LMFDB - Embedded newform 2415.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 9x^{5} + 16x^{4} + 20x^{3} - 29x^{2} - 12x + 9 $ x^7 - 2x^6 - 9x^5 + 16x^4 + 20x^3 - 29x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.76794$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76794 q^{2} +1.00000 q^{3} +5.66150 q^{4} -1.00000 q^{5} -2.76794 q^{6} -1.00000 q^{7} -10.1348 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.76794 q^{2} +1.00000 q^{3} +5.66150 q^{4} -1.00000 q^{5} -2.76794 q^{6} -1.00000 q^{7} -10.1348 q^{8} +1.00000 q^{9} +2.76794 q^{10} -6.57288 q^{11} +5.66150 q^{12} +2.49653 q^{13} +2.76794 q^{14} -1.00000 q^{15} +16.7296 q^{16} +7.53933 q^{17} -2.76794 q^{18} +1.84942 q^{19} -5.66150 q^{20} -1.00000 q^{21} +18.1933 q^{22} -1.00000 q^{23} -10.1348 q^{24} +1.00000 q^{25} -6.91024 q^{26} +1.00000 q^{27} -5.66150 q^{28} -2.09956 q^{29} +2.76794 q^{30} -10.2775 q^{31} -26.0368 q^{32} -6.57288 q^{33} -20.8684 q^{34} +1.00000 q^{35} +5.66150 q^{36} +1.43536 q^{37} -5.11909 q^{38} +2.49653 q^{39} +10.1348 q^{40} +6.03726 q^{41} +2.76794 q^{42} +2.16187 q^{43} -37.2123 q^{44} -1.00000 q^{45} +2.76794 q^{46} +0.0425406 q^{47} +16.7296 q^{48} +1.00000 q^{49} -2.76794 q^{50} +7.53933 q^{51} +14.1341 q^{52} -0.911988 q^{53} -2.76794 q^{54} +6.57288 q^{55} +10.1348 q^{56} +1.84942 q^{57} +5.81147 q^{58} -7.59151 q^{59} -5.66150 q^{60} -7.63889 q^{61} +28.4476 q^{62} -1.00000 q^{63} +38.6093 q^{64} -2.49653 q^{65} +18.1933 q^{66} +3.58454 q^{67} +42.6839 q^{68} -1.00000 q^{69} -2.76794 q^{70} +14.2069 q^{71} -10.1348 q^{72} +3.13068 q^{73} -3.97299 q^{74} +1.00000 q^{75} +10.4705 q^{76} +6.57288 q^{77} -6.91024 q^{78} -10.0986 q^{79} -16.7296 q^{80} +1.00000 q^{81} -16.7108 q^{82} +0.813825 q^{83} -5.66150 q^{84} -7.53933 q^{85} -5.98393 q^{86} -2.09956 q^{87} +66.6149 q^{88} +3.59928 q^{89} +2.76794 q^{90} -2.49653 q^{91} -5.66150 q^{92} -10.2775 q^{93} -0.117750 q^{94} -1.84942 q^{95} -26.0368 q^{96} +18.7593 q^{97} -2.76794 q^{98} -6.57288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9} + 2 q^{10} - 2 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 7 q^{15} + 10 q^{16} + 14 q^{17} - 2 q^{18} + 6 q^{19} - 8 q^{20} - 7 q^{21} + 28 q^{22} - 7 q^{23} - 6 q^{24} + 7 q^{25} + 5 q^{26} + 7 q^{27} - 8 q^{28} - 4 q^{29} + 2 q^{30} + 4 q^{31} - 19 q^{32} - 2 q^{33} - 7 q^{34} + 7 q^{35} + 8 q^{36} + 18 q^{37} + 22 q^{38} + 6 q^{39} + 6 q^{40} + 10 q^{41} + 2 q^{42} + 26 q^{43} - 29 q^{44} - 7 q^{45} + 2 q^{46} - 4 q^{47} + 10 q^{48} + 7 q^{49} - 2 q^{50} + 14 q^{51} + 18 q^{52} + 2 q^{53} - 2 q^{54} + 2 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} + 6 q^{59} - 8 q^{60} - 4 q^{61} + 4 q^{62} - 7 q^{63} + 38 q^{64} - 6 q^{65} + 28 q^{66} + 22 q^{67} + 52 q^{68} - 7 q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} + 24 q^{73} + 17 q^{74} + 7 q^{75} + 15 q^{76} + 2 q^{77} + 5 q^{78} + 2 q^{79} - 10 q^{80} + 7 q^{81} - 10 q^{82} + 26 q^{83} - 8 q^{84} - 14 q^{85} - 22 q^{86} - 4 q^{87} + 79 q^{88} + 22 q^{89} + 2 q^{90} - 6 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} - 6 q^{95} - 19 q^{96} + 44 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9 + 2 * q^10 - 2 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 7 * q^15 + 10 * q^16 + 14 * q^17 - 2 * q^18 + 6 * q^19 - 8 * q^20 - 7 * q^21 + 28 * q^22 - 7 * q^23 - 6 * q^24 + 7 * q^25 + 5 * q^26 + 7 * q^27 - 8 * q^28 - 4 * q^29 + 2 * q^30 + 4 * q^31 - 19 * q^32 - 2 * q^33 - 7 * q^34 + 7 * q^35 + 8 * q^36 + 18 * q^37 + 22 * q^38 + 6 * q^39 + 6 * q^40 + 10 * q^41 + 2 * q^42 + 26 * q^43 - 29 * q^44 - 7 * q^45 + 2 * q^46 - 4 * q^47 + 10 * q^48 + 7 * q^49 - 2 * q^50 + 14 * q^51 + 18 * q^52 + 2 * q^53 - 2 * q^54 + 2 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 + 6 * q^59 - 8 * q^60 - 4 * q^61 + 4 * q^62 - 7 * q^63 + 38 * q^64 - 6 * q^65 + 28 * q^66 + 22 * q^67 + 52 * q^68 - 7 * q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 + 24 * q^73 + 17 * q^74 + 7 * q^75 + 15 * q^76 + 2 * q^77 + 5 * q^78 + 2 * q^79 - 10 * q^80 + 7 * q^81 - 10 * q^82 + 26 * q^83 - 8 * q^84 - 14 * q^85 - 22 * q^86 - 4 * q^87 + 79 * q^88 + 22 * q^89 + 2 * q^90 - 6 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 - 6 * q^95 - 19 * q^96 + 44 * q^97 - 2 * q^98 - 2 * 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 $

$2$	−2.76794	−1.95723	−0.978615	−	0.205700i	$-0.934053\pi$
$2$	−2.76794	−1.95723	−0.978615	+	0.205700i	$0.934053\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.66150	2.83075
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.76794	−1.13001
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.1348	−3.58320
$9$	1.00000	0.333333
$10$	2.76794	0.875300
$11$	−6.57288	−1.98180	−0.990899	−	0.134609i	$-0.957022\pi$
$11$	−6.57288	−1.98180	−0.990899	+	0.134609i	$0.957022\pi$
$12$	5.66150	1.63433
$13$	2.49653	0.692412	0.346206	−	0.938158i	$-0.387470\pi$
$13$	2.49653	0.692412	0.346206	+	0.938158i	$0.387470\pi$
$14$	2.76794	0.739763
$15$	−1.00000	−0.258199
$16$	16.7296	4.18239
$17$	7.53933	1.82856	0.914278	−	0.405087i	$-0.132759\pi$
$17$	7.53933	1.82856	0.914278	+	0.405087i	$0.132759\pi$
$18$	−2.76794	−0.652410
$19$	1.84942	0.424286	0.212143	−	0.977239i	$-0.431956\pi$
$19$	1.84942	0.424286	0.212143	+	0.977239i	$0.431956\pi$
$20$	−5.66150	−1.26595
$21$	−1.00000	−0.218218
$22$	18.1933	3.87883
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−10.1348	−2.06876
$25$	1.00000	0.200000
$26$	−6.91024	−1.35521
$27$	1.00000	0.192450
$28$	−5.66150	−1.06992
$29$	−2.09956	−0.389879	−0.194940	−	0.980815i	$-0.562451\pi$
$29$	−2.09956	−0.389879	−0.194940	+	0.980815i	$0.562451\pi$
$30$	2.76794	0.505355
$31$	−10.2775	−1.84590	−0.922949	−	0.384922i	$-0.874228\pi$
$31$	−10.2775	−1.84590	−0.922949	+	0.384922i	$0.874228\pi$
$32$	−26.0368	−4.60271
$33$	−6.57288	−1.14419
$34$	−20.8684	−3.57891
$35$	1.00000	0.169031
$36$	5.66150	0.943583
$37$	1.43536	0.235972	0.117986	−	0.993015i	$-0.462356\pi$
$37$	1.43536	0.235972	0.117986	+	0.993015i	$0.462356\pi$
$38$	−5.11909	−0.830426
$39$	2.49653	0.399764
$40$	10.1348	1.60245
