LMFDB - Embedded newform 75.9.f.e.7.7

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4140 x^{13} + 1109893 x^{12} - 3063780 x^{11} + 8569800 x^{10} - 2336277960 x^{9} + \cdots + 66\!\cdots\!00 $ x^16 - 4140x^13 + 1109893x^12 - 3063780x^11 + 8569800x^10 - 2336277960x^9 + 311176823556x^8 - 1727244961920x^7 + 4854003667200x^6 - 30001722912000x^5 + 6803138028400000x^4 - 35113381084800000x^3 + 91055220768000000x^2 - 110364533280000000*x + 66884304400000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{20}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.7
Root			$-20.7939 - 20.7939i$ of defining polynomial
Character	$\chi$	$=$	75.7
Dual form			75.9.f.e.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(18.3444 + 18.3444i) q^{2} +(33.0681 - 33.0681i) q^{3} +417.032i q^{4} +1213.23 q^{6} +(1693.91 + 1693.91i) q^{7} +(-2954.03 + 2954.03i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(18.3444 + 18.3444i) q^{2} +(33.0681 - 33.0681i) q^{3} +417.032i q^{4} +1213.23 q^{6} +(1693.91 + 1693.91i) q^{7} +(-2954.03 + 2954.03i) q^{8} -2187.00i q^{9} +25244.5 q^{11} +(13790.5 + 13790.5i) q^{12} +(-11411.4 + 11411.4i) q^{13} +62147.4i q^{14} -1619.57 q^{16} +(-38525.0 - 38525.0i) q^{17} +(40119.1 - 40119.1i) q^{18} +25004.0i q^{19} +112029. q^{21} +(463094. + 463094. i) q^{22} +(-341797. + 341797. i) q^{23} +195369. i q^{24} -418671. q^{26} +(-72320.0 - 72320.0i) q^{27} +(-706414. + 706414. i) q^{28} +898012. i q^{29} +722476. q^{31} +(726523. + 726523. i) q^{32} +(834787. - 834787. i) q^{33} -1.41343e6i q^{34} +912049. q^{36} +(744870. + 744870. i) q^{37} +(-458683. + 458683. i) q^{38} +754709. i q^{39} +372769. q^{41} +(2.05510e6 + 2.05510e6i) q^{42} +(2.18643e6 - 2.18643e6i) q^{43} +1.05278e7i q^{44} -1.25401e7 q^{46} +(-4.50830e6 - 4.50830e6i) q^{47} +(-53556.0 + 53556.0i) q^{48} -26154.4i q^{49} -2.54790e6 q^{51} +(-4.75893e6 - 4.75893e6i) q^{52} +(-910386. + 910386. i) q^{53} -2.65333e6i q^{54} -1.00077e7 q^{56} +(826835. + 826835. i) q^{57} +(-1.64735e7 + 1.64735e7i) q^{58} -2.21256e7i q^{59} -1.14825e7 q^{61} +(1.32534e7 + 1.32534e7i) q^{62} +(3.70458e6 - 3.70458e6i) q^{63} +2.70698e7i q^{64} +3.06273e7 q^{66} +(-4.80945e6 - 4.80945e6i) q^{67} +(1.60662e7 - 1.60662e7i) q^{68} +2.26052e7i q^{69} +2.76149e7 q^{71} +(6.46047e6 + 6.46047e6i) q^{72} +(-1.10501e6 + 1.10501e6i) q^{73} +2.73284e7i q^{74} -1.04275e7 q^{76} +(4.27618e7 + 4.27618e7i) q^{77} +(-1.38447e7 + 1.38447e7i) q^{78} -5.65305e7i q^{79} -4.78297e6 q^{81} +(6.83822e6 + 6.83822e6i) q^{82} +(4.51308e7 - 4.51308e7i) q^{83} +4.67195e7i q^{84} +8.02173e7 q^{86} +(2.96955e7 + 2.96955e7i) q^{87} +(-7.45730e7 + 7.45730e7i) q^{88} -1.92663e7i q^{89} -3.86598e7 q^{91} +(-1.42540e8 - 1.42540e8i) q^{92} +(2.38909e7 - 2.38909e7i) q^{93} -1.65404e8i q^{94} +4.80495e7 q^{96} +(-1.54709e7 - 1.54709e7i) q^{97} +(479785. - 479785. i) q^{98} -5.52096e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8	$ 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) $ 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8 - 23616 * q^11 - 22680 * q^12 - 133420 * q^13 - 471380 * q^16 - 573300 * q^17 + 163944 * q^21 + 234700 * q^22 - 651480 * q^23 - 448848 * q^26 + 3567940 * q^28 + 1311776 * q^31 - 641460 * q^32 + 3815100 * q^33 + 5519988 * q^36 + 3607340 * q^37 - 8139840 * q^38 - 14740104 * q^41 + 9643860 * q^42 + 4805480 * q^43 + 14024216 * q^46 - 26529600 * q^47 - 3661200 * q^48 - 6168312 * q^51 + 15861080 * q^52 - 16612140 * q^53 + 10752000 * q^56 - 4714200 * q^57 - 63562980 * q^58 - 12550600 * q^61 + 35190840 * q^62 - 9928980 * q^63 + 46958616 * q^66 - 46836760 * q^67 + 197811840 * q^68 - 85681968 * q^71 + 38185020 * q^72 + 50835800 * q^73 + 101166648 * q^76 - 97175880 * q^77 - 131709240 * q^78 - 76527504 * q^81 + 181542400 * q^82 + 208234800 * q^83 - 187512576 * q^86 + 74298060 * q^87 - 138207420 * q^88 + 38623856 * q^91 - 652331400 * q^92 - 159787080 * q^93 + 531512604 * q^96 + 138370520 * q^97 + 50186520 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	18.3444	+	18.3444i	1.14652	+	1.14652i	0.987232	+	0.159292i	$0.0509211\pi$
$2$	18.3444	+	18.3444i	1.14652	+	1.14652i	0.159292	+	0.987232i	$0.449079\pi$
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$3$	33.0681	−	33.0681i	0.408248	−	0.408248i
$4$			417.032i			1.62903i
$5$		0			0
$5$		0			0
$6$	1213.23			0.936132
$7$	1693.91	+	1693.91i	0.705501	+	0.705501i	0.965586	−	0.260085i	$-0.0837505\pi$
$7$	1693.91	+	1693.91i	0.705501	+	0.705501i	−0.260085	+	0.965586i	$0.583751\pi$
$8$	−2954.03	+	2954.03i	−0.721200	+	0.721200i
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	25244.5			1.72423			0.862115	−	0.506712i	$-0.169139\pi$
$11$	25244.5			1.72423			0.862115	+	0.506712i	$0.169139\pi$
$12$	13790.5	+	13790.5i	0.665049	+	0.665049i
$13$	−11411.4	+	11411.4i	−0.399546	+	0.399546i	−0.878073	−	0.478527i	$-0.841171\pi$
$13$	−11411.4	+	11411.4i	−0.399546	+	0.399546i	0.478527	+	0.878073i	$0.341171\pi$
$14$			62147.4i			1.61775i
$15$		0			0
$16$	−1619.57			−0.0247126
$17$	−38525.0	−	38525.0i	−0.461261	−	0.461261i	0.437808	−	0.899069i	$-0.355755\pi$
$17$	−38525.0	−	38525.0i	−0.461261	−	0.461261i	−0.899069	+	0.437808i	$0.855755\pi$
$18$	40119.1	−	40119.1i	0.382174	−	0.382174i
$19$			25004.0i			0.191865i	0.995388	+	0.0959323i	$0.0305832\pi$
$19$			25004.0i			0.191865i	−0.995388	+	0.0959323i	$0.969417\pi$
$20$		0			0
$21$	112029.			0.576039
$22$	463094.	+	463094.i	1.97687	+	1.97687i
$23$	−341797.	+	341797.i	−1.22140	+	1.22140i	−0.254263	+	0.967135i	$0.581833\pi$
$23$	−341797.	+	341797.i	−1.22140	+	1.22140i	−0.967135	+	0.254263i	$0.918167\pi$
$24$			195369.i			0.588857i
$25$		0			0
$26$	−418671.			−0.916177
$27$	−72320.0	−	72320.0i	−0.136083	−	0.136083i
$28$	−706414.	+	706414.i	−1.14928	+	1.14928i
$29$			898012.i			1.26967i	0.772649	+	0.634834i	$0.218931\pi$
$29$			898012.i			1.26967i	−0.772649	+	0.634834i	$0.781069\pi$
$30$		0			0
$31$	722476.			0.782306			0.391153	−	0.920326i	$-0.372076\pi$
$31$	722476.			0.782306			0.391153	+	0.920326i	$0.372076\pi$
$32$	726523.	+	726523.i	0.692866	+	0.692866i
$33$	834787.	−	834787.i	0.703914	−	0.703914i
$34$		−	1.41343e6i		−	1.05769i
$35$		0			0
$36$	912049.			0.543011
$37$	744870.	+	744870.i	0.397442	+	0.397442i	0.877330	−	0.479888i	$-0.159323\pi$
$37$	744870.	+	744870.i	0.397442	+	0.397442i	−0.479888	+	0.877330i	$0.659323\pi$
$38$	−458683.	+	458683.i	−0.219977	+	0.219977i
$39$			754709.i			0.326228i
$40$		0			0
$41$	372769.			0.131918			0.0659591	−	0.997822i	$-0.478989\pi$
$41$	372769.			0.131918			0.0659591	+	0.997822i	$0.478989\pi$
$42$	2.05510e6	+	2.05510e6i	0.660442	+	0.660442i
$43$	2.18643e6	−	2.18643e6i	0.639530	−	0.639530i	−0.310909	−	0.950440i	$-0.600634\pi$
$43$	2.18643e6	−	2.18643e6i	0.639530	−	0.639530i	0.950440	+	0.310909i	$0.100634\pi$
$44$			1.05278e7i			2.80883i
$45$		0			0
$46$	−1.25401e7			−2.80072
$47$	−4.50830e6	−	4.50830e6i	−0.923892	−	0.923892i	0.0734097	−	0.997302i	$-0.476612\pi$
$47$	−4.50830e6	−	4.50830e6i	−0.923892	−	0.923892i	−0.997302	+	0.0734097i	$0.976612\pi$
$48$	−53556.0	+	53556.0i	−0.0100889	+	0.0100889i
$49$		−	26154.4i		−	0.00453691i
$50$		0			0
$51$	−2.54790e6			−0.376618
$52$	−4.75893e6	−	4.75893e6i	−0.650873	−	0.650873i
$53$	−910386.	+	910386.i	−0.115378	+	0.115378i	−0.762438	−	0.647061i	$-0.775998\pi$
$53$	−910386.	+	910386.i	−0.115378	+	0.115378i	0.647061	+	0.762438i	$0.275998\pi$
$54$		−	2.65333e6i		−	0.312044i
$55$		0			0
$56$	−1.00077e7			−1.01761
$57$	826835.	+	826835.i	0.0783284	+	0.0783284i
$58$	−1.64735e7	+	1.64735e7i	−1.45570	+	1.45570i
$59$		−	2.21256e7i		−	1.82594i	−0.408024	−	0.912971i	$-0.633782\pi$
$59$		−	2.21256e7i		−	1.82594i	0.408024	−	0.912971i	$-0.366218\pi$
$60$		0			0
$61$	−1.14825e7			−0.829311			−0.414655	−	0.909979i	$-0.636098\pi$
$61$	−1.14825e7			−0.829311			−0.414655	+	0.909979i	$0.636098\pi$
$62$	1.32534e7	+	1.32534e7i	0.896932	+	0.896932i
