LMFDB - Embedded newform 4235.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} -1.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} -0.585786 q^{6} +1.00000 q^{7} -1.58579 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.414214 q^{2} -1.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} -0.585786 q^{6} +1.00000 q^{7} -1.58579 q^{8} -1.00000 q^{9} -0.414214 q^{10} +2.58579 q^{12} -3.41421 q^{13} +0.414214 q^{14} +1.41421 q^{15} +3.00000 q^{16} +0.585786 q^{17} -0.414214 q^{18} +1.82843 q^{20} -1.41421 q^{21} +8.82843 q^{23} +2.24264 q^{24} +1.00000 q^{25} -1.41421 q^{26} +5.65685 q^{27} -1.82843 q^{28} +0.828427 q^{29} +0.585786 q^{30} -1.75736 q^{31} +4.41421 q^{32} +0.242641 q^{34} -1.00000 q^{35} +1.82843 q^{36} +1.17157 q^{37} +4.82843 q^{39} +1.58579 q^{40} -4.24264 q^{41} -0.585786 q^{42} -6.00000 q^{43} +1.00000 q^{45} +3.65685 q^{46} +1.41421 q^{47} -4.24264 q^{48} +1.00000 q^{49} +0.414214 q^{50} -0.828427 q^{51} +6.24264 q^{52} +2.82843 q^{53} +2.34315 q^{54} -1.58579 q^{56} +0.343146 q^{58} -7.89949 q^{59} -2.58579 q^{60} +13.8995 q^{61} -0.727922 q^{62} -1.00000 q^{63} -4.17157 q^{64} +3.41421 q^{65} +6.48528 q^{67} -1.07107 q^{68} -12.4853 q^{69} -0.414214 q^{70} +9.17157 q^{71} +1.58579 q^{72} +5.07107 q^{73} +0.485281 q^{74} -1.41421 q^{75} +2.00000 q^{78} -6.48528 q^{79} -3.00000 q^{80} -5.00000 q^{81} -1.75736 q^{82} -12.0000 q^{83} +2.58579 q^{84} -0.585786 q^{85} -2.48528 q^{86} -1.17157 q^{87} +0.828427 q^{89} +0.414214 q^{90} -3.41421 q^{91} -16.1421 q^{92} +2.48528 q^{93} +0.585786 q^{94} -6.24264 q^{96} +9.31371 q^{97} +0.414214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 2 q^{9} + 2 q^{10} + 8 q^{12} - 4 q^{13} - 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{20} + 12 q^{23} - 4 q^{24} + 2 q^{25} + 2 q^{28} - 4 q^{29} + 4 q^{30} - 12 q^{31} + 6 q^{32} - 8 q^{34} - 2 q^{35} - 2 q^{36} + 8 q^{37} + 4 q^{39} + 6 q^{40} - 4 q^{42} - 12 q^{43} + 2 q^{45} - 4 q^{46} + 2 q^{49} - 2 q^{50} + 4 q^{51} + 4 q^{52} + 16 q^{54} - 6 q^{56} + 12 q^{58} + 4 q^{59} - 8 q^{60} + 8 q^{61} + 24 q^{62} - 2 q^{63} - 14 q^{64} + 4 q^{65} - 4 q^{67} + 12 q^{68} - 8 q^{69} + 2 q^{70} + 24 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} + 4 q^{78} + 4 q^{79} - 6 q^{80} - 10 q^{81} - 12 q^{82} - 24 q^{83} + 8 q^{84} - 4 q^{85} + 12 q^{86} - 8 q^{87} - 4 q^{89} - 2 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 4 q^{94} - 4 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 2 * q^9 + 2 * q^10 + 8 * q^12 - 4 * q^13 - 2 * q^14 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^20 + 12 * q^23 - 4 * q^24 + 2 * q^25 + 2 * q^28 - 4 * q^29 + 4 * q^30 - 12 * q^31 + 6 * q^32 - 8 * q^34 - 2 * q^35 - 2 * q^36 + 8 * q^37 + 4 * q^39 + 6 * q^40 - 4 * q^42 - 12 * q^43 + 2 * q^45 - 4 * q^46 + 2 * q^49 - 2 * q^50 + 4 * q^51 + 4 * q^52 + 16 * q^54 - 6 * q^56 + 12 * q^58 + 4 * q^59 - 8 * q^60 + 8 * q^61 + 24 * q^62 - 2 * q^63 - 14 * q^64 + 4 * q^65 - 4 * q^67 + 12 * q^68 - 8 * q^69 + 2 * q^70 + 24 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 + 4 * q^78 + 4 * q^79 - 6 * q^80 - 10 * q^81 - 12 * q^82 - 24 * q^83 + 8 * q^84 - 4 * q^85 + 12 * q^86 - 8 * q^87 - 4 * q^89 - 2 * q^90 - 4 * q^91 - 4 * q^92 - 12 * q^93 + 4 * q^94 - 4 * q^96 - 4 * q^97 - 2 * q^98

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 $

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	−1.41421	−0.816497	−0.408248	−	0.912871i	$-0.633860\pi$
$3$	−1.41421	−0.816497	−0.408248	+	0.912871i	$0.633860\pi$
$4$	−1.82843	−0.914214
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.585786	−0.239146
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.58579	−0.560660
$9$	−1.00000	−0.333333
$10$	−0.414214	−0.130986
$11$	0	0
$11$	0	0
$12$	2.58579	0.746452
$13$	−3.41421	−0.946932	−0.473466	−	0.880812i	$-0.656997\pi$
$13$	−3.41421	−0.946932	−0.473466	+	0.880812i	$0.656997\pi$
$14$	0.414214	0.110703
$15$	1.41421	0.365148
$16$	3.00000	0.750000
$17$	0.585786	0.142074	0.0710370	−	0.997474i	$-0.477369\pi$
$17$	0.585786	0.142074	0.0710370	+	0.997474i	$0.477369\pi$
$18$	−0.414214	−0.0976311
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	1.82843	0.408849
$21$	−1.41421	−0.308607
$22$	0	0
$23$	8.82843	1.84085	0.920427	−	0.390914i	$-0.127841\pi$
$23$	8.82843	1.84085	0.920427	+	0.390914i	$0.127841\pi$
$24$	2.24264	0.457777
$25$	1.00000	0.200000
$26$	−1.41421	−0.277350
$27$	5.65685	1.08866
$28$	−1.82843	−0.345540
$29$	0.828427	0.153835	0.0769175	−	0.997037i	$-0.475492\pi$
$29$	0.828427	0.153835	0.0769175	+	0.997037i	$0.475492\pi$
$30$	0.585786	0.106949
$31$	−1.75736	−0.315631	−0.157816	−	0.987469i	$-0.550445\pi$
$31$	−1.75736	−0.315631	−0.157816	+	0.987469i	$0.550445\pi$
$32$	4.41421	0.780330
$33$	0	0
$34$	0.242641	0.0416125
$35$	−1.00000	−0.169031
$36$	1.82843	0.304738
$37$	1.17157	0.192605	0.0963027	−	0.995352i	$-0.469298\pi$
$37$	1.17157	0.192605	0.0963027	+	0.995352i	$0.469298\pi$
$38$	0	0
$39$	4.82843	0.773167
$40$	1.58579	0.250735
$41$	−4.24264	−0.662589	−0.331295	−	0.943527i	$-0.607485\pi$
$41$	−4.24264	−0.662589	−0.331295	+	0.943527i	$0.607485\pi$
$42$	−0.585786	−0.0903888
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	3.65685	0.539174
$47$	1.41421	0.206284	0.103142	−	0.994667i	$-0.467110\pi$
$47$	1.41421	0.206284	0.103142	+	0.994667i	$0.467110\pi$
$48$	−4.24264	−0.612372
$49$	1.00000	0.142857
$50$	0.414214	0.0585786
$51$	−0.828427	−0.116003
$52$	6.24264	0.865699
$53$	2.82843	0.388514	0.194257	−	0.980951i	$-0.437770\pi$
$53$	2.82843	0.388514	0.194257	+	0.980951i	$0.437770\pi$
$54$	2.34315	0.318862
$55$	0	0
$56$	−1.58579	−0.211910
$57$	0	0
$58$	0.343146	0.0450572
