LMFDB - Embedded newform 8035.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32037 q^{2} +2.64444 q^{3} +3.38410 q^{4} +1.00000 q^{5} -6.13607 q^{6} +4.54944 q^{7} -3.21162 q^{8} +3.99307 q^{9} +O(q^{10})$	\(q-2.32037 q^{2} +2.64444 q^{3} +3.38410 q^{4} +1.00000 q^{5} -6.13607 q^{6} +4.54944 q^{7} -3.21162 q^{8} +3.99307 q^{9} -2.32037 q^{10} +4.33503 q^{11} +8.94905 q^{12} -1.34544 q^{13} -10.5564 q^{14} +2.64444 q^{15} +0.683929 q^{16} -2.85566 q^{17} -9.26540 q^{18} -2.45105 q^{19} +3.38410 q^{20} +12.0307 q^{21} -10.0588 q^{22} +3.22525 q^{23} -8.49294 q^{24} +1.00000 q^{25} +3.12192 q^{26} +2.62613 q^{27} +15.3958 q^{28} +3.53723 q^{29} -6.13607 q^{30} +6.72082 q^{31} +4.83627 q^{32} +11.4637 q^{33} +6.62618 q^{34} +4.54944 q^{35} +13.5130 q^{36} +5.60838 q^{37} +5.68734 q^{38} -3.55794 q^{39} -3.21162 q^{40} -2.64781 q^{41} -27.9157 q^{42} -1.92594 q^{43} +14.6702 q^{44} +3.99307 q^{45} -7.48377 q^{46} +1.58251 q^{47} +1.80861 q^{48} +13.6974 q^{49} -2.32037 q^{50} -7.55164 q^{51} -4.55310 q^{52} -9.57516 q^{53} -6.09358 q^{54} +4.33503 q^{55} -14.6111 q^{56} -6.48166 q^{57} -8.20767 q^{58} +4.60243 q^{59} +8.94905 q^{60} -6.26088 q^{61} -15.5948 q^{62} +18.1663 q^{63} -12.5898 q^{64} -1.34544 q^{65} -26.6000 q^{66} -13.8298 q^{67} -9.66385 q^{68} +8.52900 q^{69} -10.5564 q^{70} -10.7191 q^{71} -12.8242 q^{72} +6.51080 q^{73} -13.0135 q^{74} +2.64444 q^{75} -8.29460 q^{76} +19.7219 q^{77} +8.25572 q^{78} -7.44392 q^{79} +0.683929 q^{80} -5.03458 q^{81} +6.14389 q^{82} +6.50425 q^{83} +40.7132 q^{84} -2.85566 q^{85} +4.46889 q^{86} +9.35401 q^{87} -13.9224 q^{88} +12.0542 q^{89} -9.26540 q^{90} -6.12100 q^{91} +10.9146 q^{92} +17.7728 q^{93} -3.67200 q^{94} -2.45105 q^{95} +12.7892 q^{96} +8.75566 q^{97} -31.7830 q^{98} +17.3101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.32037	−1.64075	−0.820373	−	0.571828i	$-0.806234\pi$
$2$	−2.32037	−1.64075	−0.820373	+	0.571828i	$0.806234\pi$
$3$	2.64444	1.52677	0.763385	−	0.645944i	$-0.223536\pi$
$3$	2.64444	1.52677	0.763385	+	0.645944i	$0.223536\pi$
$4$	3.38410	1.69205
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.13607	−2.50504
$7$	4.54944	1.71953	0.859763	−	0.510693i	$-0.170611\pi$
$7$	4.54944	1.71953	0.859763	+	0.510693i	$0.170611\pi$
$8$	−3.21162	−1.13548
$9$	3.99307	1.33102
$10$	−2.32037	−0.733764
$11$	4.33503	1.30706	0.653530	−	0.756901i	$-0.273287\pi$
$11$	4.33503	1.30706	0.653530	+	0.756901i	$0.273287\pi$
$12$	8.94905	2.58337
$13$	−1.34544	−0.373158	−0.186579	−	0.982440i	$-0.559740\pi$
$13$	−1.34544	−0.373158	−0.186579	+	0.982440i	$0.559740\pi$
$14$	−10.5564	−2.82131
$15$	2.64444	0.682792
$16$	0.683929	0.170982
$17$	−2.85566	−0.692600	−0.346300	−	0.938124i	$-0.612562\pi$
$17$	−2.85566	−0.692600	−0.346300	+	0.938124i	$0.612562\pi$
$18$	−9.26540	−2.18387
$19$	−2.45105	−0.562310	−0.281155	−	0.959662i	$-0.590717\pi$
$19$	−2.45105	−0.562310	−0.281155	+	0.959662i	$0.590717\pi$
$20$	3.38410	0.756708
$21$	12.0307	2.62532
$22$	−10.0588	−2.14455
$23$	3.22525	0.672512	0.336256	−	0.941771i	$-0.390839\pi$
$23$	3.22525	0.672512	0.336256	+	0.941771i	$0.390839\pi$
$24$	−8.49294	−1.73361
$25$	1.00000	0.200000
$26$	3.12192	0.612258
$27$	2.62613	0.505399
$28$	15.3958	2.90952
$29$	3.53723	0.656847	0.328424	−	0.944530i	$-0.393483\pi$
$29$	3.53723	0.656847	0.328424	+	0.944530i	$0.393483\pi$
$30$	−6.13607	−1.12029
$31$	6.72082	1.20709	0.603547	−	0.797327i	$-0.293753\pi$
$31$	6.72082	1.20709	0.603547	+	0.797327i	$0.293753\pi$
$32$	4.83627	0.854939
$33$	11.4637	1.99558
$34$	6.62618	1.13638
$35$	4.54944	0.768996
$36$	13.5130	2.25216
$37$	5.60838	0.922013	0.461006	−	0.887397i	$-0.347489\pi$
$37$	5.60838	0.922013	0.461006	+	0.887397i	$0.347489\pi$
$38$	5.68734	0.922608
$39$	−3.55794	−0.569726
$40$	−3.21162	−0.507801
$41$	−2.64781	−0.413519	−0.206759	−	0.978392i	$-0.566292\pi$
$41$	−2.64781	−0.413519	−0.206759	+	0.978392i	$0.566292\pi$
$42$	−27.9157	−4.30749
$43$	−1.92594	−0.293703	−0.146852	−	0.989159i	$-0.546914\pi$
$43$	−1.92594	−0.293703	−0.146852	+	0.989159i	$0.546914\pi$
$44$	14.6702	2.21161
$45$	3.99307	0.595252
$46$	−7.48377	−1.10342
$47$	1.58251	0.230833	0.115416	−	0.993317i	$-0.463180\pi$
$47$	1.58251	0.230833	0.115416	+	0.993317i	$0.463180\pi$
$48$	1.80861	0.261051
$49$	13.6974	1.95677
$50$	−2.32037	−0.328149
$51$	−7.55164	−1.05744
$52$	−4.55310	−0.631402
$53$	−9.57516	−1.31525	−0.657625	−	0.753345i	$-0.728439\pi$
$53$	−9.57516	−1.31525	−0.657625	+	0.753345i	$0.728439\pi$
$54$	−6.09358	−0.829231
$55$	4.33503	0.584535
$56$	−14.6111	−1.95248
$57$	−6.48166	−0.858517
$58$	−8.20767	−1.07772
$59$	4.60243	0.599185	0.299593	−	0.954067i	$-0.403149\pi$
$59$	4.60243	0.599185	0.299593	+	0.954067i	$0.403149\pi$
$60$	8.94905	1.15532
$61$	−6.26088	−0.801623	−0.400812	−	0.916160i	$-0.631272\pi$
$61$	−6.26088	−0.801623	−0.400812	+	0.916160i	$0.631272\pi$
$62$	−15.5948	−1.98054
$63$	18.1663	2.28873
$64$	−12.5898	−1.57372
$65$	−1.34544	−0.166881
$66$	−26.6000	−3.27424
$67$	−13.8298	−1.68958	−0.844792	−	0.535094i	$-0.820276\pi$
$67$	−13.8298	−1.68958	−0.844792	+	0.535094i	$0.820276\pi$
$68$	−9.66385	−1.17191
$69$	8.52900	1.02677
$70$	−10.5564	−1.26173
$71$	−10.7191	−1.27213	−0.636064	−	0.771636i	$-0.719439\pi$
$71$	−10.7191	−1.27213	−0.636064	+	0.771636i	$0.719439\pi$
$72$	−12.8242	−1.51135
$73$	6.51080	0.762032	0.381016	−	0.924569i	$-0.375574\pi$
$73$	6.51080	0.762032	0.381016	+	0.924569i	$0.375574\pi$
$74$	−13.0135	−1.51279
$75$	2.64444	0.305354
$76$	−8.29460	−0.951456
