LMFDB - Embedded newform 725.6.a.a.1.2

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			1.2
Root			$-1.10057$ 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)

$f(q)$	$=$	$q-4.16235 q^{2} +17.5258 q^{3} -14.6748 q^{4} -72.9487 q^{6} +220.793 q^{7} +194.277 q^{8} +64.1549 q^{9} +O(q^{10})$	\(q-4.16235 q^{2} +17.5258 q^{3} -14.6748 q^{4} -72.9487 q^{6} +220.793 q^{7} +194.277 q^{8} +64.1549 q^{9} -85.7296 q^{11} -257.189 q^{12} -1034.02 q^{13} -919.018 q^{14} -339.054 q^{16} +313.020 q^{17} -267.035 q^{18} +458.534 q^{19} +3869.58 q^{21} +356.836 q^{22} +3448.84 q^{23} +3404.87 q^{24} +4303.94 q^{26} -3134.41 q^{27} -3240.10 q^{28} -841.000 q^{29} -7983.23 q^{31} -4805.60 q^{32} -1502.48 q^{33} -1302.90 q^{34} -941.463 q^{36} -152.624 q^{37} -1908.58 q^{38} -18122.0 q^{39} -18492.2 q^{41} -16106.6 q^{42} -2072.84 q^{43} +1258.07 q^{44} -14355.3 q^{46} -15845.6 q^{47} -5942.21 q^{48} +31942.6 q^{49} +5485.94 q^{51} +15174.0 q^{52} -9240.52 q^{53} +13046.5 q^{54} +42895.0 q^{56} +8036.19 q^{57} +3500.54 q^{58} -14323.2 q^{59} -19580.2 q^{61} +33229.0 q^{62} +14165.0 q^{63} +30852.3 q^{64} +6253.86 q^{66} +9193.70 q^{67} -4593.53 q^{68} +60443.8 q^{69} -19374.7 q^{71} +12463.8 q^{72} +56912.4 q^{73} +635.276 q^{74} -6728.91 q^{76} -18928.5 q^{77} +75430.1 q^{78} +51573.6 q^{79} -70522.8 q^{81} +76971.0 q^{82} -19978.1 q^{83} -56785.5 q^{84} +8627.87 q^{86} -14739.2 q^{87} -16655.3 q^{88} +130663. q^{89} -228304. q^{91} -50611.1 q^{92} -139913. q^{93} +65954.9 q^{94} -84222.2 q^{96} -43603.5 q^{97} -132956. q^{98} -5499.97 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.16235	−0.735806	−0.367903	−	0.929864i	$-0.619924\pi$
$2$	−4.16235	−0.735806	−0.367903	+	0.929864i	$0.619924\pi$
$3$	17.5258	1.12428	0.562141	−	0.827041i	$-0.309978\pi$
$3$	17.5258	1.12428	0.562141	+	0.827041i	$0.309978\pi$
$4$	−14.6748	−0.458589
$5$	0	0
$5$	0	0
$6$	−72.9487	−0.827255
$7$	220.793	1.70310	0.851551	−	0.524272i	$-0.175663\pi$
$7$	220.793	1.70310	0.851551	+	0.524272i	$0.175663\pi$
$8$	194.277	1.07324
$9$	64.1549	0.264012
$10$	0	0
$11$	−85.7296	−0.213623	−0.106812	−	0.994279i	$-0.534064\pi$
$11$	−85.7296	−0.213623	−0.106812	+	0.994279i	$0.534064\pi$
$12$	−257.189	−0.515584
$13$	−1034.02	−1.69695	−0.848475	−	0.529235i	$-0.822479\pi$
$13$	−1034.02	−1.69695	−0.848475	+	0.529235i	$0.822479\pi$
$14$	−919.018	−1.25315
$15$	0	0
$16$	−339.054	−0.331108
$17$	313.020	0.262694	0.131347	−	0.991336i	$-0.458070\pi$
$17$	313.020	0.262694	0.131347	+	0.991336i	$0.458070\pi$
$18$	−267.035	−0.194262
$19$	458.534	0.291398	0.145699	−	0.989329i	$-0.453457\pi$
$19$	458.534	0.291398	0.145699	+	0.989329i	$0.453457\pi$
$20$	0	0
$21$	3869.58	1.91477
$22$	356.836	0.157186
$23$	3448.84	1.35942	0.679709	−	0.733482i	$-0.262106\pi$
$23$	3448.84	1.35942	0.679709	+	0.733482i	$0.262106\pi$
$24$	3404.87	1.20662
$25$	0	0
$26$	4303.94	1.24863
$27$	−3134.41	−0.827459
$28$	−3240.10	−0.781023
$29$	−841.000	−0.185695
$29$	−841.000	−0.185695
$30$	0	0
$31$	−7983.23	−1.49202	−0.746009	−	0.665936i	$-0.768033\pi$
$31$	−7983.23	−1.49202	−0.746009	+	0.665936i	$0.768033\pi$
$32$	−4805.60	−0.829608
$33$	−1502.48	−0.240173
$34$	−1302.90	−0.193292
$35$	0	0
$36$	−941.463	−0.121073
$37$	−152.624	−0.0183282	−0.00916409	−	0.999958i	$-0.502917\pi$
$37$	−152.624	−0.0183282	−0.00916409	+	0.999958i	$0.502917\pi$
$38$	−1908.58	−0.214413
$39$	−18122.0	−1.90785
$40$	0	0
$41$	−18492.2	−1.71802	−0.859011	−	0.511957i	$-0.828921\pi$
$41$	−18492.2	−1.71802	−0.859011	+	0.511957i	$0.828921\pi$
$42$	−16106.6	−1.40890
$43$	−2072.84	−0.170960	−0.0854799	−	0.996340i	$-0.527242\pi$
$43$	−2072.84	−0.170960	−0.0854799	+	0.996340i	$0.527242\pi$
$44$	1258.07	0.0979653
$45$	0	0
$46$	−14355.3	−1.00027
$47$	−15845.6	−1.04632	−0.523159	−	0.852235i	$-0.675247\pi$
$47$	−15845.6	−1.04632	−0.523159	+	0.852235i	$0.675247\pi$
$48$	−5942.21	−0.372258
$49$	31942.6	1.90055
$50$	0	0
$51$	5485.94	0.295343
$52$	15174.0	0.778203
$53$	−9240.52	−0.451863	−0.225931	−	0.974143i	$-0.572543\pi$
$53$	−9240.52	−0.451863	−0.225931	+	0.974143i	$0.572543\pi$
$54$	13046.5	0.608850
$55$	0	0
$56$	42895.0	1.82783
$57$	8036.19	0.327614
$58$	3500.54	0.136636
$59$	−14323.2	−0.535686	−0.267843	−	0.963463i	$-0.586311\pi$
$59$	−14323.2	−0.535686	−0.267843	+	0.963463i	$0.586311\pi$
$60$	0	0
$61$	−19580.2	−0.673739	−0.336870	−	0.941551i	$-0.609368\pi$
$61$	−19580.2	−0.673739	−0.336870	+	0.941551i	$0.609368\pi$
$62$	33229.0	1.09784
$63$	14165.0	0.449639
$64$	30852.3	0.941539
$65$	0	0
$66$	6253.86	0.176721
$67$	9193.70	0.250209	0.125105	−	0.992144i	$-0.460073\pi$
$67$	9193.70	0.250209	0.125105	+	0.992144i	$0.460073\pi$
$68$	−4593.53	−0.120469
$69$	60443.8	1.52837
$70$	0	0
$71$	−19374.7	−0.456131	−0.228066	−	0.973646i	$-0.573240\pi$
$71$	−19374.7	−0.456131	−0.228066	+	0.973646i	$0.573240\pi$
$72$	12463.8	0.283348
$73$	56912.4	1.24997	0.624985	−	0.780637i	$-0.285105\pi$
$73$	56912.4	1.24997	0.624985	+	0.780637i	$0.285105\pi$
$74$	635.276	0.0134860
$75$	0	0
$76$	−6728.91	−0.133632
$77$	−18928.5	−0.363822
$78$	75430.1	1.40381
$79$	51573.6	0.929736	0.464868	−	0.885380i	$-0.346102\pi$
$79$	51573.6	0.929736	0.464868	+	0.885380i	$0.346102\pi$
$80$	0	0
$81$	−70522.8	−1.19431
$82$	76971.0	1.26413
$83$	−19978.1	−0.318317	−0.159158	−	0.987253i	$-0.550878\pi$
