LMFDB - Embedded newform 6017.2.a.c.1.4

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:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.70820 q^{2} +2.96568 q^{3} +5.33437 q^{4} -1.26109 q^{5} -8.03167 q^{6} +1.85077 q^{7} -9.03015 q^{8} +5.79526 q^{9} +O(q^{10})$	\(q-2.70820 q^{2} +2.96568 q^{3} +5.33437 q^{4} -1.26109 q^{5} -8.03167 q^{6} +1.85077 q^{7} -9.03015 q^{8} +5.79526 q^{9} +3.41529 q^{10} +1.00000 q^{11} +15.8200 q^{12} -5.34816 q^{13} -5.01227 q^{14} -3.73999 q^{15} +13.7868 q^{16} +3.21050 q^{17} -15.6947 q^{18} -7.60704 q^{19} -6.72713 q^{20} +5.48880 q^{21} -2.70820 q^{22} -3.07950 q^{23} -26.7805 q^{24} -3.40965 q^{25} +14.4839 q^{26} +8.28984 q^{27} +9.87270 q^{28} -0.603421 q^{29} +10.1287 q^{30} +3.99164 q^{31} -19.2770 q^{32} +2.96568 q^{33} -8.69469 q^{34} -2.33399 q^{35} +30.9140 q^{36} -0.667363 q^{37} +20.6014 q^{38} -15.8609 q^{39} +11.3878 q^{40} +0.907812 q^{41} -14.8648 q^{42} -7.50474 q^{43} +5.33437 q^{44} -7.30835 q^{45} +8.33991 q^{46} +2.39940 q^{47} +40.8871 q^{48} -3.57465 q^{49} +9.23402 q^{50} +9.52132 q^{51} -28.5291 q^{52} +11.9695 q^{53} -22.4506 q^{54} -1.26109 q^{55} -16.7127 q^{56} -22.5600 q^{57} +1.63419 q^{58} +2.90667 q^{59} -19.9505 q^{60} +0.749237 q^{61} -10.8102 q^{62} +10.7257 q^{63} +24.6326 q^{64} +6.74452 q^{65} -8.03167 q^{66} -6.13031 q^{67} +17.1260 q^{68} -9.13281 q^{69} +6.32093 q^{70} -11.1018 q^{71} -52.3321 q^{72} +2.46272 q^{73} +1.80736 q^{74} -10.1119 q^{75} -40.5787 q^{76} +1.85077 q^{77} +42.9547 q^{78} -11.2992 q^{79} -17.3864 q^{80} +7.19924 q^{81} -2.45854 q^{82} -7.98386 q^{83} +29.2793 q^{84} -4.04874 q^{85} +20.3244 q^{86} -1.78955 q^{87} -9.03015 q^{88} +3.27238 q^{89} +19.7925 q^{90} -9.89823 q^{91} -16.4272 q^{92} +11.8379 q^{93} -6.49807 q^{94} +9.59317 q^{95} -57.1695 q^{96} -4.16250 q^{97} +9.68087 q^{98} +5.79526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.70820	−1.91499	−0.957495	−	0.288451i	$-0.906860\pi$
$2$	−2.70820	−1.91499	−0.957495	+	0.288451i	$0.906860\pi$
$3$	2.96568	1.71224	0.856118	−	0.516780i	$-0.172870\pi$
$3$	2.96568	1.71224	0.856118	+	0.516780i	$0.172870\pi$
$4$	5.33437	2.66718
$5$	−1.26109	−0.563977	−0.281989	−	0.959418i	$-0.590994\pi$
$5$	−1.26109	−0.563977	−0.281989	+	0.959418i	$0.590994\pi$
$6$	−8.03167	−3.27891
$7$	1.85077	0.699526	0.349763	−	0.936838i	$-0.386262\pi$
$7$	1.85077	0.699526	0.349763	+	0.936838i	$0.386262\pi$
$8$	−9.03015	−3.19264
$9$	5.79526	1.93175
$10$	3.41529	1.08001
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	15.8200	4.56685
$13$	−5.34816	−1.48331	−0.741657	−	0.670780i	$-0.765960\pi$
$13$	−5.34816	−1.48331	−0.741657	+	0.670780i	$0.765960\pi$
$14$	−5.01227	−1.33958
$15$	−3.73999	−0.965662
$16$	13.7868	3.44669
$17$	3.21050	0.778661	0.389330	−	0.921098i	$-0.372706\pi$
$17$	3.21050	0.778661	0.389330	+	0.921098i	$0.372706\pi$
$18$	−15.6947	−3.69929
$19$	−7.60704	−1.74517	−0.872587	−	0.488459i	$-0.837559\pi$
$19$	−7.60704	−1.74517	−0.872587	+	0.488459i	$0.837559\pi$
$20$	−6.72713	−1.50423
$21$	5.48880	1.19775
$22$	−2.70820	−0.577391
$23$	−3.07950	−0.642120	−0.321060	−	0.947059i	$-0.604039\pi$
$23$	−3.07950	−0.642120	−0.321060	+	0.947059i	$0.604039\pi$
$24$	−26.7805	−5.46655
$25$	−3.40965	−0.681930
$26$	14.4839	2.84053
$27$	8.28984	1.59538
$28$	9.87270	1.86576
$29$	−0.603421	−0.112053	−0.0560263	−	0.998429i	$-0.517843\pi$
$29$	−0.603421	−0.112053	−0.0560263	+	0.998429i	$0.517843\pi$
$30$	10.1287	1.84923
$31$	3.99164	0.716920	0.358460	−	0.933545i	$-0.383302\pi$
$31$	3.99164	0.716920	0.358460	+	0.933545i	$0.383302\pi$
$32$	−19.2770	−3.40773
$33$	2.96568	0.516259
$34$	−8.69469	−1.49113
$35$	−2.33399	−0.394517
$36$	30.9140	5.15234
$37$	−0.667363	−0.109714	−0.0548569	−	0.998494i	$-0.517470\pi$
$37$	−0.667363	−0.109714	−0.0548569	+	0.998494i	$0.517470\pi$
$38$	20.6014	3.34199
$39$	−15.8609	−2.53978
$40$	11.3878	1.80058
$41$	0.907812	0.141776	0.0708882	−	0.997484i	$-0.477417\pi$
$41$	0.907812	0.141776	0.0708882	+	0.997484i	$0.477417\pi$
$42$	−14.8648	−2.29369
$43$	−7.50474	−1.14446	−0.572231	−	0.820093i	$-0.693922\pi$
$43$	−7.50474	−1.14446	−0.572231	+	0.820093i	$0.693922\pi$
$44$	5.33437	0.804186
$45$	−7.30835	−1.08946
$46$	8.33991	1.22965
$47$	2.39940	0.349989	0.174994	−	0.984569i	$-0.444009\pi$
$47$	2.39940	0.349989	0.174994	+	0.984569i	$0.444009\pi$
$48$	40.8871	5.90154
$49$	−3.57465	−0.510664
$50$	9.23402	1.30589
$51$	9.52132	1.33325
$52$	−28.5291	−3.95627
$53$	11.9695	1.64414	0.822070	−	0.569386i	$-0.192819\pi$
$53$	11.9695	1.64414	0.822070	+	0.569386i	$0.192819\pi$
$54$	−22.4506	−3.05514
$55$	−1.26109	−0.170046
$56$	−16.7127	−2.23333
$57$	−22.5600	−2.98815
$58$	1.63419	0.214579
$59$	2.90667	0.378416	0.189208	−	0.981937i	$-0.439408\pi$
$59$	2.90667	0.378416	0.189208	+	0.981937i	$0.439408\pi$
$60$	−19.9505	−2.57560
$61$	0.749237	0.0959299	0.0479650	−	0.998849i	$-0.484726\pi$
$61$	0.749237	0.0959299	0.0479650	+	0.998849i	$0.484726\pi$
$62$	−10.8102	−1.37290
$63$	10.7257	1.35131
$64$	24.6326	3.07908
$65$	6.74452	0.836555
$66$	−8.03167	−0.988630
$67$	−6.13031	−0.748937	−0.374468	−	0.927240i	$-0.622175\pi$
$67$	−6.13031	−0.748937	−0.374468	+	0.927240i	$0.622175\pi$
$68$	17.1260	2.07683
$69$	−9.13281	−1.09946
$70$	6.32093	0.755495
$71$	−11.1018	−1.31754	−0.658770	−	0.752344i	$-0.728923\pi$
$71$	−11.1018	−1.31754	−0.658770	+	0.752344i	$0.728923\pi$
$72$	−52.3321	−6.16739
$73$	2.46272	0.288239	0.144120	−	0.989560i	$-0.453965\pi$
$73$	2.46272	0.288239	0.144120	+	0.989560i	$0.453965\pi$
