LMFDB - Embedded newform 725.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,6,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, 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("725.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	725.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:	$116.278269364$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.3257317.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 34x^{2} - 27x + 10 $ x^4 - 34x^2 - 27x + 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.275208$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.91663 q^{2} +18.2828 q^{3} +3.00648 q^{4} -108.173 q^{6} -139.558 q^{7} +171.544 q^{8} +91.2623 q^{9} +O(q^{10})$	\(q-5.91663 q^{2} +18.2828 q^{3} +3.00648 q^{4} -108.173 q^{6} -139.558 q^{7} +171.544 q^{8} +91.2623 q^{9} +533.092 q^{11} +54.9671 q^{12} +675.965 q^{13} +825.715 q^{14} -1111.17 q^{16} +268.994 q^{17} -539.965 q^{18} -2649.15 q^{19} -2551.52 q^{21} -3154.11 q^{22} -794.438 q^{23} +3136.31 q^{24} -3999.43 q^{26} -2774.20 q^{27} -419.580 q^{28} -841.000 q^{29} -4231.04 q^{31} +1084.97 q^{32} +9746.44 q^{33} -1591.54 q^{34} +274.379 q^{36} +2689.54 q^{37} +15674.0 q^{38} +12358.6 q^{39} +1395.36 q^{41} +15096.4 q^{42} +23810.5 q^{43} +1602.73 q^{44} +4700.39 q^{46} -11267.5 q^{47} -20315.3 q^{48} +2669.53 q^{49} +4917.98 q^{51} +2032.28 q^{52} +3396.67 q^{53} +16413.9 q^{54} -23940.4 q^{56} -48433.9 q^{57} +4975.88 q^{58} -2785.38 q^{59} +41551.7 q^{61} +25033.5 q^{62} -12736.4 q^{63} +29138.0 q^{64} -57666.1 q^{66} -8574.14 q^{67} +808.728 q^{68} -14524.6 q^{69} -6995.03 q^{71} +15655.5 q^{72} +4994.73 q^{73} -15913.0 q^{74} -7964.62 q^{76} -74397.5 q^{77} -73121.0 q^{78} -23856.6 q^{79} -72896.9 q^{81} -8255.84 q^{82} -43076.9 q^{83} -7671.11 q^{84} -140878. q^{86} -15375.9 q^{87} +91448.7 q^{88} +13806.4 q^{89} -94336.6 q^{91} -2388.47 q^{92} -77355.4 q^{93} +66665.5 q^{94} +19836.3 q^{96} +176400. q^{97} -15794.6 q^{98} +48651.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9}+O(q^{10}) $ 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9} - 124 q^{11} - 20 q^{12} + 460 q^{13} + 768 q^{14} - 414 q^{16} - 184 q^{17} - 3208 q^{18} - 2392 q^{19} + 992 q^{21} - 5538 q^{22} + 1192 q^{23} + 6786 q^{24} + 4724 q^{26} - 2468 q^{27} - 44 q^{28} - 3364 q^{29} - 19212 q^{31} - 6552 q^{32} + 10580 q^{33} - 7612 q^{34} - 7468 q^{36} + 10928 q^{37} + 456 q^{38} - 8732 q^{39} - 1120 q^{41} - 1844 q^{42} + 21420 q^{43} - 1932 q^{44} - 7588 q^{46} - 23772 q^{47} - 33060 q^{48} + 10452 q^{49} + 12744 q^{51} + 29062 q^{52} - 8860 q^{53} + 35410 q^{54} + 34304 q^{56} - 48944 q^{57} - 10840 q^{59} + 49448 q^{61} - 18518 q^{62} - 27488 q^{63} - 20734 q^{64} - 47744 q^{66} + 7840 q^{67} - 20724 q^{68} + 58792 q^{69} - 48744 q^{71} - 8088 q^{72} + 74992 q^{73} - 35920 q^{74} - 140792 q^{76} - 128656 q^{77} - 2982 q^{78} - 106076 q^{79} - 59692 q^{81} + 234132 q^{82} - 62888 q^{83} - 59832 q^{84} - 216014 q^{86} - 23548 q^{87} + 39426 q^{88} + 107568 q^{89} - 268896 q^{91} + 26268 q^{92} - 221460 q^{93} + 30542 q^{94} - 78606 q^{96} + 49520 q^{97} - 242304 q^{98} + 166720 q^{99}+O(q^{100}) \) 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9 - 124 * q^11 - 20 * q^12 + 460 * q^13 + 768 * q^14 - 414 * q^16 - 184 * q^17 - 3208 * q^18 - 2392 * q^19 + 992 * q^21 - 5538 * q^22 + 1192 * q^23 + 6786 * q^24 + 4724 * q^26 - 2468 * q^27 - 44 * q^28 - 3364 * q^29 - 19212 * q^31 - 6552 * q^32 + 10580 * q^33 - 7612 * q^34 - 7468 * q^36 + 10928 * q^37 + 456 * q^38 - 8732 * q^39 - 1120 * q^41 - 1844 * q^42 + 21420 * q^43 - 1932 * q^44 - 7588 * q^46 - 23772 * q^47 - 33060 * q^48 + 10452 * q^49 + 12744 * q^51 + 29062 * q^52 - 8860 * q^53 + 35410 * q^54 + 34304 * q^56 - 48944 * q^57 - 10840 * q^59 + 49448 * q^61 - 18518 * q^62 - 27488 * q^63 - 20734 * q^64 - 47744 * q^66 + 7840 * q^67 - 20724 * q^68 + 58792 * q^69 - 48744 * q^71 - 8088 * q^72 + 74992 * q^73 - 35920 * q^74 - 140792 * q^76 - 128656 * q^77 - 2982 * q^78 - 106076 * q^79 - 59692 * q^81 + 234132 * q^82 - 62888 * q^83 - 59832 * q^84 - 216014 * q^86 - 23548 * q^87 + 39426 * q^88 + 107568 * q^89 - 268896 * q^91 + 26268 * q^92 - 221460 * q^93 + 30542 * q^94 - 78606 * q^96 + 49520 * q^97 - 242304 * q^98 + 166720 * 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 $

$2$	−5.91663	−1.04592	−0.522961	−	0.852357i	$-0.675173\pi$
$2$	−5.91663	−1.04592	−0.522961	+	0.852357i	$0.675173\pi$
$3$	18.2828	1.17284	0.586422	−	0.810005i	$-0.300536\pi$
$3$	18.2828	1.17284	0.586422	+	0.810005i	$0.300536\pi$
$4$	3.00648	0.0939526
$5$	0	0
$5$	0	0
$6$	−108.173	−1.22670
$7$	−139.558	−1.07649	−0.538246	−	0.842788i	$-0.680913\pi$
$7$	−139.558	−1.07649	−0.538246	+	0.842788i	$0.680913\pi$
$8$	171.544	0.947655
$9$	91.2623	0.375565
$10$	0	0
$11$	533.092	1.32838	0.664188	−	0.747566i	$-0.268778\pi$
$11$	533.092	1.32838	0.664188	+	0.747566i	$0.268778\pi$
$12$	54.9671	0.110192
$13$	675.965	1.10934	0.554672	−	0.832069i	$-0.312844\pi$
$13$	675.965	1.10934	0.554672	+	0.832069i	$0.312844\pi$
$14$	825.715	1.12593
$15$	0	0
$16$	−1111.17	−1.08513
$17$	268.994	0.225746	0.112873	−	0.993609i	$-0.463995\pi$
$17$	268.994	0.225746	0.112873	+	0.993609i	$0.463995\pi$
$18$	−539.965	−0.392812
$19$	−2649.15	−1.68354	−0.841768	−	0.539840i	$-0.818485\pi$
$19$	−2649.15	−1.68354	−0.841768	+	0.539840i	$0.818485\pi$
$20$	0	0
$21$	−2551.52	−1.26256
$22$	−3154.11	−1.38938
$23$	−794.438	−0.313141	−0.156571	−	0.987667i	$-0.550044\pi$
$23$	−794.438	−0.313141	−0.156571	+	0.987667i	$0.550044\pi$
$24$	3136.31	1.11145
$25$	0	0
$26$	−3999.43	−1.16029
$27$	−2774.20	−0.732366
$28$	−419.580	−0.101139
$29$	−841.000	−0.185695
$29$	−841.000	−0.185695
$30$	0	0
$31$	−4231.04	−0.790756	−0.395378	−	0.918518i	$-0.629386\pi$
$31$	−4231.04	−0.790756	−0.395378	+	0.918518i	$0.629386\pi$
$32$	1084.97	0.187302
$33$	9746.44	1.55798
$34$	−1591.54	−0.236113
