LMFDB - Embedded newform 75.9.f.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.f (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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.9.f.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} -234.000 q^{11} +(4894.08 - 4894.08i) q^{12} +(11930.2 + 11930.2i) q^{13} -42210.0i q^{14} +5744.00 q^{16} +(-89012.0 + 89012.0i) q^{17} +(-16071.1 - 16071.1i) q^{18} +181693. i q^{19} +189945. q^{21} +(1719.54 - 1719.54i) q^{22} +(-269432. - 269432. i) q^{23} +196344. i q^{24} -175338. q^{26} +(72320.0 - 72320.0i) q^{27} +(-425060. - 425060. i) q^{28} -240174. i q^{29} +836725. q^{31} +(717798. - 717798. i) q^{32} +(7737.94 + 7737.94i) q^{33} -1.30820e6i q^{34} -323676. q^{36} +(-608282. + 608282. i) q^{37} +(-1.33517e6 - 1.33517e6i) q^{38} -789021. i q^{39} +2.82222e6 q^{41} +(-1.39580e6 + 1.39580e6i) q^{42} +(-2.80202e6 - 2.80202e6i) q^{43} -34632.0i q^{44} +3.95982e6 q^{46} +(5.39321e6 - 5.39321e6i) q^{47} +(-189943. - 189943. i) q^{48} -1.07323e7i q^{49} +5.88692e6 q^{51} +(-1.76568e6 + 1.76568e6i) q^{52} +(1.19258e6 + 1.19258e6i) q^{53} +1.06288e6i q^{54} +1.70528e7 q^{56} +(6.00824e6 - 6.00824e6i) q^{57} +(1.76491e6 + 1.76491e6i) q^{58} -1.27860e7i q^{59} +517403. q^{61} +(-6.14865e6 + 6.14865e6i) q^{62} +(-6.28112e6 - 6.28112e6i) q^{63} +1.20199e7i q^{64} -113724. q^{66} +(-2.06617e6 + 2.06617e6i) q^{67} +(-1.31738e7 - 1.31738e7i) q^{68} +1.78192e7i q^{69} -2.08286e7 q^{71} +(6.49273e6 - 6.49273e6i) q^{72} +(-2.88730e7 - 2.88730e7i) q^{73} -8.93988e6i q^{74} -2.68906e7 q^{76} +(672054. - 672054. i) q^{77} +(5.79810e6 + 5.79810e6i) q^{78} -4.21879e7i q^{79} -4.78297e6 q^{81} +(-2.07390e7 + 2.07390e7i) q^{82} +(6.66763e7 + 6.66763e7i) q^{83} +2.81119e7i q^{84} +4.11811e7 q^{86} +(-7.94210e6 + 7.94210e6i) q^{87} +(694695. + 694695. i) q^{88} +9.51614e7i q^{89} -6.85279e7 q^{91} +(3.98759e7 - 3.98759e7i) q^{92} +(-2.76689e7 - 2.76689e7i) q^{93} +7.92637e7i q^{94} -4.74725e7 q^{96} +(-7.08678e7 + 7.08678e7i) q^{97} +(7.88658e7 + 7.88658e7i) q^{98} -511758. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1944 q^{6}+O(q^{10}) $ 4 * q + 1944 * q^6	$ 4 q + 1944 q^{6} - 936 q^{11} + 22976 q^{16} + 759780 q^{21} - 701352 q^{26} + 3346900 q^{31} - 1294704 q^{36} + 11288880 q^{41} + 15839280 q^{46} + 23547672 q^{51} + 68211360 q^{56} + 2069612 q^{61} - 454896 q^{66} - 83314512 q^{71} - 107562256 q^{76} - 19131876 q^{81} + 164724264 q^{86} - 274111740 q^{91} - 189889920 q^{96}+O(q^{100}) $ 4 * q + 1944 * q^6 - 936 * q^11 + 22976 * q^16 + 759780 * q^21 - 701352 * q^26 + 3346900 * q^31 - 1294704 * q^36 + 11288880 * q^41 + 15839280 * q^46 + 23547672 * q^51 + 68211360 * q^56 + 2069612 * q^61 - 454896 * q^66 - 83314512 * q^71 - 107562256 * q^76 - 19131876 * q^81 + 164724264 * q^86 - 274111740 * q^91 - 189889920 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−7.34847	+	7.34847i	−0.459279	+	0.459279i	−0.898419	−	0.439140i	$-0.855283\pi$
$2$	−7.34847	+	7.34847i	−0.459279	+	0.459279i	0.439140	+	0.898419i	$0.355283\pi$
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$			148.000i			0.578125i
$5$		0			0
$5$		0			0
$6$	486.000			0.375000
$7$	−2872.03	+	2872.03i	−1.19618	+	1.19618i	−0.220878	+	0.975301i	$0.570892\pi$
$7$	−2872.03	+	2872.03i	−1.19618	+	1.19618i	−0.975301	+	0.220878i	$0.929108\pi$
$8$	−2968.78	−	2968.78i	−0.724800	−	0.724800i
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−234.000			−0.0159825			−0.00799126	−	0.999968i	$-0.502544\pi$
$11$	−234.000			−0.0159825			−0.00799126	+	0.999968i	$0.502544\pi$
$12$	4894.08	−	4894.08i	0.236019	−	0.236019i
$13$	11930.2	+	11930.2i	0.417711	+	0.417711i	0.884414	−	0.466703i	$-0.154558\pi$
$13$	11930.2	+	11930.2i	0.417711	+	0.417711i	−0.466703	+	0.884414i	$0.654558\pi$
$14$		−	42210.0i		−	1.09876i
$15$		0			0
$16$	5744.00			0.0876465
$17$	−89012.0	+	89012.0i	−1.06574	+	1.06574i	−0.0680630	+	0.997681i	$0.521682\pi$
$17$	−89012.0	+	89012.0i	−1.06574	+	1.06574i	−0.997681	+	0.0680630i	$0.978318\pi$
$18$	−16071.1	−	16071.1i	−0.153093	−	0.153093i
$19$			181693.i			1.39420i	0.716976	+	0.697098i	$0.245526\pi$
$19$			181693.i			1.39420i	−0.716976	+	0.697098i	$0.754474\pi$
$20$		0			0
$21$	189945.			0.976676
$22$	1719.54	−	1719.54i	0.00734044	−	0.00734044i
$23$	−269432.	−	269432.i	−0.962803	−	0.962803i	0.0365300	−	0.999333i	$-0.488370\pi$
$23$	−269432.	−	269432.i	−0.962803	−	0.962803i	−0.999333	+	0.0365300i	$0.988370\pi$
$24$			196344.i			0.591797i
$25$		0			0
$26$	−175338.			−0.383692
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$	−425060.	−	425060.i	−0.691541	−	0.691541i
$29$		−	240174.i		−	0.339574i	−0.985481	−	0.169787i	$-0.945692\pi$
$29$		−	240174.i		−	0.339574i	0.985481	−	0.169787i	$-0.0543079\pi$
$30$		0			0
$31$	836725.			0.906016			0.453008	−	0.891506i	$-0.350351\pi$
$31$	836725.			0.906016			0.453008	+	0.891506i	$0.350351\pi$
$32$	717798.	−	717798.i	0.684546	−	0.684546i
$33$	7737.94	+	7737.94i	0.00652483	+	0.00652483i
$34$		−	1.30820e6i		−	0.978948i
$35$		0			0
$36$	−323676.			−0.192708
$37$	−608282.	+	608282.i	−0.324562	+	0.324562i	−0.850514	−	0.525952i	$-0.823709\pi$
$37$	−608282.	+	608282.i	−0.324562	+	0.324562i	0.525952	+	0.850514i	$0.323709\pi$
$38$	−1.33517e6	−	1.33517e6i	−0.640325	−	0.640325i
$39$		−	789021.i		−	0.341059i
$40$		0			0
$41$	2.82222e6			0.998747			0.499373	−	0.866387i	$-0.333564\pi$
$41$	2.82222e6			0.998747			0.499373	+	0.866387i	$0.333564\pi$
$42$	−1.39580e6	+	1.39580e6i	−0.448567	+	0.448567i
$43$	−2.80202e6	−	2.80202e6i	−0.819590	−	0.819590i	0.166458	−	0.986049i	$-0.446767\pi$
$43$	−2.80202e6	−	2.80202e6i	−0.819590	−	0.819590i	−0.986049	+	0.166458i	$0.946767\pi$
$44$		−	34632.0i		−	0.00923989i
$45$		0			0
$46$	3.95982e6			0.884391
$47$	5.39321e6	−	5.39321e6i	1.10524	−	1.10524i	0.111471	−	0.993768i	$-0.464444\pi$
$47$	5.39321e6	−	5.39321e6i	1.10524	−	1.10524i	0.993768	−	0.111471i	$-0.0355561\pi$
$48$	−189943.	−	189943.i	−0.0357815	−	0.0357815i
$49$		−	1.07323e7i		−	1.86169i
$50$		0			0
$51$	5.88692e6			0.870176
$52$	−1.76568e6	+	1.76568e6i	−0.241489	+	0.241489i
$53$	1.19258e6	+	1.19258e6i	0.151142	+	0.151142i	0.778628	−	0.627486i	$-0.215916\pi$
$53$	1.19258e6	+	1.19258e6i	0.151142	+	0.151142i	−0.627486	+	0.778628i	$0.715916\pi$
$54$			1.06288e6i			0.125000i
$55$		0			0
$56$	1.70528e7			1.73398
$57$	6.00824e6	−	6.00824e6i	0.569178	−	0.569178i
$58$	1.76491e6	+	1.76491e6i	0.155959	+	0.155959i
$59$		−	1.27860e7i		−	1.05518i	−0.849500	−	0.527588i	$-0.823096\pi$
$59$		−	1.27860e7i		−	1.05518i	0.849500	−	0.527588i	$-0.176904\pi$
$60$		0			0
$61$	517403.			0.0373688			0.0186844	−	0.999825i	$-0.494052\pi$
$61$	517403.			0.0373688			0.0186844	+	0.999825i	$0.494052\pi$
$62$	−6.14865e6	+	6.14865e6i	−0.416115	+	0.416115i
$63$	−6.28112e6	−	6.28112e6i	−0.398726	−	0.398726i
$64$			1.20199e7i			0.716442i
$65$		0			0
$66$	−113724.			−0.00599344
$67$	−2.06617e6	+	2.06617e6i	−0.102534	+	0.102534i	−0.756513	−	0.653979i	$-0.773098\pi$
$67$	−2.06617e6	+	2.06617e6i	−0.102534	+	0.102534i	0.653979	+	0.756513i	$0.273098\pi$
$68$	−1.31738e7	−	1.31738e7i	−0.616133	−	0.616133i
$69$			1.78192e7i			0.786125i
$70$		0			0
$71$	−2.08286e7			−0.819648			−0.409824	−	0.912165i	$-0.634410\pi$
$71$	−2.08286e7			−0.819648			−0.409824	+	0.912165i	$0.634410\pi$
$72$	6.49273e6	−	6.49273e6i	0.241600	−	0.241600i
$73$	−2.88730e7	−	2.88730e7i	−1.01672	−	1.01672i	−0.999858	−	0.0168598i	$-0.994633\pi$
$73$	−2.88730e7	−	2.88730e7i	−1.01672	−	1.01672i	−0.0168598	−	0.999858i	$-0.505367\pi$
$74$		−	8.93988e6i		−	0.298129i
$75$		0			0
$76$	−2.68906e7			−0.806019
$77$	672054.	−	672054.i	0.0191180	−	0.0191180i
$78$	5.79810e6	+	5.79810e6i	0.156642	+	0.156642i
