LMFDB - Embedded newform 350.10.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,10,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("350.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	350.a (trivial)

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:	yes
Analytic conductor:	$180.262542657$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 30664x^{2} - 954173x + 15584709 $ x^4 - x^3 - 30664x^2 - 954173x + 15584709
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 3\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$188.358$ of defining polynomial
Character	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} -184.949 q^{3} +256.000 q^{4} -2959.18 q^{6} +2401.00 q^{7} +4096.00 q^{8} +14523.0 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -184.949 q^{3} +256.000 q^{4} -2959.18 q^{6} +2401.00 q^{7} +4096.00 q^{8} +14523.0 q^{9} -9145.50 q^{11} -47346.8 q^{12} -12757.9 q^{13} +38416.0 q^{14} +65536.0 q^{16} +195951. q^{17} +232368. q^{18} -10329.3 q^{19} -444062. q^{21} -146328. q^{22} -2.43266e6 q^{23} -757550. q^{24} -204126. q^{26} +954336. q^{27} +614656. q^{28} +4.66001e6 q^{29} -5.16761e6 q^{31} +1.04858e6 q^{32} +1.69145e6 q^{33} +3.13521e6 q^{34} +3.71789e6 q^{36} +3.21188e6 q^{37} -165269. q^{38} +2.35956e6 q^{39} -6.84077e6 q^{41} -7.10499e6 q^{42} +1.69448e7 q^{43} -2.34125e6 q^{44} -3.89225e7 q^{46} +1.27638e7 q^{47} -1.21208e7 q^{48} +5.76480e6 q^{49} -3.62408e7 q^{51} -3.26602e6 q^{52} -1.31021e7 q^{53} +1.52694e7 q^{54} +9.83450e6 q^{56} +1.91039e6 q^{57} +7.45602e7 q^{58} +6.40620e7 q^{59} +9.40174e7 q^{61} -8.26817e7 q^{62} +3.48697e7 q^{63} +1.67772e7 q^{64} +2.70632e7 q^{66} -1.25249e8 q^{67} +5.01634e7 q^{68} +4.49916e8 q^{69} +2.04871e8 q^{71} +5.94862e7 q^{72} +1.15647e8 q^{73} +5.13901e7 q^{74} -2.64431e6 q^{76} -2.19584e7 q^{77} +3.77529e7 q^{78} +1.12704e7 q^{79} -4.62359e8 q^{81} -1.09452e8 q^{82} -5.97163e8 q^{83} -1.13680e8 q^{84} +2.71117e8 q^{86} -8.61863e8 q^{87} -3.74600e7 q^{88} +2.42292e8 q^{89} -3.06317e7 q^{91} -6.22760e8 q^{92} +9.55742e8 q^{93} +2.04221e8 q^{94} -1.93933e8 q^{96} -9.71199e8 q^{97} +9.22368e7 q^{98} -1.32820e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 7 q^{3} + 1024 q^{4} + 112 q^{6} + 9604 q^{7} + 16384 q^{8} - 263 q^{9}+O(q^{10}) $ 4 * q + 64 * q^2 + 7 * q^3 + 1024 * q^4 + 112 * q^6 + 9604 * q^7 + 16384 * q^8 - 263 * q^9	\( 4 q + 64 q^{2} + 7 q^{3} + 1024 q^{4} + 112 q^{6} + 9604 q^{7} + 16384 q^{8} - 263 q^{9} - 36284 q^{11} + 1792 q^{12} - 182630 q^{13} + 153664 q^{14} + 262144 q^{16} - 367563 q^{17} - 4208 q^{18} + 222229 q^{19} + 16807 q^{21} - 580544 q^{22} + 182439 q^{23} + 28672 q^{24} - 2922080 q^{26} + 978355 q^{27} + 2458624 q^{28} + 255537 q^{29} - 12276460 q^{31} + 4194304 q^{32} - 3846073 q^{33} - 5881008 q^{34} - 67328 q^{36} - 4274163 q^{37} + 3555664 q^{38} - 27734218 q^{39} - 17136315 q^{41} + 268912 q^{42} - 27962067 q^{43} - 9288704 q^{44} + 2919024 q^{46} - 26065620 q^{47} + 458752 q^{48} + 23059204 q^{49} - 112821039 q^{51} - 46753280 q^{52} - 89230902 q^{53} + 15653680 q^{54} + 39337984 q^{56} - 38823861 q^{57} + 4088592 q^{58} + 96035996 q^{59} - 44213288 q^{61} - 196423360 q^{62} - 631463 q^{63} + 67108864 q^{64} - 61537168 q^{66} - 59945448 q^{67} - 94096128 q^{68} + 496450346 q^{69} - 232110635 q^{71} - 1077248 q^{72} + 28740649 q^{73} - 68386608 q^{74} + 56890624 q^{76} - 87117884 q^{77} - 443747488 q^{78} + 155306887 q^{79} - 398735816 q^{81} - 274181040 q^{82} + 383782847 q^{83} + 4302592 q^{84} - 447393072 q^{86} + 272329372 q^{87} - 148619264 q^{88} - 988710835 q^{89} - 438494630 q^{91} + 46704384 q^{92} - 1244946524 q^{93} - 417049920 q^{94} + 7340032 q^{96} - 950576942 q^{97} + 368947264 q^{98} - 1411275007 q^{99}+O(q^{100}) \) 4 * q + 64 * q^2 + 7 * q^3 + 1024 * q^4 + 112 * q^6 + 9604 * q^7 + 16384 * q^8 - 263 * q^9 - 36284 * q^11 + 1792 * q^12 - 182630 * q^13 + 153664 * q^14 + 262144 * q^16 - 367563 * q^17 - 4208 * q^18 + 222229 * q^19 + 16807 * q^21 - 580544 * q^22 + 182439 * q^23 + 28672 * q^24 - 2922080 * q^26 + 978355 * q^27 + 2458624 * q^28 + 255537 * q^29 - 12276460 * q^31 + 4194304 * q^32 - 3846073 * q^33 - 5881008 * q^34 - 67328 * q^36 - 4274163 * q^37 + 3555664 * q^38 - 27734218 * q^39 - 17136315 * q^41 + 268912 * q^42 - 27962067 * q^43 - 9288704 * q^44 + 2919024 * q^46 - 26065620 * q^47 + 458752 * q^48 + 23059204 * q^49 - 112821039 * q^51 - 46753280 * q^52 - 89230902 * q^53 + 15653680 * q^54 + 39337984 * q^56 - 38823861 * q^57 + 4088592 * q^58 + 96035996 * q^59 - 44213288 * q^61 - 196423360 * q^62 - 631463 * q^63 + 67108864 * q^64 - 61537168 * q^66 - 59945448 * q^67 - 94096128 * q^68 + 496450346 * q^69 - 232110635 * q^71 - 1077248 * q^72 + 28740649 * q^73 - 68386608 * q^74 + 56890624 * q^76 - 87117884 * q^77 - 443747488 * q^78 + 155306887 * q^79 - 398735816 * q^81 - 274181040 * q^82 + 383782847 * q^83 + 4302592 * q^84 - 447393072 * q^86 + 272329372 * q^87 - 148619264 * q^88 - 988710835 * q^89 - 438494630 * q^91 + 46704384 * q^92 - 1244946524 * q^93 - 417049920 * q^94 + 7340032 * q^96 - 950576942 * q^97 + 368947264 * q^98 - 1411275007 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−184.949	−1.31827	−0.659137	−	0.752023i	$-0.729078\pi$
$3$	−184.949	−1.31827	−0.659137	+	0.752023i	$0.729078\pi$
$4$	256.000	0.500000
$5$	0	0
$5$	0	0
$6$	−2959.18	−0.932160
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	4096.00	0.353553
$9$	14523.0	0.737845
$10$	0	0
$11$	−9145.50	−0.188339	−0.0941696	−	0.995556i	$-0.530020\pi$
$11$	−9145.50	−0.188339	−0.0941696	+	0.995556i	$0.530020\pi$
$12$	−47346.8	−0.659137
$13$	−12757.9	−0.123889	−0.0619447	−	0.998080i	$-0.519730\pi$
$13$	−12757.9	−0.123889	−0.0619447	+	0.998080i	$0.519730\pi$
$14$	38416.0	0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	195951.	0.569019	0.284510	−	0.958673i	$-0.408169\pi$
$17$	195951.	0.569019	0.284510	+	0.958673i	$0.408169\pi$
$18$	232368.	0.521735
$19$	−10329.3	−0.0181836	−0.00909182	−	0.999959i	$-0.502894\pi$
$19$	−10329.3	−0.0181836	−0.00909182	+	0.999959i	$0.502894\pi$
$20$	0	0
$21$	−444062.	−0.498260
$22$	−146328.	−0.133176
$23$	−2.43266e6	−1.81261	−0.906307	−	0.422620i	$-0.861111\pi$
$23$	−2.43266e6	−1.81261	−0.906307	+	0.422620i	$0.861111\pi$
$24$	−757550.	−0.466080
