LMFDB - Embedded newform 200.2.k.h.43.2

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			43.2
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	200.43
Dual form			200.2.k.h.107.2

$q$-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 $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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	0.505818	−	0.862640i	$-0.331191\pi$
$3$	−0.618034	−	0.618034i	−0.356822	−	0.356822i	−0.862640	+	0.505818i	$0.831191\pi$
$4$	−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	0.249455	−	0.968386i	$-0.419748\pi$
$7$	−1.90211	−	1.90211i	−0.718931	−	0.718931i	−0.968386	+	0.249455i	$0.919748\pi$
$8$	−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	−0.599139	−	0.800645i	$-0.704490\pi$
$13$	0.726543	−	0.726543i	0.201507	−	0.201507i	0.800645	+	0.599139i	$0.204490\pi$
$14$	−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	−0.575363	−	0.817898i	$-0.695139\pi$
$17$	1.00000	−	1.00000i	0.242536	−	0.242536i	0.817898	+	0.575363i	$0.195139\pi$
$18$	−3.12334	−	0.494689i	−0.736179	−	0.116599i
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$		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	−0.107356	−	0.994221i	$-0.534238\pi$
$23$	4.25325	−	4.25325i	0.886865	−	0.886865i	0.994221	+	0.107356i	$0.0342384\pi$
$24$	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	$-0.723279\pi$
$31$		−	8.50651i		−	1.52781i	0.645326	−	0.763907i	$-0.276721\pi$
$32$	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	0.644859	−	0.764302i	$-0.276916\pi$
$37$	−0.726543	−	0.726543i	−0.119443	−	0.119443i	−0.764302	+	0.644859i	$0.776916\pi$
$38$	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	0.261075	−	0.965319i	$-0.415923\pi$
$43$	−4.61803	−	4.61803i	−0.704244	−	0.704244i	−0.965319	+	0.261075i	$0.915923\pi$
$44$	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	0.908119	−	0.418713i	$-0.137519\pi$
$47$	3.35520	+	3.35520i	0.489406	+	0.489406i	−0.418713	+	0.908119i	$0.637519\pi$
$48$	−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	−0.886150	−	0.463398i	$-0.846630\pi$
$53$	−3.07768	+	3.07768i	−0.422752	+	0.422752i	0.463398	+	0.886150i	$0.346630\pi$
$54$	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	$0.00978430\pi$
$59$			0.472136i			0.0614669i	−0.999528	+	0.0307334i	$0.990216\pi$
$60$		0			0
$61$			0.898056i			0.114984i	0.998346	+	0.0574921i	$0.0183104\pi$
$61$			0.898056i			0.114984i	−0.998346	+	0.0574921i	$0.981690\pi$
$62$	−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	−0.366310	−	0.930493i	$-0.619379\pi$
$67$	4.61803	−	4.61803i	0.564183	−	0.564183i	0.930493	+	0.366310i	$0.119379\pi$
$68$	−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	$0.236815\pi$
$71$			11.4127i			1.35444i	−0.735783	+	0.677218i	$0.763185\pi$
$72$	5.63522	+	2.87129i	0.664117	+	0.338385i
$73$	4.70820	+	4.70820i	0.551054	+	0.551054i	0.926745	−	0.375691i	$-0.122595\pi$
$73$	4.70820	+	4.70820i	0.551054	+	0.551054i	−0.375691	+	0.926745i	$0.622595\pi$
$74$	−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	0.969905	−	0.243482i	$-0.0782896\pi$
$83$	6.61803	+	6.61803i	0.726424	+	0.726424i	−0.243482	+	0.969905i	$0.578290\pi$
$84$	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	$-0.958174\pi$
$89$		−	2.47214i		−	0.262046i	0.991379	−	0.131023i	$-0.0418262\pi$
$90$		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	−0.888665	−	0.458557i	$-0.848366\pi$
$97$	−4.23607	+	4.23607i	−0.430108	+	0.430108i	0.458557	+	0.888665i	$0.348366\pi$