$74$	1.80736	0.210101
$75$	−10.1119	−1.16762
$76$	−40.5787	−4.65470
$77$	1.85077	0.210915
$78$	42.9547	4.86366
$79$	−11.2992	−1.27125	−0.635627	−	0.771996i	$-0.719258\pi$
$79$	−11.2992	−1.27125	−0.635627	+	0.771996i	$0.719258\pi$
$80$	−17.3864	−1.94385
$81$	7.19924	0.799916
$82$	−2.45854	−0.271500
$83$	−7.98386	−0.876343	−0.438171	−	0.898891i	$-0.644374\pi$
$83$	−7.98386	−0.876343	−0.438171	+	0.898891i	$0.644374\pi$
$84$	29.2793	3.19463
$85$	−4.04874	−0.439147
$86$	20.3244	2.19163
$87$	−1.78955	−0.191860
$88$	−9.03015	−0.962617
$89$	3.27238	0.346872	0.173436	−	0.984845i	$-0.444513\pi$
$89$	3.27238	0.346872	0.173436	+	0.984845i	$0.444513\pi$
$90$	19.7925	2.08631
$91$	−9.89823	−1.03762
$92$	−16.4272	−1.71265
$93$	11.8379	1.22754
$94$	−6.49807	−0.670225
$95$	9.59317	0.984239
$96$	−57.1695	−5.83484
$97$	−4.16250	−0.422638	−0.211319	−	0.977417i	$-0.567776\pi$
$97$	−4.16250	−0.422638	−0.211319	+	0.977417i	$0.567776\pi$
$98$	9.68087	0.977915
$99$	5.79526	0.582445
$100$	−18.1883	−1.81883
$101$	5.79334	0.576459	0.288230	−	0.957561i	$-0.406933\pi$
$101$	5.79334	0.576459	0.288230	+	0.957561i	$0.406933\pi$
$102$	−25.7857	−2.55316
$103$	−9.57292	−0.943248	−0.471624	−	0.881800i	$-0.656332\pi$
$103$	−9.57292	−0.943248	−0.471624	+	0.881800i	$0.656332\pi$
$104$	48.2947	4.73569
$105$	−6.92188	−0.675506
$106$	−32.4159	−3.14851
$107$	−14.5234	−1.40403	−0.702016	−	0.712161i	$-0.747716\pi$
$107$	−14.5234	−1.40403	−0.702016	+	0.712161i	$0.747716\pi$
$108$	44.2211	4.25517
$109$	−2.66667	−0.255421	−0.127711	−	0.991811i	$-0.540763\pi$
$109$	−2.66667	−0.255421	−0.127711	+	0.991811i	$0.540763\pi$
$110$	3.41529	0.325635
$111$	−1.97919	−0.187856
$112$	25.5161	2.41105
$113$	11.9363	1.12287	0.561434	−	0.827521i	$-0.310250\pi$
$113$	11.9363	1.12287	0.561434	+	0.827521i	$0.310250\pi$
$114$	61.0972	5.72227
$115$	3.88353	0.362141
$116$	−3.21887	−0.298865
$117$	−30.9940	−2.86540
$118$	−7.87186	−0.724663
$119$	5.94190	0.544693
$120$	33.7727	3.08301
$121$	1.00000	0.0909091
$122$	−2.02909	−0.183705
$123$	2.69228	0.242755
$124$	21.2929	1.91216
$125$	10.6053	0.948570
$126$	−29.0474	−2.58775
$127$	16.0814	1.42700	0.713499	−	0.700657i	$-0.247109\pi$
$127$	16.0814	1.42700	0.713499	+	0.700657i	$0.247109\pi$
$128$	−28.1561	−2.48867
$129$	−22.2566	−1.95959
$130$	−18.2655	−1.60199
$131$	14.0716	1.22944	0.614722	−	0.788744i	$-0.289268\pi$
$131$	14.0716	1.22944	0.614722	+	0.788744i	$0.289268\pi$
$132$	15.8200	1.37696
$133$	−14.0789	−1.22079
$134$	16.6021	1.43421
$135$	−10.4543	−0.899759
$136$	−28.9913	−2.48598
$137$	−11.9734	−1.02295	−0.511477	−	0.859297i	$-0.670902\pi$
$137$	−11.9734	−1.02295	−0.511477	+	0.859297i	$0.670902\pi$
$138$	24.7335	2.10546
$139$	−1.75295	−0.148684	−0.0743418	−	0.997233i	$-0.523686\pi$
$139$	−1.75295	−0.148684	−0.0743418	+	0.997233i	$0.523686\pi$
$140$	−12.4504	−1.05225
$141$	7.11586	0.599264
$142$	30.0659	2.52308
$143$	−5.34816	−0.447236
$144$	79.8978	6.65815
$145$	0.760970	0.0631951
$146$	−6.66954	−0.551975
$147$	−10.6013	−0.874377
$148$	−3.55996	−0.292627
$149$	3.31700	0.271739	0.135870	−	0.990727i	$-0.456617\pi$
$149$	3.31700	0.271739	0.135870	+	0.990727i	$0.456617\pi$
$150$	27.3852	2.23599
$151$	−15.4234	−1.25514	−0.627570	−	0.778561i	$-0.715950\pi$
$151$	−15.4234	−1.25514	−0.627570	+	0.778561i	$0.715950\pi$
$152$	68.6927	5.57171
$153$	18.6057	1.50418
$154$	−5.01227	−0.403900
$155$	−5.03383	−0.404327
$156$	−84.6081	−6.77407
$157$	−10.9000	−0.869917	−0.434958	−	0.900451i	$-0.643237\pi$
$157$	−10.9000	−0.869917	−0.434958	+	0.900451i	$0.643237\pi$
$158$	30.6004	2.43444
$159$	35.4978	2.81516
$160$	24.3101	1.92188
$161$	−5.69945	−0.449179
$162$	−19.4970	−1.53183
$163$	−0.449109	−0.0351769	−0.0175885	−	0.999845i	$-0.505599\pi$
$163$	−0.449109	−0.0351769	−0.0175885	+	0.999845i	$0.505599\pi$
$164$	4.84260	0.378144
$165$	−3.73999	−0.291158
$166$	21.6219	1.67819
$167$	−21.3714	−1.65377	−0.826885	−	0.562371i	$-0.809889\pi$
$167$	−21.3714	−1.65377	−0.826885	+	0.562371i	$0.809889\pi$
$168$	−49.5647	−3.82400
$169$	15.6028	1.20022
$170$	10.9648	0.840962
$171$	−44.0847	−3.37124
$172$	−40.0330	−3.05249
$173$	15.3758	1.16900	0.584499	−	0.811394i	$-0.301291\pi$
$173$	15.3758	1.16900	0.584499	+	0.811394i	$0.301291\pi$
$174$	4.84648	0.367411
$175$	−6.31048	−0.477027
$176$	13.7868	1.03922
$177$	8.62026	0.647938
$178$	−8.86229	−0.664256
$179$	−16.8159	−1.25688	−0.628438	−	0.777860i	$-0.716305\pi$
$179$	−16.8159	−1.25688	−0.628438	+	0.777860i	$0.716305\pi$
$180$	−38.9854	−2.90580
$181$	−1.97496	−0.146798	−0.0733988	−	0.997303i	$-0.523385\pi$
$181$	−1.97496	−0.146798	−0.0733988	+	0.997303i	$0.523385\pi$
$182$	26.8064	1.98702
$183$	2.22200	0.164255
$184$	27.8083	2.05006
$185$	0.841606	0.0618761
$186$	−32.0596	−2.35072
$187$	3.21050	0.234775
$188$	12.7993	0.933485
$189$	15.3426	1.11601
$190$	−25.9803	−1.88481
$191$	−14.6931	−1.06315	−0.531577	−	0.847010i	$-0.678400\pi$
$191$	−14.6931	−1.06315	−0.531577	+	0.847010i	$0.678400\pi$
$192$	73.0525	5.27211
$193$	−0.662869	−0.0477143	−0.0238572	−	0.999715i	$-0.507595\pi$
$193$	−0.662869	−0.0477143	−0.0238572	+	0.999715i	$0.507595\pi$
$194$	11.2729	0.809347
$195$	20.0021	1.43238
$196$	−19.0685	−1.36203
$197$	−16.1645	−1.15167	−0.575837	−	0.817564i	$-0.695324\pi$
$197$	−16.1645	−1.15167	−0.575837	+	0.817564i	$0.695324\pi$
$198$	−15.6947	−1.11538
$199$	−20.0997	−1.42483	−0.712413	−	0.701760i	$-0.752398\pi$
$199$	−20.0997	−1.42483	−0.712413	+	0.701760i	$0.752398\pi$
$200$	30.7896	2.17716
$201$	−18.1805	−1.28236