$25$	0	0
$26$	−204126.	−0.0876031
$27$	954336.	0.345593
$28$	614656.	0.188982
$29$	4.66001e6	1.22348	0.611739	−	0.791060i	$-0.290470\pi$
$29$	4.66001e6	1.22348	0.611739	+	0.791060i	$0.290470\pi$
$30$	0	0
$31$	−5.16761e6	−1.00499	−0.502495	−	0.864580i	$-0.667585\pi$
$31$	−5.16761e6	−1.00499	−0.502495	+	0.864580i	$0.667585\pi$
$32$	1.04858e6	0.176777
$33$	1.69145e6	0.248282
$34$	3.13521e6	0.402357
$35$	0	0
$36$	3.71789e6	0.368922
$37$	3.21188e6	0.281742	0.140871	−	0.990028i	$-0.455010\pi$
$37$	3.21188e6	0.281742	0.140871	+	0.990028i	$0.455010\pi$
$38$	−165269.	−0.0128578
$39$	2.35956e6	0.163320
$40$	0	0
$41$	−6.84077e6	−0.378074	−0.189037	−	0.981970i	$-0.560537\pi$
$41$	−6.84077e6	−0.378074	−0.189037	+	0.981970i	$0.560537\pi$
$42$	−7.10499e6	−0.352323
$43$	1.69448e7	0.755839	0.377919	−	0.925839i	$-0.376640\pi$
$43$	1.69448e7	0.755839	0.377919	+	0.925839i	$0.376640\pi$
$44$	−2.34125e6	−0.0941696
$45$	0	0
$46$	−3.89225e7	−1.28171
$47$	1.27638e7	0.381540	0.190770	−	0.981635i	$-0.438901\pi$
$47$	1.27638e7	0.381540	0.190770	+	0.981635i	$0.438901\pi$
$48$	−1.21208e7	−0.329568
$49$	5.76480e6	0.142857
$50$	0	0
$51$	−3.62408e7	−0.750123
$52$	−3.26602e6	−0.0619447
$53$	−1.31021e7	−0.228086	−0.114043	−	0.993476i	$-0.536380\pi$
$53$	−1.31021e7	−0.228086	−0.114043	+	0.993476i	$0.536380\pi$
$54$	1.52694e7	0.244371
$55$	0	0
$56$	9.83450e6	0.133631
$57$	1.91039e6	0.0239710
$58$	7.45602e7	0.865130
$59$	6.40620e7	0.688282	0.344141	−	0.938918i	$-0.388170\pi$
$59$	6.40620e7	0.688282	0.344141	+	0.938918i	$0.388170\pi$
$60$	0	0
$61$	9.40174e7	0.869409	0.434704	−	0.900573i	$-0.356853\pi$
$61$	9.40174e7	0.869409	0.434704	+	0.900573i	$0.356853\pi$
$62$	−8.26817e7	−0.710635
$63$	3.48697e7	0.278879
$64$	1.67772e7	0.125000
$65$	0	0
$66$	2.70632e7	0.175562
$67$	−1.25249e8	−0.759345	−0.379672	−	0.925121i	$-0.623963\pi$
$67$	−1.25249e8	−0.759345	−0.379672	+	0.925121i	$0.623963\pi$
$68$	5.01634e7	0.284510
$69$	4.49916e8	2.38952
$70$	0	0
$71$	2.04871e8	0.956794	0.478397	−	0.878144i	$-0.341218\pi$
$71$	2.04871e8	0.956794	0.478397	+	0.878144i	$0.341218\pi$
$72$	5.94862e7	0.260867
$73$	1.15647e8	0.476629	0.238315	−	0.971188i	$-0.423405\pi$
$73$	1.15647e8	0.476629	0.238315	+	0.971188i	$0.423405\pi$
$74$	5.13901e7	0.199222
$75$	0	0
$76$	−2.64431e6	−0.00909182
$77$	−2.19584e7	−0.0711855
$78$	3.77529e7	0.115485
$79$	1.12704e7	0.0325549	0.0162775	−	0.999868i	$-0.494818\pi$
$79$	1.12704e7	0.0325549	0.0162775	+	0.999868i	$0.494818\pi$
$80$	0	0
$81$	−4.62359e8	−1.19343
$82$	−1.09452e8	−0.267339
$83$	−5.97163e8	−1.38115	−0.690576	−	0.723260i	$-0.742643\pi$
$83$	−5.97163e8	−1.38115	−0.690576	+	0.723260i	$0.742643\pi$
$84$	−1.13680e8	−0.249130
$85$	0	0
$86$	2.71117e8	0.534459
$87$	−8.61863e8	−1.61288
$88$	−3.74600e7	−0.0665879
$89$	2.42292e8	0.409340	0.204670	−	0.978831i	$-0.434388\pi$
$89$	2.42292e8	0.409340	0.204670	+	0.978831i	$0.434388\pi$
$90$	0	0
$91$	−3.06317e7	−0.0468258
$92$	−6.22760e8	−0.906307
$93$	9.55742e8	1.32485
$94$	2.04221e8	0.269790
$95$	0	0
$96$	−1.93933e8	−0.233040
$97$	−9.71199e8	−1.11387	−0.556936	−	0.830555i	$-0.688023\pi$
$97$	−9.71199e8	−1.11387	−0.556936	+	0.830555i	$0.688023\pi$
$98$	9.22368e7	0.101015
$99$	−1.32820e8	−0.138965
$100$	0	0
$101$	5.10288e8	0.487943	0.243971	−	0.969782i	$-0.421550\pi$
$101$	5.10288e8	0.487943	0.243971	+	0.969782i	$0.421550\pi$
$102$	−5.79853e8	−0.530417
$103$	7.00825e8	0.613539	0.306769	−	0.951784i	$-0.400752\pi$
$103$	7.00825e8	0.613539	0.306769	+	0.951784i	$0.400752\pi$
$104$	−5.22564e7	−0.0438015
$105$	0	0
$106$	−2.09633e8	−0.161281
$107$	−9.83255e8	−0.725169	−0.362584	−	0.931951i	$-0.618106\pi$
$107$	−9.83255e8	−0.725169	−0.362584	+	0.931951i	$0.618106\pi$
$108$	2.44310e8	0.172796
$109$	2.00802e9	1.36254	0.681270	−	0.732032i	$-0.261428\pi$
$109$	2.00802e9	1.36254	0.681270	+	0.732032i	$0.261428\pi$
$110$	0	0
$111$	−5.94033e8	−0.371413
$112$	1.57352e8	0.0944911
$113$	5.74189e8	0.331285	0.165643	−	0.986186i	$-0.447030\pi$
$113$	5.74189e8	0.331285	0.165643	+	0.986186i	$0.447030\pi$
$114$	3.05663e7	0.0169501
$115$	0	0
$116$	1.19296e9	0.611739
$117$	−1.85283e8	−0.0914111
$118$	1.02499e9	0.486689
$119$	4.70478e8	0.215069
$120$	0	0
$121$	−2.27431e9	−0.964528
$122$	1.50428e9	0.614765
$123$	1.26519e9	0.498405
$124$	−1.32291e9	−0.502495
$125$	0	0
$126$	5.57915e8	0.197197
$127$	−2.67783e9	−0.913412	−0.456706	−	0.889618i	$-0.650971\pi$
$127$	−2.67783e9	−0.913412	−0.456706	+	0.889618i	$0.650971\pi$
$128$	2.68435e8	0.0883883
$129$	−3.13392e9	−0.996402
$130$	0	0
$131$	−1.37966e9	−0.409309	−0.204654	−	0.978834i	$-0.565607\pi$
$131$	−1.37966e9	−0.409309	−0.204654	+	0.978834i	$0.565607\pi$
$132$	4.33011e8	0.124141
$133$	−2.48007e7	−0.00687277
$134$	−2.00399e9	−0.536938
$135$	0	0
$136$	8.02614e8	0.201179
$137$	−3.80895e8	−0.0923767	−0.0461884	−	0.998933i	$-0.514707\pi$
$137$	−3.80895e8	−0.0923767	−0.0461884	+	0.998933i	$0.514707\pi$
$138$	7.19866e9	1.68965
$139$	1.90486e8	0.0432810	0.0216405	−	0.999766i	$-0.493111\pi$
$139$	1.90486e8	0.0432810	0.0216405	+	0.999766i	$0.493111\pi$
$140$	0	0
$141$	−2.36065e9	−0.502974
$142$	3.27794e9	0.676555
$143$	1.16677e8	0.0233332
$144$	9.51779e8	0.184461
$145$	0	0
$146$	1.85035e9	0.337028
$147$	−1.06619e9	−0.188325
$148$	8.22241e8	0.140871
$149$	−3.53750e9	−0.587974	−0.293987	−	0.955809i	$-0.594982\pi$
$149$	−3.53750e9	−0.587974	−0.293987	+	0.955809i	$0.594982\pi$
$150$	0	0
$151$	−1.96605e9	−0.307751	−0.153875	−	0.988090i	$-0.549175\pi$
$151$	−1.96605e9	−0.307751	−0.153875	+	0.988090i	$0.549175\pi$
$152$	−4.23089e7	−0.00642889
$153$	2.84579e9	0.419848
$154$	−3.51334e8	−0.0503357
$155$	0	0
$156$	6.04047e8	0.0816601
$157$	−7.53875e9	−0.990264	−0.495132	−	0.868818i	$-0.664880\pi$
$157$	−7.53875e9	−0.990264	−0.495132	+	0.868818i	$0.664880\pi$
$158$	1.80326e8	0.0230198
$159$	2.42321e9	0.300680
$160$	0	0
$161$	−5.84081e9	−0.685104
$162$	−7.39775e9	−0.843882
$163$	−1.30466e10	−1.44761	−0.723807	−	0.690002i	$-0.757610\pi$
$163$	−1.30466e10	−1.44761	−0.723807	+	0.690002i	$0.757610\pi$
$164$	−1.75124e9	−0.189037
$165$	0	0
$166$	−9.55461e9	−0.976622
$167$	6.63487e9	0.660098	0.330049	−	0.943964i	$-0.392935\pi$
$167$	6.63487e9	0.660098	0.330049	+	0.943964i	$0.392935\pi$
$168$	−1.81888e9	−0.176162
$169$	−1.04417e10	−0.984651
$170$	0	0
$171$	−1.50013e8	−0.0134167
$172$	4.33788e9	0.377919
