LMFDB - Embedded newform 8085.2.a.bx.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.127775712.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} + 20x^{2} - 2x - 8 $ x^6 - 9x^4 + 20x^2 - 2*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.33025$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.33025 q^{2} -1.00000 q^{3} +3.43006 q^{4} +1.00000 q^{5} -2.33025 q^{6} +3.33238 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.33025 q^{2} -1.00000 q^{3} +3.43006 q^{4} +1.00000 q^{5} -2.33025 q^{6} +3.33238 q^{8} +1.00000 q^{9} +2.33025 q^{10} +1.00000 q^{11} -3.43006 q^{12} +6.56567 q^{13} -1.00000 q^{15} +0.905171 q^{16} +2.55550 q^{17} +2.33025 q^{18} +2.38844 q^{19} +3.43006 q^{20} +2.33025 q^{22} -3.71869 q^{23} -3.33238 q^{24} +1.00000 q^{25} +15.2996 q^{26} -1.00000 q^{27} -4.34552 q^{29} -2.33025 q^{30} +9.27917 q^{31} -4.55550 q^{32} -1.00000 q^{33} +5.95494 q^{34} +3.43006 q^{36} +6.98686 q^{37} +5.56567 q^{38} -6.56567 q^{39} +3.33238 q^{40} -5.85125 q^{41} -0.577059 q^{43} +3.43006 q^{44} +1.00000 q^{45} -8.66547 q^{46} -1.22008 q^{47} -0.905171 q^{48} +2.33025 q^{50} -2.55550 q^{51} +22.5206 q^{52} +1.71564 q^{53} -2.33025 q^{54} +1.00000 q^{55} -2.38844 q^{57} -10.1261 q^{58} +11.7696 q^{59} -3.43006 q^{60} -10.1078 q^{61} +21.6228 q^{62} -12.4258 q^{64} +6.56567 q^{65} -2.33025 q^{66} -12.1037 q^{67} +8.76550 q^{68} +3.71869 q^{69} +1.12615 q^{71} +3.33238 q^{72} -7.66678 q^{73} +16.2811 q^{74} -1.00000 q^{75} +8.19250 q^{76} -15.2996 q^{78} +0.744325 q^{79} +0.905171 q^{80} +1.00000 q^{81} -13.6349 q^{82} +12.9061 q^{83} +2.55550 q^{85} -1.34469 q^{86} +4.34552 q^{87} +3.33238 q^{88} +16.0765 q^{89} +2.33025 q^{90} -12.7553 q^{92} -9.27917 q^{93} -2.84309 q^{94} +2.38844 q^{95} +4.55550 q^{96} +4.43219 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^9	$ 6 q - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{9} + 6 q^{11} - 6 q^{12} + 4 q^{13} - 6 q^{15} - 2 q^{16} - 2 q^{17} + 13 q^{19} + 6 q^{20} - 7 q^{23} + 6 q^{25} + 26 q^{26} - 6 q^{27} + 3 q^{29} + 15 q^{31} - 10 q^{32} - 6 q^{33} + 14 q^{34} + 6 q^{36} - 11 q^{37} - 2 q^{38} - 4 q^{39} - 3 q^{41} - 4 q^{43} + 6 q^{44} + 6 q^{45} - 16 q^{46} + 19 q^{47} + 2 q^{48} + 2 q^{51} + 16 q^{52} - q^{53} + 6 q^{55} - 13 q^{57} + 22 q^{59} - 6 q^{60} + 14 q^{61} + 2 q^{62} - 10 q^{64} + 4 q^{65} - 21 q^{67} + 14 q^{68} + 7 q^{69} + 8 q^{71} + 11 q^{73} + 20 q^{74} - 6 q^{75} - 26 q^{78} - 13 q^{79} - 2 q^{80} + 6 q^{81} + 6 q^{82} + 10 q^{83} - 2 q^{85} + 36 q^{86} - 3 q^{87} + 28 q^{89} + 6 q^{92} - 15 q^{93} + 14 q^{94} + 13 q^{95} + 10 q^{96} + 6 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^9 + 6 * q^11 - 6 * q^12 + 4 * q^13 - 6 * q^15 - 2 * q^16 - 2 * q^17 + 13 * q^19 + 6 * q^20 - 7 * q^23 + 6 * q^25 + 26 * q^26 - 6 * q^27 + 3 * q^29 + 15 * q^31 - 10 * q^32 - 6 * q^33 + 14 * q^34 + 6 * q^36 - 11 * q^37 - 2 * q^38 - 4 * q^39 - 3 * q^41 - 4 * q^43 + 6 * q^44 + 6 * q^45 - 16 * q^46 + 19 * q^47 + 2 * q^48 + 2 * q^51 + 16 * q^52 - q^53 + 6 * q^55 - 13 * q^57 + 22 * q^59 - 6 * q^60 + 14 * q^61 + 2 * q^62 - 10 * q^64 + 4 * q^65 - 21 * q^67 + 14 * q^68 + 7 * q^69 + 8 * q^71 + 11 * q^73 + 20 * q^74 - 6 * q^75 - 26 * q^78 - 13 * q^79 - 2 * q^80 + 6 * q^81 + 6 * q^82 + 10 * q^83 - 2 * q^85 + 36 * q^86 - 3 * q^87 + 28 * q^89 + 6 * q^92 - 15 * q^93 + 14 * q^94 + 13 * q^95 + 10 * q^96 + 6 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.33025	1.64773	0.823867	−	0.566783i	$-0.191812\pi$
$2$	2.33025	1.64773	0.823867	+	0.566783i	$0.191812\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.43006	1.71503
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.33025	−0.951320
$7$	0	0
$7$	0	0
$8$	3.33238	1.17818
$9$	1.00000	0.333333
$10$	2.33025	0.736889
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.43006	−0.990172
$13$	6.56567	1.82099	0.910494	−	0.413522i	$-0.135701\pi$
$13$	6.56567	1.82099	0.910494	+	0.413522i	$0.135701\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	0.905171	0.226293
$17$	2.55550	0.619799	0.309899	−	0.950769i	$-0.399705\pi$
$17$	2.55550	0.619799	0.309899	+	0.950769i	$0.399705\pi$
$18$	2.33025	0.549245
$19$	2.38844	0.547947	0.273973	−	0.961737i	$-0.411662\pi$
$19$	2.38844	0.547947	0.273973	+	0.961737i	$0.411662\pi$
$20$	3.43006	0.766984
$21$	0	0
$22$	2.33025	0.496811
$23$	−3.71869	−0.775401	−0.387700	−	0.921785i	$-0.626730\pi$
$23$	−3.71869	−0.775401	−0.387700	+	0.921785i	$0.626730\pi$
$24$	−3.33238	−0.680220
$25$	1.00000	0.200000
$26$	15.2996	3.00050
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.34552	−0.806943	−0.403472	−	0.914992i	$-0.632197\pi$
$29$	−4.34552	−0.806943	−0.403472	+	0.914992i	$0.632197\pi$
$30$	−2.33025	−0.425443
$31$	9.27917	1.66659	0.833294	−	0.552830i	$-0.186452\pi$
$31$	9.27917	1.66659	0.833294	+	0.552830i	$0.186452\pi$
$32$	−4.55550	−0.805306
$33$	−1.00000	−0.174078
$34$	5.95494	1.02126
$35$	0	0
$36$	3.43006	0.571676
$37$	6.98686	1.14863	0.574316	−	0.818634i	$-0.305268\pi$
$37$	6.98686	1.14863	0.574316	+	0.818634i	$0.305268\pi$
$38$	5.56567	0.902870
$39$	−6.56567	−1.05135
$40$	3.33238	0.526896
$41$	−5.85125	−0.913811	−0.456906	−	0.889515i	$-0.651042\pi$
$41$	−5.85125	−0.913811	−0.456906	+	0.889515i	$0.651042\pi$
$42$	0	0
$43$	−0.577059	−0.0880007	−0.0440004	−	0.999032i	$-0.514010\pi$
$43$	−0.577059	−0.0880007	−0.0440004	+	0.999032i	$0.514010\pi$
$44$	3.43006	0.517100
$45$	1.00000	0.149071
$46$	−8.66547	−1.27765
$47$	−1.22008	−0.177967	−0.0889835	−	0.996033i	$-0.528362\pi$
$47$	−1.22008	−0.177967	−0.0889835	+	0.996033i	$0.528362\pi$
$48$	−0.905171	−0.130650
$49$	0	0
$50$	2.33025	0.329547
$51$	−2.55550	−0.357841