$98$	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	$0.0461855\pi$
$101$			2.90617i			0.289175i	−0.989492	+	0.144587i	$0.953815\pi$
$102$	−0.273457	+	1.72654i	−0.0270763	+	0.170953i
$103$	−3.35520	+	3.35520i	−0.330597	+	0.330597i	−0.852813	−	0.522216i	$-0.825106\pi$
$103$	−3.35520	+	3.35520i	−0.330597	+	0.330597i	0.522216	+	0.852813i	$0.325106\pi$
$104$	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	−0.749716	−	0.661760i	$-0.769810\pi$
$107$	−0.909830	+	0.909830i	−0.0879566	+	0.0879566i	0.661760	+	0.749716i	$0.269810\pi$
$108$	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	0.166793	−	0.985992i	$-0.446659\pi$
$113$	−8.70820	−	8.70820i	−0.819199	−	0.819199i	−0.985992	+	0.166793i	$0.946659\pi$
$114$	−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	0.820344	−	0.571870i	$-0.193782\pi$
$127$	2.80017	+	2.80017i	0.248475	+	0.248475i	−0.571870	+	0.820344i	$0.693782\pi$
$128$	−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	−0.433593	−	0.901109i	$-0.642754\pi$
$137$	5.47214	−	5.47214i	0.467516	−	0.467516i	0.901109	+	0.433593i	$0.142754\pi$
$138$	−1.16308	+	7.34342i	−0.0990083	+	0.625114i
$139$		−	21.4164i		−	1.81652i	−0.418411	−	0.908258i	$-0.637413\pi$
$139$		−	21.4164i		−	1.81652i	0.418411	−	0.908258i	$-0.362587\pi$
$140$		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	$-0.911970\pi$
$151$		−	6.71040i		−	0.546084i	0.962002	−	0.273042i	$-0.0880298\pi$
$152$	−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	−0.992858	−	0.119303i	$-0.961934\pi$
$157$	−13.9353	−	13.9353i	−1.11216	−	1.11216i	−0.119303	−	0.992858i	$-0.538066\pi$
$158$	−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	0.996021	+	0.0891157i	$0.0284041\pi$
$163$	13.8541	+	13.8541i	1.08514	+	1.08514i	0.0891157	+	0.996021i	$0.471596\pi$
$164$	−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	0.946426	−	0.322920i	$-0.104664\pi$
$167$	8.05748	+	8.05748i	0.623507	+	0.623507i	−0.322920	+	0.946426i	$0.604664\pi$
$168$	−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	0.107474	−	0.994208i	$-0.465724\pi$
$173$	14.4904	−	14.4904i	1.10168	−	1.10168i	0.994208	−	0.107474i	$-0.0342762\pi$
$174$	−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	$0.0907754\pi$
$179$			7.52786i			0.562659i	−0.959611	+	0.281329i	$0.909225\pi$
$180$		0			0
$181$		−	15.2169i		−	1.13106i	−0.824726	−	0.565532i	$-0.808671\pi$
$181$		−	15.2169i		−	1.13106i	0.824726	−	0.565532i	$-0.191329\pi$
$182$	−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	$0.158594\pi$
$191$			13.2088i			0.955755i	−0.878427	+	0.477877i	$0.841406\pi$
$192$	−1.09383	+	6.90617i	−0.0789404	+	0.498410i
$193$	−1.47214	−	1.47214i	−0.105967	−	0.105967i	0.652136	−	0.758102i	$-0.273873\pi$
$193$	−1.47214	−	1.47214i	−0.105967	−	0.105967i	−0.758102	+	0.652136i	$0.773873\pi$
$194$	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	0.954866	−	0.297038i	$-0.0959988\pi$
$197$	9.23305	+	9.23305i	0.657828	+	0.657828i	−0.297038	+	0.954866i	$0.595999\pi$
$198$	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	−0.0471263	−	0.998889i	$-0.515006\pi$
$223$	14.2128	−	14.2128i	0.951763	−	0.951763i	0.998889	+	0.0471263i	$0.0150063\pi$
$224$	−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	−0.323519	−	0.946222i	$-0.604866\pi$
$227$	9.38197	−	9.38197i	0.622703	−	0.622703i	0.946222	+	0.323519i	$0.104866\pi$
$228$	−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	0.504765	−	0.863257i	$-0.331579\pi$
$233$	−5.47214	−	5.47214i	−0.358492	−	0.358492i	−0.863257	+	0.504765i	$0.831579\pi$
