LMFDB - Embedded newform 49.6.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.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:	$7.85880717084$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{113})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 59x^{2} + 60x + 674 $ x^4 - 2x^3 - 59x^2 + 60*x + 674
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.22929$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.81507 q^{2} +23.5186 q^{3} +29.0754 q^{4} -74.2753 q^{5} -183.799 q^{6} +22.8562 q^{8} +310.123 q^{9} +O(q^{10})$	\(q-7.81507 q^{2} +23.5186 q^{3} +29.0754 q^{4} -74.2753 q^{5} -183.799 q^{6} +22.8562 q^{8} +310.123 q^{9} +580.467 q^{10} -424.219 q^{11} +683.811 q^{12} -252.233 q^{13} -1746.85 q^{15} -1109.03 q^{16} -1104.35 q^{17} -2423.64 q^{18} -6.47100 q^{19} -2159.58 q^{20} +3315.30 q^{22} -3612.39 q^{23} +537.546 q^{24} +2391.82 q^{25} +1971.22 q^{26} +1578.65 q^{27} -5005.02 q^{29} +13651.8 q^{30} +2821.69 q^{31} +7935.79 q^{32} -9977.03 q^{33} +8630.55 q^{34} +9016.95 q^{36} -2046.88 q^{37} +50.5713 q^{38} -5932.17 q^{39} -1697.65 q^{40} +9393.81 q^{41} +10320.8 q^{43} -12334.3 q^{44} -23034.5 q^{45} +28231.1 q^{46} +17035.6 q^{47} -26082.9 q^{48} -18692.3 q^{50} -25972.7 q^{51} -7333.78 q^{52} -39506.7 q^{53} -12337.3 q^{54} +31509.0 q^{55} -152.189 q^{57} +39114.6 q^{58} +33949.8 q^{59} -50790.3 q^{60} +28295.2 q^{61} -22051.7 q^{62} -26529.7 q^{64} +18734.7 q^{65} +77971.2 q^{66} +56100.9 q^{67} -32109.3 q^{68} -84958.2 q^{69} -15537.4 q^{71} +7088.26 q^{72} -78219.5 q^{73} +15996.5 q^{74} +56252.3 q^{75} -188.147 q^{76} +46360.3 q^{78} -45335.5 q^{79} +82373.9 q^{80} -38232.4 q^{81} -73413.3 q^{82} +1381.82 q^{83} +82025.7 q^{85} -80657.6 q^{86} -117711. q^{87} -9696.05 q^{88} -68879.4 q^{89} +180016. q^{90} -105031. q^{92} +66362.1 q^{93} -133134. q^{94} +480.635 q^{95} +186638. q^{96} +108857. q^{97} -131560. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{2} + 10 q^{4} - 270 q^{8} + 220 q^{9}+O(q^{10}) $ 4 * q - 10 * q^2 + 10 * q^4 - 270 * q^8 + 220 * q^9	$ 4 q - 10 q^{2} + 10 q^{4} - 270 q^{8} + 220 q^{9} - 1952 q^{11} - 4096 q^{15} - 1566 q^{16} - 5974 q^{18} + 3524 q^{22} - 7136 q^{23} + 2764 q^{25} - 3352 q^{29} + 25608 q^{30} + 27810 q^{32} + 27670 q^{36} - 9208 q^{37} + 2464 q^{39} + 20448 q^{43} + 1900 q^{44} + 56712 q^{46} - 43070 q^{50} - 67408 q^{51} - 102920 q^{53} - 15576 q^{57} + 96972 q^{58} - 87080 q^{60} - 40318 q^{64} - 63168 q^{65} - 22896 q^{67} - 153824 q^{71} + 77358 q^{72} + 17596 q^{74} + 133056 q^{78} - 90688 q^{79} - 17204 q^{81} + 272656 q^{85} - 161860 q^{86} + 154812 q^{88} - 212200 q^{92} + 247760 q^{93} + 108224 q^{95} - 42272 q^{99}+O(q^{100}) $ 4 * q - 10 * q^2 + 10 * q^4 - 270 * q^8 + 220 * q^9 - 1952 * q^11 - 4096 * q^15 - 1566 * q^16 - 5974 * q^18 + 3524 * q^22 - 7136 * q^23 + 2764 * q^25 - 3352 * q^29 + 25608 * q^30 + 27810 * q^32 + 27670 * q^36 - 9208 * q^37 + 2464 * q^39 + 20448 * q^43 + 1900 * q^44 + 56712 * q^46 - 43070 * q^50 - 67408 * q^51 - 102920 * q^53 - 15576 * q^57 + 96972 * q^58 - 87080 * q^60 - 40318 * q^64 - 63168 * q^65 - 22896 * q^67 - 153824 * q^71 + 77358 * q^72 + 17596 * q^74 + 133056 * q^78 - 90688 * q^79 - 17204 * q^81 + 272656 * q^85 - 161860 * q^86 + 154812 * q^88 - 212200 * q^92 + 247760 * q^93 + 108224 * q^95 - 42272 * 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 $

$2$	−7.81507	−1.38152	−0.690761	−	0.723083i	$-0.742724\pi$
$2$	−7.81507	−1.38152	−0.690761	+	0.723083i	$0.742724\pi$
$3$	23.5186	1.50872	0.754359	−	0.656462i	$-0.227948\pi$
$3$	23.5186	1.50872	0.754359	+	0.656462i	$0.227948\pi$
$4$	29.0754	0.908605
$5$	−74.2753	−1.32868	−0.664339	−	0.747432i	$-0.731287\pi$
$5$	−74.2753	−1.32868	−0.664339	+	0.747432i	$0.731287\pi$
$6$	−183.799	−2.08433
$7$	0	0
$7$	0	0
$8$	22.8562	0.126264
$9$	310.123	1.27623
$10$	580.467	1.83560
$11$	−424.219	−1.05708	−0.528541	−	0.848908i	$-0.677261\pi$
$11$	−424.219	−1.05708	−0.528541	+	0.848908i	$0.677261\pi$
$12$	683.811	1.37083
$13$	−252.233	−0.413946	−0.206973	−	0.978347i	$-0.566361\pi$
$13$	−252.233	−0.413946	−0.206973	+	0.978347i	$0.566361\pi$
$14$	0	0
$15$	−1746.85	−2.00460
$16$	−1109.03	−1.08304
$17$	−1104.35	−0.926794	−0.463397	−	0.886151i	$-0.653370\pi$
$17$	−1104.35	−0.926794	−0.463397	+	0.886151i	$0.653370\pi$
$18$	−2423.64	−1.76314
$19$	−6.47100	−0.00411232	−0.00205616	−	0.999998i	$-0.500654\pi$
$19$	−6.47100	−0.00411232	−0.00205616	+	0.999998i	$0.500654\pi$
$20$	−2159.58	−1.20724
$21$	0	0
$22$	3315.30	1.46038
$23$	−3612.39	−1.42388	−0.711942	−	0.702239i	$-0.752184\pi$
$23$	−3612.39	−1.42388	−0.711942	+	0.702239i	$0.752184\pi$
$24$	537.546	0.190497
$25$	2391.82	0.765383
$26$	1971.22	0.571876
$27$	1578.65	0.416751
$28$	0	0
$29$	−5005.02	−1.10512	−0.552561	−	0.833472i	$-0.686350\pi$
$29$	−5005.02	−1.10512	−0.552561	+	0.833472i	$0.686350\pi$
$30$	13651.8	2.76940
$31$	2821.69	0.527357	0.263679	−	0.964611i	$-0.415064\pi$
$31$	2821.69	0.527357	0.263679	+	0.964611i	$0.415064\pi$
$32$	7935.79	1.36998
$33$	−9977.03	−1.59484
$34$	8630.55	1.28039
$35$	0	0
$36$	9016.95	1.15959
$37$	−2046.88	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$37$	−2046.88	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$38$	50.5713	0.00568127
$39$	−5932.17	−0.624528
$40$	−1697.65	−0.167764
$41$	9393.81	0.872734	0.436367	−	0.899769i	$-0.356265\pi$
$41$	9393.81	0.872734	0.436367	+	0.899769i	$0.356265\pi$
$42$	0	0
$43$	10320.8	0.851218	0.425609	−	0.904907i	$-0.360060\pi$
$43$	10320.8	0.851218	0.425609	+	0.904907i	$0.360060\pi$
$44$	−12334.3	−0.960470
$45$	−23034.5	−1.69570
$46$	28231.1	1.96713
$47$	17035.6	1.12490	0.562448	−	0.826833i	$-0.309860\pi$
$47$	17035.6	1.12490	0.562448	+	0.826833i	$0.309860\pi$
$48$	−26082.9	−1.63400
$49$	0	0
$50$	−18692.3	−1.05739
$51$	−25972.7	−1.39827
$52$	−7333.78	−0.376114