$83$	−19978.1	−0.318317	−0.159158	+	0.987253i	$0.550878\pi$
$84$	−56785.5	−0.878091
$85$	0	0
$86$	8627.87	0.125793
$87$	−14739.2	−0.208774
$88$	−16655.3	−0.229269
$89$	130663.	1.74855	0.874274	−	0.485432i	$-0.161338\pi$
$89$	130663.	1.74855	0.874274	+	0.485432i	$0.161338\pi$
$90$	0	0
$91$	−228304.	−2.89008
$92$	−50611.1	−0.623414
$93$	−139913.	−1.67745
$94$	65954.9	0.769888
$95$	0	0
$96$	−84222.2	−0.932714
$97$	−43603.5	−0.470535	−0.235268	−	0.971931i	$-0.575597\pi$
$97$	−43603.5	−0.470535	−0.235268	+	0.971931i	$0.575597\pi$
$98$	−132956.	−1.39844
$99$	−5499.97	−0.0563991
$100$	0	0
$101$	−56686.0	−0.552933	−0.276467	−	0.961024i	$-0.589164\pi$
$101$	−56686.0	−0.552933	−0.276467	+	0.961024i	$0.589164\pi$
$102$	−22834.4	−0.217315
$103$	111450.	1.03511	0.517556	−	0.855649i	$-0.326842\pi$
$103$	111450.	1.03511	0.517556	+	0.855649i	$0.326842\pi$
$104$	−200886.	−1.82123
$105$	0	0
$106$	38462.3	0.332484
$107$	−189434.	−1.59955	−0.799775	−	0.600300i	$-0.795048\pi$
$107$	−189434.	−1.59955	−0.799775	+	0.600300i	$0.795048\pi$
$108$	45997.0	0.379463
$109$	100232.	0.808054	0.404027	−	0.914747i	$-0.367610\pi$
$109$	100232.	0.808054	0.404027	+	0.914747i	$0.367610\pi$
$110$	0	0
$111$	−2674.87	−0.0206061
$112$	−74860.8	−0.563910
$113$	103444.	0.762092	0.381046	−	0.924556i	$-0.375564\pi$
$113$	103444.	0.762092	0.381046	+	0.924556i	$0.375564\pi$
$114$	−33449.4	−0.241061
$115$	0	0
$116$	12341.5	0.0851578
$117$	−66337.2	−0.448015
$118$	59618.2	0.394161
$119$	69112.8	0.447395
$120$	0	0
$121$	−153701.	−0.954365
$122$	81499.5	0.495742
$123$	−324091.	−1.93154
$124$	117153.	0.684223
$125$	0	0
$126$	−58959.5	−0.330847
$127$	247538.	1.36186	0.680930	−	0.732349i	$-0.261576\pi$
$127$	247538.	1.36186	0.680930	+	0.732349i	$0.261576\pi$
$128$	25361.1	0.136818
$129$	−36328.2	−0.192207
$130$	0	0
$131$	198458.	1.01040	0.505198	−	0.863004i	$-0.331420\pi$
$131$	198458.	1.01040	0.505198	+	0.863004i	$0.331420\pi$
$132$	22048.7	0.110141
$133$	101241.	0.496281
$134$	−38267.4	−0.184106
$135$	0	0
$136$	60812.7	0.281934
$137$	−141442.	−0.643839	−0.321920	−	0.946767i	$-0.604328\pi$
$137$	−141442.	−0.643839	−0.321920	+	0.946767i	$0.604328\pi$
$138$	−251588.	−1.12459
$139$	−325330.	−1.42819	−0.714097	−	0.700047i	$-0.753162\pi$
$139$	−325330.	−1.42819	−0.714097	+	0.700047i	$0.753162\pi$
$140$	0	0
$141$	−277707.	−1.17636
$142$	80644.4	0.335624
$143$	88645.8	0.362508
$144$	−21752.0	−0.0874163
$145$	0	0
$146$	−236889.	−0.919736
$147$	559821.	2.13676
$148$	2239.74	0.00840510
$149$	−391462.	−1.44452	−0.722261	−	0.691621i	$-0.756897\pi$
$149$	−391462.	−1.44452	−0.722261	+	0.691621i	$0.756897\pi$
$150$	0	0
$151$	−216585.	−0.773013	−0.386507	−	0.922287i	$-0.626318\pi$
$151$	−216585.	−0.773013	−0.386507	+	0.922287i	$0.626318\pi$
$152$	89082.6	0.312740
$153$	20081.8	0.0693544
$154$	78787.0	0.267703
$155$	0	0
$156$	265938.	0.874920
$157$	−564396.	−1.82740	−0.913702	−	0.406385i	$-0.866789\pi$
$157$	−564396.	−1.82740	−0.913702	+	0.406385i	$0.866789\pi$
$158$	−214667.	−0.684106
$159$	−161948.	−0.508022
$160$	0	0
$161$	761480.	2.31523
$162$	293541.	0.878781
$163$	−476986.	−1.40617	−0.703083	−	0.711108i	$-0.748194\pi$
$163$	−476986.	−1.40617	−0.703083	+	0.711108i	$0.748194\pi$
$164$	271370.	0.787866
$165$	0	0
$166$	83155.9	0.234219
$167$	203397.	0.564357	0.282178	−	0.959362i	$-0.408943\pi$
$167$	203397.	0.564357	0.282178	+	0.959362i	$0.408943\pi$
$168$	751771.	2.05500
$169$	697898.	1.87964
$170$	0	0
$171$	29417.2	0.0769327
$172$	30418.6	0.0784003
$173$	95409.0	0.242367	0.121184	−	0.992630i	$-0.461331\pi$
$173$	95409.0	0.242367	0.121184	+	0.992630i	$0.461331\pi$
$174$	61349.8	0.153617
$175$	0	0
$176$	29067.0	0.0707323
$177$	−251026.	−0.602263
$178$	−543865.	−1.28659
$179$	−327011.	−0.762833	−0.381416	−	0.924403i	$-0.624564\pi$
$179$	−327011.	−0.762833	−0.381416	+	0.924403i	$0.624564\pi$
$180$	0	0
$181$	108581.	0.246353	0.123177	−	0.992385i	$-0.460692\pi$
$181$	108581.	0.246353	0.123177	+	0.992385i	$0.460692\pi$
$182$	950280.	2.12654
$183$	−343159.	−0.757473
$184$	670030.	1.45898
$185$	0	0
$186$	582366.	1.23428
$187$	−26835.1	−0.0561176
$188$	232532.	0.479830
$189$	−692056.	−1.40925
$190$	0	0
$191$	−315738.	−0.626244	−0.313122	−	0.949713i	$-0.601375\pi$
$191$	−315738.	−0.626244	−0.313122	+	0.949713i	$0.601375\pi$
$192$	540713.	1.05856
$193$	−41432.1	−0.0800651	−0.0400326	−	0.999198i	$-0.512746\pi$
$193$	−41432.1	−0.0800651	−0.0400326	+	0.999198i	$0.512746\pi$
$194$	181493.	0.346223
$195$	0	0
$196$	−468753.	−0.871573
$197$	−354739.	−0.651243	−0.325622	−	0.945500i	$-0.605574\pi$
$197$	−354739.	−0.651243	−0.325622	+	0.945500i	$0.605574\pi$
$198$	22892.8	0.0414988
$199$	−949129.	−1.69900	−0.849498	−	0.527591i	$-0.823095\pi$
$199$	−949129.	−1.69900	−0.849498	+	0.527591i	$0.823095\pi$
$200$	0	0
$201$	161127.	0.281306
$202$	235947.	0.406852
$203$	−185687.	−0.316258
$204$	−80505.4	−0.135441
$205$	0	0
$206$	−463894.	−0.761642
$207$	221260.	0.358903
$208$	350588.	0.561873
$209$	−39309.9	−0.0622495
$210$	0	0
$211$	−380574.	−0.588481	−0.294241	−	0.955731i	$-0.595067\pi$
$211$	−380574.	−0.588481	−0.294241	+	0.955731i	$0.595067\pi$
$212$	135603.	0.207219
$213$	−339558.	−0.512820
$214$	788489.	1.17696
$215$	0	0
$216$	−608944.	−0.888061
$217$	−1.76264e6	−2.54106
$218$	−417201.	−0.594571
$219$	997437.	1.40532
$220$	0	0
$221$	−323668.	−0.445779
