LMFDB - Embedded newform 1045.4.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.91078 q^{2} -7.41926 q^{3} +16.1158 q^{4} +5.00000 q^{5} +36.4343 q^{6} +29.5366 q^{7} -39.8547 q^{8} +28.0453 q^{9} +O(q^{10})$	\(q-4.91078 q^{2} -7.41926 q^{3} +16.1158 q^{4} +5.00000 q^{5} +36.4343 q^{6} +29.5366 q^{7} -39.8547 q^{8} +28.0453 q^{9} -24.5539 q^{10} -11.0000 q^{11} -119.567 q^{12} -58.0220 q^{13} -145.048 q^{14} -37.0963 q^{15} +66.7914 q^{16} +78.5868 q^{17} -137.725 q^{18} +19.0000 q^{19} +80.5788 q^{20} -219.140 q^{21} +54.0186 q^{22} +154.668 q^{23} +295.692 q^{24} +25.0000 q^{25} +284.933 q^{26} -7.75570 q^{27} +476.004 q^{28} +52.2465 q^{29} +182.172 q^{30} -168.551 q^{31} -9.16058 q^{32} +81.6118 q^{33} -385.922 q^{34} +147.683 q^{35} +451.972 q^{36} +430.950 q^{37} -93.3048 q^{38} +430.480 q^{39} -199.273 q^{40} -68.7969 q^{41} +1076.15 q^{42} +310.957 q^{43} -177.273 q^{44} +140.227 q^{45} -759.542 q^{46} -491.568 q^{47} -495.542 q^{48} +529.411 q^{49} -122.769 q^{50} -583.055 q^{51} -935.068 q^{52} +375.783 q^{53} +38.0865 q^{54} -55.0000 q^{55} -1177.17 q^{56} -140.966 q^{57} -256.571 q^{58} +176.197 q^{59} -597.834 q^{60} -45.8978 q^{61} +827.716 q^{62} +828.364 q^{63} -489.346 q^{64} -290.110 q^{65} -400.778 q^{66} -520.411 q^{67} +1266.48 q^{68} -1147.52 q^{69} -725.239 q^{70} -405.902 q^{71} -1117.74 q^{72} -762.866 q^{73} -2116.30 q^{74} -185.481 q^{75} +306.199 q^{76} -324.903 q^{77} -2113.99 q^{78} +652.742 q^{79} +333.957 q^{80} -699.683 q^{81} +337.846 q^{82} +1345.25 q^{83} -3531.60 q^{84} +392.934 q^{85} -1527.04 q^{86} -387.630 q^{87} +438.401 q^{88} +1265.33 q^{89} -688.623 q^{90} -1713.77 q^{91} +2492.59 q^{92} +1250.52 q^{93} +2413.98 q^{94} +95.0000 q^{95} +67.9647 q^{96} +254.068 q^{97} -2599.82 q^{98} -308.499 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * 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 $

$2$	−4.91078	−1.73622	−0.868111	−	0.496370i	$-0.834666\pi$
$2$	−4.91078	−1.73622	−0.868111	+	0.496370i	$0.834666\pi$
$3$	−7.41926	−1.42784	−0.713918	−	0.700229i	$-0.753081\pi$
$3$	−7.41926	−1.42784	−0.713918	+	0.700229i	$0.753081\pi$
$4$	16.1158	2.01447
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	36.4343	2.47904
$7$	29.5366	1.59483	0.797413	−	0.603434i	$-0.206201\pi$
$7$	29.5366	1.59483	0.797413	+	0.603434i	$0.206201\pi$
$8$	−39.8547	−1.76134
$9$	28.0453	1.03872
$10$	−24.5539	−0.776462
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−119.567	−2.87633
$13$	−58.0220	−1.23788	−0.618938	−	0.785439i	$-0.712437\pi$
$13$	−58.0220	−1.23788	−0.618938	+	0.785439i	$0.712437\pi$
$14$	−145.048	−2.76897
$15$	−37.0963	−0.638548
$16$	66.7914	1.04362
$17$	78.5868	1.12118	0.560591	−	0.828093i	$-0.310574\pi$
$17$	78.5868	1.12118	0.560591	+	0.828093i	$0.310574\pi$
$18$	−137.725	−1.80344
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	80.5788	0.900898
$21$	−219.140	−2.27715
$22$	54.0186	0.523491
$23$	154.668	1.40220	0.701099	−	0.713064i	$-0.252693\pi$
$23$	154.668	1.40220	0.701099	+	0.713064i	$0.252693\pi$
$24$	295.692	2.51491
$25$	25.0000	0.200000
$26$	284.933	2.14923
$27$	−7.75570	−0.0552809
$28$	476.004	3.21273
$29$	52.2465	0.334549	0.167275	−	0.985910i	$-0.446503\pi$
$29$	52.2465	0.334549	0.167275	+	0.985910i	$0.446503\pi$
$30$	182.172	1.10866
$31$	−168.551	−0.976537	−0.488268	−	0.872694i	$-0.662371\pi$
$31$	−168.551	−0.976537	−0.488268	+	0.872694i	$0.662371\pi$
$32$	−9.16058	−0.0506056
$33$	81.6118	0.430509
$34$	−385.922	−1.94662
$35$	147.683	0.713228
$36$	451.972	2.09246
$37$	430.950	1.91480	0.957401	−	0.288761i	$-0.0932434\pi$
$37$	430.950	1.91480	0.957401	+	0.288761i	$0.0932434\pi$
$38$	−93.3048	−0.398317
$39$	430.480	1.76749
$40$	−199.273	−0.787697
$41$	−68.7969	−0.262055	−0.131028	−	0.991379i	$-0.541828\pi$
$41$	−68.7969	−0.262055	−0.131028	+	0.991379i	$0.541828\pi$
$42$	1076.15	3.95364
$43$	310.957	1.10280	0.551401	−	0.834241i	$-0.314094\pi$
$43$	310.957	1.10280	0.551401	+	0.834241i	$0.314094\pi$
$44$	−177.273	−0.607385
$45$	140.227	0.464528
$46$	−759.542	−2.43453
$47$	−491.568	−1.52559	−0.762793	−	0.646643i	$-0.776172\pi$
$47$	−491.568	−1.52559	−0.762793	+	0.646643i	$0.776172\pi$
$48$	−495.542	−1.49011
$49$	529.411	1.54347
$50$	−122.769	−0.347245
$51$	−583.055	−1.60086
$52$	−935.068	−2.49366
$53$	375.783	0.973921	0.486961	−	0.873424i	$-0.338106\pi$
$53$	375.783	0.973921	0.486961	+	0.873424i	$0.338106\pi$
$54$	38.0865	0.0959800
$55$	−55.0000	−0.134840
$56$	−1177.17	−2.80904
$57$	−140.966	−0.327568
$58$	−256.571	−0.580852
$59$	176.197	0.388795	0.194398	−	0.980923i	$-0.437725\pi$
$59$	176.197	0.388795	0.194398	+	0.980923i	$0.437725\pi$
$60$	−597.834	−1.28633
$61$	−45.8978	−0.0963378	−0.0481689	−	0.998839i	$-0.515339\pi$
$61$	−45.8978	−0.0963378	−0.0481689	+	0.998839i	$0.515339\pi$
$62$	827.716	1.69549
$63$	828.364	1.65657
$64$	−489.346	−0.955753
$65$	−290.110	−0.553595
$66$	−400.778	−0.747459
$67$	−520.411	−0.948930	−0.474465	−	0.880274i	$-0.657358\pi$
$67$	−520.411	−0.948930	−0.474465	+	0.880274i	$0.657358\pi$
$68$	1266.48	2.25859
$69$	−1147.52	−2.00211
$70$	−725.239	−1.23832
$71$	−405.902	−0.678475	−0.339237	−	0.940701i	$-0.610169\pi$
$71$	−405.902	−0.678475	−0.339237	+	0.940701i	$0.610169\pi$
$72$	−1117.74	−1.82954
$73$	−762.866	−1.22311	−0.611553	−	0.791204i	$-0.709455\pi$
$73$	−762.866	−1.22311	−0.611553	+	0.791204i	$0.709455\pi$
$74$	−2116.30	−3.32452
$75$	−185.481	−0.285567
$76$	306.199	0.462151
$77$	−324.903	−0.480858
