LMFDB - Embedded newform 130.6.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,6,Mod(1,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, 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("130.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	130.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:	$20.8498965757$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.1458804.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 361x - 1139 $ x^3 - x^2 - 361*x - 1139
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$20.8905$ of defining polynomial
Character	$\chi$	$=$	130.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -27.8905 q^{3} +16.0000 q^{4} +25.0000 q^{5} +111.562 q^{6} -240.426 q^{7} -64.0000 q^{8} +534.880 q^{9} -100.000 q^{10} +544.151 q^{11} -446.248 q^{12} +169.000 q^{13} +961.702 q^{14} -697.262 q^{15} +256.000 q^{16} +1629.30 q^{17} -2139.52 q^{18} -805.920 q^{19} +400.000 q^{20} +6705.59 q^{21} -2176.61 q^{22} +373.152 q^{23} +1784.99 q^{24} +625.000 q^{25} -676.000 q^{26} -8140.67 q^{27} -3846.81 q^{28} +1503.62 q^{29} +2789.05 q^{30} -2200.08 q^{31} -1024.00 q^{32} -15176.7 q^{33} -6517.20 q^{34} -6010.64 q^{35} +8558.08 q^{36} -13109.1 q^{37} +3223.68 q^{38} -4713.49 q^{39} -1600.00 q^{40} -17099.9 q^{41} -26822.4 q^{42} -8935.58 q^{43} +8706.42 q^{44} +13372.0 q^{45} -1492.61 q^{46} +15749.7 q^{47} -7139.97 q^{48} +40997.5 q^{49} -2500.00 q^{50} -45442.0 q^{51} +2704.00 q^{52} +40379.7 q^{53} +32562.7 q^{54} +13603.8 q^{55} +15387.2 q^{56} +22477.5 q^{57} -6014.46 q^{58} -47562.1 q^{59} -11156.2 q^{60} -30280.0 q^{61} +8800.31 q^{62} -128599. q^{63} +4096.00 q^{64} +4225.00 q^{65} +60706.6 q^{66} +38769.4 q^{67} +26068.8 q^{68} -10407.4 q^{69} +24042.6 q^{70} -10519.7 q^{71} -34232.3 q^{72} +1582.12 q^{73} +52436.5 q^{74} -17431.6 q^{75} -12894.7 q^{76} -130828. q^{77} +18854.0 q^{78} -6191.23 q^{79} +6400.00 q^{80} +97071.7 q^{81} +68399.8 q^{82} +37849.2 q^{83} +107289. q^{84} +40732.5 q^{85} +35742.3 q^{86} -41936.6 q^{87} -34825.7 q^{88} +49151.0 q^{89} -53488.0 q^{90} -40631.9 q^{91} +5970.43 q^{92} +61361.3 q^{93} -62999.0 q^{94} -20148.0 q^{95} +28559.9 q^{96} -15654.2 q^{97} -163990. q^{98} +291056. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 12 q^{2} - 22 q^{3} + 48 q^{4} + 75 q^{5} + 88 q^{6} - 234 q^{7} - 192 q^{8} + 155 q^{9} - 300 q^{10} + 48 q^{11} - 352 q^{12} + 507 q^{13} + 936 q^{14} - 550 q^{15} + 768 q^{16} + 1506 q^{17} - 620 q^{18}+ \cdots + 350340 q^{99}+O(q^{100}) $ 3 * q - 12 * q^2 - 22 * q^3 + 48 * q^4 + 75 * q^5 + 88 * q^6 - 234 * q^7 - 192 * q^8 + 155 * q^9 - 300 * q^10 + 48 * q^11 - 352 * q^12 + 507 * q^13 + 936 * q^14 - 550 * q^15 + 768 * q^16 + 1506 * q^17 - 620 * q^18 - 360 * q^19 + 1200 * q^20 + 6904 * q^21 - 192 * q^22 - 2370 * q^23 + 1408 * q^24 + 1875 * q^25 - 2028 * q^26 - 10168 * q^27 - 3744 * q^28 - 3078 * q^29 + 2200 * q^30 - 5388 * q^31 - 3072 * q^32 - 22572 * q^33 - 6024 * q^34 - 5850 * q^35 + 2480 * q^36 - 25362 * q^37 + 1440 * q^38 - 3718 * q^39 - 4800 * q^40 - 15906 * q^41 - 27616 * q^42 - 39306 * q^43 + 768 * q^44 + 3875 * q^45 + 9480 * q^46 - 17778 * q^47 - 5632 * q^48 + 7767 * q^49 - 7500 * q^50 - 33972 * q^51 + 8112 * q^52 + 9246 * q^53 + 40672 * q^54 + 1200 * q^55 + 14976 * q^56 - 2996 * q^57 + 12312 * q^58 - 77760 * q^59 - 8800 * q^60 + 17982 * q^61 + 21552 * q^62 - 128762 * q^63 + 12288 * q^64 + 12675 * q^65 + 90288 * q^66 - 2922 * q^67 + 24096 * q^68 - 31860 * q^69 + 23400 * q^70 - 4944 * q^71 - 9920 * q^72 + 43278 * q^73 + 101448 * q^74 - 13750 * q^75 - 5760 * q^76 - 144420 * q^77 + 14872 * q^78 + 42120 * q^79 + 19200 * q^80 + 146519 * q^81 + 63624 * q^82 + 58098 * q^83 + 110464 * q^84 + 37650 * q^85 + 157224 * q^86 + 2016 * q^87 - 3072 * q^88 + 19614 * q^89 - 15500 * q^90 - 39546 * q^91 - 37920 * q^92 + 162796 * q^93 + 71112 * q^94 - 9000 * q^95 + 22528 * q^96 - 87078 * q^97 - 31068 * q^98 + 350340 * q^99

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−27.8905	−1.78918	−0.894588	−	0.446892i	$-0.852531\pi$
$3$	−27.8905	−1.78918	−0.894588	+	0.446892i	$0.852531\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	111.562	1.26514
$7$	−240.426	−1.85454	−0.927269	−	0.374397i	$-0.877850\pi$
$7$	−240.426	−1.85454	−0.927269	+	0.374397i	$0.877850\pi$
$8$	−64.0000	−0.353553
$9$	534.880	2.20115
$10$	−100.000	−0.316228
$11$	544.151	1.35593	0.677966	−	0.735093i	$-0.262862\pi$
$11$	544.151	1.35593	0.677966	+	0.735093i	$0.262862\pi$
$12$	−446.248	−0.894588
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	961.702	1.31136
$15$	−697.262	−0.800144
$16$	256.000	0.250000
$17$	1629.30	1.36735	0.683673	−	0.729788i	$-0.260381\pi$
$17$	1629.30	1.36735	0.683673	+	0.729788i	$0.260381\pi$
$18$	−2139.52	−1.55645
$19$	−805.920	−0.512162	−0.256081	−	0.966655i	$-0.582431\pi$
$19$	−805.920	−0.512162	−0.256081	+	0.966655i	$0.582431\pi$
$20$	400.000	0.223607
$21$	6705.59	3.31809
$22$	−2176.61	−0.958789
$23$	373.152	0.147084	0.0735421	−	0.997292i	$-0.476570\pi$
$23$	373.152	0.147084	0.0735421	+	0.997292i	$0.476570\pi$
$24$	1784.99	0.632569
$25$	625.000	0.200000
$26$	−676.000	−0.196116
$27$	−8140.67	−2.14907
$28$	−3846.81	−0.927269
$29$	1503.62	0.332003	0.166001	−	0.986126i	$-0.446914\pi$
$29$	1503.62	0.332003	0.166001	+	0.986126i	$0.446914\pi$
$30$	2789.05	0.565787
$31$	−2200.08	−0.411182	−0.205591	−	0.978638i	$-0.565912\pi$
$31$	−2200.08	−0.411182	−0.205591	+	0.978638i	$0.565912\pi$
$32$	−1024.00	−0.176777
$33$	−15176.7	−2.42600
$34$	−6517.20	−0.966860
$35$	−6010.64	−0.829374
$36$	8558.08	1.10058
$37$	−13109.1	−1.57423	−0.787117	−	0.616804i	$-0.788427\pi$
$37$	−13109.1	−1.57423	−0.787117	+	0.616804i	$0.788427\pi$
$38$	3223.68	0.362154
$39$	−4713.49	−0.496228
$40$	−1600.00	−0.158114
$41$	−17099.9	−1.58867	−0.794337	−	0.607477i	$-0.792182\pi$
$41$	−17099.9	−1.58867	−0.794337	+	0.607477i	$0.792182\pi$
$42$	−26822.4	−2.34625
$43$	−8935.58	−0.736973	−0.368487	−	0.929633i	$-0.620124\pi$
$43$	−8935.58	−0.736973	−0.368487	+	0.929633i	$0.620124\pi$
$44$	8706.42	0.677966
$45$	13372.0	0.984385
$46$	−1492.61	−0.104004
$47$	15749.7	1.03999	0.519995	−	0.854170i	$-0.325934\pi$
