LMFDB - Embedded newform 1045.4.a.d.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.22182 q^{2} +6.66604 q^{3} -3.06353 q^{4} +5.00000 q^{5} -14.8107 q^{6} -18.2528 q^{7} +24.5811 q^{8} +17.4361 q^{9} +O(q^{10})$	\(q-2.22182 q^{2} +6.66604 q^{3} -3.06353 q^{4} +5.00000 q^{5} -14.8107 q^{6} -18.2528 q^{7} +24.5811 q^{8} +17.4361 q^{9} -11.1091 q^{10} -11.0000 q^{11} -20.4216 q^{12} +18.1791 q^{13} +40.5545 q^{14} +33.3302 q^{15} -30.1066 q^{16} -33.1209 q^{17} -38.7399 q^{18} -19.0000 q^{19} -15.3176 q^{20} -121.674 q^{21} +24.4400 q^{22} +195.722 q^{23} +163.859 q^{24} +25.0000 q^{25} -40.3907 q^{26} -63.7532 q^{27} +55.9180 q^{28} +60.7265 q^{29} -74.0537 q^{30} -314.394 q^{31} -129.758 q^{32} -73.3265 q^{33} +73.5886 q^{34} -91.2641 q^{35} -53.4161 q^{36} +95.3515 q^{37} +42.2145 q^{38} +121.183 q^{39} +122.906 q^{40} +253.919 q^{41} +270.338 q^{42} +129.893 q^{43} +33.6988 q^{44} +87.1806 q^{45} -434.858 q^{46} -415.646 q^{47} -200.692 q^{48} -9.83427 q^{49} -55.5454 q^{50} -220.785 q^{51} -55.6923 q^{52} +279.953 q^{53} +141.648 q^{54} -55.0000 q^{55} -448.675 q^{56} -126.655 q^{57} -134.923 q^{58} -508.054 q^{59} -102.108 q^{60} +15.4540 q^{61} +698.525 q^{62} -318.259 q^{63} +529.151 q^{64} +90.8957 q^{65} +162.918 q^{66} -1063.35 q^{67} +101.467 q^{68} +1304.69 q^{69} +202.772 q^{70} -199.213 q^{71} +428.600 q^{72} -541.638 q^{73} -211.854 q^{74} +166.651 q^{75} +58.2070 q^{76} +200.781 q^{77} -269.246 q^{78} -826.681 q^{79} -150.533 q^{80} -895.757 q^{81} -564.161 q^{82} +1240.64 q^{83} +372.752 q^{84} -165.605 q^{85} -288.600 q^{86} +404.806 q^{87} -270.393 q^{88} -748.781 q^{89} -193.699 q^{90} -331.821 q^{91} -599.599 q^{92} -2095.76 q^{93} +923.489 q^{94} -95.0000 q^{95} -864.971 q^{96} +231.841 q^{97} +21.8500 q^{98} -191.797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.22182	−0.785531	−0.392766	−	0.919639i	$-0.628482\pi$
$2$	−2.22182	−0.785531	−0.392766	+	0.919639i	$0.628482\pi$
$3$	6.66604	1.28288	0.641440	−	0.767173i	$-0.278337\pi$
$3$	6.66604	1.28288	0.641440	+	0.767173i	$0.278337\pi$
$4$	−3.06353	−0.382941
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−14.8107	−1.00774
$7$	−18.2528	−0.985560	−0.492780	−	0.870154i	$-0.664019\pi$
$7$	−18.2528	−0.985560	−0.492780	+	0.870154i	$0.664019\pi$
$8$	24.5811	1.08634
$9$	17.4361	0.645783
$10$	−11.1091	−0.351300
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−20.4216	−0.491267
$13$	18.1791	0.387845	0.193922	−	0.981017i	$-0.437879\pi$
$13$	18.1791	0.387845	0.193922	+	0.981017i	$0.437879\pi$
$14$	40.5545	0.774188
$15$	33.3302	0.573722
$16$	−30.1066	−0.470415
$17$	−33.1209	−0.472529	−0.236265	−	0.971689i	$-0.575923\pi$
$17$	−33.1209	−0.472529	−0.236265	+	0.971689i	$0.575923\pi$
$18$	−38.7399	−0.507282
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−15.3176	−0.171256
$21$	−121.674	−1.26436
$22$	24.4400	0.236847
$23$	195.722	1.77438	0.887192	−	0.461401i	$-0.152653\pi$
$23$	195.722	1.77438	0.887192	+	0.461401i	$0.152653\pi$
$24$	163.859	1.39365
$25$	25.0000	0.200000
$26$	−40.3907	−0.304664
$27$	−63.7532	−0.454419
$28$	55.9180	0.377411
$29$	60.7265	0.388850	0.194425	−	0.980917i	$-0.437716\pi$
$29$	60.7265	0.388850	0.194425	+	0.980917i	$0.437716\pi$
$30$	−74.0537	−0.450676
$31$	−314.394	−1.82151	−0.910754	−	0.412949i	$-0.864499\pi$
$31$	−314.394	−1.82151	−0.910754	+	0.412949i	$0.864499\pi$
$32$	−129.758	−0.716817
$33$	−73.3265	−0.386803
$34$	73.5886	0.371187
$35$	−91.2641	−0.440756
$36$	−53.4161	−0.247297
$37$	95.3515	0.423667	0.211834	−	0.977306i	$-0.432056\pi$
$37$	95.3515	0.423667	0.211834	+	0.977306i	$0.432056\pi$
$38$	42.2145	0.180213
$39$	121.183	0.497559
$40$	122.906	0.485827
$41$	253.919	0.967206	0.483603	−	0.875288i	$-0.339328\pi$
$41$	253.919	0.967206	0.483603	+	0.875288i	$0.339328\pi$
$42$	270.338	0.993191
$43$	129.893	0.460664	0.230332	−	0.973112i	$-0.426019\pi$
$43$	129.893	0.460664	0.230332	+	0.973112i	$0.426019\pi$
$44$	33.6988	0.115461
$45$	87.1806	0.288803
$46$	−434.858	−1.39383
$47$	−415.646	−1.28996	−0.644981	−	0.764199i	$-0.723135\pi$
$47$	−415.646	−1.28996	−0.644981	+	0.764199i	$0.723135\pi$
$48$	−200.692	−0.603487
$49$	−9.83427	−0.0286714
$50$	−55.5454	−0.157106
$51$	−220.785	−0.606199
$52$	−55.6923	−0.148522
$53$	279.953	0.725557	0.362779	−	0.931875i	$-0.381828\pi$
$53$	279.953	0.725557	0.362779	+	0.931875i	$0.381828\pi$
$54$	141.648	0.356960
$55$	−55.0000	−0.134840
$56$	−448.675	−1.07066
$57$	−126.655	−0.294313
$58$	−134.923	−0.305453
$59$	−508.054	−1.12107	−0.560534	−	0.828131i	$-0.689404\pi$
$59$	−508.054	−1.12107	−0.560534	+	0.828131i	$0.689404\pi$
$60$	−102.108	−0.219701
$61$	15.4540	0.0324374	0.0162187	−	0.999868i	$-0.494837\pi$
$61$	15.4540	0.0324374	0.0162187	+	0.999868i	$0.494837\pi$
$62$	698.525	1.43085
$63$	−318.259	−0.636457
$64$	529.151	1.03350
$65$	90.8957	0.173450
$66$	162.918	0.303846
$67$	−1063.35	−1.93894	−0.969471	−	0.245205i	$-0.921145\pi$
$67$	−1063.35	−1.93894	−0.969471	+	0.245205i	$0.921145\pi$
$68$	101.467	0.180951
$69$	1304.69	2.27632
$70$	202.772	0.346227
$71$	−199.213	−0.332989	−0.166495	−	0.986042i	$-0.553245\pi$
$71$	−199.213	−0.332989	−0.166495	+	0.986042i	$0.553245\pi$
$72$	428.600	0.701541
$73$	−541.638	−0.868409	−0.434205	−	0.900814i	$-0.642971\pi$
$73$	−541.638	−0.868409	−0.434205	+	0.900814i	$0.642971\pi$
$74$	−211.854	−0.332804
$75$	166.651	0.256576
$76$	58.2070	0.0878527
$77$	200.781	0.297158
$78$	−269.246	−0.390848
$79$	−826.681	−1.17733	−0.588664	−	0.808378i	$-0.700346\pi$
