LMFDB - Embedded newform 605.6.a.e.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,6,Mod(1,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$97.0322109869$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 149x^{4} + 297x^{3} + 4052x^{2} - 6522x - 20692 $ x^6 - 3x^5 - 149x^4 + 297x^3 + 4052x^2 - 6522*x - 20692
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.01414$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.01414 q^{2} -13.7145 q^{3} -22.9149 q^{4} -25.0000 q^{5} -41.3374 q^{6} +131.565 q^{7} -165.521 q^{8} -54.9135 q^{9} -75.3536 q^{10} +314.266 q^{12} -598.870 q^{13} +396.555 q^{14} +342.862 q^{15} +234.373 q^{16} +1336.53 q^{17} -165.517 q^{18} -2886.27 q^{19} +572.874 q^{20} -1804.34 q^{21} -2048.71 q^{23} +2270.04 q^{24} +625.000 q^{25} -1805.08 q^{26} +4085.72 q^{27} -3014.80 q^{28} -5800.71 q^{29} +1033.43 q^{30} -9529.52 q^{31} +6003.12 q^{32} +4028.50 q^{34} -3289.12 q^{35} +1258.34 q^{36} -8187.53 q^{37} -8699.64 q^{38} +8213.18 q^{39} +4138.04 q^{40} -13471.0 q^{41} -5438.54 q^{42} +6524.24 q^{43} +1372.84 q^{45} -6175.12 q^{46} -8172.53 q^{47} -3214.29 q^{48} +502.291 q^{49} +1883.84 q^{50} -18329.8 q^{51} +13723.1 q^{52} +33262.9 q^{53} +12315.0 q^{54} -21776.8 q^{56} +39583.7 q^{57} -17484.2 q^{58} +33630.9 q^{59} -7856.65 q^{60} -46455.0 q^{61} -28723.3 q^{62} -7224.68 q^{63} +10594.3 q^{64} +14971.7 q^{65} +1838.70 q^{67} -30626.6 q^{68} +28097.0 q^{69} -9913.88 q^{70} +37198.6 q^{71} +9089.37 q^{72} -33497.7 q^{73} -24678.4 q^{74} -8571.54 q^{75} +66138.8 q^{76} +24755.7 q^{78} -38783.5 q^{79} -5859.31 q^{80} -42689.5 q^{81} -40603.6 q^{82} -350.204 q^{83} +41346.4 q^{84} -33413.3 q^{85} +19665.0 q^{86} +79553.6 q^{87} +15929.8 q^{89} +4137.93 q^{90} -78790.2 q^{91} +46946.2 q^{92} +130692. q^{93} -24633.2 q^{94} +72156.8 q^{95} -82329.6 q^{96} +25331.2 q^{97} +1513.98 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 115 q^{4} - 150 q^{5} - 325 q^{6} + 66 q^{7} - 249 q^{8} + 832 q^{9} + 75 q^{10} + 1301 q^{12} + 972 q^{13} + 2017 q^{14} + 6675 q^{16} - 712 q^{17} - 5920 q^{18} - 610 q^{19} - 2875 q^{20}+ \cdots + 351884 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 115 * q^4 - 150 * q^5 - 325 * q^6 + 66 * q^7 - 249 * q^8 + 832 * q^9 + 75 * q^10 + 1301 * q^12 + 972 * q^13 + 2017 * q^14 + 6675 * q^16 - 712 * q^17 - 5920 * q^18 - 610 * q^19 - 2875 * q^20 - 2508 * q^21 + 7100 * q^23 - 13447 * q^24 + 3750 * q^25 - 7742 * q^26 - 2520 * q^27 + 33171 * q^28 - 10964 * q^29 + 8125 * q^30 + 8868 * q^31 - 10861 * q^32 - 42673 * q^34 - 1650 * q^35 - 30116 * q^36 - 15506 * q^37 + 26185 * q^38 - 7208 * q^39 + 6225 * q^40 - 160 * q^41 - 47111 * q^42 - 7032 * q^43 - 20800 * q^45 - 1650 * q^46 - 46320 * q^47 - 22215 * q^48 + 48512 * q^49 - 1875 * q^50 + 43378 * q^51 + 145838 * q^52 + 30518 * q^53 + 56881 * q^54 - 21297 * q^56 + 5640 * q^57 + 51477 * q^58 + 120532 * q^59 - 32525 * q^60 + 9228 * q^61 + 81355 * q^62 - 222460 * q^63 + 302839 * q^64 - 24300 * q^65 + 47432 * q^67 - 78111 * q^68 + 118960 * q^69 - 50425 * q^70 + 163948 * q^71 + 212580 * q^72 - 78528 * q^73 - 133501 * q^74 + 29355 * q^76 - 138086 * q^78 + 36712 * q^79 - 166875 * q^80 + 202166 * q^81 - 128902 * q^82 - 133792 * q^83 - 119033 * q^84 + 17800 * q^85 + 83996 * q^86 + 267082 * q^87 + 254946 * q^89 + 148000 * q^90 + 167844 * q^91 - 5134 * q^92 - 224250 * q^93 - 31414 * q^94 + 15250 * q^95 - 234415 * q^96 + 17404 * q^97 + 351884 * q^98

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 $

$2$	3.01414	0.532830	0.266415	−	0.963858i	$-0.414161\pi$
$2$	3.01414	0.532830	0.266415	+	0.963858i	$0.414161\pi$
$3$	−13.7145	−0.879783	−0.439892	−	0.898051i	$-0.644983\pi$
$3$	−13.7145	−0.879783	−0.439892	+	0.898051i	$0.644983\pi$
$4$	−22.9149	−0.716092
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−41.3374	−0.468775
$7$	131.565	1.01483	0.507416	−	0.861701i	$-0.330601\pi$
$7$	131.565	1.01483	0.507416	+	0.861701i	$0.330601\pi$
$8$	−165.521	−0.914386
$9$	−54.9135	−0.225981
$10$	−75.3536	−0.238289
$11$	0	0
$11$	0	0
$12$	314.266	0.630006
$13$	−598.870	−0.982820	−0.491410	−	0.870928i	$-0.663518\pi$
$13$	−598.870	−0.982820	−0.491410	+	0.870928i	$0.663518\pi$
$14$	396.555	0.540734
$15$	342.862	0.393451
$16$	234.373	0.228879
$17$	1336.53	1.12165	0.560825	−	0.827935i	$-0.310484\pi$
$17$	1336.53	1.12165	0.560825	+	0.827935i	$0.310484\pi$
$18$	−165.517	−0.120410
$19$	−2886.27	−1.83423	−0.917114	−	0.398624i	$-0.869488\pi$
$19$	−2886.27	−1.83423	−0.917114	+	0.398624i	$0.869488\pi$
$20$	572.874	0.320246
$21$	−1804.34	−0.892833
$22$	0	0
$23$	−2048.71	−0.807536	−0.403768	−	0.914861i	$-0.632300\pi$
$23$	−2048.71	−0.807536	−0.403768	+	0.914861i	$0.632300\pi$
$24$	2270.04	0.804461
$25$	625.000	0.200000
$26$	−1805.08	−0.523676
$27$	4085.72	1.07860
$28$	−3014.80	−0.726714
$29$	−5800.71	−1.28081	−0.640407	−	0.768036i	$-0.721234\pi$
$29$	−5800.71	−1.28081	−0.640407	+	0.768036i	$0.721234\pi$
$30$	1033.43	0.209643
$31$	−9529.52	−1.78101	−0.890506	−	0.454971i	$-0.849650\pi$
$31$	−9529.52	−1.78101	−0.890506	+	0.454971i	$0.849650\pi$
$32$	6003.12	1.03634
$33$	0	0
$34$	4028.50	0.597649
$35$	−3289.12	−0.453847
$36$	1258.34	0.161824
$37$	−8187.53	−0.983215	−0.491608	−	0.870817i	$-0.663591\pi$
$37$	−8187.53	−0.983215	−0.491608	+	0.870817i	$0.663591\pi$
$38$	−8699.64	−0.977333
$39$	8213.18	0.864669
$40$	4138.04	0.408926
$41$	−13471.0	−1.25153	−0.625765	−	0.780011i	$-0.715213\pi$
$41$	−13471.0	−1.25153	−0.625765	+	0.780011i	$0.715213\pi$
$42$	−5438.54	−0.475728
$43$	6524.24	0.538095	0.269047	−	0.963127i	$-0.413291\pi$
$43$	6524.24	0.538095	0.269047	+	0.963127i	$0.413291\pi$
$44$	0	0
$45$	1372.84	0.101062
$46$	−6175.12	−0.430280
$47$	−8172.53	−0.539649	−0.269825	−	0.962909i	$-0.586966\pi$
$47$	−8172.53	−0.539649	−0.269825	+	0.962909i	$0.586966\pi$
$48$	−3214.29	−0.201364
$49$	502.291	0.0298858
$50$	1883.84	0.106566
$51$	−18329.8	−0.986808
$52$	13723.1	0.703790