$77$	19.7219	2.24752
$78$	8.25572	0.934777
$79$	−7.44392	−0.837506	−0.418753	−	0.908100i	$-0.637533\pi$
$79$	−7.44392	−0.837506	−0.418753	+	0.908100i	$0.637533\pi$
$80$	0.683929	0.0764656
$81$	−5.03458	−0.559398
$82$	6.14389	0.678479
$83$	6.50425	0.713934	0.356967	−	0.934117i	$-0.383811\pi$
$83$	6.50425	0.713934	0.356967	+	0.934117i	$0.383811\pi$
$84$	40.7132	4.44217
$85$	−2.85566	−0.309740
$86$	4.46889	0.481892
$87$	9.35401	1.00285
$88$	−13.9224	−1.48414
$89$	12.0542	1.27774	0.638870	−	0.769315i	$-0.279402\pi$
$89$	12.0542	1.27774	0.638870	+	0.769315i	$0.279402\pi$
$90$	−9.26540	−0.976658
$91$	−6.12100	−0.641655
$92$	10.9146	1.13792
$93$	17.7728	1.84295
$94$	−3.67200	−0.378738
$95$	−2.45105	−0.251473
$96$	12.7892	1.30530
$97$	8.75566	0.889002	0.444501	−	0.895778i	$-0.353381\pi$
$97$	8.75566	0.889002	0.444501	+	0.895778i	$0.353381\pi$
$98$	−31.7830	−3.21057
$99$	17.3101	1.73973
$100$	3.38410	0.338410
$101$	14.8576	1.47839	0.739194	−	0.673493i	$-0.235207\pi$
$101$	14.8576	1.47839	0.739194	+	0.673493i	$0.235207\pi$
$102$	17.5226	1.73499
$103$	−13.6659	−1.34654	−0.673270	−	0.739397i	$-0.735111\pi$
$103$	−13.6659	−1.34654	−0.673270	+	0.739397i	$0.735111\pi$
$104$	4.32104	0.423713
$105$	12.0307	1.17408
$106$	22.2179	2.15799
$107$	9.71118	0.938815	0.469408	−	0.882982i	$-0.344467\pi$
$107$	9.71118	0.938815	0.469408	+	0.882982i	$0.344467\pi$
$108$	8.88708	0.855160
$109$	2.49497	0.238975	0.119487	−	0.992836i	$-0.461875\pi$
$109$	2.49497	0.238975	0.119487	+	0.992836i	$0.461875\pi$
$110$	−10.0588	−0.959073
$111$	14.8310	1.40770
$112$	3.11150	0.294009
$113$	8.81959	0.829677	0.414839	−	0.909895i	$-0.363838\pi$
$113$	8.81959	0.829677	0.414839	+	0.909895i	$0.363838\pi$
$114$	15.0398	1.40861
$115$	3.22525	0.300756
$116$	11.9703	1.11142
$117$	−5.37245	−0.496683
$118$	−10.6793	−0.983111
$119$	−12.9917	−1.19094
$120$	−8.49294	−0.775295
$121$	7.79245	0.708405
$122$	14.5275	1.31526
$123$	−7.00198	−0.631348
$124$	22.7439	2.04246
$125$	1.00000	0.0894427
$126$	−42.1524	−3.75523
$127$	−2.91396	−0.258572	−0.129286	−	0.991607i	$-0.541269\pi$
$127$	−2.91396	−0.258572	−0.129286	+	0.991607i	$0.541269\pi$
$128$	19.5403	1.72714
$129$	−5.09304	−0.448417
$130$	3.12192	0.273810
$131$	−1.90961	−0.166843	−0.0834217	−	0.996514i	$-0.526585\pi$
$131$	−1.90961	−0.166843	−0.0834217	+	0.996514i	$0.526585\pi$
$132$	38.7944	3.37662
$133$	−11.1509	−0.966906
$134$	32.0903	2.77218
$135$	2.62613	0.226021
$136$	9.17130	0.786432
$137$	−9.97449	−0.852178	−0.426089	−	0.904681i	$-0.640109\pi$
$137$	−9.97449	−0.852178	−0.426089	+	0.904681i	$0.640109\pi$
$138$	−19.7904	−1.68467
$139$	0.250117	0.0212146	0.0106073	−	0.999944i	$-0.496624\pi$
$139$	0.250117	0.0212146	0.0106073	+	0.999944i	$0.496624\pi$
$140$	15.3958	1.30118
$141$	4.18485	0.352428
$142$	24.8723	2.08724
$143$	−5.83252	−0.487740
$144$	2.73098	0.227582
$145$	3.53723	0.293751
$146$	−15.1074	−1.25030
$147$	36.2220	2.98754
$148$	18.9793	1.56009
$149$	0.955480	0.0782760	0.0391380	−	0.999234i	$-0.487539\pi$
$149$	0.955480	0.0782760	0.0391380	+	0.999234i	$0.487539\pi$
$150$	−6.13607	−0.501008
$151$	21.5986	1.75767	0.878835	−	0.477126i	$-0.158321\pi$
$151$	21.5986	1.75767	0.878835	+	0.477126i	$0.158321\pi$
$152$	7.87184	0.638490
$153$	−11.4029	−0.921868
$154$	−45.7621	−3.68762
$155$	6.72082	0.539829
$156$	−12.0404	−0.964005
$157$	2.59811	0.207352	0.103676	−	0.994611i	$-0.466940\pi$
$157$	2.59811	0.207352	0.103676	+	0.994611i	$0.466940\pi$
$158$	17.2726	1.37414
$159$	−25.3210	−2.00808
$160$	4.83627	0.382341
$161$	14.6731	1.15640
$162$	11.6821	0.917830
$163$	2.04576	0.160236	0.0801181	−	0.996785i	$-0.474470\pi$
$163$	2.04576	0.160236	0.0801181	+	0.996785i	$0.474470\pi$
$164$	−8.96045	−0.699694
$165$	11.4637	0.892450
$166$	−15.0922	−1.17138
$167$	4.60394	0.356264	0.178132	−	0.984007i	$-0.442995\pi$
$167$	4.60394	0.356264	0.178132	+	0.984007i	$0.442995\pi$
$168$	−38.6381	−2.98099
$169$	−11.1898	−0.860753
$170$	6.62618	0.508205
$171$	−9.78723	−0.748448
$172$	−6.51757	−0.496960
$173$	3.25271	0.247299	0.123649	−	0.992326i	$-0.460540\pi$
$173$	3.25271	0.247299	0.123649	+	0.992326i	$0.460540\pi$
$174$	−21.7047	−1.64543
$175$	4.54944	0.343905
$176$	2.96485	0.223484
$177$	12.1709	0.914817
$178$	−27.9701	−2.09645
$179$	13.8170	1.03273	0.516366	−	0.856368i	$-0.327285\pi$
$179$	13.8170	1.03273	0.516366	+	0.856368i	$0.327285\pi$
$180$	13.5130	1.00720
$181$	4.62251	0.343588	0.171794	−	0.985133i	$-0.445044\pi$
$181$	4.62251	0.343588	0.171794	+	0.985133i	$0.445044\pi$
$182$	14.2030	1.05279
$183$	−16.5565	−1.22389
$184$	−10.3583	−0.763622
$185$	5.60838	0.412337
$186$	−41.2394	−3.02382
$187$	−12.3794	−0.905269
$188$	5.35536	0.390580
$189$	11.9474	0.869046
$190$	5.68734	0.412603
$191$	−5.17864	−0.374713	−0.187357	−	0.982292i	$-0.559992\pi$
$191$	−5.17864	−0.374713	−0.187357	+	0.982292i	$0.559992\pi$
$192$	−33.2929	−2.40271
$193$	19.6064	1.41130	0.705650	−	0.708561i	$-0.250655\pi$
$193$	19.6064	1.41130	0.705650	+	0.708561i	$0.250655\pi$
$194$	−20.3163	−1.45863
$195$	−3.55794	−0.254789
$196$	46.3534	3.31095
$197$	13.3605	0.951898	0.475949	−	0.879473i	$-0.342105\pi$
$197$	13.3605	0.951898	0.475949	+	0.879473i	$0.342105\pi$
$198$	−40.1657	−2.85445
$199$	−17.2051	−1.21964	−0.609820	−	0.792540i	$-0.708758\pi$
$199$	−17.2051	−1.21964	−0.609820	+	0.792540i	$0.708758\pi$
$200$	−3.21162	−0.227096
$201$	−36.5722	−2.57961
$202$	−34.4751	−2.42566
$203$	16.0924	1.12947
$204$	−25.5555	−1.78924
$205$	−2.64781	−0.184931
