LMFDB - Embedded newform 350.10.a.v.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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 19610x^{4} + 704364x^{3} + 22509888x^{2} + 142780860x + 152654544 $ x^6 - x^5 - 19610x^4 + 704364x^3 + 22509888x^2 + 142780860x + 152654544
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 5^{5} $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$103.125$ 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)

$f(q)$	$=$	$q+16.0000 q^{2} -201.043 q^{3} +256.000 q^{4} -3216.69 q^{6} -2401.00 q^{7} +4096.00 q^{8} +20735.3 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -201.043 q^{3} +256.000 q^{4} -3216.69 q^{6} -2401.00 q^{7} +4096.00 q^{8} +20735.3 q^{9} -15618.5 q^{11} -51467.0 q^{12} +29286.1 q^{13} -38416.0 q^{14} +65536.0 q^{16} -139809. q^{17} +331765. q^{18} -271017. q^{19} +482704. q^{21} -249896. q^{22} +873473. q^{23} -823472. q^{24} +468577. q^{26} -211557. q^{27} -614656. q^{28} +3.31307e6 q^{29} -6.25069e6 q^{31} +1.04858e6 q^{32} +3.13999e6 q^{33} -2.23695e6 q^{34} +5.30824e6 q^{36} +6.37553e6 q^{37} -4.33627e6 q^{38} -5.88776e6 q^{39} +7.91273e6 q^{41} +7.72327e6 q^{42} -2.12455e7 q^{43} -3.99833e6 q^{44} +1.39756e7 q^{46} -4.02228e6 q^{47} -1.31756e7 q^{48} +5.76480e6 q^{49} +2.81077e7 q^{51} +7.49723e6 q^{52} +9.13777e7 q^{53} -3.38492e6 q^{54} -9.83450e6 q^{56} +5.44861e7 q^{57} +5.30091e7 q^{58} -7.49792e7 q^{59} +1.59662e8 q^{61} -1.00011e8 q^{62} -4.97855e7 q^{63} +1.67772e7 q^{64} +5.02398e7 q^{66} +1.57308e8 q^{67} -3.57912e7 q^{68} -1.75606e8 q^{69} -3.29592e7 q^{71} +8.49318e7 q^{72} +3.35788e8 q^{73} +1.02009e8 q^{74} -6.93804e7 q^{76} +3.75000e7 q^{77} -9.42042e7 q^{78} -5.93256e7 q^{79} -3.65601e8 q^{81} +1.26604e8 q^{82} +3.97437e8 q^{83} +1.23572e8 q^{84} -3.39928e8 q^{86} -6.66069e8 q^{87} -6.39733e7 q^{88} -8.36174e8 q^{89} -7.03159e7 q^{91} +2.23609e8 q^{92} +1.25666e9 q^{93} -6.43565e7 q^{94} -2.10809e8 q^{96} -7.45068e8 q^{97} +9.22368e7 q^{98} -3.23854e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 96 q^{2} - 77 q^{3} + 1536 q^{4} - 1232 q^{6} - 14406 q^{7} + 24576 q^{8} + 12253 q^{9}+O(q^{10}) $ 6 * q + 96 * q^2 - 77 * q^3 + 1536 * q^4 - 1232 * q^6 - 14406 * q^7 + 24576 * q^8 + 12253 * q^9	\( 6 q + 96 q^{2} - 77 q^{3} + 1536 q^{4} - 1232 q^{6} - 14406 q^{7} + 24576 q^{8} + 12253 q^{9} + 15403 q^{11} - 19712 q^{12} - 31881 q^{13} - 230496 q^{14} + 393216 q^{16} + 40105 q^{17} + 196048 q^{18} - 453532 q^{19} + 184877 q^{21} + 246448 q^{22} - 1283250 q^{23} - 315392 q^{24} - 510096 q^{26} + 4542769 q^{27} - 3687936 q^{28} + 2987503 q^{29} - 10485850 q^{31} + 6291456 q^{32} - 10778125 q^{33} + 641680 q^{34} + 3136768 q^{36} + 23029642 q^{37} - 7256512 q^{38} + 387387 q^{39} - 40774792 q^{41} + 2958032 q^{42} - 28109124 q^{43} + 3943168 q^{44} - 20532000 q^{46} + 12965759 q^{47} - 5046272 q^{48} + 34588806 q^{49} - 133173023 q^{51} - 8161536 q^{52} + 52853782 q^{53} + 72684304 q^{54} - 59006976 q^{56} + 51609516 q^{57} + 47800048 q^{58} + 1392010 q^{59} - 223375386 q^{61} - 167773600 q^{62} - 29419453 q^{63} + 100663296 q^{64} - 172450000 q^{66} + 13994382 q^{67} + 10266880 q^{68} - 317796350 q^{69} - 266244592 q^{71} + 50188288 q^{72} - 40166814 q^{73} + 368474272 q^{74} - 116104192 q^{76} - 36982603 q^{77} + 6198192 q^{78} - 727619379 q^{79} - 645880646 q^{81} - 652396672 q^{82} - 1013909260 q^{83} + 47328512 q^{84} - 449745984 q^{86} - 1307973903 q^{87} + 63090688 q^{88} - 1489896214 q^{89} + 76546281 q^{91} - 328512000 q^{92} - 971293682 q^{93} + 207452144 q^{94} - 80740352 q^{96} - 2163452111 q^{97} + 553420896 q^{98} - 2691573574 q^{99}+O(q^{100}) \) 6 * q + 96 * q^2 - 77 * q^3 + 1536 * q^4 - 1232 * q^6 - 14406 * q^7 + 24576 * q^8 + 12253 * q^9 + 15403 * q^11 - 19712 * q^12 - 31881 * q^13 - 230496 * q^14 + 393216 * q^16 + 40105 * q^17 + 196048 * q^18 - 453532 * q^19 + 184877 * q^21 + 246448 * q^22 - 1283250 * q^23 - 315392 * q^24 - 510096 * q^26 + 4542769 * q^27 - 3687936 * q^28 + 2987503 * q^29 - 10485850 * q^31 + 6291456 * q^32 - 10778125 * q^33 + 641680 * q^34 + 3136768 * q^36 + 23029642 * q^37 - 7256512 * q^38 + 387387 * q^39 - 40774792 * q^41 + 2958032 * q^42 - 28109124 * q^43 + 3943168 * q^44 - 20532000 * q^46 + 12965759 * q^47 - 5046272 * q^48 + 34588806 * q^49 - 133173023 * q^51 - 8161536 * q^52 + 52853782 * q^53 + 72684304 * q^54 - 59006976 * q^56 + 51609516 * q^57 + 47800048 * q^58 + 1392010 * q^59 - 223375386 * q^61 - 167773600 * q^62 - 29419453 * q^63 + 100663296 * q^64 - 172450000 * q^66 + 13994382 * q^67 + 10266880 * q^68 - 317796350 * q^69 - 266244592 * q^71 + 50188288 * q^72 - 40166814 * q^73 + 368474272 * q^74 - 116104192 * q^76 - 36982603 * q^77 + 6198192 * q^78 - 727619379 * q^79 - 645880646 * q^81 - 652396672 * q^82 - 1013909260 * q^83 + 47328512 * q^84 - 449745984 * q^86 - 1307973903 * q^87 + 63090688 * q^88 - 1489896214 * q^89 + 76546281 * q^91 - 328512000 * q^92 - 971293682 * q^93 + 207452144 * q^94 - 80740352 * q^96 - 2163452111 * q^97 + 553420896 * q^98 - 2691573574 * 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
$3$	−201.043	−1.43299	−0.716495	−	0.697592i	$-0.754255\pi$
$3$	−201.043	−1.43299	−0.716495	+	0.697592i	$0.754255\pi$
$4$	256.000	0.500000
$5$	0	0
$5$	0	0
$6$	−3216.69	−1.01328
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	4096.00	0.353553
$9$	20735.3	1.05346
$10$	0	0
$11$	−15618.5	−0.321641	−0.160821	−	0.986984i	$-0.551414\pi$
$11$	−15618.5	−0.321641	−0.160821	+	0.986984i	$0.551414\pi$
$12$	−51467.0	−0.716495
$13$	29286.1	0.284391	0.142196	−	0.989839i	$-0.454584\pi$
$13$	29286.1	0.284391	0.142196	+	0.989839i	$0.454584\pi$
$14$	−38416.0	−0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	−139809.	−0.405991	−0.202995	−	0.979180i	$-0.565068\pi$
$17$	−139809.	−0.405991	−0.202995	+	0.979180i	$0.565068\pi$
$18$	331765.	0.744910
$19$	−271017.	−0.477096	−0.238548	−	0.971131i	$-0.576671\pi$
$19$	−271017.	−0.477096	−0.238548	+	0.971131i	$0.576671\pi$
$20$	0	0
$21$	482704.	0.541620
$22$	−249896.	−0.227435
$23$	873473.	0.650840	0.325420	−	0.945570i	$-0.394494\pi$
$23$	873473.	0.650840	0.325420	+	0.945570i	$0.394494\pi$
$24$	−823472.	−0.506639
$25$	0	0
$26$	468577.	0.201095
$27$	−211557.	−0.0766110
$28$	−614656.	−0.188982
