LMFDB - Embedded newform 300.2.e.c.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(251,300)]

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, 0]))

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

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

chi := DirichletCharacter("300.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.e (of order $2$, degree $1$, 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.4
Root			$-0.599676 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.c.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.599676 + 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} +(2.41656 + 0.400324i) q^{6} -0.936426i q^{7} +(2.73546 - 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})$	\(q+(-0.599676 + 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} +(2.41656 + 0.400324i) q^{6} -0.936426i q^{7} +(2.73546 - 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} -4.27156 q^{11} +(-1.96188 + 2.85500i) q^{12} -3.12311 q^{13} +(1.19935 + 0.561553i) q^{14} +(-0.719224 + 3.93481i) q^{16} -2.00000i q^{17} +(-0.463897 - 4.21720i) q^{18} -4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(2.56155 - 5.47091i) q^{22} -7.60669 q^{23} +(-2.48013 - 4.22480i) q^{24} +(1.87285 - 4.00000i) q^{26} +(3.80335 + 3.54042i) q^{27} +(-1.43845 + 1.19935i) q^{28} -5.12311i q^{29} -2.39871i q^{31} +(-4.60831 - 3.28078i) q^{32} +(2.00000 + 7.12311i) q^{33} +(2.56155 + 1.19935i) q^{34} +(5.67948 + 1.93481i) q^{36} +3.12311 q^{37} +(5.47091 + 2.56155i) q^{38} +(1.46228 + 5.20798i) q^{39} +7.12311i q^{41} +(0.374874 - 2.26293i) q^{42} -1.46228i q^{43} +(5.47091 + 6.56155i) q^{44} +(4.56155 - 9.74247i) q^{46} +0.936426 q^{47} +(6.89830 - 0.642976i) q^{48} +6.12311 q^{49} +(-3.33513 + 0.936426i) q^{51} +(4.00000 + 4.79741i) q^{52} -4.24621i q^{53} +(-6.81526 + 2.74813i) q^{54} +(-0.673500 - 2.56155i) q^{56} +(-7.12311 + 2.00000i) q^{57} +(6.56155 + 3.07221i) q^{58} -7.19612 q^{59} -5.12311 q^{61} +(3.07221 + 1.43845i) q^{62} +(1.46228 + 2.39871i) q^{63} +(6.96543 - 3.93481i) q^{64} +(-10.3225 - 1.71001i) q^{66} -5.20798i q^{67} +(-3.07221 + 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +6.67026 q^{71} +(-5.88391 + 6.11389i) q^{72} +8.24621 q^{73} +(-1.87285 + 4.00000i) q^{74} +(-6.56155 + 5.47091i) q^{76} +4.00000i q^{77} +(-7.54716 - 1.25025i) q^{78} +9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(-9.12311 - 4.27156i) q^{82} +4.68213 q^{83} +(2.67350 + 1.83715i) q^{84} +(1.87285 + 0.876894i) q^{86} +(-8.54312 + 2.39871i) q^{87} +(-11.6847 + 3.07221i) q^{88} -6.24621i q^{89} +2.92456i q^{91} +(9.74247 + 11.6847i) q^{92} +(-4.00000 + 1.12311i) q^{93} +(-0.561553 + 1.19935i) q^{94} +(-3.31324 + 9.22076i) q^{96} +6.00000 q^{97} +(-3.67188 + 7.84233i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 14 q^{16} - 16 q^{18} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 28 q^{28} + 16 q^{33} + 4 q^{34} + 18 q^{36} - 8 q^{37} + 12 q^{42} + 20 q^{46} + 36 q^{48} + 16 q^{49} + 32 q^{52} - 10 q^{54} - 24 q^{57} + 36 q^{58} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 24 q^{72} - 36 q^{76} - 40 q^{78} - 40 q^{82} + 16 q^{84} - 44 q^{88} - 32 q^{93} + 12 q^{94} + 42 q^{96} + 48 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 14 * q^16 - 16 * q^18 + 4 * q^21 + 4 * q^22 - 2 * q^24 - 28 * q^28 + 16 * q^33 + 4 * q^34 + 18 * q^36 - 8 * q^37 + 12 * q^42 + 20 * q^46 + 36 * q^48 + 16 * q^49 + 32 * q^52 - 10 * q^54 - 24 * q^57 + 36 * q^58 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 24 * q^72 - 36 * q^76 - 40 * q^78 - 40 * q^82 + 16 * q^84 - 44 * q^88 - 32 * q^93 + 12 * q^94 + 42 * q^96 + 48 * q^97

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 $

$2$	−0.599676	+	1.28078i	−0.424035	+	0.905646i
$2$	−0.599676	+	1.28078i	−0.424035	+	0.905646i
$3$	−0.468213	−	1.66757i	−0.270323	−	0.962770i
$3$	−0.468213	−	1.66757i	−0.270323	−	0.962770i
$4$	−1.28078	−	1.53610i	−0.640388	−	0.768051i
$5$		0			0
$5$		0			0
$6$	2.41656	+	0.400324i	0.986555	+	0.163431i
$7$		−	0.936426i		−	0.353936i	−0.984217	−	0.176968i	$-0.943371\pi$
$7$		−	0.936426i		−	0.353936i	0.984217	−	0.176968i	$-0.0566289\pi$
$8$	2.73546	−	0.719224i	0.967130	−	0.254284i
$9$	−2.56155	+	1.56155i	−0.853851	+	0.520518i
$10$		0			0
$11$	−4.27156			−1.28792			−0.643962	−	0.765058i	$-0.722710\pi$
$11$	−4.27156			−1.28792			−0.643962	+	0.765058i	$0.722710\pi$
$12$	−1.96188	+	2.85500i	−0.566345	+	0.824168i
$13$	−3.12311			−0.866194			−0.433097	−	0.901347i	$-0.642579\pi$
$13$	−3.12311			−0.866194			−0.433097	+	0.901347i	$0.642579\pi$
$14$	1.19935	+	0.561553i	0.320541	+	0.150081i
$15$		0			0
$16$	−0.719224	+	3.93481i	−0.179806	+	0.983702i
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	−0.463897	−	4.21720i	−0.109342	−	0.994004i
$19$		−	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
$22$	2.56155	−	5.47091i	0.546125	−	1.16640i
$23$	−7.60669			−1.58610			−0.793052	−	0.609154i	$-0.791509\pi$
$23$	−7.60669			−1.58610			−0.793052	+	0.609154i	$0.791509\pi$
$24$	−2.48013	−	4.22480i	−0.506254	−	0.862384i
$25$		0			0
$26$	1.87285	−	4.00000i	0.367297	−	0.784465i
$27$	3.80335	+	3.54042i	0.731954	+	0.681354i
$28$	−1.43845	+	1.19935i	−0.271841	+	0.226656i
$29$		−	5.12311i		−	0.951337i	−0.879625	−	0.475668i	$-0.842206\pi$
$29$		−	5.12311i		−	0.951337i	0.879625	−	0.475668i	$-0.157794\pi$
$30$		0			0
$31$		−	2.39871i		−	0.430820i	−0.976524	−	0.215410i	$-0.930891\pi$
$31$		−	2.39871i		−	0.430820i	0.976524	−	0.215410i	$-0.0691088\pi$
$32$	−4.60831	−	3.28078i	−0.814642	−	0.579965i
$33$	2.00000	+	7.12311i	0.348155	+	1.23997i
$34$	2.56155	+	1.19935i	0.439303	+	0.205687i
$35$		0			0
$36$	5.67948	+	1.93481i	0.946580	+	0.322468i
$37$	3.12311			0.513435			0.256718	−	0.966486i	$-0.417359\pi$
$37$	3.12311			0.513435			0.256718	+	0.966486i	$0.417359\pi$
$38$	5.47091	+	2.56155i	0.887499	+	0.415539i
$39$	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	$0.812251\pi$
$42$	0.374874	−	2.26293i	0.0578442	−	0.349177i
$43$		−	1.46228i		−	0.222995i	−0.993765	−	0.111498i	$-0.964435\pi$
$43$		−	1.46228i		−	0.222995i	0.993765	−	0.111498i	$-0.0355648\pi$
$44$	5.47091	+	6.56155i	0.824771	+	0.989191i
$45$		0			0
$46$	4.56155	−	9.74247i	0.672564	−	1.43645i
$47$	0.936426			0.136592			0.0682959	−	0.997665i	$-0.478244\pi$
$47$	0.936426			0.136592			0.0682959	+	0.997665i	$0.478244\pi$
$48$	6.89830	−	0.642976i	0.995684	−	0.0928056i
$49$	6.12311			0.874729
$50$		0			0
$51$	−3.33513	+	0.936426i	−0.467012	+	0.131126i
$52$	4.00000	+	4.79741i	0.554700	+	0.665281i
$53$		−	4.24621i		−	0.583262i	−0.956531	−	0.291631i	$-0.905802\pi$
$53$		−	4.24621i		−	0.583262i	0.956531	−	0.291631i	$-0.0941979\pi$
$54$	−6.81526	+	2.74813i	−0.927440	+	0.373973i
$55$		0			0
$56$	−0.673500	−	2.56155i	−0.0900002	−	0.342302i
$57$	−7.12311	+	2.00000i	−0.943478	+	0.264906i
$58$	6.56155	+	3.07221i	0.861574	+	0.403400i
$59$	−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	$0.606366\pi$
$62$	3.07221	+	1.43845i	0.390171	+	0.182683i
