LMFDB - Embedded newform 531.8.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, 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("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.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:	$165.876448532$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-20.3182$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.3182 q^{2} +370.104 q^{4} +84.4166 q^{5} +1532.13 q^{7} +5403.34 q^{8} +O(q^{10})$	\(q+22.3182 q^{2} +370.104 q^{4} +84.4166 q^{5} +1532.13 q^{7} +5403.34 q^{8} +1884.03 q^{10} -4639.41 q^{11} -1710.47 q^{13} +34194.5 q^{14} +73219.7 q^{16} +14226.6 q^{17} -21902.8 q^{19} +31242.9 q^{20} -103543. q^{22} +107697. q^{23} -70998.8 q^{25} -38174.6 q^{26} +567048. q^{28} +195131. q^{29} -68117.7 q^{31} +942507. q^{32} +317512. q^{34} +129337. q^{35} -309640. q^{37} -488831. q^{38} +456131. q^{40} -873409. q^{41} +159630. q^{43} -1.71706e6 q^{44} +2.40360e6 q^{46} +615386. q^{47} +1.52388e6 q^{49} -1.58457e6 q^{50} -633051. q^{52} +745946. q^{53} -391643. q^{55} +8.27862e6 q^{56} +4.35498e6 q^{58} +205379. q^{59} -2.69167e6 q^{61} -1.52027e6 q^{62} +1.16630e7 q^{64} -144392. q^{65} +2.11862e6 q^{67} +5.26531e6 q^{68} +2.88658e6 q^{70} +1.64750e6 q^{71} -2.91422e6 q^{73} -6.91062e6 q^{74} -8.10630e6 q^{76} -7.10818e6 q^{77} +171784. q^{79} +6.18095e6 q^{80} -1.94930e7 q^{82} -4.94728e6 q^{83} +1.20096e6 q^{85} +3.56266e6 q^{86} -2.50683e7 q^{88} +1.83391e6 q^{89} -2.62066e6 q^{91} +3.98589e7 q^{92} +1.37343e7 q^{94} -1.84896e6 q^{95} -1.09662e7 q^{97} +3.40104e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) $ 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * 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 $

$2$	22.3182	1.97267	0.986336	−	0.164744i	$-0.0526798\pi$
$2$	22.3182	1.97267	0.986336	+	0.164744i	$0.0526798\pi$
$3$	0	0
$3$	0	0
$4$	370.104	2.89144
$5$	84.4166	0.302018	0.151009	−	0.988532i	$-0.451748\pi$
$5$	84.4166	0.302018	0.151009	+	0.988532i	$0.451748\pi$
$6$	0	0
$7$	1532.13	1.68831	0.844156	−	0.536097i	$-0.180102\pi$
$7$	1532.13	1.68831	0.844156	+	0.536097i	$0.180102\pi$
$8$	5403.34	3.73119
$9$	0	0
$10$	1884.03	0.595782
$11$	−4639.41	−1.05097	−0.525483	−	0.850804i	$-0.676115\pi$
$11$	−4639.41	−1.05097	−0.525483	+	0.850804i	$0.676115\pi$
$12$	0	0
$13$	−1710.47	−0.215930	−0.107965	−	0.994155i	$-0.534433\pi$
$13$	−1710.47	−0.215930	−0.107965	+	0.994155i	$0.534433\pi$
$14$	34194.5	3.33049
$15$	0	0
$16$	73219.7	4.46897
$17$	14226.6	0.702310	0.351155	−	0.936317i	$-0.385789\pi$
$17$	14226.6	0.702310	0.351155	+	0.936317i	$0.385789\pi$
$18$	0	0
$19$	−21902.8	−0.732590	−0.366295	−	0.930499i	$-0.619374\pi$
$19$	−21902.8	−0.732590	−0.366295	+	0.930499i	$0.619374\pi$
$20$	31242.9	0.873266
$21$	0	0
$22$	−103543.	−2.07321
$23$	107697.	1.84567	0.922836	−	0.385194i	$-0.125865\pi$
$23$	107697.	1.84567	0.922836	+	0.385194i	$0.125865\pi$
$24$	0	0
$25$	−70998.8	−0.908785
$26$	−38174.6	−0.425959
$27$	0	0
$28$	567048.	4.88165
$29$	195131.	1.48571	0.742853	−	0.669454i	$-0.233472\pi$
$29$	195131.	1.48571	0.742853	+	0.669454i	$0.233472\pi$
$30$	0	0
$31$	−68117.7	−0.410671	−0.205336	−	0.978692i	$-0.565829\pi$
$31$	−68117.7	−0.410671	−0.205336	+	0.978692i	$0.565829\pi$
$32$	942507.	5.08463
$33$	0	0
$34$	317512.	1.38543
$35$	129337.	0.509901
$36$	0	0
$37$	−309640.	−1.00496	−0.502482	−	0.864588i	$-0.667580\pi$
$37$	−309640.	−1.00496	−0.502482	+	0.864588i	$0.667580\pi$
$38$	−488831.	−1.44516
$39$	0	0
$40$	456131.	1.12689
$41$	−873409.	−1.97913	−0.989565	−	0.144086i	$-0.953976\pi$
$41$	−873409.	−1.97913	−0.989565	+	0.144086i	$0.953976\pi$
$42$	0	0
$43$	159630.	0.306179	0.153089	−	0.988212i	$-0.451078\pi$
$43$	159630.	0.306179	0.153089	+	0.988212i	$0.451078\pi$
$44$	−1.71706e6	−3.03880
$45$	0	0
$46$	2.40360e6	3.64091
$47$	615386.	0.864580	0.432290	−	0.901735i	$-0.357706\pi$
$47$	615386.	0.864580	0.432290	+	0.901735i	$0.357706\pi$
$48$	0	0
$49$	1.52388e6	1.85040
$50$	−1.58457e6	−1.79274
$51$	0	0
$52$	−633051.	−0.624348
$53$	745946.	0.688243	0.344121	−	0.938925i	$-0.388177\pi$
$53$	745946.	0.688243	0.344121	+	0.938925i	$0.388177\pi$
$54$	0	0
$55$	−391643.	−0.317410
$56$	8.27862e6	6.29941
$57$	0	0
$58$	4.35498e6	2.93081
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−2.69167e6	−1.51833	−0.759167	−	0.650896i	$-0.774393\pi$
$61$	−2.69167e6	−1.51833	−0.759167	+	0.650896i	$0.774393\pi$
$62$	−1.52027e6	−0.810119
$63$	0	0
$64$	1.16630e7	5.56135
$65$	−144392.	−0.0652147
$66$	0	0
$67$	2.11862e6	0.860581	0.430290	−	0.902691i	$-0.358411\pi$
$67$	2.11862e6	0.860581	0.430290	+	0.902691i	$0.358411\pi$
$68$	5.26531e6	2.03068
$69$	0	0
$70$	2.88658e6	1.00587
$71$	1.64750e6	0.546289	0.273144	−	0.961973i	$-0.411936\pi$
$71$	1.64750e6	0.546289	0.273144	+	0.961973i	$0.411936\pi$
$72$	0	0
$73$	−2.91422e6	−0.876783	−0.438391	−	0.898784i	$-0.644452\pi$
$73$	−2.91422e6	−0.876783	−0.438391	+	0.898784i	$0.644452\pi$
$74$	−6.91062e6	−1.98247
$75$	0	0
$76$	−8.10630e6	−2.11824
$77$	−7.10818e6	−1.77436
$78$	0	0
$79$	171784.	0.0392002	0.0196001	−	0.999808i	$-0.493761\pi$