$59$	−7.89949	−1.02843	−0.514213	−	0.857662i	$-0.671916\pi$
$59$	−7.89949	−1.02843	−0.514213	+	0.857662i	$0.671916\pi$
$60$	−2.58579	−0.333824
$61$	13.8995	1.77965	0.889824	−	0.456304i	$-0.150827\pi$
$61$	13.8995	1.77965	0.889824	+	0.456304i	$0.150827\pi$
$62$	−0.727922	−0.0924462
$63$	−1.00000	−0.125988
$64$	−4.17157	−0.521447
$65$	3.41421	0.423481
$66$	0	0
$67$	6.48528	0.792303	0.396152	−	0.918185i	$-0.370345\pi$
$67$	6.48528	0.792303	0.396152	+	0.918185i	$0.370345\pi$
$68$	−1.07107	−0.129886
$69$	−12.4853	−1.50305
$70$	−0.414214	−0.0495080
$71$	9.17157	1.08847	0.544233	−	0.838934i	$-0.316821\pi$
$71$	9.17157	1.08847	0.544233	+	0.838934i	$0.316821\pi$
$72$	1.58579	0.186887
$73$	5.07107	0.593524	0.296762	−	0.954952i	$-0.404093\pi$
$73$	5.07107	0.593524	0.296762	+	0.954952i	$0.404093\pi$
$74$	0.485281	0.0564128
$75$	−1.41421	−0.163299
$76$	0	0
$77$	0	0
$78$	2.00000	0.226455
$79$	−6.48528	−0.729651	−0.364826	−	0.931076i	$-0.618871\pi$
$79$	−6.48528	−0.729651	−0.364826	+	0.931076i	$0.618871\pi$
$80$	−3.00000	−0.335410
$81$	−5.00000	−0.555556
$82$	−1.75736	−0.194068
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	2.58579	0.282132
$85$	−0.585786	−0.0635375
$86$	−2.48528	−0.267995
$87$	−1.17157	−0.125606
$88$	0	0
$89$	0.828427	0.0878131	0.0439065	−	0.999036i	$-0.486020\pi$
$89$	0.828427	0.0878131	0.0439065	+	0.999036i	$0.486020\pi$
$90$	0.414214	0.0436619
$91$	−3.41421	−0.357907
$92$	−16.1421	−1.68293
$93$	2.48528	0.257712
$94$	0.585786	0.0604193
$95$	0	0
$96$	−6.24264	−0.637137
$97$	9.31371	0.945664	0.472832	−	0.881153i	$-0.343232\pi$
$97$	9.31371	0.945664	0.472832	+	0.881153i	$0.343232\pi$
$98$	0.414214	0.0418419
$99$	0	0
$100$	−1.82843	−0.182843
$101$	−5.41421	−0.538734	−0.269367	−	0.963038i	$-0.586815\pi$
$101$	−5.41421	−0.538734	−0.269367	+	0.963038i	$0.586815\pi$
$102$	−0.343146	−0.0339765
$103$	−15.0711	−1.48500	−0.742498	−	0.669848i	$-0.766359\pi$
$103$	−15.0711	−1.48500	−0.742498	+	0.669848i	$0.766359\pi$
$104$	5.41421	0.530907
$105$	1.41421	0.138013
$106$	1.17157	0.113793
$107$	−19.3137	−1.86713	−0.933563	−	0.358412i	$-0.883318\pi$
$107$	−19.3137	−1.86713	−0.933563	+	0.358412i	$0.883318\pi$
$108$	−10.3431	−0.995270
$109$	4.82843	0.462479	0.231240	−	0.972897i	$-0.425722\pi$
$109$	4.82843	0.462479	0.231240	+	0.972897i	$0.425722\pi$
$110$	0	0
$111$	−1.65685	−0.157262
$112$	3.00000	0.283473
$113$	−3.65685	−0.344008	−0.172004	−	0.985096i	$-0.555024\pi$
$113$	−3.65685	−0.344008	−0.172004	+	0.985096i	$0.555024\pi$
$114$	0	0
$115$	−8.82843	−0.823255
$116$	−1.51472	−0.140638
$117$	3.41421	0.315644
$118$	−3.27208	−0.301219
$119$	0.585786	0.0536990
$120$	−2.24264	−0.204724
$121$	0	0
$122$	5.75736	0.521247
$123$	6.00000	0.541002
$124$	3.21320	0.288554
$125$	−1.00000	−0.0894427
$126$	−0.414214	−0.0369011
$127$	7.31371	0.648987	0.324493	−	0.945888i	$-0.394806\pi$
$127$	7.31371	0.648987	0.324493	+	0.945888i	$0.394806\pi$
$128$	−10.5563	−0.933058
$129$	8.48528	0.747087
$130$	1.41421	0.124035
$131$	−11.3137	−0.988483	−0.494242	−	0.869325i	$-0.664554\pi$
$131$	−11.3137	−0.988483	−0.494242	+	0.869325i	$0.664554\pi$
$132$	0	0
$133$	0	0
$134$	2.68629	0.232060
$135$	−5.65685	−0.486864
$136$	−0.928932	−0.0796553
$137$	8.48528	0.724947	0.362473	−	0.931994i	$-0.381932\pi$
$137$	8.48528	0.724947	0.362473	+	0.931994i	$0.381932\pi$
$138$	−5.17157	−0.440234
$139$	12.4853	1.05899	0.529494	−	0.848314i	$-0.322382\pi$
$139$	12.4853	1.05899	0.529494	+	0.848314i	$0.322382\pi$
$140$	1.82843	0.154530
$141$	−2.00000	−0.168430
$142$	3.79899	0.318804
$143$	0	0
$144$	−3.00000	−0.250000
$145$	−0.828427	−0.0687971
$146$	2.10051	0.173839
$147$	−1.41421	−0.116642
$148$	−2.14214	−0.176082
$149$	−11.6569	−0.954967	−0.477483	−	0.878641i	$-0.658451\pi$
$149$	−11.6569	−0.954967	−0.477483	+	0.878641i	$0.658451\pi$
$150$	−0.585786	−0.0478293
$151$	−14.4853	−1.17880	−0.589398	−	0.807843i	$-0.700635\pi$
$151$	−14.4853	−1.17880	−0.589398	+	0.807843i	$0.700635\pi$
$152$	0	0
$153$	−0.585786	−0.0473580
$154$	0	0
$155$	1.75736	0.141154
$156$	−8.82843	−0.706840
$157$	6.48528	0.517582	0.258791	−	0.965933i	$-0.416676\pi$
$157$	6.48528	0.517582	0.258791	+	0.965933i	$0.416676\pi$
$158$	−2.68629	−0.213710
$159$	−4.00000	−0.317221
$160$	−4.41421	−0.348974
$161$	8.82843	0.695778
$162$	−2.07107	−0.162718
$163$	−6.48528	−0.507966	−0.253983	−	0.967209i	$-0.581741\pi$
$163$	−6.48528	−0.507966	−0.253983	+	0.967209i	$0.581741\pi$
$164$	7.75736	0.605748
$165$	0	0
$166$	−4.97056	−0.385790
$167$	−20.4853	−1.58520	−0.792599	−	0.609743i	$-0.791273\pi$
$167$	−20.4853	−1.58520	−0.792599	+	0.609743i	$0.791273\pi$
$168$	2.24264	0.173023
$169$	−1.34315	−0.103319
$170$	−0.242641	−0.0186097
$171$	0	0
$172$	10.9706	0.836498
$173$	−2.92893	−0.222683	−0.111341	−	0.993782i	$-0.535515\pi$
$173$	−2.92893	−0.222683	−0.111341	+	0.993782i	$0.535515\pi$
$174$	−0.485281	−0.0367891
$175$	1.00000	0.0755929
$176$	0	0
$177$	11.1716	0.839707
$178$	0.343146	0.0257199
$179$	3.31371	0.247678	0.123839	−	0.992302i	$-0.460479\pi$
$179$	3.31371	0.247678	0.123839	+	0.992302i	$0.460479\pi$
$180$	−1.82843	−0.136283
$181$	−25.3137	−1.88155	−0.940777	−	0.339027i	$-0.889902\pi$
$181$	−25.3137	−1.88155	−0.940777	+	0.339027i	$0.889902\pi$
$182$	−1.41421	−0.104828
$183$	−19.6569	−1.45308
$184$	−14.0000	−1.03209
$185$	−1.17157	−0.0861358
$186$	1.02944	0.0754820
$187$	0	0
$188$	−2.58579	−0.188588
$189$	5.65685	0.411476
$190$	0	0
$191$	26.6274	1.92669	0.963346	−	0.268261i	$-0.0864491\pi$
$191$	26.6274	1.92669	0.963346	+	0.268261i	$0.0864491\pi$
$192$	5.89949	0.425759
$193$	−13.6569	−0.983042	−0.491521	−	0.870866i	$-0.663559\pi$
$193$	−13.6569	−0.983042	−0.491521	+	0.870866i	$0.663559\pi$