$53$	33262.9	1.62656	0.813280	−	0.581872i	$-0.197680\pi$
$53$	33262.9	1.62656	0.813280	+	0.581872i	$0.197680\pi$
$54$	12315.0	0.574710
$55$	0	0
$56$	−21776.8	−0.927949
$57$	39583.7	1.61372
$58$	−17484.2	−0.682456
$59$	33630.9	1.25779	0.628895	−	0.777490i	$-0.283508\pi$
$59$	33630.9	1.25779	0.628895	+	0.777490i	$0.283508\pi$
$60$	−7856.65	−0.281747
$61$	−46455.0	−1.59848	−0.799241	−	0.601011i	$-0.794765\pi$
$61$	−46455.0	−1.59848	−0.799241	+	0.601011i	$0.794765\pi$
$62$	−28723.3	−0.948977
$63$	−7224.68	−0.229333
$64$	10594.3	0.323314
$65$	14971.7	0.439531
$66$	0	0
$67$	1838.70	0.0500409	0.0250204	−	0.999687i	$-0.492035\pi$
$67$	1838.70	0.0500409	0.0250204	+	0.999687i	$0.492035\pi$
$68$	−30626.6	−0.803204
$69$	28097.0	0.710457
$70$	−9913.88	−0.241823
$71$	37198.6	0.875751	0.437875	−	0.899036i	$-0.355731\pi$
$71$	37198.6	0.875751	0.437875	+	0.899036i	$0.355731\pi$
$72$	9089.37	0.206634
$73$	−33497.7	−0.735713	−0.367856	−	0.929883i	$-0.619908\pi$
$73$	−33497.7	−0.735713	−0.367856	+	0.929883i	$0.619908\pi$
$74$	−24678.4	−0.523887
$75$	−8571.54	−0.175957
$76$	66138.8	1.31348
$77$	0	0
$78$	24755.7	0.460722
$79$	−38783.5	−0.699165	−0.349582	−	0.936906i	$-0.613677\pi$
$79$	−38783.5	−0.699165	−0.349582	+	0.936906i	$0.613677\pi$
$80$	−5859.31	−0.102358
$81$	−42689.5	−0.722951
$82$	−40603.6	−0.666853
$83$	−350.204	−0.00557990	−0.00278995	−	0.999996i	$-0.500888\pi$
$83$	−350.204	−0.00557990	−0.00278995	+	0.999996i	$0.500888\pi$
$84$	41346.4	0.639350
$85$	−33413.3	−0.501617
$86$	19665.0	0.286713
$87$	79553.6	1.12684
$88$	0	0
$89$	15929.8	0.213174	0.106587	−	0.994303i	$-0.466008\pi$
$89$	15929.8	0.213174	0.106587	+	0.994303i	$0.466008\pi$
$90$	4137.93	0.0538489
$91$	−78790.2	−0.997399
$92$	46946.2	0.578270
$93$	130692.	1.56690
$94$	−24633.2	−0.287541
$95$	72156.8	0.820292
$96$	−82329.6	−0.911754
$97$	25331.2	0.273355	0.136677	−	0.990616i	$-0.456358\pi$
$97$	25331.2	0.273355	0.136677	+	0.990616i	$0.456358\pi$
$98$	1513.98	0.0159241
$99$	0	0
$100$	−14321.8	−0.143218
$101$	22193.8	0.216485	0.108243	−	0.994125i	$-0.465478\pi$
$101$	22193.8	0.216485	0.108243	+	0.994125i	$0.465478\pi$
$102$	−55248.7	−0.525801
$103$	−125832.	−1.16869	−0.584343	−	0.811506i	$-0.698648\pi$
$103$	−125832.	−1.16869	−0.584343	+	0.811506i	$0.698648\pi$
$104$	99125.9	0.898677
$105$	45108.5	0.399287
$106$	100259.	0.866681
$107$	71187.7	0.601098	0.300549	−	0.953766i	$-0.402830\pi$
$107$	71187.7	0.601098	0.300549	+	0.953766i	$0.402830\pi$
$108$	−93624.1	−0.772375
$109$	161346.	1.30074	0.650370	−	0.759617i	$-0.274614\pi$
$109$	161346.	1.30074	0.650370	+	0.759617i	$0.274614\pi$
$110$	0	0
$111$	112288.	0.865016
$112$	30835.2	0.232274
$113$	186477.	1.37382	0.686910	−	0.726742i	$-0.258967\pi$
$113$	186477.	1.37382	0.686910	+	0.726742i	$0.258967\pi$
$114$	119311.	0.859841
$115$	51217.9	0.361141
$116$	132923.	0.917180
$117$	32886.0	0.222099
$118$	101368.	0.670188
$119$	175841.	1.13829
$120$	−56751.0	−0.359766
$121$	0	0
$122$	−140022.	−0.851719
$123$	184748.	1.10108
$124$	218368.	1.27537
$125$	−15625.0	−0.0894427
$126$	−21776.2	−0.122196
$127$	193515.	1.06465	0.532324	−	0.846541i	$-0.321319\pi$
$127$	193515.	1.06465	0.532324	+	0.846541i	$0.321319\pi$
$128$	−160167.	−0.864068
$129$	−89476.4	−0.473407
$130$	45127.0	0.234195
$131$	−38812.1	−0.197601	−0.0988004	−	0.995107i	$-0.531501\pi$
$131$	−38812.1	−0.197601	−0.0988004	+	0.995107i	$0.531501\pi$
$132$	0	0
$133$	−379732.	−1.86144
$134$	5542.12	0.0266633
$135$	−102143.	−0.482364
$136$	−221225.	−1.02562
$137$	304505.	1.38610	0.693048	−	0.720892i	$-0.256267\pi$
$137$	304505.	1.38610	0.693048	+	0.720892i	$0.256267\pi$
$138$	84688.5	0.378553
$139$	135420.	0.594493	0.297247	−	0.954801i	$-0.403932\pi$
$139$	135420.	0.594493	0.297247	+	0.954801i	$0.403932\pi$
$140$	75370.0	0.324996
$141$	112082.	0.474774
$142$	112122.	0.466627
$143$	0	0
$144$	−12870.2	−0.0517225
$145$	145018.	0.572797
$146$	−100967.	−0.392010
$147$	−6888.65	−0.0262930
$148$	187617.	0.704072
$149$	−139744.	−0.515664	−0.257832	−	0.966190i	$-0.583008\pi$
$149$	−139744.	−0.515664	−0.257832	+	0.966190i	$0.583008\pi$
$150$	−25835.8	−0.0937550
$151$	−360217.	−1.28565	−0.642823	−	0.766015i	$-0.722237\pi$
$151$	−360217.	−1.28565	−0.642823	+	0.766015i	$0.722237\pi$
$152$	477740.	1.67719
$153$	−73393.7	−0.253472
$154$	0	0
$155$	238238.	0.796493
$156$	−188205.	−0.619182
$157$	458813.	1.48555	0.742773	−	0.669543i	$-0.233510\pi$
$157$	458813.	1.48555	0.742773	+	0.669543i	$0.233510\pi$
$158$	−116899.	−0.372536
$159$	−456183.	−1.43102
$160$	−150078.	−0.463465
$161$	−269539.	−0.819514
$162$	−128672.	−0.385210
$163$	499719.	1.47318	0.736592	−	0.676337i	$-0.236434\pi$
$163$	499719.	1.47318	0.736592	+	0.676337i	$0.236434\pi$
$164$	308688.	0.896211
$165$	0	0
$166$	−1055.57	−0.00297314
$167$	328346.	0.911047	0.455524	−	0.890224i	$-0.349452\pi$
$167$	328346.	0.911047	0.455524	+	0.890224i	$0.349452\pi$
$168$	298657.	0.816394
$169$	−12647.7	−0.0340640
$170$	−100713.	−0.267277
$171$	158495.	0.414502
$172$	−149503.	−0.385325
$173$	−138676.	−0.352278	−0.176139	−	0.984365i	$-0.556361\pi$
$173$	−138676.	−0.352278	−0.176139	+	0.984365i	$0.556361\pi$
$174$	239786.	0.600414
$175$	82228.0	0.202967
$176$	0	0
$177$	−461229.	−1.10658
$178$	48014.6	0.113586
$179$	−442770.	−1.03287	−0.516435	−	0.856326i	$-0.672741\pi$
$179$	−442770.	−1.03287	−0.516435	+	0.856326i	$0.672741\pi$
$180$	−31458.5	−0.0723697
$181$	348806.	0.791385	0.395692	−	0.918383i	$-0.370505\pi$
$181$	348806.	0.791385	0.395692	+	0.918383i	$0.370505\pi$
$182$	−237485.	−0.531444
$183$	637105.	1.40632
$184$	339106.	0.738399
$185$	204688.	0.439707
$186$	393925.	0.834894
$187$	0	0
$188$	187273.	0.386438
$189$	537537.	1.09460
$190$	217491.	0.437076
$191$	−231528.	−0.459219	−0.229609	−	0.973283i	$-0.573745\pi$
$191$	−231528.	−0.459219	−0.229609	+	0.973283i	$0.573745\pi$
$192$	−145296.	−0.284446
$193$	379671.	0.733693	0.366846	−	0.930282i	$-0.380437\pi$