$52$	22.5206	3.12305
$53$	1.71564	0.235661	0.117830	−	0.993034i	$-0.462406\pi$
$53$	1.71564	0.235661	0.117830	+	0.993034i	$0.462406\pi$
$54$	−2.33025	−0.317107
$55$	1.00000	0.134840
$56$	0	0
$57$	−2.38844	−0.316357
$58$	−10.1261	−1.32963
$59$	11.7696	1.53227	0.766133	−	0.642682i	$-0.222178\pi$
$59$	11.7696	1.53227	0.766133	+	0.642682i	$0.222178\pi$
$60$	−3.43006	−0.442818
$61$	−10.1078	−1.29418	−0.647088	−	0.762415i	$-0.724013\pi$
$61$	−10.1078	−1.29418	−0.647088	+	0.762415i	$0.724013\pi$
$62$	21.6228	2.74609
$63$	0	0
$64$	−12.4258	−1.55322
$65$	6.56567	0.814371
$66$	−2.33025	−0.286834
$67$	−12.1037	−1.47870	−0.739350	−	0.673321i	$-0.764867\pi$
$67$	−12.1037	−1.47870	−0.739350	+	0.673321i	$0.764867\pi$
$68$	8.76550	1.06297
$69$	3.71869	0.447678
$70$	0	0
$71$	1.12615	0.133649	0.0668245	−	0.997765i	$-0.478713\pi$
$71$	1.12615	0.133649	0.0668245	+	0.997765i	$0.478713\pi$
$72$	3.33238	0.392725
$73$	−7.66678	−0.897329	−0.448664	−	0.893700i	$-0.648100\pi$
$73$	−7.66678	−0.897329	−0.448664	+	0.893700i	$0.648100\pi$
$74$	16.2811	1.89264
$75$	−1.00000	−0.115470
$76$	8.19250	0.939744
$77$	0	0
$78$	−15.2996	−1.73234
$79$	0.744325	0.0837431	0.0418716	−	0.999123i	$-0.486668\pi$
$79$	0.744325	0.0837431	0.0418716	+	0.999123i	$0.486668\pi$
$80$	0.905171	0.101201
$81$	1.00000	0.111111
$82$	−13.6349	−1.50572
$83$	12.9061	1.41663	0.708313	−	0.705898i	$-0.249456\pi$
$83$	12.9061	1.41663	0.708313	+	0.705898i	$0.249456\pi$
$84$	0	0
$85$	2.55550	0.277183
$86$	−1.34469	−0.145002
$87$	4.34552	0.465889
$88$	3.33238	0.355233
$89$	16.0765	1.70411	0.852054	−	0.523454i	$-0.175357\pi$
$89$	16.0765	1.70411	0.852054	+	0.523454i	$0.175357\pi$
$90$	2.33025	0.245630
$91$	0	0
$92$	−12.7553	−1.32983
$93$	−9.27917	−0.962205
$94$	−2.84309	−0.293242
$95$	2.38844	0.245049
$96$	4.55550	0.464943
$97$	4.43219	0.450021	0.225010	−	0.974356i	$-0.427758\pi$
$97$	4.43219	0.450021	0.225010	+	0.974356i	$0.427758\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	3.43006	0.343006
$101$	−10.5424	−1.04900	−0.524502	−	0.851409i	$-0.675748\pi$
$101$	−10.5424	−1.04900	−0.524502	+	0.851409i	$0.675748\pi$
$102$	−5.95494	−0.589627
$103$	−5.93083	−0.584382	−0.292191	−	0.956360i	$-0.594384\pi$
$103$	−5.93083	−0.584382	−0.292191	+	0.956360i	$0.594384\pi$
$104$	21.8793	2.14544
$105$	0	0
$106$	3.99786	0.388306
$107$	16.7846	1.62263	0.811317	−	0.584607i	$-0.198751\pi$
$107$	16.7846	1.62263	0.811317	+	0.584607i	$0.198751\pi$
$108$	−3.43006	−0.330057
$109$	−16.5688	−1.58701	−0.793504	−	0.608566i	$-0.791745\pi$
$109$	−16.5688	−1.58701	−0.793504	+	0.608566i	$0.791745\pi$
$110$	2.33025	0.222180
$111$	−6.98686	−0.663163
$112$	0	0
$113$	17.2975	1.62721	0.813606	−	0.581417i	$-0.197502\pi$
$113$	17.2975	1.62721	0.813606	+	0.581417i	$0.197502\pi$
$114$	−5.56567	−0.521272
$115$	−3.71869	−0.346770
$116$	−14.9054	−1.38393
$117$	6.56567	0.606996
$118$	27.4260	2.52477
$119$	0	0
$120$	−3.33238	−0.304204
$121$	1.00000	0.0909091
$122$	−23.5538	−2.13246
$123$	5.85125	0.527589
$124$	31.8281	2.85824
$125$	1.00000	0.0894427
$126$	0	0
$127$	−6.96467	−0.618015	−0.309007	−	0.951060i	$-0.599997\pi$
$127$	−6.96467	−0.618015	−0.309007	+	0.951060i	$0.599997\pi$
$128$	−19.8442	−1.75399
$129$	0.577059	0.0508072
$130$	15.2996	1.34187
$131$	15.6096	1.36382	0.681910	−	0.731436i	$-0.261150\pi$
$131$	15.6096	1.36382	0.681910	+	0.731436i	$0.261150\pi$
$132$	−3.43006	−0.298548
$133$	0	0
$134$	−28.2046	−2.43651
$135$	−1.00000	−0.0860663
$136$	8.51590	0.730232
$137$	2.23737	0.191151	0.0955757	−	0.995422i	$-0.469531\pi$
$137$	2.23737	0.191151	0.0955757	+	0.995422i	$0.469531\pi$
$138$	8.66547	0.737654
$139$	12.3721	1.04939	0.524693	−	0.851292i	$-0.324180\pi$
$139$	12.3721	1.04939	0.524693	+	0.851292i	$0.324180\pi$
$140$	0	0
$141$	1.22008	0.102749
$142$	2.62420	0.220218
$143$	6.56567	0.549049
$144$	0.905171	0.0754309
$145$	−4.34552	−0.360876
$146$	−17.8655	−1.47856
$147$	0	0
$148$	23.9653	1.96994
$149$	3.39043	0.277755	0.138878	−	0.990310i	$-0.455651\pi$
$149$	3.39043	0.277755	0.138878	+	0.990310i	$0.455651\pi$
$150$	−2.33025	−0.190264
$151$	−0.920629	−0.0749197	−0.0374599	−	0.999298i	$-0.511927\pi$
$151$	−0.920629	−0.0749197	−0.0374599	+	0.999298i	$0.511927\pi$
$152$	7.95921	0.645577
$153$	2.55550	0.206600
$154$	0	0
$155$	9.27917	0.745321
$156$	−22.5206	−1.80309
$157$	−19.6247	−1.56623	−0.783113	−	0.621880i	$-0.786369\pi$
$157$	−19.6247	−1.56623	−0.783113	+	0.621880i	$0.786369\pi$
$158$	1.73446	0.137986
$159$	−1.71564	−0.136059
$160$	−4.55550	−0.360144
$161$	0	0
$162$	2.33025	0.183082
$163$	10.1961	0.798617	0.399309	−	0.916817i	$-0.369250\pi$
$163$	10.1961	0.798617	0.399309	+	0.916817i	$0.369250\pi$
$164$	−20.0701	−1.56721
$165$	−1.00000	−0.0778499
$166$	30.0744	2.33422
$167$	−0.708129	−0.0547967	−0.0273983	−	0.999625i	$-0.508722\pi$
$167$	−0.708129	−0.0547967	−0.0273983	+	0.999625i	$0.508722\pi$
$168$	0	0
$169$	30.1080	2.31600
$170$	5.95494	0.456723
$171$	2.38844	0.182649
$172$	−1.97935	−0.150924
$173$	−13.5334	−1.02893	−0.514464	−	0.857512i	$-0.672009\pi$
$173$	−13.5334	−1.02893	−0.514464	+	0.857512i	$0.672009\pi$
$174$	10.1261	0.767661
$175$	0	0
$176$	0.905171	0.0682298
$177$	−11.7696	−0.884654
$178$	37.4623	2.80792
$179$	−13.9753	−1.04456	−0.522281	−	0.852774i	$-0.674919\pi$
$179$	−13.9753	−1.04456	−0.522281	+	0.852774i	$0.674919\pi$
$180$	3.43006	0.255661
$181$	9.94639	0.739309	0.369655	−	0.929169i	$-0.379476\pi$
$181$	9.94639	0.739309	0.369655	+	0.929169i	$0.379476\pi$
$182$	0	0
$183$	10.1078	0.747193
$184$	−12.3921	−0.913559
$185$	6.98686	0.513684
$186$	−21.6228	−1.58546
$187$	2.55550	0.186876
$188$	−4.18494	−0.305218
$189$	0	0
$190$	5.56567	0.403776
