LMFDB - Embedded newform 8033.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33211 q^{2} +3.25701 q^{3} +3.43872 q^{4} +3.02617 q^{5} -7.59569 q^{6} +3.43735 q^{7} -3.35525 q^{8} +7.60809 q^{9} +O(q^{10})$	\(q-2.33211 q^{2} +3.25701 q^{3} +3.43872 q^{4} +3.02617 q^{5} -7.59569 q^{6} +3.43735 q^{7} -3.35525 q^{8} +7.60809 q^{9} -7.05735 q^{10} -0.0592625 q^{11} +11.1999 q^{12} -1.20688 q^{13} -8.01626 q^{14} +9.85625 q^{15} +0.947352 q^{16} +3.11538 q^{17} -17.7429 q^{18} -4.51114 q^{19} +10.4061 q^{20} +11.1955 q^{21} +0.138206 q^{22} +5.00342 q^{23} -10.9281 q^{24} +4.15770 q^{25} +2.81457 q^{26} +15.0086 q^{27} +11.8201 q^{28} +1.00000 q^{29} -22.9858 q^{30} -7.22420 q^{31} +4.50117 q^{32} -0.193018 q^{33} -7.26541 q^{34} +10.4020 q^{35} +26.1621 q^{36} +9.07886 q^{37} +10.5204 q^{38} -3.93081 q^{39} -10.1535 q^{40} +1.70572 q^{41} -26.1090 q^{42} +9.84360 q^{43} -0.203787 q^{44} +23.0234 q^{45} -11.6685 q^{46} -10.8343 q^{47} +3.08553 q^{48} +4.81535 q^{49} -9.69621 q^{50} +10.1468 q^{51} -4.15012 q^{52} +2.09037 q^{53} -35.0016 q^{54} -0.179338 q^{55} -11.5331 q^{56} -14.6928 q^{57} -2.33211 q^{58} -8.69537 q^{59} +33.8929 q^{60} +11.2141 q^{61} +16.8476 q^{62} +26.1516 q^{63} -12.3919 q^{64} -3.65222 q^{65} +0.450139 q^{66} -8.19319 q^{67} +10.7129 q^{68} +16.2962 q^{69} -24.2586 q^{70} -14.6492 q^{71} -25.5270 q^{72} -11.8641 q^{73} -21.1729 q^{74} +13.5417 q^{75} -15.5125 q^{76} -0.203706 q^{77} +9.16707 q^{78} +0.280778 q^{79} +2.86685 q^{80} +26.0588 q^{81} -3.97792 q^{82} +9.69549 q^{83} +38.4980 q^{84} +9.42768 q^{85} -22.9563 q^{86} +3.25701 q^{87} +0.198840 q^{88} +12.1072 q^{89} -53.6930 q^{90} -4.14846 q^{91} +17.2054 q^{92} -23.5293 q^{93} +25.2667 q^{94} -13.6515 q^{95} +14.6603 q^{96} -10.3212 q^{97} -11.2299 q^{98} -0.450875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) $ 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * 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 $

$2$	−2.33211	−1.64905	−0.824524	−	0.565827i	$-0.808557\pi$
$2$	−2.33211	−1.64905	−0.824524	+	0.565827i	$0.808557\pi$
$3$	3.25701	1.88043	0.940217	−	0.340577i	$-0.110622\pi$
$3$	3.25701	1.88043	0.940217	+	0.340577i	$0.110622\pi$
$4$	3.43872	1.71936
$5$	3.02617	1.35334	0.676672	−	0.736284i	$-0.263421\pi$
$5$	3.02617	1.35334	0.676672	+	0.736284i	$0.263421\pi$
$6$	−7.59569	−3.10093
$7$	3.43735	1.29919	0.649597	−	0.760278i	$-0.274937\pi$
$7$	3.43735	1.29919	0.649597	+	0.760278i	$0.274937\pi$
$8$	−3.35525	−1.18626
$9$	7.60809	2.53603
$10$	−7.05735	−2.23173
$11$	−0.0592625	−0.0178683	−0.00893416	−	0.999960i	$-0.502844\pi$
$11$	−0.0592625	−0.0178683	−0.00893416	+	0.999960i	$0.502844\pi$
$12$	11.1999	3.23314
$13$	−1.20688	−0.334728	−0.167364	−	0.985895i	$-0.553525\pi$
$13$	−1.20688	−0.334728	−0.167364	+	0.985895i	$0.553525\pi$
$14$	−8.01626	−2.14243
$15$	9.85625	2.54487
$16$	0.947352	0.236838
$17$	3.11538	0.755592	0.377796	−	0.925889i	$-0.376682\pi$
$17$	3.11538	0.755592	0.377796	+	0.925889i	$0.376682\pi$
$18$	−17.7429	−4.18204
$19$	−4.51114	−1.03493	−0.517463	−	0.855706i	$-0.673123\pi$
$19$	−4.51114	−1.03493	−0.517463	+	0.855706i	$0.673123\pi$
$20$	10.4061	2.32689
$21$	11.1955	2.44305
$22$	0.138206	0.0294657
$23$	5.00342	1.04329	0.521643	−	0.853164i	$-0.325319\pi$
$23$	5.00342	1.04329	0.521643	+	0.853164i	$0.325319\pi$
$24$	−10.9281	−2.23068
$25$	4.15770	0.831541
$26$	2.81457	0.551982
$27$	15.0086	2.88840
$28$	11.8201	2.23378
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−22.9858	−4.19662
$31$	−7.22420	−1.29751	−0.648753	−	0.760999i	$-0.724709\pi$
$31$	−7.22420	−1.29751	−0.648753	+	0.760999i	$0.724709\pi$
$32$	4.50117	0.795701
$33$	−0.193018	−0.0336002
$34$	−7.26541	−1.24601
$35$	10.4020	1.75826
$36$	26.1621	4.36035
$37$	9.07886	1.49256	0.746278	−	0.665635i	$-0.231839\pi$
$37$	9.07886	1.49256	0.746278	+	0.665635i	$0.231839\pi$
$38$	10.5204	1.70664
$39$	−3.93081	−0.629433
$40$	−10.1535	−1.60542
$41$	1.70572	0.266389	0.133194	−	0.991090i	$-0.457477\pi$
$41$	1.70572	0.266389	0.133194	+	0.991090i	$0.457477\pi$
$42$	−26.1090	−4.02871
$43$	9.84360	1.50113	0.750567	−	0.660794i	$-0.229780\pi$
$43$	9.84360	1.50113	0.750567	+	0.660794i	$0.229780\pi$
$44$	−0.203787	−0.0307221
$45$	23.0234	3.43212
$46$	−11.6685	−1.72043
$47$	−10.8343	−1.58034	−0.790172	−	0.612885i	$-0.790009\pi$
$47$	−10.8343	−1.58034	−0.790172	+	0.612885i	$0.790009\pi$
$48$	3.08553	0.445358
$49$	4.81535	0.687907
$50$	−9.69621	−1.37125
$51$	10.1468	1.42084
$52$	−4.15012	−0.575517
$53$	2.09037	0.287135	0.143567	−	0.989641i	$-0.454143\pi$
$53$	2.09037	0.287135	0.143567	+	0.989641i	$0.454143\pi$
$54$	−35.0016	−4.76312
$55$	−0.179338	−0.0241820
$56$	−11.5331	−1.54118
$57$	−14.6928	−1.94611
$58$	−2.33211	−0.306221
$59$	−8.69537	−1.13204	−0.566020	−	0.824391i	$-0.691518\pi$
$59$	−8.69537	−1.13204	−0.566020	+	0.824391i	$0.691518\pi$
$60$	33.8929	4.37555
$61$	11.2141	1.43581	0.717907	−	0.696139i	$-0.245100\pi$
$61$	11.2141	1.43581	0.717907	+	0.696139i	$0.245100\pi$
$62$	16.8476	2.13965
$63$	26.1516	3.29480
$64$	−12.3919	−1.54899
$65$	−3.65222	−0.453002
$66$	0.450139	0.0554083
$67$	−8.19319	−1.00096	−0.500479	−	0.865749i	$-0.666843\pi$
$67$	−8.19319	−1.00096	−0.500479	+	0.865749i	$0.666843\pi$
$68$	10.7129	1.29913
$69$	16.2962	1.96183
$70$	−24.2586	−2.89945
$71$	−14.6492	−1.73854	−0.869270	−	0.494338i	$-0.835410\pi$
$71$	−14.6492	−1.73854	−0.869270	+	0.494338i	$0.835410\pi$
$72$	−25.5270	−3.00839
$73$	−11.8641	−1.38859	−0.694295	−	0.719690i	$-0.744284\pi$
$73$	−11.8641	−1.38859	−0.694295	+	0.719690i	$0.744284\pi$
$74$	−21.1729	−2.46130
$75$	13.5417	1.56366
$76$	−15.5125	−1.77941
$77$	−0.203706	−0.0232144
$78$	9.16707	1.03797
$79$	0.280778	0.0315900	0.0157950	−	0.999875i	$-0.494972\pi$
$79$	0.280778	0.0315900	0.0157950	+	0.999875i	$0.494972\pi$
$80$	2.86685	0.320523
