LMFDB - Embedded newform 1045.4.a.d.1.15

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+1.45119 q^{2} -8.75662 q^{3} -5.89406 q^{4} +5.00000 q^{5} -12.7075 q^{6} -31.7430 q^{7} -20.1629 q^{8} +49.6783 q^{9} +O(q^{10})$	\(q+1.45119 q^{2} -8.75662 q^{3} -5.89406 q^{4} +5.00000 q^{5} -12.7075 q^{6} -31.7430 q^{7} -20.1629 q^{8} +49.6783 q^{9} +7.25593 q^{10} -11.0000 q^{11} +51.6120 q^{12} +24.2701 q^{13} -46.0650 q^{14} -43.7831 q^{15} +17.8924 q^{16} +30.6308 q^{17} +72.0925 q^{18} -19.0000 q^{19} -29.4703 q^{20} +277.961 q^{21} -15.9631 q^{22} +27.2772 q^{23} +176.559 q^{24} +25.0000 q^{25} +35.2204 q^{26} -198.585 q^{27} +187.095 q^{28} +258.777 q^{29} -63.5374 q^{30} -151.503 q^{31} +187.268 q^{32} +96.3228 q^{33} +44.4510 q^{34} -158.715 q^{35} -292.807 q^{36} +297.549 q^{37} -27.5726 q^{38} -212.524 q^{39} -100.814 q^{40} -132.459 q^{41} +403.373 q^{42} +10.5691 q^{43} +64.8346 q^{44} +248.392 q^{45} +39.5844 q^{46} -517.418 q^{47} -156.676 q^{48} +664.617 q^{49} +36.2797 q^{50} -268.222 q^{51} -143.049 q^{52} +140.535 q^{53} -288.184 q^{54} -55.0000 q^{55} +640.030 q^{56} +166.376 q^{57} +375.534 q^{58} -201.930 q^{59} +258.060 q^{60} +630.247 q^{61} -219.859 q^{62} -1576.94 q^{63} +128.622 q^{64} +121.350 q^{65} +139.782 q^{66} +582.137 q^{67} -180.540 q^{68} -238.856 q^{69} -230.325 q^{70} +731.683 q^{71} -1001.66 q^{72} -958.656 q^{73} +431.799 q^{74} -218.915 q^{75} +111.987 q^{76} +349.173 q^{77} -308.412 q^{78} -562.292 q^{79} +89.4618 q^{80} +397.620 q^{81} -192.223 q^{82} -101.137 q^{83} -1638.32 q^{84} +153.154 q^{85} +15.3377 q^{86} -2266.01 q^{87} +221.792 q^{88} +670.413 q^{89} +360.463 q^{90} -770.404 q^{91} -160.774 q^{92} +1326.65 q^{93} -750.870 q^{94} -95.0000 q^{95} -1639.84 q^{96} -1496.52 q^{97} +964.483 q^{98} -546.461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18} - 418 q^{19} + 370 q^{20} - 107 q^{21} + 44 q^{22} - 361 q^{23} + 208 q^{24} + 550 q^{25} - 365 q^{26} - 1467 q^{27} - 773 q^{28} - 319 q^{29} - 45 q^{30} - 402 q^{31} - 873 q^{32} + 231 q^{33} - 717 q^{34} - 205 q^{35} + 725 q^{36} - 838 q^{37} + 76 q^{38} - 607 q^{39} - 390 q^{40} - 392 q^{41} - 1350 q^{42} - 610 q^{43} - 814 q^{44} + 1045 q^{45} - 605 q^{46} - 1866 q^{47} - 1637 q^{48} + 379 q^{49} - 100 q^{50} - 2659 q^{51} - 638 q^{52} - 1303 q^{53} + 2338 q^{54} - 1210 q^{55} + 727 q^{56} + 399 q^{57} + 44 q^{58} - 2417 q^{59} - 980 q^{60} + 918 q^{61} - 1634 q^{62} - 374 q^{63} - 1716 q^{64} - 5 q^{65} + 99 q^{66} - 2339 q^{67} + 4940 q^{68} + 127 q^{69} - 315 q^{70} - 2370 q^{71} - 3306 q^{72} + 2207 q^{73} + 2051 q^{74} - 525 q^{75} - 1406 q^{76} + 451 q^{77} + 1380 q^{78} + 586 q^{79} + 30 q^{80} + 1950 q^{81} - 1566 q^{82} - 2870 q^{83} + 3076 q^{84} + 935 q^{85} - 1246 q^{86} - 1811 q^{87} + 858 q^{88} - 1768 q^{89} - 1805 q^{90} - 2195 q^{91} - 6728 q^{92} - 2916 q^{93} + 672 q^{94} - 2090 q^{95} + 6022 q^{96} - 4022 q^{97} + 1162 q^{98} - 2299 q^{99}+O(q^{100}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9 - 20 * q^10 - 242 * q^11 - 196 * q^12 - q^13 - 63 * q^14 - 105 * q^15 + 6 * q^16 + 187 * q^17 - 361 * q^18 - 418 * q^19 + 370 * q^20 - 107 * q^21 + 44 * q^22 - 361 * q^23 + 208 * q^24 + 550 * q^25 - 365 * q^26 - 1467 * q^27 - 773 * q^28 - 319 * q^29 - 45 * q^30 - 402 * q^31 - 873 * q^32 + 231 * q^33 - 717 * q^34 - 205 * q^35 + 725 * q^36 - 838 * q^37 + 76 * q^38 - 607 * q^39 - 390 * q^40 - 392 * q^41 - 1350 * q^42 - 610 * q^43 - 814 * q^44 + 1045 * q^45 - 605 * q^46 - 1866 * q^47 - 1637 * q^48 + 379 * q^49 - 100 * q^50 - 2659 * q^51 - 638 * q^52 - 1303 * q^53 + 2338 * q^54 - 1210 * q^55 + 727 * q^56 + 399 * q^57 + 44 * q^58 - 2417 * q^59 - 980 * q^60 + 918 * q^61 - 1634 * q^62 - 374 * q^63 - 1716 * q^64 - 5 * q^65 + 99 * q^66 - 2339 * q^67 + 4940 * q^68 + 127 * q^69 - 315 * q^70 - 2370 * q^71 - 3306 * q^72 + 2207 * q^73 + 2051 * q^74 - 525 * q^75 - 1406 * q^76 + 451 * q^77 + 1380 * q^78 + 586 * q^79 + 30 * q^80 + 1950 * q^81 - 1566 * q^82 - 2870 * q^83 + 3076 * q^84 + 935 * q^85 - 1246 * q^86 - 1811 * q^87 + 858 * q^88 - 1768 * q^89 - 1805 * q^90 - 2195 * q^91 - 6728 * q^92 - 2916 * q^93 + 672 * q^94 - 2090 * q^95 + 6022 * q^96 - 4022 * q^97 + 1162 * q^98 - 2299 * 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 $

$2$	1.45119	0.513072	0.256536	−	0.966535i	$-0.417419\pi$
$2$	1.45119	0.513072	0.256536	+	0.966535i	$0.417419\pi$
$3$	−8.75662	−1.68521	−0.842606	−	0.538531i	$-0.818979\pi$
$3$	−8.75662	−1.68521	−0.842606	+	0.538531i	$0.818979\pi$
$4$	−5.89406	−0.736757
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−12.7075	−0.864635
$7$	−31.7430	−1.71396	−0.856980	−	0.515350i	$-0.827662\pi$
$7$	−31.7430	−1.71396	−0.856980	+	0.515350i	$0.827662\pi$
$8$	−20.1629	−0.891081
$9$	49.6783	1.83994
$10$	7.25593	0.229453
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	51.6120	1.24159
$13$	24.2701	0.517793	0.258896	−	0.965905i	$-0.416641\pi$
$13$	24.2701	0.517793	0.258896	+	0.965905i	$0.416641\pi$
$14$	−46.0650	−0.879385
$15$	−43.7831	−0.753649
$16$	17.8924	0.279568
$17$	30.6308	0.437003	0.218502	−	0.975837i	$-0.429883\pi$
$17$	30.6308	0.437003	0.218502	+	0.975837i	$0.429883\pi$
$18$	72.0925	0.944021
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−29.4703	−0.329488
$21$	277.961	2.88838
$22$	−15.9631	−0.154697
$23$	27.2772	0.247291	0.123646	−	0.992326i	$-0.460541\pi$
$23$	27.2772	0.247291	0.123646	+	0.992326i	$0.460541\pi$
$24$	176.559	1.50166
$25$	25.0000	0.200000
$26$	35.2204	0.265665
$27$	−198.585	−1.41547
$28$	187.095	1.26277
$29$	258.777	1.65702	0.828512	−	0.559971i	$-0.189188\pi$
$29$	258.777	1.65702	0.828512	+	0.559971i	$0.189188\pi$
$30$	−63.5374	−0.386676
$31$	−151.503	−0.877764	−0.438882	−	0.898545i	$-0.644625\pi$
$31$	−151.503	−0.877764	−0.438882	+	0.898545i	$0.644625\pi$
$32$	187.268	1.03452
$33$	96.3228	0.508110
$34$	44.4510	0.224214
$35$	−158.715	−0.766506
$36$	−292.807	−1.35559
$37$	297.549	1.32207	0.661037	−	0.750353i	$-0.270116\pi$
$37$	297.549	1.32207	0.661037	+	0.750353i	$0.270116\pi$
$38$	−27.5726	−0.117707
$39$	−212.524	−0.872590
$40$	−100.814	−0.398504