$63$	1.46228	+	2.39871i	0.184230	+	0.302209i
$64$	6.96543	−	3.93481i	0.870679	−	0.491851i
$65$		0			0
$66$	−10.3225	−	1.71001i	−1.27061	−	0.210487i
$67$		−	5.20798i		−	0.636257i	−0.948048	−	0.318128i	$-0.896946\pi$
$67$		−	5.20798i		−	0.636257i	0.948048	−	0.318128i	$-0.103054\pi$
$68$	−3.07221	+	2.56155i	−0.372560	+	0.310634i
$69$	3.56155	+	12.6847i	0.428761	+	1.52705i
$70$		0			0
$71$	6.67026			0.791615			0.395807	−	0.918334i	$-0.370465\pi$
$71$	6.67026			0.791615			0.395807	+	0.918334i	$0.370465\pi$
$72$	−5.88391	+	6.11389i	−0.693425	+	0.720529i
$73$	8.24621			0.965146			0.482573	−	0.875856i	$-0.339702\pi$
$73$	8.24621			0.965146			0.482573	+	0.875856i	$0.339702\pi$
$74$	−1.87285	+	4.00000i	−0.217715	+	0.464991i
$75$		0			0
$76$	−6.56155	+	5.47091i	−0.752662	+	0.627557i
$77$			4.00000i			0.455842i
$78$	−7.54716	−	1.25025i	−0.854547	−	0.141563i
$79$			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
$82$	−9.12311	−	4.27156i	−1.00748	−	0.471715i
$83$	4.68213			0.513931			0.256965	−	0.966421i	$-0.417277\pi$
$83$	4.68213			0.513931			0.256965	+	0.966421i	$0.417277\pi$
$84$	2.67350	+	1.83715i	0.291703	+	0.200450i
$85$		0			0
$86$	1.87285	+	0.876894i	0.201955	+	0.0945580i
$87$	−8.54312	+	2.39871i	−0.915918	+	0.257168i
$88$	−11.6847	+	3.07221i	−1.24559	+	0.327498i
$89$		−	6.24621i		−	0.662097i	−0.943614	−	0.331049i	$-0.892598\pi$
$89$		−	6.24621i		−	0.662097i	0.943614	−	0.331049i	$-0.107402\pi$
$90$		0			0
$91$			2.92456i			0.306577i
$92$	9.74247	+	11.6847i	1.01572	+	1.21821i
$93$	−4.00000	+	1.12311i	−0.414781	+	0.116461i
$94$	−0.561553	+	1.19935i	−0.0579198	+	0.123704i
$95$		0			0
$96$	−3.31324	+	9.22076i	−0.338156	+	0.941090i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	−3.67188	+	7.84233i	−0.370916	+	0.792195i
$99$	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	$-0.149965\pi$
$102$	0.800647	−	4.83311i	0.0792759	−	0.478549i
$103$			12.4041i			1.22221i	0.791549	+	0.611106i	$0.209275\pi$
$103$			12.4041i			1.22221i	−0.791549	+	0.611106i	$0.790725\pi$
$104$	−8.54312	+	2.24621i	−0.837722	+	0.220259i
$105$		0			0
$106$	5.43845	+	2.54635i	0.528229	+	0.247324i
$107$	−0.936426			−0.0905278			−0.0452639	−	0.998975i	$-0.514413\pi$
$107$	−0.936426			−0.0905278			−0.0452639	+	0.998975i	$0.514413\pi$
$108$	0.567212	−	10.3768i	0.0545800	−	0.998509i
$109$	−9.12311			−0.873835			−0.436918	−	0.899502i	$-0.643930\pi$
$109$	−9.12311			−0.873835			−0.436918	+	0.899502i	$0.643930\pi$
$110$		0			0
$111$	−1.46228	−	5.20798i	−0.138793	−	0.494320i
$112$	3.68466	+	0.673500i	0.348167	+	0.0636398i
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	1.71001	−	10.3225i	0.160157	−	0.966787i
$115$		0			0
$116$	−7.86962	+	6.56155i	−0.730676	+	0.609225i
$117$	8.00000	−	4.87689i	0.739600	−	0.450869i
$118$	4.31534	−	9.21662i	0.397259	−	0.848458i
$119$	−1.87285			−0.171684
$120$		0			0
$121$	7.24621			0.658746
$122$	3.07221	−	6.56155i	0.278144	−	0.594055i
$123$	11.8782	−	3.33513i	1.07103	−	0.300719i
$124$	−3.68466	+	3.07221i	−0.330892	+	0.275892i
$125$		0			0
$126$	−3.94910	+	0.434406i	−0.351814	+	0.0386999i
$127$			4.68213i			0.415472i	0.978185	+	0.207736i	$0.0666095\pi$
$127$			4.68213i			0.415472i	−0.978185	+	0.207736i	$0.933391\pi$
$128$	0.862603	+	11.2808i	0.0762440	+	0.997089i
$129$	−2.43845	+	0.684658i	−0.214693	+	0.0602808i
$130$		0			0
$131$	17.6121			1.53878			0.769388	−	0.638782i	$-0.220562\pi$
$131$	17.6121			1.53878			0.769388	+	0.638782i	$0.220562\pi$
$132$	8.38027	−	12.1953i	0.729409	−	1.06147i
$133$	−4.00000			−0.346844
$134$	6.67026	+	3.12311i	0.576223	+	0.269795i
$135$		0			0
$136$	−1.43845	−	5.47091i	−0.123346	−	0.469127i
$137$		−	8.24621i		−	0.704521i	−0.935902	−	0.352261i	$-0.885413\pi$
$137$		−	8.24621i		−	0.704521i	0.935902	−	0.352261i	$-0.114587\pi$
$138$	−18.3820	−	3.04514i	−1.56478	−	0.259219i
$139$		−	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
$142$	−4.00000	+	8.54312i	−0.335673	+	0.716922i
$143$	13.3405			1.11559
$144$	−4.30208	−	11.2023i	−0.358507	−	0.933527i
$145$		0			0
$146$	−4.94506	+	10.5616i	−0.409256	+	0.874080i
$147$	−2.86692	−	10.2107i	−0.236459	−	0.842163i
$148$	−4.00000	−	4.79741i	−0.328798	−	0.394345i
$149$		−	14.0000i		−	1.14692i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$		0			0
$151$			6.14441i			0.500025i	0.968243	+	0.250013i	$0.0804347\pi$
$151$			6.14441i			0.500025i	−0.968243	+	0.250013i	$0.919565\pi$
$152$	−3.07221	−	11.6847i	−0.249189	−	0.947751i
$153$	3.12311	+	5.12311i	0.252488	+	0.414179i
$154$	−5.12311	−	2.39871i	−0.412832	−	0.193293i
$155$		0			0
$156$	6.12715	−	8.91648i	0.490564	−	0.713889i
$157$	−21.3693			−1.70546			−0.852729	−	0.522354i	$-0.825054\pi$
$157$	−21.3693			−1.70546			−0.852729	+	0.522354i	$0.825054\pi$
$158$	−11.6153	−	5.43845i	−0.924065	−	0.432660i
$159$	−7.08084	+	1.98813i	−0.561547	+	0.157669i
$160$		0			0
$161$			7.12311i			0.561379i
$162$	7.77368	+	10.0782i	0.610758	+	0.791817i
$163$		−	24.1671i		−	1.89291i	−0.322834	−	0.946456i	$-0.604636\pi$
$163$		−	24.1671i		−	1.89291i	0.322834	−	0.946456i	$-0.395364\pi$
$164$	10.9418	−	9.12311i	0.854413	−	0.712395i
$165$		0			0
$166$	−2.80776	+	5.99676i	−0.217925	+	0.465439i
$167$	−2.80928			−0.217389			−0.108694	−	0.994075i	$-0.534667\pi$
$167$	−2.80928			−0.217389			−0.108694	+	0.994075i	$0.534667\pi$
$168$	−3.95622	+	2.32246i	−0.305229	+	0.179182i
$169$	−3.24621			−0.249709
$170$		0			0
$171$	6.67026	+	10.9418i	0.510088	+	0.836742i
$172$	−2.24621	+	1.87285i	−0.171272	+	0.142804i
$173$		−	2.00000i		−	0.152057i	−0.997106	−	0.0760286i	$-0.975776\pi$
$173$		−	2.00000i		−	0.152057i	0.997106	−	0.0760286i	$-0.0242240\pi$
$174$	2.05090	−	12.3803i	0.155478	−	0.938546i
$175$		0			0
$176$	3.07221	−	16.8078i	0.231576	−	1.26693i
$177$	3.36932	+	12.0000i	0.253253	+	0.901975i
$178$	8.00000	+	3.74571i	0.599625	+	0.280752i
$179$	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	$0.449557\pi$
$182$	−3.74571	−	1.75379i	−0.277650	−	0.129999i
$183$	2.39871	+	8.54312i	0.177317	+	0.631525i
$184$	−20.8078	+	5.47091i	−1.53397	+	0.403321i
$185$		0			0
$186$	0.960258	−	5.79661i	0.0704096	−	0.425028i
$187$			8.54312i			0.624735i
$188$	−1.19935	−	1.43845i	−0.0874718	−	0.104910i
$189$	3.31534	−	3.56155i	0.241156	−	0.259065i
$190$		0			0
$191$	−7.72197			−0.558742			−0.279371	−	0.960183i	$-0.590126\pi$
$191$	−7.72197			−0.558742			−0.279371	+	0.960183i	$0.590126\pi$
$192$	−9.82286	−	9.77299i	−0.708904	−	0.705305i
$193$	−16.2462			−1.16943			−0.584714	−	0.811240i	$-0.698793\pi$
$193$	−16.2462			−1.16943			−0.584714	+	0.811240i	$0.698793\pi$
$194$	−3.59806	+	7.68466i	−0.258326	+	0.551726i
$195$		0			0
$196$	−7.84233	−	9.40572i	−0.560166	−	0.671837i
$197$			12.2462i			0.872506i	0.899824	+	0.436253i	$0.143695\pi$
$197$			12.2462i			0.872506i	−0.899824	+	0.436253i	$0.856305\pi$
$198$	1.98156	+	18.0140i	0.140824	+	1.28020i
$199$			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
$202$	11.6847	+	5.47091i	0.822130	+	0.384932i
$203$	−4.79741			−0.336712
