LMFDB - Embedded newform 1045.4.a.g.1.19

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:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+4.05796 q^{2} -1.73694 q^{3} +8.46702 q^{4} -5.00000 q^{5} -7.04845 q^{6} -13.5343 q^{7} +1.89515 q^{8} -23.9830 q^{9} +O(q^{10})$	\(q+4.05796 q^{2} -1.73694 q^{3} +8.46702 q^{4} -5.00000 q^{5} -7.04845 q^{6} -13.5343 q^{7} +1.89515 q^{8} -23.9830 q^{9} -20.2898 q^{10} -11.0000 q^{11} -14.7067 q^{12} +56.9663 q^{13} -54.9215 q^{14} +8.68472 q^{15} -60.0457 q^{16} +76.4798 q^{17} -97.3221 q^{18} -19.0000 q^{19} -42.3351 q^{20} +23.5083 q^{21} -44.6375 q^{22} +108.688 q^{23} -3.29177 q^{24} +25.0000 q^{25} +231.167 q^{26} +88.5547 q^{27} -114.595 q^{28} +86.2082 q^{29} +35.2422 q^{30} -192.753 q^{31} -258.824 q^{32} +19.1064 q^{33} +310.352 q^{34} +67.6714 q^{35} -203.065 q^{36} +240.280 q^{37} -77.1012 q^{38} -98.9472 q^{39} -9.47576 q^{40} +324.580 q^{41} +95.3957 q^{42} +369.421 q^{43} -93.1372 q^{44} +119.915 q^{45} +441.050 q^{46} +299.506 q^{47} +104.296 q^{48} -159.823 q^{49} +101.449 q^{50} -132.841 q^{51} +482.335 q^{52} -119.278 q^{53} +359.351 q^{54} +55.0000 q^{55} -25.6495 q^{56} +33.0019 q^{57} +349.829 q^{58} +120.859 q^{59} +73.5337 q^{60} -331.725 q^{61} -782.185 q^{62} +324.593 q^{63} -569.932 q^{64} -284.831 q^{65} +77.5329 q^{66} +1035.13 q^{67} +647.556 q^{68} -188.784 q^{69} +274.608 q^{70} -457.482 q^{71} -45.4515 q^{72} +261.151 q^{73} +975.045 q^{74} -43.4236 q^{75} -160.873 q^{76} +148.877 q^{77} -401.524 q^{78} +736.705 q^{79} +300.229 q^{80} +493.727 q^{81} +1317.13 q^{82} +275.455 q^{83} +199.045 q^{84} -382.399 q^{85} +1499.09 q^{86} -149.739 q^{87} -20.8467 q^{88} -1201.01 q^{89} +486.610 q^{90} -770.997 q^{91} +920.260 q^{92} +334.802 q^{93} +1215.38 q^{94} +95.0000 q^{95} +449.563 q^{96} +903.648 q^{97} -648.556 q^{98} +263.813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9}+O(q^{10}) $ 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9	\( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9} - 30 q^{10} - 253 q^{11} + 44 q^{12} - 37 q^{13} + 61 q^{14} - 45 q^{15} + 588 q^{16} - 73 q^{17} + 391 q^{18} - 437 q^{19} - 460 q^{20} - 127 q^{21} - 66 q^{22} - 175 q^{23} + 16 q^{24} + 575 q^{25} + 719 q^{26} + 21 q^{27} + 253 q^{28} + 71 q^{29} + 125 q^{30} + 302 q^{31} + 1107 q^{32} - 99 q^{33} + 1267 q^{34} + 185 q^{35} + 703 q^{36} - 500 q^{37} - 114 q^{38} + 457 q^{39} - 210 q^{40} + 770 q^{41} + 2596 q^{42} - 902 q^{43} - 1012 q^{44} - 850 q^{45} - 1101 q^{46} + 356 q^{47} + 1221 q^{48} + 908 q^{49} + 150 q^{50} - 451 q^{51} - 358 q^{52} + 1327 q^{53} + 2534 q^{54} + 1265 q^{55} + 3135 q^{56} - 171 q^{57} + 1014 q^{58} + 3619 q^{59} - 220 q^{60} - 1432 q^{61} + 1826 q^{62} + 1658 q^{63} + 4006 q^{64} + 185 q^{65} + 275 q^{66} - 605 q^{67} + 5128 q^{68} + 3099 q^{69} - 305 q^{70} + 3230 q^{71} + 2152 q^{72} - 637 q^{73} + 5063 q^{74} + 225 q^{75} - 1748 q^{76} + 407 q^{77} + 7230 q^{78} + 2074 q^{79} - 2940 q^{80} + 2291 q^{81} + 530 q^{82} + 3882 q^{83} + 5096 q^{84} + 365 q^{85} + 2262 q^{86} - 27 q^{87} - 462 q^{88} - 210 q^{89} - 1955 q^{90} + 4133 q^{91} - 6064 q^{92} + 824 q^{93} - 392 q^{94} + 2185 q^{95} + 2462 q^{96} + 2032 q^{97} + 7896 q^{98} - 1870 q^{99}+O(q^{100}) \) 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9 - 30 * q^10 - 253 * q^11 + 44 * q^12 - 37 * q^13 + 61 * q^14 - 45 * q^15 + 588 * q^16 - 73 * q^17 + 391 * q^18 - 437 * q^19 - 460 * q^20 - 127 * q^21 - 66 * q^22 - 175 * q^23 + 16 * q^24 + 575 * q^25 + 719 * q^26 + 21 * q^27 + 253 * q^28 + 71 * q^29 + 125 * q^30 + 302 * q^31 + 1107 * q^32 - 99 * q^33 + 1267 * q^34 + 185 * q^35 + 703 * q^36 - 500 * q^37 - 114 * q^38 + 457 * q^39 - 210 * q^40 + 770 * q^41 + 2596 * q^42 - 902 * q^43 - 1012 * q^44 - 850 * q^45 - 1101 * q^46 + 356 * q^47 + 1221 * q^48 + 908 * q^49 + 150 * q^50 - 451 * q^51 - 358 * q^52 + 1327 * q^53 + 2534 * q^54 + 1265 * q^55 + 3135 * q^56 - 171 * q^57 + 1014 * q^58 + 3619 * q^59 - 220 * q^60 - 1432 * q^61 + 1826 * q^62 + 1658 * q^63 + 4006 * q^64 + 185 * q^65 + 275 * q^66 - 605 * q^67 + 5128 * q^68 + 3099 * q^69 - 305 * q^70 + 3230 * q^71 + 2152 * q^72 - 637 * q^73 + 5063 * q^74 + 225 * q^75 - 1748 * q^76 + 407 * q^77 + 7230 * q^78 + 2074 * q^79 - 2940 * q^80 + 2291 * q^81 + 530 * q^82 + 3882 * q^83 + 5096 * q^84 + 365 * q^85 + 2262 * q^86 - 27 * q^87 - 462 * q^88 - 210 * q^89 - 1955 * q^90 + 4133 * q^91 - 6064 * q^92 + 824 * q^93 - 392 * q^94 + 2185 * q^95 + 2462 * q^96 + 2032 * q^97 + 7896 * q^98 - 1870 * 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 $

$2$	4.05796	1.43470	0.717352	−	0.696711i	$-0.245354\pi$
$2$	4.05796	1.43470	0.717352	+	0.696711i	$0.245354\pi$
$3$	−1.73694	−0.334275	−0.167138	−	0.985934i	$-0.553452\pi$
$3$	−1.73694	−0.334275	−0.167138	+	0.985934i	$0.553452\pi$
$4$	8.46702	1.05838
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−7.04845	−0.479586
$7$	−13.5343	−0.730783	−0.365391	−	0.930854i	$-0.619065\pi$
$7$	−13.5343	−0.730783	−0.365391	+	0.930854i	$0.619065\pi$
$8$	1.89515	0.0837546
$9$	−23.9830	−0.888260
$10$	−20.2898	−0.641619
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−14.7067	−0.353789
$13$	56.9663	1.21535	0.607677	−	0.794184i	$-0.292102\pi$
$13$	56.9663	1.21535	0.607677	+	0.794184i	$0.292102\pi$
$14$	−54.9215	−1.04846
$15$	8.68472	0.149492
$16$	−60.0457	−0.938214
$17$	76.4798	1.09112	0.545561	−	0.838071i	$-0.316317\pi$
$17$	76.4798	1.09112	0.545561	+	0.838071i	$0.316317\pi$
$18$	−97.3221	−1.27439
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−42.3351	−0.473321
$21$	23.5083	0.244282
$22$	−44.6375	−0.432580
$23$	108.688	0.985345	0.492673	−	0.870215i	$-0.336020\pi$
$23$	108.688	0.985345	0.492673	+	0.870215i	$0.336020\pi$
$24$	−3.29177	−0.0279971
$25$	25.0000	0.200000
$26$	231.167	1.74367
$27$	88.5547	0.631198
$28$	−114.595	−0.773444
$29$	86.2082	0.552016	0.276008	−	0.961155i	$-0.410988\pi$
$29$	86.2082	0.552016	0.276008	+	0.961155i	$0.410988\pi$
$30$	35.2422	0.214477
$31$	−192.753	−1.11676	−0.558379	−	0.829586i	$-0.688577\pi$
$31$	−192.753	−1.11676	−0.558379	+	0.829586i	$0.688577\pi$
$32$	−258.824	−1.42982
$33$	19.1064	0.100788
$34$	310.352	1.56544
