LMFDB - Embedded newform 6025.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	7.7.31056073.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 $ x^7 - 3x^6 - 3x^5 + 11x^4 + x^3 - 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 241)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.27758$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.277577 q^{2} +0.494846 q^{3} -1.92295 q^{4} -0.137358 q^{6} -1.36627 q^{7} +1.08892 q^{8} -2.75513 q^{9} +O(q^{10})$	\(q-0.277577 q^{2} +0.494846 q^{3} -1.92295 q^{4} -0.137358 q^{6} -1.36627 q^{7} +1.08892 q^{8} -2.75513 q^{9} -4.69806 q^{11} -0.951564 q^{12} +0.0431968 q^{13} +0.379244 q^{14} +3.54364 q^{16} +7.31430 q^{17} +0.764761 q^{18} -0.697489 q^{19} -0.676090 q^{21} +1.30407 q^{22} -1.41195 q^{23} +0.538848 q^{24} -0.0119904 q^{26} -2.84790 q^{27} +2.62726 q^{28} +8.30334 q^{29} +3.39655 q^{31} -3.16148 q^{32} -2.32481 q^{33} -2.03028 q^{34} +5.29798 q^{36} -7.15948 q^{37} +0.193607 q^{38} +0.0213757 q^{39} +5.45541 q^{41} +0.187667 q^{42} +11.7568 q^{43} +9.03414 q^{44} +0.391925 q^{46} +5.24836 q^{47} +1.75356 q^{48} -5.13332 q^{49} +3.61945 q^{51} -0.0830653 q^{52} +8.57769 q^{53} +0.790512 q^{54} -1.48776 q^{56} -0.345149 q^{57} -2.30482 q^{58} -12.9925 q^{59} +10.1636 q^{61} -0.942804 q^{62} +3.76423 q^{63} -6.20973 q^{64} +0.645315 q^{66} -10.1259 q^{67} -14.0650 q^{68} -0.698697 q^{69} +1.86703 q^{71} -3.00012 q^{72} -6.47826 q^{73} +1.98731 q^{74} +1.34124 q^{76} +6.41880 q^{77} -0.00593342 q^{78} -12.9436 q^{79} +6.85611 q^{81} -1.51430 q^{82} +2.32915 q^{83} +1.30009 q^{84} -3.26342 q^{86} +4.10887 q^{87} -5.11582 q^{88} -14.5180 q^{89} -0.0590183 q^{91} +2.71511 q^{92} +1.68077 q^{93} -1.45682 q^{94} -1.56444 q^{96} +2.23725 q^{97} +1.42489 q^{98} +12.9438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	$ 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * 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 $

$2$	−0.277577	−0.196277	−0.0981383	−	0.995173i	$-0.531289\pi$
$2$	−0.277577	−0.196277	−0.0981383	+	0.995173i	$0.531289\pi$
$3$	0.494846	0.285699	0.142850	−	0.989744i	$-0.454373\pi$
$3$	0.494846	0.285699	0.142850	+	0.989744i	$0.454373\pi$
$4$	−1.92295	−0.961475
$5$	0	0
$5$	0	0
$6$	−0.137358	−0.0560761
$7$	−1.36627	−0.516400	−0.258200	−	0.966092i	$-0.583129\pi$
$7$	−1.36627	−0.516400	−0.258200	+	0.966092i	$0.583129\pi$
$8$	1.08892	0.384992
$9$	−2.75513	−0.918376
$10$	0	0
$11$	−4.69806	−1.41652	−0.708259	−	0.705952i	$-0.750519\pi$
$11$	−4.69806	−1.41652	−0.708259	+	0.705952i	$0.750519\pi$
$12$	−0.951564	−0.274693
$13$	0.0431968	0.0119806	0.00599032	−	0.999982i	$-0.498093\pi$
$13$	0.0431968	0.0119806	0.00599032	+	0.999982i	$0.498093\pi$
$14$	0.379244	0.101357
$15$	0	0
$16$	3.54364	0.885911
$17$	7.31430	1.77398	0.886989	−	0.461790i	$-0.152793\pi$
$17$	7.31430	1.77398	0.886989	+	0.461790i	$0.152793\pi$
$18$	0.764761	0.180256
$19$	−0.697489	−0.160015	−0.0800075	−	0.996794i	$-0.525494\pi$
