LMFDB - Embedded newform 2015.4.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2015,4,Mod(1,2015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2015.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2015 = 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2015.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:	$118.888848662$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	2015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37712 q^{2} +4.38088 q^{3} -2.34931 q^{4} -5.00000 q^{5} -10.4139 q^{6} +13.5532 q^{7} +24.6015 q^{8} -7.80791 q^{9} +O(q^{10})$	\(q-2.37712 q^{2} +4.38088 q^{3} -2.34931 q^{4} -5.00000 q^{5} -10.4139 q^{6} +13.5532 q^{7} +24.6015 q^{8} -7.80791 q^{9} +11.8856 q^{10} +16.1555 q^{11} -10.2920 q^{12} -13.0000 q^{13} -32.2175 q^{14} -21.9044 q^{15} -39.6863 q^{16} +28.0145 q^{17} +18.5603 q^{18} +11.6811 q^{19} +11.7465 q^{20} +59.3748 q^{21} -38.4036 q^{22} -160.222 q^{23} +107.776 q^{24} +25.0000 q^{25} +30.9025 q^{26} -152.489 q^{27} -31.8405 q^{28} +289.477 q^{29} +52.0693 q^{30} +31.0000 q^{31} -102.473 q^{32} +70.7754 q^{33} -66.5937 q^{34} -67.7658 q^{35} +18.3432 q^{36} -378.814 q^{37} -27.7674 q^{38} -56.9514 q^{39} -123.008 q^{40} +138.920 q^{41} -141.141 q^{42} +207.115 q^{43} -37.9543 q^{44} +39.0396 q^{45} +380.866 q^{46} +270.885 q^{47} -173.861 q^{48} -159.312 q^{49} -59.4280 q^{50} +122.728 q^{51} +30.5410 q^{52} -614.080 q^{53} +362.485 q^{54} -80.7777 q^{55} +333.429 q^{56} +51.1736 q^{57} -688.122 q^{58} -437.240 q^{59} +51.4601 q^{60} +592.439 q^{61} -73.6907 q^{62} -105.822 q^{63} +561.081 q^{64} +65.0000 q^{65} -168.242 q^{66} +633.022 q^{67} -65.8146 q^{68} -701.913 q^{69} +161.087 q^{70} -1013.23 q^{71} -192.087 q^{72} -420.735 q^{73} +900.485 q^{74} +109.522 q^{75} -27.4426 q^{76} +218.959 q^{77} +135.380 q^{78} -295.238 q^{79} +198.432 q^{80} -457.223 q^{81} -330.229 q^{82} +40.2055 q^{83} -139.490 q^{84} -140.072 q^{85} -492.337 q^{86} +1268.16 q^{87} +397.451 q^{88} -251.453 q^{89} -92.8017 q^{90} -176.191 q^{91} +376.410 q^{92} +135.807 q^{93} -643.925 q^{94} -58.4057 q^{95} -448.922 q^{96} +931.961 q^{97} +378.703 q^{98} -126.141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * 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 $

$2$	−2.37712	−0.840438	−0.420219	−	0.907423i	$-0.638047\pi$
$2$	−2.37712	−0.840438	−0.420219	+	0.907423i	$0.638047\pi$
$3$	4.38088	0.843100	0.421550	−	0.906805i	$-0.361486\pi$
$3$	4.38088	0.843100	0.421550	+	0.906805i	$0.361486\pi$
$4$	−2.34931	−0.293663
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−10.4139	−0.708574
$7$	13.5532	0.731802	0.365901	−	0.930654i	$-0.380761\pi$
$7$	13.5532	0.731802	0.365901	+	0.930654i	$0.380761\pi$
$8$	24.6015	1.08724
$9$	−7.80791	−0.289182
$10$	11.8856	0.375855
$11$	16.1555	0.442825	0.221413	−	0.975180i	$-0.428933\pi$
$11$	16.1555	0.442825	0.221413	+	0.975180i	$0.428933\pi$
$12$	−10.2920	−0.247588
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−32.2175	−0.615035
$15$	−21.9044	−0.377046
$16$	−39.6863	−0.620099
$17$	28.0145	0.399677	0.199838	−	0.979829i	$-0.435958\pi$
$17$	28.0145	0.399677	0.199838	+	0.979829i	$0.435958\pi$
$18$	18.5603	0.243040
$19$	11.6811	0.141044	0.0705220	−	0.997510i	$-0.477534\pi$
$19$	11.6811	0.141044	0.0705220	+	0.997510i	$0.477534\pi$
$20$	11.7465	0.131330
$21$	59.3748	0.616983
$22$	−38.4036	−0.372167
$23$	−160.222	−1.45255	−0.726273	−	0.687406i	$-0.758749\pi$
$23$	−160.222	−1.45255	−0.726273	+	0.687406i	$0.758749\pi$
$24$	107.776	0.916656
$25$	25.0000	0.200000
$26$	30.9025	0.233096
$27$	−152.489	−1.08691
$28$	−31.8405	−0.214904
$29$	289.477	1.85361	0.926803	−	0.375547i	$-0.122545\pi$
$29$	289.477	1.85361	0.926803	+	0.375547i	$0.122545\pi$
$30$	52.0693	0.316884
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−102.473	−0.566090
$33$	70.7754	0.373346
$34$	−66.5937	−0.335904
$35$	−67.7658	−0.327272
$36$	18.3432	0.0849221
$37$	−378.814	−1.68315	−0.841575	−	0.540140i	$-0.818371\pi$
$37$	−378.814	−1.68315	−0.841575	+	0.540140i	$0.818371\pi$
$38$	−27.7674	−0.118539
$39$	−56.9514	−0.233834
$40$	−123.008	−0.486230
$41$	138.920	0.529161	0.264581	−	0.964364i	$-0.414766\pi$
$41$	138.920	0.529161	0.264581	+	0.964364i	$0.414766\pi$
$42$	−141.141	−0.518536
$43$	207.115	0.734529	0.367264	−	0.930117i	$-0.380294\pi$
$43$	207.115	0.734529	0.367264	+	0.930117i	$0.380294\pi$
$44$	−37.9543	−0.130042
$45$	39.0396	0.129326
$46$	380.866	1.22078
$47$	270.885	0.840694	0.420347	−	0.907364i	$-0.361908\pi$
$47$	270.885	0.840694	0.420347	+	0.907364i	$0.361908\pi$
$48$	−173.861	−0.522805
$49$	−159.312	−0.464465
$50$	−59.4280	−0.168088
$51$	122.728	0.336968
$52$	30.5410	0.0814476
$53$	−614.080	−1.59152	−0.795758	−	0.605615i	$-0.792927\pi$
$53$	−614.080	−1.59152	−0.795758	+	0.605615i	$0.792927\pi$
$54$	362.485	0.913481
$55$	−80.7777	−0.198037
$56$	333.429	0.795648
$57$	51.1736	0.118914
$58$	−688.122	−1.55784
$59$	−437.240	−0.964811	−0.482406	−	0.875948i	$-0.660237\pi$
$59$	−437.240	−0.964811	−0.482406	+	0.875948i	$0.660237\pi$
$60$	51.4601	0.110725
$61$	592.439	1.24351	0.621754	−	0.783213i	$-0.286420\pi$
$61$	592.439	1.24351	0.621754	+	0.783213i	$0.286420\pi$
$62$	−73.6907	−0.150947
$63$	−105.822	−0.211624
$64$	561.081	1.09586
$65$	65.0000	0.124035
$66$	−168.242	−0.313774
$67$	633.022	1.15427	0.577134	−	0.816650i	$-0.304171\pi$
$67$	633.022	1.15427	0.577134	+	0.816650i	$0.304171\pi$
$68$	−65.8146	−0.117370
$69$	−701.913	−1.22464
$70$	161.087	0.275052
$71$	−1013.23	−1.69364	−0.846818	−	0.531883i	$-0.821485\pi$
$71$	−1013.23	−1.69364	−0.846818	+	0.531883i	$0.821485\pi$
