LMFDB - Embedded newform 450.2.p.h.257.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (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:	$3.59326809096$
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			257.3
Root			$0.500000 + 1.33108i$ of defining polynomial
Character	$\chi$	$=$	450.257
Dual form			450.2.p.h.443.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.73022 + 0.0795432i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.69185 - 0.370982i) q^{6} +(0.622279 - 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.98735 - 0.275255i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.73022 + 0.0795432i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.69185 - 0.370982i) q^{6} +(0.622279 - 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.98735 - 0.275255i) q^{9} +(0.991757 - 0.572591i) q^{11} +(-1.53819 - 0.796225i) q^{12} +(0.640322 + 2.38971i) q^{13} +(1.20215 - 2.08219i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.99855 - 4.99855i) q^{17} +(2.95680 + 0.507306i) q^{18} +2.78390i q^{19} +(-0.891952 + 4.06773i) q^{21} +(1.10616 - 0.296395i) q^{22} +(5.95746 - 1.59630i) q^{23} +(-1.27970 - 1.16721i) q^{24} +2.47401i q^{26} +(-5.14688 + 0.713876i) q^{27} +(1.70010 - 1.70010i) q^{28} +(0.672250 + 1.16437i) q^{29} +(1.25223 - 2.16892i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.67042 + 1.06960i) q^{33} +(6.12195 - 3.53451i) q^{34} +(2.72474 + 1.25529i) q^{36} +(8.16761 + 8.16761i) q^{37} +(-0.720527 + 2.68904i) q^{38} +(-1.29799 - 4.08381i) q^{39} +(-1.70826 - 0.986264i) q^{41} +(-1.91436 + 3.69827i) q^{42} +(-8.68498 - 2.32713i) q^{43} +1.14518 q^{44} +6.16761 q^{46} +(-11.9118 - 3.19175i) q^{47} +(-0.933998 - 1.45865i) q^{48} +(1.05598 + 0.609669i) q^{49} +(-8.25101 + 9.04622i) q^{51} +(-0.640322 + 2.38971i) q^{52} +(-1.84828 - 1.84828i) q^{53} +(-5.15627 - 0.642559i) q^{54} +(2.08219 - 1.20215i) q^{56} +(-0.221441 - 4.81678i) q^{57} +(0.347982 + 1.29869i) q^{58} +(1.31456 - 2.27688i) q^{59} +(-3.54275 - 6.13623i) q^{61} +(1.77092 - 1.77092i) q^{62} +(1.21972 - 7.10903i) q^{63} +1.00000i q^{64} +(-1.89033 + 0.600817i) q^{66} +(-0.0545285 + 0.0146109i) q^{67} +(6.82815 - 1.82960i) q^{68} +(-10.1808 + 3.23582i) q^{69} -9.10005i q^{71} +(2.30701 + 1.91774i) q^{72} +(-7.82779 + 7.82779i) q^{73} +(5.77537 + 10.0032i) q^{74} +(-1.39195 + 2.41093i) q^{76} +(-0.712623 - 2.65955i) q^{77} +(-0.196791 - 4.28060i) q^{78} +(-8.46375 + 4.88655i) q^{79} +(8.84847 - 1.64456i) q^{81} +(-1.39479 - 1.39479i) q^{82} +(-0.724794 + 2.70497i) q^{83} +(-2.80632 + 3.07678i) q^{84} +(-7.78674 - 4.49568i) q^{86} +(-1.25576 - 1.96115i) q^{87} +(1.10616 + 0.296395i) q^{88} -4.87832 q^{89} +5.94827 q^{91} +(5.95746 + 1.59630i) q^{92} +(-1.99411 + 3.85233i) q^{93} +(-10.6798 - 6.16599i) q^{94} +(-0.524648 - 1.65068i) q^{96} +(-2.08981 + 7.79929i) q^{97} +(0.862203 + 0.862203i) q^{98} +(2.80511 - 1.98351i) q^{99} +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} + 24 q^{21} - 8 q^{22} + 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{36} - 24 q^{38} + 24 q^{41} - 24 q^{42} - 32 q^{46} - 48 q^{47} - 48 q^{51} + 24 q^{56} - 24 q^{57} - 16 q^{58} - 24 q^{61} + 48 q^{63} - 48 q^{66} + 16 q^{67} + 24 q^{68} + 24 q^{72} - 16 q^{73} + 16 q^{76} + 72 q^{77} + 24 q^{81} + 16 q^{82} - 48 q^{83} - 48 q^{86} + 48 q^{87} - 8 q^{88} + 24 q^{92} - 72 q^{93} + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^16 + 24 * q^21 - 8 * q^22 + 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^36 - 24 * q^38 + 24 * q^41 - 24 * q^42 - 32 * q^46 - 48 * q^47 - 48 * q^51 + 24 * q^56 - 24 * q^57 - 16 * q^58 - 24 * q^61 + 48 * q^63 - 48 * q^66 + 16 * q^67 + 24 * q^68 + 24 * q^72 - 16 * q^73 + 16 * q^76 + 72 * q^77 + 24 * q^81 + 16 * q^82 - 48 * q^83 - 48 * q^86 + 48 * q^87 - 8 * q^88 + 24 * q^92 - 72 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.73022	+	0.0795432i	−0.998945	+	0.0459243i
$3$	−1.73022	+	0.0795432i	−0.998945	+	0.0459243i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.69185	−	0.370982i	−0.690697	−	0.151453i
$7$	0.622279	−	2.32238i	0.235199	−	0.877776i	−0.742860	−	0.669447i	$-0.766531\pi$
$7$	0.622279	−	2.32238i	0.235199	−	0.877776i	0.978059	−	0.208328i	$-0.0668023\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.98735	−	0.275255i	0.995782	−	0.0917517i
$10$		0			0
$11$	0.991757	−	0.572591i	0.299026	−	0.172643i	−0.342979	−	0.939343i	$-0.611436\pi$
$11$	0.991757	−	0.572591i	0.299026	−	0.172643i	0.642005	+	0.766700i	$0.278103\pi$
$12$	−1.53819	−	0.796225i	−0.444037	−	0.229850i
$13$	0.640322	+	2.38971i	0.177593	+	0.662788i	0.996095	+	0.0882838i	$0.0281383\pi$
$13$	0.640322	+	2.38971i	0.177593	+	0.662788i	−0.818502	+	0.574504i	$0.805195\pi$
$14$	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	0.242068	−	0.970259i	$-0.422174\pi$
$17$	4.99855	−	4.99855i	1.21233	−	1.21233i	0.970259	−	0.242068i	$-0.0778258\pi$
$18$	2.95680	+	0.507306i	0.696923	+	0.119573i
$19$			2.78390i			0.638671i	0.947642	+	0.319336i	$0.103460\pi$
$19$			2.78390i			0.638671i	−0.947642	+	0.319336i	$0.896540\pi$
$20$		0			0
$21$	−0.891952	+	4.06773i	−0.194640	+	0.887651i
$22$	1.10616	−	0.296395i	0.235834	−	0.0631917i
$23$	5.95746	−	1.59630i	1.24222	−	0.332851i	0.422891	−	0.906181i	$-0.361015\pi$
$23$	5.95746	−	1.59630i	1.24222	−	0.332851i	0.819325	+	0.573330i	$0.194349\pi$
$24$	−1.27970	−	1.16721i	−0.261217	−	0.238255i
$25$		0			0
$26$			2.47401i			0.485194i
$27$	−5.14688	+	0.713876i	−0.990518	+	0.137386i
$28$	1.70010	−	1.70010i	0.321288	−	0.321288i
$29$	0.672250	+	1.16437i	0.124834	+	0.216218i	0.921668	−	0.387980i	$-0.126827\pi$
$29$	0.672250	+	1.16437i	0.124834	+	0.216218i	−0.796834	+	0.604198i	$0.793494\pi$
$30$		0			0
$31$	1.25223	−	2.16892i	0.224907	−	0.389550i	−0.731385	−	0.681965i	$-0.761126\pi$
$31$	1.25223	−	2.16892i	0.224907	−	0.389550i	0.956292	+	0.292415i	$0.0944589\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−1.67042	+	1.06960i	−0.290782	+	0.186193i
$34$	6.12195	−	3.53451i	1.04991	−	0.606164i
$35$		0			0
$36$	2.72474	+	1.25529i	0.454124	+	0.209216i
$37$	8.16761	+	8.16761i	1.34275	+	1.34275i	0.893314	+	0.449434i	$0.148374\pi$
$37$	8.16761	+	8.16761i	1.34275	+	1.34275i	0.449434	+	0.893314i	$0.351626\pi$
$38$	−0.720527	+	2.68904i	−0.116885	+	0.436221i
$39$	−1.29799	−	4.08381i	−0.207844	−	0.653932i
$40$		0			0
$41$	−1.70826	−	0.986264i	−0.266785	−	0.154029i	0.360641	−	0.932705i	$-0.382558\pi$
$41$	−1.70826	−	0.986264i	−0.266785	−	0.154029i	−0.627426	+	0.778676i	$0.715891\pi$
$42$	−1.91436	+	3.69827i	−0.295393	+	0.570655i
$43$	−8.68498	−	2.32713i	−1.32445	−	0.354885i	−0.473805	−	0.880630i	$-0.657120\pi$
$43$	−8.68498	−	2.32713i	−1.32445	−	0.354885i	−0.850642	+	0.525745i	$0.823787\pi$
$44$	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	$-0.772665\pi$
$47$	−11.9118	−	3.19175i	−1.73751	−	0.465565i	−0.981891	+	0.189445i	$0.939331\pi$
$48$	−0.933998	−	1.45865i	−0.134811	−	0.210537i
$49$	1.05598	+	0.609669i	0.150854	+	0.0870956i
$50$		0			0
$51$	−8.25101	+	9.04622i	−1.15537	+	1.26672i
$52$	−0.640322	+	2.38971i	−0.0887967	+	0.331394i
$53$	−1.84828	−	1.84828i	−0.253881	−	0.253881i	0.568679	−	0.822560i	$-0.307455\pi$
$53$	−1.84828	−	1.84828i	−0.253881	−	0.253881i	−0.822560	+	0.568679i	$0.807455\pi$
$54$	−5.15627	−	0.642559i	−0.701679	−	0.0874413i
$55$		0			0
$56$	2.08219	−	1.20215i	0.278244	−	0.160644i
$57$	−0.221441	−	4.81678i	−0.0293305	−	0.637998i
$58$	0.347982	+	1.29869i	0.0456923	+	0.170526i
$59$	1.31456	−	2.27688i	0.171141	−	0.296424i	−0.767678	−	0.640835i	$-0.778588\pi$
$59$	1.31456	−	2.27688i	0.171141	−	0.296424i	0.938819	+	0.344411i	$0.111921\pi$
$60$		0			0
