LMFDB - Embedded newform 195.6.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,6,Mod(1,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("195.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	195.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:	$31.2748448635$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 67x^{2} + 57x + 250 $ x^4 - x^3 - 67x^2 + 57x + 250
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			1.2
Root			$-1.59162$ of defining polynomial
Character	$\chi$	$=$	195.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.59162 q^{2} -9.00000 q^{3} -25.2835 q^{4} +25.0000 q^{5} +23.3245 q^{6} -54.8537 q^{7} +148.457 q^{8} +81.0000 q^{9} -64.7904 q^{10} -290.262 q^{11} +227.552 q^{12} +169.000 q^{13} +142.160 q^{14} -225.000 q^{15} +424.330 q^{16} +300.969 q^{17} -209.921 q^{18} +2338.08 q^{19} -632.088 q^{20} +493.684 q^{21} +752.248 q^{22} +1669.33 q^{23} -1336.11 q^{24} +625.000 q^{25} -437.983 q^{26} -729.000 q^{27} +1386.90 q^{28} -2268.75 q^{29} +583.114 q^{30} -743.117 q^{31} -5850.32 q^{32} +2612.36 q^{33} -779.996 q^{34} -1371.34 q^{35} -2047.97 q^{36} +5772.74 q^{37} -6059.40 q^{38} -1521.00 q^{39} +3711.42 q^{40} -17026.7 q^{41} -1279.44 q^{42} -23533.3 q^{43} +7338.85 q^{44} +2025.00 q^{45} -4326.25 q^{46} +22075.9 q^{47} -3818.97 q^{48} -13798.1 q^{49} -1619.76 q^{50} -2708.72 q^{51} -4272.92 q^{52} -14705.3 q^{53} +1889.29 q^{54} -7256.55 q^{55} -8143.41 q^{56} -21042.7 q^{57} +5879.73 q^{58} -29292.8 q^{59} +5688.79 q^{60} +29473.2 q^{61} +1925.87 q^{62} -4443.15 q^{63} +1583.23 q^{64} +4225.00 q^{65} -6770.23 q^{66} -63057.6 q^{67} -7609.56 q^{68} -15023.9 q^{69} +3553.99 q^{70} +66763.1 q^{71} +12025.0 q^{72} -89576.2 q^{73} -14960.7 q^{74} -5625.00 q^{75} -59114.9 q^{76} +15922.0 q^{77} +3941.85 q^{78} +54278.7 q^{79} +10608.2 q^{80} +6561.00 q^{81} +44126.7 q^{82} +7985.79 q^{83} -12482.1 q^{84} +7524.22 q^{85} +60989.3 q^{86} +20418.8 q^{87} -43091.4 q^{88} -62769.6 q^{89} -5248.02 q^{90} -9270.28 q^{91} -42206.5 q^{92} +6688.06 q^{93} -57212.1 q^{94} +58451.9 q^{95} +52652.9 q^{96} -15494.6 q^{97} +35759.3 q^{98} -23511.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 36 q^{3} + 9 q^{4} + 100 q^{5} + 27 q^{6} - 87 q^{7} - 183 q^{8} + 324 q^{9} - 75 q^{10} - 631 q^{11} - 81 q^{12} + 676 q^{13} + 1344 q^{14} - 900 q^{15} - 351 q^{16} - 599 q^{17} - 243 q^{18}+ \cdots - 51111 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 36 * q^3 + 9 * q^4 + 100 * q^5 + 27 * q^6 - 87 * q^7 - 183 * q^8 + 324 * q^9 - 75 * q^10 - 631 * q^11 - 81 * q^12 + 676 * q^13 + 1344 * q^14 - 900 * q^15 - 351 * q^16 - 599 * q^17 - 243 * q^18 - 4 * q^19 + 225 * q^20 + 783 * q^21 - 1920 * q^22 + 4459 * q^23 + 1647 * q^24 + 2500 * q^25 - 507 * q^26 - 2916 * q^27 - 1048 * q^28 - 5274 * q^29 + 675 * q^30 + 2642 * q^31 - 199 * q^32 + 5679 * q^33 + 15794 * q^34 - 2175 * q^35 + 729 * q^36 - 30189 * q^37 - 26408 * q^38 - 6084 * q^39 - 4575 * q^40 - 8947 * q^41 - 12096 * q^42 - 15928 * q^43 - 29676 * q^44 + 8100 * q^45 - 14272 * q^46 - 28242 * q^47 + 3159 * q^48 - 52335 * q^49 - 1875 * q^50 + 5391 * q^51 + 1521 * q^52 - 38021 * q^53 + 2187 * q^54 - 15775 * q^55 - 2480 * q^56 + 36 * q^57 - 115014 * q^58 - 17200 * q^59 - 2025 * q^60 - 67669 * q^61 - 99568 * q^62 - 7047 * q^63 - 69455 * q^64 + 16900 * q^65 + 17280 * q^66 + 8832 * q^67 - 45054 * q^68 - 40131 * q^69 + 33600 * q^70 + 128633 * q^71 - 14823 * q^72 - 48706 * q^73 + 35026 * q^74 - 22500 * q^75 - 66036 * q^76 - 25533 * q^77 + 4563 * q^78 + 72799 * q^79 - 8775 * q^80 + 26244 * q^81 - 191810 * q^82 + 15868 * q^83 + 9432 * q^84 - 14975 * q^85 + 247924 * q^86 + 47466 * q^87 + 5204 * q^88 - 45713 * q^89 - 6075 * q^90 - 14703 * q^91 + 271408 * q^92 - 23778 * q^93 - 51544 * q^94 - 100 * q^95 + 1791 * q^96 - 148949 * q^97 + 10289 * q^98 - 51111 * 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 $

$2$	−2.59162	−0.458137	−0.229069	−	0.973410i	$-0.573568\pi$
$2$	−2.59162	−0.458137	−0.229069	+	0.973410i	$0.573568\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−25.2835	−0.790110
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	23.3245	0.264506
$7$	−54.8537	−0.423118	−0.211559	−	0.977365i	$-0.567854\pi$
$7$	−54.8537	−0.423118	−0.211559	+	0.977365i	$0.567854\pi$
$8$	148.457	0.820116
$9$	81.0000	0.333333
$10$	−64.7904	−0.204885
$11$	−290.262	−0.723283	−0.361642	−	0.932317i	$-0.617784\pi$
$11$	−290.262	−0.723283	−0.361642	+	0.932317i	$0.617784\pi$
$12$	227.552	0.456170
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	142.160	0.193846
$15$	−225.000	−0.258199
$16$	424.330	0.414384
$17$	300.969	0.252580	0.126290	−	0.991993i	$-0.459693\pi$
$17$	300.969	0.252580	0.126290	+	0.991993i	$0.459693\pi$
$18$	−209.921	−0.152712
$19$	2338.08	1.48585	0.742925	−	0.669375i	$-0.233438\pi$
$19$	2338.08	1.48585	0.742925	+	0.669375i	$0.233438\pi$
$20$	−632.088	−0.353348
$21$	493.684	0.244287
$22$	752.248	0.331363
$23$	1669.33	0.657994	0.328997	−	0.944331i	$-0.393289\pi$
$23$	1669.33	0.657994	0.328997	+	0.944331i	$0.393289\pi$
$24$	−1336.11	−0.473494
$25$	625.000	0.200000
$26$	−437.983	−0.127064
$27$	−729.000	−0.192450
$28$	1386.90	0.334310
$29$	−2268.75	−0.500947	−0.250473	−	0.968123i	$-0.580586\pi$
$29$	−2268.75	−0.500947	−0.250473	+	0.968123i	$0.580586\pi$
$30$	583.114	0.118291
$31$	−743.117	−0.138884	−0.0694421	−	0.997586i	$-0.522122\pi$
$31$	−743.117	−0.138884	−0.0694421	+	0.997586i	$0.522122\pi$
$32$	−5850.32	−1.00996
$33$	2612.36	0.417588
$34$	−779.996	−0.115716
$35$	−1371.34	−0.189224
$36$	−2047.97	−0.263370
$37$	5772.74	0.693231	0.346615	−	0.938007i	$-0.387331\pi$
$37$	5772.74	0.693231	0.346615	+	0.938007i	$0.387331\pi$
$38$	−6059.40	−0.680723
$39$	−1521.00	−0.160128
$40$	3711.42	0.366767
$41$	−17026.7	−1.58187	−0.790936	−	0.611899i	$-0.790406\pi$
$41$	−17026.7	−1.58187	−0.790936	+	0.611899i	$0.790406\pi$
$42$	−1279.44	−0.111917
$43$	−23533.3	−1.94094	−0.970470	−	0.241222i	$-0.922452\pi$
$43$	−23533.3	−1.94094	−0.970470	+	0.241222i	$0.922452\pi$
$44$	7338.85	0.571474
$45$	2025.00	0.149071
$46$	−4326.25	−0.301452
$47$	22075.9	1.45772	0.728858	−	0.684665i	$-0.240051\pi$