$53$	−39506.7	−1.93188	−0.965941	−	0.258761i	$-0.916686\pi$
$53$	−39506.7	−1.93188	−0.965941	+	0.258761i	$0.916686\pi$
$54$	−12337.3	−0.575750
$55$	31509.0	1.40452
$56$	0	0
$57$	−152.189	−0.00620433
$58$	39114.6	1.52675
$59$	33949.8	1.26972	0.634859	−	0.772628i	$-0.281058\pi$
$59$	33949.8	1.26972	0.634859	+	0.772628i	$0.281058\pi$
$60$	−50790.3	−1.82139
$61$	28295.2	0.973618	0.486809	−	0.873508i	$-0.338161\pi$
$61$	28295.2	0.973618	0.486809	+	0.873508i	$0.338161\pi$
$62$	−22051.7	−0.728556
$63$	0	0
$64$	−26529.7	−0.809621
$65$	18734.7	0.550001
$66$	77971.2	2.20330
$67$	56100.9	1.52680	0.763402	−	0.645924i	$-0.223528\pi$
$67$	56100.9	1.52680	0.763402	+	0.645924i	$0.223528\pi$
$68$	−32109.3	−0.842090
$69$	−84958.2	−2.14824
$70$	0	0
$71$	−15537.4	−0.365791	−0.182895	−	0.983132i	$-0.558547\pi$
$71$	−15537.4	−0.365791	−0.182895	+	0.983132i	$0.558547\pi$
$72$	7088.26	0.161142
$73$	−78219.5	−1.71794	−0.858970	−	0.512025i	$-0.828895\pi$
$73$	−78219.5	−1.71794	−0.858970	+	0.512025i	$0.828895\pi$
$74$	15996.5	0.339583
$75$	56252.3	1.15475
$76$	−188.147	−0.00373648
$77$	0	0
$78$	46360.3	0.862800
$79$	−45335.5	−0.817279	−0.408640	−	0.912696i	$-0.633997\pi$
$79$	−45335.5	−0.817279	−0.408640	+	0.912696i	$0.633997\pi$
$80$	82373.9	1.43901
$81$	−38232.4	−0.647469
$82$	−73413.3	−1.20570
$83$	1381.82	0.0220169	0.0110085	−	0.999939i	$-0.496496\pi$
$83$	1381.82	0.0220169	0.0110085	+	0.999939i	$0.496496\pi$
$84$	0	0
$85$	82025.7	1.23141
$86$	−80657.6	−1.17598
$87$	−117711.	−1.66732
$88$	−9696.05	−0.133471
$89$	−68879.4	−0.921753	−0.460876	−	0.887464i	$-0.652465\pi$
$89$	−68879.4	−0.921753	−0.460876	+	0.887464i	$0.652465\pi$
$90$	180016.	2.34264
$91$	0	0
$92$	−105031.	−1.29375
$93$	66362.1	0.795633
$94$	−133134.	−1.55407
$95$	480.635	0.00546395
$96$	186638.	2.06692
$97$	108857.	1.17470	0.587351	−	0.809332i	$-0.300171\pi$
$97$	108857.	1.17470	0.587351	+	0.809332i	$0.300171\pi$
$98$	0	0
$99$	−131560.	−1.34908
$100$	69543.1	0.695431
$101$	17972.3	0.175307	0.0876535	−	0.996151i	$-0.472063\pi$
$101$	17972.3	0.175307	0.0876535	+	0.996151i	$0.472063\pi$
$102$	202978.	1.93174
$103$	31773.7	0.295103	0.147552	−	0.989054i	$-0.452861\pi$
$103$	31773.7	0.295103	0.147552	+	0.989054i	$0.452861\pi$
$104$	−5765.11	−0.0522666
$105$	0	0
$106$	308747.	2.66894
$107$	8229.36	0.0694875	0.0347438	−	0.999396i	$-0.488938\pi$
$107$	8229.36	0.0694875	0.0347438	+	0.999396i	$0.488938\pi$
$108$	45899.8	0.378662
$109$	−11068.7	−0.0892338	−0.0446169	−	0.999004i	$-0.514207\pi$
$109$	−11068.7	−0.0892338	−0.0446169	+	0.999004i	$0.514207\pi$
$110$	−246245.	−1.94038
$111$	−48139.6	−0.370847
$112$	0	0
$113$	65184.3	0.480228	0.240114	−	0.970745i	$-0.422815\pi$
$113$	65184.3	0.480228	0.240114	+	0.970745i	$0.422815\pi$
$114$	1189.37	0.00857143
$115$	268311.	1.89188
$116$	−145523.	−1.00412
$117$	−78223.5	−0.528290
$118$	−265320.	−1.75414
$119$	0	0
$120$	−39926.4	−0.253109
$121$	18910.9	0.117422
$122$	−221129.	−1.34508
$123$	220929.	1.31671
$124$	82041.7	0.479160
$125$	54456.9	0.311730
$126$	0	0
$127$	−194777.	−1.07159	−0.535796	−	0.844348i	$-0.679988\pi$
$127$	−194777.	−1.07159	−0.535796	+	0.844348i	$0.679988\pi$
$128$	−46614.1	−0.251473
$129$	242730.	1.28425
$130$	−146413.	−0.759839
$131$	−236503.	−1.20409	−0.602046	−	0.798462i	$-0.705647\pi$
$131$	−236503.	−1.20409	−0.602046	+	0.798462i	$0.705647\pi$
$132$	−290086.	−1.44908
$133$	0	0
$134$	−438433.	−2.10931
$135$	−117255.	−0.553727
$136$	−25241.2	−0.117021
$137$	−200903.	−0.914503	−0.457252	−	0.889337i	$-0.651166\pi$
$137$	−200903.	−0.914503	−0.457252	+	0.889337i	$0.651166\pi$
$138$	663954.	2.96784
$139$	52985.2	0.232604	0.116302	−	0.993214i	$-0.462896\pi$
$139$	52985.2	0.232604	0.116302	+	0.993214i	$0.462896\pi$
$140$	0	0
$141$	400653.	1.69715
$142$	121426.	0.505348
$143$	107002.	0.437575
$144$	−343938.	−1.38221
$145$	371749.	1.46835
$146$	611291.	2.37337
$147$	0	0
$148$	−59513.7	−0.223338
$149$	−100770.	−0.371849	−0.185925	−	0.982564i	$-0.559528\pi$
$149$	−100770.	−0.371849	−0.185925	+	0.982564i	$0.559528\pi$
$150$	−439616.	−1.59531
$151$	−457904.	−1.63430	−0.817150	−	0.576425i	$-0.804447\pi$
$151$	−457904.	−1.63430	−0.817150	+	0.576425i	$0.804447\pi$
$152$	−147.903	−0.000519239 0
$153$	−342484.	−1.18280
$154$	0	0
$155$	−209582.	−0.700688
$156$	−172480.	−0.567450
$157$	−179037.	−0.579688	−0.289844	−	0.957074i	$-0.593603\pi$
$157$	−179037.	−0.579688	−0.289844	+	0.957074i	$0.593603\pi$
$158$	354300.	1.12909
$159$	−929141.	−2.91467
$160$	−589433.	−1.82027
$161$	0	0
$162$	298789.	0.894494
$163$	243610.	0.718168	0.359084	−	0.933305i	$-0.383089\pi$
$163$	243610.	0.718168	0.359084	+	0.933305i	$0.383089\pi$
$164$	273128.	0.792971
$165$	741047.	2.11902
$166$	−10799.0	−0.0304169
$167$	117033.	0.324725	0.162362	−	0.986731i	$-0.448089\pi$
$167$	117033.	0.324725	0.162362	+	0.986731i	$0.448089\pi$
$168$	0	0
$169$	−307671.	−0.828648
$170$	−641037.	−1.70122
$171$	−2006.81	−0.00524826
$172$	300080.	0.773421
$173$	269733.	0.685203	0.342602	−	0.939481i	$-0.388692\pi$
$173$	269733.	0.685203	0.342602	+	0.939481i	$0.388692\pi$
$174$	919919.	2.30344
$175$	0	0
$176$	470474.	1.14486
$177$	798451.	1.91564
$178$	538298.	1.27342
$179$	376525.	0.878336	0.439168	−	0.898405i	$-0.355273\pi$
$179$	376525.	0.878336	0.439168	+	0.898405i	$0.355273\pi$
$180$	−669737.	−1.54072
$181$	−434641.	−0.986131	−0.493065	−	0.869992i	$-0.664124\pi$
$181$	−434641.	−0.986131	−0.493065	+	0.869992i	$0.664124\pi$
$182$	0	0
$183$	665464.	1.46891
$184$	−82565.5	−0.179785
$185$	152032.	0.326593
$186$	−518625.	−1.09919
$187$	468485.	0.979697
$188$	495316.	1.02209
$189$	0	0
$190$	−3756.20	−0.00754857
$191$	565940.	1.12250	0.561250	−	0.827646i	$-0.310320\pi$
$191$	565940.	1.12250	0.561250	+	0.827646i	$0.310320\pi$
$192$	−623940.	−1.22149
$193$	514461.	0.994167	0.497084	−	0.867703i	$-0.334404\pi$