$72$	−192.087	−0.314411
$73$	−420.735	−0.674566	−0.337283	−	0.941403i	$-0.609508\pi$
$73$	−420.735	−0.674566	−0.337283	+	0.941403i	$0.609508\pi$
$74$	900.485	1.41458
$75$	109.522	0.168620
$76$	−27.4426	−0.0414195
$77$	218.959	0.324061
$78$	135.380	0.196523
$79$	−295.238	−0.420467	−0.210233	−	0.977651i	$-0.567422\pi$
$79$	−295.238	−0.420467	−0.210233	+	0.977651i	$0.567422\pi$
$80$	198.432	0.277316
$81$	−457.223	−0.627192
$82$	−330.229	−0.444727
$83$	40.2055	0.0531702	0.0265851	−	0.999647i	$-0.491537\pi$
$83$	40.2055	0.0531702	0.0265851	+	0.999647i	$0.491537\pi$
$84$	−139.490	−0.181185
$85$	−140.072	−0.178741
$86$	−492.337	−0.617326
$87$	1268.16	1.56278
$88$	397.451	0.481459
$89$	−251.453	−0.299483	−0.149741	−	0.988725i	$-0.547844\pi$
$89$	−251.453	−0.299483	−0.149741	+	0.988725i	$0.547844\pi$
$90$	−92.8017	−0.108691
$91$	−176.191	−0.202965
$92$	376.410	0.426560
$93$	135.807	0.151425
$94$	−643.925	−0.706551
$95$	−58.4057	−0.0630768
$96$	−448.922	−0.477270
$97$	931.961	0.975528	0.487764	−	0.872975i	$-0.337813\pi$
$97$	931.961	0.975528	0.487764	+	0.872975i	$0.337813\pi$
$98$	378.703	0.390355
$99$	−126.141	−0.128057
$100$	−58.7327	−0.0587327
$101$	58.6996	0.0578300	0.0289150	−	0.999582i	$-0.490795\pi$
$101$	58.6996	0.0578300	0.0289150	+	0.999582i	$0.490795\pi$
$102$	−291.739	−0.283201
$103$	1241.37	1.18753	0.593765	−	0.804639i	$-0.297641\pi$
$103$	1241.37	1.18753	0.593765	+	0.804639i	$0.297641\pi$
$104$	−319.820	−0.301547
$105$	−296.874	−0.275923
$106$	1459.74	1.33757
$107$	1190.08	1.07523	0.537616	−	0.843190i	$-0.319325\pi$
$107$	1190.08	1.07523	0.537616	+	0.843190i	$0.319325\pi$
$108$	358.244	0.319186
$109$	781.479	0.686716	0.343358	−	0.939205i	$-0.388436\pi$
$109$	781.479	0.686716	0.343358	+	0.939205i	$0.388436\pi$
$110$	192.018	0.166438
$111$	−1659.54	−1.41906
$112$	−537.875	−0.453790
$113$	675.284	0.562172	0.281086	−	0.959683i	$-0.409305\pi$
$113$	675.284	0.562172	0.281086	+	0.959683i	$0.409305\pi$
$114$	−121.646	−0.0999401
$115$	801.110	0.649599
$116$	−680.071	−0.544336
$117$	101.503	0.0802046
$118$	1039.37	0.810864
$119$	379.685	0.292485
$120$	−538.881	−0.409941
$121$	−1070.00	−0.803906
$122$	−1408.30	−1.04509
$123$	608.590	0.446136
$124$	−72.8285	−0.0527435
$125$	−125.000	−0.0894427
$126$	251.551	0.177857
$127$	477.545	0.333664	0.166832	−	0.985985i	$-0.446646\pi$
$127$	477.545	0.333664	0.166832	+	0.985985i	$0.446646\pi$
$128$	−513.971	−0.354915
$129$	907.346	0.619282
$130$	−154.513	−0.104244
$131$	64.6204	0.0430986	0.0215493	−	0.999768i	$-0.493140\pi$
$131$	64.6204	0.0430986	0.0215493	+	0.999768i	$0.493140\pi$
$132$	−166.273	−0.109638
$133$	158.316	0.103216
$134$	−1504.77	−0.970091
$135$	762.446	0.486081
$136$	689.199	0.434546
$137$	−1737.05	−1.08326	−0.541629	−	0.840618i	$-0.682192\pi$
$137$	−1737.05	−1.08326	−0.541629	+	0.840618i	$0.682192\pi$
$138$	1668.53	1.02924
$139$	−1463.08	−0.892780	−0.446390	−	0.894838i	$-0.647291\pi$
$139$	−1463.08	−0.892780	−0.446390	+	0.894838i	$0.647291\pi$
$140$	159.203	0.0961078
$141$	1186.71	0.708789
$142$	2408.57	1.42340
$143$	−210.022	−0.122818
$144$	309.867	0.179321
$145$	−1447.39	−0.828958
$146$	1000.14	0.566931
$147$	−697.925	−0.391591
$148$	889.949	0.494280
$149$	2009.95	1.10511	0.552557	−	0.833475i	$-0.313652\pi$
$149$	2009.95	1.10511	0.552557	+	0.833475i	$0.313652\pi$
$150$	−260.347	−0.141715
$151$	−2544.86	−1.37151	−0.685753	−	0.727834i	$-0.740527\pi$
$151$	−2544.86	−1.37151	−0.685753	+	0.727834i	$0.740527\pi$
$152$	287.374	0.153349
$153$	−218.735	−0.115579
$154$	−520.491	−0.272353
$155$	−155.000	−0.0803219
$156$	133.796	0.0686685
$157$	−2536.62	−1.28946	−0.644728	−	0.764412i	$-0.723029\pi$
$157$	−2536.62	−1.28946	−0.644728	+	0.764412i	$0.723029\pi$
$158$	701.816	0.353376
$159$	−2690.21	−1.34181
$160$	512.366	0.253163
$161$	−2171.51	−1.06298
$162$	1086.87	0.527116
$163$	−2894.50	−1.39089	−0.695445	−	0.718580i	$-0.744793\pi$
$163$	−2894.50	−1.39089	−0.695445	+	0.718580i	$0.744793\pi$
$164$	−326.365	−0.155395
$165$	−353.877	−0.166965
$166$	−95.5732	−0.0446863
$167$	721.670	0.334398	0.167199	−	0.985923i	$-0.446528\pi$
$167$	721.670	0.334398	0.167199	+	0.985923i	$0.446528\pi$
$168$	1460.71	0.670811
$169$	169.000	0.0769231
$170$	332.969	0.150221
$171$	−91.2053	−0.0407874
$172$	−486.577	−0.215704
$173$	−1654.29	−0.727014	−0.363507	−	0.931592i	$-0.618421\pi$
$173$	−1654.29	−0.727014	−0.363507	+	0.931592i	$0.618421\pi$
$174$	−3014.58	−1.31342
$175$	338.829	0.146360
$176$	−641.154	−0.274595
$177$	−1915.50	−0.813433
$178$	597.733	0.251697
$179$	−1669.40	−0.697079	−0.348539	−	0.937294i	$-0.613322\pi$
$179$	−1669.40	−0.697079	−0.348539	+	0.937294i	$0.613322\pi$
$180$	−91.7159	−0.0379783
$181$	677.423	0.278190	0.139095	−	0.990279i	$-0.455581\pi$
$181$	677.423	0.278190	0.139095	+	0.990279i	$0.455581\pi$
$182$	418.827	0.170580
$183$	2595.40	1.04840
$184$	−3941.70	−1.57927
$185$	1894.07	0.752728
$186$	−322.830	−0.127264
$187$	452.589	0.176987
$188$	−636.391	−0.246881
$189$	−2066.71	−0.795403
$190$	138.837	0.0530122
$191$	2399.12	0.908871	0.454435	−	0.890780i	$-0.349841\pi$
$191$	2399.12	0.908871	0.454435	+	0.890780i	$0.349841\pi$
$192$	2458.03	0.923922
$193$	−3204.86	−1.19529	−0.597644	−	0.801761i	$-0.703897\pi$
$193$	−3204.86	−1.19529	−0.597644	+	0.801761i	$0.703897\pi$
$194$	−2215.38	−0.819872
$195$	284.757	0.104574
$196$	374.272	0.136396
$197$	−3933.08	−1.42244	−0.711219	−	0.702970i	$-0.751857\pi$
$197$	−3933.08	−1.42244	−0.711219	+	0.702970i	$0.751857\pi$
$198$	299.852	0.107624
$199$	1985.91	0.707425	0.353712	−	0.935354i	$-0.384919\pi$