$63$	3.70458e6	−	3.70458e6i	0.235167	−	0.235167i
$64$			2.70698e7i			1.61349i
$65$		0			0
$66$	3.06273e7			1.61411
$67$	−4.80945e6	−	4.80945e6i	−0.238669	−	0.238669i	0.577630	−	0.816299i	$-0.303978\pi$
$67$	−4.80945e6	−	4.80945e6i	−0.238669	−	0.238669i	−0.816299	+	0.577630i	$0.803978\pi$
$68$	1.60662e7	−	1.60662e7i	0.751409	−	0.751409i
$69$			2.26052e7i			0.997267i
$70$		0			0
$71$	2.76149e7			1.08670			0.543351	−	0.839505i	$-0.317155\pi$
$71$	2.76149e7			1.08670			0.543351	+	0.839505i	$0.317155\pi$
$72$	6.46047e6	+	6.46047e6i	0.240400	+	0.240400i
$73$	−1.10501e6	+	1.10501e6i	−0.0389113	+	0.0389113i	−0.726295	−	0.687383i	$-0.758759\pi$
$73$	−1.10501e6	+	1.10501e6i	−0.0389113	+	0.0389113i	0.687383	+	0.726295i	$0.258759\pi$
$74$			2.73284e7i			0.911353i
$75$		0			0
$76$	−1.04275e7			−0.312554
$77$	4.27618e7	+	4.27618e7i	1.21645	+	1.21645i
$78$	−1.38447e7	+	1.38447e7i	−0.374028	+	0.374028i
$79$		−	5.65305e7i		−	1.45136i	−0.688033	−	0.725679i	$-0.741526\pi$
$79$		−	5.65305e7i		−	1.45136i	0.688033	−	0.725679i	$-0.258474\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	6.83822e6	+	6.83822e6i	0.151247	+	0.151247i
$83$	4.51308e7	−	4.51308e7i	0.950957	−	0.950957i	−0.0478955	−	0.998852i	$-0.515251\pi$
$83$	4.51308e7	−	4.51308e7i	0.950957	−	0.950957i	0.998852	+	0.0478955i	$0.0152515\pi$
$84$			4.67195e7i			0.938386i
$85$		0			0
$86$	8.02173e7			1.46647
$87$	2.96955e7	+	2.96955e7i	0.518339	+	0.518339i
$88$	−7.45730e7	+	7.45730e7i	−1.24351	+	1.24351i
$89$		−	1.92663e7i		−	0.307070i	−0.988143	−	0.153535i	$-0.950934\pi$
$89$		−	1.92663e7i		−	0.307070i	0.988143	−	0.153535i	$-0.0490659\pi$
$90$		0			0
$91$	−3.86598e7			−0.563760
$92$	−1.42540e8	−	1.42540e8i	−1.98970	−	1.98970i
$93$	2.38909e7	−	2.38909e7i	0.319375	−	0.319375i
$94$		−	1.65404e8i		−	2.11853i
$95$		0			0
$96$	4.80495e7			0.565723
$97$	−1.54709e7	−	1.54709e7i	−0.174755	−	0.174755i	0.614310	−	0.789065i	$-0.289434\pi$
$97$	−1.54709e7	−	1.54709e7i	−0.174755	−	0.174755i	−0.789065	+	0.614310i	$0.789434\pi$
$98$	479785.	−	479785.i	0.00520167	−	0.00520167i
$99$		−	5.52096e7i		−	0.574744i
$100$		0			0
$101$	−5.67557e7			−0.545411			−0.272705	−	0.962098i	$-0.587918\pi$
$101$	−5.67557e7			−0.545411			−0.272705	+	0.962098i	$0.587918\pi$
$102$	−4.67396e7	−	4.67396e7i	−0.431801	−	0.431801i
$103$	−6.87607e7	+	6.87607e7i	−0.610930	+	0.610930i	−0.943188	−	0.332258i	$-0.892189\pi$
$103$	−6.87607e7	+	6.87607e7i	−0.610930	+	0.610930i	0.332258	+	0.943188i	$0.392189\pi$
$104$		−	6.74195e7i		−	0.576305i
$105$		0			0
$106$	−3.34009e7			−0.264567
$107$	−7.29346e7	−	7.29346e7i	−0.556415	−	0.556415i	0.371870	−	0.928285i	$-0.378717\pi$
$107$	−7.29346e7	−	7.29346e7i	−0.556415	−	0.556415i	−0.928285	+	0.371870i	$0.878717\pi$
$108$	3.01597e7	−	3.01597e7i	0.221683	−	0.221683i
$109$			4.54558e7i			0.322020i	0.986953	+	0.161010i	$0.0514751\pi$
$109$			4.54558e7i			0.322020i	−0.986953	+	0.161010i	$0.948525\pi$
$110$		0			0
$111$	4.92629e7			0.324510
$112$	−2.74340e6	−	2.74340e6i	−0.0174348	−	0.0174348i
$113$	1.77929e8	−	1.77929e8i	1.09127	−	1.09127i	0.0958771	−	0.995393i	$-0.469434\pi$
$113$	1.77929e8	−	1.77929e8i	1.09127	−	1.09127i	0.995393	−	0.0958771i	$-0.0305656\pi$
$114$			3.03355e7i			0.179611i
$115$		0			0
$116$	−3.74500e8			−2.06833
$117$	2.49568e7	+	2.49568e7i	0.133182	+	0.133182i
$118$	4.05880e8	−	4.05880e8i	2.09349	−	2.09349i
$119$		−	1.30516e8i		−	0.650840i
$120$		0			0
$121$	4.22924e8			1.97297
$122$	−2.10639e8	−	2.10639e8i	−0.950824	−	0.950824i
$123$	1.23268e7	−	1.23268e7i	0.0538554	−	0.0538554i
$124$			3.01296e8i			1.27440i
$125$		0			0
$126$	1.35916e8			0.539249
$127$	2.54460e7	+	2.54460e7i	0.0978150	+	0.0978150i	0.754321	−	0.656506i	$-0.227966\pi$
$127$	2.54460e7	+	2.54460e7i	0.0978150	+	0.0978150i	−0.656506	+	0.754321i	$0.727966\pi$
$128$	−3.10589e8	+	3.10589e8i	−1.15703	+	1.15703i
$129$		−	1.44602e8i		−	0.522174i
$130$		0			0
$131$	−1.31218e8			−0.445563			−0.222782	−	0.974868i	$-0.571514\pi$
$131$	−1.31218e8			−0.445563			−0.222782	+	0.974868i	$0.571514\pi$
$132$	3.48133e8	+	3.48133e8i	1.14670	+	1.14670i
$133$	−4.23545e7	+	4.23545e7i	−0.135361	+	0.135361i
$134$		−	1.76453e8i		−	0.547279i
$135$		0			0
$136$	2.27608e8			0.665322
$137$	−5.64400e7	−	5.64400e7i	−0.160216	−	0.160216i	0.622447	−	0.782662i	$-0.286139\pi$
$137$	−5.64400e7	−	5.64400e7i	−0.160216	−	0.160216i	−0.782662	+	0.622447i	$0.786139\pi$
$138$	−4.14678e8	+	4.14678e8i	−1.14339	+	1.14339i
$139$		−	2.70591e7i		−	0.0724861i	−0.999343	−	0.0362430i	$-0.988461\pi$
$139$		−	2.70591e7i		−	0.0724861i	0.999343	−	0.0362430i	$-0.0115390\pi$
$140$		0			0
$141$	−2.98162e8			−0.754355
$142$	5.06579e8	+	5.06579e8i	1.24593	+	1.24593i
$143$	−2.88075e8	+	2.88075e8i	−0.688909	+	0.688909i
$144$			3.54199e6i			0.00823754i
$145$		0			0
$146$	−4.05416e7			−0.0892255
$147$	−864875.	−	864875.i	−0.00185218	−	0.00185218i
$148$	−3.10635e8	+	3.10635e8i	−0.647446	+	0.647446i
$149$			2.05645e8i			0.417228i	0.977998	+	0.208614i	$0.0668952\pi$
$149$			2.05645e8i			0.417228i	−0.977998	+	0.208614i	$0.933105\pi$
$150$		0			0
$151$	8.09303e6			0.0155670			0.00778348	−	0.999970i	$-0.497522\pi$
$151$	8.09303e6			0.0155670			0.00778348	+	0.999970i	$0.497522\pi$
$152$	−7.38626e7	−	7.38626e7i	−0.138373	−	0.138373i
$153$	−8.42541e7	+	8.42541e7i	−0.153754	+	0.153754i
$154$			1.56888e9i			2.78937i
$155$		0			0
$156$	−3.14738e8			−0.531436
$157$	2.95099e8	+	2.95099e8i	0.485700	+	0.485700i	0.906946	−	0.421246i	$-0.138407\pi$
$157$	2.95099e8	+	2.95099e8i	0.485700	+	0.485700i	−0.421246	+	0.906946i	$0.638407\pi$
$158$	1.03702e9	−	1.03702e9i	1.66402	−	1.66402i
$159$			6.02095e7i			0.0942055i
$160$		0			0
$161$	−1.15795e9			−1.72339
$162$	−8.77406e7	−	8.77406e7i	−0.127391	−	0.127391i
$163$	−3.32640e8	+	3.32640e8i	−0.471221	+	0.471221i	−0.902310	−	0.431089i	$-0.858130\pi$
$163$	−3.32640e8	+	3.32640e8i	−0.471221	+	0.471221i	0.431089	+	0.902310i	$0.358130\pi$
$164$			1.55457e8i			0.214899i
$165$		0			0
$166$	1.65579e9			2.18059
$167$	3.99899e8	+	3.99899e8i	0.514143	+	0.514143i	0.915793	−	0.401650i	$-0.131563\pi$
$167$	3.99899e8	+	3.99899e8i	0.514143	+	0.514143i	−0.401650	+	0.915793i	$0.631563\pi$
$168$	−3.30936e8	+	3.30936e8i	−0.415439	+	0.415439i
$169$			5.55289e8i			0.680726i
$170$		0			0
$171$	5.46837e7			0.0639549
$172$	9.11810e8	+	9.11810e8i	1.04182	+	1.04182i
$173$	−3.06134e8	+	3.06134e8i	−0.341765	+	0.341765i	−0.857030	−	0.515266i	$-0.827693\pi$
$173$	−3.06134e8	+	3.06134e8i	−0.341765	+	0.341765i	0.515266	+	0.857030i	$0.327693\pi$
$174$			1.08949e9i			1.18858i
$175$		0			0
$176$	−4.08851e7			−0.0426103
$177$	−7.31652e8	−	7.31652e8i	−0.745438	−	0.745438i
$178$	3.53428e8	−	3.53428e8i	0.352063	−	0.352063i
$179$		−	1.36846e9i		−	1.33297i	−0.745520	−	0.666483i	$-0.767799\pi$
$179$		−	1.36846e9i		−	1.33297i	0.745520	−	0.666483i	$-0.232201\pi$
$180$		0			0
$181$	−1.78886e9			−1.66672			−0.833359	−	0.552732i	$-0.813585\pi$
$181$	−1.78886e9			−1.66672			−0.833359	+	0.552732i	$0.813585\pi$
$182$	−7.09190e8	−	7.09190e8i	−0.646364	−	0.646364i
$183$	−3.79705e8	+	3.79705e8i	−0.338565	+	0.338565i
$184$		−	2.01936e9i		−	1.76174i
$185$		0			0
$186$	8.76528e8			0.732342
$187$	−9.72542e8	−	9.72542e8i	−0.795320	−	0.795320i
$188$	1.88011e9	−	1.88011e9i	1.50505	−	1.50505i
$189$		−	2.45007e8i		−	0.192013i
$190$		0			0
$191$	7.48859e8			0.562687			0.281343	−	0.959607i	$-0.409220\pi$
$191$	7.48859e8			0.562687			0.281343	+	0.959607i	$0.409220\pi$
$192$	8.95148e8	+	8.95148e8i	0.658703	+	0.658703i
$193$	−2.85639e8	+	2.85639e8i	−0.205868	+	0.205868i	−0.802509	−	0.596641i	$-0.796502\pi$
$193$	−2.85639e8	+	2.85639e8i	−0.205868	+	0.205868i	0.596641	+	0.802509i	$0.296502\pi$
$194$		−	5.67608e8i		−	0.400720i
$195$		0			0
$196$	1.09072e7			0.00739076
$197$	−1.96372e9	−	1.96372e9i	−1.30381	−	1.30381i	−0.925803	−	0.378006i	$-0.876610\pi$
$197$	−1.96372e9	−	1.96372e9i	−1.30381	−	1.30381i	−0.378006	−	0.925803i	$-0.623390\pi$