$193$	514461.	0.994167	0.497084	+	0.867703i	$0.334404\pi$
$194$	−850727.	−1.62288
$195$	440614.	0.829796
$196$	0	0
$197$	−298541.	−0.548073	−0.274037	−	0.961719i	$-0.588359\pi$
$197$	−298541.	−0.548073	−0.274037	+	0.961719i	$0.588359\pi$
$198$	1.02815e6	1.86378
$199$	−591919.	−1.05957	−0.529785	−	0.848132i	$-0.677727\pi$
$199$	−591919.	−1.05957	−0.529785	+	0.848132i	$0.677727\pi$
$200$	54668.1	0.0966404
$201$	1.31941e6	2.30351
$202$	−140455.	−0.242191
$203$	0	0
$204$	−755165.	−1.27048
$205$	−697728.	−1.15958
$206$	−248313.	−0.407692
$207$	−1.12029e6	−1.81720
$208$	279736.	0.448321
$209$	2745.12	0.00434706
$210$	0	0
$211$	−140535.	−0.217309	−0.108655	−	0.994080i	$-0.534654\pi$
$211$	−140535.	−0.217309	−0.108655	+	0.994080i	$0.534654\pi$
$212$	−1.14867e6	−1.75532
$213$	−365418.	−0.551875
$214$	−64313.1	−0.0959986
$215$	−766579.	−1.13099
$216$	36082.0	0.0526206
$217$	0	0
$218$	86502.5	0.123278
$219$	−1.83961e6	−2.59189
$220$	916136.	1.27615
$221$	278553.	0.383643
$222$	376215.	0.512334
$223$	490.526	0.000660541 0	0.000330271	−	1.00000i	$-0.499895\pi$
$223$	490.526	0.000660541 0	0.000330271		1.00000i	$0.499895\pi$
$224$	0	0
$225$	741761.	0.976804
$226$	−509420.	−0.663445
$227$	593898.	0.764975	0.382488	−	0.923961i	$-0.375067\pi$
$227$	593898.	0.764975	0.382488	+	0.923961i	$0.375067\pi$
$228$	−4424.94	−0.00563729
$229$	−35880.3	−0.0452135	−0.0226067	−	0.999744i	$-0.507197\pi$
$229$	−35880.3	−0.0452135	−0.0226067	+	0.999744i	$0.507197\pi$
$230$	−2.09687e6	−2.61368
$231$	0	0
$232$	−114396.	−0.139537
$233$	1.24822e6	1.50626	0.753131	−	0.657871i	$-0.228543\pi$
$233$	1.24822e6	1.50626	0.753131	+	0.657871i	$0.228543\pi$
$234$	611322.	0.729845
$235$	−1.26532e6	−1.49462
$236$	987102.	1.15367
$237$	−1.06623e6	−1.23304
$238$	0	0
$239$	−576943.	−0.653339	−0.326669	−	0.945139i	$-0.605926\pi$
$239$	−576943.	−0.653339	−0.326669	+	0.945139i	$0.605926\pi$
$240$	1.93732e6	2.17106
$241$	−1.38241e6	−1.53318	−0.766592	−	0.642135i	$-0.778049\pi$
$241$	−1.38241e6	−1.53318	−0.766592	+	0.642135i	$0.778049\pi$
$242$	−147790.	−0.162221
$243$	−1.28278e6	−1.39360
$244$	822694.	0.884634
$245$	0	0
$246$	−1.72658e6	−1.81906
$247$	1632.20	0.00170228
$248$	64493.2	0.0665863
$249$	32498.5	0.0332173
$250$	−425585.	−0.430662
$251$	323217.	0.323824	0.161912	−	0.986805i	$-0.448234\pi$
$251$	323217.	0.323824	0.161912	+	0.986805i	$0.448234\pi$
$252$	0	0
$253$	1.53244e6	1.50516
$254$	1.52220e6	1.48043
$255$	1.92913e6	1.85785
$256$	1.21324e6	1.15704
$257$	1.84601e6	1.74342	0.871711	−	0.490021i	$-0.163011\pi$
$257$	1.84601e6	1.74342	0.871711	+	0.490021i	$0.163011\pi$
$258$	−1.89695e6	−1.77422
$259$	0	0
$260$	544719.	0.499734
$261$	−1.55217e6	−1.41039
$262$	1.84829e6	1.66348
$263$	−458222.	−0.408495	−0.204248	−	0.978919i	$-0.565475\pi$
$263$	−458222.	−0.408495	−0.204248	+	0.978919i	$0.565475\pi$
$264$	−228037.	−0.201371
$265$	2.93437e6	2.56685
$266$	0	0
$267$	−1.61995e6	−1.39066
$268$	1.63115e6	1.38726
$269$	416958.	0.351327	0.175663	−	0.984450i	$-0.443793\pi$
$269$	416958.	0.351327	0.175663	+	0.984450i	$0.443793\pi$
$270$	916354.	0.764987
$271$	−900379.	−0.744735	−0.372368	−	0.928085i	$-0.621454\pi$
$271$	−900379.	−0.744735	−0.372368	+	0.928085i	$0.621454\pi$
$272$	1.22476e6	1.00376
$273$	0	0
$274$	1.57007e6	1.26341
$275$	−1.01466e6	−0.809073
$276$	−2.47019e6	−1.95190
$277$	−447641.	−0.350535	−0.175267	−	0.984521i	$-0.556079\pi$
$277$	−447641.	−0.350535	−0.175267	+	0.984521i	$0.556079\pi$
$278$	−414083.	−0.321348
$279$	875072.	0.673029
$280$	0	0
$281$	−768521.	−0.580617	−0.290309	−	0.956933i	$-0.593758\pi$
$281$	−768521.	−0.580617	−0.290309	+	0.956933i	$0.593758\pi$
$282$	−3.13113e6	−2.34465
$283$	−2.13220e6	−1.58256	−0.791282	−	0.611452i	$-0.790586\pi$
$283$	−2.13220e6	−1.58256	−0.791282	+	0.611452i	$0.790586\pi$
$284$	−451756.	−0.332359
$285$	11303.9	0.00824356
$286$	−836230.	−0.604520
$287$	0	0
$288$	2.46107e6	1.74841
$289$	−200275.	−0.141053
$290$	−2.90525e6	−2.02856
$291$	2.56017e6	1.77229
$292$	−2.27426e6	−1.56093
$293$	−2.42669e6	−1.65138	−0.825688	−	0.564128i	$-0.809213\pi$
$293$	−2.42669e6	−1.65138	−0.825688	+	0.564128i	$0.809213\pi$
$294$	0	0
$295$	−2.52163e6	−1.68704
$296$	−46783.9	−0.0310361
$297$	−669693.	−0.440539
$298$	787528.	0.513719
$299$	911164.	0.589411
$300$	1.63556e6	1.04921
$301$	0	0
$302$	3.57855e6	2.25782
$303$	422682.	0.264489
$304$	7176.56	0.00445382
$305$	−2.10164e6	−1.29362
$306$	2.67654e6	1.63407
$307$	2.44328e6	1.47954	0.739772	−	0.672857i	$-0.234933\pi$
$307$	2.44328e6	1.47954	0.739772	+	0.672857i	$0.234933\pi$
$308$	0	0
$309$	747271.	0.445228
$310$	1.63790e6	0.968016
$311$	−1.15465e6	−0.676938	−0.338469	−	0.940978i	$-0.609909\pi$
$311$	−1.15465e6	−0.676938	−0.338469	+	0.940978i	$0.609909\pi$
$312$	−135587.	−0.0788555
$313$	−1.65706e6	−0.956044	−0.478022	−	0.878348i	$-0.658646\pi$
$313$	−1.65706e6	−0.956044	−0.478022	+	0.878348i	$0.658646\pi$
$314$	1.39919e6	0.800852
$315$	0	0
$316$	−1.31815e6	−0.742584
$317$	821361.	0.459077	0.229539	−	0.973300i	$-0.426278\pi$
$317$	821361.	0.459077	0.229539	+	0.973300i	$0.426278\pi$
$318$	7.26130e6	4.02668
$319$	2.12322e6	1.16821
$320$	1.97050e6	1.07572
$321$	193543.	0.104837
$322$	0	0
$323$	7146.23	0.00381128
$324$	−1.11162e6	−0.588294
$325$	−603298.	−0.316828
$326$	−1.90383e6	−0.992166
$327$	−260319.	−0.134629
$328$	214707.	0.110195
$329$	0	0
$330$	−5.79134e6	−2.92748
$331$	−95670.7	−0.0479964	−0.0239982	−	0.999712i	$-0.507640\pi$
$331$	−95670.7	−0.0479964	−0.0239982	+	0.999712i	$0.507640\pi$
$332$	40177.0	0.0200047
$333$	−634785.	−0.313701
$334$	−914618.	−0.448615
$335$	−4.16691e6	−2.02863
$336$	0	0
$337$	2.37020e6	1.13687	0.568435	−	0.822728i	$-0.307549\pi$
$337$	2.37020e6	1.13687	0.568435	+	0.822728i	$0.307549\pi$
$338$	2.40447e6	1.14480
$339$	1.53304e6	0.724528
$340$	2.38493e6	1.11887
$341$	−1.19701e6	−0.557460