$41$	−132.459	−0.504553	−0.252276	−	0.967655i	$-0.581179\pi$
$41$	−132.459	−0.504553	−0.252276	+	0.967655i	$0.581179\pi$
$42$	403.373	1.48195
$43$	10.5691	0.0374831	0.0187415	−	0.999824i	$-0.494034\pi$
$43$	10.5691	0.0374831	0.0187415	+	0.999824i	$0.494034\pi$
$44$	64.8346	0.222141
$45$	248.392	0.822845
$46$	39.5844	0.126878
$47$	−517.418	−1.60581	−0.802906	−	0.596105i	$-0.796714\pi$
$47$	−517.418	−1.60581	−0.802906	+	0.596105i	$0.796714\pi$
$48$	−156.676	−0.471131
$49$	664.617	1.93766
$50$	36.2797	0.102614
$51$	−268.222	−0.736443
$52$	−143.049	−0.381488
$53$	140.535	0.364227	0.182114	−	0.983278i	$-0.441706\pi$
$53$	140.535	0.364227	0.182114	+	0.983278i	$0.441706\pi$
$54$	−288.184	−0.726239
$55$	−55.0000	−0.134840
$56$	640.030	1.52728
$57$	166.376	0.386614
$58$	375.534	0.850173
$59$	−201.930	−0.445577	−0.222788	−	0.974867i	$-0.571516\pi$
$59$	−201.930	−0.445577	−0.222788	+	0.974867i	$0.571516\pi$
$60$	258.060	0.555257
$61$	630.247	1.32287	0.661433	−	0.750004i	$-0.269949\pi$
$61$	630.247	1.32287	0.661433	+	0.750004i	$0.269949\pi$
$62$	−219.859	−0.450356
$63$	−1576.94	−3.15358
$64$	128.622	0.251215
$65$	121.350	0.231564
$66$	139.782	0.260697
$67$	582.137	1.06148	0.530742	−	0.847534i	$-0.321913\pi$
$67$	582.137	1.06148	0.530742	+	0.847534i	$0.321913\pi$
$68$	−180.540	−0.321965
$69$	−238.856	−0.416738
$70$	−230.325	−0.393273
$71$	731.683	1.22302	0.611512	−	0.791235i	$-0.290561\pi$
$71$	731.683	1.22302	0.611512	+	0.791235i	$0.290561\pi$
$72$	−1001.66	−1.63953
$73$	−958.656	−1.53702	−0.768508	−	0.639840i	$-0.779001\pi$
$73$	−958.656	−1.53702	−0.768508	+	0.639840i	$0.779001\pi$
$74$	431.799	0.678320
$75$	−218.915	−0.337042
$76$	111.987	0.169024
$77$	349.173	0.516778
$78$	−308.412	−0.447702
$79$	−562.292	−0.800794	−0.400397	−	0.916342i	$-0.631128\pi$
$79$	−562.292	−0.800794	−0.400397	+	0.916342i	$0.631128\pi$
$80$	89.4618	0.125027
$81$	397.620	0.545433
$82$	−192.223	−0.258872
$83$	−101.137	−0.133750	−0.0668752	−	0.997761i	$-0.521303\pi$
$83$	−101.137	−0.133750	−0.0668752	+	0.997761i	$0.521303\pi$
$84$	−1638.32	−2.12804
$85$	153.154	0.195434
$86$	15.3377	0.0192315
$87$	−2266.01	−2.79244
$88$	221.792	0.268671
$89$	670.413	0.798468	0.399234	−	0.916849i	$-0.369276\pi$
$89$	670.413	0.798468	0.399234	+	0.916849i	$0.369276\pi$
$90$	360.463	0.422179
$91$	−770.404	−0.887476
$92$	−160.774	−0.182194
$93$	1326.65	1.47922
$94$	−750.870	−0.823898
$95$	−95.0000	−0.102598
$96$	−1639.84	−1.74339
$97$	−1496.52	−1.56648	−0.783240	−	0.621719i	$-0.786434\pi$
$97$	−1496.52	−1.56648	−0.783240	+	0.621719i	$0.786434\pi$
$98$	964.483	0.994158
$99$	−546.461	−0.554762
$100$	−147.351	−0.147351
$101$	−166.226	−0.163763	−0.0818817	−	0.996642i	$-0.526093\pi$
$101$	−166.226	−0.163763	−0.0818817	+	0.996642i	$0.526093\pi$
$102$	−389.240	−0.377848
$103$	−99.3656	−0.0950562	−0.0475281	−	0.998870i	$-0.515134\pi$
$103$	−99.3656	−0.0950562	−0.0475281	+	0.998870i	$0.515134\pi$
$104$	−489.354	−0.461396
$105$	1389.81	1.29172
$106$	203.943	0.186875
$107$	−1064.87	−0.962099	−0.481050	−	0.876693i	$-0.659744\pi$
$107$	−1064.87	−0.962099	−0.481050	+	0.876693i	$0.659744\pi$
$108$	1170.47	1.04286
$109$	−354.815	−0.311790	−0.155895	−	0.987774i	$-0.549826\pi$
$109$	−354.815	−0.311790	−0.155895	+	0.987774i	$0.549826\pi$
$110$	−79.8153	−0.0691826
$111$	−2605.52	−2.22798
$112$	−567.957	−0.479168
$113$	150.542	0.125326	0.0626630	−	0.998035i	$-0.480041\pi$
$113$	150.542	0.125326	0.0626630	+	0.998035i	$0.480041\pi$
$114$	241.442	0.198361
$115$	136.386	0.110592
$116$	−1525.25	−1.22082
$117$	1205.70	0.952706
$118$	−293.038	−0.228613
$119$	−972.313	−0.749006
$120$	882.793	0.671563
$121$	121.000	0.0909091
$122$	914.605	0.678725
$123$	1159.90	0.850278
$124$	892.966	0.646699
$125$	125.000	0.0894427
$126$	−2288.43	−1.61801
$127$	−156.698	−0.109486	−0.0547430	−	0.998500i	$-0.517434\pi$
$127$	−156.698	−0.109486	−0.0547430	+	0.998500i	$0.517434\pi$
$128$	−1311.49	−0.905629
$129$	−92.5495	−0.0631669
$130$	176.102	0.118809
$131$	2621.52	1.74842	0.874211	−	0.485546i	$-0.161379\pi$
$131$	2621.52	1.74842	0.874211	+	0.485546i	$0.161379\pi$
$132$	−567.732	−0.374354
$133$	603.117	0.393209
$134$	844.790	0.544617
$135$	−992.926	−0.633019
$136$	−617.605	−0.389406
$137$	−2949.32	−1.83925	−0.919626	−	0.392794i	$-0.871509\pi$
$137$	−2949.32	−1.83925	−0.919626	+	0.392794i	$0.871509\pi$
$138$	−346.625	−0.213817
$139$	−155.672	−0.0949922	−0.0474961	−	0.998871i	$-0.515124\pi$
$139$	−155.672	−0.0949922	−0.0474961	+	0.998871i	$0.515124\pi$
$140$	935.475	0.564729
$141$	4530.83	2.70613
$142$	1061.81	0.627500
$143$	−266.971	−0.156120
$144$	888.862	0.514388
$145$	1293.89	0.741044
$146$	−1391.19	−0.788600
$147$	−5819.79	−3.26536
$148$	−1753.77	−0.974048
$149$	−81.9598	−0.0450632	−0.0225316	−	0.999746i	$-0.507173\pi$
$149$	−81.9598	−0.0450632	−0.0225316	+	0.999746i	$0.507173\pi$
$150$	−317.687	−0.172927
$151$	3258.21	1.75595	0.877977	−	0.478703i	$-0.158893\pi$
$151$	3258.21	1.75595	0.877977	+	0.478703i	$0.158893\pi$
$152$	383.095	0.204428
$153$	1521.69	0.804059
$154$	506.715	0.265144
$155$	−757.514	−0.392548
$156$	1252.63	0.642887
$157$	−1685.84	−0.856971	−0.428486	−	0.903549i	$-0.640953\pi$
$157$	−1685.84	−0.856971	−0.428486	+	0.903549i	$0.640953\pi$
$158$	−815.990	−0.410865
$159$	−1230.62	−0.613800
$160$	936.341	0.462651
$161$	−865.861	−0.423847
$162$	577.022	0.279846
$163$	3196.75	1.53613	0.768064	−	0.640373i	$-0.221220\pi$
$163$	3196.75	1.53613	0.768064	+	0.640373i	$0.221220\pi$
$164$	780.723	0.371733
$165$	481.614	0.227234
$166$	−146.769	−0.0686236
$167$	−1447.82	−0.670874	−0.335437	−	0.942063i	$-0.608884\pi$
$167$	−1447.82	−0.670874	−0.335437	+	0.942063i	$0.608884\pi$
$168$	−5604.49	−2.57379
$169$	−1607.96	−0.731891
$170$	222.255	0.100272
$171$	−943.888	−0.422111
$172$	−62.2948	−0.0276159
$173$	−8.57581	−0.00376882	−0.00188441	−	0.999998i	$-0.500600\pi$
$173$	−8.57581	−0.00376882	−0.00188441	+	0.999998i	$0.500600\pi$
$174$	−3288.41	−1.43272
$175$	−793.574	−0.342792
$176$	−196.816	−0.0842930
$177$	1768.22	0.750891
$178$	972.894	0.409671
$179$	911.242	0.380499	0.190250	−	0.981736i	$-0.439070\pi$
