LMFDB - Embedded newform 1075.6.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14099 q^{2} +23.1734 q^{3} -27.4162 q^{4} -49.6140 q^{6} -101.342 q^{7} +127.210 q^{8} +294.004 q^{9} +O(q^{10})$	\(q-2.14099 q^{2} +23.1734 q^{3} -27.4162 q^{4} -49.6140 q^{6} -101.342 q^{7} +127.210 q^{8} +294.004 q^{9} +303.205 q^{11} -635.324 q^{12} +946.835 q^{13} +216.973 q^{14} +604.962 q^{16} -661.512 q^{17} -629.461 q^{18} +1288.45 q^{19} -2348.44 q^{21} -649.159 q^{22} -963.647 q^{23} +2947.87 q^{24} -2027.17 q^{26} +1181.94 q^{27} +2778.41 q^{28} +2736.75 q^{29} +2497.15 q^{31} -5365.92 q^{32} +7026.27 q^{33} +1416.29 q^{34} -8060.46 q^{36} +1674.78 q^{37} -2758.57 q^{38} +21941.3 q^{39} -2222.14 q^{41} +5027.98 q^{42} -1849.00 q^{43} -8312.70 q^{44} +2063.16 q^{46} +52.2863 q^{47} +14019.0 q^{48} -6536.77 q^{49} -15329.4 q^{51} -25958.6 q^{52} +24803.9 q^{53} -2530.52 q^{54} -12891.7 q^{56} +29857.8 q^{57} -5859.36 q^{58} -18069.3 q^{59} -22242.8 q^{61} -5346.38 q^{62} -29795.0 q^{63} -7870.40 q^{64} -15043.2 q^{66} -15230.5 q^{67} +18136.1 q^{68} -22330.9 q^{69} +48480.0 q^{71} +37400.1 q^{72} +26119.3 q^{73} -3585.70 q^{74} -35324.4 q^{76} -30727.4 q^{77} -46976.2 q^{78} -65398.0 q^{79} -44053.6 q^{81} +4757.59 q^{82} -11884.5 q^{83} +64385.1 q^{84} +3958.69 q^{86} +63419.7 q^{87} +38570.5 q^{88} +41224.2 q^{89} -95954.3 q^{91} +26419.5 q^{92} +57867.4 q^{93} -111.944 q^{94} -124346. q^{96} +98842.5 q^{97} +13995.2 q^{98} +89143.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.14099	−0.378477	−0.189239	−	0.981931i	$-0.560602\pi$
$2$	−2.14099	−0.378477	−0.189239	+	0.981931i	$0.560602\pi$
$3$	23.1734	1.48657	0.743286	−	0.668974i	$-0.233266\pi$
$3$	23.1734	1.48657	0.743286	+	0.668974i	$0.233266\pi$
$4$	−27.4162	−0.856755
$5$	0	0
$5$	0	0
$6$	−49.6140	−0.562634
$7$	−101.342	−0.781709	−0.390854	−	0.920453i	$-0.627820\pi$
$7$	−101.342	−0.781709	−0.390854	+	0.920453i	$0.627820\pi$
$8$	127.210	0.702740
$9$	294.004	1.20989
$10$	0	0
$11$	303.205	0.755534	0.377767	−	0.925901i	$-0.376692\pi$
$11$	303.205	0.755534	0.377767	+	0.925901i	$0.376692\pi$
$12$	−635.324	−1.27363
$13$	946.835	1.55387	0.776937	−	0.629578i	$-0.216772\pi$
$13$	946.835	1.55387	0.776937	+	0.629578i	$0.216772\pi$
$14$	216.973	0.295859
$15$	0	0
$16$	604.962	0.590784
$17$	−661.512	−0.555156	−0.277578	−	0.960703i	$-0.589532\pi$
$17$	−661.512	−0.555156	−0.277578	+	0.960703i	$0.589532\pi$
$18$	−629.461	−0.457918
$19$	1288.45	0.818812	0.409406	−	0.912352i	$-0.365736\pi$
$19$	1288.45	0.818812	0.409406	+	0.912352i	$0.365736\pi$
$20$	0	0
$21$	−2348.44	−1.16207
$22$	−649.159	−0.285953
$23$	−963.647	−0.379838	−0.189919	−	0.981800i	$-0.560823\pi$
$23$	−963.647	−0.379838	−0.189919	+	0.981800i	$0.560823\pi$
$24$	2947.87	1.04467
$25$	0	0
$26$	−2027.17	−0.588106
$27$	1181.94	0.312022
$28$	2778.41	0.669733
$29$	2736.75	0.604283	0.302142	−	0.953263i	$-0.402298\pi$
$29$	2736.75	0.604283	0.302142	+	0.953263i	$0.402298\pi$
$30$	0	0
$31$	2497.15	0.466703	0.233352	−	0.972392i	$-0.425031\pi$
$31$	2497.15	0.466703	0.233352	+	0.972392i	$0.425031\pi$
$32$	−5365.92	−0.926338
$33$	7026.27	1.12316
$34$	1416.29	0.210114
$35$	0	0
$36$	−8060.46	−1.03658
$37$	1674.78	0.201119	0.100560	−	0.994931i	$-0.467937\pi$
$37$	1674.78	0.201119	0.100560	+	0.994931i	$0.467937\pi$
$38$	−2758.57	−0.309902
$39$	21941.3	2.30994
$40$	0	0
$41$	−2222.14	−0.206449	−0.103224	−	0.994658i	$-0.532916\pi$
$41$	−2222.14	−0.206449	−0.103224	+	0.994658i	$0.532916\pi$
$42$	5027.98	0.439816
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−8312.70	−0.647307
$45$	0	0
$46$	2063.16	0.143760
$47$	52.2863	0.00345257	0.00172629	−	0.999999i	$-0.499451\pi$
$47$	52.2863	0.00345257	0.00172629	+	0.999999i	$0.499451\pi$
$48$	14019.0	0.878242
$49$	−6536.77	−0.388932
$50$	0	0
$51$	−15329.4	−0.825279
$52$	−25958.6	−1.33129
$53$	24803.9	1.21292	0.606459	−	0.795115i	$-0.292590\pi$
$53$	24803.9	1.21292	0.606459	+	0.795115i	$0.292590\pi$
$54$	−2530.52	−0.118093
$55$	0	0
$56$	−12891.7	−0.549338
$57$	29857.8	1.21722
$58$	−5859.36	−0.228708
$59$	−18069.3	−0.675789	−0.337895	−	0.941184i	$-0.609715\pi$
$59$	−18069.3	−0.675789	−0.337895	+	0.941184i	$0.609715\pi$
$60$	0	0
$61$	−22242.8	−0.765357	−0.382679	−	0.923881i	$-0.624998\pi$
$61$	−22242.8	−0.765357	−0.382679	+	0.923881i	$0.624998\pi$
$62$	−5346.38	−0.176637
$63$	−29795.0	−0.945784
$64$	−7870.40	−0.240185
$65$	0	0
$66$	−15043.2	−0.425089
$67$	−15230.5	−0.414503	−0.207252	−	0.978288i	$-0.566452\pi$
$67$	−15230.5	−0.414503	−0.207252	+	0.978288i	$0.566452\pi$
$68$	18136.1	0.475633
$69$	−22330.9	−0.564656
$70$	0	0
$71$	48480.0	1.14134	0.570672	−	0.821178i	$-0.306683\pi$
$71$	48480.0	1.14134	0.570672	+	0.821178i	$0.306683\pi$
$72$	37400.1	0.850241
$73$	26119.3	0.573659	0.286829	−	0.957982i	$-0.407399\pi$
$73$	26119.3	0.573659	0.286829	+	0.957982i	$0.407399\pi$
$74$	−3585.70	−0.0761192
$75$	0	0
$76$	−35324.4	−0.701521
$77$	−30727.4	−0.590608
$78$	−46976.2	−0.874262
$79$	−65398.0	−1.17895	−0.589476	−	0.807786i	$-0.700666\pi$
$79$	−65398.0	−1.17895	−0.589476	+	0.807786i	$0.700666\pi$
$80$	0	0
$81$	−44053.6	−0.746051
$82$	4757.59	0.0781362
$83$	−11884.5	−0.189360	−0.0946798	−	0.995508i	$-0.530183\pi$
$83$	−11884.5	−0.189360	−0.0946798	+	0.995508i	$0.530183\pi$