$202$	−15.6896	−1.10391
$203$	−1.11679	−0.0783836
$204$	50.7902	3.55603
$205$	−1.14483	−0.0799587
$206$	25.9254	1.80631
$207$	−17.8465	−1.24042
$208$	−73.7338	−5.11252
$209$	−7.60704	−0.526190
$210$	18.7459	1.29359
$211$	22.3700	1.54001	0.770006	−	0.638036i	$-0.220253\pi$
$211$	22.3700	1.54001	0.770006	+	0.638036i	$0.220253\pi$
$212$	63.8498	4.38523
$213$	−32.9244	−2.25594
$214$	39.3324	2.68871
$215$	9.46416	0.645450
$216$	−74.8585	−5.09348
$217$	7.38762	0.501504
$218$	7.22190	0.489129
$219$	7.30363	0.493534
$220$	−6.72713	−0.453543
$221$	−17.1703	−1.15500
$222$	5.36004	0.359742
$223$	−27.0966	−1.81452	−0.907262	−	0.420567i	$-0.861831\pi$
$223$	−27.0966	−1.81452	−0.907262	+	0.420567i	$0.861831\pi$
$224$	−35.6774	−2.38380
$225$	−19.7598	−1.31732
$226$	−32.3258	−2.15028
$227$	−27.6172	−1.83302	−0.916509	−	0.400013i	$-0.869005\pi$
$227$	−27.6172	−1.83302	−0.916509	+	0.400013i	$0.869005\pi$
$228$	−120.344	−7.96995
$229$	10.4911	0.693269	0.346634	−	0.938000i	$-0.387324\pi$
$229$	10.4911	0.693269	0.346634	+	0.938000i	$0.387324\pi$
$230$	−10.5174	−0.693496
$231$	5.48880	0.361136
$232$	5.44898	0.357743
$233$	−18.5041	−1.21224	−0.606121	−	0.795372i	$-0.707275\pi$
$233$	−18.5041	−1.21224	−0.606121	+	0.795372i	$0.707275\pi$
$234$	83.9380	5.48720
$235$	−3.02587	−0.197386
$236$	15.5053	1.00931
$237$	−33.5097	−2.17669
$238$	−16.0919	−1.04308
$239$	−25.5943	−1.65556	−0.827779	−	0.561054i	$-0.810396\pi$
$239$	−25.5943	−1.65556	−0.827779	+	0.561054i	$0.810396\pi$
$240$	−51.5624	−3.32834
$241$	−12.0435	−0.775792	−0.387896	−	0.921703i	$-0.626798\pi$
$241$	−12.0435	−0.775792	−0.387896	+	0.921703i	$0.626798\pi$
$242$	−2.70820	−0.174090
$243$	−3.51887	−0.225736
$244$	3.99671	0.255863
$245$	4.50796	0.288003
$246$	−7.29124	−0.464873
$247$	40.6837	2.58864
$248$	−36.0451	−2.28887
$249$	−23.6776	−1.50051
$250$	−28.7214	−1.81650
$251$	18.6971	1.18015	0.590075	−	0.807348i	$-0.299098\pi$
$251$	18.6971	1.18015	0.590075	+	0.807348i	$0.299098\pi$
$252$	57.2148	3.60420
$253$	−3.07950	−0.193606
$254$	−43.5518	−2.73268
$255$	−12.0073	−0.751924
$256$	26.9873	1.68670
$257$	2.23407	0.139357	0.0696786	−	0.997569i	$-0.477803\pi$
$257$	2.23407	0.139357	0.0696786	+	0.997569i	$0.477803\pi$
$258$	60.2755	3.75259
$259$	−1.23514	−0.0767477
$260$	35.9778	2.23125
$261$	−3.49698	−0.216458
$262$	−38.1089	−2.35437
$263$	18.3853	1.13369	0.566843	−	0.823826i	$-0.308165\pi$
$263$	18.3853	1.13369	0.566843	+	0.823826i	$0.308165\pi$
$264$	−26.7805	−1.64823
$265$	−15.0947	−0.927258
$266$	38.1285	2.33781
$267$	9.70485	0.593927
$268$	−32.7013	−1.99755
$269$	28.4063	1.73196	0.865981	−	0.500078i	$-0.166695\pi$
$269$	28.4063	1.73196	0.865981	+	0.500078i	$0.166695\pi$
$270$	28.3122	1.72303
$271$	−10.7111	−0.650654	−0.325327	−	0.945602i	$-0.605474\pi$
$271$	−10.7111	−0.650654	−0.325327	+	0.945602i	$0.605474\pi$
$272$	44.2624	2.68380
$273$	−29.3550	−1.77664
$274$	32.4264	1.95895
$275$	−3.40965	−0.205609
$276$	−48.7177	−2.93246
$277$	−3.22663	−0.193869	−0.0969346	−	0.995291i	$-0.530904\pi$
$277$	−3.22663	−0.193869	−0.0969346	+	0.995291i	$0.530904\pi$
$278$	4.74736	0.284728
$279$	23.1326	1.38491
$280$	21.0763	1.25955
$281$	32.7063	1.95109	0.975547	−	0.219791i	$-0.0705376\pi$
$281$	32.7063	1.95109	0.975547	+	0.219791i	$0.0705376\pi$
$282$	−19.2712	−1.14758
$283$	25.4567	1.51324	0.756622	−	0.653853i	$-0.226849\pi$
$283$	25.4567	1.51324	0.756622	+	0.653853i	$0.226849\pi$
$284$	−59.2211	−3.51412
$285$	28.4503	1.68525
$286$	14.4839	0.856452
$287$	1.68015	0.0991763
$288$	−111.715	−6.58289
$289$	−6.69268	−0.393687
$290$	−2.06086	−0.121018
$291$	−12.3446	−0.723656
$292$	13.1370	0.768787
$293$	−17.5954	−1.02794	−0.513968	−	0.857809i	$-0.671825\pi$
$293$	−17.5954	−1.02794	−0.513968	+	0.857809i	$0.671825\pi$
$294$	28.7104	1.67442
$295$	−3.66558	−0.213418
$296$	6.02639	0.350277
$297$	8.28984	0.481025
$298$	−8.98311	−0.520378
$299$	16.4697	0.952465
$300$	−53.9407	−3.11427
$301$	−13.8896	−0.800581
$302$	41.7697	2.40358
$303$	17.1812	0.987034
$304$	−104.876	−6.01507
$305$	−0.944856	−0.0541023
$306$	−50.3880	−2.88049
$307$	−18.9693	−1.08264	−0.541318	−	0.840818i	$-0.682074\pi$
$307$	−18.9693	−1.08264	−0.541318	+	0.840818i	$0.682074\pi$
$308$	9.87270	0.562549
$309$	−28.3902	−1.61506
$310$	13.6326	0.774282
$311$	−9.47818	−0.537458	−0.268729	−	0.963216i	$-0.586604\pi$
$311$	−9.47818	−0.537458	−0.268729	+	0.963216i	$0.586604\pi$
$312$	143.227	8.10861
$313$	24.2524	1.37083	0.685414	−	0.728153i	$-0.259621\pi$
$313$	24.2524	1.37083	0.685414	+	0.728153i	$0.259621\pi$
$314$	29.5195	1.66588
$315$	−13.5261	−0.762109
$316$	−60.2739	−3.39067
$317$	23.9063	1.34271	0.671355	−	0.741136i	$-0.265713\pi$
$317$	23.9063	1.34271	0.671355	+	0.741136i	$0.265713\pi$
$318$	−96.1352	−5.39100
$319$	−0.603421	−0.0337851
$320$	−31.0640	−1.73653
$321$	−43.0718	−2.40403
$322$	15.4353	0.860174
$323$	−24.4224	−1.35890
$324$	38.4034	2.13352
$325$	18.2354	1.01152
$326$	1.21628	0.0673635
$327$	−7.90850	−0.437341
$328$	−8.19768	−0.452641
$329$	4.44075	0.244826
$330$	10.1287	0.557565
$331$	1.13048	0.0621370	0.0310685	−	0.999517i	$-0.490109\pi$
$331$	1.13048	0.0621370	0.0310685	+	0.999517i	$0.490109\pi$
$332$	−42.5889	−2.33737
$333$	−3.86754	−0.211940
$334$	57.8782	3.16695
$335$	7.73089	0.422383
$336$	75.6727	4.12828
$337$	26.7203	1.45555	0.727775	−	0.685816i	$-0.240555\pi$
$337$	26.7203	1.45555	0.727775	+	0.685816i	$0.240555\pi$
$338$	−42.2557	−2.29841
$339$	35.3991	1.92262
$340$	−21.5975	−1.17129
$341$	3.99164	0.216160