$179$	911.242	0.380499	0.190250	+	0.981736i	$0.439070\pi$
$180$	−1464.03	−0.606237
$181$	1334.41	0.547988	0.273994	−	0.961731i	$-0.411655\pi$
$181$	1334.41	0.547988	0.273994	+	0.961731i	$0.411655\pi$
$182$	−1118.00	−0.455339
$183$	−5518.83	−2.22931
$184$	−549.988	−0.220357
$185$	1487.75	0.591250
$186$	1925.22	0.758946
$187$	−336.939	−0.131762
$188$	3049.69	1.18309
$189$	6303.69	2.42606
$190$	−137.863	−0.0526401
$191$	3044.88	1.15351	0.576753	−	0.816918i	$-0.304319\pi$
$191$	3044.88	1.15351	0.576753	+	0.816918i	$0.304319\pi$
$192$	−1126.30	−0.423351
$193$	−4259.63	−1.58868	−0.794340	−	0.607473i	$-0.792183\pi$
$193$	−4259.63	−1.58868	−0.794340	+	0.607473i	$0.792183\pi$
$194$	−2171.73	−0.803717
$195$	−1062.62	−0.390234
$196$	−3917.29	−1.42758
$197$	−3264.51	−1.18064	−0.590322	−	0.807168i	$-0.700999\pi$
$197$	−3264.51	−1.18064	−0.590322	+	0.807168i	$0.700999\pi$
$198$	−793.018	−0.284633
$199$	−2837.81	−1.01089	−0.505445	−	0.862859i	$-0.668671\pi$
$199$	−2837.81	−1.01089	−0.505445	+	0.862859i	$0.668671\pi$
$200$	−504.072	−0.178216
$201$	−5097.55	−1.78882
$202$	−241.225	−0.0840224
$203$	−8214.35	−2.84007
$204$	1580.92	0.542580
$205$	−662.296	−0.225643
$206$	−144.198	−0.0487707
$207$	1355.09	0.455000
$208$	434.249	0.144758
$209$	209.000	0.0691714
$210$	2016.87	0.662748
$211$	−1914.28	−0.624571	−0.312286	−	0.949988i	$-0.601095\pi$
$211$	−1914.28	−0.624571	−0.312286	+	0.949988i	$0.601095\pi$
$212$	−828.324	−0.268347
$213$	−6407.06	−2.06106
$214$	−1545.32	−0.493626
$215$	52.8455	0.0167629
$216$	4004.05	1.26130
$217$	4809.15	1.50445
$218$	−514.902	−0.159971
$219$	8394.58	2.59020
$220$	324.173	0.0993443
$221$	743.412	0.226277
$222$	−3781.10	−1.14311
$223$	−4262.92	−1.28012	−0.640059	−	0.768326i	$-0.721090\pi$
$223$	−4262.92	−1.28012	−0.640059	+	0.768326i	$0.721090\pi$
$224$	−5944.45	−1.77313
$225$	1241.96	0.367988
$226$	218.465	0.0643013
$227$	5132.96	1.50082	0.750411	−	0.660971i	$-0.229855\pi$
$227$	5132.96	1.50082	0.750411	+	0.660971i	$0.229855\pi$
$228$	−980.628	−0.284841
$229$	−4266.34	−1.23113	−0.615563	−	0.788088i	$-0.711071\pi$
$229$	−4266.34	−1.23113	−0.615563	+	0.788088i	$0.711071\pi$
$230$	197.922	0.0567417
$231$	−3057.57	−0.870881
$232$	−5217.69	−1.47654
$233$	−999.594	−0.281054	−0.140527	−	0.990077i	$-0.544880\pi$
$233$	−999.594	−0.281054	−0.140527	+	0.990077i	$0.544880\pi$
$234$	1749.69	0.488807
$235$	−2587.09	−0.718141
$236$	1190.19	0.328282
$237$	4923.77	1.34951
$238$	−1411.01	−0.384294
$239$	2355.79	0.637586	0.318793	−	0.947824i	$-0.396722\pi$
$239$	2355.79	0.637586	0.318793	+	0.947824i	$0.396722\pi$
$240$	−783.382	−0.210696
$241$	5702.90	1.52430	0.762149	−	0.647401i	$-0.224144\pi$
$241$	5702.90	1.52430	0.762149	+	0.647401i	$0.224144\pi$
$242$	175.594	0.0466429
$243$	1879.99	0.496303
$244$	−3714.71	−0.974631
$245$	3323.08	0.866547
$246$	1683.22	0.436254
$247$	−461.131	−0.118790
$248$	3054.73	0.782160
$249$	885.622	0.225398
$250$	181.398	0.0458906
$251$	6527.24	1.64142	0.820708	−	0.571347i	$-0.193579\pi$
$251$	6527.24	1.64142	0.820708	+	0.571347i	$0.193579\pi$
$252$	9294.56	2.32342
$253$	−300.050	−0.0745611
$254$	−227.399	−0.0561743
$255$	−1341.11	−0.329347
$256$	−2932.19	−0.715868
$257$	4110.28	0.997635	0.498817	−	0.866707i	$-0.333768\pi$
$257$	4110.28	0.997635	0.498817	+	0.866707i	$0.333768\pi$
$258$	−134.307	−0.0324092
$259$	−9445.09	−2.26598
$260$	−715.246	−0.170606
$261$	12855.6	3.04882
$262$	3804.32	0.897066
$263$	5387.23	1.26308	0.631541	−	0.775342i	$-0.282423\pi$
$263$	5387.23	1.26308	0.631541	+	0.775342i	$0.282423\pi$
$264$	−1942.14	−0.452768
$265$	702.677	0.162887
$266$	875.235	0.201745
$267$	−5870.55	−1.34559
$268$	−3431.15	−0.782055
$269$	−3760.70	−0.852393	−0.426197	−	0.904631i	$-0.640147\pi$
$269$	−3760.70	−0.852393	−0.426197	+	0.904631i	$0.640147\pi$
$270$	−1440.92	−0.324784
$271$	3836.44	0.859952	0.429976	−	0.902840i	$-0.358522\pi$
$271$	3836.44	0.859952	0.429976	+	0.902840i	$0.358522\pi$
$272$	548.057	0.122172
$273$	6746.13	1.49558
$274$	−4280.02	−0.943669
$275$	−275.000	−0.0603023
$276$	1407.83	0.307035
$277$	−2968.70	−0.643943	−0.321971	−	0.946749i	$-0.604345\pi$
$277$	−2968.70	−0.643943	−0.321971	+	0.946749i	$0.604345\pi$
$278$	−225.909	−0.0487378
$279$	−7526.40	−1.61503
$280$	3200.15	0.683019
$281$	−3715.17	−0.788714	−0.394357	−	0.918957i	$-0.629033\pi$
$281$	−3715.17	−0.788714	−0.394357	+	0.918957i	$0.629033\pi$
$282$	6575.08	1.38844
$283$	8360.30	1.75607	0.878036	−	0.478595i	$-0.158854\pi$
$283$	8360.30	1.75607	0.878036	+	0.478595i	$0.158854\pi$
$284$	−4312.58	−0.901072
$285$	831.878	0.172899
$286$	−387.424	−0.0801010
$287$	4204.65	0.864783
$288$	9303.17	1.90345
$289$	−3974.75	−0.809028
$290$	1877.67	0.380209
$291$	13104.4	2.63985
$292$	5650.37	1.13241
$293$	−2607.26	−0.519856	−0.259928	−	0.965628i	$-0.583699\pi$
$293$	−2607.26	−0.519856	−0.259928	+	0.965628i	$0.583699\pi$
$294$	−8445.61	−1.67537
$295$	−1009.65	−0.199268
$296$	−5999.44	−1.17808
$297$	2184.44	0.426781
$298$	−118.939	−0.0231206
$299$	662.021	0.128046
$300$	1290.30	0.248318
$301$	−335.494	−0.0642444
$302$	4728.27	0.900931
$303$	1455.58	0.275976
$304$	−339.955	−0.0641373
$305$	3151.23	0.591603
$306$	2208.25	0.412540
$307$	−6699.31	−1.24544	−0.622719	−	0.782445i	$-0.713972\pi$
$307$	−6699.31	−1.24544	−0.622719	+	0.782445i	$0.713972\pi$
$308$	−2058.04	−0.380740
$309$	870.106	0.160190
$310$	−1099.29	−0.201405
$311$	1709.94	0.311774	0.155887	−	0.987775i	$-0.450176\pi$
$311$	1709.94	0.311774	0.155887	+	0.987775i	$0.450176\pi$
$312$	4285.09	0.777549
$313$	1744.52	0.315035	0.157518	−	0.987516i	$-0.449651\pi$
$313$	1744.52	0.315035	0.157518	+	0.987516i	$0.449651\pi$
$314$	−2446.47	−0.439688
$315$	−7884.69	−1.41032
$316$	3314.18	0.589991
$317$	10588.5	1.87606	0.938028	−	0.346560i	$-0.112650\pi$
$317$	10588.5	1.87606	0.938028	+	0.346560i	$0.112650\pi$
$318$	−1785.85	−0.314923
$319$	−2846.55	−0.499611
$320$	643.111	0.112347
$321$	9324.63	1.62134
$322$	−1256.53	−0.217464
$323$	−581.985	−0.100255
$324$	−2343.60	−0.401851
$325$	606.752	0.103559
$326$	4639.08	0.788145
$327$	3106.98	0.525432
$328$	2670.76	0.449598
$329$	16424.4	2.75230
$330$	698.912	0.116587