$198$	1.01279e9	−	1.01279e9i	0.658957	−	0.658957i
$199$		−	2.33013e8i		−	0.148583i	−0.997237	−	0.0742913i	$-0.976331\pi$
$199$		−	2.33013e8i		−	0.148583i	0.997237	−	0.0742913i	$-0.0236695\pi$
$200$		0			0
$201$	−3.18079e8			−0.194873
$202$	−1.04115e9	−	1.04115e9i	−0.625326	−	0.625326i
$203$	−1.52115e9	+	1.52115e9i	−0.895751	+	0.895751i
$204$		−	1.06255e9i		−	0.613523i
$205$		0			0
$206$	−2.52274e9			−1.40089
$207$	7.47510e8	+	7.47510e8i	0.407133	+	0.407133i
$208$	1.84816e7	−	1.84816e7i	0.00987383	−	0.00987383i
$209$			6.31212e8i			0.330819i
$210$		0			0
$211$	−2.23003e9			−1.12507			−0.562537	−	0.826772i	$-0.690175\pi$
$211$	−2.23003e9			−1.12507			−0.562537	+	0.826772i	$0.690175\pi$
$212$	−3.79660e8	−	3.79660e8i	−0.187954	−	0.187954i
$213$	9.13174e8	−	9.13174e8i	0.443644	−	0.443644i
$214$		−	2.67588e9i		−	1.27589i
$215$		0			0
$216$	4.27271e8			0.196286
$217$	1.22381e9	+	1.22381e9i	0.551918	+	0.551918i
$218$	−8.33857e8	+	8.33857e8i	−0.369204	+	0.369204i
$219$			7.30814e7i			0.0317710i
$220$		0			0
$221$	8.79250e8			0.368590
$222$	9.03697e8	+	9.03697e8i	0.372058	+	0.372058i
$223$	4.16515e8	−	4.16515e8i	0.168427	−	0.168427i	−0.617861	−	0.786288i	$-0.712000\pi$
$223$	4.16515e8	−	4.16515e8i	0.168427	−	0.168427i	0.786288	+	0.617861i	$0.212000\pi$
$224$			2.46132e9i			0.977635i
$225$		0			0
$226$	6.52798e9			2.50233
$227$	−3.46295e8	−	3.46295e8i	−0.130420	−	0.130420i	0.638884	−	0.769303i	$-0.279396\pi$
$227$	−3.46295e8	−	3.46295e8i	−0.130420	−	0.130420i	−0.769303	+	0.638884i	$0.779396\pi$
$228$	−3.44817e8	+	3.44817e8i	−0.127599	+	0.127599i
$229$			2.57639e9i			0.936851i	0.883503	+	0.468425i	$0.155179\pi$
$229$			2.57639e9i			0.936851i	−0.883503	+	0.468425i	$0.844821\pi$
$230$		0			0
$231$	2.82810e9			0.993224
$232$	−2.65276e9	−	2.65276e9i	−0.915683	−	0.915683i
$233$	4.53996e8	−	4.53996e8i	0.154038	−	0.154038i	−0.625881	−	0.779919i	$-0.715260\pi$
$233$	4.53996e8	−	4.53996e8i	0.154038	−	0.154038i	0.779919	+	0.625881i	$0.215260\pi$
$234$			9.15634e8i			0.305392i
$235$		0			0
$236$	9.22709e9			2.97452
$237$	−1.86936e9	−	1.86936e9i	−0.592514	−	0.592514i
$238$	2.39423e9	−	2.39423e9i	0.746203	−	0.746203i
$239$		−	1.50644e9i		−	0.461700i	−0.972989	−	0.230850i	$-0.925849\pi$
$239$		−	1.50644e9i		−	0.461700i	0.972989	−	0.230850i	$-0.0741506\pi$
$240$		0			0
$241$	−5.92568e9			−1.75659			−0.878294	−	0.478122i	$-0.841318\pi$
$241$	−5.92568e9			−1.75659			−0.878294	+	0.478122i	$0.841318\pi$
$242$	7.75828e9	+	7.75828e9i	2.26206	+	2.26206i
$243$	−1.58164e8	+	1.58164e8i	−0.0453609	+	0.0453609i
$244$		−	4.78857e9i		−	1.35097i
$245$		0			0
$246$	4.52254e8			0.123493
$247$	−2.85331e8	−	2.85331e8i	−0.0766587	−	0.0766587i
$248$	−2.13422e9	+	2.13422e9i	−0.564199	+	0.564199i
$249$		−	2.98478e9i		−	0.776453i
$250$		0			0
$251$	−9.41585e8			−0.237227			−0.118614	−	0.992940i	$-0.537845\pi$
$251$	−9.41585e8			−0.237227			−0.118614	+	0.992940i	$0.537845\pi$
$252$	1.54493e9	+	1.54493e9i	0.383094	+	0.383094i
$253$	−8.62849e9	+	8.62849e9i	−2.10597	+	2.10597i
$254$			9.33583e8i			0.224294i
$255$		0			0
$256$	−4.46525e9			−1.03965
$257$	−1.20555e9	−	1.20555e9i	−0.276346	−	0.276346i	0.555303	−	0.831648i	$-0.312602\pi$
$257$	−1.20555e9	−	1.20555e9i	−0.276346	−	0.276346i	−0.831648	+	0.555303i	$0.812602\pi$
$258$	2.65263e9	−	2.65263e9i	0.598685	−	0.598685i
$259$			2.52348e9i			0.560791i
$260$		0			0
$261$	1.96395e9			0.423222
$262$	−2.40712e9	−	2.40712e9i	−0.510849	−	0.510849i
$263$	2.85600e9	−	2.85600e9i	0.596946	−	0.596946i	−0.342553	−	0.939499i	$-0.611292\pi$
$263$	2.85600e9	−	2.85600e9i	0.596946	−	0.596946i	0.939499	+	0.342553i	$0.111292\pi$
$264$			4.93198e9i			1.01533i
$265$		0			0
$266$	−1.55393e9			−0.310388
$267$	−6.37100e8	−	6.37100e8i	−0.125361	−	0.125361i
$268$	2.00570e9	−	2.00570e9i	0.388800	−	0.388800i
$269$		−	1.27106e9i		−	0.242749i	−0.992607	−	0.121374i	$-0.961270\pi$
$269$		−	1.27106e9i		−	0.242749i	0.992607	−	0.121374i	$-0.0387301\pi$
$270$		0			0
$271$	−2.85410e9			−0.529166			−0.264583	−	0.964363i	$-0.585234\pi$
$271$	−2.85410e9			−0.529166			−0.264583	+	0.964363i	$0.585234\pi$
$272$	6.23938e7	+	6.23938e7i	0.0113990	+	0.0113990i
$273$	−1.27841e9	+	1.27841e9i	−0.230154	+	0.230154i
$274$		−	2.07071e9i		−	0.367382i
$275$		0			0
$276$	−9.42708e9			−1.62458
$277$	1.48206e9	+	1.48206e9i	0.251737	+	0.251737i	0.821683	−	0.569945i	$-0.193036\pi$
$277$	1.48206e9	+	1.48206e9i	0.251737	+	0.251737i	−0.569945	+	0.821683i	$0.693036\pi$
$278$	4.96383e8	−	4.96383e8i	0.0831070	−	0.0831070i
$279$		−	1.58006e9i		−	0.260769i
$280$		0			0
$281$	4.87341e9			0.781641			0.390820	−	0.920467i	$-0.372191\pi$
$281$	4.87341e9			0.781641			0.390820	+	0.920467i	$0.372191\pi$
$282$	−5.46959e9	−	5.46959e9i	−0.864885	−	0.864885i
$283$	5.00265e9	−	5.00265e9i	0.779928	−	0.779928i	−0.199891	−	0.979818i	$-0.564059\pi$
$283$	5.00265e9	−	5.00265e9i	0.779928	−	0.779928i	0.979818	+	0.199891i	$0.0640587\pi$
$284$			1.15163e10i			1.77027i
$285$		0			0
$286$	−1.05691e10			−1.57970
$287$	6.31437e8	+	6.31437e8i	0.0930684	+	0.0930684i
$288$	1.58890e9	−	1.58890e9i	0.230955	−	0.230955i
$289$		−	4.00741e9i		−	0.574477i
$290$		0			0
$291$	−1.02319e9			−0.142687
$292$	−4.60826e8	−	4.60826e8i	−0.0633878	−	0.0633878i
$293$	6.76531e9	−	6.76531e9i	0.917947	−	0.917947i	−0.0789332	−	0.996880i	$-0.525151\pi$
$293$	6.76531e9	−	6.76531e9i	0.917947	−	0.917947i	0.996880	+	0.0789332i	$0.0251514\pi$
$294$		−	3.17312e7i		−	0.00424715i
$295$		0			0
$296$	−4.40074e9			−0.573270
$297$	−1.82568e9	−	1.82568e9i	−0.234638	−	0.234638i
$298$	−3.77243e9	+	3.77243e9i	−0.478361	+	0.478361i
$299$		−	7.80079e9i		−	0.976009i
$300$		0			0
$301$	7.40721e9			0.902378
$302$	1.48462e8	+	1.48462e8i	0.0178479	+	0.0178479i
$303$	−1.87680e9	+	1.87680e9i	−0.222663	+	0.222663i
$304$		−	4.04956e7i		−	0.00474148i
$305$		0			0
$306$	−3.09118e9			−0.352564
$307$	1.15018e10	+	1.15018e10i	1.29483	+	1.29483i	0.931766	+	0.363060i	$0.118268\pi$
$307$	1.15018e10	+	1.15018e10i	1.29483	+	1.29483i	0.363060	+	0.931766i	$0.381732\pi$
$308$	−1.78330e10	+	1.78330e10i	−1.98163	+	1.98163i
$309$			4.54757e9i			0.498822i
$310$		0			0
$311$	−1.24742e9			−0.133343			−0.0666716	−	0.997775i	$-0.521238\pi$
$311$	−1.24742e9			−0.133343			−0.0666716	+	0.997775i	$0.521238\pi$
$312$	−2.22944e9	−	2.22944e9i	−0.235275	−	0.235275i
$313$	6.03624e9	−	6.03624e9i	0.628911	−	0.628911i	−0.318883	−	0.947794i	$-0.603308\pi$
$313$	6.03624e9	−	6.03624e9i	0.628911	−	0.628911i	0.947794	+	0.318883i	$0.103308\pi$
$314$			1.08268e10i			1.11373i
$315$		0			0
$316$	2.35750e10			2.36431
$317$	8.29996e9	+	8.29996e9i	0.821938	+	0.821938i	0.986386	−	0.164448i	$-0.0525843\pi$
$317$	8.29996e9	+	8.29996e9i	0.821938	+	0.821938i	−0.164448	+	0.986386i	$0.552584\pi$
$318$	−1.10451e9	+	1.10451e9i	−0.108009	+	0.108009i
$319$			2.26698e10i			2.18920i
$320$		0			0
$321$	−4.82362e9			−0.454311
$322$	−2.12418e10	−	2.12418e10i	−1.97591	−	1.97591i
$323$	9.63278e8	−	9.63278e8i	0.0884997	−	0.0884997i
$324$		−	1.99465e9i		−	0.181004i
$325$		0			0
$326$	−1.22042e10			−1.08053
$327$	1.50314e9	+	1.50314e9i	0.131464	+	0.131464i
$328$	−1.10117e9	+	1.10117e9i	−0.0951393	+	0.0951393i
$329$		−	1.52733e10i		−	1.30361i
$330$		0			0
$331$	−4.94937e9			−0.412324			−0.206162	−	0.978518i	$-0.566097\pi$
$331$	−4.94937e9			−0.412324			−0.206162	+	0.978518i	$0.566097\pi$
$332$	1.88210e10	+	1.88210e10i	1.54914	+	1.54914i
$333$	1.62903e9	−	1.62903e9i	0.132481	−	0.132481i
$334$			1.46718e10i			1.17895i
$335$		0			0
$336$	−1.81438e8			−0.0142354
$337$	6.01364e9	+	6.01364e9i	0.466249	+	0.466249i	0.900697	−	0.434448i	$-0.143057\pi$
$337$	6.01364e9	+	6.01364e9i	0.466249	+	0.466249i	−0.434448	+	0.900697i	$0.643057\pi$
$338$	−1.01864e10	+	1.01864e10i	−0.780468	+	0.780468i
$339$		−	1.17675e10i		−	0.891018i
$340$		0			0
$341$	1.82385e10			1.34888
$342$	1.00314e9	+	1.00314e9i	0.0733258	+	0.0733258i
$343$	9.80934e9	−	9.80934e9i	0.708702	−	0.708702i