$29$	3.31307e6	0.869840	0.434920	−	0.900469i	$-0.356777\pi$
$29$	3.31307e6	0.869840	0.434920	+	0.900469i	$0.356777\pi$
$30$	0	0
$31$	−6.25069e6	−1.21563	−0.607813	−	0.794080i	$-0.707953\pi$
$31$	−6.25069e6	−1.21563	−0.607813	+	0.794080i	$0.707953\pi$
$32$	1.04858e6	0.176777
$33$	3.13999e6	0.460909
$34$	−2.23695e6	−0.287079
$35$	0	0
$36$	5.30824e6	0.526731
$37$	6.37553e6	0.559253	0.279627	−	0.960109i	$-0.409789\pi$
$37$	6.37553e6	0.559253	0.279627	+	0.960109i	$0.409789\pi$
$38$	−4.33627e6	−0.337358
$39$	−5.88776e6	−0.407530
$40$	0	0
$41$	7.91273e6	0.437320	0.218660	−	0.975801i	$-0.429831\pi$
$41$	7.91273e6	0.437320	0.218660	+	0.975801i	$0.429831\pi$
$42$	7.72327e6	0.382983
$43$	−2.12455e7	−0.947674	−0.473837	−	0.880612i	$-0.657131\pi$
$43$	−2.12455e7	−0.947674	−0.473837	+	0.880612i	$0.657131\pi$
$44$	−3.99833e6	−0.160821
$45$	0	0
$46$	1.39756e7	0.460214
$47$	−4.02228e6	−0.120235	−0.0601177	−	0.998191i	$-0.519148\pi$
$47$	−4.02228e6	−0.120235	−0.0601177	+	0.998191i	$0.519148\pi$
$48$	−1.31756e7	−0.358248
$49$	5.76480e6	0.142857
$50$	0	0
$51$	2.81077e7	0.581781
$52$	7.49723e6	0.142196
$53$	9.13777e7	1.59074	0.795370	−	0.606125i	$-0.207277\pi$
$53$	9.13777e7	1.59074	0.795370	+	0.606125i	$0.207277\pi$
$54$	−3.38492e6	−0.0541722
$55$	0	0
$56$	−9.83450e6	−0.133631
$57$	5.44861e7	0.683674
$58$	5.30091e7	0.615070
$59$	−7.49792e7	−0.805576	−0.402788	−	0.915293i	$-0.631959\pi$
$59$	−7.49792e7	−0.805576	−0.402788	+	0.915293i	$0.631959\pi$
$60$	0	0
$61$	1.59662e8	1.47645	0.738224	−	0.674556i	$-0.235665\pi$
$61$	1.59662e8	1.47645	0.738224	+	0.674556i	$0.235665\pi$
$62$	−1.00011e8	−0.859578
$63$	−4.97855e7	−0.398171
$64$	1.67772e7	0.125000
$65$	0	0
$66$	5.02398e7	0.325912
$67$	1.57308e8	0.953702	0.476851	−	0.878984i	$-0.341778\pi$
$67$	1.57308e8	0.953702	0.476851	+	0.878984i	$0.341778\pi$
$68$	−3.57912e7	−0.202995
$69$	−1.75606e8	−0.932648
$70$	0	0
$71$	−3.29592e7	−0.153927	−0.0769633	−	0.997034i	$-0.524522\pi$
$71$	−3.29592e7	−0.153927	−0.0769633	+	0.997034i	$0.524522\pi$
$72$	8.49318e7	0.372455
$73$	3.35788e8	1.38393	0.691963	−	0.721933i	$-0.256746\pi$
$73$	3.35788e8	1.38393	0.691963	+	0.721933i	$0.256746\pi$
$74$	1.02009e8	0.395452
$75$	0	0
$76$	−6.93804e7	−0.238548
$77$	3.75000e7	0.121569
$78$	−9.42042e7	−0.288167
$79$	−5.93256e7	−0.171364	−0.0856822	−	0.996323i	$-0.527307\pi$
$79$	−5.93256e7	−0.171364	−0.0856822	+	0.996323i	$0.527307\pi$
$80$	0	0
$81$	−3.65601e8	−0.943679
$82$	1.26604e8	0.309232
$83$	3.97437e8	0.919213	0.459607	−	0.888123i	$-0.347990\pi$
$83$	3.97437e8	0.919213	0.459607	+	0.888123i	$0.347990\pi$
$84$	1.23572e8	0.270810
$85$	0	0
$86$	−3.39928e8	−0.670107
$87$	−6.66069e8	−1.24647
$88$	−6.39733e7	−0.113717
$89$	−8.36174e8	−1.41267	−0.706336	−	0.707877i	$-0.749653\pi$
$89$	−8.36174e8	−1.41267	−0.706336	+	0.707877i	$0.749653\pi$
$90$	0	0
$91$	−7.03159e7	−0.107490
$92$	2.23609e8	0.325420
$93$	1.25666e9	1.74198
$94$	−6.43565e7	−0.0850193
$95$	0	0
$96$	−2.10809e8	−0.253319
$97$	−7.45068e8	−0.854521	−0.427261	−	0.904128i	$-0.640521\pi$
$97$	−7.45068e8	−0.854521	−0.427261	+	0.904128i	$0.640521\pi$
$98$	9.22368e7	0.101015
$99$	−3.23854e8	−0.338837
$100$	0	0
$101$	−1.72732e9	−1.65168	−0.825840	−	0.563905i	$-0.809298\pi$
$101$	−1.72732e9	−1.65168	−0.825840	+	0.563905i	$0.809298\pi$
$102$	4.49723e8	0.411381
$103$	6.28769e8	0.550457	0.275229	−	0.961379i	$-0.411246\pi$
$103$	6.28769e8	0.550457	0.275229	+	0.961379i	$0.411246\pi$
$104$	1.19956e8	0.100547
$105$	0	0
$106$	1.46204e9	1.12482
$107$	−1.64943e9	−1.21648	−0.608241	−	0.793753i	$-0.708125\pi$
$107$	−1.64943e9	−1.21648	−0.608241	+	0.793753i	$0.708125\pi$
$108$	−5.41587e7	−0.0383055
$109$	1.48709e9	1.00907	0.504533	−	0.863393i	$-0.331665\pi$
$109$	1.48709e9	1.00907	0.504533	+	0.863393i	$0.331665\pi$
$110$	0	0
$111$	−1.28176e9	−0.801405
$112$	−1.57352e8	−0.0944911
$113$	1.66416e9	0.960158	0.480079	−	0.877225i	$-0.340608\pi$
$113$	1.66416e9	0.960158	0.480079	+	0.877225i	$0.340608\pi$
$114$	8.71777e8	0.483430
$115$	0	0
$116$	8.48145e8	0.434920
$117$	6.07255e8	0.299595
$118$	−1.19967e9	−0.569629
$119$	3.35682e8	0.153450
$120$	0	0
$121$	−2.11401e9	−0.896547
$122$	2.55460e9	1.04401
$123$	−1.59080e9	−0.626675
$124$	−1.60018e9	−0.607813
$125$	0	0
$126$	−7.96567e8	−0.281550
$127$	1.45106e9	0.494958	0.247479	−	0.968893i	$-0.420398\pi$
$127$	1.45106e9	0.494958	0.247479	+	0.968893i	$0.420398\pi$
$128$	2.68435e8	0.0883883
$129$	4.27126e9	1.35801
$130$	0	0
$131$	6.23775e9	1.85058	0.925289	−	0.379263i	$-0.123822\pi$
$131$	6.23775e9	1.85058	0.925289	+	0.379263i	$0.123822\pi$
$132$	8.03837e8	0.230455
$133$	6.50712e8	0.180325
$134$	2.51692e9	0.674369
$135$	0	0
$136$	−5.72659e8	−0.143539
$137$	−7.14761e9	−1.73348	−0.866739	−	0.498761i	$-0.833788\pi$
$137$	−7.14761e9	−1.73348	−0.866739	+	0.498761i	$0.833788\pi$
$138$	−2.80969e9	−0.659482
$139$	−2.17548e9	−0.494298	−0.247149	−	0.968978i	$-0.579494\pi$
$139$	−2.17548e9	−0.494298	−0.247149	+	0.968978i	$0.579494\pi$
$140$	0	0
$141$	8.08652e8	0.172296
$142$	−5.27346e8	−0.108842
$143$	−4.57404e8	−0.0914719
$144$	1.35891e9	0.263366
$145$	0	0
$146$	5.37261e9	0.978583
$147$	−1.15897e9	−0.204713
$148$	1.63214e9	0.279627
$149$	−2.76925e9	−0.460282	−0.230141	−	0.973157i	$-0.573919\pi$
$149$	−2.76925e9	−0.460282	−0.230141	+	0.973157i	$0.573919\pi$
$150$	0	0
$151$	9.61745e8	0.150544	0.0752720	−	0.997163i	$-0.476017\pi$
$151$	9.61745e8	0.150544	0.0752720	+	0.997163i	$0.476017\pi$
$152$	−1.11009e9	−0.168679
$153$	−2.89899e9	−0.427696
$154$	6.00000e8	0.0859623
$155$	0	0
$156$	−1.50727e9	−0.203765
$157$	−7.42184e9	−0.974907	−0.487454	−	0.873149i	$-0.662074\pi$
$157$	−7.42184e9	−0.974907	−0.487454	+	0.873149i	$0.662074\pi$
$158$	−9.49210e8	−0.121173
$159$	−1.83709e10	−2.27951
$160$	0	0
$161$	−2.09721e9	−0.245995
$162$	−5.84961e9	−0.667282
$163$	5.13802e8	0.0570100	0.0285050	−	0.999594i	$-0.490925\pi$
$163$	5.13802e8	0.0570100	0.0285050	+	0.999594i	$0.490925\pi$
$164$	2.02566e9	0.218660
$165$	0	0
$166$	6.35898e9	0.649982
$167$	−1.71805e10	−1.70927	−0.854636	−	0.519228i	$-0.826220\pi$
$167$	−1.71805e10	−1.70927	−0.854636	+	0.519228i	$0.826220\pi$
$168$	1.97716e9	0.191491
$169$	−9.74683e9	−0.919122
$170$	0	0
$171$	−5.61962e9	−0.502602
$172$	−5.43885e9	−0.473837
$173$	−7.60367e9	−0.645380	−0.322690	−	0.946505i	$-0.604587\pi$
