LMFDB - Embedded newform 4033.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34943 q^{2} -2.83343 q^{3} +3.51983 q^{4} -1.24434 q^{5} +6.65694 q^{6} +2.59127 q^{7} -3.57074 q^{8} +5.02830 q^{9} +O(q^{10})$	\(q-2.34943 q^{2} -2.83343 q^{3} +3.51983 q^{4} -1.24434 q^{5} +6.65694 q^{6} +2.59127 q^{7} -3.57074 q^{8} +5.02830 q^{9} +2.92348 q^{10} +1.09839 q^{11} -9.97318 q^{12} +0.239734 q^{13} -6.08801 q^{14} +3.52573 q^{15} +1.34955 q^{16} -4.85012 q^{17} -11.8137 q^{18} -7.88283 q^{19} -4.37985 q^{20} -7.34217 q^{21} -2.58060 q^{22} +6.03982 q^{23} +10.1174 q^{24} -3.45163 q^{25} -0.563239 q^{26} -5.74704 q^{27} +9.12083 q^{28} +2.81932 q^{29} -8.28347 q^{30} +3.58196 q^{31} +3.97080 q^{32} -3.11221 q^{33} +11.3950 q^{34} -3.22441 q^{35} +17.6988 q^{36} -1.00000 q^{37} +18.5202 q^{38} -0.679268 q^{39} +4.44320 q^{40} +0.0870684 q^{41} +17.2499 q^{42} -6.45930 q^{43} +3.86615 q^{44} -6.25690 q^{45} -14.1902 q^{46} +11.8836 q^{47} -3.82386 q^{48} -0.285324 q^{49} +8.10937 q^{50} +13.7425 q^{51} +0.843823 q^{52} +9.96187 q^{53} +13.5023 q^{54} -1.36677 q^{55} -9.25275 q^{56} +22.3354 q^{57} -6.62379 q^{58} +7.62537 q^{59} +12.4100 q^{60} +5.07350 q^{61} -8.41558 q^{62} +13.0297 q^{63} -12.0282 q^{64} -0.298310 q^{65} +7.31192 q^{66} -12.6458 q^{67} -17.0716 q^{68} -17.1134 q^{69} +7.57553 q^{70} -15.7528 q^{71} -17.9548 q^{72} +12.9091 q^{73} +2.34943 q^{74} +9.77993 q^{75} -27.7462 q^{76} +2.84623 q^{77} +1.59589 q^{78} -9.15991 q^{79} -1.67930 q^{80} +1.19891 q^{81} -0.204561 q^{82} -9.55755 q^{83} -25.8432 q^{84} +6.03518 q^{85} +15.1757 q^{86} -7.98832 q^{87} -3.92207 q^{88} +7.70256 q^{89} +14.7002 q^{90} +0.621215 q^{91} +21.2592 q^{92} -10.1492 q^{93} -27.9196 q^{94} +9.80889 q^{95} -11.2510 q^{96} +0.0228065 q^{97} +0.670349 q^{98} +5.52304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * 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 $

$2$	−2.34943	−1.66130	−0.830650	−	0.556795i	$-0.812031\pi$
$2$	−2.34943	−1.66130	−0.830650	+	0.556795i	$0.812031\pi$
$3$	−2.83343	−1.63588	−0.817940	−	0.575304i	$-0.804884\pi$
$3$	−2.83343	−1.63588	−0.817940	+	0.575304i	$0.804884\pi$
$4$	3.51983	1.75992
$5$	−1.24434	−0.556484	−0.278242	−	0.960511i	$-0.589752\pi$
$5$	−1.24434	−0.556484	−0.278242	+	0.960511i	$0.589752\pi$
$6$	6.65694	2.71769
$7$	2.59127	0.979408	0.489704	−	0.871889i	$-0.337105\pi$
$7$	2.59127	0.979408	0.489704	+	0.871889i	$0.337105\pi$
$8$	−3.57074	−1.26245
$9$	5.02830	1.67610
$10$	2.92348	0.924486
$11$	1.09839	0.331177	0.165589	−	0.986195i	$-0.447048\pi$
$11$	1.09839	0.331177	0.165589	+	0.986195i	$0.447048\pi$
$12$	−9.97318	−2.87901
$13$	0.239734	0.0664902	0.0332451	−	0.999447i	$-0.489416\pi$
$13$	0.239734	0.0664902	0.0332451	+	0.999447i	$0.489416\pi$
$14$	−6.08801	−1.62709
$15$	3.52573	0.910340
$16$	1.34955	0.337388
$17$	−4.85012	−1.17633	−0.588164	−	0.808742i	$-0.700149\pi$
$17$	−4.85012	−1.17633	−0.588164	+	0.808742i	$0.700149\pi$
$18$	−11.8137	−2.78450
$19$	−7.88283	−1.80845	−0.904223	−	0.427061i	$-0.859549\pi$
$19$	−7.88283	−1.80845	−0.904223	+	0.427061i	$0.859549\pi$
$20$	−4.37985	−0.979365
$21$	−7.34217	−1.60219
$22$	−2.58060	−0.550185
$23$	6.03982	1.25939	0.629695	−	0.776843i	$-0.283180\pi$
$23$	6.03982	1.25939	0.629695	+	0.776843i	$0.283180\pi$
$24$	10.1174	2.06521
$25$	−3.45163	−0.690326
$26$	−0.563239	−0.110460
$27$	−5.74704	−1.10602
$28$	9.12083	1.72368
$29$	2.81932	0.523534	0.261767	−	0.965131i	$-0.415695\pi$
$29$	2.81932	0.523534	0.261767	+	0.965131i	$0.415695\pi$
$30$	−8.28347	−1.51235
$31$	3.58196	0.643339	0.321670	−	0.946852i	$-0.395756\pi$
$31$	3.58196	0.643339	0.321670	+	0.946852i	$0.395756\pi$
$32$	3.97080	0.701945
$33$	−3.11221	−0.541766
$34$	11.3950	1.95423
$35$	−3.22441	−0.545025
$36$	17.6988	2.94980
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	18.5202	3.00437
$39$	−0.679268	−0.108770
$40$	4.44320	0.702532
$41$	0.0870684	0.0135978	0.00679890	−	0.999977i	$-0.497836\pi$
$41$	0.0870684	0.0135978	0.00679890	+	0.999977i	$0.497836\pi$
$42$	17.2499	2.66172
$43$	−6.45930	−0.985033	−0.492517	−	0.870303i	$-0.663923\pi$
$43$	−6.45930	−0.985033	−0.492517	+	0.870303i	$0.663923\pi$
$44$	3.86615	0.582844
$45$	−6.25690	−0.932723
$46$	−14.1902	−2.09222
$47$	11.8836	1.73339	0.866697	−	0.498835i	$-0.166239\pi$
$47$	11.8836	1.73339	0.866697	+	0.498835i	$0.166239\pi$
$48$	−3.82386	−0.551926
$49$	−0.285324	−0.0407606
$50$	8.10937	1.14684
$51$	13.7425	1.92433
$52$	0.843823	0.117017
$53$	9.96187	1.36837	0.684184	−	0.729309i	$-0.260158\pi$
$53$	9.96187	1.36837	0.684184	+	0.729309i	$0.260158\pi$
$54$	13.5023	1.83743
$55$	−1.36677	−0.184295
$56$	−9.25275	−1.23645
$57$	22.3354	2.95840
$58$	−6.62379	−0.869746
$59$	7.62537	0.992739	0.496369	−	0.868111i	$-0.334666\pi$
$59$	7.62537	0.992739	0.496369	+	0.868111i	$0.334666\pi$
$60$	12.4100	1.60212
$61$	5.07350	0.649595	0.324797	−	0.945784i	$-0.394704\pi$
$61$	5.07350	0.649595	0.324797	+	0.945784i	$0.394704\pi$
$62$	−8.41558	−1.06878
$63$	13.0297	1.64159
$64$	−12.0282	−1.50353
$65$	−0.298310	−0.0370007
$66$	7.31192	0.900036
$67$	−12.6458	−1.54493	−0.772465	−	0.635057i	$-0.780977\pi$
$67$	−12.6458	−1.54493	−0.772465	+	0.635057i	$0.780977\pi$
$68$	−17.0716	−2.07024
$69$	−17.1134	−2.06021
$70$	7.57553	0.905449
$71$	−15.7528	−1.86952	−0.934758	−	0.355285i	$-0.884384\pi$
$71$	−15.7528	−1.86952	−0.934758	+	0.355285i	$0.884384\pi$
$72$	−17.9548	−2.11599
$73$	12.9091	1.51089	0.755446	−	0.655211i	$-0.227420\pi$
$73$	12.9091	1.51089	0.755446	+	0.655211i	$0.227420\pi$
