LMFDB - Embedded newform 1334.4.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,4,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1334.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:	$78.7085479477$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 5 x^{18} - 327 x^{17} + 1564 x^{16} + 43869 x^{15} - 203270 x^{14} - 3103297 x^{13} + \cdots - 37580243456 $ x^19 - 5x^18 - 327x^17 + 1564x^16 + 43869x^15 - 203270x^14 - 3103297x^13 + 14176990x^12 + 123567059x^11 - 569338227x^10 - 2720149582x^9 + 13044432966x^8 + 29634597970x^7 - 156881614170x^6 - 111892601042x^5 + 797597313752x^4 - 61225108811x^3 - 836249925952x^2 - 357044713984x - 37580243456
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.67612$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.67612 q^{3} +4.00000 q^{4} +18.7156 q^{5} +7.35224 q^{6} -19.6479 q^{7} -8.00000 q^{8} -13.4861 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.67612 q^{3} +4.00000 q^{4} +18.7156 q^{5} +7.35224 q^{6} -19.6479 q^{7} -8.00000 q^{8} -13.4861 q^{9} -37.4311 q^{10} +10.0534 q^{11} -14.7045 q^{12} -19.4802 q^{13} +39.2958 q^{14} -68.8006 q^{15} +16.0000 q^{16} +31.1714 q^{17} +26.9723 q^{18} -12.4065 q^{19} +74.8622 q^{20} +72.2280 q^{21} -20.1068 q^{22} +23.0000 q^{23} +29.4090 q^{24} +225.272 q^{25} +38.9603 q^{26} +148.832 q^{27} -78.5916 q^{28} -29.0000 q^{29} +137.601 q^{30} +207.430 q^{31} -32.0000 q^{32} -36.9575 q^{33} -62.3427 q^{34} -367.721 q^{35} -53.9445 q^{36} -127.812 q^{37} +24.8131 q^{38} +71.6114 q^{39} -149.724 q^{40} -250.826 q^{41} -144.456 q^{42} -306.069 q^{43} +40.2135 q^{44} -252.400 q^{45} -46.0000 q^{46} +420.251 q^{47} -58.8179 q^{48} +43.0395 q^{49} -450.544 q^{50} -114.590 q^{51} -77.9206 q^{52} +209.524 q^{53} -297.664 q^{54} +188.155 q^{55} +157.183 q^{56} +45.6080 q^{57} +58.0000 q^{58} -728.190 q^{59} -275.203 q^{60} -853.929 q^{61} -414.861 q^{62} +264.974 q^{63} +64.0000 q^{64} -364.582 q^{65} +73.9149 q^{66} +486.336 q^{67} +124.685 q^{68} -84.5508 q^{69} +735.442 q^{70} +685.447 q^{71} +107.889 q^{72} -70.9219 q^{73} +255.624 q^{74} -828.127 q^{75} -49.6262 q^{76} -197.528 q^{77} -143.223 q^{78} +1384.88 q^{79} +299.449 q^{80} -182.999 q^{81} +501.651 q^{82} -553.517 q^{83} +288.912 q^{84} +583.389 q^{85} +612.139 q^{86} +106.608 q^{87} -80.4271 q^{88} +699.330 q^{89} +504.801 q^{90} +382.744 q^{91} +92.0000 q^{92} -762.539 q^{93} -840.503 q^{94} -232.195 q^{95} +117.636 q^{96} -1648.18 q^{97} -86.0791 q^{98} -135.581 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 38 q^{2} - 5 q^{3} + 76 q^{4} + 10 q^{6} - 13 q^{7} - 152 q^{8} + 166 q^{9}+O(q^{10}) $ 19 * q - 38 * q^2 - 5 * q^3 + 76 * q^4 + 10 * q^6 - 13 * q^7 - 152 * q^8 + 166 * q^9	\( 19 q - 38 q^{2} - 5 q^{3} + 76 q^{4} + 10 q^{6} - 13 q^{7} - 152 q^{8} + 166 q^{9} + 30 q^{11} - 20 q^{12} - 151 q^{13} + 26 q^{14} + 2 q^{15} + 304 q^{16} - 56 q^{17} - 332 q^{18} - 266 q^{19} - 239 q^{21} - 60 q^{22} + 437 q^{23} + 40 q^{24} + 395 q^{25} + 302 q^{26} - 68 q^{27} - 52 q^{28} - 551 q^{29} - 4 q^{30} - 622 q^{31} - 608 q^{32} - 291 q^{33} + 112 q^{34} + 21 q^{35} + 664 q^{36} - 183 q^{37} + 532 q^{38} - 212 q^{39} - 395 q^{41} + 478 q^{42} - 291 q^{43} + 120 q^{44} - 1018 q^{45} - 874 q^{46} - 241 q^{47} - 80 q^{48} + 1394 q^{49} - 790 q^{50} - 184 q^{51} - 604 q^{52} - 631 q^{53} + 136 q^{54} - 1765 q^{55} + 104 q^{56} + 144 q^{57} + 1102 q^{58} - 457 q^{59} + 8 q^{60} - 630 q^{61} + 1244 q^{62} + 125 q^{63} + 1216 q^{64} + 137 q^{65} + 582 q^{66} + 1421 q^{67} - 224 q^{68} - 115 q^{69} - 42 q^{70} + 983 q^{71} - 1328 q^{72} - 2532 q^{73} + 366 q^{74} - 1081 q^{75} - 1064 q^{76} - 595 q^{77} + 424 q^{78} - 4361 q^{79} - 721 q^{81} + 790 q^{82} + 1422 q^{83} - 956 q^{84} + 722 q^{85} + 582 q^{86} + 145 q^{87} - 240 q^{88} - 580 q^{89} + 2036 q^{90} - 447 q^{91} + 1748 q^{92} + 2106 q^{93} + 482 q^{94} - 310 q^{95} + 160 q^{96} - 2016 q^{97} - 2788 q^{98} - 1972 q^{99}+O(q^{100}) \) 19 * q - 38 * q^2 - 5 * q^3 + 76 * q^4 + 10 * q^6 - 13 * q^7 - 152 * q^8 + 166 * q^9 + 30 * q^11 - 20 * q^12 - 151 * q^13 + 26 * q^14 + 2 * q^15 + 304 * q^16 - 56 * q^17 - 332 * q^18 - 266 * q^19 - 239 * q^21 - 60 * q^22 + 437 * q^23 + 40 * q^24 + 395 * q^25 + 302 * q^26 - 68 * q^27 - 52 * q^28 - 551 * q^29 - 4 * q^30 - 622 * q^31 - 608 * q^32 - 291 * q^33 + 112 * q^34 + 21 * q^35 + 664 * q^36 - 183 * q^37 + 532 * q^38 - 212 * q^39 - 395 * q^41 + 478 * q^42 - 291 * q^43 + 120 * q^44 - 1018 * q^45 - 874 * q^46 - 241 * q^47 - 80 * q^48 + 1394 * q^49 - 790 * q^50 - 184 * q^51 - 604 * q^52 - 631 * q^53 + 136 * q^54 - 1765 * q^55 + 104 * q^56 + 144 * q^57 + 1102 * q^58 - 457 * q^59 + 8 * q^60 - 630 * q^61 + 1244 * q^62 + 125 * q^63 + 1216 * q^64 + 137 * q^65 + 582 * q^66 + 1421 * q^67 - 224 * q^68 - 115 * q^69 - 42 * q^70 + 983 * q^71 - 1328 * q^72 - 2532 * q^73 + 366 * q^74 - 1081 * q^75 - 1064 * q^76 - 595 * q^77 + 424 * q^78 - 4361 * q^79 - 721 * q^81 + 790 * q^82 + 1422 * q^83 - 956 * q^84 + 722 * q^85 + 582 * q^86 + 145 * q^87 - 240 * q^88 - 580 * q^89 + 2036 * q^90 - 447 * q^91 + 1748 * q^92 + 2106 * q^93 + 482 * q^94 - 310 * q^95 + 160 * q^96 - 2016 * q^97 - 2788 * q^98 - 1972 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.67612	−0.707470	−0.353735	−	0.935346i	$-0.615089\pi$
$3$	−3.67612	−0.707470	−0.353735	+	0.935346i	$0.615089\pi$
$4$	4.00000	0.500000
$5$	18.7156	1.67397	0.836985	−	0.547226i	$-0.184316\pi$
$5$	18.7156	1.67397	0.836985	+	0.547226i	$0.184316\pi$
$6$	7.35224	0.500257
$7$	−19.6479	−1.06089	−0.530443	−	0.847721i	$-0.677974\pi$
$7$	−19.6479	−1.06089	−0.530443	+	0.847721i	$0.677974\pi$
$8$	−8.00000	−0.353553
$9$	−13.4861	−0.499486
$10$	−37.4311	−1.18368
$11$	10.0534	0.275565	0.137782	−	0.990463i	$-0.456003\pi$
$11$	10.0534	0.275565	0.137782	+	0.990463i	$0.456003\pi$
$12$	−14.7045	−0.353735
$13$	−19.4802	−0.415602	−0.207801	−	0.978171i	$-0.566631\pi$
$13$	−19.4802	−0.415602	−0.207801	+	0.978171i	$0.566631\pi$
$14$	39.2958	0.750160
$15$	−68.8006	−1.18428
$16$	16.0000	0.250000
$17$	31.1714	0.444716	0.222358	−	0.974965i	$-0.428625\pi$
$17$	31.1714	0.444716	0.222358	+	0.974965i	$0.428625\pi$
$18$	26.9723	0.353190
$19$	−12.4065	−0.149803	−0.0749015	−	0.997191i	$-0.523864\pi$
$19$	−12.4065	−0.149803	−0.0749015	+	0.997191i	$0.523864\pi$