$344$			1.29176e10i			0.922458i
$345$		0			0
$346$	−1.12317e10			−0.783682
$347$	6.48632e8	+	6.48632e8i	0.0447384	+	0.0447384i	0.729122	−	0.684384i	$-0.239929\pi$
$347$	6.48632e8	+	6.48632e8i	0.0447384	+	0.0447384i	−0.684384	+	0.729122i	$0.739929\pi$
$348$	−1.23840e10	+	1.23840e10i	−0.844391	+	0.844391i
$349$		−	1.43845e10i		−	0.969604i	−0.874624	−	0.484802i	$-0.838892\pi$
$349$		−	1.43845e10i		−	0.969604i	0.874624	−	0.484802i	$-0.161108\pi$
$350$		0			0
$351$	1.65055e9			0.108743
$352$	1.83407e10	+	1.83407e10i	1.19466	+	1.19466i
$353$	−1.05059e10	+	1.05059e10i	−0.676604	+	0.676604i	−0.959230	−	0.282626i	$-0.908795\pi$
$353$	−1.05059e10	+	1.05059e10i	−0.676604	+	0.676604i	0.282626	+	0.959230i	$0.408795\pi$
$354$		−	2.68434e10i		−	1.70932i
$355$		0			0
$356$	8.03466e9			0.500228
$357$	−4.31590e9	−	4.31590e9i	−0.265704	−	0.265704i
$358$	2.51035e10	−	2.51035e10i	1.52828	−	1.52828i
$359$			9.77407e9i			0.588434i	0.955739	+	0.294217i	$0.0950588\pi$
$359$			9.77407e9i			0.588434i	−0.955739	+	0.294217i	$0.904941\pi$
$360$		0			0
$361$	1.63584e10			0.963188
$362$	−3.28155e10	−	3.28155e10i	−1.91093	−	1.91093i
$363$	1.39853e10	−	1.39853e10i	0.805462	−	0.805462i
$364$		−	1.61224e10i		−	0.918383i
$365$		0			0
$366$	−1.39309e10			−0.776344
$367$	−1.25025e10	−	1.25025e10i	−0.689182	−	0.689182i	0.272869	−	0.962051i	$-0.412027\pi$
$367$	−1.25025e10	−	1.25025e10i	−0.689182	−	0.689182i	−0.962051	+	0.272869i	$0.912027\pi$
$368$	5.53563e8	−	5.53563e8i	0.0301840	−	0.0301840i
$369$		−	8.15246e8i		−	0.0439727i
$370$		0			0
$371$	−3.08422e9			−0.162798
$372$	9.96328e9	+	9.96328e9i	0.520272	+	0.520272i
$373$	−1.92580e10	+	1.92580e10i	−0.994891	+	0.994891i	−0.999987	−	0.00509558i	$-0.998378\pi$
$373$	−1.92580e10	+	1.92580e10i	−0.994891	+	0.994891i	0.00509558	+	0.999987i	$0.498378\pi$
$374$		−	3.56814e10i		−	1.82371i
$375$		0			0
$376$	2.66353e10			1.33262
$377$	−1.02476e10	−	1.02476e10i	−0.507290	−	0.507290i
$378$	4.49449e9	−	4.49449e9i	0.220147	−	0.220147i
$379$			3.20827e10i			1.55494i	0.628918	+	0.777471i	$0.283498\pi$
$379$			3.20827e10i			1.55494i	−0.628918	+	0.777471i	$0.716502\pi$
$380$		0			0
$381$	1.68291e9			0.0798656
$382$	1.37374e10	+	1.37374e10i	0.645133	+	0.645133i
$383$	9.24061e9	−	9.24061e9i	0.429443	−	0.429443i	−0.458995	−	0.888439i	$-0.651791\pi$
$383$	9.24061e9	−	9.24061e9i	0.429443	−	0.429443i	0.888439	+	0.458995i	$0.151791\pi$
$384$			2.05412e10i			0.944715i
$385$		0			0
$386$	−1.04797e10			−0.472065
$387$	−4.78172e9	−	4.78172e9i	−0.213177	−	0.213177i
$388$	6.45186e9	−	6.45186e9i	0.284681	−	0.284681i
$389$			2.94292e10i			1.28523i	0.766190	+	0.642614i	$0.222150\pi$
$389$			2.94292e10i			1.28523i	−0.766190	+	0.642614i	$0.777850\pi$
$390$		0			0
$391$	2.63355e10			1.12677
$392$	7.72609e7	+	7.72609e7i	0.00327202	+	0.00327202i
$393$	−4.33914e9	+	4.33914e9i	−0.181901	+	0.181901i
$394$		−	7.20463e10i		−	2.98970i
$395$		0			0
$396$	2.30242e10			0.936276
$397$	−1.32741e10	−	1.32741e10i	−0.534369	−	0.534369i	0.387500	−	0.921870i	$-0.373339\pi$
$397$	−1.32741e10	−	1.32741e10i	−0.534369	−	0.534369i	−0.921870	+	0.387500i	$0.873339\pi$
$398$	4.27448e9	−	4.27448e9i	0.170353	−	0.170353i
$399$			2.80116e9i			0.110522i
$400$		0			0
$401$	1.10029e10			0.425530			0.212765	−	0.977103i	$-0.431753\pi$
$401$	1.10029e10			0.425530			0.212765	+	0.977103i	$0.431753\pi$
$402$	−5.83496e9	−	5.83496e9i	−0.223426	−	0.223426i
$403$	−8.24449e9	+	8.24449e9i	−0.312567	+	0.312567i
$404$		−	2.36689e10i		−	0.888491i
$405$		0			0
$406$	−5.58090e10			−2.05400
$407$	1.88039e10	+	1.88039e10i	0.685282	+	0.685282i
$408$	7.52657e9	−	7.52657e9i	0.271617	−	0.271617i
$409$			2.42015e9i			0.0864867i	0.999065	+	0.0432433i	$0.0137691\pi$
$409$			2.42015e9i			0.0864867i	−0.999065	+	0.0432433i	$0.986231\pi$
$410$		0			0
$411$	−3.73273e9			−0.130815
$412$	−2.86754e10	−	2.86754e10i	−0.995224	−	0.995224i
$413$	3.74787e10	−	3.74787e10i	1.28820	−	1.28820i
$414$			2.74252e10i			0.933574i
$415$		0			0
$416$	−1.65813e10			−0.553663
$417$	−8.94794e8	−	8.94794e8i	−0.0295923	−	0.0295923i
$418$	−1.15792e10	+	1.15792e10i	−0.379292	+	0.379292i
$419$		−	5.80459e10i		−	1.88328i	−0.336619	−	0.941641i	$-0.609283\pi$
$419$		−	5.80459e10i		−	1.88328i	0.336619	−	0.941641i	$-0.390717\pi$
$420$		0			0
$421$	−5.17041e10			−1.64587			−0.822936	−	0.568134i	$-0.807666\pi$
$421$	−5.17041e10			−1.64587			−0.822936	+	0.568134i	$0.807666\pi$
$422$	−4.09086e10	−	4.09086e10i	−1.28992	−	1.28992i
$423$	−9.85965e9	+	9.85965e9i	−0.307964	+	0.307964i
$424$		−	5.37862e9i		−	0.166421i
$425$		0			0
$426$	3.35032e10			1.01730
$427$	−1.94503e10	−	1.94503e10i	−0.585079	−	0.585079i
$428$	3.04161e10	−	3.04161e10i	0.906417	−	0.906417i
$429$			1.90522e10i			0.562492i
$430$		0			0
$431$	−4.03165e10			−1.16835			−0.584176	−	0.811627i	$-0.698582\pi$
$431$	−4.03165e10			−1.16835			−0.584176	+	0.811627i	$0.698582\pi$
$432$	1.17127e8	+	1.17127e8i	0.00336296	+	0.00336296i
$433$	−1.68419e10	+	1.68419e10i	−0.479114	+	0.479114i	−0.904848	−	0.425734i	$-0.860016\pi$
$433$	−1.68419e10	+	1.68419e10i	−0.479114	+	0.479114i	0.425734	+	0.904848i	$0.360016\pi$
$434$			4.49000e10i			1.26557i
$435$		0			0
$436$	−1.89565e10			−0.524581
$437$	−8.54629e9	−	8.54629e9i	−0.234343	−	0.234343i
$438$	−1.34063e9	+	1.34063e9i	−0.0364262	+	0.0364262i
$439$			2.04050e10i			0.549387i	0.961532	+	0.274693i	$0.0885764\pi$
$439$			2.04050e10i			0.549387i	−0.961532	+	0.274693i	$0.911424\pi$
$440$		0			0
$441$	−5.71996e7			−0.00151230
$442$	1.61293e10	+	1.61293e10i	0.422597	+	0.422597i
$443$	3.86803e9	−	3.86803e9i	0.100433	−	0.100433i	−0.655105	−	0.755538i	$-0.727376\pi$
$443$	3.86803e9	−	3.86803e9i	0.100433	−	0.100433i	0.755538	+	0.655105i	$0.227376\pi$
$444$			2.05442e10i			0.528637i
$445$		0			0
$446$	1.52814e10			0.386211
$447$	6.80029e9	+	6.80029e9i	0.170332	+	0.170332i
$448$	−4.58538e10	+	4.58538e10i	−1.13832	+	1.13832i
$449$			1.83588e10i			0.451709i	0.974161	+	0.225855i	$0.0725174\pi$
$449$			1.83588e10i			0.451709i	−0.974161	+	0.225855i	$0.927483\pi$
$450$		0			0
$451$	9.41036e9			0.227457
$452$	7.42020e10	+	7.42020e10i	1.77771	+	1.77771i
$453$	2.67621e8	−	2.67621e8i	0.00635518	−	0.00635518i
$454$		−	1.27051e10i		−	0.299058i
$455$		0			0
$456$	−4.88499e9			−0.112981
$457$	4.82993e10	+	4.82993e10i	1.10733	+	1.10733i	0.993501	+	0.113827i	$0.0363110\pi$
$457$	4.82993e10	+	4.82993e10i	1.10733	+	1.10733i	0.113827	+	0.993501i	$0.463689\pi$
$458$	−4.72623e10	+	4.72623e10i	−1.07412	+	1.07412i
$459$			5.57225e9i			0.125539i
$460$		0			0
$461$	5.86396e10			1.29834			0.649169	−	0.760644i	$-0.275117\pi$
$461$	5.86396e10			1.29834			0.649169	+	0.760644i	$0.275117\pi$
$462$	5.18798e10	+	5.18798e10i	1.13875	+	1.13875i
$463$	−4.96456e10	+	4.96456e10i	−1.08033	+	1.08033i	−0.0838539	+	0.996478i	$0.526723\pi$
$463$	−4.96456e10	+	4.96456e10i	−1.08033	+	1.08033i	−0.996478	+	0.0838539i	$0.973277\pi$
$464$		−	1.45439e9i		−	0.0313768i
$465$		0			0
$466$	1.66566e10			0.353217
$467$	1.29087e10	+	1.29087e10i	0.271403	+	0.271403i	0.829665	−	0.558262i	$-0.188532\pi$
$467$	1.29087e10	+	1.29087e10i	0.271403	+	0.271403i	−0.558262	+	0.829665i	$0.688532\pi$
$468$	−1.04078e10	+	1.04078e10i	−0.216958	+	0.216958i
$469$		−	1.62935e10i		−	0.336763i
$470$		0			0
$471$	1.95167e10			0.396573
$472$	6.53598e10	+	6.53598e10i	1.31687	+	1.31687i
$473$	5.51952e10	−	5.51952e10i	1.10270	−	1.10270i
$474$		−	6.85844e10i		−	1.35866i
$475$		0			0
$476$	5.44292e10			1.06024
$477$	1.99101e9	+	1.99101e9i	0.0384592	+	0.0384592i
$478$	2.76347e10	−	2.76347e10i	0.529350	−	0.529350i
$479$			6.38944e10i			1.21373i	0.794806	+	0.606864i	$0.207573\pi$
$479$			6.38944e10i			1.21373i	−0.794806	+	0.606864i	$0.792427\pi$
$480$		0			0
$481$	−1.70001e10			−0.317593
$482$	−1.08703e11	−	1.08703e11i	−2.01397	−	2.01397i
$483$	−3.82911e10	+	3.82911e10i	−0.703573	+	0.703573i
$484$			1.76373e11i			3.21403i
$485$		0			0
$486$	−5.80283e9			−0.104015