$331$	−775.546	−0.128785	−0.0643926	−	0.997925i	$-0.520511\pi$
$331$	−775.546	−0.128785	−0.0643926	+	0.997925i	$0.520511\pi$
$332$	596.110	0.0985415
$333$	14781.7	2.43253
$334$	−2101.06	−0.344207
$335$	2910.69	0.474710
$336$	4973.38	0.807500
$337$	−1549.45	−0.250456	−0.125228	−	0.992128i	$-0.539966\pi$
$337$	−1549.45	−0.250456	−0.125228	+	0.992128i	$0.539966\pi$
$338$	−2333.46	−0.375513
$339$	−1318.24	−0.211201
$340$	−902.698	−0.143987
$341$	1666.53	0.264656
$342$	−1369.76	−0.216573
$343$	−10209.1	−1.60711
$344$	−213.103	−0.0334005
$345$	−1194.28	−0.186371
$346$	−12.4451	−0.00193368
$347$	8251.21	1.27651	0.638254	−	0.769826i	$-0.279657\pi$
$347$	8251.21	1.27651	0.638254	+	0.769826i	$0.279657\pi$
$348$	13356.0	2.05735
$349$	−10048.2	−1.54116	−0.770582	−	0.637341i	$-0.780034\pi$
$349$	−10048.2	−1.54116	−0.770582	+	0.637341i	$0.780034\pi$
$350$	−1151.62	−0.175877
$351$	−4819.68	−0.732921
$352$	−2059.95	−0.311920
$353$	1397.30	0.210681	0.105341	−	0.994436i	$-0.466407\pi$
$353$	1397.30	0.210681	0.105341	+	0.994436i	$0.466407\pi$
$354$	2566.02	0.385261
$355$	3658.41	0.546953
$356$	−3951.45	−0.588277
$357$	8514.17	1.26223
$358$	1322.38	0.195224
$359$	−10359.5	−1.52300	−0.761498	−	0.648167i	$-0.775536\pi$
$359$	−10359.5	−1.52300	−0.761498	+	0.648167i	$0.775536\pi$
$360$	−5008.29	−0.733222
$361$	361.000	0.0526316
$362$	1936.48	0.281158
$363$	−1059.55	−0.153201
$364$	4540.81	0.653854
$365$	−4793.28	−0.687375
$366$	−8008.85	−1.14380
$367$	−4674.04	−0.664803	−0.332402	−	0.943138i	$-0.607859\pi$
$367$	−4674.04	−0.664803	−0.332402	+	0.943138i	$0.607859\pi$
$368$	488.054	0.0691347
$369$	−6580.35	−0.928346
$370$	2159.00	0.303354
$371$	−4461.01	−0.624270
$372$	−7819.36	−1.08982
$373$	3302.26	0.458403	0.229202	−	0.973379i	$-0.426388\pi$
$373$	3302.26	0.458403	0.229202	+	0.973379i	$0.426388\pi$
$374$	−488.961	−0.0676031
$375$	−1094.58	−0.150730
$376$	10432.6	1.43091
$377$	6280.54	0.857995
$378$	9147.83	1.24474
$379$	1950.24	0.264319	0.132160	−	0.991228i	$-0.457809\pi$
$379$	1950.24	0.264319	0.132160	+	0.991228i	$0.457809\pi$
$380$	559.935	0.0755897
$381$	1372.15	0.184507
$382$	4418.69	0.591832
$383$	1028.07	0.137159	0.0685796	−	0.997646i	$-0.478153\pi$
$383$	1028.07	0.137159	0.0685796	+	0.997646i	$0.478153\pi$
$384$	11484.2	1.52618
$385$	1745.86	0.231110
$386$	−6181.53	−0.815107
$387$	525.055	0.0689665
$388$	8820.57	1.15412
$389$	710.713	0.0926339	0.0463170	−	0.998927i	$-0.485252\pi$
$389$	710.713	0.0926339	0.0463170	+	0.998927i	$0.485252\pi$
$390$	−1542.06	−0.200218
$391$	835.524	0.108067
$392$	−13400.6	−1.72661
$393$	−22955.6	−2.94646
$394$	−4737.42	−0.605756
$395$	−2811.46	−0.358126
$396$	3220.87	0.408725
$397$	−10621.1	−1.34271	−0.671356	−	0.741135i	$-0.734288\pi$
$397$	−10621.1	−1.34271	−0.671356	+	0.741135i	$0.734288\pi$
$398$	−4118.19	−0.518659
$399$	−5281.26	−0.662641
$400$	447.309	0.0559136
$401$	−89.6882	−0.0111691	−0.00558456	−	0.999984i	$-0.501778\pi$
$401$	−89.6882	−0.0111691	−0.00558456	+	0.999984i	$0.501778\pi$
$402$	−7397.50	−0.917795
$403$	−3676.98	−0.454500
$404$	979.746	0.120654
$405$	1988.10	0.243925
$406$	−11920.6	−1.45716
$407$	−3273.04	−0.398621
$408$	5408.13	0.656231
$409$	12602.7	1.52362	0.761811	−	0.647799i	$-0.224310\pi$
$409$	12602.7	1.52362	0.761811	+	0.647799i	$0.224310\pi$
$410$	−961.116	−0.115771
$411$	25826.1	3.09953
$412$	585.667	0.0700333
$413$	6409.85	0.763700
$414$	1966.49	0.233448
$415$	−505.687	−0.0598150
$416$	4545.01	0.535667
$417$	1363.16	0.160082
$418$	303.298	0.0354899
$419$	1758.54	0.205037	0.102519	−	0.994731i	$-0.467310\pi$
$419$	1758.54	0.205037	0.102519	+	0.994731i	$0.467310\pi$
$420$	−8191.59	−0.951687
$421$	−7907.71	−0.915435	−0.457718	−	0.889098i	$-0.651333\pi$
$421$	−7907.71	−0.915435	−0.457718	+	0.889098i	$0.651333\pi$
$422$	−2777.98	−0.320450
$423$	−25704.5	−2.95460
$424$	−2833.60	−0.324556
$425$	765.770	0.0874007
$426$	−9297.85	−1.05747
$427$	−20005.9	−2.26734
$428$	6276.39	0.708833
$429$	2337.76	0.263096
$430$	76.6886	0.00860059
$431$	−3380.75	−0.377830	−0.188915	−	0.981993i	$-0.560497\pi$
$431$	−3380.75	−0.377830	−0.188915	+	0.981993i	$0.560497\pi$
$432$	−3553.16	−0.395721
$433$	−1158.52	−0.128579	−0.0642897	−	0.997931i	$-0.520478\pi$
$433$	−1158.52	−0.128579	−0.0642897	+	0.997931i	$0.520478\pi$
$434$	6978.97	0.771893
$435$	−11330.1	−1.24882
$436$	2091.30	0.229713
$437$	−518.268	−0.0567325
$438$	12182.1	1.32896
$439$	−7763.09	−0.843991	−0.421996	−	0.906598i	$-0.638670\pi$
$439$	−7763.09	−0.843991	−0.421996	+	0.906598i	$0.638670\pi$
$440$	1108.96	0.120153
$441$	33017.0	3.56517
$442$	1078.83	0.116097
$443$	1545.89	0.165796	0.0828979	−	0.996558i	$-0.473582\pi$
$443$	1545.89	0.165796	0.0828979	+	0.996558i	$0.473582\pi$
$444$	15357.1	1.64148
$445$	3352.06	0.357086
$446$	−6186.29	−0.656792
$447$	717.691	0.0759409
$448$	−4082.85	−0.430573
$449$	8623.20	0.906356	0.453178	−	0.891420i	$-0.350290\pi$
$449$	8623.20	0.906356	0.453178	+	0.891420i	$0.350290\pi$
$450$	1802.31	0.188804
$451$	1457.05	0.152128
$452$	−887.306	−0.0923348
$453$	−28530.9	−2.95915
$454$	7448.89	0.770030
$455$	−3852.02	−0.396891
$456$	−3354.61	−0.344505
$457$	−14021.6	−1.43523	−0.717617	−	0.696438i	$-0.754767\pi$
$457$	−14021.6	−1.43523	−0.717617	+	0.696438i	$0.754767\pi$
$458$	−6191.26	−0.631656
$459$	−6082.83	−0.618566
$460$	−803.868	−0.0814795
$461$	−968.363	−0.0978333	−0.0489166	−	0.998803i	$-0.515577\pi$
$461$	−968.363	−0.0978333	−0.0489166	+	0.998803i	$0.515577\pi$
$462$	−4437.11	−0.446825
$463$	−6738.21	−0.676352	−0.338176	−	0.941083i	$-0.609810\pi$
$463$	−6738.21	−0.676352	−0.338176	+	0.941083i	$0.609810\pi$
$464$	4630.13	0.463251
$465$	6633.26	0.661527
$466$	−1450.60	−0.144201
$467$	−10721.5	−1.06238	−0.531192	−	0.847252i	$-0.678256\pi$
$467$	−10721.5	−1.06238	−0.531192	+	0.847252i	$0.678256\pi$
$468$	−7106.44	−0.701913
$469$	−18478.8	−1.81934
$470$	−3754.35	−0.368458
$471$	14762.2	1.44418
$472$	4071.48	0.397045
$473$	−116.260	−0.0113016
$474$	7145.31	0.692395
$475$	−475.000	−0.0458831
$476$	5730.87	0.551836
$477$	6981.57	0.670155
$478$	3418.68	0.327128
$479$	908.841	0.0866931	0.0433465	−	0.999060i	$-0.486198\pi$