$79$	171784.	0.0392002	0.0196001	+	0.999808i	$0.493761\pi$
$80$	6.18095e6	1.34971
$81$	0	0
$82$	−1.94930e7	−3.90418
$83$	−4.94728e6	−0.949714	−0.474857	−	0.880063i	$-0.657500\pi$
$83$	−4.94728e6	−0.949714	−0.474857	+	0.880063i	$0.657500\pi$
$84$	0	0
$85$	1.20096e6	0.212110
$86$	3.56266e6	0.603990
$87$	0	0
$88$	−2.50683e7	−3.92135
$89$	1.83391e6	0.275748	0.137874	−	0.990450i	$-0.455973\pi$
$89$	1.83391e6	0.275748	0.137874	+	0.990450i	$0.455973\pi$
$90$	0	0
$91$	−2.62066e6	−0.364557
$92$	3.98589e7	5.33664
$93$	0	0
$94$	1.37343e7	1.70553
$95$	−1.84896e6	−0.221255
$96$	0	0
$97$	−1.09662e7	−1.21998	−0.609992	−	0.792408i	$-0.708827\pi$
$97$	−1.09662e7	−1.21998	−0.609992	+	0.792408i	$0.708827\pi$
$98$	3.40104e7	3.65023
$99$	0	0
$100$	−2.62770e7	−2.62770
$101$	7.80317e6	0.753610	0.376805	−	0.926293i	$-0.377023\pi$
$101$	7.80317e6	0.753610	0.376805	+	0.926293i	$0.377023\pi$
$102$	0	0
$103$	−150244.	−0.0135477	−0.00677386	−	0.999977i	$-0.502156\pi$
$103$	−150244.	−0.0135477	−0.00677386	+	0.999977i	$0.502156\pi$
$104$	−9.24223e6	−0.805675
$105$	0	0
$106$	1.66482e7	1.35768
$107$	−8.15970e6	−0.643918	−0.321959	−	0.946754i	$-0.604341\pi$
$107$	−8.15970e6	−0.643918	−0.321959	+	0.946754i	$0.604341\pi$
$108$	0	0
$109$	6.65386e6	0.492131	0.246066	−	0.969253i	$-0.420862\pi$
$109$	6.65386e6	0.492131	0.246066	+	0.969253i	$0.420862\pi$
$110$	−8.74078e6	−0.626147
$111$	0	0
$112$	1.12182e8	7.54502
$113$	−1.76235e7	−1.14899	−0.574496	−	0.818507i	$-0.694802\pi$
$113$	−1.76235e7	−1.14899	−0.574496	+	0.818507i	$0.694802\pi$
$114$	0	0
$115$	9.09137e6	0.557426
$116$	7.22187e7	4.29583
$117$	0	0
$118$	4.58370e6	0.256820
$119$	2.17970e7	1.18572
$120$	0	0
$121$	2.03695e6	0.104528
$122$	−6.00733e7	−2.99517
$123$	0	0
$124$	−2.52106e7	−1.18743
$125$	−1.25885e7	−0.576487
$126$	0	0
$127$	−2.94003e7	−1.27362	−0.636808	−	0.771023i	$-0.719745\pi$
$127$	−2.94003e7	−1.27362	−0.636808	+	0.771023i	$0.719745\pi$
$128$	1.39656e8	5.88608
$129$	0	0
$130$	−3.22257e6	−0.128647
$131$	−4.56665e6	−0.177480	−0.0887398	−	0.996055i	$-0.528284\pi$
$131$	−4.56665e6	−0.177480	−0.0887398	+	0.996055i	$0.528284\pi$
$132$	0	0
$133$	−3.35579e7	−1.23684
$134$	4.72839e7	1.69764
$135$	0	0
$136$	7.68709e7	2.62045
$137$	−3.33611e6	−0.110846	−0.0554228	−	0.998463i	$-0.517651\pi$
$137$	−3.33611e6	−0.110846	−0.0554228	+	0.998463i	$0.517651\pi$
$138$	0	0
$139$	2.57204e7	0.812317	0.406158	−	0.913803i	$-0.366868\pi$
$139$	2.57204e7	0.812317	0.406158	+	0.913803i	$0.366868\pi$
$140$	4.78682e7	1.47435
$141$	0	0
$142$	3.67694e7	1.07765
$143$	7.93556e6	0.226935
$144$	0	0
$145$	1.64723e7	0.448710
$146$	−6.50402e7	−1.72961
$147$	0	0
$148$	−1.14599e8	−2.90579
$149$	7.15213e7	1.77127	0.885633	−	0.464387i	$-0.153725\pi$
$149$	7.15213e7	1.77127	0.885633	+	0.464387i	$0.153725\pi$
$150$	0	0
$151$	3.70730e7	0.876271	0.438135	−	0.898909i	$-0.355639\pi$
$151$	3.70730e7	0.876271	0.438135	+	0.898909i	$0.355639\pi$
$152$	−1.18348e8	−2.73343
$153$	0	0
$154$	−1.58642e8	−3.50023
$155$	−5.75026e6	−0.124030
$156$	0	0
$157$	−5.84600e7	−1.20562	−0.602810	−	0.797885i	$-0.705952\pi$
$157$	−5.84600e7	−1.20562	−0.602810	+	0.797885i	$0.705952\pi$
$158$	3.83392e6	0.0773291
$159$	0	0
$160$	7.95632e7	1.53565
$161$	1.65005e8	3.11607
$162$	0	0
$163$	1.08299e8	1.95869	0.979346	−	0.202190i	$-0.0648057\pi$
$163$	1.08299e8	1.95869	0.979346	+	0.202190i	$0.0648057\pi$
$164$	−3.23252e8	−5.72253
$165$	0	0
$166$	−1.10415e8	−1.87347
$167$	6.99062e6	0.116147	0.0580735	−	0.998312i	$-0.481504\pi$
$167$	6.99062e6	0.116147	0.0580735	+	0.998312i	$0.481504\pi$
$168$	0	0
$169$	−5.98228e7	−0.953374
$170$	2.68033e7	0.418424
$171$	0	0
$172$	5.90797e7	0.885296
$173$	9.78233e7	1.43642	0.718209	−	0.695827i	$-0.244962\pi$
$173$	9.78233e7	1.43642	0.718209	+	0.695827i	$0.244962\pi$
$174$	0	0
$175$	−1.08780e8	−1.53431
$176$	−3.39696e8	−4.69674
$177$	0	0
$178$	4.09296e7	0.543961
$179$	−7.71690e7	−1.00567	−0.502837	−	0.864381i	$-0.667710\pi$
$179$	−7.71690e7	−1.00567	−0.502837	+	0.864381i	$0.667710\pi$
$180$	0	0
$181$	−6.26316e7	−0.785088	−0.392544	−	0.919733i	$-0.628405\pi$
$181$	−6.26316e7	−0.785088	−0.392544	+	0.919733i	$0.628405\pi$
$182$	−5.84885e7	−0.719152
$183$	0	0
$184$	5.81921e8	6.88655
$185$	−2.61387e7	−0.303517
$186$	0	0
$187$	−6.60028e7	−0.738103
$188$	2.27757e8	2.49988
$189$	0	0
$190$	−4.12654e7	−0.436464
$191$	2.82767e7	0.293638	0.146819	−	0.989163i	$-0.453097\pi$
$191$	2.82767e7	0.293638	0.146819	+	0.989163i	$0.453097\pi$
$192$	0	0
$193$	−3.31268e7	−0.331688	−0.165844	−	0.986152i	$-0.553035\pi$
$193$	−3.31268e7	−0.331688	−0.165844	+	0.986152i	$0.553035\pi$
$194$	−2.44746e8	−2.40663
$195$	0	0
$196$	5.63995e8	5.35031
$197$	1.09797e8	1.02320	0.511598	−	0.859225i	$-0.329054\pi$
$197$	1.09797e8	1.02320	0.511598	+	0.859225i	$0.329054\pi$
$198$	0	0
$199$	1.14654e8	1.03134	0.515671	−	0.856787i	$-0.327543\pi$
$199$	1.14654e8	1.03134	0.515671	+	0.856787i	$0.327543\pi$
$200$	−3.83631e8	−3.39085
$201$	0	0
$202$	1.74153e8	1.48663
$203$	2.98966e8	2.50834
$204$	0	0
$205$	−7.37302e7	−0.597733
