LMFDB - Embedded newform 387.8.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,8,Mod(1,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("387.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	387.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:	$120.893004862$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 $ x^11 - 2x^10 - 977x^9 + 2592x^8 + 344686x^7 - 1160956x^6 - 53409536x^5 + 209758592x^4 + 3410917248x^3 - 14180732672x^2 - 60918607872x + 238240894976
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-17.2185$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.2185 q^{2} +103.603 q^{4} +537.911 q^{5} +1471.62 q^{7} +371.288 q^{8} +O(q^{10})$	\(q-15.2185 q^{2} +103.603 q^{4} +537.911 q^{5} +1471.62 q^{7} +371.288 q^{8} -8186.21 q^{10} +3353.32 q^{11} -12401.8 q^{13} -22395.8 q^{14} -18911.6 q^{16} -20775.2 q^{17} -1067.31 q^{19} +55729.2 q^{20} -51032.5 q^{22} +17801.1 q^{23} +211224. q^{25} +188736. q^{26} +152464. q^{28} -99935.2 q^{29} -30140.3 q^{31} +240282. q^{32} +316168. q^{34} +791601. q^{35} -174672. q^{37} +16242.9 q^{38} +199720. q^{40} +45042.7 q^{41} +79507.0 q^{43} +347414. q^{44} -270907. q^{46} +319582. q^{47} +1.34212e6 q^{49} -3.21451e6 q^{50} -1.28486e6 q^{52} -72727.4 q^{53} +1.80379e6 q^{55} +546394. q^{56} +1.52086e6 q^{58} +2.67444e6 q^{59} -2.37204e6 q^{61} +458690. q^{62} -1.23604e6 q^{64} -6.67106e6 q^{65} +3.70267e6 q^{67} -2.15237e6 q^{68} -1.20470e7 q^{70} +4.04493e6 q^{71} +862213. q^{73} +2.65824e6 q^{74} -110577. q^{76} +4.93481e6 q^{77} -3.18079e6 q^{79} -1.01728e7 q^{80} -685483. q^{82} +2.05380e6 q^{83} -1.11752e7 q^{85} -1.20998e6 q^{86} +1.24505e6 q^{88} +1.05466e7 q^{89} -1.82507e7 q^{91} +1.84425e6 q^{92} -4.86356e6 q^{94} -574120. q^{95} +849791. q^{97} -2.04251e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8}+O(q^{10}) $ 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8} - 1333 q^{10} - 1333 q^{11} - 17967 q^{13} + 22352 q^{14} - 34406 q^{16} + 63095 q^{17} - 54524 q^{19} + 280995 q^{20} - 289358 q^{22} + 138139 q^{23} + 3455 q^{25} + 132946 q^{26} - 12704 q^{28} + 308658 q^{29} - 209523 q^{31} + 644934 q^{32} + 762435 q^{34} + 578892 q^{35} - 298472 q^{37} + 369707 q^{38} + 2633173 q^{40} + 1346735 q^{41} + 874577 q^{43} - 3134292 q^{44} + 3588111 q^{46} - 499284 q^{47} + 2544563 q^{49} - 3049745 q^{50} + 983088 q^{52} + 2210495 q^{53} - 1855072 q^{55} + 469976 q^{56} + 4397067 q^{58} + 5824216 q^{59} - 4453034 q^{61} - 1002789 q^{62} + 4757538 q^{64} + 2162872 q^{65} - 6859513 q^{67} + 9397005 q^{68} + 845078 q^{70} + 10726554 q^{71} - 4456898 q^{73} - 1046637 q^{74} + 5861267 q^{76} + 17019816 q^{77} - 15541320 q^{79} + 15680911 q^{80} + 20233655 q^{82} + 11146767 q^{83} - 12471976 q^{85} + 1908168 q^{86} - 24463544 q^{88} + 13531356 q^{89} - 19746448 q^{91} + 26023161 q^{92} + 20288857 q^{94} + 12291624 q^{95} - 10999901 q^{97} - 29909168 q^{98}+O(q^{100}) \) 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8 - 1333 * q^10 - 1333 * q^11 - 17967 * q^13 + 22352 * q^14 - 34406 * q^16 + 63095 * q^17 - 54524 * q^19 + 280995 * q^20 - 289358 * q^22 + 138139 * q^23 + 3455 * q^25 + 132946 * q^26 - 12704 * q^28 + 308658 * q^29 - 209523 * q^31 + 644934 * q^32 + 762435 * q^34 + 578892 * q^35 - 298472 * q^37 + 369707 * q^38 + 2633173 * q^40 + 1346735 * q^41 + 874577 * q^43 - 3134292 * q^44 + 3588111 * q^46 - 499284 * q^47 + 2544563 * q^49 - 3049745 * q^50 + 983088 * q^52 + 2210495 * q^53 - 1855072 * q^55 + 469976 * q^56 + 4397067 * q^58 + 5824216 * q^59 - 4453034 * q^61 - 1002789 * q^62 + 4757538 * q^64 + 2162872 * q^65 - 6859513 * q^67 + 9397005 * q^68 + 845078 * q^70 + 10726554 * q^71 - 4456898 * q^73 - 1046637 * q^74 + 5861267 * q^76 + 17019816 * q^77 - 15541320 * q^79 + 15680911 * q^80 + 20233655 * q^82 + 11146767 * q^83 - 12471976 * q^85 + 1908168 * q^86 - 24463544 * q^88 + 13531356 * q^89 - 19746448 * q^91 + 26023161 * q^92 + 20288857 * q^94 + 12291624 * q^95 - 10999901 * q^97 - 29909168 * q^98

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 $

$2$	−15.2185	−1.34514	−0.672569	−	0.740034i	$-0.734809\pi$
$2$	−15.2185	−1.34514	−0.672569	+	0.740034i	$0.734809\pi$
$3$	0	0
$3$	0	0
$4$	103.603	0.809397
$5$	537.911	1.92449	0.962245	−	0.272184i	$-0.0877461\pi$
$5$	537.911	1.92449	0.962245	+	0.272184i	$0.0877461\pi$
$6$	0	0
$7$	1471.62	1.62163	0.810816	−	0.585301i	$-0.199024\pi$
$7$	1471.62	1.62163	0.810816	+	0.585301i	$0.199024\pi$
$8$	371.288	0.256387
$9$	0	0
$10$	−8186.21	−2.58871
$11$	3353.32	0.759628	0.379814	−	0.925063i	$-0.375988\pi$
$11$	3353.32	0.759628	0.379814	+	0.925063i	$0.375988\pi$
$12$	0	0
$13$	−12401.8	−1.56560	−0.782802	−	0.622270i	$-0.786210\pi$
$13$	−12401.8	−1.56560	−0.782802	+	0.622270i	$0.786210\pi$
$14$	−22395.8	−2.18132
$15$	0	0
$16$	−18911.6	−1.15427
$17$	−20775.2	−1.02559	−0.512796	−	0.858511i	$-0.671390\pi$
$17$	−20775.2	−1.02559	−0.512796	+	0.858511i	$0.671390\pi$
$18$	0	0
$19$	−1067.31	−0.0356988	−0.0178494	−	0.999841i	$-0.505682\pi$
$19$	−1067.31	−0.0356988	−0.0178494	+	0.999841i	$0.505682\pi$
$20$	55729.2	1.55768
$21$	0	0
$22$	−51032.5	−1.02180
$23$	17801.1	0.305071	0.152535	−	0.988298i	$-0.451256\pi$
$23$	17801.1	0.305071	0.152535	+	0.988298i	$0.451256\pi$
$24$	0	0
$25$	211224.	2.70366
$26$	188736.	2.10596
$27$	0	0
$28$	152464.	1.31254
$29$	−99935.2	−0.760897	−0.380448	−	0.924802i	$-0.624230\pi$
$29$	−99935.2	−0.760897	−0.380448	+	0.924802i	$0.624230\pi$
$30$	0	0
$31$	−30140.3	−0.181711	−0.0908556	−	0.995864i	$-0.528960\pi$
$31$	−30140.3	−0.181711	−0.0908556	+	0.995864i	$0.528960\pi$
$32$	240282.	1.29627
$33$	0	0
$34$	316168.	1.37956