$78$	−2113.99	−3.06875
$79$	652.742	0.929610	0.464805	−	0.885413i	$-0.346124\pi$
$79$	652.742	0.929610	0.464805	+	0.885413i	$0.346124\pi$
$80$	333.957	0.466719
$81$	−699.683	−0.959784
$82$	337.846	0.454986
$83$	1345.25	1.77904	0.889519	−	0.456898i	$-0.151040\pi$
$83$	1345.25	1.77904	0.889519	+	0.456898i	$0.151040\pi$
$84$	−3531.60	−4.58725
$85$	392.934	0.501408
$86$	−1527.04	−1.91471
$87$	−387.630	−0.477682
$88$	438.401	0.531065
$89$	1265.33	1.50702	0.753509	−	0.657438i	$-0.228360\pi$
$89$	1265.33	1.50702	0.753509	+	0.657438i	$0.228360\pi$
$90$	−688.623	−0.806524
$91$	−1713.77	−1.97420
$92$	2492.59	2.82468
$93$	1250.52	1.39433
$94$	2413.98	2.64876
$95$	95.0000	0.102598
$96$	67.9647	0.0722565
$97$	254.068	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$97$	254.068	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$98$	−2599.82	−2.67981
$99$	−308.499	−0.313185
$100$	402.894	0.402894
$101$	844.012	0.831508	0.415754	−	0.909477i	$-0.363518\pi$
$101$	844.012	0.831508	0.415754	+	0.909477i	$0.363518\pi$
$102$	2863.26	2.77946
$103$	270.393	0.258666	0.129333	−	0.991601i	$-0.458716\pi$
$103$	270.393	0.258666	0.129333	+	0.991601i	$0.458716\pi$
$104$	2312.45	2.18033
$105$	−1095.70	−1.01837
$106$	−1845.39	−1.69094
$107$	1487.20	1.34368	0.671839	−	0.740698i	$-0.265505\pi$
$107$	1487.20	1.34368	0.671839	+	0.740698i	$0.265505\pi$
$108$	−124.989	−0.111362
$109$	−1916.79	−1.68436	−0.842180	−	0.539196i	$-0.818728\pi$
$109$	−1916.79	−1.68436	−0.842180	+	0.539196i	$0.818728\pi$
$110$	270.093	0.234112
$111$	−3197.33	−2.73402
$112$	1972.79	1.66439
$113$	−1526.70	−1.27097	−0.635486	−	0.772112i	$-0.719200\pi$
$113$	−1526.70	−1.27097	−0.635486	+	0.772112i	$0.719200\pi$
$114$	692.252	0.568731
$115$	773.341	0.627082
$116$	841.992	0.673939
$117$	−1627.25	−1.28580
$118$	−865.265	−0.675035
$119$	2321.19	1.78809
$120$	1478.46	1.12470
$121$	121.000	0.0909091
$122$	225.394	0.167264
$123$	510.421	0.374172
$124$	−2716.32	−1.96720
$125$	125.000	0.0894427
$126$	−4067.91	−2.87618
$127$	−1762.11	−1.23119	−0.615597	−	0.788061i	$-0.711085\pi$
$127$	−1762.11	−1.23119	−0.615597	+	0.788061i	$0.711085\pi$
$128$	2476.35	1.71001
$129$	−2307.07	−1.57462
$130$	1424.67	0.961165
$131$	−990.178	−0.660399	−0.330199	−	0.943911i	$-0.607116\pi$
$131$	−990.178	−0.660399	−0.330199	+	0.943911i	$0.607116\pi$
$132$	1315.24	0.867247
$133$	561.195	0.365878
$134$	2555.62	1.64755
$135$	−38.7785	−0.0247224
$136$	−3132.05	−1.97479
$137$	−351.475	−0.219186	−0.109593	−	0.993977i	$-0.534955\pi$
$137$	−351.475	−0.219186	−0.109593	+	0.993977i	$0.534955\pi$
$138$	5635.23	3.47611
$139$	−409.306	−0.249762	−0.124881	−	0.992172i	$-0.539855\pi$
$139$	−409.306	−0.249762	−0.124881	+	0.992172i	$0.539855\pi$
$140$	2380.02	1.43678
$141$	3647.07	2.17829
$142$	1993.30	1.17798
$143$	638.242	0.373234
$144$	1873.19	1.08402
$145$	261.233	0.149615
$146$	3746.26	2.12358
$147$	−3927.83	−2.20382
$148$	6945.08	3.85731
$149$	−881.884	−0.484877	−0.242439	−	0.970167i	$-0.577947\pi$
$149$	−881.884	−0.484877	−0.242439	+	0.970167i	$0.577947\pi$
$150$	910.858	0.495808
$151$	238.053	0.128295	0.0641473	−	0.997940i	$-0.479567\pi$
$151$	238.053	0.128295	0.0641473	+	0.997940i	$0.479567\pi$
$152$	−757.238	−0.404080
$153$	2203.99	1.16459
$154$	1595.52	0.834877
$155$	−842.755	−0.436721
$156$	6937.51	3.56054
$157$	748.865	0.380675	0.190337	−	0.981719i	$-0.439042\pi$
$157$	748.865	0.380675	0.190337	+	0.981719i	$0.439042\pi$
$158$	−3205.47	−1.61401
$159$	−2788.03	−1.39060
$160$	−45.8029	−0.0226315
$161$	4568.37	2.23626
$162$	3435.99	1.66640
$163$	−3630.61	−1.74461	−0.872305	−	0.488961i	$-0.837376\pi$
$163$	−3630.61	−1.74461	−0.872305	+	0.488961i	$0.837376\pi$
$164$	−1108.71	−0.527902
$165$	408.059	0.192529
$166$	−6606.22	−3.08881
$167$	−1756.58	−0.813940	−0.406970	−	0.913442i	$-0.633415\pi$
$167$	−1756.58	−0.813940	−0.406970	+	0.913442i	$0.633415\pi$
$168$	8733.73	4.01085
$169$	1169.55	0.532339
$170$	−1929.61	−0.870556
$171$	532.862	0.238298
$172$	5011.30	2.22156
$173$	884.826	0.388856	0.194428	−	0.980917i	$-0.437715\pi$
$173$	884.826	0.388856	0.194428	+	0.980917i	$0.437715\pi$
$174$	1903.57	0.829362
$175$	738.415	0.318965
$176$	−734.705	−0.314662
$177$	−1307.25	−0.555136
$178$	−6213.75	−2.61652
$179$	929.597	0.388164	0.194082	−	0.980985i	$-0.437827\pi$
$179$	929.597	0.388164	0.194082	+	0.980985i	$0.437827\pi$
$180$	2259.86	0.935778
$181$	−3754.06	−1.54164	−0.770820	−	0.637053i	$-0.780153\pi$
$181$	−3754.06	−1.54164	−0.770820	+	0.637053i	$0.780153\pi$
$182$	8415.95	3.42765
$183$	340.527	0.137555
$184$	−6164.25	−2.46975
$185$	2154.75	0.856326
$186$	−6141.04	−2.42088
$187$	−864.455	−0.338049
$188$	−7921.98	−3.07324
$189$	−229.077	−0.0881635
$190$	−466.524	−0.178133
$191$	534.472	0.202477	0.101238	−	0.994862i	$-0.467720\pi$
$191$	534.472	0.202477	0.101238	+	0.994862i	$0.467720\pi$
$192$	3630.58	1.36466
$193$	−1106.96	−0.412852	−0.206426	−	0.978462i	$-0.566183\pi$
$193$	−1106.96	−0.412852	−0.206426	+	0.978462i	$0.566183\pi$
$194$	−1247.67	−0.461740
$195$	2152.40	0.790444
$196$	8531.85	3.10927
$197$	3697.60	1.33728	0.668638	−	0.743588i	$-0.266878\pi$
$197$	3697.60	1.33728	0.668638	+	0.743588i	$0.266878\pi$
$198$	1514.97	0.543759
$199$	−2063.06	−0.734907	−0.367453	−	0.930042i	$-0.619770\pi$
$199$	−2063.06	−0.734907	−0.367453	+	0.930042i	$0.619770\pi$
$200$	−996.366	−0.352269
$201$	3861.06	1.35492
$202$	−4144.76	−1.44368
$203$	1543.18	0.533548
$204$	−9396.38	−3.22489
$205$	−343.984	−0.117195
$206$	−1327.84	−0.449101