$79$	−826.681	−1.17733	−0.588664	+	0.808378i	$0.700346\pi$
$80$	−150.533	−0.210376
$81$	−895.757	−1.22875
$82$	−564.161	−0.759770
$83$	1240.64	1.64070	0.820351	−	0.571861i	$-0.193778\pi$
$83$	1240.64	1.64070	0.820351	+	0.571861i	$0.193778\pi$
$84$	372.752	0.484174
$85$	−165.605	−0.211322
$86$	−288.600	−0.361866
$87$	404.806	0.498848
$88$	−270.393	−0.327545
$89$	−748.781	−0.891804	−0.445902	−	0.895082i	$-0.647117\pi$
$89$	−748.781	−0.891804	−0.445902	+	0.895082i	$0.647117\pi$
$90$	−193.699	−0.226864
$91$	−331.821	−0.382244
$92$	−599.599	−0.679484
$93$	−2095.76	−2.33678
$94$	923.489	1.01330
$95$	−95.0000	−0.102598
$96$	−864.971	−0.919591
$97$	231.841	0.242680	0.121340	−	0.992611i	$-0.461281\pi$
$97$	231.841	0.242680	0.121340	+	0.992611i	$0.461281\pi$
$98$	21.8500	0.0225222
$99$	−191.797	−0.194711
$100$	−76.5882	−0.0765882
$101$	−140.746	−0.138660	−0.0693302	−	0.997594i	$-0.522086\pi$
$101$	−140.746	−0.138660	−0.0693302	+	0.997594i	$0.522086\pi$
$102$	490.545	0.476188
$103$	−1755.72	−1.67958	−0.839789	−	0.542913i	$-0.817321\pi$
$103$	−1755.72	−1.67958	−0.839789	+	0.542913i	$0.817321\pi$
$104$	446.864	0.421333
$105$	−608.371	−0.565437
$106$	−622.005	−0.569948
$107$	724.244	0.654349	0.327175	−	0.944964i	$-0.393903\pi$
$107$	724.244	0.654349	0.327175	+	0.944964i	$0.393903\pi$
$108$	195.310	0.174016
$109$	−2003.86	−1.76087	−0.880435	−	0.474166i	$-0.842750\pi$
$109$	−2003.86	−1.76087	−0.880435	+	0.474166i	$0.842750\pi$
$110$	122.200	0.105921
$111$	635.617	0.543515
$112$	549.530	0.463623
$113$	1356.52	1.12930	0.564650	−	0.825331i	$-0.309011\pi$
$113$	1356.52	1.12930	0.564650	+	0.825331i	$0.309011\pi$
$114$	281.404	0.231192
$115$	978.609	0.793528
$116$	−186.037	−0.148906
$117$	316.974	0.250463
$118$	1128.80	0.880634
$119$	604.550	0.465706
$120$	819.295	0.623259
$121$	121.000	0.0909091
$122$	−34.3360	−0.0254806
$123$	1692.63	1.24081
$124$	963.153	0.697530
$125$	125.000	0.0894427
$126$	707.113	0.499957
$127$	289.769	0.202463	0.101232	−	0.994863i	$-0.467722\pi$
$127$	289.769	0.202463	0.101232	+	0.994863i	$0.467722\pi$
$128$	−137.614	−0.0950273
$129$	865.875	0.590977
$130$	−201.954	−0.136250
$131$	126.867	0.0846136	0.0423068	−	0.999105i	$-0.486529\pi$
$131$	126.867	0.0846136	0.0423068	+	0.999105i	$0.486529\pi$
$132$	224.638	0.148123
$133$	346.804	0.226103
$134$	2362.57	1.52310
$135$	−318.766	−0.203222
$136$	−814.150	−0.513329
$137$	−368.810	−0.229997	−0.114998	−	0.993366i	$-0.536686\pi$
$137$	−368.810	−0.229997	−0.114998	+	0.993366i	$0.536686\pi$
$138$	−2898.78	−1.78812
$139$	−14.2048	−0.00866787	−0.00433394	−	0.999991i	$-0.501380\pi$
$139$	−14.2048	−0.00866787	−0.00433394	+	0.999991i	$0.501380\pi$
$140$	279.590	0.168783
$141$	−2770.71	−1.65487
$142$	442.615	0.261574
$143$	−199.970	−0.116940
$144$	−524.942	−0.303786
$145$	303.633	0.173899
$146$	1203.42	0.682163
$147$	−65.5557	−0.0367819
$148$	−292.112	−0.162240
$149$	−314.738	−0.173049	−0.0865247	−	0.996250i	$-0.527576\pi$
$149$	−314.738	−0.173049	−0.0865247	+	0.996250i	$0.527576\pi$
$150$	−370.268	−0.201549
$151$	−240.141	−0.129420	−0.0647100	−	0.997904i	$-0.520612\pi$
$151$	−240.141	−0.129420	−0.0647100	+	0.997904i	$0.520612\pi$
$152$	−467.042	−0.249224
$153$	−577.500	−0.305151
$154$	−446.099	−0.233426
$155$	−1571.97	−0.814603
$156$	−371.247	−0.190536
$157$	1255.61	0.638269	0.319135	−	0.947709i	$-0.396608\pi$
$157$	1255.61	0.638269	0.319135	+	0.947709i	$0.396608\pi$
$158$	1836.73	0.924827
$159$	1866.18	0.930803
$160$	−648.789	−0.320570
$161$	−3572.48	−1.74876
$162$	1990.21	0.965219
$163$	−906.481	−0.435589	−0.217795	−	0.975995i	$-0.569886\pi$
$163$	−906.481	−0.435589	−0.217795	+	0.975995i	$0.569886\pi$
$164$	−777.887	−0.370383
$165$	−366.632	−0.172984
$166$	−2756.48	−1.28882
$167$	−1131.81	−0.524443	−0.262221	−	0.965008i	$-0.584455\pi$
$167$	−1131.81	−0.524443	−0.262221	+	0.965008i	$0.584455\pi$
$168$	−2990.89	−1.37352
$169$	−1866.52	−0.849576
$170$	367.943	0.166000
$171$	−331.286	−0.148153
$172$	−397.932	−0.176407
$173$	676.890	0.297474	0.148737	−	0.988877i	$-0.452479\pi$
$173$	676.890	0.297474	0.148737	+	0.988877i	$0.452479\pi$
$174$	−899.405	−0.391860
$175$	−456.321	−0.197112
$176$	331.172	0.141836
$177$	−3386.71	−1.43820
$178$	1663.65	0.700540
$179$	1493.87	0.623781	0.311891	−	0.950118i	$-0.399038\pi$
$179$	1493.87	0.623781	0.311891	+	0.950118i	$0.399038\pi$
$180$	−267.080	−0.110594
$181$	−1205.98	−0.495247	−0.247623	−	0.968856i	$-0.579650\pi$
$181$	−1205.98	−0.495247	−0.247623	+	0.968856i	$0.579650\pi$
$182$	737.245	0.300265
$183$	103.017	0.0416133
$184$	4811.07	1.92759
$185$	476.758	0.189470
$186$	4656.40	1.83561
$187$	364.330	0.142473
$188$	1273.34	0.493979
$189$	1163.68	0.447857
$190$	211.073	0.0805938
$191$	−2792.05	−1.05773	−0.528863	−	0.848707i	$-0.677381\pi$
$191$	−2792.05	−1.05773	−0.528863	+	0.848707i	$0.677381\pi$
$192$	3527.34	1.32585
$193$	−971.345	−0.362274	−0.181137	−	0.983458i	$-0.557978\pi$
$193$	−971.345	−0.362274	−0.181137	+	0.983458i	$0.557978\pi$
$194$	−515.109	−0.190632
$195$	605.914	0.222515
$196$	30.1276	0.0109794
$197$	2299.18	0.831520	0.415760	−	0.909474i	$-0.363516\pi$
$197$	2299.18	0.831520	0.415760	+	0.909474i	$0.363516\pi$
$198$	426.139	0.152951
$199$	−3024.19	−1.07728	−0.538642	−	0.842535i	$-0.681062\pi$
$199$	−3024.19	−1.07728	−0.538642	+	0.842535i	$0.681062\pi$
$200$	614.528	0.217269
$201$	−7088.35	−2.48743
$202$	312.711	0.108922
$203$	−1108.43	−0.383235
$204$	676.382	0.232138
$205$	1269.59	0.432547
$206$	3900.90	1.31936
$207$	3412.63	1.14587
$208$	−547.312	−0.182448
$209$	209.000	0.0691714