$193$	379671.	0.733693	0.366846	+	0.930282i	$0.380437\pi$
$194$	76352.0	0.145652
$195$	−205330.	−0.386692
$196$	−11510.0	−0.0214010
$197$	−277285.	−0.509050	−0.254525	−	0.967066i	$-0.581919\pi$
$197$	−277285.	−0.509050	−0.254525	+	0.967066i	$0.581919\pi$
$198$	0	0
$199$	−757833.	−1.35657	−0.678283	−	0.734801i	$-0.737276\pi$
$199$	−757833.	−1.35657	−0.678283	+	0.734801i	$0.737276\pi$
$200$	−103451.	−0.182877
$201$	−25216.8	−0.0440251
$202$	66895.3	0.115350
$203$	−763169.	−1.29981
$204$	420027.	0.706646
$205$	336776.	0.559702
$206$	−379276.	−0.622712
$207$	112502.	0.182488
$208$	−140359.	−0.224947
$209$	0	0
$210$	135964.	0.212752
$211$	301095.	0.465584	0.232792	−	0.972527i	$-0.425214\pi$
$211$	301095.	0.465584	0.232792	+	0.972527i	$0.425214\pi$
$212$	−762217.	−1.16477
$213$	−510159.	−0.770471
$214$	214570.	0.320283
$215$	−163106.	−0.240643
$216$	−676275.	−0.986255
$217$	−1.25375e6	−1.80743
$218$	486319.	0.693074
$219$	459403.	0.647268
$220$	0	0
$221$	−800409.	−1.10238
$222$	338451.	0.460907
$223$	353960.	0.476642	0.238321	−	0.971186i	$-0.423403\pi$
$223$	353960.	0.476642	0.238321	+	0.971186i	$0.423403\pi$
$224$	789799.	1.05171
$225$	−34320.9	−0.0451963
$226$	562069.	0.732013
$227$	−510395.	−0.657418	−0.328709	−	0.944431i	$-0.606614\pi$
$227$	−510395.	−0.657418	−0.328709	+	0.944431i	$0.606614\pi$
$228$	−907058.	−1.15557
$229$	−830048.	−1.04596	−0.522979	−	0.852345i	$-0.675179\pi$
$229$	−830048.	−1.04596	−0.522979	+	0.852345i	$0.675179\pi$
$230$	154378.	0.192427
$231$	0	0
$232$	960142.	1.17116
$233$	−145009.	−0.174987	−0.0874937	−	0.996165i	$-0.527886\pi$
$233$	−145009.	−0.174987	−0.0874937	+	0.996165i	$0.527886\pi$
$234$	99123.3	0.118341
$235$	204313.	0.241339
$236$	−770649.	−0.900693
$237$	531895.	0.615113
$238$	530009.	0.606514
$239$	−1.35319e6	−1.53238	−0.766188	−	0.642617i	$-0.777849\pi$
$239$	−1.35319e6	−1.53238	−0.766188	+	0.642617i	$0.777849\pi$
$240$	80357.4	0.0900529
$241$	678741.	0.752768	0.376384	−	0.926464i	$-0.377167\pi$
$241$	678741.	0.752768	0.376384	+	0.926464i	$0.377167\pi$
$242$	0	0
$243$	−407367.	−0.442558
$244$	1.06451e6	1.14466
$245$	−12557.3	−0.0133653
$246$	556857.	0.586686
$247$	1.72850e6	1.80272
$248$	1.57734e6	1.62853
$249$	4802.86	0.00490910
$250$	−47096.0	−0.0476578
$251$	1.10172e6	1.10380	0.551898	−	0.833912i	$-0.313904\pi$
$251$	1.10172e6	1.10380	0.551898	+	0.833912i	$0.313904\pi$
$252$	165553.	0.164224
$253$	0	0
$254$	583282.	0.567276
$255$	458246.	0.441314
$256$	−821785.	−0.783715
$257$	1.24112e6	1.17214	0.586071	−	0.810260i	$-0.300674\pi$
$257$	1.24112e6	1.17214	0.586071	+	0.810260i	$0.300674\pi$
$258$	−269695.	−0.252245
$259$	−1.07719e6	−0.997799
$260$	−343077.	−0.314744
$261$	318537.	0.289440
$262$	−116985.	−0.105288
$263$	207030.	0.184562	0.0922811	−	0.995733i	$-0.470584\pi$
$263$	207030.	0.184562	0.0922811	+	0.995733i	$0.470584\pi$
$264$	0	0
$265$	−831572.	−0.727420
$266$	−1.14457e6	−0.991829
$267$	−218468.	−0.187547
$268$	−42133.8	−0.0358339
$269$	1.36048e6	1.14633	0.573167	−	0.819439i	$-0.305715\pi$
$269$	1.36048e6	1.14633	0.573167	+	0.819439i	$0.305715\pi$
$270$	−307874.	−0.257018
$271$	−997686.	−0.825222	−0.412611	−	0.910907i	$-0.635383\pi$
$271$	−997686.	−0.825222	−0.412611	+	0.910907i	$0.635383\pi$
$272$	313247.	0.256723
$273$	1.08057e6	0.877494
$274$	917822.	0.738554
$275$	0	0
$276$	−643842.	−0.508752
$277$	−1.65022e6	−1.29223	−0.646117	−	0.763238i	$-0.723608\pi$
$277$	−1.65022e6	−1.29223	−0.646117	+	0.763238i	$0.723608\pi$
$278$	408176.	0.316764
$279$	523299.	0.402476
$280$	544420.	0.414991
$281$	−1.16381e6	−0.879260	−0.439630	−	0.898179i	$-0.644890\pi$
$281$	−1.16381e6	−0.879260	−0.439630	+	0.898179i	$0.644890\pi$
$282$	337831.	0.252974
$283$	1.76857e6	1.31267	0.656336	−	0.754469i	$-0.272106\pi$
$283$	1.76857e6	1.31267	0.656336	+	0.754469i	$0.272106\pi$
$284$	−852404.	−0.627118
$285$	−989592.	−0.721679
$286$	0	0
$287$	−1.77231e6	−1.27009
$288$	−329652.	−0.234194
$289$	366462.	0.258098
$290$	437104.	0.305204
$291$	−347404.	−0.240493
$292$	767598.	0.526838
$293$	−1.81234e6	−1.23331	−0.616653	−	0.787235i	$-0.711512\pi$
$293$	−1.81234e6	−1.23331	−0.616653	+	0.787235i	$0.711512\pi$
$294$	−20763.4	−0.0140097
$295$	−840771.	−0.562501
$296$	1.35521e6	0.899038
$297$	0	0
$298$	−421208.	−0.274761
$299$	1.22691e6	0.793663
$300$	196416.	0.126001
$301$	858360.	0.546076
$302$	−1.08574e6	−0.685031
$303$	−304376.	−0.190460
$304$	−676463.	−0.419817
$305$	1.16137e6	0.714863
$306$	−221219.	−0.135058
$307$	174606.	0.105734	0.0528668	−	0.998602i	$-0.483164\pi$
$307$	174606.	0.105734	0.0528668	+	0.998602i	$0.483164\pi$
$308$	0	0
$309$	1.72572e6	1.02819
$310$	718084.	0.424396
$311$	−2.56816e6	−1.50564	−0.752821	−	0.658225i	$-0.771308\pi$
$311$	−2.56816e6	−1.50564	−0.752821	+	0.658225i	$0.771308\pi$
$312$	−1.35946e6	−0.790641
$313$	328703.	0.189646	0.0948229	−	0.995494i	$-0.469772\pi$
$313$	328703.	0.189646	0.0948229	+	0.995494i	$0.469772\pi$
$314$	1.38293e6	0.791544
$315$	180617.	0.102561
$316$	888722.	0.500666
$317$	−662607.	−0.370346	−0.185173	−	0.982706i	$-0.559285\pi$
$317$	−662607.	−0.370346	−0.185173	+	0.982706i	$0.559285\pi$
$318$	−1.37500e6	−0.762491
$319$	0	0
$320$	−264859.	−0.144590
$321$	−976301.	−0.528836
$322$	−812428.	−0.436662
$323$	−3.85760e6	−2.05736
$324$	978228.	0.517699
$325$	−374294.	−0.196564
$326$	1.50623e6	0.784957
$327$	−2.21277e6	−1.14437
$328$	2.22975e6	1.14438
$329$	−1.07522e6	−0.547654
$330$	0	0
$331$	236679.	0.118738	0.0593690	−	0.998236i	$-0.481091\pi$
$331$	236679.	0.118738	0.0593690	+	0.998236i	$0.481091\pi$
$332$	8024.91	0.00399572
$333$	449606.	0.222188
$334$	989683.	0.485434
$335$	−45967.6	−0.0223790
$336$	−422888.	−0.204351
$337$	3.92672e6	1.88346	0.941728	−	0.336375i	$-0.109201\pi$
$337$	3.92672e6	1.88346	0.941728	+	0.336375i	$0.109201\pi$
$338$	−38122.1	−0.0181503
$339$	−2.55744e6	−1.20866
$340$	765664.	0.359204
$341$	0	0
$342$	477728.	0.220859
$343$	−2.14513e6	−0.984504
$344$	−1.07990e6	−0.492026