$61$	−3.54275	−	6.13623i	−0.453603	−	0.785664i	0.545004	−	0.838434i	$-0.316528\pi$
$61$	−3.54275	−	6.13623i	−0.453603	−	0.785664i	−0.998607	+	0.0527700i	$0.983195\pi$
$62$	1.77092	−	1.77092i	0.224907	−	0.224907i
$63$	1.21972	−	7.10903i	0.153670	−	0.895653i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.89033	+	0.600817i	−0.232684	+	0.0739555i
$67$	−0.0545285	+	0.0146109i	−0.00666172	+	0.00178500i	−0.262148	−	0.965028i	$-0.584431\pi$
$67$	−0.0545285	+	0.0146109i	−0.00666172	+	0.00178500i	0.255487	+	0.966813i	$0.417764\pi$
$68$	6.82815	−	1.82960i	0.828035	−	0.221871i
$69$	−10.1808	+	3.23582i	−1.22562	+	0.389547i
$70$		0			0
$71$		−	9.10005i		−	1.07998i	−0.841672	−	0.539989i	$-0.818429\pi$
$71$		−	9.10005i		−	1.07998i	0.841672	−	0.539989i	$-0.181571\pi$
$72$	2.30701	+	1.91774i	0.271883	+	0.226008i
$73$	−7.82779	+	7.82779i	−0.916174	+	0.916174i	−0.996749	−	0.0805747i	$-0.974324\pi$
$73$	−7.82779	+	7.82779i	−0.916174	+	0.916174i	0.0805747	+	0.996749i	$0.474324\pi$
$74$	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
$78$	−0.196791	−	4.28060i	−0.0222822	−	0.484682i
$79$	−8.46375	+	4.88655i	−0.952246	+	0.549779i	−0.893778	−	0.448510i	$-0.851955\pi$
$79$	−8.46375	+	4.88655i	−0.952246	+	0.549779i	−0.0584679	+	0.998289i	$0.518622\pi$
$80$		0			0
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$	−1.39479	−	1.39479i	−0.154029	−	0.154029i
$83$	−0.724794	+	2.70497i	−0.0795565	+	0.296909i	−0.994228	−	0.107290i	$-0.965783\pi$
$83$	−0.724794	+	2.70497i	−0.0795565	+	0.296909i	0.914671	+	0.404198i	$0.132449\pi$
$84$	−2.80632	+	3.07678i	−0.306194	+	0.335704i
$85$		0			0
$86$	−7.78674	−	4.49568i	−0.839666	−	0.484781i
$87$	−1.25576	−	1.96115i	−0.134632	−	0.210257i
$88$	1.10616	+	0.296395i	0.117917	+	0.0315958i
$89$	−4.87832			−0.517100			−0.258550	−	0.965998i	$-0.583245\pi$
$89$	−4.87832			−0.517100			−0.258550	+	0.965998i	$0.583245\pi$
$90$		0			0
$91$	5.94827			0.623549
$92$	5.95746	+	1.59630i	0.621108	+	0.166425i
$93$	−1.99411	+	3.85233i	−0.206780	+	0.399468i
$94$	−10.6798	−	6.16599i	−1.10154	−	0.635974i
$95$		0			0
$96$	−0.524648	−	1.65068i	−0.0535466	−	0.168472i
$97$	−2.08981	+	7.79929i	−0.212188	+	0.791898i	0.774949	+	0.632024i	$0.217775\pi$
$97$	−2.08981	+	7.79929i	−0.212188	+	0.791898i	−0.987137	+	0.159874i	$0.948891\pi$
$98$	0.862203	+	0.862203i	0.0870956	+	0.0870956i
$99$	2.80511	−	1.98351i	0.281925	−	0.199351i
$100$		0			0
$101$	−0.631074	+	0.364351i	−0.0627942	+	0.0362543i	−0.531068	−	0.847329i	$-0.678209\pi$
$101$	−0.631074	+	0.364351i	−0.0627942	+	0.0362543i	0.468274	+	0.883583i	$0.344876\pi$
$102$	−10.3112	+	6.60245i	−1.02096	+	0.653740i
$103$	−0.353393	−	1.31888i	−0.0348209	−	0.129953i	0.946327	−	0.323209i	$-0.104762\pi$
$103$	−0.353393	−	1.31888i	−0.0348209	−	0.129953i	−0.981148	+	0.193256i	$0.938095\pi$
$104$	−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	$-0.741312\pi$
$107$	0.399208	−	0.399208i	0.0385929	−	0.0385929i	0.726140	+	0.687547i	$0.241312\pi$
$108$	−4.81427	−	1.95521i	−0.463253	−	0.188140i
$109$			13.5974i			1.30239i	0.758909	+	0.651196i	$0.225732\pi$
$109$			13.5974i			1.30239i	−0.758909	+	0.651196i	$0.774268\pi$
$110$		0			0
$111$	−14.7815	−	13.4821i	−1.40300	−	1.27967i
$112$	2.32238	−	0.622279i	0.219444	−	0.0587998i
$113$	−4.94392	+	1.32472i	−0.465084	+	0.124619i	−0.483749	−	0.875207i	$-0.660725\pi$
$113$	−4.94392	+	1.32472i	−0.465084	+	0.124619i	0.0186645	+	0.999826i	$0.494059\pi$
$114$	1.03278	−	4.70996i	0.0967285	−	0.441128i
$115$		0			0
$116$			1.34450i			0.124834i
$117$	2.57064	+	6.96265i	0.237656	+	0.643697i
$118$	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
$123$	3.03412	+	1.57058i	0.273578	+	0.141614i
$124$	2.16892	−	1.25223i	0.194775	−	0.112453i
$125$		0			0
$126$	3.01811	−	6.55111i	0.268874	−	0.583619i
$127$	4.88817	+	4.88817i	0.433755	+	0.433755i	0.889904	−	0.456149i	$-0.150772\pi$
$127$	4.88817	+	4.88817i	0.433755	+	0.433755i	−0.456149	+	0.889904i	$0.650772\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	15.2121	+	3.33563i	1.33935	+	0.293686i
$130$		0			0
$131$	4.98351	+	2.87723i	0.435412	+	0.251385i	0.701649	−	0.712522i	$-0.252447\pi$
$131$	4.98351	+	2.87723i	0.435412	+	0.251385i	−0.266238	+	0.963907i	$0.585781\pi$
$132$	−1.98142	+	0.0910916i	−0.172461	+	0.00792850i
$133$	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	$-0.270128\pi$
$137$	10.0458	+	2.69177i	0.858272	+	0.229973i	0.197262	+	0.980351i	$0.436795\pi$
$138$	−10.6713	+	0.490592i	−0.908406	+	0.0417620i
$139$	−2.19537	−	1.26750i	−0.186209	−	0.107508i	0.403998	−	0.914760i	$-0.367620\pi$
$139$	−2.19537	−	1.26750i	−0.186209	−	0.107508i	−0.590207	+	0.807252i	$0.700954\pi$
$140$		0			0
$141$	20.8639	+	4.57494i	1.75706	+	0.385280i
$142$	2.35527	−	8.78997i	0.197650	−	0.737638i
$143$	2.00337	+	2.00337i	0.167531	+	0.167531i
$144$	1.73205	+	2.44949i	0.144338	+	0.204124i
$145$		0			0
$146$	−9.58705	+	5.53509i	−0.793430	+	0.458087i
$147$	−1.87557	−	0.970868i	−0.154695	−	0.0800759i
$148$	2.98955	+	11.1572i	0.245740	+	0.917114i
$149$	6.49294	−	11.2461i	0.531922	−	0.921316i	−0.467384	−	0.884055i	$-0.654803\pi$
$149$	6.49294	−	11.2461i	0.531922	−	0.921316i	0.999306	−	0.0372613i	$-0.0118634\pi$
$150$		0			0
$151$	1.58502	+	2.74534i	0.128987	+	0.223412i	0.923284	−	0.384117i	$-0.125494\pi$
$151$	1.58502	+	2.74534i	0.128987	+	0.223412i	−0.794297	+	0.607529i	$0.792161\pi$
$152$	−1.96852	+	1.96852i	−0.159668	+	0.159668i
$153$	13.5565	−	16.3083i	1.09598	−	1.31845i
$154$		−	2.75336i		−	0.221872i
$155$		0			0
$156$	0.917815	−	4.18567i	0.0734840	−	0.335122i
$157$	−10.3186	+	2.76487i	−0.823515	+	0.220660i	−0.645883	−	0.763437i	$-0.723511\pi$
$157$	−10.3186	+	2.76487i	−0.823515	+	0.220660i	−0.177633	+	0.984097i	$0.556844\pi$
$158$	−9.44008	+	2.52946i	−0.751013	+	0.201233i
$159$	3.34495	+	3.05092i	0.265272	+	0.241953i
$160$		0			0
$161$		−	14.8288i		−	1.16867i
$162$	8.97261	+	0.701625i	0.704955	+	0.0551249i
$163$	15.7354	−	15.7354i	1.23249	−	1.23249i	0.269490	−	0.963003i	$-0.413145\pi$
$163$	15.7354	−	15.7354i	1.23249	−	1.23249i	0.963003	−	0.269490i	$-0.0868552\pi$
$164$	−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	$-0.0330512\pi$
$167$	1.05230	+	3.92724i	0.0814295	+	0.303899i	−0.913185	+	0.407546i	$0.866385\pi$
$168$	−3.50702	+	2.24561i	−0.270573	+	0.173253i
$169$	5.95761	−	3.43963i	0.458277	−	0.264587i
$170$		0			0
$171$	0.766284	+	8.31648i	0.0585992	+	0.635977i
$172$	−6.35785	−	6.35785i	−0.484781	−	0.484781i
$173$	1.44105	−	5.37809i	0.109561	−	0.408889i	−0.889261	−	0.457400i	$-0.848781\pi$
$173$	1.44105	−	5.37809i	0.109561	−	0.408889i	0.998823	+	0.0485110i	$0.0154476\pi$
$174$	−0.705388	−	2.21934i	−0.0534754	−	0.168248i
$175$		0			0
$176$	0.991757	+	0.572591i	0.0747565	+	0.0431607i
$177$	−2.09336	+	4.04407i	−0.157347	+	0.303971i
$178$	−4.71209	−	1.26260i	−0.353186	−	0.0946359i
$179$	−0.310192			−0.0231848			−0.0115924	−	0.999933i	$-0.503690\pi$
$179$	−0.310192			−0.0231848			−0.0115924	+	0.999933i	$0.503690\pi$
$180$		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
$183$	6.61785	+	10.3352i	0.489206	+	0.764003i
$184$	5.34131	+	3.08381i	0.393767	+	0.227341i
$185$		0			0
$186$	−2.92322	+	3.20495i	−0.214341	+	0.234998i
$187$	2.09522	−	7.81948i	0.153218	−	0.571817i
$188$	−8.72003	−	8.72003i	−0.635974	−	0.635974i
$189$	−1.54491	+	12.3972i	−0.112375	+	0.901765i
$190$		0			0
$191$	−12.3541	+	7.13262i	−0.893909	+	0.516098i	−0.875219	−	0.483727i	$-0.839283\pi$
$191$	−12.3541	+	7.13262i	−0.893909	+	0.516098i	−0.0186896	+	0.999825i	$0.505949\pi$
$192$	−0.0795432	−	1.73022i	−0.00574054	−	0.124868i
$193$	2.48506	+	9.27437i	0.178879	+	0.667584i	0.995858	+	0.0909176i	$0.0289800\pi$
$193$	2.48506	+	9.27437i	0.178879	+	0.667584i	−0.816980	+	0.576666i	$0.804353\pi$