$222$	11133.7	0.0151621
$223$	68362.6	0.0920569	0.0460284	−	0.998940i	$-0.485344\pi$
$223$	68362.6	0.0920569	0.0460284	+	0.998940i	$0.485344\pi$
$224$	−1.06104e6	−1.41291
$225$	0	0
$226$	−430569.	−0.560753
$227$	1.07914e6	1.39000	0.694998	−	0.719012i	$-0.255405\pi$
$227$	1.07914e6	1.39000	0.694998	+	0.719012i	$0.255405\pi$
$228$	−117930.	−0.150240
$229$	−724221.	−0.912604	−0.456302	−	0.889825i	$-0.650826\pi$
$229$	−724221.	−0.912604	−0.456302	+	0.889825i	$0.650826\pi$
$230$	0	0
$231$	−331738.	−0.409039
$232$	−163387.	−0.199296
$233$	−1.37311e6	−1.65697	−0.828486	−	0.560009i	$-0.810797\pi$
$233$	−1.37311e6	−1.65697	−0.828486	+	0.560009i	$0.810797\pi$
$234$	276119.	0.329652
$235$	0	0
$236$	210191.	0.245660
$237$	903870.	1.04529
$238$	−287672.	−0.329196
$239$	1.11446e6	1.26204	0.631018	−	0.775769i	$-0.282638\pi$
$239$	1.11446e6	1.26204	0.631018	+	0.775769i	$0.282638\pi$
$240$	0	0
$241$	−1.47058e6	−1.63097	−0.815486	−	0.578776i	$-0.803530\pi$
$241$	−1.47058e6	−1.63097	−0.815486	+	0.578776i	$0.803530\pi$
$242$	639759.	0.702228
$243$	−474309.	−0.515283
$244$	287336.	0.308969
$245$	0	0
$246$	1.34898e6	1.42124
$247$	−474132.	−0.494489
$248$	−1.55096e6	−1.60129
$249$	−350133.	−0.357878
$250$	0	0
$251$	375105.	0.375810	0.187905	−	0.982187i	$-0.439830\pi$
$251$	375105.	0.375810	0.187905	+	0.982187i	$0.439830\pi$
$252$	−207868.	−0.206199
$253$	−295667.	−0.290404
$254$	−1.03034e6	−1.00207
$255$	0	0
$256$	−1.09284e6	−1.04221
$257$	471074.	0.444894	0.222447	−	0.974945i	$-0.428596\pi$
$257$	471074.	0.444894	0.222447	+	0.974945i	$0.428596\pi$
$258$	151211.	0.141427
$259$	−33698.4	−0.0312147
$260$	0	0
$261$	−53954.3	−0.0490258
$262$	−826053.	−0.743455
$263$	−1.11373e6	−0.992865	−0.496433	−	0.868075i	$-0.665357\pi$
$263$	−1.11373e6	−0.992865	−0.496433	+	0.868075i	$0.665357\pi$
$264$	−291898.	−0.257763
$265$	0	0
$266$	−421401.	−0.365167
$267$	2.28998e6	1.96586
$268$	−134916.	−0.114743
$269$	−381568.	−0.321508	−0.160754	−	0.986995i	$-0.551393\pi$
$269$	−381568.	−0.321508	−0.160754	+	0.986995i	$0.551393\pi$
$270$	0	0
$271$	1.08834e6	0.900208	0.450104	−	0.892976i	$-0.351387\pi$
$271$	1.08834e6	0.900208	0.450104	+	0.892976i	$0.351387\pi$
$272$	−106131.	−0.0869800
$273$	−4.00121e6	−3.24927
$274$	588732.	0.473741
$275$	0	0
$276$	−887003.	−0.700894
$277$	2.18958e6	1.71459	0.857295	−	0.514825i	$-0.172143\pi$
$277$	2.18958e6	1.71459	0.857295	+	0.514825i	$0.172143\pi$
$278$	1.35414e6	1.05087
$279$	−512163.	−0.393911
$280$	0	0
$281$	−1.02712e6	−0.775992	−0.387996	−	0.921661i	$-0.626833\pi$
$281$	−1.02712e6	−0.775992	−0.387996	+	0.921661i	$0.626833\pi$
$282$	1.15592e6	0.865572
$283$	−889156.	−0.659952	−0.329976	−	0.943989i	$-0.607041\pi$
$283$	−889156.	−0.659952	−0.329976	+	0.943989i	$0.607041\pi$
$284$	284321.	0.209177
$285$	0	0
$286$	−368975.	−0.266736
$287$	−4.08295e6	−2.92597
$288$	−308303.	−0.219026
$289$	−1.32188e6	−0.930992
$290$	0	0
$291$	−764188.	−0.529015
$292$	−835180.	−0.573222
$293$	482000.	0.328003	0.164001	−	0.986460i	$-0.447560\pi$
$293$	482000.	0.328003	0.164001	+	0.986460i	$0.447560\pi$
$294$	−2.33017e6	−1.57224
$295$	0	0
$296$	−29651.4	−0.0196705
$297$	268712.	0.176765
$298$	1.62940e6	1.06289
$299$	−3.56616e6	−2.30687
$300$	0	0
$301$	−457668.	−0.291162
$302$	901505.	0.568788
$303$	−993470.	−0.621653
$304$	−155468.	−0.0964842
$305$	0	0
$306$	−83587.4	−0.0510314
$307$	−229158.	−0.138768	−0.0693839	−	0.997590i	$-0.522103\pi$
$307$	−229158.	−0.138768	−0.0693839	+	0.997590i	$0.522103\pi$
$308$	277773.	0.166845
$309$	1.95326e6	1.16376
$310$	0	0
$311$	2.49699e6	1.46392	0.731958	−	0.681350i	$-0.238607\pi$
$311$	2.49699e6	1.46392	0.731958	+	0.681350i	$0.238607\pi$
$312$	−3.52069e6	−2.04758
$313$	2.78111e6	1.60457	0.802283	−	0.596944i	$-0.203619\pi$
$313$	2.78111e6	1.60457	0.802283	+	0.596944i	$0.203619\pi$
$314$	2.34921e6	1.34462
$315$	0	0
$316$	−756834.	−0.426366
$317$	−1.94375e6	−1.08641	−0.543203	−	0.839602i	$-0.682788\pi$
$317$	−1.94375e6	−1.08641	−0.543203	+	0.839602i	$0.682788\pi$
$318$	674083.	0.373806
$319$	72098.6	0.0396689
$320$	0	0
$321$	−3.31998e6	−1.79835
$322$	−3.16955e6	−1.70356
$323$	143530.	0.0765487
$324$	1.03491e6	0.547697
$325$	0	0
$326$	1.98538e6	1.03467
$327$	1.75665e6	0.908481
$328$	−3.59261e6	−1.84385
$329$	−3.49860e6	−1.78199
$330$	0	0
$331$	−60445.1	−0.0303243	−0.0151622	−	0.999885i	$-0.504826\pi$
$331$	−60445.1	−0.0303243	−0.0151622	+	0.999885i	$0.504826\pi$
$332$	293176.	0.145976
$333$	−9791.59	−0.00483886
$334$	−846611.	−0.415258
$335$	0	0
$336$	−1.31200e6	−0.633994
$337$	1.72999e6	0.829791	0.414895	−	0.909869i	$-0.363818\pi$
$337$	1.72999e6	0.829791	0.414895	+	0.909869i	$0.363818\pi$
$338$	−2.90489e6	−1.38305
$339$	1.81294e6	0.856807
$340$	0	0
$341$	684398.	0.318730
$342$	−122445.	−0.0566075
$343$	3.34184e6	1.53373
$344$	−402705.	−0.183481
$345$	0	0
$346$	−397126.	−0.178335
$347$	−1.17667e6	−0.524605	−0.262303	−	0.964986i	$-0.584482\pi$
$347$	−1.17667e6	−0.524605	−0.262303	+	0.964986i	$0.584482\pi$
$348$	216296.	0.0957415
$349$	1.20893e6	0.531297	0.265648	−	0.964070i	$-0.414414\pi$
$349$	1.20893e6	0.531297	0.265648	+	0.964070i	$0.414414\pi$
$350$	0	0
$351$	3.24103e6	1.40416
$352$	411982.	0.177224
$353$	−1.00723e6	−0.430223	−0.215111	−	0.976589i	$-0.569011\pi$
$353$	−1.00723e6	−0.430223	−0.215111	+	0.976589i	$0.569011\pi$