$81$	26.0588	2.89542
$82$	−3.97792	−0.439288
$83$	9.69549	1.06422	0.532109	−	0.846676i	$-0.321399\pi$
$83$	9.69549	1.06422	0.532109	+	0.846676i	$0.321399\pi$
$84$	38.4980	4.20048
$85$	9.42768	1.02258
$86$	−22.9563	−2.47544
$87$	3.25701	0.349188
$88$	0.198840	0.0211964
$89$	12.1072	1.28336	0.641681	−	0.766972i	$-0.278237\pi$
$89$	12.1072	1.28336	0.641681	+	0.766972i	$0.278237\pi$
$90$	−53.6930	−5.65973
$91$	−4.14846	−0.434877
$92$	17.2054	1.79378
$93$	−23.5293	−2.43987
$94$	25.2667	2.60606
$95$	−13.6515	−1.40061
$96$	14.6603	1.49626
$97$	−10.3212	−1.04796	−0.523982	−	0.851729i	$-0.675554\pi$
$97$	−10.3212	−1.04796	−0.523982	+	0.851729i	$0.675554\pi$
$98$	−11.2299	−1.13439
$99$	−0.450875	−0.0453146
$100$	14.2972	1.42972
$101$	6.75741	0.672388	0.336194	−	0.941793i	$-0.390860\pi$
$101$	6.75741	0.672388	0.336194	+	0.941793i	$0.390860\pi$
$102$	−23.6635	−2.34303
$103$	5.95944	0.587201	0.293600	−	0.955928i	$-0.405147\pi$
$103$	5.95944	0.587201	0.293600	+	0.955928i	$0.405147\pi$
$104$	4.04937	0.397074
$105$	33.8794	3.30629
$106$	−4.87497	−0.473499
$107$	−2.54222	−0.245765	−0.122883	−	0.992421i	$-0.539214\pi$
$107$	−2.54222	−0.245765	−0.122883	+	0.992421i	$0.539214\pi$
$108$	51.6103	4.96620
$109$	−15.4539	−1.48021	−0.740107	−	0.672489i	$-0.765225\pi$
$109$	−15.4539	−1.48021	−0.740107	+	0.672489i	$0.765225\pi$
$110$	0.418236	0.0398773
$111$	29.5699	2.80665
$112$	3.25638	0.307699
$113$	−17.7895	−1.67349	−0.836747	−	0.547590i	$-0.815545\pi$
$113$	−17.7895	−1.67349	−0.836747	+	0.547590i	$0.815545\pi$
$114$	34.2652	3.20923
$115$	15.1412	1.41192
$116$	3.43872	0.319277
$117$	−9.18204	−0.848880
$118$	20.2785	1.86679
$119$	10.7087	0.981661
$120$	−33.0702	−3.01888
$121$	−10.9965	−0.999681
$122$	−26.1524	−2.36773
$123$	5.55554	0.500926
$124$	−24.8420	−2.23088
$125$	−2.54893	−0.227983
$126$	−60.9884	−5.43328
$127$	−6.19228	−0.549476	−0.274738	−	0.961519i	$-0.588591\pi$
$127$	−6.19228	−0.549476	−0.274738	+	0.961519i	$0.588591\pi$
$128$	19.8969	1.75865
$129$	32.0607	2.82278
$130$	8.51736	0.747022
$131$	10.9635	0.957886	0.478943	−	0.877846i	$-0.341020\pi$
$131$	10.9635	0.957886	0.478943	+	0.877846i	$0.341020\pi$
$132$	−0.663736	−0.0577708
$133$	−15.5063	−1.34457
$134$	19.1074	1.65063
$135$	45.4185	3.90900
$136$	−10.4529	−0.896327
$137$	−3.09142	−0.264118	−0.132059	−	0.991242i	$-0.542159\pi$
$137$	−3.09142	−0.264118	−0.132059	+	0.991242i	$0.542159\pi$
$138$	−38.0044	−3.23515
$139$	21.5759	1.83004	0.915022	−	0.403404i	$-0.132173\pi$
$139$	21.5759	1.83004	0.915022	+	0.403404i	$0.132173\pi$
$140$	35.7695	3.02308
$141$	−35.2874	−2.97173
$142$	34.1635	2.86693
$143$	0.0715226	0.00598102
$144$	7.20754	0.600628
$145$	3.02617	0.251310
$146$	27.6684	2.28985
$147$	15.6836	1.29356
$148$	31.2197	2.56624
$149$	−1.75862	−0.144072	−0.0720361	−	0.997402i	$-0.522950\pi$
$149$	−1.75862	−0.144072	−0.0720361	+	0.997402i	$0.522950\pi$
$150$	−31.5806	−2.57855
$151$	−14.3586	−1.16849	−0.584244	−	0.811578i	$-0.698609\pi$
$151$	−14.3586	−1.16849	−0.584244	+	0.811578i	$0.698609\pi$
$152$	15.1360	1.22769
$153$	23.7021	1.91620
$154$	0.475064	0.0382817
$155$	−21.8617	−1.75597
$156$	−13.5170	−1.08222
$157$	12.3281	0.983888	0.491944	−	0.870627i	$-0.336286\pi$
$157$	12.3281	0.983888	0.491944	+	0.870627i	$0.336286\pi$
$158$	−0.654803	−0.0520934
$159$	6.80836	0.539938
$160$	13.6213	1.07686
$161$	17.1985	1.35543
$162$	−60.7718	−4.77469
$163$	−15.3921	−1.20561	−0.602803	−	0.797890i	$-0.705949\pi$
$163$	−15.3921	−1.20561	−0.602803	+	0.797890i	$0.705949\pi$
$164$	5.86549	0.458018
$165$	−0.584106	−0.0454726
$166$	−22.6109	−1.75495
$167$	−12.9506	−1.00215	−0.501074	−	0.865405i	$-0.667061\pi$
$167$	−12.9506	−1.00215	−0.501074	+	0.865405i	$0.667061\pi$
$168$	−37.5635	−2.89809
$169$	−11.5434	−0.887957
$170$	−21.9864	−1.68628
$171$	−34.3211	−2.62460
$172$	33.8494	2.58099
$173$	−23.4334	−1.78161	−0.890805	−	0.454387i	$-0.849858\pi$
$173$	−23.4334	−1.78161	−0.890805	+	0.454387i	$0.849858\pi$
$174$	−7.59569	−0.575827
$175$	14.2915	1.08033
$176$	−0.0561425	−0.00423190
$177$	−28.3209	−2.12873
$178$	−28.2353	−2.11632
$179$	8.90846	0.665850	0.332925	−	0.942953i	$-0.391964\pi$
$179$	8.90846	0.665850	0.332925	+	0.942953i	$0.391964\pi$
$180$	79.1709	5.90105
$181$	8.59011	0.638498	0.319249	−	0.947671i	$-0.396569\pi$
$181$	8.59011	0.638498	0.319249	+	0.947671i	$0.396569\pi$
$182$	9.67465	0.717132
$183$	36.5243	2.69995
$184$	−16.7877	−1.23761
$185$	27.4742	2.01994
$186$	54.8728	4.02347
$187$	−0.184626	−0.0135012
$188$	−37.2561	−2.71718
$189$	51.5897	3.75260
$190$	31.8367	2.30967
$191$	23.6505	1.71129	0.855646	−	0.517561i	$-0.173160\pi$
$191$	23.6505	1.71129	0.855646	+	0.517561i	$0.173160\pi$
$192$	−40.3605	−2.91277
$193$	3.29242	0.236993	0.118497	−	0.992954i	$-0.462193\pi$
$193$	3.29242	0.236993	0.118497	+	0.992954i	$0.462193\pi$
$194$	24.0702	1.72814
$195$	−11.8953	−0.851840
$196$	16.5586	1.18276
$197$	−2.30759	−0.164409	−0.0822044	−	0.996615i	$-0.526196\pi$
$197$	−2.30759	−0.164409	−0.0822044	+	0.996615i	$0.526196\pi$
$198$	1.05149	0.0747260
$199$	−2.77508	−0.196720	−0.0983600	−	0.995151i	$-0.531360\pi$
$199$	−2.77508	−0.196720	−0.0983600	+	0.995151i	$0.531360\pi$
$200$	−13.9501	−0.986422
$201$	−26.6853	−1.88223
$202$	−15.7590	−1.10880
$203$	3.43735	0.241254
$204$	34.8921	2.44294
$205$	5.16180	0.360516
$206$	−13.8980	−0.968322
$207$	38.0665	2.64580
$208$	−1.14334	−0.0792762
$209$	0.267341	0.0184924
$210$	−79.0103	−5.45223
$211$	22.4623	1.54637	0.773183	−	0.634182i	$-0.218663\pi$
$211$	22.4623	1.54637	0.773183	+	0.634182i	$0.218663\pi$
$212$	7.18821	0.493688
$213$	−47.7125	−3.26921
$214$	5.92872	0.405279
$215$	29.7884	2.03155
$216$	−50.3575	−3.42639
$217$	−24.8321	−1.68571
$218$	36.0401	2.44094
$219$	−38.6415	−2.61115
$220$	−0.616694	−0.0415775
$221$	−3.75989	−0.252918
$222$	−68.9602	−4.62830