$20$	74.8622	0.836985
$21$	72.2280	0.750545
$22$	−20.1068	−0.194854
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	29.4090	0.250128
$25$	225.272	1.80218
$26$	38.9603	0.293875
$27$	148.832	1.06084
$28$	−78.5916	−0.530443
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	137.601	0.837415
$31$	207.430	1.20179	0.600897	−	0.799327i	$-0.294810\pi$
$31$	207.430	1.20179	0.600897	+	0.799327i	$0.294810\pi$
$32$	−32.0000	−0.176777
$33$	−36.9575	−0.194954
$34$	−62.3427	−0.314462
$35$	−367.721	−1.77589
$36$	−53.9445	−0.249743
$37$	−127.812	−0.567897	−0.283949	−	0.958840i	$-0.591644\pi$
$37$	−127.812	−0.567897	−0.283949	+	0.958840i	$0.591644\pi$
$38$	24.8131	0.105927
$39$	71.6114	0.294026
$40$	−149.724	−0.591838
$41$	−250.826	−0.955424	−0.477712	−	0.878517i	$-0.658534\pi$
$41$	−250.826	−0.955424	−0.477712	+	0.878517i	$0.658534\pi$
$42$	−144.456	−0.530715
$43$	−306.069	−1.08547	−0.542734	−	0.839905i	$-0.682611\pi$
$43$	−306.069	−1.08547	−0.542734	+	0.839905i	$0.682611\pi$
$44$	40.2135	0.137782
$45$	−252.400	−0.836125
$46$	−46.0000	−0.147442
$47$	420.251	1.30425	0.652127	−	0.758110i	$-0.273877\pi$
$47$	420.251	1.30425	0.652127	+	0.758110i	$0.273877\pi$
$48$	−58.8179	−0.176867
$49$	43.0395	0.125480
$50$	−450.544	−1.27433
$51$	−114.590	−0.314623
$52$	−77.9206	−0.207801
$53$	209.524	0.543025	0.271512	−	0.962435i	$-0.412476\pi$
$53$	209.524	0.543025	0.271512	+	0.962435i	$0.412476\pi$
$54$	−297.664	−0.750128
$55$	188.155	0.461287
$56$	157.183	0.375080
$57$	45.6080	0.105981
$58$	58.0000	0.131306
$59$	−728.190	−1.60682	−0.803410	−	0.595427i	$-0.796983\pi$
$59$	−728.190	−1.60682	−0.803410	+	0.595427i	$0.796983\pi$
$60$	−275.203	−0.592142
$61$	−853.929	−1.79237	−0.896183	−	0.443684i	$-0.853671\pi$
$61$	−853.929	−1.79237	−0.896183	+	0.443684i	$0.853671\pi$
$62$	−414.861	−0.849796
$63$	264.974	0.529898
$64$	64.0000	0.125000
$65$	−364.582	−0.695705
$66$	73.9149	0.137853
$67$	486.336	0.886797	0.443399	−	0.896325i	$-0.353773\pi$
$67$	486.336	0.886797	0.443399	+	0.896325i	$0.353773\pi$
$68$	124.685	0.222358
$69$	−84.5508	−0.147518
$70$	735.442	1.25575
$71$	685.447	1.14574	0.572870	−	0.819646i	$-0.305830\pi$
$71$	685.447	1.14574	0.572870	+	0.819646i	$0.305830\pi$
$72$	107.889	0.176595
$73$	−70.9219	−0.113709	−0.0568547	−	0.998382i	$-0.518107\pi$
$73$	−70.9219	−0.113709	−0.0568547	+	0.998382i	$0.518107\pi$
$74$	255.624	0.401564
$75$	−828.127	−1.27498
$76$	−49.6262	−0.0749015
$77$	−197.528	−0.292343
$78$	−143.223	−0.207908
$79$	1384.88	1.97230	0.986149	−	0.165863i	$-0.0530409\pi$
$79$	1384.88	1.97230	0.986149	+	0.165863i	$0.0530409\pi$
$80$	299.449	0.418492
$81$	−182.999	−0.251027
$82$	501.651	0.675587
$83$	−553.517	−0.732004	−0.366002	−	0.930614i	$-0.619274\pi$
$83$	−553.517	−0.732004	−0.366002	+	0.930614i	$0.619274\pi$
$84$	288.912	0.375273
$85$	583.389	0.744441
$86$	612.139	0.767542
$87$	106.608	0.131374
$88$	−80.4271	−0.0974268
$89$	699.330	0.832908	0.416454	−	0.909157i	$-0.363273\pi$
$89$	699.330	0.832908	0.416454	+	0.909157i	$0.363273\pi$
$90$	504.801	0.591230
$91$	382.744	0.440906
$92$	92.0000	0.104257
$93$	−762.539	−0.850233
$94$	−840.503	−0.922247
$95$	−232.195	−0.250766
$96$	117.636	0.125064
$97$	−1648.18	−1.72523	−0.862617	−	0.505858i	$-0.831176\pi$
$97$	−1648.18	−1.72523	−0.862617	+	0.505858i	$0.831176\pi$
$98$	−86.0791	−0.0887275
$99$	−135.581	−0.137641
$100$	901.088	0.901088
$101$	−1021.52	−1.00639	−0.503193	−	0.864174i	$-0.667842\pi$
$101$	−1021.52	−1.00639	−0.503193	+	0.864174i	$0.667842\pi$
$102$	229.179	0.222472
$103$	1346.52	1.28812	0.644059	−	0.764976i	$-0.277249\pi$
$103$	1346.52	1.28812	0.644059	+	0.764976i	$0.277249\pi$
$104$	155.841	0.146937
$105$	1351.79	1.25639
$106$	−419.048	−0.383976
$107$	−1602.14	−1.44752	−0.723758	−	0.690054i	$-0.757587\pi$
$107$	−1602.14	−1.44752	−0.723758	+	0.690054i	$0.757587\pi$
$108$	595.328	0.530421
$109$	−947.001	−0.832167	−0.416084	−	0.909326i	$-0.636598\pi$
$109$	−947.001	−0.832167	−0.416084	+	0.909326i	$0.636598\pi$
$110$	−376.309	−0.326179
$111$	469.853	0.401770
$112$	−314.366	−0.265222
$113$	−94.4756	−0.0786506	−0.0393253	−	0.999226i	$-0.512521\pi$
$113$	−94.4756	−0.0786506	−0.0393253	+	0.999226i	$0.512521\pi$
$114$	−91.2159	−0.0749399
$115$	430.458	0.349047
$116$	−116.000	−0.0928477
$117$	262.712	0.207588
$118$	1456.38	1.13619
$119$	−612.452	−0.471793
$120$	550.405	0.418707
$121$	−1229.93	−0.924064
$122$	1707.86	1.26739
$123$	922.065	0.675933
$124$	829.721	0.600897
$125$	1876.64	1.34282
$126$	−529.948	−0.374695
$127$	2055.51	1.43620	0.718098	−	0.695942i	$-0.245013\pi$
$127$	2055.51	1.43620	0.718098	+	0.695942i	$0.245013\pi$
$128$	−128.000	−0.0883883
$129$	1125.15	0.767936
$130$	729.164	0.491938
$131$	−2789.80	−1.86066	−0.930329	−	0.366727i	$-0.880478\pi$
$131$	−2789.80	−1.86066	−0.930329	+	0.366727i	$0.880478\pi$
$132$	−147.830	−0.0974768
$133$	243.762	0.158924
$134$	−972.672	−0.627060
$135$	2785.47	1.77582
$136$	−249.371	−0.157231
$137$	141.281	0.0881053	0.0440527	−	0.999029i	$-0.485973\pi$
$137$	141.281	0.0881053	0.0440527	+	0.999029i	$0.485973\pi$
$138$	169.102	0.104311
$139$	1668.44	1.01810	0.509049	−	0.860738i	$-0.329997\pi$
$139$	1668.44	1.01810	0.509049	+	0.860738i	$0.329997\pi$
$140$	−1470.88	−0.887946
$141$	−1544.89	−0.922720
$142$	−1370.89	−0.810161
$143$	−195.842	−0.114525
$144$	−215.778	−0.124872
$145$	−542.751	−0.310848
$146$	141.844	0.0804047
$147$	−158.219	−0.0887731
$148$	−511.249	−0.283949
$149$	1249.37	0.686928	0.343464	−	0.939166i	$-0.388400\pi$
$149$	1249.37	0.686928	0.343464	+	0.939166i	$0.388400\pi$
$150$	1656.25	0.901550
$151$	2732.18	1.47246	0.736232	−	0.676729i	$-0.236603\pi$
$151$	2732.18	1.47246	0.736232	+	0.676729i	$0.236603\pi$
$152$	99.2523	0.0529633
$153$	−420.381	−0.222130
$154$	395.056	0.206717
$155$	3882.17	2.01177
$156$	286.446	0.147013
$157$	530.374	0.269608	0.134804	−	0.990872i	$-0.456960\pi$
$157$	530.374	0.269608	0.134804	+	0.990872i	$0.456960\pi$
$158$	−2769.77	−1.39463
$159$	−770.235	−0.384174
$160$	−598.898	−0.295919
$161$	−451.901	−0.221210
$162$	365.997	0.177503
$163$	−1055.10	−0.507005	−0.253502	−	0.967335i	$-0.581583\pi$
$163$	−1055.10	−0.507005	−0.253502	+	0.967335i	$0.581583\pi$
$164$	−1003.30	−0.477712
$165$	−691.679	−0.326346
$166$	1107.03	0.517605
