LMFDB - Embedded newform 1127.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1127,2,Mod(1,1127)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1127, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1127.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1127 = 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1127.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:	$8.99914030780$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 10x^{5} - x^{4} + 29x^{3} + 9x^{2} - 24x - 11 $ x^7 - 10x^5 - x^4 + 29x^3 + 9x^2 - 24x - 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 161)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.41138$ of defining polynomial
Character	$\chi$	$=$	1127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41138 q^{2} -2.22004 q^{3} +3.81476 q^{4} -0.731257 q^{5} -5.35336 q^{6} +4.37609 q^{8} +1.92856 q^{9} +O(q^{10})$	\(q+2.41138 q^{2} -2.22004 q^{3} +3.81476 q^{4} -0.731257 q^{5} -5.35336 q^{6} +4.37609 q^{8} +1.92856 q^{9} -1.76334 q^{10} -6.08962 q^{11} -8.46891 q^{12} -3.98092 q^{13} +1.62342 q^{15} +2.92289 q^{16} -2.26985 q^{17} +4.65050 q^{18} +3.73265 q^{19} -2.78957 q^{20} -14.6844 q^{22} +1.00000 q^{23} -9.71507 q^{24} -4.46526 q^{25} -9.59952 q^{26} +2.37863 q^{27} +2.92532 q^{29} +3.91468 q^{30} -0.838280 q^{31} -1.70396 q^{32} +13.5192 q^{33} -5.47348 q^{34} +7.35701 q^{36} -0.669580 q^{37} +9.00086 q^{38} +8.83779 q^{39} -3.20005 q^{40} -9.01411 q^{41} -9.88871 q^{43} -23.2304 q^{44} -1.41027 q^{45} +2.41138 q^{46} -3.52953 q^{47} -6.48893 q^{48} -10.7675 q^{50} +5.03915 q^{51} -15.1863 q^{52} +10.6520 q^{53} +5.73579 q^{54} +4.45308 q^{55} -8.28663 q^{57} +7.05406 q^{58} +8.15536 q^{59} +6.19295 q^{60} +1.50217 q^{61} -2.02141 q^{62} -9.95469 q^{64} +2.91108 q^{65} +32.5999 q^{66} +5.04290 q^{67} -8.65894 q^{68} -2.22004 q^{69} -5.82247 q^{71} +8.43956 q^{72} -6.81932 q^{73} -1.61461 q^{74} +9.91305 q^{75} +14.2392 q^{76} +21.3113 q^{78} +1.24277 q^{79} -2.13739 q^{80} -11.0663 q^{81} -21.7365 q^{82} +16.8288 q^{83} +1.65984 q^{85} -23.8454 q^{86} -6.49432 q^{87} -26.6487 q^{88} +9.64488 q^{89} -3.40071 q^{90} +3.81476 q^{92} +1.86101 q^{93} -8.51105 q^{94} -2.72953 q^{95} +3.78286 q^{96} -13.6744 q^{97} -11.7442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 5 q^{3} + 6 q^{4} - 4 q^{5} - 6 q^{6} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 5 * q^3 + 6 * q^4 - 4 * q^5 - 6 * q^6 - 3 * q^8 + 4 * q^9	$ 7 q - 5 q^{3} + 6 q^{4} - 4 q^{5} - 6 q^{6} - 3 q^{8} + 4 q^{9} + 2 q^{10} + 4 q^{11} - 9 q^{12} - 14 q^{13} - 3 q^{15} - 8 q^{16} - 4 q^{17} + 19 q^{18} - 9 q^{19} - 12 q^{20} - 10 q^{22} + 7 q^{23} + 4 q^{24} + 3 q^{25} - 14 q^{26} - 20 q^{27} - 5 q^{29} - 17 q^{30} - 10 q^{31} + 19 q^{32} - 3 q^{33} - 20 q^{34} + 4 q^{36} - 5 q^{37} + 17 q^{38} + 18 q^{39} - 4 q^{40} - 23 q^{41} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 4 q^{47} - 11 q^{48} - 9 q^{50} + 7 q^{51} - 12 q^{52} + 2 q^{53} - 15 q^{54} - 17 q^{55} - 24 q^{57} - 7 q^{58} - 7 q^{59} + 32 q^{60} - 12 q^{61} + 4 q^{62} - 9 q^{64} + 9 q^{65} + 27 q^{66} + 2 q^{67} + 12 q^{68} - 5 q^{69} - 28 q^{71} - 20 q^{72} - 59 q^{73} + 2 q^{74} + 22 q^{75} - q^{76} - 17 q^{78} - 4 q^{79} + 22 q^{80} + 11 q^{81} - 54 q^{82} + 9 q^{83} + 9 q^{85} - 15 q^{86} - 11 q^{87} - 33 q^{88} - q^{89} - 2 q^{90} + 6 q^{92} + 15 q^{93} + 14 q^{94} - 16 q^{95} - 20 q^{96} - 35 q^{97} + 18 q^{99}+O(q^{100}) $ 7 * q - 5 * q^3 + 6 * q^4 - 4 * q^5 - 6 * q^6 - 3 * q^8 + 4 * q^9 + 2 * q^10 + 4 * q^11 - 9 * q^12 - 14 * q^13 - 3 * q^15 - 8 * q^16 - 4 * q^17 + 19 * q^18 - 9 * q^19 - 12 * q^20 - 10 * q^22 + 7 * q^23 + 4 * q^24 + 3 * q^25 - 14 * q^26 - 20 * q^27 - 5 * q^29 - 17 * q^30 - 10 * q^31 + 19 * q^32 - 3 * q^33 - 20 * q^34 + 4 * q^36 - 5 * q^37 + 17 * q^38 + 18 * q^39 - 4 * q^40 - 23 * q^41 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 4 * q^47 - 11 * q^48 - 9 * q^50 + 7 * q^51 - 12 * q^52 + 2 * q^53 - 15 * q^54 - 17 * q^55 - 24 * q^57 - 7 * q^58 - 7 * q^59 + 32 * q^60 - 12 * q^61 + 4 * q^62 - 9 * q^64 + 9 * q^65 + 27 * q^66 + 2 * q^67 + 12 * q^68 - 5 * q^69 - 28 * q^71 - 20 * q^72 - 59 * q^73 + 2 * q^74 + 22 * q^75 - q^76 - 17 * q^78 - 4 * q^79 + 22 * q^80 + 11 * q^81 - 54 * q^82 + 9 * q^83 + 9 * q^85 - 15 * q^86 - 11 * q^87 - 33 * q^88 - q^89 - 2 * q^90 + 6 * q^92 + 15 * q^93 + 14 * q^94 - 16 * q^95 - 20 * q^96 - 35 * q^97 + 18 * 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 $

$2$	2.41138	1.70510	0.852552	−	0.522642i	$-0.175054\pi$
$2$	2.41138	1.70510	0.852552	+	0.522642i	$0.175054\pi$
$3$	−2.22004	−1.28174	−0.640869	−	0.767650i	$-0.721426\pi$
$3$	−2.22004	−1.28174	−0.640869	+	0.767650i	$0.721426\pi$
$4$	3.81476	1.90738
$5$	−0.731257	−0.327028	−0.163514	−	0.986541i	$-0.552283\pi$
$5$	−0.731257	−0.327028	−0.163514	+	0.986541i	$0.552283\pi$
$6$	−5.35336	−2.18550
$7$	0	0
$7$	0	0
$8$	4.37609	1.54718
$9$	1.92856	0.642854
$10$	−1.76334	−0.557617
$11$	−6.08962	−1.83609	−0.918044	−	0.396478i	$-0.870232\pi$
$11$	−6.08962	−1.83609	−0.918044	+	0.396478i	$0.870232\pi$
$12$	−8.46891	−2.44476
$13$	−3.98092	−1.10411	−0.552054	−	0.833808i	$-0.686156\pi$
$13$	−3.98092	−1.10411	−0.552054	+	0.833808i	$0.686156\pi$
$14$	0	0
$15$	1.62342	0.419165
$16$	2.92289	0.730723
$17$	−2.26985	−0.550519	−0.275260	−	0.961370i	$-0.588764\pi$
$17$	−2.26985	−0.550519	−0.275260	+	0.961370i	$0.588764\pi$
$18$	4.65050	1.09613
$19$	3.73265	0.856330	0.428165	−	0.903701i	$-0.359160\pi$
$19$	3.73265	0.856330	0.428165	+	0.903701i	$0.359160\pi$
$20$	−2.78957	−0.623768
$21$	0	0
$22$	−14.6844	−3.13072
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−9.71507	−1.98308
$25$	−4.46526	−0.893053
$26$	−9.59952	−1.88262
$27$	2.37863	0.457768
$28$	0	0
$29$	2.92532	0.543218	0.271609	−	0.962408i	$-0.412444\pi$
$29$	2.92532	0.543218	0.271609	+	0.962408i	$0.412444\pi$