$74$	2.34943	0.273116
$75$	9.77993	1.12929
$76$	−27.7462	−3.18271
$77$	2.84623	0.324358
$78$	1.59589	0.180700
$79$	−9.15991	−1.03057	−0.515285	−	0.857019i	$-0.672314\pi$
$79$	−9.15991	−1.03057	−0.515285	+	0.857019i	$0.672314\pi$
$80$	−1.67930	−0.187751
$81$	1.19891	0.133212
$82$	−0.204561	−0.0225900
$83$	−9.55755	−1.04908	−0.524539	−	0.851386i	$-0.675762\pi$
$83$	−9.55755	−1.04908	−0.524539	+	0.851386i	$0.675762\pi$
$84$	−25.8432	−2.81972
$85$	6.03518	0.654607
$86$	15.1757	1.63644
$87$	−7.98832	−0.856438
$88$	−3.92207	−0.418094
$89$	7.70256	0.816470	0.408235	−	0.912877i	$-0.366144\pi$
$89$	7.70256	0.816470	0.408235	+	0.912877i	$0.366144\pi$
$90$	14.7002	1.54953
$91$	0.621215	0.0651210
$92$	21.2592	2.21642
$93$	−10.1492	−1.05243
$94$	−27.9196	−2.87969
$95$	9.80889	1.00637
$96$	−11.2510	−1.14830
$97$	0.0228065	0.00231565	0.00115783	−	0.999999i	$-0.499631\pi$
$97$	0.0228065	0.00231565	0.00115783	+	0.999999i	$0.499631\pi$
$98$	0.670349	0.0677155
$99$	5.52304	0.555086
$100$	−12.1492	−1.21492
$101$	−3.22833	−0.321231	−0.160615	−	0.987017i	$-0.551348\pi$
$101$	−3.22833	−0.321231	−0.160615	+	0.987017i	$0.551348\pi$
$102$	−32.2870	−3.19689
$103$	4.33270	0.426913	0.213457	−	0.976953i	$-0.431528\pi$
$103$	4.33270	0.426913	0.213457	+	0.976953i	$0.431528\pi$
$104$	−0.856028	−0.0839405
$105$	9.13612	0.891594
$106$	−23.4047	−2.27327
$107$	−7.57758	−0.732552	−0.366276	−	0.930506i	$-0.619367\pi$
$107$	−7.57758	−0.732552	−0.366276	+	0.930506i	$0.619367\pi$
$108$	−20.2286	−1.94650
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	3.21113	0.306169
$111$	2.83343	0.268937
$112$	3.49706	0.330441
$113$	7.02534	0.660889	0.330444	−	0.943825i	$-0.392801\pi$
$113$	7.02534	0.660889	0.330444	+	0.943825i	$0.392801\pi$
$114$	−52.4756	−4.91479
$115$	−7.51557	−0.700830
$116$	9.92352	0.921375
$117$	1.20545	0.111444
$118$	−17.9153	−1.64924
$119$	−12.5680	−1.15210
$120$	−12.5895	−1.14926
$121$	−9.79354	−0.890322
$122$	−11.9198	−1.07917
$123$	−0.246702	−0.0222444
$124$	12.6079	1.13222
$125$	10.5167	0.940639
$126$	−30.6124	−2.72717
$127$	6.88701	0.611124	0.305562	−	0.952172i	$-0.401156\pi$
$127$	6.88701	0.611124	0.305562	+	0.952172i	$0.401156\pi$
$128$	20.3179	1.79587
$129$	18.3019	1.61140
$130$	0.700858	0.0614693
$131$	−4.77768	−0.417428	−0.208714	−	0.977977i	$-0.566928\pi$
$131$	−4.77768	−0.417428	−0.208714	+	0.977977i	$0.566928\pi$
$132$	−10.9545	−0.953463
$133$	−20.4265	−1.77121
$134$	29.7104	2.56659
$135$	7.15125	0.615482
$136$	17.3185	1.48505
$137$	3.71961	0.317788	0.158894	−	0.987296i	$-0.449207\pi$
$137$	3.71961	0.317788	0.158894	+	0.987296i	$0.449207\pi$
$138$	40.2067	3.42262
$139$	0.460045	0.0390205	0.0195103	−	0.999810i	$-0.493789\pi$
$139$	0.460045	0.0390205	0.0195103	+	0.999810i	$0.493789\pi$
$140$	−11.3494	−0.959198
$141$	−33.6712	−2.83562
$142$	37.0102	3.10583
$143$	0.263322	0.0220201
$144$	6.78596	0.565497
$145$	−3.50818	−0.291338
$146$	−30.3290	−2.51004
$147$	0.808444	0.0666794
$148$	−3.51983	−0.289328
$149$	−14.4721	−1.18560	−0.592799	−	0.805350i	$-0.701977\pi$
$149$	−14.4721	−1.18560	−0.592799	+	0.805350i	$0.701977\pi$
$150$	−22.9773	−1.87609
$151$	−14.6519	−1.19235	−0.596176	−	0.802854i	$-0.703314\pi$
$151$	−14.6519	−1.19235	−0.596176	+	0.802854i	$0.703314\pi$
$152$	28.1476	2.28307
$153$	−24.3879	−1.97164
$154$	−6.68702	−0.538855
$155$	−4.45716	−0.358008
$156$	−2.39091	−0.191426
$157$	−20.1254	−1.60618	−0.803092	−	0.595855i	$-0.796813\pi$
$157$	−20.1254	−1.60618	−0.803092	+	0.595855i	$0.796813\pi$
$158$	21.5206	1.71209
$159$	−28.2262	−2.23848
$160$	−4.94101	−0.390621
$161$	15.6508	1.23346
$162$	−2.81676	−0.221306
$163$	18.5795	1.45526	0.727628	−	0.685972i	$-0.240623\pi$
$163$	18.5795	1.45526	0.727628	+	0.685972i	$0.240623\pi$
$164$	0.306466	0.0239310
$165$	3.87263	0.301484
$166$	22.4548	1.74283
$167$	25.3430	1.96110	0.980549	−	0.196275i	$-0.0628846\pi$
$167$	25.3430	1.96110	0.980549	+	0.196275i	$0.0628846\pi$
$168$	26.2170	2.02268
$169$	−12.9425	−0.995579
$170$	−14.1793	−1.08750
$171$	−39.6373	−3.03114
$172$	−22.7356	−1.73358
$173$	7.41351	0.563638	0.281819	−	0.959468i	$-0.409062\pi$
$173$	7.41351	0.563638	0.281819	+	0.959468i	$0.409062\pi$
$174$	18.7680	1.42280
$175$	−8.94410	−0.676110
$176$	1.48234	0.111735
$177$	−21.6059	−1.62400
$178$	−18.0966	−1.35640
$179$	4.51697	0.337614	0.168807	−	0.985649i	$-0.446009\pi$
$179$	4.51697	0.337614	0.168807	+	0.985649i	$0.446009\pi$
$180$	−22.0232	−1.64151
$181$	23.4177	1.74062	0.870312	−	0.492501i	$-0.163917\pi$
$181$	23.4177	1.74062	0.870312	+	0.492501i	$0.163917\pi$
$182$	−1.45950	−0.108186
$183$	−14.3754	−1.06266
$184$	−21.5666	−1.58991
$185$	1.24434	0.0914854
$186$	23.8449	1.74839
$187$	−5.32733	−0.389573
$188$	41.8281	3.05063
$189$	−14.8921	−1.08324
$190$	−23.0453	−1.67188
$191$	23.6543	1.71156	0.855782	−	0.517337i	$-0.173076\pi$
$191$	23.6543	1.71156	0.855782	+	0.517337i	$0.173076\pi$
$192$	34.0811	2.45959
$193$	5.43382	0.391135	0.195568	−	0.980690i	$-0.437345\pi$
$193$	5.43382	0.391135	0.195568	+	0.980690i	$0.437345\pi$
$194$	−0.0535824	−0.00384699
$195$	0.845238	0.0605288
$196$	−1.00429	−0.0717352
$197$	−6.69045	−0.476675	−0.238337	−	0.971182i	$-0.576602\pi$
$197$	−6.69045	−0.476675	−0.238337	+	0.971182i	$0.576602\pi$
$198$	−12.9760	−0.922165
$199$	−7.13162	−0.505547	−0.252774	−	0.967525i	$-0.581343\pi$
$199$	−7.13162	−0.505547	−0.252774	+	0.967525i	$0.581343\pi$
$200$	12.3249	0.871500
$201$	35.8309	2.52732
$202$	7.58475	0.533661
$203$	7.30561	0.512753
$204$	48.3712	3.38666