$47$	15749.7	1.03999	0.519995	+	0.854170i	$0.325934\pi$
$48$	−7139.97	−0.447294
$49$	40997.5	2.43931
$50$	−2500.00	−0.141421
$51$	−45442.0	−2.44642
$52$	2704.00	0.138675
$53$	40379.7	1.97457	0.987286	−	0.158951i	$-0.0508112\pi$
$53$	40379.7	1.97457	0.987286	+	0.158951i	$0.0508112\pi$
$54$	32562.7	1.51962
$55$	13603.8	0.606391
$56$	15387.2	0.655678
$57$	22477.5	0.916349
$58$	−6014.46	−0.234761
$59$	−47562.1	−1.77881	−0.889407	−	0.457116i	$-0.848882\pi$
$59$	−47562.1	−1.77881	−0.889407	+	0.457116i	$0.848882\pi$
$60$	−11156.2	−0.400072
$61$	−30280.0	−1.04191	−0.520956	−	0.853584i	$-0.674424\pi$
$61$	−30280.0	−1.04191	−0.520956	+	0.853584i	$0.674424\pi$
$62$	8800.31	0.290749
$63$	−128599.	−4.08212
$64$	4096.00	0.125000
$65$	4225.00	0.124035
$66$	60706.6	1.71544
$67$	38769.4	1.05512	0.527561	−	0.849517i	$-0.323107\pi$
$67$	38769.4	1.05512	0.527561	+	0.849517i	$0.323107\pi$
$68$	26068.8	0.683673
$69$	−10407.4	−0.263160
$70$	24042.6	0.586456
$71$	−10519.7	−0.247660	−0.123830	−	0.992303i	$-0.539518\pi$
$71$	−10519.7	−0.247660	−0.123830	+	0.992303i	$0.539518\pi$
$72$	−34232.3	−0.778225
$73$	1582.12	0.0347483	0.0173742	−	0.999849i	$-0.494469\pi$
$73$	1582.12	0.0347483	0.0173742	+	0.999849i	$0.494469\pi$
$74$	52436.5	1.11315
$75$	−17431.6	−0.357835
$76$	−12894.7	−0.256081
$77$	−130828.	−2.51463
$78$	18854.0	0.350886
$79$	−6191.23	−0.111612	−0.0558058	−	0.998442i	$-0.517773\pi$
$79$	−6191.23	−0.111612	−0.0558058	+	0.998442i	$0.517773\pi$
$80$	6400.00	0.111803
$81$	97071.7	1.64392
$82$	68399.8	1.12336
$83$	37849.2	0.603062	0.301531	−	0.953456i	$-0.402502\pi$
$83$	37849.2	0.603062	0.301531	+	0.953456i	$0.402502\pi$
$84$	107289.	1.65905
$85$	40732.5	0.611496
$86$	35742.3	0.521119
$87$	−41936.6	−0.594011
$88$	−34825.7	−0.479394
$89$	49151.0	0.657744	0.328872	−	0.944374i	$-0.393331\pi$
$89$	49151.0	0.657744	0.328872	+	0.944374i	$0.393331\pi$
$90$	−53488.0	−0.696065
$91$	−40631.9	−0.514356
$92$	5970.43	0.0735421
$93$	61361.3	0.735677
$94$	−62999.0	−0.735383
$95$	−20148.0	−0.229046
$96$	28559.9	0.316285
$97$	−15654.2	−0.168928	−0.0844641	−	0.996427i	$-0.526918\pi$
$97$	−15654.2	−0.168928	−0.0844641	+	0.996427i	$0.526918\pi$
$98$	−163990.	−1.72485
$99$	291056.	2.98461
$100$	10000.0	0.100000
$101$	−138108.	−1.34714	−0.673572	−	0.739122i	$-0.735241\pi$
$101$	−138108.	−1.34714	−0.673572	+	0.739122i	$0.735241\pi$
$102$	181768.	1.72988
$103$	−47642.1	−0.442484	−0.221242	−	0.975219i	$-0.571011\pi$
$103$	−47642.1	−0.442484	−0.221242	+	0.975219i	$0.571011\pi$
$104$	−10816.0	−0.0980581
$105$	167640.	1.48390
$106$	−161519.	−1.39623
$107$	−186527.	−1.57500	−0.787501	−	0.616313i	$-0.788626\pi$
$107$	−186527.	−1.57500	−0.787501	+	0.616313i	$0.788626\pi$
$108$	−130251.	−1.07454
$109$	14407.1	0.116147	0.0580736	−	0.998312i	$-0.481504\pi$
$109$	14407.1	0.116147	0.0580736	+	0.998312i	$0.481504\pi$
$110$	−54415.1	−0.428783
$111$	365620.	2.81658
$112$	−61548.9	−0.463634
$113$	−50802.0	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$113$	−50802.0	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$114$	−89910.0	−0.647957
$115$	9328.80	0.0657781
$116$	24057.8	0.166001
$117$	90394.7	0.610490
$118$	190248.	1.25781
$119$	−391725.	−2.53580
$120$	44624.8	0.282894
$121$	135050.	0.838552
$122$	121120.	0.736742
$123$	476926.	2.84242
$124$	−35201.3	−0.205591
$125$	15625.0	0.0894427
$126$	514395.	2.88649
$127$	−182278.	−1.00282	−0.501411	−	0.865209i	$-0.667186\pi$
$127$	−182278.	−1.00282	−0.501411	+	0.865209i	$0.667186\pi$
$128$	−16384.0	−0.0883883
$129$	249218.	1.31858
$130$	−16900.0	−0.0877058
$131$	199714.	1.01679	0.508394	−	0.861124i	$-0.330239\pi$
$131$	199714.	1.01679	0.508394	+	0.861124i	$0.330239\pi$
$132$	−242826.	−1.21300
$133$	193764.	0.949824
$134$	−155078.	−0.746083
$135$	−203517.	−0.961094
$136$	−104275.	−0.483430
$137$	−345418.	−1.57233	−0.786165	−	0.618017i	$-0.787936\pi$
$137$	−345418.	−1.57233	−0.786165	+	0.618017i	$0.787936\pi$
$138$	41629.6	0.186082
$139$	183088.	0.803754	0.401877	−	0.915694i	$-0.368358\pi$
$139$	183088.	0.803754	0.401877	+	0.915694i	$0.368358\pi$
$140$	−96170.2	−0.414687
$141$	−439268.	−1.86072
$142$	42078.7	0.175122
$143$	91961.6	0.376068
$144$	136929.	0.550288
$145$	37590.4	0.148476
$146$	−6328.50	−0.0245708
$147$	−1.14344e6	−4.36435
$148$	−209746.	−0.787117
$149$	−187082.	−0.690344	−0.345172	−	0.938540i	$-0.612179\pi$
$149$	−187082.	−0.690344	−0.345172	+	0.938540i	$0.612179\pi$
$150$	69726.2	0.253028
$151$	−10616.3	−0.0378907	−0.0189454	−	0.999821i	$-0.506031\pi$
$151$	−10616.3	−0.0378907	−0.0189454	+	0.999821i	$0.506031\pi$
$152$	51578.9	0.181077
$153$	871480.	3.00974
$154$	523312.	1.77811
$155$	−55002.0	−0.183886
$156$	−75415.9	−0.248114
$157$	−335884.	−1.08753	−0.543764	−	0.839238i	$-0.683001\pi$
$157$	−335884.	−1.08753	−0.543764	+	0.839238i	$0.683001\pi$
$158$	24764.9	0.0789213
$159$	−1.12621e6	−3.53286
$160$	−25600.0	−0.0790569
$161$	−89715.3	−0.272773
$162$	−388287.	−1.16242
$163$	201881.	0.595150	0.297575	−	0.954698i	$-0.403822\pi$
$163$	201881.	0.595150	0.297575	+	0.954698i	$0.403822\pi$
$164$	−273599.	−0.794337
$165$	−379416.	−1.08494
$166$	−151397.	−0.426429
$167$	−446050.	−1.23764	−0.618818	−	0.785535i	$-0.712388\pi$
$167$	−446050.	−1.23764	−0.618818	+	0.785535i	$0.712388\pi$
$168$	−429158.	−1.17312
$169$	28561.0	0.0769231
$170$	−162930.	−0.432393
$171$	−431070.	−1.12735
$172$	−142969.	−0.368487
$173$	57408.8	0.145835	0.0729177	−	0.997338i	$-0.476769\pi$
$173$	57408.8	0.145835	0.0729177	+	0.997338i	$0.476769\pi$
$174$	167746.	0.420030
$175$	−150266.	−0.370907
$176$	139303.	0.338983
$177$	1.32653e6	3.18261
$178$	−196604.	−0.465095
$179$	87439.4	0.203974	0.101987	−	0.994786i	$-0.467480\pi$
$179$	87439.4	0.203974	0.101987	+	0.994786i	$0.467480\pi$
$180$	213952.	0.492192
$181$	21341.6	0.0484206	0.0242103	−	0.999707i	$-0.492293\pi$
$181$	21341.6	0.0484206	0.0242103	+	0.999707i	$0.492293\pi$
$182$	162528.	0.363705
$183$	844523.	1.86416
$184$	−23881.7	−0.0520021
$185$	−327728.	−0.704019
$186$	−245445.	−0.520202
$187$	886586.	1.85403
$188$	251996.	0.519995
$189$	1.95723e6	3.98553
$190$	80592.0	0.161960
$191$	307517.	0.609938	0.304969	−	0.952362i	$-0.401354\pi$
