LMFDB - Embedded newform 300.2.h.b.299.5

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			299.5
Root			$0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.b.299.7

$q$-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	$-0.443371\pi$
$7$	0.936426			0.353936			0.176968	+	0.984217i	$0.443371\pi$
$8$	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	$-0.857421\pi$
$13$		−	3.12311i		−	0.866194i	0.901347	−	0.433097i	$-0.142579\pi$
$14$	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	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	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	$0.291509\pi$
$23$			7.60669i			1.58610i	−0.609154	+	0.793052i	$0.708491\pi$
$24$	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	$-0.917359\pi$
$37$		−	3.12311i		−	0.513435i	0.966486	−	0.256718i	$-0.0826411\pi$
$38$	−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	$-0.535565\pi$
$43$	−1.46228			−0.222995			−0.111498	+	0.993765i	$0.535565\pi$
$44$	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	$0.0217562\pi$
$47$			0.936426i			0.136592i	−0.997665	+	0.0682959i	$0.978244\pi$
$48$	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	$-0.405802\pi$
$53$	4.24621			0.583262			0.291631	+	0.956531i	$0.405802\pi$
$54$	−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	$-0.396946\pi$
$67$	5.20798			0.636257			0.318128	+	0.948048i	$0.396946\pi$
$68$	−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	$0.160298\pi$
$73$			8.24621i			0.965146i	−0.875856	+	0.482573i	$0.839702\pi$
$74$	−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	$-0.917277\pi$
$83$		−	4.68213i		−	0.513931i	0.966421	−	0.256965i	$-0.0827226\pi$
$84$	−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	$-0.901476\pi$
$97$		−	6.00000i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$	−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	$-0.290725\pi$
$103$	12.4041			1.22221			0.611106	+	0.791549i	$0.290725\pi$
$104$	−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	$-0.985587\pi$
$107$		−	0.936426i		−	0.0905278i	0.998975	−	0.0452639i	$-0.0144129\pi$
$108$	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	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$	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	$-0.566609\pi$
$127$	−4.68213			−0.415472			−0.207736	+	0.978185i	$0.566609\pi$
$128$	−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	$-0.614587\pi$
$137$	−8.24621			−0.704521			−0.352261	+	0.935902i	$0.614587\pi$
$138$	−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	$0.325054\pi$
$157$			21.3693i			1.70546i	−0.522354	+	0.852729i	$0.674946\pi$
$158$	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	$-0.895364\pi$
$163$	−24.1671			−1.89291			−0.946456	+	0.322834i	$0.895364\pi$
$164$	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	$-0.965333\pi$
$167$		−	2.80928i		−	0.217389i	0.994075	−	0.108694i	$-0.0346670\pi$
$168$	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	$-0.475776\pi$
$173$	2.00000			0.152057			0.0760286	+	0.997106i	$0.475776\pi$
$174$	−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	$-0.801207\pi$
$193$		−	16.2462i		−	1.16943i	0.811240	−	0.584714i	$-0.198793\pi$
$194$	−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	$-0.356305\pi$
$197$	12.2462			0.872506			0.436253	+	0.899824i	$0.356305\pi$
$198$	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	$-0.293795\pi$
$223$	18.0227			1.20689			0.603443	+	0.797406i	$0.293795\pi$
$224$	−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	$-0.907229\pi$
$227$		−	8.65840i		−	0.574678i	0.957829	−	0.287339i	$-0.0927706\pi$
$228$	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	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$	−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	$-0.475231\pi$
$257$	2.49242			0.155473			0.0777365	+	0.996974i	$0.475231\pi$
$258$	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	$0.154123\pi$
$263$			15.0981i			0.930989i	−0.885051	+	0.465494i	$0.845877\pi$
$264$	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	$-0.986902\pi$
$277$		−	1.36932i		−	0.0822743i	0.999154	−	0.0411371i	$-0.0130981\pi$
$278$	−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	$-0.541621\pi$
$283$	−4.38684			−0.260770			−0.130385	+	0.991463i	$0.541621\pi$
$284$	−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	$-0.849780\pi$
$293$	−30.4924			−1.78139			−0.890693	+	0.454605i	$0.849780\pi$
$294$	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	$-0.425449\pi$
$307$	8.13254			0.464149			0.232074	+	0.972698i	$0.425449\pi$