$167$	−3083.90	−1.42898	−0.714488	−	0.699647i	$-0.753341\pi$
$167$	−3083.90	−1.42898	−0.714488	+	0.699647i	$0.753341\pi$
$168$	−577.824	−0.265358
$169$	−1817.52	−0.827275
$170$	−1166.78	−0.526399
$171$	167.316	0.0748245
$172$	−1224.28	−0.542734
$173$	−2702.70	−1.18776	−0.593881	−	0.804553i	$-0.702405\pi$
$173$	−2702.70	−1.18776	−0.593881	+	0.804553i	$0.702405\pi$
$174$	−213.215	−0.0928953
$175$	−4426.12	−1.91190
$176$	160.854	0.0688911
$177$	2676.92	1.13678
$178$	−1398.66	−0.588955
$179$	−2829.45	−1.18147	−0.590735	−	0.806866i	$-0.701162\pi$
$179$	−2829.45	−1.18147	−0.590735	+	0.806866i	$0.701162\pi$
$180$	−1009.60	−0.418063
$181$	2154.75	0.884868	0.442434	−	0.896801i	$-0.354115\pi$
$181$	2154.75	0.884868	0.442434	+	0.896801i	$0.354115\pi$
$182$	−765.488	−0.311768
$183$	3139.15	1.26805
$184$	−184.000	−0.0737210
$185$	−2392.08	−0.950643
$186$	1525.08	0.601205
$187$	313.378	0.122548
$188$	1681.01	0.652127
$189$	−2924.23	−1.12543
$190$	464.391	0.177318
$191$	−4014.85	−1.52096	−0.760482	−	0.649359i	$-0.775037\pi$
$191$	−4014.85	−1.52096	−0.760482	+	0.649359i	$0.775037\pi$
$192$	−235.272	−0.0884337
$193$	4334.42	1.61657	0.808287	−	0.588789i	$-0.200395\pi$
$193$	4334.42	1.61657	0.808287	+	0.588789i	$0.200395\pi$
$194$	3296.37	1.21992
$195$	1340.25	0.492190
$196$	172.158	0.0627398
$197$	−3914.95	−1.41588	−0.707941	−	0.706271i	$-0.750376\pi$
$197$	−3914.95	−1.41588	−0.707941	+	0.706271i	$0.750376\pi$
$198$	271.163	0.0973267
$199$	1746.70	0.622214	0.311107	−	0.950375i	$-0.399300\pi$
$199$	1746.70	0.622214	0.311107	+	0.950375i	$0.399300\pi$
$200$	−1802.18	−0.637165
$201$	−1787.83	−0.627382
$202$	2043.04	0.711622
$203$	569.789	0.197002
$204$	−458.359	−0.157312
$205$	−4694.34	−1.59935
$206$	−2693.03	−0.910837
$207$	−310.181	−0.104150
$208$	−311.683	−0.103900
$209$	−124.728	−0.0412804
$210$	−2703.57	−0.888402
$211$	−5561.85	−1.81466	−0.907331	−	0.420416i	$-0.861884\pi$
$211$	−5561.85	−1.81466	−0.907331	+	0.420416i	$0.861884\pi$
$212$	838.095	0.271512
$213$	−2519.79	−0.810577
$214$	3204.27	1.02355
$215$	−5728.26	−1.81704
$216$	−1190.66	−0.375064
$217$	−4075.57	−1.27497
$218$	1894.00	0.588431
$219$	260.718	0.0804459
$220$	752.619	0.230643
$221$	−607.223	−0.184825
$222$	−939.706	−0.284094
$223$	1619.51	0.486326	0.243163	−	0.969985i	$-0.421815\pi$
$223$	1619.51	0.486326	0.243163	+	0.969985i	$0.421815\pi$
$224$	628.732	0.187540
$225$	−3038.05	−0.900162
$226$	188.951	0.0556144
$227$	550.098	0.160843	0.0804213	−	0.996761i	$-0.474373\pi$
$227$	550.098	0.160843	0.0804213	+	0.996761i	$0.474373\pi$
$228$	182.432	0.0529905
$229$	−4337.54	−1.25167	−0.625836	−	0.779954i	$-0.715242\pi$
$229$	−4337.54	−1.25167	−0.625836	+	0.779954i	$0.715242\pi$
$230$	−860.915	−0.246813
$231$	726.136	0.206824
$232$	232.000	0.0656532
$233$	1611.16	0.453007	0.226504	−	0.974010i	$-0.427270\pi$
$233$	1611.16	0.453007	0.226504	+	0.974010i	$0.427270\pi$
$234$	−525.424	−0.146787
$235$	7865.23	2.18328
$236$	−2912.76	−0.803410
$237$	−5091.00	−1.39534
$238$	1224.90	0.333608
$239$	−4258.87	−1.15265	−0.576325	−	0.817221i	$-0.695514\pi$
$239$	−4258.87	−1.15265	−0.576325	+	0.817221i	$0.695514\pi$
$240$	−1100.81	−0.296071
$241$	−5143.60	−1.37481	−0.687404	−	0.726275i	$-0.741250\pi$
$241$	−5143.60	−1.37481	−0.687404	+	0.726275i	$0.741250\pi$
$242$	2459.86	0.653412
$243$	−3345.74	−0.883247
$244$	−3415.72	−0.896183
$245$	805.509	0.210049
$246$	−1844.13	−0.477957
$247$	241.681	0.0622584
$248$	−1659.44	−0.424898
$249$	2034.79	0.517871
$250$	−3753.29	−0.949515
$251$	−2536.18	−0.637778	−0.318889	−	0.947792i	$-0.603310\pi$
$251$	−2536.18	−0.637778	−0.318889	+	0.947792i	$0.603310\pi$
$252$	1059.90	0.264949
$253$	231.228	0.0574592
$254$	−4111.02	−1.01554
$255$	−2144.61	−0.526669
$256$	256.000	0.0625000
$257$	−6019.91	−1.46113	−0.730567	−	0.682841i	$-0.760744\pi$
$257$	−6019.91	−1.46113	−0.730567	+	0.682841i	$0.760744\pi$
$258$	−2250.30	−0.543013
$259$	2511.24	0.602474
$260$	−1458.33	−0.347853
$261$	391.098	0.0927523
$262$	5579.60	1.31568
$263$	1994.19	0.467556	0.233778	−	0.972290i	$-0.424891\pi$
$263$	1994.19	0.467556	0.233778	+	0.972290i	$0.424891\pi$
$264$	295.660	0.0689265
$265$	3921.35	0.909007
$266$	−487.525	−0.112376
$267$	−2570.82	−0.589257
$268$	1945.34	0.443399
$269$	367.756	0.0833549	0.0416774	−	0.999131i	$-0.486730\pi$
$269$	367.756	0.0833549	0.0416774	+	0.999131i	$0.486730\pi$
$270$	−5570.94	−1.25569
$271$	−5475.44	−1.22734	−0.613670	−	0.789563i	$-0.710308\pi$
$271$	−5475.44	−1.22734	−0.613670	+	0.789563i	$0.710308\pi$
$272$	498.742	0.111179
$273$	−1407.01	−0.311928
$274$	−282.562	−0.0622999
$275$	2264.75	0.496616
$276$	−338.203	−0.0737588
$277$	4343.45	0.942140	0.471070	−	0.882096i	$-0.343868\pi$
$277$	4343.45	0.942140	0.471070	+	0.882096i	$0.343868\pi$
$278$	−3336.89	−0.719904
$279$	−2797.43	−0.600279
$280$	2941.77	0.627873
$281$	806.274	0.171168	0.0855841	−	0.996331i	$-0.472724\pi$
$281$	806.274	0.171168	0.0855841	+	0.996331i	$0.472724\pi$
$282$	3089.79	0.652462
$283$	−3944.06	−0.828446	−0.414223	−	0.910175i	$-0.635947\pi$
$283$	−3944.06	−0.828446	−0.414223	+	0.910175i	$0.635947\pi$
$284$	2741.79	0.572870
$285$	853.578	0.177409
$286$	391.683	0.0809815
$287$	4928.19	1.01360
$288$	431.556	0.0882976
$289$	−3941.35	−0.802228
$290$	1085.50	0.219803
$291$	6058.92	1.22055
$292$	−283.688	−0.0568547
$293$	102.013	0.0203401	0.0101701	−	0.999948i	$-0.496763\pi$
$293$	102.013	0.0203401	0.0101701	+	0.999948i	$0.496763\pi$
$294$	316.437	0.0627721
$295$	−13628.5	−2.68977
$296$	1022.50	0.200782
$297$	1496.26	0.292330
$298$	−2498.74	−0.485731
$299$	−448.044	−0.0866590
$300$	−3312.51	−0.637492
$301$	6013.62	1.15156
$302$	−5464.37	−1.04119
$303$	3755.23	0.711988
$304$	−198.505	−0.0374507
$305$	−15981.7	−3.00037
$306$	840.763	0.157069
$307$	−3007.65	−0.559139	−0.279569	−	0.960125i	$-0.590192\pi$
$307$	−3007.65	−0.559139	−0.279569	+	0.960125i	$0.590192\pi$
$308$	−790.111	−0.146171
$309$	−4949.95	−0.911304
$310$	−7764.35	−1.42253
$311$	4566.04	0.832528	0.416264	−	0.909244i	$-0.363339\pi$
$311$	4566.04	0.832528	0.416264	+	0.909244i	$0.363339\pi$
$312$	−572.891	−0.103954
$313$	−648.401	−0.117092	−0.0585460	−	0.998285i	$-0.518646\pi$
$313$	−648.401	−0.117092	−0.0585460	+	0.998285i	$0.518646\pi$
$314$	−1060.75	−0.190642
$315$	4959.14	0.887034