$194$	3.85786	0.276979
$195$	−4.82843	−0.345771
$196$	−1.82843	−0.130602
$197$	18.6274	1.32715	0.663574	−	0.748110i	$-0.269039\pi$
$197$	18.6274	1.32715	0.663574	+	0.748110i	$0.269039\pi$
$198$	0	0
$199$	19.8995	1.41064	0.705319	−	0.708890i	$-0.250804\pi$
$199$	19.8995	1.41064	0.705319	+	0.708890i	$0.250804\pi$
$200$	−1.58579	−0.112132
$201$	−9.17157	−0.646913
$202$	−2.24264	−0.157792
$203$	0.828427	0.0581442
$204$	1.51472	0.106052
$205$	4.24264	0.296319
$206$	−6.24264	−0.434945
$207$	−8.82843	−0.613618
$208$	−10.2426	−0.710199
$209$	0	0
$210$	0.585786	0.0404231
$211$	−12.9706	−0.892930	−0.446465	−	0.894801i	$-0.647317\pi$
$211$	−12.9706	−0.892930	−0.446465	+	0.894801i	$0.647317\pi$
$212$	−5.17157	−0.355185
$213$	−12.9706	−0.888728
$214$	−8.00000	−0.546869
$215$	6.00000	0.409197
$216$	−8.97056	−0.610369
$217$	−1.75736	−0.119297
$218$	2.00000	0.135457
$219$	−7.17157	−0.484610
$220$	0	0
$221$	−2.00000	−0.134535
$222$	−0.686292	−0.0460609
$223$	−14.3848	−0.963276	−0.481638	−	0.876370i	$-0.659958\pi$
$223$	−14.3848	−0.963276	−0.481638	+	0.876370i	$0.659958\pi$
$224$	4.41421	0.294937
$225$	−1.00000	−0.0666667
$226$	−1.51472	−0.100758
$227$	3.31371	0.219939	0.109969	−	0.993935i	$-0.464925\pi$
$227$	3.31371	0.219939	0.109969	+	0.993935i	$0.464925\pi$
$228$	0	0
$229$	16.1421	1.06670	0.533351	−	0.845894i	$-0.320932\pi$
$229$	16.1421	1.06670	0.533351	+	0.845894i	$0.320932\pi$
$230$	−3.65685	−0.241126
$231$	0	0
$232$	−1.31371	−0.0862492
$233$	1.85786	0.121713	0.0608564	−	0.998147i	$-0.480617\pi$
$233$	1.85786	0.121713	0.0608564	+	0.998147i	$0.480617\pi$
$234$	1.41421	0.0924500
$235$	−1.41421	−0.0922531
$236$	14.4437	0.940202
$237$	9.17157	0.595758
$238$	0.242641	0.0157281
$239$	−18.3431	−1.18652	−0.593260	−	0.805011i	$-0.702159\pi$
$239$	−18.3431	−1.18652	−0.593260	+	0.805011i	$0.702159\pi$
$240$	4.24264	0.273861
$241$	−21.2132	−1.36646	−0.683231	−	0.730202i	$-0.739426\pi$
$241$	−21.2132	−1.36646	−0.683231	+	0.730202i	$0.739426\pi$
$242$	0	0
$243$	−9.89949	−0.635053
$244$	−25.4142	−1.62698
$245$	−1.00000	−0.0638877
$246$	2.48528	0.158456
$247$	0	0
$248$	2.78680	0.176962
$249$	16.9706	1.07547
$250$	−0.414214	−0.0261972
$251$	−18.7279	−1.18210	−0.591048	−	0.806636i	$-0.701286\pi$
$251$	−18.7279	−1.18210	−0.591048	+	0.806636i	$0.701286\pi$
$252$	1.82843	0.115180
$253$	0	0
$254$	3.02944	0.190084
$255$	0.828427	0.0518781
$256$	3.97056	0.248160
$257$	−12.1421	−0.757406	−0.378703	−	0.925518i	$-0.623630\pi$
$257$	−12.1421	−0.757406	−0.378703	+	0.925518i	$0.623630\pi$
$258$	3.51472	0.218817
$259$	1.17157	0.0727980
$260$	−6.24264	−0.387152
$261$	−0.828427	−0.0512784
$262$	−4.68629	−0.289520
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	−2.82843	−0.173749
$266$	0	0
$267$	−1.17157	−0.0716991
$268$	−11.8579	−0.724334
$269$	−17.3137	−1.05564	−0.527818	−	0.849358i	$-0.676990\pi$
$269$	−17.3137	−1.05564	−0.527818	+	0.849358i	$0.676990\pi$
$270$	−2.34315	−0.142599
$271$	23.7990	1.44569	0.722843	−	0.691012i	$-0.242835\pi$
$271$	23.7990	1.44569	0.722843	+	0.691012i	$0.242835\pi$
$272$	1.75736	0.106556
$273$	4.82843	0.292230
$274$	3.51472	0.212332
$275$	0	0
$276$	22.8284	1.37411
$277$	2.34315	0.140786	0.0703930	−	0.997519i	$-0.477575\pi$
$277$	2.34315	0.140786	0.0703930	+	0.997519i	$0.477575\pi$
$278$	5.17157	0.310170
$279$	1.75736	0.105210
$280$	1.58579	0.0947689
$281$	32.8284	1.95838	0.979190	−	0.202946i	$-0.0650517\pi$
$281$	32.8284	1.95838	0.979190	+	0.202946i	$0.0650517\pi$
$282$	−0.828427	−0.0493321
$283$	13.6569	0.811816	0.405908	−	0.913914i	$-0.366955\pi$
$283$	13.6569	0.811816	0.405908	+	0.913914i	$0.366955\pi$
$284$	−16.7696	−0.995090
$285$	0	0
$286$	0	0
$287$	−4.24264	−0.250435
$288$	−4.41421	−0.260110
$289$	−16.6569	−0.979815
$290$	−0.343146	−0.0201502
$291$	−13.1716	−0.772131
$292$	−9.27208	−0.542607
$293$	−12.3848	−0.723526	−0.361763	−	0.932270i	$-0.617825\pi$
$293$	−12.3848	−0.723526	−0.361763	+	0.932270i	$0.617825\pi$
$294$	−0.585786	−0.0341638
$295$	7.89949	0.459926
$296$	−1.85786	−0.107986
$297$	0	0
$298$	−4.82843	−0.279703
$299$	−30.1421	−1.74316
$300$	2.58579	0.149290
$301$	−6.00000	−0.345834
$302$	−6.00000	−0.345261
$303$	7.65685	0.439875
$304$	0	0
$305$	−13.8995	−0.795883
$306$	−0.242641	−0.0138708
$307$	6.14214	0.350550	0.175275	−	0.984519i	$-0.443919\pi$
$307$	6.14214	0.350550	0.175275	+	0.984519i	$0.443919\pi$
$308$	0	0
$309$	21.3137	1.21249
$310$	0.727922	0.0413432
$311$	20.5858	1.16731	0.583656	−	0.812001i	$-0.301622\pi$
$311$	20.5858	1.16731	0.583656	+	0.812001i	$0.301622\pi$
$312$	−7.65685	−0.433484
$313$	−19.6569	−1.11107	−0.555536	−	0.831493i	$-0.687487\pi$
$313$	−19.6569	−1.11107	−0.555536	+	0.831493i	$0.687487\pi$
$314$	2.68629	0.151596
$315$	1.00000	0.0563436
$316$	11.8579	0.667057
$317$	−24.6274	−1.38321	−0.691607	−	0.722274i	$-0.743097\pi$
$317$	−24.6274	−1.38321	−0.691607	+	0.722274i	$0.743097\pi$
$318$	−1.65685	−0.0929118
$319$	0	0
$320$	4.17157	0.233198
$321$	27.3137	1.52450
$322$	3.65685	0.203789
$323$	0	0
$324$	9.14214	0.507896
$325$	−3.41421	−0.189386
$326$	−2.68629	−0.148780
$327$	−6.82843	−0.377613
$328$	6.72792	0.371487
$329$	1.41421	0.0779681
$330$	0	0
$331$	−25.6569	−1.41023	−0.705114	−	0.709094i	$-0.749104\pi$
$331$	−25.6569	−1.41023	−0.705114	+	0.709094i	$0.749104\pi$
$332$	21.9411	1.20418
$333$	−1.17157	−0.0642018
$334$	−8.48528	−0.464294
$335$	−6.48528	−0.354329
$336$	−4.24264	−0.231455
$337$	−20.4853	−1.11590	−0.557952	−	0.829873i	$-0.688413\pi$
$337$	−20.4853	−1.11590	−0.557952	+	0.829873i	$0.688413\pi$
$338$	−0.556349	−0.0302614
$339$	5.17157	0.280881
$340$	1.07107	0.0580868
$341$	0	0
$342$	0	0
$343$	1.00000	0.0539949
