LMFDB - Embedded newform 300.2.h.a.299.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(299,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("300.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.h (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.4
Root			$0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.a.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} -0.936426 q^{7} +(-0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +O(q^{10})$	\(q+(-1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} -0.936426 q^{7} +(-0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +4.27156 q^{11} +(1.41656 - 3.16123i) q^{12} +3.12311i q^{13} +(1.19935 - 0.561553i) q^{14} +(-0.719224 - 3.93481i) q^{16} +2.00000 q^{17} +(-2.34435 + 3.53610i) q^{18} -4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(-5.47091 + 2.56155i) q^{22} -7.60669i q^{23} +(0.0814236 + 4.89830i) q^{24} +(-1.87285 - 4.00000i) q^{26} +(3.54042 - 3.80335i) q^{27} +(-1.19935 + 1.43845i) q^{28} +5.12311i q^{29} +2.39871i q^{31} +(3.28078 + 4.60831i) q^{32} +(7.12311 - 2.00000i) q^{33} +(-2.56155 + 1.19935i) q^{34} +(0.882071 - 5.93481i) q^{36} +3.12311i q^{37} +(2.56155 + 5.47091i) q^{38} +(1.46228 + 5.20798i) q^{39} +7.12311i q^{41} +(1.73707 - 1.49798i) q^{42} +1.46228 q^{43} +(5.47091 - 6.56155i) q^{44} +(4.56155 + 9.74247i) q^{46} -0.936426i q^{47} +(-3.04168 - 6.22480i) q^{48} -6.12311 q^{49} +(3.33513 - 0.936426i) q^{51} +(4.79741 + 4.00000i) q^{52} -4.24621 q^{53} +(-2.25371 + 6.99434i) q^{54} +(0.673500 - 2.56155i) q^{56} +(-2.00000 - 7.12311i) q^{57} +(-3.07221 - 6.56155i) q^{58} -7.19612 q^{59} -5.12311 q^{61} +(-1.43845 - 3.07221i) q^{62} +(-2.39871 + 1.46228i) q^{63} +(-6.96543 - 3.93481i) q^{64} +(-7.92375 + 6.83311i) q^{66} -5.20798 q^{67} +(2.56155 - 3.07221i) q^{68} +(-3.56155 - 12.6847i) q^{69} -6.67026 q^{71} +(2.42923 + 8.13012i) q^{72} -8.24621i q^{73} +(-1.87285 - 4.00000i) q^{74} +(-6.56155 - 5.47091i) q^{76} -4.00000 q^{77} +(-4.99596 - 5.79337i) q^{78} +9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(-4.27156 - 9.12311i) q^{82} +4.68213i q^{83} +(-1.32650 + 2.96026i) q^{84} +(-1.87285 + 0.876894i) q^{86} +(2.39871 + 8.54312i) q^{87} +(-3.07221 + 11.6847i) q^{88} +6.24621i q^{89} -2.92456i q^{91} +(-11.6847 - 9.74247i) q^{92} +(1.12311 + 4.00000i) q^{93} +(0.561553 + 1.19935i) q^{94} +(7.62858 + 6.14856i) q^{96} +6.00000i q^{97} +(7.84233 - 3.67188i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9	$ 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9} - 14 q^{12} - 14 q^{16} + 16 q^{17} - 18 q^{18} + 4 q^{21} + 2 q^{24} + 18 q^{32} + 24 q^{33} - 4 q^{34} + 18 q^{36} + 4 q^{38} + 16 q^{42} + 20 q^{46} + 10 q^{48} - 16 q^{49} + 32 q^{53} + 10 q^{54} - 16 q^{57} - 8 q^{61} - 28 q^{62} + 2 q^{64} - 40 q^{66} + 4 q^{68} - 12 q^{69} + 10 q^{72} - 36 q^{76} - 32 q^{77} + 8 q^{78} - 16 q^{84} - 44 q^{92} - 24 q^{93} - 12 q^{94} + 42 q^{96} + 38 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9 - 14 * q^12 - 14 * q^16 + 16 * q^17 - 18 * q^18 + 4 * q^21 + 2 * q^24 + 18 * q^32 + 24 * q^33 - 4 * q^34 + 18 * q^36 + 4 * q^38 + 16 * q^42 + 20 * q^46 + 10 * q^48 - 16 * q^49 + 32 * q^53 + 10 * q^54 - 16 * q^57 - 8 * q^61 - 28 * q^62 + 2 * q^64 - 40 * q^66 + 4 * q^68 - 12 * q^69 + 10 * q^72 - 36 * q^76 - 32 * q^77 + 8 * q^78 - 16 * q^84 - 44 * q^92 - 24 * q^93 - 12 * q^94 + 42 * q^96 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.28078	+	0.599676i	−0.905646	+	0.424035i
$2$	−1.28078	+	0.599676i	−0.905646	+	0.424035i
$3$	1.66757	−	0.468213i	0.962770	−	0.270323i
$3$	1.66757	−	0.468213i	0.962770	−	0.270323i
$4$	1.28078	−	1.53610i	0.640388	−	0.768051i
$5$		0			0
$5$		0			0
$6$	−1.85500	+	1.59968i	−0.757302	+	0.653065i
$7$	−0.936426			−0.353936			−0.176968	−	0.984217i	$-0.556629\pi$
$7$	−0.936426			−0.353936			−0.176968	+	0.984217i	$0.556629\pi$
$8$	−0.719224	+	2.73546i	−0.254284	+	0.967130i
$9$	2.56155	−	1.56155i	0.853851	−	0.520518i
$10$		0			0
$11$	4.27156			1.28792			0.643962	−	0.765058i	$-0.277290\pi$
$11$	4.27156			1.28792			0.643962	+	0.765058i	$0.277290\pi$
$12$	1.41656	−	3.16123i	0.408924	−	0.912568i
$13$			3.12311i			0.866194i	0.901347	+	0.433097i	$0.142579\pi$
$13$			3.12311i			0.866194i	−0.901347	+	0.433097i	$0.857421\pi$
$14$	1.19935	−	0.561553i	0.320541	−	0.150081i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−2.34435	+	3.53610i	−0.552569	+	0.833467i
$19$		−	4.27156i		−	0.979963i	−0.871733	−	0.489981i	$-0.837004\pi$
$19$		−	4.27156i		−	0.979963i	0.871733	−	0.489981i	$-0.162996\pi$
$20$		0			0
$21$	−1.56155	+	0.438447i	−0.340759	+	0.0956770i
$22$	−5.47091	+	2.56155i	−1.16640	+	0.546125i
$23$		−	7.60669i		−	1.58610i	−0.609154	−	0.793052i	$-0.708491\pi$
$23$		−	7.60669i		−	1.58610i	0.609154	−	0.793052i	$-0.291509\pi$
$24$	0.0814236	+	4.89830i	0.0166205	+	0.999862i
$25$		0			0
$26$	−1.87285	−	4.00000i	−0.367297	−	0.784465i
$27$	3.54042	−	3.80335i	0.681354	−	0.731954i
$28$	−1.19935	+	1.43845i	−0.226656	+	0.271841i
$29$			5.12311i			0.951337i	0.879625	+	0.475668i	$0.157794\pi$
$29$			5.12311i			0.951337i	−0.879625	+	0.475668i	$0.842206\pi$
$30$		0			0
$31$			2.39871i			0.430820i	0.976524	+	0.215410i	$0.0691088\pi$
$31$			2.39871i			0.430820i	−0.976524	+	0.215410i	$0.930891\pi$
$32$	3.28078	+	4.60831i	0.579965	+	0.814642i
$33$	7.12311	−	2.00000i	1.23997	−	0.348155i
$34$	−2.56155	+	1.19935i	−0.439303	+	0.205687i
$35$		0			0
$36$	0.882071	−	5.93481i	0.147012	−	0.989135i
$37$			3.12311i			0.513435i	0.966486	+	0.256718i	$0.0826411\pi$
$37$			3.12311i			0.513435i	−0.966486	+	0.256718i	$0.917359\pi$
$38$	2.56155	+	5.47091i	0.415539	+	0.887499i
$39$	1.46228	+	5.20798i	0.234152	+	0.833945i
$40$		0			0
$41$			7.12311i			1.11244i	0.831034	+	0.556221i	$0.187749\pi$
$41$			7.12311i			1.11244i	−0.831034	+	0.556221i	$0.812251\pi$
$42$	1.73707	−	1.49798i	0.268036	−	0.231143i
$43$	1.46228			0.222995			0.111498	−	0.993765i	$-0.464435\pi$
$43$	1.46228			0.222995			0.111498	+	0.993765i	$0.464435\pi$
$44$	5.47091	−	6.56155i	0.824771	−	0.989191i
$45$		0			0
$46$	4.56155	+	9.74247i	0.672564	+	1.43645i
$47$		−	0.936426i		−	0.136592i	−0.997665	−	0.0682959i	$-0.978244\pi$
$47$		−	0.936426i		−	0.136592i	0.997665	−	0.0682959i	$-0.0217562\pi$
$48$	−3.04168	−	6.22480i	−0.439029	−	0.898473i
$49$	−6.12311			−0.874729
$50$		0			0
$51$	3.33513	−	0.936426i	0.467012	−	0.131126i
$52$	4.79741	+	4.00000i	0.665281	+	0.554700i
$53$	−4.24621			−0.583262			−0.291631	−	0.956531i	$-0.594198\pi$
$53$	−4.24621			−0.583262			−0.291631	+	0.956531i	$0.594198\pi$
$54$	−2.25371	+	6.99434i	−0.306691	+	0.951809i
$55$		0			0
$56$	0.673500	−	2.56155i	0.0900002	−	0.342302i
$57$	−2.00000	−	7.12311i	−0.264906	−	0.943478i
$58$	−3.07221	−	6.56155i	−0.403400	−	0.861574i
$59$	−7.19612			−0.936855			−0.468427	−	0.883502i	$-0.655179\pi$
$59$	−7.19612			−0.936855			−0.468427	+	0.883502i	$0.655179\pi$
$60$		0			0
$61$	−5.12311			−0.655946			−0.327973	−	0.944687i	$-0.606366\pi$
$61$	−5.12311			−0.655946			−0.327973	+	0.944687i	$0.606366\pi$
$62$	−1.43845	−	3.07221i	−0.182683	−	0.390171i
$63$	−2.39871	+	1.46228i	−0.302209	+	0.184230i
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$		0			0
$66$	−7.92375	+	6.83311i	−0.975347	+	0.841098i
$67$	−5.20798			−0.636257			−0.318128	−	0.948048i	$-0.603054\pi$
$67$	−5.20798			−0.636257			−0.318128	+	0.948048i	$0.603054\pi$
$68$	2.56155	−	3.07221i	0.310634	−	0.372560i
$69$	−3.56155	−	12.6847i	−0.428761	−	1.52705i
$70$		0			0