$487$	3.70532e9	+	3.70532e9i	0.0658734	+	0.0658734i	0.739276	−	0.673403i	$-0.235168\pi$
$487$	3.70532e9	+	3.70532e9i	0.0658734	+	0.0658734i	−0.673403	+	0.739276i	$0.735168\pi$
$488$	3.39197e10	−	3.39197e10i	0.598098	−	0.598098i
$489$			2.19996e10i			0.384750i
$490$		0			0
$491$	6.34805e10			1.09223			0.546116	−	0.837710i	$-0.316106\pi$
$491$	6.34805e10			1.09223			0.546116	+	0.837710i	$0.316106\pi$
$492$	5.14066e9	+	5.14066e9i	0.0877321	+	0.0877321i
$493$	3.45959e10	−	3.45959e10i	0.585648	−	0.585648i
$494$		−	1.04684e10i		−	0.175782i
$495$		0			0
$496$	−1.17010e9			−0.0193328
$497$	4.67772e10	+	4.67772e10i	0.766670	+	0.766670i
$498$	5.47539e10	−	5.47539e10i	0.890222	−	0.890222i
$499$			3.41919e10i			0.551469i	0.961234	+	0.275734i	$0.0889210\pi$
$499$			3.41919e10i			0.551469i	−0.961234	+	0.275734i	$0.911079\pi$
$500$		0			0
$501$	2.64478e10			0.419796
$502$	−1.72728e10	−	1.72728e10i	−0.271987	−	0.271987i
$503$	−8.68401e10	+	8.68401e10i	−1.35659	+	1.35659i	−0.478503	+	0.878086i	$0.658820\pi$
$503$	−8.68401e10	+	8.68401e10i	−1.35659	+	1.35659i	−0.878086	+	0.478503i	$0.841180\pi$
$504$			2.18869e10i			0.339205i
$505$		0			0
$506$	−3.16568e11			−4.82909
$507$	1.83624e10	+	1.83624e10i	0.277905	+	0.277905i
$508$	−1.06118e10	+	1.06118e10i	−0.159344	+	0.159344i
$509$		−	3.25241e10i		−	0.484545i	−0.970208	−	0.242273i	$-0.922107\pi$
$509$		−	3.25241e10i		−	0.484545i	0.970208	−	0.242273i	$-0.0778929\pi$
$510$		0			0
$511$	−3.74358e9			−0.0549040
$512$	−2.40142e9	−	2.40142e9i	−0.0349453	−	0.0349453i
$513$	1.80829e9	−	1.80829e9i	0.0261095	−	0.0261095i
$514$		−	4.42301e10i		−	0.633673i
$515$		0			0
$516$	6.03037e10			0.850638
$517$	−1.13810e11	−	1.13810e11i	−1.59300	−	1.59300i
$518$	−4.62917e10	+	4.62917e10i	−0.642960	+	0.642960i
$519$			2.02465e10i			0.279050i
$520$		0			0
$521$	−1.07908e11			−1.46454			−0.732272	−	0.681013i	$-0.761540\pi$
$521$	−1.07908e11			−1.46454			−0.732272	+	0.681013i	$0.761540\pi$
$522$	3.60275e10	+	3.60275e10i	0.485234	+	0.485234i
$523$	4.65193e10	−	4.65193e10i	0.621765	−	0.621765i	−0.324218	−	0.945982i	$-0.605101\pi$
$523$	4.65193e10	−	4.65193e10i	0.621765	−	0.621765i	0.945982	+	0.324218i	$0.105101\pi$
$524$		−	5.47223e10i		−	0.725837i
$525$		0			0
$526$	1.04783e11			1.36882
$527$	−2.78334e10	−	2.78334e10i	−0.360847	−	0.360847i
$528$	−1.35199e9	+	1.35199e9i	−0.0173956	+	0.0173956i
$529$		−	1.55340e11i		−	1.98363i
$530$		0			0
$531$	−4.83887e10			−0.608647
$532$	−1.76632e10	−	1.76632e10i	−0.220507	−	0.220507i
$533$	−4.25383e9	+	4.25383e9i	−0.0527074	+	0.0527074i
$534$		−	2.33744e10i		−	0.287459i
$535$		0			0
$536$	2.84146e10			0.344256
$537$	−4.52523e10	−	4.52523e10i	−0.544181	−	0.544181i
$538$	2.33168e10	−	2.33168e10i	0.278317	−	0.278317i
$539$		−	6.60253e8i		−	0.00782267i
$540$		0			0
$541$	2.68575e10			0.313528			0.156764	−	0.987636i	$-0.449894\pi$
$541$	2.68575e10			0.313528			0.156764	+	0.987636i	$0.449894\pi$
$542$	−5.23567e10	−	5.23567e10i	−0.606702	−	0.606702i
$543$	−5.91542e10	+	5.91542e10i	−0.680435	+	0.680435i
$544$		−	5.59785e10i		−	0.639184i
$545$		0			0
$546$	−4.69032e10			−0.527754
$547$	7.70438e10	+	7.70438e10i	0.860575	+	0.860575i	0.991405	−	0.130830i	$-0.0417642\pi$
$547$	7.70438e10	+	7.70438e10i	0.860575	+	0.860575i	−0.130830	+	0.991405i	$0.541764\pi$
$548$	2.35373e10	−	2.35373e10i	0.260996	−	0.260996i
$549$			2.51122e10i			0.276437i
$550$		0			0
$551$	−2.24539e10			−0.243604
$552$	−6.67764e10	−	6.67764e10i	−0.719229	−	0.719229i
$553$	9.57575e10	−	9.57575e10i	1.02393	−	1.02393i
$554$			5.43750e10i			0.577245i
$555$		0			0
$556$	1.12845e10			0.118082
$557$	−1.17779e11	−	1.17779e11i	−1.22362	−	1.22362i	−0.966335	−	0.257288i	$-0.917171\pi$
$557$	−1.17779e11	−	1.17779e11i	−1.22362	−	1.22362i	−0.257288	−	0.966335i	$-0.582829\pi$
$558$	2.89851e10	−	2.89851e10i	0.298977	−	0.298977i
$559$			4.99005e10i			0.511043i
$560$		0			0
$561$	−6.43203e10			−0.649376
$562$	8.93996e10	+	8.93996e10i	0.896169	+	0.896169i
$563$	1.75535e10	−	1.75535e10i	0.174715	−	0.174715i	−0.614332	−	0.789047i	$-0.710575\pi$
$563$	1.75535e10	−	1.75535e10i	0.174715	−	0.174715i	0.789047	+	0.614332i	$0.210575\pi$
$564$		−	1.24343e11i		−	1.22887i
$565$		0			0
$566$	1.83541e11			1.78841
$567$	−8.10191e9	−	8.10191e9i	−0.0783890	−	0.0783890i
$568$	−8.15755e10	+	8.15755e10i	−0.783729	+	0.783729i
$569$		−	1.43630e11i		−	1.37024i	−0.728430	−	0.685121i	$-0.759749\pi$
$569$		−	1.43630e11i		−	1.37024i	0.728430	−	0.685121i	$-0.240251\pi$
$570$		0			0
$571$	−4.28147e10			−0.402762			−0.201381	−	0.979513i	$-0.564543\pi$
$571$	−4.28147e10			−0.402762			−0.201381	+	0.979513i	$0.564543\pi$
$572$	−1.20137e11	−	1.20137e11i	−1.12226	−	1.12226i
$573$	2.47634e10	−	2.47634e10i	0.229716	−	0.229716i
$574$			2.31666e10i			0.213410i
$575$		0			0
$576$	5.92017e10			0.537829
$577$	5.80226e10	+	5.80226e10i	0.523472	+	0.523472i	0.918618	−	0.395146i	$-0.129306\pi$
$577$	5.80226e10	+	5.80226e10i	0.523472	+	0.523472i	−0.395146	+	0.918618i	$0.629306\pi$
$578$	7.35134e10	−	7.35134e10i	0.658651	−	0.658651i
$579$			1.88911e10i			0.168090i
$580$		0			0
$581$	1.52895e11			1.34180
$582$	−1.87697e10	−	1.87697e10i	−0.163593	−	0.163593i
$583$	−2.29822e10	+	2.29822e10i	−0.198938	+	0.198938i
$584$		−	6.52849e9i		−	0.0561257i
$585$		0			0
$586$	2.48211e11			2.10489
$587$	1.51452e11	+	1.51452e11i	1.27562	+	1.27562i	0.943092	+	0.332531i	$0.107903\pi$
$587$	1.51452e11	+	1.51452e11i	1.27562	+	1.27562i	0.332531	+	0.943092i	$0.392097\pi$
$588$	3.60681e8	−	3.60681e8i	0.00301727	−	0.00301727i
$589$			1.80648e10i			0.150097i
$590$		0			0
$591$	−1.29873e11			−1.06456
$592$	−1.20637e9	−	1.20637e9i	−0.00982184	−	0.00982184i
$593$	8.39640e10	−	8.39640e10i	0.679007	−	0.679007i	−0.280768	−	0.959776i	$-0.590589\pi$
$593$	8.39640e10	−	8.39640e10i	0.679007	−	0.679007i	0.959776	+	0.280768i	$0.0905892\pi$
$594$		−	6.69819e10i		−	0.538036i
$595$		0			0
$596$	−8.57606e10			−0.679677
$597$	−7.70530e9	−	7.70530e9i	−0.0606586	−	0.0606586i
$598$	1.43101e11	−	1.43101e11i	1.11902	−	1.11902i
$599$		−	2.19165e11i		−	1.70241i	−0.524835	−	0.851204i	$-0.675873\pi$
$599$		−	2.19165e11i		−	1.70241i	0.524835	−	0.851204i	$-0.324127\pi$
$600$		0			0
$601$	1.93720e11			1.48483			0.742414	−	0.669941i	$-0.233681\pi$
$601$	1.93720e11			1.48483			0.742414	+	0.669941i	$0.233681\pi$
$602$	1.35881e11	+	1.35881e11i	1.03460	+	1.03460i
$603$	−1.05183e10	+	1.05183e10i	−0.0795564	+	0.0795564i
$604$			3.37506e9i			0.0253591i
$605$		0			0
$606$	−6.88575e10			−0.510577
$607$	−1.30845e11	−	1.30845e11i	−0.963834	−	0.963834i	0.0355341	−	0.999368i	$-0.488687\pi$
$607$	−1.30845e11	−	1.30845e11i	−0.963834	−	0.963834i	−0.999368	+	0.0355341i	$0.988687\pi$
$608$	−1.81660e10	+	1.81660e10i	−0.132936	+	0.132936i
$609$			1.00603e11i			0.731378i
$610$		0			0
$611$	1.02892e11			0.738275
$612$	−3.51367e10	−	3.51367e10i	−0.250470	−	0.250470i
$613$	−8.33869e10	+	8.33869e10i	−0.590549	+	0.590549i	−0.937780	−	0.347231i	$-0.887122\pi$
$613$	−8.33869e10	+	8.33869e10i	−0.590549	+	0.590549i	0.347231	+	0.937780i	$0.387122\pi$
$614$			4.21986e11i			2.96910i
$615$		0			0
$616$	−2.52640e11			−1.75460
$617$	1.10504e11	+	1.10504e11i	0.762497	+	0.762497i	0.976773	−	0.214276i	$-0.0687393\pi$
$617$	1.10504e11	+	1.10504e11i	0.762497	+	0.762497i	−0.214276	+	0.976773i	$0.568739\pi$
$618$	−8.34224e10	+	8.34224e10i	−0.571911	+	0.571911i
$619$			1.14849e11i			0.782286i	0.920330	+	0.391143i	$0.127920\pi$
$619$			1.14849e11i			0.782286i	−0.920330	+	0.391143i	$0.872080\pi$
$620$		0			0
$621$	4.94375e10			0.332422
$622$	−2.28831e10	−	2.28831e10i	−0.152881	−	0.152881i
$623$	3.26353e10	−	3.26353e10i	0.216639	−	0.216639i
$624$		−	1.22230e9i		−	0.00806195i
$625$		0			0
$626$	2.21462e11			1.44212
$627$	2.08730e10	+	2.08730e10i	0.135056	+	0.135056i
$628$	−1.23066e11	+	1.23066e11i	−0.791221	+	0.791221i
$629$		−	5.73922e10i		−	0.366649i
$630$		0			0
$631$	−2.13765e11			−1.34840			−0.674200	−	0.738549i	$-0.735512\pi$