$345$	−702426.	−0.317726
$346$	−417989.	−0.187705
$347$	97486.2	0.0434630	0.0217315	−	0.999764i	$-0.493082\pi$
$347$	97486.2	0.0434630	0.0217315	+	0.999764i	$0.493082\pi$
$348$	−1.82297e6	−0.806920
$349$	937238.	0.411895	0.205947	−	0.978563i	$-0.433972\pi$
$349$	937238.	0.411895	0.205947	+	0.978563i	$0.433972\pi$
$350$	247847.	0.108147
$351$	−2.44682e6	−1.06007
$352$	0	0
$353$	1.16848e6	0.499095	0.249548	−	0.968363i	$-0.419718\pi$
$353$	1.16848e6	0.499095	0.249548	+	0.968363i	$0.419718\pi$
$354$	−1.39021e6	−0.589620
$355$	−929965.	−0.391648
$356$	−365030.	−0.152652
$357$	−2.41156e6	−1.00145
$358$	−1.33457e6	−0.550345
$359$	846273.	0.346557	0.173278	−	0.984873i	$-0.444564\pi$
$359$	846273.	0.346557	0.173278	+	0.984873i	$0.444564\pi$
$360$	−227234.	−0.0924096
$361$	5.85448e6	2.36440
$362$	1.05135e6	0.421674
$363$	0	0
$364$	1.80547e6	0.714229
$365$	837443.	0.329021
$366$	1.92033e6	0.749328
$367$	−2.69738e6	−1.04539	−0.522694	−	0.852521i	$-0.675073\pi$
$367$	−2.69738e6	−1.04539	−0.522694	+	0.852521i	$0.675073\pi$
$368$	−480163.	−0.184828
$369$	739742.	0.282823
$370$	616960.	0.234289
$371$	4.37622e6	1.65069
$372$	−2.99481e6	−1.12205
$373$	−1.84632e6	−0.687122	−0.343561	−	0.939130i	$-0.611633\pi$
$373$	−1.84632e6	−0.687122	−0.343561	+	0.939130i	$0.611633\pi$
$374$	0	0
$375$	214288.	0.0786902
$376$	1.35273e6	0.493448
$377$	3.47387e6	1.25881
$378$	1.62021e6	0.583234
$379$	−213160.	−0.0762269	−0.0381134	−	0.999273i	$-0.512135\pi$
$379$	−213160.	−0.0762269	−0.0381134	+	0.999273i	$0.512135\pi$
$380$	−1.65347e6	−0.587404
$381$	−2.65396e6	−0.936659
$382$	−697858.	−0.244686
$383$	−4.13824e6	−1.44151	−0.720757	−	0.693188i	$-0.756206\pi$
$383$	−4.13824e6	−1.44151	−0.720757	+	0.693188i	$0.756206\pi$
$384$	2.19660e6	0.760193
$385$	0	0
$386$	1.14438e6	0.390934
$387$	−358269.	−0.121599
$388$	−580464.	−0.195747
$389$	3.62932e6	1.21605	0.608024	−	0.793918i	$-0.291962\pi$
$389$	3.62932e6	1.21605	0.608024	+	0.793918i	$0.291962\pi$
$390$	−618893.	−0.206041
$391$	−2.73817e6	−0.905772
$392$	−83140.0	−0.0273272
$393$	532287.	0.173846
$394$	−835776.	−0.271237
$395$	969588.	0.312676
$396$	0	0
$397$	−996930.	−0.317459	−0.158730	−	0.987322i	$-0.550740\pi$
$397$	−996930.	−0.317459	−0.158730	+	0.987322i	$0.550740\pi$
$398$	−2.28422e6	−0.722819
$399$	5.20782e6	1.63766
$400$	146483.	0.0457759
$401$	2.14079e6	0.664833	0.332416	−	0.943133i	$-0.392136\pi$
$401$	2.14079e6	0.664833	0.332416	+	0.943133i	$0.392136\pi$
$402$	−76007.2	−0.0234579
$403$	5.70695e6	1.75042
$404$	−508570.	−0.155023
$405$	1.06724e6	0.323313
$406$	−2.30030e6	−0.692579
$407$	0	0
$408$	3.03398e6	0.902324
$409$	2.66050e6	0.786422	0.393211	−	0.919448i	$-0.371364\pi$
$409$	2.66050e6	0.786422	0.393211	+	0.919448i	$0.371364\pi$
$410$	1.01509e6	0.298226
$411$	−4.17612e6	−1.21946
$412$	2.88343e6	0.836887
$413$	4.42464e6	1.27645
$414$	339097.	0.0972352
$415$	8755.11	0.00249541
$416$	−3.59509e6	−1.01854
$417$	−1.85722e6	−0.523025
$418$	0	0
$419$	6.75397e6	1.87942	0.939710	−	0.341973i	$-0.111095\pi$
$419$	6.75397e6	1.87942	0.939710	+	0.341973i	$0.111095\pi$
$420$	−1.03366e6	−0.285926
$421$	2.90394e6	0.798514	0.399257	−	0.916839i	$-0.369268\pi$
$421$	2.90394e6	0.798514	0.399257	+	0.916839i	$0.369268\pi$
$422$	907545.	0.248077
$423$	448782.	0.121951
$424$	−5.50572e6	−1.48730
$425$	835333.	0.224330
$426$	−1.53769e6	−0.410530
$427$	−6.11184e6	−1.62219
$428$	−1.63126e6	−0.430441
$429$	0	0
$430$	−491625.	−0.128222
$431$	530831.	0.137646	0.0688230	−	0.997629i	$-0.478076\pi$
$431$	530831.	0.137646	0.0688230	+	0.997629i	$0.478076\pi$
$432$	957582.	0.246869
$433$	−1.41701e6	−0.363207	−0.181603	−	0.983372i	$-0.558129\pi$
$433$	−1.41701e6	−0.363207	−0.181603	+	0.983372i	$0.558129\pi$
$434$	−3.77898e6	−0.963053
$435$	−1.98884e6	−0.503937
$436$	−3.69722e6	−0.931450
$437$	5.91315e6	1.48121
$438$	1.38471e6	0.344884
$439$	−5.45603e6	−1.35119	−0.675593	−	0.737275i	$-0.736112\pi$
$439$	−5.45603e6	−1.35119	−0.675593	+	0.737275i	$0.736112\pi$
$440$	0	0
$441$	−27582.6	−0.00675364
$442$	−2.41255e6	−0.587381
$443$	2.51044e6	0.607772	0.303886	−	0.952708i	$-0.401716\pi$
$443$	2.51044e6	0.607772	0.303886	+	0.952708i	$0.401716\pi$
$444$	−2.57306e6	−0.619431
$445$	−398244.	−0.0953343
$446$	1.06689e6	0.253969
$447$	1.91651e6	0.453673
$448$	1.39384e6	0.328109
$449$	81910.9	0.0191746	0.00958729	−	0.999954i	$-0.496948\pi$
$449$	81910.9	0.0191746	0.00958729	+	0.999954i	$0.496948\pi$
$450$	−103448.	−0.0240820
$451$	0	0
$452$	−4.27312e6	−0.983782
$453$	4.94018e6	1.13109
$454$	−1.53840e6	−0.350292
$455$	1.96975e6	0.446050
$456$	−6.55195e6	−1.47557
$457$	−6.82583e6	−1.52885	−0.764425	−	0.644712i	$-0.776977\pi$
$457$	−6.82583e6	−1.52885	−0.764425	+	0.644712i	$0.776977\pi$
$458$	−2.50188e6	−0.557318
$459$	5.46070e6	1.20981
$460$	−1.17365e6	−0.258610
$461$	−934822.	−0.204869	−0.102435	−	0.994740i	$-0.532663\pi$
$461$	−934822.	−0.204869	−0.102435	+	0.994740i	$0.532663\pi$
$462$	0	0
$463$	1.70121e6	0.368813	0.184406	−	0.982850i	$-0.440964\pi$
$463$	1.70121e6	0.368813	0.184406	+	0.982850i	$0.440964\pi$
$464$	−1.35953e6	−0.293152
$465$	−3.26731e6	−0.700741
$466$	−437079.	−0.0932385
$467$	6.66304e6	1.41378	0.706888	−	0.707326i	$-0.250099\pi$
$467$	6.66304e6	1.41378	0.706888	+	0.707326i	$0.250099\pi$
$468$	−753582.	−0.159043
$469$	241909.	0.0507831
$470$	615829.	0.128592
$471$	−6.29237e6	−1.30696
$472$	−5.56663e6	−1.15010
$473$	0	0
$474$	1.60321e6	0.327751
$475$	−1.80392e6	−0.366846
$476$	−4.02938e6	−0.815118
$477$	−1.82658e6	−0.367573
$478$	−4.07872e6	−0.816496
$479$	2.83033e6	0.563635	0.281817	−	0.959468i	$-0.409063\pi$
$479$	2.83033e6	0.563635	0.281817	+	0.959468i	$0.409063\pi$
$480$	2.05824e6	0.407749
$481$	4.90327e6	0.966324
$482$	2.04582e6	0.401098
$483$	3.69658e6	0.720995
$484$	0	0
$485$	−633281.	−0.122248
$486$	−1.22786e6	−0.235808
$487$	−1.27484e6	−0.243574	−0.121787	−	0.992556i	$-0.538863\pi$
$487$	−1.27484e6	−0.243574	−0.121787	+	0.992556i	$0.538863\pi$
