LMFDB - Embedded newform 95.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,4,Mod(1,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("95.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	95.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:	$5.60518145055$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 36x^{4} + 30x^{3} + 241x^{2} - 347x + 76 $ x^6 - x^5 - 36x^4 + 30x^3 + 241x^2 - 347x + 76
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.47638$ of defining polynomial
Character	$\chi$	$=$	95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.47638 q^{2} -4.48105 q^{3} +21.9908 q^{4} -5.00000 q^{5} +24.5399 q^{6} -26.3667 q^{7} -76.6187 q^{8} -6.92019 q^{9} +O(q^{10})$	\(q-5.47638 q^{2} -4.48105 q^{3} +21.9908 q^{4} -5.00000 q^{5} +24.5399 q^{6} -26.3667 q^{7} -76.6187 q^{8} -6.92019 q^{9} +27.3819 q^{10} -31.1680 q^{11} -98.5417 q^{12} +70.5976 q^{13} +144.394 q^{14} +22.4052 q^{15} +243.667 q^{16} -33.8763 q^{17} +37.8976 q^{18} -19.0000 q^{19} -109.954 q^{20} +118.151 q^{21} +170.688 q^{22} +39.6592 q^{23} +343.332 q^{24} +25.0000 q^{25} -386.619 q^{26} +151.998 q^{27} -579.824 q^{28} +199.207 q^{29} -122.700 q^{30} -55.7463 q^{31} -721.466 q^{32} +139.665 q^{33} +185.519 q^{34} +131.834 q^{35} -152.180 q^{36} +399.083 q^{37} +104.051 q^{38} -316.351 q^{39} +383.094 q^{40} -286.604 q^{41} -647.038 q^{42} -53.9994 q^{43} -685.408 q^{44} +34.6010 q^{45} -217.189 q^{46} +242.471 q^{47} -1091.89 q^{48} +352.204 q^{49} -136.910 q^{50} +151.801 q^{51} +1552.49 q^{52} -315.119 q^{53} -832.399 q^{54} +155.840 q^{55} +2020.19 q^{56} +85.1399 q^{57} -1090.93 q^{58} +52.5046 q^{59} +492.708 q^{60} +486.488 q^{61} +305.288 q^{62} +182.463 q^{63} +2001.68 q^{64} -352.988 q^{65} -764.860 q^{66} -890.930 q^{67} -744.965 q^{68} -177.715 q^{69} -721.971 q^{70} +67.7338 q^{71} +530.216 q^{72} -647.291 q^{73} -2185.53 q^{74} -112.026 q^{75} -417.824 q^{76} +821.798 q^{77} +1732.46 q^{78} +982.400 q^{79} -1218.34 q^{80} -494.266 q^{81} +1569.55 q^{82} +186.044 q^{83} +2598.22 q^{84} +169.381 q^{85} +295.721 q^{86} -892.656 q^{87} +2388.05 q^{88} +1047.22 q^{89} -189.488 q^{90} -1861.43 q^{91} +872.135 q^{92} +249.802 q^{93} -1327.86 q^{94} +95.0000 q^{95} +3232.92 q^{96} +635.901 q^{97} -1928.80 q^{98} +215.688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 5 q^{3} + 25 q^{4} - 30 q^{5} + 61 q^{6} + 5 q^{7} - 3 q^{8} + 135 q^{9}+O(q^{10}) $ 6 * q - q^2 + 5 * q^3 + 25 * q^4 - 30 * q^5 + 61 * q^6 + 5 * q^7 - 3 * q^8 + 135 * q^9	\( 6 q - q^{2} + 5 q^{3} + 25 q^{4} - 30 q^{5} + 61 q^{6} + 5 q^{7} - 3 q^{8} + 135 q^{9} + 5 q^{10} + 8 q^{11} + 35 q^{12} + 79 q^{13} + 151 q^{14} - 25 q^{15} + 285 q^{16} + 35 q^{17} - 48 q^{18} - 114 q^{19} - 125 q^{20} + 403 q^{21} + 320 q^{22} - 111 q^{23} + 365 q^{24} + 150 q^{25} - 597 q^{26} + 683 q^{27} - 581 q^{28} + 107 q^{29} - 305 q^{30} + 574 q^{31} - 1225 q^{32} - 348 q^{33} - 379 q^{34} - 25 q^{35} - 602 q^{36} + 490 q^{37} + 19 q^{38} - 205 q^{39} + 15 q^{40} - 256 q^{41} - 1469 q^{42} - 212 q^{43} - 1228 q^{44} - 675 q^{45} + 43 q^{46} + 674 q^{47} - 2429 q^{48} + 931 q^{49} - 25 q^{50} + 661 q^{51} + 1601 q^{52} - 1729 q^{53} - 797 q^{54} - 40 q^{55} + 2731 q^{56} - 95 q^{57} - 1799 q^{58} - 25 q^{59} - 175 q^{60} + 1626 q^{61} + 1642 q^{62} - 852 q^{63} + 1717 q^{64} - 395 q^{65} + 1856 q^{66} + 741 q^{67} - 2207 q^{68} + 119 q^{69} - 755 q^{70} + 792 q^{71} + 1238 q^{72} + 1529 q^{73} - 2098 q^{74} + 125 q^{75} - 475 q^{76} + 628 q^{77} - 2589 q^{78} + 62 q^{79} - 1425 q^{80} + 3278 q^{81} + 1682 q^{82} - 80 q^{83} + 1687 q^{84} - 175 q^{85} + 3086 q^{86} + 545 q^{87} + 56 q^{88} + 4256 q^{89} + 240 q^{90} + 3153 q^{91} + 3163 q^{92} - 10 q^{93} + 2208 q^{94} + 570 q^{95} + 2377 q^{96} + 1910 q^{97} - 4940 q^{98} - 444 q^{99}+O(q^{100}) \) 6 * q - q^2 + 5 * q^3 + 25 * q^4 - 30 * q^5 + 61 * q^6 + 5 * q^7 - 3 * q^8 + 135 * q^9 + 5 * q^10 + 8 * q^11 + 35 * q^12 + 79 * q^13 + 151 * q^14 - 25 * q^15 + 285 * q^16 + 35 * q^17 - 48 * q^18 - 114 * q^19 - 125 * q^20 + 403 * q^21 + 320 * q^22 - 111 * q^23 + 365 * q^24 + 150 * q^25 - 597 * q^26 + 683 * q^27 - 581 * q^28 + 107 * q^29 - 305 * q^30 + 574 * q^31 - 1225 * q^32 - 348 * q^33 - 379 * q^34 - 25 * q^35 - 602 * q^36 + 490 * q^37 + 19 * q^38 - 205 * q^39 + 15 * q^40 - 256 * q^41 - 1469 * q^42 - 212 * q^43 - 1228 * q^44 - 675 * q^45 + 43 * q^46 + 674 * q^47 - 2429 * q^48 + 931 * q^49 - 25 * q^50 + 661 * q^51 + 1601 * q^52 - 1729 * q^53 - 797 * q^54 - 40 * q^55 + 2731 * q^56 - 95 * q^57 - 1799 * q^58 - 25 * q^59 - 175 * q^60 + 1626 * q^61 + 1642 * q^62 - 852 * q^63 + 1717 * q^64 - 395 * q^65 + 1856 * q^66 + 741 * q^67 - 2207 * q^68 + 119 * q^69 - 755 * q^70 + 792 * q^71 + 1238 * q^72 + 1529 * q^73 - 2098 * q^74 + 125 * q^75 - 475 * q^76 + 628 * q^77 - 2589 * q^78 + 62 * q^79 - 1425 * q^80 + 3278 * q^81 + 1682 * q^82 - 80 * q^83 + 1687 * q^84 - 175 * q^85 + 3086 * q^86 + 545 * q^87 + 56 * q^88 + 4256 * q^89 + 240 * q^90 + 3153 * q^91 + 3163 * q^92 - 10 * q^93 + 2208 * q^94 + 570 * q^95 + 2377 * q^96 + 1910 * q^97 - 4940 * q^98 - 444 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−5.47638	−1.93619	−0.968097	−	0.250577i	$-0.919380\pi$
$2$	−5.47638	−1.93619	−0.968097	+	0.250577i	$0.919380\pi$
$3$	−4.48105	−0.862378	−0.431189	−	0.902262i	$-0.641906\pi$
$3$	−4.48105	−0.862378	−0.431189	+	0.902262i	$0.641906\pi$
$4$	21.9908	2.74884
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	24.5399	1.66973
$7$	−26.3667	−1.42367	−0.711835	−	0.702347i	$-0.752135\pi$
$7$	−26.3667	−1.42367	−0.711835	+	0.702347i	$0.752135\pi$
$8$	−76.6187	−3.38610
$9$	−6.92019	−0.256303
$10$	27.3819	0.865892
$11$	−31.1680	−0.854318	−0.427159	−	0.904176i	$-0.640486\pi$
$11$	−31.1680	−0.854318	−0.427159	+	0.904176i	$0.640486\pi$
$12$	−98.5417	−2.37054
$13$	70.5976	1.50617	0.753086	−	0.657922i	$-0.228564\pi$
$13$	70.5976	1.50617	0.753086	+	0.657922i	$0.228564\pi$
$14$	144.394	2.75650
$15$	22.4052	0.385667
$16$	243.667	3.80730
$17$	−33.8763	−0.483306	−0.241653	−	0.970363i	$-0.577690\pi$
$17$	−33.8763	−0.483306	−0.241653	+	0.970363i	$0.577690\pi$
$18$	37.8976	0.496253
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−109.954	−1.22932
$21$	118.151	1.22774
$22$	170.688	1.65413
$23$	39.6592	0.359544	0.179772	−	0.983708i	$-0.442464\pi$
