+	0.651493i
$963$		0			0
$964$			21.1332i			0.680654i
$965$		0			0
$966$		0			0
$967$	−30.9494	−	8.29288i	−0.995267	−	0.266681i	−0.275805	−	0.961213i	$-0.588945\pi$
$967$	−30.9494	−	8.29288i	−0.995267	−	0.266681i	−0.719461	+	0.694533i	$0.755611\pi$
$968$	9.35843	+	2.50758i	0.300791	+	0.0805968i
$969$		0			0
$970$		0			0
$971$		−	29.2201i		−	0.937716i	−0.883274	−	0.468858i	$-0.844666\pi$
$971$		−	29.2201i		−	0.937716i	0.883274	−	0.468858i	$-0.155334\pi$
$972$		0			0
$973$	−4.30974	−	4.30974i	−0.138164	−	0.138164i
$974$	−13.0737	+	22.6442i	−0.418907	+	0.725568i
$975$		0			0
$976$	3.54275	+	6.13623i	0.113401	+	0.196416i
$977$	−10.1124	+	37.7399i	−0.323523	+	1.20741i	0.592265	+	0.805743i	$0.298234\pi$
$977$	−10.1124	+	37.7399i	−0.323523	+	1.20741i	−0.915788	+	0.401662i	$0.868433\pi$
$978$		0			0
$979$	−4.83811	−	2.79328i	−0.154627	−	0.0892737i
$980$		0			0
$981$		0			0
$982$	−0.596101	+	0.596101i	−0.0190223	+	0.0190223i
$983$	2.96514	+	11.0660i	0.0945732	+	0.352952i	0.996954	−	0.0779867i	$-0.0248492\pi$
$983$	2.96514	+	11.0660i	0.0945732	+	0.352952i	−0.902381	+	0.430939i	$0.858182\pi$
$984$		0			0
$985$		0			0
$986$	−8.23096	+	4.75215i	−0.262127	+	0.151339i
$987$		0			0
$988$	−6.65274	+	1.78260i	−0.211652	+	0.0567119i
$989$	55.4552			1.76337
$990$		0			0
$991$	−26.7986			−0.851286			−0.425643	−	0.904891i	$-0.639952\pi$
$991$	−26.7986			−0.851286			−0.425643	+	0.904891i	$0.639952\pi$
$992$	−2.41912	+	0.648201i	−0.0768071	+	0.0205804i
$993$		0			0
$994$	−18.9480	+	10.9396i	−0.600994	+	0.346984i
$995$		0			0
$996$		0			0
$997$	−14.2233	−	53.0819i	−0.450455	−	1.68112i	−0.701116	−	0.713047i	$-0.747315\pi$
$997$	−14.2233	−	53.0819i	−0.450455	−	1.68112i	0.250661	−	0.968075i	$-0.419352\pi$
$998$	6.90650	−	6.90650i	0.218621	−	0.218621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.h.143.1		16
3.2	odd	2		450.2.p.h.443.3		16
5.2	odd	4	inner	1350.2.q.h.1007.2		16
5.3	odd	4		270.2.m.b.197.4		16
5.4	even	2		270.2.m.b.143.3		16
9.4	even	3		450.2.p.h.293.3		16
9.5	odd	6	inner	1350.2.q.h.1043.2		16
15.2	even	4		450.2.p.h.407.3		16
15.8	even	4		90.2.l.b.47.2	yes	16
15.14	odd	2		90.2.l.b.83.2	yes	16
45.4	even	6		90.2.l.b.23.2	✓	16
45.13	odd	12		90.2.l.b.77.2	yes	16
45.14	odd	6		270.2.m.b.233.4		16
45.22	odd	12		450.2.p.h.257.3		16
45.23	even	12		270.2.m.b.17.3		16
45.29	odd	6		810.2.f.c.323.6		16
45.32	even	12	inner	1350.2.q.h.557.1		16
45.34	even	6		810.2.f.c.323.3		16
45.38	even	12		810.2.f.c.647.3		16
45.43	odd	12		810.2.f.c.647.6		16
60.23	odd	4		720.2.cu.b.497.2		16
60.59	even	2		720.2.cu.b.353.1		16
180.103	even	12		720.2.cu.b.257.1		16
180.139	odd	6		720.2.cu.b.113.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	45.4	even	6
90.2.l.b.47.2	yes	16	15.8	even	4
90.2.l.b.77.2	yes	16	45.13	odd	12