$206$	31.7099	2.20933
$207$	12.8787	0.895130
$208$	−0.920186	−0.0638034
$209$	−10.6254	−0.734972
$210$	−27.9157	−1.92637
$211$	−15.1596	−1.04363	−0.521814	−	0.853059i	$-0.674744\pi$
$211$	−15.1596	−1.04363	−0.521814	+	0.853059i	$0.674744\pi$
$212$	−32.4033	−2.22547
$213$	−28.3462	−1.94225
$214$	−22.5335	−1.54036
$215$	−1.92594	−0.131348
$216$	−8.43412	−0.573869
$217$	30.5760	2.07563
$218$	−5.78925	−0.392097
$219$	17.2174	1.16345
$220$	14.6702	0.989062
$221$	3.84213	0.258449
$222$	−34.4135	−2.30968
$223$	11.6371	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$223$	11.6371	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$224$	22.0023	1.47009
$225$	3.99307	0.266205
$226$	−20.4647	−1.36129
$227$	−5.71826	−0.379534	−0.189767	−	0.981829i	$-0.560773\pi$
$227$	−5.71826	−0.379534	−0.189767	+	0.981829i	$0.560773\pi$
$228$	−21.9346	−1.45265
$229$	−14.6751	−0.969759	−0.484880	−	0.874581i	$-0.661137\pi$
$229$	−14.6751	−0.969759	−0.484880	+	0.874581i	$0.661137\pi$
$230$	−7.48377	−0.493465
$231$	52.1535	3.43145
$232$	−11.3602	−0.745836
$233$	−13.7583	−0.901337	−0.450668	−	0.892691i	$-0.648814\pi$
$233$	−13.7583	−0.901337	−0.450668	+	0.892691i	$0.648814\pi$
$234$	12.4660	0.814931
$235$	1.58251	0.103231
$236$	15.5751	1.01385
$237$	−19.6850	−1.27868
$238$	30.1454	1.95404
$239$	5.73906	0.371229	0.185614	−	0.982623i	$-0.440572\pi$
$239$	5.73906	0.371229	0.185614	+	0.982623i	$0.440572\pi$
$240$	1.80861	0.116745
$241$	2.82335	0.181868	0.0909339	−	0.995857i	$-0.471015\pi$
$241$	2.82335	0.181868	0.0909339	+	0.995857i	$0.471015\pi$
$242$	−18.0813	−1.16231
$243$	−21.1920	−1.35947
$244$	−21.1874	−1.35639
$245$	13.6974	0.875095
$246$	16.2472	1.03588
$247$	3.29774	0.209830
$248$	−21.5847	−1.37063
$249$	17.2001	1.09001
$250$	−2.32037	−0.146753
$251$	−15.3933	−0.971618	−0.485809	−	0.874065i	$-0.661475\pi$
$251$	−15.3933	−0.971618	−0.485809	+	0.874065i	$0.661475\pi$
$252$	61.4764	3.87265
$253$	13.9816	0.879013
$254$	6.76146	0.424252
$255$	−7.55164	−0.472902
$256$	−20.1612	−1.26008
$257$	−14.6277	−0.912449	−0.456224	−	0.889865i	$-0.650799\pi$
$257$	−14.6277	−0.912449	−0.456224	+	0.889865i	$0.650799\pi$
$258$	11.8177	0.735739
$259$	25.5150	1.58543
$260$	−4.55310	−0.282372
$261$	14.1244	0.874280
$262$	4.43099	0.273748
$263$	24.6072	1.51734	0.758672	−	0.651472i	$-0.225848\pi$
$263$	24.6072	1.51734	0.758672	+	0.651472i	$0.225848\pi$
$264$	−36.8171	−2.26594
$265$	−9.57516	−0.588198
$266$	25.8742	1.58645
$267$	31.8766	1.95082
$268$	−46.8016	−2.85886
$269$	−26.9657	−1.64413	−0.822063	−	0.569397i	$-0.807177\pi$
$269$	−26.9657	−1.64413	−0.822063	+	0.569397i	$0.807177\pi$
$270$	−6.09358	−0.370843
$271$	15.7753	0.958284	0.479142	−	0.877737i	$-0.340948\pi$
$271$	15.7753	0.958284	0.479142	+	0.877737i	$0.340948\pi$
$272$	−1.95307	−0.118422
$273$	−16.1866	−0.979660
$274$	23.1445	1.39821
$275$	4.33503	0.261412
$276$	28.8630	1.73735
$277$	−6.24037	−0.374948	−0.187474	−	0.982270i	$-0.560030\pi$
$277$	−6.24037	−0.374948	−0.187474	+	0.982270i	$0.560030\pi$
$278$	−0.580363	−0.0348078
$279$	26.8367	1.60667
$280$	−14.6111	−0.873178
$281$	22.1505	1.32139	0.660695	−	0.750654i	$-0.270262\pi$
$281$	22.1505	1.32139	0.660695	+	0.750654i	$0.270262\pi$
$282$	−9.71039	−0.578245
$283$	−6.06473	−0.360511	−0.180255	−	0.983620i	$-0.557692\pi$
$283$	−6.06473	−0.360511	−0.180255	+	0.983620i	$0.557692\pi$
$284$	−36.2747	−2.15251
$285$	−6.48166	−0.383941
$286$	13.5336	0.800258
$287$	−12.0461	−0.711056
$288$	19.3116	1.13795
$289$	−8.84519	−0.520305
$290$	−8.20767	−0.481971
$291$	23.1538	1.35730
$292$	22.0332	1.28940
$293$	14.4061	0.841614	0.420807	−	0.907150i	$-0.361747\pi$
$293$	14.4061	0.841614	0.420807	+	0.907150i	$0.361747\pi$
$294$	−84.0483	−4.90179
$295$	4.60243	0.267964
$296$	−18.0120	−1.04693
$297$	11.3843	0.660586
$298$	−2.21706	−0.128431
$299$	−4.33939	−0.250953
$300$	8.94905	0.516674
$301$	−8.76195	−0.505030
$302$	−50.1167	−2.88389
$303$	39.2901	2.25716
$304$	−1.67635	−0.0961450
$305$	−6.26088	−0.358497
$306$	26.4588	1.51255
$307$	−11.7899	−0.672884	−0.336442	−	0.941704i	$-0.609224\pi$
$307$	−11.7899	−0.672884	−0.336442	+	0.941704i	$0.609224\pi$
$308$	66.7410	3.80292
$309$	−36.1387	−2.05586
$310$	−15.5948	−0.885723
$311$	1.67991	0.0952588	0.0476294	−	0.998865i	$-0.484833\pi$
$311$	1.67991	0.0952588	0.0476294	+	0.998865i	$0.484833\pi$
$312$	11.4267	0.646912
$313$	−12.0379	−0.680421	−0.340210	−	0.940349i	$-0.610498\pi$
$313$	−12.0379	−0.680421	−0.340210	+	0.940349i	$0.610498\pi$
$314$	−6.02856	−0.340211
$315$	18.1663	1.02355
$316$	−25.1910	−1.41710
$317$	−33.8585	−1.90169	−0.950843	−	0.309675i	$-0.899780\pi$
$317$	−33.8585	−1.90169	−0.950843	+	0.309675i	$0.899780\pi$
$318$	58.7539	3.29476
$319$	15.3340	0.858539
$320$	−12.5898	−0.703790
$321$	25.6807	1.43335
$322$	−34.0470	−1.89736
$323$	6.99938	0.389456
$324$	−17.0375	−0.946529
$325$	−1.34544	−0.0746316
$326$	−4.74691	−0.262907
$327$	6.59781	0.364859
$328$	8.50375	0.469541
$329$	7.19952	0.396923
$330$	−26.6000	−1.46428
$331$	7.54252	0.414574	0.207287	−	0.978280i	$-0.433537\pi$
$331$	7.54252	0.414574	0.207287	+	0.978280i	$0.433537\pi$
$332$	22.0110	1.20801
$333$	22.3947	1.22722
$334$	−10.6828	−0.584539
$335$	−13.8298	−0.755605
$336$	8.22817	0.448883
$337$	−23.7388	−1.29314	−0.646568	−	0.762856i	$-0.723796\pi$
$337$	−23.7388	−1.29314	−0.646568	+	0.762856i	$0.723796\pi$
$338$	25.9644	1.41228
$339$	23.3229	1.26673
$340$	−9.66385	−0.524096
$341$	29.1349	1.57774
$342$	22.7100	1.22801
$343$	30.4694	1.64519