$194$	−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	$-0.824855\pi$
$197$	−4.62495	+	4.62495i	−0.329514	+	0.329514i	0.522887	+	0.852402i	$0.324855\pi$
$198$	3.22290	−	1.18991i	0.229042	−	0.0845633i
$199$			4.07227i			0.288675i	0.989528	+	0.144338i	$0.0461051\pi$
$199$			4.07227i			0.288675i	−0.989528	+	0.144338i	$0.953895\pi$
$200$		0			0
$201$	0.0931843	−	0.0296174i	0.00657271	−	0.00208905i
$202$	−0.703872	+	0.188602i	−0.0495243	+	0.0132700i
$203$	3.12243	−	0.836654i	0.219152	−	0.0587216i
$204$	−11.6687	+	3.70875i	−0.816972	+	0.259664i
$205$		0			0
$206$		−	1.36541i		−	0.0951324i
$207$	17.3576	−	6.40851i	1.20644	−	0.445422i
$208$	−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	0.477282	+	0.878750i	$0.341622\pi$
$211$	−7.58800	+	13.1428i	−0.522379	+	0.904788i	−0.999661	+	0.0260371i	$0.991711\pi$
$212$	−0.676517	−	2.52480i	−0.0464634	−	0.173404i
$213$	0.723847	+	15.7451i	0.0495972	+	1.07884i
$214$	0.488928	−	0.282283i	0.0334224	−	0.0192964i
$215$		0			0
$216$	−4.14418	−	3.13461i	−0.281976	−	0.213283i
$217$	−4.25782	−	4.25782i	−0.289040	−	0.289040i
$218$	−3.51926	+	13.1341i	−0.238354	+	0.889551i
$219$	12.9212	−	14.1665i	0.873133	−	0.957282i
$220$		0			0
$221$	15.1458	+	8.74443i	1.01882	+	0.588214i
$222$	−10.7884	−	16.8485i	−0.724069	−	1.13079i
$223$	−8.21978	−	2.20248i	−0.550437	−	0.147489i	−0.0271279	−	0.999632i	$-0.508636\pi$
$223$	−8.21978	−	2.20248i	−0.550437	−	0.147489i	−0.523309	+	0.852143i	$0.675303\pi$
$224$	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	$-0.652849\pi$
$227$	−19.6687	−	5.27021i	−1.30546	−	0.349796i	−0.843511	+	0.537112i	$0.819515\pi$
$228$	2.21661	−	4.28217i	0.146799	−	0.283594i
$229$	−12.2032	−	7.04551i	−0.806409	−	0.465580i	0.0392983	−	0.999228i	$-0.487488\pi$
$229$	−12.2032	−	7.04551i	−0.806409	−	0.465580i	−0.845707	+	0.533647i	$0.820821\pi$
$230$		0			0
$231$	1.44455	+	4.54492i	0.0950441	+	0.299034i
$232$	−0.347982	+	1.29869i	−0.0228461	+	0.0852630i
$233$	−0.643009	−	0.643009i	−0.0421249	−	0.0421249i	0.685731	−	0.727855i	$-0.259483\pi$
$233$	−0.643009	−	0.643009i	−0.0421249	−	0.0421249i	−0.727855	+	0.685731i	$0.759483\pi$
$234$	0.680985	+	7.39074i	0.0445174	+	0.483148i
$235$		0			0
$236$	2.27688	−	1.31456i	0.148212	−	0.0855703i
$237$	14.2555	−	9.12805i	0.925993	−	0.592931i
$238$	−4.39890	−	16.4169i	−0.285139	−	1.06415i
$239$	−5.34131	+	9.25142i	−0.345501	+	0.598425i	−0.985445	−	0.169997i	$-0.945624\pi$
$239$	−5.34131	+	9.25142i	−0.345501	+	0.598425i	0.639944	+	0.768422i	$0.278958\pi$
$240$		0			0
$241$	−10.5666	−	18.3019i	−0.680654	−	1.17893i	−0.974782	−	0.223161i	$-0.928362\pi$
$241$	−10.5666	−	18.3019i	−0.680654	−	1.17893i	0.294127	−	0.955766i	$-0.404971\pi$
$242$	−6.85084	+	6.85084i	−0.440389	+	0.440389i
$243$	−15.1790	+	3.54930i	−0.973734	+	0.227688i
$244$		−	7.08551i		−	0.453603i
$245$		0			0
$246$	2.52424	+	2.30235i	0.160940	+	0.146792i
$247$	−6.65274	+	1.78260i	−0.423303	+	0.113424i
$248$	2.41912	−	0.648201i	0.153614	−	0.0411608i
$249$	1.03889	−	4.73785i	0.0658372	−	0.300249i
$250$		0			0
$251$			24.6952i			1.55874i	0.626561	+	0.779372i	$0.284462\pi$
$251$			24.6952i			1.55874i	−0.626561	+	0.779372i	$0.715538\pi$
$252$	4.61082	−	5.54674i	0.290454	−	0.349412i
$253$	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	$-0.0309223\pi$
$257$	1.36020	+	5.07632i	0.0848467	+	0.316652i	−0.910438	+	0.413645i	$0.864256\pi$
$258$	13.8304	+	7.15914i	0.861043	+	0.445709i
$259$	24.0508	−	13.8857i	1.49444	−	0.862818i
$260$		0			0
$261$	2.32874	+	3.29334i	0.144145	+	0.203852i
$262$	4.06902	+	4.06902i	0.251385	+	0.251385i
$263$	3.86551	−	14.4263i	0.238358	−	0.889563i	−0.738249	−	0.674529i	$-0.764347\pi$
$263$	3.86551	−	14.4263i	0.238358	−	0.889563i	0.976606	−	0.215034i	$-0.0689864\pi$
$264$	−1.93748	−	0.424842i	−0.119244	−	0.0261472i
$265$		0			0
$266$	5.79660	+	3.34667i	0.355413	+	0.205198i
$267$	8.44057	−	0.388037i	0.516555	−	0.0237475i
$268$	−0.0545285	−	0.0146109i	−0.00333086	−	0.000892501i
$269$	20.0071			1.21985			0.609927	−	0.792457i	$-0.291199\pi$
$269$	20.0071			1.21985			0.609927	+	0.792457i	$0.291199\pi$
$270$		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
$273$	−10.2918	+	0.473145i	−0.622891	+	0.0286360i
$274$	9.00683	+	5.20010i	0.544123	+	0.314149i
$275$		0			0
$276$	−10.4347	−	2.28807i	−0.628095	−	0.137726i
$277$	0.723941	−	2.70178i	0.0434974	−	0.162334i	−0.940761	−	0.339071i	$-0.889887\pi$
$277$	0.723941	−	2.70178i	0.0434974	−	0.162334i	0.984258	+	0.176736i	$0.0565540\pi$
$278$	−1.79251	−	1.79251i	−0.107508	−	0.107508i
$279$	3.14383	−	6.82401i	0.188216	−	0.408543i
$280$		0			0
$281$	13.0998	−	7.56319i	0.781470	−	0.451182i	−0.0554808	−	0.998460i	$-0.517669\pi$
$281$	13.0998	−	7.56319i	0.781470	−	0.451182i	0.836951	+	0.547278i	$0.184336\pi$
$282$	18.9689	+	9.81904i	1.12958	+	0.584715i
$283$	6.22154	+	23.2191i	0.369832	+	1.38023i	0.860750	+	0.509027i	$0.169995\pi$
$283$	6.22154	+	23.2191i	0.369832	+	1.38023i	−0.490918	+	0.871206i	$0.663339\pi$
$284$	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
$288$	1.03906	+	2.81431i	0.0612271	+	0.165835i
$289$		−	32.9711i		−	1.93948i
$290$		0			0
$291$	2.99546	−	13.6607i	0.175597	−	0.800807i
$292$	−10.6930	+	2.86517i	−0.625758	+	0.167671i
$293$	−14.5851	+	3.90805i	−0.852068	+	0.228311i	−0.658318	−	0.752740i	$-0.728732\pi$
$293$	−14.5851	+	3.90805i	−0.852068	+	0.228311i	−0.193750	+	0.981051i	$0.562065\pi$
$294$	−1.56039	−	1.42322i	−0.0910035	−	0.0830039i
$295$		0			0
$296$			11.5507i			0.671374i
$297$	−4.69570	+	3.65505i	−0.272472	+	0.212088i
$298$	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
$303$	1.06292	−	0.680606i	0.0610630	−	0.0390998i
$304$	−2.41093	+	1.39195i	−0.138276	+	0.0798339i
$305$		0			0
$306$	17.3155	−	12.2439i	0.989861	−	0.699938i
$307$	−8.29531	−	8.29531i	−0.473438	−	0.473438i	0.429587	−	0.903025i	$-0.358659\pi$
$307$	−8.29531	−	8.29531i	−0.473438	−	0.473438i	−0.903025	+	0.429587i	$0.858659\pi$
$308$	0.712623	−	2.65955i	0.0406055	−	0.151542i
$309$	0.716358	+	2.25385i	0.0407522	+	0.128217i
$310$		0			0
$311$	10.8857	+	6.28488i	0.617274	+	0.356383i	0.775807	−	0.630971i	$-0.217343\pi$
$311$	10.8857	+	6.28488i	0.617274	+	0.356383i	−0.158533	+	0.987354i	$0.550676\pi$
$312$	1.96987	−	3.80550i	0.111522	−	0.215444i
$313$	−11.5304	−	3.08956i	−0.651737	−	0.174632i	−0.0822229	−	0.996614i	$-0.526202\pi$
$313$	−11.5304	−	3.08956i	−0.651737	−	0.174632i	−0.569514	+	0.821982i	$0.692869\pi$
$314$	−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	$-0.399302\pi$
$317$	1.87547	+	0.502531i	0.105337	+	0.0282249i	−0.205766	+	0.978601i	$0.565968\pi$
$318$	2.44134	+	3.81270i	0.136904	+	0.213805i
$319$	1.33342	+	0.769849i	0.0746570	+	0.0431033i
$320$		0			0
$321$	−0.658965	+	0.722473i	−0.0367798	+	0.0403245i
$322$	3.83797	−	14.3235i	0.213882	−	0.798218i
$323$	13.9155	+	13.9155i	0.774279	+	0.774279i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$		0			0
$326$	19.2719	−	11.1266i	1.06737	−	0.616247i
$327$	−1.08158	−	23.5265i	−0.0598115	−	1.30102i
$328$	−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	−0.992275	−	0.124058i	$-0.960409\pi$
$331$	−10.9811	−	19.0198i	−0.603575	−	1.04542i	0.388700	−	0.921364i	$-0.372924\pi$
$332$	−1.98017	+	1.98017i	−0.108676	+	0.108676i
$333$	26.6477	+	22.1513i	1.46028	+	1.21388i
$334$			4.06578i			0.222470i
$335$		0			0
$336$	−3.96873	+	1.26141i	−0.216512	+	0.0688156i
$337$	25.8842	−	6.93565i	1.41000	−	0.377809i	0.528076	−	0.849197i	$-0.322914\pi$
$337$	25.8842	−	6.93565i	1.41000	−	0.377809i	0.881926	+	0.471388i	$0.156247\pi$
$338$	6.64485	−	1.78048i	0.361432	−	0.0968454i
$339$	8.44871	−	2.68531i	0.458871	−	0.145846i
$340$		0			0