$35$	67.6714	0.326816
$36$	−203.065	−0.940115
$37$	240.280	1.06761	0.533807	−	0.845606i	$-0.320761\pi$
$37$	240.280	1.06761	0.533807	+	0.845606i	$0.320761\pi$
$38$	−77.1012	−0.329144
$39$	−98.9472	−0.406262
$40$	−9.47576	−0.0374562
$41$	324.580	1.23636	0.618182	−	0.786035i	$-0.287869\pi$
$41$	324.580	1.23636	0.618182	+	0.786035i	$0.287869\pi$
$42$	95.3957	0.350473
$43$	369.421	1.31014	0.655072	−	0.755567i	$-0.272638\pi$
$43$	369.421	1.31014	0.655072	+	0.755567i	$0.272638\pi$
$44$	−93.1372	−0.319113
$45$	119.915	0.397242
$46$	441.050	1.41368
$47$	299.506	0.929519	0.464760	−	0.885437i	$-0.346141\pi$
$47$	299.506	0.929519	0.464760	+	0.885437i	$0.346141\pi$
$48$	104.296	0.313622
$49$	−159.823	−0.465957
$50$	101.449	0.286941
$51$	−132.841	−0.364735
$52$	482.335	1.28630
$53$	−119.278	−0.309133	−0.154566	−	0.987982i	$-0.549398\pi$
$53$	−119.278	−0.309133	−0.154566	+	0.987982i	$0.549398\pi$
$54$	359.351	0.905583
$55$	55.0000	0.134840
$56$	−25.6495	−0.0612064
$57$	33.0019	0.0766880
$58$	349.829	0.791980
$59$	120.859	0.266686	0.133343	−	0.991070i	$-0.457429\pi$
$59$	120.859	0.266686	0.133343	+	0.991070i	$0.457429\pi$
$60$	73.5337	0.158219
$61$	−331.725	−0.696279	−0.348140	−	0.937443i	$-0.613186\pi$
$61$	−331.725	−0.696279	−0.348140	+	0.937443i	$0.613186\pi$
$62$	−782.185	−1.60222
$63$	324.593	0.649125
$64$	−569.932	−1.11315
$65$	−284.831	−0.543523
$66$	77.5329	0.144601
$67$	1035.13	1.88748	0.943739	−	0.330691i	$-0.107282\pi$
$67$	1035.13	1.88748	0.943739	+	0.330691i	$0.107282\pi$
$68$	647.556	1.15482
$69$	−188.784	−0.329376
$70$	274.608	0.468884
$71$	−457.482	−0.764691	−0.382346	−	0.924019i	$-0.624884\pi$
$71$	−457.482	−0.764691	−0.382346	+	0.924019i	$0.624884\pi$
$72$	−45.4515	−0.0743959
$73$	261.151	0.418705	0.209352	−	0.977840i	$-0.432864\pi$
$73$	261.151	0.418705	0.209352	+	0.977840i	$0.432864\pi$
$74$	975.045	1.53171
$75$	−43.4236	−0.0668550
$76$	−160.873	−0.242808
$77$	148.877	0.220339
$78$	−401.524	−0.582867
$79$	736.705	1.04919	0.524594	−	0.851353i	$-0.324217\pi$
$79$	736.705	1.04919	0.524594	+	0.851353i	$0.324217\pi$
$80$	300.229	0.419582
$81$	493.727	0.677266
$82$	1317.13	1.77382
$83$	275.455	0.364278	0.182139	−	0.983273i	$-0.441698\pi$
$83$	275.455	0.364278	0.182139	+	0.983273i	$0.441698\pi$
$84$	199.045	0.258543
$85$	−382.399	−0.487965
$86$	1499.09	1.87967
$87$	−149.739	−0.184525
$88$	−20.8467	−0.0252530
$89$	−1201.01	−1.43042	−0.715208	−	0.698911i	$-0.753668\pi$
$89$	−1201.01	−1.43042	−0.715208	+	0.698911i	$0.753668\pi$
$90$	486.610	0.569925
$91$	−770.997	−0.888159
$92$	920.260	1.04287
$93$	334.802	0.373305
$94$	1215.38	1.33359
$95$	95.0000	0.102598
$96$	449.563	0.477952
$97$	903.648	0.945892	0.472946	−	0.881091i	$-0.343191\pi$
$97$	903.648	0.945892	0.472946	+	0.881091i	$0.343191\pi$
$98$	−648.556	−0.668511
$99$	263.813	0.267821
$100$	211.676	0.211676
$101$	−1580.61	−1.55719	−0.778595	−	0.627527i	$-0.784067\pi$
$101$	−1580.61	−1.55719	−0.778595	+	0.627527i	$0.784067\pi$
$102$	−539.064	−0.523287
$103$	−76.3907	−0.0730777	−0.0365389	−	0.999332i	$-0.511633\pi$
$103$	−76.3907	−0.0730777	−0.0365389	+	0.999332i	$0.511633\pi$
$104$	107.960	0.101792
$105$	−117.541	−0.109246
$106$	−484.024	−0.443514
$107$	−599.093	−0.541276	−0.270638	−	0.962681i	$-0.587235\pi$
$107$	−599.093	−0.541276	−0.270638	+	0.962681i	$0.587235\pi$
$108$	749.794	0.668046
$109$	−790.810	−0.694916	−0.347458	−	0.937695i	$-0.612955\pi$
$109$	−790.810	−0.694916	−0.347458	+	0.937695i	$0.612955\pi$
$110$	223.188	0.193456
$111$	−417.353	−0.356877
$112$	812.676	0.685631
$113$	1431.50	1.19172	0.595859	−	0.803089i	$-0.296812\pi$
$113$	1431.50	1.19172	0.595859	+	0.803089i	$0.296812\pi$
$114$	133.920	0.110025
$115$	−543.438	−0.440660
$116$	729.927	0.584242
$117$	−1366.22	−1.07955
$118$	490.440	0.382616
$119$	−1035.10	−0.797373
$120$	16.4589	0.0125207
$121$	121.000	0.0909091
$122$	−1346.13	−0.998955
$123$	−563.778	−0.413286
$124$	−1632.05	−1.18195
$125$	−125.000	−0.0894427
$126$	1317.18	0.931303
$127$	327.214	0.228627	0.114313	−	0.993445i	$-0.463533\pi$
$127$	327.214	0.228627	0.114313	+	0.993445i	$0.463533\pi$
$128$	−242.166	−0.167224
$129$	−641.664	−0.437948
$130$	−1155.83	−0.779795
$131$	1949.74	1.30038	0.650191	−	0.759771i	$-0.274689\pi$
$131$	1949.74	1.30038	0.650191	+	0.759771i	$0.274689\pi$
$132$	161.774	0.106671
$133$	257.151	0.167653
$134$	4200.51	2.70797
$135$	−442.773	−0.282280
$136$	144.941	0.0913865
$137$	−2811.90	−1.75355	−0.876775	−	0.480900i	$-0.840310\pi$
$137$	−2811.90	−1.75355	−0.876775	+	0.480900i	$0.840310\pi$
$138$	−766.079	−0.472558
$139$	1640.99	1.00134	0.500671	−	0.865637i	$-0.333087\pi$
$139$	1640.99	1.00134	0.500671	+	0.865637i	$0.333087\pi$
$140$	572.975	0.345895
$141$	−520.225	−0.310715
$142$	−1856.44	−1.09711
$143$	−626.629	−0.366443
$144$	1440.08	0.833378
$145$	−431.041	−0.246869
$146$	1059.74	0.600717
$147$	277.604	0.155758
$148$	2034.45	1.12994
$149$	1454.27	0.799585	0.399792	−	0.916606i	$-0.369082\pi$
$149$	1454.27	0.799585	0.399792	+	0.916606i	$0.369082\pi$
$150$	−176.211	−0.0959172
$151$	1357.90	0.731818	0.365909	−	0.930651i	$-0.380758\pi$
$151$	1357.90	0.731818	0.365909	+	0.930651i	$0.380758\pi$
$152$	−36.0079	−0.0192146
$153$	−1834.22	−0.969200
$154$	604.137	0.316122
$155$	963.767	0.499430
$156$	−837.788	−0.429979
$157$	−3014.47	−1.53236	−0.766182	−	0.642623i	$-0.777846\pi$
$157$	−3014.47	−1.53236	−0.766182	+	0.642623i	$0.777846\pi$
$158$	2989.52	1.50527
$159$	207.179	0.103335
$160$	1294.12	0.639433
$161$	−1471.01	−0.720073
$162$	2003.52	0.971677
$163$	−419.730	−0.201692	−0.100846	−	0.994902i	$-0.532155\pi$
$163$	−419.730	−0.201692	−0.100846	+	0.994902i	$0.532155\pi$
$164$	2748.23	1.30854
$165$	−95.5319	−0.0450736
$166$	1117.78	0.522632
$167$	1786.44	0.827776	0.413888	−	0.910328i	$-0.364170\pi$
$167$	1786.44	0.827776	0.413888	+	0.910328i	$0.364170\pi$
$168$	44.5518	0.0204598
$169$	1048.15	0.477085
$170$	−1551.76	−0.700085
$171$	455.677	0.203781
$172$	3127.89	1.38663
$173$	1766.80	0.776456	0.388228	−	0.921563i	$-0.373087\pi$
$173$	1766.80	0.776456	0.388228	+	0.921563i	$0.373087\pi$
$174$	−607.634	−0.264739
$175$	−338.357	−0.146157
$176$	660.503	0.282882
$177$	−209.925	−0.0891465
$178$	−4873.66	−2.05223