$71$	−6.67026			−0.791615			−0.395807	−	0.918334i	$-0.629535\pi$
$71$	−6.67026			−0.791615			−0.395807	+	0.918334i	$0.629535\pi$
$72$	2.42923	+	8.13012i	0.286287	+	0.958144i
$73$		−	8.24621i		−	0.965146i	−0.875856	−	0.482573i	$-0.839702\pi$
$73$		−	8.24621i		−	0.965146i	0.875856	−	0.482573i	$-0.160298\pi$
$74$	−1.87285	−	4.00000i	−0.217715	−	0.464991i
$75$		0			0
$76$	−6.56155	−	5.47091i	−0.752662	−	0.627557i
$77$	−4.00000			−0.455842
$78$	−4.99596	−	5.79337i	−0.565681	−	0.655970i
$79$			9.06897i			1.02034i	0.860074	+	0.510169i	$0.170417\pi$
$79$			9.06897i			1.02034i	−0.860074	+	0.510169i	$0.829583\pi$
$80$		0			0
$81$	4.12311	−	8.00000i	0.458123	−	0.888889i
$82$	−4.27156	−	9.12311i	−0.471715	−	1.00748i
$83$			4.68213i			0.513931i	0.966421	+	0.256965i	$0.0827226\pi$
$83$			4.68213i			0.513931i	−0.966421	+	0.256965i	$0.917277\pi$
$84$	−1.32650	+	2.96026i	−0.144733	+	0.322991i
$85$		0			0
$86$	−1.87285	+	0.876894i	−0.201955	+	0.0945580i
$87$	2.39871	+	8.54312i	0.257168	+	0.915918i
$88$	−3.07221	+	11.6847i	−0.327498	+	1.24559i
$89$			6.24621i			0.662097i	0.943614	+	0.331049i	$0.107402\pi$
$89$			6.24621i			0.662097i	−0.943614	+	0.331049i	$0.892598\pi$
$90$		0			0
$91$		−	2.92456i		−	0.306577i
$92$	−11.6847	−	9.74247i	−1.21821	−	1.01572i
$93$	1.12311	+	4.00000i	0.116461	+	0.414781i
$94$	0.561553	+	1.19935i	0.0579198	+	0.123704i
$95$		0			0
$96$	7.62858	+	6.14856i	0.778589	+	0.627534i
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$	7.84233	−	3.67188i	0.792195	−	0.370916i
$99$	10.9418	−	6.67026i	1.09969	−	0.670387i
$100$		0			0
$101$		−	9.12311i		−	0.907783i	−0.891057	−	0.453891i	$-0.850035\pi$
$101$		−	9.12311i		−	0.907783i	0.891057	−	0.453891i	$-0.149965\pi$
$102$	−3.71001	+	3.19935i	−0.367345	+	0.316783i
$103$	−12.4041			−1.22221			−0.611106	−	0.791549i	$-0.709275\pi$
$103$	−12.4041			−1.22221			−0.611106	+	0.791549i	$0.709275\pi$
$104$	−8.54312	−	2.24621i	−0.837722	−	0.220259i
$105$		0			0
$106$	5.43845	−	2.54635i	0.528229	−	0.247324i
$107$			0.936426i			0.0905278i	0.998975	+	0.0452639i	$0.0144129\pi$
$107$			0.936426i			0.0905278i	−0.998975	+	0.0452639i	$0.985587\pi$
$108$	−1.30784	−	10.3097i	−0.125847	−	0.992050i
$109$	9.12311			0.873835			0.436918	−	0.899502i	$-0.356070\pi$
$109$	9.12311			0.873835			0.436918	+	0.899502i	$0.356070\pi$
$110$		0			0
$111$	1.46228	+	5.20798i	0.138793	+	0.494320i
$112$	0.673500	+	3.68466i	0.0636398	+	0.348167i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	6.83311	+	7.92375i	0.639980	+	0.742127i
$115$		0			0
$116$	7.86962	+	6.56155i	0.730676	+	0.609225i
$117$	4.87689	+	8.00000i	0.450869	+	0.739600i
$118$	9.21662	−	4.31534i	0.848458	−	0.397259i
$119$	−1.87285			−0.171684
$120$		0			0
$121$	7.24621			0.658746
$122$	6.56155	−	3.07221i	0.594055	−	0.278144i
$123$	3.33513	+	11.8782i	0.300719	+	1.07103i
$124$	3.68466	+	3.07221i	0.330892	+	0.275892i
$125$		0			0
$126$	2.19531	−	3.31130i	0.195574	−	0.294994i
$127$	4.68213			0.415472			0.207736	−	0.978185i	$-0.433391\pi$
$127$	4.68213			0.415472			0.207736	+	0.978185i	$0.433391\pi$
$128$	11.2808	+	0.862603i	0.997089	+	0.0762440i
$129$	2.43845	−	0.684658i	0.214693	−	0.0602808i
$130$		0			0
$131$	−17.6121			−1.53878			−0.769388	−	0.638782i	$-0.779438\pi$
$131$	−17.6121			−1.53878			−0.769388	+	0.638782i	$0.779438\pi$
$132$	6.05090	−	13.5034i	0.526663	−	1.17532i
$133$			4.00000i			0.346844i
$134$	6.67026	−	3.12311i	0.576223	−	0.269795i
$135$		0			0
$136$	−1.43845	+	5.47091i	−0.123346	+	0.469127i
$137$	8.24621			0.704521			0.352261	−	0.935902i	$-0.385413\pi$
$137$	8.24621			0.704521			0.352261	+	0.935902i	$0.385413\pi$
$138$	12.1682	+	14.1104i	1.03583	+	1.20116i
$139$		−	13.8664i		−	1.17613i	−0.808813	−	0.588066i	$-0.799890\pi$
$139$		−	13.8664i		−	1.17613i	0.808813	−	0.588066i	$-0.200110\pi$
$140$		0			0
$141$	−0.438447	−	1.56155i	−0.0369239	−	0.131506i
$142$	8.54312	−	4.00000i	0.716922	−	0.335673i
$143$			13.3405i			1.11559i
$144$	−7.98674	−	8.95611i	−0.665562	−	0.746343i
$145$		0			0
$146$	4.94506	+	10.5616i	0.409256	+	0.874080i
$147$	−10.2107	+	2.86692i	−0.842163	+	0.236459i
$148$	4.79741	+	4.00000i	0.394345	+	0.328798i
$149$			14.0000i			1.14692i	0.819232	+	0.573462i	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$		−	6.14441i		−	0.500025i	−0.968243	−	0.250013i	$-0.919565\pi$
$151$		−	6.14441i		−	0.500025i	0.968243	−	0.250013i	$-0.0804347\pi$
$152$	11.6847	+	3.07221i	0.947751	+	0.249189i
$153$	5.12311	−	3.12311i	0.414179	−	0.252488i
$154$	5.12311	−	2.39871i	0.412832	−	0.193293i
$155$		0			0
$156$	9.87285	+	4.42405i	0.790461	+	0.354208i
$157$		−	21.3693i		−	1.70546i	−0.522354	−	0.852729i	$-0.674946\pi$
$157$		−	21.3693i		−	1.70546i	0.522354	−	0.852729i	$-0.325054\pi$
$158$	−5.43845	−	11.6153i	−0.432660	−	0.924065i
$159$	−7.08084	+	1.98813i	−0.561547	+	0.157669i
$160$		0			0
$161$			7.12311i			0.561379i
$162$	−0.483365	+	12.7187i	−0.0379768	+	0.999279i
$163$	24.1671			1.89291			0.946456	−	0.322834i	$-0.104636\pi$
$163$	24.1671			1.89291			0.946456	+	0.322834i	$0.104636\pi$
$164$	10.9418	+	9.12311i	0.854413	+	0.712395i
$165$		0			0
$166$	−2.80776	−	5.99676i	−0.217925	−	0.465439i
$167$			2.80928i			0.217389i	0.994075	+	0.108694i	$0.0346670\pi$
$167$			2.80928i			0.217389i	−0.994075	+	0.108694i	$0.965333\pi$
$168$	−0.0762472	−	4.58690i	−0.00588260	−	0.353887i
$169$	3.24621			0.249709
$170$		0			0
$171$	−6.67026	−	10.9418i	−0.510088	−	0.836742i
$172$	1.87285	−	2.24621i	0.142804	−	0.171272i
$173$	−2.00000			−0.152057			−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000			−0.152057			−0.0760286	+	0.997106i	$0.524224\pi$
$174$	−8.19531	−	9.50338i	−0.621285	−	0.720449i
$175$		0			0
$176$	−3.07221	−	16.8078i	−0.231576	−	1.26693i
$177$	−12.0000	+	3.36932i	−0.901975	+	0.253253i
$178$	−3.74571	−	8.00000i	−0.280752	−	0.599625i
$179$	14.6875			1.09780			0.548899	−	0.835889i	$-0.315047\pi$
$179$	14.6875			1.09780			0.548899	+	0.835889i	$0.315047\pi$
$180$		0			0
$181$	4.24621			0.315618			0.157809	−	0.987470i	$-0.449557\pi$
$181$	4.24621			0.315618			0.157809	+	0.987470i	$0.449557\pi$
$182$	1.75379	+	3.74571i	0.129999	+	0.277650i
$183$	−8.54312	+	2.39871i	−0.631525	+	0.177317i
$184$	20.8078	+	5.47091i	1.53397	+	0.403321i
$185$		0			0
$186$	−3.83715	−	4.44961i	−0.281354	−	0.326261i
$187$	8.54312			0.624735
$188$	−1.43845	−	1.19935i	−0.104910	−	0.0874718i
$189$	−3.31534	+	3.56155i	−0.241156	+	0.259065i
$190$		0			0
$191$	7.72197			0.558742			0.279371	−	0.960183i	$-0.409874\pi$
$191$	7.72197			0.558742			0.279371	+	0.960183i	$0.409874\pi$
$192$	−13.4577	−	3.30024i	−0.971222	−	0.238175i
$193$			16.2462i			1.16943i	0.811240	+	0.584714i	$0.198793\pi$
$193$			16.2462i			1.16943i	−0.811240	+	0.584714i	$0.801207\pi$
$194$	−3.59806	−	7.68466i	−0.258326	−	0.551726i
$195$		0			0
$196$	−7.84233	+	9.40572i	−0.560166	+	0.671837i
$197$	−12.2462			−0.872506			−0.436253	−	0.899824i	$-0.643695\pi$
$197$	−12.2462			−0.872506			−0.436253	+	0.899824i	$0.643695\pi$
$198$	−10.0140	+	15.1047i	−0.711666	+	1.07344i
$199$			17.6121i			1.24849i	0.781230	+	0.624244i	$0.214593\pi$
$199$			17.6121i			1.24849i	−0.781230	+	0.624244i	$0.785407\pi$
$200$		0			0
$201$	−8.68466	+	2.43845i	−0.612569	+	0.171995i
$202$	5.47091	+	11.6847i	0.384932	+	0.822130i
$203$		−	4.79741i		−	0.336712i
$204$	2.83311	−	6.32246i	0.198357	−	0.442661i
$205$		0			0
$206$	15.8869	−	7.43845i	1.10689	−	0.518261i
$207$	−11.8782	−	19.4849i	−0.825595	−	1.35430i
$208$	12.2888	−	2.24621i	0.852077	−	0.155747i
$209$		−	18.2462i		−	1.26212i
$210$		0			0
