LMFDB - Embedded newform 3525.2.a.bi.1.4

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			1.4
Root			$-1.22883$ 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)

$f(q)$	$=$	$q-1.22883 q^{2} +1.00000 q^{3} -0.489976 q^{4} -1.22883 q^{6} -1.54483 q^{7} +3.05976 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.22883 q^{2} +1.00000 q^{3} -0.489976 q^{4} -1.22883 q^{6} -1.54483 q^{7} +3.05976 q^{8} +1.00000 q^{9} -5.30627 q^{11} -0.489976 q^{12} -1.18326 q^{13} +1.89834 q^{14} -2.77997 q^{16} -0.202968 q^{17} -1.22883 q^{18} -0.763314 q^{19} -1.54483 q^{21} +6.52050 q^{22} +0.949787 q^{23} +3.05976 q^{24} +1.45403 q^{26} +1.00000 q^{27} +0.756933 q^{28} -1.24372 q^{29} +5.77891 q^{31} -2.70340 q^{32} -5.30627 q^{33} +0.249413 q^{34} -0.489976 q^{36} -4.62516 q^{37} +0.937983 q^{38} -1.18326 q^{39} +2.66758 q^{41} +1.89834 q^{42} -9.66369 q^{43} +2.59995 q^{44} -1.16713 q^{46} +1.00000 q^{47} -2.77997 q^{48} -4.61349 q^{49} -0.202968 q^{51} +0.579770 q^{52} +5.23309 q^{53} -1.22883 q^{54} -4.72682 q^{56} -0.763314 q^{57} +1.52832 q^{58} +6.90070 q^{59} +10.6642 q^{61} -7.10130 q^{62} -1.54483 q^{63} +8.88197 q^{64} +6.52050 q^{66} +7.49480 q^{67} +0.0994496 q^{68} +0.949787 q^{69} +2.47955 q^{71} +3.05976 q^{72} -5.46468 q^{73} +5.68354 q^{74} +0.374006 q^{76} +8.19731 q^{77} +1.45403 q^{78} +12.6895 q^{79} +1.00000 q^{81} -3.27800 q^{82} +5.11278 q^{83} +0.756933 q^{84} +11.8750 q^{86} -1.24372 q^{87} -16.2359 q^{88} -11.4045 q^{89} +1.82794 q^{91} -0.465373 q^{92} +5.77891 q^{93} -1.22883 q^{94} -2.70340 q^{96} +12.7106 q^{97} +5.66919 q^{98} -5.30627 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.22883	−0.868914	−0.434457	−	0.900693i	$-0.643060\pi$
$2$	−1.22883	−0.868914	−0.434457	+	0.900693i	$0.643060\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.489976	−0.244988
$5$	0	0
$5$	0	0
$6$	−1.22883	−0.501668
$7$	−1.54483	−0.583893	−0.291946	−	0.956435i	$-0.594303\pi$
$7$	−1.54483	−0.583893	−0.291946	+	0.956435i	$0.594303\pi$
$8$	3.05976	1.08179
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.30627	−1.59990	−0.799950	−	0.600066i	$-0.795141\pi$
$11$	−5.30627	−1.59990	−0.799950	+	0.600066i	$0.795141\pi$
$12$	−0.489976	−0.141444
$13$	−1.18326	−0.328178	−0.164089	−	0.986446i	$-0.552468\pi$
$13$	−1.18326	−0.328178	−0.164089	+	0.986446i	$0.552468\pi$
$14$	1.89834	0.507353
$15$	0	0
$16$	−2.77997	−0.694993
$17$	−0.202968	−0.0492270	−0.0246135	−	0.999697i	$-0.507836\pi$
$17$	−0.202968	−0.0492270	−0.0246135	+	0.999697i	$0.507836\pi$
$18$	−1.22883	−0.289638
$19$	−0.763314	−0.175116	−0.0875581	−	0.996159i	$-0.527906\pi$
$19$	−0.763314	−0.175116	−0.0875581	+	0.996159i	$0.527906\pi$
$20$	0	0
$21$	−1.54483	−0.337111
$22$	6.52050	1.39018
$23$	0.949787	0.198044	0.0990221	−	0.995085i	$-0.468429\pi$
$23$	0.949787	0.198044	0.0990221	+	0.995085i	$0.468429\pi$
$24$	3.05976	0.624571
$25$	0	0
$26$	1.45403	0.285158
$27$	1.00000	0.192450
$28$	0.756933	0.143047
$29$	−1.24372	−0.230952	−0.115476	−	0.993310i	$-0.536839\pi$
$29$	−1.24372	−0.230952	−0.115476	+	0.993310i	$0.536839\pi$
$30$	0	0
$31$	5.77891	1.03792	0.518961	−	0.854798i	$-0.326319\pi$
$31$	5.77891	1.03792	0.518961	+	0.854798i	$0.326319\pi$
$32$	−2.70340	−0.477899
$33$	−5.30627	−0.923703
$34$	0.249413	0.0427740
$35$	0	0
$36$	−0.489976	−0.0816627
$37$	−4.62516	−0.760372	−0.380186	−	0.924910i	$-0.624140\pi$
$37$	−4.62516	−0.760372	−0.380186	+	0.924910i	$0.624140\pi$
$38$	0.937983	0.152161
$39$	−1.18326	−0.189473
$40$	0	0
$41$	2.66758	0.416606	0.208303	−	0.978064i	$-0.433206\pi$
$41$	2.66758	0.416606	0.208303	+	0.978064i	$0.433206\pi$
$42$	1.89834	0.292920
$43$	−9.66369	−1.47370	−0.736850	−	0.676057i	$-0.763687\pi$
$43$	−9.66369	−1.47370	−0.736850	+	0.676057i	$0.763687\pi$
$44$	2.59995	0.391957
$45$	0	0
$46$	−1.16713	−0.172083
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−2.77997	−0.401254
$49$	−4.61349	−0.659069
$50$	0	0
$51$	−0.202968	−0.0284212
$52$	0.579770	0.0803996
$53$	5.23309	0.718820	0.359410	−	0.933180i	$-0.382978\pi$
$53$	5.23309	0.718820	0.359410	+	0.933180i	$0.382978\pi$
$54$	−1.22883	−0.167223
$55$	0	0
$56$	−4.72682	−0.631648
$57$	−0.763314	−0.101103
$58$	1.52832	0.200678
$59$	6.90070	0.898395	0.449197	−	0.893433i	$-0.351710\pi$
$59$	6.90070	0.898395	0.449197	+	0.893433i	$0.351710\pi$
$60$	0	0
$61$	10.6642	1.36541	0.682706	−	0.730693i	$-0.260803\pi$
$61$	10.6642	1.36541	0.682706	+	0.730693i	$0.260803\pi$
$62$	−7.10130	−0.901866
$63$	−1.54483	−0.194631
$64$	8.88197	1.11025
$65$	0	0
$66$	6.52050	0.802619
$67$	7.49480	0.915636	0.457818	−	0.889046i	$-0.348631\pi$
$67$	7.49480	0.915636	0.457818	+	0.889046i	$0.348631\pi$
$68$	0.0994496	0.0120600
$69$	0.949787	0.114341
$70$	0	0
$71$	2.47955	0.294268	0.147134	−	0.989117i	$-0.452995\pi$
$71$	2.47955	0.294268	0.147134	+	0.989117i	$0.452995\pi$
$72$	3.05976	0.360596
$73$	−5.46468	−0.639592	−0.319796	−	0.947486i	$-0.603614\pi$
$73$	−5.46468	−0.639592	−0.319796	+	0.947486i	$0.603614\pi$
$74$	5.68354	0.660698
$75$	0	0
$76$	0.374006	0.0429014
$77$	8.19731	0.934170
$78$	1.45403	0.164636
$79$	12.6895	1.42768	0.713842	−	0.700306i	$-0.246953\pi$