$344$	9.51472	0.512999
$345$	12.4853	0.672185
$346$	−1.21320	−0.0652222
$347$	10.9706	0.588931	0.294465	−	0.955662i	$-0.404858\pi$
$347$	10.9706	0.588931	0.294465	+	0.955662i	$0.404858\pi$
$348$	2.14214	0.114831
$349$	−16.7279	−0.895425	−0.447713	−	0.894178i	$-0.647761\pi$
$349$	−16.7279	−0.895425	−0.447713	+	0.894178i	$0.647761\pi$
$350$	0.414214	0.0221406
$351$	−19.3137	−1.03089
$352$	0	0
$353$	−20.3431	−1.08276	−0.541378	−	0.840779i	$-0.682097\pi$
$353$	−20.3431	−1.08276	−0.541378	+	0.840779i	$0.682097\pi$
$354$	4.62742	0.245944
$355$	−9.17157	−0.486777
$356$	−1.51472	−0.0802799
$357$	−0.828427	−0.0438450
$358$	1.37258	0.0725433
$359$	27.1716	1.43406	0.717030	−	0.697042i	$-0.245501\pi$
$359$	27.1716	1.43406	0.717030	+	0.697042i	$0.245501\pi$
$360$	−1.58579	−0.0835783
$361$	−19.0000	−1.00000
$362$	−10.4853	−0.551094
$363$	0	0
$364$	6.24264	0.327203
$365$	−5.07107	−0.265432
$366$	−8.14214	−0.425596
$367$	29.6985	1.55025	0.775124	−	0.631809i	$-0.217687\pi$
$367$	29.6985	1.55025	0.775124	+	0.631809i	$0.217687\pi$
$368$	26.4853	1.38064
$369$	4.24264	0.220863
$370$	−0.485281	−0.0252286
$371$	2.82843	0.146845
$372$	−4.54416	−0.235604
$373$	19.3137	1.00003	0.500013	−	0.866018i	$-0.333329\pi$
$373$	19.3137	1.00003	0.500013	+	0.866018i	$0.333329\pi$
$374$	0	0
$375$	1.41421	0.0730297
$376$	−2.24264	−0.115655
$377$	−2.82843	−0.145671
$378$	2.34315	0.120518
$379$	−29.1716	−1.49844	−0.749222	−	0.662319i	$-0.769572\pi$
$379$	−29.1716	−1.49844	−0.749222	+	0.662319i	$0.769572\pi$
$380$	0	0
$381$	−10.3431	−0.529895
$382$	11.0294	0.564315
$383$	−5.89949	−0.301450	−0.150725	−	0.988576i	$-0.548161\pi$
$383$	−5.89949	−0.301450	−0.150725	+	0.988576i	$0.548161\pi$
$384$	14.9289	0.761839
$385$	0	0
$386$	−5.65685	−0.287926
$387$	6.00000	0.304997
$388$	−17.0294	−0.864539
$389$	38.2843	1.94109	0.970545	−	0.240921i	$-0.0774494\pi$
$389$	38.2843	1.94109	0.970545	+	0.240921i	$0.0774494\pi$
$390$	−2.00000	−0.101274
$391$	5.17157	0.261538
$392$	−1.58579	−0.0800943
$393$	16.0000	0.807093
$394$	7.71573	0.388713
$395$	6.48528	0.326310
$396$	0	0
$397$	−31.1716	−1.56446	−0.782228	−	0.622992i	$-0.785917\pi$
$397$	−31.1716	−1.56446	−0.782228	+	0.622992i	$0.785917\pi$
$398$	8.24264	0.413166
$399$	0	0
$400$	3.00000	0.150000
$401$	5.31371	0.265354	0.132677	−	0.991159i	$-0.457643\pi$
$401$	5.31371	0.265354	0.132677	+	0.991159i	$0.457643\pi$
$402$	−3.79899	−0.189476
$403$	6.00000	0.298881
$404$	9.89949	0.492518
$405$	5.00000	0.248452
$406$	0.343146	0.0170300
$407$	0	0
$408$	1.31371	0.0650383
$409$	−21.2132	−1.04893	−0.524463	−	0.851433i	$-0.675734\pi$
$409$	−21.2132	−1.04893	−0.524463	+	0.851433i	$0.675734\pi$
$410$	1.75736	0.0867898
$411$	−12.0000	−0.591916
$412$	27.5563	1.35760
$413$	−7.89949	−0.388709
$414$	−3.65685	−0.179725
$415$	12.0000	0.589057
$416$	−15.0711	−0.738920
$417$	−17.6569	−0.864660
$418$	0	0
$419$	−4.10051	−0.200323	−0.100161	−	0.994971i	$-0.531936\pi$
$419$	−4.10051	−0.200323	−0.100161	+	0.994971i	$0.531936\pi$
$420$	−2.58579	−0.126173
$421$	−28.9706	−1.41194	−0.705969	−	0.708242i	$-0.749488\pi$
$421$	−28.9706	−1.41194	−0.705969	+	0.708242i	$0.749488\pi$
$422$	−5.37258	−0.261533
$423$	−1.41421	−0.0687614
$424$	−4.48528	−0.217825
$425$	0.585786	0.0284148
$426$	−5.37258	−0.260302
$427$	13.8995	0.672644
$428$	35.3137	1.70695
$429$	0	0
$430$	2.48528	0.119851
$431$	25.1127	1.20964	0.604818	−	0.796364i	$-0.293246\pi$
$431$	25.1127	1.20964	0.604818	+	0.796364i	$0.293246\pi$
$432$	16.9706	0.816497
$433$	0.142136	0.00683060	0.00341530	−	0.999994i	$-0.498913\pi$
$433$	0.142136	0.00683060	0.00341530	+	0.999994i	$0.498913\pi$
$434$	−0.727922	−0.0349414
$435$	1.17157	0.0561726
$436$	−8.82843	−0.422805
$437$	0	0
$438$	−2.97056	−0.141939
$439$	−33.4558	−1.59676	−0.798380	−	0.602154i	$-0.794309\pi$
$439$	−33.4558	−1.59676	−0.798380	+	0.602154i	$0.794309\pi$
$440$	0	0
$441$	−1.00000	−0.0476190
$442$	−0.828427	−0.0394043
$443$	−28.6274	−1.36013	−0.680065	−	0.733152i	$-0.738048\pi$
$443$	−28.6274	−1.36013	−0.680065	+	0.733152i	$0.738048\pi$
$444$	3.02944	0.143771
$445$	−0.828427	−0.0392712
$446$	−5.95837	−0.282137
$447$	16.4853	0.779727
$448$	−4.17157	−0.197088
$449$	18.3431	0.865667	0.432833	−	0.901474i	$-0.357514\pi$
$449$	18.3431	0.865667	0.432833	+	0.901474i	$0.357514\pi$
$450$	−0.414214	−0.0195262
$451$	0	0
$452$	6.68629	0.314497
$453$	20.4853	0.962482
$454$	1.37258	0.0644185
$455$	3.41421	0.160061
$456$	0	0
$457$	−32.9706	−1.54230	−0.771149	−	0.636655i	$-0.780318\pi$
$457$	−32.9706	−1.54230	−0.771149	+	0.636655i	$0.780318\pi$
$458$	6.68629	0.312430
$459$	3.31371	0.154671
$460$	16.1421	0.752631
$461$	−6.58579	−0.306731	−0.153365	−	0.988170i	$-0.549011\pi$
$461$	−6.58579	−0.306731	−0.153365	+	0.988170i	$0.549011\pi$
$462$	0	0
$463$	40.1421	1.86556	0.932782	−	0.360442i	$-0.117374\pi$
$463$	40.1421	1.86556	0.932782	+	0.360442i	$0.117374\pi$
$464$	2.48528	0.115376
$465$	−2.48528	−0.115252
$466$	0.769553	0.0356488
$467$	12.0416	0.557220	0.278610	−	0.960404i	$-0.410126\pi$
$467$	12.0416	0.557220	0.278610	+	0.960404i	$0.410126\pi$
$468$	−6.24264	−0.288566
$469$	6.48528	0.299462
$470$	−0.585786	−0.0270203
$471$	−9.17157	−0.422604
$472$	12.5269	0.576598
$473$	0	0
$474$	3.79899	0.174493
$475$	0	0
$476$	−1.07107	−0.0490923
$477$	−2.82843	−0.129505
$478$	−7.59798	−0.347524
$479$	4.97056	0.227111	0.113555	−	0.993532i	$-0.463776\pi$
$479$	4.97056	0.227111	0.113555	+	0.993532i	$0.463776\pi$
$480$	6.24264	0.284936
$481$	−4.00000	−0.182384
$482$	−8.78680	−0.400228
$483$	−12.4853	−0.568100
$484$	0	0
$485$	−9.31371	−0.422914
$486$	−4.10051	−0.186003
$487$	15.4558	0.700371	0.350186	−	0.936680i	$-0.386119\pi$
