LMFDB - Embedded newform 200.2.k.h.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(43,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("200.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.k (of order $4$, degree $2$, 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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	200.107
Dual form			200.2.k.h.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.221232 + 1.39680i) q^{2} +(-0.618034 + 0.618034i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.00000 - 0.726543i) q^{6} +(-1.90211 + 1.90211i) q^{7} +(-1.28408 - 2.52015i) q^{8} +2.23607i q^{9} -3.23607 q^{11} +(0.793604 - 1.55754i) q^{12} +(0.726543 + 0.726543i) q^{13} +(-3.07768 - 2.23607i) q^{14} +(3.23607 - 2.35114i) q^{16} +(1.00000 + 1.00000i) q^{17} +(-3.12334 + 0.494689i) q^{18} -2.00000i q^{19} -2.35114i q^{21} +(-0.715921 - 4.52015i) q^{22} +(4.25325 + 4.25325i) q^{23} +(2.35114 + 0.763932i) q^{24} +(-0.854102 + 1.17557i) q^{26} +(-3.23607 - 3.23607i) q^{27} +(2.44246 - 4.79360i) q^{28} +6.15537 q^{29} +8.50651i q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 - 2.00000i) q^{33} +(-1.17557 + 1.61803i) q^{34} +(-1.38197 - 4.25325i) q^{36} +(-0.726543 + 0.726543i) q^{37} +(2.79360 - 0.442463i) q^{38} -0.898056 q^{39} +5.70820 q^{41} +(3.28408 - 0.520147i) q^{42} +(-4.61803 + 4.61803i) q^{43} +(6.15537 - 2.00000i) q^{44} +(-5.00000 + 6.88191i) q^{46} +(3.35520 - 3.35520i) q^{47} +(-0.546915 + 3.45309i) q^{48} -0.236068i q^{49} -1.23607 q^{51} +(-1.83099 - 0.932938i) q^{52} +(-3.07768 - 3.07768i) q^{53} +(3.80423 - 5.23607i) q^{54} +(7.23607 + 2.35114i) q^{56} +(1.23607 + 1.23607i) q^{57} +(1.36176 + 8.59783i) q^{58} -0.472136i q^{59} -0.898056i q^{61} +(-11.8819 + 1.88191i) q^{62} +(-4.25325 - 4.25325i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(3.23607 + 2.35114i) q^{66} +(4.61803 + 4.61803i) q^{67} +(-2.52015 - 1.28408i) q^{68} -5.25731 q^{69} -11.4127i q^{71} +(5.63522 - 2.87129i) q^{72} +(4.70820 - 4.70820i) q^{73} +(-1.17557 - 0.854102i) q^{74} +(1.23607 + 3.80423i) q^{76} +(6.15537 - 6.15537i) q^{77} +(-0.198678 - 1.25441i) q^{78} -2.90617 q^{79} -2.70820 q^{81} +(1.26284 + 7.97323i) q^{82} +(6.61803 - 6.61803i) q^{83} +(1.45309 + 4.47214i) q^{84} +(-7.47214 - 5.42882i) q^{86} +(-3.80423 + 3.80423i) q^{87} +(4.15537 + 8.15537i) q^{88} +2.47214i q^{89} -2.76393 q^{91} +(-10.7188 - 5.46151i) q^{92} +(-5.25731 - 5.25731i) q^{93} +(5.42882 + 3.94427i) q^{94} -4.94427 q^{96} +(-4.23607 - 4.23607i) q^{97} +(0.329740 - 0.0522257i) q^{98} -7.23607i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 4 q^{3} - 8 q^{6} - 4 q^{8} - 8 q^{11} - 12 q^{12} + 8 q^{16} + 8 q^{17} - 10 q^{18} - 12 q^{22} + 20 q^{26} - 8 q^{27} + 20 q^{28} + 32 q^{32} + 16 q^{33} - 20 q^{36} + 4 q^{38} - 8 q^{41}+ \cdots + 6 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 4 * q^3 - 8 * q^6 - 4 * q^8 - 8 * q^11 - 12 * q^12 + 8 * q^16 + 8 * q^17 - 10 * q^18 - 12 * q^22 + 20 * q^26 - 8 * q^27 + 20 * q^28 + 32 * q^32 + 16 * q^33 - 20 * q^36 + 4 * q^38 - 8 * q^41 + 20 * q^42 - 28 * q^43 - 40 * q^46 - 16 * q^48 + 8 * q^51 - 20 * q^52 + 40 * q^56 - 8 * q^57 - 20 * q^58 - 40 * q^62 + 8 * q^66 + 28 * q^67 + 4 * q^68 + 20 * q^72 - 16 * q^73 - 8 * q^76 + 40 * q^78 + 32 * q^81 + 28 * q^82 + 44 * q^83 - 24 * q^86 - 16 * q^88 - 40 * q^91 - 20 * q^92 + 32 * q^96 - 16 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$2$	0.221232	+	1.39680i	0.156434	+	0.987688i
$3$	−0.618034	+	0.618034i	−0.356822	+	0.356822i	−0.862640	−	0.505818i	$-0.831191\pi$
$3$	−0.618034	+	0.618034i	−0.356822	+	0.356822i	0.505818	+	0.862640i	$0.331191\pi$
$4$	−1.90211	+	0.618034i	−0.951057	+	0.309017i
$5$		0			0
$5$		0			0
$6$	−1.00000	−	0.726543i	−0.408248	−	0.296610i
$7$	−1.90211	+	1.90211i	−0.718931	+	0.718931i	−0.968386	−	0.249455i	$-0.919748\pi$
$7$	−1.90211	+	1.90211i	−0.718931	+	0.718931i	0.249455	+	0.968386i	$0.419748\pi$
$8$	−1.28408	−	2.52015i	−0.453990	−	0.891007i
$9$			2.23607i			0.745356i
$10$		0			0
$11$	−3.23607			−0.975711			−0.487856	−	0.872924i	$-0.662221\pi$
$11$	−3.23607			−0.975711			−0.487856	+	0.872924i	$0.662221\pi$
$12$	0.793604	−	1.55754i	0.229094	−	0.449622i
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	0.800645	−	0.599139i	$-0.204490\pi$
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	−0.599139	+	0.800645i	$0.704490\pi$
$14$	−3.07768	−	2.23607i	−0.822546	−	0.597614i
$15$		0			0
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$	−3.12334	+	0.494689i	−0.736179	+	0.116599i
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$		−	2.35114i		−	0.513061i
$22$	−0.715921	−	4.52015i	−0.152635	−	0.963699i
$23$	4.25325	+	4.25325i	0.886865	+	0.886865i	0.994221	−	0.107356i	$-0.0342384\pi$
$23$	4.25325	+	4.25325i	0.886865	+	0.886865i	−0.107356	+	0.994221i	$0.534238\pi$
$24$	2.35114	+	0.763932i	0.479925	+	0.155937i
$25$		0			0
$26$	−0.854102	+	1.17557i	−0.167503	+	0.230548i
$27$	−3.23607	−	3.23607i	−0.622782	−	0.622782i
$28$	2.44246	−	4.79360i	0.461582	−	0.905906i
$29$	6.15537			1.14302			0.571511	−	0.820594i	$-0.306357\pi$
$29$	6.15537			1.14302			0.571511	+	0.820594i	$0.306357\pi$
$30$		0			0
$31$			8.50651i			1.52781i	0.645326	+	0.763907i	$0.276721\pi$
$31$			8.50651i			1.52781i	−0.645326	+	0.763907i	$0.723279\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	2.00000	−	2.00000i	0.348155	−	0.348155i
$34$	−1.17557	+	1.61803i	−0.201609	+	0.277491i
$35$		0			0
$36$	−1.38197	−	4.25325i	−0.230328	−	0.708876i
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	−0.764302	−	0.644859i	$-0.776916\pi$
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	0.644859	+	0.764302i	$0.276916\pi$
$38$	2.79360	−	0.442463i	0.453182	−	0.0717771i
$39$	−0.898056			−0.143804
$40$		0			0
$41$	5.70820			0.891472			0.445736	−	0.895165i	$-0.352942\pi$
$41$	5.70820			0.891472			0.445736	+	0.895165i	$0.352942\pi$
$42$	3.28408	−	0.520147i	0.506744	−	0.0802604i
$43$	−4.61803	+	4.61803i	−0.704244	+	0.704244i	−0.965319	−	0.261075i	$-0.915923\pi$
$43$	−4.61803	+	4.61803i	−0.704244	+	0.704244i	0.261075	+	0.965319i	$0.415923\pi$
$44$	6.15537	−	2.00000i	0.927957	−	0.301511i
$45$		0			0
$46$	−5.00000	+	6.88191i	−0.737210	+	1.01468i
$47$	3.35520	−	3.35520i	0.489406	−	0.489406i	−0.418713	−	0.908119i	$-0.637519\pi$
$47$	3.35520	−	3.35520i	0.489406	−	0.489406i	0.908119	+	0.418713i	$0.137519\pi$
$48$	−0.546915	+	3.45309i	−0.0789404	+	0.498410i
$49$		−	0.236068i		−	0.0337240i
$50$		0			0
$51$	−1.23607			−0.173084
$52$	−1.83099	−	0.932938i	−0.253913	−	0.129375i
$53$	−3.07768	−	3.07768i	−0.422752	−	0.422752i	0.463398	−	0.886150i	$-0.346630\pi$
$53$	−3.07768	−	3.07768i	−0.422752	−	0.422752i	−0.886150	+	0.463398i	$0.846630\pi$
$54$	3.80423	−	5.23607i	0.517690	−	0.712539i
$55$		0			0
$56$	7.23607	+	2.35114i	0.966960	+	0.314184i
$57$	1.23607	+	1.23607i	0.163721	+	0.163721i
$58$	1.36176	+	8.59783i	0.178808	+	1.12895i
$59$		−	0.472136i		−	0.0614669i	−0.999528	−	0.0307334i	$-0.990216\pi$
$59$		−	0.472136i		−	0.0614669i	0.999528	−	0.0307334i	$-0.00978430\pi$
$60$		0			0
$61$		−	0.898056i		−	0.114984i	−0.998346	−	0.0574921i	$-0.981690\pi$
$61$		−	0.898056i		−	0.114984i	0.998346	−	0.0574921i	$-0.0183104\pi$
$62$	−11.8819	+	1.88191i	−1.50900	+	0.239003i
$63$	−4.25325	−	4.25325i	−0.535860	−	0.535860i
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$		0			0
$66$	3.23607	+	2.35114i	0.398332	+	0.289405i
$67$	4.61803	+	4.61803i	0.564183	+	0.564183i	0.930493	−	0.366310i	$-0.119379\pi$
$67$	4.61803	+	4.61803i	0.564183	+	0.564183i	−0.366310	+	0.930493i	$0.619379\pi$
$68$	−2.52015	−	1.28408i	−0.305613	−	0.155717i
$69$	−5.25731			−0.632906
$70$		0			0
$71$		−	11.4127i		−	1.35444i	−0.735783	−	0.677218i	$-0.763185\pi$
$71$		−	11.4127i		−	1.35444i	0.735783	−	0.677218i	$-0.236815\pi$
$72$	5.63522	−	2.87129i	0.664117	−	0.338385i
$73$	4.70820	−	4.70820i	0.551054	−	0.551054i	−0.375691	−	0.926745i	$-0.622595\pi$
$73$	4.70820	−	4.70820i	0.551054	−	0.551054i	0.926745	+	0.375691i	$0.122595\pi$
$74$	−1.17557	−	0.854102i	−0.136657	−	0.0992873i