$23$	39.6592	0.359544	0.179772	+	0.983708i	$0.442464\pi$
$24$	343.332	2.92010
$25$	25.0000	0.200000
$26$	−386.619	−2.91624
$27$	151.998	1.08341
$28$	−579.824	−3.91345
$29$	199.207	1.27558	0.637790	−	0.770211i	$-0.279849\pi$
$29$	199.207	1.27558	0.637790	+	0.770211i	$0.279849\pi$
$30$	−122.700	−0.746727
$31$	−55.7463	−0.322978	−0.161489	−	0.986874i	$-0.551630\pi$
$31$	−55.7463	−0.322978	−0.161489	+	0.986874i	$0.551630\pi$
$32$	−721.466	−3.98557
$33$	139.665	0.736746
$34$	185.519	0.935774
$35$	131.834	0.636684
$36$	−152.180	−0.704538
$37$	399.083	1.77321	0.886605	−	0.462528i	$-0.153057\pi$
$37$	399.083	1.77321	0.886605	+	0.462528i	$0.153057\pi$
$38$	104.051	0.444193
$39$	−316.351	−1.29889
$40$	383.094	1.51431
$41$	−286.604	−1.09171	−0.545854	−	0.837880i	$-0.683795\pi$
$41$	−286.604	−1.09171	−0.545854	+	0.837880i	$0.683795\pi$
$42$	−647.038	−2.37715
$43$	−53.9994	−0.191508	−0.0957539	−	0.995405i	$-0.530526\pi$
$43$	−53.9994	−0.191508	−0.0957539	+	0.995405i	$0.530526\pi$
$44$	−685.408	−2.34839
$45$	34.6010	0.114622
$46$	−217.189	−0.696146
$47$	242.471	0.752511	0.376255	−	0.926516i	$-0.377212\pi$
$47$	242.471	0.752511	0.376255	+	0.926516i	$0.377212\pi$
$48$	−1091.89	−3.28334
$49$	352.204	1.02683
$50$	−136.910	−0.387239
$51$	151.801	0.416793
$52$	1552.49	4.14023
$53$	−315.119	−0.816697	−0.408349	−	0.912826i	$-0.633895\pi$
$53$	−315.119	−0.816697	−0.408349	+	0.912826i	$0.633895\pi$
$54$	−832.399	−2.09769
$55$	155.840	0.382063
$56$	2020.19	4.82069
$57$	85.1399	0.197843
$58$	−1090.93	−2.46977
$59$	52.5046	0.115856	0.0579281	−	0.998321i	$-0.481551\pi$
$59$	52.5046	0.115856	0.0579281	+	0.998321i	$0.481551\pi$
$60$	492.708	1.06014
$61$	486.488	1.02112	0.510560	−	0.859842i	$-0.329438\pi$
$61$	486.488	1.02112	0.510560	+	0.859842i	$0.329438\pi$
$62$	305.288	0.625348
$63$	182.463	0.364891
$64$	2001.68	3.90954
$65$	−352.988	−0.673581
$66$	−764.860	−1.42648
$67$	−890.930	−1.62454	−0.812272	−	0.583278i	$-0.801770\pi$
$67$	−890.930	−1.62454	−0.812272	+	0.583278i	$0.801770\pi$
$68$	−744.965	−1.32853
$69$	−177.715	−0.310063
$70$	−721.971	−1.23274
$71$	67.7338	0.113219	0.0566093	−	0.998396i	$-0.481971\pi$
$71$	67.7338	0.113219	0.0566093	+	0.998396i	$0.481971\pi$
$72$	530.216	0.867870
$73$	−647.291	−1.03780	−0.518902	−	0.854834i	$-0.673659\pi$
$73$	−647.291	−1.03780	−0.518902	+	0.854834i	$0.673659\pi$
$74$	−2185.53	−3.43328
$75$	−112.026	−0.172476
$76$	−417.824	−0.630628
$77$	821.798	1.21627
$78$	1732.46	2.51490
$79$	982.400	1.39910	0.699548	−	0.714585i	$-0.253385\pi$
$79$	982.400	1.39910	0.699548	+	0.714585i	$0.253385\pi$
$80$	−1218.34	−1.70268
$81$	−494.266	−0.678005
$82$	1569.55	2.11376
$83$	186.044	0.246036	0.123018	−	0.992404i	$-0.460743\pi$
$83$	186.044	0.246036	0.123018	+	0.992404i	$0.460743\pi$
$84$	2598.22	3.37487
$85$	169.381	0.216141
$86$	295.721	0.370796
$87$	−892.656	−1.10003
$88$	2388.05	2.89281
$89$	1047.22	1.24725	0.623624	−	0.781724i	$-0.285660\pi$
$89$	1047.22	1.24725	0.623624	+	0.781724i	$0.285660\pi$
$90$	−189.488	−0.221931
$91$	−1861.43	−2.14429
$92$	872.135	0.988330
$93$	249.802	0.278529
$94$	−1327.86	−1.45701
$95$	95.0000	0.102598
$96$	3232.92	3.43707
$97$	635.901	0.665629	0.332815	−	0.942992i	$-0.392002\pi$
$97$	635.901	0.665629	0.332815	+	0.942992i	$0.392002\pi$
$98$	−1928.80	−1.98815
$99$	215.688	0.218965
$100$	549.769	0.549769
$101$	−881.379	−0.868322	−0.434161	−	0.900835i	$-0.642955\pi$
$101$	−881.379	−0.868322	−0.434161	+	0.900835i	$0.642955\pi$
$102$	−831.322	−0.806991
$103$	−792.294	−0.757932	−0.378966	−	0.925411i	$-0.623720\pi$
$103$	−792.294	−0.757932	−0.378966	+	0.925411i	$0.623720\pi$
$104$	−5409.10	−5.10005
$105$	−590.753	−0.549063
$106$	1725.71	1.58128
$107$	147.459	0.133228	0.0666142	−	0.997779i	$-0.478780\pi$
$107$	147.459	0.133228	0.0666142	+	0.997779i	$0.478780\pi$
$108$	3342.55	2.97812
$109$	−1210.65	−1.06385	−0.531924	−	0.846792i	$-0.678531\pi$
$109$	−1210.65	−1.06385	−0.531924	+	0.846792i	$0.678531\pi$
$110$	−853.439	−0.739747
$111$	−1788.31	−1.52918
$112$	−6424.71	−5.42034
$113$	2187.92	1.82144	0.910719	−	0.413026i	$-0.135528\pi$
$113$	2187.92	1.82144	0.910719	+	0.413026i	$0.135528\pi$
$114$	−466.259	−0.383063
$115$	−198.296	−0.160793
$116$	4380.71	3.50637
$117$	−488.549	−0.386037
$118$	−287.535	−0.224320
$119$	893.206	0.688068
$120$	−1716.66	−1.30591
$121$	−359.557	−0.270140
$122$	−2664.19	−1.97709
$123$	1284.29	0.941466
$124$	−1225.90	−0.887817
$125$	−125.000	−0.0894427
$126$	−999.236	−0.706500
$127$	−903.852	−0.631527	−0.315763	−	0.948838i	$-0.602261\pi$
$127$	−903.852	−0.631527	−0.315763	+	0.948838i	$0.602261\pi$
$128$	−5190.25	−3.58405
$129$	241.974	0.165152
$130$	1933.10	1.30418
$131$	595.310	0.397042	0.198521	−	0.980097i	$-0.436386\pi$
$131$	595.310	0.397042	0.198521	+	0.980097i	$0.436386\pi$
$132$	3071.35	2.02520
$133$	500.968	0.326612
$134$	4879.08	3.14543
$135$	−759.990	−0.484515
$136$	2595.56	1.63652
$137$	2036.38	1.26993	0.634963	−	0.772542i	$-0.281015\pi$
$137$	2036.38	1.26993	0.634963	+	0.772542i	$0.281015\pi$
$138$	973.233	0.600341
$139$	−696.600	−0.425071	−0.212535	−	0.977153i	$-0.568172\pi$
$139$	−696.600	−0.425071	−0.212535	+	0.977153i	$0.568172\pi$
$140$	2899.12	1.75015
$141$	−1086.52	−0.648949
$142$	−370.936	−0.219213
$143$	−2200.38	−1.28675
$144$	−1686.23	−0.975825
$145$	−996.034	−0.570456
$146$	3544.81	2.00939
$147$	−1578.24	−0.885520
$148$	8776.13	4.87428
$149$	2472.49	1.35942	0.679712	−	0.733479i	$-0.262105\pi$
$149$	2472.49	1.35942	0.679712	+	0.733479i	$0.262105\pi$
$150$	613.498	0.333946
$151$	−619.737	−0.333996	−0.166998	−	0.985957i	$-0.553407\pi$
$151$	−619.737	−0.333996	−0.166998	+	0.985957i	$0.553407\pi$
$152$	1455.76	0.776825
$153$	234.430	0.123873
$154$	−4500.48	−2.35493
$155$	278.731	0.144440
$156$	−6956.80	−3.57045
$157$	2387.36	1.21358	0.606790	−	0.794862i	$-0.292457\pi$
$157$	2387.36	1.21358	0.606790	+	0.794862i	$0.292457\pi$
$158$	−5380.00	−2.70892
$159$	1412.07	0.704302
$160$	3607.33	1.78240
$161$	−1045.68	−0.511871
$162$	2706.79	1.31275
$163$	−35.1973	−0.0169133	−0.00845663	−	0.999964i	$-0.502692\pi$
$163$	−35.1973	−0.0169133	−0.00845663	+	0.999964i	$0.502692\pi$
$164$	−6302.64	−3.00094
$165$	−698.326	−0.329483
$166$	−1018.85	−0.476373
$167$	1314.17	0.608942	0.304471	−	0.952522i	$-0.401520\pi$
