LMFDB - Embedded newform 450.2.p.h.407.3

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			407.3
Root			$0.500000 + 2.00333i$ of defining polynomial
Character	$\chi$	$=$	450.407
Dual form			450.2.p.h.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.0795432 + 1.73022i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.69185 + 0.370982i) q^{6} +(-2.32238 + 0.622279i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.98735 - 0.275255i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.0795432 + 1.73022i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.69185 + 0.370982i) q^{6} +(-2.32238 + 0.622279i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.98735 - 0.275255i) q^{9} +(0.991757 + 0.572591i) q^{11} +(-0.796225 - 1.53819i) q^{12} +(-2.38971 - 0.640322i) q^{13} +(-1.20215 - 2.08219i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.99855 + 4.99855i) q^{17} +(-0.507306 - 2.95680i) q^{18} +2.78390i q^{19} +(-0.891952 - 4.06773i) q^{21} +(-0.296395 + 1.10616i) q^{22} +(1.59630 - 5.95746i) q^{23} +(1.27970 - 1.16721i) q^{24} -2.47401i q^{26} +(0.713876 - 5.14688i) q^{27} +(1.70010 - 1.70010i) q^{28} +(-0.672250 + 1.16437i) q^{29} +(1.25223 + 2.16892i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.06960 + 1.67042i) q^{33} +(-6.12195 - 3.53451i) q^{34} +(2.72474 - 1.25529i) q^{36} +(8.16761 + 8.16761i) q^{37} +(-2.68904 + 0.720527i) q^{38} +(1.29799 - 4.08381i) q^{39} +(-1.70826 + 0.986264i) q^{41} +(3.69827 - 1.91436i) q^{42} +(2.32713 + 8.68498i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(-3.19175 - 11.9118i) q^{47} +(1.45865 + 0.933998i) q^{48} +(-1.05598 + 0.609669i) q^{49} +(-8.25101 - 9.04622i) q^{51} +(2.38971 - 0.640322i) q^{52} +(1.84828 + 1.84828i) q^{53} +(5.15627 - 0.642559i) q^{54} +(2.08219 + 1.20215i) q^{56} +(-4.81678 - 0.221441i) q^{57} +(-1.29869 - 0.347982i) q^{58} +(-1.31456 - 2.27688i) q^{59} +(-3.54275 + 6.13623i) q^{61} +(-1.77092 + 1.77092i) q^{62} +(7.10903 - 1.21972i) q^{63} +1.00000i q^{64} +(-1.89033 - 0.600817i) q^{66} +(0.0146109 - 0.0545285i) q^{67} +(1.82960 - 6.82815i) q^{68} +(10.1808 + 3.23582i) q^{69} +9.10005i q^{71} +(1.91774 + 2.30701i) q^{72} +(-7.82779 + 7.82779i) q^{73} +(-5.77537 + 10.0032i) q^{74} +(-1.39195 - 2.41093i) q^{76} +(-2.65955 - 0.712623i) q^{77} +(4.28060 + 0.196791i) q^{78} +(8.46375 + 4.88655i) q^{79} +(8.84847 + 1.64456i) q^{81} +(-1.39479 - 1.39479i) q^{82} +(-2.70497 + 0.724794i) q^{83} +(2.80632 + 3.07678i) q^{84} +(-7.78674 + 4.49568i) q^{86} +(-1.96115 - 1.25576i) q^{87} +(-0.296395 - 1.10616i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(1.59630 + 5.95746i) q^{92} +(-3.85233 + 1.99411i) q^{93} +(10.6798 - 6.16599i) q^{94} +(-0.524648 + 1.65068i) q^{96} +(7.79929 - 2.08981i) 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 $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.0795432	+	1.73022i	−0.0459243	+	0.998945i
$3$	−0.0795432	+	1.73022i	−0.0459243	+	0.998945i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.69185	+	0.370982i	−0.690697	+	0.151453i
$7$	−2.32238	+	0.622279i	−0.877776	+	0.235199i	−0.669447	−	0.742860i	$-0.733469\pi$
$7$	−2.32238	+	0.622279i	−0.877776	+	0.235199i	−0.208328	+	0.978059i	$0.566802\pi$
$8$	−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	0.642005	−	0.766700i	$-0.278103\pi$
$11$	0.991757	+	0.572591i	0.299026	+	0.172643i	−0.342979	+	0.939343i	$0.611436\pi$
$12$	−0.796225	−	1.53819i	−0.229850	−	0.444037i
$13$	−2.38971	−	0.640322i	−0.662788	−	0.177593i	−0.0882838	−	0.996095i	$-0.528138\pi$
$13$	−2.38971	−	0.640322i	−0.662788	−	0.177593i	−0.574504	+	0.818502i	$0.694805\pi$
$14$	−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	$0.577826\pi$
$17$	−4.99855	+	4.99855i	−1.21233	+	1.21233i	−0.970259	+	0.242068i	$0.922174\pi$
$18$	−0.507306	−	2.95680i	−0.119573	−	0.696923i
$19$			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
$22$	−0.296395	+	1.10616i	−0.0631917	+	0.235834i
$23$	1.59630	−	5.95746i	0.332851	−	1.24222i	−0.573330	−	0.819325i	$-0.694349\pi$
$23$	1.59630	−	5.95746i	0.332851	−	1.24222i	0.906181	−	0.422891i	$-0.138985\pi$
$24$	1.27970	−	1.16721i	0.261217	−	0.238255i
$25$		0			0
$26$		−	2.47401i		−	0.485194i
$27$	0.713876	−	5.14688i	0.137386	−	0.990518i
$28$	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	$0.761126\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−1.06960	+	1.67042i	−0.186193	+	0.290782i
$34$	−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	$0.351626\pi$
$38$	−2.68904	+	0.720527i	−0.436221	+	0.116885i
$39$	1.29799	−	4.08381i	0.207844	−	0.653932i
$40$		0			0
$41$	−1.70826	+	0.986264i	−0.266785	+	0.154029i	−0.627426	−	0.778676i	$-0.715891\pi$
$41$	−1.70826	+	0.986264i	−0.266785	+	0.154029i	0.360641	+	0.932705i	$0.382558\pi$
$42$	3.69827	−	1.91436i	0.570655	−	0.295393i
$43$	2.32713	+	8.68498i	0.354885	+	1.32445i	0.880630	+	0.473805i	$0.157120\pi$
$43$	2.32713	+	8.68498i	0.354885	+	1.32445i	−0.525745	+	0.850642i	$0.676213\pi$
$44$	−1.14518			−0.172643
$45$		0			0
$46$	6.16761			0.909365
$47$	−3.19175	−	11.9118i	−0.465565	−	1.73751i	−0.655010	−	0.755621i	$-0.727335\pi$
$47$	−3.19175	−	11.9118i	−0.465565	−	1.73751i	0.189445	−	0.981891i	$-0.439331\pi$
$48$	1.45865	+	0.933998i	0.210537	+	0.134811i
$49$	−1.05598	+	0.609669i	−0.150854	+	0.0870956i
$50$		0			0
$51$	−8.25101	−	9.04622i	−1.15537	−	1.26672i
$52$	2.38971	−	0.640322i	0.331394	−	0.0887967i
$53$	1.84828	+	1.84828i	0.253881	+	0.253881i	0.822560	−	0.568679i	$-0.192545\pi$
$53$	1.84828	+	1.84828i	0.253881	+	0.253881i	−0.568679	+	0.822560i	$0.692545\pi$
$54$	5.15627	−	0.642559i	0.701679	−	0.0874413i
$55$		0			0
$56$	2.08219	+	1.20215i	0.278244	+	0.160644i
$57$	−4.81678	−	0.221441i	−0.637998	−	0.0293305i
$58$	−1.29869	−	0.347982i	−0.170526	−	0.0456923i
$59$	−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
$63$	7.10903	−	1.21972i	0.895653	−	0.153670i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.89033	−	0.600817i	−0.232684	−	0.0739555i
$67$	0.0146109	−	0.0545285i	0.00178500	−	0.00666172i	−0.965028	−	0.262148i	$-0.915569\pi$
$67$	0.0146109	−	0.0545285i	0.00178500	−	0.00666172i	0.966813	+	0.255487i	$0.0822357\pi$