$84$	64385.1	0.995605
$85$	0	0
$86$	3958.69	0.0577173
$87$	63419.7	0.898310
$88$	38570.5	0.530944
$89$	41224.2	0.551667	0.275834	−	0.961205i	$-0.411046\pi$
$89$	41224.2	0.551667	0.275834	+	0.961205i	$0.411046\pi$
$90$	0	0
$91$	−95954.3	−1.21468
$92$	26419.5	0.325428
$93$	57867.4	0.693788
$94$	−111.944	−0.00130672
$95$	0	0
$96$	−124346.	−1.37707
$97$	98842.5	1.06663	0.533316	−	0.845916i	$-0.320946\pi$
$97$	98842.5	1.06663	0.533316	+	0.845916i	$0.320946\pi$
$98$	13995.2	0.147202
$99$	89143.4	0.914116
$100$	0	0
$101$	−136975.	−1.33609	−0.668047	−	0.744119i	$-0.732869\pi$
$101$	−136975.	−1.33609	−0.668047	+	0.744119i	$0.732869\pi$
$102$	32820.2	0.312350
$103$	−71699.4	−0.665921	−0.332961	−	0.942941i	$-0.608048\pi$
$103$	−71699.4	−0.665921	−0.332961	+	0.942941i	$0.608048\pi$
$104$	120446.	1.09197
$105$	0	0
$106$	−53105.1	−0.459062
$107$	95526.0	0.806608	0.403304	−	0.915066i	$-0.367862\pi$
$107$	95526.0	0.806608	0.403304	+	0.915066i	$0.367862\pi$
$108$	−32404.2	−0.267326
$109$	238586.	1.92344	0.961719	−	0.274039i	$-0.0883596\pi$
$109$	238586.	1.92344	0.961719	+	0.274039i	$0.0883596\pi$
$110$	0	0
$111$	38810.3	0.298978
$112$	−61308.2	−0.461821
$113$	141960.	1.04585	0.522927	−	0.852378i	$-0.324840\pi$
$113$	141960.	1.04585	0.522927	+	0.852378i	$0.324840\pi$
$114$	−63925.2	−0.460691
$115$	0	0
$116$	−75031.2	−0.517722
$117$	278373.	1.88002
$118$	38686.2	0.255771
$119$	67039.0	0.433970
$120$	0	0
$121$	−69118.0	−0.429168
$122$	47621.6	0.289671
$123$	−51494.5	−0.306901
$124$	−68462.3	−0.399850
$125$	0	0
$126$	63790.9	0.357958
$127$	−101884.	−0.560525	−0.280262	−	0.959923i	$-0.590421\pi$
$127$	−101884.	−0.560525	−0.280262	+	0.959923i	$0.590421\pi$
$128$	188560.	1.01724
$129$	−42847.5	−0.226700
$130$	0	0
$131$	390217.	1.98668	0.993339	−	0.115229i	$-0.0367603\pi$
$131$	390217.	1.98668	0.993339	+	0.115229i	$0.0367603\pi$
$132$	−192633.	−0.962269
$133$	−130574.	−0.640073
$134$	32608.4	0.156880
$135$	0	0
$136$	−84150.6	−0.390130
$137$	37582.5	0.171074	0.0855369	−	0.996335i	$-0.472739\pi$
$137$	37582.5	0.171074	0.0855369	+	0.996335i	$0.472739\pi$
$138$	47810.3	0.213710
$139$	250757.	1.10082	0.550410	−	0.834895i	$-0.314471\pi$
$139$	250757.	1.10082	0.550410	+	0.834895i	$0.314471\pi$
$140$	0	0
$141$	1211.65	0.00513250
$142$	−103795.	−0.431973
$143$	287085.	1.17401
$144$	177861.	0.714785
$145$	0	0
$146$	−55921.1	−0.217117
$147$	−151479.	−0.578174
$148$	−45916.1	−0.172310
$149$	−140854.	−0.519761	−0.259880	−	0.965641i	$-0.583683\pi$
$149$	−140854.	−0.519761	−0.259880	+	0.965641i	$0.583683\pi$
$150$	0	0
$151$	227060.	0.810396	0.405198	−	0.914229i	$-0.367203\pi$
$151$	227060.	0.810396	0.405198	+	0.914229i	$0.367203\pi$
$152$	163903.	0.575412
$153$	−194487.	−0.671680
$154$	65787.1	0.223532
$155$	0	0
$156$	−601547.	−1.97906
$157$	−69740.7	−0.225807	−0.112904	−	0.993606i	$-0.536015\pi$
$157$	−69740.7	−0.225807	−0.112904	+	0.993606i	$0.536015\pi$
$158$	140017.	0.446207
$159$	574791.	1.80309
$160$	0	0
$161$	97658.0	0.296923
$162$	94318.3	0.282364
$163$	256384.	0.755827	0.377913	−	0.925841i	$-0.376642\pi$
$163$	256384.	0.755827	0.377913	+	0.925841i	$0.376642\pi$
$164$	60922.6	0.176876
$165$	0	0
$166$	25444.7	0.0716683
$167$	234634.	0.651028	0.325514	−	0.945537i	$-0.394463\pi$
$167$	234634.	0.651028	0.325514	+	0.945537i	$0.394463\pi$
$168$	−298743.	−0.816630
$169$	525203.	1.41453
$170$	0	0
$171$	378810.	0.990676
$172$	50692.5	0.130654
$173$	−132057.	−0.335464	−0.167732	−	0.985833i	$-0.553644\pi$
$173$	−132057.	−0.335464	−0.167732	+	0.985833i	$0.553644\pi$
$174$	−135781.	−0.339990
$175$	0	0
$176$	183427.	0.446357
$177$	−418726.	−1.00461
$178$	−88260.7	−0.208794
$179$	174642.	0.407396	0.203698	−	0.979034i	$-0.434704\pi$
$179$	174642.	0.407396	0.203698	+	0.979034i	$0.434704\pi$
$180$	0	0
$181$	585099.	1.32749	0.663747	−	0.747957i	$-0.268965\pi$
$181$	585099.	1.32749	0.663747	+	0.747957i	$0.268965\pi$
$182$	205437.	0.459728
$183$	−515440.	−1.13776
$184$	−122585.	−0.266927
$185$	0	0
$186$	−123894.	−0.262583
$187$	−200573.	−0.419439
$188$	−1433.49	−0.00295801
$189$	−119780.	−0.243910
$190$	0	0
$191$	297030.	0.589138	0.294569	−	0.955630i	$-0.404824\pi$
$191$	297030.	0.589138	0.294569	+	0.955630i	$0.404824\pi$
$192$	−182383.	−0.357053
$193$	578242.	1.11742	0.558710	−	0.829363i	$-0.311297\pi$
$193$	578242.	1.11742	0.558710	+	0.829363i	$0.311297\pi$
$194$	−211621.	−0.403696
$195$	0	0
$196$	179213.	0.333219
$197$	387014.	0.710495	0.355248	−	0.934772i	$-0.384397\pi$
$197$	387014.	0.710495	0.355248	+	0.934772i	$0.384397\pi$
$198$	−190855.	−0.345972
$199$	126822.	0.227019	0.113509	−	0.993537i	$-0.463791\pi$
$199$	126822.	0.227019	0.113509	+	0.993537i	$0.463791\pi$
$200$	0	0
$201$	−352942.	−0.616189
$202$	293262.	0.505681
$203$	−277348.	−0.472373
$204$	420274.	0.707062
$205$	0	0
$206$	153508.	0.252036
$207$	−283316.	−0.459563
$208$	572799.	0.918003
$209$	390665.	0.618641
$210$	0	0
$211$	358329.	0.554085	0.277042	−	0.960858i	$-0.410646\pi$
$211$	358329.	0.554085	0.277042	+	0.960858i	$0.410646\pi$
$212$	−680029.	−1.03917
$213$	1.12344e6	1.69669
$214$	−204520.	−0.305283
$215$	0	0
$216$	150354.	0.219270
$217$	−253067.	−0.364826
$218$	−510810.	−0.727978
$219$	605271.	0.852785
$220$	0	0
$221$	−626342.	−0.862643
$222$	−83092.6	−0.113157