$211$		−	1.34700i		−	0.0927313i	−0.998925	−	0.0463656i	$-0.985236\pi$
$211$		−	1.34700i		−	0.0927313i	0.998925	−	0.0463656i	$-0.0147639\pi$
$212$	−5.43845	+	6.52262i	−0.373514	+	0.447975i
$213$	−11.1231	+	3.12311i	−0.762143	+	0.213992i
$214$	−0.561553	−	1.19935i	−0.0383870	−	0.0819861i
$215$		0			0
$216$	7.85753	+	12.4201i	0.534637	+	0.845082i
$217$		−	2.24621i		−	0.152483i
$218$	−11.6847	+	5.47091i	−0.791385	+	0.370537i
$219$	−3.86098	−	13.7511i	−0.260901	−	0.929213i
$220$		0			0
$221$			6.24621i			0.420166i
$222$	−4.99596	−	5.79337i	−0.335307	−	0.388826i
$223$	−18.0227			−1.20689			−0.603443	−	0.797406i	$-0.706205\pi$
$223$	−18.0227			−1.20689			−0.603443	+	0.797406i	$0.706205\pi$
$224$	−3.07221	−	4.31534i	−0.205270	−	0.288331i
$225$		0			0
$226$	17.9309	−	8.39547i	1.19274	−	0.558458i
$227$			8.65840i			0.574678i	0.957829	+	0.287339i	$0.0927706\pi$
$227$			8.65840i			0.574678i	−0.957829	+	0.287339i	$0.907229\pi$
$228$	−13.5034	−	6.05090i	−0.894283	−	0.400731i
$229$	−0.246211			−0.0162701			−0.00813505	−	0.999967i	$-0.502589\pi$
$229$	−0.246211			−0.0162701			−0.00813505	+	0.999967i	$0.502589\pi$
$230$		0			0
$231$	−6.67026	+	1.87285i	−0.438871	+	0.123225i
$232$	−14.0140	−	3.68466i	−0.920066	−	0.241910i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	−11.0436	−	7.32165i	−0.721944	−	0.478631i
$235$		0			0
$236$	−9.21662	+	11.0540i	−0.599951	+	0.719553i
$237$	4.24621	+	15.1231i	0.275821	+	0.982351i
$238$	2.39871	−	1.12311i	0.155485	−	0.0728001i
$239$	−20.8319			−1.34751			−0.673753	−	0.738957i	$-0.735319\pi$
$239$	−20.8319			−1.34751			−0.673753	+	0.738957i	$0.735319\pi$
$240$		0			0
$241$	−11.3693			−0.732362			−0.366181	−	0.930544i	$-0.619335\pi$
$241$	−11.3693			−0.732362			−0.366181	+	0.930544i	$0.619335\pi$
$242$	−9.28078	+	4.34538i	−0.596591	+	0.279332i
$243$	3.12985	−	15.2710i	0.200780	−	0.979636i
$244$	−6.56155	+	7.86962i	−0.420060	+	0.503801i
$245$		0			0
$246$	−11.3947	−	13.2134i	−0.726497	−	0.842454i
$247$	13.3405			0.848837
$248$	−6.56155	−	1.72521i	−0.416659	−	0.109551i
$249$	2.19224	+	7.80776i	0.138927	+	0.494797i
$250$		0			0
$251$	25.1035			1.58452			0.792259	−	0.610184i	$-0.208905\pi$
$251$	25.1035			1.58452			0.792259	+	0.610184i	$0.208905\pi$
$252$	−0.825994	+	5.55751i	−0.0520328	+	0.350090i
$253$		−	32.4924i		−	2.04278i
$254$	−5.99676	+	2.80776i	−0.376270	+	0.176175i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$	−2.49242			−0.155473			−0.0777365	−	0.996974i	$-0.524769\pi$
$257$	−2.49242			−0.155473			−0.0777365	+	0.996974i	$0.524769\pi$
$258$	−2.71253	+	2.33917i	−0.168875	+	0.145631i
$259$		−	2.92456i		−	0.181723i
$260$		0			0
$261$	8.00000	+	13.1231i	0.495188	+	0.812300i
$262$	22.5571	−	10.5616i	1.39359	−	0.652495i
$263$		−	15.0981i		−	0.930989i	−0.885051	−	0.465494i	$-0.845877\pi$
$263$		−	15.0981i		−	0.930989i	0.885051	−	0.465494i	$-0.154123\pi$
$264$	0.347806	+	20.9234i	0.0214060	+	1.28775i
$265$		0			0
$266$	−2.39871	−	5.12311i	−0.147074	−	0.314118i
$267$	2.92456	+	10.4160i	0.178980	+	0.637447i
$268$	−6.67026	+	8.00000i	−0.407451	+	0.488678i
$269$		−	14.0000i		−	0.853595i	−0.904347	−	0.426798i	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$		0			0
$271$			31.7738i			1.93012i	0.262032	+	0.965059i	$0.415608\pi$
$271$			31.7738i			1.93012i	−0.262032	+	0.965059i	$0.584392\pi$
$272$	−1.43845	−	7.86962i	−0.0872187	−	0.477166i
$273$	−1.36932	−	4.87689i	−0.0828748	−	0.295163i
$274$	−10.5616	+	4.94506i	−0.638047	+	0.298742i
$275$		0			0
$276$	−24.0465	−	10.7753i	−1.44743	−	0.648597i
$277$			1.36932i			0.0822743i	0.999154	+	0.0411371i	$0.0130981\pi$
$277$			1.36932i			0.0822743i	−0.999154	+	0.0411371i	$0.986902\pi$
$278$	8.31534	+	17.7597i	0.498721	+	1.06516i
$279$	3.74571	+	6.14441i	0.224250	+	0.367856i
$280$		0			0
$281$		−	27.6155i		−	1.64740i	−0.567023	−	0.823702i	$-0.691905\pi$
$281$		−	27.6155i		−	1.64740i	0.567023	−	0.823702i	$-0.308095\pi$
$282$	1.49798	+	1.73707i	0.0892034	+	0.103441i
$283$	4.38684			0.260770			0.130385	−	0.991463i	$-0.458379\pi$
$283$	4.38684			0.260770			0.130385	+	0.991463i	$0.458379\pi$
$284$	−8.54312	+	10.2462i	−0.506941	+	0.608001i
$285$		0			0
$286$	−8.00000	−	17.0862i	−0.473050	−	1.01033i
$287$		−	6.67026i		−	0.393733i
$288$	15.6000	+	6.68132i	0.919239	+	0.393701i
$289$	−13.0000			−0.764706
$290$		0			0
$291$	2.80928	+	10.0054i	0.164683	+	0.586527i
$292$	−12.6670	−	10.5616i	−0.741282	−	0.618068i
$293$	30.4924			1.78139			0.890693	−	0.454605i	$-0.150220\pi$
$293$	30.4924			1.78139			0.890693	+	0.454605i	$0.150220\pi$
$294$	11.3584	−	9.79499i	0.662434	−	0.571255i
$295$		0			0
$296$	−8.54312	−	2.24621i	−0.496559	−	0.130558i
$297$	15.1231	−	16.2462i	0.877532	−	0.942701i
$298$	−8.39547	−	17.9309i	−0.486337	−	1.03871i
$299$	23.7565			1.37387
$300$		0			0
$301$	−1.36932			−0.0789261
$302$	3.68466	+	7.86962i	0.212028	+	0.452846i
$303$	−4.27156	−	15.2134i	−0.245395	−	0.873986i
$304$	−16.8078	+	3.07221i	−0.963991	+	0.176203i
$305$		0			0
$306$	−4.68870	+	7.07221i	−0.268035	+	0.404291i
$307$	−8.13254			−0.464149			−0.232074	−	0.972698i	$-0.574551\pi$
$307$	−8.13254			−0.464149			−0.232074	+	0.972698i	$0.574551\pi$
$308$	−5.12311	+	6.14441i	−0.291916	+	0.350110i
$309$	−20.6847	+	5.80776i	−1.17671	+	0.330392i
$310$		0			0
$311$	14.1617			0.803035			0.401517	−	0.915851i	$-0.368483\pi$
$311$	14.1617			0.803035			0.401517	+	0.915851i	$0.368483\pi$
$312$	−15.2979	+	0.254294i	−0.866074	+	0.0143966i
$313$			10.4924i			0.593067i	0.955022	+	0.296533i	$0.0958306\pi$
$313$			10.4924i			0.593067i	−0.955022	+	0.296533i	$0.904169\pi$
$314$	12.8147	+	27.3693i	0.723174	+	1.54454i
$315$		0			0
$316$	13.9309	+	11.6153i	0.783673	+	0.653413i
$317$	32.7386			1.83878			0.919392	−	0.393342i	$-0.128681\pi$
$317$	32.7386			1.83878			0.919392	+	0.393342i	$0.128681\pi$
$318$	7.87673	−	6.79256i	0.441705	−	0.380908i
$319$			21.8836i			1.22525i
$320$		0			0
$321$	0.438447	+	1.56155i	0.0244717	+	0.0871574i
$322$	−4.27156	−	9.12311i	−0.238045	−	0.508411i
$323$		−	8.54312i		−	0.475352i
$324$	−7.00805	−	16.5797i	−0.389336	−	0.921096i
$325$		0			0
$326$	−30.9526	+	14.4924i	−1.71431	+	0.802661i
$327$	15.2134	−	4.27156i	0.841302	−	0.236218i
$328$	−19.4849	−	5.12311i	−1.07588	−	0.282876i
$329$			0.876894i			0.0483448i
$330$		0			0
$331$		−	28.0281i		−	1.54056i	−0.637705	−	0.770281i	$-0.720116\pi$
$331$		−	28.0281i		−	1.54056i	0.637705	−	0.770281i	$-0.279884\pi$
$332$	7.19224	+	5.99676i	0.394725	+	0.329115i
$333$	4.87689	+	8.00000i	0.267252	+	0.438397i
$334$	−1.68466	−	3.59806i	−0.0921804	−	0.196877i
$335$		0			0
$336$	2.84831	+	5.82907i	0.155388	+	0.318002i
$337$			34.4924i			1.87892i	0.342656	+	0.939461i	$0.388674\pi$
$337$			34.4924i			1.87892i	−0.342656	+	0.939461i	$0.611326\pi$
$338$	−4.15767	+	1.94668i	−0.226147	+	0.105885i
$339$	−23.3459	+	6.55498i	−1.26798	+	0.356018i
$340$		0			0
$341$			10.2462i			0.554863i
$342$	15.1047	+	10.0140i	0.816767	+	0.541497i
$343$	12.2888			0.663534
$344$	−1.05171	+	4.00000i	−0.0567042	+	0.215666i
$345$		0			0
$346$	2.56155	−	1.19935i	0.137710	−	0.0644776i
$347$		−	23.8718i		−	1.28150i	−0.767748	−	0.640752i	$-0.778623\pi$
$347$		−	23.8718i		−	1.28150i	0.767748	−	0.640752i	$-0.221377\pi$
$348$	16.1953	+	7.25716i	0.868160	+	0.389025i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	11.8782	+	11.0571i	0.634014	+	0.590184i
$352$	14.0140	+	19.6847i	0.746950	+	1.04920i
$353$	3.75379			0.199794			0.0998970	−	0.994998i	$-0.468149\pi$
$353$	3.75379			0.199794			0.0998970	+	0.994998i	$0.468149\pi$
$354$	13.3488	−	11.5115i	0.709482	−	0.611827i