$30$	3.91468	0.714720
$31$	−0.838280	−0.150559	−0.0752797	−	0.997162i	$-0.523985\pi$
$31$	−0.838280	−0.150559	−0.0752797	+	0.997162i	$0.523985\pi$
$32$	−1.70396	−0.301221
$33$	13.5192	2.35339
$34$	−5.47348	−0.938693
$35$	0	0
$36$	7.35701	1.22617
$37$	−0.669580	−0.110078	−0.0550392	−	0.998484i	$-0.517528\pi$
$37$	−0.669580	−0.110078	−0.0550392	+	0.998484i	$0.517528\pi$
$38$	9.00086	1.46013
$39$	8.83779	1.41518
$40$	−3.20005	−0.505972
$41$	−9.01411	−1.40777	−0.703884	−	0.710315i	$-0.748552\pi$
$41$	−9.01411	−1.40777	−0.703884	+	0.710315i	$0.748552\pi$
$42$	0	0
$43$	−9.88871	−1.50801	−0.754007	−	0.656867i	$-0.771881\pi$
$43$	−9.88871	−1.50801	−0.754007	+	0.656867i	$0.771881\pi$
$44$	−23.2304	−3.50212
$45$	−1.41027	−0.210231
$46$	2.41138	0.355539
$47$	−3.52953	−0.514835	−0.257418	−	0.966300i	$-0.582872\pi$
$47$	−3.52953	−0.514835	−0.257418	+	0.966300i	$0.582872\pi$
$48$	−6.48893	−0.936596
$49$	0	0
$50$	−10.7675	−1.52275
$51$	5.03915	0.705622
$52$	−15.1863	−2.10596
$53$	10.6520	1.46317	0.731586	−	0.681750i	$-0.238781\pi$
$53$	10.6520	1.46317	0.731586	+	0.681750i	$0.238781\pi$
$54$	5.73579	0.780542
$55$	4.45308	0.600453
$56$	0	0
$57$	−8.28663	−1.09759
$58$	7.05406	0.926244
$59$	8.15536	1.06174	0.530869	−	0.847454i	$-0.321866\pi$
$59$	8.15536	1.06174	0.530869	+	0.847454i	$0.321866\pi$
$60$	6.19295	0.799507
$61$	1.50217	0.192333	0.0961663	−	0.995365i	$-0.469342\pi$
$61$	1.50217	0.192333	0.0961663	+	0.995365i	$0.469342\pi$
$62$	−2.02141	−0.256720
$63$	0	0
$64$	−9.95469	−1.24434
$65$	2.91108	0.361075
$66$	32.5999	4.01277
$67$	5.04290	0.616089	0.308044	−	0.951372i	$-0.400325\pi$
$67$	5.04290	0.616089	0.308044	+	0.951372i	$0.400325\pi$
$68$	−8.65894	−1.05005
$69$	−2.22004	−0.267261
$70$	0	0
$71$	−5.82247	−0.691001	−0.345500	−	0.938419i	$-0.612291\pi$
$71$	−5.82247	−0.691001	−0.345500	+	0.938419i	$0.612291\pi$
$72$	8.43956	0.994611
$73$	−6.81932	−0.798142	−0.399071	−	0.916920i	$-0.630667\pi$
$73$	−6.81932	−0.798142	−0.399071	+	0.916920i	$0.630667\pi$
$74$	−1.61461	−0.187695
$75$	9.91305	1.14466
$76$	14.2392	1.63335
$77$	0	0
$78$	21.3113	2.41303
$79$	1.24277	0.139822	0.0699112	−	0.997553i	$-0.477728\pi$
$79$	1.24277	0.139822	0.0699112	+	0.997553i	$0.477728\pi$
$80$	−2.13739	−0.238967
$81$	−11.0663	−1.22959
$82$	−21.7365	−2.40039
$83$	16.8288	1.84720	0.923600	−	0.383357i	$-0.125232\pi$
$83$	16.8288	1.84720	0.923600	+	0.383357i	$0.125232\pi$
$84$	0	0
$85$	1.65984	0.180035
$86$	−23.8454	−2.57132
$87$	−6.49432	−0.696264
$88$	−26.6487	−2.84076
$89$	9.64488	1.02235	0.511177	−	0.859475i	$-0.329209\pi$
$89$	9.64488	1.02235	0.511177	+	0.859475i	$0.329209\pi$
$90$	−3.40071	−0.358466
$91$	0	0
$92$	3.81476	0.397717
$93$	1.86101	0.192978
$94$	−8.51105	−0.877848
$95$	−2.72953	−0.280044
$96$	3.78286	0.386087
$97$	−13.6744	−1.38842	−0.694211	−	0.719772i	$-0.744247\pi$
$97$	−13.6744	−1.38842	−0.694211	+	0.719772i	$0.744247\pi$
$98$	0	0
$99$	−11.7442	−1.18034
$100$	−17.0339	−1.70339
$101$	−14.8457	−1.47720	−0.738601	−	0.674143i	$-0.764513\pi$
$101$	−14.8457	−1.47720	−0.738601	+	0.674143i	$0.764513\pi$
$102$	12.1513	1.20316
$103$	−10.6658	−1.05094	−0.525468	−	0.850813i	$-0.676110\pi$
$103$	−10.6658	−1.05094	−0.525468	+	0.850813i	$0.676110\pi$
$104$	−17.4209	−1.70826
$105$	0	0
$106$	25.6862	2.49486
$107$	0.0658172	0.00636279	0.00318139	−	0.999995i	$-0.498987\pi$
$107$	0.0658172	0.00636279	0.00318139	+	0.999995i	$0.498987\pi$
$108$	9.07392	0.873138
$109$	−4.91792	−0.471052	−0.235526	−	0.971868i	$-0.575681\pi$
$109$	−4.91792	−0.471052	−0.235526	+	0.971868i	$0.575681\pi$
$110$	10.7381	1.02383
$111$	1.48649	0.141092
$112$	0	0
$113$	5.38682	0.506749	0.253375	−	0.967368i	$-0.418460\pi$
$113$	5.38682	0.506749	0.253375	+	0.967368i	$0.418460\pi$
$114$	−19.9822	−1.87151
$115$	−0.731257	−0.0681901
$116$	11.1594	1.03612
$117$	−7.67745	−0.709780
$118$	19.6657	1.81037
$119$	0	0
$120$	7.10422	0.648524
$121$	26.0834	2.37122
$122$	3.62230	0.327947
$123$	20.0117	1.80439
$124$	−3.19784	−0.287174
$125$	6.92154	0.619082
$126$	0	0
$127$	18.7589	1.66458	0.832290	−	0.554340i	$-0.187029\pi$
$127$	18.7589	1.66458	0.832290	+	0.554340i	$0.187029\pi$
$128$	−20.5966	−1.82050
$129$	21.9533	1.93288
$130$	7.01972	0.615670
$131$	10.8696	0.949680	0.474840	−	0.880072i	$-0.342506\pi$
$131$	10.8696	0.949680	0.474840	+	0.880072i	$0.342506\pi$
$132$	51.5724	4.48880
$133$	0	0
$134$	12.1604	1.05050
$135$	−1.73939	−0.149703
$136$	−9.93306	−0.851753
$137$	1.10893	0.0947423	0.0473712	−	0.998877i	$-0.484916\pi$
$137$	1.10893	0.0947423	0.0473712	+	0.998877i	$0.484916\pi$
$138$	−5.35336	−0.455708
$139$	−2.44650	−0.207509	−0.103755	−	0.994603i	$-0.533086\pi$
$139$	−2.44650	−0.207509	−0.103755	+	0.994603i	$0.533086\pi$
$140$	0	0
$141$	7.83569	0.659884
$142$	−14.0402	−1.17823
$143$	24.2423	2.02724
$144$	5.63698	0.469748
$145$	−2.13916	−0.177648
$146$	−16.4440	−1.36091
$147$	0	0
$148$	−2.55429	−0.209961
$149$	6.28211	0.514650	0.257325	−	0.966325i	$-0.417159\pi$
$149$	6.28211	0.514650	0.257325	+	0.966325i	$0.417159\pi$
$150$	23.9041	1.95176
$151$	−7.83871	−0.637905	−0.318952	−	0.947771i	$-0.603331\pi$
$151$	−7.83871	−0.637905	−0.318952	+	0.947771i	$0.603331\pi$
$152$	16.3344	1.32490
$153$	−4.37755	−0.353904
$154$	0	0
$155$	0.612998	0.0492372
$156$	33.7141	2.69929
$157$	−17.2651	−1.37791	−0.688954	−	0.724805i	$-0.741930\pi$
$157$	−17.2651	−1.37791	−0.688954	+	0.724805i	$0.741930\pi$
$158$	2.99679	0.238412
$159$	−23.6479	−1.87540
$160$	1.24604	0.0985078
$161$	0	0
$162$	−26.6852	−2.09658
$163$	−5.50755	−0.431385	−0.215692	−	0.976461i	$-0.569201\pi$
$163$	−5.50755	−0.431385	−0.215692	+	0.976461i	$0.569201\pi$
$164$	−34.3867	−2.68515
$165$	−9.88599	−0.769623
$166$	40.5807	3.14967
$167$	13.9018	1.07576	0.537878	−	0.843023i	$-0.319226\pi$
$167$	13.9018	1.07576	0.537878	+	0.843023i	$0.319226\pi$
$168$	0	0
$169$	2.84772	0.219055
$170$	4.00252	0.306979