$35$	0	0
$36$	274.379	0.0352853
$37$	2689.54	0.322979	0.161489	−	0.986874i	$-0.448370\pi$
$37$	2689.54	0.322979	0.161489	+	0.986874i	$0.448370\pi$
$38$	15674.0	1.76085
$39$	12358.6	1.30109
$40$	0	0
$41$	1395.36	0.129636	0.0648182	−	0.997897i	$-0.479353\pi$
$41$	1395.36	0.129636	0.0648182	+	0.997897i	$0.479353\pi$
$42$	15096.4	1.32054
$43$	23810.5	1.96380	0.981901	−	0.189395i	$-0.0606527\pi$
$43$	23810.5	1.96380	0.981901	+	0.189395i	$0.0606527\pi$
$44$	1602.73	0.124804
$45$	0	0
$46$	4700.39	0.327521
$47$	−11267.5	−0.744016	−0.372008	−	0.928229i	$-0.621331\pi$
$47$	−11267.5	−0.744016	−0.372008	+	0.928229i	$0.621331\pi$
$48$	−20315.3	−1.27268
$49$	2669.53	0.158834
$50$	0	0
$51$	4917.98	0.264766
$52$	2032.28	0.104226
$53$	3396.67	0.166097	0.0830487	−	0.996545i	$-0.473534\pi$
$53$	3396.67	0.166097	0.0830487	+	0.996545i	$0.473534\pi$
$54$	16413.9	0.765997
$55$	0	0
$56$	−23940.4	−1.02014
$57$	−48433.9	−1.97453
$58$	4975.88	0.194223
$59$	−2785.38	−0.104173	−0.0520865	−	0.998643i	$-0.516587\pi$
$59$	−2785.38	−0.104173	−0.0520865	+	0.998643i	$0.516587\pi$
$60$	0	0
$61$	41551.7	1.42976	0.714881	−	0.699246i	$-0.246481\pi$
$61$	41551.7	1.42976	0.714881	+	0.699246i	$0.246481\pi$
$62$	25033.5	0.827069
$63$	−12736.4	−0.404292
$64$	29138.0	0.889222
$65$	0	0
$66$	−57666.1	−1.62952
$67$	−8574.14	−0.233348	−0.116674	−	0.993170i	$-0.537223\pi$
$67$	−8574.14	−0.233348	−0.116674	+	0.993170i	$0.537223\pi$
$68$	808.728	0.0212095
$69$	−14524.6	−0.367266
$70$	0	0
$71$	−6995.03	−0.164681	−0.0823405	−	0.996604i	$-0.526240\pi$
$71$	−6995.03	−0.164681	−0.0823405	+	0.996604i	$0.526240\pi$
$72$	15655.5	0.355906
$73$	4994.73	0.109699	0.0548497	−	0.998495i	$-0.482532\pi$
$73$	4994.73	0.109699	0.0548497	+	0.998495i	$0.482532\pi$
$74$	−15913.0	−0.337811
$75$	0	0
$76$	−7964.62	−0.158173
$77$	−74397.5	−1.42998
$78$	−73121.0	−1.36084
$79$	−23856.6	−0.430071	−0.215036	−	0.976606i	$-0.568987\pi$
$79$	−23856.6	−0.430071	−0.215036	+	0.976606i	$0.568987\pi$
$80$	0	0
$81$	−72896.9	−1.23452
$82$	−8255.84	−0.135590
$83$	−43076.9	−0.686356	−0.343178	−	0.939270i	$-0.611503\pi$
$83$	−43076.9	−0.686356	−0.343178	+	0.939270i	$0.611503\pi$
$84$	−7671.11	−0.118621
$85$	0	0
$86$	−140878.	−2.05398
$87$	−15375.9	−0.217792
$88$	91448.7	1.25884
$89$	13806.4	0.184759	0.0923793	−	0.995724i	$-0.470553\pi$
$89$	13806.4	0.184759	0.0923793	+	0.995724i	$0.470553\pi$
$90$	0	0
$91$	−94336.6	−1.19420
$92$	−2388.47	−0.0294205
$93$	−77355.4	−0.927435
$94$	66665.5	0.778183
$95$	0	0
$96$	19836.3	0.219676
$97$	176400.	1.90357	0.951786	−	0.306762i	$-0.0992454\pi$
$97$	176400.	1.90357	0.951786	+	0.306762i	$0.0992454\pi$
$98$	−15794.6	−0.166128
$99$	48651.2	0.498891
$100$	0	0
$101$	−112043.	−1.09290	−0.546452	−	0.837490i	$-0.684022\pi$
$101$	−112043.	−1.09290	−0.546452	+	0.837490i	$0.684022\pi$
$102$	−29097.9	−0.276924
$103$	−38255.6	−0.355305	−0.177653	−	0.984093i	$-0.556850\pi$
$103$	−38255.6	−0.355305	−0.177653	+	0.984093i	$0.556850\pi$
$104$	115958.	1.05127
$105$	0	0
$106$	−20096.8	−0.173725
$107$	19410.6	0.163900	0.0819499	−	0.996636i	$-0.473885\pi$
$107$	19410.6	0.163900	0.0819499	+	0.996636i	$0.473885\pi$
$108$	−8340.58	−0.0688077
$109$	−51029.2	−0.411389	−0.205694	−	0.978616i	$-0.565945\pi$
$109$	−51029.2	−0.411389	−0.205694	+	0.978616i	$0.565945\pi$
$110$	0	0
$111$	49172.5	0.378804
$112$	155073.	1.16813
$113$	−45687.3	−0.336588	−0.168294	−	0.985737i	$-0.553826\pi$
$113$	−45687.3	−0.336588	−0.168294	+	0.985737i	$0.553826\pi$
$114$	286566.	2.06520
$115$	0	0
$116$	−2528.45	−0.0174466
$117$	61690.1	0.416630
$118$	16480.1	0.108957
$119$	−37540.4	−0.243014
$120$	0	0
$121$	123136.	0.764581
$122$	−245846.	−1.49542
$123$	25511.2	0.152043
$124$	−12720.6	−0.0742937
$125$	0	0
$126$	75356.6	0.422858
$127$	−267210.	−1.47009	−0.735044	−	0.678019i	$-0.762839\pi$
$127$	−267210.	−1.47009	−0.735044	+	0.678019i	$0.762839\pi$
$128$	−207118.	−1.11736
$129$	435324.	2.30323
$130$	0	0
$131$	−165523.	−0.842713	−0.421356	−	0.906895i	$-0.638446\pi$
$131$	−165523.	−0.842713	−0.421356	+	0.906895i	$0.638446\pi$
$132$	29302.5	0.146376
$133$	369711.	1.81231
$134$	50730.0	0.244063
$135$	0	0
$136$	46144.3	0.213930
$137$	−91000.4	−0.414230	−0.207115	−	0.978317i	$-0.566407\pi$
$137$	−91000.4	−0.414230	−0.207115	+	0.978317i	$0.566407\pi$
$138$	85936.6	0.384132
$139$	−400431.	−1.75788	−0.878942	−	0.476928i	$-0.841750\pi$
$139$	−400431.	−1.75788	−0.878942	+	0.476928i	$0.841750\pi$
$140$	0	0
$141$	−206002.	−0.872616
$142$	41387.0	0.172244
$143$	360352.	1.47362
$144$	−101408.	−0.407535
$145$	0	0
$146$	−29551.9	−0.114737
$147$	48806.6	0.186288
$148$	8086.07	0.0303447
$149$	−18312.8	−0.0675756	−0.0337878	−	0.999429i	$-0.510757\pi$
$149$	−18312.8	−0.0675756	−0.0337878	+	0.999429i	$0.510757\pi$
$150$	0	0
$151$	−17899.8	−0.0638859	−0.0319430	−	0.999490i	$-0.510169\pi$
$151$	−17899.8	−0.0638859	−0.0319430	+	0.999490i	$0.510169\pi$
$152$	−454445.	−1.59541
$153$	24549.0	0.0847824
$154$	440182.	1.49565
$155$	0	0
$156$	37155.8	0.122241
$157$	413598.	1.33915	0.669576	−	0.742744i	$-0.266476\pi$
$157$	413598.	1.33915	0.669576	+	0.742744i	$0.266476\pi$
$158$	141151.	0.449821
$159$	62100.7	0.194807
$160$	0	0
$161$	110870.	0.337094
$162$	431304.	1.29121
$163$	−178276.	−0.525562	−0.262781	−	0.964856i	$-0.584640\pi$
$163$	−178276.	−0.525562	−0.262781	+	0.964856i	$0.584640\pi$
$164$	4195.13	0.0121797
$165$	0	0
$166$	254870.	0.717875
$167$	452143.	1.25454	0.627269	−	0.778802i	$-0.284172\pi$
$167$	452143.	1.25454	0.627269	+	0.778802i	$0.284172\pi$
$168$	−437698.	−1.19647
$169$	85635.9	0.230642
$170$	0	0
$171$	−241767.	−0.632277
$172$	71586.0	0.184504
$173$	−754374.	−1.91634	−0.958168	−	0.286206i	$-0.907606\pi$
$173$	−754374.	−1.91634	−0.958168	+	0.286206i	$0.907606\pi$
$174$	90973.3	0.227793
$175$	0	0
$176$	−592356.	−1.44145
$177$	−50924.7	−0.122179
$178$	−81687.2	−0.193243
$179$	−352813.	−0.823024	−0.411512	−	0.911404i	$-0.634999\pi$