$355$		0			0
$356$	9.59482	+	8.00000i	0.508525	+	0.423999i
$357$	−3.12311	+	0.876894i	−0.165292	+	0.0464102i
$358$	−18.8114	+	8.80776i	−0.994215	+	0.465505i
$359$	1.05171			0.0555069			0.0277535	−	0.999615i	$-0.491165\pi$
$359$	1.05171			0.0555069			0.0277535	+	0.999615i	$0.491165\pi$
$360$		0			0
$361$	0.753789			0.0396731
$362$	−5.43845	+	2.54635i	−0.285838	+	0.133833i
$363$	12.0835	−	3.39277i	0.634221	−	0.178074i
$364$	−4.49242	−	3.74571i	−0.235467	−	0.196328i
$365$		0			0
$366$	9.50338	−	8.19531i	0.496749	−	0.428376i
$367$	−26.5658			−1.38672			−0.693361	−	0.720590i	$-0.743871\pi$
$367$	−26.5658			−1.38672			−0.693361	+	0.720590i	$0.743871\pi$
$368$	−29.9309	+	5.47091i	−1.56025	+	0.285191i
$369$	11.1231	+	18.2462i	0.579046	+	0.949860i
$370$		0			0
$371$	3.97626			0.206437
$372$	7.58286	+	3.39790i	0.393153	+	0.176173i
$373$		−	0.876894i		−	0.0454039i	−0.999742	−	0.0227019i	$-0.992773\pi$
$373$		−	0.876894i		−	0.0454039i	0.999742	−	0.0227019i	$-0.00722687\pi$
$374$	−10.9418	+	5.12311i	−0.565788	+	0.264909i
$375$		0			0
$376$	2.56155	+	0.673500i	0.132102	+	0.0347331i
$377$	−16.0000			−0.824042
$378$	2.11043	−	6.54968i	0.108549	−	0.336879i
$379$		−	25.1035i		−	1.28948i	−0.764402	−	0.644740i	$-0.776966\pi$
$379$		−	25.1035i		−	1.28948i	0.764402	−	0.644740i	$-0.223034\pi$
$380$		0			0
$381$	7.80776	−	2.19224i	0.400004	−	0.112312i
$382$	−9.89012	+	4.63068i	−0.506022	+	0.236926i
$383$		−	4.68213i		−	0.239246i	−0.992819	−	0.119623i	$-0.961831\pi$
$383$		−	4.68213i		−	0.239246i	0.992819	−	0.119623i	$-0.0381685\pi$
$384$	19.2153	−	3.84336i	0.980578	−	0.196131i
$385$		0			0
$386$	−9.74247	−	20.8078i	−0.495879	−	1.05909i
$387$	3.74571	−	2.28343i	0.190405	−	0.116073i
$388$	9.21662	+	7.68466i	0.467903	+	0.390129i
$389$		−	28.7386i		−	1.45711i	−0.684989	−	0.728553i	$-0.740193\pi$
$389$		−	28.7386i		−	1.45711i	0.684989	−	0.728553i	$-0.259807\pi$
$390$		0			0
$391$		−	15.2134i		−	0.769374i
$392$	4.40388	−	16.7495i	0.222430	−	0.845977i
$393$	−29.3693	+	8.24621i	−1.48149	+	0.415966i
$394$	15.6847	−	7.34376i	0.790182	−	0.369973i
$395$		0			0
$396$	3.76782	−	25.3509i	0.189340	−	1.27393i
$397$		−	23.1231i		−	1.16052i	−0.814433	−	0.580258i	$-0.802952\pi$
$397$		−	23.1231i		−	1.16052i	0.814433	−	0.580258i	$-0.197048\pi$
$398$	−10.5616	−	22.5571i	−0.529403	−	1.13069i
$399$	1.87285	+	6.67026i	0.0937599	+	0.333931i
$400$		0			0
$401$			24.0000i			1.19850i	0.800561	+	0.599251i	$0.204535\pi$
$401$			24.0000i			1.19850i	−0.800561	+	0.599251i	$0.795465\pi$
$402$	9.66083	−	8.33109i	0.481838	−	0.415517i
$403$	−7.49141			−0.373174
$404$	−14.0140	−	11.6847i	−0.697224	−	0.581333i
$405$		0			0
$406$	2.87689	+	6.14441i	0.142778	+	0.304942i
$407$			13.3405i			0.661265i
$408$	0.162847	+	9.79661i	0.00806214	+	0.485004i
$409$	−0.630683			−0.0311853			−0.0155926	−	0.999878i	$-0.504963\pi$
$409$	−0.630683			−0.0311853			−0.0155926	+	0.999878i	$0.504963\pi$
$410$		0			0
$411$	13.7511	−	3.86098i	0.678292	−	0.190448i
$412$	−15.8869	+	19.0540i	−0.782690	+	0.938722i
$413$	6.73863			0.331586
$414$	26.8980	+	17.8327i	1.32197	+	0.876432i
$415$		0			0
$416$	−14.3922	+	10.2462i	−0.705637	+	0.502362i
$417$	−6.49242	−	23.1231i	−0.317935	−	1.13234i
$418$	10.9418	+	23.3693i	0.535182	+	1.14303i
$419$	−6.14441			−0.300174			−0.150087	−	0.988673i	$-0.547955\pi$
$419$	−6.14441			−0.300174			−0.150087	+	0.988673i	$0.547955\pi$
$420$		0			0
$421$	−0.630683			−0.0307376			−0.0153688	−	0.999882i	$-0.504892\pi$
$421$	−0.630683			−0.0307376			−0.0153688	+	0.999882i	$0.504892\pi$
$422$	0.807764	+	1.72521i	0.0393213	+	0.0839817i
$423$	−1.46228	−	2.39871i	−0.0710985	−	0.116629i
$424$	3.05398	−	11.6153i	0.148314	−	0.564090i
$425$		0			0
$426$	12.3734	−	10.6703i	0.599491	−	0.516976i
$427$	4.79741			0.232163
$428$	1.43845	+	1.19935i	0.0695300	+	0.0579729i
$429$	6.24621	+	22.2462i	0.301570	+	1.07406i
$430$		0			0
$431$	−36.0453			−1.73624			−0.868121	−	0.496353i	$-0.834672\pi$
$431$	−36.0453			−1.73624			−0.868121	+	0.496353i	$0.834672\pi$
$432$	−17.5118	−	11.1954i	−0.842536	−	0.538640i
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	1.34700	+	2.87689i	0.0646581	+	0.138095i
$435$		0			0
$436$	11.6847	−	14.0140i	0.559594	−	0.671150i
$437$	−32.4924			−1.55432
$438$	13.1913	+	15.2967i	0.630303	+	0.730907i
$439$		−	29.9009i		−	1.42709i	−0.700608	−	0.713546i	$-0.747088\pi$
$439$		−	29.9009i		−	1.42709i	0.700608	−	0.713546i	$-0.252912\pi$
$440$		0			0
$441$	−15.6847	+	9.56155i	−0.746888	+	0.455312i
$442$	−3.74571	−	8.00000i	−0.178165	−	0.380521i
$443$			25.7446i			1.22316i	0.791181	+	0.611582i	$0.209467\pi$
$443$			25.7446i			1.22316i	−0.791181	+	0.611582i	$0.790533\pi$
$444$	9.87285	+	4.42405i	0.468545	+	0.209956i
$445$		0			0
$446$	23.0830	−	10.8078i	1.09301	−	0.511762i
$447$	6.55498	+	23.3459i	0.310040	+	1.10422i
$448$	6.52262	+	3.68466i	0.308165	+	0.174084i
$449$			2.63068i			0.124150i	0.998071	+	0.0620748i	$0.0197717\pi$
$449$			2.63068i			0.124150i	−0.998071	+	0.0620748i	$0.980228\pi$
$450$		0			0
$451$			30.4268i			1.43274i
$452$	−17.9309	+	21.5054i	−0.843397	+	1.01153i
$453$	−2.87689	−	10.2462i	−0.135168	−	0.481409i
$454$	−5.19224	−	11.0895i	−0.243684	−	0.520455i
$455$		0			0
$456$	20.9234	−	0.347806i	0.979827	−	0.0162875i
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	0.315342	−	0.147647i	0.0147349	−	0.00689909i
$459$	7.08084	−	7.60669i	0.330505	−	0.355050i
$460$		0			0
$461$		−	15.8617i		−	0.738755i	−0.929279	−	0.369377i	$-0.879571\pi$
$461$		−	15.8617i		−	0.738755i	0.929279	−	0.369377i	$-0.120429\pi$
$462$	7.42001	−	6.39871i	0.345210	−	0.297695i
$463$	−0.936426			−0.0435194			−0.0217597	−	0.999763i	$-0.506927\pi$
$463$	−0.936426			−0.0435194			−0.0217597	+	0.999763i	$0.506927\pi$
$464$	20.1584	−	3.68466i	0.935832	−	0.171056i
$465$		0			0
$466$	−12.8078	+	5.99676i	−0.593308	+	0.277795i
$467$		−	16.1498i		−	0.747324i	−0.927565	−	0.373662i	$-0.878102\pi$
$467$		−	16.1498i		−	0.747324i	0.927565	−	0.373662i	$-0.121898\pi$
$468$	18.5350	+	2.75480i	0.856782	+	0.127341i
$469$	4.87689			0.225194
$470$		0			0
$471$	−10.0054	−	35.6347i	−0.461024	−	1.64196i
$472$	5.17562	−	19.6847i	0.238227	−	0.906060i
$473$	6.24621			0.287201
$474$	−14.5074	−	16.8230i	−0.666348	−	0.772704i
$475$		0			0
$476$	−2.39871	+	2.87689i	−0.109944	+	0.131862i
$477$	−10.8769	+	6.63068i	−0.498019	+	0.303598i
$478$	26.6811	−	12.4924i	1.22036	−	0.571390i
$479$	22.9354			1.04794			0.523971	−	0.851736i	$-0.324450\pi$
$479$	22.9354			1.04794			0.523971	+	0.851736i	$0.324450\pi$
$480$		0			0
$481$	−9.75379			−0.444734
$482$	14.5616	−	6.81791i	0.663261	−	0.310547i
$483$	3.33513	+	11.8782i	0.151754	+	0.540479i
$484$	9.28078	−	11.1309i	0.421853	−	0.505951i
$485$		0			0
$486$	5.14904	+	21.4357i	0.233565	+	0.972341i
$487$	15.3287			0.694608			0.347304	−	0.937753i	$-0.387097\pi$
$487$	15.3287			0.694608			0.347304	+	0.937753i	$0.387097\pi$
$488$	3.68466	−	14.0140i	0.166797	−	0.634385i
$489$	40.3002	−	11.3153i	1.82244	−	0.511697i
$490$		0			0
$491$	−18.6638			−0.842285			−0.421143	−	0.906994i	$-0.638371\pi$
$491$	−18.6638			−0.842285			−0.421143	+	0.906994i	$0.638371\pi$
$492$	22.5178	+	10.0903i	1.01518	+	0.454905i
$493$			10.2462i			0.461466i
$494$	−17.0862	+	8.00000i	−0.768746	+	0.359937i
$495$		0			0
$496$	9.43845	−	1.72521i	0.423799	−	0.0774640i
$497$	6.24621			0.280181
$498$	−7.48990	−	8.68537i	−0.335630	−	0.389201i
$499$			1.57756i			0.0706212i	0.999376	+	0.0353106i	$0.0112421\pi$
$499$			1.57756i			0.0706212i	−0.999376	+	0.0353106i	$0.988758\pi$
