LMFDB - Embedded newform 6025.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 $ x^12 - 3x^11 - 14x^10 + 44x^9 + 65x^8 - 219x^7 - 123x^6 + 444x^5 + 105x^4 - 328x^3 - 45x^2 + 18*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.01020$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.01020 q^{2} -0.500591 q^{3} +2.04092 q^{4} +1.00629 q^{6} +0.852319 q^{7} -0.0822476 q^{8} -2.74941 q^{9} +O(q^{10})$	\(q-2.01020 q^{2} -0.500591 q^{3} +2.04092 q^{4} +1.00629 q^{6} +0.852319 q^{7} -0.0822476 q^{8} -2.74941 q^{9} +0.719546 q^{11} -1.02166 q^{12} +1.93309 q^{13} -1.71333 q^{14} -3.91650 q^{16} -0.439843 q^{17} +5.52687 q^{18} +5.85432 q^{19} -0.426663 q^{21} -1.44643 q^{22} +7.09215 q^{23} +0.0411724 q^{24} -3.88589 q^{26} +2.87810 q^{27} +1.73951 q^{28} +10.0222 q^{29} +5.69622 q^{31} +8.03745 q^{32} -0.360198 q^{33} +0.884173 q^{34} -5.61131 q^{36} +3.17197 q^{37} -11.7684 q^{38} -0.967685 q^{39} -6.39435 q^{41} +0.857679 q^{42} -4.29669 q^{43} +1.46853 q^{44} -14.2567 q^{46} +0.642479 q^{47} +1.96056 q^{48} -6.27355 q^{49} +0.220181 q^{51} +3.94526 q^{52} -0.729714 q^{53} -5.78557 q^{54} -0.0701012 q^{56} -2.93062 q^{57} -20.1467 q^{58} +0.348904 q^{59} +1.12656 q^{61} -11.4506 q^{62} -2.34337 q^{63} -8.32390 q^{64} +0.724072 q^{66} -12.5549 q^{67} -0.897682 q^{68} -3.55026 q^{69} +0.552289 q^{71} +0.226132 q^{72} +10.9882 q^{73} -6.37630 q^{74} +11.9482 q^{76} +0.613283 q^{77} +1.94524 q^{78} +10.9569 q^{79} +6.80748 q^{81} +12.8539 q^{82} -6.62478 q^{83} -0.870783 q^{84} +8.63722 q^{86} -5.01703 q^{87} -0.0591810 q^{88} +12.5513 q^{89} +1.64760 q^{91} +14.4745 q^{92} -2.85148 q^{93} -1.29151 q^{94} -4.02347 q^{96} +5.00536 q^{97} +12.6111 q^{98} -1.97833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	$ 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * 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 $

$2$	−2.01020	−1.42143	−0.710714	−	0.703481i	$-0.751628\pi$
$2$	−2.01020	−1.42143	−0.710714	+	0.703481i	$0.751628\pi$
$3$	−0.500591	−0.289016	−0.144508	−	0.989504i	$-0.546160\pi$
$3$	−0.500591	−0.289016	−0.144508	+	0.989504i	$0.546160\pi$
$4$	2.04092	1.02046
$5$	0	0
$5$	0	0
$6$	1.00629	0.410816
$7$	0.852319	0.322146	0.161073	−	0.986942i	$-0.448505\pi$
$7$	0.852319	0.322146	0.161073	+	0.986942i	$0.448505\pi$
$8$	−0.0822476	−0.0290789
$9$	−2.74941	−0.916470
$10$	0	0
$11$	0.719546	0.216951	0.108476	−	0.994099i	$-0.465403\pi$
$11$	0.719546	0.216951	0.108476	+	0.994099i	$0.465403\pi$
$12$	−1.02166	−0.294929
$13$	1.93309	0.536141	0.268071	−	0.963399i	$-0.413614\pi$
$13$	1.93309	0.536141	0.268071	+	0.963399i	$0.413614\pi$
$14$	−1.71333	−0.457908
$15$	0	0
$16$	−3.91650	−0.979124
$17$	−0.439843	−0.106678	−0.0533388	−	0.998576i	$-0.516986\pi$
$17$	−0.439843	−0.106678	−0.0533388	+	0.998576i	$0.516986\pi$
$18$	5.52687	1.30270
$19$	5.85432	1.34307	0.671537	−	0.740971i	$-0.265635\pi$
$19$	5.85432	1.34307	0.671537	+	0.740971i	$0.265635\pi$
$20$	0	0
$21$	−0.426663	−0.0931055
$22$	−1.44643	−0.308381
$23$	7.09215	1.47881	0.739407	−	0.673258i	$-0.235106\pi$
$23$	7.09215	1.47881	0.739407	+	0.673258i	$0.235106\pi$
$24$	0.0411724	0.00840428
$25$	0	0
$26$	−3.88589	−0.762086
$27$	2.87810	0.553891
$28$	1.73951	0.328737
$29$	10.0222	1.86108	0.930540	−	0.366190i	$-0.119338\pi$
$29$	10.0222	1.86108	0.930540	+	0.366190i	$0.119338\pi$
$30$	0	0
$31$	5.69622	1.02307	0.511536	−	0.859262i	$-0.329077\pi$
$31$	5.69622	1.02307	0.511536	+	0.859262i	$0.329077\pi$
$32$	8.03745	1.42083
$33$	−0.360198	−0.0627025
$34$	0.884173	0.151634
$35$	0	0
$36$	−5.61131	−0.935218
$37$	3.17197	0.521468	0.260734	−	0.965411i	$-0.416035\pi$
$37$	3.17197	0.521468	0.260734	+	0.965411i	$0.416035\pi$
$38$	−11.7684	−1.90908
$39$	−0.967685	−0.154954
$40$	0	0
$41$	−6.39435	−0.998630	−0.499315	−	0.866421i	$-0.666415\pi$
$41$	−6.39435	−0.998630	−0.499315	+	0.866421i	$0.666415\pi$
$42$	0.857679	0.132343
$43$	−4.29669	−0.655239	−0.327620	−	0.944810i	$-0.606246\pi$
$43$	−4.29669	−0.655239	−0.327620	+	0.944810i	$0.606246\pi$
$44$	1.46853	0.221390
$45$	0	0
$46$	−14.2567	−2.10203
$47$	0.642479	0.0937152	0.0468576	−	0.998902i	$-0.485079\pi$
$47$	0.642479	0.0937152	0.0468576	+	0.998902i	$0.485079\pi$
$48$	1.96056	0.282983
$49$	−6.27355	−0.896222
$50$	0	0
$51$	0.220181	0.0308315
$52$	3.94526	0.547110
$53$	−0.729714	−0.100234	−0.0501170	−	0.998743i	$-0.515959\pi$
$53$	−0.729714	−0.100234	−0.0501170	+	0.998743i	$0.515959\pi$
$54$	−5.78557	−0.787316
$55$	0	0
$56$	−0.0701012	−0.00936766
$57$	−2.93062	−0.388170
$58$	−20.1467	−2.64539
$59$	0.348904	0.0454234	0.0227117	−	0.999742i	$-0.492770\pi$
$59$	0.348904	0.0454234	0.0227117	+	0.999742i	$0.492770\pi$
$60$	0	0
$61$	1.12656	0.144241	0.0721204	−	0.997396i	$-0.477023\pi$
$61$	1.12656	0.144241	0.0721204	+	0.997396i	$0.477023\pi$
$62$	−11.4506	−1.45422
$63$	−2.34337	−0.295237
$64$	−8.32390	−1.04049
$65$	0	0
$66$	0.724072	0.0891270
$67$	−12.5549	−1.53383	−0.766915	−	0.641749i	$-0.778209\pi$
$67$	−12.5549	−1.53383	−0.766915	+	0.641749i	$0.778209\pi$
$68$	−0.897682	−0.108860
$69$	−3.55026	−0.427401
$70$	0	0
$71$	0.552289	0.0655446	0.0327723	−	0.999463i	$-0.489566\pi$
$71$	0.552289	0.0655446	0.0327723	+	0.999463i	$0.489566\pi$
$72$	0.226132	0.0266499
$73$	10.9882	1.28607	0.643037	−	0.765835i	$-0.277674\pi$
$73$	10.9882	1.28607	0.643037	+	0.765835i	$0.277674\pi$
$74$	−6.37630	−0.741229
$75$	0	0
$76$	11.9482	1.37055
$77$	0.613283	0.0698901
$78$	1.94524	0.220255
