LMFDB - Embedded newform 2695.2.a.t.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 26x^{5} + 15x^{4} - 60x^{3} - 2x^{2} + 37x - 9 $ x^8 - 3x^7 - 8x^6 + 26x^5 + 15x^4 - 60x^3 - 2x^2 + 37*x - 9
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			1.8
Root			$2.55022$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.55022 q^{2} +1.87460 q^{3} +4.50360 q^{4} +1.00000 q^{5} +4.78064 q^{6} +6.38473 q^{8} +0.514136 q^{9} +O(q^{10})$	\(q+2.55022 q^{2} +1.87460 q^{3} +4.50360 q^{4} +1.00000 q^{5} +4.78064 q^{6} +6.38473 q^{8} +0.514136 q^{9} +2.55022 q^{10} -1.00000 q^{11} +8.44247 q^{12} +1.50645 q^{13} +1.87460 q^{15} +7.27523 q^{16} -5.58630 q^{17} +1.31116 q^{18} +0.545798 q^{19} +4.50360 q^{20} -2.55022 q^{22} +8.58444 q^{23} +11.9688 q^{24} +1.00000 q^{25} +3.84178 q^{26} -4.66001 q^{27} +3.24142 q^{29} +4.78064 q^{30} -3.85548 q^{31} +5.78395 q^{32} -1.87460 q^{33} -14.2463 q^{34} +2.31546 q^{36} +7.90220 q^{37} +1.39190 q^{38} +2.82400 q^{39} +6.38473 q^{40} +9.58045 q^{41} -1.27678 q^{43} -4.50360 q^{44} +0.514136 q^{45} +21.8922 q^{46} -6.98804 q^{47} +13.6382 q^{48} +2.55022 q^{50} -10.4721 q^{51} +6.78446 q^{52} +4.69864 q^{53} -11.8840 q^{54} -1.00000 q^{55} +1.02316 q^{57} +8.26633 q^{58} -9.20708 q^{59} +8.44247 q^{60} -7.40295 q^{61} -9.83232 q^{62} +0.199875 q^{64} +1.50645 q^{65} -4.78064 q^{66} -11.9563 q^{67} -25.1585 q^{68} +16.0924 q^{69} -13.9114 q^{71} +3.28262 q^{72} -7.24959 q^{73} +20.1523 q^{74} +1.87460 q^{75} +2.45806 q^{76} +7.20181 q^{78} +10.2361 q^{79} +7.27523 q^{80} -10.2781 q^{81} +24.4322 q^{82} +1.53695 q^{83} -5.58630 q^{85} -3.25606 q^{86} +6.07638 q^{87} -6.38473 q^{88} -1.56271 q^{89} +1.31116 q^{90} +38.6609 q^{92} -7.22750 q^{93} -17.8210 q^{94} +0.545798 q^{95} +10.8426 q^{96} +4.93672 q^{97} -0.514136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * 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 $

$2$	2.55022	1.80328	0.901638	−	0.432492i	$-0.142366\pi$
$2$	2.55022	1.80328	0.901638	+	0.432492i	$0.142366\pi$
$3$	1.87460	1.08230	0.541151	−	0.840925i	$-0.317989\pi$
$3$	1.87460	1.08230	0.541151	+	0.840925i	$0.317989\pi$
$4$	4.50360	2.25180
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.78064	1.95169
$7$	0	0
$7$	0	0
$8$	6.38473	2.25734
$9$	0.514136	0.171379
$10$	2.55022	0.806449
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	8.44247	2.43713
$13$	1.50645	0.417815	0.208907	−	0.977935i	$-0.433009\pi$
$13$	1.50645	0.417815	0.208907	+	0.977935i	$0.433009\pi$
$14$	0	0
$15$	1.87460	0.484020
$16$	7.27523	1.81881
$17$	−5.58630	−1.35488	−0.677438	−	0.735580i	$-0.736910\pi$
$17$	−5.58630	−1.35488	−0.677438	+	0.735580i	$0.736910\pi$
$18$	1.31116	0.309043
$19$	0.545798	0.125215	0.0626074	−	0.998038i	$-0.480058\pi$
$19$	0.545798	0.125215	0.0626074	+	0.998038i	$0.480058\pi$
$20$	4.50360	1.00704
$21$	0	0
$22$	−2.55022	−0.543708
$23$	8.58444	1.78998	0.894990	−	0.446087i	$-0.147183\pi$
$23$	8.58444	1.78998	0.894990	+	0.446087i	$0.147183\pi$
$24$	11.9688	2.44313
$25$	1.00000	0.200000
$26$	3.84178	0.753435
$27$	−4.66001	−0.896819
$28$	0	0
$29$	3.24142	0.601917	0.300959	−	0.953637i	$-0.402693\pi$
$29$	3.24142	0.601917	0.300959	+	0.953637i	$0.402693\pi$
$30$	4.78064	0.872822
$31$	−3.85548	−0.692465	−0.346233	−	0.938149i	$-0.612539\pi$
$31$	−3.85548	−0.692465	−0.346233	+	0.938149i	$0.612539\pi$
$32$	5.78395	1.02247
$33$	−1.87460	−0.326326
$34$	−14.2463	−2.44321
$35$	0	0
$36$	2.31546	0.385911
$37$	7.90220	1.29911	0.649557	−	0.760313i	$-0.274955\pi$
$37$	7.90220	1.29911	0.649557	+	0.760313i	$0.274955\pi$
$38$	1.39190	0.225797
$39$	2.82400	0.452202
$40$	6.38473	1.00951
$41$	9.58045	1.49622	0.748108	−	0.663577i	$-0.230963\pi$
$41$	9.58045	1.49622	0.748108	+	0.663577i	$0.230963\pi$
$42$	0	0
$43$	−1.27678	−0.194707	−0.0973535	−	0.995250i	$-0.531038\pi$
$43$	−1.27678	−0.194707	−0.0973535	+	0.995250i	$0.531038\pi$
$44$	−4.50360	−0.678944
$45$	0.514136	0.0766428
$46$	21.8922	3.22783
$47$	−6.98804	−1.01931	−0.509655	−	0.860379i	$-0.670227\pi$
$47$	−6.98804	−1.01931	−0.509655	+	0.860379i	$0.670227\pi$
$48$	13.6382	1.96850
$49$	0	0
$50$	2.55022	0.360655
$51$	−10.4721	−1.46639
$52$	6.78446	0.940836
$53$	4.69864	0.645408	0.322704	−	0.946500i	$-0.395408\pi$
$53$	4.69864	0.645408	0.322704	+	0.946500i	$0.395408\pi$
$54$	−11.8840	−1.61721
$55$	−1.00000	−0.134840
$56$	0	0
$57$	1.02316	0.135520
$58$	8.26633	1.08542
$59$	−9.20708	−1.19866	−0.599330	−	0.800502i	$-0.704566\pi$
$59$	−9.20708	−1.19866	−0.599330	+	0.800502i	$0.704566\pi$
$60$	8.44247	1.08992
$61$	−7.40295	−0.947851	−0.473925	−	0.880565i	$-0.657163\pi$
$61$	−7.40295	−0.947851	−0.473925	+	0.880565i	$0.657163\pi$
$62$	−9.83232	−1.24871
$63$	0	0
$64$	0.199875	0.0249843
$65$	1.50645	0.186852
$66$	−4.78064	−0.588456
$67$	−11.9563	−1.46069	−0.730346	−	0.683077i	$-0.760641\pi$
$67$	−11.9563	−1.46069	−0.730346	+	0.683077i	$0.760641\pi$
$68$	−25.1585	−3.05091
$69$	16.0924	1.93730
$70$	0	0
$71$	−13.9114	−1.65098	−0.825489	−	0.564418i	$-0.809101\pi$
$71$	−13.9114	−1.65098	−0.825489	+	0.564418i	$0.809101\pi$
$72$	3.28262	0.386860
$73$	−7.24959	−0.848500	−0.424250	−	0.905545i	$-0.639462\pi$
$73$	−7.24959	−0.848500	−0.424250	+	0.905545i	$0.639462\pi$
$74$	20.1523	2.34266
$75$	1.87460	0.216460