$68$	1.82960	−	6.82815i	0.221871	−	0.828035i
$69$	10.1808	+	3.23582i	1.22562	+	0.389547i
$70$		0			0
$71$			9.10005i			1.07998i	0.841672	+	0.539989i	$0.181571\pi$
$71$			9.10005i			1.07998i	−0.841672	+	0.539989i	$0.818429\pi$
$72$	1.91774	+	2.30701i	0.226008	+	0.271883i
$73$	−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
$77$	−2.65955	−	0.712623i	−0.303083	−	0.0812109i
$78$	4.28060	+	0.196791i	0.484682	+	0.0222822i
$79$	8.46375	+	4.88655i	0.952246	+	0.549779i	0.893778	−	0.448510i	$-0.148045\pi$
$79$	8.46375	+	4.88655i	0.952246	+	0.549779i	0.0584679	+	0.998289i	$0.481378\pi$
$80$		0			0
$81$	8.84847	+	1.64456i	0.983163	+	0.182729i
$82$	−1.39479	−	1.39479i	−0.154029	−	0.154029i
$83$	−2.70497	+	0.724794i	−0.296909	+	0.0795565i	−0.404198	−	0.914671i	$-0.632449\pi$
$83$	−2.70497	+	0.724794i	−0.296909	+	0.0795565i	0.107290	+	0.994228i	$0.465783\pi$
$84$	2.80632	+	3.07678i	0.306194	+	0.335704i
$85$		0			0
$86$	−7.78674	+	4.49568i	−0.839666	+	0.484781i
$87$	−1.96115	−	1.25576i	−0.210257	−	0.134632i
$88$	−0.296395	−	1.10616i	−0.0315958	−	0.117917i
$89$	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
$92$	1.59630	+	5.95746i	0.166425	+	0.621108i
$93$	−3.85233	+	1.99411i	−0.399468	+	0.206780i
$94$	10.6798	−	6.16599i	1.10154	−	0.635974i
$95$		0			0
$96$	−0.524648	+	1.65068i	−0.0535466	+	0.168472i
$97$	7.79929	−	2.08981i	0.791898	−	0.212188i	0.159874	−	0.987137i	$-0.448891\pi$
$97$	7.79929	−	2.08981i	0.791898	−	0.212188i	0.632024	+	0.774949i	$0.282225\pi$
$98$	−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	0.468274	−	0.883583i	$-0.344876\pi$
$101$	−0.631074	−	0.364351i	−0.0627942	−	0.0362543i	−0.531068	+	0.847329i	$0.678209\pi$
$102$	6.60245	−	10.3112i	0.653740	−	1.02096i
$103$	1.31888	+	0.353393i	0.129953	+	0.0348209i	0.323209	−	0.946327i	$-0.395238\pi$
$103$	1.31888	+	0.353393i	0.129953	+	0.0348209i	−0.193256	+	0.981148i	$0.561905\pi$
$104$	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	−0.726140	−	0.687547i	$-0.758688\pi$
$107$	−0.399208	+	0.399208i	−0.0385929	+	0.0385929i	0.687547	+	0.726140i	$0.258688\pi$
$108$	1.95521	+	4.81427i	0.188140	+	0.463253i
$109$			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
$112$	−0.622279	+	2.32238i	−0.0587998	+	0.219444i
$113$	−1.32472	+	4.94392i	−0.124619	+	0.465084i	−0.999826	−	0.0186645i	$-0.994059\pi$
$113$	−1.32472	+	4.94392i	−0.124619	+	0.465084i	0.875207	+	0.483749i	$0.160725\pi$
$114$	−1.03278	−	4.70996i	−0.0967285	−	0.441128i
$115$		0			0
$116$		−	1.34450i		−	0.124834i
$117$	6.96265	+	2.57064i	0.643697	+	0.237656i
$118$	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
$122$	−6.84408	−	1.83386i	−0.619633	−	0.166030i
$123$	−1.57058	−	3.03412i	−0.141614	−	0.273578i
$124$	−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	$0.650772\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−15.2121	+	3.33563i	−1.33935	+	0.293686i
$130$		0			0
$131$	4.98351	−	2.87723i	0.435412	−	0.251385i	−0.266238	−	0.963907i	$-0.585781\pi$
$131$	4.98351	−	2.87723i	0.435412	−	0.251385i	0.701649	+	0.712522i	$0.252447\pi$
$132$	0.0910916	−	1.98142i	0.00792850	−	0.172461i
$133$	−1.73236	−	6.46527i	−0.150215	−	0.560610i
$134$	0.0564521			0.00487672
$135$		0			0
$136$	7.06902			0.606164
$137$	2.69177	+	10.0458i	0.229973	+	0.858272i	0.980351	+	0.197262i	$0.0632051\pi$
$137$	2.69177	+	10.0458i	0.229973	+	0.858272i	−0.750377	+	0.661010i	$0.770128\pi$
$138$	−0.490592	+	10.6713i	−0.0417620	+	0.908406i
$139$	2.19537	−	1.26750i	0.186209	−	0.107508i	−0.403998	−	0.914760i	$-0.632380\pi$
$139$	2.19537	−	1.26750i	0.186209	−	0.107508i	0.590207	+	0.807252i	$0.299046\pi$
$140$		0			0
$141$	20.8639	−	4.57494i	1.75706	−	0.385280i
$142$	−8.78997	+	2.35527i	−0.737638	+	0.197650i
$143$	−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
$147$	−0.970868	−	1.87557i	−0.0800759	−	0.154695i
$148$	−11.1572	−	2.98955i	−0.917114	−	0.245740i
$149$	−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
$153$	16.3083	−	13.5565i	1.31845	−	1.09598i
$154$		−	2.75336i		−	0.221872i
$155$		0			0
$156$	0.917815	+	4.18567i	0.0734840	+	0.335122i
$157$	2.76487	−	10.3186i	0.220660	−	0.823515i	−0.763437	−	0.645883i	$-0.776489\pi$
$157$	2.76487	−	10.3186i	0.220660	−	0.823515i	0.984097	−	0.177633i	$-0.0568439\pi$
$158$	−2.52946	+	9.44008i	−0.201233	+	0.751013i
$159$	−3.34495	+	3.05092i	−0.265272	+	0.241953i
$160$		0			0
$161$			14.8288i			1.16867i
$162$	0.701625	+	8.97261i	0.0551249	+	0.704955i
$163$	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
$167$	3.92724	+	1.05230i	0.303899	+	0.0814295i	0.407546	−	0.913185i	$-0.366385\pi$
$167$	3.92724	+	1.05230i	0.303899	+	0.0814295i	−0.103647	+	0.994614i	$0.533051\pi$
$168$	−2.24561	+	3.50702i	−0.173253	+	0.270573i
$169$	−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
$173$	5.37809	−	1.44105i	0.408889	−	0.109561i	−0.0485110	−	0.998823i	$-0.515448\pi$
$173$	5.37809	−	1.44105i	0.408889	−	0.109561i	0.457400	+	0.889261i	$0.348781\pi$
$174$	0.705388	−	2.21934i	0.0534754	−	0.168248i
$175$		0			0
$176$	0.991757	−	0.572591i	0.0747565	−	0.0431607i
$177$	4.04407	−	2.09336i	0.303971	−	0.157347i
$178$	1.26260	+	4.71209i	0.0946359	+	0.353186i
$179$	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	$0.463553\pi$
$182$	1.53953	+	5.74559i	0.114117	+	0.425892i
$183$	−10.3352	−	6.61785i	−0.764003	−	0.489206i
$184$	−5.34131	+	3.08381i	−0.393767	+	0.227341i
$185$		0			0
$186$	−2.92322	−	3.20495i	−0.214341	−	0.234998i
$187$	−7.81948	+	2.09522i	−0.571817	+	0.153218i
$188$	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	−0.0186896	−	0.999825i	$-0.505949\pi$
$191$	−12.3541	−	7.13262i	−0.893909	−	0.516098i	−0.875219	+	0.483727i	$0.839283\pi$
$192$	−1.73022	−	0.0795432i	−0.124868	−	0.00574054i
$193$	−9.27437	−	2.48506i	−0.667584	−	0.178879i	−0.0909176	−	0.995858i	$-0.528980\pi$
$193$	−9.27437	−	2.48506i	−0.667584	−	0.178879i	−0.576666	+	0.816980i	$0.695647\pi$
$194$	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	−0.522887	−	0.852402i	$-0.675145\pi$
$197$	4.62495	−	4.62495i	0.329514	−	0.329514i	0.852402	+	0.522887i	$0.175145\pi$
$198$	1.18991	−	3.22290i	0.0845633	−	0.229042i
$199$			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