$199$	1985.91	0.707425	0.353712	+	0.935354i	$0.384919\pi$
$200$	615.038	0.217449
$201$	2773.19	0.973163
$202$	−139.536	−0.0486026
$203$	3923.34	1.35647
$204$	−288.326	−0.0989551
$205$	−694.599	−0.236648
$206$	−2950.88	−0.998046
$207$	1251.00	0.420050
$208$	515.922	0.171984
$209$	188.715	0.0624579
$210$	705.704	0.231896
$211$	1878.19	0.612795	0.306397	−	0.951904i	$-0.400876\pi$
$211$	1878.19	0.612795	0.306397	+	0.951904i	$0.400876\pi$
$212$	1442.66	0.467370
$213$	−4438.83	−1.42790
$214$	−2828.97	−0.903666
$215$	−1035.58	−0.328491
$216$	−3751.47	−1.18174
$217$	420.148	0.131436
$218$	−1857.67	−0.577143
$219$	−1843.19	−0.568727
$220$	189.772	0.0581564
$221$	−364.188	−0.110850
$222$	3944.91	1.19264
$223$	2377.98	0.714088	0.357044	−	0.934088i	$-0.383785\pi$
$223$	2377.98	0.714088	0.357044	+	0.934088i	$0.383785\pi$
$224$	−1388.84	−0.414266
$225$	−195.198	−0.0578364
$226$	−1605.23	−0.472471
$227$	482.237	0.141001	0.0705004	−	0.997512i	$-0.477540\pi$
$227$	482.237	0.141001	0.0705004	+	0.997512i	$0.477540\pi$
$228$	−120.223	−0.0349208
$229$	−5303.97	−1.53055	−0.765276	−	0.643702i	$-0.777398\pi$
$229$	−5303.97	−1.53055	−0.765276	+	0.643702i	$0.777398\pi$
$230$	−1904.33	−0.545948
$231$	959.231	0.273216
$232$	7121.59	2.01532
$233$	−5955.28	−1.67443	−0.837217	−	0.546870i	$-0.815819\pi$
$233$	−5955.28	−1.67443	−0.837217	+	0.546870i	$0.815819\pi$
$234$	−241.284	−0.0674071
$235$	−1354.42	−0.375970
$236$	1027.21	0.283330
$237$	−1293.40	−0.354496
$238$	−902.556	−0.245815
$239$	149.018	0.0403314	0.0201657	−	0.999797i	$-0.493581\pi$
$239$	149.018	0.0403314	0.0201657	+	0.999797i	$0.493581\pi$
$240$	869.304	0.233806
$241$	3764.25	1.00613	0.503063	−	0.864250i	$-0.332206\pi$
$241$	3764.25	1.00613	0.503063	+	0.864250i	$0.332206\pi$
$242$	2543.51	0.675633
$243$	2114.17	0.558124
$244$	−1391.82	−0.365173
$245$	796.558	0.207715
$246$	−1446.69	−0.374950
$247$	−151.855	−0.0391186
$248$	762.647	0.195275
$249$	176.135	0.0448278
$250$	297.140	0.0751711
$251$	−6377.38	−1.60373	−0.801866	−	0.597503i	$-0.796159\pi$
$251$	−6377.38	−1.60373	−0.801866	+	0.597503i	$0.796159\pi$
$252$	248.608	0.0621462
$253$	−2588.47	−0.643225
$254$	−1135.18	−0.280424
$255$	−613.640	−0.150697
$256$	−3266.88	−0.797578
$257$	3017.65	0.732435	0.366217	−	0.930529i	$-0.380653\pi$
$257$	3017.65	0.732435	0.366217	+	0.930529i	$0.380653\pi$
$258$	−2156.87	−0.520468
$259$	−5134.12	−1.23173
$260$	−152.705	−0.0364245
$261$	−2260.21	−0.536030
$262$	−153.610	−0.0362217
$263$	1263.57	0.296256	0.148128	−	0.988968i	$-0.452675\pi$
$263$	1263.57	0.296256	0.148128	+	0.988968i	$0.452675\pi$
$264$	1741.18	0.405918
$265$	3070.40	0.711747
$266$	−376.337	−0.0867470
$267$	−1101.58	−0.252494
$268$	−1487.16	−0.338966
$269$	1075.56	0.243784	0.121892	−	0.992543i	$-0.461104\pi$
$269$	1075.56	0.243784	0.121892	+	0.992543i	$0.461104\pi$
$270$	−1812.42	−0.408521
$271$	−3674.52	−0.823658	−0.411829	−	0.911261i	$-0.635110\pi$
$271$	−3674.52	−0.823658	−0.411829	+	0.911261i	$0.635110\pi$
$272$	−1111.79	−0.247839
$273$	−771.872	−0.171120
$274$	4129.18	0.910412
$275$	403.888	0.0885651
$276$	1649.01	0.359633
$277$	1133.06	0.245771	0.122886	−	0.992421i	$-0.460785\pi$
$277$	1133.06	0.245771	0.122886	+	0.992421i	$0.460785\pi$
$278$	3477.91	0.750327
$279$	−242.045	−0.0519386
$280$	−1667.14	−0.355825
$281$	3974.62	0.843793	0.421897	−	0.906644i	$-0.361365\pi$
$281$	3974.62	0.843793	0.421897	+	0.906644i	$0.361365\pi$
$282$	−2820.96	−0.595693
$283$	−5865.94	−1.23213	−0.616067	−	0.787694i	$-0.711275\pi$
$283$	−5865.94	−1.23213	−0.616067	+	0.787694i	$0.711275\pi$
$284$	2380.39	0.497359
$285$	−255.868	−0.0531801
$286$	499.247	0.103221
$287$	1882.80	0.387241
$288$	800.102	0.163703
$289$	−4128.19	−0.840258
$290$	3440.61	0.696688
$291$	4082.81	0.822468
$292$	988.436	0.198095
$293$	−6721.68	−1.34022	−0.670110	−	0.742262i	$-0.733753\pi$
$293$	−6721.68	−1.34022	−0.670110	+	0.742262i	$0.733753\pi$
$294$	1659.05	0.329108
$295$	2186.20	0.431477
$296$	−9319.39	−1.83000
$297$	−2463.55	−0.481311
$298$	−4777.90	−0.928779
$299$	2082.88	0.402864
$300$	−257.301	−0.0495175
$301$	2807.06	0.537530
$302$	6049.43	1.15267
$303$	257.156	0.0487565
$304$	−463.581	−0.0874612
$305$	−2962.19	−0.556114
$306$	519.958	0.0971373
$307$	−1600.37	−0.297518	−0.148759	−	0.988874i	$-0.547528\pi$
$307$	−1600.37	−0.297518	−0.148759	+	0.988874i	$0.547528\pi$
$308$	−514.401	−0.0951647
$309$	5438.28	1.00121
$310$	368.453	0.0675056
$311$	6564.16	1.19685	0.598423	−	0.801180i	$-0.295794\pi$
$311$	6564.16	1.19685	0.598423	+	0.801180i	$0.295794\pi$
$312$	−1401.09	−0.254235
$313$	−9218.25	−1.66468	−0.832342	−	0.554263i	$-0.813000\pi$
$313$	−9218.25	−1.66468	−0.832342	+	0.554263i	$0.813000\pi$
$314$	6029.85	1.08371
$315$	529.110	0.0946411
$316$	693.604	0.123476
$317$	8824.76	1.56356	0.781779	−	0.623556i	$-0.214313\pi$
$317$	8824.76	1.56356	0.781779	+	0.623556i	$0.214313\pi$
$318$	6394.94	1.12771
$319$	4676.66	0.820824
$320$	−2805.41	−0.490084
$321$	5213.62	0.906528
$322$	5161.95	0.893367
$323$	327.241	0.0563720
$324$	1074.16	0.184183
$325$	−325.000	−0.0554700
$326$	6880.58	1.16896
$327$	3423.56	0.578971
$328$	3417.64	0.575328
$329$	3671.35	0.615221
$330$	841.208	0.140324
$331$	−2641.74	−0.438680	−0.219340	−	0.975648i	$-0.570390\pi$
$331$	−2641.74	−0.438680	−0.219340	+	0.975648i	$0.570390\pi$
$332$	−94.4550	−0.0156141
$333$	2957.74	0.486737
$334$	−1715.49	−0.281041
$335$	−3165.11	−0.516204
$336$	−2356.37	−0.382590
$337$	7215.13	1.16627	0.583135	−	0.812375i	$-0.301826\pi$
$337$	7215.13	1.16627	0.583135	+	0.812375i	$0.301826\pi$
$338$	−401.733	−0.0646491