$76$	2.45806	0.281959
$77$	0	0
$78$	7.20181	0.815444
$79$	10.2361	1.15165	0.575823	−	0.817574i	$-0.304682\pi$
$79$	10.2361	1.15165	0.575823	+	0.817574i	$0.304682\pi$
$80$	7.27523	0.813395
$81$	−10.2781	−1.14201
$82$	24.4322	2.69809
$83$	1.53695	0.168702	0.0843512	−	0.996436i	$-0.473118\pi$
$83$	1.53695	0.168702	0.0843512	+	0.996436i	$0.473118\pi$
$84$	0	0
$85$	−5.58630	−0.605919
$86$	−3.25606	−0.351110
$87$	6.07638	0.651456
$88$	−6.38473	−0.680614
$89$	−1.56271	−0.165647	−0.0828235	−	0.996564i	$-0.526394\pi$
$89$	−1.56271	−0.165647	−0.0828235	+	0.996564i	$0.526394\pi$
$90$	1.31116	0.138208
$91$	0	0
$92$	38.6609	4.03068
$93$	−7.22750	−0.749457
$94$	−17.8210	−1.83810
$95$	0.545798	0.0559977
$96$	10.8426	1.10662
$97$	4.93672	0.501248	0.250624	−	0.968085i	$-0.419364\pi$
$97$	4.93672	0.501248	0.250624	+	0.968085i	$0.419364\pi$
$98$	0	0
$99$	−0.514136	−0.0516726
$100$	4.50360	0.450360
$101$	−14.0136	−1.39441	−0.697204	−	0.716873i	$-0.745573\pi$
$101$	−14.0136	−1.39441	−0.697204	+	0.716873i	$0.745573\pi$
$102$	−26.7061	−2.64430
$103$	−6.36893	−0.627549	−0.313774	−	0.949498i	$-0.601594\pi$
$103$	−6.36893	−0.627549	−0.313774	+	0.949498i	$0.601594\pi$
$104$	9.61829	0.943151
$105$	0	0
$106$	11.9826	1.16385
$107$	−15.1014	−1.45991	−0.729955	−	0.683495i	$-0.760459\pi$
$107$	−15.1014	−1.45991	−0.729955	+	0.683495i	$0.760459\pi$
$108$	−20.9868	−2.01946
$109$	2.21862	0.212506	0.106253	−	0.994339i	$-0.466115\pi$
$109$	2.21862	0.212506	0.106253	+	0.994339i	$0.466115\pi$
$110$	−2.55022	−0.243154
$111$	14.8135	1.40603
$112$	0	0
$113$	−10.8293	−1.01873	−0.509367	−	0.860549i	$-0.670121\pi$
$113$	−10.8293	−1.01873	−0.509367	+	0.860549i	$0.670121\pi$
$114$	2.60927	0.244380
$115$	8.58444	0.800503
$116$	14.5981	1.35540
$117$	0.774521	0.0716045
$118$	−23.4800	−2.16151
$119$	0	0
$120$	11.9688	1.09260
$121$	1.00000	0.0909091
$122$	−18.8791	−1.70924
$123$	17.9595	1.61936
$124$	−17.3636	−1.55929
$125$	1.00000	0.0894427
$126$	0	0
$127$	3.80250	0.337417	0.168709	−	0.985666i	$-0.446040\pi$
$127$	3.80250	0.337417	0.168709	+	0.985666i	$0.446040\pi$
$128$	−11.0582	−0.977415
$129$	−2.39345	−0.210732
$130$	3.84178	0.336946
$131$	14.9423	1.30552	0.652758	−	0.757566i	$-0.273612\pi$
$131$	14.9423	1.30552	0.652758	+	0.757566i	$0.273612\pi$
$132$	−8.44247	−0.734822
$133$	0	0
$134$	−30.4911	−2.63403
$135$	−4.66001	−0.401070
$136$	−35.6670	−3.05842
$137$	−4.67182	−0.399141	−0.199570	−	0.979883i	$-0.563955\pi$
$137$	−4.67182	−0.399141	−0.199570	+	0.979883i	$0.563955\pi$
$138$	41.0391	3.49348
$139$	−14.6424	−1.24195	−0.620977	−	0.783829i	$-0.713264\pi$
$139$	−14.6424	−1.24195	−0.620977	+	0.783829i	$0.713264\pi$
$140$	0	0
$141$	−13.0998	−1.10320
$142$	−35.4770	−2.97717
$143$	−1.50645	−0.125976
$144$	3.74046	0.311705
$145$	3.24142	0.269185
$146$	−18.4880	−1.53008
$147$	0	0
$148$	35.5884	2.92534
$149$	8.76407	0.717980	0.358990	−	0.933341i	$-0.383121\pi$
$149$	8.76407	0.717980	0.358990	+	0.933341i	$0.383121\pi$
$150$	4.78064	0.390338
$151$	17.7555	1.44492	0.722461	−	0.691411i	$-0.243011\pi$
$151$	17.7555	1.44492	0.722461	+	0.691411i	$0.243011\pi$
$152$	3.48477	0.282652
$153$	−2.87212	−0.232197
$154$	0	0
$155$	−3.85548	−0.309680
$156$	12.7182	1.01827
$157$	12.3861	0.988519	0.494259	−	0.869314i	$-0.335439\pi$
$157$	12.3861	0.988519	0.494259	+	0.869314i	$0.335439\pi$
$158$	26.1042	2.07673
$159$	8.80809	0.698527
$160$	5.78395	0.457262
$161$	0	0
$162$	−26.2113	−2.05935
$163$	−6.69879	−0.524689	−0.262345	−	0.964974i	$-0.584496\pi$
$163$	−6.69879	−0.524689	−0.262345	+	0.964974i	$0.584496\pi$
$164$	43.1465	3.36918
$165$	−1.87460	−0.145938
$166$	3.91956	0.304217
$167$	18.1713	1.40613	0.703067	−	0.711124i	$-0.251813\pi$
$167$	18.1713	1.40613	0.703067	+	0.711124i	$0.251813\pi$
$168$	0	0
$169$	−10.7306	−0.825431
$170$	−14.2463	−1.09264
$171$	0.280614	0.0214591
$172$	−5.75011	−0.438442
$173$	8.20909	0.624126	0.312063	−	0.950061i	$-0.398980\pi$
$173$	8.20909	0.624126	0.312063	+	0.950061i	$0.398980\pi$
$174$	15.4961	1.17475
$175$	0	0
$176$	−7.27523	−0.548391
$177$	−17.2596	−1.29731
$178$	−3.98525	−0.298707
$179$	0.230038	0.0171939	0.00859693	−	0.999963i	$-0.497263\pi$
$179$	0.230038	0.0171939	0.00859693	+	0.999963i	$0.497263\pi$
$180$	2.31546	0.172584
$181$	−5.75456	−0.427733	−0.213866	−	0.976863i	$-0.568606\pi$
$181$	−5.75456	−0.427733	−0.213866	+	0.976863i	$0.568606\pi$
$182$	0	0
$183$	−13.8776	−1.02586
$184$	54.8093	4.04060
$185$	7.90220	0.580981
$186$	−18.4317	−1.35148
$187$	5.58630	0.408510
$188$	−31.4713	−2.29528
$189$	0	0
$190$	1.39190	0.100979
$191$	21.5078	1.55625	0.778125	−	0.628110i	$-0.216171\pi$
$191$	21.5078	1.55625	0.778125	+	0.628110i	$0.216171\pi$
$192$	0.374686	0.0270406
$193$	2.12721	0.153120	0.0765598	−	0.997065i	$-0.475606\pi$
$193$	2.12721	0.153120	0.0765598	+	0.997065i	$0.475606\pi$
$194$	12.5897	0.903887
$195$	2.82400	0.202231
$196$	0	0
$197$	−1.54764	−0.110265	−0.0551325	−	0.998479i	$-0.517558\pi$
$197$	−1.54764	−0.110265	−0.0551325	+	0.998479i	$0.517558\pi$
$198$	−1.31116	−0.0931799
$199$	10.9180	0.773960	0.386980	−	0.922088i	$-0.373518\pi$
$199$	10.9180	0.773960	0.386980	+	0.922088i	$0.373518\pi$
$200$	6.38473	0.451468
$201$	−22.4133	−1.58091
$202$	−35.7378	−2.51450
$203$	0	0
$204$	−47.1621	−3.30201