$341$		−	2.86806i		−	0.155314i
$342$	−1.41229	+	8.23144i	−0.0763680	+	0.445105i
$343$	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	0.778679	+	0.627423i	$0.215890\pi$
$347$	7.78712	+	29.0619i	0.418035	+	1.56013i	−0.360644	+	0.932704i	$0.617443\pi$
$348$	−0.106946	−	2.32628i	−0.00573290	−	0.124702i
$349$	−22.2846	+	12.8660i	−1.19287	+	0.688702i	−0.958956	−	0.283556i	$-0.908486\pi$
$349$	−22.2846	+	12.8660i	−1.19287	+	0.688702i	−0.233911	+	0.972258i	$0.575152\pi$
$350$		0			0
$351$	−5.00162	−	11.8425i	−0.266967	−	0.632104i
$352$	0.809767	+	0.809767i	0.0431607	+	0.0431607i
$353$	4.03627	−	15.0636i	0.214829	−	0.801752i	−0.771398	−	0.636353i	$-0.780442\pi$
$353$	4.03627	−	15.0636i	0.214829	−	0.801752i	0.986227	−	0.165399i	$-0.0528912\pi$
$354$	−3.06872	+	3.36447i	−0.163100	+	0.178819i
$355$		0			0
$356$	−4.22474	−	2.43916i	−0.223911	−	0.129275i
$357$	15.8743	+	24.7912i	0.840156	+	1.31209i
$358$	−0.299622	−	0.0802835i	−0.0158355	−	0.00424312i
$359$	−22.9830			−1.21300			−0.606498	−	0.795085i	$-0.707426\pi$
$359$	−22.9830			−1.21300			−0.606498	+	0.795085i	$0.707426\pi$
$360$		0			0
$361$	11.2499			0.592099
$362$	2.96941	+	0.795652i	0.156069	+	0.0418185i
$363$	7.71427	−	14.9028i	0.404894	−	0.782196i
$364$	5.15136	+	2.97414i	0.270004	+	0.155887i
$365$		0			0
$366$	3.71739	+	11.6959i	0.194311	+	0.611355i
$367$	0.901720	−	3.36526i	0.0470694	−	0.175665i	−0.938389	−	0.345580i	$-0.887682\pi$
$367$	0.901720	−	3.36526i	0.0470694	−	0.175665i	0.985459	+	0.169914i	$0.0543490\pi$
$368$	4.36116	+	4.36116i	0.227341	+	0.227341i
$369$	−5.37464	−	2.47611i	−0.279792	−	0.128901i
$370$		0			0
$371$	−5.44254	+	3.14225i	−0.282563	+	0.163138i
$372$	−3.65312	+	2.33916i	−0.189405	+	0.121280i
$373$	−5.91894	−	22.0898i	−0.306471	−	1.14377i	−0.931671	−	0.363302i	$-0.881649\pi$
$373$	−5.91894	−	22.0898i	−0.306471	−	1.14377i	0.625200	−	0.780464i	$-0.285017\pi$
$374$	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
$378$	−4.70090	+	11.5749i	−0.241788	+	0.595351i
$379$			36.3113i			1.86519i	0.360927	+	0.932594i	$0.382460\pi$
$379$			36.3113i			1.86519i	−0.360927	+	0.932594i	$0.617540\pi$
$380$		0			0
$381$	−8.84644	−	8.06880i	−0.453217	−	0.413377i
$382$	−13.7792	+	3.69212i	−0.705003	+	0.188905i
$383$	−16.0342	+	4.29635i	−0.819308	+	0.219533i	−0.644044	−	0.764988i	$-0.722745\pi$
$383$	−16.0342	+	4.29635i	−0.819308	+	0.219533i	−0.175264	+	0.984521i	$0.556078\pi$
$384$	0.370982	−	1.69185i	0.0189316	−	0.0863371i
$385$		0			0
$386$			9.60153i			0.488705i
$387$	−26.5856	−	4.56137i	−1.35142	−	0.231867i
$388$	−5.70947	+	5.70947i	−0.289855	+	0.289855i
$389$	−11.7878	−	20.4171i	−0.597667	−	1.03519i	−0.993164	−	0.116723i	$-0.962761\pi$
$389$	−11.7878	−	20.4171i	−0.597667	−	1.03519i	0.395497	−	0.918467i	$-0.370572\pi$
$390$		0			0
$391$	21.7995	−	37.7578i	1.10245	−	1.90950i
$392$	0.315588	+	1.17779i	0.0159396	+	0.0594874i
$393$	−8.85146	−	4.58185i	−0.446497	−	0.231124i
$394$	−5.66439	+	3.27034i	−0.285368	+	0.164757i
$395$		0			0
$396$	3.42106	−	0.315217i	0.171915	−	0.0158403i
$397$	−27.6509	−	27.6509i	−1.38776	−	1.38776i	−0.830011	−	0.557748i	$-0.811666\pi$
$397$	−27.6509	−	27.6509i	−1.38776	−	1.38776i	−0.557748	−	0.830011i	$-0.688334\pi$
$398$	−1.05398	+	3.93351i	−0.0528312	+	0.197169i
$399$	−11.3242	−	2.48311i	−0.566917	−	0.124311i
$400$		0			0
$401$	−26.4658	−	15.2801i	−1.32164	−	0.763050i	−0.337651	−	0.941272i	$-0.609632\pi$
$401$	−26.4658	−	15.2801i	−1.32164	−	0.763050i	−0.983990	+	0.178222i	$0.942966\pi$
$402$	0.0976747	−	0.00449038i	0.00487157	−	0.000223960i
$403$	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
$408$	−12.2310	+	0.562293i	−0.605524	+	0.0278376i
$409$	−2.43668	−	1.40682i	−0.120486	−	0.0695626i	0.438546	−	0.898709i	$-0.355494\pi$
$409$	−2.43668	−	1.40682i	−0.120486	−	0.0695626i	−0.559032	+	0.829146i	$0.688827\pi$
$410$		0			0
$411$	−17.5956	−	3.85828i	−0.867928	−	0.190315i
$412$	0.353393	−	1.31888i	0.0174104	−	0.0649766i
$413$	−4.46974	−	4.46974i	−0.219942	−	0.219942i
$414$	18.4248	−	1.69767i	0.905529	−	0.0834358i
$415$		0			0
$416$	−2.14256	+	1.23701i	−0.105048	+	0.0606493i
$417$	3.89931	+	2.01843i	0.190950	+	0.0988429i
$418$	0.825136	+	3.07945i	0.0403587	+	0.150621i
$419$	−2.23812	+	3.87654i	−0.109339	+	0.189381i	−0.915503	−	0.402311i	$-0.868207\pi$
$419$	−2.23812	+	3.87654i	−0.109339	+	0.189381i	0.806163	+	0.591693i	$0.201540\pi$
$420$		0			0
$421$	2.85177	+	4.93941i	0.138987	+	0.240732i	0.927113	−	0.374781i	$-0.122282\pi$
$421$	2.85177	+	4.93941i	0.138987	+	0.240732i	−0.788127	+	0.615513i	$0.788949\pi$
$422$	−10.7310	+	10.7310i	−0.522379	+	0.522379i
$423$	−36.4632	−	6.25609i	−1.77290	−	0.304181i
$424$		−	2.61386i		−	0.126940i
$425$		0			0
$426$	−3.37595	+	15.3960i	−0.163565	+	0.745937i
$427$	−16.4552	+	4.40916i	−0.796324	+	0.213374i
$428$	0.545328	−	0.146120i	0.0263594	−	0.00706299i
$429$	−3.62564	−	3.30693i	−0.175048	−	0.159660i
$430$		0			0
$431$			28.4120i			1.36856i	0.729221	+	0.684278i	$0.239883\pi$
$431$			28.4120i			1.36856i	−0.729221	+	0.684278i	$0.760117\pi$
$432$	−3.19168	−	4.10039i	−0.153560	−	0.197280i
$433$	−20.2290	+	20.2290i	−0.972142	+	0.972142i	−0.999622	−	0.0274806i	$-0.991252\pi$
$433$	−20.2290	+	20.2290i	−0.972142	+	0.972142i	0.0274806	+	0.999622i	$0.491252\pi$
$434$	−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
$438$	16.1475	−	10.3395i	0.771555	−	0.494041i
$439$	12.4785	−	7.20447i	0.595567	−	0.343851i	−0.171729	−	0.985144i	$-0.554935\pi$
$439$	12.4785	−	7.20447i	0.595567	−	0.343851i	0.767296	+	0.641293i	$0.221602\pi$
$440$		0			0
$441$	3.32239	+	1.53063i	0.158209	+	0.0728871i
$442$	12.3665	+	12.3665i	0.588214	+	0.588214i
$443$	−6.94511	+	25.9195i	−0.329972	+	1.23147i	0.579246	+	0.815153i	$0.303347\pi$
$443$	−6.94511	+	25.9195i	−0.329972	+	1.23147i	−0.909218	+	0.416320i	$0.863320\pi$
$444$	−6.06007	−	19.0666i	−0.287598	−	0.904860i
$445$		0			0
$446$	−7.36965	−	4.25487i	−0.348963	−	0.201474i
$447$	−10.3397	+	19.9747i	−0.489050	+	0.944772i
$448$	2.32238	+	0.622279i	0.109722	+	0.0293999i
$449$	−1.72288			−0.0813077			−0.0406538	−	0.999173i	$-0.512944\pi$
$449$	−1.72288			−0.0813077			−0.0406538	+	0.999173i	$0.512944\pi$
$450$		0			0
$451$	−2.25891			−0.106368
$452$	−4.94392	−	1.32472i	−0.232542	−	0.0623095i
$453$	−2.96081	−	4.62397i	−0.139111	−	0.217253i
$454$	−17.6345	−	10.1813i	−0.827626	−	0.477830i
$455$		0			0
$456$	3.24939	−	3.56256i	0.152167	−	0.166832i
$457$	3.30155	−	12.3215i	0.154440	−	0.576377i	−0.844713	−	0.535220i	$-0.820229\pi$
$457$	3.30155	−	12.3215i	0.154440	−	0.576377i	0.999153	−	0.0411576i	$-0.0131046\pi$
$458$	−9.96386	−	9.96386i	−0.465580	−	0.465580i
$459$	−22.1586	+	29.2953i	−1.03428	+	1.36739i
$460$		0			0
$461$	8.72418	−	5.03691i	0.406326	−	0.234592i	−0.282884	−	0.959154i	$-0.591291\pi$
$461$	8.72418	−	5.03691i	0.406326	−	0.234592i	0.689210	+	0.724562i	$0.257958\pi$
$462$	0.219011	+	4.76393i	0.0101893	+	0.221638i
$463$	−9.90706	−	36.9737i	−0.460420	−	1.71831i	−0.671644	−	0.740874i	$-0.734412\pi$
$463$	−9.90706	−	36.9737i	−0.460420	−	1.71831i	0.211224	−	0.977438i	$-0.432255\pi$
$464$	−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	$-0.592535\pi$
$467$	14.5094	−	14.5094i	0.671413	−	0.671413i	0.958042	+	0.286629i	$0.0925347\pi$
$468$	−1.25508	+	7.31516i	−0.0580162	+	0.338143i
$469$			0.135728i			0.00626733i
$470$		0			0
$471$	17.6336	−	5.60461i	0.812513	−	0.258247i
$472$	2.53953	−	0.680464i	0.116891	−	0.0313209i
$473$	−9.94589	+	2.66499i	−0.457313	+	0.122537i
$474$	16.1322	−	5.12743i	0.740979	−	0.235511i
$475$		0			0
$476$		−	16.9961i		−	0.779013i
$477$	−6.03020	−	5.01270i	−0.276104	−	0.229516i
$478$	−7.55375	+	7.55375i	−0.345501	+	0.345501i