$79$		−	4.21879e7i		−	1.08313i	−0.840659	−	0.541564i	$-0.817832\pi$
$79$		−	4.21879e7i		−	1.08313i	0.840659	−	0.541564i	$-0.182168\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	−2.07390e7	+	2.07390e7i	−0.458704	+	0.458704i
$83$	6.66763e7	+	6.66763e7i	1.40494	+	1.40494i	0.783302	+	0.621642i	$0.213534\pi$
$83$	6.66763e7	+	6.66763e7i	1.40494	+	1.40494i	0.621642	+	0.783302i	$0.286466\pi$
$84$			2.81119e7i			0.564641i
$85$		0			0
$86$	4.11811e7			0.752842
$87$	−7.94210e6	+	7.94210e6i	−0.138630	+	0.138630i
$88$	694695.	+	694695.i	0.0115841	+	0.0115841i
$89$			9.51614e7i			1.51670i	0.651845	+	0.758352i	$0.273995\pi$
$89$			9.51614e7i			1.51670i	−0.651845	+	0.758352i	$0.726005\pi$
$90$		0			0
$91$	−6.85279e7			−0.999314
$92$	3.98759e7	−	3.98759e7i	0.556620	−	0.556620i
$93$	−2.76689e7	−	2.76689e7i	−0.369880	−	0.369880i
$94$			7.92637e7i			1.01523i
$95$		0			0
$96$	−4.74725e7			−0.558929
$97$	−7.08678e7	+	7.08678e7i	−0.800501	+	0.800501i	−0.983174	−	0.182672i	$-0.941525\pi$
$97$	−7.08678e7	+	7.08678e7i	−0.800501	+	0.800501i	0.182672	+	0.983174i	$0.441525\pi$
$98$	7.88658e7	+	7.88658e7i	0.855036	+	0.855036i
$99$		−	511758.i		−	0.00532750i
$100$		0			0
$101$	−8.63379e7			−0.829690			−0.414845	−	0.909892i	$-0.636164\pi$
$101$	−8.63379e7			−0.829690			−0.414845	+	0.909892i	$0.636164\pi$
$102$	−4.32598e7	+	4.32598e7i	−0.399654	+	0.399654i
$103$	7.61161e7	+	7.61161e7i	0.676282	+	0.676282i	0.959157	−	0.282875i	$-0.0912881\pi$
$103$	7.61161e7	+	7.61161e7i	0.676282	+	0.676282i	−0.282875	+	0.959157i	$0.591288\pi$
$104$		−	7.08366e7i		−	0.605514i
$105$		0			0
$106$	−1.75273e7			−0.138833
$107$	1.09281e8	−	1.09281e8i	0.833701	−	0.833701i	−0.154320	−	0.988021i	$-0.549319\pi$
$107$	1.09281e8	−	1.09281e8i	0.833701	−	0.833701i	0.988021	+	0.154320i	$0.0493186\pi$
$108$	1.07034e7	+	1.07034e7i	0.0786728	+	0.0786728i
$109$			5.04631e7i			0.357494i	0.983895	+	0.178747i	$0.0572043\pi$
$109$			5.04631e7i			0.357494i	−0.983895	+	0.178747i	$0.942796\pi$
$110$		0			0
$111$	4.02295e7			0.265004
$112$	−1.64969e7	+	1.64969e7i	−0.104841	+	0.104841i
$113$	1.21244e8	+	1.21244e8i	0.743611	+	0.743611i	0.973271	−	0.229660i	$-0.0737615\pi$
$113$	1.21244e8	+	1.21244e8i	0.743611	+	0.743611i	−0.229660	+	0.973271i	$0.573762\pi$
$114$			8.83028e7i			0.522823i
$115$		0			0
$116$	3.55458e7			0.196316
$117$	−2.60914e7	+	2.60914e7i	−0.139237	+	0.139237i
$118$	9.39572e7	+	9.39572e7i	0.484621	+	0.484621i
$119$		−	5.11290e8i		−	2.54964i
$120$		0			0
$121$	−2.14304e8			−0.999745
$122$	−3.80212e6	+	3.80212e6i	−0.0171627	+	0.0171627i
$123$	−9.33255e7	−	9.33255e7i	−0.407737	−	0.407737i
$124$			1.23835e8i			0.523791i
$125$		0			0
$126$	9.23133e7			0.366254
$127$	9.55780e7	−	9.55780e7i	0.367403	−	0.367403i	−0.499126	−	0.866529i	$-0.666346\pi$
$127$	9.55780e7	−	9.55780e7i	0.367403	−	0.367403i	0.866529	+	0.499126i	$0.166346\pi$
$128$	9.54285e7	+	9.54285e7i	0.355499	+	0.355499i
$129$			1.85315e8i			0.669193i
$130$		0			0
$131$	−3.13838e8			−1.06566			−0.532832	−	0.846221i	$-0.678872\pi$
$131$	−3.13838e8			−1.06566			−0.532832	+	0.846221i	$0.678872\pi$
$132$	−1.14521e6	+	1.14521e6i	−0.00377217	+	0.00377217i
$133$	−5.21827e8	−	5.21827e8i	−1.66771	−	1.66771i
$134$		−	3.03664e7i		−	0.0941834i
$135$		0			0
$136$	5.28514e8			1.54490
$137$	−5.04691e7	+	5.04691e7i	−0.143266	+	0.143266i	−0.775102	−	0.631836i	$-0.782302\pi$
$137$	−5.04691e7	+	5.04691e7i	−0.143266	+	0.143266i	0.631836	+	0.775102i	$0.282302\pi$
$138$	−1.30944e8	−	1.30944e8i	−0.361051	−	0.361051i
$139$			5.26688e8i			1.41089i	0.708763	+	0.705446i	$0.249253\pi$
$139$			5.26688e8i			1.41089i	−0.708763	+	0.705446i	$0.750747\pi$
$140$		0			0
$141$	−3.56687e8			−0.902423
$142$	1.53059e8	−	1.53059e8i	0.376447	−	0.376447i
$143$	−2.79168e6	−	2.79168e6i	−0.00667607	−	0.00667607i
$144$			1.25621e7i			0.0292155i
$145$		0			0
$146$	4.24345e8			0.933915
$147$	−3.54896e8	+	3.54896e8i	−0.760032	+	0.760032i
$148$	−9.00257e7	−	9.00257e7i	−0.187638	−	0.187638i
$149$		−	8.99246e8i		−	1.82446i	−0.409683	−	0.912228i	$-0.634361\pi$
$149$		−	8.99246e8i		−	1.82446i	0.409683	−	0.912228i	$-0.365639\pi$
$150$		0			0
$151$	8.05999e8			1.55034			0.775170	−	0.631753i	$-0.217664\pi$
$151$	8.05999e8			1.55034			0.775170	+	0.631753i	$0.217664\pi$
$152$	5.39407e8	−	5.39407e8i	1.01051	−	1.01051i
$153$	−1.94669e8	−	1.94669e8i	−0.355248	−	0.355248i
$154$			9.87714e6i			0.0175610i
$155$		0			0
$156$	1.16775e8			0.197175
$157$	−4.78600e8	+	4.78600e8i	−0.787724	+	0.787724i	−0.981121	−	0.193397i	$-0.938050\pi$
$157$	−4.78600e8	+	4.78600e8i	−0.787724	+	0.787724i	0.193397	+	0.981121i	$0.438050\pi$
$158$	3.10017e8	+	3.10017e8i	0.497458	+	0.497458i
$159$		−	7.88729e7i		−	0.123407i
$160$		0			0
$161$	1.54763e9			2.30337
$162$	3.51475e7	−	3.51475e7i	0.0510310	−	0.0510310i
$163$	−4.56533e8	−	4.56533e8i	−0.646729	−	0.646729i	0.305472	−	0.952201i	$-0.401186\pi$
$163$	−4.56533e8	−	4.56533e8i	−0.646729	−	0.646729i	−0.952201	+	0.305472i	$0.901186\pi$
$164$			4.17689e8i			0.577401i
$165$		0			0
$166$	−9.79937e8			−1.29052
$167$	−2.74258e8	+	2.74258e8i	−0.352609	+	0.352609i	−0.861079	−	0.508470i	$-0.830211\pi$
$167$	−2.74258e8	+	2.74258e8i	−0.352609	+	0.352609i	0.508470	+	0.861079i	$0.330211\pi$
$168$	−5.63905e8	−	5.63905e8i	−0.707895	−	0.707895i
$169$		−	5.31069e8i		−	0.651035i
$170$		0			0
$171$	−3.97363e8			−0.464732
$172$	4.14698e8	−	4.14698e8i	0.473826	−	0.473826i
$173$	1.75277e8	+	1.75277e8i	0.195677	+	0.195677i	0.798144	−	0.602467i	$-0.205815\pi$
$173$	1.75277e8	+	1.75277e8i	0.195677	+	0.195677i	−0.602467	+	0.798144i	$0.705815\pi$
$174$		−	1.16725e8i		−	0.127340i
$175$		0			0
$176$	−1.34410e6			−0.00140081
$177$	−4.22807e8	+	4.22807e8i	−0.430774	+	0.430774i
$178$	−6.99291e8	−	6.99291e8i	−0.696591	−	0.696591i
$179$		−	1.65138e9i		−	1.60855i	−0.594255	−	0.804277i	$-0.702553\pi$
$179$		−	1.65138e9i		−	1.60855i	0.594255	−	0.804277i	$-0.297447\pi$
$180$		0			0
$181$	−3.19153e8			−0.297362			−0.148681	−	0.988885i	$-0.547503\pi$
$181$	−3.19153e8			−0.297362			−0.148681	+	0.988885i	$0.547503\pi$
$182$	5.03575e8	−	5.03575e8i	0.458964	−	0.458964i
$183$	−1.71095e7	−	1.71095e7i	−0.0152558	−	0.0152558i
$184$			1.59977e9i			1.39568i
$185$		0			0
$186$	4.06648e8			0.339756
$187$	2.08288e7	−	2.08288e7i	0.0170333	−	0.0170333i
$188$	7.98195e8	+	7.98195e8i	0.638966	+	0.638966i
$189$			4.15410e8i			0.325559i
$190$		0			0
$191$	−1.13627e9			−0.853785			−0.426893	−	0.904302i	$-0.640392\pi$
$191$	−1.13627e9			−0.853785			−0.426893	+	0.904302i	$0.640392\pi$
$192$	3.97476e8	−	3.97476e8i	0.292486	−	0.292486i
$193$	1.71674e9	+	1.71674e9i	1.23730	+	1.23730i	0.961101	+	0.276197i	$0.0890742\pi$
$193$	1.71674e9	+	1.71674e9i	1.23730	+	1.23730i	0.276197	+	0.961101i	$0.410926\pi$
$194$		−	1.04154e9i		−	0.735307i
$195$		0			0
$196$	1.58838e9			1.07629
$197$	4.17614e8	−	4.17614e8i	0.277275	−	0.277275i	−0.554745	−	0.832020i	$-0.687184\pi$
$197$	4.17614e8	−	4.17614e8i	0.277275	−	0.277275i	0.832020	+	0.554745i	$0.187184\pi$
$198$	3.76064e6	+	3.76064e6i	0.00244681	+	0.00244681i
$199$		−	1.06994e9i		−	0.682258i	−0.940017	−	0.341129i	$-0.889191\pi$
$199$		−	1.06994e9i		−	0.682258i	0.940017	−	0.341129i	$-0.110809\pi$
$200$		0			0
$201$	1.36649e8			0.0837186
$202$	6.34451e8	−	6.34451e8i	0.381059	−	0.381059i
$203$	6.89786e8	+	6.89786e8i	0.406191	+	0.406191i
$204$			8.71264e8i			0.503071i
$205$		0			0
$206$	−1.11867e9			−0.621205
$207$	5.89247e8	−	5.89247e8i	0.320934	−	0.320934i
$208$	6.85273e7	+	6.85273e7i	0.0366109	+	0.0366109i
$209$		−	4.25162e7i		−	0.0222828i
$210$		0			0
$211$	−2.26915e9			−1.14481			−0.572406	−	0.819971i	$-0.693990\pi$
$211$	−2.26915e9			−1.14481			−0.572406	+	0.819971i	$0.693990\pi$
$212$	−1.76502e8	+	1.76502e8i	−0.0873790	+	0.0873790i
