LMFDB - Embedded newform 350.10.a.n.1.3

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:	$0$
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			1.3
Root			$-153.773$ 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)

$f(q)$	$=$	$q-16.0000 q^{2} +54.9868 q^{3} +256.000 q^{4} -879.788 q^{6} -2401.00 q^{7} -4096.00 q^{8} -16659.5 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} +54.9868 q^{3} +256.000 q^{4} -879.788 q^{6} -2401.00 q^{7} -4096.00 q^{8} -16659.5 q^{9} -26937.0 q^{11} +14076.6 q^{12} +47442.1 q^{13} +38416.0 q^{14} +65536.0 q^{16} -61784.2 q^{17} +266551. q^{18} +714484. q^{19} -132023. q^{21} +430992. q^{22} -1.92694e6 q^{23} -225226. q^{24} -759074. q^{26} -1.99835e6 q^{27} -614656. q^{28} -5.23852e6 q^{29} +4.79435e6 q^{31} -1.04858e6 q^{32} -1.48118e6 q^{33} +988547. q^{34} -4.26482e6 q^{36} -1.18872e7 q^{37} -1.14317e7 q^{38} +2.60869e6 q^{39} -3.42477e7 q^{41} +2.11237e6 q^{42} +3.91880e7 q^{43} -6.89587e6 q^{44} +3.08310e7 q^{46} +4.85434e7 q^{47} +3.60361e6 q^{48} +5.76480e6 q^{49} -3.39731e6 q^{51} +1.21452e7 q^{52} -8.99282e7 q^{53} +3.19737e7 q^{54} +9.83450e6 q^{56} +3.92871e7 q^{57} +8.38163e7 q^{58} +7.46218e7 q^{59} -1.52790e8 q^{61} -7.67097e7 q^{62} +3.99994e7 q^{63} +1.67772e7 q^{64} +2.36989e7 q^{66} -7.84743e6 q^{67} -1.58167e7 q^{68} -1.05956e8 q^{69} -1.32897e7 q^{71} +6.82371e7 q^{72} +3.24970e8 q^{73} +1.90195e8 q^{74} +1.82908e8 q^{76} +6.46757e7 q^{77} -4.17390e7 q^{78} +5.86543e8 q^{79} +2.18025e8 q^{81} +5.47963e8 q^{82} -8.52632e8 q^{83} -3.37979e7 q^{84} -6.27008e8 q^{86} -2.88049e8 q^{87} +1.10334e8 q^{88} -5.68916e8 q^{89} -1.13909e8 q^{91} -4.93296e8 q^{92} +2.63626e8 q^{93} -7.76694e8 q^{94} -5.76578e7 q^{96} +1.43376e9 q^{97} -9.22368e7 q^{98} +4.48756e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	54.9868	0.391934	0.195967	−	0.980611i	$-0.437216\pi$
$3$	54.9868	0.391934	0.195967	+	0.980611i	$0.437216\pi$
$4$	256.000	0.500000
$5$	0	0
$5$	0	0
$6$	−879.788	−0.277139
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−4096.00	−0.353553
$9$	−16659.5	−0.846388
$10$	0	0
$11$	−26937.0	−0.554731	−0.277365	−	0.960765i	$-0.589461\pi$
$11$	−26937.0	−0.554731	−0.277365	+	0.960765i	$0.589461\pi$
$12$	14076.6	0.195967
$13$	47442.1	0.460701	0.230350	−	0.973108i	$-0.426013\pi$
$13$	47442.1	0.460701	0.230350	+	0.973108i	$0.426013\pi$
$14$	38416.0	0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	−61784.2	−0.179414	−0.0897071	−	0.995968i	$-0.528593\pi$
$17$	−61784.2	−0.179414	−0.0897071	+	0.995968i	$0.528593\pi$
$18$	266551.	0.598487
$19$	714484.	1.25777	0.628885	−	0.777499i	$-0.283512\pi$
$19$	714484.	1.25777	0.628885	+	0.777499i	$0.283512\pi$
$20$	0	0
$21$	−132023.	−0.148137
$22$	430992.	0.392254
$23$	−1.92694e6	−1.43580	−0.717898	−	0.696148i	$-0.754896\pi$
$23$	−1.92694e6	−1.43580	−0.717898	+	0.696148i	$0.754896\pi$
$24$	−225226.	−0.138569
$25$	0	0
$26$	−759074.	−0.325765
$27$	−1.99835e6	−0.723661
$28$	−614656.	−0.188982
$29$	−5.23852e6	−1.37536	−0.687682	−	0.726012i	$-0.741372\pi$
$29$	−5.23852e6	−1.37536	−0.687682	+	0.726012i	$0.741372\pi$
$30$	0	0
$31$	4.79435e6	0.932400	0.466200	−	0.884679i	$-0.345623\pi$
$31$	4.79435e6	0.932400	0.466200	+	0.884679i	$0.345623\pi$
$32$	−1.04858e6	−0.176777
$33$	−1.48118e6	−0.217418
$34$	988547.	0.126865
$35$	0	0
$36$	−4.26482e6	−0.423194
$37$	−1.18872e7	−1.04273	−0.521365	−	0.853334i	$-0.674577\pi$
$37$	−1.18872e7	−1.04273	−0.521365	+	0.853334i	$0.674577\pi$
$38$	−1.14317e7	−0.889377
$39$	2.60869e6	0.180564
$40$	0	0
$41$	−3.42477e7	−1.89280	−0.946398	−	0.323004i	$-0.895307\pi$
$41$	−3.42477e7	−1.89280	−0.946398	+	0.323004i	$0.895307\pi$
$42$	2.11237e6	0.104749
$43$	3.91880e7	1.74802	0.874008	−	0.485912i	$-0.161513\pi$
$43$	3.91880e7	1.74802	0.874008	+	0.485912i	$0.161513\pi$
$44$	−6.89587e6	−0.277365
$45$	0	0
$46$	3.08310e7	1.01526
$47$	4.85434e7	1.45107	0.725537	−	0.688183i	$-0.241591\pi$
$47$	4.85434e7	1.45107	0.725537	+	0.688183i	$0.241591\pi$
$48$	3.60361e6	0.0979834
$49$	5.76480e6	0.142857
$50$	0	0
$51$	−3.39731e6	−0.0703185
$52$	1.21452e7	0.230350
$53$	−8.99282e7	−1.56550	−0.782752	−	0.622333i	$-0.786185\pi$
$53$	−8.99282e7	−1.56550	−0.782752	+	0.622333i	$0.786185\pi$
$54$	3.19737e7	0.511706
$55$	0	0
$56$	9.83450e6	0.133631
$57$	3.92871e7	0.492962
$58$	8.38163e7	0.972529
$59$	7.46218e7	0.801737	0.400868	−	0.916136i	$-0.368708\pi$
$59$	7.46218e7	0.801737	0.400868	+	0.916136i	$0.368708\pi$
$60$	0	0
$61$	−1.52790e8	−1.41290	−0.706449	−	0.707764i	$-0.749704\pi$
$61$	−1.52790e8	−1.41290	−0.706449	+	0.707764i	$0.749704\pi$
$62$	−7.67097e7	−0.659307
$63$	3.99994e7	0.319905
$64$	1.67772e7	0.125000
$65$	0	0
$66$	2.36989e7	0.153737
$67$	−7.84743e6	−0.0475763	−0.0237881	−	0.999717i	$-0.507573\pi$
$67$	−7.84743e6	−0.0475763	−0.0237881	+	0.999717i	$0.507573\pi$
$68$	−1.58167e7	−0.0897071
$69$	−1.05956e8	−0.562737
$70$	0	0
$71$	−1.32897e7	−0.0620658	−0.0310329	−	0.999518i	$-0.509880\pi$
$71$	−1.32897e7	−0.0620658	−0.0310329	+	0.999518i	$0.509880\pi$
$72$	6.82371e7	0.299243
$73$	3.24970e8	1.33934	0.669669	−	0.742660i	$-0.266436\pi$
$73$	3.24970e8	1.33934	0.669669	+	0.742660i	$0.266436\pi$
$74$	1.90195e8	0.737321
$75$	0	0
$76$	1.82908e8	0.628885
$77$	6.46757e7	0.209668
$78$	−4.17390e7	−0.127678
$79$	5.86543e8	1.69425	0.847125	−	0.531393i	$-0.178331\pi$
$79$	5.86543e8	1.69425	0.847125	+	0.531393i	$0.178331\pi$
$80$	0	0
$81$	2.18025e8	0.562761
$82$	5.47963e8	1.33841
$83$	−8.52632e8	−1.97202	−0.986008	−	0.166699i	$-0.946689\pi$
