LMFDB - Embedded newform 6017.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75999 q^{2} -3.06184 q^{3} +5.61754 q^{4} -2.40388 q^{5} +8.45065 q^{6} -3.94507 q^{7} -9.98436 q^{8} +6.37487 q^{9} +O(q^{10})$	\(q-2.75999 q^{2} -3.06184 q^{3} +5.61754 q^{4} -2.40388 q^{5} +8.45065 q^{6} -3.94507 q^{7} -9.98436 q^{8} +6.37487 q^{9} +6.63467 q^{10} -1.00000 q^{11} -17.2000 q^{12} -2.78559 q^{13} +10.8884 q^{14} +7.36028 q^{15} +16.3217 q^{16} +7.23996 q^{17} -17.5946 q^{18} -1.05610 q^{19} -13.5039 q^{20} +12.0792 q^{21} +2.75999 q^{22} -4.23645 q^{23} +30.5705 q^{24} +0.778618 q^{25} +7.68820 q^{26} -10.3333 q^{27} -22.1616 q^{28} -1.68996 q^{29} -20.3143 q^{30} -10.5153 q^{31} -25.0789 q^{32} +3.06184 q^{33} -19.9822 q^{34} +9.48347 q^{35} +35.8111 q^{36} +3.71189 q^{37} +2.91483 q^{38} +8.52904 q^{39} +24.0012 q^{40} +6.10424 q^{41} -33.3384 q^{42} -11.4430 q^{43} -5.61754 q^{44} -15.3244 q^{45} +11.6925 q^{46} -12.0766 q^{47} -49.9743 q^{48} +8.56361 q^{49} -2.14898 q^{50} -22.1676 q^{51} -15.6482 q^{52} -3.28997 q^{53} +28.5198 q^{54} +2.40388 q^{55} +39.3891 q^{56} +3.23362 q^{57} +4.66427 q^{58} +10.6109 q^{59} +41.3467 q^{60} -9.45911 q^{61} +29.0221 q^{62} -25.1493 q^{63} +36.5741 q^{64} +6.69622 q^{65} -8.45065 q^{66} +9.23146 q^{67} +40.6707 q^{68} +12.9713 q^{69} -26.1743 q^{70} +1.56085 q^{71} -63.6490 q^{72} +6.70131 q^{73} -10.2448 q^{74} -2.38400 q^{75} -5.93270 q^{76} +3.94507 q^{77} -23.5401 q^{78} -0.599747 q^{79} -39.2352 q^{80} +12.5144 q^{81} -16.8476 q^{82} -2.99112 q^{83} +67.8553 q^{84} -17.4040 q^{85} +31.5825 q^{86} +5.17439 q^{87} +9.98436 q^{88} -11.4507 q^{89} +42.2952 q^{90} +10.9894 q^{91} -23.7984 q^{92} +32.1962 q^{93} +33.3313 q^{94} +2.53874 q^{95} +76.7875 q^{96} +1.96658 q^{97} -23.6355 q^{98} -6.37487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * 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 $

$2$	−2.75999	−1.95161	−0.975803	−	0.218650i	$-0.929835\pi$
$2$	−2.75999	−1.95161	−0.975803	+	0.218650i	$0.929835\pi$
$3$	−3.06184	−1.76775	−0.883877	−	0.467719i	$-0.845076\pi$
$3$	−3.06184	−1.76775	−0.883877	+	0.467719i	$0.845076\pi$
$4$	5.61754	2.80877
$5$	−2.40388	−1.07505	−0.537523	−	0.843249i	$-0.680640\pi$
$5$	−2.40388	−1.07505	−0.537523	+	0.843249i	$0.680640\pi$
$6$	8.45065	3.44996
$7$	−3.94507	−1.49110	−0.745549	−	0.666451i	$-0.767813\pi$
$7$	−3.94507	−1.49110	−0.745549	+	0.666451i	$0.767813\pi$
$8$	−9.98436	−3.53001
$9$	6.37487	2.12496
$10$	6.63467	2.09807
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−17.2000	−4.96521
$13$	−2.78559	−0.772584	−0.386292	−	0.922376i	$-0.626244\pi$
$13$	−2.78559	−0.772584	−0.386292	+	0.922376i	$0.626244\pi$
$14$	10.8884	2.91004
$15$	7.36028	1.90042
$16$	16.3217	4.08041
$17$	7.23996	1.75595	0.877974	−	0.478709i	$-0.158895\pi$
$17$	7.23996	1.75595	0.877974	+	0.478709i	$0.158895\pi$
$18$	−17.5946	−4.14708
$19$	−1.05610	−0.242287	−0.121143	−	0.992635i	$-0.538656\pi$
$19$	−1.05610	−0.242287	−0.121143	+	0.992635i	$0.538656\pi$
$20$	−13.5039	−3.01956
$21$	12.0792	2.63589
$22$	2.75999	0.588432
$23$	−4.23645	−0.883361	−0.441680	−	0.897173i	$-0.645617\pi$
$23$	−4.23645	−0.883361	−0.441680	+	0.897173i	$0.645617\pi$
$24$	30.5705	6.24018
$25$	0.778618	0.155724
$26$	7.68820	1.50778
$27$	−10.3333	−1.98865
$28$	−22.1616	−4.18815
$29$	−1.68996	−0.313818	−0.156909	−	0.987613i	$-0.550153\pi$
$29$	−1.68996	−0.313818	−0.156909	+	0.987613i	$0.550153\pi$
$30$	−20.3143	−3.70887
$31$	−10.5153	−1.88861	−0.944303	−	0.329078i	$-0.893262\pi$
$31$	−10.5153	−1.88861	−0.944303	+	0.329078i	$0.893262\pi$
$32$	−25.0789	−4.43336
$33$	3.06184	0.532998
$34$	−19.9822	−3.42692
$35$	9.48347	1.60300
$36$	35.8111	5.96851
$37$	3.71189	0.610230	0.305115	−	0.952315i	$-0.401305\pi$
$37$	3.71189	0.610230	0.305115	+	0.952315i	$0.401305\pi$
$38$	2.91483	0.472848
$39$	8.52904	1.36574
$40$	24.0012	3.79492
$41$	6.10424	0.953322	0.476661	−	0.879087i	$-0.341847\pi$
$41$	6.10424	0.953322	0.476661	+	0.879087i	$0.341847\pi$
$42$	−33.3384	−5.14423
$43$	−11.4430	−1.74504	−0.872520	−	0.488579i	$-0.837515\pi$
$43$	−11.4430	−1.74504	−0.872520	+	0.488579i	$0.837515\pi$
$44$	−5.61754	−0.846876
$45$	−15.3244	−2.28443
$46$	11.6925	1.72397
$47$	−12.0766	−1.76155	−0.880777	−	0.473531i	$-0.842979\pi$
$47$	−12.0766	−1.76155	−0.880777	+	0.473531i	$0.842979\pi$
$48$	−49.9743	−7.21317
$49$	8.56361	1.22337
$50$	−2.14898	−0.303911
$51$	−22.1676	−3.10408
$52$	−15.6482	−2.17001
$53$	−3.28997	−0.451913	−0.225956	−	0.974137i	$-0.572551\pi$
$53$	−3.28997	−0.451913	−0.225956	+	0.974137i	$0.572551\pi$
$54$	28.5198	3.88106
$55$	2.40388	0.324139
$56$	39.3891	5.26358
$57$	3.23362	0.428304
$58$	4.66427	0.612449
$59$	10.6109	1.38142	0.690708	−	0.723134i	$-0.257299\pi$
$59$	10.6109	1.38142	0.690708	+	0.723134i	$0.257299\pi$
$60$	41.3467	5.33783
$61$	−9.45911	−1.21111	−0.605557	−	0.795802i	$-0.707050\pi$
$61$	−9.45911	−1.21111	−0.605557	+	0.795802i	$0.707050\pi$
$62$	29.0221	3.68582
$63$	−25.1493	−3.16852
$64$	36.5741	4.57176
$65$	6.69622	0.830564
$66$	−8.45065	−1.04020
$67$	9.23146	1.12780	0.563901	−	0.825842i	$-0.309300\pi$
$67$	9.23146	1.12780	0.563901	+	0.825842i	$0.309300\pi$
$68$	40.6707	4.93205
$69$	12.9713	1.56156
$70$	−26.1743	−3.12842
$71$	1.56085	0.185239	0.0926196	−	0.995702i	$-0.470476\pi$
$71$	1.56085	0.185239	0.0926196	+	0.995702i	$0.470476\pi$
$72$	−63.6490	−7.50111
$73$	6.70131	0.784329	0.392165	−	0.919895i	$-0.371726\pi$
$73$	6.70131	0.784329	0.392165	+	0.919895i	$0.371726\pi$