$223$	10.4609	0.700511	0.350255	−	0.936654i	$-0.386095\pi$
$223$	10.4609	0.700511	0.350255	+	0.936654i	$0.386095\pi$
$224$	15.4721	1.03377
$225$	31.6322	2.10881
$226$	41.4869	2.75967
$227$	−2.12020	−0.140723	−0.0703613	−	0.997522i	$-0.522415\pi$
$227$	−2.12020	−0.140723	−0.0703613	+	0.997522i	$0.522415\pi$
$228$	−50.5244	−3.34606
$229$	15.2463	1.00750	0.503751	−	0.863849i	$-0.331953\pi$
$229$	15.2463	1.00750	0.503751	+	0.863849i	$0.331953\pi$
$230$	−35.3109	−2.32833
$231$	−0.663471	−0.0436532
$232$	−3.35525	−0.220283
$233$	−23.3623	−1.53052	−0.765258	−	0.643724i	$-0.777389\pi$
$233$	−23.3623	−1.53052	−0.765258	+	0.643724i	$0.777389\pi$
$234$	21.4135	1.39984
$235$	−32.7864	−2.13875
$236$	−29.9009	−1.94638
$237$	0.914495	0.0594028
$238$	−24.9737	−1.61881
$239$	23.0676	1.49212	0.746059	−	0.665879i	$-0.231943\pi$
$239$	23.0676	1.49212	0.746059	+	0.665879i	$0.231943\pi$
$240$	9.33734	0.602723
$241$	−6.85810	−0.441769	−0.220885	−	0.975300i	$-0.570894\pi$
$241$	−6.85810	−0.441769	−0.220885	+	0.975300i	$0.570894\pi$
$242$	25.6450	1.64852
$243$	39.8479	2.55624
$244$	38.5620	2.46868
$245$	14.5721	0.930976
$246$	−12.9561	−0.826052
$247$	5.44439	0.346418
$248$	24.2390	1.53918
$249$	31.5783	2.00119
$250$	5.94438	0.375955
$251$	−11.3317	−0.715252	−0.357626	−	0.933865i	$-0.616414\pi$
$251$	−11.3317	−0.715252	−0.357626	+	0.933865i	$0.616414\pi$
$252$	89.9282	5.66494
$253$	−0.296515	−0.0186418
$254$	14.4411	0.906112
$255$	30.7060	1.92289
$256$	−21.6179	−1.35112
$257$	−14.1698	−0.883890	−0.441945	−	0.897042i	$-0.645711\pi$
$257$	−14.1698	−0.883890	−0.441945	+	0.897042i	$0.645711\pi$
$258$	−74.7689	−4.65491
$259$	31.2072	1.93912
$260$	−12.5590	−0.778873
$261$	7.60809	0.470929
$262$	−25.5681	−1.57960
$263$	−21.1845	−1.30629	−0.653147	−	0.757231i	$-0.726552\pi$
$263$	−21.1845	−1.30629	−0.653147	+	0.757231i	$0.726552\pi$
$264$	0.647624	0.0398585
$265$	6.32582	0.388592
$266$	36.1624	2.21726
$267$	39.4332	2.41328
$268$	−28.1741	−1.72101
$269$	3.34796	0.204129	0.102064	−	0.994778i	$-0.467455\pi$
$269$	3.34796	0.204129	0.102064	+	0.994778i	$0.467455\pi$
$270$	−105.921	−6.44614
$271$	2.98694	0.181444	0.0907219	−	0.995876i	$-0.471083\pi$
$271$	2.98694	0.181444	0.0907219	+	0.995876i	$0.471083\pi$
$272$	2.95137	0.178953
$273$	−13.5116	−0.817757
$274$	7.20951	0.435543
$275$	−0.246396	−0.0148582
$276$	56.0380	3.37309
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−50.3173	−3.01783
$279$	−54.9624	−3.29051
$280$	−34.9013	−2.08575
$281$	3.72794	0.222390	0.111195	−	0.993799i	$-0.464532\pi$
$281$	3.72794	0.222390	0.111195	+	0.993799i	$0.464532\pi$
$282$	82.2939	4.90053
$283$	23.8295	1.41652	0.708258	−	0.705953i	$-0.249481\pi$
$283$	23.8295	1.41652	0.708258	+	0.705953i	$0.249481\pi$
$284$	−50.3745	−2.98917
$285$	−44.4629	−2.63375
$286$	−0.166798	−0.00986299
$287$	5.86315	0.346091
$288$	34.2453	2.01792
$289$	−7.29438	−0.429081
$290$	−7.05735	−0.414422
$291$	−33.6164	−1.97063
$292$	−40.7974	−2.38749
$293$	−6.58255	−0.384557	−0.192278	−	0.981340i	$-0.561588\pi$
$293$	−6.58255	−0.384557	−0.192278	+	0.981340i	$0.561588\pi$
$294$	−36.5759	−2.13315
$295$	−26.3137	−1.53204
$296$	−30.4618	−1.77056
$297$	−0.889446	−0.0516109
$298$	4.10130	0.237582
$299$	−6.03852	−0.349217
$300$	46.5660	2.68849
$301$	33.8359	1.95027
$302$	33.4858	1.92689
$303$	22.0089	1.26438
$304$	−4.27363	−0.245110
$305$	33.9357	1.94315
$306$	−55.2759	−3.15991
$307$	26.2480	1.49805	0.749026	−	0.662540i	$-0.230522\pi$
$307$	26.2480	1.49805	0.749026	+	0.662540i	$0.230522\pi$
$308$	−0.700487	−0.0399140
$309$	19.4099	1.10419
$310$	50.9837	2.89568
$311$	−26.9295	−1.52703	−0.763516	−	0.645789i	$-0.776529\pi$
$311$	−26.9295	−1.52703	−0.763516	+	0.645789i	$0.776529\pi$
$312$	13.1888	0.746671
$313$	1.57532	0.0890422	0.0445211	−	0.999008i	$-0.485824\pi$
$313$	1.57532	0.0890422	0.0445211	+	0.999008i	$0.485824\pi$
$314$	−28.7504	−1.62248
$315$	79.1393	4.45900
$316$	0.965516	0.0543145
$317$	−23.3273	−1.31019	−0.655097	−	0.755545i	$-0.727372\pi$
$317$	−23.3273	−1.31019	−0.655097	+	0.755545i	$0.727372\pi$
$318$	−15.8778	−0.890384
$319$	−0.0592625	−0.00331806
$320$	−37.5000	−2.09631
$321$	−8.28002	−0.462146
$322$	−40.1087	−2.23517
$323$	−14.0539	−0.781981
$324$	89.6088	4.97827
$325$	−5.01784	−0.278340
$326$	35.8961	1.98810
$327$	−50.3334	−2.78345
$328$	−5.72311	−0.316006
$329$	−37.2412	−2.05318
$330$	1.36220	0.0749865
$331$	0.535641	0.0294415	0.0147207	−	0.999892i	$-0.495314\pi$
$331$	0.535641	0.0294415	0.0147207	+	0.999892i	$0.495314\pi$
$332$	33.3401	1.82977
$333$	69.0728	3.78517
$334$	30.2022	1.65259
$335$	−24.7940	−1.35464
$336$	10.6060	0.578607
$337$	32.7772	1.78549	0.892743	−	0.450565i	$-0.148778\pi$
$337$	32.7772	1.78549	0.892743	+	0.450565i	$0.148778\pi$
$338$	26.9205	1.46428
$339$	−57.9404	−3.14689
$340$	32.4192	1.75818
$341$	0.428124	0.0231842
$342$	80.0405	4.32810
$343$	−7.50939	−0.405469
$344$	−33.0277	−1.78073
$345$	49.3150	2.65503
$346$	54.6492	2.93796
$347$	20.2081	1.08483	0.542414	−	0.840111i	$-0.317510\pi$
$347$	20.2081	1.08483	0.542414	+	0.840111i	$0.317510\pi$
$348$	11.1999	0.600379
$349$	11.6831	0.625383	0.312692	−	0.949855i	$-0.398769\pi$
$349$	11.6831	0.625383	0.312692	+	0.949855i	$0.398769\pi$
$350$	−33.3292	−1.78152
$351$	−18.1135	−0.966829
$352$	−0.266750	−0.0142178
$353$	−12.3889	−0.659393	−0.329697	−	0.944087i	$-0.606946\pi$
$353$	−12.3889	−0.659393	−0.329697	+	0.944087i	$0.606946\pi$
$354$	66.0473	3.51037
$355$	−44.3309	−2.35284
$356$	41.6333	2.20656
$357$	34.8782	1.84595
$358$	−20.7755	−1.09802
$359$	17.8253	0.940782	0.470391	−	0.882458i	$-0.344113\pi$
$359$	17.8253	0.940782	0.470391	+	0.882458i	$0.344113\pi$
$360$	−77.2491	−4.07138
$361$	1.35034	0.0710707
$362$	−20.0330	−1.05291
$363$	−35.8156	−1.87983
$364$	−14.2654	−0.747709
$365$	−35.9029	−1.87924
$366$	−85.1785	−4.45235