$179$	−352813.	−0.823024	−0.411512	+	0.911404i	$0.634999\pi$
$180$	0	0
$181$	227087.	0.515224	0.257612	−	0.966248i	$-0.417064\pi$
$181$	227087.	0.515224	0.257612	+	0.966248i	$0.417064\pi$
$182$	558154.	1.24904
$183$	759683.	1.67689
$184$	−136281.	−0.296750
$185$	0	0
$186$	457683.	0.970024
$187$	143399.	0.299876
$188$	−33875.5	−0.0699023
$189$	387162.	0.788385
$190$	0	0
$191$	183415.	0.363790	0.181895	−	0.983318i	$-0.441777\pi$
$191$	183415.	0.363790	0.181895	+	0.983318i	$0.441777\pi$
$192$	532726.	1.04292
$193$	−997005.	−1.92665	−0.963327	−	0.268329i	$-0.913529\pi$
$193$	−997005.	−1.92665	−0.963327	+	0.268329i	$0.913529\pi$
$194$	−1.04369e6	−1.99099
$195$	0	0
$196$	8025.90	0.0149229
$197$	861288.	1.58119	0.790593	−	0.612342i	$-0.209773\pi$
$197$	861288.	1.58119	0.790593	+	0.612342i	$0.209773\pi$
$198$	−287851.	−0.521801
$199$	−837743.	−1.49961	−0.749805	−	0.661659i	$-0.769853\pi$
$199$	−837743.	−1.49961	−0.749805	+	0.661659i	$0.769853\pi$
$200$	0	0
$201$	−156760.	−0.273681
$202$	662918.	1.14309
$203$	117369.	0.199899
$204$	14785.8	0.0248754
$205$	0	0
$206$	226344.	0.371621
$207$	−72502.2	−0.117605
$208$	−751111.	−1.20378
$209$	−1.41224e6	−2.23637
$210$	0	0
$211$	−637594.	−0.985912	−0.492956	−	0.870054i	$-0.664084\pi$
$211$	−637594.	−0.985912	−0.492956	+	0.870054i	$0.664084\pi$
$212$	10212.0	0.0156053
$213$	−127889.	−0.193145
$214$	−114845.	−0.171426
$215$	0	0
$216$	−475896.	−0.694030
$217$	590477.	0.851243
$218$	301921.	0.430281
$219$	91317.8	0.128660
$220$	0	0
$221$	181831.	0.250430
$222$	−290935.	−0.396199
$223$	−45526.9	−0.0613064	−0.0306532	−	0.999530i	$-0.509759\pi$
$223$	−45526.9	−0.0613064	−0.0306532	+	0.999530i	$0.509759\pi$
$224$	−151416.	−0.201629
$225$	0	0
$226$	270315.	0.352045
$227$	−1.33313e6	−1.71715	−0.858575	−	0.512688i	$-0.828650\pi$
$227$	−1.33313e6	−1.71715	−0.858575	+	0.512688i	$0.828650\pi$
$228$	−145616.	−0.185512
$229$	830883.	1.04701	0.523506	−	0.852022i	$-0.324624\pi$
$229$	830883.	1.04701	0.523506	+	0.852022i	$0.324624\pi$
$230$	0	0
$231$	−1.36020e6	−1.67715
$232$	−144268.	−0.175975
$233$	−767627.	−0.926319	−0.463159	−	0.886275i	$-0.653284\pi$
$233$	−767627.	−0.926319	−0.463159	+	0.886275i	$0.653284\pi$
$234$	−364997.	−0.435763
$235$	0	0
$236$	−8374.22	−0.00978733
$237$	−436166.	−0.504407
$238$	222113.	0.254174
$239$	−1.22858e6	−1.39126	−0.695631	−	0.718399i	$-0.744875\pi$
$239$	−1.22858e6	−1.39126	−0.695631	+	0.718399i	$0.744875\pi$
$240$	0	0
$241$	304030.	0.337190	0.168595	−	0.985685i	$-0.446077\pi$
$241$	304030.	0.337190	0.168595	+	0.985685i	$0.446077\pi$
$242$	−728553.	−0.799692
$243$	−658633.	−0.715530
$244$	124924.	0.134330
$245$	0	0
$246$	−150940.	−0.159026
$247$	−1.79073e6	−1.86762
$248$	−725809.	−0.749364
$249$	−787569.	−0.804989
$250$	0	0
$251$	850953.	0.852553	0.426276	−	0.904593i	$-0.359825\pi$
$251$	850953.	0.852553	0.426276	+	0.904593i	$0.359825\pi$
$252$	−38291.8	−0.0379843
$253$	−423509.	−0.415969
$254$	1.58098e6	1.53760
$255$	0	0
$256$	293022.	0.279448
$257$	−28252.8	−0.0266826	−0.0133413	−	0.999911i	$-0.504247\pi$
$257$	−28252.8	−0.0266826	−0.0133413	+	0.999911i	$0.504247\pi$
$258$	−2.57565e6	−2.40900
$259$	−375348.	−0.347684
$260$	0	0
$261$	−76751.6	−0.0697406
$262$	979337.	0.881412
$263$	−393978.	−0.351223	−0.175611	−	0.984460i	$-0.556190\pi$
$263$	−393978.	−0.351223	−0.175611	+	0.984460i	$0.556190\pi$
$264$	1.67194e6	1.47643
$265$	0	0
$266$	−2.18744e6	−1.89554
$267$	252420.	0.216693
$268$	−25778.0	−0.0219236
$269$	453727.	0.382309	0.191154	−	0.981560i	$-0.438777\pi$
$269$	453727.	0.382309	0.191154	+	0.981560i	$0.438777\pi$
$270$	0	0
$271$	−1.54312e6	−1.27637	−0.638186	−	0.769882i	$-0.720315\pi$
$271$	−1.54312e6	−1.27637	−0.638186	+	0.769882i	$0.720315\pi$
$272$	−298898.	−0.244963
$273$	−1.72474e6	−1.40061
$274$	538416.	0.433253
$275$	0	0
$276$	−43667.9	−0.0345056
$277$	1.13023e6	0.885050	0.442525	−	0.896756i	$-0.354083\pi$
$277$	1.13023e6	0.885050	0.442525	+	0.896756i	$0.354083\pi$
$278$	2.36920e6	1.83861
$279$	−386134.	−0.296980
$280$	0	0
$281$	−1.17984e6	−0.891371	−0.445685	−	0.895190i	$-0.647040\pi$
$281$	−1.17984e6	−0.891371	−0.445685	+	0.895190i	$0.647040\pi$
$282$	1.21884e6	0.912688
$283$	−345340.	−0.256319	−0.128160	−	0.991754i	$-0.540907\pi$
$283$	−345340.	−0.256319	−0.128160	+	0.991754i	$0.540907\pi$
$284$	−21030.5	−0.0154722
$285$	0	0
$286$	−2.13207e6	−1.54130
$287$	−194734.	−0.139553
$288$	99016.6	0.0703440
$289$	−1.34750e6	−0.949039
$290$	0	0
$291$	3.22509e6	2.23260
$292$	15016.6	0.0103066
$293$	−2.40825e6	−1.63883	−0.819414	−	0.573202i	$-0.805701\pi$
$293$	−2.40825e6	−1.63883	−0.819414	+	0.573202i	$0.805701\pi$
$294$	−288770.	−0.194843
$295$	0	0
$296$	461374.	0.306072
$297$	−1.47890e6	−0.972856
$298$	108350.	0.0706788
$299$	−537013.	−0.347381
$300$	0	0
$301$	−3.32296e6	−2.11402
$302$	105906.	0.0668197
$303$	−2.04847e6	−1.28181
$304$	2.94365e6	1.82685
$305$	0	0
$306$	−145248.	−0.0886758
$307$	−595416.	−0.360558	−0.180279	−	0.983616i	$-0.557700\pi$
$307$	−595416.	−0.360558	−0.180279	+	0.983616i	$0.557700\pi$
$308$	−223675.	−0.134351
$309$	−699420.	−0.416718
$310$	0	0
$311$	999900.	0.586213	0.293107	−	0.956080i	$-0.405311\pi$
$311$	999900.	0.586213	0.293107	+	0.956080i	$0.405311\pi$
$312$	2.12004e6	1.23298
$313$	365270.	0.210743	0.105371	−	0.994433i	$-0.466397\pi$
$313$	365270.	0.210743	0.105371	+	0.994433i	$0.466397\pi$
$314$	−2.44711e6	−1.40065
$315$	0	0
$316$	−71724.5	−0.0404064
$317$	−1.60635e6	−0.897823	−0.448912	−	0.893576i	$-0.648188\pi$
$317$	−1.60635e6	−0.897823	−0.448912	+	0.893576i	$0.648188\pi$
$318$	−367427.	−0.203752
$319$	−448331.	−0.246673
$320$	0	0
$321$	354880.	0.192229
$322$	−655979.	−0.352574
$323$	−712606.	−0.380052
$324$	−219164.	−0.115986
$325$	0	0
$326$	1.05479e6	0.549697
$327$	−932959.	−0.482495
$328$	239366.	0.122851
$329$	1.57247e6	0.800928
$330$	0	0
$331$	−535124.	−0.268463	−0.134232	−	0.990950i	$-0.542857\pi$