$79$	10.9569	1.23275	0.616375	−	0.787453i	$-0.288600\pi$
$79$	10.9569	1.23275	0.616375	+	0.787453i	$0.288600\pi$
$80$	0	0
$81$	6.80748	0.756386
$82$	12.8539	1.41948
$83$	−6.62478	−0.727164	−0.363582	−	0.931562i	$-0.618446\pi$
$83$	−6.62478	−0.727164	−0.363582	+	0.931562i	$0.618446\pi$
$84$	−0.870783	−0.0950102
$85$	0	0
$86$	8.63722	0.931375
$87$	−5.01703	−0.537882
$88$	−0.0591810	−0.00630871
$89$	12.5513	1.33044	0.665219	−	0.746648i	$-0.268338\pi$
$89$	12.5513	1.33044	0.665219	+	0.746648i	$0.268338\pi$
$90$	0	0
$91$	1.64760	0.172716
$92$	14.4745	1.50907
$93$	−2.85148	−0.295684
$94$	−1.29151	−0.133209
$95$	0	0
$96$	−4.02347	−0.410644
$97$	5.00536	0.508217	0.254108	−	0.967176i	$-0.418218\pi$
$97$	5.00536	0.508217	0.254108	+	0.967176i	$0.418218\pi$
$98$	12.6111	1.27391
$99$	−1.97833	−0.198829
$100$	0	0
$101$	0.191991	0.0191038	0.00955192	−	0.999954i	$-0.496959\pi$
$101$	0.191991	0.0191038	0.00955192	+	0.999954i	$0.496959\pi$
$102$	−0.442609	−0.0438248
$103$	3.97237	0.391409	0.195705	−	0.980663i	$-0.437301\pi$
$103$	3.97237	0.391409	0.195705	+	0.980663i	$0.437301\pi$
$104$	−0.158992	−0.0155904
$105$	0	0
$106$	1.46687	0.142475
$107$	−6.70922	−0.648605	−0.324303	−	0.945953i	$-0.605130\pi$
$107$	−6.70922	−0.648605	−0.324303	+	0.945953i	$0.605130\pi$
$108$	5.87396	0.565222
$109$	4.03051	0.386053	0.193027	−	0.981194i	$-0.438170\pi$
$109$	4.03051	0.386053	0.193027	+	0.981194i	$0.438170\pi$
$110$	0	0
$111$	−1.58786	−0.150713
$112$	−3.33810	−0.315421
$113$	−0.430322	−0.0404813	−0.0202407	−	0.999795i	$-0.506443\pi$
$113$	−0.430322	−0.0404813	−0.0202407	+	0.999795i	$0.506443\pi$
$114$	5.89114	0.551756
$115$	0	0
$116$	20.4545	1.89915
$117$	−5.31484	−0.491357
$118$	−0.701368	−0.0645661
$119$	−0.374886	−0.0343658
$120$	0	0
$121$	−10.4823	−0.952932
$122$	−2.26461	−0.205028
$123$	3.20095	0.288620
$124$	11.6255	1.04400
$125$	0	0
$126$	4.71065	0.419658
$127$	0.0290958	0.00258183	0.00129092	−	0.999999i	$-0.499589\pi$
$127$	0.0290958	0.00258183	0.00129092	+	0.999999i	$0.499589\pi$
$128$	0.657843	0.0581457
$129$	2.15088	0.189375
$130$	0	0
$131$	−7.50804	−0.655980	−0.327990	−	0.944681i	$-0.606371\pi$
$131$	−7.50804	−0.655980	−0.327990	+	0.944681i	$0.606371\pi$
$132$	−0.735134	−0.0639852
$133$	4.98975	0.432666
$134$	25.2380	2.18023
$135$	0	0
$136$	0.0361760	0.00310207
$137$	2.79071	0.238427	0.119213	−	0.992869i	$-0.461963\pi$
$137$	2.79071	0.238427	0.119213	+	0.992869i	$0.461963\pi$
$138$	7.13675	0.607520
$139$	5.56312	0.471858	0.235929	−	0.971770i	$-0.424187\pi$
$139$	5.56312	0.471858	0.235929	+	0.971770i	$0.424187\pi$
$140$	0	0
$141$	−0.321619	−0.0270852
$142$	−1.11021	−0.0931669
$143$	1.39094	0.116317
$144$	10.7680	0.897337
$145$	0	0
$146$	−22.0886	−1.82806
$147$	3.14048	0.259023
$148$	6.47372	0.532136
$149$	14.8309	1.21500	0.607499	−	0.794321i	$-0.292173\pi$
$149$	14.8309	1.21500	0.607499	+	0.794321i	$0.292173\pi$
$150$	0	0
$151$	−19.6745	−1.60109	−0.800543	−	0.599276i	$-0.795455\pi$
$151$	−19.6745	−1.60109	−0.800543	+	0.599276i	$0.795455\pi$
$152$	−0.481504	−0.0390551
$153$	1.20931	0.0977667
$154$	−1.23282	−0.0993437
$155$	0	0
$156$	−1.97496	−0.158124
$157$	−14.3437	−1.14475	−0.572377	−	0.819991i	$-0.693978\pi$
$157$	−14.3437	−1.14475	−0.572377	+	0.819991i	$0.693978\pi$
$158$	−22.0256	−1.75227
$159$	0.365288	0.0289692
$160$	0	0
$161$	6.04477	0.476395
$162$	−13.6844	−1.07515
$163$	−4.99007	−0.390853	−0.195426	−	0.980718i	$-0.562609\pi$
$163$	−4.99007	−0.390853	−0.195426	+	0.980718i	$0.562609\pi$
$164$	−13.0503	−1.01906
$165$	0	0
$166$	13.3172	1.03361
$167$	−15.6290	−1.20941	−0.604703	−	0.796451i	$-0.706708\pi$
$167$	−15.6290	−1.20941	−0.604703	+	0.796451i	$0.706708\pi$
$168$	0.0350920	0.00270741
$169$	−9.26318	−0.712552
$170$	0	0
$171$	−16.0959	−1.23089
$172$	−8.76918	−0.668644
$173$	−0.833365	−0.0633596	−0.0316798	−	0.999498i	$-0.510086\pi$
$173$	−0.833365	−0.0633596	−0.0316798	+	0.999498i	$0.510086\pi$
$174$	10.0853	0.764561
$175$	0	0
$176$	−2.81810	−0.212422
$177$	−0.174658	−0.0131281
$178$	−25.2307	−1.89112
$179$	14.9985	1.12104	0.560520	−	0.828141i	$-0.310601\pi$
$179$	14.9985	1.12104	0.560520	+	0.828141i	$0.310601\pi$
$180$	0	0
$181$	−14.9752	−1.11310	−0.556550	−	0.830814i	$-0.687875\pi$
$181$	−14.9752	−1.11310	−0.556550	+	0.830814i	$0.687875\pi$
$182$	−3.31202	−0.245503
$183$	−0.563944	−0.0416879
$184$	−0.583312	−0.0430023
$185$	0	0
$186$	5.73204	0.420294
$187$	−0.316487	−0.0231438
$188$	1.31125	0.0956324
$189$	2.45306	0.178434
$190$	0	0
$191$	8.51858	0.616383	0.308191	−	0.951324i	$-0.400276\pi$
$191$	8.51858	0.616383	0.308191	+	0.951324i	$0.400276\pi$
$192$	4.16687	0.300718
$193$	23.5303	1.69375	0.846874	−	0.531793i	$-0.178482\pi$
$193$	23.5303	1.69375	0.846874	+	0.531793i	$0.178482\pi$
$194$	−10.0618	−0.722394
$195$	0	0
$196$	−12.8038	−0.914556
$197$	26.7548	1.90620	0.953102	−	0.302649i	$-0.0978710\pi$
$197$	26.7548	1.90620	0.953102	+	0.302649i	$0.0978710\pi$
$198$	3.97684	0.282622
$199$	−19.5915	−1.38880	−0.694401	−	0.719589i	$-0.744330\pi$
$199$	−19.5915	−1.38880	−0.694401	+	0.719589i	$0.744330\pi$
$200$	0	0
$201$	6.28488	0.443301
$202$	−0.385941	−0.0271547
$203$	8.54213	0.599540
$204$	0.449371	0.0314623
$205$	0	0
$206$	−7.98527	−0.556360
$207$	−19.4992	−1.35529
$208$	−7.57092	−0.524949
$209$	4.21246	0.291382
$210$	0	0
$211$	4.58617	0.315725	0.157862	−	0.987461i	$-0.449540\pi$
$211$	4.58617	0.315725	0.157862	+	0.987461i	$0.449540\pi$