$223$	−665174.	−0.895721	−0.447861	−	0.894103i	$-0.647814\pi$
$223$	−665174.	−0.895721	−0.447861	+	0.894103i	$0.647814\pi$
$224$	543794.	0.724127
$225$	0	0
$226$	−303936.	−0.395832
$227$	−269962.	−0.347727	−0.173864	−	0.984770i	$-0.555625\pi$
$227$	−269962.	−0.347727	−0.173864	+	0.984770i	$0.555625\pi$
$228$	−818585.	−1.04286
$229$	368831.	0.464771	0.232386	−	0.972624i	$-0.425347\pi$
$229$	368831.	0.464771	0.232386	+	0.972624i	$0.425347\pi$
$230$	0	0
$231$	−712057.	−0.877980
$232$	348141.	0.424654
$233$	−855037.	−1.03180	−0.515900	−	0.856649i	$-0.672542\pi$
$233$	−855037.	−1.03180	−0.515900	+	0.856649i	$0.672542\pi$
$234$	−595995.	−0.711546
$235$	0	0
$236$	495391.	0.578985
$237$	−1.51549e6	−1.75260
$238$	−143530.	−0.164248
$239$	−1.35994e6	−1.54001	−0.770005	−	0.638038i	$-0.779746\pi$
$239$	−1.35994e6	−1.54001	−0.770005	+	0.638038i	$0.779746\pi$
$240$	0	0
$241$	−780045.	−0.865121	−0.432561	−	0.901605i	$-0.642390\pi$
$241$	−780045.	−0.865121	−0.432561	+	0.901605i	$0.642390\pi$
$242$	147981.	0.162431
$243$	−1.30808e6	−1.42108
$244$	609811.	0.655724
$245$	0	0
$246$	110249.	0.116155
$247$	1.21995e6	1.27233
$248$	317662.	0.327971
$249$	−275405.	−0.281496
$250$	0	0
$251$	185775.	0.186124	0.0930619	−	0.995660i	$-0.470335\pi$
$251$	185775.	0.186124	0.0930619	+	0.995660i	$0.470335\pi$
$252$	816864.	0.810305
$253$	−292182.	−0.286980
$254$	218132.	0.212146
$255$	0	0
$256$	−151853.	−0.144818
$257$	190595.	0.180002	0.0900012	−	0.995942i	$-0.471313\pi$
$257$	190595.	0.180002	0.0900012	+	0.995942i	$0.471313\pi$
$258$	91736.2	0.0858008
$259$	−169726.	−0.157217
$260$	0	0
$261$	804616.	0.731118
$262$	−835451.	−0.751913
$263$	−1.60189e6	−1.42805	−0.714024	−	0.700121i	$-0.753129\pi$
$263$	−1.60189e6	−1.42805	−0.714024	+	0.700121i	$0.753129\pi$
$264$	893808.	0.789286
$265$	0	0
$266$	279559.	0.242253
$267$	955302.	0.820092
$268$	417563.	0.355128
$269$	1.57004e6	1.32291	0.661457	−	0.749983i	$-0.269939\pi$
$269$	1.57004e6	1.32291	0.661457	+	0.749983i	$0.269939\pi$
$270$	0	0
$271$	1.57739e6	1.30471	0.652357	−	0.757912i	$-0.273780\pi$
$271$	1.57739e6	1.30471	0.652357	+	0.757912i	$0.273780\pi$
$272$	−400190.	−0.327977
$273$	−2.22358e6	−1.80570
$274$	−80463.7	−0.0647476
$275$	0	0
$276$	612228.	0.483772
$277$	−7891.72	−0.00617977	−0.00308988	−	0.999995i	$-0.500984\pi$
$277$	−7891.72	−0.00617977	−0.00308988	+	0.999995i	$0.500984\pi$
$278$	−536869.	−0.416636
$279$	734173.	0.564661
$280$	0	0
$281$	1.89466e6	1.43141	0.715707	−	0.698401i	$-0.246105\pi$
$281$	1.89466e6	1.43141	0.715707	+	0.698401i	$0.246105\pi$
$282$	−2594.13	−0.00194253
$283$	−76292.8	−0.0566262	−0.0283131	−	0.999599i	$-0.509014\pi$
$283$	−76292.8	−0.0566262	−0.0283131	+	0.999599i	$0.509014\pi$
$284$	−1.32913e6	−0.977852
$285$	0	0
$286$	−614646.	−0.444334
$287$	225197.	0.161383
$288$	−1.57760e6	−1.12077
$289$	−982259.	−0.691802
$290$	0	0
$291$	2.29051e6	1.58562
$292$	−716090.	−0.491485
$293$	786014.	0.534886	0.267443	−	0.963574i	$-0.413821\pi$
$293$	786014.	0.534886	0.267443	+	0.963574i	$0.413821\pi$
$294$	324315.	0.218826
$295$	0	0
$296$	213048.	0.141335
$297$	358369.	0.235743
$298$	301567.	0.196718
$299$	−912414.	−0.590220
$300$	0	0
$301$	187382.	0.119209
$302$	−486133.	−0.306717
$303$	−3.17416e6	−1.98620
$304$	779465.	0.483741
$305$	0	0
$306$	416395.	0.254216
$307$	382004.	0.231325	0.115662	−	0.993289i	$-0.463101\pi$
$307$	382004.	0.231325	0.115662	+	0.993289i	$0.463101\pi$
$308$	842427.	0.506006
$309$	−1.66152e6	−0.989939
$310$	0	0
$311$	−1.66972e6	−0.978907	−0.489454	−	0.872029i	$-0.662804\pi$
$311$	−1.66972e6	−0.978907	−0.489454	+	0.872029i	$0.662804\pi$
$312$	2.79115e6	1.62329
$313$	−2.89171e6	−1.66837	−0.834187	−	0.551482i	$-0.814063\pi$
$313$	−2.89171e6	−1.66837	−0.834187	+	0.551482i	$0.814063\pi$
$314$	149314.	0.0854629
$315$	0	0
$316$	1.79296e6	1.01007
$317$	−286174.	−0.159949	−0.0799745	−	0.996797i	$-0.525484\pi$
$317$	−286174.	−0.159949	−0.0799745	+	0.996797i	$0.525484\pi$
$318$	−1.23062e6	−0.682428
$319$	829796.	0.456556
$320$	0	0
$321$	2.21366e6	1.19908
$322$	−209085.	−0.112378
$323$	−852326.	−0.454569
$324$	1.20778e6	0.639183
$325$	0	0
$326$	−548917.	−0.286063
$327$	5.52883e6	2.85933
$328$	−282678.	−0.145080
$329$	−5298.80	−0.00269891
$330$	0	0
$331$	2.18138e6	1.09436	0.547180	−	0.837015i	$-0.315701\pi$
$331$	2.18138e6	1.09436	0.547180	+	0.837015i	$0.315701\pi$
$332$	325828.	0.162235
$333$	492393.	0.243333
$334$	−502349.	−0.246399
$335$	0	0
$336$	−1.42072e6	−0.686529
$337$	1.81952e6	0.872733	0.436367	−	0.899769i	$-0.356265\pi$
$337$	1.81952e6	0.872733	0.436367	+	0.899769i	$0.356265\pi$
$338$	−1.12446e6	−0.535366
$339$	3.28969e6	1.55473
$340$	0	0
$341$	757148.	0.352610
$342$	−811030.	−0.374948
$343$	2.36571e6	1.08574
$344$	−235210.	−0.107167
$345$	0	0
$346$	282733.	0.126965
$347$	2.41292e6	1.07577	0.537884	−	0.843019i	$-0.319224\pi$
$347$	2.41292e6	1.07577	0.537884	+	0.843019i	$0.319224\pi$
$348$	−1.73872e6	−0.769631
$349$	1.37016e6	0.602153	0.301077	−	0.953600i	$-0.402654\pi$
$349$	1.37016e6	0.602153	0.301077	+	0.953600i	$0.402654\pi$
$350$	0	0
$351$	1.11910e6	0.484843
$352$	−1.62697e6	−0.699880
$353$	3.23386e6	1.38129	0.690645	−	0.723194i	$-0.257327\pi$
$353$	3.23386e6	1.38129	0.690645	+	0.723194i	$0.257327\pi$
$354$	896489.	0.380222
$355$	0	0