$354$	1.04486e6	0.443149
$355$	0	0
$356$	−1.91746e6	−0.801865
$357$	1.21126e6	0.502998
$358$	1.36113e6	0.561297
$359$	1.10145e6	0.451055	0.225527	−	0.974237i	$-0.427589\pi$
$359$	1.10145e6	0.451055	0.225527	+	0.974237i	$0.427589\pi$
$360$	0	0
$361$	−2.26585e6	−0.915087
$362$	−451953.	−0.181268
$363$	−2.69375e6	−1.07298
$364$	3.35032e6	1.32536
$365$	0	0
$366$	1.42835e6	0.557354
$367$	−2.99288e6	−1.15991	−0.579955	−	0.814648i	$-0.696930\pi$
$367$	−2.99288e6	−1.15991	−0.579955	+	0.814648i	$0.696930\pi$
$368$	−1.16934e6	−0.450114
$369$	−1.18636e6	−0.453578
$370$	0	0
$371$	−2.04024e6	−0.769568
$372$	2.05320e6	0.769260
$373$	−4.23178e6	−1.57489	−0.787446	−	0.616384i	$-0.788597\pi$
$373$	−4.23178e6	−1.57489	−0.787446	+	0.616384i	$0.788597\pi$
$374$	111697.	0.0412917
$375$	0	0
$376$	−3.07844e6	−1.12295
$377$	869608.	0.315116
$378$	2.88058e6	1.03693
$379$	1.06268e6	0.380018	0.190009	−	0.981782i	$-0.439148\pi$
$379$	1.06268e6	0.380018	0.190009	+	0.981782i	$0.439148\pi$
$380$	0	0
$381$	4.33831e6	1.53112
$382$	1.31421e6	0.460794
$383$	3.75736e6	1.30884	0.654418	−	0.756133i	$-0.272913\pi$
$383$	3.75736e6	1.30884	0.654418	+	0.756133i	$0.272913\pi$
$384$	444474.	0.153822
$385$	0	0
$386$	172455.	0.0589125
$387$	−132983.	−0.0451354
$388$	639875.	0.215782
$389$	−3.88561e6	−1.30192	−0.650961	−	0.759112i	$-0.725634\pi$
$389$	−3.88561e6	−1.30192	−0.650961	+	0.759112i	$0.725634\pi$
$390$	0	0
$391$	1.07956e6	0.357111
$392$	6.20571e6	2.03975
$393$	3.47815e6	1.13597
$394$	1.47655e6	0.479189
$395$	0	0
$396$	80711.2	0.0258640
$397$	−719537.	−0.229127	−0.114564	−	0.993416i	$-0.536547\pi$
$397$	−719537.	−0.229127	−0.114564	+	0.993416i	$0.536547\pi$
$398$	3.95061e6	1.25013
$399$	1.77433e6	0.557960
$400$	0	0
$401$	−1.57519e6	−0.489185	−0.244592	−	0.969626i	$-0.578654\pi$
$401$	−1.57519e6	−0.489185	−0.244592	+	0.969626i	$0.578654\pi$
$402$	−670668.	−0.206987
$403$	8.25479e6	2.53188
$404$	831859.	0.253569
$405$	0	0
$406$	772894.	0.232705
$407$	13084.4	0.00391533
$408$	1.06579e6	0.316973
$409$	−3.35355e6	−0.991279	−0.495639	−	0.868528i	$-0.665066\pi$
$409$	−3.35355e6	−0.991279	−0.495639	+	0.868528i	$0.665066\pi$
$410$	0	0
$411$	−2.47889e6	−0.723857
$412$	−1.63551e6	−0.474691
$413$	−3.16247e6	−0.912328
$414$	−920961.	−0.264083
$415$	0	0
$416$	4.96907e6	1.40780
$417$	−5.70168e6	−1.60569
$418$	163622.	0.0458036
$419$	6.79853e6	1.89182	0.945911	−	0.324427i	$-0.105171\pi$
$419$	6.79853e6	1.89182	0.945911	+	0.324427i	$0.105171\pi$
$420$	0	0
$421$	−1.77259e6	−0.487420	−0.243710	−	0.969848i	$-0.578365\pi$
$421$	−1.77259e6	−0.487420	−0.243710	+	0.969848i	$0.578365\pi$
$422$	1.58408e6	0.433008
$423$	−1.01657e6	−0.276241
$424$	−1.79522e6	−0.484957
$425$	0	0
$426$	1.41336e6	0.377337
$427$	−4.32317e6	−1.14745
$428$	2.77991e6	0.733536
$429$	1.55359e6	0.407562
$430$	0	0
$431$	1.30221e6	0.337666	0.168833	−	0.985645i	$-0.446000\pi$
$431$	1.30221e6	0.337666	0.168833	+	0.985645i	$0.446000\pi$
$432$	1.06273e6	0.273978
$433$	−2.15386e6	−0.552074	−0.276037	−	0.961147i	$-0.589021\pi$
$433$	−2.15386e6	−0.552074	−0.276037	+	0.961147i	$0.589021\pi$
$434$	7.33673e6	1.86973
$435$	0	0
$436$	−1.47089e6	−0.370564
$437$	1.58141e6	0.396133
$438$	−4.15168e6	−1.03404
$439$	−5.81916e6	−1.44112	−0.720558	−	0.693394i	$-0.756114\pi$
$439$	−5.81916e6	−1.44112	−0.720558	+	0.693394i	$0.756114\pi$
$440$	0	0
$441$	2.04927e6	0.501769
$442$	1.34722e6	0.328007
$443$	−4.34332e6	−1.05151	−0.525754	−	0.850637i	$-0.676217\pi$
$443$	−4.34332e6	−1.05151	−0.525754	+	0.850637i	$0.676217\pi$
$444$	39253.3	0.00944970
$445$	0	0
$446$	−284549.	−0.0677361
$447$	−6.86070e6	−1.62405
$448$	6.81198e6	1.60354
$449$	2.68108e6	0.627615	0.313807	−	0.949487i	$-0.398395\pi$
$449$	2.68108e6	0.627615	0.313807	+	0.949487i	$0.398395\pi$
$450$	0	0
$451$	1.58533e6	0.367010
$452$	−1.51802e6	−0.349487
$453$	−3.79584e6	−0.869086
$454$	−4.49176e6	−1.02277
$455$	0	0
$456$	1.56125e6	0.351609
$457$	4.29834e6	0.962743	0.481371	−	0.876517i	$-0.340139\pi$
$457$	4.29834e6	0.962743	0.481371	+	0.876517i	$0.340139\pi$
$458$	3.01446e6	0.671500
$459$	−981134.	−0.217369
$460$	0	0
$461$	2.28441e6	0.500636	0.250318	−	0.968164i	$-0.419465\pi$
$461$	2.28441e6	0.500636	0.250318	+	0.968164i	$0.419465\pi$
$462$	1.38081e6	0.300974
$463$	−1.51960e6	−0.329440	−0.164720	−	0.986340i	$-0.552672\pi$
$463$	−1.51960e6	−0.329440	−0.164720	+	0.986340i	$0.552672\pi$
$464$	285144.	0.0614851
$465$	0	0
$466$	5.71536e6	1.21921
$467$	4.71846e6	1.00117	0.500585	−	0.865687i	$-0.333118\pi$
$467$	4.71846e6	1.00117	0.500585	+	0.865687i	$0.333118\pi$
$468$	973488.	0.205455
$469$	2.02991e6	0.426132
$470$	0	0
$471$	−9.89151e6	−2.05452
$472$	−2.78267e6	−0.574919
$473$	177703.	0.0365210
$474$	−3.76222e6	−0.769128
$475$	0	0
$476$	−1.01422e6	−0.205170
$477$	−592824.	−0.119297
$478$	−4.63879e6	−0.928614
$479$	5.85157e6	1.16529	0.582644	−	0.812727i	$-0.302018\pi$
$479$	5.85157e6	1.16529	0.582644	+	0.812727i	$0.302018\pi$
$480$	0	0
$481$	157816.	0.0311020
$482$	6.12108e6	1.20008
$483$	1.33456e7	2.60297
$484$	2.25554e6	0.437661
$485$	0	0
$486$	1.97424e6	0.379149
$487$	−1.83575e6	−0.350745	−0.175372	−	0.984502i	$-0.556113\pi$
$487$	−1.83575e6	−0.350745	−0.175372	+	0.984502i	$0.556113\pi$
$488$	−3.80398e6	−0.723083
$489$	−8.35958e6	−1.58093
$490$	0	0
$491$	−5.75635e6	−1.07757	−0.538783	−	0.842445i	$-0.681116\pi$