$171$	7.19866	0.550495
$172$	−37.7231	−2.87636
$173$	−13.3335	−1.01373	−0.506864	−	0.862026i	$-0.669195\pi$
$173$	−13.3335	−1.01373	−0.506864	+	0.862026i	$0.669195\pi$
$174$	−15.6603	−1.18720
$175$	0	0
$176$	−17.7993	−1.34167
$177$	−18.1052	−1.36087
$178$	23.2575	1.74322
$179$	21.5230	1.60870	0.804352	−	0.594154i	$-0.202513\pi$
$179$	21.5230	1.60870	0.804352	+	0.594154i	$0.202513\pi$
$180$	−5.37986	−0.400991
$181$	19.0363	1.41496	0.707480	−	0.706734i	$-0.249832\pi$
$181$	19.0363	1.41496	0.707480	+	0.706734i	$0.249832\pi$
$182$	0	0
$183$	−3.33486	−0.246520
$184$	4.37609	0.322609
$185$	0.489635	0.0359987
$186$	4.48761	0.329048
$187$	13.8225	1.01080
$188$	−13.4643	−0.981987
$189$	0	0
$190$	−6.58194	−0.477504
$191$	9.21621	0.666861	0.333431	−	0.942775i	$-0.391794\pi$
$191$	9.21621	0.666861	0.333431	+	0.942775i	$0.391794\pi$
$192$	22.0998	1.59491
$193$	−1.75650	−0.126436	−0.0632178	−	0.998000i	$-0.520136\pi$
$193$	−1.75650	−0.126436	−0.0632178	+	0.998000i	$0.520136\pi$
$194$	−32.9741	−2.36740
$195$	−6.46270	−0.462803
$196$	0	0
$197$	−22.8252	−1.62623	−0.813114	−	0.582104i	$-0.802229\pi$
$197$	−22.8252	−1.62623	−0.813114	+	0.582104i	$0.802229\pi$
$198$	−28.3198	−2.01260
$199$	−11.0549	−0.783659	−0.391829	−	0.920038i	$-0.628158\pi$
$199$	−11.0549	−0.783659	−0.391829	+	0.920038i	$0.628158\pi$
$200$	−19.5404	−1.38171
$201$	−11.1954	−0.789665
$202$	−35.7987	−2.51878
$203$	0	0
$204$	19.2232	1.34589
$205$	6.59163	0.460380
$206$	−25.7194	−1.79196
$207$	1.92856	0.134044
$208$	−11.6358	−0.806798
$209$	−22.7304	−1.57230
$210$	0	0
$211$	6.81925	0.469456	0.234728	−	0.972061i	$-0.424580\pi$
$211$	6.81925	0.469456	0.234728	+	0.972061i	$0.424580\pi$
$212$	40.6350	2.79083
$213$	12.9261	0.885682
$214$	0.158710	0.0108492
$215$	7.23119	0.493163
$216$	10.4091	0.708250
$217$	0	0
$218$	−11.8590	−0.803192
$219$	15.1391	1.02301
$220$	16.9874	1.14529
$221$	9.03609	0.607833
$222$	3.58450	0.240576
$223$	−14.2311	−0.952987	−0.476494	−	0.879178i	$-0.658092\pi$
$223$	−14.2311	−0.952987	−0.476494	+	0.879178i	$0.658092\pi$
$224$	0	0
$225$	−8.61154	−0.574102
$226$	12.9897	0.864060
$227$	2.49001	0.165268	0.0826340	−	0.996580i	$-0.473667\pi$
$227$	2.49001	0.165268	0.0826340	+	0.996580i	$0.473667\pi$
$228$	−31.6115	−2.09352
$229$	13.2315	0.874361	0.437181	−	0.899374i	$-0.355977\pi$
$229$	13.2315	0.874361	0.437181	+	0.899374i	$0.355977\pi$
$230$	−1.76334	−0.116271
$231$	0	0
$232$	12.8015	0.840457
$233$	−28.9905	−1.89923	−0.949617	−	0.313413i	$-0.898528\pi$
$233$	−28.9905	−1.89923	−0.949617	+	0.313413i	$0.898528\pi$
$234$	−18.5133	−1.21025
$235$	2.58100	0.168366
$236$	31.1108	2.02514
$237$	−2.75899	−0.179216
$238$	0	0
$239$	−1.30148	−0.0841857	−0.0420929	−	0.999114i	$-0.513403\pi$
$239$	−1.30148	−0.0841857	−0.0420929	+	0.999114i	$0.513403\pi$
$240$	4.74508	0.306293
$241$	−20.2462	−1.30417	−0.652087	−	0.758144i	$-0.726106\pi$
$241$	−20.2462	−1.30417	−0.652087	+	0.758144i	$0.726106\pi$
$242$	62.8971	4.04318
$243$	17.4318	1.11825
$244$	5.73041	0.366852
$245$	0	0
$246$	48.2557	3.07667
$247$	−14.8594	−0.945481
$248$	−3.66839	−0.232943
$249$	−37.3605	−2.36763
$250$	16.6905	1.05560
$251$	10.5102	0.663397	0.331698	−	0.943386i	$-0.392378\pi$
$251$	10.5102	0.663397	0.331698	+	0.943386i	$0.392378\pi$
$252$	0	0
$253$	−6.08962	−0.382851
$254$	45.2348	2.83828
$255$	−3.68491	−0.230758
$256$	−29.7570	−1.85981
$257$	0.226436	0.0141247	0.00706234	−	0.999975i	$-0.497752\pi$
$257$	0.226436	0.0141247	0.00706234	+	0.999975i	$0.497752\pi$
$258$	52.9378	3.29576
$259$	0	0
$260$	11.1051	0.688707
$261$	5.64166	0.349210
$262$	26.2107	1.61930
$263$	0.959772	0.0591821	0.0295911	−	0.999562i	$-0.490580\pi$
$263$	0.959772	0.0591821	0.0295911	+	0.999562i	$0.490580\pi$
$264$	59.1611	3.64111
$265$	−7.78939	−0.478498
$266$	0	0
$267$	−21.4120	−1.31039
$268$	19.2375	1.17512
$269$	7.57538	0.461879	0.230940	−	0.972968i	$-0.425820\pi$
$269$	7.57538	0.461879	0.230940	+	0.972968i	$0.425820\pi$
$270$	−4.19434	−0.255259
$271$	−23.2052	−1.40961	−0.704807	−	0.709399i	$-0.748966\pi$
$271$	−23.2052	−1.40961	−0.704807	+	0.709399i	$0.748966\pi$
$272$	−6.63453	−0.402277
$273$	0	0
$274$	2.67406	0.161546
$275$	27.1917	1.63972
$276$	−8.46891	−0.509769
$277$	−18.8389	−1.13192	−0.565960	−	0.824433i	$-0.691494\pi$
$277$	−18.8389	−1.13192	−0.565960	+	0.824433i	$0.691494\pi$
$278$	−5.89944	−0.353825
$279$	−1.61667	−0.0967878
$280$	0	0
$281$	−2.46071	−0.146794	−0.0733968	−	0.997303i	$-0.523384\pi$
$281$	−2.46071	−0.146794	−0.0733968	+	0.997303i	$0.523384\pi$
$282$	18.8948	1.12517
$283$	−14.0604	−0.835807	−0.417903	−	0.908491i	$-0.637235\pi$
$283$	−14.0604	−0.835807	−0.417903	+	0.908491i	$0.637235\pi$
$284$	−22.2114	−1.31800
$285$	6.05966	0.358943
$286$	58.4574	3.45666
$287$	0	0
$288$	−3.28620	−0.193641
$289$	−11.8478	−0.696928
$290$	−5.15833	−0.302908
$291$	30.3576	1.77959
$292$	−26.0141	−1.52236
$293$	12.2918	0.718096	0.359048	−	0.933319i	$-0.383101\pi$
$293$	12.2918	0.718096	0.359048	+	0.933319i	$0.383101\pi$
$294$	0	0
$295$	−5.96367	−0.347218
$296$	−2.93014	−0.170311
$297$	−14.4850	−0.840502
$298$	15.1486	0.877533
$299$	−3.98092	−0.230222
$300$	37.8159	2.18330
$301$	0	0
$302$	−18.9021	−1.08769
$303$	32.9580	1.89339
$304$	10.9102	0.625740
$305$	−1.09847	−0.0628982
$306$	−10.5559	−0.603443
$307$	4.14337	0.236475	0.118237	−	0.992985i	$-0.462276\pi$
$307$	4.14337	0.236475	0.118237	+	0.992985i	$0.462276\pi$
$308$	0	0
$309$	23.6786	1.34703
$310$	1.47817	0.0839546
$311$	−23.3491	−1.32401	−0.662003	−	0.749501i	$-0.730293\pi$
$311$	−23.3491	−1.32401	−0.662003	+	0.749501i	$0.730293\pi$
$312$	38.6749	2.18954
$313$	−20.9478	−1.18404	−0.592020	−	0.805923i	$-0.701669\pi$
$313$	−20.9478	−1.18404	−0.592020	+	0.805923i	$0.701669\pi$
$314$	−41.6328	−2.34948
$315$	0	0
$316$	4.74087	0.266695
$317$	−9.43527	−0.529937	−0.264969	−	0.964257i	$-0.585362\pi$