$83$	−8.52632e8	−1.97202	−0.986008	+	0.166699i	$0.946689\pi$
$84$	−3.37979e7	−0.0740685
$85$	0	0
$86$	−6.27008e8	−1.23603
$87$	−2.88049e8	−0.539051
$88$	1.10334e8	0.196127
$89$	−5.68916e8	−0.961155	−0.480577	−	0.876952i	$-0.659573\pi$
$89$	−5.68916e8	−0.961155	−0.480577	+	0.876952i	$0.659573\pi$
$90$	0	0
$91$	−1.13909e8	−0.174129
$92$	−4.93296e8	−0.717898
$93$	2.63626e8	0.365439
$94$	−7.76694e8	−1.02606
$95$	0	0
$96$	−5.76578e7	−0.0692847
$97$	1.43376e9	1.64438	0.822190	−	0.569213i	$-0.192752\pi$
$97$	1.43376e9	1.64438	0.822190	+	0.569213i	$0.192752\pi$
$98$	−9.22368e7	−0.101015
$99$	4.48756e8	0.469517
$100$	0	0
$101$	−1.66792e7	−0.0159489	−0.00797444	−	0.999968i	$-0.502538\pi$
$101$	−1.66792e7	−0.0159489	−0.00797444	+	0.999968i	$0.502538\pi$
$102$	5.43570e7	0.0497227
$103$	−7.03526e8	−0.615903	−0.307952	−	0.951402i	$-0.599644\pi$
$103$	−7.03526e8	−0.615903	−0.307952	+	0.951402i	$0.599644\pi$
$104$	−1.94323e8	−0.162882
$105$	0	0
$106$	1.43885e9	1.10698
$107$	6.40461e8	0.472352	0.236176	−	0.971710i	$-0.424106\pi$
$107$	6.40461e8	0.472352	0.236176	+	0.971710i	$0.424106\pi$
$108$	−5.11579e8	−0.361831
$109$	−9.44605e8	−0.640960	−0.320480	−	0.947255i	$-0.603844\pi$
$109$	−9.44605e8	−0.640960	−0.320480	+	0.947255i	$0.603844\pi$
$110$	0	0
$111$	−6.53639e8	−0.408681
$112$	−1.57352e8	−0.0944911
$113$	1.36755e9	0.789022	0.394511	−	0.918891i	$-0.370914\pi$
$113$	1.36755e9	0.789022	0.394511	+	0.918891i	$0.370914\pi$
$114$	−6.28594e8	−0.348577
$115$	0	0
$116$	−1.34106e9	−0.687682
$117$	−7.90360e8	−0.389932
$118$	−1.19395e9	−0.566914
$119$	1.48344e8	0.0678122
$120$	0	0
$121$	−1.63235e9	−0.692274
$122$	2.44464e9	0.999070
$123$	−1.88317e9	−0.741850
$124$	1.22735e9	0.466200
$125$	0	0
$126$	−6.39990e8	−0.226207
$127$	2.88715e9	0.984809	0.492405	−	0.870366i	$-0.336118\pi$
$127$	2.88715e9	0.984809	0.492405	+	0.870366i	$0.336118\pi$
$128$	−2.68435e8	−0.0883883
$129$	2.15482e9	0.685106
$130$	0	0
$131$	−2.14502e9	−0.636371	−0.318185	−	0.948029i	$-0.603073\pi$
$131$	−2.14502e9	−0.636371	−0.318185	+	0.948029i	$0.603073\pi$
$132$	−3.79182e8	−0.108709
$133$	−1.71547e9	−0.475392
$134$	1.25559e8	0.0336415
$135$	0	0
$136$	2.53068e8	0.0634325
$137$	1.54736e9	0.375274	0.187637	−	0.982238i	$-0.439917\pi$
$137$	1.54736e9	0.375274	0.187637	+	0.982238i	$0.439917\pi$
$138$	1.69530e9	0.397915
$139$	−9.43851e8	−0.214455	−0.107228	−	0.994234i	$-0.534197\pi$
$139$	−9.43851e8	−0.214455	−0.107228	+	0.994234i	$0.534197\pi$
$140$	0	0
$141$	2.66924e9	0.568725
$142$	2.12635e8	0.0438872
$143$	−1.27795e9	−0.255565
$144$	−1.09179e9	−0.211597
$145$	0	0
$146$	−5.19952e9	−0.947055
$147$	3.16988e8	0.0559905
$148$	−3.04312e9	−0.521365
$149$	−8.39046e9	−1.39459	−0.697296	−	0.716783i	$-0.745614\pi$
$149$	−8.39046e9	−1.39459	−0.697296	+	0.716783i	$0.745614\pi$
$150$	0	0
$151$	−2.13222e8	−0.0333761	−0.0166880	−	0.999861i	$-0.505312\pi$
$151$	−2.13222e8	−0.0333761	−0.0166880	+	0.999861i	$0.505312\pi$
$152$	−2.92652e9	−0.444689
$153$	1.02929e9	0.151854
$154$	−1.03481e9	−0.148258
$155$	0	0
$156$	6.67824e8	0.0902820
$157$	−5.81675e8	−0.0764068	−0.0382034	−	0.999270i	$-0.512163\pi$
$157$	−5.81675e8	−0.0764068	−0.0382034	+	0.999270i	$0.512163\pi$
$158$	−9.38468e9	−1.19802
$159$	−4.94486e9	−0.613574
$160$	0	0
$161$	4.62658e9	0.542680
$162$	−3.48840e9	−0.397932
$163$	1.18196e10	1.31147	0.655733	−	0.754993i	$-0.272360\pi$
$163$	1.18196e10	1.31147	0.655733	+	0.754993i	$0.272360\pi$
$164$	−8.76740e9	−0.946398
$165$	0	0
$166$	1.36421e10	1.39443
$167$	1.37597e10	1.36894	0.684470	−	0.729041i	$-0.260033\pi$
$167$	1.37597e10	1.36894	0.684470	+	0.729041i	$0.260033\pi$
$168$	5.40767e8	0.0523743
$169$	−8.35375e9	−0.787755
$170$	0	0
$171$	−1.19029e10	−1.06456
$172$	1.00321e10	0.874008
$173$	−1.07898e10	−0.915810	−0.457905	−	0.889001i	$-0.651400\pi$
$173$	−1.07898e10	−0.915810	−0.457905	+	0.889001i	$0.651400\pi$
$174$	4.60879e9	0.381167
$175$	0	0
$176$	−1.76534e9	−0.138683
$177$	4.10321e9	0.314228
$178$	9.10266e9	0.679639
$179$	8.78729e9	0.639759	0.319879	−	0.947458i	$-0.396358\pi$
$179$	8.78729e9	0.639759	0.319879	+	0.947458i	$0.396358\pi$
$180$	0	0
$181$	−1.20534e10	−0.834750	−0.417375	−	0.908734i	$-0.637050\pi$
$181$	−1.20534e10	−0.834750	−0.417375	+	0.908734i	$0.637050\pi$
$182$	1.82254e9	0.123127
$183$	−8.40143e9	−0.553762
$184$	7.89274e9	0.507630
$185$	0	0
$186$	−4.21802e9	−0.258404
$187$	1.66428e9	0.0995266
$188$	1.24271e10	0.725537
$189$	4.79805e9	0.273518
$190$	0	0
$191$	2.62284e10	1.42601	0.713004	−	0.701160i	$-0.247334\pi$
$191$	2.62284e10	1.42601	0.713004	+	0.701160i	$0.247334\pi$
$192$	9.22525e8	0.0489917
$193$	3.29657e10	1.71023	0.855115	−	0.518438i	$-0.173486\pi$
$193$	3.29657e10	1.71023	0.855115	+	0.518438i	$0.173486\pi$
$194$	−2.29401e10	−1.16275
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	2.52084e10	1.19247	0.596236	−	0.802809i	$-0.296662\pi$
$197$	2.52084e10	1.19247	0.596236	+	0.802809i	$0.296662\pi$
$198$	−7.18009e9	−0.331999
$199$	−3.56701e10	−1.61237	−0.806186	−	0.591662i	$-0.798472\pi$
$199$	−3.56701e10	−1.61237	−0.806186	+	0.591662i	$0.798472\pi$
$200$	0	0
$201$	−4.31505e8	−0.0186467
$202$	2.66868e8	0.0112776
$203$	1.25777e10	0.519839
$204$	−8.69712e8	−0.0351592
$205$	0	0
$206$	1.12564e10	0.435509
$207$	3.21018e10	1.21524
$208$	3.10917e9	0.115175
$209$	−1.92460e10	−0.697723
$210$	0	0
$211$	−6.41609e9	−0.222843	−0.111422	−	0.993773i	$-0.535540\pi$
$211$	−6.41609e9	−0.222843	−0.111422	+	0.993773i	$0.535540\pi$
$212$	−2.30216e10	−0.782752
$213$	−7.30757e8	−0.0243257
$214$	−1.02474e10	−0.334003
$215$	0	0