$191$	307517.	0.609938	0.304969	+	0.952362i	$0.401354\pi$
$192$	−114239.	−0.223647
$193$	182409.	0.352496	0.176248	−	0.984346i	$-0.443604\pi$
$193$	182409.	0.352496	0.176248	+	0.984346i	$0.443604\pi$
$194$	62616.9	0.119450
$195$	−117837.	−0.221920
$196$	655959.	1.21965
$197$	−152508.	−0.279980	−0.139990	−	0.990153i	$-0.544707\pi$
$197$	−152508.	−0.279980	−0.139990	+	0.990153i	$0.544707\pi$
$198$	−1.16422e6	−2.11044
$199$	−586606.	−1.05006	−0.525029	−	0.851084i	$-0.675946\pi$
$199$	−586606.	−1.05006	−0.525029	+	0.851084i	$0.675946\pi$
$200$	−40000.0	−0.0707107
$201$	−1.08130e6	−1.88780
$202$	552430.	0.952574
$203$	−361508.	−0.615711
$204$	−727072.	−1.22321
$205$	−427498.	−0.710477
$206$	190568.	0.312884
$207$	199592.	0.323755
$208$	43264.0	0.0693375
$209$	−438542.	−0.694458
$210$	−670559.	−1.04927
$211$	−207041.	−0.320147	−0.160073	−	0.987105i	$-0.551173\pi$
$211$	−207041.	−0.320147	−0.160073	+	0.987105i	$0.551173\pi$
$212$	646075.	0.987286
$213$	293399.	0.443108
$214$	746106.	1.11369
$215$	−223390.	−0.329585
$216$	521003.	0.759812
$217$	528955.	0.762552
$218$	−57628.2	−0.0821285
$219$	−44126.3	−0.0621708
$220$	217661.	0.303196
$221$	275352.	0.379234
$222$	−1.46248e6	−1.99162
$223$	−1.04889e6	−1.41243	−0.706214	−	0.707998i	$-0.749599\pi$
$223$	−1.04889e6	−1.41243	−0.706214	+	0.707998i	$0.749599\pi$
$224$	246196.	0.327839
$225$	334300.	0.440230
$226$	203208.	0.264649
$227$	−100709.	−0.129719	−0.0648593	−	0.997894i	$-0.520660\pi$
$227$	−100709.	−0.129719	−0.0648593	+	0.997894i	$0.520660\pi$
$228$	359640.	0.458174
$229$	487174.	0.613896	0.306948	−	0.951726i	$-0.400692\pi$
$229$	487174.	0.613896	0.306948	+	0.951726i	$0.400692\pi$
$230$	−37315.2	−0.0465121
$231$	3.64886e6	4.49911
$232$	−96231.4	−0.117381
$233$	−832844.	−1.00502	−0.502509	−	0.864572i	$-0.667590\pi$
$233$	−832844.	−1.00502	−0.502509	+	0.864572i	$0.667590\pi$
$234$	−361579.	−0.431681
$235$	393744.	0.465097
$236$	−760993.	−0.889407
$237$	172677.	0.199693
$238$	1.56690e6	1.79308
$239$	1.34919e6	1.52785	0.763923	−	0.645308i	$-0.223271\pi$
$239$	1.34919e6	1.52785	0.763923	+	0.645308i	$0.223271\pi$
$240$	−178499.	−0.200036
$241$	−1.66283e6	−1.84419	−0.922096	−	0.386962i	$-0.873524\pi$
$241$	−1.66283e6	−1.84419	−0.922096	+	0.386962i	$0.873524\pi$
$242$	−540199.	−0.592946
$243$	−729193.	−0.792185
$244$	−484479.	−0.520956
$245$	1.02494e6	1.09089
$246$	−1.90770e6	−2.00989
$247$	−136200.	−0.142048
$248$	140805.	0.145375
$249$	−1.05563e6	−1.07898
$250$	−62500.0	−0.0632456
$251$	−291273.	−0.291820	−0.145910	−	0.989298i	$-0.546611\pi$
$251$	−291273.	−0.291820	−0.145910	+	0.989298i	$0.546611\pi$
$252$	−2.05758e6	−2.04106
$253$	203051.	0.199436
$254$	729110.	0.709102
$255$	−1.13605e6	−1.09407
$256$	65536.0	0.0625000
$257$	−548204.	−0.517737	−0.258868	−	0.965913i	$-0.583350\pi$
$257$	−548204.	−0.517737	−0.258868	+	0.965913i	$0.583350\pi$
$258$	−996872.	−0.932374
$259$	3.15177e6	2.91947
$260$	67600.0	0.0620174
$261$	804253.	0.730788
$262$	−798857.	−0.718978
$263$	818412.	0.729596	0.364798	−	0.931087i	$-0.381138\pi$
$263$	818412.	0.729596	0.364798	+	0.931087i	$0.381138\pi$
$264$	971306.	0.857721
$265$	1.00949e6	0.883056
$266$	−775055.	−0.671627
$267$	−1.37085e6	−1.17682
$268$	620311.	0.527561
$269$	−939455.	−0.791581	−0.395790	−	0.918341i	$-0.629529\pi$
$269$	−939455.	−0.791581	−0.395790	+	0.918341i	$0.629529\pi$
$270$	814067.	0.679596
$271$	−1.52416e6	−1.26069	−0.630345	−	0.776315i	$-0.717087\pi$
$271$	−1.52416e6	−1.26069	−0.630345	+	0.776315i	$0.717087\pi$
$272$	417101.	0.341837
$273$	1.13324e6	0.920274
$274$	1.38167e6	1.11180
$275$	340095.	0.271186
$276$	−166518.	−0.131580
$277$	−439704.	−0.344319	−0.172159	−	0.985069i	$-0.555074\pi$
$277$	−439704.	−0.344319	−0.172159	+	0.985069i	$0.555074\pi$
$278$	−732352.	−0.568340
$279$	−1.17678e6	−0.905074
$280$	384681.	0.293228
$281$	−592033.	−0.447280	−0.223640	−	0.974672i	$-0.571794\pi$
$281$	−592033.	−0.447280	−0.223640	+	0.974672i	$0.571794\pi$
$282$	1.75707e6	1.31573
$283$	−777226.	−0.576875	−0.288437	−	0.957499i	$-0.593136\pi$
$283$	−777226.	−0.576875	−0.288437	+	0.957499i	$0.593136\pi$
$284$	−168315.	−0.123830
$285$	561938.	0.409804
$286$	−367846.	−0.265920
$287$	4.11126e6	2.94626
$288$	−547717.	−0.389112
$289$	1.23476e6	0.869637
$290$	−150362.	−0.104988
$291$	436604.	0.302242
$292$	25314.0	0.0173742
$293$	609025.	0.414444	0.207222	−	0.978294i	$-0.433558\pi$
$293$	609025.	0.414444	0.207222	+	0.978294i	$0.433558\pi$
$294$	4.57376e6	3.08606
$295$	−1.18905e6	−0.795510
$296$	838984.	0.556576
$297$	−4.42976e6	−2.91400
$298$	748326.	0.488147
$299$	63062.7	0.0407938
$300$	−278905.	−0.178918
$301$	2.14834e6	1.36674
$302$	42465.4	0.0267928
$303$	3.85189e6	2.41028
$304$	−206315.	−0.128041
$305$	−756999.	−0.465957
$306$	−3.48592e6	−2.12821
$307$	−2.66761e6	−1.61538	−0.807692	−	0.589604i	$-0.799284\pi$
$307$	−2.66761e6	−1.61538	−0.807692	+	0.589604i	$0.799284\pi$
$308$	−2.09325e6	−1.25731
$309$	1.32876e6	0.791682
$310$	220008.	0.130027
$311$	−1.62320e6	−0.951634	−0.475817	−	0.879544i	$-0.657847\pi$
$311$	−1.62320e6	−0.951634	−0.475817	+	0.879544i	$0.657847\pi$
$312$	301664.	0.175443
$313$	592115.	0.341622	0.170811	−	0.985304i	$-0.445361\pi$
$313$	592115.	0.341622	0.170811	+	0.985304i	$0.445361\pi$
$314$	1.34354e6	0.768998
$315$	−3.21497e6	−1.82558
$316$	−99059.7	−0.0558058
$317$	−2.61036e6	−1.45899	−0.729494	−	0.683987i	$-0.760244\pi$
$317$	−2.61036e6	−1.45899	−0.729494	+	0.683987i	$0.760244\pi$
$318$	4.50484e6	2.49811
$319$	818194.	0.450173
$320$	102400.	0.0559017
$321$	5.20232e6	2.81796
$322$	358861.	0.192880
$323$	−1.31308e6	−0.700304
$324$	1.55315e6	0.821959
$325$	105625.	0.0554700
$326$	−807524.	−0.420834
$327$	−401820.	−0.207808
$328$	1.09440e6	0.561681
$329$	−3.78664e6	−1.92870
$330$	1.51767e6	0.767169
$331$	818785.	0.410771	0.205386	−	0.978681i	$-0.434155\pi$
$331$	818785.	0.410771	0.205386	+	0.978681i	$0.434155\pi$
$332$	605588.	0.301531
$333$	−7.01180e6	−3.46513
$334$	1.78420e6	0.875140
$335$	969236.	0.471864
$336$	1.71663e6	0.829523
$337$	3.28910e6	1.57762	0.788809	−	0.614638i	$-0.210698\pi$
$337$	3.28910e6	1.57762	0.788809	+	0.614638i	$0.210698\pi$
$338$	−114244.	−0.0543928
$339$	1.41689e6	0.669634