$234$	−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	−0.852622	−	0.522529i	$-0.824989\pi$
$257$	−5.29180	+	5.29180i	−0.330093	+	0.330093i	0.522529	+	0.852622i	$0.324989\pi$
$258$	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	−0.899514	−	0.436893i	$-0.856079\pi$
$263$	−7.50245	+	7.50245i	−0.462621	+	0.462621i	0.436893	+	0.899514i	$0.356079\pi$
$264$	−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	$0.175252\pi$
$271$			17.2250i			1.04635i	−0.852227	+	0.523173i	$0.824748\pi$
$272$	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	0.373051	−	0.927811i	$-0.378312\pi$
$277$	−9.23305	−	9.23305i	−0.554760	−	0.554760i	−0.927811	+	0.373051i	$0.878312\pi$
$278$	−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	0.186903	−	0.982378i	$-0.440155\pi$
$283$	−13.3820	−	13.3820i	−0.795475	−	0.795475i	−0.982378	+	0.186903i	$0.940155\pi$
$284$	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	−0.611469	−	0.791269i	$-0.709421\pi$
$293$	3.07768	−	3.07768i	0.179800	−	0.179800i	0.791269	+	0.611469i	$0.209421\pi$
$294$	−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	−0.204769	−	0.978810i	$-0.565644\pi$
$307$	13.5623	−	13.5623i	0.774042	−	0.774042i	0.978810	+	0.204769i	$0.0656442\pi$
$308$	−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	$-0.799041\pi$
$311$		−	20.8172i		−	1.18044i	0.807243	−	0.590219i	$-0.200959\pi$
$312$	1.15317	−	2.26323i	0.0652857	−	0.128130i
$313$	1.76393	+	1.76393i	0.0997033	+	0.0997033i	0.755199	−	0.655496i	$-0.227540\pi$
$313$	1.76393	+	1.76393i	0.0997033	+	0.0997033i	−0.655496	+	0.755199i	$0.727540\pi$
$314$	−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	0.586587	−	0.809886i	$-0.300471\pi$
$317$	−3.97574	−	3.97574i	−0.223300	−	0.223300i	−0.809886	+	0.586587i	$0.800471\pi$
$318$	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	0.0905410	−	0.995893i	$-0.471140\pi$
$337$	19.9443	−	19.9443i	1.08643	−	1.08643i	0.995893	−	0.0905410i	$-0.0288596\pi$
$338$	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	−0.590740	+	0.806862i	$0.701164\pi$
$347$	−26.0344	+	26.0344i	−1.39760	+	1.39760i	−0.806862	+	0.590740i	$0.798836\pi$
$348$	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	0.976191	+	0.216914i	$0.0695992\pi$
$353$	22.4164	+	22.4164i	1.19311	+	1.19311i	0.216914	+	0.976191i	$0.430401\pi$
$354$	−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	0.949835	−	0.312753i	$-0.101251\pi$
$367$	12.2047	+	12.2047i	0.637082	+	0.637082i	−0.312753	+	0.949835i	$0.601251\pi$
$368$	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	−0.177956	+	0.984038i	$0.556948\pi$
$373$	−22.4418	+	22.4418i	−1.16199	+	1.16199i	−0.984038	+	0.177956i	$0.943052\pi$
$374$	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	$-0.999089\pi$
$379$		−	0.111456i		−	0.00572512i	0.999996	−	0.00286256i	$-0.000911182\pi$
$380$		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	−0.732294	−	0.680989i	$-0.761550\pi$
$383$	−1.00406	+	1.00406i	−0.0513049	+	0.0513049i	0.680989	+	0.732294i	$0.261550\pi$
$384$	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	0.965053	+	0.262055i	$0.0844002\pi$
$397$	24.4500	+	24.4500i	1.22711	+	1.22711i	0.262055	+	0.965053i	$0.415600\pi$
$398$	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	$0.179291\pi$
$409$			21.5967i			1.06789i	−0.845519	+	0.533945i	$0.820709\pi$
$410$		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	$0.248733\pi$
$419$			28.8328i			1.40858i	−0.709915	+	0.704288i	$0.751267\pi$
$420$		0			0