$500$		0			0
$501$	1.31534	+	4.68466i	0.0587651	+	0.209295i
$502$	−32.1520	+	15.0540i	−1.43501	+	0.671892i
$503$			19.8955i			0.887097i	0.896250	+	0.443549i	$0.146281\pi$
$503$			19.8955i			0.887097i	−0.896250	+	0.443549i	$0.853719\pi$
$504$	−2.27479	−	7.61326i	−0.101327	−	0.339121i
$505$		0			0
$506$	19.4849	+	41.6155i	0.866211	+	1.85004i
$507$	5.41327	−	1.51992i	0.240412	−	0.0675020i
$508$	5.99676	−	7.19224i	0.266063	−	0.319104i
$509$		−	2.87689i		−	0.127516i	−0.997965	−	0.0637581i	$-0.979691\pi$
$509$		−	2.87689i		−	0.127516i	0.997965	−	0.0637581i	$-0.0203086\pi$
$510$		0			0
$511$			7.72197i			0.341600i
$512$	15.7732	−	16.2236i	0.697083	−	0.716990i
$513$	−16.2462	−	15.1231i	−0.717288	−	0.667701i
$514$	3.19224	−	1.49465i	0.140803	−	0.0659261i
$515$		0			0
$516$	2.07140	−	4.62260i	0.0911883	−	0.203499i
$517$		−	4.00000i		−	0.175920i
$518$	1.75379	+	3.74571i	0.0770571	+	0.164577i
$519$	−3.33513	+	0.936426i	−0.146396	+	0.0411046i
$520$		0			0
$521$		−	21.7538i		−	0.953051i	−0.879161	−	0.476525i	$-0.841896\pi$
$521$		−	21.7538i		−	0.953051i	0.879161	−	0.476525i	$-0.158104\pi$
$522$	−18.1158	−	12.0104i	−0.792908	−	0.525679i
$523$	−0.641132			−0.0280348			−0.0140174	−	0.999902i	$-0.504462\pi$
$523$	−0.641132			−0.0280348			−0.0140174	+	0.999902i	$0.504462\pi$
$524$	−22.5571	+	27.0540i	−0.985413	+	1.18186i
$525$		0			0
$526$	9.05398	+	19.3373i	0.394772	+	0.843146i
$527$			4.79741i			0.208979i
$528$	−12.9927	−	26.5896i	−0.565436	−	1.15716i
$529$	−34.8617			−1.51573
$530$		0			0
$531$	−18.4332	+	11.2371i	−0.799934	+	0.487649i
$532$	6.14441	+	5.12311i	0.266394	+	0.222115i
$533$	−22.2462			−0.963590
$534$	−9.99192	−	11.5867i	−0.432393	−	0.501407i
$535$		0			0
$536$	3.74571	−	14.2462i	0.161790	−	0.615343i
$537$	24.4924	−	6.87689i	1.05693	−	0.296760i
$538$	8.39547	+	17.9309i	0.361954	+	0.773055i
$539$	−26.1552			−1.12658
$540$		0			0
$541$	38.9848			1.67609			0.838045	−	0.545602i	$-0.183699\pi$
$541$	38.9848			1.67609			0.838045	+	0.545602i	$0.183699\pi$
$542$	−19.0540	−	40.6951i	−0.818438	−	1.74800i
$543$	7.08084	−	1.98813i	0.303868	−	0.0853189i
$544$	6.56155	+	9.21662i	0.281324	+	0.395159i
$545$		0			0
$546$	4.67835	+	5.42506i	0.200215	+	0.232171i
$547$	−25.2188			−1.07828			−0.539139	−	0.842217i	$-0.681250\pi$
$547$	−25.2188			−1.07828			−0.539139	+	0.842217i	$0.681250\pi$
$548$	10.5616	−	12.6670i	0.451167	−	0.541109i
$549$	−13.1231	+	8.00000i	−0.560080	+	0.341432i
$550$		0			0
$551$	21.8836			0.932275
$552$	37.2599	−	0.619364i	1.58589	−	0.0263619i
$553$		−	8.49242i		−	0.361135i
$554$	−0.821147	−	1.75379i	−0.0348872	−	0.0745113i
$555$		0			0
$556$	−21.3002	−	17.7597i	−0.903329	−	0.753180i
$557$	19.7538			0.836995			0.418497	−	0.908218i	$-0.362557\pi$
$557$	19.7538			0.836995			0.418497	+	0.908218i	$0.362557\pi$
$558$	−8.48207	−	5.62341i	−0.359075	−	0.238058i
$559$			4.56685i			0.193157i
$560$		0			0
$561$	14.2462	−	4.00000i	0.601476	−	0.168880i
$562$	16.5604	+	35.3693i	0.698558	+	1.49196i
$563$			36.1606i			1.52399i	0.647584	+	0.761994i	$0.275779\pi$
$563$			36.1606i			1.52399i	−0.647584	+	0.761994i	$0.724221\pi$
$564$	−2.96026	−	1.32650i	−0.124649	−	0.0558557i
$565$		0			0
$566$	−5.61856	+	2.63068i	−0.236166	+	0.110576i
$567$	−3.86098	+	7.49141i	−0.162146	+	0.314610i
$568$	4.79741	−	18.2462i	0.201295	−	0.765594i
$569$			4.87689i			0.204450i	0.994761	+	0.102225i	$0.0325962\pi$
$569$			4.87689i			0.204450i	−0.994761	+	0.102225i	$0.967404\pi$
$570$		0			0
$571$		−	16.7909i		−	0.702679i	−0.936248	−	0.351339i	$-0.885726\pi$
$571$		−	16.7909i		−	0.702679i	0.936248	−	0.351339i	$-0.114274\pi$
$572$	20.4924	+	17.0862i	0.856831	+	0.714411i
$573$	12.8769	−	3.61553i	0.537940	−	0.151041i
$574$	4.00000	+	8.54312i	0.166957	+	0.356583i
$575$		0			0
$576$	−23.9867	+	0.797675i	−0.999448	+	0.0332364i
$577$			15.7538i			0.655839i	0.944706	+	0.327919i	$0.106347\pi$
$577$			15.7538i			0.655839i	−0.944706	+	0.327919i	$0.893653\pi$
$578$	16.6501	−	7.79579i	0.692553	−	0.324262i
$579$	7.60669	+	27.0916i	0.316123	+	1.12589i
$580$		0			0
$581$		−	4.38447i		−	0.181899i
$582$	−9.59806	−	11.1300i	−0.397852	−	0.461354i
$583$	−18.1379			−0.751197
$584$	22.5571	+	5.93087i	0.933421	+	0.245421i
$585$		0			0
$586$	−39.0540	+	18.2856i	−1.61330	+	0.755371i
$587$			38.0335i			1.56981i	0.619617	+	0.784904i	$0.287288\pi$
$587$			38.0335i			1.56981i	−0.619617	+	0.784904i	$0.712712\pi$
$588$	−8.67372	+	19.3565i	−0.357698	+	0.798250i
$589$	10.2462			0.422188
$590$		0			0
$591$	−20.4214	+	5.73384i	−0.840023	+	0.235859i
$592$	12.2888	−	2.24621i	0.505067	−	0.0923187i
$593$	8.24621			0.338631			0.169316	−	0.985562i	$-0.445844\pi$
$593$	8.24621			0.338631			0.169316	+	0.985562i	$0.445844\pi$
$594$	−9.62685	+	29.8767i	−0.394994	+	1.22586i
$595$		0			0
$596$	21.5054	+	17.9309i	0.880897	+	0.734477i
$597$	8.24621	+	29.3693i	0.337495	+	1.20201i
$598$	−30.4268	+	14.2462i	−1.24424	+	0.582571i
$599$	36.8665			1.50632			0.753162	−	0.657836i	$-0.228528\pi$
$599$	36.8665			1.50632			0.753162	+	0.657836i	$0.228528\pi$
$600$		0			0
$601$	14.8769			0.606841			0.303421	−	0.952857i	$-0.401871\pi$
$601$	14.8769			0.606841			0.303421	+	0.952857i	$0.401871\pi$
$602$	1.75379	−	0.821147i	0.0714791	−	0.0334675i
$603$	−13.3405	+	8.13254i	−0.543268	+	0.331183i
$604$	−9.43845	−	7.86962i	−0.384045	−	0.320210i
$605$		0			0
$606$	14.5940	+	16.9234i	0.592841	+	0.687466i
$607$	−29.4903			−1.19698			−0.598488	−	0.801132i	$-0.704232\pi$
$607$	−29.4903			−1.19698			−0.598488	+	0.801132i	$0.704232\pi$
$608$	19.6847	−	14.0140i	0.798318	−	0.568344i
$609$	−2.24621	−	8.00000i	−0.0910211	−	0.324176i
$610$		0			0
$611$	2.92456			0.118315
$612$	1.76414	−	11.8696i	0.0713112	−	0.479801i
$613$			0.876894i			0.0354174i	0.999843	+	0.0177087i	$0.00563715\pi$
$613$			0.876894i			0.0354174i	−0.999843	+	0.0177087i	$0.994363\pi$
$614$	10.4160	−	4.87689i	0.420354	−	0.196815i
$615$		0			0
$616$	2.87689	−	10.9418i	0.115913	−	0.440859i
$617$	−14.0000			−0.563619			−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000			−0.563619			−0.281809	+	0.959470i	$0.590935\pi$
$618$	23.0096	−	19.8425i	0.925584	−	0.798184i
$619$			20.3061i			0.816171i	0.912944	+	0.408085i	$0.133803\pi$
$619$			20.3061i			0.816171i	−0.912944	+	0.408085i	$0.866197\pi$
$620$		0			0
$621$	−28.9309	−	26.9309i	−1.16096	−	1.08070i
$622$	−18.1379	+	8.49242i	−0.727265	+	0.340515i
$623$		−	5.84912i		−	0.234340i
$624$	19.4407	−	9.49949i	0.778252	−	0.380284i
$625$		0			0
$626$	−6.29206	−	13.4384i	−0.251481	−	0.537108i
$627$	−8.54312	−	30.4268i	−0.341179	−	1.21513i
$628$	−32.8255	−	27.3693i	−1.30988	−	1.09215i
$629$			6.24621i			0.249053i
$630$		0			0
$631$		−	30.1315i		−	1.19951i	−0.800182	−	0.599757i	$-0.795264\pi$
$631$		−	30.1315i		−	1.19951i	0.800182	−	0.599757i	$-0.204736\pi$
$632$	−24.8078	−	6.52262i	−0.986800	−	0.259456i
$633$	−0.630683	−	2.24621i	−0.0250674	−	0.0892789i
$634$	−41.9309	+	19.6326i	−1.66529	+	0.779710i
$635$		0			0
$636$	−6.01499	+	13.4232i	−0.238510	+	0.532266i
$637$		−	19.1231i		−	0.757685i
$638$	−13.1231	−	28.0281i	−0.519549	−	1.10964i
$639$	−17.0862	+	10.4160i	−0.675921	+	0.412049i
$640$		0			0
$641$		−	47.6155i		−	1.88070i	−0.340208	−	0.940350i	$-0.610498\pi$
$641$		−	47.6155i		−	1.88070i	0.340208	−	0.940350i	$-0.389502\pi$
$642$	−1.49798	−	1.73707i	−0.0591205	−	0.0685568i
$643$	−20.4214			−0.805340			−0.402670	−	0.915345i	$-0.631918\pi$
$643$	−20.4214			−0.805340			−0.402670	+	0.915345i	$0.631918\pi$
$644$	10.9418	+	9.12311i	0.431168	+	0.359501i
$645$		0			0