$210$	1351.69	0.444168
$211$	1493.91	0.487416	0.243708	−	0.969849i	$-0.421636\pi$
$211$	1493.91	0.487416	0.243708	+	0.969849i	$0.421636\pi$
$212$	−857.644	−0.277846
$213$	−1327.96	−0.427186
$214$	−1609.14	−0.514012
$215$	649.467	0.206015
$216$	−1567.13	−0.493655
$217$	5738.57	1.79521
$218$	4452.21	1.38322
$219$	−3610.58	−1.11407
$220$	168.494	0.0516357
$221$	−602.109	−0.183268
$222$	−1412.23	−0.426948
$223$	−1582.36	−0.475170	−0.237585	−	0.971367i	$-0.576356\pi$
$223$	−1582.36	−0.475170	−0.237585	+	0.971367i	$0.576356\pi$
$224$	2368.45	0.706466
$225$	435.903	0.129157
$226$	−3013.94	−0.887100
$227$	−6779.73	−1.98232	−0.991159	−	0.132679i	$-0.957642\pi$
$227$	−6779.73	−1.98232	−0.991159	+	0.132679i	$0.957642\pi$
$228$	388.010	0.112704
$229$	−2313.78	−0.667680	−0.333840	−	0.942630i	$-0.608344\pi$
$229$	−2313.78	−0.667680	−0.333840	+	0.942630i	$0.608344\pi$
$230$	−2174.29	−0.623341
$231$	1338.42	0.381218
$232$	1492.73	0.422424
$233$	644.852	0.181312	0.0906559	−	0.995882i	$-0.471104\pi$
$233$	644.852	0.181312	0.0906559	+	0.995882i	$0.471104\pi$
$234$	−704.258	−0.196747
$235$	−2078.23	−0.576888
$236$	1556.44	0.429303
$237$	−5510.69	−1.51037
$238$	−1343.20	−0.365827
$239$	−6239.33	−1.68866	−0.844328	−	0.535826i	$-0.820000\pi$
$239$	−6239.33	−1.68866	−0.844328	+	0.535826i	$0.820000\pi$
$240$	−1003.46	−0.269887
$241$	−5462.03	−1.45992	−0.729959	−	0.683491i	$-0.760461\pi$
$241$	−5462.03	−1.45992	−0.729959	+	0.683491i	$0.760461\pi$
$242$	−268.840	−0.0714119
$243$	−4249.82	−1.12192
$244$	−47.3437	−0.0124216
$245$	−49.1714	−0.0128222
$246$	−3760.72	−0.974694
$247$	−345.403	−0.0889777
$248$	−7728.15	−1.97878
$249$	8270.18	2.10482
$250$	−277.727	−0.0702600
$251$	1024.59	0.257655	0.128827	−	0.991667i	$-0.458879\pi$
$251$	1024.59	0.257655	0.128827	+	0.991667i	$0.458879\pi$
$252$	974.994	0.243726
$253$	−2152.94	−0.534997
$254$	−643.814	−0.159041
$255$	−1103.93	−0.271100
$256$	−3927.45	−0.958851
$257$	7891.55	1.91541	0.957707	−	0.287746i	$-0.0929058\pi$
$257$	7891.55	1.91541	0.957707	+	0.287746i	$0.0929058\pi$
$258$	−1923.82	−0.464231
$259$	−1740.44	−0.417550
$260$	−278.461	−0.0664209
$261$	1058.84	0.251112
$262$	−281.874	−0.0664666
$263$	−6314.58	−1.48051	−0.740254	−	0.672327i	$-0.765295\pi$
$263$	−6314.58	−1.48051	−0.740254	+	0.672327i	$0.765295\pi$
$264$	−1802.45	−0.420201
$265$	1399.77	0.324479
$266$	−770.535	−0.177611
$267$	−4991.40	−1.14408
$268$	3257.61	0.742500
$269$	−1170.37	−0.265273	−0.132637	−	0.991165i	$-0.542344\pi$
$269$	−1170.37	−0.265273	−0.132637	+	0.991165i	$0.542344\pi$
$270$	708.240	0.159637
$271$	−1066.94	−0.239159	−0.119580	−	0.992825i	$-0.538155\pi$
$271$	−1066.94	−0.239159	−0.119580	+	0.992825i	$0.538155\pi$
$272$	997.158	0.222285
$273$	−2211.93	−0.490374
$274$	819.428	0.180670
$275$	−275.000	−0.0603023
$276$	−3996.95	−0.871697
$277$	127.141	0.0275783	0.0137891	−	0.999905i	$-0.495611\pi$
$277$	127.141	0.0275783	0.0137891	+	0.999905i	$0.495611\pi$
$278$	31.5604	0.00680888
$279$	−5481.81	−1.17630
$280$	−2243.38	−0.478812
$281$	7621.04	1.61791	0.808956	−	0.587870i	$-0.200033\pi$
$281$	7621.04	1.61791	0.808956	+	0.587870i	$0.200033\pi$
$282$	6156.02	1.29995
$283$	−2476.96	−0.520284	−0.260142	−	0.965570i	$-0.583769\pi$
$283$	−2476.96	−0.520284	−0.260142	+	0.965570i	$0.583769\pi$
$284$	610.295	0.127515
$285$	−633.274	−0.131621
$286$	444.298	0.0918597
$287$	−4634.73	−0.953239
$288$	−2262.47	−0.462908
$289$	−3816.01	−0.776716
$290$	−674.616	−0.136603
$291$	1545.46	0.311329
$292$	1659.32	0.332549
$293$	−1659.01	−0.330785	−0.165393	−	0.986228i	$-0.552889\pi$
$293$	−1659.01	−0.330785	−0.165393	+	0.986228i	$0.552889\pi$
$294$	145.653	0.0288933
$295$	−2540.27	−0.501357
$296$	2343.85	0.460248
$297$	701.285	0.137012
$298$	699.291	0.135936
$299$	3558.05	0.688186
$300$	−510.540	−0.0982535
$301$	−2370.92	−0.454012
$302$	533.550	0.101663
$303$	−938.216	−0.177885
$304$	572.025	0.107921
$305$	77.2700	0.0145064
$306$	1283.10	0.239706
$307$	−5099.02	−0.947937	−0.473968	−	0.880542i	$-0.657179\pi$
$307$	−5099.02	−0.947937	−0.473968	+	0.880542i	$0.657179\pi$
$308$	−615.098	−0.113794
$309$	−11703.7	−2.15470
$310$	3492.63	0.639896
$311$	7162.04	1.30586	0.652929	−	0.757419i	$-0.273540\pi$
$311$	7162.04	1.30586	0.652929	+	0.757419i	$0.273540\pi$
$312$	2978.81	0.540519
$313$	−5148.02	−0.929659	−0.464829	−	0.885400i	$-0.653884\pi$
$313$	−5148.02	−0.929659	−0.464829	+	0.885400i	$0.653884\pi$
$314$	−2789.73	−0.501380
$315$	−1591.29	−0.284632
$316$	2532.56	0.450847
$317$	−5036.02	−0.892275	−0.446137	−	0.894965i	$-0.647201\pi$
$317$	−5036.02	−0.892275	−0.446137	+	0.894965i	$0.647201\pi$
$318$	−4146.31	−0.731175
$319$	−667.992	−0.117243
$320$	2645.75	0.462194
$321$	4827.84	0.839452
$322$	7937.39	1.37371
$323$	629.297	0.108406
$324$	2744.18	0.470538
$325$	454.478	0.0775690
$326$	2014.04	0.342169
$327$	−13357.8	−2.25899
$328$	6241.61	1.05072
$329$	7586.71	1.27133
$330$	814.590	0.135884
$331$	6520.36	1.08275	0.541377	−	0.840780i	$-0.317903\pi$
$331$	6520.36	1.08275	0.541377	+	0.840780i	$0.317903\pi$
$332$	−3800.74	−0.628292
$333$	1662.56	0.273597
$334$	2514.67	0.411966
$335$	−5316.76	−0.867121
$336$	3663.19	0.594772
$337$	14.8569	0.00240150	0.00120075	−	0.999999i	$-0.499618\pi$
$337$	14.8569	0.00240150	0.00120075	+	0.999999i	$0.499618\pi$
$338$	4147.06	0.667369
$339$	9042.63	1.44876
$340$	507.334	0.0809237
$341$	3458.33	0.549205
$342$	736.058	0.116379
$343$	6440.22	1.01382
$344$	3192.93	0.500440
$345$	6523.45	1.01800
$346$	−1503.93	−0.233675
$347$	11282.7	1.74549	0.872747	−	0.488173i	$-0.162336\pi$