$207$	4337.72	1.45649
$208$	−3875.37	−1.29187
$209$	−209.000	−0.0691714
$210$	5380.73	1.76812
$211$	−1416.04	−0.462012	−0.231006	−	0.972952i	$-0.574202\pi$
$211$	−1416.04	−0.462012	−0.231006	+	0.972952i	$0.574202\pi$
$212$	6056.03	1.96193
$213$	3011.49	0.968751
$214$	−7303.33	−2.33292
$215$	1554.78	0.493188
$216$	309.101	0.0973687
$217$	−4978.42	−1.55741
$218$	9412.94	2.92442
$219$	5659.90	1.74639
$220$	−886.366	−0.271631
$221$	−4559.76	−1.38789
$222$	15701.4	4.74687
$223$	5000.97	1.50175	0.750873	−	0.660446i	$-0.229633\pi$
$223$	5000.97	1.50175	0.750873	+	0.660446i	$0.229633\pi$
$224$	−270.573	−0.0807071
$225$	701.134	0.207743
$226$	7497.29	2.20669
$227$	4971.27	1.45355	0.726773	−	0.686878i	$-0.241019\pi$
$227$	4971.27	1.45355	0.726773	+	0.686878i	$0.241019\pi$
$228$	−2271.77	−0.659876
$229$	6480.47	1.87005	0.935026	−	0.354580i	$-0.115376\pi$
$229$	6480.47	1.87005	0.935026	+	0.354580i	$0.115376\pi$
$230$	−3797.71	−1.08875
$231$	2410.54	0.686587
$232$	−2082.27	−0.589257
$233$	−6054.55	−1.70235	−0.851174	−	0.524884i	$-0.824109\pi$
$233$	−6054.55	−1.70235	−0.851174	+	0.524884i	$0.824109\pi$
$234$	7991.05	2.23244
$235$	−2457.84	−0.682262
$236$	2839.55	0.783216
$237$	−4842.86	−1.32733
$238$	−11398.8	−3.10452
$239$	1676.62	0.453772	0.226886	−	0.973921i	$-0.427146\pi$
$239$	1676.62	0.453772	0.226886	+	0.973921i	$0.427146\pi$
$240$	−2477.71	−0.666399
$241$	3810.34	1.01845	0.509223	−	0.860634i	$-0.329933\pi$
$241$	3810.34	1.01845	0.509223	+	0.860634i	$0.329933\pi$
$242$	−594.204	−0.157838
$243$	5400.53	1.42570
$244$	−739.677	−0.194070
$245$	2647.05	0.690261
$246$	−2506.57	−0.649646
$247$	−1102.42	−0.283988
$248$	6717.54	1.72002
$249$	−9980.74	−2.54017
$250$	−613.847	−0.155292
$251$	6144.12	1.54507	0.772536	−	0.634971i	$-0.218988\pi$
$251$	6144.12	1.54507	0.772536	+	0.634971i	$0.218988\pi$
$252$	13349.7	3.33711
$253$	−1701.35	−0.422779
$254$	8653.32	2.13763
$255$	−2915.28	−0.715928
$256$	−8246.06	−2.01320
$257$	5944.10	1.44274	0.721368	−	0.692552i	$-0.243514\pi$
$257$	5944.10	1.44274	0.721368	+	0.692552i	$0.243514\pi$
$258$	11329.5	2.73389
$259$	12728.8	3.05378
$260$	−4675.34	−1.11520
$261$	1465.27	0.347502
$262$	4862.54	1.14660
$263$	−1293.59	−0.303293	−0.151646	−	0.988435i	$-0.548457\pi$
$263$	−1293.59	−0.303293	−0.151646	+	0.988435i	$0.548457\pi$
$264$	−3252.61	−0.758274
$265$	1878.92	0.435551
$266$	−2755.91	−0.635246
$267$	−9387.80	−2.15178
$268$	−8386.81	−1.91159
$269$	−2763.05	−0.626269	−0.313135	−	0.949709i	$-0.601379\pi$
$269$	−2763.05	−0.626269	−0.313135	+	0.949709i	$0.601379\pi$
$270$	190.433	0.0429236
$271$	−5393.84	−1.20905	−0.604525	−	0.796586i	$-0.706637\pi$
$271$	−5393.84	−1.20905	−0.604525	+	0.796586i	$0.706637\pi$
$272$	5248.92	1.17008
$273$	12714.9	2.81883
$274$	1726.02	0.380556
$275$	−275.000	−0.0603023
$276$	−18493.2	−4.03319
$277$	1565.26	0.339522	0.169761	−	0.985485i	$-0.445700\pi$
$277$	1565.26	0.339522	0.169761	+	0.985485i	$0.445700\pi$
$278$	2010.01	0.433642
$279$	−4727.07	−1.01435
$280$	−5885.85	−1.25624
$281$	2921.65	0.620253	0.310127	−	0.950695i	$-0.399629\pi$
$281$	2921.65	0.620253	0.310127	+	0.950695i	$0.399629\pi$
$282$	−17909.9	−3.78199
$283$	−4440.73	−0.932770	−0.466385	−	0.884582i	$-0.654444\pi$
$283$	−4440.73	−0.932770	−0.466385	+	0.884582i	$0.654444\pi$
$284$	−6541.42	−1.36677
$285$	−704.829	−0.146493
$286$	−3134.26	−0.648017
$287$	−2032.03	−0.417933
$288$	−256.912	−0.0525648
$289$	1262.88	0.257049
$290$	−1282.86	−0.259765
$291$	−1884.99	−0.379726
$292$	−12294.2	−2.46391
$293$	4552.87	0.907787	0.453893	−	0.891056i	$-0.350035\pi$
$293$	4552.87	0.907787	0.453893	+	0.891056i	$0.350035\pi$
$294$	19288.7	3.82633
$295$	880.986	0.173875
$296$	−17175.3	−3.37262
$297$	85.3127	0.0166678
$298$	4330.74	0.841855
$299$	−8974.16	−1.73575
$300$	−2989.17	−0.575266
$301$	9184.60	1.75878
$302$	−1169.03	−0.222748
$303$	−6261.94	−1.18726
$304$	1269.04	0.239422
$305$	−229.489	−0.0430836
$306$	−10823.3	−2.02199
$307$	7691.31	1.42986	0.714929	−	0.699197i	$-0.246459\pi$
$307$	7691.31	1.42986	0.714929	+	0.699197i	$0.246459\pi$
$308$	−5236.05	−0.968674
$309$	−2006.11	−0.369332
$310$	4138.58	0.758244
$311$	2570.35	0.468653	0.234327	−	0.972158i	$-0.424711\pi$
$311$	2570.35	0.468653	0.234327	+	0.972158i	$0.424711\pi$
$312$	−17156.6	−3.11315
$313$	6420.39	1.15943	0.579716	−	0.814819i	$-0.303164\pi$
$313$	6420.39	1.15943	0.579716	+	0.814819i	$0.303164\pi$
$314$	−3677.51	−0.660936
$315$	4141.82	0.740842
$316$	10519.4	1.87267
$317$	−6188.17	−1.09641	−0.548205	−	0.836344i	$-0.684689\pi$
$317$	−6188.17	−1.09641	−0.548205	+	0.836344i	$0.684689\pi$
$318$	13691.4	2.41439
$319$	−574.712	−0.100870
$320$	−2446.73	−0.427426
$321$	−11033.9	−1.91855
$322$	−22434.3	−3.88265
$323$	1493.15	0.257217
$324$	−11275.9	−1.93346
$325$	−1450.55	−0.247575
$326$	17829.1	3.02903
$327$	14221.2	2.40499
$328$	2741.88	0.461569
$329$	−14519.2	−2.43304
$330$	−2003.89	−0.334274
$331$	6547.56	1.08727	0.543635	−	0.839322i	$-0.317048\pi$
$331$	6547.56	1.08727	0.543635	+	0.839322i	$0.317048\pi$
$332$	21679.7	3.58382
$333$	12086.1	1.98894
$334$	8626.16	1.41318
$335$	−2602.05	−0.424374
$336$	−14636.6	−2.37647
$337$	−11893.6	−1.92250	−0.961252	−	0.275670i	$-0.911100\pi$
$337$	−11893.6	−1.92250	−0.961252	+	0.275670i	$0.911100\pi$
$338$	−5743.40	−0.924259
$339$	11327.0	1.81474
$340$	6332.42	1.01007
$341$	1854.06	0.294437
$342$	−2616.77	−0.413738
$343$	5505.93	0.866742
$344$	−12393.1	−1.94241
$345$	−5737.62	−0.895371
$346$	−4345.19	−0.675141