$205$	−0.108342	−0.00756696
$206$	−10.1794	−0.709231
$207$	30.3700	2.11086
$208$	0.323534	0.0224330
$209$	−8.65843	−0.598916
$210$	−21.4647	−1.48121
$211$	−13.4435	−0.925492	−0.462746	−	0.886491i	$-0.653136\pi$
$211$	−13.4435	−0.925492	−0.462746	+	0.886491i	$0.653136\pi$
$212$	35.0641	2.40821
$213$	44.6344	3.05830
$214$	17.8030	1.21699
$215$	8.03753	0.548155
$216$	20.5212	1.39629
$217$	9.28183	0.630092
$218$	−2.34943	−0.159124
$219$	−36.5769	−2.47164
$220$	−4.81079	−0.324343
$221$	−1.16274	−0.0782143
$222$	−6.65694	−0.446785
$223$	−7.99246	−0.535215	−0.267607	−	0.963528i	$-0.586233\pi$
$223$	−7.99246	−0.535215	−0.267607	+	0.963528i	$0.586233\pi$
$224$	10.2894	0.687490
$225$	−17.3558	−1.15706
$226$	−16.5056	−1.09793
$227$	−3.76213	−0.249701	−0.124851	−	0.992176i	$-0.539845\pi$
$227$	−3.76213	−0.249701	−0.124851	+	0.992176i	$0.539845\pi$
$228$	78.6169	5.20653
$229$	20.6705	1.36595	0.682974	−	0.730443i	$-0.260686\pi$
$229$	20.6705	1.36595	0.682974	+	0.730443i	$0.260686\pi$
$230$	17.6573	1.16429
$231$	−8.06457	−0.530610
$232$	−10.0670	−0.660934
$233$	−5.86757	−0.384398	−0.192199	−	0.981356i	$-0.561562\pi$
$233$	−5.86757	−0.384398	−0.192199	+	0.981356i	$0.561562\pi$
$234$	−2.83213	−0.185142
$235$	−14.7871	−0.964606
$236$	26.8400	1.74714
$237$	25.9539	1.68589
$238$	29.5276	1.91399
$239$	22.6293	1.46376	0.731882	−	0.681431i	$-0.238642\pi$
$239$	22.6293	1.46376	0.731882	+	0.681431i	$0.238642\pi$
$240$	4.75817	0.307138
$241$	−27.9146	−1.79814	−0.899070	−	0.437805i	$-0.855756\pi$
$241$	−27.9146	−1.79814	−0.899070	+	0.437805i	$0.855756\pi$
$242$	23.0093	1.47909
$243$	13.8441	0.888099
$244$	17.8579	1.14323
$245$	0.355039	0.0226826
$246$	0.579609	0.0369545
$247$	−1.88978	−0.120244
$248$	−12.7903	−0.812183
$249$	27.0806	1.71616
$250$	−24.7082	−1.56268
$251$	−26.3640	−1.66408	−0.832039	−	0.554717i	$-0.812827\pi$
$251$	−26.3640	−1.66408	−0.832039	+	0.554717i	$0.812827\pi$
$252$	45.8623	2.88905
$253$	6.63408	0.417081
$254$	−16.1806	−1.01526
$255$	−17.1002	−1.07086
$256$	−23.6791	−1.47994
$257$	−14.7336	−0.919059	−0.459529	−	0.888163i	$-0.651982\pi$
$257$	−14.7336	−0.919059	−0.459529	+	0.888163i	$0.651982\pi$
$258$	−42.9992	−2.67701
$259$	−2.59127	−0.161014
$260$	−1.05000	−0.0651182
$261$	14.1764	0.877495
$262$	11.2248	0.693472
$263$	−10.9769	−0.676864	−0.338432	−	0.940991i	$-0.609896\pi$
$263$	−10.9769	−0.676864	−0.338432	+	0.940991i	$0.609896\pi$
$264$	11.1129	0.683952
$265$	−12.3959	−0.761475
$266$	47.9908	2.94250
$267$	−21.8246	−1.33565
$268$	−44.5111	−2.71895
$269$	−22.1587	−1.35104	−0.675521	−	0.737341i	$-0.736081\pi$
$269$	−22.1587	−1.35104	−0.675521	+	0.737341i	$0.736081\pi$
$270$	−16.8014	−1.02250
$271$	30.6249	1.86033	0.930166	−	0.367139i	$-0.119663\pi$
$271$	30.6249	1.86033	0.930166	+	0.367139i	$0.119663\pi$
$272$	−6.54550	−0.396879
$273$	−1.76017	−0.106530
$274$	−8.73898	−0.527941
$275$	−3.79124	−0.228620
$276$	−60.2362	−3.62580
$277$	−25.1698	−1.51231	−0.756155	−	0.654393i	$-0.772924\pi$
$277$	−25.1698	−1.51231	−0.756155	+	0.654393i	$0.772924\pi$
$278$	−1.08085	−0.0648248
$279$	18.0112	1.07830
$280$	11.5135	0.688065
$281$	−21.2509	−1.26772	−0.633862	−	0.773446i	$-0.718531\pi$
$281$	−21.2509	−1.26772	−0.633862	+	0.773446i	$0.718531\pi$
$282$	79.1081	4.71082
$283$	17.9933	1.06959	0.534796	−	0.844981i	$-0.320389\pi$
$283$	17.9933	1.06959	0.534796	+	0.844981i	$0.320389\pi$
$284$	−55.4473	−3.29019
$285$	−27.7928	−1.64630
$286$	−0.618656	−0.0365819
$287$	0.225618	0.0133178
$288$	19.9664	1.17653
$289$	6.52370	0.383747
$290$	8.24222	0.484000
$291$	−0.0646206	−0.00378813
$292$	45.4378	2.65904
$293$	−26.5068	−1.54855	−0.774273	−	0.632852i	$-0.781884\pi$
$293$	−26.5068	−1.54855	−0.774273	+	0.632852i	$0.781884\pi$
$294$	−1.89939	−0.110774
$295$	−9.48852	−0.552443
$296$	3.57074	0.207545
$297$	−6.31250	−0.366288
$298$	34.0012	1.96963
$299$	1.44795	0.0837371
$300$	34.4237	1.98745
$301$	−16.7378	−0.964749
$302$	34.4236	1.98085
$303$	9.14724	0.525495
$304$	−10.6383	−0.610149
$305$	−6.31313	−0.361489
$306$	57.2977	3.27549
$307$	15.0819	0.860768	0.430384	−	0.902646i	$-0.358378\pi$
$307$	15.0819	0.860768	0.430384	+	0.902646i	$0.358378\pi$
$308$	10.0182	0.570842
$309$	−12.2764	−0.698379
$310$	10.4718	0.594759
$311$	−2.69323	−0.152719	−0.0763594	−	0.997080i	$-0.524330\pi$
$311$	−2.69323	−0.152719	−0.0763594	+	0.997080i	$0.524330\pi$
$312$	2.42549	0.137316
$313$	19.0679	1.07778	0.538891	−	0.842375i	$-0.318843\pi$
$313$	19.0679	1.07778	0.538891	+	0.842375i	$0.318843\pi$
$314$	47.2833	2.66835
$315$	−16.2133	−0.913516
$316$	−32.2413	−1.81372
$317$	−2.04802	−0.115029	−0.0575143	−	0.998345i	$-0.518317\pi$
$317$	−2.04802	−0.115029	−0.0575143	+	0.998345i	$0.518317\pi$
$318$	66.3156	3.71879
$319$	3.09671	0.173383
$320$	14.9672	0.836690
$321$	21.4705	1.19837
$322$	−36.7705	−2.04914
$323$	38.2327	2.12733
$324$	4.21996	0.234442
$325$	−0.827472	−0.0458999
$326$	−43.6512	−2.41762
$327$	−2.83343	−0.156689
$328$	−0.310899	−0.0171665
$329$	30.7935	1.69770
$330$	−9.09849	−0.500855
$331$	−8.81596	−0.484569	−0.242285	−	0.970205i	$-0.577897\pi$
$331$	−8.81596	−0.484569	−0.242285	+	0.970205i	$0.577897\pi$
$332$	−33.6410	−1.84629
$333$	−5.02830	−0.275549
$334$	−59.5416	−3.25797
$335$	15.7356	0.859729
$336$	−9.90865	−0.540561
$337$	0.464004	0.0252759	0.0126379	−	0.999920i	$-0.495977\pi$
$337$	0.464004	0.0252759	0.0126379	+	0.999920i	$0.495977\pi$
$338$	30.4076	1.65395
$339$	−19.9058	−1.08113
$340$	21.2428	1.15205
$341$	3.93439	0.213059
$342$	93.1251	5.03563
$343$	−18.8782	−1.01933