$167$	1314.17	0.608942	0.304471	+	0.952522i	$0.401520\pi$
$168$	−9052.55	−4.15726
$169$	2787.02	1.26856
$170$	−927.597	−0.418491
$171$	131.484	0.0588000
$172$	−1187.49	−0.526425
$173$	2395.48	1.05275	0.526374	−	0.850253i	$-0.323551\pi$
$173$	2395.48	1.05275	0.526374	+	0.850253i	$0.323551\pi$
$174$	4888.53	2.12987
$175$	−659.168	−0.284734
$176$	−7594.62	−3.25265
$177$	−235.276	−0.0999119
$178$	−5734.97	−2.41491
$179$	3027.22	1.26405	0.632026	−	0.774947i	$-0.282224\pi$
$179$	3027.22	1.26405	0.632026	+	0.774947i	$0.282224\pi$
$180$	760.901	0.315079
$181$	134.324	0.0551614	0.0275807	−	0.999620i	$-0.491220\pi$
$181$	134.324	0.0551614	0.0275807	+	0.999620i	$0.491220\pi$
$182$	10193.9	4.15176
$183$	−2179.97	−0.880592
$184$	−3038.63	−1.21745
$185$	−1995.41	−0.793004
$186$	−1368.01	−0.539287
$187$	1055.85	0.412897
$188$	5332.12	2.06853
$189$	−4007.69	−1.54242
$190$	−520.256	−0.198649
$191$	−415.085	−0.157249	−0.0786243	−	0.996904i	$-0.525053\pi$
$191$	−415.085	−0.157249	−0.0786243	+	0.996904i	$0.525053\pi$
$192$	−8969.64	−3.37150
$193$	3151.47	1.17538	0.587688	−	0.809087i	$-0.300038\pi$
$193$	3151.47	1.17538	0.587688	+	0.809087i	$0.300038\pi$
$194$	−3482.44	−1.28879
$195$	1581.76	0.580882
$196$	7745.24	2.82261
$197$	−2579.87	−0.933037	−0.466519	−	0.884511i	$-0.654492\pi$
$197$	−2579.87	−0.933037	−0.466519	+	0.884511i	$0.654492\pi$
$198$	−1181.19	−0.423958
$199$	−251.981	−0.0897609	−0.0448805	−	0.998992i	$-0.514291\pi$
$199$	−251.981	−0.0897609	−0.0448805	+	0.998992i	$0.514291\pi$
$200$	−1915.47	−0.677220
$201$	3992.30	1.40097
$202$	4826.77	1.68124
$203$	−5252.43	−1.81600
$204$	3338.22	1.14570
$205$	1433.02	0.488227
$206$	4338.90	1.46750
$207$	−274.449	−0.0921523
$208$	17202.3	5.73445
$209$	592.192	0.195994
$210$	3235.19	1.06309
$211$	973.736	0.317700	0.158850	−	0.987303i	$-0.449221\pi$
$211$	973.736	0.317700	0.158850	+	0.987303i	$0.449221\pi$
$212$	−6929.71	−2.24497
$213$	−303.519	−0.0976373
$214$	−807.544	−0.257956
$215$	269.997	0.0856449
$216$	−11645.9	−3.66853
$217$	1469.85	0.459814
$218$	6629.99	2.05981
$219$	2900.54	0.894980
$220$	3427.04	1.05023
$221$	−2391.58	−0.727942
$222$	9793.46	2.96078
$223$	1494.06	0.448653	0.224326	−	0.974514i	$-0.427982\pi$
$223$	1494.06	0.448653	0.224326	+	0.974514i	$0.427982\pi$
$224$	19022.7	5.67414
$225$	−173.005	−0.0512607
$226$	−11981.9	−3.52666
$227$	−6216.39	−1.81761	−0.908803	−	0.417225i	$-0.863003\pi$
$227$	−6216.39	−1.81761	−0.908803	+	0.417225i	$0.863003\pi$
$228$	1872.29	0.543840
$229$	−1958.14	−0.565054	−0.282527	−	0.959259i	$-0.591173\pi$
$229$	−1958.14	−0.565054	−0.282527	+	0.959259i	$0.591173\pi$
$230$	1085.94	0.311326
$231$	−3682.52	−1.04888
$232$	−15263.0	−4.31924
$233$	−5873.23	−1.65137	−0.825683	−	0.564135i	$-0.809210\pi$
$233$	−5873.23	−1.65137	−0.825683	+	0.564135i	$0.809210\pi$
$234$	2675.48	0.747443
$235$	−1212.35	−0.336533
$236$	1154.62	0.318471
$237$	−4402.18	−1.20655
$238$	−4891.54	−1.33223
$239$	1939.79	0.524998	0.262499	−	0.964932i	$-0.415453\pi$
$239$	1939.79	0.524998	0.262499	+	0.964932i	$0.415453\pi$
$240$	5459.43	1.46835
$241$	5291.29	1.41428	0.707141	−	0.707073i	$-0.249985\pi$
$241$	5291.29	1.41428	0.707141	+	0.707073i	$0.249985\pi$
$242$	1969.07	0.523044
$243$	−1889.12	−0.498712
$244$	10698.2	2.80690
$245$	−1761.02	−0.459214
$246$	−7033.25	−1.82286
$247$	−1341.35	−0.345540
$248$	4271.21	1.09364
$249$	−833.672	−0.212176
$250$	684.548	0.173178
$251$	4840.48	1.21724	0.608622	−	0.793460i	$-0.291723\pi$
$251$	4840.48	1.21724	0.608622	+	0.793460i	$0.291723\pi$
$252$	4012.50	1.00303
$253$	−1236.10	−0.307165
$254$	4949.84	1.22276
$255$	−759.006	−0.186395
$256$	12410.3	3.02987
$257$	3789.33	0.919734	0.459867	−	0.887988i	$-0.347897\pi$
$257$	3789.33	0.919734	0.459867	+	0.887988i	$0.347897\pi$
$258$	−1325.14	−0.319766
$259$	−10522.5	−2.52446
$260$	−7762.47	−1.85157
$261$	−1378.55	−0.326935
$262$	−3260.14	−0.768749
$263$	4565.76	1.07048	0.535241	−	0.844699i	$-0.320221\pi$
$263$	4565.76	1.07048	0.535241	+	0.844699i	$0.320221\pi$
$264$	−10701.0	−2.49470
$265$	1575.60	0.365238
$266$	−2743.49	−0.632384
$267$	−4692.64	−1.07560
$268$	−19592.2	−4.46562
$269$	7250.89	1.64347	0.821737	−	0.569867i	$-0.193005\pi$
$269$	7250.89	1.64347	0.821737	+	0.569867i	$0.193005\pi$
$270$	4162.00	0.938115
$271$	−5540.92	−1.24202	−0.621009	−	0.783803i	$-0.713277\pi$
$271$	−5540.92	−1.24202	−0.621009	+	0.783803i	$0.713277\pi$
$272$	−8254.54	−1.84009
$273$	8341.15	1.84919
$274$	−11152.0	−2.45882
$275$	−779.200	−0.170864
$276$	−3908.08	−0.852314
$277$	1096.10	0.237755	0.118877	−	0.992909i	$-0.462070\pi$
$277$	1096.10	0.237755	0.118877	+	0.992909i	$0.462070\pi$
$278$	3814.85	0.823019
$279$	385.775	0.0827804
$280$	−10100.9	−2.15588
$281$	914.520	0.194148	0.0970742	−	0.995277i	$-0.469052\pi$
$281$	914.520	0.194148	0.0970742	+	0.995277i	$0.469052\pi$
$282$	5950.22	1.25649
$283$	6105.82	1.28252	0.641260	−	0.767324i	$-0.278412\pi$
$283$	6105.82	1.28252	0.641260	+	0.767324i	$0.278412\pi$
$284$	1489.52	0.311221
$285$	−425.700	−0.0884782
$286$	12050.1	2.49140
$287$	7556.81	1.55423
$288$	4992.68	1.02152
$289$	−3765.40	−0.766415
$290$	5454.67	1.10451
$291$	−2849.51	−0.574024
$292$	−14234.4	−2.85276
$293$	−5455.61	−1.08778	−0.543891	−	0.839156i	$-0.683050\pi$
$293$	−5455.61	−1.08778	−0.543891	+	0.839156i	$0.683050\pi$
$294$	8643.07	1.71454
$295$	−262.523	−0.0518125
$296$	−30577.2	−6.00427
$297$	−4737.47	−0.925576
$298$	−13540.3	−2.63211
$299$	2799.84	0.541535
$300$	−2463.54	−0.474109
$301$	1423.79	0.272644
$302$	3393.92	0.646682
$303$	3949.50	0.748822
$304$	−4629.68	−0.873455
$305$	−2432.44	−0.456659
$306$	−1283.83	−0.239842
$307$	−4872.78	−0.905877	−0.452939	−	0.891542i	$-0.649624\pi$
$307$	−4872.78	−0.905877	−0.452939	+	0.891542i	$0.649624\pi$
$308$	18072.0	3.34333
$309$	3550.31	0.653625
$310$	−1526.44	−0.279664
$311$	−178.055	−0.0324648	−0.0162324	−	0.999868i	$-0.505167\pi$
$311$	−178.055	−0.0324648	−0.0162324	+	0.999868i	$0.505167\pi$
$312$	24238.4	4.39818
$313$	1774.63	0.320472	0.160236	−	0.987079i	$-0.448774\pi$
$313$	1774.63	0.320472	0.160236	+	0.987079i	$0.448774\pi$
$314$	−13074.1	−2.34973
$315$	−912.314	−0.163184
$316$	21603.7	3.84590
$317$	2224.27	0.394093	0.197047	−	0.980394i	$-0.436865\pi$
$317$	2224.27	0.394093	0.197047	+	0.980394i	$0.436865\pi$
$318$	−7733.01	−1.36367