$491$	−5.75635e6	−1.07757	−0.538783	+	0.842445i	$0.681116\pi$
$492$	4.75599e6	0.885784
$493$	−263250.	−0.0487811
$494$	1.97350e6	0.363848
$495$	0	0
$496$	2.70675e6	0.494019
$497$	−4.27781e6	−0.776838
$498$	1.45738e6	0.263329
$499$	4.10166e6	0.737409	0.368705	−	0.929547i	$-0.379801\pi$
$499$	4.10166e6	0.737409	0.368705	+	0.929547i	$0.379801\pi$
$500$	0	0
$501$	3.56471e6	0.634497
$502$	−1.56132e6	−0.276523
$503$	1.12157e6	0.197654	0.0988270	−	0.995105i	$-0.468491\pi$
$503$	1.12157e6	0.197654	0.0988270	+	0.995105i	$0.468491\pi$
$504$	2.75193e6	0.482570
$505$	0	0
$506$	1.23067e6	0.213681
$507$	1.22312e7	2.11325
$508$	−3.63258e6	−0.624534
$509$	−2.68902e6	−0.460045	−0.230023	−	0.973185i	$-0.573880\pi$
$509$	−2.68902e6	−0.460045	−0.230023	+	0.973185i	$0.573880\pi$
$510$	0	0
$511$	1.25659e7	2.12883
$512$	3.73721e6	0.630047
$513$	−1.43723e6	−0.241120
$514$	−1.96078e6	−0.327356
$515$	0	0
$516$	533111.	0.0881441
$517$	1.35844e6	0.223518
$518$	140264.	0.0229680
$519$	1.67212e6	0.272489
$520$	0	0
$521$	2.88911e6	0.466305	0.233152	−	0.972440i	$-0.425096\pi$
$521$	2.88911e6	0.466305	0.233152	+	0.972440i	$0.425096\pi$
$522$	224576.	0.0360735
$523$	1.40417e6	0.224474	0.112237	−	0.993681i	$-0.464198\pi$
$523$	1.40417e6	0.224474	0.112237	+	0.993681i	$0.464198\pi$
$524$	−2.91235e6	−0.463356
$525$	0	0
$526$	4.63573e6	0.730557
$527$	−2.49891e6	−0.391945
$528$	509423.	0.0795231
$529$	5.45814e6	0.848019
$530$	0	0
$531$	−918904.	−0.141428
$532$	−1.48570e6	−0.227589
$533$	1.91212e7	2.91540
$534$	−9.53169e6	−1.44650
$535$	0	0
$536$	1.78612e6	0.268534
$537$	−5.73113e6	−0.857640
$538$	1.58822e6	0.236568
$539$	−2.73843e6	−0.406003
$540$	0	0
$541$	−211154.	−0.0310174	−0.0155087	−	0.999880i	$-0.504937\pi$
$541$	−211154.	−0.0310174	−0.0155087	+	0.999880i	$0.504937\pi$
$542$	−4.53007e6	−0.662379
$543$	1.90298e6	0.276971
$544$	−1.50425e6	−0.217933
$545$	0	0
$546$	1.66545e7	2.39083
$547$	4.61571e6	0.659584	0.329792	−	0.944054i	$-0.393021\pi$
$547$	4.61571e6	0.659584	0.329792	+	0.944054i	$0.393021\pi$
$548$	2.07564e6	0.295257
$549$	−1.25616e6	−0.177875
$550$	0	0
$551$	−385627.	−0.0541113
$552$	1.17428e7	1.64031
$553$	1.13871e7	1.58343
$554$	−9.11378e6	−1.26161
$555$	0	0
$556$	4.77416e6	0.654953
$557$	−1.01209e7	−1.38223	−0.691114	−	0.722746i	$-0.742880\pi$
$557$	−1.01209e7	−1.38223	−0.691114	+	0.722746i	$0.742880\pi$
$558$	2.13180e6	0.289842
$559$	2.14335e6	0.290110
$560$	0	0
$561$	−470308.	−0.0630921
$562$	4.27525e6	0.570980
$563$	−3.84774e6	−0.511604	−0.255802	−	0.966729i	$-0.582340\pi$
$563$	−3.84774e6	−0.511604	−0.255802	+	0.966729i	$0.582340\pi$
$564$	4.07531e6	0.539465
$565$	0	0
$566$	3.70098e6	0.485597
$567$	−1.55709e7	−2.03403
$568$	−3.76406e6	−0.489538
$569$	4.38443e6	0.567718	0.283859	−	0.958866i	$-0.408385\pi$
$569$	4.38443e6	0.567718	0.283859	+	0.958866i	$0.408385\pi$
$570$	0	0
$571$	2.61241e6	0.335313	0.167656	−	0.985845i	$-0.446380\pi$
$571$	2.61241e6	0.335313	0.167656	+	0.985845i	$0.446380\pi$
$572$	−1.30086e6	−0.166242
$573$	−5.53357e6	−0.704075
$574$	1.69947e7	2.15295
$575$	0	0
$576$	1.97933e6	0.248577
$577$	7.06124e6	0.882961	0.441480	−	0.897271i	$-0.354453\pi$
$577$	7.06124e6	0.882961	0.441480	+	0.897271i	$0.354453\pi$
$578$	5.50211e6	0.685030
$579$	−726132.	−0.0900159
$580$	0	0
$581$	−4.41103e6	−0.542125
$582$	3.18082e6	0.389252
$583$	792186.	0.0965285
$584$	1.10568e7	1.34152
$585$	0	0
$586$	−2.00625e6	−0.241347
$587$	8.18957e6	0.980993	0.490496	−	0.871443i	$-0.336815\pi$
$587$	8.18957e6	0.980993	0.490496	+	0.871443i	$0.336815\pi$
$588$	−8.21528e6	−0.979894
$589$	−3.66058e6	−0.434772
$590$	0	0
$591$	−6.21710e6	−0.732182
$592$	51747.9	0.00606860
$593$	9.78828e6	1.14306	0.571531	−	0.820580i	$-0.306350\pi$
$593$	9.78828e6	1.14306	0.571531	+	0.820580i	$0.306350\pi$
$594$	−1.11847e6	−0.130065
$595$	0	0
$596$	5.74465e6	0.662442
$597$	−1.66343e7	−1.91015
$598$	1.48436e7	1.69741
$599$	4.44247e6	0.505892	0.252946	−	0.967480i	$-0.418600\pi$
$599$	4.44247e6	0.505892	0.252946	+	0.967480i	$0.418600\pi$
$600$	0	0
$601$	248973.	0.0281168	0.0140584	−	0.999901i	$-0.495525\pi$
$601$	248973.	0.0281168	0.0140584	+	0.999901i	$0.495525\pi$
$602$	1.90498e6	0.214239
$603$	589821.	0.0660582
$604$	3.17836e6	0.354495
$605$	0	0
$606$	4.13517e6	0.457417
$607$	5.61487e6	0.618540	0.309270	−	0.950974i	$-0.399915\pi$
$607$	5.61487e6	0.618540	0.309270	+	0.950974i	$0.399915\pi$
$608$	−2.20353e6	−0.241747
$609$	−3.25432e6	−0.355563
$610$	0	0
$611$	1.63846e7	1.77555
$612$	−294697.	−0.0318051
$613$	−7.11213e6	−0.764449	−0.382225	−	0.924069i	$-0.624842\pi$
$613$	−7.11213e6	−0.764449	−0.382225	+	0.924069i	$0.624842\pi$
$614$	953834.	0.102106
$615$	0	0
$616$	−3.67737e6	−0.390468
$617$	−872669.	−0.0922862	−0.0461431	−	0.998935i	$-0.514693\pi$
$617$	−872669.	−0.0922862	−0.0461431	+	0.998935i	$0.514693\pi$
$618$	−8.13014e6	−0.856301
$619$	−9.40244e6	−0.986312	−0.493156	−	0.869941i	$-0.664157\pi$
$619$	−9.40244e6	−0.986312	−0.493156	+	0.869941i	$0.664157\pi$
$620$	0	0
$621$	−1.08101e7	−1.12486
$622$	−1.03934e7	−1.07716
$623$	2.88495e7	2.97796
$624$	6.14434e6	0.631704
$625$	0	0
$626$	−1.15760e7	−1.18065
$627$	−688939.	−0.0699861
$628$	8.28242e6	0.838027
$629$	−47774.5	−0.00481470
$630$	0	0
$631$	−1.90990e7	−1.90957	−0.954786	−	0.297293i	$-0.903916\pi$
$631$	−1.90990e7	−1.90957	−0.954786	+	0.297293i	$0.903916\pi$