$75$		0			0
$76$	1.23607	+	3.80423i	0.141787	+	0.436375i
$77$	6.15537	−	6.15537i	0.701469	−	0.701469i
$78$	−0.198678	−	1.25441i	−0.0224959	−	0.142034i
$79$	−2.90617			−0.326970			−0.163485	−	0.986546i	$-0.552273\pi$
$79$	−2.90617			−0.326970			−0.163485	+	0.986546i	$0.552273\pi$
$80$		0			0
$81$	−2.70820			−0.300912
$82$	1.26284	+	7.97323i	0.139457	+	0.880496i
$83$	6.61803	−	6.61803i	0.726424	−	0.726424i	−0.243482	−	0.969905i	$-0.578290\pi$
$83$	6.61803	−	6.61803i	0.726424	−	0.726424i	0.969905	+	0.243482i	$0.0782896\pi$
$84$	1.45309	+	4.47214i	0.158545	+	0.487950i
$85$		0			0
$86$	−7.47214	−	5.42882i	−0.805741	−	0.585405i
$87$	−3.80423	+	3.80423i	−0.407856	+	0.407856i
$88$	4.15537	+	8.15537i	0.442964	+	0.869365i
$89$			2.47214i			0.262046i	0.991379	+	0.131023i	$0.0418262\pi$
$89$			2.47214i			0.262046i	−0.991379	+	0.131023i	$0.958174\pi$
$90$		0			0
$91$	−2.76393			−0.289739
$92$	−10.7188	−	5.46151i	−1.11751	−	0.569402i
$93$	−5.25731	−	5.25731i	−0.545158	−	0.545158i
$94$	5.42882	+	3.94427i	0.559940	+	0.406821i
$95$		0			0
$96$	−4.94427			−0.504623
$97$	−4.23607	−	4.23607i	−0.430108	−	0.430108i	0.458557	−	0.888665i	$-0.348366\pi$
$97$	−4.23607	−	4.23607i	−0.430108	−	0.430108i	−0.888665	+	0.458557i	$0.848366\pi$
$98$	0.329740	−	0.0522257i	0.0333088	−	0.00527560i
$99$		−	7.23607i		−	0.727252i
$100$		0			0
$101$		−	2.90617i		−	0.289175i	−0.989492	−	0.144587i	$-0.953815\pi$
$101$		−	2.90617i		−	0.289175i	0.989492	−	0.144587i	$-0.0461855\pi$
$102$	−0.273457	−	1.72654i	−0.0270763	−	0.170953i
$103$	−3.35520	−	3.35520i	−0.330597	−	0.330597i	0.522216	−	0.852813i	$-0.325106\pi$
$103$	−3.35520	−	3.35520i	−0.330597	−	0.330597i	−0.852813	+	0.522216i	$0.825106\pi$
$104$	0.898056	−	2.76393i	0.0880616	−	0.271026i
$105$		0			0
$106$	3.61803	−	4.97980i	0.351415	−	0.483681i
$107$	−0.909830	−	0.909830i	−0.0879566	−	0.0879566i	0.661760	−	0.749716i	$-0.269810\pi$
$107$	−0.909830	−	0.909830i	−0.0879566	−	0.0879566i	−0.749716	+	0.661760i	$0.769810\pi$
$108$	8.15537	+	4.15537i	0.784751	+	0.399850i
$109$	−14.6619			−1.40435			−0.702176	−	0.712003i	$-0.747788\pi$
$109$	−14.6619			−1.40435			−0.702176	+	0.712003i	$0.747788\pi$
$110$		0			0
$111$		−	0.898056i		−	0.0852397i
$112$	−1.68323	+	10.6275i	−0.159050	+	1.00420i
$113$	−8.70820	+	8.70820i	−0.819199	+	0.819199i	−0.985992	−	0.166793i	$-0.946659\pi$
$113$	−8.70820	+	8.70820i	−0.819199	+	0.819199i	0.166793	+	0.985992i	$0.446659\pi$
$114$	−1.45309	+	2.00000i	−0.136094	+	0.187317i
$115$		0			0
$116$	−11.7082	+	3.80423i	−1.08708	+	0.353214i
$117$	−1.62460	+	1.62460i	−0.150194	+	0.150194i
$118$	0.659481	−	0.104451i	0.0607101	−	0.00961554i
$119$	−3.80423			−0.348733
$120$		0			0
$121$	−0.527864			−0.0479876
$122$	1.25441	−	0.198678i	0.113569	−	0.0179875i
$123$	−3.52786	+	3.52786i	−0.318097	+	0.318097i
$124$	−5.25731	−	16.1803i	−0.472120	−	1.45304i
$125$		0			0
$126$	5.00000	−	6.88191i	0.445435	−	0.613089i
$127$	2.80017	−	2.80017i	0.248475	−	0.248475i	−0.571870	−	0.820344i	$-0.693782\pi$
$127$	2.80017	−	2.80017i	0.248475	−	0.248475i	0.820344	+	0.571870i	$0.193782\pi$
$128$	−10.0806	−	5.13632i	−0.891007	−	0.453990i
$129$		−	5.70820i		−	0.502579i
$130$		0			0
$131$	13.7082			1.19769			0.598846	−	0.800864i	$-0.295626\pi$
$131$	13.7082			1.19769			0.598846	+	0.800864i	$0.295626\pi$
$132$	−2.56816	+	5.04029i	−0.223529	+	0.438701i
$133$	3.80423	+	3.80423i	0.329868	+	0.329868i
$134$	−5.42882	+	7.47214i	−0.468979	+	0.645494i
$135$		0			0
$136$	1.23607	−	3.80423i	0.105992	−	0.326210i
$137$	5.47214	+	5.47214i	0.467516	+	0.467516i	0.901109	−	0.433593i	$-0.142754\pi$
$137$	5.47214	+	5.47214i	0.467516	+	0.467516i	−0.433593	+	0.901109i	$0.642754\pi$
$138$	−1.16308	−	7.34342i	−0.0990083	−	0.625114i
$139$			21.4164i			1.81652i	0.418411	+	0.908258i	$0.362587\pi$
$139$			21.4164i			1.81652i	−0.418411	+	0.908258i	$0.637413\pi$
$140$		0			0
$141$			4.14725i			0.349262i
$142$	15.9413	−	2.52485i	1.33776	−	0.211880i
$143$	−2.35114	−	2.35114i	−0.196612	−	0.196612i
$144$	5.25731	+	7.23607i	0.438109	+	0.603006i
$145$		0			0
$146$	7.61803	+	5.53483i	0.630473	+	0.458065i
$147$	0.145898	+	0.145898i	0.0120335	+	0.0120335i
$148$	0.932938	−	1.83099i	0.0766870	−	0.150507i
$149$	12.8658			1.05400			0.527002	−	0.849864i	$-0.323316\pi$
$149$	12.8658			1.05400			0.527002	+	0.849864i	$0.323316\pi$
$150$		0			0
$151$			6.71040i			0.546084i	0.962002	+	0.273042i	$0.0880298\pi$
$151$			6.71040i			0.546084i	−0.962002	+	0.273042i	$0.911970\pi$
$152$	−5.04029	+	2.56816i	−0.408822	+	0.208305i
$153$	−2.23607	+	2.23607i	−0.180775	+	0.180775i
$154$	9.95959	+	7.23607i	0.802567	+	0.583099i
$155$		0			0
$156$	1.70820	−	0.555029i	0.136766	−	0.0444379i
$157$	−13.9353	+	13.9353i	−1.11216	+	1.11216i	−0.119303	+	0.992858i	$0.538066\pi$
$157$	−13.9353	+	13.9353i	−1.11216	+	1.11216i	−0.992858	+	0.119303i	$0.961934\pi$
$158$	−0.642937	−	4.05934i	−0.0511493	−	0.322944i
$159$	3.80423			0.301695
$160$		0			0
$161$	−16.1803			−1.27519
$162$	−0.599141	−	3.78283i	−0.0470729	−	0.297207i
$163$	13.8541	−	13.8541i	1.08514	−	1.08514i	0.0891157	−	0.996021i	$-0.471596\pi$
$163$	13.8541	−	13.8541i	1.08514	−	1.08514i	0.996021	−	0.0891157i	$-0.0284041\pi$
$164$	−10.8576	+	3.52786i	−0.847840	+	0.275480i
$165$		0			0
$166$	10.7082	+	7.77997i	0.831118	+	0.603842i
$167$	8.05748	−	8.05748i	0.623507	−	0.623507i	−0.322920	−	0.946426i	$-0.604664\pi$
$167$	8.05748	−	8.05748i	0.623507	−	0.623507i	0.946426	+	0.322920i	$0.104664\pi$
$168$	−5.92522	+	3.01905i	−0.457141	+	0.232925i
$169$		−	11.9443i		−	0.918790i
$170$		0			0
$171$	4.47214			0.341993
$172$	5.92992	−	11.6381i	0.452152	−	0.887399i
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.994208	+	0.107474i	$0.0342762\pi$
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.107474	+	0.994208i	$0.465724\pi$
$174$	−6.15537	−	4.47214i	−0.466637	−	0.339032i
$175$		0			0
$176$	−10.4721	+	7.60845i	−0.789367	+	0.573509i
$177$	0.291796	+	0.291796i	0.0219327	+	0.0219327i
$178$	−3.45309	+	0.546915i	−0.258820	+	0.0409930i
$179$		−	7.52786i		−	0.562659i	−0.959611	−	0.281329i	$-0.909225\pi$
$179$		−	7.52786i		−	0.562659i	0.959611	−	0.281329i	$-0.0907754\pi$
$180$		0			0
$181$			15.2169i			1.13106i	0.824726	+	0.565532i	$0.191329\pi$
$181$			15.2169i			1.13106i	−0.824726	+	0.565532i	$0.808671\pi$
$182$	−0.611469	−	3.86067i	−0.0453251	−	0.286172i
$183$	0.555029	+	0.555029i	0.0410289	+	0.0410289i
$184$	5.25731	−	16.1803i	0.387574	−	1.19283i
$185$		0			0
$186$	6.18034	−	8.50651i	0.453165	−	0.623727i
$187$	−3.23607	−	3.23607i	−0.236645	−	0.236645i
$188$	−4.30834	+	8.45559i	−0.314218	+	0.616687i
$189$	12.3107			0.895474
$190$		0			0
$191$		−	13.2088i		−	0.955755i	−0.878427	−	0.477877i	$-0.841406\pi$
$191$		−	13.2088i		−	0.955755i	0.878427	−	0.477877i	$-0.158594\pi$
$192$	−1.09383	−	6.90617i	−0.0789404	−	0.498410i
$193$	−1.47214	+	1.47214i	−0.105967	+	0.105967i	−0.758102	−	0.652136i	$-0.773873\pi$
$193$	−1.47214	+	1.47214i	−0.105967	+	0.105967i	0.652136	+	0.758102i	$0.273873\pi$
$194$	4.97980	−	6.85410i	0.357529	−	0.492096i
$195$		0			0
$196$	0.145898	+	0.449028i	0.0104213	+	0.0320734i
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	−0.297038	−	0.954866i	$-0.595999\pi$
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	0.954866	+	0.297038i	$0.0959988\pi$
$198$	10.1074	−	1.60085i	0.718299	−	0.113767i
$199$	21.7153			1.53936			0.769678	−	0.638432i	$-0.220417\pi$
$199$	21.7153			1.53936			0.769678	+	0.638432i	$0.220417\pi$
$200$		0			0
$201$	−5.70820			−0.402626
$202$	4.05934	−	0.642937i	0.285615	−	0.0452369i
$203$	−11.7082	+	11.7082i	−0.821755	+	0.821755i
$204$	2.35114	−	0.763932i	0.164613	−	0.0534859i
$205$		0			0
$206$	3.94427	−	5.42882i	0.274810	−	0.378244i
$207$	−9.51057	+	9.51057i	−0.661030	+	0.661030i
$208$	4.05934	+	0.642937i	0.281465	+	0.0445797i
$209$			6.47214i			0.447687i
$210$		0			0
$211$	2.29180			0.157774			0.0788869	−	0.996884i	$-0.474863\pi$
$211$	2.29180			0.157774			0.0788869	+	0.996884i	$0.474863\pi$
$212$	7.75621	+	3.95199i	0.532699	+	0.271424i