$216$	8.18526e9	0.255853
$217$	−1.15112e10	−0.352414
$218$	1.51137e10	0.453227
$219$	1.78690e10	0.524932
$220$	0	0
$221$	−2.93117e9	−0.0826563
$222$	1.04582e10	0.288981
$223$	−3.20212e10	−0.867094	−0.433547	−	0.901131i	$-0.642738\pi$
$223$	−3.20212e10	−0.867094	−0.433547	+	0.901131i	$0.642738\pi$
$224$	2.51763e9	0.0668153
$225$	0	0
$226$	−2.18808e10	−0.557923
$227$	2.43392e10	0.608401	0.304200	−	0.952608i	$-0.401611\pi$
$227$	2.43392e10	0.608401	0.304200	+	0.952608i	$0.401611\pi$
$228$	1.00575e10	0.246481
$229$	4.05160e10	0.973570	0.486785	−	0.873522i	$-0.338169\pi$
$229$	4.05160e10	0.973570	0.486785	+	0.873522i	$0.338169\pi$
$230$	0	0
$231$	3.55631e9	0.0821761
$232$	2.14570e10	0.486265
$233$	7.77106e10	1.72734	0.863672	−	0.504054i	$-0.168159\pi$
$233$	7.77106e10	1.72734	0.863672	+	0.504054i	$0.168159\pi$
$234$	1.26458e10	0.275723
$235$	0	0
$236$	1.91032e10	0.400868
$237$	3.22521e10	0.664034
$238$	−2.37350e9	−0.0479505
$239$	1.17585e10	0.233111	0.116556	−	0.993184i	$-0.462815\pi$
$239$	1.17585e10	0.233111	0.116556	+	0.993184i	$0.462815\pi$
$240$	0	0
$241$	6.06811e10	1.15871	0.579357	−	0.815074i	$-0.303304\pi$
$241$	6.06811e10	1.15871	0.579357	+	0.815074i	$0.303304\pi$
$242$	2.61175e10	0.489512
$243$	5.13221e10	0.944226
$244$	−3.91143e10	−0.706449
$245$	0	0
$246$	3.01307e10	0.524567
$247$	3.38966e10	0.579455
$248$	−1.96377e10	−0.329653
$249$	−4.68835e10	−0.772899
$250$	0	0
$251$	2.23859e10	0.355994	0.177997	−	0.984031i	$-0.443038\pi$
$251$	2.23859e10	0.355994	0.177997	+	0.984031i	$0.443038\pi$
$252$	1.02398e10	0.159952
$253$	5.19059e10	0.796480
$254$	−4.61943e10	−0.696365
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	3.22872e10	0.461670	0.230835	−	0.972993i	$-0.425854\pi$
$257$	3.22872e10	0.461670	0.230835	+	0.972993i	$0.425854\pi$
$258$	−3.44772e10	−0.484443
$259$	2.85412e10	0.394115
$260$	0	0
$261$	8.72709e10	1.16409
$262$	3.43203e10	0.449982
$263$	−1.06597e11	−1.37386	−0.686930	−	0.726724i	$-0.741042\pi$
$263$	−1.06597e11	−1.37386	−0.686930	+	0.726724i	$0.741042\pi$
$264$	6.06691e9	0.0768687
$265$	0	0
$266$	2.74476e10	0.336153
$267$	−3.12829e10	−0.376709
$268$	−2.00894e9	−0.0237881
$269$	5.83050e10	0.678923	0.339462	−	0.940620i	$-0.389755\pi$
$269$	5.83050e10	0.678923	0.339462	+	0.940620i	$0.389755\pi$
$270$	0	0
$271$	1.76430e11	1.98705	0.993527	−	0.113597i	$-0.0362372\pi$
$271$	1.76430e11	1.98705	0.993527	+	0.113597i	$0.0362372\pi$
$272$	−4.04909e9	−0.0448536
$273$	−6.26346e9	−0.0682468
$274$	−2.47577e10	−0.265359
$275$	0	0
$276$	−2.71248e10	−0.281368
$277$	−1.01835e10	−0.103930	−0.0519649	−	0.998649i	$-0.516548\pi$
$277$	−1.01835e10	−0.103930	−0.0519649	+	0.998649i	$0.516548\pi$
$278$	1.51016e10	0.151643
$279$	−7.98713e10	−0.789173
$280$	0	0
$281$	1.42149e11	1.36008	0.680041	−	0.733174i	$-0.261962\pi$
$281$	1.42149e11	1.36008	0.680041	+	0.733174i	$0.261962\pi$
$282$	−4.27079e10	−0.402149
$283$	8.74627e10	0.810558	0.405279	−	0.914193i	$-0.367174\pi$
$283$	8.74627e10	0.810558	0.405279	+	0.914193i	$0.367174\pi$
$284$	−3.40216e9	−0.0310329
$285$	0	0
$286$	2.04472e10	0.180712
$287$	8.22286e10	0.715409
$288$	1.74687e10	0.149622
$289$	−1.14771e11	−0.967811
$290$	0	0
$291$	7.88376e10	0.644488
$292$	8.31923e10	0.669669
$293$	−1.84704e10	−0.146410	−0.0732051	−	0.997317i	$-0.523323\pi$
$293$	−1.84704e10	−0.146410	−0.0732051	+	0.997317i	$0.523323\pi$
$294$	−5.07180e9	−0.0395913
$295$	0	0
$296$	4.86900e10	0.368661
$297$	5.38297e10	0.401437
$298$	1.34247e11	0.986126
$299$	−9.14181e10	−0.661472
$300$	0	0
$301$	−9.40904e10	−0.660688
$302$	3.41155e9	0.0236004
$303$	−9.17137e8	−0.00625090
$304$	4.68244e10	0.314442
$305$	0	0
$306$	−1.64686e10	−0.107377
$307$	8.28529e10	0.532335	0.266168	−	0.963927i	$-0.414243\pi$
$307$	8.28529e10	0.532335	0.266168	+	0.963927i	$0.414243\pi$
$308$	1.65570e10	0.104834
$309$	−3.86846e10	−0.241393
$310$	0	0
$311$	1.36248e11	0.825865	0.412932	−	0.910762i	$-0.364505\pi$
$311$	1.36248e11	0.825865	0.412932	+	0.910762i	$0.364505\pi$
$312$	−1.06852e10	−0.0638390
$313$	−4.17539e10	−0.245894	−0.122947	−	0.992413i	$-0.539234\pi$
$313$	−4.17539e10	−0.245894	−0.122947	+	0.992413i	$0.539234\pi$
$314$	9.30680e9	0.0540278
$315$	0	0
$316$	1.50155e11	0.847125
$317$	3.02932e11	1.68492	0.842458	−	0.538761i	$-0.181108\pi$
$317$	3.02932e11	1.68492	0.842458	+	0.538761i	$0.181108\pi$
$318$	7.91177e10	0.433862
$319$	1.41110e11	0.762957
$320$	0	0
$321$	3.52169e10	0.185131
$322$	−7.40253e10	−0.383733
$323$	−4.41438e10	−0.225662
$324$	5.58144e10	0.281380
$325$	0	0
$326$	−1.89113e11	−0.927347
$327$	−5.19407e10	−0.251214
$328$	1.40278e11	0.669204
$329$	−1.16553e11	−0.548455
$330$	0	0
$331$	2.07799e10	0.0951521	0.0475760	−	0.998868i	$-0.484850\pi$
$331$	2.07799e10	0.0951521	0.0475760	+	0.998868i	$0.484850\pi$
$332$	−2.18274e11	−0.986008
$333$	1.98034e11	0.882554
$334$	−2.20155e11	−0.967987
$335$	0	0
$336$	−8.65227e9	−0.0370342
$337$	4.52094e10	0.190939	0.0954693	−	0.995432i	$-0.469565\pi$
$337$	4.52094e10	0.190939	0.0954693	+	0.995432i	$0.469565\pi$
$338$	1.33660e11	0.557027
$339$	7.51970e10	0.309244
$340$	0	0
$341$	−1.29146e11	−0.517231
$342$	1.90447e11	0.752758
$343$	−1.38413e10	−0.0539949
$344$	−1.60514e11	−0.618017
$345$	0	0
$346$	1.72636e11	0.647575
$347$	4.80358e11	1.77862	0.889308	−	0.457308i	$-0.151186\pi$
$347$	4.80358e11	1.77862	0.889308	+	0.457308i	$0.151186\pi$
$348$	−7.37406e10	−0.269526
$349$	−2.04156e11	−0.736627	−0.368314	−	0.929702i	$-0.620065\pi$
$349$	−2.04156e11	−0.736627	−0.368314	+	0.929702i	$0.620065\pi$
$350$	0	0
$351$	−9.48061e10	−0.333391