$367$	10.1483	0.529739	0.264869	−	0.964284i	$-0.414671\pi$
$367$	10.1483	0.529739	0.264869	+	0.964284i	$0.414671\pi$
$368$	4.74000	0.247090
$369$	12.9773	0.675570
$370$	−64.0727	−3.33098
$371$	7.18534	0.373044
$372$	−80.9106	−4.19502
$373$	−14.1070	−0.730431	−0.365215	−	0.930923i	$-0.619005\pi$
$373$	−14.1070	−0.730431	−0.365215	+	0.930923i	$0.619005\pi$
$374$	0.430566	0.0222641
$375$	−8.30189	−0.428708
$376$	36.3517	1.87470
$377$	−1.20688	−0.0621574
$378$	−120.313	−6.18822
$379$	35.6823	1.83287	0.916437	−	0.400179i	$-0.131052\pi$
$379$	35.6823	1.83287	0.916437	+	0.400179i	$0.131052\pi$
$380$	−46.9435	−2.40815
$381$	−20.1683	−1.03325
$382$	−55.1556	−2.82200
$383$	13.2178	0.675399	0.337700	−	0.941254i	$-0.390351\pi$
$383$	13.2178	0.675399	0.337700	+	0.941254i	$0.390351\pi$
$384$	64.8043	3.30703
$385$	−0.616448	−0.0314171
$386$	−7.67826	−0.390813
$387$	74.8910	3.80692
$388$	−35.4919	−1.80183
$389$	15.6451	0.793236	0.396618	−	0.917984i	$-0.370184\pi$
$389$	15.6451	0.793236	0.396618	+	0.917984i	$0.370184\pi$
$390$	27.7411	1.40473
$391$	15.5876	0.788298
$392$	−16.1567	−0.816036
$393$	35.7082	1.80124
$394$	5.38154	0.271118
$395$	0.849681	0.0427521
$396$	−1.55043	−0.0779121
$397$	29.5793	1.48454	0.742271	−	0.670100i	$-0.233749\pi$
$397$	29.5793	1.48454	0.742271	+	0.670100i	$0.233749\pi$
$398$	6.47177	0.324401
$399$	−50.5042	−2.52837
$400$	3.93881	0.196940
$401$	−15.9174	−0.794877	−0.397438	−	0.917629i	$-0.630101\pi$
$401$	−15.9174	−0.794877	−0.397438	+	0.917629i	$0.630101\pi$
$402$	62.2329	3.10389
$403$	8.71873	0.434311
$404$	23.2368	1.15608
$405$	78.8583	3.91850
$406$	−8.01626	−0.397840
$407$	−0.538036	−0.0266695
$408$	−34.0451	−1.68548
$409$	−0.475986	−0.0235360	−0.0117680	−	0.999931i	$-0.503746\pi$
$409$	−0.475986	−0.0235360	−0.0117680	+	0.999931i	$0.503746\pi$
$410$	−12.0379	−0.594508
$411$	−10.0688	−0.496656
$412$	20.4928	1.00961
$413$	−29.8890	−1.47074
$414$	−88.7751	−4.36306
$415$	29.3402	1.44025
$416$	−5.43236	−0.266343
$417$	70.2728	3.44128
$418$	−0.623468	−0.0304948
$419$	−6.45610	−0.315401	−0.157701	−	0.987487i	$-0.550408\pi$
$419$	−6.45610	−0.315401	−0.157701	+	0.987487i	$0.550408\pi$
$420$	116.502	5.68470
$421$	−2.64268	−0.128796	−0.0643981	−	0.997924i	$-0.520513\pi$
$421$	−2.64268	−0.128796	−0.0643981	+	0.997924i	$0.520513\pi$
$422$	−52.3844	−2.55003
$423$	−82.4283	−4.00780
$424$	−7.01372	−0.340616
$425$	12.9528	0.628305
$426$	111.271	5.39108
$427$	38.5466	1.86540
$428$	−8.74197	−0.422559
$429$	0.232950	0.0112469
$430$	−69.4697	−3.35013
$431$	−2.35915	−0.113636	−0.0568181	−	0.998385i	$-0.518096\pi$
$431$	−2.35915	−0.113636	−0.0568181	+	0.998385i	$0.518096\pi$
$432$	14.2184	0.684084
$433$	14.1123	0.678194	0.339097	−	0.940751i	$-0.389879\pi$
$433$	14.1123	0.678194	0.339097	+	0.940751i	$0.389879\pi$
$434$	57.9111	2.77982
$435$	9.85625	0.472571
$436$	−53.1416	−2.54502
$437$	−22.5711	−1.07972
$438$	90.1161	4.30592
$439$	0.0795677	0.00379756	0.00189878	−	0.999998i	$-0.499396\pi$
$439$	0.0795677	0.00379756	0.00189878	+	0.999998i	$0.499396\pi$
$440$	0.601725	0.0286861
$441$	36.6356	1.74455
$442$	8.76846	0.417073
$443$	2.82433	0.134188	0.0670941	−	0.997747i	$-0.478627\pi$
$443$	2.82433	0.134188	0.0670941	+	0.997747i	$0.478627\pi$
$444$	101.683	4.82564
$445$	36.6385	1.73683
$446$	−24.3958	−1.15518
$447$	−5.72785	−0.270918
$448$	−42.5953	−2.01244
$449$	5.75335	0.271517	0.135759	−	0.990742i	$-0.456653\pi$
$449$	5.75335	0.271517	0.135759	+	0.990742i	$0.456653\pi$
$450$	−73.7696	−3.47753
$451$	−0.101085	−0.00475992
$452$	−61.1730	−2.87734
$453$	−46.7661	−2.19726
$454$	4.94453	0.232058
$455$	−12.5539	−0.588538
$456$	49.2980	2.30859
$457$	−40.5488	−1.89679	−0.948397	−	0.317086i	$-0.897296\pi$
$457$	−40.5488	−1.89679	−0.948397	+	0.317086i	$0.897296\pi$
$458$	−35.5559	−1.66142
$459$	46.7575	2.18245
$460$	52.0663	2.42761
$461$	−27.5167	−1.28158	−0.640790	−	0.767716i	$-0.721393\pi$
$461$	−27.5167	−1.28158	−0.640790	+	0.767716i	$0.721393\pi$
$462$	1.54729	0.0719862
$463$	−22.0541	−1.02494	−0.512471	−	0.858704i	$-0.671270\pi$
$463$	−22.0541	−1.02494	−0.512471	+	0.858704i	$0.671270\pi$
$464$	0.947352	0.0439797
$465$	−71.2036	−3.30199
$466$	54.4834	2.52389
$467$	−17.9999	−0.832935	−0.416467	−	0.909151i	$-0.636732\pi$
$467$	−17.9999	−0.832935	−0.416467	+	0.909151i	$0.636732\pi$
$468$	−31.5745	−1.45953
$469$	−28.1628	−1.30044
$470$	76.4614	3.52690
$471$	40.1526	1.85014
$472$	29.1751	1.34289
$473$	−0.583356	−0.0268227
$474$	−2.13270	−0.0979581
$475$	−18.7560	−0.860583
$476$	36.8241	1.68783
$477$	15.9037	0.728183
$478$	−53.7961	−2.46058
$479$	−39.8366	−1.82018	−0.910090	−	0.414410i	$-0.863988\pi$
$479$	−39.8366	−1.82018	−0.910090	+	0.414410i	$0.863988\pi$
$480$	44.3647	2.02496
$481$	−10.9571	−0.499600
$482$	15.9938	0.728499
$483$	56.0156	2.54880
$484$	−37.8138	−1.71881
$485$	−31.2338	−1.41826
$486$	−92.9294	−4.21537
$487$	−6.36823	−0.288572	−0.144286	−	0.989536i	$-0.546089\pi$
$487$	−6.36823	−0.288572	−0.144286	+	0.989536i	$0.546089\pi$
$488$	−37.6259	−1.70325
$489$	−50.1323	−2.26706
$490$	−33.9836	−1.53522
$491$	−4.84772	−0.218775	−0.109387	−	0.993999i	$-0.534889\pi$
$491$	−4.84772	−0.218775	−0.109387	+	0.993999i	$0.534889\pi$
$492$	19.1040	0.861273
$493$	3.11538	0.140310
$494$	−12.6969	−0.571260
$495$	−1.36442	−0.0613263
$496$	−6.84386	−0.307298
$497$	−50.3544	−2.25870
$498$	−73.6439	−3.30006
$499$	−11.0470	−0.494531	−0.247266	−	0.968948i	$-0.579532\pi$
$499$	−11.0470	−0.494531	−0.247266	+	0.968948i	$0.579532\pi$
$500$	−8.76506	−0.391985
$501$	−42.1802	−1.88447
$502$	26.4268	1.17948
$503$	26.0271	1.16049	0.580247	−	0.814441i	$-0.302956\pi$
$503$	26.0271	1.16049	0.580247	+	0.814441i	$0.302956\pi$
$504$	−87.7452	−3.90848
$505$	20.4491	0.909972
$506$	0.691505	0.0307412
$507$	−37.5971	−1.66974
$508$	−21.2935	−0.944747
$509$	−12.9963	−0.576050	−0.288025	−	0.957623i	$-0.592999\pi$