$347$	11282.7	1.74549	0.872747	+	0.488173i	$0.162336\pi$
$348$	−1240.13	−0.191029
$349$	6827.95	1.04725	0.523627	−	0.851947i	$-0.324578\pi$
$349$	6827.95	1.04725	0.523627	+	0.851947i	$0.324578\pi$
$350$	1013.86	0.154838
$351$	−1158.98	−0.176244
$352$	1427.34	0.216129
$353$	−10326.3	−1.55698	−0.778491	−	0.627656i	$-0.784015\pi$
$353$	−10326.3	−1.55698	−0.778491	+	0.627656i	$0.784015\pi$
$354$	7524.65	1.12975
$355$	−996.066	−0.148917
$356$	2293.91	0.341508
$357$	4029.96	0.597445
$358$	−3319.10	−0.489999
$359$	61.0431	0.00897418	0.00448709	−	0.999990i	$-0.498572\pi$
$359$	61.0431	0.00897418	0.00448709	+	0.999990i	$0.498572\pi$
$360$	2143.00	0.313739
$361$	361.000	0.0526316
$362$	2679.46	0.389032
$363$	806.591	0.116626
$364$	1016.54	0.146377
$365$	−2708.19	−0.388365
$366$	−228.885	−0.0326886
$367$	2768.40	0.393758	0.196879	−	0.980428i	$-0.436919\pi$
$367$	2768.40	0.393758	0.196879	+	0.980428i	$0.436919\pi$
$368$	−5892.52	−0.834697
$369$	4427.36	0.624604
$370$	−1059.27	−0.148834
$371$	−5109.94	−0.715080
$372$	6420.42	0.894848
$373$	6075.06	0.843310	0.421655	−	0.906756i	$-0.361449\pi$
$373$	6075.06	0.843310	0.421655	+	0.906756i	$0.361449\pi$
$374$	−809.475	−0.111917
$375$	833.255	0.114744
$376$	−10217.1	−1.40134
$377$	1103.96	0.150813
$378$	−2585.48	−0.351806
$379$	477.122	0.0646651	0.0323326	−	0.999477i	$-0.489706\pi$
$379$	477.122	0.0646651	0.0323326	+	0.999477i	$0.489706\pi$
$380$	291.035	0.0392889
$381$	1931.61	0.259736
$382$	6203.43	0.830877
$383$	−422.858	−0.0564152	−0.0282076	−	0.999602i	$-0.508980\pi$
$383$	−422.858	−0.0564152	−0.0282076	+	0.999602i	$0.508980\pi$
$384$	−917.342	−0.121909
$385$	1003.91	0.132893
$386$	2158.15	0.284578
$387$	2264.84	0.297489
$388$	−710.252	−0.0929320
$389$	7109.21	0.926610	0.463305	−	0.886199i	$-0.346663\pi$
$389$	7109.21	0.926610	0.463305	+	0.886199i	$0.346663\pi$
$390$	−1346.23	−0.174792
$391$	−6482.49	−0.838449
$392$	−241.738	−0.0311469
$393$	845.698	0.108549
$394$	−5108.35	−0.653185
$395$	−4133.40	−0.526517
$396$	587.577	0.0745627
$397$	−6219.70	−0.786292	−0.393146	−	0.919476i	$-0.628613\pi$
$397$	−6219.70	−0.786292	−0.393146	+	0.919476i	$0.628613\pi$
$398$	6719.20	0.846239
$399$	2311.81	0.290063
$400$	−752.665	−0.0940831
$401$	−12573.8	−1.56585	−0.782927	−	0.622113i	$-0.786274\pi$
$401$	−12573.8	−1.56585	−0.782927	+	0.622113i	$0.786274\pi$
$402$	15749.0	1.95395
$403$	−5715.40	−0.706463
$404$	431.178	0.0530987
$405$	−4478.78	−0.549513
$406$	2462.73	0.301043
$407$	−1048.87	−0.127741
$408$	−5427.16	−0.658540
$409$	9786.85	1.18320	0.591600	−	0.806232i	$-0.298497\pi$
$409$	9786.85	1.18320	0.591600	+	0.806232i	$0.298497\pi$
$410$	−2820.80	−0.339779
$411$	−2458.50	−0.295058
$412$	5378.71	0.643179
$413$	9273.43	1.10488
$414$	−7582.24	−0.900113
$415$	6203.21	0.733744
$416$	−2358.88	−0.278014
$417$	−94.6897	−0.0111198
$418$	−464.360	−0.0543363
$419$	−983.445	−0.114665	−0.0573323	−	0.998355i	$-0.518259\pi$
$419$	−983.445	−0.114665	−0.0573323	+	0.998355i	$0.518259\pi$
$420$	1863.76	0.216529
$421$	6765.60	0.783219	0.391609	−	0.920132i	$-0.371918\pi$
$421$	6765.60	0.783219	0.391609	+	0.920132i	$0.371918\pi$
$422$	−3319.19	−0.382880
$423$	−7247.26	−0.833035
$424$	6881.57	0.788204
$425$	−828.023	−0.0945059
$426$	2950.49	0.335568
$427$	−282.079	−0.0319690
$428$	−2218.74	−0.250577
$429$	−1333.01	−0.150020
$430$	−1443.00	−0.161831
$431$	14082.1	1.57380	0.786902	−	0.617078i	$-0.211684\pi$
$431$	14082.1	1.57380	0.786902	+	0.617078i	$0.211684\pi$
$432$	1919.39	0.213766
$433$	−1107.78	−0.122948	−0.0614739	−	0.998109i	$-0.519580\pi$
$433$	−1107.78	−0.122948	−0.0614739	+	0.998109i	$0.519580\pi$
$434$	−12750.1	−1.41019
$435$	2024.03	0.223091
$436$	6138.88	0.674310
$437$	−3718.71	−0.407072
$438$	8022.05	0.875133
$439$	16027.5	1.74248	0.871242	−	0.490854i	$-0.163315\pi$
$439$	16027.5	1.74248	0.871242	+	0.490854i	$0.163315\pi$
$440$	−1351.96	−0.146482
$441$	−171.472	−0.0185155
$442$	1337.78	0.143963
$443$	−15195.0	−1.62965	−0.814825	−	0.579707i	$-0.803167\pi$
$443$	−15195.0	−1.62965	−0.814825	+	0.579707i	$0.803167\pi$
$444$	−1947.23	−0.208134
$445$	−3743.90	−0.398827
$446$	3515.72	0.373260
$447$	−2098.06	−0.222002
$448$	−9658.50	−1.01857
$449$	9760.81	1.02593	0.512963	−	0.858411i	$-0.328548\pi$
$449$	9760.81	1.02593	0.512963	+	0.858411i	$0.328548\pi$
$450$	−968.497	−0.101456
$451$	−2793.10	−0.291623
$452$	−4155.74	−0.432455
$453$	−1600.79	−0.166030
$454$	15063.3	1.55717
$455$	−1659.10	−0.170945
$456$	−3113.32	−0.319725
$457$	347.056	0.0355242	0.0177621	−	0.999842i	$-0.494346\pi$
$457$	347.056	0.0355242	0.0177621	+	0.999842i	$0.494346\pi$
$458$	5140.79	0.524483
$459$	2111.56	0.214726
$460$	−2998.00	−0.303875
$461$	9947.42	1.00498	0.502492	−	0.864582i	$-0.332417\pi$
$461$	9947.42	1.00498	0.502492	+	0.864582i	$0.332417\pi$
$462$	−2973.71	−0.299458
$463$	5827.37	0.584927	0.292463	−	0.956277i	$-0.405525\pi$
$463$	5827.37	0.584927	0.292463	+	0.956277i	$0.405525\pi$
$464$	−1828.27	−0.182921
$465$	−10478.8	−1.04504
$466$	−1432.74	−0.142426
$467$	3598.16	0.356537	0.178269	−	0.983982i	$-0.442950\pi$
$467$	3598.16	0.356537	0.178269	+	0.983982i	$0.442950\pi$
$468$	−971.057	−0.0959127
$469$	19409.2	1.91094
$470$	4617.45	0.453164
$471$	8369.92	0.818823
$472$	−12488.6	−1.21786
$473$	−1428.83	−0.138896
$474$	12243.7	1.18644
$475$	−475.000	−0.0458831
$476$	−1852.06	−0.178338
$477$	4881.30	0.468552
$478$	13862.7	1.32649
$479$	5858.21	0.558807	0.279404	−	0.960174i	$-0.409863\pi$
$479$	5858.21	0.558807	0.279404	+	0.960174i	$0.409863\pi$
