LMFDB - Embedded newform 33.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(1,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("33.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{97}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 24 $ x^2 - x - 24
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.42443$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.42443 q^{2} -3.00000 q^{3} +11.5756 q^{4} +2.84886 q^{5} +13.2733 q^{6} +31.6977 q^{7} -15.8199 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.42443 q^{2} -3.00000 q^{3} +11.5756 q^{4} +2.84886 q^{5} +13.2733 q^{6} +31.6977 q^{7} -15.8199 q^{8} +9.00000 q^{9} -12.6046 q^{10} -11.0000 q^{11} -34.7267 q^{12} +5.15114 q^{13} -140.244 q^{14} -8.54657 q^{15} -22.6107 q^{16} +121.942 q^{17} -39.8199 q^{18} +34.8489 q^{19} +32.9772 q^{20} -95.0931 q^{21} +48.6687 q^{22} +116.244 q^{23} +47.4596 q^{24} -116.884 q^{25} -22.7909 q^{26} -27.0000 q^{27} +366.919 q^{28} -69.4534 q^{29} +37.8137 q^{30} +140.605 q^{31} +226.598 q^{32} +33.0000 q^{33} -539.524 q^{34} +90.3023 q^{35} +104.180 q^{36} -420.070 q^{37} -154.186 q^{38} -15.4534 q^{39} -45.0685 q^{40} -322.058 q^{41} +420.733 q^{42} +321.035 q^{43} -127.331 q^{44} +25.6397 q^{45} -514.315 q^{46} -231.408 q^{47} +67.8322 q^{48} +661.745 q^{49} +517.145 q^{50} -365.826 q^{51} +59.6274 q^{52} +4.91916 q^{53} +119.460 q^{54} -31.3374 q^{55} -501.453 q^{56} -104.547 q^{57} +307.292 q^{58} +406.443 q^{59} -98.9315 q^{60} -556.431 q^{61} -622.095 q^{62} +285.279 q^{63} -821.683 q^{64} +14.6749 q^{65} -146.006 q^{66} +84.7452 q^{67} +1411.55 q^{68} -348.733 q^{69} -399.536 q^{70} +49.0808 q^{71} -142.379 q^{72} +785.884 q^{73} +1858.57 q^{74} +350.652 q^{75} +403.395 q^{76} -348.675 q^{77} +68.3726 q^{78} -383.118 q^{79} -64.4147 q^{80} +81.0000 q^{81} +1424.92 q^{82} -930.211 q^{83} -1100.76 q^{84} +347.395 q^{85} -1420.40 q^{86} +208.360 q^{87} +174.018 q^{88} -732.559 q^{89} -113.441 q^{90} +163.279 q^{91} +1345.59 q^{92} -421.814 q^{93} +1023.85 q^{94} +99.2794 q^{95} -679.795 q^{96} -1171.49 q^{97} -2927.84 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 6 q^{3} + 33 q^{4} - 14 q^{5} - 3 q^{6} + 24 q^{7} + 57 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + q^2 - 6 * q^3 + 33 * q^4 - 14 * q^5 - 3 * q^6 + 24 * q^7 + 57 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} + 33 q^{4} - 14 q^{5} - 3 q^{6} + 24 q^{7} + 57 q^{8} + 18 q^{9} - 104 q^{10} - 22 q^{11} - 99 q^{12} + 30 q^{13} - 182 q^{14} + 42 q^{15} + 201 q^{16} + 106 q^{17} + 9 q^{18} + 50 q^{19} - 328 q^{20} - 72 q^{21} - 11 q^{22} + 134 q^{23} - 171 q^{24} + 42 q^{25} + 112 q^{26} - 54 q^{27} + 202 q^{28} - 198 q^{29} + 312 q^{30} + 360 q^{31} + 857 q^{32} + 66 q^{33} - 626 q^{34} + 220 q^{35} + 297 q^{36} - 328 q^{37} - 72 q^{38} - 90 q^{39} - 1272 q^{40} - 782 q^{41} + 546 q^{42} + 386 q^{43} - 363 q^{44} - 126 q^{45} - 418 q^{46} + 266 q^{47} - 603 q^{48} + 378 q^{49} + 1379 q^{50} - 318 q^{51} + 592 q^{52} - 522 q^{53} - 27 q^{54} + 154 q^{55} - 1062 q^{56} - 150 q^{57} - 390 q^{58} - 172 q^{59} + 984 q^{60} - 778 q^{61} + 568 q^{62} + 216 q^{63} + 809 q^{64} - 404 q^{65} + 33 q^{66} - 776 q^{67} + 1070 q^{68} - 402 q^{69} + 304 q^{70} + 630 q^{71} + 513 q^{72} + 1296 q^{73} + 2358 q^{74} - 126 q^{75} + 728 q^{76} - 264 q^{77} - 336 q^{78} + 652 q^{79} - 3832 q^{80} + 162 q^{81} - 1070 q^{82} - 324 q^{83} - 606 q^{84} + 616 q^{85} - 1068 q^{86} + 594 q^{87} - 627 q^{88} - 756 q^{89} - 936 q^{90} - 28 q^{91} + 1726 q^{92} - 1080 q^{93} + 3722 q^{94} - 156 q^{95} - 2571 q^{96} - 452 q^{97} - 4467 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 + 33 * q^4 - 14 * q^5 - 3 * q^6 + 24 * q^7 + 57 * q^8 + 18 * q^9 - 104 * q^10 - 22 * q^11 - 99 * q^12 + 30 * q^13 - 182 * q^14 + 42 * q^15 + 201 * q^16 + 106 * q^17 + 9 * q^18 + 50 * q^19 - 328 * q^20 - 72 * q^21 - 11 * q^22 + 134 * q^23 - 171 * q^24 + 42 * q^25 + 112 * q^26 - 54 * q^27 + 202 * q^28 - 198 * q^29 + 312 * q^30 + 360 * q^31 + 857 * q^32 + 66 * q^33 - 626 * q^34 + 220 * q^35 + 297 * q^36 - 328 * q^37 - 72 * q^38 - 90 * q^39 - 1272 * q^40 - 782 * q^41 + 546 * q^42 + 386 * q^43 - 363 * q^44 - 126 * q^45 - 418 * q^46 + 266 * q^47 - 603 * q^48 + 378 * q^49 + 1379 * q^50 - 318 * q^51 + 592 * q^52 - 522 * q^53 - 27 * q^54 + 154 * q^55 - 1062 * q^56 - 150 * q^57 - 390 * q^58 - 172 * q^59 + 984 * q^60 - 778 * q^61 + 568 * q^62 + 216 * q^63 + 809 * q^64 - 404 * q^65 + 33 * q^66 - 776 * q^67 + 1070 * q^68 - 402 * q^69 + 304 * q^70 + 630 * q^71 + 513 * q^72 + 1296 * q^73 + 2358 * q^74 - 126 * q^75 + 728 * q^76 - 264 * q^77 - 336 * q^78 + 652 * q^79 - 3832 * q^80 + 162 * q^81 - 1070 * q^82 - 324 * q^83 - 606 * q^84 + 616 * q^85 - 1068 * q^86 + 594 * q^87 - 627 * q^88 - 756 * q^89 - 936 * q^90 - 28 * q^91 + 1726 * q^92 - 1080 * q^93 + 3722 * q^94 - 156 * q^95 - 2571 * q^96 - 452 * q^97 - 4467 * q^98 - 198 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−4.42443	−1.56427	−0.782136	−	0.623108i	$-0.785870\pi$
$2$	−4.42443	−1.56427	−0.782136	+	0.623108i	$0.785870\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	11.5756	1.44695
$5$	2.84886	0.254810	0.127405	−	0.991851i	$-0.459335\pi$
$5$	2.84886	0.254810	0.127405	+	0.991851i	$0.459335\pi$
$6$	13.2733	0.903133
$7$	31.6977	1.71152	0.855758	−	0.517377i	$-0.173091\pi$
$7$	31.6977	1.71152	0.855758	+	0.517377i	$0.173091\pi$
$8$	−15.8199	−0.699146
$9$	9.00000	0.333333
$10$	−12.6046	−0.398591
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−34.7267	−0.835395
$13$	5.15114	0.109898	0.0549488	−	0.998489i	$-0.482500\pi$
$13$	5.15114	0.109898	0.0549488	+	0.998489i	$0.482500\pi$
$14$	−140.244	−2.67728
$15$	−8.54657	−0.147114
$16$	−22.6107	−0.353293
$17$	121.942	1.73972	0.869861	−	0.493297i	$-0.164208\pi$
$17$	121.942	1.73972	0.869861	+	0.493297i	$0.164208\pi$
$18$	−39.8199	−0.521424
$19$	34.8489	0.420783	0.210391	−	0.977617i	$-0.432526\pi$
$19$	34.8489	0.420783	0.210391	+	0.977617i	$0.432526\pi$
$20$	32.9772	0.368696
$21$	−95.0931	−0.988144
$22$	48.6687	0.471646
$23$	116.244	1.05385	0.526926	−	0.849911i	$-0.323344\pi$
$23$	116.244	1.05385	0.526926	+	0.849911i	$0.323344\pi$
$24$	47.4596	0.403652
$25$	−116.884	−0.935072
$26$	−22.7909	−0.171910
$27$	−27.0000	−0.192450
$28$	366.919	2.47647
$29$	−69.4534	−0.444730	−0.222365	−	0.974963i	$-0.571378\pi$