$317$	−9.43527	−0.529937	−0.264969	+	0.964257i	$0.585362\pi$
$318$	−57.0242	−3.19776
$319$	−17.8141	−0.997396
$320$	7.27944	0.406933
$321$	−0.146117	−0.00815543
$322$	0	0
$323$	−8.47257	−0.471426
$324$	−42.2154	−2.34530
$325$	17.7759	0.986027
$326$	−13.2808	−0.735557
$327$	10.9180	0.603765
$328$	−39.4465	−2.17807
$329$	0	0
$330$	−23.8389	−1.31229
$331$	22.2584	1.22343	0.611717	−	0.791077i	$-0.290479\pi$
$331$	22.2584	1.22343	0.611717	+	0.791077i	$0.290479\pi$
$332$	64.1979	3.52332
$333$	−1.29133	−0.0707643
$334$	33.5226	1.83428
$335$	−3.68766	−0.201478
$336$	0	0
$337$	−6.76320	−0.368415	−0.184208	−	0.982887i	$-0.558972\pi$
$337$	−6.76320	−0.368415	−0.184208	+	0.982887i	$0.558972\pi$
$338$	6.86693	0.373512
$339$	−11.9589	−0.649520
$340$	6.33191	0.343396
$341$	5.10480	0.276440
$342$	17.3587	0.938651
$343$	0	0
$344$	−43.2738	−2.33317
$345$	1.62342	0.0874019
$346$	−32.1522	−1.72851
$347$	−14.2918	−0.767226	−0.383613	−	0.923494i	$-0.625320\pi$
$347$	−14.2918	−0.767226	−0.383613	+	0.923494i	$0.625320\pi$
$348$	−24.7743	−1.32804
$349$	−11.6590	−0.624093	−0.312046	−	0.950067i	$-0.601014\pi$
$349$	−11.6590	−0.624093	−0.312046	+	0.950067i	$0.601014\pi$
$350$	0	0
$351$	−9.46914	−0.505425
$352$	10.3765	0.553068
$353$	5.25902	0.279909	0.139955	−	0.990158i	$-0.455304\pi$
$353$	5.25902	0.279909	0.139955	+	0.990158i	$0.455304\pi$
$354$	−43.6585	−2.32043
$355$	4.25773	0.225977
$356$	36.7929	1.95002
$357$	0	0
$358$	51.9001	2.74301
$359$	−19.6433	−1.03673	−0.518366	−	0.855159i	$-0.673459\pi$
$359$	−19.6433	−1.03673	−0.518366	+	0.855159i	$0.673459\pi$
$360$	−6.17149	−0.325266
$361$	−5.06729	−0.266699
$362$	45.9039	2.41265
$363$	−57.9061	−3.03928
$364$	0	0
$365$	4.98668	0.261015
$366$	−8.04163	−0.420343
$367$	12.2450	0.639182	0.319591	−	0.947556i	$-0.396455\pi$
$367$	12.2450	0.639182	0.319591	+	0.947556i	$0.396455\pi$
$368$	2.92289	0.152366
$369$	−17.3843	−0.904989
$370$	1.18070	0.0613816
$371$	0	0
$372$	7.09932	0.368083
$373$	−4.34581	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$373$	−4.34581	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$374$	33.3314	1.72352
$375$	−15.3661	−0.793501
$376$	−15.4455	−0.796543
$377$	−11.6455	−0.599772
$378$	0	0
$379$	−4.48867	−0.230568	−0.115284	−	0.993333i	$-0.536778\pi$
$379$	−4.48867	−0.230568	−0.115284	+	0.993333i	$0.536778\pi$
$380$	−10.4125	−0.534151
$381$	−41.6454	−2.13356
$382$	22.2238	1.13707
$383$	−8.04137	−0.410895	−0.205447	−	0.978668i	$-0.565865\pi$
$383$	−8.04137	−0.410895	−0.205447	+	0.978668i	$0.565865\pi$
$384$	45.7253	2.33341
$385$	0	0
$386$	−4.23559	−0.215586
$387$	−19.0710	−0.969432
$388$	−52.1645	−2.64825
$389$	−24.6380	−1.24920	−0.624599	−	0.780946i	$-0.714738\pi$
$389$	−24.6380	−1.24920	−0.624599	+	0.780946i	$0.714738\pi$
$390$	−15.5840	−0.789128
$391$	−2.26985	−0.114791
$392$	0	0
$393$	−24.1309	−1.21724
$394$	−55.0403	−2.77289
$395$	−0.908783	−0.0457259
$396$	−44.8013	−2.25135
$397$	10.3379	0.518842	0.259421	−	0.965764i	$-0.416468\pi$
$397$	10.3379	0.518842	0.259421	+	0.965764i	$0.416468\pi$
$398$	−26.6575	−1.33622
$399$	0	0
$400$	−13.0515	−0.652574
$401$	−21.5233	−1.07482	−0.537411	−	0.843321i	$-0.680597\pi$
$401$	−21.5233	−1.07482	−0.537411	+	0.843321i	$0.680597\pi$
$402$	−26.9965	−1.34646
$403$	3.33712	0.166234
$404$	−56.6328	−2.81759
$405$	8.09234	0.402112
$406$	0	0
$407$	4.07749	0.202113
$408$	22.0518	1.09172
$409$	−22.5835	−1.11668	−0.558340	−	0.829612i	$-0.688562\pi$
$409$	−22.5835	−1.11668	−0.558340	+	0.829612i	$0.688562\pi$
$410$	15.8949	0.784995
$411$	−2.46187	−0.121435
$412$	−40.6877	−2.00454
$413$	0	0
$414$	4.65050	0.228560
$415$	−12.3062	−0.604087
$416$	6.78334	0.332581
$417$	5.43131	0.265973
$418$	−54.8118	−2.68093
$419$	−5.64094	−0.275578	−0.137789	−	0.990462i	$-0.544000\pi$
$419$	−5.64094	−0.275578	−0.137789	+	0.990462i	$0.544000\pi$
$420$	0	0
$421$	19.0576	0.928809	0.464405	−	0.885623i	$-0.346268\pi$
$421$	19.0576	0.928809	0.464405	+	0.885623i	$0.346268\pi$
$422$	16.4438	0.800472
$423$	−6.80692	−0.330964
$424$	46.6143	2.26379
$425$	10.1355	0.491643
$426$	31.1698	1.51018
$427$	0	0
$428$	0.251077	0.0121363
$429$	−53.8187	−2.59839
$430$	17.4372	0.840894
$431$	17.1053	0.823932	0.411966	−	0.911199i	$-0.364842\pi$
$431$	17.1053	0.823932	0.411966	+	0.911199i	$0.364842\pi$
$432$	6.95249	0.334502
$433$	9.05939	0.435366	0.217683	−	0.976019i	$-0.430150\pi$
$433$	9.05939	0.435366	0.217683	+	0.976019i	$0.430150\pi$
$434$	0	0
$435$	4.74902	0.227698
$436$	−18.7607	−0.898475
$437$	3.73265	0.178557
$438$	36.5063	1.74434
$439$	−34.9683	−1.66895	−0.834473	−	0.551048i	$-0.814228\pi$
$439$	−34.9683	−1.66895	−0.834473	+	0.551048i	$0.814228\pi$
$440$	19.4870	0.929009
$441$	0	0
$442$	21.7895	1.03642
$443$	−37.7785	−1.79491	−0.897456	−	0.441103i	$-0.854587\pi$
$443$	−37.7785	−1.79491	−0.897456	+	0.441103i	$0.854587\pi$
$444$	5.67062	0.269116
$445$	−7.05289	−0.334339
$446$	−34.3167	−1.62494
$447$	−13.9465	−0.659647
$448$	0	0
$449$	16.4904	0.778232	0.389116	−	0.921189i	$-0.372781\pi$
$449$	16.4904	0.778232	0.389116	+	0.921189i	$0.372781\pi$
$450$	−20.7657	−0.978905
$451$	54.8925	2.58478
$452$	20.5494	0.966564
$453$	17.4022	0.817627
$454$	6.00437	0.281799
$455$	0	0
$456$	−36.2630	−1.69817
$457$	5.50926	0.257713	0.128856	−	0.991663i	$-0.458869\pi$
$457$	5.50926	0.257713	0.128856	+	0.991663i	$0.458869\pi$
$458$	31.9062	1.49088
$459$	−5.39914	−0.252010
$460$	−2.78957	−0.130065
$461$	−3.59487	−0.167430	−0.0837149	−	0.996490i	$-0.526679\pi$
$461$	−3.59487	−0.167430	−0.0837149	+	0.996490i	$0.526679\pi$
$462$	0	0
$463$	9.85049	0.457791	0.228896	−	0.973451i	$-0.426489\pi$
$463$	9.85049	0.457791	0.228896	+	0.973451i	$0.426489\pi$
$464$	8.55040	0.396942
$465$	−1.36088	−0.0631092
$466$	−69.9073	−3.23839
$467$	−18.5841	−0.859971	−0.429985	−	0.902836i	$-0.641481\pi$
$467$	−18.5841	−0.859971	−0.429985	+	0.902836i	$0.641481\pi$