$342$	119.390	6.45590
$343$	−19.5713	−1.05675
$344$	67.7689	3.65385
$345$	11.5173	0.620071
$346$	−41.6407	−2.23862
$347$	−13.3911	−0.718871	−0.359435	−	0.933170i	$-0.617031\pi$
$347$	−13.3911	−0.718871	−0.359435	+	0.933170i	$0.617031\pi$
$348$	−9.54614	−0.511727
$349$	4.38597	0.234776	0.117388	−	0.993086i	$-0.462548\pi$
$349$	4.38597	0.234776	0.117388	+	0.993086i	$0.462548\pi$
$350$	17.0901	0.913502
$351$	−44.3354	−2.36645
$352$	−19.2770	−1.02747
$353$	2.18438	0.116263	0.0581313	−	0.998309i	$-0.481486\pi$
$353$	2.18438	0.116263	0.0581313	+	0.998309i	$0.481486\pi$
$354$	−23.3454	−1.24080
$355$	14.0004	0.743063
$356$	17.4561	0.925172
$357$	17.6218	0.932644
$358$	45.5408	2.40690
$359$	2.27025	0.119819	0.0599096	−	0.998204i	$-0.480919\pi$
$359$	2.27025	0.119819	0.0599096	+	0.998204i	$0.480919\pi$
$360$	65.9955	3.47827
$361$	38.8670	2.04563
$362$	5.34859	0.281116
$363$	2.96568	0.155658
$364$	−52.8008	−2.76751
$365$	−3.10571	−0.162560
$366$	−6.01762	−0.314546
$367$	−10.7058	−0.558841	−0.279420	−	0.960169i	$-0.590142\pi$
$367$	−10.7058	−0.558841	−0.279420	+	0.960169i	$0.590142\pi$
$368$	−42.4563	−2.21319
$369$	5.26101	0.273877
$370$	−2.27924	−0.118492
$371$	22.1529	1.15012
$372$	63.1479	3.27407
$373$	−4.26136	−0.220645	−0.110322	−	0.993896i	$-0.535188\pi$
$373$	−4.26136	−0.220645	−0.110322	+	0.993896i	$0.535188\pi$
$374$	−8.69469	−0.449592
$375$	31.4520	1.62418
$376$	−21.6670	−1.11739
$377$	3.22720	0.166209
$378$	−41.5509	−2.13715
$379$	36.3236	1.86582	0.932910	−	0.360110i	$-0.117261\pi$
$379$	36.3236	1.86582	0.932910	+	0.360110i	$0.117261\pi$
$380$	51.1735	2.62515
$381$	47.6924	2.44336
$382$	39.7919	2.03593
$383$	−21.7319	−1.11045	−0.555224	−	0.831701i	$-0.687368\pi$
$383$	−21.7319	−1.11045	−0.555224	+	0.831701i	$0.687368\pi$
$384$	−83.5021	−4.26120
$385$	−2.33399	−0.118951
$386$	1.79518	0.0913724
$387$	−43.4919	−2.21082
$388$	−22.2043	−1.12725
$389$	−11.2709	−0.571460	−0.285730	−	0.958310i	$-0.592236\pi$
$389$	−11.2709	−0.571460	−0.285730	+	0.958310i	$0.592236\pi$
$390$	−54.1698	−2.74299
$391$	−9.88673	−0.499993
$392$	32.2796	1.63037
$393$	41.7320	2.10510
$394$	43.7768	2.20544
$395$	14.2493	0.716959
$396$	30.9140	1.55349
$397$	10.1721	0.510522	0.255261	−	0.966872i	$-0.417839\pi$
$397$	10.1721	0.510522	0.255261	+	0.966872i	$0.417839\pi$
$398$	54.4340	2.72853
$399$	−41.7535	−2.09029
$400$	−47.0080	−2.35040
$401$	22.6399	1.13058	0.565292	−	0.824891i	$-0.308764\pi$
$401$	22.6399	1.13058	0.565292	+	0.824891i	$0.308764\pi$
$402$	49.2366	2.45570
$403$	−21.3480	−1.06342
$404$	30.9038	1.53752
$405$	−9.07891	−0.451134
$406$	3.02451	0.150104
$407$	−0.667363	−0.0330800
$408$	−85.9789	−4.25659
$409$	−15.6624	−0.774454	−0.387227	−	0.921984i	$-0.626567\pi$
$409$	−15.6624	−0.774454	−0.387227	+	0.921984i	$0.626567\pi$
$410$	3.10045	0.153120
$411$	−35.5092	−1.75154
$412$	−51.0655	−2.51582
$413$	5.37959	0.264712
$414$	48.3319	2.37538
$415$	10.0684	0.494237
$416$	103.097	5.05473
$417$	−5.19870	−0.254582
$418$	20.6014	1.00765
$419$	−16.9011	−0.825673	−0.412836	−	0.910805i	$-0.635462\pi$
$419$	−16.9011	−0.825673	−0.412836	+	0.910805i	$0.635462\pi$
$420$	−36.9238	−1.80170
$421$	−9.78715	−0.476996	−0.238498	−	0.971143i	$-0.576655\pi$
$421$	−9.78715	−0.476996	−0.238498	+	0.971143i	$0.576655\pi$
$422$	−60.5824	−2.94911
$423$	13.9052	0.676092
$424$	−108.087	−5.24915
$425$	−10.9467	−0.530992
$426$	89.1659	4.32010
$427$	1.38667	0.0671055
$428$	−77.4732	−3.74481
$429$	−15.8609	−0.765773
$430$	−25.6309	−1.23603
$431$	0.102479	0.00493624	0.00246812	−	0.999997i	$-0.499214\pi$
$431$	0.102479	0.00493624	0.00246812	+	0.999997i	$0.499214\pi$
$432$	114.290	5.49878
$433$	17.3195	0.832323	0.416161	−	0.909291i	$-0.363375\pi$
$433$	17.3195	0.832323	0.416161	+	0.909291i	$0.363375\pi$
$434$	−20.0072	−0.960376
$435$	2.25679	0.108205
$436$	−14.2250	−0.681255
$437$	23.4259	1.12061
$438$	−19.7797	−0.945112
$439$	0.0191838	0.000915595 0	0.000457797	−	1.00000i	$-0.499854\pi$
$439$	0.0191838	0.000915595 0	0.000457797		1.00000i	$0.499854\pi$
$440$	11.3878	0.542894
$441$	−20.7160	−0.986476
$442$	46.5006	2.21181
$443$	20.2494	0.962077	0.481038	−	0.876700i	$-0.340260\pi$
$443$	20.2494	0.962077	0.481038	+	0.876700i	$0.340260\pi$
$444$	−10.5577	−0.501047
$445$	−4.12678	−0.195628
$446$	73.3831	3.47479
$447$	9.83716	0.465282
$448$	45.5894	2.15390
$449$	11.8043	0.557077	0.278539	−	0.960425i	$-0.410150\pi$
$449$	11.8043	0.557077	0.278539	+	0.960425i	$0.410150\pi$
$450$	53.5135	2.52265
$451$	0.907812	0.0427472
$452$	63.6724	2.99490
$453$	−45.7409	−2.14909
$454$	74.7930	3.51021
$455$	12.4826	0.585192
$456$	203.721	9.54009
$457$	29.4288	1.37662	0.688310	−	0.725416i	$-0.258353\pi$
$457$	29.4288	1.37662	0.688310	+	0.725416i	$0.258353\pi$
$458$	−28.4119	−1.32760
$459$	26.6145	1.24226
$460$	20.7162	0.965897
$461$	29.6630	1.38154	0.690771	−	0.723074i	$-0.257271\pi$
$461$	29.6630	1.38154	0.690771	+	0.723074i	$0.257271\pi$
$462$	−14.8648	−0.691572
$463$	−3.98757	−0.185318	−0.0926591	−	0.995698i	$-0.529537\pi$
$463$	−3.98757	−0.185318	−0.0926591	+	0.995698i	$0.529537\pi$
$464$	−8.31922	−0.386210
$465$	−14.9287	−0.692303
$466$	50.1128	2.32143
$467$	−41.2377	−1.90825	−0.954127	−	0.299402i	$-0.903213\pi$
$467$	−41.2377	−1.90825	−0.954127	+	0.299402i	$0.903213\pi$
$468$	−165.333	−7.64254
$469$	−11.3458	−0.523901
$470$	8.19467	0.377992
$471$	−32.3260	−1.48950
$472$	−26.2477	−1.20815
$473$	−7.50474	−0.345068
$474$	90.7510	4.16833
$475$	25.9373	1.19009
$476$	31.6963	1.45280
$477$	69.3665	3.17607