$344$	6.18538	0.333494
$345$	8.52900	0.459186
$346$	−7.54748	−0.405755
$347$	2.99093	0.160562	0.0802809	−	0.996772i	$-0.474418\pi$
$347$	2.99093	0.160562	0.0802809	+	0.996772i	$0.474418\pi$
$348$	31.6549	1.69688
$349$	23.6467	1.26578	0.632890	−	0.774242i	$-0.281868\pi$
$349$	23.6467	1.26578	0.632890	+	0.774242i	$0.281868\pi$
$350$	−10.5564	−0.564261
$351$	−3.53330	−0.188594
$352$	20.9653	1.11746
$353$	29.6987	1.58070	0.790351	−	0.612654i	$-0.209898\pi$
$353$	29.6987	1.58070	0.790351	+	0.612654i	$0.209898\pi$
$354$	−28.2408	−1.50098
$355$	−10.7191	−0.568913
$356$	40.7925	2.16200
$357$	−34.3557	−1.81830
$358$	−32.0605	−1.69445
$359$	−29.3925	−1.55128	−0.775639	−	0.631176i	$-0.782572\pi$
$359$	−29.3925	−1.55128	−0.775639	+	0.631176i	$0.782572\pi$
$360$	−12.8242	−0.675896
$361$	−12.9923	−0.683808
$362$	−10.7259	−0.563741
$363$	20.6067	1.08157
$364$	−20.7141	−1.08571
$365$	6.51080	0.340791
$366$	38.4172	2.00810
$367$	−27.8774	−1.45519	−0.727594	−	0.686008i	$-0.759362\pi$
$367$	−27.8774	−1.45519	−0.727594	+	0.686008i	$0.759362\pi$
$368$	2.20585	0.114988
$369$	−10.5729	−0.550403
$370$	−13.0135	−0.676540
$371$	−43.5616	−2.26161
$372$	60.1450	3.11837
$373$	−30.9115	−1.60053	−0.800267	−	0.599643i	$-0.795309\pi$
$373$	−30.9115	−1.60053	−0.800267	+	0.599643i	$0.795309\pi$
$374$	28.7247	1.48532
$375$	2.64444	0.136558
$376$	−5.08241	−0.262105
$377$	−4.75914	−0.245108
$378$	−27.7224	−1.42588
$379$	−22.6232	−1.16207	−0.581037	−	0.813877i	$-0.697353\pi$
$379$	−22.6232	−1.16207	−0.581037	+	0.813877i	$0.697353\pi$
$380$	−8.29460	−0.425504
$381$	−7.70581	−0.394780
$382$	12.0163	0.614809
$383$	−2.18637	−0.111718	−0.0558592	−	0.998439i	$-0.517790\pi$
$383$	−2.18637	−0.111718	−0.0558592	+	0.998439i	$0.517790\pi$
$384$	51.6733	2.63694
$385$	19.7219	1.00512
$386$	−45.4940	−2.31558
$387$	−7.69042	−0.390926
$388$	29.6300	1.50424
$389$	−3.00667	−0.152444	−0.0762221	−	0.997091i	$-0.524286\pi$
$389$	−3.00667	−0.152444	−0.0762221	+	0.997091i	$0.524286\pi$
$390$	8.25572	0.418045
$391$	−9.21024	−0.465782
$392$	−43.9908	−2.22187
$393$	−5.04985	−0.254731
$394$	−31.0013	−1.56182
$395$	−7.44392	−0.374544
$396$	58.5790	2.94371
$397$	−20.0766	−1.00762	−0.503808	−	0.863816i	$-0.668068\pi$
$397$	−20.0766	−1.00762	−0.503808	+	0.863816i	$0.668068\pi$
$398$	39.9222	2.00112
$399$	−29.4879	−1.47624
$400$	0.683929	0.0341965
$401$	11.9906	0.598781	0.299391	−	0.954131i	$-0.403217\pi$
$401$	11.9906	0.598781	0.299391	+	0.954131i	$0.403217\pi$
$402$	84.8610	4.23248
$403$	−9.04246	−0.450437
$404$	50.2796	2.50150
$405$	−5.03458	−0.250170
$406$	−37.3403	−1.85317
$407$	24.3125	1.20513
$408$	24.2530	1.20070
$409$	−10.9065	−0.539290	−0.269645	−	0.962960i	$-0.586906\pi$
$409$	−10.9065	−0.539290	−0.269645	+	0.962960i	$0.586906\pi$
$410$	6.14389	0.303425
$411$	−26.3770	−1.30108
$412$	−46.2467	−2.27841
$413$	20.9385	1.03031
$414$	−29.8832	−1.46868
$415$	6.50425	0.319281
$416$	−6.50691	−0.319028
$417$	0.661419	0.0323898
$418$	24.6547	1.20590
$419$	31.4908	1.53843	0.769214	−	0.638991i	$-0.220648\pi$
$419$	31.4908	1.53843	0.769214	+	0.638991i	$0.220648\pi$
$420$	40.7132	1.98660
$421$	39.1240	1.90679	0.953394	−	0.301727i	$-0.0975630\pi$
$421$	39.1240	1.90679	0.953394	+	0.301727i	$0.0975630\pi$
$422$	35.1758	1.71233
$423$	6.31907	0.307244
$424$	30.7518	1.49344
$425$	−2.85566	−0.138520
$426$	65.7735	3.18674
$427$	−28.4835	−1.37841
$428$	32.8636	1.58852
$429$	−15.4238	−0.744666
$430$	4.46889	0.215509
$431$	1.49541	0.0720315	0.0360157	−	0.999351i	$-0.488533\pi$
$431$	1.49541	0.0720315	0.0360157	+	0.999351i	$0.488533\pi$
$432$	1.79609	0.0864142
$433$	26.9556	1.29540	0.647701	−	0.761895i	$-0.275731\pi$
$433$	26.9556	1.29540	0.647701	+	0.761895i	$0.275731\pi$
$434$	−70.9474	−3.40558
$435$	9.35401	0.448490
$436$	8.44323	0.404357
$437$	−7.90526	−0.378160
$438$	−39.9508	−1.90892
$439$	−4.13259	−0.197238	−0.0986189	−	0.995125i	$-0.531442\pi$
$439$	−4.13259	−0.197238	−0.0986189	+	0.995125i	$0.531442\pi$
$440$	−13.9224	−0.663726
$441$	54.6947	2.60451
$442$	−8.91514	−0.424050
$443$	3.53038	0.167733	0.0838667	−	0.996477i	$-0.473273\pi$
$443$	3.53038	0.167733	0.0838667	+	0.996477i	$0.473273\pi$
$444$	50.1897	2.38190
$445$	12.0542	0.571423
$446$	−27.0024	−1.27860
$447$	2.52671	0.119509
$448$	−57.2764	−2.70606
$449$	4.00427	0.188973	0.0944867	−	0.995526i	$-0.469879\pi$
$449$	4.00427	0.188973	0.0944867	+	0.995526i	$0.469879\pi$
$450$	−9.26540	−0.436775
$451$	−11.4783	−0.540493
$452$	29.8464	1.40386
$453$	57.1163	2.68356
$454$	13.2685	0.622720
$455$	−6.12100	−0.286957
$456$	20.8166	0.974827
$457$	−20.2031	−0.945059	−0.472530	−	0.881315i	$-0.656659\pi$
$457$	−20.2031	−0.945059	−0.472530	+	0.881315i	$0.656659\pi$
$458$	34.0516	1.59113
$459$	−7.49934	−0.350039
$460$	10.9146	0.508895
$461$	24.8642	1.15804	0.579022	−	0.815312i	$-0.303435\pi$
$461$	24.8642	1.15804	0.579022	+	0.815312i	$0.303435\pi$
$462$	−121.015	−5.63014
$463$	−4.56220	−0.212024	−0.106012	−	0.994365i	$-0.533808\pi$
$463$	−4.56220	−0.212024	−0.106012	+	0.994365i	$0.533808\pi$
$464$	2.41922	0.112309
$465$	17.7728	0.824194
$466$	31.9243	1.47887
$467$	23.4269	1.08407	0.542034	−	0.840357i	$-0.317654\pi$
$467$	23.4269	1.08407	0.542034	+	0.840357i	$0.317654\pi$
$468$	−18.1809	−0.840412
$469$	−62.9181	−2.90529
$470$	−3.67200	−0.169377
$471$	6.87055	0.316578
$472$	−14.7812	−0.680362
$473$	−8.34900	−0.383887
$474$	45.6764	2.09799
$475$	−2.45105	−0.112462
$476$	−43.9651	−2.01514
$477$	−38.2343	−1.75063
$478$	−13.3167	−0.609092