$213$	7.05342	+	7.05342i	0.483293	+	0.483293i
$214$	1.06957	−	1.47214i	0.0731143	−	0.100633i
$215$		0			0
$216$	−4.00000	+	12.3107i	−0.272166	+	0.837639i
$217$	−16.1803	−	16.1803i	−1.09839	−	1.09839i
$218$	−3.24367	−	20.4797i	−0.219689	−	1.38706i
$219$			5.81966i			0.393256i
$220$		0			0
$221$			1.45309i			0.0977451i
$222$	1.25441	−	0.198678i	0.0841903	−	0.0133344i
$223$	14.2128	+	14.2128i	0.951763	+	0.951763i	0.998889	−	0.0471263i	$-0.0150063\pi$
$223$	14.2128	+	14.2128i	0.951763	+	0.951763i	−0.0471263	+	0.998889i	$0.515006\pi$
$224$	−15.2169			−1.01672
$225$		0			0
$226$	−14.0902	−	10.2371i	−0.937264	−	0.680962i
$227$	9.38197	+	9.38197i	0.622703	+	0.622703i	0.946222	−	0.323519i	$-0.104866\pi$
$227$	9.38197	+	9.38197i	0.622703	+	0.622703i	−0.323519	+	0.946222i	$0.604866\pi$
$228$	−3.11507	−	1.58721i	−0.206301	−	0.105115i
$229$	−7.95148			−0.525449			−0.262724	−	0.964871i	$-0.584621\pi$
$229$	−7.95148			−0.525449			−0.262724	+	0.964871i	$0.584621\pi$
$230$		0			0
$231$			7.60845i			0.500599i
$232$	−7.90398	−	15.5124i	−0.518922	−	1.01844i
$233$	−5.47214	+	5.47214i	−0.358492	+	0.358492i	−0.863257	−	0.504765i	$-0.831579\pi$
$233$	−5.47214	+	5.47214i	−0.358492	+	0.358492i	0.504765	+	0.863257i	$0.331579\pi$
$234$	−2.62866	−	1.90983i	−0.171841	−	0.124849i
$235$		0			0
$236$	0.291796	+	0.898056i	0.0189943	+	0.0584585i
$237$	1.79611	−	1.79611i	0.116670	−	0.116670i
$238$	−0.841616	−	5.31375i	−0.0545538	−	0.344439i
$239$	13.4208			0.868119			0.434059	−	0.900884i	$-0.357081\pi$
$239$	13.4208			0.868119			0.434059	+	0.900884i	$0.357081\pi$
$240$		0			0
$241$	11.2361			0.723779			0.361889	−	0.932221i	$-0.382132\pi$
$241$	11.2361			0.723779			0.361889	+	0.932221i	$0.382132\pi$
$242$	−0.116780	−	0.737322i	−0.00750692	−	0.0473968i
$243$	11.3820	−	11.3820i	0.730153	−	0.730153i
$244$	0.555029	+	1.70820i	0.0355321	+	0.109357i
$245$		0			0
$246$	−5.70820	−	4.14725i	−0.363942	−	0.264419i
$247$	1.45309	−	1.45309i	0.0924576	−	0.0924576i
$248$	21.4377	−	10.9230i	1.36129	−	0.693613i
$249$			8.18034i			0.518408i
$250$		0			0
$251$	0.180340			0.0113830			0.00569148	−	0.999984i	$-0.498188\pi$
$251$	0.180340			0.0113830			0.00569148	+	0.999984i	$0.498188\pi$
$252$	10.7188	+	5.46151i	0.675223	+	0.344043i
$253$	−13.7638	−	13.7638i	−0.865324	−	0.865324i
$254$	4.53077	+	3.29180i	0.284286	+	0.206546i
$255$		0			0
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−5.29180	−	5.29180i	−0.330093	−	0.330093i	0.522529	−	0.852622i	$-0.324989\pi$
$257$	−5.29180	−	5.29180i	−0.330093	−	0.330093i	−0.852622	+	0.522529i	$0.824989\pi$
$258$	7.97323	−	1.26284i	0.496392	−	0.0786207i
$259$		−	2.76393i		−	0.171742i
$260$		0			0
$261$			13.7638i			0.851959i
$262$	3.03269	+	19.1477i	0.187360	+	1.18295i
$263$	−7.50245	−	7.50245i	−0.462621	−	0.462621i	0.436893	−	0.899514i	$-0.356079\pi$
$263$	−7.50245	−	7.50245i	−0.462621	−	0.462621i	−0.899514	+	0.436893i	$0.856079\pi$
$264$	−7.60845	−	2.47214i	−0.468268	−	0.152149i
$265$		0			0
$266$	−4.47214	+	6.15537i	−0.274204	+	0.377410i
$267$	−1.52786	−	1.52786i	−0.0935038	−	0.0935038i
$268$	−11.6381	−	5.92992i	−0.710912	−	0.362228i
$269$	−20.4742			−1.24833			−0.624167	−	0.781291i	$-0.714562\pi$
$269$	−20.4742			−1.24833			−0.624167	+	0.781291i	$0.714562\pi$
$270$		0			0
$271$		−	17.2250i		−	1.04635i	−0.852227	−	0.523173i	$-0.824748\pi$
$271$		−	17.2250i		−	1.04635i	0.852227	−	0.523173i	$-0.175252\pi$
$272$	5.58721	+	0.884927i	0.338774	+	0.0536566i
$273$	1.70820	−	1.70820i	0.103385	−	0.103385i
$274$	−6.43288	+	8.85410i	−0.388625	+	0.534896i
$275$		0			0
$276$	10.0000	−	3.24920i	0.601929	−	0.195579i
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	−0.927811	−	0.373051i	$-0.878312\pi$
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	0.373051	+	0.927811i	$0.378312\pi$
$278$	−29.9145	+	4.73799i	−1.79415	+	0.284166i
$279$	−19.0211			−1.13877
$280$		0			0
$281$	−9.70820			−0.579143			−0.289571	−	0.957156i	$-0.593513\pi$
$281$	−9.70820			−0.579143			−0.289571	+	0.957156i	$0.593513\pi$
$282$	−5.79289	+	0.917504i	−0.344962	+	0.0546366i
$283$	−13.3820	+	13.3820i	−0.795475	+	0.795475i	−0.982378	−	0.186903i	$-0.940155\pi$
$283$	−13.3820	+	13.3820i	−0.795475	+	0.795475i	0.186903	+	0.982378i	$0.440155\pi$
$284$	7.05342	+	21.7082i	0.418544	+	1.28814i
$285$		0			0
$286$	2.76393	−	3.80423i	0.163435	−	0.224949i
$287$	−10.8576	+	10.8576i	−0.640907	+	0.640907i
$288$	−8.94427	+	8.94427i	−0.527046	+	0.527046i
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$	5.23607			0.306944
$292$	−6.04571	+	11.8654i	−0.353798	+	0.694368i
$293$	3.07768	+	3.07768i	0.179800	+	0.179800i	0.791269	−	0.611469i	$-0.209421\pi$
$293$	3.07768	+	3.07768i	0.179800	+	0.179800i	−0.611469	+	0.791269i	$0.709421\pi$
$294$	−0.171513	+	0.236068i	−0.0100029	+	0.0137678i
$295$		0			0
$296$	2.76393	+	0.898056i	0.160650	+	0.0521984i
$297$	10.4721	+	10.4721i	0.607655	+	0.607655i
$298$	2.84632	+	17.9709i	0.164883	+	1.04103i
$299$			6.18034i			0.357418i
$300$		0			0
$301$		−	17.5680i		−	1.01261i
$302$	−9.37310	+	1.48455i	−0.539361	+	0.0854264i
$303$	1.79611	+	1.79611i	0.103184	+	0.103184i
$304$	−4.70228	−	6.47214i	−0.269694	−	0.371202i
$305$		0			0
$306$	−3.61803	−	2.62866i	−0.206829	−	0.150270i
$307$	13.5623	+	13.5623i	0.774042	+	0.774042i	0.978810	−	0.204769i	$-0.0656442\pi$
$307$	13.5623	+	13.5623i	0.774042	+	0.774042i	−0.204769	+	0.978810i	$0.565644\pi$
$308$	−7.90398	+	15.5124i	−0.450371	+	0.883903i
$309$	4.14725			0.235929
$310$		0			0
$311$			20.8172i			1.18044i	0.807243	+	0.590219i	$0.200959\pi$
$311$			20.8172i			1.18044i	−0.807243	+	0.590219i	$0.799041\pi$
$312$	1.15317	+	2.26323i	0.0652857	+	0.128130i
$313$	1.76393	−	1.76393i	0.0997033	−	0.0997033i	−0.655496	−	0.755199i	$-0.727540\pi$
$313$	1.76393	−	1.76393i	0.0997033	−	0.0997033i	0.755199	+	0.655496i	$0.227540\pi$
$314$	−22.5478	−	16.3820i	−1.27245	−	0.924488i
$315$		0			0
$316$	5.52786	−	1.79611i	0.310967	−	0.101039i
$317$	−3.97574	+	3.97574i	−0.223300	+	0.223300i	−0.809886	−	0.586587i	$-0.800471\pi$
$317$	−3.97574	+	3.97574i	−0.223300	+	0.223300i	0.586587	+	0.809886i	$0.300471\pi$
$318$	0.841616	+	5.31375i	0.0471955	+	0.297980i
$319$	−19.9192			−1.11526
$320$		0			0
$321$	1.12461			0.0627697
$322$	−3.57960	−	22.6007i	−0.199484	−	1.25949i
$323$	2.00000	−	2.00000i	0.111283	−	0.111283i
$324$	5.15131	−	1.67376i	0.286184	−	0.0929868i
$325$		0			0
$326$	22.4164	+	16.2865i	1.24153	+	0.902024i
$327$	9.06154	−	9.06154i	0.501104	−	0.501104i
$328$	−7.32979	−	14.3855i	−0.404720	−	0.794307i
$329$			12.7639i			0.703698i
$330$		0			0
$331$	−30.0689			−1.65274			−0.826368	−	0.563131i	$-0.809597\pi$
$331$	−30.0689			−1.65274			−0.826368	+	0.563131i	$0.809597\pi$
$332$	−8.49808	+	16.6784i	−0.466393	+	0.915347i
$333$	−1.62460	−	1.62460i	−0.0890274	−	0.0890274i
$334$	13.0373	+	9.47214i	0.713368	+	0.518292i
$335$		0			0
$336$	−5.52786	−	7.60845i	−0.301570	−	0.415075i
$337$	19.9443	+	19.9443i	1.08643	+	1.08643i	0.995893	+	0.0905410i	$0.0288596\pi$
$337$	19.9443	+	19.9443i	1.08643	+	1.08643i	0.0905410	+	0.995893i	$0.471140\pi$
$338$	16.6838	−	2.64245i	0.907478	−	0.143730i
$339$		−	10.7639i		−	0.584617i
$340$		0			0
$341$		−	27.5276i		−	1.49071i
$342$	0.989378	+	6.24669i	0.0534995	+	0.337782i
$343$	−12.8658	−	12.8658i	−0.694686	−	0.694686i
$344$	17.5680	+	5.70820i	0.947206	+	0.307766i
$345$		0			0
$346$	−17.0344	+	23.4459i	−0.915777	+	1.26046i
$347$	−26.0344	−	26.0344i	−1.39760	−	1.39760i	−0.806862	−	0.590740i	$-0.798836\pi$
$347$	−26.0344	−	26.0344i	−1.39760	−	1.39760i	−0.590740	−	0.806862i	$-0.701164\pi$
$348$	4.88493	−	9.58721i	0.261860	−	0.513928i
$349$	16.6700			0.892324			0.446162	−	0.894952i	$-0.352791\pi$
$349$	16.6700			0.892324			0.446162	+	0.894952i	$0.352791\pi$
$350$		0			0
$351$		−	4.70228i		−	0.250989i
$352$	−12.9443	−	12.9443i	−0.689932	−	0.689932i
$353$	22.4164	−	22.4164i	1.19311	−	1.19311i	0.216914	−	0.976191i	$-0.430401\pi$
$353$	22.4164	−	22.4164i	1.19311	−	1.19311i	0.976191	−	0.216914i	$-0.0695992\pi$
$354$	−0.343027	+	0.472136i	−0.0182317	+	0.0250937i
$355$		0			0