$342$	15683.4	0.00725060
$343$	0	0
$344$	235894.	0.107478
$345$	6.31029e6	2.85431
$346$	−2.10799e6	−0.946624
$347$	490571.	0.218715	0.109358	−	0.994002i	$-0.465121\pi$
$347$	490571.	0.218715	0.109358	+	0.994002i	$0.465121\pi$
$348$	−3.42249e6	−1.51493
$349$	−4.21208e6	−1.85111	−0.925557	−	0.378607i	$-0.876403\pi$
$349$	−4.21208e6	−1.85111	−0.925557	+	0.378607i	$0.876403\pi$
$350$	0	0
$351$	−398188.	−0.172512
$352$	−3.36651e6	−1.44818
$353$	3.17378e6	1.35563	0.677814	−	0.735234i	$-0.262928\pi$
$353$	3.17378e6	1.35563	0.677814	+	0.735234i	$0.262928\pi$
$354$	−6.23995e6	−2.64651
$355$	1.15405e6	0.486018
$356$	−2.00269e6	−0.837509
$357$	0	0
$358$	−2.94257e6	−1.21344
$359$	−3.40098e6	−1.39273	−0.696366	−	0.717687i	$-0.745201\pi$
$359$	−3.40098e6	−1.39273	−0.696366	+	0.717687i	$0.745201\pi$
$360$	−526483.	−0.214105
$361$	−2.47606e6	−0.999983
$362$	3.39675e6	1.36236
$363$	444757.	0.177156
$364$	0	0
$365$	5.80978e6	2.28259
$366$	−5.20065e6	−2.02934
$367$	1.96872e6	0.762988	0.381494	−	0.924371i	$-0.375410\pi$
$367$	1.96872e6	0.762988	0.381494	+	0.924371i	$0.375410\pi$
$368$	4.00626e6	1.54213
$369$	2.91324e6	1.11381
$370$	−1.18814e6	−0.451196
$371$	0	0
$372$	1.92950e6	0.722917
$373$	−3.47889e6	−1.29470	−0.647349	−	0.762194i	$-0.724122\pi$
$373$	−3.47889e6	−1.29470	−0.647349	+	0.762194i	$0.724122\pi$
$374$	−3.66124e6	−1.35347
$375$	1.28075e6	0.470312
$376$	389369.	0.142034
$377$	1.26243e6	0.457462
$378$	0	0
$379$	−421294.	−0.150656	−0.0753281	−	0.997159i	$-0.524000\pi$
$379$	−421294.	−0.150656	−0.0753281	+	0.997159i	$0.524000\pi$
$380$	13974.7	0.00496457
$381$	−4.58089e6	−1.61673
$382$	−4.42286e6	−1.55076
$383$	2.66910e6	0.929754	0.464877	−	0.885375i	$-0.346099\pi$
$383$	2.66910e6	0.929754	0.464877	+	0.885375i	$0.346099\pi$
$384$	−1.09630e6	−0.379402
$385$	0	0
$386$	−4.02055e6	−1.37346
$387$	3.20071e6	1.08635
$388$	3.16506e6	1.06734
$389$	3.10178e6	1.03929	0.519645	−	0.854382i	$-0.326064\pi$
$389$	3.10178e6	1.03929	0.519645	+	0.854382i	$0.326064\pi$
$390$	−3.44343e6	−1.14638
$391$	3.98933e6	1.31965
$392$	0	0
$393$	−5.56223e6	−1.81663
$394$	2.33312e6	0.757176
$395$	3.36731e6	1.08590
$396$	−3.82516e6	−1.22578
$397$	613257.	0.195284	0.0976419	−	0.995222i	$-0.468870\pi$
$397$	613257.	0.195284	0.0976419	+	0.995222i	$0.468870\pi$
$398$	4.62589e6	1.46382
$399$	0	0
$400$	−2.65262e6	−0.828942
$401$	2.82223e6	0.876459	0.438229	−	0.898863i	$-0.355606\pi$
$401$	2.82223e6	0.876459	0.438229	+	0.898863i	$0.355606\pi$
$402$	−1.03113e7	−3.18236
$403$	−711724.	−0.218298
$404$	522550.	0.159285
$405$	2.83973e6	0.860278
$406$	0	0
$407$	868324.	0.259834
$408$	−593637.	−0.176551
$409$	2.28350e6	0.674983	0.337492	−	0.941329i	$-0.390422\pi$
$409$	2.28350e6	0.674983	0.337492	+	0.941329i	$0.390422\pi$
$410$	5.45279e6	1.60199
$411$	−4.72496e6	−1.37973
$412$	923831.	0.268132
$413$	0	0
$414$	8.75511e6	2.51050
$415$	−102635.	−0.0292534
$416$	−2.00167e6	−0.567100
$417$	1.24614e6	0.350934
$418$	−21453.3	−0.00600556
$419$	−2.65270e6	−0.738163	−0.369082	−	0.929397i	$-0.620328\pi$
$419$	−2.65270e6	−0.738163	−0.369082	+	0.929397i	$0.620328\pi$
$420$	0	0
$421$	2.93674e6	0.807532	0.403766	−	0.914862i	$-0.367701\pi$
$421$	2.93674e6	0.807532	0.403766	+	0.914862i	$0.367701\pi$
$422$	1.09829e6	0.300218
$423$	5.28314e6	1.43562
$424$	−902974.	−0.243927
$425$	−2.64140e6	−0.709353
$426$	2.85577e6	0.762428
$427$	0	0
$428$	239272.	0.0631367
$429$	2.51654e6	0.660177
$430$	5.99087e6	1.56249
$431$	−2.44565e6	−0.634164	−0.317082	−	0.948398i	$-0.602703\pi$
$431$	−2.44565e6	−0.634164	−0.317082	+	0.948398i	$0.602703\pi$
$432$	−1.75078e6	−0.451358
$433$	−2.11718e6	−0.542673	−0.271336	−	0.962485i	$-0.587466\pi$
$433$	−2.11718e6	−0.542673	−0.271336	+	0.962485i	$0.587466\pi$
$434$	0	0
$435$	8.74301e6	2.21533
$436$	−321826.	−0.0810783
$437$	23375.7	0.00585547
$438$	1.43767e7	3.58075
$439$	4.64764e6	1.15099	0.575495	−	0.817806i	$-0.304810\pi$
$439$	4.64764e6	1.15099	0.575495	+	0.817806i	$0.304810\pi$
$440$	720178.	0.177340
$441$	0	0
$442$	−2.17691e6	−0.530012
$443$	4.42925e6	1.07231	0.536155	−	0.844119i	$-0.319876\pi$
$443$	4.42925e6	1.07231	0.536155	+	0.844119i	$0.319876\pi$
$444$	−1.39968e6	−0.336954
$445$	5.11604e6	1.22471
$446$	−3833.50	−0.000912553 0
$447$	−2.36998e6	−0.561016
$448$	0	0
$449$	−6.70171e6	−1.56881	−0.784404	−	0.620250i	$-0.787031\pi$
$449$	−6.70171e6	−1.56881	−0.784404	+	0.620250i	$0.787031\pi$
$450$	−5.79691e6	−1.34948
$451$	−3.98503e6	−0.922551
$452$	1.89526e6	0.436337
$453$	−1.07692e7	−2.46570
$454$	−4.64136e6	−1.05683
$455$	0	0
$456$	−3478.46	−0.000783385 0
$457$	−5.88344e6	−1.31777	−0.658887	−	0.752242i	$-0.728972\pi$
$457$	−5.88344e6	−1.31777	−0.658887	+	0.752242i	$0.728972\pi$
$458$	280407.	0.0624634
$459$	−1.74338e6	−0.386242
$460$	7.80124e6	1.71897
$461$	1.54764e6	0.339171	0.169585	−	0.985515i	$-0.445757\pi$
$461$	1.54764e6	0.339171	0.169585	+	0.985515i	$0.445757\pi$
$462$	0	0
$463$	−3.93764e6	−0.853656	−0.426828	−	0.904333i	$-0.640369\pi$
$463$	−3.93764e6	−0.853656	−0.426828	+	0.904333i	$0.640369\pi$
$464$	5.55074e6	1.19689
$465$	−4.92907e6	−1.05714
$466$	−9.75491e6	−2.08093
$467$	−6.81586e6	−1.44620	−0.723100	−	0.690743i	$-0.757284\pi$
$467$	−6.81586e6	−1.44620	−0.723100	+	0.690743i	$0.757284\pi$
$468$	−2.27438e6	−0.480007
$469$	0	0
$470$	9.88860e6	2.06486
$471$	−4.21070e6	−0.874585
$472$	775964.	0.160320
$473$	−4.37827e6	−0.899807
$474$	8.33263e6	1.70348
$475$	−15477.5	−0.00314750
$476$	0	0
$477$	−1.22519e7	−2.46552
$478$	4.50885e6	0.902602
$479$	−5.20406e6	−1.03634	−0.518171	−	0.855277i	$-0.673387\pi$
$479$	−5.20406e6	−1.03634	−0.518171	+	0.855277i	$0.673387\pi$
$480$	−1.38626e7	−2.74627
$481$	516291.	0.101749
$482$	1.08036e7	2.11813
$483$	0	0
$484$	549840.	0.106690
$485$	−8.08540e6	−1.56080
$486$	1.00251e7	1.92529
$487$	−154998.	−0.0296145	−0.0148073	−	0.999890i	$-0.504713\pi$