$479$	−35.1980	−1.60824	−0.804118	−	0.594469i	$-0.797362\pi$
$479$	−35.1980	−1.60824	−0.804118	+	0.594469i	$0.797362\pi$
$480$	12.7892	0.583746
$481$	−7.54575	−0.344057
$482$	−6.55120	−0.298399
$483$	38.8022	1.76556
$484$	26.3704	1.19866
$485$	8.75566	0.397574
$486$	49.1733	2.23055
$487$	−10.1913	−0.461813	−0.230906	−	0.972976i	$-0.574169\pi$
$487$	−10.1913	−0.461813	−0.230906	+	0.972976i	$0.574169\pi$
$488$	20.1075	0.910226
$489$	5.40989	0.244644
$490$	−31.7830	−1.43581
$491$	15.9025	0.717669	0.358834	−	0.933401i	$-0.383174\pi$
$491$	15.9025	0.717669	0.358834	+	0.933401i	$0.383174\pi$
$492$	−23.6954	−1.06827
$493$	−10.1011	−0.454933
$494$	−7.65197	−0.344279
$495$	17.3101	0.778030
$496$	4.59656	0.206392
$497$	−48.7661	−2.18746
$498$	−39.9106	−1.78843
$499$	3.12949	0.140095	0.0700476	−	0.997544i	$-0.477685\pi$
$499$	3.12949	0.140095	0.0700476	+	0.997544i	$0.477685\pi$
$500$	3.38410	0.151342
$501$	12.1749	0.543933
$502$	35.7182	1.59418
$503$	−11.8563	−0.528648	−0.264324	−	0.964434i	$-0.585149\pi$
$503$	−11.8563	−0.528648	−0.264324	+	0.964434i	$0.585149\pi$
$504$	−58.3430	−2.59881
$505$	14.8576	0.661155
$506$	−32.4423	−1.44224
$507$	−29.5908	−1.31417
$508$	−9.86114	−0.437517
$509$	36.2396	1.60629	0.803146	−	0.595783i	$-0.203158\pi$
$509$	36.2396	1.60629	0.803146	+	0.595783i	$0.203158\pi$
$510$	17.5226	0.775912
$511$	29.6205	1.31033
$512$	7.70070	0.340326
$513$	−6.43677	−0.284191
$514$	33.9415	1.49710
$515$	−13.6659	−0.602191
$516$	−17.2353	−0.758744
$517$	6.86021	0.301712
$518$	−59.2042	−2.60128
$519$	8.60160	0.377568
$520$	4.32104	0.189490
$521$	25.3687	1.11142	0.555712	−	0.831375i	$-0.312446\pi$
$521$	25.3687	1.11142	0.555712	+	0.831375i	$0.312446\pi$
$522$	−32.7739	−1.43447
$523$	−25.2585	−1.10448	−0.552239	−	0.833686i	$-0.686226\pi$
$523$	−25.2585	−1.10448	−0.552239	+	0.833686i	$0.686226\pi$
$524$	−6.46231	−0.282307
$525$	12.0307	0.525064
$526$	−57.0977	−2.48958
$527$	−19.1924	−0.836034
$528$	7.84038	0.341209
$529$	−12.5977	−0.547728
$530$	22.2179	0.965083
$531$	18.3778	0.797530
$532$	−37.7358	−1.63605
$533$	3.56247	0.154308
$534$	−73.9653	−3.20079
$535$	9.71118	0.419851
$536$	44.4162	1.91849
$537$	36.5383	1.57674
$538$	62.5702	2.69759
$539$	59.3786	2.55762
$540$	8.88708	0.382439
$541$	−24.9068	−1.07083	−0.535414	−	0.844590i	$-0.679844\pi$
$541$	−24.9068	−1.07083	−0.535414	+	0.844590i	$0.679844\pi$
$542$	−36.6046	−1.57230
$543$	12.2240	0.524580
$544$	−13.8108	−0.592131
$545$	2.49497	0.106873
$546$	37.5589	1.60737
$547$	26.6515	1.13954	0.569768	−	0.821805i	$-0.307033\pi$
$547$	26.6515	1.13954	0.569768	+	0.821805i	$0.307033\pi$
$548$	−33.7547	−1.44193
$549$	−25.0002	−1.06698
$550$	−10.0588	−0.428911
$551$	−8.66993	−0.369352
$552$	−27.3919	−1.16588
$553$	−33.8657	−1.44011
$554$	14.4800	0.615194
$555$	14.8310	0.629543
$556$	0.846420	0.0358962
$557$	−3.92451	−0.166287	−0.0831434	−	0.996538i	$-0.526496\pi$
$557$	−3.92451	−0.166287	−0.0831434	+	0.996538i	$0.526496\pi$
$558$	−62.2710	−2.63614
$559$	2.59124	0.109598
$560$	3.11150	0.131485
$561$	−32.7365	−1.38214
$562$	−51.3974	−2.16807
$563$	−19.9387	−0.840317	−0.420159	−	0.907451i	$-0.638026\pi$
$563$	−19.9387	−0.840317	−0.420159	+	0.907451i	$0.638026\pi$
$564$	14.1620	0.596326
$565$	8.81959	0.371043
$566$	14.0724	0.591507
$567$	−22.9045	−0.961899
$568$	34.4258	1.44447
$569$	−22.6758	−0.950621	−0.475310	−	0.879818i	$-0.657664\pi$
$569$	−22.6758	−0.950621	−0.475310	+	0.879818i	$0.657664\pi$
$570$	15.0398	0.629949
$571$	−5.36019	−0.224317	−0.112158	−	0.993690i	$-0.535776\pi$
$571$	−5.36019	−0.224317	−0.112158	+	0.993690i	$0.535776\pi$
$572$	−19.7378	−0.825280
$573$	−13.6946	−0.572100
$574$	27.9513	1.16666
$575$	3.22525	0.134502
$576$	−50.2719	−2.09466
$577$	−43.3315	−1.80391	−0.901956	−	0.431828i	$-0.857869\pi$
$577$	−43.3315	−1.80391	−0.901956	+	0.431828i	$0.857869\pi$
$578$	20.5241	0.853689
$579$	51.8480	2.15473
$580$	11.9703	0.497041
$581$	29.5907	1.22763
$582$	−53.7254	−2.22699
$583$	−41.5086	−1.71911
$584$	−20.9102	−0.865270
$585$	−5.37245	−0.222123
$586$	−33.4274	−1.38088
$587$	5.08639	0.209938	0.104969	−	0.994476i	$-0.466526\pi$
$587$	5.08639	0.209938	0.104969	+	0.994476i	$0.466526\pi$
$588$	122.579	5.05506
$589$	−16.4731	−0.678761
$590$	−10.6793	−0.439661
$591$	35.3311	1.45333
$592$	3.83574	0.157648
$593$	−18.9775	−0.779311	−0.389655	−	0.920961i	$-0.627406\pi$
$593$	−18.9775	−0.779311	−0.389655	+	0.920961i	$0.627406\pi$
$594$	−26.4158	−1.08385
$595$	−12.9917	−0.532606
$596$	3.23344	0.132447
$597$	−45.4980	−1.86211
$598$	10.0690	0.411751
$599$	−34.5583	−1.41201	−0.706007	−	0.708205i	$-0.749505\pi$
$599$	−34.5583	−1.41201	−0.706007	+	0.708205i	$0.749505\pi$
$600$	−8.49294	−0.346723
$601$	25.0349	1.02119	0.510597	−	0.859820i	$-0.329424\pi$
$601$	25.0349	1.02119	0.510597	+	0.859820i	$0.329424\pi$
$602$	20.3309	0.828627
$603$	−55.2236	−2.24888
$604$	73.0918	2.97406
$605$	7.79245	0.316808
$606$	−91.1674	−3.70342
$607$	0.469295	0.0190481	0.00952406	−	0.999955i	$-0.496968\pi$
$607$	0.469295	0.0190481	0.00952406	+	0.999955i	$0.496968\pi$
$608$	−11.8539	−0.480741
$609$	42.5555	1.72444
$610$	14.5275	0.588202
$611$	−2.12917	−0.0861370
$612$	−38.5885	−1.55985
$613$	−15.6484	−0.632035	−0.316017	−	0.948753i	$-0.602346\pi$
$613$	−15.6484	−0.632035	−0.316017	+	0.948753i	$0.602346\pi$
$614$	27.3569	1.10403
$615$	−7.00198	−0.282347
$616$	−63.3393	−2.55201
$617$	−36.6104	−1.47388	−0.736939	−	0.675959i	$-0.763729\pi$
$617$	−36.6104	−1.47388	−0.736939	+	0.675959i	$0.763729\pi$