$421$			28.4257i			1.38538i	0.721234	+	0.692692i	$0.243575\pi$
$421$			28.4257i			1.38538i	−0.721234	+	0.692692i	$0.756425\pi$
$422$	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	$-0.848527\pi$
$431$		−	19.0211i		−	0.916216i	0.888897	−	0.458108i	$-0.151473\pi$
$432$	−18.0806	+	2.86368i	−0.869903	+	0.137779i
$433$	−0.819660	−	0.819660i	−0.0393904	−	0.0393904i	0.687137	−	0.726528i	$-0.258867\pi$
$433$	−0.819660	−	0.819660i	−0.0393904	−	0.0393904i	−0.726528	+	0.687137i	$0.758867\pi$
$434$	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	0.732530	−	0.680735i	$-0.238339\pi$
$443$	1.09017	+	1.09017i	0.0517955	+	0.0517955i	−0.680735	+	0.732530i	$0.738339\pi$
$444$	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	$-0.863704\pi$
$449$		−	17.5967i		−	0.830442i	0.909721	−	0.415221i	$-0.136296\pi$
$450$		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	−0.895860	−	0.444336i	$-0.853440\pi$
$457$	−9.65248	+	9.65248i	−0.451524	+	0.451524i	0.444336	+	0.895860i	$0.353440\pi$
$458$	−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	$-0.778501\pi$
$461$		−	27.5276i		−	1.28209i	0.767503	−	0.641045i	$-0.221499\pi$
$462$	−10.6275	−	1.68323i	−0.494436	−	0.0783110i
$463$	2.45714	−	2.45714i	0.114193	−	0.114193i	−0.647701	−	0.761894i	$-0.724270\pi$
$463$	2.45714	−	2.45714i	0.114193	−	0.114193i	0.761894	+	0.647701i	$0.224270\pi$
$464$	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	−0.141851	−	0.989888i	$-0.545305\pi$
$467$	18.3262	−	18.3262i	0.848037	−	0.848037i	0.989888	+	0.141851i	$0.0453054\pi$
$468$	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	0.133872	−	0.990999i	$-0.457259\pi$
$487$	−18.9151	−	18.9151i	−0.857126	−	0.857126i	−0.990999	+	0.133872i	$0.957259\pi$
$488$	−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	$-0.914264\pi$
$499$		−	11.8885i		−	0.532204i	0.963945	−	0.266102i	$-0.0857359\pi$
$500$		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	−0.233746	−	0.972298i	$-0.575098\pi$
$503$	16.5640	−	16.5640i	0.738552	−	0.738552i	0.972298	+	0.233746i	$0.0750984\pi$
$504$	−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	−0.990877	−	0.134770i	$-0.956970\pi$
$523$	−25.7426	−	25.7426i	−1.12565	−	1.12565i	−0.134770	−	0.990877i	$-0.543030\pi$
$524$	−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	$0.0852531\pi$
$541$			12.3107i			0.529280i	−0.964347	+	0.264640i	$0.914747\pi$
$542$	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	−0.909679	−	0.415311i	$-0.863673\pi$
$547$	−11.5623	+	11.5623i	−0.494369	+	0.494369i	0.415311	+	0.909679i	$0.363673\pi$
$548$	−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	0.00207187	−	0.999998i	$-0.499341\pi$
$557$	−23.5519	−	23.5519i	−0.997926	−	0.997926i	−0.999998	+	0.00207187i	$0.999341\pi$
$558$	−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	0.792370	−	0.610041i	$-0.208847\pi$
$563$	4.32624	+	4.32624i	0.182329	+	0.182329i	−0.610041	+	0.792370i	$0.708847\pi$
$564$	−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	$0.192500\pi$
$569$			27.1246i			1.13712i	−0.822641	+	0.568561i	$0.807500\pi$
$570$		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	−0.0969307	+	0.995291i	$0.530903\pi$
$577$	−26.2361	+	26.2361i	−1.09222	+	1.09222i	−0.995291	+	0.0969307i	$0.969097\pi$
$578$	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	−0.965562	−	0.260175i	$-0.916220\pi$
$587$	−17.0902	+	17.0902i	−0.705387	+	0.705387i	0.260175	+	0.965562i	$0.416220\pi$
$588$	−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	0.150247	−	0.988648i	$-0.451993\pi$