$331$	−535124.	−0.268463	−0.134232	+	0.990950i	$0.542857\pi$
$332$	−129510.	−0.0644850
$333$	245454.	0.121299
$334$	−2.67516e6	−1.31215
$335$	0	0
$336$	2.83517e6	1.37003
$337$	−1.93303e6	−0.927178	−0.463589	−	0.886050i	$-0.653439\pi$
$337$	−1.93303e6	−0.927178	−0.463589	+	0.886050i	$0.653439\pi$
$338$	−506676.	−0.241234
$339$	−835293.	−0.394766
$340$	0	0
$341$	−2.25553e6	−1.05042
$342$	1.43045e6	0.661312
$343$	1.97300e6	0.905508
$344$	4.08455e6	1.86101
$345$	0	0
$346$	4.46335e6	2.00434
$347$	2.83701e6	1.26485	0.632423	−	0.774623i	$-0.282060\pi$
$347$	2.83701e6	1.26485	0.632423	+	0.774623i	$0.282060\pi$
$348$	−46227.3	−0.0204621
$349$	1.11395e6	0.489555	0.244778	−	0.969579i	$-0.421285\pi$
$349$	1.11395e6	0.489555	0.244778	+	0.969579i	$0.421285\pi$
$350$	0	0
$351$	−1.87526e6	−0.812445
$352$	578388.	0.248807
$353$	3.49053e6	1.49092	0.745461	−	0.666549i	$-0.232229\pi$
$353$	3.49053e6	1.49092	0.745461	+	0.666549i	$0.232229\pi$
$354$	301303.	0.127789
$355$	0	0
$356$	41508.7	0.0173586
$357$	−686345.	−0.285018
$358$	2.08746e6	0.860819
$359$	469676.	0.192337	0.0961684	−	0.995365i	$-0.469341\pi$
$359$	469676.	0.192337	0.0961684	+	0.995365i	$0.469341\pi$
$360$	0	0
$361$	4.54189e6	1.83429
$362$	−1.34359e6	−0.538884
$363$	2.25128e6	0.896735
$364$	−283621.	−0.112198
$365$	0	0
$366$	−4.49476e6	−1.75390
$367$	−2.70229e6	−1.04729	−0.523645	−	0.851936i	$-0.675428\pi$
$367$	−2.70229e6	−1.04729	−0.523645	+	0.851936i	$0.675428\pi$
$368$	882755.	0.339798
$369$	127344.	0.0486869
$370$	0	0
$371$	−474033.	−0.178803
$372$	−232568.	−0.0871349
$373$	−2.77666e6	−1.03336	−0.516678	−	0.856180i	$-0.672832\pi$
$373$	−2.77666e6	−1.03336	−0.516678	+	0.856180i	$0.672832\pi$
$374$	−848438.	−0.313647
$375$	0	0
$376$	−1.93287e6	−0.705071
$377$	−568487.	−0.206000
$378$	−2.29070e6	−0.824590
$379$	−4.41837e6	−1.58002	−0.790012	−	0.613091i	$-0.789926\pi$
$379$	−4.41837e6	−1.58002	−0.790012	+	0.613091i	$0.789926\pi$
$380$	0	0
$381$	−4.88536e6	−1.72419
$382$	−1.08520e6	−0.380496
$383$	−1.37796e6	−0.479999	−0.239999	−	0.970773i	$-0.577147\pi$
$383$	−1.37796e6	−0.479999	−0.239999	+	0.970773i	$0.577147\pi$
$384$	−3.78670e6	−1.31049
$385$	0	0
$386$	5.89891e6	2.01513
$387$	2.17300e6	0.737535
$388$	530344.	0.178846
$389$	649334.	0.217568	0.108784	−	0.994065i	$-0.465304\pi$
$389$	649334.	0.217568	0.108784	+	0.994065i	$0.465304\pi$
$390$	0	0
$391$	−213699.	−0.0706906
$392$	457941.	0.150520
$393$	−3.02623e6	−0.988371
$394$	−5.09592e6	−1.65380
$395$	0	0
$396$	146269.	0.0468721
$397$	2.52909e6	0.805356	0.402678	−	0.915342i	$-0.368079\pi$
$397$	2.52909e6	0.805356	0.402678	+	0.915342i	$0.368079\pi$
$398$	4.95661e6	1.56847
$399$	6.75936e6	2.12556
$400$	0	0
$401$	−3.64231e6	−1.13114	−0.565569	−	0.824701i	$-0.691344\pi$
$401$	−3.64231e6	−1.13114	−0.565569	+	0.824701i	$0.691344\pi$
$402$	927488.	0.286248
$403$	−2.86003e6	−0.877220
$404$	−336856.	−0.102681
$405$	0	0
$406$	−694426.	−0.209079
$407$	1.43377e6	0.429037
$408$	843650.	0.250906
$409$	2.68522e6	0.793729	0.396865	−	0.917877i	$-0.370098\pi$
$409$	2.68522e6	0.793729	0.396865	+	0.917877i	$0.370098\pi$
$410$	0	0
$411$	−1.66375e6	−0.485828
$412$	−115015.	−0.0333819
$413$	388724.	0.112141
$414$	428969.	0.123006
$415$	0	0
$416$	733401.	0.207782
$417$	−7.32101e6	−2.06173
$418$	8.35570e6	2.33906
$419$	−4.33500e6	−1.20630	−0.603148	−	0.797629i	$-0.706087\pi$
$419$	−4.33500e6	−1.20630	−0.603148	+	0.797629i	$0.706087\pi$
$420$	0	0
$421$	3.38962e6	0.932063	0.466032	−	0.884768i	$-0.345683\pi$
$421$	3.38962e6	0.932063	0.466032	+	0.884768i	$0.345683\pi$
$422$	3.77241e6	1.03119
$423$	−1.02830e6	−0.279426
$424$	582677.	0.157403
$425$	0	0
$426$	756672.	0.202015
$427$	−5.79888e6	−1.53913
$428$	58357.6	0.0153988
$429$	6.58826e6	1.72833
$430$	0	0
$431$	290831.	0.0754132	0.0377066	−	0.999289i	$-0.487995\pi$
$431$	290831.	0.0754132	0.0377066	+	0.999289i	$0.487995\pi$
$432$	3.08260e6	0.794709
$433$	2.64162e6	0.677097	0.338549	−	0.940949i	$-0.390064\pi$
$433$	2.64162e6	0.677097	0.338549	+	0.940949i	$0.390064\pi$
$434$	−3.49363e6	−0.890333
$435$	0	0
$436$	−153418.	−0.0386511
$437$	2.10458e6	0.527185
$438$	−540293.	−0.134569
$439$	5.65486e6	1.40043	0.700214	−	0.713933i	$-0.253088\pi$
$439$	5.65486e6	1.40043	0.700214	+	0.713933i	$0.253088\pi$
$440$	0	0
$441$	243627.	0.0596526
$442$	−1.07583e6	−0.261931
$443$	−1.31778e6	−0.319031	−0.159515	−	0.987195i	$-0.550993\pi$
$443$	−1.31778e6	−0.319031	−0.159515	+	0.987195i	$0.550993\pi$
$444$	147836.	0.0355896
$445$	0	0
$446$	269366.	0.0641217
$447$	−334810.	−0.0792556
$448$	−4.06646e6	−0.957241
$449$	−6.50617e6	−1.52303	−0.761517	−	0.648145i	$-0.775545\pi$
$449$	−6.50617e6	−1.52303	−0.761517	+	0.648145i	$0.775545\pi$
$450$	0	0
$451$	743857.	0.172206
$452$	−137358.	−0.0316234
$453$	−327259.	−0.0749283
$454$	7.88764e6	1.79601
$455$	0	0
$456$	−8.30855e6	−1.87117
$457$	3.50691e6	0.785477	0.392739	−	0.919650i	$-0.371528\pi$
$457$	3.50691e6	0.785477	0.392739	+	0.919650i	$0.371528\pi$
$458$	−4.91603e6	−1.09509
$459$	−746244.	−0.165329
$460$	0	0
$461$	−1.22247e6	−0.267908	−0.133954	−	0.990988i	$-0.542767\pi$
$461$	−1.22247e6	−0.267908	−0.133954	+	0.990988i	$0.542767\pi$
$462$	8.04778e6	1.75417
$463$	−382178.	−0.0828540	−0.0414270	−	0.999142i	$-0.513190\pi$
$463$	−382178.	−0.0828540	−0.0414270	+	0.999142i	$0.513190\pi$
$464$	934493.	0.201503
$465$	0	0
$466$	4.54176e6	0.968857
$467$	1.81409e6	0.384916	0.192458	−	0.981305i	$-0.438354\pi$
$467$	1.81409e6	0.384916	0.192458	+	0.981305i	$0.438354\pi$
$468$	185470.	0.0391435
$469$	1.19659e6	0.251197
$470$	0	0
$471$	7.56175e6	1.57062
$472$	−477816.	−0.0987200
$473$	1.26932e7	2.60867
$474$	2.58063e6	0.527570
$475$	0	0
$476$	−112865.	−0.0228318
$477$	309987.	0.0623804
$478$	7.26906e6	1.45515
$479$	4.87397e6	0.970609	0.485304	−	0.874345i	$-0.338709\pi$
$479$	4.87397e6	0.970609	0.485304	+	0.874345i	$0.338709\pi$
$480$	0	0
$481$	1.81804e6	0.358294