$47$	22075.9	1.45772	0.728858	+	0.684665i	$0.240051\pi$
$48$	−3818.97	−0.239245
$49$	−13798.1	−0.820972
$50$	−1619.76	−0.0916275
$51$	−2708.72	−0.145827
$52$	−4272.92	−0.219137
$53$	−14705.3	−0.719093	−0.359546	−	0.933127i	$-0.617069\pi$
$53$	−14705.3	−0.719093	−0.359546	+	0.933127i	$0.617069\pi$
$54$	1889.29	0.0881686
$55$	−7256.55	−0.323462
$56$	−8143.41	−0.347006
$57$	−21042.7	−0.857856
$58$	5879.73	0.229502
$59$	−29292.8	−1.09555	−0.547774	−	0.836626i	$-0.684525\pi$
$59$	−29292.8	−1.09555	−0.547774	+	0.836626i	$0.684525\pi$
$60$	5688.79	0.204006
$61$	29473.2	1.01415	0.507076	−	0.861901i	$-0.330726\pi$
$61$	29473.2	1.01415	0.507076	+	0.861901i	$0.330726\pi$
$62$	1925.87	0.0636281
$63$	−4443.15	−0.141039
$64$	1583.23	0.0483165
$65$	4225.00	0.124035
$66$	−6770.23	−0.191313
$67$	−63057.6	−1.71613	−0.858066	−	0.513539i	$-0.828334\pi$
$67$	−63057.6	−1.71613	−0.858066	+	0.513539i	$0.828334\pi$
$68$	−7609.56	−0.199566
$69$	−15023.9	−0.379893
$70$	3553.99	0.0866905
$71$	66763.1	1.57178	0.785888	−	0.618368i	$-0.212206\pi$
$71$	66763.1	1.57178	0.785888	+	0.618368i	$0.212206\pi$
$72$	12025.0	0.273372
$73$	−89576.2	−1.96737	−0.983684	−	0.179905i	$-0.942421\pi$
$73$	−89576.2	−1.96737	−0.983684	+	0.179905i	$0.942421\pi$
$74$	−14960.7	−0.317595
$75$	−5625.00	−0.115470
$76$	−59114.9	−1.17399
$77$	15922.0	0.306034
$78$	3941.85	0.0733607
$79$	54278.7	0.978501	0.489251	−	0.872143i	$-0.337270\pi$
$79$	54278.7	0.978501	0.489251	+	0.872143i	$0.337270\pi$
$80$	10608.2	0.185318
$81$	6561.00	0.111111
$82$	44126.7	0.724714
$83$	7985.79	0.127240	0.0636198	−	0.997974i	$-0.479735\pi$
$83$	7985.79	0.127240	0.0636198	+	0.997974i	$0.479735\pi$
$84$	−12482.1	−0.193014
$85$	7524.22	0.112957
$86$	60989.3	0.889217
$87$	20418.8	0.289222
$88$	−43091.4	−0.593176
$89$	−62769.6	−0.839990	−0.419995	−	0.907526i	$-0.637968\pi$
$89$	−62769.6	−0.839990	−0.419995	+	0.907526i	$0.637968\pi$
$90$	−5248.02	−0.0682951
$91$	−9270.28	−0.117352
$92$	−42206.5	−0.519888
$93$	6688.06	0.0801849
$94$	−57212.1	−0.667834
$95$	58451.9	0.664492
$96$	52652.9	0.583101
$97$	−15494.6	−0.167205	−0.0836026	−	0.996499i	$-0.526643\pi$
$97$	−15494.6	−0.167205	−0.0836026	+	0.996499i	$0.526643\pi$
$98$	35759.3	0.376118
$99$	−23511.2	−0.241094
$100$	−15802.2	−0.158022
$101$	−41988.4	−0.409568	−0.204784	−	0.978807i	$-0.565649\pi$
$101$	−41988.4	−0.409568	−0.204784	+	0.978807i	$0.565649\pi$
$102$	7019.96	0.0668089
$103$	−105241.	−0.977447	−0.488724	−	0.872439i	$-0.662537\pi$
$103$	−105241.	−0.977447	−0.488724	+	0.872439i	$0.662537\pi$
$104$	25089.2	0.227459
$105$	12342.1	0.109248
$106$	38110.5	0.329443
$107$	13869.3	0.117110	0.0585552	−	0.998284i	$-0.481351\pi$
$107$	13869.3	0.117110	0.0585552	+	0.998284i	$0.481351\pi$
$108$	18431.7	0.152057
$109$	−167225.	−1.34814	−0.674072	−	0.738666i	$-0.735456\pi$
$109$	−167225.	−1.34814	−0.674072	+	0.738666i	$0.735456\pi$
$110$	18806.2	0.148190
$111$	−51954.7	−0.400237
$112$	−23276.1	−0.175333
$113$	−62253.5	−0.458635	−0.229318	−	0.973352i	$-0.573649\pi$
$113$	−62253.5	−0.458635	−0.229318	+	0.973352i	$0.573649\pi$
$114$	54534.6	0.393016
$115$	41733.2	0.294264
$116$	57362.0	0.395803
$117$	13689.0	0.0924500
$118$	75915.8	0.501911
$119$	−16509.3	−0.106871
$120$	−33402.8	−0.211753
$121$	−76799.0	−0.476861
$122$	−76383.2	−0.464621
$123$	153240.	0.913294
$124$	18788.6	0.109734
$125$	15625.0	0.0894427
$126$	11514.9	0.0646153
$127$	151671.	0.834437	0.417219	−	0.908806i	$-0.363005\pi$
$127$	151671.	0.834437	0.417219	+	0.908806i	$0.363005\pi$
$128$	183107.	0.987826
$129$	211800.	1.12060
$130$	−10949.6	−0.0568249
$131$	380790.	1.93868	0.969342	−	0.245716i	$-0.0790231\pi$
$131$	380790.	1.93868	0.969342	+	0.245716i	$0.0790231\pi$
$132$	−66049.6	−0.329940
$133$	−128252.	−0.628689
$134$	163421.	0.786224
$135$	−18225.0	−0.0860663
$136$	44680.9	0.207145
$137$	141642.	0.644748	0.322374	−	0.946612i	$-0.395519\pi$
$137$	141642.	0.644748	0.322374	+	0.946612i	$0.395519\pi$
$138$	38936.3	0.174043
$139$	274401.	1.20461	0.602307	−	0.798264i	$-0.294248\pi$
$139$	274401.	1.20461	0.602307	+	0.798264i	$0.294248\pi$
$140$	34672.4	0.149508
$141$	−198683.	−0.841613
$142$	−173024.	−0.720090
$143$	−49054.3	−0.200603
$144$	34370.7	0.138128
$145$	−56718.8	−0.224030
$146$	232147.	0.901325
$147$	124183.	0.473988
$148$	−145955.	−0.547729
$149$	241413.	0.890831	0.445415	−	0.895324i	$-0.353056\pi$
$149$	241413.	0.890831	0.445415	+	0.895324i	$0.353056\pi$
$150$	14577.8	0.0529011
$151$	168939.	0.602959	0.301479	−	0.953473i	$-0.402520\pi$
$151$	168939.	0.602959	0.301479	+	0.953473i	$0.402520\pi$
$152$	347104.	1.21857
$153$	24378.5	0.0841934
$154$	−41263.6	−0.140206
$155$	−18577.9	−0.0621109
$156$	38456.2	0.126519
$157$	−351585.	−1.13837	−0.569183	−	0.822211i	$-0.692740\pi$
$157$	−351585.	−1.13837	−0.569183	+	0.822211i	$0.692740\pi$
$158$	−140669.	−0.448288
$159$	132348.	0.415168
$160$	−146258.	−0.451668
$161$	−91568.8	−0.278409
$162$	−17003.6	−0.0509041
$163$	−370754.	−1.09299	−0.546495	−	0.837462i	$-0.684038\pi$
$163$	−370754.	−1.09299	−0.546495	+	0.837462i	$0.684038\pi$
$164$	430495.	1.24985
$165$	65308.9	0.186751
$166$	−20696.1	−0.0582932
$167$	−708309.	−1.96531	−0.982656	−	0.185439i	$-0.940629\pi$
$167$	−708309.	−1.96531	−0.982656	+	0.185439i	$0.940629\pi$
$168$	73290.7	0.200344
$169$	28561.0	0.0769231
$170$	−19499.9	−0.0517500
$171$	189384.	0.495283
$172$	595005.	1.53356
$173$	−57046.9	−0.144916	−0.0724580	−	0.997371i	$-0.523084\pi$
$173$	−57046.9	−0.144916	−0.0724580	+	0.997371i	$0.523084\pi$
$174$	−52917.6	−0.132503
$175$	−34283.6	−0.0846235
$176$	−123167.	−0.299717
$177$	263635.	0.632515
$178$	162675.	0.384831
$179$	−186253.	−0.434481	−0.217241	−	0.976118i	$-0.569706\pi$
$179$	−186253.	−0.434481	−0.217241	+	0.976118i	$0.569706\pi$
$180$	−51199.1	−0.117783
$181$	75693.0	0.171735	0.0858676	−	0.996307i	$-0.472634\pi$
$181$	75693.0	0.171735	0.0858676	+	0.996307i	$0.472634\pi$
$182$	24025.0	0.0537632
$183$	−265259.	−0.585521
$184$	247823.	0.539631
$185$	144319.	0.310022
$186$	−17332.9	−0.0367357
$187$	−87359.8	−0.182687
$188$	−558156.	−1.15176
$189$	39988.4	0.0814290
$190$	−151485.	−0.304429
$191$	−305399.	−0.605737	−0.302869	−	0.953032i	$-0.597944\pi$