$632$	1.00196e7	0.997829
$633$	−6.66987e6	−0.661619
$634$	8.09056e6	0.799384
$635$	0	0
$636$	2.37656e6	0.232973
$637$	−3.30292e7	−3.22515
$638$	−300099.	−0.0291886
$639$	−1.24298e6	−0.120424
$640$	0	0
$641$	−4.06757e6	−0.391012	−0.195506	−	0.980703i	$-0.562635\pi$
$641$	−4.06757e6	−0.391012	−0.195506	+	0.980703i	$0.562635\pi$
$642$	1.38189e7	1.32324
$643$	1.00899e6	0.0962410	0.0481205	−	0.998842i	$-0.484677\pi$
$643$	1.00899e6	0.0962410	0.0481205	+	0.998842i	$0.484677\pi$
$644$	−1.11746e7	−1.06174
$645$	0	0
$646$	−597424.	−0.0563250
$647$	−1.99986e7	−1.87819	−0.939095	−	0.343657i	$-0.888334\pi$
$647$	−1.99986e7	−1.87819	−0.939095	+	0.343657i	$0.888334\pi$
$648$	−1.37010e7	−1.28178
$649$	1.22792e6	0.114435
$650$	0	0
$651$	−3.08918e7	−2.85687
$652$	6.99970e6	0.644852
$653$	1.16599e7	1.07007	0.535035	−	0.844830i	$-0.320298\pi$
$653$	1.16599e7	1.07007	0.535035	+	0.844830i	$0.320298\pi$
$654$	−7.31179e6	−0.668466
$655$	0	0
$656$	6.26986e6	0.568850
$657$	3.65121e6	0.330007
$658$	1.45624e7	1.31120
$659$	1.40204e7	1.25761	0.628806	−	0.777562i	$-0.283544\pi$
$659$	1.40204e7	1.25761	0.628806	+	0.777562i	$0.283544\pi$
$660$	0	0
$661$	5.39932e6	0.480657	0.240328	−	0.970692i	$-0.422745\pi$
$661$	5.39932e6	0.480657	0.240328	+	0.970692i	$0.422745\pi$
$662$	251594.	0.0223128
$663$	−5.67256e6	−0.501182
$664$	−3.88129e6	−0.341630
$665$	0	0
$666$	40756.0	0.00356046
$667$	−2.90047e6	−0.252438
$668$	−2.98482e6	−0.258808
$669$	1.19811e6	0.103498
$670$	0	0
$671$	1.67860e6	0.143926
$672$	−1.85957e7	−1.58851
$673$	−2.37236e6	−0.201903	−0.100951	−	0.994891i	$-0.532189\pi$
$673$	−2.37236e6	−0.201903	−0.100951	+	0.994891i	$0.532189\pi$
$674$	−7.20082e6	−0.610565
$675$	0	0
$676$	−1.02415e7	−0.861983
$677$	−1.48279e7	−1.24339	−0.621695	−	0.783260i	$-0.713556\pi$
$677$	−1.48279e7	−1.24339	−0.621695	+	0.783260i	$0.713556\pi$
$678$	−7.54607e6	−0.630444
$679$	−9.62736e6	−0.801369
$680$	0	0
$681$	1.89128e7	1.56275
$682$	−2.84871e6	−0.234524
$683$	1.45710e7	1.19519	0.597594	−	0.801799i	$-0.296123\pi$
$683$	1.45710e7	1.19519	0.597594	+	0.801799i	$0.296123\pi$
$684$	−431692.	−0.0352805
$685$	0	0
$686$	−1.39099e7	−1.12853
$687$	−1.26926e7	−1.02603
$688$	702804.	0.0566061
$689$	9.55485e6	0.766789
$690$	0	0
$691$	−2.39101e6	−0.190496	−0.0952480	−	0.995454i	$-0.530364\pi$
$691$	−2.39101e6	−0.190496	−0.0952480	+	0.995454i	$0.530364\pi$
$692$	−1.40011e6	−0.111147
$693$	−1.21436e6	−0.0960534
$694$	4.89773e6	0.386008
$695$	0	0
$696$	−2.86349e6	−0.224065
$697$	−5.78844e6	−0.451315
$698$	−5.03198e6	−0.390932
$699$	−2.40649e7	−1.86291
$700$	0	0
$701$	−2.67685e6	−0.205745	−0.102872	−	0.994695i	$-0.532803\pi$
$701$	−2.67685e6	−0.205745	−0.102872	+	0.994695i	$0.532803\pi$
$702$	−1.34903e7	−1.03319
$703$	−69983.4	−0.00534080
$704$	−2.64496e6	−0.201135
$705$	0	0
$706$	4.19246e6	0.316561
$707$	−1.25159e7	−0.941701
$708$	3.68377e6	0.276191
$709$	1.61177e7	1.20417	0.602085	−	0.798432i	$-0.294337\pi$
$709$	1.61177e7	1.20417	0.602085	+	0.798432i	$0.294337\pi$
$710$	0	0
$711$	3.30870e6	0.245461
$712$	2.53848e7	1.87661
$713$	−2.75329e7	−2.02828
$714$	−5.04168e6	−0.370109
$715$	0	0
$716$	4.79883e6	0.349826
$717$	1.95319e7	1.41888
$718$	−4.58463e6	−0.331889
$719$	2.74012e7	1.97673	0.988363	−	0.152111i	$-0.0486070\pi$
$719$	2.74012e7	1.97673	0.988363	+	0.152111i	$0.0486070\pi$
$720$	0	0
$721$	2.46074e7	1.76290
$722$	9.43124e6	0.673327
$723$	−2.57732e7	−1.83367
$724$	−1.59341e6	−0.112975
$725$	0	0
$726$	1.12123e7	0.789503
$727$	1.44905e7	1.01683	0.508413	−	0.861113i	$-0.330232\pi$
$727$	1.44905e7	1.01683	0.508413	+	0.861113i	$0.330232\pi$
$728$	−4.43542e7	−3.10175
$729$	8.82438e6	0.614986
$730$	0	0
$731$	−648840.	−0.0449101
$732$	5.03580e6	0.347369
$733$	−9.24243e6	−0.635370	−0.317685	−	0.948196i	$-0.602905\pi$
$733$	−9.24243e6	−0.635370	−0.317685	+	0.948196i	$0.602905\pi$
$734$	1.24574e7	0.853470
$735$	0	0
$736$	−1.65737e7	−1.12778
$737$	−788172.	−0.0534505
$738$	4.93807e6	0.333746
$739$	−270924.	−0.0182489	−0.00912445	−	0.999958i	$-0.502904\pi$
$739$	−270924.	−0.0182489	−0.00912445	+	0.999958i	$0.502904\pi$
$740$	0	0
$741$	−8.30955e6	−0.555945
$742$	8.49221e6	0.566253
$743$	−1.56128e7	−1.03755	−0.518776	−	0.854910i	$-0.673612\pi$
$743$	−1.56128e7	−1.03755	−0.518776	+	0.854910i	$0.673612\pi$
$744$	−2.71818e7	−1.80031
$745$	0	0
$746$	1.76141e7	1.15882
$747$	−1.28169e6	−0.0840394
$748$	393801.	0.0257349
$749$	−4.18257e7	−2.72420
$750$	0	0
$751$	2.81796e6	0.182320	0.0911600	−	0.995836i	$-0.470943\pi$
$751$	2.81796e6	0.182320	0.0911600	+	0.995836i	$0.470943\pi$
$752$	5.37251e6	0.346444
$753$	6.57403e6	0.422517
$754$	−3.61961e6	−0.231864
$755$	0	0
$756$	1.01558e7	0.646264
$757$	−1.47622e6	−0.0936293	−0.0468146	−	0.998904i	$-0.514907\pi$
$757$	−1.47622e6	−0.0936293	−0.0468146	+	0.998904i	$0.514907\pi$
$758$	−4.42325e6	−0.279620
$759$	−5.18182e6	−0.326496
$760$	0	0
$761$	−1.59710e7	−0.999700	−0.499850	−	0.866112i	$-0.666612\pi$
$761$	−1.59710e7	−0.999700	−0.499850	+	0.866112i	$0.666612\pi$
$762$	−1.80576e7	−1.12660
$763$	2.21305e7	1.37620
$764$	4.63340e6	0.287188
$765$	0	0
$766$	−1.56394e7	−0.963051
$767$	1.48104e7	0.909033
$768$	−1.91529e7	−1.17174
$769$	−2.69038e7	−1.64058	−0.820291	−	0.571947i	$-0.806188\pi$
$769$	−2.69038e7	−1.64058	−0.820291	+	0.571947i	$0.806188\pi$
$770$	0	0
$771$	8.25597e6	0.500187