$74$	−10.2448	−1.19093
$75$	−2.38400	−0.275281
$76$	−5.93270	−0.680527
$77$	3.94507	0.449583
$78$	−23.5401	−2.66539
$79$	−0.599747	−0.0674768	−0.0337384	−	0.999431i	$-0.510741\pi$
$79$	−0.599747	−0.0674768	−0.0337384	+	0.999431i	$0.510741\pi$
$80$	−39.2352	−4.38663
$81$	12.5144	1.39048
$82$	−16.8476	−1.86051
$83$	−2.99112	−0.328318	−0.164159	−	0.986434i	$-0.552491\pi$
$83$	−2.99112	−0.328318	−0.164159	+	0.986434i	$0.552491\pi$
$84$	67.8553	7.40362
$85$	−17.4040	−1.88772
$86$	31.5825	3.40563
$87$	5.17439	0.554753
$88$	9.98436	1.06434
$89$	−11.4507	−1.21377	−0.606886	−	0.794789i	$-0.707581\pi$
$89$	−11.4507	−1.21377	−0.606886	+	0.794789i	$0.707581\pi$
$90$	42.2952	4.45830
$91$	10.9894	1.15200
$92$	−23.7984	−2.48116
$93$	32.1962	3.33859
$94$	33.3313	3.43786
$95$	2.53874	0.260469
$96$	76.7875	7.83709
$97$	1.96658	0.199676	0.0998381	−	0.995004i	$-0.468168\pi$
$97$	1.96658	0.199676	0.0998381	+	0.995004i	$0.468168\pi$
$98$	−23.6355	−2.38754
$99$	−6.37487	−0.640698
$100$	4.37392	0.437392
$101$	8.62325	0.858045	0.429023	−	0.903294i	$-0.358858\pi$
$101$	8.62325	0.858045	0.429023	+	0.903294i	$0.358858\pi$
$102$	61.1823	6.05795
$103$	−15.0289	−1.48084	−0.740420	−	0.672144i	$-0.765374\pi$
$103$	−15.0289	−1.48084	−0.740420	+	0.672144i	$0.765374\pi$
$104$	27.8124	2.72723
$105$	−29.0369	−2.83371
$106$	9.08029	0.881956
$107$	5.76415	0.557242	0.278621	−	0.960401i	$-0.410123\pi$
$107$	5.76415	0.557242	0.278621	+	0.960401i	$0.410123\pi$
$108$	−58.0478	−5.58565
$109$	0.682357	0.0653579	0.0326790	−	0.999466i	$-0.489596\pi$
$109$	0.682357	0.0653579	0.0326790	+	0.999466i	$0.489596\pi$
$110$	−6.63467	−0.632591
$111$	−11.3652	−1.07874
$112$	−64.3901	−6.08430
$113$	0.271003	0.0254938	0.0127469	−	0.999919i	$-0.495942\pi$
$113$	0.271003	0.0254938	0.0127469	+	0.999919i	$0.495942\pi$
$114$	−8.92476	−0.835880
$115$	10.1839	0.949653
$116$	−9.49342	−0.881442
$117$	−17.7578	−1.64171
$118$	−29.2858	−2.69598
$119$	−28.5622	−2.61829
$120$	−73.4878	−6.70848
$121$	1.00000	0.0909091
$122$	26.1070	2.36362
$123$	−18.6902	−1.68524
$124$	−59.0702	−5.30466
$125$	10.1477	0.907636
$126$	69.4119	6.18370
$127$	17.3483	1.53941	0.769705	−	0.638400i	$-0.220404\pi$
$127$	17.3483	1.53941	0.769705	+	0.638400i	$0.220404\pi$
$128$	−50.7863	−4.48891
$129$	35.0366	3.08480
$130$	−18.4815	−1.62093
$131$	−9.22448	−0.805946	−0.402973	−	0.915212i	$-0.632023\pi$
$131$	−9.22448	−0.805946	−0.402973	+	0.915212i	$0.632023\pi$
$132$	17.2000	1.49707
$133$	4.16641	0.361273
$134$	−25.4787	−2.20103
$135$	24.8400	2.13789
$136$	−72.2864	−6.19850
$137$	−2.78742	−0.238146	−0.119073	−	0.992886i	$-0.537992\pi$
$137$	−2.78742	−0.238146	−0.119073	+	0.992886i	$0.537992\pi$
$138$	−35.8007	−3.04756
$139$	9.26977	0.786252	0.393126	−	0.919485i	$-0.371394\pi$
$139$	9.26977	0.786252	0.393126	+	0.919485i	$0.371394\pi$
$140$	53.2737	4.50245
$141$	36.9767	3.11400
$142$	−4.30794	−0.361514
$143$	2.78559	0.232943
$144$	104.048	8.67070
$145$	4.06246	0.337369
$146$	−18.4955	−1.53070
$147$	−26.2204	−2.16262
$148$	20.8517	1.71400
$149$	8.41204	0.689141	0.344570	−	0.938760i	$-0.388025\pi$
$149$	8.41204	0.689141	0.344570	+	0.938760i	$0.388025\pi$
$150$	6.57983	0.537241
$151$	−12.0347	−0.979366	−0.489683	−	0.871900i	$-0.662888\pi$
$151$	−12.0347	−0.979366	−0.489683	+	0.871900i	$0.662888\pi$
$152$	10.5445	0.855274
$153$	46.1538	3.73131
$154$	−10.8884	−0.877409
$155$	25.2775	2.03034
$156$	47.9122	3.83605
$157$	8.77923	0.700659	0.350329	−	0.936627i	$-0.386070\pi$
$157$	8.77923	0.700659	0.350329	+	0.936627i	$0.386070\pi$
$158$	1.65529	0.131688
$159$	10.0734	0.798871
$160$	60.2865	4.76606
$161$	16.7131	1.31718
$162$	−34.5395	−2.71368
$163$	−12.4366	−0.974111	−0.487056	−	0.873371i	$-0.661929\pi$
$163$	−12.4366	−0.974111	−0.487056	+	0.873371i	$0.661929\pi$
$164$	34.2908	2.67766
$165$	−7.36028	−0.572997
$166$	8.25546	0.640748
$167$	8.23294	0.637084	0.318542	−	0.947909i	$-0.396807\pi$
$167$	8.23294	0.637084	0.318542	+	0.947909i	$0.396807\pi$
$168$	−120.603	−9.30472
$169$	−5.24047	−0.403113
$170$	48.0347	3.68410
$171$	−6.73252	−0.514849
$172$	−64.2814	−4.90141
$173$	13.5006	1.02643	0.513217	−	0.858259i	$-0.328454\pi$
$173$	13.5006	1.02643	0.513217	+	0.858259i	$0.328454\pi$
$174$	−14.2813	−1.08266
$175$	−3.07171	−0.232199
$176$	−16.3217	−1.23029
$177$	−32.4887	−2.44200
$178$	31.6038	2.36880
$179$	9.13912	0.683090	0.341545	−	0.939865i	$-0.389050\pi$
$179$	9.13912	0.683090	0.341545	+	0.939865i	$0.389050\pi$
$180$	−86.0854	−6.41642
$181$	0.584539	0.0434485	0.0217242	−	0.999764i	$-0.493084\pi$
$181$	0.584539	0.0434485	0.0217242	+	0.999764i	$0.493084\pi$
$182$	−30.3305	−2.24825
$183$	28.9623	2.14095
$184$	42.2982	3.11827
$185$	−8.92291	−0.656025
$186$	−88.8612	−6.51562
$187$	−7.23996	−0.529438
$188$	−67.8408	−4.94780
$189$	40.7657	2.96527
$190$	−7.00690	−0.508334
$191$	26.8640	1.94381	0.971907	−	0.235365i	$-0.0756286\pi$
$191$	26.8640	1.94381	0.971907	+	0.235365i	$0.0756286\pi$
$192$	−111.984	−8.08174
$193$	−18.3041	−1.31756	−0.658780	−	0.752336i	$-0.728927\pi$
$193$	−18.3041	−1.31756	−0.658780	+	0.752336i	$0.728927\pi$
$194$	−5.42775	−0.389689
$195$	−20.5028	−1.46823
$196$	48.1064	3.43617
$197$	21.0973	1.50312	0.751560	−	0.659665i	$-0.229302\pi$
$197$	21.0973	1.50312	0.751560	+	0.659665i	$0.229302\pi$
$198$	17.5946	1.25039
$199$	−21.4336	−1.51939	−0.759695	−	0.650279i	$-0.774652\pi$
$199$	−21.4336	−1.51939	−0.759695	+	0.650279i	$0.774652\pi$
$200$	−7.77401	−0.549705
$201$	−28.2653	−1.99368