$316$	5539.53	0.986149
$317$	4019.65	0.712196	0.356098	−	0.934449i	$-0.384107\pi$
$317$	4019.65	0.712196	0.356098	+	0.934449i	$0.384107\pi$
$318$	1540.47	0.271652
$319$	−291.548	−0.0511711
$320$	1197.80	0.209246
$321$	5889.64	1.02407
$322$	903.803	0.156419
$323$	−386.729	−0.0666197
$324$	−731.994	−0.125513
$325$	−4388.33	−0.748987
$326$	2110.20	0.358506
$327$	3481.29	0.588733
$328$	2006.60	0.337793
$329$	−8257.05	−1.38367
$330$	1383.36	0.230762
$331$	−7008.43	−1.16380	−0.581901	−	0.813260i	$-0.697691\pi$
$331$	−7008.43	−1.16380	−0.581901	+	0.813260i	$0.697691\pi$
$332$	−2214.07	−0.366002
$333$	1723.69	0.283657
$334$	6167.79	1.01044
$335$	9102.05	1.48447
$336$	1155.65	0.187636
$337$	−3117.33	−0.503893	−0.251947	−	0.967741i	$-0.581071\pi$
$337$	−3117.33	−0.503893	−0.251947	+	0.967741i	$0.581071\pi$
$338$	3635.05	0.584972
$339$	347.304	0.0556429
$340$	2333.56	0.372220
$341$	2085.38	0.331172
$342$	−334.633	−0.0529089
$343$	5893.59	0.927767
$344$	2448.55	0.383771
$345$	−1582.41	−0.246940
$346$	5405.41	0.839874
$347$	10126.5	1.56663	0.783313	−	0.621627i	$-0.213528\pi$
$347$	10126.5	1.56663	0.783313	+	0.621627i	$0.213528\pi$
$348$	426.430	0.0656869
$349$	418.001	0.0641120	0.0320560	−	0.999486i	$-0.489795\pi$
$349$	418.001	0.0641120	0.0320560	+	0.999486i	$0.489795\pi$
$350$	8852.23	1.35192
$351$	−2899.27	−0.440888
$352$	−321.708	−0.0487134
$353$	10375.9	1.56446	0.782230	−	0.622990i	$-0.214082\pi$
$353$	10375.9	1.56446	0.782230	+	0.622990i	$0.214082\pi$
$354$	−5353.83	−0.803822
$355$	12828.5	1.91794
$356$	2797.32	0.416454
$357$	2251.45	0.333779
$358$	5658.90	0.835425
$359$	1895.71	0.278695	0.139348	−	0.990244i	$-0.455499\pi$
$359$	1895.71	0.278695	0.139348	+	0.990244i	$0.455499\pi$
$360$	2019.20	0.295615
$361$	−6705.08	−0.977559
$362$	−4309.49	−0.625696
$363$	4521.37	0.653748
$364$	1530.98	0.220453
$365$	−1327.34	−0.190346
$366$	−6278.29	−0.896644
$367$	−11322.0	−1.61037	−0.805185	−	0.593024i	$-0.797934\pi$
$367$	−11322.0	−1.61037	−0.805185	+	0.593024i	$0.797934\pi$
$368$	368.000	0.0521286
$369$	3382.67	0.477221
$370$	4784.15	0.672206
$371$	−4116.70	−0.576087
$372$	−3050.16	−0.425116
$373$	−9241.50	−1.28286	−0.641430	−	0.767182i	$-0.721659\pi$
$373$	−9241.50	−1.28286	−0.641430	+	0.767182i	$0.721659\pi$
$374$	−626.756	−0.0866545
$375$	−6898.77	−0.950002
$376$	−3362.01	−0.461123
$377$	564.925	0.0771753
$378$	5848.47	0.795801
$379$	−1973.61	−0.267487	−0.133744	−	0.991016i	$-0.542700\pi$
$379$	−1973.61	−0.267487	−0.133744	+	0.991016i	$0.542700\pi$
$380$	−928.781	−0.125383
$381$	−7556.30	−1.01607
$382$	8029.70	1.07548
$383$	11158.3	1.48867	0.744337	−	0.667804i	$-0.232766\pi$
$383$	11158.3	1.48867	0.744337	+	0.667804i	$0.232766\pi$
$384$	470.543	0.0625321
$385$	−3696.84	−0.489373
$386$	−8668.85	−1.14309
$387$	4127.69	0.542177
$388$	−6592.73	−0.862617
$389$	−9366.76	−1.22086	−0.610429	−	0.792071i	$-0.709003\pi$
$389$	−9366.76	−1.22086	−0.610429	+	0.792071i	$0.709003\pi$
$390$	−2680.49	−0.348031
$391$	716.942	0.0927297
$392$	−344.316	−0.0443638
$393$	10255.6	1.31636
$394$	7829.90	1.00118
$395$	25918.9	3.30157
$396$	−542.325	−0.0688204
$397$	−4483.48	−0.566799	−0.283400	−	0.959002i	$-0.591462\pi$
$397$	−4483.48	−0.566799	−0.283400	+	0.959002i	$0.591462\pi$
$398$	−3493.41	−0.439972
$399$	−896.100	−0.112434
$400$	3604.35	0.450544
$401$	6412.37	0.798549	0.399275	−	0.916831i	$-0.369262\pi$
$401$	6412.37	0.798549	0.399275	+	0.916831i	$0.369262\pi$
$402$	3575.66	0.443626
$403$	−4040.78	−0.499468
$404$	−4086.08	−0.503193
$405$	−3424.92	−0.420211
$406$	−1139.58	−0.139301
$407$	−1284.95	−0.156492
$408$	916.718	0.111236
$409$	−13294.9	−1.60731	−0.803657	−	0.595092i	$-0.797115\pi$
$409$	−13294.9	−1.60731	−0.803657	+	0.595092i	$0.797115\pi$
$410$	9388.68	1.13091
$411$	−519.365	−0.0623319
$412$	5386.06	0.644059
$413$	14307.4	1.70465
$414$	620.362	0.0736453
$415$	−10359.4	−1.22535
$416$	623.365	0.0734687
$417$	−6133.40	−0.720274
$418$	249.456	0.0291896
$419$	2374.51	0.276856	0.138428	−	0.990373i	$-0.455795\pi$
$419$	2374.51	0.276856	0.138428	+	0.990373i	$0.455795\pi$
$420$	5407.15	0.628195
$421$	−13116.7	−1.51845	−0.759227	−	0.650826i	$-0.774423\pi$
$421$	−13116.7	−1.51845	−0.759227	+	0.650826i	$0.774423\pi$
$422$	11123.7	1.28316
$423$	−5667.56	−0.651457
$424$	−1676.19	−0.191988
$425$	7022.03	0.801456
$426$	5039.57	0.573165
$427$	16777.9	1.90150
$428$	−6408.54	−0.723758
$429$	719.937	0.0810231
$430$	11456.5	1.28484
$431$	−9608.67	−1.07386	−0.536929	−	0.843627i	$-0.680416\pi$
$431$	−9608.67	−1.07386	−0.536929	+	0.843627i	$0.680416\pi$
$432$	2381.31	0.265210
$433$	17012.3	1.88813	0.944066	−	0.329757i	$-0.106967\pi$
$433$	17012.3	1.88813	0.944066	+	0.329757i	$0.106967\pi$
$434$	8151.14	0.901537
$435$	1995.22	0.219916
$436$	−3788.00	−0.416084
$437$	−285.350	−0.0312361
$438$	−521.435	−0.0568839
$439$	3087.48	0.335666	0.167833	−	0.985815i	$-0.446323\pi$
$439$	3087.48	0.335666	0.167833	+	0.985815i	$0.446323\pi$
$440$	−1505.24	−0.163089
$441$	−580.437	−0.0626754
$442$	1214.45	0.130691
$443$	−4027.96	−0.431996	−0.215998	−	0.976394i	$-0.569301\pi$
$443$	−4027.96	−0.431996	−0.215998	+	0.976394i	$0.569301\pi$
$444$	1879.41	0.200885
$445$	13088.3	1.39426
$446$	−3239.03	−0.343884
$447$	−4592.83	−0.485981
$448$	−1257.46	−0.132611
$449$	−3436.61	−0.361211	−0.180606	−	0.983556i	$-0.557806\pi$
$449$	−3436.61	−0.361211	−0.180606	+	0.983556i	$0.557806\pi$
$450$	6076.09	0.636511
$451$	−2521.65	−0.263281
$452$	−377.903	−0.0393253
$453$	−10043.8	−1.04172
$454$	−1100.20	−0.113733
$455$	7163.27	0.738064
$456$	−364.864	−0.0374700
$457$	−11157.8	−1.14210	−0.571050	−	0.820915i	$-0.693464\pi$
$457$	−11157.8	−1.14210	−0.571050	+	0.820915i	$0.693464\pi$
$458$	8675.09	0.885066
$459$	4639.30	0.471773
$460$	1721.83	0.174523
$461$	−2121.65	−0.214350	−0.107175	−	0.994240i	$-0.534180\pi$
$461$	−2121.65	−0.214350	−0.107175	+	0.994240i	$0.534180\pi$
$462$	−1452.27	−0.146246
$463$	12339.7	1.23860	0.619301	−	0.785154i	$-0.287416\pi$
$463$	12339.7	1.23860	0.619301	+	0.785154i	$0.287416\pi$
$464$	−464.000	−0.0464238
$465$	−14271.3	−1.42326
$466$	−3222.32	−0.320325
$467$	−13596.2	−1.34723	−0.673615	−	0.739082i	$-0.735259\pi$
$467$	−13596.2	−1.34723	−0.673615	+	0.739082i	$0.735259\pi$
$468$	1050.85	0.103794
$469$	−9555.48	−0.940791