$206$	−3.35318e6	−0.0267252
$207$	0	0
$208$	−1.25240e8	−0.964985
$209$	1.01616e8	0.769927
$210$	0	0
$211$	−1.35295e8	−0.991502	−0.495751	−	0.868465i	$-0.665107\pi$
$211$	−1.35295e8	−0.991502	−0.495751	+	0.868465i	$0.665107\pi$
$212$	2.76077e8	1.99001
$213$	0	0
$214$	−1.82110e8	−1.27024
$215$	1.34754e7	0.0924714
$216$	0	0
$217$	−1.04365e8	−0.693341
$218$	1.48502e8	0.970814
$219$	0	0
$220$	−1.44949e8	−0.917772
$221$	−2.43341e7	−0.151650
$222$	0	0
$223$	9.14456e7	0.552199	0.276100	−	0.961129i	$-0.410958\pi$
$223$	9.14456e7	0.552199	0.276100	+	0.961129i	$0.410958\pi$
$224$	1.44404e9	8.58445
$225$	0	0
$226$	−3.93325e8	−2.26659
$227$	8.92462e7	0.506406	0.253203	−	0.967413i	$-0.418516\pi$
$227$	8.92462e7	0.506406	0.253203	+	0.967413i	$0.418516\pi$
$228$	0	0
$229$	2.51758e8	1.38535	0.692673	−	0.721251i	$-0.256433\pi$
$229$	2.51758e8	1.38535	0.692673	+	0.721251i	$0.256433\pi$
$230$	2.02903e8	1.09962
$231$	0	0
$232$	1.05436e9	5.54345
$233$	−3.50359e8	−1.81455	−0.907273	−	0.420542i	$-0.861840\pi$
$233$	−3.50359e8	−1.81455	−0.907273	+	0.420542i	$0.861840\pi$
$234$	0	0
$235$	5.19488e7	0.261119
$236$	7.60116e7	0.376433
$237$	0	0
$238$	4.86470e8	2.33903
$239$	−1.94400e8	−0.921092	−0.460546	−	0.887636i	$-0.652346\pi$
$239$	−1.94400e8	−0.921092	−0.460546	+	0.887636i	$0.652346\pi$
$240$	0	0
$241$	6.19386e7	0.285038	0.142519	−	0.989792i	$-0.454480\pi$
$241$	6.19386e7	0.285038	0.142519	+	0.989792i	$0.454480\pi$
$242$	4.54612e7	0.206199
$243$	0	0
$244$	−9.96197e8	−4.39017
$245$	1.28641e8	0.558853
$246$	0	0
$247$	3.74639e7	0.158188
$248$	−3.68063e8	−1.53229
$249$	0	0
$250$	−2.80954e8	−1.13722
$251$	−2.42156e8	−0.966577	−0.483289	−	0.875461i	$-0.660558\pi$
$251$	−2.42156e8	−0.966577	−0.483289	+	0.875461i	$0.660558\pi$
$252$	0	0
$253$	−4.99648e8	−1.93974
$254$	−6.56162e8	−2.51243
$255$	0	0
$256$	1.62403e9	6.04996
$257$	3.80530e8	1.39837	0.699187	−	0.714939i	$-0.253546\pi$
$257$	3.80530e8	1.39837	0.699187	+	0.714939i	$0.253546\pi$
$258$	0	0
$259$	−4.74409e8	−1.69669
$260$	−5.34400e7	−0.188564
$261$	0	0
$262$	−1.01920e8	−0.350109
$263$	1.88914e8	0.640353	0.320176	−	0.947358i	$-0.396258\pi$
$263$	1.88914e8	0.640353	0.320176	+	0.947358i	$0.396258\pi$
$264$	0	0
$265$	6.29702e7	0.207862
$266$	−7.48953e8	−2.43988
$267$	0	0
$268$	7.84110e8	2.48832
$269$	−2.07575e8	−0.650194	−0.325097	−	0.945681i	$-0.605397\pi$
$269$	−2.07575e8	−0.650194	−0.325097	+	0.945681i	$0.605397\pi$
$270$	0	0
$271$	−7.81832e7	−0.238628	−0.119314	−	0.992857i	$-0.538069\pi$
$271$	−7.81832e7	−0.238628	−0.119314	+	0.992857i	$0.538069\pi$
$272$	1.04166e9	3.13860
$273$	0	0
$274$	−7.44562e7	−0.218662
$275$	3.29393e8	0.955102
$276$	0	0
$277$	−1.30983e8	−0.370284	−0.185142	−	0.982712i	$-0.559274\pi$
$277$	−1.30983e8	−0.370284	−0.185142	+	0.982712i	$0.559274\pi$
$278$	5.74033e8	1.60243
$279$	0	0
$280$	6.98853e8	1.90253
$281$	−1.69682e8	−0.456209	−0.228105	−	0.973637i	$-0.573253\pi$
$281$	−1.69682e8	−0.456209	−0.228105	+	0.973637i	$0.573253\pi$
$282$	0	0
$283$	2.01304e8	0.527958	0.263979	−	0.964528i	$-0.414965\pi$
$283$	2.01304e8	0.527958	0.263979	+	0.964528i	$0.414965\pi$
$284$	6.09748e8	1.57956
$285$	0	0
$286$	1.77108e8	0.447668
$287$	−1.33818e9	−3.34139
$288$	0	0
$289$	−2.07944e8	−0.506761
$290$	3.67632e8	0.885158
$291$	0	0
$292$	−1.07856e9	−2.53516
$293$	4.63019e7	0.107538	0.0537691	−	0.998553i	$-0.482877\pi$
$293$	4.63019e7	0.107538	0.0537691	+	0.998553i	$0.482877\pi$
$294$	0	0
$295$	1.73374e7	0.0393194
$296$	−1.67309e9	−3.74971
$297$	0	0
$298$	1.59623e9	3.49413
$299$	−1.84211e8	−0.398536
$300$	0	0
$301$	2.44574e8	0.516925
$302$	8.27404e8	1.72859
$303$	0	0
$304$	−1.60371e9	−3.27393
$305$	−2.27221e8	−0.458564
$306$	0	0
$307$	−8.24546e8	−1.62641	−0.813206	−	0.581975i	$-0.802280\pi$
$307$	−8.24546e8	−1.62641	−0.813206	+	0.581975i	$0.802280\pi$
$308$	−2.63077e9	−5.13044
$309$	0	0
$310$	−1.28336e8	−0.244671
$311$	−8.21297e8	−1.54824	−0.774121	−	0.633038i	$-0.781808\pi$
$311$	−8.21297e8	−1.54824	−0.774121	+	0.633038i	$0.781808\pi$
$312$	0	0
$313$	4.00974e8	0.739113	0.369557	−	0.929208i	$-0.379510\pi$
$313$	4.00974e8	0.739113	0.369557	+	0.929208i	$0.379510\pi$
$314$	−1.30472e9	−2.37829
$315$	0	0
$316$	6.35779e7	0.113345
$317$	−2.03257e8	−0.358375	−0.179187	−	0.983815i	$-0.557347\pi$
$317$	−2.03257e8	−0.358375	−0.179187	+	0.983815i	$0.557347\pi$
$318$	0	0
$319$	−9.05292e8	−1.56143
$320$	9.84549e8	1.67963
$321$	0	0
$322$	3.68263e9	6.14699
$323$	−3.11601e8	−0.514505
$324$	0	0
$325$	1.21441e8	0.196234
$326$	2.41704e9	3.86386
$327$	0	0
$328$	−4.71932e9	−7.38451
$329$	9.42853e8	1.45968
$330$	0	0
$331$	4.59053e8	0.695769	0.347884	−	0.937537i	$-0.386900\pi$
$331$	4.59053e8	0.695769	0.347884	+	0.937537i	$0.386900\pi$
$332$	−1.83101e9	−2.74604
$333$	0	0
$334$	1.56018e8	0.229120
$335$	1.78847e8	0.259911
$336$	0	0
$337$	−1.03100e9	−1.46741	−0.733706	−	0.679467i	$-0.762211\pi$
$337$	−1.03100e9	−1.46741	−0.733706	+	0.679467i	$0.762211\pi$
$338$	−1.33514e9	−1.88070
$339$	0	0
$340$	4.44479e8	0.613303
$341$	3.16026e8	0.431601
$342$	0	0
$343$	1.07301e9	1.43574
$344$	8.62534e8	1.14241