$487$	−154998.	−0.0296145	−0.0148073	+	0.999890i	$0.504713\pi$
$488$	646723.	0.122933
$489$	5.72936e6	1.08351
$490$	0	0
$491$	−1.61951e6	−0.303165	−0.151583	−	0.988445i	$-0.548437\pi$
$491$	−1.61951e6	−0.303165	−0.151583	+	0.988445i	$0.548437\pi$
$492$	6.42359e6	1.19637
$493$	5.52727e6	1.02422
$494$	−12755.8	−0.00235174
$495$	9.77168e6	1.79249
$496$	−3.12935e6	−0.571150
$497$	0	0
$498$	−253978.	−0.0458905
$499$	4.10674e6	0.738322	0.369161	−	0.929366i	$-0.379645\pi$
$499$	4.10674e6	0.738322	0.369161	+	0.929366i	$0.379645\pi$
$500$	1.58336e6	0.283239
$501$	2.75244e6	0.489918
$502$	−2.52596e6	−0.447371
$503$	−3.40748e6	−0.600501	−0.300250	−	0.953860i	$-0.597070\pi$
$503$	−3.40748e6	−0.600501	−0.300250	+	0.953860i	$0.597070\pi$
$504$	0	0
$505$	−1.33490e6	−0.232927
$506$	−1.19762e7	−2.07941
$507$	−7.23599e6	−1.25020
$508$	−5.66322e6	−0.973654
$509$	1.07091e7	1.83213	0.916067	−	0.401025i	$-0.131346\pi$
$509$	1.07091e7	1.83213	0.916067	+	0.401025i	$0.131346\pi$
$510$	−1.50763e7	−2.56666
$511$	0	0
$512$	−7.98992e6	−1.34700
$513$	−10215.4	−0.00171381
$514$	−1.44267e7	−2.40858
$515$	−2.36000e6	−0.392097
$516$	7.05746e6	1.16687
$517$	−7.22682e6	−1.18911
$518$	0	0
$519$	6.34374e6	1.03378
$520$	428205.	0.0694454
$521$	7.92001e6	1.27830	0.639148	−	0.769084i	$-0.279287\pi$
$521$	7.92001e6	1.27830	0.639148	+	0.769084i	$0.279287\pi$
$522$	1.21303e7	1.94848
$523$	−8.32746e6	−1.33125	−0.665623	−	0.746288i	$-0.731834\pi$
$523$	−8.32746e6	−1.33125	−0.665623	+	0.746288i	$0.731834\pi$
$524$	−6.87643e6	−1.09404
$525$	0	0
$526$	3.58104e6	0.564345
$527$	−3.11612e6	−0.488752
$528$	1.10649e7	1.72728
$529$	6.61298e6	1.02744
$530$	−2.29323e7	−3.54616
$531$	1.05286e7	1.62045
$532$	0	0
$533$	−2.36943e6	−0.361265
$534$	1.26600e7	1.92124
$535$	−611239.	−0.0923265
$536$	1.28226e6	0.192780
$537$	8.85532e6	1.32516
$538$	−3.25856e6	−0.485366
$539$	0	0
$540$	−3.40922e6	−0.503119
$541$	623261.	0.0915539	0.0457770	−	0.998952i	$-0.485424\pi$
$541$	623261.	0.0915539	0.0457770	+	0.998952i	$0.485424\pi$
$542$	7.03653e6	1.02887
$543$	−1.02221e7	−1.48779
$544$	−8.76386e6	−1.26969
$545$	822129.	0.118563
$546$	0	0
$547$	1.05691e7	1.51032	0.755159	−	0.655541i	$-0.227559\pi$
$547$	1.05691e7	1.51032	0.755159	+	0.655541i	$0.227559\pi$
$548$	−5.84133e6	−0.830922
$549$	8.77502e6	1.24256
$550$	7.92962e6	1.11775
$551$	32387.5	0.00454462
$552$	−1.94182e6	−0.271245
$553$	0	0
$554$	3.49835e6	0.484272
$555$	3.57559e6	0.492737
$556$	1.54056e6	0.211345
$557$	−1.35398e7	−1.84916	−0.924579	−	0.380991i	$-0.875583\pi$
$557$	−1.35398e7	−1.84916	−0.924579	+	0.380991i	$0.875583\pi$
$558$	−6.83875e6	−0.929804
$559$	−2.60324e6	−0.352359
$560$	0	0
$561$	1.10181e7	1.47809
$562$	6.00605e6	0.802136
$563$	−1.39757e7	−1.85824	−0.929122	−	0.369774i	$-0.879435\pi$
$563$	−1.39757e7	−1.85824	−0.929122	+	0.369774i	$0.879435\pi$
$564$	1.16491e7	1.54204
$565$	−4.84159e6	−0.638068
$566$	1.66633e7	2.18635
$567$	0	0
$568$	−355127.	−0.0461862
$569$	−5.61993e6	−0.727697	−0.363848	−	0.931458i	$-0.618537\pi$
$569$	−5.61993e6	−0.727697	−0.363848	+	0.931458i	$0.618537\pi$
$570$	−88340.5	−0.0113887
$571$	8.70790e6	1.11769	0.558847	−	0.829271i	$-0.311244\pi$
$571$	8.70790e6	1.11769	0.558847	+	0.829271i	$0.311244\pi$
$572$	3.11113e6	0.397583
$573$	1.33101e7	1.69354
$574$	0	0
$575$	−8.64019e6	−1.08982
$576$	−8.22747e6	−1.03326
$577$	−6.63992e6	−0.830278	−0.415139	−	0.909758i	$-0.636267\pi$
$577$	−6.63992e6	−0.830278	−0.415139	+	0.909758i	$0.636267\pi$
$578$	1.56517e6	0.194868
$579$	1.20994e7	1.49992
$580$	1.08087e7	1.33415
$581$	0	0
$582$	−2.00079e7	−2.44846
$583$	1.67595e7	2.04216
$584$	−1.78780e6	−0.216914
$585$	5.81007e6	0.701927
$586$	1.89648e7	2.28141
$587$	−1.36652e7	−1.63689	−0.818446	−	0.574583i	$-0.805164\pi$
$587$	−1.36652e7	−1.63689	−0.818446	+	0.574583i	$0.805164\pi$
$588$	0	0
$589$	−18259.2	−0.00216866
$590$	1.97067e7	2.33069
$591$	−7.02126e6	−0.826888
$592$	2.27006e6	0.266215
$593$	−7.02589e6	−0.820474	−0.410237	−	0.911979i	$-0.634554\pi$
$593$	−7.02589e6	−0.820474	−0.410237	+	0.911979i	$0.634554\pi$
$594$	5.23370e6	0.608615
$595$	0	0
$596$	−2.92994e6	−0.337864
$597$	−1.39211e7	−1.59859
$598$	−7.12081e6	−0.814285
$599$	−3.58663e6	−0.408432	−0.204216	−	0.978926i	$-0.565464\pi$
$599$	−3.58663e6	−0.408432	−0.204216	+	0.978926i	$0.565464\pi$
$600$	1.28572e6	0.145803
$601$	1.58600e7	1.79108	0.895542	−	0.444977i	$-0.146788\pi$
$601$	1.58600e7	1.79108	0.895542	+	0.444977i	$0.146788\pi$
$602$	0	0
$603$	1.73982e7	1.94855
$604$	−1.33137e7	−1.48493
$605$	−1.40461e6	−0.156015
$606$	−3.30329e6	−0.365397
$607$	6.44170e6	0.709625	0.354812	−	0.934938i	$-0.384545\pi$
$607$	6.44170e6	0.709625	0.354812	+	0.934938i	$0.384545\pi$
$608$	−51352.5	−0.00563381
$609$	0	0
$610$	1.64244e7	1.78717
$611$	−4.29694e6	−0.465647
$612$	−9.95784e6	−1.07470
$613$	−4.58865e6	−0.493212	−0.246606	−	0.969116i	$-0.579315\pi$
$613$	−4.58865e6	−0.493212	−0.246606	+	0.969116i	$0.579315\pi$
$614$	−1.90944e7	−2.04402
$615$	−1.64096e7	−1.74948
$616$	0	0
$617$	1.47104e6	0.155565	0.0777825	−	0.996970i	$-0.475216\pi$
$617$	1.47104e6	0.155565	0.0777825	+	0.996970i	$0.475216\pi$
$618$	−5.83998e6	−0.615092
$619$	−3.13569e6	−0.328932	−0.164466	−	0.986383i	$-0.552590\pi$
$619$	−3.13569e6	−0.328932	−0.164466	+	0.986383i	$0.552590\pi$
$620$	−6.09367e6	−0.636649
$621$	−5.70269e6	−0.593404
$622$	9.02366e6	0.935205
$623$	0	0
$624$	6.57898e6	0.676390
$625$	−1.15193e7	−1.17957
$626$	1.29501e7	1.32080
$627$	64561.3	0.00655849
$628$	−5.20557e6	−0.526707
$629$	2.26046e6	0.227809
$630$	0	0
$631$	484547.	0.0484465	0.0242233	−	0.999707i	$-0.492289\pi$
$631$	484547.	0.0484465	0.0242233	+	0.999707i	$0.492289\pi$
$632$	−1.03620e6	−0.103193
$633$	−3.30518e6	−0.327858
$634$	−6.41899e6	−0.634226
$635$	1.44672e7	1.42380
$636$	−2.70151e7	−2.64828
$637$	0	0
$638$	−1.65932e7	−1.61390
$639$	−4.81851e6	−0.466832