$470$	−15730.5	−1.54381
$471$	−1949.72	−0.190740
$472$	5825.52	0.568096
$473$	−3077.03	−0.299117
$474$	10182.0	0.986655
$475$	−2794.85	−0.269971
$476$	−2449.81	−0.235896
$477$	−2825.67	−0.271233
$478$	8517.74	0.815047
$479$	18975.4	1.81004	0.905018	−	0.425374i	$-0.139857\pi$
$479$	18975.4	1.81004	0.905018	+	0.425374i	$0.139857\pi$
$480$	2201.62	0.209354
$481$	2489.80	0.236019
$482$	10287.2	0.972136
$483$	1661.24	0.156499
$484$	−4919.72	−0.462032
$485$	−30846.7	−2.88799
$486$	6691.47	0.624550
$487$	−2184.12	−0.203228	−0.101614	−	0.994824i	$-0.532401\pi$
$487$	−2184.12	−0.203228	−0.101614	+	0.994824i	$0.532401\pi$
$488$	6831.43	0.633697
$489$	3878.67	0.358690
$490$	−1611.02	−0.148527
$491$	15035.3	1.38195	0.690973	−	0.722880i	$-0.257182\pi$
$491$	15035.3	1.38195	0.690973	+	0.722880i	$0.257182\pi$
$492$	3688.26	0.337967
$493$	−903.970	−0.0825817
$494$	−483.363	−0.0440233
$495$	−2537.48	−0.230406
$496$	3318.89	0.300448
$497$	−13467.6	−1.21550
$498$	−4069.59	−0.366190
$499$	5555.51	0.498394	0.249197	−	0.968453i	$-0.419833\pi$
$499$	5555.51	0.498394	0.249197	+	0.968453i	$0.419833\pi$
$500$	7506.57	0.671408
$501$	11336.8	1.01096
$502$	5072.36	0.450977
$503$	−18062.0	−1.60108	−0.800540	−	0.599279i	$-0.795454\pi$
$503$	−18062.0	−1.60108	−0.800540	+	0.599279i	$0.795454\pi$
$504$	−2119.79	−0.187347
$505$	−19118.3	−1.68466
$506$	−462.456	−0.0406298
$507$	6681.44	0.585272
$508$	8222.03	0.718098
$509$	−7314.77	−0.636978	−0.318489	−	0.947927i	$-0.603175\pi$
$509$	−7314.77	−0.636978	−0.318489	+	0.947927i	$0.603175\pi$
$510$	4289.22	0.372412
$511$	1393.47	0.120633
$512$	−512.000	−0.0441942
$513$	−1846.49	−0.158917
$514$	12039.8	1.03318
$515$	25200.8	2.15627
$516$	4500.59	0.383968
$517$	4224.95	0.359406
$518$	−5022.48	−0.426014
$519$	9935.47	0.840306
$520$	2916.66	0.245969
$521$	6409.03	0.538934	0.269467	−	0.963010i	$-0.413153\pi$
$521$	6409.03	0.538934	0.269467	+	0.963010i	$0.413153\pi$
$522$	−782.196	−0.0655858
$523$	−9805.47	−0.819815	−0.409908	−	0.912127i	$-0.634439\pi$
$523$	−9805.47	−0.819815	−0.409908	+	0.912127i	$0.634439\pi$
$524$	−11159.2	−0.930329
$525$	16270.9	1.35261
$526$	−3988.39	−0.330612
$527$	6465.89	0.534456
$528$	−591.319	−0.0487384
$529$	529.000	0.0434783
$530$	−7842.71	−0.642765
$531$	9820.47	0.802584
$532$	975.050	0.0794620
$533$	4886.12	0.397076
$534$	5141.64	0.416668
$535$	−29984.8	−2.42310
$536$	−3890.69	−0.313530
$537$	10401.4	0.835854
$538$	−735.511	−0.0589408
$539$	432.693	0.0345778
$540$	11141.9	0.887908
$541$	−5421.49	−0.430846	−0.215423	−	0.976521i	$-0.569113\pi$
$541$	−5421.49	−0.430846	−0.215423	+	0.976521i	$0.569113\pi$
$542$	10950.9	0.867861
$543$	−7921.11	−0.626017
$544$	−997.484	−0.0786154
$545$	−17723.6	−1.39302
$546$	2814.03	0.220566
$547$	−4283.32	−0.334811	−0.167405	−	0.985888i	$-0.553539\pi$
$547$	−4283.32	−0.334811	−0.167405	+	0.985888i	$0.553539\pi$
$548$	565.123	0.0440527
$549$	11516.2	0.895263
$550$	−4529.49	−0.351160
$551$	359.790	0.0278177
$552$	676.406	0.0521554
$553$	−27210.0	−2.09238
$554$	−8686.90	−0.666193
$555$	8793.56	0.672551
$556$	6673.78	0.509049
$557$	11724.8	0.891915	0.445957	−	0.895054i	$-0.352863\pi$
$557$	11724.8	0.891915	0.445957	+	0.895054i	$0.352863\pi$
$558$	5594.87	0.424462
$559$	5962.28	0.451123
$560$	−5883.54	−0.443973
$561$	−1152.02	−0.0866990
$562$	−1612.55	−0.121034
$563$	−21750.9	−1.62823	−0.814113	−	0.580707i	$-0.802776\pi$
$563$	−21750.9	−1.62823	−0.814113	+	0.580707i	$0.802776\pi$
$564$	−6179.58	−0.461360
$565$	−1768.16	−0.131659
$566$	7888.12	0.585800
$567$	3595.54	0.266311
$568$	−5483.58	−0.405081
$569$	−8218.27	−0.605497	−0.302749	−	0.953070i	$-0.597904\pi$
$569$	−8218.27	−0.605497	−0.302749	+	0.953070i	$0.597904\pi$
$570$	−1707.16	−0.125447
$571$	25365.1	1.85901	0.929505	−	0.368809i	$-0.120234\pi$
$571$	25365.1	1.85901	0.929505	+	0.368809i	$0.120234\pi$
$572$	−783.366	−0.0572626
$573$	14759.1	1.07604
$574$	−9856.38	−0.716720
$575$	5181.25	0.375779
$576$	−863.113	−0.0624358
$577$	−0.882099	−6.36434e−5 0	−3.18217e−5	−	1.00000i	$-0.500010\pi$
$577$	−0.882099	−6.36434e−5 0	−3.18217e−5		1.00000i	$0.500010\pi$
$578$	7882.69	0.567261
$579$	−15933.9	−1.14368
$580$	−2171.00	−0.155424
$581$	10875.4	0.776573
$582$	−12117.8	−0.863059
$583$	2106.42	0.149638
$584$	567.375	0.0402023
$585$	4916.80	0.347495
$586$	−204.026	−0.0143827
$587$	13722.7	0.964902	0.482451	−	0.875923i	$-0.339747\pi$
$587$	13722.7	0.964902	0.482451	+	0.875923i	$0.339747\pi$
$588$	−632.874	−0.0443865
$589$	−2573.49	−0.180032
$590$	27257.0	1.90195
$591$	14391.8	1.00169
$592$	−2044.99	−0.141974
$593$	−12337.8	−0.854390	−0.427195	−	0.904159i	$-0.640498\pi$
$593$	−12337.8	−0.854390	−0.427195	+	0.904159i	$0.640498\pi$
$594$	−2992.53	−0.206709
$595$	−11462.4	−0.789767
$596$	4997.47	0.343464
$597$	−6421.09	−0.440197
$598$	896.087	0.0612772
$599$	−5173.36	−0.352884	−0.176442	−	0.984311i	$-0.556459\pi$
$599$	−5173.36	−0.352884	−0.176442	+	0.984311i	$0.556459\pi$
$600$	6625.01	0.450775
$601$	4017.34	0.272664	0.136332	−	0.990663i	$-0.456469\pi$
$601$	4017.34	0.272664	0.136332	+	0.990663i	$0.456469\pi$
$602$	−12027.2	−0.814275
$603$	−6558.79	−0.442943
$604$	10928.7	0.736232
$605$	−23018.8	−1.54686
$606$	−7510.46	−0.503451
$607$	−15752.3	−1.05332	−0.526661	−	0.850075i	$-0.676556\pi$
$607$	−15752.3	−1.05332	−0.526661	+	0.850075i	$0.676556\pi$
$608$	397.009	0.0264817
$609$	−2094.61	−0.139373
$610$	31963.5	2.12158
$611$	−8186.56	−0.542050
$612$	−1681.53	−0.111065
$613$	−11479.8	−0.756389	−0.378195	−	0.925726i	$-0.623455\pi$
$613$	−11479.8	−0.756389	−0.378195	+	0.925726i	$0.623455\pi$
$614$	6015.30	0.395371
$615$	17257.0	1.13149
$616$	1580.22	0.103359
$617$	−9138.54	−0.596278	−0.298139	−	0.954522i	$-0.596366\pi$
$617$	−9138.54	−0.596278	−0.298139	+	0.954522i	$0.596366\pi$
$618$	9899.91	0.644389
$619$	−20057.7	−1.30240	−0.651201	−	0.758905i	$-0.725735\pi$
$619$	−20057.7	−1.30240	−0.651201	+	0.758905i	$0.725735\pi$
$620$	15528.7	1.00588
$621$	3423.13	0.221201
$622$	−9132.08	−0.588686
$623$	−13740.3	−0.883620
$624$	1145.78	0.0735064
$625$	6963.43	0.445660
$626$	1296.80	0.0827966
$627$	458.514	0.0292046
$628$	2121.50	0.134804
$629$	−3984.08	−0.252553
$630$	−9918.27	−0.627228
$631$	9362.16	0.590653	0.295326	−	0.955396i	$-0.404572\pi$