$345$	0	0
$346$	2.18324e9	2.83358
$347$	−8.50881e8	−1.09324	−0.546620	−	0.837381i	$-0.684086\pi$
$347$	−8.50881e8	−1.09324	−0.546620	+	0.837381i	$0.684086\pi$
$348$	0	0
$349$	−7.28476e8	−0.917331	−0.458666	−	0.888609i	$-0.651672\pi$
$349$	−7.28476e8	−0.917331	−0.458666	+	0.888609i	$0.651672\pi$
$350$	−2.42777e9	−3.02670
$351$	0	0
$352$	−4.37268e9	−5.34377
$353$	−1.14502e9	−1.38548	−0.692741	−	0.721186i	$-0.743597\pi$
$353$	−1.14502e9	−1.38548	−0.692741	+	0.721186i	$0.743597\pi$
$354$	0	0
$355$	1.39077e8	0.164989
$356$	6.78737e8	0.797309
$357$	0	0
$358$	−1.72228e9	−1.98387
$359$	−4.66157e8	−0.531743	−0.265871	−	0.964008i	$-0.585660\pi$
$359$	−4.66157e8	−0.531743	−0.265871	+	0.964008i	$0.585660\pi$
$360$	0	0
$361$	−4.14141e8	−0.463312
$362$	−1.39783e9	−1.54872
$363$	0	0
$364$	−9.69917e8	−1.05409
$365$	−2.46008e8	−0.264804
$366$	0	0
$367$	1.98730e8	0.209861	0.104930	−	0.994480i	$-0.466538\pi$
$367$	1.98730e8	0.209861	0.104930	+	0.994480i	$0.466538\pi$
$368$	7.88551e9	8.24826
$369$	0	0
$370$	−5.83370e8	−0.598740
$371$	1.14289e9	1.16197
$372$	0	0
$373$	9.45866e8	0.943732	0.471866	−	0.881670i	$-0.343581\pi$
$373$	9.45866e8	0.943732	0.471866	+	0.881670i	$0.343581\pi$
$374$	−1.47307e9	−1.45604
$375$	0	0
$376$	3.32514e9	3.22591
$377$	−3.33765e8	−0.320809
$378$	0	0
$379$	−1.07925e9	−1.01832	−0.509162	−	0.860671i	$-0.670044\pi$
$379$	−1.07925e9	−1.01832	−0.509162	+	0.860671i	$0.670044\pi$
$380$	−6.84306e8	−0.639746
$381$	0	0
$382$	6.31086e8	0.579251
$383$	5.46503e8	0.497046	0.248523	−	0.968626i	$-0.420055\pi$
$383$	5.46503e8	0.497046	0.248523	+	0.968626i	$0.420055\pi$
$384$	0	0
$385$	−6.00048e8	−0.535888
$386$	−7.39333e8	−0.654311
$387$	0	0
$388$	−4.05863e9	−3.52751
$389$	6.83446e8	0.588682	0.294341	−	0.955700i	$-0.404900\pi$
$389$	6.83446e8	0.588682	0.294341	+	0.955700i	$0.404900\pi$
$390$	0	0
$391$	1.53215e9	1.29623
$392$	8.23405e9	6.90418
$393$	0	0
$394$	2.45048e9	2.01843
$395$	1.45014e7	0.0118391
$396$	0	0
$397$	−1.21932e9	−0.978030	−0.489015	−	0.872275i	$-0.662644\pi$
$397$	−1.21932e9	−0.978030	−0.489015	+	0.872275i	$0.662644\pi$
$398$	2.55887e9	2.03450
$399$	0	0
$400$	−5.19851e9	−4.06134
$401$	1.27738e9	0.989268	0.494634	−	0.869101i	$-0.335302\pi$
$401$	1.27738e9	0.989268	0.494634	+	0.869101i	$0.335302\pi$
$402$	0	0
$403$	1.16513e8	0.0886762
$404$	2.88799e9	2.17902
$405$	0	0
$406$	6.67240e9	4.94813
$407$	1.43655e9	1.05618
$408$	0	0
$409$	−1.52758e9	−1.10401	−0.552004	−	0.833842i	$-0.686137\pi$
$409$	−1.52758e9	−1.10401	−0.552004	+	0.833842i	$0.686137\pi$
$410$	−1.64553e9	−1.17913
$411$	0	0
$412$	−5.56058e7	−0.0391724
$413$	3.14668e8	0.219800
$414$	0	0
$415$	−4.17632e8	−0.286831
$416$	−1.61213e9	−1.09792
$417$	0	0
$418$	2.26789e9	1.51881
$419$	−2.15816e9	−1.43329	−0.716645	−	0.697438i	$-0.754323\pi$
$419$	−2.15816e9	−1.43329	−0.716645	+	0.697438i	$0.754323\pi$
$420$	0	0
$421$	−4.86121e8	−0.317509	−0.158755	−	0.987318i	$-0.550748\pi$
$421$	−4.86121e8	−0.317509	−0.158755	+	0.987318i	$0.550748\pi$
$422$	−3.01955e9	−1.95591
$423$	0	0
$424$	4.03059e9	2.56796
$425$	−1.01007e9	−0.638249
$426$	0	0
$427$	−4.12399e9	−2.56342
$428$	−3.01994e9	−1.86185
$429$	0	0
$430$	3.00747e8	0.182416
$431$	−8.97584e8	−0.540013	−0.270007	−	0.962858i	$-0.587026\pi$
$431$	−8.97584e8	−0.540013	−0.270007	+	0.962858i	$0.587026\pi$
$432$	0	0
$433$	−1.07413e8	−0.0635843	−0.0317921	−	0.999495i	$-0.510121\pi$
$433$	−1.07413e8	−0.0635843	−0.0317921	+	0.999495i	$0.510121\pi$
$434$	−2.32925e9	−1.36773
$435$	0	0
$436$	2.46262e9	1.42297
$437$	−2.35885e9	−1.35212
$438$	0	0
$439$	−4.23839e8	−0.239097	−0.119549	−	0.992828i	$-0.538145\pi$
$439$	−4.23839e8	−0.239097	−0.119549	+	0.992828i	$0.538145\pi$
$440$	−2.11618e9	−1.18432
$441$	0	0
$442$	−5.43094e8	−0.299155
$443$	1.56918e9	0.857552	0.428776	−	0.903411i	$-0.358945\pi$
$443$	1.56918e9	0.857552	0.428776	+	0.903411i	$0.358945\pi$
$444$	0	0
$445$	1.54812e8	0.0832809
$446$	2.04091e9	1.08931
$447$	0	0
$448$	1.78692e10	9.38929
$449$	6.52660e8	0.340271	0.170135	−	0.985421i	$-0.445580\pi$
$449$	6.52660e8	0.340271	0.170135	+	0.985421i	$0.445580\pi$
$450$	0	0
$451$	4.05210e9	2.08000
$452$	−6.52252e9	−3.32224
$453$	0	0
$454$	1.99182e9	0.998974
$455$	−2.21227e8	−0.110103
$456$	0	0
$457$	−3.14784e9	−1.54278	−0.771392	−	0.636360i	$-0.780439\pi$
$457$	−3.14784e9	−1.54278	−0.771392	+	0.636360i	$0.780439\pi$
$458$	5.61879e9	2.73284
$459$	0	0
$460$	3.36475e9	1.61176
$461$	−3.81603e9	−1.81409	−0.907044	−	0.421037i	$-0.861666\pi$
$461$	−3.81603e9	−1.81409	−0.907044	+	0.421037i	$0.861666\pi$
$462$	0	0
$463$	7.32034e8	0.342766	0.171383	−	0.985204i	$-0.445176\pi$
$463$	7.32034e8	0.342766	0.171383	+	0.985204i	$0.445176\pi$
$464$	1.42874e10	6.63958
$465$	0	0
$466$	−7.81941e9	−3.57951
$467$	9.56937e8	0.434785	0.217392	−	0.976084i	$-0.430245\pi$
$467$	9.56937e8	0.434785	0.217392	+	0.976084i	$0.430245\pi$
$468$	0	0
$469$	3.24601e9	1.45293
$470$	1.15941e9	0.515102
$471$	0	0
$472$	1.10973e9	0.485759
$473$	−7.40589e8	−0.321783
$474$	0	0
$475$	1.55507e9	0.665767
$476$	8.06714e9	3.42843
$477$	0	0
$478$	−4.33866e9	−1.81701