$480$	−4324.85	−0.411254
$481$	1733.41	0.164317
$482$	12135.6	1.14681
$483$	−23814.3	−2.24345
$484$	−370.687	−0.0348128
$485$	1159.21	0.108530
$486$	9442.32	0.881301
$487$	851.396	0.0792206	0.0396103	−	0.999215i	$-0.487388\pi$
$487$	851.396	0.0792206	0.0396103	+	0.999215i	$0.487388\pi$
$488$	379.877	0.0352382
$489$	−6042.64	−0.558809
$490$	109.250	0.0100723
$491$	−8740.75	−0.803390	−0.401695	−	0.915774i	$-0.631579\pi$
$491$	−8740.75	−0.803390	−0.401695	+	0.915774i	$0.631579\pi$
$492$	−5185.43	−0.475157
$493$	−2011.32	−0.183743
$494$	767.423	0.0698948
$495$	−958.987	−0.0870773
$496$	9465.32	0.856865
$497$	3636.20	0.328181
$498$	−18374.8	−1.65340
$499$	−2291.80	−0.205601	−0.102800	−	0.994702i	$-0.532780\pi$
$499$	−2291.80	−0.205601	−0.102800	+	0.994702i	$0.532780\pi$
$500$	−382.941	−0.0342513
$501$	−7544.68	−0.672798
$502$	−2276.45	−0.202396
$503$	12381.6	1.09755	0.548775	−	0.835970i	$-0.315095\pi$
$503$	12381.6	1.09755	0.548775	+	0.835970i	$0.315095\pi$
$504$	−7823.16	−0.691411
$505$	−703.728	−0.0620108
$506$	4783.44	0.420257
$507$	−12442.3	−1.08990
$508$	−887.715	−0.0775315
$509$	−15958.7	−1.38970	−0.694851	−	0.719154i	$-0.744530\pi$
$509$	−15958.7	−1.38970	−0.694851	+	0.719154i	$0.744530\pi$
$510$	2452.72	0.212958
$511$	9886.42	0.855870
$512$	9827.00	0.848234
$513$	1211.31	0.104251
$514$	−17533.6	−1.50462
$515$	−8778.62	−0.751130
$516$	−2652.63	−0.226309
$517$	4572.11	0.388938
$518$	3866.93	0.327998
$519$	4512.18	0.381624
$520$	2234.32	0.188426
$521$	14887.5	1.25189	0.625944	−	0.779868i	$-0.284714\pi$
$521$	14887.5	1.25189	0.625944	+	0.779868i	$0.284714\pi$
$522$	−2352.54	−0.197256
$523$	8610.57	0.719912	0.359956	−	0.932969i	$-0.382792\pi$
$523$	8610.57	0.719912	0.359956	+	0.932969i	$0.382792\pi$
$524$	−388.659	−0.0324020
$525$	−3041.85	−0.252871
$526$	14029.8	1.16299
$527$	10413.0	0.860716
$528$	2207.61	0.181958
$529$	26140.0	2.14844
$530$	−3110.02	−0.254888
$531$	−8858.50	−0.723966
$532$	−1062.44	−0.0865841
$533$	4616.02	0.375126
$534$	11090.0	0.898709
$535$	3621.22	0.292634
$536$	−26138.4	−2.10636
$537$	9958.18	0.800237
$538$	2600.34	0.208380
$539$	108.177	0.00864474
$540$	976.548	0.0778221
$541$	14053.2	1.11681	0.558404	−	0.829569i	$-0.311414\pi$
$541$	14053.2	1.11681	0.558404	+	0.829569i	$0.311414\pi$
$542$	2370.55	0.187867
$543$	−8039.11	−0.635343
$544$	4297.70	0.338717
$545$	−10019.3	−0.787485
$546$	4914.50	0.385204
$547$	14025.4	1.09632	0.548158	−	0.836375i	$-0.315329\pi$
$547$	14025.4	1.09632	0.548158	+	0.836375i	$0.315329\pi$
$548$	1129.86	0.0880752
$549$	269.458	0.0209475
$550$	611.000	0.0473693
$551$	−1153.80	−0.0892082
$552$	32070.8	2.47287
$553$	15089.3	1.16033
$554$	−282.485	−0.0216636
$555$	3178.09	0.243067
$556$	43.5167	0.00331928
$557$	25643.2	1.95070	0.975349	−	0.220668i	$-0.0708237\pi$
$557$	25643.2	1.95070	0.975349	+	0.220668i	$0.0708237\pi$
$558$	12179.6	0.924019
$559$	2361.35	0.178666
$560$	2747.65	0.207338
$561$	2428.64	0.182776
$562$	−16932.6	−1.27092
$563$	−15650.1	−1.17153	−0.585767	−	0.810479i	$-0.699207\pi$
$563$	−15650.1	−1.17153	−0.585767	+	0.810479i	$0.699207\pi$
$564$	8488.16	0.633716
$565$	6782.61	0.505038
$566$	5503.36	0.408699
$567$	16350.1	1.21100
$568$	−4896.89	−0.361741
$569$	8801.96	0.648502	0.324251	−	0.945971i	$-0.394888\pi$
$569$	8801.96	0.648502	0.324251	+	0.945971i	$0.394888\pi$
$570$	1407.02	0.103392
$571$	3920.57	0.287339	0.143669	−	0.989626i	$-0.454110\pi$
$571$	3920.57	0.287339	0.143669	+	0.989626i	$0.454110\pi$
$572$	612.615	0.0447810
$573$	−18611.9	−1.35694
$574$	10297.5	0.748799
$575$	4893.05	0.354877
$576$	9226.34	0.667415
$577$	−5848.88	−0.421997	−0.210998	−	0.977486i	$-0.567671\pi$
$577$	−5848.88	−0.421997	−0.210998	+	0.977486i	$0.567671\pi$
$578$	8478.47	0.610134
$579$	−6475.02	−0.464754
$580$	−930.187	−0.0665930
$581$	−22645.2	−1.61701
$582$	−3433.74	−0.244559
$583$	−3079.49	−0.218764
$584$	−13314.1	−0.943391
$585$	1584.87	0.112011
$586$	3686.01	0.259842
$587$	9808.35	0.689666	0.344833	−	0.938664i	$-0.387936\pi$
$587$	9808.35	0.689666	0.344833	+	0.938664i	$0.387936\pi$
$588$	200.832	0.0140853
$589$	5973.48	0.417883
$590$	5644.02	0.393831
$591$	15326.4	1.06674
$592$	−2870.71	−0.199300
$593$	−22382.9	−1.55001	−0.775003	−	0.631957i	$-0.782252\pi$
$593$	−22382.9	−1.55001	−0.775003	+	0.631957i	$0.782252\pi$
$594$	−1558.13	−0.107628
$595$	3022.75	0.208270
$596$	964.209	0.0662677
$597$	−20159.4	−1.38203
$598$	−7905.34	−0.540591
$599$	−22433.9	−1.53026	−0.765128	−	0.643878i	$-0.777324\pi$
$599$	−22433.9	−1.53026	−0.765128	+	0.643878i	$0.777324\pi$
$600$	4096.47	0.278730
$601$	20878.4	1.41705	0.708526	−	0.705685i	$-0.249361\pi$
$601$	20878.4	1.41705	0.708526	+	0.705685i	$0.249361\pi$
$602$	5267.76	0.356641
$603$	−18540.7	−1.25214
$604$	735.679	0.0495602
$605$	605.000	0.0406558
$606$	2084.54	0.139734
$607$	3740.81	0.250140	0.125070	−	0.992148i	$-0.460085\pi$
$607$	3740.81	0.250140	0.125070	+	0.992148i	$0.460085\pi$
$608$	2465.40	0.164449
$609$	−7388.85	−0.491644
$610$	−171.680	−0.0113953
$611$	−7556.08	−0.500305
$612$	1769.19	0.116855
$613$	29248.3	1.92712	0.963562	−	0.267486i	$-0.0861931\pi$
$613$	29248.3	1.92712	0.963562	+	0.267486i	$0.0861931\pi$
$614$	11329.1	0.744634
$615$	8463.16	0.554907
$616$	4935.43	0.322815
$617$	−16276.7	−1.06203	−0.531016	−	0.847362i	$-0.678190\pi$
$617$	−16276.7	−1.06203	−0.531016	+	0.847362i	$0.678190\pi$
$618$	26003.5	1.69258
$619$	8832.74	0.573534	0.286767	−	0.958000i	$-0.407419\pi$
$619$	8832.74	0.573534	0.286767	+	0.958000i	$0.407419\pi$
$620$	4815.77	0.311945