$202$	0.188602	−	0.703872i	0.0132700	−	0.0495243i
$203$	0.836654	−	3.12243i	0.0587216	−	0.219152i
$204$	11.6687	+	3.70875i	0.816972	+	0.259664i
$205$		0			0
$206$			1.36541i			0.0951324i
$207$	−6.40851	+	17.3576i	−0.445422	+	1.20644i
$208$	−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	$-0.341622\pi$
$212$	−2.52480	−	0.676517i	−0.173404	−	0.0464634i
$213$	−15.7451	−	0.723847i	−1.07884	−	0.0495972i
$214$	−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
$218$	−13.1341	+	3.51926i	−0.889551	+	0.238354i
$219$	−12.9212	−	14.1665i	−0.873133	−	0.957282i
$220$		0			0
$221$	15.1458	−	8.74443i	1.01882	−	0.588214i
$222$	−16.8485	−	10.7884i	−1.13079	−	0.724069i
$223$	2.20248	+	8.21978i	0.147489	+	0.550437i	0.999632	+	0.0271279i	$0.00863613\pi$
$223$	2.20248	+	8.21978i	0.147489	+	0.550437i	−0.852143	+	0.523309i	$0.824697\pi$
$224$	−2.40430			−0.160644
$225$		0			0
$226$	−5.11832			−0.340465
$227$	−5.27021	−	19.6687i	−0.349796	−	1.30546i	−0.886908	−	0.461946i	$-0.847151\pi$
$227$	−5.27021	−	19.6687i	−0.349796	−	1.30546i	0.537112	−	0.843511i	$-0.319515\pi$
$228$	4.28217	−	2.21661i	0.283594	−	0.146799i
$229$	12.2032	−	7.04551i	0.806409	−	0.465580i	−0.0392983	−	0.999228i	$-0.512512\pi$
$229$	12.2032	−	7.04551i	0.806409	−	0.465580i	0.845707	+	0.533647i	$0.179179\pi$
$230$		0			0
$231$	1.44455	−	4.54492i	0.0950441	−	0.299034i
$232$	1.29869	−	0.347982i	0.0852630	−	0.0228461i
$233$	0.643009	+	0.643009i	0.0421249	+	0.0421249i	0.727855	−	0.685731i	$-0.240517\pi$
$233$	0.643009	+	0.643009i	0.0421249	+	0.0421249i	−0.685731	+	0.727855i	$0.740517\pi$
$234$	−0.680985	+	7.39074i	−0.0445174	+	0.483148i
$235$		0			0
$236$	2.27688	+	1.31456i	0.148212	+	0.0855703i
$237$	−9.12805	+	14.2555i	−0.592931	+	0.925993i
$238$	16.4169	+	4.39890i	1.06415	+	0.285139i
$239$	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
$243$	−3.54930	+	15.1790i	−0.227688	+	0.973734i
$244$		−	7.08551i		−	0.453603i
$245$		0			0
$246$	2.52424	−	2.30235i	0.160940	−	0.146792i
$247$	1.78260	−	6.65274i	0.113424	−	0.423303i
$248$	0.648201	−	2.41912i	0.0411608	−	0.153614i
$249$	−1.03889	−	4.73785i	−0.0658372	−	0.300249i
$250$		0			0
$251$		−	24.6952i		−	1.55874i	−0.626561	−	0.779372i	$-0.715538\pi$
$251$		−	24.6952i		−	1.55874i	0.626561	−	0.779372i	$-0.284462\pi$
$252$	−5.54674	+	4.61082i	−0.349412	+	0.290454i
$253$	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
$257$	5.07632	+	1.36020i	0.316652	+	0.0848467i	0.413645	−	0.910438i	$-0.364256\pi$
$257$	5.07632	+	1.36020i	0.316652	+	0.0848467i	−0.0969925	+	0.995285i	$0.530922\pi$
$258$	−7.15914	−	13.8304i	−0.445709	−	0.861043i
$259$	−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
$263$	14.4263	−	3.86551i	0.889563	−	0.238358i	0.215034	−	0.976606i	$-0.431014\pi$
$263$	14.4263	−	3.86551i	0.889563	−	0.238358i	0.674529	+	0.738249i	$0.264347\pi$
$264$	1.93748	−	0.424842i	0.119244	−	0.0261472i
$265$		0			0
$266$	5.79660	−	3.34667i	0.355413	−	0.205198i
$267$	−0.388037	+	8.44057i	−0.0237475	+	0.516555i
$268$	0.0146109	+	0.0545285i	0.000892501	+	0.00333086i
$269$	−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	$0.529308\pi$
$272$	1.82960	+	6.82815i	0.110936	+	0.414018i
$273$	−0.473145	+	10.2918i	−0.0286360	+	0.622891i
$274$	−9.00683	+	5.20010i	−0.544123	+	0.314149i
$275$		0			0
$276$	−10.4347	+	2.28807i	−0.628095	+	0.137726i
$277$	−2.70178	+	0.723941i	−0.162334	+	0.0434974i	−0.339071	−	0.940761i	$-0.610113\pi$
$277$	−2.70178	+	0.723941i	−0.162334	+	0.0434974i	0.176736	+	0.984258i	$0.443446\pi$
$278$	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	0.836951	−	0.547278i	$-0.184336\pi$
$281$	13.0998	+	7.56319i	0.781470	+	0.451182i	−0.0554808	+	0.998460i	$0.517669\pi$
$282$	9.81904	+	18.9689i	0.584715	+	1.12958i
$283$	−23.2191	−	6.22154i	−1.38023	−	0.369832i	−0.509027	−	0.860750i	$-0.669995\pi$
$283$	−23.2191	−	6.22154i	−1.38023	−	0.369832i	−0.871206	+	0.490918i	$0.836661\pi$
$284$	−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
$288$	−2.81431	−	1.03906i	−0.165835	−	0.0612271i
$289$		−	32.9711i		−	1.93948i
$290$		0			0
$291$	2.99546	+	13.6607i	0.175597	+	0.800807i
$292$	2.86517	−	10.6930i	0.167671	−	0.625758i
$293$	−3.90805	+	14.5851i	−0.228311	+	0.852068i	0.752740	+	0.658318i	$0.228732\pi$
$293$	−3.90805	+	14.5851i	−0.228311	+	0.852068i	−0.981051	+	0.193750i	$0.937935\pi$
$294$	1.56039	−	1.42322i	0.0910035	−	0.0830039i
$295$		0			0
$296$		−	11.5507i		−	0.671374i
$297$	3.65505	−	4.69570i	0.212088	−	0.272472i
$298$	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
$302$	3.06203	+	0.820468i	0.176200	+	0.0472126i
$303$	0.680606	−	1.06292i	0.0390998	−	0.0610630i
$304$	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	$0.858659\pi$
$308$	2.65955	−	0.712623i	0.151542	−	0.0406055i
$309$	−0.716358	+	2.25385i	−0.0407522	+	0.128217i
$310$		0			0
$311$	10.8857	−	6.28488i	0.617274	−	0.356383i	−0.158533	−	0.987354i	$-0.550676\pi$
$311$	10.8857	−	6.28488i	0.617274	−	0.356383i	0.775807	+	0.630971i	$0.217343\pi$
$312$	−3.80550	+	1.96987i	−0.215444	+	0.111522i
$313$	3.08956	+	11.5304i	0.174632	+	0.651737i	0.996614	+	0.0822229i	$0.0262019\pi$
$313$	3.08956	+	11.5304i	0.174632	+	0.651737i	−0.821982	+	0.569514i	$0.807131\pi$
$314$	10.6826			0.602855
$315$		0			0
$316$	−9.77309			−0.549779
$317$	0.502531	+	1.87547i	0.0282249	+	0.105337i	0.978601	−	0.205766i	$-0.0659684\pi$
$317$	0.502531	+	1.87547i	0.0282249	+	0.105337i	−0.950376	+	0.311102i	$0.899302\pi$
$318$	−3.81270	−	2.44134i	−0.213805	−	0.136904i
$319$	−1.33342	+	0.769849i	−0.0746570	+	0.0431033i
$320$		0			0
$321$	−0.658965	−	0.722473i	−0.0367798	−	0.0403245i
$322$	−14.3235	+	3.83797i	−0.798218	+	0.213882i
$323$	−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
$327$	−23.5265	−	1.08158i	−1.30102	−	0.0598115i
$328$	1.90532	+	0.510528i	0.105203	+	0.0281892i
$329$	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
$333$	−22.1513	−	26.6477i	−1.21388	−	1.46028i
$334$			4.06578i			0.222470i
$335$		0			0
$336$	−3.96873	−	1.26141i	−0.216512	−	0.0688156i
$337$	−6.93565	+	25.8842i	−0.377809	+	1.41000i	0.471388	+	0.881926i	$0.343753\pi$
$337$	−6.93565	+	25.8842i	−0.377809	+	1.41000i	−0.849197	+	0.528076i	$0.822914\pi$