$202$	−23.8001	−1.67457
$203$	6.66702	0.467933
$204$	−124.527	−8.71866
$205$	−14.6738	−1.02487
$206$	41.4796	2.89002
$207$	−27.0068	−1.87710
$208$	−45.4655	−3.15246
$209$	1.05610	0.0730522
$210$	80.1414	5.53028
$211$	22.9009	1.57656	0.788280	−	0.615316i	$-0.210972\pi$
$211$	22.9009	1.57656	0.788280	+	0.615316i	$0.210972\pi$
$212$	−18.4816	−1.26932
$213$	−4.77908	−0.327457
$214$	−15.9090	−1.08752
$215$	27.5075	1.87600
$216$	103.172	7.01993
$217$	41.4837	2.81610
$218$	−1.88330	−0.127553
$219$	−20.5184	−1.38650
$220$	13.5039	0.910430
$221$	−20.1676	−1.35662
$222$	31.3678	2.10527
$223$	−11.3395	−0.759350	−0.379675	−	0.925120i	$-0.623964\pi$
$223$	−11.3395	−0.759350	−0.379675	+	0.925120i	$0.623964\pi$
$224$	98.9379	6.61057
$225$	4.96359	0.330906
$226$	−0.747966	−0.0497539
$227$	11.6936	0.776133	0.388067	−	0.921631i	$-0.373143\pi$
$227$	11.6936	0.776133	0.388067	+	0.921631i	$0.373143\pi$
$228$	18.1650	1.20301
$229$	4.70907	0.311184	0.155592	−	0.987821i	$-0.450271\pi$
$229$	4.70907	0.311184	0.155592	+	0.987821i	$0.450271\pi$
$230$	−28.1074	−1.85335
$231$	−12.0792	−0.794752
$232$	16.8732	1.10778
$233$	14.3376	0.939285	0.469642	−	0.882857i	$-0.344383\pi$
$233$	14.3376	0.939285	0.469642	+	0.882857i	$0.344383\pi$
$234$	49.0113	3.20397
$235$	29.0307	1.89375
$236$	59.6069	3.88008
$237$	1.83633	0.119282
$238$	78.8312	5.10987
$239$	18.8931	1.22210	0.611048	−	0.791594i	$-0.290748\pi$
$239$	18.8931	1.22210	0.611048	+	0.791594i	$0.290748\pi$
$240$	120.132	7.75449
$241$	−14.9014	−0.959886	−0.479943	−	0.877300i	$-0.659343\pi$
$241$	−14.9014	−0.959886	−0.479943	+	0.877300i	$0.659343\pi$
$242$	−2.75999	−0.177419
$243$	−7.31701	−0.469386
$244$	−53.1369	−3.40174
$245$	−20.5858	−1.31518
$246$	51.5848	3.28892
$247$	2.94187	0.187187
$248$	104.989	6.66679
$249$	9.15834	0.580386
$250$	−28.0075	−1.77135
$251$	16.5292	1.04331	0.521655	−	0.853156i	$-0.325315\pi$
$251$	16.5292	1.04331	0.521655	+	0.853156i	$0.325315\pi$
$252$	−141.277	−8.89963
$253$	4.23645	0.266343
$254$	−47.8810	−3.00432
$255$	53.2881	3.33703
$256$	67.0214	4.18884
$257$	3.48507	0.217393	0.108696	−	0.994075i	$-0.465332\pi$
$257$	3.48507	0.217393	0.108696	+	0.994075i	$0.465332\pi$
$258$	−96.7006	−6.02032
$259$	−14.6437	−0.909913
$260$	37.6163	2.33286
$261$	−10.7733	−0.666849
$262$	25.4595	1.57289
$263$	5.60219	0.345446	0.172723	−	0.984970i	$-0.444743\pi$
$263$	5.60219	0.345446	0.172723	+	0.984970i	$0.444743\pi$
$264$	−30.5705	−1.88149
$265$	7.90869	0.485827
$266$	−11.4992	−0.705063
$267$	35.0602	2.14565
$268$	51.8581	3.16774
$269$	22.6546	1.38127	0.690637	−	0.723202i	$-0.257330\pi$
$269$	22.6546	1.38127	0.690637	+	0.723202i	$0.257330\pi$
$270$	−68.5581	−4.17231
$271$	−31.5352	−1.91562	−0.957812	−	0.287395i	$-0.907211\pi$
$271$	−31.5352	−1.91562	−0.957812	+	0.287395i	$0.907211\pi$
$272$	118.168	7.16499
$273$	−33.6477	−2.03645
$274$	7.69326	0.464767
$275$	−0.778618	−0.0469524
$276$	72.8669	4.38607
$277$	16.9404	1.01785	0.508926	−	0.860811i	$-0.330043\pi$
$277$	16.9404	1.01785	0.508926	+	0.860811i	$0.330043\pi$
$278$	−25.5845	−1.53445
$279$	−67.0337	−4.01320
$280$	−94.6864	−5.65859
$281$	−25.1904	−1.50274	−0.751368	−	0.659884i	$-0.770606\pi$
$281$	−25.1904	−1.50274	−0.751368	+	0.659884i	$0.770606\pi$
$282$	−102.055	−6.07730
$283$	24.1084	1.43309	0.716547	−	0.697538i	$-0.245721\pi$
$283$	24.1084	1.43309	0.716547	+	0.697538i	$0.245721\pi$
$284$	8.76815	0.520294
$285$	−7.77322	−0.460446
$286$	−7.68820	−0.454613
$287$	−24.0817	−1.42150
$288$	−159.874	−9.42069
$289$	35.4170	2.08335
$290$	−11.2123	−0.658411
$291$	−6.02136	−0.352978
$292$	37.6449	2.20300
$293$	−1.07378	−0.0627306	−0.0313653	−	0.999508i	$-0.509986\pi$
$293$	−1.07378	−0.0627306	−0.0313653	+	0.999508i	$0.509986\pi$
$294$	72.3680	4.22059
$295$	−25.5072	−1.48508
$296$	−37.0608	−2.15412
$297$	10.3333	0.599600
$298$	−23.2171	−1.34493
$299$	11.8010	0.682471
$300$	−13.3922	−0.773201
$301$	45.1434	2.60202
$302$	33.2155	1.91134
$303$	−26.4030	−1.51681
$304$	−17.2374	−0.988630
$305$	22.7385	1.30200
$306$	−127.384	−7.28205
$307$	19.4711	1.11127	0.555637	−	0.831425i	$-0.312474\pi$
$307$	19.4711	1.11127	0.555637	+	0.831425i	$0.312474\pi$
$308$	22.1616	1.26277
$309$	46.0161	2.61776
$310$	−69.7656	−3.96242
$311$	−4.37453	−0.248057	−0.124029	−	0.992279i	$-0.539581\pi$
$311$	−4.37453	−0.248057	−0.124029	+	0.992279i	$0.539581\pi$
$312$	−85.1571	−4.82107
$313$	−12.3334	−0.697125	−0.348562	−	0.937286i	$-0.613330\pi$
$313$	−12.3334	−0.697125	−0.348562	+	0.937286i	$0.613330\pi$
$314$	−24.2306	−1.36741
$315$	60.4559	3.40630
$316$	−3.36910	−0.189527
$317$	14.0094	0.786847	0.393424	−	0.919357i	$-0.371291\pi$
$317$	14.0094	0.786847	0.393424	+	0.919357i	$0.371291\pi$
$318$	−27.8024	−1.55908
$319$	1.68996	0.0946197
$320$	−87.9195	−4.91485
$321$	−17.6489	−0.985066
$322$	−46.1280	−2.57061
$323$	−7.64614	−0.425443
$324$	70.2998	3.90555
$325$	−2.16891	−0.120310
$326$	34.3249	1.90108
$327$	−2.08927	−0.115537
$328$	−60.9470	−3.36523
$329$	47.6431	2.62665
$330$	20.3143	1.11827
$331$	−12.1888	−0.669957	−0.334978	−	0.942226i	$-0.608729\pi$
$331$	−12.1888	−0.669957	−0.334978	+	0.942226i	$0.608729\pi$
$332$	−16.8027	−0.922170
$333$	23.6628	1.29671
$334$	−22.7228	−1.24334
$335$	−22.1913	−1.21244
$336$	197.152	10.7555
$337$	33.5102	1.82542	0.912709	−	0.408609i	$-0.133986\pi$
$337$	33.5102	1.82542	0.912709	+	0.408609i	$0.133986\pi$
$338$	14.4636	0.786719
$339$	−0.829768	−0.0450668
$340$	−97.7674	−5.30218
$341$	10.5153	0.569436