$468$	−29.2877	−1.35382
$469$	0	0
$470$	6.22377	0.287081
$471$	38.3292	1.76612
$472$	35.6886	1.64270
$473$	60.2184	2.76885
$474$	−6.65298	−0.305582
$475$	−16.6673	−0.764747
$476$	0	0
$477$	20.5431	0.940605
$478$	−3.13837	−0.143546
$479$	17.3898	0.794559	0.397279	−	0.917698i	$-0.369954\pi$
$479$	17.3898	0.794559	0.397279	+	0.917698i	$0.369954\pi$
$480$	−2.76625	−0.126261
$481$	2.66554	0.121538
$482$	−48.8214	−2.22375
$483$	0	0
$484$	99.5020	4.52282
$485$	9.99948	0.454053
$486$	42.0347	1.90673
$487$	−11.3906	−0.516157	−0.258078	−	0.966124i	$-0.583089\pi$
$487$	−11.3906	−0.516157	−0.258078	+	0.966124i	$0.583089\pi$
$488$	6.57361	0.297573
$489$	12.2270	0.552923
$490$	0	0
$491$	−0.434813	−0.0196229	−0.00981143	−	0.999952i	$-0.503123\pi$
$491$	−0.434813	−0.0196229	−0.00981143	+	0.999952i	$0.503123\pi$
$492$	76.3397	3.44166
$493$	−6.64004	−0.299052
$494$	−35.8317	−1.61214
$495$	8.58803	0.386003
$496$	−2.45020	−0.110017
$497$	0	0
$498$	−90.0905	−4.03705
$499$	20.1108	0.900281	0.450141	−	0.892958i	$-0.351374\pi$
$499$	20.1108	0.900281	0.450141	+	0.892958i	$0.351374\pi$
$500$	26.4040	1.18082
$501$	−30.8626	−1.37884
$502$	25.3441	1.13116
$503$	5.36537	0.239230	0.119615	−	0.992820i	$-0.461834\pi$
$503$	5.36537	0.239230	0.119615	+	0.992820i	$0.461834\pi$
$504$	0	0
$505$	10.8560	0.483087
$506$	−14.6844	−0.652801
$507$	−6.32204	−0.280771
$508$	71.5606	3.17499
$509$	−12.9009	−0.571821	−0.285911	−	0.958256i	$-0.592296\pi$
$509$	−12.9009	−0.571821	−0.285911	+	0.958256i	$0.592296\pi$
$510$	−8.88574	−0.393467
$511$	0	0
$512$	−30.5622	−1.35067
$513$	8.87861	0.392000
$514$	0.546023	0.0240840
$515$	7.79948	0.343686
$516$	83.7466	3.68674
$517$	21.4935	0.945283
$518$	0	0
$519$	29.6008	1.29933
$520$	12.7391	0.558648
$521$	−16.9193	−0.741249	−0.370624	−	0.928783i	$-0.620856\pi$
$521$	−16.9193	−0.741249	−0.370624	+	0.928783i	$0.620856\pi$
$522$	13.6042	0.595439
$523$	15.7926	0.690562	0.345281	−	0.938499i	$-0.387784\pi$
$523$	15.7926	0.690562	0.345281	+	0.938499i	$0.387784\pi$
$524$	41.4649	1.81140
$525$	0	0
$526$	2.31438	0.100912
$527$	1.90277	0.0828859
$528$	39.5151	1.71967
$529$	1.00000	0.0434783
$530$	−18.7832	−0.815890
$531$	15.7281	0.682542
$532$	0	0
$533$	35.8844	1.55433
$534$	−51.6325	−2.23436
$535$	−0.0481293	−0.00208081
$536$	22.0682	0.953201
$537$	−47.7818	−2.06194
$538$	18.2671	0.787552
$539$	0	0
$540$	−6.63537	−0.285541
$541$	21.0781	0.906220	0.453110	−	0.891455i	$-0.350314\pi$
$541$	21.0781	0.906220	0.453110	+	0.891455i	$0.350314\pi$
$542$	−55.9565	−2.40354
$543$	−42.2613	−1.81361
$544$	3.86774	0.165828
$545$	3.59627	0.154047
$546$	0	0
$547$	−26.2415	−1.12201	−0.561003	−	0.827814i	$-0.689584\pi$
$547$	−26.2415	−1.12201	−0.561003	+	0.827814i	$0.689584\pi$
$548$	4.23031	0.180710
$549$	2.89702	0.123642
$550$	65.5697	2.79590
$551$	10.9192	0.465174
$552$	−9.71507	−0.413501
$553$	0	0
$554$	−45.4278	−1.93004
$555$	−1.08701	−0.0461409
$556$	−9.33281	−0.395799
$557$	−14.2328	−0.603064	−0.301532	−	0.953456i	$-0.597498\pi$
$557$	−14.2328	−0.603064	−0.301532	+	0.953456i	$0.597498\pi$
$558$	−3.89842	−0.165033
$559$	39.3661	1.66501
$560$	0	0
$561$	−30.6865	−1.29558
$562$	−5.93371	−0.250298
$563$	0.656705	0.0276768	0.0138384	−	0.999904i	$-0.495595\pi$
$563$	0.656705	0.0276768	0.0138384	+	0.999904i	$0.495595\pi$
$564$	29.8913	1.25865
$565$	−3.93915	−0.165721
$566$	−33.9051	−1.42514
$567$	0	0
$568$	−25.4797	−1.06910
$569$	28.0704	1.17677	0.588387	−	0.808580i	$-0.299763\pi$
$569$	28.0704	1.17677	0.588387	+	0.808580i	$0.299763\pi$
$570$	14.6122	0.612036
$571$	25.3982	1.06288	0.531440	−	0.847096i	$-0.321651\pi$
$571$	25.3982	1.06288	0.531440	+	0.847096i	$0.321651\pi$
$572$	92.4785	3.86672
$573$	−20.4603	−0.854742
$574$	0	0
$575$	−4.46526	−0.186214
$576$	−19.1982	−0.799927
$577$	41.9630	1.74694	0.873472	−	0.486874i	$-0.161863\pi$
$577$	41.9630	1.74694	0.873472	+	0.486874i	$0.161863\pi$
$578$	−28.5695	−1.18834
$579$	3.89949	0.162057
$580$	−8.16039	−0.338842
$581$	0	0
$582$	73.2038	3.03439
$583$	−64.8669	−2.68651
$584$	−29.8420	−1.23487
$585$	5.61419	0.232118
$586$	29.6403	1.22443
$587$	24.3930	1.00681	0.503404	−	0.864051i	$-0.332081\pi$
$587$	24.3930	1.00681	0.503404	+	0.864051i	$0.332081\pi$
$588$	0	0
$589$	−3.12901	−0.128929
$590$	−14.3807	−0.592043
$591$	50.6728	2.08440
$592$	−1.95711	−0.0804368
$593$	11.4468	0.470065	0.235033	−	0.971987i	$-0.424480\pi$
$593$	11.4468	0.470065	0.235033	+	0.971987i	$0.424480\pi$
$594$	−34.9288	−1.43314
$595$	0	0
$596$	23.9648	0.981635
$597$	24.5422	1.00445
$598$	−9.59952	−0.392553
$599$	−2.13657	−0.0872979	−0.0436490	−	0.999047i	$-0.513898\pi$
$599$	−2.13657	−0.0872979	−0.0436490	+	0.999047i	$0.513898\pi$
$600$	43.3804	1.77100
$601$	28.0654	1.14481	0.572406	−	0.819970i	$-0.306010\pi$
$601$	28.0654	1.14481	0.572406	+	0.819970i	$0.306010\pi$
$602$	0	0
$603$	9.72555	0.396055
$604$	−29.9028	−1.21673
$605$	−19.0737	−0.775456
$606$	79.4743	3.22842
$607$	42.9663	1.74395	0.871973	−	0.489553i	$-0.162840\pi$
$607$	42.9663	1.74395	0.871973	+	0.489553i	$0.162840\pi$
$608$	−6.36031	−0.257945
$609$	0	0
$610$	−2.64883	−0.107248
$611$	14.0508	0.568434
$612$	−16.6993	−0.675029
$613$	1.37712	0.0556215	0.0278107	−	0.999613i	$-0.491146\pi$
$613$	1.37712	0.0556215	0.0278107	+	0.999613i	$0.491146\pi$
$614$	9.99125	0.403214
$615$	−14.6337	−0.590086
$616$	0	0
$617$	25.9576	1.04501	0.522507	−	0.852635i	$-0.324997\pi$
$617$	25.9576	1.04501	0.522507	+	0.852635i	$0.324997\pi$
$618$	57.0981	2.29682
$619$	−26.9260	−1.08225	−0.541125	−	0.840942i	$-0.682001\pi$
$619$	−26.9260	−1.08225	−0.541125	+	0.840942i	$0.682001\pi$
$620$	2.33844	0.0939141
$621$	2.37863	0.0954512
$622$	−56.3036	−2.25757
$623$	0	0
$624$	25.8319	1.03410
$625$	17.2649	0.690595
$626$	−50.5132	−2.01891
$627$	50.4624	2.01527
$628$	−65.8624	−2.62820
$629$	1.51985	0.0606003
$630$	0	0
$631$	−0.354568	−0.0141151	−0.00705756	−	0.999975i	$-0.502247\pi$