$339$	2958.34	0.473967
$340$	329.073	0.0524897
$341$	500.822	0.0795338
$342$	216.806	0.0342793
$343$	−6807.91	−1.07170
$344$	5095.35	0.798612
$345$	3509.56	0.547677
$346$	3932.44	0.611010
$347$	−10384.3	−1.60651	−0.803255	−	0.595636i	$-0.796900\pi$
$347$	−10384.3	−1.60651	−0.803255	+	0.595636i	$0.796900\pi$
$348$	−2979.31	−0.458930
$349$	−7298.59	−1.11944	−0.559720	−	0.828682i	$-0.689091\pi$
$349$	−7298.59	−1.11944	−0.559720	+	0.828682i	$0.689091\pi$
$350$	−805.437	−0.123007
$351$	1982.36	0.301454
$352$	−1655.51	−0.250679
$353$	−2465.29	−0.371712	−0.185856	−	0.982577i	$-0.559506\pi$
$353$	−2465.29	−0.371712	−0.185856	+	0.982577i	$0.559506\pi$
$354$	4553.36	0.683640
$355$	5066.15	0.757417
$356$	590.740	0.0879471
$357$	1663.35	0.246594
$358$	3968.37	0.585852
$359$	−2574.74	−0.378523	−0.189261	−	0.981927i	$-0.560609\pi$
$359$	−2574.74	−0.378523	−0.189261	+	0.981927i	$0.560609\pi$
$360$	960.433	0.140609
$361$	−6722.55	−0.980107
$362$	−1610.31	−0.233802
$363$	−4687.53	−0.677773
$364$	413.927	0.0596035
$365$	2103.68	0.301675
$366$	−6169.57	−0.881117
$367$	−10796.3	−1.53559	−0.767794	−	0.640697i	$-0.778646\pi$
$367$	−10796.3	−1.53559	−0.767794	+	0.640697i	$0.778646\pi$
$368$	6358.62	0.900722
$369$	−1084.67	−0.153024
$370$	−4502.42	−0.632621
$371$	−8322.72	−1.16467
$372$	−319.053	−0.0444681
$373$	8592.15	1.19272	0.596360	−	0.802717i	$-0.296613\pi$
$373$	8592.15	1.19272	0.596360	+	0.802717i	$0.296613\pi$
$374$	−1075.86	−0.148747
$375$	−547.610	−0.0754092
$376$	6664.18	0.914039
$377$	−3763.21	−0.514098
$378$	4912.82	0.668487
$379$	3315.43	0.449346	0.224673	−	0.974434i	$-0.427869\pi$
$379$	3315.43	0.449346	0.224673	+	0.974434i	$0.427869\pi$
$380$	137.213	0.0185233
$381$	2092.07	0.281312
$382$	−5703.00	−0.763850
$383$	−7754.37	−1.03454	−0.517271	−	0.855822i	$-0.673052\pi$
$383$	−7754.37	−1.03454	−0.517271	+	0.855822i	$0.673052\pi$
$384$	−2251.65	−0.299229
$385$	−1094.79	−0.144924
$386$	7618.33	1.00457
$387$	−1617.14	−0.212413
$388$	−2189.46	−0.286477
$389$	−11725.8	−1.52833	−0.764165	−	0.645020i	$-0.776849\pi$
$389$	−11725.8	−1.52833	−0.764165	+	0.645020i	$0.776849\pi$
$390$	−676.901	−0.0878878
$391$	−4488.53	−0.580549
$392$	−3919.31	−0.504987
$393$	283.094	0.0363364
$394$	9349.40	1.19547
$395$	1476.19	0.188038
$396$	296.344	0.0376057
$397$	−5688.89	−0.719187	−0.359594	−	0.933109i	$-0.617085\pi$
$397$	−5688.89	−0.719187	−0.359594	+	0.933109i	$0.617085\pi$
$398$	−4720.75	−0.594547
$399$	693.565	0.0870217
$400$	−992.158	−0.124020
$401$	−11762.9	−1.46487	−0.732434	−	0.680838i	$-0.761616\pi$
$401$	−11762.9	−1.46487	−0.732434	+	0.680838i	$0.761616\pi$
$402$	−6592.20	−0.817884
$403$	−403.000	−0.0498135
$404$	−137.903	−0.0169826
$405$	2286.11	0.280489
$406$	−9326.23	−1.14003
$407$	−6119.94	−0.745342
$408$	3019.30	0.366366
$409$	2692.42	0.325506	0.162753	−	0.986667i	$-0.447963\pi$
$409$	2692.42	0.325506	0.162753	+	0.986667i	$0.447963\pi$
$410$	1651.14	0.198888
$411$	−7609.81	−0.913295
$412$	−2916.35	−0.348734
$413$	−5925.99	−0.706051
$414$	−2973.77	−0.353026
$415$	−201.027	−0.0237784
$416$	1332.15	0.157005
$417$	−6409.56	−0.752703
$418$	−448.598	−0.0524920
$419$	−4098.02	−0.477807	−0.238904	−	0.971043i	$-0.576788\pi$
$419$	−4098.02	−0.477807	−0.238904	+	0.971043i	$0.576788\pi$
$420$	697.448	0.0810285
$421$	15027.1	1.73961	0.869807	−	0.493392i	$-0.164243\pi$
$421$	15027.1	1.73961	0.869807	+	0.493392i	$0.164243\pi$
$422$	−4464.67	−0.515016
$423$	−2115.04	−0.243113
$424$	−15107.3	−1.73037
$425$	700.362	0.0799354
$426$	10551.6	1.20007
$427$	8029.42	0.910002
$428$	−2795.87	−0.315756
$429$	−920.081	−0.103548
$430$	2461.69	0.276077
$431$	1047.12	0.117026	0.0585128	−	0.998287i	$-0.481364\pi$
$431$	1047.12	0.117026	0.0585128	+	0.998287i	$0.481364\pi$
$432$	6051.73	0.673991
$433$	−5814.07	−0.645280	−0.322640	−	0.946522i	$-0.604570\pi$
$433$	−5814.07	−0.645280	−0.322640	+	0.946522i	$0.604570\pi$
$434$	−998.742	−0.110464
$435$	−6340.82	−0.698895
$436$	−1835.93	−0.201663
$437$	−1871.57	−0.204873
$438$	4381.48	0.477980
$439$	−1337.85	−0.145448	−0.0727242	−	0.997352i	$-0.523169\pi$
$439$	−1337.85	−0.145448	−0.0727242	+	0.997352i	$0.523169\pi$
$440$	−1987.25	−0.215315
$441$	1243.89	0.134315
$442$	865.718	0.0931630
$443$	2160.45	0.231707	0.115853	−	0.993266i	$-0.463040\pi$
$443$	2160.45	0.231707	0.115853	+	0.993266i	$0.463040\pi$
$444$	3898.76	0.416727
$445$	1257.26	0.133933
$446$	−5652.75	−0.600147
$447$	8805.36	0.931721
$448$	7604.43	0.801954
$449$	174.561	0.0183475	0.00917377	−	0.999958i	$-0.497080\pi$
$449$	174.561	0.0183475	0.00917377	+	0.999958i	$0.497080\pi$
$450$	464.008	0.0486079
$451$	2244.32	0.234326
$452$	−1586.45	−0.165089
$453$	−11148.7	−1.15632
$454$	−1146.33	−0.118502
$455$	880.956	0.0907689
$456$	1258.95	0.129289
$457$	−8463.92	−0.866357	−0.433179	−	0.901308i	$-0.642608\pi$
$457$	−8463.92	−0.866357	−0.433179	+	0.901308i	$0.642608\pi$
$458$	12608.2	1.28633
$459$	−4271.90	−0.434413
$460$	−1882.05	−0.190763
$461$	1290.04	0.130332	0.0651659	−	0.997874i	$-0.479242\pi$
$461$	1290.04	0.130332	0.0651659	+	0.997874i	$0.479242\pi$
$462$	−2280.21	−0.229621
$463$	−17673.2	−1.77396	−0.886981	−	0.461806i	$-0.847202\pi$
$463$	−17673.2	−1.77396	−0.886981	+	0.461806i	$0.847202\pi$
$464$	−11488.3	−1.14942
$465$	−679.036	−0.0677194
$466$	14156.4	1.40726
$467$	12864.9	1.27477	0.637385	−	0.770545i	$-0.280016\pi$
$467$	12864.9	1.27477	0.637385	+	0.770545i	$0.280016\pi$
$468$	−238.461	−0.0235532
$469$	8579.45	0.844696
$470$	3219.63	0.315979
$471$	−11112.6	−1.08714
$472$	−10756.8	−1.04899
$473$	3346.06	0.325268
$474$	3074.57	0.297932