$213$	6.88763e8	+	6.88763e8i	0.334620	+	0.334620i
$214$			1.60610e9i			0.765803i
$215$		0			0
$216$	−4.29404e8			−0.197266
$217$	−2.40310e9	+	2.40310e9i	−1.08376	+	1.08376i
$218$	−3.70827e8	−	3.70827e8i	−0.164189	−	0.164189i
$219$			1.90955e9i			0.830146i
$220$		0			0
$221$	−2.12387e9			−0.890346
$222$	−2.95625e8	+	2.95625e8i	−0.121711	+	0.121711i
$223$	−1.99573e9	−	1.99573e9i	−0.807015	−	0.807015i	0.177166	−	0.984181i	$-0.443307\pi$
$223$	−1.99573e9	−	1.99573e9i	−0.807015	−	0.807015i	−0.984181	+	0.177166i	$0.943307\pi$
$224$			4.12307e9i			1.63768i
$225$		0			0
$226$	−1.78191e9			−0.683050
$227$	−1.32121e9	+	1.32121e9i	−0.497588	+	0.497588i	−0.910686	−	0.413099i	$-0.864446\pi$
$227$	−1.32121e9	+	1.32121e9i	−0.497588	+	0.497588i	0.413099	+	0.910686i	$0.364446\pi$
$228$	8.89220e8	+	8.89220e8i	0.329056	+	0.329056i
$229$		−	2.03118e9i		−	0.738595i	−0.929311	−	0.369297i	$-0.879598\pi$
$229$		−	2.03118e9i		−	0.738595i	0.929311	−	0.369297i	$-0.120402\pi$
$230$		0			0
$231$	−4.44471e7			−0.0156097
$232$	−7.13024e8	+	7.13024e8i	−0.246123	+	0.246123i
$233$	1.51062e9	+	1.51062e9i	0.512545	+	0.512545i	0.915305	−	0.402760i	$-0.131949\pi$
$233$	1.51062e9	+	1.51062e9i	0.512545	+	0.512545i	−0.402760	+	0.915305i	$0.631949\pi$
$234$		−	3.83464e8i		−	0.127897i
$235$		0			0
$236$	1.89232e9			0.610024
$237$	−1.39508e9	+	1.39508e9i	−0.442185	+	0.442185i
$238$	3.75720e9	+	3.75720e9i	1.17100	+	1.17100i
$239$			3.44530e9i			1.05593i	0.849266	+	0.527965i	$0.177045\pi$
$239$			3.44530e9i			1.05593i	−0.849266	+	0.527965i	$0.822955\pi$
$240$		0			0
$241$	2.45959e7			0.00729112			0.00364556	−	0.999993i	$-0.498840\pi$
$241$	2.45959e7			0.00729112			0.00364556	+	0.999993i	$0.498840\pi$
$242$	1.57481e9	−	1.57481e9i	0.459162	−	0.459162i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$			7.65756e7i			0.0216039i
$245$		0			0
$246$	1.37160e9			0.374530
$247$	−2.16764e9	+	2.16764e9i	−0.582371	+	0.582371i
$248$	−2.48405e9	−	2.48405e9i	−0.656681	−	0.656681i
$249$		−	4.40972e9i		−	1.14713i
$250$		0			0
$251$	−3.62820e9			−0.914106			−0.457053	−	0.889440i	$-0.651095\pi$
$251$	−3.62820e9			−0.914106			−0.457053	+	0.889440i	$0.651095\pi$
$252$	9.29606e8	−	9.29606e8i	0.230514	−	0.230514i
$253$	6.30470e7	+	6.30470e7i	0.0153880	+	0.0153880i
$254$			1.40470e9i			0.337482i
$255$		0			0
$256$	−4.47960e9			−1.04299
$257$	1.05639e9	−	1.05639e9i	0.242154	−	0.242154i	−0.575586	−	0.817741i	$-0.695226\pi$
$257$	1.05639e9	−	1.05639e9i	0.242154	−	0.242154i	0.817741	+	0.575586i	$0.195226\pi$
$258$	−1.36178e9	−	1.36178e9i	−0.307346	−	0.307346i
$259$		−	3.49400e9i		−	0.776469i
$260$		0			0
$261$	5.25261e8			0.113191
$262$	2.30623e9	−	2.30623e9i	0.489438	−	0.489438i
$263$	−2.89677e9	−	2.89677e9i	−0.605468	−	0.605468i	0.336290	−	0.941758i	$-0.390828\pi$
$263$	−2.89677e9	−	2.89677e9i	−0.605468	−	0.605468i	−0.941758	+	0.336290i	$0.890828\pi$
$264$		−	4.59445e7i		−	0.00945840i
$265$		0			0
$266$	7.66926e9			1.53189
$267$	3.14681e9	−	3.14681e9i	0.619192	−	0.619192i
$268$	−3.05794e8	−	3.05794e8i	−0.0592774	−	0.0592774i
$269$			4.75635e9i			0.908374i	0.890906	+	0.454187i	$0.150070\pi$
$269$			4.75635e9i			0.908374i	−0.890906	+	0.454187i	$0.849930\pi$
$270$		0			0
$271$	4.98291e9			0.923860			0.461930	−	0.886916i	$-0.347157\pi$
$271$	4.98291e9			0.923860			0.461930	+	0.886916i	$0.347157\pi$
$272$	−5.11285e8	+	5.11285e8i	−0.0934087	+	0.0934087i
$273$	2.26609e9	+	2.26609e9i	0.407968	+	0.407968i
$274$		−	7.41741e8i		−	0.131598i
$275$		0			0
$276$	−2.63724e9			−0.454479
$277$	2.27910e9	−	2.27910e9i	0.387119	−	0.387119i	−0.486539	−	0.873659i	$-0.661741\pi$
$277$	2.27910e9	−	2.27910e9i	0.387119	−	0.387119i	0.873659	+	0.486539i	$0.161741\pi$
$278$	−3.87035e9	−	3.87035e9i	−0.647994	−	0.647994i
$279$			1.82992e9i			0.302005i
$280$		0			0
$281$	−1.00667e9			−0.161459			−0.0807294	−	0.996736i	$-0.525725\pi$
$281$	−1.00667e9			−0.161459			−0.0807294	+	0.996736i	$0.525725\pi$
$282$	2.62110e9	−	2.62110e9i	0.414464	−	0.414464i
$283$	−3.14496e9	−	3.14496e9i	−0.490308	−	0.490308i	0.418095	−	0.908403i	$-0.362698\pi$
$283$	−3.14496e9	−	3.14496e9i	−0.490308	−	0.490308i	−0.908403	+	0.418095i	$0.862698\pi$
$284$		−	3.08264e9i		−	0.473859i
$285$		0			0
$286$	4.10291e7			0.00613236
$287$	−8.10549e9	+	8.10549e9i	−1.19468	+	1.19468i
$288$	1.56983e9	+	1.56983e9i	0.228182	+	0.228182i
$289$		−	8.87052e9i		−	1.27162i
$290$		0			0
$291$	4.68693e9			0.653607
$292$	4.27320e9	−	4.27320e9i	0.587790	−	0.587790i
$293$	−3.60077e9	−	3.60077e9i	−0.488568	−	0.488568i	0.419286	−	0.907854i	$-0.362280\pi$
$293$	−3.60077e9	−	3.60077e9i	−0.488568	−	0.488568i	−0.907854	+	0.419286i	$0.862280\pi$
$294$		−	5.21589e9i		−	0.698134i
$295$		0			0
$296$	3.61171e9			0.470485
$297$	−1.69229e7	+	1.69229e7i	−0.00217494	+	0.00217494i
$298$	6.60808e9	+	6.60808e9i	0.837935	+	0.837935i
$299$		−	6.42877e9i		−	0.804346i
$300$		0			0
$301$	1.60949e10			1.96075
$302$	−5.92286e9	+	5.92286e9i	−0.712039	+	0.712039i
$303$	2.85503e9	+	2.85503e9i	0.338719	+	0.338719i
$304$			1.04364e9i			0.122196i
$305$		0			0
$306$	2.86104e9			0.326316
$307$	1.23211e10	−	1.23211e10i	1.38706	−	1.38706i	0.555644	−	0.831420i	$-0.312472\pi$
$307$	1.23211e10	−	1.23211e10i	1.38706	−	1.38706i	0.831420	−	0.555644i	$-0.187528\pi$
$308$	9.94640e7	+	9.94640e7i	0.0110526	+	0.0110526i
$309$		−	5.03403e9i		−	0.552182i
$310$		0			0
$311$	−8.62846e9			−0.922341			−0.461170	−	0.887312i	$-0.652570\pi$
$311$	−8.62846e9			−0.922341			−0.461170	+	0.887312i	$0.652570\pi$
$312$	−2.34243e9	+	2.34243e9i	−0.247200	+	0.247200i
$313$	−2.96428e9	−	2.96428e9i	−0.308846	−	0.308846i	0.535616	−	0.844462i	$-0.320079\pi$
$313$	−2.96428e9	−	2.96428e9i	−0.308846	−	0.308846i	−0.844462	+	0.535616i	$0.820079\pi$
$314$		−	7.03396e9i		−	0.723571i
$315$		0			0
$316$	6.24381e9			0.626183
$317$	1.98335e9	−	1.98335e9i	0.196409	−	0.196409i	−0.602050	−	0.798459i	$-0.705649\pi$
$317$	1.98335e9	−	1.98335e9i	0.196409	−	0.196409i	0.798459	+	0.602050i	$0.205649\pi$
$318$	5.79595e8	+	5.79595e8i	0.0566782	+	0.0566782i
$319$			5.62007e7i			0.00542724i
$320$		0			0
$321$	−7.22745e9			−0.680714
$322$	−1.13727e10	+	1.13727e10i	−1.05789	+	1.05789i
$323$	−1.61729e10	−	1.61729e10i	−1.48586	−	1.48586i
$324$		−	7.07879e8i		−	0.0642361i
$325$		0			0
$326$	6.70964e9			0.594058
$327$	1.66872e9	−	1.66872e9i	0.145946	−	0.145946i
$328$	−8.37855e9	−	8.37855e9i	−0.723892	−	0.723892i
$329$			3.09789e10i			2.64413i
$330$		0			0
$331$	−4.30793e9			−0.358886			−0.179443	−	0.983768i	$-0.557430\pi$
$331$	−4.30793e9			−0.358886			−0.179443	+	0.983768i	$0.557430\pi$
$332$	−9.86809e9	+	9.86809e9i	−0.812233	+	0.812233i
$333$	−1.33031e9	−	1.33031e9i	−0.108187	−	0.108187i
$334$		−	4.03075e9i		−	0.323892i
$335$		0			0
$336$	1.09104e9			0.0856023
$337$	1.18877e8	−	1.18877e8i	0.00921677	−	0.00921677i	−0.702483	−	0.711700i	$-0.747925\pi$
$337$	1.18877e8	−	1.18877e8i	0.00921677	−	0.00921677i	0.711700	+	0.702483i	$0.247925\pi$
$338$	3.90255e9	+	3.90255e9i	0.299007	+	0.299007i
$339$		−	8.01860e9i		−	0.607156i
$340$		0			0
$341$	−1.95794e8			−0.0144804
$342$	2.92001e9	−	2.92001e9i	0.213442	−	0.213442i
$343$	1.42667e10	+	1.42667e10i	1.03074	+	1.03074i
$344$			1.66372e10i			1.18808i
$345$		0			0
$346$	−2.57603e9			−0.179741
$347$	1.63550e10	−	1.63550e10i	1.12806	−	1.12806i	0.137569	−	0.990492i	$-0.456071\pi$
$347$	1.63550e10	−	1.63550e10i	1.12806	−	1.12806i	0.990492	−	0.137569i	$-0.0439289\pi$
$348$	−1.17543e9	−	1.17543e9i	−0.0801457	−	0.0801457i
$349$			2.63406e10i			1.77552i	0.460310	+	0.887758i	$0.347738\pi$
$349$			2.63406e10i			1.77552i	−0.460310	+	0.887758i	$0.652262\pi$
$350$		0			0
$351$	1.72559e9			0.113686
$352$	−1.67965e8	+	1.67965e8i	−0.0109408	+	0.0109408i