$79$	12.6895	1.42768	0.713842	+	0.700306i	$0.246953\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.27800	−0.361995
$83$	5.11278	0.561200	0.280600	−	0.959825i	$-0.409467\pi$
$83$	5.11278	0.561200	0.280600	+	0.959825i	$0.409467\pi$
$84$	0.756933	0.0825881
$85$	0	0
$86$	11.8750	1.28052
$87$	−1.24372	−0.133340
$88$	−16.2359	−1.73075
$89$	−11.4045	−1.20888	−0.604438	−	0.796652i	$-0.706602\pi$
$89$	−11.4045	−1.20888	−0.604438	+	0.796652i	$0.706602\pi$
$90$	0	0
$91$	1.82794	0.191620
$92$	−0.465373	−0.0485185
$93$	5.77891	0.599245
$94$	−1.22883	−0.126744
$95$	0	0
$96$	−2.70340	−0.275915
$97$	12.7106	1.29057	0.645285	−	0.763942i	$-0.276739\pi$
$97$	12.7106	1.29057	0.645285	+	0.763942i	$0.276739\pi$
$98$	5.66919	0.572675
$99$	−5.30627	−0.533300
$100$	0	0
$101$	2.38330	0.237147	0.118574	−	0.992945i	$-0.462168\pi$
$101$	2.38330	0.237147	0.118574	+	0.992945i	$0.462168\pi$
$102$	0.249413	0.0246956
$103$	−4.57143	−0.450437	−0.225218	−	0.974308i	$-0.572310\pi$
$103$	−4.57143	−0.450437	−0.225218	+	0.974308i	$0.572310\pi$
$104$	−3.62049	−0.355019
$105$	0	0
$106$	−6.43058	−0.624593
$107$	−13.4303	−1.29836	−0.649179	−	0.760636i	$-0.724887\pi$
$107$	−13.4303	−1.29836	−0.649179	+	0.760636i	$0.724887\pi$
$108$	−0.489976	−0.0471480
$109$	−1.05666	−0.101210	−0.0506049	−	0.998719i	$-0.516115\pi$
$109$	−1.05666	−0.101210	−0.0506049	+	0.998719i	$0.516115\pi$
$110$	0	0
$111$	−4.62516	−0.439001
$112$	4.29459	0.405801
$113$	1.49638	0.140768	0.0703839	−	0.997520i	$-0.477578\pi$
$113$	1.49638	0.140768	0.0703839	+	0.997520i	$0.477578\pi$
$114$	0.937983	0.0878502
$115$	0	0
$116$	0.609392	0.0565806
$117$	−1.18326	−0.109393
$118$	−8.47979	−0.780628
$119$	0.313552	0.0287433
$120$	0	0
$121$	17.1565	1.55968
$122$	−13.1045	−1.18643
$123$	2.66758	0.240528
$124$	−2.83153	−0.254279
$125$	0	0
$126$	1.89834	0.169118
$127$	−14.3633	−1.27454	−0.637269	−	0.770642i	$-0.719936\pi$
$127$	−14.3633	−1.27454	−0.637269	+	0.770642i	$0.719936\pi$
$128$	−5.50762	−0.486809
$129$	−9.66369	−0.850841
$130$	0	0
$131$	18.0891	1.58046	0.790228	−	0.612813i	$-0.209962\pi$
$131$	18.0891	1.58046	0.790228	+	0.612813i	$0.209962\pi$
$132$	2.59995	0.226296
$133$	1.17919	0.102249
$134$	−9.20984	−0.795609
$135$	0	0
$136$	−0.621033	−0.0532532
$137$	3.13238	0.267617	0.133809	−	0.991007i	$-0.457279\pi$
$137$	3.13238	0.267617	0.133809	+	0.991007i	$0.457279\pi$
$138$	−1.16713	−0.0993525
$139$	9.28678	0.787694	0.393847	−	0.919176i	$-0.371144\pi$
$139$	9.28678	0.787694	0.393847	+	0.919176i	$0.371144\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−3.04694	−0.255694
$143$	6.27870	0.525052
$144$	−2.77997	−0.231664
$145$	0	0
$146$	6.71516	0.555750
$147$	−4.61349	−0.380514
$148$	2.26622	0.186282
$149$	17.7245	1.45205	0.726023	−	0.687670i	$-0.241366\pi$
$149$	17.7245	1.45205	0.726023	+	0.687670i	$0.241366\pi$
$150$	0	0
$151$	19.4229	1.58061	0.790306	−	0.612712i	$-0.209921\pi$
$151$	19.4229	1.58061	0.790306	+	0.612712i	$0.209921\pi$
$152$	−2.33556	−0.189439
$153$	−0.202968	−0.0164090
$154$	−10.0731	−0.811714
$155$	0	0
$156$	0.579770	0.0464188
$157$	−13.6755	−1.09142	−0.545711	−	0.837973i	$-0.683740\pi$
$157$	−13.6755	−1.09142	−0.545711	+	0.837973i	$0.683740\pi$
$158$	−15.5933	−1.24054
$159$	5.23309	0.415011
$160$	0	0
$161$	−1.46726	−0.115637
$162$	−1.22883	−0.0965460
$163$	−19.3212	−1.51335	−0.756676	−	0.653790i	$-0.773178\pi$
$163$	−19.3212	−1.51335	−0.756676	+	0.653790i	$0.773178\pi$
$164$	−1.30705	−0.102064
$165$	0	0
$166$	−6.28274	−0.487635
$167$	19.3742	1.49922	0.749611	−	0.661879i	$-0.230241\pi$
$167$	19.3742	1.49922	0.749611	+	0.661879i	$0.230241\pi$
$168$	−4.72682	−0.364682
$169$	−11.5999	−0.892299
$170$	0	0
$171$	−0.763314	−0.0583721
$172$	4.73498	0.361039
$173$	−3.62837	−0.275860	−0.137930	−	0.990442i	$-0.544045\pi$
$173$	−3.62837	−0.275860	−0.137930	+	0.990442i	$0.544045\pi$
$174$	1.52832	0.115861
$175$	0	0
$176$	14.7513	1.11192
$177$	6.90070	0.518688
$178$	14.0142	1.05041
$179$	12.9338	0.966716	0.483358	−	0.875423i	$-0.339417\pi$
$179$	12.9338	0.966716	0.483358	+	0.875423i	$0.339417\pi$
$180$	0	0
$181$	7.42347	0.551783	0.275891	−	0.961189i	$-0.411027\pi$
$181$	7.42347	0.551783	0.275891	+	0.961189i	$0.411027\pi$
$182$	−2.24623	−0.166502
$183$	10.6642	0.788321
$184$	2.90612	0.214242
$185$	0	0
$186$	−7.10130	−0.520692
$187$	1.07700	0.0787583
$188$	−0.489976	−0.0357352
$189$	−1.54483	−0.112370
$190$	0	0
$191$	12.1100	0.876247	0.438124	−	0.898915i	$-0.355643\pi$
$191$	12.1100	0.876247	0.438124	+	0.898915i	$0.355643\pi$
$192$	8.88197	0.641001
$193$	1.59738	0.114982	0.0574908	−	0.998346i	$-0.481690\pi$
$193$	1.59738	0.114982	0.0574908	+	0.998346i	$0.481690\pi$
$194$	−15.6192	−1.12139
$195$	0	0
$196$	2.26050	0.161464
$197$	2.88292	0.205400	0.102700	−	0.994712i	$-0.467252\pi$
$197$	2.88292	0.205400	0.102700	+	0.994712i	$0.467252\pi$
$198$	6.52050	0.463392
$199$	−7.89509	−0.559668	−0.279834	−	0.960048i	$-0.590279\pi$
$199$	−7.89509	−0.559668	−0.279834	+	0.960048i	$0.590279\pi$
$200$	0	0
$201$	7.49480	0.528643
$202$	−2.92867	−0.206061
$203$	1.92134	0.134851
$204$	0.0994496	0.00696286
$205$	0	0
$206$	5.61751	0.391391
$207$	0.949787	0.0660148
$208$	3.28943	0.228081
$209$	4.05035	0.280169
$210$	0	0