$631$	9362.16	0.590653	0.295326	+	0.955396i	$0.404572\pi$
$632$	−11079.1	−0.697313
$633$	20446.1	1.28382
$634$	−8039.31	−0.503599
$635$	38470.0	2.40415
$636$	−3080.94	−0.192087
$637$	−838.417	−0.0521496
$638$	583.096	0.0361834
$639$	−9244.03	−0.572282
$640$	−2395.59	−0.147959
$641$	8876.33	0.546948	0.273474	−	0.961879i	$-0.411827\pi$
$641$	8876.33	0.546948	0.273474	+	0.961879i	$0.411827\pi$
$642$	−11779.3	−0.724130
$643$	23010.6	1.41128	0.705638	−	0.708573i	$-0.250661\pi$
$643$	23010.6	1.41128	0.705638	+	0.708573i	$0.250661\pi$
$644$	−1807.61	−0.110605
$645$	21057.8	1.28550
$646$	773.458	0.0471073
$647$	−15695.7	−0.953729	−0.476864	−	0.878977i	$-0.658227\pi$
$647$	−15695.7	−0.953729	−0.476864	+	0.878977i	$0.658227\pi$
$648$	1463.99	0.0887514
$649$	−7320.78	−0.442782
$650$	8776.66	0.529614
$651$	14982.3	0.902000
$652$	−4220.40	−0.253502
$653$	27595.6	1.65375	0.826874	−	0.562387i	$-0.190117\pi$
$653$	27595.6	1.65375	0.826874	+	0.562387i	$0.190117\pi$
$654$	−6962.58	−0.416297
$655$	−52212.7	−3.11468
$656$	−4013.21	−0.238856
$657$	956.462	0.0567963
$658$	16514.1	0.978399
$659$	−32186.3	−1.90258	−0.951289	−	0.308300i	$-0.900240\pi$
$659$	−32186.3	−1.90258	−0.951289	+	0.308300i	$0.900240\pi$
$660$	−2766.72	−0.163173
$661$	25527.6	1.50213	0.751066	−	0.660227i	$-0.229540\pi$
$661$	25527.6	1.50213	0.751066	+	0.660227i	$0.229540\pi$
$662$	14016.9	0.822932
$663$	2232.23	0.130758
$664$	4428.13	0.258803
$665$	4562.15	0.266034
$666$	−3447.38	−0.200576
$667$	−667.000	−0.0387202
$668$	−12335.6	−0.714488
$669$	−5953.53	−0.344061
$670$	−18204.1	−1.04968
$671$	−8584.88	−0.493913
$672$	−2311.30	−0.132679
$673$	18972.1	1.08666	0.543328	−	0.839520i	$-0.317164\pi$
$673$	18972.1	1.08666	0.543328	+	0.839520i	$0.317164\pi$
$674$	6234.67	0.356306
$675$	33527.6	1.91182
$676$	−7270.09	−0.413638
$677$	10226.3	0.580543	0.290272	−	0.956944i	$-0.406254\pi$
$677$	10226.3	0.580543	0.290272	+	0.956944i	$0.406254\pi$
$678$	−694.608	−0.0393455
$679$	32383.3	1.83028
$680$	−4667.12	−0.263200
$681$	−2022.23	−0.113791
$682$	−4170.76	−0.234174
$683$	−5068.35	−0.283946	−0.141973	−	0.989871i	$-0.545345\pi$
$683$	−5068.35	−0.283946	−0.141973	+	0.989871i	$0.545345\pi$
$684$	669.265	0.0374123
$685$	2644.15	0.147486
$686$	−11787.2	−0.656030
$687$	15945.3	0.885521
$688$	−4897.11	−0.271367
$689$	−4081.56	−0.225682
$690$	3164.83	0.174613
$691$	−23153.1	−1.27466	−0.637328	−	0.770593i	$-0.719960\pi$
$691$	−23153.1	−1.27466	−0.637328	+	0.770593i	$0.719960\pi$
$692$	−10810.8	−0.593881
$693$	2663.89	0.146021
$694$	−20253.0	−1.10777
$695$	31225.9	1.70427
$696$	−852.860	−0.0464477
$697$	−7818.58	−0.424892
$698$	−836.002	−0.0453340
$699$	−5922.83	−0.320489
$700$	−17704.5	−0.955951
$701$	−3667.24	−0.197589	−0.0987945	−	0.995108i	$-0.531499\pi$
$701$	−3667.24	−0.197589	−0.0987945	+	0.995108i	$0.531499\pi$
$702$	5798.54	0.311755
$703$	1585.71	0.0850727
$704$	643.417	0.0344456
$705$	−28913.6	−1.54461
$706$	−20751.8	−1.10624
$707$	20070.7	1.06766
$708$	10707.7	0.568388
$709$	19814.0	1.04955	0.524775	−	0.851241i	$-0.324149\pi$
$709$	19814.0	1.04955	0.524775	+	0.851241i	$0.324149\pi$
$710$	−25657.0	−1.35619
$711$	−18676.7	−0.985136
$712$	−5594.64	−0.294477
$713$	4770.90	0.250591
$714$	−4502.89	−0.236018
$715$	−3665.28	−0.191712
$716$	−11317.8	−0.590735
$717$	15656.1	0.815465
$718$	−3791.41	−0.197067
$719$	27169.8	1.40927	0.704633	−	0.709572i	$-0.251112\pi$
$719$	27169.8	1.40927	0.704633	+	0.709572i	$0.251112\pi$
$720$	−4038.41	−0.209031
$721$	−26456.2	−1.36655
$722$	13410.2	0.691239
$723$	18908.5	0.972635
$724$	8618.99	0.442434
$725$	−6532.88	−0.334656
$726$	−9042.74	−0.462269
$727$	24937.2	1.27217	0.636086	−	0.771618i	$-0.280552\pi$
$727$	24937.2	1.27217	0.636086	+	0.771618i	$0.280552\pi$
$728$	−3061.95	−0.155884
$729$	17240.3	0.875898
$730$	2654.69	0.134595
$731$	−9540.60	−0.482725
$732$	12556.6	0.634023
$733$	−9870.52	−0.497375	−0.248688	−	0.968584i	$-0.579999\pi$
$733$	−9870.52	−0.497375	−0.248688	+	0.968584i	$0.579999\pi$
$734$	22644.1	1.13870
$735$	−2961.15	−0.148603
$736$	−736.000	−0.0368605
$737$	4889.32	0.244370
$738$	−6765.33	−0.337446
$739$	−28424.8	−1.41492	−0.707459	−	0.706755i	$-0.750158\pi$
$739$	−28424.8	−1.41492	−0.707459	+	0.706755i	$0.750158\pi$
$740$	−9568.30	−0.475321
$741$	−888.450	−0.0440459
$742$	8233.40	0.407355
$743$	−4280.52	−0.211355	−0.105678	−	0.994400i	$-0.533701\pi$
$743$	−4280.52	−0.211355	−0.105678	+	0.994400i	$0.533701\pi$
$744$	6100.31	0.300603
$745$	23382.6	1.14990
$746$	18483.0	0.907119
$747$	7464.80	0.365626
$748$	1253.51	0.0612740
$749$	31478.6	1.53565
$750$	13797.5	0.671753
$751$	5042.08	0.244991	0.122495	−	0.992469i	$-0.460910\pi$
$751$	5042.08	0.244991	0.122495	+	0.992469i	$0.460910\pi$
$752$	6724.02	0.326064
$753$	9323.31	0.451209
$754$	−1129.85	−0.0545712
$755$	51134.3	2.46486
$756$	−11696.9	−0.562716
$757$	−13429.4	−0.644780	−0.322390	−	0.946607i	$-0.604486\pi$
$757$	−13429.4	−0.644780	−0.322390	+	0.946607i	$0.604486\pi$
$758$	3947.23	0.189142
$759$	−850.022	−0.0406506
$760$	1857.56	0.0886590
$761$	28535.4	1.35927	0.679636	−	0.733549i	$-0.262138\pi$
$761$	28535.4	1.35927	0.679636	+	0.733549i	$0.262138\pi$
$762$	15112.6	0.718467
$763$	18606.6	0.882835
$764$	−16059.4	−0.760482
$765$	−7867.67	−0.371838
$766$	−22316.6	−1.05265
$767$	14185.3	0.667797
$768$	−941.087	−0.0442169
$769$	−13963.1	−0.654774	−0.327387	−	0.944890i	$-0.606168\pi$
$769$	−13963.1	−0.654774	−0.327387	+	0.944890i	$0.606168\pi$
$770$	7393.68	0.346039
$771$	22129.9	1.03371
$772$	17337.7	0.808287
$773$	39780.8	1.85099	0.925496	−	0.378757i	$-0.123648\pi$
$773$	39780.8	1.85099	0.925496	+	0.378757i	$0.123648\pi$
$774$	−8255.38	−0.383377
$775$	46728.2	2.16584
$776$	13185.5	0.609962
$777$	−9231.62	−0.426232
$778$	18733.5	0.863277
$779$	3111.88	0.143125
$780$	5360.99	0.246095
$781$	6891.06	0.315726
$782$	−1433.88	−0.0655698
$783$	−4316.13	−0.196993
$784$	688.633	0.0313699
$785$	9926.24	0.451316
$786$	−20511.3	−0.930806
$787$	−3085.62	−0.139759	−0.0698796	−	0.997555i	$-0.522261\pi$
$787$	−3085.62	−0.139759	−0.0698796	+	0.997555i	$0.522261\pi$
$788$	−15659.8	−0.707941
$789$	−7330.90	−0.330782
$790$	−51837.7	−2.33456
$791$	1856.25	0.0834394
$792$	1084.65	0.0486634
$793$	16634.7	0.744911
$794$	8966.95	0.400787
$795$	−14415.4	−0.643095