$41$	6.03726	0.942861	0.471431	−	0.881903i	$-0.343738\pi$
$41$	6.03726	0.942861	0.471431	+	0.881903i	$0.343738\pi$
$42$	2.76794	0.427103
$43$	2.16187	0.329682	0.164841	−	0.986320i	$-0.447289\pi$
$43$	2.16187	0.329682	0.164841	+	0.986320i	$0.447289\pi$
$44$	−37.2123	−5.60997
$45$	−1.00000	−0.149071
$46$	2.76794	0.408111
$47$	0.0425406	0.00620518	0.00310259	−	0.999995i	$-0.499012\pi$
$47$	0.0425406	0.00620518	0.00310259	+	0.999995i	$0.499012\pi$
$48$	16.7296	2.41471
$49$	1.00000	0.142857
$50$	−2.76794	−0.391446
$51$	7.53933	1.05572
$52$	14.1341	1.96005
$53$	−0.911988	−0.125271	−0.0626356	−	0.998036i	$-0.519951\pi$
$53$	−0.911988	−0.125271	−0.0626356	+	0.998036i	$0.519951\pi$
$54$	−2.76794	−0.376669
$55$	6.57288	0.886287
$56$	10.1348	1.35432
$57$	1.84942	0.244962
$58$	5.81147	0.763083
$59$	−7.59151	−0.988330	−0.494165	−	0.869368i	$-0.664526\pi$
$59$	−7.59151	−0.988330	−0.494165	+	0.869368i	$0.664526\pi$
$60$	−5.66150	−0.730896
$61$	−7.63889	−0.978060	−0.489030	−	0.872267i	$-0.662649\pi$
$61$	−7.63889	−0.978060	−0.489030	+	0.872267i	$0.662649\pi$
$62$	28.4476	3.61285
$63$	−1.00000	−0.125988
$64$	38.6093	4.82616
$65$	−2.49653	−0.309656
$66$	18.1933	2.23945
$67$	3.58454	0.437921	0.218961	−	0.975734i	$-0.429733\pi$
$67$	3.58454	0.437921	0.218961	+	0.975734i	$0.429733\pi$
$68$	42.6839	5.17618
$69$	−1.00000	−0.120386
$70$	−2.76794	−0.330832
$71$	14.2069	1.68605	0.843026	−	0.537873i	$-0.180772\pi$
$71$	14.2069	1.68605	0.843026	+	0.537873i	$0.180772\pi$
$72$	−10.1348	−1.19440
$73$	3.13068	0.366418	0.183209	−	0.983074i	$-0.441351\pi$
$73$	3.13068	0.366418	0.183209	+	0.983074i	$0.441351\pi$
$74$	−3.97299	−0.461851
$75$	1.00000	0.115470
$76$	10.4705	1.20105
$77$	6.57288	0.749049
$78$	−6.91024	−0.782431
$79$	−10.0986	−1.13618	−0.568088	−	0.822968i	$-0.692317\pi$
$79$	−10.0986	−1.13618	−0.568088	+	0.822968i	$0.692317\pi$
$80$	−16.7296	−1.87042
$81$	1.00000	0.111111
$82$	−16.7108	−1.84540
$83$	0.813825	0.0893289	0.0446644	−	0.999002i	$-0.485778\pi$
$83$	0.813825	0.0893289	0.0446644	+	0.999002i	$0.485778\pi$
$84$	−5.66150	−0.617720
$85$	−7.53933	−0.817755
$86$	−5.98393	−0.645264
$87$	−2.09956	−0.225097
$88$	66.6149	7.10117
$89$	3.59928	0.381523	0.190761	−	0.981636i	$-0.438904\pi$
$89$	3.59928	0.381523	0.190761	+	0.981636i	$0.438904\pi$
$90$	2.76794	0.291767
$91$	−2.49653	−0.261707
$92$	−5.66150	−0.590252
$93$	−10.2775	−1.06573
$94$	−0.117750	−0.0121450
$95$	−1.84942	−0.189747
$96$	−26.0368	−2.65737
$97$	18.7593	1.90472	0.952360	−	0.304976i	$-0.0986485\pi$
$97$	18.7593	1.90472	0.952360	+	0.304976i	$0.0986485\pi$
$98$	−2.76794	−0.279604
$99$	−6.57288	−0.660599
$100$	5.66150	0.566150
$101$	0.0403095	0.00401094	0.00200547	−	0.999998i	$-0.499362\pi$
$101$	0.0403095	0.00401094	0.00200547	+	0.999998i	$0.499362\pi$
$102$	−20.8684	−2.06628
$103$	−5.08995	−0.501528	−0.250764	−	0.968048i	$-0.580682\pi$
$103$	−5.08995	−0.501528	−0.250764	+	0.968048i	$0.580682\pi$
$104$	−25.3018	−2.48105
$105$	1.00000	0.0975900
$106$	2.52433	0.245185
$107$	11.5220	1.11387	0.556937	−	0.830555i	$-0.311977\pi$
$107$	11.5220	1.11387	0.556937	+	0.830555i	$0.311977\pi$
$108$	5.66150	0.544778
$109$	10.3725	0.993504	0.496752	−	0.867893i	$-0.334526\pi$
$109$	10.3725	0.993504	0.496752	+	0.867893i	$0.334526\pi$
$110$	−18.1933	−1.73467
$111$	1.43536	0.136238
$112$	−16.7296	−1.58080
$113$	12.1598	1.14390	0.571948	−	0.820290i	$-0.306188\pi$
$113$	12.1598	1.14390	0.571948	+	0.820290i	$0.306188\pi$
$114$	−5.11909	−0.479446
$115$	1.00000	0.0932505
$116$	−11.8867	−1.10365
$117$	2.49653	0.230804
$118$	21.0128	1.93439
$119$	−7.53933	−0.691129
$120$	10.1348	0.925178
$121$	32.2027	2.92752
$122$	21.1440	1.91429
$123$	6.03726	0.544361
$124$	−58.1862	−5.22528
$125$	−1.00000	−0.0894427
$126$	2.76794	0.246588
$127$	−6.77327	−0.601031	−0.300515	−	0.953777i	$-0.597159\pi$
$127$	−6.77327	−0.601031	−0.300515	+	0.953777i	$0.597159\pi$
$128$	−54.7946	−4.84321
$129$	2.16187	0.190342
$130$	6.91024	0.606068
$131$	−15.4331	−1.34839	−0.674197	−	0.738551i	$-0.735510\pi$
$131$	−15.4331	−1.34839	−0.674197	+	0.738551i	$0.735510\pi$
$132$	−37.2123	−3.23892
$133$	−1.84942	−0.160365
$134$	−9.92179	−0.857112
$135$	−1.00000	−0.0860663
$136$	−76.4097	−6.55208
$137$	21.6020	1.84558	0.922791	−	0.385302i	$-0.125903\pi$
$137$	21.6020	1.84558	0.922791	+	0.385302i	$0.125903\pi$
$138$	2.76794	0.235623
$139$	6.41642	0.544234	0.272117	−	0.962264i	$-0.412276\pi$
$139$	6.41642	0.544234	0.272117	+	0.962264i	$0.412276\pi$
$140$	5.66150	0.478484
$141$	0.0425406	0.00358256
$142$	−39.3239	−3.29999
$143$	−16.4094	−1.37222
$144$	16.7296	1.39413
$145$	2.09956	0.174359
$146$	−8.66554	−0.717165
$147$	1.00000	0.0824786
$148$	8.12629	0.667977
$149$	11.7288	0.960858	0.480429	−	0.877034i	$-0.340481\pi$
$149$	11.7288	0.960858	0.480429	+	0.877034i	$0.340481\pi$
$150$	−2.76794	−0.226001
$151$	−15.1968	−1.23670	−0.618348	−	0.785904i	$-0.712198\pi$
$151$	−15.1968	−1.23670	−0.618348	+	0.785904i	$0.712198\pi$
$152$	−18.7435	−1.52030
$153$	7.53933	0.609519
$154$	−18.1933	−1.46606
$155$	10.2775	0.825511
$156$	14.1341	1.13163
$157$	−3.18657	−0.254316	−0.127158	−	0.991882i	$-0.540586\pi$
$157$	−3.18657	−0.254316	−0.127158	+	0.991882i	$0.540586\pi$
$158$	27.9522	2.22376
$159$	−0.911988	−0.0723254
$160$	26.0368	2.05839
$161$	1.00000	0.0788110
$162$	−2.76794	−0.217470
$163$	6.12247	0.479549	0.239774	−	0.970829i	$-0.422927\pi$
$163$	6.12247	0.479549	0.239774	+	0.970829i	$0.422927\pi$
$164$	34.1799	2.66900
$165$	6.57288	0.511698
$166$	−2.25262	−0.174837
$167$	−8.29377	−0.641791	−0.320896	−	0.947115i	$-0.603984\pi$
$167$	−8.29377	−0.641791	−0.320896	+	0.947115i	$0.603984\pi$
$168$	10.1348	0.781918
$169$	−6.76735	−0.520565
$170$	20.8684	1.60054
$171$	1.84942	0.141429
$172$	12.2394	0.933247
$173$	4.94324	0.375827	0.187914	−	0.982186i	$-0.439827\pi$
$173$	4.94324	0.375827	0.187914	+	0.982186i	$0.439827\pi$
$174$	5.81147	0.440566
$175$	−1.00000	−0.0755929
$176$	−109.961	−8.28866
$177$	−7.59151	−0.570612
$178$	−9.96259	−0.746728
$179$	11.4213	0.853671	0.426836	−	0.904329i	$-0.359628\pi$
$179$	11.4213	0.853671	0.426836	+	0.904329i	$0.359628\pi$