$204$	5.71001	+	3.92375i	0.399780	+	0.274718i
$205$		0			0
$206$	−15.8869	−	7.43845i	−1.10689	−	0.518261i
$207$	19.4849	−	11.8782i	1.35430	−	0.825595i
$208$	2.24621	−	12.2888i	0.155747	−	0.852077i
$209$			18.2462i			1.26212i
$210$		0			0
$211$			1.34700i			0.0927313i	0.998925	+	0.0463656i	$0.0147639\pi$
$211$			1.34700i			0.0927313i	−0.998925	+	0.0463656i	$0.985236\pi$
$212$	−6.52262	+	5.43845i	−0.447975	+	0.373514i
$213$	−3.12311	−	11.1231i	−0.213992	−	0.762143i
$214$	0.561553	−	1.19935i	0.0383870	−	0.0819861i
$215$		0			0
$216$	12.9502	+	6.94920i	0.881152	+	0.472833i
$217$	−2.24621			−0.152483
$218$	5.47091	−	11.6847i	0.370537	−	0.791385i
$219$	−3.86098	−	13.7511i	−0.260901	−	0.929213i
$220$		0			0
$221$			6.24621i			0.420166i
$222$	7.54716	+	1.25025i	0.506532	+	0.0839115i
$223$			18.0227i			1.20689i	0.797406	+	0.603443i	$0.206205\pi$
$223$			18.0227i			1.20689i	−0.797406	+	0.603443i	$0.793795\pi$
$224$	−3.07221	+	4.31534i	−0.205270	+	0.288331i
$225$		0			0
$226$	17.9309	+	8.39547i	1.19274	+	0.558458i
$227$	−8.65840			−0.574678			−0.287339	−	0.957829i	$-0.592771\pi$
$227$	−8.65840			−0.574678			−0.287339	+	0.957829i	$0.592771\pi$
$228$	12.1953	+	8.38027i	0.807654	+	0.554997i
$229$	0.246211			0.0162701			0.00813505	−	0.999967i	$-0.497411\pi$
$229$	0.246211			0.0162701			0.00813505	+	0.999967i	$0.497411\pi$
$230$		0			0
$231$	6.67026	−	1.87285i	0.438871	−	0.123225i
$232$	−3.68466	−	14.0140i	−0.241910	−	0.920066i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	1.44880	+	13.1708i	0.0947110	+	0.861000i
$235$		0			0
$236$	9.21662	+	11.0540i	0.599951	+	0.719553i
$237$	15.1231	−	4.24621i	0.982351	−	0.275821i
$238$	1.12311	−	2.39871i	0.0728001	−	0.155485i
$239$	−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	$0.619335\pi$
$242$	−4.34538	+	9.28078i	−0.279332	+	0.596591i
$243$	−15.2710	−	3.12985i	−0.979636	−	0.200780i
$244$	6.56155	+	7.86962i	0.420060	+	0.503801i
$245$		0			0
$246$	−2.85155	+	17.2134i	−0.181808	+	1.09749i
$247$			13.3405i			0.848837i
$248$	−1.72521	−	6.56155i	−0.109551	−	0.416659i
$249$	−2.19224	−	7.80776i	−0.138927	−	0.494797i
$250$		0			0
$251$	−25.1035			−1.58452			−0.792259	−	0.610184i	$-0.791095\pi$
$251$	−25.1035			−1.58452			−0.792259	+	0.610184i	$0.791095\pi$
$252$	1.81181	−	5.31842i	0.114133	−	0.335029i
$253$	32.4924			2.04278
$254$	−5.99676	−	2.80776i	−0.376270	−	0.176175i
$255$		0			0
$256$	−14.9654	−	5.66001i	−0.935340	−	0.353751i
$257$			2.49242i			0.155473i	0.996974	+	0.0777365i	$0.0247693\pi$
$257$			2.49242i			0.155473i	−0.996974	+	0.0777365i	$0.975231\pi$
$258$	0.585385	−	3.53368i	0.0364445	−	0.219997i
$259$		−	2.92456i		−	0.181723i
$260$		0			0
$261$	8.00000	+	13.1231i	0.495188	+	0.812300i
$262$	−10.5616	+	22.5571i	−0.652495	+	1.39359i
$263$	−15.0981			−0.930989			−0.465494	−	0.885051i	$-0.654123\pi$
$263$	−15.0981			−0.930989			−0.465494	+	0.885051i	$0.654123\pi$
$264$	10.5940	+	18.0465i	0.652017	+	1.11068i
$265$		0			0
$266$	2.39871	−	5.12311i	0.147074	−	0.314118i
$267$	−10.4160	+	2.92456i	−0.637447	+	0.178980i
$268$	−8.00000	+	6.67026i	−0.488678	+	0.407451i
$269$			14.0000i			0.853595i	0.904347	+	0.426798i	$0.140358\pi$
$269$			14.0000i			0.853595i	−0.904347	+	0.426798i	$0.859642\pi$
$270$		0			0
$271$		−	31.7738i		−	1.93012i	−0.262032	−	0.965059i	$-0.584392\pi$
$271$		−	31.7738i		−	1.93012i	0.262032	−	0.965059i	$-0.415608\pi$
$272$	7.86962	+	1.43845i	0.477166	+	0.0872187i
$273$	4.87689	−	1.36932i	0.295163	−	0.0828748i
$274$	10.5616	+	4.94506i	0.638047	+	0.298742i
$275$		0			0
$276$	14.9234	−	21.7171i	0.898282	−	1.30722i
$277$	1.36932			0.0822743			0.0411371	−	0.999154i	$-0.486902\pi$
$277$	1.36932			0.0822743			0.0411371	+	0.999154i	$0.486902\pi$
$278$	17.7597	+	8.31534i	1.06516	+	0.498721i
$279$	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	$-0.308095\pi$
$282$	2.26293	+	0.374874i	0.134755	+	0.0223234i
$283$		−	4.38684i		−	0.260770i	−0.991463	−	0.130385i	$-0.958379\pi$
$283$		−	4.38684i		−	0.260770i	0.991463	−	0.130385i	$-0.0416214\pi$
$284$	−8.54312	−	10.2462i	−0.506941	−	0.608001i
$285$		0			0
$286$	−8.00000	+	17.0862i	−0.473050	+	1.01033i
$287$	6.67026			0.393733
$288$	16.9275	+	1.20777i	0.997464	+	0.0711682i
$289$	13.0000			0.764706
$290$		0			0
$291$	−2.80928	−	10.0054i	−0.164683	−	0.586527i
$292$	−10.5616	−	12.6670i	−0.618068	−	0.741282i
$293$			30.4924i			1.78139i	0.454605	+	0.890693i	$0.349780\pi$
$293$			30.4924i			1.78139i	−0.454605	+	0.890693i	$0.650220\pi$
$294$	14.7968	+	2.45122i	0.862968	+	0.142958i
$295$		0			0
$296$	8.54312	−	2.24621i	0.496559	−	0.130558i
$297$	−16.2462	−	15.1231i	−0.942701	−	0.877532i
$298$	17.9309	+	8.39547i	1.03871	+	0.486337i
$299$	23.7565			1.37387
$300$		0			0
$301$	−1.36932			−0.0789261
$302$	−7.86962	−	3.68466i	−0.452846	−	0.212028i
$303$	−15.2134	+	4.27156i	−0.873986	+	0.245395i
$304$	16.8078	+	3.07221i	0.963991	+	0.176203i
$305$		0			0
$306$	−8.43441	+	0.927794i	−0.482163	+	0.0530385i
$307$		−	8.13254i		−	0.464149i	−0.972698	−	0.232074i	$-0.925449\pi$
$307$		−	8.13254i		−	0.464149i	0.972698	−	0.232074i	$-0.0745513\pi$
$308$	6.14441	−	5.12311i	0.350110	−	0.291916i
$309$	20.6847	−	5.80776i	1.17671	−	0.330392i
$310$		0			0
$311$	−14.1617			−0.803035			−0.401517	−	0.915851i	$-0.631517\pi$
$311$	−14.1617			−0.803035			−0.401517	+	0.915851i	$0.631517\pi$
$312$	7.74571	+	13.1945i	0.438514	+	0.746992i
$313$	−10.4924			−0.593067			−0.296533	−	0.955022i	$-0.595831\pi$
$313$	−10.4924			−0.593067			−0.296533	+	0.955022i	$0.595831\pi$
$314$	12.8147	−	27.3693i	0.723174	−	1.54454i
$315$		0			0
$316$	13.9309	−	11.6153i	0.783673	−	0.653413i
$317$		−	32.7386i		−	1.83878i	−0.393342	−	0.919392i	$-0.628681\pi$
$317$		−	32.7386i		−	1.83878i	0.393342	−	0.919392i	$-0.371319\pi$
$318$	1.69986	−	10.2612i	0.0953233	−	0.575420i
$319$			21.8836i			1.22525i
$320$		0			0
$321$	0.438447	+	1.56155i	0.0244717	+	0.0871574i
$322$	−9.12311	−	4.27156i	−0.508411	−	0.238045i
$323$	−8.54312			−0.475352
$324$	−17.5696	+	3.91270i	−0.976089	+	0.217372i
$325$		0			0
$326$	30.9526	+	14.4924i	1.71431	+	0.802661i
$327$	4.27156	+	15.2134i	0.236218	+	0.841302i
$328$	5.12311	+	19.4849i	0.282876	+	1.07588i
$329$		−	0.876894i		−	0.0483448i
$330$		0			0
$331$			28.0281i			1.54056i	0.637705	+	0.770281i	$0.279884\pi$
$331$			28.0281i			1.54056i	−0.637705	+	0.770281i	$0.720116\pi$
$332$	−5.99676	−	7.19224i	−0.329115	−	0.394725i
$333$	−8.00000	+	4.87689i	−0.438397	+	0.267252i
$334$	1.68466	−	3.59806i	0.0921804	−	0.196877i
$335$		0			0
$336$	−0.602100	−	6.45975i	−0.0328473	−	0.352408i
$337$	34.4924			1.87892			0.939461	−	0.342656i	$-0.111326\pi$
$337$	34.4924			1.87892			0.939461	+	0.342656i	$0.111326\pi$
$338$	1.94668	−	4.15767i	0.105885	−	0.226147i
$339$	−23.3459	+	6.55498i	−1.26798	+	0.356018i
$340$		0			0
$341$			10.2462i			0.554863i
$342$	−18.0140	+	1.98156i	−0.974087	+	0.107151i
$343$		−	12.2888i		−	0.663534i
$344$	−1.05171	−	4.00000i	−0.0567042	−	0.215666i
$345$		0			0
$346$	2.56155	+	1.19935i	0.137710	+	0.0644776i
