LMFDB - Embedded newform 722.4.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,4,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.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:	$42.5993790241$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.253788.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 63x + 15 $ x^3 - x^2 - 63*x + 15
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-7.57650$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -9.57650 q^{3} +4.00000 q^{4} +15.7782 q^{5} -19.1530 q^{6} +16.5765 q^{7} +8.00000 q^{8} +64.7093 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -9.57650 q^{3} +4.00000 q^{4} +15.7782 q^{5} -19.1530 q^{6} +16.5765 q^{7} +8.00000 q^{8} +64.7093 q^{9} +31.5563 q^{10} +16.0285 q^{11} -38.3060 q^{12} +67.1043 q^{13} +33.1530 q^{14} -151.099 q^{15} +16.0000 q^{16} +39.6050 q^{17} +129.419 q^{18} +63.1126 q^{20} -158.745 q^{21} +32.0569 q^{22} -47.6808 q^{23} -76.6120 q^{24} +123.950 q^{25} +134.209 q^{26} -361.123 q^{27} +66.3060 q^{28} +118.404 q^{29} -302.199 q^{30} -120.050 q^{31} +32.0000 q^{32} -153.497 q^{33} +79.2099 q^{34} +261.546 q^{35} +258.837 q^{36} -22.0924 q^{37} -642.624 q^{39} +126.225 q^{40} -109.102 q^{41} -317.490 q^{42} -360.624 q^{43} +64.1139 q^{44} +1020.99 q^{45} -95.3617 q^{46} +192.945 q^{47} -153.224 q^{48} -68.2197 q^{49} +247.900 q^{50} -379.277 q^{51} +268.417 q^{52} -217.844 q^{53} -722.246 q^{54} +252.900 q^{55} +132.612 q^{56} +236.808 q^{58} -423.190 q^{59} -604.398 q^{60} +563.920 q^{61} -240.099 q^{62} +1072.65 q^{63} +64.0000 q^{64} +1058.78 q^{65} -306.993 q^{66} +942.852 q^{67} +158.420 q^{68} +456.615 q^{69} +523.093 q^{70} +665.745 q^{71} +517.674 q^{72} -186.946 q^{73} -44.1848 q^{74} -1187.01 q^{75} +265.696 q^{77} -1285.25 q^{78} +876.354 q^{79} +252.450 q^{80} +1711.14 q^{81} -218.203 q^{82} -476.297 q^{83} -634.979 q^{84} +624.893 q^{85} -721.249 q^{86} -1133.90 q^{87} +128.228 q^{88} +964.740 q^{89} +2041.99 q^{90} +1112.35 q^{91} -190.723 q^{92} +1149.65 q^{93} +385.890 q^{94} -306.448 q^{96} +1585.92 q^{97} -136.439 q^{98} +1037.19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9} + 2 q^{10} + 4 q^{11} - 20 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} + 48 q^{16} + 51 q^{17} + 108 q^{18} + 4 q^{20} - 170 q^{21} + 8 q^{22} - 47 q^{23} - 40 q^{24} + 338 q^{25} + 258 q^{26} - 359 q^{27} + 104 q^{28} - 125 q^{29} - 154 q^{30} + 50 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} + 84 q^{35} + 216 q^{36} + 188 q^{37} - 773 q^{39} + 8 q^{40} + 475 q^{41} - 340 q^{42} + 73 q^{43} + 16 q^{44} + 1594 q^{45} - 94 q^{46} + 241 q^{47} - 80 q^{48} - 677 q^{49} + 676 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} - 718 q^{54} + 1838 q^{55} + 208 q^{56} - 250 q^{58} - 1065 q^{59} - 308 q^{60} + 981 q^{61} + 100 q^{62} + 872 q^{63} + 192 q^{64} - 293 q^{65} + 548 q^{66} + 877 q^{67} + 204 q^{68} + 763 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} - 667 q^{73} + 376 q^{74} - 2292 q^{75} - 246 q^{77} - 1546 q^{78} + 1671 q^{79} + 16 q^{80} + 1287 q^{81} + 950 q^{82} + 588 q^{83} - 680 q^{84} + 1929 q^{85} + 146 q^{86} - 3215 q^{87} + 32 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} - 188 q^{92} + 3138 q^{93} + 482 q^{94} - 160 q^{96} - 985 q^{97} - 1354 q^{98} + 3184 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9 + 2 * q^10 + 4 * q^11 - 20 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 + 48 * q^16 + 51 * q^17 + 108 * q^18 + 4 * q^20 - 170 * q^21 + 8 * q^22 - 47 * q^23 - 40 * q^24 + 338 * q^25 + 258 * q^26 - 359 * q^27 + 104 * q^28 - 125 * q^29 - 154 * q^30 + 50 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 + 84 * q^35 + 216 * q^36 + 188 * q^37 - 773 * q^39 + 8 * q^40 + 475 * q^41 - 340 * q^42 + 73 * q^43 + 16 * q^44 + 1594 * q^45 - 94 * q^46 + 241 * q^47 - 80 * q^48 - 677 * q^49 + 676 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 - 718 * q^54 + 1838 * q^55 + 208 * q^56 - 250 * q^58 - 1065 * q^59 - 308 * q^60 + 981 * q^61 + 100 * q^62 + 872 * q^63 + 192 * q^64 - 293 * q^65 + 548 * q^66 + 877 * q^67 + 204 * q^68 + 763 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 - 667 * q^73 + 376 * q^74 - 2292 * q^75 - 246 * q^77 - 1546 * q^78 + 1671 * q^79 + 16 * q^80 + 1287 * q^81 + 950 * q^82 + 588 * q^83 - 680 * q^84 + 1929 * q^85 + 146 * q^86 - 3215 * q^87 + 32 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 - 188 * q^92 + 3138 * q^93 + 482 * q^94 - 160 * q^96 - 985 * q^97 - 1354 * q^98 + 3184 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−9.57650	−1.84300	−0.921499	−	0.388381i	$-0.873034\pi$
$3$	−9.57650	−1.84300	−0.921499	+	0.388381i	$0.873034\pi$
$4$	4.00000	0.500000
$5$	15.7782	1.41124	0.705620	−	0.708590i	$-0.250668\pi$
$5$	15.7782	1.41124	0.705620	+	0.708590i	$0.250668\pi$
$6$	−19.1530	−1.30320
$7$	16.5765	0.895047	0.447523	−	0.894272i	$-0.352306\pi$
$7$	16.5765	0.895047	0.447523	+	0.894272i	$0.352306\pi$
$8$	8.00000	0.353553
$9$	64.7093	2.39664
$10$	31.5563	0.997898
$11$	16.0285	0.439342	0.219671	−	0.975574i	$-0.429502\pi$
$11$	16.0285	0.439342	0.219671	+	0.975574i	$0.429502\pi$
$12$	−38.3060	−0.921499
$13$	67.1043	1.43165	0.715823	−	0.698282i	$-0.246052\pi$
$13$	67.1043	1.43165	0.715823	+	0.698282i	$0.246052\pi$
$14$	33.1530	0.632894
$15$	−151.099	−2.60091
$16$	16.0000	0.250000
$17$	39.6050	0.565036	0.282518	−	0.959262i	$-0.408830\pi$
$17$	39.6050	0.565036	0.282518	+	0.959262i	$0.408830\pi$
$18$	129.419	1.69468
$19$	0	0
$19$	0	0
$20$	63.1126	0.705620
$21$	−158.745	−1.64957
$22$	32.0569	0.310662
$23$	−47.6808	−0.432267	−0.216133	−	0.976364i	$-0.569345\pi$
$23$	−47.6808	−0.432267	−0.216133	+	0.976364i	$0.569345\pi$
$24$	−76.6120	−0.651598
$25$	123.950	0.991601
$26$	134.209	1.01233
$27$	−361.123	−2.57401
$28$	66.3060	0.447523
$29$	118.404	0.758176	0.379088	−	0.925361i	$-0.376238\pi$
$29$	118.404	0.758176	0.379088	+	0.925361i	$0.376238\pi$
$30$	−302.199	−1.83912
$31$	−120.050	−0.695533	−0.347767	−	0.937581i	$-0.613060\pi$
$31$	−120.050	−0.695533	−0.347767	+	0.937581i	$0.613060\pi$
$32$	32.0000	0.176777