$340$	651720.	0.305748
$341$	−1.19718e6	−0.557535
$342$	1.72428e6	0.797155
$343$	−5.81600e6	−2.66925
$344$	571877.	0.260559
$345$	−260185.	−0.117689
$346$	−229635.	−0.103121
$347$	139108.	0.0620195	0.0310098	−	0.999519i	$-0.490128\pi$
$347$	139108.	0.0620195	0.0310098	+	0.999519i	$0.490128\pi$
$348$	−670985.	−0.297006
$349$	1.41781e6	0.623097	0.311549	−	0.950230i	$-0.399152\pi$
$349$	1.41781e6	0.623097	0.311549	+	0.950230i	$0.399152\pi$
$350$	601064.	0.262271
$351$	−1.37577e6	−0.596045
$352$	−557211.	−0.239697
$353$	2.45675e6	1.04936	0.524679	−	0.851300i	$-0.324185\pi$
$353$	2.45675e6	1.04936	0.524679	+	0.851300i	$0.324185\pi$
$354$	−5.30612e6	−2.25045
$355$	−262992.	−0.110757
$356$	786416.	0.328872
$357$	1.09254e7	4.53698
$358$	−349758.	−0.144231
$359$	−2.88601e6	−1.18185	−0.590924	−	0.806727i	$-0.701237\pi$
$359$	−2.88601e6	−1.18185	−0.590924	+	0.806727i	$0.701237\pi$
$360$	−855808.	−0.348033
$361$	−1.82659e6	−0.737690
$362$	−85366.4	−0.0342386
$363$	−3.76660e6	−1.50032
$364$	−650111.	−0.257178
$365$	39553.1	0.0155399
$366$	−3.37809e6	−1.31816
$367$	−2.83587e6	−1.09906	−0.549530	−	0.835474i	$-0.685193\pi$
$367$	−2.83587e6	−1.09906	−0.549530	+	0.835474i	$0.685193\pi$
$368$	95526.9	0.0367711
$369$	−9.14641e6	−3.49691
$370$	1.31091e6	0.497816
$371$	−9.70831e6	−3.66192
$372$	981781.	0.367838
$373$	5.02691e6	1.87081	0.935403	−	0.353583i	$-0.115037\pi$
$373$	5.02691e6	1.87081	0.935403	+	0.353583i	$0.115037\pi$
$374$	−3.54634e6	−1.31100
$375$	−435789.	−0.160029
$376$	−1.00798e6	−0.367692
$377$	254111.	0.0920810
$378$	−7.82891e6	−2.81820
$379$	2.14892e6	0.768462	0.384231	−	0.923237i	$-0.374467\pi$
$379$	2.14892e6	0.768462	0.384231	+	0.923237i	$0.374467\pi$
$380$	−322368.	−0.114523
$381$	5.08381e6	1.79423
$382$	−1.23007e6	−0.431291
$383$	832971.	0.290157	0.145078	−	0.989420i	$-0.453657\pi$
$383$	832971.	0.290157	0.145078	+	0.989420i	$0.453657\pi$
$384$	456958.	0.158142
$385$	−3.27070e6	−1.12458
$386$	−729637.	−0.249252
$387$	−4.77946e6	−1.62219
$388$	−250468.	−0.0844641
$389$	−725243.	−0.243002	−0.121501	−	0.992591i	$-0.538771\pi$
$389$	−725243.	−0.243002	−0.121501	+	0.992591i	$0.538771\pi$
$390$	471349.	0.156921
$391$	607976.	0.201115
$392$	−2.62384e6	−0.862426
$393$	−5.57013e6	−1.81921
$394$	610032.	0.197976
$395$	−154781.	−0.0499142
$396$	4.65689e6	1.49231
$397$	2.42654e6	0.772701	0.386351	−	0.922352i	$-0.373735\pi$
$397$	2.42654e6	0.772701	0.386351	+	0.922352i	$0.373735\pi$
$398$	2.34642e6	0.742504
$399$	−5.40417e6	−1.69940
$400$	160000.	0.0500000
$401$	−2.14376e6	−0.665758	−0.332879	−	0.942970i	$-0.608020\pi$
$401$	−2.14376e6	−0.665758	−0.332879	+	0.942970i	$0.608020\pi$
$402$	4.32519e6	1.33487
$403$	−371813.	−0.114041
$404$	−2.20972e6	−0.673572
$405$	2.42679e6	0.735182
$406$	1.44603e6	0.435374
$407$	−7.13335e6	−2.13455
$408$	2.90829e6	0.864942
$409$	−3.66144e6	−1.08229	−0.541145	−	0.840929i	$-0.682009\pi$
$409$	−3.66144e6	−1.08229	−0.541145	+	0.840929i	$0.682009\pi$
$410$	1.70999e6	0.502383
$411$	9.63388e6	2.81317
$412$	−762273.	−0.221242
$413$	1.14351e7	3.29888
$414$	−798366.	−0.228929
$415$	946231.	0.269698
$416$	−173056.	−0.0490290
$417$	−5.10642e6	−1.43806
$418$	1.75417e6	0.491056
$419$	3.03786e6	0.845341	0.422671	−	0.906283i	$-0.361093\pi$
$419$	3.03786e6	0.845341	0.422671	+	0.906283i	$0.361093\pi$
$420$	2.68224e6	0.741948
$421$	−1.88663e6	−0.518777	−0.259389	−	0.965773i	$-0.583521\pi$
$421$	−1.88663e6	−0.518777	−0.259389	+	0.965773i	$0.583521\pi$
$422$	828162.	0.226378
$423$	8.42422e6	2.28917
$424$	−2.58430e6	−0.698117
$425$	1.01831e6	0.273469
$426$	−1.17360e6	−0.313325
$427$	7.28008e6	1.93226
$428$	−2.98442e6	−0.787501
$429$	−2.56485e6	−0.672852
$430$	893558.	0.233051
$431$	717193.	0.185970	0.0929850	−	0.995668i	$-0.470359\pi$
$431$	717193.	0.185970	0.0929850	+	0.995668i	$0.470359\pi$
$432$	−2.08401e6	−0.537268
$433$	2.64569e6	0.678140	0.339070	−	0.940761i	$-0.389888\pi$
$433$	2.64569e6	0.678140	0.339070	+	0.940761i	$0.389888\pi$
$434$	−2.11582e6	−0.539206
$435$	−1.04841e6	−0.265650
$436$	230513.	0.0580736
$437$	−300731.	−0.0753310
$438$	176505.	0.0439614
$439$	4.47973e6	1.10941	0.554704	−	0.832048i	$-0.312832\pi$
$439$	4.47973e6	1.10941	0.554704	+	0.832048i	$0.312832\pi$
$440$	−870642.	−0.214392
$441$	2.19287e7	5.36929
$442$	−1.10141e6	−0.268159
$443$	4.30731e6	1.04279	0.521395	−	0.853315i	$-0.325412\pi$
$443$	4.30731e6	1.04279	0.521395	+	0.853315i	$0.325412\pi$
$444$	5.84992e6	1.40829
$445$	1.22877e6	0.294152
$446$	4.19555e6	0.998738
$447$	5.21780e6	1.23515
$448$	−984783.	−0.231817
$449$	−25272.9	−0.00591615	−0.00295808	−	0.999996i	$-0.500942\pi$
$449$	−25272.9	−0.00591615	−0.00295808	+	0.999996i	$0.500942\pi$
$450$	−1.33720e6	−0.311290
$451$	−9.30495e6	−2.15413
$452$	−812832.	−0.187135
$453$	296095.	0.0677932
$454$	402835.	0.0917250
$455$	−1.01580e6	−0.230027
$456$	−1.43856e6	−0.323978
$457$	1.14360e6	0.256143	0.128072	−	0.991765i	$-0.459121\pi$
$457$	1.14360e6	0.256143	0.128072	+	0.991765i	$0.459121\pi$
$458$	−1.94869e6	−0.434090
$459$	−1.32636e7	−2.93853
$460$	149261.	0.0328890
$461$	−8.34911e6	−1.82973	−0.914867	−	0.403755i	$-0.867705\pi$
$461$	−8.34911e6	−1.82973	−0.914867	+	0.403755i	$0.867705\pi$
$462$	−1.45954e7	−3.18135
$463$	−3.41596e6	−0.740561	−0.370280	−	0.928920i	$-0.620738\pi$
$463$	−3.41596e6	−0.740561	−0.370280	+	0.928920i	$0.620738\pi$
$464$	384925.	0.0830007
$465$	1.53403e6	0.329005
$466$	3.33138e6	0.710655
$467$	5.67105e6	1.20329	0.601646	−	0.798763i	$-0.294512\pi$
$467$	5.67105e6	1.20329	0.601646	+	0.798763i	$0.294512\pi$
$468$	1.44632e6	0.305245
$469$	−9.32116e6	−1.95676
$470$	−1.57497e6	−0.328873
$471$	9.36797e6	1.94578
$472$	3.04397e6	0.628906
$473$	−4.86231e6	−0.999286
$474$	−690706.	−0.141204
$475$	−503700.	−0.102432
$476$	−6.26760e6	−1.26790
$477$	2.15983e7	4.34633
$478$	−5.39677e6	−1.08035
$479$	−6.16340e6	−1.22739	−0.613694	−	0.789544i	$-0.710317\pi$
$479$	−6.16340e6	−1.22739	−0.613694	+	0.789544i	$0.710317\pi$
$480$	713997.	0.141447
$481$	−2.21544e6	−0.436614
$482$	6.65133e6	1.30404
$483$	2.50220e6	0.488039
$484$	2.16080e6	0.419276
$485$	−391356.	−0.0755470
$486$	2.91677e6	0.560160
$487$	−7.32701e6	−1.39992	−0.699962	−	0.714180i	$-0.746800\pi$