$308$	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	$-0.904169\pi$
$313$		−	10.4924i		−	0.593067i	0.955022	−	0.296533i	$-0.0958306\pi$
$314$	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	$-0.871319\pi$
$317$	−32.7386			−1.83878			−0.919392	+	0.393342i	$0.871319\pi$
$318$	−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	$-0.611326\pi$
$337$		−	34.4924i		−	1.87892i	0.342656	−	0.939461i	$-0.388674\pi$
$338$	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	$0.221377\pi$
$347$			23.8718i			1.28150i	−0.767748	+	0.640752i	$0.778623\pi$
$348$	−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	$-0.531851\pi$
$353$	−3.75379			−0.199794			−0.0998970	+	0.994998i	$0.531851\pi$
$354$	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	$-0.256129\pi$
$367$	26.5658			1.38672			0.693361	+	0.720590i	$0.256129\pi$
$368$	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	$0.00722687\pi$
$373$			0.876894i			0.0454039i	−0.999742	+	0.0227019i	$0.992773\pi$
$374$	−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	$0.0381685\pi$
$383$			4.68213i			0.239246i	−0.992819	+	0.119623i	$0.961831\pi$
$384$	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	$0.197048\pi$
$397$			23.1231i			1.16052i	−0.814433	+	0.580258i	$0.802952\pi$
$398$	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	$-0.857627\pi$
$433$		−	18.0000i		−	0.865025i	0.901628	−	0.432512i	$-0.142373\pi$
$434$	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	$-0.790533\pi$
$443$		−	25.7446i		−	1.22316i	0.791181	−	0.611582i	$-0.209467\pi$
$444$	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	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$	−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	$-0.493073\pi$
$463$	0.936426			0.0435194			0.0217597	+	0.999763i	$0.493073\pi$
$464$	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	$0.121898\pi$
$467$			16.1498i			0.747324i	−0.927565	+	0.373662i	$0.878102\pi$
$468$	−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	$-0.612903\pi$
$487$	−15.3287			−0.694608			−0.347304	+	0.937753i	$0.612903\pi$
$488$	−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	$-0.853719\pi$
$503$		−	19.8955i		−	0.887097i	0.896250	−	0.443549i	$-0.146281\pi$
$504$	−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	$-0.495538\pi$
$523$	0.641132			0.0280348			0.0140174	+	0.999902i	$0.495538\pi$
$524$	−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	$-0.318750\pi$
$547$	25.2188			1.07828			0.539139	+	0.842217i	$0.318750\pi$
$548$	−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	$-0.637443\pi$
$557$	−19.7538			−0.836995			−0.418497	+	0.908218i	$0.637443\pi$
$558$	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	$-0.724221\pi$
$563$		−	36.1606i		−	1.52399i	0.647584	−	0.761994i	$-0.275779\pi$
$564$	−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	$-0.893653\pi$
$577$		−	15.7538i		−	0.655839i	0.944706	−	0.327919i	$-0.106347\pi$
$578$	−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	$-0.712712\pi$
$587$		−	38.0335i		−	1.56981i	0.619617	−	0.784904i	$-0.287288\pi$
$588$	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	$-0.554156\pi$
$593$	−8.24621			−0.338631			−0.169316	+	0.985562i	$0.554156\pi$
$594$	−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	$-0.295768\pi$
$607$	29.4903			1.19698			0.598488	+	0.801132i	$0.295768\pi$
$608$	−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	$-0.994363\pi$
$613$		−	0.876894i		−	0.0354174i	0.999843	−	0.0177087i	$-0.00563715\pi$
$614$	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	$-0.409065\pi$
$617$	14.0000			0.563619			0.281809	+	0.959470i	$0.409065\pi$
$618$	−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	$-0.368082\pi$
$643$	20.4214			0.805340			0.402670	+	0.915345i	$0.368082\pi$
$644$	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	$-0.977265\pi$
$647$		−	3.63043i		−	0.142727i	0.997450	−	0.0713634i	$-0.0227350\pi$
$648$	−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	$-0.322942\pi$
$653$	26.9848			1.05600			0.527999	+	0.849245i	$0.322942\pi$
$654$	−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	$0.0648177\pi$
$673$			10.4924i			0.404453i	−0.979339	+	0.202227i	$0.935182\pi$
$674$	−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	$-0.730643\pi$
$677$	−34.4924			−1.32565			−0.662826	+	0.748774i	$0.730643\pi$
$678$	−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	$0.243192\pi$
$683$			36.1606i			1.38365i	−0.722067	+	0.691823i	$0.756808\pi$
$684$	−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	$-0.663966\pi$