$173$	−7.60367e9	−0.645380	−0.322690	+	0.946505i	$0.604587\pi$
$174$	−1.06571e10	−0.881389
$175$	0	0
$176$	−1.02357e9	−0.0804103
$177$	1.50740e10	1.15438
$178$	−1.33788e10	−0.998910
$179$	−1.61995e10	−1.17941	−0.589703	−	0.807620i	$-0.700755\pi$
$179$	−1.61995e10	−1.17941	−0.589703	+	0.807620i	$0.700755\pi$
$180$	0	0
$181$	−2.00837e10	−1.39088	−0.695441	−	0.718583i	$-0.744791\pi$
$181$	−2.00837e10	−1.39088	−0.695441	+	0.718583i	$0.744791\pi$
$182$	−1.12505e9	−0.0760067
$183$	−3.20990e10	−2.11574
$184$	3.57775e9	0.230107
$185$	0	0
$186$	2.01065e10	1.23177
$187$	2.18361e9	0.130583
$188$	−1.02970e9	−0.0601177
$189$	5.07949e8	0.0289562
$190$	0	0
$191$	−4.08580e9	−0.222140	−0.111070	−	0.993813i	$-0.535428\pi$
$191$	−4.08580e9	−0.222140	−0.111070	+	0.993813i	$0.535428\pi$
$192$	−3.37294e9	−0.179124
$193$	−2.35391e10	−1.22119	−0.610594	−	0.791944i	$-0.709069\pi$
$193$	−2.35391e10	−1.22119	−0.610594	+	0.791944i	$0.709069\pi$
$194$	−1.19211e10	−0.604238
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	2.49930e10	1.18228	0.591140	−	0.806569i	$-0.298678\pi$
$197$	2.49930e10	1.18228	0.591140	+	0.806569i	$0.298678\pi$
$198$	−5.18166e9	−0.239594
$199$	−5.92459e9	−0.267805	−0.133903	−	0.990994i	$-0.542751\pi$
$199$	−5.92459e9	−0.267805	−0.133903	+	0.990994i	$0.542751\pi$
$200$	0	0
$201$	−3.16256e10	−1.36665
$202$	−2.76371e10	−1.16791
$203$	−7.95467e9	−0.328769
$204$	7.19557e9	0.290891
$205$	0	0
$206$	1.00603e10	0.389232
$207$	1.81117e10	0.685636
$208$	1.91929e9	0.0710978
$209$	4.23288e9	0.153454
$210$	0	0
$211$	−5.00436e10	−1.73811	−0.869055	−	0.494716i	$-0.835272\pi$
$211$	−5.00436e10	−1.73811	−0.869055	+	0.494716i	$0.835272\pi$
$212$	2.33927e10	0.795370
$213$	6.62621e9	0.220575
$214$	−2.63908e10	−0.860182
$215$	0	0
$216$	−8.66539e8	−0.0270861
$217$	1.50079e10	0.459464
$218$	2.37935e10	0.713517
$219$	−6.75079e10	−1.98315
$220$	0	0
$221$	−4.09447e9	−0.115460
$222$	−2.05081e10	−0.566679
$223$	9.17747e9	0.248514	0.124257	−	0.992250i	$-0.460345\pi$
$223$	9.17747e9	0.248514	0.124257	+	0.992250i	$0.460345\pi$
$224$	−2.51763e9	−0.0668153
$225$	0	0
$226$	2.66266e10	0.678935
$227$	−4.88804e10	−1.22185	−0.610926	−	0.791688i	$-0.709203\pi$
$227$	−4.88804e10	−1.22185	−0.610926	+	0.791688i	$0.709203\pi$
$228$	1.39484e10	0.341837
$229$	1.07277e10	0.257778	0.128889	−	0.991659i	$-0.458859\pi$
$229$	1.07277e10	0.257778	0.128889	+	0.991659i	$0.458859\pi$
$230$	0	0
$231$	−7.53911e9	−0.174207
$232$	1.35703e10	0.307535
$233$	7.90863e10	1.75792	0.878961	−	0.476895i	$-0.158238\pi$
$233$	7.90863e10	1.75792	0.878961	+	0.476895i	$0.158238\pi$
$234$	9.71609e9	0.211846
$235$	0	0
$236$	−1.91947e10	−0.402788
$237$	1.19270e10	0.245564
$238$	5.37092e9	0.108506
$239$	7.03817e10	1.39530	0.697652	−	0.716436i	$-0.254228\pi$
$239$	7.03817e10	1.39530	0.697652	+	0.716436i	$0.254228\pi$
$240$	0	0
$241$	3.22499e9	0.0615816	0.0307908	−	0.999526i	$-0.490197\pi$
$241$	3.22499e9	0.0615816	0.0307908	+	0.999526i	$0.490197\pi$
$242$	−3.38242e10	−0.633954
$243$	7.76656e10	1.42889
$244$	4.08735e10	0.738224
$245$	0	0
$246$	−2.54528e10	−0.443126
$247$	−7.93702e9	−0.135682
$248$	−2.56028e10	−0.429789
$249$	−7.99018e10	−1.31722
$250$	0	0
$251$	−1.09992e11	−1.74916	−0.874580	−	0.484881i	$-0.838863\pi$
$251$	−1.09992e11	−1.74916	−0.874580	+	0.484881i	$0.838863\pi$
$252$	−1.27451e10	−0.199086
$253$	−1.36423e10	−0.209337
$254$	2.32169e10	0.349988
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	−1.98467e10	−0.283785	−0.141892	−	0.989882i	$-0.545319\pi$
$257$	−1.98467e10	−0.283785	−0.141892	+	0.989882i	$0.545319\pi$
$258$	6.83402e10	0.960257
$259$	−1.53077e10	−0.211378
$260$	0	0
$261$	6.86974e10	0.916343
$262$	9.98040e10	1.30856
$263$	−8.60804e10	−1.10944	−0.554719	−	0.832038i	$-0.687174\pi$
$263$	−8.60804e10	−1.10944	−0.554719	+	0.832038i	$0.687174\pi$
$264$	1.28614e10	0.162956
$265$	0	0
$266$	1.04114e10	0.127509
$267$	1.68107e11	2.02435
$268$	4.02707e10	0.476851
$269$	−1.06232e11	−1.23700	−0.618498	−	0.785786i	$-0.712259\pi$
$269$	−1.06232e11	−1.23700	−0.618498	+	0.785786i	$0.712259\pi$
$270$	0	0
$271$	−2.66290e10	−0.299912	−0.149956	−	0.988693i	$-0.547913\pi$
$271$	−2.66290e10	−0.299912	−0.149956	+	0.988693i	$0.547913\pi$
$272$	−9.16255e9	−0.101498
$273$	1.41365e10	0.154032
$274$	−1.14362e11	−1.22575
$275$	0	0
$276$	−4.49551e10	−0.466324
$277$	1.59378e11	1.62655	0.813276	−	0.581878i	$-0.197682\pi$
$277$	1.59378e11	1.62655	0.813276	+	0.581878i	$0.197682\pi$
$278$	−3.48077e10	−0.349521
$279$	−1.29610e11	−1.28062
$280$	0	0
$281$	−5.32719e10	−0.509706	−0.254853	−	0.966980i	$-0.582027\pi$
$281$	−5.32719e10	−0.509706	−0.254853	+	0.966980i	$0.582027\pi$
$282$	1.29384e10	0.121832
$283$	−2.09521e10	−0.194173	−0.0970863	−	0.995276i	$-0.530952\pi$
$283$	−2.09521e10	−0.194173	−0.0970863	+	0.995276i	$0.530952\pi$
$284$	−8.43754e9	−0.0769633
$285$	0	0
$286$	−7.31847e9	−0.0646804
$287$	−1.89985e10	−0.165291
$288$	2.17425e10	0.186228
$289$	−9.90412e10	−0.835171
$290$	0	0
$291$	1.49791e11	1.22452
$292$	8.59618e10	0.691963
$293$	1.50217e11	1.19073	0.595366	−	0.803455i	$-0.297007\pi$
$293$	1.50217e11	1.19073	0.595366	+	0.803455i	$0.297007\pi$
$294$	−1.85436e10	−0.144754
$295$	0	0
$296$	2.61142e10	0.197726
$297$	3.30421e9	0.0246413
$298$	−4.43080e10	−0.325468
$299$	2.55806e10	0.185093
$300$	0	0
$301$	5.10105e10	0.358187
$302$	1.53879e10	0.106451
$303$	3.47265e11	2.36684
$304$	−1.77614e10	−0.119274
$305$	0	0
$306$	−4.63838e10	−0.302427
$307$	−6.95420e10	−0.446812	−0.223406	−	0.974725i	$-0.571718\pi$
$307$	−6.95420e10	−0.446812	−0.223406	+	0.974725i	$0.571718\pi$
$308$	9.60000e9	0.0607845
$309$	−1.26410e11	−0.788800
$310$	0	0
$311$	−1.35026e11	−0.818455	−0.409228	−	0.912432i	$-0.634202\pi$
$311$	−1.35026e11	−0.818455	−0.409228	+	0.912432i	$0.634202\pi$
$312$	−2.41163e10	−0.144084
$313$	2.79797e10	0.164776	0.0823881	−	0.996600i	$-0.473745\pi$
$313$	2.79797e10	0.164776	0.0823881	+	0.996600i	$0.473745\pi$
$314$	−1.18749e11	−0.689364
$315$	0	0
$316$	−1.51874e10	−0.0856822
$317$	6.80226e9	0.0378344	0.0189172	−	0.999821i	$-0.493978\pi$
$317$	6.80226e9	0.0378344	0.0189172	+	0.999821i	$0.493978\pi$
$318$	−2.93934e11	−1.61186
$319$	−5.17451e10	−0.279776
$320$	0	0
$321$	3.31605e11	1.74321
$322$	−3.35554e10	−0.173944
$323$	3.78907e10	0.193696
$324$	−9.35938e10	−0.471840
$325$	0	0