$173$	−1.60973e10	−1.36630	−0.683151	−	0.730277i	$-0.739391\pi$
$173$	−1.60973e10	−1.36630	−0.683151	+	0.730277i	$0.739391\pi$
$174$	−1.37898e10	−1.14048
$175$	0	0
$176$	−5.99360e8	−0.0470848
$177$	−1.18482e10	−0.907344
$178$	3.87668e9	0.289447
$179$	−1.92583e10	−1.40210	−0.701049	−	0.713113i	$-0.747285\pi$
$179$	−1.92583e10	−1.40210	−0.701049	+	0.713113i	$0.747285\pi$
$180$	0	0
$181$	1.23010e10	0.851899	0.425949	−	0.904747i	$-0.359940\pi$
$181$	1.23010e10	0.851899	0.425949	+	0.904747i	$0.359940\pi$
$182$	−4.90108e8	−0.0331108
$183$	−1.73884e10	−1.14612
$184$	−9.96416e9	−0.640856
$185$	0	0
$186$	1.52919e10	0.936812
$187$	−1.79207e9	−0.107169
$188$	3.26754e9	0.190770
$189$	2.29136e9	0.130622
$190$	0	0
$191$	−3.16654e10	−1.72161	−0.860805	−	0.508935i	$-0.830039\pi$
$191$	−3.16654e10	−1.72161	−0.860805	+	0.508935i	$0.830039\pi$
$192$	−3.10292e9	−0.164784
$193$	−1.87232e10	−0.971343	−0.485671	−	0.874141i	$-0.661425\pi$
$193$	−1.87232e10	−0.971343	−0.485671	+	0.874141i	$0.661425\pi$
$194$	−1.55392e10	−0.787627
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	−1.70648e10	−0.807239	−0.403619	−	0.914927i	$-0.632248\pi$
$197$	−1.70648e10	−0.807239	−0.403619	+	0.914927i	$0.632248\pi$
$198$	−2.12512e9	−0.0982631
$199$	−3.62470e9	−0.163845	−0.0819225	−	0.996639i	$-0.526106\pi$
$199$	−3.62470e9	−0.163845	−0.0819225	+	0.996639i	$0.526106\pi$
$200$	0	0
$201$	2.31647e10	1.00102
$202$	8.16460e9	0.345028
$203$	1.11887e10	0.462431
$204$	−9.27765e9	−0.375061
$205$	0	0
$206$	1.12132e10	0.433837
$207$	−3.53294e10	−1.33743
$208$	−8.36102e8	−0.0309724
$209$	9.44669e7	0.00342469
$210$	0	0
$211$	1.14427e10	0.397428	0.198714	−	0.980058i	$-0.436323\pi$
$211$	1.14427e10	0.397428	0.198714	+	0.980058i	$0.436323\pi$
$212$	−3.35413e9	−0.114043
$213$	−3.78906e10	−1.26132
$214$	−1.57321e10	−0.512772
$215$	0	0
$216$	3.90896e9	0.122185
$217$	−1.24074e10	−0.379851
$218$	3.21284e10	0.963461
$219$	−2.13887e10	−0.628327
$220$	0	0
$221$	−2.49992e9	−0.0704954
$222$	−9.50452e9	−0.262629
$223$	−5.35226e10	−1.44932	−0.724662	−	0.689104i	$-0.758004\pi$
$223$	−5.35226e10	−1.44932	−0.724662	+	0.689104i	$0.758004\pi$
$224$	2.51763e9	0.0668153
$225$	0	0
$226$	9.18702e9	0.234254
$227$	−1.64337e10	−0.410789	−0.205395	−	0.978679i	$-0.565848\pi$
$227$	−1.64337e10	−0.410789	−0.205395	+	0.978679i	$0.565848\pi$
$228$	4.89061e8	0.0119855
$229$	2.20751e9	0.0530448	0.0265224	−	0.999648i	$-0.491557\pi$
$229$	2.20751e9	0.0530448	0.0265224	+	0.999648i	$0.491557\pi$
$230$	0	0
$231$	4.06117e9	0.0938419
$232$	1.90874e10	0.432565
$233$	−9.93425e9	−0.220818	−0.110409	−	0.993886i	$-0.535216\pi$
$233$	−9.93425e9	−0.220818	−0.110409	+	0.993886i	$0.535216\pi$
$234$	−2.96453e9	−0.0646374
$235$	0	0
$236$	1.63999e10	0.344141
$237$	−2.08444e9	−0.0429163
$238$	7.52764e9	0.152077
$239$	−2.78139e10	−0.551405	−0.275702	−	0.961243i	$-0.588910\pi$
$239$	−2.78139e10	−0.551405	−0.275702	+	0.961243i	$0.588910\pi$
$240$	0	0
$241$	1.22545e10	0.234002	0.117001	−	0.993132i	$-0.462672\pi$
$241$	1.22545e10	0.234002	0.117001	+	0.993132i	$0.462672\pi$
$242$	−3.63889e10	−0.682025
$243$	6.67285e10	1.22767
$244$	2.40685e10	0.434704
$245$	0	0
$246$	2.02430e10	0.352426
$247$	1.31781e8	0.00225276
$248$	−2.11665e10	−0.355318
$249$	1.10445e11	1.82074
$250$	0	0
$251$	5.23734e10	0.832873	0.416436	−	0.909165i	$-0.363279\pi$
$251$	5.23734e10	0.832873	0.416436	+	0.909165i	$0.363279\pi$
$252$	8.92665e9	0.139440
$253$	2.22479e10	0.341386
$254$	−4.28453e10	−0.645880
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−1.15695e11	−1.65430	−0.827149	−	0.561983i	$-0.810039\pi$
$257$	−1.15695e11	−1.65430	−0.827149	+	0.561983i	$0.810039\pi$
$258$	−5.01428e10	−0.704562
$259$	7.71172e9	0.106488
$260$	0	0
$261$	6.76773e10	0.902737
$262$	−2.20745e10	−0.289425
$263$	−5.95846e10	−0.767951	−0.383975	−	0.923343i	$-0.625445\pi$
$263$	−5.95846e10	−0.767951	−0.383975	+	0.923343i	$0.625445\pi$
$264$	6.92817e9	0.0877811
$265$	0	0
$266$	−3.96811e8	−0.00485978
$267$	−4.48116e10	−0.539623
$268$	−3.20638e10	−0.379672
$269$	1.37245e11	1.59812	0.799062	−	0.601249i	$-0.205330\pi$
$269$	1.37245e11	1.59812	0.799062	+	0.601249i	$0.205330\pi$
$270$	0	0
$271$	8.81462e10	0.992754	0.496377	−	0.868107i	$-0.334663\pi$
$271$	8.81462e10	0.992754	0.496377	+	0.868107i	$0.334663\pi$
$272$	1.28418e10	0.142255
$273$	5.66530e9	0.0617292
$274$	−6.09432e9	−0.0653202
$275$	0	0
$276$	1.15179e11	1.19476
$277$	−7.18053e10	−0.732820	−0.366410	−	0.930453i	$-0.619413\pi$
$277$	−7.18053e10	−0.732820	−0.366410	+	0.930453i	$0.619413\pi$
$278$	3.04778e9	0.0306043
$279$	−7.50491e10	−0.741527
$280$	0	0
$281$	1.39478e10	0.133453	0.0667265	−	0.997771i	$-0.478744\pi$
$281$	1.39478e10	0.133453	0.0667265	+	0.997771i	$0.478744\pi$
$282$	−3.77704e10	−0.355657
$283$	5.69305e10	0.527602	0.263801	−	0.964577i	$-0.415024\pi$
$283$	5.69305e10	0.527602	0.263801	+	0.964577i	$0.415024\pi$
$284$	5.24470e10	0.478397
$285$	0	0
$286$	1.86684e9	0.0164991
$287$	−1.64247e10	−0.142899
$288$	1.52285e10	0.130434
$289$	−8.01912e10	−0.676217
$290$	0	0
$291$	1.79622e11	1.46839
$292$	2.96056e10	0.238315
$293$	2.60372e10	0.206390	0.103195	−	0.994661i	$-0.467093\pi$
$293$	2.60372e10	0.206390	0.103195	+	0.994661i	$0.467093\pi$
$294$	−1.70591e10	−0.133166
$295$	0	0
$296$	1.31559e10	0.0996108
$297$	−8.72788e9	−0.0650886
$298$	−5.66000e10	−0.415761
$299$	3.10356e10	0.224564
$300$	0	0
$301$	4.06845e10	0.285680
$302$	−3.14568e10	−0.217613
$303$	−9.43770e10	−0.643242
$304$	−6.76943e8	−0.00454591
$305$	0	0
$306$	4.55327e10	0.296877
$307$	−1.39216e11	−0.894470	−0.447235	−	0.894417i	$-0.647591\pi$
$307$	−1.39216e11	−0.894470	−0.447235	+	0.894417i	$0.647591\pi$
$308$	−5.62134e9	−0.0355927
$309$	−1.29617e11	−0.808812
$310$	0	0
$311$	2.80742e11	1.70171	0.850855	−	0.525400i	$-0.176084\pi$
$311$	2.80742e11	1.70171	0.850855	+	0.525400i	$0.176084\pi$
$312$	9.66475e9	0.0577424
$313$	1.32418e10	0.0779826	0.0389913	−	0.999240i	$-0.487586\pi$
$313$	1.32418e10	0.0779826	0.0389913	+	0.999240i	$0.487586\pi$
$314$	−1.20620e11	−0.700222
$315$	0	0
$316$	2.88522e9	0.0162775
$317$	8.58533e9	0.0477519	0.0238759	−	0.999715i	$-0.492399\pi$
$317$	8.58533e9	0.0477519	0.0238759	+	0.999715i	$0.492399\pi$
$318$	3.87714e10	0.212613
$319$	−4.26182e10	−0.230429
$320$	0	0
$321$	1.81852e11	0.955970