$356$	−1.13021e6	−0.472643
$357$	1.55352e6	0.645128
$358$	−373908.	−0.154190
$359$	−2.96966e6	−1.21610	−0.608051	−	0.793898i	$-0.708049\pi$
$359$	−2.96966e6	−1.21610	−0.608051	+	0.793898i	$0.708049\pi$
$360$	0	0
$361$	−815990.	−0.329547
$362$	−1.25269e6	−0.502427
$363$	−1.60169e6	−0.637989
$364$	2.63070e6	1.04068
$365$	0	0
$366$	1.10355e6	0.430616
$367$	416084.	0.161256	0.0806281	−	0.996744i	$-0.474307\pi$
$367$	416084.	0.161256	0.0806281	+	0.996744i	$0.474307\pi$
$368$	−582970.	−0.224402
$369$	−653319.	−0.249781
$370$	0	0
$371$	−2.51368e6	−0.948148
$372$	−1.58650e6	−0.594406
$373$	3.12680e6	1.16367	0.581833	−	0.813308i	$-0.302336\pi$
$373$	3.12680e6	1.16367	0.581833	+	0.813308i	$0.302336\pi$
$374$	429426.	0.158748
$375$	0	0
$376$	6651.31	0.00242626
$377$	2.59125e6	0.938980
$378$	256448.	0.0923145
$379$	3.97807e6	1.42257	0.711286	−	0.702902i	$-0.248113\pi$
$379$	3.97807e6	1.42257	0.711286	+	0.702902i	$0.248113\pi$
$380$	0	0
$381$	−2.36098e6	−0.833260
$382$	−635939.	−0.222975
$383$	−256479.	−0.0893419	−0.0446709	−	0.999002i	$-0.514224\pi$
$383$	−256479.	−0.0893419	−0.0446709	+	0.999002i	$0.514224\pi$
$384$	4.36957e6	1.51220
$385$	0	0
$386$	−1.23801e6	−0.422918
$387$	−543614.	−0.184507
$388$	−2.70988e6	−0.913842
$389$	−1.40124e6	−0.469503	−0.234752	−	0.972055i	$-0.575428\pi$
$389$	−1.40124e6	−0.469503	−0.234752	+	0.972055i	$0.575428\pi$
$390$	0	0
$391$	637463.	0.210869
$392$	−831540.	−0.273318
$393$	9.04262e6	2.95334
$394$	−828594.	−0.268906
$395$	0	0
$396$	−2.44397e6	−0.783173
$397$	4.07266e6	1.29689	0.648444	−	0.761263i	$-0.275420\pi$
$397$	4.07266e6	1.29689	0.648444	+	0.761263i	$0.275420\pi$
$398$	−271525.	−0.0859215
$399$	−3.02585e6	−0.951513
$400$	0	0
$401$	4.63646e6	1.43988	0.719938	−	0.694038i	$-0.244170\pi$
$401$	4.63646e6	1.43988	0.719938	+	0.694038i	$0.244170\pi$
$402$	755647.	0.233214
$403$	2.36439e6	0.725198
$404$	3.75532e6	1.14470
$405$	0	0
$406$	593800.	0.178783
$407$	507802.	0.151953
$408$	−1.95005e6	−0.579957
$409$	−3.64510e6	−1.07746	−0.538730	−	0.842478i	$-0.681096\pi$
$409$	−3.64510e6	−1.07746	−0.538730	+	0.842478i	$0.681096\pi$
$410$	0	0
$411$	870911.	0.254313
$412$	1.96572e6	0.570531
$413$	1.83118e6	0.528270
$414$	606578.	0.173934
$415$	0	0
$416$	−5.08064e6	−1.43941
$417$	5.81088e6	1.63645
$418$	−836410.	−0.234142
$419$	1.79257e6	0.498817	0.249409	−	0.968398i	$-0.419764\pi$
$419$	1.79257e6	0.498817	0.249409	+	0.968398i	$0.419764\pi$
$420$	0	0
$421$	−1.04497e6	−0.287341	−0.143671	−	0.989626i	$-0.545891\pi$
$421$	−1.04497e6	−0.287341	−0.143671	+	0.989626i	$0.545891\pi$
$422$	−767180.	−0.209709
$423$	15372.4	0.00417725
$424$	3.15530e6	0.852365
$425$	0	0
$426$	−2.40528e6	−0.642158
$427$	2.25413e6	0.598287
$428$	−2.61896e6	−0.691065
$429$	6.65271e6	1.74524
$430$	0	0
$431$	−4.01423e6	−1.04090	−0.520450	−	0.853892i	$-0.674236\pi$
$431$	−4.01423e6	−1.04090	−0.520450	+	0.853892i	$0.674236\pi$
$432$	715028.	0.184337
$433$	−2.37417e6	−0.608543	−0.304272	−	0.952585i	$-0.598413\pi$
$433$	−2.37417e6	−0.608543	−0.304272	+	0.952585i	$0.598413\pi$
$434$	541814.	0.138078
$435$	0	0
$436$	−6.54110e6	−1.64791
$437$	−1.24161e6	−0.311016
$438$	−1.29588e6	−0.322760
$439$	2.15367e6	0.533356	0.266678	−	0.963786i	$-0.414074\pi$
$439$	2.15367e6	0.533356	0.266678	+	0.963786i	$0.414074\pi$
$440$	0	0
$441$	−1.92184e6	−0.470566
$442$	1.34099e6	0.326491
$443$	−3.15788e6	−0.764515	−0.382257	−	0.924056i	$-0.624853\pi$
$443$	−3.15788e6	−0.764515	−0.382257	+	0.924056i	$0.624853\pi$
$444$	−1.06403e6	−0.256151
$445$	0	0
$446$	1.42413e6	0.339010
$447$	−3.26406e6	−0.772661
$448$	797603.	0.187755
$449$	3.98611e6	0.933111	0.466556	−	0.884492i	$-0.345495\pi$
$449$	3.98611e6	0.933111	0.466556	+	0.884492i	$0.345495\pi$
$450$	0	0
$451$	−673763.	−0.155979
$452$	−3.89200e6	−0.896040
$453$	5.26173e6	1.20471
$454$	577987.	0.131607
$455$	0	0
$456$	3.79819e6	0.855391
$457$	−1.22640e6	−0.274689	−0.137344	−	0.990523i	$-0.543857\pi$
$457$	−1.22640e6	−0.274689	−0.137344	+	0.990523i	$0.543857\pi$
$458$	−789665.	−0.175905
$459$	−781865.	−0.173221
$460$	0	0
$461$	1.60134e6	0.350940	0.175470	−	0.984485i	$-0.443856\pi$
$461$	1.60134e6	0.350940	0.175470	+	0.984485i	$0.443856\pi$
$462$	1.52451e6	0.332296
$463$	−2.60752e6	−0.565294	−0.282647	−	0.959224i	$-0.591213\pi$
$463$	−2.60752e6	−0.565294	−0.282647	+	0.959224i	$0.591213\pi$
$464$	1.65563e6	0.357000
$465$	0	0
$466$	1.83063e6	0.390513
$467$	−6.26319e6	−1.32893	−0.664467	−	0.747318i	$-0.731341\pi$
$467$	−6.26319e6	−1.32893	−0.664467	+	0.747318i	$0.731341\pi$
$468$	−7.63193e6	−1.61072
$469$	1.54349e6	0.324021
$470$	0	0
$471$	−1.61613e6	−0.335678
$472$	−2.29859e6	−0.474904
$473$	−560625.	−0.115218
$474$	3.24465e6	0.663319
$475$	0	0
$476$	−1.83795e6	−0.371806
$477$	7.29246e6	1.46750
$478$	2.91161e6	0.582859
$479$	−1.98635e6	−0.395564	−0.197782	−	0.980246i	$-0.563374\pi$
$479$	−1.98635e6	−0.395564	−0.197782	+	0.980246i	$0.563374\pi$
$480$	0	0
$481$	1.58574e6	0.312514
$482$	1.67007e6	0.327429
$483$	2.26306e6	0.441396
$484$	1.89495e6	0.367692
$485$	0	0
$486$	2.80059e6	0.537847
$487$	5.21331e6	0.996073	0.498036	−	0.867156i	$-0.334055\pi$
$487$	5.21331e6	0.996073	0.498036	+	0.867156i	$0.334055\pi$
$488$	−2.82949e6	−0.537847
$489$	5.94128e6	1.12359
$490$	0	0
$491$	7.81135e6	1.46225	0.731126	−	0.682242i	$-0.238995\pi$