$356$	−1.52786	−	4.70228i	−0.0809766	−	0.249220i
$357$	2.35114	−	2.35114i	0.124436	−	0.124436i
$358$	10.5149	−	1.66540i	0.555732	−	0.0880193i
$359$	−19.9192			−1.05129			−0.525647	−	0.850703i	$-0.676177\pi$
$359$	−19.9192			−1.05129			−0.525647	+	0.850703i	$0.676177\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	−21.2550	+	3.36646i	−1.11714	+	0.176937i
$363$	0.326238	−	0.326238i	0.0171231	−	0.0171231i
$364$	5.25731	−	1.70820i	0.275558	−	0.0895342i
$365$		0			0
$366$	−0.652476	+	0.898056i	−0.0341055	+	0.0469421i
$367$	12.2047	−	12.2047i	0.637082	−	0.637082i	−0.312753	−	0.949835i	$-0.601251\pi$
$367$	12.2047	−	12.2047i	0.637082	−	0.637082i	0.949835	+	0.312753i	$0.101251\pi$
$368$	23.7638	+	3.76382i	1.23877	+	0.196203i
$369$			12.7639i			0.664464i
$370$		0			0
$371$	11.7082			0.607860
$372$	13.2492	+	6.75080i	0.686939	+	0.350013i
$373$	−22.4418	−	22.4418i	−1.16199	−	1.16199i	−0.984038	−	0.177956i	$-0.943052\pi$
$373$	−22.4418	−	22.4418i	−1.16199	−	1.16199i	−0.177956	−	0.984038i	$-0.556948\pi$
$374$	3.80423	−	5.23607i	0.196712	−	0.270751i
$375$		0			0
$376$	−12.7639	−	4.14725i	−0.658250	−	0.213878i
$377$	4.47214	+	4.47214i	0.230327	+	0.230327i
$378$	2.72353	+	17.1957i	0.140083	+	0.884449i
$379$			0.111456i			0.00572512i	0.999996	+	0.00286256i	$0.000911182\pi$
$379$			0.111456i			0.00572512i	−0.999996	+	0.00286256i	$0.999089\pi$
$380$		0			0
$381$			3.46120i			0.177323i
$382$	18.4501	−	2.92220i	0.943988	−	0.149513i
$383$	−1.00406	−	1.00406i	−0.0513049	−	0.0513049i	0.680989	−	0.732294i	$-0.261550\pi$
$383$	−1.00406	−	1.00406i	−0.0513049	−	0.0513049i	−0.732294	+	0.680989i	$0.761550\pi$
$384$	9.40456	−	3.05573i	0.479925	−	0.155937i
$385$		0			0
$386$	−2.38197	−	1.73060i	−0.121239	−	0.0880852i
$387$	−10.3262	−	10.3262i	−0.524912	−	0.524912i
$388$	10.6755	+	5.43945i	0.541967	+	0.276146i
$389$	4.14725			0.210274			0.105137	−	0.994458i	$-0.466472\pi$
$389$	4.14725			0.210274			0.105137	+	0.994458i	$0.466472\pi$
$390$		0			0
$391$			8.50651i			0.430193i
$392$	−0.594926	+	0.303130i	−0.0300483	+	0.0153104i
$393$	−8.47214	+	8.47214i	−0.427363	+	0.427363i
$394$	14.9394	+	10.8541i	0.752636	+	0.546822i
$395$		0			0
$396$	4.47214	+	13.7638i	0.224733	+	0.691658i
$397$	24.4500	−	24.4500i	1.22711	−	1.22711i	0.262055	−	0.965053i	$-0.415600\pi$
$397$	24.4500	−	24.4500i	1.22711	−	1.22711i	0.965053	−	0.262055i	$-0.0844002\pi$
$398$	4.80411	+	30.3320i	0.240808	+	1.52040i
$399$	−4.70228			−0.235409
$400$		0			0
$401$	31.8885			1.59244			0.796219	−	0.605009i	$-0.206830\pi$
$401$	31.8885			1.59244			0.796219	+	0.605009i	$0.206830\pi$
$402$	−1.26284	−	7.97323i	−0.0629845	−	0.397669i
$403$	−6.18034	+	6.18034i	−0.307865	+	0.307865i
$404$	1.79611	+	5.52786i	0.0893599	+	0.275022i
$405$		0			0
$406$	−18.9443	−	13.7638i	−0.940188	−	0.683087i
$407$	2.35114	−	2.35114i	0.116542	−	0.116542i
$408$	1.58721	+	3.11507i	0.0785786	+	0.154219i
$409$		−	21.5967i		−	1.06789i	−0.845519	−	0.533945i	$-0.820709\pi$
$409$		−	21.5967i		−	1.06789i	0.845519	−	0.533945i	$-0.179291\pi$
$410$		0			0
$411$	−6.76393			−0.333640
$412$	8.45559	+	4.30834i	0.416577	+	0.212257i
$413$	0.898056	+	0.898056i	0.0441904	+	0.0441904i
$414$	−15.3884	−	11.1803i	−0.756299	−	0.549484i
$415$		0			0
$416$			5.81234i			0.284973i
$417$	−13.2361	−	13.2361i	−0.648173	−	0.648173i
$418$	−9.04029	+	1.43184i	−0.442175	+	0.0700337i
$419$		−	28.8328i		−	1.40858i	−0.709915	−	0.704288i	$-0.751267\pi$
$419$		−	28.8328i		−	1.40858i	0.709915	−	0.704288i	$-0.248733\pi$
$420$		0			0
$421$		−	28.4257i		−	1.38538i	−0.721234	−	0.692692i	$-0.756425\pi$
$421$		−	28.4257i		−	1.38538i	0.721234	−	0.692692i	$-0.243575\pi$
$422$	0.507018	+	3.20119i	0.0246813	+	0.155831i
$423$	7.50245	+	7.50245i	0.364782	+	0.364782i
$424$	−3.80423	+	11.7082i	−0.184750	+	0.568601i
$425$		0			0
$426$	−8.29180	+	11.4127i	−0.401739	+	0.552946i
$427$	1.70820	+	1.70820i	0.0826658	+	0.0826658i
$428$	2.29291	+	1.16829i	0.110832	+	0.0564716i
$429$	2.90617			0.140311
$430$		0			0
$431$			19.0211i			0.916216i	0.888897	+	0.458108i	$0.151473\pi$
$431$			19.0211i			0.916216i	−0.888897	+	0.458108i	$0.848527\pi$
$432$	−18.0806	−	2.86368i	−0.869903	−	0.137779i
$433$	−0.819660	+	0.819660i	−0.0393904	+	0.0393904i	−0.726528	−	0.687137i	$-0.758867\pi$
$433$	−0.819660	+	0.819660i	−0.0393904	+	0.0393904i	0.687137	+	0.726528i	$0.258867\pi$
$434$	19.0211	−	26.1803i	0.913043	−	1.25670i
$435$		0			0
$436$	27.8885	−	9.06154i	1.33562	−	0.433969i
$437$	8.50651	−	8.50651i	0.406921	−	0.406921i
$438$	−8.12891	+	1.28749i	−0.388415	+	0.0615188i
$439$	35.1361			1.67695			0.838477	−	0.544937i	$-0.183446\pi$
$439$	35.1361			1.67695			0.838477	+	0.544937i	$0.183446\pi$
$440$		0			0
$441$	0.527864			0.0251364
$442$	−2.02967	+	0.321469i	−0.0965417	+	0.0152907i
$443$	1.09017	−	1.09017i	0.0517955	−	0.0517955i	−0.680735	−	0.732530i	$-0.738339\pi$
$443$	1.09017	−	1.09017i	0.0517955	−	0.0517955i	0.732530	+	0.680735i	$0.238339\pi$
$444$	0.555029	+	1.70820i	0.0263405	+	0.0810678i
$445$		0			0
$446$	−16.7082	+	22.9969i	−0.791156	+	1.08893i
$447$	−7.95148	+	7.95148i	−0.376092	+	0.376092i
$448$	−3.36646	−	21.2550i	−0.159050	−	1.00420i
$449$			17.5967i			0.830442i	0.909721	+	0.415221i	$0.136296\pi$
$449$			17.5967i			0.830442i	−0.909721	+	0.415221i	$0.863704\pi$
$450$		0			0
$451$	−18.4721			−0.869819
$452$	11.1820	−	21.9460i	0.525958	−	1.03225i
$453$	−4.14725	−	4.14725i	−0.194855	−	0.194855i
$454$	−11.0292	+	15.1803i	−0.517624	+	0.712449i
$455$		0			0
$456$	1.52786	−	4.70228i	0.0715488	−	0.220205i
$457$	−9.65248	−	9.65248i	−0.451524	−	0.451524i	0.444336	−	0.895860i	$-0.353440\pi$
$457$	−9.65248	−	9.65248i	−0.451524	−	0.451524i	−0.895860	+	0.444336i	$0.853440\pi$
$458$	−1.75912	−	11.1066i	−0.0821983	−	0.518979i
$459$		−	6.47214i		−	0.302093i
$460$		0			0
$461$			27.5276i			1.28209i	0.767503	+	0.641045i	$0.221499\pi$
$461$			27.5276i			1.28209i	−0.767503	+	0.641045i	$0.778501\pi$
$462$	−10.6275	+	1.68323i	−0.494436	+	0.0783110i
$463$	2.45714	+	2.45714i	0.114193	+	0.114193i	0.761894	−	0.647701i	$-0.224270\pi$
$463$	2.45714	+	2.45714i	0.114193	+	0.114193i	−0.647701	+	0.761894i	$0.724270\pi$
$464$	19.9192	−	14.4721i	0.924725	−	0.671852i
$465$		0			0
$466$	−8.85410	−	6.43288i	−0.410158	−	0.297997i
$467$	18.3262	+	18.3262i	0.848037	+	0.848037i	0.989888	−	0.141851i	$-0.0453054\pi$
$467$	18.3262	+	18.3262i	0.848037	+	0.848037i	−0.141851	+	0.989888i	$0.545305\pi$
$468$	2.08611	−	4.09423i	0.0964306	−	0.189256i
$469$	−17.5680			−0.811217
$470$		0			0
$471$		−	17.2250i		−	0.793687i
$472$	−1.18985	+	0.606260i	−0.0547674	+	0.0279054i
$473$	14.9443	−	14.9443i	0.687138	−	0.687138i
$474$	2.90617	+	2.11146i	0.133485	+	0.0969824i
$475$		0			0
$476$	7.23607	−	2.35114i	0.331665	−	0.107764i
$477$	6.88191	−	6.88191i	0.315101	−	0.315101i
$478$	2.96911	+	18.7462i	0.135804	+	0.857431i
$479$	4.70228			0.214853			0.107426	−	0.994213i	$-0.465739\pi$
$479$	4.70228			0.214853			0.107426	+	0.994213i	$0.465739\pi$
$480$		0			0
$481$	−1.05573			−0.0481371
$482$	2.48577	+	15.6946i	0.113224	+	0.714868i
$483$	10.0000	−	10.0000i	0.455016	−	0.455016i
$484$	1.00406	−	0.326238i	0.0456390	−	0.0148290i
$485$		0			0
$486$	18.4164	+	13.3803i	0.835385	+	0.606943i
$487$	−18.9151	+	18.9151i	−0.857126	+	0.857126i	−0.990999	−	0.133872i	$-0.957259\pi$
$487$	−18.9151	+	18.9151i	−0.857126	+	0.857126i	0.133872	+	0.990999i	$0.457259\pi$
$488$	−2.26323	+	1.15317i	−0.102452	+	0.0522018i
$489$			17.1246i			0.774402i
$490$		0			0
$491$	−15.2361			−0.687594			−0.343797	−	0.939044i	$-0.611713\pi$
$491$	−15.2361			−0.687594			−0.343797	+	0.939044i	$0.611713\pi$
$492$	4.53006	−	8.89074i	0.204231	−	0.400825i
$493$	6.15537	+	6.15537i	0.277224	+	0.277224i
$494$	2.35114	+	1.70820i	0.105783	+	0.0768557i
$495$		0			0
$496$	20.0000	+	27.5276i	0.898027	+	1.23603i
$497$	21.7082	+	21.7082i	0.973746	+	0.973746i
$498$	−11.4263	+	1.80975i	−0.512026	+	0.0810969i
$499$			11.8885i			0.532204i	0.963945	+	0.266102i	$0.0857359\pi$
$499$			11.8885i			0.532204i	−0.963945	+	0.266102i	$0.914264\pi$
$500$		0			0