$205$	9.58045	0.669128
$206$	−16.2421	−1.13164
$207$	4.41357	0.306764
$208$	10.9598	0.759925
$209$	−0.545798	−0.0377537
$210$	0	0
$211$	−2.00275	−0.137875	−0.0689376	−	0.997621i	$-0.521961\pi$
$211$	−2.00275	−0.137875	−0.0689376	+	0.997621i	$0.521961\pi$
$212$	21.1608	1.45333
$213$	−26.0783	−1.78686
$214$	−38.5119	−2.63262
$215$	−1.27678	−0.0870756
$216$	−29.7529	−2.02443
$217$	0	0
$218$	5.65797	0.383206
$219$	−13.5901	−0.918334
$220$	−4.50360	−0.303633
$221$	−8.41549	−0.566087
$222$	37.7776	2.53546
$223$	−19.5356	−1.30820	−0.654102	−	0.756407i	$-0.726953\pi$
$223$	−19.5356	−1.30820	−0.654102	+	0.756407i	$0.726953\pi$
$224$	0	0
$225$	0.514136	0.0342757
$226$	−27.6171	−1.83706
$227$	13.5755	0.901039	0.450519	−	0.892767i	$-0.351239\pi$
$227$	13.5755	0.901039	0.450519	+	0.892767i	$0.351239\pi$
$228$	4.60788	0.305165
$229$	−12.1277	−0.801422	−0.400711	−	0.916205i	$-0.631237\pi$
$229$	−12.1277	−0.801422	−0.400711	+	0.916205i	$0.631237\pi$
$230$	21.8922	1.44353
$231$	0	0
$232$	20.6956	1.35873
$233$	27.4097	1.79567	0.897833	−	0.440335i	$-0.145140\pi$
$233$	27.4097	1.79567	0.897833	+	0.440335i	$0.145140\pi$
$234$	1.97520	0.129123
$235$	−6.98804	−0.455849
$236$	−41.4650	−2.69914
$237$	19.1885	1.24643
$238$	0	0
$239$	30.0460	1.94352	0.971758	−	0.235981i	$-0.0758305\pi$
$239$	30.0460	1.94352	0.971758	+	0.235981i	$0.0758305\pi$
$240$	13.6382	0.880340
$241$	−25.5729	−1.64729	−0.823647	−	0.567102i	$-0.808064\pi$
$241$	−25.5729	−1.64729	−0.823647	+	0.567102i	$0.808064\pi$
$242$	2.55022	0.163934
$243$	−5.28728	−0.339179
$244$	−33.3400	−2.13437
$245$	0	0
$246$	45.8007	2.92015
$247$	0.822219	0.0523166
$248$	−24.6162	−1.56313
$249$	2.88117	0.182587
$250$	2.55022	0.161290
$251$	19.6680	1.24144	0.620718	−	0.784034i	$-0.286841\pi$
$251$	19.6680	1.24144	0.620718	+	0.784034i	$0.286841\pi$
$252$	0	0
$253$	−8.58444	−0.539699
$254$	9.69719	0.608456
$255$	−10.4721	−0.655788
$256$	−28.6005	−1.78753
$257$	−4.43044	−0.276363	−0.138182	−	0.990407i	$-0.544126\pi$
$257$	−4.43044	−0.276363	−0.138182	+	0.990407i	$0.544126\pi$
$258$	−6.10383	−0.380008
$259$	0	0
$260$	6.78446	0.420754
$261$	1.66653	0.103156
$262$	38.1061	2.35421
$263$	−12.4297	−0.766445	−0.383223	−	0.923656i	$-0.625186\pi$
$263$	−12.4297	−0.766445	−0.383223	+	0.923656i	$0.625186\pi$
$264$	−11.9688	−0.736630
$265$	4.69864	0.288635
$266$	0	0
$267$	−2.92946	−0.179280
$268$	−53.8464	−3.28919
$269$	19.4842	1.18797	0.593987	−	0.804475i	$-0.297553\pi$
$269$	19.4842	1.18797	0.593987	+	0.804475i	$0.297553\pi$
$270$	−11.8840	−0.723239
$271$	24.9067	1.51298	0.756488	−	0.654008i	$-0.226914\pi$
$271$	24.9067	1.51298	0.756488	+	0.654008i	$0.226914\pi$
$272$	−40.6416	−2.46426
$273$	0	0
$274$	−11.9142	−0.719761
$275$	−1.00000	−0.0603023
$276$	72.4738	4.36241
$277$	14.5773	0.875863	0.437932	−	0.899008i	$-0.355711\pi$
$277$	14.5773	0.875863	0.437932	+	0.899008i	$0.355711\pi$
$278$	−37.3413	−2.23958
$279$	−1.98224	−0.118674
$280$	0	0
$281$	−21.7901	−1.29989	−0.649945	−	0.759982i	$-0.725208\pi$
$281$	−21.7901	−1.29989	−0.649945	+	0.759982i	$0.725208\pi$
$282$	−33.4073	−1.98938
$283$	17.2867	1.02759	0.513794	−	0.857913i	$-0.328239\pi$
$283$	17.2867	1.02759	0.513794	+	0.857913i	$0.328239\pi$
$284$	−62.6514	−3.71767
$285$	1.02316	0.0606065
$286$	−3.84178	−0.227169
$287$	0	0
$288$	2.97374	0.175229
$289$	14.2067	0.835689
$290$	8.26633	0.485415
$291$	9.25438	0.542501
$292$	−32.6493	−1.91065
$293$	−8.39824	−0.490631	−0.245315	−	0.969443i	$-0.578891\pi$
$293$	−8.39824	−0.490631	−0.245315	+	0.969443i	$0.578891\pi$
$294$	0	0
$295$	−9.20708	−0.536057
$296$	50.4534	2.93254
$297$	4.66001	0.270401
$298$	22.3503	1.29472
$299$	12.9320	0.747880
$300$	8.44247	0.487426
$301$	0	0
$302$	45.2804	2.60559
$303$	−26.2700	−1.50917
$304$	3.97081	0.227742
$305$	−7.40295	−0.423892
$306$	−7.32451	−0.418715
$307$	29.9045	1.70674	0.853369	−	0.521307i	$-0.174555\pi$
$307$	29.9045	1.70674	0.853369	+	0.521307i	$0.174555\pi$
$308$	0	0
$309$	−11.9392	−0.679198
$310$	−9.83232	−0.558438
$311$	−18.4959	−1.04881	−0.524404	−	0.851470i	$-0.675712\pi$
$311$	−18.4959	−1.04881	−0.524404	+	0.851470i	$0.675712\pi$
$312$	18.0305	1.02077
$313$	25.3658	1.43376	0.716881	−	0.697195i	$-0.245569\pi$
$313$	25.3658	1.43376	0.716881	+	0.697195i	$0.245569\pi$
$314$	31.5872	1.78257
$315$	0	0
$316$	46.0991	2.59328
$317$	3.95375	0.222065	0.111032	−	0.993817i	$-0.464584\pi$
$317$	3.95375	0.222065	0.111032	+	0.993817i	$0.464584\pi$
$318$	22.4625	1.25964
$319$	−3.24142	−0.181485
$320$	0.199875	0.0111733
$321$	−28.3092	−1.58006
$322$	0	0
$323$	−3.04899	−0.169650
$324$	−46.2883	−2.57157
$325$	1.50645	0.0835629
$326$	−17.0834	−0.946159
$327$	4.15904	0.229995
$328$	61.1686	3.37747
$329$	0	0
$330$	−4.78064	−0.263166
$331$	−15.4704	−0.850331	−0.425165	−	0.905116i	$-0.639784\pi$
$331$	−15.4704	−0.850331	−0.425165	+	0.905116i	$0.639784\pi$
$332$	6.92182	0.379884
$333$	4.06280	0.222640
$334$	46.3406	2.53565
$335$	−11.9563	−0.653242
$336$	0	0
$337$	18.2385	0.993512	0.496756	−	0.867890i	$-0.334524\pi$
$337$	18.2385	0.993512	0.496756	+	0.867890i	$0.334524\pi$
$338$	−27.3654	−1.48848
$339$	−20.3006	−1.10258
$340$	−25.1585	−1.36441
$341$	3.85548	0.208786
$342$	0.715628	0.0386967
$343$	0	0
$344$	−8.15189	−0.439520
$345$	16.0924	0.866387