$621$	−12477.9	−0.806313
$622$	−15912.7	−1.02579
$623$	13667.4	0.878927
$624$	−3648.40	−0.234059
$625$	625.000	0.0400000
$626$	11438.0	0.730276
$627$	1393.20	0.0887387
$628$	−3846.58	−0.244419
$629$	−3158.13	−0.200195
$630$	3535.56	0.223588
$631$	22905.6	1.44510	0.722551	−	0.691318i	$-0.242969\pi$
$631$	22905.6	1.44510	0.722551	+	0.691318i	$0.242969\pi$
$632$	−20320.8	−1.27898
$633$	9958.45	0.625297
$634$	11189.1	0.700910
$635$	1448.84	0.0905443
$636$	−5717.09	−0.356443
$637$	−178.779	−0.0111200
$638$	1484.16	0.0920977
$639$	−3473.51	−0.215039
$640$	−688.071	−0.0424975
$641$	1367.86	0.0842859	0.0421429	−	0.999112i	$-0.486582\pi$
$641$	1367.86	0.0842859	0.0421429	+	0.999112i	$0.486582\pi$
$642$	−10726.6	−0.659415
$643$	10853.8	0.665677	0.332838	−	0.942984i	$-0.391994\pi$
$643$	10853.8	0.665677	0.332838	+	0.942984i	$0.391994\pi$
$644$	10944.4	0.669672
$645$	4329.38	0.264293
$646$	−1398.18	−0.0851560
$647$	−26086.3	−1.58510	−0.792550	−	0.609806i	$-0.791247\pi$
$647$	−26086.3	−1.58510	−0.792550	+	0.609806i	$0.791247\pi$
$648$	−22018.7	−1.33484
$649$	5588.60	0.338015
$650$	−1009.77	−0.0609328
$651$	38253.6	2.30303
$652$	2777.03	0.166805
$653$	−19168.9	−1.14875	−0.574376	−	0.818591i	$-0.694755\pi$
$653$	−19168.9	−1.14875	−0.574376	+	0.818591i	$0.694755\pi$
$654$	29678.6	1.77450
$655$	634.333	0.0378404
$656$	−7644.62	−0.454988
$657$	−9444.06	−0.560804
$658$	−16856.3	−0.998673
$659$	−7157.29	−0.423078	−0.211539	−	0.977370i	$-0.567848\pi$
$659$	−7157.29	−0.423078	−0.211539	+	0.977370i	$0.567848\pi$
$660$	1123.19	0.0662425
$661$	2926.68	0.172216	0.0861079	−	0.996286i	$-0.472557\pi$
$661$	2926.68	0.172216	0.0861079	+	0.996286i	$0.472557\pi$
$662$	−14487.1	−0.850537
$663$	−4013.69	−0.235111
$664$	30496.4	1.78236
$665$	1734.02	0.101116
$666$	−3693.91	−0.214919
$667$	11885.5	0.689968
$668$	3467.33	0.200831
$669$	−10548.1	−0.609586
$670$	11812.9	0.681151
$671$	−169.994	−0.00978025
$672$	15788.2	0.906312
$673$	−28206.4	−1.61557	−0.807783	−	0.589480i	$-0.799333\pi$
$673$	−28206.4	−1.61557	−0.807783	+	0.589480i	$0.799333\pi$
$674$	−33.0092	−0.00188645
$675$	−1593.83	−0.0908837
$676$	5718.13	0.325338
$677$	557.192	0.0316317	0.0158158	−	0.999875i	$-0.494965\pi$
$677$	557.192	0.0316317	0.0158158	+	0.999875i	$0.494965\pi$
$678$	−20091.1	−1.13804
$679$	−4231.76	−0.239175
$680$	−4070.75	−0.229568
$681$	−45193.9	−2.54308
$682$	−7683.78	−0.431418
$683$	9535.92	0.534234	0.267117	−	0.963664i	$-0.413929\pi$
$683$	9535.92	0.534234	0.267117	+	0.963664i	$0.413929\pi$
$684$	1014.90	0.0567337
$685$	−1844.05	−0.102858
$686$	−14309.0	−0.796385
$687$	−15423.7	−0.856553
$688$	−3910.65	−0.216704
$689$	5089.31	0.281404
$690$	−14493.9	−0.799672
$691$	−5273.21	−0.290307	−0.145154	−	0.989409i	$-0.546368\pi$
$691$	−5273.21	−0.290307	−0.145154	+	0.989409i	$0.546368\pi$
$692$	−2073.67	−0.113915
$693$	3500.85	0.191899
$694$	−25068.1	−1.37114
$695$	−71.0239	−0.00387639
$696$	9950.59	0.541920
$697$	−8410.02	−0.457033
$698$	−15170.5	−0.822651
$699$	4298.61	0.232601
$700$	1397.95	0.0754823
$701$	−5414.59	−0.291735	−0.145867	−	0.989304i	$-0.546597\pi$
$701$	−5414.59	−0.291735	−0.145867	+	0.989304i	$0.546597\pi$
$702$	2575.04	0.138445
$703$	−1811.68	−0.0971960
$704$	−5820.66	−0.311611
$705$	−13853.6	−0.740079
$706$	22943.2	1.22306
$707$	2569.00	0.136658
$708$	10375.3	0.550744
$709$	−20941.8	−1.10929	−0.554645	−	0.832087i	$-0.687146\pi$
$709$	−20941.8	−1.10929	−0.554645	+	0.832087i	$0.687146\pi$
$710$	2213.08	0.116979
$711$	−14414.1	−0.760297
$712$	−18405.9	−0.968806
$713$	−61533.7	−3.23205
$714$	−8953.83	−0.469312
$715$	−999.852	−0.0522970
$716$	−4576.50	−0.238871
$717$	−41591.7	−2.16634
$718$	−135.627	−0.00704950
$719$	22139.2	1.14833	0.574167	−	0.818738i	$-0.305326\pi$
$719$	22139.2	1.14833	0.574167	+	0.818738i	$0.305326\pi$
$720$	−2624.71	−0.135857
$721$	32046.9	1.65533
$722$	−802.076	−0.0413437
$723$	−36410.1	−1.87290
$724$	3694.55	0.189650
$725$	1518.16	0.0777699
$726$	−1792.10	−0.0916130
$727$	−27076.4	−1.38130	−0.690652	−	0.723187i	$-0.742676\pi$
$727$	−27076.4	−1.38130	−0.690652	+	0.723187i	$0.742676\pi$
$728$	−8156.53	−0.415249
$729$	−4144.03	−0.210539
$730$	6017.10	0.305072
$731$	−4302.19	−0.217678
$732$	−315.595	−0.0159354
$733$	−4722.46	−0.237965	−0.118982	−	0.992896i	$-0.537963\pi$
$733$	−4722.46	−0.237965	−0.118982	+	0.992896i	$0.537963\pi$
$734$	−6150.88	−0.309310
$735$	−327.778	−0.0164494
$736$	−25396.4	−1.27191
$737$	11696.9	0.584613
$738$	−9836.78	−0.490646
$739$	24853.2	1.23713	0.618566	−	0.785733i	$-0.287714\pi$
$739$	24853.2	1.23713	0.618566	+	0.785733i	$0.287714\pi$
$740$	−1460.56	−0.0725558
$741$	−2302.47	−0.114148
$742$	11353.3	0.561718
$743$	12230.5	0.603893	0.301946	−	0.953325i	$-0.402364\pi$
$743$	12230.5	0.603893	0.301946	+	0.953325i	$0.402364\pi$
$744$	−51516.2	−2.53854
$745$	−1573.69	−0.0773900
$746$	−13497.7	−0.662446
$747$	21632.0	1.05954
$748$	−1116.13	−0.0545587
$749$	−13219.5	−0.644900
$750$	−1851.34	−0.0901352
$751$	−9967.80	−0.484328	−0.242164	−	0.970235i	$-0.577857\pi$
$751$	−9967.80	−0.484328	−0.242164	+	0.970235i	$0.577857\pi$
$752$	12513.7	0.606818
$753$	6829.94	0.330540
$754$	−2452.79	−0.118469
$755$	−1200.71	−0.0578783
$756$	−3564.95	−0.171503
$757$	4480.75	0.215133	0.107566	−	0.994198i	$-0.465694\pi$
$757$	4480.75	0.215133	0.107566	+	0.994198i	$0.465694\pi$
$758$	−1060.08	−0.0507965
$759$	−14351.6	−0.686337
$760$	−2335.21	−0.111456
$761$	10231.3	0.487365	0.243683	−	0.969855i	$-0.421644\pi$
$761$	10231.3	0.487365	0.243683	+	0.969855i	$0.421644\pi$