$322$	−9.34529e10	−0.484441
$323$	−2.02404e9	−0.0103468
$324$	−1.18364e11	−0.596715
$325$	0	0
$326$	−2.08746e11	−1.02362
$327$	−3.71381e11	−1.79620
$328$	−2.80198e10	−0.133670
$329$	3.06459e10	0.144209
$330$	0	0
$331$	1.54965e11	0.709590	0.354795	−	0.934944i	$-0.384551\pi$
$331$	1.54965e11	0.709590	0.354795	+	0.934944i	$0.384551\pi$
$332$	−1.52874e11	−0.690576
$333$	4.66461e10	0.207882
$334$	1.06158e11	0.466760
$335$	0	0
$336$	−2.91020e10	−0.124565
$337$	−9.47955e10	−0.400362	−0.200181	−	0.979759i	$-0.564153\pi$
$337$	−9.47955e10	−0.400362	−0.200181	+	0.979759i	$0.564153\pi$
$338$	−1.67068e11	−0.696254
$339$	−1.06195e11	−0.436724
$340$	0	0
$341$	4.72604e10	0.189279
$342$	−2.40020e9	−0.00948704
$343$	1.38413e10	0.0539949
$344$	6.94060e10	0.267229
$345$	0	0
$346$	−2.57557e11	−0.966121
$347$	−2.34378e9	−0.00867830	−0.00433915	−	0.999991i	$-0.501381\pi$
$347$	−2.34378e9	−0.00867830	−0.00433915	+	0.999991i	$0.501381\pi$
$348$	−2.20637e11	−0.806439
$349$	−3.75953e11	−1.35650	−0.678250	−	0.734832i	$-0.737261\pi$
$349$	−3.75953e11	−1.35650	−0.678250	+	0.734832i	$0.737261\pi$
$350$	0	0
$351$	−1.21753e10	−0.0428153
$352$	−9.58976e9	−0.0332940
$353$	3.30165e11	1.13173	0.565867	−	0.824497i	$-0.308542\pi$
$353$	3.30165e11	1.13173	0.565867	+	0.824497i	$0.308542\pi$
$354$	−1.89571e11	−0.641589
$355$	0	0
$356$	6.20268e10	0.204670
$357$	−8.70142e10	−0.283520
$358$	−3.08132e11	−0.991433
$359$	−1.83725e11	−0.583773	−0.291887	−	0.956453i	$-0.594283\pi$
$359$	−1.83725e11	−0.583773	−0.291887	+	0.956453i	$0.594283\pi$
$360$	0	0
$361$	−3.22581e11	−0.999669
$362$	1.96817e11	0.602383
$363$	4.20630e11	1.27151
$364$	−7.84172e9	−0.0234129
$365$	0	0
$366$	−2.78214e11	−0.810428
$367$	−7.26307e10	−0.208989	−0.104494	−	0.994525i	$-0.533322\pi$
$367$	−7.26307e10	−0.208989	−0.104494	+	0.994525i	$0.533322\pi$
$368$	−1.59427e11	−0.453154
$369$	−9.93484e10	−0.278960
$370$	0	0
$371$	−3.14581e10	−0.0862084
$372$	2.44670e11	0.662426
$373$	−6.15713e11	−1.64698	−0.823490	−	0.567331i	$-0.807976\pi$
$373$	−6.15713e11	−1.64698	−0.823490	+	0.567331i	$0.807976\pi$
$374$	−2.86731e10	−0.0757796
$375$	0	0
$376$	5.22806e10	0.134895
$377$	−5.94520e10	−0.151576
$378$	3.66618e10	0.0923635
$379$	−1.07045e11	−0.266495	−0.133248	−	0.991083i	$-0.542541\pi$
$379$	−1.07045e11	−0.266495	−0.133248	+	0.991083i	$0.542541\pi$
$380$	0	0
$381$	4.95261e11	1.20413
$382$	−5.06646e11	−1.21736
$383$	−4.29799e11	−1.02064	−0.510318	−	0.859986i	$-0.670472\pi$
$383$	−4.29799e11	−1.02064	−0.510318	+	0.859986i	$0.670472\pi$
$384$	−4.96468e10	−0.116520
$385$	0	0
$386$	−2.99571e11	−0.686843
$387$	2.46090e11	0.557691
$388$	−2.48627e11	−0.556936
$389$	5.33893e11	1.18217	0.591087	−	0.806608i	$-0.298699\pi$
$389$	5.33893e11	1.18217	0.591087	+	0.806608i	$0.298699\pi$
$390$	0	0
$391$	−4.76681e11	−1.03141
$392$	2.36126e10	0.0505076
$393$	2.55166e11	0.539581
$394$	−2.73036e11	−0.570804
$395$	0	0
$396$	−3.40019e10	−0.0694825
$397$	2.35660e11	0.476133	0.238067	−	0.971249i	$-0.423486\pi$
$397$	2.35660e11	0.476133	0.238067	+	0.971249i	$0.423486\pi$
$398$	−5.79952e10	−0.115856
$399$	4.58686e9	0.00906019
$400$	0	0
$401$	−5.77945e11	−1.11619	−0.558094	−	0.829778i	$-0.688467\pi$
$401$	−5.77945e11	−1.11619	−0.558094	+	0.829778i	$0.688467\pi$
$402$	3.70635e11	0.707831
$403$	6.59278e10	0.124508
$404$	1.30634e11	0.243971
$405$	0	0
$406$	1.79019e11	0.326988
$407$	−2.93743e10	−0.0530630
$408$	−1.48442e11	−0.265208
$409$	1.68833e11	0.298334	0.149167	−	0.988812i	$-0.452341\pi$
$409$	1.68833e11	0.298334	0.149167	+	0.988812i	$0.452341\pi$
$410$	0	0
$411$	7.04460e10	0.121778
$412$	1.79411e11	0.306769
$413$	1.53813e11	0.260146
$414$	−5.65271e11	−0.945704
$415$	0	0
$416$	−1.33776e10	−0.0219008
$417$	−3.52302e10	−0.0570561
$418$	1.51147e9	0.00242162
$419$	−5.98516e11	−0.948665	−0.474333	−	0.880346i	$-0.657311\pi$
$419$	−5.98516e11	−0.948665	−0.474333	+	0.880346i	$0.657311\pi$
$420$	0	0
$421$	7.51464e10	0.116584	0.0582920	−	0.998300i	$-0.481435\pi$
$421$	7.51464e10	0.116584	0.0582920	+	0.998300i	$0.481435\pi$
$422$	1.83084e11	0.281024
$423$	1.85369e11	0.281517
$424$	−5.36661e10	−0.0806406
$425$	0	0
$426$	−6.06250e11	−0.891885
$427$	2.25736e11	0.328606
$428$	−2.51713e11	−0.362584
$429$	−2.15793e10	−0.0307596
$430$	0	0
$431$	−1.13736e12	−1.58763	−0.793815	−	0.608159i	$-0.791908\pi$
$431$	−1.13736e12	−1.58763	−0.793815	+	0.608159i	$0.791908\pi$
$432$	6.25434e10	0.0863981
$433$	8.19900e11	1.12090	0.560448	−	0.828190i	$-0.310629\pi$
$433$	8.19900e11	1.12090	0.560448	+	0.828190i	$0.310629\pi$
$434$	−1.98519e11	−0.268595
$435$	0	0
$436$	5.14054e11	0.681270
$437$	2.51277e10	0.0329599
$438$	−3.42219e11	−0.444295
$439$	9.07439e11	1.16608	0.583039	−	0.812444i	$-0.301864\pi$
$439$	9.07439e11	1.16608	0.583039	+	0.812444i	$0.301864\pi$
$440$	0	0
$441$	8.37222e10	0.105406
$442$	−3.99987e10	−0.0498478
$443$	6.53202e11	0.805806	0.402903	−	0.915243i	$-0.368001\pi$
$443$	6.53202e11	0.805806	0.402903	+	0.915243i	$0.368001\pi$
$444$	−1.52072e11	−0.185706
$445$	0	0
$446$	−8.56362e11	−1.02483
$447$	6.54256e11	0.775111
$448$	4.02821e10	0.0472456
$449$	−4.55908e11	−0.529382	−0.264691	−	0.964333i	$-0.585270\pi$
$449$	−4.55908e11	−0.529382	−0.264691	+	0.964333i	$0.585270\pi$
$450$	0	0
$451$	6.25622e10	0.0712062
$452$	1.46992e11	0.165643
$453$	3.63619e11	0.405699
$454$	−2.62939e11	−0.290472
$455$	0	0
$456$	7.82497e9	0.00847503
$457$	3.85725e11	0.413671	0.206835	−	0.978376i	$-0.433684\pi$
$457$	3.85725e11	0.413671	0.206835	+	0.978376i	$0.433684\pi$
$458$	3.53201e10	0.0375083
$459$	1.87003e11	0.196649
$460$	0	0
$461$	−7.85020e11	−0.809518	−0.404759	−	0.914423i	$-0.632645\pi$
$461$	−7.85020e11	−0.809518	−0.404759	+	0.914423i	$0.632645\pi$
$462$	6.49787e10	0.0663563
$463$	1.10144e12	1.11390	0.556952	−	0.830545i	$-0.311971\pi$
$463$	1.10144e12	1.11390	0.556952	+	0.830545i	$0.311971\pi$
$464$	3.05399e11	0.305869
$465$	0	0
$466$	−1.58948e11	−0.156142
$467$	−2.03124e12	−1.97622	−0.988112	−	0.153736i	$-0.950869\pi$
$467$	−2.03124e12	−1.97622	−0.988112	+	0.153736i	$0.950869\pi$
$468$	−4.74324e10	−0.0457056
$469$	−3.00724e11	−0.287005
$470$	0	0
$471$	1.39428e12	1.30544
$472$	2.62398e11	0.243344
$473$	−1.54969e11	−0.142354
$474$	−3.33511e10	−0.0303464
$475$	0	0
$476$	1.20442e11	0.107534
$477$	−1.90281e11	−0.168292
$478$	−4.45022e11	−0.389902