$352$	2.82455e10	0.0980634
$353$	−3.37988e10	−0.115855	−0.0579276	−	0.998321i	$-0.518449\pi$
$353$	−3.37988e10	−0.115855	−0.0579276	+	0.998321i	$0.518449\pi$
$354$	−6.56514e10	−0.222192
$355$	0	0
$356$	−1.45643e11	−0.480577
$357$	8.15694e9	0.0265779
$358$	−1.40597e11	−0.452378
$359$	4.99600e10	0.158744	0.0793720	−	0.996845i	$-0.474709\pi$
$359$	4.99600e10	0.158744	0.0793720	+	0.996845i	$0.474709\pi$
$360$	0	0
$361$	1.87799e11	0.581984
$362$	1.92855e11	0.590257
$363$	−8.97574e10	−0.271325
$364$	−2.91606e10	−0.0870643
$365$	0	0
$366$	1.34423e11	0.391569
$367$	6.15726e11	1.77170	0.885850	−	0.463973i	$-0.153576\pi$
$367$	6.15726e11	1.77170	0.885850	+	0.463973i	$0.153576\pi$
$368$	−1.26284e11	−0.358949
$369$	5.70547e11	1.60204
$370$	0	0
$371$	2.15918e11	0.591705
$372$	6.74883e10	0.182720
$373$	−1.95235e11	−0.522238	−0.261119	−	0.965307i	$-0.584091\pi$
$373$	−1.95235e11	−0.522238	−0.261119	+	0.965307i	$0.584091\pi$
$374$	−2.66285e10	−0.0703759
$375$	0	0
$376$	−1.98834e11	−0.513032
$377$	−2.48527e11	−0.633631
$378$	−7.67688e10	−0.193407
$379$	−4.25292e11	−1.05879	−0.529397	−	0.848374i	$-0.677582\pi$
$379$	−4.25292e11	−1.05879	−0.529397	+	0.848374i	$0.677582\pi$
$380$	0	0
$381$	1.58755e11	0.385980
$382$	−4.19655e11	−1.00834
$383$	−6.86115e9	−0.0162931	−0.00814653	−	0.999967i	$-0.502593\pi$
$383$	−6.86115e9	−0.0162931	−0.00814653	+	0.999967i	$0.502593\pi$
$384$	−1.47604e10	−0.0346424
$385$	0	0
$386$	−5.27452e11	−1.20932
$387$	−6.52851e11	−1.47950
$388$	3.67041e11	0.822190
$389$	−3.41482e11	−0.756128	−0.378064	−	0.925780i	$-0.623410\pi$
$389$	−3.41482e11	−0.756128	−0.378064	+	0.925780i	$0.623410\pi$
$390$	0	0
$391$	1.19054e11	0.257602
$392$	−2.36126e10	−0.0505076
$393$	−1.17948e11	−0.249415
$394$	−4.03335e11	−0.843205
$395$	0	0
$396$	1.14881e11	0.234759
$397$	4.00666e11	0.809516	0.404758	−	0.914424i	$-0.367356\pi$
$397$	4.00666e11	0.809516	0.404758	+	0.914424i	$0.367356\pi$
$398$	5.70721e11	1.14012
$399$	−9.43284e10	−0.186322
$400$	0	0
$401$	−3.65541e11	−0.705970	−0.352985	−	0.935629i	$-0.614833\pi$
$401$	−3.65541e11	−0.705970	−0.352985	+	0.935629i	$0.614833\pi$
$402$	6.90407e9	0.0131852
$403$	2.27454e11	0.429558
$404$	−4.26988e9	−0.00797444
$405$	0	0
$406$	−2.01243e11	−0.367582
$407$	3.20205e11	0.578434
$408$	1.39154e10	0.0248613
$409$	1.94966e11	0.344512	0.172256	−	0.985052i	$-0.444894\pi$
$409$	1.94966e11	0.344512	0.172256	+	0.985052i	$0.444894\pi$
$410$	0	0
$411$	8.50842e10	0.147082
$412$	−1.80103e11	−0.307952
$413$	−1.79167e11	−0.303028
$414$	−5.13628e11	−0.859305
$415$	0	0
$416$	−4.97467e10	−0.0814412
$417$	−5.18993e10	−0.0840523
$418$	3.07937e11	0.493365
$419$	7.64968e11	1.21250	0.606248	−	0.795276i	$-0.292674\pi$
$419$	7.64968e11	1.21250	0.606248	+	0.795276i	$0.292674\pi$
$420$	0	0
$421$	−1.12953e12	−1.75238	−0.876189	−	0.481968i	$-0.839922\pi$
$421$	−1.12953e12	−1.75238	−0.876189	+	0.481968i	$0.839922\pi$
$422$	1.02657e11	0.157574
$423$	−8.08706e11	−1.22817
$424$	3.68346e11	0.553489
$425$	0	0
$426$	1.16921e10	0.0172008
$427$	3.66849e11	0.534025
$428$	1.63958e11	0.236176
$429$	−7.02702e10	−0.100164
$430$	0	0
$431$	−7.41987e11	−1.03573	−0.517867	−	0.855461i	$-0.673274\pi$
$431$	−7.41987e11	−1.03573	−0.517867	+	0.855461i	$0.673274\pi$
$432$	−1.30964e11	−0.180915
$433$	−5.33419e11	−0.729244	−0.364622	−	0.931156i	$-0.618802\pi$
$433$	−5.33419e11	−0.729244	−0.364622	+	0.931156i	$0.618802\pi$
$434$	1.84180e11	0.249195
$435$	0	0
$436$	−2.41819e11	−0.320480
$437$	−1.37677e12	−1.80590
$438$	−2.85905e11	−0.371183
$439$	−3.95968e11	−0.508826	−0.254413	−	0.967096i	$-0.581882\pi$
$439$	−3.95968e11	−0.508826	−0.254413	+	0.967096i	$0.581882\pi$
$440$	0	0
$441$	−9.60385e10	−0.120913
$442$	4.68987e10	0.0584468
$443$	8.27906e11	1.02133	0.510663	−	0.859781i	$-0.329400\pi$
$443$	8.27906e11	1.02133	0.510663	+	0.859781i	$0.329400\pi$
$444$	−1.67331e11	−0.204340
$445$	0	0
$446$	5.12340e11	0.613128
$447$	−4.61364e11	−0.546588
$448$	−4.02821e10	−0.0472456
$449$	1.57691e12	1.83105	0.915523	−	0.402266i	$-0.131777\pi$
$449$	1.57691e12	1.83105	0.915523	+	0.402266i	$0.131777\pi$
$450$	0	0
$451$	9.22529e11	1.04999
$452$	3.50092e11	0.394511
$453$	−1.17244e10	−0.0130812
$454$	−3.89427e11	−0.430204
$455$	0	0
$456$	−1.60920e11	−0.174288
$457$	1.15676e12	1.24057	0.620284	−	0.784377i	$-0.287017\pi$
$457$	1.15676e12	1.24057	0.620284	+	0.784377i	$0.287017\pi$
$458$	−6.48257e11	−0.688418
$459$	1.23467e11	0.129835
$460$	0	0
$461$	3.24289e11	0.334409	0.167204	−	0.985922i	$-0.446526\pi$
$461$	3.24289e11	0.334409	0.167204	+	0.985922i	$0.446526\pi$
$462$	−5.69009e10	−0.0581073
$463$	−8.55827e11	−0.865509	−0.432754	−	0.901512i	$-0.642458\pi$
$463$	−8.55827e11	−0.865509	−0.432754	+	0.901512i	$0.642458\pi$
$464$	−3.43312e11	−0.343841
$465$	0	0
$466$	−1.24337e12	−1.22142
$467$	−8.84354e11	−0.860400	−0.430200	−	0.902734i	$-0.641557\pi$
$467$	−8.84354e11	−0.860400	−0.430200	+	0.902734i	$0.641557\pi$
$468$	−2.02332e11	−0.194966
$469$	1.88417e10	0.0179822
$470$	0	0
$471$	−3.19844e10	−0.0299464
$472$	−3.05651e11	−0.283457
$473$	−1.05561e12	−0.969677
$474$	−5.16033e11	−0.469543
$475$	0	0
$476$	3.79760e10	0.0339061
$477$	1.49815e12	1.32502
$478$	−1.88137e11	−0.164834
$479$	−4.38193e11	−0.380326	−0.190163	−	0.981753i	$-0.560902\pi$
$479$	−4.38193e11	−0.380326	−0.190163	+	0.981753i	$0.560902\pi$
$480$	0	0
$481$	−5.63954e11	−0.480386
$482$	−9.70897e11	−0.819335
$483$	2.54401e11	0.212694
$484$	−4.17881e11	−0.346137
$485$	0	0
$486$	−8.21153e11	−0.667669
$487$	−1.13497e11	−0.0914330	−0.0457165	−	0.998954i	$-0.514557\pi$