$211$	−10.5868	−0.728825	−0.364412	−	0.931238i	$-0.618730\pi$
$211$	−10.5868	−0.728825	−0.364412	+	0.931238i	$0.618730\pi$
$212$	−2.56409	−0.176103
$213$	2.47955	0.169896
$214$	16.5036	1.12816
$215$	0	0
$216$	3.05976	0.208190
$217$	−8.92746	−0.606035
$218$	1.29846	0.0879426
$219$	−5.46468	−0.369269
$220$	0	0
$221$	0.240164	0.0161552
$222$	5.68354	0.381454
$223$	0.155542	0.0104158	0.00520792	−	0.999986i	$-0.498342\pi$
$223$	0.155542	0.0104158	0.00520792	+	0.999986i	$0.498342\pi$
$224$	4.17631	0.279042
$225$	0	0
$226$	−1.83880	−0.122315
$227$	12.6761	0.841345	0.420672	−	0.907213i	$-0.361794\pi$
$227$	12.6761	0.841345	0.420672	+	0.907213i	$0.361794\pi$
$228$	0.374006	0.0247691
$229$	−13.6316	−0.900803	−0.450402	−	0.892826i	$-0.648719\pi$
$229$	−13.6316	−0.900803	−0.450402	+	0.892826i	$0.648719\pi$
$230$	0	0
$231$	8.19731	0.539343
$232$	−3.80547	−0.249841
$233$	3.91747	0.256642	0.128321	−	0.991733i	$-0.459041\pi$
$233$	3.91747	0.256642	0.128321	+	0.991733i	$0.459041\pi$
$234$	1.45403	0.0950527
$235$	0	0
$236$	−3.38118	−0.220096
$237$	12.6895	0.824274
$238$	−0.385302	−0.0249754
$239$	26.1812	1.69352	0.846760	−	0.531976i	$-0.178550\pi$
$239$	26.1812	1.69352	0.846760	+	0.531976i	$0.178550\pi$
$240$	0	0
$241$	−21.7180	−1.39898	−0.699489	−	0.714644i	$-0.746589\pi$
$241$	−21.7180	−1.39898	−0.699489	+	0.714644i	$0.746589\pi$
$242$	−21.0824	−1.35523
$243$	1.00000	0.0641500
$244$	−5.22521	−0.334510
$245$	0	0
$246$	−3.27800	−0.208998
$247$	0.903200	0.0574692
$248$	17.6821	1.12281
$249$	5.11278	0.324009
$250$	0	0
$251$	24.3104	1.53446	0.767231	−	0.641371i	$-0.221634\pi$
$251$	24.3104	1.53446	0.767231	+	0.641371i	$0.221634\pi$
$252$	0.756933	0.0476823
$253$	−5.03983	−0.316851
$254$	17.6501	1.10746
$255$	0	0
$256$	−10.9960	−0.687250
$257$	25.4288	1.58621	0.793103	−	0.609088i	$-0.208464\pi$
$257$	25.4288	1.58621	0.793103	+	0.609088i	$0.208464\pi$
$258$	11.8750	0.739308
$259$	7.14511	0.443976
$260$	0	0
$261$	−1.24372	−0.0769841
$262$	−22.2285	−1.37328
$263$	9.58117	0.590800	0.295400	−	0.955374i	$-0.404547\pi$
$263$	9.58117	0.590800	0.295400	+	0.955374i	$0.404547\pi$
$264$	−16.2359	−0.999251
$265$	0	0
$266$	−1.44903	−0.0888457
$267$	−11.4045	−0.697945
$268$	−3.67228	−0.224320
$269$	17.6402	1.07554	0.537770	−	0.843092i	$-0.319267\pi$
$269$	17.6402	1.07554	0.537770	+	0.843092i	$0.319267\pi$
$270$	0	0
$271$	−16.8243	−1.02200	−0.511002	−	0.859579i	$-0.670726\pi$
$271$	−16.8243	−1.02200	−0.511002	+	0.859579i	$0.670726\pi$
$272$	0.564245	0.0342124
$273$	1.82794	0.110632
$274$	−3.84916	−0.232536
$275$	0	0
$276$	−0.465373	−0.0280122
$277$	24.0266	1.44362	0.721810	−	0.692091i	$-0.243310\pi$
$277$	24.0266	1.44362	0.721810	+	0.692091i	$0.243310\pi$
$278$	−11.4119	−0.684439
$279$	5.77891	0.345974
$280$	0	0
$281$	25.0266	1.49296	0.746482	−	0.665406i	$-0.231742\pi$
$281$	25.0266	1.49296	0.746482	+	0.665406i	$0.231742\pi$
$282$	−1.22883	−0.0731758
$283$	19.3174	1.14830	0.574151	−	0.818749i	$-0.305332\pi$
$283$	19.3174	1.14830	0.574151	+	0.818749i	$0.305332\pi$
$284$	−1.21492	−0.0720922
$285$	0	0
$286$	−7.71546	−0.456225
$287$	−4.12097	−0.243253
$288$	−2.70340	−0.159300
$289$	−16.9588	−0.997577
$290$	0	0
$291$	12.7106	0.745111
$292$	2.67756	0.156692
$293$	−18.1029	−1.05758	−0.528791	−	0.848752i	$-0.677355\pi$
$293$	−18.1029	−1.05758	−0.528791	+	0.848752i	$0.677355\pi$
$294$	5.66919	0.330634
$295$	0	0
$296$	−14.1519	−0.822561
$297$	−5.30627	−0.307901
$298$	−21.7804	−1.26170
$299$	−1.12385	−0.0649937
$300$	0	0
$301$	14.9288	0.860482
$302$	−23.8674	−1.37342
$303$	2.38330	0.136917
$304$	2.12199	0.121705
$305$	0	0
$306$	0.249413	0.0142580
$307$	5.93879	0.338945	0.169472	−	0.985535i	$-0.445794\pi$
$307$	5.93879	0.338945	0.169472	+	0.985535i	$0.445794\pi$
$308$	−4.01649	−0.228861
$309$	−4.57143	−0.260060
$310$	0	0
$311$	−15.1976	−0.861776	−0.430888	−	0.902405i	$-0.641800\pi$
$311$	−15.1976	−0.861776	−0.430888	+	0.902405i	$0.641800\pi$
$312$	−3.62049	−0.204970
$313$	−16.6263	−0.939774	−0.469887	−	0.882727i	$-0.655705\pi$
$313$	−16.6263	−0.939774	−0.469887	+	0.882727i	$0.655705\pi$
$314$	16.8048	0.948352
$315$	0	0
$316$	−6.21758	−0.349766
$317$	−1.96987	−0.110639	−0.0553193	−	0.998469i	$-0.517618\pi$
$317$	−1.96987	−0.110639	−0.0553193	+	0.998469i	$0.517618\pi$
$318$	−6.43058	−0.360609
$319$	6.59949	0.369501
$320$	0	0
$321$	−13.4303	−0.749607
$322$	1.80302	0.100478
$323$	0.154928	0.00862045
$324$	−0.489976	−0.0272209
$325$	0	0
$326$	23.7424	1.31497
$327$	−1.05666	−0.0584335
$328$	8.16215	0.450679
$329$	−1.54483	−0.0851695
$330$	0	0
$331$	23.5199	1.29277	0.646384	−	0.763012i	$-0.276280\pi$
$331$	23.5199	1.29277	0.646384	+	0.763012i	$0.276280\pi$
$332$	−2.50514	−0.137487
$333$	−4.62516	−0.253457
$334$	−23.8076	−1.30270
$335$	0	0
$336$	4.29459	0.234289
$337$	2.44780	0.133340	0.0666701	−	0.997775i	$-0.478763\pi$
$337$	2.44780	0.133340	0.0666701	+	0.997775i	$0.478763\pi$
$338$	14.2543	0.775332
$339$	1.49638	0.0812723
$340$	0	0
$341$	−30.6644	−1.66057
$342$	0.937983	0.0507203
$343$	17.9409	0.968718
$344$	−29.5686	−1.59423
$345$	0	0
$346$	4.45865	0.239698
$347$	36.0156	1.93342	0.966709	−	0.255877i	$-0.0823641\pi$
$347$	36.0156	1.93342	0.966709	+	0.255877i	$0.0823641\pi$