$347$	2153.86	0.333214	0.166607	−	0.986023i	$-0.446719\pi$
$347$	2153.86	0.333214	0.166607	+	0.986023i	$0.446719\pi$
$348$	−6246.95	−0.962275
$349$	−6073.33	−0.931512	−0.465756	−	0.884913i	$-0.654218\pi$
$349$	−6073.33	−0.931512	−0.465756	+	0.884913i	$0.654218\pi$
$350$	−3626.19	−0.553795
$351$	450.001	0.0684310
$352$	100.766	0.0152582
$353$	−2032.45	−0.306449	−0.153225	−	0.988191i	$-0.548966\pi$
$353$	−2032.45	−0.306449	−0.153225	+	0.988191i	$0.548966\pi$
$354$	6419.63	0.963840
$355$	−2029.51	−0.303423
$356$	20391.7	3.03584
$357$	−17221.5	−2.55310
$358$	−4565.04	−0.673939
$359$	−10160.0	−1.49367	−0.746834	−	0.665011i	$-0.768427\pi$
$359$	−10160.0	−1.49367	−0.746834	+	0.665011i	$0.768427\pi$
$360$	−5588.69	−0.818194
$361$	361.000	0.0526316
$362$	18435.3	2.67663
$363$	−897.730	−0.129803
$364$	−27618.7	−3.97696
$365$	−3814.33	−0.546989
$366$	−1672.25	−0.238826
$367$	−2985.41	−0.424624	−0.212312	−	0.977202i	$-0.568099\pi$
$367$	−2985.41	−0.424624	−0.212312	+	0.977202i	$0.568099\pi$
$368$	10330.5	1.46336
$369$	−1929.43	−0.272201
$370$	−10581.5	−1.48677
$371$	11099.4	1.55324
$372$	20153.1	2.80884
$373$	−6078.39	−0.843773	−0.421886	−	0.906649i	$-0.638632\pi$
$373$	−6078.39	−0.843773	−0.421886	+	0.906649i	$0.638632\pi$
$374$	4245.15	0.586928
$375$	−927.407	−0.127710
$376$	19591.3	2.68708
$377$	−3031.45	−0.414131
$378$	1124.95	0.153071
$379$	6265.83	0.849219	0.424609	−	0.905377i	$-0.360411\pi$
$379$	6265.83	0.849219	0.424609	+	0.905377i	$0.360411\pi$
$380$	1531.00	0.206680
$381$	13073.5	1.75794
$382$	−2624.67	−0.351544
$383$	14422.9	1.92421	0.962106	−	0.272676i	$-0.0879086\pi$
$383$	14422.9	1.92421	0.962106	+	0.272676i	$0.0879086\pi$
$384$	−18372.7	−2.44161
$385$	−1624.51	−0.215046
$386$	5436.01	0.716802
$387$	8720.89	1.14550
$388$	4094.49	0.535738
$389$	−9777.04	−1.27433	−0.637167	−	0.770726i	$-0.719894\pi$
$389$	−9777.04	−1.27433	−0.637167	+	0.770726i	$0.719894\pi$
$390$	−10570.0	−1.37239
$391$	12154.9	1.57212
$392$	−21099.5	−2.71858
$393$	7346.38	0.942941
$394$	−18158.1	−2.32181
$395$	3263.71	0.415734
$396$	−4971.69	−0.630901
$397$	6467.82	0.817659	0.408830	−	0.912611i	$-0.365937\pi$
$397$	6467.82	0.817659	0.408830	+	0.912611i	$0.365937\pi$
$398$	10131.2	1.27596
$399$	−4163.65	−0.522414
$400$	1669.79	0.208723
$401$	−8442.10	−1.05132	−0.525659	−	0.850696i	$-0.676181\pi$
$401$	−8442.10	−1.05132	−0.525659	+	0.850696i	$0.676181\pi$
$402$	−18960.8	−2.35244
$403$	9779.66	1.20883
$404$	13601.9	1.67505
$405$	−3498.41	−0.429229
$406$	−7578.24	−0.926359
$407$	−4740.45	−0.577335
$408$	23237.5	2.81967
$409$	6326.92	0.764905	0.382453	−	0.923975i	$-0.375080\pi$
$409$	6326.92	0.764905	0.382453	+	0.923975i	$0.375080\pi$
$410$	1689.23	0.203476
$411$	2607.68	0.312962
$412$	4357.58	0.521074
$413$	5204.27	0.620061
$414$	−21301.6	−2.52878
$415$	6726.24	0.795610
$416$	531.515	0.0626435
$417$	3036.75	0.356619
$418$	1026.35	0.120097
$419$	2750.29	0.320669	0.160334	−	0.987063i	$-0.448743\pi$
$419$	2750.29	0.320669	0.160334	+	0.987063i	$0.448743\pi$
$420$	−17658.0	−2.05148
$421$	6452.09	0.746925	0.373463	−	0.927645i	$-0.378170\pi$
$421$	6452.09	0.746925	0.373463	+	0.927645i	$0.378170\pi$
$422$	6953.88	0.802155
$423$	−13786.2	−1.58465
$424$	−14976.7	−1.71541
$425$	1964.67	0.224236
$426$	−14788.8	−1.68197
$427$	−1355.66	−0.153642
$428$	23967.4	2.70680
$429$	−4735.28	−0.532917
$430$	−7635.20	−0.856283
$431$	6343.22	0.708914	0.354457	−	0.935072i	$-0.384666\pi$
$431$	6343.22	0.708914	0.354457	+	0.935072i	$0.384666\pi$
$432$	−518.014	−0.0576921
$433$	13669.3	1.51710	0.758550	−	0.651615i	$-0.225908\pi$
$433$	13669.3	1.51710	0.758550	+	0.651615i	$0.225908\pi$
$434$	24447.9	2.70400
$435$	−1938.15	−0.213626
$436$	−30890.5	−3.39309
$437$	2938.70	0.321686
$438$	−27794.5	−3.03213
$439$	−4291.06	−0.466517	−0.233258	−	0.972415i	$-0.574939\pi$
$439$	−4291.06	−0.466517	−0.233258	+	0.972415i	$0.574939\pi$
$440$	2192.01	0.237500
$441$	14847.5	1.60323
$442$	22392.0	2.40968
$443$	−425.303	−0.0456134	−0.0228067	−	0.999740i	$-0.507260\pi$
$443$	−425.303	−0.0456134	−0.0228067	+	0.999740i	$0.507260\pi$
$444$	−51527.3	−5.50761
$445$	6326.64	0.673959
$446$	−24558.6	−2.60737
$447$	6542.92	0.692326
$448$	−14453.6	−1.52426
$449$	−12510.0	−1.31488	−0.657440	−	0.753507i	$-0.728361\pi$
$449$	−12510.0	−1.31488	−0.657440	+	0.753507i	$0.728361\pi$
$450$	−3443.11	−0.360689
$451$	756.765	0.0790126
$452$	−24603.9	−2.56033
$453$	−1766.18	−0.183184
$454$	−24412.8	−2.52368
$455$	−8568.86	−0.882889
$456$	5618.15	0.576960
$457$	8697.95	0.890313	0.445157	−	0.895453i	$-0.353148\pi$
$457$	8697.95	0.890313	0.445157	+	0.895453i	$0.353148\pi$
$458$	−31824.2	−3.24683
$459$	−609.496	−0.0619800
$460$	12463.0	1.26324
$461$	4637.71	0.468546	0.234273	−	0.972171i	$-0.424729\pi$
$461$	4637.71	0.468546	0.234273	+	0.972171i	$0.424729\pi$
$462$	−11837.6	−1.19207
$463$	5117.63	0.513685	0.256843	−	0.966453i	$-0.417318\pi$
$463$	5117.63	0.513685	0.256843	+	0.966453i	$0.417318\pi$
$464$	3489.62	0.349141
$465$	6252.61	0.623565
$466$	29732.6	2.95565
$467$	14250.5	1.41206	0.706032	−	0.708180i	$-0.250483\pi$
$467$	14250.5	1.41206	0.706032	+	0.708180i	$0.250483\pi$
$468$	−26224.3	−2.59021
$469$	−15371.2	−1.51338
$470$	12069.9	1.18456
$471$	−5556.02	−0.543541
$472$	−7022.28	−0.684802
$473$	−3420.52	−0.332507
$474$	23782.2	2.30454
$475$	475.000	0.0458831
$476$	37407.7	3.60205
$477$	10539.0	1.01163
$478$	−8233.50	−0.787849
$479$	5482.95	0.523011	0.261506	−	0.965202i	$-0.415781\pi$