$491$	7.81135e6	1.46225	0.731126	+	0.682242i	$0.238995\pi$
$492$	1.41178e6	0.262939
$493$	−1.81039e6	−0.335471
$494$	−2.61191e6	−0.481549
$495$	0	0
$496$	1.51068e6	0.275721
$497$	−4.91306e6	−0.892198
$498$	589639.	0.106540
$499$	1.10822e6	0.199238	0.0996191	−	0.995026i	$-0.468238\pi$
$499$	1.10822e6	0.199238	0.0996191	+	0.995026i	$0.468238\pi$
$500$	0	0
$501$	5.43725e6	0.967799
$502$	−397742.	−0.0704437
$503$	5.63874e6	0.993716	0.496858	−	0.867832i	$-0.334487\pi$
$503$	5.63874e6	0.993716	0.496858	+	0.867832i	$0.334487\pi$
$504$	−3.79021e6	−0.664640
$505$	0	0
$506$	625560.	0.108616
$507$	1.21707e7	2.10279
$508$	2.79325e6	0.480232
$509$	1.85028e6	0.316550	0.158275	−	0.987395i	$-0.449407\pi$
$509$	1.85028e6	0.316550	0.158275	+	0.987395i	$0.449407\pi$
$510$	0	0
$511$	−2.64698e6	−0.448434
$512$	−5.70880e6	−0.962433
$513$	1.52287e6	0.255487
$514$	−408062.	−0.0681269
$515$	0	0
$516$	1.17471e6	0.194226
$517$	15853.4	0.00260854
$518$	363382.	0.0595030
$519$	−3.06020e6	−0.498691
$520$	0	0
$521$	−4.59177e6	−0.741115	−0.370558	−	0.928809i	$-0.620833\pi$
$521$	−4.59177e6	−0.741115	−0.370558	+	0.928809i	$0.620833\pi$
$522$	−1.72268e6	−0.276712
$523$	5.06618e6	0.809890	0.404945	−	0.914341i	$-0.367291\pi$
$523$	5.06618e6	0.809890	0.404945	+	0.914341i	$0.367291\pi$
$524$	−1.06982e7	−1.70210
$525$	0	0
$526$	3.42963e6	0.540484
$527$	−1.65190e6	−0.259093
$528$	4.25063e6	0.663542
$529$	−5.50773e6	−0.855723
$530$	0	0
$531$	−5.31245e6	−0.817633
$532$	3.57985e6	0.548385
$533$	−2.10400e6	−0.320795
$534$	−2.04529e6	−0.310386
$535$	0	0
$536$	−1.93747e6	−0.291288
$537$	4.04705e6	0.605623
$538$	−3.36145e6	−0.500693
$539$	−1.98198e6	−0.293851
$540$	0	0
$541$	9.26992e6	1.36170	0.680852	−	0.732421i	$-0.261610\pi$
$541$	9.26992e6	1.36170	0.680852	+	0.732421i	$0.261610\pi$
$542$	−3.37718e6	−0.493805
$543$	1.35587e7	1.97342
$544$	3.54962e6	0.514262
$545$	0	0
$546$	4.76067e6	0.683418
$547$	1.36420e6	0.194943	0.0974717	−	0.995238i	$-0.468924\pi$
$547$	1.36420e6	0.194943	0.0974717	+	0.995238i	$0.468924\pi$
$548$	−1.03037e6	−0.146568
$549$	−6.53947e6	−0.926001
$550$	0	0
$551$	3.52617e6	0.494794
$552$	−2.84071e6	−0.396806
$553$	6.62757e6	0.921598
$554$	16896.1	0.00233890
$555$	0	0
$556$	−6.87480e6	−0.943133
$557$	2.36218e6	0.322608	0.161304	−	0.986905i	$-0.448430\pi$
$557$	2.36218e6	0.322608	0.161304	+	0.986905i	$0.448430\pi$
$558$	−1.57186e6	−0.213712
$559$	−1.75070e6	−0.236964
$560$	0	0
$561$	−4.64796e6	−0.623527
$562$	−4.05645e6	−0.541758
$563$	3.92025e6	0.521246	0.260623	−	0.965441i	$-0.416072\pi$
$563$	3.92025e6	0.521246	0.260623	+	0.965441i	$0.416072\pi$
$564$	−33218.7	−0.00439729
$565$	0	0
$566$	163342.	0.0214317
$567$	4.46448e6	0.583195
$568$	6.16711e6	0.802068
$569$	5.98608e6	0.775108	0.387554	−	0.921847i	$-0.373320\pi$
$569$	5.98608e6	0.775108	0.387554	+	0.921847i	$0.373320\pi$
$570$	0	0
$571$	4.83971e6	0.621197	0.310598	−	0.950541i	$-0.399471\pi$
$571$	4.83971e6	0.621197	0.310598	+	0.950541i	$0.399471\pi$
$572$	−7.87076e6	−1.00583
$573$	6.88318e6	0.875795
$574$	−482144.	−0.0610797
$575$	0	0
$576$	−2.31393e6	−0.290599
$577$	4.16039e6	0.520229	0.260115	−	0.965578i	$-0.416240\pi$
$577$	4.16039e6	0.520229	0.260115	+	0.965578i	$0.416240\pi$
$578$	2.10301e6	0.261831
$579$	1.33998e7	1.66112
$580$	0	0
$581$	1.20440e6	0.148024
$582$	−4.90397e6	−0.600123
$583$	7.52067e6	0.916400
$584$	3.32262e6	0.403133
$585$	0	0
$586$	−1.68285e6	−0.202442
$587$	−3.70349e6	−0.443625	−0.221812	−	0.975089i	$-0.571197\pi$
$587$	−3.70349e6	−0.443625	−0.221812	+	0.975089i	$0.571197\pi$
$588$	4.15297e6	0.495354
$589$	3.21746e6	0.382142
$590$	0	0
$591$	8.96841e6	1.05620
$592$	1.01318e6	0.118818
$593$	2.88760e6	0.337210	0.168605	−	0.985684i	$-0.446074\pi$
$593$	2.88760e6	0.337210	0.168605	+	0.985684i	$0.446074\pi$
$594$	−767265.	−0.0892235
$595$	0	0
$596$	3.86167e6	0.445308
$597$	2.93889e6	0.337480
$598$	1.95347e6	0.223385
$599$	−7.93475e6	−0.903579	−0.451790	−	0.892125i	$-0.649214\pi$
$599$	−7.93475e6	−0.903579	−0.451790	+	0.892125i	$0.649214\pi$
$600$	0	0
$601$	8.07159e6	0.911534	0.455767	−	0.890099i	$-0.349365\pi$
$601$	8.07159e6	0.911534	0.455767	+	0.890099i	$0.349365\pi$
$602$	−401182.	−0.0451181
$603$	−4.47784e6	−0.501505
$604$	−6.22510e6	−0.694311
$605$	0	0
$606$	6.79586e6	0.751731
$607$	−1.65297e7	−1.82093	−0.910466	−	0.413584i	$-0.864277\pi$
$607$	−1.65297e7	−1.82093	−0.910466	+	0.413584i	$0.864277\pi$
$608$	−6.91374e6	−0.758497
$609$	−6.42709e6	−0.702216
$610$	0	0
$611$	49506.5	0.00536486
$612$	5.33209e6	0.575465
$613$	−1.18970e7	−1.27875	−0.639374	−	0.768896i	$-0.720807\pi$
$613$	−1.18970e7	−1.27875	−0.639374	+	0.768896i	$0.720807\pi$
$614$	−817868.	−0.0875512
$615$	0	0
$616$	−3.90882e6	−0.415043
$617$	−6.87626e6	−0.727176	−0.363588	−	0.931560i	$-0.618448\pi$
$617$	−6.87626e6	−0.727176	−0.363588	+	0.931560i	$0.618448\pi$
$618$	3.55729e6	0.374670
$619$	8.46240e6	0.887702	0.443851	−	0.896101i	$-0.353612\pi$
$619$	8.46240e6	0.887702	0.443851	+	0.896101i	$0.353612\pi$
$620$	0	0
$621$	−1.13897e6	−0.118518
$622$	3.57485e6	0.370494
$623$	−4.17775e6	−0.431243
$624$	1.32737e7	1.36468
$625$	0	0
$626$	6.19112e6	0.631442
$627$	9.05301e6	0.919653
$628$	1.91202e6	0.193461
$629$	−1.10789e6	−0.111653
$630$	0	0