$348$	0.609392	0.0326668
$349$	22.4477	1.20160	0.600798	−	0.799401i	$-0.294850\pi$
$349$	22.4477	1.20160	0.600798	+	0.799401i	$0.294850\pi$
$350$	0	0
$351$	−1.18326	−0.0631578
$352$	14.3450	0.764591
$353$	−15.1135	−0.804412	−0.402206	−	0.915549i	$-0.631756\pi$
$353$	−15.1135	−0.804412	−0.402206	+	0.915549i	$0.631756\pi$
$354$	−8.47979	−0.450696
$355$	0	0
$356$	5.58794	0.296160
$357$	0.313552	0.0165949
$358$	−15.8934	−0.839993
$359$	14.9500	0.789031	0.394515	−	0.918889i	$-0.370912\pi$
$359$	14.9500	0.789031	0.394515	+	0.918889i	$0.370912\pi$
$360$	0	0
$361$	−18.4174	−0.969334
$362$	−9.12219	−0.479452
$363$	17.1565	0.900483
$364$	−0.895649	−0.0469448
$365$	0	0
$366$	−13.1045	−0.684984
$367$	−23.6379	−1.23389	−0.616944	−	0.787007i	$-0.711629\pi$
$367$	−23.6379	−1.23389	−0.616944	+	0.787007i	$0.711629\pi$
$368$	−2.64038	−0.137639
$369$	2.66758	0.138869
$370$	0	0
$371$	−8.08426	−0.419714
$372$	−2.83153	−0.146808
$373$	28.1670	1.45843	0.729216	−	0.684283i	$-0.239885\pi$
$373$	28.1670	1.45843	0.729216	+	0.684283i	$0.239885\pi$
$374$	−1.32345	−0.0684342
$375$	0	0
$376$	3.05976	0.157795
$377$	1.47164	0.0757934
$378$	1.89834	0.0976401
$379$	27.4787	1.41149	0.705743	−	0.708468i	$-0.250613\pi$
$379$	27.4787	1.41149	0.705743	+	0.708468i	$0.250613\pi$
$380$	0	0
$381$	−14.3633	−0.735854
$382$	−14.8811	−0.761384
$383$	12.2495	0.625922	0.312961	−	0.949766i	$-0.398679\pi$
$383$	12.2495	0.625922	0.312961	+	0.949766i	$0.398679\pi$
$384$	−5.50762	−0.281059
$385$	0	0
$386$	−1.96290	−0.0999092
$387$	−9.66369	−0.491233
$388$	−6.22792	−0.316175
$389$	0.461856	0.0234170	0.0117085	−	0.999931i	$-0.496273\pi$
$389$	0.461856	0.0234170	0.0117085	+	0.999931i	$0.496273\pi$
$390$	0	0
$391$	−0.192776	−0.00974912
$392$	−14.1161	−0.712973
$393$	18.0891	0.912477
$394$	−3.54262	−0.178475
$395$	0	0
$396$	2.59995	0.130652
$397$	−31.9407	−1.60306	−0.801528	−	0.597957i	$-0.795979\pi$
$397$	−31.9407	−1.60306	−0.801528	+	0.597957i	$0.795979\pi$
$398$	9.70172	0.486303
$399$	1.17919	0.0590336
$400$	0	0
$401$	−17.7000	−0.883897	−0.441949	−	0.897040i	$-0.645713\pi$
$401$	−17.7000	−0.883897	−0.441949	+	0.897040i	$0.645713\pi$
$402$	−9.20984	−0.459345
$403$	−6.83796	−0.340623
$404$	−1.16776	−0.0580983
$405$	0	0
$406$	−2.36100	−0.117174
$407$	24.5424	1.21652
$408$	−0.621033	−0.0307457
$409$	6.00486	0.296921	0.148461	−	0.988918i	$-0.452568\pi$
$409$	6.00486	0.296921	0.148461	+	0.988918i	$0.452568\pi$
$410$	0	0
$411$	3.13238	0.154509
$412$	2.23989	0.110352
$413$	−10.6604	−0.524566
$414$	−1.16713	−0.0573612
$415$	0	0
$416$	3.19883	0.156836
$417$	9.28678	0.454775
$418$	−4.97719	−0.243442
$419$	24.2422	1.18431	0.592155	−	0.805824i	$-0.298277\pi$
$419$	24.2422	1.18431	0.592155	+	0.805824i	$0.298277\pi$
$420$	0	0
$421$	11.8857	0.579272	0.289636	−	0.957137i	$-0.406466\pi$
$421$	11.8857	0.579272	0.289636	+	0.957137i	$0.406466\pi$
$422$	13.0094	0.633286
$423$	1.00000	0.0486217
$424$	16.0120	0.777611
$425$	0	0
$426$	−3.04694	−0.147625
$427$	−16.4744	−0.797254
$428$	6.58054	0.318082
$429$	6.27870	0.303139
$430$	0	0
$431$	−14.1068	−0.679501	−0.339751	−	0.940516i	$-0.610343\pi$
$431$	−14.1068	−0.679501	−0.339751	+	0.940516i	$0.610343\pi$
$432$	−2.77997	−0.133751
$433$	24.9404	1.19856	0.599280	−	0.800540i	$-0.295454\pi$
$433$	24.9404	1.19856	0.599280	+	0.800540i	$0.295454\pi$
$434$	10.9703	0.526593
$435$	0	0
$436$	0.517739	0.0247952
$437$	−0.724986	−0.0346808
$438$	6.71516	0.320863
$439$	−6.31573	−0.301433	−0.150717	−	0.988577i	$-0.548158\pi$
$439$	−6.31573	−0.301433	−0.150717	+	0.988577i	$0.548158\pi$
$440$	0	0
$441$	−4.61349	−0.219690
$442$	−0.295121	−0.0140375
$443$	−1.78753	−0.0849282	−0.0424641	−	0.999098i	$-0.513521\pi$
$443$	−1.78753	−0.0849282	−0.0424641	+	0.999098i	$0.513521\pi$
$444$	2.26622	0.107550
$445$	0	0
$446$	−0.191134	−0.00905047
$447$	17.7245	0.838340
$448$	−13.7212	−0.648264
$449$	3.89922	0.184015	0.0920077	−	0.995758i	$-0.470672\pi$
$449$	3.89922	0.184015	0.0920077	+	0.995758i	$0.470672\pi$
$450$	0	0
$451$	−14.1549	−0.666528
$452$	−0.733192	−0.0344864
$453$	19.4229	0.912567
$454$	−15.5768	−0.731056
$455$	0	0
$456$	−2.33556	−0.109372
$457$	16.7078	0.781556	0.390778	−	0.920485i	$-0.372206\pi$
$457$	16.7078	0.781556	0.390778	+	0.920485i	$0.372206\pi$
$458$	16.7510	0.782721
$459$	−0.202968	−0.00947374
$460$	0	0
$461$	−12.7831	−0.595370	−0.297685	−	0.954664i	$-0.596215\pi$
$461$	−12.7831	−0.595370	−0.297685	+	0.954664i	$0.596215\pi$
$462$	−10.0731	−0.468643
$463$	−13.0363	−0.605849	−0.302924	−	0.953015i	$-0.597963\pi$
$463$	−13.0363	−0.605849	−0.302924	+	0.953015i	$0.597963\pi$
$464$	3.45749	0.160510
$465$	0	0
$466$	−4.81390	−0.223000
$467$	−23.4370	−1.08454	−0.542268	−	0.840206i	$-0.682434\pi$
$467$	−23.4370	−1.08454	−0.542268	+	0.840206i	$0.682434\pi$
$468$	0.579770	0.0267999
$469$	−11.5782	−0.534633
$470$	0	0
$471$	−13.6755	−0.630133
$472$	21.1145	0.971872
$473$	51.2782	2.35777
$474$	−15.5933	−0.716224
$475$	0	0
$476$	−0.153633	−0.00704176
$477$	5.23309	0.239607
$478$	−32.1722	−1.47152
$479$	−9.34360	−0.426920	−0.213460	−	0.976952i	$-0.568473\pi$
$479$	−9.34360	−0.426920	−0.213460	+	0.976952i	$0.568473\pi$
$480$	0	0
$481$	5.47277	0.249537