$319$	−6208.88	−1.08975
$320$	−10008.4	−1.74840
$321$	−660.773	−0.114893
$322$	5726.55	0.991082
$323$	643.649	0.110878
$324$	−10869.3	−1.86373
$325$	1764.94	0.301235
$326$	192.754	0.0327474
$327$	5424.99	0.917439
$328$	21959.2	3.69663
$329$	−6393.16	−1.07133
$330$	3824.30	0.637942
$331$	6013.21	0.998537	0.499269	−	0.866447i	$-0.333602\pi$
$331$	6013.21	0.998537	0.499269	+	0.866447i	$0.333602\pi$
$332$	4091.24	0.676314
$333$	−2761.73	−0.454480
$334$	−7196.89	−1.17903
$335$	4454.65	0.726518
$336$	28789.4	4.67438
$337$	−7996.78	−1.29262	−0.646309	−	0.763076i	$-0.723688\pi$
$337$	−7996.78	−1.29262	−0.646309	+	0.763076i	$0.723688\pi$
$338$	−15262.8	−2.45617
$339$	−9804.19	−1.57077
$340$	3724.82	0.594138
$341$	1737.50	0.275926
$342$	−720.055	−0.113848
$343$	−242.686	−0.0382035
$344$	4137.37	0.648465
$345$	888.573	0.138664
$346$	−13118.6	−2.03832
$347$	−6462.16	−0.999731	−0.499866	−	0.866103i	$-0.666617\pi$
$347$	−6462.16	−0.999731	−0.499866	+	0.866103i	$0.666617\pi$
$348$	−19630.2	−3.02382
$349$	5416.48	0.830767	0.415384	−	0.909646i	$-0.363647\pi$
$349$	5416.48	0.830767	0.415384	+	0.909646i	$0.363647\pi$
$350$	3609.86	0.551300
$351$	10730.7	1.63180
$352$	22486.6	3.40495
$353$	6098.66	0.919544	0.459772	−	0.888037i	$-0.347931\pi$
$353$	6098.66	0.919544	0.459772	+	0.888037i	$0.347931\pi$
$354$	1288.46	0.193449
$355$	−338.669	−0.0506329
$356$	23029.2	3.42849
$357$	−4002.50	−0.593375
$358$	−16578.2	−2.44745
$359$	4177.62	0.614169	0.307084	−	0.951682i	$-0.400647\pi$
$359$	4177.62	0.614169	0.307084	+	0.951682i	$0.400647\pi$
$360$	−2651.08	−0.388123
$361$	361.000	0.0526316
$362$	−735.609	−0.106803
$363$	1611.19	0.232963
$364$	−40934.2	−5.89433
$365$	3236.46	0.464120
$366$	11938.4	1.70500
$367$	7914.32	1.12568	0.562840	−	0.826566i	$-0.309709\pi$
$367$	7914.32	1.12568	0.562840	+	0.826566i	$0.309709\pi$
$368$	9663.64	1.36889
$369$	1983.36	0.279809
$370$	10927.6	1.53541
$371$	8308.66	1.16271
$372$	5493.33	0.765634
$373$	−1243.10	−0.172562	−0.0862809	−	0.996271i	$-0.527498\pi$
$373$	−1243.10	−0.172562	−0.0862809	+	0.996271i	$0.527498\pi$
$374$	−5782.26	−0.799449
$375$	560.131	0.0771335
$376$	−18577.8	−2.54808
$377$	14063.5	1.92124
$378$	21947.6	2.98642
$379$	13010.5	1.76334	0.881668	−	0.471871i	$-0.156421\pi$
$379$	13010.5	1.76334	0.881668	+	0.471871i	$0.156421\pi$
$380$	2089.12	0.282026
$381$	4050.21	0.544615
$382$	2273.16	0.304464
$383$	4933.63	0.658216	0.329108	−	0.944292i	$-0.393252\pi$
$383$	4933.63	0.658216	0.329108	+	0.944292i	$0.393252\pi$
$384$	23257.8	3.09080
$385$	−4108.99	−0.543931
$386$	−17258.6	−2.27576
$387$	373.686	0.0490841
$388$	13984.0	1.82971
$389$	−2598.50	−0.338687	−0.169343	−	0.985557i	$-0.554165\pi$
$389$	−2598.50	−0.338687	−0.169343	+	0.985557i	$0.554165\pi$
$390$	−8662.30	−1.12470
$391$	−1343.50	−0.173770
$392$	−26985.4	−3.47697
$393$	−2667.61	−0.342400
$394$	14128.4	1.80654
$395$	−4912.00	−0.625695
$396$	4743.15	0.601900
$397$	3037.97	0.384059	0.192029	−	0.981389i	$-0.438493\pi$
$397$	3037.97	0.384059	0.192029	+	0.981389i	$0.438493\pi$
$398$	1379.94	0.173795
$399$	−2244.86	−0.281663
$400$	6091.68	0.761461
$401$	5081.96	0.632871	0.316435	−	0.948614i	$-0.397514\pi$
$401$	5081.96	0.632871	0.316435	+	0.948614i	$0.397514\pi$
$402$	−21863.4	−2.71255
$403$	−3935.55	−0.486461
$404$	−19382.2	−2.38688
$405$	2471.33	0.303213
$406$	28764.3	3.51613
$407$	−12438.6	−1.51489
$408$	−11630.8	−1.41130
$409$	6955.75	0.840929	0.420464	−	0.907309i	$-0.361867\pi$
$409$	6955.75	0.840929	0.420464	+	0.907309i	$0.361867\pi$
$410$	−7847.77	−0.945301
$411$	−9125.13	−1.09516
$412$	−17423.1	−2.08344
$413$	−1384.37	−0.164941
$414$	1502.99	0.178425
$415$	−930.219	−0.110031
$416$	−50933.7	−6.00296
$417$	3121.50	0.366572
$418$	−3243.07	−0.379482
$419$	−5306.37	−0.618695	−0.309347	−	0.950949i	$-0.600111\pi$
$419$	−5306.37	−0.618695	−0.309347	+	0.950949i	$0.600111\pi$
$420$	−12991.1	−1.50929
$421$	−7769.31	−0.899413	−0.449707	−	0.893176i	$-0.648471\pi$
$421$	−7769.31	−0.899413	−0.449707	+	0.893176i	$0.648471\pi$
$422$	−5332.55	−0.615129
$423$	−1677.94	−0.192871
$424$	24144.0	2.76542
$425$	−846.907	−0.0966612
$426$	1662.18	0.189045
$427$	−12827.1	−1.45374
$428$	3242.74	0.366224
$429$	9860.03	1.10967
$430$	−1478.61	−0.165825
$431$	8028.59	0.897270	0.448635	−	0.893715i	$-0.351910\pi$
$431$	8028.59	0.897270	0.448635	+	0.893715i	$0.351910\pi$
$432$	37037.0	4.12487
$433$	12643.7	1.40327	0.701637	−	0.712534i	$-0.252453\pi$
$433$	12643.7	1.40327	0.701637	+	0.712534i	$0.252453\pi$
$434$	−8049.44	−0.890289
$435$	4463.28	0.491949
$436$	−26623.1	−2.92435
$437$	−753.524	−0.0824850
$438$	−15884.5	−1.73285
$439$	5725.64	0.622483	0.311241	−	0.950331i	$-0.399255\pi$
$439$	5725.64	0.622483	0.311241	+	0.950331i	$0.399255\pi$
$440$	−11940.3	−1.29370
$441$	−2437.32	−0.263181
$442$	13097.2	1.40944
$443$	−12743.9	−1.36678	−0.683390	−	0.730054i	$-0.739495\pi$
$443$	−12743.9	−1.36678	−0.683390	+	0.730054i	$0.739495\pi$
$444$	−39326.3	−4.20347
$445$	−5236.10	−0.557786
$446$	−8182.03	−0.868678
$447$	−11079.3	−1.17234
$448$	−52777.8	−5.56589
$449$	8739.02	0.918530	0.459265	−	0.888299i	$-0.348113\pi$
$449$	8739.02	0.918530	0.459265	+	0.888299i	$0.348113\pi$
$450$	947.441	0.0992506
$451$	8932.87	0.932666
$452$	48114.1	5.00685
$453$	2777.07	0.288031
$454$	34043.4	3.51924
$455$	9307.13	0.958956
$456$	−6523.31	−0.669917
$457$	−5574.87	−0.570638	−0.285319	−	0.958433i	$-0.592099\pi$
$457$	−5574.87	−0.570638	−0.285319	+	0.958433i	$0.592099\pi$
$458$	10723.5	1.09405
$459$	−5149.13	−0.523618
$460$	−4360.67	−0.441995
$461$	−6896.15	−0.696715	−0.348358	−	0.937362i	$-0.613261\pi$
$461$	−6896.15	−0.696715	−0.348358	+	0.937362i	$0.613261\pi$
$462$	20166.9	2.03084
$463$	8436.08	0.846777	0.423388	−	0.905948i	$-0.360841\pi$
$463$	8436.08	0.846777	0.423388	+	0.905948i	$0.360841\pi$
$464$	48540.2	4.85652
$465$	−1249.01	−0.124562
$466$	32164.1	3.19736
$467$	−11640.2	−1.15341	−0.576707	−	0.816951i	$-0.695663\pi$
$467$	−11640.2	−1.15341	−0.576707	+	0.816951i	$0.695663\pi$
$468$	−10743.6	−1.06116
$469$	23490.9	2.31281
$470$	6639.31	0.651593
$471$	−10697.9	−1.04657
$472$	−4022.83	−0.392301
$473$	1683.05	0.163609
$474$	24108.0	2.33612
$475$	−475.000	−0.0458831
$476$	19642.3	1.89139
$477$	2180.69	0.209322
$478$	−10623.0	−1.01650