$33$	−153.497	−0.809707
$34$	79.2099	0.399541
$35$	261.546	1.26313
$36$	258.837	1.19832
$37$	−22.0924	−0.0981614	−0.0490807	−	0.998795i	$-0.515629\pi$
$37$	−22.0924	−0.0981614	−0.0490807	+	0.998795i	$0.515629\pi$
$38$	0	0
$39$	−642.624	−2.63852
$40$	126.225	0.498949
$41$	−109.102	−0.415580	−0.207790	−	0.978173i	$-0.566627\pi$
$41$	−109.102	−0.415580	−0.207790	+	0.978173i	$0.566627\pi$
$42$	−317.490	−1.16642
$43$	−360.624	−1.27895	−0.639473	−	0.768813i	$-0.720848\pi$
$43$	−360.624	−1.27895	−0.639473	+	0.768813i	$0.720848\pi$
$44$	64.1139	0.219671
$45$	1020.99	3.38224
$46$	−95.3617	−0.305659
$47$	192.945	0.598807	0.299404	−	0.954127i	$-0.403212\pi$
$47$	192.945	0.598807	0.299404	+	0.954127i	$0.403212\pi$
$48$	−153.224	−0.460749
$49$	−68.2197	−0.198891
$50$	247.900	0.701168
$51$	−379.277	−1.04136
$52$	268.417	0.715823
$53$	−217.844	−0.564589	−0.282294	−	0.959328i	$-0.591095\pi$
$53$	−217.844	−0.564589	−0.282294	+	0.959328i	$0.591095\pi$
$54$	−722.246	−1.82010
$55$	252.900	0.620018
$56$	132.612	0.316447
$57$	0	0
$58$	236.808	0.536111
$59$	−423.190	−0.933807	−0.466903	−	0.884308i	$-0.654630\pi$
$59$	−423.190	−0.933807	−0.466903	+	0.884308i	$0.654630\pi$
$60$	−604.398	−1.30046
$61$	563.920	1.18365	0.591824	−	0.806067i	$-0.298408\pi$
$61$	563.920	1.18365	0.591824	+	0.806067i	$0.298408\pi$
$62$	−240.099	−0.491816
$63$	1072.65	2.14511
$64$	64.0000	0.125000
$65$	1058.78	2.02040
$66$	−306.993	−0.572549
$67$	942.852	1.71922	0.859610	−	0.510951i	$-0.170707\pi$
$67$	942.852	1.71922	0.859610	+	0.510951i	$0.170707\pi$
$68$	158.420	0.282518
$69$	456.615	0.796667
$70$	523.093	0.893165
$71$	665.745	1.11281	0.556404	−	0.830912i	$-0.312181\pi$
$71$	665.745	1.11281	0.556404	+	0.830912i	$0.312181\pi$
$72$	517.674	0.847340
$73$	−186.946	−0.299730	−0.149865	−	0.988706i	$-0.547884\pi$
$73$	−186.946	−0.299730	−0.149865	+	0.988706i	$0.547884\pi$
$74$	−44.1848	−0.0694106
$75$	−1187.01	−1.82752
$76$	0	0
$77$	265.696	0.393232
$78$	−1285.25	−1.86572
$79$	876.354	1.24807	0.624035	−	0.781397i	$-0.285492\pi$
$79$	876.354	1.24807	0.624035	+	0.781397i	$0.285492\pi$
$80$	252.450	0.352810
$81$	1711.14	2.34725
$82$	−218.203	−0.293860
$83$	−476.297	−0.629885	−0.314942	−	0.949111i	$-0.601985\pi$
$83$	−476.297	−0.629885	−0.314942	+	0.949111i	$0.601985\pi$
$84$	−634.979	−0.824785
$85$	624.893	0.797402
$86$	−721.249	−0.904352
$87$	−1133.90	−1.39732
$88$	128.228	0.155331
$89$	964.740	1.14901	0.574507	−	0.818500i	$-0.305194\pi$
$89$	964.740	1.14901	0.574507	+	0.818500i	$0.305194\pi$
$90$	2041.99	2.39160
$91$	1112.35	1.28139
$92$	−190.723	−0.216133
$93$	1149.65	1.28187
$94$	385.890	0.423421
$95$	0	0
$96$	−306.448	−0.325799
$97$	1585.92	1.66006	0.830031	−	0.557718i	$-0.188323\pi$
$97$	1585.92	1.66006	0.830031	+	0.557718i	$0.188323\pi$
$98$	−136.439	−0.140637
$99$	1037.19	1.05295
$100$	495.800	0.495800
$101$	−1043.83	−1.02836	−0.514181	−	0.857682i	$-0.671904\pi$
$101$	−1043.83	−1.02836	−0.514181	+	0.857682i	$0.671904\pi$
$102$	−758.554	−0.736353
$103$	−1427.83	−1.36591	−0.682954	−	0.730461i	$-0.739305\pi$
$103$	−1427.83	−1.36591	−0.682954	+	0.730461i	$0.739305\pi$
$104$	536.835	0.506163
$105$	−2504.70	−2.32794
$106$	−435.688	−0.399225
$107$	−500.924	−0.452581	−0.226290	−	0.974060i	$-0.572660\pi$
$107$	−500.924	−0.452581	−0.226290	+	0.974060i	$0.572660\pi$
$108$	−1444.49	−1.28700
$109$	−1212.92	−1.06584	−0.532922	−	0.846164i	$-0.678906\pi$
$109$	−1212.92	−1.06584	−0.532922	+	0.846164i	$0.678906\pi$
$110$	505.799	0.438419
$111$	211.568	0.180911
$112$	265.224	0.223762
$113$	−738.956	−0.615178	−0.307589	−	0.951519i	$-0.599522\pi$
$113$	−738.956	−0.615178	−0.307589	+	0.951519i	$0.599522\pi$
$114$	0	0
$115$	−752.315	−0.610033
$116$	473.617	0.379088
$117$	4342.27	3.43114
$118$	−846.379	−0.660301
$119$	656.512	0.505734
$120$	−1208.80	−0.919562
$121$	−1074.09	−0.806978
$122$	1127.84	0.836966
$123$	1044.81	0.765914
$124$	−480.198	−0.347767
$125$	−16.5658	−0.0118535
$126$	2145.31	1.51682
$127$	−238.908	−0.166926	−0.0834632	−	0.996511i	$-0.526598\pi$
$127$	−238.908	−0.166926	−0.0834632	+	0.996511i	$0.526598\pi$
$128$	128.000	0.0883883
$129$	3453.52	2.35710
$130$	2117.56	1.42864
$131$	265.249	0.176907	0.0884537	−	0.996080i	$-0.471807\pi$
$131$	265.249	0.176907	0.0884537	+	0.996080i	$0.471807\pi$
$132$	−613.986	−0.404853
$133$	0	0
$134$	1885.70	1.21567
$135$	−5697.85	−3.63254
$136$	316.840	0.199770
$137$	2438.45	1.52066	0.760331	−	0.649536i	$-0.225037\pi$
$137$	2438.45	1.52066	0.760331	+	0.649536i	$0.225037\pi$
$138$	913.231	0.563329
$139$	−366.795	−0.223821	−0.111910	−	0.993718i	$-0.535697\pi$
$139$	−366.795	−0.223821	−0.111910	+	0.993718i	$0.535697\pi$
$140$	1046.19	0.631563
$141$	−1847.74	−1.10360
$142$	1331.49	0.786875
$143$	1075.58	0.628982
$144$	1035.35	0.599160
$145$	1868.20	1.06997
$146$	−373.891	−0.211941
$147$	653.306	0.366556
$148$	−88.3697	−0.0490807
$149$	−2241.76	−1.23256	−0.616281	−	0.787526i	$-0.711362\pi$
$149$	−2241.76	−1.23256	−0.616281	+	0.787526i	$0.711362\pi$
$150$	−2374.02	−1.29225
$151$	638.195	0.343944	0.171972	−	0.985102i	$-0.444986\pi$
$151$	638.195	0.343944	0.171972	+	0.985102i	$0.444986\pi$
$152$	0	0
$153$	2562.81	1.35419
$154$	531.392	0.278057
$155$	−1894.16	−0.981565
$156$	−2570.50	−1.31926
$157$	2125.99	1.08072	0.540358	−	0.841435i	$-0.318289\pi$
$157$	2125.99	1.08072	0.540358	+	0.841435i	$0.318289\pi$
$158$	1752.71	0.882519
$159$	2086.18	1.04054
$160$	504.901	0.249474
$161$	−790.381	−0.386899
$162$	3422.28	1.65975
$163$	−160.043	−0.0769053	−0.0384526	−	0.999260i	$-0.512243\pi$
$163$	−160.043	−0.0769053	−0.0384526	+	0.999260i	$0.512243\pi$
$164$	−436.406	−0.207790
$165$	−2421.89	−1.14269
$166$	−952.595	−0.445396
$167$	−2102.16	−0.974072	−0.487036	−	0.873382i	$-0.661922\pi$
$167$	−2102.16	−0.974072	−0.487036	+	0.873382i	$0.661922\pi$
$168$	−1269.96	−0.583211
$169$	2305.99	1.04961
$170$	1249.79	0.563848
$171$	0	0
$172$	−1442.50	−0.639473
$173$	405.464	0.178190	0.0890949	−	0.996023i	$-0.471603\pi$
$173$	405.464	0.178190	0.0890949	+	0.996023i	$0.471603\pi$
$174$	−2267.79	−0.988052
$175$	2054.66	0.887529