$479$	908.841	0.0866931	0.0433465	+	0.999060i	$0.486198\pi$
$480$	−8199.18	−0.779665
$481$	7221.54	0.684561
$482$	8275.97	0.782075
$483$	7582.01	0.714272
$484$	−713.181	−0.0669779
$485$	−7482.60	−0.700551
$486$	2728.22	0.254639
$487$	−18569.4	−1.72784	−0.863921	−	0.503627i	$-0.831998\pi$
$487$	−18569.4	−1.72784	−0.863921	+	0.503627i	$0.831998\pi$
$488$	−12707.6	−1.17878
$489$	−27992.7	−2.58870
$490$	4822.42	0.444601
$491$	−4411.57	−0.405481	−0.202741	−	0.979232i	$-0.564985\pi$
$491$	−4411.57	−0.405481	−0.202741	+	0.979232i	$0.564985\pi$
$492$	−6836.49	−0.626448
$493$	7926.55	0.724125
$494$	−669.188	−0.0609477
$495$	−2732.31	−0.248097
$496$	−2710.74	−0.245395
$497$	−23225.8	−2.09622
$498$	1285.20	0.115645
$499$	3757.02	0.337049	0.168524	−	0.985697i	$-0.446100\pi$
$499$	3757.02	0.337049	0.168524	+	0.985697i	$0.446100\pi$
$500$	−736.757	−0.0658976
$501$	12678.0	1.13056
$502$	9472.24	0.842165
$503$	8065.44	0.714950	0.357475	−	0.933923i	$-0.383638\pi$
$503$	8065.44	0.714950	0.357475	+	0.933923i	$0.383638\pi$
$504$	31795.6	2.81010
$505$	−831.130	−0.0732372
$506$	−435.428	−0.0382552
$507$	14080.3	1.23339
$508$	923.589	0.0806647
$509$	−10956.4	−0.954098	−0.477049	−	0.878877i	$-0.658294\pi$
$509$	−10956.4	−0.954098	−0.477049	+	0.878877i	$0.658294\pi$
$510$	−1946.20	−0.168979
$511$	30430.6	2.63439
$512$	6236.76	0.538337
$513$	3773.12	0.324732
$514$	5964.78	0.511859
$515$	−496.828	−0.0425104
$516$	545.492	0.0465386
$517$	5691.60	0.484171
$518$	−13706.6	−1.16261
$519$	75.0950	0.00635126
$520$	−2446.77	−0.206342
$521$	−4504.15	−0.378753	−0.189377	−	0.981905i	$-0.560647\pi$
$521$	−4504.15	−0.378753	−0.189377	+	0.981905i	$0.560647\pi$
$522$	18655.9	1.56426
$523$	3412.31	0.285296	0.142648	−	0.989773i	$-0.454438\pi$
$523$	3412.31	0.285296	0.142648	+	0.989773i	$0.454438\pi$
$524$	−15451.4	−1.28816
$525$	6949.03	0.577677
$526$	7817.87	0.648052
$527$	−4640.65	−0.383586
$528$	1723.44	0.142051
$529$	−11423.0	−0.938847
$530$	1019.72	0.0835729
$531$	−10031.5	−0.819833
$532$	−3554.80	−0.289700
$533$	−3214.80	−0.261254
$534$	−8519.26	−0.690383
$535$	−5324.34	−0.430264
$536$	−11737.6	−0.945868
$537$	−7979.39	−0.641222
$538$	−5457.47	−0.437339
$539$	−7310.78	−0.584226
$540$	5852.36	0.466381
$541$	−11550.2	−0.917895	−0.458947	−	0.888463i	$-0.651773\pi$
$541$	−11550.2	−0.917895	−0.458947	+	0.888463i	$0.651773\pi$
$542$	5567.39	0.441217
$543$	−11684.9	−0.923476
$544$	5736.17	0.452089
$545$	−1774.07	−0.139437
$546$	9789.90	0.767343
$547$	−4244.23	−0.331755	−0.165878	−	0.986146i	$-0.553046\pi$
$547$	−4244.23	−0.331755	−0.165878	+	0.986146i	$0.553046\pi$
$548$	17383.5	1.35508
$549$	31309.6	2.43399
$550$	−399.076	−0.0309394
$551$	−4916.76	−0.380147
$552$	4816.03	0.371348
$553$	17848.8	1.37253
$554$	−4308.14	−0.330389
$555$	−13027.6	−0.996381
$556$	917.539	0.0699862
$557$	14833.5	1.12840	0.564199	−	0.825639i	$-0.309185\pi$
$557$	14833.5	1.12840	0.564199	+	0.825639i	$0.309185\pi$
$558$	−10922.2	−0.828628
$559$	256.513	0.0194085
$560$	−2839.78	−0.214291
$561$	2950.44	0.222046
$562$	−5391.41	−0.404667
$563$	−23829.3	−1.78381	−0.891907	−	0.452220i	$-0.850632\pi$
$563$	−23829.3	−1.78381	−0.891907	+	0.452220i	$0.850632\pi$
$564$	−26705.0	−1.99376
$565$	752.712	0.0560475
$566$	12132.4	0.900991
$567$	−12621.7	−0.934850
$568$	−14752.8	−1.08981
$569$	23710.9	1.74695	0.873473	−	0.486873i	$-0.161863\pi$
$569$	23710.9	1.74695	0.873473	+	0.486873i	$0.161863\pi$
$570$	1207.21	0.0887097
$571$	14430.7	1.05763	0.528815	−	0.848737i	$-0.322636\pi$
$571$	14430.7	1.05763	0.528815	+	0.848737i	$0.322636\pi$
$572$	1573.54	0.115023
$573$	−26662.8	−1.94390
$574$	6101.74	0.443696
$575$	681.931	0.0494583
$576$	6389.73	0.462220
$577$	12294.9	0.887075	0.443538	−	0.896256i	$-0.353723\pi$
$577$	12294.9	0.887075	0.443538	+	0.896256i	$0.353723\pi$
$578$	−5768.11	−0.415090
$579$	37300.0	2.67726
$580$	−7626.23	−0.545969
$581$	3210.41	0.229243
$582$	19017.0	1.35443
$583$	−1545.89	−0.109819
$584$	19329.3	1.36961
$585$	6028.48	0.426063
$586$	−3783.63	−0.266724
$587$	5484.87	0.385664	0.192832	−	0.981232i	$-0.438233\pi$
$587$	5484.87	0.385664	0.192832	+	0.981232i	$0.438233\pi$
$588$	34302.2	2.40578
$589$	2878.55	0.201373
$590$	−1465.19	−0.102239
$591$	28586.1	1.98964
$592$	5323.85	0.369610
$593$	−3781.22	−0.261848	−0.130924	−	0.991392i	$-0.541794\pi$
$593$	−3781.22	−0.261848	−0.130924	+	0.991392i	$0.541794\pi$
$594$	3170.03	0.218969
$595$	−4861.56	−0.334966
$596$	483.076	0.0332006
$597$	24849.6	1.70356
$598$	960.716	0.0656966
$599$	−23029.8	−1.57090	−0.785452	−	0.618922i	$-0.787570\pi$
$599$	−23029.8	−1.57090	−0.785452	+	0.618922i	$0.787570\pi$
$600$	4413.96	0.300332
$601$	−16.3054	−0.00110667	−0.000553337	−	1.00000i	$-0.500176\pi$
$601$	−16.3054	−0.00110667	−0.000553337		1.00000i	$0.500176\pi$
$602$	−486.865	−0.0329620
$603$	28919.6	1.95306
$604$	−19204.0	−1.29371
$605$	605.000	0.0406558
$606$	2112.31	0.141596
$607$	−22449.1	−1.50112	−0.750560	−	0.660803i	$-0.770216\pi$
$607$	−22449.1	−1.50112	−0.750560	+	0.660803i	$0.770216\pi$
$608$	−3558.09	−0.237335
$609$	71929.9	4.78612
$610$	4573.03	0.303535
$611$	−12557.8	−0.831478
$612$	−8968.91	−0.592396
$613$	5683.47	0.374475	0.187238	−	0.982315i	$-0.440047\pi$
$613$	5683.47	0.374475	0.187238	+	0.982315i	$0.440047\pi$
$614$	−9721.95	−0.639000
$615$	5799.48	0.380256
$616$	−7040.33	−0.460492
$617$	11124.4	0.725851	0.362926	−	0.931818i	$-0.381778\pi$
$617$	11124.4	0.725851	0.362926	+	0.931818i	$0.381778\pi$
$618$	1262.69	0.0821889
$619$	−24459.3	−1.58821	−0.794104	−	0.607781i	$-0.792060\pi$
$619$	−24459.3	−1.58821	−0.794104	+	0.607781i	$0.792060\pi$
$620$	4464.83	0.289213
$621$	−5416.86	−0.350034
$622$	2481.44	0.159963
$623$	−21280.9	−1.36854
$624$	−3802.55	−0.243948
$625$	625.000	0.0400000
$626$	2531.62	0.161636
$627$	−1830.13	−0.116569
$628$	9936.42	0.631380
$629$	9114.16	0.577751
$630$	−11442.2	−0.723597
$631$	9467.37	0.597290	0.298645	−	0.954364i	$-0.403465\pi$
$631$	9467.37	0.597290	0.298645	+	0.954364i	$0.403465\pi$
$632$	11337.4	0.713573
$633$	16762.6	1.05253
$634$	15365.9	0.962552
$635$	−783.492	−0.0489637
$636$	7253.32	0.452221