$509$	−12.9963	−0.576050	−0.288025	+	0.957623i	$0.592999\pi$
$510$	−71.6097	−3.17093
$511$	−40.7811	−1.80405
$512$	10.6214	0.469403
$513$	−67.7058	−2.98928
$514$	33.0455	1.45758
$515$	18.0343	0.794685
$516$	110.248	4.85338
$517$	0.642067	0.0282381
$518$	−72.7785	−3.19770
$519$	−76.3228	−3.35020
$520$	12.2541	0.537377
$521$	11.5820	0.507419	0.253709	−	0.967280i	$-0.418349\pi$
$521$	11.5820	0.507419	0.253709	+	0.967280i	$0.418349\pi$
$522$	−17.7429	−0.776585
$523$	−23.5486	−1.02971	−0.514854	−	0.857278i	$-0.672154\pi$
$523$	−23.5486	−1.02971	−0.514854	+	0.857278i	$0.672154\pi$
$524$	37.7004	1.64695
$525$	46.5474	2.03150
$526$	49.4046	2.15414
$527$	−22.5062	−0.980384
$528$	−0.182856	−0.00795780
$529$	2.03422	0.0884444
$530$	−14.7525	−0.640807
$531$	−66.1552	−2.87089
$532$	−53.3219	−2.31180
$533$	−2.05860	−0.0891677
$534$	−91.9625	−3.97961
$535$	−7.69318	−0.332605
$536$	27.4902	1.18739
$537$	29.0149	1.25209
$538$	−7.80779	−0.336618
$539$	−0.285370	−0.0122917
$540$	156.182	6.72098
$541$	9.90982	0.426056	0.213028	−	0.977046i	$-0.431667\pi$
$541$	9.90982	0.426056	0.213028	+	0.977046i	$0.431667\pi$
$542$	−6.96586	−0.299209
$543$	27.9780	1.20065
$544$	14.0229	0.601226
$545$	−46.7661	−2.00324
$546$	31.5104	1.34852
$547$	15.4309	0.659779	0.329889	−	0.944020i	$-0.392989\pi$
$547$	15.4309	0.659779	0.329889	+	0.944020i	$0.392989\pi$
$548$	−10.6305	−0.454113
$549$	85.3176	3.64127
$550$	0.574622	0.0245019
$551$	−4.51114	−0.192181
$552$	−54.6777	−2.32724
$553$	0.965130	0.0410415
$554$	2.33211	0.0990817
$555$	89.4836	3.79837
$556$	74.1935	3.14650
$557$	43.0706	1.82496	0.912480	−	0.409122i	$-0.134165\pi$
$557$	43.0706	1.82496	0.912480	+	0.409122i	$0.134165\pi$
$558$	128.178	5.42621
$559$	−11.8800	−0.502471
$560$	9.85435	0.416422
$561$	−0.601327	−0.0253880
$562$	−8.69395	−0.366732
$563$	−6.14713	−0.259071	−0.129535	−	0.991575i	$-0.541349\pi$
$563$	−6.14713	−0.259071	−0.129535	+	0.991575i	$0.541349\pi$
$564$	−121.343	−5.10948
$565$	−53.8340	−2.26481
$566$	−55.5729	−2.33590
$567$	89.5731	3.76171
$568$	49.1516	2.06236
$569$	−44.9052	−1.88252	−0.941262	−	0.337677i	$-0.890359\pi$
$569$	−44.9052	−1.88252	−0.941262	+	0.337677i	$0.890359\pi$
$570$	103.692	4.34319
$571$	36.9757	1.54739	0.773693	−	0.633561i	$-0.218407\pi$
$571$	36.9757	1.54739	0.773693	+	0.633561i	$0.218407\pi$
$572$	0.245946	0.0102835
$573$	77.0299	3.21797
$574$	−13.6735	−0.570721
$575$	20.8027	0.867534
$576$	−94.2787	−3.92828
$577$	−8.67584	−0.361180	−0.180590	−	0.983558i	$-0.557801\pi$
$577$	−8.67584	−0.361180	−0.180590	+	0.983558i	$0.557801\pi$
$578$	17.0113	0.707575
$579$	10.7234	0.445650
$580$	10.4061	0.432092
$581$	33.3268	1.38263
$582$	78.3969	3.24966
$583$	−0.123881	−0.00513062
$584$	39.8071	1.64723
$585$	−27.7864	−1.14883
$586$	15.3512	0.634152
$587$	17.5978	0.726340	0.363170	−	0.931723i	$-0.381694\pi$
$587$	17.5978	0.726340	0.363170	+	0.931723i	$0.381694\pi$
$588$	53.9316	2.22410
$589$	32.5894	1.34282
$590$	61.3663	2.52641
$591$	−7.51582	−0.309160
$592$	8.60088	0.353494
$593$	−2.41064	−0.0989929	−0.0494965	−	0.998774i	$-0.515762\pi$
$593$	−2.41064	−0.0989929	−0.0494965	+	0.998774i	$0.515762\pi$
$594$	2.07428	0.0851089
$595$	32.4062	1.32853
$596$	−6.04742	−0.247712
$597$	−9.03844	−0.369919
$598$	14.0825	0.575875
$599$	−10.0067	−0.408862	−0.204431	−	0.978881i	$-0.565534\pi$
$599$	−10.0067	−0.408862	−0.204431	+	0.978881i	$0.565534\pi$
$600$	−45.4356	−1.85490
$601$	18.2283	0.743546	0.371773	−	0.928324i	$-0.378750\pi$
$601$	18.2283	0.743546	0.371773	+	0.928324i	$0.378750\pi$
$602$	−78.9088	−3.21608
$603$	−62.3345	−2.53846
$604$	−49.3752	−2.00905
$605$	−33.2772	−1.35291
$606$	−51.3272	−2.08502
$607$	−4.14795	−0.168360	−0.0841800	−	0.996451i	$-0.526827\pi$
$607$	−4.14795	−0.168360	−0.0841800	+	0.996451i	$0.526827\pi$
$608$	−20.3054	−0.823492
$609$	11.1955	0.453663
$610$	−79.1416	−3.20435
$611$	13.0757	0.528985
$612$	81.5050	3.29464
$613$	−3.69430	−0.149211	−0.0746056	−	0.997213i	$-0.523770\pi$
$613$	−3.69430	−0.149211	−0.0746056	+	0.997213i	$0.523770\pi$
$614$	−61.2131	−2.47036
$615$	16.8120	0.677926
$616$	0.683483	0.0275383
$617$	−28.2858	−1.13874	−0.569372	−	0.822080i	$-0.692813\pi$
$617$	−28.2858	−1.13874	−0.569372	+	0.822080i	$0.692813\pi$
$618$	−45.2660	−1.82087
$619$	−17.2502	−0.693342	−0.346671	−	0.937987i	$-0.612688\pi$
$619$	−17.2502	−0.693342	−0.346671	+	0.937987i	$0.612688\pi$
$620$	−75.1761	−3.01915
$621$	75.0943	3.01343
$622$	62.8025	2.51815
$623$	41.6167	1.66734
$624$	−3.72386	−0.149074
$625$	−28.5020	−1.14008
$626$	−3.67381	−0.146835
$627$	0.870732	0.0347737
$628$	42.3928	1.69166
$629$	28.2841	1.12776
$630$	−184.561	−7.35310
$631$	−16.9315	−0.674033	−0.337017	−	0.941499i	$-0.609418\pi$
$631$	−16.9315	−0.674033	−0.337017	+	0.941499i	$0.609418\pi$
$632$	−0.942078	−0.0374739
$633$	73.1598	2.90784
$634$	54.4018	2.16057
$635$	−18.7389	−0.743630
$636$	23.4120	0.928347
$637$	−5.81154	−0.230262
$638$	0.138206	0.00547165
$639$	−111.452	−4.40899
$640$	60.2114	2.38006
$641$	−40.3609	−1.59416	−0.797080	−	0.603873i	$-0.793623\pi$
$641$	−40.3609	−1.59416	−0.797080	+	0.603873i	$0.793623\pi$
$642$	19.3099	0.762100
$643$	17.7171	0.698696	0.349348	−	0.936993i	$-0.386403\pi$
$643$	17.7171	0.698696	0.349348	+	0.936993i	$0.386403\pi$
$644$	59.1408	2.33047
$645$	97.0210	3.82020
$646$	32.7752	1.28952
$647$	−4.65095	−0.182848	−0.0914239	−	0.995812i	$-0.529142\pi$
$647$	−4.65095	−0.182848	−0.0914239	+	0.995812i	$0.529142\pi$
$648$	−87.4336	−3.43472
$649$	0.515309	0.0202277
$650$	11.7021	0.458996
$651$	−80.8783	−3.16987
$652$	−52.9292	−2.07287
$653$	45.2699	1.77155	0.885774	−	0.464117i	$-0.153628\pi$
$653$	45.2699	1.77155	0.885774	+	0.464117i	$0.153628\pi$
$654$	117.383	4.59003
$655$	33.1774	1.29635
$656$	1.61592	0.0630910
$657$	−90.2633	−3.52151
$658$	86.8505	3.38578