$796$	6986.81	0.311107
$797$	11141.4	0.495168	0.247584	−	0.968866i	$-0.420363\pi$
$797$	11141.4	0.495168	0.247584	+	0.968866i	$0.420363\pi$
$798$	1792.20	0.0795027
$799$	13099.8	0.580022
$800$	−7208.70	−0.318583
$801$	−9431.25	−0.416026
$802$	−12824.7	−0.564660
$803$	−713.005	−0.0313343
$804$	−7151.32	−0.313691
$805$	−8457.58	−0.370299
$806$	8081.55	0.353177
$807$	−1351.91	−0.0589710
$808$	8172.16	0.355811
$809$	6080.54	0.264253	0.132126	−	0.991233i	$-0.457820\pi$
$809$	6080.54	0.264253	0.132126	+	0.991233i	$0.457820\pi$
$810$	6849.84	0.297134
$811$	−17173.9	−0.743596	−0.371798	−	0.928314i	$-0.621259\pi$
$811$	−17173.9	−0.743596	−0.371798	+	0.928314i	$0.621259\pi$
$812$	2279.16	0.0985008
$813$	20128.4	0.868306
$814$	2569.89	0.110657
$815$	−19746.8	−0.848710
$816$	−1833.44	−0.0786558
$817$	3797.26	0.162606
$818$	26589.8	1.13654
$819$	−5161.74	−0.220227
$820$	−18777.4	−0.799675
$821$	−10854.0	−0.461399	−0.230699	−	0.973025i	$-0.574101\pi$
$821$	−10854.0	−0.461399	−0.230699	+	0.973025i	$0.574101\pi$
$822$	1038.73	0.0440753
$823$	16928.5	0.716999	0.358500	−	0.933530i	$-0.383288\pi$
$823$	16928.5	0.716999	0.358500	+	0.933530i	$0.383288\pi$
$824$	−10772.1	−0.455418
$825$	−8325.48	−0.351341
$826$	−28614.8	−1.20537
$827$	−13297.9	−0.559146	−0.279573	−	0.960125i	$-0.590193\pi$
$827$	−13297.9	−0.559146	−0.279573	+	0.960125i	$0.590193\pi$
$828$	−1240.72	−0.0520751
$829$	−33125.7	−1.38782	−0.693910	−	0.720061i	$-0.744114\pi$
$829$	−33125.7	−1.38782	−0.693910	+	0.720061i	$0.744114\pi$
$830$	20718.7	0.866456
$831$	−15967.1	−0.666535
$832$	−1246.73	−0.0519502
$833$	1341.60	0.0558028
$834$	12266.8	0.509310
$835$	−57716.8	−2.39206
$836$	−498.911	−0.0206402
$837$	30872.3	1.27491
$838$	−4749.03	−0.195767
$839$	−29845.5	−1.22810	−0.614052	−	0.789265i	$-0.710462\pi$
$839$	−29845.5	−1.22810	−0.614052	+	0.789265i	$0.710462\pi$
$840$	−10814.3	−0.444201
$841$	841.000	0.0344828
$842$	26233.4	1.07371
$843$	−2963.96	−0.121096
$844$	−22247.4	−0.907331
$845$	−34016.0	−1.38483
$846$	11335.1	0.460650
$847$	24165.5	0.980327
$848$	3352.38	0.135756
$849$	14498.8	0.586100
$850$	−14044.1	−0.566715
$851$	−2939.68	−0.118415
$852$	−10079.1	−0.405289
$853$	45337.9	1.81986	0.909930	−	0.414762i	$-0.136135\pi$
$853$	45337.9	1.81986	0.909930	+	0.414762i	$0.136135\pi$
$854$	−33555.8	−1.34456
$855$	3131.42	0.125254
$856$	12817.1	0.511774
$857$	−6985.04	−0.278418	−0.139209	−	0.990263i	$-0.544456\pi$
$857$	−6985.04	−0.278418	−0.139209	+	0.990263i	$0.544456\pi$
$858$	−1439.87	−0.0572920
$859$	−24537.3	−0.974625	−0.487313	−	0.873228i	$-0.662023\pi$
$859$	−24537.3	−0.974625	−0.487313	+	0.873228i	$0.662023\pi$
$860$	−22913.0	−0.908520
$861$	−18116.6	−0.717088
$862$	19217.3	0.759333
$863$	3745.97	0.147757	0.0738786	−	0.997267i	$-0.476462\pi$
$863$	3745.97	0.147757	0.0738786	+	0.997267i	$0.476462\pi$
$864$	−4762.62	−0.187532
$865$	−50582.6	−1.98828
$866$	−34024.7	−1.33511
$867$	14488.9	0.567552
$868$	−16302.3	−0.637483
$869$	13922.8	0.543495
$870$	−3990.44	−0.155504
$871$	−9473.90	−0.368555
$872$	7576.01	0.294216
$873$	22227.6	0.861731
$874$	570.701	0.0220872
$875$	−36872.1	−1.42458
$876$	1042.87	0.0402230
$877$	−9016.63	−0.347172	−0.173586	−	0.984819i	$-0.555535\pi$
$877$	−9016.63	−0.347172	−0.173586	+	0.984819i	$0.555535\pi$
$878$	−6174.96	−0.237352
$879$	−375.012	−0.0143900
$880$	3010.47	0.115322
$881$	27912.2	1.06741	0.533703	−	0.845672i	$-0.320800\pi$
$881$	27912.2	1.06741	0.533703	+	0.845672i	$0.320800\pi$
$882$	1160.87	0.0443182
$883$	17589.0	0.670347	0.335173	−	0.942156i	$-0.391205\pi$
$883$	17589.0	0.670347	0.335173	+	0.942156i	$0.391205\pi$
$884$	−2428.89	−0.0924124
$885$	50100.0	1.90293
$886$	8055.93	0.305467
$887$	29548.2	1.11852	0.559262	−	0.828991i	$-0.311085\pi$
$887$	29548.2	1.11852	0.559262	+	0.828991i	$0.311085\pi$
$888$	−3758.82	−0.142047
$889$	−40386.4	−1.52364
$890$	−26176.7	−0.985892
$891$	−1839.76	−0.0691741
$892$	6478.06	0.243163
$893$	−5213.87	−0.195381
$894$	9185.66	0.343640
$895$	−52954.7	−1.97774
$896$	2514.93	0.0937700
$897$	1647.06	0.0613086
$898$	6873.22	0.255415
$899$	−6015.48	−0.223167
$900$	−12152.2	−0.450081
$901$	6531.15	0.241492
$902$	5043.29	0.186168
$903$	−22106.8	−0.814693
$904$	755.805	0.0278072
$905$	40327.3	1.48124
$906$	20087.7	0.736610
$907$	30371.2	1.11186	0.555930	−	0.831229i	$-0.312362\pi$
$907$	30371.2	1.11186	0.555930	+	0.831229i	$0.312362\pi$
$908$	2200.39	0.0804213
$909$	13776.3	0.502676
$910$	−14326.5	−0.521890
$911$	−29887.2	−1.08694	−0.543472	−	0.839427i	$-0.682891\pi$
$911$	−29887.2	−1.08694	−0.543472	+	0.839427i	$0.682891\pi$
$912$	729.727	0.0264953
$913$	−5564.72	−0.201714
$914$	22315.6	0.807587
$915$	58750.8	2.12267
$916$	−17350.2	−0.625836
$917$	54813.7	1.97395
$918$	−9278.59	−0.333594
$919$	20888.4	0.749778	0.374889	−	0.927070i	$-0.377681\pi$
$919$	20888.4	0.749778	0.374889	+	0.927070i	$0.377681\pi$
$920$	−3443.66	−0.123407
$921$	11056.5	0.395574
$922$	4243.30	0.151568
$923$	−13352.6	−0.476172
$924$	2904.54	0.103412
$925$	−28792.5	−1.02345
$926$	−24679.3	−0.875824
$927$	−18159.3	−0.643397
$928$	928.000	0.0328266
$929$	16830.9	0.594406	0.297203	−	0.954814i	$-0.403946\pi$
$929$	16830.9	0.594406	0.297203	+	0.954814i	$0.403946\pi$
$930$	28542.7	1.00640
$931$	−533.972	−0.0187972
$932$	6444.65	0.226504
$933$	−16785.3	−0.588989
$934$	27192.4	0.952635
$935$	5865.04	0.205142
$936$	−2101.70	−0.0733933
$937$	−28372.7	−0.989215	−0.494607	−	0.869117i	$-0.664688\pi$
$937$	−28372.7	−0.989215	−0.494607	+	0.869117i	$0.664688\pi$
$938$	19111.0	0.665240
$939$	2383.60	0.0828391
$940$	31460.9	1.09164
$941$	−9741.12	−0.337462	−0.168731	−	0.985662i	$-0.553967\pi$
$941$	−9741.12	−0.337462	−0.168731	+	0.985662i	$0.553967\pi$
$942$	3899.44	0.134873
$943$	−5768.99	−0.199220
$944$	−11651.0	−0.401705
$945$	−54728.6	−1.88394
$946$	6154.07	0.211507
$947$	−4731.32	−0.162352	−0.0811759	−	0.996700i	$-0.525868\pi$
$947$	−4731.32	−0.162352	−0.0811759	+	0.996700i	$0.525868\pi$
$948$	−20364.0	−0.697671
$949$	1381.57	0.0472578
$950$	5589.69	0.190898
$951$	−14776.7	−0.503857
$952$	4899.61	0.166804
$953$	25650.5	0.871881	0.435940	−	0.899976i	$-0.356416\pi$
$953$	25650.5	0.871881	0.435940	+	0.899976i	$0.356416\pi$
$954$	5651.33	0.191791
$955$	−75140.1	−2.54605
$956$	−17035.5	−0.576325
$957$	1071.77	0.0362020