$344$	23.0645	1.24355
$345$	21.2948	1.14647
$346$	−17.4175	−0.936372
$347$	15.9277	0.855043	0.427522	−	0.904005i	$-0.359387\pi$
$347$	15.9277	0.855043	0.427522	+	0.904005i	$0.359387\pi$
$348$	−28.1175	−1.50726
$349$	−30.0314	−1.60755	−0.803773	−	0.594936i	$-0.797177\pi$
$349$	−30.0314	−1.60755	−0.803773	+	0.594936i	$0.797177\pi$
$350$	21.0136	1.12322
$351$	−1.37776	−0.0735394
$352$	4.36149	0.232468
$353$	−2.99548	−0.159434	−0.0797168	−	0.996818i	$-0.525402\pi$
$353$	−2.99548	−0.159434	−0.0797168	+	0.996818i	$0.525402\pi$
$354$	50.7617	2.69795
$355$	19.6018	1.04036
$356$	27.1117	1.43692
$357$	35.6104	1.88470
$358$	−10.6123	−0.560878
$359$	−17.5610	−0.926833	−0.463417	−	0.886140i	$-0.653377\pi$
$359$	−17.5610	−0.926833	−0.463417	+	0.886140i	$0.653377\pi$
$360$	22.3418	1.17751
$361$	43.1391	2.27048
$362$	−55.0183	−2.89170
$363$	27.7493	1.45646
$364$	2.18657	0.114608
$365$	−16.0632	−0.840787
$366$	33.7740	1.76539
$367$	23.3722	1.22002	0.610010	−	0.792394i	$-0.291165\pi$
$367$	23.3722	1.22002	0.610010	+	0.792394i	$0.291165\pi$
$368$	8.15106	0.424903
$369$	0.437806	0.0227913
$370$	−2.92348	−0.151985
$371$	25.8139	1.34019
$372$	−35.7236	−1.85218
$373$	−20.0561	−1.03847	−0.519233	−	0.854632i	$-0.673782\pi$
$373$	−20.0561	−1.03847	−0.519233	+	0.854632i	$0.673782\pi$
$374$	12.5162	0.647198
$375$	−29.7982	−1.53877
$376$	−42.4331	−2.18832
$377$	0.675886	0.0348099
$378$	34.9881	1.79959
$379$	30.0503	1.54358	0.771789	−	0.635878i	$-0.219362\pi$
$379$	30.0503	1.54358	0.771789	+	0.635878i	$0.219362\pi$
$380$	34.5257	1.77113
$381$	−19.5138	−0.999725
$382$	−55.5741	−2.84342
$383$	14.7765	0.755043	0.377522	−	0.926001i	$-0.376776\pi$
$383$	14.7765	0.755043	0.377522	+	0.926001i	$0.376776\pi$
$384$	−57.5693	−2.93782
$385$	−3.54166	−0.180500
$386$	−12.7664	−0.649793
$387$	−32.4793	−1.65101
$388$	0.0802751	0.00407535
$389$	−14.3150	−0.725801	−0.362901	−	0.931828i	$-0.618214\pi$
$389$	−14.3150	−0.725801	−0.362901	+	0.931828i	$0.618214\pi$
$390$	−1.98583	−0.100556
$391$	−29.2939	−1.48146
$392$	1.01882	0.0514581
$393$	13.5372	0.682861
$394$	15.7188	0.791900
$395$	11.3980	0.573496
$396$	19.4402	0.976906
$397$	11.6372	0.584056	0.292028	−	0.956410i	$-0.405670\pi$
$397$	11.6372	0.584056	0.292028	+	0.956410i	$0.405670\pi$
$398$	16.7553	0.839865
$399$	57.8771	2.89748
$400$	−4.65816	−0.232908
$401$	18.5480	0.926245	0.463122	−	0.886294i	$-0.346729\pi$
$401$	18.5480	0.926245	0.463122	+	0.886294i	$0.346729\pi$
$402$	−84.1824	−4.19863
$403$	0.858718	0.0427758
$404$	−11.3632	−0.565339
$405$	−1.49185	−0.0741305
$406$	−17.1640	−0.851836
$407$	−1.09839	−0.0544452
$408$	−49.0708	−2.42937
$409$	26.6700	1.31874	0.659372	−	0.751817i	$-0.270822\pi$
$409$	26.6700	1.31874	0.659372	+	0.751817i	$0.270822\pi$
$410$	0.254543	0.0125710
$411$	−10.5392	−0.519863
$412$	15.2504	0.751332
$413$	19.7594	0.972296
$414$	−71.3524	−3.50678
$415$	11.8928	0.583795
$416$	0.951936	0.0466725
$417$	−1.30350	−0.0638329
$418$	20.3424	0.994979
$419$	21.7437	1.06225	0.531124	−	0.847294i	$-0.321770\pi$
$419$	21.7437	1.06225	0.531124	+	0.847294i	$0.321770\pi$
$420$	32.1576	1.56913
$421$	1.62359	0.0791292	0.0395646	−	0.999217i	$-0.487403\pi$
$421$	1.62359	0.0791292	0.0395646	+	0.999217i	$0.487403\pi$
$422$	31.5847	1.53752
$423$	59.7541	2.90534
$424$	−35.5713	−1.72749
$425$	16.7408	0.812049
$426$	−104.866	−5.08076
$427$	13.1468	0.636218
$428$	−26.6718	−1.28923
$429$	−0.746102	−0.0360222
$430$	−18.8836	−0.910650
$431$	−8.37592	−0.403454	−0.201727	−	0.979442i	$-0.564655\pi$
$431$	−8.37592	−0.403454	−0.201727	+	0.979442i	$0.564655\pi$
$432$	−7.75594	−0.373158
$433$	29.2555	1.40593	0.702964	−	0.711226i	$-0.251860\pi$
$433$	29.2555	1.40593	0.702964	+	0.711226i	$0.251860\pi$
$434$	−21.8070	−1.04677
$435$	9.94015	0.476594
$436$	3.51983	0.168569
$437$	−47.6109	−2.27754
$438$	85.9349	4.10613
$439$	31.7015	1.51303	0.756516	−	0.653976i	$-0.226900\pi$
$439$	31.7015	1.51303	0.756516	+	0.653976i	$0.226900\pi$
$440$	4.88037	0.232663
$441$	−1.43470	−0.0683188
$442$	2.73178	0.129937
$443$	8.56937	0.407143	0.203571	−	0.979060i	$-0.434745\pi$
$443$	8.56937	0.407143	0.203571	+	0.979060i	$0.434745\pi$
$444$	9.97318	0.473306
$445$	−9.58457	−0.454352
$446$	18.7777	0.889152
$447$	41.0055	1.93950
$448$	−31.1684	−1.47257
$449$	4.39393	0.207362	0.103681	−	0.994611i	$-0.466938\pi$
$449$	4.39393	0.207362	0.103681	+	0.994611i	$0.466938\pi$
$450$	40.7763	1.92222
$451$	0.0956351	0.00450328
$452$	24.7280	1.16311
$453$	41.5150	1.95054
$454$	8.83887	0.414829
$455$	−0.773000	−0.0362388
$456$	−79.7540	−3.73483
$457$	14.7721	0.691011	0.345505	−	0.938417i	$-0.387708\pi$
$457$	14.7721	0.691011	0.345505	+	0.938417i	$0.387708\pi$
$458$	−48.5640	−2.26925
$459$	27.8739	1.30104
$460$	−26.4535	−1.23340
$461$	−22.2274	−1.03523	−0.517616	−	0.855613i	$-0.673180\pi$
$461$	−22.2274	−1.03523	−0.517616	+	0.855613i	$0.673180\pi$
$462$	18.9472	0.881502
$463$	3.79191	0.176225	0.0881124	−	0.996111i	$-0.471917\pi$
$463$	3.79191	0.176225	0.0881124	+	0.996111i	$0.471917\pi$
$464$	3.80482	0.176634
$465$	12.6290	0.585658
$466$	13.7855	0.638599
$467$	25.7854	1.19320	0.596602	−	0.802537i	$-0.296517\pi$
$467$	25.7854	1.19320	0.596602	+	0.802537i	$0.296517\pi$
$468$	4.24300	0.196133
$469$	−32.7687	−1.51312
$470$	34.7414	1.60250
$471$	57.0239	2.62752
$472$	−27.2282	−1.25328
$473$	−7.09483	−0.326221
$474$	−60.9770	−2.80077
$475$	27.2086	1.24842
$476$	−44.2372	−2.02761
$477$	50.0913	2.29352
$478$	−53.1659	−2.43175
$479$	1.14188	0.0521737	0.0260868	−	0.999660i	$-0.491695\pi$