$475$	292.028	0.0282088
$476$	−891.996	−0.0858920
$477$	4794.68	0.460238
$478$	−354.234	−0.0338960
$479$	−9363.06	−0.893130	−0.446565	−	0.894751i	$-0.647353\pi$
$479$	−9363.06	−0.893130	−0.446565	+	0.894751i	$0.647353\pi$
$480$	2244.61	0.213442
$481$	4924.58	0.466822
$482$	−8948.06	−0.845587
$483$	−9513.14	−0.896196
$484$	2513.75	0.236078
$485$	−4659.80	−0.436270
$486$	−5025.64	−0.469069
$487$	13231.0	1.23111	0.615557	−	0.788092i	$-0.288931\pi$
$487$	13231.0	1.23111	0.615557	+	0.788092i	$0.288931\pi$
$488$	14574.9	1.35200
$489$	−12680.5	−1.17266
$490$	−1893.51	−0.174572
$491$	1046.12	0.0961525	0.0480762	−	0.998844i	$-0.484691\pi$
$491$	1046.12	0.0961525	0.0480762	+	0.998844i	$0.484691\pi$
$492$	−1429.77	−0.131014
$493$	8109.56	0.740844
$494$	360.977	0.0328767
$495$	630.705	0.0572689
$496$	−1230.28	−0.111373
$497$	−13732.5	−1.23941
$498$	−418.695	−0.0376750
$499$	−11286.9	−1.01257	−0.506284	−	0.862367i	$-0.668981\pi$
$499$	−11286.9	−1.01257	−0.506284	+	0.862367i	$0.668981\pi$
$500$	293.663	0.0262660
$501$	3161.55	0.281931
$502$	15159.8	1.34784
$503$	−15365.9	−1.36209	−0.681044	−	0.732242i	$-0.738474\pi$
$503$	−15365.9	−1.36209	−0.681044	+	0.732242i	$0.738474\pi$
$504$	−2603.38	−0.230087
$505$	−293.498	−0.0258624
$506$	6153.10	0.540591
$507$	740.368	0.0648539
$508$	−1121.90	−0.0979848
$509$	4956.54	0.431620	0.215810	−	0.976435i	$-0.430761\pi$
$509$	4956.54	0.431620	0.215810	+	0.976435i	$0.430761\pi$
$510$	1458.69	0.126651
$511$	−5702.29	−0.493649
$512$	11877.5	1.02523
$513$	−1781.25	−0.153302
$514$	−7173.31	−0.615566
$515$	−6206.84	−0.531079
$516$	−2131.63	−0.181860
$517$	4376.29	0.372280
$518$	12204.4	1.03520
$519$	−7247.24	−0.612945
$520$	1599.10	0.134856
$521$	−13733.8	−1.15487	−0.577435	−	0.816437i	$-0.695946\pi$
$521$	−13733.8	−1.15487	−0.577435	+	0.816437i	$0.695946\pi$
$522$	5372.80	0.450500
$523$	−22041.0	−1.84281	−0.921403	−	0.388609i	$-0.872956\pi$
$523$	−22041.0	−1.84281	−0.921403	+	0.388609i	$0.872956\pi$
$524$	−151.813	−0.0126565
$525$	1484.37	0.123397
$526$	−3003.66	−0.248985
$527$	868.449	0.0717841
$528$	−2808.82	−0.231511
$529$	13504.1	1.10989
$530$	−7298.70	−0.598180
$531$	3413.94	0.279006
$532$	−371.934	−0.0303109
$533$	−1805.96	−0.146763
$534$	2618.60	0.212206
$535$	−5950.42	−0.480858
$536$	15573.3	1.25497
$537$	−7313.45	−0.587707
$538$	−2556.73	−0.204886
$539$	−2573.77	−0.205677
$540$	−1791.22	−0.142744
$541$	−13134.2	−1.04378	−0.521888	−	0.853014i	$-0.674772\pi$
$541$	−13134.2	−1.04378	−0.521888	+	0.853014i	$0.674772\pi$
$542$	8734.77	0.692234
$543$	2967.71	0.234542
$544$	−2870.73	−0.226253
$545$	−3907.39	−0.307109
$546$	1834.83	0.143816
$547$	7532.53	0.588789	0.294395	−	0.955684i	$-0.404882\pi$
$547$	7532.53	0.588789	0.294395	+	0.955684i	$0.404882\pi$
$548$	4080.87	0.318113
$549$	−4625.71	−0.359600
$550$	−960.091	−0.0744335
$551$	3381.42	0.261440
$552$	−17268.1	−1.33149
$553$	−4001.41	−0.307698
$554$	−2693.41	−0.206556
$555$	8297.68	0.634625
$556$	3437.21	0.262177
$557$	19920.9	1.51540	0.757698	−	0.652606i	$-0.226324\pi$
$557$	19920.9	1.51540	0.757698	+	0.652606i	$0.226324\pi$
$558$	575.370	0.0436512
$559$	−2692.50	−0.203722
$560$	2689.38	0.202941
$561$	1982.74	0.149218
$562$	−9448.14	−0.709156
$563$	−20033.3	−1.49965	−0.749823	−	0.661638i	$-0.769862\pi$
$563$	−20033.3	−1.49965	−0.749823	+	0.661638i	$0.769862\pi$
$564$	−2787.95	−0.208145
$565$	−3376.42	−0.251411
$566$	13944.0	1.03553
$567$	−6196.82	−0.458980
$568$	−24927.0	−1.84140
$569$	−4708.95	−0.346941	−0.173470	−	0.984839i	$-0.555498\pi$
$569$	−4708.95	−0.346941	−0.173470	+	0.984839i	$0.555498\pi$
$570$	608.229	0.0446946
$571$	−13486.3	−0.988417	−0.494208	−	0.869344i	$-0.664542\pi$
$571$	−13486.3	−0.988417	−0.494208	+	0.869344i	$0.664542\pi$
$572$	493.406	0.0360670
$573$	10510.3	0.766269
$574$	−4475.64	−0.325453
$575$	−4005.55	−0.290509
$576$	−4380.87	−0.316904
$577$	12897.9	0.930584	0.465292	−	0.885157i	$-0.345949\pi$
$577$	12897.9	0.930584	0.465292	+	0.885157i	$0.345949\pi$
$578$	9813.20	0.706185
$579$	−14040.1	−1.00775
$580$	3400.36	0.243435
$581$	544.912	0.0389101
$582$	−9705.31	−0.691234
$583$	−9920.79	−0.704763
$584$	−10350.7	−0.733418
$585$	−507.514	−0.0358686
$586$	15978.2	1.12637
$587$	5127.02	0.360502	0.180251	−	0.983621i	$-0.442309\pi$
$587$	5127.02	0.360502	0.180251	+	0.983621i	$0.442309\pi$
$588$	1639.64	0.114996
$589$	362.115	0.0253323
$590$	−5196.86	−0.362630
$591$	−17230.3	−1.19926
$592$	15033.7	1.04372
$593$	6151.91	0.426018	0.213009	−	0.977050i	$-0.431674\pi$
$593$	6151.91	0.426018	0.213009	+	0.977050i	$0.431674\pi$
$594$	5856.14	0.404512
$595$	−1898.42	−0.130803
$596$	−4722.00	−0.324531
$597$	8700.03	0.596430
$598$	−4951.26	−0.338582
$599$	−4157.76	−0.283608	−0.141804	−	0.989895i	$-0.545290\pi$
$599$	−4157.76	−0.283608	−0.141804	+	0.989895i	$0.545290\pi$
$600$	2694.41	0.183331
$601$	4345.14	0.294912	0.147456	−	0.989069i	$-0.452892\pi$
$601$	4345.14	0.294912	0.147456	+	0.989069i	$0.452892\pi$
$602$	−6672.73	−0.451761
$603$	−4942.58	−0.333793
$604$	5978.65	0.402761
$605$	5349.99	0.359518
$606$	−611.290	−0.0409768
$607$	−21569.0	−1.44227	−0.721136	−	0.692794i	$-0.756380\pi$
$607$	−21569.0	−1.44227	−0.721136	+	0.692794i	$0.756380\pi$
$608$	−1197.00	−0.0798436
$609$	17187.7	1.14364
$610$	7041.48	0.467379
$611$	−3521.50	−0.233166
$612$	513.875	0.0339414
$613$	−16207.7	−1.06790	−0.533949	−	0.845517i	$-0.679293\pi$
$613$	−16207.7	−1.06790	−0.533949	+	0.845517i	$0.679293\pi$
$614$	3804.27	0.250045
$615$	−3042.95	−0.199518
$616$	5386.72	0.352333
$617$	15530.8	1.01337	0.506683	−	0.862133i	$-0.330872\pi$