$35$	791601.	3.12081
$36$	0	0
$37$	−174672.	−0.566913	−0.283457	−	0.958985i	$-0.591481\pi$
$37$	−174672.	−0.566913	−0.283457	+	0.958985i	$0.591481\pi$
$38$	16242.9	0.0480199
$39$	0	0
$40$	199720.	0.493414
$41$	45042.7	0.102066	0.0510330	−	0.998697i	$-0.483749\pi$
$41$	45042.7	0.102066	0.0510330	+	0.998697i	$0.483749\pi$
$42$	0	0
$43$	79507.0	0.152499
$43$	79507.0	0.152499
$44$	347414.	0.614841
$45$	0	0
$46$	−270907.	−0.410362
$47$	319582.	0.448993	0.224497	−	0.974475i	$-0.427926\pi$
$47$	319582.	0.448993	0.224497	+	0.974475i	$0.427926\pi$
$48$	0	0
$49$	1.34212e6	1.62969
$50$	−3.21451e6	−3.63680
$51$	0	0
$52$	−1.28486e6	−1.26720
$53$	−72727.4	−0.0671016	−0.0335508	−	0.999437i	$-0.510682\pi$
$53$	−72727.4	−0.0671016	−0.0335508	+	0.999437i	$0.510682\pi$
$54$	0	0
$55$	1.80379e6	1.46190
$56$	546394.	0.415765
$57$	0	0
$58$	1.52086e6	1.02351
$59$	2.67444e6	1.69531	0.847657	−	0.530544i	$-0.178012\pi$
$59$	2.67444e6	1.69531	0.847657	+	0.530544i	$0.178012\pi$
$60$	0	0
$61$	−2.37204e6	−1.33804	−0.669019	−	0.743246i	$-0.733285\pi$
$61$	−2.37204e6	−1.33804	−0.669019	+	0.743246i	$0.733285\pi$
$62$	458690.	0.244427
$63$	0	0
$64$	−1.23604e6	−0.589390
$65$	−6.67106e6	−3.01299
$66$	0	0
$67$	3.70267e6	1.50402	0.752009	−	0.659153i	$-0.229085\pi$
$67$	3.70267e6	1.50402	0.752009	+	0.659153i	$0.229085\pi$
$68$	−2.15237e6	−0.830111
$69$	0	0
$70$	−1.20470e7	−4.19793
$71$	4.04493e6	1.34124	0.670620	−	0.741801i	$-0.266028\pi$
$71$	4.04493e6	1.34124	0.670620	+	0.741801i	$0.266028\pi$
$72$	0	0
$73$	862213.	0.259409	0.129704	−	0.991553i	$-0.458597\pi$
$73$	862213.	0.259409	0.129704	+	0.991553i	$0.458597\pi$
$74$	2.65824e6	0.762577
$75$	0	0
$76$	−110577.	−0.0288945
$77$	4.93481e6	1.23184
$78$	0	0
$79$	−3.18079e6	−0.725839	−0.362920	−	0.931820i	$-0.618220\pi$
$79$	−3.18079e6	−0.725839	−0.362920	+	0.931820i	$0.618220\pi$
$80$	−1.01728e7	−2.22139
$81$	0	0
$82$	−685483.	−0.137293
$83$	2.05380e6	0.394262	0.197131	−	0.980377i	$-0.436838\pi$
$83$	2.05380e6	0.394262	0.197131	+	0.980377i	$0.436838\pi$
$84$	0	0
$85$	−1.11752e7	−1.97374
$86$	−1.20998e6	−0.205132
$87$	0	0
$88$	1.24505e6	0.194759
$89$	1.05466e7	1.58580	0.792899	−	0.609353i	$-0.208571\pi$
$89$	1.05466e7	1.58580	0.792899	+	0.609353i	$0.208571\pi$
$90$	0	0
$91$	−1.82507e7	−2.53883
$92$	1.84425e6	0.246923
$93$	0	0
$94$	−4.86356e6	−0.603958
$95$	−574120.	−0.0687021
$96$	0	0
$97$	849791.	0.0945390	0.0472695	−	0.998882i	$-0.484948\pi$
$97$	849791.	0.0945390	0.0472695	+	0.998882i	$0.484948\pi$
$98$	−2.04251e7	−2.19216
$99$	0	0
$100$	2.18834e7	2.18834
$101$	−106287.	−0.0102649	−0.00513244	−	0.999987i	$-0.501634\pi$
$101$	−106287.	−0.0102649	−0.00513244	+	0.999987i	$0.501634\pi$
$102$	0	0
$103$	9.84740e6	0.887956	0.443978	−	0.896038i	$-0.353567\pi$
$103$	9.84740e6	0.887956	0.443978	+	0.896038i	$0.353567\pi$
$104$	−4.60463e6	−0.401401
$105$	0	0
$106$	1.10680e6	0.0902609
$107$	7.20095e6	0.568260	0.284130	−	0.958786i	$-0.408295\pi$
$107$	7.20095e6	0.568260	0.284130	+	0.958786i	$0.408295\pi$
$108$	0	0
$109$	5.59758e6	0.414007	0.207003	−	0.978340i	$-0.433629\pi$
$109$	5.59758e6	0.414007	0.207003	+	0.978340i	$0.433629\pi$
$110$	−2.74510e7	−1.96645
$111$	0	0
$112$	−2.78307e7	−1.87181
$113$	2.45481e7	1.60046	0.800229	−	0.599695i	$-0.204711\pi$
$113$	2.45481e7	1.60046	0.800229	+	0.599695i	$0.204711\pi$
$114$	0	0
$115$	9.57543e6	0.587105
$116$	−1.03536e7	−0.615868
$117$	0	0
$118$	−4.07009e7	−2.28043
$119$	−3.05732e7	−1.66313
$120$	0	0
$121$	−8.24241e6	−0.422966
$122$	3.60990e7	1.79985
$123$	0	0
$124$	−3.12262e6	−0.147077
$125$	7.15953e7	3.27868
$126$	0	0
$127$	3.30101e7	1.42999	0.714995	−	0.699129i	$-0.246429\pi$
$127$	3.30101e7	1.42999	0.714995	+	0.699129i	$0.246429\pi$
$128$	−1.19454e7	−0.503460
$129$	0	0
$130$	1.01524e8	4.05289
$131$	2.31631e7	0.900216	0.450108	−	0.892974i	$-0.351385\pi$
$131$	2.31631e7	0.900216	0.450108	+	0.892974i	$0.351385\pi$
$132$	0	0
$133$	−1.57068e6	−0.0578904
$134$	−5.63490e7	−2.02311
$135$	0	0
$136$	−7.71359e6	−0.262948
$137$	−4.28026e7	−1.42216	−0.711079	−	0.703112i	$-0.751793\pi$
$137$	−4.28026e7	−1.42216	−0.711079	+	0.703112i	$0.751793\pi$
$138$	0	0
$139$	1.99694e6	0.0630688	0.0315344	−	0.999503i	$-0.489961\pi$
$139$	1.99694e6	0.0630688	0.0315344	+	0.999503i	$0.489961\pi$
$140$	8.20121e7	2.52598
$141$	0	0
$142$	−6.15577e7	−1.80415
$143$	−4.15871e7	−1.18928
$144$	0	0
$145$	−5.37563e7	−1.46434
$146$	−1.31216e7	−0.348941
$147$	0	0
$148$	−1.80965e7	−0.458858
$149$	−4.86799e7	−1.20558	−0.602792	−	0.797898i	$-0.705945\pi$
$149$	−4.86799e7	−1.20558	−0.602792	+	0.797898i	$0.705945\pi$
$150$	0	0
$151$	2.21291e7	0.523051	0.261525	−	0.965197i	$-0.415775\pi$
$151$	2.21291e7	0.523051	0.261525	+	0.965197i	$0.415775\pi$
$152$	−396280.	−0.00915272
$153$	0	0
$154$	−7.51004e7	−1.65699
$155$	−1.62128e7	−0.349702
$156$	0	0
$157$	−1.06571e7	−0.219782	−0.109891	−	0.993944i	$-0.535050\pi$
$157$	−1.06571e7	−0.219782	−0.109891	+	0.993944i	$0.535050\pi$
$158$	4.84069e7	0.976354
$159$	0	0
$160$	1.29250e8	2.49466
$161$	2.61965e7	0.494712
$162$	0	0
$163$	1.16225e7	0.210205	0.105103	−	0.994461i	$-0.466483\pi$
$163$	1.16225e7	0.210205	0.105103	+	0.994461i	$0.466483\pi$
$164$	4.66656e6	0.0826120
$165$	0	0
$166$	−3.12557e7	−0.530336
$167$	1.81744e7	0.301962	0.150981	−	0.988537i	$-0.451757\pi$
$167$	1.81744e7	0.301962	0.150981	+	0.988537i	$0.451757\pi$
$168$	0	0
$169$	9.10556e7	1.45112
$170$	1.70070e8	2.65495
$171$	0	0
$172$	8.23715e6	0.123432
$173$	8.49183e7	1.24692	0.623462	−	0.781854i	$-0.285726\pi$
$173$	8.49183e7	1.24692	0.623462	+	0.781854i	$0.285726\pi$
$174$	0	0
$175$	3.10841e8	4.38435
$176$	−6.34167e7	−0.876818
$177$	0	0