$478$	69.3146	3.17038
$479$	−3.12730	−0.142890	−0.0714449	−	0.997445i	$-0.522761\pi$
$479$	−3.12730	−0.142890	−0.0714449	+	0.997445i	$0.522761\pi$
$480$	72.0960	3.29072
$481$	3.56917	0.162740
$482$	32.6164	1.48563
$483$	−16.9027	−0.769101
$484$	5.33437	0.242471
$485$	5.24929	0.238358
$486$	9.52982	0.432282
$487$	−5.68093	−0.257427	−0.128714	−	0.991682i	$-0.541085\pi$
$487$	−5.68093	−0.257427	−0.128714	+	0.991682i	$0.541085\pi$
$488$	−6.76572	−0.306270
$489$	−1.33191	−0.0602312
$490$	−12.2085	−0.551522
$491$	28.0152	1.26431	0.632155	−	0.774842i	$-0.282171\pi$
$491$	28.0152	1.26431	0.632155	+	0.774842i	$0.282171\pi$
$492$	14.3616	0.647472
$493$	−1.93728	−0.0872509
$494$	−110.180	−4.95722
$495$	−7.30835	−0.328486
$496$	55.0318	2.47100
$497$	−20.5469	−0.921654
$498$	64.1237	2.87345
$499$	29.8915	1.33813	0.669063	−	0.743206i	$-0.266696\pi$
$499$	29.8915	1.33813	0.669063	+	0.743206i	$0.266696\pi$
$500$	56.5728	2.53001
$501$	−63.3808	−2.83164
$502$	−50.6355	−2.25997
$503$	17.1935	0.766619	0.383310	−	0.923620i	$-0.374784\pi$
$503$	17.1935	0.766619	0.383310	+	0.923620i	$0.374784\pi$
$504$	−96.8547	−4.31425
$505$	−7.30594	−0.325110
$506$	8.33991	0.370754
$507$	46.2731	2.05506
$508$	85.7844	3.80607
$509$	−11.4147	−0.505949	−0.252975	−	0.967473i	$-0.581409\pi$
$509$	−11.4147	−0.505949	−0.252975	+	0.967473i	$0.581409\pi$
$510$	32.5181	1.43993
$511$	4.55793	0.201631
$512$	−16.7748	−0.741348
$513$	−63.0611	−2.78422
$514$	−6.05031	−0.266868
$515$	12.0723	0.531970
$516$	−118.725	−5.22658
$517$	2.39940	0.105526
$518$	3.34500	0.146971
$519$	45.5996	2.00160
$520$	−60.9041	−2.67082
$521$	38.0825	1.66843	0.834213	−	0.551442i	$-0.185922\pi$
$521$	38.0825	1.66843	0.834213	+	0.551442i	$0.185922\pi$
$522$	9.47054	0.414514
$523$	−6.71485	−0.293620	−0.146810	−	0.989165i	$-0.546901\pi$
$523$	−6.71485	−0.293620	−0.146810	+	0.989165i	$0.546901\pi$
$524$	75.0633	3.27916
$525$	−18.7149	−0.816783
$526$	−49.7911	−2.17100
$527$	12.8152	0.558238
$528$	40.8871	1.77938
$529$	−13.5167	−0.587682
$530$	40.8794	1.77569
$531$	16.8449	0.731007
$532$	−75.1020	−3.25608
$533$	−4.85513	−0.210299
$534$	−26.2827	−1.13736
$535$	18.3154	0.791842
$536$	55.3576	2.39109
$537$	−49.8704	−2.15207
$538$	−76.9300	−3.31669
$539$	−3.57465	−0.153971
$540$	−55.7668	−2.39982
$541$	−36.0432	−1.54962	−0.774810	−	0.632194i	$-0.782154\pi$
$541$	−36.0432	−1.54962	−0.774810	+	0.632194i	$0.782154\pi$
$542$	29.0079	1.24600
$543$	−5.85710	−0.251352
$544$	−61.8889	−2.65347
$545$	3.36292	0.144052
$546$	79.4993	3.40225
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−63.8704	−2.72841
$549$	4.34202	0.185313
$550$	9.23402	0.393740
$551$	4.59025	0.195551
$552$	82.4706	3.51018
$553$	−20.9122	−0.889275
$554$	8.73836	0.371258
$555$	2.49594	0.105947
$556$	−9.35091	−0.396567
$557$	−15.7749	−0.668404	−0.334202	−	0.942501i	$-0.608467\pi$
$557$	−15.7749	−0.668404	−0.334202	+	0.942501i	$0.608467\pi$
$558$	−62.6478	−2.65209
$559$	40.1366	1.69760
$560$	−32.1782	−1.35978
$561$	9.52132	0.401990
$562$	−88.5753	−3.73632
$563$	9.12226	0.384458	0.192229	−	0.981350i	$-0.438428\pi$
$563$	9.12226	0.384458	0.192229	+	0.981350i	$0.438428\pi$
$564$	37.9586	1.59835
$565$	−15.0527	−0.633272
$566$	−68.9419	−2.89784
$567$	13.3242	0.559562
$568$	100.251	4.20643
$569$	11.6914	0.490130	0.245065	−	0.969507i	$-0.421191\pi$
$569$	11.6914	0.490130	0.245065	+	0.969507i	$0.421191\pi$
$570$	−77.0491	−3.22723
$571$	3.59023	0.150246	0.0751231	−	0.997174i	$-0.476065\pi$
$571$	3.59023	0.150246	0.0751231	+	0.997174i	$0.476065\pi$
$572$	−28.5291	−1.19286
$573$	−43.5750	−1.82037
$574$	−4.55020	−0.189922
$575$	10.5000	0.437880
$576$	142.752	5.94802
$577$	−39.3583	−1.63851	−0.819255	−	0.573430i	$-0.805613\pi$
$577$	−39.3583	−1.63851	−0.819255	+	0.573430i	$0.805613\pi$
$578$	18.1252	0.753907
$579$	−1.96586	−0.0816982
$580$	4.05929	0.168553
$581$	−14.7763	−0.613024
$582$	33.4318	1.38579
$583$	11.9695	0.495727
$584$	−22.2387	−0.920244
$585$	39.0863	1.61602
$586$	47.6520	1.96849
$587$	−30.1683	−1.24518	−0.622590	−	0.782548i	$-0.713920\pi$
$587$	−30.1683	−1.24518	−0.622590	+	0.782548i	$0.713920\pi$
$588$	−56.5510	−2.33212
$589$	−30.3646	−1.25115
$590$	9.92714	0.408694
$591$	−47.9388	−1.97194
$592$	−9.20077	−0.378149
$593$	5.38500	0.221136	0.110568	−	0.993869i	$-0.464733\pi$
$593$	5.38500	0.221136	0.110568	+	0.993869i	$0.464733\pi$
$594$	−22.4506	−0.921159
$595$	−7.49329	−0.307195
$596$	17.6941	0.724779
$597$	−59.6092	−2.43964
$598$	−44.6032	−1.82396
$599$	8.98567	0.367145	0.183572	−	0.983006i	$-0.441234\pi$
$599$	8.98567	0.367145	0.183572	+	0.983006i	$0.441234\pi$
$600$	91.3122	3.72780
$601$	−1.08029	−0.0440660	−0.0220330	−	0.999757i	$-0.507014\pi$
$601$	−1.08029	−0.0440660	−0.0220330	+	0.999757i	$0.507014\pi$
$602$	37.6157	1.53310
$603$	−35.5267	−1.44676
$604$	−82.2741	−3.34769
$605$	−1.26109	−0.0512707
$606$	−46.5302	−1.89016
$607$	−22.1977	−0.900978	−0.450489	−	0.892782i	$-0.648750\pi$
$607$	−22.1977	−0.900978	−0.450489	+	0.892782i	$0.648750\pi$
$608$	146.641	5.94708
$609$	−3.31206	−0.134211
$610$	2.55886	0.103605
$611$	−12.8324	−0.519143
$612$	99.2496	4.01193
$613$	−28.9653	−1.16990	−0.584949	−	0.811070i	$-0.698885\pi$
$613$	−28.9653	−1.16990	−0.584949	+	0.811070i	$0.698885\pi$
$614$	51.3727	2.07323
$615$	−3.39521	−0.136908
$616$	−16.7127	−0.673376
$617$	16.1433	0.649905	0.324953	−	0.945730i	$-0.394652\pi$
$617$	16.1433	0.649905	0.324953	+	0.945730i	$0.394652\pi$
$618$	76.8865	3.09283
$619$	−41.7313	−1.67732	−0.838660	−	0.544655i	$-0.816661\pi$