$342$	18.5817	1.00478
$343$	−6.16854	−0.333070
$344$	114.251	6.16000
$345$	−31.1815	−1.67875
$346$	−37.2616	−2.00319
$347$	14.6345	0.785621	0.392810	−	0.919619i	$-0.371503\pi$
$347$	14.6345	0.785621	0.392810	+	0.919619i	$0.371503\pi$
$348$	29.0673	1.55817
$349$	−9.48925	−0.507948	−0.253974	−	0.967211i	$-0.581738\pi$
$349$	−9.48925	−0.507948	−0.253974	+	0.967211i	$0.581738\pi$
$350$	8.47787	0.453161
$351$	28.7844	1.53640
$352$	25.0789	1.33671
$353$	−3.56043	−0.189503	−0.0947514	−	0.995501i	$-0.530206\pi$
$353$	−3.56043	−0.189503	−0.0947514	+	0.995501i	$0.530206\pi$
$354$	89.6685	4.76583
$355$	−3.75210	−0.199141
$356$	−64.3247	−3.40920
$357$	87.4528	4.62849
$358$	−25.2239	−1.33312
$359$	5.51488	0.291064	0.145532	−	0.989354i	$-0.453511\pi$
$359$	5.51488	0.291064	0.145532	+	0.989354i	$0.453511\pi$
$360$	153.004	8.06404
$361$	−17.8846	−0.941297
$362$	−1.61332	−0.0847943
$363$	−3.06184	−0.160705
$364$	61.7332	3.23570
$365$	−16.1091	−0.843190
$366$	−79.9356	−4.17830
$367$	27.3618	1.42827	0.714137	−	0.700006i	$-0.246819\pi$
$367$	27.3618	1.42827	0.714137	+	0.700006i	$0.246819\pi$
$368$	−69.1458	−3.60448
$369$	38.9137	2.02577
$370$	24.6271	1.28030
$371$	12.9792	0.673846
$372$	180.863	9.37733
$373$	−20.7712	−1.07549	−0.537745	−	0.843107i	$-0.680724\pi$
$373$	−20.7712	−1.07549	−0.537745	+	0.843107i	$0.680724\pi$
$374$	19.9822	1.03325
$375$	−31.0706	−1.60448
$376$	120.577	6.21830
$377$	4.70754	0.242451
$378$	−112.513	−5.78703
$379$	−8.19945	−0.421177	−0.210589	−	0.977575i	$-0.567538\pi$
$379$	−8.19945	−0.421177	−0.210589	+	0.977575i	$0.567538\pi$
$380$	14.2615	0.731598
$381$	−53.1176	−2.72130
$382$	−74.1445	−3.79356
$383$	19.8770	1.01567	0.507833	−	0.861455i	$-0.330447\pi$
$383$	19.8770	1.01567	0.507833	+	0.861455i	$0.330447\pi$
$384$	155.499	7.93530
$385$	−9.48347	−0.483322
$386$	50.5192	2.57136
$387$	−72.9476	−3.70813
$388$	11.0474	0.560844
$389$	−29.4693	−1.49415	−0.747075	−	0.664740i	$-0.768543\pi$
$389$	−29.4693	−1.49415	−0.747075	+	0.664740i	$0.768543\pi$
$390$	56.5874	2.86541
$391$	−30.6717	−1.55113
$392$	−85.5022	−4.31851
$393$	28.2439	1.42472
$394$	−58.2283	−2.93350
$395$	1.44172	0.0725407
$396$	−35.8111	−1.79957
$397$	−14.6003	−0.732769	−0.366384	−	0.930464i	$-0.619404\pi$
$397$	−14.6003	−0.732769	−0.366384	+	0.930464i	$0.619404\pi$
$398$	59.1566	2.96525
$399$	−12.7569	−0.638642
$400$	12.7083	0.635417
$401$	−8.10143	−0.404566	−0.202283	−	0.979327i	$-0.564836\pi$
$401$	−8.10143	−0.404566	−0.202283	+	0.979327i	$0.564836\pi$
$402$	78.0118	3.89088
$403$	29.2914	1.45911
$404$	48.4414	2.41005
$405$	−30.0829	−1.49483
$406$	−18.4009	−0.913222
$407$	−3.71189	−0.183991
$408$	221.329	10.9574
$409$	9.84011	0.486562	0.243281	−	0.969956i	$-0.421776\pi$
$409$	9.84011	0.486562	0.243281	+	0.969956i	$0.421776\pi$
$410$	40.4996	2.00013
$411$	8.53465	0.420983
$412$	−84.4254	−4.15934
$413$	−41.8606	−2.05982
$414$	74.5385	3.66337
$415$	7.19029	0.352957
$416$	69.8595	3.42514
$417$	−28.3826	−1.38990
$418$	−2.91483	−0.142569
$419$	28.4913	1.39189	0.695947	−	0.718094i	$-0.254985\pi$
$419$	28.4913	1.39189	0.695947	+	0.718094i	$0.254985\pi$
$420$	−163.116	−7.95923
$421$	3.08406	0.150308	0.0751539	−	0.997172i	$-0.476055\pi$
$421$	3.08406	0.150308	0.0751539	+	0.997172i	$0.476055\pi$
$422$	−63.2061	−3.07683
$423$	−76.9868	−3.74323
$424$	32.8483	1.59525
$425$	5.63716	0.273443
$426$	13.1902	0.639068
$427$	37.3169	1.80589
$428$	32.3803	1.56516
$429$	−8.52904	−0.411786
$430$	−75.9204	−3.66121
$431$	13.0471	0.628457	0.314228	−	0.949347i	$-0.398254\pi$
$431$	13.0471	0.628457	0.314228	+	0.949347i	$0.398254\pi$
$432$	−168.657	−8.11450
$433$	−23.4986	−1.12927	−0.564635	−	0.825341i	$-0.690983\pi$
$433$	−23.4986	−1.12927	−0.564635	+	0.825341i	$0.690983\pi$
$434$	−114.494	−5.49591
$435$	−12.4386	−0.596385
$436$	3.83316	0.183575
$437$	4.47413	0.214027
$438$	56.6304	2.70591
$439$	23.0266	1.09900	0.549500	−	0.835494i	$-0.314818\pi$
$439$	23.0266	1.09900	0.549500	+	0.835494i	$0.314818\pi$
$440$	−24.0012	−1.14421
$441$	54.5919	2.59961
$442$	55.6623	2.64758
$443$	19.3017	0.917053	0.458526	−	0.888681i	$-0.348377\pi$
$443$	19.3017	0.917053	0.458526	+	0.888681i	$0.348377\pi$
$444$	−63.8445	−3.02992
$445$	27.5261	1.30486
$446$	31.2969	1.48195
$447$	−25.7563	−1.21823
$448$	−144.287	−6.81694
$449$	−39.2749	−1.85350	−0.926749	−	0.375681i	$-0.877409\pi$
$449$	−39.2749	−1.85350	−0.926749	+	0.375681i	$0.877409\pi$
$450$	−13.6995	−0.645798
$451$	−6.10424	−0.287437
$452$	1.52237	0.0716063
$453$	36.8482	1.73128
$454$	−32.2743	−1.51471
$455$	−26.4171	−1.23845
$456$	−32.2856	−1.51191
$457$	31.9768	1.49581	0.747905	−	0.663806i	$-0.231060\pi$
$457$	31.9768	1.49581	0.747905	+	0.663806i	$0.231060\pi$
$458$	−12.9970	−0.607310
$459$	−74.8127	−3.49196
$460$	57.2084	2.66736
$461$	−12.3711	−0.576180	−0.288090	−	0.957603i	$-0.593020\pi$
$461$	−12.3711	−0.576180	−0.288090	+	0.957603i	$0.593020\pi$
$462$	33.3384	1.55104
$463$	−23.7965	−1.10592	−0.552959	−	0.833208i	$-0.686502\pi$
$463$	−23.7965	−1.10592	−0.552959	+	0.833208i	$0.686502\pi$
$464$	−27.5830	−1.28051
$465$	−77.3957	−3.58914
$466$	−39.5715	−1.83311
$467$	−33.3296	−1.54231	−0.771155	−	0.636648i	$-0.780320\pi$
$467$	−33.3296	−1.54231	−0.771155	+	0.636648i	$0.780320\pi$
$468$	−99.7551	−4.61118
$469$	−36.4188	−1.68166
$470$	−80.1243	−3.69586
$471$	−26.8806	−1.23859
$472$	−105.943	−4.87640
$473$	11.4430	0.526149
$474$	−5.06825	−0.232792
$475$	−0.822301	−0.0377298
$476$	−160.449	−7.35417