$501$			9.95959i			0.444962i
$502$	0.0398969	+	0.251899i	0.00178069	+	0.0112428i
$503$	16.5640	+	16.5640i	0.738552	+	0.738552i	0.972298	−	0.233746i	$-0.0750984\pi$
$503$	16.5640	+	16.5640i	0.738552	+	0.738552i	−0.233746	+	0.972298i	$0.575098\pi$
$504$	−5.25731	+	16.1803i	−0.234179	+	0.720730i
$505$		0			0
$506$	16.1803	−	22.2703i	0.719304	−	0.990037i
$507$	7.38197	+	7.38197i	0.327845	+	0.327845i
$508$	−3.59564	+	7.05684i	−0.159531	+	0.313097i
$509$	10.8576			0.481257			0.240628	−	0.970617i	$-0.422646\pi$
$509$	10.8576			0.481257			0.240628	+	0.970617i	$0.422646\pi$
$510$		0			0
$511$			17.9111i			0.792339i
$512$	22.3488	+	3.53971i	0.987688	+	0.156434i
$513$	−6.47214	+	6.47214i	−0.285752	+	0.285752i
$514$	6.22088	−	8.56231i	0.274391	−	0.377667i
$515$		0			0
$516$	3.52786	+	10.8576i	0.155306	+	0.477981i
$517$	−10.8576	+	10.8576i	−0.477519	+	0.477519i
$518$	3.86067	−	0.611469i	0.169628	−	0.0268664i
$519$	−17.9111			−0.786209
$520$		0			0
$521$	−0.472136			−0.0206847			−0.0103423	−	0.999947i	$-0.503292\pi$
$521$	−0.472136			−0.0206847			−0.0103423	+	0.999947i	$0.503292\pi$
$522$	−19.2253	+	3.04499i	−0.841470	+	0.133276i
$523$	−25.7426	+	25.7426i	−1.12565	+	1.12565i	−0.134770	+	0.990877i	$0.543030\pi$
$523$	−25.7426	+	25.7426i	−1.12565	+	1.12565i	−0.990877	+	0.134770i	$0.956970\pi$
$524$	−26.0746	+	8.47214i	−1.13907	+	0.370107i
$525$		0			0
$526$	8.81966	−	12.1392i	0.384555	−	0.529295i
$527$	−8.50651	+	8.50651i	−0.370549	+	0.370549i
$528$	1.76985	−	11.1744i	0.0770230	−	0.486304i
$529$			13.1803i			0.573058i
$530$		0			0
$531$	1.05573			0.0458147
$532$	−9.58721	−	4.88493i	−0.415658	−	0.211788i
$533$	4.14725	+	4.14725i	0.179637	+	0.179637i
$534$	1.79611	−	2.47214i	0.0777254	−	0.106980i
$535$		0			0
$536$	5.70820	−	17.5680i	0.246557	−	0.758824i
$537$	4.65248	+	4.65248i	0.200769	+	0.200769i
$538$	−4.52955	−	28.5984i	−0.195283	−	1.23297i
$539$			0.763932i			0.0329049i
$540$		0			0
$541$		−	12.3107i		−	0.529280i	−0.964347	−	0.264640i	$-0.914747\pi$
$541$		−	12.3107i		−	0.529280i	0.964347	−	0.264640i	$-0.0852531\pi$
$542$	24.0599	−	3.81072i	1.03346	−	0.163684i
$543$	−9.40456	−	9.40456i	−0.403588	−	0.403588i
$544$			8.00000i			0.342997i
$545$		0			0
$546$	2.76393	+	2.00811i	0.118285	+	0.0859394i
$547$	−11.5623	−	11.5623i	−0.494369	−	0.494369i	0.415311	−	0.909679i	$-0.363673\pi$
$547$	−11.5623	−	11.5623i	−0.494369	−	0.494369i	−0.909679	+	0.415311i	$0.863673\pi$
$548$	−13.7906	−	7.02666i	−0.589105	−	0.300164i
$549$	2.00811			0.0857042
$550$		0			0
$551$		−	12.3107i		−	0.524455i
$552$	6.75080	+	13.2492i	0.287333	+	0.563923i
$553$	5.52786	−	5.52786i	0.235069	−	0.235069i
$554$	−14.9394	−	10.8541i	−0.634714	−	0.461147i
$555$		0			0
$556$	−13.2361	−	40.7364i	−0.561334	−	1.72761i
$557$	−23.5519	+	23.5519i	−0.997926	+	0.997926i	−0.999998	−	0.00207187i	$-0.999341\pi$
$557$	−23.5519	+	23.5519i	−0.997926	+	0.997926i	0.00207187	+	0.999998i	$0.499341\pi$
$558$	−4.20808	−	26.5688i	−0.178142	−	1.12475i
$559$	−6.71040			−0.283820
$560$		0			0
$561$	4.00000			0.168880
$562$	−2.14776	−	13.5604i	−0.0905979	−	0.572013i
$563$	4.32624	−	4.32624i	0.182329	−	0.182329i	−0.610041	−	0.792370i	$-0.708847\pi$
$563$	4.32624	−	4.32624i	0.182329	−	0.182329i	0.792370	+	0.610041i	$0.208847\pi$
$564$	−2.56314	−	7.88854i	−0.107928	−	0.332168i
$565$		0			0
$566$	−21.6525	−	15.7314i	−0.910121	−	0.661242i
$567$	5.15131	−	5.15131i	0.216335	−	0.216335i
$568$	−28.7616	+	14.6548i	−1.20681	+	0.614901i
$569$		−	27.1246i		−	1.13712i	−0.822641	−	0.568561i	$-0.807500\pi$
$569$		−	27.1246i		−	1.13712i	0.822641	−	0.568561i	$-0.192500\pi$
$570$		0			0
$571$	22.6525			0.947977			0.473988	−	0.880531i	$-0.342814\pi$
$571$	22.6525			0.947977			0.473988	+	0.880531i	$0.342814\pi$
$572$	5.92522	+	3.01905i	0.247746	+	0.126233i
$573$	8.16348	+	8.16348i	0.341034	+	0.341034i
$574$	−17.5680	−	12.7639i	−0.733276	−	0.532756i
$575$		0			0
$576$	−14.4721	−	10.5146i	−0.603006	−	0.438109i
$577$	−26.2361	−	26.2361i	−1.09222	−	1.09222i	−0.995291	−	0.0969307i	$-0.969097\pi$
$577$	−26.2361	−	26.2361i	−1.09222	−	1.09222i	−0.0969307	−	0.995291i	$-0.530903\pi$
$578$	20.9520	−	3.31848i	0.871490	−	0.138030i
$579$		−	1.81966i		−	0.0756225i
$580$		0			0
$581$			25.1765i			1.04450i
$582$	1.15838	+	7.31375i	0.0480166	+	0.303165i
$583$	9.95959	+	9.95959i	0.412484	+	0.412484i
$584$	−17.9111	−	5.81966i	−0.741165	−	0.240819i
$585$		0			0
$586$	−3.61803	+	4.97980i	−0.149460	+	0.205714i
$587$	−17.0902	−	17.0902i	−0.705387	−	0.705387i	0.260175	−	0.965562i	$-0.416220\pi$
$587$	−17.0902	−	17.0902i	−0.705387	−	0.705387i	−0.965562	+	0.260175i	$0.916220\pi$
$588$	−0.367684	−	0.187345i	−0.0151631	−	0.00772596i
$589$	17.0130			0.701009
$590$		0			0
$591$			11.4127i			0.469455i
$592$	−0.642937	+	4.05934i	−0.0264246	+	0.166838i
$593$	−20.4164	+	20.4164i	−0.838401	+	0.838401i	−0.988648	−	0.150247i	$-0.951993\pi$
$593$	−20.4164	+	20.4164i	−0.838401	+	0.838401i	0.150247	+	0.988648i	$0.451993\pi$
$594$	−12.3107	+	16.9443i	−0.505116	+	0.695232i
$595$		0			0
$596$	−24.4721	+	7.95148i	−1.00242	+	0.325705i
$597$	−13.4208	+	13.4208i	−0.549276	+	0.549276i
$598$	−8.63271	+	1.36729i	−0.353018	+	0.0559125i
$599$	−6.49839			−0.265517			−0.132759	−	0.991148i	$-0.542383\pi$
$599$	−6.49839			−0.265517			−0.132759	+	0.991148i	$0.542383\pi$
$600$		0			0
$601$	−17.7082			−0.722333			−0.361166	−	0.932501i	$-0.617621\pi$
$601$	−17.7082			−0.722333			−0.361166	+	0.932501i	$0.617621\pi$
$602$	24.5391	−	3.88661i	1.00014	−	0.158406i
$603$	−10.3262	+	10.3262i	−0.420517	+	0.420517i
$604$	−4.14725	−	12.7639i	−0.168749	−	0.519357i
$605$		0			0
$606$	−2.11146	+	2.90617i	−0.0857720	+	0.118055i
$607$	32.6789	−	32.6789i	1.32640	−	1.32640i	0.417908	−	0.908489i	$-0.362763\pi$
$607$	32.6789	−	32.6789i	1.32640	−	1.32640i	0.908489	−	0.417908i	$-0.137237\pi$
$608$	8.00000	−	8.00000i	0.324443	−	0.324443i
$609$		−	14.4721i		−	0.586441i
$610$		0			0
$611$	4.87539			0.197237
$612$	2.87129	−	5.63522i	0.116065	−	0.227790i
$613$	19.5357	+	19.5357i	0.789038	+	0.789038i	0.981337	−	0.192298i	$-0.0615941\pi$
$613$	19.5357	+	19.5357i	0.789038	+	0.789038i	−0.192298	+	0.981337i	$0.561594\pi$
$614$	−15.9434	+	21.9443i	−0.643425	+	0.885599i
$615$		0			0
$616$	−23.4164	−	7.60845i	−0.943474	−	0.306553i
$617$	−4.88854	−	4.88854i	−0.196805	−	0.196805i	0.601824	−	0.798629i	$-0.294441\pi$
$617$	−4.88854	−	4.88854i	−0.196805	−	0.196805i	−0.798629	+	0.601824i	$0.794441\pi$
$618$	0.917504	+	5.79289i	0.0369074	+	0.233024i
$619$			35.3050i			1.41903i	0.704692	+	0.709513i	$0.251085\pi$
$619$			35.3050i			1.41903i	−0.704692	+	0.709513i	$0.748915\pi$
$620$		0			0
$621$		−	27.5276i		−	1.10465i
$622$	−29.0776	+	4.60543i	−1.16590	+	0.184661i
$623$	−4.70228	−	4.70228i	−0.188393	−	0.188393i
$624$	−2.90617	+	2.11146i	−0.116340	+	0.0845259i
$625$		0			0
$626$	2.85410	+	2.07363i	0.114073	+	0.0828788i
$627$	−4.00000	−	4.00000i	−0.159745	−	0.159745i
$628$	17.8941	−	35.1191i	0.714051	−	1.40140i
$629$	−1.45309			−0.0579383
$630$		0			0
$631$		−	22.6134i		−	0.900223i	−0.892972	−	0.450112i	$-0.851384\pi$
$631$		−	22.6134i		−	0.900223i	0.892972	−	0.450112i	$-0.148616\pi$
$632$	3.73175	+	7.32398i	0.148441	+	0.291332i
$633$	−1.41641	+	1.41641i	−0.0562972	+	0.0562972i
$634$	−6.43288	−	4.67376i	−0.255482	−	0.185619i
$635$		0			0
$636$	−7.23607	+	2.35114i	−0.286929	+	0.0932288i
$637$	0.171513	−	0.171513i	0.00679561	−	0.00679561i
$638$	−4.40676	−	27.8232i	−0.174465	−	1.10153i
$639$	25.5195			1.00954
$640$		0			0
$641$	−38.6525			−1.52668			−0.763341	−	0.645996i	$-0.776442\pi$
$641$	−38.6525			−1.52668			−0.763341	+	0.645996i	$0.776442\pi$
$642$	0.248800	+	1.57086i	0.00981935	+	0.0619969i
$643$	11.5623	−	11.5623i	0.455973	−	0.455973i	−0.441358	−	0.897331i	$-0.645503\pi$
$643$	11.5623	−	11.5623i	0.455973	−	0.455973i	0.897331	+	0.441358i	$0.145503\pi$
$644$	30.7768	−	10.0000i	1.21278	−	0.394055i
$645$		0			0
$646$	3.23607	+	2.35114i	0.127321	+	0.0925044i
$647$	−20.0252	+	20.0252i	−0.787271	+	0.787271i	−0.981046	−	0.193775i	$-0.937927\pi$
$647$	−20.0252	+	20.0252i	−0.787271	+	0.787271i	0.193775	+	0.981046i	$0.437927\pi$