$479$	5482.95	0.523011	0.261506	+	0.965202i	$0.415781\pi$
$480$	339.824	0.0323141
$481$	−25004.5	−2.37029
$482$	−18711.7	−1.76825
$483$	−33893.9	−3.19302
$484$	1950.01	0.183134
$485$	1270.34	0.118934
$486$	−26520.8	−2.47533
$487$	−512.001	−0.0476406	−0.0238203	−	0.999716i	$-0.507583\pi$
$487$	−512.001	−0.0476406	−0.0238203	+	0.999716i	$0.507583\pi$
$488$	1829.24	0.169684
$489$	26936.4	2.49102
$490$	−12999.1	−1.19845
$491$	15543.7	1.42867	0.714337	−	0.699802i	$-0.246728\pi$
$491$	15543.7	1.42867	0.714337	+	0.699802i	$0.246728\pi$
$492$	8225.83	0.753758
$493$	4105.89	0.375091
$494$	5413.73	0.493067
$495$	−1542.49	−0.140061
$496$	−11257.8	−1.01913
$497$	−11989.0	−1.08205
$498$	49013.2	4.41031
$499$	13388.9	1.20114	0.600570	−	0.799572i	$-0.294941\pi$
$499$	13388.9	1.20114	0.600570	+	0.799572i	$0.294941\pi$
$500$	2014.47	0.180180
$501$	13032.5	1.16217
$502$	−30172.4	−2.68259
$503$	−3240.66	−0.287264	−0.143632	−	0.989631i	$-0.545878\pi$
$503$	−3240.66	−0.287264	−0.143632	+	0.989631i	$0.545878\pi$
$504$	−33014.2	−2.91779
$505$	4220.06	0.371862
$506$	8354.96	0.734038
$507$	−8677.18	−0.760093
$508$	−28397.7	−2.48020
$509$	15488.6	1.34877	0.674383	−	0.738382i	$-0.264410\pi$
$509$	15488.6	1.34877	0.674383	+	0.738382i	$0.264410\pi$
$510$	14316.3	1.24301
$511$	−22532.5	−1.95064
$512$	20683.7	1.78535
$513$	−147.358	−0.0126823
$514$	−29190.2	−2.50491
$515$	1351.96	0.115679
$516$	−37180.1	−3.17202
$517$	5407.24	0.459981
$518$	−62508.3	−5.30204
$519$	−6564.75	−0.555223
$520$	11562.2	0.975072
$521$	4881.48	0.410483	0.205241	−	0.978711i	$-0.434202\pi$
$521$	4881.48	0.410483	0.205241	+	0.978711i	$0.434202\pi$
$522$	−7195.63	−0.603341
$523$	15112.0	1.26348	0.631740	−	0.775180i	$-0.282341\pi$
$523$	15112.0	1.26348	0.631740	+	0.775180i	$0.282341\pi$
$524$	−15957.5	−1.33035
$525$	−5478.49	−0.455430
$526$	6352.52	0.526584
$527$	−13245.9	−1.09488
$528$	5450.97	0.449286
$529$	11755.3	0.966160
$530$	−9226.95	−0.756213
$531$	4941.51	0.403848
$532$	9044.08	0.737050
$533$	3991.73	0.324392
$534$	46101.4	3.73596
$535$	7436.02	0.600911
$536$	20740.8	1.67139
$537$	−6896.92	−0.554234
$538$	13568.7	1.08734
$539$	−5823.52	−0.465374
$540$	−624.945	−0.0498025
$541$	−23194.0	−1.84323	−0.921617	−	0.388102i	$-0.873131\pi$
$541$	−23194.0	−1.84323	−0.921617	+	0.388102i	$0.873131\pi$
$542$	26487.9	2.09918
$543$	27852.3	2.20121
$544$	−719.901	−0.0567380
$545$	−9583.96	−0.753269
$546$	−62440.1	−4.89412
$547$	15259.8	1.19280	0.596402	−	0.802686i	$-0.296596\pi$
$547$	15259.8	1.19280	0.596402	+	0.802686i	$0.296596\pi$
$548$	−5664.28	−0.441544
$549$	−1287.22	−0.100068
$550$	1350.46	0.104698
$551$	992.684	0.0767509
$552$	45734.1	3.52640
$553$	19279.8	1.48257
$554$	−7686.66	−0.589485
$555$	−15986.6	−1.22269
$556$	−6596.28	−0.503138
$557$	−10708.1	−0.814572	−0.407286	−	0.913301i	$-0.633525\pi$
$557$	−10708.1	−0.814572	−0.407286	+	0.913301i	$0.633525\pi$
$558$	23213.6	1.76113
$559$	−18042.3	−1.36513
$560$	9863.95	0.744336
$561$	6413.61	0.482679
$562$	−14347.6	−1.07690
$563$	−7838.99	−0.586810	−0.293405	−	0.955988i	$-0.594788\pi$
$563$	−7838.99	−0.586810	−0.293405	+	0.955988i	$0.594788\pi$
$564$	58775.2	4.38809
$565$	−7633.50	−0.568396
$566$	21807.4	1.61950
$567$	−20666.3	−1.53069
$568$	16177.1	1.19503
$569$	8985.97	0.662059	0.331029	−	0.943620i	$-0.392604\pi$
$569$	8985.97	0.662059	0.331029	+	0.943620i	$0.392604\pi$
$570$	3461.26	0.254344
$571$	10754.0	0.788162	0.394081	−	0.919076i	$-0.371063\pi$
$571$	10754.0	0.788162	0.394081	+	0.919076i	$0.371063\pi$
$572$	10285.7	0.751868
$573$	−3965.38	−0.289103
$574$	9978.83	0.725624
$575$	3866.71	0.280440
$576$	−13723.9	−0.992757
$577$	−3766.66	−0.271764	−0.135882	−	0.990725i	$-0.543387\pi$
$577$	−3766.66	−0.271764	−0.135882	+	0.990725i	$0.543387\pi$
$578$	−6201.74	−0.446295
$579$	8212.78	0.589485
$580$	4209.96	0.301395
$581$	39734.0	2.83726
$582$	9256.78	0.659289
$583$	−4133.62	−0.293648
$584$	30403.7	2.15431
$585$	−8136.23	−0.575029
$586$	−22358.1	−1.57612
$587$	−6693.33	−0.470636	−0.235318	−	0.971918i	$-0.575613\pi$
$587$	−6693.33	−0.470636	−0.235318	+	0.971918i	$0.575613\pi$
$588$	−63300.0	−4.43953
$589$	−3202.47	−0.224033
$590$	−4326.33	−0.301885
$591$	−27433.5	−1.90941
$592$	28783.7	1.99832
$593$	19700.3	1.36424	0.682120	−	0.731240i	$-0.261058\pi$
$593$	19700.3	1.36424	0.682120	+	0.731240i	$0.261058\pi$
$594$	−418.952	−0.0289391
$595$	11605.9	0.799658
$596$	−14212.2	−0.976770
$597$	15306.4	1.04933
$598$	44070.1	3.01365
$599$	25833.1	1.76212	0.881061	−	0.473003i	$-0.156830\pi$
$599$	25833.1	1.76212	0.881061	+	0.473003i	$0.156830\pi$
$600$	7392.30	0.502982
$601$	−2666.51	−0.180981	−0.0904903	−	0.995897i	$-0.528843\pi$
$601$	−2666.51	−0.180981	−0.0904903	+	0.995897i	$0.528843\pi$
$602$	−45103.5	−3.05363
$603$	−14595.1	−0.985669
$604$	3836.41	0.258446
$605$	605.000	0.0406558
$606$	30751.0	2.06134
$607$	−21766.2	−1.45546	−0.727729	−	0.685865i	$-0.759424\pi$
$607$	−21766.2	−1.45546	−0.727729	+	0.685865i	$0.759424\pi$
$608$	−174.051	−0.0116097
$609$	−11449.3	−0.761820
$610$	1126.97	0.0748027
$611$	28521.7	1.88849
$612$	35519.0	2.34603
$613$	−11855.3	−0.781126	−0.390563	−	0.920576i	$-0.627720\pi$
$613$	−11855.3	−0.781126	−0.390563	+	0.920576i	$0.627720\pi$
$614$	−37770.3	−2.48255
$615$	2552.11	0.167335
$616$	12948.9	0.846957
$617$	19483.5	1.27128	0.635638	−	0.771987i	$-0.280737\pi$
$617$	19483.5	1.27128	0.635638	+	0.771987i	$0.280737\pi$
$618$	9851.57	0.641243
$619$	−6612.23	−0.429351	−0.214675	−	0.976685i	$-0.568869\pi$