$191$	12.4829	0.903230	0.451615	−	0.892213i	$-0.350848\pi$
$191$	12.4829	0.903230	0.451615	+	0.892213i	$0.350848\pi$
$192$	12.4258	0.896753
$193$	1.71866	0.123712	0.0618561	−	0.998085i	$-0.480298\pi$
$193$	1.71866	0.123712	0.0618561	+	0.998085i	$0.480298\pi$
$194$	10.3281	0.741515
$195$	−6.56567	−0.470177
$196$	0	0
$197$	0.0590259	0.00420542	0.00210271	−	0.999998i	$-0.499331\pi$
$197$	0.0590259	0.00420542	0.00210271	+	0.999998i	$0.499331\pi$
$198$	2.33025	0.165604
$199$	−21.3818	−1.51571	−0.757856	−	0.652422i	$-0.773753\pi$
$199$	−21.3818	−1.51571	−0.757856	+	0.652422i	$0.773753\pi$
$200$	3.33238	0.235635
$201$	12.1037	0.853728
$202$	−24.5663	−1.72848
$203$	0	0
$204$	−8.76550	−0.613707
$205$	−5.85125	−0.408669
$206$	−13.8203	−0.962906
$207$	−3.71869	−0.258467
$208$	5.94305	0.412076
$209$	2.38844	0.165212
$210$	0	0
$211$	16.1643	1.11280	0.556398	−	0.830916i	$-0.312183\pi$
$211$	16.1643	1.11280	0.556398	+	0.830916i	$0.312183\pi$
$212$	5.88473	0.404165
$213$	−1.12615	−0.0771623
$214$	39.1124	2.67367
$215$	−0.577059	−0.0393551
$216$	−3.33238	−0.226740
$217$	0	0
$218$	−38.6095	−2.61497
$219$	7.66678	0.518073
$220$	3.43006	0.231254
$221$	16.7785	1.12865
$222$	−16.2811	−1.09272
$223$	9.06835	0.607262	0.303631	−	0.952790i	$-0.401801\pi$
$223$	9.06835	0.607262	0.303631	+	0.952790i	$0.401801\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	40.3074	2.68121
$227$	13.3174	0.883904	0.441952	−	0.897039i	$-0.354286\pi$
$227$	13.3174	0.883904	0.441952	+	0.897039i	$0.354286\pi$
$228$	−8.19250	−0.542561
$229$	−17.9433	−1.18573	−0.592864	−	0.805303i	$-0.702003\pi$
$229$	−17.9433	−1.18573	−0.592864	+	0.805303i	$0.702003\pi$
$230$	−8.66547	−0.571384
$231$	0	0
$232$	−14.4809	−0.950721
$233$	8.66091	0.567395	0.283698	−	0.958914i	$-0.408439\pi$
$233$	8.66091	0.567395	0.283698	+	0.958914i	$0.408439\pi$
$234$	15.2996	1.00017
$235$	−1.22008	−0.0795893
$236$	40.3702	2.62788
$237$	−0.744325	−0.0483491
$238$	0	0
$239$	−5.89784	−0.381499	−0.190750	−	0.981639i	$-0.561092\pi$
$239$	−5.89784	−0.381499	−0.190750	+	0.981639i	$0.561092\pi$
$240$	−0.905171	−0.0584285
$241$	−25.7444	−1.65834	−0.829170	−	0.558997i	$-0.811186\pi$
$241$	−25.7444	−1.65834	−0.829170	+	0.558997i	$0.811186\pi$
$242$	2.33025	0.149794
$243$	−1.00000	−0.0641500
$244$	−34.6704	−2.21955
$245$	0	0
$246$	13.6349	0.869327
$247$	15.6817	0.997804
$248$	30.9218	1.96353
$249$	−12.9061	−0.817890
$250$	2.33025	0.147378
$251$	20.9817	1.32435	0.662176	−	0.749348i	$-0.269633\pi$
$251$	20.9817	1.32435	0.662176	+	0.749348i	$0.269633\pi$
$252$	0	0
$253$	−3.71869	−0.233792
$254$	−16.2294	−1.01832
$255$	−2.55550	−0.160031
$256$	−21.3902	−1.33689
$257$	13.7452	0.857404	0.428702	−	0.903446i	$-0.358971\pi$
$257$	13.7452	0.857404	0.428702	+	0.903446i	$0.358971\pi$
$258$	1.34469	0.0837168
$259$	0	0
$260$	22.5206	1.39667
$261$	−4.34552	−0.268981
$262$	36.3743	2.24721
$263$	−26.4249	−1.62943	−0.814713	−	0.579864i	$-0.803106\pi$
$263$	−26.4249	−1.62943	−0.814713	+	0.579864i	$0.803106\pi$
$264$	−3.33238	−0.205094
$265$	1.71564	0.105391
$266$	0	0
$267$	−16.0765	−0.983867
$268$	−41.5163	−2.53601
$269$	21.5035	1.31109	0.655546	−	0.755155i	$-0.272438\pi$
$269$	21.5035	1.31109	0.655546	+	0.755155i	$0.272438\pi$
$270$	−2.33025	−0.141814
$271$	−12.9964	−0.789473	−0.394736	−	0.918794i	$-0.629164\pi$
$271$	−12.9964	−0.789473	−0.394736	+	0.918794i	$0.629164\pi$
$272$	2.31316	0.140256
$273$	0	0
$274$	5.21363	0.314967
$275$	1.00000	0.0603023
$276$	12.7553	0.767780
$277$	−15.1834	−0.912285	−0.456142	−	0.889907i	$-0.650769\pi$
$277$	−15.1834	−0.912285	−0.456142	+	0.889907i	$0.650769\pi$
$278$	28.8300	1.72911
$279$	9.27917	0.555529
$280$	0	0
$281$	9.45336	0.563940	0.281970	−	0.959423i	$-0.409012\pi$
$281$	9.45336	0.563940	0.281970	+	0.959423i	$0.409012\pi$
$282$	2.84309	0.169304
$283$	18.1802	1.08070	0.540351	−	0.841440i	$-0.318292\pi$
$283$	18.1802	1.08070	0.540351	+	0.841440i	$0.318292\pi$
$284$	3.86274	0.229212
$285$	−2.38844	−0.141479
$286$	15.2996	0.904686
$287$	0	0
$288$	−4.55550	−0.268435
$289$	−10.4694	−0.615849
$290$	−10.1261	−0.594628
$291$	−4.43219	−0.259820
$292$	−26.2975	−1.53894
$293$	−28.7950	−1.68222	−0.841112	−	0.540862i	$-0.818098\pi$
$293$	−28.7950	−1.68222	−0.841112	+	0.540862i	$0.818098\pi$
$294$	0	0
$295$	11.7696	0.685250
$296$	23.2829	1.35329
$297$	−1.00000	−0.0580259
$298$	7.90055	0.457667
$299$	−24.4157	−1.41200
$300$	−3.43006	−0.198034
$301$	0	0
$302$	−2.14529	−0.123448
$303$	10.5424	0.605642
$304$	2.16195	0.123996
$305$	−10.1078	−0.578773
$306$	5.95494	0.340421
$307$	25.7537	1.46984	0.734920	−	0.678154i	$-0.237220\pi$
$307$	25.7537	1.46984	0.734920	+	0.678154i	$0.237220\pi$
$308$	0	0
$309$	5.93083	0.337393
$310$	21.6228	1.22809
$311$	6.95499	0.394381	0.197191	−	0.980365i	$-0.436818\pi$
$311$	6.95499	0.394381	0.197191	+	0.980365i	$0.436818\pi$
$312$	−21.8793	−1.23867
$313$	15.9445	0.901235	0.450618	−	0.892717i	$-0.351204\pi$
$313$	15.9445	0.901235	0.450618	+	0.892717i	$0.351204\pi$
$314$	−45.7305	−2.58072
$315$	0	0
$316$	2.55308	0.143622
$317$	6.11558	0.343485	0.171743	−	0.985142i	$-0.445060\pi$
$317$	6.11558	0.343485	0.171743	+	0.985142i	$0.445060\pi$
$318$	−3.99786	−0.224189
$319$	−4.34552	−0.243302
$320$	−12.4258	−0.694622
$321$	−16.7846	−0.936828
$322$	0	0
$323$	6.10366	0.339617
$324$	3.43006	0.190559
$325$	6.56567	0.364198
$326$	23.7594	1.31591
$327$	16.5688	0.916259
$328$	−19.4986	−1.07663
$329$	0	0
$330$	−2.33025	−0.128276
$331$	2.21500	0.121747	0.0608737	−	0.998145i	$-0.480611\pi$
$331$	2.21500	0.121747	0.0608737	+	0.998145i	$0.480611\pi$
$332$	44.2686	2.42955
$333$	6.98686	0.382878
$334$	−1.65012	−0.0902904
$335$	−12.1037	−0.661295
$336$	0	0