$29$	−69.4534	−0.444730	−0.222365	+	0.974963i	$0.571378\pi$
$30$	37.8137	0.230127
$31$	140.605	0.814623	0.407312	−	0.913289i	$-0.366466\pi$
$31$	140.605	0.814623	0.407312	+	0.913289i	$0.366466\pi$
$32$	226.598	1.25179
$33$	33.0000	0.174078
$34$	−539.524	−2.72140
$35$	90.3023	0.436111
$36$	104.180	0.482315
$37$	−420.070	−1.86646	−0.933232	−	0.359276i	$-0.883024\pi$
$37$	−420.070	−1.86646	−0.933232	+	0.359276i	$0.883024\pi$
$38$	−154.186	−0.658219
$39$	−15.4534	−0.0634495
$40$	−45.0685	−0.178149
$41$	−322.058	−1.22676	−0.613378	−	0.789789i	$-0.710190\pi$
$41$	−322.058	−1.22676	−0.613378	+	0.789789i	$0.710190\pi$
$42$	420.733	1.54573
$43$	321.035	1.13854	0.569272	−	0.822149i	$-0.307225\pi$
$43$	321.035	1.13854	0.569272	+	0.822149i	$0.307225\pi$
$44$	−127.331	−0.436271
$45$	25.6397	0.0849365
$46$	−514.315	−1.64851
$47$	−231.408	−0.718176	−0.359088	−	0.933304i	$-0.616912\pi$
$47$	−231.408	−0.718176	−0.359088	+	0.933304i	$0.616912\pi$
$48$	67.8322	0.203974
$49$	661.745	1.92929
$50$	517.145	1.46271
$51$	−365.826	−1.00443
$52$	59.6274	0.159016
$53$	4.91916	0.0127490	0.00637452	−	0.999980i	$-0.497971\pi$
$53$	4.91916	0.0127490	0.00637452	+	0.999980i	$0.497971\pi$
$54$	119.460	0.301044
$55$	−31.3374	−0.0768280
$56$	−501.453	−1.19660
$57$	−104.547	−0.242939
$58$	307.292	0.695679
$59$	406.443	0.896854	0.448427	−	0.893820i	$-0.351984\pi$
$59$	406.443	0.896854	0.448427	+	0.893820i	$0.351984\pi$
$60$	−98.9315	−0.212867
$61$	−556.431	−1.16793	−0.583964	−	0.811779i	$-0.698499\pi$
$61$	−556.431	−1.16793	−0.583964	+	0.811779i	$0.698499\pi$
$62$	−622.095	−1.27429
$63$	285.279	0.570505
$64$	−821.683	−1.60485
$65$	14.6749	0.0280030
$66$	−146.006	−0.272305
$67$	84.7452	0.154526	0.0772632	−	0.997011i	$-0.475382\pi$
$67$	84.7452	0.154526	0.0772632	+	0.997011i	$0.475382\pi$
$68$	1411.55	2.51728
$69$	−348.733	−0.608442
$70$	−399.536	−0.682196
$71$	49.0808	0.0820398	0.0410199	−	0.999158i	$-0.486939\pi$
$71$	49.0808	0.0820398	0.0410199	+	0.999158i	$0.486939\pi$
$72$	−142.379	−0.233049
$73$	785.884	1.26001	0.630005	−	0.776591i	$-0.283053\pi$
$73$	785.884	1.26001	0.630005	+	0.776591i	$0.283053\pi$
$74$	1858.57	2.91966
$75$	350.652	0.539864
$76$	403.395	0.608850
$77$	−348.675	−0.516041
$78$	68.3726	0.0992522
$79$	−383.118	−0.545622	−0.272811	−	0.962068i	$-0.587953\pi$
$79$	−383.118	−0.545622	−0.272811	+	0.962068i	$0.587953\pi$
$80$	−64.4147	−0.0900223
$81$	81.0000	0.111111
$82$	1424.92	1.91898
$83$	−930.211	−1.23017	−0.615084	−	0.788462i	$-0.710878\pi$
$83$	−930.211	−1.23017	−0.615084	+	0.788462i	$0.710878\pi$
$84$	−1100.76	−1.42979
$85$	347.395	0.443298
$86$	−1420.40	−1.78099
$87$	208.360	0.256765
$88$	174.018	0.210800
$89$	−732.559	−0.872484	−0.436242	−	0.899829i	$-0.643691\pi$
$89$	−732.559	−0.872484	−0.436242	+	0.899829i	$0.643691\pi$
$90$	−113.441	−0.132864
$91$	163.279	0.188092
$92$	1345.59	1.52487
$93$	−421.814	−0.470323
$94$	1023.85	1.12342
$95$	99.2794	0.107220
$96$	−679.795	−0.722722
$97$	−1171.49	−1.22626	−0.613128	−	0.789984i	$-0.710089\pi$
$97$	−1171.49	−1.22626	−0.613128	+	0.789984i	$0.710089\pi$
$98$	−2927.84	−3.01793
$99$	−99.0000	−0.100504
$100$	−1353.00	−1.35300
$101$	−1221.27	−1.20318	−0.601589	−	0.798806i	$-0.705465\pi$
$101$	−1221.27	−1.20318	−0.601589	+	0.798806i	$0.705465\pi$
$102$	1618.57	1.57120
$103$	516.745	0.494334	0.247167	−	0.968973i	$-0.420500\pi$
$103$	516.745	0.494334	0.247167	+	0.968973i	$0.420500\pi$
$104$	−81.4903	−0.0768345
$105$	−270.907	−0.251789
$106$	−21.7645	−0.0199430
$107$	−152.025	−0.137353	−0.0686765	−	0.997639i	$-0.521878\pi$
$107$	−152.025	−0.137353	−0.0686765	+	0.997639i	$0.521878\pi$
$108$	−312.540	−0.278465
$109$	2170.32	1.90714	0.953572	−	0.301164i	$-0.0973752\pi$
$109$	2170.32	1.90714	0.953572	+	0.301164i	$0.0973752\pi$
$110$	138.650	0.120180
$111$	1260.21	1.07760
$112$	−716.708	−0.604666
$113$	−646.397	−0.538123	−0.269062	−	0.963123i	$-0.586714\pi$
$113$	−646.397	−0.538123	−0.269062	+	0.963123i	$0.586714\pi$
$114$	462.559	0.380023
$115$	331.163	0.268532
$116$	−803.963	−0.643501
$117$	46.3603	0.0366326
$118$	−1798.28	−1.40292
$119$	3865.28	2.97756
$120$	135.206	0.102854
$121$	121.000	0.0909091
$122$	2461.89	1.82696
$123$	966.174	0.708268
$124$	1627.58	1.17872
$125$	−689.093	−0.493075
$126$	−1262.20	−0.892425
$127$	−993.304	−0.694027	−0.347014	−	0.937860i	$-0.612804\pi$
$127$	−993.304	−0.694027	−0.347014	+	0.937860i	$0.612804\pi$
$128$	1822.69	1.25863
$129$	−963.105	−0.657339
$130$	−64.9279	−0.0438043
$131$	385.814	0.257318	0.128659	−	0.991689i	$-0.458933\pi$
$131$	385.814	0.257318	0.128659	+	0.991689i	$0.458933\pi$
$132$	381.994	0.251881
$133$	1104.63	0.720177
$134$	−374.949	−0.241721
$135$	−76.9192	−0.0490381
$136$	−1929.11	−1.21632
$137$	884.840	0.551803	0.275901	−	0.961186i	$-0.411024\pi$
$137$	884.840	0.551803	0.275901	+	0.961186i	$0.411024\pi$
$138$	1542.94	0.951769
$139$	−1091.94	−0.666312	−0.333156	−	0.942872i	$-0.608114\pi$
$139$	−1091.94	−0.666312	−0.333156	+	0.942872i	$0.608114\pi$
$140$	1045.30	0.631029
$141$	694.223	0.414639
$142$	−217.155	−0.128333
$143$	−56.6626	−0.0331354
$144$	−203.497	−0.117764
$145$	−197.863	−0.113322
$146$	−3477.09	−1.97100
$147$	−1985.24	−1.11387
$148$	−4862.55	−2.70067
$149$	297.014	0.163304	0.0816522	−	0.996661i	$-0.473980\pi$
$149$	297.014	0.163304	0.0816522	+	0.996661i	$0.473980\pi$
$150$	−1551.43	−0.844494
$151$	−1887.86	−1.01743	−0.508716	−	0.860935i	$-0.669880\pi$
$151$	−1887.86	−1.01743	−0.508716	+	0.860935i	$0.669880\pi$
$152$	−551.304	−0.294189
$153$	1097.48	0.579907
$154$	1542.69	0.807229
$155$	400.562	0.207574
$156$	−178.882	−0.0918080
$157$	−56.5343	−0.0287384	−0.0143692	−	0.999897i	$-0.504574\pi$
$157$	−56.5343	−0.0287384	−0.0143692	+	0.999897i	$0.504574\pi$
$158$	1695.08	0.853501
$159$	−14.7575	−0.00736066
$160$	645.547	0.318968
$161$	3684.68	1.80369
$162$	−358.379	−0.173808
$163$	−49.2338	−0.0236582	−0.0118291	−	0.999930i	$-0.503765\pi$
$163$	−49.2338	−0.0236582	−0.0118291	+	0.999930i	$0.503765\pi$
$164$	−3728.01	−1.77505
$165$	94.0123	0.0443567
$166$	4115.65	1.92432
$167$	2068.75	0.958589	0.479294	−	0.877654i	$-0.340893\pi$
$167$	2068.75	0.958589	0.479294	+	0.877654i	$0.340893\pi$
$168$	1504.36	0.690857
$169$	−2170.47	−0.987923
$170$	−1537.03	−0.693438
$171$	313.640	0.140261
$172$	3716.17	1.64741
$173$	−604.012	−0.265446	−0.132723	−	0.991153i	$-0.542372\pi$