$191$	−305399.	−0.605737	−0.302869	+	0.953032i	$0.597944\pi$
$192$	−14249.1	−0.0278955
$193$	−741845.	−1.43357	−0.716787	−	0.697292i	$-0.754388\pi$
$193$	−741845.	−1.43357	−0.716787	+	0.697292i	$0.754388\pi$
$194$	40155.9	0.0766029
$195$	−38025.0	−0.0716115
$196$	348864.	0.648658
$197$	603512.	1.10795	0.553975	−	0.832533i	$-0.313110\pi$
$197$	603512.	1.10795	0.553975	+	0.832533i	$0.313110\pi$
$198$	60932.1	0.110454
$199$	343396.	0.614698	0.307349	−	0.951597i	$-0.400558\pi$
$199$	343396.	0.614698	0.307349	+	0.951597i	$0.400558\pi$
$200$	92785.6	0.164023
$201$	567519.	0.990809
$202$	108818.	0.187639
$203$	124449.	0.211959
$204$	68486.0	0.115220
$205$	−425668.	−0.707435
$206$	272745.	0.447805
$207$	135215.	0.219331
$208$	71711.7	0.114930
$209$	−678655.	−1.07469
$210$	−31986.0	−0.0500508
$211$	−960164.	−1.48470	−0.742351	−	0.670011i	$-0.766289\pi$
$211$	−960164.	−1.48470	−0.742351	+	0.670011i	$0.766289\pi$
$212$	371802.	0.568162
$213$	−600868.	−0.907466
$214$	−35943.9	−0.0536526
$215$	−588333.	−0.868015
$216$	−108225.	−0.157831
$217$	40762.8	0.0587644
$218$	433384.	0.617635
$219$	806186.	1.13586
$220$	183471.	0.255571
$221$	50863.8	0.0700532
$222$	134647.	0.183363
$223$	−625536.	−0.842346	−0.421173	−	0.906980i	$-0.638381\pi$
$223$	−625536.	−0.842346	−0.421173	+	0.906980i	$0.638381\pi$
$224$	320912.	0.427332
$225$	50625.0	0.0666667
$226$	161337.	0.210118
$227$	−1.40089e6	−1.80443	−0.902215	−	0.431287i	$-0.858060\pi$
$227$	−1.40089e6	−1.80443	−0.902215	+	0.431287i	$0.858060\pi$
$228$	532034.	0.677801
$229$	−825220.	−1.03988	−0.519938	−	0.854204i	$-0.674045\pi$
$229$	−825220.	−1.03988	−0.519938	+	0.854204i	$0.674045\pi$
$230$	−108156.	−0.134813
$231$	−143298.	−0.176689
$232$	−336812.	−0.410835
$233$	−1.25079e6	−1.50937	−0.754684	−	0.656088i	$-0.772210\pi$
$233$	−1.25079e6	−1.50937	−0.754684	+	0.656088i	$0.772210\pi$
$234$	−35476.6	−0.0423548
$235$	551896.	0.651910
$236$	740626.	0.865604
$237$	−488508.	−0.564938
$238$	42785.7	0.0489617
$239$	900688.	1.01995	0.509976	−	0.860189i	$-0.329654\pi$
$239$	900688.	1.01995	0.509976	+	0.860189i	$0.329654\pi$
$240$	−95474.2	−0.106994
$241$	137571.	0.152575	0.0762876	−	0.997086i	$-0.475693\pi$
$241$	137571.	0.152575	0.0762876	+	0.997086i	$0.475693\pi$
$242$	199033.	0.218468
$243$	−59049.0	−0.0641500
$244$	−745187.	−0.801292
$245$	−344952.	−0.367150
$246$	−397140.	−0.418414
$247$	395135.	0.412101
$248$	−110321.	−0.113901
$249$	−71872.1	−0.0734618
$250$	−40494.0	−0.0409770
$251$	1.45062e6	1.45334	0.726671	−	0.686985i	$-0.241066\pi$
$251$	1.45062e6	1.45334	0.726671	+	0.686985i	$0.241066\pi$
$252$	112339.	0.111437
$253$	−484542.	−0.475916
$254$	−393073.	−0.382287
$255$	−67718.0	−0.0652159
$256$	−525207.	−0.500876
$257$	−197792.	−0.186799	−0.0933997	−	0.995629i	$-0.529773\pi$
$257$	−197792.	−0.186799	−0.0933997	+	0.995629i	$0.529773\pi$
$258$	−548904.	−0.513390
$259$	−316656.	−0.293318
$260$	−106823.	−0.0980011
$261$	−183769.	−0.166982
$262$	−986861.	−0.888183
$263$	−504026.	−0.449328	−0.224664	−	0.974436i	$-0.572128\pi$
$263$	−504026.	−0.449328	−0.224664	+	0.974436i	$0.572128\pi$
$264$	387823.	0.342471
$265$	−367633.	−0.321588
$266$	332381.	0.288026
$267$	564926.	0.484968
$268$	1.59432e6	1.35593
$269$	−371314.	−0.312867	−0.156434	−	0.987688i	$-0.550000\pi$
$269$	−371314.	−0.312867	−0.156434	+	0.987688i	$0.550000\pi$
$270$	47232.2	0.0394302
$271$	−1.41828e6	−1.17311	−0.586556	−	0.809909i	$-0.699516\pi$
$271$	−1.41828e6	−1.17311	−0.586556	+	0.809909i	$0.699516\pi$
$272$	127710.	0.104665
$273$	83432.5	0.0677530
$274$	−367081.	−0.295383
$275$	−181414.	−0.144657
$276$	379858.	0.300157
$277$	353077.	0.276484	0.138242	−	0.990398i	$-0.455855\pi$
$277$	353077.	0.276484	0.138242	+	0.990398i	$0.455855\pi$
$278$	−711141.	−0.551879
$279$	−60192.5	−0.0462948
$280$	−203585.	−0.155186
$281$	1.02661e6	0.775600	0.387800	−	0.921744i	$-0.373235\pi$
$281$	1.02661e6	0.775600	0.387800	+	0.921744i	$0.373235\pi$
$282$	514909.	0.385574
$283$	−1.71763e6	−1.27487	−0.637433	−	0.770506i	$-0.720004\pi$
$283$	−1.71763e6	−1.27487	−0.637433	+	0.770506i	$0.720004\pi$
$284$	−1.68801e6	−1.24188
$285$	−526068.	−0.383645
$286$	127130.	0.0919036
$287$	933979.	0.669318
$288$	−473876.	−0.336654
$289$	−1.32927e6	−0.936203
$290$	146993.	0.102637
$291$	139451.	0.0965360
$292$	2.26480e6	1.55444
$293$	−510871.	−0.347650	−0.173825	−	0.984777i	$-0.555613\pi$
$293$	−510871.	−0.347650	−0.173825	+	0.984777i	$0.555613\pi$
$294$	−321834.	−0.217152
$295$	−732321.	−0.489944
$296$	857003.	0.568530
$297$	211601.	0.139196
$298$	−625650.	−0.408123
$299$	282116.	0.182495
$300$	142220.	0.0912341
$301$	1.29089e6	0.821246
$302$	−437825.	−0.276238
$303$	377896.	0.236464
$304$	992116.	0.615713
$305$	736830.	0.453542
$306$	−63179.7	−0.0385721
$307$	982994.	0.595257	0.297629	−	0.954682i	$-0.403804\pi$
$307$	982994.	0.595257	0.297629	+	0.954682i	$0.403804\pi$
$308$	−402563.	−0.241800
$309$	947172.	0.564330
$310$	48146.9	0.0284553
$311$	127598.	0.0748069	0.0374034	−	0.999300i	$-0.488091\pi$
$311$	127598.	0.0748069	0.0374034	+	0.999300i	$0.488091\pi$
$312$	−225803.	−0.131324
$313$	−1.48526e6	−0.856924	−0.428462	−	0.903560i	$-0.640944\pi$
$313$	−1.48526e6	−0.856924	−0.428462	+	0.903560i	$0.640944\pi$
$314$	911174.	0.521528
$315$	−111079.	−0.0630746
$316$	−1.37236e6	−0.773124
$317$	187925.	0.105036	0.0525179	−	0.998620i	$-0.483275\pi$
$317$	187925.	0.105036	0.0525179	+	0.998620i	$0.483275\pi$
$318$	−342995.	−0.190204
$319$	658532.	0.362327
$320$	39580.9	0.0216078
$321$	−124824.	−0.0676137
$322$	237311.	0.127549
$323$	703689.	0.375296
$324$	−165885.	−0.0877900
$325$	105625.	0.0554700
$326$	960851.	0.500740
$327$	1.50503e6	0.778351
$328$	−2.52773e6	−1.29732
$329$	−1.21094e6	−0.616785
$330$	−169256.	−0.0855576
$331$	−349254.	−0.175215	−0.0876075	−	0.996155i	$-0.527922\pi$
$331$	−349254.	−0.175215	−0.0876075	+	0.996155i	$0.527922\pi$
$332$	−201909.	−0.100533
$333$	467592.	0.231077
$334$	1.83566e6	0.900383
$335$	−1.57644e6	−0.767478
$336$	209485.	0.101229
$337$	898203.	0.430824	0.215412	−	0.976523i	$-0.430891\pi$
$337$	898203.	0.430824	0.215412	+	0.976523i	$0.430891\pi$
$338$	−74019.1	−0.0352413
$339$	560281.	0.264793