$346$	20.9350	1.12547
$347$	−31.4428	−1.68794	−0.843968	−	0.536394i	$-0.819786\pi$
$347$	−31.4428	−1.68794	−0.843968	+	0.536394i	$0.819786\pi$
$348$	27.3656	1.46695
$349$	12.4702	0.667516	0.333758	−	0.942659i	$-0.391683\pi$
$349$	12.4702	0.667516	0.333758	+	0.942659i	$0.391683\pi$
$350$	0	0
$351$	−7.02008	−0.374704
$352$	−5.78395	−0.308286
$353$	3.16843	0.168639	0.0843194	−	0.996439i	$-0.473128\pi$
$353$	3.16843	0.168639	0.0843194	+	0.996439i	$0.473128\pi$
$354$	−44.0158	−2.33941
$355$	−13.9114	−0.738340
$356$	−7.03783	−0.373004
$357$	0	0
$358$	0.586647	0.0310053
$359$	4.33906	0.229007	0.114503	−	0.993423i	$-0.463472\pi$
$359$	4.33906	0.229007	0.114503	+	0.993423i	$0.463472\pi$
$360$	3.28262	0.173009
$361$	−18.7021	−0.984321
$362$	−14.6754	−0.771320
$363$	1.87460	0.0983911
$364$	0	0
$365$	−7.24959	−0.379461
$366$	−35.3909	−1.84991
$367$	20.9574	1.09397	0.546983	−	0.837144i	$-0.315776\pi$
$367$	20.9574	1.09397	0.546983	+	0.837144i	$0.315776\pi$
$368$	62.4538	3.25563
$369$	4.92565	0.256419
$370$	20.1523	1.04767
$371$	0	0
$372$	−32.5498	−1.68763
$373$	−1.61000	−0.0833628	−0.0416814	−	0.999131i	$-0.513271\pi$
$373$	−1.61000	−0.0833628	−0.0416814	+	0.999131i	$0.513271\pi$
$374$	14.2463	0.736657
$375$	1.87460	0.0968041
$376$	−44.6167	−2.30093
$377$	4.88305	0.251490
$378$	0	0
$379$	−8.45646	−0.434379	−0.217189	−	0.976129i	$-0.569689\pi$
$379$	−8.45646	−0.434379	−0.217189	+	0.976129i	$0.569689\pi$
$380$	2.45806	0.126096
$381$	7.12817	0.365187
$382$	54.8495	2.80635
$383$	−4.06325	−0.207622	−0.103811	−	0.994597i	$-0.533104\pi$
$383$	−4.06325	−0.207622	−0.103811	+	0.994597i	$0.533104\pi$
$384$	−20.7297	−1.05786
$385$	0	0
$386$	5.42484	0.276117
$387$	−0.656438	−0.0333686
$388$	22.2330	1.12871
$389$	14.6562	0.743098	0.371549	−	0.928413i	$-0.378827\pi$
$389$	14.6562	0.743098	0.371549	+	0.928413i	$0.378827\pi$
$390$	7.20181	0.364678
$391$	−47.9552	−2.42520
$392$	0	0
$393$	28.0109	1.41296
$394$	−3.94682	−0.198838
$395$	10.2361	0.515032
$396$	−2.31546	−0.116356
$397$	19.7009	0.988762	0.494381	−	0.869245i	$-0.335395\pi$
$397$	19.7009	0.988762	0.494381	+	0.869245i	$0.335395\pi$
$398$	27.8434	1.39566
$399$	0	0
$400$	7.27523	0.363762
$401$	38.2507	1.91015	0.955074	−	0.296366i	$-0.0957748\pi$
$401$	38.2507	1.91015	0.955074	+	0.296366i	$0.0957748\pi$
$402$	−57.1587	−2.85082
$403$	−5.80810	−0.289322
$404$	−63.1118	−3.13993
$405$	−10.2781	−0.510721
$406$	0	0
$407$	−7.90220	−0.391697
$408$	−66.8614	−3.31013
$409$	1.98751	0.0982761	0.0491381	−	0.998792i	$-0.484353\pi$
$409$	1.98751	0.0982761	0.0491381	+	0.998792i	$0.484353\pi$
$410$	24.4322	1.20662
$411$	−8.75781	−0.431991
$412$	−28.6831	−1.41312
$413$	0	0
$414$	11.2556	0.553180
$415$	1.53695	0.0754460
$416$	8.71325	0.427202
$417$	−27.4487	−1.34417
$418$	−1.39190	−0.0680802
$419$	25.4653	1.24406	0.622031	−	0.782993i	$-0.286308\pi$
$419$	25.4653	1.24406	0.622031	+	0.782993i	$0.286308\pi$
$420$	0	0
$421$	31.0909	1.51528	0.757638	−	0.652675i	$-0.226353\pi$
$421$	31.0909	1.51528	0.757638	+	0.652675i	$0.226353\pi$
$422$	−5.10745	−0.248627
$423$	−3.59280	−0.174688
$424$	29.9996	1.45691
$425$	−5.58630	−0.270975
$426$	−66.5054	−3.22220
$427$	0	0
$428$	−68.0108	−3.28743
$429$	−2.82400	−0.136344
$430$	−3.25606	−0.157021
$431$	8.14470	0.392316	0.196158	−	0.980572i	$-0.437153\pi$
$431$	8.14470	0.392316	0.196158	+	0.980572i	$0.437153\pi$
$432$	−33.9026	−1.63114
$433$	−1.81370	−0.0871607	−0.0435804	−	0.999050i	$-0.513876\pi$
$433$	−1.81370	−0.0871607	−0.0435804	+	0.999050i	$0.513876\pi$
$434$	0	0
$435$	6.07638	0.291340
$436$	9.99180	0.478521
$437$	4.68537	0.224132
$438$	−34.6577	−1.65601
$439$	−2.98755	−0.142588	−0.0712939	−	0.997455i	$-0.522713\pi$
$439$	−2.98755	−0.142588	−0.0712939	+	0.997455i	$0.522713\pi$
$440$	−6.38473	−0.304380
$441$	0	0
$442$	−21.4613	−1.02081
$443$	−33.5844	−1.59564	−0.797822	−	0.602893i	$-0.794014\pi$
$443$	−33.5844	−1.59564	−0.797822	+	0.602893i	$0.794014\pi$
$444$	66.7140	3.16611
$445$	−1.56271	−0.0740796
$446$	−49.8201	−2.35905
$447$	16.4291	0.777072
$448$	0	0
$449$	32.6748	1.54202	0.771011	−	0.636822i	$-0.219752\pi$
$449$	32.6748	1.54202	0.771011	+	0.636822i	$0.219752\pi$
$450$	1.31116	0.0618086
$451$	−9.58045	−0.451126
$452$	−48.7709	−2.29399
$453$	33.2845	1.56384
$454$	34.6205	1.62482
$455$	0	0
$456$	6.53257	0.305915
$457$	−28.0848	−1.31375	−0.656877	−	0.753998i	$-0.728123\pi$
$457$	−28.0848	−1.31375	−0.656877	+	0.753998i	$0.728123\pi$
$458$	−30.9283	−1.44518
$459$	26.0322	1.21508
$460$	38.6609	1.80257
$461$	−3.33883	−0.155505	−0.0777524	−	0.996973i	$-0.524774\pi$
$461$	−3.33883	−0.155505	−0.0777524	+	0.996973i	$0.524774\pi$
$462$	0	0
$463$	−7.52155	−0.349556	−0.174778	−	0.984608i	$-0.555921\pi$
$463$	−7.52155	−0.349556	−0.174778	+	0.984608i	$0.555921\pi$
$464$	23.5821	1.09477
$465$	−7.22750	−0.335167
$466$	69.9006	3.23808
$467$	−20.3706	−0.942637	−0.471319	−	0.881963i	$-0.656222\pi$
$467$	−20.3706	−0.942637	−0.471319	+	0.881963i	$0.656222\pi$
$468$	3.48814	0.161239
$469$	0	0
$470$	−17.8210	−0.822022
$471$	23.2190	1.06988
$472$	−58.7847	−2.70578
$473$	1.27678	0.0587064
$474$	48.9349	2.24766
$475$	0.545798	0.0250429
$476$	0	0
$477$	2.41574	0.110609
$478$	76.6238	3.50469
$479$	2.71883	0.124226	0.0621132	−	0.998069i	$-0.480216\pi$