$772$	608009.	0.0367170
$773$	−2.10506e7	−1.26711	−0.633556	−	0.773697i	$-0.718405\pi$
$773$	−2.10506e7	−1.26711	−0.633556	+	0.773697i	$0.718405\pi$
$774$	553520.	0.0332109
$775$	0	0
$776$	−8.47116e6	−0.504997
$777$	−590592.	−0.0350942
$778$	1.61732e7	0.957962
$779$	−8.47930e6	−0.500629
$780$	0	0
$781$	1.66099e6	0.0974403
$782$	−4.49349e6	−0.262765
$783$	2.63604e6	0.153655
$784$	−1.08303e7	−0.629288
$785$	0	0
$786$	−1.44773e7	−0.835854
$787$	1.46428e7	0.842728	0.421364	−	0.906892i	$-0.361552\pi$
$787$	1.46428e7	0.842728	0.421364	+	0.906892i	$0.361552\pi$
$788$	5.20574e6	0.298653
$789$	−1.95190e7	−1.11626
$790$	0	0
$791$	2.28396e7	1.29792
$792$	−1.06852e6	−0.0605297
$793$	2.02462e7	1.14330
$794$	2.99496e6	0.168593
$795$	0	0
$796$	1.39283e7	0.779141
$797$	1.53622e7	0.856660	0.428330	−	0.903622i	$-0.359102\pi$
$797$	1.53622e7	0.856660	0.428330	+	0.903622i	$0.359102\pi$
$798$	−7.38540e6	−0.410551
$799$	−4.96000e6	−0.274862
$800$	0	0
$801$	8.38267e6	0.461638
$802$	6.55651e6	0.359945
$803$	−4.87907e6	−0.267023
$804$	−2.36452e6	−0.129004
$805$	0	0
$806$	−3.43593e7	−1.86298
$807$	−6.68730e6	−0.361466
$808$	−1.10128e7	−0.593430
$809$	−7.26215e6	−0.390116	−0.195058	−	0.980792i	$-0.562490\pi$
$809$	−7.26215e6	−0.390116	−0.195058	+	0.980792i	$0.562490\pi$
$810$	0	0
$811$	4.17728e6	0.223019	0.111510	−	0.993763i	$-0.464431\pi$
$811$	4.17728e6	0.223019	0.111510	+	0.993763i	$0.464431\pi$
$812$	2.72493e6	0.145032
$813$	1.90741e7	1.01209
$814$	−54461.9	−0.00288092
$815$	0	0
$816$	−1.86003e6	−0.0977901
$817$	−950466.	−0.0498174
$818$	1.39586e7	0.729390
$819$	−1.46468e7	−0.763015
$820$	0	0
$821$	2.70285e7	1.39947	0.699736	−	0.714402i	$-0.253301\pi$
$821$	2.70285e7	1.39947	0.699736	+	0.714402i	$0.253301\pi$
$822$	1.03180e7	0.532619
$823$	6.95032e6	0.357689	0.178844	−	0.983877i	$-0.442764\pi$
$823$	6.95032e6	0.357689	0.178844	+	0.983877i	$0.442764\pi$
$824$	2.16522e7	1.11092
$825$	0	0
$826$	1.31633e7	0.671297
$827$	370060.	0.0188152	0.00940759	−	0.999956i	$-0.497005\pi$
$827$	370060.	0.0188152	0.00940759	+	0.999956i	$0.497005\pi$
$828$	−3.24695e6	−0.164589
$829$	1.38451e7	0.699698	0.349849	−	0.936806i	$-0.386233\pi$
$829$	1.38451e7	0.699698	0.349849	+	0.936806i	$0.386233\pi$
$830$	0	0
$831$	3.83741e7	1.92768
$832$	−3.19018e7	−1.59774
$833$	9.99869e6	0.499264
$834$	2.37324e7	1.18148
$835$	0	0
$836$	576867.	0.0285469
$837$	2.50227e7	1.23458
$838$	−2.82979e7	−1.39201
$839$	1.86174e7	0.913089	0.456544	−	0.889701i	$-0.349087\pi$
$839$	1.86174e7	0.913089	0.456544	+	0.889701i	$0.349087\pi$
$840$	0	0
$841$	707281.	0.0344828
$842$	7.37815e6	0.358647
$843$	−1.80012e7	−0.872435
$844$	5.58486e6	0.269871
$845$	0	0
$846$	4.23133e6	0.203260
$847$	−3.39362e7	−1.62538
$848$	3.13304e6	0.149615
$849$	−1.55832e7	−0.741972
$850$	0	0
$851$	−526376.	−0.0249157
$852$	4.98296e6	0.235174
$853$	−2.15389e6	−0.101356	−0.0506782	−	0.998715i	$-0.516138\pi$
$853$	−2.15389e6	−0.101356	−0.0506782	+	0.998715i	$0.516138\pi$
$854$	1.79945e7	0.844298
$855$	0	0
$856$	−3.68026e7	−1.71670
$857$	3.33513e7	1.55118	0.775588	−	0.631239i	$-0.217453\pi$
$857$	3.33513e7	1.55118	0.775588	+	0.631239i	$0.217453\pi$
$858$	−6.46659e6	−0.299887
$859$	−3.11061e7	−1.43834	−0.719171	−	0.694833i	$-0.755478\pi$
$859$	−3.11061e7	−1.43834	−0.719171	+	0.694833i	$0.755478\pi$
$860$	0	0
$861$	−7.15571e7	−3.28961
$862$	−5.42025e6	−0.248457
$863$	1.59387e7	0.728494	0.364247	−	0.931302i	$-0.381326\pi$
$863$	1.59387e7	0.728494	0.364247	+	0.931302i	$0.381326\pi$
$864$	1.50627e7	0.686467
$865$	0	0
$866$	8.96511e6	0.406220
$867$	−2.31670e7	−1.04670
$868$	2.58665e7	1.16530
$869$	−4.42138e6	−0.198613
$870$	0	0
$871$	−9.50644e6	−0.424593
$872$	1.94728e7	0.867235
$873$	−2.79738e6	−0.124227
$874$	−6.58238e6	−0.291477
$875$	0	0
$876$	−1.46372e7	−0.644464
$877$	−666578.	−0.0292652	−0.0146326	−	0.999893i	$-0.504658\pi$
$877$	−666578.	−0.0292652	−0.0146326	+	0.999893i	$0.504658\pi$
$878$	2.42214e7	1.06038
$879$	8.44745e6	0.368768
$880$	0	0
$881$	−2.30910e7	−1.00231	−0.501155	−	0.865358i	$-0.667091\pi$
$881$	−2.30910e7	−1.00231	−0.501155	+	0.865358i	$0.667091\pi$
$882$	−8.52980e6	−0.369205
$883$	−3.85060e6	−0.166198	−0.0830992	−	0.996541i	$-0.526482\pi$
$883$	−3.85060e6	−0.166198	−0.0830992	+	0.996541i	$0.526482\pi$
$884$	4.74978e6	0.204429
$885$	0	0
$886$	1.80784e7	0.773706
$887$	4.14426e7	1.76863	0.884316	−	0.466889i	$-0.154625\pi$
$887$	4.14426e7	1.76863	0.884316	+	0.466889i	$0.154625\pi$
$888$	−519665.	−0.0221152
$889$	5.46547e7	2.31939
$890$	0	0
$891$	6.04589e6	0.255133
$892$	−1.00321e6	−0.0422163
$893$	−7.26574e6	−0.304896
$894$	2.85566e7	1.19499
$895$	0	0
$896$	5.59955e6	0.233015
$897$	−6.24999e7	−2.59357
$898$	−1.11596e7	−0.461803
$899$	6.71389e6	0.277061
$900$	0	0
$901$	−2.89247e6	−0.118702
$902$	−6.59869e6	−0.270048
$903$	−8.02102e6	−0.327348
$904$	2.00967e7	0.817907
$905$	0	0
$906$	1.57996e7	0.639479
$907$	4.63163e7	1.86946	0.934729	−	0.355363i	$-0.115643\pi$
$907$	4.63163e7	1.86946	0.934729	+	0.355363i	$0.115643\pi$
$908$	−1.58362e7	−0.637436
$909$	−3.63669e6	−0.145981
$910$	0	0
$911$	2.69515e6	0.107594	0.0537969	−	0.998552i	$-0.482868\pi$
$911$	2.69515e6	0.107594	0.0537969	+	0.998552i	$0.482868\pi$
$912$	−2.72470e6	−0.108476
$913$	1.71272e6	0.0679999
$914$	−1.78912e7	−0.708392
$915$	0	0
$916$	1.06278e7	0.418510