$479$	8.54579e11	0.741724	0.370862	−	0.928688i	$-0.379062\pi$
$479$	8.54579e11	0.741724	0.370862	+	0.928688i	$0.379062\pi$
$480$	0	0
$481$	−4.09768e10	−0.0349048
$482$	1.96072e11	0.165464
$483$	1.08025e12	0.903154
$484$	−5.82223e11	−0.482264
$485$	0	0
$486$	1.06766e12	0.868097
$487$	−2.14946e12	−1.73161	−0.865803	−	0.500385i	$-0.833192\pi$
$487$	−2.14946e12	−1.73161	−0.865803	+	0.500385i	$0.833192\pi$
$488$	3.85095e11	0.307382
$489$	2.41295e12	1.90835
$490$	0	0
$491$	1.50434e12	1.16810	0.584050	−	0.811718i	$-0.301467\pi$
$491$	1.50434e12	1.16810	0.584050	+	0.811718i	$0.301467\pi$
$492$	3.23889e11	0.249203
$493$	9.13133e11	0.696182
$494$	2.10849e9	0.00159294
$495$	0	0
$496$	−3.38664e11	−0.251248
$497$	4.91896e11	0.361634
$498$	1.76711e12	1.28745
$499$	1.65677e12	1.19622	0.598109	−	0.801415i	$-0.295919\pi$
$499$	1.65677e12	1.19622	0.598109	+	0.801415i	$0.295919\pi$
$500$	0	0
$501$	−1.22711e12	−0.870190
$502$	8.37974e11	0.588930
$503$	7.50706e11	0.522894	0.261447	−	0.965218i	$-0.415800\pi$
$503$	7.50706e11	0.522894	0.261447	+	0.965218i	$0.415800\pi$
$504$	1.42826e11	0.0985986
$505$	0	0
$506$	3.55966e11	0.241396
$507$	1.93118e12	1.29804
$508$	−6.85525e11	−0.456706
$509$	1.01686e12	0.671480	0.335740	−	0.941955i	$-0.391014\pi$
$509$	1.01686e12	0.671480	0.335740	+	0.941955i	$0.391014\pi$
$510$	0	0
$511$	2.77668e11	0.180149
$512$	6.87195e10	0.0441942
$513$	−9.85764e9	−0.00628413
$514$	−1.85111e12	−1.16977
$515$	0	0
$516$	−8.02284e11	−0.498201
$517$	−1.16732e11	−0.0718590
$518$	1.23388e11	0.0752987
$519$	2.97718e12	1.80116
$520$	0	0
$521$	2.47067e11	0.146908	0.0734539	−	0.997299i	$-0.476598\pi$
$521$	2.47067e11	0.146908	0.0734539	+	0.997299i	$0.476598\pi$
$522$	1.08284e12	0.638331
$523$	−2.44458e12	−1.42872	−0.714359	−	0.699779i	$-0.753282\pi$
$523$	−2.44458e12	−1.42872	−0.714359	+	0.699779i	$0.753282\pi$
$524$	−3.53193e11	−0.204654
$525$	0	0
$526$	−9.53354e11	−0.543023
$527$	−1.01260e12	−0.571859
$528$	1.10851e11	0.0620706
$529$	4.11666e12	2.28557
$530$	0	0
$531$	9.30372e11	0.507845
$532$	−6.34898e9	−0.00343638
$533$	8.72738e10	0.0468394
$534$	−7.16986e11	−0.381571
$535$	0	0
$536$	−5.13021e11	−0.268469
$537$	3.56179e12	1.84835
$538$	2.19591e12	1.13004
$539$	−5.27220e10	−0.0269056
$540$	0	0
$541$	−2.14650e12	−1.07732	−0.538658	−	0.842524i	$-0.681069\pi$
$541$	−2.14650e12	−1.07732	−0.538658	+	0.842524i	$0.681069\pi$
$542$	1.41034e12	0.701983
$543$	−2.27506e12	−1.12304
$544$	2.05469e11	0.100589
$545$	0	0
$546$	9.06447e10	0.0436491
$547$	−2.47600e12	−1.18252	−0.591259	−	0.806482i	$-0.701369\pi$
$547$	−2.47600e12	−1.18252	−0.591259	+	0.806482i	$0.701369\pi$
$548$	−9.75091e10	−0.0461884
$549$	1.36541e12	0.641489
$550$	0	0
$551$	−4.81348e10	−0.0222473
$552$	1.84286e12	0.844823
$553$	2.70602e10	0.0123046
$554$	−1.14888e12	−0.518182
$555$	0	0
$556$	4.87645e10	0.0216405
$557$	2.30979e12	1.01678	0.508388	−	0.861128i	$-0.330242\pi$
$557$	2.30979e12	1.01678	0.508388	+	0.861128i	$0.330242\pi$
$558$	−1.20079e12	−0.524339
$559$	−2.16180e11	−0.0936404
$560$	0	0
$561$	3.31441e11	0.141277
$562$	2.23165e11	0.0943655
$563$	2.15348e12	0.903344	0.451672	−	0.892184i	$-0.350828\pi$
$563$	2.15348e12	0.903344	0.451672	+	0.892184i	$0.350828\pi$
$564$	−6.04327e11	−0.251487
$565$	0	0
$566$	9.10888e11	0.373071
$567$	−1.11012e12	−0.451074
$568$	8.39152e11	0.338278
$569$	4.45987e12	1.78368	0.891841	−	0.452349i	$-0.149414\pi$
$569$	4.45987e12	1.78368	0.891841	+	0.452349i	$0.149414\pi$
$570$	0	0
$571$	−2.93833e12	−1.15675	−0.578373	−	0.815772i	$-0.696312\pi$
$571$	−2.93833e12	−1.15675	−0.578373	+	0.815772i	$0.696312\pi$
$572$	2.98694e10	0.0116666
$573$	5.85647e12	2.26955
$574$	−2.62795e11	−0.101045
$575$	0	0
$576$	2.43655e11	0.0922306
$577$	2.89323e12	1.08665	0.543327	−	0.839521i	$-0.317164\pi$
$577$	2.89323e12	1.08665	0.543327	+	0.839521i	$0.317164\pi$
$578$	−1.28306e12	−0.478158
$579$	3.46283e12	1.28050
$580$	0	0
$581$	−1.43379e12	−0.522027
$582$	2.87395e12	1.03831
$583$	1.19825e11	0.0429575
$584$	4.73689e11	0.168514
$585$	0	0
$586$	4.16595e11	0.145940
$587$	3.74697e12	1.30259	0.651296	−	0.758824i	$-0.274226\pi$
$587$	3.74697e12	1.30259	0.651296	+	0.758824i	$0.274226\pi$
$588$	−2.72945e11	−0.0941624
$589$	5.33779e10	0.0182744
$590$	0	0
$591$	3.15610e12	1.06416
$592$	2.10494e11	0.0704355
$593$	−2.99959e12	−0.996129	−0.498065	−	0.867140i	$-0.665956\pi$
$593$	−2.99959e12	−0.996129	−0.498065	+	0.867140i	$0.665956\pi$
$594$	−1.39646e11	−0.0460246
$595$	0	0
$596$	−9.05600e11	−0.293987
$597$	6.70383e11	0.215993
$598$	4.96569e11	0.158791
$599$	1.12884e12	0.358271	0.179135	−	0.983824i	$-0.442670\pi$
$599$	1.12884e12	0.358271	0.179135	+	0.983824i	$0.442670\pi$
$600$	0	0
$601$	3.52400e12	1.10180	0.550898	−	0.834573i	$-0.314285\pi$
$601$	3.52400e12	1.10180	0.550898	+	0.834573i	$0.314285\pi$
$602$	6.50952e11	0.202006
$603$	−1.81900e12	−0.560278
$604$	−5.03310e11	−0.153875
$605$	0	0
$606$	−1.51003e12	−0.454841
$607$	−2.42156e12	−0.724014	−0.362007	−	0.932175i	$-0.617908\pi$
$607$	−2.42156e12	−0.724014	−0.362007	+	0.932175i	$0.617908\pi$
$608$	−1.08311e10	−0.00321444
$609$	−2.06933e12	−0.609611
$610$	0	0
$611$	−1.62840e11	−0.0472688
$612$	7.28523e11	0.209924
$613$	−4.89467e12	−1.40008	−0.700038	−	0.714106i	$-0.746834\pi$
$613$	−4.89467e12	−1.40008	−0.700038	+	0.714106i	$0.746834\pi$
$614$	−2.22745e12	−0.632486
$615$	0	0
$616$	−8.99414e10	−0.0251679
$617$	3.00988e12	0.836116	0.418058	−	0.908420i	$-0.362711\pi$
$617$	3.00988e12	0.836116	0.418058	+	0.908420i	$0.362711\pi$
$618$	−2.07387e12	−0.571916
$619$	−4.52183e12	−1.23796	−0.618979	−	0.785407i	$-0.712453\pi$
$619$	−4.52183e12	−1.23796	−0.618979	+	0.785407i	$0.712453\pi$
$620$	0	0
$621$	−2.32157e12	−0.626426
$622$	4.49187e12	1.20329
$623$	5.81744e11	0.154716
$624$	1.54636e11	0.0408300
$625$	0	0
$626$	2.11869e11	0.0551420
$627$	−1.74715e10	−0.00451468
$628$	−1.92992e12	−0.495132
$629$	6.29370e11	0.160317
$630$	0	0
$631$	−1.41264e12	−0.354732	−0.177366	−	0.984145i	$-0.556758\pi$
$631$	−1.41264e12	−0.354732	−0.177366	+	0.984145i	$0.556758\pi$
$632$	4.61635e10	0.0115099
$633$	−2.11632e12	−0.523919
$634$	1.37365e11	0.0337657
$635$	0	0
$636$	6.20342e11	0.150340
$637$	−7.35468e10	−0.0176985
$638$	−6.81891e11	−0.162938
$639$	2.97534e12	0.705965
$640$	0	0
$641$	−6.11799e12	−1.43136	−0.715678	−	0.698430i	$-0.753882\pi$