$347$	23.8718			1.28150			0.640752	−	0.767748i	$-0.278623\pi$
$347$	23.8718			1.28150			0.640752	+	0.767748i	$0.278623\pi$
$348$	14.6265	+	10.0509i	0.784062	+	0.538785i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−11.8782	−	11.0571i	−0.634014	−	0.590184i
$352$	19.6847	+	14.0140i	1.04920	+	0.746950i
$353$			3.75379i			0.199794i	0.994998	+	0.0998970i	$0.0318513\pi$
$353$			3.75379i			0.199794i	−0.994998	+	0.0998970i	$0.968149\pi$
$354$	−17.3898	−	2.88078i	−0.924258	−	0.153111i
$355$		0			0
$356$	−9.59482	+	8.00000i	−0.508525	+	0.423999i
$357$	0.876894	+	3.12311i	0.0464102	+	0.165292i
$358$	−8.80776	+	18.8114i	−0.465505	+	0.994215i
$359$	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
$362$	−2.54635	+	5.43845i	−0.133833	+	0.285838i
$363$	−3.39277	−	12.0835i	−0.178074	−	0.634221i
$364$	4.49242	−	3.74571i	0.235467	−	0.196328i
$365$		0			0
$366$	−12.3803	−	2.05090i	−0.647127	−	0.107202i
$367$		−	26.5658i		−	1.38672i	−0.720590	−	0.693361i	$-0.756129\pi$
$367$		−	26.5658i		−	1.38672i	0.720590	−	0.693361i	$-0.243871\pi$
$368$	5.47091	−	29.9309i	0.285191	−	1.56025i
$369$	−11.1231	−	18.2462i	−0.579046	−	0.949860i
$370$		0			0
$371$	−3.97626			−0.206437
$372$	6.84831	+	4.70596i	0.355068	+	0.243993i
$373$	0.876894			0.0454039			0.0227019	−	0.999742i	$-0.492773\pi$
$373$	0.876894			0.0454039			0.0227019	+	0.999742i	$0.492773\pi$
$374$	−10.9418	−	5.12311i	−0.565788	−	0.264909i
$375$		0			0
$376$	2.56155	−	0.673500i	0.132102	−	0.0347331i
$377$			16.0000i			0.824042i
$378$	2.57342	+	6.38199i	0.132362	+	0.328254i
$379$		−	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
$382$	4.63068	−	9.89012i	0.236926	−	0.506022i
$383$	−4.68213			−0.239246			−0.119623	−	0.992819i	$-0.538169\pi$
$383$	−4.68213			−0.239246			−0.119623	+	0.992819i	$0.538169\pi$
$384$	18.4076	−	6.72026i	0.939357	−	0.342942i
$385$		0			0
$386$	9.74247	−	20.8078i	0.495879	−	1.05909i
$387$	2.28343	+	3.74571i	0.116073	+	0.190405i
$388$	−7.68466	−	9.21662i	−0.390129	−	0.467903i
$389$			28.7386i			1.45711i	0.684989	+	0.728553i	$0.259807\pi$
$389$			28.7386i			1.45711i	−0.684989	+	0.728553i	$0.740193\pi$
$390$		0			0
$391$			15.2134i			0.769374i
$392$	16.7495	−	4.40388i	0.845977	−	0.222430i
$393$	−8.24621	−	29.3693i	−0.415966	−	1.48149i
$394$	−15.6847	−	7.34376i	−0.790182	−	0.369973i
$395$		0			0
$396$	−24.2602	−	8.26465i	−1.21912	−	0.415314i
$397$	−23.1231			−1.16052			−0.580258	−	0.814433i	$-0.697048\pi$
$397$	−23.1231			−1.16052			−0.580258	+	0.814433i	$0.697048\pi$
$398$	−22.5571	−	10.5616i	−1.13069	−	0.529403i
$399$	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	$0.795465\pi$
$402$	2.08488	−	12.5854i	0.103984	−	0.627702i
$403$			7.49141i			0.373174i
$404$	−14.0140	+	11.6847i	−0.697224	+	0.581333i
$405$		0			0
$406$	2.87689	−	6.14441i	0.142778	−	0.304942i
$407$	−13.3405			−0.661265
$408$	−8.44961	+	4.96026i	−0.418318	+	0.245569i
$409$	0.630683			0.0311853			0.0155926	−	0.999878i	$-0.495037\pi$
$409$	0.630683			0.0311853			0.0155926	+	0.999878i	$0.495037\pi$
$410$		0			0
$411$	−13.7511	+	3.86098i	−0.678292	+	0.190448i
$412$	19.0540	−	15.8869i	0.938722	−	0.782690i
$413$			6.73863i			0.331586i
$414$	3.52872	+	32.0790i	0.173427	+	1.57659i
$415$		0			0
$416$	14.3922	+	10.2462i	0.705637	+	0.502362i
$417$	−23.1231	+	6.49242i	−1.13234	+	0.317935i
$418$	−23.3693	−	10.9418i	−1.14303	−	0.535182i
$419$	−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	$0.504892\pi$
$422$	−1.72521	−	0.807764i	−0.0839817	−	0.0393213i
$423$	−2.39871	+	1.46228i	−0.116629	+	0.0710985i
$424$	−3.05398	−	11.6153i	−0.148314	−	0.564090i
$425$		0			0
$426$	16.1191	+	2.67026i	0.780971	+	0.129375i
$427$			4.79741i			0.232163i
$428$	1.19935	+	1.43845i	0.0579729	+	0.0695300i
$429$	−6.24621	−	22.2462i	−0.301570	−	1.07406i
$430$		0			0
$431$	36.0453			1.73624			0.868121	−	0.496353i	$-0.165328\pi$
$431$	36.0453			1.73624			0.868121	+	0.496353i	$0.165328\pi$
$432$	−16.6663	+	12.4191i	−0.801859	+	0.597513i
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$	1.34700	−	2.87689i	0.0646581	−	0.138095i
$435$		0			0
$436$	11.6847	+	14.0140i	0.559594	+	0.671150i
$437$			32.4924i			1.55432i
$438$	19.9274	+	3.30115i	0.952169	+	0.157735i
$439$		−	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
$442$	−8.00000	−	3.74571i	−0.380521	−	0.178165i
$443$	25.7446			1.22316			0.611582	−	0.791181i	$-0.290533\pi$
$443$	25.7446			1.22316			0.611582	+	0.791181i	$0.290533\pi$
$444$	−6.12715	+	8.91648i	−0.290782	+	0.423157i
$445$		0			0
$446$	−23.0830	−	10.8078i	−1.09301	−	0.511762i
$447$	−23.3459	+	6.55498i	−1.10422	+	0.310040i
$448$	−3.68466	−	6.52262i	−0.174084	−	0.308165i
$449$		−	2.63068i		−	0.124150i	−0.998071	−	0.0620748i	$-0.980228\pi$
$449$		−	2.63068i		−	0.124150i	0.998071	−	0.0620748i	$-0.0197717\pi$
$450$		0			0
$451$		−	30.4268i		−	1.43274i
$452$	−21.5054	+	17.9309i	−1.01153	+	0.843397i
$453$	10.2462	−	2.87689i	0.481409	−	0.135168i
$454$	5.19224	−	11.0895i	0.243684	−	0.520455i
$455$		0			0
$456$	−18.0465	+	10.5940i	−0.845104	+	0.496110i
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$	−0.147647	+	0.315342i	−0.00689909	+	0.0147349i
$459$	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	$-0.120429\pi$
$462$	−1.60129	+	9.66622i	−0.0744990	+	0.449713i
$463$			0.936426i			0.0435194i	0.999763	+	0.0217597i	$0.00692688\pi$
$463$			0.936426i			0.0435194i	−0.999763	+	0.0217597i	$0.993073\pi$
$464$	20.1584	+	3.68466i	0.935832	+	0.171056i
$465$		0			0
$466$	−12.8078	−	5.99676i	−0.593308	−	0.277795i
$467$	16.1498			0.747324			0.373662	−	0.927565i	$-0.378102\pi$
$467$	16.1498			0.747324			0.373662	+	0.927565i	$0.378102\pi$
$468$	−17.7376	−	6.04261i	−0.819922	−	0.279320i
$469$	−4.87689			−0.225194
$470$		0			0
$471$	10.0054	+	35.6347i	0.461024	+	1.64196i
$472$	−19.6847	+	5.17562i	−0.906060	+	0.238227i
$473$			6.24621i			0.287201i
$474$	−3.63052	+	21.9157i	−0.166755	+	1.00662i
$475$		0			0
$476$	2.39871	+	2.87689i	0.109944	+	0.131862i
$477$	6.63068	+	10.8769i	0.303598	+	0.498019i
$478$	12.4924	−	26.6811i	0.571390	−	1.22036i
$479$	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
$482$	6.81791	−	14.5616i	0.310547	−	0.663261i
$483$	11.8782	−	3.33513i	0.540479	−	0.151754i
$484$	−9.28078	−	11.1309i	−0.421853	−	0.505951i
$485$		0			0
$486$	13.1663	−	17.6819i	0.597236	−	0.802066i
$487$			15.3287i			0.694608i	0.937753	+	0.347304i	$0.112903\pi$
$487$			15.3287i			0.694608i	−0.937753	+	0.347304i	$0.887097\pi$
$488$	−14.0140	+	3.68466i	−0.634385	+	0.166797i
$489$	−40.3002	+	11.3153i	−1.82244	+	0.511697i
$490$		0			0
$491$	18.6638			0.842285			0.421143	−	0.906994i	$-0.361629\pi$
$491$	18.6638			0.842285			0.421143	+	0.906994i	$0.361629\pi$
$492$	−20.3365	−	13.9747i	−0.916840	−	0.630026i
$493$	−10.2462			−0.461466
$494$	−17.0862	−	8.00000i	−0.768746	−	0.359937i
$495$		0			0
$496$	9.43845	+	1.72521i	0.423799	+	0.0774640i
$497$		−	6.24621i		−	0.280181i
$498$	11.3146	+	1.87437i	0.507021	+	0.0839924i
$499$			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