$178$	−1.60504e8	−2.13312
$179$	1.24796e8	1.62636	0.813179	−	0.582014i	$-0.197735\pi$
$179$	1.24796e8	1.62636	0.813179	+	0.582014i	$0.197735\pi$
$180$	0	0
$181$	1.02160e7	0.128058	0.0640289	−	0.997948i	$-0.479605\pi$
$181$	1.02160e7	0.128058	0.0640289	+	0.997948i	$0.479605\pi$
$182$	2.77748e8	3.41508
$183$	0	0
$184$	6.60935e6	0.0782161
$185$	−9.39579e7	−1.09102
$186$	0	0
$187$	−6.96660e7	−0.779067
$188$	3.31096e7	0.363414
$189$	0	0
$190$	8.73724e6	0.0924138
$191$	1.39911e8	1.45290	0.726449	−	0.687221i	$-0.241169\pi$
$191$	1.39911e8	1.45290	0.726449	+	0.687221i	$0.241169\pi$
$192$	0	0
$193$	7.00658e7	0.701545	0.350773	−	0.936461i	$-0.385919\pi$
$193$	7.00658e7	0.701545	0.350773	+	0.936461i	$0.385919\pi$
$194$	−1.29325e7	−0.127168
$195$	0	0
$196$	1.39047e8	1.31907
$197$	−1.41757e8	−1.32103	−0.660513	−	0.750814i	$-0.729661\pi$
$197$	−1.41757e8	−1.32103	−0.660513	+	0.750814i	$0.729661\pi$
$198$	0	0
$199$	−1.58549e8	−1.42620	−0.713098	−	0.701065i	$-0.752708\pi$
$199$	−1.58549e8	−1.42620	−0.713098	+	0.701065i	$0.752708\pi$
$200$	7.84248e7	0.693184
$201$	0	0
$202$	1.61752e6	0.0138077
$203$	−1.47067e8	−1.23389
$204$	0	0
$205$	2.42290e7	0.196425
$206$	−1.49863e8	−1.19442
$207$	0	0
$208$	2.34538e8	1.80714
$209$	−3.57904e6	−0.0271178
$210$	0	0
$211$	2.65269e8	1.94400	0.972002	−	0.234972i	$-0.0755000\pi$
$211$	2.65269e8	1.94400	0.972002	+	0.234972i	$0.0755000\pi$
$212$	−7.53477e6	−0.0543118
$213$	0	0
$214$	−1.09588e8	−0.764388
$215$	4.27677e7	0.293482
$216$	0	0
$217$	−4.43551e7	−0.294669
$218$	−8.51868e7	−0.556897
$219$	0	0
$220$	1.86878e8	1.18325
$221$	2.57650e8	1.60567
$222$	0	0
$223$	1.05872e8	0.639315	0.319658	−	0.947533i	$-0.396432\pi$
$223$	1.05872e8	0.639315	0.319658	+	0.947533i	$0.396432\pi$
$224$	3.53603e8	2.10207
$225$	0	0
$226$	−3.73586e8	−2.15284
$227$	−1.29359e8	−0.734014	−0.367007	−	0.930218i	$-0.619618\pi$
$227$	−1.29359e8	−0.734014	−0.367007	+	0.930218i	$0.619618\pi$
$228$	0	0
$229$	−9.87515e7	−0.543400	−0.271700	−	0.962382i	$-0.587586\pi$
$229$	−9.87515e7	−0.543400	−0.271700	+	0.962382i	$0.587586\pi$
$230$	−1.45724e8	−0.789738
$231$	0	0
$232$	−3.71047e7	−0.195084
$233$	−3.20820e8	−1.66156	−0.830779	−	0.556602i	$-0.812105\pi$
$233$	−3.20820e8	−1.66156	−0.830779	+	0.556602i	$0.812105\pi$
$234$	0	0
$235$	1.71907e8	0.864083
$236$	2.77079e8	1.37218
$237$	0	0
$238$	4.65278e8	2.23714
$239$	−1.03848e8	−0.492045	−0.246023	−	0.969264i	$-0.579124\pi$
$239$	−1.03848e8	−0.492045	−0.246023	+	0.969264i	$0.579124\pi$
$240$	0	0
$241$	7.62277e7	0.350795	0.175397	−	0.984498i	$-0.443879\pi$
$241$	7.62277e7	0.350795	0.175397	+	0.984498i	$0.443879\pi$
$242$	1.25437e8	0.568948
$243$	0	0
$244$	−2.45751e8	−1.08300
$245$	7.21942e8	3.13632
$246$	0	0
$247$	1.32366e7	0.0558903
$248$	−1.11907e7	−0.0465884
$249$	0	0
$250$	−1.08957e9	−4.41028
$251$	4.49350e8	1.79360	0.896802	−	0.442432i	$-0.145884\pi$
$251$	4.49350e8	1.79360	0.896802	+	0.442432i	$0.145884\pi$
$252$	0	0
$253$	5.96929e7	0.231740
$254$	−5.02364e8	−1.92354
$255$	0	0
$256$	3.40004e8	1.26661
$257$	−8.54500e7	−0.314012	−0.157006	−	0.987598i	$-0.550184\pi$
$257$	−8.54500e7	−0.314012	−0.157006	+	0.987598i	$0.550184\pi$
$258$	0	0
$259$	−2.57050e8	−0.919325
$260$	−6.91141e8	−2.43871
$261$	0	0
$262$	−3.52507e8	−1.21092
$263$	1.42757e8	0.483896	0.241948	−	0.970289i	$-0.422214\pi$
$263$	1.42757e8	0.483896	0.241948	+	0.970289i	$0.422214\pi$
$264$	0	0
$265$	−3.91209e7	−0.129136
$266$	2.39034e7	0.0778706
$267$	0	0
$268$	3.83607e8	1.21735
$269$	−1.00980e8	−0.316302	−0.158151	−	0.987415i	$-0.550553\pi$
$269$	−1.00980e8	−0.316302	−0.158151	+	0.987415i	$0.550553\pi$
$270$	0	0
$271$	9.22392e7	0.281529	0.140765	−	0.990043i	$-0.455044\pi$
$271$	9.22392e7	0.281529	0.140765	+	0.990043i	$0.455044\pi$
$272$	3.92893e8	1.18381
$273$	0	0
$274$	6.51391e8	1.91300
$275$	7.08301e8	2.05378
$276$	0	0
$277$	1.50780e8	0.426249	0.213125	−	0.977025i	$-0.431636\pi$
$277$	1.50780e8	0.426249	0.213125	+	0.977025i	$0.431636\pi$
$278$	−3.03905e7	−0.0848362
$279$	0	0
$280$	2.93912e8	0.800136
$281$	−2.04352e8	−0.549424	−0.274712	−	0.961527i	$-0.588582\pi$
$281$	−2.04352e8	−0.549424	−0.274712	+	0.961527i	$0.588582\pi$
$282$	0	0
$283$	−1.63381e8	−0.428499	−0.214250	−	0.976779i	$-0.568731\pi$
$283$	−1.63381e8	−0.428499	−0.214250	+	0.976779i	$0.568731\pi$
$284$	4.19066e8	1.08560
$285$	0	0
$286$	6.32894e8	1.59974
$287$	6.62858e7	0.165514
$288$	0	0
$289$	2.12708e7	0.0518372
$290$	8.18090e8	1.96974
$291$	0	0
$292$	8.93278e7	0.209965
$293$	−4.41998e8	−1.02656	−0.513279	−	0.858222i	$-0.671569\pi$
$293$	−4.41998e8	−1.02656	−0.513279	+	0.858222i	$0.671569\pi$
$294$	0	0
$295$	1.43861e9	3.26262
$296$	−6.48535e7	−0.145349
$297$	0	0
$298$	7.40835e8	1.62168
$299$	−2.20766e8	−0.477620
$300$	0	0
$301$	1.17004e8	0.247297
$302$	−3.36771e8	−0.703576
$303$	0	0
$304$	2.01846e7	0.0412062
$305$	−1.27595e9	−2.57504
$306$	0	0
$307$	−4.00924e8	−0.790820	−0.395410	−	0.918505i	$-0.629397\pi$
$307$	−4.00924e8	−0.790820	−0.395410	+	0.918505i	$0.629397\pi$
$308$	5.11261e8	0.997045
$309$	0	0
$310$	2.46735e8	0.470397
$311$	−3.36264e8	−0.633897	−0.316948	−	0.948443i	$-0.602658\pi$
$311$	−3.36264e8	−0.633897	−0.316948	+	0.948443i	$0.602658\pi$
$312$	0	0
$313$	−1.24177e7	−0.0228895	−0.0114448	−	0.999935i	$-0.503643\pi$
$313$	−1.24177e7	−0.0228895	−0.0114448	+	0.999935i	$0.503643\pi$
$314$	1.62186e8	0.295637
$315$	0	0
$316$	−3.29539e8	−0.587492
$317$	8.50201e8	1.49904	0.749521	−	0.661980i	$-0.230284\pi$
$317$	8.50201e8	1.49904	0.749521	+	0.661980i	$0.230284\pi$
$318$	0	0
$319$	−3.35115e8	−0.577998
$320$	−6.64880e8	−1.13427
$321$	0	0
$322$	−3.98671e8	−0.665456
$323$	2.21736e7	0.0366124
$324$	0	0