$646$	5.12311	+	10.9418i	0.201566	+	0.430500i
$647$			3.63043i			0.142727i	0.997450	+	0.0713634i	$0.0227350\pi$
$647$			3.63043i			0.142727i	−0.997450	+	0.0713634i	$0.977265\pi$
$648$	18.9182	+	17.0324i	0.743177	+	0.669094i
$649$	−30.7386			−1.20660
$650$		0			0
$651$	−1.05171	−	3.74571i	−0.0412196	−	0.146806i
$652$	30.9526	−	37.1231i	1.21220	−	1.45385i
$653$	−26.9848			−1.05600			−0.527999	−	0.849245i	$-0.677058\pi$
$653$	−26.9848			−1.05600			−0.527999	+	0.849245i	$0.677058\pi$
$654$	−16.9234	+	14.5940i	−0.661757	+	0.570671i
$655$		0			0
$656$	28.0281	−	5.12311i	1.09431	−	0.200024i
$657$	−12.8769	−	21.1231i	−0.502375	−	0.824091i
$658$	−0.525853	−	1.12311i	−0.0204999	−	0.0437832i
$659$	−26.9764			−1.05085			−0.525425	−	0.850840i	$-0.676094\pi$
$659$	−26.9764			−1.05085			−0.525425	+	0.850840i	$0.676094\pi$
$660$		0			0
$661$	−46.1080			−1.79339			−0.896696	−	0.442647i	$-0.854039\pi$
$661$	−46.1080			−1.79339			−0.896696	+	0.442647i	$0.854039\pi$
$662$	16.8078	+	35.8977i	0.653252	+	1.39520i
$663$	2.92456	+	10.4160i	0.113580	+	0.404523i
$664$	−12.8078	−	3.36750i	−0.497038	−	0.130684i
$665$		0			0
$666$	−11.0436	−	7.32165i	−0.427932	−	0.283708i
$667$	38.9699			1.50892
$668$	4.31534	+	3.59806i	0.166966	+	0.139213i
$669$	−30.0540	+	8.43845i	−1.16195	+	0.326249i
$670$		0			0
$671$	−21.8836			−0.844809
$672$	−7.14361	−	5.75767i	−0.275571	−	0.222107i
$673$		−	10.4924i		−	0.404453i	−0.979339	−	0.202227i	$-0.935182\pi$
$673$		−	10.4924i		−	0.404453i	0.979339	−	0.202227i	$-0.0648177\pi$
$674$	−20.6843	−	44.1771i	−0.796729	−	1.70164i
$675$		0			0
$676$	4.15767	−	4.98651i	0.159910	−	0.191789i
$677$	34.4924			1.32565			0.662826	−	0.748774i	$-0.269357\pi$
$677$	34.4924			1.32565			0.662826	+	0.748774i	$0.269357\pi$
$678$	25.9700	−	22.3955i	0.997373	−	0.860093i
$679$		−	5.61856i		−	0.215620i
$680$		0			0
$681$	4.05398	+	14.4384i	0.155349	+	0.553282i
$682$	−6.14441	−	13.1231i	−0.235282	−	0.502510i
$683$		−	36.1606i		−	1.38365i	−0.722067	−	0.691823i	$-0.756808\pi$
$683$		−	36.1606i		−	1.38365i	0.722067	−	0.691823i	$-0.243192\pi$
$684$	−25.3509	−	3.76782i	−0.969315	−	0.144066i
$685$		0			0
$686$	−15.7392	+	7.36932i	−0.600927	+	0.281362i
$687$	−0.410574	+	0.115279i	−0.0156644	+	0.00439818i
$688$	−1.05171	−	5.75379i	−0.0400959	−	0.219361i
$689$		−	13.2614i		−	0.505218i
$690$		0			0
$691$			29.0798i			1.10625i	0.833100	+	0.553123i	$0.186564\pi$
$691$			29.0798i			1.10625i	−0.833100	+	0.553123i	$0.813436\pi$
$692$	−2.56155	+	3.07221i	−0.0973756	+	0.116788i
$693$	−10.2462	+	6.24621i	−0.389221	+	0.237274i
$694$	14.3153	+	30.5744i	0.543403	+	1.16059i
$695$		0			0
$696$	−25.0945	+	0.417142i	−0.951205	+	0.0158117i
$697$			14.2462i			0.539614i
$698$	−17.9309	+	8.39547i	−0.678693	+	0.317773i
$699$	16.6757	−	4.68213i	0.630731	−	0.177094i
$700$		0			0
$701$			50.4924i			1.90707i	0.301278	+	0.953536i	$0.402587\pi$
$701$			50.4924i			1.90707i	−0.301278	+	0.953536i	$0.597413\pi$
$702$	−21.8441	−	7.03857i	−0.824451	−	0.265654i
$703$	13.3405			0.503148
$704$	−29.7533	−	16.8078i	−1.12137	−	0.633466i
$705$		0			0
$706$	−4.80776	+	2.25106i	−0.180943	+	0.0847197i
$707$			8.54312i			0.321297i
$708$	−10.1937	+	22.7486i	−0.383103	+	0.854944i
$709$	26.4924			0.994944			0.497472	−	0.867480i	$-0.334262\pi$
$709$	26.4924			0.994944			0.497472	+	0.867480i	$0.334262\pi$
$710$		0			0
$711$	14.1617	+	23.2306i	0.531104	+	0.871217i
$712$	−17.0862	−	4.49242i	−0.640334	−	0.168361i
$713$	18.2462			0.683326
$714$	3.47415	−	2.99596i	0.130017	−	0.112121i
$715$		0			0
$716$	18.8114	−	22.5616i	0.703016	−	0.843165i
$717$	−34.7386	+	9.75379i	−1.29734	+	0.364262i
$718$	−1.34700	+	0.630683i	−0.0502696	+	0.0235369i
$719$	−5.84912			−0.218135			−0.109068	−	0.994034i	$-0.534787\pi$
$719$	−5.84912			−0.218135			−0.109068	+	0.994034i	$0.534787\pi$
$720$		0			0
$721$	11.6155			0.432585
$722$	−0.965435	+	0.452029i	−0.0359298	+	0.0168228i
$723$	−18.9591	+	5.32326i	−0.705096	+	0.197974i
$724$	5.43845	−	6.52262i	0.202118	−	0.242411i
$725$		0			0
$726$	−13.4417	+	11.5916i	−0.498870	+	0.430204i
$727$	26.5658			0.985270			0.492635	−	0.870236i	$-0.336034\pi$
$727$	26.5658			0.985270			0.492635	+	0.870236i	$0.336034\pi$
$728$	8.00000	+	2.10341i	0.296500	+	0.0779576i
$729$	−1.93087	−	26.9309i	−0.0715137	−	0.997440i
$730$		0			0
$731$	2.92456			0.108169
$732$	−7.25716	+	16.1953i	−0.268233	+	0.598596i
$733$		−	35.1231i		−	1.29730i	−0.761086	−	0.648651i	$-0.775334\pi$
$733$		−	35.1231i		−	1.29730i	0.761086	−	0.648651i	$-0.224666\pi$
$734$	34.0248	−	15.9309i	1.25588	−	0.588019i
$735$		0			0
$736$	35.0540	−	24.9559i	1.29211	−	0.919885i
$737$	−22.2462			−0.819450
$738$	−25.1880	−	16.6991i	−0.927184	−	0.614701i
$739$			18.6638i			0.686559i	0.939233	+	0.343279i	$0.111538\pi$
$739$			18.6638i			0.686559i	−0.939233	+	0.343279i	$0.888462\pi$
$740$		0			0
$741$	22.2462	−	6.24621i	0.817235	−	0.229460i
$742$	−5.09271	+	2.38447i	−0.186959	+	0.0875367i
$743$			12.4041i			0.455062i	0.973771	+	0.227531i	$0.0730654\pi$
$743$			12.4041i			0.455062i	−0.973771	+	0.227531i	$0.926935\pi$
$744$	−11.7496	+	0.195311i	−0.430761	+	0.00716046i
$745$		0			0
$746$	0.525853	+	1.12311i	0.0192528	+	0.0411198i
$747$	7.31140	+	11.9935i	0.267510	+	0.438820i
$748$	10.9418	−	13.1231i	0.400073	−	0.479828i
$749$		−	0.876894i		−	0.0320410i
$750$		0			0
$751$			15.7392i			0.574333i	0.957881	+	0.287166i	$0.0927133\pi$
$751$			15.7392i			0.574333i	−0.957881	+	0.287166i	$0.907287\pi$
$752$	−3.68466	+	0.673500i	−0.134366	+	0.0245600i
$753$	41.8617	−	11.7538i	1.52553	−	0.428332i
$754$	20.4924	−	9.59482i	0.746290	−	0.349423i
$755$		0			0
$756$	1.22470	+	9.65426i	0.0445419	+	0.351122i
$757$		−	19.1231i		−	0.695041i	−0.937672	−	0.347521i	$-0.887024\pi$
$757$		−	19.1231i		−	0.695041i	0.937672	−	0.347521i	$-0.112976\pi$
$758$	15.0540	+	32.1520i	0.546785	+	1.16781i
$759$	−15.2134	−	54.1833i	−0.552211	−	1.96673i
$760$		0			0
$761$			51.2311i			1.85712i	0.371177	+	0.928562i	$0.378954\pi$
$761$			51.2311i			1.85712i	−0.371177	+	0.928562i	$0.621046\pi$
$762$	−8.68537	+	7.48990i	−0.314638	+	0.271330i
$763$	−8.54312			−0.309282
$764$	9.89012	−	11.8617i	0.357812	−	0.429143i
$765$		0			0
$766$	2.80776	+	5.99676i	0.101449	+	0.216672i
$767$		−	22.4742i		−	0.811498i
$768$	−22.3058	+	16.4455i	−0.804890	+	0.593424i
$769$	26.9848			0.973098			0.486549	−	0.873653i	$-0.338255\pi$
$769$	26.9848			0.973098			0.486549	+	0.873653i	$0.338255\pi$
$770$		0			0
$771$	−4.15628	+	1.16699i	−0.149685	+	0.0420279i
$772$	24.9559	+	20.8078i	0.898181	+	0.748888i
$773$	−16.2462			−0.584336			−0.292168	−	0.956367i	$-0.594377\pi$
$773$	−16.2462			−0.584336			−0.292168	+	0.956367i	$0.594377\pi$
$774$	−3.42809	+	5.17077i	−0.123220	+	0.185859i
$775$		0			0
$776$	−16.4127	−	4.31534i	−0.589183	−	0.154912i
$777$	−1.36932	−	4.87689i	−0.0491240	−	0.174958i
$778$	17.2339	+	36.8078i	0.617865	+	1.31962i
$779$	30.4268			1.09015
$780$		0			0
$781$	−28.4924			−1.01954
$782$	9.12311	+	19.4849i	0.326242	+	0.696780i
$783$	19.4849	+	18.1379i	0.696335	+	0.648197i
$784$	4.40388	+	24.0932i	0.157282	+	0.860473i
$785$		0			0
$786$	32.6705	−	28.1736i	1.16532	−	1.00492i
$787$	−13.9817			−0.498392			−0.249196	−	0.968453i	$-0.580166\pi$
$787$	−13.9817			−0.498392			−0.249196	+	0.968453i	$0.580166\pi$
$788$	−15.6847	+	18.8114i	−0.558743	+	0.670130i
$789$	−7.06913	−	25.1771i	−0.251668	−	0.896328i
$790$		0			0
$791$	13.1100			0.466137
$792$	10.3766	+	34.7283i	0.368716	+	1.23402i
$793$		−	16.0000i		−	0.568177i
$794$	13.8664	+	29.6155i	0.492099	+	1.05102i