$180$	−5.66150	−0.421983
$181$	12.6985	0.943869	0.471935	−	0.881634i	$-0.343556\pi$
$181$	12.6985	0.943869	0.471935	+	0.881634i	$0.343556\pi$
$182$	6.91024	0.512221
$183$	−7.63889	−0.564683
$184$	10.1348	0.747148
$185$	−1.43536	−0.105530
$186$	28.4476	2.08588
$187$	−49.5551	−3.62383
$188$	0.240843	0.0175653
$189$	−1.00000	−0.0727393
$190$	5.11909	0.371378
$191$	21.8530	1.58123	0.790615	−	0.612314i	$-0.209761\pi$
$191$	21.8530	1.58123	0.790615	+	0.612314i	$0.209761\pi$
$192$	38.6093	2.78639
$193$	26.4290	1.90240	0.951199	−	0.308578i	$-0.0998532\pi$
$193$	26.4290	1.90240	0.951199	+	0.308578i	$0.0998532\pi$
$194$	−51.9247	−3.72798
$195$	−2.49653	−0.178780
$196$	5.66150	0.404393
$197$	−5.94891	−0.423842	−0.211921	−	0.977287i	$-0.567972\pi$
$197$	−5.94891	−0.423842	−0.211921	+	0.977287i	$0.567972\pi$
$198$	18.1933	1.29294
$199$	13.0831	0.927433	0.463717	−	0.885984i	$-0.346516\pi$
$199$	13.0831	0.927433	0.463717	+	0.885984i	$0.346516\pi$
$200$	−10.1348	−0.716640
$201$	3.58454	0.252834
$202$	−0.111574	−0.00785033
$203$	2.09956	0.147361
$204$	42.6839	2.98847
$205$	−6.03726	−0.421660
$206$	14.0887	0.981605
$207$	−1.00000	−0.0695048
$208$	41.7658	2.89594
$209$	−12.1560	−0.840849
$210$	−2.76794	−0.191006
$211$	4.23625	0.291636	0.145818	−	0.989311i	$-0.453419\pi$
$211$	4.23625	0.291636	0.145818	+	0.989311i	$0.453419\pi$
$212$	−5.16322	−0.354611
$213$	14.2069	0.973442
$214$	−31.8922	−2.18011
$215$	−2.16187	−0.147438
$216$	−10.1348	−0.689587
$217$	10.2775	0.697684
$218$	−28.7104	−1.94452
$219$	3.13068	0.211552
$220$	37.2123	2.50886
$221$	18.8221	1.26611
$222$	−3.97299	−0.266650
$223$	23.0574	1.54404	0.772020	−	0.635598i	$-0.219246\pi$
$223$	23.0574	1.54404	0.772020	+	0.635598i	$0.219246\pi$
$224$	26.0368	1.73966
$225$	1.00000	0.0666667
$226$	−33.6575	−2.23887
$227$	−21.4242	−1.42198	−0.710988	−	0.703204i	$-0.751752\pi$
$227$	−21.4242	−1.42198	−0.710988	+	0.703204i	$0.751752\pi$
$228$	10.4705	0.693425
$229$	−2.34849	−0.155193	−0.0775963	−	0.996985i	$-0.524725\pi$
$229$	−2.34849	−0.155193	−0.0775963	+	0.996985i	$0.524725\pi$
$230$	−2.76794	−0.182513
$231$	6.57288	0.432464
$232$	21.2787	1.39701
$233$	−19.5422	−1.28025	−0.640125	−	0.768271i	$-0.721117\pi$
$233$	−19.5422	−1.28025	−0.640125	+	0.768271i	$0.721117\pi$
$234$	−6.91024	−0.451737
$235$	−0.0425406	−0.00277504
$236$	−42.9793	−2.79771
$237$	−10.0986	−0.655972
$238$	20.8684	1.35270
$239$	12.5452	0.811482	0.405741	−	0.913988i	$-0.367013\pi$
$239$	12.5452	0.811482	0.405741	+	0.913988i	$0.367013\pi$
$240$	−16.7296	−1.07989
$241$	−25.8404	−1.66453	−0.832264	−	0.554380i	$-0.812955\pi$
$241$	−25.8404	−1.66453	−0.832264	+	0.554380i	$0.812955\pi$
$242$	−89.1353	−5.72983
$243$	1.00000	0.0641500
$244$	−43.2476	−2.76864
$245$	−1.00000	−0.0638877
$246$	−16.7108	−1.06544
$247$	4.61713	0.293781
$248$	104.161	6.61422
$249$	0.813825	0.0515741
$250$	2.76794	0.175060
$251$	25.8124	1.62926	0.814632	−	0.579978i	$-0.196939\pi$
$251$	25.8124	1.62926	0.814632	+	0.579978i	$0.196939\pi$
$252$	−5.66150	−0.356641
$253$	6.57288	0.413233
$254$	18.7480	1.17636
$255$	−7.53933	−0.472131
$256$	74.4497	4.65310
$257$	−3.29760	−0.205699	−0.102849	−	0.994697i	$-0.532796\pi$
$257$	−3.29760	−0.205699	−0.102849	+	0.994697i	$0.532796\pi$
$258$	−5.98393	−0.372543
$259$	−1.43536	−0.0891890
$260$	−14.1341	−0.876559
$261$	−2.09956	−0.129960
$262$	42.7179	2.63912
$263$	1.20646	0.0743938	0.0371969	−	0.999308i	$-0.488157\pi$
$263$	1.20646	0.0743938	0.0371969	+	0.999308i	$0.488157\pi$
$264$	66.6149	4.09986
$265$	0.911988	0.0560230
$266$	5.11909	0.313871
$267$	3.59928	0.220272
$268$	20.2939	1.23965
$269$	5.44946	0.332259	0.166130	−	0.986104i	$-0.446873\pi$
$269$	5.44946	0.332259	0.166130	+	0.986104i	$0.446873\pi$
$270$	2.76794	0.168452
$271$	6.72789	0.408690	0.204345	−	0.978899i	$-0.434494\pi$
$271$	6.72789	0.408690	0.204345	+	0.978899i	$0.434494\pi$
$272$	126.130	7.64774
$273$	−2.49653	−0.151097
$274$	−59.7930	−3.61223
$275$	−6.57288	−0.396360
$276$	−5.66150	−0.340782
$277$	24.9697	1.50029	0.750143	−	0.661276i	$-0.229985\pi$
$277$	24.9697	1.50029	0.750143	+	0.661276i	$0.229985\pi$
$278$	−17.7603	−1.06519
$279$	−10.2775	−0.615299
$280$	−10.1348	−0.605671
$281$	−12.7752	−0.762104	−0.381052	−	0.924554i	$-0.624438\pi$
$281$	−12.7752	−0.762104	−0.381052	+	0.924554i	$0.624438\pi$
$282$	−0.117750	−0.00701190
$283$	11.1065	0.660213	0.330107	−	0.943944i	$-0.392915\pi$
$283$	11.1065	0.660213	0.330107	+	0.943944i	$0.392915\pi$
$284$	80.4325	4.77279
$285$	−1.84942	−0.109550
$286$	45.4202	2.68575
$287$	−6.03726	−0.356368
$288$	−26.0368	−1.53424
$289$	39.8415	2.34362
$290$	−5.81147	−0.341261
$291$	18.7593	1.09969
$292$	17.7243	1.03724
$293$	15.6763	0.915818	0.457909	−	0.888999i	$-0.348599\pi$
$293$	15.6763	0.915818	0.457909	+	0.888999i	$0.348599\pi$
$294$	−2.76794	−0.161430
$295$	7.59151	0.441995
$296$	−14.5471	−0.845534
$297$	−6.57288	−0.381397
$298$	−32.4645	−1.88062
$299$	−2.49653	−0.144378
$300$	5.66150	0.326867
$301$	−2.16187	−0.124608
$302$	42.0638	2.42050
$303$	0.0403095	0.00231572
$304$	30.9400	1.77453
$305$	7.63889	0.437402
$306$	−20.8684	−1.19297
$307$	24.3219	1.38812	0.694061	−	0.719916i	$-0.255820\pi$
$307$	24.3219	1.38812	0.694061	+	0.719916i	$0.255820\pi$
$308$	37.2123	2.12037
$309$	−5.08995	−0.289557
$310$	−28.4476	−1.61571
$311$	30.2730	1.71663	0.858313	−	0.513127i	$-0.171513\pi$
$311$	30.2730	1.71663	0.858313	+	0.513127i	$0.171513\pi$
$312$	−25.3018	−1.43243
$313$	−15.9200	−0.899854	−0.449927	−	0.893065i	$-0.648550\pi$
$313$	−15.9200	−0.899854	−0.449927	+	0.893065i	$0.648550\pi$
$314$	8.82024	0.497755
$315$	1.00000	0.0563436
$316$	−57.1730	−3.21623
$317$	−24.5847	−1.38081	−0.690407	−	0.723421i	$-0.742569\pi$
$317$	−24.5847	−1.38081	−0.690407	+	0.723421i	$0.742569\pi$
$318$	2.52433	0.141557
$319$	13.8002	0.772662
$320$	−38.6093	−2.15833
$321$	11.5220	0.643095
$322$	−2.76794	−0.154251
$323$	13.9434	0.775831
$324$	5.66150	0.314528
$325$	2.49653	0.138482
$326$	−16.9466	−0.938587
$327$	10.3725	0.573600
$328$	−61.1865	−3.37846
$329$	−0.0425406	−0.00234534
$330$	−18.1933	−1.00151
$331$	3.35409	0.184358	0.0921788	−	0.995742i	$-0.470617\pi$