$482$	−1.79883e6	−0.352674
$483$	2.02703e6	0.395359
$484$	370208.	0.0718344
$485$	0	0
$486$	3.89689e6	0.748389
$487$	1.84954e6	0.353379	0.176690	−	0.984267i	$-0.443461\pi$
$487$	1.84954e6	0.353379	0.176690	+	0.984267i	$0.443461\pi$
$488$	7.12793e6	1.35492
$489$	−3.25939e6	−0.616403
$490$	0	0
$491$	−5.47088e6	−1.02413	−0.512063	−	0.858948i	$-0.671119\pi$
$491$	−5.47088e6	−1.02413	−0.512063	+	0.858948i	$0.671119\pi$
$492$	76699.0	0.0142849
$493$	−226224.	−0.0419201
$494$	1.05951e7	1.95338
$495$	0	0
$496$	4.70140e6	0.858070
$497$	976215.	0.177278
$498$	4.65975e6	0.841956
$499$	5.27760e6	0.948823	0.474411	−	0.880303i	$-0.342661\pi$
$499$	5.27760e6	0.948823	0.474411	+	0.880303i	$0.342661\pi$
$500$	0	0
$501$	8.26645e6	1.47138
$502$	−5.03477e6	−0.891703
$503$	−6.07721e6	−1.07099	−0.535494	−	0.844539i	$-0.679875\pi$
$503$	−6.07721e6	−1.07099	−0.535494	+	0.844539i	$0.679875\pi$
$504$	−2.18485e6	−0.383130
$505$	0	0
$506$	2.50574e6	0.435071
$507$	1.56567e6	0.270508
$508$	−803363.	−0.138119
$509$	4.28972e6	0.733896	0.366948	−	0.930242i	$-0.380403\pi$
$509$	4.28972e6	0.733896	0.366948	+	0.930242i	$0.380403\pi$
$510$	0	0
$511$	−697056.	−0.118091
$512$	4.89407e6	0.825078
$513$	7.34926e6	1.23296
$514$	167161.	0.0279079
$515$	0	0
$516$	1.30879e6	0.216395
$517$	−6.00661e6	−0.988333
$518$	2.22079e6	0.363650
$519$	−1.37921e7	−2.24756
$520$	0	0
$521$	3.12541e6	0.504444	0.252222	−	0.967669i	$-0.418839\pi$
$521$	3.12541e6	0.504444	0.252222	+	0.967669i	$0.418839\pi$
$522$	454110.	0.0729433
$523$	6.57035e6	1.05035	0.525176	−	0.850994i	$-0.324000\pi$
$523$	6.57035e6	1.05035	0.525176	+	0.850994i	$0.324000\pi$
$524$	−497642.	−0.0791751
$525$	0	0
$526$	2.33102e6	0.367352
$527$	−1.13813e6	−0.178510
$528$	−1.08299e7	−1.69060
$529$	−5.80521e6	−0.901942
$530$	0	0
$531$	−254201.	−0.0391237
$532$	1.11153e6	0.170271
$533$	943216.	0.143811
$534$	−1.49347e6	−0.226644
$535$	0	0
$536$	−1.47084e6	−0.221133
$537$	−6.45043e6	−0.965279
$538$	−2.68453e6	−0.399865
$539$	1.42311e6	0.210992
$540$	0	0
$541$	−6.72381e6	−0.987694	−0.493847	−	0.869549i	$-0.664410\pi$
$541$	−6.72381e6	−0.987694	−0.493847	+	0.869549i	$0.664410\pi$
$542$	9.13008e6	1.33499
$543$	4.15180e6	0.604278
$544$	291850.	0.0422827
$545$	0	0
$546$	1.02046e7	1.46493
$547$	−1.19150e6	−0.170264	−0.0851322	−	0.996370i	$-0.527131\pi$
$547$	−1.19150e6	−0.170264	−0.0851322	+	0.996370i	$0.527131\pi$
$548$	−273591.	−0.0389180
$549$	3.79210e6	0.536969
$550$	0	0
$551$	2.22793e6	0.312625
$552$	−2.49160e6	−0.348042
$553$	3.32939e6	0.462968
$554$	−6.68716e6	−0.925693
$555$	0	0
$556$	−1.20389e6	−0.165158
$557$	−2.43064e6	−0.331958	−0.165979	−	0.986129i	$-0.553078\pi$
$557$	−2.43064e6	−0.331958	−0.165979	+	0.986129i	$0.553078\pi$
$558$	2.28461e6	0.310618
$559$	1.60951e7	2.17853
$560$	0	0
$561$	2.62174e6	0.351708
$562$	6.98069e6	0.932304
$563$	1.05702e7	1.40544	0.702721	−	0.711466i	$-0.251968\pi$
$563$	1.05702e7	1.40544	0.702721	+	0.711466i	$0.251968\pi$
$564$	−619341.	−0.0819846
$565$	0	0
$566$	2.04325e6	0.268090
$567$	1.01734e7	1.32895
$568$	−1.19995e6	−0.156061
$569$	5.17877e6	0.670573	0.335286	−	0.942116i	$-0.391167\pi$
$569$	5.17877e6	0.670573	0.335286	+	0.942116i	$0.391167\pi$
$570$	0	0
$571$	−3.92258e6	−0.503479	−0.251739	−	0.967795i	$-0.581003\pi$
$571$	−3.92258e6	−0.503479	−0.251739	+	0.967795i	$0.581003\pi$
$572$	1.08339e6	0.138451
$573$	3.35335e6	0.426670
$574$	1.15217e6	0.145961
$575$	0	0
$576$	2.65920e6	0.333961
$577$	−1.12133e7	−1.40215	−0.701074	−	0.713089i	$-0.747296\pi$
$577$	−1.12133e7	−1.40215	−0.701074	+	0.713089i	$0.747296\pi$
$578$	7.97265e6	0.992620
$579$	−1.82281e7	−2.25967
$580$	0	0
$581$	6.01174e6	0.738857
$582$	−1.90817e7	−2.33512
$583$	1.81074e6	0.220640
$584$	856814.	0.103957
$585$	0	0
$586$	1.42487e7	1.71409
$587$	−1.03337e7	−1.23783	−0.618915	−	0.785458i	$-0.712427\pi$
$587$	−1.03337e7	−1.23783	−0.618915	+	0.785458i	$0.712427\pi$
$588$	146736.	0.0175023
$589$	1.12086e7	1.33127
$590$	0	0
$591$	1.57468e7	1.85448
$592$	−2.98853e6	−0.350472
$593$	1.58653e7	1.85272	0.926362	−	0.376634i	$-0.122919\pi$
$593$	1.58653e7	1.85272	0.926362	+	0.376634i	$0.122919\pi$
$594$	8.75012e6	1.01753
$595$	0	0
$596$	−55057.2	−0.00634890
$597$	−1.53163e7	−1.75881
$598$	3.17730e6	0.363334
$599$	−9.66314e6	−1.10040	−0.550201	−	0.835032i	$-0.685449\pi$
$599$	−9.66314e6	−1.10040	−0.550201	+	0.835032i	$0.685449\pi$
$600$	0	0
$601$	−1.07881e7	−1.21831	−0.609155	−	0.793051i	$-0.708491\pi$
$601$	−1.07881e7	−1.21831	−0.609155	+	0.793051i	$0.708491\pi$
$602$	1.96607e7	2.21110
$603$	−782495.	−0.0876372
$604$	−53815.4	−0.00600225
$605$	0	0
$606$	1.21200e7	1.34067
$607$	−6.76786e6	−0.745555	−0.372778	−	0.927921i	$-0.621595\pi$
$607$	−6.76786e6	−0.745555	−0.372778	+	0.927921i	$0.621595\pi$
$608$	−2.87424e6	−0.315329
$609$	2.14583e6	0.234451
$610$	0	0
$611$	−7.61643e6	−0.825370
$612$	73806.3	0.00796553
$613$	−2.91439e6	−0.313253	−0.156627	−	0.987658i	$-0.550062\pi$
$613$	−2.91439e6	−0.313253	−0.156627	+	0.987658i	$0.550062\pi$
$614$	3.52286e6	0.377115
$615$	0	0
$616$	−1.27624e7	−1.35513
$617$	1.01418e7	1.07251	0.536254	−	0.844056i	$-0.319839\pi$
$617$	1.01418e7	1.07251	0.536254	+	0.844056i	$0.319839\pi$
$618$	4.13821e6	0.435854
$619$	−6.89280e6	−0.723051	−0.361526	−	0.932362i	$-0.617744\pi$
$619$	−6.89280e6	−0.723051	−0.361526	+	0.932362i	$0.617744\pi$
$620$	0	0
$621$	2.20393e6	0.229334
$622$	−5.91603e6	−0.613133
$623$	−1.92680e6	−0.198891
$624$	−1.37324e7	−1.41184
$625$	0	0
$626$	−2.16116e6	−0.220420
$627$	−2.58198e7	−2.62291
$628$	1.24348e6	0.125817
$629$	723472.	0.0729113
$630$	0	0
$631$	−7.52515e6	−0.752388	−0.376194	−	0.926541i	$-0.622767\pi$
$631$	−7.52515e6	−0.752388	−0.376194	+	0.926541i	$0.622767\pi$
$632$	−4.09245e6	−0.407559
$633$	−1.16570e7	−1.15632
$634$	9.50415e6	0.939053
$635$	0	0
$636$	186705.	0.0183026
$637$	1.80451e6	0.176202
$638$	2.65261e6	0.258001
$639$	−638382.	−0.0618484
$640$	0	0