90.2.l.b.83.2	yes	16	15.14	odd	2
270.2.m.b.17.3		16	45.23	even	12
270.2.m.b.143.3		16	5.4	even	2
270.2.m.b.197.4		16	5.3	odd	4
270.2.m.b.233.4		16	45.14	odd	6
450.2.p.h.257.3		16	45.22	odd	12
450.2.p.h.293.3		16	9.4	even	3
450.2.p.h.407.3		16	15.2	even	4
450.2.p.h.443.3		16	3.2	odd	2
720.2.cu.b.113.2		16	180.139	odd	6
720.2.cu.b.257.1		16	180.103	even	12
720.2.cu.b.353.1		16	60.59	even	2
720.2.cu.b.497.2		16	60.23	odd	4
810.2.f.c.323.3		16	45.34	even	6
810.2.f.c.323.6		16	45.29	odd	6
810.2.f.c.647.3		16	45.38	even	12
810.2.f.c.647.6		16	45.43	odd	12
1350.2.q.h.143.1		16	1.1	even	1	trivial
1350.2.q.h.557.1		16	45.32	even	12	inner
1350.2.q.h.1007.2		16	5.2	odd	4	inner
1350.2.q.h.1043.2		16	9.5	odd	6	inner

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:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(0.622279 + 2.32238i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(0.622279 + 2.32238i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.991757 - 0.572591i) q^{11} +(0.640322 - 2.38971i) q^{13} +(-1.20215 - 2.08219i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.99855 - 4.99855i) q^{17} -2.78390i q^{19} +(1.10616 + 0.296395i) q^{22} +(-5.95746 - 1.59630i) q^{23} +2.47401i q^{26} +(1.70010 + 1.70010i) q^{28} +(-0.672250 + 1.16437i) q^{29} +(1.25223 + 2.16892i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(6.12195 + 3.53451i) q^{34} +(8.16761 - 8.16761i) q^{37} +(0.720527 + 2.68904i) q^{38} +(1.70826 - 0.986264i) q^{41} +(-8.68498 + 2.32713i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(11.9118 - 3.19175i) q^{47} +(1.05598 - 0.609669i) q^{49} +(-0.640322 - 2.38971i) q^{52} +(1.84828 - 1.84828i) q^{53} +(-2.08219 - 1.20215i) q^{56} +(0.347982 - 1.29869i) q^{58} +(-1.31456 - 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(-1.77092 - 1.77092i) q^{62} -1.00000i q^{64} +(-0.0545285 - 0.0146109i) q^{67} +(-6.82815 - 1.82960i) q^{68} -9.10005i q^{71} +(-7.82779 - 7.82779i) q^{73} +(-5.77537 + 10.0032i) q^{74} +(-1.39195 - 2.41093i) q^{76} +(0.712623 - 2.65955i) q^{77} +(-8.46375 - 4.88655i) q^{79} +(-1.39479 + 1.39479i) q^{82} +(0.724794 + 2.70497i) q^{83} +(7.78674 - 4.49568i) q^{86} +(1.10616 - 0.296395i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(-5.95746 + 1.59630i) q^{92} +(-10.6798 + 6.16599i) q^{94} +(-2.08981 - 7.79929i) q^{97} +(-0.862203 + 0.862203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^16 - 8 * q^22 - 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^38 - 24 * q^41 - 32 * q^46 + 48 * q^47 - 24 * q^56 - 16 * q^58 - 24 * q^61 + 16 * q^67 - 24 * q^68 - 16 * q^73 + 16 * q^76 - 72 * q^77 + 16 * q^82 + 48 * q^83 + 48 * q^86 - 8 * q^88 - 24 * q^92 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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