$637$	16130.3	1.00331
$638$	−4130.87	−0.256337
$639$	36348.8	2.25029
$640$	−6557.45	−0.405009
$641$	−14142.1	−0.871419	−0.435709	−	0.900087i	$-0.643502\pi$
$641$	−14142.1	−0.871419	−0.435709	+	0.900087i	$0.643502\pi$
$642$	13531.8	0.831865
$643$	−22524.4	−1.38145	−0.690727	−	0.723115i	$-0.742709\pi$
$643$	−22524.4	−1.38145	−0.690727	+	0.723115i	$0.742709\pi$
$644$	5103.43	0.312272
$645$	−462.747	−0.0282491
$646$	−844.569	−0.0514383
$647$	−25657.7	−1.55906	−0.779528	−	0.626367i	$-0.784541\pi$
$647$	−25657.7	−1.55906	−0.779528	+	0.626367i	$0.784541\pi$
$648$	−8017.17	−0.486025
$649$	2221.23	0.134346
$650$	880.510	0.0531330
$651$	−42111.9	−2.53532
$652$	−18841.8	−1.13175
$653$	26310.9	1.57676	0.788381	−	0.615187i	$-0.210919\pi$
$653$	26310.9	1.57676	0.788381	+	0.615187i	$0.210919\pi$
$654$	4508.80	0.269584
$655$	13107.6	0.781918
$656$	−2370.01	−0.141057
$657$	−47624.4	−2.82802
$658$	23834.9	1.41213
$659$	−7543.17	−0.445888	−0.222944	−	0.974831i	$-0.571567\pi$
$659$	−7543.17	−0.445888	−0.222944	+	0.974831i	$0.571567\pi$
$660$	−2838.66	−0.167416
$661$	−9601.69	−0.564996	−0.282498	−	0.959268i	$-0.591163\pi$
$661$	−9601.69	−0.564996	−0.282498	+	0.959268i	$0.591163\pi$
$662$	−1125.46	−0.0660760
$663$	−6509.77	−0.381325
$664$	2039.22	0.119182
$665$	3015.58	0.175849
$666$	21451.1	1.24807
$667$	7058.73	0.409768
$668$	8533.55	0.494271
$669$	37328.7	2.15727
$670$	4223.95	0.243560
$671$	−6932.71	−0.398859
$672$	52053.2	2.98809
$673$	−28263.8	−1.61886	−0.809428	−	0.587219i	$-0.800223\pi$
$673$	−28263.8	−1.61886	−0.809428	+	0.587219i	$0.800223\pi$
$674$	−2248.54	−0.128502
$675$	−4964.63	−0.283094
$676$	9477.43	0.539226
$677$	−27284.8	−1.54895	−0.774477	−	0.632602i	$-0.781987\pi$
$677$	−27284.8	−1.54895	−0.774477	+	0.632602i	$0.781987\pi$
$678$	−1913.02	−0.108361
$679$	47504.0	2.68488
$680$	−3088.02	−0.174148
$681$	−44947.4	−2.52920
$682$	2418.45	0.135788
$683$	2891.34	0.161982	0.0809912	−	0.996715i	$-0.474191\pi$
$683$	2891.34	0.161982	0.0809912	+	0.996715i	$0.474191\pi$
$684$	5563.33	0.310993
$685$	−14746.6	−0.822539
$686$	−14815.3	−0.824562
$687$	37358.7	2.07471
$688$	189.106	0.0104791
$689$	3410.81	0.188594
$690$	−1733.13	−0.0956217
$691$	−5429.70	−0.298922	−0.149461	−	0.988768i	$-0.547754\pi$
$691$	−5429.70	−0.298922	−0.149461	+	0.988768i	$0.547754\pi$
$692$	50.5463	0.00277671
$693$	17346.3	0.950840
$694$	11974.0	0.654941
$695$	−778.359	−0.0424818
$696$	45689.3	2.48829
$697$	−4057.33	−0.220491
$698$	−14581.8	−0.790728
$699$	8753.06	0.473635
$700$	4677.37	0.252554
$701$	−21386.7	−1.15230	−0.576152	−	0.817342i	$-0.695446\pi$
$701$	−21386.7	−1.15230	−0.576152	+	0.817342i	$0.695446\pi$
$702$	−6994.25	−0.376041
$703$	−5653.43	−0.303305
$704$	−1414.84	−0.0757442
$705$	22654.2	1.21022
$706$	2027.74	0.108095
$707$	5276.51	0.280684
$708$	−10422.0	−0.553224
$709$	−23348.5	−1.23677	−0.618386	−	0.785875i	$-0.712213\pi$
$709$	−23348.5	−1.23677	−0.618386	+	0.785875i	$0.712213\pi$
$710$	5309.04	0.280626
$711$	−27933.7	−1.47341
$712$	−13517.5	−0.711500
$713$	−4132.58	−0.217063
$714$	12355.6	0.647617
$715$	−1334.85	−0.0698192
$716$	−5370.91	−0.280336
$717$	−20628.7	−1.07447
$718$	−15033.6	−0.781407
$719$	−33935.6	−1.76020	−0.880101	−	0.474787i	$-0.842525\pi$
$719$	−33935.6	−1.76020	−0.880101	+	0.474787i	$0.842525\pi$
$720$	4444.31	0.230041
$721$	3154.16	0.162922
$722$	523.878	0.0270038
$723$	−49938.1	−2.56876
$724$	−7865.09	−0.403734
$725$	6469.43	0.331405
$726$	−1537.61	−0.0786032
$727$	−27928.6	−1.42478	−0.712390	−	0.701784i	$-0.752387\pi$
$727$	−27928.6	−1.42478	−0.712390	+	0.701784i	$0.752387\pi$
$728$	15533.6	0.790813
$729$	−27198.1	−1.38181
$730$	−6955.95	−0.352673
$731$	323.740	0.0163802
$732$	32528.3	1.64246
$733$	18309.4	0.922609	0.461304	−	0.887242i	$-0.347382\pi$
$733$	18309.4	0.922609	0.461304	+	0.887242i	$0.347382\pi$
$734$	−6782.90	−0.341092
$735$	−29099.0	−1.46031
$736$	5108.16	0.255828
$737$	−6403.51	−0.320049
$738$	−9549.32	−0.476308
$739$	−7444.81	−0.370584	−0.185292	−	0.982683i	$-0.559323\pi$
$739$	−7444.81	−0.370584	−0.185292	+	0.982683i	$0.559323\pi$
$740$	−8768.85	−0.435607
$741$	4037.95	0.200186
$742$	−6473.77	−0.320296
$743$	−29640.4	−1.46353	−0.731765	−	0.681557i	$-0.761303\pi$
$743$	−29640.4	−1.46353	−0.731765	+	0.681557i	$0.761303\pi$
$744$	−26749.1	−1.31810
$745$	−409.799	−0.0201529
$746$	4792.19	0.235194
$747$	−5024.34	−0.246092
$748$	1985.94	0.0970762
$749$	33802.1	1.64900
$750$	−1588.44	−0.0773353
$751$	15529.5	0.754566	0.377283	−	0.926098i	$-0.376858\pi$
$751$	15529.5	0.754566	0.377283	+	0.926098i	$0.376858\pi$
$752$	−9257.83	−0.448934
$753$	−57156.5	−2.76613
$754$	9114.23	0.440213
$755$	16291.0	0.785286
$756$	−37154.3	−1.78742
$757$	20982.9	1.00744	0.503722	−	0.863866i	$-0.331963\pi$
$757$	20982.9	1.00744	0.503722	+	0.863866i	$0.331963\pi$
$758$	2830.16	0.135615
$759$	2627.42	0.125651
$760$	1915.47	0.0914230
$761$	−39897.6	−1.90051	−0.950254	−	0.311475i	$-0.899177\pi$
$761$	−39897.6	−1.90051	−0.950254	+	0.311475i	$0.899177\pi$
$762$	1991.24	0.0946655
$763$	11262.9	0.534395
$764$	−17946.7	−0.849854
$765$	7608.43	0.359586
$766$	1491.92	0.0703725
$767$	−4900.85	−0.230716
$768$	25676.1	1.20639
$769$	5168.42	0.242364	0.121182	−	0.992630i	$-0.461331\pi$
$769$	5168.42	0.242364	0.121182	+	0.992630i	$0.461331\pi$
$770$	2533.57	0.118576
$771$	−35992.1	−1.68123
$772$	25106.5	1.17047
$773$	6789.92	0.315933	0.157967	−	0.987444i	$-0.449506\pi$
$773$	6789.92	0.315933	0.157967	+	0.987444i	$0.449506\pi$
$774$	761.952	0.0353848
$775$	−3787.57	−0.175553
$776$	30174.1	1.39586
$777$	82707.0	3.81866
$778$	1031.38	0.0475279
$779$	2516.73	0.115752
$780$	6263.13	0.287508
$781$	−8048.51	−0.368756
$782$	1212.50	0.0554462
$783$	−51389.3	−2.34547
$784$	11891.6	0.541707
$785$	−8429.19	−0.383249
$786$	−33312.9	−1.51175
$787$	6796.71	0.307848	0.153924	−	0.988083i	$-0.450809\pi$
$787$	6796.71	0.307848	0.153924	+	0.988083i	$0.450809\pi$
$788$	19241.2	0.869848
$789$	−47173.9	−2.12856
$790$	−4079.95	−0.183744
$791$	−4778.66	−0.214804
$792$	11018.2	0.494338
$793$	15296.1	0.684970
$794$	−15413.2	−0.688908
$795$	−6153.08	−0.274500