$479$	2.71883	0.124226	0.0621132	+	0.998069i	$0.480216\pi$
$480$	10.8426	0.494896
$481$	11.9043	0.542789
$482$	−65.2164	−2.97053
$483$	0	0
$484$	4.50360	0.204709
$485$	4.93672	0.224165
$486$	−13.4837	−0.611633
$487$	−9.70510	−0.439780	−0.219890	−	0.975525i	$-0.570570\pi$
$487$	−9.70510	−0.439780	−0.219890	+	0.975525i	$0.570570\pi$
$488$	−47.2658	−2.13962
$489$	−12.5576	−0.567873
$490$	0	0
$491$	2.33255	0.105266	0.0526331	−	0.998614i	$-0.483239\pi$
$491$	2.33255	0.105266	0.0526331	+	0.998614i	$0.483239\pi$
$492$	80.8826	3.64647
$493$	−18.1075	−0.815523
$494$	2.09684	0.0943411
$495$	−0.514136	−0.0231087
$496$	−28.0495	−1.25946
$497$	0	0
$498$	7.34762	0.329255
$499$	−30.0300	−1.34433	−0.672164	−	0.740403i	$-0.734635\pi$
$499$	−30.0300	−1.34433	−0.672164	+	0.740403i	$0.734635\pi$
$500$	4.50360	0.201407
$501$	34.0639	1.52186
$502$	50.1577	2.23865
$503$	33.3655	1.48769	0.743847	−	0.668350i	$-0.232999\pi$
$503$	33.3655	1.48769	0.743847	+	0.668350i	$0.232999\pi$
$504$	0	0
$505$	−14.0136	−0.623598
$506$	−21.8922	−0.973226
$507$	−20.1156	−0.893366
$508$	17.1249	0.759796
$509$	13.9388	0.617824	0.308912	−	0.951091i	$-0.400035\pi$
$509$	13.9388	0.617824	0.308912	+	0.951091i	$0.400035\pi$
$510$	−26.7061	−1.18257
$511$	0	0
$512$	−50.8211	−2.24600
$513$	−2.54342	−0.112295
$514$	−11.2986	−0.498359
$515$	−6.36893	−0.280648
$516$	−10.7792	−0.474526
$517$	6.98804	0.307334
$518$	0	0
$519$	15.3888	0.675493
$520$	9.61829	0.421790
$521$	−18.5558	−0.812946	−0.406473	−	0.913663i	$-0.633242\pi$
$521$	−18.5558	−0.812946	−0.406473	+	0.913663i	$0.633242\pi$
$522$	4.25002	0.186018
$523$	8.24920	0.360712	0.180356	−	0.983601i	$-0.442275\pi$
$523$	8.24920	0.360712	0.180356	+	0.983601i	$0.442275\pi$
$524$	67.2943	2.93976
$525$	0	0
$526$	−31.6983	−1.38211
$527$	21.5379	0.938204
$528$	−13.6382	−0.593525
$529$	50.6926	2.20403
$530$	11.9826	0.520489
$531$	−4.73369	−0.205425
$532$	0	0
$533$	14.4325	0.625141
$534$	−7.47076	−0.323292
$535$	−15.1014	−0.652892
$536$	−76.3376	−3.29728
$537$	0.431230	0.0186090
$538$	49.6890	2.14224
$539$	0	0
$540$	−20.9868	−0.903129
$541$	−34.6430	−1.48942	−0.744709	−	0.667389i	$-0.767412\pi$
$541$	−34.6430	−1.48942	−0.744709	+	0.667389i	$0.767412\pi$
$542$	63.5175	2.72831
$543$	−10.7875	−0.462936
$544$	−32.3109	−1.38532
$545$	2.21862	0.0950354
$546$	0	0
$547$	0.156894	0.00670828	0.00335414	−	0.999994i	$-0.498932\pi$
$547$	0.156894	0.00670828	0.00335414	+	0.999994i	$0.498932\pi$
$548$	−21.0400	−0.898786
$549$	−3.80612	−0.162441
$550$	−2.55022	−0.108742
$551$	1.76916	0.0753689
$552$	102.746	4.37315
$553$	0	0
$554$	37.1752	1.57942
$555$	14.8135	0.628797
$556$	−65.9436	−2.79663
$557$	35.6939	1.51240	0.756199	−	0.654342i	$-0.227054\pi$
$557$	35.6939	1.51240	0.756199	+	0.654342i	$0.227054\pi$
$558$	−5.05515	−0.214001
$559$	−1.92341	−0.0813515
$560$	0	0
$561$	10.4721	0.442132
$562$	−55.5695	−2.34406
$563$	−40.9476	−1.72574	−0.862868	−	0.505429i	$-0.831334\pi$
$563$	−40.9476	−1.72574	−0.862868	+	0.505429i	$0.831334\pi$
$564$	−58.9963	−2.48419
$565$	−10.8293	−0.455592
$566$	44.0849	1.85303
$567$	0	0
$568$	−88.8204	−3.72682
$569$	31.3133	1.31272	0.656361	−	0.754447i	$-0.272095\pi$
$569$	31.3133	1.31272	0.656361	+	0.754447i	$0.272095\pi$
$570$	2.60927	0.109290
$571$	−6.57532	−0.275169	−0.137584	−	0.990490i	$-0.543934\pi$
$571$	−6.57532	−0.275169	−0.137584	+	0.990490i	$0.543934\pi$
$572$	−6.78446	−0.283673
$573$	40.3186	1.68433
$574$	0	0
$575$	8.58444	0.357996
$576$	0.102763	0.00428178
$577$	−17.7367	−0.738389	−0.369195	−	0.929352i	$-0.620366\pi$
$577$	−17.7367	−0.738389	−0.369195	+	0.929352i	$0.620366\pi$
$578$	36.2302	1.50698
$579$	3.98767	0.165722
$580$	14.5981	0.606152
$581$	0	0
$582$	23.6007	0.978279
$583$	−4.69864	−0.194598
$584$	−46.2866	−1.91536
$585$	0.774521	0.0320225
$586$	−21.4173	−0.884742
$587$	−27.4297	−1.13214	−0.566072	−	0.824356i	$-0.691538\pi$
$587$	−27.4297	−1.13214	−0.566072	+	0.824356i	$0.691538\pi$
$588$	0	0
$589$	−2.10432	−0.0867068
$590$	−23.4800	−0.966658
$591$	−2.90122	−0.119340
$592$	57.4903	2.36284
$593$	−30.7587	−1.26311	−0.631554	−	0.775332i	$-0.717582\pi$
$593$	−30.7587	−1.26311	−0.631554	+	0.775332i	$0.717582\pi$
$594$	11.8840	0.487608
$595$	0	0
$596$	39.4699	1.61675
$597$	20.4670	0.837659
$598$	32.9795	1.34863
$599$	−14.6139	−0.597108	−0.298554	−	0.954393i	$-0.596504\pi$
$599$	−14.6139	−0.597108	−0.298554	+	0.954393i	$0.596504\pi$
$600$	11.9688	0.488625
$601$	15.8405	0.646149	0.323075	−	0.946373i	$-0.395284\pi$
$601$	15.8405	0.646149	0.323075	+	0.946373i	$0.395284\pi$
$602$	0	0
$603$	−6.14715	−0.250331
$604$	79.9637	3.25368
$605$	1.00000	0.0406558
$606$	−66.9942	−2.72145
$607$	7.79643	0.316447	0.158224	−	0.987403i	$-0.449423\pi$
$607$	7.79643	0.316447	0.158224	+	0.987403i	$0.449423\pi$
$608$	3.15687	0.128028
$609$	0	0
$610$	−18.8791	−0.764394
$611$	−10.5271	−0.425883
$612$	−12.9349	−0.522861
$613$	−25.4912	−1.02958	−0.514789	−	0.857317i	$-0.672130\pi$
$613$	−25.4912	−1.02958	−0.514789	+	0.857317i	$0.672130\pi$
$614$	76.2629	3.07772
$615$	17.9595	0.724199
$616$	0	0
$617$	−19.9703	−0.803973	−0.401986	−	0.915646i	$-0.631680\pi$
$617$	−19.9703	−0.803973	−0.401986	+	0.915646i	$0.631680\pi$
$618$	−30.4476	−1.22478
$619$	34.4581	1.38499	0.692494	−	0.721424i	$-0.256512\pi$