$337$	−12.9876	−0.707480	−0.353740	−	0.935344i	$-0.615090\pi$
$337$	−12.9876	−0.707480	−0.353740	+	0.935344i	$0.615090\pi$
$338$	70.1591	3.81615
$339$	−17.2975	−0.939471
$340$	8.76550	0.475376
$341$	9.27917	0.502495
$342$	5.56567	0.300957
$343$	0	0
$344$	−1.92298	−0.103680
$345$	3.71869	0.200208
$346$	−31.5362	−1.69540
$347$	−5.86289	−0.314736	−0.157368	−	0.987540i	$-0.550301\pi$
$347$	−5.86289	−0.314736	−0.157368	+	0.987540i	$0.550301\pi$
$348$	14.9054	0.799012
$349$	−9.96125	−0.533213	−0.266607	−	0.963805i	$-0.585902\pi$
$349$	−9.96125	−0.533213	−0.266607	+	0.963805i	$0.585902\pi$
$350$	0	0
$351$	−6.56567	−0.350449
$352$	−4.55550	−0.242809
$353$	−6.91306	−0.367945	−0.183973	−	0.982931i	$-0.558896\pi$
$353$	−6.91306	−0.367945	−0.183973	+	0.982931i	$0.558896\pi$
$354$	−27.4260	−1.45767
$355$	1.12615	0.0597696
$356$	55.1434	2.92259
$357$	0	0
$358$	−32.5659	−1.72116
$359$	5.09607	0.268960	0.134480	−	0.990916i	$-0.457064\pi$
$359$	5.09607	0.268960	0.134480	+	0.990916i	$0.457064\pi$
$360$	3.33238	0.175632
$361$	−13.2953	−0.699754
$362$	23.1776	1.21819
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−7.66678	−0.401298
$366$	23.5538	1.23118
$367$	15.6679	0.817858	0.408929	−	0.912566i	$-0.365902\pi$
$367$	15.6679	0.817858	0.408929	+	0.912566i	$0.365902\pi$
$368$	−3.36605	−0.175468
$369$	−5.85125	−0.304604
$370$	16.2811	0.846415
$371$	0	0
$372$	−31.8281	−1.65021
$373$	−22.0542	−1.14192	−0.570962	−	0.820976i	$-0.693430\pi$
$373$	−22.0542	−1.14192	−0.570962	+	0.820976i	$0.693430\pi$
$374$	5.95494	0.307923
$375$	−1.00000	−0.0516398
$376$	−4.06578	−0.209676
$377$	−28.5312	−1.46943
$378$	0	0
$379$	7.40055	0.380141	0.190070	−	0.981770i	$-0.439128\pi$
$379$	7.40055	0.380141	0.190070	+	0.981770i	$0.439128\pi$
$380$	8.19250	0.420266
$381$	6.96467	0.356811
$382$	29.0882	1.48828
$383$	16.8001	0.858445	0.429223	−	0.903199i	$-0.358788\pi$
$383$	16.8001	0.858445	0.429223	+	0.903199i	$0.358788\pi$
$384$	19.8442	1.01267
$385$	0	0
$386$	4.00491	0.203845
$387$	−0.577059	−0.0293336
$388$	15.2027	0.771798
$389$	−17.9625	−0.910737	−0.455369	−	0.890303i	$-0.650493\pi$
$389$	−17.9625	−0.910737	−0.455369	+	0.890303i	$0.650493\pi$
$390$	−15.2996	−0.774727
$391$	−9.50310	−0.480593
$392$	0	0
$393$	−15.6096	−0.787402
$394$	0.137545	0.00692941
$395$	0.744325	0.0374511
$396$	3.43006	0.172367
$397$	0.443236	0.0222454	0.0111227	−	0.999938i	$-0.496459\pi$
$397$	0.443236	0.0222454	0.0111227	+	0.999938i	$0.496459\pi$
$398$	−49.8248	−2.49749
$399$	0	0
$400$	0.905171	0.0452585
$401$	29.6287	1.47959	0.739793	−	0.672834i	$-0.234923\pi$
$401$	29.6287	1.47959	0.739793	+	0.672834i	$0.234923\pi$
$402$	28.2046	1.40672
$403$	60.9239	3.03484
$404$	−36.1609	−1.79907
$405$	1.00000	0.0496904
$406$	0	0
$407$	6.98686	0.346326
$408$	−8.51590	−0.421600
$409$	−8.99186	−0.444619	−0.222310	−	0.974976i	$-0.571360\pi$
$409$	−8.99186	−0.444619	−0.222310	+	0.974976i	$0.571360\pi$
$410$	−13.6349	−0.673378
$411$	−2.23737	−0.110361
$412$	−20.3431	−1.00223
$413$	0	0
$414$	−8.66547	−0.425885
$415$	12.9061	0.633535
$416$	−29.9099	−1.46645
$417$	−12.3721	−0.605863
$418$	5.56567	0.272226
$419$	−16.4514	−0.803704	−0.401852	−	0.915705i	$-0.631633\pi$
$419$	−16.4514	−0.803704	−0.401852	+	0.915705i	$0.631633\pi$
$420$	0	0
$421$	−28.4904	−1.38854	−0.694268	−	0.719717i	$-0.744272\pi$
$421$	−28.4904	−1.38854	−0.694268	+	0.719717i	$0.744272\pi$
$422$	37.6668	1.83359
$423$	−1.22008	−0.0593223
$424$	5.71716	0.277650
$425$	2.55550	0.123960
$426$	−2.62420	−0.127143
$427$	0	0
$428$	57.5723	2.78286
$429$	−6.56567	−0.316993
$430$	−1.34469	−0.0648468
$431$	27.6688	1.33276	0.666379	−	0.745613i	$-0.267843\pi$
$431$	27.6688	1.33276	0.666379	+	0.745613i	$0.267843\pi$
$432$	−0.905171	−0.0435500
$433$	31.9507	1.53545	0.767727	−	0.640777i	$-0.221388\pi$
$433$	31.9507	1.53545	0.767727	+	0.640777i	$0.221388\pi$
$434$	0	0
$435$	4.34552	0.208352
$436$	−56.8321	−2.72176
$437$	−8.88189	−0.424878
$438$	17.8655	0.853647
$439$	−34.0895	−1.62701	−0.813503	−	0.581561i	$-0.802442\pi$
$439$	−34.0895	−1.62701	−0.813503	+	0.581561i	$0.802442\pi$
$440$	3.33238	0.158865
$441$	0	0
$442$	39.0982	1.85971
$443$	−41.1418	−1.95471	−0.977353	−	0.211615i	$-0.932128\pi$
$443$	−41.1418	−1.95471	−0.977353	+	0.211615i	$0.932128\pi$
$444$	−23.9653	−1.13734
$445$	16.0765	0.762100
$446$	21.1315	1.00061
$447$	−3.39043	−0.160362
$448$	0	0
$449$	−32.0369	−1.51191	−0.755957	−	0.654621i	$-0.772828\pi$
$449$	−32.0369	−1.51191	−0.755957	+	0.654621i	$0.772828\pi$
$450$	2.33025	0.109849
$451$	−5.85125	−0.275524
$452$	59.3314	2.79071
$453$	0.920629	0.0432549
$454$	31.0327	1.45644
$455$	0	0
$456$	−7.95921	−0.372724
$457$	−21.5638	−1.00871	−0.504357	−	0.863495i	$-0.668270\pi$
$457$	−21.5638	−1.00871	−0.504357	+	0.863495i	$0.668270\pi$
$458$	−41.8124	−1.95376
$459$	−2.55550	−0.119280
$460$	−12.7553	−0.594720
$461$	23.9259	1.11434	0.557171	−	0.830398i	$-0.311887\pi$
$461$	23.9259	1.11434	0.557171	+	0.830398i	$0.311887\pi$
$462$	0	0
$463$	−15.7595	−0.732407	−0.366203	−	0.930535i	$-0.619343\pi$
$463$	−15.7595	−0.732407	−0.366203	+	0.930535i	$0.619343\pi$
$464$	−3.93344	−0.182605
$465$	−9.27917	−0.430311
$466$	20.1821	0.934916
$467$	−0.419691	−0.0194210	−0.00971050	−	0.999953i	$-0.503091\pi$
$467$	−0.419691	−0.0194210	−0.00971050	+	0.999953i	$0.503091\pi$
$468$	22.5206	1.04102
$469$	0	0
$470$	−2.84309	−0.131142
$471$	19.6247	0.904261
$472$	39.2207	1.80528
$473$	−0.577059	−0.0265332
$474$	−1.73446	−0.0796665
$475$	2.38844	0.109589
$476$	0	0
$477$	1.71564	0.0785536
$478$	−13.7434	−0.628610
$479$	−31.9291	−1.45888	−0.729439	−	0.684046i	$-0.760219\pi$
$479$	−31.9291	−1.45888	−0.729439	+	0.684046i	$0.760219\pi$
$480$	4.55550	0.207929