$331$	3.35409	0.184358	0.0921788	+	0.995742i	$0.470617\pi$
$332$	4.60747	0.252868
$333$	1.43536	0.0786573
$334$	22.9567	1.25613
$335$	−3.58454	−0.195844
$336$	−16.7296	−0.912673
$337$	0.0787670	0.00429071	0.00214536	−	0.999998i	$-0.499317\pi$
$337$	0.0787670	0.00429071	0.00214536	+	0.999998i	$0.499317\pi$
$338$	18.7316	1.01887
$339$	12.1598	0.660428
$340$	−42.6839	−2.31486
$341$	67.5529	3.65820
$342$	−5.11909	−0.276809
$343$	−1.00000	−0.0539949
$344$	−21.9101	−1.18132
$345$	1.00000	0.0538382
$346$	−13.6826	−0.735581
$347$	−35.9589	−1.93038	−0.965188	−	0.261557i	$-0.915764\pi$
$347$	−35.9589	−1.93038	−0.965188	+	0.261557i	$0.915764\pi$
$348$	−11.8867	−0.637193
$349$	−17.4538	−0.934281	−0.467141	−	0.884183i	$-0.654716\pi$
$349$	−17.4538	−0.934281	−0.467141	+	0.884183i	$0.654716\pi$
$350$	2.76794	0.147953
$351$	2.49653	0.133255
$352$	171.137	9.12163
$353$	8.10861	0.431578	0.215789	−	0.976440i	$-0.430768\pi$
$353$	8.10861	0.431578	0.215789	+	0.976440i	$0.430768\pi$
$354$	21.0128	1.11682
$355$	−14.2069	−0.754025
$356$	20.3773	1.07999
$357$	−7.53933	−0.399024
$358$	−31.6136	−1.67083
$359$	23.0754	1.21787	0.608937	−	0.793218i	$-0.291596\pi$
$359$	23.0754	1.21787	0.608937	+	0.793218i	$0.291596\pi$
$360$	10.1348	0.534152
$361$	−15.5796	−0.819981
$362$	−35.1486	−1.84737
$363$	32.2027	1.69021
$364$	−14.1341	−0.740827
$365$	−3.13068	−0.163867
$366$	21.1440	1.10522
$367$	10.4332	0.544608	0.272304	−	0.962211i	$-0.412214\pi$
$367$	10.4332	0.544608	0.272304	+	0.962211i	$0.412214\pi$
$368$	−16.7296	−0.872089
$369$	6.03726	0.314287
$370$	3.97299	0.206546
$371$	0.911988	0.0473481
$372$	−58.1862	−3.01681
$373$	−14.3073	−0.740805	−0.370403	−	0.928871i	$-0.620780\pi$
$373$	−14.3073	−0.740805	−0.370403	+	0.928871i	$0.620780\pi$
$374$	137.166	7.09267
$375$	−1.00000	−0.0516398
$376$	−0.431141	−0.0222344
$377$	−5.24162	−0.269957
$378$	2.76794	0.142368
$379$	−4.81863	−0.247516	−0.123758	−	0.992312i	$-0.539495\pi$
$379$	−4.81863	−0.247516	−0.123758	+	0.992312i	$0.539495\pi$
$380$	−10.4705	−0.537125
$381$	−6.77327	−0.347005
$382$	−60.4879	−3.09483
$383$	13.0401	0.666317	0.333158	−	0.942871i	$-0.391886\pi$
$383$	13.0401	0.666317	0.333158	+	0.942871i	$0.391886\pi$
$384$	−54.7946	−2.79623
$385$	−6.57288	−0.334985
$386$	−73.1538	−3.72343
$387$	2.16187	0.109894
$388$	106.206	5.39178
$389$	17.2883	0.876553	0.438276	−	0.898840i	$-0.355589\pi$
$389$	17.2883	0.876553	0.438276	+	0.898840i	$0.355589\pi$
$390$	6.91024	0.349914
$391$	−7.53933	−0.381280
$392$	−10.1348	−0.511885
$393$	−15.4331	−0.778496
$394$	16.4662	0.829557
$395$	10.0986	0.508114
$396$	−37.2123	−1.86999
$397$	4.09644	0.205594	0.102797	−	0.994702i	$-0.467221\pi$
$397$	4.09644	0.205594	0.102797	+	0.994702i	$0.467221\pi$
$398$	−36.2131	−1.81520
$399$	−1.84942	−0.0925868
$400$	16.7296	0.836479
$401$	−19.4741	−0.972491	−0.486245	−	0.873822i	$-0.661634\pi$
$401$	−19.4741	−0.972491	−0.486245	+	0.873822i	$0.661634\pi$
$402$	−9.92179	−0.494854
$403$	−25.6581	−1.27812
$404$	0.228212	0.0113540
$405$	−1.00000	−0.0496904
$406$	−5.81147	−0.288418
$407$	−9.43445	−0.467648
$408$	−76.4097	−3.78284
$409$	23.7657	1.17514	0.587569	−	0.809174i	$-0.300085\pi$
$409$	23.7657	1.17514	0.587569	+	0.809174i	$0.300085\pi$
$410$	16.7108	0.825286
$411$	21.6020	1.06555
$412$	−28.8168	−1.41970
$413$	7.59151	0.373554
$414$	2.76794	0.136037
$415$	−0.813825	−0.0399491
$416$	−65.0017	−3.18697
$417$	6.41642	0.314213
$418$	33.6471	1.64574
$419$	−29.8737	−1.45943	−0.729713	−	0.683754i	$-0.760346\pi$
$419$	−29.8737	−1.45943	−0.729713	+	0.683754i	$0.760346\pi$
$420$	5.66150	0.276253
$421$	0.556619	0.0271279	0.0135640	−	0.999908i	$-0.495682\pi$
$421$	0.556619	0.0271279	0.0135640	+	0.999908i	$0.495682\pi$
$422$	−11.7257	−0.570798
$423$	0.0425406	0.00206839
$424$	9.24283	0.448872
$425$	7.53933	0.365711
$426$	−39.3239	−1.90525
$427$	7.63889	0.369672
$428$	65.2317	3.15310
$429$	−16.4094	−0.792252
$430$	5.98393	0.288571
$431$	−13.7401	−0.661838	−0.330919	−	0.943659i	$-0.607359\pi$
$431$	−13.7401	−0.661838	−0.330919	+	0.943659i	$0.607359\pi$
$432$	16.7296	0.804902
$433$	−20.2005	−0.970772	−0.485386	−	0.874300i	$-0.661321\pi$
$433$	−20.2005	−0.970772	−0.485386	+	0.874300i	$0.661321\pi$
$434$	−28.4476	−1.36553
$435$	2.09956	0.100666
$436$	58.7238	2.81236
$437$	−1.84942	−0.0884698
$438$	−8.66554	−0.414055
$439$	−12.9422	−0.617696	−0.308848	−	0.951111i	$-0.599943\pi$
$439$	−12.9422	−0.617696	−0.308848	+	0.951111i	$0.599943\pi$
$440$	−66.6149	−3.17574
$441$	1.00000	0.0476190
$442$	−52.0986	−2.47808
$443$	10.9817	0.521754	0.260877	−	0.965372i	$-0.415988\pi$
$443$	10.9817	0.521754	0.260877	+	0.965372i	$0.415988\pi$
$444$	8.12629	0.385657
$445$	−3.59928	−0.170622
$446$	−63.8216	−3.02204
$447$	11.7288	0.554751
$448$	−38.6093	−1.82412
$449$	7.72857	0.364734	0.182367	−	0.983231i	$-0.441624\pi$
$449$	7.72857	0.364734	0.182367	+	0.983231i	$0.441624\pi$
$450$	−2.76794	−0.130482
$451$	−39.6822	−1.86856
$452$	68.8426	3.23808
$453$	−15.1968	−0.714007
$454$	59.3010	2.78314
$455$	2.49653	0.117039
$456$	−18.7435	−0.877746
$457$	13.0179	0.608953	0.304476	−	0.952520i	$-0.401519\pi$
$457$	13.0179	0.608953	0.304476	+	0.952520i	$0.401519\pi$
$458$	6.50048	0.303748
$459$	7.53933	0.351906
$460$	5.66150	0.263969
$461$	−10.8293	−0.504369	−0.252185	−	0.967679i	$-0.581149\pi$
$461$	−10.8293	−0.504369	−0.252185	+	0.967679i	$0.581149\pi$
$462$	−18.1933	−0.846431
$463$	−13.2948	−0.617860	−0.308930	−	0.951085i	$-0.599971\pi$
$463$	−13.2948	−0.617860	−0.308930	+	0.951085i	$0.599971\pi$
$464$	−35.1248	−1.63063
$465$	10.2775	0.476609
$466$	54.0916	2.50574
$467$	26.3532	1.21948	0.609740	−	0.792602i	$-0.291274\pi$
$467$	26.3532	1.21948	0.609740	+	0.792602i	$0.291274\pi$
$468$	14.1341	0.653348
$469$	−3.58454	−0.165519
$470$	0.117750	0.00543139
$471$	−3.18657	−0.146829
$472$	76.9385	3.54138
$473$	−14.2097	−0.653363
$474$	27.9522	1.28389
$475$	1.84942	0.0848572
$476$	−42.6839	−1.95641
$477$	−0.911988	−0.0417571
$478$	−34.7244	−1.58826
$479$	−10.2773	−0.469584	−0.234792	−	0.972046i	$-0.575441\pi$
$479$	−10.2773	−0.469584	−0.234792	+	0.972046i	$0.575441\pi$