$479$	−3.19983e9	−1.33031	−0.665154	−	0.746706i	$-0.731634\pi$
$479$	−3.19983e9	−1.33031	−0.665154	+	0.746706i	$0.731634\pi$
$480$	0	0
$481$	5.29629e8	0.217002
$482$	1.38236e9	0.562286
$483$	0	0
$484$	7.53884e8	0.302236
$485$	−9.25727e8	−0.368457
$486$	0	0
$487$	−3.55741e8	−0.139567	−0.0697834	−	0.997562i	$-0.522231\pi$
$487$	−3.55741e8	−0.139567	−0.0697834	+	0.997562i	$0.522231\pi$
$488$	−1.45440e10	−5.66518
$489$	0	0
$490$	2.87104e9	1.10243
$491$	1.77516e7	0.00676788	0.00338394	−	0.999994i	$-0.498923\pi$
$491$	1.77516e7	0.00676788	0.00338394	+	0.999994i	$0.498923\pi$
$492$	0	0
$493$	2.77604e9	1.04343
$494$	8.36129e8	0.312054
$495$	0	0
$496$	−4.98755e9	−1.83528
$497$	2.52419e9	0.922306
$498$	0	0
$499$	1.97045e9	0.709927	0.354963	−	0.934880i	$-0.384493\pi$
$499$	1.97045e9	0.709927	0.354963	+	0.934880i	$0.384493\pi$
$500$	−4.65906e9	−1.66688
$501$	0	0
$502$	−5.40449e9	−1.90674
$503$	4.77882e9	1.67430	0.837148	−	0.546976i	$-0.184221\pi$
$503$	4.77882e9	1.67430	0.837148	+	0.546976i	$0.184221\pi$
$504$	0	0
$505$	6.58717e8	0.227604
$506$	−1.11513e10	−3.82647
$507$	0	0
$508$	−1.08812e10	−3.68258
$509$	2.21746e9	0.745321	0.372660	−	0.927968i	$-0.378446\pi$
$509$	2.21746e9	0.745321	0.372660	+	0.927968i	$0.378446\pi$
$510$	0	0
$511$	−4.46496e9	−1.48028
$512$	1.83694e10	6.04852
$513$	0	0
$514$	8.49277e9	2.75853
$515$	−1.26831e7	−0.00409165
$516$	0	0
$517$	−2.85503e9	−0.908644
$518$	−1.05880e10	−3.34702
$519$	0	0
$520$	−7.80197e8	−0.243328
$521$	2.05916e9	0.637908	0.318954	−	0.947770i	$-0.396668\pi$
$521$	2.05916e9	0.637908	0.318954	+	0.947770i	$0.396668\pi$
$522$	0	0
$523$	4.60384e9	1.40723	0.703614	−	0.710582i	$-0.251568\pi$
$523$	4.60384e9	1.40723	0.703614	+	0.710582i	$0.251568\pi$
$524$	−1.69014e9	−0.513171
$525$	0	0
$526$	4.21623e9	1.26321
$527$	−9.69081e8	−0.288418
$528$	0	0
$529$	8.19372e9	2.40650
$530$	1.40538e9	0.410043
$531$	0	0
$532$	−1.24199e10	−3.57625
$533$	1.49394e9	0.427354
$534$	0	0
$535$	−6.88814e8	−0.194475
$536$	1.14476e10	3.21099
$537$	0	0
$538$	−4.63272e9	−1.28262
$539$	−7.06992e9	−1.94470
$540$	0	0
$541$	−5.44524e9	−1.47852	−0.739258	−	0.673422i	$-0.764824\pi$
$541$	−5.44524e9	−1.47852	−0.739258	+	0.673422i	$0.764824\pi$
$542$	−1.74491e9	−0.470735
$543$	0	0
$544$	1.34086e10	3.57099
$545$	5.61696e8	0.148632
$546$	0	0
$547$	−2.09397e9	−0.547035	−0.273518	−	0.961867i	$-0.588187\pi$
$547$	−2.09397e9	−0.547035	−0.273518	+	0.961867i	$0.588187\pi$
$548$	−1.23471e9	−0.320503
$549$	0	0
$550$	7.35147e9	1.88410
$551$	−4.27390e9	−1.08841
$552$	0	0
$553$	2.63196e8	0.0661821
$554$	−2.92330e9	−0.730449
$555$	0	0
$556$	9.51921e9	2.34876
$557$	−4.55263e9	−1.11627	−0.558135	−	0.829750i	$-0.688483\pi$
$557$	−4.55263e9	−1.11627	−0.558135	+	0.829750i	$0.688483\pi$
$558$	0	0
$559$	−2.73042e8	−0.0661131
$560$	9.47003e9	2.27873
$561$	0	0
$562$	−3.78701e9	−0.899952
$563$	2.34649e9	0.554166	0.277083	−	0.960846i	$-0.410632\pi$
$563$	2.34649e9	0.554166	0.277083	+	0.960846i	$0.410632\pi$
$564$	0	0
$565$	−1.48771e9	−0.347016
$566$	4.49274e9	1.04149
$567$	0	0
$568$	8.90202e9	2.03831
$569$	2.75800e9	0.627626	0.313813	−	0.949485i	$-0.398394\pi$
$569$	2.75800e9	0.627626	0.313813	+	0.949485i	$0.398394\pi$
$570$	0	0
$571$	−1.49430e9	−0.335901	−0.167950	−	0.985795i	$-0.553715\pi$
$571$	−1.49430e9	−0.335901	−0.167950	+	0.985795i	$0.553715\pi$
$572$	2.93698e9	0.656168
$573$	0	0
$574$	−2.98658e10	−6.59147
$575$	−7.64633e9	−1.67732
$576$	0	0
$577$	−5.27606e8	−0.114339	−0.0571695	−	0.998364i	$-0.518208\pi$
$577$	−5.27606e8	−0.114339	−0.0571695	+	0.998364i	$0.518208\pi$
$578$	−4.64094e9	−0.999673
$579$	0	0
$580$	6.09646e9	1.29742
$581$	−7.57987e9	−1.60341
$582$	0	0
$583$	−3.46075e9	−0.723319
$584$	−1.57465e10	−3.27144
$585$	0	0
$586$	1.03338e9	0.212138
$587$	3.02681e9	0.617664	0.308832	−	0.951117i	$-0.400062\pi$
$587$	3.02681e9	0.617664	0.308832	+	0.951117i	$0.400062\pi$
$588$	0	0
$589$	1.49197e9	0.300854
$590$	3.86940e8	0.0775643
$591$	0	0
$592$	−2.26717e10	−4.49116
$593$	7.55687e9	1.48816	0.744081	−	0.668089i	$-0.232887\pi$
$593$	7.55687e9	1.48816	0.744081	+	0.668089i	$0.232887\pi$
$594$	0	0
$595$	1.84002e9	0.358108
$596$	2.64703e10	5.12150
$597$	0	0
$598$	−4.11127e9	−0.786181
$599$	7.21826e9	1.37227	0.686133	−	0.727476i	$-0.259307\pi$
$599$	7.21826e9	1.37227	0.686133	+	0.727476i	$0.259307\pi$
$600$	0	0
$601$	−4.11700e9	−0.773607	−0.386803	−	0.922162i	$-0.626421\pi$
$601$	−4.11700e9	−0.773607	−0.386803	+	0.922162i	$0.626421\pi$
$602$	5.45846e9	1.01972
$603$	0	0
$604$	1.37209e10	2.53368
$605$	1.71952e8	0.0315693
$606$	0	0
$607$	3.42535e9	0.621649	0.310824	−	0.950467i	$-0.399395\pi$
$607$	3.42535e9	0.621649	0.310824	+	0.950467i	$0.399395\pi$
$608$	−2.06435e10	−3.72495
$609$	0	0
$610$	−5.07118e9	−0.904596
$611$	−1.05260e9	−0.186689
$612$	0	0
$613$	−8.07359e9	−1.41565	−0.707823	−	0.706390i	$-0.750323\pi$
$613$	−8.07359e9	−1.41565	−0.707823	+	0.706390i	$0.750323\pi$
$614$	−1.84024e10	−3.20838
$615$	0	0
$616$	−3.84079e10	−6.62046
$617$	7.36421e9	1.26220	0.631100	−	0.775702i	$-0.282604\pi$