$479$	1.14188	0.0521737	0.0260868	+	0.999660i	$0.491695\pi$
$480$	14.0000	0.639009
$481$	−0.239734	−0.0109309
$482$	65.5835	2.98725
$483$	−44.3454	−2.01778
$484$	−34.4716	−1.56689
$485$	−0.0283790	−0.00128862
$486$	−32.5258	−1.47540
$487$	20.6326	0.934953	0.467476	−	0.884006i	$-0.345163\pi$
$487$	20.6326	0.934953	0.467476	+	0.884006i	$0.345163\pi$
$488$	−18.1161	−0.820080
$489$	−52.6435	−2.38062
$490$	−0.834140	−0.0376826
$491$	−10.4982	−0.473778	−0.236889	−	0.971537i	$-0.576128\pi$
$491$	−10.4982	−0.473778	−0.236889	+	0.971537i	$0.576128\pi$
$492$	−0.868349	−0.0391482
$493$	−13.6740	−0.615847
$494$	4.43992	0.199761
$495$	−6.87252	−0.308897
$496$	4.83405	0.217055
$497$	−40.8198	−1.83102
$498$	−63.6241	−2.85106
$499$	40.0946	1.79488	0.897441	−	0.441134i	$-0.145424\pi$
$499$	40.0946	1.79488	0.897441	+	0.441134i	$0.145424\pi$
$500$	37.0169	1.65545
$501$	−71.8074	−3.20812
$502$	61.9403	2.76453
$503$	29.4335	1.31238	0.656188	−	0.754598i	$-0.272168\pi$
$503$	29.4335	1.31238	0.656188	+	0.754598i	$0.272168\pi$
$504$	−46.5256	−2.07242
$505$	4.01713	0.178760
$506$	−15.5863	−0.692897
$507$	36.6717	1.62865
$508$	24.2411	1.07553
$509$	21.6107	0.957878	0.478939	−	0.877848i	$-0.341022\pi$
$509$	21.6107	0.957878	0.478939	+	0.877848i	$0.341022\pi$
$510$	40.1759	1.77902
$511$	33.4509	1.47978
$512$	14.9966	0.662763
$513$	45.3030	2.00017
$514$	34.6157	1.52683
$515$	−5.39133	−0.237570
$516$	64.4197	2.83592
$517$	13.0528	0.574061
$518$	6.08801	0.267492
$519$	−21.0056	−0.922044
$520$	1.06519	0.0467115
$521$	2.52635	0.110681	0.0553407	−	0.998468i	$-0.482375\pi$
$521$	2.52635	0.110681	0.0553407	+	0.998468i	$0.482375\pi$
$522$	−33.3064	−1.45778
$523$	21.8794	0.956718	0.478359	−	0.878164i	$-0.341232\pi$
$523$	21.8794	0.956718	0.478359	+	0.878164i	$0.341232\pi$
$524$	−16.8166	−0.734637
$525$	25.3424	1.10603
$526$	25.7894	1.12447
$527$	−17.3730	−0.756778
$528$	−4.20009	−0.182786
$529$	13.4794	0.586063
$530$	29.1234	1.26504
$531$	38.3427	1.66393
$532$	−71.8980	−3.11717
$533$	0.0208733	0.000904121 0
$534$	51.2755	2.21891
$535$	9.42905	0.407654
$536$	45.1549	1.95039
$537$	−12.7985	−0.552296
$538$	52.0604	2.24448
$539$	−0.313397	−0.0134990
$540$	25.1712	1.08320
$541$	−1.35098	−0.0580833	−0.0290416	−	0.999578i	$-0.509246\pi$
$541$	−1.35098	−0.0580833	−0.0290416	+	0.999578i	$0.509246\pi$
$542$	−71.9512	−3.09057
$543$	−66.3523	−2.84745
$544$	−19.2589	−0.825717
$545$	−1.24434	−0.0533015
$546$	4.13539	0.176979
$547$	−7.54143	−0.322448	−0.161224	−	0.986918i	$-0.551544\pi$
$547$	−7.54143	−0.322448	−0.161224	+	0.986918i	$0.551544\pi$
$548$	13.0924	0.559280
$549$	25.5111	1.08879
$550$	8.90725	0.379807
$551$	−22.2242	−0.946783
$552$	61.1075	2.60091
$553$	−23.7358	−1.00935
$554$	59.1349	2.51240
$555$	−3.52573	−0.149659
$556$	1.61928	0.0686729
$557$	33.4849	1.41880	0.709399	−	0.704807i	$-0.248966\pi$
$557$	33.4849	1.41880	0.709399	+	0.704807i	$0.248966\pi$
$558$	−42.3161	−1.79138
$559$	−1.54851	−0.0654951
$560$	−4.35151	−0.183885
$561$	15.0946	0.637294
$562$	49.9276	2.10607
$563$	−16.6713	−0.702612	−0.351306	−	0.936261i	$-0.614262\pi$
$563$	−16.6713	−0.702612	−0.351306	+	0.936261i	$0.614262\pi$
$564$	−118.517	−4.99046
$565$	−8.74189	−0.367774
$566$	−42.2741	−1.77691
$567$	3.10670	0.130469
$568$	56.2493	2.36017
$569$	41.2856	1.73078	0.865391	−	0.501098i	$-0.167070\pi$
$569$	41.2856	1.73078	0.865391	+	0.501098i	$0.167070\pi$
$570$	65.2972	2.73500
$571$	−15.7083	−0.657371	−0.328686	−	0.944439i	$-0.606606\pi$
$571$	−15.7083	−0.657371	−0.328686	+	0.944439i	$0.606606\pi$
$572$	0.926848	0.0387535
$573$	−67.0227	−2.79991
$574$	−0.530073	−0.0221248
$575$	−20.8472	−0.869389
$576$	−60.4816	−2.52007
$577$	−19.3224	−0.804401	−0.402201	−	0.915552i	$-0.631755\pi$
$577$	−19.3224	−0.804401	−0.402201	+	0.915552i	$0.631755\pi$
$578$	−15.3270	−0.637518
$579$	−15.3963	−0.639850
$580$	−12.3482	−0.512731
$581$	−24.7662	−1.02747
$582$	0.151822	0.00629321
$583$	10.9420	0.453173
$584$	−46.0950	−1.90742
$585$	−1.49999	−0.0620170
$586$	62.2760	2.57260
$587$	23.9069	0.986744	0.493372	−	0.869818i	$-0.335764\pi$
$587$	23.9069	0.986744	0.493372	+	0.869818i	$0.335764\pi$
$588$	2.84559	0.117350
$589$	−28.2360	−1.16344
$590$	22.2926	0.917774
$591$	18.9569	0.779782
$592$	−1.34955	−0.0554663
$593$	−32.5487	−1.33662	−0.668308	−	0.743885i	$-0.732981\pi$
$593$	−32.5487	−1.33662	−0.668308	+	0.743885i	$0.732981\pi$
$594$	14.8308	0.608515
$595$	15.6388	0.641128
$596$	−50.9393	−2.08655
$597$	20.2069	0.827014
$598$	−3.40186	−0.139112
$599$	−36.3476	−1.48512	−0.742561	−	0.669778i	$-0.766389\pi$
$599$	−36.3476	−1.48512	−0.742561	+	0.669778i	$0.766389\pi$
$600$	−34.9216	−1.42567
$601$	15.0949	0.615735	0.307867	−	0.951429i	$-0.400385\pi$
$601$	15.0949	0.615735	0.307867	+	0.951429i	$0.400385\pi$
$602$	39.3243	1.60274
$603$	−63.5869	−2.58946
$604$	−51.5721	−2.09844
$605$	12.1865	0.495450
$606$	−21.4908	−0.873005
$607$	3.27670	0.132997	0.0664986	−	0.997787i	$-0.478817\pi$
$607$	3.27670	0.132997	0.0664986	+	0.997787i	$0.478817\pi$
$608$	−31.3012	−1.26943
$609$	−20.6999	−0.838802
$610$	14.8323	0.600542
$611$	2.84889	0.115254
$612$	−85.8412	−3.46993
$613$	−41.3958	−1.67196	−0.835979	−	0.548761i	$-0.815100\pi$
$613$	−41.3958	−1.67196	−0.835979	+	0.548761i	$0.815100\pi$
$614$	−35.4338	−1.42999
$615$	0.306980	0.0123786
$616$	−10.1631	−0.409485
$617$	6.95984	0.280193	0.140096	−	0.990138i	$-0.455259\pi$
$617$	6.95984	0.280193	0.140096	+	0.990138i	$0.455259\pi$
$618$	28.8425	1.16022