$958$	−37950.8	−1.27989
$959$	−2775.87	−0.0934697
$960$	−4403.24	−0.148035
$961$	13236.4	0.444307
$962$	−4979.60	−0.166891
$963$	21606.6	0.723015
$964$	−20574.4	−0.687404
$965$	81121.1	2.70610
$966$	−3322.49	−0.110662
$967$	−11273.0	−0.374886	−0.187443	−	0.982275i	$-0.560020\pi$
$967$	−11273.0	−0.374886	−0.187443	+	0.982275i	$0.560020\pi$
$968$	9839.44	0.326706
$969$	1421.66	0.0471315
$970$	61693.3	2.04212
$971$	−26943.2	−0.890474	−0.445237	−	0.895413i	$-0.646881\pi$
$971$	−26943.2	−0.890474	−0.445237	+	0.895413i	$0.646881\pi$
$972$	−13382.9	−0.441624
$973$	−32781.4	−1.08009
$974$	4368.24	0.143704
$975$	16132.0	0.529886
$976$	−13662.9	−0.448092
$977$	−14890.2	−0.487595	−0.243798	−	0.969826i	$-0.578393\pi$
$977$	−14890.2	−0.487595	−0.243798	+	0.969826i	$0.578393\pi$
$978$	−7757.34	−0.253632
$979$	7030.63	0.229520
$980$	3222.03	0.105025
$981$	12771.4	0.415656
$982$	−30070.7	−0.977184
$983$	−28529.7	−0.925692	−0.462846	−	0.886439i	$-0.653172\pi$
$983$	−28529.7	−0.925692	−0.462846	+	0.886439i	$0.653172\pi$
$984$	−7376.52	−0.238979
$985$	−73270.5	−2.37014
$986$	1807.94	0.0583940
$987$	30353.9	0.978901
$988$	966.726	0.0311292
$989$	−7039.59	−0.226336
$990$	5074.96	0.162922
$991$	−33216.2	−1.06473	−0.532365	−	0.846515i	$-0.678697\pi$
$991$	−33216.2	−1.06473	−0.532365	+	0.846515i	$0.678697\pi$
$992$	−6637.77	−0.212449
$993$	25763.8	0.823354
$994$	26935.2	0.859489
$995$	32690.5	1.04157
$996$	8139.18	0.258935
$997$	29870.5	0.948856	0.474428	−	0.880294i	$-0.342655\pi$
$997$	29870.5	0.948856	0.474428	+	0.880294i	$0.342655\pi$
$998$	−11111.0	−0.352418
$999$	−19022.5	−0.602449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.4.a.d.1.7	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.4.a.d.1.7	✓	19	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.67612 q^{3} +4.00000 q^{4} +18.7156 q^{5} +7.35224 q^{6} -19.6479 q^{7} -8.00000 q^{8} -13.4861 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.67612 q^{3} +4.00000 q^{4} +18.7156 q^{5} +7.35224 q^{6} -19.6479 q^{7} -8.00000 q^{8} -13.4861 q^{9} -37.4311 q^{10} +10.0534 q^{11} -14.7045 q^{12} -19.4802 q^{13} +39.2958 q^{14} -68.8006 q^{15} +16.0000 q^{16} +31.1714 q^{17} +26.9723 q^{18} -12.4065 q^{19} +74.8622 q^{20} +72.2280 q^{21} -20.1068 q^{22} +23.0000 q^{23} +29.4090 q^{24} +225.272 q^{25} +38.9603 q^{26} +148.832 q^{27} -78.5916 q^{28} -29.0000 q^{29} +137.601 q^{30} +207.430 q^{31} -32.0000 q^{32} -36.9575 q^{33} -62.3427 q^{34} -367.721 q^{35} -53.9445 q^{36} -127.812 q^{37} +24.8131 q^{38} +71.6114 q^{39} -149.724 q^{40} -250.826 q^{41} -144.456 q^{42} -306.069 q^{43} +40.2135 q^{44} -252.400 q^{45} -46.0000 q^{46} +420.251 q^{47} -58.8179 q^{48} +43.0395 q^{49} -450.544 q^{50} -114.590 q^{51} -77.9206 q^{52} +209.524 q^{53} -297.664 q^{54} +188.155 q^{55} +157.183 q^{56} +45.6080 q^{57} +58.0000 q^{58} -728.190 q^{59} -275.203 q^{60} -853.929 q^{61} -414.861 q^{62} +264.974 q^{63} +64.0000 q^{64} -364.582 q^{65} +73.9149 q^{66} +486.336 q^{67} +124.685 q^{68} -84.5508 q^{69} +735.442 q^{70} +685.447 q^{71} +107.889 q^{72} -70.9219 q^{73} +255.624 q^{74} -828.127 q^{75} -49.6262 q^{76} -197.528 q^{77} -143.223 q^{78} +1384.88 q^{79} +299.449 q^{80} -182.999 q^{81} +501.651 q^{82} -553.517 q^{83} +288.912 q^{84} +583.389 q^{85} +612.139 q^{86} +106.608 q^{87} -80.4271 q^{88} +699.330 q^{89} +504.801 q^{90} +382.744 q^{91} +92.0000 q^{92} -762.539 q^{93} -840.503 q^{94} -232.195 q^{95} +117.636 q^{96} -1648.18 q^{97} -86.0791 q^{98} -135.581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 38 q^{2} - 5 q^{3} + 76 q^{4} + 10 q^{6} - 13 q^{7} - 152 q^{8} + 166 q^{9}+O(q^{10}) \) 19 * q - 38 * q^2 - 5 * q^3 + 76 * q^4 + 10 * q^6 - 13 * q^7 - 152 * q^8 + 166 * q^9	\( 19 q - 38 q^{2} - 5 q^{3} + 76 q^{4} + 10 q^{6} - 13 q^{7} - 152 q^{8} + 166 q^{9} + 30 q^{11} - 20 q^{12} - 151 q^{13} + 26 q^{14} + 2 q^{15} + 304 q^{16} - 56 q^{17} - 332 q^{18} - 266 q^{19} - 239 q^{21} - 60 q^{22} + 437 q^{23} + 40 q^{24} + 395 q^{25} + 302 q^{26} - 68 q^{27} - 52 q^{28} - 551 q^{29} - 4 q^{30} - 622 q^{31} - 608 q^{32} - 291 q^{33} + 112 q^{34} + 21 q^{35} + 664 q^{36} - 183 q^{37} + 532 q^{38} - 212 q^{39} - 395 q^{41} + 478 q^{42} - 291 q^{43} + 120 q^{44} - 1018 q^{45} - 874 q^{46} - 241 q^{47} - 80 q^{48} + 1394 q^{49} - 790 q^{50} - 184 q^{51} - 604 q^{52} - 631 q^{53} + 136 q^{54} - 1765 q^{55} + 104 q^{56} + 144 q^{57} + 1102 q^{58} - 457 q^{59} + 8 q^{60} - 630 q^{61} + 1244 q^{62} + 125 q^{63} + 1216 q^{64} + 137 q^{65} + 582 q^{66} + 1421 q^{67} - 224 q^{68} - 115 q^{69} - 42 q^{70} + 983 q^{71} - 1328 q^{72} - 2532 q^{73} + 366 q^{74} - 1081 q^{75} - 1064 q^{76} - 595 q^{77} + 424 q^{78} - 4361 q^{79} - 721 q^{81} + 790 q^{82} + 1422 q^{83} - 956 q^{84} + 722 q^{85} + 582 q^{86} + 145 q^{87} - 240 q^{88} - 580 q^{89} + 2036 q^{90} - 447 q^{91} + 1748 q^{92} + 2106 q^{93} + 482 q^{94} - 310 q^{95} + 160 q^{96} - 2016 q^{97} - 2788 q^{98} - 1972 q^{99}+O(q^{100}) \) 19 * q - 38 * q^2 - 5 * q^3 + 76 * q^4 + 10 * q^6 - 13 * q^7 - 152 * q^8 + 166 * q^9 + 30 * q^11 - 20 * q^12 - 151 * q^13 + 26 * q^14 + 2 * q^15 + 304 * q^16 - 56 * q^17 - 332 * q^18 - 266 * q^19 - 239 * q^21 - 60 * q^22 + 437 * q^23 + 40 * q^24 + 395 * q^25 + 302 * q^26 - 68 * q^27 - 52 * q^28 - 551 * q^29 - 4 * q^30 - 622 * q^31 - 608 * q^32 - 291 * q^33 + 112 * q^34 + 21 * q^35 + 664 * q^36 - 183 * q^37 + 532 * q^38 - 212 * q^39 - 395 * q^41 + 478 * q^42 - 291 * q^43 + 120 * q^44 - 1018 * q^45 - 874 * q^46 - 241 * q^47 - 80 * q^48 + 1394 * q^49 - 790 * q^50 - 184 * q^51 - 604 * q^52 - 631 * q^53 + 136 * q^54 - 1765 * q^55 + 104 * q^56 + 144 * q^57 + 1102 * q^58 - 457 * q^59 + 8 * q^60 - 630 * q^61 + 1244 * q^62 + 125 * q^63 + 1216 * q^64 + 137 * q^65 + 582 * q^66 + 1421 * q^67 - 224 * q^68 - 115 * q^69 - 42 * q^70 + 983 * q^71 - 1328 * q^72 - 2532 * q^73 + 366 * q^74 - 1081 * q^75 - 1064 * q^76 - 595 * q^77 + 424 * q^78 - 4361 * q^79 - 721 * q^81 + 790 * q^82 + 1422 * q^83 - 956 * q^84 + 722 * q^85 + 582 * q^86 + 145 * q^87 - 240 * q^88 - 580 * q^89 + 2036 * q^90 - 447 * q^91 + 1748 * q^92 + 2106 * q^93 + 482 * q^94 - 310 * q^95 + 160 * q^96 - 2016 * q^97 - 2788 * q^98 - 1972 * q^99

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