$480$	26.0368	1.18841
$481$	3.58342	0.163390
$482$	71.5247	3.25786
$483$	1.00000	0.0455016
$484$	182.316	8.28708
$485$	−18.7593	−0.851817
$486$	−2.76794	−0.125556
$487$	−3.83125	−0.173610	−0.0868052	−	0.996225i	$-0.527666\pi$
$487$	−3.83125	−0.173610	−0.0868052	+	0.996225i	$0.527666\pi$
$488$	77.4188	3.50458
$489$	6.12247	0.276868
$490$	2.76794	0.125043
$491$	29.4815	1.33048	0.665240	−	0.746629i	$-0.268329\pi$
$491$	29.4815	1.33048	0.665240	+	0.746629i	$0.268329\pi$
$492$	34.1799	1.54095
$493$	−15.8293	−0.712916
$494$	−12.7799	−0.574997
$495$	6.57288	0.295429
$496$	−171.939	−7.72027
$497$	−14.2069	−0.637268
$498$	−2.25262	−0.100942
$499$	−35.7458	−1.60020	−0.800100	−	0.599867i	$-0.795220\pi$
$499$	−35.7458	−1.60020	−0.800100	+	0.599867i	$0.795220\pi$
$500$	−5.66150	−0.253190
$501$	−8.29377	−0.370538
$502$	−71.4472	−3.18885
$503$	36.9094	1.64571	0.822854	−	0.568253i	$-0.192380\pi$
$503$	36.9094	1.64571	0.822854	+	0.568253i	$0.192380\pi$
$504$	10.1348	0.451440
$505$	−0.0403095	−0.00179375
$506$	−18.1933	−0.808793
$507$	−6.76735	−0.300549
$508$	−38.3469	−1.70137
$509$	11.1675	0.494989	0.247494	−	0.968889i	$-0.420393\pi$
$509$	11.1675	0.494989	0.247494	+	0.968889i	$0.420393\pi$
$510$	20.8684	0.924069
$511$	−3.13068	−0.138493
$512$	−96.4830	−4.26399
$513$	1.84942	0.0816539
$514$	9.12758	0.402600
$515$	5.08995	0.224290
$516$	12.2394	0.538810
$517$	−0.279614	−0.0122974
$518$	3.97299	0.174563
$519$	4.94324	0.216984
$520$	25.3018	1.10956
$521$	−2.42439	−0.106214	−0.0531072	−	0.998589i	$-0.516912\pi$
$521$	−2.42439	−0.106214	−0.0531072	+	0.998589i	$0.516912\pi$
$522$	5.81147	0.254361
$523$	17.7340	0.775454	0.387727	−	0.921774i	$-0.373260\pi$
$523$	17.7340	0.775454	0.387727	+	0.921774i	$0.373260\pi$
$524$	−87.3744	−3.81697
$525$	−1.00000	−0.0436436
$526$	−3.33942	−0.145606
$527$	−77.4857	−3.37533
$528$	−109.961	−4.78546
$529$	1.00000	0.0434783
$530$	−2.52433	−0.109650
$531$	−7.59151	−0.329443
$532$	−10.4705	−0.453953
$533$	15.0722	0.652849
$534$	−9.96259	−0.431123
$535$	−11.5220	−0.498139
$536$	−36.3286	−1.56916
$537$	11.4213	0.492867
$538$	−15.0838	−0.650308
$539$	−6.57288	−0.283114
$540$	−5.66150	−0.243632
$541$	−38.9595	−1.67500	−0.837501	−	0.546436i	$-0.815984\pi$
$541$	−38.9595	−1.67500	−0.837501	+	0.546436i	$0.815984\pi$
$542$	−18.6224	−0.799900
$543$	12.6985	0.544943
$544$	−196.300	−8.41631
$545$	−10.3725	−0.444308
$546$	6.91024	0.295731
$547$	−15.8963	−0.679677	−0.339839	−	0.940484i	$-0.610372\pi$
$547$	−15.8963	−0.679677	−0.339839	+	0.940484i	$0.610372\pi$
$548$	122.300	5.22438
$549$	−7.63889	−0.326020
$550$	18.1933	0.775767
$551$	−3.88298	−0.165420
$552$	10.1348	0.431366
$553$	10.0986	0.429434
$554$	−69.1148	−2.93640
$555$	−1.43536	−0.0609277
$556$	36.3265	1.54059
$557$	−23.4360	−0.993017	−0.496508	−	0.868032i	$-0.665385\pi$
$557$	−23.4360	−0.993017	−0.496508	+	0.868032i	$0.665385\pi$
$558$	28.4476	1.20428
$559$	5.39717	0.228276
$560$	16.7296	0.706953
$561$	−49.5551	−2.09222
$562$	35.3610	1.49161
$563$	16.9808	0.715656	0.357828	−	0.933787i	$-0.383517\pi$
$563$	16.9808	0.715656	0.357828	+	0.933787i	$0.383517\pi$
$564$	0.240843	0.0101413
$565$	−12.1598	−0.511566
$566$	−30.7422	−1.29219
$567$	−1.00000	−0.0419961
$568$	−143.985	−6.04146
$569$	22.0357	0.923786	0.461893	−	0.886936i	$-0.347170\pi$
$569$	22.0357	0.923786	0.461893	+	0.886936i	$0.347170\pi$
$570$	5.11909	0.214415
$571$	1.64991	0.0690464	0.0345232	−	0.999404i	$-0.489009\pi$
$571$	1.64991	0.0690464	0.0345232	+	0.999404i	$0.489009\pi$
$572$	−92.9016	−3.88441
$573$	21.8530	0.912923
$574$	16.7108	0.697494
$575$	−1.00000	−0.0417029
$576$	38.6093	1.60872
$577$	−5.15378	−0.214555	−0.107277	−	0.994229i	$-0.534213\pi$
$577$	−5.15378	−0.214555	−0.107277	+	0.994229i	$0.534213\pi$
$578$	−110.279	−4.58700
$579$	26.4290	1.09835
$580$	11.8867	0.493567
$581$	−0.813825	−0.0337631
$582$	−51.9247	−2.15235
$583$	5.99439	0.248262
$584$	−31.7289	−1.31295
$585$	−2.49653	−0.103219
$586$	−43.3910	−1.79247
$587$	22.5028	0.928791	0.464395	−	0.885628i	$-0.346272\pi$
$587$	22.5028	0.928791	0.464395	+	0.885628i	$0.346272\pi$
$588$	5.66150	0.233476
$589$	−19.0075	−0.783189
$590$	−21.0128	−0.865085
$591$	−5.94891	−0.244705
$592$	24.0130	0.986927
$593$	−20.6302	−0.847182	−0.423591	−	0.905853i	$-0.639231\pi$
$593$	−20.6302	−0.847182	−0.423591	+	0.905853i	$0.639231\pi$
$594$	18.1933	0.746482
$595$	7.53933	0.309082
$596$	66.4024	2.71995
$597$	13.0831	0.535454
$598$	6.91024	0.282581
$599$	−24.0982	−0.984628	−0.492314	−	0.870418i	$-0.663849\pi$
$599$	−24.0982	−0.984628	−0.492314	+	0.870418i	$0.663849\pi$
$600$	−10.1348	−0.413752
$601$	13.0049	0.530480	0.265240	−	0.964182i	$-0.414549\pi$
$601$	13.0049	0.530480	0.265240	+	0.964182i	$0.414549\pi$
$602$	5.98393	0.243887
$603$	3.58454	0.145974
$604$	−86.0365	−3.50078
$605$	−32.2027	−1.30923
$606$	−0.111574	−0.00453239
$607$	−14.5583	−0.590903	−0.295452	−	0.955358i	$-0.595470\pi$
$607$	−14.5583	−0.590903	−0.295452	+	0.955358i	$0.595470\pi$
$608$	−48.1531	−1.95286
$609$	2.09956	0.0850786
$610$	−21.1440	−0.856096
$611$	0.106204	0.00429654
$612$	42.6839	1.72539
$613$	4.18647	0.169090	0.0845450	−	0.996420i	$-0.473056\pi$
$613$	4.18647	0.169090	0.0845450	+	0.996420i	$0.473056\pi$
$614$	−67.3215	−2.71687
$615$	−6.03726	−0.243446
$616$	−66.6149	−2.68399
$617$	35.6470	1.43509	0.717546	−	0.696511i	$-0.245265\pi$
$617$	35.6470	1.43509	0.717546	+	0.696511i	$0.245265\pi$
$618$	14.0887	0.566730
$619$	−37.6931	−1.51501	−0.757507	−	0.652827i	$-0.773583\pi$
$619$	−37.6931	−1.51501	−0.757507	+	0.652827i	$0.773583\pi$
$620$	58.1862	2.33681
$621$	−1.00000	−0.0401286
$622$	−83.7939	−3.35983
$623$	−3.59928	−0.144202
$624$	41.7658	1.67197
$625$	1.00000	0.0400000
$626$	44.0658	1.76122
$627$	−12.1560	−0.485465
$628$	−18.0408	−0.719905
$629$	10.8217	0.431488
$630$	−2.76794	−0.110277
$631$	40.9177	1.62891	0.814454	−	0.580228i	$-0.197037\pi$
$631$	40.9177	1.62891	0.814454	+	0.580228i	$0.197037\pi$
$632$	102.347	4.07115
$633$	4.23625	0.168376
$634$	68.0490	2.70257
$635$	6.77327	0.268789
$636$	−5.16322	−0.204735
$637$	2.49653	0.0989160