$481$	45.8734	2.09165
$482$	−59.9907	−2.73250
$483$	0	0
$484$	3.43006	0.155912
$485$	4.43219	0.201255
$486$	−2.33025	−0.105702
$487$	9.01768	0.408630	0.204315	−	0.978905i	$-0.434503\pi$
$487$	9.01768	0.408630	0.204315	+	0.978905i	$0.434503\pi$
$488$	−33.6832	−1.52477
$489$	−10.1961	−0.461082
$490$	0	0
$491$	26.8024	1.20957	0.604787	−	0.796388i	$-0.293258\pi$
$491$	26.8024	1.20957	0.604787	+	0.796388i	$0.293258\pi$
$492$	20.0701	0.904830
$493$	−11.1050	−0.500142
$494$	36.5423	1.64412
$495$	1.00000	0.0449467
$496$	8.39923	0.377137
$497$	0	0
$498$	−30.0744	−1.34767
$499$	−13.4874	−0.603780	−0.301890	−	0.953343i	$-0.597618\pi$
$499$	−13.4874	−0.603780	−0.301890	+	0.953343i	$0.597618\pi$
$500$	3.43006	0.153397
$501$	0.708129	0.0316369
$502$	48.8925	2.18218
$503$	−0.989318	−0.0441115	−0.0220557	−	0.999757i	$-0.507021\pi$
$503$	−0.989318	−0.0441115	−0.0220557	+	0.999757i	$0.507021\pi$
$504$	0	0
$505$	−10.5424	−0.469129
$506$	−8.66547	−0.385227
$507$	−30.1080	−1.33714
$508$	−23.8892	−1.05991
$509$	13.6416	0.604655	0.302328	−	0.953204i	$-0.402236\pi$
$509$	13.6416	0.604655	0.302328	+	0.953204i	$0.402236\pi$
$510$	−5.95494	−0.263689
$511$	0	0
$512$	−10.1563	−0.448847
$513$	−2.38844	−0.105452
$514$	32.0298	1.41277
$515$	−5.93083	−0.261343
$516$	1.97935	0.0871358
$517$	−1.22008	−0.0536591
$518$	0	0
$519$	13.5334	0.594051
$520$	21.8793	0.959472
$521$	−30.3215	−1.32841	−0.664204	−	0.747552i	$-0.731229\pi$
$521$	−30.3215	−1.32841	−0.664204	+	0.747552i	$0.731229\pi$
$522$	−10.1261	−0.443209
$523$	9.56645	0.418312	0.209156	−	0.977882i	$-0.432928\pi$
$523$	9.56645	0.418312	0.209156	+	0.977882i	$0.432928\pi$
$524$	53.5419	2.33899
$525$	0	0
$526$	−61.5765	−2.68486
$527$	23.7129	1.03295
$528$	−0.905171	−0.0393925
$529$	−9.17133	−0.398753
$530$	3.99786	0.173656
$531$	11.7696	0.510755
$532$	0	0
$533$	−38.4173	−1.66404
$534$	−37.4623	−1.62115
$535$	16.7846	0.725664
$536$	−40.3341	−1.74217
$537$	13.9753	0.603078
$538$	50.1085	2.16033
$539$	0	0
$540$	−3.43006	−0.147606
$541$	22.7800	0.979390	0.489695	−	0.871894i	$-0.337108\pi$
$541$	22.7800	0.979390	0.489695	+	0.871894i	$0.337108\pi$
$542$	−30.2847	−1.30084
$543$	−9.94639	−0.426840
$544$	−11.6416	−0.499128
$545$	−16.5688	−0.709731
$546$	0	0
$547$	−41.7796	−1.78637	−0.893184	−	0.449691i	$-0.851534\pi$
$547$	−41.7796	−1.78637	−0.893184	+	0.449691i	$0.851534\pi$
$548$	7.67430	0.327830
$549$	−10.1078	−0.431392
$550$	2.33025	0.0993621
$551$	−10.3790	−0.442162
$552$	12.3921	0.527443
$553$	0	0
$554$	−35.3812	−1.50320
$555$	−6.98686	−0.296576
$556$	42.4369	1.79973
$557$	−14.6582	−0.621090	−0.310545	−	0.950559i	$-0.600511\pi$
$557$	−14.6582	−0.621090	−0.310545	+	0.950559i	$0.600511\pi$
$558$	21.6228	0.915364
$559$	−3.78878	−0.160248
$560$	0	0
$561$	−2.55550	−0.107893
$562$	22.0287	0.929224
$563$	−10.5178	−0.443274	−0.221637	−	0.975129i	$-0.571140\pi$
$563$	−10.5178	−0.443274	−0.221637	+	0.975129i	$0.571140\pi$
$564$	4.18494	0.176218
$565$	17.2975	0.727711
$566$	42.3644	1.78071
$567$	0	0
$568$	3.75275	0.157462
$569$	−5.00689	−0.209900	−0.104950	−	0.994478i	$-0.533468\pi$
$569$	−5.00689	−0.209900	−0.104950	+	0.994478i	$0.533468\pi$
$570$	−5.56567	−0.233120
$571$	−8.53669	−0.357249	−0.178625	−	0.983917i	$-0.557165\pi$
$571$	−8.53669	−0.357249	−0.178625	+	0.983917i	$0.557165\pi$
$572$	22.5206	0.941634
$573$	−12.4829	−0.521480
$574$	0	0
$575$	−3.71869	−0.155080
$576$	−12.4258	−0.517741
$577$	−7.15949	−0.298054	−0.149027	−	0.988833i	$-0.547614\pi$
$577$	−7.15949	−0.298054	−0.149027	+	0.988833i	$0.547614\pi$
$578$	−24.3964	−1.01476
$579$	−1.71866	−0.0714252
$580$	−14.9054	−0.618912
$581$	0	0
$582$	−10.3281	−0.428114
$583$	1.71564	0.0710544
$584$	−25.5487	−1.05721
$585$	6.56567	0.271457
$586$	−67.0995	−2.77186
$587$	−29.4112	−1.21393	−0.606964	−	0.794729i	$-0.707613\pi$
$587$	−29.4112	−1.21393	−0.606964	+	0.794729i	$0.707613\pi$
$588$	0	0
$589$	22.1628	0.913201
$590$	27.4260	1.12911
$591$	−0.0590259	−0.00242800
$592$	6.32430	0.259927
$593$	−1.54545	−0.0634642	−0.0317321	−	0.999496i	$-0.510102\pi$
$593$	−1.54545	−0.0634642	−0.0317321	+	0.999496i	$0.510102\pi$
$594$	−2.33025	−0.0956112
$595$	0	0
$596$	11.6294	0.476358
$597$	21.3818	0.875097
$598$	−56.8946	−2.32659
$599$	10.5213	0.429890	0.214945	−	0.976626i	$-0.431043\pi$
$599$	10.5213	0.429890	0.214945	+	0.976626i	$0.431043\pi$
$600$	−3.33238	−0.136044
$601$	35.8037	1.46046	0.730232	−	0.683199i	$-0.239412\pi$
$601$	35.8037	1.46046	0.730232	+	0.683199i	$0.239412\pi$
$602$	0	0
$603$	−12.1037	−0.492900
$604$	−3.15781	−0.128489
$605$	1.00000	0.0406558
$606$	24.5663	0.997938
$607$	−0.564007	−0.0228923	−0.0114462	−	0.999934i	$-0.503644\pi$
$607$	−0.564007	−0.0228923	−0.0114462	+	0.999934i	$0.503644\pi$
$608$	−10.8805	−0.441264
$609$	0	0
$610$	−23.5538	−0.953664
$611$	−8.01064	−0.324076
$612$	8.76550	0.354324
$613$	−13.6564	−0.551576	−0.275788	−	0.961218i	$-0.588939\pi$
$613$	−13.6564	−0.551576	−0.275788	+	0.961218i	$0.588939\pi$
$614$	60.0124	2.42190
$615$	5.85125	0.235945
$616$	0	0
$617$	−26.4948	−1.06664	−0.533320	−	0.845913i	$-0.679056\pi$
$617$	−26.4948	−1.06664	−0.533320	+	0.845913i	$0.679056\pi$
$618$	13.8203	0.555934
$619$	−12.2166	−0.491025	−0.245513	−	0.969393i	$-0.578956\pi$
$619$	−12.2166	−0.491025	−0.245513	+	0.969393i	$0.578956\pi$
$620$	31.8281	1.27825
$621$	3.71869	0.149226
$622$	16.2069	0.649836
$623$	0	0
$624$	−5.94305	−0.237912
$625$	1.00000	0.0400000
$626$	37.1546	1.48500
$627$	−2.38844	−0.0953853
$628$	−67.3140	−2.68612
$629$	17.8549	0.711921
$630$	0	0
$631$	−15.4089	−0.613417	−0.306709	−	0.951803i	$-0.599228\pi$
$631$	−15.4089	−0.613417	−0.306709	+	0.951803i	$0.599228\pi$
$632$	2.48038	0.0986641