$212$	−1.48928	−0.102284
$213$	−0.276471	−0.0189435
$214$	13.4869	0.921946
$215$	0	0
$216$	−0.236717	−0.0161065
$217$	4.85500	0.329579
$218$	−8.10215	−0.548747
$219$	−5.50060	−0.371696
$220$	0	0
$221$	−0.850254	−0.0571943
$222$	3.19191	0.214227
$223$	11.8124	0.791018	0.395509	−	0.918462i	$-0.370568\pi$
$223$	11.8124	0.791018	0.395509	+	0.918462i	$0.370568\pi$
$224$	6.85047	0.457716
$225$	0	0
$226$	0.865035	0.0575413
$227$	10.4668	0.694703	0.347352	−	0.937735i	$-0.387081\pi$
$227$	10.4668	0.694703	0.347352	+	0.937735i	$0.387081\pi$
$228$	−5.98114	−0.396111
$229$	−28.8373	−1.90562	−0.952811	−	0.303563i	$-0.901824\pi$
$229$	−28.8373	−1.90562	−0.952811	+	0.303563i	$0.901824\pi$
$230$	0	0
$231$	−0.307004	−0.0201994
$232$	−0.824304	−0.0541182
$233$	−0.483058	−0.0316462	−0.0158231	−	0.999875i	$-0.505037\pi$
$233$	−0.483058	−0.0316462	−0.0158231	+	0.999875i	$0.505037\pi$
$234$	10.6839	0.698429
$235$	0	0
$236$	0.712084	0.0463527
$237$	−5.48494	−0.356285
$238$	0.753597	0.0488485
$239$	−2.08293	−0.134734	−0.0673668	−	0.997728i	$-0.521460\pi$
$239$	−2.08293	−0.134734	−0.0673668	+	0.997728i	$0.521460\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	21.0715	1.35452
$243$	−12.0421	−0.772499
$244$	2.29921	0.147192
$245$	0	0
$246$	−6.43456	−0.410253
$247$	11.3169	0.720077
$248$	−0.468501	−0.0297498
$249$	3.31631	0.210162
$250$	0	0
$251$	−9.67130	−0.610447	−0.305223	−	0.952281i	$-0.598731\pi$
$251$	−9.67130	−0.610447	−0.305223	+	0.952281i	$0.598731\pi$
$252$	−4.78262	−0.301277
$253$	5.10313	0.320831
$254$	−0.0584884	−0.00366989
$255$	0	0
$256$	15.3254	0.957838
$257$	16.0352	1.00025	0.500123	−	0.865954i	$-0.333288\pi$
$257$	16.0352	1.00025	0.500123	+	0.865954i	$0.333288\pi$
$258$	−4.32371	−0.269183
$259$	2.70353	0.167989
$260$	0	0
$261$	−27.5552	−1.70562
$262$	15.0927	0.932429
$263$	−26.9402	−1.66120	−0.830602	−	0.556867i	$-0.812003\pi$
$263$	−26.9402	−1.66120	−0.830602	+	0.556867i	$0.812003\pi$
$264$	0.0296254	0.00182332
$265$	0	0
$266$	−10.0304	−0.615004
$267$	−6.28308	−0.384518
$268$	−25.6236	−1.56521
$269$	30.7223	1.87317	0.936585	−	0.350441i	$-0.113968\pi$
$269$	30.7223	1.87317	0.936585	+	0.350441i	$0.113968\pi$
$270$	0	0
$271$	−32.2539	−1.95928	−0.979641	−	0.200757i	$-0.935660\pi$
$271$	−32.2539	−1.95928	−0.979641	+	0.200757i	$0.935660\pi$
$272$	1.72264	0.104451
$273$	−0.824776	−0.0499177
$274$	−5.60990	−0.338906
$275$	0	0
$276$	−7.24579	−0.436145
$277$	−9.84003	−0.591230	−0.295615	−	0.955307i	$-0.595525\pi$
$277$	−9.84003	−0.591230	−0.295615	+	0.955307i	$0.595525\pi$
$278$	−11.1830	−0.670712
$279$	−15.6612	−0.937614
$280$	0	0
$281$	0.0623558	0.00371983	0.00185992	−	0.999998i	$-0.499408\pi$
$281$	0.0623558	0.00371983	0.00185992	+	0.999998i	$0.499408\pi$
$282$	0.646519	0.0384997
$283$	23.1136	1.37396	0.686979	−	0.726677i	$-0.258936\pi$
$283$	23.1136	1.37396	0.686979	+	0.726677i	$0.258936\pi$
$284$	1.12717	0.0668855
$285$	0	0
$286$	−2.79608	−0.165336
$287$	−5.45002	−0.321705
$288$	−22.0982	−1.30215
$289$	−16.8065	−0.988620
$290$	0	0
$291$	−2.50564	−0.146883
$292$	22.4260	1.31238
$293$	7.59717	0.443831	0.221916	−	0.975066i	$-0.428769\pi$
$293$	7.59717	0.443831	0.221916	+	0.975066i	$0.428769\pi$
$294$	−6.31301	−0.368182
$295$	0	0
$296$	−0.260887	−0.0151637
$297$	2.07093	0.120167
$298$	−29.8132	−1.72703
$299$	13.7097	0.792854
$300$	0	0
$301$	−3.66215	−0.211083
$302$	39.5497	2.27583
$303$	−0.0961090	−0.00552132
$304$	−22.9284	−1.31504
$305$	0	0
$306$	−2.43095	−0.138968
$307$	15.3566	0.876447	0.438224	−	0.898866i	$-0.355608\pi$
$307$	15.3566	0.876447	0.438224	+	0.898866i	$0.355608\pi$
$308$	1.25166	0.0713198
$309$	−1.98853	−0.113124
$310$	0	0
$311$	25.0513	1.42053	0.710263	−	0.703936i	$-0.248576\pi$
$311$	25.0513	1.42053	0.710263	+	0.703936i	$0.248576\pi$
$312$	0.0795897	0.00450588
$313$	8.95197	0.505995	0.252997	−	0.967467i	$-0.418584\pi$
$313$	8.95197	0.505995	0.252997	+	0.967467i	$0.418584\pi$
$314$	28.8338	1.62718
$315$	0	0
$316$	22.3622	1.25797
$317$	−20.7326	−1.16446	−0.582228	−	0.813025i	$-0.697819\pi$
$317$	−20.7326	−1.16446	−0.582228	+	0.813025i	$0.697819\pi$
$318$	−0.734303	−0.0411777
$319$	7.21146	0.403764
$320$	0	0
$321$	3.35858	0.187457
$322$	−12.1512	−0.677161
$323$	−2.57498	−0.143276
$324$	13.8935	0.771860
$325$	0	0
$326$	10.0311	0.555569
$327$	−2.01764	−0.111576
$328$	0.525920	0.0290391
$329$	0.547597	0.0301900
$330$	0	0
$331$	6.99950	0.384727	0.192364	−	0.981324i	$-0.438385\pi$
$331$	6.99950	0.384727	0.192364	+	0.981324i	$0.438385\pi$
$332$	−13.5206	−0.742040
$333$	−8.72103	−0.477910
$334$	31.4174	1.71908
$335$	0	0
$336$	1.67102	0.0911618
$337$	−1.75653	−0.0956843	−0.0478421	−	0.998855i	$-0.515234\pi$
$337$	−1.75653	−0.0956843	−0.0478421	+	0.998855i	$0.515234\pi$
$338$	18.6209	1.01284
$339$	0.215415	0.0116998
$340$	0	0
$341$	4.09870	0.221957
$342$	32.3561	1.74962
$343$	−11.3133	−0.610861
$344$	0.353393	0.0190536
$345$	0	0
$346$	1.67523	0.0900611
$347$	11.0359	0.592440	0.296220	−	0.955120i	$-0.404274\pi$
$347$	11.0359	0.592440	0.296220	+	0.955120i	$0.404274\pi$
$348$	−10.2393	−0.548886
$349$	−22.8659	−1.22398	−0.611992	−	0.790864i	$-0.709631\pi$
$349$	−22.8659	−1.22398	−0.611992	+	0.790864i	$0.709631\pi$
$350$	0	0
$351$	5.56361	0.296964
$352$	5.78332	0.308252
$353$	19.2684	1.02556	0.512778	−	0.858522i	$-0.328617\pi$
$353$	19.2684	1.02556	0.512778	+	0.858522i	$0.328617\pi$
$354$	0.351098	0.0186607
$355$	0	0
$356$	25.6162	1.35766
$357$	0.187665	0.00993226