$641$	−6.11799e12	−1.43136	−0.715678	+	0.698430i	$0.753882\pi$
$642$	2.90963e12	0.675973
$643$	−5.03448e11	−0.116146	−0.0580732	−	0.998312i	$-0.518496\pi$
$643$	−5.03448e11	−0.116146	−0.0580732	+	0.998312i	$0.518496\pi$
$644$	−1.49525e12	−0.342552
$645$	0	0
$646$	−3.23846e10	−0.00731632
$647$	5.22457e12	1.17215	0.586073	−	0.810258i	$-0.300673\pi$
$647$	5.22457e12	1.17215	0.586073	+	0.810258i	$0.300673\pi$
$648$	−1.89382e12	−0.421941
$649$	−5.85879e11	−0.129630
$650$	0	0
$651$	2.29474e12	0.500747
$652$	−3.33993e12	−0.723807
$653$	1.99808e11	0.0430035	0.0215018	−	0.999769i	$-0.493155\pi$
$653$	1.99808e11	0.0430035	0.0215018	+	0.999769i	$0.493155\pi$
$654$	−5.94210e12	−1.27011
$655$	0	0
$656$	−4.48316e11	−0.0945186
$657$	1.67954e12	0.351678
$658$	4.90335e11	0.101971
$659$	−5.38091e12	−1.11140	−0.555702	−	0.831382i	$-0.687550\pi$
$659$	−5.38091e12	−1.11140	−0.555702	+	0.831382i	$0.687550\pi$
$660$	0	0
$661$	2.41478e12	0.492006	0.246003	−	0.969269i	$-0.420883\pi$
$661$	2.41478e12	0.492006	0.246003	+	0.969269i	$0.420883\pi$
$662$	2.47944e12	0.501756
$663$	4.62357e11	0.0929323
$664$	−2.44598e12	−0.488311
$665$	0	0
$666$	7.46338e11	0.146995
$667$	−1.13362e13	−2.21769
$668$	1.69853e12	0.330049
$669$	9.89894e12	1.91061
$670$	0	0
$671$	−8.59837e11	−0.163744
$672$	−4.65632e11	−0.0880808
$673$	1.06168e13	1.99493	0.997463	−	0.0711807i	$-0.0226767\pi$
$673$	1.06168e13	1.99493	0.997463	+	0.0711807i	$0.0226767\pi$
$674$	−1.51673e12	−0.283099
$675$	0	0
$676$	−2.67308e12	−0.492326
$677$	−7.97493e12	−1.45908	−0.729538	−	0.683940i	$-0.760265\pi$
$677$	−7.97493e12	−1.45908	−0.729538	+	0.683940i	$0.760265\pi$
$678$	−1.69913e12	−0.308811
$679$	−2.33185e12	−0.421004
$680$	0	0
$681$	3.03939e12	0.541532
$682$	7.56166e11	0.133840
$683$	−8.63770e12	−1.51882	−0.759408	−	0.650615i	$-0.774511\pi$
$683$	−8.63770e12	−1.51882	−0.759408	+	0.650615i	$0.774511\pi$
$684$	−3.84033e10	−0.00670835
$685$	0	0
$686$	2.21461e11	0.0381802
$687$	−4.08276e11	−0.0699276
$688$	1.11050e12	0.188960
$689$	1.67155e11	0.0282575
$690$	0	0
$691$	−7.28867e12	−1.21618	−0.608089	−	0.793869i	$-0.708064\pi$
$691$	−7.28867e12	−1.21618	−0.608089	+	0.793869i	$0.708064\pi$
$692$	−4.12092e12	−0.683151
$693$	−3.18901e11	−0.0525238
$694$	−3.75005e10	−0.00613648
$695$	0	0
$696$	−3.53019e12	−0.570239
$697$	−1.34045e12	−0.215132
$698$	−6.01525e12	−0.959190
$699$	1.83733e12	0.291098
$700$	0	0
$701$	2.95893e12	0.462810	0.231405	−	0.972857i	$-0.425668\pi$
$701$	2.95893e12	0.462810	0.231405	+	0.972857i	$0.425668\pi$
$702$	−1.94805e11	−0.0302750
$703$	−3.31765e10	−0.00512309
$704$	−1.53436e11	−0.0235424
$705$	0	0
$706$	5.28263e12	0.800257
$707$	1.22520e12	0.184425
$708$	−3.03313e12	−0.453672
$709$	−6.21704e12	−0.924008	−0.462004	−	0.886878i	$-0.652869\pi$
$709$	−6.21704e12	−0.924008	−0.462004	+	0.886878i	$0.652869\pi$
$710$	0	0
$711$	1.63680e11	0.0240205
$712$	9.92430e11	0.144724
$713$	1.25710e13	1.82166
$714$	−1.39223e12	−0.200479
$715$	0	0
$716$	−4.93011e12	−0.701049
$717$	5.14413e12	0.726902
$718$	−2.93961e12	−0.412790
$719$	−9.91499e12	−1.38361	−0.691803	−	0.722087i	$-0.743183\pi$
$719$	−9.91499e12	−1.38361	−0.691803	+	0.722087i	$0.743183\pi$
$720$	0	0
$721$	1.68268e12	0.231896
$722$	−5.16130e12	−0.706873
$723$	−2.26646e12	−0.308479
$724$	3.14906e12	0.425949
$725$	0	0
$726$	6.73008e12	0.899095
$727$	1.06689e11	0.0141649	0.00708247	−	0.999975i	$-0.497746\pi$
$727$	1.06689e11	0.0141649	0.00708247	+	0.999975i	$0.497746\pi$
$728$	−1.25468e11	−0.0165554
$729$	−3.24073e12	−0.424980
$730$	0	0
$731$	3.32035e12	0.430087
$732$	−4.45143e12	−0.573059
$733$	8.46143e12	1.08262	0.541310	−	0.840823i	$-0.317929\pi$
$733$	8.46143e12	1.08262	0.541310	+	0.840823i	$0.317929\pi$
$734$	−1.16209e12	−0.147777
$735$	0	0
$736$	−2.55082e12	−0.320428
$737$	1.14547e12	0.143014
$738$	−1.58957e12	−0.197255
$739$	−2.27314e12	−0.280366	−0.140183	−	0.990126i	$-0.544769\pi$
$739$	−2.27314e12	−0.280366	−0.140183	+	0.990126i	$0.544769\pi$
$740$	0	0
$741$	−2.43726e10	−0.00296975
$742$	−5.03329e11	−0.0609586
$743$	1.22616e13	1.47604	0.738021	−	0.674778i	$-0.235760\pi$
$743$	1.22616e13	1.47604	0.738021	+	0.674778i	$0.235760\pi$
$744$	3.91472e12	0.468406
$745$	0	0
$746$	−9.85140e12	−1.16459
$747$	−8.67260e12	−1.01908
$748$	−4.58770e11	−0.0535843
$749$	−2.36079e12	−0.274088
$750$	0	0
$751$	8.69236e12	0.997144	0.498572	−	0.866848i	$-0.333858\pi$
$751$	8.69236e12	0.997144	0.498572	+	0.866848i	$0.333858\pi$
$752$	8.36490e11	0.0953851
$753$	−9.68638e12	−1.09795
$754$	−9.51232e11	−0.107180
$755$	0	0
$756$	5.86588e11	0.0653108
$757$	5.74839e12	0.636231	0.318116	−	0.948052i	$-0.396950\pi$
$757$	5.74839e12	0.636231	0.318116	+	0.948052i	$0.396950\pi$
$758$	−1.71272e12	−0.188441
$759$	−4.11471e12	−0.450040
$760$	0	0
$761$	−3.06164e11	−0.0330920	−0.0165460	−	0.999863i	$-0.505267\pi$
$761$	−3.06164e11	−0.0330920	−0.0165460	+	0.999863i	$0.505267\pi$
$762$	7.92418e12	0.851446
$763$	4.82126e12	0.514992
$764$	−8.10634e12	−0.860805
$765$	0	0
$766$	−6.87678e12	−0.721698
$767$	−8.17297e11	−0.0852709
$768$	−7.94348e11	−0.0823921
$769$	1.16297e13	1.19922	0.599611	−	0.800291i	$-0.295322\pi$
$769$	1.16297e13	1.19922	0.599611	+	0.800291i	$0.295322\pi$
$770$	0	0
$771$	2.13975e13	2.18082
$772$	−4.79314e12	−0.485671
$773$	1.73446e13	1.74725	0.873627	−	0.486596i	$-0.161761\pi$
$773$	1.73446e13	1.74725	0.873627	+	0.486596i	$0.161761\pi$
$774$	3.93743e12	0.394347
$775$	0	0
$776$	−3.97803e12	−0.393813
$777$	−1.42627e12	−0.140381
$778$	8.54229e12	0.835923
$779$	7.06605e10	0.00687477
$780$	0	0
$781$	−1.87365e12	−0.180202
$782$	−7.62689e12	−0.729318
$783$	4.44722e12	0.422825
$784$	3.77802e11	0.0357143
$785$	0	0
$786$	4.08266e12	0.381541
$787$	−2.05847e13	−1.91275	−0.956377	−	0.292137i	$-0.905634\pi$
$787$	−2.05847e13	−1.91275	−0.956377	+	0.292137i	$0.905634\pi$
$788$	−4.36858e12	−0.403619
$789$	1.10201e13	1.01237
$790$	0	0
$791$	1.37863e12	0.125214
$792$	−5.44031e11	−0.0491315
$793$	−1.19947e12	−0.107711
$794$	3.77056e12	0.336677
$795$	0	0
$796$	−9.27923e11	−0.0819225
$797$	2.50358e12	0.219786	0.109893	−	0.993943i	$-0.464949\pi$
$797$	2.50358e12	0.219786	0.109893	+	0.993943i	$0.464949\pi$
$798$	7.33897e10	0.00640652
$799$	2.50108e12	0.217104
$800$	0	0
$801$	3.51881e12	0.302030
$802$	−9.24712e12	−0.789263
$803$	−1.05765e12	−0.0897679