$638$	−38.1981	−1.51228
$639$	14.2069	0.562017
$640$	54.7946	2.16595
$641$	33.5438	1.32490	0.662451	−	0.749105i	$-0.269516\pi$
$641$	33.5438	1.32490	0.662451	+	0.749105i	$0.269516\pi$
$642$	−31.8922	−1.25868
$643$	33.5936	1.32480	0.662402	−	0.749149i	$-0.269537\pi$
$643$	33.5936	1.32480	0.662402	+	0.749149i	$0.269537\pi$
$644$	5.66150	0.223094
$645$	−2.16187	−0.0851235
$646$	−38.5945	−1.51848
$647$	−25.2775	−0.993761	−0.496880	−	0.867819i	$-0.665521\pi$
$647$	−25.2775	−0.993761	−0.496880	+	0.867819i	$0.665521\pi$
$648$	−10.1348	−0.398133
$649$	49.8980	1.95867
$650$	−6.91024	−0.271042
$651$	10.2775	0.402808
$652$	34.6623	1.35748
$653$	8.29026	0.324423	0.162212	−	0.986756i	$-0.448137\pi$
$653$	8.29026	0.324423	0.162212	+	0.986756i	$0.448137\pi$
$654$	−28.7104	−1.12267
$655$	15.4331	0.603020
$656$	101.001	3.94342
$657$	3.13068	0.122139
$658$	0.117750	0.00459037
$659$	2.76672	0.107776	0.0538881	−	0.998547i	$-0.482839\pi$
$659$	2.76672	0.107776	0.0538881	+	0.998547i	$0.482839\pi$
$660$	37.2123	1.44849
$661$	−16.8894	−0.656922	−0.328461	−	0.944517i	$-0.606530\pi$
$661$	−16.8894	−0.656922	−0.328461	+	0.944517i	$0.606530\pi$
$662$	−9.28393	−0.360830
$663$	18.8221	0.730992
$664$	−8.24796	−0.320083
$665$	1.84942	0.0717175
$666$	−3.97299	−0.153950
$667$	2.09956	0.0812954
$668$	−46.9552	−1.81675
$669$	23.0574	0.891452
$670$	9.92179	0.383312
$671$	50.2095	1.93832
$672$	26.0368	1.00439
$673$	−37.6808	−1.45249	−0.726244	−	0.687437i	$-0.758736\pi$
$673$	−37.6808	−1.45249	−0.726244	+	0.687437i	$0.758736\pi$
$674$	−0.218022	−0.00839791
$675$	1.00000	0.0384900
$676$	−38.3133	−1.47359
$677$	−17.7477	−0.682099	−0.341049	−	0.940045i	$-0.610782\pi$
$677$	−17.7477	−0.682099	−0.341049	+	0.940045i	$0.610782\pi$
$678$	−33.6575	−1.29261
$679$	−18.7593	−0.719916
$680$	76.4097	2.93018
$681$	−21.4242	−0.820979
$682$	−186.983	−7.15993
$683$	0.765559	0.0292933	0.0146466	−	0.999893i	$-0.495338\pi$
$683$	0.765559	0.0292933	0.0146466	+	0.999893i	$0.495338\pi$
$684$	10.4705	0.400349
$685$	−21.6020	−0.825369
$686$	2.76794	0.105680
$687$	−2.34849	−0.0896005
$688$	36.1671	1.37886
$689$	−2.27680	−0.0867393
$690$	−2.76794	−0.105374
$691$	21.1362	0.804057	0.402029	−	0.915627i	$-0.368305\pi$
$691$	21.1362	0.804057	0.402029	+	0.915627i	$0.368305\pi$
$692$	27.9861	1.06387
$693$	6.57288	0.249683
$694$	99.5322	3.77819
$695$	−6.41642	−0.243389
$696$	21.2787	0.806567
$697$	45.5169	1.72407
$698$	48.3111	1.82860
$699$	−19.5422	−0.739152
$700$	−5.66150	−0.213985
$701$	0.161875	0.00611393	0.00305696	−	0.999995i	$-0.499027\pi$
$701$	0.161875	0.00611393	0.00305696	+	0.999995i	$0.499027\pi$
$702$	−6.91024	−0.260810
$703$	2.65459	0.100120
$704$	−253.774	−9.56448
$705$	−0.0425406	−0.00160217
$706$	−22.4442	−0.844697
$707$	−0.0403095	−0.00151599
$708$	−42.9793	−1.61526
$709$	−33.6654	−1.26433	−0.632165	−	0.774834i	$-0.717834\pi$
$709$	−33.6654	−1.26433	−0.632165	+	0.774834i	$0.717834\pi$
$710$	39.3239	1.47580
$711$	−10.0986	−0.378726
$712$	−36.4780	−1.36707
$713$	10.2775	0.384896
$714$	20.8684	0.780981
$715$	16.4094	0.613676
$716$	64.6619	2.41653
$717$	12.5452	0.468510
$718$	−63.8714	−2.38366
$719$	16.1536	0.602426	0.301213	−	0.953557i	$-0.402609\pi$
$719$	16.1536	0.602426	0.301213	+	0.953557i	$0.402609\pi$
$720$	−16.7296	−0.623474
$721$	5.08995	0.189560
$722$	43.1235	1.60489
$723$	−25.8404	−0.961015
$724$	71.8923	2.67186
$725$	−2.09956	−0.0779758
$726$	−89.1353	−3.30812
$727$	10.0550	0.372921	0.186461	−	0.982462i	$-0.440298\pi$
$727$	10.0550	0.372921	0.186461	+	0.982462i	$0.440298\pi$
$728$	25.3018	0.937749
$729$	1.00000	0.0370370
$730$	8.66554	0.320726
$731$	16.2990	0.602842
$732$	−43.2476	−1.59848
$733$	−37.7617	−1.39476	−0.697381	−	0.716701i	$-0.745651\pi$
$733$	−37.7617	−1.39476	−0.697381	+	0.716701i	$0.745651\pi$
$734$	−28.8785	−1.06592
$735$	−1.00000	−0.0368856
$736$	26.0368	0.959731
$737$	−23.5607	−0.867871
$738$	−16.7108	−0.615132
$739$	−34.4024	−1.26551	−0.632756	−	0.774351i	$-0.718076\pi$
$739$	−34.4024	−1.26551	−0.632756	+	0.774351i	$0.718076\pi$
$740$	−8.12629	−0.298728
$741$	4.61713	0.169614
$742$	−2.52433	−0.0926711
$743$	−20.3187	−0.745419	−0.372710	−	0.927948i	$-0.621571\pi$
$743$	−20.3187	−0.745419	−0.372710	+	0.927948i	$0.621571\pi$
$744$	104.161	3.81872
$745$	−11.7288	−0.429709
$746$	39.6018	1.44993
$747$	0.813825	0.0297763
$748$	−280.556	−10.2581
$749$	−11.5220	−0.421004
$750$	2.76794	0.101071
$751$	40.8153	1.48937	0.744686	−	0.667415i	$-0.232599\pi$
$751$	40.8153	1.48937	0.744686	+	0.667415i	$0.232599\pi$
$752$	0.711686	0.0259525
$753$	25.8124	0.940656
$754$	14.5085	0.528368
$755$	15.1968	0.553067
$756$	−5.66150	−0.205907
$757$	12.2580	0.445525	0.222763	−	0.974873i	$-0.428493\pi$
$757$	12.2580	0.445525	0.222763	+	0.974873i	$0.428493\pi$
$758$	13.3377	0.484446
$759$	6.57288	0.238580
$760$	18.7435	0.679899
$761$	−2.59013	−0.0938923	−0.0469462	−	0.998897i	$-0.514949\pi$
$761$	−2.59013	−0.0938923	−0.0469462	+	0.998897i	$0.514949\pi$
$762$	18.7480	0.679169
$763$	−10.3725	−0.375509
$764$	123.721	4.47606
$765$	−7.53933	−0.272585
$766$	−36.0942	−1.30414
$767$	−18.9524	−0.684332
$768$	74.4497	2.68647
$769$	48.5443	1.75055	0.875277	−	0.483623i	$-0.160679\pi$
$769$	48.5443	1.75055	0.875277	+	0.483623i	$0.160679\pi$
$770$	18.1933	0.655643
$771$	−3.29760	−0.118760
$772$	149.628	5.38521
$773$	30.8534	1.10972	0.554859	−	0.831944i	$-0.312772\pi$
$773$	30.8534	1.10972	0.554859	+	0.831944i	$0.312772\pi$
$774$	−5.98393	−0.215088
$775$	−10.2775	−0.369180
$776$	−190.122	−6.82499
$777$	−1.43536	−0.0514933
$778$	−47.8531	−1.71561
$779$	11.1654	0.400043
$780$	−14.1341	−0.506082
$781$	−93.3804	−3.34141
$782$	20.8684	0.746253
$783$	−2.09956	−0.0750323
$784$	16.7296	0.597485
$785$	3.18657	0.113734
$786$	42.7179	1.52370
$787$	16.1445	0.575488	0.287744	−	0.957707i	$-0.407095\pi$
$787$	16.1445	0.575488	0.287744	+	0.957707i	$0.407095\pi$
$788$	−33.6798	−1.19979
$789$	1.20646	0.0429513
$790$	−27.9522	−0.994495
$791$	−12.1598	−0.432352
$792$	66.6149	2.36706
$793$	−19.0707	−0.677221
$794$	−11.3387	−0.402395
$795$	0.911988	0.0323449
$796$	74.0697	2.62533