$358$	−30.1500	−1.59348
$359$	20.1999	1.06611	0.533056	−	0.846080i	$-0.321043\pi$
$359$	20.1999	1.06611	0.533056	+	0.846080i	$0.321043\pi$
$360$	0	0
$361$	15.2731	0.803847
$362$	30.1033	1.58219
$363$	5.24732	0.275413
$364$	3.36262	0.176249
$365$	0	0
$366$	1.13364	0.0592564
$367$	−3.91082	−0.204143	−0.102072	−	0.994777i	$-0.532547\pi$
$367$	−3.91082	−0.204143	−0.102072	+	0.994777i	$0.532547\pi$
$368$	−27.7764	−1.44794
$369$	17.5807	0.915214
$370$	0	0
$371$	−0.621949	−0.0322900
$372$	−5.81962	−0.301733
$373$	−9.05376	−0.468786	−0.234393	−	0.972142i	$-0.575310\pi$
$373$	−9.05376	−0.468786	−0.234393	+	0.972142i	$0.575310\pi$
$374$	0.636204	0.0328973
$375$	0	0
$376$	−0.0528424	−0.00272514
$377$	19.3738	0.997802
$378$	−4.93115	−0.253631
$379$	28.2491	1.45106	0.725530	−	0.688191i	$-0.241595\pi$
$379$	28.2491	1.45106	0.725530	+	0.688191i	$0.241595\pi$
$380$	0	0
$381$	−0.0145651	−0.000746192 0
$382$	−17.1241	−0.876144
$383$	−31.6901	−1.61929	−0.809645	−	0.586920i	$-0.800340\pi$
$383$	−31.6901	−1.61929	−0.809645	+	0.586920i	$0.800340\pi$
$384$	−0.329310	−0.0168050
$385$	0	0
$386$	−47.3007	−2.40754
$387$	11.8134	0.600507
$388$	10.2155	0.518614
$389$	23.1689	1.17471	0.587355	−	0.809330i	$-0.300169\pi$
$389$	23.1689	1.17471	0.587355	+	0.809330i	$0.300169\pi$
$390$	0	0
$391$	−3.11943	−0.157756
$392$	0.515985	0.0260612
$393$	3.75845	0.189589
$394$	−53.7827	−2.70953
$395$	0	0
$396$	−4.03760	−0.202897
$397$	−30.6366	−1.53761	−0.768804	−	0.639484i	$-0.779148\pi$
$397$	−30.6366	−1.53761	−0.768804	+	0.639484i	$0.779148\pi$
$398$	39.3828	1.97408
$399$	−2.49782	−0.125047
$400$	0	0
$401$	−8.47109	−0.423026	−0.211513	−	0.977375i	$-0.567839\pi$
$401$	−8.47109	−0.423026	−0.211513	+	0.977375i	$0.567839\pi$
$402$	−12.6339	−0.630121
$403$	11.0113	0.548511
$404$	0.391838	0.0194947
$405$	0	0
$406$	−17.1714	−0.852203
$407$	2.28238	0.113133
$408$	−0.0181094	−0.000896548 0
$409$	23.2857	1.15140	0.575702	−	0.817660i	$-0.304729\pi$
$409$	23.2857	1.15140	0.575702	+	0.817660i	$0.304729\pi$
$410$	0	0
$411$	−1.39701	−0.0689092
$412$	8.10727	0.399416
$413$	0.297377	0.0146330
$414$	39.1974	1.92645
$415$	0	0
$416$	15.5371	0.761767
$417$	−2.78485	−0.136375
$418$	−8.46789	−0.414178
$419$	−9.29059	−0.453875	−0.226937	−	0.973909i	$-0.572871\pi$
$419$	−9.29059	−0.453875	−0.226937	+	0.973909i	$0.572871\pi$
$420$	0	0
$421$	15.4991	0.755380	0.377690	−	0.925932i	$-0.376719\pi$
$421$	15.4991	0.755380	0.377690	+	0.925932i	$0.376719\pi$
$422$	−9.21913	−0.448780
$423$	−1.76644	−0.0858871
$424$	0.0600172	0.00291469
$425$	0	0
$426$	0.555762	0.0269268
$427$	0.960185	0.0464666
$428$	−13.6930	−0.661874
$429$	−0.696294	−0.0336174
$430$	0	0
$431$	−19.5308	−0.940765	−0.470382	−	0.882463i	$-0.655884\pi$
$431$	−19.5308	−0.940765	−0.470382	+	0.882463i	$0.655884\pi$
$432$	−11.2721	−0.542328
$433$	5.89329	0.283213	0.141607	−	0.989923i	$-0.454773\pi$
$433$	5.89329	0.283213	0.141607	+	0.989923i	$0.454773\pi$
$434$	−9.75953	−0.468472
$435$	0	0
$436$	8.22594	0.393951
$437$	41.5197	1.98616
$438$	11.0573	0.528340
$439$	22.1839	1.05878	0.529390	−	0.848379i	$-0.322421\pi$
$439$	22.1839	1.05878	0.529390	+	0.848379i	$0.322421\pi$
$440$	0	0
$441$	17.2486	0.821360
$442$	1.70918	0.0812975
$443$	14.6268	0.694940	0.347470	−	0.937691i	$-0.387041\pi$
$443$	14.6268	0.694940	0.347470	+	0.937691i	$0.387041\pi$
$444$	−3.24068	−0.153796
$445$	0	0
$446$	−23.7454	−1.12438
$447$	−7.42423	−0.351154
$448$	−7.09462	−0.335189
$449$	−34.2308	−1.61545	−0.807726	−	0.589558i	$-0.799302\pi$
$449$	−34.2308	−1.61545	−0.807726	+	0.589558i	$0.799302\pi$
$450$	0	0
$451$	−4.60103	−0.216654
$452$	−0.878251	−0.0413095
$453$	9.84886	0.462740
$454$	−21.0403	−0.987470
$455$	0	0
$456$	0.241036	0.0112876
$457$	24.3534	1.13921	0.569603	−	0.821920i	$-0.307097\pi$
$457$	24.3534	1.13921	0.569603	+	0.821920i	$0.307097\pi$
$458$	57.9688	2.70871
$459$	−1.26591	−0.0590877
$460$	0	0
$461$	10.3474	0.481924	0.240962	−	0.970535i	$-0.422537\pi$
$461$	10.3474	0.481924	0.240962	+	0.970535i	$0.422537\pi$
$462$	0.617140	0.0287119
$463$	−30.7015	−1.42682	−0.713409	−	0.700748i	$-0.752850\pi$
$463$	−30.7015	−1.42682	−0.713409	+	0.700748i	$0.752850\pi$
$464$	−39.2520	−1.82223
$465$	0	0
$466$	0.971044	0.0449828
$467$	20.5093	0.949056	0.474528	−	0.880240i	$-0.342619\pi$
$467$	20.5093	0.949056	0.474528	+	0.880240i	$0.342619\pi$
$468$	−10.8471	−0.501409
$469$	−10.7008	−0.494117
$470$	0	0
$471$	7.18033	0.330852
$472$	−0.0286965	−0.00132086
$473$	−3.09167	−0.142155
$474$	11.0258	0.506433
$475$	0	0
$476$	−0.765111	−0.0350688
$477$	2.00628	0.0918614
$478$	4.18711	0.191514
$479$	28.0475	1.28152	0.640761	−	0.767740i	$-0.278619\pi$
$479$	28.0475	1.28152	0.640761	+	0.767740i	$0.278619\pi$
$480$	0	0
$481$	6.13168	0.279581
$482$	−2.01020	−0.0915622
$483$	−3.02596	−0.137686
$484$	−21.3934	−0.972427
$485$	0	0
$486$	24.2070	1.09805
$487$	−10.9035	−0.494085	−0.247043	−	0.969005i	$-0.579459\pi$
$487$	−10.9035	−0.494085	−0.247043	+	0.969005i	$0.579459\pi$
$488$	−0.0926566	−0.00419437
$489$	2.49798	0.112963
$490$	0	0
$491$	−27.6672	−1.24860	−0.624301	−	0.781184i	$-0.714616\pi$
$491$	−27.6672	−1.24860	−0.624301	+	0.781184i	$0.714616\pi$
$492$	6.53287	0.294525
$493$	−4.40820	−0.198536
$494$	−22.7493	−1.02354
$495$	0	0
$496$	−22.3092	−1.00171
$497$	0.470726	0.0211149
$498$	−6.66645	−0.298731
$499$	−17.3522	−0.776792	−0.388396	−	0.921493i	$-0.626971\pi$
$499$	−17.3522	−0.776792	−0.388396	+	0.921493i	$0.626971\pi$