$340$	−190239.	−0.0892487
$341$	215699.	0.100453
$342$	−490811.	−0.226908
$343$	1.67880e6	0.770485
$344$	−3.49368e6	−1.59180
$345$	−375599.	−0.169893
$346$	147844.	0.0663914
$347$	1.00900e6	0.449851	0.224925	−	0.974376i	$-0.427786\pi$
$347$	1.00900e6	0.449851	0.224925	+	0.974376i	$0.427786\pi$
$348$	−516258.	−0.228517
$349$	−93616.8	−0.0411425	−0.0205712	−	0.999788i	$-0.506548\pi$
$349$	−93616.8	−0.0411425	−0.0205712	+	0.999788i	$0.506548\pi$
$350$	88849.9	0.0387692
$351$	−123201.	−0.0533761
$352$	1.69813e6	0.730488
$353$	−378686.	−0.161749	−0.0808746	−	0.996724i	$-0.525771\pi$
$353$	−378686.	−0.161749	−0.0808746	+	0.996724i	$0.525771\pi$
$354$	−683242.	−0.289779
$355$	1.66908e6	0.702920
$356$	1.58704e6	0.663685
$357$	148583.	0.0617021
$358$	482697.	0.199052
$359$	1.23245e6	0.504702	0.252351	−	0.967636i	$-0.418796\pi$
$359$	1.23245e6	0.504702	0.252351	+	0.967636i	$0.418796\pi$
$360$	300625.	0.122256
$361$	2.99051e6	1.20775
$362$	−196167.	−0.0786783
$363$	691191.	0.275316
$364$	234385.	0.0927208
$365$	−2.23941e6	−0.879834
$366$	687449.	0.268249
$367$	2.65963e6	1.03076	0.515378	−	0.856963i	$-0.327652\pi$
$367$	2.65963e6	1.03076	0.515378	+	0.856963i	$0.327652\pi$
$368$	708345.	0.272662
$369$	−1.37916e6	−0.527291
$370$	−374018.	−0.142033
$371$	806642.	0.304261
$372$	−169098.	−0.0633549
$373$	−2.15129e6	−0.800620	−0.400310	−	0.916380i	$-0.631098\pi$
$373$	−2.15129e6	−0.800620	−0.400310	+	0.916380i	$0.631098\pi$
$374$	226403.	0.0836958
$375$	−140625.	−0.0516398
$376$	3.27731e6	1.19550
$377$	−383419.	−0.138938
$378$	−103634.	−0.0373057
$379$	286584.	0.102484	0.0512418	−	0.998686i	$-0.483682\pi$
$379$	286584.	0.102484	0.0512418	+	0.998686i	$0.483682\pi$
$380$	−1.47787e6	−0.525022
$381$	−1.36504e6	−0.481762
$382$	791477.	0.277511
$383$	2.49736e6	0.869931	0.434966	−	0.900447i	$-0.356760\pi$
$383$	2.49736e6	0.869931	0.434966	+	0.900447i	$0.356760\pi$
$384$	−1.64796e6	−0.570321
$385$	398049.	0.136863
$386$	1.92258e6	0.656774
$387$	−1.90620e6	−0.646980
$388$	391757.	0.132111
$389$	4.84505e6	1.62339	0.811697	−	0.584079i	$-0.198544\pi$
$389$	4.84505e6	1.62339	0.811697	+	0.584079i	$0.198544\pi$
$390$	98546.2	0.0328079
$391$	502416.	0.166196
$392$	−2.04842e6	−0.673292
$393$	−3.42711e6	−1.11930
$394$	−1.56407e6	−0.507593
$395$	1.35697e6	0.437599
$396$	594447.	0.190491
$397$	−898099.	−0.285988	−0.142994	−	0.989724i	$-0.545673\pi$
$397$	−898099.	−0.285988	−0.142994	+	0.989724i	$0.545673\pi$
$398$	−889949.	−0.281616
$399$	1.15427e6	0.362974
$400$	265206.	0.0828769
$401$	−3.15459e6	−0.979676	−0.489838	−	0.871813i	$-0.662944\pi$
$401$	−3.15459e6	−0.979676	−0.489838	+	0.871813i	$0.662944\pi$
$402$	−1.47079e6	−0.453927
$403$	−125587.	−0.0385196
$404$	1.06162e6	0.323604
$405$	164025.	0.0496904
$406$	−322525.	−0.0971065
$407$	−1.67561e6	−0.501402
$408$	−402128.	−0.119595
$409$	3.05248e6	0.902286	0.451143	−	0.892452i	$-0.351016\pi$
$409$	3.05248e6	0.902286	0.451143	+	0.892452i	$0.351016\pi$
$410$	1.10317e6	0.324102
$411$	−1.27478e6	−0.372246
$412$	2.66087e6	0.772291
$413$	1.60682e6	0.463546
$414$	−350427.	−0.100484
$415$	199645.	0.0569033
$416$	−988704.	−0.280113
$417$	−2.46961e6	−0.695485
$418$	1.75881e6	0.492356
$419$	−4.54407e6	−1.26448	−0.632238	−	0.774774i	$-0.717863\pi$
$419$	−4.54407e6	−1.26448	−0.632238	+	0.774774i	$0.717863\pi$
$420$	−312052.	−0.0863183
$421$	2.76813e6	0.761169	0.380585	−	0.924746i	$-0.375723\pi$
$421$	2.76813e6	0.761169	0.380585	+	0.924746i	$0.375723\pi$
$422$	2.48838e6	0.680197
$423$	1.78814e6	0.485905
$424$	−2.18311e6	−0.589739
$425$	188106.	0.0505161
$426$	1.55722e6	0.415744
$427$	−1.61672e6	−0.429105
$428$	−350665.	−0.0925301
$429$	441488.	0.115818
$430$	1.52473e6	0.397670
$431$	4.41610e6	1.14511	0.572553	−	0.819868i	$-0.305953\pi$
$431$	4.41610e6	1.14511	0.572553	+	0.819868i	$0.305953\pi$
$432$	−309336.	−0.0797483
$433$	−863694.	−0.221381	−0.110690	−	0.993855i	$-0.535306\pi$
$433$	−863694.	−0.221381	−0.110690	+	0.993855i	$0.535306\pi$
$434$	−105641.	−0.0269222
$435$	510469.	0.129344
$436$	4.22805e6	1.06518
$437$	3.90302e6	0.977680
$438$	−2.08932e6	−0.520380
$439$	−6.45914e6	−1.59961	−0.799803	−	0.600262i	$-0.795063\pi$
$439$	−6.45914e6	−1.59961	−0.799803	+	0.600262i	$0.795063\pi$
$440$	−1.07728e6	−0.265277
$441$	−1.11764e6	−0.273657
$442$	−131819.	−0.0320940
$443$	−6.66037e6	−1.61246	−0.806231	−	0.591601i	$-0.798496\pi$
$443$	−6.66037e6	−1.61246	−0.806231	+	0.591601i	$0.798496\pi$
$444$	1.31360e6	0.316231
$445$	−1.56924e6	−0.375655
$446$	1.62115e6	0.385910
$447$	−2.17272e6	−0.514321
$448$	−86846.3	−0.0204436
$449$	−3.86595e6	−0.904984	−0.452492	−	0.891769i	$-0.649465\pi$
$449$	−3.86595e6	−0.904984	−0.452492	+	0.891769i	$0.649465\pi$
$450$	−131201.	−0.0305425
$451$	4.94221e6	1.14414
$452$	1.57399e6	0.362373
$453$	−1.52045e6	−0.348118
$454$	3.63057e6	0.826676
$455$	−231757.	−0.0524813
$456$	−3.12393e6	−0.703542
$457$	6.31227e6	1.41382	0.706912	−	0.707302i	$-0.250088\pi$
$457$	6.31227e6	1.41382	0.706912	+	0.707302i	$0.250088\pi$
$458$	2.13865e6	0.476406
$459$	−219406.	−0.0486091
$460$	−1.05516e6	−0.232501
$461$	−5.36464e6	−1.17568	−0.587839	−	0.808978i	$-0.700021\pi$
$461$	−5.36464e6	−1.17568	−0.587839	+	0.808978i	$0.700021\pi$
$462$	371372.	0.0809477
$463$	2.43236e6	0.527321	0.263660	−	0.964616i	$-0.415070\pi$
$463$	2.43236e6	0.527321	0.263660	+	0.964616i	$0.415070\pi$
$464$	−962698.	−0.207585
$465$	167201.	0.0358598
$466$	3.24157e6	0.691498
$467$	−1.25881e6	−0.267097	−0.133549	−	0.991042i	$-0.542637\pi$
$467$	−1.25881e6	−0.267097	−0.133549	+	0.991042i	$0.542637\pi$
$468$	−346106.	−0.0730457
$469$	3.45895e6	0.726126
$470$	−1.43030e6	−0.298664
$471$	3.16427e6	0.657236
$472$	−4.34872e6	−0.898477
$473$	6.83083e6	1.40385
$474$	1.26602e6	0.258819
$475$	1.46130e6	0.297170
$476$	417413.	0.0844400
$477$	−1.19113e6	−0.239698
$478$	−2.33424e6	−0.467278
$479$	992576.	0.197663	0.0988314	−	0.995104i	$-0.468490\pi$
$479$	992576.	0.197663	0.0988314	+	0.995104i	$0.468490\pi$
$480$	1.31632e6	0.260771
$481$	975593.	0.192268
$482$	−356531.	−0.0699004
$483$	824119.	0.160739
$484$	1.94175e6	0.376773
$485$	−387364.	−0.0747764
$486$	153032.	0.0293895
$487$	−1.27849e6	−0.244272	−0.122136	−	0.992513i	$-0.538974\pi$