$641$	−278549.	−0.0267767	−0.0133883	−	0.999910i	$-0.504262\pi$
$641$	−278549.	−0.0267767	−0.0133883	+	0.999910i	$0.504262\pi$
$642$	−2.09969e6	−0.201057
$643$	3.63623e6	0.346836	0.173418	−	0.984848i	$-0.444519\pi$
$643$	3.63623e6	0.346836	0.173418	+	0.984848i	$0.444519\pi$
$644$	333330.	0.0316709
$645$	0	0
$646$	4.21622e6	0.397505
$647$	1.08234e7	1.01649	0.508243	−	0.861214i	$-0.330295\pi$
$647$	1.08234e7	1.01649	0.508243	+	0.861214i	$0.330295\pi$
$648$	−1.25050e7	−1.16989
$649$	−1.48487e6	−0.138381
$650$	0	0
$651$	1.07956e7	0.998376
$652$	−535984.	−0.0493779
$653$	−8.86232e6	−0.813326	−0.406663	−	0.913578i	$-0.633308\pi$
$653$	−8.86232e6	−0.813326	−0.406663	+	0.913578i	$0.633308\pi$
$654$	5.51997e6	0.504652
$655$	0	0
$656$	−1.55048e6	−0.140672
$657$	455830.	0.0411993
$658$	−9.30373e6	−0.837708
$659$	−4.94619e6	−0.443667	−0.221833	−	0.975085i	$-0.571204\pi$
$659$	−4.94619e6	−0.443667	−0.221833	+	0.975085i	$0.571204\pi$
$660$	0	0
$661$	−6.34440e6	−0.564790	−0.282395	−	0.959298i	$-0.591129\pi$
$661$	−6.34440e6	−0.564790	−0.282395	+	0.959298i	$0.591129\pi$
$662$	3.16613e6	0.280791
$663$	3.32438e6	0.293716
$664$	−7.38958e6	−0.650429
$665$	0	0
$666$	−1.45226e6	−0.126870
$667$	668122.	0.0581489
$668$	1.35936e6	0.117867
$669$	−832361.	−0.0719029
$670$	0	0
$671$	2.21509e7	1.89926
$672$	−2.76832e6	−0.236479
$673$	−1.00239e7	−0.853095	−0.426548	−	0.904465i	$-0.640270\pi$
$673$	−1.00239e7	−0.853095	−0.426548	+	0.904465i	$0.640270\pi$
$674$	1.14370e7	0.969756
$675$	0	0
$676$	257463.	0.0216695
$677$	−3.44231e6	−0.288654	−0.144327	−	0.989530i	$-0.546102\pi$
$677$	−3.44231e6	−0.288654	−0.144327	+	0.989530i	$0.546102\pi$
$678$	4.94212e6	0.412894
$679$	−2.46181e7	−2.04918
$680$	0	0
$681$	−2.43734e7	−2.01395
$682$	1.33452e7	1.09866
$683$	−2.51352e6	−0.206172	−0.103086	−	0.994672i	$-0.532872\pi$
$683$	−2.51352e6	−0.206172	−0.103086	+	0.994672i	$0.532872\pi$
$684$	−726869.	−0.0594041
$685$	0	0
$686$	−1.16735e7	−0.947090
$687$	1.51909e7	1.22798
$688$	−2.64575e7	−2.13097
$689$	2.29603e6	0.184259
$690$	0	0
$691$	−2.01696e7	−1.60695	−0.803474	−	0.595340i	$-0.797017\pi$
$691$	−2.01696e7	−1.60695	−0.803474	+	0.595340i	$0.797017\pi$
$692$	−2.26802e6	−0.180045
$693$	−6.78968e6	−0.537052
$694$	−1.67856e7	−1.32293
$695$	0	0
$696$	−2.63764e6	−0.206391
$697$	375345.	0.0292650
$698$	−6.59082e6	−0.512037
$699$	−1.40344e7	−1.08643
$700$	0	0
$701$	1.67322e6	0.128605	0.0643025	−	0.997930i	$-0.479518\pi$
$701$	1.67322e6	0.128605	0.0643025	+	0.997930i	$0.479518\pi$
$702$	1.10952e7	0.849754
$703$	−7.12499e6	−0.543746
$704$	1.55333e7	1.18122
$705$	0	0
$706$	−2.06522e7	−1.55939
$707$	1.56366e7	1.17650
$708$	−153104.	−0.0114790
$709$	6.28913e6	0.469867	0.234933	−	0.972011i	$-0.424513\pi$
$709$	6.28913e6	0.469867	0.234933	+	0.972011i	$0.424513\pi$
$710$	0	0
$711$	−2.17721e6	−0.161520
$712$	2.36840e6	0.175087
$713$	3.36130e6	0.247619
$714$	4.06085e6	0.298107
$715$	0	0
$716$	−1.06073e6	−0.0773253
$717$	−2.24620e7	−1.63173
$718$	−2.77890e6	−0.201169
$719$	2.87519e6	0.207417	0.103709	−	0.994608i	$-0.466929\pi$
$719$	2.87519e6	0.207417	0.103709	+	0.994608i	$0.466929\pi$
$720$	0	0
$721$	5.33888e6	0.382483
$722$	−2.68726e7	−1.91852
$723$	5.55854e6	0.395471
$724$	682734.	0.0484067
$725$	0	0
$726$	−1.33200e7	−0.937914
$727$	−2.76368e6	−0.193933	−0.0969665	−	0.995288i	$-0.530914\pi$
$727$	−2.76368e6	−0.193933	−0.0969665	+	0.995288i	$0.530914\pi$
$728$	−1.61829e7	−1.13169
$729$	5.67227e6	0.395310
$730$	0	0
$731$	6.40490e6	0.443321
$732$	2.28397e6	0.157548
$733$	1.06643e7	0.733115	0.366557	−	0.930395i	$-0.380536\pi$
$733$	1.06643e7	0.733115	0.366557	+	0.930395i	$0.380536\pi$
$734$	1.59885e7	1.09538
$735$	0	0
$736$	−861940.	−0.0586520
$737$	−4.57081e6	−0.309973
$738$	−753446.	−0.0509227
$739$	−3.98603e6	−0.268491	−0.134245	−	0.990948i	$-0.542861\pi$
$739$	−3.98603e6	−0.268491	−0.134245	+	0.990948i	$0.542861\pi$
$740$	0	0
$741$	−3.27397e7	−2.19043
$742$	2.80468e6	0.187014
$743$	2.19748e7	1.46034	0.730170	−	0.683266i	$-0.239441\pi$
$743$	2.19748e7	1.46034	0.730170	+	0.683266i	$0.239441\pi$
$744$	−1.32698e7	−0.878888
$745$	0	0
$746$	1.64285e7	1.08081
$747$	−3.93130e6	−0.257771
$748$	431127.	0.0281741
$749$	−2.70891e6	−0.176437
$750$	0	0
$751$	−1.84068e7	−1.19091	−0.595456	−	0.803388i	$-0.703028\pi$
$751$	−1.84068e7	−1.19091	−0.595456	+	0.803388i	$0.703028\pi$
$752$	1.25201e7	0.807351
$753$	1.55578e7	0.999912
$754$	3.36352e6	0.215460
$755$	0	0
$756$	1.16400e6	0.0740709
$757$	−2.78199e7	−1.76447	−0.882237	−	0.470805i	$-0.843963\pi$
$757$	−2.78199e7	−1.76447	−0.882237	+	0.470805i	$0.843963\pi$
$758$	2.61418e7	1.65258
$759$	−7.74295e6	−0.487867
$760$	0	0
$761$	1.96481e6	0.122987	0.0614935	−	0.998107i	$-0.480414\pi$
$761$	1.96481e6	0.122987	0.0614935	+	0.998107i	$0.480414\pi$
$762$	2.89048e7	1.80336
$763$	7.12155e6	0.442857
$764$	551434.	0.0341791
$765$	0	0
$766$	8.15288e6	0.502041
$767$	−1.88282e6	−0.115564
$768$	5.35728e6	0.327749
$769$	−1.16064e7	−0.707754	−0.353877	−	0.935292i	$-0.615137\pi$
$769$	−1.16064e7	−0.707754	−0.353877	+	0.935292i	$0.615137\pi$
$770$	0	0
$771$	−516541.	−0.0312946
$772$	−2.99748e6	−0.181014
$773$	−2.10057e7	−1.26441	−0.632207	−	0.774800i	$-0.717851\pi$
$773$	−2.10057e7	−1.26441	−0.632207	+	0.774800i	$0.717851\pi$
$774$	−1.28568e7	−0.771404
$775$	0	0
$776$	3.02604e7	1.80393
$777$	−6.86243e6	−0.407779
$778$	−3.84187e6	−0.227559
$779$	−3.69652e6	−0.218248
$780$	0	0
$781$	−3.72900e6	−0.218758
$782$	1.26438e6	0.0739368
$783$	2.33310e6	0.135997
$784$	−2.96630e6	−0.172355
$785$	0	0
$786$	1.79051e7	1.03376
$787$	8.11927e6	0.467283	0.233642	−	0.972323i	$-0.424936\pi$
$787$	8.11927e6	0.467283	0.233642	+	0.972323i	$0.424936\pi$
$788$	2.58945e6	0.148557
$789$	−7.20304e6	−0.411930
$790$	0	0
$791$	6.37604e6	0.362335
$792$	8.34582e6	0.472776
$793$	2.80875e7	1.58610
$794$	−1.49637e7	−0.842340
$795$	0	0
$796$	−2.51866e6	−0.140892
$797$	1.42204e7	0.792985	0.396493	−	0.918038i	$-0.370227\pi$