$631$	−0.354568	−0.0141151	−0.00705756	+	0.999975i	$0.502247\pi$
$632$	5.43846	0.216330
$633$	−15.1390	−0.601720
$634$	−22.7520	−0.903599
$635$	−13.7176	−0.544365
$636$	−90.2113	−3.57711
$637$	0	0
$638$	−42.9565	−1.70067
$639$	−11.2290	−0.444212
$640$	15.0614	0.595356
$641$	−15.4596	−0.610617	−0.305309	−	0.952253i	$-0.598760\pi$
$641$	−15.4596	−0.610617	−0.305309	+	0.952253i	$0.598760\pi$
$642$	−0.352343	−0.0139059
$643$	−27.8179	−1.09703	−0.548516	−	0.836140i	$-0.684807\pi$
$643$	−27.8179	−1.09703	−0.548516	+	0.836140i	$0.684807\pi$
$644$	0	0
$645$	−16.0535	−0.632106
$646$	−20.4306	−0.803831
$647$	4.16295	0.163662	0.0818312	−	0.996646i	$-0.473923\pi$
$647$	4.16295	0.163662	0.0818312	+	0.996646i	$0.473923\pi$
$648$	−48.4273	−1.90240
$649$	−49.6630	−1.94944
$650$	42.8644	1.68128
$651$	0	0
$652$	−21.0100	−0.822816
$653$	−16.9409	−0.662949	−0.331475	−	0.943464i	$-0.607546\pi$
$653$	−16.9409	−0.662949	−0.331475	+	0.943464i	$0.607546\pi$
$654$	26.3274	1.02948
$655$	−7.94846	−0.310572
$656$	−26.3473	−1.02869
$657$	−13.1515	−0.513088
$658$	0	0
$659$	44.2490	1.72370	0.861848	−	0.507167i	$-0.169307\pi$
$659$	44.2490	1.72370	0.861848	+	0.507167i	$0.169307\pi$
$660$	−37.7127	−1.46797
$661$	17.2914	0.672557	0.336278	−	0.941763i	$-0.390832\pi$
$661$	17.2914	0.672557	0.336278	+	0.941763i	$0.390832\pi$
$662$	53.6735	2.08608
$663$	−20.0604	−0.779083
$664$	73.6443	2.85795
$665$	0	0
$666$	−3.11388	−0.120660
$667$	2.92532	0.113269
$668$	53.0322	2.05188
$669$	31.5936	1.22148
$670$	−8.89236	−0.343542
$671$	−9.14761	−0.353140
$672$	0	0
$673$	8.44788	0.325642	0.162821	−	0.986656i	$-0.447941\pi$
$673$	8.44788	0.325642	0.162821	+	0.986656i	$0.447941\pi$
$674$	−16.3087	−0.628186
$675$	−10.6212	−0.408811
$676$	10.8634	0.417822
$677$	6.53305	0.251085	0.125543	−	0.992088i	$-0.459933\pi$
$677$	6.53305	0.251085	0.125543	+	0.992088i	$0.459933\pi$
$678$	−28.8375	−1.10750
$679$	0	0
$680$	7.26362	0.278547
$681$	−5.52792	−0.211830
$682$	12.3096	0.471360
$683$	−15.0182	−0.574654	−0.287327	−	0.957833i	$-0.592767\pi$
$683$	−15.0182	−0.574654	−0.287327	+	0.957833i	$0.592767\pi$
$684$	27.4612	1.05000
$685$	−0.810914	−0.0309834
$686$	0	0
$687$	−29.3744	−1.12070
$688$	−28.9036	−1.10194
$689$	−42.4049	−1.61550
$690$	3.91468	0.149029
$691$	6.43131	0.244658	0.122329	−	0.992490i	$-0.460964\pi$
$691$	6.43131	0.244658	0.122329	+	0.992490i	$0.460964\pi$
$692$	−50.8641	−1.93356
$693$	0	0
$694$	−34.4631	−1.30820
$695$	1.78902	0.0678614
$696$	−28.4197	−1.07725
$697$	20.4607	0.775003
$698$	−28.1143	−1.06414
$699$	64.3601	2.43432
$700$	0	0
$701$	−7.68566	−0.290284	−0.145142	−	0.989411i	$-0.546364\pi$
$701$	−7.68566	−0.290284	−0.145142	+	0.989411i	$0.546364\pi$
$702$	−22.8337	−0.861803
$703$	−2.49931	−0.0942633
$704$	60.6203	2.28471
$705$	−5.72990	−0.215801
$706$	12.6815	0.477275
$707$	0	0
$708$	−69.0670	−2.59570
$709$	25.7927	0.968666	0.484333	−	0.874884i	$-0.339062\pi$
$709$	25.7927	0.968666	0.484333	+	0.874884i	$0.339062\pi$
$710$	10.2670	0.385314
$711$	2.39676	0.0898854
$712$	42.2068	1.58177
$713$	−0.838280	−0.0313938
$714$	0	0
$715$	−17.7273	−0.662965
$716$	82.1051	3.06841
$717$	2.88933	0.107904
$718$	−47.3674	−1.76774
$719$	−30.0919	−1.12224	−0.561120	−	0.827734i	$-0.689629\pi$
$719$	−30.0919	−1.12224	−0.561120	+	0.827734i	$0.689629\pi$
$720$	−4.12208	−0.153621
$721$	0	0
$722$	−12.2192	−0.454750
$723$	44.9473	1.67161
$724$	72.6191	2.69887
$725$	−13.0623	−0.485122
$726$	−139.634	−5.18230
$727$	2.48183	0.0920459	0.0460230	−	0.998940i	$-0.485345\pi$
$727$	2.48183	0.0920459	0.0460230	+	0.998940i	$0.485345\pi$
$728$	0	0
$729$	−5.50016	−0.203710
$730$	12.0248	0.445058
$731$	22.4459	0.830191
$732$	−12.7217	−0.470208
$733$	−52.0908	−1.92402	−0.962009	−	0.273019i	$-0.911978\pi$
$733$	−52.0908	−1.92402	−0.962009	+	0.273019i	$0.911978\pi$
$734$	29.5273	1.08987
$735$	0	0
$736$	−1.70396	−0.0628089
$737$	−30.7093	−1.13119
$738$	−41.9201	−1.54310
$739$	5.12904	0.188675	0.0943373	−	0.995540i	$-0.469927\pi$
$739$	5.12904	0.188675	0.0943373	+	0.995540i	$0.469927\pi$
$740$	1.86784	0.0686633
$741$	32.9884	1.21186
$742$	0	0
$743$	30.5585	1.12108	0.560541	−	0.828127i	$-0.310593\pi$
$743$	30.5585	1.12108	0.560541	+	0.828127i	$0.310593\pi$
$744$	8.14395	0.298572
$745$	−4.59384	−0.168305
$746$	−10.4794	−0.383678
$747$	32.4554	1.18748
$748$	52.7296	1.92799
$749$	0	0
$750$	−37.0535	−1.35300
$751$	−3.40453	−0.124233	−0.0621165	−	0.998069i	$-0.519785\pi$
$751$	−3.40453	−0.124233	−0.0621165	+	0.998069i	$0.519785\pi$
$752$	−10.3164	−0.376202
$753$	−23.3330	−0.850301
$754$	−28.0817	−1.02267
$755$	5.73211	0.208613
$756$	0	0
$757$	−25.4057	−0.923384	−0.461692	−	0.887040i	$-0.652757\pi$
$757$	−25.4057	−0.923384	−0.461692	+	0.887040i	$0.652757\pi$
$758$	−10.8239	−0.393142
$759$	13.5192	0.490715
$760$	−11.9447	−0.433279
$761$	3.31880	0.120306	0.0601531	−	0.998189i	$-0.480841\pi$
$761$	3.31880	0.120306	0.0601531	+	0.998189i	$0.480841\pi$
$762$	−100.423	−3.63794
$763$	0	0
$764$	35.1576	1.27196
$765$	3.20111	0.115736
$766$	−19.3908	−0.700619
$767$	−32.4658	−1.17227
$768$	66.0616	2.38379
$769$	39.4967	1.42429	0.712143	−	0.702035i	$-0.247725\pi$
$769$	39.4967	1.42429	0.712143	+	0.702035i	$0.247725\pi$
$770$	0	0
$771$	−0.502696	−0.0181041
$772$	−6.70063	−0.241161
$773$	0.397843	0.0143094	0.00715472	−	0.999974i	$-0.497723\pi$
$773$	0.397843	0.0143094	0.00715472	+	0.999974i	$0.497723\pi$
$774$	−45.9874	−1.65298
$775$	3.74314	0.134458
$776$	−59.8403	−2.14814
$777$	0	0
$778$	−59.4117	−2.13001
$779$	−33.6466	−1.20551
$780$	−24.6537	−0.882742
$781$	35.4566	1.26874
$782$	−5.47348	−0.195731
$783$	6.95826	0.248668
$784$	0	0
$785$	12.6253	0.450615
$786$	−58.1888	−2.07552
$787$	−20.8893	−0.744624	−0.372312	−	0.928108i	$-0.621435\pi$
$787$	−20.8893	−0.744624	−0.372312	+	0.928108i	$0.621435\pi$
$788$	−87.0727	−3.10184