$487$	−1.27849e6	−0.244272	−0.122136	+	0.992513i	$0.538974\pi$
$488$	4.37550e6	0.831722
$489$	3.33678e6	0.631039
$490$	893982.	0.168205
$491$	4.18445e6	0.783312	0.391656	−	0.920112i	$-0.371902\pi$
$491$	4.18445e6	0.783312	0.391656	+	0.920112i	$0.371902\pi$
$492$	−3.87446e6	−0.721603
$493$	−682823.	−0.126529
$494$	−1.02404e6	−0.188799
$495$	−587781.	−0.107821
$496$	−315327.	−0.0575515
$497$	−3.66221e6	−0.665046
$498$	186265.	0.0336556
$499$	9.34504e6	1.68008	0.840039	−	0.542525i	$-0.182532\pi$
$499$	9.34504e6	1.68008	0.840039	+	0.542525i	$0.182532\pi$
$500$	−395055.	−0.0706696
$501$	6.37478e6	1.13467
$502$	−3.75944e6	−0.665830
$503$	3.48626e6	0.614384	0.307192	−	0.951648i	$-0.400611\pi$
$503$	3.48626e6	0.614384	0.307192	+	0.951648i	$0.400611\pi$
$504$	−659617.	−0.115669
$505$	−1.04971e6	−0.183165
$506$	1.25575e6	0.218035
$507$	−257049.	−0.0444116
$508$	−3.83478e6	−0.659297
$509$	4.36939e6	0.747527	0.373763	−	0.927524i	$-0.378067\pi$
$509$	4.36939e6	0.747527	0.373763	+	0.927524i	$0.378067\pi$
$510$	175499.	0.0298779
$511$	4.91359e6	0.832428
$512$	−4.49829e6	−0.758356
$513$	−1.70446e6	−0.285952
$514$	512600.	0.0855798
$515$	−2.63103e6	−0.437128
$516$	−5.35505e6	−0.885399
$517$	−6.40778e6	−1.05434
$518$	820652.	0.134380
$519$	513422.	0.0836673
$520$	627230.	0.101723
$521$	−7.27566e6	−1.17430	−0.587149	−	0.809479i	$-0.699750\pi$
$521$	−7.27566e6	−1.17430	−0.587149	+	0.809479i	$0.699750\pi$
$522$	476258.	0.0765008
$523$	−6.97883e6	−1.11565	−0.557825	−	0.829958i	$-0.688364\pi$
$523$	−6.97883e6	−1.11565	−0.557825	+	0.829958i	$0.688364\pi$
$524$	−9.62771e6	−1.53177
$525$	308552.	0.0488574
$526$	1.30624e6	0.205854
$527$	−223655.	−0.0350794
$528$	1.10850e6	0.173042
$529$	−3.64969e6	−0.567044
$530$	952763.	0.147331
$531$	−2.37272e6	−0.365183
$532$	3.24267e6	0.496734
$533$	−2.87752e6	−0.438732
$534$	−1.46407e6	−0.222182
$535$	346733.	0.0523733
$536$	−9.36134e6	−1.40743
$537$	1.67628e6	0.250848
$538$	962303.	0.143336
$539$	4.00505e6	0.593795
$540$	460792.	0.0680019
$541$	−1.20446e7	−1.76929	−0.884643	−	0.466270i	$-0.845598\pi$
$541$	−1.20446e7	−1.76929	−0.884643	+	0.466270i	$0.845598\pi$
$542$	3.67564e6	0.537446
$543$	−681237.	−0.0991514
$544$	−1.76076e6	−0.255096
$545$	−4.18064e6	−0.602908
$546$	−216225.	−0.0310402
$547$	−680290.	−0.0972133	−0.0486066	−	0.998818i	$-0.515478\pi$
$547$	−680290.	−0.0972133	−0.0486066	+	0.998818i	$0.515478\pi$
$548$	−3.58121e6	−0.509422
$549$	2.38733e6	0.338051
$550$	470155.	0.0662726
$551$	−5.30452e6	−0.744332
$552$	−2.23041e6	−0.311556
$553$	−2.97739e6	−0.414021
$554$	−915039.	−0.126668
$555$	−1.29887e6	−0.178991
$556$	−6.93782e6	−0.951779
$557$	−9.83821e6	−1.34363	−0.671813	−	0.740721i	$-0.734484\pi$
$557$	−9.83821e6	−1.34363	−0.671813	+	0.740721i	$0.734484\pi$
$558$	155996.	0.0212094
$559$	−3.97713e6	−0.538320
$560$	−581902.	−0.0784114
$561$	786239.	0.105474
$562$	−2.66057e6	−0.355331
$563$	−5.26909e6	−0.700591	−0.350296	−	0.936639i	$-0.613919\pi$
$563$	−5.26909e6	−0.700591	−0.350296	+	0.936639i	$0.613919\pi$
$564$	5.02340e6	0.664967
$565$	−1.55634e6	−0.205108
$566$	4.45145e6	0.584064
$567$	−359895.	−0.0470131
$568$	9.91145e6	1.28904
$569$	−5.43793e6	−0.704130	−0.352065	−	0.935976i	$-0.614520\pi$
$569$	−5.43793e6	−0.704130	−0.352065	+	0.935976i	$0.614520\pi$
$570$	1.36336e6	0.175762
$571$	−1.22762e7	−1.57570	−0.787851	−	0.615865i	$-0.788806\pi$
$571$	−1.22762e7	−1.57570	−0.787851	+	0.615865i	$0.788806\pi$
$572$	1.24027e6	0.158498
$573$	2.74859e6	0.349722
$574$	−2.42051e6	−0.306639
$575$	1.04333e6	0.131599
$576$	128242.	0.0161055
$577$	5.41452e6	0.677049	0.338525	−	0.940958i	$-0.390072\pi$
$577$	5.41452e6	0.677049	0.338525	+	0.940958i	$0.390072\pi$
$578$	3.44497e6	0.428910
$579$	6.67661e6	0.827674
$580$	1.43405e6	0.177009
$581$	−438050.	−0.0538373
$582$	−361403.	−0.0442267
$583$	4.26839e6	0.520108
$584$	−1.32982e7	−1.61347
$585$	342225.	0.0413449
$586$	1.32398e6	0.159271
$587$	4.91081e6	0.588244	0.294122	−	0.955768i	$-0.404973\pi$
$587$	4.91081e6	0.588244	0.294122	+	0.955768i	$0.404973\pi$
$588$	−3.13977e6	−0.374503
$589$	−1.73747e6	−0.206361
$590$	1.89789e6	0.224462
$591$	−5.43161e6	−0.639675
$592$	2.44955e6	0.287264
$593$	1.35145e7	1.57820	0.789100	−	0.614265i	$-0.210547\pi$
$593$	1.35145e7	1.57820	0.789100	+	0.614265i	$0.210547\pi$
$594$	−548388.	−0.0637708
$595$	−412732.	−0.0477942
$596$	−6.10377e6	−0.703854
$597$	−3.09056e6	−0.354896
$598$	−731137.	−0.0836076
$599$	−5.00902e6	−0.570409	−0.285204	−	0.958467i	$-0.592061\pi$
$599$	−5.00902e6	−0.570409	−0.285204	+	0.958467i	$0.592061\pi$
$600$	−835070.	−0.0946989
$601$	747198.	0.0843819	0.0421910	−	0.999110i	$-0.486566\pi$
$601$	747198.	0.0843819	0.0421910	+	0.999110i	$0.486566\pi$
$602$	−3.34549e6	−0.376243
$603$	−5.10767e6	−0.572044
$604$	−4.27138e6	−0.476404
$605$	−1.91997e6	−0.213259
$606$	−979361.	−0.108333
$607$	8.01852e6	0.883329	0.441665	−	0.897180i	$-0.354388\pi$
$607$	8.01852e6	0.883329	0.441665	+	0.897180i	$0.354388\pi$
$608$	−1.36785e7	−1.50065
$609$	−1.12004e6	−0.122375
$610$	−1.90958e6	−0.207785
$611$	3.73082e6	0.404298
$612$	−616374.	−0.0665221
$613$	−4.05917e6	−0.436301	−0.218151	−	0.975915i	$-0.570002\pi$
$613$	−4.05917e6	−0.436301	−0.218151	+	0.975915i	$0.570002\pi$
$614$	−2.54754e6	−0.272710
$615$	3.83101e6	0.408438
$616$	2.36372e6	0.250983
$617$	1.52799e6	0.161588	0.0807938	−	0.996731i	$-0.474254\pi$
$617$	1.52799e6	0.161588	0.0807938	+	0.996731i	$0.474254\pi$
$618$	−2.45471e6	−0.258540
$619$	7.43720e6	0.780158	0.390079	−	0.920781i	$-0.372448\pi$
$619$	7.43720e6	0.780158	0.390079	+	0.920781i	$0.372448\pi$
$620$	469716.	0.0490745
$621$	−1.21694e6	−0.126631
$622$	−330684.	−0.0342718
$623$	3.44314e6	0.355415
$624$	−645405.	−0.0663546
$625$	390625.	0.0400000
$626$	3.84923e6	0.392589
$627$	6.10790e6	0.620473
$628$	8.88932e6	0.899434
$629$	1.73742e6	0.175096
$630$	287874.	0.0288968
$631$	−9.85344e6	−0.985178	−0.492589	−	0.870262i	$-0.663949\pi$
$631$	−9.85344e6	−0.985178	−0.492589	+	0.870262i	$0.663949\pi$
$632$	8.05804e6	0.802485
$633$	8.64147e6	0.857193
$634$	−487030.	−0.0481208
$635$	3.79178e6	0.373172
$636$	−3.34622e6	−0.328029
$637$	−2.33187e6	−0.227697