$487$	15.4558	0.700371	0.350186	+	0.936680i	$0.386119\pi$
$488$	−22.0416	−0.997778
$489$	9.17157	0.414753
$490$	−0.414214	−0.0187123
$491$	−20.1421	−0.909002	−0.454501	−	0.890746i	$-0.650182\pi$
$491$	−20.1421	−0.909002	−0.454501	+	0.890746i	$0.650182\pi$
$492$	−10.9706	−0.494591
$493$	0.485281	0.0218560
$494$	0	0
$495$	0	0
$496$	−5.27208	−0.236723
$497$	9.17157	0.411401
$498$	7.02944	0.314997
$499$	6.82843	0.305682	0.152841	−	0.988251i	$-0.451158\pi$
$499$	6.82843	0.305682	0.152841	+	0.988251i	$0.451158\pi$
$500$	1.82843	0.0817697
$501$	28.9706	1.29431
$502$	−7.75736	−0.346228
$503$	−18.3431	−0.817880	−0.408940	−	0.912561i	$-0.634102\pi$
$503$	−18.3431	−0.817880	−0.408940	+	0.912561i	$0.634102\pi$
$504$	1.58579	0.0706365
$505$	5.41421	0.240929
$506$	0	0
$507$	1.89949	0.0843595
$508$	−13.3726	−0.593312
$509$	12.8284	0.568610	0.284305	−	0.958734i	$-0.408237\pi$
$509$	12.8284	0.568610	0.284305	+	0.958734i	$0.408237\pi$
$510$	0.343146	0.0151947
$511$	5.07107	0.224331
$512$	22.7574	1.00574
$513$	0	0
$514$	−5.02944	−0.221839
$515$	15.0711	0.664111
$516$	−15.5147	−0.682997
$517$	0	0
$518$	0.485281	0.0213220
$519$	4.14214	0.181820
$520$	−5.41421	−0.237429
$521$	2.68629	0.117689	0.0588443	−	0.998267i	$-0.481258\pi$
$521$	2.68629	0.117689	0.0588443	+	0.998267i	$0.481258\pi$
$522$	−0.343146	−0.0150191
$523$	−1.17157	−0.0512293	−0.0256147	−	0.999672i	$-0.508154\pi$
$523$	−1.17157	−0.0512293	−0.0256147	+	0.999672i	$0.508154\pi$
$524$	20.6863	0.903685
$525$	−1.41421	−0.0617213
$526$	−4.97056	−0.216727
$527$	−1.02944	−0.0448430
$528$	0	0
$529$	54.9411	2.38874
$530$	−1.17157	−0.0508899
$531$	7.89949	0.342809
$532$	0	0
$533$	14.4853	0.627427
$534$	−0.485281	−0.0210002
$535$	19.3137	0.835004
$536$	−10.2843	−0.444213
$537$	−4.68629	−0.202228
$538$	−7.17157	−0.309188
$539$	0	0
$540$	10.3431	0.445098
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	9.85786	0.423432
$543$	35.7990	1.53628
$544$	2.58579	0.110865
$545$	−4.82843	−0.206827
$546$	2.00000	0.0855921
$547$	−3.02944	−0.129529	−0.0647647	−	0.997901i	$-0.520630\pi$
$547$	−3.02944	−0.129529	−0.0647647	+	0.997901i	$0.520630\pi$
$548$	−15.5147	−0.662756
$549$	−13.8995	−0.593216
$550$	0	0
$551$	0	0
$552$	19.7990	0.842701
$553$	−6.48528	−0.275782
$554$	0.970563	0.0412353
$555$	1.65685	0.0703295
$556$	−22.8284	−0.968141
$557$	−17.6569	−0.748145	−0.374072	−	0.927399i	$-0.622039\pi$
$557$	−17.6569	−0.748145	−0.374072	+	0.927399i	$0.622039\pi$
$558$	0.727922	0.0308154
$559$	20.4853	0.866435
$560$	−3.00000	−0.126773
$561$	0	0
$562$	13.5980	0.573596
$563$	19.7990	0.834428	0.417214	−	0.908808i	$-0.363007\pi$
$563$	19.7990	0.834428	0.417214	+	0.908808i	$0.363007\pi$
$564$	3.65685	0.153981
$565$	3.65685	0.153845
$566$	5.65685	0.237775
$567$	−5.00000	−0.209980
$568$	−14.5442	−0.610259
$569$	12.1421	0.509025	0.254512	−	0.967070i	$-0.418085\pi$
$569$	12.1421	0.509025	0.254512	+	0.967070i	$0.418085\pi$
$570$	0	0
$571$	36.0000	1.50655	0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000	1.50655	0.753277	+	0.657704i	$0.228472\pi$
$572$	0	0
$573$	−37.6569	−1.57314
$574$	−1.75736	−0.0733508
$575$	8.82843	0.368171
$576$	4.17157	0.173816
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	−6.89949	−0.286981
$579$	19.3137	0.802650
$580$	1.51472	0.0628953
$581$	−12.0000	−0.497844
$582$	−5.45584	−0.226152
$583$	0	0
$584$	−8.04163	−0.332765
$585$	−3.41421	−0.141160
$586$	−5.12994	−0.211916
$587$	−27.5563	−1.13737	−0.568686	−	0.822555i	$-0.692548\pi$
$587$	−27.5563	−1.13737	−0.568686	+	0.822555i	$0.692548\pi$
$588$	2.58579	0.106636
$589$	0	0
$590$	3.27208	0.134709
$591$	−26.3431	−1.08361
$592$	3.51472	0.144454
$593$	−18.7279	−0.769064	−0.384532	−	0.923112i	$-0.625637\pi$
$593$	−18.7279	−0.769064	−0.384532	+	0.923112i	$0.625637\pi$
$594$	0	0
$595$	−0.585786	−0.0240149
$596$	21.3137	0.873044
$597$	−28.1421	−1.15178
$598$	−12.4853	−0.510561
$599$	−9.85786	−0.402781	−0.201391	−	0.979511i	$-0.564546\pi$
$599$	−9.85786	−0.402781	−0.201391	+	0.979511i	$0.564546\pi$
$600$	2.24264	0.0915554
$601$	−19.2721	−0.786124	−0.393062	−	0.919512i	$-0.628584\pi$
$601$	−19.2721	−0.786124	−0.393062	+	0.919512i	$0.628584\pi$
$602$	−2.48528	−0.101293
$603$	−6.48528	−0.264101
$604$	26.4853	1.07767
$605$	0	0
$606$	3.17157	0.128836
$607$	−25.1716	−1.02168	−0.510841	−	0.859675i	$-0.670666\pi$
$607$	−25.1716	−1.02168	−0.510841	+	0.859675i	$0.670666\pi$
$608$	0	0
$609$	−1.17157	−0.0474745
$610$	−5.75736	−0.233109
$611$	−4.82843	−0.195337
$612$	1.07107	0.0432954
$613$	20.4853	0.827393	0.413696	−	0.910415i	$-0.364238\pi$
$613$	20.4853	0.827393	0.413696	+	0.910415i	$0.364238\pi$
$614$	2.54416	0.102674
$615$	−6.00000	−0.241943
$616$	0	0
$617$	−2.82843	−0.113868	−0.0569341	−	0.998378i	$-0.518132\pi$
$617$	−2.82843	−0.113868	−0.0569341	+	0.998378i	$0.518132\pi$
$618$	8.82843	0.355131
$619$	12.1005	0.486360	0.243180	−	0.969981i	$-0.421809\pi$
$619$	12.1005	0.486360	0.243180	+	0.969981i	$0.421809\pi$
$620$	−3.21320	−0.129045
$621$	49.9411	2.00407
$622$	8.52691	0.341898
$623$	0.828427	0.0331902
$624$	14.4853	0.579875
$625$	1.00000	0.0400000
$626$	−8.14214	−0.325425
$627$	0	0
$628$	−11.8579	−0.473180
$629$	0.686292	0.0273642
$630$	0.414214	0.0165027
$631$	7.02944	0.279837	0.139919	−	0.990163i	$-0.455316\pi$
$631$	7.02944	0.279837	0.139919	+	0.990163i	$0.455316\pi$
$632$	10.2843	0.409086
$633$	18.3431	0.729075
$634$	−10.2010	−0.405134
$635$	−7.31371	−0.290236
$636$	7.31371	0.290007
$637$	−3.41421	−0.135276
$638$	0	0
$639$	−9.17157	−0.362822
$640$	10.5563	0.417276
$641$	36.0000	1.42191	0.710957	−	0.703235i	$-0.248262\pi$
$641$	36.0000	1.42191	0.710957	+	0.703235i	$0.248262\pi$