$500$	0	0
$501$	7.82371	0.349538
$502$	19.4413	0.867706
$503$	26.4875	1.18102	0.590510	−	0.807030i	$-0.298926\pi$
$503$	26.4875	1.18102	0.590510	+	0.807030i	$0.298926\pi$
$504$	0.192737	0.00858518
$505$	0	0
$506$	−10.2583	−0.456038
$507$	4.63706	0.205939
$508$	0.0593820	0.00263465
$509$	3.50048	0.155156	0.0775780	−	0.996986i	$-0.475281\pi$
$509$	3.50048	0.155156	0.0775780	+	0.996986i	$0.475281\pi$
$510$	0	0
$511$	9.36547	0.414304
$512$	−32.1229	−1.41964
$513$	16.8493	0.743916
$514$	−32.2339	−1.42178
$515$	0	0
$516$	4.38977	0.193249
$517$	0.462293	0.0203316
$518$	−5.43464	−0.238784
$519$	0.417175	0.0183119
$520$	0	0
$521$	8.93651	0.391516	0.195758	−	0.980652i	$-0.437283\pi$
$521$	8.93651	0.391516	0.195758	+	0.980652i	$0.437283\pi$
$522$	55.3915	2.42442
$523$	−6.13438	−0.268238	−0.134119	−	0.990965i	$-0.542820\pi$
$523$	−6.13438	−0.268238	−0.134119	+	0.990965i	$0.542820\pi$
$524$	−15.3233	−0.669400
$525$	0	0
$526$	54.1552	2.36128
$527$	−2.50544	−0.109139
$528$	1.41071	0.0613935
$529$	27.2986	1.18689
$530$	0	0
$531$	−0.959280	−0.0416292
$532$	10.1837	0.441517
$533$	−12.3608	−0.535407
$534$	12.6303	0.546565
$535$	0	0
$536$	1.03261	0.0446021
$537$	−7.50810	−0.323999
$538$	−61.7580	−2.66258
$539$	−4.51411	−0.194437
$540$	0	0
$541$	32.8484	1.41226	0.706132	−	0.708081i	$-0.250439\pi$
$541$	32.8484	1.41226	0.706132	+	0.708081i	$0.250439\pi$
$542$	64.8368	2.78498
$543$	7.49647	0.321704
$544$	−3.53521	−0.151571
$545$	0	0
$546$	1.65797	0.0709544
$547$	27.5818	1.17931	0.589656	−	0.807655i	$-0.299263\pi$
$547$	27.5818	1.17931	0.589656	+	0.807655i	$0.299263\pi$
$548$	5.69561	0.243304
$549$	−3.09736	−0.132192
$550$	0	0
$551$	58.6733	2.49957
$552$	0.292001	0.0124284
$553$	9.33879	0.397126
$554$	19.7805	0.840391
$555$	0	0
$556$	11.3539	0.481511
$557$	−12.3393	−0.522834	−0.261417	−	0.965226i	$-0.584190\pi$
$557$	−12.3393	−0.522834	−0.261417	+	0.965226i	$0.584190\pi$
$558$	31.4823	1.33275
$559$	−8.30587	−0.351301
$560$	0	0
$561$	0.158431	0.00668895
$562$	−0.125348	−0.00528748
$563$	35.3473	1.48971	0.744855	−	0.667227i	$-0.232519\pi$
$563$	35.3473	1.48971	0.744855	+	0.667227i	$0.232519\pi$
$564$	−0.656397	−0.0276393
$565$	0	0
$566$	−46.4629	−1.95298
$567$	5.80214	0.243667
$568$	−0.0454244	−0.00190597
$569$	19.0099	0.796938	0.398469	−	0.917182i	$-0.369542\pi$
$569$	19.0099	0.796938	0.398469	+	0.917182i	$0.369542\pi$
$570$	0	0
$571$	23.9059	1.00043	0.500215	−	0.865901i	$-0.333254\pi$
$571$	23.9059	1.00043	0.500215	+	0.865901i	$0.333254\pi$
$572$	2.83880	0.118696
$573$	−4.26432	−0.178145
$574$	10.9557	0.457280
$575$	0	0
$576$	22.8858	0.953576
$577$	−24.7986	−1.03238	−0.516190	−	0.856474i	$-0.672650\pi$
$577$	−24.7986	−1.03238	−0.516190	+	0.856474i	$0.672650\pi$
$578$	33.7845	1.40525
$579$	−11.7791	−0.489521
$580$	0	0
$581$	−5.64643	−0.234253
$582$	5.03683	0.208784
$583$	−0.525063	−0.0217459
$584$	−0.903755	−0.0373977
$585$	0	0
$586$	−15.2718	−0.630874
$587$	45.8195	1.89117	0.945586	−	0.325373i	$-0.105490\pi$
$587$	45.8195	1.89117	0.945586	+	0.325373i	$0.105490\pi$
$588$	6.40946	0.264322
$589$	33.3475	1.37406
$590$	0	0
$591$	−13.3932	−0.550924
$592$	−12.4230	−0.510582
$593$	−12.9205	−0.530581	−0.265290	−	0.964169i	$-0.585468\pi$
$593$	−12.9205	−0.530581	−0.265290	+	0.964169i	$0.585468\pi$
$594$	−4.16298	−0.170809
$595$	0	0
$596$	30.2687	1.23985
$597$	9.80730	0.401386
$598$	−27.5593	−1.12698
$599$	26.4741	1.08170	0.540851	−	0.841118i	$-0.318102\pi$
$599$	26.4741	1.08170	0.540851	+	0.841118i	$0.318102\pi$
$600$	0	0
$601$	12.3729	0.504702	0.252351	−	0.967636i	$-0.418796\pi$
$601$	12.3729	0.504702	0.252351	+	0.967636i	$0.418796\pi$
$602$	7.36166	0.300039
$603$	34.5186	1.40571
$604$	−40.1539	−1.63384
$605$	0	0
$606$	0.193199	0.00784816
$607$	6.58880	0.267431	0.133716	−	0.991020i	$-0.457309\pi$
$607$	6.58880	0.267431	0.133716	+	0.991020i	$0.457309\pi$
$608$	47.0538	1.90828
$609$	−4.27611	−0.173277
$610$	0	0
$611$	1.24197	0.0502446
$612$	2.46809	0.0997668
$613$	32.6185	1.31745	0.658724	−	0.752384i	$-0.271096\pi$
$613$	32.6185	1.31745	0.658724	+	0.752384i	$0.271096\pi$
$614$	−30.8699	−1.24581
$615$	0	0
$616$	−0.0504410	−0.00203233
$617$	−44.7802	−1.80278	−0.901391	−	0.433006i	$-0.857453\pi$
$617$	−44.7802	−1.80278	−0.901391	+	0.433006i	$0.857453\pi$
$618$	3.99735	0.160797
$619$	36.4386	1.46459	0.732296	−	0.680986i	$-0.238449\pi$
$619$	36.4386	1.46459	0.732296	+	0.680986i	$0.238449\pi$
$620$	0	0
$621$	20.4119	0.819102
$622$	−50.3581	−2.01918
$623$	10.6977	0.428596
$624$	3.78993	0.151719
$625$	0	0
$626$	−17.9953	−0.719235
$627$	−2.10872	−0.0842140
$628$	−29.2743	−1.16817
$629$	−1.39517	−0.0556290
$630$	0	0
$631$	19.4629	0.774804	0.387402	−	0.921911i	$-0.373373\pi$
$631$	19.4629	0.774804	0.387402	+	0.921911i	$0.373373\pi$
$632$	−0.901181	−0.0358470
$633$	−2.29579	−0.0912496
$634$	41.6767	1.65519
$635$	0	0
$636$	0.745522	0.0295619
$637$	−12.1273	−0.480502
$638$	−14.4965	−0.573921
$639$	−1.51847	−0.0600696
$640$	0	0
$641$	27.8560	1.10025	0.550123	−	0.835084i	$-0.314581\pi$
$641$	27.8560	1.10025	0.550123	+	0.835084i	$0.314581\pi$
$642$	−6.75142	−0.266457
$643$	5.63664	0.222288	0.111144	−	0.993804i	$-0.464549\pi$
$643$	5.63664	0.222288	0.111144	+	0.993804i	$0.464549\pi$
$644$	12.3369	0.486140
$645$	0	0
$646$	5.17624	0.203656
$647$	17.7323	0.697127	0.348563	−	0.937285i	$-0.386670\pi$
$647$	17.7323	0.697127	0.348563	+	0.937285i	$0.386670\pi$
$648$	−0.559899	−0.0219949