$640$	3.46228e6	0.334127
$641$	3.04085e6	0.292314	0.146157	−	0.989261i	$-0.453310\pi$
$641$	3.04085e6	0.292314	0.146157	+	0.989261i	$0.453310\pi$
$642$	−1.51255e6	−0.144835
$643$	5.25888e6	0.501609	0.250805	−	0.968038i	$-0.419305\pi$
$643$	5.25888e6	0.501609	0.250805	+	0.968038i	$0.419305\pi$
$644$	0	0
$645$	−1.80288e7	−1.70635
$646$	−55848.3	−0.00526536
$647$	2.11970e7	1.99074	0.995368	−	0.0961386i	$-0.0306492\pi$
$647$	2.11970e7	1.99074	0.995368	+	0.0961386i	$0.0306492\pi$
$648$	−873849.	−0.0817521
$649$	−1.44021e7	−1.34219
$650$	4.71481e6	0.437705
$651$	0	0
$652$	7.08305e6	0.652531
$653$	1.30106e7	1.19403	0.597013	−	0.802232i	$-0.296354\pi$
$653$	1.30106e7	1.19403	0.597013	+	0.802232i	$0.296354\pi$
$654$	2.03442e6	0.185992
$655$	1.75664e7	1.59985
$656$	−1.04181e7	−0.945208
$657$	−2.42577e7	−2.19248
$658$	0	0
$659$	−1.59874e7	−1.43405	−0.717024	−	0.697049i	$-0.754496\pi$
$659$	−1.59874e7	−1.43405	−0.717024	+	0.697049i	$0.754496\pi$
$660$	2.15462e7	1.92536
$661$	4.03142e6	0.358884	0.179442	−	0.983769i	$-0.442571\pi$
$661$	4.03142e6	0.358884	0.179442	+	0.983769i	$0.442571\pi$
$662$	747673.	0.0663082
$663$	6.55117e6	0.578809
$664$	31583.3	0.00277995
$665$	0	0
$666$	4.96089e6	0.433385
$667$	1.80800e7	1.57357
$668$	3.40276e6	0.295047
$669$	11536.5	0.000996570 0
$670$	3.25647e7	2.80260
$671$	−1.20034e7	−1.02919
$672$	0	0
$673$	2.98234e6	0.253816	0.126908	−	0.991914i	$-0.459495\pi$
$673$	2.98234e6	0.253816	0.126908	+	0.991914i	$0.459495\pi$
$674$	−1.85233e7	−1.57061
$675$	3.77585e6	0.318974
$676$	−8.94566e6	−0.752914
$677$	1.94696e6	0.163262	0.0816309	−	0.996663i	$-0.473987\pi$
$677$	1.94696e6	0.163262	0.0816309	+	0.996663i	$0.473987\pi$
$678$	−1.19808e7	−1.00095
$679$	0	0
$680$	1.87480e6	0.155483
$681$	1.39676e7	1.15413
$682$	9.35476e6	0.770144
$683$	1.19940e7	0.983812	0.491906	−	0.870648i	$-0.336300\pi$
$683$	1.19940e7	0.983812	0.491906	+	0.870648i	$0.336300\pi$
$684$	−58348.7	−0.00476860
$685$	1.49221e7	1.21508
$686$	0	0
$687$	−843854.	−0.0682143
$688$	−1.14461e7	−0.921905
$689$	9.96490e6	0.799696
$690$	−4.93154e7	−3.94330
$691$	−8.66304e6	−0.690201	−0.345100	−	0.938566i	$-0.612155\pi$
$691$	−8.66304e6	−0.690201	−0.345100	+	0.938566i	$0.612155\pi$
$692$	7.84260e6	0.622579
$693$	0	0
$694$	−3.83385e6	−0.302160
$695$	−3.93549e6	−0.309056
$696$	−2.69043e6	−0.210522
$697$	−1.03740e7	−0.808845
$698$	3.29177e7	2.55736
$699$	2.93563e7	2.27252
$700$	0	0
$701$	−8.13382e6	−0.625172	−0.312586	−	0.949889i	$-0.601195\pi$
$701$	−8.13382e6	−0.625172	−0.312586	+	0.949889i	$0.601195\pi$
$702$	3.11187e6	0.238330
$703$	13245.3	0.00101082
$704$	1.12544e7	0.855835
$705$	−2.97586e7	−2.25497
$706$	−2.48033e7	−1.87283
$707$	0	0
$708$	2.32152e7	1.74056
$709$	2.21326e7	1.65355	0.826773	−	0.562535i	$-0.190174\pi$
$709$	2.21326e7	1.65355	0.826773	+	0.562535i	$0.190174\pi$
$710$	−9.01895e6	−0.671445
$711$	−1.40596e7	−1.04303
$712$	−1.57432e6	−0.116384
$713$	−1.01930e7	−0.750896
$714$	0	0
$715$	−7.94762e6	−0.581396
$716$	1.09476e7	0.798061
$717$	−1.35689e7	−0.985704
$718$	2.65789e7	1.92409
$719$	−7.23196e6	−0.521716	−0.260858	−	0.965377i	$-0.584005\pi$
$719$	−7.23196e6	−0.521716	−0.260858	+	0.965377i	$0.584005\pi$
$720$	2.55461e7	1.83651
$721$	0	0
$722$	1.93506e7	1.38150
$723$	−3.25123e7	−2.31314
$724$	−1.26374e7	−0.896004
$725$	−1.19711e7	−0.845843
$726$	−3.47581e6	−0.244745
$727$	−1.70200e7	−1.19433	−0.597163	−	0.802120i	$-0.703705\pi$
$727$	−1.70200e7	−1.19433	−0.597163	+	0.802120i	$0.703705\pi$
$728$	0	0
$729$	−2.08788e7	−1.45508
$730$	−4.54039e7	−3.15345
$731$	−1.13977e7	−0.788904
$732$	1.93486e7	1.33466
$733$	1.00011e6	0.0687525	0.0343763	−	0.999409i	$-0.489056\pi$
$733$	1.00011e6	0.0687525	0.0343763	+	0.999409i	$0.489056\pi$
$734$	−1.53857e7	−1.05409
$735$	0	0
$736$	−2.86671e7	−1.95070
$737$	−2.37991e7	−1.61396
$738$	−2.27672e7	−1.53875
$739$	3.25979e6	0.219572	0.109786	−	0.993955i	$-0.464983\pi$
$739$	3.25979e6	0.219572	0.109786	+	0.993955i	$0.464983\pi$
$740$	4.42040e6	0.296744
$741$	38387.1	0.00256826
$742$	0	0
$743$	1.36125e7	0.904617	0.452309	−	0.891861i	$-0.350601\pi$
$743$	1.36125e7	0.904617	0.452309	+	0.891861i	$0.350601\pi$
$744$	1.51679e6	0.100460
$745$	7.48475e6	0.494068
$746$	2.71878e7	1.78865
$747$	428536.	0.0280986
$748$	1.36214e7	0.890158
$749$	0	0
$750$	−1.00092e7	−0.649747
$751$	6.56544e6	0.424780	0.212390	−	0.977185i	$-0.431875\pi$
$751$	6.56544e6	0.424780	0.212390	+	0.977185i	$0.431875\pi$
$752$	−1.88931e7	−1.21831
$753$	7.60160e6	0.488560
$754$	−9.86600e6	−0.631994
$755$	3.40110e7	2.17146
$756$	0	0
$757$	2.62531e7	1.66510	0.832551	−	0.553948i	$-0.186879\pi$
$757$	2.62531e7	1.66510	0.832551	+	0.553948i	$0.186879\pi$
$758$	3.29244e6	0.208135
$759$	3.60409e7	2.27086
$760$	10985.5	0.000689901 0
$761$	−5.25111e6	−0.328692	−0.164346	−	0.986403i	$-0.552551\pi$
$761$	−5.25111e6	−0.328692	−0.164346	+	0.986403i	$0.552551\pi$
$762$	3.58000e7	2.23355
$763$	0	0
$764$	1.64549e7	1.01991
$765$	2.54381e7	1.57156
$766$	−2.08592e7	−1.28448
$767$	−8.56327e6	−0.525595
$768$	2.85337e7	1.74564
$769$	−1.77307e7	−1.08121	−0.540605	−	0.841277i	$-0.681805\pi$
$769$	−1.77307e7	−1.08121	−0.540605	+	0.841277i	$0.681805\pi$
$770$	0	0
$771$	4.34156e7	2.63033
$772$	1.49581e7	0.903305
$773$	3.82592e6	0.230296	0.115148	−	0.993348i	$-0.463266\pi$
$773$	3.82592e6	0.230296	0.115148	+	0.993348i	$0.463266\pi$
$774$	−2.50138e7	−1.50082
$775$	6.74898e6	0.403631
$776$	2.48807e6	0.148323
$777$	0	0
$778$	−2.42406e7	−1.43580
$779$	−60787.3	−0.00358896
$780$	1.28110e7	0.753957
$781$	6.59126e6	0.386671
$782$	−3.11769e7	−1.82312
$783$	−7.90117e6	−0.460561
$784$	0	0
$785$	1.32980e7	0.770218
$786$	4.34692e7	2.50972
$787$	2.94263e7	1.69355	0.846777	−	0.531948i	$-0.178540\pi$
$787$	2.94263e7	1.69355	0.846777	+	0.531948i	$0.178540\pi$
$788$	−8.68019e6	−0.497982
$789$	−1.07767e7	−0.616304