$173$	−604.012	−0.265446	−0.132723	+	0.991153i	$0.542372\pi$
$174$	−921.875	−0.401650
$175$	−3704.96	−1.60039
$176$	248.718	0.106522
$177$	−1219.33	−0.517799
$178$	3241.15	1.36480
$179$	−2132.02	−0.890251	−0.445126	−	0.895468i	$-0.646841\pi$
$179$	−2132.02	−0.890251	−0.445126	+	0.895468i	$0.646841\pi$
$180$	296.794	0.122899
$181$	−589.371	−0.242031	−0.121015	−	0.992651i	$-0.538615\pi$
$181$	−589.371	−0.242031	−0.121015	+	0.992651i	$0.538615\pi$
$182$	−722.418	−0.294226
$183$	1669.29	0.674304
$184$	−1838.97	−0.736796
$185$	−1196.72	−0.475593
$186$	1866.28	0.735713
$187$	−1341.36	−0.524546
$188$	−2678.68	−1.03916
$189$	−855.838	−0.329381
$190$	−439.255	−0.167720
$191$	−2160.90	−0.818624	−0.409312	−	0.912395i	$-0.634231\pi$
$191$	−2160.90	−0.818624	−0.409312	+	0.912395i	$0.634231\pi$
$192$	2465.05	0.926560
$193$	−1490.91	−0.556052	−0.278026	−	0.960574i	$-0.589680\pi$
$193$	−1490.91	−0.556052	−0.278026	+	0.960574i	$0.589680\pi$
$194$	5183.18	1.91820
$195$	−44.0246	−0.0161675
$196$	7660.08	2.79157
$197$	−230.529	−0.0833732	−0.0416866	−	0.999131i	$-0.513273\pi$
$197$	−230.529	−0.0833732	−0.0416866	+	0.999131i	$0.513273\pi$
$198$	438.018	0.157215
$199$	22.4007	0.00797963	0.00398982	−	0.999992i	$-0.498730\pi$
$199$	22.4007	0.00797963	0.00398982	+	0.999992i	$0.498730\pi$
$200$	1849.09	0.653752
$201$	−254.236	−0.0892159
$202$	5403.43	1.88210
$203$	−2201.51	−0.761163
$204$	−4234.65	−1.45336
$205$	−917.497	−0.312589
$206$	−2286.30	−0.773273
$207$	1046.20	0.351284
$208$	−116.471	−0.0388260
$209$	−383.337	−0.126871
$210$	1198.61	0.393866
$211$	−1051.64	−0.343117	−0.171558	−	0.985174i	$-0.554880\pi$
$211$	−1051.64	−0.343117	−0.171558	+	0.985174i	$0.554880\pi$
$212$	56.9421	0.0184472
$213$	−147.243	−0.0473657
$214$	672.622	0.214857
$215$	914.583	0.290112
$216$	427.136	0.134551
$217$	4456.84	1.39424
$218$	−9602.42	−2.98329
$219$	−2357.65	−0.727467
$220$	−362.749	−0.111166
$221$	628.141	0.191191
$222$	−5575.71	−1.68566
$223$	3861.80	1.15966	0.579832	−	0.814736i	$-0.303118\pi$
$223$	3861.80	1.15966	0.579832	+	0.814736i	$0.303118\pi$
$224$	7182.65	2.14246
$225$	−1051.96	−0.311691
$226$	2859.94	0.841771
$227$	−872.721	−0.255174	−0.127587	−	0.991827i	$-0.540723\pi$
$227$	−872.721	−0.255174	−0.127587	+	0.991827i	$0.540723\pi$
$228$	−1210.19	−0.351520
$229$	1841.72	0.531459	0.265730	−	0.964048i	$-0.414387\pi$
$229$	1841.72	0.531459	0.265730	+	0.964048i	$0.414387\pi$
$230$	−1465.21	−0.420057
$231$	1046.02	0.297937
$232$	1098.74	0.310931
$233$	3932.14	1.10559	0.552796	−	0.833317i	$-0.313561\pi$
$233$	3932.14	1.10559	0.552796	+	0.833317i	$0.313561\pi$
$234$	−205.118	−0.0573033
$235$	−659.248	−0.182998
$236$	4704.81	1.29770
$237$	1149.35	0.315015
$238$	−17101.7	−4.65772
$239$	4772.10	1.29155	0.645777	−	0.763526i	$-0.276534\pi$
$239$	4772.10	1.29155	0.645777	+	0.763526i	$0.276534\pi$
$240$	193.244	0.0519744
$241$	3988.84	1.06616	0.533078	−	0.846066i	$-0.321035\pi$
$241$	3988.84	1.06616	0.533078	+	0.846066i	$0.321035\pi$
$242$	−535.356	−0.142207
$243$	−243.000	−0.0641500
$244$	−6441.00	−1.68993
$245$	1885.22	0.491601
$246$	−4274.77	−1.10792
$247$	179.511	0.0462431
$248$	−2224.34	−0.569540
$249$	2790.63	0.710238
$250$	3048.84	0.771303
$251$	−5474.22	−1.37661	−0.688306	−	0.725421i	$-0.741645\pi$
$251$	−5474.22	−1.37661	−0.688306	+	0.725421i	$0.741645\pi$
$252$	3302.27	0.825491
$253$	−1278.69	−0.317749
$254$	4394.80	1.08565
$255$	−1042.19	−0.255938
$256$	−1490.90	−0.363989
$257$	−6434.01	−1.56164	−0.780822	−	0.624754i	$-0.785199\pi$
$257$	−6434.01	−1.56164	−0.780822	+	0.624754i	$0.785199\pi$
$258$	4261.19	1.02826
$259$	−13315.3	−3.19448
$260$	169.870	0.0405188
$261$	−625.081	−0.148243
$262$	−1707.01	−0.402516
$263$	7589.00	1.77931	0.889654	−	0.456636i	$-0.150946\pi$
$263$	7589.00	1.77931	0.889654	+	0.456636i	$0.150946\pi$
$264$	−522.055	−0.121706
$265$	14.0140	0.00324858
$266$	−4887.35	−1.12655
$267$	2197.68	0.503729
$268$	980.974	0.223591
$269$	478.178	0.108383	0.0541914	−	0.998531i	$-0.482742\pi$
$269$	478.178	0.108383	0.0541914	+	0.998531i	$0.482742\pi$
$270$	340.323	0.0767090
$271$	−122.323	−0.0274192	−0.0137096	−	0.999906i	$-0.504364\pi$
$271$	−122.323	−0.0274192	−0.0137096	+	0.999906i	$0.504364\pi$
$272$	−2757.20	−0.614631
$273$	−489.838	−0.108595
$274$	−3914.91	−0.863170
$275$	1285.72	0.281935
$276$	−4036.78	−0.880383
$277$	8199.41	1.77854	0.889269	−	0.457385i	$-0.151214\pi$
$277$	8199.41	1.77854	0.889269	+	0.457385i	$0.151214\pi$
$278$	4831.22	1.04229
$279$	1265.44	0.271541
$280$	−1428.57	−0.304905
$281$	6943.79	1.47413	0.737067	−	0.675820i	$-0.236210\pi$
$281$	6943.79	1.47413	0.737067	+	0.675820i	$0.236210\pi$
$282$	−3071.54	−0.648609
$283$	1035.14	0.217429	0.108715	−	0.994073i	$-0.465327\pi$
$283$	1035.14	0.217429	0.108715	+	0.994073i	$0.465327\pi$
$284$	568.139	0.118707
$285$	−297.838	−0.0619032
$286$	250.699	0.0518328
$287$	−10208.5	−2.09961
$288$	2039.39	0.417264
$289$	9956.85	2.02663
$290$	875.430	0.177266
$291$	3514.47	0.707979
$292$	9097.06	1.82317
$293$	−6144.81	−1.22520	−0.612600	−	0.790393i	$-0.709876\pi$
$293$	−6144.81	−1.22520	−0.612600	+	0.790393i	$0.709876\pi$
$294$	8783.53	1.74240
$295$	1157.90	0.228527
$296$	6645.45	1.30493
$297$	297.000	0.0580259
$298$	−1314.12	−0.255452
$299$	598.791	0.115816
$300$	4059.00	0.781154
$301$	10176.1	1.94864
$302$	8352.72	1.59154
$303$	3663.81	0.694655
$304$	−787.958	−0.148659
$305$	−1585.19	−0.297599
$306$	−4855.71	−0.907133
$307$	−2186.09	−0.406406	−0.203203	−	0.979137i	$-0.565135\pi$
$307$	−2186.09	−0.406406	−0.203203	+	0.979137i	$0.565135\pi$
$308$	−4036.11	−0.746684
$309$	−1550.24	−0.285404
$310$	−1772.26	−0.324702
$311$	−7484.83	−1.36471	−0.682357	−	0.731019i	$-0.739045\pi$
$311$	−7484.83	−1.36471	−0.682357	+	0.731019i	$0.739045\pi$
$312$	244.471	0.0443604
$313$	−6833.33	−1.23400	−0.617001	−	0.786962i	$-0.711653\pi$
$313$	−6833.33	−1.23400	−0.617001	+	0.786962i	$0.711653\pi$
$314$	250.132	0.0449546
$315$	812.721	0.145370
$316$	−4434.81	−0.789485
$317$	924.265	0.163760	0.0818800	−	0.996642i	$-0.473908\pi$
$317$	924.265	0.163760	0.0818800	+	0.996642i	$0.473908\pi$
$318$	65.2934	0.0115141
$319$	763.988	0.134091
$320$	−2340.86	−0.408931
$321$	456.074	0.0793008
$322$	−16302.6	−2.82145
$323$	4249.54	0.732046
$324$	937.621	0.160772
$325$	−602.086	−0.102762
$326$	217.831	0.0370078
$327$	−6510.95	−1.10109
$328$	5094.91	0.857681