$482$	26.6877	1.21559
$483$	−1.46726	−0.0667628
$484$	−8.40628	−0.382104
$485$	0	0
$486$	−1.22883	−0.0557409
$487$	−5.86645	−0.265834	−0.132917	−	0.991127i	$-0.542434\pi$
$487$	−5.86645	−0.265834	−0.132917	+	0.991127i	$0.542434\pi$
$488$	32.6299	1.47709
$489$	−19.3212	−0.873734
$490$	0	0
$491$	−32.6094	−1.47164	−0.735820	−	0.677177i	$-0.763203\pi$
$491$	−32.6094	−1.47164	−0.735820	+	0.677177i	$0.763203\pi$
$492$	−1.30705	−0.0589264
$493$	0.252435	0.0113691
$494$	−1.10988	−0.0499358
$495$	0	0
$496$	−16.0652	−0.721349
$497$	−3.83049	−0.171821
$498$	−6.28274	−0.281536
$499$	−14.4230	−0.645661	−0.322831	−	0.946457i	$-0.604634\pi$
$499$	−14.4230	−0.645661	−0.322831	+	0.946457i	$0.604634\pi$
$500$	0	0
$501$	19.3742	0.865576
$502$	−29.8734	−1.33331
$503$	27.4384	1.22342	0.611710	−	0.791082i	$-0.290482\pi$
$503$	27.4384	1.22342	0.611710	+	0.791082i	$0.290482\pi$
$504$	−4.72682	−0.210549
$505$	0	0
$506$	6.19309	0.275316
$507$	−11.5999	−0.515169
$508$	7.03768	0.312247
$509$	10.2857	0.455906	0.227953	−	0.973672i	$-0.426797\pi$
$509$	10.2857	0.455906	0.227953	+	0.973672i	$0.426797\pi$
$510$	0	0
$511$	8.44202	0.373453
$512$	24.5275	1.08397
$513$	−0.763314	−0.0337011
$514$	−31.2477	−1.37828
$515$	0	0
$516$	4.73498	0.208446
$517$	−5.30627	−0.233369
$518$	−8.78013	−0.385777
$519$	−3.62837	−0.159268
$520$	0	0
$521$	−7.44464	−0.326156	−0.163078	−	0.986613i	$-0.552142\pi$
$521$	−7.44464	−0.326156	−0.163078	+	0.986613i	$0.552142\pi$
$522$	1.52832	0.0668926
$523$	0.676793	0.0295941	0.0147971	−	0.999891i	$-0.495290\pi$
$523$	0.676793	0.0295941	0.0147971	+	0.999891i	$0.495290\pi$
$524$	−8.86326	−0.387193
$525$	0	0
$526$	−11.7736	−0.513355
$527$	−1.17293	−0.0510938
$528$	14.7513	0.641967
$529$	−22.0979	−0.960778
$530$	0	0
$531$	6.90070	0.299465
$532$	−0.577777	−0.0250498
$533$	−3.15644	−0.136721
$534$	14.0142	0.606454
$535$	0	0
$536$	22.9323	0.990524
$537$	12.9338	0.558134
$538$	−21.6768	−0.934552
$539$	24.4804	1.05445
$540$	0	0
$541$	−9.54109	−0.410204	−0.205102	−	0.978741i	$-0.565753\pi$
$541$	−9.54109	−0.410204	−0.205102	+	0.978741i	$0.565753\pi$
$542$	20.6742	0.888034
$543$	7.42347	0.318572
$544$	0.548705	0.0235255
$545$	0	0
$546$	−2.24623	−0.0961298
$547$	25.4767	1.08930	0.544652	−	0.838662i	$-0.316662\pi$
$547$	25.4767	1.08930	0.544652	+	0.838662i	$0.316662\pi$
$548$	−1.53479	−0.0655630
$549$	10.6642	0.455138
$550$	0	0
$551$	0.949346	0.0404435
$552$	2.90612	0.123693
$553$	−19.6032	−0.833615
$554$	−29.5246	−1.25438
$555$	0	0
$556$	−4.55030	−0.192976
$557$	36.4571	1.54474	0.772369	−	0.635174i	$-0.219072\pi$
$557$	36.4571	1.54474	0.772369	+	0.635174i	$0.219072\pi$
$558$	−7.10130	−0.300622
$559$	11.4347	0.483635
$560$	0	0
$561$	1.07700	0.0454711
$562$	−30.7535	−1.29726
$563$	−30.8565	−1.30045	−0.650224	−	0.759743i	$-0.725325\pi$
$563$	−30.8565	−1.30045	−0.650224	+	0.759743i	$0.725325\pi$
$564$	−0.489976	−0.0206317
$565$	0	0
$566$	−23.7379	−0.997776
$567$	−1.54483	−0.0648770
$568$	7.58681	0.318335
$569$	−17.1583	−0.719313	−0.359656	−	0.933085i	$-0.617106\pi$
$569$	−17.1583	−0.719313	−0.359656	+	0.933085i	$0.617106\pi$
$570$	0	0
$571$	33.5660	1.40469	0.702346	−	0.711836i	$-0.252136\pi$
$571$	33.5660	1.40469	0.702346	+	0.711836i	$0.252136\pi$
$572$	−3.07642	−0.128631
$573$	12.1100	0.505902
$574$	5.06397	0.211366
$575$	0	0
$576$	8.88197	0.370082
$577$	−10.9190	−0.454566	−0.227283	−	0.973829i	$-0.572984\pi$
$577$	−10.9190	−0.454566	−0.227283	+	0.973829i	$0.572984\pi$
$578$	20.8395	0.866809
$579$	1.59738	0.0663847
$580$	0	0
$581$	−7.89840	−0.327681
$582$	−15.6192	−0.647438
$583$	−27.7682	−1.15004
$584$	−16.7206	−0.691903
$585$	0	0
$586$	22.2454	0.918948
$587$	38.6211	1.59406	0.797032	−	0.603937i	$-0.206402\pi$
$587$	38.6211	1.59406	0.797032	+	0.603937i	$0.206402\pi$
$588$	2.26050	0.0932214
$589$	−4.41112	−0.181757
$590$	0	0
$591$	2.88292	0.118588
$592$	12.8578	0.528453
$593$	−36.3554	−1.49294	−0.746469	−	0.665420i	$-0.768252\pi$
$593$	−36.3554	−1.49294	−0.746469	+	0.665420i	$0.768252\pi$
$594$	6.52050	0.267540
$595$	0	0
$596$	−8.68458	−0.355734
$597$	−7.89509	−0.323124
$598$	1.38102	0.0564739
$599$	−18.6920	−0.763733	−0.381867	−	0.924217i	$-0.624719\pi$
$599$	−18.6920	−0.763733	−0.381867	+	0.924217i	$0.624719\pi$
$600$	0	0
$601$	−46.7942	−1.90878	−0.954388	−	0.298570i	$-0.903490\pi$
$601$	−46.7942	−1.90878	−0.954388	+	0.298570i	$0.903490\pi$
$602$	−18.3450	−0.747685
$603$	7.49480	0.305212
$604$	−9.51676	−0.387231
$605$	0	0
$606$	−2.92867	−0.118969
$607$	−21.0398	−0.853980	−0.426990	−	0.904256i	$-0.640426\pi$
$607$	−21.0398	−0.853980	−0.426990	+	0.904256i	$0.640426\pi$
$608$	2.06355	0.0836879
$609$	1.92134	0.0778565
$610$	0	0
$611$	−1.18326	−0.0478696
$612$	0.0994496	0.00402001
$613$	−31.3799	−1.26742	−0.633711	−	0.773570i	$-0.718469\pi$
$613$	−31.3799	−1.26742	−0.633711	+	0.773570i	$0.718469\pi$
$614$	−7.29777	−0.294514
$615$	0	0
$616$	25.0818	1.01057
$617$	−15.3165	−0.616619	−0.308309	−	0.951286i	$-0.599763\pi$
$617$	−15.3165	−0.616619	−0.308309	+	0.951286i	$0.599763\pi$
$618$	5.61751	0.225970
$619$	35.2822	1.41811	0.709055	−	0.705153i	$-0.249122\pi$
$619$	35.2822	1.41811	0.709055	+	0.705153i	$0.249122\pi$
$620$	0	0