$648$	3.47755	+	6.82507i	0.136611	+	0.268114i
$649$			1.52786i			0.0599739i
$650$		0			0
$651$	20.0000			0.783862
$652$	−17.7898	+	34.9144i	−0.696701	+	1.36735i
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	0.194661	−	0.980871i	$-0.437639\pi$
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	−0.980871	+	0.194661i	$0.937639\pi$
$654$	14.6619	+	10.6525i	0.573325	+	0.416545i
$655$		0			0
$656$	18.4721	−	13.4208i	0.721216	−	0.523994i
$657$	10.5279	+	10.5279i	0.410731	+	0.410731i
$658$	−17.8287	+	2.82379i	−0.695035	+	0.110083i
$659$			18.0000i			0.701180i	0.936529	+	0.350590i	$0.114019\pi$
$659$			18.0000i			0.701180i	−0.936529	+	0.350590i	$0.885981\pi$
$660$		0			0
$661$			3.80423i			0.147967i	0.997259	+	0.0739836i	$0.0235713\pi$
$661$			3.80423i			0.147967i	−0.997259	+	0.0739836i	$0.976429\pi$
$662$	−6.65219	−	42.0003i	−0.258545	−	1.63239i
$663$	−0.898056	−	0.898056i	−0.0348776	−	0.0348776i
$664$	−25.1765	−	8.18034i	−0.977038	−	0.317459i
$665$		0			0
$666$	1.90983	−	2.62866i	0.0740044	−	0.101858i
$667$	26.1803	+	26.1803i	1.01371	+	1.01371i
$668$	−10.3464	+	20.3060i	−0.400316	+	0.785664i
$669$	−17.5680			−0.679220
$670$		0			0
$671$			2.90617i			0.112191i
$672$	9.40456	−	9.40456i	0.362789	−	0.362789i
$673$	17.2918	−	17.2918i	0.666550	−	0.666550i	−0.290366	−	0.956916i	$-0.593777\pi$
$673$	17.2918	−	17.2918i	0.666550	−	0.666550i	0.956916	+	0.290366i	$0.0937770\pi$
$674$	−23.4459	+	32.2705i	−0.903102	+	1.24301i
$675$		0			0
$676$	7.38197	+	22.7194i	0.283922	+	0.873821i
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	−0.840625	−	0.541617i	$-0.817812\pi$
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	0.541617	+	0.840625i	$0.317812\pi$
$678$	15.0351	−	2.38132i	0.577419	−	0.0914542i
$679$	16.1150			0.618435
$680$		0			0
$681$	−11.5967			−0.444388
$682$	38.4507	−	6.08999i	1.47235	−	0.233198i
$683$	22.7984	−	22.7984i	0.872356	−	0.872356i	−0.120373	−	0.992729i	$-0.538409\pi$
$683$	22.7984	−	22.7984i	0.872356	−	0.872356i	0.992729	+	0.120373i	$0.0384091\pi$
$684$	−8.50651	+	2.76393i	−0.325254	+	0.105682i
$685$		0			0
$686$	15.1246	−	20.8172i	0.577460	−	0.794806i
$687$	4.91428	−	4.91428i	0.187492	−	0.187492i
$688$	−4.08662	+	25.8019i	−0.155801	+	0.983689i
$689$		−	4.47214i		−	0.170375i
$690$		0			0
$691$	9.12461			0.347117			0.173558	−	0.984824i	$-0.444473\pi$
$691$	9.12461			0.347117			0.173558	+	0.984824i	$0.444473\pi$
$692$	−36.5178	−	18.6068i	−1.38820	−	0.707323i
$693$	13.7638	+	13.7638i	0.522844	+	0.522844i
$694$	30.6053	−	42.1246i	1.16176	−	1.59903i
$695$		0			0
$696$	14.4721	+	4.70228i	0.548565	+	0.178240i
$697$	5.70820	+	5.70820i	0.216214	+	0.216214i
$698$	3.68793	+	23.2847i	0.139590	+	0.881338i
$699$		−	6.76393i		−	0.255835i
$700$		0			0
$701$			19.7072i			0.744330i	0.928167	+	0.372165i	$0.121384\pi$
$701$			19.7072i			0.744330i	−0.928167	+	0.372165i	$0.878616\pi$
$702$	6.56816	−	1.04029i	0.247899	−	0.0392634i
$703$	1.45309	+	1.45309i	0.0548041	+	0.0548041i
$704$	15.2169	−	20.9443i	0.573509	−	0.789367i
$705$		0			0
$706$	36.2705	+	26.3521i	1.36506	+	0.991773i
$707$	5.52786	+	5.52786i	0.207897	+	0.207897i
$708$	−0.735369	−	0.374689i	−0.0276369	−	0.0140817i
$709$	−3.24920			−0.122026			−0.0610131	−	0.998137i	$-0.519433\pi$
$709$	−3.24920			−0.122026			−0.0610131	+	0.998137i	$0.519433\pi$
$710$		0			0
$711$		−	6.49839i		−	0.243709i
$712$	6.23015	−	3.17442i	0.233485	−	0.118966i
$713$	−36.1803	+	36.1803i	−1.35496	+	1.35496i
$714$	3.80423	+	2.76393i	0.142370	+	0.103438i
$715$		0			0
$716$	4.65248	+	14.3188i	0.173871	+	0.535120i
$717$	−8.29451	+	8.29451i	−0.309764	+	0.309764i
$718$	−4.40676	−	27.8232i	−0.164459	−	1.03835i
$719$	−4.01623			−0.149780			−0.0748900	−	0.997192i	$-0.523861\pi$
$719$	−4.01623			−0.149780			−0.0748900	+	0.997192i	$0.523861\pi$
$720$		0			0
$721$	12.7639			0.475354
$722$	3.31848	+	20.9520i	0.123501	+	0.779754i
$723$	−6.94427	+	6.94427i	−0.258260	+	0.258260i
$724$	−9.40456	−	28.9443i	−0.349518	−	1.07571i
$725$		0			0
$726$	0.527864	+	0.383516i	0.0195909	+	0.0142336i
$727$	−9.51057	+	9.51057i	−0.352727	+	0.352727i	−0.861123	−	0.508396i	$-0.830239\pi$
$727$	−9.51057	+	9.51057i	−0.352727	+	0.352727i	0.508396	+	0.861123i	$0.330239\pi$
$728$	3.54911	+	6.96552i	0.131539	+	0.258159i
$729$			5.94427i			0.220158i
$730$		0			0
$731$	−9.23607			−0.341608
$732$	−1.39875	−	0.712701i	−0.0516995	−	0.0263422i
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	0.966303	−	0.257407i	$-0.0828680\pi$
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	−0.257407	+	0.966303i	$0.582868\pi$
$734$	19.7477	+	14.3475i	0.728900	+	0.529577i
$735$		0			0
$736$			34.0260i			1.25422i
$737$	−14.9443	−	14.9443i	−0.550479	−	0.550479i
$738$	−17.8287	+	2.82379i	−0.656283	+	0.103945i
$739$		−	9.41641i		−	0.346388i	−0.984888	−	0.173194i	$-0.944591\pi$
$739$		−	9.41641i		−	0.346388i	0.984888	−	0.173194i	$-0.0554088\pi$
$740$		0			0
$741$			1.79611i			0.0659818i
$742$	2.59023	+	16.3540i	0.0950902	+	0.600376i
$743$	4.80828	+	4.80828i	0.176399	+	0.176399i	0.789784	−	0.613385i	$-0.210193\pi$
$743$	4.80828	+	4.80828i	0.176399	+	0.176399i	−0.613385	+	0.789784i	$0.710193\pi$
$744$	−6.49839	+	20.0000i	−0.238243	+	0.733236i
$745$		0			0
$746$	26.3820	−	36.3117i	0.965912	−	1.32946i
$747$	14.7984	+	14.7984i	0.541444	+	0.541444i
$748$	8.15537	+	4.15537i	0.298190	+	0.151935i
$749$	3.46120			0.126469
$750$		0			0
$751$			11.4127i			0.416455i	0.978080	+	0.208227i	$0.0667694\pi$
$751$			11.4127i			0.416455i	−0.978080	+	0.208227i	$0.933231\pi$
$752$	2.96911	−	18.7462i	0.108272	−	0.683603i
$753$	−0.111456	+	0.111456i	−0.00406169	+	0.00406169i
$754$	−5.25731	+	7.23607i	−0.191460	+	0.263522i
$755$		0			0
$756$	−23.4164	+	7.60845i	−0.851647	+	0.276717i
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.166709	−	0.986006i	$-0.446686\pi$
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.986006	−	0.166709i	$-0.0533140\pi$
$758$	−0.155682	+	0.0246576i	−0.00565463	+	0.000895606i
$759$	17.0130			0.617533
$760$		0			0
$761$	2.94427			0.106730			0.0533649	−	0.998575i	$-0.483005\pi$
$761$	2.94427			0.106730			0.0533649	+	0.998575i	$0.483005\pi$
$762$	−4.83461	+	0.765727i	−0.175139	+	0.0277394i
$763$	27.8885	−	27.8885i	1.00963	−	1.00963i
$764$	8.16348	+	25.1246i	0.295344	+	0.908977i
$765$		0			0
$766$	1.18034	−	1.62460i	0.0426474	−	0.0586991i
$767$	0.343027	−	0.343027i	0.0123860	−	0.0123860i
$768$	6.34884	+	12.4603i	0.229094	+	0.449622i
$769$		−	6.47214i		−	0.233391i	−0.993168	−	0.116696i	$-0.962770\pi$
$769$		−	6.47214i		−	0.233391i	0.993168	−	0.116696i	$-0.0372302\pi$
$770$		0			0
$771$	6.54102			0.235569
$772$	1.89034	−	3.71000i	0.0680348	−	0.133526i
$773$	−31.5034	−	31.5034i	−1.13310	−	1.13310i	−0.989659	−	0.143439i	$-0.954184\pi$
$773$	−31.5034	−	31.5034i	−1.13310	−	1.13310i	−0.143439	−	0.989659i	$-0.545816\pi$
$774$	12.1392	−	16.7082i	0.436335	−	0.600564i
$775$		0			0
$776$	−5.23607	+	16.1150i	−0.187964	+	0.578493i
$777$	1.70820	+	1.70820i	0.0612815	+	0.0612815i
$778$	0.917504	+	5.79289i	0.0328941	+	0.207685i
$779$		−	11.4164i		−	0.409035i
$780$		0			0
$781$			36.9322i			1.32154i
$782$	−11.8819	+	1.88191i	−0.424896	+	0.0672969i
$783$	−19.9192	−	19.9192i	−0.711854	−	0.711854i
$784$	−0.555029	−	0.763932i	−0.0198225	−	0.0272833i
$785$		0			0
$786$	−13.7082	−	9.95959i	−0.488955	−	0.355247i
$787$	−17.8541	−	17.8541i	−0.636430	−	0.636430i	0.313243	−	0.949673i	$-0.398585\pi$
$787$	−17.8541	−	17.8541i	−0.636430	−	0.636430i	−0.949673	+	0.313243i	$0.898585\pi$
$788$	−11.8560	+	23.2686i	−0.422351	+	0.828911i
$789$	9.27354			0.330147
$790$		0			0
$791$		−	33.1280i		−	1.17790i
$792$	−18.2360	+	9.29168i	−0.647986	+	0.330166i
$793$	0.652476	−	0.652476i	0.0231701	−	0.0231701i
$794$	39.5609	+	28.7426i	1.40396	+	1.02004i
$795$		0			0
$796$	−41.3050	+	13.4208i	−1.46402	+	0.475687i
$797$	14.8334	−	14.8334i	0.525426	−	0.525426i	−0.393779	−	0.919205i	$-0.628833\pi$
$797$	14.8334	−	14.8334i	0.525426	−	0.525426i	0.919205	+	0.393779i	$0.128833\pi$
$798$	−1.04029	−	6.56816i	−0.0368260	−	0.232510i