$329$	−7335.10	−1.22917
$330$	−415.951	−0.0693859
$331$	−9820.46	−1.63076	−0.815380	−	0.578927i	$-0.803472\pi$
$331$	−9820.46	−1.63076	−0.815380	+	0.578927i	$0.803472\pi$
$332$	−10767.7	−1.77999
$333$	−3780.63	−0.622154
$334$	−9153.02	−1.49949
$335$	241.427	0.0393748
$336$	2150.12	0.349104
$337$	600.808	0.0971161	0.0485580	−	0.998820i	$-0.484537\pi$
$337$	600.808	0.0971161	0.0485580	+	0.998820i	$0.484537\pi$
$338$	9603.07	1.54538
$339$	1939.19	0.310686
$340$	4021.30	0.641428
$341$	−1546.65	−0.245618
$342$	−1387.68	−0.219406
$343$	10103.5	1.59049
$344$	−5078.73	−0.796008
$345$	−993.490	−0.155037
$346$	2672.41	0.415230
$347$	−3143.41	−0.486303	−0.243152	−	0.969988i	$-0.578181\pi$
$347$	−3143.41	−0.486303	−0.243152	+	0.969988i	$0.578181\pi$
$348$	2411.89	0.371525
$349$	720.663	0.110533	0.0552667	−	0.998472i	$-0.482399\pi$
$349$	720.663	0.110533	0.0552667	+	0.998472i	$0.482399\pi$
$350$	16392.3	2.50345
$351$	−139.081	−0.0211498
$352$	−2492.58	−0.377429
$353$	1207.12	0.182007	0.0910034	−	0.995851i	$-0.470993\pi$
$353$	1207.12	0.182007	0.0910034	+	0.995851i	$0.470993\pi$
$354$	5394.83	0.809978
$355$	139.824	0.0209045
$356$	−8479.79	−1.26244
$357$	−11595.8	−1.71910
$358$	9432.99	1.39260
$359$	8748.31	1.28612	0.643062	−	0.765814i	$-0.277664\pi$
$359$	8748.31	1.28612	0.643062	+	0.765814i	$0.277664\pi$
$360$	−405.617	−0.0593830
$361$	−5644.56	−0.822942
$362$	2607.63	0.378602
$363$	−363.000	−0.0524864
$364$	1890.05	0.272158
$365$	2238.87	0.321063
$366$	−7385.66	−1.05479
$367$	−6730.45	−0.957293	−0.478647	−	0.878008i	$-0.658872\pi$
$367$	−6730.45	−0.957293	−0.478647	+	0.878008i	$0.658872\pi$
$368$	−2628.37	−0.372318
$369$	−2898.52	−0.408919
$370$	5294.81	0.743956
$371$	155.926	0.0218202
$372$	−4882.73	−0.680532
$373$	−227.394	−0.0315657	−0.0157828	−	0.999875i	$-0.505024\pi$
$373$	−227.394	−0.0315657	−0.0157828	+	0.999875i	$0.505024\pi$
$374$	5934.76	0.820533
$375$	2067.28	0.284677
$376$	3660.84	0.502110
$377$	−357.764	−0.0488748
$378$	3786.60	0.515242
$379$	11356.2	1.53913	0.769565	−	0.638568i	$-0.220473\pi$
$379$	11356.2	1.53913	0.769565	+	0.638568i	$0.220473\pi$
$380$	1149.22	0.155141
$381$	2979.91	0.400697
$382$	9560.74	1.28055
$383$	10753.6	1.43468	0.717338	−	0.696725i	$-0.245360\pi$
$383$	10753.6	1.43468	0.717338	+	0.696725i	$0.245360\pi$
$384$	−5468.07	−0.726670
$385$	−993.325	−0.131492
$386$	6596.43	0.869817
$387$	2889.32	0.379515
$388$	−13560.7	−1.77433
$389$	−11727.1	−1.52850	−0.764252	−	0.644918i	$-0.776891\pi$
$389$	−11727.1	−1.52850	−0.764252	+	0.644918i	$0.776891\pi$
$390$	194.784	0.0252904
$391$	14175.1	1.83341
$392$	−10468.7	−1.34885
$393$	−1157.44	−0.148563
$394$	1019.96	0.130418
$395$	−1091.45	−0.139030
$396$	−1145.98	−0.145424
$397$	−359.905	−0.0454990	−0.0227495	−	0.999741i	$-0.507242\pi$
$397$	−359.905	−0.0454990	−0.0227495	+	0.999741i	$0.507242\pi$
$398$	−99.1105	−0.0124823
$399$	−3313.89	−0.415794
$400$	2642.83	0.330354
$401$	−4066.71	−0.506438	−0.253219	−	0.967409i	$-0.581489\pi$
$401$	−4066.71	−0.506438	−0.253219	+	0.967409i	$0.581489\pi$
$402$	1124.85	0.139558
$403$	724.274	0.0895252
$404$	−14136.9	−1.74093
$405$	230.757	0.0283122
$406$	9740.45	1.19067
$407$	4620.77	0.562760
$408$	5787.32	0.702242
$409$	−13488.8	−1.63076	−0.815379	−	0.578927i	$-0.803472\pi$
$409$	−13488.8	−1.63076	−0.815379	+	0.578927i	$0.803472\pi$
$410$	4059.40	0.488975
$411$	−2654.52	−0.318584
$412$	5981.62	0.715275
$413$	12883.3	1.53498
$414$	−4628.83	−0.549504
$415$	−2650.04	−0.313459
$416$	1167.24	0.137569
$417$	3275.83	0.384695
$418$	1696.05	0.198460
$419$	−7040.12	−0.820841	−0.410420	−	0.911896i	$-0.634618\pi$
$419$	−7040.12	−0.820841	−0.410420	+	0.911896i	$0.634618\pi$
$420$	−3135.90	−0.364325
$421$	9171.74	1.06177	0.530883	−	0.847445i	$-0.321860\pi$
$421$	9171.74	1.06177	0.530883	+	0.847445i	$0.321860\pi$
$422$	4652.89	0.536728
$423$	−2082.67	−0.239392
$424$	−77.8204	−0.00891343
$425$	−14253.1	−1.62677
$426$	651.464	0.0740928
$427$	−17637.6	−1.99893
$428$	−1759.77	−0.198742
$429$	169.988	0.0191307
$430$	−4046.51	−0.453814
$431$	992.995	0.110976	0.0554882	−	0.998459i	$-0.482328\pi$
$431$	992.995	0.110976	0.0554882	+	0.998459i	$0.482328\pi$
$432$	610.490	0.0679912
$433$	3790.21	0.420660	0.210330	−	0.977630i	$-0.432546\pi$
$433$	3790.21	0.420660	0.210330	+	0.977630i	$0.432546\pi$
$434$	−19719.0	−2.18097
$435$	593.589	0.0654262
$436$	25122.7	2.75954
$437$	4050.98	0.443443
$438$	10431.3	1.13796
$439$	−5136.97	−0.558483	−0.279242	−	0.960221i	$-0.590083\pi$
$439$	−5136.97	−0.558483	−0.279242	+	0.960221i	$0.590083\pi$
$440$	495.754	0.0537139
$441$	5955.71	0.643095
$442$	−2779.16	−0.299075
$443$	10676.8	1.14508	0.572541	−	0.819876i	$-0.305958\pi$
$443$	10676.8	1.14508	0.572541	+	0.819876i	$0.305958\pi$
$444$	14587.7	1.55923
$445$	−2086.96	−0.222317
$446$	−17086.2	−1.81403
$447$	−891.042	−0.0942838
$448$	−26045.5	−2.74672
$449$	10529.9	1.10676	0.553379	−	0.832929i	$-0.313338\pi$
$449$	10529.9	1.10676	0.553379	+	0.832929i	$0.313338\pi$
$450$	4654.30	0.487569
$451$	3542.64	0.369881
$452$	−7482.42	−0.778636
$453$	5663.59	0.587414
$454$	3861.29	0.399162
$455$	465.160	0.0479275
$456$	1653.91	0.169850
$457$	−14072.5	−1.44045	−0.720225	−	0.693741i	$-0.755961\pi$
$457$	−14072.5	−1.44045	−0.720225	+	0.693741i	$0.755961\pi$
$458$	−8148.55	−0.831347
$459$	−3292.43	−0.334810
$460$	3833.41	0.388551
$461$	−30.8173	−0.00311346	−0.00155673	−	0.999999i	$-0.500496\pi$
$461$	−30.8173	−0.00311346	−0.00155673	+	0.999999i	$0.500496\pi$
$462$	−4628.06	−0.466054
$463$	17591.3	1.76573	0.882867	−	0.469622i	$-0.155610\pi$
$463$	17591.3	1.76573	0.882867	+	0.469622i	$0.155610\pi$
$464$	1570.39	0.157120
$465$	−1201.69	−0.119843
$466$	−17397.5	−1.72945
$467$	13273.1	1.31522	0.657609	−	0.753360i	$-0.271568\pi$
$467$	13273.1	1.31522	0.657609	+	0.753360i	$0.271568\pi$
$468$	536.647	0.0530053
$469$	2686.23	0.264474
$470$	2916.79	0.286259
$471$	169.603	0.0165921
$472$	−6429.87	−0.627031
$473$	−3531.39	−0.343284
$474$	−5085.23	−0.492769
$475$	−4073.27	−0.393462
$476$	44742.9	4.30837
$477$	44.2724	0.00424968
$478$	−21113.8	−2.02034
$479$	2496.68	0.238155	0.119077	−	0.992885i	$-0.462006\pi$
$479$	2496.68	0.238155	0.119077	+	0.992885i	$0.462006\pi$
$480$	−1936.64	−0.184156
$481$	−2163.84	−0.205120
$482$	−17648.3	−1.66776
$483$	−11054.0	−1.04136
$484$	1400.64	0.131541
$485$	−3337.41	−0.312462
$486$	1075.14	0.100348