$338$	1.78048	−	6.64485i	0.0968454	−	0.361432i
$339$	−8.44871	−	2.68531i	−0.458871	−	0.145846i
$340$		0			0
$341$			2.86806i			0.155314i
$342$	8.23144	−	1.41229i	0.445105	−	0.0763680i
$343$	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
$347$	29.0619	+	7.78712i	1.56013	+	0.418035i	0.932704	−	0.360644i	$-0.117443\pi$
$347$	29.0619	+	7.78712i	1.56013	+	0.418035i	0.627423	+	0.778679i	$0.284110\pi$
$348$	2.32628	+	0.106946i	0.124702	+	0.00573290i
$349$	22.2846	+	12.8660i	1.19287	+	0.688702i	0.958956	−	0.283556i	$-0.0915143\pi$
$349$	22.2846	+	12.8660i	1.19287	+	0.688702i	0.233911	+	0.972258i	$0.424848\pi$
$350$		0			0
$351$	−5.00162	+	11.8425i	−0.266967	+	0.632104i
$352$	0.809767	+	0.809767i	0.0431607	+	0.0431607i
$353$	15.0636	−	4.03627i	0.801752	−	0.214829i	0.165399	−	0.986227i	$-0.447109\pi$
$353$	15.0636	−	4.03627i	0.801752	−	0.214829i	0.636353	+	0.771398i	$0.280442\pi$
$354$	3.06872	+	3.36447i	0.163100	+	0.178819i
$355$		0			0
$356$	−4.22474	+	2.43916i	−0.223911	+	0.129275i
$357$	24.7912	+	15.8743i	1.31209	+	0.840156i
$358$	0.0802835	+	0.299622i	0.00424312	+	0.0158355i
$359$	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
$362$	0.795652	+	2.96941i	0.0418185	+	0.156069i
$363$	14.9028	−	7.71427i	0.782196	−	0.404894i
$364$	−5.15136	+	2.97414i	−0.270004	+	0.155887i
$365$		0			0
$366$	3.71739	−	11.6959i	0.194311	−	0.611355i
$367$	−3.36526	+	0.901720i	−0.175665	+	0.0470694i	−0.345580	−	0.938389i	$-0.612318\pi$
$367$	−3.36526	+	0.901720i	−0.175665	+	0.0470694i	0.169914	+	0.985459i	$0.445651\pi$
$368$	−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
$372$	2.33916	−	3.65312i	0.121280	−	0.189405i
$373$	22.0898	+	5.91894i	1.14377	+	0.306471i	0.780464	−	0.625200i	$-0.214983\pi$
$373$	22.0898	+	5.91894i	1.14377	+	0.306471i	0.363302	+	0.931671i	$0.381649\pi$
$374$	−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
$378$	−11.5749	+	4.70090i	−0.595351	+	0.241788i
$379$			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
$382$	3.69212	−	13.7792i	0.188905	−	0.705003i
$383$	−4.29635	+	16.0342i	−0.219533	+	0.819308i	0.764988	+	0.644044i	$0.222745\pi$
$383$	−4.29635	+	16.0342i	−0.219533	+	0.819308i	−0.984521	+	0.175264i	$0.943922\pi$
$384$	−0.370982	−	1.69185i	−0.0189316	−	0.0863371i
$385$		0			0
$386$		−	9.60153i		−	0.488705i
$387$	−4.56137	−	26.5856i	−0.231867	−	1.35142i
$388$	−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
$392$	1.17779	+	0.315588i	0.0594874	+	0.0159396i
$393$	4.58185	+	8.85146i	0.231124	+	0.446497i
$394$	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	$-0.688334\pi$
$398$	−3.93351	+	1.05398i	−0.197169	+	0.0528312i
$399$	11.3242	−	2.48311i	0.566917	−	0.124311i
$400$		0			0
$401$	−26.4658	+	15.2801i	−1.32164	+	0.763050i	−0.983990	−	0.178222i	$-0.942966\pi$
$401$	−26.4658	+	15.2801i	−1.32164	+	0.763050i	−0.337651	+	0.941272i	$0.609632\pi$
$402$	−0.00449038	+	0.0976747i	−0.000223960	+	0.00487157i
$403$	−1.60366	−	5.98494i	−0.0798840	−	0.298131i
$404$	0.728702			0.0362543
$405$		0			0
$406$	3.23258			0.160430
$407$	3.42359	+	12.7770i	0.169701	+	0.633332i
$408$	−0.562293	+	12.2310i	−0.0278376	+	0.605524i
$409$	2.43668	−	1.40682i	0.120486	−	0.0695626i	−0.438546	−	0.898709i	$-0.644506\pi$
$409$	2.43668	−	1.40682i	0.120486	−	0.0695626i	0.559032	+	0.829146i	$0.311173\pi$
$410$		0			0
$411$	−17.5956	+	3.85828i	−0.867928	+	0.190315i
$412$	−1.31888	+	0.353393i	−0.0649766	+	0.0174104i
$413$	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
$417$	2.01843	+	3.89931i	0.0988429	+	0.190950i
$418$	−3.07945	−	0.825136i	−0.150621	−	0.0403587i
$419$	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
$423$	6.25609	+	36.4632i	0.304181	+	1.77290i
$424$		−	2.61386i		−	0.126940i
$425$		0			0
$426$	−3.37595	−	15.3960i	−0.163565	−	0.745937i
$427$	4.40916	−	16.4552i	0.213374	−	0.796324i
$428$	0.146120	−	0.545328i	0.00706299	−	0.0263594i
$429$	3.62564	−	3.30693i	0.175048	−	0.159660i
$430$		0			0
$431$		−	28.4120i		−	1.36856i	−0.729221	−	0.684278i	$-0.760117\pi$
$431$		−	28.4120i		−	1.36856i	0.729221	−	0.684278i	$-0.239883\pi$
$432$	−4.10039	−	3.19168i	−0.197280	−	0.153560i
$433$	−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
$437$	16.5850	+	4.44393i	0.793368	+	0.212582i
$438$	10.3395	−	16.1475i	0.494041	−	0.771555i
$439$	−12.4785	−	7.20447i	−0.595567	−	0.343851i	0.171729	−	0.985144i	$-0.445065\pi$
$439$	−12.4785	−	7.20447i	−0.595567	−	0.343851i	−0.767296	+	0.641293i	$0.778398\pi$
$440$		0			0
$441$	3.32239	−	1.53063i	0.158209	−	0.0728871i
$442$	12.3665	+	12.3665i	0.588214	+	0.588214i
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.815153	−	0.579246i	$-0.803347\pi$
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.416320	+	0.909218i	$0.636680\pi$
$444$	6.06007	−	19.0666i	0.287598	−	0.904860i
$445$		0			0
$446$	−7.36965	+	4.25487i	−0.348963	+	0.201474i
$447$	19.9747	−	10.3397i	0.944772	−	0.489050i
$448$	−0.622279	−	2.32238i	−0.0293999	−	0.109722i
$449$	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
$452$	−1.32472	−	4.94392i	−0.0623095	−	0.232542i
$453$	4.62397	+	2.96081i	0.217253	+	0.139111i
$454$	17.6345	−	10.1813i	0.827626	−	0.477830i
$455$		0			0
$456$	3.24939	+	3.56256i	0.152167	+	0.166832i
$457$	−12.3215	+	3.30155i	−0.576377	+	0.154440i	−0.535220	−	0.844713i	$-0.679771\pi$
$457$	−12.3215	+	3.30155i	−0.576377	+	0.154440i	−0.0411576	+	0.999153i	$0.513105\pi$
$458$	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	0.689210	−	0.724562i	$-0.257958\pi$
$461$	8.72418	+	5.03691i	0.406326	+	0.234592i	−0.282884	+	0.959154i	$0.591291\pi$
$462$	4.76393	+	0.219011i	0.221638	+	0.0101893i
$463$	36.9737	+	9.90706i	1.71831	+	0.460420i	0.977438	−	0.211224i	$-0.0677450\pi$
$463$	36.9737	+	9.90706i	1.71831	+	0.460420i	0.740874	+	0.671644i	$0.234412\pi$
$464$	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	−0.958042	−	0.286629i	$-0.907465\pi$
$467$	−14.5094	+	14.5094i	−0.671413	+	0.671413i	0.286629	+	0.958042i	$0.407465\pi$
$468$	−7.31516	+	1.25508i	−0.338143	+	0.0580162i
$469$			0.135728i			0.00626733i
$470$		0			0
$471$	17.6336	+	5.60461i	0.812513	+	0.258247i
$472$	−0.680464	+	2.53953i	−0.0313209	+	0.116891i
$473$	−2.66499	+	9.94589i	−0.122537	+	0.457313i