$799$	6.71040			0.237397
$800$		0			0
$801$	−5.52786			−0.195317
$802$	7.05476	+	44.5420i	0.249112	+	1.57283i
$803$	−15.2361	+	15.2361i	−0.537669	+	0.537669i
$804$	10.8576	−	3.52786i	0.382920	−	0.124418i
$805$		0			0
$806$	−10.0000	−	7.26543i	−0.352235	−	0.255914i
$807$	12.6538	−	12.6538i	0.445433	−	0.445433i
$808$	−7.32398	+	3.73175i	−0.257657	+	0.131283i
$809$		−	4.94427i		−	0.173831i	−0.996216	−	0.0869157i	$-0.972299\pi$
$809$		−	4.94427i		−	0.173831i	0.996216	−	0.0869157i	$-0.0277011\pi$
$810$		0			0
$811$	26.0689			0.915402			0.457701	−	0.889106i	$-0.348673\pi$
$811$	26.0689			0.915402			0.457701	+	0.889106i	$0.348673\pi$
$812$	15.0343	−	29.5064i	0.527599	−	1.03547i
$813$	10.6456	+	10.6456i	0.373359	+	0.373359i
$814$	3.80423	+	2.76393i	0.133338	+	0.0968758i
$815$		0			0
$816$	−4.00000	+	2.90617i	−0.140028	+	0.101736i
$817$	9.23607	+	9.23607i	0.323129	+	0.323129i
$818$	30.1664	−	4.77789i	1.05474	−	0.167055i
$819$		−	6.18034i		−	0.215959i
$820$		0			0
$821$			17.9111i			0.625101i	0.949901	+	0.312550i	$0.101183\pi$
$821$			17.9111i			0.625101i	−0.949901	+	0.312550i	$0.898817\pi$
$822$	−1.49640	−	9.44788i	−0.0521928	−	0.329532i
$823$	−13.8698	−	13.8698i	−0.483472	−	0.483472i	0.422767	−	0.906238i	$-0.361059\pi$
$823$	−13.8698	−	13.8698i	−0.483472	−	0.483472i	−0.906238	+	0.422767i	$0.861059\pi$
$824$	−4.14725	+	12.7639i	−0.144476	+	0.444653i
$825$		0			0
$826$	−1.05573	+	1.45309i	−0.0367335	+	0.0505593i
$827$	−8.14590	−	8.14590i	−0.283261	−	0.283261i	0.551147	−	0.834408i	$-0.314190\pi$
$827$	−8.14590	−	8.14590i	−0.283261	−	0.283261i	−0.834408	+	0.551147i	$0.814190\pi$
$828$	12.2123	−	23.9680i	0.424407	−	0.832946i
$829$	−54.5002			−1.89287			−0.946436	−	0.322892i	$-0.895345\pi$
$829$	−54.5002			−1.89287			−0.946436	+	0.322892i	$0.895345\pi$
$830$		0			0
$831$		−	11.4127i		−	0.395901i
$832$	−8.11869	+	1.28587i	−0.281465	+	0.0445797i
$833$	0.236068	−	0.236068i	0.00817927	−	0.00817927i
$834$	15.5599	−	21.4164i	0.538796	−	0.741590i
$835$		0			0
$836$	−4.00000	−	12.3107i	−0.138343	−	0.425776i
$837$	27.5276	−	27.5276i	0.951494	−	0.951494i
$838$	40.2737	−	6.37873i	1.39123	−	0.220350i
$839$	−15.2169			−0.525346			−0.262673	−	0.964885i	$-0.584604\pi$
$839$	−15.2169			−0.525346			−0.262673	+	0.964885i	$0.584604\pi$
$840$		0			0
$841$	8.88854			0.306502
$842$	39.7051	−	6.28867i	1.36833	−	0.216722i
$843$	6.00000	−	6.00000i	0.206651	−	0.206651i
$844$	−4.35926	+	1.41641i	−0.150052	+	0.0487548i
$845$		0			0
$846$	−8.81966	+	12.1392i	−0.303226	+	0.417355i
$847$	1.00406	−	1.00406i	0.0344998	−	0.0344998i
$848$	−17.1957	−	2.72353i	−0.590501	−	0.0935262i
$849$		−	16.5410i		−	0.567686i
$850$		0			0
$851$	−6.18034			−0.211859
$852$	−17.7757	−	9.05715i	−0.608984	−	0.310293i
$853$	18.8496	+	18.8496i	0.645399	+	0.645399i	0.951877	−	0.306479i	$-0.0991509\pi$
$853$	18.8496	+	18.8496i	0.645399	+	0.645399i	−0.306479	+	0.951877i	$0.599151\pi$
$854$	−2.00811	+	2.76393i	−0.0687163	+	0.0945798i
$855$		0			0
$856$	−1.12461	+	3.46120i	−0.0384384	+	0.118301i
$857$	−35.8328	−	35.8328i	−1.22403	−	1.22403i	−0.966188	−	0.257837i	$-0.916990\pi$
$857$	−35.8328	−	35.8328i	−1.22403	−	1.22403i	−0.257837	−	0.966188i	$-0.583010\pi$
$858$	0.642937	+	4.05934i	0.0219495	+	0.138584i
$859$		−	16.4721i		−	0.562022i	−0.959705	−	0.281011i	$-0.909330\pi$
$859$		−	16.4721i		−	0.562022i	0.959705	−	0.281011i	$-0.0906697\pi$
$860$		0			0
$861$		−	13.4208i		−	0.457379i
$862$	−26.5688	+	4.20808i	−0.904935	+	0.143328i
$863$	−35.5851	−	35.5851i	−1.21133	−	1.21133i	−0.970589	−	0.240743i	$-0.922609\pi$
$863$	−35.5851	−	35.5851i	−1.21133	−	1.21133i	−0.240743	−	0.970589i	$-0.577391\pi$
$864$		−	25.8885i		−	0.880746i
$865$		0			0
$866$	−1.32624	−	0.963568i	−0.0450674	−	0.0327434i
$867$	9.27051	+	9.27051i	0.314843	+	0.314843i
$868$	40.7768	+	20.7768i	1.38406	+	0.705212i
$869$	9.40456			0.319028
$870$		0			0
$871$			6.71040i			0.227373i
$872$	18.8270	+	36.9501i	0.637563	+	1.25129i
$873$	9.47214	−	9.47214i	0.320583	−	0.320583i
$874$	13.7638	+	10.0000i	0.465568	+	0.338255i
$875$		0			0
$876$	−3.59675	−	11.0697i	−0.121523	−	0.374009i
$877$	−21.5438	+	21.5438i	−0.727482	+	0.727482i	−0.970118	−	0.242636i	$-0.921988\pi$
$877$	−21.5438	+	21.5438i	−0.727482	+	0.727482i	0.242636	+	0.970118i	$0.421988\pi$
$878$	7.77322	+	49.0782i	0.262333	+	1.65631i
$879$	−3.80423			−0.128313
$880$		0			0
$881$	6.87539			0.231638			0.115819	−	0.993270i	$-0.463051\pi$
$881$	6.87539			0.231638			0.115819	+	0.993270i	$0.463051\pi$
$882$	0.116780	+	0.737322i	0.00393220	+	0.0248269i
$883$	2.79837	−	2.79837i	0.0941728	−	0.0941728i	−0.658451	−	0.752624i	$-0.728788\pi$
$883$	2.79837	−	2.79837i	0.0941728	−	0.0941728i	0.752624	+	0.658451i	$0.228788\pi$
$884$	−0.898056	−	2.76393i	−0.0302049	−	0.0929611i
$885$		0			0
$886$	1.76393	+	1.28157i	0.0592605	+	0.0430552i
$887$	11.5187	−	11.5187i	0.386759	−	0.386759i	−0.486770	−	0.873530i	$-0.661825\pi$
$887$	11.5187	−	11.5187i	0.386759	−	0.386759i	0.873530	+	0.486770i	$0.161825\pi$
$888$	−2.26323	+	1.15317i	−0.0759491	+	0.0386980i
$889$			10.6525i			0.357273i
$890$		0			0
$891$	8.76393			0.293603
$892$	−35.8185	−	18.2504i	−1.19929	−	0.611069i
$893$	−6.71040	−	6.71040i	−0.224555	−	0.224555i
$894$	−12.8658	−	9.34752i	−0.430295	−	0.312628i
$895$		0			0
$896$	28.9443	−	9.40456i	0.966960	−	0.314184i
$897$	−3.81966	−	3.81966i	−0.127535	−	0.127535i
$898$	−24.5792	+	3.89296i	−0.820218	+	0.129910i
$899$			52.3607i			1.74633i
$900$		0			0
$901$		−	6.15537i		−	0.205065i
$902$	−4.08662	−	25.8019i	−0.136070	−	0.859110i
$903$	10.8576	+	10.8576i	0.361320	+	0.361320i
$904$	33.1280	+	10.7639i	1.10182	+	0.358003i
$905$		0			0
$906$	4.87539	−	6.71040i	0.161974	−	0.222938i
$907$	7.67376	+	7.67376i	0.254803	+	0.254803i	0.822936	−	0.568133i	$-0.192334\pi$
$907$	7.67376	+	7.67376i	0.254803	+	0.254803i	−0.568133	+	0.822936i	$0.692334\pi$
$908$	−23.6439	−	12.0472i	−0.784651	−	0.399800i
$909$	6.49839			0.215538
$910$		0			0
$911$		−	10.3026i		−	0.341341i	−0.985328	−	0.170671i	$-0.945407\pi$
$911$		−	10.3026i		−	0.341341i	0.985328	−	0.170671i	$-0.0545934\pi$
$912$	6.90617	+	1.09383i	0.228686	+	0.0362203i
$913$	−21.4164	+	21.4164i	−0.708780	+	0.708780i
$914$	11.3472	−	15.6180i	0.375331	−	0.516599i
$915$		0			0
$916$	15.1246	−	4.91428i	0.499731	−	0.162373i
$917$	−26.0746	+	26.0746i	−0.861058	+	0.861058i
$918$	9.04029	−	1.43184i	0.298374	−	0.0472578i
$919$	−18.1231			−0.597825			−0.298913	−	0.954281i	$-0.596624\pi$
$919$	−18.1231			−0.597825			−0.298913	+	0.954281i	$0.596624\pi$
$920$		0			0
$921$	−16.7639			−0.552390
$922$	−38.4507	+	6.08999i	−1.26631	+	0.200563i
$923$	8.29180	−	8.29180i	0.272928	−	0.272928i
$924$	−4.70228	−	14.4721i	−0.154694	−	0.476098i
$925$		0			0
$926$	−2.88854	+	3.97574i	−0.0949234	+	0.130651i
$927$	7.50245	−	7.50245i	0.246413	−	0.246413i
$928$	24.6215	+	24.6215i	0.808239	+	0.808239i
$929$		−	36.6525i		−	1.20253i	−0.799050	−	0.601264i	$-0.794664\pi$
$929$		−	36.6525i		−	1.20253i	0.799050	−	0.601264i	$-0.205336\pi$
$930$		0			0
$931$	−0.472136			−0.0154736
$932$	7.02666	−	13.7906i	0.230166	−	0.451726i
$933$	−12.8658	−	12.8658i	−0.421206	−	0.421206i
$934$	−21.5438	+	29.6525i	−0.704934	+	0.970259i
$935$		0			0
$936$	6.18034	+	2.00811i	0.202011	+	0.0656373i
$937$	42.3050	+	42.3050i	1.38204	+	1.38204i	0.840987	+	0.541056i	$0.181975\pi$
$937$	42.3050	+	42.3050i	1.38204	+	1.38204i	0.541056	+	0.840987i	$0.318025\pi$
$938$	−3.88661	−	24.5391i	−0.126902	−	0.801230i
$939$			2.18034i			0.0711527i
$940$		0			0
$941$		−	37.6183i		−	1.22632i	−0.789959	−	0.613160i	$-0.789898\pi$
$941$		−	37.6183i		−	1.22632i	0.789959	−	0.613160i	$-0.210102\pi$
$942$	24.0599	−	3.81072i	0.783915	−	0.124160i
$943$	24.2784	+	24.2784i	0.790615	+	0.790615i
$944$	−1.11006	−	1.52786i	−0.0361293	−	0.0497277i
$945$		0			0
$946$	24.1803	+	17.5680i	0.786171	+	0.571186i
$947$	2.14590	+	2.14590i	0.0697323	+	0.0697323i	0.741113	−	0.671381i	$-0.234298\pi$
$947$	2.14590	+	2.14590i	0.0697323	+	0.0697323i	−0.671381	+	0.741113i	$0.734298\pi$
$948$	−2.30635	+	4.52647i	−0.0749068	+	0.147013i