$619$	−6612.23	−0.429351	−0.214675	+	0.976685i	$0.568869\pi$
$620$	−13581.6	−0.879760
$621$	−1199.56	−0.0775148
$622$	−12622.4	−0.813687
$623$	37373.5	2.40343
$624$	28752.4	1.84458
$625$	625.000	0.0400000
$626$	−31529.1	−2.01303
$627$	1550.62	0.0987655
$628$	12068.5	0.766857
$629$	33866.9	2.14684
$630$	−20339.6	−1.28627
$631$	−3662.93	−0.231092	−0.115546	−	0.993302i	$-0.536862\pi$
$631$	−3662.93	−0.231092	−0.115546	+	0.993302i	$0.536862\pi$
$632$	−26014.8	−1.63736
$633$	10506.0	0.659677
$634$	30388.7	1.90361
$635$	−8810.53	−0.550607
$636$	−44931.2	−2.80132
$637$	−30717.4	−1.91063
$638$	2822.28	0.175134
$639$	−11383.7	−0.704743
$640$	12381.8	0.764738
$641$	−10211.4	−0.629217	−0.314608	−	0.949222i	$-0.601873\pi$
$641$	−10211.4	−0.629217	−0.314608	+	0.949222i	$0.601873\pi$
$642$	54185.3	3.33103
$643$	18114.7	1.11100	0.555501	−	0.831516i	$-0.312527\pi$
$643$	18114.7	1.11100	0.555501	+	0.831516i	$0.312527\pi$
$644$	73622.8	4.50488
$645$	−11535.3	−0.704191
$646$	−7332.52	−0.446586
$647$	10291.6	0.625356	0.312678	−	0.949859i	$-0.398774\pi$
$647$	10291.6	0.625356	0.312678	+	0.949859i	$0.398774\pi$
$648$	27885.6	1.69051
$649$	−1938.17	−0.117226
$650$	7123.33	0.429846
$651$	36936.2	2.22372
$652$	−58510.1	−3.51446
$653$	−4865.51	−0.291581	−0.145790	−	0.989316i	$-0.546572\pi$
$653$	−4865.51	−0.291581	−0.145790	+	0.989316i	$0.546572\pi$
$654$	−69837.0	−4.17560
$655$	−4950.89	−0.295339
$656$	−4595.04	−0.273485
$657$	−21394.8	−1.27046
$658$	71300.8	4.22431
$659$	−1746.17	−0.103219	−0.0516093	−	0.998667i	$-0.516435\pi$
$659$	−1746.17	−0.103219	−0.0516093	+	0.998667i	$0.516435\pi$
$660$	6576.18	0.387844
$661$	18996.6	1.11782	0.558911	−	0.829227i	$-0.311219\pi$
$661$	18996.6	1.11782	0.558911	+	0.829227i	$0.311219\pi$
$662$	−32153.6	−1.88774
$663$	33830.0	1.98167
$664$	−53614.4	−3.13350
$665$	2805.98	0.163626
$666$	−59352.3	−3.45324
$667$	8080.88	0.469105
$668$	−28308.6	−1.63966
$669$	−37103.4	−2.14425
$670$	12778.1	0.736809
$671$	504.876	0.0290470
$672$	2007.45	0.115237
$673$	−4527.02	−0.259292	−0.129646	−	0.991560i	$-0.541384\pi$
$673$	−4527.02	−0.259292	−0.129646	+	0.991560i	$0.541384\pi$
$674$	58406.7	3.33790
$675$	−193.893	−0.0110562
$676$	18848.2	1.07238
$677$	−22199.3	−1.26025	−0.630124	−	0.776495i	$-0.716996\pi$
$677$	−22199.3	−1.26025	−0.630124	+	0.776495i	$0.716996\pi$
$678$	−55624.3	−3.15079
$679$	7504.30	0.424136
$680$	−15660.2	−0.883152
$681$	−36883.1	−2.07542
$682$	−9104.88	−0.511208
$683$	24173.5	1.35428	0.677141	−	0.735853i	$-0.263219\pi$
$683$	24173.5	1.35428	0.677141	+	0.735853i	$0.263219\pi$
$684$	8587.46	0.480044
$685$	−1757.37	−0.0980231
$686$	−27038.4	−1.50486
$687$	−48080.3	−2.67013
$688$	20769.2	1.15090
$689$	−21803.7	−1.20559
$690$	28176.2	1.55456
$691$	6547.71	0.360473	0.180236	−	0.983623i	$-0.442314\pi$
$691$	6547.71	0.360473	0.180236	+	0.983623i	$0.442314\pi$
$692$	14259.6	0.783338
$693$	−9112.01	−0.499475
$694$	−10577.1	−0.578533
$695$	−2046.53	−0.111697
$696$	15448.9	0.841362
$697$	−5406.52	−0.293812
$698$	29824.8	1.61731
$699$	44920.3	2.43067
$700$	11900.1	0.642546
$701$	11.9468	0.000643689 0	0.000321845	−	1.00000i	$-0.499898\pi$
$701$	11.9468	0.000643689 0	0.000321845		1.00000i	$0.499898\pi$
$702$	−2209.86	−0.118811
$703$	8188.04	0.439286
$704$	5382.80	0.288170
$705$	18235.3	0.974159
$706$	9980.93	0.532064
$707$	24929.2	1.32611
$708$	−21067.3	−1.11830
$709$	16212.7	0.858789	0.429394	−	0.903117i	$-0.358727\pi$
$709$	16212.7	0.858789	0.429394	+	0.903117i	$0.358727\pi$
$710$	9966.48	0.526810
$711$	18306.4	0.965601
$712$	−50429.3	−2.65438
$713$	−26069.5	−1.36930
$714$	84570.8	4.43275
$715$	3191.21	0.166915
$716$	14981.1	0.781944
$717$	−12439.3	−0.647912
$718$	49893.7	2.59334
$719$	22244.3	1.15379	0.576893	−	0.816820i	$-0.304265\pi$
$719$	22244.3	1.15379	0.576893	+	0.816820i	$0.304265\pi$
$720$	9365.94	0.484789
$721$	7986.48	0.412527
$722$	−1772.79	−0.0913801
$723$	−28269.9	−1.45418
$724$	−60499.4	−3.10559
$725$	1306.16	0.0669099
$726$	4408.55	0.225367
$727$	−15092.4	−0.769938	−0.384969	−	0.922930i	$-0.625788\pi$
$727$	−15092.4	−0.769938	−0.384969	+	0.922930i	$0.625788\pi$
$728$	68301.8	3.47724
$729$	−21176.5	−1.07588
$730$	18731.3	0.949695
$731$	24437.1	1.23644
$732$	5487.85	0.277100
$733$	−22072.1	−1.11221	−0.556106	−	0.831112i	$-0.687705\pi$
$733$	−22072.1	−1.11221	−0.556106	+	0.831112i	$0.687705\pi$
$734$	14660.7	0.737242
$735$	−19639.2	−0.985580
$736$	−1416.85	−0.0709590
$737$	5724.52	0.286113
$738$	9475.01	0.472602
$739$	32110.5	1.59838	0.799192	−	0.601076i	$-0.205261\pi$
$739$	32110.5	1.59838	0.799192	+	0.601076i	$0.205261\pi$
$740$	34725.4	1.72504
$741$	8179.12	0.405489
$742$	−54506.5	−2.69676
$743$	−10963.7	−0.541343	−0.270672	−	0.962672i	$-0.587246\pi$
$743$	−10963.7	−0.541343	−0.270672	+	0.962672i	$0.587246\pi$
$744$	−49839.1	−2.45590
$745$	−4409.42	−0.216844
$746$	29849.6	1.46498
$747$	37727.9	1.84792
$748$	−13931.3	−0.680989
$749$	43927.0	2.14293
$750$	4554.29	0.221732
$751$	17845.3	0.867089	0.433544	−	0.901132i	$-0.357263\pi$
$751$	17845.3	0.867089	0.433544	+	0.901132i	$0.357263\pi$
$752$	−32832.5	−1.59212
$753$	−45584.8	−2.20611
$754$	14886.8	0.719024
$755$	1190.27	0.0573751
$756$	−3691.75	−0.177603
$757$	−467.526	−0.0224472	−0.0112236	−	0.999937i	$-0.503573\pi$
$757$	−467.526	−0.0224472	−0.0112236	+	0.999937i	$0.503573\pi$
$758$	−30770.1	−1.47443
$759$	12622.8	0.603659
$760$	−3786.19	−0.180710
$761$	9393.37	0.447450	0.223725	−	0.974652i	$-0.428178\pi$