$617$	7.36421e9	1.26220	0.631100	+	0.775702i	$0.282604\pi$
$618$	0	0
$619$	9.33576e9	1.58210	0.791048	−	0.611755i	$-0.209536\pi$
$619$	9.33576e9	1.58210	0.791048	+	0.611755i	$0.209536\pi$
$620$	−2.12820e9	−0.358625
$621$	0	0
$622$	−1.83299e10	−3.05417
$623$	2.80979e9	0.465549
$624$	0	0
$625$	4.48410e9	0.734676
$626$	8.94903e9	1.45803
$627$	0	0
$628$	−2.16363e10	−3.48597
$629$	−4.40511e9	−0.705796
$630$	0	0
$631$	1.58549e9	0.251225	0.125612	−	0.992079i	$-0.459910\pi$
$631$	1.58549e9	0.251225	0.125612	+	0.992079i	$0.459910\pi$
$632$	9.28206e8	0.146263
$633$	0	0
$634$	−4.53633e9	−0.706956
$635$	−2.48187e9	−0.384655
$636$	0	0
$637$	−2.60655e9	−0.399556
$638$	−2.02045e10	−3.08018
$639$	0	0
$640$	1.17893e10	1.77770
$641$	−7.99377e9	−1.19880	−0.599402	−	0.800448i	$-0.704595\pi$
$641$	−7.99377e9	−1.19880	−0.599402	+	0.800448i	$0.704595\pi$
$642$	0	0
$643$	−2.26242e9	−0.335610	−0.167805	−	0.985820i	$-0.553668\pi$
$643$	−2.26242e9	−0.335610	−0.167805	+	0.985820i	$0.553668\pi$
$644$	6.10691e10	9.00992
$645$	0	0
$646$	−6.95438e9	−1.01495
$647$	−4.58044e8	−0.0664879	−0.0332439	−	0.999447i	$-0.510584\pi$
$647$	−4.58044e8	−0.0664879	−0.0332439	+	0.999447i	$0.510584\pi$
$648$	0	0
$649$	−9.52837e8	−0.136824
$650$	2.71035e9	0.387105
$651$	0	0
$652$	4.00818e10	5.66344
$653$	−8.67155e9	−1.21871	−0.609355	−	0.792897i	$-0.708572\pi$
$653$	−8.67155e9	−1.21871	−0.609355	+	0.792897i	$0.708572\pi$
$654$	0	0
$655$	−3.85501e8	−0.0536020
$656$	−6.39507e10	−8.84468
$657$	0	0
$658$	2.10428e10	2.87947
$659$	−8.76494e9	−1.19303	−0.596513	−	0.802603i	$-0.703448\pi$
$659$	−8.76494e9	−1.19303	−0.596513	+	0.802603i	$0.703448\pi$
$660$	0	0
$661$	1.58045e9	0.212850	0.106425	−	0.994321i	$-0.466060\pi$
$661$	1.58045e9	0.212850	0.106425	+	0.994321i	$0.466060\pi$
$662$	1.02453e10	1.37252
$663$	0	0
$664$	−2.67318e10	−3.54356
$665$	−2.83284e9	−0.373548
$666$	0	0
$667$	2.10149e10	2.74213
$668$	2.58726e9	0.335832
$669$	0	0
$670$	3.99155e9	0.512719
$671$	1.24877e10	1.59572
$672$	0	0
$673$	−2.26086e9	−0.285905	−0.142952	−	0.989730i	$-0.545660\pi$
$673$	−2.26086e9	−0.285905	−0.142952	+	0.989730i	$0.545660\pi$
$674$	−2.30100e10	−2.89472
$675$	0	0
$676$	−2.21407e10	−2.75662
$677$	−6.78561e9	−0.840483	−0.420241	−	0.907412i	$-0.638055\pi$
$677$	−6.78561e9	−0.840483	−0.420241	+	0.907412i	$0.638055\pi$
$678$	0	0
$679$	−1.68016e10	−2.05971
$680$	6.48918e9	0.791423
$681$	0	0
$682$	7.05314e9	0.851407
$683$	7.74627e9	0.930294	0.465147	−	0.885234i	$-0.346002\pi$
$683$	7.74627e9	0.930294	0.465147	+	0.885234i	$0.346002\pi$
$684$	0	0
$685$	−2.81623e8	−0.0334774
$686$	2.39477e10	2.83224
$687$	0	0
$688$	1.16880e10	1.36830
$689$	−1.27592e9	−0.148612
$690$	0	0
$691$	−5.90227e9	−0.680528	−0.340264	−	0.940330i	$-0.610516\pi$
$691$	−5.90227e9	−0.680528	−0.340264	+	0.940330i	$0.610516\pi$
$692$	3.62048e10	4.15331
$693$	0	0
$694$	−1.89902e10	−2.15660
$695$	2.17122e9	0.245334
$696$	0	0
$697$	−1.24256e10	−1.38996
$698$	−1.62583e10	−1.80959
$699$	0	0
$700$	−4.02597e10	−4.43637
$701$	1.01648e10	1.11452	0.557259	−	0.830339i	$-0.311853\pi$
$701$	1.01648e10	1.11452	0.557259	+	0.830339i	$0.311853\pi$
$702$	0	0
$703$	6.78196e9	0.736227
$704$	−5.41094e10	−5.84478
$705$	0	0
$706$	−2.55548e10	−2.73310
$707$	1.19555e10	1.27233
$708$	0	0
$709$	−7.24332e9	−0.763266	−0.381633	−	0.924314i	$-0.624638\pi$
$709$	−7.24332e9	−0.763266	−0.381633	+	0.924314i	$0.624638\pi$
$710$	3.10395e9	0.325469
$711$	0	0
$712$	9.90922e9	1.02887
$713$	−7.33604e9	−0.757964
$714$	0	0
$715$	6.69892e8	0.0685384
$716$	−2.85606e10	−2.90784
$717$	0	0
$718$	−1.04038e10	−1.04895
$719$	−1.37810e10	−1.38270	−0.691350	−	0.722520i	$-0.742984\pi$
$719$	−1.37810e10	−1.38270	−0.691350	+	0.722520i	$0.742984\pi$
$720$	0	0
$721$	−2.30193e8	−0.0228728
$722$	−9.24290e9	−0.913962
$723$	0	0
$724$	−2.31802e10	−2.27003
$725$	−1.38541e10	−1.35019
$726$	0	0
$727$	−1.04638e10	−1.00999	−0.504996	−	0.863122i	$-0.668506\pi$
$727$	−1.04638e10	−1.00999	−0.504996	+	0.863122i	$0.668506\pi$
$728$	−1.41603e10	−1.36023
$729$	0	0
$730$	−5.49047e9	−0.522372
$731$	2.27099e9	0.215032
$732$	0	0
$733$	−6.09625e9	−0.571740	−0.285870	−	0.958268i	$-0.592283\pi$
$733$	−6.09625e9	−0.571740	−0.285870	+	0.958268i	$0.592283\pi$
$734$	4.43530e9	0.413987
$735$	0	0
$736$	1.01505e11	9.38456
$737$	−9.82915e9	−0.904440
$738$	0	0
$739$	1.62223e10	1.47862	0.739308	−	0.673367i	$-0.235153\pi$
$739$	1.62223e10	1.47862	0.739308	+	0.673367i	$0.235153\pi$
$740$	−9.67405e9	−0.877601
$741$	0	0
$742$	2.55072e10	2.29218
$743$	2.03461e10	1.81978	0.909891	−	0.414847i	$-0.136165\pi$
$743$	2.03461e10	1.81978	0.909891	+	0.414847i	$0.136165\pi$
$744$	0	0
$745$	6.03758e9	0.534954
$746$	2.11101e10	1.86167
$747$	0	0
$748$	−2.44279e10	−2.13418
$749$	−1.25017e10	−1.08714
$750$	0	0
$751$	6.71015e9	0.578086	0.289043	−	0.957316i	$-0.406663\pi$
$751$	6.71015e9	0.578086	0.289043	+	0.957316i	$0.406663\pi$
$752$	4.50584e10	3.86379
$753$	0	0
$754$	−7.44905e9	−0.632850
$755$	3.12957e9	0.264649
$756$	0	0
$757$	7.51213e9	0.629401	0.314700	−	0.949191i	$-0.398096\pi$
$757$	7.51213e9	0.629401	0.314700	+	0.949191i	$0.398096\pi$