$176$	256.455	0.109836
$177$	4052.68	1.72100
$178$	1929.48	0.812476
$179$	1628.76	0.680107	0.340053	−	0.940406i	$-0.389555\pi$
$179$	1628.76	0.680107	0.340053	+	0.940406i	$0.389555\pi$
$180$	4083.97	1.69112
$181$	−2836.84	−1.16497	−0.582487	−	0.812840i	$-0.697921\pi$
$181$	−2836.84	−1.16497	−0.582487	+	0.812840i	$0.697921\pi$
$182$	2224.71	0.906079
$183$	−5400.38	−2.18146
$184$	−381.447	−0.152829
$185$	−348.577	−0.138529
$186$	2299.31	0.906416
$187$	634.807	0.248244
$188$	771.781	0.299404
$189$	−5986.15	−2.30386
$190$	0	0
$191$	3521.85	1.33420	0.667099	−	0.744969i	$-0.267536\pi$
$191$	3521.85	1.33420	0.667099	+	0.744969i	$0.267536\pi$
$192$	−612.896	−0.230375
$193$	−4735.39	−1.76612	−0.883060	−	0.469261i	$-0.844520\pi$
$193$	−4735.39	−1.76612	−0.883060	+	0.469261i	$0.844520\pi$
$194$	3171.84	1.17384
$195$	−10139.4	−3.72359
$196$	−272.879	−0.0994457
$197$	2357.30	0.852541	0.426270	−	0.904596i	$-0.359827\pi$
$197$	2357.30	0.852541	0.426270	+	0.904596i	$0.359827\pi$
$198$	2074.38	0.744545
$199$	685.156	0.244067	0.122034	−	0.992526i	$-0.461058\pi$
$199$	685.156	0.244067	0.122034	+	0.992526i	$0.461058\pi$
$200$	991.601	0.350584
$201$	−9029.22	−3.16852
$202$	−2087.65	−0.727162
$203$	1962.73	0.678603
$204$	−1517.11	−0.520680
$205$	−1721.42	−0.586484
$206$	−2855.67	−0.965843
$207$	−3085.39	−1.03599
$208$	1073.67	0.357911
$209$	0	0
$210$	−5009.40	−1.64610
$211$	531.020	0.173255	0.0866277	−	0.996241i	$-0.472391\pi$
$211$	531.020	0.173255	0.0866277	+	0.996241i	$0.472391\pi$
$212$	−871.377	−0.282294
$213$	−6375.51	−2.05090
$214$	−1001.85	−0.320023
$215$	−5689.99	−1.80490
$216$	−2888.98	−0.910048
$217$	−1990.00	−0.622535
$218$	−2425.85	−0.753665
$219$	1790.28	0.552403
$220$	1011.60	0.310009
$221$	2657.66	0.808932
$222$	423.136	0.127924
$223$	−4851.71	−1.45693	−0.728463	−	0.685085i	$-0.759765\pi$
$223$	−4851.71	−1.45693	−0.728463	+	0.685085i	$0.759765\pi$
$224$	530.448	0.158223
$225$	8020.72	2.37651
$226$	−1477.91	−0.434997
$227$	3971.88	1.16134	0.580668	−	0.814141i	$-0.302792\pi$
$227$	3971.88	1.16134	0.580668	+	0.814141i	$0.302792\pi$
$228$	0	0
$229$	−78.9844	−0.0227923	−0.0113961	−	0.999935i	$-0.503628\pi$
$229$	−78.9844	−0.0227923	−0.0113961	+	0.999935i	$0.503628\pi$
$230$	−1504.63	−0.431358
$231$	−2544.44	−0.724725
$232$	947.233	0.268056
$233$	−1643.29	−0.462042	−0.231021	−	0.972949i	$-0.574207\pi$
$233$	−1643.29	−0.462042	−0.231021	+	0.972949i	$0.574207\pi$
$234$	8684.55	2.42618
$235$	3044.32	0.845061
$236$	−1692.76	−0.466903
$237$	−8392.40	−2.30019
$238$	1313.02	0.357608
$239$	−6316.74	−1.70961	−0.854803	−	0.518952i	$-0.826322\pi$
$239$	−6316.74	−1.70961	−0.854803	+	0.518952i	$0.826322\pi$
$240$	−2417.59	−0.650228
$241$	3494.65	0.934068	0.467034	−	0.884239i	$-0.345322\pi$
$241$	3494.65	0.934068	0.467034	+	0.884239i	$0.345322\pi$
$242$	−2148.18	−0.570620
$243$	−6636.43	−1.75196
$244$	2255.68	0.591824
$245$	−1076.38	−0.280684
$246$	2089.62	0.541583
$247$	0	0
$248$	−960.396	−0.245908
$249$	4561.26	1.16088
$250$	−33.1316	−0.00838171
$251$	3630.37	0.912936	0.456468	−	0.889740i	$-0.349114\pi$
$251$	3630.37	0.912936	0.456468	+	0.889740i	$0.349114\pi$
$252$	4290.61	1.07255
$253$	−764.251	−0.189913
$254$	−477.816	−0.118035
$255$	−5984.29	−1.46961
$256$	256.000	0.0625000
$257$	1549.42	0.376070	0.188035	−	0.982162i	$-0.439788\pi$
$257$	1549.42	0.376070	0.188035	+	0.982162i	$0.439788\pi$
$258$	6907.04	1.66672
$259$	−366.215	−0.0878590
$260$	4235.13	1.01020
$261$	7661.85	1.81708
$262$	530.497	0.125092
$263$	−3809.81	−0.893243	−0.446622	−	0.894723i	$-0.647373\pi$
$263$	−3809.81	−0.893243	−0.446622	+	0.894723i	$0.647373\pi$
$264$	−1227.97	−0.286275
$265$	−3437.18	−0.796771
$266$	0	0
$267$	−9238.83	−2.11763
$268$	3771.41	0.859610
$269$	3376.40	0.765289	0.382644	−	0.923896i	$-0.375013\pi$
$269$	3376.40	0.765289	0.382644	+	0.923896i	$0.375013\pi$
$270$	−11395.7	−2.56859
$271$	−3525.50	−0.790254	−0.395127	−	0.918627i	$-0.629299\pi$
$271$	−3525.50	−0.790254	−0.395127	+	0.918627i	$0.629299\pi$
$272$	633.679	0.141259
$273$	−10652.5	−2.36160
$274$	4876.90	1.07527
$275$	1986.73	0.435652
$276$	1826.46	0.398334
$277$	6557.88	1.42247	0.711236	−	0.702953i	$-0.248136\pi$
$277$	6557.88	1.42247	0.711236	+	0.702953i	$0.248136\pi$
$278$	−733.589	−0.158265
$279$	−7768.32	−1.66694
$280$	2092.37	0.446583
$281$	−7887.80	−1.67454	−0.837272	−	0.546787i	$-0.815851\pi$
$281$	−7887.80	−1.67454	−0.837272	+	0.546787i	$0.815851\pi$
$282$	−3695.48	−0.780363
$283$	2072.73	0.435375	0.217687	−	0.976019i	$-0.430149\pi$
$283$	2072.73	0.435375	0.217687	+	0.976019i	$0.430149\pi$
$284$	2662.98	0.556404
$285$	0	0
$286$	2151.16	0.444758
$287$	−1808.52	−0.371964
$288$	2070.70	0.423670
$289$	−3344.45	−0.680734
$290$	3736.40	0.756582
$291$	−15187.6	−3.05949
$292$	−747.782	−0.149865
$293$	7820.84	1.55938	0.779690	−	0.626165i	$-0.215376\pi$
$293$	7820.84	1.55938	0.779690	+	0.626165i	$0.215376\pi$
$294$	1306.61	0.259194
$295$	−6677.15	−1.31783
$296$	−176.739	−0.0347053
$297$	−5788.25	−1.13087
$298$	−4483.51	−0.871553
$299$	−3199.59	−0.618853
$300$	−4748.03	−0.913759
$301$	−5977.89	−1.14472
$302$	1276.39	0.243205
$303$	9996.20	1.89527
$304$	0	0
$305$	8897.62	1.67041
$306$	5125.62	0.957556
$307$	5937.79	1.10387	0.551934	−	0.833888i	$-0.313890\pi$
$307$	5937.79	1.10387	0.551934	+	0.833888i	$0.313890\pi$
$308$	1062.78	0.196616
$309$	13673.6	2.51737
$310$	−3788.32	−0.694071
$311$	1832.63	0.334145	0.167073	−	0.985945i	$-0.446569\pi$
$311$	1832.63	0.334145	0.167073	+	0.985945i	$0.446569\pi$
$312$	−5141.00	−0.932858
$313$	−938.332	−0.169449	−0.0847247	−	0.996404i	$-0.527001\pi$
$313$	−938.332	−0.169449	−0.0847247	+	0.996404i	$0.527001\pi$
$314$	4251.98	0.764182
$315$	16924.5	3.02726
$316$	3505.42	0.624035
$317$	7411.46	1.31315	0.656576	−	0.754260i	$-0.272004\pi$
$317$	7411.46	1.31315	0.656576	+	0.754260i	$0.272004\pi$
$318$	4172.37	0.735770
$319$	1897.84	0.333099
$320$	1009.80	0.176405
$321$	4797.10	0.834106
$322$	−1580.76	−0.273579
$323$	0	0
$324$	6844.57	1.17362
$325$	8317.59	1.41962
$326$	−320.087	−0.0543802
$327$	11615.6	1.96435
$328$	−872.812	−0.146930