$487$	−7.32701e6	−1.39992	−0.699962	+	0.714180i	$0.746800\pi$
$488$	1.93792e6	0.368371
$489$	−5.63056e6	−1.06483
$490$	−4.09975e6	−0.771377
$491$	8.89739e6	1.66555	0.832777	−	0.553608i	$-0.186750\pi$
$491$	8.89739e6	1.66555	0.832777	+	0.553608i	$0.186750\pi$
$492$	7.63081e6	1.42121
$493$	2.44984e6	0.453963
$494$	544802.	0.100443
$495$	7.27639e6	1.33476
$496$	−563220.	−0.102795
$497$	2.52920e6	0.459295
$498$	4.22254e6	0.762957
$499$	3.02237e6	0.543371	0.271686	−	0.962386i	$-0.412419\pi$
$499$	3.02237e6	0.543371	0.271686	+	0.962386i	$0.412419\pi$
$500$	250000.	0.0447214
$501$	1.24406e7	2.21435
$502$	1.16509e6	0.206348
$503$	−7.48799e6	−1.31961	−0.659805	−	0.751437i	$-0.729361\pi$
$503$	−7.48799e6	−1.31961	−0.659805	+	0.751437i	$0.729361\pi$
$504$	8.23032e6	1.44325
$505$	−3.45269e6	−0.602461
$506$	−812205.	−0.141023
$507$	−796581.	−0.137629
$508$	−2.91644e6	−0.501411
$509$	4.87997e6	0.834878	0.417439	−	0.908705i	$-0.362928\pi$
$509$	4.87997e6	0.834878	0.417439	+	0.908705i	$0.362928\pi$
$510$	4.54420e6	0.773627
$511$	−380383.	−0.0644420
$512$	−262144.	−0.0441942
$513$	6.56073e6	1.10067
$514$	2.19281e6	0.366095
$515$	−1.19105e6	−0.197885
$516$	3.98749e6	0.659288
$517$	8.57024e6	1.41015
$518$	−1.26071e7	−2.06438
$519$	−1.60116e6	−0.260925
$520$	−270400.	−0.0438529
$521$	−3.79679e6	−0.612805	−0.306403	−	0.951902i	$-0.599125\pi$
$521$	−3.79679e6	−0.612805	−0.306403	+	0.951902i	$0.599125\pi$
$522$	−3.21701e6	−0.516745
$523$	−5.66643e6	−0.905848	−0.452924	−	0.891549i	$-0.649619\pi$
$523$	−5.66643e6	−0.905848	−0.452924	+	0.891549i	$0.649619\pi$
$524$	3.19543e6	0.508394
$525$	4.19099e6	0.663619
$526$	−3.27365e6	−0.515902
$527$	−3.58459e6	−0.562228
$528$	−3.88522e6	−0.606500
$529$	−6.29710e6	−0.978366
$530$	−4.03797e6	−0.624415
$531$	−2.54400e7	−3.91544
$532$	3.10022e6	0.474912
$533$	−2.88989e6	−0.440619
$534$	5.48338e6	0.832138
$535$	−4.66316e6	−0.704362
$536$	−2.48124e6	−0.373042
$537$	−2.43873e6	−0.364945
$538$	3.75782e6	0.559732
$539$	2.23088e7	3.30754
$540$	−3.25627e6	−0.480547
$541$	1.15648e7	1.69881	0.849403	−	0.527745i	$-0.176962\pi$
$541$	1.15648e7	1.69881	0.849403	+	0.527745i	$0.176962\pi$
$542$	6.09665e6	0.891442
$543$	−595228.	−0.0866330
$544$	−1.66840e6	−0.241715
$545$	360176.	0.0519426
$546$	−4.53298e6	−0.650732
$547$	−1.28104e7	−1.83060	−0.915299	−	0.402776i	$-0.868045\pi$
$547$	−1.28104e7	−1.83060	−0.915299	+	0.402776i	$0.868045\pi$
$548$	−5.52669e6	−0.786165
$549$	−1.61961e7	−2.29340
$550$	−1.36038e6	−0.191758
$551$	−1.21179e6	−0.170039
$552$	666073.	0.0930410
$553$	1.48853e6	0.206988
$554$	1.75881e6	0.243470
$555$	9.14050e6	1.25961
$556$	2.92941e6	0.401877
$557$	3.51737e6	0.480374	0.240187	−	0.970727i	$-0.422791\pi$
$557$	3.51737e6	0.480374	0.240187	+	0.970727i	$0.422791\pi$
$558$	4.70711e6	0.639984
$559$	−1.51011e6	−0.204400
$560$	−1.53872e6	−0.207344
$561$	−2.47273e7	−3.31719
$562$	2.36813e6	0.316275
$563$	9.45258e6	1.25684	0.628419	−	0.777875i	$-0.283702\pi$
$563$	9.45258e6	1.25684	0.628419	+	0.777875i	$0.283702\pi$
$564$	−7.02829e6	−0.930362
$565$	−1.27005e6	−0.167378
$566$	3.10891e6	0.407912
$567$	−2.33385e7	−3.04871
$568$	673259.	0.0875611
$569$	1.11315e7	1.44136	0.720679	−	0.693269i	$-0.243830\pi$
$569$	1.11315e7	1.44136	0.720679	+	0.693269i	$0.243830\pi$
$570$	−2.24775e6	−0.289775
$571$	4.92935e6	0.632702	0.316351	−	0.948642i	$-0.397542\pi$
$571$	4.92935e6	0.632702	0.316351	+	0.948642i	$0.397542\pi$
$572$	1.47139e6	0.188034
$573$	−8.57680e6	−1.09129
$574$	−1.64450e7	−2.08332
$575$	233220.	0.0294169
$576$	2.19087e6	0.275144
$577$	1.09437e7	1.36843	0.684217	−	0.729279i	$-0.260144\pi$
$577$	1.09437e7	1.36843	0.684217	+	0.729279i	$0.260144\pi$
$578$	−4.93904e6	−0.614926
$579$	−5.08749e6	−0.630677
$580$	601446.	0.0742381
$581$	−9.09993e6	−1.11840
$582$	−1.74642e6	−0.213718
$583$	2.19727e7	2.67739
$584$	−101256.	−0.0122854
$585$	2.25987e6	0.273019
$586$	−2.43610e6	−0.293056
$587$	7.96444e6	0.954025	0.477013	−	0.878896i	$-0.341720\pi$
$587$	7.96444e6	0.954025	0.477013	+	0.878896i	$0.341720\pi$
$588$	−1.82950e7	−2.18218
$589$	1.77309e6	0.210592
$590$	4.75621e6	0.562510
$591$	4.25352e6	0.500934
$592$	−3.35593e6	−0.393558
$593$	−1.19793e7	−1.39892	−0.699460	−	0.714671i	$-0.746576\pi$
$593$	−1.19793e7	−1.39892	−0.699460	+	0.714671i	$0.746576\pi$
$594$	1.77190e7	2.06051
$595$	−9.79313e6	−1.13404
$596$	−2.99330e6	−0.345172
$597$	1.63607e7	1.87874
$598$	−252251.	−0.0288456
$599$	7.45663e6	0.849132	0.424566	−	0.905397i	$-0.360427\pi$
$599$	7.45663e6	0.849132	0.424566	+	0.905397i	$0.360427\pi$
$600$	1.11562e6	0.126514
$601$	−1.04196e7	−1.17670	−0.588351	−	0.808606i	$-0.700223\pi$
$601$	−1.04196e7	−1.17670	−0.588351	+	0.808606i	$0.700223\pi$
$602$	−8.59337e6	−0.966434
$603$	2.07370e7	2.32248
$604$	−169862.	−0.0189454
$605$	3.37624e6	0.375012
$606$	−1.54075e7	−1.70432
$607$	571939.	0.0630054	0.0315027	−	0.999504i	$-0.489971\pi$
$607$	571939.	0.0630054	0.0315027	+	0.999504i	$0.489971\pi$
$608$	825262.	0.0905384
$609$	1.00826e7	1.10162
$610$	3.02800e6	0.329481
$611$	2.66171e6	0.288441
$612$	1.39437e7	1.50487
$613$	−1.61323e7	−1.73398	−0.866991	−	0.498323i	$-0.833949\pi$
$613$	−1.61323e7	−1.73398	−0.866991	+	0.498323i	$0.833949\pi$
$614$	1.06704e7	1.14225
$615$	1.19231e7	1.27117
$616$	8.37299e6	0.889055
$617$	−6.39133e6	−0.675894	−0.337947	−	0.941165i	$-0.609732\pi$
$617$	−6.39133e6	−0.675894	−0.337947	+	0.941165i	$0.609732\pi$
$618$	−5.31505e6	−0.559804
$619$	1.27062e7	1.33287	0.666435	−	0.745563i	$-0.267819\pi$
$619$	1.27062e7	1.33287	0.666435	+	0.745563i	$0.267819\pi$
$620$	−880031.	−0.0919431
$621$	−3.03771e6	−0.316095
$622$	6.49278e6	0.672907
$623$	−1.18172e7	−1.21981
$624$	−1.20665e6	−0.124057
$625$	390625.	0.0400000
$626$	−2.36846e6	−0.241563
$627$	1.22312e7	1.24251
$628$	−5.37414e6	−0.543764
$629$	−2.13587e7	−2.15252
$630$	1.28599e7	1.29088
$631$	−694354.	−0.0694237	−0.0347118	−	0.999397i	$-0.511051\pi$
$631$	−694354.	−0.0694237	−0.0347118	+	0.999397i	$0.511051\pi$
$632$	396239.	0.0394607
$633$	5.77447e6	0.572799
$634$	1.04414e7	1.03166
$635$	−4.55694e6	−0.448476
$636$	−1.80193e7	−1.76643
$637$	6.92857e6	0.676542
$638$	−3.27278e6	−0.318321
$639$	−5.62676e6	−0.545138