$502$	15.0540	−	32.1520i	0.671892	−	1.43501i
$503$	19.8955			0.887097			0.443549	−	0.896250i	$-0.353719\pi$
$503$	19.8955			0.887097			0.443549	+	0.896250i	$0.353719\pi$
$504$	5.72521	+	5.50985i	0.255021	+	0.245428i
$505$		0			0
$506$	−19.4849	+	41.6155i	−0.866211	+	1.85004i
$507$	1.51992	+	5.41327i	0.0675020	+	0.240412i
$508$	7.19224	−	5.99676i	0.319104	−	0.266063i
$509$			2.87689i			0.127516i	0.997965	+	0.0637581i	$0.0203086\pi$
$509$			2.87689i			0.127516i	−0.997965	+	0.0637581i	$0.979691\pi$
$510$		0			0
$511$		−	7.72197i		−	0.341600i
$512$	16.2236	−	15.7732i	0.716990	−	0.697083i
$513$	15.1231	−	16.2462i	0.667701	−	0.717288i
$514$	−3.19224	−	1.49465i	−0.140803	−	0.0659261i
$515$		0			0
$516$	4.17481	+	2.86881i	0.183786	+	0.126292i
$517$	−4.00000			−0.175920
$518$	3.74571	+	1.75379i	0.164577	+	0.0770571i
$519$	−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	$-0.158104\pi$
$522$	−21.6052	+	2.37659i	−0.945633	+	0.104021i
$523$			0.641132i			0.0280348i	0.999902	+	0.0140174i	$0.00446202\pi$
$523$			0.641132i			0.0280348i	−0.999902	+	0.0140174i	$0.995538\pi$
$524$	−22.5571	−	27.0540i	−0.985413	−	1.18186i
$525$		0			0
$526$	9.05398	−	19.3373i	0.394772	−	0.843146i
$527$	−4.79741			−0.208979
$528$	−29.4665	+	2.74651i	−1.28236	+	0.119527i
$529$	34.8617			1.51573
$530$		0			0
$531$	18.4332	−	11.2371i	0.799934	−	0.487649i
$532$	5.12311	+	6.14441i	0.222115	+	0.266394i
$533$		−	22.2462i		−	0.963590i
$534$	2.50051	−	15.0943i	0.108207	−	0.653195i
$535$		0			0
$536$	−3.74571	−	14.2462i	−0.161790	−	0.615343i
$537$	−6.87689	−	24.4924i	−0.296760	−	1.05693i
$538$	−17.9309	−	8.39547i	−0.773055	−	0.361954i
$539$	−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	$0.183699\pi$
$542$	40.6951	+	19.0540i	1.74800	+	0.818438i
$543$	−1.98813	−	7.08084i	−0.0853189	−	0.303868i
$544$	−6.56155	+	9.21662i	−0.281324	+	0.395159i
$545$		0			0
$546$	−1.17077	+	7.06736i	−0.0501043	+	0.302455i
$547$		−	25.2188i		−	1.07828i	−0.842217	−	0.539139i	$-0.818750\pi$
$547$		−	25.2188i		−	1.07828i	0.842217	−	0.539139i	$-0.181250\pi$
$548$	−12.6670	+	10.5616i	−0.541109	+	0.451167i
$549$	13.1231	−	8.00000i	0.560080	−	0.341432i
$550$		0			0
$551$	−21.8836			−0.932275
$552$	18.8656	+	32.1368i	0.802972	+	1.36783i
$553$	8.49242			0.361135
$554$	−0.821147	+	1.75379i	−0.0348872	+	0.0745113i
$555$		0			0
$556$	−21.3002	+	17.7597i	−0.903329	+	0.753180i
$557$		−	19.7538i		−	0.836995i	−0.908218	−	0.418497i	$-0.862557\pi$
$557$		−	19.7538i		−	0.836995i	0.908218	−	0.418497i	$-0.137443\pi$
$558$	−10.1158	+	1.11275i	−0.428237	+	0.0471066i
$559$			4.56685i			0.193157i
$560$		0			0
$561$	14.2462	−	4.00000i	0.601476	−	0.168880i
$562$	35.3693	+	16.5604i	1.49196	+	0.698558i
$563$	36.1606			1.52399			0.761994	−	0.647584i	$-0.224221\pi$
$563$	36.1606			1.52399			0.761994	+	0.647584i	$0.224221\pi$
$564$	−1.83715	+	2.67350i	−0.0773581	+	0.112575i
$565$		0			0
$566$	5.61856	+	2.63068i	0.236166	+	0.110576i
$567$	−7.49141	−	3.86098i	−0.314610	−	0.162146i
$568$	18.2462	−	4.79741i	0.765594	−	0.201295i
$569$		−	4.87689i		−	0.204450i	−0.994761	−	0.102225i	$-0.967404\pi$
$569$		−	4.87689i		−	0.204450i	0.994761	−	0.102225i	$-0.0325962\pi$
$570$		0			0
$571$			16.7909i			0.702679i	0.936248	+	0.351339i	$0.114274\pi$
$571$			16.7909i			0.702679i	−0.936248	+	0.351339i	$0.885726\pi$
$572$	−17.0862	−	20.4924i	−0.714411	−	0.856831i
$573$	3.61553	+	12.8769i	0.151041	+	0.537940i
$574$	−4.00000	+	8.54312i	−0.166957	+	0.356583i
$575$		0			0
$576$	−11.6979	+	20.9561i	−0.487413	+	0.873171i
$577$	15.7538			0.655839			0.327919	−	0.944706i	$-0.393653\pi$
$577$	15.7538			0.655839			0.327919	+	0.944706i	$0.393653\pi$
$578$	−7.79579	+	16.6501i	−0.324262	+	0.692553i
$579$	7.60669	+	27.0916i	0.316123	+	1.12589i
$580$		0			0
$581$		−	4.38447i		−	0.181899i
$582$	14.4993	+	2.40194i	0.601017	+	0.0995637i
$583$			18.1379i			0.751197i
$584$	22.5571	−	5.93087i	0.933421	−	0.245421i
$585$		0			0
$586$	−39.0540	−	18.2856i	−1.61330	−	0.755371i
$587$	−38.0335			−1.56981			−0.784904	−	0.619617i	$-0.787288\pi$
$587$	−38.0335			−1.56981			−0.784904	+	0.619617i	$0.787288\pi$
$588$	−12.0128	+	17.4815i	−0.495399	+	0.720924i
$589$	−10.2462			−0.422188
$590$		0			0
$591$	20.4214	−	5.73384i	0.840023	−	0.235859i
$592$	−2.24621	+	12.2888i	−0.0923187	+	0.505067i
$593$			8.24621i			0.338631i	0.985562	+	0.169316i	$0.0541557\pi$
$593$			8.24621i			0.338631i	−0.985562	+	0.169316i	$0.945844\pi$
$594$	29.1118	−	11.7388i	1.19447	−	0.481649i
$595$		0			0
$596$	−21.5054	+	17.9309i	−0.880897	+	0.734477i
$597$	29.3693	−	8.24621i	1.20201	−	0.337495i
$598$	−14.2462	+	30.4268i	−0.582571	+	1.24424i
$599$	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	$0.401871\pi$
$602$	0.821147	−	1.75379i	0.0334675	−	0.0714791i
$603$	8.13254	+	13.3405i	0.331183	+	0.543268i
$604$	9.43845	−	7.86962i	0.384045	−	0.320210i
$605$		0			0
$606$	3.65219	−	22.0465i	0.148360	−	0.895578i
$607$		−	29.4903i		−	1.19698i	−0.801132	−	0.598488i	$-0.795768\pi$
$607$		−	29.4903i		−	1.19698i	0.801132	−	0.598488i	$-0.204232\pi$
$608$	−14.0140	+	19.6847i	−0.568344	+	0.798318i
$609$	2.24621	+	8.00000i	0.0910211	+	0.324176i
$610$		0			0
$611$	−2.92456			−0.118315
$612$	3.86962	−	11.3590i	0.156420	−	0.459159i
$613$	−0.876894			−0.0354174			−0.0177087	−	0.999843i	$-0.505637\pi$
$613$	−0.876894			−0.0354174			−0.0177087	+	0.999843i	$0.505637\pi$
$614$	10.4160	+	4.87689i	0.420354	+	0.196815i
$615$		0			0
$616$	2.87689	+	10.9418i	0.115913	+	0.440859i
$617$			14.0000i			0.563619i	0.959470	+	0.281809i	$0.0909346\pi$
$617$			14.0000i			0.563619i	−0.959470	+	0.281809i	$0.909065\pi$
$618$	−4.96565	+	29.9752i	−0.199748	+	1.20578i
$619$			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
$622$	8.49242	−	18.1379i	0.340515	−	0.727265i
$623$	−5.84912			−0.234340
$624$	−21.5441	+	2.00808i	−0.862455	+	0.0803877i
$625$		0			0
$626$	6.29206	−	13.4384i	0.251481	−	0.537108i
$627$	30.4268	−	8.54312i	1.21513	−	0.341179i
$628$	27.3693	+	32.8255i	1.09215	+	1.30988i
$629$		−	6.24621i		−	0.249053i
$630$		0			0
$631$			30.1315i			1.19951i	0.800182	+	0.599757i	$0.204736\pi$
$631$			30.1315i			1.19951i	−0.800182	+	0.599757i	$0.795264\pi$
$632$	6.52262	+	24.8078i	0.259456	+	0.986800i
$633$	2.24621	−	0.630683i	0.0892789	−	0.0250674i
$634$	41.9309	+	19.6326i	1.66529	+	0.779710i
$635$		0			0
$636$	12.1229	+	8.33054i	0.480706	+	0.330327i
$637$	−19.1231			−0.757685
$638$	−28.0281	−	13.1231i	−1.10964	−	0.519549i
$639$	−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	$-0.389502\pi$
$642$	−2.26293	−	0.374874i	−0.0893106	−	0.0147951i
$643$			20.4214i			0.805340i	0.915345	+	0.402670i	$0.131918\pi$
$643$			20.4214i			0.805340i	−0.915345	+	0.402670i	$0.868082\pi$
$644$	10.9418	−	9.12311i	0.431168	−	0.359501i
$645$		0			0
$646$	5.12311	−	10.9418i	0.201566	−	0.430500i
$647$	−3.63043			−0.142727			−0.0713634	−	0.997450i	$-0.522735\pi$
$647$	−3.63043			−0.142727			−0.0713634	+	0.997450i	$0.522735\pi$
$648$	5.52478	−	24.8491i	0.217034	−	0.976164i