$796$	16726.2	0.744780
$797$	−25165.2	−1.11844	−0.559219	−	0.829020i	$-0.688899\pi$
$797$	−25165.2	−1.11844	−0.559219	+	0.829020i	$0.688899\pi$
$798$	−7664.10	−0.339982
$799$	−15848.9	−0.701746
$800$	4681.70	0.206904
$801$	33305.0	1.46913
$802$	−130.154	−0.00573056
$803$	10545.2	0.463428
$804$	30045.3	1.31793
$805$	−4329.31	−0.189550
$806$	−5335.99	−0.233191
$807$	32931.0	1.43646
$808$	3351.59	0.145927
$809$	37452.7	1.62765	0.813824	−	0.581111i	$-0.197382\pi$
$809$	37452.7	1.62765	0.813824	+	0.581111i	$0.197382\pi$
$810$	2885.11	0.125151
$811$	10543.5	0.456515	0.228258	−	0.973601i	$-0.426697\pi$
$811$	10543.5	0.456515	0.228258	+	0.973601i	$0.426697\pi$
$812$	48415.9	2.09244
$813$	−33594.2	−1.44920
$814$	−4749.79	−0.204521
$815$	15983.8	0.686978
$816$	−4799.13	−0.205886
$817$	−200.813	−0.00859920
$818$	18288.8	0.781728
$819$	−38272.4	−1.63290
$820$	3903.61	0.166244
$821$	−21866.8	−0.929545	−0.464773	−	0.885430i	$-0.653864\pi$
$821$	−21866.8	−0.929545	−0.464773	+	0.885430i	$0.653864\pi$
$822$	37478.5	1.59028
$823$	−32222.6	−1.36478	−0.682388	−	0.730991i	$-0.739058\pi$
$823$	−32222.6	−1.36478	−0.682388	+	0.730991i	$0.739058\pi$
$824$	2003.50	0.0847028
$825$	2408.07	0.101622
$826$	9301.89	0.391833
$827$	−25604.8	−1.07662	−0.538311	−	0.842747i	$-0.680937\pi$
$827$	−25604.8	−1.07662	−0.538311	+	0.842747i	$0.680937\pi$
$828$	−7986.96	−0.335225
$829$	18104.3	0.758490	0.379245	−	0.925296i	$-0.376184\pi$
$829$	18104.3	0.758490	0.379245	+	0.925296i	$0.376184\pi$
$830$	−733.847	−0.0306894
$831$	25995.8	1.08518
$832$	3121.67	0.130077
$833$	20357.7	0.846763
$834$	1978.20	0.0821336
$835$	−7239.12	−0.300024
$836$	−1231.86	−0.0509626
$837$	30086.2	1.24245
$838$	2551.98	0.105199
$839$	38044.3	1.56547	0.782737	−	0.622352i	$-0.213823\pi$
$839$	38044.3	1.56547	0.782737	+	0.622352i	$0.213823\pi$
$840$	−28022.5	−1.15103
$841$	42576.6	1.74573
$842$	−11475.6	−0.469684
$843$	32532.4	1.32915
$844$	11282.9	0.460157
$845$	−8039.82	−0.327311
$846$	−37302.0	−1.51592
$847$	−3840.90	−0.155815
$848$	2514.51	0.101826
$849$	−73207.9	−2.95935
$850$	1111.28	0.0448429
$851$	8116.32	0.326938
$852$	37763.6	1.51850
$853$	20853.9	0.837072	0.418536	−	0.908200i	$-0.362543\pi$
$853$	20853.9	0.837072	0.418536	+	0.908200i	$0.362543\pi$
$854$	−29032.3	−1.16331
$855$	−4719.44	−0.188774
$856$	21470.8	0.857309
$857$	−30034.3	−1.19714	−0.598571	−	0.801069i	$-0.704265\pi$
$857$	−30034.3	−1.19714	−0.598571	+	0.801069i	$0.704265\pi$
$858$	3392.53	0.134987
$859$	47412.6	1.88323	0.941616	−	0.336688i	$-0.109307\pi$
$859$	47412.6	1.88323	0.941616	+	0.336688i	$0.109307\pi$
$860$	−311.474	−0.0123502
$861$	−36818.5	−1.45734
$862$	−4906.09	−0.193854
$863$	14590.3	0.575504	0.287752	−	0.957705i	$-0.407092\pi$
$863$	14590.3	0.575504	0.287752	+	0.957705i	$0.407092\pi$
$864$	−37188.7	−1.46433
$865$	−42.8790	−0.00168547
$866$	−1681.23	−0.0659705
$867$	34805.4	1.36338
$868$	−28345.4	−1.10842
$869$	6185.21	0.241449
$870$	−16442.0	−0.640732
$871$	14128.5	0.549628
$872$	7154.08	0.277830
$873$	−74344.6	−2.88223
$874$	−752.103	−0.0291079
$875$	−3967.87	−0.153301
$876$	−49478.2	−1.90835
$877$	−17597.2	−0.677555	−0.338778	−	0.940866i	$-0.610013\pi$
$877$	−17597.2	−0.677555	−0.338778	+	0.940866i	$0.610013\pi$
$878$	−11265.7	−0.433028
$879$	22830.8	0.876068
$880$	−984.080	−0.0376970
$881$	−42581.3	−1.62838	−0.814189	−	0.580600i	$-0.802818\pi$
$881$	−42581.3	−1.62838	−0.814189	+	0.580600i	$0.802818\pi$
$882$	47913.9	1.82919
$883$	31943.4	1.21742	0.608709	−	0.793393i	$-0.291688\pi$
$883$	31943.4	1.21742	0.608709	+	0.793393i	$0.291688\pi$
$884$	−4381.71	−0.166711
$885$	8841.11	0.335809
$886$	2243.38	0.0850652
$887$	28138.7	1.06517	0.532585	−	0.846377i	$-0.321221\pi$
$887$	28138.7	1.06517	0.532585	+	0.846377i	$0.321221\pi$
$888$	52534.8	1.98531
$889$	4974.07	0.187655
$890$	4864.47	0.183211
$891$	−4373.83	−0.164454
$892$	25125.9	0.943135
$893$	9830.94	0.368399
$894$	1041.50	0.0389632
$895$	4556.21	0.170165
$896$	41630.6	1.55221
$897$	−5797.06	−0.215784
$898$	12513.9	0.465026
$899$	−39205.4	−1.45448
$900$	−7320.17	−0.271117
$901$	4304.71	0.159168
$902$	2114.46	0.0780528
$903$	2937.80	0.108265
$904$	−3035.37	−0.111676
$905$	6672.05	0.245068
$906$	−41403.6	−1.51826
$907$	−28345.6	−1.03771	−0.518854	−	0.854863i	$-0.673641\pi$
$907$	−28345.6	−1.03771	−0.518854	+	0.854863i	$0.673641\pi$
$908$	−30254.0	−1.10574
$909$	−8257.83	−0.301314
$910$	−5590.00	−0.203634
$911$	10968.2	0.398895	0.199448	−	0.979908i	$-0.436085\pi$
$911$	10968.2	0.398895	0.199448	+	0.979908i	$0.436085\pi$
$912$	2976.85	0.108085
$913$	1112.51	0.0403273
$914$	−20347.9	−0.736379
$915$	−27594.1	−0.996977
$916$	25146.1	0.907041
$917$	−83214.8	−2.99672
$918$	−8827.32	−0.317369
$919$	19919.0	0.714980	0.357490	−	0.933917i	$-0.383633\pi$
$919$	19919.0	0.714980	0.357490	+	0.933917i	$0.383633\pi$
$920$	−2749.94	−0.0985465
$921$	58663.3	2.09883
$922$	−1405.27	−0.0501955
$923$	17758.0	0.633273
$924$	18021.5	0.641628
$925$	7438.73	0.264415
$926$	−9778.40	−0.347017
$927$	−4936.32	−0.174897
$928$	48460.7	1.71422
$929$	14067.6	0.496816	0.248408	−	0.968656i	$-0.420093\pi$
$929$	14067.6	0.496816	0.248408	+	0.968656i	$0.420093\pi$
$930$	9626.09	0.339411
$931$	−12627.7	−0.444529
$932$	5891.66	0.207068
$933$	−14973.3	−0.525406
$934$	−15558.9	−0.545079
$935$	−1684.69	−0.0589255
$936$	−24310.3	−0.848939
$937$	−35236.7	−1.22853	−0.614265	−	0.789100i	$-0.710547\pi$
$937$	−35236.7	−1.22853	−0.614265	+	0.789100i	$0.710547\pi$
$938$	−26816.1	−0.933452
$939$	−15276.1	−0.530901
$940$	15248.5	0.529096
$941$	32917.6	1.14036	0.570182	−	0.821518i	$-0.306873\pi$
$941$	32917.6	1.14036	0.570182	+	0.821518i	$0.306873\pi$
$942$	21422.8	0.740967
$943$	−3613.12	−0.124772
$944$	−3613.00	−0.124569
$945$	31518.4	1.08497
$946$	−168.715	−0.00579852
$947$	43197.8	1.48230	0.741152	−	0.671338i	$-0.234280\pi$
$947$	43197.8	1.48230	0.741152	+	0.671338i	$0.234280\pi$
$948$	−29021.0	−0.994259
$949$	−23266.7	−0.795856
$950$	−689.314	−0.0235414
$951$	−92719.4	−3.16155
$952$	19604.6	0.667426
$953$	−38712.8	−1.31588	−0.657938	−	0.753072i	$-0.728571\pi$
$953$	−38712.8	−1.31588	−0.657938	+	0.753072i	$0.728571\pi$