$179$	−3658.66	−1.52771	−0.763857	−	0.645385i	$-0.776697\pi$
$179$	−3658.66	−1.52771	−0.763857	+	0.645385i	$0.776697\pi$
$180$	1015.32	0.420432
$181$	−863.803	−0.354729	−0.177365	−	0.984145i	$-0.556757\pi$
$181$	−863.803	−0.354729	−0.177365	+	0.984145i	$0.556757\pi$
$182$	−3128.67	−1.27425
$183$	576.188	0.232749
$184$	205.979	0.0825272
$185$	−1201.40	−0.477452
$186$	1358.61	0.535582
$187$	−841.278	−0.328986
$188$	2535.92	0.983782
$189$	−1198.52	−0.461269
$190$	385.506	0.147198
$191$	4246.55	1.60874	0.804371	−	0.594128i	$-0.202503\pi$
$191$	4246.55	1.60874	0.804371	+	0.594128i	$0.202503\pi$
$192$	989.940	0.372098
$193$	4404.63	1.64276	0.821379	−	0.570383i	$-0.193205\pi$
$193$	4404.63	1.64276	0.821379	+	0.570383i	$0.193205\pi$
$194$	3666.96	1.35708
$195$	494.736	0.181686
$196$	−1353.23	−0.493158
$197$	661.778	0.239339	0.119669	−	0.992814i	$-0.461817\pi$
$197$	661.778	0.239339	0.119669	+	0.992814i	$0.461817\pi$
$198$	1070.54	0.384243
$199$	−3718.81	−1.32472	−0.662360	−	0.749186i	$-0.730445\pi$
$199$	−3718.81	−1.32472	−0.662360	+	0.749186i	$0.730445\pi$
$200$	47.3788	0.0167509
$201$	−1797.96	−0.630937
$202$	−6414.03	−2.23411
$203$	−1166.77	−0.403404
$204$	−1124.77	−0.386027
$205$	−1622.90	−0.552919
$206$	−309.990	−0.104845
$207$	−2606.66	−0.875243
$208$	−3420.58	−1.14026
$209$	209.000	0.0691714
$210$	−476.978	−0.156736
$211$	2064.77	0.673671	0.336835	−	0.941564i	$-0.390643\pi$
$211$	2064.77	0.673671	0.336835	+	0.941564i	$0.390643\pi$
$212$	−1009.93	−0.327179
$213$	794.620	0.255617
$214$	−2431.09	−0.776571
$215$	−1847.10	−0.585914
$216$	167.825	0.0528658
$217$	2608.78	0.816108
$218$	−3209.07	−0.997000
$219$	−453.605	−0.139963
$220$	465.686	0.142712
$221$	4356.77	1.32610
$222$	−1693.60	−0.512013
$223$	2859.05	0.858547	0.429273	−	0.903175i	$-0.358770\pi$
$223$	2859.05	0.858547	0.429273	+	0.903175i	$0.358770\pi$
$224$	3503.00	1.04488
$225$	−599.576	−0.177652
$226$	5808.96	1.70976
$227$	2009.87	0.587663	0.293832	−	0.955857i	$-0.405070\pi$
$227$	2009.87	0.587663	0.293832	+	0.955857i	$0.405070\pi$
$228$	279.428	0.0811648
$229$	3504.19	1.01119	0.505597	−	0.862770i	$-0.331272\pi$
$229$	3504.19	1.01119	0.505597	+	0.862770i	$0.331272\pi$
$230$	−2205.25	−0.632217
$231$	−258.591	−0.0736539
$232$	163.378	0.0462339
$233$	6771.46	1.90392	0.951959	−	0.306225i	$-0.0990660\pi$
$233$	6771.46	1.90392	0.951959	+	0.306225i	$0.0990660\pi$
$234$	−5544.08	−1.54884
$235$	−1497.53	−0.415694
$236$	1023.31	0.282254
$237$	−1279.62	−0.350717
$238$	−4200.39	−1.14399
$239$	−5533.17	−1.49754	−0.748768	−	0.662832i	$-0.769354\pi$
$239$	−5533.17	−1.49754	−0.748768	+	0.662832i	$0.769354\pi$
$240$	−521.480	−0.140256
$241$	5204.90	1.39119	0.695595	−	0.718434i	$-0.255141\pi$
$241$	5204.90	1.39119	0.695595	+	0.718434i	$0.255141\pi$
$242$	491.013	0.130428
$243$	−3248.55	−0.857592
$244$	−2808.72	−0.736926
$245$	799.116	0.208382
$246$	−2287.79	−0.592943
$247$	−1082.36	−0.278821
$248$	−365.297	−0.0935337
$249$	−478.450	−0.121769
$250$	−507.245	−0.128324
$251$	5532.31	1.39122	0.695610	−	0.718419i	$-0.255134\pi$
$251$	5532.31	1.39122	0.695610	+	0.718419i	$0.255134\pi$
$252$	2748.34	0.687019
$253$	−1195.56	−0.297093
$254$	1327.82	0.328012
$255$	664.206	0.163114
$256$	3576.76	0.873231
$257$	−1891.82	−0.459177	−0.229589	−	0.973288i	$-0.573738\pi$
$257$	−1891.82	−0.459177	−0.229589	+	0.973288i	$0.573738\pi$
$258$	−2603.84	−0.628326
$259$	−3252.01	−0.780194
$260$	−2411.67	−0.575252
$261$	−2067.53	−0.490334
$262$	7911.98	1.86566
$263$	−129.230	−0.0302991	−0.0151495	−	0.999885i	$-0.504822\pi$
$263$	−129.230	−0.0302991	−0.0151495	+	0.999885i	$0.504822\pi$
$264$	36.2095	0.00844144
$265$	596.388	0.138248
$266$	1043.51	0.240533
$267$	2086.09	0.478153
$268$	8764.45	1.99766
$269$	−3009.85	−0.682208	−0.341104	−	0.940026i	$-0.610801\pi$
$269$	−3009.85	−0.682208	−0.341104	+	0.940026i	$0.610801\pi$
$270$	−1796.76	−0.404989
$271$	6922.66	1.55174	0.775870	−	0.630892i	$-0.217311\pi$
$271$	6922.66	1.55174	0.775870	+	0.630892i	$0.217311\pi$
$272$	−4592.29	−1.02371
$273$	1339.18	0.296890
$274$	−11410.6	−2.51583
$275$	−275.000	−0.0603023
$276$	−1598.44	−0.348605
$277$	239.162	0.0518767	0.0259383	−	0.999664i	$-0.491743\pi$
$277$	239.162	0.0518767	0.0259383	+	0.999664i	$0.491743\pi$
$278$	6659.05	1.43663
$279$	4622.81	0.991972
$280$	128.248	0.0273723
$281$	−6941.49	−1.47365	−0.736823	−	0.676085i	$-0.763675\pi$
$281$	−6941.49	−1.47365	−0.736823	+	0.676085i	$0.763675\pi$
$282$	−2111.05	−0.445784
$283$	−3132.69	−0.658019	−0.329009	−	0.944327i	$-0.606715\pi$
$283$	−3132.69	−0.658019	−0.329009	+	0.944327i	$0.606715\pi$
$284$	−3873.51	−0.809332
$285$	−165.010	−0.0342959
$286$	−2542.83	−0.525737
$287$	−4392.96	−0.903513
$288$	6207.39	1.27005
$289$	936.160	0.190548
$290$	−1749.15	−0.354184
$291$	−1569.59	−0.316188
$292$	2211.17	0.443148
$293$	−2061.87	−0.411112	−0.205556	−	0.978645i	$-0.565900\pi$
$293$	−2061.87	−0.411112	−0.205556	+	0.978645i	$0.565900\pi$
$294$	1126.51	0.223466
$295$	−604.294	−0.119266
$296$	455.367	0.0894177
$297$	−974.101	−0.190313
$298$	5901.35	1.14717
$299$	6191.53	1.19754
$300$	−367.669	−0.0707579
$301$	−4999.85	−0.957430
$302$	5510.31	1.04994
$303$	2745.43	0.520530
$304$	1140.87	0.215241
$305$	1658.62	0.311385
$306$	−7443.17	−1.39052
$307$	−8489.31	−1.57821	−0.789105	−	0.614258i	$-0.789455\pi$
$307$	−8489.31	−1.57821	−0.789105	+	0.614258i	$0.789455\pi$
$308$	1260.55	0.233202
$309$	132.686	0.0244281
$310$	3910.92	0.716534
$311$	−6251.05	−1.13976	−0.569879	−	0.821729i	$-0.693010\pi$
$311$	−6251.05	−1.13976	−0.569879	+	0.821729i	$0.693010\pi$
$312$	−187.520	−0.0340264
$313$	−3356.73	−0.606178	−0.303089	−	0.952962i	$-0.598018\pi$
$313$	−3356.73	−0.606178	−0.303089	+	0.952962i	$0.598018\pi$
$314$	−12232.6	−2.19849
$315$	−1622.96	−0.290298
$316$	6237.70	1.11044
$317$	−3183.30	−0.564013	−0.282007	−	0.959412i	$-0.591000\pi$
$317$	−3183.30	−0.564013	−0.282007	+	0.959412i	$0.591000\pi$
$318$	840.722	0.148256
$319$	−948.291	−0.166439
$320$	2849.66	0.497815
$321$	1040.59	0.180935
$322$	−5969.29	−1.03309
$323$	−1453.12	−0.250321
$324$	4180.40	0.716803
$325$	1424.16	0.243071
$326$	−1703.24	−0.289368
$327$	1373.59	0.232293
$328$	615.129	0.103551