$19$	−0.697489	−0.160015	−0.0800075	+	0.996794i	$0.525494\pi$
$20$	0	0
$21$	−0.676090	−0.147535
$22$	1.30407	0.278030
$23$	−1.41195	−0.294412	−0.147206	−	0.989106i	$-0.547028\pi$
$23$	−1.41195	−0.294412	−0.147206	+	0.989106i	$0.547028\pi$
$24$	0.538848	0.109992
$25$	0	0
$26$	−0.0119904	−0.00235152
$27$	−2.84790	−0.548078
$28$	2.62726	0.496506
$29$	8.30334	1.54189	0.770946	−	0.636901i	$-0.219784\pi$
$29$	8.30334	1.54189	0.770946	+	0.636901i	$0.219784\pi$
$30$	0	0
$31$	3.39655	0.610038	0.305019	−	0.952346i	$-0.401337\pi$
$31$	3.39655	0.610038	0.305019	+	0.952346i	$0.401337\pi$
$32$	−3.16148	−0.558875
$33$	−2.32481	−0.404698
$34$	−2.03028	−0.348191
$35$	0	0
$36$	5.29798	0.882996
$37$	−7.15948	−1.17701	−0.588506	−	0.808493i	$-0.700284\pi$
$37$	−7.15948	−1.17701	−0.588506	+	0.808493i	$0.700284\pi$
$38$	0.193607	0.0314072
$39$	0.0213757	0.00342286
$40$	0	0
$41$	5.45541	0.851992	0.425996	−	0.904725i	$-0.359924\pi$
$41$	5.45541	0.851992	0.425996	+	0.904725i	$0.359924\pi$
$42$	0.187667	0.0289577
$43$	11.7568	1.79290	0.896448	−	0.443149i	$-0.146139\pi$
$43$	11.7568	1.79290	0.896448	+	0.443149i	$0.146139\pi$
$44$	9.03414	1.36195
$45$	0	0
$46$	0.391925	0.0577862
$47$	5.24836	0.765551	0.382776	−	0.923841i	$-0.374968\pi$
$47$	5.24836	0.765551	0.382776	+	0.923841i	$0.374968\pi$
$48$	1.75356	0.253104
$49$	−5.13332	−0.733331
$50$	0	0
$51$	3.61945	0.506824
$52$	−0.0830653	−0.0115191
$53$	8.57769	1.17824	0.589118	−	0.808047i	$-0.299475\pi$
$53$	8.57769	1.17824	0.589118	+	0.808047i	$0.299475\pi$
$54$	0.790512	0.107575
$55$	0	0
$56$	−1.48776	−0.198810
$57$	−0.345149	−0.0457162
$58$	−2.30482	−0.302637
$59$	−12.9925	−1.69148	−0.845738	−	0.533598i	$-0.820840\pi$
$59$	−12.9925	−1.69148	−0.845738	+	0.533598i	$0.820840\pi$
$60$	0	0
$61$	10.1636	1.30132	0.650658	−	0.759371i	$-0.274493\pi$
$61$	10.1636	1.30132	0.650658	+	0.759371i	$0.274493\pi$
$62$	−0.942804	−0.119736
$63$	3.76423	0.474249
$64$	−6.20973	−0.776216
$65$	0	0
$66$	0.645315	0.0794328
$67$	−10.1259	−1.23707	−0.618536	−	0.785757i	$-0.712274\pi$
$67$	−10.1259	−1.23707	−0.618536	+	0.785757i	$0.712274\pi$
$68$	−14.0650	−1.70564
$69$	−0.698697	−0.0841132
$70$	0	0
$71$	1.86703	0.221576	0.110788	−	0.993844i	$-0.464663\pi$
$71$	1.86703	0.221576	0.110788	+	0.993844i	$0.464663\pi$
$72$	−3.00012	−0.353567
$73$	−6.47826	−0.758223	−0.379111	−	0.925351i	$-0.623770\pi$
$73$	−6.47826	−0.758223	−0.379111	+	0.925351i	$0.623770\pi$
$74$	1.98731	0.231020
$75$	0	0
$76$	1.34124	0.153850
$77$	6.41880	0.731490
$78$	−0.00593342	−0.000671827 0
$79$	−12.9436	−1.45627	−0.728136	−	0.685432i	$-0.759613\pi$
$79$	−12.9436	−1.45627	−0.728136	+	0.685432i	$0.759613\pi$
$80$	0	0
$81$	6.85611	0.761790
$82$	−1.51430	−0.167226
$83$	2.32915	0.255657	0.127829	−	0.991796i	$-0.459199\pi$
$83$	2.32915	0.255657	0.127829	+	0.991796i	$0.459199\pi$
$84$	1.30009	0.141851
$85$	0	0
$86$	−3.26342	−0.351904
$87$	4.10887	0.440517
$88$	−5.11582	−0.545348