$761$	9393.37	0.447450	0.223725	+	0.974652i	$0.428178\pi$
$762$	−64201.2	−3.05218
$763$	−56615.5	−2.68626
$764$	8613.42	0.407883
$765$	11020.0	0.520821
$766$	−70827.4	−3.34086
$767$	−10223.3	−0.481281
$768$	61179.6	2.87452
$769$	−8741.12	−0.409900	−0.204950	−	0.978772i	$-0.565703\pi$
$769$	−8741.12	−0.409900	−0.204950	+	0.978772i	$0.565703\pi$
$770$	7977.62	0.373368
$771$	−44100.8	−2.05999
$772$	−17839.4	−0.831677
$773$	−15358.9	−0.714645	−0.357323	−	0.933981i	$-0.616310\pi$
$773$	−15358.9	−0.714645	−0.357323	+	0.933981i	$0.616310\pi$
$774$	−42826.4	−1.98884
$775$	−4213.77	−0.195307
$776$	−10125.8	−0.468421
$777$	−94438.1	−4.36029
$778$	48012.9	2.21253
$779$	−1307.14	−0.0601196
$780$	34687.5	1.59232
$781$	4464.92	0.204568
$782$	−59689.9	−2.72955
$783$	−405.208	−0.0184942
$784$	35360.1	1.61079
$785$	3744.33	0.170243
$786$	−36076.4	−1.63716
$787$	29561.1	1.33893	0.669467	−	0.742842i	$-0.266523\pi$
$787$	29561.1	1.33893	0.669467	+	0.742842i	$0.266523\pi$
$788$	59589.6	2.69390
$789$	9597.45	0.433052
$790$	−16027.4	−0.721807
$791$	−45093.5	−2.02698
$792$	12295.1	0.551626
$793$	2663.08	0.119254
$794$	−31762.0	−1.41964
$795$	−13940.2	−0.621895
$796$	−33247.8	−1.48045
$797$	−19952.0	−0.886747	−0.443374	−	0.896337i	$-0.646218\pi$
$797$	−19952.0	−0.886747	−0.443374	+	0.896337i	$0.646218\pi$
$798$	20446.8	0.907027
$799$	−38630.7	−1.71046
$800$	−229.015	−0.0101211
$801$	35486.6	1.56536
$802$	41457.3	1.82532
$803$	8391.52	0.368780
$804$	62223.9	2.72944
$805$	22841.9	1.00009
$806$	−48025.7	−2.09880
$807$	20499.8	0.894210
$808$	−33637.8	−1.46457
$809$	−6328.01	−0.275007	−0.137504	−	0.990501i	$-0.543908\pi$
$809$	−6328.01	−0.275007	−0.137504	+	0.990501i	$0.543908\pi$
$810$	17179.9	0.745236
$811$	−18769.4	−0.812679	−0.406340	−	0.913722i	$-0.633195\pi$
$811$	−18769.4	−0.812679	−0.406340	+	0.913722i	$0.633195\pi$
$812$	24869.6	1.07482
$813$	40018.3	1.72632
$814$	23279.3	1.00238
$815$	−18153.1	−0.780214
$816$	−38943.1	−1.67069
$817$	5908.18	0.253000
$818$	−31070.1	−1.32805
$819$	−48063.3	−2.05063
$820$	−5543.57	−0.236085
$821$	17443.4	0.741509	0.370754	−	0.928731i	$-0.379099\pi$
$821$	17443.4	0.741509	0.370754	+	0.928731i	$0.379099\pi$
$822$	−12805.8	−0.543372
$823$	26048.6	1.10328	0.551639	−	0.834083i	$-0.314002\pi$
$823$	26048.6	1.10328	0.551639	+	0.834083i	$0.314002\pi$
$824$	−10776.4	−0.455599
$825$	2040.30	0.0861018
$826$	−25557.0	−1.07656
$827$	−14290.0	−0.600863	−0.300431	−	0.953803i	$-0.597131\pi$
$827$	−14290.0	−0.600863	−0.300431	+	0.953803i	$0.597131\pi$
$828$	69905.7	2.93405
$829$	6898.78	0.289028	0.144514	−	0.989503i	$-0.453838\pi$
$829$	6898.78	0.289028	0.144514	+	0.989503i	$0.453838\pi$
$830$	−33031.1	−1.38136
$831$	−11613.1	−0.484781
$832$	28392.8	1.18310
$833$	41604.7	1.73051
$834$	−14912.8	−0.619170
$835$	−8782.88	−0.364005
$836$	−3368.19	−0.139344
$837$	1307.23	0.0539839
$838$	−13506.0	−0.556753
$839$	−18154.8	−0.747047	−0.373524	−	0.927621i	$-0.621850\pi$
$839$	−18154.8	−0.747047	−0.373524	+	0.927621i	$0.621850\pi$
$840$	43668.7	1.79370
$841$	−21659.3	−0.888077
$842$	−31684.8	−1.29683
$843$	−21676.5	−0.885620
$844$	−22820.6	−0.930708
$845$	5847.75	0.238069
$846$	67700.9	2.75131
$847$	3573.93	0.144984
$848$	25099.1	1.01640
$849$	32946.9	1.33184
$850$	−9648.06	−0.389324
$851$	66654.2	2.68493
$852$	48532.4	1.95152
$853$	−727.222	−0.0291906	−0.0145953	−	0.999893i	$-0.504646\pi$
$853$	−727.222	−0.0291906	−0.0145953	+	0.999893i	$0.504646\pi$
$854$	6657.37	0.266757
$855$	2664.31	0.106570
$856$	−59272.0	−2.36668
$857$	−32732.0	−1.30467	−0.652336	−	0.757930i	$-0.726211\pi$
$857$	−32732.0	−1.30467	−0.652336	+	0.757930i	$0.726211\pi$
$858$	23253.9	0.925262
$859$	23406.4	0.929704	0.464852	−	0.885388i	$-0.346108\pi$
$859$	23406.4	0.929704	0.464852	+	0.885388i	$0.346108\pi$
$860$	25056.5	0.993511
$861$	15076.1	0.596739
$862$	−31150.1	−1.23083
$863$	−18303.7	−0.721974	−0.360987	−	0.932571i	$-0.617560\pi$
$863$	−18303.7	−0.721974	−0.360987	+	0.932571i	$0.617560\pi$
$864$	71.0468	0.00279752
$865$	4424.13	0.173902
$866$	−67126.9	−2.63402
$867$	−9369.65	−0.367024
$868$	−80231.0	−3.13735
$869$	−7180.16	−0.280288
$870$	9517.83	0.370902
$871$	30195.3	1.17466
$872$	76393.1	2.96674
$873$	7125.42	0.276241
$874$	−14431.3	−0.558519
$875$	3692.07	0.142646
$876$	91213.5	3.51806
$877$	−754.119	−0.0290362	−0.0145181	−	0.999895i	$-0.504621\pi$
$877$	−754.119	−0.0290362	−0.0145181	+	0.999895i	$0.504621\pi$
$878$	21072.4	0.809977
$879$	−33778.9	−1.29617
$880$	−3673.53	−0.140721
$881$	4941.44	0.188969	0.0944844	−	0.995526i	$-0.469880\pi$
$881$	4941.44	0.188969	0.0944844	+	0.995526i	$0.469880\pi$
$882$	−72912.8	−2.78356
$883$	45905.6	1.74954	0.874771	−	0.484537i	$-0.161012\pi$
$883$	45905.6	1.74954	0.874771	+	0.484537i	$0.161012\pi$
$884$	−73484.0	−2.79585
$885$	−6536.26	−0.248264
$886$	2088.57	0.0791950
$887$	−18780.6	−0.710927	−0.355463	−	0.934690i	$-0.615677\pi$
$887$	−18780.6	−0.710927	−0.355463	+	0.934690i	$0.615677\pi$
$888$	127428.	4.81556
$889$	−52046.6	−1.96354
$890$	−31068.8	−1.17014
$891$	7696.51	0.289386
$892$	80594.3	3.02522
$893$	−9339.79	−0.349993
$894$	−32130.8	−1.20203
$895$	4647.98	0.173592
$896$	73143.0	2.72716
$897$	66581.6	2.47837
$898$	61433.6	2.28293
$899$	−8806.20	−0.326700
$900$	11299.3	0.418492
$901$	29531.6	1.09194
$902$	−3716.31	−0.137184
$903$	−68142.9	−2.51124
$904$	60846.1	2.23862
$905$	−18770.3	−0.689442
$906$	8673.31	0.318048
$907$	12109.2	0.443305	0.221653	−	0.975126i	$-0.428855\pi$