$329$	−4053.60	−0.679276
$330$	−387.665	−0.0646674
$331$	4520.74	0.750702	0.375351	−	0.926883i	$-0.377522\pi$
$331$	4520.74	0.750702	0.375351	+	0.926883i	$0.377522\pi$
$332$	2332.28	0.385544
$333$	−5762.64	−0.948320
$334$	7249.29	1.18761
$335$	−5175.64	−0.844106
$336$	−1411.57	−0.229189
$337$	−7930.88	−1.28197	−0.640983	−	0.767555i	$-0.721473\pi$
$337$	−7930.88	−1.28197	−0.640983	+	0.767555i	$0.721473\pi$
$338$	4253.37	0.684476
$339$	−2486.43	−0.398361
$340$	−3237.78	−0.516451
$341$	2120.29	0.336715
$342$	1849.12	0.292365
$343$	6805.35	1.07130
$344$	700.108	0.109731
$345$	943.922	0.147302
$346$	7169.58	1.11399
$347$	−6380.06	−0.987030	−0.493515	−	0.869737i	$-0.664288\pi$
$347$	−6380.06	−0.987030	−0.493515	+	0.869737i	$0.664288\pi$
$348$	−1267.84	−0.195297
$349$	−10190.6	−1.56301	−0.781507	−	0.623896i	$-0.785549\pi$
$349$	−10190.6	−1.56301	−0.781507	+	0.623896i	$0.785549\pi$
$350$	−1373.04	−0.209691
$351$	5044.63	0.767129
$352$	2847.07	0.431106
$353$	11440.1	1.72492	0.862459	−	0.506128i	$-0.168923\pi$
$353$	11440.1	1.72492	0.862459	+	0.506128i	$0.168923\pi$
$354$	−851.867	−0.127899
$355$	2287.41	0.341980
$356$	−10169.0	−1.51392
$357$	1797.91	0.266542
$358$	−14846.7	−2.19182
$359$	7594.08	1.11644	0.558218	−	0.829695i	$-0.311485\pi$
$359$	7594.08	1.11644	0.558218	+	0.829695i	$0.311485\pi$
$360$	227.257	0.0332709
$361$	361.000	0.0526316
$362$	−3505.28	−0.508931
$363$	−210.170	−0.0303886
$364$	−6528.05	−0.940008
$365$	−1305.76	−0.187250
$366$	2338.15	0.333926
$367$	3150.17	0.448059	0.224030	−	0.974582i	$-0.428079\pi$
$367$	3150.17	0.448059	0.224030	+	0.974582i	$0.428079\pi$
$368$	−6526.23	−0.924465
$369$	−7784.42	−1.09821
$370$	−4875.23	−0.685003
$371$	1614.34	0.225909
$372$	2834.77	0.395097
$373$	3798.98	0.527355	0.263678	−	0.964611i	$-0.415064\pi$
$373$	3798.98	0.527355	0.263678	+	0.964611i	$0.415064\pi$
$374$	−3413.87	−0.471997
$375$	217.118	0.0298985
$376$	567.609	0.0778516
$377$	4910.96	0.670895
$378$	−4863.56	−0.661784
$379$	−4431.32	−0.600585	−0.300293	−	0.953847i	$-0.597084\pi$
$379$	−4431.32	−0.600585	−0.300293	+	0.953847i	$0.597084\pi$
$380$	804.367	0.108587
$381$	−568.353	−0.0764242
$382$	17232.3	2.30807
$383$	8701.34	1.16088	0.580441	−	0.814302i	$-0.302880\pi$
$383$	8701.34	1.16088	0.580441	+	0.814302i	$0.302880\pi$
$384$	420.629	0.0558988
$385$	−744.385	−0.0985387
$386$	17873.8	2.35687
$387$	−8859.83	−1.16375
$388$	7651.21	1.00111
$389$	11738.6	1.53000	0.765001	−	0.644029i	$-0.222738\pi$
$389$	11738.6	1.53000	0.765001	+	0.644029i	$0.222738\pi$
$390$	2007.62	0.260666
$391$	8312.41	1.07513
$392$	−302.889	−0.0390261
$393$	−3386.60	−0.434685
$394$	2685.47	0.343380
$395$	−3683.52	−0.469211
$396$	2233.71	0.283455
$397$	6040.61	0.763652	0.381826	−	0.924234i	$-0.375295\pi$
$397$	6040.61	0.763652	0.381826	+	0.924234i	$0.375295\pi$
$398$	−15090.8	−1.90058
$399$	−446.658	−0.0560422
$400$	−1501.14	−0.187643
$401$	−11867.9	−1.47795	−0.738973	−	0.673735i	$-0.764689\pi$
$401$	−11867.9	−1.47795	−0.738973	+	0.673735i	$0.764689\pi$
$402$	−7296.05	−0.905208
$403$	−10980.4	−1.35726
$404$	−13383.0	−1.64810
$405$	−2468.64	−0.302883
$406$	−4734.69	−0.578765
$407$	−2643.08	−0.321898
$408$	−251.754	−0.0305482
$409$	−3579.79	−0.432786	−0.216393	−	0.976306i	$-0.569429\pi$
$409$	−3579.79	−0.432786	−0.216393	+	0.976306i	$0.569429\pi$
$410$	−6585.67	−0.793275
$411$	4884.11	0.586168
$412$	−646.802	−0.0773438
$413$	−1635.74	−0.194889
$414$	−10577.7	−1.25571
$415$	−1377.27	−0.162910
$416$	−14744.2	−1.73773
$417$	−2850.30	−0.334724
$418$	848.113	0.0992406
$419$	−12214.3	−1.42412	−0.712060	−	0.702119i	$-0.752238\pi$
$419$	−12214.3	−1.42412	−0.712060	+	0.702119i	$0.752238\pi$
$420$	−995.226	−0.115624
$421$	1098.76	0.127198	0.0635991	−	0.997976i	$-0.479742\pi$
$421$	1098.76	0.127198	0.0635991	+	0.997976i	$0.479742\pi$
$422$	8378.74	0.966519
$423$	−7183.05	−0.825655
$424$	−226.049	−0.0258913
$425$	1912.00	0.218224
$426$	3224.53	0.366735
$427$	4489.66	0.508829
$428$	−5072.53	−0.572874
$429$	1088.42	0.122493
$430$	−7495.47	−0.840613
$431$	−4836.21	−0.540491	−0.270246	−	0.962791i	$-0.587105\pi$
$431$	−4836.21	−0.540491	−0.270246	+	0.962791i	$0.587105\pi$
$432$	−5317.33	−0.592199
$433$	−10179.5	−1.12978	−0.564892	−	0.825165i	$-0.691082\pi$
$433$	−10179.5	−1.12978	−0.564892	+	0.825165i	$0.691082\pi$
$434$	10586.3	1.17087
$435$	748.695	0.0825222
$436$	−6695.81	−0.735484
$437$	−2065.06	−0.226054
$438$	−1840.71	−0.200805
$439$	4696.99	0.510650	0.255325	−	0.966855i	$-0.417818\pi$
$439$	4696.99	0.510650	0.255325	+	0.966855i	$0.417818\pi$
$440$	104.233	0.0112935
$441$	3833.04	0.413891
$442$	17679.6	1.90256
$443$	13914.2	1.49229	0.746147	−	0.665782i	$-0.231902\pi$
$443$	13914.2	1.49229	0.746147	+	0.665782i	$0.231902\pi$
$444$	−3533.73	−0.377711
$445$	6005.06	0.639702
$446$	11601.9	1.23176
$447$	−2525.98	−0.267281
$448$	7713.62	0.813469
$449$	1397.69	0.146906	0.0734532	−	0.997299i	$-0.476598\pi$
$449$	1397.69	0.146906	0.0734532	+	0.997299i	$0.476598\pi$
$450$	−2433.05	−0.254878
$451$	−3570.38	−0.372778
$452$	12120.5	1.26129
$453$	−2358.60	−0.244629
$454$	8155.95	0.843123
$455$	3854.99	0.397197
$456$	62.5437	0.00642297
$457$	10978.0	1.12369	0.561847	−	0.827241i	$-0.310091\pi$
$457$	10978.0	1.12369	0.561847	+	0.827241i	$0.310091\pi$
$458$	14219.9	1.45077
$459$	6772.64	0.688715
$460$	−4601.30	−0.466384
$461$	8741.16	0.883116	0.441558	−	0.897233i	$-0.354426\pi$
$461$	8741.16	0.883116	0.441558	+	0.897233i	$0.354426\pi$
$462$	−1049.35	−0.105672
$463$	−7546.09	−0.757444	−0.378722	−	0.925511i	$-0.623636\pi$
$463$	−7546.09	−0.757444	−0.378722	+	0.925511i	$0.623636\pi$
$464$	−5176.44	−0.517910
$465$	−1674.01	−0.166947
$466$	27478.3	2.73156
$467$	14340.9	1.42102	0.710510	−	0.703687i	$-0.248464\pi$
$467$	14340.9	1.42102	0.710510	+	0.703687i	$0.248464\pi$
$468$	−11567.8	−1.14257
$469$	−14009.7	−1.37934
$470$	−6076.91	−0.596398
$471$	5235.97	0.512231
$472$	229.046	0.0223362
$473$	−4063.63	−0.395023
$474$	−5192.63	−0.503176
$475$	−475.000	−0.0458831
$476$	−8764.21	−0.843922
$477$	2860.64	0.274590
$478$	−22453.4	−2.14852
$479$	3117.77	0.297400	0.148700	−	0.988882i	$-0.452491\pi$
$479$	3117.77	0.297400	0.148700	+	0.988882i	$0.452491\pi$