$326$	8.22083e9	0.0403122
$327$	−2.98970e11	−1.44598
$328$	3.24106e10	0.154616
$329$	9.65750e9	0.0454447
$330$	0	0
$331$	6.81462e10	0.312044	0.156022	−	0.987754i	$-0.450133\pi$
$331$	6.81462e10	0.312044	0.156022	+	0.987754i	$0.450133\pi$
$332$	1.01744e11	0.459607
$333$	1.32199e11	0.589152
$334$	−2.74888e11	−1.20864
$335$	0	0
$336$	3.16345e10	0.135405
$337$	4.12449e11	1.74195	0.870975	−	0.491327i	$-0.163488\pi$
$337$	4.12449e11	1.74195	0.870975	+	0.491327i	$0.163488\pi$
$338$	−1.55949e11	−0.649917
$339$	−3.34568e11	−1.37590
$340$	0	0
$341$	9.76263e10	0.390996
$342$	−8.99139e10	−0.355393
$343$	−1.38413e10	−0.0539949
$344$	−8.70216e10	−0.335053
$345$	0	0
$346$	−1.21659e11	−0.456353
$347$	−9.76937e10	−0.361730	−0.180865	−	0.983508i	$-0.557890\pi$
$347$	−9.76937e10	−0.361730	−0.180865	+	0.983508i	$0.557890\pi$
$348$	−1.70514e11	−0.623236
$349$	−1.77906e11	−0.641913	−0.320956	−	0.947094i	$-0.604004\pi$
$349$	−1.77906e11	−0.641913	−0.320956	+	0.947094i	$0.604004\pi$
$350$	0	0
$351$	−6.19569e9	−0.0217875
$352$	−1.63772e10	−0.0568587
$353$	−5.05930e11	−1.73422	−0.867110	−	0.498117i	$-0.834025\pi$
$353$	−5.05930e11	−1.73422	−0.867110	+	0.498117i	$0.834025\pi$
$354$	2.41185e11	0.816272
$355$	0	0
$356$	−2.14060e11	−0.706336
$357$	−6.74866e10	−0.219893
$358$	−2.59192e11	−0.833965
$359$	2.26820e11	0.720702	0.360351	−	0.932817i	$-0.382657\pi$
$359$	2.26820e11	0.720702	0.360351	+	0.932817i	$0.382657\pi$
$360$	0	0
$361$	−2.49237e11	−0.772380
$362$	−3.21339e11	−0.983503
$363$	4.25007e11	1.28474
$364$	−1.80009e10	−0.0537449
$365$	0	0
$366$	−5.13584e11	−1.49605
$367$	−8.91653e10	−0.256566	−0.128283	−	0.991738i	$-0.540947\pi$
$367$	−8.91653e10	−0.256566	−0.128283	+	0.991738i	$0.540947\pi$
$368$	5.72440e10	0.162710
$369$	1.64073e11	0.460700
$370$	0	0
$371$	−2.19398e11	−0.601243
$372$	3.21704e11	0.870991
$373$	2.45130e11	0.655703	0.327852	−	0.944729i	$-0.393675\pi$
$373$	2.45130e11	0.655703	0.327852	+	0.944729i	$0.393675\pi$
$374$	3.49378e10	0.0923365
$375$	0	0
$376$	−1.64753e10	−0.0425096
$377$	9.70267e10	0.247375
$378$	8.12719e9	0.0204752
$379$	−3.41880e11	−0.851133	−0.425567	−	0.904927i	$-0.639925\pi$
$379$	−3.41880e11	−0.851133	−0.425567	+	0.904927i	$0.639925\pi$
$380$	0	0
$381$	−2.91725e11	−0.709270
$382$	−6.53728e10	−0.157077
$383$	1.39360e11	0.330935	0.165468	−	0.986215i	$-0.447087\pi$
$383$	1.39360e11	0.330935	0.165468	+	0.986215i	$0.447087\pi$
$384$	−5.39671e10	−0.126660
$385$	0	0
$386$	−3.76626e11	−0.863510
$387$	−4.40532e11	−0.998339
$388$	−1.90737e11	−0.427261
$389$	7.50059e11	1.66082	0.830410	−	0.557153i	$-0.188106\pi$
$389$	7.50059e11	1.66082	0.830410	+	0.557153i	$0.188106\pi$
$390$	0	0
$391$	−1.22120e11	−0.264235
$392$	2.36126e10	0.0505076
$393$	−1.25406e12	−2.65186
$394$	3.99888e11	0.835999
$395$	0	0
$396$	−8.29066e10	−0.169419
$397$	−6.29880e11	−1.27262	−0.636312	−	0.771432i	$-0.719541\pi$
$397$	−6.29880e11	−1.27262	−0.636312	+	0.771432i	$0.719541\pi$
$398$	−9.47934e10	−0.189367
$399$	−1.30821e11	−0.258404
$400$	0	0
$401$	−1.63259e11	−0.315303	−0.157652	−	0.987495i	$-0.550392\pi$
$401$	−1.63259e11	−0.315303	−0.157652	+	0.987495i	$0.550392\pi$
$402$	−5.06009e11	−0.966365
$403$	−1.83058e11	−0.345713
$404$	−4.42193e11	−0.825840
$405$	0	0
$406$	−1.27275e11	−0.232474
$407$	−9.95762e10	−0.179879
$408$	1.15129e11	0.205691
$409$	6.51936e11	1.15199	0.575996	−	0.817452i	$-0.304614\pi$
$409$	6.51936e11	1.15199	0.575996	+	0.817452i	$0.304614\pi$
$410$	0	0
$411$	1.43698e12	2.48406
$412$	1.60965e11	0.275229
$413$	1.80025e11	0.304479
$414$	2.89788e11	0.484818
$415$	0	0
$416$	3.07087e10	0.0502737
$417$	4.37365e11	0.708324
$418$	6.77260e10	0.108508
$419$	−4.74478e11	−0.752060	−0.376030	−	0.926607i	$-0.622711\pi$
$419$	−4.74478e11	−0.752060	−0.376030	+	0.926607i	$0.622711\pi$
$420$	0	0
$421$	1.46001e11	0.226510	0.113255	−	0.993566i	$-0.463872\pi$
$421$	1.46001e11	0.226510	0.113255	+	0.993566i	$0.463872\pi$
$422$	−8.00697e11	−1.22903
$423$	−8.34033e10	−0.126663
$424$	3.74283e11	0.562411
$425$	0	0
$426$	1.06019e11	0.155970
$427$	−3.83349e11	−0.558045
$428$	−4.22253e11	−0.608241
$429$	9.19579e10	0.131078
$430$	0	0
$431$	−4.41387e11	−0.616129	−0.308064	−	0.951365i	$-0.599681\pi$
$431$	−4.41387e11	−0.616129	−0.308064	+	0.951365i	$0.599681\pi$
$432$	−1.38646e10	−0.0191528
$433$	1.35346e11	0.185033	0.0925165	−	0.995711i	$-0.470509\pi$
$433$	1.35346e11	0.185033	0.0925165	+	0.995711i	$0.470509\pi$
$434$	2.40126e11	0.324890
$435$	0	0
$436$	3.80696e11	0.504533
$437$	−2.36726e11	−0.310513
$438$	−1.08013e12	−1.40230
$439$	7.39550e10	0.0950336	0.0475168	−	0.998870i	$-0.484869\pi$
$439$	7.39550e10	0.0950336	0.0475168	+	0.998870i	$0.484869\pi$
$440$	0	0
$441$	1.19535e11	0.150495
$442$	−6.55115e10	−0.0816427
$443$	−9.68867e10	−0.119522	−0.0597610	−	0.998213i	$-0.519034\pi$
$443$	−9.68867e10	−0.119522	−0.0597610	+	0.998213i	$0.519034\pi$
$444$	−3.28130e11	−0.400702
$445$	0	0
$446$	1.46840e11	0.175726
$447$	5.56738e11	0.659579
$448$	−4.02821e10	−0.0472456
$449$	1.31869e12	1.53120	0.765602	−	0.643314i	$-0.222441\pi$
$449$	1.31869e12	1.53120	0.765602	+	0.643314i	$0.222441\pi$
$450$	0	0
$451$	−1.23585e11	−0.140660
$452$	4.26026e11	0.480079
$453$	−1.93352e11	−0.215728
$454$	−7.82087e11	−0.863980
$455$	0	0
$456$	2.23175e11	0.241715
$457$	−3.66535e11	−0.393091	−0.196546	−	0.980495i	$-0.562972\pi$
$457$	−3.66535e11	−0.393091	−0.196546	+	0.980495i	$0.562972\pi$
$458$	1.71643e11	0.182276
$459$	2.95777e10	0.0311034
$460$	0	0
$461$	−1.09415e12	−1.12829	−0.564146	−	0.825675i	$-0.690795\pi$
$461$	−1.09415e12	−1.12829	−0.564146	+	0.825675i	$0.690795\pi$
$462$	−1.20626e11	−0.123183
$463$	1.06833e12	1.08042	0.540210	−	0.841530i	$-0.318345\pi$
$463$	1.06833e12	1.08042	0.540210	+	0.841530i	$0.318345\pi$
$464$	2.17125e11	0.217460
$465$	0	0
$466$	1.26538e12	1.24304
$467$	−4.76995e11	−0.464074	−0.232037	−	0.972707i	$-0.574539\pi$
$467$	−4.76995e11	−0.464074	−0.232037	+	0.972707i	$0.574539\pi$
$468$	1.55457e11	0.149798
$469$	−3.77695e11	−0.360466
$470$	0	0
$471$	1.49211e12	1.39703
$472$	−3.07115e11	−0.284814
$473$	3.31823e11	0.304811
$474$	1.90832e11	0.173640
$475$	0	0
$476$	8.59347e10	0.0767251
$477$	1.89474e12	1.67578
$478$	1.12611e12	0.986629
$479$	−4.85334e11	−0.421241	−0.210621	−	0.977568i	$-0.567548\pi$
$479$	−4.85334e11	−0.421241	−0.210621	+	0.977568i	$0.567548\pi$