$479$	2.27813	+	3.94584i	0.104091	+	0.180290i	0.913366	−	0.407139i	$-0.133473\pi$
$479$	2.27813	+	3.94584i	0.104091	+	0.180290i	−0.809276	+	0.587429i	$0.800140\pi$
$480$		0			0
$481$	−14.2884	+	24.7482i	−0.651493	+	1.12842i
$482$	−5.46967	−	20.4131i	−0.249137	−	0.929791i
$483$	1.17953	+	25.6571i	0.0536705	+	1.16744i
$484$	−8.39054	+	4.84428i	−0.381388	+	0.220194i
$485$		0			0
$486$	−15.5804	−	0.500258i	−0.706743	−	0.0226921i
$487$	18.4889	+	18.4889i	0.837814	+	0.837814i	0.988571	−	0.150757i	$-0.0481710\pi$
$487$	18.4889	+	18.4889i	0.837814	+	0.837814i	−0.150757	+	0.988571i	$0.548171\pi$
$488$	1.83386	−	6.84408i	0.0830151	−	0.309817i
$489$	−25.9741	+	28.4774i	−1.17459	+	1.28779i
$490$		0			0
$491$	−0.730071	−	0.421507i	−0.0329476	−	0.0190223i	0.483436	−	0.875380i	$-0.339389\pi$
$491$	−0.730071	−	0.421507i	−0.0329476	−	0.0190223i	−0.516383	+	0.856358i	$0.672722\pi$
$492$	1.84234	+	2.87722i	0.0830590	+	0.129715i
$493$	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
$498$	2.22974	−	4.30753i	0.0999171	−	0.193025i
$499$	−8.45869	−	4.88363i	−0.378663	−	0.218621i	0.298573	−	0.954387i	$-0.403489\pi$
$499$	−8.45869	−	4.88363i	−0.378663	−	0.218621i	−0.677236	+	0.735765i	$0.736823\pi$
$500$		0			0
$501$	−2.13310	−	6.71130i	−0.0953000	−	0.299839i
$502$	−6.39158	+	23.8537i	−0.285270	+	1.06464i
$503$	−22.3161	−	22.3161i	−0.995025	−	0.995025i	0.00496279	−	0.999988i	$-0.498420\pi$
$503$	−22.3161	−	22.3161i	−0.995025	−	0.995025i	−0.999988	+	0.00496279i	$0.998420\pi$
$504$	5.88931	−	4.16437i	0.262331	−	0.185496i
$505$		0			0
$506$	6.11678	−	3.53152i	0.271924	−	0.156995i
$507$	−10.0344	+	6.42521i	−0.445643	+	0.285354i
$508$	1.78919	+	6.67736i	0.0793826	+	0.296260i
$509$	3.83647	−	6.64497i	0.170049	−	0.294533i	−0.768388	−	0.639984i	$-0.778941\pi$
$509$	3.83647	−	6.64497i	0.170049	−	0.294533i	0.938437	+	0.345451i	$0.112274\pi$
$510$		0			0
$511$	13.3080	+	23.0501i	0.588712	+	1.01968i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.98736	−	14.3284i	−0.0877442	−	0.632615i
$514$			5.25539i			0.231805i
$515$		0			0
$516$	11.5062	+	10.4948i	0.506533	+	0.462007i
$517$	−13.6412	+	3.65514i	−0.599938	+	0.160753i
$518$	26.8252	−	7.18779i	1.17863	−	0.315813i
$519$	−2.06556	+	9.41992i	−0.0906678	+	0.413489i
$520$		0			0
$521$		−	23.2333i		−	1.01787i	−0.860805	−	0.508934i	$-0.830040\pi$
$521$		−	23.2333i		−	1.01787i	0.860805	−	0.508934i	$-0.169960\pi$
$522$	1.39701	+	3.78384i	0.0611456	+	0.165614i
$523$	3.86103	−	3.86103i	0.168831	−	0.168831i	−0.617634	−	0.786465i	$-0.711909\pi$
$523$	3.86103	−	3.86103i	0.168831	−	0.168831i	0.786465	+	0.617634i	$0.211909\pi$
$524$	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
$528$	−1.76151	−	0.911824i	−0.0766598	−	0.0396820i
$529$	13.0246	−	7.51973i	0.566285	−	0.326945i
$530$		0			0
$531$	3.30031	−	7.16366i	0.143221	−	0.310876i
$532$	4.73291	+	4.73291i	0.205198	+	0.205198i
$533$	1.26305	−	4.71378i	0.0547089	−	0.204176i
$534$	8.25340	+	1.80977i	0.357160	+	0.0783163i
$535$		0			0
$536$	−0.0488889	−	0.0282260i	−0.00211168	−	0.00121918i
$537$	0.536701	−	0.0246737i	0.0231604	−	0.00106475i
$538$	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
$543$	−5.31899	+	0.244529i	−0.228260	+	0.0104937i
$544$	6.12195	+	3.53451i	0.262477	+	0.151541i
$545$		0			0
$546$	−10.0636	−	2.20670i	−0.430683	−	0.0944381i
$547$	−7.10984	+	26.5343i	−0.303995	+	1.13452i	0.629812	+	0.776747i	$0.283132\pi$
$547$	−7.10984	+	26.5343i	−0.303995	+	1.13452i	−0.933807	+	0.357777i	$0.883535\pi$
$548$	7.35405	+	7.35405i	0.314149	+	0.314149i
$549$	−12.2725	−	17.3559i	−0.523776	−	0.740731i
$550$		0			0
$551$	−3.24150	+	1.87148i	−0.138092	+	0.0797277i
$552$	−9.48696	−	4.91081i	−0.403792	−	0.209018i
$553$	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	$-0.615003\pi$
$557$	13.7347	−	13.7347i	0.581958	−	0.581958i	0.935441	+	0.353483i	$0.115003\pi$
$558$	4.80289	−	5.77780i	0.203323	−	0.244594i
$559$		−	22.2447i		−	0.940852i
$560$		0			0
$561$	−3.00322	+	13.6961i	−0.126796	+	0.578250i
$562$	14.6110	−	3.91500i	0.616326	−	0.165144i
$563$	14.3759	−	3.85201i	0.605872	−	0.162343i	0.0571749	−	0.998364i	$-0.481791\pi$
$563$	14.3759	−	3.85201i	0.605872	−	0.162343i	0.548697	+	0.836021i	$0.315124\pi$
$564$	15.7812	+	14.3940i	0.664509	+	0.606096i
$565$		0			0
$566$			24.0382i			1.01040i
$567$	1.68692	−	21.5729i	0.0708439	−	0.905975i
$568$	6.43471	−	6.43471i	0.269994	−	0.269994i
$569$	14.7082	+	25.4753i	0.616599	+	1.06798i	0.990102	+	0.140351i	$0.0448232\pi$
$569$	14.7082	+	25.4753i	0.616599	+	1.06798i	−0.373503	+	0.927629i	$0.621843\pi$
$570$		0			0
$571$	15.2909	−	26.4847i	0.639906	−	1.10835i	−0.345548	−	0.938401i	$-0.612307\pi$
$571$	15.2909	−	26.4847i	0.639906	−	1.10835i	0.985453	−	0.169948i	$-0.0543599\pi$
$572$	0.733286	+	2.73666i	0.0306602	+	0.114426i
$573$	20.8079	−	13.3237i	0.869264	−	0.556606i
$574$	−4.10717	+	2.37128i	−0.171430	+	0.0989751i
$575$		0			0
$576$	0.275255	+	2.98735i	0.0114690	+	0.124473i
$577$	2.75877	+	2.75877i	0.114849	+	0.114849i	0.762196	−	0.647347i	$-0.224121\pi$
$577$	2.75877	+	2.75877i	0.114849	+	0.114849i	−0.647347	+	0.762196i	$0.724121\pi$
$578$	8.53354	−	31.8476i	0.354949	−	1.32469i
$579$	−5.03742	−	15.8491i	−0.209348	−	0.658665i
$580$		0			0
$581$	5.83093	+	3.36649i	0.241908	+	0.139665i
$582$	6.42905	−	12.4200i	0.266493	−	0.514825i
$583$	−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	$-0.308878\pi$
$587$	15.5484	+	4.16617i	0.641750	+	0.171956i	0.0767539	+	0.997050i	$0.475544\pi$
$588$	−1.13886	−	1.77858i	−0.0469658	−	0.0733475i
$589$	6.03808	+	3.48608i	0.248795	+	0.143642i
$590$		0			0
$591$	7.63432	−	8.37008i	0.314034	−	0.344299i
$592$	−2.98955	+	11.1572i	−0.122870	+	0.458557i
$593$	31.4829	+	31.4829i	1.29285	+	1.29285i	0.933018	+	0.359830i	$0.117165\pi$
$593$	31.4829	+	31.4829i	1.29285	+	1.29285i	0.359830	+	0.933018i	$0.382835\pi$
$594$	−5.48169	+	2.31517i	−0.224917	+	0.0949927i
$595$		0			0
$596$	11.2461	−	6.49294i	0.460658	−	0.265961i
$597$	−0.323921	−	7.04593i	−0.0132572	−	0.288371i
$598$	3.94926	+	14.7388i	0.161497	+	0.602716i
$599$	−0.0708577	+	0.122729i	−0.00289517	+	0.00501457i	−0.867469	−	0.497491i	$-0.834255\pi$
$599$	−0.0708577	+	0.122729i	−0.00289517	+	0.00501457i	0.864574	+	0.502505i	$0.167588\pi$
$600$		0			0
$601$	21.9425	+	38.0055i	0.895052	+	1.55028i	0.833740	+	0.552157i	$0.186195\pi$
$601$	21.9425	+	38.0055i	0.895052	+	1.55028i	0.0613115	+	0.998119i	$0.480472\pi$
$602$	−15.2862	+	15.2862i	−0.623018	+	0.623018i
$603$	−0.158874	+	0.0586570i	−0.00646984	+	0.00238870i
$604$			3.17004i			0.128987i
$605$		0			0
$606$	1.20285	−	0.382312i	0.0488626	−	0.0155304i
$607$	32.2841	−	8.65049i	1.31037	−	0.351113i	0.465008	−	0.885306i	$-0.346051\pi$
$607$	32.2841	−	8.65049i	1.31037	−	0.351113i	0.845362	+	0.534194i	$0.179385\pi$
$608$	−2.68904	+	0.720527i	−0.109055	+	0.0292212i
$609$	−5.33596	+	1.69597i	−0.216224	+	0.0687240i
$610$		0			0
$611$		−	30.5095i		−	1.23428i
$612$	19.8944	−	7.34512i	0.804185	−	0.296909i
$613$	−6.75021	+	6.75021i	−0.272638	+	0.272638i	−0.830161	−	0.557523i	$-0.811752\pi$
$613$	−6.75021	+	6.75021i	−0.272638	+	0.272638i	0.557523	+	0.830161i	$0.311752\pi$
$614$	−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	−0.894021	−	0.448025i	$-0.852128\pi$
$617$	−8.53953	−	31.8700i	−0.343789	−	1.28304i	0.550232	−	0.835012i	$-0.314539\pi$
$618$	0.108609	+	2.36246i	0.00436889	+	0.0950320i
$619$	13.2360	−	7.64183i	0.532001	−	0.307151i	−0.209830	−	0.977738i	$-0.567291\pi$
$619$	13.2360	−	7.64183i	0.532001	−	0.307151i	0.741831	+	0.670587i	$0.233958\pi$
$620$		0			0
$621$	−29.5228	+	12.4688i	−1.18471	+	0.500357i
$622$	8.88817	+	8.88817i	0.356383	+	0.356383i
$623$	−3.03567	+	11.3293i	−0.121622	+	0.453898i