$795$		0			0
$796$	27.0540	+	22.5571i	0.958903	+	0.799517i
$797$	−36.7386			−1.30135			−0.650675	−	0.759357i	$-0.725514\pi$
$797$	−36.7386			−1.30135			−0.650675	+	0.759357i	$0.725514\pi$
$798$	−6.39871	−	7.42001i	−0.226512	−	0.262666i
$799$		−	1.87285i		−	0.0662568i
$800$		0			0
$801$	9.75379	+	16.0000i	0.344633	+	0.565332i
$802$	−14.3922	−	30.7386i	−0.508207	−	1.08542i
$803$		−	35.2242i		−	1.24303i
$804$	−7.37740	+	16.4636i	−0.260181	+	0.580628i
$805$		0			0
$806$	9.59482	−	4.49242i	0.337963	−	0.158239i
$807$	−6.55498	−	23.3459i	−0.230746	−	0.821815i
$808$	24.9559	+	6.56155i	0.877944	+	0.230835i
$809$			46.2462i			1.62593i	0.582312	+	0.812965i	$0.302148\pi$
$809$			46.2462i			1.62593i	−0.582312	+	0.812965i	$0.697852\pi$
$810$		0			0
$811$		−	25.9246i		−	0.910337i	−0.890405	−	0.455169i	$-0.849579\pi$
$811$		−	25.9246i		−	0.910337i	0.890405	−	0.455169i	$-0.150421\pi$
$812$	−7.36932	−	6.14441i	−0.258612	−	0.215627i
$813$	14.8769	+	52.9848i	0.521755	+	1.85826i
$814$	−8.00000	−	17.0862i	−0.280400	−	0.598872i
$815$		0			0
$816$	−6.08336	−	12.4496i	−0.212960	−	0.435823i
$817$		−	6.24621i		−	0.218527i
$818$	0.807764	−	0.378206i	0.0282428	−	0.0132237i
$819$	−4.56685	−	7.49141i	−0.159579	−	0.261771i
$820$		0			0
$821$		−	29.2311i		−	1.02017i	−0.860124	−	0.510085i	$-0.829614\pi$
$821$		−	29.2311i		−	1.02017i	0.860124	−	0.510085i	$-0.170386\pi$
$822$	−15.2967	+	13.1913i	−0.533535	+	0.460098i
$823$	46.8071			1.63159			0.815797	−	0.578338i	$-0.196299\pi$
$823$	46.8071			1.63159			0.815797	+	0.578338i	$0.196299\pi$
$824$	8.92132	−	33.9309i	0.310789	−	1.18204i
$825$		0			0
$826$	−8.63068	+	4.04100i	−0.300300	+	0.140604i
$827$			13.2252i			0.459887i	0.973204	+	0.229943i	$0.0738541\pi$
$827$			13.2252i			0.459887i	−0.973204	+	0.229943i	$0.926146\pi$
$828$	−45.1443	−	6.70964i	−1.56887	−	0.233176i
$829$	17.1231			0.594710			0.297355	−	0.954767i	$-0.403896\pi$
$829$	17.1231			0.594710			0.297355	+	0.954767i	$0.403896\pi$
$830$		0			0
$831$	0.641132	+	2.28343i	0.0222406	+	0.0792112i
$832$	12.2888	−	21.7538i	0.426038	−	0.754177i
$833$	−12.2462			−0.424306
$834$	22.1817	+	25.7222i	0.768090	+	0.890686i
$835$		0			0
$836$	−28.0281	−	23.3693i	−0.969371	−	0.808245i
$837$	9.12311	+	8.49242i	0.315341	+	0.293541i
$838$	7.86962	−	3.68466i	0.271851	−	0.127284i
$839$	−48.5647			−1.67664			−0.838320	−	0.545179i	$-0.816462\pi$
$839$	−48.5647			−1.67664			−0.838320	+	0.545179i	$0.816462\pi$
$840$		0			0
$841$	2.75379			0.0949582
$842$	0.807764	−	0.378206i	0.0278374	−	0.0130338i
$843$	−12.9300	−	46.0507i	−0.445331	−	1.58607i
$844$	−2.06913	−	1.72521i	−0.0712224	−	0.0593840i
$845$		0			0
$846$	3.31130	+	2.19531i	0.113845	+	0.0754764i
$847$	−6.78554			−0.233154
$848$	3.05398	+	16.7080i	0.104874	+	0.573756i
$849$	7.31534	−	2.05398i	0.251062	−	0.0704923i
$850$		0			0
$851$	23.7565			0.814362
$852$	−9.44880	+	21.0862i	−0.323711	+	0.722402i
$853$			49.8617i			1.70723i	0.520902	+	0.853617i	$0.325596\pi$
$853$			49.8617i			1.70723i	−0.520902	+	0.853617i	$0.674404\pi$
$854$	−6.14441	+	2.87689i	−0.210257	+	0.0984453i
$855$		0			0
$856$	−2.56155	−	0.673500i	−0.0875521	−	0.0230198i
$857$	28.7386			0.981693			0.490847	−	0.871246i	$-0.336688\pi$
$857$	28.7386			0.981693			0.490847	+	0.871246i	$0.336688\pi$
$858$	−21.3405	−	24.7467i	−0.728554	−	0.844839i
$859$			37.3923i			1.27581i	0.770115	+	0.637905i	$0.220199\pi$
$859$			37.3923i			1.27581i	−0.770115	+	0.637905i	$0.779801\pi$
$860$		0			0
$861$	−3.12311	−	11.1231i	−0.106435	−	0.379074i
$862$	46.1660	−	21.6155i	1.57242	−	0.736228i
$863$		−	27.6175i		−	0.940110i	−0.882637	−	0.470055i	$-0.844234\pi$
$863$		−	27.6175i		−	0.940110i	0.882637	−	0.470055i	$-0.155766\pi$
$864$	29.1423	+	3.83742i	0.991442	+	0.130552i
$865$		0			0
$866$	−10.7942	−	23.0540i	−0.366801	−	0.783406i
$867$	−21.6784	+	6.08677i	−0.736236	+	0.206718i
$868$	−3.45041	−	2.87689i	−0.117115	−	0.0976482i
$869$			38.7386i			1.31412i
$870$		0			0
$871$		−	16.2651i		−	0.551121i
$872$	−6.56155	+	24.9559i	−0.222202	+	0.845112i
$873$	9.36932	+	15.3693i	0.317103	+	0.520173i
$874$	41.6155	−	19.4849i	1.40767	−	0.659088i
$875$		0			0
$876$	−26.0682	−	11.6812i	−0.880762	−	0.394672i
$877$			3.61553i			0.122088i	0.998135	+	0.0610439i	$0.0194430\pi$
$877$			3.61553i			0.122088i	−0.998135	+	0.0610439i	$0.980557\pi$
$878$	17.9309	+	38.2964i	0.605138	+	1.29244i
$879$	50.8481	−	14.2770i	1.71506	−	0.481550i
$880$		0			0
$881$			25.3693i			0.854714i	0.904083	+	0.427357i	$0.140555\pi$
$881$			25.3693i			0.854714i	−0.904083	+	0.427357i	$0.859445\pi$
$882$	14.3547	−	21.6519i	0.483348	−	0.729058i
$883$	10.8265			0.364342			0.182171	−	0.983267i	$-0.441688\pi$
$883$	10.8265			0.364342			0.182171	+	0.983267i	$0.441688\pi$
$884$	9.59482	+	8.00000i	0.322709	+	0.269069i
$885$		0			0
$886$	−15.4384	−	32.9731i	−0.518665	−	1.10775i
$887$		−	53.4774i		−	1.79560i	−0.440408	−	0.897798i	$-0.645166\pi$
$887$		−	53.4774i		−	1.79560i	0.440408	−	0.897798i	$-0.354834\pi$
$888$	−15.2979	+	0.254294i	−0.513364	+	0.00853356i
$889$	−4.38447			−0.147050
$890$		0			0
$891$	17.6121	−	34.1725i	0.590027	−	1.14482i
$892$	−23.0830	+	27.6847i	−0.772876	+	0.926951i
$893$	−4.00000			−0.133855
$894$	−22.3955	−	25.9700i	−0.749017	−	0.868568i
$895$		0			0
$896$	−10.5636	−	0.807764i	−0.352906	−	0.0269855i
$897$	39.6155	−	11.1231i	1.32272	−	0.371390i
$898$	−1.57756	−	3.36932i	−0.0526438	−	0.112436i
$899$	−12.2888			−0.409855
$900$		0			0
$901$	−8.49242			−0.282924
$902$	−18.2462	−	38.9699i	−0.607532	−	1.29756i
$903$	−2.28343	+	0.641132i	−0.0759877	+	0.0213355i
$904$	10.0691	−	38.2964i	0.334894	−	1.27372i
$905$		0			0
$906$	9.82907	+	11.3979i	0.326549	+	0.378670i
$907$	35.8653			1.19089			0.595444	−	0.803397i	$-0.296976\pi$
$907$	35.8653			1.19089			0.595444	+	0.803397i	$0.296976\pi$
$908$	13.3002	+	11.0895i	0.441382	+	0.368017i
$909$	−14.2462	−	23.3693i	−0.472517	−	0.775111i
$910$		0			0
$911$	41.8944			1.38802			0.694012	−	0.719963i	$-0.255841\pi$
$911$	41.8944			1.38802			0.694012	+	0.719963i	$0.255841\pi$
$912$	−26.5896	+	12.9927i	−0.880470	+	0.430232i
$913$			20.0000i			0.661903i
$914$	−5.99676	−	12.8078i	−0.198355	−	0.423643i
$915$		0			0
$916$	−0.315342	+	0.378206i	−0.0104192	+	0.0124963i
$917$	16.4924			0.544628
$918$	−4.50742	+	13.9887i	−0.148767	+	0.461695i
$919$		−	50.1423i		−	1.65404i	−0.562172	−	0.827020i	$-0.690034\pi$
$919$		−	50.1423i		−	1.65404i	0.562172	−	0.827020i	$-0.309966\pi$
$920$		0			0
$921$	−13.5616	+	3.80776i	−0.446868	+	0.125470i
$922$	9.51191	+	20.3153i	0.313258	+	0.669050i
$923$		−	20.8319i		−	0.685692i
$924$	−5.66622	+	12.6449i	−0.186405	+	0.415987i
$925$		0			0
$926$	1.19935	−	0.561553i	0.0394132	−	0.0184538i
$927$	−31.7738	+	19.3697i	−1.04359	+	0.636183i
$928$	−23.6089	+	16.8078i	−0.774998	+	0.551742i
$929$			24.8769i			0.816184i	0.912941	+	0.408092i	$0.133806\pi$
$929$			24.8769i			0.816184i	−0.912941	+	0.408092i	$0.866194\pi$
$930$		0			0
$931$			26.1552i			0.857202i
$932$	12.8078	−	15.3610i	0.419532	−	0.503167i
$933$	23.6155	−	6.63068i	0.773138	−	0.217079i
$934$	9.68466	+	20.6843i	0.316892	+	0.676811i
$935$		0			0
$936$	−25.3912	+	7.58674i	−0.829938	+	0.247980i
$937$		−	10.4924i		−	0.342773i	−0.985204	−	0.171386i	$-0.945175\pi$
$937$		−	10.4924i		−	0.342773i	0.985204	−	0.171386i	$-0.0548246\pi$
$938$	−6.24621	+	2.92456i	−0.203946	+	0.0954902i
$939$	4.91269	+	17.4968i	0.160320	+	0.570987i
$940$		0			0
$941$			9.12311i			0.297405i	0.988882	+	0.148702i	$0.0475096\pi$
$941$			9.12311i			0.297405i	−0.988882	+	0.148702i	$0.952490\pi$