$474$	−16.1322	−	5.12743i	−0.740979	−	0.235511i
$475$		0			0
$476$			16.9961i			0.779013i
$477$	−5.01270	−	6.03020i	−0.229516	−	0.276104i
$478$	−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
$482$	−20.4131	−	5.46967i	−0.929791	−	0.249137i
$483$	−25.6571	−	1.17953i	−1.16744	−	0.0536705i
$484$	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	$0.548171\pi$
$488$	6.84408	−	1.83386i	0.309817	−	0.0830151i
$489$	25.9741	+	28.4774i	1.17459	+	1.28779i
$490$		0			0
$491$	−0.730071	+	0.421507i	−0.0329476	+	0.0190223i	−0.516383	−	0.856358i	$-0.672722\pi$
$491$	−0.730071	+	0.421507i	−0.0329476	+	0.0190223i	0.483436	+	0.875380i	$0.339389\pi$
$492$	2.87722	+	1.84234i	0.129715	+	0.0830590i
$493$	−2.45989	−	9.18045i	−0.110788	−	0.413467i
$494$	6.88742			0.309880
$495$		0			0
$496$	2.50446			0.112453
$497$	−5.66277	−	21.1337i	−0.254010	−	0.947978i
$498$	4.30753	−	2.22974i	0.193025	−	0.0999171i
$499$	8.45869	−	4.88363i	0.378663	−	0.218621i	−0.298573	−	0.954387i	$-0.596511\pi$
$499$	8.45869	−	4.88363i	0.378663	−	0.218621i	0.677236	+	0.735765i	$0.263177\pi$
$500$		0			0
$501$	−2.13310	+	6.71130i	−0.0953000	+	0.299839i
$502$	23.8537	−	6.39158i	1.06464	−	0.285270i
$503$	22.3161	+	22.3161i	0.995025	+	0.995025i	0.999988	−	0.00496279i	$-0.00157971\pi$
$503$	22.3161	+	22.3161i	0.995025	+	0.995025i	−0.00496279	+	0.999988i	$0.501580\pi$
$504$	−5.88931	−	4.16437i	−0.262331	−	0.185496i
$505$		0			0
$506$	6.11678	+	3.53152i	0.271924	+	0.156995i
$507$	6.42521	−	10.0344i	0.285354	−	0.445643i
$508$	−6.67736	−	1.78919i	−0.296260	−	0.0793826i
$509$	−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
$513$	14.3284	+	1.98736i	0.632615	+	0.0877442i
$514$			5.25539i			0.231805i
$515$		0			0
$516$	11.5062	−	10.4948i	0.506533	−	0.462007i
$517$	3.65514	−	13.6412i	0.160753	−	0.599938i
$518$	7.18779	−	26.8252i	0.315813	−	1.17863i
$519$	2.06556	+	9.41992i	0.0906678	+	0.413489i
$520$		0			0
$521$			23.2333i			1.01787i	0.860805	+	0.508934i	$0.169960\pi$
$521$			23.2333i			1.01787i	−0.860805	+	0.508934i	$0.830040\pi$
$522$	3.78384	+	1.39701i	0.165614	+	0.0611456i
$523$	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
$527$	−17.1008	−	4.58215i	−0.744923	−	0.199602i
$528$	0.911824	+	1.76151i	0.0396820	+	0.0766598i
$529$	−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
$533$	4.71378	−	1.26305i	0.204176	−	0.0547089i
$534$	−8.25340	+	1.80977i	−0.357160	+	0.0783163i
$535$		0			0
$536$	−0.0488889	+	0.0282260i	−0.00211168	+	0.00121918i
$537$	−0.0246737	+	0.536701i	−0.00106475	+	0.0231604i
$538$	−5.17822	−	19.3254i	−0.223249	−	0.833176i
$539$	−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	$0.651923\pi$
$542$	−0.783481	−	2.92399i	−0.0336534	−	0.125596i
$543$	−0.244529	+	5.31899i	−0.0104937	+	0.228260i
$544$	−6.12195	+	3.53451i	−0.262477	+	0.151541i
$545$		0			0
$546$	−10.0636	+	2.20670i	−0.430683	+	0.0944381i
$547$	26.5343	−	7.10984i	1.13452	−	0.303995i	0.357777	−	0.933807i	$-0.383535\pi$
$547$	26.5343	−	7.10984i	1.13452	−	0.303995i	0.776747	+	0.629812i	$0.216868\pi$
$548$	−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
$552$	−4.91081	−	9.48696i	−0.209018	−	0.403792i
$553$	−22.6968	−	6.08159i	−0.965166	−	0.258615i
$554$	−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	−0.935441	−	0.353483i	$-0.884997\pi$
$557$	−13.7347	+	13.7347i	−0.581958	+	0.581958i	0.353483	+	0.935441i	$0.384997\pi$
$558$	5.77780	−	4.80289i	0.244594	−	0.203323i
$559$		−	22.2447i		−	0.940852i
$560$		0			0
$561$	−3.00322	−	13.6961i	−0.126796	−	0.578250i
$562$	−3.91500	+	14.6110i	−0.165144	+	0.616326i
$563$	3.85201	−	14.3759i	0.162343	−	0.605872i	−0.836021	−	0.548697i	$-0.815124\pi$
$563$	3.85201	−	14.3759i	0.162343	−	0.605872i	0.998364	−	0.0571749i	$-0.0182093\pi$
$564$	−15.7812	+	14.3940i	−0.664509	+	0.606096i
$565$		0			0
$566$		−	24.0382i		−	1.01040i
$567$	−21.5729	+	1.68692i	−0.905975	+	0.0708439i
$568$	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	$0.612307\pi$
$572$	2.73666	+	0.733286i	0.114426	+	0.0306602i
$573$	13.3237	−	20.8079i	0.556606	−	0.869264i
$574$	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	$0.724121\pi$
$578$	31.8476	−	8.53354i	1.32469	−	0.354949i
$579$	5.03742	−	15.8491i	0.209348	−	0.658665i
$580$		0			0
$581$	5.83093	−	3.36649i	0.241908	−	0.139665i
$582$	−12.4200	+	6.42905i	−0.514825	+	0.266493i
$583$	0.774736	+	2.89135i	0.0320863	+	0.119748i
$584$	11.0702			0.458087
$585$		0			0
$586$	−15.0996			−0.623757
$587$	4.16617	+	15.5484i	0.171956	+	0.641750i	0.997050	+	0.0767539i	$0.0244556\pi$
$587$	4.16617	+	15.5484i	0.171956	+	0.641750i	−0.825094	+	0.564996i	$0.808878\pi$
$588$	1.77858	+	1.13886i	0.0733475	+	0.0469658i
$589$	−6.03808	+	3.48608i	−0.248795	+	0.143642i
$590$		0			0
$591$	7.63432	+	8.37008i	0.314034	+	0.344299i
$592$	11.1572	−	2.98955i	0.458557	−	0.122870i
$593$	−31.4829	−	31.4829i	−1.29285	−	1.29285i	−0.933018	−	0.359830i	$-0.882835\pi$
$593$	−31.4829	−	31.4829i	−1.29285	−	1.29285i	−0.359830	−	0.933018i	$-0.617165\pi$
$594$	5.48169	+	2.31517i	0.224917	+	0.0949927i
$595$		0			0
$596$	11.2461	+	6.49294i	0.460658	+	0.265961i
$597$	−7.04593	−	0.323921i	−0.288371	−	0.0132572i
$598$	−14.7388	−	3.94926i	−0.602716	−	0.161497i
$599$	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
$603$	−0.0586570	+	0.158874i	−0.00238870	+	0.00646984i
$604$			3.17004i			0.128987i
$605$		0			0
$606$	1.20285	+	0.382312i	0.0488626	+	0.0155304i
$607$	−8.65049	+	32.2841i	−0.351113	+	1.31037i	0.534194	+	0.845362i	$0.320615\pi$
$607$	−8.65049	+	32.2841i	−0.351113	+	1.31037i	−0.885306	+	0.465008i	$0.846051\pi$
$608$	−0.720527	+	2.68904i	−0.0292212	+	0.109055i
$609$	5.33596	+	1.69597i	0.216224	+	0.0687240i
$610$		0			0
$611$			30.5095i			1.23428i
$612$	−7.34512	+	19.8944i	−0.296909	+	0.804185i
$613$	−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
$617$	−31.8700	−	8.53953i	−1.28304	−	0.343789i	−0.448025	−	0.894021i	$-0.647872\pi$
$617$	−31.8700	−	8.53953i	−1.28304	−	0.343789i	−0.835012	+	0.550232i	$0.814539\pi$
$618$	−2.36246	−	0.108609i	−0.0950320	−	0.00436889i
$619$	−13.2360	−	7.64183i	−0.532001	−	0.307151i	0.209830	−	0.977738i	$-0.432709\pi$
$619$	−13.2360	−	7.64183i	−0.532001	−	0.307151i	−0.741831	+	0.670587i	$0.766042\pi$