$633$	−16.1643	−0.642473
$634$	14.2508	0.565973
$635$	−6.96467	−0.276385
$636$	−5.88473	−0.233345
$637$	0	0
$638$	−10.1261	−0.400898
$639$	1.12615	0.0445497
$640$	−19.8442	−0.784409
$641$	−13.9149	−0.549607	−0.274803	−	0.961500i	$-0.588613\pi$
$641$	−13.9149	−0.549607	−0.274803	+	0.961500i	$0.588613\pi$
$642$	−39.1124	−1.54364
$643$	16.1658	0.637519	0.318759	−	0.947836i	$-0.396734\pi$
$643$	16.1658	0.637519	0.318759	+	0.947836i	$0.396734\pi$
$644$	0	0
$645$	0.577059	0.0227217
$646$	14.2230	0.559598
$647$	29.6850	1.16704	0.583519	−	0.812100i	$-0.301675\pi$
$647$	29.6850	1.16704	0.583519	+	0.812100i	$0.301675\pi$
$648$	3.33238	0.130908
$649$	11.7696	0.461995
$650$	15.2996	0.600101
$651$	0	0
$652$	34.9731	1.36965
$653$	−0.310300	−0.0121430	−0.00607149	−	0.999982i	$-0.501933\pi$
$653$	−0.310300	−0.0121430	−0.00607149	+	0.999982i	$0.501933\pi$
$654$	38.6095	1.50975
$655$	15.6096	0.609919
$656$	−5.29638	−0.206789
$657$	−7.66678	−0.299110
$658$	0	0
$659$	22.0773	0.860008	0.430004	−	0.902827i	$-0.358512\pi$
$659$	22.0773	0.860008	0.430004	+	0.902827i	$0.358512\pi$
$660$	−3.43006	−0.133515
$661$	−44.4597	−1.72928	−0.864641	−	0.502390i	$-0.832454\pi$
$661$	−44.4597	−1.72928	−0.864641	+	0.502390i	$0.832454\pi$
$662$	5.16150	0.200607
$663$	−16.7785	−0.651624
$664$	43.0080	1.66904
$665$	0	0
$666$	16.2811	0.630880
$667$	16.1597	0.625704
$668$	−2.42892	−0.0939779
$669$	−9.06835	−0.350603
$670$	−28.2046	−1.08964
$671$	−10.1078	−0.390209
$672$	0	0
$673$	−5.27727	−0.203424	−0.101712	−	0.994814i	$-0.532432\pi$
$673$	−5.27727	−0.203424	−0.101712	+	0.994814i	$0.532432\pi$
$674$	−30.2643	−1.16574
$675$	−1.00000	−0.0384900
$676$	103.272	3.97200
$677$	−47.1912	−1.81371	−0.906853	−	0.421447i	$-0.861522\pi$
$677$	−47.1912	−1.81371	−0.906853	+	0.421447i	$0.861522\pi$
$678$	−40.3074	−1.54800
$679$	0	0
$680$	8.51590	0.326570
$681$	−13.3174	−0.510322
$682$	21.6228	0.827978
$683$	−16.9902	−0.650113	−0.325057	−	0.945695i	$-0.605383\pi$
$683$	−16.9902	−0.650113	−0.325057	+	0.945695i	$0.605383\pi$
$684$	8.19250	0.313248
$685$	2.23737	0.0854855
$686$	0	0
$687$	17.9433	0.684580
$688$	−0.522337	−0.0199139
$689$	11.2643	0.429136
$690$	8.66547	0.329889
$691$	−11.6357	−0.442642	−0.221321	−	0.975201i	$-0.571037\pi$
$691$	−11.6357	−0.442642	−0.221321	+	0.975201i	$0.571037\pi$
$692$	−46.4204	−1.76464
$693$	0	0
$694$	−13.6620	−0.518602
$695$	12.3721	0.469299
$696$	14.4809	0.548899
$697$	−14.9528	−0.566379
$698$	−23.2122	−0.878594
$699$	−8.66091	−0.327586
$700$	0	0
$701$	6.31631	0.238564	0.119282	−	0.992860i	$-0.461941\pi$
$701$	6.31631	0.238564	0.119282	+	0.992860i	$0.461941\pi$
$702$	−15.2996	−0.577447
$703$	16.6877	0.629389
$704$	−12.4258	−0.468314
$705$	1.22008	0.0459509
$706$	−16.1091	−0.606276
$707$	0	0
$708$	−40.3702	−1.51721
$709$	16.9654	0.637147	0.318574	−	0.947898i	$-0.396796\pi$
$709$	16.9654	0.637147	0.318574	+	0.947898i	$0.396796\pi$
$710$	2.62420	0.0984845
$711$	0.744325	0.0279144
$712$	53.5731	2.00774
$713$	−34.5064	−1.29227
$714$	0	0
$715$	6.56567	0.245542
$716$	−47.9360	−1.79145
$717$	5.89784	0.220259
$718$	11.8751	0.443175
$719$	9.53294	0.355519	0.177759	−	0.984074i	$-0.443115\pi$
$719$	9.53294	0.355519	0.177759	+	0.984074i	$0.443115\pi$
$720$	0.905171	0.0337337
$721$	0	0
$722$	−30.9814	−1.15301
$723$	25.7444	0.957443
$724$	34.1167	1.26794
$725$	−4.34552	−0.161389
$726$	−2.33025	−0.0864836
$727$	−45.7753	−1.69771	−0.848855	−	0.528625i	$-0.822708\pi$
$727$	−45.7753	−1.69771	−0.848855	+	0.528625i	$0.822708\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−17.8655	−0.661232
$731$	−1.47467	−0.0545427
$732$	34.6704	1.28146
$733$	−6.54970	−0.241919	−0.120959	−	0.992657i	$-0.538597\pi$
$733$	−6.54970	−0.241919	−0.120959	+	0.992657i	$0.538597\pi$
$734$	36.5101	1.34761
$735$	0	0
$736$	16.9405	0.624435
$737$	−12.1037	−0.445845
$738$	−13.6349	−0.501906
$739$	−20.6539	−0.759768	−0.379884	−	0.925034i	$-0.624036\pi$
$739$	−20.6539	−0.759768	−0.379884	+	0.925034i	$0.624036\pi$
$740$	23.9653	0.880983
$741$	−15.6817	−0.576083
$742$	0	0
$743$	39.7387	1.45787	0.728936	−	0.684582i	$-0.240015\pi$
$743$	39.7387	1.45787	0.728936	+	0.684582i	$0.240015\pi$
$744$	−30.9218	−1.13365
$745$	3.39043	0.124216
$746$	−51.3918	−1.88159
$747$	12.9061	0.472209
$748$	8.76550	0.320498
$749$	0	0
$750$	−2.33025	−0.0850886
$751$	42.5246	1.55175	0.775873	−	0.630889i	$-0.217310\pi$
$751$	42.5246	1.55175	0.775873	+	0.630889i	$0.217310\pi$
$752$	−1.10438	−0.0402726
$753$	−20.9817	−0.764615
$754$	−66.4849	−2.42124
$755$	−0.920629	−0.0335051
$756$	0	0
$757$	−37.5157	−1.36353	−0.681767	−	0.731570i	$-0.738788\pi$
$757$	−37.5157	−1.36353	−0.681767	+	0.731570i	$0.738788\pi$
$758$	17.2451	0.626371
$759$	3.71869	0.134980
$760$	7.95921	0.288711
$761$	−44.9932	−1.63100	−0.815501	−	0.578755i	$-0.803539\pi$
$761$	−44.9932	−1.63100	−0.815501	+	0.578755i	$0.803539\pi$
$762$	16.2294	0.587930
$763$	0	0
$764$	42.8170	1.54906
$765$	2.55550	0.0923942
$766$	39.1484	1.41449
$767$	77.2750	2.79024
$768$	21.3902	0.771854
$769$	−0.330307	−0.0119112	−0.00595559	−	0.999982i	$-0.501896\pi$
$769$	−0.330307	−0.0119112	−0.00595559	+	0.999982i	$0.501896\pi$
$770$	0	0
$771$	−13.7452	−0.495023
$772$	5.89511	0.212170
$773$	−7.69570	−0.276795	−0.138398	−	0.990377i	$-0.544195\pi$
$773$	−7.69570	−0.276795	−0.138398	+	0.990377i	$0.544195\pi$
$774$	−1.34469	−0.0483339
$775$	9.27917	0.333318
$776$	14.7698	0.530204
$777$	0	0
$778$	−41.8572	−1.50065
$779$	−13.9754	−0.500720
$780$	−22.5206	−0.806367
$781$	1.12615	0.0402967
$782$	−22.1446	−0.791889
$783$	4.34552	0.155296
$784$	0	0
$785$	−19.6247	−0.700437
$786$	−36.3743	−1.29743
$787$	27.0391	0.963839	0.481919	−	0.876216i	$-0.339940\pi$