$479$	896.018	0.0854700	0.0427350	−	0.999086i	$-0.486393\pi$
$479$	896.018	0.0854700	0.0427350	+	0.999086i	$0.486393\pi$
$480$	−16164.6	−1.53711
$481$	28174.3	2.67076
$482$	−28977.1	−2.73832
$483$	4685.75	0.441427
$484$	−7906.93	−0.742574
$485$	−3179.51	−0.297678
$486$	10345.5	0.965603
$487$	−17952.6	−1.67045	−0.835225	−	0.549908i	$-0.814663\pi$
$487$	−17952.6	−1.67045	−0.835225	+	0.549908i	$0.814663\pi$
$488$	−37274.1	−3.45762
$489$	157.721	0.0145856
$490$	9644.02	0.889128
$491$	−5157.83	−0.474073	−0.237036	−	0.971501i	$-0.576176\pi$
$491$	−5157.83	−0.474073	−0.237036	+	0.971501i	$0.576176\pi$
$492$	28242.4	2.58794
$493$	−6748.39	−0.616495
$494$	7345.77	0.669032
$495$	−1078.44	−0.0979240
$496$	−13583.5	−1.22968
$497$	−1785.92	−0.161186
$498$	4565.50	0.410814
$499$	−15067.5	−1.35173	−0.675865	−	0.737025i	$-0.736230\pi$
$499$	−15067.5	−1.35173	−0.675865	+	0.737025i	$0.736230\pi$
$500$	−2748.84	−0.245864
$501$	−5888.85	−0.525139
$502$	−26508.3	−2.35682
$503$	821.915	0.0728576	0.0364288	−	0.999336i	$-0.488402\pi$
$503$	821.915	0.0728576	0.0364288	+	0.999336i	$0.488402\pi$
$504$	−13980.1	−1.23556
$505$	4406.89	0.388325
$506$	6769.33	0.594730
$507$	−12488.8	−1.09398
$508$	−19876.4	−1.73597
$509$	−10837.3	−0.943725	−0.471862	−	0.881672i	$-0.656418\pi$
$509$	−10837.3	−0.943725	−0.471862	+	0.881672i	$0.656418\pi$
$510$	4156.61	0.360897
$511$	17067.0	1.47749
$512$	−26441.8	−2.28237
$513$	−2887.96	−0.248551
$514$	−20751.8	−1.78078
$515$	3961.47	0.338958
$516$	5321.19	0.453978
$517$	−7557.32	−0.642883
$518$	57625.2	4.88785
$519$	−10734.3	−0.907867
$520$	27045.5	2.28081
$521$	−20597.2	−1.73202	−0.866009	−	0.500028i	$-0.833323\pi$
$521$	−20597.2	−1.73202	−0.866009	+	0.500028i	$0.833323\pi$
$522$	7549.47	0.633010
$523$	10804.1	0.903306	0.451653	−	0.892194i	$-0.350835\pi$
$523$	10804.1	0.903306	0.451653	+	0.892194i	$0.350835\pi$
$524$	13091.3	1.09141
$525$	2953.77	0.245548
$526$	−25003.8	−2.07266
$527$	1888.48	0.156097
$528$	34031.9	2.80501
$529$	−10594.2	−0.870728
$530$	−8628.57	−0.707172
$531$	−363.342	−0.0296943
$532$	11016.7	0.897806
$533$	−20233.6	−1.64430
$534$	25698.7	2.08257
$535$	−737.297	−0.0595815
$536$	68262.0	5.50087
$537$	−13565.1	−1.09009
$538$	−39708.6	−3.18208
$539$	−10977.5	−0.877243
$540$	−16712.8	−1.33186
$541$	3569.38	0.283659	0.141830	−	0.989891i	$-0.454701\pi$
$541$	3569.38	0.283659	0.141830	+	0.989891i	$0.454701\pi$
$542$	30344.2	2.40479
$543$	−601.912	−0.0475700
$544$	24440.6	1.92625
$545$	6053.26	0.475767
$546$	−45679.3	−3.58039
$547$	4519.85	0.353300	0.176650	−	0.984274i	$-0.443474\pi$
$547$	4519.85	0.353300	0.176650	+	0.984274i	$0.443474\pi$
$548$	44781.6	3.49083
$549$	−3366.59	−0.261717
$550$	4267.19	0.330825
$551$	−3784.93	−0.292638
$552$	13616.3	1.04990
$553$	−25902.7	−1.99185
$554$	−6002.64	−0.460339
$555$	8941.54	0.683869
$556$	−15318.8	−1.16845
$557$	−11591.5	−0.881772	−0.440886	−	0.897563i	$-0.645336\pi$
$557$	−11591.5	−0.881772	−0.440886	+	0.897563i	$0.645336\pi$
$558$	−2112.65	−0.160279
$559$	−3812.23	−0.288444
$560$	32123.6	2.42405
$561$	−4731.34	−0.356074
$562$	−5008.26	−0.375909
$563$	12751.6	0.954555	0.477277	−	0.878753i	$-0.341624\pi$
$563$	12751.6	0.954555	0.477277	+	0.878753i	$0.341624\pi$
$564$	−23893.5	−1.78386
$565$	−10939.6	−0.814572
$566$	−33437.8	−2.48321
$567$	13032.2	0.965255
$568$	−5189.68	−0.383370
$569$	−7021.18	−0.517299	−0.258650	−	0.965971i	$-0.583278\pi$
$569$	−7021.18	−0.517299	−0.258650	+	0.965971i	$0.583278\pi$
$570$	2331.29	0.171311
$571$	3906.50	0.286308	0.143154	−	0.989700i	$-0.454276\pi$
$571$	3906.50	0.286308	0.143154	+	0.989700i	$0.454276\pi$
$572$	−48388.1	−3.53708
$573$	1860.02	0.135608
$574$	−41384.0	−3.00929
$575$	991.479	0.0719087
$576$	−13852.0	−1.00203
$577$	10680.2	0.770579	0.385290	−	0.922796i	$-0.374102\pi$
$577$	10680.2	0.770579	0.385290	+	0.922796i	$0.374102\pi$
$578$	20620.8	1.48393
$579$	−14121.9	−1.01362
$580$	−21903.6	−1.56810
$581$	−4905.37	−0.350273
$582$	15605.0	1.11142
$583$	9821.63	0.697719
$584$	49594.6	3.51411
$585$	2442.74	0.172641
$586$	29877.0	2.10616
$587$	−3371.04	−0.237032	−0.118516	−	0.992952i	$-0.537814\pi$
$587$	−3371.04	−0.237032	−0.118516	+	0.992952i	$0.537814\pi$
$588$	−34706.8	−2.43416
$589$	1059.18	0.0740963
$590$	1437.68	0.100319
$591$	11560.5	0.804631
$592$	97243.4	6.75115
$593$	−16065.2	−1.11251	−0.556257	−	0.831011i	$-0.687763\pi$
$593$	−16065.2	−1.11251	−0.556257	+	0.831011i	$0.687763\pi$
$594$	25944.2	1.79209
$595$	−4466.03	−0.307713
$596$	54371.9	3.73684
$597$	1129.14	0.0774079
$598$	−15333.0	−1.04852
$599$	9870.16	0.673262	0.336631	−	0.941637i	$-0.390713\pi$
$599$	9870.16	0.673262	0.336631	+	0.941637i	$0.390713\pi$
$600$	8583.31	0.584020
$601$	−16016.2	−1.08704	−0.543521	−	0.839395i	$-0.682909\pi$
$601$	−16016.2	−1.08704	−0.543521	+	0.839395i	$0.682909\pi$
$602$	−7797.20	−0.527891
$603$	6165.41	0.416376
$604$	−13628.5	−0.918104
$605$	1797.78	0.120810
$606$	−21629.0	−1.44986
$607$	14462.3	0.967064	0.483532	−	0.875327i	$-0.339354\pi$
$607$	14462.3	0.967064	0.483532	+	0.875327i	$0.339354\pi$
$608$	13707.8	0.914353
$609$	23536.4	1.56608
$610$	13321.0	0.884180
$611$	17117.8	1.13341
$612$	5155.30	0.340508
$613$	−25748.6	−1.69653	−0.848267	−	0.529568i	$-0.822354\pi$
$613$	−25748.6	−1.69653	−0.848267	+	0.529568i	$0.822354\pi$
$614$	26685.2	1.75395
$615$	−6421.44	−0.421036
$616$	−62965.1	−4.11840
$617$	17032.3	1.11134	0.555670	−	0.831403i	$-0.312462\pi$
$617$	17032.3	1.11134	0.555670	+	0.831403i	$0.312462\pi$
$618$	−19442.8	−1.26554
$619$	11618.4	0.754412	0.377206	−	0.926129i	$-0.376885\pi$
$619$	11618.4	0.754412	0.377206	+	0.926129i	$0.376885\pi$
$620$	6129.51	0.397044
$621$	6028.11	0.389533
$622$	975.095	0.0628581
$623$	−27611.8	−1.77567
$624$	−77084.5	−4.94527
$625$	625.000	0.0400000
$626$	−9718.54	−0.620497
$627$	−2653.64	−0.169021
$628$	52499.8	3.33594
$629$	−13519.4	−0.857003
$630$	4996.18	0.315957
$631$	−14829.2	−0.935567	−0.467783	−	0.883843i	$-0.654947\pi$
$631$	−14829.2	−0.935567	−0.467783	+	0.883843i	$0.654947\pi$
$632$	−75270.2	−4.73748
$633$	−4363.36	−0.273978
$634$	−12181.0	−0.763041
$635$	4519.26	0.282427
$636$	31052.4	1.93602
$637$	24864.8	1.54659
$638$	34002.2	2.10997
$639$	−468.731	−0.0290183
$640$	25951.3	1.60283
$641$	−21754.9	−1.34051	−0.670256	−	0.742130i	$-0.733816\pi$
$641$	−21754.9	−1.34051	−0.670256	+	0.742130i	$0.733816\pi$