$638$	−1.70666e6	−0.165995
$639$	5.40781e6	0.523926
$640$	4.57768e6	0.441769
$641$	−6.42503e6	−0.617633	−0.308816	−	0.951122i	$-0.599933\pi$
$641$	−6.42503e6	−0.617633	−0.308816	+	0.951122i	$0.599933\pi$
$642$	323495.	0.0309763
$643$	−8.19208e6	−0.781388	−0.390694	−	0.920521i	$-0.627765\pi$
$643$	−8.19208e6	−0.781388	−0.390694	+	0.920521i	$0.627765\pi$
$644$	2.31518e6	0.219974
$645$	5.29500e6	0.501149
$646$	−1.82369e6	−0.171937
$647$	8.72113e6	0.819053	0.409526	−	0.912298i	$-0.365694\pi$
$647$	8.72113e6	0.819053	0.409526	+	0.912298i	$0.365694\pi$
$648$	974026.	0.0911240
$649$	8.50260e6	0.792391
$650$	−273739.	−0.0254129
$651$	−366865.	−0.0339276
$652$	9.37396e6	0.863583
$653$	1.51333e7	1.38884	0.694419	−	0.719571i	$-0.255662\pi$
$653$	1.51333e7	1.38884	0.694419	+	0.719571i	$0.255662\pi$
$654$	−3.90046e6	−0.356592
$655$	9.51974e6	0.867006
$656$	−7.22494e6	−0.655503
$657$	−7.25567e6	−0.655789
$658$	3.13830e6	0.282572
$659$	1.96144e7	1.75938	0.879692	−	0.475544i	$-0.157749\pi$
$659$	1.96144e7	1.75938	0.879692	+	0.475544i	$0.157749\pi$
$660$	−1.65124e6	−0.147554
$661$	−1.84242e7	−1.64015	−0.820076	−	0.572255i	$-0.806069\pi$
$661$	−1.84242e7	−1.64015	−0.820076	+	0.572255i	$0.806069\pi$
$662$	905132.	0.0802725
$663$	−457774.	−0.0404452
$664$	1.18555e6	0.104351
$665$	−3.20631e6	−0.281158
$666$	−1.21182e6	−0.105865
$667$	−3.78729e6	−0.329620
$668$	1.79085e7	1.55281
$669$	5.62983e6	0.486328
$670$	4.08553e6	0.351610
$671$	−8.55495e6	−0.733519
$672$	−2.88821e6	−0.246720
$673$	−7.42806e6	−0.632176	−0.316088	−	0.948730i	$-0.602369\pi$
$673$	−7.42806e6	−0.632176	−0.316088	+	0.948730i	$0.602369\pi$
$674$	−2.32780e6	−0.197377
$675$	−455625.	−0.0384900
$676$	−722123.	−0.0607777
$677$	−471546.	−0.0395415	−0.0197707	−	0.999805i	$-0.506294\pi$
$677$	−471546.	−0.0395415	−0.0197707	+	0.999805i	$0.506294\pi$
$678$	−1.45203e6	−0.121312
$679$	849934.	0.0707475
$680$	1.11702e6	0.0926381
$681$	1.26080e7	1.04179
$682$	−559008.	−0.0460211
$683$	1.68803e7	1.38461	0.692305	−	0.721605i	$-0.256595\pi$
$683$	1.68803e7	1.38461	0.692305	+	0.721605i	$0.256595\pi$
$684$	−4.78830e6	−0.391328
$685$	3.54105e6	0.288340
$686$	−4.35081e6	−0.352988
$687$	7.42698e6	0.600372
$688$	−9.98588e6	−0.804295
$689$	−2.48520e6	−0.199440
$690$	973407.	0.0778344
$691$	1.28298e7	1.02218	0.511088	−	0.859528i	$-0.329243\pi$
$691$	1.28298e7	1.02218	0.511088	+	0.859528i	$0.329243\pi$
$692$	1.44235e6	0.114500
$693$	1.28968e6	0.102011
$694$	−2.61495e6	−0.206093
$695$	6.86002e6	0.538720
$696$	3.03130e6	0.237196
$697$	−5.12451e6	−0.399550
$698$	242619.	0.0188489
$699$	1.12571e7	0.871434
$700$	866810.	0.0668619
$701$	1.23572e7	0.949783	0.474892	−	0.880044i	$-0.342487\pi$
$701$	1.23572e7	0.949783	0.474892	+	0.880044i	$0.342487\pi$
$702$	319290.	0.0244536
$703$	1.34971e7	1.03004
$704$	−459553.	−0.0349465
$705$	−4.96707e6	−0.376381
$706$	981408.	0.0741033
$707$	2.30322e6	0.173296
$708$	−6.66564e6	−0.499756
$709$	1.11669e7	0.834293	0.417146	−	0.908839i	$-0.363030\pi$
$709$	1.11669e7	0.834293	0.417146	+	0.908839i	$0.363030\pi$
$710$	−4.32561e6	−0.322034
$711$	4.39657e6	0.326167
$712$	−9.31858e6	−0.688889
$713$	−1.24051e6	−0.0913850
$714$	−385071.	−0.0282680
$715$	−1.22636e6	−0.0897123
$716$	4.70914e6	0.343288
$717$	−8.10620e6	−0.588870
$718$	−3.19405e6	−0.231223
$719$	1.22097e6	0.0880807	0.0440404	−	0.999030i	$-0.485977\pi$
$719$	1.22097e6	0.0880807	0.0440404	+	0.999030i	$0.485977\pi$
$720$	859267.	0.0617728
$721$	5.77288e6	0.413575
$722$	−7.75025e6	−0.553315
$723$	−1.23814e6	−0.0880893
$724$	−1.91379e6	−0.135690
$725$	−1.41797e6	−0.100189
$726$	−1.79130e6	−0.126133
$727$	−1.16677e7	−0.818749	−0.409374	−	0.912366i	$-0.634253\pi$
$727$	−1.16677e7	−0.818749	−0.409374	+	0.912366i	$0.634253\pi$
$728$	−1.37624e6	−0.0962420
$729$	531441.	0.0370370
$730$	5.80368e6	0.403085
$731$	−7.08280e6	−0.490243
$732$	6.70668e6	0.462626
$733$	4.81700e6	0.331144	0.165572	−	0.986198i	$-0.447053\pi$
$733$	4.81700e6	0.331144	0.165572	+	0.986198i	$0.447053\pi$
$734$	−6.89273e6	−0.472228
$735$	3.10457e6	0.211974
$736$	−9.76610e6	−0.664548
$737$	1.83032e7	1.24125
$738$	3.57426e6	0.241571
$739$	−1.36673e6	−0.0920599	−0.0460299	−	0.998940i	$-0.514657\pi$
$739$	−1.36673e6	−0.0920599	−0.0460299	+	0.998940i	$0.514657\pi$
$740$	−3.64888e6	−0.244952
$741$	−3.55622e6	−0.237926
$742$	−2.09051e6	−0.139393
$743$	2.43212e7	1.61626	0.808132	−	0.589001i	$-0.200479\pi$
$743$	2.43212e7	1.61626	0.808132	+	0.589001i	$0.200479\pi$
$744$	992888.	0.0657609
$745$	6.03533e6	0.398392
$746$	5.57531e6	0.366794
$747$	646849.	0.0424132
$748$	2.20877e6	0.144343
$749$	−760783.	−0.0495514
$750$	364446.	0.0236581
$751$	−1.63033e7	−1.05481	−0.527406	−	0.849614i	$-0.676835\pi$
$751$	−1.63033e7	−1.05481	−0.527406	+	0.849614i	$0.676835\pi$
$752$	9.36744e6	0.604055
$753$	−1.30555e7	−0.839088
$754$	993674.	0.0636525
$755$	4.22348e6	0.269651
$756$	−1.01105e6	−0.0643379
$757$	1.66431e6	0.105559	0.0527795	−	0.998606i	$-0.483192\pi$
$757$	1.66431e6	0.105559	0.0527795	+	0.998606i	$0.483192\pi$
$758$	−742716.	−0.0469515
$759$	4.36088e6	0.274770
$760$	8.67759e6	0.544961
$761$	5.48618e6	0.343407	0.171703	−	0.985149i	$-0.445073\pi$
$761$	5.48618e6	0.343407	0.171703	+	0.985149i	$0.445073\pi$
$762$	3.53766e6	0.220713
$763$	9.17294e6	0.570423
$764$	7.72156e6	0.478599
$765$	609462.	0.0376524
$766$	−6.47221e6	−0.398548
$767$	−4.95049e6	−0.303850
$768$	4.72686e6	0.289181
$769$	3.23567e6	0.197309	0.0986547	−	0.995122i	$-0.468546\pi$
$769$	3.23567e6	0.197309	0.0986547	+	0.995122i	$0.468546\pi$
$770$	−1.03159e6	−0.0627018
$771$	1.78013e6	0.107849
$772$	1.87565e7	1.13268
$773$	1.81094e7	1.09007	0.545037	−	0.838412i	$-0.316515\pi$
$773$	1.81094e7	1.09007	0.545037	+	0.838412i	$0.316515\pi$
$774$	4.94014e6	0.296406
$775$	−464448.	−0.0277769
$776$	−2.30027e6	−0.137128
$777$	2.84991e6	0.169347
$778$	−1.25565e7	−0.743737
$779$	−3.98098e7	−2.35042
$780$	961406.	0.0565810
$781$	−1.93788e7	−1.13684
$782$	−1.30207e6	−0.0761407
$783$	1.65392e6	0.0964073
$784$	−5.85493e6	−0.340198
$785$	−8.78964e6	−0.509093
$786$	8.88175e6	0.512793
$787$	−2.22828e7	−1.28243	−0.641213	−	0.767363i	$-0.721568\pi$