$480$	−2247.82	−0.213746
$481$	13687.8	1.29753
$482$	21121.3	1.99595
$483$	2555.06	0.240702
$484$	1024.51	0.0962161
$485$	−4518.24	−0.423016
$486$	−13182.5	−1.23039
$487$	−6537.13	−0.608266	−0.304133	−	0.952630i	$-0.598367\pi$
$487$	−6537.13	−0.608266	−0.304133	+	0.952630i	$0.598367\pi$
$488$	−628.669	−0.0583166
$489$	729.047	0.0674205
$490$	3242.78	0.298967
$491$	13922.8	1.27968	0.639842	−	0.768506i	$-0.279000\pi$
$491$	13922.8	1.27968	0.639842	+	0.768506i	$0.279000\pi$
$492$	−4773.52	−0.437412
$493$	6593.19	0.602317
$494$	−4392.17	−0.400026
$495$	−1319.07	−0.119773
$496$	11574.0	1.04776
$497$	6191.68	0.558823
$498$	−1941.53	−0.174703
$499$	−11122.4	−0.997808	−0.498904	−	0.866657i	$-0.666264\pi$
$499$	−11122.4	−0.997808	−0.498904	+	0.866657i	$0.666264\pi$
$500$	−1058.38	−0.0946642
$501$	−3102.94	−0.276705
$502$	22449.9	1.99599
$503$	8019.77	0.710902	0.355451	−	0.934695i	$-0.384327\pi$
$503$	8019.77	0.710902	0.355451	+	0.934695i	$0.384327\pi$
$504$	615.153	0.0543672
$505$	7903.03	0.696397
$506$	−4851.55	−0.426240
$507$	−1820.59	−0.159478
$508$	2770.53	0.241973
$509$	−12772.5	−1.11224	−0.556120	−	0.831102i	$-0.687711\pi$
$509$	−12772.5	−1.11224	−0.556120	+	0.831102i	$0.687711\pi$
$510$	2695.32	0.234021
$511$	−3534.49	−0.305982
$512$	16451.7	1.42005
$513$	−1682.54	−0.144807
$514$	−7676.93	−0.658784
$515$	381.954	0.0326813
$516$	−5432.98	−0.463515
$517$	−3294.56	−0.280261
$518$	−13196.5	−1.11935
$519$	−3068.83	−0.259550
$520$	−539.798	−0.0455226
$521$	11109.6	0.934203	0.467101	−	0.884204i	$-0.345298\pi$
$521$	11109.6	0.934203	0.467101	+	0.884204i	$0.345298\pi$
$522$	−8389.97	−0.703484
$523$	−5989.80	−0.500795	−0.250398	−	0.968143i	$-0.580561\pi$
$523$	−5989.80	−0.500795	−0.250398	+	0.968143i	$0.580561\pi$
$524$	16508.5	1.37629
$525$	587.707	0.0488565
$526$	−524.409	−0.0434702
$527$	−14741.7	−1.21852
$528$	−1147.26	−0.0945605
$529$	−354.001	−0.0290952
$530$	2420.12	0.198346
$531$	−2898.56	−0.236887
$532$	2177.31	0.177440
$533$	18490.1	1.50262
$534$	8465.27	0.686008
$535$	2995.46	0.242066
$536$	1961.72	0.158085
$537$	6354.88	0.510677
$538$	−12213.8	−0.978766
$539$	1758.06	0.140491
$540$	−3748.97	−0.298759
$541$	−1076.19	−0.0855249	−0.0427625	−	0.999085i	$-0.513616\pi$
$541$	−1076.19	−0.0855249	−0.0427625	+	0.999085i	$0.513616\pi$
$542$	28091.9	2.22629
$543$	1500.38	0.118577
$544$	−19794.8	−1.56010
$545$	3954.05	0.310776
$546$	5434.33	0.425949
$547$	15391.0	1.20306	0.601529	−	0.798851i	$-0.294558\pi$
$547$	15391.0	1.20306	0.601529	+	0.798851i	$0.294558\pi$
$548$	−23808.4	−1.85592
$549$	7955.77	0.618477
$550$	−1115.94	−0.0865159
$551$	−1637.96	−0.126641
$552$	−357.775	−0.0275868
$553$	−9970.77	−0.766728
$554$	970.508	0.0744277
$555$	2086.76	0.159600
$556$	13894.3	1.05980
$557$	6003.50	0.456690	0.228345	−	0.973580i	$-0.426669\pi$
$557$	6003.50	0.456690	0.228345	+	0.973580i	$0.426669\pi$
$558$	18759.2	1.42319
$559$	21044.5	1.59229
$560$	−4063.38	−0.306623
$561$	1461.25	0.109972
$562$	−28168.3	−2.11425
$563$	9856.55	0.737840	0.368920	−	0.929461i	$-0.379728\pi$
$563$	9856.55	0.737840	0.368920	+	0.929461i	$0.379728\pi$
$564$	−4404.75	−0.328854
$565$	−7157.49	−0.532952
$566$	−12712.3	−0.944063
$567$	−6682.24	−0.494934
$568$	−866.997	−0.0640464
$569$	22908.9	1.68786	0.843929	−	0.536455i	$-0.180237\pi$
$569$	22908.9	1.68786	0.843929	+	0.536455i	$0.180237\pi$
$570$	−669.602	−0.0492045
$571$	−6367.65	−0.466686	−0.233343	−	0.972394i	$-0.574966\pi$
$571$	−6367.65	−0.466686	−0.233343	+	0.972394i	$0.574966\pi$
$572$	−5305.68	−0.387835
$573$	−7376.02	−0.537762
$574$	−17826.5	−1.29627
$575$	2717.19	0.197069
$576$	13668.7	0.988765
$577$	−20212.0	−1.45830	−0.729150	−	0.684354i	$-0.760084\pi$
$577$	−20212.0	−1.45830	−0.729150	+	0.684354i	$0.760084\pi$
$578$	3798.90	0.273379
$579$	−7650.60	−0.549133
$580$	−3649.63	−0.261281
$581$	−3728.09	−0.266208
$582$	−6369.31	−0.453637
$583$	1312.05	0.0932071
$584$	494.921	0.0350685
$585$	6831.12	0.482790
$586$	−8366.99	−0.589825
$587$	8897.31	0.625607	0.312804	−	0.949818i	$-0.398732\pi$
$587$	8897.31	0.625607	0.312804	+	0.949818i	$0.398732\pi$
$588$	2350.48	0.164851
$589$	3662.31	0.256202
$590$	−2452.20	−0.171111
$591$	−1149.47	−0.0800049
$592$	−14427.8	−1.00165
$593$	15781.3	1.09285	0.546424	−	0.837509i	$-0.315989\pi$
$593$	15781.3	1.09285	0.546424	+	0.837509i	$0.315989\pi$
$594$	−3952.86	−0.273044
$595$	5175.50	0.356596
$596$	12313.3	0.846263
$597$	6459.36	0.442821
$598$	25125.0	1.71812
$599$	−16726.2	−1.14092	−0.570461	−	0.821325i	$-0.693235\pi$
$599$	−16726.2	−1.14092	−0.570461	+	0.821325i	$0.693235\pi$
$600$	−82.2943	−0.00559942
$601$	12881.0	0.874255	0.437127	−	0.899400i	$-0.355996\pi$
$601$	12881.0	0.874255	0.437127	+	0.899400i	$0.355996\pi$
$602$	−20289.2	−1.37363
$603$	−24825.5	−1.67657
$604$	11497.4	0.774540
$605$	−605.000	−0.0406558
$606$	11140.8	0.746807
$607$	−3583.03	−0.239589	−0.119795	−	0.992799i	$-0.538224\pi$
$607$	−3583.03	−0.239589	−0.119795	+	0.992799i	$0.538224\pi$
$608$	4917.66	0.328022
$609$	2026.61	0.134848
$610$	6730.63	0.446746
$611$	17061.7	1.12969
$612$	−15530.4	−1.02578
$613$	23897.2	1.57455	0.787276	−	0.616601i	$-0.211491\pi$
$613$	23897.2	1.57455	0.787276	+	0.616601i	$0.211491\pi$
$614$	−34449.3	−2.26427
$615$	2818.89	0.184827
$616$	282.145	0.0184544
$617$	−22689.6	−1.48047	−0.740235	−	0.672349i	$-0.765286\pi$
$617$	−22689.6	−1.48047	−0.740235	+	0.672349i	$0.765286\pi$
$618$	538.436	0.0350471
$619$	−11240.1	−0.729848	−0.364924	−	0.931037i	$-0.618905\pi$
$619$	−11240.1	−0.729848	−0.364924	+	0.931037i	$0.618905\pi$
$620$	8160.23	0.528585
$621$	9624.80	0.621948
$622$	−25366.5	−1.63522
$623$	16254.8	1.04532
$624$	5941.36	0.381161
$625$	625.000	0.0400000
$626$	−13621.5	−0.869687
$627$	−363.021	−0.0231223
$628$	−25523.6	−1.62182
$629$	18376.5	1.16490
$630$	−6585.92	−0.416491
$631$	8627.64	0.544312	0.272156	−	0.962253i	$-0.412263\pi$
$631$	8627.64	0.544312	0.272156	+	0.962253i	$0.412263\pi$
$632$	1396.17	0.0878743
$633$	−3586.39	−0.225191
$634$	−12917.7	−0.809192
$635$	−1636.07	−0.102245
$636$	1754.19	0.109368
$637$	−9104.53	−0.566302
$638$	−3848.12	−0.238791
$639$	10971.8	0.679245
$640$	1210.83	0.0747848
$641$	−13698.6	−0.844092	−0.422046	−	0.906575i	$-0.638688\pi$