$488$	7.68930e6	1.46163
$489$	−6.85338e6	−1.29608
$490$	−37849.4	−0.00712146
$491$	171346.	0.0320754	0.0160377	−	0.999871i	$-0.494895\pi$
$491$	171346.	0.0320754	0.0160377	+	0.999871i	$0.494895\pi$
$492$	−4.23349e6	−0.788471
$493$	−7.75283e6	−1.43662
$494$	5.20995e6	0.960542
$495$	0	0
$496$	−2.23346e6	−0.407637
$497$	4.89402e6	0.888741
$498$	14476.5	0.00261572
$499$	4.83367e6	0.869011	0.434506	−	0.900669i	$-0.356923\pi$
$499$	4.83367e6	0.869011	0.434506	+	0.900669i	$0.356923\pi$
$500$	358046.	0.0640492
$501$	−4.50309e6	−0.801524
$502$	3.32076e6	0.588136
$503$	1.06055e6	0.186901	0.0934506	−	0.995624i	$-0.470210\pi$
$503$	1.06055e6	0.186901	0.0934506	+	0.995624i	$0.470210\pi$
$504$	1.19584e6	0.209699
$505$	−554845.	−0.0968152
$506$	0	0
$507$	173457.	0.0299690
$508$	−4.43439e6	−0.762385
$509$	−4.30052e6	−0.735744	−0.367872	−	0.929876i	$-0.619913\pi$
$509$	−4.30052e6	−0.735744	−0.367872	+	0.929876i	$0.619913\pi$
$510$	1.38122e6	0.235146
$511$	−4.40712e6	−0.746625
$512$	2.64837e6	0.446481
$513$	−1.17925e7	−1.97840
$514$	3.74091e6	0.624552
$515$	3.14580e6	0.522653
$516$	2.05035e6	0.339003
$517$	0	0
$518$	−3.24681e6	−0.531658
$519$	1.90187e6	0.309929
$520$	−2.47815e6	−0.401901
$521$	−8.98238e6	−1.44976	−0.724882	−	0.688873i	$-0.758106\pi$
$521$	−8.98238e6	−1.44976	−0.724882	+	0.688873i	$0.758106\pi$
$522$	960117.	0.154223
$523$	2.53721e6	0.405604	0.202802	−	0.979220i	$-0.434995\pi$
$523$	2.53721e6	0.405604	0.202802	+	0.979220i	$0.434995\pi$
$524$	889376.	0.141500
$525$	−1.12771e6	−0.178567
$526$	624017.	0.0983404
$527$	−1.27365e7	−1.99767
$528$	0	0
$529$	−2.23911e6	−0.347886
$530$	−2.50648e6	−0.387591
$531$	−1.84679e6	−0.284237
$532$	8.70154e6	1.33296
$533$	8.06740e6	1.23003
$534$	−658494.	−0.0999307
$535$	−1.77969e6	−0.268819
$536$	−304345.	−0.0457567
$537$	6.07236e6	0.908702
$538$	4.10068e6	0.610801
$539$	0	0
$540$	2.34060e6	0.345417
$541$	−1.11058e7	−1.63139	−0.815696	−	0.578481i	$-0.803646\pi$
$541$	−1.11058e7	−1.63139	−0.815696	+	0.578481i	$0.803646\pi$
$542$	−3.00717e6	−0.439703
$543$	−4.78369e6	−0.696247
$544$	8.02337e6	1.16241
$545$	−4.03364e6	−0.581709
$546$	3.25698e6	0.467556
$547$	−8.21202e6	−1.17350	−0.586748	−	0.809769i	$-0.699592\pi$
$547$	−8.21202e6	−1.17350	−0.586748	+	0.809769i	$0.699592\pi$
$548$	−6.97772e6	−0.992572
$549$	2.55101e6	0.361227
$550$	0	0
$551$	1.67424e7	2.34931
$552$	−4.65066e6	−0.649631
$553$	−5.10255e6	−0.709535
$554$	−4.97399e6	−0.688542
$555$	−2.80719e6	−0.386847
$556$	−3.10315e6	−0.425712
$557$	1.80394e6	0.246368	0.123184	−	0.992384i	$-0.460690\pi$
$557$	1.80394e6	0.246368	0.123184	+	0.992384i	$0.460690\pi$
$558$	1.57730e6	0.214451
$559$	−3.90717e6	−0.528850
$560$	−770879.	−0.103876
$561$	0	0
$562$	−3.50790e6	−0.468496
$563$	−7.24282e6	−0.963024	−0.481512	−	0.876440i	$-0.659912\pi$
$563$	−7.24282e6	−0.963024	−0.481512	+	0.876440i	$0.659912\pi$
$564$	−2.56835e6	−0.339982
$565$	−4.66193e6	−0.614391
$566$	5.33072e6	0.699431
$567$	−5.61644e6	−0.733674
$568$	−6.15717e6	−0.800774
$569$	465183.	0.0602342	0.0301171	−	0.999546i	$-0.490412\pi$
$569$	465183.	0.0602342	0.0301171	+	0.999546i	$0.490412\pi$
$570$	−2.98277e6	−0.384533
$571$	−6.14795e6	−0.789114	−0.394557	−	0.918871i	$-0.629102\pi$
$571$	−6.14795e6	−0.789114	−0.394557	+	0.918871i	$0.629102\pi$
$572$	0	0
$573$	3.17528e6	0.404013
$574$	−5.34201e6	−0.676745
$575$	−1.28045e6	−0.161507
$576$	−581772.	−0.0730629
$577$	−1.42512e6	−0.178201	−0.0891007	−	0.996023i	$-0.528399\pi$
$577$	−1.42512e6	−0.178201	−0.0891007	+	0.996023i	$0.528399\pi$
$578$	1.10457e6	0.137522
$579$	−5.20698e6	−0.645491
$580$	−3.32307e6	−0.410176
$581$	−46074.6	−0.00566266
$582$	−1.04713e6	−0.128142
$583$	0	0
$584$	5.54459e6	0.672725
$585$	−822151.	−0.0993258
$586$	−5.46265e6	−0.657143
$587$	1.18717e7	1.42206	0.711032	−	0.703159i	$-0.248228\pi$
$587$	1.18717e7	1.42206	0.711032	+	0.703159i	$0.248228\pi$
$588$	157853.	0.0188282
$589$	2.75048e7	3.26678
$590$	−2.53421e6	−0.299717
$591$	3.80281e6	0.447854
$592$	−1.91893e6	−0.225038
$593$	−5.50367e6	−0.642710	−0.321355	−	0.946959i	$-0.604138\pi$
$593$	−5.50367e6	−0.642710	−0.321355	+	0.946959i	$0.604138\pi$
$594$	0	0
$595$	−4.39601e6	−0.509057
$596$	3.20222e6	0.369263
$597$	1.03933e7	1.19348
$598$	3.69809e6	0.422888
$599$	−1.25304e7	−1.42692	−0.713458	−	0.700698i	$-0.752872\pi$
$599$	−1.25304e7	−1.42692	−0.713458	+	0.700698i	$0.752872\pi$
$600$	1.41877e6	0.160892
$601$	1.13744e7	1.28452	0.642261	−	0.766486i	$-0.277997\pi$
$601$	1.13744e7	1.28452	0.642261	+	0.766486i	$0.277997\pi$
$602$	2.58722e6	0.290966
$603$	−100970.	−0.0113083
$604$	8.25434e6	0.920641
$605$	0	0
$606$	−917433.	−0.101483
$607$	4.72621e6	0.520645	0.260323	−	0.965522i	$-0.416171\pi$
$607$	4.72621e6	0.520645	0.260323	+	0.965522i	$0.416171\pi$
$608$	−1.73266e7	−1.90088
$609$	1.04665e7	1.14355
$610$	3.50055e6	0.380901
$611$	4.89428e6	0.530378
$612$	1.68181e6	0.181509
$613$	652666.	0.0701519	0.0350760	−	0.999385i	$-0.488833\pi$
$613$	652666.	0.0701519	0.0350760	+	0.999385i	$0.488833\pi$
$614$	526287.	0.0563380
$615$	−4.61870e6	−0.492416
$616$	0	0
$617$	−1.41008e7	−1.49118	−0.745592	−	0.666403i	$-0.767833\pi$
$617$	−1.41008e7	−1.49118	−0.745592	+	0.666403i	$0.767833\pi$
$618$	5.20156e6	0.547851
$619$	1.77166e7	1.85847	0.929233	−	0.369493i	$-0.120469\pi$
$619$	1.77166e7	1.85847	0.929233	+	0.369493i	$0.120469\pi$
$620$	−5.45921e6	−0.570362
$621$	−8.37048e6	−0.871007
$622$	−7.74082e6	−0.802252
$623$	2.09580e6	0.216336
$624$	1.92494e6	0.197905
$625$	390625.	0.0400000
$626$	990759.	0.101049
$627$	0	0
$628$	−1.05137e7	−1.06379
$629$	−1.09429e7	−1.10282
$630$	544406.	0.0546476
$631$	1.82506e7	1.82475	0.912374	−	0.409358i	$-0.134247\pi$
$631$	1.82506e7	1.82475	0.912374	+	0.409358i	$0.134247\pi$
$632$	6.41951e6	0.639306
$633$	−4.12936e6	−0.409613
$634$	−1.99719e6	−0.197332
$635$	−4.83788e6	−0.476125
$636$	1.04534e7	1.02474
$637$	−300807.	−0.0293724
$638$	0	0
$639$	−2.04270e6	−0.197904