$487$	−1.13497e11	−0.0914330	−0.0457165	+	0.998954i	$0.514557\pi$
$488$	6.25828e11	0.499535
$489$	6.49919e11	0.514008
$490$	0	0
$491$	1.37729e11	0.106945	0.0534723	−	0.998569i	$-0.482971\pi$
$491$	1.37729e11	0.106945	0.0534723	+	0.998569i	$0.482971\pi$
$492$	−4.82091e11	−0.370925
$493$	3.23658e11	0.246760
$494$	−5.42346e11	−0.409737
$495$	0	0
$496$	3.14203e11	0.233100
$497$	3.19086e10	0.0234587
$498$	7.50136e11	0.546522
$499$	2.27758e12	1.64445	0.822224	−	0.569164i	$-0.192733\pi$
$499$	2.27758e12	1.64445	0.822224	+	0.569164i	$0.192733\pi$
$500$	0	0
$501$	7.56601e11	0.536534
$502$	−3.58174e11	−0.251726
$503$	−1.58061e12	−1.10095	−0.550476	−	0.834851i	$-0.685554\pi$
$503$	−1.58061e12	−1.10095	−0.550476	+	0.834851i	$0.685554\pi$
$504$	−1.63837e11	−0.113103
$505$	0	0
$506$	−8.30495e11	−0.563196
$507$	−4.59345e11	−0.308748
$508$	7.39109e11	0.492405
$509$	2.45533e12	1.62136	0.810682	−	0.585487i	$-0.199097\pi$
$509$	2.45533e12	1.62136	0.810682	+	0.585487i	$0.199097\pi$
$510$	0	0
$511$	−7.80253e11	−0.506222
$512$	−6.87195e10	−0.0441942
$513$	−1.42779e12	−0.910199
$514$	−5.16596e11	−0.326450
$515$	0	0
$516$	5.51634e11	0.342553
$517$	−1.30761e12	−0.804955
$518$	−4.56659e11	−0.278681
$519$	−5.93295e11	−0.358937
$520$	0	0
$521$	1.24919e12	0.742779	0.371390	−	0.928477i	$-0.378881\pi$
$521$	1.24919e12	0.742779	0.371390	+	0.928477i	$0.378881\pi$
$522$	−1.39633e12	−0.823137
$523$	−7.83895e11	−0.458142	−0.229071	−	0.973410i	$-0.573569\pi$
$523$	−7.83895e11	−0.458142	−0.229071	+	0.973410i	$0.573569\pi$
$524$	−5.49125e11	−0.318185
$525$	0	0
$526$	1.70554e12	0.971465
$527$	−2.96215e11	−0.167286
$528$	−9.70705e10	−0.0543544
$529$	1.91194e12	1.06151
$530$	0	0
$531$	−1.24316e12	−0.678581
$532$	−4.39162e11	−0.237696
$533$	−1.62478e12	−0.872012
$534$	5.00526e11	0.266373
$535$	0	0
$536$	3.21431e10	0.0168208
$537$	4.83184e11	0.250743
$538$	−9.32880e11	−0.480071
$539$	−1.55286e11	−0.0792472
$540$	0	0
$541$	2.22696e12	1.11770	0.558849	−	0.829269i	$-0.311243\pi$
$541$	2.22696e12	1.11770	0.558849	+	0.829269i	$0.311243\pi$
$542$	−2.82287e12	−1.40506
$543$	−6.62778e11	−0.327166
$544$	6.47854e10	0.0317163
$545$	0	0
$546$	1.00215e11	0.0482578
$547$	−2.30598e12	−1.10132	−0.550659	−	0.834730i	$-0.685623\pi$
$547$	−2.30598e12	−1.10132	−0.550659	+	0.834730i	$0.685623\pi$
$548$	3.96124e11	0.187637
$549$	2.54540e12	1.19586
$550$	0	0
$551$	−3.74284e12	−1.72989
$552$	4.33996e11	0.198957
$553$	−1.40829e12	−0.640367
$554$	1.62937e11	0.0734895
$555$	0	0
$556$	−2.41626e11	−0.107228
$557$	2.38221e11	0.104865	0.0524327	−	0.998624i	$-0.483302\pi$
$557$	2.38221e11	0.104865	0.0524327	+	0.998624i	$0.483302\pi$
$558$	1.27794e12	0.558029
$559$	1.85916e12	0.805312
$560$	0	0
$561$	9.15133e10	0.0390078
$562$	−2.27438e12	−0.961723
$563$	2.15766e12	0.905099	0.452550	−	0.891739i	$-0.350515\pi$
$563$	2.15766e12	0.905099	0.452550	+	0.891739i	$0.350515\pi$
$564$	6.83326e11	0.284362
$565$	0	0
$566$	−1.39940e12	−0.573151
$567$	−5.23478e11	−0.212704
$568$	5.44346e10	0.0219436
$569$	−2.01543e12	−0.806051	−0.403025	−	0.915189i	$-0.632041\pi$
$569$	−2.01543e12	−0.806051	−0.403025	+	0.915189i	$0.632041\pi$
$570$	0	0
$571$	−1.83068e12	−0.720693	−0.360347	−	0.932818i	$-0.617342\pi$
$571$	−1.83068e12	−0.720693	−0.360347	+	0.932818i	$0.617342\pi$
$572$	−3.27155e11	−0.127782
$573$	1.44222e12	0.558900
$574$	−1.31566e12	−0.505871
$575$	0	0
$576$	−2.79499e11	−0.105799
$577$	−2.41292e12	−0.906257	−0.453128	−	0.891445i	$-0.649692\pi$
$577$	−2.41292e12	−0.906257	−0.453128	+	0.891445i	$0.649692\pi$
$578$	1.83633e12	0.684345
$579$	1.81268e12	0.670297
$580$	0	0
$581$	2.04717e12	0.745352
$582$	−1.26140e12	−0.455722
$583$	2.42239e12	0.868433
$584$	−1.33108e12	−0.473528
$585$	0	0
$586$	2.95526e11	0.103528
$587$	1.63649e12	0.568907	0.284454	−	0.958690i	$-0.408188\pi$
$587$	1.63649e12	0.568907	0.284454	+	0.958690i	$0.408188\pi$
$588$	8.11489e10	0.0279953
$589$	3.42549e12	1.17274
$590$	0	0
$591$	1.38613e12	0.467370
$592$	−7.79040e11	−0.260682
$593$	5.72144e11	0.190003	0.0950013	−	0.995477i	$-0.469714\pi$
$593$	5.72144e11	0.190003	0.0950013	+	0.995477i	$0.469714\pi$
$594$	−8.61274e11	−0.283859
$595$	0	0
$596$	−2.14796e12	−0.697296
$597$	−1.96138e12	−0.631943
$598$	1.46269e12	0.467731
$599$	5.63032e12	1.78695	0.893475	−	0.449114i	$-0.148260\pi$
$599$	5.63032e12	1.78695	0.893475	+	0.449114i	$0.148260\pi$
$600$	0	0
$601$	−4.98614e12	−1.55894	−0.779471	−	0.626439i	$-0.784512\pi$
$601$	−4.98614e12	−1.55894	−0.779471	+	0.626439i	$0.784512\pi$
$602$	1.50545e12	0.467177
$603$	1.30734e11	0.0402680
$604$	−5.45848e10	−0.0166880
$605$	0	0
$606$	1.46742e10	0.00442005
$607$	1.22820e12	0.367215	0.183608	−	0.983000i	$-0.441222\pi$
$607$	1.22820e12	0.367215	0.183608	+	0.983000i	$0.441222\pi$
$608$	−7.49190e11	−0.222344
$609$	6.91606e11	0.203742
$610$	0	0
$611$	2.30300e12	0.668511
$612$	2.63498e11	0.0759271
$613$	2.15391e12	0.616106	0.308053	−	0.951369i	$-0.400323\pi$
$613$	2.15391e12	0.616106	0.308053	+	0.951369i	$0.400323\pi$
$614$	−1.32565e12	−0.376418
$615$	0	0
$616$	−2.64912e11	−0.0741290
$617$	−1.87667e12	−0.521321	−0.260660	−	0.965431i	$-0.583940\pi$
$617$	−1.87667e12	−0.521321	−0.260660	+	0.965431i	$0.583940\pi$
$618$	6.18954e11	0.170691
$619$	2.24620e12	0.614951	0.307475	−	0.951556i	$-0.400516\pi$
$619$	2.24620e12	0.614951	0.307475	+	0.951556i	$0.400516\pi$
$620$	0	0
$621$	3.85071e12	1.03903
$622$	−2.17997e12	−0.583975
$623$	1.36597e12	0.363282
$624$	1.70963e11	0.0451410
$625$	0	0
$626$	6.68062e11	0.173873