$325$	−2.61955e9	−4.23287
$326$	−1.76877e8	−0.282755
$327$	0	0
$328$	1.67238e7	0.0261684
$329$	4.70303e8	0.728102
$330$	0	0
$331$	−4.63676e8	−0.702775	−0.351388	−	0.936230i	$-0.614290\pi$
$331$	−4.63676e8	−0.702775	−0.351388	+	0.936230i	$0.614290\pi$
$332$	2.12779e8	0.319114
$333$	0	0
$334$	−2.76587e8	−0.406180
$335$	1.99171e9	2.89447
$336$	0	0
$337$	−8.51629e8	−1.21212	−0.606060	−	0.795419i	$-0.707251\pi$
$337$	−8.51629e8	−1.21212	−0.606060	+	0.795419i	$0.707251\pi$
$338$	−1.38573e9	−1.95196
$339$	0	0
$340$	−1.15779e9	−1.59754
$341$	−1.01070e8	−0.138033
$342$	0	0
$343$	7.63148e8	1.02113
$344$	2.95200e7	0.0390986
$345$	0	0
$346$	−1.29233e9	−1.67729
$347$	−9.08191e8	−1.16687	−0.583437	−	0.812159i	$-0.698292\pi$
$347$	−9.08191e8	−1.16687	−0.583437	+	0.812159i	$0.698292\pi$
$348$	0	0
$349$	−1.24649e9	−1.56963	−0.784817	−	0.619728i	$-0.787243\pi$
$349$	−1.24649e9	−1.56963	−0.784817	+	0.619728i	$0.787243\pi$
$350$	−4.73053e9	−5.89755
$351$	0	0
$352$	8.05741e8	0.984683
$353$	−7.48315e8	−0.905467	−0.452734	−	0.891646i	$-0.649551\pi$
$353$	−7.48315e8	−0.905467	−0.452734	+	0.891646i	$0.649551\pi$
$354$	0	0
$355$	2.17581e9	2.58120
$356$	1.09266e9	1.28354
$357$	0	0
$358$	−1.89921e9	−2.18768
$359$	5.31954e8	0.606798	0.303399	−	0.952864i	$-0.401879\pi$
$359$	5.31954e8	0.606798	0.303399	+	0.952864i	$0.401879\pi$
$360$	0	0
$361$	−8.92733e8	−0.998726
$362$	−1.55472e8	−0.172256
$363$	0	0
$364$	−1.89082e9	−2.05493
$365$	4.63794e8	0.499230
$366$	0	0
$367$	1.07856e9	1.13897	0.569485	−	0.822001i	$-0.307142\pi$
$367$	1.07856e9	1.13897	0.569485	+	0.822001i	$0.307142\pi$
$368$	−3.36648e8	−0.352135
$369$	0	0
$370$	1.42990e9	1.46757
$371$	−1.07027e8	−0.108814
$372$	0	0
$373$	−1.07870e9	−1.07626	−0.538132	−	0.842860i	$-0.680870\pi$
$373$	−1.07870e9	−1.07626	−0.538132	+	0.842860i	$0.680870\pi$
$374$	1.06021e9	1.04795
$375$	0	0
$376$	1.18657e8	0.115116
$377$	1.23937e9	1.19126
$378$	0	0
$379$	−7.68170e8	−0.724803	−0.362401	−	0.932022i	$-0.618043\pi$
$379$	−7.68170e8	−0.724803	−0.362401	+	0.932022i	$0.618043\pi$
$380$	−5.94804e7	−0.0556073
$381$	0	0
$382$	−2.12924e9	−1.95435
$383$	−2.81285e8	−0.255829	−0.127915	−	0.991785i	$-0.540828\pi$
$383$	−2.81285e8	−0.255829	−0.127915	+	0.991785i	$0.540828\pi$
$384$	0	0
$385$	2.65449e9	2.37066
$386$	−1.06630e9	−0.943675
$387$	0	0
$388$	8.80407e7	0.0765196
$389$	1.52136e9	1.31041	0.655206	−	0.755450i	$-0.272582\pi$
$389$	1.52136e9	1.31041	0.655206	+	0.755450i	$0.272582\pi$
$390$	0	0
$391$	−3.69822e8	−0.312878
$392$	4.98313e8	0.417831
$393$	0	0
$394$	2.15732e9	1.77696
$395$	−1.71098e9	−1.39687
$396$	0	0
$397$	9.64243e8	0.773428	0.386714	−	0.922200i	$-0.373610\pi$
$397$	9.64243e8	0.773428	0.386714	+	0.922200i	$0.373610\pi$
$398$	2.41289e9	1.91843
$399$	0	0
$400$	−3.99458e9	−3.12077
$401$	−1.46162e9	−1.13195	−0.565977	−	0.824421i	$-0.691501\pi$
$401$	−1.46162e9	−1.13195	−0.565977	+	0.824421i	$0.691501\pi$
$402$	0	0
$403$	3.73793e8	0.284488
$404$	−1.10116e7	−0.00830836
$405$	0	0
$406$	2.23813e9	1.65976
$407$	−5.85730e8	−0.430643
$408$	0	0
$409$	−1.40198e9	−1.01324	−0.506619	−	0.862170i	$-0.669105\pi$
$409$	−1.40198e9	−1.01324	−0.506619	+	0.862170i	$0.669105\pi$
$410$	−3.68729e8	−0.264219
$411$	0	0
$412$	1.02022e9	0.718709
$413$	3.93575e9	2.74918
$414$	0	0
$415$	1.10476e9	0.758753
$416$	−2.97992e9	−2.02945
$417$	0	0
$418$	5.44677e7	0.0364772
$419$	−2.20128e9	−1.46193	−0.730964	−	0.682416i	$-0.760929\pi$
$419$	−2.20128e9	−1.46193	−0.730964	+	0.682416i	$0.760929\pi$
$420$	0	0
$421$	1.37650e9	0.899061	0.449530	−	0.893265i	$-0.351591\pi$
$421$	1.37650e9	0.899061	0.449530	+	0.893265i	$0.351591\pi$
$422$	−4.03699e9	−2.61495
$423$	0	0
$424$	−2.70028e7	−0.0172040
$425$	−4.38822e9	−2.77285
$426$	0	0
$427$	−3.49075e9	−2.16980
$428$	7.46039e8	0.459948
$429$	0	0
$430$	−6.50861e8	−0.394774
$431$	1.13829e9	0.684832	0.342416	−	0.939548i	$-0.388755\pi$
$431$	1.13829e9	0.684832	0.342416	+	0.939548i	$0.388755\pi$
$432$	0	0
$433$	−3.25059e8	−0.192422	−0.0962111	−	0.995361i	$-0.530672\pi$
$433$	−3.25059e8	−0.192422	−0.0962111	+	0.995361i	$0.530672\pi$
$434$	6.75018e8	0.396370
$435$	0	0
$436$	5.79925e8	0.335096
$437$	−1.89994e7	−0.0108907
$438$	0	0
$439$	−2.09252e9	−1.18044	−0.590219	−	0.807243i	$-0.700959\pi$
$439$	−2.09252e9	−1.18044	−0.590219	+	0.807243i	$0.700959\pi$
$440$	6.69725e8	0.374811
$441$	0	0
$442$	−3.92104e9	−2.15985
$443$	1.93713e9	1.05863	0.529316	−	0.848425i	$-0.322449\pi$
$443$	1.93713e9	1.05863	0.529316	+	0.848425i	$0.322449\pi$
$444$	0	0
$445$	5.67314e9	3.05185
$446$	−1.61122e9	−0.859968
$447$	0	0
$448$	−1.81898e9	−0.955773
$449$	1.43342e9	0.747329	0.373665	−	0.927564i	$-0.378101\pi$
$449$	1.43342e9	0.747329	0.373665	+	0.927564i	$0.378101\pi$
$450$	0	0
$451$	1.51043e8	0.0775322
$452$	2.54326e9	1.29541
$453$	0	0
$454$	1.96864e9	0.987351
$455$	−9.81725e9	−4.88596
$456$	0	0
$457$	3.05243e8	0.149602	0.0748012	−	0.997198i	$-0.476168\pi$
$457$	3.05243e8	0.149602	0.0748012	+	0.997198i	$0.476168\pi$
$458$	1.50285e9	0.730948
$459$	0	0
$460$	9.92042e8	0.475202
$461$	3.07533e9	1.46197	0.730986	−	0.682392i	$-0.239060\pi$
$461$	3.07533e9	1.46197	0.730986	+	0.682392i	$0.239060\pi$
$462$	0	0
$463$	−6.71289e8	−0.314323	−0.157162	−	0.987573i	$-0.550234\pi$
$463$	−6.71289e8	−0.314323	−0.157162	+	0.987573i	$0.550234\pi$
$464$	1.88994e9	0.878283
$465$	0	0
$466$	4.88240e9	2.23503
$467$	−1.81833e9	−0.826160	−0.413080	−	0.910695i	$-0.635547\pi$
$467$	−1.81833e9	−0.826160	−0.413080	+	0.910695i	$0.635547\pi$
$468$	0	0
$469$	5.44891e9	2.43896
$470$	−2.61616e9	−1.16231
$471$	0	0
$472$	9.92986e8	0.434657
$473$	2.66612e8	0.115842
$474$	0	0
$475$	−2.25442e8	−0.0965176