$649$	0.251053	0.00985468
$650$	0	0
$651$	−2.43037	−0.0952536
$652$	−10.1843	−0.398849
$653$	−14.1435	−0.553477	−0.276739	−	0.960945i	$-0.589254\pi$
$653$	−14.1435	−0.553477	−0.276739	+	0.960945i	$0.589254\pi$
$654$	4.05586	0.158597
$655$	0	0
$656$	25.0434	0.977782
$657$	−30.2111	−1.17865
$658$	−1.10078	−0.0429129
$659$	20.0695	0.781798	0.390899	−	0.920434i	$-0.372164\pi$
$659$	20.0695	0.781798	0.390899	+	0.920434i	$0.372164\pi$
$660$	0	0
$661$	−6.85193	−0.266509	−0.133255	−	0.991082i	$-0.542543\pi$
$661$	−6.85193	−0.266509	−0.133255	+	0.991082i	$0.542543\pi$
$662$	−14.0704	−0.546862
$663$	0.425629	0.0165301
$664$	0.544873	0.0211452
$665$	0	0
$666$	17.5310	0.679314
$667$	71.0791	2.75219
$668$	−31.8974	−1.23415
$669$	−5.91319	−0.228617
$670$	0	0
$671$	0.810610	0.0312932
$672$	−3.42928	−0.132287
$673$	−17.5575	−0.676791	−0.338396	−	0.941004i	$-0.609884\pi$
$673$	−17.5575	−0.676791	−0.338396	+	0.941004i	$0.609884\pi$
$674$	3.53098	0.136008
$675$	0	0
$676$	−18.9054	−0.727129
$677$	−22.0052	−0.845728	−0.422864	−	0.906193i	$-0.638975\pi$
$677$	−22.0052	−0.845728	−0.422864	+	0.906193i	$0.638975\pi$
$678$	−0.433028	−0.0166304
$679$	4.26616	0.163720
$680$	0	0
$681$	−5.23956	−0.200780
$682$	−8.23921	−0.315496
$683$	−32.7325	−1.25248	−0.626238	−	0.779632i	$-0.715406\pi$
$683$	−32.7325	−1.25248	−0.626238	+	0.779632i	$0.715406\pi$
$684$	−32.8504	−1.25607
$685$	0	0
$686$	22.7420	0.868294
$687$	14.4357	0.550756
$688$	16.8280	0.641560
$689$	−1.41060	−0.0537396
$690$	0	0
$691$	−42.8793	−1.63121	−0.815604	−	0.578611i	$-0.803595\pi$
$691$	−42.8793	−1.63121	−0.815604	+	0.578611i	$0.803595\pi$
$692$	−1.70083	−0.0646558
$693$	−1.68617	−0.0640521
$694$	−22.1844	−0.842110
$695$	0	0
$696$	0.412639	0.0156410
$697$	2.81251	0.106531
$698$	45.9651	1.73980
$699$	0.241814	0.00914626
$700$	0	0
$701$	−9.59945	−0.362566	−0.181283	−	0.983431i	$-0.558025\pi$
$701$	−9.59945	−0.362566	−0.181283	+	0.983431i	$0.558025\pi$
$702$	−11.1840	−0.422113
$703$	18.5697	0.700370
$704$	−5.98944	−0.225735
$705$	0	0
$706$	−38.7335	−1.45775
$707$	0.163638	0.00615423
$708$	−0.356462	−0.0133967
$709$	−20.6550	−0.775717	−0.387858	−	0.921719i	$-0.626785\pi$
$709$	−20.6550	−0.775717	−0.387858	+	0.921719i	$0.626785\pi$
$710$	0	0
$711$	−30.1251	−1.12978
$712$	−1.03232	−0.0386877
$713$	40.3984	1.51293
$714$	−0.377244	−0.0141180
$715$	0	0
$716$	30.6106	1.14397
$717$	1.04270	0.0389402
$718$	−40.6060	−1.51540
$719$	−36.5196	−1.36195	−0.680975	−	0.732307i	$-0.738444\pi$
$719$	−36.5196	−1.36195	−0.680975	+	0.732307i	$0.738444\pi$
$720$	0	0
$721$	3.38572	0.126091
$722$	−30.7020	−1.14261
$723$	−0.500591	−0.0186172
$724$	−30.5632	−1.13587
$725$	0	0
$726$	−10.5482	−0.391479
$727$	−53.4718	−1.98316	−0.991579	−	0.129503i	$-0.958662\pi$
$727$	−53.4718	−1.98316	−0.991579	+	0.129503i	$0.958662\pi$
$728$	−0.135512	−0.00502239
$729$	−14.3943	−0.533122
$730$	0	0
$731$	1.88987	0.0698993
$732$	−1.15096	−0.0425408
$733$	47.4390	1.75220	0.876100	−	0.482129i	$-0.160136\pi$
$733$	47.4390	1.75220	0.876100	+	0.482129i	$0.160136\pi$
$734$	7.86154	0.290175
$735$	0	0
$736$	57.0027	2.10115
$737$	−9.03386	−0.332766
$738$	−35.3407	−1.30091
$739$	24.6810	0.907904	0.453952	−	0.891026i	$-0.350014\pi$
$739$	24.6810	0.907904	0.453952	+	0.891026i	$0.350014\pi$
$740$	0	0
$741$	−5.66514	−0.208114
$742$	1.25024	0.0458979
$743$	41.1925	1.51121	0.755603	−	0.655030i	$-0.227344\pi$
$743$	41.1925	1.51121	0.755603	+	0.655030i	$0.227344\pi$
$744$	0.234527	0.00859818
$745$	0	0
$746$	18.1999	0.666345
$747$	18.2142	0.666424
$748$	−0.645924	−0.0236173
$749$	−5.71840	−0.208946
$750$	0	0
$751$	−16.0787	−0.586719	−0.293360	−	0.956002i	$-0.594773\pi$
$751$	−16.0787	−0.586719	−0.293360	+	0.956002i	$0.594773\pi$
$752$	−2.51627	−0.0917588
$753$	4.84136	0.176429
$754$	−38.9453	−1.41830
$755$	0	0
$756$	5.00649	0.182084
$757$	38.0614	1.38336	0.691682	−	0.722202i	$-0.256870\pi$
$757$	38.0614	1.38336	0.691682	+	0.722202i	$0.256870\pi$
$758$	−56.7865	−2.06258
$759$	−2.55458	−0.0927253
$760$	0	0
$761$	29.7253	1.07754	0.538770	−	0.842453i	$-0.318889\pi$
$761$	29.7253	1.07754	0.538770	+	0.842453i	$0.318889\pi$
$762$	0.0292788	0.00106066
$763$	3.43528	0.124366
$764$	17.3857	0.628992
$765$	0	0
$766$	63.7036	2.30170
$767$	0.674461	0.0243534
$768$	−7.67176	−0.276831
$769$	−50.1093	−1.80699	−0.903494	−	0.428602i	$-0.859006\pi$
$769$	−50.1093	−1.80699	−0.903494	+	0.428602i	$0.859006\pi$
$770$	0	0
$771$	−8.02705	−0.289087
$772$	48.0234	1.72840
$773$	−1.44897	−0.0521159	−0.0260579	−	0.999660i	$-0.508295\pi$
$773$	−1.44897	−0.0521159	−0.0260579	+	0.999660i	$0.508295\pi$
$774$	−23.7473	−0.853577
$775$	0	0
$776$	−0.411679	−0.0147784
$777$	−1.35336	−0.0485515
$778$	−46.5742	−1.66976
$779$	−37.4346	−1.34123
$780$	0	0
$781$	0.397397	0.0142200
$782$	6.27069	0.224239
$783$	28.8450	1.03084
$784$	24.5703	0.877512
$785$	0	0
$786$	−7.55525	−0.269487
$787$	−10.5396	−0.375695	−0.187848	−	0.982198i	$-0.560151\pi$
$787$	−10.5396	−0.375695	−0.187848	+	0.982198i	$0.560151\pi$
$788$	54.6044	1.94520
$789$	13.4860	0.480115
$790$	0	0
$791$	−0.366772	−0.0130409
$792$	0.162713	0.00578174
$793$	2.17773	0.0773335
$794$	61.5858	2.18560
$795$	0	0
$796$	−39.9845	−1.41721
$797$	−31.2275	−1.10614	−0.553068	−	0.833136i	$-0.686543\pi$
$797$	−31.2275	−1.10614	−0.553068	+	0.833136i	$0.686543\pi$
$798$	5.02113	0.177746
$799$	−0.282590	−0.00999731
$800$	0	0
$801$	−34.5087	−1.21931
$802$	17.0286	0.601301