$89$	−14.5180	−1.53890	−0.769450	−	0.638707i	$-0.779470\pi$
$89$	−14.5180	−1.53890	−0.769450	+	0.638707i	$0.779470\pi$
$90$	0	0
$91$	−0.0590183	−0.00618680
$92$	2.71511	0.283070
$93$	1.68077	0.174287
$94$	−1.45682	−0.150260
$95$	0	0
$96$	−1.56444	−0.159670
$97$	2.23725	0.227158	0.113579	−	0.993529i	$-0.463769\pi$
$97$	2.23725	0.227158	0.113579	+	0.993529i	$0.463769\pi$
$98$	1.42489	0.143936
$99$	12.9438	1.30090
$100$	0	0
$101$	−4.01607	−0.399614	−0.199807	−	0.979835i	$-0.564031\pi$
$101$	−4.01607	−0.399614	−0.199807	+	0.979835i	$0.564031\pi$
$102$	−1.00468	−0.0994778
$103$	5.25187	0.517482	0.258741	−	0.965947i	$-0.416692\pi$
$103$	5.25187	0.517482	0.258741	+	0.965947i	$0.416692\pi$
$104$	0.0470379	0.00461245
$105$	0	0
$106$	−2.38097	−0.231260
$107$	−5.60385	−0.541745	−0.270873	−	0.962615i	$-0.587312\pi$
$107$	−5.60385	−0.541745	−0.270873	+	0.962615i	$0.587312\pi$
$108$	5.47637	0.526964
$109$	−4.77557	−0.457416	−0.228708	−	0.973495i	$-0.573450\pi$
$109$	−4.77557	−0.457416	−0.228708	+	0.973495i	$0.573450\pi$
$110$	0	0
$111$	−3.54284	−0.336271
$112$	−4.84155	−0.457484
$113$	12.6186	1.18706	0.593531	−	0.804811i	$-0.297733\pi$
$113$	12.6186	1.18706	0.593531	+	0.804811i	$0.297733\pi$
$114$	0.0958056	0.00897301
$115$	0	0
$116$	−15.9669	−1.48249
$117$	−0.119013	−0.0110027
$118$	3.60642	0.331997
$119$	−9.99327	−0.916082
$120$	0	0
$121$	11.0718	1.00653
$122$	−2.82118	−0.255418
$123$	2.69959	0.243413
$124$	−6.53139	−0.586536
$125$	0	0
$126$	−1.04487	−0.0930840
$127$	−0.427651	−0.0379479	−0.0189740	−	0.999820i	$-0.506040\pi$
$127$	−0.427651	−0.0379479	−0.0189740	+	0.999820i	$0.506040\pi$
$128$	8.04663	0.711229
$129$	5.81780	0.512229
$130$	0	0
$131$	−13.3633	−1.16756	−0.583780	−	0.811912i	$-0.698427\pi$
$131$	−13.3633	−1.16756	−0.583780	+	0.811912i	$0.698427\pi$
$132$	4.47050	0.389107
$133$	0.952955	0.0826317
$134$	2.81071	0.242808
$135$	0	0
$136$	7.96470	0.682967
$137$	−11.2702	−0.962874	−0.481437	−	0.876481i	$-0.659885\pi$
$137$	−11.2702	−0.962874	−0.481437	+	0.876481i	$0.659885\pi$
$138$	0.193942	0.0165095
$139$	−0.927184	−0.0786427	−0.0393214	−	0.999227i	$-0.512520\pi$
$139$	−0.927184	−0.0786427	−0.0393214	+	0.999227i	$0.512520\pi$
$140$	0	0
$141$	2.59713	0.218717
$142$	−0.518245	−0.0434902
$143$	−0.202941	−0.0169708
$144$	−9.76319	−0.813599
$145$	0	0
$146$	1.79822	0.148821
$147$	−2.54020	−0.209512
$148$	13.7673	1.13167
$149$	12.8757	1.05481	0.527407	−	0.849612i	$-0.323164\pi$
$149$	12.8757	1.05481	0.527407	+	0.849612i	$0.323164\pi$
$150$	0	0
$151$	−21.2436	−1.72878	−0.864390	−	0.502823i	$-0.832295\pi$
$151$	−21.2436	−1.72878	−0.864390	+	0.502823i	$0.832295\pi$
$152$	−0.759511	−0.0616045
$153$	−20.1518	−1.62918
$154$	−1.78171	−0.143574
$155$	0	0
$156$	−0.0411045	−0.00329099
$157$	−17.1798	−1.37110	−0.685550	−	0.728026i	$-0.740438\pi$
$157$	−17.1798	−1.37110	−0.685550	+	0.728026i	$0.740438\pi$
$158$	3.59286	0.285832
$159$	4.24463	0.336621
$160$	0	0
$161$	1.92910	0.152034
$162$	−1.90310	−0.149522