$787$	−2.22828e7	−1.28243	−0.641213	+	0.767363i	$0.721568\pi$
$788$	−1.52589e7	−0.875403
$789$	4.53623e6	0.259420
$790$	−3.51674e6	−0.200480
$791$	3.41484e6	0.194057
$792$	−3.49040e6	−0.197725
$793$	4.98097e6	0.281275
$794$	2.32753e6	0.131022
$795$	3.30870e6	0.185669
$796$	−8.68225e6	−0.485679
$797$	1.23718e7	0.689900	0.344950	−	0.938621i	$-0.387896\pi$
$797$	1.23718e7	0.689900	0.344950	+	0.938621i	$0.387896\pi$
$798$	−2.99143e6	−0.166292
$799$	6.64415e6	0.368190
$800$	−3.65645e6	−0.201992
$801$	−5.08433e6	−0.279997
$802$	8.17550e6	0.448826
$803$	2.60006e7	1.42296
$804$	−1.43489e7	−0.782849
$805$	−2.28922e6	−0.124508
$806$	325473.	0.0176473
$807$	3.34182e6	0.180634
$808$	−6.23348e6	−0.335894
$809$	−45723.1	−0.00245620	−0.00122810	−	0.999999i	$-0.500391\pi$
$809$	−45723.1	−0.00245620	−0.00122810	+	0.999999i	$0.500391\pi$
$810$	−425090.	−0.0227650
$811$	1.48379e6	0.0792174	0.0396087	−	0.999215i	$-0.487389\pi$
$811$	1.48379e6	0.0792174	0.0396087	+	0.999215i	$0.487389\pi$
$812$	−3.14652e6	−0.167471
$813$	1.27645e7	0.677296
$814$	4.34253e6	0.229711
$815$	−9.26884e6	−0.488800
$816$	−1.14939e6	−0.0604285
$817$	−5.50227e7	−2.88395
$818$	−7.91085e6	−0.413371
$819$	−750893.	−0.0391172
$820$	1.07624e7	0.558951
$821$	3.27057e7	1.69342	0.846711	−	0.532054i	$-0.178579\pi$
$821$	3.27057e7	1.69342	0.846711	+	0.532054i	$0.178579\pi$
$822$	3.30373e6	0.170540
$823$	1.73238e7	0.891543	0.445772	−	0.895147i	$-0.352929\pi$
$823$	1.73238e7	0.891543	0.445772	+	0.895147i	$0.352929\pi$
$824$	−1.56238e7	−0.801620
$825$	1.63272e6	0.0835176
$826$	−4.16426e6	−0.212367
$827$	1.24591e7	0.633463	0.316732	−	0.948515i	$-0.397415\pi$
$827$	1.24591e7	0.633463	0.316732	+	0.948515i	$0.397415\pi$
$828$	−3.41872e6	−0.173296
$829$	−1.86441e7	−0.942226	−0.471113	−	0.882073i	$-0.656148\pi$
$829$	−1.86441e7	−0.942226	−0.471113	+	0.882073i	$0.656148\pi$
$830$	−517402.	−0.0260695
$831$	−3.17769e6	−0.159628
$832$	267567.	0.0134006
$833$	−4.15279e6	−0.207361
$834$	6.40027e6	0.318627
$835$	−1.77077e7	−0.878914
$836$	1.71588e7	0.849124
$837$	541733.	0.0267283
$838$	1.17765e7	0.579303
$839$	−1.05408e7	−0.516974	−0.258487	−	0.966015i	$-0.583224\pi$
$839$	−1.05408e7	−0.516974	−0.258487	+	0.966015i	$0.583224\pi$
$840$	1.83227e6	0.0895965
$841$	−1.53639e7	−0.749052
$842$	−7.17393e6	−0.348720
$843$	−9.23945e6	−0.447793
$844$	2.42763e7	1.17308
$845$	714025.	0.0344010
$846$	−4.63418e6	−0.222611
$847$	4.21271e6	0.201768
$848$	−6.23990e6	−0.297981
$849$	1.54587e7	0.736044
$850$	−487497.	−0.0231433
$851$	9.63659e6	0.456142
$852$	1.51921e7	0.716998
$853$	−3.76226e7	−1.77042	−0.885210	−	0.465191i	$-0.845985\pi$
$853$	−3.76226e7	−1.77042	−0.885210	+	0.465191i	$0.845985\pi$
$854$	4.18991e6	0.196589
$855$	4.73461e6	0.221497
$856$	2.05899e6	0.0960441
$857$	−1.67479e7	−0.778949	−0.389475	−	0.921037i	$-0.627343\pi$
$857$	−1.67479e7	−0.778949	−0.389475	+	0.921037i	$0.627343\pi$
$858$	−1.14417e6	−0.0530606
$859$	−6.07022e6	−0.280686	−0.140343	−	0.990103i	$-0.544821\pi$
$859$	−6.07022e6	−0.280686	−0.140343	+	0.990103i	$0.544821\pi$
$860$	1.48751e7	0.685827
$861$	−8.40581e6	−0.386431
$862$	−1.14448e7	−0.524616
$863$	3.14068e7	1.43548	0.717738	−	0.696313i	$-0.245177\pi$
$863$	3.14068e7	1.43548	0.717738	+	0.696313i	$0.245177\pi$
$864$	4.26488e6	0.194367
$865$	−1.42617e6	−0.0648084
$866$	2.23836e6	0.101423
$867$	1.19635e7	0.540517
$868$	−1.03063e6	−0.0464303
$869$	−1.57550e7	−0.707734
$870$	−1.32294e6	−0.0592573
$871$	−1.06567e7	−0.475969
$872$	−2.48258e7	−1.10563
$873$	−1.25506e6	−0.0557351
$874$	−1.01151e7	−0.447912
$875$	−857090.	−0.0378448
$876$	−2.03832e7	−0.897455
$877$	−1.88402e7	−0.827152	−0.413576	−	0.910469i	$-0.635720\pi$
$877$	−1.88402e7	−0.827152	−0.413576	+	0.910469i	$0.635720\pi$
$878$	1.67396e7	0.732840
$879$	4.59784e6	0.200716
$880$	−3.07917e6	−0.134038
$881$	−1.75384e7	−0.761292	−0.380646	−	0.924721i	$-0.624298\pi$
$881$	−1.75384e7	−0.761292	−0.380646	+	0.924721i	$0.624298\pi$
$882$	2.89650e6	0.125373
$883$	−2.44702e6	−0.105618	−0.0528088	−	0.998605i	$-0.516817\pi$
$883$	−2.44702e6	−0.105618	−0.0528088	+	0.998605i	$0.516817\pi$
$884$	−1.28602e6	−0.0553497
$885$	6.59089e6	0.282869
$886$	1.72611e7	0.738729
$887$	−4.43486e7	−1.89265	−0.946327	−	0.323212i	$-0.895237\pi$
$887$	−4.43486e7	−1.89265	−0.946327	+	0.323212i	$0.895237\pi$
$888$	−7.71303e6	−0.328241
$889$	−8.31973e6	−0.353065
$890$	4.06687e6	0.172102
$891$	−1.90441e6	−0.0803648
$892$	1.58158e7	0.665546
$893$	5.16151e7	2.16595
$894$	5.63085e6	0.235630
$895$	−4.65633e6	−0.194306
$896$	−1.00441e7	−0.417966
$897$	−2.53905e6	−0.105363
$898$	1.00191e7	0.414607
$899$	1.68595e6	0.0695737
$900$	−1.27998e6	−0.0526740
$901$	−4.42584e6	−0.181629
$902$	−1.28083e7	−0.524174
$903$	−1.16180e7	−0.474146
$904$	−9.24196e6	−0.376134
$905$	1.89233e6	0.0768023
$906$	3.94043e6	0.159486
$907$	1.55585e7	0.627984	0.313992	−	0.949426i	$-0.398334\pi$
$907$	1.55585e7	0.627984	0.313992	+	0.949426i	$0.398334\pi$
$908$	3.54195e7	1.42570
$909$	−3.40106e6	−0.136523
$910$	600625.	0.0240436
$911$	2.10345e7	0.839722	0.419861	−	0.907588i	$-0.362079\pi$
$911$	2.10345e7	0.839722	0.419861	+	0.907588i	$0.362079\pi$
$912$	−8.92904e6	−0.355482
$913$	−2.31797e6	−0.0920303
$914$	−1.63590e7	−0.647725
$915$	−6.63147e6	−0.261853
$916$	2.08645e7	0.821616
$917$	−2.08877e7	−0.820291
$918$	568617.	0.0222696
$919$	3.03776e7	1.18649	0.593245	−	0.805022i	$-0.297846\pi$
$919$	3.03776e7	1.18649	0.593245	+	0.805022i	$0.297846\pi$
$920$	6.19558e6	0.241331
$921$	−8.84694e6	−0.343672
$922$	1.39031e7	0.538622
$923$	1.12830e7	0.435932
$924$	3.62307e6	0.139604
$925$	3.60796e6	0.138646
$926$	−6.30373e6	−0.241585
$927$	−8.52455e6	−0.325816
$928$	1.32729e7	0.505937
$929$	−1.65938e7	−0.630823	−0.315412	−	0.948955i	$-0.602143\pi$
$929$	−1.65938e7	−0.630823	−0.315412	+	0.948955i	$0.602143\pi$
$930$	−433322.	−0.0164287
$931$	−3.22610e7	−1.21984
$932$	3.16244e7	1.19257
$933$	−1.14838e6	−0.0431898
$934$	3.26236e6	0.122367
$935$	−2.18400e6	−0.0817001
$936$	2.03223e6	0.0758198
$937$	7.72391e6	0.287401	0.143701	−	0.989621i	$-0.454100\pi$
$937$	7.72391e6	0.287401	0.143701	+	0.989621i	$0.454100\pi$
$938$	−8.96426e6	−0.332665
$939$	1.33674e7	0.494745
$940$	−1.39539e7	−0.515081