$803$	7.90654	0.279016
$804$	12.8269	0.452370
$805$	0	0
$806$	−22.1349	−0.779669
$807$	−15.3793	−0.541376
$808$	−0.0157908	−0.000555519 0
$809$	−38.9547	−1.36957	−0.684787	−	0.728743i	$-0.740105\pi$
$809$	−38.9547	−1.36957	−0.684787	+	0.728743i	$0.740105\pi$
$810$	0	0
$811$	3.89413	0.136741	0.0683707	−	0.997660i	$-0.478220\pi$
$811$	3.89413	0.136741	0.0683707	+	0.997660i	$0.478220\pi$
$812$	17.4338	0.611805
$813$	16.1460	0.566264
$814$	−4.58804	−0.160811
$815$	0	0
$816$	−0.862339	−0.0301879
$817$	−25.1542	−0.880035
$818$	−46.8090	−1.63664
$819$	−4.52994	−0.158289
$820$	0	0
$821$	−14.5536	−0.507923	−0.253962	−	0.967214i	$-0.581734\pi$
$821$	−14.5536	−0.507923	−0.253962	+	0.967214i	$0.581734\pi$
$822$	2.80826	0.0979495
$823$	−37.0978	−1.29315	−0.646575	−	0.762851i	$-0.723799\pi$
$823$	−37.0978	−1.29315	−0.646575	+	0.762851i	$0.723799\pi$
$824$	−0.326718	−0.0113818
$825$	0	0
$826$	−0.597789	−0.0207997
$827$	46.8558	1.62934	0.814668	−	0.579928i	$-0.196919\pi$
$827$	46.8558	1.62934	0.814668	+	0.579928i	$0.196919\pi$
$828$	−39.7962	−1.38301
$829$	43.4487	1.50904	0.754518	−	0.656280i	$-0.227871\pi$
$829$	43.4487	1.50904	0.754518	+	0.656280i	$0.227871\pi$
$830$	0	0
$831$	4.92583	0.170875
$832$	−16.0908	−0.557849
$833$	2.75938	0.0956068
$834$	5.59811	0.193847
$835$	0	0
$836$	8.59727	0.297343
$837$	16.3943	0.566670
$838$	18.6760	0.645150
$839$	45.0114	1.55397	0.776983	−	0.629521i	$-0.216749\pi$
$839$	45.0114	1.55397	0.776983	+	0.629521i	$0.216749\pi$
$840$	0	0
$841$	71.4450	2.46362
$842$	−31.1563	−1.07372
$843$	−0.0312147	−0.00107509
$844$	9.35998	0.322184
$845$	0	0
$846$	3.55090	0.122082
$847$	−8.93422	−0.306983
$848$	2.85792	0.0981415
$849$	−11.5704	−0.397096
$850$	0	0
$851$	22.4961	0.771155
$852$	−0.564253	−0.0193310
$853$	−5.62487	−0.192592	−0.0962959	−	0.995353i	$-0.530700\pi$
$853$	−5.62487	−0.192592	−0.0962959	+	0.995353i	$0.530700\pi$
$854$	−1.93017	−0.0660490
$855$	0	0
$856$	0.551818	0.0188607
$857$	1.42125	0.0485491	0.0242746	−	0.999705i	$-0.492272\pi$
$857$	1.42125	0.0485491	0.0242746	+	0.999705i	$0.492272\pi$
$858$	1.39969	0.0477847
$859$	−2.58506	−0.0882010	−0.0441005	−	0.999027i	$-0.514042\pi$
$859$	−2.58506	−0.0882010	−0.0441005	+	0.999027i	$0.514042\pi$
$860$	0	0
$861$	2.72823	0.0929779
$862$	39.2608	1.33723
$863$	46.3980	1.57941	0.789703	−	0.613490i	$-0.210235\pi$
$863$	46.3980	1.57941	0.789703	+	0.613490i	$0.210235\pi$
$864$	23.1326	0.786986
$865$	0	0
$866$	−11.8467	−0.402567
$867$	8.41320	0.285727
$868$	9.90864	0.336321
$869$	7.88402	0.267447
$870$	0	0
$871$	−24.2698	−0.822349
$872$	−0.331500	−0.0112260
$873$	−13.7618	−0.465765
$874$	−83.4630	−2.82318
$875$	0	0
$876$	−11.2263	−0.379300
$877$	9.47791	0.320046	0.160023	−	0.987113i	$-0.448843\pi$
$877$	9.47791	0.320046	0.160023	+	0.987113i	$0.448843\pi$
$878$	−44.5941	−1.50498
$879$	−3.80307	−0.128274
$880$	0	0
$881$	50.5681	1.70368	0.851841	−	0.523800i	$-0.175486\pi$
$881$	50.5681	1.70368	0.851841	+	0.523800i	$0.175486\pi$
$882$	−34.6731	−1.16750
$883$	18.3321	0.616925	0.308462	−	0.951237i	$-0.400186\pi$
$883$	18.3321	0.616925	0.308462	+	0.951237i	$0.400186\pi$
$884$	−1.73530	−0.0583643
$885$	0	0
$886$	−29.4028	−0.987807
$887$	−22.4382	−0.753401	−0.376701	−	0.926335i	$-0.622941\pi$
$887$	−22.4382	−0.753401	−0.376701	+	0.926335i	$0.622941\pi$
$888$	0.130597	0.00438256
$889$	0.0247989	0.000831728 0
$890$	0	0
$891$	4.89829	0.164099
$892$	24.1082	0.807201
$893$	3.76128	0.125866
$894$	14.9242	0.499140
$895$	0	0
$896$	0.560692	0.0187314
$897$	−6.86296	−0.229148
$898$	68.8109	2.29625
$899$	57.0888	1.90402
$900$	0	0
$901$	0.320960	0.0106927
$902$	9.24900	0.307958
$903$	1.83324	0.0610064
$904$	0.0353930	0.00117715
$905$	0	0
$906$	−19.7982	−0.657751
$907$	44.1063	1.46452	0.732262	−	0.681023i	$-0.238465\pi$
$907$	44.1063	1.46452	0.732262	+	0.681023i	$0.238465\pi$
$908$	21.3618	0.708915
$909$	−0.527862	−0.0175081
$910$	0	0
$911$	36.5594	1.21127	0.605633	−	0.795744i	$-0.292920\pi$
$911$	36.5594	1.21127	0.605633	+	0.795744i	$0.292920\pi$
$912$	11.4778	0.380067
$913$	−4.76684	−0.157759
$914$	−48.9554	−1.61930
$915$	0	0
$916$	−58.8545	−1.94461
$917$	−6.39924	−0.211322
$918$	2.54474	0.0839889
$919$	−47.3887	−1.56321	−0.781605	−	0.623774i	$-0.785599\pi$
$919$	−47.3887	−1.56321	−0.781605	+	0.623774i	$0.785599\pi$
$920$	0	0
$921$	−7.68737	−0.253307
$922$	−20.8003	−0.685021
$923$	1.06762	0.0351412
$924$	−0.626568	−0.0206126
$925$	0	0
$926$	61.7162	2.02812
$927$	−10.9217	−0.358715
$928$	80.5531	2.64428
$929$	23.8472	0.782400	0.391200	−	0.920306i	$-0.372060\pi$
$929$	23.8472	0.782400	0.391200	+	0.920306i	$0.372060\pi$
$930$	0	0
$931$	−36.7274	−1.20369
$932$	−0.985880	−0.0322936
$933$	−12.5404	−0.410555
$934$	−41.2278	−1.34901
$935$	0	0
$936$	0.437133	0.0142881
$937$	−31.9624	−1.04417	−0.522083	−	0.852895i	$-0.674845\pi$
$937$	−31.9624	−1.04417	−0.522083	+	0.852895i	$0.674845\pi$
$938$	21.5108	0.702352
$939$	−4.48127	−0.146241
$940$	0	0
$941$	23.8740	0.778271	0.389136	−	0.921180i	$-0.372774\pi$
$941$	23.8740	0.778271	0.389136	+	0.921180i	$0.372774\pi$
$942$	−14.4339	−0.470283
$943$	−45.3497	−1.47679
$944$	−1.36648	−0.0444752
$945$	0	0
$946$	6.21488	0.202063
$947$	−44.4722	−1.44515	−0.722575	−	0.691292i	$-0.757042\pi$
$947$	−44.4722	−1.44515	−0.722575	+	0.691292i	$0.757042\pi$
$948$	−11.1943	−0.363574
$949$	21.2412	0.689518
$950$	0	0
$951$	10.3785	0.336547
$952$	0.0308335	0.000999319 0