$640$	−409600.	−0.0395285
$641$	−8.71863e6	−0.838114	−0.419057	−	0.907960i	$-0.637639\pi$
$641$	−8.71863e6	−0.838114	−0.419057	+	0.907960i	$0.637639\pi$
$642$	−2.08093e7	−1.99260
$643$	5.98737e6	0.571096	0.285548	−	0.958364i	$-0.407824\pi$
$643$	5.98737e6	0.571096	0.285548	+	0.958364i	$0.407824\pi$
$644$	−1.43544e6	−0.136387
$645$	6.23045e6	0.589685
$646$	5.25234e6	0.495189
$647$	−1.09581e7	−1.02914	−0.514571	−	0.857448i	$-0.672049\pi$
$647$	−1.09581e7	−1.02914	−0.514571	+	0.857448i	$0.672049\pi$
$648$	−6.21259e6	−0.581212
$649$	−2.58810e7	−2.41195
$650$	−422500.	−0.0392232
$651$	−1.47528e7	−1.36434
$652$	3.23009e6	0.297575
$653$	6.47503e6	0.594236	0.297118	−	0.954841i	$-0.403975\pi$
$653$	6.47503e6	0.594236	0.297118	+	0.954841i	$0.403975\pi$
$654$	1.60728e6	0.146942
$655$	4.99285e6	0.454722
$656$	−4.37758e6	−0.397169
$657$	846247.	0.0764863
$658$	1.51466e7	1.36380
$659$	501723.	0.0450039	0.0225020	−	0.999747i	$-0.492837\pi$
$659$	501723.	0.0450039	0.0225020	+	0.999747i	$0.492837\pi$
$660$	−6.07066e6	−0.542471
$661$	4.00659e6	0.356674	0.178337	−	0.983969i	$-0.442928\pi$
$661$	4.00659e6	0.356674	0.178337	+	0.983969i	$0.442928\pi$
$662$	−3.27514e6	−0.290459
$663$	−7.67969e6	−0.678516
$664$	−2.42235e6	−0.213215
$665$	4.84409e6	0.424774
$666$	2.80472e7	2.45021
$667$	561077.	0.0488324
$668$	−7.13681e6	−0.618818
$669$	2.92540e7	2.52708
$670$	−3.87694e6	−0.333659
$671$	−1.64769e7	−1.41276
$672$	−6.86652e6	−0.586562
$673$	8.17473e6	0.695722	0.347861	−	0.937546i	$-0.386908\pi$
$673$	8.17473e6	0.695722	0.347861	+	0.937546i	$0.386908\pi$
$674$	−1.31564e7	−1.11554
$675$	−5.08792e6	−0.429814
$676$	456976.	0.0384615
$677$	1.00935e6	0.0846392	0.0423196	−	0.999104i	$-0.486525\pi$
$677$	1.00935e6	0.0846392	0.0423196	+	0.999104i	$0.486525\pi$
$678$	−5.66757e6	−0.473503
$679$	3.76368e6	0.313284
$680$	−2.60688e6	−0.216196
$681$	2.80882e6	0.232090
$682$	4.78870e6	0.394237
$683$	1.99189e7	1.63386	0.816928	−	0.576739i	$-0.195675\pi$
$683$	1.99189e7	1.63386	0.816928	+	0.576739i	$0.195675\pi$
$684$	−6.89712e6	−0.563674
$685$	−8.63545e6	−0.703167
$686$	2.32640e7	1.88745
$687$	−1.35875e7	−1.09837
$688$	−2.28751e6	−0.184243
$689$	6.82417e6	0.547648
$690$	1.04074e6	0.0832184
$691$	−677407.	−0.0539703	−0.0269851	−	0.999636i	$-0.508591\pi$
$691$	−677407.	−0.0539703	−0.0269851	+	0.999636i	$0.508591\pi$
$692$	918541.	0.0729177
$693$	−6.99772e7	−5.53508
$694$	−556432.	−0.0438544
$695$	4.57720e6	0.359450
$696$	2.68394e6	0.210015
$697$	−2.78609e7	−2.17227
$698$	−5.67126e6	−0.440596
$699$	2.32284e7	1.79815
$700$	−2.40426e6	−0.185454
$701$	1.04542e7	0.803518	0.401759	−	0.915745i	$-0.368399\pi$
$701$	1.04542e7	0.803518	0.401759	+	0.915745i	$0.368399\pi$
$702$	5.50310e6	0.421468
$703$	1.05649e7	0.806263
$704$	2.22884e6	0.169492
$705$	−1.09817e7	−0.832141
$706$	−9.82700e6	−0.742009
$707$	3.32046e7	2.49833
$708$	2.12245e7	1.59131
$709$	−2.25125e7	−1.68193	−0.840964	−	0.541091i	$-0.818011\pi$
$709$	−2.25125e7	−1.68193	−0.840964	+	0.541091i	$0.818011\pi$
$710$	1.05197e6	0.0783170
$711$	−3.31157e6	−0.245674
$712$	−3.14566e6	−0.232548
$713$	−820964.	−0.0604784
$714$	−4.37017e7	−3.20813
$715$	2.29904e6	0.168183
$716$	1.39903e6	0.101987
$717$	−3.76297e7	−2.73358
$718$	1.15440e7	0.835693
$719$	−2.77678e6	−0.200317	−0.100159	−	0.994971i	$-0.531935\pi$
$719$	−2.77678e6	−0.200317	−0.100159	+	0.994971i	$0.531935\pi$
$720$	3.42323e6	0.246096
$721$	1.14544e7	0.820603
$722$	7.30637e6	0.521625
$723$	4.63772e7	3.29958
$724$	341466.	0.0242103
$725$	939759.	0.0664006
$726$	1.50664e7	1.06089
$727$	2.76872e6	0.194287	0.0971434	−	0.995270i	$-0.469029\pi$
$727$	2.76872e6	0.194287	0.0971434	+	0.995270i	$0.469029\pi$
$728$	2.60044e6	0.181852
$729$	−3.25086e6	−0.226558
$730$	−158212.	−0.0109884
$731$	−1.45587e7	−1.00770
$732$	1.35124e7	0.932081
$733$	−1.80998e7	−1.24427	−0.622133	−	0.782911i	$-0.713734\pi$
$733$	−1.80998e7	−1.24427	−0.622133	+	0.782911i	$0.713734\pi$
$734$	1.13435e7	0.777152
$735$	−2.85860e7	−1.95180
$736$	−382108.	−0.0260011
$737$	2.10964e7	1.43067
$738$	3.65857e7	2.47269
$739$	−3.57016e6	−0.240479	−0.120239	−	0.992745i	$-0.538366\pi$
$739$	−3.57016e6	−0.240479	−0.120239	+	0.992745i	$0.538366\pi$
$740$	−5.24365e6	−0.352009
$741$	3.79870e6	0.254149
$742$	3.88332e7	2.58937
$743$	−1.73285e7	−1.15157	−0.575783	−	0.817603i	$-0.695303\pi$
$743$	−1.73285e7	−1.15157	−0.575783	+	0.817603i	$0.695303\pi$
$744$	−3.92712e6	−0.260101
$745$	−4.67704e6	−0.308731
$746$	−2.01076e7	−1.32286
$747$	2.02448e7	1.32743
$748$	1.41854e7	0.927015
$749$	4.48457e7	2.92090
$750$	1.74316e6	0.113157
$751$	3.04634e6	0.197096	0.0985480	−	0.995132i	$-0.468580\pi$
$751$	3.04634e6	0.197096	0.0985480	+	0.995132i	$0.468580\pi$
$752$	4.03193e6	0.259997
$753$	8.12374e6	0.522118
$754$	−1.01644e6	−0.0651111
$755$	−265409.	−0.0169452
$756$	3.13156e7	1.99277
$757$	−8.98398e6	−0.569808	−0.284904	−	0.958556i	$-0.591962\pi$
$757$	−8.98398e6	−0.569808	−0.284904	+	0.958556i	$0.591962\pi$
$758$	−8.59568e6	−0.543384
$759$	−5.66320e6	−0.356827
$760$	1.28947e6	0.0809800
$761$	1.31757e7	0.824731	0.412366	−	0.911018i	$-0.364703\pi$
$761$	1.31757e7	0.824731	0.412366	+	0.911018i	$0.364703\pi$
$762$	−2.03352e7	−1.26871
$763$	−3.46382e6	−0.215399
$764$	4.92027e6	0.304969
$765$	2.17870e7	1.34600
$766$	−3.33188e6	−0.205172
$767$	−8.03799e6	−0.493354
$768$	−1.82783e6	−0.111824
$769$	3.53661e6	0.215661	0.107830	−	0.994169i	$-0.465610\pi$
$769$	3.53661e6	0.215661	0.107830	+	0.994169i	$0.465610\pi$
$770$	1.30828e7	0.795195
$771$	1.52897e7	0.926322
$772$	2.91855e6	0.176248
$773$	−3.14397e7	−1.89247	−0.946235	−	0.323479i	$-0.895147\pi$
$773$	−3.14397e7	−1.89247	−0.946235	+	0.323479i	$0.895147\pi$
$774$	1.91179e7	1.14706
$775$	−1.37505e6	−0.0822364
$776$	1.00187e6	0.0597251
$777$	−8.79044e7	−5.22346
$778$	2.90097e6	0.171828
$779$	1.37812e7	0.813659
$780$	−1.88540e6	−0.110960
$781$	−5.72429e6	−0.335810
$782$	−2.43191e6	−0.142210
$783$	−1.22404e7	−0.713498
$784$	1.04953e7	0.609827
$785$	−8.39710e6	−0.486357
$786$	2.22805e7	1.28638
$787$	1.27213e7	0.732139	0.366069	−	0.930588i	$-0.380703\pi$
$787$	1.27213e7	0.732139	0.366069	+	0.930588i	$0.380703\pi$
$788$	−2.44013e6	−0.139990