$163$	−11.1081	−0.870055	−0.435028	−	0.900417i	$-0.643261\pi$
$163$	−11.1081	−0.870055	−0.435028	+	0.900417i	$0.643261\pi$
$164$	−10.4905	−0.819170
$165$	0	0
$166$	−0.646519	−0.0501796
$167$	22.3791	1.73174	0.865872	−	0.500266i	$-0.166764\pi$
$167$	22.3791	1.73174	0.865872	+	0.500266i	$0.166764\pi$
$168$	−0.736209	−0.0567998
$169$	−12.9981	−0.999856
$170$	0	0
$171$	1.92167	0.146954
$172$	−22.6078	−1.72383
$173$	−4.16100	−0.316355	−0.158178	−	0.987411i	$-0.550562\pi$
$173$	−4.16100	−0.316355	−0.158178	+	0.987411i	$0.550562\pi$
$174$	−1.14053	−0.0864633
$175$	0	0
$176$	−16.6482	−1.25491
$177$	−6.42927	−0.483254
$178$	4.02985	0.302050
$179$	−5.79009	−0.432772	−0.216386	−	0.976308i	$-0.569427\pi$
$179$	−5.79009	−0.432772	−0.216386	+	0.976308i	$0.569427\pi$
$180$	0	0
$181$	17.4917	1.30015	0.650076	−	0.759869i	$-0.274737\pi$
$181$	17.4917	1.30015	0.650076	+	0.759869i	$0.274737\pi$
$182$	0.0163821	0.00121432
$183$	5.02941	0.371785
$184$	−1.53750	−0.113346
$185$	0	0
$186$	−0.466542	−0.0342085
$187$	−34.3630	−2.51287
$188$	−10.0923	−0.736059
$189$	3.89099	0.283028
$190$	0	0
$191$	−21.6074	−1.56346	−0.781728	−	0.623620i	$-0.785661\pi$
$191$	−21.6074	−1.56346	−0.781728	+	0.623620i	$0.785661\pi$
$192$	−3.07286	−0.221764
$193$	−2.30886	−0.166195	−0.0830977	−	0.996541i	$-0.526481\pi$
$193$	−2.30886	−0.166195	−0.0830977	+	0.996541i	$0.526481\pi$
$194$	−0.621008	−0.0445858
$195$	0	0
$196$	9.87112	0.705080
$197$	−1.91876	−0.136706	−0.0683531	−	0.997661i	$-0.521774\pi$
$197$	−1.91876	−0.136706	−0.0683531	+	0.997661i	$0.521774\pi$
$198$	−3.59289	−0.255336
$199$	21.2430	1.50588	0.752938	−	0.658091i	$-0.228636\pi$
$199$	21.2430	1.50588	0.752938	+	0.658091i	$0.228636\pi$
$200$	0	0
$201$	−5.01074	−0.353430
$202$	1.11477	0.0784349
$203$	−11.3446	−0.796232
$204$	−6.96002	−0.487299
$205$	0	0
$206$	−1.45780	−0.101570
$207$	3.89010	0.270381
$208$	0.153074	0.0106138
$209$	3.27685	0.226664
$210$	0	0
$211$	−19.0961	−1.31463	−0.657314	−	0.753616i	$-0.728308\pi$
$211$	−19.0961	−1.31463	−0.657314	+	0.753616i	$0.728308\pi$
$212$	−16.4945	−1.13285
$213$	0.923892	0.0633040
$214$	1.55550	0.106332
$215$	0	0
$216$	−3.10114	−0.211006
$217$	−4.64058	−0.315023
$218$	1.32559	0.0897802
$219$	−3.20574	−0.216624
$220$	0	0
$221$	0.315954	0.0212534
$222$	0.983410	0.0660022
$223$	−8.41781	−0.563698	−0.281849	−	0.959459i	$-0.590948\pi$
$223$	−8.41781	−0.563698	−0.281849	+	0.959459i	$0.590948\pi$
$224$	4.31942	0.288603
$225$	0	0
$226$	−3.50265	−0.232993
$227$	−1.82854	−0.121364	−0.0606821	−	0.998157i	$-0.519328\pi$
$227$	−1.82854	−0.121364	−0.0606821	+	0.998157i	$0.519328\pi$
$228$	0.663705	0.0439550
$229$	2.52038	0.166551	0.0832756	−	0.996527i	$-0.473462\pi$
$229$	2.52038	0.166551	0.0832756	+	0.996527i	$0.473462\pi$
$230$	0	0
$231$	3.17631	0.208986
$232$	9.04169	0.593616
$233$	−16.3812	−1.07317	−0.536585	−	0.843847i	$-0.680286\pi$
$233$	−16.3812	−1.07317	−0.536585	+	0.843847i	$0.680286\pi$
