LMFDB - Embedded newform 3525.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} + \cdots - 2 $ x^13 - 3x^12 - 17x^11 + 51x^10 + 106x^9 - 316x^8 - 288x^7 + 852x^6 + 309x^5 - 923x^4 - 107x^3 + 293x^2 + 12x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.32477$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32477 q^{2} +1.00000 q^{3} +3.40453 q^{4} -2.32477 q^{6} -4.29166 q^{7} -3.26521 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.32477 q^{2} +1.00000 q^{3} +3.40453 q^{4} -2.32477 q^{6} -4.29166 q^{7} -3.26521 q^{8} +1.00000 q^{9} -3.02713 q^{11} +3.40453 q^{12} -3.00342 q^{13} +9.97710 q^{14} +0.781783 q^{16} +0.421785 q^{17} -2.32477 q^{18} +4.21461 q^{19} -4.29166 q^{21} +7.03736 q^{22} -2.52032 q^{23} -3.26521 q^{24} +6.98224 q^{26} +1.00000 q^{27} -14.6111 q^{28} -0.653085 q^{29} +0.762027 q^{31} +4.71296 q^{32} -3.02713 q^{33} -0.980551 q^{34} +3.40453 q^{36} -6.53533 q^{37} -9.79798 q^{38} -3.00342 q^{39} +1.69035 q^{41} +9.97710 q^{42} -2.62536 q^{43} -10.3060 q^{44} +5.85915 q^{46} +1.00000 q^{47} +0.781783 q^{48} +11.4183 q^{49} +0.421785 q^{51} -10.2252 q^{52} -6.40027 q^{53} -2.32477 q^{54} +14.0132 q^{56} +4.21461 q^{57} +1.51827 q^{58} +0.907548 q^{59} -13.3935 q^{61} -1.77153 q^{62} -4.29166 q^{63} -12.5201 q^{64} +7.03736 q^{66} -12.1504 q^{67} +1.43598 q^{68} -2.52032 q^{69} +4.47678 q^{71} -3.26521 q^{72} +9.94599 q^{73} +15.1931 q^{74} +14.3488 q^{76} +12.9914 q^{77} +6.98224 q^{78} -6.97049 q^{79} +1.00000 q^{81} -3.92966 q^{82} +17.2004 q^{83} -14.6111 q^{84} +6.10335 q^{86} -0.653085 q^{87} +9.88422 q^{88} +17.6260 q^{89} +12.8896 q^{91} -8.58051 q^{92} +0.762027 q^{93} -2.32477 q^{94} +4.71296 q^{96} -11.5760 q^{97} -26.5450 q^{98} -3.02713 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	$ 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) $ 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * 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 $

$2$	−2.32477	−1.64386	−0.821929	−	0.569590i	$-0.807102\pi$
$2$	−2.32477	−1.64386	−0.821929	+	0.569590i	$0.807102\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.40453	1.70227
$5$	0	0
$5$	0	0
$6$	−2.32477	−0.949081
$7$	−4.29166	−1.62210	−0.811048	−	0.584980i	$-0.801102\pi$
$7$	−4.29166	−1.62210	−0.811048	+	0.584980i	$0.801102\pi$
$8$	−3.26521	−1.15443
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.02713	−0.912714	−0.456357	−	0.889797i	$-0.650846\pi$
$11$	−3.02713	−0.912714	−0.456357	+	0.889797i	$0.650846\pi$
$12$	3.40453	0.982804
$13$	−3.00342	−0.832998	−0.416499	−	0.909136i	$-0.636743\pi$
$13$	−3.00342	−0.832998	−0.416499	+	0.909136i	$0.636743\pi$
$14$	9.97710	2.66649
$15$	0	0
$16$	0.781783	0.195446
$17$	0.421785	0.102298	0.0511489	−	0.998691i	$-0.483712\pi$
$17$	0.421785	0.102298	0.0511489	+	0.998691i	$0.483712\pi$
$18$	−2.32477	−0.547952
$19$	4.21461	0.966898	0.483449	−	0.875373i	$-0.339384\pi$
$19$	4.21461	0.966898	0.483449	+	0.875373i	$0.339384\pi$
$20$	0	0
$21$	−4.29166	−0.936517
$22$	7.03736	1.50037
$23$	−2.52032	−0.525523	−0.262762	−	0.964861i	$-0.584633\pi$
$23$	−2.52032	−0.525523	−0.262762	+	0.964861i	$0.584633\pi$
$24$	−3.26521	−0.666508
$25$	0	0
$26$	6.98224	1.36933
$27$	1.00000	0.192450
$28$	−14.6111	−2.76124
$29$	−0.653085	−0.121275	−0.0606374	−	0.998160i	$-0.519313\pi$
$29$	−0.653085	−0.121275	−0.0606374	+	0.998160i	$0.519313\pi$
$30$	0	0
$31$	0.762027	0.136864	0.0684320	−	0.997656i	$-0.478200\pi$
$31$	0.762027	0.136864	0.0684320	+	0.997656i	$0.478200\pi$
$32$	4.71296	0.833142
$33$	−3.02713	−0.526956
$34$	−0.980551	−0.168163
$35$	0	0
$36$	3.40453	0.567422
$37$	−6.53533	−1.07440	−0.537201	−	0.843454i	$-0.680518\pi$
$37$	−6.53533	−1.07440	−0.537201	+	0.843454i	$0.680518\pi$
$38$	−9.79798	−1.58944
$39$	−3.00342	−0.480932
$40$	0	0
$41$	1.69035	0.263988	0.131994	−	0.991251i	$-0.457862\pi$
$41$	1.69035	0.263988	0.131994	+	0.991251i	$0.457862\pi$
$42$	9.97710	1.53950
$43$	−2.62536	−0.400364	−0.200182	−	0.979759i	$-0.564153\pi$
$43$	−2.62536	−0.400364	−0.200182	+	0.979759i	$0.564153\pi$
$44$	−10.3060	−1.55368
$45$	0	0
$46$	5.85915	0.863885
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	0.781783	0.112841
$49$	11.4183	1.63119
$50$	0	0
$51$	0.421785	0.0590617
$52$	−10.2252	−1.41798
$53$	−6.40027	−0.879144	−0.439572	−	0.898207i	$-0.644870\pi$
$53$	−6.40027	−0.879144	−0.439572	+	0.898207i	$0.644870\pi$
$54$	−2.32477	−0.316360
$55$	0	0
$56$	14.0132	1.87259
$57$	4.21461	0.558239
$58$	1.51827	0.199358
$59$	0.907548	0.118153	0.0590763	−	0.998253i	$-0.481184\pi$
$59$	0.907548	0.118153	0.0590763	+	0.998253i	$0.481184\pi$
$60$	0	0
$61$	−13.3935	−1.71486	−0.857428	−	0.514604i	$-0.827939\pi$
$61$	−13.3935	−1.71486	−0.857428	+	0.514604i	$0.827939\pi$
$62$	−1.77153	−0.224985
$63$	−4.29166	−0.540698
$64$	−12.5201	−1.56501
$65$	0	0
$66$	7.03736	0.866240
$67$	−12.1504	−1.48440	−0.742202	−	0.670177i	$-0.766218\pi$
$67$	−12.1504	−1.48440	−0.742202	+	0.670177i	$0.766218\pi$
$68$	1.43598	0.174138
$69$	−2.52032	−0.303411
$70$	0	0
$71$	4.47678	0.531296	0.265648	−	0.964070i	$-0.414414\pi$
$71$	4.47678	0.531296	0.265648	+	0.964070i	$0.414414\pi$
$72$	−3.26521	−0.384809
$73$	9.94599	1.16409	0.582045	−	0.813157i	$-0.302253\pi$
$73$	9.94599	1.16409	0.582045	+	0.813157i	$0.302253\pi$
$74$	15.1931	1.76616