$621$	0.949787	0.0381136
$622$	18.6752	0.748809
$623$	17.6181	0.705854
$624$	3.28943	0.131683
$625$	0	0
$626$	20.4309	0.816583
$627$	4.05035	0.161755
$628$	6.70066	0.267386
$629$	0.938760	0.0374308
$630$	0	0
$631$	29.8599	1.18870	0.594352	−	0.804205i	$-0.297409\pi$
$631$	29.8599	1.18870	0.594352	+	0.804205i	$0.297409\pi$
$632$	38.8269	1.54445
$633$	−10.5868	−0.420787
$634$	2.42063	0.0961355
$635$	0	0
$636$	−2.56409	−0.101673
$637$	5.45896	0.216292
$638$	−8.10966	−0.321064
$639$	2.47955	0.0980893
$640$	0	0
$641$	37.0614	1.46384	0.731919	−	0.681392i	$-0.238625\pi$
$641$	37.0614	1.46384	0.731919	+	0.681392i	$0.238625\pi$
$642$	16.5036	0.651345
$643$	35.3309	1.39331	0.696657	−	0.717404i	$-0.254670\pi$
$643$	35.3309	1.39331	0.696657	+	0.717404i	$0.254670\pi$
$644$	0.718925	0.0283296
$645$	0	0
$646$	−0.190381	−0.00749043
$647$	7.83353	0.307968	0.153984	−	0.988073i	$-0.450790\pi$
$647$	7.83353	0.307968	0.153984	+	0.988073i	$0.450790\pi$
$648$	3.05976	0.120199
$649$	−36.6170	−1.43734
$650$	0	0
$651$	−8.92746	−0.349895
$652$	9.46692	0.370753
$653$	3.92576	0.153627	0.0768134	−	0.997045i	$-0.475525\pi$
$653$	3.92576	0.153627	0.0768134	+	0.997045i	$0.475525\pi$
$654$	1.29846	0.0507737
$655$	0	0
$656$	−7.41579	−0.289538
$657$	−5.46468	−0.213197
$658$	1.89834	0.0740050
$659$	5.75144	0.224044	0.112022	−	0.993706i	$-0.464267\pi$
$659$	5.75144	0.224044	0.112022	+	0.993706i	$0.464267\pi$
$660$	0	0
$661$	30.1100	1.17114	0.585572	−	0.810621i	$-0.300870\pi$
$661$	30.1100	1.17114	0.585572	+	0.810621i	$0.300870\pi$
$662$	−28.9019	−1.12330
$663$	0.240164	0.00932721
$664$	15.6439	0.607100
$665$	0	0
$666$	5.68354	0.220233
$667$	−1.18127	−0.0457388
$668$	−9.49291	−0.367292
$669$	0.155542	0.00601359
$670$	0	0
$671$	−56.5872	−2.18452
$672$	4.17631	0.161105
$673$	−19.7218	−0.760220	−0.380110	−	0.924941i	$-0.624114\pi$
$673$	−19.7218	−0.760220	−0.380110	+	0.924941i	$0.624114\pi$
$674$	−3.00793	−0.115861
$675$	0	0
$676$	5.68367	0.218603
$677$	32.2913	1.24106	0.620528	−	0.784184i	$-0.286918\pi$
$677$	32.2913	1.24106	0.620528	+	0.784184i	$0.286918\pi$
$678$	−1.83880	−0.0706186
$679$	−19.6358	−0.753555
$680$	0	0
$681$	12.6761	0.485751
$682$	37.6814	1.44290
$683$	34.9548	1.33751	0.668753	−	0.743484i	$-0.266828\pi$
$683$	34.9548	1.33751	0.668753	+	0.743484i	$0.266828\pi$
$684$	0.374006	0.0143005
$685$	0	0
$686$	−22.0463	−0.841733
$687$	−13.6316	−0.520079
$688$	26.8648	1.02421
$689$	−6.19211	−0.235901
$690$	0	0
$691$	−20.5301	−0.781003	−0.390501	−	0.920602i	$-0.627698\pi$
$691$	−20.5301	−0.781003	−0.390501	+	0.920602i	$0.627698\pi$
$692$	1.77782	0.0675824
$693$	8.19731	0.311390
$694$	−44.2571	−1.67997
$695$	0	0
$696$	−3.80547	−0.144246
$697$	−0.541434	−0.0205083
$698$	−27.5844	−1.04408
$699$	3.91747	0.148172
$700$	0	0
$701$	−30.1643	−1.13929	−0.569645	−	0.821891i	$-0.692919\pi$
$701$	−30.1643	−1.13929	−0.569645	+	0.821891i	$0.692919\pi$
$702$	1.45403	0.0548787
$703$	3.53045	0.133154
$704$	−47.1301	−1.77628
$705$	0	0
$706$	18.5720	0.698965
$707$	−3.68181	−0.138469
$708$	−3.38118	−0.127073
$709$	31.3261	1.17648	0.588238	−	0.808688i	$-0.299822\pi$
$709$	31.3261	1.17648	0.588238	+	0.808688i	$0.299822\pi$
$710$	0	0
$711$	12.6895	0.475895
$712$	−34.8951	−1.30775
$713$	5.48873	0.205555
$714$	−0.385302	−0.0144196
$715$	0	0
$716$	−6.33725	−0.236834
$717$	26.1812	0.977754
$718$	−18.3710	−0.685600
$719$	−2.56869	−0.0957961	−0.0478980	−	0.998852i	$-0.515252\pi$
$719$	−2.56869	−0.0957961	−0.0478980	+	0.998852i	$0.515252\pi$
$720$	0	0
$721$	7.06211	0.263007
$722$	22.6318	0.842268
$723$	−21.7180	−0.807700
$724$	−3.63733	−0.135180
$725$	0	0
$726$	−21.0824	−0.782442
$727$	−13.0525	−0.484090	−0.242045	−	0.970265i	$-0.577818\pi$
$727$	−13.0525	−0.484090	−0.242045	+	0.970265i	$0.577818\pi$
$728$	5.59306	0.207293
$729$	1.00000	0.0370370
$730$	0	0
$731$	1.96142	0.0725458
$732$	−5.22521	−0.193129
$733$	−22.7460	−0.840143	−0.420072	−	0.907491i	$-0.637995\pi$
$733$	−22.7460	−0.840143	−0.420072	+	0.907491i	$0.637995\pi$
$734$	29.0469	1.07214
$735$	0	0
$736$	−2.56766	−0.0946452
$737$	−39.7695	−1.46493
$738$	−3.27800	−0.120665
$739$	5.98809	0.220276	0.110138	−	0.993916i	$-0.464871\pi$
$739$	5.98809	0.220276	0.110138	+	0.993916i	$0.464871\pi$
$740$	0	0
$741$	0.903200	0.0331799
$742$	9.93419	0.364695
$743$	−41.0514	−1.50603	−0.753015	−	0.658004i	$-0.771401\pi$
$743$	−41.0514	−1.50603	−0.753015	+	0.658004i	$0.771401\pi$
$744$	17.6821	0.648256
$745$	0	0
$746$	−34.6125	−1.26725
$747$	5.11278	0.187067
$748$	−0.527706	−0.0192949
$749$	20.7476	0.758102
$750$	0	0
$751$	15.9215	0.580985	0.290492	−	0.956877i	$-0.406181\pi$
$751$	15.9215	0.580985	0.290492	+	0.956877i	$0.406181\pi$
$752$	−2.77997	−0.101375
$753$	24.3104	0.885922
$754$	−1.80840	−0.0658579
$755$	0	0
$756$	0.756933	0.0275294
$757$	20.5963	0.748585	0.374293	−	0.927311i	$-0.377886\pi$
$757$	20.5963	0.748585	0.374293	+	0.927311i	$0.377886\pi$
$758$	−33.7667	−1.22646
$759$	−5.03983	−0.182934
$760$	0	0
$761$	5.43504	0.197020	0.0985101	−	0.995136i	$-0.468592\pi$
$761$	5.43504	0.197020	0.0985101	+	0.995136i	$0.468592\pi$
$762$	17.6501	0.639394
$763$	1.63237	0.0590956
$764$	−5.93360	−0.214670
$765$	0	0