$642$	3618.64	0.222456
$643$	31416.8	1.92684	0.963421	−	0.267994i	$-0.0863608\pi$
$643$	31416.8	1.92684	0.963421	+	0.267994i	$0.0863608\pi$
$644$	−22995.3	−1.40705
$645$	−1209.87	−0.0738583
$646$	−3524.87	−0.214681
$647$	19497.7	1.18475	0.592374	−	0.805663i	$-0.298191\pi$
$647$	19497.7	1.18475	0.592374	+	0.805663i	$0.298191\pi$
$648$	37870.0	2.29579
$649$	−1636.46	−0.0989780
$650$	−9665.48	−0.583248
$651$	−6586.45	−0.396534
$652$	−774.015	−0.0464920
$653$	−17253.6	−1.03397	−0.516986	−	0.855994i	$-0.672946\pi$
$653$	−17253.6	−1.03397	−0.516986	+	0.855994i	$0.672946\pi$
$654$	−29709.3	−1.77634
$655$	−2976.55	−0.177562
$656$	−69836.1	−4.15646
$657$	4479.38	0.265993
$658$	35011.4	2.07429
$659$	11126.9	0.657727	0.328863	−	0.944378i	$-0.393334\pi$
$659$	11126.9	0.657727	0.328863	+	0.944378i	$0.393334\pi$
$660$	−15356.7	−0.905697
$661$	3148.00	0.185239	0.0926195	−	0.995702i	$-0.470476\pi$
$661$	3148.00	0.185239	0.0926195	+	0.995702i	$0.470476\pi$
$662$	−32930.6	−1.93336
$663$	10716.8	0.627762
$664$	−14254.4	−0.833102
$665$	−2504.84	−0.146065
$666$	15124.3	0.879961
$667$	7900.38	0.458626
$668$	28899.6	1.67389
$669$	−6694.95	−0.386908
$670$	−24395.4	−1.40668
$671$	−15162.8	−0.872362
$672$	−85241.6	−4.89325
$673$	792.453	0.0453890	0.0226945	−	0.999742i	$-0.492775\pi$
$673$	792.453	0.0453890	0.0226945	+	0.999742i	$0.492775\pi$
$674$	43793.4	2.50276
$675$	3799.95	0.216682
$676$	61288.6	3.48706
$677$	−25746.5	−1.46162	−0.730810	−	0.682581i	$-0.760857\pi$
$677$	−25746.5	−1.46162	−0.730810	+	0.682581i	$0.760857\pi$
$678$	53691.5	3.04131
$679$	−16766.6	−0.947636
$680$	−12977.8	−0.731875
$681$	27856.0	1.56746
$682$	−9515.20	−0.534246
$683$	14638.1	0.820075	0.410038	−	0.912069i	$-0.365516\pi$
$683$	14638.1	0.820075	0.410038	+	0.912069i	$0.365516\pi$
$684$	2891.43	0.161632
$685$	−10181.9	−0.567928
$686$	1329.04	0.0739693
$687$	8774.52	0.487291
$688$	−13157.9	−0.729128
$689$	−22246.7	−1.23009
$690$	−4866.17	−0.268481
$691$	30987.7	1.70597	0.852987	−	0.521931i	$-0.174788\pi$
$691$	30987.7	1.70597	0.852987	+	0.521931i	$0.174788\pi$
$692$	52678.5	2.89384
$693$	−5687.00	−0.311733
$694$	35389.2	1.93567
$695$	3483.00	0.190097
$696$	68394.2	3.72482
$697$	9709.08	0.527629
$698$	−29662.7	−1.60853
$699$	26318.2	1.42410
$700$	−14495.6	−0.782689
$701$	1662.96	0.0895992	0.0447996	−	0.998996i	$-0.485735\pi$
$701$	1662.96	0.0895992	0.0447996	+	0.998996i	$0.485735\pi$
$702$	−58765.4	−3.15948
$703$	−7582.57	−0.406802
$704$	−62388.4	−3.33999
$705$	5432.62	0.290219
$706$	−33398.6	−1.78041
$707$	23239.1	1.23620
$708$	−5173.89	−0.274642
$709$	−17483.4	−0.926099	−0.463050	−	0.886332i	$-0.653245\pi$
$709$	−17483.4	−0.926099	−0.463050	+	0.886332i	$0.653245\pi$
$710$	1854.68	0.0980351
$711$	−6798.40	−0.358593
$712$	−80236.6	−4.22331
$713$	−2210.85	−0.116125
$714$	21919.2	1.14889
$715$	11001.9	0.575452
$716$	66570.9	3.47468
$717$	−8692.29	−0.452747
$718$	−22878.3	−1.18915
$719$	28989.2	1.50364	0.751819	−	0.659370i	$-0.229177\pi$
$719$	28989.2	1.50364	0.751819	+	0.659370i	$0.229177\pi$
$720$	8431.13	0.436402
$721$	20890.2	1.07905
$722$	−1976.97	−0.101905
$723$	−23710.5	−1.21965
$724$	2953.89	0.151630
$725$	4980.17	0.255116
$726$	−8823.51	−0.451062
$727$	32401.8	1.65298	0.826489	−	0.562953i	$-0.190335\pi$
$727$	32401.8	1.65298	0.826489	+	0.562953i	$0.190335\pi$
$728$	142620.	7.26079
$729$	21810.4	1.10808
$730$	−17724.1	−0.898626
$731$	1829.30	0.0925568
$732$	−47939.3	−2.42061
$733$	694.988	0.0350204	0.0175102	−	0.999847i	$-0.494426\pi$
$733$	694.988	0.0350204	0.0175102	+	0.999847i	$0.494426\pi$
$734$	−43341.9	−2.17953
$735$	7891.22	0.396017
$736$	−28612.7	−1.43299
$737$	27768.5	1.38788
$738$	−10861.6	−0.541763
$739$	−5366.18	−0.267115	−0.133558	−	0.991041i	$-0.542640\pi$
$739$	−5366.18	−0.267115	−0.133558	+	0.991041i	$0.542640\pi$
$740$	−43880.6	−2.17984
$741$	6010.67	0.297986
$742$	−45501.4	−2.25123
$743$	−1895.53	−0.0935940	−0.0467970	−	0.998904i	$-0.514901\pi$
$743$	−1895.53	−0.0935940	−0.0467970	+	0.998904i	$0.514901\pi$
$744$	−19139.5	−0.943129
$745$	−12362.4	−0.607953
$746$	6807.72	0.334113
$747$	−1287.46	−0.0630598
$748$	23219.0	1.13499
$749$	−3888.02	−0.189673
$750$	−3067.49	−0.149345
$751$	−28262.3	−1.37324	−0.686622	−	0.727014i	$-0.740907\pi$
$751$	−28262.3	−1.37324	−0.686622	+	0.727014i	$0.740907\pi$
$752$	59082.2	2.86504
$753$	−21690.4	−1.04972
$754$	−77017.2	−3.71990
$755$	3098.68	0.149368
$756$	−88132.2	−4.23986
$757$	−6100.51	−0.292902	−0.146451	−	0.989218i	$-0.546785\pi$
$757$	−6100.51	−0.292902	−0.146451	+	0.989218i	$0.546785\pi$
$758$	−71250.4	−3.41416
$759$	5539.01	0.264892
$760$	−7278.78	−0.347407
$761$	21151.0	1.00752	0.503761	−	0.863843i	$-0.331949\pi$
$761$	21151.0	1.00752	0.503761	+	0.863843i	$0.331949\pi$
$762$	−22180.5	−1.05448
$763$	31920.9	1.51457
$764$	−9128.03	−0.432252
$765$	−1172.15	−0.0553977
$766$	−27018.4	−1.27443
$767$	3706.70	0.174499
$768$	−55611.4	−2.61289
$769$	−18502.3	−0.867631	−0.433815	−	0.901002i	$-0.642833\pi$
$769$	−18502.3	−0.867631	−0.433815	+	0.901002i	$0.642833\pi$
$770$	22502.4	1.05316
$771$	−16980.2	−0.793159
$772$	69303.2	3.23093
$773$	−27014.9	−1.25700	−0.628498	−	0.777811i	$-0.716330\pi$
$773$	−27014.9	−1.25700	−0.628498	+	0.777811i	$0.716330\pi$
$774$	−2046.45	−0.0950363
$775$	−1393.66	−0.0645956
$776$	−48722.0	−2.25389
$777$	47151.8	2.17704
$778$	14230.4	0.655764
$779$	5445.48	0.250455
$780$	34784.0	1.59675
$781$	−2111.13	−0.0967248
$782$	7357.54	0.336452
$783$	30279.1	1.38197
$784$	85820.7	3.90947
$785$	−11936.8	−0.542729
$786$	14608.9	0.662953
$787$	9479.87	0.429379	0.214689	−	0.976682i	$-0.431126\pi$
$787$	9479.87	0.429379	0.214689	+	0.976682i	$0.431126\pi$
$788$	−56733.4	−2.56477
$789$	−20459.4	−0.923161
$790$	26900.0	1.21147
$791$	−57688.4	−2.59313
$792$	−16525.8	−0.741437
$793$	34344.8	1.53798
$794$	−16637.1	−0.743612
$795$	−7060.33	−0.314974
$796$	−5541.24	−0.246739
$797$	1351.71	0.0600754	0.0300377	−	0.999549i	$-0.490437\pi$
$797$	1351.71	0.0600754	0.0300377	+	0.999549i	$0.490437\pi$
$798$	12293.7	0.545355
$799$	−8214.00	−0.363693
$800$	−18036.6	−0.797115
$801$	−7246.96	−0.319674
$802$	−27830.8	−1.22536
$803$	20174.8	0.886615
$804$	87793.8	3.85105
$805$	5228.41	0.228916
$806$	21552.6	0.941882
$807$	−32491.6	−1.41730
$808$	67530.1	2.94023