$353$	−4.48404e9	−	4.48404e9i	−0.288783	−	0.288783i	0.547816	−	0.836599i	$-0.315459\pi$
$353$	−4.48404e9	−	4.48404e9i	−0.288783	−	0.288783i	−0.836599	+	0.547816i	$0.815459\pi$
$354$		−	6.21398e9i		−	0.395691i
$355$		0			0
$356$	−1.40839e10			−0.876845
$357$	−1.69074e10	+	1.69074e10i	−1.04089	+	1.04089i
$358$	1.21351e10	+	1.21351e10i	0.738775	+	0.738775i
$359$		−	1.76017e10i		−	1.05968i	−0.848097	−	0.529841i	$-0.822251\pi$
$359$		−	1.76017e10i		−	1.05968i	0.848097	−	0.529841i	$-0.177749\pi$
$360$		0			0
$361$	−1.60288e10			−0.943782
$362$	2.34529e9	−	2.34529e9i	0.136572	−	0.136572i
$363$	7.08663e9	+	7.08663e9i	0.408144	+	0.408144i
$364$		−	1.01421e10i		−	0.577729i
$365$		0			0
$366$	2.51458e8			0.0140133
$367$	5.58417e9	−	5.58417e9i	0.307818	−	0.307818i	−0.536245	−	0.844063i	$-0.680158\pi$
$367$	5.58417e9	−	5.58417e9i	0.307818	−	0.307818i	0.844063	+	0.536245i	$0.180158\pi$
$368$	−1.54762e9	−	1.54762e9i	−0.0843863	−	0.0843863i
$369$			6.17220e9i			0.332916i
$370$		0			0
$371$	−6.85026e9			−0.361586
$372$	4.09500e9	−	4.09500e9i	0.213837	−	0.213837i
$373$	1.94503e9	+	1.94503e9i	0.100483	+	0.100483i	0.755561	−	0.655078i	$-0.227364\pi$
$373$	1.94503e9	+	1.94503e9i	0.100483	+	0.100483i	−0.655078	+	0.755561i	$0.727364\pi$
$374$			3.06120e8i			0.0156461i
$375$		0			0
$376$	−3.20225e10			−1.60215
$377$	2.86533e9	−	2.86533e9i	0.141844	−	0.141844i
$378$	−3.05263e9	−	3.05263e9i	−0.149522	−	0.149522i
$379$			1.29779e10i			0.628996i	0.949258	+	0.314498i	$0.101836\pi$
$379$			1.29779e10i			0.628996i	−0.949258	+	0.314498i	$0.898164\pi$
$380$		0			0
$381$	−6.32117e9			−0.299984
$382$	8.34986e9	−	8.34986e9i	0.392126	−	0.392126i
$383$	1.84005e10	+	1.84005e10i	0.855135	+	0.855135i	0.990760	−	0.135625i	$-0.0433044\pi$
$383$	1.84005e10	+	1.84005e10i	0.855135	+	0.855135i	−0.135625	+	0.990760i	$0.543304\pi$
$384$		−	6.31128e9i		−	0.290264i
$385$		0			0
$386$	−2.52308e10			−1.13653
$387$	6.12801e9	−	6.12801e9i	0.273197	−	0.273197i
$388$	−1.04884e10	−	1.04884e10i	−0.462790	−	0.462790i
$389$			1.69662e9i			0.0740944i	0.999314	+	0.0370472i	$0.0117952\pi$
$389$			1.69662e9i			0.0740944i	−0.999314	+	0.0370472i	$0.988205\pi$
$390$		0			0
$391$	4.79653e10			2.05220
$392$	−3.18618e10	+	3.18618e10i	−1.34935	+	1.34935i
$393$	1.03780e10	+	1.03780e10i	0.435056	+	0.435056i
$394$			6.13765e9i			0.254693i
$395$		0			0
$396$	7.57402e7			0.00307996
$397$	−1.61839e10	+	1.61839e10i	−0.651510	+	0.651510i	−0.953357	−	0.301846i	$-0.902397\pi$
$397$	−1.61839e10	+	1.61839e10i	−0.651510	+	0.651510i	0.301846	+	0.953357i	$0.402397\pi$
$398$	7.86245e9	+	7.86245e9i	0.313347	+	0.313347i
$399$			3.45117e10i			1.36168i
$400$		0			0
$401$	−3.67977e9			−0.142313			−0.0711563	−	0.997465i	$-0.522669\pi$
$401$	−3.67977e9			−0.142313			−0.0711563	+	0.997465i	$0.522669\pi$
$402$	−1.00416e9	+	1.00416e9i	−0.0384502	+	0.0384502i
$403$	9.98233e9	+	9.98233e9i	0.378453	+	0.378453i
$404$		−	1.27780e10i		−	0.479664i
$405$		0			0
$406$	−1.01377e10			−0.373110
$407$	1.42338e8	−	1.42338e8i	0.00518732	−	0.00518732i
$408$	−1.74770e10	−	1.74770e10i	−0.630704	−	0.630704i
$409$		−	2.44824e10i		−	0.874905i	−0.899242	−	0.437452i	$-0.855881\pi$
$409$		−	2.44824e10i		−	0.874905i	0.899242	−	0.437452i	$-0.144119\pi$
$410$		0			0
$411$	3.33783e9			0.116976
$412$	−1.12652e10	+	1.12652e10i	−0.390976	+	0.390976i
$413$	3.67216e10	+	3.67216e10i	1.26218	+	1.26218i
$414$			8.66013e9i			0.294797i
$415$		0			0
$416$	1.71270e10			0.571885
$417$	1.74166e10	−	1.74166e10i	0.575995	−	0.575995i
$418$	3.12429e8	+	3.12429e8i	0.0102340	+	0.0102340i
$419$		−	2.07283e10i		−	0.672522i	−0.941769	−	0.336261i	$-0.890838\pi$
$419$		−	2.07283e10i		−	0.672522i	0.941769	−	0.336261i	$-0.109162\pi$
$420$		0			0
$421$	−1.53035e10			−0.487150			−0.243575	−	0.969882i	$-0.578320\pi$
$421$	−1.53035e10			−0.487150			−0.243575	+	0.969882i	$0.578320\pi$
$422$	1.66748e10	−	1.66748e10i	0.525788	−	0.525788i
$423$	1.17950e10	+	1.17950e10i	0.368413	+	0.368413i
$424$		−	7.08104e9i		−	0.219095i
$425$		0			0
$426$	−1.01227e10			−0.307368
$427$	−1.48600e9	+	1.48600e9i	−0.0446998	+	0.0446998i
$428$	1.61736e10	+	1.61736e10i	0.481983	+	0.481983i
$429$			1.84631e8i			0.00545099i
$430$		0			0
$431$	3.04251e10			0.881705			0.440852	−	0.897580i	$-0.354676\pi$
$431$	3.04251e10			0.881705			0.440852	+	0.897580i	$0.354676\pi$
$432$	4.15406e8	−	4.15406e8i	0.0119272	−	0.0119272i
$433$	−3.30421e9	−	3.30421e9i	−0.0939974	−	0.0939974i	0.658544	−	0.752542i	$-0.271172\pi$
$433$	−3.30421e9	−	3.30421e9i	−0.0939974	−	0.0939974i	−0.752542	+	0.658544i	$0.771172\pi$
$434$		−	3.53182e10i		−	0.995495i
$435$		0			0
$436$	−7.46855e9			−0.206676
$437$	4.89538e10	−	4.89538e10i	1.34234	−	1.34234i
$438$	−1.40323e10	−	1.40323e10i	−0.381269	−	0.381269i
$439$			3.09771e10i			0.834032i	0.908899	+	0.417016i	$0.136924\pi$
$439$			3.09771e10i			0.834032i	−0.908899	+	0.417016i	$0.863076\pi$
$440$		0			0
$441$	2.34715e10			0.620563
$442$	1.56072e10	−	1.56072e10i	0.408917	−	0.408917i
$443$	−3.59125e10	−	3.59125e10i	−0.932460	−	0.932460i	0.0653990	−	0.997859i	$-0.479168\pi$
$443$	−3.59125e10	−	3.59125e10i	−0.932460	−	0.932460i	−0.997859	+	0.0653990i	$0.979168\pi$
$444$			5.95396e9i			0.153205i
$445$		0			0
$446$	2.93311e10			0.741291
$447$	−2.97364e10	+	2.97364e10i	−0.744831	+	0.744831i
$448$	−3.45215e10	−	3.45215e10i	−0.856993	−	0.856993i
$449$			3.25449e10i			0.800751i	0.916351	+	0.400376i	$0.131120\pi$
$449$			3.25449e10i			0.800751i	−0.916351	+	0.400376i	$0.868880\pi$
$450$		0			0
$451$	−6.60399e8			−0.0159625
$452$	−1.79441e10	+	1.79441e10i	−0.429900	+	0.429900i
$453$	−2.66529e10	−	2.66529e10i	−0.632924	−	0.632924i
$454$		−	1.94178e10i		−	0.457064i
$455$		0			0
$456$	−3.56743e10			−0.825081
$457$	−1.89124e10	+	1.89124e10i	−0.433593	+	0.433593i	−0.889849	−	0.456256i	$-0.849190\pi$
$457$	−1.89124e10	+	1.89124e10i	−0.433593	+	0.433593i	0.456256	+	0.889849i	$0.349190\pi$
$458$	1.49261e10	+	1.49261e10i	0.339221	+	0.339221i
$459$			1.28747e10i			0.290059i
$460$		0			0
$461$	3.64502e10			0.807042			0.403521	−	0.914970i	$-0.367786\pi$
$461$	3.64502e10			0.807042			0.403521	+	0.914970i	$0.367786\pi$
$462$	3.26618e8	−	3.26618e8i	0.00716923	−	0.00716923i
$463$	−5.92927e10	−	5.92927e10i	−1.29026	−	1.29026i	−0.934625	−	0.355636i	$-0.884264\pi$
$463$	−5.92927e10	−	5.92927e10i	−1.29026	−	1.29026i	−0.355636	−	0.934625i	$-0.615736\pi$
$464$		−	1.37956e9i		−	0.0297624i
$465$		0			0
$466$	−2.22015e10			−0.470803
$467$	3.42203e10	−	3.42203e10i	0.719476	−	0.719476i	−0.249021	−	0.968498i	$-0.580109\pi$
$467$	3.42203e10	−	3.42203e10i	0.719476	−	0.719476i	0.968498	+	0.249021i	$0.0801090\pi$
$468$	−3.86153e9	−	3.86153e9i	−0.0804964	−	0.0804964i
$469$		−	1.18682e10i		−	0.245298i
$470$		0			0
$471$	3.16528e10			0.643174
$472$	−3.79587e10	+	3.79587e10i	−0.764792	+	0.764792i
$473$	6.55672e8	+	6.55672e8i	0.0130991	+	0.0130991i
$474$		−	2.05033e10i		−	0.406173i
$475$		0			0
$476$	7.56709e10			1.47401
$477$	−2.60818e9	+	2.60818e9i	−0.0503807	+	0.0503807i
$478$	−2.53177e10	−	2.53177e10i	−0.484967	−	0.484967i
$479$		−	4.05336e10i		−	0.769970i	−0.922923	−	0.384985i	$-0.874207\pi$
$479$		−	4.05336e10i		−	0.769970i	0.922923	−	0.384985i	$-0.125793\pi$
$480$		0			0
$481$	−1.45139e10			−0.271146
$482$	−1.80742e8	+	1.80742e8i	−0.00334866	+	0.00334866i
$483$	−5.11772e10	−	5.11772e10i	−0.940346	−	0.940346i
$484$		−	3.17170e10i		−	0.577977i
$485$		0			0
$486$	−2.32452e9			−0.0416667
$487$	−3.57760e10	+	3.57760e10i	−0.636028	+	0.636028i	−0.949573	−	0.313545i	$-0.898483\pi$
$487$	−3.57760e10	+	3.57760e10i	−0.636028	+	0.636028i	0.313545	+	0.949573i	$0.398483\pi$
$488$	−1.53606e9	−	1.53606e9i	−0.0270849	−	0.0270849i
$489$			3.01934e10i			0.528052i
$490$		0			0