$619$	−41.7313	−1.67732	−0.838660	+	0.544655i	$0.816661\pi$
$620$	−26.8523	−1.07841
$621$	−25.5285	−1.02443
$622$	25.6688	1.02923
$623$	6.05644	0.242646
$624$	−218.671	−8.75384
$625$	3.67393	0.146957
$626$	−65.6805	−2.62512
$627$	−22.5600	−0.900961
$628$	−58.1448	−2.32023
$629$	−2.14257	−0.0854299
$630$	36.6314	1.45943
$631$	−21.3161	−0.848582	−0.424291	−	0.905526i	$-0.639477\pi$
$631$	−21.3161	−0.848582	−0.424291	+	0.905526i	$0.639477\pi$
$632$	102.033	4.05866
$633$	66.3422	2.63686
$634$	−64.7430	−2.57127
$635$	−20.2802	−0.804794
$636$	189.358	7.50854
$637$	19.1178	0.757474
$638$	1.63419	0.0646981
$639$	−64.3378	−2.54516
$640$	35.5075	1.40356
$641$	−10.1135	−0.399457	−0.199729	−	0.979851i	$-0.564006\pi$
$641$	−10.1135	−0.399457	−0.199729	+	0.979851i	$0.564006\pi$
$642$	116.647	4.60370
$643$	−26.2851	−1.03658	−0.518292	−	0.855204i	$-0.673432\pi$
$643$	−26.2851	−1.03658	−0.518292	+	0.855204i	$0.673432\pi$
$644$	−30.4029	−1.19804
$645$	28.0677	1.10516
$646$	66.1408	2.60228
$647$	−13.8508	−0.544530	−0.272265	−	0.962222i	$-0.587773\pi$
$647$	−13.8508	−0.544530	−0.272265	+	0.962222i	$0.587773\pi$
$648$	−65.0102	−2.55384
$649$	2.90667	0.114097
$650$	−49.3850	−1.93704
$651$	21.9093	0.858694
$652$	−2.39571	−0.0938234
$653$	−30.5105	−1.19397	−0.596985	−	0.802253i	$-0.703635\pi$
$653$	−30.5105	−1.19397	−0.596985	+	0.802253i	$0.703635\pi$
$654$	21.4178	0.837504
$655$	−17.7456	−0.693379
$656$	12.5158	0.488659
$657$	14.2721	0.556807
$658$	−12.0264	−0.468840
$659$	37.8830	1.47571	0.737855	−	0.674959i	$-0.235839\pi$
$659$	37.8830	1.47571	0.737855	+	0.674959i	$0.235839\pi$
$660$	−19.9505	−0.776573
$661$	41.1371	1.60005	0.800023	−	0.599969i	$-0.204820\pi$
$661$	41.1371	1.60005	0.800023	+	0.599969i	$0.204820\pi$
$662$	−3.06158	−0.118992
$663$	−50.9216	−1.97763
$664$	72.0955	2.79785
$665$	17.7548	0.688500
$666$	10.4741	0.405863
$667$	1.85823	0.0719511
$668$	−114.003	−4.41091
$669$	−80.3599	−3.10689
$670$	−20.9368	−0.808860
$671$	0.749237	0.0289240
$672$	−105.808	−4.08162
$673$	40.9094	1.57694	0.788471	−	0.615072i	$-0.210873\pi$
$673$	40.9094	1.57694	0.788471	+	0.615072i	$0.210873\pi$
$674$	−72.3641	−2.78736
$675$	−28.2654	−1.08794
$676$	83.2313	3.20121
$677$	0.586737	0.0225501	0.0112751	−	0.999936i	$-0.496411\pi$
$677$	0.586737	0.0225501	0.0112751	+	0.999936i	$0.496411\pi$
$678$	−95.8680	−3.68179
$679$	−7.70383	−0.295646
$680$	36.5607	1.40204
$681$	−81.9038	−3.13856
$682$	−10.8102	−0.413943
$683$	6.99564	0.267681	0.133840	−	0.991003i	$-0.457269\pi$
$683$	6.99564	0.267681	0.133840	+	0.991003i	$0.457269\pi$
$684$	−235.164	−8.99173
$685$	15.0995	0.576923
$686$	53.0029	2.02366
$687$	31.1131	1.18704
$688$	−103.466	−3.94460
$689$	−64.0150	−2.43878
$690$	−31.1912	−1.18743
$691$	40.5622	1.54306	0.771530	−	0.636193i	$-0.219492\pi$
$691$	40.5622	1.54306	0.771530	+	0.636193i	$0.219492\pi$
$692$	82.0200	3.11793
$693$	10.7257	0.407436
$694$	36.2658	1.37663
$695$	2.21064	0.0838542
$696$	16.1599	0.612541
$697$	2.91453	0.110396
$698$	−11.8781	−0.449593
$699$	−54.8772	−2.07565
$700$	−33.6624	−1.27232
$701$	−11.9868	−0.452736	−0.226368	−	0.974042i	$-0.572685\pi$
$701$	−11.9868	−0.452736	−0.226368	+	0.974042i	$0.572685\pi$
$702$	120.069	4.53173
$703$	5.07666	0.191470
$704$	24.6326	0.928377
$705$	−8.97376	−0.337971
$706$	−5.91574	−0.222642
$707$	10.7222	0.403248
$708$	45.9836	1.72817
$709$	−28.1864	−1.05856	−0.529281	−	0.848447i	$-0.677538\pi$
$709$	−28.1864	−1.05856	−0.529281	+	0.848447i	$0.677538\pi$
$710$	−37.9159	−1.42296
$711$	−65.4815	−2.45575
$712$	−29.5501	−1.10744
$713$	−12.2923	−0.460349
$714$	−47.7234	−1.78600
$715$	6.74452	0.252231
$716$	−89.7020	−3.35232
$717$	−75.9046	−2.83471
$718$	−6.14829	−0.229452
$719$	−28.2604	−1.05393	−0.526967	−	0.849886i	$-0.676671\pi$
$719$	−28.2604	−1.05393	−0.526967	+	0.849886i	$0.676671\pi$
$720$	−100.758	−3.75505
$721$	−17.7173	−0.659826
$722$	−105.260	−3.91736
$723$	−35.7173	−1.32834
$724$	−10.5352	−0.391536
$725$	2.05745	0.0764119
$726$	−8.03167	−0.298083
$727$	−0.523961	−0.0194326	−0.00971632	−	0.999953i	$-0.503093\pi$
$727$	−0.523961	−0.0194326	−0.00971632	+	0.999953i	$0.503093\pi$
$728$	89.3825	3.31273
$729$	−32.0336	−1.18643
$730$	8.41090	0.311302
$731$	−24.0940	−0.891148
$732$	11.8529	0.438098
$733$	1.22762	0.0453433	0.0226716	−	0.999743i	$-0.492783\pi$
$733$	1.22762	0.0453433	0.0226716	+	0.999743i	$0.492783\pi$
$734$	28.9936	1.07017
$735$	13.3692	0.493129
$736$	59.3636	2.18817
$737$	−6.13031	−0.225813
$738$	−14.2479	−0.524472
$739$	8.01240	0.294741	0.147370	−	0.989081i	$-0.452919\pi$
$739$	8.01240	0.294741	0.147370	+	0.989081i	$0.452919\pi$
$740$	4.48944	0.165035
$741$	120.655	4.43236
$742$	−59.9944	−2.20247
$743$	17.6933	0.649104	0.324552	−	0.945868i	$-0.394786\pi$
$743$	17.6933	0.649104	0.324552	+	0.945868i	$0.394786\pi$
$744$	−106.898	−3.91908
$745$	−4.18304	−0.153255
$746$	11.5406	0.422532
$747$	−46.2685	−1.69288
$748$	17.1260	0.626188
$749$	−26.8795	−0.982156
$750$	−85.1785	−3.11028
$751$	−6.38702	−0.233066	−0.116533	−	0.993187i	$-0.537178\pi$
$751$	−6.38702	−0.233066	−0.116533	+	0.993187i	$0.537178\pi$
$752$	33.0800	1.20630
$753$	55.4496	2.02070
$754$	−8.73990	−0.318288
$755$	19.4503	0.707870
$756$	81.8431	2.97660
$757$	41.2391	1.49886	0.749430	−	0.662084i	$-0.230328\pi$
$757$	41.2391	1.49886	0.749430	+	0.662084i	$0.230328\pi$
$758$	−98.3718	−3.57303
$759$	−9.13281	−0.331500
$760$	−86.6278	−3.14232
$761$	23.6428	0.857051	0.428525	−	0.903530i	$-0.359033\pi$