$641$	−13698.6	−0.844092	−0.422046	+	0.906575i	$0.638688\pi$
$642$	4222.67	0.259588
$643$	30043.0	1.84258	0.921290	−	0.388876i	$-0.127137\pi$
$643$	30043.0	1.84258	0.921290	+	0.388876i	$0.127137\pi$
$644$	−12455.1	−0.762109
$645$	3208.32	0.195856
$646$	−5896.68	−0.359136
$647$	16898.0	1.02679	0.513393	−	0.858154i	$-0.328388\pi$
$647$	16898.0	1.02679	0.513393	+	0.858154i	$0.328388\pi$
$648$	935.688	0.0567242
$649$	−1329.45	−0.0804088
$650$	5779.17	0.348735
$651$	−4531.30	−0.272804
$652$	−3553.86	−0.213466
$653$	−18268.2	−1.09478	−0.547389	−	0.836878i	$-0.684378\pi$
$653$	−18268.2	−1.09478	−0.547389	+	0.836878i	$0.684378\pi$
$654$	5573.98	0.333272
$655$	−9748.72	−0.581548
$656$	−19489.7	−1.15997
$657$	−6263.19	−0.371919
$658$	−16449.3	−0.974561
$659$	−9985.59	−0.590263	−0.295131	−	0.955457i	$-0.595363\pi$
$659$	−9985.59	−0.590263	−0.295131	+	0.955457i	$0.595363\pi$
$660$	−808.871	−0.0477049
$661$	641.763	0.0377635	0.0188817	−	0.999822i	$-0.493989\pi$
$661$	641.763	0.0377635	0.0188817	+	0.999822i	$0.493989\pi$
$662$	18345.0	1.07704
$663$	−7567.46	−0.443282
$664$	522.029	0.0305100
$665$	−1285.76	−0.0749767
$666$	−23384.5	−1.36056
$667$	9369.77	0.543926
$668$	15125.8	0.876100
$669$	−4966.00	−0.286991
$670$	−21002.5	−1.21104
$671$	3648.97	0.209936
$672$	−6084.52	−0.349279
$673$	−8092.74	−0.463525	−0.231762	−	0.972772i	$-0.574449\pi$
$673$	−8092.74	−0.463525	−0.231762	+	0.972772i	$0.574449\pi$
$674$	−32183.2	−1.83924
$675$	2213.87	0.126240
$676$	8874.75	0.504936
$677$	5139.63	0.291776	0.145888	−	0.989301i	$-0.453396\pi$
$677$	5139.63	0.291776	0.145888	+	0.989301i	$0.453396\pi$
$678$	−10089.8	−0.571531
$679$	−12230.2	−0.691241
$680$	−724.704	−0.0408693
$681$	−3491.03	−0.196441
$682$	8604.03	0.483087
$683$	−20071.5	−1.12447	−0.562236	−	0.826977i	$-0.690059\pi$
$683$	−20071.5	−1.12447	−0.562236	+	0.826977i	$0.690059\pi$
$684$	3858.23	0.215677
$685$	14059.5	0.784212
$686$	27615.8	1.53699
$687$	−6086.59	−0.338017
$688$	−22182.1	−1.22920
$689$	−6794.80	−0.375706
$690$	3830.39	0.211334
$691$	−30417.5	−1.67458	−0.837292	−	0.546756i	$-0.815863\pi$
$691$	−30417.5	−1.67458	−0.837292	+	0.546756i	$0.815863\pi$
$692$	14959.5	0.821784
$693$	−3570.52	−0.195719
$694$	−25890.0	−1.41610
$695$	−8204.93	−0.447814
$696$	−283.778	−0.0154548
$697$	24823.8	1.34902
$698$	−41353.2	−2.24246
$699$	−11761.6	−0.636433
$700$	−2864.88	−0.154689
$701$	8822.49	0.475351	0.237675	−	0.971345i	$-0.423615\pi$
$701$	8822.49	0.475351	0.237675	+	0.971345i	$0.423615\pi$
$702$	20470.9	1.10060
$703$	−4565.32	−0.244928
$704$	6269.25	0.335627
$705$	2601.12	0.138956
$706$	46423.5	2.47475
$707$	21392.4	1.13797
$708$	−1777.44	−0.0943506
$709$	12325.3	0.652872	0.326436	−	0.945219i	$-0.394152\pi$
$709$	12325.3	0.652872	0.326436	+	0.945219i	$0.394152\pi$
$710$	9282.20	0.490641
$711$	−17668.4	−0.931951
$712$	−2276.10	−0.119804
$713$	−20949.9	−1.10039
$714$	7295.84	0.382409
$715$	3133.14	0.163878
$716$	−30977.9	−1.61690
$717$	9610.81	0.500589
$718$	30816.5	1.60176
$719$	−3323.49	−0.172386	−0.0861929	−	0.996278i	$-0.527470\pi$
$719$	−3323.49	−0.172386	−0.0861929	+	0.996278i	$0.527470\pi$
$720$	−7200.39	−0.372698
$721$	1033.89	0.0534039
$722$	1464.92	0.0755108
$723$	−9040.62	−0.465041
$724$	−7313.84	−0.375437
$725$	2155.21	0.110403
$726$	−852.862	−0.0435987
$727$	14578.7	0.743731	0.371866	−	0.928287i	$-0.378718\pi$
$727$	14578.7	0.743731	0.371866	+	0.928287i	$0.378718\pi$
$728$	−1461.16	−0.0743875
$729$	−7688.08	−0.390595
$730$	−5298.70	−0.268649
$731$	28253.2	1.42953
$732$	4878.59	0.246336
$733$	28721.1	1.44725	0.723627	−	0.690191i	$-0.242474\pi$
$733$	28721.1	1.44725	0.723627	+	0.690191i	$0.242474\pi$
$734$	12783.3	0.642833
$735$	−1388.02	−0.0696570
$736$	−28131.0	−1.40886
$737$	−11386.4	−0.569096
$738$	−31588.8	−1.57561
$739$	−4818.66	−0.239861	−0.119930	−	0.992782i	$-0.538267\pi$
$739$	−4818.66	−0.239861	−0.119930	+	0.992782i	$0.538267\pi$
$740$	−10172.3	−0.505324
$741$	1880.00	0.0932030
$742$	6550.91	0.324113
$743$	−26090.9	−1.28826	−0.644132	−	0.764914i	$-0.722781\pi$
$743$	−26090.9	−1.28826	−0.644132	+	0.764914i	$0.722781\pi$
$744$	634.500	0.0312660
$745$	−7271.33	−0.357585
$746$	15416.1	0.756599
$747$	−6606.24	−0.323574
$748$	−7123.12	−0.348191
$749$	8108.29	0.395555
$750$	881.056	0.0428955
$751$	13971.8	0.678880	0.339440	−	0.940628i	$-0.389763\pi$
$751$	13971.8	0.678880	0.339440	+	0.940628i	$0.389763\pi$
$752$	−17984.0	−0.872088
$753$	−9609.32	−0.465051
$754$	19928.5	0.962536
$755$	−6789.51	−0.327279
$756$	−10147.9	−0.488197
$757$	−5629.85	−0.270304	−0.135152	−	0.990825i	$-0.543152\pi$
$757$	−5629.85	−0.270304	−0.135152	+	0.990825i	$0.543152\pi$
$758$	−17982.1	−0.861663
$759$	2076.63	0.0993107
$760$	180.039	0.00859305
$761$	−3863.28	−0.184026	−0.0920130	−	0.995758i	$-0.529330\pi$
$761$	−3863.28	−0.184026	−0.0920130	+	0.995758i	$0.529330\pi$
$762$	−2306.35	−0.109646
$763$	10703.0	0.507833
$764$	35955.6	1.70266
$765$	9171.08	0.433440
$766$	35309.7	1.66552
$767$	6884.87	0.324118
$768$	−6212.63	−0.291900
$769$	12427.7	0.582775	0.291387	−	0.956605i	$-0.405883\pi$
$769$	12427.7	0.582775	0.291387	+	0.956605i	$0.405883\pi$
$770$	−3020.68	−0.141374
$771$	3285.99	0.153492
$772$	37294.1	1.73866
$773$	−40557.1	−1.88711	−0.943555	−	0.331214i	$-0.892542\pi$
$773$	−40557.1	−1.88711	−0.943555	+	0.331214i	$0.892542\pi$
$774$	−35952.8	−1.66963
$775$	−4818.83	−0.223352
$776$	1712.55	0.0792229
$777$	5648.57	0.260800
$778$	47634.8	2.19510
$779$	−6167.03	−0.283641
$780$	4188.94	0.192293
$781$	5032.30	0.230563
$782$	33731.4	1.54250
$783$	7634.14	0.348432
$784$	9596.70	0.437168
$785$	15072.4	0.685294
$786$	−13742.7	−0.623645
$787$	3699.86	0.167581	0.0837903	−	0.996483i	$-0.473297\pi$
$787$	3699.86	0.167581	0.0837903	+	0.996483i	$0.473297\pi$
$788$	5603.29	0.253311
$789$	224.465	0.0101282
$790$	−14947.6	−0.673179
$791$	−19374.3	−0.870886
$792$	499.966	0.0224312
$793$	−18897.1	−0.846225
$794$	24512.6	1.09561
$795$	−1035.89	−0.0462130
$796$	−31487.2	−1.40205
$797$	−12269.6	−0.545307	−0.272654	−	0.962112i	$-0.587901\pi$
$797$	−12269.6	−0.545307	−0.272654	+	0.962112i	$0.587901\pi$
$798$	−1812.52	−0.0804040
$799$	22906.1	1.01422
$800$	−6470.61	−0.285963