$949$	6.84142			0.222082
$950$		0			0
$951$		−	4.91428i		−	0.159357i
$952$	4.88493	+	9.58721i	0.158321	+	0.310723i
$953$	29.1803	−	29.1803i	0.945244	−	0.945244i	−0.0533329	−	0.998577i	$-0.516984\pi$
$953$	29.1803	−	29.1803i	0.945244	−	0.945244i	0.998577	+	0.0533329i	$0.0169844\pi$
$954$	11.1352	+	8.09017i	0.360514	+	0.261929i
$955$		0			0
$956$	−25.5279	+	8.29451i	−0.825630	+	0.268263i
$957$	12.3107	−	12.3107i	0.397950	−	0.397950i
$958$	1.04029	+	6.56816i	0.0336104	+	0.212208i
$959$	−20.8172			−0.672224
$960$		0			0
$961$	−41.3607			−1.33422
$962$	−0.233561	−	1.47464i	−0.00753029	−	0.0475444i
$963$	2.03444	−	2.03444i	0.0655590	−	0.0655590i
$964$	−21.3723	+	6.94427i	−0.688355	+	0.223660i
$965$		0			0
$966$	16.1803	+	11.7557i	0.520594	+	0.378234i
$967$	10.9637	−	10.9637i	0.352567	−	0.352567i	−0.508497	−	0.861064i	$-0.669799\pi$
$967$	10.9637	−	10.9637i	0.352567	−	0.352567i	0.861064	+	0.508497i	$0.169799\pi$
$968$	0.677819	+	1.33030i	0.0217859	+	0.0427573i
$969$			2.47214i			0.0794164i
$970$		0			0
$971$	−15.5967			−0.500523			−0.250262	−	0.968178i	$-0.580517\pi$
$971$	−15.5967			−0.500523			−0.250262	+	0.968178i	$0.580517\pi$
$972$	−14.6153	+	28.6842i	−0.468787	+	0.920047i
$973$	−40.7364	−	40.7364i	−1.30595	−	1.30595i
$974$	−30.6053	−	22.2361i	−0.980658	−	0.712490i
$975$		0			0
$976$	−2.11146	−	2.90617i	−0.0675861	−	0.0930242i
$977$	23.7639	+	23.7639i	0.760276	+	0.760276i	0.976372	−	0.216096i	$-0.0693326\pi$
$977$	23.7639	+	23.7639i	0.760276	+	0.760276i	−0.216096	+	0.976372i	$0.569333\pi$
$978$	−23.9197	+	3.78851i	−0.764868	+	0.121143i
$979$		−	8.00000i		−	0.255681i
$980$		0			0
$981$		−	32.7849i		−	1.04674i
$982$	−3.37070	−	21.2818i	−0.107563	−	0.679129i
$983$	−18.0171	−	18.0171i	−0.574655	−	0.574655i	0.358770	−	0.933426i	$-0.383196\pi$
$983$	−18.0171	−	18.0171i	−0.574655	−	0.574655i	−0.933426	+	0.358770i	$0.883196\pi$
$984$	13.4208	+	4.36068i	0.427839	+	0.139013i
$985$		0			0
$986$	−7.23607	+	9.95959i	−0.230443	+	0.317178i
$987$	−7.88854	−	7.88854i	−0.251095	−	0.251095i
$988$	−1.86588	+	3.66199i	−0.0593614	+	0.116503i
$989$	−39.2833			−1.24914
$990$		0			0
$991$		−	14.3188i		−	0.454853i	−0.973795	−	0.227427i	$-0.926969\pi$
$991$		−	14.3188i		−	0.454853i	0.973795	−	0.227427i	$-0.0730312\pi$
$992$	−34.0260	+	34.0260i	−1.08033	+	1.08033i
$993$	18.5836	−	18.5836i	0.589732	−	0.589732i
$994$	−25.5195	+	35.1246i	−0.809430	+	1.11409i
$995$		0			0
$996$	−5.05573	−	15.5599i	−0.160197	−	0.493035i
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	−0.993934	−	0.109979i	$-0.964922\pi$
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	0.109979	+	0.993934i	$0.464922\pi$
$998$	−16.6059	+	2.63012i	−0.525652	+	0.0832551i
$999$	4.70228			0.148774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.k.h.107.2		8
4.3	odd	2		800.2.o.g.207.4		8
5.2	odd	4		40.2.k.a.3.1	✓	8
5.3	odd	4	inner	200.2.k.h.43.4		8
5.4	even	2		40.2.k.a.27.3	yes	8
8.3	odd	2	inner	200.2.k.h.107.4		8
8.5	even	2		800.2.o.g.207.3		8
15.2	even	4		360.2.w.c.163.4		8
15.14	odd	2		360.2.w.c.307.2		8
20.3	even	4		800.2.o.g.143.3		8
20.7	even	4		160.2.o.a.143.2		8
20.19	odd	2		160.2.o.a.47.1		8
40.3	even	4	inner	200.2.k.h.43.2		8
40.13	odd	4		800.2.o.g.143.4		8
40.19	odd	2		40.2.k.a.27.1	yes	8
40.27	even	4		40.2.k.a.3.3	yes	8
40.29	even	2		160.2.o.a.47.2		8
40.37	odd	4		160.2.o.a.143.1		8
60.47	odd	4		1440.2.bi.c.1423.2		8
60.59	even	2		1440.2.bi.c.847.3		8
80.19	odd	4		1280.2.n.q.767.2		8
80.27	even	4		1280.2.n.q.1023.1		8
80.29	even	4		1280.2.n.m.767.4		8
80.37	odd	4		1280.2.n.m.1023.3		8
80.59	odd	4		1280.2.n.m.767.3		8
80.67	even	4		1280.2.n.m.1023.4		8
80.69	even	4		1280.2.n.q.767.1		8
80.77	odd	4		1280.2.n.q.1023.2		8
120.29	odd	2		1440.2.bi.c.847.2		8
120.59	even	2		360.2.w.c.307.4		8
120.77	even	4		1440.2.bi.c.1423.3		8
120.107	odd	4		360.2.w.c.163.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.1	✓	8	5.2	odd	4
40.2.k.a.3.3	yes	8	40.27	even	4
40.2.k.a.27.1	yes	8	40.19	odd	2
40.2.k.a.27.3	yes	8	5.4	even	2
160.2.o.a.47.1		8	20.19	odd	2
160.2.o.a.47.2		8	40.29	even	2
160.2.o.a.143.1		8	40.37	odd	4
160.2.o.a.143.2		8	20.7	even	4
200.2.k.h.43.2		8	40.3	even	4	inner
200.2.k.h.43.4		8	5.3	odd	4	inner
200.2.k.h.107.2		8	1.1	even	1	trivial
200.2.k.h.107.4		8	8.3	odd	2	inner
360.2.w.c.163.2		8	120.107	odd	4
360.2.w.c.163.4		8	15.2	even	4
360.2.w.c.307.2		8	15.14	odd	2
360.2.w.c.307.4		8	120.59	even	2
800.2.o.g.143.3		8	20.3	even	4
800.2.o.g.143.4		8	40.13	odd	4
800.2.o.g.207.3		8	8.5	even	2
800.2.o.g.207.4		8	4.3	odd	2
1280.2.n.m.767.3		8	80.59	odd	4
1280.2.n.m.767.4		8	80.29	even	4
1280.2.n.m.1023.3		8	80.37	odd	4
1280.2.n.m.1023.4		8	80.67	even	4
1280.2.n.q.767.1		8	80.69	even	4
1280.2.n.q.767.2		8	80.19	odd	4
1280.2.n.q.1023.1		8	80.27	even	4
1280.2.n.q.1023.2		8	80.77	odd	4
1440.2.bi.c.847.2		8	120.29	odd	2
1440.2.bi.c.847.3		8	60.59	even	2
1440.2.bi.c.1423.2		8	60.47	odd	4
1440.2.bi.c.1423.3		8	120.77	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 + 1.39680i) q^{2} +(-0.618034 + 0.618034i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(-1.00000 - 0.726543i) q^{6} +(-1.90211 + 1.90211i) q^{7} +(-1.28408 - 2.52015i) q^{8} +2.23607i q^{9} -3.23607 q^{11} +(0.793604 - 1.55754i) q^{12} +(0.726543 + 0.726543i) q^{13} +(-3.07768 - 2.23607i) q^{14} +(3.23607 - 2.35114i) q^{16} +(1.00000 + 1.00000i) q^{17} +(-3.12334 + 0.494689i) q^{18} -2.00000i q^{19} -2.35114i q^{21} +(-0.715921 - 4.52015i) q^{22} +(4.25325 + 4.25325i) q^{23} +(2.35114 + 0.763932i) q^{24} +(-0.854102 + 1.17557i) q^{26} +(-3.23607 - 3.23607i) q^{27} +(2.44246 - 4.79360i) q^{28} +6.15537 q^{29} +8.50651i q^{31} +(4.00000 + 4.00000i) q^{32} +(2.00000 - 2.00000i) q^{33} +(-1.17557 + 1.61803i) q^{34} +(-1.38197 - 4.25325i) q^{36} +(-0.726543 + 0.726543i) q^{37} +(2.79360 - 0.442463i) q^{38} -0.898056 q^{39} +5.70820 q^{41} +(3.28408 - 0.520147i) q^{42} +(-4.61803 + 4.61803i) q^{43} +(6.15537 - 2.00000i) q^{44} +(-5.00000 + 6.88191i) q^{46} +(3.35520 - 3.35520i) q^{47} +(-0.546915 + 3.45309i) q^{48} -0.236068i q^{49} -1.23607 q^{51} +(-1.83099 - 0.932938i) q^{52} +(-3.07768 - 3.07768i) q^{53} +(3.80423 - 5.23607i) q^{54} +(7.23607 + 2.35114i) q^{56} +(1.23607 + 1.23607i) q^{57} +(1.36176 + 8.59783i) q^{58} -0.472136i q^{59} -0.898056i q^{61} +(-11.8819 + 1.88191i) q^{62} +(-4.25325 - 4.25325i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(3.23607 + 2.35114i) q^{66} +(4.61803 + 4.61803i) q^{67} +(-2.52015 - 1.28408i) q^{68} -5.25731 q^{69} -11.4127i q^{71} +(5.63522 - 2.87129i) q^{72} +(4.70820 - 4.70820i) q^{73} +(-1.17557 - 0.854102i) q^{74} +(1.23607 + 3.80423i) q^{76} +(6.15537 - 6.15537i) q^{77} +(-0.198678 - 1.25441i) q^{78} -2.90617 q^{79} -2.70820 q^{81} +(1.26284 + 7.97323i) q^{82} +(6.61803 - 6.61803i) q^{83} +(1.45309 + 4.47214i) q^{84} +(-7.47214 - 5.42882i) q^{86} +(-3.80423 + 3.80423i) q^{87} +(4.15537 + 8.15537i) q^{88} +2.47214i q^{89} -2.76393 q^{91} +(-10.7188 - 5.46151i) q^{92} +(-5.25731 - 5.25731i) q^{93} +(5.42882 + 3.94427i) q^{94} -4.94427 q^{96} +(-4.23607 - 4.23607i) q^{97} +(0.329740 - 0.0522257i) q^{98} -7.23607i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{3} - 8 q^{6} - 4 q^{8} - 8 q^{11} - 12 q^{12} + 8 q^{16} + 8 q^{17} - 10 q^{18} - 12 q^{22} + 20 q^{26} - 8 q^{27} + 20 q^{28} + 32 q^{32} + 16 q^{33} - 20 q^{36} + 4 q^{38} - 8 q^{41}+ \cdots + 6 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 4 * q^3 - 8 * q^6 - 4 * q^8 - 8 * q^11 - 12 * q^12 + 8 * q^16 + 8 * q^17 - 10 * q^18 - 12 * q^22 + 20 * q^26 - 8 * q^27 + 20 * q^28 + 32 * q^32 + 16 * q^33 - 20 * q^36 + 4 * q^38 - 8 * q^41 + 20 * q^42 - 28 * q^43 - 40 * q^46 - 16 * q^48 + 8 * q^51 - 20 * q^52 + 40 * q^56 - 8 * q^57 - 20 * q^58 - 40 * q^62 + 8 * q^66 + 28 * q^67 + 4 * q^68 + 20 * q^72 - 16 * q^73 - 8 * q^76 + 40 * q^78 + 32 * q^81 + 28 * q^82 + 44 * q^83 - 24 * q^86 - 16 * q^88 - 40 * q^91 - 20 * q^92 + 32 * q^96 - 16 * q^97 + 6 * q^98

Introduction

L-functions

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