$329$	3198.36	0.535961
$330$	−4843.78	−0.808005
$331$	5412.69	0.898817	0.449408	−	0.893326i	$-0.351635\pi$
$331$	5412.69	0.898817	0.449408	+	0.893326i	$0.351635\pi$
$332$	−1905.19	−0.314942
$333$	−1429.58	−0.235258
$334$	−4204.32	−0.688773
$335$	14876.5	2.42623
$336$	−2539.92	−0.412392
$337$	−9273.57	−1.49900	−0.749501	−	0.662003i	$-0.769706\pi$
$337$	−9273.57	−1.49900	−0.749501	+	0.662003i	$0.769706\pi$
$338$	4611.98	0.742186
$339$	7076.61	1.13377
$340$	2499.57	0.398701
$341$	−1924.21	−0.305577
$342$	0	0
$343$	−6816.58	−1.07306
$344$	−2885.00	−0.452176
$345$	7204.55	1.12429
$346$	810.927	0.125999
$347$	−9674.48	−1.49670	−0.748348	−	0.663307i	$-0.769153\pi$
$347$	−9674.48	−1.49670	−0.748348	+	0.663307i	$0.769153\pi$
$348$	−4535.59	−0.698658
$349$	1300.56	0.199477	0.0997387	−	0.995014i	$-0.468199\pi$
$349$	1300.56	0.199477	0.0997387	+	0.995014i	$0.468199\pi$
$350$	4109.32	0.627578
$351$	−24232.9	−3.68506
$352$	512.911	0.0776655
$353$	11985.4	1.80713	0.903564	−	0.428454i	$-0.140942\pi$
$353$	11985.4	1.80713	0.903564	+	0.428454i	$0.140942\pi$
$354$	8105.35	1.21693
$355$	10504.2	1.57044
$356$	3858.96	0.574507
$357$	−6287.08	−0.932066
$358$	3257.52	0.480908
$359$	−4407.90	−0.648022	−0.324011	−	0.946053i	$-0.605031\pi$
$359$	−4407.90	−0.648022	−0.324011	+	0.946053i	$0.605031\pi$
$360$	8167.95	1.19580
$361$	0	0
$362$	−5673.68	−0.823762
$363$	10286.0	1.48726
$364$	4449.42	0.640695
$365$	−2949.66	−0.422992
$366$	−10800.8	−1.54253
$367$	6260.08	0.890391	0.445196	−	0.895433i	$-0.353134\pi$
$367$	6260.08	0.890391	0.445196	+	0.895433i	$0.353134\pi$
$368$	−762.893	−0.108067
$369$	−7059.88	−0.995997
$370$	−697.155	−0.0979550
$371$	−3611.09	−0.505333
$372$	4598.62	0.640933
$373$	2745.24	0.381081	0.190541	−	0.981679i	$-0.438976\pi$
$373$	2745.24	0.381081	0.190541	+	0.981679i	$0.438976\pi$
$374$	1269.61	0.175535
$375$	158.642	0.0218460
$376$	1543.56	0.211710
$377$	7945.43	1.08544
$378$	−11972.3	−1.62907
$379$	−10772.3	−1.45998	−0.729992	−	0.683455i	$-0.760476\pi$
$379$	−10772.3	−1.45998	−0.729992	+	0.683455i	$0.760476\pi$
$380$	0	0
$381$	2287.90	0.307645
$382$	7043.70	0.943421
$383$	3379.95	0.450933	0.225466	−	0.974251i	$-0.427609\pi$
$383$	3379.95	0.450933	0.225466	+	0.974251i	$0.427609\pi$
$384$	−1225.79	−0.162900
$385$	4192.19	0.554945
$386$	−9470.78	−1.24883
$387$	−23335.8	−3.06518
$388$	6343.69	0.830031
$389$	4702.56	0.612929	0.306464	−	0.951882i	$-0.400854\pi$
$389$	4702.56	0.612929	0.306464	+	0.951882i	$0.400854\pi$
$390$	−20278.9	−2.63297
$391$	−1888.40	−0.244246
$392$	−545.758	−0.0703187
$393$	−2540.15	−0.326040
$394$	4714.60	0.602837
$395$	13827.2	1.76133
$396$	4148.76	0.526473
$397$	251.499	0.0317943	0.0158972	−	0.999874i	$-0.494940\pi$
$397$	251.499	0.0317943	0.0158972	+	0.999874i	$0.494940\pi$
$398$	1370.31	0.172582
$399$	0	0
$400$	1983.20	0.247900
$401$	6450.33	0.803277	0.401638	−	0.915798i	$-0.368441\pi$
$401$	6450.33	0.803277	0.401638	+	0.915798i	$0.368441\pi$
$402$	−18058.4	−2.24048
$403$	−8055.84	−0.995757
$404$	−4175.31	−0.514181
$405$	26998.7	3.31253
$406$	3925.45	0.479845
$407$	−354.108	−0.0431264
$408$	−3034.21	−0.368176
$409$	−2015.92	−0.243718	−0.121859	−	0.992547i	$-0.538886\pi$
$409$	−2015.92	−0.243718	−0.121859	+	0.992547i	$0.538886\pi$
$410$	−3442.84	−0.414707
$411$	−23351.8	−2.80258
$412$	−5711.33	−0.682954
$413$	−7015.00	−0.835801
$414$	−6170.79	−0.732555
$415$	−7515.09	−0.888919
$416$	2147.34	0.253082
$417$	3512.61	0.412501
$418$	0	0
$419$	−10124.5	−1.18046	−0.590232	−	0.807234i	$-0.700964\pi$
$419$	−10124.5	−1.18046	−0.590232	+	0.807234i	$0.700964\pi$
$420$	−10018.8	−1.16397
$421$	−3146.27	−0.364227	−0.182114	−	0.983278i	$-0.558294\pi$
$421$	−3146.27	−0.364227	−0.182114	+	0.983278i	$0.558294\pi$
$422$	1062.04	0.122510
$423$	12485.3	1.43513
$424$	−1742.75	−0.199612
$425$	4909.04	0.560290
$426$	−12751.0	−1.45021
$427$	9347.82	1.05942
$428$	−2003.70	−0.226290
$429$	−10300.3	−1.15921
$430$	−11380.0	−1.27626
$431$	−11662.3	−1.30337	−0.651687	−	0.758488i	$-0.725938\pi$
$431$	−11662.3	−1.30337	−0.651687	+	0.758488i	$0.725938\pi$
$432$	−5777.97	−0.643501
$433$	8969.04	0.995438	0.497719	−	0.867338i	$-0.334171\pi$
$433$	8969.04	0.995438	0.497719	+	0.867338i	$0.334171\pi$
$434$	−3980.00	−0.440198
$435$	−17890.8	−1.97195
$436$	−4851.69	−0.532922
$437$	0	0
$438$	3580.57	0.390608
$439$	−98.3073	−0.0106878	−0.00534391	−	0.999986i	$-0.501701\pi$
$439$	−98.3073	−0.0106878	−0.00534391	+	0.999986i	$0.501701\pi$
$440$	2023.20	0.219209
$441$	−4414.45	−0.476671
$442$	5315.33	0.572001
$443$	−9320.46	−0.999613	−0.499806	−	0.866137i	$-0.666595\pi$
$443$	−9320.46	−0.999613	−0.499806	+	0.866137i	$0.666595\pi$
$444$	846.272	0.0904556
$445$	15221.8	1.62154
$446$	−9703.42	−1.03020
$447$	21468.2	2.27161
$448$	1060.90	0.111881
$449$	−9992.53	−1.05028	−0.525141	−	0.851015i	$-0.675987\pi$
$449$	−9992.53	−1.05028	−0.525141	+	0.851015i	$0.675987\pi$
$450$	16041.4	1.68045
$451$	−1748.73	−0.182582
$452$	−2955.82	−0.307589
$453$	−6111.67	−0.633888
$454$	7943.77	0.821188
$455$	17550.9	1.80835
$456$	0	0
$457$	−1536.89	−0.157314	−0.0786572	−	0.996902i	$-0.525063\pi$
$457$	−1536.89	−0.157314	−0.0786572	+	0.996902i	$0.525063\pi$
$458$	−157.969	−0.0161166
$459$	−14302.3	−1.45441
$460$	−3009.26	−0.305016
$461$	−16624.9	−1.67961	−0.839804	−	0.542889i	$-0.817330\pi$
$461$	−16624.9	−1.67961	−0.839804	+	0.542889i	$0.817330\pi$
$462$	−5088.87	−0.512458
$463$	7191.48	0.721850	0.360925	−	0.932595i	$-0.382461\pi$
$463$	7191.48	0.721850	0.360925	+	0.932595i	$0.382461\pi$
$464$	1894.47	0.189544
$465$	18139.4	1.80902
$466$	−3286.59	−0.326713
$467$	−7001.51	−0.693772	−0.346886	−	0.937907i	$-0.612761\pi$
$467$	−7001.51	−0.693772	−0.346886	+	0.937907i	$0.612761\pi$
$468$	17369.1	1.71557
$469$	15629.2	1.53878
$470$	6088.64	0.597549
$471$	−20359.5	−1.99176
$472$	−3385.52	−0.330151
$473$	−5780.26	−0.561895
$474$	−16784.8	−1.62648
$475$	0	0
$476$	2626.05	0.252867
$477$	−14096.5	−1.35312
$478$	−12633.5	−1.20887
$479$	1911.84	0.182367	0.0911837	−	0.995834i	$-0.470935\pi$
$479$	1911.84	0.182367	0.0911837	+	0.995834i	$0.470935\pi$
$480$	−4835.18	−0.459781