$234$	0.0330352	0.00215958
$235$	0	0
$236$	24.9839	1.62631
$237$	−6.40510	−0.416056
$238$	2.77390	0.179805
$239$	−10.7430	−0.694909	−0.347455	−	0.937697i	$-0.612954\pi$
$239$	−10.7430	−0.694909	−0.347455	+	0.937697i	$0.612954\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−3.07327	−0.197557
$243$	11.9364	0.765721
$244$	−19.5441	−1.25118
$245$	0	0
$246$	−0.749343	−0.0477764
$247$	−0.0301293	−0.00191708
$248$	3.69857	0.234860
$249$	1.15257	0.0730411
$250$	0	0
$251$	23.8819	1.50741	0.753706	−	0.657212i	$-0.228264\pi$
$251$	23.8819	1.50741	0.753706	+	0.657212i	$0.228264\pi$
$252$	−7.23844	−0.455979
$253$	6.63342	0.417040
$254$	0.118706	0.00744829
$255$	0	0
$256$	10.1859	0.636619
$257$	−5.25407	−0.327740	−0.163870	−	0.986482i	$-0.552398\pi$
$257$	−5.25407	−0.327740	−0.163870	+	0.986482i	$0.552398\pi$
$258$	−1.61489	−0.100539
$259$	9.78175	0.607808
$260$	0	0
$261$	−22.8768	−1.41604
$262$	3.70936	0.229165
$263$	1.10964	0.0684235	0.0342118	−	0.999415i	$-0.489108\pi$
$263$	1.10964	0.0684235	0.0342118	+	0.999415i	$0.489108\pi$
$264$	−2.53154	−0.155806
$265$	0	0
$266$	−0.264519	−0.0162187
$267$	−7.18414	−0.439662
$268$	19.4715	1.18941
$269$	−2.84634	−0.173544	−0.0867722	−	0.996228i	$-0.527655\pi$
$269$	−2.84634	−0.173544	−0.0867722	+	0.996228i	$0.527655\pi$
$270$	0	0
$271$	13.1029	0.795946	0.397973	−	0.917397i	$-0.369714\pi$
$271$	13.1029	0.795946	0.397973	+	0.917397i	$0.369714\pi$
$272$	25.9193	1.57159
$273$	−0.0292049	−0.00176756
$274$	3.12834	0.188990
$275$	0	0
$276$	1.34356	0.0808728
$277$	23.4634	1.40978	0.704888	−	0.709318i	$-0.250997\pi$
$277$	23.4634	1.40978	0.704888	+	0.709318i	$0.250997\pi$
$278$	0.257365	0.0154357
$279$	−9.35792	−0.560244
$280$	0	0
$281$	8.91165	0.531625	0.265812	−	0.964025i	$-0.414360\pi$
$281$	8.91165	0.531625	0.265812	+	0.964025i	$0.414360\pi$
$282$	−0.720903	−0.0429291
$283$	15.8040	0.939453	0.469726	−	0.882812i	$-0.344353\pi$
$283$	15.8040	0.939453	0.469726	+	0.882812i	$0.344353\pi$
$284$	−3.59021	−0.213040
$285$	0	0
$286$	0.0563318	0.00333097
$287$	−7.45354	−0.439968
$288$	8.71027	0.513258
$289$	36.4990	2.14700
$290$	0	0
$291$	1.10709	0.0648988
$292$	12.4574	0.729013
$293$	−32.9425	−1.92452	−0.962261	−	0.272127i	$-0.912273\pi$
$293$	−32.9425	−1.92452	−0.962261	+	0.272127i	$0.912273\pi$
$294$	0.705102	0.0411224
$295$	0	0
$296$	−7.79611	−0.453140
$297$	13.3796	0.776363
$298$	−3.57399	−0.207036
$299$	−0.0609917	−0.00352724
$300$	0	0
$301$	−16.0629	−0.925851
$302$	5.89674	0.339319
$303$	−1.98733	−0.114169
$304$	−2.47165	−0.141759
$305$	0	0
$306$	5.59369	0.319770
$307$	−20.2343	−1.15483	−0.577416	−	0.816450i	$-0.695939\pi$
$307$	−20.2343	−1.15483	−0.577416	+	0.816450i	$0.695939\pi$
$308$	−12.3430	−0.703309
$309$	2.59886	0.147844
$310$	0	0
$311$	2.27289	0.128884	0.0644420	−	0.997921i	$-0.479473\pi$
$311$	2.27289	0.128884	0.0644420	+	0.997921i	$0.479473\pi$
$312$	0.0232765	0.00131777
$313$	−13.1142	−0.741257	−0.370629	−	0.928781i	$-0.620858\pi$