$801$	28803.9	1.27058
$802$	−48159.5	−2.12041
$803$	−2872.66	−0.126244
$804$	−15223.4	−0.667770
$805$	7355.04	0.322026
$806$	−44558.1	−1.94726
$807$	5227.94	0.228045
$808$	−2995.49	−0.130422
$809$	−15057.5	−0.654382	−0.327191	−	0.944958i	$-0.606102\pi$
$809$	−15057.5	−0.654382	−0.327191	+	0.944958i	$0.606102\pi$
$810$	−10017.6	−0.434547
$811$	−5323.01	−0.230476	−0.115238	−	0.993338i	$-0.536763\pi$
$811$	−5323.01	−0.230476	−0.115238	+	0.993338i	$0.536763\pi$
$812$	−9879.04	−0.426954
$813$	−12024.3	−0.518708
$814$	−10725.5	−0.461829
$815$	2098.65	0.0901993
$816$	7976.54	0.342200
$817$	−7019.00	−0.300567
$818$	−14526.7	−0.620920
$819$	18490.8	0.788916
$820$	−13741.1	−0.585197
$821$	7519.48	0.319649	0.159824	−	0.987145i	$-0.448907\pi$
$821$	7519.48	0.319649	0.159824	+	0.987145i	$0.448907\pi$
$822$	19819.5	0.840979
$823$	35036.2	1.48394	0.741972	−	0.670430i	$-0.233890\pi$
$823$	35036.2	1.48394	0.741972	+	0.670430i	$0.233890\pi$
$824$	−144.772	−0.00612060
$825$	477.660	0.0201575
$826$	−6637.75	−0.279609
$827$	33630.6	1.41409	0.707044	−	0.707170i	$-0.250028\pi$
$827$	33630.6	1.41409	0.707044	+	0.707170i	$0.250028\pi$
$828$	−22070.6	−0.926337
$829$	16592.5	0.695152	0.347576	−	0.937652i	$-0.387005\pi$
$829$	16592.5	0.695152	0.347576	+	0.937652i	$0.387005\pi$
$830$	−5588.92	−0.233728
$831$	−415.411	−0.0173411
$832$	−32466.9	−1.35287
$833$	−12223.2	−0.508416
$834$	−11566.4	−0.480230
$835$	−8932.19	−0.370193
$836$	1769.61	0.0732095
$837$	−17069.2	−0.704896
$838$	−49565.0	−2.04319
$839$	6564.43	0.270118	0.135059	−	0.990838i	$-0.456878\pi$
$839$	6564.43	0.270118	0.135059	+	0.990838i	$0.456878\pi$
$840$	−222.759	−0.00914989
$841$	−16957.1	−0.695278
$842$	4458.74	0.182492
$843$	12057.0	0.492603
$844$	17482.4	0.712998
$845$	−5240.77	−0.213359
$846$	−29148.5	−1.18457
$847$	−1637.65	−0.0664348
$848$	7162.11	0.290033
$849$	5441.31	0.219959
$850$	7758.80	0.313088
$851$	26115.4	1.05197
$852$	6728.06	0.270540
$853$	−1930.69	−0.0774979	−0.0387489	−	0.999249i	$-0.512337\pi$
$853$	−1930.69	−0.0774979	−0.0387489	+	0.999249i	$0.512337\pi$
$854$	18218.8	0.730019
$855$	−2278.39	−0.0911336
$856$	−1135.37	−0.0453343
$857$	1748.76	0.0697043	0.0348521	−	0.999392i	$-0.488904\pi$
$857$	1748.76	0.0697043	0.0348521	+	0.999392i	$0.488904\pi$
$858$	4416.76	0.175741
$859$	36849.5	1.46366	0.731832	−	0.681485i	$-0.238666\pi$
$859$	36849.5	1.46366	0.731832	+	0.681485i	$0.238666\pi$
$860$	−15639.5	−0.620118
$861$	7630.33	0.302022
$862$	−19625.1	−0.775446
$863$	39558.5	1.56036	0.780178	−	0.625557i	$-0.215128\pi$
$863$	39558.5	1.56036	0.780178	+	0.625557i	$0.215128\pi$
$864$	−22920.1	−0.902497
$865$	−8833.98	−0.347242
$866$	−41308.0	−1.62091
$867$	−1626.06	−0.0636953
$868$	22088.6	0.863750
$869$	−8103.75	−0.316342
$870$	3038.17	0.118395
$871$	58967.4	2.29395
$872$	−1498.70	−0.0582025
$873$	−21672.2	−0.840198
$874$	−8379.95	−0.324320
$875$	1691.79	0.0653632
$876$	−3840.68	−0.148133
$877$	−29758.5	−1.14581	−0.572903	−	0.819623i	$-0.694183\pi$
$877$	−29758.5	−1.14581	−0.572903	+	0.819623i	$0.694183\pi$
$878$	19060.2	0.732632
$879$	3581.36	0.137425
$880$	−3302.51	−0.126509
$881$	−21477.1	−0.821317	−0.410659	−	0.911789i	$-0.634701\pi$
$881$	−21477.1	−0.821317	−0.410659	+	0.911789i	$0.634701\pi$
$882$	15554.3	0.593811
$883$	−39264.7	−1.49645	−0.748223	−	0.663447i	$-0.769093\pi$
$883$	−39264.7	−1.49645	−0.748223	+	0.663447i	$0.769093\pi$
$884$	36888.8	1.40351
$885$	1049.62	0.0398675
$886$	56463.4	2.14100
$887$	20028.5	0.758165	0.379082	−	0.925363i	$-0.376240\pi$
$887$	20028.5	0.758165	0.379082	+	0.925363i	$0.376240\pi$
$888$	−790.946	−0.0298901
$889$	−4428.61	−0.167076
$890$	24368.3	0.917783
$891$	−5431.00	−0.204203
$892$	24207.6	0.908666
$893$	−5690.61	−0.213246
$894$	−10250.3	−0.383470
$895$	18293.3	0.683215
$896$	3277.54	0.122204
$897$	−10754.3	−0.400309
$898$	5671.76	0.210767
$899$	−16616.9	−0.616469
$900$	−5076.62	−0.188023
$901$	−9122.33	−0.337302
$902$	−14488.5	−0.534826
$903$	8684.46	0.320045
$904$	2712.91	0.0998118
$905$	4319.01	0.158640
$906$	−9571.10	−0.350970
$907$	34349.1	1.25749	0.628745	−	0.777612i	$-0.283569\pi$
$907$	34349.1	1.25749	0.628745	+	0.777612i	$0.283569\pi$
$908$	17017.6	0.621969
$909$	37907.7	1.38319
$910$	15643.4	0.569860
$911$	−50959.5	−1.85331	−0.926654	−	0.375916i	$-0.877328\pi$
$911$	−50959.5	−1.85331	−0.926654	+	0.375916i	$0.877328\pi$
$912$	−1981.63	−0.0719498
$913$	−3030.00	−0.109834
$914$	44548.1	1.61217
$915$	−2880.94	−0.104088
$916$	29670.1	1.07023
$917$	−26388.4	−0.950296
$918$	27483.1	0.988102
$919$	−40259.5	−1.44509	−0.722546	−	0.691323i	$-0.757028\pi$
$919$	−40259.5	−1.44509	−0.722546	+	0.691323i	$0.757028\pi$
$920$	−1029.90	−0.0369073
$921$	14745.5	0.527556
$922$	35471.3	1.26701
$923$	−26061.0	−0.929370
$924$	−2189.50	−0.0779537
$925$	6006.99	0.213523
$926$	−30621.7	−1.08671
$927$	1832.08	0.0649120
$928$	−22312.8	−0.789281
$929$	21585.3	0.762317	0.381158	−	0.924510i	$-0.375525\pi$
$929$	21585.3	0.762317	0.381158	+	0.924510i	$0.375525\pi$
$930$	−6793.06	−0.239520
$931$	3036.64	0.106898
$932$	57334.1	2.01506
$933$	10857.7	0.380993
$934$	58194.6	2.03874
$935$	4206.39	0.147127
$936$	−2589.20	−0.0904173
$937$	20017.8	0.697923	0.348962	−	0.937137i	$-0.386534\pi$
$937$	20017.8	0.697923	0.348962	+	0.937137i	$0.386534\pi$
$938$	−56850.8	−1.97894
$939$	5830.46	0.202630
$940$	−12679.6	−0.439961
$941$	−26730.7	−0.926031	−0.463015	−	0.886350i	$-0.653233\pi$
$941$	−26730.7	−0.926031	−0.463015	+	0.886350i	$0.653233\pi$
$942$	21247.4	0.734901
$943$	35277.9	1.21825
$944$	−7257.05	−0.250209
$945$	5992.62	0.206286
$946$	−16490.0	−0.566741
$947$	−44404.3	−1.52370	−0.761851	−	0.647752i	$-0.775709\pi$
$947$	−44404.3	−1.52370	−0.761851	+	0.647752i	$0.775709\pi$
$948$	−10834.5	−0.371191
$949$	14876.8	0.508874
$950$	−1927.53	−0.0658288
$951$	5529.22	0.188536
$952$	−1961.67	−0.0667837
$953$	45994.5	1.56339	0.781694	−	0.623662i	$-0.214356\pi$
$953$	45994.5	1.56339	0.781694	+	0.623662i	$0.214356\pi$
$954$	11608.3	0.393956
$955$	−21232.8	−0.719451
$956$	−46849.5	−1.58496
$957$	1647.13	0.0556365
$958$	12651.8	0.426681
$959$	38057.0	1.28146
$960$	−4949.70	−0.166407
$961$	7362.84	0.247150
$962$	55544.7	1.86157
$963$	14368.1	0.480793