$762$	−4291.69	−0.204031
$763$	36576.1	1.73544
$764$	8553.52	0.405047
$765$	−2887.50	−0.136468
$766$	939.513	0.0443159
$767$	−9235.98	−0.434801
$768$	−26180.6	−1.23009
$769$	−40573.7	−1.90263	−0.951316	−	0.308216i	$-0.900268\pi$
$769$	−40573.7	−1.90263	−0.951316	+	0.308216i	$0.900268\pi$
$770$	−2230.49	−0.104391
$771$	52605.4	2.45725
$772$	2975.74	0.138730
$773$	1364.20	0.0634759	0.0317379	−	0.999496i	$-0.489896\pi$
$773$	1364.20	0.0634759	0.0317379	+	0.999496i	$0.489896\pi$
$774$	−5032.06	−0.233687
$775$	−7859.84	−0.364302
$776$	5698.93	0.263633
$777$	−11601.8	−0.535666
$778$	−15795.4	−0.727881
$779$	−4824.45	−0.221892
$780$	−1856.24	−0.0852101
$781$	2191.34	0.100400
$782$	14402.9	0.658627
$783$	−3871.51	−0.176701
$784$	296.076	0.0134874
$785$	6278.03	0.285443
$786$	−1878.99	−0.0852688
$787$	−33408.0	−1.51317	−0.756586	−	0.653894i	$-0.773134\pi$
$787$	−33408.0	−1.51317	−0.756586	+	0.653894i	$0.773134\pi$
$788$	−7043.59	−0.318423
$789$	−42093.3	−1.89932
$790$	9183.67	0.413595
$791$	−24760.4	−1.11299
$792$	−4714.60	−0.211523
$793$	280.940	0.0125807
$794$	13819.0	0.617657
$795$	9330.90	0.416268
$796$	9264.70	0.412536
$797$	8161.66	0.362736	0.181368	−	0.983415i	$-0.441947\pi$
$797$	8161.66	0.362736	0.181368	+	0.983415i	$0.441947\pi$
$798$	−5136.42	−0.227854
$799$	13766.6	0.609545
$800$	−3243.94	−0.143363
$801$	−13055.8	−0.575912
$802$	27936.8	1.23003
$803$	5958.01	0.261835
$804$	21715.4	0.952539
$805$	−17862.4	−0.782070
$806$	12698.6	0.554948
$807$	−7801.71	−0.340314
$808$	−3459.68	−0.150633
$809$	−6195.79	−0.269261	−0.134631	−	0.990896i	$-0.542985\pi$
$809$	−6195.79	−0.269261	−0.134631	+	0.990896i	$0.542985\pi$
$810$	9951.04	0.431659
$811$	2905.90	0.125820	0.0629100	−	0.998019i	$-0.479962\pi$
$811$	2905.90	0.125820	0.0629100	+	0.998019i	$0.479962\pi$
$812$	3395.71	0.146756
$813$	−7112.28	−0.306812
$814$	2330.39	0.100344
$815$	−4532.41	−0.194802
$816$	6647.09	0.285165
$817$	−2467.98	−0.105684
$818$	−21744.6	−0.929440
$819$	−5785.67	−0.246847
$820$	−3889.43	−0.165640
$821$	31700.5	1.34757	0.673784	−	0.738928i	$-0.264668\pi$
$821$	31700.5	1.34757	0.673784	+	0.738928i	$0.264668\pi$
$822$	5462.34	0.231778
$823$	43438.9	1.83984	0.919918	−	0.392112i	$-0.128255\pi$
$823$	43438.9	1.83984	0.919918	+	0.392112i	$0.128255\pi$
$824$	−43157.7	−1.82460
$825$	−1833.16	−0.0773606
$826$	−20603.9	−0.867918
$827$	−12339.3	−0.518839	−0.259419	−	0.965765i	$-0.583531\pi$
$827$	−12339.3	−0.518839	−0.259419	+	0.965765i	$0.583531\pi$
$828$	−10454.7	−0.438799
$829$	−4932.33	−0.206643	−0.103321	−	0.994648i	$-0.532947\pi$
$829$	−4932.33	−0.206643	−0.103321	+	0.994648i	$0.532947\pi$
$830$	−13782.4	−0.576379
$831$	847.529	0.0353796
$832$	9619.50	0.400837
$833$	325.720	0.0135481
$834$	210.383	0.00873498
$835$	−5659.04	−0.234538
$836$	−640.277	−0.0264886
$837$	20043.6	0.827727
$838$	2185.04	0.0900726
$839$	11908.0	0.489999	0.244999	−	0.969523i	$-0.421212\pi$
$839$	11908.0	0.489999	0.244999	+	0.969523i	$0.421212\pi$
$840$	−14954.4	−0.614259
$841$	−20701.3	−0.848796
$842$	−15031.9	−0.615243
$843$	50802.2	2.07559
$844$	−4576.62	−0.186652
$845$	−9332.60	−0.379942
$846$	16102.1	0.654375
$847$	−2208.59	−0.0895964
$848$	−8428.43	−0.341313
$849$	−16511.6	−0.667462
$850$	1839.72	0.0742373
$851$	18662.4	0.751749
$852$	4068.25	0.163587
$853$	−38952.9	−1.56357	−0.781784	−	0.623550i	$-0.785690\pi$
$853$	−38952.9	−1.56357	−0.781784	+	0.623550i	$0.785690\pi$
$854$	626.728	0.0251127
$855$	−1656.43	−0.0662559
$856$	17802.8	0.710848
$857$	−24232.8	−0.965902	−0.482951	−	0.875647i	$-0.660435\pi$
$857$	−24232.8	−0.965902	−0.482951	+	0.875647i	$0.660435\pi$
$858$	2961.71	0.117845
$859$	6876.07	0.273118	0.136559	−	0.990632i	$-0.456396\pi$
$859$	6876.07	0.273118	0.136559	+	0.990632i	$0.456396\pi$
$860$	−1989.66	−0.0788917
$861$	−30895.3	−1.22289
$862$	−31287.8	−1.23627
$863$	−38602.9	−1.52266	−0.761331	−	0.648364i	$-0.775454\pi$
$863$	−38602.9	−1.52266	−0.761331	+	0.648364i	$0.775454\pi$
$864$	8272.47	0.325735
$865$	3384.45	0.133034
$866$	2461.28	0.0965793
$867$	−25437.7	−0.996434
$868$	−17580.3	−0.687458
$869$	9093.49	0.354978
$870$	−4497.02	−0.175245
$871$	−19330.8	−0.752009
$872$	−49257.1	−1.91291
$873$	4042.42	0.156718
$874$	8262.31	0.319767
$875$	−2281.60	−0.0881512
$876$	11061.1	0.426621
$877$	9753.98	0.375563	0.187781	−	0.982211i	$-0.439870\pi$
$877$	9753.98	0.375563	0.187781	+	0.982211i	$0.439870\pi$
$878$	−35610.2	−1.36878
$879$	−11059.0	−0.424358
$880$	1655.86	0.0634308
$881$	1555.23	0.0594744	0.0297372	−	0.999558i	$-0.490533\pi$
$881$	1555.23	0.0594744	0.0297372	+	0.999558i	$0.490533\pi$
$882$	380.979	0.0145445
$883$	4540.46	0.173045	0.0865225	−	0.996250i	$-0.472425\pi$
$883$	4540.46	0.173045	0.0865225	+	0.996250i	$0.472425\pi$
$884$	1844.58	0.0701809
$885$	−16933.6	−0.643181
$886$	33760.5	1.28014
$887$	−28275.1	−1.07033	−0.535166	−	0.844747i	$-0.679751\pi$
$887$	−28275.1	−1.07033	−0.535166	+	0.844747i	$0.679751\pi$
$888$	15624.2	0.590444
$889$	−5289.10	−0.199540
$890$	8318.27	0.313291
$891$	9853.33	0.370481
$892$	4847.61	0.181962
$893$	7897.27	0.295937
$894$	4661.50	0.174389
$895$	7469.33	0.278963
$896$	2511.85	0.0936551
$897$	23718.1	0.882860
$898$	−21686.7	−0.805897
$899$	−19092.0	−0.708293
$900$	−1335.40	−0.0494593
$901$	−9272.31	−0.342847
$902$	6205.77	0.229079
$903$	−15804.7	−0.582444
$904$	33344.9	1.22681
$905$	−6029.89	−0.221481
$906$	3556.67	0.130422
$907$	35498.7	1.29958	0.649788	−	0.760115i	$-0.274857\pi$
$907$	35498.7	1.29958	0.649788	+	0.760115i	$0.274857\pi$
$908$	20769.9	0.759111