$649$	30.7386			1.20660
$650$		0			0
$651$	1.05171	+	3.74571i	0.0412196	+	0.146806i
$652$	−37.1231	+	30.9526i	−1.45385	+	1.21220i
$653$		−	26.9848i		−	1.05600i	−0.849245	−	0.527999i	$-0.822942\pi$
$653$		−	26.9848i		−	1.05600i	0.849245	−	0.527999i	$-0.177058\pi$
$654$	−22.0465	−	3.65219i	−0.862086	−	0.142812i
$655$		0			0
$656$	−28.0281	−	5.12311i	−1.09431	−	0.200024i
$657$	−21.1231	+	12.8769i	−0.824091	+	0.502375i
$658$	1.12311	+	0.525853i	0.0437832	+	0.0204999i
$659$	−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	$0.854039\pi$
$662$	−35.8977	−	16.8078i	−1.39520	−	0.653252i
$663$	10.4160	−	2.92456i	0.404523	−	0.113580i
$664$	12.8078	−	3.36750i	0.497038	−	0.130684i
$665$		0			0
$666$	−1.44880	−	13.1708i	−0.0561399	−	0.510357i
$667$			38.9699i			1.50892i
$668$	3.59806	+	4.31534i	0.139213	+	0.166966i
$669$	30.0540	−	8.43845i	1.16195	−	0.326249i
$670$		0			0
$671$	21.8836			0.844809
$672$	8.63456	+	3.10261i	0.333086	+	0.119686i
$673$	10.4924			0.404453			0.202227	−	0.979339i	$-0.435182\pi$
$673$	10.4924			0.404453			0.202227	+	0.979339i	$0.435182\pi$
$674$	−20.6843	+	44.1771i	−0.796729	+	1.70164i
$675$		0			0
$676$	4.15767	+	4.98651i	0.159910	+	0.191789i
$677$		−	34.4924i		−	1.32565i	−0.748774	−	0.662826i	$-0.769357\pi$
$677$		−	34.4924i		−	1.32565i	0.748774	−	0.662826i	$-0.230643\pi$
$678$	5.60453	−	33.8318i	0.215241	−	1.29930i
$679$		−	5.61856i		−	0.215620i
$680$		0			0
$681$	4.05398	+	14.4384i	0.155349	+	0.553282i
$682$	−13.1231	−	6.14441i	−0.502510	−	0.235282i
$683$	−36.1606			−1.38365			−0.691823	−	0.722067i	$-0.743192\pi$
$683$	−36.1606			−1.38365			−0.691823	+	0.722067i	$0.743192\pi$
$684$	8.26465	−	24.2602i	0.316007	−	0.927613i
$685$		0			0
$686$	15.7392	+	7.36932i	0.600927	+	0.281362i
$687$	−0.115279	−	0.410574i	−0.00439818	−	0.0156644i
$688$	5.75379	+	1.05171i	0.219361	+	0.0400959i
$689$			13.2614i			0.505218i
$690$		0			0
$691$		−	29.0798i		−	1.10625i	−0.833100	−	0.553123i	$-0.813436\pi$
$691$		−	29.0798i		−	1.10625i	0.833100	−	0.553123i	$-0.186564\pi$
$692$	−3.07221	+	2.56155i	−0.116788	+	0.0973756i
$693$	−6.24621	−	10.2462i	−0.237274	−	0.389221i
$694$	−14.3153	+	30.5744i	−0.543403	+	1.16059i
$695$		0			0
$696$	−21.6441	+	12.7060i	−0.820418	+	0.481618i
$697$	14.2462			0.539614
$698$	8.39547	−	17.9309i	0.317773	−	0.678693i
$699$	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	$0.597413\pi$
$702$	21.2848	−	8.58270i	0.803342	−	0.323933i
$703$		−	13.3405i		−	0.503148i
$704$	−29.7533	+	16.8078i	−1.12137	+	0.633466i
$705$		0			0
$706$	−4.80776	−	2.25106i	−0.180943	−	0.0847197i
$707$	−8.54312			−0.321297
$708$	14.1179	−	20.5449i	0.530583	−	0.772126i
$709$	−26.4924			−0.994944			−0.497472	−	0.867480i	$-0.665738\pi$
$709$	−26.4924			−0.994944			−0.497472	+	0.867480i	$0.665738\pi$
$710$		0			0
$711$	−14.1617	−	23.2306i	−0.531104	−	0.871217i
$712$	−4.49242	−	17.0862i	−0.168361	−	0.640334i
$713$			18.2462i			0.683326i
$714$	−4.52585	−	0.749747i	−0.169376	−	0.0280586i
$715$		0			0
$716$	−18.8114	−	22.5616i	−0.703016	−	0.843165i
$717$	9.75379	+	34.7386i	0.364262	+	1.29734i
$718$	−0.630683	+	1.34700i	−0.0235369	+	0.0502696i
$719$	−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
$722$	−0.452029	+	0.965435i	−0.0168228	+	0.0359298i
$723$	5.32326	+	18.9591i	0.197974	+	0.705096i
$724$	−5.43845	−	6.52262i	−0.202118	−	0.242411i
$725$		0			0
$726$	17.5109	+	2.90083i	0.649889	+	0.107660i
$727$			26.5658i			0.985270i	0.870236	+	0.492635i	$0.163966\pi$
$727$			26.5658i			0.985270i	−0.870236	+	0.492635i	$0.836034\pi$
$728$	2.10341	+	8.00000i	0.0779576	+	0.296500i
$729$	1.93087	+	26.9309i	0.0715137	+	0.997440i
$730$		0			0
$731$	−2.92456			−0.108169
$732$	10.0509	−	14.6265i	0.371492	−	0.540610i
$733$	35.1231			1.29730			0.648651	−	0.761086i	$-0.275334\pi$
$733$	35.1231			1.29730			0.648651	+	0.761086i	$0.275334\pi$
$734$	34.0248	+	15.9309i	1.25588	+	0.588019i
$735$		0			0
$736$	35.0540	+	24.9559i	1.29211	+	0.919885i
$737$			22.2462i			0.819450i
$738$	30.0396	−	3.30439i	1.10577	−	0.121636i
$739$			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
$742$	2.38447	−	5.09271i	0.0875367	−	0.186959i
$743$	12.4041			0.455062			0.227531	−	0.973771i	$-0.426935\pi$
$743$	12.4041			0.455062			0.227531	+	0.973771i	$0.426935\pi$
$744$	−10.1341	+	5.94910i	−0.371533	+	0.218105i
$745$		0			0
$746$	−0.525853	+	1.12311i	−0.0192528	+	0.0411198i
$747$	−11.9935	+	7.31140i	−0.438820	+	0.267510i
$748$	13.1231	−	10.9418i	0.479828	−	0.400073i
$749$			0.876894i			0.0320410i
$750$		0			0
$751$		−	15.7392i		−	0.574333i	−0.957881	−	0.287166i	$-0.907287\pi$
$751$		−	15.7392i		−	0.574333i	0.957881	−	0.287166i	$-0.0927133\pi$
$752$	−0.673500	+	3.68466i	−0.0245600	+	0.134366i
$753$	11.7538	+	41.8617i	0.428332	+	1.52553i
$754$	−20.4924	−	9.59482i	−0.746290	−	0.349423i
$755$		0			0
$756$	−9.71712	−	0.531153i	−0.353408	−	0.0193178i
$757$	−19.1231			−0.695041			−0.347521	−	0.937672i	$-0.612976\pi$
$757$	−19.1231			−0.695041			−0.347521	+	0.937672i	$0.612976\pi$
$758$	32.1520	+	15.0540i	1.16781	+	0.546785i
$759$	−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	$0.621046\pi$
$762$	−1.87437	+	11.3146i	−0.0679012	+	0.409886i
$763$			8.54312i			0.309282i
$764$	9.89012	+	11.8617i	0.357812	+	0.429143i
$765$		0			0
$766$	2.80776	−	5.99676i	0.101449	−	0.216672i
$767$	22.4742			0.811498
$768$	−2.43143	+	27.6059i	−0.0877368	+	0.996144i
$769$	−26.9848			−0.973098			−0.486549	−	0.873653i	$-0.661745\pi$
$769$	−26.9848			−0.973098			−0.486549	+	0.873653i	$0.661745\pi$
$770$		0			0
$771$	4.15628	−	1.16699i	0.149685	−	0.0420279i
$772$	20.8078	+	24.9559i	0.748888	+	0.898181i
$773$		−	16.2462i		−	0.584336i	−0.956367	−	0.292168i	$-0.905623\pi$
$773$		−	16.2462i		−	0.584336i	0.956367	−	0.292168i	$-0.0943766\pi$
$774$	−6.16673	+	0.678347i	−0.221658	+	0.0243827i
$775$		0			0
$776$	16.4127	−	4.31534i	0.589183	−	0.154912i
$777$	−4.87689	+	1.36932i	−0.174958	+	0.0491240i
$778$	−36.8078	−	17.2339i	−1.31962	−	0.617865i
$779$	30.4268			1.09015
$780$		0			0
$781$	−28.4924			−1.01954
$782$	−19.4849	−	9.12311i	−0.696780	−	0.326242i
$783$	18.1379	−	19.4849i	0.648197	−	0.696335i
$784$	−4.40388	+	24.0932i	−0.157282	+	0.860473i
$785$		0			0
$786$	42.5606	+	7.05053i	1.51809	+	0.251484i
$787$		−	13.9817i		−	0.498392i	−0.968453	−	0.249196i	$-0.919834\pi$
$787$		−	13.9817i		−	0.498392i	0.968453	−	0.249196i	$-0.0801664\pi$
$788$	18.8114	−	15.6847i	0.670130	−	0.558743i
$789$	7.06913	+	25.1771i	0.251668	+	0.896328i
$790$		0			0
$791$	−13.1100			−0.466137
$792$	25.1335	−	26.1158i	0.893079	−	0.927986i
$793$	16.0000			0.568177
$794$	13.8664	−	29.6155i	0.492099	−	1.05102i
$795$		0			0
$796$	27.0540	−	22.5571i	0.958903	−	0.799517i
$797$			36.7386i			1.30135i	0.759357	+	0.650675i	$0.225514\pi$
$797$			36.7386i			1.30135i	−0.759357	+	0.650675i	$0.774486\pi$
$798$	−9.66622	−	1.60129i	−0.342181	−	0.0566852i
$799$		−	1.87285i		−	0.0662568i
$800$		0			0
$801$	9.75379	+	16.0000i	0.344633	+	0.565332i
$802$	−30.7386	−	14.3922i	−1.08542	−	0.508207i