$477$	−20.9732	−0.960295
$478$	−52.1448	−2.38505
$479$	−26.5979	−1.21529	−0.607645	−	0.794209i	$-0.707885\pi$
$479$	−26.5979	−1.21529	−0.607645	+	0.794209i	$0.707885\pi$
$480$	−184.588	−8.42523
$481$	−10.3398	−0.471454
$482$	41.1278	1.87332
$483$	−51.1729	−2.32845
$484$	5.61754	0.255343
$485$	−4.72742	−0.214661
$486$	20.1949	0.916058
$487$	27.8219	1.26073	0.630365	−	0.776299i	$-0.282905\pi$
$487$	27.8219	1.26073	0.630365	+	0.776299i	$0.282905\pi$
$488$	94.4432	4.27524
$489$	38.0790	1.72199
$490$	56.8167	2.56672
$491$	14.3122	0.645902	0.322951	−	0.946416i	$-0.395325\pi$
$491$	14.3122	0.645902	0.322951	+	0.946416i	$0.395325\pi$
$492$	−104.993	−4.73345
$493$	−12.2352	−0.551048
$494$	−8.11954	−0.365315
$495$	15.3244	0.688780
$496$	−171.627	−7.70629
$497$	−6.15768	−0.276210
$498$	−25.2769	−1.13269
$499$	−13.1097	−0.586873	−0.293436	−	0.955979i	$-0.594799\pi$
$499$	−13.1097	−0.586873	−0.293436	+	0.955979i	$0.594799\pi$
$500$	57.0050	2.54934
$501$	−25.2079	−1.12621
$502$	−45.6203	−2.03613
$503$	−23.4553	−1.04582	−0.522911	−	0.852387i	$-0.675154\pi$
$503$	−23.4553	−1.04582	−0.522911	+	0.852387i	$0.675154\pi$
$504$	251.100	11.1849
$505$	−20.7292	−0.922438
$506$	−11.6925	−0.519797
$507$	16.0455	0.712605
$508$	97.4545	4.32384
$509$	18.3194	0.811994	0.405997	−	0.913874i	$-0.366924\pi$
$509$	18.3194	0.811994	0.405997	+	0.913874i	$0.366924\pi$
$510$	−147.075	−6.51258
$511$	−26.4372	−1.16951
$512$	−83.4058	−3.68605
$513$	10.9130	0.481823
$514$	−9.61875	−0.424265
$515$	36.1276	1.59197
$516$	196.819	8.66449
$517$	12.0766	0.531129
$518$	40.4163	1.77579
$519$	−41.3368	−1.81448
$520$	−66.8575	−2.93189
$521$	30.9856	1.35751	0.678753	−	0.734367i	$-0.262521\pi$
$521$	30.9856	1.35751	0.678753	+	0.734367i	$0.262521\pi$
$522$	29.7341	1.30143
$523$	−22.1917	−0.970377	−0.485189	−	0.874410i	$-0.661249\pi$
$523$	−22.1917	−0.970377	−0.485189	+	0.874410i	$0.661249\pi$
$524$	−51.8189	−2.26372
$525$	9.40508	0.410471
$526$	−15.4620	−0.674174
$527$	−76.1304	−3.31629
$528$	49.9743	2.17485
$529$	−5.05251	−0.219674
$530$	−21.8279	−0.948143
$531$	67.6428	2.93545
$532$	23.4049	1.01473
$533$	−17.0039	−0.736522
$534$	−96.7658	−4.18747
$535$	−13.8563	−0.599060
$536$	−92.1703	−3.98115
$537$	−27.9825	−1.20754
$538$	−62.5264	−2.69570
$539$	−8.56361	−0.368861
$540$	139.540	6.00483
$541$	15.8641	0.682049	0.341024	−	0.940054i	$-0.389226\pi$
$541$	15.8641	0.682049	0.341024	+	0.940054i	$0.389226\pi$
$542$	87.0367	3.73855
$543$	−1.78977	−0.0768062
$544$	−181.570	−7.78474
$545$	−1.64030	−0.0702627
$546$	92.8673	3.97435
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−15.6585	−0.668896
$549$	−60.3006	−2.57357
$550$	2.14898	0.0916327
$551$	1.78477	0.0760339
$552$	−129.510	−5.51233
$553$	2.36605	0.100615
$554$	−46.7554	−1.98645
$555$	27.3205	1.15969
$556$	52.0733	2.20840
$557$	−16.6607	−0.705937	−0.352968	−	0.935635i	$-0.614828\pi$
$557$	−16.6607	−0.705937	−0.352968	+	0.935635i	$0.614828\pi$
$558$	185.012	7.83220
$559$	31.8755	1.34819
$560$	154.786	6.54090
$561$	22.1676	0.935917
$562$	69.5253	2.93275
$563$	−16.4801	−0.694553	−0.347276	−	0.937763i	$-0.612893\pi$
$563$	−16.4801	−0.694553	−0.347276	+	0.937763i	$0.612893\pi$
$564$	207.718	8.74650
$565$	−0.651458	−0.0274070
$566$	−66.5389	−2.79684
$567$	−49.3700	−2.07335
$568$	−15.5841	−0.653895
$569$	19.6759	0.824858	0.412429	−	0.910990i	$-0.364680\pi$
$569$	19.6759	0.824858	0.412429	+	0.910990i	$0.364680\pi$
$570$	21.4540	0.898609
$571$	4.69088	0.196307	0.0981536	−	0.995171i	$-0.468706\pi$
$571$	4.69088	0.196307	0.0981536	+	0.995171i	$0.468706\pi$
$572$	15.6482	0.654283
$573$	−82.2534	−3.43619
$574$	66.4652	2.77420
$575$	−3.29858	−0.137560
$576$	233.155	9.71478
$577$	28.0301	1.16691	0.583455	−	0.812146i	$-0.301701\pi$
$577$	28.0301	1.16691	0.583455	+	0.812146i	$0.301701\pi$
$578$	−97.7505	−4.06588
$579$	56.0443	2.32912
$580$	22.8210	0.947591
$581$	11.8002	0.489555
$582$	16.6189	0.688875
$583$	3.28997	0.136257
$584$	−66.9083	−2.76869
$585$	42.6875	1.76491
$586$	2.96361	0.122425
$587$	−19.6259	−0.810049	−0.405025	−	0.914306i	$-0.632737\pi$
$587$	−19.6259	−0.810049	−0.405025	+	0.914306i	$0.632737\pi$
$588$	−147.294	−6.07431
$589$	11.1053	0.457584
$590$	70.3995	2.89830
$591$	−64.5965	−2.65715
$592$	60.5841	2.48999
$593$	−26.2679	−1.07870	−0.539348	−	0.842083i	$-0.681329\pi$
$593$	−26.2679	−1.07870	−0.539348	+	0.842083i	$0.681329\pi$
$594$	−28.5198	−1.17018
$595$	68.6599	2.81478
$596$	47.2549	1.93564
$597$	65.6264	2.68591
$598$	−32.5707	−1.33191
$599$	−33.5957	−1.37268	−0.686341	−	0.727280i	$-0.740784\pi$
$599$	−33.5957	−1.37268	−0.686341	+	0.727280i	$0.740784\pi$
$600$	23.8028	0.971744
$601$	−17.7286	−0.723163	−0.361582	−	0.932341i	$-0.617763\pi$
$601$	−17.7286	−0.723163	−0.361582	+	0.932341i	$0.617763\pi$
$602$	−124.595	−5.07813
$603$	58.8494	2.39653
$604$	−67.6051	−2.75081
$605$	−2.40388	−0.0977314
$606$	72.8720	2.96022
$607$	38.0183	1.54312	0.771558	−	0.636159i	$-0.219478\pi$
$607$	38.0183	1.54312	0.771558	+	0.636159i	$0.219478\pi$
$608$	26.4859	1.07414
$609$	−20.4134	−0.827191
$610$	−62.7580	−2.54100
$611$	33.6405	1.36095
$612$	259.271	10.4804
$613$	−5.43837	−0.219654	−0.109827	−	0.993951i	$-0.535030\pi$
$613$	−5.43837	−0.219654	−0.109827	+	0.993951i	$0.535030\pi$
$614$	−53.7400	−2.16877
$615$	44.9289	1.81171
$616$	−39.3891	−1.58703
$617$	−15.6897	−0.631642	−0.315821	−	0.948819i	$-0.602280\pi$
$617$	−15.6897	−0.631642	−0.315821	+	0.948819i	$0.602280\pi$
$618$	−127.004	−5.10884