$942$	34.1840	+	39.6401i	1.11377	+	1.29155i
$943$	54.1833			1.76445
$944$	5.17562	+	28.3153i	0.168452	+	0.921586i
$945$		0			0
$946$	−8.00000	+	3.74571i	−0.260102	+	0.121783i
$947$		−	25.5141i		−	0.829096i	−0.910027	−	0.414548i	$-0.863940\pi$
$947$		−	25.5141i		−	0.829096i	0.910027	−	0.414548i	$-0.136060\pi$
$948$	28.6691	+	12.8467i	0.931129	+	0.417241i
$949$	25.7538			0.836003
$950$		0			0
$951$	54.5938	−	15.3287i	1.77033	−	0.497066i
$952$	1.34700	−	5.12311i	0.0436565	−	0.166041i
$953$	−10.4924			−0.339883			−0.169941	−	0.985454i	$-0.554358\pi$
$953$	−10.4924			−0.339883			−0.169941	+	0.985454i	$0.554358\pi$
$954$	9.95461	−	15.0150i	0.322292	−	0.486130i
$955$		0			0
$956$	−26.6811	+	32.0000i	−0.862927	+	1.03495i
$957$	10.2462	+	36.4924i	0.331213	+	1.17963i
$958$	−29.3751	+	13.7538i	−0.949065	+	0.444365i
$959$	−7.72197			−0.249355
$960$		0			0
$961$	25.2462			0.814394
$962$	12.4924	−	5.84912i	0.402772	−	0.188583i
$963$	1.46228	+	2.39871i	0.0471213	+	0.0772972i
$964$	−14.5616	+	17.4644i	−0.468996	+	0.562492i
$965$		0			0
$966$	−11.3947	−	13.2134i	−0.366617	−	0.425134i
$967$	23.6412			0.760250			0.380125	−	0.924935i	$-0.375881\pi$
$967$	23.6412			0.760250			0.380125	+	0.924935i	$0.375881\pi$
$968$	−5.21165	+	19.8217i	−0.167509	+	0.637093i
$969$	−4.00000	−	14.2462i	−0.128499	−	0.457654i
$970$		0			0
$971$	−41.5991			−1.33498			−0.667490	−	0.744619i	$-0.732631\pi$
$971$	−41.5991			−1.33498			−0.667490	+	0.744619i	$0.732631\pi$
$972$	−19.4492	−	24.3665i	−0.623834	−	0.781557i
$973$			12.9848i			0.416275i
$974$	−19.6326	+	9.19224i	−0.629069	+	0.294538i
$975$		0			0
$976$	3.68466	+	20.1584i	0.117943	+	0.645256i
$977$	48.2462			1.54353			0.771767	−	0.635906i	$-0.219373\pi$
$977$	48.2462			1.54353			0.771767	+	0.635906i	$0.219373\pi$
$978$	−44.8300	+	38.6595i	−1.43350	+	1.23619i
$979$			26.6811i			0.852730i
$980$		0			0
$981$	23.3693	−	14.2462i	0.746125	−	0.454847i
$982$	23.9041	−	11.1922i	0.762812	−	0.357159i
$983$		−	3.03984i		−	0.0969558i	−0.998824	−	0.0484779i	$-0.984563\pi$
$983$		−	3.03984i		−	0.0969558i	0.998824	−	0.0484779i	$-0.0154370\pi$
$984$	−34.8911	+	0.579989i	−1.11229	+	0.0184894i
$985$		0			0
$986$	−6.14441	−	13.1231i	−0.195678	−	0.417925i
$987$	0.410574	+	1.46228i	0.0130687	+	0.0465449i
$988$	17.0862	−	20.4924i	0.543586	−	0.651951i
$989$		−	11.1231i		−	0.353694i
$990$		0			0
$991$			16.7909i			0.533382i	0.963782	+	0.266691i	$0.0859303\pi$
$991$			16.7909i			0.533382i	−0.963782	+	0.266691i	$0.914070\pi$
$992$	−11.0540	+	7.86962i	−0.350964	+	0.249861i
$993$	−13.1231	−	46.7386i	−0.416449	−	1.48321i
$994$	−8.00000	+	3.74571i	−0.253745	+	0.118807i
$995$		0			0
$996$	14.8013	+	6.63250i	0.468997	+	0.210159i
$997$		−	7.61553i		−	0.241186i	−0.992702	−	0.120593i	$-0.961520\pi$
$997$		−	7.61553i		−	0.241186i	0.992702	−	0.120593i	$-0.0384796\pi$
$998$	−0.946025	−	2.02050i	−0.0299459	−	0.0639578i
$999$	11.8782	+	11.0571i	0.375811	+	0.349831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.h.a.299.4		8
3.2	odd	2		300.2.h.b.299.6		8
4.3	odd	2	inner	300.2.h.a.299.1		8
5.2	odd	4		60.2.e.a.11.3	✓	8
5.3	odd	4		300.2.e.c.251.6		8
5.4	even	2		300.2.h.b.299.5		8
12.11	even	2		300.2.h.b.299.7		8
15.2	even	4		60.2.e.a.11.6	yes	8
15.8	even	4		300.2.e.c.251.3		8
15.14	odd	2	inner	300.2.h.a.299.3		8
20.3	even	4		300.2.e.c.251.4		8
20.7	even	4		60.2.e.a.11.5	yes	8
20.19	odd	2		300.2.h.b.299.8		8
40.27	even	4		960.2.h.g.191.3		8
40.37	odd	4		960.2.h.g.191.6		8
60.23	odd	4		300.2.e.c.251.5		8
60.47	odd	4		60.2.e.a.11.4	yes	8
60.59	even	2	inner	300.2.h.a.299.2		8
120.77	even	4		960.2.h.g.191.4		8
120.107	odd	4		960.2.h.g.191.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.e.a.11.3	✓	8	5.2	odd	4
60.2.e.a.11.4	yes	8	60.47	odd	4
60.2.e.a.11.5	yes	8	20.7	even	4
60.2.e.a.11.6	yes	8	15.2	even	4
300.2.e.c.251.3		8	15.8	even	4
300.2.e.c.251.4		8	20.3	even	4
300.2.e.c.251.5		8	60.23	odd	4
300.2.e.c.251.6		8	5.3	odd	4
300.2.h.a.299.1		8	4.3	odd	2	inner
300.2.h.a.299.2		8	60.59	even	2	inner
300.2.h.a.299.3		8	15.14	odd	2	inner
300.2.h.a.299.4		8	1.1	even	1	trivial
300.2.h.b.299.5		8	5.4	even	2
300.2.h.b.299.6		8	3.2	odd	2
300.2.h.b.299.7		8	12.11	even	2
300.2.h.b.299.8		8	20.19	odd	2
960.2.h.g.191.3		8	40.27	even	4
960.2.h.g.191.4		8	120.77	even	4
960.2.h.g.191.5		8	120.107	odd	4
960.2.h.g.191.6		8	40.37	odd	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} -0.936426 q^{7} +(-0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +O(q^{10})\)	\(q+(-1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} -0.936426 q^{7} +(-0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +4.27156 q^{11} +(1.41656 - 3.16123i) q^{12} +3.12311i q^{13} +(1.19935 - 0.561553i) q^{14} +(-0.719224 - 3.93481i) q^{16} +2.00000 q^{17} +(-2.34435 + 3.53610i) q^{18} -4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(-5.47091 + 2.56155i) q^{22} -7.60669i q^{23} +(0.0814236 + 4.89830i) q^{24} +(-1.87285 - 4.00000i) q^{26} +(3.54042 - 3.80335i) q^{27} +(-1.19935 + 1.43845i) q^{28} +5.12311i q^{29} +2.39871i q^{31} +(3.28078 + 4.60831i) q^{32} +(7.12311 - 2.00000i) q^{33} +(-2.56155 + 1.19935i) q^{34} +(0.882071 - 5.93481i) q^{36} +3.12311i q^{37} +(2.56155 + 5.47091i) q^{38} +(1.46228 + 5.20798i) q^{39} +7.12311i q^{41} +(1.73707 - 1.49798i) q^{42} +1.46228 q^{43} +(5.47091 - 6.56155i) q^{44} +(4.56155 + 9.74247i) q^{46} -0.936426i q^{47} +(-3.04168 - 6.22480i) q^{48} -6.12311 q^{49} +(3.33513 - 0.936426i) q^{51} +(4.79741 + 4.00000i) q^{52} -4.24621 q^{53} +(-2.25371 + 6.99434i) q^{54} +(0.673500 - 2.56155i) q^{56} +(-2.00000 - 7.12311i) q^{57} +(-3.07221 - 6.56155i) q^{58} -7.19612 q^{59} -5.12311 q^{61} +(-1.43845 - 3.07221i) q^{62} +(-2.39871 + 1.46228i) q^{63} +(-6.96543 - 3.93481i) q^{64} +(-7.92375 + 6.83311i) q^{66} -5.20798 q^{67} +(2.56155 - 3.07221i) q^{68} +(-3.56155 - 12.6847i) q^{69} -6.67026 q^{71} +(2.42923 + 8.13012i) q^{72} -8.24621i q^{73} +(-1.87285 - 4.00000i) q^{74} +(-6.56155 - 5.47091i) q^{76} -4.00000 q^{77} +(-4.99596 - 5.79337i) q^{78} +9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(-4.27156 - 9.12311i) q^{82} +4.68213i q^{83} +(-1.32650 + 2.96026i) q^{84} +(-1.87285 + 0.876894i) q^{86} +(2.39871 + 8.54312i) q^{87} +(-3.07221 + 11.6847i) q^{88} +6.24621i q^{89} -2.92456i q^{91} +(-11.6847 - 9.74247i) q^{92} +(1.12311 + 4.00000i) q^{93} +(0.561553 + 1.19935i) q^{94} +(7.62858 + 6.14856i) q^{96} +6.00000i q^{97} +(7.84233 - 3.67188i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9	\( 8 q - 2 q^{2} + 2 q^{4} - 6 q^{6} - 14 q^{8} + 4 q^{9} - 14 q^{12} - 14 q^{16} + 16 q^{17} - 18 q^{18} + 4 q^{21} + 2 q^{24} + 18 q^{32} + 24 q^{33} - 4 q^{34} + 18 q^{36} + 4 q^{38} + 16 q^{42} + 20 q^{46} + 10 q^{48} - 16 q^{49} + 32 q^{53} + 10 q^{54} - 16 q^{57} - 8 q^{61} - 28 q^{62} + 2 q^{64} - 40 q^{66} + 4 q^{68} - 12 q^{69} + 10 q^{72} - 36 q^{76} - 32 q^{77} + 8 q^{78} - 16 q^{84} - 44 q^{92} - 24 q^{93} - 12 q^{94} + 42 q^{96} + 38 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^4 - 6 * q^6 - 14 * q^8 + 4 * q^9 - 14 * q^12 - 14 * q^16 + 16 * q^17 - 18 * q^18 + 4 * q^21 + 2 * q^24 + 18 * q^32 + 24 * q^33 - 4 * q^34 + 18 * q^36 + 4 * q^38 + 16 * q^42 + 20 * q^46 + 10 * q^48 - 16 * q^49 + 32 * q^53 + 10 * q^54 - 16 * q^57 - 8 * q^61 - 28 * q^62 + 2 * q^64 - 40 * q^66 + 4 * q^68 - 12 * q^69 + 10 * q^72 - 36 * q^76 - 32 * q^77 + 8 * q^78 - 16 * q^84 - 44 * q^92 - 24 * q^93 - 12 * q^94 + 42 * q^96 + 38 * q^98

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