$75$	0	0
$76$	14.3488	1.64592
$77$	12.9914	1.48051
$78$	6.98224	0.790583
$79$	−6.97049	−0.784241	−0.392121	−	0.919914i	$-0.628258\pi$
$79$	−6.97049	−0.784241	−0.392121	+	0.919914i	$0.628258\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.92966	−0.433958
$83$	17.2004	1.88798	0.943992	−	0.329968i	$-0.107038\pi$
$83$	17.2004	1.88798	0.943992	+	0.329968i	$0.107038\pi$
$84$	−14.6111	−1.59420
$85$	0	0
$86$	6.10335	0.658141
$87$	−0.653085	−0.0700180
$88$	9.88422	1.05366
$89$	17.6260	1.86836	0.934178	−	0.356808i	$-0.116135\pi$
$89$	17.6260	1.86836	0.934178	+	0.356808i	$0.116135\pi$
$90$	0	0
$91$	12.8896	1.35120
$92$	−8.58051	−0.894580
$93$	0.762027	0.0790185
$94$	−2.32477	−0.239781
$95$	0	0
$96$	4.71296	0.481015
$97$	−11.5760	−1.17536	−0.587682	−	0.809092i	$-0.699959\pi$
$97$	−11.5760	−1.17536	−0.587682	+	0.809092i	$0.699959\pi$
$98$	−26.5450	−2.68145
$99$	−3.02713	−0.304238
$100$	0	0
$101$	−15.5523	−1.54751	−0.773755	−	0.633484i	$-0.781624\pi$
$101$	−15.5523	−1.54751	−0.773755	+	0.633484i	$0.781624\pi$
$102$	−0.980551	−0.0970890
$103$	1.73292	0.170750	0.0853750	−	0.996349i	$-0.472791\pi$
$103$	1.73292	0.170750	0.0853750	+	0.996349i	$0.472791\pi$
$104$	9.80679	0.961635
$105$	0	0
$106$	14.8791	1.44519
$107$	15.4056	1.48932	0.744660	−	0.667444i	$-0.232612\pi$
$107$	15.4056	1.48932	0.744660	+	0.667444i	$0.232612\pi$
$108$	3.40453	0.327601
$109$	15.7878	1.51220	0.756100	−	0.654456i	$-0.227102\pi$
$109$	15.7878	1.51220	0.756100	+	0.654456i	$0.227102\pi$
$110$	0	0
$111$	−6.53533	−0.620306
$112$	−3.35515	−0.317031
$113$	3.73971	0.351802	0.175901	−	0.984408i	$-0.443716\pi$
$113$	3.73971	0.351802	0.175901	+	0.984408i	$0.443716\pi$
$114$	−9.79798	−0.917665
$115$	0	0
$116$	−2.22345	−0.206442
$117$	−3.00342	−0.277666
$118$	−2.10984	−0.194226
$119$	−1.81016	−0.165937
$120$	0	0
$121$	−1.83649	−0.166954
$122$	31.1366	2.81898
$123$	1.69035	0.152414
$124$	2.59435	0.232979
$125$	0	0
$126$	9.97710	0.888831
$127$	0.615447	0.0546121	0.0273060	−	0.999627i	$-0.491307\pi$
$127$	0.615447	0.0546121	0.0273060	+	0.999627i	$0.491307\pi$
$128$	19.6804	1.73951
$129$	−2.62536	−0.231150
$130$	0	0
$131$	22.1614	1.93625	0.968125	−	0.250468i	$-0.0805844\pi$
$131$	22.1614	1.93625	0.968125	+	0.250468i	$0.0805844\pi$
$132$	−10.3060	−0.897019
$133$	−18.0877	−1.56840
$134$	28.2467	2.44015
$135$	0	0
$136$	−1.37722	−0.118095
$137$	13.2832	1.13486	0.567432	−	0.823420i	$-0.307937\pi$
$137$	13.2832	1.13486	0.567432	+	0.823420i	$0.307937\pi$
$138$	5.85915	0.498764
$139$	23.4020	1.98493	0.992466	−	0.122520i	$-0.0390976\pi$
$139$	23.4020	1.98493	0.992466	+	0.122520i	$0.0390976\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−10.4075	−0.873374
$143$	9.09173	0.760289
$144$	0.781783	0.0651485
$145$	0	0
$146$	−23.1221	−1.91360
$147$	11.4183	0.941770
$148$	−22.2498	−1.82892
$149$	6.36654	0.521567	0.260784	−	0.965397i	$-0.416019\pi$
$149$	6.36654	0.521567	0.260784	+	0.965397i	$0.416019\pi$
$150$	0	0
$151$	−2.80047	−0.227899	−0.113950	−	0.993487i	$-0.536350\pi$
$151$	−2.80047	−0.227899	−0.113950	+	0.993487i	$0.536350\pi$
$152$	−13.7616	−1.11621
$153$	0.421785	0.0340993
$154$	−30.2020	−2.43374
$155$	0	0
$156$	−10.2252	−0.818674
$157$	−7.69012	−0.613739	−0.306869	−	0.951752i	$-0.599281\pi$
$157$	−7.69012	−0.613739	−0.306869	+	0.951752i	$0.599281\pi$
$158$	16.2048	1.28918
$159$	−6.40027	−0.507574
$160$	0	0
$161$	10.8164	0.852448
$162$	−2.32477	−0.182651
$163$	−11.5626	−0.905655	−0.452828	−	0.891598i	$-0.649585\pi$
$163$	−11.5626	−0.905655	−0.452828	+	0.891598i	$0.649585\pi$
$164$	5.75485	0.449378
$165$	0	0
$166$	−39.9868	−3.10358
$167$	−16.6662	−1.28967	−0.644835	−	0.764322i	$-0.723074\pi$
$167$	−16.6662	−1.28967	−0.644835	+	0.764322i	$0.723074\pi$
$168$	14.0132	1.08114
$169$	−3.97949	−0.306114
$170$	0	0
$171$	4.21461	0.322299
$172$	−8.93813	−0.681526
$173$	0.789286	0.0600083	0.0300042	−	0.999550i	$-0.490448\pi$
$173$	0.789286	0.0600083	0.0300042	+	0.999550i	$0.490448\pi$
$174$	1.51827	0.115100
$175$	0	0
$176$	−2.36656	−0.178386
$177$	0.907548	0.0682155
$178$	−40.9764	−3.07131
$179$	0.716809	0.0535768	0.0267884	−	0.999641i	$-0.491472\pi$
$179$	0.716809	0.0535768	0.0267884	+	0.999641i	$0.491472\pi$
$180$	0	0
$181$	16.2947	1.21118	0.605588	−	0.795778i	$-0.292938\pi$
$181$	16.2947	1.21118	0.605588	+	0.795778i	$0.292938\pi$
$182$	−29.9654	−2.22118
$183$	−13.3935	−0.990073
$184$	8.22938	0.606678
$185$	0	0
$186$	−1.77153	−0.129895
$187$	−1.27680	−0.0933687
$188$	3.40453	0.248301
$189$	−4.29166	−0.312172
$190$	0	0
$191$	−4.79543	−0.346985	−0.173493	−	0.984835i	$-0.555505\pi$
$191$	−4.79543	−0.346985	−0.173493	+	0.984835i	$0.555505\pi$
$192$	−12.5201	−0.903560
$193$	14.2758	1.02759	0.513797	−	0.857912i	$-0.328238\pi$
$193$	14.2758	1.02759	0.513797	+	0.857912i	$0.328238\pi$
$194$	26.9115	1.93213
$195$	0	0
$196$	38.8742	2.77673
$197$	16.0371	1.14259	0.571297	−	0.820743i	$-0.306440\pi$
$197$	16.0371	1.14259	0.571297	+	0.820743i	$0.306440\pi$
$198$	7.03736	0.500124
$199$	−21.8940	−1.55202	−0.776012	−	0.630718i	$-0.782760\pi$
$199$	−21.8940	−1.55202	−0.776012	+	0.630718i	$0.782760\pi$
$200$	0	0
$201$	−12.1504	−0.857021
$202$	36.1554	2.54389
$203$	2.80282	0.196719
$204$	1.43598	0.100539
$205$	0	0
$206$	−4.02864	−0.280689
$207$	−2.52032	−0.175174
$208$	−2.34802	−0.162806