$631$	−1.01368e7	−1.01351	−0.506756	−	0.862090i	$-0.669155\pi$
$631$	−1.01368e7	−1.01351	−0.506756	+	0.862090i	$0.669155\pi$
$632$	−8.31924e6	−0.828497
$633$	8.30369e6	0.823686
$634$	612696.	0.0605371
$635$	0	0
$636$	−1.57585e7	−1.54480
$637$	−6.18925e6	−0.604351
$638$	−1.77659e6	−0.172796
$639$	1.42533e7	1.38090
$640$	0	0
$641$	4.41055e6	0.423983	0.211991	−	0.977272i	$-0.432005\pi$
$641$	4.41055e6	0.423983	0.211991	+	0.977272i	$0.432005\pi$
$642$	−4.73942e6	−0.453825
$643$	−1.73310e7	−1.65309	−0.826543	−	0.562874i	$-0.809696\pi$
$643$	−1.73310e7	−1.65309	−0.826543	+	0.562874i	$0.809696\pi$
$644$	−2.67741e6	−0.254390
$645$	0	0
$646$	1.82482e6	0.172044
$647$	−9.66092e6	−0.907314	−0.453657	−	0.891176i	$-0.649881\pi$
$647$	−9.66092e6	−0.907314	−0.453657	+	0.891176i	$0.649881\pi$
$648$	−5.60403e6	−0.524280
$649$	−5.47869e6	−0.510582
$650$	0	0
$651$	−5.86441e6	−0.542340
$652$	−7.02907e6	−0.647558
$653$	1.38135e7	1.26772	0.633858	−	0.773449i	$-0.281470\pi$
$653$	1.38135e7	1.26772	0.633858	+	0.773449i	$0.281470\pi$
$654$	−1.18372e7	−1.08219
$655$	0	0
$656$	−1.34431e6	−0.121966
$657$	7.67917e6	0.694066
$658$	11344.7	0.00102148
$659$	4.67535e6	0.419373	0.209687	−	0.977769i	$-0.432756\pi$
$659$	4.67535e6	0.419373	0.209687	+	0.977769i	$0.432756\pi$
$660$	0	0
$661$	9.74412e6	0.867439	0.433719	−	0.901048i	$-0.357201\pi$
$661$	9.74412e6	0.867439	0.433719	+	0.901048i	$0.357201\pi$
$662$	−4.67031e6	−0.414191
$663$	−1.45145e7	−1.28238
$664$	−1.51183e6	−0.133071
$665$	0	0
$666$	−1.05421e6	−0.0920961
$667$	−2.63726e6	−0.229530
$668$	−6.43276e6	−0.557771
$669$	−1.54143e7	−1.33155
$670$	0	0
$671$	−6.74411e6	−0.578254
$672$	1.26015e7	1.07647
$673$	−1.34161e7	−1.14180	−0.570900	−	0.821019i	$-0.693406\pi$
$673$	−1.34161e7	−1.14180	−0.570900	+	0.821019i	$0.693406\pi$
$674$	−3.89557e6	−0.330310
$675$	0	0
$676$	−1.43991e7	−1.21190
$677$	−1.44900e7	−1.21506	−0.607528	−	0.794298i	$-0.707839\pi$
$677$	−1.44900e7	−1.21506	−0.607528	+	0.794298i	$0.707839\pi$
$678$	−7.04321e6	−0.588432
$679$	−1.00169e7	−0.833795
$680$	0	0
$681$	−6.25593e6	−0.516921
$682$	−1.62105e6	−0.133455
$683$	−1.69229e7	−1.38810	−0.694052	−	0.719925i	$-0.744176\pi$
$683$	−1.69229e7	−1.38810	−0.694052	+	0.719925i	$0.744176\pi$
$684$	−1.03855e7	−0.848766
$685$	0	0
$686$	−5.06496e6	−0.410928
$687$	8.54706e6	0.690915
$688$	−1.11858e6	−0.0900936
$689$	2.34852e7	1.88472
$690$	0	0
$691$	−1.58530e7	−1.26304	−0.631521	−	0.775359i	$-0.717569\pi$
$691$	−1.58530e7	−1.26304	−0.631521	+	0.775359i	$0.717569\pi$
$692$	3.62049e6	0.287410
$693$	−9.03398e6	−0.714572
$694$	−5.16603e6	−0.407154
$695$	0	0
$696$	8.06759e6	0.631278
$697$	1.46997e6	0.114611
$698$	−2.93350e6	−0.227901
$699$	−1.98141e7	−1.53384
$700$	0	0
$701$	−1.55449e7	−1.19479	−0.597396	−	0.801947i	$-0.703798\pi$
$701$	−1.55449e7	−1.19479	−0.597396	+	0.801947i	$0.703798\pi$
$702$	−2.39598e6	−0.183502
$703$	2.15788e6	0.164679
$704$	−2.38634e6	−0.181468
$705$	0	0
$706$	−6.92368e6	−0.522787
$707$	1.38813e7	1.04444
$708$	1.14799e7	0.860703
$709$	−141986.	−0.0106079	−0.00530396	−	0.999986i	$-0.501688\pi$
$709$	−141986.	−0.0106079	−0.00530396	+	0.999986i	$0.501688\pi$
$710$	0	0
$711$	−1.92273e7	−1.42641
$712$	5.24411e6	0.387678
$713$	−2.40637e6	−0.177272
$714$	−3.32607e6	−0.244166
$715$	0	0
$716$	−4.78802e6	−0.349038
$717$	−3.15143e7	−2.28933
$718$	6.35801e6	0.460268
$719$	2.84973e6	0.205580	0.102790	−	0.994703i	$-0.467223\pi$
$719$	2.84973e6	0.205580	0.102790	+	0.994703i	$0.467223\pi$
$720$	0	0
$721$	7.26617e6	0.520556
$722$	1.74703e6	0.124726
$723$	−1.80763e7	−1.28606
$724$	−1.60412e7	−1.13734
$725$	0	0
$726$	3.42922e6	0.241464
$727$	−2.11993e7	−1.48760	−0.743799	−	0.668403i	$-0.766978\pi$
$727$	−2.11993e7	−1.48760	−0.743799	+	0.668403i	$0.766978\pi$
$728$	−1.22063e7	−0.853602
$729$	−1.96076e7	−1.36649
$730$	0	0
$731$	1.22314e6	0.0846605
$732$	1.41314e7	0.974780
$733$	−2.07197e7	−1.42437	−0.712186	−	0.701990i	$-0.752295\pi$
$733$	−2.07197e7	−1.42437	−0.712186	+	0.701990i	$0.752295\pi$
$734$	−890833.	−0.0610318
$735$	0	0
$736$	5.17085e6	0.351858
$737$	−4.61797e6	−0.313171
$738$	1.39875e6	0.0945364
$739$	−725048.	−0.0488377	−0.0244189	−	0.999702i	$-0.507774\pi$
$739$	−725048.	−0.0488377	−0.0244189	+	0.999702i	$0.507774\pi$
$740$	0	0
$741$	2.82704e7	1.89141
$742$	5.38178e6	0.358853
$743$	1.93455e7	1.28561	0.642804	−	0.766030i	$-0.277771\pi$
$743$	1.93455e7	1.28561	0.642804	+	0.766030i	$0.277771\pi$
$744$	7.36128e6	0.487552
$745$	0	0
$746$	−6.69446e6	−0.440422
$747$	−3.49411e6	−0.229105
$748$	5.49895e6	0.359357
$749$	−9.68081e6	−0.630532
$750$	0	0
$751$	1.46491e7	0.947787	0.473893	−	0.880582i	$-0.342848\pi$
$751$	1.46491e7	0.947787	0.473893	+	0.880582i	$0.342848\pi$
$752$	31631.2	0.00203972
$753$	4.30502e6	0.276686
$754$	−5.54785e6	−0.355383
$755$	0	0
$756$	3.28391e6	0.208971
$757$	7.52536e6	0.477296	0.238648	−	0.971106i	$-0.423296\pi$
$757$	7.52536e6	0.477296	0.238648	+	0.971106i	$0.423296\pi$
$758$	−8.51702e6	−0.538412
$759$	−6.77084e6	−0.426617
$760$	0	0
$761$	1.73339e6	0.108501	0.0542507	−	0.998527i	$-0.482723\pi$
$761$	1.73339e6	0.108501	0.0542507	+	0.998527i	$0.482723\pi$
$762$	5.05485e6	0.315370
$763$	−2.41788e7	−1.50357
$764$	−8.14342e6	−0.504747
$765$	0	0
$766$	549120.	0.0338139
$767$	−1.71086e7	−1.05009
$768$	−3.51894e6	−0.215282