$491$	−5.52678e10			−0.950925			−0.475462	−	0.879736i	$-0.657719\pi$
$491$	−5.52678e10			−0.950925			−0.475462	+	0.879736i	$0.657719\pi$
$492$	1.38122e10	−	1.38122e10i	0.235723	−	0.235723i
$493$	2.13784e10	+	2.13784e10i	0.361899	+	0.361899i
$494$		−	3.18577e10i		−	0.534942i
$495$		0			0
$496$	4.80615e9			0.0794091
$497$	5.98204e10	−	5.98204e10i	0.980446	−	0.980446i
$498$	3.24047e10	+	3.24047e10i	0.526854	+	0.526854i
$499$			2.17632e10i			0.351011i	0.984478	+	0.175506i	$0.0561560\pi$
$499$			2.17632e10i			0.351011i	−0.984478	+	0.175506i	$0.943844\pi$
$500$		0			0
$501$	1.81384e10			0.287904
$502$	2.66617e10	−	2.66617e10i	0.419830	−	0.419830i
$503$	1.36083e10	+	1.36083e10i	0.212585	+	0.212585i	0.805365	−	0.592779i	$-0.201969\pi$
$503$	1.36083e10	+	1.36083e10i	0.212585	+	0.212585i	−0.592779	+	0.805365i	$0.701969\pi$
$504$			3.72946e10i			0.577994i
$505$		0			0
$506$	−9.26598e8			−0.0141348
$507$	−1.75615e10	+	1.75615e10i	−0.265784	+	0.265784i
$508$	1.41455e10	+	1.41455e10i	0.212405	+	0.212405i
$509$		−	8.50274e10i		−	1.26674i	−0.773849	−	0.633370i	$-0.781671\pi$
$509$		−	8.50274e10i		−	1.26674i	0.773849	−	0.633370i	$-0.218329\pi$
$510$		0			0
$511$	1.65848e11			2.43235
$512$	8.48852e9	−	8.48852e9i	0.123524	−	0.123524i
$513$	1.31400e10	+	1.31400e10i	0.189726	+	0.189726i
$514$			1.55257e10i			0.222433i
$515$		0			0
$516$	−2.74266e10			−0.386877
$517$	−1.26201e9	+	1.26201e9i	−0.0176645	+	0.0176645i
$518$	2.56756e10	+	2.56756e10i	0.356616	+	0.356616i
$519$		−	1.15921e10i		−	0.159770i
$520$		0			0
$521$	−1.04749e11			−1.42167			−0.710836	−	0.703358i	$-0.751683\pi$
$521$	−1.04749e11			−1.42167			−0.710836	+	0.703358i	$0.751683\pi$
$522$	−3.85986e9	+	3.85986e9i	−0.0519864	+	0.0519864i
$523$	−1.81952e10	−	1.81952e10i	−0.243192	−	0.243192i	0.574977	−	0.818169i	$-0.305011\pi$
$523$	−1.81952e10	−	1.81952e10i	−0.243192	−	0.243192i	−0.818169	+	0.574977i	$0.805011\pi$
$524$		−	4.64480e10i		−	0.616087i
$525$		0			0
$526$	4.25737e10			0.556158
$527$	−7.44786e10	+	7.44786e10i	−0.965581	+	0.965581i
$528$	4.44467e7	+	4.44467e7i	0.000571879	+	0.000571879i
$529$			6.68758e10i			0.853977i
$530$		0			0
$531$	2.79629e10			0.351726
$532$	7.72304e10	−	7.72304e10i	0.964144	−	0.964144i
$533$	3.36698e10	+	3.36698e10i	0.417187	+	0.417187i
$534$			4.62485e10i			0.568764i
$535$		0			0
$536$	1.22680e10			0.148633
$537$	−5.46081e10	+	5.46081e10i	−0.656689	+	0.656689i
$538$	−3.49519e10	−	3.49519e10i	−0.417198	−	0.417198i
$539$			2.51135e9i			0.0297545i
$540$		0			0
$541$	−6.68793e10			−0.780733			−0.390367	−	0.920660i	$-0.627652\pi$
$541$	−6.68793e10			−0.780733			−0.390367	+	0.920660i	$0.627652\pi$
$542$	−3.66168e10	+	3.66168e10i	−0.424310	+	0.424310i
$543$	1.05538e10	+	1.05538e10i	0.121397	+	0.121397i
$544$			1.27785e11i			1.45910i
$545$		0			0
$546$	−3.33046e10			−0.374743
$547$	−1.80208e9	+	1.80208e9i	−0.0201291	+	0.0201291i	−0.717100	−	0.696971i	$-0.754531\pi$
$547$	−1.80208e9	+	1.80208e9i	−0.0201291	+	0.0201291i	0.696971	+	0.717100i	$0.254531\pi$
$548$	−7.46942e9	−	7.46942e9i	−0.0828256	−	0.0828256i
$549$			1.13156e9i			0.0124563i
$550$		0			0
$551$	4.36379e10			0.473432
$552$	5.29013e10	−	5.29013e10i	0.569784	−	0.569784i
$553$	1.21165e11	+	1.21165e11i	1.29562	+	1.29562i
$554$			3.34958e10i			0.355592i
$555$		0			0
$556$	−7.79498e10			−0.815672
$557$	2.12113e10	−	2.12113e10i	0.220367	−	0.220367i	−0.588286	−	0.808653i	$-0.700197\pi$
$557$	2.12113e10	−	2.12113e10i	0.220367	−	0.220367i	0.808653	+	0.588286i	$0.200197\pi$
$558$	−1.34471e10	−	1.34471e10i	−0.138705	−	0.138705i
$559$		−	6.68575e10i		−	0.684704i
$560$		0			0
$561$	−1.37754e9			−0.0139076
$562$	7.39748e9	−	7.39748e9i	0.0741547	−	0.0741547i
$563$	2.95427e10	+	2.95427e10i	0.294047	+	0.294047i	0.838677	−	0.544629i	$-0.183330\pi$
$563$	2.95427e10	+	2.95427e10i	0.294047	+	0.294047i	−0.544629	+	0.838677i	$0.683330\pi$
$564$		−	5.27896e10i		−	0.521713i
$565$		0			0
$566$	4.62212e10			0.450377
$567$	1.37368e10	−	1.37368e10i	0.132909	−	0.132909i
$568$	6.18356e10	+	6.18356e10i	0.594081	+	0.594081i
$569$		−	6.53964e10i		−	0.623886i	−0.950101	−	0.311943i	$-0.899020\pi$
$569$		−	6.53964e10i		−	0.623886i	0.950101	−	0.311943i	$-0.100980\pi$
$570$		0			0
$571$	−1.87778e11			−1.76644			−0.883221	−	0.468957i	$-0.844630\pi$
$571$	−1.87778e11			−1.76644			−0.883221	+	0.468957i	$0.844630\pi$
$572$	4.13168e8	−	4.13168e8i	0.00385960	−	0.00385960i
$573$	3.75744e10	+	3.75744e10i	0.348556	+	0.348556i
$574$		−	1.19126e11i		−	1.09738i
$575$		0			0
$576$	−2.62875e10			−0.238814
$577$	9.25087e7	−	9.25087e7i	0.000834602	−	0.000834602i	−0.706689	−	0.707524i	$-0.749812\pi$
$577$	9.25087e7	−	9.25087e7i	0.000834602	−	0.000834602i	0.707524	+	0.706689i	$0.249812\pi$
$578$	6.51847e10	+	6.51847e10i	0.584029	+	0.584029i
$579$		−	1.13538e11i		−	1.01025i
$580$		0			0
$581$	−3.82992e11			−3.36113
$582$	−3.44418e10	+	3.44418e10i	−0.300188	+	0.300188i
$583$	−2.79064e8	−	2.79064e8i	−0.00241563	−	0.00241563i
$584$			1.71435e11i			1.47383i
$585$		0			0
$586$	5.29204e10			0.448779
$587$	1.12620e11	−	1.12620e11i	0.948560	−	0.948560i	−0.0501803	−	0.998740i	$-0.515980\pi$
$587$	1.12620e11	−	1.12620e11i	0.948560	−	0.948560i	0.998740	+	0.0501803i	$0.0159796\pi$
$588$	−5.25246e10	−	5.25246e10i	−0.439393	−	0.439393i
$589$			1.52027e11i			1.26316i
$590$		0			0
$591$	−2.76194e10			−0.226394
$592$	−3.49397e9	+	3.49397e9i	−0.0284467	+	0.0284467i
$593$	−1.37020e11	−	1.37020e11i	−1.10807	−	1.10807i	−0.993405	−	0.114661i	$-0.963422\pi$
$593$	−1.37020e11	−	1.37020e11i	−1.10807	−	1.10807i	−0.114661	−	0.993405i	$-0.536578\pi$
$594$		−	2.48714e8i		−	0.00199781i
$595$		0			0
$596$	1.33088e11			1.05476
$597$	−3.53810e10	+	3.53810e10i	−0.278531	+	0.278531i
$598$	4.72416e10	+	4.72416e10i	0.369420	+	0.369420i
$599$			1.62549e11i			1.26263i	0.775525	+	0.631317i	$0.217485\pi$
$599$			1.62549e11i			1.26263i	−0.775525	+	0.631317i	$0.782515\pi$
$600$		0			0
$601$	1.32519e10			0.101574			0.0507869	−	0.998710i	$-0.483827\pi$
$601$	1.32519e10			0.101574			0.0507869	+	0.998710i	$0.483827\pi$
$602$	−1.18273e11	+	1.18273e11i	−0.900534	+	0.900534i
$603$	−4.51872e9	−	4.51872e9i	−0.0341780	−	0.0341780i
$604$			1.19288e11i			0.896290i
$605$		0			0
$606$	−4.19602e10			−0.311134
$607$	−8.11866e10	+	8.11866e10i	−0.598039	+	0.598039i	−0.939791	−	0.341751i	$-0.888980\pi$
$607$	−8.11866e10	+	8.11866e10i	−0.598039	+	0.598039i	0.341751	+	0.939791i	$0.388980\pi$
$608$	1.30419e11	+	1.30419e11i	0.954391	+	0.954391i
$609$		−	4.56199e10i		−	0.331654i
$610$		0			0
$611$	1.28685e11			0.923340
$612$	2.88111e10	−	2.88111e10i	0.205378	−	0.205378i
$613$	−4.13613e10	−	4.13613e10i	−0.292922	−	0.292922i	0.545311	−	0.838234i	$-0.316411\pi$
$613$	−4.13613e10	−	4.13613e10i	−0.292922	−	0.292922i	−0.838234	+	0.545311i	$0.816411\pi$
$614$			1.81083e11i			1.27410i
$615$		0			0
$616$	−3.99036e9			−0.0277134
$617$	−1.45292e11	+	1.45292e11i	−1.00254	+	1.00254i	−0.00254243	+	0.999997i	$0.500809\pi$
$617$	−1.45292e11	+	1.45292e11i	−1.00254	+	1.00254i	−0.999997	+	0.00254243i	$0.999191\pi$
$618$	3.69924e10	+	3.69924e10i	0.253606	+	0.253606i
$619$		−	1.15947e11i		−	0.789765i	−0.918732	−	0.394882i	$-0.870785\pi$
$619$		−	1.15947e11i		−	0.789765i	0.918732	−	0.394882i	$-0.129215\pi$
$620$		0			0
$621$	−3.89706e10			−0.262042
$622$	6.34059e10	−	6.34059e10i	0.423612	−	0.423612i
$623$	−2.73306e11	−	2.73306e11i	−1.81425	−	1.81425i
$624$		−	4.53214e9i		−	0.0298927i
$625$		0			0
$626$	4.35658e10			0.283693
$627$	−1.40593e9	+	1.40593e9i	−0.00909690	+	0.00909690i
$628$	−7.08328e10	−	7.08328e10i	−0.455403	−	0.455403i
$629$		−	1.08289e11i		−	0.691800i
$630$		0			0
$631$	−3.77923e10			−0.238389			−0.119194	−	0.992871i	$-0.538031\pi$
$631$	−3.77923e10			−0.238389			−0.119194	+	0.992871i	$0.538031\pi$