$797$	−13.0900	−0.463672	−0.231836	−	0.972755i	$-0.574473\pi$
$797$	−13.0900	−0.463672	−0.231836	+	0.972755i	$0.574473\pi$
$798$	5.11909	0.181214
$799$	0.320728	0.0113465
$800$	−26.0368	−0.920541
$801$	3.59928	0.127174
$802$	53.9032	1.90339
$803$	−20.5776	−0.726167
$804$	20.2939	0.715709
$805$	−1.00000	−0.0352454
$806$	71.0202	2.50158
$807$	5.44946	0.191830
$808$	−0.408529	−0.0143720
$809$	−48.1903	−1.69428	−0.847141	−	0.531368i	$-0.821678\pi$
$809$	−48.1903	−1.69428	−0.847141	+	0.531368i	$0.821678\pi$
$810$	2.76794	0.0972555
$811$	11.3036	0.396924	0.198462	−	0.980109i	$-0.436405\pi$
$811$	11.3036	0.396924	0.198462	+	0.980109i	$0.436405\pi$
$812$	11.8867	0.417141
$813$	6.72789	0.235957
$814$	26.1140	0.915295
$815$	−6.12247	−0.214461
$816$	126.130	4.41542
$817$	3.99821	0.139880
$818$	−65.7821	−2.30002
$819$	−2.49653	−0.0872357
$820$	−34.1799	−1.19361
$821$	15.9176	0.555527	0.277764	−	0.960649i	$-0.410407\pi$
$821$	15.9176	0.555527	0.277764	+	0.960649i	$0.410407\pi$
$822$	−59.7930	−2.08552
$823$	−15.0971	−0.526251	−0.263126	−	0.964762i	$-0.584753\pi$
$823$	−15.0971	−0.526251	−0.263126	+	0.964762i	$0.584753\pi$
$824$	51.5857	1.79707
$825$	−6.57288	−0.228838
$826$	−21.0128	−0.731130
$827$	1.57621	0.0548101	0.0274050	−	0.999624i	$-0.491276\pi$
$827$	1.57621	0.0548101	0.0274050	+	0.999624i	$0.491276\pi$
$828$	−5.66150	−0.196751
$829$	−46.1227	−1.60191	−0.800953	−	0.598727i	$-0.795673\pi$
$829$	−46.1227	−1.60191	−0.800953	+	0.598727i	$0.795673\pi$
$830$	2.25262	0.0781896
$831$	24.9697	0.866190
$832$	96.3892	3.34169
$833$	7.53933	0.261222
$834$	−17.7603	−0.614988
$835$	8.29377	0.287018
$836$	−68.8213	−2.38023
$837$	−10.2775	−0.355243
$838$	82.6886	2.85643
$839$	37.4722	1.29368	0.646842	−	0.762624i	$-0.276089\pi$
$839$	37.4722	1.29368	0.646842	+	0.762624i	$0.276089\pi$
$840$	−10.1348	−0.349684
$841$	−24.5918	−0.847994
$842$	−1.54069	−0.0530956
$843$	−12.7752	−0.440001
$844$	23.9835	0.825548
$845$	6.76735	0.232804
$846$	−0.117750	−0.00404832
$847$	−32.2027	−1.10650
$848$	−15.2572	−0.523933
$849$	11.1065	0.381174
$850$	−20.8684	−0.715781
$851$	−1.43536	−0.0492035
$852$	80.4325	2.75557
$853$	10.5068	0.359745	0.179872	−	0.983690i	$-0.442432\pi$
$853$	10.5068	0.359745	0.179872	+	0.983690i	$0.442432\pi$
$854$	−21.1440	−0.723533
$855$	−1.84942	−0.0632489
$856$	−116.773	−3.99123
$857$	−1.30404	−0.0445450	−0.0222725	−	0.999752i	$-0.507090\pi$
$857$	−1.30404	−0.0445450	−0.0222725	+	0.999752i	$0.507090\pi$
$858$	45.4202	1.55062
$859$	31.6095	1.07850	0.539252	−	0.842145i	$-0.318707\pi$
$859$	31.6095	1.07850	0.539252	+	0.842145i	$0.318707\pi$
$860$	−12.2394	−0.417361
$861$	−6.03726	−0.205749
$862$	38.0319	1.29537
$863$	7.76336	0.264268	0.132134	−	0.991232i	$-0.457817\pi$
$863$	7.76336	0.264268	0.132134	+	0.991232i	$0.457817\pi$
$864$	−26.0368	−0.885791
$865$	−4.94324	−0.168075
$866$	55.9137	1.90002
$867$	39.8415	1.35309
$868$	58.1862	1.97497
$869$	66.3766	2.25167
$870$	−5.81147	−0.197027
$871$	8.94890	0.303222
$872$	−105.123	−3.55992
$873$	18.7593	0.634907
$874$	5.11909	0.173156
$875$	1.00000	0.0338062
$876$	17.7243	0.598850
$877$	13.9749	0.471899	0.235949	−	0.971765i	$-0.424180\pi$
$877$	13.9749	0.471899	0.235949	+	0.971765i	$0.424180\pi$
$878$	35.8231	1.20897
$879$	15.6763	0.528748
$880$	109.961	3.70680
$881$	48.9169	1.64805	0.824027	−	0.566551i	$-0.191723\pi$
$881$	48.9169	1.64805	0.824027	+	0.566551i	$0.191723\pi$
$882$	−2.76794	−0.0932014
$883$	17.4977	0.588846	0.294423	−	0.955675i	$-0.404873\pi$
$883$	17.4977	0.588846	0.294423	+	0.955675i	$0.404873\pi$
$884$	106.562	3.58405
$885$	7.59151	0.255186
$886$	−30.3966	−1.02119
$887$	−26.8435	−0.901318	−0.450659	−	0.892696i	$-0.648811\pi$
$887$	−26.8435	−0.901318	−0.450659	+	0.892696i	$0.648811\pi$
$888$	−14.5471	−0.488169
$889$	6.77327	0.227168
$890$	9.96259	0.333947
$891$	−6.57288	−0.220200
$892$	130.540	4.37079
$893$	0.0786754	0.00263277
$894$	−32.4645	−1.08578
$895$	−11.4213	−0.381773
$896$	54.7946	1.83056
$897$	−2.49653	−0.0833566
$898$	−21.3922	−0.713868
$899$	21.5783	0.719677
$900$	5.66150	0.188717
$901$	−6.87578	−0.229065
$902$	109.838	3.65720
$903$	−2.16187	−0.0719425
$904$	−123.237	−4.09880
$905$	−12.6985	−0.422111
$906$	42.0638	1.39748
$907$	−24.3665	−0.809077	−0.404538	−	0.914521i	$-0.632568\pi$
$907$	−24.3665	−0.809077	−0.404538	+	0.914521i	$0.632568\pi$
$908$	−121.293	−4.02526
$909$	0.0403095	0.00133698
$910$	−6.91024	−0.229072
$911$	−9.10011	−0.301500	−0.150750	−	0.988572i	$-0.548169\pi$
$911$	−9.10011	−0.301500	−0.150750	+	0.988572i	$0.548169\pi$
$912$	30.9400	1.02453
$913$	−5.34917	−0.177032
$914$	−36.0328	−1.19186
$915$	7.63889	0.252534
$916$	−13.2960	−0.439311
$917$	15.4331	0.509645
$918$	−20.8684	−0.688761
$919$	−14.6107	−0.481963	−0.240982	−	0.970530i	$-0.577469\pi$
$919$	−14.6107	−0.481963	−0.240982	+	0.970530i	$0.577469\pi$
$920$	−10.1348	−0.334135
$921$	24.3219	0.801433
$922$	29.9748	0.987167
$923$	35.4680	1.16744
$924$	37.2123	1.22420
$925$	1.43536	0.0471944
$926$	36.7991	1.20929
$927$	−5.08995	−0.167176
$928$	54.6660	1.79450
$929$	−45.0067	−1.47662	−0.738310	−	0.674461i	$-0.764376\pi$
$929$	−45.0067	−1.47662	−0.738310	+	0.674461i	$0.764376\pi$
$930$	−28.4476	−0.932833
$931$	1.84942	0.0606123
$932$	−110.638	−3.62407
$933$	30.2730	0.991094
$934$	−72.9440	−2.38680
$935$	49.5551	1.62063
$936$	−25.3018	−0.827017
$937$	−37.3243	−1.21933	−0.609667	−	0.792658i	$-0.708697\pi$
$937$	−37.3243	−1.21933	−0.609667	+	0.792658i	$0.708697\pi$
$938$	9.92179	0.323958
$939$	−15.9200	−0.519531
$940$	−0.240843	−0.00785545
$941$	−0.950957	−0.0310003	−0.0155002	−	0.999880i	$-0.504934\pi$
$941$	−0.950957	−0.0310003	−0.0155002	+	0.999880i	$0.504934\pi$
$942$	8.82024	0.287379
$943$	−6.03726	−0.196600
$944$	−127.003	−4.13358
$945$	1.00000	0.0325300
$946$	39.3316	1.27878
$947$	−24.3565	−0.791481	−0.395741	−	0.918362i	$-0.629512\pi$
$947$	−24.3565	−0.791481	−0.395741	+	0.918362i	$0.629512\pi$
$948$	−57.1730	−1.85689
$949$	7.81583	0.253713
$950$	−5.11909	−0.166085
$951$	−24.5847	−0.797213
$952$	76.4097	2.47645
$953$	−15.4909	−0.501800	−0.250900	−	0.968013i	$-0.580726\pi$