$659$	10.6805	0.416054	0.208027	−	0.978123i	$-0.433296\pi$
$659$	10.6805	0.416054	0.208027	+	0.978123i	$0.433296\pi$
$660$	−2.00858	−0.0781838
$661$	−22.8203	−0.887608	−0.443804	−	0.896124i	$-0.646371\pi$
$661$	−22.8203	−0.887608	−0.443804	+	0.896124i	$0.646371\pi$
$662$	−1.24917	−0.0485504
$663$	−12.2460	−0.475595
$664$	−32.5308	−1.26244
$665$	−46.9248	−1.81967
$666$	−161.085	−6.24192
$667$	5.00342	0.193733
$668$	−44.5335	−1.72305
$669$	34.0711	1.31726
$670$	57.8222	2.23387
$671$	−0.664573	−0.0256556
$672$	50.3926	1.94394
$673$	−42.3155	−1.63114	−0.815572	−	0.578656i	$-0.803577\pi$
$673$	−42.3155	−1.63114	−0.815572	+	0.578656i	$0.803577\pi$
$674$	−76.4399	−2.94435
$675$	62.4012	2.40183
$676$	−39.6947	−1.52672
$677$	3.84723	0.147861	0.0739306	−	0.997263i	$-0.476446\pi$
$677$	3.84723	0.147861	0.0739306	+	0.997263i	$0.476446\pi$
$678$	135.123	5.18938
$679$	−35.4777	−1.36151
$680$	−31.6322	−1.21304
$681$	−6.90550	−0.264619
$682$	−0.998431	−0.0382319
$683$	−6.26642	−0.239778	−0.119889	−	0.992787i	$-0.538254\pi$
$683$	−6.26642	−0.239778	−0.119889	+	0.992787i	$0.538254\pi$
$684$	−118.021	−4.51264
$685$	−9.35515	−0.357442
$686$	17.5127	0.668638
$687$	49.6572	1.89454
$688$	9.32535	0.355526
$689$	−2.52283	−0.0961120
$690$	−115.008	−4.37827
$691$	−36.6195	−1.39307	−0.696537	−	0.717521i	$-0.745277\pi$
$691$	−36.6195	−1.39307	−0.696537	+	0.717521i	$0.745277\pi$
$692$	−80.5809	−3.06323
$693$	−1.54981	−0.0588725
$694$	−47.1275	−1.78893
$695$	65.2923	2.47668
$696$	−10.9281	−0.414227
$697$	5.31398	0.201281
$698$	−27.2463	−1.03129
$699$	−76.0912	−2.87803
$700$	49.1444	1.85748
$701$	−37.4223	−1.41342	−0.706711	−	0.707502i	$-0.749822\pi$
$701$	−37.4223	−1.41342	−0.706711	+	0.707502i	$0.749822\pi$
$702$	42.2427	1.59435
$703$	−40.9560	−1.54468
$704$	0.734375	0.0276778
$705$	−106.786	−4.02178
$706$	28.8922	1.08737
$707$	23.2276	0.873563
$708$	−97.3875	−3.66005
$709$	−12.3760	−0.464792	−0.232396	−	0.972621i	$-0.574656\pi$
$709$	−12.3760	−0.464792	−0.232396	+	0.972621i	$0.574656\pi$
$710$	103.384	3.87995
$711$	2.13618	0.0801131
$712$	−40.6227	−1.52240
$713$	−36.1457	−1.35367
$714$	−81.3396	−3.04406
$715$	0.216440	0.00809438
$716$	30.6337	1.14484
$717$	75.1313	2.80583
$718$	−41.5704	−1.55139
$719$	−26.2191	−0.977806	−0.488903	−	0.872338i	$-0.662603\pi$
$719$	−26.2191	−0.977806	−0.488903	+	0.872338i	$0.662603\pi$
$720$	21.8112	0.812857
$721$	20.4846	0.762888
$722$	−3.14915	−0.117199
$723$	−22.3369	−0.830718
$724$	29.5390	1.09781
$725$	4.15770	0.154413
$726$	83.5259	3.09994
$727$	−11.7647	−0.436329	−0.218164	−	0.975912i	$-0.570007\pi$
$727$	−11.7647	−0.436329	−0.218164	+	0.975912i	$0.570007\pi$
$728$	13.9191	0.515876
$729$	51.6084	1.91142
$730$	83.7293	3.09896
$731$	30.6666	1.13424
$732$	125.597	4.64219
$733$	−17.0144	−0.628442	−0.314221	−	0.949350i	$-0.601743\pi$
$733$	−17.0144	−0.628442	−0.314221	+	0.949350i	$0.601743\pi$
$734$	−23.6670	−0.873565
$735$	47.4613	1.75064
$736$	22.5212	0.830144
$737$	0.485549	0.0178854
$738$	−30.2644	−1.11405
$739$	29.8527	1.09815	0.549074	−	0.835773i	$-0.314980\pi$
$739$	29.8527	1.09815	0.549074	+	0.835773i	$0.314980\pi$
$740$	94.4760	3.47301
$741$	17.7324	0.651417
$742$	−16.7570	−0.615168
$743$	−4.80595	−0.176313	−0.0881566	−	0.996107i	$-0.528098\pi$
$743$	−4.80595	−0.176313	−0.0881566	+	0.996107i	$0.528098\pi$
$744$	78.9465	2.89432
$745$	−5.32190	−0.194979
$746$	32.8989	1.20452
$747$	73.7642	2.69889
$748$	−0.634875	−0.0232133
$749$	−8.73848	−0.319297
$750$	19.3609	0.706959
$751$	41.8405	1.52678	0.763391	−	0.645936i	$-0.223533\pi$
$751$	41.8405	1.52678	0.763391	+	0.645936i	$0.223533\pi$
$752$	−10.2639	−0.374286
$753$	−36.9075	−1.34498
$754$	2.81457	0.102501
$755$	−43.4516	−1.58137
$756$	177.403	6.45207
$757$	−17.7978	−0.646871	−0.323436	−	0.946250i	$-0.604838\pi$
$757$	−17.7978	−0.646871	−0.323436	+	0.946250i	$0.604838\pi$
$758$	−83.2148	−3.02250
$759$	−0.965752	−0.0350546
$760$	45.8040	1.66149
$761$	31.7013	1.14917	0.574586	−	0.818444i	$-0.305163\pi$
$761$	31.7013	1.14917	0.574586	+	0.818444i	$0.305163\pi$
$762$	47.0346	1.70388
$763$	−53.1204	−1.92309
$764$	81.3275	2.94233
$765$	71.7267	2.59328
$766$	−30.8254	−1.11377
$767$	10.4943	0.378925
$768$	−70.4096	−2.54069
$769$	46.0810	1.66172	0.830862	−	0.556479i	$-0.187848\pi$
$769$	46.0810	1.66172	0.830862	+	0.556479i	$0.187848\pi$
$770$	1.43762	0.0518083
$771$	−46.1512	−1.66210
$772$	11.3217	0.407477
$773$	16.6957	0.600502	0.300251	−	0.953860i	$-0.402930\pi$
$773$	16.6957	0.600502	0.300251	+	0.953860i	$0.402930\pi$
$774$	−174.654	−6.27780
$775$	−30.0361	−1.07893
$776$	34.6303	1.24316
$777$	101.642	3.64639
$778$	−36.4859	−1.30808
$779$	−7.69474	−0.275693
$780$	−40.9046	−1.46462
$781$	0.868148	0.0310648
$782$	−36.3519	−1.29994
$783$	15.0086	0.536363
$784$	4.56183	0.162923
$785$	37.3069	1.33154
$786$	−83.2754	−2.97033
$787$	25.9755	0.925926	0.462963	−	0.886377i	$-0.346786\pi$
$787$	25.9755	0.925926	0.462963	+	0.886377i	$0.346786\pi$
$788$	−7.93514	−0.282678
$789$	−68.9982	−2.45640
$790$	−1.98155	−0.0705002
$791$	−61.1486	−2.17419
$792$	1.51280	0.0537548
$793$	−13.5340	−0.480607
$794$	−68.9820	−2.44808
$795$	20.6032	0.730722
$796$	−9.54271	−0.338232
$797$	−44.6960	−1.58321	−0.791606	−	0.611031i	$-0.790755\pi$
$797$	−44.6960	−1.58321	−0.791606	+	0.611031i	$0.790755\pi$
$798$	117.781	4.16941
$799$	−33.7530	−1.19410
$800$	18.7145	0.661658
$801$	92.1127	3.25464
$802$	37.1211	1.31079
$803$	0.703098	0.0248118
$804$	−91.7632	−3.23624
$805$	52.0456	1.83436
$806$	−20.3330	−0.716200
$807$	10.9043	0.383850
$808$	−22.6728	−0.797626
$809$	−30.0180	−1.05538	−0.527689	−	0.849438i	$-0.676941\pi$
$809$	−30.0180	−1.05538	−0.527689	+	0.849438i	$0.676941\pi$
$810$	−183.906	−6.46180
$811$	42.6346	1.49710	0.748551	−	0.663077i	$-0.230750\pi$
$811$	42.6346	1.49710	0.748551	+	0.663077i	$0.230750\pi$
$812$	11.8201	0.414803