$209$	−12.7582	−0.882501
$210$	0	0
$211$	12.1566	0.836892	0.418446	−	0.908242i	$-0.362575\pi$
$211$	12.1566	0.836892	0.418446	+	0.908242i	$0.362575\pi$
$212$	−21.7899	−1.49654
$213$	4.47678	0.306744
$214$	−35.8145	−2.44823
$215$	0	0
$216$	−3.26521	−0.222169
$217$	−3.27036	−0.222007
$218$	−36.7030	−2.48584
$219$	9.94599	0.672088
$220$	0	0
$221$	−1.26680	−0.0852139
$222$	15.1931	1.01970
$223$	21.4395	1.43570	0.717849	−	0.696199i	$-0.245127\pi$
$223$	21.4395	1.43570	0.717849	+	0.696199i	$0.245127\pi$
$224$	−20.2264	−1.35144
$225$	0	0
$226$	−8.69394	−0.578313
$227$	9.30673	0.617709	0.308855	−	0.951109i	$-0.400054\pi$
$227$	9.30673	0.617709	0.308855	+	0.951109i	$0.400054\pi$
$228$	14.3488	0.950271
$229$	1.89462	0.125200	0.0626000	−	0.998039i	$-0.480061\pi$
$229$	1.89462	0.125200	0.0626000	+	0.998039i	$0.480061\pi$
$230$	0	0
$231$	12.9914	0.854772
$232$	2.13246	0.140003
$233$	22.1293	1.44974	0.724870	−	0.688886i	$-0.241900\pi$
$233$	22.1293	1.44974	0.724870	+	0.688886i	$0.241900\pi$
$234$	6.98224	0.456443
$235$	0	0
$236$	3.08978	0.201127
$237$	−6.97049	−0.452782
$238$	4.20819	0.272777
$239$	−22.4595	−1.45279	−0.726393	−	0.687280i	$-0.758805\pi$
$239$	−22.4595	−1.45279	−0.726393	+	0.687280i	$0.758805\pi$
$240$	0	0
$241$	−9.98074	−0.642916	−0.321458	−	0.946924i	$-0.604173\pi$
$241$	−9.98074	−0.642916	−0.321458	+	0.946924i	$0.604173\pi$
$242$	4.26941	0.274448
$243$	1.00000	0.0641500
$244$	−45.5985	−2.91914
$245$	0	0
$246$	−3.92966	−0.250546
$247$	−12.6582	−0.805424
$248$	−2.48818	−0.157999
$249$	17.2004	1.09003
$250$	0	0
$251$	−21.0666	−1.32971	−0.664856	−	0.746971i	$-0.731507\pi$
$251$	−21.0666	−1.32971	−0.664856	+	0.746971i	$0.731507\pi$
$252$	−14.6111	−0.920413
$253$	7.62933	0.479652
$254$	−1.43077	−0.0897745
$255$	0	0
$256$	−20.7120	−1.29450
$257$	−19.3155	−1.20487	−0.602434	−	0.798169i	$-0.705802\pi$
$257$	−19.3155	−1.20487	−0.602434	+	0.798169i	$0.705802\pi$
$258$	6.10335	0.379978
$259$	28.0474	1.74278
$260$	0	0
$261$	−0.653085	−0.0404249
$262$	−51.5200	−3.18292
$263$	30.9674	1.90953	0.954765	−	0.297360i	$-0.0961062\pi$
$263$	30.9674	1.90953	0.954765	+	0.297360i	$0.0961062\pi$
$264$	9.88422	0.608331
$265$	0	0
$266$	42.0496	2.57823
$267$	17.6260	1.07870
$268$	−41.3663	−2.52685
$269$	8.49408	0.517893	0.258947	−	0.965892i	$-0.416625\pi$
$269$	8.49408	0.517893	0.258947	+	0.965892i	$0.416625\pi$
$270$	0	0
$271$	10.0506	0.610528	0.305264	−	0.952268i	$-0.401255\pi$
$271$	10.0506	0.610528	0.305264	+	0.952268i	$0.401255\pi$
$272$	0.329744	0.0199937
$273$	12.8896	0.780117
$274$	−30.8804	−1.86555
$275$	0	0
$276$	−8.58051	−0.516486
$277$	17.3360	1.04162	0.520811	−	0.853672i	$-0.325630\pi$
$277$	17.3360	1.04162	0.520811	+	0.853672i	$0.325630\pi$
$278$	−54.4042	−3.26295
$279$	0.762027	0.0456213
$280$	0	0
$281$	−7.56882	−0.451518	−0.225759	−	0.974183i	$-0.572486\pi$
$281$	−7.56882	−0.451518	−0.225759	+	0.974183i	$0.572486\pi$
$282$	−2.32477	−0.138438
$283$	0.356970	0.0212197	0.0106098	−	0.999944i	$-0.496623\pi$
$283$	0.356970	0.0212197	0.0106098	+	0.999944i	$0.496623\pi$
$284$	15.2413	0.904407
$285$	0	0
$286$	−21.1361	−1.24981
$287$	−7.25440	−0.428214
$288$	4.71296	0.277714
$289$	−16.8221	−0.989535
$290$	0	0
$291$	−11.5760	−0.678596
$292$	33.8614	1.98159
$293$	−2.52855	−0.147720	−0.0738598	−	0.997269i	$-0.523532\pi$
$293$	−2.52855	−0.147720	−0.0738598	+	0.997269i	$0.523532\pi$
$294$	−26.5450	−1.54813
$295$	0	0
$296$	21.3392	1.24032
$297$	−3.02713	−0.175652
$298$	−14.8007	−0.857382
$299$	7.56957	0.437760
$300$	0	0
$301$	11.2672	0.649428
$302$	6.51044	0.374634
$303$	−15.5523	−0.893456
$304$	3.29491	0.188976
$305$	0	0
$306$	−0.980551	−0.0560544
$307$	0.777839	0.0443936	0.0221968	−	0.999754i	$-0.492934\pi$
$307$	0.777839	0.0443936	0.0221968	+	0.999754i	$0.492934\pi$
$308$	44.2297	2.52022
$309$	1.73292	0.0985826
$310$	0	0
$311$	−5.00666	−0.283902	−0.141951	−	0.989874i	$-0.545337\pi$
$311$	−5.00666	−0.283902	−0.141951	+	0.989874i	$0.545337\pi$
$312$	9.80679	0.555200
$313$	5.86776	0.331665	0.165833	−	0.986154i	$-0.446969\pi$
$313$	5.86776	0.331665	0.165833	+	0.986154i	$0.446969\pi$
$314$	17.8777	1.00890
$315$	0	0
$316$	−23.7313	−1.33499
$317$	−1.21922	−0.0684780	−0.0342390	−	0.999414i	$-0.510901\pi$
$317$	−1.21922	−0.0684780	−0.0342390	+	0.999414i	$0.510901\pi$
$318$	14.8791	0.834380
$319$	1.97697	0.110689
$320$	0	0
$321$	15.4056	0.859859
$322$	−25.1455	−1.40130
$323$	1.77766	0.0989116
$324$	3.40453	0.189141
$325$	0	0
$326$	26.8804	1.48877
$327$	15.7878	0.873069
$328$	−5.51934	−0.304755
$329$	−4.29166	−0.236607
$330$	0	0
$331$	12.1088	0.665561	0.332781	−	0.943004i	$-0.392013\pi$
$331$	12.1088	0.665561	0.332781	+	0.943004i	$0.392013\pi$
$332$	58.5592	3.21385
$333$	−6.53533	−0.358134
$334$	38.7450	2.12003
$335$	0	0
$336$	−3.35515	−0.183038
$337$	16.3135	0.888652	0.444326	−	0.895865i	$-0.353443\pi$
$337$	16.3135	0.888652	0.444326	+	0.895865i	$0.353443\pi$
$338$	9.25137	0.503208
$339$	3.73971	0.203113
$340$	0	0
$341$	−2.30675	−0.124918
$342$	−9.79798	−0.529814
$343$	−18.9621	−1.02385
$344$	8.57236	0.462191
$345$	0	0
$346$	−1.83490	−0.0986451
$347$	8.01238	0.430127	0.215063	−	0.976600i	$-0.431004\pi$
$347$	8.01238	0.430127	0.215063	+	0.976600i	$0.431004\pi$
$348$	−2.22345	−0.119189
$349$	−22.7233	−1.21635	−0.608176	−	0.793802i	$-0.708099\pi$