$953$	54.1645	1.75456	0.877280	−	0.479980i	$-0.159356\pi$
$953$	54.1645	1.75456	0.877280	+	0.479980i	$0.159356\pi$
$954$	−4.03303	−0.130574
$955$	0	0
$956$	−4.25109	−0.137490
$957$	−3.60999	−0.116694
$958$	−56.3811	−1.82159
$959$	2.37858	0.0768083
$960$	0	0
$961$	1.44694	0.0466756
$962$	−12.3259	−0.397404
$963$	18.4464	0.594427
$964$	2.04092	0.0657334
$965$	0	0
$966$	6.08278	0.195710
$967$	35.3826	1.13783	0.568914	−	0.822397i	$-0.307364\pi$
$967$	35.3826	1.13783	0.568914	+	0.822397i	$0.307364\pi$
$968$	0.862140	0.0277102
$969$	1.28901	0.0414090
$970$	0	0
$971$	−8.91001	−0.285936	−0.142968	−	0.989727i	$-0.545665\pi$
$971$	−8.91001	−0.285936	−0.142968	+	0.989727i	$0.545665\pi$
$972$	−24.5768	−0.788302
$973$	4.74155	0.152007
$974$	21.9183	0.702307
$975$	0	0
$976$	−4.41215	−0.141230
$977$	−21.0250	−0.672650	−0.336325	−	0.941746i	$-0.609184\pi$
$977$	−21.0250	−0.672650	−0.336325	+	0.941746i	$0.609184\pi$
$978$	−5.02146	−0.160568
$979$	9.03126	0.288640
$980$	0	0
$981$	−11.0815	−0.353806
$982$	55.6166	1.77480
$983$	33.5818	1.07109	0.535546	−	0.844506i	$-0.320106\pi$
$983$	33.5818	1.07109	0.535546	+	0.844506i	$0.320106\pi$
$984$	−0.263271	−0.00839276
$985$	0	0
$986$	8.86138	0.282204
$987$	−0.274122	−0.00872540
$988$	23.0968	0.734808
$989$	−30.4728	−0.968978
$990$	0	0
$991$	−32.0529	−1.01819	−0.509097	−	0.860709i	$-0.670021\pi$
$991$	−32.0529	−1.01819	−0.509097	+	0.860709i	$0.670021\pi$
$992$	45.7831	1.45361
$993$	−3.50389	−0.111192
$994$	−0.946255	−0.0300134
$995$	0	0
$996$	6.76830	0.214462
$997$	−37.4198	−1.18510	−0.592548	−	0.805535i	$-0.701878\pi$
$997$	−37.4198	−1.18510	−0.592548	+	0.805535i	$0.701878\pi$
$998$	34.8815	1.10415
$999$	9.12924	0.288836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.h.1.3		12
5.4	even	2		241.2.a.b.1.10	✓	12
15.14	odd	2		2169.2.a.h.1.3		12
20.19	odd	2		3856.2.a.n.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.b.1.10	✓	12	5.4	even	2
2169.2.a.h.1.3		12	15.14	odd	2
3856.2.a.n.1.6		12	20.19	odd	2
6025.2.a.h.1.3		12	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01020 q^{2} -0.500591 q^{3} +2.04092 q^{4} +1.00629 q^{6} +0.852319 q^{7} -0.0822476 q^{8} -2.74941 q^{9} +O(q^{10})\)	\(q-2.01020 q^{2} -0.500591 q^{3} +2.04092 q^{4} +1.00629 q^{6} +0.852319 q^{7} -0.0822476 q^{8} -2.74941 q^{9} +0.719546 q^{11} -1.02166 q^{12} +1.93309 q^{13} -1.71333 q^{14} -3.91650 q^{16} -0.439843 q^{17} +5.52687 q^{18} +5.85432 q^{19} -0.426663 q^{21} -1.44643 q^{22} +7.09215 q^{23} +0.0411724 q^{24} -3.88589 q^{26} +2.87810 q^{27} +1.73951 q^{28} +10.0222 q^{29} +5.69622 q^{31} +8.03745 q^{32} -0.360198 q^{33} +0.884173 q^{34} -5.61131 q^{36} +3.17197 q^{37} -11.7684 q^{38} -0.967685 q^{39} -6.39435 q^{41} +0.857679 q^{42} -4.29669 q^{43} +1.46853 q^{44} -14.2567 q^{46} +0.642479 q^{47} +1.96056 q^{48} -6.27355 q^{49} +0.220181 q^{51} +3.94526 q^{52} -0.729714 q^{53} -5.78557 q^{54} -0.0701012 q^{56} -2.93062 q^{57} -20.1467 q^{58} +0.348904 q^{59} +1.12656 q^{61} -11.4506 q^{62} -2.34337 q^{63} -8.32390 q^{64} +0.724072 q^{66} -12.5549 q^{67} -0.897682 q^{68} -3.55026 q^{69} +0.552289 q^{71} +0.226132 q^{72} +10.9882 q^{73} -6.37630 q^{74} +11.9482 q^{76} +0.613283 q^{77} +1.94524 q^{78} +10.9569 q^{79} +6.80748 q^{81} +12.8539 q^{82} -6.62478 q^{83} -0.870783 q^{84} +8.63722 q^{86} -5.01703 q^{87} -0.0591810 q^{88} +12.5513 q^{89} +1.64760 q^{91} +14.4745 q^{92} -2.85148 q^{93} -1.29151 q^{94} -4.02347 q^{96} +5.00536 q^{97} +12.6111 q^{98} -1.97833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9	\( 12 q - 3 q^{2} - q^{3} + 13 q^{4} - q^{6} - 3 q^{7} - 9 q^{8} + 15 q^{9} + 22 q^{11} + 7 q^{12} + 5 q^{13} + 6 q^{14} + 15 q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - 14 q^{21} + 12 q^{22} - 32 q^{23} - 15 q^{24} + 8 q^{26} + 5 q^{27} + 11 q^{28} + 6 q^{29} + 8 q^{31} - q^{32} + 24 q^{33} - 19 q^{34} - 8 q^{36} + 8 q^{37} + 10 q^{38} + 31 q^{39} - q^{41} + 49 q^{42} + 2 q^{43} + 42 q^{44} - 25 q^{46} - 34 q^{47} + 49 q^{48} - 9 q^{49} - 3 q^{51} + 41 q^{52} - 5 q^{53} - 40 q^{54} + q^{56} + 22 q^{57} + 33 q^{58} + 26 q^{59} - 26 q^{61} + 17 q^{62} + 4 q^{63} + 13 q^{64} - 2 q^{66} - 6 q^{67} + 35 q^{68} - 2 q^{69} + 94 q^{71} - 17 q^{72} + 22 q^{73} + 26 q^{74} - 20 q^{76} + 7 q^{77} - 54 q^{78} + 9 q^{79} + 4 q^{81} - 15 q^{82} + 8 q^{83} + 2 q^{84} + 9 q^{86} - 4 q^{87} - 6 q^{88} - 3 q^{89} - 20 q^{91} - 36 q^{92} - 12 q^{93} + 48 q^{94} - 23 q^{96} + 29 q^{97} - 28 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - q^3 + 13 * q^4 - q^6 - 3 * q^7 - 9 * q^8 + 15 * q^9 + 22 * q^11 + 7 * q^12 + 5 * q^13 + 6 * q^14 + 15 * q^16 + 4 * q^17 + q^18 - 6 * q^19 - 14 * q^21 + 12 * q^22 - 32 * q^23 - 15 * q^24 + 8 * q^26 + 5 * q^27 + 11 * q^28 + 6 * q^29 + 8 * q^31 - q^32 + 24 * q^33 - 19 * q^34 - 8 * q^36 + 8 * q^37 + 10 * q^38 + 31 * q^39 - q^41 + 49 * q^42 + 2 * q^43 + 42 * q^44 - 25 * q^46 - 34 * q^47 + 49 * q^48 - 9 * q^49 - 3 * q^51 + 41 * q^52 - 5 * q^53 - 40 * q^54 + q^56 + 22 * q^57 + 33 * q^58 + 26 * q^59 - 26 * q^61 + 17 * q^62 + 4 * q^63 + 13 * q^64 - 2 * q^66 - 6 * q^67 + 35 * q^68 - 2 * q^69 + 94 * q^71 - 17 * q^72 + 22 * q^73 + 26 * q^74 - 20 * q^76 + 7 * q^77 - 54 * q^78 + 9 * q^79 + 4 * q^81 - 15 * q^82 + 8 * q^83 + 2 * q^84 + 9 * q^86 - 4 * q^87 - 6 * q^88 - 3 * q^89 - 20 * q^91 - 36 * q^92 - 12 * q^93 + 48 * q^94 - 23 * q^96 + 29 * q^97 - 28 * q^98 + 36 * q^99

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