$917$	4.38183e7	1.72081
$918$	4.08383e6	0.159941
$919$	1.39792e7	0.546000	0.273000	−	0.962014i	$-0.411984\pi$
$919$	1.39792e7	0.546000	0.273000	+	0.962014i	$0.411984\pi$
$920$	0	0
$921$	−4.01618e6	−0.156014
$922$	−9.50852e6	−0.368371
$923$	2.00338e7	0.774032
$924$	4.86820e6	0.187581
$925$	0	0
$926$	6.32510e6	0.242404
$927$	7.15007e6	0.273282
$928$	4.04151e6	0.154054
$929$	−7.25580e6	−0.275833	−0.137916	−	0.990444i	$-0.544041\pi$
$929$	−7.25580e6	−0.275833	−0.137916	+	0.990444i	$0.544041\pi$
$930$	0	0
$931$	1.46468e7	0.553819
$932$	2.01502e7	0.759869
$933$	4.37619e7	1.64586
$934$	−1.96399e7	−0.736667
$935$	0	0
$936$	−1.28878e7	−0.480827
$937$	−3.95850e6	−0.147293	−0.0736464	−	0.997284i	$-0.523464\pi$
$937$	−3.95850e6	−0.147293	−0.0736464	+	0.997284i	$0.523464\pi$
$938$	−8.44918e6	−0.313550
$939$	4.87413e7	1.80399
$940$	0	0
$941$	−4.07672e7	−1.50085	−0.750425	−	0.660956i	$-0.770151\pi$
$941$	−4.07672e7	−1.50085	−0.750425	+	0.660956i	$0.770151\pi$
$942$	4.11719e7	1.51173
$943$	−6.37766e7	−2.33551
$944$	4.85635e6	0.177370
$945$	0	0
$946$	−739664.	−0.0268724
$947$	2.67878e7	0.970650	0.485325	−	0.874334i	$-0.338701\pi$
$947$	2.67878e7	0.970650	0.485325	+	0.874334i	$0.338701\pi$
$948$	−1.32641e7	−0.479356
$949$	−5.88484e7	−2.12114
$950$	0	0
$951$	−3.40658e7	−1.22143
$952$	1.34270e7	0.480162
$953$	1.81430e7	0.647107	0.323553	−	0.946210i	$-0.395123\pi$
$953$	1.81430e7	0.647107	0.323553	+	0.946210i	$0.395123\pi$
$954$	2.46754e6	0.0877796
$955$	0	0
$956$	−1.63546e7	−0.578755
$957$	1.26359e6	0.0445990
$958$	−2.43563e7	−0.857427
$959$	−3.12294e7	−1.09652
$960$	0	0
$961$	3.51028e7	1.22612
$962$	−656886.	−0.0228851
$963$	−1.21531e7	−0.422300
$964$	2.15806e7	0.747946
$965$	0	0
$966$	−5.55489e7	−1.91528
$967$	1.40529e7	0.483282	0.241641	−	0.970366i	$-0.422314\pi$
$967$	1.40529e7	0.483282	0.241641	+	0.970366i	$0.422314\pi$
$968$	−2.98607e7	−1.02426
$969$	2.51549e6	0.0860624
$970$	0	0
$971$	1.77622e7	0.604573	0.302287	−	0.953217i	$-0.402250\pi$
$971$	1.77622e7	0.604573	0.302287	+	0.953217i	$0.402250\pi$
$972$	6.96041e6	0.236303
$973$	−7.18306e7	−2.43236
$974$	7.64103e6	0.258080
$975$	0	0
$976$	6.63873e6	0.223080
$977$	1.66625e7	0.558474	0.279237	−	0.960222i	$-0.409918\pi$
$977$	1.66625e7	0.558474	0.279237	+	0.960222i	$0.409918\pi$
$978$	3.47955e7	1.16326
$979$	−1.12017e7	−0.373531
$980$	0	0
$981$	6.43037e6	0.213336
$982$	2.39600e7	0.792880
$983$	2.28571e7	0.754461	0.377231	−	0.926119i	$-0.376876\pi$
$983$	2.28571e7	0.754461	0.377231	+	0.926119i	$0.376876\pi$
$984$	−6.29635e7	−2.07301
$985$	0	0
$986$	1.09574e6	0.0358934
$987$	−6.13159e7	−2.00346
$988$	6.95781e6	0.226767
$989$	−7.14888e6	−0.232406
$990$	0	0
$991$	−2.52864e7	−0.817904	−0.408952	−	0.912556i	$-0.634106\pi$
$991$	−2.52864e7	−0.817904	−0.408952	+	0.912556i	$0.634106\pi$
$992$	3.83642e7	1.23779
$993$	−1.05935e6	−0.0340931
$994$	1.78057e7	0.571602
$995$	0	0
$996$	5.13815e6	0.164119
$997$	−4.44014e7	−1.41468	−0.707340	−	0.706873i	$-0.750105\pi$
$997$	−4.44014e7	−1.41468	−0.707340	+	0.706873i	$0.750105\pi$
$998$	−1.70726e7	−0.542590
$999$	478387.	0.0151658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.6.a.a.1.2		4
5.4	even	2		29.6.a.a.1.3	✓	4
15.14	odd	2		261.6.a.a.1.2		4
20.19	odd	2		464.6.a.i.1.3		4
145.144	even	2		841.6.a.a.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.a.1.3	✓	4	5.4	even	2
261.6.a.a.1.2		4	15.14	odd	2
464.6.a.i.1.3		4	20.19	odd	2
725.6.a.a.1.2		4	1.1	even	1	trivial
841.6.a.a.1.2		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)

\(f(q)\)	\(=\)	\(q-4.16235 q^{2} +17.5258 q^{3} -14.6748 q^{4} -72.9487 q^{6} +220.793 q^{7} +194.277 q^{8} +64.1549 q^{9} +O(q^{10})\)	\(q-4.16235 q^{2} +17.5258 q^{3} -14.6748 q^{4} -72.9487 q^{6} +220.793 q^{7} +194.277 q^{8} +64.1549 q^{9} -85.7296 q^{11} -257.189 q^{12} -1034.02 q^{13} -919.018 q^{14} -339.054 q^{16} +313.020 q^{17} -267.035 q^{18} +458.534 q^{19} +3869.58 q^{21} +356.836 q^{22} +3448.84 q^{23} +3404.87 q^{24} +4303.94 q^{26} -3134.41 q^{27} -3240.10 q^{28} -841.000 q^{29} -7983.23 q^{31} -4805.60 q^{32} -1502.48 q^{33} -1302.90 q^{34} -941.463 q^{36} -152.624 q^{37} -1908.58 q^{38} -18122.0 q^{39} -18492.2 q^{41} -16106.6 q^{42} -2072.84 q^{43} +1258.07 q^{44} -14355.3 q^{46} -15845.6 q^{47} -5942.21 q^{48} +31942.6 q^{49} +5485.94 q^{51} +15174.0 q^{52} -9240.52 q^{53} +13046.5 q^{54} +42895.0 q^{56} +8036.19 q^{57} +3500.54 q^{58} -14323.2 q^{59} -19580.2 q^{61} +33229.0 q^{62} +14165.0 q^{63} +30852.3 q^{64} +6253.86 q^{66} +9193.70 q^{67} -4593.53 q^{68} +60443.8 q^{69} -19374.7 q^{71} +12463.8 q^{72} +56912.4 q^{73} +635.276 q^{74} -6728.91 q^{76} -18928.5 q^{77} +75430.1 q^{78} +51573.6 q^{79} -70522.8 q^{81} +76971.0 q^{82} -19978.1 q^{83} -56785.5 q^{84} +8627.87 q^{86} -14739.2 q^{87} -16655.3 q^{88} +130663. q^{89} -228304. q^{91} -50611.1 q^{92} -139913. q^{93} +65954.9 q^{94} -84222.2 q^{96} -43603.5 q^{97} -132956. q^{98} -5499.97 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 28 q^{3} + 10 q^{4} - 194 q^{6} + 208 q^{7} + 504 q^{8} - 280 q^{9}+O(q^{10}) \) 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

Introduction

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Varieties

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Database

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