$487$	−3464.42	−0.322357	−0.161178	−	0.986925i	$-0.551529\pi$
$487$	−3464.42	−0.322357	−0.161178	+	0.986925i	$0.551529\pi$
$488$	8802.65	0.816552
$489$	147.701	0.0136591
$490$	−8341.01	−0.768997
$491$	−16224.6	−1.49125	−0.745625	−	0.666366i	$-0.767849\pi$
$491$	−16224.6	−1.49125	−0.745625	+	0.666366i	$0.767849\pi$
$492$	11184.0	1.02483
$493$	−8469.29	−0.773707
$494$	−794.236	−0.0723367
$495$	−282.037	−0.0256093
$496$	−3179.17	−0.287800
$497$	1555.75	0.140412
$498$	−12347.0	−1.11100
$499$	9993.81	0.896562	0.448281	−	0.893893i	$-0.352036\pi$
$499$	9993.81	0.896562	0.448281	+	0.893893i	$0.352036\pi$
$500$	−7976.65	−0.713453
$501$	−6206.24	−0.553441
$502$	24220.3	2.15340
$503$	−15334.8	−1.35933	−0.679667	−	0.733520i	$-0.737876\pi$
$503$	−15334.8	−1.35933	−0.679667	+	0.733520i	$0.737876\pi$
$504$	−4513.08	−0.398866
$505$	−3479.23	−0.306581
$506$	5657.46	0.497045
$507$	6511.40	0.570377
$508$	−11498.1	−1.00422
$509$	−7291.23	−0.634927	−0.317464	−	0.948270i	$-0.602831\pi$
$509$	−7291.23	−0.634927	−0.317464	+	0.948270i	$0.602831\pi$
$510$	4611.08	0.400357
$511$	24910.7	2.15653
$512$	−7985.14	−0.689251
$513$	−940.919	−0.0809797
$514$	28466.8	2.44283
$515$	1472.13	0.125961
$516$	−11148.5	−0.951134
$517$	2545.49	0.216538
$518$	58912.5	4.99704
$519$	1812.04	0.153255
$520$	−232.154	−0.0195782
$521$	16794.3	1.41223	0.706114	−	0.708098i	$-0.250447\pi$
$521$	16794.3	1.41223	0.706114	+	0.708098i	$0.250447\pi$
$522$	2765.63	0.231893
$523$	−21009.4	−1.75655	−0.878275	−	0.478157i	$-0.841305\pi$
$523$	−21009.4	−1.75655	−0.878275	+	0.478157i	$0.841305\pi$
$524$	4466.01	0.372326
$525$	11114.9	0.923986
$526$	−33577.0	−2.78332
$527$	17145.6	1.41722
$528$	−746.154	−0.0615003
$529$	1345.73	0.110605
$530$	−62.0039	−0.00508166
$531$	3657.99	0.298951
$532$	12786.7	1.04206
$533$	−1658.97	−0.134818
$534$	−9723.46	−0.787969
$535$	−433.097	−0.0349989
$536$	−1340.66	−0.108036
$537$	6396.07	0.513987
$538$	−2115.66	−0.169540
$539$	−7279.20	−0.581702
$540$	−890.383	−0.0709555
$541$	−16802.8	−1.33532	−0.667662	−	0.744464i	$-0.732705\pi$
$541$	−16802.8	−1.33532	−0.667662	+	0.744464i	$0.732705\pi$
$542$	541.211	0.0428911
$543$	1768.11	0.139737
$544$	27631.9	2.17777
$545$	6182.93	0.485959
$546$	2167.25	0.169872
$547$	16784.5	1.31198	0.655990	−	0.754770i	$-0.272251\pi$
$547$	16784.5	1.31198	0.655990	+	0.754770i	$0.272251\pi$
$548$	10242.5	0.798429
$549$	−5007.88	−0.389309
$550$	−5688.59	−0.441023
$551$	−2420.37	−0.187135
$552$	5516.91	0.425390
$553$	−12144.0	−0.933840
$554$	−36277.7	−2.78212
$555$	3590.16	0.274584
$556$	−12639.9	−0.964117
$557$	18127.0	1.37893	0.689467	−	0.724317i	$-0.257845\pi$
$557$	18127.0	1.37893	0.689467	+	0.724317i	$0.257845\pi$
$558$	−5598.85	−0.424764
$559$	1653.70	0.125123
$560$	−2041.80	−0.154075
$561$	4024.09	0.302847
$562$	−30722.3	−2.30595
$563$	2090.88	0.156518	0.0782592	−	0.996933i	$-0.475064\pi$
$563$	2090.88	0.156518	0.0782592	+	0.996933i	$0.475064\pi$
$564$	8036.03	0.599961
$565$	−1841.49	−0.137119
$566$	−4579.89	−0.340119
$567$	2567.51	0.190168
$568$	−776.452	−0.0573578
$569$	6249.23	0.460424	0.230212	−	0.973140i	$-0.426058\pi$
$569$	6249.23	0.460424	0.230212	+	0.973140i	$0.426058\pi$
$570$	1317.76	0.0968335
$571$	6048.79	0.443317	0.221659	−	0.975124i	$-0.428853\pi$
$571$	6048.79	0.443317	0.221659	+	0.975124i	$0.428853\pi$
$572$	−655.902	−0.0479451
$573$	6482.69	0.472633
$574$	45166.8	3.28437
$575$	−13587.1	−0.985428
$576$	−7395.15	−0.534950
$577$	−15729.1	−1.13486	−0.567429	−	0.823423i	$-0.692062\pi$
$577$	−15729.1	−1.13486	−0.567429	+	0.823423i	$0.692062\pi$
$578$	−44053.4	−3.17021
$579$	4472.73	0.321037
$580$	−2290.38	−0.163970
$581$	−29485.6	−2.10545
$582$	−15549.5	−1.10747
$583$	−54.1108	−0.00384398
$584$	−12432.6	−0.880931
$585$	132.074	0.00933433
$586$	27187.3	1.91655
$587$	15620.5	1.09835	0.549173	−	0.835709i	$-0.314943\pi$
$587$	15620.5	1.09835	0.549173	+	0.835709i	$0.314943\pi$
$588$	−22980.2	−1.61172
$589$	4899.91	0.342780
$590$	−5123.04	−0.357478
$591$	691.587	0.0481355
$592$	9498.09	0.659407
$593$	−493.541	−0.0341776	−0.0170888	−	0.999854i	$-0.505440\pi$
$593$	−493.541	−0.0341776	−0.0170888	+	0.999854i	$0.505440\pi$
$594$	−1314.06	−0.0907683
$595$	11011.6	0.758711
$596$	3438.11	0.236293
$597$	−67.2022	−0.00460704
$598$	−2649.31	−0.181168
$599$	−12455.1	−0.849585	−0.424793	−	0.905291i	$-0.639653\pi$
$599$	−12455.1	−0.849585	−0.424793	+	0.905291i	$0.639653\pi$
$600$	−5547.27	−0.377444
$601$	12454.8	0.845329	0.422664	−	0.906286i	$-0.361095\pi$
$601$	12454.8	0.845329	0.422664	+	0.906286i	$0.361095\pi$
$602$	−45023.3	−3.04820
$603$	762.707	0.0515088
$604$	−21853.1	−1.47217
$605$	344.712	0.0231645
$606$	−16210.3	−1.08663
$607$	−4243.19	−0.283733	−0.141867	−	0.989886i	$-0.545310\pi$
$607$	−4243.19	−0.283733	−0.141867	+	0.989886i	$0.545310\pi$
$608$	7896.70	0.526732
$609$	6604.54	0.439458
$610$	7013.57	0.465526
$611$	−1192.01	−0.0789259
$612$	12703.9	0.839095
$613$	5733.14	0.377748	0.188874	−	0.982001i	$-0.439516\pi$
$613$	5733.14	0.377748	0.188874	+	0.982001i	$0.439516\pi$
$614$	9672.18	0.635729
$615$	2752.49	0.180473
$616$	5515.99	0.360788
$617$	15642.1	1.02063	0.510314	−	0.859988i	$-0.329529\pi$
$617$	15642.1	1.02063	0.510314	+	0.859988i	$0.329529\pi$
$618$	6858.91	0.446449
$619$	−7467.40	−0.484879	−0.242440	−	0.970167i	$-0.577948\pi$
$619$	−7467.40	−0.484879	−0.242440	+	0.970167i	$0.577948\pi$
$620$	4636.74	0.300348
$621$	−3138.60	−0.202814
$622$	33116.1	2.13478
$623$	−23220.4	−1.49327
$624$	349.413	0.0224162
$625$	12647.4	0.809432
$626$	30233.6	1.93031
$627$	1150.01	0.0732489
$628$	−654.416	−0.0415829
$629$	−51224.2	−3.24713
$630$	−3595.82	−0.227399
$631$	−1486.38	−0.0937745	−0.0468872	−	0.998900i	$-0.514930\pi$
$631$	−1486.38	−0.0937745	−0.0468872	+	0.998900i	$0.514930\pi$
$632$	6060.87	0.381469
$633$	3154.91	0.198099
$634$	−4089.35	−0.256165
$635$	−2829.78	−0.176845
$636$	−170.826	−0.0106505
$637$	3408.74	0.212024
$638$	−3380.21	−0.209755
$639$	441.728	0.0273466
$640$	5192.58	0.320711
$641$	12386.0	0.763211	0.381606	−	0.924325i	$-0.375371\pi$
$641$	12386.0	0.763211	0.381606	+	0.924325i	$0.375371\pi$
$642$	−2017.87	−0.124048
$643$	−14458.1	−0.886737	−0.443369	−	0.896339i	$-0.646217\pi$
$643$	−14458.1	−0.886737	−0.443369	+	0.896339i	$0.646217\pi$
$644$	42652.3	2.60984
$645$	−2743.75	−0.167496
$646$	−18801.8	−1.14512