$954$	10131.6	0.343838
$955$	15224.4	0.515864
$956$	−13885.1	−0.469746
$957$	24926.1	0.841951
$958$	1318.90	0.0444798
$959$	93620.3	3.15241
$960$	−5631.48	−0.189328
$961$	−6837.92	−0.229530
$962$	10479.8	0.351229
$963$	−52900.8	−1.77020
$964$	−33613.2	−1.12304
$965$	−21298.2	−0.710479
$966$	11002.9	0.366473
$967$	33850.7	1.12571	0.562856	−	0.826555i	$-0.309702\pi$
$967$	33850.7	1.12571	0.562856	+	0.826555i	$0.309702\pi$
$968$	−2439.71	−0.0810074
$969$	5096.22	0.168952
$970$	−10858.6	−0.359433
$971$	−7386.85	−0.244135	−0.122068	−	0.992522i	$-0.538952\pi$
$971$	−7386.85	−0.244135	−0.122068	+	0.992522i	$0.538952\pi$
$972$	−11080.8	−0.365655
$973$	4941.49	0.162813
$974$	−26947.6	−0.886507
$975$	−5313.09	−0.174518
$976$	11276.6	0.369831
$977$	−17341.5	−0.567864	−0.283932	−	0.958844i	$-0.591639\pi$
$977$	−17341.5	−0.567864	−0.283932	+	0.958844i	$0.591639\pi$
$978$	−40622.7	−1.32819
$979$	−7374.54	−0.240747
$980$	−19586.4	−0.638435
$981$	−17626.6	−0.573674
$982$	−6402.01	−0.208041
$983$	7292.90	0.236630	0.118315	−	0.992976i	$-0.462251\pi$
$983$	7292.90	0.236630	0.118315	+	0.992976i	$0.462251\pi$
$984$	−23386.8	−0.757667
$985$	−16322.6	−0.528000
$986$	11502.9	0.371528
$987$	−143822.	−4.63820
$988$	2717.93	0.0875192
$989$	288.296	0.00926923
$990$	−3965.09	−0.127292
$991$	43404.9	1.39132	0.695662	−	0.718369i	$-0.255111\pi$
$991$	43404.9	1.39132	0.695662	+	0.718369i	$0.255111\pi$
$992$	−28371.6	−0.908065
$993$	6791.16	0.217030
$994$	−33705.0	−1.07551
$995$	−14189.0	−0.452083
$996$	−5219.91	−0.166063
$997$	23181.7	0.736380	0.368190	−	0.929751i	$-0.379978\pi$
$997$	23181.7	0.736380	0.368190	+	0.929751i	$0.379978\pi$
$998$	5452.14	0.172930
$999$	−59088.9	−1.87136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.d.1.15	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.d.1.15	✓	22	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)

\(f(q)\)	\(=\)	\(q+1.45119 q^{2} -8.75662 q^{3} -5.89406 q^{4} +5.00000 q^{5} -12.7075 q^{6} -31.7430 q^{7} -20.1629 q^{8} +49.6783 q^{9} +O(q^{10})\)	\(q+1.45119 q^{2} -8.75662 q^{3} -5.89406 q^{4} +5.00000 q^{5} -12.7075 q^{6} -31.7430 q^{7} -20.1629 q^{8} +49.6783 q^{9} +7.25593 q^{10} -11.0000 q^{11} +51.6120 q^{12} +24.2701 q^{13} -46.0650 q^{14} -43.7831 q^{15} +17.8924 q^{16} +30.6308 q^{17} +72.0925 q^{18} -19.0000 q^{19} -29.4703 q^{20} +277.961 q^{21} -15.9631 q^{22} +27.2772 q^{23} +176.559 q^{24} +25.0000 q^{25} +35.2204 q^{26} -198.585 q^{27} +187.095 q^{28} +258.777 q^{29} -63.5374 q^{30} -151.503 q^{31} +187.268 q^{32} +96.3228 q^{33} +44.4510 q^{34} -158.715 q^{35} -292.807 q^{36} +297.549 q^{37} -27.5726 q^{38} -212.524 q^{39} -100.814 q^{40} -132.459 q^{41} +403.373 q^{42} +10.5691 q^{43} +64.8346 q^{44} +248.392 q^{45} +39.5844 q^{46} -517.418 q^{47} -156.676 q^{48} +664.617 q^{49} +36.2797 q^{50} -268.222 q^{51} -143.049 q^{52} +140.535 q^{53} -288.184 q^{54} -55.0000 q^{55} +640.030 q^{56} +166.376 q^{57} +375.534 q^{58} -201.930 q^{59} +258.060 q^{60} +630.247 q^{61} -219.859 q^{62} -1576.94 q^{63} +128.622 q^{64} +121.350 q^{65} +139.782 q^{66} +582.137 q^{67} -180.540 q^{68} -238.856 q^{69} -230.325 q^{70} +731.683 q^{71} -1001.66 q^{72} -958.656 q^{73} +431.799 q^{74} -218.915 q^{75} +111.987 q^{76} +349.173 q^{77} -308.412 q^{78} -562.292 q^{79} +89.4618 q^{80} +397.620 q^{81} -192.223 q^{82} -101.137 q^{83} -1638.32 q^{84} +153.154 q^{85} +15.3377 q^{86} -2266.01 q^{87} +221.792 q^{88} +670.413 q^{89} +360.463 q^{90} -770.404 q^{91} -160.774 q^{92} +1326.65 q^{93} -750.870 q^{94} -95.0000 q^{95} -1639.84 q^{96} -1496.52 q^{97} +964.483 q^{98} -546.461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18} - 418 q^{19} + 370 q^{20} - 107 q^{21} + 44 q^{22} - 361 q^{23} + 208 q^{24} + 550 q^{25} - 365 q^{26} - 1467 q^{27} - 773 q^{28} - 319 q^{29} - 45 q^{30} - 402 q^{31} - 873 q^{32} + 231 q^{33} - 717 q^{34} - 205 q^{35} + 725 q^{36} - 838 q^{37} + 76 q^{38} - 607 q^{39} - 390 q^{40} - 392 q^{41} - 1350 q^{42} - 610 q^{43} - 814 q^{44} + 1045 q^{45} - 605 q^{46} - 1866 q^{47} - 1637 q^{48} + 379 q^{49} - 100 q^{50} - 2659 q^{51} - 638 q^{52} - 1303 q^{53} + 2338 q^{54} - 1210 q^{55} + 727 q^{56} + 399 q^{57} + 44 q^{58} - 2417 q^{59} - 980 q^{60} + 918 q^{61} - 1634 q^{62} - 374 q^{63} - 1716 q^{64} - 5 q^{65} + 99 q^{66} - 2339 q^{67} + 4940 q^{68} + 127 q^{69} - 315 q^{70} - 2370 q^{71} - 3306 q^{72} + 2207 q^{73} + 2051 q^{74} - 525 q^{75} - 1406 q^{76} + 451 q^{77} + 1380 q^{78} + 586 q^{79} + 30 q^{80} + 1950 q^{81} - 1566 q^{82} - 2870 q^{83} + 3076 q^{84} + 935 q^{85} - 1246 q^{86} - 1811 q^{87} + 858 q^{88} - 1768 q^{89} - 1805 q^{90} - 2195 q^{91} - 6728 q^{92} - 2916 q^{93} + 672 q^{94} - 2090 q^{95} + 6022 q^{96} - 4022 q^{97} + 1162 q^{98} - 2299 q^{99}+O(q^{100}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9 - 20 * q^10 - 242 * q^11 - 196 * q^12 - q^13 - 63 * q^14 - 105 * q^15 + 6 * q^16 + 187 * q^17 - 361 * q^18 - 418 * q^19 + 370 * q^20 - 107 * q^21 + 44 * q^22 - 361 * q^23 + 208 * q^24 + 550 * q^25 - 365 * q^26 - 1467 * q^27 - 773 * q^28 - 319 * q^29 - 45 * q^30 - 402 * q^31 - 873 * q^32 + 231 * q^33 - 717 * q^34 - 205 * q^35 + 725 * q^36 - 838 * q^37 + 76 * q^38 - 607 * q^39 - 390 * q^40 - 392 * q^41 - 1350 * q^42 - 610 * q^43 - 814 * q^44 + 1045 * q^45 - 605 * q^46 - 1866 * q^47 - 1637 * q^48 + 379 * q^49 - 100 * q^50 - 2659 * q^51 - 638 * q^52 - 1303 * q^53 + 2338 * q^54 - 1210 * q^55 + 727 * q^56 + 399 * q^57 + 44 * q^58 - 2417 * q^59 - 980 * q^60 + 918 * q^61 - 1634 * q^62 - 374 * q^63 - 1716 * q^64 - 5 * q^65 + 99 * q^66 - 2339 * q^67 + 4940 * q^68 + 127 * q^69 - 315 * q^70 - 2370 * q^71 - 3306 * q^72 + 2207 * q^73 + 2051 * q^74 - 525 * q^75 - 1406 * q^76 + 451 * q^77 + 1380 * q^78 + 586 * q^79 + 30 * q^80 + 1950 * q^81 - 1566 * q^82 - 2870 * q^83 + 3076 * q^84 + 935 * q^85 - 1246 * q^86 - 1811 * q^87 + 858 * q^88 - 1768 * q^89 - 1805 * q^90 - 2195 * q^91 - 6728 * q^92 - 2916 * q^93 + 672 * q^94 - 2090 * q^95 + 6022 * q^96 - 4022 * q^97 + 1162 * q^98 - 2299 * q^99

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