$627$	−1.05828e12	−0.273461
$628$	−1.48909e11	−0.0382034
$629$	7.34441e11	0.187081
$630$	0	0
$631$	7.19648e12	1.80713	0.903563	−	0.428456i	$-0.140942\pi$
$631$	7.19648e12	1.80713	0.903563	+	0.428456i	$0.140942\pi$
$632$	−2.40248e12	−0.599008
$633$	−3.52800e11	−0.0873397
$634$	−4.84691e12	−1.19142
$635$	0	0
$636$	−1.26588e12	−0.306787
$637$	2.73494e11	0.0658144
$638$	−2.25776e12	−0.539492
$639$	2.21399e11	0.0525318
$640$	0	0
$641$	−5.26314e12	−1.23136	−0.615678	−	0.787998i	$-0.711118\pi$
$641$	−5.26314e12	−1.23136	−0.615678	+	0.787998i	$0.711118\pi$
$642$	−5.63470e11	−0.130907
$643$	−6.94208e12	−1.60155	−0.800775	−	0.598966i	$-0.795579\pi$
$643$	−6.94208e12	−1.60155	−0.800775	+	0.598966i	$0.795579\pi$
$644$	1.18440e12	0.271340
$645$	0	0
$646$	7.06300e11	0.159567
$647$	5.47976e10	0.0122940	0.00614699	−	0.999981i	$-0.498043\pi$
$647$	5.47976e10	0.0122940	0.00614699	+	0.999981i	$0.498043\pi$
$648$	−8.93031e11	−0.198966
$649$	−2.01009e12	−0.444748
$650$	0	0
$651$	−6.32966e11	−0.138123
$652$	3.02581e12	0.655733
$653$	−2.59017e12	−0.557468	−0.278734	−	0.960368i	$-0.589915\pi$
$653$	−2.59017e12	−0.557468	−0.278734	+	0.960368i	$0.589915\pi$
$654$	8.31052e11	0.177635
$655$	0	0
$656$	−2.24445e12	−0.473199
$657$	−5.41382e12	−1.13360
$658$	1.86484e12	0.387816
$659$	−4.09336e12	−0.845464	−0.422732	−	0.906255i	$-0.638929\pi$
$659$	−4.09336e12	−0.845464	−0.422732	+	0.906255i	$0.638929\pi$
$660$	0	0
$661$	−4.98709e12	−1.01611	−0.508055	−	0.861325i	$-0.669635\pi$
$661$	−4.98709e12	−1.01611	−0.508055	+	0.861325i	$0.669635\pi$
$662$	−3.32479e11	−0.0672827
$663$	−1.61176e11	−0.0323958
$664$	3.49238e12	0.697213
$665$	0	0
$666$	−3.16855e12	−0.624060
$667$	1.00943e13	1.97474
$668$	3.52248e12	0.684470
$669$	−1.76074e12	−0.339843
$670$	0	0
$671$	4.11571e12	0.783778
$672$	1.38436e11	0.0261872
$673$	1.93550e12	0.363686	0.181843	−	0.983328i	$-0.441794\pi$
$673$	1.93550e12	0.363686	0.181843	+	0.983328i	$0.441794\pi$
$674$	−7.23350e11	−0.135014
$675$	0	0
$676$	−2.13856e12	−0.393877
$677$	−7.03944e12	−1.28792	−0.643961	−	0.765059i	$-0.722710\pi$
$677$	−7.03944e12	−1.28792	−0.643961	+	0.765059i	$0.722710\pi$
$678$	−1.20315e12	−0.218669
$679$	−3.44245e12	−0.621517
$680$	0	0
$681$	1.33833e12	0.238453
$682$	2.06633e12	0.365738
$683$	1.46949e12	0.258389	0.129194	−	0.991619i	$-0.458761\pi$
$683$	1.46949e12	0.258389	0.129194	+	0.991619i	$0.458761\pi$
$684$	−3.04714e12	−0.532280
$685$	0	0
$686$	2.21461e11	0.0381802
$687$	2.22785e12	0.381575
$688$	2.56823e12	0.437004
$689$	−4.26638e12	−0.721229
$690$	0	0
$691$	6.97562e12	1.16394	0.581971	−	0.813209i	$-0.302282\pi$
$691$	6.97562e12	1.16394	0.581971	+	0.813209i	$0.302282\pi$
$692$	−2.76218e12	−0.457905
$693$	−1.07746e12	−0.177461
$694$	−7.68573e12	−1.25767
$695$	0	0
$696$	1.17985e12	0.190583
$697$	2.11596e12	0.339594
$698$	3.26650e12	0.520874
$699$	4.27306e12	0.677004
$700$	0	0
$701$	−1.45105e12	−0.226962	−0.113481	−	0.993540i	$-0.536200\pi$
$701$	−1.45105e12	−0.226962	−0.113481	+	0.993540i	$0.536200\pi$
$702$	1.51690e12	0.235743
$703$	−8.49321e12	−1.31151
$704$	−4.51928e11	−0.0693413
$705$	0	0
$706$	5.40781e11	0.0819220
$707$	4.00468e10	0.00602811
$708$	1.05042e12	0.157114
$709$	1.10227e13	1.63824	0.819121	−	0.573620i	$-0.194462\pi$
$709$	1.10227e13	1.63824	0.819121	+	0.573620i	$0.194462\pi$
$710$	0	0
$711$	−9.77148e12	−1.43399
$712$	2.33028e12	0.339820
$713$	−9.23843e12	−1.33874
$714$	−1.30511e11	−0.0187934
$715$	0	0
$716$	2.24955e12	0.319879
$717$	6.46564e11	0.0913641
$718$	−7.99360e11	−0.112249
$719$	6.34436e12	0.885336	0.442668	−	0.896686i	$-0.354032\pi$
$719$	6.34436e12	0.885336	0.442668	+	0.896686i	$0.354032\pi$
$720$	0	0
$721$	1.68917e12	0.232790
$722$	−3.00478e12	−0.411525
$723$	3.33665e12	0.454139
$724$	−3.08567e12	−0.417375
$725$	0	0
$726$	1.43612e12	0.191856
$727$	6.38267e12	0.847418	0.423709	−	0.905798i	$-0.360728\pi$
$727$	6.38267e12	0.847418	0.423709	+	0.905798i	$0.360728\pi$
$728$	4.66569e11	0.0615637
$729$	−1.46935e12	−0.192687
$730$	0	0
$731$	−2.42120e12	−0.313619
$732$	−2.15077e12	−0.276881
$733$	6.10811e12	0.781518	0.390759	−	0.920493i	$-0.372213\pi$
$733$	6.10811e12	0.781518	0.390759	+	0.920493i	$0.372213\pi$
$734$	−9.85161e12	−1.25278
$735$	0	0
$736$	2.02054e12	0.253815
$737$	2.11386e11	0.0263920
$738$	−9.12876e12	−1.13281
$739$	−3.54007e12	−0.436628	−0.218314	−	0.975879i	$-0.570056\pi$
$739$	−3.54007e12	−0.436628	−0.218314	+	0.975879i	$0.570056\pi$
$740$	0	0
$741$	1.86386e12	0.227108
$742$	−3.45468e12	−0.418399
$743$	−5.50051e12	−0.662145	−0.331073	−	0.943605i	$-0.607410\pi$
$743$	−5.50051e12	−0.662145	−0.331073	+	0.943605i	$0.607410\pi$
$744$	−1.07981e12	−0.129202
$745$	0	0
$746$	3.12376e12	0.369278
$747$	1.42044e13	1.66909
$748$	4.26056e11	0.0497633
$749$	−1.53775e12	−0.178532
$750$	0	0
$751$	−9.13357e11	−0.104776	−0.0523879	−	0.998627i	$-0.516683\pi$
$751$	−9.13357e11	−0.104776	−0.0523879	+	0.998627i	$0.516683\pi$
$752$	3.18134e12	0.362769
$753$	1.23093e12	0.139526
$754$	3.97642e12	0.448045
$755$	0	0
$756$	1.22830e12	0.136759
$757$	1.67378e13	1.85254	0.926269	−	0.376863i	$-0.122997\pi$
$757$	1.67378e13	1.85254	0.926269	+	0.376863i	$0.122997\pi$
$758$	6.80468e12	0.748680
$759$	2.85414e12	0.312167
$760$	0	0
$761$	5.39474e12	0.583095	0.291548	−	0.956556i	$-0.405830\pi$
$761$	5.39474e12	0.583095	0.291548	+	0.956556i	$0.405830\pi$
$762$	−2.54008e12	−0.272929
$763$	2.26800e12	0.242260
$764$	6.71448e12	0.713004
$765$	0	0
$766$	1.09778e11	0.0115209
$767$	3.54022e12	0.369361
$768$	2.36166e11	0.0244958