$803$	−35.2242			−1.24303
$804$	14.8688	+	10.2174i	0.524383	+	0.360341i
$805$		0			0
$806$	−9.59482	−	4.49242i	−0.337963	−	0.158239i
$807$	23.3459	−	6.55498i	0.821815	−	0.230746i
$808$	−6.56155	−	24.9559i	−0.230835	−	0.877944i
$809$		−	46.2462i		−	1.62593i	−0.582312	−	0.812965i	$-0.697852\pi$
$809$		−	46.2462i		−	1.62593i	0.582312	−	0.812965i	$-0.302148\pi$
$810$		0			0
$811$			25.9246i			0.910337i	0.890405	+	0.455169i	$0.150421\pi$
$811$			25.9246i			0.910337i	−0.890405	+	0.455169i	$0.849579\pi$
$812$	6.14441	+	7.36932i	0.215627	+	0.258612i
$813$	−52.9848	+	14.8769i	−1.85826	+	0.521755i
$814$	8.00000	−	17.0862i	0.280400	−	0.598872i
$815$		0			0
$816$	−1.28595	−	13.7966i	−0.0450174	−	0.482978i
$817$	−6.24621			−0.218527
$818$	−0.378206	+	0.807764i	−0.0132237	+	0.0282428i
$819$	−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	$-0.170386\pi$
$822$	3.30115	−	19.9274i	0.115141	−	0.695049i
$823$		−	46.8071i		−	1.63159i	−0.578338	−	0.815797i	$-0.696299\pi$
$823$		−	46.8071i		−	1.63159i	0.578338	−	0.815797i	$-0.303701\pi$
$824$	8.92132	+	33.9309i	0.310789	+	1.18204i
$825$		0			0
$826$	−8.63068	−	4.04100i	−0.300300	−	0.140604i
$827$	−13.2252			−0.459887			−0.229943	−	0.973204i	$-0.573854\pi$
$827$	−13.2252			−0.459887			−0.229943	+	0.973204i	$0.573854\pi$
$828$	−43.2021	−	14.7175i	−1.50138	−	0.511468i
$829$	−17.1231			−0.594710			−0.297355	−	0.954767i	$-0.596104\pi$
$829$	−17.1231			−0.594710			−0.297355	+	0.954767i	$0.596104\pi$
$830$		0			0
$831$	−0.641132	−	2.28343i	−0.0222406	−	0.0792112i
$832$	−21.7538	+	12.2888i	−0.754177	+	0.426038i
$833$		−	12.2462i		−	0.424306i
$834$	5.55104	−	33.5089i	0.192217	−	1.16032i
$835$		0			0
$836$	28.0281	−	23.3693i	0.969371	−	0.808245i
$837$	8.49242	−	9.12311i	0.293541	−	0.315341i
$838$	3.68466	−	7.86962i	0.127284	−	0.271851i
$839$	−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
$842$	0.378206	−	0.807764i	0.0130338	−	0.0278374i
$843$	−46.0507	+	12.9300i	−1.58607	+	0.445331i
$844$	2.06913	−	1.72521i	0.0712224	−	0.0593840i
$845$		0			0
$846$	−0.434406	−	3.94910i	−0.0149352	−	0.135773i
$847$		−	6.78554i		−	0.233154i
$848$	16.7080	+	3.05398i	0.573756	+	0.104874i
$849$	−7.31534	+	2.05398i	−0.251062	+	0.0704923i
$850$		0			0
$851$	−23.7565			−0.814362
$852$	−13.0862	+	19.0436i	−0.448327	+	0.652424i
$853$	−49.8617			−1.70723			−0.853617	−	0.520902i	$-0.825596\pi$
$853$	−49.8617			−1.70723			−0.853617	+	0.520902i	$0.825596\pi$
$854$	−6.14441	−	2.87689i	−0.210257	−	0.0984453i
$855$		0			0
$856$	−2.56155	+	0.673500i	−0.0875521	+	0.0230198i
$857$		−	28.7386i		−	0.981693i	−0.871246	−	0.490847i	$-0.836688\pi$
$857$		−	28.7386i		−	0.981693i	0.871246	−	0.490847i	$-0.163312\pi$
$858$	32.2381	+	5.34053i	1.10059	+	0.182323i
$859$			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
$862$	−21.6155	+	46.1660i	−0.736228	+	1.57242i
$863$	−27.6175			−0.940110			−0.470055	−	0.882637i	$-0.655766\pi$
$863$	−27.6175			−0.940110			−0.470055	+	0.882637i	$0.655766\pi$
$864$	−5.91167	−	28.7933i	−0.201119	−	0.979567i
$865$		0			0
$866$	10.7942	−	23.0540i	0.366801	−	0.783406i
$867$	−6.08677	−	21.6784i	−0.206718	−	0.736236i
$868$	2.87689	+	3.45041i	0.0976482	+	0.117115i
$869$		−	38.7386i		−	1.31412i
$870$		0			0
$871$			16.2651i			0.551121i
$872$	−24.9559	+	6.56155i	−0.845112	+	0.222202i
$873$	−15.3693	+	9.36932i	−0.520173	+	0.317103i
$874$	−41.6155	−	19.4849i	−1.40767	−	0.659088i
$875$		0			0
$876$	−16.1780	+	23.5430i	−0.546606	+	0.795443i
$877$	3.61553			0.122088			0.0610439	−	0.998135i	$-0.480557\pi$
$877$	3.61553			0.122088			0.0610439	+	0.998135i	$0.480557\pi$
$878$	38.2964	+	17.9309i	1.29244	+	0.605138i
$879$	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	$0.859445\pi$
$882$	−2.84049	−	25.8224i	−0.0956443	−	0.869485i
$883$		−	10.8265i		−	0.364342i	−0.983267	−	0.182171i	$-0.941688\pi$
$883$		−	10.8265i		−	0.364342i	0.983267	−	0.182171i	$-0.0583125\pi$
$884$	9.59482	−	8.00000i	0.322709	−	0.269069i
$885$		0			0
$886$	−15.4384	+	32.9731i	−0.518665	+	1.10775i
$887$	53.4774			1.79560			0.897798	−	0.440408i	$-0.145166\pi$
$887$	53.4774			1.79560			0.897798	+	0.440408i	$0.145166\pi$
$888$	−7.74571	−	13.1945i	−0.259929	−	0.442779i
$889$	4.38447			0.147050
$890$		0			0
$891$	−17.6121	+	34.1725i	−0.590027	+	1.14482i
$892$	27.6847	−	23.0830i	0.926951	−	0.772876i
$893$		−	4.00000i		−	0.133855i
$894$	5.60453	−	33.8318i	0.187444	−	1.13150i
$895$		0			0
$896$	10.5636	−	0.807764i	0.352906	−	0.0269855i
$897$	−11.1231	−	39.6155i	−0.371390	−	1.32272i
$898$	3.36932	+	1.57756i	0.112436	+	0.0526438i
$899$	−12.2888			−0.409855
$900$		0			0
$901$	−8.49242			−0.282924
$902$	38.9699	+	18.2462i	1.29756	+	0.607532i
$903$	0.641132	+	2.28343i	0.0213355	+	0.0759877i
$904$	−10.0691	−	38.2964i	−0.334894	−	1.27372i
$905$		0			0
$906$	−2.45975	+	14.8483i	−0.0817198	+	0.493302i
$907$			35.8653i			1.19089i	0.803397	+	0.595444i	$0.203024\pi$
$907$			35.8653i			1.19089i	−0.803397	+	0.595444i	$0.796976\pi$
$908$	11.0895	+	13.3002i	0.368017	+	0.441382i
$909$	14.2462	+	23.3693i	0.472517	+	0.775111i
$910$		0			0
$911$	−41.8944			−1.38802			−0.694012	−	0.719963i	$-0.744159\pi$
$911$	−41.8944			−1.38802			−0.694012	+	0.719963i	$0.744159\pi$
$912$	−2.74651	−	29.4665i	−0.0909461	−	0.975733i
$913$	−20.0000			−0.661903
$914$	−5.99676	+	12.8078i	−0.198355	+	0.423643i
$915$		0			0
$916$	−0.315342	−	0.378206i	−0.0104192	−	0.0124963i
$917$		−	16.4924i		−	0.544628i
$918$	5.49626	+	13.6305i	0.181404	+	0.449874i
$919$		−	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
$922$	20.3153	+	9.51191i	0.669050	+	0.313258i
$923$	−20.8319			−0.685692
$924$	−11.4200	−	7.84751i	−0.375691	−	0.258164i
$925$		0			0
$926$	−1.19935	−	0.561553i	−0.0394132	−	0.0184538i
$927$	−19.3697	−	31.7738i	−0.636183	−	1.04359i
$928$	−16.8078	+	23.6089i	−0.551742	+	0.774998i
$929$		−	24.8769i		−	0.816184i	−0.912941	−	0.408092i	$-0.866194\pi$
$929$		−	24.8769i		−	0.816184i	0.912941	−	0.408092i	$-0.133806\pi$
$930$		0			0
$931$		−	26.1552i		−	0.857202i
$932$	15.3610	−	12.8078i	0.503167	−	0.419532i
$933$	6.63068	+	23.6155i	0.217079	+	0.773138i
$934$	−9.68466	+	20.6843i	−0.316892	+	0.676811i
$935$		0			0
$936$	18.3761	−	19.0943i	0.600641	−	0.624117i
$937$	−10.4924			−0.342773			−0.171386	−	0.985204i	$-0.554825\pi$
$937$	−10.4924			−0.342773			−0.171386	+	0.985204i	$0.554825\pi$
$938$	2.92456	−	6.24621i	0.0954902	−	0.203946i
$939$	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	$0.952490\pi$
$942$	−51.6401	−	8.55464i	−1.68253	−	0.278725i
$943$		−	54.1833i		−	1.76445i
$944$	5.17562	−	28.3153i	0.168452	−	0.921586i
$945$		0			0
$946$	−8.00000	−	3.74571i	−0.260102	−	0.121783i
$947$	25.5141			0.829096			0.414548	−	0.910027i	$-0.363940\pi$
$947$	25.5141			0.829096			0.414548	+	0.910027i	$0.363940\pi$
$948$	−25.8919	−	17.7922i	−0.840931	−	0.577864i
$949$	−25.7538			−0.836003
$950$		0			0
$951$	−54.5938	+	15.3287i	−1.77033	+	0.497066i
$952$	−5.12311	+	1.34700i	−0.166041	+	0.0436565i
$953$		−	10.4924i		−	0.339883i	−0.985454	−	0.169941i	$-0.945642\pi$