$619$	34.4581	1.38499	0.692494	+	0.721424i	$0.256512\pi$
$620$	−17.3636	−0.697338
$621$	−40.0036	−1.60529
$622$	−47.1686	−1.89129
$623$	0	0
$624$	20.5452	0.822468
$625$	1.00000	0.0400000
$626$	64.6884	2.58547
$627$	−1.02316	−0.0408609
$628$	55.7821	2.22595
$629$	−44.1440	−1.76014
$630$	0	0
$631$	−21.1687	−0.842714	−0.421357	−	0.906895i	$-0.638446\pi$
$631$	−21.1687	−0.842714	−0.421357	+	0.906895i	$0.638446\pi$
$632$	65.3544	2.59966
$633$	−3.75437	−0.149223
$634$	10.0829	0.400444
$635$	3.80250	0.150897
$636$	39.6681	1.57294
$637$	0	0
$638$	−8.26633	−0.327267
$639$	−7.15234	−0.282942
$640$	−11.0582	−0.437113
$641$	−3.06718	−0.121146	−0.0605732	−	0.998164i	$-0.519293\pi$
$641$	−3.06718	−0.121146	−0.0605732	+	0.998164i	$0.519293\pi$
$642$	−72.1945	−2.84929
$643$	16.0289	0.632117	0.316058	−	0.948740i	$-0.397640\pi$
$643$	16.0289	0.632117	0.316058	+	0.948740i	$0.397640\pi$
$644$	0	0
$645$	−2.39345	−0.0942422
$646$	−7.77559	−0.305926
$647$	−33.7054	−1.32510	−0.662548	−	0.749020i	$-0.730525\pi$
$647$	−33.7054	−1.32510	−0.662548	+	0.749020i	$0.730525\pi$
$648$	−65.6227	−2.57790
$649$	9.20708	0.361409
$650$	3.84178	0.150687
$651$	0	0
$652$	−30.1687	−1.18150
$653$	27.8905	1.09144	0.545721	−	0.837967i	$-0.316256\pi$
$653$	27.8905	1.09144	0.545721	+	0.837967i	$0.316256\pi$
$654$	10.6065	0.414745
$655$	14.9423	0.583845
$656$	69.7000	2.72133
$657$	−3.72727	−0.145415
$658$	0	0
$659$	9.12210	0.355346	0.177673	−	0.984090i	$-0.443143\pi$
$659$	9.12210	0.355346	0.177673	+	0.984090i	$0.443143\pi$
$660$	−8.44247	−0.328623
$661$	23.3070	0.906538	0.453269	−	0.891374i	$-0.350258\pi$
$661$	23.3070	0.906538	0.453269	+	0.891374i	$0.350258\pi$
$662$	−39.4529	−1.53338
$663$	−15.7757	−0.612677
$664$	9.81302	0.380819
$665$	0	0
$666$	10.3610	0.401482
$667$	27.8258	1.07742
$668$	81.8361	3.16633
$669$	−36.6216	−1.41587
$670$	−30.4911	−1.17797
$671$	7.40295	0.285788
$672$	0	0
$673$	−10.6792	−0.411655	−0.205827	−	0.978588i	$-0.565989\pi$
$673$	−10.6792	−0.411655	−0.205827	+	0.978588i	$0.565989\pi$
$674$	46.5120	1.79158
$675$	−4.66001	−0.179364
$676$	−48.3264	−1.85871
$677$	−21.2496	−0.816689	−0.408344	−	0.912828i	$-0.633894\pi$
$677$	−21.2496	−0.816689	−0.408344	+	0.912828i	$0.633894\pi$
$678$	−51.7710	−1.98825
$679$	0	0
$680$	−35.6670	−1.36777
$681$	25.4487	0.975197
$682$	9.83232	0.376499
$683$	35.8442	1.37154	0.685770	−	0.727819i	$-0.259466\pi$
$683$	35.8442	1.37154	0.685770	+	0.727819i	$0.259466\pi$
$684$	1.26378	0.0483217
$685$	−4.67182	−0.178501
$686$	0	0
$687$	−22.7346	−0.867381
$688$	−9.28887	−0.354135
$689$	7.07828	0.269661
$690$	41.0391	1.56233
$691$	−29.8516	−1.13561	−0.567804	−	0.823164i	$-0.692207\pi$
$691$	−29.8516	−1.13561	−0.567804	+	0.823164i	$0.692207\pi$
$692$	36.9705	1.40541
$693$	0	0
$694$	−80.1858	−3.04381
$695$	−14.6424	−0.555419
$696$	38.7960	1.47056
$697$	−53.5192	−2.02719
$698$	31.8018	1.20372
$699$	51.3822	1.94345
$700$	0	0
$701$	−11.7181	−0.442587	−0.221294	−	0.975207i	$-0.571028\pi$
$701$	−11.7181	−0.442587	−0.221294	+	0.975207i	$0.571028\pi$
$702$	−17.9027	−0.675695
$703$	4.31301	0.162668
$704$	−0.199875	−0.00753306
$705$	−13.0998	−0.493367
$706$	8.08019	0.304102
$707$	0	0
$708$	−77.7305	−2.92129
$709$	−31.1243	−1.16890	−0.584449	−	0.811431i	$-0.698689\pi$
$709$	−31.1243	−1.16890	−0.584449	+	0.811431i	$0.698689\pi$
$710$	−35.4770	−1.33143
$711$	5.26272	0.197367
$712$	−9.97749	−0.373922
$713$	−33.0972	−1.23950
$714$	0	0
$715$	−1.50645	−0.0563381
$716$	1.03600	0.0387172
$717$	56.3243	2.10347
$718$	11.0655	0.412962
$719$	35.1180	1.30968	0.654840	−	0.755768i	$-0.272736\pi$
$719$	35.1180	1.30968	0.654840	+	0.755768i	$0.272736\pi$
$720$	3.74046	0.139399
$721$	0	0
$722$	−47.6944	−1.77500
$723$	−47.9390	−1.78287
$724$	−25.9162	−0.963169
$725$	3.24142	0.120383
$726$	4.78064	0.177426
$727$	−36.0570	−1.33728	−0.668640	−	0.743587i	$-0.733123\pi$
$727$	−36.0570	−1.33728	−0.668640	+	0.743587i	$0.733123\pi$
$728$	0	0
$729$	20.9227	0.774914
$730$	−18.4880	−0.684272
$731$	7.13247	0.263804
$732$	−62.4992	−2.31004
$733$	−18.4578	−0.681753	−0.340877	−	0.940108i	$-0.610724\pi$
$733$	−18.4578	−0.681753	−0.340877	+	0.940108i	$0.610724\pi$
$734$	53.4458	1.97272
$735$	0	0
$736$	49.6520	1.83020
$737$	11.9563	0.440415
$738$	12.5615	0.462394
$739$	18.6221	0.685024	0.342512	−	0.939513i	$-0.388722\pi$
$739$	18.6221	0.685024	0.342512	+	0.939513i	$0.388722\pi$
$740$	35.5884	1.30825
$741$	1.54133	0.0566223
$742$	0	0
$743$	4.24611	0.155775	0.0778873	−	0.996962i	$-0.475183\pi$
$743$	4.24611	0.155775	0.0778873	+	0.996962i	$0.475183\pi$
$744$	−46.1456	−1.69178
$745$	8.76407	0.321091
$746$	−4.10586	−0.150326
$747$	0.790202	0.0289120
$748$	25.1585	0.919884
$749$	0	0
$750$	4.78064	0.174564
$751$	16.4886	0.601677	0.300838	−	0.953675i	$-0.402734\pi$
$751$	16.4886	0.601677	0.300838	+	0.953675i	$0.402734\pi$
$752$	−50.8396	−1.85393
$753$	36.8697	1.34361
$754$	12.4528	0.453505
$755$	17.7555	0.646189
$756$	0	0
$757$	−28.8402	−1.04822	−0.524108	−	0.851652i	$-0.675601\pi$
$757$	−28.8402	−1.04822	−0.524108	+	0.851652i	$0.675601\pi$
$758$	−21.5658	−0.783305
$759$	−16.0924	−0.584118
$760$	3.48477	0.126406
$761$	−30.8735	−1.11916	−0.559582	−	0.828775i	$-0.689038\pi$