$813$	9.72849	0.341193
$814$	1.25476	0.0439792
$815$	−46.5792	−1.63160
$816$	9.61262	0.336509
$817$	−44.4058	−1.55356
$818$	1.11005	0.0388120
$819$	−31.5619	−1.10286
$820$	17.7500	0.619856
$821$	45.5999	1.59145	0.795723	−	0.605660i	$-0.207091\pi$
$821$	45.5999	1.59145	0.795723	+	0.605660i	$0.207091\pi$
$822$	23.4814	0.819009
$823$	4.08744	0.142479	0.0712396	−	0.997459i	$-0.477305\pi$
$823$	4.08744	0.142479	0.0712396	+	0.997459i	$0.477305\pi$
$824$	−19.9954	−0.696572
$825$	−0.802513	−0.0279399
$826$	69.7043	2.42532
$827$	29.8035	1.03637	0.518185	−	0.855269i	$-0.326608\pi$
$827$	29.8035	1.03637	0.518185	+	0.855269i	$0.326608\pi$
$828$	130.900	4.54909
$829$	−16.0250	−0.556570	−0.278285	−	0.960499i	$-0.589766\pi$
$829$	−16.0250	−0.556570	−0.278285	+	0.960499i	$0.589766\pi$
$830$	−68.4245	−2.37505
$831$	−3.25701	−0.112984
$832$	14.9555	0.518489
$833$	15.0017	0.519777
$834$	−163.884	−5.67483
$835$	−39.1907	−1.35625
$836$	0.919311	0.0317950
$837$	−108.425	−3.74772
$838$	15.0563	0.520112
$839$	−29.2520	−1.00989	−0.504945	−	0.863152i	$-0.668487\pi$
$839$	−29.2520	−1.00989	−0.504945	+	0.863152i	$0.668487\pi$
$840$	−113.674	−3.92211
$841$	1.00000	0.0344828
$842$	6.16300	0.212391
$843$	12.1419	0.418190
$844$	77.2415	2.65876
$845$	−34.9324	−1.20171
$846$	192.232	6.60906
$847$	−37.7987	−1.29878
$848$	1.98032	0.0680044
$849$	77.6128	2.66367
$850$	−30.2074	−1.03611
$851$	45.4254	1.55716
$852$	−164.070	−5.62094
$853$	49.9708	1.71097	0.855484	−	0.517830i	$-0.173260\pi$
$853$	49.9708	1.71097	0.855484	+	0.517830i	$0.173260\pi$
$854$	−89.8948	−3.07614
$855$	−103.862	−3.55199
$856$	8.52976	0.291541
$857$	−54.5535	−1.86351	−0.931756	−	0.363086i	$-0.881723\pi$
$857$	−54.5535	−1.86351	−0.931756	+	0.363086i	$0.881723\pi$
$858$	−0.543263	−0.0185467
$859$	1.92759	0.0657685	0.0328843	−	0.999459i	$-0.489531\pi$
$859$	1.92759	0.0657685	0.0328843	+	0.999459i	$0.489531\pi$
$860$	102.434	3.49297
$861$	19.0963	0.650801
$862$	5.50178	0.187392
$863$	31.3650	1.06768	0.533839	−	0.845586i	$-0.320749\pi$
$863$	31.3650	1.06768	0.533839	+	0.845586i	$0.320749\pi$
$864$	67.5561	2.29831
$865$	−70.9135	−2.41113
$866$	−32.9114	−1.11837
$867$	−23.7578	−0.806858
$868$	−85.3906	−2.89835
$869$	−0.0166396	−0.000564459 0
$870$	−22.9858	−0.779293
$871$	9.88818	0.335048
$872$	51.8516	1.75592
$873$	−78.5250	−2.65767
$874$	52.6382	1.78051
$875$	−8.76156	−0.296195
$876$	−132.877	−4.48951
$877$	−28.5982	−0.965693	−0.482847	−	0.875705i	$-0.660397\pi$
$877$	−28.5982	−0.965693	−0.482847	+	0.875705i	$0.660397\pi$
$878$	−0.185560	−0.00626236
$879$	−21.4394	−0.723133
$880$	−0.169897	−0.00572721
$881$	−2.73305	−0.0920790	−0.0460395	−	0.998940i	$-0.514660\pi$
$881$	−2.73305	−0.0920790	−0.0460395	+	0.998940i	$0.514660\pi$
$882$	−85.4382	−2.87685
$883$	−4.82306	−0.162309	−0.0811544	−	0.996702i	$-0.525861\pi$
$883$	−4.82306	−0.162309	−0.0811544	+	0.996702i	$0.525861\pi$
$884$	−12.9292	−0.434856
$885$	−85.7038	−2.88090
$886$	−6.58664	−0.221283
$887$	50.4550	1.69411	0.847056	−	0.531503i	$-0.178373\pi$
$887$	50.4550	1.69411	0.847056	+	0.531503i	$0.178373\pi$
$888$	−99.2143	−3.32941
$889$	−21.2850	−0.713876
$890$	−85.4448	−2.86412
$891$	−1.54431	−0.0517363
$892$	35.9720	1.20443
$893$	48.8750	1.63554
$894$	13.3580	0.446757
$895$	26.9585	0.901124
$896$	68.3925	2.28483
$897$	−19.6675	−0.656679
$898$	−13.4174	−0.447745
$899$	−7.22420	−0.240941
$900$	108.774	3.62581
$901$	6.51232	0.216957
$902$	0.235742	0.00784934
$903$	110.204	3.66735
$904$	59.6881	1.98520
$905$	25.9951	0.864107
$906$	109.063	3.62339
$907$	35.3885	1.17506	0.587528	−	0.809204i	$-0.300101\pi$
$907$	35.3885	1.17506	0.587528	+	0.809204i	$0.300101\pi$
$908$	−7.29077	−0.241953
$909$	51.4110	1.70520
$910$	29.2771	0.970527
$911$	−23.7827	−0.787956	−0.393978	−	0.919120i	$-0.628901\pi$
$911$	−23.7827	−0.787956	−0.393978	+	0.919120i	$0.628901\pi$
$912$	−13.9193	−0.460912
$913$	−0.574579	−0.0190158
$914$	94.5641	3.12790
$915$	110.529	3.65396
$916$	52.4276	1.73226
$917$	37.6854	1.24448
$918$	−109.043	−3.59897
$919$	−2.61276	−0.0861871	−0.0430935	−	0.999071i	$-0.513721\pi$
$919$	−2.61276	−0.0861871	−0.0430935	+	0.999071i	$0.513721\pi$
$920$	−50.8025	−1.67491
$921$	85.4899	2.81699
$922$	64.1718	2.11339
$923$	17.6798	0.581937
$924$	−2.28149	−0.0750555
$925$	37.7472	1.24112
$926$	51.4326	1.69018
$927$	45.3399	1.48916
$928$	4.50117	0.147758
$929$	40.4023	1.32556	0.662778	−	0.748816i	$-0.269377\pi$
$929$	40.4023	1.32556	0.662778	+	0.748816i	$0.269377\pi$
$930$	166.054	5.44514
$931$	−21.7227	−0.711933
$932$	−80.3365	−2.63151
$933$	−87.7096	−2.87148
$934$	41.9776	1.37355
$935$	−0.558708	−0.0182717
$936$	30.8080	1.00699
$937$	0.150816	0.00492694	0.00246347	−	0.999997i	$-0.499216\pi$
$937$	0.150816	0.00492694	0.00246347	+	0.999997i	$0.499216\pi$
$938$	65.6787	2.14449
$939$	5.13082	0.167438
$940$	−112.743	−3.67728
$941$	−1.45535	−0.0474429	−0.0237215	−	0.999719i	$-0.507551\pi$
$941$	−1.45535	−0.0474429	−0.0237215	+	0.999719i	$0.507551\pi$
$942$	−93.6402	−3.05096
$943$	8.53444	0.277920
$944$	−8.23757	−0.268110
$945$	156.119	5.07856
$946$	1.36045	0.0442320
$947$	−50.2241	−1.63206	−0.816032	−	0.578007i	$-0.803831\pi$
$947$	−50.2241	−1.63206	−0.816032	+	0.578007i	$0.803831\pi$
$948$	3.14469	0.102135
$949$	14.3186	0.464800
$950$	43.7409	1.41914
$951$	−75.9773	−2.46373
$952$	−35.9302	−1.16450
$953$	−23.9459	−0.775684	−0.387842	−	0.921726i	$-0.626779\pi$
$953$	−23.9459	−0.775684	−0.387842	+	0.921726i	$0.626779\pi$
$954$	−37.0892	−1.20081
$955$	71.5705	2.31597
$956$	79.3230	2.56549
$957$	−0.193018	−0.00623940
$958$	92.9032	3.00157
$959$	−10.6263	−0.343140
$960$	−122.138	−3.94198
$961$	21.1891	0.683519
$962$	25.5531	0.823864
$963$	−19.3414	−0.623269
$964$	−23.5831	−0.759560
$965$	9.96341	0.320734
$966$	−130.634	−4.20309
$967$	33.7667	1.08587	0.542933	−	0.839776i	$-0.317314\pi$