$640$	4.00417e6	0.386423
$641$	7.36294e6	0.707793	0.353896	−	0.935285i	$-0.384857\pi$
$641$	7.36294e6	0.707793	0.353896	+	0.935285i	$0.384857\pi$
$642$	−2.94271e6	−0.281780
$643$	−1.47916e7	−1.41087	−0.705436	−	0.708774i	$-0.749249\pi$
$643$	−1.47916e7	−1.41087	−0.705436	+	0.708774i	$0.749249\pi$
$644$	6.17646e6	0.586847
$645$	2.23691e6	0.211714
$646$	−1.16274e7	−1.09622
$647$	3.78301e6	0.355285	0.177643	−	0.984095i	$-0.443153\pi$
$647$	3.78301e6	0.355285	0.177643	+	0.984095i	$0.443153\pi$
$648$	7.06603e6	0.661056
$649$	0	0
$650$	−1.12817e6	−0.104735
$651$	1.71945e7	1.59015
$652$	−1.14510e7	−1.05494
$653$	1.31122e6	0.120335	0.0601677	−	0.998188i	$-0.480836\pi$
$653$	1.31122e6	0.120335	0.0601677	+	0.998188i	$0.480836\pi$
$654$	−6.66960e6	−0.609755
$655$	970302.	0.0883697
$656$	−3.15724e6	−0.286450
$657$	1.83948e6	0.166257
$658$	−3.24086e6	−0.291807
$659$	−4.43005e6	−0.397370	−0.198685	−	0.980063i	$-0.563667\pi$
$659$	−4.43005e6	−0.397370	−0.198685	+	0.980063i	$0.563667\pi$
$660$	0	0
$661$	−1.01783e7	−0.906093	−0.453046	−	0.891487i	$-0.649663\pi$
$661$	−1.01783e7	−0.906093	−0.453046	+	0.891487i	$0.649663\pi$
$662$	713384.	0.0632672
$663$	1.09772e7	0.969856
$664$	57966.3	0.00510218
$665$	9.49330e6	0.832459
$666$	1.35518e6	0.118389
$667$	1.18840e7	1.03430
$668$	−7.52404e6	−0.652394
$669$	−4.85438e6	−0.419342
$670$	−138553.	−0.0119242
$671$	0	0
$672$	−1.08317e7	−0.925278
$673$	9.77223e6	0.831680	0.415840	−	0.909438i	$-0.363488\pi$
$673$	9.77223e6	0.831680	0.415840	+	0.909438i	$0.363488\pi$
$674$	1.18357e7	1.00356
$675$	2.55358e6	0.215720
$676$	289822.	0.0243930
$677$	9.08811e6	0.762082	0.381041	−	0.924558i	$-0.375566\pi$
$677$	9.08811e6	0.762082	0.381041	+	0.924558i	$0.375566\pi$
$678$	−7.70848e6	−0.644013
$679$	3.33270e6	0.277410
$680$	5.53062e6	0.458671
$681$	6.99979e6	0.578385
$682$	0	0
$683$	1.80408e7	1.47980	0.739900	−	0.672717i	$-0.234873\pi$
$683$	1.80408e7	1.47980	0.739900	+	0.672717i	$0.234873\pi$
$684$	−3.63191e6	−0.296821
$685$	−7.61263e6	−0.619881
$686$	−6.46572e6	−0.524573
$687$	1.13837e7	0.920217
$688$	1.52910e6	0.123159
$689$	−1.99201e7	−1.59862
$690$	−2.11721e6	−0.169294
$691$	1.44102e7	1.14808	0.574042	−	0.818826i	$-0.305375\pi$
$691$	1.44102e7	1.14808	0.574042	+	0.818826i	$0.305375\pi$
$692$	3.17775e6	0.252264
$693$	0	0
$694$	293837.	0.0231584
$695$	−3.38551e6	−0.265865
$696$	−1.31678e7	−1.03036
$697$	−1.80045e7	−1.40378
$698$	2.82497e6	0.219470
$699$	1.98873e6	0.153951
$700$	−1.88425e6	−0.145343
$701$	6.70799e6	0.515582	0.257791	−	0.966201i	$-0.417005\pi$
$701$	6.70799e6	0.515582	0.257791	+	0.966201i	$0.417005\pi$
$702$	−7.37506e6	−0.564836
$703$	2.36315e7	1.80344
$704$	0	0
$705$	−2.80204e6	−0.212326
$706$	3.52196e6	0.265933
$707$	2.91992e6	0.219696
$708$	1.05690e7	0.792414
$709$	844897.	0.0631231	0.0315616	−	0.999502i	$-0.489952\pi$
$709$	844897.	0.0631231	0.0315616	+	0.999502i	$0.489952\pi$
$710$	−2.80305e6	−0.208682
$711$	2.12974e6	0.157998
$712$	−2.63672e6	−0.194923
$713$	1.95233e7	1.43823
$714$	−7.26879e6	−0.533601
$715$	0	0
$716$	1.01461e7	0.739630
$717$	1.85583e7	1.34816
$718$	2.55079e6	0.184656
$719$	−2.61886e7	−1.88925	−0.944627	−	0.328147i	$-0.893576\pi$
$719$	−2.61886e7	−1.88925	−0.944627	+	0.328147i	$0.893576\pi$
$720$	321756.	0.0231310
$721$	−1.65551e7	−1.18602
$722$	1.76462e7	1.25982
$723$	−9.30856e6	−0.662273
$724$	−7.99287e6	−0.566704
$725$	−3.62544e6	−0.256163
$726$	0	0
$727$	−33141.0	−0.00232557	−0.00116278	−	0.999999i	$-0.500370\pi$
$727$	−33141.0	−0.00232557	−0.00116278	+	0.999999i	$0.500370\pi$
$728$	1.30415e7	0.912007
$729$	1.59604e7	1.11231
$730$	2.52417e6	0.175312
$731$	8.71985e6	0.603554
$732$	−1.45992e7	−1.00705
$733$	1.72231e7	1.18400	0.591998	−	0.805939i	$-0.298339\pi$
$733$	1.72231e7	1.18400	0.591998	+	0.805939i	$0.298339\pi$
$734$	−8.13029e6	−0.557014
$735$	172216.	0.0117586
$736$	−1.22987e7	−0.836882
$737$	0	0
$738$	2.22969e6	0.150697
$739$	1.91027e7	1.28672	0.643360	−	0.765563i	$-0.277540\pi$
$739$	1.91027e7	1.28672	0.643360	+	0.765563i	$0.277540\pi$
$740$	−4.69042e6	−0.314871
$741$	−2.37055e7	−1.58600
$742$	1.31906e7	0.879536
$743$	−8.56931e6	−0.569474	−0.284737	−	0.958606i	$-0.591906\pi$
$743$	−8.56931e6	−0.569474	−0.284737	+	0.958606i	$0.591906\pi$
$744$	−2.16324e7	−1.43276
$745$	3.49359e6	0.230612
$746$	−5.56506e6	−0.366119
$747$	19230.9	0.00126095
$748$	0	0
$749$	9.36579e6	0.610014
$750$	645896.	0.0419285
$751$	4.61377e6	0.298508	0.149254	−	0.988799i	$-0.452313\pi$
$751$	4.61377e6	0.298508	0.149254	+	0.988799i	$0.452313\pi$
$752$	−1.91542e6	−0.123515
$753$	−1.51096e7	−0.971101
$754$	1.04707e7	0.670732
$755$	9.00541e6	0.574958
$756$	−1.23176e7	−0.783832
$757$	1.39463e7	0.884544	0.442272	−	0.896881i	$-0.354173\pi$
$757$	1.39463e7	0.884544	0.442272	+	0.896881i	$0.354173\pi$
$758$	−642496.	−0.0406160
$759$	0	0
$760$	−1.19435e7	−0.750063
$761$	3.14364e6	0.196776	0.0983878	−	0.995148i	$-0.468631\pi$
$761$	3.14364e6	0.196776	0.0983878	+	0.995148i	$0.468631\pi$
$762$	−7.99941e6	−0.499080
$763$	2.12274e7	1.32003
$764$	5.30545e6	0.328843
$765$	1.83484e6	0.113356
$766$	−1.24733e7	−0.768082
$767$	−2.01405e7	−1.23618
$768$	1.12703e7	0.689500
$769$	−845337.	−0.0515482	−0.0257741	−	0.999668i	$-0.508205\pi$
$769$	−845337.	−0.0515482	−0.0257741	+	0.999668i	$0.508205\pi$
$770$	0	0
$771$	−1.70213e7	−1.03123
$772$	−8.70014e6	−0.525391
$773$	3.14976e7	1.89596	0.947978	−	0.318336i	$-0.103124\pi$
$773$	3.14976e7	1.89596	0.947978	+	0.318336i	$0.103124\pi$
$774$	−1.07987e6	−0.0647918
$775$	−5.95595e6	−0.356202
$776$	−4.19286e6	−0.249952
$777$	1.47731e7	0.877847
$778$	1.09393e7	0.647948
$779$	3.88811e7	2.29559
$780$	4.70511e6	0.276907
$781$	0	0
$782$	−8.25325e6	−0.482623
$783$	−2.37001e7	−1.38148
$784$	117723.	0.00684025
$785$	−1.14703e7	−0.664356
$786$	1.60439e6	0.0926303
$787$	−1.52029e7	−0.874963	−0.437481	−	0.899227i	$-0.644129\pi$
$787$	−1.52029e7	−0.874963	−0.437481	+	0.899227i	$0.644129\pi$
$788$	6.35396e6	0.364527