$769$	2.13968e7	1.30477	0.652383	−	0.757890i	$-0.273769\pi$
$769$	2.13968e7	1.30477	0.652383	+	0.757890i	$0.273769\pi$
$770$	0	0
$771$	4.41672e6	0.267586
$772$	−1.58532e7	−0.957355
$773$	2.35101e7	1.41516	0.707580	−	0.706634i	$-0.249787\pi$
$773$	2.35101e7	1.41516	0.707580	+	0.706634i	$0.249787\pi$
$774$	1.16387e6	0.0698318
$775$	0	0
$776$	1.25737e7	0.749565
$777$	−3.93312e6	−0.233714
$778$	3.00005e6	0.177696
$779$	−2.86312e6	−0.169043
$780$	0	0
$781$	1.46993e7	0.862324
$782$	−1.36480e6	−0.0798093
$783$	3.23467e6	0.188550
$784$	−3.95450e6	−0.229774
$785$	0	0
$786$	−1.93602e7	−1.11777
$787$	−2.22992e7	−1.28337	−0.641687	−	0.766967i	$-0.721765\pi$
$787$	−2.22992e7	−1.28337	−0.641687	+	0.766967i	$0.721765\pi$
$788$	−1.06104e7	−0.608720
$789$	−3.71211e7	−2.12290
$790$	0	0
$791$	−1.43866e7	−0.817552
$792$	1.13399e7	0.642386
$793$	−2.10602e7	−1.18927
$794$	−8.71954e6	−0.490843
$795$	0	0
$796$	−3.47697e6	−0.194499
$797$	−2.22307e7	−1.23967	−0.619837	−	0.784730i	$-0.712801\pi$
$797$	−2.22307e7	−1.23967	−0.619837	+	0.784730i	$0.712801\pi$
$798$	6.47832e6	0.360126
$799$	−34588.0	−0.00191672
$800$	0	0
$801$	1.21201e7	0.667458
$802$	−9.92661e6	−0.544961
$803$	7.91948e6	0.433419
$804$	9.67632e6	0.527923
$805$	0	0
$806$	−5.06214e6	−0.274471
$807$	3.63832e7	1.96660
$808$	−1.74245e7	−0.938927
$809$	−2.88799e7	−1.55140	−0.775701	−	0.631101i	$-0.782603\pi$
$809$	−2.88799e7	−1.55140	−0.775701	+	0.631101i	$0.782603\pi$
$810$	0	0
$811$	−2.42224e7	−1.29320	−0.646600	−	0.762829i	$-0.723810\pi$
$811$	−2.42224e7	−1.29320	−0.646600	+	0.762829i	$0.723810\pi$
$812$	7.60382e6	0.404708
$813$	3.65534e7	1.93955
$814$	−1.08720e6	−0.0575106
$815$	0	0
$816$	−9.27373e6	−0.487561
$817$	−2.38235e6	−0.124868
$818$	7.80413e6	0.407794
$819$	−2.82110e7	−1.46963
$820$	0	0
$821$	2.56568e7	1.32845	0.664225	−	0.747532i	$-0.268762\pi$
$821$	2.56568e7	1.32845	0.664225	+	0.747532i	$0.268762\pi$
$822$	−1.86461e6	−0.0962519
$823$	−2.88133e7	−1.48284	−0.741419	−	0.671043i	$-0.765847\pi$
$823$	−2.88133e7	−1.48284	−0.741419	+	0.671043i	$0.765847\pi$
$824$	−9.12085e6	−0.467969
$825$	0	0
$826$	−3.92054e6	−0.199938
$827$	−3.52668e7	−1.79309	−0.896544	−	0.442954i	$-0.853930\pi$
$827$	−3.52668e7	−1.79309	−0.896544	+	0.442954i	$0.853930\pi$
$828$	7.76744e6	0.393733
$829$	1.23200e7	0.622621	0.311310	−	0.950308i	$-0.399232\pi$
$829$	1.23200e7	0.622621	0.311310	+	0.950308i	$0.399232\pi$
$830$	0	0
$831$	−182878.	−0.00918667
$832$	−7.45197e6	−0.373218
$833$	4.32415e6	0.215918
$834$	−1.24411e7	−0.619358
$835$	0	0
$836$	−1.07105e7	−0.530023
$837$	2.95148e6	0.145622
$838$	−3.83788e6	−0.188791
$839$	2.53906e7	1.24528	0.622641	−	0.782508i	$-0.286060\pi$
$839$	2.53906e7	1.24528	0.622641	+	0.782508i	$0.286060\pi$
$840$	0	0
$841$	−1.30213e7	−0.634842
$842$	2.23727e6	0.108752
$843$	4.39056e7	2.12790
$844$	−9.82401e6	−0.474715
$845$	0	0
$846$	−32912.1	−0.00158099
$847$	7.00456e6	0.335484
$848$	1.50055e7	0.716571
$849$	−1.76796e6	−0.0841789
$850$	0	0
$851$	−1.61390e6	−0.0763928
$852$	−3.08005e7	−1.45365
$853$	1.60901e7	0.757159	0.378580	−	0.925569i	$-0.376413\pi$
$853$	1.60901e7	0.757159	0.378580	+	0.925569i	$0.376413\pi$
$854$	−4.82607e6	−0.226438
$855$	0	0
$856$	1.21518e7	0.566835
$857$	2.49452e7	1.16020	0.580102	−	0.814544i	$-0.303013\pi$
$857$	2.49452e7	1.16020	0.580102	+	0.814544i	$0.303013\pi$
$858$	−1.42434e7	−0.660535
$859$	−1.99775e7	−0.923757	−0.461879	−	0.886943i	$-0.652824\pi$
$859$	−1.99775e7	−0.923757	−0.461879	+	0.886943i	$0.652824\pi$
$860$	0	0
$861$	5.21856e6	0.239907
$862$	8.59444e6	0.393957
$863$	3.70446e7	1.69316	0.846580	−	0.532261i	$-0.178657\pi$
$863$	3.70446e7	1.69316	0.846580	+	0.532261i	$0.178657\pi$
$864$	−6.34218e6	−0.289038
$865$	0	0
$866$	5.08307e6	0.230320
$867$	−2.27622e7	−1.02841
$868$	6.93812e6	0.312566
$869$	−1.98290e7	−0.890739
$870$	0	0
$871$	−1.44208e7	−0.644086
$872$	3.03504e7	1.35168
$873$	2.90601e7	1.29051
$874$	2.65828e6	0.117713
$875$	0	0
$876$	−1.65942e7	−0.730627
$877$	−1.16178e7	−0.510064	−0.255032	−	0.966933i	$-0.582086\pi$
$877$	−1.16178e7	−0.510064	−0.255032	+	0.966933i	$0.582086\pi$
$878$	−4.61098e6	−0.201863
$879$	1.82146e7	0.795146
$880$	0	0
$881$	2.07720e7	0.901653	0.450826	−	0.892612i	$-0.351129\pi$
$881$	2.07720e7	0.901653	0.450826	+	0.892612i	$0.351129\pi$
$882$	4.11464e6	0.178099
$883$	2.98792e7	1.28964	0.644819	−	0.764336i	$-0.276933\pi$
$883$	2.98792e7	1.28964	0.644819	+	0.764336i	$0.276933\pi$
$884$	1.71719e7	0.739073
$885$	0	0
$886$	6.76099e6	0.289352
$887$	−3.09233e7	−1.31970	−0.659852	−	0.751396i	$-0.729381\pi$
$887$	−3.09233e7	−1.31970	−0.659852	+	0.751396i	$0.729381\pi$
$888$	4.93704e6	0.210104
$889$	1.03251e7	0.438167
$890$	0	0
$891$	−1.33572e7	−0.563667
$892$	1.82365e7	0.767414
$893$	67368.3	0.00282701
$894$	6.98832e6	0.292435
$895$	0	0
$896$	−1.91091e7	−0.795188
$897$	−2.11437e7	−0.877404
$898$	−8.53423e6	−0.353162
$899$	6.83409e6	0.282021
$900$	0	0
$901$	−1.64081e7	−0.673358
$902$	1.44252e6	0.0590345
$903$	4.34226e6	0.177213
$904$	1.80587e7	0.734963
$905$	0	0
$906$	−1.12653e7	−0.455956
$907$	4.60660e6	0.185935	0.0929677	−	0.995669i	$-0.470365\pi$
$907$	4.60660e6	0.185935	0.0929677	+	0.995669i	$0.470365\pi$
$908$	7.40133e6	0.297917
$909$	−4.02711e7	−1.61653
$910$	0	0