$804$	5.93016e12	0.500512
$805$	0	0
$806$	1.05485e12	0.0880402
$807$	−2.53832e13	−2.10676
$808$	2.09014e12	0.172514
$809$	3.08739e12	0.253410	0.126705	−	0.991940i	$-0.459560\pi$
$809$	3.08739e12	0.253410	0.126705	+	0.991940i	$0.459560\pi$
$810$	0	0
$811$	−2.21381e12	−0.179700	−0.0898498	−	0.995955i	$-0.528639\pi$
$811$	−2.21381e12	−0.179700	−0.0898498	+	0.995955i	$0.528639\pi$
$812$	2.86430e12	0.231216
$813$	−1.63025e13	−1.30872
$814$	−4.69988e11	−0.0375212
$815$	0	0
$816$	−2.37508e12	−0.187531
$817$	−1.75029e11	−0.0137439
$818$	2.70133e12	0.210954
$819$	−4.44864e11	−0.0345502
$820$	0	0
$821$	−1.20316e13	−0.924228	−0.462114	−	0.886821i	$-0.652909\pi$
$821$	−1.20316e13	−0.924228	−0.462114	+	0.886821i	$0.652909\pi$
$822$	1.12714e12	0.0861099
$823$	−5.34967e12	−0.406469	−0.203235	−	0.979130i	$-0.565145\pi$
$823$	−5.34967e12	−0.406469	−0.203235	+	0.979130i	$0.565145\pi$
$824$	2.87058e12	0.216919
$825$	0	0
$826$	2.46101e12	0.183951
$827$	−2.00953e13	−1.49390	−0.746948	−	0.664882i	$-0.768482\pi$
$827$	−2.00953e13	−1.49390	−0.746948	+	0.664882i	$0.768482\pi$
$828$	−9.04434e12	−0.668714
$829$	9.97930e11	0.0733845	0.0366923	−	0.999327i	$-0.488318\pi$
$829$	9.97930e11	0.0733845	0.0366923	+	0.999327i	$0.488318\pi$
$830$	0	0
$831$	1.32803e13	0.966057
$832$	−2.14042e11	−0.0154862
$833$	1.12962e12	0.0812884
$834$	−5.63683e11	−0.0403448
$835$	0	0
$836$	2.41835e10	0.00171234
$837$	−4.93163e12	−0.347317
$838$	−9.57626e12	−0.670808
$839$	−2.81839e13	−1.96369	−0.981843	−	0.189696i	$-0.939250\pi$
$839$	−2.81839e13	−1.96369	−0.981843	+	0.189696i	$0.939250\pi$
$840$	0	0
$841$	7.20857e12	0.496898
$842$	1.20234e12	0.0824373
$843$	−2.57963e12	−0.175928
$844$	2.92934e12	0.198714
$845$	0	0
$846$	2.96590e12	0.199063
$847$	−5.46061e12	−0.364557
$848$	−8.58658e11	−0.0570215
$849$	−1.05292e13	−0.695523
$850$	0	0
$851$	−7.81339e12	−0.510689
$852$	−9.70000e12	−0.630658
$853$	2.66795e13	1.72547	0.862733	−	0.505659i	$-0.168751\pi$
$853$	2.66795e13	1.72547	0.862733	+	0.505659i	$0.168751\pi$
$854$	3.61177e12	0.232359
$855$	0	0
$856$	−4.02741e12	−0.256386
$857$	6.51094e11	0.0412316	0.0206158	−	0.999787i	$-0.493437\pi$
$857$	6.51094e11	0.0412316	0.0206158	+	0.999787i	$0.493437\pi$
$858$	−3.45269e11	−0.0217503
$859$	1.02299e13	0.641066	0.320533	−	0.947237i	$-0.396138\pi$
$859$	1.02299e13	0.641066	0.320533	+	0.947237i	$0.396138\pi$
$860$	0	0
$861$	3.03772e12	0.188380
$862$	−1.81977e13	−1.12262
$863$	−2.08353e12	−0.127865	−0.0639323	−	0.997954i	$-0.520364\pi$
$863$	−2.08353e12	−0.127865	−0.0639323	+	0.997954i	$0.520364\pi$
$864$	1.00069e12	0.0610927
$865$	0	0
$866$	1.31184e13	0.792593
$867$	1.48312e13	0.891439
$868$	−3.17630e12	−0.189925
$869$	−1.03073e11	−0.00613137
$870$	0	0
$871$	1.59792e12	0.0940748
$872$	8.22486e12	0.481731
$873$	−1.41047e13	−0.821865
$874$	4.02043e11	0.0233062
$875$	0	0
$876$	−5.47551e12	−0.314164
$877$	−9.80888e12	−0.559914	−0.279957	−	0.960013i	$-0.590320\pi$
$877$	−9.80888e12	−0.559914	−0.279957	+	0.960013i	$0.590320\pi$
$878$	1.45190e13	0.824541
$879$	−4.81554e12	−0.272079
$880$	0	0
$881$	−1.81332e13	−1.01410	−0.507051	−	0.861916i	$-0.669265\pi$
$881$	−1.81332e13	−1.01410	−0.507051	+	0.861916i	$0.669265\pi$
$882$	1.33955e12	0.0745336
$883$	−2.63986e13	−1.46136	−0.730681	−	0.682719i	$-0.760797\pi$
$883$	−2.63986e13	−1.46136	−0.730681	+	0.682719i	$0.760797\pi$
$884$	−6.39980e11	−0.0352477
$885$	0	0
$886$	1.04512e13	0.569791
$887$	−1.92841e13	−1.04603	−0.523015	−	0.852324i	$-0.675193\pi$
$887$	−1.92841e13	−1.04603	−0.523015	+	0.852324i	$0.675193\pi$
$888$	−2.43316e12	−0.131314
$889$	−6.42947e12	−0.345237
$890$	0	0
$891$	4.22851e12	0.224770
$892$	−1.37018e13	−0.724662
$893$	−1.31842e11	−0.00693779
$894$	1.04681e13	0.548086
$895$	0	0
$896$	6.44514e11	0.0334077
$897$	−5.73999e12	−0.296036
$898$	−7.29453e12	−0.374329
$899$	−2.40811e13	−1.22958
$900$	0	0
$901$	−2.56736e12	−0.129785
$902$	1.00100e12	0.0503504
$903$	−7.52455e12	−0.376604
$904$	2.35188e12	0.117127
$905$	0	0
$906$	5.81790e12	0.286873
$907$	−1.82552e13	−0.895682	−0.447841	−	0.894113i	$-0.647807\pi$
$907$	−1.82552e13	−0.895682	−0.447841	+	0.894113i	$0.647807\pi$
$908$	−4.20703e12	−0.205395
$909$	7.41091e12	0.360026
$910$	0	0
$911$	3.19168e13	1.53528	0.767638	−	0.640883i	$-0.221432\pi$
$911$	3.19168e13	1.53528	0.767638	+	0.640883i	$0.221432\pi$
$912$	1.25200e11	0.00599275
$913$	5.46136e12	0.260125
$914$	6.17160e12	0.292509
$915$	0	0
$916$	5.65122e11	0.0265224
$917$	−3.31256e12	−0.154704
$918$	2.99205e12	0.139052
$919$	−3.70916e13	−1.71536	−0.857680	−	0.514184i	$-0.828095\pi$
$919$	−3.70916e13	−1.71536	−0.857680	+	0.514184i	$0.828095\pi$
$920$	0	0
$921$	2.57478e13	1.17916
$922$	−1.25603e13	−0.572415
$923$	−2.61373e12	−0.118537
$924$	1.03966e12	0.0469210
$925$	0	0
$926$	1.76231e13	0.787649
$927$	1.01781e13	0.452696
$928$	4.88638e12	0.216282
$929$	−3.71833e12	−0.163786	−0.0818931	−	0.996641i	$-0.526097\pi$
$929$	−3.71833e12	−0.163786	−0.0818931	+	0.996641i	$0.526097\pi$
$930$	0	0
$931$	−5.95465e10	−0.00259766
$932$	−2.54317e12	−0.110409
$933$	−5.19228e13	−2.24332
$934$	−3.24999e13	−1.39740
$935$	0	0
$936$	−7.58919e11	−0.0323187
$937$	2.93891e13	1.24554	0.622772	−	0.782404i	$-0.286007\pi$
$937$	2.93891e13	1.24554	0.622772	+	0.782404i	$0.286007\pi$
$938$	−4.81158e12	−0.202943
$939$	−2.44905e12	−0.102802
$940$	0	0
$941$	−2.17930e13	−0.906076	−0.453038	−	0.891491i	$-0.649660\pi$
$941$	−2.17930e13	−0.906076	−0.453038	+	0.891491i	$0.649660\pi$
$942$	2.23085e13	0.923084
$943$	1.66412e13	0.685303
$944$	4.19837e12	0.172071
$945$	0	0
$946$	−2.47950e12	−0.100659
$947$	3.28464e13	1.32713	0.663564	−	0.748120i	$-0.269043\pi$
$947$	3.28464e13	1.32713	0.663564	+	0.748120i	$0.269043\pi$
$948$	−5.33617e11	−0.0214582
$949$	−1.47541e12	−0.0590493
$950$	0	0
$951$	−1.58785e12	−0.0629500
$952$	1.92708e12	0.0760384
$953$	−3.12975e13	−1.22911	−0.614556	−	0.788873i	$-0.710665\pi$
$953$	−3.12975e13	−1.22911	−0.614556	+	0.788873i	$0.710665\pi$
$954$	−3.04450e12	−0.119000
$955$	0	0
$956$	−7.12035e12	−0.275702
$957$	7.88217e12	0.303768
$958$	1.36733e13	0.524478
$959$	−9.14528e11	−0.0349151
$960$	0	0
$961$	2.64542e11	0.0100055
$962$	−6.55630e11	−0.0246814
$963$	−1.42798e13	−0.535062
$964$	3.13716e12	0.117001
$965$	0	0
$966$	1.72840e13	0.638626
$967$	2.46796e13	0.907651	0.453825	−	0.891091i	$-0.350059\pi$