$617$	15530.8	1.01337	0.506683	+	0.862133i	$0.330872\pi$
$618$	−12927.4	−0.841453
$619$	−26546.7	−1.72375	−0.861875	−	0.507120i	$-0.830710\pi$
$619$	−26546.7	−1.72375	−0.861875	+	0.507120i	$0.830710\pi$
$620$	364.143	0.0235876
$621$	24432.1	1.57879
$622$	−15603.8	−1.00588
$623$	−3407.98	−0.219162
$624$	2260.19	0.145000
$625$	625.000	0.0400000
$626$	21912.9	1.39906
$627$	826.737	0.0526582
$628$	5959.31	0.378666
$629$	−10612.3	−0.672716
$630$	−1257.76	−0.0795400
$631$	−1112.92	−0.0702134	−0.0351067	−	0.999384i	$-0.511177\pi$
$631$	−1112.92	−0.0702134	−0.0351067	+	0.999384i	$0.511177\pi$
$632$	−7263.31	−0.457150
$633$	8228.11	0.516648
$634$	−20977.5	−1.31407
$635$	−2387.73	−0.149219
$636$	6320.12	0.394040
$637$	2071.05	0.128820
$638$	−11117.0	−0.689852
$639$	7911.20	0.489769
$640$	2569.86	0.158723
$641$	13889.2	0.855837	0.427918	−	0.903817i	$-0.359247\pi$
$641$	13889.2	0.855837	0.427918	+	0.903817i	$0.359247\pi$
$642$	−12393.4	−0.761881
$643$	15214.9	0.933150	0.466575	−	0.884482i	$-0.345488\pi$
$643$	15214.9	0.933150	0.466575	+	0.884482i	$0.345488\pi$
$644$	5101.55	0.312157
$645$	−4536.73	−0.276951
$646$	−777.890	−0.0473772
$647$	9779.52	0.594239	0.297119	−	0.954840i	$-0.403974\pi$
$647$	9779.52	0.594239	0.297119	+	0.954840i	$0.403974\pi$
$648$	−11248.4	−0.681911
$649$	−7063.86	−0.427243
$650$	772.564	0.0466191
$651$	1840.62	0.110813
$652$	6800.08	0.408453
$653$	10582.6	0.634192	0.317096	−	0.948393i	$-0.397292\pi$
$653$	10582.6	0.634192	0.317096	+	0.948393i	$0.397292\pi$
$654$	−8138.21	−0.486589
$655$	−323.102	−0.0192743
$656$	−5513.21	−0.328132
$657$	3285.06	0.195072
$658$	−8727.23	−0.517056
$659$	−13417.9	−0.793151	−0.396575	−	0.918002i	$-0.629801\pi$
$659$	−13417.9	−0.793151	−0.396575	+	0.918002i	$0.629801\pi$
$660$	831.366	0.0490316
$661$	21407.9	1.25971	0.629857	−	0.776711i	$-0.283113\pi$
$661$	21407.9	1.25971	0.629857	+	0.776711i	$0.283113\pi$
$662$	6279.73	0.368684
$663$	−1595.46	−0.0934580
$664$	989.117	0.0578090
$665$	−791.582	−0.0461597
$666$	−7030.91	−0.409072
$667$	−46380.6	−2.69245
$668$	−1695.42	−0.0982004
$669$	10417.7	0.602048
$670$	7523.84	0.433838
$671$	9571.16	0.550657
$672$	−6084.32	−0.349268
$673$	1.58332	9.06873e−5 0	4.53437e−5	−	1.00000i	$-0.499986\pi$
$673$	1.58332	9.06873e−5 0	4.53437e−5		1.00000i	$0.499986\pi$
$674$	−17151.2	−0.980179
$675$	−3812.23	−0.217382
$676$	−397.033	−0.0225895
$677$	7911.96	0.449160	0.224580	−	0.974456i	$-0.427899\pi$
$677$	7911.96	0.449160	0.224580	+	0.974456i	$0.427899\pi$
$678$	−7032.32	−0.398340
$679$	12631.0	0.713894
$680$	−3445.99	−0.194335
$681$	2112.62	0.118878
$682$	−1190.51	−0.0668432
$683$	16322.6	0.914444	0.457222	−	0.889353i	$-0.348844\pi$
$683$	16322.6	0.914444	0.457222	+	0.889353i	$0.348844\pi$
$684$	214.269	0.0119778
$685$	8685.26	0.484448
$686$	16183.2	0.900697
$687$	−23236.1	−1.29041
$688$	−8219.63	−0.455480
$689$	7983.03	0.441407
$690$	−8342.65	−0.460289
$691$	−7027.36	−0.386879	−0.193440	−	0.981112i	$-0.561964\pi$
$691$	−7027.36	−0.386879	−0.193440	+	0.981112i	$0.561964\pi$
$692$	3886.43	0.213497
$693$	−1709.61	−0.0937125
$694$	24684.7	1.35017
$695$	7315.38	0.399264
$696$	31198.8	1.69912
$697$	3891.76	0.211494
$698$	17349.6	0.940821
$699$	−26089.4	−1.41172
$700$	−796.014	−0.0429807
$701$	−7589.08	−0.408895	−0.204448	−	0.978877i	$-0.565540\pi$
$701$	−7589.08	−0.408895	−0.204448	+	0.978877i	$0.565540\pi$
$702$	−4712.30	−0.253354
$703$	−4424.97	−0.237398
$704$	9064.57	0.485275
$705$	−5933.56	−0.316980
$706$	5860.29	0.312401
$707$	795.566	0.0423201
$708$	4500.09	0.238875
$709$	6994.18	0.370482	0.185241	−	0.982693i	$-0.440693\pi$
$709$	6994.18	0.370482	0.185241	+	0.982693i	$0.440693\pi$
$710$	−12042.8	−0.636562
$711$	2305.19	0.121591
$712$	−6186.12	−0.325611
$713$	−4966.88	−0.260885
$714$	−3953.99	−0.207247
$715$	1050.11	0.0549257
$716$	3921.94	0.204706
$717$	652.831	0.0340034
$718$	6120.46	0.318125
$719$	11213.4	0.581624	0.290812	−	0.956780i	$-0.406075\pi$
$719$	11213.4	0.581624	0.290812	+	0.956780i	$0.406075\pi$
$720$	−1549.34	−0.0801949
$721$	16824.5	0.869037
$722$	15980.3	0.823719
$723$	16490.7	0.848265
$724$	−1591.47	−0.0816943
$725$	7236.93	0.370721
$726$	11142.8	0.569627
$727$	19245.1	0.981789	0.490894	−	0.871219i	$-0.336670\pi$
$727$	19245.1	0.981789	0.490894	+	0.871219i	$0.336670\pi$
$728$	−4334.57	−0.220673
$729$	21606.9	1.09775
$730$	−5000.69	−0.253539
$731$	5802.22	0.293574
$732$	−6097.39	−0.307877
$733$	−33875.6	−1.70699	−0.853495	−	0.521101i	$-0.825522\pi$
$733$	−33875.6	−1.70699	−0.853495	+	0.521101i	$0.825522\pi$
$734$	25664.0	1.29057
$735$	3489.62	0.175125
$736$	16418.4	0.822272
$737$	10226.8	0.511139
$738$	2578.40	0.128607
$739$	4460.73	0.222044	0.111022	−	0.993818i	$-0.464588\pi$
$739$	4460.73	0.222044	0.111022	+	0.993818i	$0.464588\pi$
$740$	−4449.75	−0.221049
$741$	−665.257	−0.0329809
$742$	19784.1	0.978837
$743$	15187.8	0.749916	0.374958	−	0.927042i	$-0.377657\pi$
$743$	15187.8	0.749916	0.374958	+	0.927042i	$0.377657\pi$
$744$	3341.06	0.164636
$745$	−10049.8	−0.494222
$746$	−20424.6	−1.00241
$747$	−313.921	−0.0153759
$748$	−1063.27	−0.0519746
$749$	16129.4	0.786857
$750$	1301.73	0.0633768
$751$	−38688.0	−1.87982	−0.939910	−	0.341423i	$-0.889091\pi$
$751$	−38688.0	−1.87982	−0.939910	+	0.341423i	$0.889091\pi$
$752$	−10750.4	−0.521313
$753$	−27938.5	−1.35211
$754$	8945.59	0.432068
$755$	12724.3	0.613356
$756$	4855.34	0.233581
$757$	−2685.88	−0.128956	−0.0644782	−	0.997919i	$-0.520538\pi$
$757$	−2685.88	−0.128956	−0.0644782	+	0.997919i	$0.520538\pi$
$758$	−7881.17	−0.377648
$759$	−11339.8	−0.542303