$953$	−15.4909	−0.501800	−0.250900	+	0.968013i	$0.580726\pi$
$954$	2.52433	0.0817282
$955$	−21.8530	−0.707147
$956$	71.0247	2.29710
$957$	13.8002	0.446096
$958$	28.4471	0.919084
$959$	−21.6020	−0.697564
$960$	−38.6093	−1.24611
$961$	74.6276	2.40734
$962$	−9.91869	−0.319791
$963$	11.5220	0.371291
$964$	−146.295	−4.71186
$965$	−26.4290	−0.850778
$966$	−2.76794	−0.0890571
$967$	3.90208	0.125483	0.0627413	−	0.998030i	$-0.480016\pi$
$967$	3.90208	0.125483	0.0627413	+	0.998030i	$0.480016\pi$
$968$	−326.369	−10.4899
$969$	13.9434	0.447926
$970$	51.9247	1.66720
$971$	−26.4962	−0.850304	−0.425152	−	0.905122i	$-0.639779\pi$
$971$	−26.4962	−0.850304	−0.425152	+	0.905122i	$0.639779\pi$
$972$	5.66150	0.181593
$973$	−6.41642	−0.205701
$974$	10.6047	0.339796
$975$	2.49653	0.0799529
$976$	−127.795	−4.09063
$977$	18.0147	0.576341	0.288170	−	0.957579i	$-0.406953\pi$
$977$	18.0147	0.576341	0.288170	+	0.957579i	$0.406953\pi$
$978$	−16.9466	−0.541893
$979$	−23.6576	−0.756101
$980$	−5.66150	−0.180850
$981$	10.3725	0.331168
$982$	−81.6030	−2.60406
$983$	38.2564	1.22019	0.610095	−	0.792329i	$-0.291131\pi$
$983$	38.2564	1.22019	0.610095	+	0.792329i	$0.291131\pi$
$984$	−61.1865	−1.95055
$985$	5.94891	0.189548
$986$	43.8146	1.39534
$987$	−0.0425406	−0.00135408
$988$	26.1399	0.831620
$989$	−2.16187	−0.0687435
$990$	−18.1933	−0.578222
$991$	51.3913	1.63250	0.816249	−	0.577700i	$-0.196050\pi$
$991$	51.3913	1.63250	0.816249	+	0.577700i	$0.196050\pi$
$992$	267.594	8.49613
$993$	3.35409	0.106439
$994$	39.3239	1.24728
$995$	−13.0831	−0.414761
$996$	4.60747	0.145993
$997$	2.23720	0.0708529	0.0354265	−	0.999372i	$-0.488721\pi$
$997$	2.23720	0.0708529	0.0354265	+	0.999372i	$0.488721\pi$
$998$	98.9422	3.13196
$999$	1.43536	0.0454128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.r.1.1	✓	7
3.2	odd	2		7245.2.a.bn.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.r.1.1	✓	7	1.1	even	1	trivial
7245.2.a.bn.1.7		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76794 q^{2} +1.00000 q^{3} +5.66150 q^{4} -1.00000 q^{5} -2.76794 q^{6} -1.00000 q^{7} -10.1348 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.76794 q^{2} +1.00000 q^{3} +5.66150 q^{4} -1.00000 q^{5} -2.76794 q^{6} -1.00000 q^{7} -10.1348 q^{8} +1.00000 q^{9} +2.76794 q^{10} -6.57288 q^{11} +5.66150 q^{12} +2.49653 q^{13} +2.76794 q^{14} -1.00000 q^{15} +16.7296 q^{16} +7.53933 q^{17} -2.76794 q^{18} +1.84942 q^{19} -5.66150 q^{20} -1.00000 q^{21} +18.1933 q^{22} -1.00000 q^{23} -10.1348 q^{24} +1.00000 q^{25} -6.91024 q^{26} +1.00000 q^{27} -5.66150 q^{28} -2.09956 q^{29} +2.76794 q^{30} -10.2775 q^{31} -26.0368 q^{32} -6.57288 q^{33} -20.8684 q^{34} +1.00000 q^{35} +5.66150 q^{36} +1.43536 q^{37} -5.11909 q^{38} +2.49653 q^{39} +10.1348 q^{40} +6.03726 q^{41} +2.76794 q^{42} +2.16187 q^{43} -37.2123 q^{44} -1.00000 q^{45} +2.76794 q^{46} +0.0425406 q^{47} +16.7296 q^{48} +1.00000 q^{49} -2.76794 q^{50} +7.53933 q^{51} +14.1341 q^{52} -0.911988 q^{53} -2.76794 q^{54} +6.57288 q^{55} +10.1348 q^{56} +1.84942 q^{57} +5.81147 q^{58} -7.59151 q^{59} -5.66150 q^{60} -7.63889 q^{61} +28.4476 q^{62} -1.00000 q^{63} +38.6093 q^{64} -2.49653 q^{65} +18.1933 q^{66} +3.58454 q^{67} +42.6839 q^{68} -1.00000 q^{69} -2.76794 q^{70} +14.2069 q^{71} -10.1348 q^{72} +3.13068 q^{73} -3.97299 q^{74} +1.00000 q^{75} +10.4705 q^{76} +6.57288 q^{77} -6.91024 q^{78} -10.0986 q^{79} -16.7296 q^{80} +1.00000 q^{81} -16.7108 q^{82} +0.813825 q^{83} -5.66150 q^{84} -7.53933 q^{85} -5.98393 q^{86} -2.09956 q^{87} +66.6149 q^{88} +3.59928 q^{89} +2.76794 q^{90} -2.49653 q^{91} -5.66150 q^{92} -10.2775 q^{93} -0.117750 q^{94} -1.84942 q^{95} -26.0368 q^{96} +18.7593 q^{97} -2.76794 q^{98} -6.57288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 8 q^{4} - 7 q^{5} - 2 q^{6} - 7 q^{7} - 6 q^{8} + 7 q^{9} + 2 q^{10} - 2 q^{11} + 8 q^{12} + 6 q^{13} + 2 q^{14} - 7 q^{15} + 10 q^{16} + 14 q^{17} - 2 q^{18} + 6 q^{19} - 8 q^{20} - 7 q^{21} + 28 q^{22} - 7 q^{23} - 6 q^{24} + 7 q^{25} + 5 q^{26} + 7 q^{27} - 8 q^{28} - 4 q^{29} + 2 q^{30} + 4 q^{31} - 19 q^{32} - 2 q^{33} - 7 q^{34} + 7 q^{35} + 8 q^{36} + 18 q^{37} + 22 q^{38} + 6 q^{39} + 6 q^{40} + 10 q^{41} + 2 q^{42} + 26 q^{43} - 29 q^{44} - 7 q^{45} + 2 q^{46} - 4 q^{47} + 10 q^{48} + 7 q^{49} - 2 q^{50} + 14 q^{51} + 18 q^{52} + 2 q^{53} - 2 q^{54} + 2 q^{55} + 6 q^{56} + 6 q^{57} + 12 q^{58} + 6 q^{59} - 8 q^{60} - 4 q^{61} + 4 q^{62} - 7 q^{63} + 38 q^{64} - 6 q^{65} + 28 q^{66} + 22 q^{67} + 52 q^{68} - 7 q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} + 24 q^{73} + 17 q^{74} + 7 q^{75} + 15 q^{76} + 2 q^{77} + 5 q^{78} + 2 q^{79} - 10 q^{80} + 7 q^{81} - 10 q^{82} + 26 q^{83} - 8 q^{84} - 14 q^{85} - 22 q^{86} - 4 q^{87} + 79 q^{88} + 22 q^{89} + 2 q^{90} - 6 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} - 6 q^{95} - 19 q^{96} + 44 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 8 * q^4 - 7 * q^5 - 2 * q^6 - 7 * q^7 - 6 * q^8 + 7 * q^9 + 2 * q^10 - 2 * q^11 + 8 * q^12 + 6 * q^13 + 2 * q^14 - 7 * q^15 + 10 * q^16 + 14 * q^17 - 2 * q^18 + 6 * q^19 - 8 * q^20 - 7 * q^21 + 28 * q^22 - 7 * q^23 - 6 * q^24 + 7 * q^25 + 5 * q^26 + 7 * q^27 - 8 * q^28 - 4 * q^29 + 2 * q^30 + 4 * q^31 - 19 * q^32 - 2 * q^33 - 7 * q^34 + 7 * q^35 + 8 * q^36 + 18 * q^37 + 22 * q^38 + 6 * q^39 + 6 * q^40 + 10 * q^41 + 2 * q^42 + 26 * q^43 - 29 * q^44 - 7 * q^45 + 2 * q^46 - 4 * q^47 + 10 * q^48 + 7 * q^49 - 2 * q^50 + 14 * q^51 + 18 * q^52 + 2 * q^53 - 2 * q^54 + 2 * q^55 + 6 * q^56 + 6 * q^57 + 12 * q^58 + 6 * q^59 - 8 * q^60 - 4 * q^61 + 4 * q^62 - 7 * q^63 + 38 * q^64 - 6 * q^65 + 28 * q^66 + 22 * q^67 + 52 * q^68 - 7 * q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 + 24 * q^73 + 17 * q^74 + 7 * q^75 + 15 * q^76 + 2 * q^77 + 5 * q^78 + 2 * q^79 - 10 * q^80 + 7 * q^81 - 10 * q^82 + 26 * q^83 - 8 * q^84 - 14 * q^85 - 22 * q^86 - 4 * q^87 + 79 * q^88 + 22 * q^89 + 2 * q^90 - 6 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 - 6 * q^95 - 19 * q^96 + 44 * q^97 - 2 * q^98 - 2 * q^99

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