$620$		0			0
$621$	−29.5228	−	12.4688i	−1.18471	−	0.500357i
$622$	8.88817	+	8.88817i	0.356383	+	0.356383i
$623$	−11.3293	+	3.03567i	−0.453898	+	0.121622i
$624$	−2.88769	−	3.16599i	−0.115600	−	0.126741i
$625$		0			0
$626$	−10.3379	+	5.96858i	−0.413185	+	0.238552i
$627$	−4.65028	−	2.97766i	−0.185714	−	0.118916i
$628$	2.76487	+	10.3186i	0.110330	+	0.411758i
$629$	−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	$0.430810\pi$
$632$	−2.52946	−	9.44008i	−0.100617	−	0.375506i
$633$	23.3435	−	12.0835i	0.927823	−	0.480276i
$634$	−1.68150	+	0.970815i	−0.0667809	+	0.0385560i
$635$		0			0
$636$	1.37136	−	4.31465i	0.0543778	−	0.171087i
$637$	2.91387	−	0.780770i	0.115452	−	0.0309352i
$638$	−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	−0.0305804	−	0.999532i	$-0.509736\pi$
$641$	−23.0771	−	13.3236i	−0.911491	−	0.526250i	−0.880911	+	0.473283i	$0.843069\pi$
$642$	0.527303	−	0.823501i	0.0208110	−	0.0325010i
$643$	−13.6969	−	3.67008i	−0.540153	−	0.144734i	−0.0215806	−	0.999767i	$-0.506870\pi$
$643$	−13.6969	−	3.67008i	−0.540153	−	0.144734i	−0.518573	+	0.855033i	$0.673537\pi$
$644$	−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	−0.993400	−	0.114702i	$-0.963409\pi$
$647$	−22.3507	+	22.3507i	−0.878698	+	0.878698i	0.114702	+	0.993400i	$0.463409\pi$
$648$	−5.09393	−	7.41970i	−0.200108	−	0.291473i
$649$		−	3.01081i		−	0.118185i
$650$		0			0
$651$	7.70566	−	7.02830i	0.302009	−	0.275461i
$652$	−5.75956	+	21.4950i	−0.225562	+	0.841809i
$653$	−6.60293	+	24.6425i	−0.258393	+	0.964334i	0.707779	+	0.706434i	$0.249697\pi$
$653$	−6.60293	+	24.6425i	−0.258393	+	0.964334i	−0.966172	+	0.257900i	$0.916969\pi$
$654$	−5.04438	−	23.0048i	−0.197251	−	0.899558i
$655$		0			0
$656$			1.97253i			0.0770143i
$657$	25.5390	−	21.2297i	0.996370	−	0.828249i
$658$	−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	$0.844271\pi$
$662$	−21.2138	−	5.68423i	−0.824499	−	0.220924i
$663$	13.9251	+	26.9012i	0.540805	+	1.04476i
$664$	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
$668$	−3.92724	+	1.05230i	−0.151950	+	0.0407148i
$669$	−14.3973	+	3.15696i	−0.556630	+	0.122055i
$670$		0			0
$671$	−7.02711	+	4.05710i	−0.271278	+	0.156623i
$672$	0.191246	−	4.15998i	0.00737747	−	0.160475i
$673$	−3.61246	−	13.4819i	−0.139250	−	0.519688i	−0.999944	−	0.0105656i	$-0.996637\pi$
$673$	−3.61246	−	13.4819i	−0.139250	−	0.519688i	0.860694	−	0.509122i	$-0.170030\pi$
$674$	−26.7973			−1.03219
$675$		0			0
$676$	6.87925			0.264587
$677$	0.458071	+	1.70954i	0.0176051	+	0.0657031i	0.974170	−	0.225818i	$-0.0725054\pi$
$677$	0.458071	+	1.70954i	0.0176051	+	0.0657031i	−0.956564	+	0.291521i	$0.905839\pi$
$678$	0.407128	−	8.85583i	0.0156356	−	0.340106i
$679$	−16.8124	+	9.70666i	−0.645202	+	0.372508i
$680$		0			0
$681$	34.4504	−	7.55413i	1.32014	−	0.289475i
$682$	−2.77034	+	0.742309i	−0.106082	+	0.0284245i
$683$	−22.8964	−	22.8964i	−0.876105	−	0.876105i	0.117024	−	0.993129i	$-0.462665\pi$
$683$	−22.8964	−	22.8964i	−0.876105	−	0.876105i	−0.993129	+	0.117024i	$0.962665\pi$
$684$	3.49462	+	7.58543i	0.133620	+	0.290036i
$685$		0			0
$686$	17.1142	+	9.88088i	0.653423	+	0.377254i
$687$	11.2196	+	21.6747i	0.428055	+	0.826940i
$688$	8.68498	+	2.32713i	0.331112	+	0.0887211i
$689$	−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
$693$	7.74883	+	2.86090i	0.294354	+	0.108677i
$694$			30.0871i			1.14209i
$695$		0			0
$696$	0.498785	+	2.27470i	0.0189064	+	0.0862222i
$697$	3.60893	−	13.4687i	0.136698	−	0.510164i
$698$	−6.65994	+	24.8552i	−0.252082	+	0.940784i
$699$	−1.16370	+	1.06140i	−0.0440150	+	0.0401459i
$700$		0			0
$701$			26.0321i			0.983220i	0.870816	+	0.491610i	$0.163591\pi$
$701$			26.0321i			0.983220i	−0.870816	+	0.491610i	$0.836409\pi$
$702$	−12.7335	−	1.76614i	−0.480593	−	0.0666586i
$703$	−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
$707$	1.69232	+	0.453456i	0.0636462	+	0.0170540i
$708$	−2.45558	+	3.83494i	−0.0922865	+	0.144126i
$709$	2.58254	+	1.49103i	0.0969892	+	0.0559968i	0.547710	−	0.836668i	$-0.315500\pi$
$709$	2.58254	+	1.49103i	0.0969892	+	0.0559968i	−0.450721	+	0.892665i	$0.648833\pi$
$710$		0			0
$711$	−23.9391	−	16.9275i	−0.897786	−	0.634831i
$712$	−3.44949	−	3.44949i	−0.129275	−	0.129275i
$713$	14.9202	−	3.99786i	0.558766	−	0.149721i
$714$	−8.91694	+	28.0551i	−0.333708	+	1.04993i
$715$		0			0
$716$	−0.268634	+	0.155096i	−0.0100393	+	0.00579621i
$717$	−16.4319	+	8.50577i	−0.613660	+	0.317654i
$718$	5.94843	+	22.1999i	0.221994	+	0.828491i
$719$	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
$722$	2.91168	+	10.8665i	0.108362	+	0.404411i
$723$	−30.8258	−	19.7384i	−1.14643	−	0.734077i
$724$	−2.66230	+	1.53708i	−0.0989437	+	0.0571252i
$725$		0			0
$726$	11.3086	+	12.3984i	0.419700	+	0.460149i
$727$	−20.8204	+	5.57881i	−0.772185	+	0.206906i	−0.623337	−	0.781954i	$-0.714223\pi$
$727$	−20.8204	+	5.57881i	−0.772185	+	0.206906i	−0.148849	+	0.988860i	$0.547557\pi$
$728$	−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
$732$	12.2595	+	0.563604i	0.453125	+	0.0208314i
$733$	−6.52116	−	1.74734i	−0.240865	−	0.0645395i	0.136367	−	0.990658i	$-0.456457\pi$
$733$	−6.52116	−	1.74734i	−0.240865	−	0.0645395i	−0.377232	+	0.926119i	$0.623124\pi$
$734$	−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
$738$	3.78279	+	4.55064i	0.139247	+	0.167511i
$739$		−	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
$742$	1.62655	−	6.07037i	0.0597125	−	0.222850i
$743$	8.77270	−	32.7401i	0.321839	−	1.20112i	−0.595613	−	0.803272i	$-0.703091\pi$
$743$	8.77270	−	32.7401i	0.321839	−	1.20112i	0.917452	−	0.397848i	$-0.130243\pi$
$744$	4.13406	+	1.31396i	0.151562	+	0.0481720i
$745$		0			0
$746$			22.8690i			0.837295i
$747$	8.28018	−	1.42065i	0.302956	−	0.0519790i
$748$	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	$0.754664\pi$
$752$	−11.9118	−	3.19175i	−0.434378	−	0.116391i
$753$	42.7281	+	1.96433i	1.55710	+	0.0715843i
$754$	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	$0.740878\pi$
$758$	−35.0741	+	9.39806i	−1.27395	+	0.341353i
$759$	8.24404	+	9.03857i	0.299240	+	0.328079i
$760$		0			0
$761$	−29.7531	+	17.1780i	−1.07855	+	0.622702i	−0.930505	−	0.366279i	$-0.880632\pi$