$618$	83.8549	3.37314
$619$	−13.5619	−0.545097	−0.272549	−	0.962142i	$-0.587867\pi$
$619$	−13.5619	−0.545097	−0.272549	+	0.962142i	$0.587867\pi$
$620$	22.7439	0.913417
$621$	8.46993	0.339887
$622$	−3.89800	−0.156296
$623$	54.8398	2.19711
$624$	−2.43338	−0.0974132
$625$	1.00000	0.0400000
$626$	27.9323	1.11640
$627$	−28.0982	−1.12213
$628$	8.79225	0.350849
$629$	−16.0157	−0.638586
$630$	−42.1524	−1.67939
$631$	−7.44155	−0.296243	−0.148122	−	0.988969i	$-0.547323\pi$
$631$	−7.44155	−0.296243	−0.148122	+	0.988969i	$0.547323\pi$
$632$	23.9070	0.950970
$633$	−40.0886	−1.59338
$634$	78.5642	3.12018
$635$	−2.91396	−0.115637
$636$	−85.6887	−3.39778
$637$	−18.4290	−0.730185
$638$	−35.5805	−1.40864
$639$	−42.8024	−1.69324
$640$	19.5403	0.772400
$641$	30.6232	1.20954	0.604771	−	0.796399i	$-0.293264\pi$
$641$	30.6232	1.20954	0.604771	+	0.796399i	$0.293264\pi$
$642$	−59.5885	−2.35177
$643$	30.7851	1.21405	0.607024	−	0.794684i	$-0.292363\pi$
$643$	30.7851	1.21405	0.607024	+	0.794684i	$0.292363\pi$
$644$	49.6552	1.95669
$645$	−5.09304	−0.200538
$646$	−16.2411	−0.638998
$647$	−7.25823	−0.285350	−0.142675	−	0.989770i	$-0.545570\pi$
$647$	−7.25823	−0.285350	−0.142675	+	0.989770i	$0.545570\pi$
$648$	16.1691	0.635184
$649$	19.9516	0.783171
$650$	3.12192	0.122452
$651$	80.8563	3.16901
$652$	6.92305	0.271128
$653$	−32.3115	−1.26445	−0.632223	−	0.774786i	$-0.717857\pi$
$653$	−32.3115	−1.26445	−0.632223	+	0.774786i	$0.717857\pi$
$654$	−15.3093	−0.598642
$655$	−1.90961	−0.0746146
$656$	−1.81092	−0.0707044
$657$	25.9981	1.01428
$658$	−16.7055	−0.651249
$659$	−20.3727	−0.793606	−0.396803	−	0.917904i	$-0.629880\pi$
$659$	−20.3727	−0.793606	−0.396803	+	0.917904i	$0.629880\pi$
$660$	38.7944	1.51007
$661$	−30.5661	−1.18888	−0.594441	−	0.804139i	$-0.702627\pi$
$661$	−30.5661	−1.18888	−0.594441	+	0.804139i	$0.702627\pi$
$662$	−17.5014	−0.680212
$663$	10.1603	0.394593
$664$	−20.8892	−0.810656
$665$	−11.1509	−0.432414
$666$	−51.9639	−2.01356
$667$	11.4085	0.441738
$668$	15.5802	0.602816
$669$	30.7737	1.18978
$670$	32.0903	1.23976
$671$	−27.1411	−1.04777
$672$	58.1838	2.24449
$673$	−3.16739	−0.122094	−0.0610469	−	0.998135i	$-0.519444\pi$
$673$	−3.16739	−0.122094	−0.0610469	+	0.998135i	$0.519444\pi$
$674$	55.0828	2.12171
$675$	2.62613	0.101080
$676$	−37.8674	−1.45644
$677$	4.30938	0.165623	0.0828115	−	0.996565i	$-0.473610\pi$
$677$	4.30938	0.165623	0.0828115	+	0.996565i	$0.473610\pi$
$678$	−54.1177	−2.07838
$679$	39.8333	1.52866
$680$	9.17130	0.351703
$681$	−15.1216	−0.579461
$682$	−67.6037	−2.58868
$683$	14.4689	0.553636	0.276818	−	0.960922i	$-0.410720\pi$
$683$	14.4689	0.553636	0.276818	+	0.960922i	$0.410720\pi$
$684$	−33.1210	−1.26641
$685$	−9.97449	−0.381106
$686$	−70.7002	−2.69935
$687$	−38.8075	−1.48060
$688$	−1.31721	−0.0502181
$689$	12.8828	0.490796
$690$	−19.7904	−0.753407
$691$	16.4279	0.624947	0.312474	−	0.949926i	$-0.398842\pi$
$691$	16.4279	0.624947	0.312474	+	0.949926i	$0.398842\pi$
$692$	11.0075	0.418442
$693$	78.7512	2.99151
$694$	−6.94006	−0.263441
$695$	0.250117	0.00948747
$696$	−30.0415	−1.13872
$697$	7.56126	0.286403
$698$	−54.8691	−2.07683
$699$	−36.3831	−1.37613
$700$	15.3958	0.581905
$701$	36.6139	1.38289	0.691443	−	0.722431i	$-0.256975\pi$
$701$	36.6139	1.38289	0.691443	+	0.722431i	$0.256975\pi$
$702$	8.19855	0.309434
$703$	−13.7464	−0.518457
$704$	−54.5770	−2.05695
$705$	4.18485	0.157611
$706$	−68.9119	−2.59353
$707$	67.5938	2.54213
$708$	41.1874	1.54792
$709$	1.94397	0.0730074	0.0365037	−	0.999334i	$-0.488378\pi$
$709$	1.94397	0.0730074	0.0365037	+	0.999334i	$0.488378\pi$
$710$	24.8723	0.933443
$711$	−29.7241	−1.11474
$712$	−38.7134	−1.45085
$713$	21.6763	0.811785
$714$	79.7178	2.98336
$715$	−5.83252	−0.218124
$716$	46.7581	1.74743
$717$	15.1766	0.566781
$718$	68.2015	2.54526
$719$	−35.6397	−1.32914	−0.664568	−	0.747228i	$-0.731384\pi$
$719$	−35.6397	−1.32914	−0.664568	+	0.747228i	$0.731384\pi$
$720$	2.73098	0.101778
$721$	−62.1722	−2.31541
$722$	30.1470	1.12196
$723$	7.46618	0.277670
$724$	15.6430	0.581368
$725$	3.53723	0.131369
$726$	−47.8150	−1.77458
$727$	16.2009	0.600860	0.300430	−	0.953804i	$-0.402870\pi$
$727$	16.2009	0.600860	0.300430	+	0.953804i	$0.402870\pi$
$728$	19.6583	0.728586
$729$	−40.9374	−1.51620
$730$	−15.1074	−0.559152
$731$	5.49984	0.203419
$732$	−56.0289	−2.07089
$733$	−51.4687	−1.90104	−0.950521	−	0.310661i	$-0.899450\pi$
$733$	−51.4687	−1.90104	−0.950521	+	0.310661i	$0.899450\pi$
$734$	64.6858	2.38760
$735$	36.2220	1.33607
$736$	15.5982	0.574957
$737$	−59.9528	−2.20839
$738$	24.5330	0.903073
$739$	36.1962	1.33150	0.665749	−	0.746176i	$-0.268112\pi$
$739$	36.1962	1.33150	0.665749	+	0.746176i	$0.268112\pi$
$740$	18.9793	0.697694
$741$	8.72069	0.320363
$742$	101.079	3.71072
$743$	37.7260	1.38403	0.692017	−	0.721881i	$-0.256722\pi$
$743$	37.7260	1.38403	0.692017	+	0.721881i	$0.256722\pi$
$744$	−57.0795	−2.09263
$745$	0.955480	0.0350061
$746$	71.7259	2.62607
$747$	25.9719	0.950264
$748$	−41.8930	−1.53176
$749$	44.1804	1.61432
$750$	−6.13607	−0.224058
$751$	50.6770	1.84923	0.924615	−	0.380904i	$-0.124387\pi$
$751$	50.6770	1.84923	0.924615	+	0.380904i	$0.124387\pi$
$752$	1.08232	0.0394683
$753$	−40.7068	−1.48344
$754$	11.0429	0.402160
$755$	21.5986	0.786054
$756$	40.4312	1.47047
$757$	−39.9617	−1.45243	−0.726217	−	0.687465i	$-0.758723\pi$
$757$	−39.9617	−1.45243	−0.726217	+	0.687465i	$0.758723\pi$
$758$	52.4940	1.90667
$759$	36.9734	1.34205
$760$	7.87184	0.285542
$761$	23.4731	0.850900	0.425450	−	0.904982i	$-0.360116\pi$