$787$	27.0391	0.963839	0.481919	+	0.876216i	$0.339940\pi$
$788$	0.202462	0.00721241
$789$	26.4249	0.940750
$790$	1.73446	0.0617094
$791$	0	0
$792$	3.33238	0.118411
$793$	−66.3647	−2.35668
$794$	1.03285	0.0366545
$795$	−1.71564	−0.0608474
$796$	−73.3406	−2.59949
$797$	13.7899	0.488465	0.244232	−	0.969717i	$-0.421464\pi$
$797$	13.7899	0.488465	0.244232	+	0.969717i	$0.421464\pi$
$798$	0	0
$799$	−3.11791	−0.110304
$800$	−4.55550	−0.161061
$801$	16.0765	0.568036
$802$	69.0422	2.43796
$803$	−7.66678	−0.270555
$804$	41.5163	1.46417
$805$	0	0
$806$	141.968	5.00060
$807$	−21.5035	−0.756960
$808$	−35.1312	−1.23591
$809$	24.3164	0.854919	0.427460	−	0.904034i	$-0.359409\pi$
$809$	24.3164	0.854919	0.427460	+	0.904034i	$0.359409\pi$
$810$	2.33025	0.0818766
$811$	−25.5442	−0.896978	−0.448489	−	0.893788i	$-0.648038\pi$
$811$	−25.5442	−0.896978	−0.448489	+	0.893788i	$0.648038\pi$
$812$	0	0
$813$	12.9964	0.455802
$814$	16.2811	0.570653
$815$	10.1961	0.357153
$816$	−2.31316	−0.0809768
$817$	−1.37827	−0.0482197
$818$	−20.9533	−0.732614
$819$	0	0
$820$	−20.0701	−0.700878
$821$	32.5200	1.13496	0.567478	−	0.823389i	$-0.307919\pi$
$821$	32.5200	1.13496	0.567478	+	0.823389i	$0.307919\pi$
$822$	−5.21363	−0.181846
$823$	−46.8394	−1.63272	−0.816359	−	0.577544i	$-0.804011\pi$
$823$	−46.8394	−1.63272	−0.816359	+	0.577544i	$0.804011\pi$
$824$	−19.7638	−0.688504
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	36.2843	1.26173	0.630864	−	0.775893i	$-0.282701\pi$
$827$	36.2843	1.26173	0.630864	+	0.775893i	$0.282701\pi$
$828$	−12.7553	−0.443278
$829$	38.5594	1.33922	0.669612	−	0.742711i	$-0.266461\pi$
$829$	38.5594	1.33922	0.669612	+	0.742711i	$0.266461\pi$
$830$	30.0744	1.04390
$831$	15.1834	0.526708
$832$	−81.5835	−2.82840
$833$	0	0
$834$	−28.8300	−0.998301
$835$	−0.708129	−0.0245058
$836$	8.19250	0.283343
$837$	−9.27917	−0.320735
$838$	−38.3358	−1.32429
$839$	40.9551	1.41393	0.706964	−	0.707249i	$-0.250064\pi$
$839$	40.9551	1.41393	0.706964	+	0.707249i	$0.250064\pi$
$840$	0	0
$841$	−10.1164	−0.348843
$842$	−66.3896	−2.28794
$843$	−9.45336	−0.325591
$844$	55.4445	1.90848
$845$	30.1080	1.03575
$846$	−2.84309	−0.0977474
$847$	0	0
$848$	1.55294	0.0533283
$849$	−18.1802	−0.623943
$850$	5.95494	0.204253
$851$	−25.9820	−0.890651
$852$	−3.86274	−0.132335
$853$	−55.8708	−1.91298	−0.956489	−	0.291768i	$-0.905756\pi$
$853$	−55.8708	−1.91298	−0.956489	+	0.291768i	$0.905756\pi$
$854$	0	0
$855$	2.38844	0.0816831
$856$	55.9329	1.91175
$857$	−6.09782	−0.208298	−0.104149	−	0.994562i	$-0.533212\pi$
$857$	−6.09782	−0.208298	−0.104149	+	0.994562i	$0.533212\pi$
$858$	−15.2996	−0.522321
$859$	−27.9037	−0.952062	−0.476031	−	0.879428i	$-0.657925\pi$
$859$	−27.9037	−0.952062	−0.476031	+	0.879428i	$0.657925\pi$
$860$	−1.97935	−0.0674951
$861$	0	0
$862$	64.4751	2.19603
$863$	−30.5230	−1.03901	−0.519507	−	0.854466i	$-0.673885\pi$
$863$	−30.5230	−1.03901	−0.519507	+	0.854466i	$0.673885\pi$
$864$	4.55550	0.154981
$865$	−13.5334	−0.460150
$866$	74.4531	2.53002
$867$	10.4694	0.355561
$868$	0	0
$869$	0.744325	0.0252495
$870$	10.1261	0.343308
$871$	−79.4688	−2.69270
$872$	−55.2138	−1.86977
$873$	4.43219	0.150007
$874$	−20.6970	−0.700086
$875$	0	0
$876$	26.2975	0.888510
$877$	−36.1262	−1.21989	−0.609947	−	0.792442i	$-0.708809\pi$
$877$	−36.1262	−1.21989	−0.609947	+	0.792442i	$0.708809\pi$
$878$	−79.4371	−2.68087
$879$	28.7950	0.971232
$880$	0.905171	0.0305133
$881$	42.0321	1.41610	0.708048	−	0.706164i	$-0.249576\pi$
$881$	42.0321	1.41610	0.708048	+	0.706164i	$0.249576\pi$
$882$	0	0
$883$	−37.1106	−1.24887	−0.624436	−	0.781076i	$-0.714671\pi$
$883$	−37.1106	−1.24887	−0.624436	+	0.781076i	$0.714671\pi$
$884$	57.5513	1.93566
$885$	−11.7696	−0.395629
$886$	−95.8706	−3.22084
$887$	−27.8091	−0.933738	−0.466869	−	0.884326i	$-0.654618\pi$
$887$	−27.8091	−0.933738	−0.466869	+	0.884326i	$0.654618\pi$
$888$	−23.2829	−0.781323
$889$	0	0
$890$	37.4623	1.25574
$891$	1.00000	0.0335013
$892$	31.1049	1.04147
$893$	−2.91409	−0.0975164
$894$	−7.90055	−0.264234
$895$	−13.9753	−0.467142
$896$	0	0
$897$	24.4157	0.815216
$898$	−74.6539	−2.49123
$899$	−40.3228	−1.34484
$900$	3.43006	0.114335
$901$	4.38430	0.146062
$902$	−13.6349	−0.453991
$903$	0	0
$904$	57.6419	1.91714
$905$	9.94639	0.330629
$906$	2.14529	0.0712726
$907$	14.9836	0.497523	0.248761	−	0.968565i	$-0.419977\pi$
$907$	14.9836	0.497523	0.248761	+	0.968565i	$0.419977\pi$
$908$	45.6793	1.51592
$909$	−10.5424	−0.349668
$910$	0	0
$911$	−24.1417	−0.799851	−0.399925	−	0.916548i	$-0.630964\pi$
$911$	−24.1417	−0.799851	−0.399925	+	0.916548i	$0.630964\pi$
$912$	−2.16195	−0.0715893
$913$	12.9061	0.427129
$914$	−50.2491	−1.66209
$915$	10.1078	0.334155
$916$	−61.5466	−2.03356
$917$	0	0
$918$	−5.95494	−0.196542
$919$	−27.3335	−0.901649	−0.450825	−	0.892613i	$-0.648870\pi$
$919$	−27.3335	−0.901649	−0.450825	+	0.892613i	$0.648870\pi$
$920$	−12.3921	−0.408556
$921$	−25.7537	−0.848612
$922$	55.7534	1.83614
$923$	7.39390	0.243373
$924$	0	0
$925$	6.98686	0.229727
$926$	−36.7236	−1.20681
$927$	−5.93083	−0.194794
$928$	19.7960	0.649836
$929$	9.52488	0.312501	0.156251	−	0.987717i	$-0.450059\pi$
$929$	9.52488	0.312501	0.156251	+	0.987717i	$0.450059\pi$
$930$	−21.6228	−0.709038
$931$	0	0
$932$	29.7074	0.973099
$933$	−6.95499	−0.227696
$934$	−0.977984	−0.0320006
$935$	2.55550	0.0835737
$936$	21.8793	0.715148
$937$	−9.95761	−0.325301	−0.162650	−	0.986684i	$-0.552004\pi$
$937$	−9.95761	−0.325301	−0.162650	+	0.986684i	$0.552004\pi$
$938$	0	0
$939$	−15.9445	−0.520328
$940$	−4.18494	−0.136498
$941$	−21.2617	−0.693113	−0.346556	−	0.938029i	$-0.612649\pi$
$941$	−21.2617	−0.693113	−0.346556	+	0.938029i	$0.612649\pi$