$624$	2.88769	−	3.16599i	0.115600	−	0.126741i
$625$		0			0
$626$	−10.3379	−	5.96858i	−0.413185	−	0.238552i
$627$	−2.97766	−	4.65028i	−0.118916	−	0.185714i
$628$	−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
$633$	12.0835	−	23.3435i	0.480276	−	0.927823i
$634$	1.68150	+	0.970815i	0.0667809	+	0.0385560i
$635$		0			0
$636$	1.37136	+	4.31465i	0.0543778	+	0.171087i
$637$	−0.780770	+	2.91387i	−0.0309352	+	0.115452i
$638$	1.08873	+	1.08873i	0.0431033	+	0.0431033i
$639$	−2.50484	−	27.1850i	−0.0990897	−	1.07542i
$640$		0			0
$641$	−23.0771	+	13.3236i	−0.911491	+	0.526250i	−0.880911	−	0.473283i	$-0.843069\pi$
$641$	−23.0771	+	13.3236i	−0.911491	+	0.526250i	−0.0305804	+	0.999532i	$0.509736\pi$
$642$	−0.823501	+	0.527303i	−0.0325010	+	0.0208110i
$643$	3.67008	+	13.6969i	0.144734	+	0.540153i	0.999767	+	0.0215806i	$0.00686984\pi$
$643$	3.67008	+	13.6969i	0.144734	+	0.540153i	−0.855033	+	0.518573i	$0.826463\pi$
$644$	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	$-0.536591\pi$
$647$	22.3507	−	22.3507i	0.878698	−	0.878698i	0.993400	+	0.114702i	$0.0365912\pi$
$648$	7.41970	+	5.09393i	0.291473	+	0.200108i
$649$		−	3.01081i		−	0.118185i
$650$		0			0
$651$	7.70566	+	7.02830i	0.302009	+	0.275461i
$652$	21.4950	−	5.75956i	0.841809	−	0.225562i
$653$	−24.6425	+	6.60293i	−0.964334	+	0.258393i	−0.706434	−	0.707779i	$-0.749697\pi$
$653$	−24.6425	+	6.60293i	−0.964334	+	0.258393i	−0.257900	+	0.966172i	$0.583031\pi$
$654$	5.04438	−	23.0048i	0.197251	−	0.899558i
$655$		0			0
$656$		−	1.97253i		−	0.0770143i
$657$	−21.2297	+	25.5390i	−0.828249	+	0.996370i
$658$	−20.9656	+	20.9656i	−0.817323	+	0.817323i
$659$	−10.2346	−	17.7269i	−0.398684	−	0.690540i	0.594880	−	0.803814i	$-0.297200\pi$
$659$	−10.2346	−	17.7269i	−0.398684	−	0.690540i	−0.993564	+	0.113274i	$0.963866\pi$
$660$		0			0
$661$	−0.883223	+	1.52979i	−0.0343534	+	0.0595018i	−0.882691	−	0.469954i	$-0.844271\pi$
$661$	−0.883223	+	1.52979i	−0.0343534	+	0.0595018i	0.848338	+	0.529456i	$0.177604\pi$
$662$	−5.68423	−	21.2138i	−0.220924	−	0.824499i
$663$	−26.9012	−	13.9251i	−1.04476	−	0.540805i
$664$	−2.42521	+	1.40019i	−0.0941163	+	0.0543381i
$665$		0			0
$666$	20.0065	+	28.2934i	0.775236	+	1.09635i
$667$	5.86358	+	5.86358i	0.227039	+	0.227039i
$668$	−1.05230	+	3.92724i	−0.0407148	+	0.151950i
$669$	14.3973	+	3.15696i	0.556630	+	0.122055i
$670$		0			0
$671$	−7.02711	−	4.05710i	−0.271278	−	0.156623i
$672$	−4.15998	+	0.191246i	−0.160475	+	0.00737747i
$673$	13.4819	+	3.61246i	0.519688	+	0.139250i	0.509122	−	0.860694i	$-0.329970\pi$
$673$	13.4819	+	3.61246i	0.519688	+	0.139250i	0.0105656	+	0.999944i	$0.496637\pi$
$674$	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	$-0.405839\pi$
$677$	1.70954	+	0.458071i	0.0657031	+	0.0176051i	−0.225818	+	0.974170i	$0.572505\pi$
$678$	8.85583	−	0.407128i	0.340106	−	0.0156356i
$679$	16.8124	+	9.70666i	0.645202	+	0.372508i
$680$		0			0
$681$	34.4504	+	7.55413i	1.32014	+	0.289475i
$682$	0.742309	−	2.77034i	0.0284245	−	0.106082i
$683$	22.8964	+	22.8964i	0.876105	+	0.876105i	0.993129	−	0.117024i	$-0.0373354\pi$
$683$	22.8964	+	22.8964i	0.876105	+	0.876105i	−0.117024	+	0.993129i	$0.537335\pi$
$684$	−3.49462	+	7.58543i	−0.133620	+	0.290036i
$685$		0			0
$686$	17.1142	−	9.88088i	0.653423	−	0.377254i
$687$	21.6747	+	11.2196i	0.826940	+	0.428055i
$688$	−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	0.997157	−	0.0753461i	$-0.0240062\pi$
$691$	11.3908	+	19.7295i	0.433327	+	0.750545i	−0.563830	+	0.825891i	$0.690673\pi$
$692$	3.93703	−	3.93703i	0.149664	−	0.149664i
$693$	−2.86090	−	7.74883i	−0.108677	−	0.294354i
$694$			30.0871i			1.14209i
$695$		0			0
$696$	0.498785	−	2.27470i	0.0189064	−	0.0862222i
$697$	−13.4687	+	3.60893i	−0.510164	+	0.136698i
$698$	−24.8552	+	6.65994i	−0.940784	+	0.252082i
$699$	1.16370	+	1.06140i	0.0440150	+	0.0401459i
$700$		0			0
$701$		−	26.0321i		−	0.983220i	−0.870816	−	0.491610i	$-0.836409\pi$
$701$		−	26.0321i		−	0.983220i	0.870816	−	0.491610i	$-0.163591\pi$
$702$	−1.76614	−	12.7335i	−0.0666586	−	0.480593i
$703$	−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
$708$	−3.83494	+	2.45558i	−0.144126	+	0.0922865i
$709$	−2.58254	+	1.49103i	−0.0969892	+	0.0559968i	−0.547710	−	0.836668i	$-0.684500\pi$
$709$	−2.58254	+	1.49103i	−0.0969892	+	0.0559968i	0.450721	+	0.892665i	$0.351167\pi$
$710$		0			0
$711$	−23.9391	+	16.9275i	−0.897786	+	0.634831i
$712$	−3.44949	−	3.44949i	−0.129275	−	0.129275i
$713$	3.99786	−	14.9202i	0.149721	−	0.558766i
$714$	8.91694	+	28.0551i	0.333708	+	1.04993i
$715$		0			0
$716$	−0.268634	−	0.155096i	−0.0100393	−	0.00579621i
$717$	8.50577	−	16.4319i	0.317654	−	0.613660i
$718$	−22.1999	−	5.94843i	−0.828491	−	0.221994i
$719$	−7.38853			−0.275546			−0.137773	−	0.990464i	$-0.543994\pi$
$719$	−7.38853			−0.275546			−0.137773	+	0.990464i	$0.543994\pi$
$720$		0			0
$721$	−3.28285			−0.122260
$722$	10.8665	+	2.91168i	0.404411	+	0.108362i
$723$	19.7384	+	30.8258i	0.734077	+	1.14643i
$724$	2.66230	+	1.53708i	0.0989437	+	0.0571252i
$725$		0			0
$726$	11.3086	−	12.3984i	0.419700	−	0.460149i
$727$	5.57881	−	20.8204i	0.206906	−	0.772185i	−0.781954	−	0.623337i	$-0.785777\pi$
$727$	5.57881	−	20.8204i	0.206906	−	0.772185i	0.988860	−	0.148849i	$-0.0475567\pi$
$728$	4.20607	+	4.20607i	0.155887	+	0.155887i
$729$	25.9808	−	7.34847i	0.962250	−	0.272166i
$730$		0			0
$731$	−55.0446	+	31.7800i	−2.03590	+	1.17543i
$732$	0.563604	+	12.2595i	0.0208314	+	0.453125i
$733$	1.74734	+	6.52116i	0.0645395	+	0.240865i	0.990658	−	0.136367i	$-0.0435427\pi$
$733$	1.74734	+	6.52116i	0.0645395	+	0.240865i	−0.926119	+	0.377232i	$0.876876\pi$
$734$	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
$738$	−4.55064	−	3.78279i	−0.167511	−	0.139247i
$739$		−	12.8637i		−	0.473200i	−0.971607	−	0.236600i	$-0.923967\pi$
$739$		−	12.8637i		−	0.473200i	0.971607	−	0.236600i	$-0.0760331\pi$
$740$		0			0
$741$	11.3689	−	3.61347i	0.417648	−	0.132744i
$742$	−6.07037	+	1.62655i	−0.222850	+	0.0597125i
$743$	32.7401	−	8.77270i	1.20112	−	0.321839i	0.397848	−	0.917452i	$-0.369757\pi$
$743$	32.7401	−	8.77270i	1.20112	−	0.321839i	0.803272	+	0.595613i	$0.203091\pi$
$744$	−4.13406	+	1.31396i	−0.151562	+	0.0481720i
$745$		0			0
$746$		−	22.8690i		−	0.837295i
$747$	−1.42065	+	8.28018i	−0.0519790	+	0.302956i
$748$	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	−0.717392	−	0.696670i	$-0.754664\pi$
$751$	6.70415	−	11.6119i	0.244638	−	0.423725i	0.962030	+	0.272945i	$0.0879975\pi$
$752$	−3.19175	−	11.9118i	−0.116391	−	0.434378i
$753$	−1.96433	−	42.7281i	−0.0715843	−	1.55710i
$754$	−2.88067	+	1.66316i	−0.104908	+	0.0605686i
$755$		0			0
$756$	−7.53654	+	9.96386i	−0.274101	+	0.362382i
$757$	1.11492	+	1.11492i	0.0405223	+	0.0405223i	0.727078	−	0.686555i	$-0.240878\pi$
$757$	1.11492	+	1.11492i	0.0405223	+	0.0405223i	−0.686555	+	0.727078i	$0.740878\pi$
$758$	−9.39806	+	35.0741i	−0.341353	+	1.27395i
$759$	−8.24404	+	9.03857i	−0.299240	+	0.328079i
$760$		0			0
$761$	−29.7531	−	17.1780i	−1.07855	−	0.622702i	−0.148046	−	0.988981i	$-0.547298\pi$
$761$	−29.7531	−	17.1780i	−1.07855	−	0.622702i	−0.930505	+	0.366279i	$0.880632\pi$
$762$	−6.45665	−	10.0835i	−0.233900	−	0.365286i
$763$	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
$768$	0.796225	−	1.53819i	0.0287313	−	0.0555046i
$769$	14.4890	+	8.36522i	0.522486	+	0.301658i	0.737951	−	0.674854i	$-0.235793\pi$
$769$	14.4890	+	8.36522i	0.522486	+	0.301658i	−0.215465	+	0.976512i	$0.569127\pi$
$770$		0			0
$771$	−2.75723	−	8.67497i	−0.0992992	−	0.312421i
$772$	−2.48506	+	9.27437i	−0.0894393	+	0.333792i
$773$	−5.20827	−	5.20827i	−0.187328	−	0.187328i	0.607212	−	0.794540i	$-0.292288\pi$
$773$	−5.20827	−	5.20827i	−0.187328	−	0.187328i	−0.794540	+	0.607212i	$0.792288\pi$