$769$	−9.78812e12	−1.00932	−0.504662	−	0.863317i	$-0.668383\pi$
$769$	−9.78812e12	−1.00932	−0.504662	+	0.863317i	$0.668383\pi$
$770$	0	0
$771$	1.77537e12	0.180944
$772$	8.43923e12	0.855115
$773$	−7.07450e12	−0.712670	−0.356335	−	0.934358i	$-0.615974\pi$
$773$	−7.07450e12	−0.712670	−0.356335	+	0.934358i	$0.615974\pi$
$774$	1.04456e13	1.04616
$775$	0	0
$776$	−5.87266e12	−0.581376
$777$	1.56939e12	0.154467
$778$	5.46372e12	0.534663
$779$	−2.44694e13	−2.38070
$780$	0	0
$781$	3.57984e11	0.0344298
$782$	−1.90487e12	−0.182152
$783$	1.04684e13	0.995298
$784$	3.77802e11	0.0357143
$785$	0	0
$786$	1.88716e12	0.176363
$787$	−7.32359e12	−0.680515	−0.340258	−	0.940332i	$-0.610514\pi$
$787$	−7.32359e12	−0.680515	−0.340258	+	0.940332i	$0.610514\pi$
$788$	6.45336e12	0.596236
$789$	−5.86140e12	−0.538462
$790$	0	0
$791$	−3.28348e12	−0.298222
$792$	−1.83810e12	−0.165999
$793$	−7.24868e12	−0.650923
$794$	−6.41066e12	−0.572414
$795$	0	0
$796$	−9.13154e12	−0.806186
$797$	−1.02782e13	−0.902311	−0.451155	−	0.892445i	$-0.648988\pi$
$797$	−1.02782e13	−0.902311	−0.451155	+	0.892445i	$0.648988\pi$
$798$	1.50925e12	0.131750
$799$	−2.99921e12	−0.260343
$800$	0	0
$801$	9.47784e12	0.813510
$802$	5.84866e12	0.499196
$803$	−8.75371e12	−0.742972
$804$	−1.10465e11	−0.00932337
$805$	0	0
$806$	−3.63927e12	−0.303743
$807$	3.20600e12	0.266093
$808$	6.83181e10	0.00563878
$809$	3.96140e12	0.325147	0.162574	−	0.986696i	$-0.448020\pi$
$809$	3.96140e12	0.325147	0.162574	+	0.986696i	$0.448020\pi$
$810$	0	0
$811$	−1.21594e12	−0.0987004	−0.0493502	−	0.998782i	$-0.515715\pi$
$811$	−1.21594e12	−0.0987004	−0.0493502	+	0.998782i	$0.515715\pi$
$812$	3.21989e12	0.259919
$813$	9.70129e12	0.778793
$814$	−5.12329e12	−0.409015
$815$	0	0
$816$	−2.22646e11	−0.0175796
$817$	2.79992e13	2.19860
$818$	−3.11946e12	−0.243607
$819$	1.89765e12	0.147380
$820$	0	0
$821$	−2.84827e12	−0.218794	−0.109397	−	0.993998i	$-0.534892\pi$
$821$	−2.84827e12	−0.218794	−0.109397	+	0.993998i	$0.534892\pi$
$822$	−1.36135e12	−0.104003
$823$	−1.37078e12	−0.104153	−0.0520763	−	0.998643i	$-0.516584\pi$
$823$	−1.37078e12	−0.104153	−0.0520763	+	0.998643i	$0.516584\pi$
$824$	2.88164e12	0.217755
$825$	0	0
$826$	2.86667e12	0.214273
$827$	8.96772e12	0.666664	0.333332	−	0.942809i	$-0.391827\pi$
$827$	8.96772e12	0.666664	0.333332	+	0.942809i	$0.391827\pi$
$828$	8.21805e12	0.607620
$829$	5.32115e12	0.391301	0.195650	−	0.980674i	$-0.437318\pi$
$829$	5.32115e12	0.391301	0.195650	+	0.980674i	$0.437318\pi$
$830$	0	0
$831$	−5.59960e11	−0.0407336
$832$	7.95947e11	0.0575876
$833$	−3.56173e11	−0.0256306
$834$	8.30389e11	0.0594339
$835$	0	0
$836$	−4.92699e12	−0.348862
$837$	−9.58082e12	−0.674742
$838$	−1.22395e13	−0.857364
$839$	2.18214e13	1.52039	0.760194	−	0.649696i	$-0.225104\pi$
$839$	2.18214e13	1.52039	0.760194	+	0.649696i	$0.225104\pi$
$840$	0	0
$841$	1.29350e13	0.891627
$842$	1.80725e13	1.23912
$843$	7.81631e12	0.533062
$844$	−1.64252e12	−0.111422
$845$	0	0
$846$	1.29393e13	0.868449
$847$	3.91926e12	0.261655
$848$	−5.89353e12	−0.391376
$849$	4.80929e12	0.317685
$850$	0	0
$851$	2.29059e13	1.49715
$852$	−1.87074e11	−0.0121628
$853$	−6.98289e11	−0.0451611	−0.0225806	−	0.999745i	$-0.507188\pi$
$853$	−6.98289e11	−0.0451611	−0.0225806	+	0.999745i	$0.507188\pi$
$854$	−5.86958e12	−0.377613
$855$	0	0
$856$	−2.62333e12	−0.167002
$857$	2.15156e13	1.36251	0.681255	−	0.732046i	$-0.261434\pi$
$857$	2.15156e13	1.36251	0.681255	+	0.732046i	$0.261434\pi$
$858$	1.12432e12	0.0708269
$859$	−2.75786e13	−1.72824	−0.864118	−	0.503290i	$-0.832123\pi$
$859$	−2.75786e13	−1.72824	−0.864118	+	0.503290i	$0.832123\pi$
$860$	0	0
$861$	4.52149e12	0.280393
$862$	1.18718e13	0.732375
$863$	1.72832e13	1.06066	0.530330	−	0.847791i	$-0.322068\pi$
$863$	1.72832e13	1.06066	0.530330	+	0.847791i	$0.322068\pi$
$864$	2.09543e12	0.127926
$865$	0	0
$866$	8.53470e12	0.515653
$867$	−6.31086e12	−0.379317
$868$	−2.94688e12	−0.176207
$869$	−1.57997e13	−0.939853
$870$	0	0
$871$	−3.72298e11	−0.0219184
$872$	3.86910e12	0.226614
$873$	−2.38856e13	−1.39178
$874$	2.20283e13	1.27696
$875$	0	0
$876$	4.57447e12	0.262466
$877$	7.60620e12	0.434180	0.217090	−	0.976152i	$-0.430344\pi$
$877$	7.60620e12	0.434180	0.217090	+	0.976152i	$0.430344\pi$
$878$	6.33548e12	0.359794
$879$	−1.01563e12	−0.0573831
$880$	0	0
$881$	−3.41351e13	−1.90902	−0.954509	−	0.298183i	$-0.903619\pi$
$881$	−3.41351e13	−1.90902	−0.954509	+	0.298183i	$0.903619\pi$
$882$	1.53662e12	0.0854981
$883$	−8.76331e12	−0.485116	−0.242558	−	0.970137i	$-0.577986\pi$
$883$	−8.76331e12	−0.485116	−0.242558	+	0.970137i	$0.577986\pi$
$884$	−7.50380e11	−0.0413281
$885$	0	0
$886$	−1.32465e13	−0.722187
$887$	1.28020e13	0.694420	0.347210	−	0.937787i	$-0.387129\pi$
$887$	1.28020e13	0.694420	0.347210	+	0.937787i	$0.387129\pi$
$888$	2.67730e12	0.144491
$889$	−6.93204e12	−0.372223
$890$	0	0
$891$	−5.87294e12	−0.312181
$892$	−8.19744e12	−0.433547
$893$	3.46834e13	1.82512
$894$	7.38182e12	0.386496
$895$	0	0
$896$	6.44514e11	0.0334077
$897$	−5.02678e12	−0.259253
$898$	−2.52306e13	−1.29474
$899$	−2.51153e13	−1.28239
$900$	0	0
$901$	5.55614e12	0.280874
$902$	−1.47605e13	−0.742456
$903$	−5.17373e12	−0.258946
$904$	−5.60147e12	−0.278962
$905$	0	0
$906$	1.87590e11	0.00924981
$907$	−2.36419e13	−1.15998	−0.579989	−	0.814624i	$-0.696943\pi$
$907$	−2.36419e13	−1.15998	−0.579989	+	0.814624i	$0.696943\pi$
$908$	6.23083e12	0.304200
$909$	2.77867e11	0.0134989
$910$	0	0
$911$	3.42719e13	1.64856	0.824282	−	0.566179i	$-0.191579\pi$
$911$	3.42719e13	1.64856	0.824282	+	0.566179i	$0.191579\pi$