$967$	2.46796e13	0.907651	0.453825	+	0.891091i	$0.350059\pi$
$968$	−9.31556e12	−0.341012
$969$	3.74343e11	0.0136400
$970$	0	0
$971$	−1.25554e13	−0.453255	−0.226628	−	0.973981i	$-0.572770\pi$
$971$	−1.25554e13	−0.453255	−0.226628	+	0.973981i	$0.572770\pi$
$972$	1.70825e13	0.613837
$973$	4.57357e11	0.0163587
$974$	−3.43914e13	−1.22443
$975$	0	0
$976$	6.16153e12	0.217352
$977$	3.57675e13	1.25592	0.627962	−	0.778244i	$-0.283889\pi$
$977$	3.57675e13	1.25592	0.627962	+	0.778244i	$0.283889\pi$
$978$	3.86072e13	1.34941
$979$	−2.21589e12	−0.0770948
$980$	0	0
$981$	2.91625e13	1.00534
$982$	2.40695e13	0.825971
$983$	−2.30282e13	−0.786628	−0.393314	−	0.919404i	$-0.628671\pi$
$983$	−2.30282e13	−0.786628	−0.393314	+	0.919404i	$0.628671\pi$
$984$	5.18222e12	0.176213
$985$	0	0
$986$	1.46101e13	0.492275
$987$	−5.66792e12	−0.190106
$988$	3.37358e10	0.00112638
$989$	−4.12209e13	−1.37004
$990$	0	0
$991$	−3.62816e13	−1.19497	−0.597483	−	0.801882i	$-0.703832\pi$
$991$	−3.62816e13	−1.19497	−0.597483	+	0.801882i	$0.703832\pi$
$992$	−5.41863e12	−0.177659
$993$	−2.86605e13	−0.935433
$994$	7.87033e12	0.255714
$995$	0	0
$996$	2.82738e13	0.910368
$997$	1.48926e13	0.477357	0.238678	−	0.971099i	$-0.423286\pi$
$997$	1.48926e13	0.477357	0.238678	+	0.971099i	$0.423286\pi$
$998$	2.65083e13	0.845853
$999$	3.06521e12	0.0973679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.10.a.o.1.1	yes	4
5.2	odd	4		350.10.c.m.99.8		8
5.3	odd	4		350.10.c.m.99.1		8
5.4	even	2		350.10.a.n.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.10.a.n.1.4	✓	4	5.4	even	2
350.10.a.o.1.1	yes	4	1.1	even	1	trivial
350.10.c.m.99.1		8	5.3	odd	4
350.10.c.m.99.8		8	5.2	odd	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -184.949 q^{3} +256.000 q^{4} -2959.18 q^{6} +2401.00 q^{7} +4096.00 q^{8} +14523.0 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -184.949 q^{3} +256.000 q^{4} -2959.18 q^{6} +2401.00 q^{7} +4096.00 q^{8} +14523.0 q^{9} -9145.50 q^{11} -47346.8 q^{12} -12757.9 q^{13} +38416.0 q^{14} +65536.0 q^{16} +195951. q^{17} +232368. q^{18} -10329.3 q^{19} -444062. q^{21} -146328. q^{22} -2.43266e6 q^{23} -757550. q^{24} -204126. q^{26} +954336. q^{27} +614656. q^{28} +4.66001e6 q^{29} -5.16761e6 q^{31} +1.04858e6 q^{32} +1.69145e6 q^{33} +3.13521e6 q^{34} +3.71789e6 q^{36} +3.21188e6 q^{37} -165269. q^{38} +2.35956e6 q^{39} -6.84077e6 q^{41} -7.10499e6 q^{42} +1.69448e7 q^{43} -2.34125e6 q^{44} -3.89225e7 q^{46} +1.27638e7 q^{47} -1.21208e7 q^{48} +5.76480e6 q^{49} -3.62408e7 q^{51} -3.26602e6 q^{52} -1.31021e7 q^{53} +1.52694e7 q^{54} +9.83450e6 q^{56} +1.91039e6 q^{57} +7.45602e7 q^{58} +6.40620e7 q^{59} +9.40174e7 q^{61} -8.26817e7 q^{62} +3.48697e7 q^{63} +1.67772e7 q^{64} +2.70632e7 q^{66} -1.25249e8 q^{67} +5.01634e7 q^{68} +4.49916e8 q^{69} +2.04871e8 q^{71} +5.94862e7 q^{72} +1.15647e8 q^{73} +5.13901e7 q^{74} -2.64431e6 q^{76} -2.19584e7 q^{77} +3.77529e7 q^{78} +1.12704e7 q^{79} -4.62359e8 q^{81} -1.09452e8 q^{82} -5.97163e8 q^{83} -1.13680e8 q^{84} +2.71117e8 q^{86} -8.61863e8 q^{87} -3.74600e7 q^{88} +2.42292e8 q^{89} -3.06317e7 q^{91} -6.22760e8 q^{92} +9.55742e8 q^{93} +2.04221e8 q^{94} -1.93933e8 q^{96} -9.71199e8 q^{97} +9.22368e7 q^{98} -1.32820e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 7 q^{3} + 1024 q^{4} + 112 q^{6} + 9604 q^{7} + 16384 q^{8} - 263 q^{9}+O(q^{10}) \) 4 * q + 64 * q^2 + 7 * q^3 + 1024 * q^4 + 112 * q^6 + 9604 * q^7 + 16384 * q^8 - 263 * q^9	\( 4 q + 64 q^{2} + 7 q^{3} + 1024 q^{4} + 112 q^{6} + 9604 q^{7} + 16384 q^{8} - 263 q^{9} - 36284 q^{11} + 1792 q^{12} - 182630 q^{13} + 153664 q^{14} + 262144 q^{16} - 367563 q^{17} - 4208 q^{18} + 222229 q^{19} + 16807 q^{21} - 580544 q^{22} + 182439 q^{23} + 28672 q^{24} - 2922080 q^{26} + 978355 q^{27} + 2458624 q^{28} + 255537 q^{29} - 12276460 q^{31} + 4194304 q^{32} - 3846073 q^{33} - 5881008 q^{34} - 67328 q^{36} - 4274163 q^{37} + 3555664 q^{38} - 27734218 q^{39} - 17136315 q^{41} + 268912 q^{42} - 27962067 q^{43} - 9288704 q^{44} + 2919024 q^{46} - 26065620 q^{47} + 458752 q^{48} + 23059204 q^{49} - 112821039 q^{51} - 46753280 q^{52} - 89230902 q^{53} + 15653680 q^{54} + 39337984 q^{56} - 38823861 q^{57} + 4088592 q^{58} + 96035996 q^{59} - 44213288 q^{61} - 196423360 q^{62} - 631463 q^{63} + 67108864 q^{64} - 61537168 q^{66} - 59945448 q^{67} - 94096128 q^{68} + 496450346 q^{69} - 232110635 q^{71} - 1077248 q^{72} + 28740649 q^{73} - 68386608 q^{74} + 56890624 q^{76} - 87117884 q^{77} - 443747488 q^{78} + 155306887 q^{79} - 398735816 q^{81} - 274181040 q^{82} + 383782847 q^{83} + 4302592 q^{84} - 447393072 q^{86} + 272329372 q^{87} - 148619264 q^{88} - 988710835 q^{89} - 438494630 q^{91} + 46704384 q^{92} - 1244946524 q^{93} - 417049920 q^{94} + 7340032 q^{96} - 950576942 q^{97} + 368947264 q^{98} - 1411275007 q^{99}+O(q^{100}) \) 4 * q + 64 * q^2 + 7 * q^3 + 1024 * q^4 + 112 * q^6 + 9604 * q^7 + 16384 * q^8 - 263 * q^9 - 36284 * q^11 + 1792 * q^12 - 182630 * q^13 + 153664 * q^14 + 262144 * q^16 - 367563 * q^17 - 4208 * q^18 + 222229 * q^19 + 16807 * q^21 - 580544 * q^22 + 182439 * q^23 + 28672 * q^24 - 2922080 * q^26 + 978355 * q^27 + 2458624 * q^28 + 255537 * q^29 - 12276460 * q^31 + 4194304 * q^32 - 3846073 * q^33 - 5881008 * q^34 - 67328 * q^36 - 4274163 * q^37 + 3555664 * q^38 - 27734218 * q^39 - 17136315 * q^41 + 268912 * q^42 - 27962067 * q^43 - 9288704 * q^44 + 2919024 * q^46 - 26065620 * q^47 + 458752 * q^48 + 23059204 * q^49 - 112821039 * q^51 - 46753280 * q^52 - 89230902 * q^53 + 15653680 * q^54 + 39337984 * q^56 - 38823861 * q^57 + 4088592 * q^58 + 96035996 * q^59 - 44213288 * q^61 - 196423360 * q^62 - 631463 * q^63 + 67108864 * q^64 - 61537168 * q^66 - 59945448 * q^67 - 94096128 * q^68 + 496450346 * q^69 - 232110635 * q^71 - 1077248 * q^72 + 28740649 * q^73 - 68386608 * q^74 + 56890624 * q^76 - 87117884 * q^77 - 443747488 * q^78 + 155306887 * q^79 - 398735816 * q^81 - 274181040 * q^82 + 383782847 * q^83 + 4302592 * q^84 - 447393072 * q^86 + 272329372 * q^87 - 148619264 * q^88 - 988710835 * q^89 - 438494630 * q^91 + 46704384 * q^92 - 1244946524 * q^93 - 417049920 * q^94 + 7340032 * q^96 - 950576942 * q^97 + 368947264 * q^98 - 1411275007 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more