$774$	−24.4991	−	11.2868i	−0.880604	−	0.405696i
$775$		0			0
$776$	−6.99265	+	4.03721i	−0.251022	+	0.144927i
$777$	−40.5087	+	25.9385i	−1.45324	+	0.930539i
$778$	−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
$783$	−4.29121	−	5.51297i	−0.153355	−	0.197018i
$784$			1.21934i			0.0435478i
$785$		0			0
$786$	−7.36398	−	6.71666i	−0.262665	−	0.239575i
$787$	44.6815	−	11.9724i	1.59272	−	0.426769i	0.649888	−	0.760030i	$-0.274816\pi$
$787$	44.6815	−	11.9724i	1.59272	−	0.426769i	0.942834	+	0.333262i	$0.108149\pi$
$788$	−6.31780	+	1.69285i	−0.225062	+	0.0603053i
$789$	−5.54069	+	25.2682i	−0.197254	+	0.899571i
$790$		0			0
$791$			12.3060i			0.437550i
$792$	3.38607	+	0.580958i	0.120319	+	0.0206434i
$793$	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	−0.631434	−	0.775430i	$-0.717533\pi$
$797$	−13.3339	−	49.7628i	−0.472311	−	1.76269i	0.159123	−	0.987259i	$-0.449134\pi$
$798$	−10.2956	−	5.32941i	−0.364461	−	0.188659i
$799$	−75.4958	+	43.5875i	−2.67085	+	1.54202i
$800$		0			0
$801$	−14.5732	+	1.34278i	−0.514919	+	0.0474448i
$802$	−21.6093	−	21.6093i	−0.763050	−	0.763050i
$803$	−3.28114	+	12.2454i	−0.115789	+	0.432131i
$804$	0.0955087	+	0.0209427i	0.00336833	+	0.000738592i
$805$		0			0
$806$	5.36595	+	3.09803i	0.189008	+	0.109124i
$807$	−34.6168	+	1.59143i	−1.21857	+	0.0560210i
$808$	−0.703872	−	0.188602i	−0.0247621	−	0.00663499i
$809$	−18.0260			−0.633762			−0.316881	−	0.948465i	$-0.602636\pi$
$809$	−18.0260			−0.633762			−0.316881	+	0.948465i	$0.602636\pi$
$810$		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
$813$	5.23762	−	0.240788i	0.183691	−	0.00844481i
$814$	11.4555	+	6.61386i	0.401517	+	0.231816i
$815$		0			0
$816$	−11.9598	−	2.62248i	−0.418675	−	0.0918051i
$817$	6.47852	−	24.1782i	0.226655	−	0.845886i
$818$	−1.98954	−	1.98954i	−0.0695626	−	0.0695626i
$819$	17.7696	−	1.63729i	0.620918	−	0.0572117i
$820$		0			0
$821$	5.91006	−	3.41218i	0.206263	−	0.119086i	−0.393311	−	0.919406i	$-0.628670\pi$
$821$	5.91006	−	3.41218i	0.206263	−	0.119086i	0.599573	+	0.800320i	$0.295337\pi$
$822$	−15.9975	−	8.28090i	−0.557976	−	0.288829i
$823$	−5.27529	−	19.6876i	−0.183885	−	0.686268i	−0.994866	−	0.101196i	$-0.967733\pi$
$823$	−5.27529	−	19.6876i	−0.183885	−	0.686268i	0.810982	−	0.585072i	$-0.198934\pi$
$824$	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	−0.0384654	+	0.999260i	$0.512247\pi$
$827$	−29.8425	+	29.8425i	−1.03773	+	1.03773i	−0.999260	+	0.0384654i	$0.987753\pi$
$828$	18.2364	+	3.12887i	0.633758	+	0.108736i
$829$		−	20.4152i		−	0.709050i	−0.935047	−	0.354525i	$-0.884643\pi$
$829$		−	20.4152i		−	0.709050i	0.935047	−	0.354525i	$-0.115357\pi$
$830$		0			0
$831$	−1.03767	+	4.73227i	−0.0359964	+	0.164161i
$832$	−2.38971	+	0.640322i	−0.0828484	+	0.0221992i
$833$	8.32583	−	2.23090i	0.288473	−	0.0772961i
$834$	3.24403	+	2.95887i	0.112332	+	0.102457i
$835$		0			0
$836$			3.18808i			0.110262i
$837$	−4.89673	+	12.0571i	−0.169256	+	0.416755i
$838$	−3.16518	+	3.16518i	−0.109339	+	0.109339i
$839$	9.70261	+	16.8054i	0.334971	+	0.580187i	0.983479	−	0.181021i	$-0.0579400\pi$
$839$	9.70261	+	16.8054i	0.334971	+	0.580187i	−0.648508	+	0.761208i	$0.724607\pi$
$840$		0			0
$841$	13.5962	−	23.5492i	0.468833	−	0.812043i
$842$	1.47618	+	5.50919i	0.0508726	+	0.189859i
$843$	−22.0640	+	14.1280i	−0.759926	+	0.486595i
$844$	−13.1428	+	7.58800i	−0.452394	+	0.261190i
$845$		0			0
$846$	−33.6015	−	15.4803i	−1.15524	−	0.532223i
$847$	16.4715	+	16.4715i	0.565967	+	0.565967i
$848$	0.676517	−	2.52480i	0.0232317	−	0.0867018i
$849$	−12.6116	−	39.6794i	−0.432828	−	1.36179i
$850$		0			0
$851$	61.6961	+	35.6203i	2.11492	+	1.22105i
$852$	−7.24569	+	13.9976i	−0.248233	+	0.479550i
$853$	0.496213	+	0.132960i	0.0169900	+	0.00455246i	0.267304	−	0.963612i	$-0.413867\pi$
$853$	0.496213	+	0.132960i	0.0169900	+	0.00455246i	−0.250314	+	0.968165i	$0.580534\pi$
$854$	−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	$-0.141332\pi$
$857$	43.0427	+	11.5332i	1.47031	+	0.393968i	0.567272	+	0.823530i	$0.307999\pi$
$858$	−2.64620	−	4.13263i	−0.0903399	−	0.141086i
$859$	25.5432	+	14.7474i	0.871522	+	0.503174i	0.867854	−	0.496820i	$-0.165499\pi$
$859$	25.5432	+	14.7474i	0.871522	+	0.503174i	0.00366859	+	0.999993i	$0.498832\pi$
$860$		0			0
$861$	5.53554	−	6.06903i	0.188651	−	0.206832i
$862$	−7.35356	+	27.4438i	−0.250463	+	0.934741i
$863$	6.17951	+	6.17951i	0.210353	+	0.210353i	0.804417	−	0.594064i	$-0.202478\pi$
$863$	6.17951	+	6.17951i	0.210353	+	0.210353i	−0.594064	+	0.804417i	$0.702478\pi$
$864$	−2.02166	−	4.78674i	−0.0687783	−	0.162848i
$865$		0			0
$866$	−24.7753	+	14.3040i	−0.841899	+	0.486071i
$867$	2.62263	+	57.0473i	0.0890691	+	1.93743i
$868$	−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
$873$	−4.09620	+	23.8744i	−0.138635	+	0.808026i
$874$			17.1700i			0.580785i
$875$		0			0
$876$	18.2733	−	5.80794i	0.617398	−	0.196232i
$877$	−20.0896	+	5.38298i	−0.678376	+	0.181770i	−0.581525	−	0.813528i	$-0.697544\pi$
$877$	−20.0896	+	5.38298i	−0.678376	+	0.181770i	−0.0968513	+	0.995299i	$0.530877\pi$
$878$	13.9180	−	3.72931i	0.469709	−	0.125858i
$879$	24.9245	−	7.92195i	0.840684	−	0.267201i
$880$		0			0
$881$			28.3087i			0.953745i	0.878972	+	0.476873i	$0.158230\pi$
$881$			28.3087i			0.953745i	−0.878972	+	0.476873i	$0.841770\pi$
$882$	2.81302	+	2.33837i	0.0947194	+	0.0787371i
$883$	−15.1647	+	15.1647i	−0.510333	+	0.510333i	−0.914629	−	0.404295i	$-0.867517\pi$
$883$	−15.1647	+	15.1647i	−0.510333	+	0.510333i	0.404295	+	0.914629i	$0.367517\pi$
$884$	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	0.779796	+	0.626034i	$0.215323\pi$
$887$	12.4339	+	46.4040i	0.417490	+	1.55809i	−0.362306	+	0.932059i	$0.618011\pi$
$888$	−0.918784	−	19.9854i	−0.0308324	−	0.670665i
$889$	14.3940	−	8.31036i	0.482758	−	0.278721i
$890$		0			0
$891$	7.83387	−	6.69757i	0.262445	−	0.224377i
$892$	−6.01730	−	6.01730i	−0.201474	−	0.201474i
$893$	8.88553	−	33.1613i	0.297343	−	1.10970i
$894$	−15.1572	+	16.6180i	−0.506933	+	0.555789i
$895$		0			0
$896$	2.08219	+	1.20215i	0.0695609	+	0.0401610i
$897$	−14.2517	−	22.2571i	−0.475849	−	0.743144i
$898$	−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
$903$	17.2127	−	33.2524i	0.572804	−	1.10657i
$904$	−4.43259	−	2.55916i	−0.147426	−	0.0851164i
$905$		0			0
$906$	−1.66316	−	5.23273i	−0.0552546	−	0.173846i
$907$	−9.66001	+	36.0516i	−0.320755	+	1.19707i	0.597755	+	0.801679i	$0.296059\pi$
$907$	−9.66001	+	36.0516i	−0.320755	+	1.19707i	−0.918511	+	0.395396i	$0.870607\pi$
$908$	−14.3985	−	14.3985i	−0.477830	−	0.477830i
$909$	−1.78495	+	1.26215i	−0.0592030	+	0.0418628i
$910$		0			0
$911$	46.5957	−	26.9020i	1.54378	−	0.891304i	0.545189	−	0.838313i	$-0.316458\pi$
$911$	46.5957	−	26.9020i	1.54378	−	0.891304i	0.998595	−	0.0529906i	$-0.0168753\pi$
$912$	4.06073	−	2.60016i	0.134464	−	0.0860999i
$913$	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
$918$	−28.9858	+	22.5620i	−0.956673	+	0.744658i
$919$		−	23.1668i		−	0.764203i	−0.924120	−	0.382101i	$-0.875201\pi$
$919$		−	23.1668i		−	0.764203i	0.924120	−	0.382101i	$-0.124799\pi$
$920$		0			0
$921$	15.0126	+	13.6929i	0.494681	+	0.451196i
$922$	9.73056	−	2.60729i	0.320459	−	0.0858667i
$923$	21.7465	−	5.82696i	0.715795	−	0.191797i
$924$	−1.02145	+	4.65829i	−0.0336032	+	0.153247i
$925$		0			0
$926$		−	38.2779i		−	1.25789i
$927$	−1.41874	−	3.84268i	−0.0465974	−	0.126210i
$928$	−0.950705	+	0.950705i	−0.0312084	+	0.0312084i
$929$	−6.78350	−	11.7494i	−0.222559	−	0.385484i	0.733025	−	0.680202i	$-0.238108\pi$
$929$	−6.78350	−	11.7494i	−0.222559	−	0.385484i	−0.955584	+	0.294717i	$0.904774\pi$
$930$		0			0
$931$	−1.69726	+	2.93974i	−0.0556255	+	0.0963462i