$797$	1.42204e7	0.792985	0.396493	+	0.918038i	$0.370227\pi$
$798$	−3.99926e7	−2.22317
$799$	−3.03089e6	−0.167959
$800$	0	0
$801$	1.26000e6	0.0693889
$802$	2.15502e7	1.18308
$803$	2.66265e6	0.145722
$804$	−471295.	−0.0257130
$805$	0	0
$806$	1.69218e7	0.917504
$807$	8.29542e6	0.448389
$808$	−1.92203e7	−1.03570
$809$	2.40784e7	1.29347	0.646736	−	0.762714i	$-0.276134\pi$
$809$	2.40784e7	1.29347	0.646736	+	0.762714i	$0.276134\pi$
$810$	0	0
$811$	2.71158e7	1.44767	0.723836	−	0.689972i	$-0.242377\pi$
$811$	2.71158e7	1.44767	0.723836	+	0.689972i	$0.242377\pi$
$812$	352867.	0.0187811
$813$	−2.82127e7	−1.49699
$814$	−8.48311e6	−0.448739
$815$	0	0
$816$	−5.46471e6	−0.287304
$817$	−6.30776e7	−3.30613
$818$	−1.58875e7	−0.830179
$819$	−8.60937e6	−0.448499
$820$	0	0
$821$	−1.57023e7	−0.813025	−0.406513	−	0.913645i	$-0.633255\pi$
$821$	−1.57023e7	−0.813025	−0.406513	+	0.913645i	$0.633255\pi$
$822$	9.84377e6	0.508138
$823$	1.52411e7	0.784364	0.392182	−	0.919888i	$-0.371720\pi$
$823$	1.52411e7	0.784364	0.392182	+	0.919888i	$0.371720\pi$
$824$	−6.56250e6	−0.336707
$825$	0	0
$826$	−2.29993e6	−0.117291
$827$	2.27417e7	1.15627	0.578136	−	0.815940i	$-0.303780\pi$
$827$	2.27417e7	1.15627	0.578136	+	0.815940i	$0.303780\pi$
$828$	−217977.	−0.0110493
$829$	1.10029e7	0.556060	0.278030	−	0.960572i	$-0.410319\pi$
$829$	1.10029e7	0.556060	0.278030	+	0.960572i	$0.410319\pi$
$830$	0	0
$831$	2.06638e7	1.03803
$832$	1.96963e7	0.986453
$833$	718089.	0.0358563
$834$	4.33157e7	2.15640
$835$	0	0
$836$	−4.24588e6	−0.210113
$837$	1.17377e7	0.579123
$838$	2.56486e7	1.26169
$839$	−2.33372e7	−1.14458	−0.572288	−	0.820053i	$-0.693944\pi$
$839$	−2.33372e7	−1.14458	−0.572288	+	0.820053i	$0.693944\pi$
$840$	0	0
$841$	707281.	0.0344828
$842$	−2.00551e7	−0.974866
$843$	−2.15709e7	−1.04544
$844$	−1.91692e6	−0.0926291
$845$	0	0
$846$	6.08405e6	0.292258
$847$	−1.71847e7	−0.823065
$848$	−3.77427e6	−0.180237
$849$	−6.31380e6	−0.300622
$850$	0	0
$851$	−2.13667e6	−0.101138
$852$	−384496.	−0.0181465
$853$	−1.63119e7	−0.767595	−0.383797	−	0.923417i	$-0.625384\pi$
$853$	−1.63119e7	−0.767595	−0.383797	+	0.923417i	$0.625384\pi$
$854$	3.43098e7	1.60981
$855$	0	0
$856$	3.32976e6	0.155321
$857$	1.11103e7	0.516743	0.258372	−	0.966046i	$-0.416814\pi$
$857$	1.11103e7	0.516743	0.258372	+	0.966046i	$0.416814\pi$
$858$	−3.89803e7	−1.80770
$859$	2.94971e7	1.36394	0.681971	−	0.731379i	$-0.261123\pi$
$859$	2.94971e7	1.36394	0.681971	+	0.731379i	$0.261123\pi$
$860$	0	0
$861$	−3.56030e6	−0.163674
$862$	−1.72074e6	−0.0788764
$863$	−2.33489e7	−1.06718	−0.533592	−	0.845742i	$-0.679158\pi$
$863$	−2.33489e7	−1.06718	−0.533592	+	0.845742i	$0.679158\pi$
$864$	−3.00991e6	−0.137173
$865$	0	0
$866$	−1.56295e7	−0.708191
$867$	−2.46361e7	−1.11307
$868$	1.77526e6	0.0799765
$869$	−1.27178e7	−0.571296
$870$	0	0
$871$	−5.79582e6	−0.258863
$872$	−8.75374e6	−0.389855
$873$	1.60987e7	0.714915
$874$	−1.24520e7	−0.551394
$875$	0	0
$876$	274545.	0.0120880
$877$	3.29425e7	1.44630	0.723149	−	0.690692i	$-0.242694\pi$
$877$	3.29425e7	1.44630	0.723149	+	0.690692i	$0.242694\pi$
$878$	−3.34577e7	−1.46474
$879$	−4.40297e7	−1.92209
$880$	0	0
$881$	3.22782e7	1.40110	0.700550	−	0.713603i	$-0.252938\pi$
$881$	3.22782e7	1.40110	0.700550	+	0.713603i	$0.252938\pi$
$882$	−1.44145e6	−0.0623920
$883$	1.31542e7	0.567758	0.283879	−	0.958860i	$-0.408379\pi$
$883$	1.31542e7	0.567758	0.283879	+	0.958860i	$0.408379\pi$
$884$	546672.	0.0235286
$885$	0	0
$886$	7.79679e6	0.333681
$887$	5.84285e6	0.249354	0.124677	−	0.992197i	$-0.460211\pi$
$887$	5.84285e6	0.249354	0.124677	+	0.992197i	$0.460211\pi$
$888$	8.43523e6	0.358975
$889$	3.72914e7	1.58254
$890$	0	0
$891$	−3.88608e7	−1.63990
$892$	−136876.	−0.00575990
$893$	2.98492e7	1.25258
$894$	1.98095e6	0.0828952
$895$	0	0
$896$	2.89050e7	1.20283
$897$	−9.81811e6	−0.407424
$898$	3.84946e7	1.59297
$899$	3.55830e6	0.146840
$900$	0	0
$901$	913684.	0.0374959
$902$	−4.40112e6	−0.180114
$903$	−6.07531e7	−2.47941
$904$	−7.83737e6	−0.318970
$905$	0	0
$906$	1.93627e6	0.0783691
$907$	2.27296e7	0.917431	0.458716	−	0.888583i	$-0.348310\pi$
$907$	2.27296e7	0.917431	0.458716	+	0.888583i	$0.348310\pi$
$908$	−4.00804e6	−0.161331
$909$	−1.02253e7	−0.410457
$910$	0	0
$911$	2.85916e7	1.14141	0.570706	−	0.821154i	$-0.306670\pi$
$911$	2.85916e7	1.14141	0.570706	+	0.821154i	$0.306670\pi$
$912$	5.38183e7	2.14261
$913$	−2.29640e7	−0.911738
$914$	−2.07491e7	−0.821548
$915$	0	0
$916$	2.49804e6	0.0983695
$917$	2.31001e7	0.907173
$918$	4.41525e6	0.172921
$919$	4.07727e7	1.59250	0.796252	−	0.604966i	$-0.206813\pi$
$919$	4.07727e7	1.59250	0.796252	+	0.604966i	$0.206813\pi$
$920$	0	0
$921$	−1.08859e7	−0.422878
$922$	7.23289e6	0.280210
$923$	−4.72840e6	−0.182688
$924$	−4.08941e6	−0.157573
$925$	0	0
$926$	2.26121e6	0.0866588
$927$	−3.49129e6	−0.133440
$928$	−912458.	−0.0347811
$929$	−4.12838e7	−1.56943	−0.784713	−	0.619860i	$-0.787190\pi$
$929$	−4.12838e7	−1.56943	−0.784713	+	0.619860i	$0.787190\pi$
$930$	0	0
$931$	−7.07198e6	−0.267403
$932$	−2.30786e6	−0.0870301
$933$	1.82810e7	0.687537
$934$	−1.07333e7	−0.402592
$935$	0	0
$936$	1.05826e7	0.394822
$937$	−4.54057e7	−1.68951	−0.844755	−	0.535153i	$-0.820254\pi$
$937$	−4.54057e7	−1.68951	−0.844755	+	0.535153i	$0.820254\pi$
$938$	−7.07979e6	−0.262732
$939$	6.67817e6	0.247169
$940$	0	0
$941$	4.70900e7	1.73362	0.866812	−	0.498635i	$-0.166165\pi$
$941$	4.70900e7	1.73362	0.866812	+	0.498635i	$0.166165\pi$
$942$	−4.47401e7	−1.64274
$943$	−1.10853e6	−0.0405946
$944$	3.09503e6	0.113041
$945$	0	0
$946$	−7.51010e7	−2.72846
$947$	−2.49040e6	−0.0902390	−0.0451195	−	0.998982i	$-0.514367\pi$
$947$	−2.49040e6	−0.0902390	−0.0451195	+	0.998982i	$0.514367\pi$
$948$	−1.31133e6	−0.0473904
$949$	3.37626e6	0.121694
$950$	0	0
$951$	−2.93686e7	−1.05301
$952$	−6.43983e6	−0.230294
$953$	1.43265e7	0.510985	0.255493	−	0.966811i	$-0.417762\pi$