$349$	−22.7233	−1.21635	−0.608176	+	0.793802i	$0.708099\pi$
$350$	0	0
$351$	−3.00342	−0.160311
$352$	−14.2667	−0.760420
$353$	−25.7000	−1.36787	−0.683936	−	0.729542i	$-0.739733\pi$
$353$	−25.7000	−1.36787	−0.683936	+	0.729542i	$0.739733\pi$
$354$	−2.10984	−0.112136
$355$	0	0
$356$	60.0084	3.18044
$357$	−1.81016	−0.0958037
$358$	−1.66641	−0.0880727
$359$	27.7951	1.46697	0.733485	−	0.679706i	$-0.237892\pi$
$359$	27.7951	1.46697	0.733485	+	0.679706i	$0.237892\pi$
$360$	0	0
$361$	−1.23706	−0.0651082
$362$	−37.8814	−1.99100
$363$	−1.83649	−0.0963907
$364$	43.8832	2.30011
$365$	0	0
$366$	31.1366	1.62754
$367$	26.9289	1.40568	0.702838	−	0.711350i	$-0.251916\pi$
$367$	26.9289	1.40568	0.702838	+	0.711350i	$0.251916\pi$
$368$	−1.97034	−0.102711
$369$	1.69035	0.0879960
$370$	0	0
$371$	27.4678	1.42606
$372$	2.59435	0.134511
$373$	19.2585	0.997165	0.498583	−	0.866842i	$-0.333854\pi$
$373$	19.2585	0.997165	0.498583	+	0.866842i	$0.333854\pi$
$374$	2.96825	0.153485
$375$	0	0
$376$	−3.26521	−0.168390
$377$	1.96149	0.101022
$378$	9.97710	0.513167
$379$	−2.49547	−0.128184	−0.0640918	−	0.997944i	$-0.520415\pi$
$379$	−2.49547	−0.128184	−0.0640918	+	0.997944i	$0.520415\pi$
$380$	0	0
$381$	0.615447	0.0315303
$382$	11.1482	0.570394
$383$	35.5758	1.81784	0.908919	−	0.416974i	$-0.136909\pi$
$383$	35.5758	1.81784	0.908919	+	0.416974i	$0.136909\pi$
$384$	19.6804	1.00431
$385$	0	0
$386$	−33.1879	−1.68922
$387$	−2.62536	−0.133455
$388$	−39.4108	−2.00078
$389$	6.03708	0.306092	0.153046	−	0.988219i	$-0.451092\pi$
$389$	6.03708	0.306092	0.153046	+	0.988219i	$0.451092\pi$
$390$	0	0
$391$	−1.06303	−0.0537599
$392$	−37.2833	−1.88309
$393$	22.1614	1.11789
$394$	−37.2824	−1.87826
$395$	0	0
$396$	−10.3060	−0.517894
$397$	7.99151	0.401083	0.200541	−	0.979685i	$-0.435730\pi$
$397$	7.99151	0.401083	0.200541	+	0.979685i	$0.435730\pi$
$398$	50.8984	2.55131
$399$	−18.0877	−0.905517
$400$	0	0
$401$	−11.2517	−0.561883	−0.280941	−	0.959725i	$-0.590647\pi$
$401$	−11.2517	−0.561883	−0.280941	+	0.959725i	$0.590647\pi$
$402$	28.2467	1.40882
$403$	−2.28868	−0.114007
$404$	−52.9483	−2.63428
$405$	0	0
$406$	−6.51589	−0.323378
$407$	19.7833	0.980622
$408$	−1.37722	−0.0681824
$409$	−23.2671	−1.15048	−0.575242	−	0.817984i	$-0.695092\pi$
$409$	−23.2671	−1.15048	−0.575242	+	0.817984i	$0.695092\pi$
$410$	0	0
$411$	13.2832	0.655214
$412$	5.89980	0.290662
$413$	−3.89489	−0.191655
$414$	5.85915	0.287962
$415$	0	0
$416$	−14.1550	−0.694005
$417$	23.4020	1.14600
$418$	29.6598	1.45071
$419$	−13.0360	−0.636850	−0.318425	−	0.947948i	$-0.603154\pi$
$419$	−13.0360	−0.636850	−0.318425	+	0.947948i	$0.603154\pi$
$420$	0	0
$421$	25.4063	1.23823	0.619113	−	0.785302i	$-0.287492\pi$
$421$	25.4063	1.23823	0.619113	+	0.785302i	$0.287492\pi$
$422$	−28.2612	−1.37573
$423$	1.00000	0.0486217
$424$	20.8982	1.01491
$425$	0	0
$426$	−10.4075	−0.504243
$427$	57.4802	2.78166
$428$	52.4490	2.53522
$429$	9.09173	0.438953
$430$	0	0
$431$	35.8462	1.72665	0.863324	−	0.504649i	$-0.168378\pi$
$431$	35.8462	1.72665	0.863324	+	0.504649i	$0.168378\pi$
$432$	0.781783	0.0376135
$433$	−30.4573	−1.46368	−0.731842	−	0.681474i	$-0.761339\pi$
$433$	−30.4573	−1.46368	−0.731842	+	0.681474i	$0.761339\pi$
$434$	7.60282	0.364947
$435$	0	0
$436$	53.7502	2.57417
$437$	−10.6222	−0.508127
$438$	−23.1221	−1.10482
$439$	11.9042	0.568158	0.284079	−	0.958801i	$-0.408312\pi$
$439$	11.9042	0.568158	0.284079	+	0.958801i	$0.408312\pi$
$440$	0	0
$441$	11.4183	0.543731
$442$	2.94500	0.140080
$443$	−7.06574	−0.335703	−0.167852	−	0.985812i	$-0.553683\pi$
$443$	−7.06574	−0.335703	−0.167852	+	0.985812i	$0.553683\pi$
$444$	−22.2498	−1.05593
$445$	0	0
$446$	−49.8419	−2.36008
$447$	6.36654	0.301127
$448$	53.7320	2.53860
$449$	−26.6196	−1.25626	−0.628128	−	0.778110i	$-0.716179\pi$
$449$	−26.6196	−1.25626	−0.628128	+	0.778110i	$0.716179\pi$
$450$	0	0
$451$	−5.11690	−0.240945
$452$	12.7320	0.598861
$453$	−2.80047	−0.131578
$454$	−21.6360	−1.01543
$455$	0	0
$456$	−13.7616	−0.644446
$457$	3.05663	0.142983	0.0714917	−	0.997441i	$-0.477224\pi$
$457$	3.05663	0.142983	0.0714917	+	0.997441i	$0.477224\pi$
$458$	−4.40454	−0.205811
$459$	0.421785	0.0196872
$460$	0	0
$461$	−12.1241	−0.564674	−0.282337	−	0.959315i	$-0.591110\pi$
$461$	−12.1241	−0.564674	−0.282337	+	0.959315i	$0.591110\pi$
$462$	−30.2020	−1.40512
$463$	25.4102	1.18091	0.590455	−	0.807070i	$-0.298948\pi$
$463$	25.4102	1.18091	0.590455	+	0.807070i	$0.298948\pi$
$464$	−0.510570	−0.0237026
$465$	0	0
$466$	−51.4455	−2.38317
$467$	42.6356	1.97294	0.986471	−	0.163937i	$-0.0524193\pi$
$467$	42.6356	1.97294	0.986471	+	0.163937i	$0.0524193\pi$
$468$	−10.2252	−0.472662
$469$	52.1452	2.40784
$470$	0	0
$471$	−7.69012	−0.354342
$472$	−2.96334	−0.136399
$473$	7.94731	0.365418
$474$	16.2048	0.744309
$475$	0	0
$476$	−6.16274	−0.282469
$477$	−6.40027	−0.293048
$478$	52.2131	2.38817
$479$	33.1908	1.51653	0.758264	−	0.651947i	$-0.226048\pi$
$479$	33.1908	1.51653	0.758264	+	0.651947i	$0.226048\pi$
$480$	0	0
$481$	19.6283	0.894975
$482$	23.2029	1.05686
$483$	10.8164	0.492161
$484$	−6.25239	−0.284200
$485$	0	0
$486$	−2.32477	−0.105453
$487$	32.5896	1.47678	0.738389	−	0.674376i	$-0.235587\pi$
$487$	32.5896	1.47678	0.738389	+	0.674376i	$0.235587\pi$
$488$	43.7325	1.97968