$761$	23.4731	0.850900	0.425450	+	0.904982i	$0.360116\pi$
$762$	17.8803	0.647735
$763$	11.3507	0.410924
$764$	−17.5250	−0.634033
$765$	−11.4029	−0.412272
$766$	5.07318	0.183302
$767$	−6.19229	−0.223591
$768$	−53.3152	−1.92384
$769$	−13.6008	−0.490458	−0.245229	−	0.969465i	$-0.578863\pi$
$769$	−13.6008	−0.490458	−0.245229	+	0.969465i	$0.578863\pi$
$770$	−45.7621	−1.64915
$771$	−38.6820	−1.39310
$772$	66.3500	2.38799
$773$	−26.7691	−0.962817	−0.481408	−	0.876496i	$-0.659875\pi$
$773$	−26.7691	−0.962817	−0.481408	+	0.876496i	$0.659875\pi$
$774$	17.8446	0.641411
$775$	6.72082	0.241419
$776$	−28.1198	−1.00944
$777$	67.4730	2.42058
$778$	6.97658	0.250122
$779$	6.48992	0.232525
$780$	−12.0404	−0.431116
$781$	−46.4678	−1.66275
$782$	21.3711	0.764230
$783$	9.28922	0.331970
$784$	9.36805	0.334573
$785$	2.59811	0.0927304
$786$	11.7175	0.417950
$787$	15.1146	0.538776	0.269388	−	0.963032i	$-0.413179\pi$
$787$	15.1146	0.538776	0.269388	+	0.963032i	$0.413179\pi$
$788$	45.2133	1.61066
$789$	65.0723	2.31664
$790$	17.2726	0.614532
$791$	40.1242	1.42665
$792$	−55.5934	−1.97542
$793$	8.42364	0.299132
$794$	46.5850	1.65324
$795$	−25.3210	−0.898042
$796$	−58.2239	−2.06369
$797$	9.34859	0.331144	0.165572	−	0.986198i	$-0.447053\pi$
$797$	9.34859	0.331144	0.165572	+	0.986198i	$0.447053\pi$
$798$	68.4228	2.42214
$799$	−4.51911	−0.159875
$800$	4.83627	0.170988
$801$	48.1332	1.70070
$802$	−27.8225	−0.982448
$803$	28.2245	0.996021
$804$	−123.764	−4.36482
$805$	14.6731	0.517159
$806$	20.9818	0.739053
$807$	−71.3091	−2.51020
$808$	−47.7169	−1.67868
$809$	7.00155	0.246161	0.123081	−	0.992397i	$-0.460723\pi$
$809$	7.00155	0.246161	0.123081	+	0.992397i	$0.460723\pi$
$810$	11.6821	0.410466
$811$	4.44382	0.156044	0.0780218	−	0.996952i	$-0.475140\pi$
$811$	4.44382	0.156044	0.0780218	+	0.996952i	$0.475140\pi$
$812$	54.4584	1.91111
$813$	41.7170	1.46308
$814$	−56.4139	−1.97731
$815$	2.04576	0.0716598
$816$	−5.16479	−0.180804
$817$	4.72058	0.165152
$818$	25.3070	0.884838
$819$	−24.4416	−0.854059
$820$	−8.96045	−0.312913
$821$	29.7236	1.03736	0.518680	−	0.854968i	$-0.326423\pi$
$821$	29.7236	1.03736	0.518680	+	0.854968i	$0.326423\pi$
$822$	61.2042	2.13474
$823$	−10.5331	−0.367163	−0.183581	−	0.983005i	$-0.558769\pi$
$823$	−10.5331	−0.367163	−0.183581	+	0.983005i	$0.558769\pi$
$824$	43.8896	1.52897
$825$	11.4637	0.399116
$826$	−48.5849	−1.69049
$827$	2.46758	0.0858060	0.0429030	−	0.999079i	$-0.486339\pi$
$827$	2.46758	0.0858060	0.0429030	+	0.999079i	$0.486339\pi$
$828$	43.5827	1.51460
$829$	14.3389	0.498011	0.249005	−	0.968502i	$-0.419896\pi$
$829$	14.3389	0.498011	0.249005	+	0.968502i	$0.419896\pi$
$830$	−15.0922	−0.523859
$831$	−16.5023	−0.572459
$832$	16.9388	0.587247
$833$	−39.1152	−1.35526
$834$	−1.53474	−0.0531435
$835$	4.60394	0.159326
$836$	−35.9573	−1.24361
$837$	17.6497	0.610064
$838$	−73.0703	−2.52417
$839$	28.5870	0.986932	0.493466	−	0.869765i	$-0.335730\pi$
$839$	28.5870	0.986932	0.493466	+	0.869765i	$0.335730\pi$
$840$	−38.6381	−1.33314
$841$	−16.4880	−0.568551
$842$	−90.7821	−3.12856
$843$	58.5758	2.01746
$844$	−51.3015	−1.76587
$845$	−11.1898	−0.384940
$846$	−14.6626	−0.504109
$847$	35.4513	1.21812
$848$	−6.54874	−0.224885
$849$	−16.0378	−0.550417
$850$	6.62618	0.227276
$851$	18.0885	0.620064
$852$	−95.9262	−3.28638
$853$	0.727424	0.0249065	0.0124533	−	0.999922i	$-0.496036\pi$
$853$	0.727424	0.0249065	0.0124533	+	0.999922i	$0.496036\pi$
$854$	66.0921	2.26163
$855$	−9.78723	−0.334716
$856$	−31.1886	−1.06600
$857$	−52.0075	−1.77654	−0.888270	−	0.459321i	$-0.848093\pi$
$857$	−52.0075	−1.77654	−0.888270	+	0.459321i	$0.848093\pi$
$858$	35.7888	1.22181
$859$	12.3236	0.420474	0.210237	−	0.977650i	$-0.432576\pi$
$859$	12.3236	0.420474	0.210237	+	0.977650i	$0.432576\pi$
$860$	−6.51757	−0.222247
$861$	−31.8551	−1.08562
$862$	−3.46990	−0.118185
$863$	−15.9895	−0.544288	−0.272144	−	0.962257i	$-0.587733\pi$
$863$	−15.9895	−0.544288	−0.272144	+	0.962257i	$0.587733\pi$
$864$	12.7007	0.432085
$865$	3.25271	0.110595
$866$	−62.5468	−2.12543
$867$	−23.3906	−0.794386
$868$	103.472	3.51207
$869$	−32.2696	−1.09467
$870$	−21.7047	−0.735859
$871$	18.6072	0.630482
$872$	−8.01289	−0.271351
$873$	34.9620	1.18328
$874$	18.3431	0.620465
$875$	4.54944	0.153799
$876$	58.2655	1.96861
$877$	−28.3157	−0.956154	−0.478077	−	0.878318i	$-0.658666\pi$
$877$	−28.3157	−0.956154	−0.478077	+	0.878318i	$0.658666\pi$
$878$	9.58913	0.323617
$879$	38.0961	1.28495
$880$	2.96485	0.0999451
$881$	5.90164	0.198831	0.0994156	−	0.995046i	$-0.468303\pi$
$881$	5.90164	0.198831	0.0994156	+	0.995046i	$0.468303\pi$
$882$	−126.912	−4.27334
$883$	−9.69872	−0.326388	−0.163194	−	0.986594i	$-0.552180\pi$
$883$	−9.69872	−0.326388	−0.163194	+	0.986594i	$0.552180\pi$
$884$	13.0021	0.437309
$885$	12.1709	0.409119
$886$	−8.19178	−0.275208
$887$	−26.5324	−0.890872	−0.445436	−	0.895314i	$-0.646951\pi$
$887$	−26.5324	−0.890872	−0.445436	+	0.895314i	$0.646951\pi$
$888$	−47.6317	−1.59841
$889$	−13.2569	−0.444622
$890$	−27.9701	−0.937560
$891$	−21.8250	−0.731166
$892$	39.3812	1.31858
$893$	−3.87881	−0.129799
$894$	−5.86290	−0.196085
$895$	13.8170	0.461852
$896$	88.8976	2.96986
$897$	−11.4753	−0.383148
$898$	−9.29138	−0.310057
$899$	23.7731	0.792877
$900$	13.5130	0.450432
$901$	27.3434	0.910942
$902$	26.6339	0.886813
$903$	−23.1705	−0.771065
$904$	−28.3252	−0.942081
$905$	4.62251	0.153657
$906$	−132.531	−4.40304
$907$	5.13863	0.170625	0.0853127	−	0.996354i	$-0.472811\pi$