$967$	33.7667	1.08587	0.542933	+	0.839776i	$0.317314\pi$
$968$	36.8959	1.18588
$969$	−45.7737	−1.47046
$970$	72.8406	2.33877
$971$	23.5795	0.756704	0.378352	−	0.925662i	$-0.376491\pi$
$971$	23.5795	0.756704	0.378352	+	0.925662i	$0.376491\pi$
$972$	137.026	4.39510
$973$	74.1638	2.37758
$974$	14.8514	0.475869
$975$	−16.3431	−0.523399
$976$	10.6237	0.340055
$977$	54.0777	1.73010	0.865049	−	0.501688i	$-0.167287\pi$
$977$	54.0777	1.73010	0.865049	+	0.501688i	$0.167287\pi$
$978$	116.914	3.73849
$979$	−0.717503	−0.0229315
$980$	50.1093	1.60068
$981$	−117.575	−3.75387
$982$	11.3054	0.360770
$983$	11.0128	0.351253	0.175627	−	0.984457i	$-0.443805\pi$
$983$	11.0128	0.351253	0.175627	+	0.984457i	$0.443805\pi$
$984$	−18.6402	−0.594228
$985$	−6.98315	−0.222502
$986$	−7.26541	−0.231378
$987$	−121.295	−3.86086
$988$	18.7217	0.595618
$989$	49.2517	1.56611
$990$	3.18198	0.101130
$991$	53.7720	1.70812	0.854061	−	0.520172i	$-0.174132\pi$
$991$	53.7720	1.70812	0.854061	+	0.520172i	$0.174132\pi$
$992$	−32.5173	−1.03243
$993$	1.74459	0.0553628
$994$	117.432	3.72471
$995$	−8.39785	−0.266230
$996$	108.589	3.44077
$997$	22.1491	0.701468	0.350734	−	0.936475i	$-0.385932\pi$
$997$	22.1491	0.701468	0.350734	+	0.936475i	$0.385932\pi$
$998$	25.7627	0.815506
$999$	136.261	4.31110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.d.1.20	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.d.1.20	✓	168	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33211 q^{2} +3.25701 q^{3} +3.43872 q^{4} +3.02617 q^{5} -7.59569 q^{6} +3.43735 q^{7} -3.35525 q^{8} +7.60809 q^{9} +O(q^{10})\)	\(q-2.33211 q^{2} +3.25701 q^{3} +3.43872 q^{4} +3.02617 q^{5} -7.59569 q^{6} +3.43735 q^{7} -3.35525 q^{8} +7.60809 q^{9} -7.05735 q^{10} -0.0592625 q^{11} +11.1999 q^{12} -1.20688 q^{13} -8.01626 q^{14} +9.85625 q^{15} +0.947352 q^{16} +3.11538 q^{17} -17.7429 q^{18} -4.51114 q^{19} +10.4061 q^{20} +11.1955 q^{21} +0.138206 q^{22} +5.00342 q^{23} -10.9281 q^{24} +4.15770 q^{25} +2.81457 q^{26} +15.0086 q^{27} +11.8201 q^{28} +1.00000 q^{29} -22.9858 q^{30} -7.22420 q^{31} +4.50117 q^{32} -0.193018 q^{33} -7.26541 q^{34} +10.4020 q^{35} +26.1621 q^{36} +9.07886 q^{37} +10.5204 q^{38} -3.93081 q^{39} -10.1535 q^{40} +1.70572 q^{41} -26.1090 q^{42} +9.84360 q^{43} -0.203787 q^{44} +23.0234 q^{45} -11.6685 q^{46} -10.8343 q^{47} +3.08553 q^{48} +4.81535 q^{49} -9.69621 q^{50} +10.1468 q^{51} -4.15012 q^{52} +2.09037 q^{53} -35.0016 q^{54} -0.179338 q^{55} -11.5331 q^{56} -14.6928 q^{57} -2.33211 q^{58} -8.69537 q^{59} +33.8929 q^{60} +11.2141 q^{61} +16.8476 q^{62} +26.1516 q^{63} -12.3919 q^{64} -3.65222 q^{65} +0.450139 q^{66} -8.19319 q^{67} +10.7129 q^{68} +16.2962 q^{69} -24.2586 q^{70} -14.6492 q^{71} -25.5270 q^{72} -11.8641 q^{73} -21.1729 q^{74} +13.5417 q^{75} -15.5125 q^{76} -0.203706 q^{77} +9.16707 q^{78} +0.280778 q^{79} +2.86685 q^{80} +26.0588 q^{81} -3.97792 q^{82} +9.69549 q^{83} +38.4980 q^{84} +9.42768 q^{85} -22.9563 q^{86} +3.25701 q^{87} +0.198840 q^{88} +12.1072 q^{89} -53.6930 q^{90} -4.14846 q^{91} +17.2054 q^{92} -23.5293 q^{93} +25.2667 q^{94} -13.6515 q^{95} +14.6603 q^{96} -10.3212 q^{97} -11.2299 q^{98} -0.450875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9}+O(q^{10}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9	\( 168 q + 12 q^{2} + 35 q^{3} + 184 q^{4} + 12 q^{5} + 10 q^{6} + 74 q^{7} + 39 q^{8} + 183 q^{9} + 41 q^{10} + 29 q^{11} + 82 q^{12} + 62 q^{13} + 23 q^{14} + 31 q^{15} + 204 q^{16} + 56 q^{17} + 35 q^{18} + 83 q^{19} + 6 q^{20} + 30 q^{21} + 56 q^{22} + 54 q^{23} + 28 q^{24} + 210 q^{25} + 21 q^{26} + 140 q^{27} + 151 q^{28} + 168 q^{29} + 29 q^{30} + 72 q^{31} + 40 q^{32} + 32 q^{33} + 34 q^{34} + 18 q^{35} + 152 q^{36} + 42 q^{37} + 29 q^{38} + 70 q^{39} + 97 q^{40} + 41 q^{41} - 20 q^{42} + 119 q^{43} + 37 q^{44} + 22 q^{45} + 24 q^{46} + 119 q^{47} + 135 q^{48} + 216 q^{49} + 38 q^{50} + 18 q^{51} + 154 q^{52} - 7 q^{53} + 35 q^{54} + 224 q^{55} + 46 q^{56} + 12 q^{57} + 12 q^{58} + 25 q^{59} + 13 q^{60} + 82 q^{61} + 27 q^{62} + 211 q^{63} + 217 q^{64} + 8 q^{65} - 6 q^{66} + 76 q^{67} + 132 q^{68} + 36 q^{69} + 39 q^{70} + 32 q^{71} + 39 q^{72} + 89 q^{73} - q^{74} + 123 q^{75} + 180 q^{76} + 68 q^{77} - 54 q^{78} + 176 q^{79} - 11 q^{80} + 192 q^{81} + 51 q^{82} + 76 q^{83} + 86 q^{84} + 65 q^{85} - 72 q^{86} + 35 q^{87} + 178 q^{88} + 55 q^{89} + 2 q^{90} + 80 q^{91} + 44 q^{92} + 39 q^{93} + 89 q^{94} + 77 q^{95} - 68 q^{96} + 82 q^{97} + 80 q^{98} + 67 q^{99}+O(q^{100}) \) 168 * q + 12 * q^2 + 35 * q^3 + 184 * q^4 + 12 * q^5 + 10 * q^6 + 74 * q^7 + 39 * q^8 + 183 * q^9 + 41 * q^10 + 29 * q^11 + 82 * q^12 + 62 * q^13 + 23 * q^14 + 31 * q^15 + 204 * q^16 + 56 * q^17 + 35 * q^18 + 83 * q^19 + 6 * q^20 + 30 * q^21 + 56 * q^22 + 54 * q^23 + 28 * q^24 + 210 * q^25 + 21 * q^26 + 140 * q^27 + 151 * q^28 + 168 * q^29 + 29 * q^30 + 72 * q^31 + 40 * q^32 + 32 * q^33 + 34 * q^34 + 18 * q^35 + 152 * q^36 + 42 * q^37 + 29 * q^38 + 70 * q^39 + 97 * q^40 + 41 * q^41 - 20 * q^42 + 119 * q^43 + 37 * q^44 + 22 * q^45 + 24 * q^46 + 119 * q^47 + 135 * q^48 + 216 * q^49 + 38 * q^50 + 18 * q^51 + 154 * q^52 - 7 * q^53 + 35 * q^54 + 224 * q^55 + 46 * q^56 + 12 * q^57 + 12 * q^58 + 25 * q^59 + 13 * q^60 + 82 * q^61 + 27 * q^62 + 211 * q^63 + 217 * q^64 + 8 * q^65 - 6 * q^66 + 76 * q^67 + 132 * q^68 + 36 * q^69 + 39 * q^70 + 32 * q^71 + 39 * q^72 + 89 * q^73 - q^74 + 123 * q^75 + 180 * q^76 + 68 * q^77 - 54 * q^78 + 176 * q^79 - 11 * q^80 + 192 * q^81 + 51 * q^82 + 76 * q^83 + 86 * q^84 + 65 * q^85 - 72 * q^86 + 35 * q^87 + 178 * q^88 + 55 * q^89 + 2 * q^90 + 80 * q^91 + 44 * q^92 + 39 * q^93 + 89 * q^94 + 77 * q^95 - 68 * q^96 + 82 * q^97 + 80 * q^98 + 67 * q^99

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