$476$	−3.16747e9	−1.34613
$477$	0	0
$478$	1.58041e9	0.661869
$479$	2.05954e9	0.856240	0.428120	−	0.903722i	$-0.359176\pi$
$479$	2.05954e9	0.856240	0.428120	+	0.903722i	$0.359176\pi$
$480$	0	0
$481$	2.16624e9	0.887562
$482$	−1.16007e9	−0.471867
$483$	0	0
$484$	−8.53937e8	−0.342348
$485$	4.57112e8	0.181939
$486$	0	0
$487$	−2.54877e9	−0.999954	−0.499977	−	0.866039i	$-0.666658\pi$
$487$	−2.54877e9	−0.999954	−0.499977	+	0.866039i	$0.666658\pi$
$488$	−8.80711e8	−0.343055
$489$	0	0
$490$	−1.09869e10	−4.21879
$491$	−2.32288e9	−0.885607	−0.442804	−	0.896619i	$-0.646016\pi$
$491$	−2.32288e9	−0.885607	−0.442804	+	0.896619i	$0.646016\pi$
$492$	0	0
$493$	2.07618e9	0.780369
$494$	−2.01441e8	−0.0751802
$495$	0	0
$496$	5.70002e8	0.209744
$497$	5.95259e9	2.17500
$498$	0	0
$499$	5.35418e9	1.92904	0.964520	−	0.264009i	$-0.0850450\pi$
$499$	5.35418e9	1.92904	0.964520	+	0.264009i	$0.0850450\pi$
$500$	7.41748e9	2.65376
$501$	0	0
$502$	−6.83843e9	−2.41265
$503$	4.36661e9	1.52988	0.764938	−	0.644104i	$-0.222770\pi$
$503$	4.36661e9	1.52988	0.764938	+	0.644104i	$0.222770\pi$
$504$	0	0
$505$	−5.71727e7	−0.0197546
$506$	−9.08437e8	−0.311722
$507$	0	0
$508$	3.41994e9	1.15743
$509$	−3.03093e9	−1.01874	−0.509371	−	0.860547i	$-0.670122\pi$
$509$	−3.03093e9	−1.01874	−0.509371	+	0.860547i	$0.670122\pi$
$510$	0	0
$511$	1.26885e9	0.420666
$512$	−3.64534e9	−1.20031
$513$	0	0
$514$	1.30042e9	0.422389
$515$	5.29703e9	1.70886
$516$	0	0
$517$	1.07166e9	0.341068
$518$	3.91192e9	1.23662
$519$	0	0
$520$	−2.47688e9	−0.772492
$521$	−7.54943e8	−0.233874	−0.116937	−	0.993139i	$-0.537308\pi$
$521$	−7.54943e8	−0.233874	−0.116937	+	0.993139i	$0.537308\pi$
$522$	0	0
$523$	1.20927e9	0.369630	0.184815	−	0.982773i	$-0.440831\pi$
$523$	1.20927e9	0.369630	0.184815	+	0.982773i	$0.440831\pi$
$524$	2.39976e9	0.728632
$525$	0	0
$526$	−2.17255e9	−0.650908
$527$	6.26171e8	0.186361
$528$	0	0
$529$	−3.08794e9	−0.906932
$530$	5.95362e8	0.173706
$531$	0	0
$532$	−1.62727e8	−0.0468563
$533$	−5.58610e8	−0.159795
$534$	0	0
$535$	3.87347e9	1.09361
$536$	1.37476e9	0.385610
$537$	0	0
$538$	1.53676e9	0.425470
$539$	4.50056e9	1.23796
$540$	0	0
$541$	3.74130e9	1.01586	0.507928	−	0.861400i	$-0.330412\pi$
$541$	3.74130e9	1.01586	0.507928	+	0.861400i	$0.330412\pi$
$542$	−1.40374e9	−0.378696
$543$	0	0
$544$	−4.99190e9	−1.32944
$545$	3.01100e9	0.796752
$546$	0	0
$547$	1.07121e8	0.0279845	0.0139923	−	0.999902i	$-0.495546\pi$
$547$	1.07121e8	0.0279845	0.0139923	+	0.999902i	$0.495546\pi$
$548$	−4.43447e9	−1.15109
$549$	0	0
$550$	−1.07793e10	−2.76261
$551$	1.06662e8	0.0271631
$552$	0	0
$553$	−4.68091e9	−1.17704
$554$	−2.29464e9	−0.573364
$555$	0	0
$556$	2.06889e8	0.0510477
$557$	1.84003e9	0.451160	0.225580	−	0.974225i	$-0.427572\pi$
$557$	1.84003e9	0.451160	0.225580	+	0.974225i	$0.427572\pi$
$558$	0	0
$559$	−9.86028e8	−0.238753
$560$	−1.49704e10	−3.60227
$561$	0	0
$562$	3.10994e9	0.739051
$563$	2.91696e8	0.0688892	0.0344446	−	0.999407i	$-0.489034\pi$
$563$	2.91696e8	0.0688892	0.0344446	+	0.999407i	$0.489034\pi$
$564$	0	0
$565$	1.32047e10	3.08006
$566$	2.48642e9	0.576391
$567$	0	0
$568$	1.50183e9	0.343876
$569$	−1.23531e9	−0.281114	−0.140557	−	0.990073i	$-0.544889\pi$
$569$	−1.23531e9	−0.281114	−0.140557	+	0.990073i	$0.544889\pi$
$570$	0	0
$571$	6.32334e9	1.42141	0.710706	−	0.703489i	$-0.248375\pi$
$571$	6.32334e9	1.42141	0.710706	+	0.703489i	$0.248375\pi$
$572$	−4.30855e9	−0.962597
$573$	0	0
$574$	−1.00877e9	−0.222639
$575$	3.76002e9	0.824808
$576$	0	0
$577$	−2.79809e9	−0.606381	−0.303191	−	0.952930i	$-0.598052\pi$
$577$	−2.79809e9	−0.606381	−0.303191	+	0.952930i	$0.598052\pi$
$578$	−3.23710e8	−0.0697282
$579$	0	0
$580$	−5.56931e9	−1.18523
$581$	3.02241e9	0.639347
$582$	0	0
$583$	−2.43878e8	−0.0509722
$584$	3.20129e8	0.0665090
$585$	0	0
$586$	6.72654e9	1.38086
$587$	−2.66505e9	−0.543841	−0.271921	−	0.962320i	$-0.587659\pi$
$587$	−2.66505e9	−0.543841	−0.271921	+	0.962320i	$0.587659\pi$
$588$	0	0
$589$	3.21691e7	0.00648688
$590$	−2.18935e10	−4.38867
$591$	0	0
$592$	3.30332e9	0.654373
$593$	2.31869e9	0.456616	0.228308	−	0.973589i	$-0.426681\pi$
$593$	2.31869e9	0.456616	0.228308	+	0.973589i	$0.426681\pi$
$594$	0	0
$595$	−1.64457e10	−3.20068
$596$	−5.04337e9	−0.975797
$597$	0	0
$598$	3.35972e9	0.642465
$599$	2.38951e9	0.454271	0.227135	−	0.973863i	$-0.427064\pi$
$599$	2.38951e9	0.454271	0.227135	+	0.973863i	$0.427064\pi$
$600$	0	0
$601$	−5.85741e9	−1.10064	−0.550320	−	0.834954i	$-0.685494\pi$
$601$	−5.85741e9	−1.10064	−0.550320	+	0.834954i	$0.685494\pi$
$602$	−1.78063e9	−0.332648
$603$	0	0
$604$	2.29263e9	0.423356
$605$	−4.43369e9	−0.813994
$606$	0	0
$607$	1.64112e8	0.0297838	0.0148919	−	0.999889i	$-0.495260\pi$
$607$	1.64112e8	0.0297838	0.0148919	+	0.999889i	$0.495260\pi$
$608$	−2.56456e8	−0.0462753
$609$	0	0
$610$	1.94180e10	3.46379
$611$	−3.96339e9	−0.702946
$612$	0	0
$613$	−6.13717e9	−1.07611	−0.538055	−	0.842910i	$-0.680841\pi$
$613$	−6.13717e9	−1.07611	−0.538055	+	0.842910i	$0.680841\pi$
$614$	6.10146e9	1.06376
$615$	0	0
$616$	1.83224e9	0.315827
$617$	1.73030e9	0.296567	0.148284	−	0.988945i	$-0.452625\pi$
$617$	1.73030e9	0.296567	0.148284	+	0.988945i	$0.452625\pi$
$618$	0	0
$619$	3.65743e9	0.619811	0.309906	−	0.950767i	$-0.399703\pi$
$619$	3.65743e9	0.619811	0.309906	+	0.950767i	$0.399703\pi$
$620$	−1.67969e9	−0.283047
$621$	0	0
$622$	5.11743e9	0.852679
$623$	1.55206e10	2.57158
$624$	0	0
$625$	2.20101e10	3.60613
$626$	1.88979e8	0.0307896
$627$	0	0
$628$	−1.10411e9	−0.177891
$629$	3.62884e9	0.581421
$630$	0	0
$631$	−8.67078e9	−1.37390	−0.686951	−	0.726704i	$-0.741051\pi$
$631$	−8.67078e9	−1.37390	−0.686951	+	0.726704i	$0.741051\pi$