$761$	−29.7531	+	17.1780i	−1.07855	+	0.622702i	−0.148046	+	0.988981i	$0.547298\pi$
$762$	−10.0835	−	6.45665i	−0.365286	−	0.233900i
$763$	−8.46136	−	31.5782i	−0.306322	−	1.14321i
$764$	14.2652			0.516098
$765$		0			0
$766$	−16.5998			−0.599775
$767$	1.68348	+	6.28282i	0.0607869	+	0.226860i
$768$	1.53819	−	0.796225i	0.0555046	−	0.0287313i
$769$	−14.4890	+	8.36522i	−0.522486	+	0.301658i	−0.737951	−	0.674854i	$-0.764207\pi$
$769$	−14.4890	+	8.36522i	−0.522486	+	0.301658i	0.215465	+	0.976512i	$0.430873\pi$
$770$		0			0
$771$	−2.75723	+	8.67497i	−0.0992992	+	0.312421i
$772$	9.27437	−	2.48506i	0.333792	−	0.0894393i
$773$	5.20827	+	5.20827i	0.187328	+	0.187328i	0.794540	−	0.607212i	$-0.207712\pi$
$773$	5.20827	+	5.20827i	0.187328	+	0.187328i	−0.607212	+	0.794540i	$0.707712\pi$
$774$	24.4991	−	11.2868i	0.880604	−	0.405696i
$775$		0			0
$776$	−6.99265	−	4.03721i	−0.251022	−	0.144927i
$777$	25.9385	−	40.5087i	0.930539	−	1.45324i
$778$	22.7724	+	6.10184i	0.816429	+	0.218761i
$779$	−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
$783$	5.51297	+	4.29121i	0.197018	+	0.153355i
$784$			1.21934i			0.0435478i
$785$		0			0
$786$	−7.36398	+	6.71666i	−0.262665	+	0.239575i
$787$	−11.9724	+	44.6815i	−0.426769	+	1.59272i	0.333262	+	0.942834i	$0.391851\pi$
$787$	−11.9724	+	44.6815i	−0.426769	+	1.59272i	−0.760030	+	0.649888i	$0.774816\pi$
$788$	−1.69285	+	6.31780i	−0.0603053	+	0.225062i
$789$	5.54069	+	25.2682i	0.197254	+	0.899571i
$790$		0			0
$791$		−	12.3060i		−	0.437550i
$792$	0.580958	+	3.38607i	0.0206434	+	0.120319i
$793$	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
$797$	−49.7628	−	13.3339i	−1.76269	−	0.472311i	−0.775430	−	0.631434i	$-0.782467\pi$
$797$	−49.7628	−	13.3339i	−1.76269	−	0.472311i	−0.987259	+	0.159123i	$0.949134\pi$
$798$	5.32941	+	10.2956i	0.188659	+	0.364461i
$799$	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
$803$	−12.2454	+	3.28114i	−0.432131	+	0.115789i
$804$	−0.0955087	+	0.0209427i	−0.00336833	+	0.000738592i
$805$		0			0
$806$	5.36595	−	3.09803i	0.189008	−	0.109124i
$807$	1.59143	−	34.6168i	0.0560210	−	1.21857i
$808$	0.188602	+	0.703872i	0.00663499	+	0.0247621i
$809$	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	$0.193065\pi$
$812$	0.836654	+	3.12243i	0.0293608	+	0.109576i
$813$	0.240788	−	5.23762i	0.00844481	−	0.183691i
$814$	−11.4555	+	6.61386i	−0.401517	+	0.231816i
$815$		0			0
$816$	−11.9598	+	2.62248i	−0.418675	+	0.0918051i
$817$	−24.1782	+	6.47852i	−0.845886	+	0.226655i
$818$	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	0.599573	−	0.800320i	$-0.295337\pi$
$821$	5.91006	+	3.41218i	0.206263	+	0.119086i	−0.393311	+	0.919406i	$0.628670\pi$
$822$	−8.28090	−	15.9975i	−0.288829	−	0.557976i
$823$	19.6876	+	5.27529i	0.686268	+	0.183885i	0.585072	−	0.810982i	$-0.301066\pi$
$823$	19.6876	+	5.27529i	0.686268	+	0.183885i	0.101196	+	0.994866i	$0.467733\pi$
$824$	−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	$-0.487753\pi$
$827$	29.8425	−	29.8425i	1.03773	−	1.03773i	0.999260	−	0.0384654i	$-0.0122469\pi$
$828$	−3.12887	−	18.2364i	−0.108736	−	0.633758i
$829$		−	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
$832$	0.640322	−	2.38971i	0.0221992	−	0.0828484i
$833$	2.23090	−	8.32583i	0.0772961	−	0.288473i
$834$	−3.24403	+	2.95887i	−0.112332	+	0.102457i
$835$		0			0
$836$		−	3.18808i		−	0.110262i
$837$	12.0571	−	4.89673i	0.416755	−	0.169256i
$838$	−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
$842$	5.50919	+	1.47618i	0.189859	+	0.0508726i
$843$	−14.1280	+	22.0640i	−0.486595	+	0.759926i
$844$	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
$848$	2.52480	−	0.676517i	0.0867018	−	0.0232317i
$849$	12.6116	−	39.6794i	0.432828	−	1.36179i
$850$		0			0
$851$	61.6961	−	35.6203i	2.11492	−	1.22105i
$852$	13.9976	−	7.24569i	0.479550	−	0.248233i
$853$	−0.132960	−	0.496213i	−0.00455246	−	0.0169900i	0.963612	−	0.267304i	$-0.0861328\pi$
$853$	−0.132960	−	0.496213i	−0.00455246	−	0.0169900i	−0.968165	+	0.250314i	$0.919466\pi$
$854$	17.0357			0.582949
$855$		0			0
$856$	0.564565			0.0192964
$857$	11.5332	+	43.0427i	0.393968	+	1.47031i	0.823530	+	0.567272i	$0.192001\pi$
$857$	11.5332	+	43.0427i	0.393968	+	1.47031i	−0.429562	+	0.903037i	$0.641332\pi$
$858$	4.13263	+	2.64620i	0.141086	+	0.0903399i
$859$	−25.5432	+	14.7474i	−0.871522	+	0.503174i	−0.867854	−	0.496820i	$-0.834501\pi$
$859$	−25.5432	+	14.7474i	−0.871522	+	0.503174i	−0.00366859	+	0.999993i	$0.501168\pi$
$860$		0			0
$861$	5.53554	+	6.06903i	0.188651	+	0.206832i
$862$	27.4438	−	7.35356i	0.934741	−	0.250463i
$863$	−6.17951	−	6.17951i	−0.210353	−	0.210353i	0.594064	−	0.804417i	$-0.297522\pi$
$863$	−6.17951	−	6.17951i	−0.210353	−	0.210353i	−0.804417	+	0.594064i	$0.797522\pi$
$864$	2.02166	−	4.78674i	0.0687783	−	0.162848i
$865$		0			0
$866$	−24.7753	−	14.3040i	−0.841899	−	0.486071i
$867$	57.0473	+	2.62263i	1.93743	+	0.0890691i
$868$	5.81629	+	1.55847i	0.197418	+	0.0528979i
$869$	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
$873$	−23.8744	+	4.09620i	−0.808026	+	0.138635i
$874$			17.1700i			0.580785i
$875$		0			0
$876$	18.2733	+	5.80794i	0.617398	+	0.196232i
$877$	5.38298	−	20.0896i	0.181770	−	0.678376i	−0.813528	−	0.581525i	$-0.802456\pi$
$877$	5.38298	−	20.0896i	0.181770	−	0.678376i	0.995299	−	0.0968513i	$-0.0308771\pi$
$878$	3.72931	−	13.9180i	0.125858	−	0.469709i
$879$	−24.9245	−	7.92195i	−0.840684	−	0.267201i
$880$		0			0
$881$		−	28.3087i		−	0.953745i	−0.878972	−	0.476873i	$-0.841770\pi$
$881$		−	28.3087i		−	0.953745i	0.878972	−	0.476873i	$-0.158230\pi$
$882$	2.33837	+	2.81302i	0.0787371	+	0.0947194i
$883$	−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
$887$	46.4040	+	12.4339i	1.55809	+	0.417490i	0.932059	−	0.362306i	$-0.118011\pi$
$887$	46.4040	+	12.4339i	1.55809	+	0.417490i	0.626034	+	0.779796i	$0.284677\pi$
$888$	19.9854	+	0.918784i	0.670665	+	0.0308324i
$889$	−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
$893$	33.1613	−	8.88553i	1.10970	−	0.297343i
$894$	15.1572	+	16.6180i	0.506933	+	0.555789i
$895$		0			0
$896$	2.08219	−	1.20215i	0.0695609	−	0.0401610i
$897$	−22.2571	−	14.2517i	−0.743144	−	0.475849i
$898$	0.445914	+	1.66417i	0.0148803	+	0.0555342i
$899$	−3.36724			−0.112304