$789$	−2.13073	−0.0758560
$790$	−2.19142	−0.0779674
$791$	0	0
$792$	−51.3936	−1.82619
$793$	−5.98000	−0.212356
$794$	24.9285	0.884681
$795$	17.2927	0.613310
$796$	−42.1717	−1.49474
$797$	33.1117	1.17288	0.586438	−	0.809994i	$-0.300530\pi$
$797$	33.1117	1.17288	0.586438	+	0.809994i	$0.300530\pi$
$798$	0	0
$799$	8.01151	0.283427
$800$	7.60865	0.269006
$801$	18.6007	0.657225
$802$	−51.9009	−1.83268
$803$	41.5271	1.46546
$804$	−42.7079	−1.50619
$805$	0	0
$806$	8.04708	0.283446
$807$	−16.8176	−0.592008
$808$	−64.9661	−2.28550
$809$	15.9819	0.561894	0.280947	−	0.959723i	$-0.409351\pi$
$809$	15.9819	0.561894	0.280947	+	0.959723i	$0.409351\pi$
$810$	19.5137	0.685642
$811$	−53.4394	−1.87651	−0.938256	−	0.345942i	$-0.887559\pi$
$811$	−53.4394	−1.87651	−0.938256	+	0.345942i	$0.887559\pi$
$812$	0	0
$813$	51.5163	1.80676
$814$	9.83238	0.344625
$815$	4.02744	0.141075
$816$	14.7289	0.515614
$817$	−36.9111	−1.29136
$818$	−54.4574	−1.90406
$819$	0	0
$820$	25.1455	0.878120
$821$	−29.3485	−1.02427	−0.512136	−	0.858905i	$-0.671145\pi$
$821$	−29.3485	−1.02427	−0.512136	+	0.858905i	$0.671145\pi$
$822$	−5.93650	−0.207059
$823$	31.9526	1.11380	0.556899	−	0.830580i	$-0.311991\pi$
$823$	31.9526	1.11380	0.556899	+	0.830580i	$0.311991\pi$
$824$	−46.6747	−1.62599
$825$	−60.3666	−2.10170
$826$	0	0
$827$	20.6922	0.719538	0.359769	−	0.933041i	$-0.382856\pi$
$827$	20.6922	0.719538	0.359769	+	0.933041i	$0.382856\pi$
$828$	7.35701	0.255674
$829$	29.8409	1.03642	0.518208	−	0.855254i	$-0.326599\pi$
$829$	29.8409	1.03642	0.518208	+	0.855254i	$0.326599\pi$
$830$	−29.6749	−1.03003
$831$	41.8230	1.45083
$832$	39.6288	1.37388
$833$	0	0
$834$	13.0970	0.453511
$835$	−10.1658	−0.351802
$836$	−86.7112	−2.99897
$837$	−1.99396	−0.0689213
$838$	−13.6025	−0.469889
$839$	52.3353	1.80682	0.903408	−	0.428781i	$-0.141057\pi$
$839$	52.3353	1.80682	0.903408	+	0.428781i	$0.141057\pi$
$840$	0	0
$841$	−20.4425	−0.704914
$842$	45.9551	1.58372
$843$	5.46286	0.188151
$844$	26.0138	0.895432
$845$	−2.08241	−0.0716372
$846$	−16.4141	−0.564328
$847$	0	0
$848$	31.1348	1.06917
$849$	31.2147	1.07129
$850$	24.4405	0.838302
$851$	−0.669580	−0.0229529
$852$	49.3100	1.68933
$853$	−54.0342	−1.85010	−0.925048	−	0.379850i	$-0.875975\pi$
$853$	−54.0342	−1.85010	−0.925048	+	0.379850i	$0.875975\pi$
$854$	0	0
$855$	−5.26407	−0.180027
$856$	0.288022	0.00984438
$857$	−13.1955	−0.450751	−0.225375	−	0.974272i	$-0.572361\pi$
$857$	−13.1955	−0.450751	−0.225375	+	0.974272i	$0.572361\pi$
$858$	−129.777	−4.43053
$859$	37.6889	1.28593	0.642964	−	0.765897i	$-0.277705\pi$
$859$	37.6889	1.28593	0.642964	+	0.765897i	$0.277705\pi$
$860$	27.5853	0.940650
$861$	0	0
$862$	41.2473	1.40489
$863$	−30.3152	−1.03194	−0.515971	−	0.856606i	$-0.672569\pi$
$863$	−30.3152	−1.03194	−0.515971	+	0.856606i	$0.672569\pi$
$864$	−4.05310	−0.137889
$865$	9.75022	0.331517
$866$	21.8456	0.742345
$867$	26.3025	0.893280
$868$	0	0
$869$	−7.56798	−0.256726
$870$	11.4517	0.388249
$871$	−20.0754	−0.680229
$872$	−21.5213	−0.728802
$873$	−26.3719	−0.892553
$874$	9.00086	0.304459
$875$	0	0
$876$	57.7523	1.95127
$877$	−20.4516	−0.690601	−0.345301	−	0.938492i	$-0.612223\pi$
$877$	−20.4516	−0.690601	−0.345301	+	0.938492i	$0.612223\pi$
$878$	−84.3220	−2.84573
$879$	−27.2883	−0.920412
$880$	13.0159	0.438765
$881$	−17.8506	−0.601401	−0.300701	−	0.953719i	$-0.597221\pi$
$881$	−17.8506	−0.601401	−0.300701	+	0.953719i	$0.597221\pi$
$882$	0	0
$883$	39.5257	1.33015	0.665073	−	0.746778i	$-0.268400\pi$
$883$	39.5257	1.33015	0.665073	+	0.746778i	$0.268400\pi$
$884$	34.4705	1.15937
$885$	13.2396	0.445043
$886$	−91.0985	−3.06051
$887$	3.73404	0.125377	0.0626884	−	0.998033i	$-0.480033\pi$
$887$	3.73404	0.125377	0.0626884	+	0.998033i	$0.480033\pi$
$888$	6.50502	0.218294
$889$	0	0
$890$	−17.0072	−0.570083
$891$	67.3897	2.25764
$892$	−54.2884	−1.81771
$893$	−13.1745	−0.440869
$894$	−33.6304	−1.12477
$895$	−15.7388	−0.526091
$896$	0	0
$897$	8.83779	0.295085
$898$	39.7647	1.32697
$899$	−2.45224	−0.0817867
$900$	−32.8510	−1.09503
$901$	−24.1785	−0.805504
$902$	132.367	4.40733
$903$	0	0
$904$	23.5732	0.784032
$905$	−13.9205	−0.462732
$906$	41.9634	1.39414
$907$	15.6914	0.521025	0.260513	−	0.965470i	$-0.416108\pi$
$907$	15.6914	0.521025	0.260513	+	0.965470i	$0.416108\pi$
$908$	9.49881	0.315229
$909$	−28.6309	−0.949625
$910$	0	0
$911$	19.5638	0.648177	0.324088	−	0.946027i	$-0.394942\pi$
$911$	19.5638	0.648177	0.324088	+	0.946027i	$0.394942\pi$
$912$	−24.2209	−0.802035
$913$	−102.481	−3.39162
$914$	13.2849	0.439427
$915$	2.43864	0.0806191
$916$	50.4750	1.66774
$917$	0	0
$918$	−13.0194	−0.429704
$919$	−4.44638	−0.146673	−0.0733363	−	0.997307i	$-0.523365\pi$
$919$	−4.44638	−0.146673	−0.0733363	+	0.997307i	$0.523365\pi$
$920$	−3.20005	−0.105502
$921$	−9.19843	−0.303099
$922$	−8.66861	−0.285485
$923$	23.1788	0.762939
$924$	0	0
$925$	2.98985	0.0983057
$926$	23.7533	0.780582
$927$	−20.5697	−0.675599
$928$	−4.98464	−0.163629
$929$	37.4763	1.22956	0.614778	−	0.788700i	$-0.289246\pi$
$929$	37.4763	1.22956	0.614778	+	0.788700i	$0.289246\pi$
$930$	−3.28160	−0.107608
$931$	0	0
$932$	−110.592	−3.62256
$933$	51.8359	1.69703
$934$	−44.8134	−1.46634
$935$	−10.1078	−0.330561
$936$	−33.5972	−1.09816
$937$	17.5118	0.572084	0.286042	−	0.958217i	$-0.407660\pi$
$937$	17.5118	0.572084	0.286042	+	0.958217i	$0.407660\pi$
$938$	0	0
$939$	46.5049	1.51763
$940$	9.84589	0.321137
$941$	−13.1220	−0.427764	−0.213882	−	0.976860i	$-0.568611\pi$
$941$	−13.1220	−0.427764	−0.213882	+	0.976860i	$0.568611\pi$
$942$	92.4264	3.01141
$943$	−9.01411	−0.293540
$944$	23.8372	0.775836
$945$	0	0
$946$	145.210	4.72117
$947$	0.640820	0.0208239	0.0104119	−	0.999946i	$-0.496686\pi$
$947$	0.640820	0.0208239	0.0104119	+	0.999946i	$0.496686\pi$
$948$	−10.5249	−0.341833
$949$	27.1472	0.881235
$950$	−40.1912	−1.30397
$951$	20.9466	0.679241
$952$	0	0