$907$	12109.2	0.443305	0.221653	+	0.975126i	$0.428855\pi$
$908$	80115.7	2.92812
$909$	23670.6	0.863701
$910$	42079.8	1.53289
$911$	−44874.8	−1.63202	−0.816009	−	0.578040i	$-0.803818\pi$
$911$	−44874.8	−1.63202	−0.816009	+	0.578040i	$0.803818\pi$
$912$	−9415.31	−0.341855
$913$	−14797.7	−0.536400
$914$	−42713.7	−1.54578
$915$	1702.64	0.0615163
$916$	104438.	3.76716
$917$	−29246.5	−1.05322
$918$	2993.10	0.107611
$919$	−21089.1	−0.756981	−0.378491	−	0.925605i	$-0.623557\pi$
$919$	−21089.1	−0.756981	−0.378491	+	0.925605i	$0.623557\pi$
$920$	−30821.2	−1.10451
$921$	−57063.8	−2.04160
$922$	−22774.8	−0.813500
$923$	23551.2	0.839868
$924$	38847.6	1.38311
$925$	10773.7	0.382960
$926$	−25131.5	−0.891872
$927$	7583.25	0.268680
$928$	−478.609	−0.0169301
$929$	25612.7	0.904548	0.452274	−	0.891879i	$-0.350613\pi$
$929$	25612.7	0.904548	0.452274	+	0.891879i	$0.350613\pi$
$930$	−30705.2	−1.08265
$931$	10058.8	0.354097
$932$	−97573.7	−3.42933
$933$	−19070.1	−0.669160
$934$	−69981.0	−2.45166
$935$	−4322.27	−0.151180
$936$	64853.3	2.26474
$937$	−35956.2	−1.25362	−0.626808	−	0.779173i	$-0.715639\pi$
$937$	−35956.2	−1.25362	−0.626808	+	0.779173i	$0.715639\pi$
$938$	75484.4	2.62756
$939$	−47634.5	−1.65548
$940$	−39609.9	−1.37440
$941$	16220.3	0.561920	0.280960	−	0.959720i	$-0.409347\pi$
$941$	16220.3	0.561920	0.280960	+	0.959720i	$0.409347\pi$
$942$	27284.4	0.943709
$943$	−10640.7	−0.367453
$944$	11768.5	0.405753
$945$	−1145.39	−0.0394279
$946$	16797.4	0.577306
$947$	54192.0	1.85956	0.929779	−	0.368117i	$-0.119997\pi$
$947$	54192.0	1.85956	0.929779	+	0.368117i	$0.119997\pi$
$948$	−78046.3	−2.67387
$949$	44263.0	1.51405
$950$	−2332.62	−0.0796634
$951$	45911.6	1.56549
$952$	−92510.1	−3.14944
$953$	−56735.1	−1.92847	−0.964234	−	0.265054i	$-0.914610\pi$
$953$	−56735.1	−1.92847	−0.964234	+	0.265054i	$0.914610\pi$
$954$	−51754.6	−1.75641
$955$	2672.36	0.0905503
$956$	27020.0	0.914109
$957$	4263.93	0.144027
$958$	−26925.5	−0.908064
$959$	−10381.4	−0.349564
$960$	18152.9	0.610294
$961$	−1381.58	−0.0463758
$962$	122792.	4.11535
$963$	41709.2	1.39570
$964$	61406.5	2.05163
$965$	−5534.78	−0.184633
$966$	166446.	5.54379
$967$	31459.8	1.04620	0.523102	−	0.852270i	$-0.324775\pi$
$967$	31459.8	1.04620	0.523102	+	0.852270i	$0.324775\pi$
$968$	−4822.41	−0.160122
$969$	−11078.1	−0.367263
$970$	−6238.35	−0.206496
$971$	15371.3	0.508020	0.254010	−	0.967202i	$-0.418250\pi$
$971$	15371.3	0.508020	0.254010	+	0.967202i	$0.418250\pi$
$972$	87033.6	2.87202
$973$	−12089.5	−0.398327
$974$	2514.33	0.0827148
$975$	10762.0	0.353497
$976$	−3065.58	−0.100540
$977$	−17366.3	−0.568678	−0.284339	−	0.958724i	$-0.591774\pi$
$977$	−17366.3	−0.568678	−0.284339	+	0.958724i	$0.591774\pi$
$978$	−132279.	−4.32496
$979$	−13918.6	−0.454383
$980$	42659.2	1.39051
$981$	−53757.1	−1.74957
$982$	−76331.9	−2.48050
$983$	41841.5	1.35762	0.678808	−	0.734316i	$-0.262497\pi$
$983$	41841.5	1.35762	0.678808	+	0.734316i	$0.262497\pi$
$984$	−20342.7	−0.659045
$985$	18488.0	0.598048
$986$	−20163.1	−0.651241
$987$	107722.	3.47399
$988$	−17766.3	−0.572086
$989$	48095.1	1.54635
$990$	7574.85	0.243176
$991$	−6025.65	−0.193149	−0.0965747	−	0.995326i	$-0.530789\pi$
$991$	−6025.65	−0.193149	−0.0965747	+	0.995326i	$0.530789\pi$
$992$	1544.03	0.0494182
$993$	−48578.0	−1.55244
$994$	58875.2	1.87868
$995$	−10315.3	−0.328660
$996$	−160847.	−5.11710
$997$	7222.12	0.229415	0.114708	−	0.993399i	$-0.463407\pi$
$997$	7222.12	0.229415	0.114708	+	0.993399i	$0.463407\pi$
$998$	−65749.8	−2.08544
$999$	−3342.32	−0.105852

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.2	✓	24	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-4.91078 q^{2} -7.41926 q^{3} +16.1158 q^{4} +5.00000 q^{5} +36.4343 q^{6} +29.5366 q^{7} -39.8547 q^{8} +28.0453 q^{9} +O(q^{10})\)	\(q-4.91078 q^{2} -7.41926 q^{3} +16.1158 q^{4} +5.00000 q^{5} +36.4343 q^{6} +29.5366 q^{7} -39.8547 q^{8} +28.0453 q^{9} -24.5539 q^{10} -11.0000 q^{11} -119.567 q^{12} -58.0220 q^{13} -145.048 q^{14} -37.0963 q^{15} +66.7914 q^{16} +78.5868 q^{17} -137.725 q^{18} +19.0000 q^{19} +80.5788 q^{20} -219.140 q^{21} +54.0186 q^{22} +154.668 q^{23} +295.692 q^{24} +25.0000 q^{25} +284.933 q^{26} -7.75570 q^{27} +476.004 q^{28} +52.2465 q^{29} +182.172 q^{30} -168.551 q^{31} -9.16058 q^{32} +81.6118 q^{33} -385.922 q^{34} +147.683 q^{35} +451.972 q^{36} +430.950 q^{37} -93.3048 q^{38} +430.480 q^{39} -199.273 q^{40} -68.7969 q^{41} +1076.15 q^{42} +310.957 q^{43} -177.273 q^{44} +140.227 q^{45} -759.542 q^{46} -491.568 q^{47} -495.542 q^{48} +529.411 q^{49} -122.769 q^{50} -583.055 q^{51} -935.068 q^{52} +375.783 q^{53} +38.0865 q^{54} -55.0000 q^{55} -1177.17 q^{56} -140.966 q^{57} -256.571 q^{58} +176.197 q^{59} -597.834 q^{60} -45.8978 q^{61} +827.716 q^{62} +828.364 q^{63} -489.346 q^{64} -290.110 q^{65} -400.778 q^{66} -520.411 q^{67} +1266.48 q^{68} -1147.52 q^{69} -725.239 q^{70} -405.902 q^{71} -1117.74 q^{72} -762.866 q^{73} -2116.30 q^{74} -185.481 q^{75} +306.199 q^{76} -324.903 q^{77} -2113.99 q^{78} +652.742 q^{79} +333.957 q^{80} -699.683 q^{81} +337.846 q^{82} +1345.25 q^{83} -3531.60 q^{84} +392.934 q^{85} -1527.04 q^{86} -387.630 q^{87} +438.401 q^{88} +1265.33 q^{89} -688.623 q^{90} -1713.77 q^{91} +2492.59 q^{92} +1250.52 q^{93} +2413.98 q^{94} +95.0000 q^{95} +67.9647 q^{96} +254.068 q^{97} -2599.82 q^{98} -308.499 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * q^99

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