$632$	−1.18099e9	−0.186096
$633$	0	0
$634$	−1.29388e10	−2.01642
$635$	1.77565e10	2.75200
$636$	0	0
$637$	−1.66447e10	−2.55145
$638$	5.09995e9	0.777487
$639$	0	0
$640$	−6.42555e9	−0.968903
$641$	−5.26409e9	−0.789442	−0.394721	−	0.918801i	$-0.629159\pi$
$641$	−5.26409e9	−0.789442	−0.394721	+	0.918801i	$0.629159\pi$
$642$	0	0
$643$	−3.46768e9	−0.514399	−0.257200	−	0.966358i	$-0.582800\pi$
$643$	−3.46768e9	−0.514399	−0.257200	+	0.966358i	$0.582800\pi$
$644$	2.71403e9	0.400419
$645$	0	0
$646$	−3.37450e8	−0.0492488
$647$	−3.80535e9	−0.552369	−0.276185	−	0.961105i	$-0.589070\pi$
$647$	−3.80535e9	−0.552369	−0.276185	+	0.961105i	$0.589070\pi$
$648$	0	0
$649$	8.96824e9	1.28781
$650$	3.98656e10	5.69379
$651$	0	0
$652$	1.20413e9	0.170140
$653$	−2.84050e9	−0.399207	−0.199603	−	0.979877i	$-0.563965\pi$
$653$	−2.84050e9	−0.399207	−0.199603	+	0.979877i	$0.563965\pi$
$654$	0	0
$655$	1.24597e10	1.73246
$656$	−8.51831e8	−0.117812
$657$	0	0
$658$	−7.15731e9	−0.979398
$659$	−3.52181e9	−0.479365	−0.239683	−	0.970851i	$-0.577043\pi$
$659$	−3.52181e9	−0.479365	−0.239683	+	0.970851i	$0.577043\pi$
$660$	0	0
$661$	7.62689e9	1.02717	0.513585	−	0.858039i	$-0.328317\pi$
$661$	7.62689e9	1.02717	0.513585	+	0.858039i	$0.328317\pi$
$662$	7.05645e9	0.945330
$663$	0	0
$664$	7.62551e8	0.101084
$665$	−8.44885e8	−0.111409
$666$	0	0
$667$	−1.77896e9	−0.232127
$668$	1.88292e9	0.244407
$669$	0	0
$670$	−3.03108e10	−3.89346
$671$	−7.95422e9	−1.01641
$672$	0	0
$673$	1.76513e9	0.223216	0.111608	−	0.993752i	$-0.464400\pi$
$673$	1.76513e9	0.223216	0.111608	+	0.993752i	$0.464400\pi$
$674$	1.29605e10	1.63047
$675$	0	0
$676$	9.43362e9	1.17453
$677$	1.21822e10	1.50892	0.754461	−	0.656345i	$-0.227898\pi$
$677$	1.21822e10	1.50892	0.754461	+	0.656345i	$0.227898\pi$
$678$	0	0
$679$	1.25057e9	0.153307
$680$	−4.14923e9	−0.506041
$681$	0	0
$682$	1.53814e9	0.185673
$683$	−9.06722e9	−1.08893	−0.544467	−	0.838782i	$-0.683268\pi$
$683$	−9.06722e9	−1.08893	−0.544467	+	0.838782i	$0.683268\pi$
$684$	0	0
$685$	−2.30240e10	−2.73693
$686$	−1.16140e10	−1.37356
$687$	0	0
$688$	−1.50361e9	−0.176025
$689$	9.01949e8	0.105055
$690$	0	0
$691$	1.27877e10	1.47441	0.737206	−	0.675668i	$-0.236145\pi$
$691$	1.27877e10	1.47441	0.737206	+	0.675668i	$0.236145\pi$
$692$	8.79778e9	1.00926
$693$	0	0
$694$	1.38213e10	1.56961
$695$	1.07418e9	0.121375
$696$	0	0
$697$	−9.35772e8	−0.104678
$698$	1.89696e10	2.11137
$699$	0	0
$700$	3.22040e10	3.54868
$701$	−1.61492e10	−1.77068	−0.885338	−	0.464948i	$-0.846073\pi$
$701$	−1.61492e10	−1.77068	−0.885338	+	0.464948i	$0.846073\pi$
$702$	0	0
$703$	1.86429e8	0.0202381
$704$	−4.14484e9	−0.447717
$705$	0	0
$706$	1.13882e10	1.21798
$707$	−1.56413e8	−0.0166458
$708$	0	0
$709$	−4.31415e9	−0.454604	−0.227302	−	0.973824i	$-0.572991\pi$
$709$	−4.31415e9	−0.454604	−0.227302	+	0.973824i	$0.572991\pi$
$710$	−3.31126e10	−3.47207
$711$	0	0
$712$	3.91583e9	0.406578
$713$	−5.36532e8	−0.0554348
$714$	0	0
$715$	−2.23702e10	−2.28875
$716$	1.29293e10	1.31637
$717$	0	0
$718$	−8.09555e9	−0.816227
$719$	−8.62138e9	−0.865019	−0.432509	−	0.901629i	$-0.642372\pi$
$719$	−8.62138e9	−0.865019	−0.432509	+	0.901629i	$0.642372\pi$
$720$	0	0
$721$	1.44916e10	1.43994
$722$	1.35861e10	1.34342
$723$	0	0
$724$	1.05841e9	0.103650
$725$	−2.11087e10	−2.05721
$726$	0	0
$727$	−1.50745e10	−1.45503	−0.727517	−	0.686089i	$-0.759326\pi$
$727$	−1.50745e10	−1.45503	−0.727517	+	0.686089i	$0.759326\pi$
$728$	−6.77626e9	−0.650924
$729$	0	0
$730$	−7.05826e9	−0.671533
$731$	−1.65177e9	−0.156401
$732$	0	0
$733$	1.41082e10	1.32315	0.661574	−	0.749880i	$-0.269889\pi$
$733$	1.41082e10	1.32315	0.661574	+	0.749880i	$0.269889\pi$
$734$	−1.64141e10	−1.53207
$735$	0	0
$736$	4.27729e9	0.395454
$737$	1.24162e10	1.14249
$738$	0	0
$739$	−2.01127e10	−1.83322	−0.916611	−	0.399781i	$-0.869086\pi$
$739$	−2.01127e10	−1.83322	−0.916611	+	0.399781i	$0.869086\pi$
$740$	−9.73431e9	−0.883068
$741$	0	0
$742$	1.62879e9	0.146370
$743$	−7.77437e9	−0.695352	−0.347676	−	0.937615i	$-0.613029\pi$
$743$	−7.77437e9	−0.695352	−0.347676	+	0.937615i	$0.613029\pi$
$744$	0	0
$745$	−2.61855e10	−2.32014
$746$	1.64162e10	1.44772
$747$	0	0
$748$	−7.21759e9	−0.630575
$749$	1.05971e10	0.921508
$750$	0	0
$751$	−1.36165e10	−1.17307	−0.586536	−	0.809923i	$-0.699509\pi$
$751$	−1.36165e10	−1.17307	−0.586536	+	0.809923i	$0.699509\pi$
$752$	−6.04381e9	−0.518261
$753$	0	0
$754$	−1.88614e10	−1.60241
$755$	1.19035e10	1.00661
$756$	0	0
$757$	1.37437e10	1.15151	0.575756	−	0.817622i	$-0.304708\pi$
$757$	1.37437e10	1.15151	0.575756	+	0.817622i	$0.304708\pi$
$758$	1.16904e10	0.974960
$759$	0	0
$760$	−2.13164e8	−0.0176143
$761$	−9.87644e9	−0.812370	−0.406185	−	0.913791i	$-0.633141\pi$
$761$	−9.87644e9	−0.812370	−0.406185	+	0.913791i	$0.633141\pi$
$762$	0	0
$763$	8.23751e9	0.671367
$764$	1.44952e10	1.17597
$765$	0	0
$766$	4.28073e9	0.344126
$767$	−3.31678e10	−2.65419
$768$	0	0
$769$	1.45345e10	1.15254	0.576272	−	0.817258i	$-0.304507\pi$
$769$	1.45345e10	1.15254	0.576272	+	0.817258i	$0.304507\pi$
$770$	−4.03974e10	−3.18886
$771$	0	0
$772$	7.25902e9	0.567829
$773$	1.27560e10	0.993312	0.496656	−	0.867947i	$-0.334561\pi$
$773$	1.27560e10	0.993312	0.496656	+	0.867947i	$0.334561\pi$
$774$	0	0
$775$	−6.36635e9	−0.491286
$776$	3.15517e8	0.0242386
$777$	0	0
$778$	−2.31528e10	−1.76269
$779$	−4.80747e7	−0.00364364
$780$	0	0
$781$	1.35639e10	1.01884
$782$	5.62814e9	0.420864
$783$	0	0
$784$	−2.53817e10	−1.88111
$785$	−5.73260e9	−0.422968
$786$	0	0
$787$	−8.63446e9	−0.631428	−0.315714	−	0.948854i	$-0.602244\pi$
$787$	−8.63446e9	−0.631428	−0.315714	+	0.948854i	$0.602244\pi$
$788$	−1.46864e10	−1.06924
$789$	0	0