$789$	−2.28259e7	−1.30538
$790$	619123.	0.0352947
$791$	1.22141e7	0.694097
$792$	−1.86276e7	−1.05522
$793$	−5.11731e6	−0.288974
$794$	−9.70617e6	−0.546382
$795$	−2.81552e7	−1.57994
$796$	−9.38569e6	−0.525029
$797$	1.84237e7	1.02738	0.513689	−	0.857977i	$-0.328279\pi$
$797$	1.84237e7	1.02738	0.513689	+	0.857977i	$0.328279\pi$
$798$	2.16167e7	1.20166
$799$	2.56610e7	1.42203
$800$	−640000.	−0.0353553
$801$	2.62899e7	1.44780
$802$	8.57506e6	0.470762
$803$	860915.	0.0471164
$804$	−1.73008e7	−0.943899
$805$	−2.24288e6	−0.121988
$806$	1.48725e6	0.0806394
$807$	2.62019e7	1.41628
$808$	8.83888e6	0.476287
$809$	2.10360e7	1.13004	0.565018	−	0.825079i	$-0.308869\pi$
$809$	2.10360e7	1.13004	0.565018	+	0.825079i	$0.308869\pi$
$810$	−9.70717e6	−0.519852
$811$	3.53571e7	1.88767	0.943833	−	0.330424i	$-0.107192\pi$
$811$	3.53571e7	1.88767	0.943833	+	0.330424i	$0.107192\pi$
$812$	−5.78412e6	−0.307856
$813$	4.25097e7	2.25560
$814$	2.85334e7	1.50936
$815$	5.04702e6	0.266159
$816$	−1.16331e7	−0.611606
$817$	7.20136e6	0.377450
$818$	1.46458e7	0.765295
$819$	−2.17332e7	−1.13218
$820$	−6.83998e6	−0.355238
$821$	1.72038e7	0.890770	0.445385	−	0.895339i	$-0.353067\pi$
$821$	1.72038e7	0.890770	0.445385	+	0.895339i	$0.353067\pi$
$822$	−3.85355e7	−1.98921
$823$	−947098.	−0.0487411	−0.0243705	−	0.999703i	$-0.507758\pi$
$823$	−947098.	−0.0487411	−0.0243705	+	0.999703i	$0.507758\pi$
$824$	3.04909e6	0.156442
$825$	−9.48541e6	−0.485200
$826$	−4.57405e7	−2.33266
$827$	−3.05385e7	−1.55269	−0.776345	−	0.630308i	$-0.782928\pi$
$827$	−3.05385e7	−1.55269	−0.776345	+	0.630308i	$0.782928\pi$
$828$	3.19346e6	0.161877
$829$	−1.57415e7	−0.795538	−0.397769	−	0.917486i	$-0.630215\pi$
$829$	−1.57415e7	−0.795538	−0.397769	+	0.917486i	$0.630215\pi$
$830$	−3.78492e6	−0.190705
$831$	1.22636e7	0.616047
$832$	692224.	0.0346688
$833$	6.67971e7	3.33538
$834$	2.04257e7	1.01686
$835$	−1.11513e7	−0.553487
$836$	−7.01668e6	−0.347229
$837$	1.79101e7	0.883659
$838$	−1.21514e7	−0.597746
$839$	2.07700e7	1.01867	0.509333	−	0.860570i	$-0.329892\pi$
$839$	2.07700e7	1.01867	0.509333	+	0.860570i	$0.329892\pi$
$840$	−1.07289e7	−0.524637
$841$	−1.82503e7	−0.889774
$842$	7.54651e6	0.366831
$843$	1.65121e7	0.800263
$844$	−3.31265e6	−0.160073
$845$	714025.	0.0344010
$846$	−3.36969e7	−1.61869
$847$	−3.24694e7	−1.55513
$848$	1.03372e7	0.493643
$849$	2.16772e7	1.03213
$850$	−4.07325e6	−0.193372
$851$	−4.89169e6	−0.231545
$852$	4.69438e6	0.221554
$853$	−1.91838e7	−0.902740	−0.451370	−	0.892337i	$-0.649064\pi$
$853$	−1.91838e7	−0.902740	−0.451370	+	0.892337i	$0.649064\pi$
$854$	−2.91203e7	−1.36632
$855$	−1.07768e7	−0.504165
$856$	1.19377e7	0.556847
$857$	2.64211e7	1.22885	0.614425	−	0.788975i	$-0.289388\pi$
$857$	2.64211e7	1.22885	0.614425	+	0.788975i	$0.289388\pi$
$858$	1.02594e7	0.475778
$859$	−3.30576e7	−1.52858	−0.764289	−	0.644873i	$-0.776910\pi$
$859$	−3.30576e7	−1.52858	−0.764289	+	0.644873i	$0.776910\pi$
$860$	−3.57423e6	−0.164792
$861$	−1.14665e8	−5.27137
$862$	−2.86877e6	−0.131501
$863$	1.19324e7	0.545380	0.272690	−	0.962102i	$-0.412087\pi$
$863$	1.19324e7	0.545380	0.272690	+	0.962102i	$0.412087\pi$
$864$	8.33605e6	0.379906
$865$	1.43522e6	0.0652196
$866$	−1.05828e7	−0.479518
$867$	−3.44381e7	−1.55593
$868$	8.46328e6	0.381276
$869$	−3.36897e6	−0.151338
$870$	4.19366e6	0.187843
$871$	6.55203e6	0.292638
$872$	−922051.	−0.0410643
$873$	−8.37313e6	−0.371837
$874$	1.20292e6	0.0532671
$875$	−3.75665e6	−0.165875
$876$	−706020.	−0.0310854
$877$	3.88434e6	0.170537	0.0852684	−	0.996358i	$-0.472825\pi$
$877$	3.88434e6	0.170537	0.0852684	+	0.996358i	$0.472825\pi$
$878$	−1.79189e7	−0.784469
$879$	−1.69860e7	−0.741513
$880$	3.48257e6	0.151598
$881$	−8.93397e6	−0.387797	−0.193899	−	0.981022i	$-0.562113\pi$
$881$	−8.93397e6	−0.387797	−0.193899	+	0.981022i	$0.562113\pi$
$882$	−8.77148e7	−3.79666
$883$	−4.32552e6	−0.186697	−0.0933484	−	0.995634i	$-0.529757\pi$
$883$	−4.32552e6	−0.186697	−0.0933484	+	0.995634i	$0.529757\pi$
$884$	4.40563e6	0.189617
$885$	3.31632e7	1.42331
$886$	−1.72292e7	−0.737364
$887$	3.55552e7	1.51738	0.758689	−	0.651453i	$-0.225840\pi$
$887$	3.55552e7	1.51738	0.758689	+	0.651453i	$0.225840\pi$
$888$	−2.33997e7	−0.995812
$889$	4.38242e7	1.85977
$890$	−4.91510e6	−0.207997
$891$	5.28217e7	2.22904
$892$	−1.67822e7	−0.706214
$893$	−1.26930e7	−0.532643
$894$	−2.08712e7	−0.873380
$895$	2.18599e6	0.0912199
$896$	3.93913e6	0.163919
$897$	−1.75885e6	−0.0729874
$898$	101092.	0.00418335
$899$	−3.30807e6	−0.136514
$900$	5.34880e6	0.220115
$901$	6.57906e7	2.69993
$902$	3.72198e7	1.52320
$903$	−5.99184e7	−2.44535
$904$	3.25133e6	0.132324
$905$	533540.	0.0216544
$906$	−1.18438e6	−0.0479370
$907$	2.44157e7	0.985486	0.492743	−	0.870175i	$-0.335994\pi$
$907$	2.44157e7	0.985486	0.492743	+	0.870175i	$0.335994\pi$
$908$	−1.61134e6	−0.0648593
$909$	−7.38709e7	−2.96527
$910$	4.06319e6	0.162654
$911$	3.00267e7	1.19870	0.599352	−	0.800486i	$-0.295425\pi$
$911$	3.00267e7	1.19870	0.599352	+	0.800486i	$0.295425\pi$
$912$	5.75424e6	0.229087
$913$	2.05957e7	0.817711
$914$	−4.57439e6	−0.181120
$915$	2.11131e7	0.833679
$916$	7.79478e6	0.306948
$917$	−4.80164e7	−1.88567
$918$	5.30544e7	2.07785
$919$	−1.30118e7	−0.508216	−0.254108	−	0.967176i	$-0.581782\pi$
$919$	−1.30118e7	−0.508216	−0.254108	+	0.967176i	$0.581782\pi$
$920$	−597043.	−0.0232561
$921$	7.44009e7	2.89021
$922$	3.33964e7	1.29382
$923$	−1.77782e6	−0.0686886
$924$	5.83817e7	2.24956
$925$	−8.19320e6	−0.314847
$926$	1.36639e7	0.523656
$927$	−2.54828e7	−0.973975
$928$	−1.53970e6	−0.0586904
$929$	−5.16678e7	−1.96418	−0.982089	−	0.188419i	$-0.939664\pi$
$929$	−5.16678e7	−1.96418	−0.982089	+	0.188419i	$0.939664\pi$
$930$	−6.13613e6	−0.232641
$931$	−3.30407e7	−1.24932
$932$	−1.33255e7	−0.502509
$933$	4.52717e7	1.70264
$934$	−2.26842e7	−0.850857
$935$	2.21646e7	0.829147
$936$	−5.78526e6	−0.215841
$937$	−4.04703e6	−0.150587	−0.0752936	−	0.997161i	$-0.523989\pi$
$937$	−4.04703e6	−0.150587	−0.0752936	+	0.997161i	$0.523989\pi$
$938$	3.72846e7	1.38364
$939$	−1.65144e7	−0.611221
$940$	6.29990e6	0.232549
$941$	−4.43008e7	−1.63094	−0.815470	−	0.578799i	$-0.803521\pi$
$941$	−4.43008e7	−1.63094	−0.815470	+	0.578799i	$0.803521\pi$