$900$		0			0
$901$	−18.4774			−0.615573
$902$	−0.584648	−	2.18194i	−0.0194666	−	0.0726505i
$903$	33.2524	−	17.2127i	1.10657	−	0.572804i
$904$	4.43259	−	2.55916i	0.147426	−	0.0851164i
$905$		0			0
$906$	−1.66316	+	5.23273i	−0.0552546	+	0.173846i
$907$	36.0516	−	9.66001i	1.19707	−	0.320755i	0.395396	−	0.918511i	$-0.370607\pi$
$907$	36.0516	−	9.66001i	1.19707	−	0.320755i	0.801679	+	0.597755i	$0.203941\pi$
$908$	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	0.998595	+	0.0529906i	$0.0168753\pi$
$911$	46.5957	+	26.9020i	1.54378	+	0.891304i	0.545189	+	0.838313i	$0.316458\pi$
$912$	−2.60016	+	4.06073i	−0.0860999	+	0.134464i
$913$	−3.09768	−	0.830022i	−0.102518	−	0.0274697i
$914$	−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
$918$	−22.5620	+	28.9858i	−0.744658	+	0.956673i
$919$		−	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
$922$	−2.60729	+	9.73056i	−0.0858667	+	0.320459i
$923$	5.82696	−	21.7465i	0.191797	−	0.715795i
$924$	1.02145	+	4.65829i	0.0336032	+	0.153247i
$925$		0			0
$926$			38.2779i			1.25789i
$927$	−3.84268	−	1.41874i	−0.126210	−	0.0465974i
$928$	−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
$932$	−0.878367	−	0.235358i	−0.0287719	−	0.00770940i
$933$	10.0084	+	19.3347i	0.327659	+	0.632989i
$934$	−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	$0.698742\pi$
$938$	−0.131103	+	0.0351289i	−0.00428066	+	0.00114700i
$939$	−20.1959	+	4.42847i	−0.659069	+	0.144518i
$940$		0			0
$941$	−14.5976	+	8.42791i	−0.475867	+	0.274742i	−0.718693	−	0.695328i	$-0.755259\pi$
$941$	−14.5976	+	8.42791i	−0.475867	+	0.274742i	0.242825	+	0.970070i	$0.421926\pi$
$942$	−0.849730	+	18.4833i	−0.0276857	+	0.602219i
$943$	3.14874	+	11.7513i	0.102537	+	0.382673i
$944$	−2.62911			−0.0855703
$945$		0			0
$946$	−10.2967			−0.334776
$947$	−9.92745	−	37.0498i	−0.322599	−	1.20396i	−0.916704	−	0.399568i	$-0.869160\pi$
$947$	−9.92745	−	37.0498i	−0.322599	−	1.20396i	0.594105	−	0.804388i	$-0.297506\pi$
$948$	0.777383	−	16.9096i	0.0252482	−	0.549199i
$949$	23.7185	−	13.6939i	0.769935	−	0.444522i
$950$		0			0
$951$	−3.28496	+	0.720309i	−0.106522	+	0.0233576i
$952$	−16.4169	+	4.39890i	−0.532076	+	0.142569i
$953$	18.8861	+	18.8861i	0.611780	+	0.611780i	0.943410	−	0.331630i	$-0.107598\pi$
$953$	18.8861	+	18.8861i	0.611780	+	0.611780i	−0.331630	+	0.943410i	$0.607598\pi$
$954$	4.52734	−	6.40262i	0.146578	−	0.207293i
$955$		0			0
$956$	−9.25142	−	5.34131i	−0.299212	−	0.172750i
$957$	−1.22595	−	2.36835i	−0.0396292	−	0.0765578i
$958$	−4.40102	−	1.17925i	−0.142190	−	0.0380998i
$959$	−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
$963$	1.30246	−	1.08269i	0.0419711	−	0.0348891i
$964$		−	21.1332i		−	0.680654i
$965$		0			0
$966$	−5.50122	−	25.0882i	−0.176999	−	0.807199i
$967$	8.29288	−	30.9494i	0.266681	−	0.995267i	−0.694533	−	0.719461i	$-0.744389\pi$
$967$	8.29288	−	30.9494i	0.266681	−	0.995267i	0.961213	−	0.275805i	$-0.0889446\pi$
$968$	−2.50758	+	9.35843i	−0.0805968	+	0.300791i
$969$	25.1838	−	22.9700i	0.809020	−	0.737904i
$970$		0			0
$971$			29.2201i			0.937716i	0.883274	+	0.468858i	$0.155334\pi$
$971$			29.2201i			0.937716i	−0.883274	+	0.468858i	$0.844666\pi$
$972$	−4.51572	−	14.9201i	−0.144842	−	0.478561i
$973$	−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
$977$	37.7399	+	10.1124i	1.20741	+	0.323523i	0.805743	−	0.592265i	$-0.201766\pi$
$977$	37.7399	+	10.1124i	1.20741	+	0.323523i	0.401662	+	0.915788i	$0.368433\pi$
$978$	−20.7845	+	32.4596i	−0.664615	+	1.03794i
$979$	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
$983$	−11.0660	+	2.96514i	−0.352952	+	0.0945732i	−0.430939	−	0.902381i	$-0.641818\pi$
$983$	−11.0660	+	2.96514i	−0.352952	+	0.0945732i	0.0779867	+	0.996954i	$0.475151\pi$
$984$	−1.03488	+	3.25601i	−0.0329908	+	0.103798i
$985$		0			0
$986$	8.23096	−	4.75215i	0.262127	−	0.151339i
$987$	−45.6070	+	23.6079i	−1.45169	+	0.751448i
$988$	1.78260	+	6.65274i	0.0567119	+	0.211652i
$989$	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	$0.639952\pi$
$992$	0.648201	+	2.41912i	0.0205804	+	0.0768071i
$993$	−32.0350	−	20.5126i	−1.01660	−	0.650949i
$994$	18.9480	−	10.9396i	0.600994	−	0.346984i
$995$		0			0
$996$	3.26863	+	3.58365i	0.103571	+	0.113552i
$997$	53.0819	−	14.2233i	1.68112	−	0.450455i	0.713047	−	0.701116i	$-0.247315\pi$
$997$	53.0819	−	14.2233i	1.68112	−	0.450455i	0.968075	+	0.250661i	$0.0806479\pi$
$998$	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.407.3		16
3.2	odd	2		1350.2.q.h.1007.2		16
5.2	odd	4		90.2.l.b.83.2	yes	16
5.3	odd	4	inner	450.2.p.h.443.3		16
5.4	even	2		90.2.l.b.47.2	yes	16
9.4	even	3		1350.2.q.h.557.1		16
9.5	odd	6	inner	450.2.p.h.257.3		16
15.2	even	4		270.2.m.b.143.3		16
15.8	even	4		1350.2.q.h.143.1		16
15.14	odd	2		270.2.m.b.197.4		16
20.7	even	4		720.2.cu.b.353.1		16
20.19	odd	2		720.2.cu.b.497.2		16
45.2	even	12		810.2.f.c.323.3		16
45.4	even	6		270.2.m.b.17.3		16
45.7	odd	12		810.2.f.c.323.6		16
45.13	odd	12		1350.2.q.h.1043.2		16
45.14	odd	6		90.2.l.b.77.2	yes	16
45.22	odd	12		270.2.m.b.233.4		16
45.23	even	12	inner	450.2.p.h.293.3		16
45.29	odd	6		810.2.f.c.647.6		16
45.32	even	12		90.2.l.b.23.2	✓	16
45.34	even	6		810.2.f.c.647.3		16
180.59	even	6		720.2.cu.b.257.1		16
180.167	odd	12		720.2.cu.b.113.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	45.32	even	12
90.2.l.b.47.2	yes	16	5.4	even	2
90.2.l.b.77.2	yes	16	45.14	odd	6
90.2.l.b.83.2	yes	16	5.2	odd	4
270.2.m.b.17.3		16	45.4	even	6
270.2.m.b.143.3		16	15.2	even	4
270.2.m.b.197.4		16	15.14	odd	2
270.2.m.b.233.4		16	45.22	odd	12
450.2.p.h.257.3		16	9.5	odd	6	inner
450.2.p.h.293.3		16	45.23	even	12	inner
450.2.p.h.407.3		16	1.1	even	1	trivial
450.2.p.h.443.3		16	5.3	odd	4	inner
720.2.cu.b.113.2		16	180.167	odd	12
720.2.cu.b.257.1		16	180.59	even	6
720.2.cu.b.353.1		16	20.7	even	4
720.2.cu.b.497.2		16	20.19	odd	2
810.2.f.c.323.3		16	45.2	even	12
810.2.f.c.323.6		16	45.7	odd	12
810.2.f.c.647.3		16	45.34	even	6
810.2.f.c.647.6		16	45.29	odd	6
1350.2.q.h.143.1		16	15.8	even	4
1350.2.q.h.557.1		16	9.4	even	3
1350.2.q.h.1007.2		16	3.2	odd	2
1350.2.q.h.1043.2		16	45.13	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

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