$790$	2.60386e10	1.87898
$791$	3.61255e10	2.59535
$792$	0	0
$793$	2.94176e10	2.09484
$794$	−1.46743e10	−1.04037
$795$	0	0
$796$	−1.64262e10	−1.15436
$797$	2.05828e10	1.44012	0.720061	−	0.693911i	$-0.244114\pi$
$797$	2.05828e10	1.44012	0.720061	+	0.693911i	$0.244114\pi$
$798$	0	0
$799$	−6.63939e9	−0.460484
$800$	5.07532e10	3.50468
$801$	0	0
$802$	2.22436e10	1.52263
$803$	2.89128e9	0.197054
$804$	0	0
$805$	1.40914e10	0.952069
$806$	−5.68858e9	−0.382676
$807$	0	0
$808$	−3.94629e7	−0.00263178
$809$	−1.96518e9	−0.130492	−0.0652459	−	0.997869i	$-0.520783\pi$
$809$	−1.96518e9	−0.130492	−0.0652459	+	0.997869i	$0.520783\pi$
$810$	0	0
$811$	−9.82285e9	−0.646643	−0.323321	−	0.946289i	$-0.604799\pi$
$811$	−9.82285e9	−0.646643	−0.323321	+	0.946289i	$0.604799\pi$
$812$	−1.52365e10	−0.998711
$813$	0	0
$814$	8.91394e9	0.579274
$815$	6.25189e9	0.404538
$816$	0	0
$817$	−8.48588e7	−0.00544402
$818$	2.13361e10	1.36295
$819$	0	0
$820$	2.51019e9	0.158986
$821$	−1.17346e10	−0.740060	−0.370030	−	0.929020i	$-0.620653\pi$
$821$	−1.17346e10	−0.740060	−0.370030	+	0.929020i	$0.620653\pi$
$822$	0	0
$823$	−1.25381e10	−0.784029	−0.392015	−	0.919959i	$-0.628222\pi$
$823$	−1.25381e10	−0.784029	−0.392015	+	0.919959i	$0.628222\pi$
$824$	3.65622e9	0.227660
$825$	0	0
$826$	−5.98963e10	−3.69802
$827$	7.60873e9	0.467782	0.233891	−	0.972263i	$-0.424854\pi$
$827$	7.60873e9	0.467782	0.233891	+	0.972263i	$0.424854\pi$
$828$	0	0
$829$	−1.26864e10	−0.773388	−0.386694	−	0.922208i	$-0.626383\pi$
$829$	−1.26864e10	−0.773388	−0.386694	+	0.922208i	$0.626383\pi$
$830$	−1.68128e10	−1.02063
$831$	0	0
$832$	1.53291e10	0.922752
$833$	−2.78828e10	−1.67140
$834$	0	0
$835$	9.77620e9	0.581122
$836$	−3.70799e8	−0.0219491
$837$	0	0
$838$	3.35002e10	1.96650
$839$	1.25954e10	0.736282	0.368141	−	0.929770i	$-0.379994\pi$
$839$	1.25954e10	0.736282	0.368141	+	0.929770i	$0.379994\pi$
$840$	0	0
$841$	−7.26283e9	−0.421036
$842$	−2.09483e10	−1.20936
$843$	0	0
$844$	2.74826e10	1.57347
$845$	4.89798e10	2.79266
$846$	0	0
$847$	−1.21297e10	−0.685895
$848$	1.37539e9	0.0774535
$849$	0	0
$850$	6.67821e10	3.72987
$851$	−3.10936e9	−0.172949
$852$	0	0
$853$	−1.68559e10	−0.929890	−0.464945	−	0.885340i	$-0.653926\pi$
$853$	−1.68559e10	−0.929890	−0.464945	+	0.885340i	$0.653926\pi$
$854$	5.31239e10	2.91869
$855$	0	0
$856$	2.67363e9	0.145694
$857$	−3.15667e9	−0.171315	−0.0856577	−	0.996325i	$-0.527299\pi$
$857$	−3.15667e9	−0.171315	−0.0856577	+	0.996325i	$0.527299\pi$
$858$	0	0
$859$	1.47310e10	0.792969	0.396484	−	0.918041i	$-0.370230\pi$
$859$	1.47310e10	0.792969	0.396484	+	0.918041i	$0.370230\pi$
$860$	4.43086e9	0.237544
$861$	0	0
$862$	−1.73231e10	−0.921194
$863$	−2.38879e10	−1.26514	−0.632571	−	0.774502i	$-0.718000\pi$
$863$	−2.38879e10	−1.26514	−0.632571	+	0.774502i	$0.718000\pi$
$864$	0	0
$865$	4.56785e10	2.39969
$866$	4.94692e9	0.258834
$867$	0	0
$868$	−4.59531e9	−0.238504
$869$	−1.06662e10	−0.551367
$870$	0	0
$871$	−4.59196e10	−2.35470
$872$	2.07831e9	0.106146
$873$	0	0
$874$	2.89142e8	0.0146495
$875$	1.05361e11	5.31682
$876$	0	0
$877$	2.26234e10	1.13255	0.566277	−	0.824215i	$-0.308383\pi$
$877$	2.26234e10	1.13255	0.566277	+	0.824215i	$0.308383\pi$
$878$	3.18450e10	1.58785
$879$	0	0
$880$	−3.41126e10	−1.68743
$881$	1.42978e8	0.00704454	0.00352227	−	0.999994i	$-0.498879\pi$
$881$	1.42978e8	0.00704454	0.00352227	+	0.999994i	$0.498879\pi$
$882$	0	0
$883$	−8.28063e9	−0.404763	−0.202381	−	0.979307i	$-0.564868\pi$
$883$	−8.28063e9	−0.404763	−0.202381	+	0.979307i	$0.564868\pi$
$884$	2.66932e10	1.29963
$885$	0	0
$886$	−2.94802e10	−1.42401
$887$	3.14829e10	1.51475	0.757376	−	0.652979i	$-0.226481\pi$
$887$	3.14829e10	1.51475	0.757376	+	0.652979i	$0.226481\pi$
$888$	0	0
$889$	4.85782e10	2.31892
$890$	−8.63367e10	−4.10516
$891$	0	0
$892$	1.09687e10	0.517460
$893$	−3.41094e8	−0.0160285
$894$	0	0
$895$	6.71294e10	3.12991
$896$	−1.75790e10	−0.816426
$897$	0	0
$898$	−2.18145e10	−1.00526
$899$	3.01208e9	0.138263
$900$	0	0
$901$	1.51093e9	0.0688188
$902$	−2.29864e9	−0.104292
$903$	0	0
$904$	9.11443e9	0.410336
$905$	5.49531e9	0.246446
$906$	0	0
$907$	−2.58557e10	−1.15062	−0.575308	−	0.817937i	$-0.695118\pi$
$907$	−2.58557e10	−1.15062	−0.575308	+	0.817937i	$0.695118\pi$
$908$	−1.34019e10	−0.594109
$909$	0	0
$910$	1.49404e11	6.57230
$911$	−1.27853e10	−0.560271	−0.280136	−	0.959960i	$-0.590379\pi$
$911$	−1.27853e10	−0.560271	−0.280136	+	0.959960i	$0.590379\pi$
$912$	0	0
$913$	6.88704e9	0.299492
$914$	−4.64534e9	−0.201236
$915$	0	0
$916$	−1.02309e10	−0.439826
$917$	3.40872e10	1.45982
$918$	0	0
$919$	−2.07808e10	−0.883197	−0.441599	−	0.897213i	$-0.645588\pi$
$919$	−2.07808e10	−0.883197	−0.441599	+	0.897213i	$0.645588\pi$
$920$	3.55524e9	0.150526
$921$	0	0
$922$	−4.68020e10	−1.96656
$923$	−5.01643e10	−2.09985
$924$	0	0
$925$	−3.68948e10	−1.53274
$926$	1.02160e10	0.422808
$927$	0	0
$928$	−2.40126e10	−0.986328
$929$	−3.30915e10	−1.35414	−0.677068	−	0.735921i	$-0.736750\pi$
$929$	−3.30915e10	−1.35414	−0.677068	+	0.735921i	$0.736750\pi$
$930$	0	0
$931$	−1.43246e9	−0.0581780
$932$	−3.32379e10	−1.34486
$933$	0	0
$934$	2.76723e10	1.11130
$935$	−3.74741e10	−1.49931
$936$	0	0
$937$	−2.83321e9	−0.112510	−0.0562548	−	0.998416i	$-0.517916\pi$
$937$	−2.83321e9	−0.112510	−0.0562548	+	0.998416i	$0.517916\pi$
$938$	−8.29243e10	−3.28074
$939$	0	0
$940$	1.78100e10	0.699387
$941$	4.17032e10	1.63157	0.815786	−	0.578354i	$-0.196305\pi$
$941$	4.17032e10	1.63157	0.815786	+	0.578354i	$0.196305\pi$
$942$	0	0
$943$	8.01812e8	0.0311373
$944$	−5.05779e10	−1.95686
$945$	0	0
$946$	−4.05744e9	−0.155824
$947$	−1.58387e10	−0.606032	−0.303016	−	0.952985i	$-0.597994\pi$