$760$	−1436.87	−0.0685799
$761$	30024.8	1.43022	0.715110	−	0.699012i	$-0.246377\pi$
$761$	30024.8	1.43022	0.715110	+	0.699012i	$0.246377\pi$
$762$	−4973.09	−0.236425
$763$	10591.5	0.502541
$764$	−5636.27	−0.266902
$765$	1093.67	0.0516887
$766$	18433.0	0.869469
$767$	5684.13	0.267590
$768$	−14311.8	−0.672438
$769$	20883.3	0.979285	0.489643	−	0.871923i	$-0.337127\pi$
$769$	20883.3	0.979285	0.489643	+	0.871923i	$0.337127\pi$
$770$	2602.45	0.121800
$771$	13219.9	0.617516
$772$	7529.20	0.351013
$773$	−14763.4	−0.686937	−0.343469	−	0.939164i	$-0.611602\pi$
$773$	−14763.4	−0.686937	−0.343469	+	0.939164i	$0.611602\pi$
$774$	3844.12	0.178520
$775$	775.000	0.0359211
$776$	22927.7	1.06064
$777$	−22492.0	−1.03847
$778$	27873.6	1.28447
$779$	1622.74	0.0746350
$780$	−668.982	−0.0307095
$781$	−16369.3	−0.749985
$782$	10669.8	0.487916
$783$	−44142.2	−2.01470
$784$	6322.49	0.288014
$785$	12683.1	0.576662
$786$	−672.948	−0.0305385
$787$	−7351.43	−0.332974	−0.166487	−	0.986044i	$-0.553242\pi$
$787$	−7351.43	−0.332974	−0.166487	+	0.986044i	$0.553242\pi$
$788$	9240.01	0.417718
$789$	5535.56	0.249773
$790$	−3509.08	−0.158035
$791$	9152.24	0.411399
$792$	−3103.26	−0.139229
$793$	−7701.70	−0.344887
$794$	13523.2	0.604433
$795$	13451.0	0.600074
$796$	−4665.52	−0.207745
$797$	−9951.03	−0.442263	−0.221132	−	0.975244i	$-0.570975\pi$
$797$	−9951.03	−0.442263	−0.221132	+	0.975244i	$0.570975\pi$
$798$	−1648.69	−0.0731364
$799$	7588.69	0.336006
$800$	−2561.83	−0.113218
$801$	1963.32	0.0866050
$802$	27961.9	1.23113
$803$	−6797.20	−0.298715
$804$	−6515.08	−0.285782
$805$	10857.6	0.475378
$806$	957.979	0.0418652
$807$	4711.89	0.205535
$808$	1444.10	0.0628754
$809$	12909.0	0.561007	0.280504	−	0.959853i	$-0.409499\pi$
$809$	12909.0	0.561007	0.280504	+	0.959853i	$0.409499\pi$
$810$	−5434.36	−0.235733
$811$	22432.3	0.971276	0.485638	−	0.874160i	$-0.338587\pi$
$811$	22432.3	0.971276	0.485638	+	0.874160i	$0.338587\pi$
$812$	−9217.12	−0.398347
$813$	−16097.6	−0.694426
$814$	14547.8	0.626414
$815$	14472.5	0.622025
$816$	−4870.62	−0.208953
$817$	2419.34	0.103601
$818$	−6400.21	−0.273567
$819$	1375.69	0.0586939
$820$	1631.83	0.0694949
$821$	−8176.69	−0.347586	−0.173793	−	0.984782i	$-0.555602\pi$
$821$	−8176.69	−0.347586	−0.173793	+	0.984782i	$0.555602\pi$
$822$	18089.4	0.767568
$823$	12817.3	0.542873	0.271437	−	0.962456i	$-0.412501\pi$
$823$	12817.3	0.542873	0.271437	+	0.962456i	$0.412501\pi$
$824$	30539.5	1.29114
$825$	1769.39	0.0746692
$826$	14086.8	0.593392
$827$	40631.7	1.70847	0.854234	−	0.519888i	$-0.174026\pi$
$827$	40631.7	1.70847	0.854234	+	0.519888i	$0.174026\pi$
$828$	−2938.98	−0.123353
$829$	−21802.2	−0.913417	−0.456708	−	0.889616i	$-0.650972\pi$
$829$	−21802.2	−0.913417	−0.456708	+	0.889616i	$0.650972\pi$
$830$	477.866	0.0199843
$831$	4963.78	0.207210
$832$	−7294.06	−0.303937
$833$	−4463.03	−0.185636
$834$	15236.3	0.632601
$835$	−3608.35	−0.149547
$836$	−443.349	−0.0183416
$837$	−4727.17	−0.195215
$838$	9741.48	0.401568
$839$	16438.1	0.676408	0.338204	−	0.941073i	$-0.390181\pi$
$839$	16438.1	0.676408	0.338204	+	0.941073i	$0.390181\pi$
$840$	−7303.55	−0.299996
$841$	59408.1	2.43586
$842$	−35721.3	−1.46204
$843$	17412.3	0.711402
$844$	−4412.44	−0.179955
$845$	−845.000	−0.0344010
$846$	5027.71	0.204322
$847$	−14501.9	−0.588300
$848$	24370.5	0.986896
$849$	−25698.0	−1.03881
$850$	−1664.84	−0.0671808
$851$	60694.2	2.44485
$852$	10428.2	0.419323
$853$	45925.3	1.84344	0.921718	−	0.387860i	$-0.126785\pi$
$853$	45925.3	1.84344	0.921718	+	0.387860i	$0.126785\pi$
$854$	−19086.9	−0.764801
$855$	456.026	0.0182407
$856$	29277.9	1.16904
$857$	2681.37	0.106877	0.0534387	−	0.998571i	$-0.482982\pi$
$857$	2681.37	0.106877	0.0534387	+	0.998571i	$0.482982\pi$
$858$	2187.14	0.0870254
$859$	−17643.6	−0.700804	−0.350402	−	0.936599i	$-0.613955\pi$
$859$	−17643.6	−0.700804	−0.350402	+	0.936599i	$0.613955\pi$
$860$	2432.88	0.0964659
$861$	8248.33	0.326483
$862$	−2489.13	−0.0983528
$863$	19402.8	0.765330	0.382665	−	0.923887i	$-0.375006\pi$
$863$	19402.8	0.765330	0.382665	+	0.923887i	$0.375006\pi$
$864$	15626.1	0.615288
$865$	8271.45	0.325130
$866$	13820.7	0.542318
$867$	−18085.1	−0.708422
$868$	−987.057	−0.0385978
$869$	−4769.73	−0.186193
$870$	15072.9	0.587378
$871$	−8229.28	−0.320136
$872$	19225.6	0.746628
$873$	−7276.67	−0.282105
$874$	4448.95	0.172183
$875$	−1694.15	−0.0654544
$876$	4330.22	0.167014
$877$	29762.1	1.14594	0.572972	−	0.819575i	$-0.305790\pi$
$877$	29762.1	1.14594	0.572972	+	0.819575i	$0.305790\pi$
$878$	3180.22	0.122240
$879$	−29446.9	−1.12994
$880$	3205.77	0.122803
$881$	32597.4	1.24658	0.623288	−	0.781992i	$-0.285796\pi$
$881$	32597.4	1.24658	0.623288	+	0.781992i	$0.285796\pi$
$882$	−2956.88	−0.112883
$883$	−9970.26	−0.379984	−0.189992	−	0.981786i	$-0.560846\pi$
$883$	−9970.26	−0.379984	−0.189992	+	0.981786i	$0.560846\pi$
$884$	855.590	0.0325527
$885$	9577.48	0.363778
$886$	−5135.65	−0.194735
$887$	−2624.10	−0.0993332	−0.0496666	−	0.998766i	$-0.515816\pi$
$887$	−2624.10	−0.0993332	−0.0496666	+	0.998766i	$0.515816\pi$
$888$	−40827.1	−1.54287
$889$	6472.25	0.244176
$890$	−2988.67	−0.112562
$891$	−7386.68	−0.277736
$892$	−5586.61	−0.209701
$893$	3164.24	0.118575
$894$	−20931.4	−0.783054
$895$	8347.02	0.311743
$896$	−6965.94	−0.259727
$897$	9124.86	0.339655
$898$	−414.952	−0.0154200
$899$	8973.80	0.332918
$900$	458.580	0.0169844
$901$	−17203.1	−0.636092
$902$	−5335.02	−0.196937
$903$	12297.4	0.453192
$904$	16613.0	0.611218
$905$	−3387.12	−0.124411
$906$	26501.8	0.971814
$907$	−42506.3	−1.55612	−0.778059	−	0.628191i	$-0.783796\pi$