$631$	−2.13765e11			−1.34840			−0.674200	+	0.738549i	$0.735512\pi$
$632$	1.66993e11	+	1.66993e11i	1.04672	+	1.04672i
$633$	−7.37430e10	+	7.37430e10i	−0.459310	+	0.459310i
$634$			3.04515e11i			1.88474i
$635$		0			0
$636$	−2.51093e10			−0.153464
$637$	2.98459e8	+	2.98459e8i	0.00181270	+	0.00181270i
$638$	−4.15864e11	+	4.15864e11i	−2.50997	+	2.50997i
$639$		−	6.03939e10i		−	0.362234i
$640$		0			0
$641$	−2.37058e11			−1.40418			−0.702091	−	0.712088i	$-0.747750\pi$
$641$	−2.37058e11			−1.40418			−0.702091	+	0.712088i	$0.747750\pi$
$642$	−8.84863e10	−	8.84863e10i	−0.520878	−	0.520878i
$643$	2.09456e10	−	2.09456e10i	0.122532	−	0.122532i	−0.643182	−	0.765714i	$-0.722386\pi$
$643$	2.09456e10	−	2.09456e10i	0.122532	−	0.122532i	0.765714	+	0.643182i	$0.222386\pi$
$644$		−	4.82901e11i		−	2.80746i
$645$		0			0
$646$	3.53415e10			0.202934
$647$	1.58224e11	+	1.58224e11i	0.902935	+	0.902935i	0.995689	−	0.0927543i	$-0.0295671\pi$
$647$	1.58224e11	+	1.58224e11i	0.902935	+	0.902935i	−0.0927543	+	0.995689i	$0.529567\pi$
$648$	1.41291e10	−	1.41291e10i	0.0801333	−	0.0801333i
$649$		−	5.58549e11i		−	3.14835i
$650$		0			0
$651$	8.09381e10			0.450639
$652$	−1.38722e11	−	1.38722e11i	−0.767634	−	0.767634i
$653$	6.63522e9	−	6.63522e9i	0.0364924	−	0.0364924i	−0.688625	−	0.725118i	$-0.741785\pi$
$653$	6.63522e9	−	6.63522e9i	0.0364924	−	0.0364924i	0.725118	+	0.688625i	$0.241785\pi$
$654$			5.51482e10i			0.301453i
$655$		0			0
$656$	−6.03725e8			−0.00326005
$657$	2.41666e9	+	2.41666e9i	0.0129704	+	0.0129704i
$658$	2.80179e11	−	2.80179e11i	1.49462	−	1.49462i
$659$			3.66062e11i			1.94095i	0.241209	+	0.970473i	$0.422456\pi$
$659$			3.66062e11i			1.94095i	−0.241209	+	0.970473i	$0.577544\pi$
$660$		0			0
$661$	1.59529e11			0.835666			0.417833	−	0.908524i	$-0.362790\pi$
$661$	1.59529e11			0.835666			0.417833	+	0.908524i	$0.362790\pi$
$662$	−9.07931e10	−	9.07931e10i	−0.472739	−	0.472739i
$663$	2.90751e10	−	2.90751e10i	0.150476	−	0.150476i
$664$			2.66636e11i			1.37166i
$665$		0			0
$666$	5.97671e10			0.303784
$667$	−3.06938e11	−	3.06938e11i	−1.55077	−	1.55077i
$668$	−1.66771e11	+	1.66771e11i	−0.837556	+	0.837556i
$669$		−	2.75467e10i		−	0.137520i
$670$		0			0
$671$	−2.89870e11			−1.42992
$672$	8.13914e10	+	8.13914e10i	0.399118	+	0.399118i
$673$	−8.74717e10	+	8.74717e10i	−0.426390	+	0.426390i	−0.887397	−	0.461007i	$-0.847488\pi$
$673$	−8.74717e10	+	8.74717e10i	−0.426390	+	0.426390i	0.461007	+	0.887397i	$0.347488\pi$
$674$			2.20633e11i			1.06913i
$675$		0			0
$676$	−2.31573e11			−1.10892
$677$	−3.15797e10	−	3.15797e10i	−0.150333	−	0.150333i	0.627934	−	0.778267i	$-0.283901\pi$
$677$	−3.15797e10	−	3.15797e10i	−0.150333	−	0.150333i	−0.778267	+	0.627934i	$0.783901\pi$
$678$	2.15868e11	−	2.15868e11i	1.02157	−	1.02157i
$679$		−	5.24126e10i		−	0.246579i
$680$		0			0
$681$	−2.29026e10			−0.106487
$682$	3.34574e11	+	3.34574e11i	1.54652	+	1.54652i
$683$	2.24956e11	−	2.24956e11i	1.03375	−	1.03375i	0.0343374	−	0.999410i	$-0.489068\pi$
$683$	2.24956e11	−	2.24956e11i	1.03375	−	1.03375i	0.999410	−	0.0343374i	$-0.0109321\pi$
$684$			2.28049e10i			0.104185i
$685$		0			0
$686$	3.59893e11			1.62509
$687$	8.51965e10	+	8.51965e10i	0.382468	+	0.382468i
$688$	−3.54106e9	+	3.54106e9i	−0.0158045	+	0.0158045i
$689$		−	2.07776e10i		−	0.0921974i
$690$		0			0
$691$	−2.09892e11			−0.920628			−0.460314	−	0.887756i	$-0.652263\pi$
$691$	−2.09892e11			−0.920628			−0.460314	+	0.887756i	$0.652263\pi$
$692$	−1.27668e11	−	1.27668e11i	−0.556745	−	0.556745i
$693$	9.35200e10	−	9.35200e10i	0.405482	−	0.405482i
$694$			2.37975e10i			0.102587i
$695$		0			0
$696$	−1.75443e11			−0.747652
$697$	−1.43609e10	−	1.43609e10i	−0.0608487	−	0.0608487i
$698$	2.63875e11	−	2.63875e11i	1.11167	−	1.11167i
$699$		−	3.00256e10i		−	0.125772i
$700$		0			0
$701$	−1.70201e9			−0.00704839			−0.00352420	−	0.999994i	$-0.501122\pi$
$701$	−1.70201e9			−0.00704839			−0.00352420	+	0.999994i	$0.501122\pi$
$702$	3.02783e10	+	3.02783e10i	0.124676	+	0.124676i
$703$	−1.86247e10	+	1.86247e10i	−0.0762551	+	0.0762551i
$704$			6.83363e11i			2.78202i
$705$		0			0
$706$	−3.85449e11			−1.55149
$707$	−9.61389e10	−	9.61389e10i	−0.384788	−	0.384788i
$708$	3.05122e11	−	3.05122e11i	1.21434	−	1.21434i
$709$			1.77464e11i			0.702303i	0.936319	+	0.351151i	$0.114210\pi$
$709$			1.77464e11i			0.702303i	−0.936319	+	0.351151i	$0.885790\pi$
$710$		0			0
$711$	−1.23632e11			−0.483786
$712$	5.69133e10	+	5.69133e10i	0.221459	+	0.221459i
$713$	−2.46940e11	+	2.46940e11i	−0.955507	+	0.955507i
$714$		−	1.58345e11i		−	0.609273i
$715$		0			0
$716$	5.70691e11			2.17144
$717$	−4.98151e10	−	4.98151e10i	−0.188488	−	0.188488i
$718$	−1.79299e11	+	1.79299e11i	−0.674653	+	0.674653i
$719$			3.16656e11i			1.18487i	0.805617	+	0.592437i	$0.201834\pi$
$719$			3.16656e11i			1.18487i	−0.805617	+	0.592437i	$0.798166\pi$
$720$		0			0
$721$	−2.32949e11			−0.862023
$722$	3.00084e11	+	3.00084e11i	1.10432	+	1.10432i
$723$	−1.95951e11	+	1.95951e11i	−0.717124	+	0.717124i
$724$		−	7.46012e11i		−	2.71514i
$725$		0			0
$726$	5.13103e11			1.84696
$727$	9.61447e10	+	9.61447e10i	0.344182	+	0.344182i	0.857937	−	0.513755i	$-0.171746\pi$
$727$	9.61447e10	+	9.61447e10i	0.344182	+	0.344182i	−0.513755	+	0.857937i	$0.671746\pi$
$728$	1.14202e11	−	1.14202e11i	0.406583	−	0.406583i
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−1.68464e11			−0.589981
$732$	−1.58349e11	−	1.58349e11i	−0.551532	−	0.551532i
$733$	−3.46829e11	+	3.46829e11i	−1.20143	+	1.20143i	−0.227701	+	0.973731i	$0.573121\pi$
$733$	−3.46829e11	+	3.46829e11i	−1.20143	+	1.20143i	−0.973731	+	0.227701i	$0.926879\pi$
$734$		−	4.58702e11i		−	1.58033i
$735$		0			0
$736$	−4.96647e11			−1.69253
$737$	−1.21412e11	−	1.21412e11i	−0.411521	−	0.411521i
$738$	1.49552e10	−	1.49552e10i	0.0504158	−	0.0504158i
$739$		−	9.39715e10i		−	0.315078i	−0.987513	−	0.157539i	$-0.949644\pi$
$739$		−	9.39715e10i		−	0.315078i	0.987513	−	0.157539i	$-0.0503560\pi$
$740$		0			0
$741$	−1.88707e10			−0.0625916
$742$	−5.65781e10	−	5.65781e10i	−0.186652	−	0.186652i
$743$	−1.57217e11	+	1.57217e11i	−0.515876	+	0.515876i	−0.916321	−	0.400445i	$-0.868856\pi$
$743$	−1.57217e11	+	1.57217e11i	−0.515876	+	0.515876i	0.400445	+	0.916321i	$0.368856\pi$
$744$			1.41149e11i			0.460667i
$745$		0			0
$746$	−7.06552e11			−2.28133
$747$	−9.87011e10	−	9.87011e10i	−0.316986	−	0.316986i
$748$	4.05581e11	−	4.05581e11i	1.29560	−	1.29560i
$749$		−	2.47089e11i		−	0.785102i
$750$		0			0
$751$	3.33116e11			1.04722			0.523608	−	0.851959i	$-0.324586\pi$
$751$	3.33116e11			1.04722			0.523608	+	0.851959i	$0.324586\pi$
$752$	7.30149e9	+	7.30149e9i	0.0228318	+	0.0228318i
$753$	−3.11364e10	+	3.11364e10i	−0.0968476	+	0.0968476i
$754$		−	3.75971e11i		−	1.16324i
$755$		0			0
$756$	1.02176e11			0.312795
$757$	−2.85750e11	−	2.85750e11i	−0.870167	−	0.870167i	0.122323	−	0.992490i	$-0.460965\pi$
$757$	−2.85750e11	−	2.85750e11i	−0.870167	−	0.870167i	−0.992490	+	0.122323i	$0.960965\pi$
$758$	−5.88538e11	+	5.88538e11i	−1.78278	+	1.78278i
$759$			5.70656e11i			1.71952i
$760$		0			0
$761$	5.31249e11			1.58402			0.792008	−	0.610511i	$-0.209036\pi$
$761$	5.31249e11			1.58402			0.792008	+	0.610511i	$0.209036\pi$
$762$	3.08718e10	+	3.08718e10i	0.0915678	+	0.0915678i
$763$	−7.69979e10	+	7.69979e10i	−0.227185	+	0.227185i
$764$			3.12298e11i			0.916634i
$765$		0			0
$766$	3.39027e11			0.984733
$767$	2.52485e11	+	2.52485e11i	0.729548	+	0.729548i
$768$	−1.47657e11	+	1.47657e11i	−0.424434	+	0.424434i
$769$			2.07421e11i			0.593126i	0.955013	+	0.296563i	$0.0958404\pi$
$769$			2.07421e11i			0.593126i	−0.955013	+	0.296563i	$0.904160\pi$
$770$		0			0
$771$	−7.97305e10			−0.225635
$772$	−1.19121e11	−	1.19121e11i	−0.335365	−	0.335365i
$773$	3.26780e11	−	3.26780e11i	0.915245	−	0.915245i	−0.0814340	−	0.996679i	$-0.525950\pi$
$773$	3.26780e11	−	3.26780e11i	0.915245	−	0.915245i	0.996679	+	0.0814340i	$0.0259500\pi$
$774$		−	1.75435e11i		−	0.488824i