$619$	43.1471	1.73423	0.867114	−	0.498111i	$-0.165973\pi$
$619$	43.1471	1.73423	0.867114	+	0.498111i	$0.165973\pi$
$620$	141.997	5.70275
$621$	43.7765	1.75669
$622$	12.0737	0.484110
$623$	45.1738	1.80985
$624$	139.208	5.57278
$625$	−28.2868	−1.13147
$626$	34.0400	1.36051
$627$	−3.23362	−0.129138
$628$	49.3176	1.96799
$629$	26.8739	1.07153
$630$	−166.857	−6.64776
$631$	39.7966	1.58428	0.792138	−	0.610342i	$-0.208968\pi$
$631$	39.7966	1.58428	0.792138	+	0.610342i	$0.208968\pi$
$632$	5.98809	0.238193
$633$	−70.1188	−2.78697
$634$	−38.6658	−1.53562
$635$	−41.7031	−1.65494
$636$	56.5876	2.24384
$637$	−23.8547	−0.945158
$638$	−4.66427	−0.184660
$639$	9.95023	0.393625
$640$	122.084	4.82579
$641$	5.84987	0.231056	0.115528	−	0.993304i	$-0.463144\pi$
$641$	5.84987	0.231056	0.115528	+	0.993304i	$0.463144\pi$
$642$	48.7108	1.92246
$643$	−20.0893	−0.792243	−0.396121	−	0.918198i	$-0.629644\pi$
$643$	−20.0893	−0.792243	−0.396121	+	0.918198i	$0.629644\pi$
$644$	93.8865	3.69965
$645$	−84.2236	−3.31630
$646$	21.1033	0.830297
$647$	−38.5461	−1.51541	−0.757703	−	0.652600i	$-0.773678\pi$
$647$	−38.5461	−1.51541	−0.757703	+	0.652600i	$0.773678\pi$
$648$	−124.948	−4.90841
$649$	−10.6109	−0.416512
$650$	5.98618	0.234797
$651$	−127.016	−4.97817
$652$	−69.8632	−2.73605
$653$	−16.1030	−0.630161	−0.315080	−	0.949065i	$-0.602031\pi$
$653$	−16.1030	−0.630161	−0.315080	+	0.949065i	$0.602031\pi$
$654$	5.76635	0.225482
$655$	22.1745	0.866429
$656$	99.6313	3.88995
$657$	42.7200	1.66667
$658$	−131.494	−5.12619
$659$	9.37501	0.365198	0.182599	−	0.983187i	$-0.441549\pi$
$659$	9.37501	0.365198	0.182599	+	0.983187i	$0.441549\pi$
$660$	−41.3467	−1.60942
$661$	−5.83160	−0.226823	−0.113412	−	0.993548i	$-0.536178\pi$
$661$	−5.83160	−0.226823	−0.113412	+	0.993548i	$0.536178\pi$
$662$	33.6409	1.30749
$663$	61.7499	2.39817
$664$	29.8645	1.15897
$665$	−10.0155	−0.388385
$666$	−65.3090	−2.53067
$667$	7.15943	0.277214
$668$	46.2488	1.78942
$669$	34.7198	1.34234
$670$	61.2477	2.36621
$671$	9.45911	0.365165
$672$	−302.932	−11.6859
$673$	23.5521	0.907869	0.453934	−	0.891035i	$-0.350020\pi$
$673$	23.5521	0.907869	0.453934	+	0.891035i	$0.350020\pi$
$674$	−92.4879	−3.56250
$675$	−8.04571	−0.309679
$676$	−29.4386	−1.13225
$677$	−1.40539	−0.0540136	−0.0270068	−	0.999635i	$-0.508598\pi$
$677$	−1.40539	−0.0540136	−0.0270068	+	0.999635i	$0.508598\pi$
$678$	2.29015	0.0879527
$679$	−7.75831	−0.297737
$680$	173.767	6.66368
$681$	−35.8040	−1.37201
$682$	−29.0221	−1.11132
$683$	−19.4596	−0.744601	−0.372301	−	0.928112i	$-0.621431\pi$
$683$	−19.4596	−0.744601	−0.372301	+	0.928112i	$0.621431\pi$
$684$	−37.8202	−1.44609
$685$	6.70062	0.256018
$686$	17.0251	0.650021
$687$	−14.4184	−0.550098
$688$	−186.769	−7.12048
$689$	9.16453	0.349141
$690$	86.0605	3.27627
$691$	29.9056	1.13766	0.568831	−	0.822454i	$-0.307396\pi$
$691$	29.9056	1.13766	0.568831	+	0.822454i	$0.307396\pi$
$692$	75.8402	2.88301
$693$	25.1493	0.955344
$694$	−40.3910	−1.53322
$695$	−22.2834	−0.845257
$696$	−51.6630	−1.95828
$697$	44.1944	1.67398
$698$	26.1902	0.991315
$699$	−43.8993	−1.66043
$700$	−17.2554	−0.652194
$701$	17.6725	0.667480	0.333740	−	0.942665i	$-0.391689\pi$
$701$	17.6725	0.667480	0.333740	+	0.942665i	$0.391689\pi$
$702$	−79.4446	−2.99844
$703$	−3.92013	−0.147851
$704$	−36.5741	−1.37844
$705$	−88.8873	−3.34769
$706$	9.82676	0.369835
$707$	−34.0193	−1.27943
$708$	−182.507	−6.85902
$709$	−5.68864	−0.213641	−0.106821	−	0.994278i	$-0.534067\pi$
$709$	−5.68864	−0.213641	−0.106821	+	0.994278i	$0.534067\pi$
$710$	10.3557	0.388644
$711$	−3.82331	−0.143385
$712$	114.328	4.28462
$713$	44.5476	1.66832
$714$	−241.369	−9.03300
$715$	−6.69622	−0.250424
$716$	51.3393	1.91864
$717$	−57.8478	−2.16036
$718$	−15.2210	−0.568043
$719$	25.6103	0.955103	0.477551	−	0.878604i	$-0.341524\pi$
$719$	25.6103	0.955103	0.477551	+	0.878604i	$0.341524\pi$
$720$	−250.119	−9.32140
$721$	59.2901	2.20808
$722$	49.3614	1.83704
$723$	45.6258	1.69684
$724$	3.28367	0.122037
$725$	−1.31583	−0.0488689
$726$	8.45065	0.313633
$727$	−14.6863	−0.544685	−0.272342	−	0.962200i	$-0.587798\pi$
$727$	−14.6863	−0.544685	−0.272342	+	0.962200i	$0.587798\pi$
$728$	−109.722	−4.06656
$729$	−15.1395	−0.560723
$730$	44.4610	1.64558
$731$	−82.8467	−3.06420
$732$	162.697	6.01344
$733$	−49.3716	−1.82358	−0.911791	−	0.410654i	$-0.865301\pi$
$733$	−49.3716	−1.82358	−0.911791	+	0.410654i	$0.865301\pi$
$734$	−75.5182	−2.78743
$735$	63.0306	2.32492
$736$	106.245	3.91625
$737$	−9.23146	−0.340045
$738$	−107.401	−3.95350
$739$	9.37819	0.344982	0.172491	−	0.985011i	$-0.444818\pi$
$739$	9.37819	0.344982	0.172491	+	0.985011i	$0.444818\pi$
$740$	−50.1248	−1.84262
$741$	−9.00755	−0.330901
$742$	−35.8224	−1.31508
$743$	9.83837	0.360935	0.180467	−	0.983581i	$-0.442239\pi$
$743$	9.83837	0.360935	0.180467	+	0.983581i	$0.442239\pi$
$744$	−321.459	−11.7852
$745$	−20.2215	−0.740858
$746$	57.3282	2.09894
$747$	−19.0680	−0.697662
$748$	−40.6707	−1.48707
$749$	−22.7400	−0.830902
$750$	85.7544	3.13131
$751$	15.3832	0.561342	0.280671	−	0.959804i	$-0.409443\pi$
$751$	15.3832	0.561342	0.280671	+	0.959804i	$0.409443\pi$
$752$	−197.110	−7.18787
$753$	−50.6096	−1.84432
$754$	−12.9928	−0.473169
$755$	28.9298	1.05286
$756$	229.003	8.32875
$757$	25.0112	0.909048	0.454524	−	0.890734i	$-0.349809\pi$
$757$	25.0112	0.909048	0.454524	+	0.890734i	$0.349809\pi$
$758$	22.6304	0.821973
$759$	−12.9713	−0.470829
$760$	−25.3477	−0.919458
$761$	−22.1686	−0.803610	−0.401805	−	0.915725i	$-0.631617\pi$