$907$	−42506.3	−1.55612	−0.778059	+	0.628191i	$0.783796\pi$
$908$	−1132.92	−0.0414068
$909$	−458.322	−0.0167234
$910$	−2094.14	−0.0762857
$911$	19580.2	0.712096	0.356048	−	0.934468i	$-0.384124\pi$
$911$	19580.2	0.712096	0.356048	+	0.934468i	$0.384124\pi$
$912$	−2030.89	−0.0737385
$913$	649.541	0.0235451
$914$	20119.7	0.728120
$915$	−12977.0	−0.468860
$916$	12460.7	0.449467
$917$	875.811	0.0315396
$918$	10154.8	0.365097
$919$	33710.1	1.21000	0.605002	−	0.796224i	$-0.293172\pi$
$919$	33710.1	1.21000	0.605002	+	0.796224i	$0.293172\pi$
$920$	19708.5	0.706272
$921$	−7011.02	−0.250837
$922$	−3066.57	−0.109536
$923$	13172.0	0.469730
$924$	−2253.53	−0.0802334
$925$	−9470.34	−0.336630
$926$	42011.4	1.49091
$927$	−9692.49	−0.343412
$928$	−29663.7	−1.04931
$929$	−6825.54	−0.241053	−0.120527	−	0.992710i	$-0.538458\pi$
$929$	−6825.54	−0.241053	−0.120527	+	0.992710i	$0.538458\pi$
$930$	1614.15	0.0569140
$931$	−1860.94	−0.0655101
$932$	13990.8	0.491720
$933$	28756.8	1.00906
$934$	−30581.5	−1.07137
$935$	−2262.94	−0.0791510
$936$	2497.13	0.0872020
$937$	640.311	0.0223245	0.0111622	−	0.999938i	$-0.496447\pi$
$937$	640.311	0.0223245	0.0111622	+	0.999938i	$0.496447\pi$
$938$	−20394.4	−0.709915
$939$	−40384.0	−1.40350
$940$	3181.96	0.110408
$941$	−43295.3	−1.49988	−0.749940	−	0.661505i	$-0.769918\pi$
$941$	−43295.3	−1.49988	−0.749940	+	0.661505i	$0.769918\pi$
$942$	26416.1	0.913675
$943$	−22258.0	−0.768632
$944$	17352.5	0.598278
$945$	10333.6	0.355715
$946$	−7953.97	−0.273368
$947$	−17802.5	−0.610881	−0.305440	−	0.952211i	$-0.598804\pi$
$947$	−17802.5	−0.610881	−0.305440	+	0.952211i	$0.598804\pi$
$948$	3038.60	0.104102
$949$	5469.56	0.187091
$950$	−694.186	−0.0237078
$951$	38660.2	1.31824
$952$	9340.83	0.318002
$953$	32275.2	1.09706	0.548530	−	0.836131i	$-0.315188\pi$
$953$	32275.2	1.09706	0.548530	+	0.836131i	$0.315188\pi$
$954$	−11397.5	−0.386801
$955$	−11995.6	−0.406459
$956$	−350.090	−0.0118438
$957$	20487.9	0.692037
$958$	22257.1	0.750621
$959$	−23542.6	−0.792731
$960$	−12290.1	−0.413190
$961$	961.000	0.0322581
$962$	−11706.3	−0.392335
$963$	−9292.08	−0.310938
$964$	−8843.37	−0.295462
$965$	16024.3	0.534549
$966$	22613.9	0.753198
$967$	2624.14	0.0872663	0.0436331	−	0.999048i	$-0.486107\pi$
$967$	2624.14	0.0872663	0.0436331	+	0.999048i	$0.486107\pi$
$968$	−26323.6	−0.874042
$969$	1433.60	0.0475273
$970$	11076.9	0.366658
$971$	8300.63	0.274336	0.137168	−	0.990548i	$-0.456200\pi$
$971$	8300.63	0.274336	0.137168	+	0.990548i	$0.456200\pi$
$972$	−4966.84	−0.163901
$973$	−19829.3	−0.653339
$974$	−31451.6	−1.03468
$975$	−1423.79	−0.0467668
$976$	−23511.7	−0.771097
$977$	22149.5	0.725307	0.362653	−	0.931924i	$-0.381871\pi$
$977$	22149.5	0.725307	0.362653	+	0.931924i	$0.381871\pi$
$978$	30143.0	0.985548
$979$	−4062.36	−0.132618
$980$	−1871.36	−0.0609983
$981$	−6101.72	−0.198586
$982$	−2486.76	−0.0808102
$983$	−32763.9	−1.06308	−0.531540	−	0.847033i	$-0.678386\pi$
$983$	−32763.9	−1.06308	−0.531540	+	0.847033i	$0.678386\pi$
$984$	14972.3	0.485059
$985$	19665.4	0.636134
$986$	−19277.4	−0.622634
$987$	16083.7	0.518693
$988$	356.753	0.0114877
$989$	−33184.4	−1.06694
$990$	−1499.26	−0.0481310
$991$	−1808.91	−0.0579837	−0.0289919	−	0.999580i	$-0.509230\pi$
$991$	−1808.91	−0.0579837	−0.0289919	+	0.999580i	$0.509230\pi$
$992$	−3176.67	−0.101673
$993$	−11573.1	−0.369851
$994$	32643.7	1.04165
$995$	−9929.56	−0.316370
$996$	−413.796	−0.0131643
$997$	−40939.6	−1.30047	−0.650236	−	0.759733i	$-0.725330\pi$
$997$	−40939.6	−1.30047	−0.650236	+	0.759733i	$0.725330\pi$
$998$	26830.3	0.851001
$999$	57765.0	1.82943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.14	✓	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2015 = 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37712 q^{2} +4.38088 q^{3} -2.34931 q^{4} -5.00000 q^{5} -10.4139 q^{6} +13.5532 q^{7} +24.6015 q^{8} -7.80791 q^{9} +O(q^{10})\)	\(q-2.37712 q^{2} +4.38088 q^{3} -2.34931 q^{4} -5.00000 q^{5} -10.4139 q^{6} +13.5532 q^{7} +24.6015 q^{8} -7.80791 q^{9} +11.8856 q^{10} +16.1555 q^{11} -10.2920 q^{12} -13.0000 q^{13} -32.2175 q^{14} -21.9044 q^{15} -39.6863 q^{16} +28.0145 q^{17} +18.5603 q^{18} +11.6811 q^{19} +11.7465 q^{20} +59.3748 q^{21} -38.4036 q^{22} -160.222 q^{23} +107.776 q^{24} +25.0000 q^{25} +30.9025 q^{26} -152.489 q^{27} -31.8405 q^{28} +289.477 q^{29} +52.0693 q^{30} +31.0000 q^{31} -102.473 q^{32} +70.7754 q^{33} -66.5937 q^{34} -67.7658 q^{35} +18.3432 q^{36} -378.814 q^{37} -27.7674 q^{38} -56.9514 q^{39} -123.008 q^{40} +138.920 q^{41} -141.141 q^{42} +207.115 q^{43} -37.9543 q^{44} +39.0396 q^{45} +380.866 q^{46} +270.885 q^{47} -173.861 q^{48} -159.312 q^{49} -59.4280 q^{50} +122.728 q^{51} +30.5410 q^{52} -614.080 q^{53} +362.485 q^{54} -80.7777 q^{55} +333.429 q^{56} +51.1736 q^{57} -688.122 q^{58} -437.240 q^{59} +51.4601 q^{60} +592.439 q^{61} -73.6907 q^{62} -105.822 q^{63} +561.081 q^{64} +65.0000 q^{65} -168.242 q^{66} +633.022 q^{67} -65.8146 q^{68} -701.913 q^{69} +161.087 q^{70} -1013.23 q^{71} -192.087 q^{72} -420.735 q^{73} +900.485 q^{74} +109.522 q^{75} -27.4426 q^{76} +218.959 q^{77} +135.380 q^{78} -295.238 q^{79} +198.432 q^{80} -457.223 q^{81} -330.229 q^{82} +40.2055 q^{83} -139.490 q^{84} -140.072 q^{85} -492.337 q^{86} +1268.16 q^{87} +397.451 q^{88} -251.453 q^{89} -92.8017 q^{90} -176.191 q^{91} +376.410 q^{92} +135.807 q^{93} -643.925 q^{94} -58.4057 q^{95} -448.922 q^{96} +931.961 q^{97} +378.703 q^{98} -126.141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * q^99

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