$953$	1.43265e7	0.510985	0.255493	+	0.966811i	$0.417762\pi$
$954$	−1.83408e6	−0.0652450
$955$	0	0
$956$	−3.69371e6	−0.130713
$957$	−8.19676e6	−0.289309
$958$	−2.88375e7	−1.01518
$959$	1.26999e7	0.445916
$960$	0	0
$961$	−1.07275e7	−0.374704
$962$	−1.07566e7	−0.374748
$963$	1.77145e6	0.0615550
$964$	914063.	0.0316799
$965$	0	0
$966$	−1.19932e7	−0.413515
$967$	1.92616e7	0.662407	0.331204	−	0.943559i	$-0.392545\pi$
$967$	1.92616e7	0.662407	0.331204	+	0.943559i	$0.392545\pi$
$968$	2.11233e7	0.724559
$969$	−1.30285e7	−0.445742
$970$	0	0
$971$	−3.31255e7	−1.12749	−0.563747	−	0.825948i	$-0.690641\pi$
$971$	−3.31255e7	−1.12749	−0.563747	+	0.825948i	$0.690641\pi$
$972$	−1.98017e6	−0.0672259
$973$	5.58834e7	1.89235
$974$	−1.09430e7	−0.369607
$975$	0	0
$976$	−4.61709e7	−1.55147
$977$	5.00959e7	1.67906	0.839529	−	0.543314i	$-0.182831\pi$
$977$	5.00959e7	1.67906	0.839529	+	0.543314i	$0.182831\pi$
$978$	1.92846e7	0.644709
$979$	7.36008e6	0.245429
$980$	0	0
$981$	−4.65704e6	−0.154503
$982$	3.23692e7	1.07116
$983$	6.69976e6	0.221144	0.110572	−	0.993868i	$-0.464732\pi$
$983$	6.69976e6	0.221144	0.110572	+	0.993868i	$0.464732\pi$
$984$	4.37629e6	0.144085
$985$	0	0
$986$	1.33849e6	0.0438451
$987$	2.87493e7	0.939364
$988$	−5.38381e6	−0.175468
$989$	−1.89160e7	−0.614948
$990$	0	0
$991$	−3.54819e7	−1.14768	−0.573842	−	0.818966i	$-0.694548\pi$
$991$	−3.54819e7	−1.14768	−0.573842	+	0.818966i	$0.694548\pi$
$992$	−4.59054e6	−0.148110
$993$	−9.78359e6	−0.314866
$994$	−5.77590e6	−0.185419
$995$	0	0
$996$	−2.36781e6	−0.0756309
$997$	2.99768e7	0.955097	0.477549	−	0.878605i	$-0.341525\pi$
$997$	2.99768e7	0.955097	0.477549	+	0.878605i	$0.341525\pi$
$998$	−3.12256e7	−0.992395
$999$	−7.46132e6	−0.236538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.6.a.a.1.1		4
5.4	even	2		29.6.a.a.1.4	✓	4
15.14	odd	2		261.6.a.a.1.1		4
20.19	odd	2		464.6.a.i.1.4		4
145.144	even	2		841.6.a.a.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.a.1.4	✓	4	5.4	even	2
261.6.a.a.1.1		4	15.14	odd	2
464.6.a.i.1.4		4	20.19	odd	2
725.6.a.a.1.1		4	1.1	even	1	trivial
841.6.a.a.1.1		4	145.144	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q-5.91663 q^{2} +18.2828 q^{3} +3.00648 q^{4} -108.173 q^{6} -139.558 q^{7} +171.544 q^{8} +91.2623 q^{9} +O(q^{10})\)	\(q-5.91663 q^{2} +18.2828 q^{3} +3.00648 q^{4} -108.173 q^{6} -139.558 q^{7} +171.544 q^{8} +91.2623 q^{9} +533.092 q^{11} +54.9671 q^{12} +675.965 q^{13} +825.715 q^{14} -1111.17 q^{16} +268.994 q^{17} -539.965 q^{18} -2649.15 q^{19} -2551.52 q^{21} -3154.11 q^{22} -794.438 q^{23} +3136.31 q^{24} -3999.43 q^{26} -2774.20 q^{27} -419.580 q^{28} -841.000 q^{29} -4231.04 q^{31} +1084.97 q^{32} +9746.44 q^{33} -1591.54 q^{34} +274.379 q^{36} +2689.54 q^{37} +15674.0 q^{38} +12358.6 q^{39} +1395.36 q^{41} +15096.4 q^{42} +23810.5 q^{43} +1602.73 q^{44} +4700.39 q^{46} -11267.5 q^{47} -20315.3 q^{48} +2669.53 q^{49} +4917.98 q^{51} +2032.28 q^{52} +3396.67 q^{53} +16413.9 q^{54} -23940.4 q^{56} -48433.9 q^{57} +4975.88 q^{58} -2785.38 q^{59} +41551.7 q^{61} +25033.5 q^{62} -12736.4 q^{63} +29138.0 q^{64} -57666.1 q^{66} -8574.14 q^{67} +808.728 q^{68} -14524.6 q^{69} -6995.03 q^{71} +15655.5 q^{72} +4994.73 q^{73} -15913.0 q^{74} -7964.62 q^{76} -74397.5 q^{77} -73121.0 q^{78} -23856.6 q^{79} -72896.9 q^{81} -8255.84 q^{82} -43076.9 q^{83} -7671.11 q^{84} -140878. q^{86} -15375.9 q^{87} +91448.7 q^{88} +13806.4 q^{89} -94336.6 q^{91} -2388.47 q^{92} -77355.4 q^{93} +66665.5 q^{94} +19836.3 q^{96} +176400. q^{97} -15794.6 q^{98} +48651.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9}+O(q^{10}) \) 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9} - 124 q^{11} - 20 q^{12} + 460 q^{13} + 768 q^{14} - 414 q^{16} - 184 q^{17} - 3208 q^{18} - 2392 q^{19} + 992 q^{21} - 5538 q^{22} + 1192 q^{23} + 6786 q^{24} + 4724 q^{26} - 2468 q^{27} - 44 q^{28} - 3364 q^{29} - 19212 q^{31} - 6552 q^{32} + 10580 q^{33} - 7612 q^{34} - 7468 q^{36} + 10928 q^{37} + 456 q^{38} - 8732 q^{39} - 1120 q^{41} - 1844 q^{42} + 21420 q^{43} - 1932 q^{44} - 7588 q^{46} - 23772 q^{47} - 33060 q^{48} + 10452 q^{49} + 12744 q^{51} + 29062 q^{52} - 8860 q^{53} + 35410 q^{54} + 34304 q^{56} - 48944 q^{57} - 10840 q^{59} + 49448 q^{61} - 18518 q^{62} - 27488 q^{63} - 20734 q^{64} - 47744 q^{66} + 7840 q^{67} - 20724 q^{68} + 58792 q^{69} - 48744 q^{71} - 8088 q^{72} + 74992 q^{73} - 35920 q^{74} - 140792 q^{76} - 128656 q^{77} - 2982 q^{78} - 106076 q^{79} - 59692 q^{81} + 234132 q^{82} - 62888 q^{83} - 59832 q^{84} - 216014 q^{86} - 23548 q^{87} + 39426 q^{88} + 107568 q^{89} - 268896 q^{91} + 26268 q^{92} - 221460 q^{93} + 30542 q^{94} - 78606 q^{96} + 49520 q^{97} - 242304 q^{98} + 166720 q^{99}+O(q^{100}) \) 4 * q + 28 * q^3 + 10 * q^4 - 194 * q^6 + 208 * q^7 + 504 * q^8 - 280 * q^9 - 124 * q^11 - 20 * q^12 + 460 * q^13 + 768 * q^14 - 414 * q^16 - 184 * q^17 - 3208 * q^18 - 2392 * q^19 + 992 * q^21 - 5538 * q^22 + 1192 * q^23 + 6786 * q^24 + 4724 * q^26 - 2468 * q^27 - 44 * q^28 - 3364 * q^29 - 19212 * q^31 - 6552 * q^32 + 10580 * q^33 - 7612 * q^34 - 7468 * q^36 + 10928 * q^37 + 456 * q^38 - 8732 * q^39 - 1120 * q^41 - 1844 * q^42 + 21420 * q^43 - 1932 * q^44 - 7588 * q^46 - 23772 * q^47 - 33060 * q^48 + 10452 * q^49 + 12744 * q^51 + 29062 * q^52 - 8860 * q^53 + 35410 * q^54 + 34304 * q^56 - 48944 * q^57 - 10840 * q^59 + 49448 * q^61 - 18518 * q^62 - 27488 * q^63 - 20734 * q^64 - 47744 * q^66 + 7840 * q^67 - 20724 * q^68 + 58792 * q^69 - 48744 * q^71 - 8088 * q^72 + 74992 * q^73 - 35920 * q^74 - 140792 * q^76 - 128656 * q^77 - 2982 * q^78 - 106076 * q^79 - 59692 * q^81 + 234132 * q^82 - 62888 * q^83 - 59832 * q^84 - 216014 * q^86 - 23548 * q^87 + 39426 * q^88 + 107568 * q^89 - 268896 * q^91 + 26268 * q^92 - 221460 * q^93 + 30542 * q^94 - 78606 * q^96 + 49520 * q^97 - 242304 * q^98 + 166720 * q^99

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