$642$	11.3137	0.446516
$643$	16.2426	0.640547	0.320274	−	0.947325i	$-0.396225\pi$
$643$	16.2426	0.640547	0.320274	+	0.947325i	$0.396225\pi$
$644$	−16.1421	−0.636089
$645$	−8.48528	−0.334108
$646$	0	0
$647$	30.5858	1.20245	0.601226	−	0.799079i	$-0.294679\pi$
$647$	30.5858	1.20245	0.601226	+	0.799079i	$0.294679\pi$
$648$	7.92893	0.311478
$649$	0	0
$650$	−1.41421	−0.0554700
$651$	2.48528	0.0974059
$652$	11.8579	0.464390
$653$	−6.68629	−0.261655	−0.130827	−	0.991405i	$-0.541763\pi$
$653$	−6.68629	−0.261655	−0.130827	+	0.991405i	$0.541763\pi$
$654$	−2.82843	−0.110600
$655$	11.3137	0.442063
$656$	−12.7279	−0.496942
$657$	−5.07107	−0.197841
$658$	0.585786	0.0228363
$659$	43.4558	1.69280	0.846400	−	0.532548i	$-0.178765\pi$
$659$	43.4558	1.69280	0.846400	+	0.532548i	$0.178765\pi$
$660$	0	0
$661$	17.7990	0.692300	0.346150	−	0.938179i	$-0.387489\pi$
$661$	17.7990	0.692300	0.346150	+	0.938179i	$0.387489\pi$
$662$	−10.6274	−0.413046
$663$	2.82843	0.109847
$664$	19.0294	0.738485
$665$	0	0
$666$	−0.485281	−0.0188043
$667$	7.31371	0.283188
$668$	37.4558	1.44921
$669$	20.3431	0.786511
$670$	−2.68629	−0.103780
$671$	0	0
$672$	−6.24264	−0.240815
$673$	−11.5147	−0.443860	−0.221930	−	0.975063i	$-0.571236\pi$
$673$	−11.5147	−0.443860	−0.221930	+	0.975063i	$0.571236\pi$
$674$	−8.48528	−0.326841
$675$	5.65685	0.217732
$676$	2.45584	0.0944555
$677$	−10.4437	−0.401382	−0.200691	−	0.979655i	$-0.564319\pi$
$677$	−10.4437	−0.401382	−0.200691	+	0.979655i	$0.564319\pi$
$678$	2.14214	0.0822682
$679$	9.31371	0.357427
$680$	0.928932	0.0356229
$681$	−4.68629	−0.179579
$682$	0	0
$683$	17.3137	0.662491	0.331245	−	0.943545i	$-0.392531\pi$
$683$	17.3137	0.662491	0.331245	+	0.943545i	$0.392531\pi$
$684$	0	0
$685$	−8.48528	−0.324206
$686$	0.414214	0.0158147
$687$	−22.8284	−0.870959
$688$	−18.0000	−0.686244
$689$	−9.65685	−0.367897
$690$	5.17157	0.196878
$691$	24.5858	0.935287	0.467644	−	0.883917i	$-0.345103\pi$
$691$	24.5858	0.935287	0.467644	+	0.883917i	$0.345103\pi$
$692$	5.35534	0.203579
$693$	0	0
$694$	4.54416	0.172494
$695$	−12.4853	−0.473594
$696$	1.85786	0.0704222
$697$	−2.48528	−0.0941367
$698$	−6.92893	−0.262264
$699$	−2.62742	−0.0993780
$700$	−1.82843	−0.0691080
$701$	50.7696	1.91754	0.958770	−	0.284184i	$-0.0917226\pi$
$701$	50.7696	1.91754	0.958770	+	0.284184i	$0.0917226\pi$
$702$	−8.00000	−0.301941
$703$	0	0
$704$	0	0
$705$	2.00000	0.0753244
$706$	−8.42641	−0.317132
$707$	−5.41421	−0.203622
$708$	−20.4264	−0.767671
$709$	−32.6274	−1.22535	−0.612674	−	0.790336i	$-0.709906\pi$
$709$	−32.6274	−1.22535	−0.612674	+	0.790336i	$0.709906\pi$
$710$	−3.79899	−0.142574
$711$	6.48528	0.243217
$712$	−1.31371	−0.0492333
$713$	−15.5147	−0.581031
$714$	−0.343146	−0.0128419
$715$	0	0
$716$	−6.05887	−0.226431
$717$	25.9411	0.968789
$718$	11.2548	0.420027
$719$	36.3848	1.35692	0.678462	−	0.734636i	$-0.262647\pi$
$719$	36.3848	1.35692	0.678462	+	0.734636i	$0.262647\pi$
$720$	3.00000	0.111803
$721$	−15.0711	−0.561276
$722$	−7.87006	−0.292893
$723$	30.0000	1.11571
$724$	46.2843	1.72014
$725$	0.828427	0.0307670
$726$	0	0
$727$	−45.6985	−1.69486	−0.847431	−	0.530905i	$-0.821852\pi$
$727$	−45.6985	−1.69486	−0.847431	+	0.530905i	$0.821852\pi$
$728$	5.41421	0.200664
$729$	29.0000	1.07407
$730$	−2.10051	−0.0777432
$731$	−3.51472	−0.129997
$732$	35.9411	1.32842
$733$	−50.7279	−1.87368	−0.936839	−	0.349760i	$-0.886263\pi$
$733$	−50.7279	−1.87368	−0.936839	+	0.349760i	$0.886263\pi$
$734$	12.3015	0.454057
$735$	1.41421	0.0521641
$736$	38.9706	1.43647
$737$	0	0
$738$	1.75736	0.0646893
$739$	28.0000	1.03000	0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000	1.03000	0.514998	+	0.857191i	$0.327793\pi$
$740$	2.14214	0.0787465
$741$	0	0
$742$	1.17157	0.0430098
$743$	15.3137	0.561805	0.280903	−	0.959736i	$-0.409366\pi$
$743$	15.3137	0.561805	0.280903	+	0.959736i	$0.409366\pi$
$744$	−3.94113	−0.144489
$745$	11.6569	0.427074
$746$	8.00000	0.292901
$747$	12.0000	0.439057
$748$	0	0
$749$	−19.3137	−0.705708
$750$	0.585786	0.0213899
$751$	33.4558	1.22082	0.610411	−	0.792085i	$-0.291004\pi$
$751$	33.4558	1.22082	0.610411	+	0.792085i	$0.291004\pi$
$752$	4.24264	0.154713
$753$	26.4853	0.965177
$754$	−1.17157	−0.0426662
$755$	14.4853	0.527173
$756$	−10.3431	−0.376177
$757$	24.6274	0.895099	0.447549	−	0.894259i	$-0.352297\pi$
$757$	24.6274	0.895099	0.447549	+	0.894259i	$0.352297\pi$
$758$	−12.0833	−0.438884
$759$	0	0
$760$	0	0
$761$	2.78680	0.101021	0.0505106	−	0.998724i	$-0.483915\pi$
$761$	2.78680	0.101021	0.0505106	+	0.998724i	$0.483915\pi$
$762$	−4.28427	−0.155203
$763$	4.82843	0.174801
$764$	−48.6863	−1.76141
$765$	0.585786	0.0211792
$766$	−2.44365	−0.0882927
$767$	26.9706	0.973851
$768$	−5.61522	−0.202622
$769$	0.242641	0.00874985	0.00437492	−	0.999990i	$-0.498607\pi$
$769$	0.242641	0.00874985	0.00437492	+	0.999990i	$0.498607\pi$
$770$	0	0
$771$	17.1716	0.618419
$772$	24.9706	0.898710
$773$	−13.3137	−0.478861	−0.239430	−	0.970914i	$-0.576961\pi$
$773$	−13.3137	−0.478861	−0.239430	+	0.970914i	$0.576961\pi$
$774$	2.48528	0.0893316
$775$	−1.75736	−0.0631262
$776$	−14.7696	−0.530196
$777$	−1.65685	−0.0594393
$778$	15.8579	0.568532
$779$	0	0
$780$	8.82843	0.316108
$781$	0	0
$782$	2.14214	0.0766026
$783$	4.68629	0.167474
$784$	3.00000	0.107143
$785$	−6.48528	−0.231470
$786$	6.62742	0.236392
$787$	−45.4558	−1.62033	−0.810163	−	0.586205i	$-0.800621\pi$
$787$	−45.4558	−1.62033	−0.810163	+	0.586205i	$0.800621\pi$
$788$	−34.0589	−1.21330
$789$	16.9706	0.604168
$790$	2.68629	0.0955740
$791$	−3.65685	−0.130023
$792$	0	0
$793$	−47.4558	−1.68521
$794$	−12.9117	−0.458219
$795$	4.00000	0.141865
$796$	−36.3848	−1.28962
$797$	−40.1421	−1.42191	−0.710954	−	0.703239i	$-0.751736\pi$