$941$	−9.62960e6	−0.354515	−0.177257	−	0.984165i	$-0.556722\pi$
$941$	−9.62960e6	−0.354515	−0.177257	+	0.984165i	$0.556722\pi$
$942$	−8.20057e6	−0.301104
$943$	−2.84232e7	−1.04086
$944$	−1.24298e7	−0.453978
$945$	999709.	0.0364162
$946$	−1.77029e7	−0.643156
$947$	−166328.	−0.00602685	−0.00301343	−	0.999995i	$-0.500959\pi$
$947$	−166328.	−0.00602685	−0.00301343	+	0.999995i	$0.500959\pi$
$948$	1.23512e7	0.446363
$949$	−1.51384e7	−0.545650
$950$	−3.78712e6	−0.136145
$951$	−1.69133e6	−0.0606424
$952$	−2.45091e6	−0.0876468
$953$	−1.98203e7	−0.706932	−0.353466	−	0.935447i	$-0.614997\pi$
$953$	−1.98203e7	−0.706932	−0.353466	+	0.935447i	$0.614997\pi$
$954$	3.08695e6	0.109814
$955$	−7.63497e6	−0.270894
$956$	−2.27726e7	−0.805875
$957$	−5.92679e6	−0.209189
$958$	−2.57238e6	−0.0905567
$959$	−7.76959e6	−0.272804
$960$	−356228.	−0.0124753
$961$	−2.80769e7	−0.980711
$962$	−2.52836e6	−0.0880850
$963$	1.12341e6	0.0390368
$964$	−3.47828e6	−0.120551
$965$	−1.85461e7	−0.641114
$966$	−2.13580e6	−0.0736407
$967$	−5.44138e7	−1.87130	−0.935648	−	0.352934i	$-0.885184\pi$
$967$	−5.44138e7	−1.87130	−0.935648	+	0.352934i	$0.885184\pi$
$968$	−1.14013e7	−0.391082
$969$	−6.33320e6	−0.216677
$970$	1.00390e6	0.0342579
$971$	4.15925e7	1.41569	0.707843	−	0.706370i	$-0.249668\pi$
$971$	4.15925e7	1.41569	0.707843	+	0.706370i	$0.249668\pi$
$972$	1.49297e6	0.0506856
$973$	−1.50519e7	−0.509694
$974$	3.31335e6	0.111910
$975$	−950625.	−0.0320256
$976$	1.25064e7	0.420249
$977$	−1.21355e7	−0.406743	−0.203371	−	0.979102i	$-0.565190\pi$
$977$	−1.21355e7	−0.406743	−0.203371	+	0.979102i	$0.565190\pi$
$978$	−8.64766e6	−0.289102
$979$	1.82196e7	0.607551
$980$	8.72160e6	0.290089
$981$	−1.35453e7	−0.449381
$982$	−1.08445e7	−0.358864
$983$	3.35695e7	1.10805	0.554027	−	0.832499i	$-0.313090\pi$
$983$	3.35695e7	1.10805	0.554027	+	0.832499i	$0.313090\pi$
$984$	2.27496e7	0.749007
$985$	1.50878e7	0.495490
$986$	1.76962e6	0.0579678
$987$	1.08985e7	0.356101
$988$	−9.99041e6	−0.325605
$989$	−3.92848e7	−1.27713
$990$	1.52330e6	0.0493967
$991$	7.36811e6	0.238326	0.119163	−	0.992875i	$-0.461979\pi$
$991$	7.36811e6	0.238326	0.119163	+	0.992875i	$0.461979\pi$
$992$	4.34747e6	0.140268
$993$	3.14329e6	0.101160
$994$	9.49103e6	0.304683
$995$	8.58489e6	0.274901
$996$	1.81718e6	0.0580430
$997$	3.35011e7	1.06738	0.533692	−	0.845679i	$-0.320804\pi$
$997$	3.35011e7	1.06738	0.533692	+	0.845679i	$0.320804\pi$
$998$	−2.42187e7	−0.769707
$999$	−4.20833e6	−0.133412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.6.a.d.1.2	✓	4
3.2	odd	2		585.6.a.e.1.3		4
5.4	even	2		975.6.a.g.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.6.a.d.1.2	✓	4	1.1	even	1	trivial
585.6.a.e.1.3		4	3.2	odd	2
975.6.a.g.1.3		4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	195.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59162 q^{2} -9.00000 q^{3} -25.2835 q^{4} +25.0000 q^{5} +23.3245 q^{6} -54.8537 q^{7} +148.457 q^{8} +81.0000 q^{9} -64.7904 q^{10} -290.262 q^{11} +227.552 q^{12} +169.000 q^{13} +142.160 q^{14} -225.000 q^{15} +424.330 q^{16} +300.969 q^{17} -209.921 q^{18} +2338.08 q^{19} -632.088 q^{20} +493.684 q^{21} +752.248 q^{22} +1669.33 q^{23} -1336.11 q^{24} +625.000 q^{25} -437.983 q^{26} -729.000 q^{27} +1386.90 q^{28} -2268.75 q^{29} +583.114 q^{30} -743.117 q^{31} -5850.32 q^{32} +2612.36 q^{33} -779.996 q^{34} -1371.34 q^{35} -2047.97 q^{36} +5772.74 q^{37} -6059.40 q^{38} -1521.00 q^{39} +3711.42 q^{40} -17026.7 q^{41} -1279.44 q^{42} -23533.3 q^{43} +7338.85 q^{44} +2025.00 q^{45} -4326.25 q^{46} +22075.9 q^{47} -3818.97 q^{48} -13798.1 q^{49} -1619.76 q^{50} -2708.72 q^{51} -4272.92 q^{52} -14705.3 q^{53} +1889.29 q^{54} -7256.55 q^{55} -8143.41 q^{56} -21042.7 q^{57} +5879.73 q^{58} -29292.8 q^{59} +5688.79 q^{60} +29473.2 q^{61} +1925.87 q^{62} -4443.15 q^{63} +1583.23 q^{64} +4225.00 q^{65} -6770.23 q^{66} -63057.6 q^{67} -7609.56 q^{68} -15023.9 q^{69} +3553.99 q^{70} +66763.1 q^{71} +12025.0 q^{72} -89576.2 q^{73} -14960.7 q^{74} -5625.00 q^{75} -59114.9 q^{76} +15922.0 q^{77} +3941.85 q^{78} +54278.7 q^{79} +10608.2 q^{80} +6561.00 q^{81} +44126.7 q^{82} +7985.79 q^{83} -12482.1 q^{84} +7524.22 q^{85} +60989.3 q^{86} +20418.8 q^{87} -43091.4 q^{88} -62769.6 q^{89} -5248.02 q^{90} -9270.28 q^{91} -42206.5 q^{92} +6688.06 q^{93} -57212.1 q^{94} +58451.9 q^{95} +52652.9 q^{96} -15494.6 q^{97} +35759.3 q^{98} -23511.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 36 q^{3} + 9 q^{4} + 100 q^{5} + 27 q^{6} - 87 q^{7} - 183 q^{8} + 324 q^{9} - 75 q^{10} - 631 q^{11} - 81 q^{12} + 676 q^{13} + 1344 q^{14} - 900 q^{15} - 351 q^{16} - 599 q^{17} - 243 q^{18}+ \cdots - 51111 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 36 * q^3 + 9 * q^4 + 100 * q^5 + 27 * q^6 - 87 * q^7 - 183 * q^8 + 324 * q^9 - 75 * q^10 - 631 * q^11 - 81 * q^12 + 676 * q^13 + 1344 * q^14 - 900 * q^15 - 351 * q^16 - 599 * q^17 - 243 * q^18 - 4 * q^19 + 225 * q^20 + 783 * q^21 - 1920 * q^22 + 4459 * q^23 + 1647 * q^24 + 2500 * q^25 - 507 * q^26 - 2916 * q^27 - 1048 * q^28 - 5274 * q^29 + 675 * q^30 + 2642 * q^31 - 199 * q^32 + 5679 * q^33 + 15794 * q^34 - 2175 * q^35 + 729 * q^36 - 30189 * q^37 - 26408 * q^38 - 6084 * q^39 - 4575 * q^40 - 8947 * q^41 - 12096 * q^42 - 15928 * q^43 - 29676 * q^44 + 8100 * q^45 - 14272 * q^46 - 28242 * q^47 + 3159 * q^48 - 52335 * q^49 - 1875 * q^50 + 5391 * q^51 + 1521 * q^52 - 38021 * q^53 + 2187 * q^54 - 15775 * q^55 - 2480 * q^56 + 36 * q^57 - 115014 * q^58 - 17200 * q^59 - 2025 * q^60 - 67669 * q^61 - 99568 * q^62 - 7047 * q^63 - 69455 * q^64 + 16900 * q^65 + 17280 * q^66 + 8832 * q^67 - 45054 * q^68 - 40131 * q^69 + 33600 * q^70 + 128633 * q^71 - 14823 * q^72 - 48706 * q^73 + 35026 * q^74 - 22500 * q^75 - 66036 * q^76 - 25533 * q^77 + 4563 * q^78 + 72799 * q^79 - 8775 * q^80 + 26244 * q^81 - 191810 * q^82 + 15868 * q^83 + 9432 * q^84 - 14975 * q^85 + 247924 * q^86 + 47466 * q^87 + 5204 * q^88 - 45713 * q^89 - 6075 * q^90 - 14703 * q^91 + 271408 * q^92 - 23778 * q^93 - 51544 * q^94 - 100 * q^95 + 1791 * q^96 - 148949 * q^97 + 10289 * q^98 - 51111 * q^99

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