$480$	0	0
$481$	1.86714e11	0.159047
$482$	5.15998e10	0.0435448
$483$	4.21629e11	0.352508
$484$	−5.41187e11	−0.448273
$485$	0	0
$486$	1.24265e12	1.01038
$487$	6.47331e11	0.521490	0.260745	−	0.965408i	$-0.416032\pi$
$487$	6.47331e11	0.521490	0.260745	+	0.965408i	$0.416032\pi$
$488$	6.53977e11	0.522003
$489$	−1.03296e11	−0.0816948
$490$	0	0
$491$	−3.97775e11	−0.308866	−0.154433	−	0.988003i	$-0.549355\pi$
$491$	−3.97775e11	−0.308866	−0.154433	+	0.988003i	$0.549355\pi$
$492$	−4.07245e11	−0.313338
$493$	−4.63198e11	−0.353147
$494$	−1.26992e11	−0.0959415
$495$	0	0
$496$	−4.09645e11	−0.303907
$497$	7.91349e10	0.0581788
$498$	−1.27843e12	−0.931418
$499$	−2.18635e12	−1.57859	−0.789293	−	0.614017i	$-0.789553\pi$
$499$	−2.18635e12	−1.57859	−0.789293	+	0.614017i	$0.789553\pi$
$500$	0	0
$501$	3.45402e12	2.44937
$502$	−1.75987e12	−1.23684
$503$	2.69639e12	1.87814	0.939068	−	0.343730i	$-0.111691\pi$
$503$	2.69639e12	1.87814	0.939068	+	0.343730i	$0.111691\pi$
$504$	−2.03921e11	−0.140775
$505$	0	0
$506$	−2.18277e11	−0.148024
$507$	1.95953e12	1.31709
$508$	3.71471e11	0.247479
$509$	2.82393e12	1.86476	0.932381	−	0.361476i	$-0.117727\pi$
$509$	2.82393e12	1.86476	0.932381	+	0.361476i	$0.117727\pi$
$510$	0	0
$511$	−8.06228e11	−0.523075
$512$	6.87195e10	0.0441942
$513$	5.73357e10	0.0365508
$514$	−3.17547e11	−0.200666
$515$	0	0
$516$	1.09344e12	0.679004
$517$	6.28220e10	0.0386727
$518$	−2.44922e11	−0.149467
$519$	1.52866e12	0.924824
$520$	0	0
$521$	−2.82836e12	−1.68176	−0.840882	−	0.541219i	$-0.817963\pi$
$521$	−2.82836e12	−1.68176	−0.840882	+	0.541219i	$0.817963\pi$
$522$	1.09916e12	0.647953
$523$	2.81319e12	1.64415	0.822074	−	0.569380i	$-0.192817\pi$
$523$	2.81319e12	1.64415	0.822074	+	0.569380i	$0.192817\pi$
$524$	1.59686e12	0.925289
$525$	0	0
$526$	−1.37729e12	−0.784492
$527$	8.73905e11	0.493533
$528$	2.05782e11	0.115227
$529$	−1.03820e12	−0.576407
$530$	0	0
$531$	−1.55472e12	−0.848644
$532$	1.66582e11	0.0901626
$533$	2.31733e11	0.124370
$534$	2.68971e12	1.43143
$535$	0	0
$536$	6.44332e11	0.337185
$537$	3.25680e12	1.69008
$538$	−1.69971e12	−0.874689
$539$	−9.00375e10	−0.0459488
$540$	0	0
$541$	1.96722e12	0.987337	0.493668	−	0.869650i	$-0.335656\pi$
$541$	1.96722e12	0.987337	0.493668	+	0.869650i	$0.335656\pi$
$542$	−4.26065e11	−0.212070
$543$	4.03769e12	1.99312
$544$	−1.46601e11	−0.0717697
$545$	0	0
$546$	2.26184e11	0.108917
$547$	−1.89427e11	−0.0904689	−0.0452345	−	0.998976i	$-0.514403\pi$
$547$	−1.89427e11	−0.0904689	−0.0452345	+	0.998976i	$0.514403\pi$
$548$	−1.82979e12	−0.866739
$549$	3.31065e12	1.55538
$550$	0	0
$551$	−8.97898e11	−0.414997
$552$	−7.19281e11	−0.329741
$553$	1.42441e11	0.0647696
$554$	2.55004e12	1.15015
$555$	0	0
$556$	−5.56923e11	−0.247149
$557$	−7.51468e10	−0.0330797	−0.0165399	−	0.999863i	$-0.505265\pi$
$557$	−7.51468e10	−0.0330797	−0.0165399	+	0.999863i	$0.505265\pi$
$558$	−2.07376e12	−0.905533
$559$	−6.22197e11	−0.269510
$560$	0	0
$561$	−4.39000e11	−0.187125
$562$	−8.52350e11	−0.360417
$563$	−7.92094e11	−0.332268	−0.166134	−	0.986103i	$-0.553128\pi$
$563$	−7.92094e11	−0.332268	−0.166134	+	0.986103i	$0.553128\pi$
$564$	2.07015e11	0.0861481
$565$	0	0
$566$	−3.35233e11	−0.137301
$567$	8.77807e11	0.356677
$568$	−1.35001e11	−0.0544212
$569$	1.81892e12	0.727459	0.363730	−	0.931505i	$-0.381503\pi$
$569$	1.81892e12	0.727459	0.363730	+	0.931505i	$0.381503\pi$
$570$	0	0
$571$	4.05446e12	1.59614	0.798068	−	0.602567i	$-0.205855\pi$
$571$	4.05446e12	1.59614	0.798068	+	0.602567i	$0.205855\pi$
$572$	−1.17095e11	−0.0457360
$573$	8.21422e11	0.318325
$574$	−3.03976e11	−0.116879
$575$	0	0
$576$	3.47881e11	0.131683
$577$	1.08566e12	0.407758	0.203879	−	0.978996i	$-0.434645\pi$
$577$	1.08566e12	0.407758	0.203879	+	0.978996i	$0.434645\pi$
$578$	−1.58466e12	−0.590555
$579$	4.73238e12	1.74995
$580$	0	0
$581$	−9.54245e11	−0.347430
$582$	2.39665e12	0.865867
$583$	−1.42718e12	−0.511648
$584$	1.37539e12	0.489292
$585$	0	0
$586$	2.40347e12	0.841974
$587$	−3.71279e12	−1.29071	−0.645355	−	0.763882i	$-0.723291\pi$
$587$	−3.71279e12	−1.29071	−0.645355	+	0.763882i	$0.723291\pi$
$588$	−2.96697e11	−0.102356
$589$	1.69404e12	0.579970
$590$	0	0
$591$	−5.02467e12	−1.69420
$592$	4.17827e11	0.139813
$593$	7.00484e11	0.232623	0.116311	−	0.993213i	$-0.462893\pi$
$593$	7.00484e11	0.232623	0.116311	+	0.993213i	$0.462893\pi$
$594$	5.28673e10	0.0174240
$595$	0	0
$596$	−7.08928e11	−0.230141
$597$	1.19110e12	0.383763
$598$	4.09290e11	0.130881
$599$	4.49331e12	1.42609	0.713043	−	0.701120i	$-0.247316\pi$
$599$	4.49331e12	1.42609	0.713043	+	0.701120i	$0.247316\pi$
$600$	0	0
$601$	−2.44210e12	−0.763534	−0.381767	−	0.924259i	$-0.624684\pi$
$601$	−2.44210e12	−0.763534	−0.381767	+	0.924259i	$0.624684\pi$
$602$	8.16168e11	0.253277
$603$	3.26182e12	1.00469
$604$	2.46207e11	0.0752720
$605$	0	0
$606$	5.55624e12	1.67361
$607$	−3.54731e12	−1.06060	−0.530299	−	0.847811i	$-0.677920\pi$
$607$	−3.54731e12	−1.06060	−0.530299	+	0.847811i	$0.677920\pi$
$608$	−2.84182e11	−0.0843394
$609$	1.59923e12	0.471122
$610$	0	0
$611$	−1.17797e11	−0.0341939
$612$	−7.42142e11	−0.213848
$613$	−2.08138e12	−0.595359	−0.297679	−	0.954666i	$-0.596213\pi$
$613$	−2.08138e12	−0.595359	−0.297679	+	0.954666i	$0.596213\pi$
$614$	−1.11267e12	−0.315944
$615$	0	0
$616$	1.53600e11	0.0429811
$617$	−2.42245e12	−0.672933	−0.336467	−	0.941695i	$-0.609232\pi$
$617$	−2.42245e12	−0.672933	−0.336467	+	0.941695i	$0.609232\pi$
$618$	−2.02255e12	−0.557766
$619$	−5.86646e12	−1.60608	−0.803042	−	0.595922i	$-0.796787\pi$
$619$	−5.86646e12	−1.60608	−0.803042	+	0.595922i	$0.796787\pi$
$620$	0	0
$621$	−1.84790e11	−0.0498615
$622$	−2.16041e12	−0.578735
$623$	2.00765e12	0.533940
$624$	−3.85860e11	−0.101882
$625$	0	0
$626$	4.47676e11	0.116514
$627$	−8.50990e11	−0.219898
$628$	−1.89999e12	−0.487454
$629$	−8.91359e11	−0.227052
$630$	0	0
$631$	−3.08036e12	−0.773515	−0.386758	−	0.922181i	$-0.626405\pi$
$631$	−3.08036e12	−0.773515	−0.386758	+	0.922181i	$0.626405\pi$
$632$	−2.42998e11	−0.0605865
$633$	1.00609e13	2.49070
$634$	1.08836e11	0.0267529
$635$	0	0
$636$	−4.70294e12	−1.13976
$637$	1.68828e11	0.0406273
$638$	−8.27922e11	−0.197832
$639$	−6.83418e11	−0.162156
$640$	0	0
$641$	8.02920e12	1.87850	0.939250	−	0.343233i	$-0.111522\pi$
$641$	8.02920e12	1.87850	0.939250	+	0.343233i	$0.111522\pi$