$481$	−1482.50	−0.140532
$482$	6989.31	0.660486
$483$	7569.08	0.713054
$484$	−4296.35	−0.403489
$485$	25022.9	2.34275
$486$	−13272.9	−1.23883
$487$	6061.32	0.563993	0.281997	−	0.959415i	$-0.409003\pi$
$487$	6061.32	0.563993	0.281997	+	0.959415i	$0.409003\pi$
$488$	4511.36	0.418483
$489$	1532.65	0.141736
$490$	−2152.76	−0.198473
$491$	6439.02	0.591831	0.295916	−	0.955214i	$-0.404375\pi$
$491$	6439.02	0.591831	0.295916	+	0.955214i	$0.404375\pi$
$492$	4179.24	0.382957
$493$	4689.39	0.428397
$494$	0	0
$495$	16365.0	1.48596
$496$	−1920.79	−0.173883
$497$	11035.7	0.996016
$498$	9122.52	0.820863
$499$	16458.1	1.47649	0.738244	−	0.674534i	$-0.235655\pi$
$499$	16458.1	1.47649	0.738244	+	0.674534i	$0.235655\pi$
$500$	−66.2633	−0.00592677
$501$	20131.3	1.79521
$502$	7260.74	0.645543
$503$	−2724.84	−0.241540	−0.120770	−	0.992681i	$-0.538536\pi$
$503$	−2724.84	−0.241540	−0.120770	+	0.992681i	$0.538536\pi$
$504$	8581.23	0.758409
$505$	−16469.7	−1.45127
$506$	−1528.50	−0.134289
$507$	−22083.3	−1.93443
$508$	−955.632	−0.0834632
$509$	−5460.82	−0.475533	−0.237767	−	0.971322i	$-0.576415\pi$
$509$	−5460.82	−0.475533	−0.237767	+	0.971322i	$0.576415\pi$
$510$	−11968.6	−1.03917
$511$	−3098.90	−0.268273
$512$	512.000	0.0441942
$513$	0	0
$514$	3098.83	0.265921
$515$	−22528.6	−1.92763
$516$	13814.1	1.17855
$517$	3092.62	0.263081
$518$	−732.430	−0.0621257
$519$	−3882.92	−0.328403
$520$	8470.26	0.714318
$521$	−7411.04	−0.623193	−0.311596	−	0.950215i	$-0.600864\pi$
$521$	−7411.04	−0.623193	−0.311596	+	0.950215i	$0.600864\pi$
$522$	15323.7	1.28487
$523$	799.420	0.0668379	0.0334189	−	0.999441i	$-0.489360\pi$
$523$	799.420	0.0668379	0.0334189	+	0.999441i	$0.489360\pi$
$524$	1060.99	0.0884537
$525$	−19676.4	−1.63571
$526$	−7619.62	−0.631618
$527$	−4754.56	−0.393001
$528$	−2455.95	−0.202427
$529$	−9893.54	−0.813145
$530$	−6874.36	−0.563402
$531$	−27384.3	−2.23800
$532$	0	0
$533$	−7321.19	−0.594964
$534$	−18477.7	−1.49739
$535$	−7903.66	−0.638701
$536$	7542.81	0.607836
$537$	−15597.8	−1.25343
$538$	6752.80	0.541141
$539$	−1093.46	−0.0873814
$540$	−22791.4	−1.81627
$541$	5895.13	0.468487	0.234243	−	0.972178i	$-0.424739\pi$
$541$	5895.13	0.468487	0.234243	+	0.972178i	$0.424739\pi$
$542$	−7051.00	−0.558794
$543$	27167.0	2.14705
$544$	1267.36	0.0998852
$545$	−19137.7	−1.50416
$546$	−21304.9	−1.66990
$547$	−11491.3	−0.898230	−0.449115	−	0.893474i	$-0.648261\pi$
$547$	−11491.3	−0.898230	−0.449115	+	0.893474i	$0.648261\pi$
$548$	9753.79	0.760331
$549$	36490.9	2.83678
$550$	3973.46	0.308053
$551$	0	0
$552$	3652.92	0.281664
$553$	14526.9	1.11708
$554$	13115.8	1.00584
$555$	3338.15	0.255309
$556$	−1467.18	−0.111910
$557$	−2244.60	−0.170748	−0.0853740	−	0.996349i	$-0.527209\pi$
$557$	−2244.60	−0.170748	−0.0853740	+	0.996349i	$0.527209\pi$
$558$	−15536.6	−1.17871
$559$	−24199.5	−1.83100
$560$	4184.74	0.315782
$561$	−6079.23	−0.457514
$562$	−15775.6	−1.18408
$563$	19529.8	1.46196	0.730978	−	0.682401i	$-0.239064\pi$
$563$	19529.8	1.46196	0.730978	+	0.682401i	$0.239064\pi$
$564$	−7390.96	−0.551800
$565$	−11659.4	−0.868165
$566$	4145.46	0.307857
$567$	28364.7	2.10089
$568$	5325.96	0.393437
$569$	3300.68	0.243184	0.121592	−	0.992580i	$-0.461200\pi$
$569$	3300.68	0.243184	0.121592	+	0.992580i	$0.461200\pi$
$570$	0	0
$571$	3080.76	0.225789	0.112895	−	0.993607i	$-0.463988\pi$
$571$	3080.76	0.225789	0.112895	+	0.993607i	$0.463988\pi$
$572$	4302.32	0.314491
$573$	−33727.0	−2.45893
$574$	−3617.04	−0.263018
$575$	−5910.04	−0.428636
$576$	4141.40	0.299580
$577$	4946.52	0.356892	0.178446	−	0.983950i	$-0.442893\pi$
$577$	4946.52	0.356892	0.178446	+	0.983950i	$0.442893\pi$
$578$	−6688.89	−0.481352
$579$	45348.5	3.25495
$580$	7472.80	0.534984
$581$	−7895.34	−0.563776
$582$	−30375.2	−2.16339
$583$	−3491.71	−0.248048
$584$	−1495.56	−0.105971
$585$	68513.1	4.84217
$586$	15641.7	1.10265
$587$	14556.0	1.02350	0.511748	−	0.859136i	$-0.328998\pi$
$587$	14556.0	1.02350	0.511748	+	0.859136i	$0.328998\pi$
$588$	2613.22	0.183278
$589$	0	0
$590$	−13354.3	−0.931844
$591$	−22574.7	−1.57123
$592$	−353.479	−0.0245403
$593$	−20617.2	−1.42774	−0.713869	−	0.700279i	$-0.753059\pi$
$593$	−20617.2	−1.42774	−0.713869	+	0.700279i	$0.753059\pi$
$594$	−11576.5	−0.799645
$595$	10358.5	0.713712
$596$	−8967.02	−0.616281
$597$	−6561.39	−0.449816
$598$	−6399.18	−0.437595
$599$	−21304.5	−1.45322	−0.726608	−	0.687052i	$-0.758904\pi$
$599$	−21304.5	−1.45322	−0.726608	+	0.687052i	$0.758904\pi$
$600$	−9496.06	−0.646125
$601$	26351.4	1.78852	0.894258	−	0.447553i	$-0.147704\pi$
$601$	26351.4	1.78852	0.894258	+	0.447553i	$0.147704\pi$
$602$	−11955.8	−0.809437
$603$	61011.3	4.12035
$604$	2552.78	0.171972
$605$	−16947.1	−1.13884
$606$	19992.4	1.34016
$607$	−24027.8	−1.60669	−0.803344	−	0.595516i	$-0.796948\pi$
$607$	−24027.8	−1.60669	−0.803344	+	0.595516i	$0.796948\pi$
$608$	0	0
$609$	−18796.0	−1.25066
$610$	17795.2	1.18116
$611$	12947.5	0.857280
$612$	10251.2	0.677094
$613$	15238.0	1.00401	0.502004	−	0.864865i	$-0.332596\pi$
$613$	15238.0	1.00401	0.502004	+	0.864865i	$0.332596\pi$
$614$	11875.6	0.780553
$615$	16485.2	1.08089
$616$	2125.57	0.139028
$617$	−28130.8	−1.83550	−0.917751	−	0.397156i	$-0.869997\pi$
$617$	−28130.8	−1.83550	−0.917751	+	0.397156i	$0.869997\pi$
$618$	27347.3	1.78005
$619$	9482.23	0.615708	0.307854	−	0.951434i	$-0.400389\pi$
$619$	9482.23	0.615708	0.307854	+	0.951434i	$0.400389\pi$
$620$	−7576.64	−0.490782
$621$	17218.6	1.11266
$622$	3665.27	0.236276
$623$	15992.0	1.02842
$624$	−10282.0	−0.659630
$625$	−15755.1	−1.00833
$626$	−1876.66	−0.119819
$627$	0	0
$628$	8503.96	0.540358
$629$	−874.969	−0.0554647
$630$	33849.0	2.14060
$631$	−1701.40	−0.107340	−0.0536702	−	0.998559i	$-0.517092\pi$
$631$	−1701.40	−0.107340	−0.0536702	+	0.998559i	$0.517092\pi$
$632$	7010.83	0.441259
$633$	−5085.31	−0.319309
$634$	14822.9	0.928539
$635$	−3769.53	−0.235573
$636$	8344.74	0.520268
$637$	−4577.84	−0.284742
$638$	3795.67	0.235536
$639$	43079.9	2.66700
$640$	2019.60	0.124737
$641$	−21631.5	−1.33291	−0.666454	−	0.745546i	$-0.732189\pi$
$641$	−21631.5	−1.33291	−0.666454	+	0.745546i	$0.732189\pi$