$809$	1647.64	0.0716042	0.0358021	−	0.999359i	$-0.488601\pi$
$809$	1647.64	0.0716042	0.0358021	+	0.999359i	$0.488601\pi$
$810$	−13533.9	−0.587079
$811$	−27370.0	−1.18507	−0.592535	−	0.805545i	$-0.701873\pi$
$811$	−27370.0	−1.18507	−0.592535	+	0.805545i	$0.701873\pi$
$812$	−115505.	−4.99191
$813$	24829.1	1.07109
$814$	68118.5	2.93311
$815$	175.986	0.00756384
$816$	36989.0	1.58686
$817$	1025.99	0.0439349
$818$	−38092.4	−1.62820
$819$	12881.4	0.549589
$820$	31513.2	1.34206
$821$	−11200.8	−0.476138	−0.238069	−	0.971248i	$-0.576514\pi$
$821$	−11200.8	−0.476138	−0.238069	+	0.971248i	$0.576514\pi$
$822$	49972.7	2.12044
$823$	7539.86	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$823$	7539.86	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$824$	60704.6	2.56644
$825$	3491.63	0.147349
$826$	7581.36	0.319357
$827$	−12931.4	−0.543734	−0.271867	−	0.962335i	$-0.587641\pi$
$827$	−12931.4	−0.543734	−0.271867	+	0.962335i	$0.587641\pi$
$828$	−6035.34	−0.253312
$829$	12317.3	0.516041	0.258020	−	0.966139i	$-0.416930\pi$
$829$	12317.3	0.516041	0.258020	+	0.966139i	$0.416930\pi$
$830$	5094.24	0.213040
$831$	−4911.66	−0.205034
$832$	141314.	5.88844
$833$	−11931.4	−0.496275
$834$	−17094.5	−0.709754
$835$	−6570.84	−0.272327
$836$	13022.7	0.538757
$837$	−8473.32	−0.349917
$838$	29059.7	1.19791
$839$	27322.2	1.12427	0.562137	−	0.827044i	$-0.309979\pi$
$839$	27322.2	1.12427	0.562137	+	0.827044i	$0.309979\pi$
$840$	45262.8	1.85918
$841$	15294.4	0.627102
$842$	42547.7	1.74144
$843$	−4098.01	−0.167429
$844$	21413.2	0.873308
$845$	−13935.1	−0.567315
$846$	9189.07	0.373436
$847$	9480.34	0.384591
$848$	−76784.3	−3.10941
$849$	−27360.5	−1.10602
$850$	4637.98	0.187155
$851$	15827.3	0.637546
$852$	−6674.60	−0.268390
$853$	46078.6	1.84959	0.924796	−	0.380463i	$-0.124235\pi$
$853$	46078.6	1.84959	0.924796	+	0.380463i	$0.124235\pi$
$854$	70246.0	2.81472
$855$	−657.418	−0.0262962
$856$	−11298.2	−0.451125
$857$	33825.6	1.34826	0.674131	−	0.738612i	$-0.264518\pi$
$857$	33825.6	1.34826	0.674131	+	0.738612i	$0.264518\pi$
$858$	−53997.3	−2.14853
$859$	5998.21	0.238249	0.119125	−	0.992879i	$-0.461991\pi$
$859$	5998.21	0.238249	0.119125	+	0.992879i	$0.461991\pi$
$860$	5937.44	0.235424
$861$	−33862.4	−1.34034
$862$	−43967.6	−1.73729
$863$	−40044.7	−1.57953	−0.789767	−	0.613407i	$-0.789799\pi$
$863$	−40044.7	−1.57953	−0.789767	+	0.613407i	$0.789799\pi$
$864$	−109661.	−4.31801
$865$	−11977.4	−0.470803
$866$	−69241.8	−2.71701
$867$	16872.9	0.660940
$868$	32323.0	1.26396
$869$	−30619.4	−1.19527
$870$	−24442.6	−0.952509
$871$	−62897.5	−2.44684
$872$	92758.6	3.60230
$873$	−4400.56	−0.170603
$874$	4126.58	0.159707
$875$	3295.84	0.127337
$876$	63785.2	2.46016
$877$	−3352.48	−0.129082	−0.0645412	−	0.997915i	$-0.520558\pi$
$877$	−3352.48	−0.129082	−0.0645412	+	0.997915i	$0.520558\pi$
$878$	−31355.8	−1.20525
$879$	24446.9	0.938080
$880$	37973.1	1.45463
$881$	−4231.78	−0.161830	−0.0809150	−	0.996721i	$-0.525784\pi$
$881$	−4231.78	−0.161830	−0.0809150	+	0.996721i	$0.525784\pi$
$882$	13347.7	0.509570
$883$	35080.8	1.33699	0.668495	−	0.743716i	$-0.266939\pi$
$883$	35080.8	1.33699	0.668495	+	0.743716i	$0.266939\pi$
$884$	−52592.7	−2.00100
$885$	1176.38	0.0446819
$886$	69790.7	2.64635
$887$	24426.3	0.924639	0.462320	−	0.886713i	$-0.347017\pi$
$887$	24426.3	0.924639	0.462320	+	0.886713i	$0.347017\pi$
$888$	137018.	5.17795
$889$	23831.6	0.899085
$890$	28674.9	1.07998
$891$	15405.3	0.579232
$892$	32855.5	1.23328
$893$	−4606.94	−0.172638
$894$	60674.7	2.26987
$895$	−15136.1	−0.565301
$896$	136850.	5.10250
$897$	−12546.2	−0.467008
$898$	−47858.2	−1.77845
$899$	−11105.0	−0.411984
$900$	−3804.51	−0.140908
$901$	10675.1	0.394715
$902$	−48919.8	−1.80582
$903$	−6380.06	−0.235122
$904$	−167636.	−6.16758
$905$	−671.620	−0.0246689
$906$	−15208.3	−0.557684
$907$	47768.1	1.74875	0.874373	−	0.485254i	$-0.161273\pi$
$907$	47768.1	1.74875	0.874373	+	0.485254i	$0.161273\pi$
$908$	−136703.	−4.99632
$909$	6099.31	0.222554
$910$	−50969.4	−1.85673
$911$	6505.92	0.236609	0.118304	−	0.992977i	$-0.462254\pi$
$911$	6505.92	0.236609	0.118304	+	0.992977i	$0.462254\pi$
$912$	20745.8	0.753249
$913$	−5798.61	−0.210193
$914$	30530.1	1.10486
$915$	10899.9	0.393813
$916$	−43061.0	−1.55325
$917$	−15696.4	−0.565256
$918$	28198.6	1.01383
$919$	−12010.8	−0.431122	−0.215561	−	0.976490i	$-0.569158\pi$
$919$	−12010.8	−0.431122	−0.215561	+	0.976490i	$0.569158\pi$
$920$	15193.2	0.544461
$921$	21835.2	0.781209
$922$	37765.9	1.34898
$923$	4781.84	0.170527
$924$	−80981.3	−2.88321
$925$	9977.06	0.354642
$926$	−46199.2	−1.63952
$927$	5482.83	0.194261
$928$	−143721.	−5.08391
$929$	14515.2	0.512624	0.256312	−	0.966594i	$-0.417493\pi$
$929$	14515.2	0.512624	0.256312	+	0.966594i	$0.417493\pi$
$930$	6840.05	0.241176
$931$	−6691.88	−0.235572
$932$	−129157.	−4.53935
$933$	797.871	0.0279969
$934$	63746.2	2.23323
$935$	−5279.27	−0.184653
$936$	37432.0	1.30716
$937$	−30316.3	−1.05698	−0.528491	−	0.848939i	$-0.677242\pi$
$937$	−30316.3	−1.05698	−0.528491	+	0.848939i	$0.677242\pi$
$938$	−128645.	−4.47806
$939$	−7952.19	−0.276369
$940$	−26660.6	−0.925077
$941$	33809.6	1.17127	0.585633	−	0.810576i	$-0.300846\pi$
$941$	33809.6	1.17127	0.585633	+	0.810576i	$0.300846\pi$
$942$	58585.7	2.02635
$943$	−11366.5	−0.392517
$944$	12793.7	0.441099
$945$	20038.5	0.689789
$946$	−9217.04	−0.316778
$947$	−53269.3	−1.82790	−0.913949	−	0.405828i	$-0.866983\pi$
$947$	−53269.3	−1.82790	−0.913949	+	0.405828i	$0.866983\pi$
$948$	−96807.3	−3.31662
$949$	−45697.2	−1.56311
$950$	2601.28	0.0888386
$951$	−9967.08	−0.339858
$952$	−68436.3	−2.32987
$953$	−29677.7	−1.00877	−0.504384	−	0.863479i	$-0.668280\pi$
$953$	−29677.7	−1.00877	−0.504384	+	0.863479i	$0.668280\pi$
$954$	−11942.3	−0.405289
$955$	2075.42	0.0703237
$956$	42657.4	1.44314
$957$	27822.3	0.939777
$958$	−4906.94	−0.165486
$959$	−53692.7	−1.80795
$960$	44848.2	1.50778
$961$	−26683.4	−0.895685
$962$	−154293.	−5.17111
$963$	−1020.45	−0.0341469
$964$	116359.	3.88764
$965$	−15757.3	−0.525644
$966$	−25661.0	−0.854688
$967$	−32706.1	−1.08765	−0.543825	−	0.839198i	$-0.683025\pi$
$967$	−32706.1	−1.08765	−0.543825	+	0.839198i	$0.683025\pi$
$968$	27548.8	0.914723
$969$	−2884.22	−0.0956188
$970$	17412.2	0.576363
$971$	−34661.4	−1.14556	−0.572780	−	0.819709i	$-0.694135\pi$