$642$	5.30569e12	1.23263
$643$	−8.21210e12	−1.89454	−0.947272	−	0.320430i	$-0.896173\pi$
$643$	−8.21210e12	−1.89454	−0.947272	+	0.320430i	$0.896173\pi$
$644$	−5.36886e11	−0.122997
$645$	0	0
$646$	6.06252e11	0.136964
$647$	−5.88696e12	−1.32075	−0.660377	−	0.750934i	$-0.729604\pi$
$647$	−5.88696e12	−1.32075	−0.660377	+	0.750934i	$0.729604\pi$
$648$	−1.49750e12	−0.333641
$649$	1.17106e12	0.259107
$650$	0	0
$651$	−3.01723e12	−0.658407
$652$	1.31533e11	0.0285050
$653$	−3.10572e12	−0.668425	−0.334213	−	0.942498i	$-0.608470\pi$
$653$	−3.10572e12	−0.668425	−0.334213	+	0.942498i	$0.608470\pi$
$654$	−4.78352e12	−1.02246
$655$	0	0
$656$	5.18569e11	0.109330
$657$	6.96267e12	1.45791
$658$	1.54520e11	0.0321343
$659$	−6.48568e12	−1.33959	−0.669793	−	0.742547i	$-0.733617\pi$
$659$	−6.48568e12	−1.33959	−0.669793	+	0.742547i	$0.733617\pi$
$660$	0	0
$661$	−3.76148e12	−0.766394	−0.383197	−	0.923667i	$-0.625177\pi$
$661$	−3.76148e12	−0.766394	−0.383197	+	0.923667i	$0.625177\pi$
$662$	1.09034e12	0.220648
$663$	8.23164e11	0.165453
$664$	1.62790e12	0.324991
$665$	0	0
$666$	2.11518e12	0.416594
$667$	2.89388e12	0.566127
$668$	−4.39820e12	−0.854636
$669$	−1.84507e12	−0.356119
$670$	0	0
$671$	−2.49368e12	−0.474887
$672$	5.06152e11	0.0957457
$673$	−1.57852e12	−0.296607	−0.148303	−	0.988942i	$-0.547381\pi$
$673$	−1.57852e12	−0.296607	−0.148303	+	0.988942i	$0.547381\pi$
$674$	6.59919e12	1.23175
$675$	0	0
$676$	−2.49519e12	−0.459561
$677$	6.10156e12	1.11633	0.558164	−	0.829730i	$-0.311506\pi$
$677$	6.10156e12	1.11633	0.558164	+	0.829730i	$0.311506\pi$
$678$	−5.35309e12	−0.972907
$679$	1.78891e12	0.322979
$680$	0	0
$681$	9.82707e12	1.75090
$682$	1.56202e12	0.276476
$683$	−2.97384e12	−0.522907	−0.261454	−	0.965216i	$-0.584202\pi$
$683$	−2.97384e12	−0.522907	−0.261454	+	0.965216i	$0.584202\pi$
$684$	−1.43862e12	−0.251301
$685$	0	0
$686$	−2.21461e11	−0.0381802
$687$	−2.15672e12	−0.369393
$688$	−1.39235e12	−0.236919
$689$	2.67610e12	0.452392
$690$	0	0
$691$	1.10345e13	1.84121	0.920603	−	0.390500i	$-0.127698\pi$
$691$	1.10345e13	1.84121	0.920603	+	0.390500i	$0.127698\pi$
$692$	−1.94654e12	−0.322690
$693$	7.77574e11	0.128068
$694$	−1.56310e12	−0.255781
$695$	0	0
$696$	−2.72822e12	−0.440694
$697$	−1.10627e12	−0.177548
$698$	−2.84650e12	−0.453901
$699$	−1.58997e13	−2.51908
$700$	0	0
$701$	−1.06601e12	−0.166737	−0.0833684	−	0.996519i	$-0.526568\pi$
$701$	−1.06601e12	−0.166737	−0.0833684	+	0.996519i	$0.526568\pi$
$702$	−9.91310e10	−0.0154061
$703$	−1.72788e12	−0.266817
$704$	−2.62035e11	−0.0402052
$705$	0	0
$706$	−8.09488e12	−1.22628
$707$	4.14729e12	0.624276
$708$	3.85896e12	0.577192
$709$	5.15092e12	0.765556	0.382778	−	0.923840i	$-0.374967\pi$
$709$	5.15092e12	0.765556	0.382778	+	0.923840i	$0.374967\pi$
$710$	0	0
$711$	−1.23013e12	−0.180526
$712$	−3.42497e12	−0.499455
$713$	−5.45981e12	−0.791179
$714$	−1.07979e12	−0.155488
$715$	0	0
$716$	−4.14707e12	−0.589703
$717$	−1.41497e13	−1.99946
$718$	3.62912e12	0.509613
$719$	−7.14930e12	−0.997662	−0.498831	−	0.866699i	$-0.666237\pi$
$719$	−7.14930e12	−0.997662	−0.498831	+	0.866699i	$0.666237\pi$
$720$	0	0
$721$	−1.50967e12	−0.208053
$722$	−3.98780e12	−0.546155
$723$	−6.48361e11	−0.0882459
$724$	−5.14143e12	−0.695441
$725$	0	0
$726$	6.80011e12	0.908451
$727$	6.60804e12	0.877340	0.438670	−	0.898648i	$-0.355450\pi$
$727$	6.60804e12	0.877340	0.438670	+	0.898648i	$0.355450\pi$
$728$	−2.88014e11	−0.0380034
$729$	−8.41800e12	−1.10391
$730$	0	0
$731$	2.97032e12	0.384747
$732$	−8.21734e12	−1.05787
$733$	−3.15031e12	−0.403075	−0.201537	−	0.979481i	$-0.564594\pi$
$733$	−3.15031e12	−0.403075	−0.201537	+	0.979481i	$0.564594\pi$
$734$	−1.42664e12	−0.181419
$735$	0	0
$736$	9.15903e11	0.115053
$737$	−2.45691e12	−0.306750
$738$	2.62517e12	0.325764
$739$	8.91714e12	1.09983	0.549915	−	0.835221i	$-0.314660\pi$
$739$	8.91714e12	1.09983	0.549915	+	0.835221i	$0.314660\pi$
$740$	0	0
$741$	1.59568e12	0.194431
$742$	−3.51037e12	−0.425143
$743$	2.01761e12	0.242878	0.121439	−	0.992599i	$-0.461249\pi$
$743$	2.01761e12	0.242878	0.121439	+	0.992599i	$0.461249\pi$
$744$	5.14727e12	0.615883
$745$	0	0
$746$	3.92209e12	0.463652
$747$	8.24096e12	0.968357
$748$	5.59005e11	0.0652917
$749$	3.96027e12	0.459787
$750$	0	0
$751$	5.57535e12	0.639576	0.319788	−	0.947489i	$-0.396388\pi$
$751$	5.57535e12	0.639576	0.319788	+	0.947489i	$0.396388\pi$
$752$	−2.63604e11	−0.0300588
$753$	2.21131e13	2.50653
$754$	1.55243e12	0.174920
$755$	0	0
$756$	1.30035e11	0.0144781
$757$	−9.24800e12	−1.02357	−0.511783	−	0.859115i	$-0.671015\pi$
$757$	−9.24800e12	−1.02357	−0.511783	+	0.859115i	$0.671015\pi$
$758$	−5.47008e12	−0.601842
$759$	2.74270e12	0.299978
$760$	0	0
$761$	5.63867e12	0.609461	0.304730	−	0.952439i	$-0.401434\pi$
$761$	5.63867e12	0.609461	0.304730	+	0.952439i	$0.401434\pi$
$762$	−4.66760e12	−0.501530
$763$	−3.57051e12	−0.381391
$764$	−1.04597e12	−0.111070
$765$	0	0
$766$	2.22976e12	0.234007
$767$	−2.19585e12	−0.229099
$768$	−8.63473e11	−0.0895619
$769$	−3.02171e12	−0.311591	−0.155795	−	0.987789i	$-0.549794\pi$
$769$	−3.02171e12	−0.311591	−0.155795	+	0.987789i	$0.549794\pi$
$770$	0	0
$771$	3.99004e12	0.406661
$772$	−6.02602e12	−0.610594
$773$	1.04201e13	1.04970	0.524848	−	0.851196i	$-0.324122\pi$
$773$	1.04201e13	1.04970	0.524848	+	0.851196i	$0.324122\pi$
$774$	−7.04851e12	−0.705932
$775$	0	0
$776$	−3.05180e12	−0.302119
$777$	3.07750e12	0.302903
$778$	1.20010e13	1.17438
$779$	−2.14449e12	−0.208643
$780$	0	0
$781$	5.14772e11	0.0495091
$782$	−1.95392e12	−0.186843
$783$	−7.00904e11	−0.0666393
$784$	3.77802e11	0.0357143
$785$	0	0
$786$	−2.00649e13	−1.87515
$787$	5.20975e12	0.484095	0.242047	−	0.970264i	$-0.422181\pi$
$787$	5.20975e12	0.484095	0.242047	+	0.970264i	$0.422181\pi$
$788$	6.39821e12	0.591140
$789$	1.73059e13	1.58982
$790$	0	0
$791$	−3.99566e12	−0.362906
$792$	−1.32651e12	−0.119797
$793$	4.67588e12	0.419889
$794$	−1.00781e13	−0.899881
$795$	0	0
$796$	−1.51670e12	−0.133903
$797$	−4.43164e12	−0.389047	−0.194523	−	0.980898i	$-0.562316\pi$
$797$	−4.43164e12	−0.389047	−0.194523	+	0.980898i	$0.562316\pi$
$798$	−2.09314e12	−0.182719
$799$	5.62353e11	0.0488145
$800$	0	0
$801$	−1.73383e13	−1.48820
$802$	−2.61215e12	−0.222953
$803$	−5.24451e12	−0.445128
$804$	−8.09615e12	−0.683323
$805$	0	0
$806$	−2.92893e12	−0.244456