$642$	9594.20	0.589802
$643$	−5444.61	−0.333926	−0.166963	−	0.985963i	$-0.553396\pi$
$643$	−5444.61	−0.333926	−0.166963	+	0.985963i	$0.553396\pi$
$644$	−3161.52	−0.193450
$645$	54490.2	3.32643
$646$	0	0
$647$	27393.8	1.66454	0.832272	−	0.554367i	$-0.187040\pi$
$647$	27393.8	1.66454	0.832272	+	0.554367i	$0.187040\pi$
$648$	13689.1	0.829877
$649$	−6783.08	−0.410261
$650$	16635.2	1.00382
$651$	19057.2	1.14733
$652$	−640.173	−0.0384526
$653$	−23390.6	−1.40175	−0.700875	−	0.713284i	$-0.747207\pi$
$653$	−23390.6	−1.40175	−0.700875	+	0.713284i	$0.747207\pi$
$654$	23231.1	1.38900
$655$	4185.13	0.249659
$656$	−1745.62	−0.103895
$657$	−12097.1	−0.718346
$658$	6396.71	0.378981
$659$	20059.0	1.18572	0.592860	−	0.805306i	$-0.297999\pi$
$659$	20059.0	1.18572	0.592860	+	0.805306i	$0.297999\pi$
$660$	−9687.57	−0.571346
$661$	−23237.8	−1.36739	−0.683696	−	0.729767i	$-0.739628\pi$
$661$	−23237.8	−1.36739	−0.683696	+	0.729767i	$0.739628\pi$
$662$	10825.4	0.635559
$663$	−25451.1	−1.49086
$664$	−3810.38	−0.222698
$665$	0	0
$666$	−2859.17	−0.166352
$667$	−5645.61	−0.327734
$668$	−8408.64	−0.487036
$669$	46462.4	2.68511
$670$	29752.9	1.71561
$671$	9038.77	0.520027
$672$	−5079.83	−0.291605
$673$	10185.3	0.583378	0.291689	−	0.956513i	$-0.405783\pi$
$673$	10185.3	0.583378	0.291689	+	0.956513i	$0.405783\pi$
$674$	−18547.1	−1.05995
$675$	−44761.2	−2.55239
$676$	9223.97	0.524805
$677$	−3202.89	−0.181827	−0.0909136	−	0.995859i	$-0.528979\pi$
$677$	−3202.89	−0.181827	−0.0909136	+	0.995859i	$0.528979\pi$
$678$	14153.2	0.801698
$679$	26289.0	1.48583
$680$	4999.15	0.281924
$681$	−38036.7	−2.14034
$682$	−3848.42	−0.216076
$683$	−1625.51	−0.0910662	−0.0455331	−	0.998963i	$-0.514499\pi$
$683$	−1625.51	−0.0910662	−0.0455331	+	0.998963i	$0.514499\pi$
$684$	0	0
$685$	38474.2	2.14602
$686$	−13633.2	−0.758771
$687$	756.394	0.0420061
$688$	−5769.99	−0.319737
$689$	−14618.3	−0.808291
$690$	14409.1	0.794992
$691$	839.130	0.0461968	0.0230984	−	0.999733i	$-0.492647\pi$
$691$	839.130	0.0461968	0.0230984	+	0.999733i	$0.492647\pi$
$692$	1621.85	0.0890949
$693$	17193.0	0.942435
$694$	−19349.0	−1.05832
$695$	−5787.34	−0.315865
$696$	−9071.18	−0.494026
$697$	−4320.96	−0.234818
$698$	2601.13	0.141052
$699$	15737.0	0.851542
$700$	8218.63	0.443764
$701$	−1458.13	−0.0785631	−0.0392816	−	0.999228i	$-0.512507\pi$
$701$	−1458.13	−0.0785631	−0.0392816	+	0.999228i	$0.512507\pi$
$702$	−48465.8	−2.60573
$703$	0	0
$704$	1025.82	0.0549178
$705$	−29153.9	−1.55745
$706$	23970.7	1.27783
$707$	−17303.0	−0.920432
$708$	16210.7	0.860502
$709$	−32319.9	−1.71199	−0.855993	−	0.516987i	$-0.827053\pi$
$709$	−32319.9	−1.71199	−0.855993	+	0.516987i	$0.827053\pi$
$710$	21008.5	1.11047
$711$	56708.2	2.99117
$712$	7717.92	0.406238
$713$	5724.06	0.300656
$714$	−12574.2	−0.659070
$715$	16970.7	0.887646
$716$	6515.03	0.340053
$717$	60492.2	3.15080
$718$	−8815.79	−0.458221
$719$	−5771.67	−0.299370	−0.149685	−	0.988734i	$-0.547826\pi$
$719$	−5771.67	−0.299370	−0.149685	+	0.988734i	$0.547826\pi$
$720$	16335.9	0.845559
$721$	−23668.5	−1.22255
$722$	0	0
$723$	−33466.6	−1.72149
$724$	−11347.4	−0.582487
$725$	14676.2	0.751808
$726$	20572.0	1.05165
$727$	5452.31	0.278150	0.139075	−	0.990282i	$-0.455587\pi$
$727$	5452.31	0.278150	0.139075	+	0.990282i	$0.455587\pi$
$728$	8898.84	0.453040
$729$	17352.9	0.881618
$730$	−5899.31	−0.299100
$731$	−14282.5	−0.722651
$732$	−21601.5	−1.09073
$733$	9558.30	0.481643	0.240821	−	0.970569i	$-0.422583\pi$
$733$	9558.30	0.481643	0.240821	+	0.970569i	$0.422583\pi$
$734$	12520.2	0.629602
$735$	10308.0	0.517299
$736$	−1525.79	−0.0764147
$737$	15112.5	0.755326
$738$	−14119.8	−0.704276
$739$	12953.5	0.644792	0.322396	−	0.946605i	$-0.395512\pi$
$739$	12953.5	0.644792	0.322396	+	0.946605i	$0.395512\pi$
$740$	−1394.31	−0.0692647
$741$	0	0
$742$	−7222.19	−0.357325
$743$	183.959	0.00908317	0.00454158	−	0.999990i	$-0.498554\pi$
$743$	183.959	0.00908317	0.00454158	+	0.999990i	$0.498554\pi$
$744$	9197.23	0.453208
$745$	−35370.8	−1.73944
$746$	5490.49	0.269465
$747$	−30820.9	−1.50961
$748$	2539.23	0.124122
$749$	−8303.57	−0.405081
$750$	317.285	0.0154475
$751$	−10494.4	−0.509914	−0.254957	−	0.966952i	$-0.582061\pi$
$751$	−10494.4	−0.509914	−0.254957	+	0.966952i	$0.582061\pi$
$752$	3087.12	0.149702
$753$	−34766.2	−1.68254
$754$	15890.9	0.767521
$755$	10069.5	0.485388
$756$	−23944.6	−1.15193
$757$	−9462.49	−0.454320	−0.227160	−	0.973857i	$-0.572944\pi$
$757$	−9462.49	−0.454320	−0.227160	+	0.973857i	$0.572944\pi$
$758$	−21544.5	−1.03237
$759$	7318.84	0.350009
$760$	0	0
$761$	−38400.1	−1.82918	−0.914588	−	0.404388i	$-0.867485\pi$
$761$	−38400.1	−1.82918	−0.914588	+	0.404388i	$0.867485\pi$
$762$	4575.80	0.217538
$763$	−20106.0	−0.953980
$764$	14087.4	0.667099
$765$	40436.4	1.91109
$766$	6759.89	0.318858
$767$	−28397.9	−1.33688
$768$	−2451.58	−0.115187
$769$	−3071.86	−0.144050	−0.0720249	−	0.997403i	$-0.522946\pi$
$769$	−3071.86	−0.144050	−0.0720249	+	0.997403i	$0.522946\pi$
$770$	8384.38	0.392405
$771$	−14838.0	−0.693095
$772$	−18941.6	−0.883060
$773$	−7177.33	−0.333960	−0.166980	−	0.985960i	$-0.553401\pi$
$773$	−7177.33	−0.333960	−0.166980	+	0.985960i	$0.553401\pi$
$774$	−46671.5	−2.16741
$775$	−14880.1	−0.689691
$776$	12687.4	0.586920
$777$	3507.06	0.161924
$778$	9405.12	0.433406
$779$	0	0
$780$	−40557.7	−1.86179
$781$	10670.9	0.488904
$782$	−3776.80	−0.172708
$783$	−42758.5	−1.95155
$784$	−1091.52	−0.0497228
$785$	33544.2	1.52515
$786$	−5080.31	−0.230545
$787$	−40299.0	−1.82529	−0.912645	−	0.408754i	$-0.865963\pi$
$787$	−40299.0	−1.82529	−0.912645	+	0.408754i	$0.865963\pi$
$788$	9429.19	0.426270
$789$	36484.6	1.64625
$790$	27654.5	1.24545
$791$	−12249.3	−0.550613
$792$	8297.53	0.372272
$793$	37841.5	1.69457
$794$	502.997	0.0224820
$795$	32916.1	1.46845
$796$	2740.62	0.122034
$797$	33505.8	1.48913	0.744565	−	0.667550i	$-0.232657\pi$
$797$	33505.8	1.48913	0.744565	+	0.667550i	$0.232657\pi$
$798$	0	0
$799$	7641.59	0.338348
$800$	3966.40	0.175292
$801$	62427.7	2.75377
$802$	12900.7	0.568003
$803$	−2996.45	−0.131684
$804$	−36116.9	−1.58426