$313$	−13.1142	−0.741257	−0.370629	+	0.928781i	$0.620858\pi$
$314$	4.76873	0.269115
$315$	0	0
$316$	24.8900	1.40017
$317$	7.86525	0.441757	0.220878	−	0.975301i	$-0.429108\pi$
$317$	7.86525	0.441757	0.220878	+	0.975301i	$0.429108\pi$
$318$	−1.17821	−0.0660709
$319$	−39.0096	−2.18412
$320$	0	0
$321$	−2.77304	−0.154776
$322$	−0.535473	−0.0298407
$323$	−5.10164	−0.283863
$324$	−13.1840	−0.732443
$325$	0	0
$326$	3.08336	0.170772
$327$	−2.36317	−0.130683
$328$	5.94051	0.328010
$329$	−7.17065	−0.395331
$330$	0	0
$331$	−19.3752	−1.06496	−0.532480	−	0.846443i	$-0.678740\pi$
$331$	−19.3752	−1.06496	−0.532480	+	0.846443i	$0.678740\pi$
$332$	−4.47884	−0.245808
$333$	19.7253	1.08094
$334$	−6.21192	−0.339901
$335$	0	0
$336$	−2.39582	−0.130703
$337$	26.2459	1.42970	0.714852	−	0.699276i	$-0.246494\pi$
$337$	26.2459	1.42970	0.714852	+	0.699276i	$0.246494\pi$
$338$	3.60798	0.196249
$339$	6.24428	0.339143
$340$	0	0
$341$	−15.9572	−0.864130
$342$	−0.533412	−0.0288436
$343$	16.5773	0.895092
$344$	12.8022	0.690250
$345$	0	0
$346$	1.15500	0.0620931
$347$	3.65189	0.196044	0.0980219	−	0.995184i	$-0.468748\pi$
$347$	3.65189	0.196044	0.0980219	+	0.995184i	$0.468748\pi$
$348$	−7.90116	−0.423547
$349$	−0.818652	−0.0438214	−0.0219107	−	0.999760i	$-0.506975\pi$
$349$	−0.818652	−0.0438214	−0.0219107	+	0.999760i	$0.506975\pi$
$350$	0	0
$351$	−0.123020	−0.00656633
$352$	14.8528	0.791658
$353$	28.5367	1.51886	0.759428	−	0.650591i	$-0.225479\pi$
$353$	28.5367	1.51886	0.759428	+	0.650591i	$0.225479\pi$
$354$	1.78462	0.0948514
$355$	0	0
$356$	27.9173	1.47961
$357$	−4.94513	−0.261724
$358$	1.60720	0.0849430
$359$	−15.8623	−0.837180	−0.418590	−	0.908175i	$-0.637476\pi$
$359$	−15.8623	−0.837180	−0.418590	+	0.908175i	$0.637476\pi$
$360$	0	0
$361$	−18.5135	−0.974395
$362$	−4.85531	−0.255189
$363$	5.47882	0.287563
$364$	0.113489	0.00594845
$365$	0	0
$366$	−1.39605	−0.0729727
$367$	−13.9937	−0.730463	−0.365232	−	0.930917i	$-0.619010\pi$
$367$	−13.9937	−0.730463	−0.365232	+	0.930917i	$0.619010\pi$
$368$	−5.00344	−0.260822
$369$	−15.0304	−0.782449
$370$	0	0
$371$	−11.7194	−0.608441
$372$	−3.23203	−0.167573
$373$	−12.2336	−0.633434	−0.316717	−	0.948520i	$-0.602581\pi$
$373$	−12.2336	−0.633434	−0.316717	+	0.948520i	$0.602581\pi$
$374$	9.53839	0.493218
$375$	0	0
$376$	5.71505	0.294731
$377$	0.358678	0.0184728
$378$	−1.08005	−0.0555517
$379$	0.284829	0.0146307	0.00731535	−	0.999973i	$-0.497671\pi$
$379$	0.284829	0.0146307	0.00731535	+	0.999973i	$0.497671\pi$
$380$	0	0
$381$	−0.211621	−0.0108417
$382$	5.99772	0.306870
$383$	−29.8268	−1.52408	−0.762038	−	0.647532i	$-0.775801\pi$
$383$	−29.8268	−1.52408	−0.762038	+	0.647532i	$0.775801\pi$
$384$	3.98184	0.203197
$385$	0	0
$386$	0.640887	0.0326203
$387$	−32.3915	−1.64655
$388$	−4.30211	−0.218407
$389$	−8.88544	−0.450510	−0.225255	−	0.974300i	$-0.572321\pi$
$389$	−8.88544	−0.450510	−0.225255	+	0.974300i	$0.572321\pi$
$390$	0	0
$391$	−10.3274	−0.522280
$392$	−5.58978	−0.282327