$647$	15792.8	0.959625	0.479813	−	0.877371i	$-0.340705\pi$
$647$	15792.8	0.959625	0.479813	+	0.877371i	$0.340705\pi$
$648$	−1281.41	−0.0776828
$649$	−4470.87	−0.270412
$650$	2663.89	0.160748
$651$	−13370.5	−0.804965
$652$	−569.909	−0.0342321
$653$	−3179.93	−0.190567	−0.0952837	−	0.995450i	$-0.530376\pi$
$653$	−3179.93	−0.190567	−0.0952837	+	0.995450i	$0.530376\pi$
$654$	28807.3	1.72240
$655$	1099.13	0.0655672
$656$	7281.96	0.433404
$657$	7072.96	0.420003
$658$	32453.6	1.92276
$659$	11593.5	0.685308	0.342654	−	0.939462i	$-0.388674\pi$
$659$	11593.5	0.685308	0.342654	+	0.939462i	$0.388674\pi$
$660$	1088.25	0.0641817
$661$	3233.88	0.190293	0.0951464	−	0.995463i	$-0.469668\pi$
$661$	3233.88	0.190293	0.0951464	+	0.995463i	$0.469668\pi$
$662$	43449.9	2.55095
$663$	−1884.42	−0.110384
$664$	14715.8	0.860066
$665$	3146.93	0.183508
$666$	16727.1	0.973219
$667$	−8073.56	−0.468680
$668$	23946.9	1.38703
$669$	−11585.4	−0.669532
$670$	−1068.18	−0.0615929
$671$	6120.74	0.352144
$672$	−21548.0	−1.23695
$673$	−5495.72	−0.314776	−0.157388	−	0.987537i	$-0.550307\pi$
$673$	−5495.72	−0.314776	−0.157388	+	0.987537i	$0.550307\pi$
$674$	−2658.23	−0.151916
$675$	3155.87	0.179955
$676$	−25124.4	−1.42947
$677$	33836.7	1.92090	0.960451	−	0.278448i	$-0.0898200\pi$
$677$	33836.7	1.92090	0.960451	+	0.278448i	$0.0898200\pi$
$678$	−8579.82	−0.485997
$679$	−37133.6	−2.09876
$680$	−5495.75	−0.309930
$681$	2618.16	0.147325
$682$	6843.04	0.384214
$683$	−21080.3	−1.18099	−0.590493	−	0.807043i	$-0.701067\pi$
$683$	−21080.3	−1.18099	−0.590493	+	0.807043i	$0.701067\pi$
$684$	3630.56	0.202950
$685$	2520.78	0.140605
$686$	−44702.2	−2.48796
$687$	−5525.16	−0.306838
$688$	−7258.84	−0.402239
$689$	25.3393	0.00140109
$690$	4395.63	0.242520
$691$	11811.3	0.650253	0.325127	−	0.945671i	$-0.394593\pi$
$691$	11811.3	0.650253	0.325127	+	0.945671i	$0.394593\pi$
$692$	−6991.79	−0.384087
$693$	−3138.07	−0.172014
$694$	13907.8	0.760711
$695$	−3110.79	−0.169783
$696$	−3296.23	−0.179516
$697$	−39272.4	−2.13422
$698$	−3188.52	−0.172904
$699$	−11796.4	−0.638313
$700$	−42887.0	−2.31568
$701$	4244.99	0.228718	0.114359	−	0.993440i	$-0.463519\pi$
$701$	4244.99	0.228718	0.114359	+	0.993440i	$0.463519\pi$
$702$	615.353	0.0330841
$703$	−14639.0	−0.785376
$704$	9038.51	0.483880
$705$	1977.74	0.105654
$706$	−5340.81	−0.284708
$707$	−38711.5	−2.05926
$708$	−14114.4	−0.749227
$709$	−898.822	−0.0476107	−0.0238053	−	0.999717i	$-0.507578\pi$
$709$	−898.822	−0.0476107	−0.0238053	+	0.999717i	$0.507578\pi$
$710$	−618.643	−0.0327004
$711$	−3448.06	−0.181874
$712$	11589.0	0.609993
$713$	16344.5	0.858493
$714$	51305.0	2.68913
$715$	−161.424	−0.00844322
$716$	−24679.4	−1.28815
$717$	−14316.3	−0.745679
$718$	−38706.3	−2.01185
$719$	10741.8	0.557165	0.278582	−	0.960412i	$-0.410135\pi$
$719$	10741.8	0.557165	0.278582	+	0.960412i	$0.410135\pi$
$720$	−579.733	−0.0300074
$721$	16379.6	0.846061
$722$	24973.9	1.28730
$723$	−11966.5	−0.615546
$724$	−6822.30	−0.350206
$725$	8117.99	0.415855
$726$	1606.07	0.0821030
$727$	16794.2	0.856758	0.428379	−	0.903599i	$-0.359085\pi$
$727$	16794.2	0.856758	0.428379	+	0.903599i	$0.359085\pi$
$728$	−2583.06	−0.131503
$729$	729.000	0.0370370
$730$	−9905.73	−0.502229
$731$	39147.7	1.98075
$732$	19323.0	0.975681
$733$	8659.40	0.436347	0.218173	−	0.975910i	$-0.429990\pi$
$733$	8659.40	0.436347	0.218173	+	0.975910i	$0.429990\pi$
$734$	29778.4	1.49747
$735$	−5655.65	−0.283826
$736$	26340.8	1.31920
$737$	−932.197	−0.0465915
$738$	12824.3	0.639660
$739$	16705.7	0.831567	0.415783	−	0.909464i	$-0.363507\pi$
$739$	16705.7	0.831567	0.415783	+	0.909464i	$0.363507\pi$
$740$	−13852.7	−0.688157
$741$	−538.534	−0.0266984
$742$	−689.884	−0.0341327
$743$	1292.12	0.0637996	0.0318998	−	0.999491i	$-0.489844\pi$
$743$	1292.12	0.0637996	0.0318998	+	0.999491i	$0.489844\pi$
$744$	6673.03	0.328824
$745$	846.151	0.0416115
$746$	1006.09	0.0493773
$747$	−8371.90	−0.410056
$748$	−15527.0	−0.758990
$749$	−4818.83	−0.235082
$750$	−9146.53	−0.445312
$751$	−14980.4	−0.727886	−0.363943	−	0.931421i	$-0.618570\pi$
$751$	−14980.4	−0.727886	−0.363943	+	0.931421i	$0.618570\pi$
$752$	5232.30	0.253726
$753$	16422.7	0.794787
$754$	1582.90	0.0764535
$755$	−5378.25	−0.259251
$756$	−9906.82	−0.476597
$757$	3003.41	0.144202	0.0721010	−	0.997397i	$-0.477030\pi$
$757$	3003.41	0.144202	0.0721010	+	0.997397i	$0.477030\pi$
$758$	−50244.8	−2.40762
$759$	3836.06	0.183452
$760$	−1570.59	−0.0749621
$761$	−20375.0	−0.970555	−0.485277	−	0.874360i	$-0.661281\pi$
$761$	−20375.0	−0.970555	−0.485277	+	0.874360i	$0.661281\pi$
$762$	−13184.4	−0.626799
$763$	68794.1	3.26411
$764$	−25013.6	−1.18450
$765$	3126.56	0.147766
$766$	−47578.4	−2.24422
$767$	2093.65	0.0985621
$768$	4472.70	0.210149
$769$	−12372.4	−0.580184	−0.290092	−	0.956999i	$-0.593686\pi$
$769$	−12372.4	−0.580184	−0.290092	+	0.956999i	$0.593686\pi$
$770$	4394.90	0.205690
$771$	19302.0	0.901615
$772$	−17258.1	−0.804578
$773$	21023.6	0.978225	0.489113	−	0.872221i	$-0.337321\pi$
$773$	21023.6	0.978225	0.489113	+	0.872221i	$0.337321\pi$
$774$	−12783.6	−0.593664
$775$	−16434.4	−0.761732
$776$	18532.8	0.857331
$777$	39945.8	1.84433
$778$	51885.7	2.39099
$779$	−11223.4	−0.516198
$780$	−509.610	−0.0233935
$781$	−539.889	−0.0247359
$782$	−62716.6	−2.86795
$783$	1875.24	0.0855884
$784$	−14962.5	−0.681602
$785$	−161.058	−0.00732281
$786$	5121.02	0.232393
$787$	30286.2	1.37177	0.685886	−	0.727709i	$-0.259415\pi$
$787$	30286.2	1.37177	0.685886	+	0.727709i	$0.259415\pi$
$788$	−2668.51	−0.120637
$789$	−22767.0	−1.02728
$790$	4829.03	0.217480
$791$	−20489.3	−0.921007
$792$	1566.17	0.0702668
$793$	−2866.25	−0.128353
$794$	1592.37	0.0711729
$795$	−42.0420	−0.00187557
$796$	259.301	0.0115461
$797$	32337.8	1.43722	0.718610	−	0.695413i	$-0.244779\pi$
$797$	32337.8	1.43722	0.718610	+	0.695413i	$0.244779\pi$
$798$	14662.1	0.650415
$799$	−28218.3	−1.24943
$800$	−26485.7	−1.17052
$801$	−6593.03	−0.290828
$802$	17992.9	0.792207
$803$	−8644.72	−0.379907
$804$	−2942.92	−0.129091
$805$	10497.1	0.459596
$806$	−3204.50	−0.140042
$807$	−1434.53	−0.0625749
$808$	19320.3	0.841197
$809$	−891.707	−0.0387525	−0.0193762	−	0.999812i	$-0.506168\pi$
$809$	−891.707	−0.0387525	−0.0193762	+	0.999812i	$0.506168\pi$
$810$	−1020.97	−0.0442879
$811$	−10114.9	−0.437957	−0.218978	−	0.975730i	$-0.570272\pi$
$811$	−10114.9	−0.437957	−0.218978	+	0.975730i	$0.570272\pi$