$953$	9.62197	0.311686	0.155843	−	0.987782i	$-0.450191\pi$
$953$	9.62197	0.311686	0.155843	+	0.987782i	$0.450191\pi$
$954$	49.5373	1.60383
$955$	−6.73942	−0.218082
$956$	−4.96484	−0.160574
$957$	39.5479	1.27840
$958$	41.9334	1.35481
$959$	0	0
$960$	−16.1606	−0.521582
$961$	−30.2973	−0.977332
$962$	6.42765	0.207236
$963$	0.126932	0.00409034
$964$	−77.2345	−2.48756
$965$	1.28445	0.0413480
$966$	0	0
$967$	−51.9876	−1.67181	−0.835904	−	0.548876i	$-0.815056\pi$
$967$	−51.9876	−1.67181	−0.835904	+	0.548876i	$0.815056\pi$
$968$	114.143	3.66870
$969$	18.8094	0.604245
$970$	24.1126	0.774208
$971$	53.8409	1.72784	0.863918	−	0.503633i	$-0.168004\pi$
$971$	53.8409	1.72784	0.863918	+	0.503633i	$0.168004\pi$
$972$	66.4981	2.13293
$973$	0	0
$974$	−27.4671	−0.880101
$975$	−39.4630	−1.26383
$976$	4.39067	0.140542
$977$	−32.3250	−1.03417	−0.517084	−	0.855935i	$-0.672983\pi$
$977$	−32.3250	−1.03417	−0.517084	+	0.855935i	$0.672983\pi$
$978$	29.4839	0.942791
$979$	−58.7336	−1.87713
$980$	0	0
$981$	−9.48452	−0.302817
$982$	−1.04850	−0.0334590
$983$	28.9238	0.922525	0.461262	−	0.887264i	$-0.347397\pi$
$983$	28.9238	0.922525	0.461262	+	0.887264i	$0.347397\pi$
$984$	87.5727	2.79172
$985$	16.6911	0.531822
$986$	−16.0117	−0.509915
$987$	0	0
$988$	−56.6851	−1.80339
$989$	−9.88871	−0.314443
$990$	20.7090	0.658176
$991$	33.6609	1.06927	0.534637	−	0.845082i	$-0.320448\pi$
$991$	33.6609	1.06927	0.534637	+	0.845082i	$0.320448\pi$
$992$	1.42840	0.0453517
$993$	−49.4145	−1.56812
$994$	0	0
$995$	8.08395	0.256279
$996$	−142.522	−4.51597
$997$	−14.3991	−0.456023	−0.228012	−	0.973658i	$-0.573222\pi$
$997$	−14.3991	−0.456023	−0.228012	+	0.973658i	$0.573222\pi$
$998$	48.4947	1.53507
$999$	−1.59268	−0.0503903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1127.2.a.k.1.7		7
7.3	odd	6		161.2.e.a.93.1	✓	14
7.5	odd	6		161.2.e.a.116.1	yes	14
7.6	odd	2		1127.2.a.n.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.e.a.93.1	✓	14	7.3	odd	6
161.2.e.a.116.1	yes	14	7.5	odd	6
1127.2.a.k.1.7		7	1.1	even	1	trivial
1127.2.a.n.1.7		7	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1127.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41138 q^{2} -2.22004 q^{3} +3.81476 q^{4} -0.731257 q^{5} -5.35336 q^{6} +4.37609 q^{8} +1.92856 q^{9} +O(q^{10})\)	\(q+2.41138 q^{2} -2.22004 q^{3} +3.81476 q^{4} -0.731257 q^{5} -5.35336 q^{6} +4.37609 q^{8} +1.92856 q^{9} -1.76334 q^{10} -6.08962 q^{11} -8.46891 q^{12} -3.98092 q^{13} +1.62342 q^{15} +2.92289 q^{16} -2.26985 q^{17} +4.65050 q^{18} +3.73265 q^{19} -2.78957 q^{20} -14.6844 q^{22} +1.00000 q^{23} -9.71507 q^{24} -4.46526 q^{25} -9.59952 q^{26} +2.37863 q^{27} +2.92532 q^{29} +3.91468 q^{30} -0.838280 q^{31} -1.70396 q^{32} +13.5192 q^{33} -5.47348 q^{34} +7.35701 q^{36} -0.669580 q^{37} +9.00086 q^{38} +8.83779 q^{39} -3.20005 q^{40} -9.01411 q^{41} -9.88871 q^{43} -23.2304 q^{44} -1.41027 q^{45} +2.41138 q^{46} -3.52953 q^{47} -6.48893 q^{48} -10.7675 q^{50} +5.03915 q^{51} -15.1863 q^{52} +10.6520 q^{53} +5.73579 q^{54} +4.45308 q^{55} -8.28663 q^{57} +7.05406 q^{58} +8.15536 q^{59} +6.19295 q^{60} +1.50217 q^{61} -2.02141 q^{62} -9.95469 q^{64} +2.91108 q^{65} +32.5999 q^{66} +5.04290 q^{67} -8.65894 q^{68} -2.22004 q^{69} -5.82247 q^{71} +8.43956 q^{72} -6.81932 q^{73} -1.61461 q^{74} +9.91305 q^{75} +14.2392 q^{76} +21.3113 q^{78} +1.24277 q^{79} -2.13739 q^{80} -11.0663 q^{81} -21.7365 q^{82} +16.8288 q^{83} +1.65984 q^{85} -23.8454 q^{86} -6.49432 q^{87} -26.6487 q^{88} +9.64488 q^{89} -3.40071 q^{90} +3.81476 q^{92} +1.86101 q^{93} -8.51105 q^{94} -2.72953 q^{95} +3.78286 q^{96} -13.6744 q^{97} -11.7442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 5 q^{3} + 6 q^{4} - 4 q^{5} - 6 q^{6} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 5 * q^3 + 6 * q^4 - 4 * q^5 - 6 * q^6 - 3 * q^8 + 4 * q^9	\( 7 q - 5 q^{3} + 6 q^{4} - 4 q^{5} - 6 q^{6} - 3 q^{8} + 4 q^{9} + 2 q^{10} + 4 q^{11} - 9 q^{12} - 14 q^{13} - 3 q^{15} - 8 q^{16} - 4 q^{17} + 19 q^{18} - 9 q^{19} - 12 q^{20} - 10 q^{22} + 7 q^{23} + 4 q^{24} + 3 q^{25} - 14 q^{26} - 20 q^{27} - 5 q^{29} - 17 q^{30} - 10 q^{31} + 19 q^{32} - 3 q^{33} - 20 q^{34} + 4 q^{36} - 5 q^{37} + 17 q^{38} + 18 q^{39} - 4 q^{40} - 23 q^{41} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 4 q^{47} - 11 q^{48} - 9 q^{50} + 7 q^{51} - 12 q^{52} + 2 q^{53} - 15 q^{54} - 17 q^{55} - 24 q^{57} - 7 q^{58} - 7 q^{59} + 32 q^{60} - 12 q^{61} + 4 q^{62} - 9 q^{64} + 9 q^{65} + 27 q^{66} + 2 q^{67} + 12 q^{68} - 5 q^{69} - 28 q^{71} - 20 q^{72} - 59 q^{73} + 2 q^{74} + 22 q^{75} - q^{76} - 17 q^{78} - 4 q^{79} + 22 q^{80} + 11 q^{81} - 54 q^{82} + 9 q^{83} + 9 q^{85} - 15 q^{86} - 11 q^{87} - 33 q^{88} - q^{89} - 2 q^{90} + 6 q^{92} + 15 q^{93} + 14 q^{94} - 16 q^{95} - 20 q^{96} - 35 q^{97} + 18 q^{99}+O(q^{100}) \) 7 * q - 5 * q^3 + 6 * q^4 - 4 * q^5 - 6 * q^6 - 3 * q^8 + 4 * q^9 + 2 * q^10 + 4 * q^11 - 9 * q^12 - 14 * q^13 - 3 * q^15 - 8 * q^16 - 4 * q^17 + 19 * q^18 - 9 * q^19 - 12 * q^20 - 10 * q^22 + 7 * q^23 + 4 * q^24 + 3 * q^25 - 14 * q^26 - 20 * q^27 - 5 * q^29 - 17 * q^30 - 10 * q^31 + 19 * q^32 - 3 * q^33 - 20 * q^34 + 4 * q^36 - 5 * q^37 + 17 * q^38 + 18 * q^39 - 4 * q^40 - 23 * q^41 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 4 * q^47 - 11 * q^48 - 9 * q^50 + 7 * q^51 - 12 * q^52 + 2 * q^53 - 15 * q^54 - 17 * q^55 - 24 * q^57 - 7 * q^58 - 7 * q^59 + 32 * q^60 - 12 * q^61 + 4 * q^62 - 9 * q^64 + 9 * q^65 + 27 * q^66 + 2 * q^67 + 12 * q^68 - 5 * q^69 - 28 * q^71 - 20 * q^72 - 59 * q^73 + 2 * q^74 + 22 * q^75 - q^76 - 17 * q^78 - 4 * q^79 + 22 * q^80 + 11 * q^81 - 54 * q^82 + 9 * q^83 + 9 * q^85 - 15 * q^86 - 11 * q^87 - 33 * q^88 - q^89 - 2 * q^90 + 6 * q^92 + 15 * q^93 + 14 * q^94 - 16 * q^95 - 20 * q^96 - 35 * q^97 + 18 * q^99

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