$632$	−1.25247e11	+	1.25247e11i	−0.785052	+	0.785052i
$633$	7.50366e10	+	7.50366e10i	0.467367	+	0.467367i
$634$			2.91491e10i			0.180413i
$635$		0			0
$636$	1.16732e10			0.0713446
$637$	1.28039e11	−	1.28039e11i	0.777648	−	0.777648i
$638$	−4.12989e8	−	4.12989e8i	−0.00249262	−	0.00249262i
$639$		−	4.55522e10i		−	0.273216i
$640$		0			0
$641$	−1.49659e10			−0.0886484			−0.0443242	−	0.999017i	$-0.514113\pi$
$641$	−1.49659e10			−0.0886484			−0.0443242	+	0.999017i	$0.514113\pi$
$642$	5.31107e10	−	5.31107e10i	0.312638	−	0.312638i
$643$	1.62422e11	+	1.62422e11i	0.950170	+	0.950170i	0.998816	−	0.0486457i	$-0.0154905\pi$
$643$	1.62422e11	+	1.62422e11i	0.950170	+	0.950170i	−0.0486457	+	0.998816i	$0.515491\pi$
$644$			2.29049e11i			1.33164i
$645$		0			0
$646$	2.37692e11			1.36485
$647$	7.96349e10	−	7.96349e10i	0.454450	−	0.454450i	−0.442378	−	0.896829i	$-0.645865\pi$
$647$	7.96349e10	−	7.96349e10i	0.454450	−	0.454450i	0.896829	+	0.442378i	$0.145865\pi$
$648$	1.41996e10	+	1.41996e10i	0.0805334	+	0.0805334i
$649$			2.99191e9i			0.0168644i
$650$		0			0
$651$	1.58932e11			0.884885
$652$	6.75669e10	−	6.75669e10i	0.373890	−	0.373890i
$653$	3.49865e9	+	3.49865e9i	0.0192419	+	0.0192419i	0.716662	−	0.697420i	$-0.245669\pi$
$653$	3.49865e9	+	3.49865e9i	0.0192419	+	0.0192419i	−0.697420	+	0.716662i	$0.745669\pi$
$654$			2.45251e10i			0.134060i
$655$		0			0
$656$	1.62108e10			0.0875367
$657$	6.31452e10	−	6.31452e10i	0.338906	−	0.338906i
$658$	−2.27647e11	−	2.27647e11i	−1.21439	−	1.21439i
$659$		−	2.49093e11i		−	1.32075i	−0.750938	−	0.660373i	$-0.770398\pi$
$659$		−	2.49093e11i		−	1.32075i	0.750938	−	0.660373i	$-0.229602\pi$
$660$		0			0
$661$	8.01902e9			0.0420064			0.0210032	−	0.999779i	$-0.493314\pi$
$661$	8.01902e9			0.0420064			0.0210032	+	0.999779i	$0.493314\pi$
$662$	3.16567e10	−	3.16567e10i	0.164829	−	0.164829i
$663$	7.02323e10	+	7.02323e10i	0.363482	+	0.363482i
$664$		−	3.95894e11i		−	2.03661i
$665$		0			0
$666$	1.95515e10			0.0993765
$667$	−6.47105e10	+	6.47105e10i	−0.326942	+	0.326942i
$668$	−4.05902e10	−	4.05902e10i	−0.203852	−	0.203852i
$669$			1.31990e11i			0.658925i
$670$		0			0
$671$	−1.21072e8			−0.000597248
$672$	1.36342e11	−	1.36342e11i	0.668580	−	0.668580i
$673$	1.75658e11	+	1.75658e11i	0.856264	+	0.856264i	0.990896	−	0.134632i	$-0.0429852\pi$
$673$	1.75658e11	+	1.75658e11i	0.856264	+	0.856264i	−0.134632	+	0.990896i	$0.542985\pi$
$674$			1.74713e9i			0.00846614i
$675$		0			0
$676$	7.85983e10			0.376380
$677$	−1.49210e11	+	1.49210e11i	−0.710301	+	0.710301i	−0.966598	−	0.256297i	$-0.917498\pi$
$677$	−1.49210e11	+	1.49210e11i	−0.710301	+	0.710301i	0.256297	+	0.966598i	$0.417498\pi$
$678$	5.89245e10	+	5.89245e10i	0.278854	+	0.278854i
$679$		−	4.07068e11i		−	1.91509i
$680$		0			0
$681$	8.73801e10			0.406279
$682$	1.43878e9	−	1.43878e9i	0.00665056	−	0.00665056i
$683$	−2.32934e11	−	2.32934e11i	−1.07041	−	1.07041i	−0.997326	−	0.0730842i	$-0.976716\pi$
$683$	−2.32934e11	−	2.32934e11i	−1.07041	−	1.07041i	−0.0730842	−	0.997326i	$-0.523284\pi$
$684$		−	5.88097e10i		−	0.268673i
$685$		0			0
$686$	−2.09677e11			−0.946792
$687$	−6.71672e10	+	6.71672e10i	−0.301530	+	0.301530i
$688$	−1.60948e10	−	1.60948e10i	−0.0718342	−	0.0718342i
$689$			2.84556e10i			0.126267i
$690$		0			0
$691$	2.85720e11			1.25322			0.626611	−	0.779332i	$-0.284441\pi$
$691$	2.85720e11			1.25322			0.626611	+	0.779332i	$0.284441\pi$
$692$	−2.59410e10	+	2.59410e10i	−0.113126	+	0.113126i
$693$	1.46978e9	+	1.46978e9i	0.00637265	+	0.00637265i
$694$			2.40368e11i			1.03619i
$695$		0			0
$696$	4.71567e10			0.200959
$697$	−2.51211e11	+	2.51211e11i	−1.06441	+	1.06441i
$698$	−1.93563e11	−	1.93563e11i	−0.815458	−	0.815458i
$699$		−	9.99068e10i		−	0.418491i
$700$		0			0
$701$	−6.05393e10			−0.250706			−0.125353	−	0.992112i	$-0.540006\pi$
$701$	−6.05393e10			−0.250706			−0.125353	+	0.992112i	$0.540006\pi$
$702$	−1.26804e10	+	1.26804e10i	−0.0522139	+	0.0522139i
$703$	−1.10521e11	−	1.10521e11i	−0.452503	−	0.452503i
$704$		−	2.81266e9i		−	0.0114505i
$705$		0			0
$706$	6.59017e10			0.265264
$707$	2.47965e11	−	2.47965e11i	0.992458	−	0.992458i
$708$	−6.25755e10	−	6.25755e10i	−0.249041	−	0.249041i
$709$		−	1.05416e10i		−	0.0417178i	−0.999782	−	0.0208589i	$-0.993360\pi$
$709$		−	1.05416e10i		−	0.0417178i	0.999782	−	0.0208589i	$-0.00664007\pi$
$710$		0			0
$711$	9.22650e10			0.361043
$712$	2.82513e11	−	2.82513e11i	1.09931	−	1.09931i
$713$	−2.25440e11	−	2.25440e11i	−0.872315	−	0.872315i
$714$		−	2.48487e11i		−	0.956116i
$715$		0			0
$716$	2.44405e11			0.929945
$717$	1.13929e11	−	1.13929e11i	0.431082	−	0.431082i
$718$	1.29345e11	+	1.29345e11i	0.486690	+	0.486690i
$719$			4.26585e10i			0.159621i	0.996810	+	0.0798104i	$0.0254315\pi$
$719$			4.26585e10i			0.159621i	−0.996810	+	0.0798104i	$0.974569\pi$
$720$		0			0
$721$	−4.37215e11			−1.61791
$722$	1.17787e11	−	1.17787e11i	0.433460	−	0.433460i
$723$	−8.13339e8	−	8.13339e8i	−0.00297659	−	0.00297659i
$724$		−	4.72347e10i		−	0.171912i
$725$		0			0
$726$	−1.04152e11			−0.374904
$727$	−5.57133e10	+	5.57133e10i	−0.199444	+	0.199444i	−0.799762	−	0.600318i	$-0.795041\pi$
$727$	−5.57133e10	+	5.57133e10i	−0.199444	+	0.199444i	0.600318	+	0.799762i	$0.295041\pi$
$728$	2.03444e11	+	2.03444e11i	0.724303	+	0.724303i
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	4.98826e11			1.74695
$732$	2.53221e9	−	2.53221e9i	0.00881974	−	0.00881974i
$733$	6.92078e10	+	6.92078e10i	0.239739	+	0.239739i	0.816742	−	0.577003i	$-0.195778\pi$
$733$	6.92078e10	+	6.92078e10i	0.239739	+	0.239739i	−0.577003	+	0.816742i	$0.695778\pi$
$734$			8.20702e10i			0.282749i
$735$		0			0
$736$	−3.86795e11			−1.31817
$737$	4.83484e8	−	4.83484e8i	0.00163875	−	0.00163875i
$738$	−4.53562e10	−	4.53562e10i	−0.152901	−	0.152901i
$739$		−	5.42380e11i		−	1.81855i	−0.416193	−	0.909276i	$-0.636636\pi$
$739$		−	5.42380e11i		−	1.81855i	0.416193	−	0.909276i	$-0.363364\pi$
$740$		0			0
$741$	1.43360e11			0.475504
$742$	5.03389e10	−	5.03389e10i	0.166069	−	0.166069i
$743$	1.05763e11	+	1.05763e11i	0.347038	+	0.347038i	0.859005	−	0.511967i	$-0.171083\pi$
$743$	1.05763e11	+	1.05763e11i	0.347038	+	0.347038i	−0.511967	+	0.859005i	$0.671083\pi$
$744$			1.64286e11i			0.536178i
$745$		0			0
$746$	−2.85860e10			−0.0922992
$747$	−1.45821e11	+	1.45821e11i	−0.468314	+	0.468314i
$748$	3.08266e9	+	3.08266e9i	0.00984736	+	0.00984736i
$749$			6.27717e11i			1.99451i
$750$		0			0
$751$	4.27682e11			1.34450			0.672251	−	0.740323i	$-0.265328\pi$
$751$	4.27682e11			1.34450			0.672251	+	0.740323i	$0.265328\pi$
$752$	3.09786e10	−	3.09786e10i	0.0968703	−	0.0968703i
$753$	1.19978e11	+	1.19978e11i	0.373182	+	0.373182i
$754$			4.21116e10i			0.130292i
$755$		0			0
$756$	−6.14806e10			−0.188214
$757$	−2.41193e11	+	2.41193e11i	−0.734482	+	0.734482i	−0.971504	−	0.237022i	$-0.923829\pi$
$757$	−2.41193e11	+	2.41193e11i	−0.734482	+	0.734482i	0.237022	+	0.971504i	$0.423829\pi$
$758$	−9.53677e10	−	9.53677e10i	−0.288885	−	0.288885i
$759$		−	4.16969e9i		−	0.0125643i
$760$		0			0
$761$	−4.31324e11			−1.28607			−0.643035	−	0.765837i	$-0.722325\pi$
$761$	−4.31324e11			−1.28607			−0.643035	+	0.765837i	$0.722325\pi$
$762$	4.64509e10	−	4.64509e10i	0.137776	−	0.137776i
$763$	−1.44931e11	−	1.44931e11i	−0.427627	−	0.427627i
$764$		−	1.68168e11i		−	0.493595i
$765$		0			0
$766$	−2.70431e11			−0.785491
$767$	1.52540e11	−	1.52540e11i	0.440759	−	0.440759i
$768$	1.48132e11	+	1.48132e11i	0.425798	+	0.425798i
$769$			3.88788e11i			1.11175i	0.831265	+	0.555876i	$0.187617\pi$
$769$			3.88788e11i			1.11175i	−0.831265	+	0.555876i	$0.812383\pi$
$770$		0			0
$771$	−6.98658e10			−0.197718
$772$	−2.54077e11	+	2.54077e11i	−0.715313	+	0.715313i