$593$	−20.4164	−	20.4164i	−0.838401	−	0.838401i	−0.988648	+	0.150247i	$0.951993\pi$
$594$	−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	0.908489	+	0.417908i	$0.137237\pi$
$607$	32.6789	+	32.6789i	1.32640	+	1.32640i	0.417908	+	0.908489i	$0.362763\pi$
$608$	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	−0.192298	−	0.981337i	$-0.561594\pi$
$613$	19.5357	−	19.5357i	0.789038	−	0.789038i	0.981337	+	0.192298i	$0.0615941\pi$
$614$	−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	−0.798629	−	0.601824i	$-0.794441\pi$
$617$	−4.88854	+	4.88854i	−0.196805	+	0.196805i	0.601824	+	0.798629i	$0.294441\pi$
$618$	0.917504	−	5.79289i	0.0369074	−	0.233024i
$619$		−	35.3050i		−	1.41903i	−0.704692	−	0.709513i	$-0.748915\pi$
$619$		−	35.3050i		−	1.41903i	0.704692	−	0.709513i	$-0.251085\pi$
$620$		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	$0.148616\pi$
$631$			22.6134i			0.900223i	−0.892972	+	0.450112i	$0.851384\pi$
$632$	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	0.897331	−	0.441358i	$-0.145503\pi$
$643$	11.5623	+	11.5623i	0.455973	+	0.455973i	−0.441358	+	0.897331i	$0.645503\pi$
$644$	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	0.193775	−	0.981046i	$-0.437927\pi$
$647$	−20.0252	−	20.0252i	−0.787271	−	0.787271i	−0.981046	+	0.193775i	$0.937927\pi$
$648$	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	−0.980871	−	0.194661i	$-0.937639\pi$
$653$	−20.0907	+	20.0907i	−0.786210	+	0.786210i	0.194661	+	0.980871i	$0.437639\pi$
$654$	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	$-0.885981\pi$
$659$		−	18.0000i		−	0.701180i	0.936529	−	0.350590i	$-0.114019\pi$
$660$		0			0
$661$		−	3.80423i		−	0.147967i	−0.997259	−	0.0739836i	$-0.976429\pi$
$661$		−	3.80423i		−	0.147967i	0.997259	−	0.0739836i	$-0.0235713\pi$
$662$	−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	0.956916	−	0.290366i	$-0.0937770\pi$
$673$	17.2918	+	17.2918i	0.666550	+	0.666550i	−0.290366	+	0.956916i	$0.593777\pi$
$674$	−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	0.541617	−	0.840625i	$-0.317812\pi$
$677$	−7.77997	−	7.77997i	−0.299008	−	0.299008i	−0.840625	+	0.541617i	$0.817812\pi$
$678$	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	0.992729	−	0.120373i	$-0.0384091\pi$
$683$	22.7984	+	22.7984i	0.872356	+	0.872356i	−0.120373	+	0.992729i	$0.538409\pi$
$684$	−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	$-0.878616\pi$
$701$		−	19.7072i		−	0.744330i	0.928167	−	0.372165i	$-0.121384\pi$
$702$	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	0.508396	−	0.861123i	$-0.330239\pi$
$727$	−9.51057	−	9.51057i	−0.352727	−	0.352727i	−0.861123	+	0.508396i	$0.830239\pi$
$728$	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	−0.257407	−	0.966303i	$-0.582868\pi$
$733$	19.1926	−	19.1926i	0.708896	−	0.708896i	0.966303	+	0.257407i	$0.0828680\pi$
$734$	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	$0.0554088\pi$
$739$			9.41641i			0.346388i	−0.984888	+	0.173194i	$0.944591\pi$
$740$		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	−0.613385	−	0.789784i	$-0.710193\pi$
$743$	4.80828	−	4.80828i	0.176399	−	0.176399i	0.789784	+	0.613385i	$0.210193\pi$
$744$	−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	$-0.933231\pi$
$751$		−	11.4127i		−	0.416455i	0.978080	−	0.208227i	$-0.0667694\pi$
$752$	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	0.986006	+	0.166709i	$0.0533140\pi$
$757$	31.7154	+	31.7154i	1.15272	+	1.15272i	0.166709	+	0.986006i	$0.446686\pi$