$619$	15.5731	0.625934	0.312967	−	0.949764i	$-0.398677\pi$
$619$	15.5731	0.625934	0.312967	+	0.949764i	$0.398677\pi$
$620$	−15.6885	−0.630064
$621$	−34.7111	−1.39291
$622$	6.32755	0.253712
$623$	19.9594	0.799657
$624$	−0.916709	−0.0366977
$625$	4.17188	0.166875
$626$	−44.7988	−1.79052
$627$	24.5330	0.979755
$628$	−70.8381	−2.82675
$629$	4.85012	0.193387
$630$	38.0921	1.51762
$631$	−35.2224	−1.40218	−0.701091	−	0.713072i	$-0.747303\pi$
$631$	−35.2224	−1.40218	−0.701091	+	0.713072i	$0.747303\pi$
$632$	32.7077	1.30104
$633$	38.0913	1.51399
$634$	4.81169	0.191097
$635$	−8.56976	−0.340081
$636$	−99.3516	−3.93955
$637$	−0.0684019	−0.00271018
$638$	−7.27551	−0.288040
$639$	−79.2099	−3.13350
$640$	−25.2823	−0.999371
$641$	7.77632	0.307146	0.153573	−	0.988137i	$-0.450922\pi$
$641$	7.77632	0.307146	0.153573	+	0.988137i	$0.450922\pi$
$642$	−50.4435	−1.99085
$643$	−25.8229	−1.01836	−0.509178	−	0.860661i	$-0.670051\pi$
$643$	−25.8229	−1.01836	−0.509178	+	0.860661i	$0.670051\pi$
$644$	55.0882	2.17078
$645$	−22.7738	−0.896716
$646$	−89.8252	−3.53412
$647$	35.2202	1.38465	0.692324	−	0.721587i	$-0.256587\pi$
$647$	35.2202	1.38465	0.692324	+	0.721587i	$0.256587\pi$
$648$	−4.28100	−0.168174
$649$	8.37564	0.328773
$650$	1.94409	0.0762535
$651$	−26.2994	−1.03075
$652$	65.3966	2.56113
$653$	−2.43483	−0.0952823	−0.0476411	−	0.998865i	$-0.515170\pi$
$653$	−2.43483	−0.0952823	−0.0476411	+	0.998865i	$0.515170\pi$
$654$	6.65694	0.260307
$655$	5.94503	0.232292
$656$	0.117503	0.00458774
$657$	64.9107	2.53241
$658$	−72.3472	−2.82039
$659$	32.1296	1.25159	0.625796	−	0.779987i	$-0.284774\pi$
$659$	32.1296	1.25159	0.625796	+	0.779987i	$0.284774\pi$
$660$	13.6310	0.530587
$661$	−9.67465	−0.376300	−0.188150	−	0.982140i	$-0.560249\pi$
$661$	−9.67465	−0.376300	−0.188150	+	0.982140i	$0.560249\pi$
$662$	20.7125	0.805015
$663$	3.29454	0.127949
$664$	34.1276	1.32441
$665$	25.4175	0.985648
$666$	11.8137	0.457770
$667$	17.0282	0.659333
$668$	89.2030	3.45137
$669$	22.6460	0.875546
$670$	−36.9698	−1.42827
$671$	5.57268	0.215131
$672$	−29.1543	−1.12465
$673$	−19.5024	−0.751763	−0.375881	−	0.926668i	$-0.622660\pi$
$673$	−19.5024	−0.751763	−0.375881	+	0.926668i	$0.622660\pi$
$674$	−1.09015	−0.0419908
$675$	19.8366	0.763513
$676$	−45.5555	−1.75214
$677$	32.4033	1.24536	0.622680	−	0.782476i	$-0.286044\pi$
$677$	32.4033	1.24536	0.622680	+	0.782476i	$0.286044\pi$
$678$	46.7673	1.79609
$679$	0.0590978	0.00226797
$680$	−21.5501	−0.826408
$681$	10.6597	0.408481
$682$	−9.24359	−0.353955
$683$	35.3718	1.35346	0.676732	−	0.736229i	$-0.263395\pi$
$683$	35.3718	1.35346	0.676732	+	0.736229i	$0.263395\pi$
$684$	−139.517	−5.33455
$685$	−4.62845	−0.176844
$686$	44.3531	1.69341
$687$	−58.5684	−2.23453
$688$	−8.71716	−0.332339
$689$	2.38820	0.0909831
$690$	−50.0307	−1.90464
$691$	2.95205	0.112301	0.0561506	−	0.998422i	$-0.482117\pi$
$691$	2.95205	0.112301	0.0561506	+	0.998422i	$0.482117\pi$
$692$	26.0943	0.991956
$693$	14.3117	0.543656
$694$	−37.4210	−1.42048
$695$	−0.572451	−0.0217143
$696$	28.5242	1.08121
$697$	−0.422292	−0.0159955
$698$	70.5568	2.67062
$699$	16.6253	0.628828
$700$	−31.4817	−1.18990
$701$	−35.8597	−1.35440	−0.677201	−	0.735799i	$-0.736807\pi$
$701$	−35.8597	−1.35440	−0.677201	+	0.735799i	$0.736807\pi$
$702$	3.23696	0.122171
$703$	7.88283	0.297307
$704$	−13.2117	−0.497935
$705$	41.8982	1.57798
$706$	7.03769	0.264867
$707$	−8.36547	−0.314616
$708$	−76.0492	−2.85811
$709$	37.2687	1.39965	0.699827	−	0.714312i	$-0.253260\pi$
$709$	37.2687	1.39965	0.699827	+	0.714312i	$0.253260\pi$
$710$	−46.0531	−1.72834
$711$	−46.0588	−1.72734
$712$	−27.5039	−1.03075
$713$	21.6344	0.810215
$714$	−83.6643	−3.13106
$715$	−0.327661	−0.0122538
$716$	15.8990	0.594172
$717$	−64.1183	−2.39454
$718$	41.2584	1.53975
$719$	−39.3127	−1.46612	−0.733058	−	0.680166i	$-0.761908\pi$
$719$	−39.3127	−1.46612	−0.733058	+	0.680166i	$0.761908\pi$
$720$	−8.44401	−0.314690
$721$	11.2272	0.418122
$722$	−101.352	−3.77194
$723$	79.0941	2.94154
$724$	82.4264	3.06335
$725$	−9.73123	−0.361409
$726$	−65.1950	−2.41961
$727$	−6.40092	−0.237397	−0.118699	−	0.992930i	$-0.537872\pi$
$727$	−6.40092	−0.237397	−0.118699	+	0.992930i	$0.537872\pi$
$728$	−2.21820	−0.0822119
$729$	−42.8230	−1.58604
$730$	37.7394	1.39680
$731$	31.3284	1.15872
$732$	−50.5989	−1.87019
$733$	4.75644	0.175683	0.0878416	−	0.996134i	$-0.472003\pi$
$733$	4.75644	0.175683	0.0878416	+	0.996134i	$0.472003\pi$
$734$	−54.9114	−2.02682
$735$	−1.00598	−0.0371060
$736$	23.9829	0.884022
$737$	−13.8900	−0.511646
$738$	−1.02860	−0.0378631
$739$	−5.64593	−0.207689	−0.103844	−	0.994594i	$-0.533114\pi$
$739$	−5.64593	−0.207689	−0.103844	+	0.994594i	$0.533114\pi$
$740$	4.37985	0.161007
$741$	5.35456	0.196705
$742$	−60.6480	−2.22646
$743$	49.6223	1.82047	0.910233	−	0.414096i	$-0.135902\pi$
$743$	49.6223	1.82047	0.910233	+	0.414096i	$0.135902\pi$
$744$	36.2403	1.32863
$745$	18.0081	0.659767
$746$	47.1205	1.72520
$747$	−48.0583	−1.75836
$748$	−18.7513	−0.685616
$749$	−19.6355	−0.717467
$750$	70.0088	2.55636
$751$	−9.89052	−0.360910	−0.180455	−	0.983583i	$-0.557757\pi$
$751$	−9.89052	−0.360910	−0.180455	+	0.983583i	$0.557757\pi$
$752$	16.0375	0.584827
$753$	74.7003	2.72223
$754$	−1.58795	−0.0578296
$755$	18.2318	0.663525
$756$	−52.4178	−1.90642
$757$	−4.99680	−0.181612	−0.0908058	−	0.995869i	$-0.528944\pi$
$757$	−4.99680	−0.181612	−0.0908058	+	0.995869i	$0.528944\pi$
$758$	−70.6011	−2.56435
$759$	−18.7972	−0.682295
$760$	−35.0250	−1.27049
$761$	−11.2036	−0.406132	−0.203066	−	0.979165i	$-0.565091\pi$