$911$	−4.03643e7	−1.61139	−0.805697	−	0.592328i	$-0.798209\pi$
$911$	−4.03643e7	−1.61139	−0.805697	+	0.592328i	$0.798209\pi$
$912$	1.80628e7	0.719115
$913$	−3.60345e6	−0.143068
$914$	2.62571e6	0.103963
$915$	0	0
$916$	−1.01119e7	−0.398195
$917$	−3.95454e7	−1.55300
$918$	1.67397e6	0.0655602
$919$	1.64186e7	0.641279	0.320639	−	0.947201i	$-0.396102\pi$
$919$	1.64186e7	0.641279	0.320639	+	0.947201i	$0.396102\pi$
$920$	0	0
$921$	8.85231e6	0.343881
$922$	−3.42847e6	−0.132823
$923$	4.59025e7	1.77350
$924$	1.95219e7	0.752214
$925$	0	0
$926$	5.58267e6	0.213951
$927$	−2.10799e7	−0.805694
$928$	−1.46852e7	−0.559770
$929$	1.70584e7	0.648485	0.324243	−	0.945974i	$-0.394891\pi$
$929$	1.70584e7	0.648485	0.324243	+	0.945974i	$0.394891\pi$
$930$	0	0
$931$	−8.42232e6	−0.318462
$932$	2.34418e7	0.883999
$933$	−3.86929e7	−1.45522
$934$	1.34094e7	0.502972
$935$	0	0
$936$	3.54117e7	1.32117
$937$	−4.43462e7	−1.65009	−0.825044	−	0.565069i	$-0.808850\pi$
$937$	−4.43462e7	−1.65009	−0.825044	+	0.565069i	$0.808850\pi$
$938$	−3.30461e6	−0.122635
$939$	−6.70105e7	−2.48016
$940$	0	0
$941$	1.11272e6	0.0409648	0.0204824	−	0.999790i	$-0.493480\pi$
$941$	1.11272e6	0.0409648	0.0204824	+	0.999790i	$0.493480\pi$
$942$	3.46011e6	0.127047
$943$	2.14136e6	0.0784170
$944$	−1.09312e7	−0.399245
$945$	0	0
$946$	1.20029e6	0.0436074
$947$	1.85354e7	0.671624	0.335812	−	0.941929i	$-0.390989\pi$
$947$	1.85354e7	0.671624	0.335812	+	0.941929i	$0.390989\pi$
$948$	4.15489e7	1.50155
$949$	2.47306e7	0.891394
$950$	0	0
$951$	−6.63161e6	−0.237776
$952$	8.52800e6	0.304968
$953$	1.80811e7	0.644901	0.322450	−	0.946586i	$-0.395493\pi$
$953$	1.80811e7	0.644901	0.322450	+	0.946586i	$0.395493\pi$
$954$	−1.56131e7	−0.555416
$955$	0	0
$956$	3.72842e7	1.31941
$957$	1.92291e7	0.678704
$958$	4.25276e6	0.149712
$959$	−3.80869e6	−0.133730
$960$	0	0
$961$	−2.23934e7	−0.782188
$962$	−3.39506e6	−0.118280
$963$	2.80851e7	0.975909
$964$	2.13858e7	0.741197
$965$	0	0
$966$	−4.84520e6	−0.167059
$967$	3.04133e7	1.04592	0.522958	−	0.852358i	$-0.324828\pi$
$967$	3.04133e7	1.04592	0.522958	+	0.852358i	$0.324828\pi$
$968$	−8.79246e6	−0.301594
$969$	−1.97513e7	−0.675749
$970$	0	0
$971$	−3.87322e7	−1.31833	−0.659164	−	0.751999i	$-0.729090\pi$
$971$	−3.87322e7	−1.31833	−0.659164	+	0.751999i	$0.729090\pi$
$972$	3.58625e7	1.21752
$973$	−2.54123e7	−0.860520
$974$	−1.11617e7	−0.376991
$975$	0	0
$976$	−1.34560e7	−0.452161
$977$	−4.84602e6	−0.162423	−0.0812117	−	0.996697i	$-0.525879\pi$
$977$	−4.84602e6	−0.162423	−0.0812117	+	0.996697i	$0.525879\pi$
$978$	−1.27202e7	−0.425254
$979$	1.24994e7	0.416803
$980$	0	0
$981$	7.01452e7	2.32715
$982$	−1.67240e7	−0.553430
$983$	3.28144e7	1.08313	0.541565	−	0.840659i	$-0.317832\pi$
$983$	3.28144e7	1.08313	0.541565	+	0.840659i	$0.317832\pi$
$984$	−6.55058e6	−0.215671
$985$	0	0
$986$	3.87604e6	0.126968
$987$	−122791.	−0.00401212
$988$	−3.34464e7	−1.09008
$989$	1.78178e6	0.0579247
$990$	0	0
$991$	2.94422e7	0.952326	0.476163	−	0.879357i	$-0.342027\pi$
$991$	2.94422e7	0.952326	0.476163	+	0.879357i	$0.342027\pi$
$992$	−1.33995e7	−0.432325
$993$	5.05498e7	1.62684
$994$	1.05188e7	0.337677
$995$	0	0
$996$	7.55054e6	0.241173
$997$	4.07284e7	1.29766	0.648828	−	0.760935i	$-0.275259\pi$
$997$	4.07284e7	1.29766	0.648828	+	0.760935i	$0.275259\pi$
$998$	−2.37268e6	−0.0754072
$999$	1.97949e6	0.0627537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.i.1.15	✓	37
5.4	even	2		1075.6.a.j.1.23	yes	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.15	✓	37	1.1	even	1	trivial
1075.6.a.j.1.23	yes	37	5.4	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14099 q^{2} +23.1734 q^{3} -27.4162 q^{4} -49.6140 q^{6} -101.342 q^{7} +127.210 q^{8} +294.004 q^{9} +O(q^{10})\)	\(q-2.14099 q^{2} +23.1734 q^{3} -27.4162 q^{4} -49.6140 q^{6} -101.342 q^{7} +127.210 q^{8} +294.004 q^{9} +303.205 q^{11} -635.324 q^{12} +946.835 q^{13} +216.973 q^{14} +604.962 q^{16} -661.512 q^{17} -629.461 q^{18} +1288.45 q^{19} -2348.44 q^{21} -649.159 q^{22} -963.647 q^{23} +2947.87 q^{24} -2027.17 q^{26} +1181.94 q^{27} +2778.41 q^{28} +2736.75 q^{29} +2497.15 q^{31} -5365.92 q^{32} +7026.27 q^{33} +1416.29 q^{34} -8060.46 q^{36} +1674.78 q^{37} -2758.57 q^{38} +21941.3 q^{39} -2222.14 q^{41} +5027.98 q^{42} -1849.00 q^{43} -8312.70 q^{44} +2063.16 q^{46} +52.2863 q^{47} +14019.0 q^{48} -6536.77 q^{49} -15329.4 q^{51} -25958.6 q^{52} +24803.9 q^{53} -2530.52 q^{54} -12891.7 q^{56} +29857.8 q^{57} -5859.36 q^{58} -18069.3 q^{59} -22242.8 q^{61} -5346.38 q^{62} -29795.0 q^{63} -7870.40 q^{64} -15043.2 q^{66} -15230.5 q^{67} +18136.1 q^{68} -22330.9 q^{69} +48480.0 q^{71} +37400.1 q^{72} +26119.3 q^{73} -3585.70 q^{74} -35324.4 q^{76} -30727.4 q^{77} -46976.2 q^{78} -65398.0 q^{79} -44053.6 q^{81} +4757.59 q^{82} -11884.5 q^{83} +64385.1 q^{84} +3958.69 q^{86} +63419.7 q^{87} +38570.5 q^{88} +41224.2 q^{89} -95954.3 q^{91} +26419.5 q^{92} +57867.4 q^{93} -111.944 q^{94} -124346. q^{96} +98842.5 q^{97} +13995.2 q^{98} +89143.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * q^99

Introduction

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Modular forms

Varieties

Fields

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Groups

Database

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