$807$	2.13571e13	1.77260
$808$	−7.07509e12	−0.583957
$809$	1.51138e13	1.24052	0.620261	−	0.784396i	$-0.287027\pi$
$809$	1.51138e13	1.24052	0.620261	+	0.784396i	$0.287027\pi$
$810$	0	0
$811$	−1.54577e13	−1.25473	−0.627364	−	0.778726i	$-0.715866\pi$
$811$	−1.54577e13	−1.25473	−0.627364	+	0.778726i	$0.715866\pi$
$812$	−2.03640e12	−0.164384
$813$	5.35358e12	0.429771
$814$	−1.59322e12	−0.127194
$815$	0	0
$816$	1.84207e12	0.145445
$817$	5.75790e12	0.452131
$818$	1.04310e13	0.814582
$819$	−1.45802e12	−0.113236
$820$	0	0
$821$	1.35717e13	1.04253	0.521267	−	0.853394i	$-0.325460\pi$
$821$	1.35717e13	1.04253	0.521267	+	0.853394i	$0.325460\pi$
$822$	2.29916e13	1.75649
$823$	−1.26218e13	−0.959011	−0.479506	−	0.877539i	$-0.659184\pi$
$823$	−1.26218e13	−0.959011	−0.479506	+	0.877539i	$0.659184\pi$
$824$	2.57544e12	0.194616
$825$	0	0
$826$	2.88040e12	0.215299
$827$	−2.20948e13	−1.64254	−0.821270	−	0.570540i	$-0.806734\pi$
$827$	−2.20948e13	−1.64254	−0.821270	+	0.570540i	$0.806734\pi$
$828$	4.63660e12	0.342818
$829$	−7.09788e12	−0.521955	−0.260978	−	0.965345i	$-0.584045\pi$
$829$	−7.09788e12	−0.521955	−0.260978	+	0.965345i	$0.584045\pi$
$830$	0	0
$831$	−3.20417e13	−2.33083
$832$	4.91339e11	0.0355489
$833$	−8.05974e11	−0.0579987
$834$	6.99785e12	0.500861
$835$	0	0
$836$	1.08362e12	0.0767268
$837$	1.32238e12	0.0931304
$838$	−7.59164e12	−0.531787
$839$	−2.47192e13	−1.72229	−0.861144	−	0.508362i	$-0.830251\pi$
$839$	−2.47192e13	−1.72229	−0.861144	+	0.508362i	$0.830251\pi$
$840$	0	0
$841$	−3.53073e12	−0.243379
$842$	2.33602e12	0.160166
$843$	1.07099e13	0.730404
$844$	−1.28112e13	−0.869055
$845$	0	0
$846$	−1.33445e12	−0.0895646
$847$	5.07574e12	0.338863
$848$	5.98853e12	0.397685
$849$	4.21227e12	0.278248
$850$	0	0
$851$	5.56886e12	0.363985
$852$	1.69631e12	0.110288
$853$	8.35049e12	0.540059	0.270030	−	0.962852i	$-0.412966\pi$
$853$	8.35049e12	0.540059	0.270030	+	0.962852i	$0.412966\pi$
$854$	−6.13359e12	−0.394597
$855$	0	0
$856$	−6.75605e12	−0.430091
$857$	−5.66058e12	−0.358465	−0.179233	−	0.983807i	$-0.557361\pi$
$857$	−5.66058e12	−0.358465	−0.179233	+	0.983807i	$0.557361\pi$
$858$	1.47133e12	0.0926865
$859$	−9.99170e12	−0.626138	−0.313069	−	0.949730i	$-0.601357\pi$
$859$	−9.99170e12	−0.626138	−0.313069	+	0.949730i	$0.601357\pi$
$860$	0	0
$861$	3.81951e12	0.236861
$862$	−7.06219e12	−0.435669
$863$	−9.53908e12	−0.585407	−0.292704	−	0.956203i	$-0.594555\pi$
$863$	−9.53908e12	−0.585407	−0.292704	+	0.956203i	$0.594555\pi$
$864$	−2.21834e11	−0.0135430
$865$	0	0
$866$	2.16553e12	0.130838
$867$	1.99115e13	1.19679
$868$	3.84202e12	0.229732
$869$	9.26577e11	0.0551179
$870$	0	0
$871$	4.60692e12	0.271224
$872$	6.09114e12	0.356758
$873$	−1.54492e13	−0.900206
$874$	−3.78762e12	−0.219566
$875$	0	0
$876$	−1.72820e13	−0.991576
$877$	−1.27850e13	−0.729799	−0.364900	−	0.931047i	$-0.618897\pi$
$877$	−1.27850e13	−0.729799	−0.364900	+	0.931047i	$0.618897\pi$
$878$	1.18328e12	0.0671989
$879$	−3.02000e13	−1.70631
$880$	0	0
$881$	−1.50900e13	−0.843913	−0.421957	−	0.906616i	$-0.638657\pi$
$881$	−1.50900e13	−0.843913	−0.421957	+	0.906616i	$0.638657\pi$
$882$	1.91256e12	0.106416
$883$	−1.48974e12	−0.0824685	−0.0412342	−	0.999150i	$-0.513129\pi$
$883$	−1.48974e12	−0.0824685	−0.0412342	+	0.999150i	$0.513129\pi$
$884$	−1.04818e12	−0.0577301
$885$	0	0
$886$	−1.55019e12	−0.0845148
$887$	−1.92566e13	−1.04453	−0.522267	−	0.852782i	$-0.674914\pi$
$887$	−1.92566e13	−1.04453	−0.522267	+	0.852782i	$0.674914\pi$
$888$	−5.25007e12	−0.283339
$889$	−3.48399e12	−0.187076
$890$	0	0
$891$	5.71013e12	0.303526
$892$	2.34943e12	0.124257
$893$	1.09011e12	0.0573638
$894$	8.90781e12	0.466393
$895$	0	0
$896$	−6.44514e11	−0.0334077
$897$	−5.14280e12	−0.265237
$898$	2.10990e13	1.08273
$899$	−2.07089e13	−1.05740
$900$	0	0
$901$	−1.27755e13	−0.645826
$902$	−1.97736e12	−0.0994618
$903$	−1.02553e13	−0.513279
$904$	6.81641e12	0.339467
$905$	0	0
$906$	−3.09363e12	−0.152543
$907$	−4.29875e12	−0.210916	−0.105458	−	0.994424i	$-0.533631\pi$
$907$	−4.29875e12	−0.210916	−0.105458	+	0.994424i	$0.533631\pi$
$908$	−1.25134e13	−0.610926
$909$	−3.58164e13	−1.73998
$910$	0	0
$911$	1.55780e13	0.749339	0.374669	−	0.927158i	$-0.377756\pi$
$911$	1.55780e13	0.749339	0.374669	+	0.927158i	$0.377756\pi$
$912$	3.57080e12	0.170918
$913$	−6.20736e12	−0.295657
$914$	−5.86457e12	−0.277957
$915$	0	0
$916$	2.74628e12	0.128889
$917$	−1.49768e13	−0.699453
$918$	4.73244e11	0.0219934
$919$	−3.15200e13	−1.45769	−0.728846	−	0.684677i	$-0.759943\pi$
$919$	−3.15200e13	−1.45769	−0.728846	+	0.684677i	$0.759943\pi$
$920$	0	0
$921$	1.39809e13	0.640277
$922$	−1.75064e13	−0.797823
$923$	−9.65244e11	−0.0437753
$924$	−1.93001e12	−0.0871036
$925$	0	0
$926$	1.70933e13	0.763972
$927$	1.30377e13	0.579886
$928$	3.47400e12	0.153767
$929$	1.29506e13	0.570453	0.285227	−	0.958460i	$-0.407931\pi$
$929$	1.29506e13	0.570453	0.285227	+	0.958460i	$0.407931\pi$
$930$	0	0
$931$	−1.56236e12	−0.0681565
$932$	2.02461e13	0.878961
$933$	2.71460e13	1.17284
$934$	−7.63192e12	−0.328150
$935$	0	0
$936$	2.48732e12	0.105923
$937$	3.67767e13	1.55864	0.779318	−	0.626628i	$-0.215566\pi$
$937$	3.67767e13	1.55864	0.779318	+	0.626628i	$0.215566\pi$
$938$	−6.04313e12	−0.254888
$939$	−5.62513e12	−0.236123
$940$	0	0
$941$	2.14183e13	0.890494	0.445247	−	0.895408i	$-0.353116\pi$
$941$	2.14183e13	0.890494	0.445247	+	0.895408i	$0.353116\pi$
$942$	2.38738e13	0.987852
$943$	6.91156e12	0.284625
$944$	−4.91384e12	−0.201394
$945$	0	0
$946$	5.30916e12	0.215534
$947$	4.33771e12	0.175261	0.0876306	−	0.996153i	$-0.472071\pi$
$947$	4.33771e12	0.175261	0.0876306	+	0.996153i	$0.472071\pi$
$948$	3.05331e12	0.122782
$949$	9.83392e12	0.393576
$950$	0	0
$951$	−1.36755e12	−0.0542163
$952$	1.37496e12	0.0542528
$953$	−3.24424e13	−1.27408	−0.637038	−	0.770833i	$-0.719840\pi$
$953$	−3.24424e13	−1.27408	−0.637038	+	0.770833i	$0.719840\pi$
$954$	3.03159e13	1.18496
$955$	0	0
$956$	1.80177e13	0.697652
$957$	1.04030e13	0.400917
$958$	−7.76534e12	−0.297863
$959$	1.71614e13	0.655193
$960$	0	0
$961$	1.26315e13	0.477747
$962$	2.98743e12	0.112463
$963$	−3.42013e13	−1.28152
$964$	8.25596e11	0.0307908
$965$	0	0
$966$	6.74607e12	0.249261
$967$	−3.83198e13	−1.40930	−0.704652	−	0.709553i	$-0.748897\pi$
$967$	−3.83198e13	−1.40930	−0.704652	+	0.709553i	$0.748897\pi$