$489$	−11.5626	−0.522880
$490$	0	0
$491$	20.4201	0.921545	0.460773	−	0.887518i	$-0.347572\pi$
$491$	20.4201	0.921545	0.460773	+	0.887518i	$0.347572\pi$
$492$	5.75485	0.259448
$493$	−0.275461	−0.0124061
$494$	29.4274	1.32400
$495$	0	0
$496$	0.595739	0.0267495
$497$	−19.2128	−0.861812
$498$	−39.9868	−1.79185
$499$	35.7094	1.59857	0.799287	−	0.600949i	$-0.205211\pi$
$499$	35.7094	1.59857	0.799287	+	0.600949i	$0.205211\pi$
$500$	0	0
$501$	−16.6662	−0.744591
$502$	48.9749	2.18586
$503$	−21.9162	−0.977195	−0.488597	−	0.872509i	$-0.662491\pi$
$503$	−21.9162	−0.977195	−0.488597	+	0.872509i	$0.662491\pi$
$504$	14.0132	0.624197
$505$	0	0
$506$	−17.7364	−0.788480
$507$	−3.97949	−0.176735
$508$	2.09531	0.0929643
$509$	10.6788	0.473327	0.236664	−	0.971592i	$-0.423946\pi$
$509$	10.6788	0.473327	0.236664	+	0.971592i	$0.423946\pi$
$510$	0	0
$511$	−42.6848	−1.88826
$512$	8.78988	0.388462
$513$	4.21461	0.186080
$514$	44.9040	1.98063
$515$	0	0
$516$	−8.93813	−0.393479
$517$	−3.02713	−0.133133
$518$	−65.2037	−2.86489
$519$	0.789286	0.0346458
$520$	0	0
$521$	−18.5819	−0.814090	−0.407045	−	0.913408i	$-0.633441\pi$
$521$	−18.5819	−0.814090	−0.407045	+	0.913408i	$0.633441\pi$
$522$	1.51827	0.0664528
$523$	38.7361	1.69381	0.846906	−	0.531743i	$-0.178463\pi$
$523$	38.7361	1.69381	0.846906	+	0.531743i	$0.178463\pi$
$524$	75.4492	3.29601
$525$	0	0
$526$	−71.9919	−3.13900
$527$	0.321411	0.0140009
$528$	−2.36656	−0.102991
$529$	−16.6480	−0.723826
$530$	0	0
$531$	0.907548	0.0393842
$532$	−61.5801	−2.66984
$533$	−5.07682	−0.219901
$534$	−40.9764	−1.77322
$535$	0	0
$536$	39.6735	1.71363
$537$	0.716809	0.0309326
$538$	−19.7467	−0.851343
$539$	−34.5648	−1.48881
$540$	0	0
$541$	−32.4457	−1.39495	−0.697475	−	0.716609i	$-0.745693\pi$
$541$	−32.4457	−1.39495	−0.697475	+	0.716609i	$0.745693\pi$
$542$	−23.3652	−1.00362
$543$	16.2947	0.699273
$544$	1.98786	0.0852286
$545$	0	0
$546$	−29.9654	−1.28240
$547$	−23.4811	−1.00398	−0.501990	−	0.864874i	$-0.667398\pi$
$547$	−23.4811	−1.00398	−0.501990	+	0.864874i	$0.667398\pi$
$548$	45.2232	1.93184
$549$	−13.3935	−0.571619
$550$	0	0
$551$	−2.75250	−0.117260
$552$	8.22938	0.350266
$553$	29.9150	1.27211
$554$	−40.3022	−1.71228
$555$	0	0
$556$	79.6729	3.37888
$557$	−19.2411	−0.815274	−0.407637	−	0.913144i	$-0.633647\pi$
$557$	−19.2411	−0.815274	−0.407637	+	0.913144i	$0.633647\pi$
$558$	−1.77153	−0.0749950
$559$	7.88506	0.333502
$560$	0	0
$561$	−1.27680	−0.0539064
$562$	17.5957	0.742231
$563$	−15.2020	−0.640690	−0.320345	−	0.947301i	$-0.603799\pi$
$563$	−15.2020	−0.640690	−0.320345	+	0.947301i	$0.603799\pi$
$564$	3.40453	0.143357
$565$	0	0
$566$	−0.829871	−0.0348821
$567$	−4.29166	−0.180233
$568$	−14.6176	−0.613342
$569$	9.86920	0.413738	0.206869	−	0.978369i	$-0.433673\pi$
$569$	9.86920	0.413738	0.206869	+	0.978369i	$0.433673\pi$
$570$	0	0
$571$	−1.72069	−0.0720085	−0.0360042	−	0.999352i	$-0.511463\pi$
$571$	−1.72069	−0.0720085	−0.0360042	+	0.999352i	$0.511463\pi$
$572$	30.9531	1.29421
$573$	−4.79543	−0.200332
$574$	16.8648	0.703922
$575$	0	0
$576$	−12.5201	−0.521671
$577$	30.1271	1.25421	0.627104	−	0.778936i	$-0.284240\pi$
$577$	30.1271	1.25421	0.627104	+	0.778936i	$0.284240\pi$
$578$	39.1074	1.62665
$579$	14.2758	0.593282
$580$	0	0
$581$	−73.8181	−3.06249
$582$	26.9115	1.11552
$583$	19.3744	0.802407
$584$	−32.4757	−1.34386
$585$	0	0
$586$	5.87829	0.242830
$587$	1.88672	0.0778732	0.0389366	−	0.999242i	$-0.487603\pi$
$587$	1.88672	0.0778732	0.0389366	+	0.999242i	$0.487603\pi$
$588$	38.8742	1.60314
$589$	3.21165	0.132334
$590$	0	0
$591$	16.0371	0.659677
$592$	−5.10921	−0.209987
$593$	−11.8287	−0.485747	−0.242873	−	0.970058i	$-0.578090\pi$
$593$	−11.8287	−0.485747	−0.242873	+	0.970058i	$0.578090\pi$
$594$	7.03736	0.288747
$595$	0	0
$596$	21.6751	0.887847
$597$	−21.8940	−0.896061
$598$	−17.5975	−0.719614
$599$	−23.1897	−0.947505	−0.473752	−	0.880658i	$-0.657101\pi$
$599$	−23.1897	−0.947505	−0.473752	+	0.880658i	$0.657101\pi$
$600$	0	0
$601$	20.1226	0.820820	0.410410	−	0.911901i	$-0.365386\pi$
$601$	20.1226	0.820820	0.410410	+	0.911901i	$0.365386\pi$
$602$	−26.1935	−1.06757
$603$	−12.1504	−0.494801
$604$	−9.53430	−0.387945
$605$	0	0
$606$	36.1554	1.46871
$607$	−47.7078	−1.93640	−0.968201	−	0.250174i	$-0.919512\pi$
$607$	−47.7078	−1.93640	−0.968201	+	0.250174i	$0.919512\pi$
$608$	19.8633	0.805563
$609$	2.80282	0.113576
$610$	0	0
$611$	−3.00342	−0.121505
$612$	1.43598	0.0580461
$613$	11.7203	0.473377	0.236689	−	0.971586i	$-0.423938\pi$
$613$	11.7203	0.473377	0.236689	+	0.971586i	$0.423938\pi$
$614$	−1.80829	−0.0729768
$615$	0	0
$616$	−42.4197	−1.70914
$617$	48.0701	1.93523	0.967615	−	0.252433i	$-0.0812306\pi$
$617$	48.0701	1.93523	0.967615	+	0.252433i	$0.0812306\pi$
$618$	−4.02864	−0.162056
$619$	5.81535	0.233739	0.116869	−	0.993147i	$-0.462714\pi$
$619$	5.81535	0.233739	0.116869	+	0.993147i	$0.462714\pi$
$620$	0	0
$621$	−2.52032	−0.101137
$622$	11.6393	0.466694
$623$	−75.6449	−3.03065
$624$	−2.34802	−0.0939960
$625$	0	0
$626$	−13.6412	−0.545210
$627$	−12.7582	−0.509512
$628$	−26.1813	−1.04475
$629$	−2.75651	−0.109909
$630$	0	0
$631$	6.11522	0.243443	0.121722	−	0.992564i	$-0.461158\pi$
$631$	6.11522	0.243443	0.121722	+	0.992564i	$0.461158\pi$
$632$	22.7601	0.905349
$633$	12.1566	0.483180
$634$	2.83439	0.112568