$932$	−0.235358	−	0.878367i	−0.00770940	−	0.0287719i
$933$	−19.3347	−	10.0084i	−0.632989	−	0.327659i
$934$	17.7703	−	10.2597i	0.581461	−	0.335706i
$935$		0			0
$936$	−3.10562	+	6.74106i	−0.101510	+	0.220338i
$937$	6.94086	+	6.94086i	0.226748	+	0.226748i	0.811333	−	0.584585i	$-0.198742\pi$
$937$	6.94086	+	6.94086i	0.226748	+	0.226748i	−0.584585	+	0.811333i	$0.698742\pi$
$938$	−0.0351289	+	0.131103i	−0.00114700	+	0.00428066i
$939$	20.1959	+	4.42847i	0.659069	+	0.144518i
$940$		0			0
$941$	−14.5976	−	8.42791i	−0.475867	−	0.274742i	0.242825	−	0.970070i	$-0.421926\pi$
$941$	−14.5976	−	8.42791i	−0.475867	−	0.274742i	−0.718693	+	0.695328i	$0.755259\pi$
$942$	18.4833	−	0.849730i	0.602219	−	0.0276857i
$943$	−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	$-0.630840\pi$
$947$	−37.0498	−	9.92745i	−1.20396	−	0.322599i	−0.804388	+	0.594105i	$0.797506\pi$
$948$	16.9096	−	0.777383i	0.549199	−	0.0252482i
$949$	−23.7185	−	13.6939i	−0.769935	−	0.444522i
$950$		0			0
$951$	−3.28496	−	0.720309i	−0.106522	−	0.0233576i
$952$	4.39890	−	16.4169i	0.142569	−	0.532076i
$953$	−18.8861	−	18.8861i	−0.611780	−	0.611780i	0.331630	−	0.943410i	$-0.392402\pi$
$953$	−18.8861	−	18.8861i	−0.611780	−	0.611780i	−0.943410	+	0.331630i	$0.892402\pi$
$954$	−4.52734	−	6.40262i	−0.146578	−	0.207293i
$955$		0			0
$956$	−9.25142	+	5.34131i	−0.299212	+	0.172750i
$957$	−2.36835	−	1.22595i	−0.0765578	−	0.0396292i
$958$	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
$963$	1.08269	−	1.30246i	0.0348891	−	0.0419711i
$964$		−	21.1332i		−	0.680654i
$965$		0			0
$966$	−5.50122	+	25.0882i	−0.176999	+	0.807199i
$967$	−30.9494	+	8.29288i	−0.995267	+	0.266681i	−0.719461	−	0.694533i	$-0.755611\pi$
$967$	−30.9494	+	8.29288i	−0.995267	+	0.266681i	−0.275805	+	0.961213i	$0.588945\pi$
$968$	−9.35843	+	2.50758i	−0.300791	+	0.0805968i
$969$	−25.1838	−	22.9700i	−0.809020	−	0.737904i
$970$		0			0
$971$		−	29.2201i		−	0.937716i	−0.883274	−	0.468858i	$-0.844666\pi$
$971$		−	29.2201i		−	0.937716i	0.883274	−	0.468858i	$-0.155334\pi$
$972$	−14.9201	−	4.51572i	−0.478561	−	0.144842i
$973$	−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	0.915788	+	0.401662i	$0.131567\pi$
$977$	10.1124	+	37.7399i	0.323523	+	1.20741i	−0.592265	+	0.805743i	$0.701766\pi$
$978$	−32.4596	+	20.7845i	−1.03794	+	0.664615i
$979$	−4.83811	+	2.79328i	−0.154627	+	0.0892737i
$980$		0			0
$981$	3.74275	+	40.6201i	0.119497	+	1.29690i
$982$	−0.596101	−	0.596101i	−0.0190223	−	0.0190223i
$983$	−2.96514	+	11.0660i	−0.0945732	+	0.352952i	−0.996954	−	0.0779867i	$-0.975151\pi$
$983$	−2.96514	+	11.0660i	−0.0945732	+	0.352952i	0.902381	+	0.430939i	$0.141818\pi$
$984$	1.03488	+	3.25601i	0.0329908	+	0.103798i
$985$		0			0
$986$	8.23096	+	4.75215i	0.262127	+	0.151339i
$987$	23.6079	−	45.6070i	0.751448	−	1.45169i
$988$	−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
$993$	20.5126	+	32.0350i	0.650949	+	1.01660i
$994$	−18.9480	−	10.9396i	−0.600994	−	0.346984i
$995$		0			0
$996$	3.26863	−	3.58365i	0.103571	−	0.113552i
$997$	−14.2233	+	53.0819i	−0.450455	+	1.68112i	0.250661	+	0.968075i	$0.419352\pi$
$997$	−14.2233	+	53.0819i	−0.450455	+	1.68112i	−0.701116	+	0.713047i	$0.747315\pi$
$998$	−6.90650	−	6.90650i	−0.218621	−	0.218621i
$999$	−47.8684	−	36.2071i	−1.51449	−	1.14554i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	5.2	odd	4
90.2.l.b.47.2	yes	16	45.29	odd	6
90.2.l.b.77.2	yes	16	5.4	even	2
90.2.l.b.83.2	yes	16	45.2	even	12
270.2.m.b.17.3		16	15.14	odd	2
270.2.m.b.143.3		16	45.7	odd	12
270.2.m.b.197.4		16	45.34	even	6
270.2.m.b.233.4		16	15.2	even	4
450.2.p.h.257.3		16	1.1	even	1	trivial
450.2.p.h.293.3		16	5.3	odd	4	inner
450.2.p.h.407.3		16	9.2	odd	6	inner
450.2.p.h.443.3		16	45.38	even	12	inner
720.2.cu.b.113.2		16	20.7	even	4
720.2.cu.b.257.1		16	20.19	odd	2
720.2.cu.b.353.1		16	180.47	odd	12
720.2.cu.b.497.2		16	180.119	even	6
810.2.f.c.323.3		16	45.22	odd	12
810.2.f.c.323.6		16	45.32	even	12
810.2.f.c.647.3		16	45.14	odd	6
810.2.f.c.647.6		16	45.4	even	6
1350.2.q.h.143.1		16	45.43	odd	12
1350.2.q.h.557.1		16	3.2	odd	2
1350.2.q.h.1007.2		16	9.7	even	3
1350.2.q.h.1043.2		16	15.8	even	4

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.73022 + 0.0795432i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.69185 - 0.370982i) q^{6} +(0.622279 - 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.98735 - 0.275255i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.73022 + 0.0795432i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.69185 - 0.370982i) q^{6} +(0.622279 - 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.98735 - 0.275255i) q^{9} +(0.991757 - 0.572591i) q^{11} +(-1.53819 - 0.796225i) q^{12} +(0.640322 + 2.38971i) q^{13} +(1.20215 - 2.08219i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.99855 - 4.99855i) q^{17} +(2.95680 + 0.507306i) q^{18} +2.78390i q^{19} +(-0.891952 + 4.06773i) q^{21} +(1.10616 - 0.296395i) q^{22} +(5.95746 - 1.59630i) q^{23} +(-1.27970 - 1.16721i) q^{24} +2.47401i q^{26} +(-5.14688 + 0.713876i) q^{27} +(1.70010 - 1.70010i) q^{28} +(0.672250 + 1.16437i) q^{29} +(1.25223 - 2.16892i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-1.67042 + 1.06960i) q^{33} +(6.12195 - 3.53451i) q^{34} +(2.72474 + 1.25529i) q^{36} +(8.16761 + 8.16761i) q^{37} +(-0.720527 + 2.68904i) q^{38} +(-1.29799 - 4.08381i) q^{39} +(-1.70826 - 0.986264i) q^{41} +(-1.91436 + 3.69827i) q^{42} +(-8.68498 - 2.32713i) q^{43} +1.14518 q^{44} +6.16761 q^{46} +(-11.9118 - 3.19175i) q^{47} +(-0.933998 - 1.45865i) q^{48} +(1.05598 + 0.609669i) q^{49} +(-8.25101 + 9.04622i) q^{51} +(-0.640322 + 2.38971i) q^{52} +(-1.84828 - 1.84828i) q^{53} +(-5.15627 - 0.642559i) q^{54} +(2.08219 - 1.20215i) q^{56} +(-0.221441 - 4.81678i) q^{57} +(0.347982 + 1.29869i) q^{58} +(1.31456 - 2.27688i) q^{59} +(-3.54275 - 6.13623i) q^{61} +(1.77092 - 1.77092i) q^{62} +(1.21972 - 7.10903i) q^{63} +1.00000i q^{64} +(-1.89033 + 0.600817i) q^{66} +(-0.0545285 + 0.0146109i) q^{67} +(6.82815 - 1.82960i) q^{68} +(-10.1808 + 3.23582i) q^{69} -9.10005i q^{71} +(2.30701 + 1.91774i) q^{72} +(-7.82779 + 7.82779i) q^{73} +(5.77537 + 10.0032i) q^{74} +(-1.39195 + 2.41093i) q^{76} +(-0.712623 - 2.65955i) q^{77} +(-0.196791 - 4.28060i) q^{78} +(-8.46375 + 4.88655i) q^{79} +(8.84847 - 1.64456i) q^{81} +(-1.39479 - 1.39479i) q^{82} +(-0.724794 + 2.70497i) q^{83} +(-2.80632 + 3.07678i) q^{84} +(-7.78674 - 4.49568i) q^{86} +(-1.25576 - 1.96115i) q^{87} +(1.10616 + 0.296395i) q^{88} -4.87832 q^{89} +5.94827 q^{91} +(5.95746 + 1.59630i) q^{92} +(-1.99411 + 3.85233i) q^{93} +(-10.6798 - 6.16599i) q^{94} +(-0.524648 - 1.65068i) q^{96} +(-2.08981 + 7.79929i) q^{97} +(0.862203 + 0.862203i) q^{98} +(2.80511 - 1.98351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{16} + 24 q^{21} - 8 q^{22} + 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{36} - 24 q^{38} + 24 q^{41} - 24 q^{42} - 32 q^{46} - 48 q^{47} - 48 q^{51} + 24 q^{56} - 24 q^{57} - 16 q^{58} - 24 q^{61} + 48 q^{63} - 48 q^{66} + 16 q^{67} + 24 q^{68} + 24 q^{72} - 16 q^{73} + 16 q^{76} + 72 q^{77} + 24 q^{81} + 16 q^{82} - 48 q^{83} - 48 q^{86} + 48 q^{87} - 8 q^{88} + 24 q^{92} - 72 q^{93} + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^16 + 24 * q^21 - 8 * q^22 + 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^36 - 24 * q^38 + 24 * q^41 - 24 * q^42 - 32 * q^46 - 48 * q^47 - 48 * q^51 + 24 * q^56 - 24 * q^57 - 16 * q^58 - 24 * q^61 + 48 * q^63 - 48 * q^66 + 16 * q^67 + 24 * q^68 + 24 * q^72 - 16 * q^73 + 16 * q^76 + 72 * q^77 + 24 * q^81 + 16 * q^82 - 48 * q^83 - 48 * q^86 + 48 * q^87 - 8 * q^88 + 24 * q^92 - 72 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more