$942$	45.7305	1.48998
$943$	21.7590	0.708570
$944$	10.6535	0.346741
$945$	0	0
$946$	−1.34469	−0.0437197
$947$	−9.61638	−0.312491	−0.156245	−	0.987718i	$-0.549939\pi$
$947$	−9.61638	−0.312491	−0.156245	+	0.987718i	$0.549939\pi$
$948$	−2.55308	−0.0829201
$949$	−50.3375	−1.63403
$950$	5.56567	0.180574
$951$	−6.11558	−0.198311
$952$	0	0
$953$	−16.6598	−0.539665	−0.269833	−	0.962907i	$-0.586968\pi$
$953$	−16.6598	−0.539665	−0.269833	+	0.962907i	$0.586968\pi$
$954$	3.99786	0.129435
$955$	12.4829	0.403937
$956$	−20.2299	−0.654282
$957$	4.34552	0.140471
$958$	−74.4027	−2.40384
$959$	0	0
$960$	12.4258	0.401040
$961$	55.1029	1.77751
$962$	106.896	3.44648
$963$	16.7846	0.540878
$964$	−88.3046	−2.84410
$965$	1.71866	0.0553257
$966$	0	0
$967$	8.39085	0.269831	0.134916	−	0.990857i	$-0.456924\pi$
$967$	8.39085	0.269831	0.134916	+	0.990857i	$0.456924\pi$
$968$	3.33238	0.107107
$969$	−6.10366	−0.196078
$970$	10.3281	0.331616
$971$	−47.8541	−1.53571	−0.767855	−	0.640623i	$-0.778676\pi$
$971$	−47.8541	−1.53571	−0.767855	+	0.640623i	$0.778676\pi$
$972$	−3.43006	−0.110019
$973$	0	0
$974$	21.0134	0.673314
$975$	−6.56567	−0.210270
$976$	−9.14932	−0.292863
$977$	27.5644	0.881862	0.440931	−	0.897541i	$-0.354648\pi$
$977$	27.5644	0.881862	0.440931	+	0.897541i	$0.354648\pi$
$978$	−23.7594	−0.759740
$979$	16.0765	0.513808
$980$	0	0
$981$	−16.5688	−0.529002
$982$	62.4561	1.99306
$983$	−14.6530	−0.467359	−0.233680	−	0.972314i	$-0.575077\pi$
$983$	−14.6530	−0.467359	−0.233680	+	0.972314i	$0.575077\pi$
$984$	19.4986	0.621593
$985$	0.0590259	0.00188072
$986$	−25.8773	−0.824102
$987$	0	0
$988$	53.7892	1.71126
$989$	2.14591	0.0682358
$990$	2.33025	0.0740601
$991$	47.0503	1.49460	0.747301	−	0.664486i	$-0.231349\pi$
$991$	47.0503	1.49460	0.747301	+	0.664486i	$0.231349\pi$
$992$	−42.2712	−1.34211
$993$	−2.21500	−0.0702909
$994$	0	0
$995$	−21.3818	−0.677847
$996$	−44.2686	−1.40270
$997$	−9.86987	−0.312582	−0.156291	−	0.987711i	$-0.549954\pi$
$997$	−9.86987	−0.312582	−0.156291	+	0.987711i	$0.549954\pi$
$998$	−31.4291	−0.994869
$999$	−6.98686	−0.221054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.bx.1.6		6
7.3	odd	6		1155.2.q.h.331.1	✓	12
7.5	odd	6		1155.2.q.h.991.1	yes	12
7.6	odd	2		8085.2.a.bz.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.h.331.1	✓	12	7.3	odd	6
1155.2.q.h.991.1	yes	12	7.5	odd	6
8085.2.a.bx.1.6		6	1.1	even	1	trivial
8085.2.a.bz.1.6		6	7.6	odd	2

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:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q+2.33025 q^{2} -1.00000 q^{3} +3.43006 q^{4} +1.00000 q^{5} -2.33025 q^{6} +3.33238 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.33025 q^{2} -1.00000 q^{3} +3.43006 q^{4} +1.00000 q^{5} -2.33025 q^{6} +3.33238 q^{8} +1.00000 q^{9} +2.33025 q^{10} +1.00000 q^{11} -3.43006 q^{12} +6.56567 q^{13} -1.00000 q^{15} +0.905171 q^{16} +2.55550 q^{17} +2.33025 q^{18} +2.38844 q^{19} +3.43006 q^{20} +2.33025 q^{22} -3.71869 q^{23} -3.33238 q^{24} +1.00000 q^{25} +15.2996 q^{26} -1.00000 q^{27} -4.34552 q^{29} -2.33025 q^{30} +9.27917 q^{31} -4.55550 q^{32} -1.00000 q^{33} +5.95494 q^{34} +3.43006 q^{36} +6.98686 q^{37} +5.56567 q^{38} -6.56567 q^{39} +3.33238 q^{40} -5.85125 q^{41} -0.577059 q^{43} +3.43006 q^{44} +1.00000 q^{45} -8.66547 q^{46} -1.22008 q^{47} -0.905171 q^{48} +2.33025 q^{50} -2.55550 q^{51} +22.5206 q^{52} +1.71564 q^{53} -2.33025 q^{54} +1.00000 q^{55} -2.38844 q^{57} -10.1261 q^{58} +11.7696 q^{59} -3.43006 q^{60} -10.1078 q^{61} +21.6228 q^{62} -12.4258 q^{64} +6.56567 q^{65} -2.33025 q^{66} -12.1037 q^{67} +8.76550 q^{68} +3.71869 q^{69} +1.12615 q^{71} +3.33238 q^{72} -7.66678 q^{73} +16.2811 q^{74} -1.00000 q^{75} +8.19250 q^{76} -15.2996 q^{78} +0.744325 q^{79} +0.905171 q^{80} +1.00000 q^{81} -13.6349 q^{82} +12.9061 q^{83} +2.55550 q^{85} -1.34469 q^{86} +4.34552 q^{87} +3.33238 q^{88} +16.0765 q^{89} +2.33025 q^{90} -12.7553 q^{92} -9.27917 q^{93} -2.84309 q^{94} +2.38844 q^{95} +4.55550 q^{96} +4.43219 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^9	\( 6 q - 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{9} + 6 q^{11} - 6 q^{12} + 4 q^{13} - 6 q^{15} - 2 q^{16} - 2 q^{17} + 13 q^{19} + 6 q^{20} - 7 q^{23} + 6 q^{25} + 26 q^{26} - 6 q^{27} + 3 q^{29} + 15 q^{31} - 10 q^{32} - 6 q^{33} + 14 q^{34} + 6 q^{36} - 11 q^{37} - 2 q^{38} - 4 q^{39} - 3 q^{41} - 4 q^{43} + 6 q^{44} + 6 q^{45} - 16 q^{46} + 19 q^{47} + 2 q^{48} + 2 q^{51} + 16 q^{52} - q^{53} + 6 q^{55} - 13 q^{57} + 22 q^{59} - 6 q^{60} + 14 q^{61} + 2 q^{62} - 10 q^{64} + 4 q^{65} - 21 q^{67} + 14 q^{68} + 7 q^{69} + 8 q^{71} + 11 q^{73} + 20 q^{74} - 6 q^{75} - 26 q^{78} - 13 q^{79} - 2 q^{80} + 6 q^{81} + 6 q^{82} + 10 q^{83} - 2 q^{85} + 36 q^{86} - 3 q^{87} + 28 q^{89} + 6 q^{92} - 15 q^{93} + 14 q^{94} + 13 q^{95} + 10 q^{96} + 6 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^9 + 6 * q^11 - 6 * q^12 + 4 * q^13 - 6 * q^15 - 2 * q^16 - 2 * q^17 + 13 * q^19 + 6 * q^20 - 7 * q^23 + 6 * q^25 + 26 * q^26 - 6 * q^27 + 3 * q^29 + 15 * q^31 - 10 * q^32 - 6 * q^33 + 14 * q^34 + 6 * q^36 - 11 * q^37 - 2 * q^38 - 4 * q^39 - 3 * q^41 - 4 * q^43 + 6 * q^44 + 6 * q^45 - 16 * q^46 + 19 * q^47 + 2 * q^48 + 2 * q^51 + 16 * q^52 - q^53 + 6 * q^55 - 13 * q^57 + 22 * q^59 - 6 * q^60 + 14 * q^61 + 2 * q^62 - 10 * q^64 + 4 * q^65 - 21 * q^67 + 14 * q^68 + 7 * q^69 + 8 * q^71 + 11 * q^73 + 20 * q^74 - 6 * q^75 - 26 * q^78 - 13 * q^79 - 2 * q^80 + 6 * q^81 + 6 * q^82 + 10 * q^83 - 2 * q^85 + 36 * q^86 - 3 * q^87 + 28 * q^89 + 6 * q^92 - 15 * q^93 + 14 * q^94 + 13 * q^95 + 10 * q^96 + 6 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more