$761$	−30.8735	−1.11916	−0.559582	+	0.828775i	$0.689038\pi$
$762$	18.1784	0.658533
$763$	0	0
$764$	96.8625	3.50436
$765$	−2.87212	−0.103842
$766$	−10.3622	−0.374400
$767$	−13.8700	−0.500818
$768$	−53.6146	−1.93465
$769$	−11.8955	−0.428962	−0.214481	−	0.976728i	$-0.568806\pi$
$769$	−11.8955	−0.428962	−0.214481	+	0.976728i	$0.568806\pi$
$770$	0	0
$771$	−8.30532	−0.299109
$772$	9.58009	0.344795
$773$	21.6620	0.779129	0.389565	−	0.920999i	$-0.372625\pi$
$773$	21.6620	0.779129	0.389565	+	0.920999i	$0.372625\pi$
$774$	−1.67406	−0.0601728
$775$	−3.85548	−0.138493
$776$	31.5196	1.13149
$777$	0	0
$778$	37.3764	1.34001
$779$	5.22899	0.187348
$780$	12.7182	0.455384
$781$	13.9114	0.497789
$782$	−122.296	−4.37330
$783$	−15.1051	−0.539811
$784$	0	0
$785$	12.3861	0.442079
$786$	71.4339	2.54796
$787$	10.6770	0.380592	0.190296	−	0.981727i	$-0.439055\pi$
$787$	10.6770	0.380592	0.190296	+	0.981727i	$0.439055\pi$
$788$	−6.96997	−0.248295
$789$	−23.3007	−0.829526
$790$	26.1042	0.928744
$791$	0	0
$792$	−3.28262	−0.116643
$793$	−11.1522	−0.396026
$794$	50.2416	1.78301
$795$	8.80809	0.312391
$796$	49.1705	1.74280
$797$	14.9964	0.531199	0.265599	−	0.964084i	$-0.414430\pi$
$797$	14.9964	0.531199	0.265599	+	0.964084i	$0.414430\pi$
$798$	0	0
$799$	39.0373	1.38104
$800$	5.78395	0.204494
$801$	−0.803446	−0.0283884
$802$	97.5476	3.44452
$803$	7.24959	0.255832
$804$	−100.941	−3.55990
$805$	0	0
$806$	−14.8119	−0.521727
$807$	36.5252	1.28575
$808$	−89.4732	−3.14766
$809$	29.0254	1.02048	0.510240	−	0.860032i	$-0.329557\pi$
$809$	29.0254	1.02048	0.510240	+	0.860032i	$0.329557\pi$
$810$	−26.2113	−0.920971
$811$	11.8393	0.415733	0.207866	−	0.978157i	$-0.433348\pi$
$811$	11.8393	0.415733	0.207866	+	0.978157i	$0.433348\pi$
$812$	0	0
$813$	46.6902	1.63750
$814$	−20.1523	−0.706338
$815$	−6.69879	−0.234648
$816$	−76.1868	−2.66707
$817$	−0.696864	−0.0243802
$818$	5.06859	0.177219
$819$	0	0
$820$	43.1465	1.50674
$821$	−1.70716	−0.0595801	−0.0297901	−	0.999556i	$-0.509484\pi$
$821$	−1.70716	−0.0595801	−0.0297901	+	0.999556i	$0.509484\pi$
$822$	−22.3343	−0.778999
$823$	−26.7554	−0.932633	−0.466317	−	0.884618i	$-0.654419\pi$
$823$	−26.7554	−0.932633	−0.466317	+	0.884618i	$0.654419\pi$
$824$	−40.6639	−1.41659
$825$	−1.87460	−0.0652653
$826$	0	0
$827$	11.8564	0.412289	0.206144	−	0.978522i	$-0.433908\pi$
$827$	11.8564	0.412289	0.206144	+	0.978522i	$0.433908\pi$
$828$	19.8770	0.690772
$829$	4.15574	0.144335	0.0721675	−	0.997393i	$-0.477008\pi$
$829$	4.15574	0.144335	0.0721675	+	0.997393i	$0.477008\pi$
$830$	3.91956	0.136050
$831$	27.3266	0.947949
$832$	0.301102	0.0104388
$833$	0	0
$834$	−70.0002	−2.42391
$835$	18.1713	0.628842
$836$	−2.45806	−0.0850137
$837$	17.9666	0.621016
$838$	64.9420	2.24338
$839$	−47.3111	−1.63336	−0.816680	−	0.577091i	$-0.804188\pi$
$839$	−47.3111	−1.63336	−0.816680	+	0.577091i	$0.804188\pi$
$840$	0	0
$841$	−18.4932	−0.637696
$842$	79.2884	2.73246
$843$	−40.8478	−1.40687
$844$	−9.01960	−0.310468
$845$	−10.7306	−0.369144
$846$	−9.16242	−0.315010
$847$	0	0
$848$	34.1837	1.17387
$849$	32.4057	1.11216
$850$	−14.2463	−0.488643
$851$	67.8359	2.32539
$852$	−117.446	−4.02365
$853$	14.2151	0.486716	0.243358	−	0.969937i	$-0.421751\pi$
$853$	14.2151	0.486716	0.243358	+	0.969937i	$0.421751\pi$
$854$	0	0
$855$	0.280614	0.00959681
$856$	−96.4185	−3.29552
$857$	−15.0118	−0.512795	−0.256397	−	0.966571i	$-0.582536\pi$
$857$	−15.0118	−0.512795	−0.256397	+	0.966571i	$0.582536\pi$
$858$	−7.20181	−0.245866
$859$	−27.9217	−0.952676	−0.476338	−	0.879262i	$-0.658036\pi$
$859$	−27.9217	−0.952676	−0.476338	+	0.879262i	$0.658036\pi$
$860$	−5.75011	−0.196077
$861$	0	0
$862$	20.7707	0.707454
$863$	30.8807	1.05119	0.525596	−	0.850734i	$-0.323842\pi$
$863$	30.8807	1.05119	0.525596	+	0.850734i	$0.323842\pi$
$864$	−26.9533	−0.916969
$865$	8.20909	0.279117
$866$	−4.62532	−0.157175
$867$	26.6319	0.904468
$868$	0	0
$869$	−10.2361	−0.347234
$870$	15.4961	0.525366
$871$	−18.0116	−0.610299
$872$	14.1653	0.479698
$873$	2.53814	0.0859031
$874$	11.9487	0.404171
$875$	0	0
$876$	−61.2044	−2.06791
$877$	15.8856	0.536420	0.268210	−	0.963360i	$-0.413568\pi$
$877$	15.8856	0.536420	0.268210	+	0.963360i	$0.413568\pi$
$878$	−7.61889	−0.257125
$879$	−15.7434	−0.531011
$880$	−7.27523	−0.245248
$881$	34.4657	1.16118	0.580590	−	0.814196i	$-0.302822\pi$
$881$	34.4657	1.16118	0.580590	+	0.814196i	$0.302822\pi$
$882$	0	0
$883$	27.8356	0.936743	0.468372	−	0.883532i	$-0.344841\pi$
$883$	27.8356	0.936743	0.468372	+	0.883532i	$0.344841\pi$
$884$	−37.9000	−1.27472
$885$	−17.2596	−0.580176
$886$	−85.6475	−2.87738
$887$	−1.99326	−0.0669270	−0.0334635	−	0.999440i	$-0.510654\pi$
$887$	−1.99326	−0.0669270	−0.0334635	+	0.999440i	$0.510654\pi$
$888$	94.5800	3.17390
$889$	0	0
$890$	−3.98525	−0.133586
$891$	10.2781	0.344328
$892$	−87.9808	−2.94581
$893$	−3.81406	−0.127633
$894$	41.8979	1.40127
$895$	0.230038	0.00768933
$896$	0	0
$897$	24.2425	0.809432
$898$	83.3279	2.78069
$899$	−12.4972	−0.416807
$900$	2.31546	0.0771821
$901$	−26.2480	−0.874448
$902$	−24.4322	−0.813504
$903$	0	0
$904$	−69.1421	−2.29963
$905$	−5.75456	−0.191288
$906$	84.8827	2.82004
$907$	22.4511	0.745476	0.372738	−	0.927937i	$-0.378419\pi$
$907$	22.4511	0.745476	0.372738	+	0.927937i	$0.378419\pi$
$908$	61.1387	2.02896