$761$	−22.1686	−0.803610	−0.401805	+	0.915725i	$0.631617\pi$
$762$	146.604	5.31090
$763$	−2.69195	−0.0974550
$764$	150.910	5.45972
$765$	−110.948	−4.01133
$766$	−54.8603	−1.98218
$767$	−29.5575	−1.06726
$768$	−205.209	−7.40484
$769$	11.9510	0.430963	0.215482	−	0.976508i	$-0.430868\pi$
$769$	11.9510	0.430963	0.215482	+	0.976508i	$0.430868\pi$
$770$	26.1743	0.943255
$771$	−10.6707	−0.384297
$772$	−102.824	−3.70072
$773$	−14.8035	−0.532446	−0.266223	−	0.963911i	$-0.585776\pi$
$773$	−14.8035	−0.532446	−0.266223	+	0.963911i	$0.585776\pi$
$774$	201.334	7.23682
$775$	−8.18741	−0.294101
$776$	−19.6351	−0.704858
$777$	44.8366	1.60850
$778$	81.3348	2.91599
$779$	−6.44671	−0.230977
$780$	−115.175	−4.12393
$781$	−1.56085	−0.0558517
$782$	84.6536	3.02720
$783$	17.4629	0.624073
$784$	139.772	4.99187
$785$	−21.1042	−0.753240
$786$	−77.9528	−2.78048
$787$	19.5570	0.697132	0.348566	−	0.937284i	$-0.386669\pi$
$787$	19.5570	0.697132	0.348566	+	0.937284i	$0.386669\pi$
$788$	118.515	4.22192
$789$	−17.1530	−0.610664
$790$	−3.97912	−0.141571
$791$	−1.06913	−0.0380138
$792$	63.6490	2.26167
$793$	26.3492	0.935688
$794$	40.2967	1.43008
$795$	−24.2151	−0.858823
$796$	−120.404	−4.26762
$797$	−9.77480	−0.346241	−0.173121	−	0.984901i	$-0.555385\pi$
$797$	−9.77480	−0.346241	−0.173121	+	0.984901i	$0.555385\pi$
$798$	35.2088	1.24638
$799$	−87.4341	−3.09320
$800$	−19.5269	−0.690379
$801$	−72.9967	−2.57921
$802$	22.3598	0.789553
$803$	−6.70131	−0.236484
$804$	−158.781	−5.59978
$805$	−40.1762	−1.41603
$806$	−80.8439	−2.84760
$807$	−69.3647	−2.44175
$808$	−86.0976	−3.02890
$809$	−46.8900	−1.64857	−0.824283	−	0.566178i	$-0.808421\pi$
$809$	−46.8900	−1.64857	−0.824283	+	0.566178i	$0.808421\pi$
$810$	83.0286	2.91733
$811$	5.06767	0.177950	0.0889750	−	0.996034i	$-0.471641\pi$
$811$	5.06767	0.177950	0.0889750	+	0.996034i	$0.471641\pi$
$812$	37.4522	1.31432
$813$	96.5556	3.38635
$814$	10.2448	0.359079
$815$	29.8961	1.04721
$816$	−361.812	−12.6659
$817$	12.0850	0.422800
$818$	−27.1586	−0.949578
$819$	70.0558	2.44795
$820$	−82.4308	−2.87861
$821$	20.4105	0.712331	0.356166	−	0.934423i	$-0.384084\pi$
$821$	20.4105	0.712331	0.356166	+	0.934423i	$0.384084\pi$
$822$	−23.5555	−0.821594
$823$	8.39516	0.292637	0.146318	−	0.989238i	$-0.453258\pi$
$823$	8.39516	0.292637	0.146318	+	0.989238i	$0.453258\pi$
$824$	150.054	5.22738
$825$	2.38400	0.0830004
$826$	115.535	4.01997
$827$	16.0121	0.556795	0.278397	−	0.960466i	$-0.410197\pi$
$827$	16.0121	0.556795	0.278397	+	0.960466i	$0.410197\pi$
$828$	−151.712	−5.27235
$829$	28.3576	0.984901	0.492450	−	0.870341i	$-0.336101\pi$
$829$	28.3576	0.984901	0.492450	+	0.870341i	$0.336101\pi$
$830$	−19.8451	−0.688834
$831$	−51.8689	−1.79931
$832$	−101.880	−3.53207
$833$	62.0001	2.14818
$834$	78.3356	2.71254
$835$	−19.7910	−0.684894
$836$	5.93270	0.205187
$837$	108.658	3.75577
$838$	−78.6358	−2.71643
$839$	−16.3577	−0.564730	−0.282365	−	0.959307i	$-0.591119\pi$
$839$	−16.3577	−0.564730	−0.282365	+	0.959307i	$0.591119\pi$
$840$	289.915	10.0030
$841$	−26.1440	−0.901518
$842$	−8.51196	−0.293342
$843$	77.1291	2.65647
$844$	128.646	4.42819
$845$	12.5974	0.433365
$846$	212.483	7.30531
$847$	−3.94507	−0.135554
$848$	−53.6978	−1.84399
$849$	−73.8160	−2.53336
$850$	−15.5585	−0.533652
$851$	−15.7252	−0.539053
$852$	−26.8467	−0.919752
$853$	−27.4894	−0.941218	−0.470609	−	0.882342i	$-0.655966\pi$
$853$	−27.4894	−0.941218	−0.470609	+	0.882342i	$0.655966\pi$
$854$	−102.994	−3.52439
$855$	16.1841	0.553486
$856$	−57.5514	−1.96707
$857$	10.8236	0.369726	0.184863	−	0.982764i	$-0.440816\pi$
$857$	10.8236	0.369726	0.184863	+	0.982764i	$0.440816\pi$
$858$	23.5401	0.803644
$859$	−46.1117	−1.57331	−0.786655	−	0.617393i	$-0.788189\pi$
$859$	−46.1117	−1.57331	−0.786655	+	0.617393i	$0.788189\pi$
$860$	154.525	5.26924
$861$	73.7343	2.51286
$862$	−36.0099	−1.22650
$863$	35.1562	1.19673	0.598365	−	0.801224i	$-0.295817\pi$
$863$	35.1562	1.19673	0.598365	+	0.801224i	$0.295817\pi$
$864$	259.148	8.81638
$865$	−32.4538	−1.10346
$866$	64.8558	2.20389
$867$	−108.441	−3.68285
$868$	233.036	7.90976
$869$	0.599747	0.0203450
$870$	34.3304	1.16391
$871$	−25.7151	−0.871323
$872$	−6.81290	−0.230714
$873$	12.5367	0.424303
$874$	−12.3485	−0.417696
$875$	−40.0333	−1.35337
$876$	−115.263	−3.89436
$877$	−53.2363	−1.79766	−0.898831	−	0.438295i	$-0.855582\pi$
$877$	−53.2363	−1.79766	−0.898831	+	0.438295i	$0.855582\pi$
$878$	−63.5532	−2.14482
$879$	3.28773	0.110892
$880$	39.2352	1.32262
$881$	−9.97667	−0.336123	−0.168061	−	0.985777i	$-0.553751\pi$
$881$	−9.97667	−0.336123	−0.168061	+	0.985777i	$0.553751\pi$
$882$	−150.673	−5.07342
$883$	−36.4521	−1.22671	−0.613356	−	0.789806i	$-0.710181\pi$
$883$	−36.4521	−1.22671	−0.613356	+	0.789806i	$0.710181\pi$
$884$	−113.292	−3.81043
$885$	78.0989	2.62527
$886$	−53.2725	−1.78973
$887$	11.0733	0.371804	0.185902	−	0.982568i	$-0.440479\pi$
$887$	11.0733	0.371804	0.185902	+	0.982568i	$0.440479\pi$
$888$	113.474	3.80795
$889$	−68.4402	−2.29541
$890$	−75.9716	−2.54657
$891$	−12.5144	−0.419247
$892$	−63.7001	−2.13284
$893$	12.7541	0.426801
$894$	71.0871	2.37751
$895$	−21.9693	−0.734353
$896$	200.356	6.69341
$897$	−36.1328	−1.20644
$898$	108.398	3.61730
$899$	17.7705	0.592678
$900$	27.8832	0.929438
$901$	−23.8193	−0.793535
$902$	16.8476	0.560965
$903$	−138.222	−4.59974
$904$	−2.70579	−0.0899934
$905$	−1.40516	−0.0467091
$906$	−101.701	−3.37878
$907$	42.9563	1.42634	0.713170	−	0.700991i	$-0.247259\pi$