$947$	−1.58387e10	−0.606032	−0.303016	+	0.952985i	$0.597994\pi$
$948$	0	0
$949$	−1.06930e10	−0.406132
$950$	3.43089e9	0.129830
$951$	0	0
$952$	−1.13515e10	−0.426405
$953$	2.37238e10	0.887889	0.443944	−	0.896054i	$-0.353579\pi$
$953$	2.37238e10	0.887889	0.443944	+	0.896054i	$0.353579\pi$
$954$	0	0
$955$	7.52597e10	2.79609
$956$	−1.07589e10	−0.398260
$957$	0	0
$958$	−3.13431e10	−1.15176
$959$	−6.29891e10	−2.30622
$960$	0	0
$961$	−2.66042e10	−0.966981
$962$	−3.29669e10	−1.19389
$963$	0	0
$964$	7.89740e9	0.283932
$965$	3.76892e10	1.35012
$966$	0	0
$967$	8.66320e9	0.308096	0.154048	−	0.988063i	$-0.450769\pi$
$967$	8.66320e9	0.308096	0.154048	+	0.988063i	$0.450769\pi$
$968$	−3.06031e9	−0.108443
$969$	0	0
$970$	−6.95656e9	−0.244734
$971$	2.16268e10	0.758098	0.379049	−	0.925377i	$-0.376251\pi$
$971$	2.16268e10	0.758098	0.379049	+	0.925377i	$0.376251\pi$
$972$	0	0
$973$	2.93874e9	0.102274
$974$	3.87885e10	1.34508
$975$	0	0
$976$	4.48592e10	1.54446
$977$	−3.39448e9	−0.116451	−0.0582255	−	0.998303i	$-0.518544\pi$
$977$	−3.39448e9	−0.116451	−0.0582255	+	0.998303i	$0.518544\pi$
$978$	0	0
$979$	3.53662e10	1.20462
$980$	7.47952e10	2.53853
$981$	0	0
$982$	3.53507e10	1.19126
$983$	−1.20191e10	−0.403585	−0.201792	−	0.979428i	$-0.564677\pi$
$983$	−1.20191e10	−0.403585	−0.201792	+	0.979428i	$0.564677\pi$
$984$	0	0
$985$	−7.62525e10	−2.54230
$986$	−3.15963e10	−1.04970
$987$	0	0
$988$	1.37135e9	0.0452374
$989$	1.41532e9	0.0465228
$990$	0	0
$991$	−4.37960e10	−1.42948	−0.714738	−	0.699393i	$-0.753454\pi$
$991$	−4.37960e10	−1.42948	−0.714738	+	0.699393i	$0.753454\pi$
$992$	−7.24216e9	−0.235547
$993$	0	0
$994$	−9.05895e10	−2.92567
$995$	−8.52855e10	−2.74470
$996$	0	0
$997$	−8.81226e9	−0.281614	−0.140807	−	0.990037i	$-0.544970\pi$
$997$	−8.81226e9	−0.281614	−0.140807	+	0.990037i	$0.544970\pi$
$998$	−8.14827e10	−2.59483
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.b.1.2		11
3.2	odd	2		43.8.a.a.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.a.1.10	✓	11	3.2	odd	2
387.8.a.b.1.2		11	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q-15.2185 q^{2} +103.603 q^{4} +537.911 q^{5} +1471.62 q^{7} +371.288 q^{8} +O(q^{10})\)	\(q-15.2185 q^{2} +103.603 q^{4} +537.911 q^{5} +1471.62 q^{7} +371.288 q^{8} -8186.21 q^{10} +3353.32 q^{11} -12401.8 q^{13} -22395.8 q^{14} -18911.6 q^{16} -20775.2 q^{17} -1067.31 q^{19} +55729.2 q^{20} -51032.5 q^{22} +17801.1 q^{23} +211224. q^{25} +188736. q^{26} +152464. q^{28} -99935.2 q^{29} -30140.3 q^{31} +240282. q^{32} +316168. q^{34} +791601. q^{35} -174672. q^{37} +16242.9 q^{38} +199720. q^{40} +45042.7 q^{41} +79507.0 q^{43} +347414. q^{44} -270907. q^{46} +319582. q^{47} +1.34212e6 q^{49} -3.21451e6 q^{50} -1.28486e6 q^{52} -72727.4 q^{53} +1.80379e6 q^{55} +546394. q^{56} +1.52086e6 q^{58} +2.67444e6 q^{59} -2.37204e6 q^{61} +458690. q^{62} -1.23604e6 q^{64} -6.67106e6 q^{65} +3.70267e6 q^{67} -2.15237e6 q^{68} -1.20470e7 q^{70} +4.04493e6 q^{71} +862213. q^{73} +2.65824e6 q^{74} -110577. q^{76} +4.93481e6 q^{77} -3.18079e6 q^{79} -1.01728e7 q^{80} -685483. q^{82} +2.05380e6 q^{83} -1.11752e7 q^{85} -1.20998e6 q^{86} +1.24505e6 q^{88} +1.05466e7 q^{89} -1.82507e7 q^{91} +1.84425e6 q^{92} -4.86356e6 q^{94} -574120. q^{95} +849791. q^{97} -2.04251e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8}+O(q^{10}) \) 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8	\( 11 q + 24 q^{2} + 602 q^{4} + 752 q^{5} - 12 q^{7} + 3810 q^{8} - 1333 q^{10} - 1333 q^{11} - 17967 q^{13} + 22352 q^{14} - 34406 q^{16} + 63095 q^{17} - 54524 q^{19} + 280995 q^{20} - 289358 q^{22} + 138139 q^{23} + 3455 q^{25} + 132946 q^{26} - 12704 q^{28} + 308658 q^{29} - 209523 q^{31} + 644934 q^{32} + 762435 q^{34} + 578892 q^{35} - 298472 q^{37} + 369707 q^{38} + 2633173 q^{40} + 1346735 q^{41} + 874577 q^{43} - 3134292 q^{44} + 3588111 q^{46} - 499284 q^{47} + 2544563 q^{49} - 3049745 q^{50} + 983088 q^{52} + 2210495 q^{53} - 1855072 q^{55} + 469976 q^{56} + 4397067 q^{58} + 5824216 q^{59} - 4453034 q^{61} - 1002789 q^{62} + 4757538 q^{64} + 2162872 q^{65} - 6859513 q^{67} + 9397005 q^{68} + 845078 q^{70} + 10726554 q^{71} - 4456898 q^{73} - 1046637 q^{74} + 5861267 q^{76} + 17019816 q^{77} - 15541320 q^{79} + 15680911 q^{80} + 20233655 q^{82} + 11146767 q^{83} - 12471976 q^{85} + 1908168 q^{86} - 24463544 q^{88} + 13531356 q^{89} - 19746448 q^{91} + 26023161 q^{92} + 20288857 q^{94} + 12291624 q^{95} - 10999901 q^{97} - 29909168 q^{98}+O(q^{100}) \) 11 * q + 24 * q^2 + 602 * q^4 + 752 * q^5 - 12 * q^7 + 3810 * q^8 - 1333 * q^10 - 1333 * q^11 - 17967 * q^13 + 22352 * q^14 - 34406 * q^16 + 63095 * q^17 - 54524 * q^19 + 280995 * q^20 - 289358 * q^22 + 138139 * q^23 + 3455 * q^25 + 132946 * q^26 - 12704 * q^28 + 308658 * q^29 - 209523 * q^31 + 644934 * q^32 + 762435 * q^34 + 578892 * q^35 - 298472 * q^37 + 369707 * q^38 + 2633173 * q^40 + 1346735 * q^41 + 874577 * q^43 - 3134292 * q^44 + 3588111 * q^46 - 499284 * q^47 + 2544563 * q^49 - 3049745 * q^50 + 983088 * q^52 + 2210495 * q^53 - 1855072 * q^55 + 469976 * q^56 + 4397067 * q^58 + 5824216 * q^59 - 4453034 * q^61 - 1002789 * q^62 + 4757538 * q^64 + 2162872 * q^65 - 6859513 * q^67 + 9397005 * q^68 + 845078 * q^70 + 10726554 * q^71 - 4456898 * q^73 - 1046637 * q^74 + 5861267 * q^76 + 17019816 * q^77 - 15541320 * q^79 + 15680911 * q^80 + 20233655 * q^82 + 11146767 * q^83 - 12471976 * q^85 + 1908168 * q^86 - 24463544 * q^88 + 13531356 * q^89 - 19746448 * q^91 + 26023161 * q^92 + 20288857 * q^94 + 12291624 * q^95 - 10999901 * q^97 - 29909168 * q^98

Introduction

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