$909$	−2454.06	−0.0895445
$910$	3686.22	0.134283
$911$	10826.4	0.393738	0.196869	−	0.980430i	$-0.436923\pi$
$911$	10826.4	0.393738	0.196869	+	0.980430i	$0.436923\pi$
$912$	3813.14	0.138449
$913$	−13647.1	−0.494690
$914$	−771.094	−0.0279054
$915$	515.085	0.0186100
$916$	7088.32	0.255682
$917$	−2315.67	−0.0833918
$918$	−4691.51	−0.168674
$919$	961.133	0.0344993	0.0172496	−	0.999851i	$-0.494509\pi$
$919$	961.133	0.0344993	0.0172496	+	0.999851i	$0.494509\pi$
$920$	24055.3	0.862044
$921$	−33990.3	−1.21609
$922$	−22101.4	−0.789446
$923$	−3621.52	−0.129148
$924$	−4100.27	−0.145984
$925$	2383.79	0.0847335
$926$	−12947.4	−0.459478
$927$	−30613.0	−1.08464
$928$	−7879.74	−0.278734
$929$	−35506.0	−1.25394	−0.626971	−	0.779042i	$-0.715706\pi$
$929$	−35506.0	−1.25394	−0.626971	+	0.779042i	$0.715706\pi$
$930$	23282.0	0.820910
$931$	186.851	0.00657766
$932$	−1975.52	−0.0694317
$933$	47742.5	1.67526
$934$	−7994.46	−0.280071
$935$	1821.65	0.0637159
$936$	7791.57	0.272089
$937$	39159.2	1.36529	0.682643	−	0.730752i	$-0.260830\pi$
$937$	39159.2	1.36529	0.682643	+	0.730752i	$0.260830\pi$
$938$	−43123.7	−1.50111
$939$	−34316.9	−1.19264
$940$	6366.71	0.220914
$941$	−15721.2	−0.544629	−0.272315	−	0.962208i	$-0.587789\pi$
$941$	−15721.2	−0.544629	−0.272315	+	0.962208i	$0.587789\pi$
$942$	−18596.4	−0.643211
$943$	49697.4	1.71619
$944$	15295.8	0.527368
$945$	5818.38	0.200288
$946$	3174.60	0.109107
$947$	−22412.0	−0.769051	−0.384525	−	0.923114i	$-0.625635\pi$
$947$	−22412.0	−0.769051	−0.384525	+	0.923114i	$0.625635\pi$
$948$	16882.1	0.578383
$949$	−9846.50	−0.336808
$950$	1055.36	0.0360426
$951$	−33570.3	−1.14468
$952$	14860.5	0.505917
$953$	40576.5	1.37923	0.689613	−	0.724178i	$-0.257781\pi$
$953$	40576.5	1.37923	0.689613	+	0.724178i	$0.257781\pi$
$954$	−10845.4	−0.368062
$955$	−13960.3	−0.473029
$956$	19114.4	0.646656
$957$	−4452.86	−0.150408
$958$	−13015.9	−0.438960
$959$	6731.82	0.226676
$960$	17636.7	0.592940
$961$	69052.3	2.31789
$962$	−3851.32	−0.129076
$963$	12628.0	0.422567
$964$	16733.1	0.559062
$965$	−4856.72	−0.162014
$966$	52911.0	1.76230
$967$	−21584.6	−0.717802	−0.358901	−	0.933376i	$-0.616848\pi$
$967$	−21584.6	−0.717802	−0.358901	+	0.933376i	$0.616848\pi$
$968$	2974.32	0.0987585
$969$	4194.92	0.139072
$970$	−2575.55	−0.0852534
$971$	38709.2	1.27934	0.639669	−	0.768650i	$-0.279071\pi$
$971$	38709.2	1.27934	0.639669	+	0.768650i	$0.279071\pi$
$972$	13019.4	0.429628
$973$	259.277	0.00854271
$974$	−1891.65	−0.0622303
$975$	3029.57	0.0995117
$976$	−465.267	−0.0152591
$977$	21879.5	0.716465	0.358232	−	0.933632i	$-0.383380\pi$
$977$	21879.5	0.716465	0.358232	+	0.933632i	$0.383380\pi$
$978$	13425.6	0.438962
$979$	8236.59	0.268889
$980$	150.638	0.00491015
$981$	−34939.6	−1.13714
$982$	19420.3	0.631088
$983$	−20001.4	−0.648978	−0.324489	−	0.945889i	$-0.605192\pi$
$983$	−20001.4	−0.648978	−0.324489	+	0.945889i	$0.605192\pi$
$984$	41606.8	1.34794
$985$	11495.9	0.371867
$986$	4468.78	0.144336
$987$	50573.4	1.63097
$988$	1058.15	0.0340732
$989$	25423.0	0.817395
$990$	2130.69	0.0684019
$991$	50334.2	1.61344	0.806720	−	0.590933i	$-0.201240\pi$
$991$	50334.2	1.61344	0.806720	+	0.590933i	$0.201240\pi$
$992$	40795.0	1.30569
$993$	43465.0	1.38904
$994$	−8078.98	−0.257796
$995$	−15121.0	−0.481776
$996$	−25335.9	−0.806023
$997$	−9903.28	−0.314584	−0.157292	−	0.987552i	$-0.550276\pi$
$997$	−9903.28	−0.314584	−0.157292	+	0.987552i	$0.550276\pi$
$998$	5091.95	0.161506
$999$	−6078.96	−0.192522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.d.1.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.d.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.22182 q^{2} +6.66604 q^{3} -3.06353 q^{4} +5.00000 q^{5} -14.8107 q^{6} -18.2528 q^{7} +24.5811 q^{8} +17.4361 q^{9} +O(q^{10})\)	\(q-2.22182 q^{2} +6.66604 q^{3} -3.06353 q^{4} +5.00000 q^{5} -14.8107 q^{6} -18.2528 q^{7} +24.5811 q^{8} +17.4361 q^{9} -11.1091 q^{10} -11.0000 q^{11} -20.4216 q^{12} +18.1791 q^{13} +40.5545 q^{14} +33.3302 q^{15} -30.1066 q^{16} -33.1209 q^{17} -38.7399 q^{18} -19.0000 q^{19} -15.3176 q^{20} -121.674 q^{21} +24.4400 q^{22} +195.722 q^{23} +163.859 q^{24} +25.0000 q^{25} -40.3907 q^{26} -63.7532 q^{27} +55.9180 q^{28} +60.7265 q^{29} -74.0537 q^{30} -314.394 q^{31} -129.758 q^{32} -73.3265 q^{33} +73.5886 q^{34} -91.2641 q^{35} -53.4161 q^{36} +95.3515 q^{37} +42.2145 q^{38} +121.183 q^{39} +122.906 q^{40} +253.919 q^{41} +270.338 q^{42} +129.893 q^{43} +33.6988 q^{44} +87.1806 q^{45} -434.858 q^{46} -415.646 q^{47} -200.692 q^{48} -9.83427 q^{49} -55.5454 q^{50} -220.785 q^{51} -55.6923 q^{52} +279.953 q^{53} +141.648 q^{54} -55.0000 q^{55} -448.675 q^{56} -126.655 q^{57} -134.923 q^{58} -508.054 q^{59} -102.108 q^{60} +15.4540 q^{61} +698.525 q^{62} -318.259 q^{63} +529.151 q^{64} +90.8957 q^{65} +162.918 q^{66} -1063.35 q^{67} +101.467 q^{68} +1304.69 q^{69} +202.772 q^{70} -199.213 q^{71} +428.600 q^{72} -541.638 q^{73} -211.854 q^{74} +166.651 q^{75} +58.2070 q^{76} +200.781 q^{77} -269.246 q^{78} -826.681 q^{79} -150.533 q^{80} -895.757 q^{81} -564.161 q^{82} +1240.64 q^{83} +372.752 q^{84} -165.605 q^{85} -288.600 q^{86} +404.806 q^{87} -270.393 q^{88} -748.781 q^{89} -193.699 q^{90} -331.821 q^{91} -599.599 q^{92} -2095.76 q^{93} +923.489 q^{94} -95.0000 q^{95} -864.971 q^{96} +231.841 q^{97} +21.8500 q^{98} -191.797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) \) 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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