$393$	−6.61279	−0.333571
$394$	0.532605	0.0268322
$395$	0	0
$396$	−24.8902	−1.25078
$397$	29.5831	1.48473	0.742367	−	0.669993i	$-0.233703\pi$
$397$	29.5831	1.48473	0.742367	+	0.669993i	$0.233703\pi$
$398$	−5.89657	−0.295569
$399$	0.471566	0.0236078
$400$	0	0
$401$	6.30306	0.314760	0.157380	−	0.987538i	$-0.449695\pi$
$401$	6.30306	0.314760	0.157380	+	0.987538i	$0.449695\pi$
$402$	1.39087	0.0693701
$403$	0.146720	0.00730864
$404$	7.72270	0.384219
$405$	0	0
$406$	3.14899	0.156282
$407$	33.6357	1.66726
$408$	3.94130	0.195123
$409$	−7.63163	−0.377360	−0.188680	−	0.982039i	$-0.560421\pi$
$409$	−7.63163	−0.377360	−0.188680	+	0.982039i	$0.560421\pi$
$410$	0	0
$411$	−5.57699	−0.275092
$412$	−10.0991	−0.497546
$413$	17.7512	0.873478
$414$	−1.07980	−0.0530694
$415$	0	0
$416$	−0.136566	−0.00669568
$417$	−0.458813	−0.0224682
$418$	−0.909578	−0.0444889
$419$	2.34760	0.114688	0.0573439	−	0.998354i	$-0.481737\pi$
$419$	2.34760	0.114688	0.0573439	+	0.998354i	$0.481737\pi$
$420$	0	0
$421$	8.61693	0.419963	0.209982	−	0.977705i	$-0.432660\pi$
$421$	8.61693	0.419963	0.209982	+	0.977705i	$0.432660\pi$
$422$	5.30064	0.258031
$423$	−14.4599	−0.703064
$424$	9.34043	0.453611
$425$	0	0
$426$	−0.256451	−0.0124251
$427$	−13.8862	−0.671999
$428$	10.7759	0.520875
$429$	−0.100425	−0.00484854
$430$	0	0
$431$	−2.73295	−0.131641	−0.0658207	−	0.997831i	$-0.520967\pi$
$431$	−2.73295	−0.131641	−0.0658207	+	0.997831i	$0.520967\pi$
$432$	−10.0919	−0.485549
$433$	−14.8768	−0.714934	−0.357467	−	0.933926i	$-0.616360\pi$
$433$	−14.8768	−0.714934	−0.357467	+	0.933926i	$0.616360\pi$
$434$	1.28812	0.0618317
$435$	0	0
$436$	9.18318	0.439795
$437$	0.984819	0.0471103
$438$	0.889839	0.0425182
$439$	−19.8115	−0.945552	−0.472776	−	0.881183i	$-0.656748\pi$
$439$	−19.8115	−0.945552	−0.472776	+	0.881183i	$0.656748\pi$
$440$	0	0
$441$	14.1430	0.673474
$442$	−0.0877017	−0.00417154
$443$	39.5818	1.88059	0.940293	−	0.340366i	$-0.110551\pi$
$443$	39.5818	1.88059	0.940293	+	0.340366i	$0.110551\pi$
$444$	6.81270	0.323316
$445$	0	0
$446$	2.33659	0.110641
$447$	6.37146	0.301360
$448$	8.48414	0.400838
$449$	−22.9205	−1.08169	−0.540843	−	0.841124i	$-0.681895\pi$
$449$	−22.9205	−1.08169	−0.540843	+	0.841124i	$0.681895\pi$
$450$	0	0
$451$	−25.6299	−1.20686
$452$	−24.2650	−1.14133
$453$	−10.5123	−0.493911
$454$	0.507560	0.0238210
$455$	0	0
$456$	−0.375841	−0.0176003
$457$	9.66494	0.452107	0.226053	−	0.974115i	$-0.427418\pi$
$457$	9.66494	0.452107	0.226053	+	0.974115i	$0.427418\pi$
$458$	−0.699599	−0.0326901
$459$	−20.8304	−0.972279
$460$	0	0
$461$	6.28046	0.292510	0.146255	−	0.989247i	$-0.453278\pi$
$461$	6.28046	0.292510	0.146255	+	0.989247i	$0.453278\pi$
$462$	−0.881672	−0.0410191
$463$	7.64337	0.355218	0.177609	−	0.984101i	$-0.443164\pi$
$463$	7.64337	0.355218	0.177609	+	0.984101i	$0.443164\pi$
$464$	29.4241	1.36598
$465$	0	0
$466$	4.54705	0.210638
$467$	−25.8943	−1.19824	−0.599122	−	0.800658i	$-0.704484\pi$