$953$		−	10.4924i		−	0.339883i	0.985454	−	0.169941i	$-0.0543579\pi$
$954$	−17.9071	+	1.96981i	−0.579765	+	0.0637748i
$955$		0			0
$956$	26.6811	+	32.0000i	0.862927	+	1.03495i
$957$	36.4924	−	10.2462i	1.17963	−	0.331213i
$958$	−13.7538	+	29.3751i	−0.444365	+	0.949065i
$959$	−7.72197			−0.249355
$960$		0			0
$961$	25.2462			0.814394
$962$	5.84912	−	12.4924i	0.188583	−	0.402772i
$963$	2.39871	−	1.46228i	0.0772972	−	0.0471213i
$964$	14.5616	+	17.4644i	0.468996	+	0.562492i
$965$		0			0
$966$	−2.85155	+	17.2134i	−0.0917470	+	0.553831i
$967$			23.6412i			0.760250i	0.924935	+	0.380125i	$0.124119\pi$
$967$			23.6412i			0.760250i	−0.924935	+	0.380125i	$0.875881\pi$
$968$	19.8217	−	5.21165i	0.637093	−	0.167509i
$969$	4.00000	+	14.2462i	0.128499	+	0.457654i
$970$		0			0
$971$	41.5991			1.33498			0.667490	−	0.744619i	$-0.267369\pi$
$971$	41.5991			1.33498			0.667490	+	0.744619i	$0.267369\pi$
$972$	14.7510	+	27.4665i	0.473139	+	0.880988i
$973$	−12.9848			−0.416275
$974$	−19.6326	−	9.19224i	−0.629069	−	0.294538i
$975$		0			0
$976$	3.68466	−	20.1584i	0.117943	−	0.645256i
$977$		−	48.2462i		−	1.54353i	−0.635906	−	0.771767i	$-0.719373\pi$
$977$		−	48.2462i		−	1.54353i	0.635906	−	0.771767i	$-0.280627\pi$
$978$	9.67465	−	58.4011i	0.309361	−	1.86746i
$979$			26.6811i			0.852730i
$980$		0			0
$981$	23.3693	−	14.2462i	0.746125	−	0.454847i
$982$	−11.1922	+	23.9041i	−0.357159	+	0.762812i
$983$	−3.03984			−0.0969558			−0.0484779	−	0.998824i	$-0.515437\pi$
$983$	−3.03984			−0.0969558			−0.0484779	+	0.998824i	$0.515437\pi$
$984$	30.0937	−	17.6662i	0.959353	−	0.563179i
$985$		0			0
$986$	6.14441	−	13.1231i	0.195678	−	0.417925i
$987$	−1.46228	+	0.410574i	−0.0465449	+	0.0130687i
$988$	20.4924	−	17.0862i	0.651951	−	0.543586i
$989$			11.1231i			0.353694i
$990$		0			0
$991$		−	16.7909i		−	0.533382i	−0.963782	−	0.266691i	$-0.914070\pi$
$991$		−	16.7909i		−	0.533382i	0.963782	−	0.266691i	$-0.0859303\pi$
$992$	−7.86962	+	11.0540i	−0.249861	+	0.350964i
$993$	46.7386	−	13.1231i	1.48321	−	0.416449i
$994$	8.00000	+	3.74571i	0.253745	+	0.118807i
$995$		0			0
$996$	−9.18576	+	13.3675i	−0.291062	+	0.423565i
$997$	−7.61553			−0.241186			−0.120593	−	0.992702i	$-0.538480\pi$
$997$	−7.61553			−0.241186			−0.120593	+	0.992702i	$0.538480\pi$
$998$	−2.02050	−	0.946025i	−0.0639578	−	0.0299459i
$999$	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.e.c.251.4		8
3.2	odd	2	inner	300.2.e.c.251.5		8
4.3	odd	2	inner	300.2.e.c.251.6		8
5.2	odd	4		300.2.h.a.299.1		8
5.3	odd	4		300.2.h.b.299.8		8
5.4	even	2		60.2.e.a.11.5	yes	8
12.11	even	2	inner	300.2.e.c.251.3		8
15.2	even	4		300.2.h.b.299.7		8
15.8	even	4		300.2.h.a.299.2		8
15.14	odd	2		60.2.e.a.11.4	yes	8
20.3	even	4		300.2.h.b.299.5		8
20.7	even	4		300.2.h.a.299.4		8
20.19	odd	2		60.2.e.a.11.3	✓	8
40.19	odd	2		960.2.h.g.191.6		8
40.29	even	2		960.2.h.g.191.3		8
60.23	odd	4		300.2.h.a.299.3		8
60.47	odd	4		300.2.h.b.299.6		8
60.59	even	2		60.2.e.a.11.6	yes	8
120.29	odd	2		960.2.h.g.191.5		8
120.59	even	2		960.2.h.g.191.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.e.a.11.3	✓	8	20.19	odd	2
60.2.e.a.11.4	yes	8	15.14	odd	2
60.2.e.a.11.5	yes	8	5.4	even	2
60.2.e.a.11.6	yes	8	60.59	even	2
300.2.e.c.251.3		8	12.11	even	2	inner
300.2.e.c.251.4		8	1.1	even	1	trivial
300.2.e.c.251.5		8	3.2	odd	2	inner
300.2.e.c.251.6		8	4.3	odd	2	inner
300.2.h.a.299.1		8	5.2	odd	4
300.2.h.a.299.2		8	15.8	even	4
300.2.h.a.299.3		8	60.23	odd	4
300.2.h.a.299.4		8	20.7	even	4
300.2.h.b.299.5		8	20.3	even	4
300.2.h.b.299.6		8	60.47	odd	4
300.2.h.b.299.7		8	15.2	even	4
300.2.h.b.299.8		8	5.3	odd	4
960.2.h.g.191.3		8	40.29	even	2
960.2.h.g.191.4		8	120.59	even	2
960.2.h.g.191.5		8	120.29	odd	2
960.2.h.g.191.6		8	40.19	odd	2

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599676 + 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} +(2.41656 + 0.400324i) q^{6} -0.936426i q^{7} +(2.73546 - 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})\)	\(q+(-0.599676 + 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 - 1.53610i) q^{4} +(2.41656 + 0.400324i) q^{6} -0.936426i q^{7} +(2.73546 - 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} -4.27156 q^{11} +(-1.96188 + 2.85500i) q^{12} -3.12311 q^{13} +(1.19935 + 0.561553i) q^{14} +(-0.719224 + 3.93481i) q^{16} -2.00000i q^{17} +(-0.463897 - 4.21720i) q^{18} -4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(2.56155 - 5.47091i) q^{22} -7.60669 q^{23} +(-2.48013 - 4.22480i) q^{24} +(1.87285 - 4.00000i) q^{26} +(3.80335 + 3.54042i) q^{27} +(-1.43845 + 1.19935i) q^{28} -5.12311i q^{29} -2.39871i q^{31} +(-4.60831 - 3.28078i) q^{32} +(2.00000 + 7.12311i) q^{33} +(2.56155 + 1.19935i) q^{34} +(5.67948 + 1.93481i) q^{36} +3.12311 q^{37} +(5.47091 + 2.56155i) q^{38} +(1.46228 + 5.20798i) q^{39} +7.12311i q^{41} +(0.374874 - 2.26293i) q^{42} -1.46228i q^{43} +(5.47091 + 6.56155i) q^{44} +(4.56155 - 9.74247i) q^{46} +0.936426 q^{47} +(6.89830 - 0.642976i) q^{48} +6.12311 q^{49} +(-3.33513 + 0.936426i) q^{51} +(4.00000 + 4.79741i) q^{52} -4.24621i q^{53} +(-6.81526 + 2.74813i) q^{54} +(-0.673500 - 2.56155i) q^{56} +(-7.12311 + 2.00000i) q^{57} +(6.56155 + 3.07221i) q^{58} -7.19612 q^{59} -5.12311 q^{61} +(3.07221 + 1.43845i) q^{62} +(1.46228 + 2.39871i) q^{63} +(6.96543 - 3.93481i) q^{64} +(-10.3225 - 1.71001i) q^{66} -5.20798i q^{67} +(-3.07221 + 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +6.67026 q^{71} +(-5.88391 + 6.11389i) q^{72} +8.24621 q^{73} +(-1.87285 + 4.00000i) q^{74} +(-6.56155 + 5.47091i) q^{76} +4.00000i q^{77} +(-7.54716 - 1.25025i) q^{78} +9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(-9.12311 - 4.27156i) q^{82} +4.68213 q^{83} +(2.67350 + 1.83715i) q^{84} +(1.87285 + 0.876894i) q^{86} +(-8.54312 + 2.39871i) q^{87} +(-11.6847 + 3.07221i) q^{88} -6.24621i q^{89} +2.92456i q^{91} +(9.74247 + 11.6847i) q^{92} +(-4.00000 + 1.12311i) q^{93} +(-0.561553 + 1.19935i) q^{94} +(-3.31324 + 9.22076i) q^{96} +6.00000 q^{97} +(-3.67188 + 7.84233i) q^{98} +(10.9418 - 6.67026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 14 q^{16} - 16 q^{18} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 28 q^{28} + 16 q^{33} + 4 q^{34} + 18 q^{36} - 8 q^{37} + 12 q^{42} + 20 q^{46} + 36 q^{48} + 16 q^{49} + 32 q^{52} - 10 q^{54} - 24 q^{57} + 36 q^{58} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 24 q^{72} - 36 q^{76} - 40 q^{78} - 40 q^{82} + 16 q^{84} - 44 q^{88} - 32 q^{93} + 12 q^{94} + 42 q^{96} + 48 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 14 * q^16 - 16 * q^18 + 4 * q^21 + 4 * q^22 - 2 * q^24 - 28 * q^28 + 16 * q^33 + 4 * q^34 + 18 * q^36 - 8 * q^37 + 12 * q^42 + 20 * q^46 + 36 * q^48 + 16 * q^49 + 32 * q^52 - 10 * q^54 - 24 * q^57 + 36 * q^58 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 24 * q^72 - 36 * q^76 - 40 * q^78 - 40 * q^82 + 16 * q^84 - 44 * q^88 - 32 * q^93 + 12 * q^94 + 42 * q^96 + 48 * q^97

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