$773$	2.51696e11	+	2.51696e11i	0.704951	+	0.704951i	0.965469	−	0.260518i	$-0.0838933\pi$
$773$	2.51696e11	+	2.51696e11i	0.704951	+	0.704951i	−0.260518	+	0.965469i	$0.583893\pi$
$774$			9.00630e10i			0.250947i
$775$		0			0
$776$	4.20782e11			1.16041
$777$	−1.15540e11	+	1.15540e11i	−0.316992	+	0.316992i
$778$	−1.24675e10	−	1.24675e10i	−0.0340300	−	0.0340300i
$779$			5.12778e11i			1.39245i
$780$		0			0
$781$	4.87390e9			0.0131000
$782$	−3.52472e11	+	3.52472e11i	−0.942534	+	0.942534i
$783$	−1.73694e10	−	1.73694e10i	−0.0462101	−	0.0462101i
$784$		−	6.16462e10i		−	0.163171i
$785$		0			0
$786$	−1.52525e11			−0.399624
$787$	−1.31260e10	+	1.31260e10i	−0.0342162	+	0.0342162i	−0.724008	−	0.689792i	$-0.757702\pi$
$787$	−1.31260e10	+	1.31260e10i	−0.0342162	+	0.0342162i	0.689792	+	0.724008i	$0.257702\pi$
$788$	6.18069e10	+	6.18069e10i	0.160299	+	0.160299i
$789$			1.91582e11i			0.494363i
$790$		0			0
$791$	−6.96431e11			−1.77898
$792$	−1.51930e9	+	1.51930e9i	−0.00386138	+	0.00386138i
$793$	6.17274e9	+	6.17274e9i	0.0156094	+	0.0156094i
$794$		−	2.37854e11i		−	0.598451i
$795$		0			0
$796$	1.58352e11			0.394430
$797$	−3.27472e11	+	3.27472e11i	−0.811598	+	0.811598i	−0.984873	−	0.173275i	$-0.944565\pi$
$797$	−3.27472e11	+	3.27472e11i	−0.811598	+	0.811598i	0.173275	+	0.984873i	$0.444565\pi$
$798$	−2.53608e11	−	2.53608e11i	−0.625391	−	0.625391i
$799$			9.60121e11i			2.35580i
$800$		0			0
$801$	−2.08118e11			−0.505568
$802$	2.70407e10	−	2.70407e10i	0.0653613	−	0.0653613i
$803$	6.75628e9	+	6.75628e9i	0.0162497	+	0.0162497i
$804$			2.02240e10i			0.0483998i
$805$		0			0
$806$	−1.46710e11			−0.347631
$807$	1.57284e11	−	1.57284e11i	0.370842	−	0.370842i
$808$	2.56318e11	+	2.56318e11i	0.601359	+	0.601359i
$809$		−	4.89700e11i		−	1.14324i	−0.820520	−	0.571618i	$-0.806316\pi$
$809$		−	4.89700e11i		−	1.14324i	0.820520	−	0.571618i	$-0.193684\pi$
$810$		0			0
$811$	−3.61409e10			−0.0835441			−0.0417721	−	0.999127i	$-0.513300\pi$
$811$	−3.61409e10			−0.0835441			−0.0417721	+	0.999127i	$0.513300\pi$
$812$	−1.02088e11	+	1.02088e11i	−0.234829	+	0.234829i
$813$	−1.64775e11	−	1.64775e11i	−0.377164	−	0.377164i
$814$			2.09193e9i			0.00476486i
$815$		0			0
$816$	3.38145e10			0.0762679
$817$	5.09107e11	−	5.09107e11i	1.14267	−	1.14267i
$818$	1.79908e11	+	1.79908e11i	0.401826	+	0.401826i
$819$		−	1.49871e11i		−	0.333105i
$820$		0			0
$821$	−4.23338e11			−0.931782			−0.465891	−	0.884842i	$-0.654266\pi$
$821$	−4.23338e11			−0.931782			−0.465891	+	0.884842i	$0.654266\pi$
$822$	−2.45280e10	+	2.45280e10i	−0.0537247	+	0.0537247i
$823$	−4.30103e11	−	4.30103e11i	−0.937504	−	0.937504i	0.0606548	−	0.998159i	$-0.480681\pi$
$823$	−4.30103e11	−	4.30103e11i	−0.937504	−	0.937504i	−0.998159	+	0.0606548i	$0.980681\pi$
$824$		−	4.51944e11i		−	0.980339i
$825$		0			0
$826$	−5.39695e11			−1.15939
$827$	−6.80948e10	+	6.80948e10i	−0.145577	+	0.145577i	−0.776139	−	0.630562i	$-0.782824\pi$
$827$	−6.80948e10	+	6.80948e10i	−0.145577	+	0.145577i	0.630562	+	0.776139i	$0.282824\pi$
$828$	8.72086e10	+	8.72086e10i	0.185540	+	0.185540i
$829$			1.19925e11i			0.253917i	0.991908	+	0.126959i	$0.0405216\pi$
$829$			1.19925e11i			0.253917i	−0.991908	+	0.126959i	$0.959478\pi$
$830$		0			0
$831$	−1.50731e11			−0.316081
$832$	−1.43400e11	+	1.43400e11i	−0.299266	+	0.299266i
$833$	9.55301e11	+	9.55301e11i	1.98409	+	1.98409i
$834$			2.55970e11i			0.529085i
$835$		0			0
$836$	6.29239e9			0.0128822
$837$	6.05119e10	−	6.05119e10i	0.123293	−	0.123293i
$838$	1.52321e11	+	1.52321e11i	0.308876	+	0.308876i
$839$		−	6.96840e11i		−	1.40632i	−0.711030	−	0.703162i	$-0.751771\pi$
$839$		−	6.96840e11i		−	1.40632i	0.711030	−	0.703162i	$-0.248229\pi$
$840$		0			0
$841$	4.42563e11			0.884690
$842$	1.12457e11	−	1.12457e11i	0.223738	−	0.223738i
$843$	3.32887e10	+	3.32887e10i	0.0659153	+	0.0659153i
$844$		−	3.35835e11i		−	0.661844i
$845$		0			0
$846$	−1.73350e11			−0.338409
$847$	6.15487e11	−	6.15487e11i	1.19587	−	1.19587i
$848$	6.85020e9	+	6.85020e9i	0.0132471	+	0.0132471i
$849$			2.07996e11i			0.400335i
$850$		0			0
$851$	3.27781e11			0.624979
$852$	−1.01937e11	+	1.01937e11i	−0.193452	+	0.193452i
$853$	7.32617e11	+	7.32617e11i	1.38382	+	1.38382i	0.837711	+	0.546114i	$0.183894\pi$
$853$	7.32617e11	+	7.32617e11i	1.38382	+	1.38382i	0.546114	+	0.837711i	$0.316106\pi$
$854$		−	2.18396e10i		−	0.0410594i
$855$		0			0
$856$	−6.48864e11			−1.20853
$857$	4.50953e11	−	4.50953e11i	0.836003	−	0.836003i	−0.152327	−	0.988330i	$-0.548677\pi$
$857$	4.50953e11	−	4.50953e11i	0.836003	−	0.836003i	0.988330	+	0.152327i	$0.0486768\pi$
$858$	−1.35675e9	−	1.35675e9i	−0.00250353	−	0.00250353i
$859$			3.74865e11i			0.688498i	0.938878	+	0.344249i	$0.111866\pi$
$859$			3.74865e11i			0.688498i	−0.938878	+	0.344249i	$0.888134\pi$
$860$		0			0
$861$	5.36067e11			0.975452
$862$	−2.23578e11	+	2.23578e11i	−0.404949	+	0.404949i
$863$	−3.89133e11	−	3.89133e11i	−0.701545	−	0.701545i	0.263197	−	0.964742i	$-0.415223\pi$
$863$	−3.89133e11	−	3.89133e11i	−0.701545	−	0.701545i	−0.964742	+	0.263197i	$0.915223\pi$
$864$		−	1.03822e11i		−	0.186310i
$865$		0			0
$866$	4.85618e10			0.0863421
$867$	−2.93331e11	+	2.93331e11i	−0.519137	+	0.519137i
$868$	−3.55658e11	−	3.55658e11i	−0.626548	−	0.626548i
$869$			9.87198e9i			0.0173111i
$870$		0			0
$871$	−4.92999e10			−0.0856590
$872$	1.49814e11	−	1.49814e11i	0.259111	−	0.259111i
$873$	−1.54988e11	−	1.54988e11i	−0.266834	−	0.266834i
$874$			7.19472e11i			1.23301i
$875$		0			0
$876$	−2.82614e11			−0.479928
$877$	−6.11606e11	+	6.11606e11i	−1.03389	+	1.03389i	−0.0344816	+	0.999405i	$0.510978\pi$
$877$	−6.11606e11	+	6.11606e11i	−1.03389	+	1.03389i	−0.999405	+	0.0344816i	$0.989022\pi$
$878$	−2.27634e11	−	2.27634e11i	−0.383053	−	0.383053i
$879$			2.38142e11i			0.398914i
$880$		0			0
$881$	7.94059e11			1.31810			0.659051	−	0.752098i	$-0.270958\pi$
$881$	7.94059e11			1.31810			0.659051	+	0.752098i	$0.270958\pi$
$882$	−1.72479e11	+	1.72479e11i	−0.285012	+	0.285012i
$883$	−3.03612e11	−	3.03612e11i	−0.499433	−	0.499433i	0.411829	−	0.911261i	$-0.364890\pi$
$883$	−3.03612e11	−	3.03612e11i	−0.499433	−	0.499433i	−0.911261	+	0.411829i	$0.864890\pi$
$884$		−	3.14333e11i		−	0.514731i
$885$		0			0
$886$	5.27803e11			0.856519
$887$	4.14795e11	−	4.14795e11i	0.670099	−	0.670099i	−0.287639	−	0.957739i	$-0.592870\pi$
$887$	4.14795e11	−	4.14795e11i	0.670099	−	0.670099i	0.957739	+	0.287639i	$0.0928705\pi$
$888$	−1.19432e11	−	1.19432e11i	−0.192075	−	0.192075i
$889$			5.49005e11i			0.878961i
$890$		0			0
$891$	1.11921e9			0.00177583
$892$	2.95368e11	−	2.95368e11i	0.466556	−	0.466556i
$893$	9.79909e11	+	9.79909e11i	1.54092	+	1.54092i
$894$		−	4.37034e11i		−	0.684171i
$895$		0			0
$896$	−5.48146e11			−0.850481
$897$	−2.12587e11	+	2.12587e11i	−0.328373	+	0.328373i
$898$	−2.39155e11	−	2.39155e11i	−0.367769	−	0.367769i
$899$		−	2.00960e11i		−	0.307659i
$900$		0			0
$901$	−2.12308e11			−0.322157
$902$	4.85293e9	−	4.85293e9i	0.00733124	−	0.00733124i
$903$	−5.32229e11	−	5.32229e11i	−0.800475	−	0.800475i
$904$		−	7.19892e11i		−	1.07794i
$905$		0			0
$906$	3.91716e11			0.581377
$907$	−3.55586e10	+	3.55586e10i	−0.0525431	+	0.0525431i	−0.732890	−	0.680347i	$-0.761829\pi$
$907$	−3.55586e10	+	3.55586e10i	−0.0525431	+	0.0525431i	0.680347	+	0.732890i	$0.261829\pi$
$908$	−1.95540e11	−	1.95540e11i	−0.287668	−	0.287668i
$909$		−	1.88821e11i		−	0.276563i
$910$		0			0
$911$	6.34952e11			0.921866			0.460933	−	0.887435i	$-0.347515\pi$
$911$	6.34952e11			0.921866			0.460933	+	0.887435i	$0.347515\pi$
$912$	3.45114e10	−	3.45114e10i	0.0498865	−	0.0498865i
$913$	−1.56022e10	−	1.56022e10i	−0.0224545	−	0.0224545i
$914$		−	2.77955e11i		−	0.398280i
$915$		0			0
$916$	3.00614e11			0.427000
$917$	9.01352e11	−	9.01352e11i	1.27473	−	1.27473i