$805$	−12470.8	−0.546008
$806$	−16111.7	−0.704107
$807$	−32334.1	−1.41043
$808$	−8350.61	−0.363581
$809$	−20863.7	−0.906710	−0.453355	−	0.891330i	$-0.649773\pi$
$809$	−20863.7	−0.906710	−0.453355	+	0.891330i	$0.649773\pi$
$810$	53997.3	2.34231
$811$	−17457.6	−0.755882	−0.377941	−	0.925830i	$-0.623368\pi$
$811$	−17457.6	−0.755882	−0.377941	+	0.925830i	$0.623368\pi$
$812$	7850.90	0.339301
$813$	33761.9	1.45644
$814$	−708.215	−0.0304950
$815$	−2525.19	−0.108532
$816$	−6068.43	−0.260340
$817$	0	0
$818$	−4031.84	−0.172335
$819$	71979.7	3.07103
$820$	−6885.68	−0.293242
$821$	29271.5	1.24432	0.622158	−	0.782892i	$-0.286256\pi$
$821$	29271.5	1.24432	0.622158	+	0.782892i	$0.286256\pi$
$822$	−46703.6	−1.98172
$823$	38677.3	1.63816	0.819080	−	0.573679i	$-0.194484\pi$
$823$	38677.3	1.63816	0.819080	+	0.573679i	$0.194484\pi$
$824$	−11422.7	−0.482922
$825$	−19025.9	−0.802906
$826$	−14030.0	−0.591000
$827$	−4642.12	−0.195190	−0.0975951	−	0.995226i	$-0.531115\pi$
$827$	−4642.12	−0.195190	−0.0975951	+	0.995226i	$0.531115\pi$
$828$	−12341.6	−0.517994
$829$	7918.14	0.331735	0.165868	−	0.986148i	$-0.446958\pi$
$829$	7918.14	0.331735	0.165868	+	0.986148i	$0.446958\pi$
$830$	−15030.2	−0.628561
$831$	−62801.5	−2.62161
$832$	4294.68	0.178956
$833$	−2701.84	−0.112381
$834$	7025.21	0.291683
$835$	−33168.2	−1.37465
$836$	0	0
$837$	43352.6	1.79031
$838$	−20249.0	−0.834714
$839$	−8123.84	−0.334286	−0.167143	−	0.985933i	$-0.553454\pi$
$839$	−8123.84	−0.334286	−0.167143	+	0.985933i	$0.553454\pi$
$840$	−20037.6	−0.823051
$841$	−10369.5	−0.425169
$842$	−6292.53	−0.257547
$843$	75537.5	3.08618
$844$	2124.08	0.0866277
$845$	36384.3	1.48125
$846$	24970.7	1.01479
$847$	−17804.6	−0.722283
$848$	−3485.51	−0.141147
$849$	−19849.5	−0.802395
$850$	9818.08	0.396185
$851$	1053.38	0.0424319
$852$	−25502.0	−1.02545
$853$	45188.8	1.81388	0.906938	−	0.421265i	$-0.138414\pi$
$853$	45188.8	1.81388	0.906938	+	0.421265i	$0.138414\pi$
$854$	18695.6	0.749124
$855$	0	0
$856$	−4007.39	−0.160012
$857$	−30492.3	−1.21540	−0.607700	−	0.794166i	$-0.707908\pi$
$857$	−30492.3	−1.21540	−0.607700	+	0.794166i	$0.707908\pi$
$858$	−20600.6	−0.819687
$859$	−39054.5	−1.55125	−0.775625	−	0.631194i	$-0.782565\pi$
$859$	−39054.5	−1.55125	−0.775625	+	0.631194i	$0.782565\pi$
$860$	−22760.0	−0.902451
$861$	17319.3	0.685529
$862$	−23324.6	−0.921624
$863$	21510.4	0.848461	0.424230	−	0.905554i	$-0.360545\pi$
$863$	21510.4	0.848461	0.424230	+	0.905554i	$0.360545\pi$
$864$	−11555.9	−0.455024
$865$	6397.47	0.251469
$866$	17938.1	0.703881
$867$	32028.1	1.25459
$868$	−7960.00	−0.311267
$869$	14046.6	0.548330
$870$	−35781.6	−1.39438
$871$	63269.4	2.46131
$872$	−9703.39	−0.376833
$873$	102624.	3.97857
$874$	0	0
$875$	−274.603	−0.0106095
$876$	7161.14	0.276201
$877$	−8398.90	−0.323387	−0.161694	−	0.986841i	$-0.551696\pi$
$877$	−8398.90	−0.323387	−0.161694	+	0.986841i	$0.551696\pi$
$878$	−196.615	−0.00755742
$879$	−74896.3	−2.87394
$880$	4046.39	0.155004
$881$	−46320.2	−1.77136	−0.885679	−	0.464298i	$-0.846307\pi$
$881$	−46320.2	−1.77136	−0.885679	+	0.464298i	$0.846307\pi$
$882$	−8828.90	−0.337057
$883$	32004.0	1.21973	0.609863	−	0.792506i	$-0.291224\pi$
$883$	32004.0	1.21973	0.609863	+	0.792506i	$0.291224\pi$
$884$	10630.7	0.404466
$885$	63943.7	2.42875
$886$	−18640.9	−0.706833
$887$	33565.5	1.27060	0.635298	−	0.772267i	$-0.280877\pi$
$887$	33565.5	1.27060	0.635298	+	0.772267i	$0.280877\pi$
$888$	1692.54	0.0639618
$889$	−3960.26	−0.149407
$890$	30443.6	1.14660
$891$	27427.0	1.03124
$892$	−19406.8	−0.728463
$893$	0	0
$894$	42936.3	1.60627
$895$	25698.8	0.959794
$896$	2121.79	0.0791117
$897$	30640.9	1.14054
$898$	−19985.1	−0.742661
$899$	−14214.4	−0.527336
$900$	32082.9	1.18826
$901$	−8627.71	−0.319013
$902$	−3497.46	−0.129105
$903$	57247.3	2.10971
$904$	−5911.65	−0.217498
$905$	−44760.1	−1.64406
$906$	−12223.3	−0.448227
$907$	−39968.4	−1.46321	−0.731604	−	0.681730i	$-0.761228\pi$
$907$	−39968.4	−1.46321	−0.731604	+	0.681730i	$0.761228\pi$
$908$	15887.5	0.580668
$909$	−67545.3	−2.46462
$910$	35101.8	1.27870
$911$	−38734.2	−1.40869	−0.704347	−	0.709855i	$-0.748760\pi$
$911$	−38734.2	−1.40869	−0.704347	+	0.709855i	$0.748760\pi$
$912$	0	0
$913$	−7634.32	−0.276735
$914$	−3073.78	−0.111238
$915$	−85208.0	−3.07857
$916$	−315.938	−0.0113961
$917$	4396.89	0.158340
$918$	−28604.5	−1.02842
$919$	7565.87	0.271572	0.135786	−	0.990738i	$-0.456644\pi$
$919$	7565.87	0.271572	0.135786	+	0.990738i	$0.456644\pi$
$920$	−6018.52	−0.215679
$921$	−56863.2	−2.03443
$922$	−33249.8	−1.18766
$923$	44674.4	1.59315
$924$	−10177.7	−0.362363
$925$	−2738.36	−0.0973369
$926$	14383.0	0.510425
$927$	−92394.1	−3.27359
$928$	3788.93	0.134028
$929$	−23716.8	−0.837592	−0.418796	−	0.908080i	$-0.637548\pi$
$929$	−23716.8	−0.837592	−0.418796	+	0.908080i	$0.637548\pi$
$930$	36278.8	1.27917
$931$	0	0
$932$	−6573.17	−0.231021
$933$	−17550.2	−0.615829
$934$	−14003.0	−0.490571
$935$	10016.1	0.350332
$936$	34738.2	1.21309
$937$	44583.9	1.55442	0.777210	−	0.629242i	$-0.216634\pi$
$937$	44583.9	1.55442	0.777210	+	0.629242i	$0.216634\pi$
$938$	31258.4	1.08808
$939$	8985.93	0.312295
$940$	12177.3	0.422531
$941$	40172.4	1.39169	0.695846	−	0.718191i	$-0.255030\pi$
$941$	40172.4	1.39169	0.695846	+	0.718191i	$0.255030\pi$
$942$	−40719.1	−1.40839
$943$	5202.05	0.179642
$944$	−6771.04	−0.233452
$945$	−94450.5	−3.25129
$946$	−11560.5	−0.397320
$947$	−42974.7	−1.47465	−0.737324	−	0.675539i	$-0.763911\pi$
$947$	−42974.7	−1.47465	−0.737324	+	0.675539i	$0.763911\pi$
$948$	−33569.6	−1.15009
$949$	−12544.9	−0.429108
$950$	0	0
$951$	−70975.8	−2.42014
$952$	5252.09	0.178804
$953$	−32782.0	−1.11428	−0.557141	−	0.830418i	$-0.688102\pi$
$953$	−32782.0	−1.11428	−0.557141	+	0.830418i	$0.688102\pi$
$954$	−28193.1	−0.956798
$955$	55568.3	1.88288
$956$	−25267.0	−0.854803
$957$	−18174.6	−0.613900
$958$	3823.67	0.128953
$959$	40420.9	1.36106
$960$	−9670.36	−0.325114
$961$	−15379.1	−0.516234
$962$	−2964.99	−0.0993713
$963$	−32414.4	−1.08467
$964$	13978.6	0.467034
$965$	−74715.7	−2.49242
$966$	15138.2	0.504205
$967$	19763.8	0.657251	0.328626	−	0.944460i	$-0.393415\pi$