$758$	−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	$0.0372302\pi$
$769$			6.47214i			0.233391i	−0.993168	+	0.116696i	$0.962770\pi$
$770$		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	−0.143439	+	0.989659i	$0.545816\pi$
$773$	−31.5034	+	31.5034i	−1.13310	+	1.13310i	−0.989659	+	0.143439i	$0.954184\pi$
$774$	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	−0.949673	−	0.313243i	$-0.898585\pi$
$787$	−17.8541	+	17.8541i	−0.636430	+	0.636430i	0.313243	+	0.949673i	$0.398585\pi$
$788$	−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	0.919205	−	0.393779i	$-0.128833\pi$
$797$	14.8334	+	14.8334i	0.525426	+	0.525426i	−0.393779	+	0.919205i	$0.628833\pi$
$798$	−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	$0.0277011\pi$
$809$			4.94427i			0.173831i	−0.996216	+	0.0869157i	$0.972299\pi$
$810$		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	$-0.898817\pi$
$821$		−	17.9111i		−	0.625101i	0.949901	−	0.312550i	$-0.101183\pi$
$822$	−1.49640	+	9.44788i	−0.0521928	+	0.329532i
$823$	−13.8698	+	13.8698i	−0.483472	+	0.483472i	−0.906238	−	0.422767i	$-0.861059\pi$
$823$	−13.8698	+	13.8698i	−0.483472	+	0.483472i	0.422767	+	0.906238i	$0.361059\pi$
$824$	−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	−0.834408	−	0.551147i	$-0.814190\pi$
$827$	−8.14590	+	8.14590i	−0.283261	+	0.283261i	0.551147	+	0.834408i	$0.314190\pi$
$828$	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	−0.306479	−	0.951877i	$-0.599151\pi$
$853$	18.8496	−	18.8496i	0.645399	−	0.645399i	0.951877	+	0.306479i	$0.0991509\pi$
$854$	−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	−0.257837	+	0.966188i	$0.583010\pi$
$857$	−35.8328	+	35.8328i	−1.22403	+	1.22403i	−0.966188	+	0.257837i	$0.916990\pi$
$858$	0.642937	−	4.05934i	0.0219495	−	0.138584i
$859$			16.4721i			0.562022i	0.959705	+	0.281011i	$0.0906697\pi$
$859$			16.4721i			0.562022i	−0.959705	+	0.281011i	$0.909330\pi$
$860$		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	−0.240743	+	0.970589i	$0.577391\pi$
$863$	−35.5851	+	35.5851i	−1.21133	+	1.21133i	−0.970589	+	0.240743i	$0.922609\pi$
$864$			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	0.242636	−	0.970118i	$-0.421988\pi$
$877$	−21.5438	−	21.5438i	−0.727482	−	0.727482i	−0.970118	+	0.242636i	$0.921988\pi$
$878$	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	0.752624	−	0.658451i	$-0.228788\pi$
$883$	2.79837	+	2.79837i	0.0941728	+	0.0941728i	−0.658451	+	0.752624i	$0.728788\pi$
$884$	−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	0.873530	−	0.486770i	$-0.161825\pi$
$887$	11.5187	+	11.5187i	0.386759	+	0.386759i	−0.486770	+	0.873530i	$0.661825\pi$
$888$	−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	−0.568133	−	0.822936i	$-0.692334\pi$
$907$	7.67376	−	7.67376i	0.254803	−	0.254803i	0.822936	+	0.568133i	$0.192334\pi$
$908$	−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	$0.0545934\pi$
$911$			10.3026i			0.341341i	−0.985328	+	0.170671i	$0.945407\pi$
$912$	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	$0.205336\pi$
$929$			36.6525i			1.20253i	−0.799050	+	0.601264i	$0.794664\pi$
$930$		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	0.541056	−	0.840987i	$-0.318025\pi$
$937$	42.3050	−	42.3050i	1.38204	−	1.38204i	0.840987	−	0.541056i	$-0.181975\pi$
$938$	−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	$0.210102\pi$
$941$			37.6183i			1.22632i	−0.789959	+	0.613160i	$0.789898\pi$
$942$	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	−0.671381	−	0.741113i	$-0.734298\pi$