$635$	0	0
$636$	−21.7899	−0.864027
$637$	−34.2941	−1.35878
$638$	−4.59599	−0.181957
$639$	4.47678	0.177099
$640$	0	0
$641$	−11.2085	−0.442709	−0.221355	−	0.975193i	$-0.571048\pi$
$641$	−11.2085	−0.442709	−0.221355	+	0.975193i	$0.571048\pi$
$642$	−35.8145	−1.41349
$643$	−13.4090	−0.528801	−0.264400	−	0.964413i	$-0.585174\pi$
$643$	−13.4090	−0.528801	−0.264400	+	0.964413i	$0.585174\pi$
$644$	36.8247	1.45109
$645$	0	0
$646$	−4.13264	−0.162597
$647$	−49.3679	−1.94085	−0.970426	−	0.241400i	$-0.922393\pi$
$647$	−49.3679	−1.94085	−0.970426	+	0.241400i	$0.922393\pi$
$648$	−3.26521	−0.128270
$649$	−2.74726	−0.107840
$650$	0	0
$651$	−3.27036	−0.128176
$652$	−39.3654	−1.54167
$653$	25.6966	1.00559	0.502793	−	0.864407i	$-0.332306\pi$
$653$	25.6966	1.00559	0.502793	+	0.864407i	$0.332306\pi$
$654$	−36.7030	−1.43520
$655$	0	0
$656$	1.32148	0.0515953
$657$	9.94599	0.388030
$658$	9.97710	0.388948
$659$	−31.4108	−1.22359	−0.611796	−	0.791016i	$-0.709553\pi$
$659$	−31.4108	−1.22359	−0.611796	+	0.791016i	$0.709553\pi$
$660$	0	0
$661$	12.2205	0.475322	0.237661	−	0.971348i	$-0.423619\pi$
$661$	12.2205	0.475322	0.237661	+	0.971348i	$0.423619\pi$
$662$	−28.1502	−1.09409
$663$	−1.26680	−0.0491983
$664$	−56.1628	−2.17954
$665$	0	0
$666$	15.1931	0.588721
$667$	1.64598	0.0637327
$668$	−56.7406	−2.19536
$669$	21.4395	0.828901
$670$	0	0
$671$	40.5437	1.56517
$672$	−20.2264	−0.780252
$673$	−44.4513	−1.71347	−0.856736	−	0.515756i	$-0.827511\pi$
$673$	−44.4513	−1.71347	−0.856736	+	0.515756i	$0.827511\pi$
$674$	−37.9250	−1.46082
$675$	0	0
$676$	−13.5483	−0.521088
$677$	−21.8401	−0.839382	−0.419691	−	0.907667i	$-0.637862\pi$
$677$	−21.8401	−0.839382	−0.419691	+	0.907667i	$0.637862\pi$
$678$	−8.69394	−0.333889
$679$	49.6802	1.90655
$680$	0	0
$681$	9.30673	0.356635
$682$	5.36266	0.205347
$683$	−8.30406	−0.317746	−0.158873	−	0.987299i	$-0.550786\pi$
$683$	−8.30406	−0.317746	−0.158873	+	0.987299i	$0.550786\pi$
$684$	14.3488	0.548640
$685$	0	0
$686$	44.0823	1.68307
$687$	1.89462	0.0722842
$688$	−2.05246	−0.0782494
$689$	19.2227	0.732325
$690$	0	0
$691$	6.58504	0.250507	0.125253	−	0.992125i	$-0.460026\pi$
$691$	6.58504	0.250507	0.125253	+	0.992125i	$0.460026\pi$
$692$	2.68715	0.102150
$693$	12.9914	0.493503
$694$	−18.6269	−0.707067
$695$	0	0
$696$	2.13246	0.0808307
$697$	0.712963	0.0270054
$698$	52.8265	1.99951
$699$	22.1293	0.837008
$700$	0	0
$701$	16.6043	0.627137	0.313569	−	0.949566i	$-0.398475\pi$
$701$	16.6043	0.627137	0.313569	+	0.949566i	$0.398475\pi$
$702$	6.98224	0.263528
$703$	−27.5439	−1.03884
$704$	37.8999	1.42841
$705$	0	0
$706$	59.7464	2.24859
$707$	66.7452	2.51021
$708$	3.08978	0.116121
$709$	−32.0839	−1.20494	−0.602468	−	0.798143i	$-0.705816\pi$
$709$	−32.0839	−1.20494	−0.602468	+	0.798143i	$0.705816\pi$
$710$	0	0
$711$	−6.97049	−0.261414
$712$	−57.5527	−2.15688
$713$	−1.92055	−0.0719252
$714$	4.20819	0.157488
$715$	0	0
$716$	2.44040	0.0912021
$717$	−22.4595	−0.838766
$718$	−64.6171	−2.41149
$719$	6.15261	0.229454	0.114727	−	0.993397i	$-0.463401\pi$
$719$	6.15261	0.229454	0.114727	+	0.993397i	$0.463401\pi$
$720$	0	0
$721$	−7.43712	−0.276973
$722$	2.87586	0.107029
$723$	−9.98074	−0.371188
$724$	55.4759	2.06174
$725$	0	0
$726$	4.26941	0.158453
$727$	20.2328	0.750395	0.375197	−	0.926945i	$-0.377575\pi$
$727$	20.2328	0.750395	0.375197	+	0.926945i	$0.377575\pi$
$728$	−42.0874	−1.55986
$729$	1.00000	0.0370370
$730$	0	0
$731$	−1.10734	−0.0409564
$732$	−45.5985	−1.68537
$733$	−10.9025	−0.402695	−0.201347	−	0.979520i	$-0.564532\pi$
$733$	−10.9025	−0.402695	−0.201347	+	0.979520i	$0.564532\pi$
$734$	−62.6033	−2.31073
$735$	0	0
$736$	−11.8782	−0.437835
$737$	36.7807	1.35484
$738$	−3.92966	−0.144653
$739$	−40.6598	−1.49569	−0.747847	−	0.663872i	$-0.768912\pi$
$739$	−40.6598	−1.49569	−0.747847	+	0.663872i	$0.768912\pi$
$740$	0	0
$741$	−12.6582	−0.465012
$742$	−63.8561	−2.34423
$743$	−0.947853	−0.0347733	−0.0173867	−	0.999849i	$-0.505535\pi$
$743$	−0.947853	−0.0347733	−0.0173867	+	0.999849i	$0.505535\pi$
$744$	−2.48818	−0.0912210
$745$	0	0
$746$	−44.7714	−1.63920
$747$	17.2004	0.629328
$748$	−4.34690	−0.158938
$749$	−66.1158	−2.41582
$750$	0	0
$751$	11.9434	0.435821	0.217911	−	0.975969i	$-0.430076\pi$
$751$	11.9434	0.435821	0.217911	+	0.975969i	$0.430076\pi$
$752$	0.781783	0.0285087
$753$	−21.0666	−0.767710
$754$	−4.55999	−0.166065
$755$	0	0
$756$	−14.6111	−0.531401
$757$	31.6773	1.15133	0.575666	−	0.817685i	$-0.304743\pi$
$757$	31.6773	1.15133	0.575666	+	0.817685i	$0.304743\pi$
$758$	5.80137	0.210715
$759$	7.62933	0.276927
$760$	0	0
$761$	−6.49897	−0.235587	−0.117794	−	0.993038i	$-0.537582\pi$
$761$	−6.49897	−0.235587	−0.117794	+	0.993038i	$0.537582\pi$
$762$	−1.43077	−0.0518313
$763$	−67.7560	−2.45293
$764$	−16.3262	−0.590661
$765$	0	0
$766$	−82.7053	−2.98827
$767$	−2.72574	−0.0984209
$768$	−20.7120	−0.747381
$769$	−26.5178	−0.956256	−0.478128	−	0.878290i	$-0.658685\pi$
$769$	−26.5178	−0.956256	−0.478128	+	0.878290i	$0.658685\pi$
$770$	0	0
$771$	−19.3155	−0.695631
$772$	48.6024	1.74924
$773$	−14.3221	−0.515132	−0.257566	−	0.966261i	$-0.582920\pi$
$773$	−14.3221	−0.515132	−0.257566	+	0.966261i	$0.582920\pi$
$774$	6.10335	0.219380
$775$	0	0
$776$	37.7980	1.35687
$777$	28.0474	1.00620
$778$	−14.0348	−0.503172
$779$	7.12416	0.255249