$761$	−11.2036	−0.406132	−0.203066	+	0.979165i	$0.565091\pi$
$762$	45.8465	1.66084
$763$	2.59127	0.0938102
$764$	83.2591	3.01221
$765$	30.3467	1.09719
$766$	−34.7164	−1.25435
$767$	1.82806	0.0660074
$768$	67.0930	2.42101
$769$	33.8927	1.22220	0.611100	−	0.791553i	$-0.290727\pi$
$769$	33.8927	1.22220	0.611100	+	0.791553i	$0.290727\pi$
$770$	8.32090	0.299864
$771$	41.7466	1.50347
$772$	19.1261	0.688365
$773$	−51.4497	−1.85052	−0.925259	−	0.379336i	$-0.876152\pi$
$773$	−51.4497	−1.85052	−0.925259	+	0.379336i	$0.876152\pi$
$774$	76.3079	2.74283
$775$	−12.3636	−0.444114
$776$	−0.0814362	−0.00292339
$777$	7.34217	0.263399
$778$	33.6322	1.20577
$779$	−0.686346	−0.0245909
$780$	2.97510	0.106526
$781$	−17.3028	−0.619141
$782$	68.8240	2.46114
$783$	−16.2027	−0.579038
$784$	−0.385060	−0.0137521
$785$	25.0428	0.893816
$786$	−31.8047	−1.13444
$787$	30.7247	1.09522	0.547609	−	0.836734i	$-0.315538\pi$
$787$	30.7247	1.09522	0.547609	+	0.836734i	$0.315538\pi$
$788$	−23.5493	−0.838908
$789$	31.1022	1.10727
$790$	−26.7788	−0.952749
$791$	18.2046	0.647279
$792$	−19.7214	−0.700768
$793$	1.21629	0.0431917
$794$	−27.3409	−0.970292
$795$	35.1229	1.24568
$796$	−25.1021	−0.889721
$797$	53.9378	1.91057	0.955287	−	0.295680i	$-0.0955462\pi$
$797$	53.9378	1.91057	0.955287	+	0.295680i	$0.0955462\pi$
$798$	−135.978	−4.81358
$799$	−57.6367	−2.03904
$800$	−13.7057	−0.484571
$801$	38.7308	1.36849
$802$	−43.5774	−1.53877
$803$	14.1792	0.500373
$804$	126.119	4.44787
$805$	−19.4749	−0.686398
$806$	−2.01750	−0.0710634
$807$	62.7851	2.21014
$808$	11.5275	0.405537
$809$	17.8127	0.626262	0.313131	−	0.949710i	$-0.398622\pi$
$809$	17.8127	0.626262	0.313131	+	0.949710i	$0.398622\pi$
$810$	3.50499	0.123153
$811$	22.4451	0.788153	0.394076	−	0.919078i	$-0.371065\pi$
$811$	22.4451	0.788153	0.394076	+	0.919078i	$0.371065\pi$
$812$	25.7145	0.902402
$813$	−86.7735	−3.04328
$814$	2.58060	0.0904498
$815$	−23.1191	−0.809827
$816$	18.5462	0.649246
$817$	50.9176	1.78138
$818$	−62.6593	−2.19083
$819$	3.12366	0.109149
$820$	−0.381347	−0.0133172
$821$	27.2395	0.950664	0.475332	−	0.879807i	$-0.342328\pi$
$821$	27.2395	0.950664	0.475332	+	0.879807i	$0.342328\pi$
$822$	24.7612	0.863648
$823$	13.2146	0.460633	0.230317	−	0.973116i	$-0.426024\pi$
$823$	13.2146	0.460633	0.230317	+	0.973116i	$0.426024\pi$
$824$	−15.4709	−0.538956
$825$	10.7422	0.373995
$826$	−46.4234	−1.61528
$827$	18.3494	0.638072	0.319036	−	0.947743i	$-0.396641\pi$
$827$	18.3494	0.638072	0.319036	+	0.947743i	$0.396641\pi$
$828$	106.897	3.71494
$829$	22.0800	0.766871	0.383435	−	0.923568i	$-0.374741\pi$
$829$	22.0800	0.766871	0.383435	+	0.923568i	$0.374741\pi$
$830$	−27.9413	−0.969858
$831$	71.3169	2.47396
$832$	−2.88358	−0.0999700
$833$	1.38386	0.0479478
$834$	3.06249	0.106046
$835$	−31.5352	−1.09132
$836$	−30.4762	−1.05404
$837$	−20.5857	−0.711545
$838$	−51.0853	−1.76471
$839$	30.9080	1.06706	0.533531	−	0.845781i	$-0.320865\pi$
$839$	30.9080	1.06706	0.533531	+	0.845781i	$0.320865\pi$
$840$	−32.6227	−1.12559
$841$	−21.0515	−0.725912
$842$	−3.81453	−0.131457
$843$	60.2129	2.07384
$844$	−47.3190	−1.62879
$845$	16.1049	0.554024
$846$	−140.388	−4.82664
$847$	−25.3777	−0.871988
$848$	13.4441	0.461671
$849$	−50.9827	−1.74972
$850$	−39.3314	−1.34906
$851$	−6.03982	−0.207042
$852$	157.106	5.38235
$853$	−26.0093	−0.890542	−0.445271	−	0.895396i	$-0.646893\pi$
$853$	−26.0093	−0.890542	−0.445271	+	0.895396i	$0.646893\pi$
$854$	−30.8875	−1.05695
$855$	49.3221	1.68678
$856$	27.0576	0.924809
$857$	−48.8508	−1.66871	−0.834356	−	0.551227i	$-0.814160\pi$
$857$	−48.8508	−1.66871	−0.834356	+	0.551227i	$0.814160\pi$
$858$	1.75292	0.0598436
$859$	−39.0221	−1.33142	−0.665708	−	0.746212i	$-0.731870\pi$
$859$	−39.0221	−1.33142	−0.665708	+	0.746212i	$0.731870\pi$
$860$	28.2908	0.964707
$861$	−0.639271	−0.0217863
$862$	19.6787	0.670258
$863$	40.6481	1.38368	0.691840	−	0.722051i	$-0.256801\pi$
$863$	40.6481	1.38368	0.691840	+	0.722051i	$0.256801\pi$
$864$	−22.8204	−0.776364
$865$	−9.22489	−0.313656
$866$	−68.7337	−2.33567
$867$	−18.4844	−0.627763
$868$	32.6705	1.10891
$869$	−10.0612	−0.341302
$870$	−23.3537	−0.791765
$871$	−3.03163	−0.102723
$872$	−3.57074	−0.120921
$873$	0.114678	0.00388126
$874$	111.859	3.78367
$875$	27.2515	0.921269
$876$	−128.744	−4.34987
$877$	−40.8012	−1.37776	−0.688879	−	0.724876i	$-0.741897\pi$
$877$	−40.8012	−1.37776	−0.688879	+	0.724876i	$0.741897\pi$
$878$	−74.4806	−2.51360
$879$	75.1051	2.53323
$880$	−1.84453	−0.0621789
$881$	10.7036	0.360614	0.180307	−	0.983610i	$-0.442291\pi$
$881$	10.7036	0.360614	0.180307	+	0.983610i	$0.442291\pi$
$882$	3.37072	0.113498
$883$	−53.5816	−1.80317	−0.901583	−	0.432607i	$-0.857594\pi$
$883$	−53.5816	−1.80317	−0.901583	+	0.432607i	$0.857594\pi$
$884$	−4.09265	−0.137651
$885$	26.8850	0.903730
$886$	−20.1331	−0.676386
$887$	51.6078	1.73282	0.866410	−	0.499333i	$-0.166422\pi$
$887$	51.6078	1.73282	0.866410	+	0.499333i	$0.166422\pi$
$888$	−10.1174	−0.339519
$889$	17.8461	0.598539
$890$	22.5183	0.754815
$891$	1.31687	0.0441169
$892$	−28.1321	−0.941933
$893$	−93.6760	−3.13475
$894$	−96.3398	−3.22208
$895$	−5.62062	−0.187877
$896$	52.6492	1.75889
$897$	−4.10266	−0.136984
$898$	−10.3232	−0.344491
$899$	10.0987	0.336810
$900$	−61.0896	−2.03632
$901$	−48.3163	−1.60965
$902$	−0.224688	−0.00748130
$903$	47.4252	1.57821
$904$	−25.0857	−0.834338
$905$	−29.1395	−0.968629
$906$	−97.5366	−3.24044
$907$	−10.5361	−0.349845	−0.174923	−	0.984582i	$-0.555968\pi$
$907$	−10.5361	−0.349845	−0.174923	+	0.984582i	$0.555968\pi$