$727$	−26.5658			−0.985270			−0.492635	+	0.870236i	$0.663966\pi$
$728$	−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	$0.224666\pi$
$733$			35.1231i			1.29730i	−0.761086	+	0.648651i	$0.775334\pi$
$734$	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	$-0.926935\pi$
$743$		−	12.4041i		−	0.455062i	0.973771	−	0.227531i	$-0.0730654\pi$
$744$	−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	$0.112976\pi$
$757$			19.1231i			0.695041i	−0.937672	+	0.347521i	$0.887024\pi$
$758$	−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	$-0.405623\pi$
$773$	16.2462			0.584336			0.292168	+	0.956367i	$0.405623\pi$
$774$	−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	$-0.419834\pi$
$787$	13.9817			0.498392			0.249196	+	0.968453i	$0.419834\pi$
$788$	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	$-0.274486\pi$
$797$	36.7386			1.30135			0.650675	+	0.759357i	$0.274486\pi$
$798$	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	$-0.803701\pi$
$823$	−46.8071			−1.63159			−0.815797	+	0.578338i	$0.803701\pi$
$824$	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	$-0.926146\pi$
$827$		−	13.2252i		−	0.459887i	0.973204	−	0.229943i	$-0.0738541\pi$
$828$	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	$-0.674404\pi$
$853$		−	49.8617i		−	1.70723i	0.520902	−	0.853617i	$-0.325596\pi$
$854$	−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	$-0.663312\pi$
$857$	−28.7386			−0.981693			−0.490847	+	0.871246i	$0.663312\pi$
$858$	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	$0.155766\pi$
$863$			27.6175i			0.940110i	−0.882637	+	0.470055i	$0.844234\pi$
$864$	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	$-0.980557\pi$
$877$		−	3.61553i		−	0.122088i	0.998135	−	0.0610439i	$-0.0194430\pi$
$878$	−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	$-0.558312\pi$
$883$	−10.8265			−0.364342			−0.182171	+	0.983267i	$0.558312\pi$
$884$	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	$0.354834\pi$
$887$			53.4774i			1.79560i	−0.440408	+	0.897798i	$0.645166\pi$
$888$	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	$-0.703024\pi$
$907$	−35.8653			−1.19089			−0.595444	+	0.803397i	$0.703024\pi$
$908$	−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	$0.0548246\pi$
$937$			10.4924i			0.342773i	−0.985204	+	0.171386i	$0.945175\pi$
$938$	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	$0.136060\pi$
$947$			25.5141i			0.829096i	−0.910027	+	0.414548i	$0.863940\pi$
$948$	−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	$-0.445642\pi$
$953$	10.4924			0.339883			0.169941	+	0.985454i	$0.445642\pi$
$954$	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	$-0.624119\pi$
$967$	−23.6412			−0.760250			−0.380125	+	0.924935i	$0.624119\pi$
$968$	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	$-0.780627\pi$
$977$	−48.2462			−1.54353			−0.771767	+	0.635906i	$0.780627\pi$
$978$	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	$0.0154370\pi$
$983$			3.03984i			0.0969558i	−0.998824	+	0.0484779i	$0.984563\pi$
$984$	−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	$0.0384796\pi$
$997$			7.61553i			0.241186i	−0.992702	+	0.120593i	$0.961520\pi$
$998$	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.b.299.5		8
3.2	odd	2		300.2.h.a.299.3		8
4.3	odd	2	inner	300.2.h.b.299.8		8
5.2	odd	4		300.2.e.c.251.6		8
5.3	odd	4		60.2.e.a.11.3	✓	8
5.4	even	2		300.2.h.a.299.4		8
12.11	even	2		300.2.h.a.299.2		8
15.2	even	4		300.2.e.c.251.3		8
15.8	even	4		60.2.e.a.11.6	yes	8
15.14	odd	2	inner	300.2.h.b.299.6		8
20.3	even	4		60.2.e.a.11.5	yes	8
20.7	even	4		300.2.e.c.251.4		8
20.19	odd	2		300.2.h.a.299.1		8
40.3	even	4		960.2.h.g.191.3		8
40.13	odd	4		960.2.h.g.191.6		8
60.23	odd	4		60.2.e.a.11.4	yes	8
60.47	odd	4		300.2.e.c.251.5		8
60.59	even	2	inner	300.2.h.b.299.7		8
120.53	even	4		960.2.h.g.191.4		8
120.83	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	5.3	odd	4
60.2.e.a.11.4	yes	8	60.23	odd	4
60.2.e.a.11.5	yes	8	20.3	even	4
60.2.e.a.11.6	yes	8	15.8	even	4
300.2.e.c.251.3		8	15.2	even	4
300.2.e.c.251.4		8	20.7	even	4
300.2.e.c.251.5		8	60.47	odd	4
300.2.e.c.251.6		8	5.2	odd	4
300.2.h.a.299.1		8	20.19	odd	2
300.2.h.a.299.2		8	12.11	even	2
300.2.h.a.299.3		8	3.2	odd	2
300.2.h.a.299.4		8	5.4	even	2
300.2.h.b.299.5		8	1.1	even	1	trivial
300.2.h.b.299.6		8	15.14	odd	2	inner
300.2.h.b.299.7		8	60.59	even	2	inner
300.2.h.b.299.8		8	4.3	odd	2	inner
960.2.h.g.191.3		8	40.3	even	4
960.2.h.g.191.4		8	120.53	even	4
960.2.h.g.191.5		8	120.83	odd	4
960.2.h.g.191.6		8	40.13	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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