$967$	19763.8	0.657251	0.328626	+	0.944460i	$0.393415\pi$
$968$	−8592.71	−0.285310
$969$	0	0
$970$	50045.8	1.65657
$971$	−13853.8	−0.457866	−0.228933	−	0.973442i	$-0.573524\pi$
$971$	−13853.8	−0.457866	−0.228933	+	0.973442i	$0.573524\pi$
$972$	−26545.7	−0.875982
$973$	−6080.17	−0.200330
$974$	12122.6	0.398803
$975$	−79653.4	−2.61636
$976$	9022.72	0.295912
$977$	−53113.0	−1.73924	−0.869620	−	0.493722i	$-0.835636\pi$
$977$	−53113.0	−1.73924	−0.869620	+	0.493722i	$0.835636\pi$
$978$	3065.31	0.100223
$979$	15463.3	0.504810
$980$	−4305.53	−0.140342
$981$	−78487.4	−2.55444
$982$	12878.0	0.418488
$983$	17345.8	0.562812	0.281406	−	0.959589i	$-0.409199\pi$
$983$	17345.8	0.562812	0.281406	+	0.959589i	$0.409199\pi$
$984$	8358.48	0.270791
$985$	37193.8	1.20314
$986$	9378.78	0.302922
$987$	−30629.0	−0.987774
$988$	0	0
$989$	17194.9	0.552847
$990$	32729.9	1.05073
$991$	6633.39	0.212630	0.106315	−	0.994332i	$-0.466095\pi$
$991$	6633.39	0.212630	0.106315	+	0.994332i	$0.466095\pi$
$992$	−3841.58	−0.122954
$993$	−51834.6	−1.65652
$994$	22071.4	0.704290
$995$	10810.5	0.344438
$996$	18245.0	0.580438
$997$	−20612.6	−0.654772	−0.327386	−	0.944891i	$-0.606168\pi$
$997$	−20612.6	−0.654772	−0.327386	+	0.944891i	$0.606168\pi$
$998$	32916.3	1.04403
$999$	7978.08	0.252668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.k.1.1		3
19.8	odd	6		38.4.c.c.7.1	✓	6
19.12	odd	6		38.4.c.c.11.1	yes	6
19.18	odd	2		722.4.a.j.1.3		3
57.8	even	6		342.4.g.f.235.3		6
57.50	even	6		342.4.g.f.163.3		6
76.27	even	6		304.4.i.e.273.3		6
76.31	even	6		304.4.i.e.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.1	✓	6	19.8	odd	6
38.4.c.c.11.1	yes	6	19.12	odd	6
304.4.i.e.49.3		6	76.31	even	6
304.4.i.e.273.3		6	76.27	even	6
342.4.g.f.163.3		6	57.50	even	6
342.4.g.f.235.3		6	57.8	even	6
722.4.a.j.1.3		3	19.18	odd	2
722.4.a.k.1.1		3	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -9.57650 q^{3} +4.00000 q^{4} +15.7782 q^{5} -19.1530 q^{6} +16.5765 q^{7} +8.00000 q^{8} +64.7093 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -9.57650 q^{3} +4.00000 q^{4} +15.7782 q^{5} -19.1530 q^{6} +16.5765 q^{7} +8.00000 q^{8} +64.7093 q^{9} +31.5563 q^{10} +16.0285 q^{11} -38.3060 q^{12} +67.1043 q^{13} +33.1530 q^{14} -151.099 q^{15} +16.0000 q^{16} +39.6050 q^{17} +129.419 q^{18} +63.1126 q^{20} -158.745 q^{21} +32.0569 q^{22} -47.6808 q^{23} -76.6120 q^{24} +123.950 q^{25} +134.209 q^{26} -361.123 q^{27} +66.3060 q^{28} +118.404 q^{29} -302.199 q^{30} -120.050 q^{31} +32.0000 q^{32} -153.497 q^{33} +79.2099 q^{34} +261.546 q^{35} +258.837 q^{36} -22.0924 q^{37} -642.624 q^{39} +126.225 q^{40} -109.102 q^{41} -317.490 q^{42} -360.624 q^{43} +64.1139 q^{44} +1020.99 q^{45} -95.3617 q^{46} +192.945 q^{47} -153.224 q^{48} -68.2197 q^{49} +247.900 q^{50} -379.277 q^{51} +268.417 q^{52} -217.844 q^{53} -722.246 q^{54} +252.900 q^{55} +132.612 q^{56} +236.808 q^{58} -423.190 q^{59} -604.398 q^{60} +563.920 q^{61} -240.099 q^{62} +1072.65 q^{63} +64.0000 q^{64} +1058.78 q^{65} -306.993 q^{66} +942.852 q^{67} +158.420 q^{68} +456.615 q^{69} +523.093 q^{70} +665.745 q^{71} +517.674 q^{72} -186.946 q^{73} -44.1848 q^{74} -1187.01 q^{75} +265.696 q^{77} -1285.25 q^{78} +876.354 q^{79} +252.450 q^{80} +1711.14 q^{81} -218.203 q^{82} -476.297 q^{83} -634.979 q^{84} +624.893 q^{85} -721.249 q^{86} -1133.90 q^{87} +128.228 q^{88} +964.740 q^{89} +2041.99 q^{90} +1112.35 q^{91} -190.723 q^{92} +1149.65 q^{93} +385.890 q^{94} -306.448 q^{96} +1585.92 q^{97} -136.439 q^{98} +1037.19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9	\( 3 q + 6 q^{2} - 5 q^{3} + 12 q^{4} + q^{5} - 10 q^{6} + 26 q^{7} + 24 q^{8} + 54 q^{9} + 2 q^{10} + 4 q^{11} - 20 q^{12} + 129 q^{13} + 52 q^{14} - 77 q^{15} + 48 q^{16} + 51 q^{17} + 108 q^{18} + 4 q^{20} - 170 q^{21} + 8 q^{22} - 47 q^{23} - 40 q^{24} + 338 q^{25} + 258 q^{26} - 359 q^{27} + 104 q^{28} - 125 q^{29} - 154 q^{30} + 50 q^{31} + 96 q^{32} + 274 q^{33} + 102 q^{34} + 84 q^{35} + 216 q^{36} + 188 q^{37} - 773 q^{39} + 8 q^{40} + 475 q^{41} - 340 q^{42} + 73 q^{43} + 16 q^{44} + 1594 q^{45} - 94 q^{46} + 241 q^{47} - 80 q^{48} - 677 q^{49} + 676 q^{50} + 69 q^{51} + 516 q^{52} + 29 q^{53} - 718 q^{54} + 1838 q^{55} + 208 q^{56} - 250 q^{58} - 1065 q^{59} - 308 q^{60} + 981 q^{61} + 100 q^{62} + 872 q^{63} + 192 q^{64} - 293 q^{65} + 548 q^{66} + 877 q^{67} + 204 q^{68} + 763 q^{69} + 168 q^{70} + 2135 q^{71} + 432 q^{72} - 667 q^{73} + 376 q^{74} - 2292 q^{75} - 246 q^{77} - 1546 q^{78} + 1671 q^{79} + 16 q^{80} + 1287 q^{81} + 950 q^{82} + 588 q^{83} - 680 q^{84} + 1929 q^{85} + 146 q^{86} - 3215 q^{87} + 32 q^{88} + 693 q^{89} + 3188 q^{90} + 1676 q^{91} - 188 q^{92} + 3138 q^{93} + 482 q^{94} - 160 q^{96} - 985 q^{97} - 1354 q^{98} + 3184 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 5 * q^3 + 12 * q^4 + q^5 - 10 * q^6 + 26 * q^7 + 24 * q^8 + 54 * q^9 + 2 * q^10 + 4 * q^11 - 20 * q^12 + 129 * q^13 + 52 * q^14 - 77 * q^15 + 48 * q^16 + 51 * q^17 + 108 * q^18 + 4 * q^20 - 170 * q^21 + 8 * q^22 - 47 * q^23 - 40 * q^24 + 338 * q^25 + 258 * q^26 - 359 * q^27 + 104 * q^28 - 125 * q^29 - 154 * q^30 + 50 * q^31 + 96 * q^32 + 274 * q^33 + 102 * q^34 + 84 * q^35 + 216 * q^36 + 188 * q^37 - 773 * q^39 + 8 * q^40 + 475 * q^41 - 340 * q^42 + 73 * q^43 + 16 * q^44 + 1594 * q^45 - 94 * q^46 + 241 * q^47 - 80 * q^48 - 677 * q^49 + 676 * q^50 + 69 * q^51 + 516 * q^52 + 29 * q^53 - 718 * q^54 + 1838 * q^55 + 208 * q^56 - 250 * q^58 - 1065 * q^59 - 308 * q^60 + 981 * q^61 + 100 * q^62 + 872 * q^63 + 192 * q^64 - 293 * q^65 + 548 * q^66 + 877 * q^67 + 204 * q^68 + 763 * q^69 + 168 * q^70 + 2135 * q^71 + 432 * q^72 - 667 * q^73 + 376 * q^74 - 2292 * q^75 - 246 * q^77 - 1546 * q^78 + 1671 * q^79 + 16 * q^80 + 1287 * q^81 + 950 * q^82 + 588 * q^83 - 680 * q^84 + 1929 * q^85 + 146 * q^86 - 3215 * q^87 + 32 * q^88 + 693 * q^89 + 3188 * q^90 + 1676 * q^91 - 188 * q^92 + 3138 * q^93 + 482 * q^94 - 160 * q^96 - 985 * q^97 - 1354 * q^98 + 3184 * q^99

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