$780$	0	0
$781$	−13.5518	−0.484921
$782$	2.47130	0.0883736
$783$	−0.653085	−0.0233393
$784$	8.92667	0.318809
$785$	0	0
$786$	−51.5200	−1.83766
$787$	−23.4770	−0.836863	−0.418432	−	0.908248i	$-0.637420\pi$
$787$	−23.4770	−0.836863	−0.418432	+	0.908248i	$0.637420\pi$
$788$	54.5988	1.94500
$789$	30.9674	1.10247
$790$	0	0
$791$	−16.0496	−0.570657
$792$	9.88422	0.351220
$793$	40.2261	1.42847
$794$	−18.5784	−0.659322
$795$	0	0
$796$	−74.5388	−2.64196
$797$	−2.55713	−0.0905781	−0.0452891	−	0.998974i	$-0.514421\pi$
$797$	−2.55713	−0.0905781	−0.0452891	+	0.998974i	$0.514421\pi$
$798$	42.0496	1.48854
$799$	0.421785	0.0149217
$800$	0	0
$801$	17.6260	0.622785
$802$	26.1575	0.923655
$803$	−30.1078	−1.06248
$804$	−41.3663	−1.45888
$805$	0	0
$806$	5.32065	0.187412
$807$	8.49408	0.299006
$808$	50.7815	1.78649
$809$	21.7612	0.765083	0.382541	−	0.923938i	$-0.375049\pi$
$809$	21.7612	0.765083	0.382541	+	0.923938i	$0.375049\pi$
$810$	0	0
$811$	−43.6108	−1.53138	−0.765692	−	0.643208i	$-0.777603\pi$
$811$	−43.6108	−1.53138	−0.765692	+	0.643208i	$0.777603\pi$
$812$	9.54229	0.334869
$813$	10.0506	0.352489
$814$	−45.9915	−1.61200
$815$	0	0
$816$	0.329744	0.0115434
$817$	−11.0649	−0.387111
$818$	54.0905	1.89123
$819$	12.8896	0.450401
$820$	0	0
$821$	37.0595	1.29339	0.646693	−	0.762751i	$-0.276152\pi$
$821$	37.0595	1.29339	0.646693	+	0.762751i	$0.276152\pi$
$822$	−30.8804	−1.07708
$823$	−49.3081	−1.71877	−0.859387	−	0.511327i	$-0.829154\pi$
$823$	−49.3081	−1.71877	−0.859387	+	0.511327i	$0.829154\pi$
$824$	−5.65836	−0.197118
$825$	0	0
$826$	9.05470	0.315053
$827$	−9.24817	−0.321590	−0.160795	−	0.986988i	$-0.551406\pi$
$827$	−9.24817	−0.321590	−0.160795	+	0.986988i	$0.551406\pi$
$828$	−8.58051	−0.298193
$829$	−11.8158	−0.410380	−0.205190	−	0.978722i	$-0.565781\pi$
$829$	−11.8158	−0.410380	−0.205190	+	0.978722i	$0.565781\pi$
$830$	0	0
$831$	17.3360	0.601381
$832$	37.6031	1.30365
$833$	4.81609	0.166868
$834$	−54.4042	−1.88386
$835$	0	0
$836$	−43.4356	−1.50225
$837$	0.762027	0.0263395
$838$	30.3056	1.04689
$839$	3.44348	0.118882	0.0594411	−	0.998232i	$-0.481068\pi$
$839$	3.44348	0.118882	0.0594411	+	0.998232i	$0.481068\pi$
$840$	0	0
$841$	−28.5735	−0.985292
$842$	−59.0636	−2.03547
$843$	−7.56882	−0.260684
$844$	41.3874	1.42461
$845$	0	0
$846$	−2.32477	−0.0799271
$847$	7.88159	0.270815
$848$	−5.00362	−0.171825
$849$	0.356970	0.0122512
$850$	0	0
$851$	16.4711	0.564623
$852$	15.2413	0.522160
$853$	28.3720	0.971438	0.485719	−	0.874115i	$-0.338558\pi$
$853$	28.3720	0.971438	0.485719	+	0.874115i	$0.338558\pi$
$854$	−133.628	−4.57265
$855$	0	0
$856$	−50.3027	−1.71931
$857$	−31.8798	−1.08899	−0.544497	−	0.838763i	$-0.683279\pi$
$857$	−31.8798	−1.08899	−0.544497	+	0.838763i	$0.683279\pi$
$858$	−21.1361	−0.721576
$859$	37.1820	1.26863	0.634317	−	0.773073i	$-0.281281\pi$
$859$	37.1820	1.26863	0.634317	+	0.773073i	$0.281281\pi$
$860$	0	0
$861$	−7.25440	−0.247229
$862$	−83.3339	−2.83836
$863$	36.0740	1.22797	0.613986	−	0.789317i	$-0.289565\pi$
$863$	36.0740	1.22797	0.613986	+	0.789317i	$0.289565\pi$
$864$	4.71296	0.160338
$865$	0	0
$866$	70.8061	2.40609
$867$	−16.8221	−0.571308
$868$	−11.1341	−0.377914
$869$	21.1006	0.715788
$870$	0	0
$871$	36.4926	1.23651
$872$	−51.5506	−1.74572
$873$	−11.5760	−0.391788
$874$	24.6940	0.835289
$875$	0	0
$876$	33.8614	1.14407
$877$	38.5747	1.30258	0.651288	−	0.758831i	$-0.274229\pi$
$877$	38.5747	1.30258	0.651288	+	0.758831i	$0.274229\pi$
$878$	−27.6746	−0.933971
$879$	−2.52855	−0.0852859
$880$	0	0
$881$	−52.9486	−1.78388	−0.891942	−	0.452149i	$-0.850657\pi$
$881$	−52.9486	−1.78388	−0.891942	+	0.452149i	$0.850657\pi$
$882$	−26.5450	−0.893816
$883$	6.21477	0.209144	0.104572	−	0.994517i	$-0.466653\pi$
$883$	6.21477	0.209144	0.104572	+	0.994517i	$0.466653\pi$
$884$	−4.31285	−0.145057
$885$	0	0
$886$	16.4262	0.551848
$887$	−39.3949	−1.32275	−0.661376	−	0.750054i	$-0.730027\pi$
$887$	−39.3949	−1.32275	−0.661376	+	0.750054i	$0.730027\pi$
$888$	21.3392	0.716098
$889$	−2.64129	−0.0885860
$890$	0	0
$891$	−3.02713	−0.101413
$892$	72.9917	2.44394
$893$	4.21461	0.141037
$894$	−14.8007	−0.495010
$895$	0	0
$896$	−84.4614	−2.82166
$897$	7.56957	0.252741
$898$	61.8843	2.06511
$899$	−0.497668	−0.0165982
$900$	0	0
$901$	−2.69954	−0.0899346
$902$	11.8956	0.396080
$903$	11.2672	0.374948
$904$	−12.2109	−0.406130
$905$	0	0
$906$	6.51044	0.216295
$907$	−15.2802	−0.507370	−0.253685	−	0.967287i	$-0.581643\pi$
$907$	−15.2802	−0.507370	−0.253685	+	0.967287i	$0.581643\pi$
$908$	31.6851	1.05151
$909$	−15.5523	−0.515837
$910$	0	0
$911$	−14.6342	−0.484853	−0.242426	−	0.970170i	$-0.577943\pi$
$911$	−14.6342	−0.484853	−0.242426	+	0.970170i	$0.577943\pi$
$912$	3.29491	0.109105
$913$	−52.0677	−1.72319
$914$	−7.10596	−0.235044
$915$	0	0
$916$	6.45029	0.213124
$917$	−95.1092	−3.14078
$918$	−0.980551	−0.0323630
$919$	51.1748	1.68810	0.844051	−	0.536263i	$-0.180165\pi$
$919$	51.1748	1.68810	0.844051	+	0.536263i	$0.180165\pi$
$920$	0	0
$921$	0.777839	0.0256307
$922$	28.1856	0.928243
$923$	−13.4456	−0.442568
$924$	44.2297	1.45505
$925$	0	0
$926$	−59.0727	−1.94125
$927$	1.73292	0.0569167
$928$	−3.07796	−0.101039
$929$	23.8439	0.782293	0.391147	−	0.920328i	$-0.372079\pi$
$929$	23.8439	0.782293	0.391147	+	0.920328i	$0.372079\pi$
$930$	0	0