$797$	−40.1421	−1.42191	−0.710954	+	0.703239i	$0.751736\pi$
$798$	0	0
$799$	0.828427	0.0293076
$800$	4.41421	0.156066
$801$	−0.828427	−0.0292710
$802$	2.20101	0.0777204
$803$	0	0
$804$	16.7696	0.591417
$805$	−8.82843	−0.311161
$806$	2.48528	0.0875403
$807$	24.4853	0.861923
$808$	8.58579	0.302047
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	2.07107	0.0727699
$811$	41.4558	1.45571	0.727856	−	0.685730i	$-0.240517\pi$
$811$	41.4558	1.45571	0.727856	+	0.685730i	$0.240517\pi$
$812$	−1.51472	−0.0531562
$813$	−33.6569	−1.18040
$814$	0	0
$815$	6.48528	0.227169
$816$	−2.48528	−0.0870023
$817$	0	0
$818$	−8.78680	−0.307223
$819$	3.41421	0.119302
$820$	−7.75736	−0.270899
$821$	−12.3431	−0.430779	−0.215389	−	0.976528i	$-0.569102\pi$
$821$	−12.3431	−0.430779	−0.215389	+	0.976528i	$0.569102\pi$
$822$	−4.97056	−0.173368
$823$	−35.9411	−1.25283	−0.626414	−	0.779490i	$-0.715478\pi$
$823$	−35.9411	−1.25283	−0.626414	+	0.779490i	$0.715478\pi$
$824$	23.8995	0.832578
$825$	0	0
$826$	−3.27208	−0.113850
$827$	−40.6274	−1.41275	−0.706377	−	0.707836i	$-0.749672\pi$
$827$	−40.6274	−1.41275	−0.706377	+	0.707836i	$0.749672\pi$
$828$	16.1421	0.560978
$829$	1.02944	0.0357538	0.0178769	−	0.999840i	$-0.494309\pi$
$829$	1.02944	0.0357538	0.0178769	+	0.999840i	$0.494309\pi$
$830$	4.97056	0.172531
$831$	−3.31371	−0.114951
$832$	14.2426	0.493775
$833$	0.585786	0.0202963
$834$	−7.31371	−0.253253
$835$	20.4853	0.708922
$836$	0	0
$837$	−9.94113	−0.343616
$838$	−1.69848	−0.0586732
$839$	−32.5858	−1.12499	−0.562493	−	0.826802i	$-0.690158\pi$
$839$	−32.5858	−1.12499	−0.562493	+	0.826802i	$0.690158\pi$
$840$	−2.24264	−0.0773785
$841$	−28.3137	−0.976335
$842$	−12.0000	−0.413547
$843$	−46.4264	−1.59901
$844$	23.7157	0.816329
$845$	1.34315	0.0462056
$846$	−0.585786	−0.0201398
$847$	0	0
$848$	8.48528	0.291386
$849$	−19.3137	−0.662845
$850$	0.242641	0.00832251
$851$	10.3431	0.354558
$852$	23.7157	0.812487
$853$	−52.6690	−1.80335	−0.901677	−	0.432410i	$-0.857663\pi$
$853$	−52.6690	−1.80335	−0.901677	+	0.432410i	$0.857663\pi$
$854$	5.75736	0.197013
$855$	0	0
$856$	30.6274	1.04682
$857$	30.0416	1.02620	0.513101	−	0.858328i	$-0.328497\pi$
$857$	30.0416	1.02620	0.513101	+	0.858328i	$0.328497\pi$
$858$	0	0
$859$	−46.0416	−1.57092	−0.785460	−	0.618912i	$-0.787574\pi$
$859$	−46.0416	−1.57092	−0.785460	+	0.618912i	$0.787574\pi$
$860$	−10.9706	−0.374093
$861$	6.00000	0.204479
$862$	10.4020	0.354294
$863$	35.6569	1.21377	0.606887	−	0.794788i	$-0.292418\pi$
$863$	35.6569	1.21377	0.606887	+	0.794788i	$0.292418\pi$
$864$	24.9706	0.849516
$865$	2.92893	0.0995867
$866$	0.0588745	0.00200064
$867$	23.5563	0.800016
$868$	3.21320	0.109063
$869$	0	0
$870$	0.485281	0.0164526
$871$	−22.1421	−0.750258
$872$	−7.65685	−0.259294
$873$	−9.31371	−0.315221
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	13.1127	0.443037
$877$	−20.4853	−0.691739	−0.345869	−	0.938283i	$-0.612416\pi$
$877$	−20.4853	−0.691739	−0.345869	+	0.938283i	$0.612416\pi$
$878$	−13.8579	−0.467680
$879$	17.5147	0.590757
$880$	0	0
$881$	−16.6274	−0.560192	−0.280096	−	0.959972i	$-0.590366\pi$
$881$	−16.6274	−0.560192	−0.280096	+	0.959972i	$0.590366\pi$
$882$	−0.414214	−0.0139473
$883$	21.3137	0.717263	0.358632	−	0.933479i	$-0.383243\pi$
$883$	21.3137	0.717263	0.358632	+	0.933479i	$0.383243\pi$
$884$	3.65685	0.122993
$885$	−11.1716	−0.375528
$886$	−11.8579	−0.398373
$887$	22.8284	0.766504	0.383252	−	0.923644i	$-0.374804\pi$
$887$	22.8284	0.766504	0.383252	+	0.923644i	$0.374804\pi$
$888$	2.62742	0.0881703
$889$	7.31371	0.245294
$890$	−0.343146	−0.0115023
$891$	0	0
$892$	26.3015	0.880640
$893$	0	0
$894$	6.82843	0.228377
$895$	−3.31371	−0.110765
$896$	−10.5563	−0.352663
$897$	42.6274	1.42329
$898$	7.59798	0.253548
$899$	−1.45584	−0.0485551
$900$	1.82843	0.0609476
$901$	1.65685	0.0551978
$902$	0	0
$903$	8.48528	0.282372
$904$	5.79899	0.192872
$905$	25.3137	0.841456
$906$	8.48528	0.281905
$907$	−48.4264	−1.60797	−0.803986	−	0.594648i	$-0.797291\pi$
$907$	−48.4264	−1.60797	−0.803986	+	0.594648i	$0.797291\pi$
$908$	−6.05887	−0.201071
$909$	5.41421	0.179578
$910$	1.41421	0.0468807
$911$	−20.4853	−0.678708	−0.339354	−	0.940659i	$-0.610208\pi$
$911$	−20.4853	−0.678708	−0.339354	+	0.940659i	$0.610208\pi$
$912$	0	0
$913$	0	0
$914$	−13.6569	−0.451729
$915$	19.6569	0.649836
$916$	−29.5147	−0.975194
$917$	−11.3137	−0.373612
$918$	1.37258	0.0453020
$919$	41.9411	1.38351	0.691755	−	0.722132i	$-0.256838\pi$
$919$	41.9411	1.38351	0.691755	+	0.722132i	$0.256838\pi$
$920$	14.0000	0.461566
$921$	−8.68629	−0.286223
$922$	−2.72792	−0.0898393
$923$	−31.3137	−1.03070
$924$	0	0
$925$	1.17157	0.0385211
$926$	16.6274	0.546411
$927$	15.0711	0.494999
$928$	3.65685	0.120042
$929$	6.68629	0.219370	0.109685	−	0.993966i	$-0.465016\pi$
$929$	6.68629	0.219370	0.109685	+	0.993966i	$0.465016\pi$
$930$	−1.02944	−0.0337566
$931$	0	0
$932$	−3.39697	−0.111271
$933$	−29.1127	−0.953107
$934$	4.98781	0.163206
$935$	0	0
$936$	−5.41421	−0.176969
$937$	17.2721	0.564254	0.282127	−	0.959377i	$-0.408960\pi$
$937$	17.2721	0.564254	0.282127	+	0.959377i	$0.408960\pi$
$938$	2.68629	0.0877105
$939$	27.7990	0.907186
$940$	2.58579	0.0843391
$941$	5.61522	0.183051	0.0915255	−	0.995803i	$-0.470826\pi$
$941$	5.61522	0.183051	0.0915255	+	0.995803i	$0.470826\pi$
$942$	−3.79899	−0.123778
$943$	−37.4558	−1.21973
$944$	−23.6985	−0.771320
$945$	−5.65685	−0.184017
$946$	0	0
$947$	−25.5980	−0.831823	−0.415911	−	0.909405i	$-0.636537\pi$
$947$	−25.5980	−0.831823	−0.415911	+	0.909405i	$0.636537\pi$
$948$	−16.7696	−0.544650
$949$	−17.3137	−0.562027
$950$	0	0
$951$	34.8284	1.12939
$952$	−0.928932	−0.0301069