$758$	−2.40870e10	−2.00882
$759$	0	0
$760$	−9.99053e9	−0.825545
$761$	−1.17043e10	−0.962721	−0.481361	−	0.876523i	$-0.659857\pi$
$761$	−1.17043e10	−0.962721	−0.481361	+	0.876523i	$0.659857\pi$
$762$	0	0
$763$	1.01946e10	0.830871
$764$	1.04653e10	0.849035
$765$	0	0
$766$	1.21970e10	0.980509
$767$	−3.51294e8	−0.0281117
$768$	0	0
$769$	−2.01241e9	−0.159579	−0.0797894	−	0.996812i	$-0.525425\pi$
$769$	−2.01241e9	−0.159579	−0.0797894	+	0.996812i	$0.525425\pi$
$770$	−1.33920e10	−1.05713
$771$	0	0
$772$	−1.22604e10	−0.959055
$773$	5.06105e9	0.394105	0.197053	−	0.980393i	$-0.436863\pi$
$773$	5.06105e9	0.394105	0.197053	+	0.980393i	$0.436863\pi$
$774$	0	0
$775$	4.83628e9	0.373212
$776$	−5.92539e10	−4.55199
$777$	0	0
$778$	1.52533e10	1.16128
$779$	1.91301e10	1.44989
$780$	0	0
$781$	−7.64344e9	−0.574130
$782$	3.41949e10	2.55704
$783$	0	0
$784$	1.11578e11	8.26938
$785$	−4.93499e9	−0.364119
$786$	0	0
$787$	−1.29130e10	−0.944311	−0.472155	−	0.881515i	$-0.656524\pi$
$787$	−1.29130e10	−0.944311	−0.472155	+	0.881515i	$0.656524\pi$
$788$	4.06364e10	2.95851
$789$	0	0
$790$	3.23646e8	0.0233548
$791$	−2.70015e10	−1.93986
$792$	0	0
$793$	4.60401e9	0.327854
$794$	−2.72132e10	−1.92933
$795$	0	0
$796$	4.24338e10	2.98206
$797$	1.75345e10	1.22684	0.613422	−	0.789755i	$-0.289792\pi$
$797$	1.75345e10	1.22684	0.613422	+	0.789755i	$0.289792\pi$
$798$	0	0
$799$	8.75483e9	0.607203
$800$	−6.69169e10	−4.62084
$801$	0	0
$802$	2.85088e10	1.95150
$803$	1.35203e10	0.921468
$804$	0	0
$805$	1.39292e10	0.941109
$806$	2.60037e9	0.174929
$807$	0	0
$808$	4.21632e10	2.81186
$809$	−3.03994e9	−0.201858	−0.100929	−	0.994894i	$-0.532181\pi$
$809$	−3.03994e9	−0.201858	−0.100929	+	0.994894i	$0.532181\pi$
$810$	0	0
$811$	1.35418e10	0.891465	0.445733	−	0.895166i	$-0.352943\pi$
$811$	1.35418e10	0.891465	0.445733	+	0.895166i	$0.352943\pi$
$812$	1.10649e11	7.25270
$813$	0	0
$814$	3.20612e10	2.08350
$815$	9.14220e9	0.591560
$816$	0	0
$817$	−3.49634e9	−0.224303
$818$	−3.40929e10	−2.17785
$819$	0	0
$820$	−2.72879e10	−1.72831
$821$	1.44424e10	0.910834	0.455417	−	0.890278i	$-0.349490\pi$
$821$	1.44424e10	0.910834	0.455417	+	0.890278i	$0.349490\pi$
$822$	0	0
$823$	1.58161e10	0.989009	0.494504	−	0.869175i	$-0.335350\pi$
$823$	1.58161e10	0.989009	0.494504	+	0.869175i	$0.335350\pi$
$824$	−8.11818e8	−0.0505491
$825$	0	0
$826$	7.02283e9	0.433593
$827$	2.91022e10	1.78919	0.894594	−	0.446879i	$-0.147465\pi$
$827$	2.91022e10	1.78919	0.894594	+	0.446879i	$0.147465\pi$
$828$	0	0
$829$	−1.38090e10	−0.841825	−0.420913	−	0.907101i	$-0.638290\pi$
$829$	−1.38090e10	−0.841825	−0.420913	+	0.907101i	$0.638290\pi$
$830$	−9.32081e9	−0.565823
$831$	0	0
$832$	−1.99492e10	−1.20086
$833$	2.16796e10	1.29955
$834$	0	0
$835$	5.90124e8	0.0350785
$836$	3.76084e10	2.22620
$837$	0	0
$838$	−4.81663e10	−2.82741
$839$	−2.26960e10	−1.32673	−0.663366	−	0.748295i	$-0.730873\pi$
$839$	−2.26960e10	−1.32673	−0.663366	+	0.748295i	$0.730873\pi$
$840$	0	0
$841$	2.08262e10	1.20732
$842$	−1.08494e10	−0.626342
$843$	0	0
$844$	−5.00733e10	−2.86687
$845$	−5.05004e9	−0.287936
$846$	0	0
$847$	3.12088e9	0.176476
$848$	5.46179e10	3.07574
$849$	0	0
$850$	−2.25430e10	−1.25906
$851$	−3.33471e10	−1.85483
$852$	0	0
$853$	−2.76986e9	−0.152804	−0.0764022	−	0.997077i	$-0.524343\pi$
$853$	−2.76986e9	−0.152804	−0.0764022	+	0.997077i	$0.524343\pi$
$854$	−9.20402e10	−5.05679
$855$	0	0
$856$	−4.40896e10	−2.40258
$857$	−8.53606e9	−0.463260	−0.231630	−	0.972804i	$-0.574406\pi$
$857$	−8.53606e9	−0.463260	−0.231630	+	0.972804i	$0.574406\pi$
$858$	0	0
$859$	−7.27081e9	−0.391387	−0.195694	−	0.980665i	$-0.562696\pi$
$859$	−7.27081e9	−0.391387	−0.195694	+	0.980665i	$0.562696\pi$
$860$	4.98730e9	0.267375
$861$	0	0
$862$	−2.00325e10	−1.06527
$863$	−2.06289e10	−1.09254	−0.546270	−	0.837609i	$-0.683953\pi$
$863$	−2.06289e10	−1.09254	−0.546270	+	0.837609i	$0.683953\pi$
$864$	0	0
$865$	8.25791e9	0.433824
$866$	−2.39727e9	−0.125431
$867$	0	0
$868$	−3.86260e10	−2.00475
$869$	−7.96976e8	−0.0411980
$870$	0	0
$871$	−3.62383e9	−0.185825
$872$	3.59530e10	1.83623
$873$	0	0
$874$	−5.26454e10	−2.66729
$875$	−1.92873e10	−0.973291
$876$	0	0
$877$	1.04224e10	0.521760	0.260880	−	0.965371i	$-0.415987\pi$
$877$	1.04224e10	0.521760	0.260880	+	0.965371i	$0.415987\pi$
$878$	−9.45934e9	−0.471661
$879$	0	0
$880$	−2.86760e10	−1.41850
$881$	−3.28267e10	−1.61738	−0.808690	−	0.588235i	$-0.799823\pi$
$881$	−3.28267e10	−1.61738	−0.808690	+	0.588235i	$0.799823\pi$
$882$	0	0
$883$	2.09738e10	1.02522	0.512608	−	0.858623i	$-0.328680\pi$
$883$	2.09738e10	1.02522	0.512608	+	0.858623i	$0.328680\pi$
$884$	−9.00613e9	−0.438486
$885$	0	0
$886$	3.50214e10	1.69167
$887$	−4.36272e9	−0.209906	−0.104953	−	0.994477i	$-0.533469\pi$
$887$	−4.36272e9	−0.209906	−0.104953	+	0.994477i	$0.533469\pi$
$888$	0	0
$889$	−4.50451e10	−2.15026
$890$	3.45514e9	0.164286
$891$	0	0
$892$	3.38444e10	1.59665
$893$	−1.34787e10	−0.633383
$894$	0	0
$895$	−6.51434e9	−0.303732
$896$	2.13972e11	9.93754
$897$	0	0
$898$	1.45662e10	0.671243
$899$	−1.32919e10	−0.610137
$900$	0	0