$931$	48.1239	1.57720
$932$	75.3400	2.46784
$933$	−5.00666	−0.163911
$934$	−99.1178	−3.24323
$935$	0	0
$936$	9.80679	0.320545
$937$	−2.80007	−0.0914744	−0.0457372	−	0.998954i	$-0.514564\pi$
$937$	−2.80007	−0.0914744	−0.0457372	+	0.998954i	$0.514564\pi$
$938$	−121.225	−3.95815
$939$	5.86776	0.191487
$940$	0	0
$941$	−24.3169	−0.792708	−0.396354	−	0.918098i	$-0.629725\pi$
$941$	−24.3169	−0.792708	−0.396354	+	0.918098i	$0.629725\pi$
$942$	17.8777	0.582488
$943$	−4.26022	−0.138732
$944$	0.709505	0.0230924
$945$	0	0
$946$	−18.4756	−0.600694
$947$	−6.63541	−0.215622	−0.107811	−	0.994171i	$-0.534384\pi$
$947$	−6.63541	−0.215622	−0.107811	+	0.994171i	$0.534384\pi$
$948$	−23.7313	−0.770756
$949$	−29.8719	−0.969684
$950$	0	0
$951$	−1.21922	−0.0395358
$952$	5.91055	0.191562
$953$	18.7781	0.608283	0.304141	−	0.952627i	$-0.401630\pi$
$953$	18.7781	0.608283	0.304141	+	0.952627i	$0.401630\pi$
$954$	14.8791	0.481729
$955$	0	0
$956$	−76.4642	−2.47303
$957$	1.97697	0.0639064
$958$	−77.1609	−2.49296
$959$	−57.0072	−1.84086
$960$	0	0
$961$	−30.4193	−0.981268
$962$	−45.6313	−1.47121
$963$	15.4056	0.496440
$964$	−33.9798	−1.09441
$965$	0	0
$966$	−25.1455	−0.809043
$967$	−1.53904	−0.0494920	−0.0247460	−	0.999694i	$-0.507878\pi$
$967$	−1.53904	−0.0494920	−0.0247460	+	0.999694i	$0.507878\pi$
$968$	5.99653	0.192736
$969$	1.77766	0.0571066
$970$	0	0
$971$	7.03155	0.225653	0.112827	−	0.993615i	$-0.464010\pi$
$971$	7.03155	0.225653	0.112827	+	0.993615i	$0.464010\pi$
$972$	3.40453	0.109200
$973$	−100.433	−3.21975
$974$	−75.7632	−2.42761
$975$	0	0
$976$	−10.4708	−0.335161
$977$	38.4016	1.22858	0.614289	−	0.789081i	$-0.289443\pi$
$977$	38.4016	1.22858	0.614289	+	0.789081i	$0.289443\pi$
$978$	26.8804	0.859540
$979$	−53.3563	−1.70527
$980$	0	0
$981$	15.7878	0.504067
$982$	−47.4719	−1.51489
$983$	31.4909	1.00440	0.502202	−	0.864750i	$-0.332523\pi$
$983$	31.4909	1.00440	0.502202	+	0.864750i	$0.332523\pi$
$984$	−5.51934	−0.175950
$985$	0	0
$986$	0.640383	0.0203939
$987$	−4.29166	−0.136605
$988$	−43.0954	−1.37105
$989$	6.61675	0.210400
$990$	0	0
$991$	−7.32146	−0.232574	−0.116287	−	0.993216i	$-0.537099\pi$
$991$	−7.32146	−0.232574	−0.116287	+	0.993216i	$0.537099\pi$
$992$	3.59140	0.114027
$993$	12.1088	0.384262
$994$	44.6653	1.41670
$995$	0	0
$996$	58.5592	1.85552
$997$	−56.1733	−1.77903	−0.889513	−	0.456911i	$-0.848956\pi$
$997$	−56.1733	−1.77903	−0.889513	+	0.456911i	$0.848956\pi$
$998$	−83.0161	−2.62783
$999$	−6.53533	−0.206769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.1		13
5.2	odd	4		705.2.c.c.424.4	✓	26
5.3	odd	4		705.2.c.c.424.23	yes	26
5.4	even	2		3525.2.a.bh.1.13		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.4	✓	26	5.2	odd	4
705.2.c.c.424.23	yes	26	5.3	odd	4
3525.2.a.bh.1.13		13	5.4	even	2
3525.2.a.bi.1.1		13	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32477 q^{2} +1.00000 q^{3} +3.40453 q^{4} -2.32477 q^{6} -4.29166 q^{7} -3.26521 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.32477 q^{2} +1.00000 q^{3} +3.40453 q^{4} -2.32477 q^{6} -4.29166 q^{7} -3.26521 q^{8} +1.00000 q^{9} -3.02713 q^{11} +3.40453 q^{12} -3.00342 q^{13} +9.97710 q^{14} +0.781783 q^{16} +0.421785 q^{17} -2.32477 q^{18} +4.21461 q^{19} -4.29166 q^{21} +7.03736 q^{22} -2.52032 q^{23} -3.26521 q^{24} +6.98224 q^{26} +1.00000 q^{27} -14.6111 q^{28} -0.653085 q^{29} +0.762027 q^{31} +4.71296 q^{32} -3.02713 q^{33} -0.980551 q^{34} +3.40453 q^{36} -6.53533 q^{37} -9.79798 q^{38} -3.00342 q^{39} +1.69035 q^{41} +9.97710 q^{42} -2.62536 q^{43} -10.3060 q^{44} +5.85915 q^{46} +1.00000 q^{47} +0.781783 q^{48} +11.4183 q^{49} +0.421785 q^{51} -10.2252 q^{52} -6.40027 q^{53} -2.32477 q^{54} +14.0132 q^{56} +4.21461 q^{57} +1.51827 q^{58} +0.907548 q^{59} -13.3935 q^{61} -1.77153 q^{62} -4.29166 q^{63} -12.5201 q^{64} +7.03736 q^{66} -12.1504 q^{67} +1.43598 q^{68} -2.52032 q^{69} +4.47678 q^{71} -3.26521 q^{72} +9.94599 q^{73} +15.1931 q^{74} +14.3488 q^{76} +12.9914 q^{77} +6.98224 q^{78} -6.97049 q^{79} +1.00000 q^{81} -3.92966 q^{82} +17.2004 q^{83} -14.6111 q^{84} +6.10335 q^{86} -0.653085 q^{87} +9.88422 q^{88} +17.6260 q^{89} +12.8896 q^{91} -8.58051 q^{92} +0.762027 q^{93} -2.32477 q^{94} +4.71296 q^{96} -11.5760 q^{97} -26.5450 q^{98} -3.02713 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) \) 13 * q + 3 * q^2 + 13 * q^3 + 17 * q^4 + 3 * q^6 - 4 * q^7 + 15 * q^8 + 13 * q^9 + 16 * q^11 + 17 * q^12 - 8 * q^13 - 4 * q^14 + 29 * q^16 + 12 * q^17 + 3 * q^18 + 28 * q^19 - 4 * q^21 + 6 * q^23 + 15 * q^24 + 4 * q^26 + 13 * q^27 - 20 * q^28 + 12 * q^29 + 26 * q^31 + 53 * q^32 + 16 * q^33 + 8 * q^34 + 17 * q^36 - 4 * q^37 + 2 * q^38 - 8 * q^39 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^44 + 16 * q^46 + 13 * q^47 + 29 * q^48 + 21 * q^49 + 12 * q^51 - 32 * q^52 + 6 * q^53 + 3 * q^54 + 28 * q^57 - 4 * q^58 + 34 * q^59 + 24 * q^61 + 30 * q^62 - 4 * q^63 + 13 * q^64 - 24 * q^67 + 44 * q^68 + 6 * q^69 + 20 * q^71 + 15 * q^72 - 6 * q^73 + 20 * q^74 + 66 * q^76 - 2 * q^77 + 4 * q^78 + 6 * q^79 + 13 * q^81 + 20 * q^82 + 14 * q^83 - 20 * q^84 + 48 * q^86 + 12 * q^87 - 22 * q^88 + 36 * q^89 + 4 * q^91 + 4 * q^92 + 26 * q^93 + 3 * q^94 + 53 * q^96 - 32 * q^97 - 39 * q^98 + 16 * q^99

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