$766$	−15.0526	−0.543873
$767$	−8.16533	−0.294833
$768$	−10.9960	−0.396784
$769$	7.80427	0.281429	0.140715	−	0.990050i	$-0.455060\pi$
$769$	7.80427	0.281429	0.140715	+	0.990050i	$0.455060\pi$
$770$	0	0
$771$	25.4288	0.915796
$772$	−0.782676	−0.0281691
$773$	5.08913	0.183043	0.0915216	−	0.995803i	$-0.470827\pi$
$773$	5.08913	0.183043	0.0915216	+	0.995803i	$0.470827\pi$
$774$	11.8750	0.426839
$775$	0	0
$776$	38.8915	1.39612
$777$	7.14511	0.256329
$778$	−0.567542	−0.0203474
$779$	−2.03620	−0.0729545
$780$	0	0
$781$	−13.1571	−0.470799
$782$	0.236890	0.00847115
$783$	−1.24372	−0.0444468
$784$	12.8254	0.458048
$785$	0	0
$786$	−22.2285	−0.792864
$787$	−18.3282	−0.653328	−0.326664	−	0.945140i	$-0.605925\pi$
$787$	−18.3282	−0.653328	−0.326664	+	0.945140i	$0.605925\pi$
$788$	−1.41257	−0.0503205
$789$	9.58117	0.341099
$790$	0	0
$791$	−2.31166	−0.0821933
$792$	−16.2359	−0.576918
$793$	−12.6185	−0.448098
$794$	39.2497	1.39292
$795$	0	0
$796$	3.86841	0.137112
$797$	−50.9584	−1.80504	−0.902520	−	0.430647i	$-0.858285\pi$
$797$	−50.9584	−1.80504	−0.902520	+	0.430647i	$0.858285\pi$
$798$	−1.44903	−0.0512951
$799$	−0.202968	−0.00718049
$800$	0	0
$801$	−11.4045	−0.402959
$802$	21.7503	0.768031
$803$	28.9970	1.02328
$804$	−3.67228	−0.129511
$805$	0	0
$806$	8.40269	0.295972
$807$	17.6402	0.620963
$808$	7.29233	0.256543
$809$	−28.1936	−0.991233	−0.495617	−	0.868541i	$-0.665058\pi$
$809$	−28.1936	−0.991233	−0.495617	+	0.868541i	$0.665058\pi$
$810$	0	0
$811$	−37.6202	−1.32102	−0.660512	−	0.750815i	$-0.729661\pi$
$811$	−37.6202	−1.32102	−0.660512	+	0.750815i	$0.729661\pi$
$812$	−0.941409	−0.0330370
$813$	−16.8243	−0.590054
$814$	−30.1584	−1.05705
$815$	0	0
$816$	0.564245	0.0197525
$817$	7.37643	0.258069
$818$	−7.37895	−0.257999
$819$	1.82794	0.0638735
$820$	0	0
$821$	−4.04014	−0.141002	−0.0705009	−	0.997512i	$-0.522460\pi$
$821$	−4.04014	−0.141002	−0.0705009	+	0.997512i	$0.522460\pi$
$822$	−3.84916	−0.134255
$823$	−10.8231	−0.377270	−0.188635	−	0.982047i	$-0.560406\pi$
$823$	−10.8231	−0.377270	−0.188635	+	0.982047i	$0.560406\pi$
$824$	−13.9875	−0.487277
$825$	0	0
$826$	13.0999	0.455803
$827$	52.2716	1.81766	0.908831	−	0.417165i	$-0.136976\pi$
$827$	52.2716	1.81766	0.908831	+	0.417165i	$0.136976\pi$
$828$	−0.465373	−0.0161728
$829$	12.5114	0.434538	0.217269	−	0.976112i	$-0.430285\pi$
$829$	12.5114	0.434538	0.217269	+	0.976112i	$0.430285\pi$
$830$	0	0
$831$	24.0266	0.833474
$832$	−10.5097	−0.364358
$833$	0.936390	0.0324440
$834$	−11.4119	−0.395161
$835$	0	0
$836$	−1.98458	−0.0686380
$837$	5.77891	0.199748
$838$	−29.7896	−1.02906
$839$	−30.3456	−1.04765	−0.523824	−	0.851827i	$-0.675495\pi$
$839$	−30.3456	−1.04765	−0.523824	+	0.851827i	$0.675495\pi$
$840$	0	0
$841$	−27.4532	−0.946661
$842$	−14.6055	−0.503337
$843$	25.0266	0.861963
$844$	5.18728	0.178553
$845$	0	0
$846$	−1.22883	−0.0422481
$847$	−26.5040	−0.910687
$848$	−14.5478	−0.499575
$849$	19.3174	0.662973
$850$	0	0
$851$	−4.39292	−0.150587
$852$	−1.21492	−0.0416224
$853$	−31.0174	−1.06202	−0.531008	−	0.847367i	$-0.678187\pi$
$853$	−31.0174	−1.06202	−0.531008	+	0.847367i	$0.678187\pi$
$854$	20.2443	0.692746
$855$	0	0
$856$	−41.0935	−1.40455
$857$	−2.96500	−0.101282	−0.0506412	−	0.998717i	$-0.516126\pi$
$857$	−2.96500	−0.101282	−0.0506412	+	0.998717i	$0.516126\pi$
$858$	−7.71546	−0.263401
$859$	34.3194	1.17096	0.585482	−	0.810685i	$-0.300905\pi$
$859$	34.3194	1.17096	0.585482	+	0.810685i	$0.300905\pi$
$860$	0	0
$861$	−4.12097	−0.140442
$862$	17.3349	0.590428
$863$	−52.4031	−1.78382	−0.891911	−	0.452210i	$-0.850636\pi$
$863$	−52.4031	−1.78382	−0.891911	+	0.452210i	$0.850636\pi$
$864$	−2.70340	−0.0919717
$865$	0	0
$866$	−30.6475	−1.04145
$867$	−16.9588	−0.575951
$868$	4.37424	0.148472
$869$	−67.3341	−2.28415
$870$	0	0
$871$	−8.86831	−0.300491
$872$	−3.23313	−0.109487
$873$	12.7106	0.430190
$874$	0.890885	0.0301346
$875$	0	0
$876$	2.67756	0.0904664
$877$	11.0483	0.373074	0.186537	−	0.982448i	$-0.440274\pi$
$877$	11.0483	0.373074	0.186537	+	0.982448i	$0.440274\pi$
$878$	7.76096	0.261920
$879$	−18.1029	−0.610595
$880$	0	0
$881$	−34.5976	−1.16562	−0.582811	−	0.812608i	$-0.698047\pi$
$881$	−34.5976	−1.16562	−0.582811	+	0.812608i	$0.698047\pi$
$882$	5.66919	0.190892
$883$	−31.2615	−1.05203	−0.526017	−	0.850474i	$-0.676315\pi$
$883$	−31.2615	−1.05203	−0.526017	+	0.850474i	$0.676315\pi$
$884$	−0.117675	−0.00395783
$885$	0	0
$886$	2.19657	0.0737953
$887$	−42.6829	−1.43315	−0.716576	−	0.697509i	$-0.754292\pi$
$887$	−42.6829	−1.43315	−0.716576	+	0.697509i	$0.754292\pi$
$888$	−14.1519	−0.474906
$889$	22.1889	0.744193
$890$	0	0
$891$	−5.30627	−0.177767
$892$	−0.0762117	−0.00255176
$893$	−0.763314	−0.0255433
$894$	−21.7804	−0.728445
$895$	0	0
$896$	8.50836	0.284244
$897$	−1.12385	−0.0375241
$898$	−4.79147	−0.159894
$899$	−7.18732	−0.239711
$900$	0	0
$901$	−1.06215	−0.0353854
$902$	17.3940	0.579156
$903$	14.9288	0.496800
$904$	4.57857	0.152281
$905$	0	0
$906$	−23.8674	−0.792942
$907$	−39.8208	−1.32223	−0.661114	−	0.750285i	$-0.729916\pi$
$907$	−39.8208	−1.32223	−0.661114	+	0.750285i	$0.729916\pi$
$908$	−6.21101	−0.206120
$909$	2.38330	0.0790492
$910$	0	0
$911$	4.04419	0.133990	0.0669950	−	0.997753i	$-0.478659\pi$