$947$	2.14590	−	2.14590i	0.0697323	−	0.0697323i	0.741113	+	0.671381i	$0.234298\pi$
$948$	−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	0.998577	−	0.0533329i	$-0.0169844\pi$
$953$	29.1803	+	29.1803i	0.945244	+	0.945244i	−0.0533329	+	0.998577i	$0.516984\pi$
$954$	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	0.861064	−	0.508497i	$-0.169799\pi$
$967$	10.9637	+	10.9637i	0.352567	+	0.352567i	−0.508497	+	0.861064i	$0.669799\pi$
$968$	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	−0.216096	−	0.976372i	$-0.569333\pi$
$977$	23.7639	−	23.7639i	0.760276	−	0.760276i	0.976372	+	0.216096i	$0.0693326\pi$
$978$	−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	−0.933426	−	0.358770i	$-0.883196\pi$
$983$	−18.0171	+	18.0171i	−0.574655	+	0.574655i	0.358770	+	0.933426i	$0.383196\pi$
$984$	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	$0.0730312\pi$
$991$			14.3188i			0.454853i	−0.973795	+	0.227427i	$0.926969\pi$
$992$	−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	0.109979	−	0.993934i	$-0.464922\pi$
$997$	−27.9112	−	27.9112i	−0.883955	−	0.883955i	−0.993934	+	0.109979i	$0.964922\pi$
$998$	−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.43.2		8
4.3	odd	2		800.2.o.g.143.4		8
5.2	odd	4	inner	200.2.k.h.107.4		8
5.3	odd	4		40.2.k.a.27.1	yes	8
5.4	even	2		40.2.k.a.3.3	yes	8
8.3	odd	2	inner	200.2.k.h.43.4		8
8.5	even	2		800.2.o.g.143.3		8
15.8	even	4		360.2.w.c.307.4		8
15.14	odd	2		360.2.w.c.163.2		8
20.3	even	4		160.2.o.a.47.2		8
20.7	even	4		800.2.o.g.207.3		8
20.19	odd	2		160.2.o.a.143.1		8
40.3	even	4		40.2.k.a.27.3	yes	8
40.13	odd	4		160.2.o.a.47.1		8
40.19	odd	2		40.2.k.a.3.1	✓	8
40.27	even	4	inner	200.2.k.h.107.2		8
40.29	even	2		160.2.o.a.143.2		8
40.37	odd	4		800.2.o.g.207.4		8
60.23	odd	4		1440.2.bi.c.847.2		8
60.59	even	2		1440.2.bi.c.1423.3		8
80.3	even	4		1280.2.n.q.767.1		8
80.13	odd	4		1280.2.n.m.767.3		8
80.19	odd	4		1280.2.n.m.1023.3		8
80.29	even	4		1280.2.n.q.1023.1		8
80.43	even	4		1280.2.n.m.767.4		8
80.53	odd	4		1280.2.n.q.767.2		8
80.59	odd	4		1280.2.n.q.1023.2		8
80.69	even	4		1280.2.n.m.1023.4		8
120.29	odd	2		1440.2.bi.c.1423.2		8
120.53	even	4		1440.2.bi.c.847.3		8
120.59	even	2		360.2.w.c.163.4		8
120.83	odd	4		360.2.w.c.307.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.1	✓	8	40.19	odd	2
40.2.k.a.3.3	yes	8	5.4	even	2
40.2.k.a.27.1	yes	8	5.3	odd	4
40.2.k.a.27.3	yes	8	40.3	even	4
160.2.o.a.47.1		8	40.13	odd	4
160.2.o.a.47.2		8	20.3	even	4
160.2.o.a.143.1		8	20.19	odd	2
160.2.o.a.143.2		8	40.29	even	2
200.2.k.h.43.2		8	1.1	even	1	trivial
200.2.k.h.43.4		8	8.3	odd	2	inner
200.2.k.h.107.2		8	40.27	even	4	inner
200.2.k.h.107.4		8	5.2	odd	4	inner
360.2.w.c.163.2		8	15.14	odd	2
360.2.w.c.163.4		8	120.59	even	2
360.2.w.c.307.2		8	120.83	odd	4
360.2.w.c.307.4		8	15.8	even	4
800.2.o.g.143.3		8	8.5	even	2
800.2.o.g.143.4		8	4.3	odd	2
800.2.o.g.207.3		8	20.7	even	4
800.2.o.g.207.4		8	40.37	odd	4
1280.2.n.m.767.3		8	80.13	odd	4
1280.2.n.m.767.4		8	80.43	even	4
1280.2.n.m.1023.3		8	80.19	odd	4
1280.2.n.m.1023.4		8	80.69	even	4
1280.2.n.q.767.1		8	80.3	even	4
1280.2.n.q.767.2		8	80.53	odd	4
1280.2.n.q.1023.1		8	80.29	even	4
1280.2.n.q.1023.2		8	80.59	odd	4
1440.2.bi.c.847.2		8	60.23	odd	4
1440.2.bi.c.847.3		8	120.53	even	4
1440.2.bi.c.1423.2		8	120.29	odd	2
1440.2.bi.c.1423.3		8	60.59	even	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
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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