$964$	44070.0	1.47241
$965$	−22023.1	−0.734663
$966$	10368.3	0.345337
$967$	−10394.6	−0.345676	−0.172838	−	0.984950i	$-0.555294\pi$
$967$	−10394.6	−0.345676	−0.172838	+	0.984950i	$0.555294\pi$
$968$	229.313	0.00761406
$969$	2523.98	0.0836759
$970$	−18334.8	−0.606903
$971$	14613.1	0.482963	0.241481	−	0.970405i	$-0.422367\pi$
$971$	14613.1	0.482963	0.241481	+	0.970405i	$0.422367\pi$
$972$	−27505.6	−0.907656
$973$	−22209.6	−0.731764
$974$	−26527.4	−0.872682
$975$	−2473.68	−0.0812525
$976$	19918.7	0.653259
$977$	−52557.5	−1.72105	−0.860523	−	0.509411i	$-0.829863\pi$
$977$	−52557.5	−1.72105	−0.860523	+	0.509411i	$0.829863\pi$
$978$	2958.44	0.0967286
$979$	13211.1	0.431287
$980$	6766.13	0.220547
$981$	18966.0	0.617266
$982$	56497.9	1.83597
$983$	33220.4	1.07789	0.538945	−	0.842341i	$-0.318823\pi$
$983$	33220.4	1.07789	0.538945	+	0.842341i	$0.318823\pi$
$984$	−1068.44	−0.0346146
$985$	−3308.89	−0.107035
$986$	26754.9	0.864147
$987$	7040.87	0.227065
$988$	−9164.36	−0.295098
$989$	40151.5	1.29094
$990$	−5352.72	−0.171839
$991$	25500.8	0.817416	0.408708	−	0.912665i	$-0.365979\pi$
$991$	25500.8	0.817416	0.408708	+	0.912665i	$0.365979\pi$
$992$	49889.2	1.59676
$993$	−7852.28	−0.250941
$994$	25125.6	0.801746
$995$	18594.0	0.592433
$996$	−4051.05	−0.128878
$997$	−24293.2	−0.771687	−0.385844	−	0.922564i	$-0.626090\pi$
$997$	−24293.2	−0.771687	−0.385844	+	0.922564i	$0.626090\pi$
$998$	−45134.2	−1.43156
$999$	21277.9	0.673877

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.g.1.19	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.g.1.19	✓	23	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)

\(f(q)\)	\(=\)	\(q+4.05796 q^{2} -1.73694 q^{3} +8.46702 q^{4} -5.00000 q^{5} -7.04845 q^{6} -13.5343 q^{7} +1.89515 q^{8} -23.9830 q^{9} +O(q^{10})\)	\(q+4.05796 q^{2} -1.73694 q^{3} +8.46702 q^{4} -5.00000 q^{5} -7.04845 q^{6} -13.5343 q^{7} +1.89515 q^{8} -23.9830 q^{9} -20.2898 q^{10} -11.0000 q^{11} -14.7067 q^{12} +56.9663 q^{13} -54.9215 q^{14} +8.68472 q^{15} -60.0457 q^{16} +76.4798 q^{17} -97.3221 q^{18} -19.0000 q^{19} -42.3351 q^{20} +23.5083 q^{21} -44.6375 q^{22} +108.688 q^{23} -3.29177 q^{24} +25.0000 q^{25} +231.167 q^{26} +88.5547 q^{27} -114.595 q^{28} +86.2082 q^{29} +35.2422 q^{30} -192.753 q^{31} -258.824 q^{32} +19.1064 q^{33} +310.352 q^{34} +67.6714 q^{35} -203.065 q^{36} +240.280 q^{37} -77.1012 q^{38} -98.9472 q^{39} -9.47576 q^{40} +324.580 q^{41} +95.3957 q^{42} +369.421 q^{43} -93.1372 q^{44} +119.915 q^{45} +441.050 q^{46} +299.506 q^{47} +104.296 q^{48} -159.823 q^{49} +101.449 q^{50} -132.841 q^{51} +482.335 q^{52} -119.278 q^{53} +359.351 q^{54} +55.0000 q^{55} -25.6495 q^{56} +33.0019 q^{57} +349.829 q^{58} +120.859 q^{59} +73.5337 q^{60} -331.725 q^{61} -782.185 q^{62} +324.593 q^{63} -569.932 q^{64} -284.831 q^{65} +77.5329 q^{66} +1035.13 q^{67} +647.556 q^{68} -188.784 q^{69} +274.608 q^{70} -457.482 q^{71} -45.4515 q^{72} +261.151 q^{73} +975.045 q^{74} -43.4236 q^{75} -160.873 q^{76} +148.877 q^{77} -401.524 q^{78} +736.705 q^{79} +300.229 q^{80} +493.727 q^{81} +1317.13 q^{82} +275.455 q^{83} +199.045 q^{84} -382.399 q^{85} +1499.09 q^{86} -149.739 q^{87} -20.8467 q^{88} -1201.01 q^{89} +486.610 q^{90} -770.997 q^{91} +920.260 q^{92} +334.802 q^{93} +1215.38 q^{94} +95.0000 q^{95} +449.563 q^{96} +903.648 q^{97} -648.556 q^{98} +263.813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9}+O(q^{10}) \) 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9	\( 23 q + 6 q^{2} + 9 q^{3} + 92 q^{4} - 115 q^{5} - 25 q^{6} - 37 q^{7} + 42 q^{8} + 170 q^{9} - 30 q^{10} - 253 q^{11} + 44 q^{12} - 37 q^{13} + 61 q^{14} - 45 q^{15} + 588 q^{16} - 73 q^{17} + 391 q^{18} - 437 q^{19} - 460 q^{20} - 127 q^{21} - 66 q^{22} - 175 q^{23} + 16 q^{24} + 575 q^{25} + 719 q^{26} + 21 q^{27} + 253 q^{28} + 71 q^{29} + 125 q^{30} + 302 q^{31} + 1107 q^{32} - 99 q^{33} + 1267 q^{34} + 185 q^{35} + 703 q^{36} - 500 q^{37} - 114 q^{38} + 457 q^{39} - 210 q^{40} + 770 q^{41} + 2596 q^{42} - 902 q^{43} - 1012 q^{44} - 850 q^{45} - 1101 q^{46} + 356 q^{47} + 1221 q^{48} + 908 q^{49} + 150 q^{50} - 451 q^{51} - 358 q^{52} + 1327 q^{53} + 2534 q^{54} + 1265 q^{55} + 3135 q^{56} - 171 q^{57} + 1014 q^{58} + 3619 q^{59} - 220 q^{60} - 1432 q^{61} + 1826 q^{62} + 1658 q^{63} + 4006 q^{64} + 185 q^{65} + 275 q^{66} - 605 q^{67} + 5128 q^{68} + 3099 q^{69} - 305 q^{70} + 3230 q^{71} + 2152 q^{72} - 637 q^{73} + 5063 q^{74} + 225 q^{75} - 1748 q^{76} + 407 q^{77} + 7230 q^{78} + 2074 q^{79} - 2940 q^{80} + 2291 q^{81} + 530 q^{82} + 3882 q^{83} + 5096 q^{84} + 365 q^{85} + 2262 q^{86} - 27 q^{87} - 462 q^{88} - 210 q^{89} - 1955 q^{90} + 4133 q^{91} - 6064 q^{92} + 824 q^{93} - 392 q^{94} + 2185 q^{95} + 2462 q^{96} + 2032 q^{97} + 7896 q^{98} - 1870 q^{99}+O(q^{100}) \) 23 * q + 6 * q^2 + 9 * q^3 + 92 * q^4 - 115 * q^5 - 25 * q^6 - 37 * q^7 + 42 * q^8 + 170 * q^9 - 30 * q^10 - 253 * q^11 + 44 * q^12 - 37 * q^13 + 61 * q^14 - 45 * q^15 + 588 * q^16 - 73 * q^17 + 391 * q^18 - 437 * q^19 - 460 * q^20 - 127 * q^21 - 66 * q^22 - 175 * q^23 + 16 * q^24 + 575 * q^25 + 719 * q^26 + 21 * q^27 + 253 * q^28 + 71 * q^29 + 125 * q^30 + 302 * q^31 + 1107 * q^32 - 99 * q^33 + 1267 * q^34 + 185 * q^35 + 703 * q^36 - 500 * q^37 - 114 * q^38 + 457 * q^39 - 210 * q^40 + 770 * q^41 + 2596 * q^42 - 902 * q^43 - 1012 * q^44 - 850 * q^45 - 1101 * q^46 + 356 * q^47 + 1221 * q^48 + 908 * q^49 + 150 * q^50 - 451 * q^51 - 358 * q^52 + 1327 * q^53 + 2534 * q^54 + 1265 * q^55 + 3135 * q^56 - 171 * q^57 + 1014 * q^58 + 3619 * q^59 - 220 * q^60 - 1432 * q^61 + 1826 * q^62 + 1658 * q^63 + 4006 * q^64 + 185 * q^65 + 275 * q^66 - 605 * q^67 + 5128 * q^68 + 3099 * q^69 - 305 * q^70 + 3230 * q^71 + 2152 * q^72 - 637 * q^73 + 5063 * q^74 + 225 * q^75 - 1748 * q^76 + 407 * q^77 + 7230 * q^78 + 2074 * q^79 - 2940 * q^80 + 2291 * q^81 + 530 * q^82 + 3882 * q^83 + 5096 * q^84 + 365 * q^85 + 2262 * q^86 - 27 * q^87 - 462 * q^88 - 210 * q^89 - 1955 * q^90 + 4133 * q^91 - 6064 * q^92 + 824 * q^93 - 392 * q^94 + 2185 * q^95 + 2462 * q^96 + 2032 * q^97 + 7896 * q^98 - 1870 * q^99

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