$901$	1.06122e10	0.483360
$902$	9.04359e10	4.10315
$903$	0	0
$904$	−9.52256e10	−4.28711
$905$	−5.28714e9	−0.237111
$906$	0	0
$907$	9.67343e9	0.430482	0.215241	−	0.976561i	$-0.430946\pi$
$907$	9.67343e9	0.430482	0.215241	+	0.976561i	$0.430946\pi$
$908$	3.30304e10	1.46424
$909$	0	0
$910$	−4.93740e9	−0.217197
$911$	−1.13862e10	−0.498959	−0.249480	−	0.968380i	$-0.580260\pi$
$911$	−1.13862e10	−0.498959	−0.249480	+	0.968380i	$0.580260\pi$
$912$	0	0
$913$	2.29524e10	0.998116
$914$	−7.02542e10	−3.04341
$915$	0	0
$916$	9.31765e10	4.00564
$917$	−6.99671e9	−0.299641
$918$	0	0
$919$	−1.74980e9	−0.0743676	−0.0371838	−	0.999308i	$-0.511839\pi$
$919$	−1.74980e9	−0.0743676	−0.0371838	+	0.999308i	$0.511839\pi$
$920$	4.91237e10	2.07986
$921$	0	0
$922$	−8.51670e10	−3.57860
$923$	−2.81800e9	−0.117960
$924$	0	0
$925$	2.19841e10	0.913297
$926$	1.63377e10	0.676165
$927$	0	0
$928$	1.83912e11	7.55428
$929$	5.01633e9	0.205273	0.102636	−	0.994719i	$-0.467272\pi$
$929$	5.01633e9	0.205273	0.102636	+	0.994719i	$0.467272\pi$
$930$	0	0
$931$	−3.33772e10	−1.35558
$932$	−1.29669e11	−5.24665
$933$	0	0
$934$	2.13572e10	0.857688
$935$	−5.57173e9	−0.222920
$936$	0	0
$937$	2.41581e10	0.959343	0.479672	−	0.877448i	$-0.340756\pi$
$937$	2.41581e10	0.959343	0.479672	+	0.877448i	$0.340756\pi$
$938$	7.24452e10	2.86615
$939$	0	0
$940$	1.92265e10	0.755009
$941$	2.00603e10	0.784826	0.392413	−	0.919789i	$-0.371640\pi$
$941$	2.00603e10	0.784826	0.392413	+	0.919789i	$0.371640\pi$
$942$	0	0
$943$	−9.40632e10	−3.65282
$944$	1.50378e10	0.581811
$945$	0	0
$946$	−1.65286e10	−0.634772
$947$	1.33454e10	0.510632	0.255316	−	0.966858i	$-0.417820\pi$
$947$	1.33454e10	0.510632	0.255316	+	0.966858i	$0.417820\pi$
$948$	0	0
$949$	4.98467e9	0.189324
$950$	3.47064e10	1.31334
$951$	0	0
$952$	1.17776e11	4.42414
$953$	4.58477e10	1.71590	0.857950	−	0.513733i	$-0.171738\pi$
$953$	4.58477e10	1.71590	0.857950	+	0.513733i	$0.171738\pi$
$954$	0	0
$955$	2.38702e9	0.0886838
$956$	−7.19481e10	−2.66328
$957$	0	0
$958$	−7.14146e10	−2.62426
$959$	−5.11136e9	−0.187142
$960$	0	0
$961$	−2.28726e10	−0.831349
$962$	1.18204e10	0.428074
$963$	0	0
$964$	2.29237e10	0.824168
$965$	−2.79645e9	−0.100176
$966$	0	0
$967$	2.81641e10	1.00162	0.500810	−	0.865557i	$-0.333036\pi$
$967$	2.81641e10	1.00162	0.500810	+	0.865557i	$0.333036\pi$
$968$	1.10063e10	0.390013
$969$	0	0
$970$	−2.06606e10	−0.726845
$971$	−2.91527e10	−1.02191	−0.510954	−	0.859608i	$-0.670708\pi$
$971$	−2.91527e10	−1.02191	−0.510954	+	0.859608i	$0.670708\pi$
$972$	0	0
$973$	3.94070e10	1.37144
$974$	−7.93951e9	−0.275320
$975$	0	0
$976$	−1.97083e11	−6.78539
$977$	−2.18798e10	−0.750607	−0.375303	−	0.926902i	$-0.622461\pi$
$977$	−2.18798e10	−0.750607	−0.375303	+	0.926902i	$0.622461\pi$
$978$	0	0
$979$	−8.50825e9	−0.289802
$980$	4.76105e10	1.61589
$981$	0	0
$982$	3.96185e8	0.0133508
$983$	−7.16781e9	−0.240685	−0.120342	−	0.992732i	$-0.538399\pi$
$983$	−7.16781e9	−0.240685	−0.120342	+	0.992732i	$0.538399\pi$
$984$	0	0
$985$	9.26870e9	0.309024
$986$	6.19564e10	2.05834
$987$	0	0
$988$	1.38656e10	0.457391
$989$	1.71916e10	0.565105
$990$	0	0
$991$	−3.83800e9	−0.125270	−0.0626350	−	0.998037i	$-0.519950\pi$
$991$	−3.83800e9	−0.125270	−0.0626350	+	0.998037i	$0.519950\pi$
$992$	−6.42014e10	−2.08811
$993$	0	0
$994$	5.63355e10	1.81941
$995$	9.67868e9	0.311484
$996$	0	0
$997$	5.63360e10	1.80033	0.900166	−	0.435547i	$-0.143445\pi$
$997$	5.63360e10	1.80033	0.900166	+	0.435547i	$0.143445\pi$
$998$	4.39770e10	1.40045
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.17		17
3.2	odd	2		177.8.a.b.1.1	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.1	✓	17	3.2	odd	2
531.8.a.d.1.17		17	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q+22.3182 q^{2} +370.104 q^{4} +84.4166 q^{5} +1532.13 q^{7} +5403.34 q^{8} +O(q^{10})\)	\(q+22.3182 q^{2} +370.104 q^{4} +84.4166 q^{5} +1532.13 q^{7} +5403.34 q^{8} +1884.03 q^{10} -4639.41 q^{11} -1710.47 q^{13} +34194.5 q^{14} +73219.7 q^{16} +14226.6 q^{17} -21902.8 q^{19} +31242.9 q^{20} -103543. q^{22} +107697. q^{23} -70998.8 q^{25} -38174.6 q^{26} +567048. q^{28} +195131. q^{29} -68117.7 q^{31} +942507. q^{32} +317512. q^{34} +129337. q^{35} -309640. q^{37} -488831. q^{38} +456131. q^{40} -873409. q^{41} +159630. q^{43} -1.71706e6 q^{44} +2.40360e6 q^{46} +615386. q^{47} +1.52388e6 q^{49} -1.58457e6 q^{50} -633051. q^{52} +745946. q^{53} -391643. q^{55} +8.27862e6 q^{56} +4.35498e6 q^{58} +205379. q^{59} -2.69167e6 q^{61} -1.52027e6 q^{62} +1.16630e7 q^{64} -144392. q^{65} +2.11862e6 q^{67} +5.26531e6 q^{68} +2.88658e6 q^{70} +1.64750e6 q^{71} -2.91422e6 q^{73} -6.91062e6 q^{74} -8.10630e6 q^{76} -7.10818e6 q^{77} +171784. q^{79} +6.18095e6 q^{80} -1.94930e7 q^{82} -4.94728e6 q^{83} +1.20096e6 q^{85} +3.56266e6 q^{86} -2.50683e7 q^{88} +1.83391e6 q^{89} -2.62066e6 q^{91} +3.98589e7 q^{92} +1.37343e7 q^{94} -1.84896e6 q^{95} -1.09662e7 q^{97} +3.40104e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * q^98

Introduction

L-functions

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