$907$	42.9563	1.42634	0.713170	+	0.700991i	$0.247259\pi$
$908$	65.6894	2.17998
$909$	54.9721	1.82331
$910$	72.9108	2.41697
$911$	−28.1967	−0.934199	−0.467099	−	0.884205i	$-0.654701\pi$
$911$	−28.1967	−0.934199	−0.467099	+	0.884205i	$0.654701\pi$
$912$	52.7780	1.74766
$913$	2.99112	0.0989917
$914$	−88.2555	−2.91923
$915$	−69.6217	−2.30162
$916$	26.4534	0.874045
$917$	36.3912	1.20174
$918$	206.482	6.81493
$919$	5.07924	0.167549	0.0837744	−	0.996485i	$-0.473303\pi$
$919$	5.07924	0.167549	0.0837744	+	0.996485i	$0.473303\pi$
$920$	−101.680	−3.35228
$921$	−59.6174	−1.96446
$922$	34.1441	1.12448
$923$	−4.34790	−0.143113
$924$	−67.8553	−2.23228
$925$	2.89014	0.0950273
$926$	65.6782	2.15832
$927$	−95.8072	−3.14672
$928$	42.3823	1.39127
$929$	−26.0711	−0.855365	−0.427683	−	0.903929i	$-0.640670\pi$
$929$	−26.0711	−0.855365	−0.427683	+	0.903929i	$0.640670\pi$
$930$	213.611	7.00459
$931$	−9.04405	−0.296407
$932$	80.5418	2.63823
$933$	13.3941	0.438504
$934$	91.9893	3.00998
$935$	17.4040	0.569170
$936$	177.300	5.79524
$937$	−22.7172	−0.742140	−0.371070	−	0.928605i	$-0.621009\pi$
$937$	−22.7172	−0.742140	−0.371070	+	0.928605i	$0.621009\pi$
$938$	100.515	3.28195
$939$	37.7629	1.23235
$940$	163.081	5.31911
$941$	2.03799	0.0664367	0.0332184	−	0.999448i	$-0.489424\pi$
$941$	2.03799	0.0664367	0.0332184	+	0.999448i	$0.489424\pi$
$942$	74.1901	2.41725
$943$	−25.8603	−0.842127
$944$	173.187	5.63675
$945$	−97.9956	−3.18780
$946$	−31.5825	−1.02684
$947$	6.40540	0.208147	0.104074	−	0.994570i	$-0.466812\pi$
$947$	6.40540	0.208147	0.104074	+	0.994570i	$0.466812\pi$
$948$	10.3157	0.335037
$949$	−18.6671	−0.605961
$950$	2.26954	0.0736337
$951$	−42.8946	−1.39095
$952$	285.175	9.24258
$953$	25.5427	0.827409	0.413704	−	0.910411i	$-0.364235\pi$
$953$	25.5427	0.827409	0.413704	+	0.910411i	$0.364235\pi$
$954$	57.8857	1.87412
$955$	−64.5778	−2.08969
$956$	106.133	3.43258
$957$	−5.17439	−0.167264
$958$	73.4099	2.37177
$959$	10.9966	0.355099
$960$	269.195	8.68825
$961$	79.5718	2.56683
$962$	28.5377	0.920093
$963$	36.7457	1.18411
$964$	−83.7094	−2.69610
$965$	44.0008	1.41644
$966$	141.236	4.54421
$967$	−31.2696	−1.00556	−0.502782	−	0.864414i	$-0.667690\pi$
$967$	−31.2696	−1.00556	−0.502782	+	0.864414i	$0.667690\pi$
$968$	−9.98436	−0.320910
$969$	23.4113	0.752079
$970$	13.0476	0.418934
$971$	24.3312	0.780824	0.390412	−	0.920640i	$-0.372333\pi$
$971$	24.3312	0.780824	0.390412	+	0.920640i	$0.372333\pi$
$972$	−41.1036	−1.31840
$973$	−36.5699	−1.17238
$974$	−76.7881	−2.46045
$975$	6.64087	0.212678
$976$	−154.388	−4.94185
$977$	27.1812	0.869605	0.434802	−	0.900526i	$-0.356818\pi$
$977$	27.1812	0.869605	0.434802	+	0.900526i	$0.356818\pi$
$978$	−105.097	−3.36065
$979$	11.4507	0.365966
$980$	−115.642	−3.69404
$981$	4.34993	0.138883
$982$	−39.5016	−1.26055
$983$	18.7834	0.599097	0.299549	−	0.954081i	$-0.403164\pi$
$983$	18.7834	0.599097	0.299549	+	0.954081i	$0.403164\pi$
$984$	186.610	5.94891
$985$	−50.7153	−1.61592
$986$	33.7691	1.07543
$987$	−145.876	−4.64327
$988$	16.5261	0.525765
$989$	48.4776	1.54150
$990$	−42.2952	−1.34423
$991$	0.0382755	0.00121586	0.000607931	−	1.00000i	$-0.499806\pi$
$991$	0.0382755	0.00121586	0.000607931		1.00000i	$0.499806\pi$
$992$	263.712	8.37286
$993$	37.3202	1.18432
$994$	16.9951	0.539053
$995$	51.5238	1.63341
$996$	51.4473	1.63017
$997$	−14.9446	−0.473300	−0.236650	−	0.971595i	$-0.576050\pi$
$997$	−14.9446	−0.473300	−0.236650	+	0.971595i	$0.576050\pi$
$998$	36.1828	1.14535
$999$	−38.3561	−1.21353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.1	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.1	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75999 q^{2} -3.06184 q^{3} +5.61754 q^{4} -2.40388 q^{5} +8.45065 q^{6} -3.94507 q^{7} -9.98436 q^{8} +6.37487 q^{9} +O(q^{10})\)	\(q-2.75999 q^{2} -3.06184 q^{3} +5.61754 q^{4} -2.40388 q^{5} +8.45065 q^{6} -3.94507 q^{7} -9.98436 q^{8} +6.37487 q^{9} +6.63467 q^{10} -1.00000 q^{11} -17.2000 q^{12} -2.78559 q^{13} +10.8884 q^{14} +7.36028 q^{15} +16.3217 q^{16} +7.23996 q^{17} -17.5946 q^{18} -1.05610 q^{19} -13.5039 q^{20} +12.0792 q^{21} +2.75999 q^{22} -4.23645 q^{23} +30.5705 q^{24} +0.778618 q^{25} +7.68820 q^{26} -10.3333 q^{27} -22.1616 q^{28} -1.68996 q^{29} -20.3143 q^{30} -10.5153 q^{31} -25.0789 q^{32} +3.06184 q^{33} -19.9822 q^{34} +9.48347 q^{35} +35.8111 q^{36} +3.71189 q^{37} +2.91483 q^{38} +8.52904 q^{39} +24.0012 q^{40} +6.10424 q^{41} -33.3384 q^{42} -11.4430 q^{43} -5.61754 q^{44} -15.3244 q^{45} +11.6925 q^{46} -12.0766 q^{47} -49.9743 q^{48} +8.56361 q^{49} -2.14898 q^{50} -22.1676 q^{51} -15.6482 q^{52} -3.28997 q^{53} +28.5198 q^{54} +2.40388 q^{55} +39.3891 q^{56} +3.23362 q^{57} +4.66427 q^{58} +10.6109 q^{59} +41.3467 q^{60} -9.45911 q^{61} +29.0221 q^{62} -25.1493 q^{63} +36.5741 q^{64} +6.69622 q^{65} -8.45065 q^{66} +9.23146 q^{67} +40.6707 q^{68} +12.9713 q^{69} -26.1743 q^{70} +1.56085 q^{71} -63.6490 q^{72} +6.70131 q^{73} -10.2448 q^{74} -2.38400 q^{75} -5.93270 q^{76} +3.94507 q^{77} -23.5401 q^{78} -0.599747 q^{79} -39.2352 q^{80} +12.5144 q^{81} -16.8476 q^{82} -2.99112 q^{83} +67.8553 q^{84} -17.4040 q^{85} +31.5825 q^{86} +5.17439 q^{87} +9.98436 q^{88} -11.4507 q^{89} +42.2952 q^{90} +10.9894 q^{91} -23.7984 q^{92} +32.1962 q^{93} +33.3313 q^{94} +2.53874 q^{95} +76.7875 q^{96} +1.96658 q^{97} -23.6355 q^{98} -6.37487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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