$775$		0			0
$776$	9.14031e10			0.252066
$777$	8.34468e10	+	8.34468e10i	0.228942	+	0.228942i
$778$	−5.39861e11	+	5.39861e11i	−1.47354	+	1.47354i
$779$			9.32072e9i			0.0253104i
$780$		0			0
$781$	6.97124e11			1.87373
$782$	4.83108e11	+	4.83108e11i	1.29186	+	1.29186i
$783$	6.49442e10	−	6.49442e10i	0.172780	−	0.172780i
$784$			4.23587e7i			0.000112119i
$785$		0			0
$786$	−1.59198e11			−0.417106
$787$	1.66899e11	+	1.66899e11i	0.435067	+	0.435067i	0.890348	−	0.455281i	$-0.150461\pi$
$787$	1.66899e11	+	1.66899e11i	0.435067	+	0.435067i	−0.455281	+	0.890348i	$0.650461\pi$
$788$	8.18933e11	−	8.18933e11i	2.12395	−	2.12395i
$789$		−	1.88885e11i		−	0.487404i
$790$		0			0
$791$	6.02790e11			1.53978
$792$	1.63091e11	+	1.63091e11i	0.414505	+	0.414505i
$793$	1.31032e11	−	1.31032e11i	0.331348	−	0.331348i
$794$		−	4.87008e11i		−	1.22533i
$795$		0			0
$796$	9.71739e10			0.242046
$797$	−2.34819e11	−	2.34819e11i	−0.581968	−	0.581968i	0.353476	−	0.935444i	$-0.385000\pi$
$797$	−2.34819e11	−	2.34819e11i	−0.581968	−	0.581968i	−0.935444	+	0.353476i	$0.885000\pi$
$798$	−5.13856e10	+	5.13856e10i	−0.126716	+	0.126716i
$799$			3.47364e11i			0.852311i
$800$		0			0
$801$	−4.21354e10			−0.102357
$802$	2.01841e11	+	2.01841e11i	0.487880	+	0.487880i
$803$	−2.78955e10	+	2.78955e10i	−0.0670921	+	0.0670921i
$804$		−	1.32649e11i		−	0.317454i
$805$		0			0
$806$	−3.02480e11			−0.716731
$807$	−4.20315e10	−	4.20315e10i	−0.0991017	−	0.0991017i
$808$	1.67658e11	−	1.67658e11i	0.393350	−	0.393350i
$809$		−	4.00874e11i		−	0.935865i	−0.883764	−	0.467933i	$-0.844999\pi$
$809$		−	4.00874e11i		−	0.935865i	0.883764	−	0.467933i	$-0.155001\pi$
$810$		0			0
$811$	−6.94082e11			−1.60445			−0.802227	−	0.597019i	$-0.796352\pi$
$811$	−6.94082e11			−1.60445			−0.802227	+	0.597019i	$0.796352\pi$
$812$	−6.34368e11	−	6.34368e11i	−1.45921	−	1.45921i
$813$	−9.43798e10	+	9.43798e10i	−0.216031	+	0.216031i
$814$			6.89890e11i			1.57138i
$815$		0			0
$816$	4.12649e9			0.00930722
$817$	5.46694e10	+	5.46694e10i	0.122703	+	0.122703i
$818$	−4.43962e10	+	4.43962e10i	−0.0991590	+	0.0991590i
$819$			8.45490e10i			0.187920i
$820$		0			0
$821$	−2.52988e10			−0.0556836			−0.0278418	−	0.999612i	$-0.508863\pi$
$821$	−2.52988e10			−0.0556836			−0.0278418	+	0.999612i	$0.508863\pi$
$822$	−6.84746e10	−	6.84746e10i	−0.149983	−	0.149983i
$823$	−2.30906e10	+	2.30906e10i	−0.0503310	+	0.0503310i	−0.731824	−	0.681493i	$-0.761331\pi$
$823$	−2.30906e10	+	2.30906e10i	−0.0503310	+	0.0503310i	0.681493	+	0.731824i	$0.261331\pi$
$824$		−	4.06243e11i		−	0.881205i
$825$		0			0
$826$	1.37505e12			2.95391
$827$	2.60632e11	+	2.60632e11i	0.557193	+	0.557193i	0.928507	−	0.371314i	$-0.121093\pi$
$827$	2.60632e11	+	2.60632e11i	0.557193	+	0.557193i	−0.371314	+	0.928507i	$0.621093\pi$
$828$	−3.11736e11	+	3.11736e11i	−0.663232	+	0.663232i
$829$			7.75807e11i			1.64261i	0.570487	+	0.821307i	$0.306755\pi$
$829$			7.75807e11i			1.64261i	−0.570487	+	0.821307i	$0.693245\pi$
$830$		0			0
$831$	9.80179e10			0.205542
$832$	−3.08905e11	−	3.08905e11i	−0.644662	−	0.644662i
$833$	−1.00760e9	+	1.00760e9i	−0.00209270	+	0.00209270i
$834$		−	3.28289e10i		−	0.0678566i
$835$		0			0
$836$	−2.63236e11			−0.538914
$837$	−5.22495e10	−	5.22495e10i	−0.106458	−	0.106458i
$838$	1.06482e12	−	1.06482e12i	2.15923	−	2.15923i
$839$			1.87384e11i			0.378169i	0.981961	+	0.189084i	$0.0605519\pi$
$839$			1.87384e11i			0.378169i	−0.981961	+	0.189084i	$0.939448\pi$
$840$		0			0
$841$	−3.06178e11			−0.612055
$842$	−9.48479e11	−	9.48479e11i	−1.88703	−	1.88703i
$843$	1.61154e11	−	1.61154e11i	0.319104	−	0.319104i
$844$		−	9.29995e11i		−	1.83278i
$845$		0			0
$846$	−3.61738e11			−0.706176
$847$	7.16394e11	+	7.16394e11i	1.39193	+	1.39193i
$848$	1.47443e9	−	1.47443e9i	0.00285129	−	0.00285129i
$849$		−	3.30856e11i		−	0.636808i
$850$		0			0
$851$	−5.09189e11			−0.970870
$852$	3.80823e11	+	3.80823e11i	0.722711	+	0.722711i
$853$	3.73371e11	−	3.73371e11i	0.705252	−	0.705252i	−0.260281	−	0.965533i	$-0.583815\pi$
$853$	3.73371e11	−	3.73371e11i	0.705252	−	0.705252i	0.965533	+	0.260281i	$0.0838153\pi$
$854$		−	7.13607e11i		−	1.34161i
$855$		0			0
$856$	4.30903e11			0.802572
$857$	−2.90762e11	−	2.90762e11i	−0.539032	−	0.539032i	0.384213	−	0.923245i	$-0.374473\pi$
$857$	−2.90762e11	−	2.90762e11i	−0.539032	−	0.539032i	−0.923245	+	0.384213i	$0.874473\pi$
$858$	−3.49501e11	+	3.49501e11i	−0.644910	+	0.644910i
$859$			2.07200e10i			0.0380554i	0.999819	+	0.0190277i	$0.00605707\pi$
$859$			2.07200e10i			0.0380554i	−0.999819	+	0.0190277i	$0.993943\pi$
$860$		0			0
$861$	4.17608e10			0.0759900
$862$	−7.39581e11	−	7.39581e11i	−1.33954	−	1.33954i
$863$	1.63832e11	−	1.63832e11i	0.295363	−	0.295363i	−0.543831	−	0.839195i	$-0.683027\pi$
$863$	1.63832e11	−	1.63832e11i	0.295363	−	0.295363i	0.839195	+	0.543831i	$0.183027\pi$
$864$		−	1.05084e11i		−	0.188574i
$865$		0			0
$866$	−6.17908e11			−1.09863
$867$	−1.32517e11	−	1.32517e11i	−0.234529	−	0.234529i
$868$	−5.10367e11	+	5.10367e11i	−0.899092	+	0.899092i
$869$		−	1.42708e12i		−	2.50248i
$870$		0			0
$871$	1.09765e11			0.190719
$872$	−1.34278e11	−	1.34278e11i	−0.232241	−	0.232241i
$873$	−3.38349e10	+	3.38349e10i	−0.0582515	+	0.0582515i
$874$		−	3.13553e11i		−	0.537360i
$875$		0			0
$876$	−3.04773e10			−0.0517559
$877$	−1.27543e11	−	1.27543e11i	−0.215605	−	0.215605i	0.591038	−	0.806644i	$-0.298718\pi$
$877$	−1.27543e11	−	1.27543e11i	−0.215605	−	0.215605i	−0.806644	+	0.591038i	$0.798718\pi$
$878$	−3.74317e11	+	3.74317e11i	−0.629885	+	0.629885i
$879$		−	4.47432e11i		−	0.749500i
$880$		0			0
$881$	−2.51076e11			−0.416775			−0.208387	−	0.978046i	$-0.566821\pi$
$881$	−2.51076e11			−0.416775			−0.208387	+	0.978046i	$0.566821\pi$
$882$	−1.04929e9	−	1.04929e9i	−0.00173389	−	0.00173389i
$883$	−3.45510e11	+	3.45510e11i	−0.568352	+	0.568352i	−0.931667	−	0.363314i	$-0.881645\pi$
$883$	−3.45510e11	+	3.45510e11i	−0.568352	+	0.568352i	0.363314	+	0.931667i	$0.381645\pi$
$884$			3.66676e11i			0.600445i
$885$		0			0
$886$	1.41913e11			0.230297
$887$	1.54768e11	+	1.54768e11i	0.250028	+	0.250028i	0.820982	−	0.570954i	$-0.193427\pi$
$887$	1.54768e11	+	1.54768e11i	0.250028	+	0.250028i	−0.570954	+	0.820982i	$0.693427\pi$
$888$	−1.45524e11	+	1.45524e11i	−0.234036	+	0.234036i
$889$			8.62065e10i			0.138017i
$890$		0			0
$891$	−1.20743e11			−0.191581
$892$	1.73700e11	+	1.73700e11i	0.274373	+	0.274373i
$893$	1.12725e11	−	1.12725e11i	0.177262	−	0.177262i
$894$			2.49494e11i			0.390580i
$895$		0			0
$896$	−1.05222e12			−1.63258
$897$	−2.57957e11	−	2.57957e11i	−0.398454	−	0.398454i
$898$	−3.36781e11	+	3.36781e11i	−0.517895	+	0.517895i
$899$			6.48792e11i			0.993269i
$900$		0			0
$901$	7.01452e10			0.106438
$902$	1.72627e11	+	1.72627e11i	0.260785	+	0.260785i
$903$	2.44942e11	−	2.44942e11i	0.368394	−	0.368394i
$904$			1.05121e12i			1.57405i
$905$		0			0
$906$	9.81869e9			0.0145727
$907$	4.03611e11	+	4.03611e11i	0.596394	+	0.596394i	0.939351	−	0.342957i	$-0.111428\pi$
$907$	4.03611e11	+	4.03611e11i	0.596394	+	0.596394i	−0.342957	+	0.939351i	$0.611428\pi$
$908$	1.44416e11	−	1.44416e11i	0.212458	−	0.212458i
$909$			1.24125e11i			0.181804i
$910$		0			0
$911$	7.31868e11			1.06257			0.531287	−	0.847192i	$-0.321709\pi$
$911$	7.31868e11			1.06257			0.531287	+	0.847192i	$0.321709\pi$
$912$	−1.33911e9	−	1.33911e9i	−0.00193570	−	0.00193570i
$913$	1.13930e12	−	1.13930e12i	1.63967	−	1.63967i
$914$			1.77204e12i			2.53915i
$915$		0			0
$916$	−1.07444e12			−1.52616
$917$	−2.22272e11	−	2.22272e11i	−0.314345	−	0.314345i
$918$	−1.02219e11	+	1.02219e11i	−0.143934	+	0.143934i
$919$			4.73733e11i			0.664158i	0.943252	+	0.332079i	$0.107750\pi$
$919$			4.73733e11i			0.664158i	−0.943252	+	0.332079i	$0.892250\pi$
$920$		0			0
$921$	7.60684e11			1.05722
$922$	1.07571e12	+	1.07571e12i	1.48857	+	1.48857i
$923$	−3.15126e11	+	3.15126e11i	−0.434188	+	0.434188i
$924$			1.17941e12i			1.61799i
$925$		0			0
$926$	−1.82144e12			−2.47725