$971$	−34661.4	−1.14556	−0.572780	+	0.819709i	$0.694135\pi$
$972$	−41543.2	−1.37088
$973$	18367.1	0.605160
$974$	98315.2	3.23431
$975$	−7908.78	−0.259778
$976$	118541.	3.88771
$977$	4915.45	0.160961	0.0804806	−	0.996756i	$-0.474354\pi$
$977$	4915.45	0.160961	0.0804806	+	0.996756i	$0.474354\pi$
$978$	−863.739	−0.0282406
$979$	−32639.7	−1.06555
$980$	−38726.2	−1.26231
$981$	8377.94	0.272668
$982$	28246.3	0.917896
$983$	25257.7	0.819529	0.409765	−	0.912191i	$-0.365611\pi$
$983$	25257.7	0.819529	0.409765	+	0.912191i	$0.365611\pi$
$984$	−98400.4	−3.18790
$985$	12899.4	0.417267
$986$	36956.7	1.19365
$987$	28648.1	0.923889
$988$	−29497.4	−0.949835
$989$	−2141.57	−0.0688554
$990$	5905.96	0.189600
$991$	−48379.1	−1.55077	−0.775385	−	0.631489i	$-0.782444\pi$
$991$	−48379.1	−1.55077	−0.775385	+	0.631489i	$0.782444\pi$
$992$	40219.0	1.28725
$993$	−26945.5	−0.861117
$994$	9780.37	0.312087
$995$	1259.90	0.0401423
$996$	−18333.1	−0.583239
$997$	3520.96	0.111846	0.0559228	−	0.998435i	$-0.482190\pi$
$997$	3520.96	0.111846	0.0559228	+	0.998435i	$0.482190\pi$
$998$	82515.3	2.61721
$999$	60659.8	1.92111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.4.a.g.1.1	✓	6
3.2	odd	2		855.4.a.r.1.6		6
4.3	odd	2		1520.4.a.y.1.5		6
5.2	odd	4		475.4.b.i.324.1		12
5.3	odd	4		475.4.b.i.324.12		12
5.4	even	2		475.4.a.i.1.6		6
19.18	odd	2		1805.4.a.m.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.a.g.1.1	✓	6	1.1	even	1	trivial
475.4.a.i.1.6		6	5.4	even	2
475.4.b.i.324.1		12	5.2	odd	4
475.4.b.i.324.12		12	5.3	odd	4
855.4.a.r.1.6		6	3.2	odd	2
1520.4.a.y.1.5		6	4.3	odd	2
1805.4.a.m.1.6		6	19.18	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.a (trivial)

\(f(q)\)	\(=\)	\(q-5.47638 q^{2} -4.48105 q^{3} +21.9908 q^{4} -5.00000 q^{5} +24.5399 q^{6} -26.3667 q^{7} -76.6187 q^{8} -6.92019 q^{9} +O(q^{10})\)	\(q-5.47638 q^{2} -4.48105 q^{3} +21.9908 q^{4} -5.00000 q^{5} +24.5399 q^{6} -26.3667 q^{7} -76.6187 q^{8} -6.92019 q^{9} +27.3819 q^{10} -31.1680 q^{11} -98.5417 q^{12} +70.5976 q^{13} +144.394 q^{14} +22.4052 q^{15} +243.667 q^{16} -33.8763 q^{17} +37.8976 q^{18} -19.0000 q^{19} -109.954 q^{20} +118.151 q^{21} +170.688 q^{22} +39.6592 q^{23} +343.332 q^{24} +25.0000 q^{25} -386.619 q^{26} +151.998 q^{27} -579.824 q^{28} +199.207 q^{29} -122.700 q^{30} -55.7463 q^{31} -721.466 q^{32} +139.665 q^{33} +185.519 q^{34} +131.834 q^{35} -152.180 q^{36} +399.083 q^{37} +104.051 q^{38} -316.351 q^{39} +383.094 q^{40} -286.604 q^{41} -647.038 q^{42} -53.9994 q^{43} -685.408 q^{44} +34.6010 q^{45} -217.189 q^{46} +242.471 q^{47} -1091.89 q^{48} +352.204 q^{49} -136.910 q^{50} +151.801 q^{51} +1552.49 q^{52} -315.119 q^{53} -832.399 q^{54} +155.840 q^{55} +2020.19 q^{56} +85.1399 q^{57} -1090.93 q^{58} +52.5046 q^{59} +492.708 q^{60} +486.488 q^{61} +305.288 q^{62} +182.463 q^{63} +2001.68 q^{64} -352.988 q^{65} -764.860 q^{66} -890.930 q^{67} -744.965 q^{68} -177.715 q^{69} -721.971 q^{70} +67.7338 q^{71} +530.216 q^{72} -647.291 q^{73} -2185.53 q^{74} -112.026 q^{75} -417.824 q^{76} +821.798 q^{77} +1732.46 q^{78} +982.400 q^{79} -1218.34 q^{80} -494.266 q^{81} +1569.55 q^{82} +186.044 q^{83} +2598.22 q^{84} +169.381 q^{85} +295.721 q^{86} -892.656 q^{87} +2388.05 q^{88} +1047.22 q^{89} -189.488 q^{90} -1861.43 q^{91} +872.135 q^{92} +249.802 q^{93} -1327.86 q^{94} +95.0000 q^{95} +3232.92 q^{96} +635.901 q^{97} -1928.80 q^{98} +215.688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 5 q^{3} + 25 q^{4} - 30 q^{5} + 61 q^{6} + 5 q^{7} - 3 q^{8} + 135 q^{9}+O(q^{10}) \) 6 * q - q^2 + 5 * q^3 + 25 * q^4 - 30 * q^5 + 61 * q^6 + 5 * q^7 - 3 * q^8 + 135 * q^9	\( 6 q - q^{2} + 5 q^{3} + 25 q^{4} - 30 q^{5} + 61 q^{6} + 5 q^{7} - 3 q^{8} + 135 q^{9} + 5 q^{10} + 8 q^{11} + 35 q^{12} + 79 q^{13} + 151 q^{14} - 25 q^{15} + 285 q^{16} + 35 q^{17} - 48 q^{18} - 114 q^{19} - 125 q^{20} + 403 q^{21} + 320 q^{22} - 111 q^{23} + 365 q^{24} + 150 q^{25} - 597 q^{26} + 683 q^{27} - 581 q^{28} + 107 q^{29} - 305 q^{30} + 574 q^{31} - 1225 q^{32} - 348 q^{33} - 379 q^{34} - 25 q^{35} - 602 q^{36} + 490 q^{37} + 19 q^{38} - 205 q^{39} + 15 q^{40} - 256 q^{41} - 1469 q^{42} - 212 q^{43} - 1228 q^{44} - 675 q^{45} + 43 q^{46} + 674 q^{47} - 2429 q^{48} + 931 q^{49} - 25 q^{50} + 661 q^{51} + 1601 q^{52} - 1729 q^{53} - 797 q^{54} - 40 q^{55} + 2731 q^{56} - 95 q^{57} - 1799 q^{58} - 25 q^{59} - 175 q^{60} + 1626 q^{61} + 1642 q^{62} - 852 q^{63} + 1717 q^{64} - 395 q^{65} + 1856 q^{66} + 741 q^{67} - 2207 q^{68} + 119 q^{69} - 755 q^{70} + 792 q^{71} + 1238 q^{72} + 1529 q^{73} - 2098 q^{74} + 125 q^{75} - 475 q^{76} + 628 q^{77} - 2589 q^{78} + 62 q^{79} - 1425 q^{80} + 3278 q^{81} + 1682 q^{82} - 80 q^{83} + 1687 q^{84} - 175 q^{85} + 3086 q^{86} + 545 q^{87} + 56 q^{88} + 4256 q^{89} + 240 q^{90} + 3153 q^{91} + 3163 q^{92} - 10 q^{93} + 2208 q^{94} + 570 q^{95} + 2377 q^{96} + 1910 q^{97} - 4940 q^{98} - 444 q^{99}+O(q^{100}) \) 6 * q - q^2 + 5 * q^3 + 25 * q^4 - 30 * q^5 + 61 * q^6 + 5 * q^7 - 3 * q^8 + 135 * q^9 + 5 * q^10 + 8 * q^11 + 35 * q^12 + 79 * q^13 + 151 * q^14 - 25 * q^15 + 285 * q^16 + 35 * q^17 - 48 * q^18 - 114 * q^19 - 125 * q^20 + 403 * q^21 + 320 * q^22 - 111 * q^23 + 365 * q^24 + 150 * q^25 - 597 * q^26 + 683 * q^27 - 581 * q^28 + 107 * q^29 - 305 * q^30 + 574 * q^31 - 1225 * q^32 - 348 * q^33 - 379 * q^34 - 25 * q^35 - 602 * q^36 + 490 * q^37 + 19 * q^38 - 205 * q^39 + 15 * q^40 - 256 * q^41 - 1469 * q^42 - 212 * q^43 - 1228 * q^44 - 675 * q^45 + 43 * q^46 + 674 * q^47 - 2429 * q^48 + 931 * q^49 - 25 * q^50 + 661 * q^51 + 1601 * q^52 - 1729 * q^53 - 797 * q^54 - 40 * q^55 + 2731 * q^56 - 95 * q^57 - 1799 * q^58 - 25 * q^59 - 175 * q^60 + 1626 * q^61 + 1642 * q^62 - 852 * q^63 + 1717 * q^64 - 395 * q^65 + 1856 * q^66 + 741 * q^67 - 2207 * q^68 + 119 * q^69 - 755 * q^70 + 792 * q^71 + 1238 * q^72 + 1529 * q^73 - 2098 * q^74 + 125 * q^75 - 475 * q^76 + 628 * q^77 - 2589 * q^78 + 62 * q^79 - 1425 * q^80 + 3278 * q^81 + 1682 * q^82 - 80 * q^83 + 1687 * q^84 - 175 * q^85 + 3086 * q^86 + 545 * q^87 + 56 * q^88 + 4256 * q^89 + 240 * q^90 + 3153 * q^91 + 3163 * q^92 - 10 * q^93 + 2208 * q^94 + 570 * q^95 + 2377 * q^96 + 1910 * q^97 - 4940 * q^98 - 444 * q^99

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