$812$	−25483.8	−1.10136
$813$	366.970	0.0158305
$814$	−20444.3	−0.880309
$815$	−140.260	−0.00602833
$816$	8271.59	0.354857
$817$	11187.7	0.479080
$818$	59680.4	2.55095
$819$	1469.51	0.0626972
$820$	−10620.6	−0.452300
$821$	10833.5	0.460525	0.230262	−	0.973129i	$-0.426042\pi$
$821$	10833.5	0.460525	0.230262	+	0.973129i	$0.426042\pi$
$822$	11744.7	0.498351
$823$	31958.5	1.35359	0.676794	−	0.736173i	$-0.263369\pi$
$823$	31958.5	1.35359	0.676794	+	0.736173i	$0.263369\pi$
$824$	−8174.84	−0.345612
$825$	−3857.17	−0.162775
$826$	−57001.3	−2.40112
$827$	34847.3	1.46525	0.732624	−	0.680634i	$-0.238296\pi$
$827$	34847.3	1.46525	0.732624	+	0.680634i	$0.238296\pi$
$828$	12110.3	0.508289
$829$	6537.91	0.273910	0.136955	−	0.990577i	$-0.456268\pi$
$829$	6537.91	0.273910	0.136955	+	0.990577i	$0.456268\pi$
$830$	11724.9	0.490334
$831$	−24598.2	−1.02684
$832$	−4232.60	−0.176369
$833$	80694.5	3.35642
$834$	−14493.7	−0.601768
$835$	5893.56	0.244258
$836$	−4437.35	−0.183575
$837$	−3796.32	−0.156774
$838$	31148.5	1.28402
$839$	2710.34	0.111527	0.0557635	−	0.998444i	$-0.482241\pi$
$839$	2710.34	0.111527	0.0557635	+	0.998444i	$0.482241\pi$
$840$	4285.71	0.176037
$841$	−19565.2	−0.802215
$842$	−40579.7	−1.66089
$843$	−20831.4	−0.851092
$844$	−12173.3	−0.496471
$845$	−6183.35	−0.251732
$846$	9214.62	0.374474
$847$	3835.42	0.155592
$848$	−111.226	−0.00450414
$849$	−3105.41	−0.125533
$850$	63061.7	2.54470
$851$	−48830.8	−1.96698
$852$	−1704.42	−0.0685356
$853$	9759.32	0.391738	0.195869	−	0.980630i	$-0.437247\pi$
$853$	9759.32	0.391738	0.195869	+	0.980630i	$0.437247\pi$
$854$	78036.2	3.12687
$855$	893.515	0.0357398
$856$	2405.01	0.0960298
$857$	−13649.8	−0.544072	−0.272036	−	0.962287i	$-0.587697\pi$
$857$	−13649.8	−0.544072	−0.272036	+	0.962287i	$0.587697\pi$
$858$	−752.098	−0.0299257
$859$	7796.42	0.309674	0.154837	−	0.987940i	$-0.450515\pi$
$859$	7796.42	0.309674	0.154837	+	0.987940i	$0.450515\pi$
$860$	10586.8	0.419776
$861$	30625.5	1.21221
$862$	−4393.43	−0.173597
$863$	7183.57	0.283350	0.141675	−	0.989913i	$-0.454751\pi$
$863$	7183.57	0.283350	0.141675	+	0.989913i	$0.454751\pi$
$864$	−6118.16	−0.240907
$865$	−1720.75	−0.0676383
$866$	−16769.5	−0.658026
$867$	−29870.6	−1.17008
$868$	51590.5	2.01739
$869$	4214.30	0.164511
$870$	−2626.29	−0.102344
$871$	436.534	0.0169821
$872$	−34334.1	−1.33337
$873$	−10543.4	−0.408752
$874$	−17923.3	−0.693666
$875$	−21842.7	−0.843905
$876$	−27291.2	−1.05261
$877$	17063.1	0.656991	0.328495	−	0.944506i	$-0.393458\pi$
$877$	17063.1	0.656991	0.328495	+	0.944506i	$0.393458\pi$
$878$	22728.2	0.873620
$879$	18434.4	0.707369
$880$	708.562	0.0271428
$881$	−32174.9	−1.23042	−0.615210	−	0.788363i	$-0.710929\pi$
$881$	−32174.9	−1.23042	−0.615210	+	0.788363i	$0.710929\pi$
$882$	−26350.6	−1.00598
$883$	2843.68	0.108378	0.0541889	−	0.998531i	$-0.482743\pi$
$883$	2843.68	0.108378	0.0541889	+	0.998531i	$0.482743\pi$
$884$	7271.09	0.276644
$885$	−3473.69	−0.131940
$886$	−47238.9	−1.79122
$887$	−31417.8	−1.18930	−0.594649	−	0.803985i	$-0.702709\pi$
$887$	−31417.8	−1.18930	−0.594649	+	0.803985i	$0.702709\pi$
$888$	−19936.4	−0.753401
$889$	−31485.5	−1.18784
$890$	9233.59	0.347765
$891$	−891.000	−0.0335013
$892$	44702.5	1.67797
$893$	−8064.30	−0.302196
$894$	3942.35	0.147485
$895$	−6073.83	−0.226845
$896$	57775.1	2.15416
$897$	−1796.37	−0.0668664
$898$	−46588.6	−1.73127
$899$	−9765.47	−0.362288
$900$	−12177.0	−0.451000
$901$	599.852	0.0221798
$902$	−15674.1	−0.578594
$903$	−30528.2	−1.12505
$904$	10225.9	0.376227
$905$	−1679.03	−0.0616718
$906$	−25058.1	−0.918875
$907$	12253.1	0.448573	0.224287	−	0.974523i	$-0.427995\pi$
$907$	12253.1	0.448573	0.224287	+	0.974523i	$0.427995\pi$
$908$	−10102.2	−0.369223
$909$	−10991.4	−0.401059
$910$	−2058.07	−0.0749717
$911$	−48422.4	−1.76104	−0.880518	−	0.474012i	$-0.842805\pi$
$911$	−48422.4	−1.76104	−0.880518	+	0.474012i	$0.842805\pi$
$912$	2363.87	0.0858286
$913$	10232.3	0.370909
$914$	62262.9	2.25326
$915$	4755.57	0.171819
$916$	21318.9	0.768993
$917$	12229.4	0.440404
$918$	14567.1	0.523733
$919$	5546.18	0.199077	0.0995385	−	0.995034i	$-0.468263\pi$
$919$	5546.18	0.199077	0.0995385	+	0.995034i	$0.468263\pi$
$920$	−5238.96	−0.187743
$921$	6558.26	0.234638
$922$	136.349	0.00487030
$923$	252.822	0.00901598
$924$	12108.3	0.431098
$925$	49099.5	1.74528
$926$	−77831.3	−2.76209
$927$	4650.71	0.164778
$928$	−15738.0	−0.556709
$929$	−35684.5	−1.26025	−0.630125	−	0.776494i	$-0.716996\pi$
$929$	−35684.5	−1.26025	−0.630125	+	0.776494i	$0.716996\pi$
$930$	5316.78	0.187467
$931$	23061.1	0.811811
$932$	45516.7	1.59973
$933$	22454.5	0.787918
$934$	−58726.0	−2.05736
$935$	−3821.35	−0.133659
$936$	−733.413	−0.0256115
$937$	−48903.6	−1.70503	−0.852514	−	0.522705i	$-0.824923\pi$
$937$	−48903.6	−1.70503	−0.852514	+	0.522705i	$0.824923\pi$
$938$	−11885.0	−0.413710
$939$	20500.0	0.712451
$940$	−7631.17	−0.264789
$941$	−23741.9	−0.822490	−0.411245	−	0.911525i	$-0.634906\pi$
$941$	−23741.9	−0.822490	−0.411245	+	0.911525i	$0.634906\pi$
$942$	−750.396	−0.0259546
$943$	−37437.4	−1.29282
$944$	−9189.97	−0.316852
$945$	−2438.16	−0.0839295
$946$	15624.4	0.536989
$947$	37612.4	1.29064	0.645321	−	0.763911i	$-0.276724\pi$
$947$	37612.4	1.29064	0.645321	+	0.763911i	$0.276724\pi$
$948$	13304.4	0.455810
$949$	4048.20	0.138472
$950$	18021.9	0.615482
$951$	−2772.80	−0.0945469
$952$	−61148.2	−2.08175
$953$	−48294.3	−1.64156	−0.820779	−	0.571246i	$-0.806460\pi$
$953$	−48294.3	−1.64156	−0.820779	+	0.571246i	$0.806460\pi$
$954$	−195.880	−0.00664765
$955$	−6156.09	−0.208593
$956$	55239.8	1.86881
$957$	−2291.96	−0.0774176
$958$	−11046.4	−0.372539
$959$	28047.4	0.944419
$960$	7022.57	0.236096
$961$	−10021.4	−0.336389
$962$	9573.76	0.320863
$963$	−1368.22	−0.0457843
$964$	46173.1	1.54267
$965$	−4247.39	−0.141687
$966$	48907.8	1.62897
$967$	1840.92	0.0612204	0.0306102	−	0.999531i	$-0.490255\pi$
$967$	1840.92	0.0612204	0.0306102	+	0.999531i	$0.490255\pi$
$968$	−1914.20	−0.0635587
$969$	−12748.6	−0.422647
$970$	14766.1	0.488775
$971$	31461.8	1.03981	0.519906	−	0.854223i	$-0.325967\pi$
$971$	31461.8	1.03981	0.519906	+	0.854223i	$0.325967\pi$
$972$	−2812.86	−0.0928217
$973$	−34612.1	−1.14040
$974$	15328.1	0.504254
$975$	1806.26	0.0593298
$976$	12581.3	0.412620
$977$	−7040.11	−0.230535	−0.115268	−	0.993334i	$-0.536773\pi$
$977$	−7040.11	−0.230535	−0.115268	+	0.993334i	$0.536773\pi$