$927$	1.50380e11	+	1.50380e11i	0.203643	+	0.203643i
$928$	−6.52426e11	+	6.52426e11i	−0.879709	+	0.879709i
$929$			5.24458e11i			0.704122i	0.935977	+	0.352061i	$0.114519\pi$
$929$			5.24458e11i			0.704122i	−0.935977	+	0.352061i	$0.885481\pi$
$930$		0			0
$931$	6.53963e8			0.000870472
$932$	1.89331e11	+	1.89331e11i	0.250933	+	0.250933i
$933$	−4.12498e10	+	4.12498e10i	−0.0544371	+	0.0544371i
$934$			4.73604e11i			0.622340i
$935$		0			0
$936$	−1.47446e11			−0.192102
$937$	−1.25037e11	−	1.25037e11i	−0.162211	−	0.162211i	0.621334	−	0.783545i	$-0.286591\pi$
$937$	−1.25037e11	−	1.25037e11i	−0.162211	−	0.162211i	−0.783545	+	0.621334i	$0.786591\pi$
$938$	2.98895e11	−	2.98895e11i	0.386106	−	0.386106i
$939$		−	3.99214e11i		−	0.513503i
$940$		0			0
$941$	9.45647e11			1.20606			0.603032	−	0.797717i	$-0.293959\pi$
$941$	9.45647e11			1.20606			0.603032	+	0.797717i	$0.293959\pi$
$942$	3.58022e11	+	3.58022e11i	0.454680	+	0.454680i
$943$	−1.27411e11	+	1.27411e11i	−0.161125	+	0.161125i
$944$			3.58339e10i			0.0451238i
$945$		0			0
$946$	2.02504e12			2.52854
$947$	−7.70617e11	−	7.70617e11i	−0.958161	−	0.958161i	0.0409978	−	0.999159i	$-0.486946\pi$
$947$	−7.70617e11	−	7.70617e11i	−0.958161	−	0.958161i	−0.999159	+	0.0409978i	$0.986946\pi$
$948$	7.79582e11	−	7.79582e11i	0.965225	−	0.965225i
$949$		−	2.52196e10i		−	0.0310937i
$950$		0			0
$951$	5.48928e11			0.671109
$952$	3.85547e11	+	3.85547e11i	0.469386	+	0.469386i
$953$	4.05642e10	−	4.05642e10i	0.0491781	−	0.0491781i	−0.682090	−	0.731268i	$-0.738929\pi$
$953$	4.05642e10	−	4.05642e10i	0.0491781	−	0.0491781i	0.731268	+	0.682090i	$0.238929\pi$
$954$			7.30478e10i			0.0881888i
$955$		0			0
$956$	6.28233e11			0.752124
$957$	7.49648e11	+	7.49648e11i	0.893737	+	0.893737i
$958$	−1.17210e12	+	1.17210e12i	−1.39157	+	1.39157i
$959$		−	1.91208e11i		−	0.226064i
$960$		0			0
$961$	−3.30919e11			−0.387997
$962$	−3.11856e11	−	3.11856e11i	−0.364127	−	0.364127i
$963$	−1.59508e11	+	1.59508e11i	−0.185472	+	0.185472i
$964$		−	2.47120e12i		−	2.86154i
$965$		0			0
$966$	−1.40485e12			−1.61333
$967$	1.06450e12	+	1.06450e12i	1.21742	+	1.21742i	0.968534	+	0.248881i	$0.0800628\pi$
$967$	1.06450e12	+	1.06450e12i	1.21742	+	1.21742i	0.248881	+	0.968534i	$0.419937\pi$
$968$	−1.24933e12	+	1.24933e12i	−1.42291	+	1.42291i
$969$		−	6.37076e10i		−	0.0722597i
$970$		0			0
$971$	1.95776e11			0.220233			0.110116	−	0.993919i	$-0.464878\pi$
$971$	1.95776e11			0.220233			0.110116	+	0.993919i	$0.464878\pi$
$972$	−6.59594e10	−	6.59594e10i	−0.0738944	−	0.0738944i
$973$	4.58357e10	−	4.58357e10i	0.0511390	−	0.0511390i
$974$			1.35944e11i			0.151051i
$975$		0			0
$976$	1.85967e10			0.0204944
$977$	7.97681e11	+	7.97681e11i	0.875490	+	0.875490i	0.993064	−	0.117574i	$-0.0375117\pi$
$977$	7.97681e11	+	7.97681e11i	0.875490	+	0.875490i	−0.117574	+	0.993064i	$0.537512\pi$
$978$	−4.03568e11	+	4.03568e11i	−0.441125	+	0.441125i
$979$		−	4.86367e11i		−	0.529460i
$980$		0			0
$981$	9.94117e10			0.107340
$982$	1.16451e12	+	1.16451e12i	1.25227	+	1.25227i
$983$	6.95183e11	−	6.95183e11i	0.744535	−	0.744535i	−0.228912	−	0.973447i	$-0.573517\pi$
$983$	6.95183e11	−	6.95183e11i	0.744535	−	0.744535i	0.973447	+	0.228912i	$0.0735168\pi$
$984$			7.28274e10i			0.0776809i
$985$		0			0
$986$	1.26928e12			1.34292
$987$	−5.05059e11	−	5.05059e11i	−0.532198	−	0.532198i
$988$	1.18992e11	−	1.18992e11i	0.124879	−	0.124879i
$989$			1.49463e12i			1.56224i
$990$		0			0
$991$	1.19169e12			1.23557			0.617786	−	0.786346i	$-0.288030\pi$
$991$	1.19169e12			1.23557			0.617786	+	0.786346i	$0.288030\pi$
$992$	5.24895e11	+	5.24895e11i	0.542033	+	0.542033i
$993$	−1.63666e11	+	1.63666e11i	−0.168330	+	0.168330i
$994$			1.71620e12i			1.75801i
$995$		0			0
$996$	1.24475e12			1.26487
$997$	−7.71264e11	−	7.71264e11i	−0.780589	−	0.780589i	0.199341	−	0.979930i	$-0.436120\pi$
$997$	−7.71264e11	−	7.71264e11i	−0.780589	−	0.780589i	−0.979930	+	0.199341i	$0.936120\pi$
$998$	−6.27229e11	+	6.27229e11i	−0.632272	+	0.632272i
$999$		−	1.07738e11i		−	0.108170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.e.7.7		16
5.2	odd	4		15.9.f.a.13.2	yes	16
5.3	odd	4	inner	75.9.f.e.43.7		16
5.4	even	2		15.9.f.a.7.2	✓	16
15.2	even	4		45.9.g.c.28.7		16
15.14	odd	2		45.9.g.c.37.7		16
20.7	even	4		240.9.bg.d.193.7		16
20.19	odd	2		240.9.bg.d.97.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.f.a.7.2	✓	16	5.4	even	2
15.9.f.a.13.2	yes	16	5.2	odd	4
45.9.g.c.28.7		16	15.2	even	4
45.9.g.c.37.7		16	15.14	odd	2
75.9.f.e.7.7		16	1.1	even	1	trivial
75.9.f.e.43.7		16	5.3	odd	4	inner
240.9.bg.d.97.7		16	20.19	odd	2
240.9.bg.d.193.7		16	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(18.3444 + 18.3444i) q^{2} +(33.0681 - 33.0681i) q^{3} +417.032i q^{4} +1213.23 q^{6} +(1693.91 + 1693.91i) q^{7} +(-2954.03 + 2954.03i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(18.3444 + 18.3444i) q^{2} +(33.0681 - 33.0681i) q^{3} +417.032i q^{4} +1213.23 q^{6} +(1693.91 + 1693.91i) q^{7} +(-2954.03 + 2954.03i) q^{8} -2187.00i q^{9} +25244.5 q^{11} +(13790.5 + 13790.5i) q^{12} +(-11411.4 + 11411.4i) q^{13} +62147.4i q^{14} -1619.57 q^{16} +(-38525.0 - 38525.0i) q^{17} +(40119.1 - 40119.1i) q^{18} +25004.0i q^{19} +112029. q^{21} +(463094. + 463094. i) q^{22} +(-341797. + 341797. i) q^{23} +195369. i q^{24} -418671. q^{26} +(-72320.0 - 72320.0i) q^{27} +(-706414. + 706414. i) q^{28} +898012. i q^{29} +722476. q^{31} +(726523. + 726523. i) q^{32} +(834787. - 834787. i) q^{33} -1.41343e6i q^{34} +912049. q^{36} +(744870. + 744870. i) q^{37} +(-458683. + 458683. i) q^{38} +754709. i q^{39} +372769. q^{41} +(2.05510e6 + 2.05510e6i) q^{42} +(2.18643e6 - 2.18643e6i) q^{43} +1.05278e7i q^{44} -1.25401e7 q^{46} +(-4.50830e6 - 4.50830e6i) q^{47} +(-53556.0 + 53556.0i) q^{48} -26154.4i q^{49} -2.54790e6 q^{51} +(-4.75893e6 - 4.75893e6i) q^{52} +(-910386. + 910386. i) q^{53} -2.65333e6i q^{54} -1.00077e7 q^{56} +(826835. + 826835. i) q^{57} +(-1.64735e7 + 1.64735e7i) q^{58} -2.21256e7i q^{59} -1.14825e7 q^{61} +(1.32534e7 + 1.32534e7i) q^{62} +(3.70458e6 - 3.70458e6i) q^{63} +2.70698e7i q^{64} +3.06273e7 q^{66} +(-4.80945e6 - 4.80945e6i) q^{67} +(1.60662e7 - 1.60662e7i) q^{68} +2.26052e7i q^{69} +2.76149e7 q^{71} +(6.46047e6 + 6.46047e6i) q^{72} +(-1.10501e6 + 1.10501e6i) q^{73} +2.73284e7i q^{74} -1.04275e7 q^{76} +(4.27618e7 + 4.27618e7i) q^{77} +(-1.38447e7 + 1.38447e7i) q^{78} -5.65305e7i q^{79} -4.78297e6 q^{81} +(6.83822e6 + 6.83822e6i) q^{82} +(4.51308e7 - 4.51308e7i) q^{83} +4.67195e7i q^{84} +8.02173e7 q^{86} +(2.96955e7 + 2.96955e7i) q^{87} +(-7.45730e7 + 7.45730e7i) q^{88} -1.92663e7i q^{89} -3.86598e7 q^{91} +(-1.42540e8 - 1.42540e8i) q^{92} +(2.38909e7 - 2.38909e7i) q^{93} -1.65404e8i q^{94} +4.80495e7 q^{96} +(-1.54709e7 - 1.54709e7i) q^{97} +(479785. - 479785. i) q^{98} -5.52096e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) \) 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8 - 23616 * q^11 - 22680 * q^12 - 133420 * q^13 - 471380 * q^16 - 573300 * q^17 + 163944 * q^21 + 234700 * q^22 - 651480 * q^23 - 448848 * q^26 + 3567940 * q^28 + 1311776 * q^31 - 641460 * q^32 + 3815100 * q^33 + 5519988 * q^36 + 3607340 * q^37 - 8139840 * q^38 - 14740104 * q^41 + 9643860 * q^42 + 4805480 * q^43 + 14024216 * q^46 - 26529600 * q^47 - 3661200 * q^48 - 6168312 * q^51 + 15861080 * q^52 - 16612140 * q^53 + 10752000 * q^56 - 4714200 * q^57 - 63562980 * q^58 - 12550600 * q^61 + 35190840 * q^62 - 9928980 * q^63 + 46958616 * q^66 - 46836760 * q^67 + 197811840 * q^68 - 85681968 * q^71 + 38185020 * q^72 + 50835800 * q^73 + 101166648 * q^76 - 97175880 * q^77 - 131709240 * q^78 - 76527504 * q^81 + 181542400 * q^82 + 208234800 * q^83 - 187512576 * q^86 + 74298060 * q^87 - 138207420 * q^88 + 38623856 * q^91 - 652331400 * q^92 - 159787080 * q^93 + 531512604 * q^96 + 138370520 * q^97 + 50186520 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more