$953$	−41.2548	−1.33638	−0.668188	−	0.743993i	$-0.732930\pi$
$953$	−41.2548	−1.33638	−0.668188	+	0.743993i	$0.732930\pi$
$954$	−1.17157	−0.0379311
$955$	−26.6274	−0.861643
$956$	33.5391	1.08473
$957$	0	0
$958$	2.05887	0.0665192
$959$	8.48528	0.274004
$960$	−5.89949	−0.190405
$961$	−27.9117	−0.900377
$962$	−1.65685	−0.0534191
$963$	19.3137	0.622376
$964$	38.7868	1.24924
$965$	13.6569	0.439630
$966$	−5.17157	−0.166393
$967$	5.02944	0.161736	0.0808679	−	0.996725i	$-0.474231\pi$
$967$	5.02944	0.161736	0.0808679	+	0.996725i	$0.474231\pi$
$968$	0	0
$969$	0	0
$970$	−3.85786	−0.123869
$971$	−12.5858	−0.403897	−0.201949	−	0.979396i	$-0.564727\pi$
$971$	−12.5858	−0.403897	−0.201949	+	0.979396i	$0.564727\pi$
$972$	18.1005	0.580574
$973$	12.4853	0.400260
$974$	6.40202	0.205134
$975$	4.82843	0.154633
$976$	41.6985	1.33474
$977$	−9.31371	−0.297972	−0.148986	−	0.988839i	$-0.547601\pi$
$977$	−9.31371	−0.297972	−0.148986	+	0.988839i	$0.547601\pi$
$978$	3.79899	0.121478
$979$	0	0
$980$	1.82843	0.0584070
$981$	−4.82843	−0.154160
$982$	−8.34315	−0.266240
$983$	14.1005	0.449736	0.224868	−	0.974389i	$-0.427805\pi$
$983$	14.1005	0.449736	0.224868	+	0.974389i	$0.427805\pi$
$984$	−9.51472	−0.303318
$985$	−18.6274	−0.593519
$986$	0.201010	0.00640147
$987$	−2.00000	−0.0636607
$988$	0	0
$989$	−52.9706	−1.68437
$990$	0	0
$991$	−37.4558	−1.18982	−0.594912	−	0.803791i	$-0.702813\pi$
$991$	−37.4558	−1.18982	−0.594912	+	0.803791i	$0.702813\pi$
$992$	−7.75736	−0.246296
$993$	36.2843	1.15145
$994$	3.79899	0.120497
$995$	−19.8995	−0.630856
$996$	−31.0294	−0.983205
$997$	−30.2426	−0.957794	−0.478897	−	0.877871i	$-0.658963\pi$
$997$	−30.2426	−0.957794	−0.478897	+	0.877871i	$0.658963\pi$
$998$	2.82843	0.0895323
$999$	6.62742	0.209682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.h.1.2		2
11.10	odd	2		385.2.a.d.1.1	✓	2
33.32	even	2		3465.2.a.u.1.2		2
44.43	even	2		6160.2.a.y.1.2		2
55.32	even	4		1925.2.b.j.1849.2		4
55.43	even	4		1925.2.b.j.1849.3		4
55.54	odd	2		1925.2.a.n.1.2		2
77.76	even	2		2695.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.d.1.1	✓	2	11.10	odd	2
1925.2.a.n.1.2		2	55.54	odd	2
1925.2.b.j.1849.2		4	55.32	even	4
1925.2.b.j.1849.3		4	55.43	even	4
2695.2.a.e.1.1		2	77.76	even	2
3465.2.a.u.1.2		2	33.32	even	2
4235.2.a.h.1.2		2	1.1	even	1	trivial
6160.2.a.y.1.2		2	44.43	even	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} -1.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} -0.585786 q^{6} +1.00000 q^{7} -1.58579 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} -1.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} -0.585786 q^{6} +1.00000 q^{7} -1.58579 q^{8} -1.00000 q^{9} -0.414214 q^{10} +2.58579 q^{12} -3.41421 q^{13} +0.414214 q^{14} +1.41421 q^{15} +3.00000 q^{16} +0.585786 q^{17} -0.414214 q^{18} +1.82843 q^{20} -1.41421 q^{21} +8.82843 q^{23} +2.24264 q^{24} +1.00000 q^{25} -1.41421 q^{26} +5.65685 q^{27} -1.82843 q^{28} +0.828427 q^{29} +0.585786 q^{30} -1.75736 q^{31} +4.41421 q^{32} +0.242641 q^{34} -1.00000 q^{35} +1.82843 q^{36} +1.17157 q^{37} +4.82843 q^{39} +1.58579 q^{40} -4.24264 q^{41} -0.585786 q^{42} -6.00000 q^{43} +1.00000 q^{45} +3.65685 q^{46} +1.41421 q^{47} -4.24264 q^{48} +1.00000 q^{49} +0.414214 q^{50} -0.828427 q^{51} +6.24264 q^{52} +2.82843 q^{53} +2.34315 q^{54} -1.58579 q^{56} +0.343146 q^{58} -7.89949 q^{59} -2.58579 q^{60} +13.8995 q^{61} -0.727922 q^{62} -1.00000 q^{63} -4.17157 q^{64} +3.41421 q^{65} +6.48528 q^{67} -1.07107 q^{68} -12.4853 q^{69} -0.414214 q^{70} +9.17157 q^{71} +1.58579 q^{72} +5.07107 q^{73} +0.485281 q^{74} -1.41421 q^{75} +2.00000 q^{78} -6.48528 q^{79} -3.00000 q^{80} -5.00000 q^{81} -1.75736 q^{82} -12.0000 q^{83} +2.58579 q^{84} -0.585786 q^{85} -2.48528 q^{86} -1.17157 q^{87} +0.828427 q^{89} +0.414214 q^{90} -3.41421 q^{91} -16.1421 q^{92} +2.48528 q^{93} +0.585786 q^{94} -6.24264 q^{96} +9.31371 q^{97} +0.414214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{7} - 6 q^{8} - 2 q^{9} + 2 q^{10} + 8 q^{12} - 4 q^{13} - 2 q^{14} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{20} + 12 q^{23} - 4 q^{24} + 2 q^{25} + 2 q^{28} - 4 q^{29} + 4 q^{30} - 12 q^{31} + 6 q^{32} - 8 q^{34} - 2 q^{35} - 2 q^{36} + 8 q^{37} + 4 q^{39} + 6 q^{40} - 4 q^{42} - 12 q^{43} + 2 q^{45} - 4 q^{46} + 2 q^{49} - 2 q^{50} + 4 q^{51} + 4 q^{52} + 16 q^{54} - 6 q^{56} + 12 q^{58} + 4 q^{59} - 8 q^{60} + 8 q^{61} + 24 q^{62} - 2 q^{63} - 14 q^{64} + 4 q^{65} - 4 q^{67} + 12 q^{68} - 8 q^{69} + 2 q^{70} + 24 q^{71} + 6 q^{72} - 4 q^{73} - 16 q^{74} + 4 q^{78} + 4 q^{79} - 6 q^{80} - 10 q^{81} - 12 q^{82} - 24 q^{83} + 8 q^{84} - 4 q^{85} + 12 q^{86} - 8 q^{87} - 4 q^{89} - 2 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 4 q^{94} - 4 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^7 - 6 * q^8 - 2 * q^9 + 2 * q^10 + 8 * q^12 - 4 * q^13 - 2 * q^14 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^20 + 12 * q^23 - 4 * q^24 + 2 * q^25 + 2 * q^28 - 4 * q^29 + 4 * q^30 - 12 * q^31 + 6 * q^32 - 8 * q^34 - 2 * q^35 - 2 * q^36 + 8 * q^37 + 4 * q^39 + 6 * q^40 - 4 * q^42 - 12 * q^43 + 2 * q^45 - 4 * q^46 + 2 * q^49 - 2 * q^50 + 4 * q^51 + 4 * q^52 + 16 * q^54 - 6 * q^56 + 12 * q^58 + 4 * q^59 - 8 * q^60 + 8 * q^61 + 24 * q^62 - 2 * q^63 - 14 * q^64 + 4 * q^65 - 4 * q^67 + 12 * q^68 - 8 * q^69 + 2 * q^70 + 24 * q^71 + 6 * q^72 - 4 * q^73 - 16 * q^74 + 4 * q^78 + 4 * q^79 - 6 * q^80 - 10 * q^81 - 12 * q^82 - 24 * q^83 + 8 * q^84 - 4 * q^85 + 12 * q^86 - 8 * q^87 - 4 * q^89 - 2 * q^90 - 4 * q^91 - 4 * q^92 - 12 * q^93 + 4 * q^94 - 4 * q^96 - 4 * q^97 - 2 * q^98

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