$908$	−13.2421	−0.439453
$909$	−16.2330	−0.538415
$910$	1.81611	0.0602035
$911$	40.5698	1.34414	0.672069	−	0.740489i	$-0.265406\pi$
$911$	40.5698	1.34414	0.672069	+	0.740489i	$0.265406\pi$
$912$	30.1428	0.998129
$913$	−10.4979	−0.347431
$914$	−34.7061	−1.14798
$915$	17.8878	0.591352
$916$	72.7568	2.40395
$917$	−12.3802	−0.408832
$918$	−65.4877	−2.16142
$919$	−12.2919	−0.405473	−0.202736	−	0.979233i	$-0.564983\pi$
$919$	−12.2919	−0.405473	−0.202736	+	0.979233i	$0.564983\pi$
$920$	26.8362	0.884762
$921$	−42.7334	−1.40811
$922$	52.2217	1.71983
$923$	−3.77649	−0.124305
$924$	−28.3859	−0.933829
$925$	3.45163	0.113489
$926$	−8.90883	−0.292762
$927$	21.7861	0.715550
$928$	11.1949	0.367492
$929$	22.1181	0.725671	0.362835	−	0.931853i	$-0.381809\pi$
$929$	22.1181	0.725671	0.362835	+	0.931853i	$0.381809\pi$
$930$	−29.6711	−0.972953
$931$	2.24916	0.0737133
$932$	−20.6529	−0.676507
$933$	7.63105	0.249830
$934$	−60.5810	−1.98227
$935$	6.62899	0.216791
$936$	−4.30437	−0.140693
$937$	10.8880	0.355696	0.177848	−	0.984058i	$-0.443086\pi$
$937$	10.8880	0.355696	0.177848	+	0.984058i	$0.443086\pi$
$938$	76.9878	2.51374
$939$	−54.0275	−1.76312
$940$	−52.0482	−1.69763
$941$	11.6164	0.378682	0.189341	−	0.981911i	$-0.439365\pi$
$941$	11.6164	0.378682	0.189341	+	0.981911i	$0.439365\pi$
$942$	−133.974	−4.36510
$943$	0.525878	0.0171249
$944$	10.2908	0.334939
$945$	18.5308	0.602807
$946$	16.6688	0.541950
$947$	−2.17662	−0.0707305	−0.0353653	−	0.999374i	$-0.511259\pi$
$947$	−2.17662	−0.0707305	−0.0353653	+	0.999374i	$0.511259\pi$
$948$	91.3535	2.96702
$949$	3.09474	0.100460
$950$	−63.9248	−2.07399
$951$	5.80293	0.188173
$952$	44.8770	1.45447
$953$	−7.52353	−0.243711	−0.121856	−	0.992548i	$-0.538884\pi$
$953$	−7.52353	−0.243711	−0.121856	+	0.992548i	$0.538884\pi$
$954$	−117.686	−3.81023
$955$	−29.4339	−0.952458
$956$	79.6512	2.57610
$957$	−8.77430	−0.283633
$958$	−2.68276	−0.0866761
$959$	9.63852	0.311244
$960$	−42.4083	−1.36872
$961$	−18.1695	−0.586114
$962$	0.563239	0.0181595
$963$	−38.1023	−1.22783
$964$	−98.2548	−3.16458
$965$	−6.76150	−0.217660
$966$	104.186	3.35215
$967$	13.9851	0.449729	0.224865	−	0.974390i	$-0.427806\pi$
$967$	13.9851	0.449729	0.224865	+	0.974390i	$0.427806\pi$
$968$	34.9702	1.12398
$969$	−108.330	−3.48005
$970$	0.0666745	0.00214079
$971$	6.12620	0.196599	0.0982996	−	0.995157i	$-0.468660\pi$
$971$	6.12620	0.196599	0.0982996	+	0.995157i	$0.468660\pi$
$972$	48.7289	1.56298
$973$	1.19210	0.0382170
$974$	−48.4749	−1.55324
$975$	2.34458	0.0750867
$976$	6.84695	0.219166
$977$	43.0908	1.37860	0.689299	−	0.724477i	$-0.257919\pi$
$977$	43.0908	1.37860	0.689299	+	0.724477i	$0.257919\pi$
$978$	123.682	3.95493
$979$	8.46042	0.270396
$980$	1.24968	0.0399195
$981$	5.02830	0.160541
$982$	24.6649	0.787088
$983$	−25.5366	−0.814492	−0.407246	−	0.913318i	$-0.633511\pi$
$983$	−25.5366	−0.814492	−0.407246	+	0.913318i	$0.633511\pi$
$984$	0.880909	0.0280823
$985$	8.32517	0.265262
$986$	32.1262	1.02311
$987$	−87.2510	−2.77723
$988$	−6.65172	−0.211619
$989$	−39.0130	−1.24054
$990$	16.1465	0.513170
$991$	−4.16414	−0.132278	−0.0661391	−	0.997810i	$-0.521068\pi$
$991$	−4.16414	−0.132278	−0.0661391	+	0.997810i	$0.521068\pi$
$992$	14.2233	0.451589
$993$	24.9794	0.792697
$994$	95.9034	3.04187
$995$	8.87413	0.281329
$996$	95.3192	3.02031
$997$	3.27624	0.103760	0.0518798	−	0.998653i	$-0.483479\pi$
$997$	3.27624	0.103760	0.0518798	+	0.998653i	$0.483479\pi$
$998$	−94.1996	−2.98184
$999$	5.74704	0.181828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.9	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.9	✓	82	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34943 q^{2} -2.83343 q^{3} +3.51983 q^{4} -1.24434 q^{5} +6.65694 q^{6} +2.59127 q^{7} -3.57074 q^{8} +5.02830 q^{9} +O(q^{10})\)	\(q-2.34943 q^{2} -2.83343 q^{3} +3.51983 q^{4} -1.24434 q^{5} +6.65694 q^{6} +2.59127 q^{7} -3.57074 q^{8} +5.02830 q^{9} +2.92348 q^{10} +1.09839 q^{11} -9.97318 q^{12} +0.239734 q^{13} -6.08801 q^{14} +3.52573 q^{15} +1.34955 q^{16} -4.85012 q^{17} -11.8137 q^{18} -7.88283 q^{19} -4.37985 q^{20} -7.34217 q^{21} -2.58060 q^{22} +6.03982 q^{23} +10.1174 q^{24} -3.45163 q^{25} -0.563239 q^{26} -5.74704 q^{27} +9.12083 q^{28} +2.81932 q^{29} -8.28347 q^{30} +3.58196 q^{31} +3.97080 q^{32} -3.11221 q^{33} +11.3950 q^{34} -3.22441 q^{35} +17.6988 q^{36} -1.00000 q^{37} +18.5202 q^{38} -0.679268 q^{39} +4.44320 q^{40} +0.0870684 q^{41} +17.2499 q^{42} -6.45930 q^{43} +3.86615 q^{44} -6.25690 q^{45} -14.1902 q^{46} +11.8836 q^{47} -3.82386 q^{48} -0.285324 q^{49} +8.10937 q^{50} +13.7425 q^{51} +0.843823 q^{52} +9.96187 q^{53} +13.5023 q^{54} -1.36677 q^{55} -9.25275 q^{56} +22.3354 q^{57} -6.62379 q^{58} +7.62537 q^{59} +12.4100 q^{60} +5.07350 q^{61} -8.41558 q^{62} +13.0297 q^{63} -12.0282 q^{64} -0.298310 q^{65} +7.31192 q^{66} -12.6458 q^{67} -17.0716 q^{68} -17.1134 q^{69} +7.57553 q^{70} -15.7528 q^{71} -17.9548 q^{72} +12.9091 q^{73} +2.34943 q^{74} +9.77993 q^{75} -27.7462 q^{76} +2.84623 q^{77} +1.59589 q^{78} -9.15991 q^{79} -1.67930 q^{80} +1.19891 q^{81} -0.204561 q^{82} -9.55755 q^{83} -25.8432 q^{84} +6.03518 q^{85} +15.1757 q^{86} -7.98832 q^{87} -3.92207 q^{88} +7.70256 q^{89} +14.7002 q^{90} +0.621215 q^{91} +21.2592 q^{92} -10.1492 q^{93} -27.9196 q^{94} +9.80889 q^{95} -11.2510 q^{96} +0.0228065 q^{97} +0.670349 q^{98} +5.52304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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