$912$	2.57472e12	0.123241
$913$	2.29674e13	1.09394
$914$	−1.85082e13	−0.877214
$915$	0	0
$916$	1.03721e13	0.486785
$917$	5.15019e12	0.240526
$918$	−1.97547e12	−0.0918073
$919$	3.74339e11	0.0173119	0.00865595	−	0.999963i	$-0.497245\pi$
$919$	3.74339e11	0.0173119	0.00865595	+	0.999963i	$0.497245\pi$
$920$	0	0
$921$	4.55581e12	0.208640
$922$	−5.18862e12	−0.236463
$923$	−6.30491e11	−0.0285938
$924$	9.10415e11	0.0410881
$925$	0	0
$926$	1.36932e13	0.612007
$927$	1.17204e13	0.521293
$928$	5.49299e12	0.243132
$929$	4.92429e12	0.216907	0.108453	−	0.994102i	$-0.465410\pi$
$929$	4.92429e12	0.216907	0.108453	+	0.994102i	$0.465410\pi$
$930$	0	0
$931$	4.11886e12	0.179681
$932$	1.98939e13	0.863672
$933$	7.49185e12	0.323684
$934$	1.41497e13	0.608394
$935$	0	0
$936$	3.23731e12	0.137862
$937$	−1.95047e13	−0.826629	−0.413314	−	0.910588i	$-0.635629\pi$
$937$	−1.95047e13	−0.826629	−0.413314	+	0.910588i	$0.635629\pi$
$938$	−3.01467e11	−0.0127153
$939$	−2.29591e12	−0.0963739
$940$	0	0
$941$	−1.28738e13	−0.535247	−0.267624	−	0.963524i	$-0.586238\pi$
$941$	−1.28738e13	−0.535247	−0.267624	+	0.963524i	$0.586238\pi$
$942$	5.11751e11	0.0211753
$943$	6.59932e13	2.71767
$944$	4.89042e12	0.200434
$945$	0	0
$946$	1.68897e13	0.685666
$947$	1.40089e13	0.566017	0.283008	−	0.959117i	$-0.408668\pi$
$947$	1.40089e13	0.566017	0.283008	+	0.959117i	$0.408668\pi$
$948$	8.25653e12	0.332017
$949$	1.54173e13	0.617034
$950$	0	0
$951$	1.66573e13	0.660376
$952$	−6.07616e11	−0.0239752
$953$	3.52164e13	1.38301	0.691507	−	0.722369i	$-0.256947\pi$
$953$	3.52164e13	1.38301	0.691507	+	0.722369i	$0.256947\pi$
$954$	−2.39705e13	−0.936934
$955$	0	0
$956$	3.01019e12	0.116556
$957$	7.75918e12	0.299028
$958$	7.01109e12	0.268931
$959$	−3.71521e12	−0.141840
$960$	0	0
$961$	−3.45379e12	−0.130629
$962$	9.02326e12	0.339685
$963$	−1.06697e13	−0.399793
$964$	1.55343e13	0.579357
$965$	0	0
$966$	−4.07041e12	−0.150398
$967$	−5.16277e12	−0.189873	−0.0949367	−	0.995483i	$-0.530265\pi$
$967$	−5.16277e12	−0.189873	−0.0949367	+	0.995483i	$0.530265\pi$
$968$	6.68609e12	0.244756
$969$	−2.42732e12	−0.0884444
$970$	0	0
$971$	−2.86438e13	−1.03406	−0.517029	−	0.855968i	$-0.672962\pi$
$971$	−2.86438e13	−1.03406	−0.517029	+	0.855968i	$0.672962\pi$
$972$	1.31385e13	0.472113
$973$	2.26619e12	0.0810565
$974$	1.81595e12	0.0646529
$975$	0	0
$976$	−1.00133e13	−0.353225
$977$	−3.11356e13	−1.09328	−0.546640	−	0.837367i	$-0.684094\pi$
$977$	−3.11356e13	−1.09328	−0.546640	+	0.837367i	$0.684094\pi$
$978$	−1.03987e13	−0.363458
$979$	1.53249e13	0.533182
$980$	0	0
$981$	1.57366e13	0.542501
$982$	−2.20367e12	−0.0756213
$983$	−3.08942e13	−1.05532	−0.527662	−	0.849454i	$-0.676931\pi$
$983$	−3.08942e13	−1.05532	−0.527662	+	0.849454i	$0.676931\pi$
$984$	7.71346e12	0.262284
$985$	0	0
$986$	−5.17852e12	−0.174486
$987$	−6.40885e12	−0.214958
$988$	8.67753e12	0.289728
$989$	−7.55129e13	−2.50979
$990$	0	0
$991$	5.62999e12	0.185428	0.0927142	−	0.995693i	$-0.470446\pi$
$991$	5.62999e12	0.185428	0.0927142	+	0.995693i	$0.470446\pi$
$992$	−5.02724e12	−0.164827
$993$	1.14262e12	0.0372933
$994$	−5.10537e11	−0.0165878
$995$	0	0
$996$	−1.20022e13	−0.386450
$997$	−4.99702e13	−1.60171	−0.800853	−	0.598861i	$-0.795620\pi$
$997$	−4.99702e13	−1.60171	−0.800853	+	0.598861i	$0.795620\pi$
$998$	−3.64412e13	−1.16280
$999$	2.37548e13	0.754583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.10.a.n.1.3	✓	4
5.2	odd	4		350.10.c.m.99.2		8
5.3	odd	4		350.10.c.m.99.7		8
5.4	even	2		350.10.a.o.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.10.a.n.1.3	✓	4	1.1	even	1	trivial
350.10.a.o.1.2	yes	4	5.4	even	2
350.10.c.m.99.2		8	5.2	odd	4
350.10.c.m.99.7		8	5.3	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)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +54.9868 q^{3} +256.000 q^{4} -879.788 q^{6} -2401.00 q^{7} -4096.00 q^{8} -16659.5 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} +54.9868 q^{3} +256.000 q^{4} -879.788 q^{6} -2401.00 q^{7} -4096.00 q^{8} -16659.5 q^{9} -26937.0 q^{11} +14076.6 q^{12} +47442.1 q^{13} +38416.0 q^{14} +65536.0 q^{16} -61784.2 q^{17} +266551. q^{18} +714484. q^{19} -132023. q^{21} +430992. q^{22} -1.92694e6 q^{23} -225226. q^{24} -759074. q^{26} -1.99835e6 q^{27} -614656. q^{28} -5.23852e6 q^{29} +4.79435e6 q^{31} -1.04858e6 q^{32} -1.48118e6 q^{33} +988547. q^{34} -4.26482e6 q^{36} -1.18872e7 q^{37} -1.14317e7 q^{38} +2.60869e6 q^{39} -3.42477e7 q^{41} +2.11237e6 q^{42} +3.91880e7 q^{43} -6.89587e6 q^{44} +3.08310e7 q^{46} +4.85434e7 q^{47} +3.60361e6 q^{48} +5.76480e6 q^{49} -3.39731e6 q^{51} +1.21452e7 q^{52} -8.99282e7 q^{53} +3.19737e7 q^{54} +9.83450e6 q^{56} +3.92871e7 q^{57} +8.38163e7 q^{58} +7.46218e7 q^{59} -1.52790e8 q^{61} -7.67097e7 q^{62} +3.99994e7 q^{63} +1.67772e7 q^{64} +2.36989e7 q^{66} -7.84743e6 q^{67} -1.58167e7 q^{68} -1.05956e8 q^{69} -1.32897e7 q^{71} +6.82371e7 q^{72} +3.24970e8 q^{73} +1.90195e8 q^{74} +1.82908e8 q^{76} +6.46757e7 q^{77} -4.17390e7 q^{78} +5.86543e8 q^{79} +2.18025e8 q^{81} +5.47963e8 q^{82} -8.52632e8 q^{83} -3.37979e7 q^{84} -6.27008e8 q^{86} -2.88049e8 q^{87} +1.10334e8 q^{88} -5.68916e8 q^{89} -1.13909e8 q^{91} -4.93296e8 q^{92} +2.63626e8 q^{93} -7.76694e8 q^{94} -5.76578e7 q^{96} +1.43376e9 q^{97} -9.22368e7 q^{98} +4.48756e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} - 7 q^{3} + 1024 q^{4} + 112 q^{6} - 9604 q^{7} - 16384 q^{8} - 263 q^{9}+O(q^{10}) \) 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

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