$761$	23.6428	0.857051	0.428525	+	0.903530i	$0.359033\pi$
$762$	−129.161	−4.67900
$763$	−4.93540	−0.178674
$764$	−78.3783	−2.83563
$765$	−23.4635	−0.848324
$766$	58.8544	2.12650
$767$	−15.5454	−0.561310
$768$	80.0356	2.88804
$769$	15.5818	0.561894	0.280947	−	0.959723i	$-0.409351\pi$
$769$	15.5818	0.561894	0.280947	+	0.959723i	$0.409351\pi$
$770$	6.32093	0.227790
$771$	6.62552	0.238612
$772$	−3.53599	−0.127263
$773$	43.2206	1.55454	0.777268	−	0.629170i	$-0.216605\pi$
$773$	43.2206	1.55454	0.777268	+	0.629170i	$0.216605\pi$
$774$	117.785	4.23369
$775$	−13.6101	−0.488889
$776$	37.5880	1.34933
$777$	−3.66302	−0.131410
$778$	30.5240	1.09434
$779$	−6.90576	−0.247425
$780$	106.699	3.82042
$781$	−11.1018	−0.397253
$782$	26.7753	0.957482
$783$	−5.00227	−0.178766
$784$	−49.2827	−1.76010
$785$	13.7459	0.490613
$786$	−113.019	−4.03124
$787$	36.7308	1.30931	0.654655	−	0.755927i	$-0.272814\pi$
$787$	36.7308	1.30931	0.654655	+	0.755927i	$0.272814\pi$
$788$	−86.2275	−3.07173
$789$	54.5249	1.94114
$790$	−38.5899	−1.37297
$791$	22.0913	0.785475
$792$	−52.3321	−1.85954
$793$	−4.00704	−0.142294
$794$	−27.5480	−0.977643
$795$	−44.7660	−1.58768
$796$	−107.219	−3.80028
$797$	−29.4984	−1.04489	−0.522443	−	0.852674i	$-0.674979\pi$
$797$	−29.4984	−1.04489	−0.522443	+	0.852674i	$0.674979\pi$
$798$	113.077	4.00288
$799$	7.70329	0.272523
$800$	65.7279	2.32383
$801$	18.9643	0.670071
$802$	−61.3135	−2.16506
$803$	2.46272	0.0869074
$804$	−96.9817	−3.42028
$805$	7.18753	0.253327
$806$	57.8146	2.03643
$807$	84.2439	2.96553
$808$	−52.3148	−1.84043
$809$	45.9270	1.61471	0.807354	−	0.590067i	$-0.200899\pi$
$809$	45.9270	1.61471	0.807354	+	0.590067i	$0.200899\pi$
$810$	24.5875	0.863918
$811$	20.9065	0.734127	0.367063	−	0.930196i	$-0.380363\pi$
$811$	20.9065	0.734127	0.367063	+	0.930196i	$0.380363\pi$
$812$	−5.95740	−0.209064
$813$	−31.7658	−1.11407
$814$	1.80736	0.0633478
$815$	0.566368	0.0198390
$816$	131.268	4.59530
$817$	57.0888	1.99728
$818$	42.4169	1.48307
$819$	−57.3628	−2.00442
$820$	−6.10697	−0.213265
$821$	−12.5474	−0.437906	−0.218953	−	0.975735i	$-0.570264\pi$
$821$	−12.5474	−0.437906	−0.218953	+	0.975735i	$0.570264\pi$
$822$	96.1662	3.35418
$823$	−38.7451	−1.35057	−0.675284	−	0.737558i	$-0.735979\pi$
$823$	−38.7451	−1.35057	−0.675284	+	0.737558i	$0.735979\pi$
$824$	86.4449	3.01145
$825$	−10.1119	−0.352052
$826$	−14.5690	−0.506921
$827$	−33.6839	−1.17130	−0.585652	−	0.810562i	$-0.699162\pi$
$827$	−33.6839	−1.17130	−0.585652	+	0.810562i	$0.699162\pi$
$828$	−95.1997	−3.30842
$829$	35.6829	1.23932	0.619659	−	0.784871i	$-0.287271\pi$
$829$	35.6829	1.23932	0.619659	+	0.784871i	$0.287271\pi$
$830$	−27.2672	−0.946459
$831$	−9.56914	−0.331950
$832$	−131.739	−4.56724
$833$	−11.4764	−0.397634
$834$	14.0791	0.487521
$835$	26.9513	0.932689
$836$	−40.5787	−1.40344
$837$	33.0901	1.14376
$838$	45.7716	1.58115
$839$	22.7138	0.784166	0.392083	−	0.919930i	$-0.371755\pi$
$839$	22.7138	0.784166	0.392083	+	0.919930i	$0.371755\pi$
$840$	62.5056	2.15665
$841$	−28.6359	−0.987444
$842$	26.5056	0.913443
$843$	96.9964	3.34073
$844$	119.330	4.10750
$845$	−19.6766	−0.676896
$846$	−37.6580	−1.29471
$847$	1.85077	0.0635933
$848$	165.021	5.66684
$849$	75.4964	2.59103
$850$	29.6458	1.01684
$851$	2.05514	0.0704494
$852$	−175.631	−6.01701
$853$	12.5561	0.429912	0.214956	−	0.976624i	$-0.431039\pi$
$853$	12.5561	0.429912	0.214956	+	0.976624i	$0.431039\pi$
$854$	−3.75537	−0.128506
$855$	55.5949	1.90131
$856$	131.149	4.48257
$857$	−5.87810	−0.200792	−0.100396	−	0.994948i	$-0.532011\pi$
$857$	−5.87810	−0.200792	−0.100396	+	0.994948i	$0.532011\pi$
$858$	42.9547	1.46645
$859$	44.7161	1.52569	0.762847	−	0.646579i	$-0.223801\pi$
$859$	44.7161	1.52569	0.762847	+	0.646579i	$0.223801\pi$
$860$	50.4853	1.72154
$861$	4.98280	0.169813
$862$	−0.277534	−0.00945286
$863$	−34.9347	−1.18919	−0.594595	−	0.804026i	$-0.702688\pi$
$863$	−34.9347	−1.18919	−0.594595	+	0.804026i	$0.702688\pi$
$864$	−159.804	−5.43663
$865$	−19.3903	−0.659289
$866$	−46.9048	−1.59389
$867$	−19.8484	−0.674086
$868$	39.4083	1.33760
$869$	−11.2992	−0.383298
$870$	−6.11185	−0.207211
$871$	32.7859	1.11091
$872$	24.0805	0.815467
$873$	−24.1228	−0.816432
$874$	−63.4420	−2.14596
$875$	19.6281	0.663549
$876$	38.9603	1.31635
$877$	−45.9861	−1.55284	−0.776421	−	0.630215i	$-0.782967\pi$
$877$	−45.9861	−1.55284	−0.776421	+	0.630215i	$0.782967\pi$
$878$	−0.0519538	−0.00175335
$879$	−52.1824	−1.76007
$880$	−17.3864	−0.586094
$881$	−2.04730	−0.0689753	−0.0344876	−	0.999405i	$-0.510980\pi$
$881$	−2.04730	−0.0689753	−0.0344876	+	0.999405i	$0.510980\pi$
$882$	56.1031	1.88909
$883$	15.5665	0.523853	0.261926	−	0.965088i	$-0.415642\pi$
$883$	15.5665	0.523853	0.261926	+	0.965088i	$0.415642\pi$
$884$	−91.5926	−3.08059
$885$	−10.8709	−0.365423
$886$	−54.8394	−1.84237
$887$	5.24540	0.176123	0.0880616	−	0.996115i	$-0.471933\pi$
$887$	5.24540	0.176123	0.0880616	+	0.996115i	$0.471933\pi$
$888$	17.8723	0.599757
$889$	29.7631	0.998222
$890$	11.1762	0.374626
$891$	7.19924	0.241184
$892$	−144.543	−4.83967
$893$	−18.2523	−0.610792
$894$	−26.6410	−0.891010
$895$	21.2063	0.708850
$896$	−52.1106	−1.74089
$897$	48.8437	1.63084
$898$	−31.9683	−1.06680
$899$	−2.40864	−0.0803327
$900$	−105.406	−3.51353
$901$	38.4282	1.28023
$902$	−2.45854	−0.0818604
$903$	−41.1920	−1.37078
$904$	−107.786	−3.58491
$905$	2.49060	0.0827905
$906$	123.876	4.11549
$907$	21.4012	0.710617	0.355308	−	0.934749i	$-0.384376\pi$
$907$	21.4012	0.710617	0.355308	+	0.934749i	$0.384376\pi$