$968$	−8.65899e12	−0.316977
$969$	−7.61767e12	−0.277565
$970$	0	0
$971$	6.62920e12	0.239317	0.119659	−	0.992815i	$-0.461820\pi$
$971$	6.62920e12	0.239317	0.119659	+	0.992815i	$0.461820\pi$
$972$	1.98824e13	0.714447
$973$	5.22333e12	0.186827
$974$	1.03573e13	0.368749
$975$	0	0
$976$	1.04636e13	0.369112
$977$	−2.52226e13	−0.885655	−0.442828	−	0.896607i	$-0.646025\pi$
$977$	−2.52226e13	−0.885655	−0.442828	+	0.896607i	$0.646025\pi$
$978$	−1.65274e12	−0.0577670
$979$	1.30598e13	0.454374
$980$	0	0
$981$	3.08353e13	1.06301
$982$	−6.36440e12	−0.218401
$983$	−2.73832e13	−0.935391	−0.467695	−	0.883890i	$-0.654916\pi$
$983$	−2.73832e13	−0.935391	−0.467695	+	0.883890i	$0.654916\pi$
$984$	−6.51592e12	−0.221563
$985$	0	0
$986$	−7.41117e12	−0.249713
$987$	−1.94157e12	−0.0651218
$988$	−2.03188e12	−0.0678409
$989$	−1.85574e13	−0.616785
$990$	0	0
$991$	−2.54798e13	−0.839197	−0.419599	−	0.907710i	$-0.637829\pi$
$991$	−2.54798e13	−0.839197	−0.419599	+	0.907710i	$0.637829\pi$
$992$	−6.55432e12	−0.214894
$993$	−1.37003e13	−0.447156
$994$	1.26616e12	0.0411386
$995$	0	0
$996$	−2.04549e13	−0.658612
$997$	−2.00966e13	−0.644162	−0.322081	−	0.946712i	$-0.604382\pi$
$997$	−2.00966e13	−0.644162	−0.322081	+	0.946712i	$0.604382\pi$
$998$	−3.49817e13	−1.11623
$999$	−1.34879e12	−0.0428450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.10.a.v.1.1		6
5.2	odd	4		70.10.c.a.29.12	yes	12
5.3	odd	4		70.10.c.a.29.1	✓	12
5.4	even	2		350.10.a.u.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.10.c.a.29.1	✓	12	5.3	odd	4
70.10.c.a.29.12	yes	12	5.2	odd	4
350.10.a.u.1.6		6	5.4	even	2
350.10.a.v.1.1		6	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -201.043 q^{3} +256.000 q^{4} -3216.69 q^{6} -2401.00 q^{7} +4096.00 q^{8} +20735.3 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -201.043 q^{3} +256.000 q^{4} -3216.69 q^{6} -2401.00 q^{7} +4096.00 q^{8} +20735.3 q^{9} -15618.5 q^{11} -51467.0 q^{12} +29286.1 q^{13} -38416.0 q^{14} +65536.0 q^{16} -139809. q^{17} +331765. q^{18} -271017. q^{19} +482704. q^{21} -249896. q^{22} +873473. q^{23} -823472. q^{24} +468577. q^{26} -211557. q^{27} -614656. q^{28} +3.31307e6 q^{29} -6.25069e6 q^{31} +1.04858e6 q^{32} +3.13999e6 q^{33} -2.23695e6 q^{34} +5.30824e6 q^{36} +6.37553e6 q^{37} -4.33627e6 q^{38} -5.88776e6 q^{39} +7.91273e6 q^{41} +7.72327e6 q^{42} -2.12455e7 q^{43} -3.99833e6 q^{44} +1.39756e7 q^{46} -4.02228e6 q^{47} -1.31756e7 q^{48} +5.76480e6 q^{49} +2.81077e7 q^{51} +7.49723e6 q^{52} +9.13777e7 q^{53} -3.38492e6 q^{54} -9.83450e6 q^{56} +5.44861e7 q^{57} +5.30091e7 q^{58} -7.49792e7 q^{59} +1.59662e8 q^{61} -1.00011e8 q^{62} -4.97855e7 q^{63} +1.67772e7 q^{64} +5.02398e7 q^{66} +1.57308e8 q^{67} -3.57912e7 q^{68} -1.75606e8 q^{69} -3.29592e7 q^{71} +8.49318e7 q^{72} +3.35788e8 q^{73} +1.02009e8 q^{74} -6.93804e7 q^{76} +3.75000e7 q^{77} -9.42042e7 q^{78} -5.93256e7 q^{79} -3.65601e8 q^{81} +1.26604e8 q^{82} +3.97437e8 q^{83} +1.23572e8 q^{84} -3.39928e8 q^{86} -6.66069e8 q^{87} -6.39733e7 q^{88} -8.36174e8 q^{89} -7.03159e7 q^{91} +2.23609e8 q^{92} +1.25666e9 q^{93} -6.43565e7 q^{94} -2.10809e8 q^{96} -7.45068e8 q^{97} +9.22368e7 q^{98} -3.23854e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 96 q^{2} - 77 q^{3} + 1536 q^{4} - 1232 q^{6} - 14406 q^{7} + 24576 q^{8} + 12253 q^{9}+O(q^{10}) \) 6 * q + 96 * q^2 - 77 * q^3 + 1536 * q^4 - 1232 * q^6 - 14406 * q^7 + 24576 * q^8 + 12253 * q^9	\( 6 q + 96 q^{2} - 77 q^{3} + 1536 q^{4} - 1232 q^{6} - 14406 q^{7} + 24576 q^{8} + 12253 q^{9} + 15403 q^{11} - 19712 q^{12} - 31881 q^{13} - 230496 q^{14} + 393216 q^{16} + 40105 q^{17} + 196048 q^{18} - 453532 q^{19} + 184877 q^{21} + 246448 q^{22} - 1283250 q^{23} - 315392 q^{24} - 510096 q^{26} + 4542769 q^{27} - 3687936 q^{28} + 2987503 q^{29} - 10485850 q^{31} + 6291456 q^{32} - 10778125 q^{33} + 641680 q^{34} + 3136768 q^{36} + 23029642 q^{37} - 7256512 q^{38} + 387387 q^{39} - 40774792 q^{41} + 2958032 q^{42} - 28109124 q^{43} + 3943168 q^{44} - 20532000 q^{46} + 12965759 q^{47} - 5046272 q^{48} + 34588806 q^{49} - 133173023 q^{51} - 8161536 q^{52} + 52853782 q^{53} + 72684304 q^{54} - 59006976 q^{56} + 51609516 q^{57} + 47800048 q^{58} + 1392010 q^{59} - 223375386 q^{61} - 167773600 q^{62} - 29419453 q^{63} + 100663296 q^{64} - 172450000 q^{66} + 13994382 q^{67} + 10266880 q^{68} - 317796350 q^{69} - 266244592 q^{71} + 50188288 q^{72} - 40166814 q^{73} + 368474272 q^{74} - 116104192 q^{76} - 36982603 q^{77} + 6198192 q^{78} - 727619379 q^{79} - 645880646 q^{81} - 652396672 q^{82} - 1013909260 q^{83} + 47328512 q^{84} - 449745984 q^{86} - 1307973903 q^{87} + 63090688 q^{88} - 1489896214 q^{89} + 76546281 q^{91} - 328512000 q^{92} - 971293682 q^{93} + 207452144 q^{94} - 80740352 q^{96} - 2163452111 q^{97} + 553420896 q^{98} - 2691573574 q^{99}+O(q^{100}) \) 6 * q + 96 * q^2 - 77 * q^3 + 1536 * q^4 - 1232 * q^6 - 14406 * q^7 + 24576 * q^8 + 12253 * q^9 + 15403 * q^11 - 19712 * q^12 - 31881 * q^13 - 230496 * q^14 + 393216 * q^16 + 40105 * q^17 + 196048 * q^18 - 453532 * q^19 + 184877 * q^21 + 246448 * q^22 - 1283250 * q^23 - 315392 * q^24 - 510096 * q^26 + 4542769 * q^27 - 3687936 * q^28 + 2987503 * q^29 - 10485850 * q^31 + 6291456 * q^32 - 10778125 * q^33 + 641680 * q^34 + 3136768 * q^36 + 23029642 * q^37 - 7256512 * q^38 + 387387 * q^39 - 40774792 * q^41 + 2958032 * q^42 - 28109124 * q^43 + 3943168 * q^44 - 20532000 * q^46 + 12965759 * q^47 - 5046272 * q^48 + 34588806 * q^49 - 133173023 * q^51 - 8161536 * q^52 + 52853782 * q^53 + 72684304 * q^54 - 59006976 * q^56 + 51609516 * q^57 + 47800048 * q^58 + 1392010 * q^59 - 223375386 * q^61 - 167773600 * q^62 - 29419453 * q^63 + 100663296 * q^64 - 172450000 * q^66 + 13994382 * q^67 + 10266880 * q^68 - 317796350 * q^69 - 266244592 * q^71 + 50188288 * q^72 - 40166814 * q^73 + 368474272 * q^74 - 116104192 * q^76 - 36982603 * q^77 + 6198192 * q^78 - 727619379 * q^79 - 645880646 * q^81 - 652396672 * q^82 - 1013909260 * q^83 + 47328512 * q^84 - 449745984 * q^86 - 1307973903 * q^87 + 63090688 * q^88 - 1489896214 * q^89 + 76546281 * q^91 - 328512000 * q^92 - 971293682 * q^93 + 207452144 * q^94 - 80740352 * q^96 - 2163452111 * q^97 + 553420896 * q^98 - 2691573574 * q^99

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