$978$	−653.494	−0.0213665
$979$	8058.15	0.263064
$980$	21822.5	0.711320
$981$	19532.9	0.635715
$982$	71784.4	2.33272
$983$	−24610.9	−0.798541	−0.399270	−	0.916833i	$-0.630737\pi$
$983$	−24610.9	−0.798541	−0.399270	+	0.916833i	$0.630737\pi$
$984$	−15284.7	−0.495183
$985$	−656.744	−0.0212443
$986$	37471.8	1.21029
$987$	22005.3	0.709662
$988$	2077.95	0.0669112
$989$	37318.5	1.19986
$990$	1247.85	0.0400599
$991$	−40003.3	−1.28229	−0.641144	−	0.767421i	$-0.721540\pi$
$991$	−40003.3	−1.28229	−0.641144	+	0.767421i	$0.721540\pi$
$992$	31860.8	1.01974
$993$	29461.4	0.941519
$994$	−6883.31	−0.219643
$995$	63.8165	0.00203329
$996$	32303.2	1.02768
$997$	−7342.61	−0.233242	−0.116621	−	0.993176i	$-0.537206\pi$
$997$	−7342.61	−0.233242	−0.116621	+	0.993176i	$0.537206\pi$
$998$	−44216.9	−1.40247
$999$	11341.9	0.359201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.a.c.1.1	✓	2
3.2	odd	2		99.4.a.f.1.2		2
4.3	odd	2		528.4.a.p.1.2		2
5.2	odd	4		825.4.c.h.199.2		4
5.3	odd	4		825.4.c.h.199.3		4
5.4	even	2		825.4.a.l.1.2		2
7.6	odd	2		1617.4.a.k.1.1		2
8.3	odd	2		2112.4.a.bg.1.1		2
8.5	even	2		2112.4.a.bn.1.1		2
11.10	odd	2		363.4.a.i.1.2		2
12.11	even	2		1584.4.a.bj.1.1		2
15.14	odd	2		2475.4.a.p.1.1		2
33.32	even	2		1089.4.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.a.c.1.1	✓	2	1.1	even	1	trivial
99.4.a.f.1.2		2	3.2	odd	2
363.4.a.i.1.2		2	11.10	odd	2
528.4.a.p.1.2		2	4.3	odd	2
825.4.a.l.1.2		2	5.4	even	2
825.4.c.h.199.2		4	5.2	odd	4
825.4.c.h.199.3		4	5.3	odd	4
1089.4.a.u.1.1		2	33.32	even	2
1584.4.a.bj.1.1		2	12.11	even	2
1617.4.a.k.1.1		2	7.6	odd	2
2112.4.a.bg.1.1		2	8.3	odd	2
2112.4.a.bn.1.1		2	8.5	even	2
2475.4.a.p.1.1		2	15.14	odd	2

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q-4.42443 q^{2} -3.00000 q^{3} +11.5756 q^{4} +2.84886 q^{5} +13.2733 q^{6} +31.6977 q^{7} -15.8199 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.42443 q^{2} -3.00000 q^{3} +11.5756 q^{4} +2.84886 q^{5} +13.2733 q^{6} +31.6977 q^{7} -15.8199 q^{8} +9.00000 q^{9} -12.6046 q^{10} -11.0000 q^{11} -34.7267 q^{12} +5.15114 q^{13} -140.244 q^{14} -8.54657 q^{15} -22.6107 q^{16} +121.942 q^{17} -39.8199 q^{18} +34.8489 q^{19} +32.9772 q^{20} -95.0931 q^{21} +48.6687 q^{22} +116.244 q^{23} +47.4596 q^{24} -116.884 q^{25} -22.7909 q^{26} -27.0000 q^{27} +366.919 q^{28} -69.4534 q^{29} +37.8137 q^{30} +140.605 q^{31} +226.598 q^{32} +33.0000 q^{33} -539.524 q^{34} +90.3023 q^{35} +104.180 q^{36} -420.070 q^{37} -154.186 q^{38} -15.4534 q^{39} -45.0685 q^{40} -322.058 q^{41} +420.733 q^{42} +321.035 q^{43} -127.331 q^{44} +25.6397 q^{45} -514.315 q^{46} -231.408 q^{47} +67.8322 q^{48} +661.745 q^{49} +517.145 q^{50} -365.826 q^{51} +59.6274 q^{52} +4.91916 q^{53} +119.460 q^{54} -31.3374 q^{55} -501.453 q^{56} -104.547 q^{57} +307.292 q^{58} +406.443 q^{59} -98.9315 q^{60} -556.431 q^{61} -622.095 q^{62} +285.279 q^{63} -821.683 q^{64} +14.6749 q^{65} -146.006 q^{66} +84.7452 q^{67} +1411.55 q^{68} -348.733 q^{69} -399.536 q^{70} +49.0808 q^{71} -142.379 q^{72} +785.884 q^{73} +1858.57 q^{74} +350.652 q^{75} +403.395 q^{76} -348.675 q^{77} +68.3726 q^{78} -383.118 q^{79} -64.4147 q^{80} +81.0000 q^{81} +1424.92 q^{82} -930.211 q^{83} -1100.76 q^{84} +347.395 q^{85} -1420.40 q^{86} +208.360 q^{87} +174.018 q^{88} -732.559 q^{89} -113.441 q^{90} +163.279 q^{91} +1345.59 q^{92} -421.814 q^{93} +1023.85 q^{94} +99.2794 q^{95} -679.795 q^{96} -1171.49 q^{97} -2927.84 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 6 q^{3} + 33 q^{4} - 14 q^{5} - 3 q^{6} + 24 q^{7} + 57 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + q^2 - 6 * q^3 + 33 * q^4 - 14 * q^5 - 3 * q^6 + 24 * q^7 + 57 * q^8 + 18 * q^9	\( 2 q + q^{2} - 6 q^{3} + 33 q^{4} - 14 q^{5} - 3 q^{6} + 24 q^{7} + 57 q^{8} + 18 q^{9} - 104 q^{10} - 22 q^{11} - 99 q^{12} + 30 q^{13} - 182 q^{14} + 42 q^{15} + 201 q^{16} + 106 q^{17} + 9 q^{18} + 50 q^{19} - 328 q^{20} - 72 q^{21} - 11 q^{22} + 134 q^{23} - 171 q^{24} + 42 q^{25} + 112 q^{26} - 54 q^{27} + 202 q^{28} - 198 q^{29} + 312 q^{30} + 360 q^{31} + 857 q^{32} + 66 q^{33} - 626 q^{34} + 220 q^{35} + 297 q^{36} - 328 q^{37} - 72 q^{38} - 90 q^{39} - 1272 q^{40} - 782 q^{41} + 546 q^{42} + 386 q^{43} - 363 q^{44} - 126 q^{45} - 418 q^{46} + 266 q^{47} - 603 q^{48} + 378 q^{49} + 1379 q^{50} - 318 q^{51} + 592 q^{52} - 522 q^{53} - 27 q^{54} + 154 q^{55} - 1062 q^{56} - 150 q^{57} - 390 q^{58} - 172 q^{59} + 984 q^{60} - 778 q^{61} + 568 q^{62} + 216 q^{63} + 809 q^{64} - 404 q^{65} + 33 q^{66} - 776 q^{67} + 1070 q^{68} - 402 q^{69} + 304 q^{70} + 630 q^{71} + 513 q^{72} + 1296 q^{73} + 2358 q^{74} - 126 q^{75} + 728 q^{76} - 264 q^{77} - 336 q^{78} + 652 q^{79} - 3832 q^{80} + 162 q^{81} - 1070 q^{82} - 324 q^{83} - 606 q^{84} + 616 q^{85} - 1068 q^{86} + 594 q^{87} - 627 q^{88} - 756 q^{89} - 936 q^{90} - 28 q^{91} + 1726 q^{92} - 1080 q^{93} + 3722 q^{94} - 156 q^{95} - 2571 q^{96} - 452 q^{97} - 4467 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q + q^2 - 6 * q^3 + 33 * q^4 - 14 * q^5 - 3 * q^6 + 24 * q^7 + 57 * q^8 + 18 * q^9 - 104 * q^10 - 22 * q^11 - 99 * q^12 + 30 * q^13 - 182 * q^14 + 42 * q^15 + 201 * q^16 + 106 * q^17 + 9 * q^18 + 50 * q^19 - 328 * q^20 - 72 * q^21 - 11 * q^22 + 134 * q^23 - 171 * q^24 + 42 * q^25 + 112 * q^26 - 54 * q^27 + 202 * q^28 - 198 * q^29 + 312 * q^30 + 360 * q^31 + 857 * q^32 + 66 * q^33 - 626 * q^34 + 220 * q^35 + 297 * q^36 - 328 * q^37 - 72 * q^38 - 90 * q^39 - 1272 * q^40 - 782 * q^41 + 546 * q^42 + 386 * q^43 - 363 * q^44 - 126 * q^45 - 418 * q^46 + 266 * q^47 - 603 * q^48 + 378 * q^49 + 1379 * q^50 - 318 * q^51 + 592 * q^52 - 522 * q^53 - 27 * q^54 + 154 * q^55 - 1062 * q^56 - 150 * q^57 - 390 * q^58 - 172 * q^59 + 984 * q^60 - 778 * q^61 + 568 * q^62 + 216 * q^63 + 809 * q^64 - 404 * q^65 + 33 * q^66 - 776 * q^67 + 1070 * q^68 - 402 * q^69 + 304 * q^70 + 630 * q^71 + 513 * q^72 + 1296 * q^73 + 2358 * q^74 - 126 * q^75 + 728 * q^76 - 264 * q^77 - 336 * q^78 + 652 * q^79 - 3832 * q^80 + 162 * q^81 - 1070 * q^82 - 324 * q^83 - 606 * q^84 + 616 * q^85 - 1068 * q^86 + 594 * q^87 - 627 * q^88 - 756 * q^89 - 936 * q^90 - 28 * q^91 + 1726 * q^92 - 1080 * q^93 + 3722 * q^94 - 156 * q^95 - 2571 * q^96 - 452 * q^97 - 4467 * q^98 - 198 * q^99

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