$907$	5.13863	0.170625	0.0853127	+	0.996354i	$0.472811\pi$
$908$	−19.3512	−0.642191
$909$	59.3275	1.96777
$910$	14.2030	0.470824
$911$	−17.6236	−0.583896	−0.291948	−	0.956434i	$-0.594303\pi$
$911$	−17.6236	−0.583896	−0.291948	+	0.956434i	$0.594303\pi$
$912$	−4.43300	−0.146791
$913$	28.1961	0.933154
$914$	46.8785	1.55060
$915$	−16.5565	−0.547342
$916$	−49.6621	−1.64088
$917$	−8.68765	−0.286892
$918$	17.4012	0.574326
$919$	−47.7484	−1.57508	−0.787538	−	0.616267i	$-0.788644\pi$
$919$	−47.7484	−1.57508	−0.787538	+	0.616267i	$0.788644\pi$
$920$	−10.3583	−0.341502
$921$	−31.1777	−1.02734
$922$	−57.6941	−1.90006
$923$	14.4220	0.474705
$924$	176.493	5.80618
$925$	5.60838	0.184403
$926$	10.5860	0.347877
$927$	−54.5689	−1.79228
$928$	17.1070	0.561565
$929$	31.7089	1.04033	0.520167	−	0.854064i	$-0.325870\pi$
$929$	31.7089	1.04033	0.520167	+	0.854064i	$0.325870\pi$
$930$	−41.2394	−1.35229
$931$	−33.5730	−1.10031
$932$	−46.5595	−1.52511
$933$	4.44242	0.145438
$934$	−54.3590	−1.77868
$935$	−12.3794	−0.404849
$936$	17.2542	0.563972
$937$	−51.9131	−1.69593	−0.847964	−	0.530055i	$-0.822171\pi$
$937$	−51.9131	−1.69593	−0.847964	+	0.530055i	$0.822171\pi$
$938$	145.993	4.76684
$939$	−31.8335	−1.03885
$940$	5.35536	0.174673
$941$	27.2287	0.887629	0.443815	−	0.896119i	$-0.353625\pi$
$941$	27.2287	0.887629	0.443815	+	0.896119i	$0.353625\pi$
$942$	−15.9422	−0.519424
$943$	−8.53986	−0.278096
$944$	3.14774	0.102450
$945$	11.9474	0.388649
$946$	19.3727	0.629862
$947$	45.5752	1.48100	0.740498	−	0.672059i	$-0.234590\pi$
$947$	45.5752	1.48100	0.740498	+	0.672059i	$0.234590\pi$
$948$	−66.6160	−2.16359
$949$	−8.75990	−0.284358
$950$	5.68734	0.184522
$951$	−89.5370	−2.90343
$952$	41.7243	1.35229
$953$	43.8420	1.42018	0.710091	−	0.704110i	$-0.248654\pi$
$953$	43.8420	1.42018	0.710091	+	0.704110i	$0.248654\pi$
$954$	88.7177	2.87234
$955$	−5.17864	−0.167577
$956$	19.4215	0.628137
$957$	40.5499	1.31079
$958$	81.6722	2.63871
$959$	−45.3783	−1.46534
$960$	−33.2929	−1.07452
$961$	14.1694	0.457077
$962$	17.5089	0.564510
$963$	38.7775	1.24959
$964$	9.55449	0.307729
$965$	19.6064	0.631152
$966$	−90.0352	−2.89684
$967$	23.8995	0.768556	0.384278	−	0.923217i	$-0.374450\pi$
$967$	23.8995	0.768556	0.384278	+	0.923217i	$0.374450\pi$
$968$	−25.0264	−0.804378
$969$	18.5094	0.594609
$970$	−20.3163	−0.652318
$971$	31.5030	1.01098	0.505489	−	0.862833i	$-0.331312\pi$
$971$	31.5030	1.01098	0.505489	+	0.862833i	$0.331312\pi$
$972$	−71.7160	−2.30029
$973$	1.13789	0.0364791
$974$	23.6476	0.757718
$975$	−3.55794	−0.113945
$976$	−4.28200	−0.137063
$977$	24.9857	0.799362	0.399681	−	0.916654i	$-0.369121\pi$
$977$	24.9857	0.799362	0.399681	+	0.916654i	$0.369121\pi$
$978$	−12.5529	−0.401399
$979$	52.2552	1.67008
$980$	46.3534	1.48070
$981$	9.96260	0.318081
$982$	−36.8996	−1.17751
$983$	28.3870	0.905406	0.452703	−	0.891661i	$-0.350460\pi$
$983$	28.3870	0.905406	0.452703	+	0.891661i	$0.350460\pi$
$984$	22.4877	0.716881
$985$	13.3605	0.425702
$986$	23.4383	0.746429
$987$	19.0387	0.606009
$988$	11.1599	0.355043
$989$	−6.21165	−0.197519
$990$	−40.1657	−1.27655
$991$	−14.0053	−0.444893	−0.222446	−	0.974945i	$-0.571404\pi$
$991$	−14.0053	−0.444893	−0.222446	+	0.974945i	$0.571404\pi$
$992$	32.5037	1.03199
$993$	19.9458	0.632960
$994$	113.155	3.58907
$995$	−17.2051	−0.545439
$996$	58.2069	1.84436
$997$	−59.2548	−1.87662	−0.938309	−	0.345797i	$-0.887609\pi$
$997$	−59.2548	−1.87662	−0.938309	+	0.345797i	$0.887609\pi$
$998$	−7.26156	−0.229861
$999$	14.7283	0.465984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.16	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.16	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32037 q^{2} +2.64444 q^{3} +3.38410 q^{4} +1.00000 q^{5} -6.13607 q^{6} +4.54944 q^{7} -3.21162 q^{8} +3.99307 q^{9} +O(q^{10})\)	\(q-2.32037 q^{2} +2.64444 q^{3} +3.38410 q^{4} +1.00000 q^{5} -6.13607 q^{6} +4.54944 q^{7} -3.21162 q^{8} +3.99307 q^{9} -2.32037 q^{10} +4.33503 q^{11} +8.94905 q^{12} -1.34544 q^{13} -10.5564 q^{14} +2.64444 q^{15} +0.683929 q^{16} -2.85566 q^{17} -9.26540 q^{18} -2.45105 q^{19} +3.38410 q^{20} +12.0307 q^{21} -10.0588 q^{22} +3.22525 q^{23} -8.49294 q^{24} +1.00000 q^{25} +3.12192 q^{26} +2.62613 q^{27} +15.3958 q^{28} +3.53723 q^{29} -6.13607 q^{30} +6.72082 q^{31} +4.83627 q^{32} +11.4637 q^{33} +6.62618 q^{34} +4.54944 q^{35} +13.5130 q^{36} +5.60838 q^{37} +5.68734 q^{38} -3.55794 q^{39} -3.21162 q^{40} -2.64781 q^{41} -27.9157 q^{42} -1.92594 q^{43} +14.6702 q^{44} +3.99307 q^{45} -7.48377 q^{46} +1.58251 q^{47} +1.80861 q^{48} +13.6974 q^{49} -2.32037 q^{50} -7.55164 q^{51} -4.55310 q^{52} -9.57516 q^{53} -6.09358 q^{54} +4.33503 q^{55} -14.6111 q^{56} -6.48166 q^{57} -8.20767 q^{58} +4.60243 q^{59} +8.94905 q^{60} -6.26088 q^{61} -15.5948 q^{62} +18.1663 q^{63} -12.5898 q^{64} -1.34544 q^{65} -26.6000 q^{66} -13.8298 q^{67} -9.66385 q^{68} +8.52900 q^{69} -10.5564 q^{70} -10.7191 q^{71} -12.8242 q^{72} +6.51080 q^{73} -13.0135 q^{74} +2.64444 q^{75} -8.29460 q^{76} +19.7219 q^{77} +8.25572 q^{78} -7.44392 q^{79} +0.683929 q^{80} -5.03458 q^{81} +6.14389 q^{82} +6.50425 q^{83} +40.7132 q^{84} -2.85566 q^{85} +4.46889 q^{86} +9.35401 q^{87} -13.9224 q^{88} +12.0542 q^{89} -9.26540 q^{90} -6.12100 q^{91} +10.9146 q^{92} +17.7728 q^{93} -3.67200 q^{94} -2.45105 q^{95} +12.7892 q^{96} +8.75566 q^{97} -31.7830 q^{98} +17.3101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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