$918$	−9.46093e10	−	9.46093e10i	−0.133218	−	0.133218i
$919$		−	6.02787e11i		−	0.845087i	−0.906343	−	0.422544i	$-0.861137\pi$
$919$		−	6.02787e11i		−	0.845087i	0.906343	−	0.422544i	$-0.138863\pi$
$920$		0			0
$921$	−8.14872e11			−1.13253
$922$	−2.67853e11	+	2.67853e11i	−0.370658	+	0.370658i
$923$	−2.48491e11	−	2.48491e11i	−0.342376	−	0.342376i
$924$		−	6.57818e9i		−	0.00902438i
$925$		0			0
$926$	8.71421e11			1.18518
$927$	−1.66466e11	+	1.66466e11i	−0.225427	+	0.225427i
$928$	−1.72397e11	−	1.72397e11i	−0.232454	−	0.232454i
$929$		−	4.56084e11i		−	0.612325i	−0.951979	−	0.306162i	$-0.900955\pi$
$929$		−	4.56084e11i		−	0.612325i	0.951979	−	0.306162i	$-0.0990451\pi$
$930$		0			0
$931$	1.94998e12			2.59556
$932$	−2.23572e11	+	2.23572e11i	−0.296315	+	0.296315i
$933$	2.85327e11	+	2.85327e11i	0.376544	+	0.376544i
$934$			5.02934e11i			0.660881i
$935$		0			0
$936$	1.54920e11			0.201838
$937$	5.21851e11	−	5.21851e11i	0.676999	−	0.676999i	−0.282321	−	0.959320i	$-0.591104\pi$
$937$	5.21851e11	−	5.21851e11i	0.676999	−	0.676999i	0.959320	+	0.282321i	$0.0911043\pi$
$938$	8.72132e10	+	8.72132e10i	0.112660	+	0.112660i
$939$			1.96046e11i			0.252172i
$940$		0			0
$941$	−4.50973e11			−0.575164			−0.287582	−	0.957756i	$-0.592851\pi$
$941$	−4.50973e11			−0.575164			−0.287582	+	0.957756i	$0.592851\pi$
$942$	−2.32600e11	+	2.32600e11i	−0.295397	+	0.295397i
$943$	−7.60395e11	−	7.60395e11i	−0.961596	−	0.961596i
$944$		−	7.34425e10i		−	0.0924825i
$945$		0			0
$946$	−9.63637e9			−0.0120323
$947$	−6.03954e11	+	6.03954e11i	−0.750938	+	0.750938i	−0.974654	−	0.223717i	$-0.928181\pi$
$947$	−6.03954e11	+	6.03954e11i	−0.750938	+	0.750938i	0.223717	+	0.974654i	$0.428181\pi$
$948$	−2.06471e11	−	2.06471e11i	−0.255638	−	0.255638i
$949$		−	6.88923e11i		−	0.849388i
$950$		0			0
$951$	−1.31171e11			−0.160367
$952$	−1.51791e12	+	1.51791e12i	−1.84798	+	1.84798i
$953$	−3.12224e11	−	3.12224e11i	−0.378525	−	0.378525i	0.492045	−	0.870570i	$-0.336250\pi$
$953$	−3.12224e11	−	3.12224e11i	−0.378525	−	0.378525i	−0.870570	+	0.492045i	$0.836250\pi$
$954$		−	3.83322e10i		−	0.0462776i
$955$		0			0
$956$	−5.09904e11			−0.610460
$957$	1.85845e9	−	1.85845e9i	0.00221566	−	0.00221566i
$958$	2.97860e11	+	2.97860e11i	0.353631	+	0.353631i
$959$		−	2.89897e11i		−	0.342744i
$960$		0			0
$961$	−1.52782e11			−0.179135
$962$	1.06655e11	−	1.06655e11i	0.124532	−	0.124532i
$963$	2.38998e11	+	2.38998e11i	0.277900	+	0.277900i
$964$			3.64019e9i			0.00421518i
$965$		0			0
$966$	7.52148e11			0.863763
$967$	4.38145e11	−	4.38145e11i	0.501086	−	0.501086i	−0.410689	−	0.911775i	$-0.634712\pi$
$967$	4.38145e11	−	4.38145e11i	0.501086	−	0.501086i	0.911775	+	0.410689i	$0.134712\pi$
$968$	6.36222e11	+	6.36222e11i	0.724615	+	0.724615i
$969$			1.06961e12i			1.21320i
$970$		0			0
$971$	6.08079e11			0.684042			0.342021	−	0.939692i	$-0.388889\pi$
$971$	6.08079e11			0.684042			0.342021	+	0.939692i	$0.388889\pi$
$972$	−2.34082e10	+	2.34082e10i	−0.0262243	+	0.0262243i
$973$	−1.51266e12	−	1.51266e12i	−1.68768	−	1.68768i
$974$		−	5.25798e11i		−	0.584229i
$975$		0			0
$976$	2.97196e9			0.00327525
$977$	4.16556e10	−	4.16556e10i	0.0457188	−	0.0457188i	−0.683878	−	0.729597i	$-0.739708\pi$
$977$	4.16556e10	−	4.16556e10i	0.0457188	−	0.0457188i	0.729597	+	0.683878i	$0.239708\pi$
$978$	−2.21875e11	−	2.21875e11i	−0.242523	−	0.242523i
$979$		−	2.22678e10i		−	0.0242407i
$980$		0			0
$981$	−1.10363e11			−0.119165
$982$	4.06134e11	−	4.06134e11i	0.436740	−	0.436740i
$983$	−1.07485e12	−	1.07485e12i	−1.15116	−	1.15116i	−0.986321	−	0.164835i	$-0.947291\pi$
$983$	−1.07485e12	−	1.07485e12i	−1.15116	−	1.15116i	−0.164835	−	0.986321i	$-0.552709\pi$
$984$			5.54126e11i			0.591055i
$985$		0			0
$986$	−3.14197e11			−0.332425
$987$	1.02441e12	−	1.02441e12i	1.07946	−	1.07946i
$988$	−3.20811e11	−	3.20811e11i	−0.336683	−	0.336683i
$989$			1.50990e12i			1.57821i
$990$		0			0
$991$	−1.59918e12			−1.65807			−0.829036	−	0.559195i	$-0.811110\pi$
$991$	−1.59918e12			−1.65807			−0.829036	+	0.559195i	$0.811110\pi$
$992$	6.00600e11	−	6.00600e11i	0.620210	−	0.620210i
$993$	1.42455e11	+	1.42455e11i	0.146514	+	0.146514i
$994$			8.79176e11i			0.900597i
$995$		0			0
$996$	6.52638e11			0.663185
$997$	1.98545e11	−	1.98545e11i	0.200946	−	0.200946i	−0.599459	−	0.800405i	$-0.704618\pi$
$997$	1.98545e11	−	1.98545e11i	0.200946	−	0.200946i	0.800405	+	0.599459i	$0.204618\pi$
$998$	−1.59926e11	−	1.59926e11i	−0.161212	−	0.161212i
$999$			8.79818e10i			0.0883346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.a.43.1	yes	4
5.2	odd	4	inner	75.9.f.a.7.1	✓	4
5.3	odd	4	inner	75.9.f.a.7.2	yes	4
5.4	even	2	inner	75.9.f.a.43.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.f.a.7.1	✓	4	5.2	odd	4	inner
75.9.f.a.7.2	yes	4	5.3	odd	4	inner
75.9.f.a.43.1	yes	4	1.1	even	1	trivial
75.9.f.a.43.2	yes	4	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-7.34847 + 7.34847i) q^{2} +(-33.0681 - 33.0681i) q^{3} +148.000i q^{4} +486.000 q^{6} +(-2872.03 + 2872.03i) q^{7} +(-2968.78 - 2968.78i) q^{8} +2187.00i q^{9} -234.000 q^{11} +(4894.08 - 4894.08i) q^{12} +(11930.2 + 11930.2i) q^{13} -42210.0i q^{14} +5744.00 q^{16} +(-89012.0 + 89012.0i) q^{17} +(-16071.1 - 16071.1i) q^{18} +181693. i q^{19} +189945. q^{21} +(1719.54 - 1719.54i) q^{22} +(-269432. - 269432. i) q^{23} +196344. i q^{24} -175338. q^{26} +(72320.0 - 72320.0i) q^{27} +(-425060. - 425060. i) q^{28} -240174. i q^{29} +836725. q^{31} +(717798. - 717798. i) q^{32} +(7737.94 + 7737.94i) q^{33} -1.30820e6i q^{34} -323676. q^{36} +(-608282. + 608282. i) q^{37} +(-1.33517e6 - 1.33517e6i) q^{38} -789021. i q^{39} +2.82222e6 q^{41} +(-1.39580e6 + 1.39580e6i) q^{42} +(-2.80202e6 - 2.80202e6i) q^{43} -34632.0i q^{44} +3.95982e6 q^{46} +(5.39321e6 - 5.39321e6i) q^{47} +(-189943. - 189943. i) q^{48} -1.07323e7i q^{49} +5.88692e6 q^{51} +(-1.76568e6 + 1.76568e6i) q^{52} +(1.19258e6 + 1.19258e6i) q^{53} +1.06288e6i q^{54} +1.70528e7 q^{56} +(6.00824e6 - 6.00824e6i) q^{57} +(1.76491e6 + 1.76491e6i) q^{58} -1.27860e7i q^{59} +517403. q^{61} +(-6.14865e6 + 6.14865e6i) q^{62} +(-6.28112e6 - 6.28112e6i) q^{63} +1.20199e7i q^{64} -113724. q^{66} +(-2.06617e6 + 2.06617e6i) q^{67} +(-1.31738e7 - 1.31738e7i) q^{68} +1.78192e7i q^{69} -2.08286e7 q^{71} +(6.49273e6 - 6.49273e6i) q^{72} +(-2.88730e7 - 2.88730e7i) q^{73} -8.93988e6i q^{74} -2.68906e7 q^{76} +(672054. - 672054. i) q^{77} +(5.79810e6 + 5.79810e6i) q^{78} -4.21879e7i q^{79} -4.78297e6 q^{81} +(-2.07390e7 + 2.07390e7i) q^{82} +(6.66763e7 + 6.66763e7i) q^{83} +2.81119e7i q^{84} +4.11811e7 q^{86} +(-7.94210e6 + 7.94210e6i) q^{87} +(694695. + 694695. i) q^{88} +9.51614e7i q^{89} -6.85279e7 q^{91} +(3.98759e7 - 3.98759e7i) q^{92} +(-2.76689e7 - 2.76689e7i) q^{93} +7.92637e7i q^{94} -4.74725e7 q^{96} +(-7.08678e7 + 7.08678e7i) q^{97} +(7.88658e7 + 7.88658e7i) q^{98} -511758. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1944 q^{6}+O(q^{10}) \) 4 * q + 1944 * q^6	\( 4 q + 1944 q^{6} - 936 q^{11} + 22976 q^{16} + 759780 q^{21} - 701352 q^{26} + 3346900 q^{31} - 1294704 q^{36} + 11288880 q^{41} + 15839280 q^{46} + 23547672 q^{51} + 68211360 q^{56} + 2069612 q^{61} - 454896 q^{66} - 83314512 q^{71} - 107562256 q^{76} - 19131876 q^{81} + 164724264 q^{86} - 274111740 q^{91} - 189889920 q^{96}+O(q^{100}) \) 4 * q + 1944 * q^6 - 936 * q^11 + 22976 * q^16 + 759780 * q^21 - 701352 * q^26 + 3346900 * q^31 - 1294704 * q^36 + 11288880 * q^41 + 15839280 * q^46 + 23547672 * q^51 + 68211360 * q^56 + 2069612 * q^61 - 454896 * q^66 - 83314512 * q^71 - 107562256 * q^76 - 19131876 * q^81 + 164724264 * q^86 - 274111740 * q^91 - 189889920 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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