$911$	4.04419	0.133990	0.0669950	+	0.997753i	$0.478659\pi$
$912$	2.12199	0.0702661
$913$	−27.1298	−0.897865
$914$	−20.5310	−0.679105
$915$	0	0
$916$	6.67918	0.220686
$917$	−27.9447	−0.922817
$918$	0.249413	0.00823187
$919$	−19.9320	−0.657496	−0.328748	−	0.944418i	$-0.606627\pi$
$919$	−19.9320	−0.657496	−0.328748	+	0.944418i	$0.606627\pi$
$920$	0	0
$921$	5.93879	0.195690
$922$	15.7083	0.517325
$923$	−2.93395	−0.0965721
$924$	−4.01649	−0.132133
$925$	0	0
$926$	16.0194	0.526431
$927$	−4.57143	−0.150146
$928$	3.36227	0.110372
$929$	−48.2701	−1.58369	−0.791846	−	0.610721i	$-0.790880\pi$
$929$	−48.2701	−1.58369	−0.791846	+	0.610721i	$0.790880\pi$
$930$	0	0
$931$	3.52154	0.115414
$932$	−1.91947	−0.0628742
$933$	−15.1976	−0.497547
$934$	28.8001	0.942369
$935$	0	0
$936$	−3.62049	−0.118340
$937$	15.0013	0.490070	0.245035	−	0.969514i	$-0.421201\pi$
$937$	15.0013	0.490070	0.245035	+	0.969514i	$0.421201\pi$
$938$	14.2277	0.464550
$939$	−16.6263	−0.542579
$940$	0	0
$941$	11.1333	0.362934	0.181467	−	0.983397i	$-0.441915\pi$
$941$	11.1333	0.362934	0.181467	+	0.983397i	$0.441915\pi$
$942$	16.8048	0.547531
$943$	2.53363	0.0825065
$944$	−19.1837	−0.624378
$945$	0	0
$946$	−63.0122	−2.04870
$947$	−47.4062	−1.54049	−0.770247	−	0.637746i	$-0.779867\pi$
$947$	−47.4062	−1.54049	−0.770247	+	0.637746i	$0.779867\pi$
$948$	−6.21758	−0.201937
$949$	6.46614	0.209900
$950$	0	0
$951$	−1.96987	−0.0638773
$952$	0.959394	0.0310941
$953$	20.0790	0.650422	0.325211	−	0.945641i	$-0.394565\pi$
$953$	20.0790	0.650422	0.325211	+	0.945641i	$0.394565\pi$
$954$	−6.43058	−0.208198
$955$	0	0
$956$	−12.8282	−0.414892
$957$	6.59949	0.213331
$958$	11.4817	0.370957
$959$	−4.83901	−0.156260
$960$	0	0
$961$	2.39579	0.0772835
$962$	−6.72511	−0.216826
$963$	−13.4303	−0.432786
$964$	10.6413	0.342733
$965$	0	0
$966$	1.80302	0.0580112
$967$	−26.7220	−0.859321	−0.429660	−	0.902991i	$-0.641367\pi$
$967$	−26.7220	−0.859321	−0.429660	+	0.902991i	$0.641367\pi$
$968$	52.4947	1.68724
$969$	0.154928	0.00497702
$970$	0	0
$971$	−6.08762	−0.195361	−0.0976805	−	0.995218i	$-0.531142\pi$
$971$	−6.08762	−0.195361	−0.0976805	+	0.995218i	$0.531142\pi$
$972$	−0.489976	−0.0157160
$973$	−14.3465	−0.459929
$974$	7.20887	0.230987
$975$	0	0
$976$	−29.6462	−0.948952
$977$	−7.15004	−0.228750	−0.114375	−	0.993438i	$-0.536487\pi$
$977$	−7.15004	−0.228750	−0.114375	+	0.993438i	$0.536487\pi$
$978$	23.7424	0.759200
$979$	60.5155	1.93408
$980$	0	0
$981$	−1.05666	−0.0337366
$982$	40.0714	1.27873
$983$	−26.3688	−0.841034	−0.420517	−	0.907285i	$-0.638151\pi$
$983$	−26.3688	−0.841034	−0.420517	+	0.907285i	$0.638151\pi$
$984$	8.16215	0.260200
$985$	0	0
$986$	−0.310199	−0.00987876
$987$	−1.54483	−0.0491726
$988$	−0.442547	−0.0140793
$989$	−9.17845	−0.291858
$990$	0	0
$991$	−54.3223	−1.72561	−0.862803	−	0.505540i	$-0.831293\pi$
$991$	−54.3223	−1.72561	−0.862803	+	0.505540i	$0.831293\pi$
$992$	−15.6227	−0.496022
$993$	23.5199	0.746380
$994$	4.70702	0.149298
$995$	0	0
$996$	−2.50514	−0.0793784
$997$	−50.9587	−1.61388	−0.806938	−	0.590635i	$-0.798877\pi$
$997$	−50.9587	−1.61388	−0.806938	+	0.590635i	$0.798877\pi$
$998$	17.7234	0.561024
$999$	−4.62516	−0.146334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bi.1.4		13
5.2	odd	4		705.2.c.c.424.9	✓	26
5.3	odd	4		705.2.c.c.424.18	yes	26
5.4	even	2		3525.2.a.bh.1.10		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.c.424.9	✓	26	5.2	odd	4
705.2.c.c.424.18	yes	26	5.3	odd	4
3525.2.a.bh.1.10		13	5.4	even	2
3525.2.a.bi.1.4		13	1.1	even	1	trivial

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-1.22883 q^{2} +1.00000 q^{3} -0.489976 q^{4} -1.22883 q^{6} -1.54483 q^{7} +3.05976 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.22883 q^{2} +1.00000 q^{3} -0.489976 q^{4} -1.22883 q^{6} -1.54483 q^{7} +3.05976 q^{8} +1.00000 q^{9} -5.30627 q^{11} -0.489976 q^{12} -1.18326 q^{13} +1.89834 q^{14} -2.77997 q^{16} -0.202968 q^{17} -1.22883 q^{18} -0.763314 q^{19} -1.54483 q^{21} +6.52050 q^{22} +0.949787 q^{23} +3.05976 q^{24} +1.45403 q^{26} +1.00000 q^{27} +0.756933 q^{28} -1.24372 q^{29} +5.77891 q^{31} -2.70340 q^{32} -5.30627 q^{33} +0.249413 q^{34} -0.489976 q^{36} -4.62516 q^{37} +0.937983 q^{38} -1.18326 q^{39} +2.66758 q^{41} +1.89834 q^{42} -9.66369 q^{43} +2.59995 q^{44} -1.16713 q^{46} +1.00000 q^{47} -2.77997 q^{48} -4.61349 q^{49} -0.202968 q^{51} +0.579770 q^{52} +5.23309 q^{53} -1.22883 q^{54} -4.72682 q^{56} -0.763314 q^{57} +1.52832 q^{58} +6.90070 q^{59} +10.6642 q^{61} -7.10130 q^{62} -1.54483 q^{63} +8.88197 q^{64} +6.52050 q^{66} +7.49480 q^{67} +0.0994496 q^{68} +0.949787 q^{69} +2.47955 q^{71} +3.05976 q^{72} -5.46468 q^{73} +5.68354 q^{74} +0.374006 q^{76} +8.19731 q^{77} +1.45403 q^{78} +12.6895 q^{79} +1.00000 q^{81} -3.27800 q^{82} +5.11278 q^{83} +0.756933 q^{84} +11.8750 q^{86} -1.24372 q^{87} -16.2359 q^{88} -11.4045 q^{89} +1.82794 q^{91} -0.465373 q^{92} +5.77891 q^{93} -1.22883 q^{94} -2.70340 q^{96} +12.7106 q^{97} +5.66919 q^{98} -5.30627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 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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