$790$	−2.63157e7	−1.50020
$791$	0	0
$792$	−3.00697e6	−0.170340
$793$	−7.13700e6	−0.403026
$794$	−4.79265e6	−0.269789
$795$	6.90122e7	3.87265
$796$	−1.72102e7	−0.962730
$797$	1.35805e7	0.757305	0.378653	−	0.925539i	$-0.376387\pi$
$797$	1.35805e7	0.757305	0.378653	+	0.925539i	$0.376387\pi$
$798$	0	0
$799$	−1.88132e7	−1.04255
$800$	1.89810e7	1.04856
$801$	−2.13611e7	−1.17637
$802$	−2.20559e7	−1.21085
$803$	3.31822e7	1.81600
$804$	3.83624e7	2.09299
$805$	0	0
$806$	5.56218e6	0.301583
$807$	9.80625e6	0.530053
$808$	410778.	0.0221350
$809$	−1.15714e7	−0.621604	−0.310802	−	0.950475i	$-0.600598\pi$
$809$	−1.15714e7	−0.621604	−0.310802	+	0.950475i	$0.600598\pi$
$810$	−2.21927e7	−1.18849
$811$	−3.52530e6	−0.188210	−0.0941052	−	0.995562i	$-0.529999\pi$
$811$	−3.52530e6	−0.188210	−0.0941052	+	0.995562i	$0.529999\pi$
$812$	0	0
$813$	−2.11756e7	−1.12360
$814$	−6.78602e6	−0.358966
$815$	−1.80942e7	−0.954214
$816$	2.88046e7	1.51439
$817$	−66785.7	−0.00350049
$818$	−1.78457e7	−0.932505
$819$	0	0
$820$	−2.02867e7	−1.05360
$821$	1.78951e7	0.926567	0.463283	−	0.886210i	$-0.346671\pi$
$821$	1.78951e7	0.926567	0.463283	+	0.886210i	$0.346671\pi$
$822$	3.69259e7	1.90612
$823$	−3.61421e7	−1.86000	−0.930001	−	0.367557i	$-0.880194\pi$
$823$	−3.61421e7	−1.86000	−0.930001	+	0.367557i	$0.880194\pi$
$824$	726226.	0.0372610
$825$	−2.38633e7	−1.22066
$826$	0	0
$827$	−1.00605e7	−0.511512	−0.255756	−	0.966741i	$-0.582324\pi$
$827$	−1.00605e7	−0.511512	−0.255756	+	0.966741i	$0.582324\pi$
$828$	−3.25727e7	−1.65112
$829$	2.03654e7	1.02921	0.514607	−	0.857426i	$-0.327938\pi$
$829$	2.03654e7	1.02921	0.514607	+	0.857426i	$0.327938\pi$
$830$	802102.	0.0404142
$831$	−1.05279e7	−0.528858
$832$	6.69166e6	0.335140
$833$	0	0
$834$	−9.73865e6	−0.484823
$835$	−8.69263e6	−0.431454
$836$	79815.4	0.00394976
$837$	4.45446e6	0.219777
$838$	2.07310e7	1.01979
$839$	−5.95014e6	−0.291825	−0.145912	−	0.989298i	$-0.546612\pi$
$839$	−5.95014e6	−0.291825	−0.145912	+	0.989298i	$0.546612\pi$
$840$	0	0
$841$	4.53905e6	0.221297
$842$	−2.29508e7	−1.11562
$843$	−1.80745e7	−0.875987
$844$	−4.08611e6	−0.197448
$845$	2.28524e7	1.10101
$846$	−4.12881e7	−1.98335
$847$	0	0
$848$	4.38143e7	2.09231
$849$	−5.01462e7	−2.38764
$850$	2.06428e7	0.979987
$851$	7.39411e6	0.349995
$852$	−1.06247e7	−0.501436
$853$	1.59836e7	0.752146	0.376073	−	0.926590i	$-0.377274\pi$
$853$	1.59836e7	0.752146	0.376073	+	0.926590i	$0.377274\pi$
$854$	0	0
$855$	149056.	0.00697325
$856$	188092.	0.00877378
$857$	−2.34591e6	−0.109109	−0.0545544	−	0.998511i	$-0.517374\pi$
$857$	−2.34591e6	−0.109109	−0.0545544	+	0.998511i	$0.517374\pi$
$858$	−1.96669e7	−0.912050
$859$	−1.30223e7	−0.602152	−0.301076	−	0.953600i	$-0.597346\pi$
$859$	−1.30223e7	−0.602152	−0.301076	+	0.953600i	$0.597346\pi$
$860$	−2.22886e7	−1.02763
$861$	0	0
$862$	1.91130e7	0.876112
$863$	1.96688e7	0.898983	0.449492	−	0.893285i	$-0.351605\pi$
$863$	1.96688e7	0.898983	0.449492	+	0.893285i	$0.351605\pi$
$864$	1.25278e7	0.570941
$865$	−2.00345e7	−0.910414
$866$	1.65459e7	0.749715
$867$	−4.71019e6	−0.212809
$868$	0	0
$869$	1.92322e7	0.863931
$870$	−6.83273e7	−3.06053
$871$	−1.41505e7	−0.632015
$872$	−252988.	−0.0112670
$873$	3.37592e7	1.49919
$874$	−182683.	−0.00808946
$875$	0	0
$876$	−5.34874e7	−2.35500
$877$	2.34581e7	1.02990	0.514950	−	0.857221i	$-0.327811\pi$
$877$	2.34581e7	1.02990	0.514950	+	0.857221i	$0.327811\pi$
$878$	−3.63217e7	−1.59012
$879$	−5.70724e7	−2.49146
$880$	−3.49446e7	−1.52115
$881$	4.59257e6	0.199350	0.0996750	−	0.995020i	$-0.468220\pi$
$881$	4.59257e6	0.199350	0.0996750	+	0.995020i	$0.468220\pi$
$882$	0	0
$883$	−1.23402e7	−0.532622	−0.266311	−	0.963887i	$-0.585805\pi$
$883$	−1.23402e7	−0.532622	−0.266311	+	0.963887i	$0.585805\pi$
$884$	8.09903e6	0.348580
$885$	−5.93052e7	−2.54527
$886$	−3.46149e7	−1.48142
$887$	1.36554e7	0.582769	0.291384	−	0.956606i	$-0.405884\pi$
$887$	1.36554e7	0.582769	0.291384	+	0.956606i	$0.405884\pi$
$888$	−1.10029e6	−0.0468247
$889$	0	0
$890$	−3.99822e7	−1.69197
$891$	1.62189e7	0.684428
$892$	14262.2	0.000600171 0
$893$	−110237.	−0.00462594
$894$	1.85215e7	0.775056
$895$	−2.79665e7	−1.16703
$896$	0	0
$897$	2.14293e7	0.889255
$898$	5.23744e7	2.16735
$899$	−1.41226e7	−0.582795
$900$	2.15670e7	0.887529
$901$	4.36291e7	1.79046
$902$	3.11433e7	1.27453
$903$	0	0
$904$	1.48987e6	0.0606355
$905$	3.22831e7	1.31025
$906$	8.41624e7	3.40642
$907$	7.39599e6	0.298523	0.149262	−	0.988798i	$-0.452310\pi$
$907$	7.39599e6	0.298523	0.149262	+	0.988798i	$0.452310\pi$
$908$	1.72678e7	0.695060
$909$	5.57362e6	0.223732
$910$	0	0
$911$	−3.51041e7	−1.40140	−0.700699	−	0.713457i	$-0.747129\pi$
$911$	−3.51041e7	−1.40140	−0.700699	+	0.713457i	$0.747129\pi$
$912$	168783.	0.00671955
$913$	−586195.	−0.0232737
$914$	4.59795e7	1.82053
$915$	−4.94275e7	−1.95171
$916$	−1.04323e6	−0.0410812
$917$	0	0
$918$	1.36246e7	0.533602
$919$	−4.81337e7	−1.88001	−0.940005	−	0.341159i	$-0.889180\pi$
$919$	−4.81337e7	−1.88001	−0.940005	+	0.341159i	$0.889180\pi$
$920$	6.13258e6	0.238877
$921$	5.74626e7	2.23221
$922$	−1.20949e7	−0.468572
$923$	3.91905e6	0.151418
$924$	0	0
$925$	−4.89577e6	−0.188134
$926$	3.07729e7	1.17935
$927$	9.85376e6	0.376619
$928$	−3.97188e7	−1.51400
$929$	−1.83602e7	−0.697971	−0.348986	−	0.937128i	$-0.613474\pi$
$929$	−1.83602e7	−0.697971	−0.348986	+	0.937128i	$0.613474\pi$
$930$	3.85210e7	1.46046
$931$	0	0
$932$	3.62924e7	1.36860
$933$	−2.71557e7	−1.02131
$934$	5.32665e7	1.99796
$935$	−3.47969e7	−1.30170
$936$	−1.78789e6	−0.0667041
$937$	2.27081e7	0.844951	0.422475	−	0.906374i	$-0.361161\pi$
$937$	2.27081e7	0.844951	0.422475	+	0.906374i	$0.361161\pi$
$938$	0	0
$939$	−3.89718e7	−1.44240
$940$	−3.67898e7	−1.35802
$941$	4.15801e7	1.53078	0.765389	−	0.643568i	$-0.222547\pi$
$941$	4.15801e7	1.53078	0.765389	+	0.643568i	$0.222547\pi$
$942$	3.29069e7	1.20826