$942$	−3.74719e7	−1.37587
$943$	−6.38088e6	−0.233669
$944$	−1.21759e7	−0.444704
$945$	4.89307e7	1.78239
$946$	1.94492e7	0.706602
$947$	−3.60463e7	−1.30613	−0.653064	−	0.757303i	$-0.726517\pi$
$947$	−3.60463e7	−1.30613	−0.653064	+	0.757303i	$0.726517\pi$
$948$	2.76283e6	0.0998464
$949$	267379.	0.00963745
$950$	2.01480e6	0.0724307
$951$	7.28042e7	2.61039
$952$	2.50704e7	0.896539
$953$	−1.31248e7	−0.468123	−0.234061	−	0.972222i	$-0.575202\pi$
$953$	−1.31248e7	−0.468123	−0.234061	+	0.972222i	$0.575202\pi$
$954$	−8.63931e7	−3.07332
$955$	7.68792e6	0.272773
$956$	2.15871e7	0.763923
$957$	−2.28198e7	−0.805439
$958$	2.46536e7	0.867894
$959$	8.30473e7	2.91594
$960$	−2.85599e6	−0.100018
$961$	−2.37888e7	−0.830929
$962$	8.86176e6	0.308733
$963$	−9.97693e7	−3.46682
$964$	−2.66053e7	−0.922096
$965$	4.56023e6	0.157641
$966$	−1.00088e7	−0.345096
$967$	2.48150e7	0.853390	0.426695	−	0.904396i	$-0.359678\pi$
$967$	2.48150e7	0.853390	0.426695	+	0.904396i	$0.359678\pi$
$968$	−8.64318e6	−0.296473
$969$	3.66226e7	1.25297
$970$	1.56542e6	0.0534198
$971$	−3.54227e6	−0.120569	−0.0602843	−	0.998181i	$-0.519201\pi$
$971$	−3.54227e6	−0.120569	−0.0602843	+	0.998181i	$0.519201\pi$
$972$	−1.16671e7	−0.396093
$973$	−4.40191e7	−1.49059
$974$	2.93080e7	0.989896
$975$	−2.94593e6	−0.0992456
$976$	−7.75167e6	−0.260478
$977$	9.16916e6	0.307322	0.153661	−	0.988124i	$-0.450894\pi$
$977$	9.16916e6	0.307322	0.153661	+	0.988124i	$0.450894\pi$
$978$	2.25222e7	0.752947
$979$	2.67456e7	0.891857
$980$	1.63990e7	0.545446
$981$	7.70604e6	0.255658
$982$	−3.55895e7	−1.17772
$983$	−3.05912e7	−1.00975	−0.504874	−	0.863193i	$-0.668461\pi$
$983$	−3.05912e7	−1.00975	−0.504874	+	0.863193i	$0.668461\pi$
$984$	−3.05233e7	−1.00495
$985$	−3.81270e6	−0.125211
$986$	−9.79936e6	−0.321000
$987$	1.05611e8	3.45078
$988$	−2.17921e6	−0.0710242
$989$	−3.33433e6	−0.108397
$990$	−2.91056e7	−0.943817
$991$	3.47852e7	1.12515	0.562575	−	0.826746i	$-0.309811\pi$
$991$	3.47852e7	1.12515	0.562575	+	0.826746i	$0.309811\pi$
$992$	2.25288e6	0.0726874
$993$	−2.28363e7	−0.734942
$994$	−1.01168e7	−0.324771
$995$	−1.46651e7	−0.469600
$996$	−1.68902e7	−0.539492
$997$	−4.21812e7	−1.34394	−0.671972	−	0.740577i	$-0.734552\pi$
$997$	−4.21812e7	−1.34394	−0.671972	+	0.740577i	$0.734552\pi$
$998$	−1.20895e7	−0.384222
$999$	1.06717e8	3.38314

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.6.a.f.1.1	✓	3
4.3	odd	2		1040.6.a.l.1.3		3
5.2	odd	4		650.6.b.j.599.3		6
5.3	odd	4		650.6.b.j.599.4		6
5.4	even	2		650.6.a.j.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.f.1.1	✓	3	1.1	even	1	trivial
650.6.a.j.1.3		3	5.4	even	2
650.6.b.j.599.3		6	5.2	odd	4
650.6.b.j.599.4		6	5.3	odd	4
1040.6.a.l.1.3		3	4.3	odd	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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -27.8905 q^{3} +16.0000 q^{4} +25.0000 q^{5} +111.562 q^{6} -240.426 q^{7} -64.0000 q^{8} +534.880 q^{9} -100.000 q^{10} +544.151 q^{11} -446.248 q^{12} +169.000 q^{13} +961.702 q^{14} -697.262 q^{15} +256.000 q^{16} +1629.30 q^{17} -2139.52 q^{18} -805.920 q^{19} +400.000 q^{20} +6705.59 q^{21} -2176.61 q^{22} +373.152 q^{23} +1784.99 q^{24} +625.000 q^{25} -676.000 q^{26} -8140.67 q^{27} -3846.81 q^{28} +1503.62 q^{29} +2789.05 q^{30} -2200.08 q^{31} -1024.00 q^{32} -15176.7 q^{33} -6517.20 q^{34} -6010.64 q^{35} +8558.08 q^{36} -13109.1 q^{37} +3223.68 q^{38} -4713.49 q^{39} -1600.00 q^{40} -17099.9 q^{41} -26822.4 q^{42} -8935.58 q^{43} +8706.42 q^{44} +13372.0 q^{45} -1492.61 q^{46} +15749.7 q^{47} -7139.97 q^{48} +40997.5 q^{49} -2500.00 q^{50} -45442.0 q^{51} +2704.00 q^{52} +40379.7 q^{53} +32562.7 q^{54} +13603.8 q^{55} +15387.2 q^{56} +22477.5 q^{57} -6014.46 q^{58} -47562.1 q^{59} -11156.2 q^{60} -30280.0 q^{61} +8800.31 q^{62} -128599. q^{63} +4096.00 q^{64} +4225.00 q^{65} +60706.6 q^{66} +38769.4 q^{67} +26068.8 q^{68} -10407.4 q^{69} +24042.6 q^{70} -10519.7 q^{71} -34232.3 q^{72} +1582.12 q^{73} +52436.5 q^{74} -17431.6 q^{75} -12894.7 q^{76} -130828. q^{77} +18854.0 q^{78} -6191.23 q^{79} +6400.00 q^{80} +97071.7 q^{81} +68399.8 q^{82} +37849.2 q^{83} +107289. q^{84} +40732.5 q^{85} +35742.3 q^{86} -41936.6 q^{87} -34825.7 q^{88} +49151.0 q^{89} -53488.0 q^{90} -40631.9 q^{91} +5970.43 q^{92} +61361.3 q^{93} -62999.0 q^{94} -20148.0 q^{95} +28559.9 q^{96} -15654.2 q^{97} -163990. q^{98} +291056. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} - 22 q^{3} + 48 q^{4} + 75 q^{5} + 88 q^{6} - 234 q^{7} - 192 q^{8} + 155 q^{9} - 300 q^{10} + 48 q^{11} - 352 q^{12} + 507 q^{13} + 936 q^{14} - 550 q^{15} + 768 q^{16} + 1506 q^{17} - 620 q^{18}+ \cdots + 350340 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 - 22 * q^3 + 48 * q^4 + 75 * q^5 + 88 * q^6 - 234 * q^7 - 192 * q^8 + 155 * q^9 - 300 * q^10 + 48 * q^11 - 352 * q^12 + 507 * q^13 + 936 * q^14 - 550 * q^15 + 768 * q^16 + 1506 * q^17 - 620 * q^18 - 360 * q^19 + 1200 * q^20 + 6904 * q^21 - 192 * q^22 - 2370 * q^23 + 1408 * q^24 + 1875 * q^25 - 2028 * q^26 - 10168 * q^27 - 3744 * q^28 - 3078 * q^29 + 2200 * q^30 - 5388 * q^31 - 3072 * q^32 - 22572 * q^33 - 6024 * q^34 - 5850 * q^35 + 2480 * q^36 - 25362 * q^37 + 1440 * q^38 - 3718 * q^39 - 4800 * q^40 - 15906 * q^41 - 27616 * q^42 - 39306 * q^43 + 768 * q^44 + 3875 * q^45 + 9480 * q^46 - 17778 * q^47 - 5632 * q^48 + 7767 * q^49 - 7500 * q^50 - 33972 * q^51 + 8112 * q^52 + 9246 * q^53 + 40672 * q^54 + 1200 * q^55 + 14976 * q^56 - 2996 * q^57 + 12312 * q^58 - 77760 * q^59 - 8800 * q^60 + 17982 * q^61 + 21552 * q^62 - 128762 * q^63 + 12288 * q^64 + 12675 * q^65 + 90288 * q^66 - 2922 * q^67 + 24096 * q^68 - 31860 * q^69 + 23400 * q^70 - 4944 * q^71 - 9920 * q^72 + 43278 * q^73 + 101448 * q^74 - 13750 * q^75 - 5760 * q^76 - 144420 * q^77 + 14872 * q^78 + 42120 * q^79 + 19200 * q^80 + 146519 * q^81 + 63624 * q^82 + 58098 * q^83 + 110464 * q^84 + 37650 * q^85 + 157224 * q^86 + 2016 * q^87 - 3072 * q^88 + 19614 * q^89 - 15500 * q^90 - 39546 * q^91 - 37920 * q^92 + 162796 * q^93 + 71112 * q^94 - 9000 * q^95 + 22528 * q^96 - 87078 * q^97 - 31068 * q^98 + 350340 * q^99

Introduction

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