$908$	−147.320	−4.88900
$909$	33.5739	1.11358
$910$	−33.8054	−1.12064
$911$	8.09467	0.268189	0.134094	−	0.990969i	$-0.457188\pi$
$911$	8.09467	0.268189	0.134094	+	0.990969i	$0.457188\pi$
$912$	−311.030	−10.2992
$913$	−7.98386	−0.264227
$914$	−79.6992	−2.63621
$915$	−2.80214	−0.0926359
$916$	55.9632	1.84908
$917$	26.0434	0.860028
$918$	−72.0776	−2.37892
$919$	22.2669	0.734517	0.367258	−	0.930119i	$-0.380297\pi$
$919$	22.2669	0.734517	0.367258	+	0.930119i	$0.380297\pi$
$920$	−35.0689	−1.15619
$921$	−56.2569	−1.85373
$922$	−80.3333	−2.64564
$923$	59.3742	1.95433
$924$	29.2793	0.963217
$925$	2.27547	0.0748171
$926$	10.7992	0.354883
$927$	−55.4775	−1.82212
$928$	11.6322	0.381845
$929$	−55.4811	−1.82028	−0.910138	−	0.414305i	$-0.864025\pi$
$929$	−55.4811	−1.82028	−0.910138	+	0.414305i	$0.864025\pi$
$930$	40.4300	1.32575
$931$	27.1925	0.891197
$932$	−98.7076	−3.23328
$933$	−28.1093	−0.920256
$934$	111.680	3.65429
$935$	−4.04874	−0.132408
$936$	279.880	9.14818
$937$	−25.5277	−0.833953	−0.416976	−	0.908917i	$-0.636910\pi$
$937$	−25.5277	−0.833953	−0.416976	+	0.908917i	$0.636910\pi$
$938$	30.7268	1.00326
$939$	71.9250	2.34718
$940$	−16.1411	−0.526464
$941$	1.17540	0.0383169	0.0191584	−	0.999816i	$-0.493901\pi$
$941$	1.17540	0.0383169	0.0191584	+	0.999816i	$0.493901\pi$
$942$	87.5454	2.85238
$943$	−2.79561	−0.0910374
$944$	40.0736	1.30428
$945$	−19.3484	−0.629404
$946$	20.3244	0.660802
$947$	50.2495	1.63289	0.816444	−	0.577424i	$-0.195942\pi$
$947$	50.2495	1.63289	0.816444	+	0.577424i	$0.195942\pi$
$948$	−178.753	−5.80563
$949$	−13.1710	−0.427549
$950$	−70.2435	−2.27900
$951$	70.8983	2.29904
$952$	−53.6563	−1.73901
$953$	−43.3113	−1.40299	−0.701495	−	0.712675i	$-0.747484\pi$
$953$	−43.3113	−1.40299	−0.701495	+	0.712675i	$0.747484\pi$
$954$	−187.859	−6.08215
$955$	18.5293	0.599595
$956$	−136.530	−4.41568
$957$	−1.78955	−0.0578481
$958$	8.46936	0.273633
$959$	−22.1600	−0.715583
$960$	−92.1259	−2.97335
$961$	−15.0668	−0.486025
$962$	−9.66604	−0.311645
$963$	−84.1669	−2.71224
$964$	−64.2447	−2.06918
$965$	0.835938	0.0269098
$966$	45.7761	1.47282
$967$	6.88835	0.221514	0.110757	−	0.993847i	$-0.464672\pi$
$967$	6.88835	0.221514	0.110757	+	0.993847i	$0.464672\pi$
$968$	−9.03015	−0.290240
$969$	−72.4290	−2.32676
$970$	−14.2162	−0.456453
$971$	−39.6340	−1.27192	−0.635958	−	0.771723i	$-0.719395\pi$
$971$	−39.6340	−1.27192	−0.635958	+	0.771723i	$0.719395\pi$
$972$	−18.7710	−0.602079
$973$	−3.24432	−0.104008
$974$	15.3851	0.492971
$975$	54.0802	1.73195
$976$	10.3295	0.330641
$977$	−28.0212	−0.896479	−0.448240	−	0.893914i	$-0.647949\pi$
$977$	−28.0212	−0.896479	−0.448240	+	0.893914i	$0.647949\pi$
$978$	3.60710	0.115342
$979$	3.27238	0.104586
$980$	24.0471	0.768156
$981$	−15.4541	−0.493410
$982$	−75.8710	−2.42114
$983$	55.6586	1.77523	0.887617	−	0.460582i	$-0.152359\pi$
$983$	55.6586	1.77523	0.887617	+	0.460582i	$0.152359\pi$
$984$	−24.3117	−0.775029
$985$	20.3849	0.649518
$986$	5.24656	0.167085
$987$	13.1698	0.419200
$988$	217.022	6.90438
$989$	23.1108	0.734881
$990$	19.7925	0.629047
$991$	−56.2914	−1.78816	−0.894078	−	0.447912i	$-0.852168\pi$
$991$	−56.2914	−1.78816	−0.894078	+	0.447912i	$0.852168\pi$
$992$	−76.9471	−2.44307
$993$	3.35265	0.106393
$994$	55.6452	1.76496
$995$	25.3475	0.803570
$996$	−126.305	−4.00213
$997$	−11.5970	−0.367279	−0.183640	−	0.982994i	$-0.558788\pi$
$997$	−11.5970	−0.367279	−0.183640	+	0.982994i	$0.558788\pi$
$998$	−80.9522	−2.56250
$999$	−5.53234	−0.175035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.4	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.4	✓	106	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)

\(f(q)\)	\(=\)	\(q-2.70820 q^{2} +2.96568 q^{3} +5.33437 q^{4} -1.26109 q^{5} -8.03167 q^{6} +1.85077 q^{7} -9.03015 q^{8} +5.79526 q^{9} +O(q^{10})\)	\(q-2.70820 q^{2} +2.96568 q^{3} +5.33437 q^{4} -1.26109 q^{5} -8.03167 q^{6} +1.85077 q^{7} -9.03015 q^{8} +5.79526 q^{9} +3.41529 q^{10} +1.00000 q^{11} +15.8200 q^{12} -5.34816 q^{13} -5.01227 q^{14} -3.73999 q^{15} +13.7868 q^{16} +3.21050 q^{17} -15.6947 q^{18} -7.60704 q^{19} -6.72713 q^{20} +5.48880 q^{21} -2.70820 q^{22} -3.07950 q^{23} -26.7805 q^{24} -3.40965 q^{25} +14.4839 q^{26} +8.28984 q^{27} +9.87270 q^{28} -0.603421 q^{29} +10.1287 q^{30} +3.99164 q^{31} -19.2770 q^{32} +2.96568 q^{33} -8.69469 q^{34} -2.33399 q^{35} +30.9140 q^{36} -0.667363 q^{37} +20.6014 q^{38} -15.8609 q^{39} +11.3878 q^{40} +0.907812 q^{41} -14.8648 q^{42} -7.50474 q^{43} +5.33437 q^{44} -7.30835 q^{45} +8.33991 q^{46} +2.39940 q^{47} +40.8871 q^{48} -3.57465 q^{49} +9.23402 q^{50} +9.52132 q^{51} -28.5291 q^{52} +11.9695 q^{53} -22.4506 q^{54} -1.26109 q^{55} -16.7127 q^{56} -22.5600 q^{57} +1.63419 q^{58} +2.90667 q^{59} -19.9505 q^{60} +0.749237 q^{61} -10.8102 q^{62} +10.7257 q^{63} +24.6326 q^{64} +6.74452 q^{65} -8.03167 q^{66} -6.13031 q^{67} +17.1260 q^{68} -9.13281 q^{69} +6.32093 q^{70} -11.1018 q^{71} -52.3321 q^{72} +2.46272 q^{73} +1.80736 q^{74} -10.1119 q^{75} -40.5787 q^{76} +1.85077 q^{77} +42.9547 q^{78} -11.2992 q^{79} -17.3864 q^{80} +7.19924 q^{81} -2.45854 q^{82} -7.98386 q^{83} +29.2793 q^{84} -4.04874 q^{85} +20.3244 q^{86} -1.78955 q^{87} -9.03015 q^{88} +3.27238 q^{89} +19.7925 q^{90} -9.89823 q^{91} -16.4272 q^{92} +11.8379 q^{93} -6.49807 q^{94} +9.59317 q^{95} -57.1695 q^{96} -4.16250 q^{97} +9.68087 q^{98} +5.79526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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