$943$	−3.39340e7	−1.24267
$944$	−3.76515e7	−1.37516
$945$	0	0
$946$	3.42165e7	1.24310
$947$	1.55341e7	0.562874	0.281437	−	0.959580i	$-0.409189\pi$
$947$	1.55341e7	0.562874	0.281437	+	0.959580i	$0.409189\pi$
$948$	−3.10009e7	−1.12035
$949$	1.97296e7	0.711135
$950$	120958.	0.00434835
$951$	1.93172e7	0.692618
$952$	0	0
$953$	3.94908e7	1.40852	0.704262	−	0.709940i	$-0.251278\pi$
$953$	3.94908e7	1.40852	0.704262	+	0.709940i	$0.251278\pi$
$954$	9.57499e7	3.40618
$955$	−4.20354e7	−1.49144
$956$	−1.67748e7	−0.593627
$957$	4.99352e7	1.76249
$958$	4.06701e7	1.43173
$959$	0	0
$960$	4.63433e7	1.62296
$961$	−2.06672e7	−0.721894
$962$	−4.03485e6	−0.140569
$963$	2.55212e6	0.0886819
$964$	−4.01941e7	−1.39306
$965$	−3.82118e7	−1.32093
$966$	0	0
$967$	−1.87472e7	−0.644718	−0.322359	−	0.946617i	$-0.604476\pi$
$967$	−1.87472e7	−0.644718	−0.322359	+	0.946617i	$0.604476\pi$
$968$	432231.	0.0148261
$969$	168069.	0.00575014
$970$	6.31880e7	2.15628
$971$	−5.35423e7	−1.82242	−0.911211	−	0.411940i	$-0.864851\pi$
$971$	−5.35423e7	−1.82242	−0.911211	+	0.411940i	$0.864851\pi$
$972$	−3.72974e7	−1.26623
$973$	0	0
$974$	1.21132e6	0.0409131
$975$	−1.41887e7	−0.478004
$976$	−3.13804e7	−1.05447
$977$	4.46104e7	1.49520	0.747600	−	0.664149i	$-0.231206\pi$
$977$	4.46104e7	1.49520	0.747600	+	0.664149i	$0.231206\pi$
$978$	−4.47754e7	−1.49690
$979$	2.92200e7	0.974368
$980$	0	0
$981$	−3.43265e6	−0.113883
$982$	1.26566e7	0.418829
$983$	−2.00068e7	−0.660380	−0.330190	−	0.943914i	$-0.607113\pi$
$983$	−2.00068e7	−0.660380	−0.330190	+	0.943914i	$0.607113\pi$
$984$	5.04960e6	0.166253
$985$	2.21742e7	0.728213
$986$	−4.31961e7	−1.41498
$987$	0	0
$988$	47456.9	0.00154670
$989$	−3.72826e7	−1.21204
$990$	−7.63664e7	−2.47636
$991$	3.24635e7	1.05005	0.525026	−	0.851086i	$-0.324056\pi$
$991$	3.24635e7	1.05005	0.525026	+	0.851086i	$0.324056\pi$
$992$	2.23923e7	0.722471
$993$	−2.25004e6	−0.0724130
$994$	0	0
$995$	4.39649e7	1.40783
$996$	944905.	0.0301814
$997$	2.78940e7	0.888736	0.444368	−	0.895844i	$-0.353428\pi$
$997$	2.78940e7	0.888736	0.444368	+	0.895844i	$0.353428\pi$
$998$	−3.20945e7	−1.02001
$999$	−3.23130e6	−0.102439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.a.g.1.2	yes	4
3.2	odd	2		441.6.a.z.1.4		4
4.3	odd	2		784.6.a.bf.1.1		4
7.2	even	3		49.6.c.h.18.3		8
7.3	odd	6		49.6.c.h.30.4		8
7.4	even	3		49.6.c.h.30.3		8
7.5	odd	6		49.6.c.h.18.4		8
7.6	odd	2	inner	49.6.a.g.1.1	✓	4
21.20	even	2		441.6.a.z.1.3		4
28.27	even	2		784.6.a.bf.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.a.g.1.1	✓	4	7.6	odd	2	inner
49.6.a.g.1.2	yes	4	1.1	even	1	trivial
49.6.c.h.18.3		8	7.2	even	3
49.6.c.h.18.4		8	7.5	odd	6
49.6.c.h.30.3		8	7.4	even	3
49.6.c.h.30.4		8	7.3	odd	6
441.6.a.z.1.3		4	21.20	even	2
441.6.a.z.1.4		4	3.2	odd	2
784.6.a.bf.1.1		4	4.3	odd	2
784.6.a.bf.1.4		4	28.27	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-7.81507 q^{2} +23.5186 q^{3} +29.0754 q^{4} -74.2753 q^{5} -183.799 q^{6} +22.8562 q^{8} +310.123 q^{9} +O(q^{10})\)	\(q-7.81507 q^{2} +23.5186 q^{3} +29.0754 q^{4} -74.2753 q^{5} -183.799 q^{6} +22.8562 q^{8} +310.123 q^{9} +580.467 q^{10} -424.219 q^{11} +683.811 q^{12} -252.233 q^{13} -1746.85 q^{15} -1109.03 q^{16} -1104.35 q^{17} -2423.64 q^{18} -6.47100 q^{19} -2159.58 q^{20} +3315.30 q^{22} -3612.39 q^{23} +537.546 q^{24} +2391.82 q^{25} +1971.22 q^{26} +1578.65 q^{27} -5005.02 q^{29} +13651.8 q^{30} +2821.69 q^{31} +7935.79 q^{32} -9977.03 q^{33} +8630.55 q^{34} +9016.95 q^{36} -2046.88 q^{37} +50.5713 q^{38} -5932.17 q^{39} -1697.65 q^{40} +9393.81 q^{41} +10320.8 q^{43} -12334.3 q^{44} -23034.5 q^{45} +28231.1 q^{46} +17035.6 q^{47} -26082.9 q^{48} -18692.3 q^{50} -25972.7 q^{51} -7333.78 q^{52} -39506.7 q^{53} -12337.3 q^{54} +31509.0 q^{55} -152.189 q^{57} +39114.6 q^{58} +33949.8 q^{59} -50790.3 q^{60} +28295.2 q^{61} -22051.7 q^{62} -26529.7 q^{64} +18734.7 q^{65} +77971.2 q^{66} +56100.9 q^{67} -32109.3 q^{68} -84958.2 q^{69} -15537.4 q^{71} +7088.26 q^{72} -78219.5 q^{73} +15996.5 q^{74} +56252.3 q^{75} -188.147 q^{76} +46360.3 q^{78} -45335.5 q^{79} +82373.9 q^{80} -38232.4 q^{81} -73413.3 q^{82} +1381.82 q^{83} +82025.7 q^{85} -80657.6 q^{86} -117711. q^{87} -9696.05 q^{88} -68879.4 q^{89} +180016. q^{90} -105031. q^{92} +66362.1 q^{93} -133134. q^{94} +480.635 q^{95} +186638. q^{96} +108857. q^{97} -131560. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{2} + 10 q^{4} - 270 q^{8} + 220 q^{9}+O(q^{10}) \) 4 * q - 10 * q^2 + 10 * q^4 - 270 * q^8 + 220 * q^9	\( 4 q - 10 q^{2} + 10 q^{4} - 270 q^{8} + 220 q^{9} - 1952 q^{11} - 4096 q^{15} - 1566 q^{16} - 5974 q^{18} + 3524 q^{22} - 7136 q^{23} + 2764 q^{25} - 3352 q^{29} + 25608 q^{30} + 27810 q^{32} + 27670 q^{36} - 9208 q^{37} + 2464 q^{39} + 20448 q^{43} + 1900 q^{44} + 56712 q^{46} - 43070 q^{50} - 67408 q^{51} - 102920 q^{53} - 15576 q^{57} + 96972 q^{58} - 87080 q^{60} - 40318 q^{64} - 63168 q^{65} - 22896 q^{67} - 153824 q^{71} + 77358 q^{72} + 17596 q^{74} + 133056 q^{78} - 90688 q^{79} - 17204 q^{81} + 272656 q^{85} - 161860 q^{86} + 154812 q^{88} - 212200 q^{92} + 247760 q^{93} + 108224 q^{95} - 42272 q^{99}+O(q^{100}) \) 4 * q - 10 * q^2 + 10 * q^4 - 270 * q^8 + 220 * q^9 - 1952 * q^11 - 4096 * q^15 - 1566 * q^16 - 5974 * q^18 + 3524 * q^22 - 7136 * q^23 + 2764 * q^25 - 3352 * q^29 + 25608 * q^30 + 27810 * q^32 + 27670 * q^36 - 9208 * q^37 + 2464 * q^39 + 20448 * q^43 + 1900 * q^44 + 56712 * q^46 - 43070 * q^50 - 67408 * q^51 - 102920 * q^53 - 15576 * q^57 + 96972 * q^58 - 87080 * q^60 - 40318 * q^64 - 63168 * q^65 - 22896 * q^67 - 153824 * q^71 + 77358 * q^72 + 17596 * q^74 + 133056 * q^78 - 90688 * q^79 - 17204 * q^81 + 272656 * q^85 - 161860 * q^86 + 154812 * q^88 - 212200 * q^92 + 247760 * q^93 + 108224 * q^95 - 42272 * q^99

Introduction

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