$789$	−2.83930e6	−0.162375
$790$	2.92248e6	0.166603
$791$	2.45339e7	1.39420
$792$	0	0
$793$	2.78205e7	1.57102
$794$	−3.00489e6	−0.169152
$795$	1.14046e7	0.639972
$796$	1.73657e7	0.971426
$797$	−1.07063e7	−0.597028	−0.298514	−	0.954405i	$-0.596491\pi$
$797$	−1.07063e7	−0.597028	−0.298514	+	0.954405i	$0.596491\pi$
$798$	1.56971e7	0.872595
$799$	−1.09228e7	−0.605297
$800$	3.75195e6	0.207268
$801$	−874759.	−0.0481734
$802$	6.45264e6	0.354243
$803$	0	0
$804$	577842.	0.0315260
$805$	6.73847e6	0.366498
$806$	1.72016e7	0.932674
$807$	−1.86582e7	−1.00852
$808$	−3.67355e6	−0.197951
$809$	1.40395e7	0.754187	0.377093	−	0.926175i	$-0.376924\pi$
$809$	1.40395e7	0.754187	0.377093	+	0.926175i	$0.376924\pi$
$810$	3.21681e6	0.172271
$811$	2.41715e7	1.29048	0.645241	−	0.763979i	$-0.276757\pi$
$811$	2.41715e7	1.29048	0.645241	+	0.763979i	$0.276757\pi$
$812$	1.74880e7	0.930785
$813$	1.36827e7	0.726017
$814$	0	0
$815$	−1.24930e7	−0.658828
$816$	−4.29601e6	−0.225860
$817$	−1.88307e7	−0.986988
$818$	8.01914e6	0.419029
$819$	4.32665e6	0.225394
$820$	−7.71720e6	−0.400798
$821$	7.98241e6	0.413310	0.206655	−	0.978414i	$-0.433742\pi$
$821$	7.98241e6	0.413310	0.206655	+	0.978414i	$0.433742\pi$
$822$	−1.25874e7	−0.649767
$823$	−9.23481e6	−0.475257	−0.237628	−	0.971356i	$-0.576370\pi$
$823$	−9.23481e6	−0.475257	−0.237628	+	0.971356i	$0.576370\pi$
$824$	2.08279e7	1.06863
$825$	0	0
$826$	1.33365e7	0.680129
$827$	2.39844e7	1.21945	0.609727	−	0.792611i	$-0.291279\pi$
$827$	2.39844e7	1.21945	0.609727	+	0.792611i	$0.291279\pi$
$828$	−2.57798e6	−0.130678
$829$	−3.50444e7	−1.77105	−0.885527	−	0.464588i	$-0.846202\pi$
$829$	−3.50444e7	−1.77105	−0.885527	+	0.464588i	$0.846202\pi$
$830$	26389.2	0.00132963
$831$	2.26318e7	1.13689
$832$	−6.34463e6	−0.317759
$833$	671328.	0.0335214
$834$	−5.59792e6	−0.278684
$835$	−8.20866e6	−0.407433
$836$	0	0
$837$	−3.89350e7	−1.92100
$838$	2.03574e7	1.00141
$839$	−2.28211e7	−1.11926	−0.559631	−	0.828742i	$-0.689057\pi$
$839$	−2.28211e7	−1.11926	−0.559631	+	0.828742i	$0.689057\pi$
$840$	−7.46643e6	−0.365102
$841$	1.31371e7	0.640484
$842$	8.75289e6	0.425472
$843$	1.59611e7	0.773558
$844$	−6.89958e6	−0.333401
$845$	316193.	0.0152339
$846$	1.35269e6	0.0649791
$847$	0	0
$848$	7.79591e6	0.372286
$849$	−2.42550e7	−1.15487
$850$	2.51781e6	0.119530
$851$	1.67739e7	0.793982
$852$	1.16903e7	0.551728
$853$	5.73956e6	0.270088	0.135044	−	0.990840i	$-0.456882\pi$
$853$	5.73956e6	0.270088	0.135044	+	0.990840i	$0.456882\pi$
$854$	−1.84220e7	−0.864353
$855$	−3.96238e6	−0.185371
$856$	−1.17831e7	−0.549635
$857$	−3.73797e7	−1.73854	−0.869268	−	0.494340i	$-0.835410\pi$
$857$	−3.73797e7	−1.73854	−0.869268	+	0.494340i	$0.835410\pi$
$858$	0	0
$859$	3.64400e7	1.68498	0.842491	−	0.538710i	$-0.181088\pi$
$859$	3.64400e7	1.68498	0.842491	+	0.538710i	$0.181088\pi$
$860$	3.73756e6	0.172323
$861$	2.43063e7	1.11741
$862$	1.60000e6	0.0733419
$863$	2.78829e7	1.27442	0.637208	−	0.770692i	$-0.280089\pi$
$863$	2.78829e7	1.27442	0.637208	+	0.770692i	$0.280089\pi$
$864$	2.45271e7	1.11779
$865$	3.46690e6	0.157544
$866$	−4.27108e6	−0.193527
$867$	−5.02583e6	−0.227070
$868$	2.87296e7	1.29429
$869$	0	0
$870$	−5.99465e6	−0.268513
$871$	−1.10114e6	−0.0491812
$872$	−2.67062e7	−1.18938
$873$	−1.39103e6	−0.0617732
$874$	1.78231e7	0.789231
$875$	−2.05570e6	−0.0907694
$876$	−1.05272e7	−0.463503
$877$	−4.44232e7	−1.95034	−0.975172	−	0.221450i	$-0.928921\pi$
$877$	−4.44232e7	−1.95034	−0.975172	+	0.221450i	$0.928921\pi$
$878$	−1.64452e7	−0.719953
$879$	2.48553e7	1.08504
$880$	0	0
$881$	−2.91300e7	−1.26445	−0.632223	−	0.774786i	$-0.717858\pi$
$881$	−2.91300e7	−1.26445	−0.632223	+	0.774786i	$0.717858\pi$
$882$	−83137.8	−0.00359855
$883$	−7.25628e6	−0.313193	−0.156597	−	0.987663i	$-0.550052\pi$
$883$	−7.25628e6	−0.313193	−0.156597	+	0.987663i	$0.550052\pi$
$884$	1.83413e7	0.789405
$885$	1.15307e7	0.494879
$886$	7.56683e6	0.323839
$887$	4.35823e7	1.85995	0.929974	−	0.367625i	$-0.119829\pi$
$887$	4.35823e7	1.85995	0.929974	+	0.367625i	$0.119829\pi$
$888$	−1.85860e7	−0.790959
$889$	2.54598e7	1.08044
$890$	−1.20036e6	−0.0507970
$891$	0	0
$892$	−8.11098e6	−0.341320
$893$	2.35881e7	0.989840
$894$	5.77664e6	0.241730
$895$	1.10693e7	0.461914
$896$	−2.10723e7	−0.876885
$897$	−1.68265e7	−0.698251
$898$	246891.	0.0102168
$899$	5.52780e7	2.28115
$900$	786462.	0.0323647
$901$	4.44569e7	1.82443
$902$	0	0
$903$	−1.17719e7	−0.480429
$904$	−3.08660e7	−1.25620
$905$	−8.72015e6	−0.353918
$906$	1.48904e7	0.602679
$907$	3.30488e7	1.33394	0.666972	−	0.745083i	$-0.267590\pi$
$907$	3.30488e7	1.33394	0.666972	+	0.745083i	$0.267590\pi$
$908$	1.16957e7	0.470772
$909$	−1.21874e6	−0.0489217
$910$	5.93712e6	0.237669
$911$	1.86352e7	0.743939	0.371969	−	0.928245i	$-0.378683\pi$
$911$	1.86352e7	0.743939	0.371969	+	0.928245i	$0.378683\pi$
$912$	9.27733e6	0.369348
$913$	0	0
$914$	−2.05740e7	−0.814618
$915$	−1.59276e7	−0.628924
$916$	1.90205e7	0.749002
$917$	−5.10630e6	−0.200532
$918$	1.64593e7	0.644623
$919$	1.31035e7	0.511800	0.255900	−	0.966703i	$-0.417628\pi$
$919$	1.31035e7	0.511800	0.255900	+	0.966703i	$0.417628\pi$
$920$	−8.47766e6	−0.330222
$921$	−2.39462e6	−0.0930226
$922$	−2.81769e6	−0.109160
$923$	−2.22771e7	−0.860706
$924$	0	0
$925$	−5.11721e6	−0.196643
$926$	5.12769e6	0.196514
$927$	6.90988e6	0.264102
$928$	−3.48223e7	−1.32736
$929$	−3.29446e7	−1.25241	−0.626203	−	0.779660i	$-0.715392\pi$
$929$	−3.29446e7	−1.25241	−0.626203	+	0.779660i	$0.715392\pi$
$930$	−9.84813e6	−0.373376
$931$	−1.44975e6	−0.0548174
$932$	3.32288e6	0.125307
$933$	3.52210e7	1.32464
$934$	2.00834e7	0.753302
$935$	0	0
$936$	−5.44335e6	−0.203084
$937$	−2.74601e7	−1.02177	−0.510885	−	0.859649i	$-0.670682\pi$
$937$	−2.74601e7	−1.02177	−0.510885	+	0.859649i	$0.670682\pi$
$938$	729147.	0.0270588
$939$	−4.50799e6	−0.166847
$940$	−4.68182e6	−0.172821
$941$	2.95875e7	1.08927	0.544633	−	0.838674i	$-0.316669\pi$
$941$	2.95875e7	1.08927	0.544633	+	0.838674i	$0.316669\pi$