$909$	−7.20491	−0.238972
$910$	0	0
$911$	−46.8664	−1.55275	−0.776376	−	0.630270i	$-0.782944\pi$
$911$	−46.8664	−1.55275	−0.776376	+	0.630270i	$0.782944\pi$
$912$	7.44369	0.246485
$913$	−1.53695	−0.0508657
$914$	−71.6224	−2.36906
$915$	−13.8776	−0.458779
$916$	−54.6184	−1.80464
$917$	0	0
$918$	66.3877	2.19112
$919$	1.95268	0.0644128	0.0322064	−	0.999481i	$-0.489747\pi$
$919$	1.95268	0.0644128	0.0322064	+	0.999481i	$0.489747\pi$
$920$	54.8093	1.80701
$921$	56.0590	1.84721
$922$	−8.51474	−0.280418
$923$	−20.9568	−0.689803
$924$	0	0
$925$	7.90220	0.259823
$926$	−19.1816	−0.630346
$927$	−3.27449	−0.107548
$928$	18.7482	0.615441
$929$	−25.7120	−0.843584	−0.421792	−	0.906693i	$-0.638599\pi$
$929$	−25.7120	−0.843584	−0.421792	+	0.906693i	$0.638599\pi$
$930$	−18.4317	−0.604399
$931$	0	0
$932$	123.442	4.04348
$933$	−34.6725	−1.13513
$934$	−51.9493	−1.69983
$935$	5.58630	0.182691
$936$	4.94511	0.161636
$937$	21.4546	0.700890	0.350445	−	0.936583i	$-0.386030\pi$
$937$	21.4546	0.700890	0.350445	+	0.936583i	$0.386030\pi$
$938$	0	0
$939$	47.5509	1.55176
$940$	−31.4713	−1.02648
$941$	−0.316562	−0.0103196	−0.00515981	−	0.999987i	$-0.501642\pi$
$941$	−0.316562	−0.0103196	−0.00515981	+	0.999987i	$0.501642\pi$
$942$	59.2135	1.92928
$943$	82.2428	2.67819
$944$	−66.9836	−2.18013
$945$	0	0
$946$	3.25606	0.105864
$947$	−47.6464	−1.54830	−0.774150	−	0.633002i	$-0.781823\pi$
$947$	−47.6464	−1.54830	−0.774150	+	0.633002i	$0.781823\pi$
$948$	86.4175	2.80671
$949$	−10.9212	−0.354516
$950$	1.39190	0.0451593
$951$	7.41171	0.240341
$952$	0	0
$953$	49.4224	1.60095	0.800475	−	0.599367i	$-0.204581\pi$
$953$	49.4224	1.60095	0.800475	+	0.599367i	$0.204581\pi$
$954$	6.16066	0.199459
$955$	21.5078	0.695976
$956$	135.315	4.37641
$957$	−6.07638	−0.196421
$958$	6.93360	0.224014
$959$	0	0
$960$	0.374686	0.0120929
$961$	−16.1352	−0.520492
$962$	30.3585	0.978797
$963$	−7.76419	−0.250197
$964$	−115.170	−3.70938
$965$	2.12721	0.0684772
$966$	0	0
$967$	25.3951	0.816653	0.408326	−	0.912836i	$-0.366113\pi$
$967$	25.3951	0.816653	0.408326	+	0.912836i	$0.366113\pi$
$968$	6.38473	0.205213
$969$	−5.71565	−0.183613
$970$	12.5897	0.404231
$971$	38.7782	1.24445	0.622225	−	0.782838i	$-0.286229\pi$
$971$	38.7782	1.24445	0.622225	+	0.782838i	$0.286229\pi$
$972$	−23.8118	−0.763764
$973$	0	0
$974$	−24.7501	−0.793044
$975$	2.82400	0.0904404
$976$	−53.8582	−1.72396
$977$	9.88817	0.316351	0.158175	−	0.987411i	$-0.449439\pi$
$977$	9.88817	0.316351	0.158175	+	0.987411i	$0.449439\pi$
$978$	−32.0245	−1.02403
$979$	1.56271	0.0499445
$980$	0	0
$981$	1.14067	0.0364189
$982$	5.94849	0.189824
$983$	−29.3543	−0.936257	−0.468129	−	0.883660i	$-0.655072\pi$
$983$	−29.3543	−0.936257	−0.468129	+	0.883660i	$0.655072\pi$
$984$	114.667	3.65544
$985$	−1.54764	−0.0493120
$986$	−46.1782	−1.47061
$987$	0	0
$988$	3.70295	0.117806
$989$	−10.9604	−0.348522
$990$	−1.31116	−0.0416713
$991$	−46.0218	−1.46193	−0.730965	−	0.682415i	$-0.760930\pi$
$991$	−46.0218	−1.46193	−0.730965	+	0.682415i	$0.760930\pi$
$992$	−22.2999	−0.708024
$993$	−29.0009	−0.920315
$994$	0	0
$995$	10.9180	0.346125
$996$	12.9757	0.411150
$997$	15.9728	0.505862	0.252931	−	0.967484i	$-0.418605\pi$
$997$	15.9728	0.505862	0.252931	+	0.967484i	$0.418605\pi$
$998$	−76.5830	−2.42419
$999$	−36.8243	−1.16507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.t.1.8		8
7.2	even	3		385.2.i.c.221.1	✓	16
7.4	even	3		385.2.i.c.331.1	yes	16
7.6	odd	2		2695.2.a.s.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.1	✓	16	7.2	even	3
385.2.i.c.331.1	yes	16	7.4	even	3
2695.2.a.s.1.8		8	7.6	odd	2
2695.2.a.t.1.8		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q+2.55022 q^{2} +1.87460 q^{3} +4.50360 q^{4} +1.00000 q^{5} +4.78064 q^{6} +6.38473 q^{8} +0.514136 q^{9} +O(q^{10})\)	\(q+2.55022 q^{2} +1.87460 q^{3} +4.50360 q^{4} +1.00000 q^{5} +4.78064 q^{6} +6.38473 q^{8} +0.514136 q^{9} +2.55022 q^{10} -1.00000 q^{11} +8.44247 q^{12} +1.50645 q^{13} +1.87460 q^{15} +7.27523 q^{16} -5.58630 q^{17} +1.31116 q^{18} +0.545798 q^{19} +4.50360 q^{20} -2.55022 q^{22} +8.58444 q^{23} +11.9688 q^{24} +1.00000 q^{25} +3.84178 q^{26} -4.66001 q^{27} +3.24142 q^{29} +4.78064 q^{30} -3.85548 q^{31} +5.78395 q^{32} -1.87460 q^{33} -14.2463 q^{34} +2.31546 q^{36} +7.90220 q^{37} +1.39190 q^{38} +2.82400 q^{39} +6.38473 q^{40} +9.58045 q^{41} -1.27678 q^{43} -4.50360 q^{44} +0.514136 q^{45} +21.8922 q^{46} -6.98804 q^{47} +13.6382 q^{48} +2.55022 q^{50} -10.4721 q^{51} +6.78446 q^{52} +4.69864 q^{53} -11.8840 q^{54} -1.00000 q^{55} +1.02316 q^{57} +8.26633 q^{58} -9.20708 q^{59} +8.44247 q^{60} -7.40295 q^{61} -9.83232 q^{62} +0.199875 q^{64} +1.50645 q^{65} -4.78064 q^{66} -11.9563 q^{67} -25.1585 q^{68} +16.0924 q^{69} -13.9114 q^{71} +3.28262 q^{72} -7.24959 q^{73} +20.1523 q^{74} +1.87460 q^{75} +2.45806 q^{76} +7.20181 q^{78} +10.2361 q^{79} +7.27523 q^{80} -10.2781 q^{81} +24.4322 q^{82} +1.53695 q^{83} -5.58630 q^{85} -3.25606 q^{86} +6.07638 q^{87} -6.38473 q^{88} -1.56271 q^{89} +1.31116 q^{90} +38.6609 q^{92} -7.22750 q^{93} -17.8210 q^{94} +0.545798 q^{95} +10.8426 q^{96} +4.93672 q^{97} -0.514136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * q^99

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