$942$	−1.89661e7	−0.696387
$943$	2.75983e7	1.01066
$944$	7.88215e6	0.287882
$945$	−1.34384e7	−0.489519
$946$	0	0
$947$	−1.22561e7	−0.444097	−0.222048	−	0.975036i	$-0.571274\pi$
$947$	−1.22561e7	−0.444097	−0.222048	+	0.975036i	$0.571274\pi$
$948$	−1.21883e7	−0.440478
$949$	2.00608e7	0.723073
$950$	−5.43728e6	−0.195467
$951$	9.08729e6	0.325824
$952$	−2.91054e7	−1.04083
$953$	−3.84538e7	−1.37154	−0.685768	−	0.727820i	$-0.740534\pi$
$953$	−3.84538e7	−1.37154	−0.685768	+	0.727820i	$0.740534\pi$
$954$	−5.50558e6	−0.195854
$955$	5.78819e6	0.205369
$956$	3.10083e7	1.09732
$957$	0	0
$958$	8.53101e6	0.300322
$959$	4.00621e7	1.40666
$960$	3.63239e6	0.127208
$961$	6.21827e7	2.17200
$962$	1.47791e7	0.514887
$963$	−3.90916e6	−0.135837
$964$	−1.55533e7	−0.539051
$965$	−9.49178e6	−0.328117
$966$	1.11420e7	0.384168
$967$	1.37466e7	0.472747	0.236373	−	0.971662i	$-0.424041\pi$
$967$	1.37466e7	0.472747	0.236373	+	0.971662i	$0.424041\pi$
$968$	0	0
$969$	5.29049e7	1.81003
$970$	−1.90880e6	−0.0651375
$971$	−4.57484e7	−1.55714	−0.778571	−	0.627557i	$-0.784055\pi$
$971$	−4.57484e7	−1.55714	−0.778571	+	0.627557i	$0.784055\pi$
$972$	9.33479e6	0.316912
$973$	1.78165e7	0.603311
$974$	−3.84254e6	−0.129784
$975$	5.13324e6	0.172934
$976$	−1.08878e7	−0.365860
$977$	−4.27421e6	−0.143258	−0.0716291	−	0.997431i	$-0.522820\pi$
$977$	−4.27421e6	−0.143258	−0.0716291	+	0.997431i	$0.522820\pi$
$978$	−2.06571e7	−0.690592
$979$	0	0
$980$	287749.	0.00957082
$981$	−8.86005e6	−0.293943
$982$	516463.	0.0170907
$983$	−1.33055e7	−0.439186	−0.219593	−	0.975592i	$-0.570473\pi$
$983$	−1.33055e7	−0.439186	−0.219593	+	0.975592i	$0.570473\pi$
$984$	−3.05798e7	−1.00681
$985$	6.93212e6	0.227654
$986$	−2.33682e7	−0.765477
$987$	1.47460e7	0.481817
$988$	−3.96085e7	−1.29091
$989$	−1.33663e7	−0.434531
$990$	0	0
$991$	3.66440e7	1.18527	0.592637	−	0.805470i	$-0.298087\pi$
$991$	3.66440e7	1.18527	0.592637	+	0.805470i	$0.298087\pi$
$992$	−5.72069e7	−1.84573
$993$	−3.24593e6	−0.104464
$994$	1.47513e7	0.473548
$995$	1.89458e7	0.606675
$996$	−110057.	−0.00351537
$997$	5.33614e7	1.70016	0.850079	−	0.526655i	$-0.176554\pi$
$997$	5.33614e7	1.70016	0.850079	+	0.526655i	$0.176554\pi$
$998$	1.45694e7	0.463036
$999$	−3.34520e7	−1.06049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.e.1.4		6
11.10	odd	2		55.6.a.d.1.3	✓	6
33.32	even	2		495.6.a.l.1.4		6
44.43	even	2		880.6.a.u.1.5		6
55.32	even	4		275.6.b.f.199.5		12
55.43	even	4		275.6.b.f.199.8		12
55.54	odd	2		275.6.a.f.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.a.d.1.3	✓	6	11.10	odd	2
275.6.a.f.1.4		6	55.54	odd	2
275.6.b.f.199.5		12	55.32	even	4
275.6.b.f.199.8		12	55.43	even	4
495.6.a.l.1.4		6	33.32	even	2
605.6.a.e.1.4		6	1.1	even	1	trivial
880.6.a.u.1.5		6	44.43	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+3.01414 q^{2} -13.7145 q^{3} -22.9149 q^{4} -25.0000 q^{5} -41.3374 q^{6} +131.565 q^{7} -165.521 q^{8} -54.9135 q^{9} -75.3536 q^{10} +314.266 q^{12} -598.870 q^{13} +396.555 q^{14} +342.862 q^{15} +234.373 q^{16} +1336.53 q^{17} -165.517 q^{18} -2886.27 q^{19} +572.874 q^{20} -1804.34 q^{21} -2048.71 q^{23} +2270.04 q^{24} +625.000 q^{25} -1805.08 q^{26} +4085.72 q^{27} -3014.80 q^{28} -5800.71 q^{29} +1033.43 q^{30} -9529.52 q^{31} +6003.12 q^{32} +4028.50 q^{34} -3289.12 q^{35} +1258.34 q^{36} -8187.53 q^{37} -8699.64 q^{38} +8213.18 q^{39} +4138.04 q^{40} -13471.0 q^{41} -5438.54 q^{42} +6524.24 q^{43} +1372.84 q^{45} -6175.12 q^{46} -8172.53 q^{47} -3214.29 q^{48} +502.291 q^{49} +1883.84 q^{50} -18329.8 q^{51} +13723.1 q^{52} +33262.9 q^{53} +12315.0 q^{54} -21776.8 q^{56} +39583.7 q^{57} -17484.2 q^{58} +33630.9 q^{59} -7856.65 q^{60} -46455.0 q^{61} -28723.3 q^{62} -7224.68 q^{63} +10594.3 q^{64} +14971.7 q^{65} +1838.70 q^{67} -30626.6 q^{68} +28097.0 q^{69} -9913.88 q^{70} +37198.6 q^{71} +9089.37 q^{72} -33497.7 q^{73} -24678.4 q^{74} -8571.54 q^{75} +66138.8 q^{76} +24755.7 q^{78} -38783.5 q^{79} -5859.31 q^{80} -42689.5 q^{81} -40603.6 q^{82} -350.204 q^{83} +41346.4 q^{84} -33413.3 q^{85} +19665.0 q^{86} +79553.6 q^{87} +15929.8 q^{89} +4137.93 q^{90} -78790.2 q^{91} +46946.2 q^{92} +130692. q^{93} -24633.2 q^{94} +72156.8 q^{95} -82329.6 q^{96} +25331.2 q^{97} +1513.98 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 115 q^{4} - 150 q^{5} - 325 q^{6} + 66 q^{7} - 249 q^{8} + 832 q^{9} + 75 q^{10} + 1301 q^{12} + 972 q^{13} + 2017 q^{14} + 6675 q^{16} - 712 q^{17} - 5920 q^{18} - 610 q^{19} - 2875 q^{20}+ \cdots + 351884 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 115 * q^4 - 150 * q^5 - 325 * q^6 + 66 * q^7 - 249 * q^8 + 832 * q^9 + 75 * q^10 + 1301 * q^12 + 972 * q^13 + 2017 * q^14 + 6675 * q^16 - 712 * q^17 - 5920 * q^18 - 610 * q^19 - 2875 * q^20 - 2508 * q^21 + 7100 * q^23 - 13447 * q^24 + 3750 * q^25 - 7742 * q^26 - 2520 * q^27 + 33171 * q^28 - 10964 * q^29 + 8125 * q^30 + 8868 * q^31 - 10861 * q^32 - 42673 * q^34 - 1650 * q^35 - 30116 * q^36 - 15506 * q^37 + 26185 * q^38 - 7208 * q^39 + 6225 * q^40 - 160 * q^41 - 47111 * q^42 - 7032 * q^43 - 20800 * q^45 - 1650 * q^46 - 46320 * q^47 - 22215 * q^48 + 48512 * q^49 - 1875 * q^50 + 43378 * q^51 + 145838 * q^52 + 30518 * q^53 + 56881 * q^54 - 21297 * q^56 + 5640 * q^57 + 51477 * q^58 + 120532 * q^59 - 32525 * q^60 + 9228 * q^61 + 81355 * q^62 - 222460 * q^63 + 302839 * q^64 - 24300 * q^65 + 47432 * q^67 - 78111 * q^68 + 118960 * q^69 - 50425 * q^70 + 163948 * q^71 + 212580 * q^72 - 78528 * q^73 - 133501 * q^74 + 29355 * q^76 - 138086 * q^78 + 36712 * q^79 - 166875 * q^80 + 202166 * q^81 - 128902 * q^82 - 133792 * q^83 - 119033 * q^84 + 17800 * q^85 + 83996 * q^86 + 267082 * q^87 + 254946 * q^89 + 148000 * q^90 + 167844 * q^91 - 5134 * q^92 - 224250 * q^93 - 31414 * q^94 + 15250 * q^95 - 234415 * q^96 + 17404 * q^97 + 351884 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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