$467$	−25.8943	−1.19824	−0.599122	+	0.800658i	$0.704484\pi$
$468$	0.228856	0.0105789
$469$	13.8346	0.638823
$470$	0	0
$471$	−8.50136	−0.391722
$472$	−14.1478	−0.651205
$473$	−55.2342	−2.53967
$474$	1.77791	0.0816621
$475$	0	0
$476$	19.2166	0.880790
$477$	−23.6326	−1.08206
$478$	2.98202	0.136394
$479$	12.6131	0.576309	0.288155	−	0.957584i	$-0.406958\pi$
$479$	12.6131	0.576309	0.288155	+	0.957584i	$0.406958\pi$
$480$	0	0
$481$	−0.309267	−0.0141013
$482$	0.277577	0.0126433
$483$	0.954605	0.0434360
$484$	−21.2905	−0.967749
$485$	0	0
$486$	−3.31328	−0.150293
$487$	−31.7807	−1.44012	−0.720061	−	0.693910i	$-0.755886\pi$
$487$	−31.7807	−1.44012	−0.720061	+	0.693910i	$0.755886\pi$
$488$	11.0674	0.500996
$489$	−5.49680	−0.248574
$490$	0	0
$491$	−10.2151	−0.461001	−0.230500	−	0.973072i	$-0.574036\pi$
$491$	−10.2151	−0.461001	−0.230500	+	0.973072i	$0.574036\pi$
$492$	−5.19117	−0.234036
$493$	60.7331	2.73528
$494$	0.00836321	0.000376278 0
$495$	0	0
$496$	12.0361	0.540439
$497$	−2.55086	−0.114422
$498$	−0.319927	−0.0143363
$499$	−9.35390	−0.418738	−0.209369	−	0.977837i	$-0.567141\pi$
$499$	−9.35390	−0.418738	−0.209369	+	0.977837i	$0.567141\pi$
$500$	0	0
$501$	11.0742	0.494758
$502$	−6.62907	−0.295870
$503$	13.7659	0.613792	0.306896	−	0.951743i	$-0.400710\pi$
$503$	13.7659	0.613792	0.306896	+	0.951743i	$0.400710\pi$
$504$	4.09896	0.182582
$505$	0	0
$506$	−1.84129	−0.0818552
$507$	−6.43207	−0.285658
$508$	0.822353	0.0364860
$509$	22.6367	1.00335	0.501677	−	0.865055i	$-0.332717\pi$
$509$	22.6367	1.00335	0.501677	+	0.865055i	$0.332717\pi$
$510$	0	0
$511$	8.85102	0.391546
$512$	−18.9206	−0.836182
$513$	1.98638	0.0877008
$514$	1.45841	0.0643277
$515$	0	0
$516$	−11.1873	−0.492496
$517$	−24.6571	−1.08442
$518$	−2.71519	−0.119299
$519$	−2.05905	−0.0903824
$520$	0	0
$521$	−10.8738	−0.476389	−0.238194	−	0.971218i	$-0.576555\pi$
$521$	−10.8738	−0.476389	−0.238194	+	0.971218i	$0.576555\pi$
$522$	6.35007	0.277935
$523$	3.43232	0.150085	0.0750424	−	0.997180i	$-0.476091\pi$
$523$	3.43232	0.150085	0.0750424	+	0.997180i	$0.476091\pi$
$524$	25.6970	1.12258
$525$	0	0
$526$	−0.308011	−0.0134299
$527$	24.8434	1.08219
$528$	−8.23831	−0.358526
$529$	−21.0064	−0.913322
$530$	0	0
$531$	35.7959	1.55341
$532$	−1.83249	−0.0794483
$533$	0.235656	0.0102074
$534$	1.99415	0.0862955
$535$	0	0
$536$	−11.0263	−0.476263
$537$	−2.86520	−0.123643
$538$	0.790079	0.0340627
$539$	24.1167	1.03878
$540$	0	0
$541$	−1.00758	−0.0433193	−0.0216597	−	0.999765i	$-0.506895\pi$
$541$	−1.00758	−0.0433193	−0.0216597	+	0.999765i	$0.506895\pi$
$542$	−3.63707	−0.156226
$543$	8.65571	0.371452
$544$	−23.1240	−0.991433
$545$	0	0
$546$	0.00810662	0.000346931 0
$547$	−10.6391	−0.454894	−0.227447	−	0.973791i	$-0.573038\pi$
$547$	−10.6391	−0.454894	−0.227447	+	0.973791i	$0.573038\pi$
$548$	21.6720	0.925780
$549$	−28.0020	−1.19510
$550$	0	0
$551$	−5.79149	−0.246726
$552$	−0.760826	−0.0323829
$553$	17.6844	0.752019
$554$	−6.51289	−0.276706
$555$	0	0
$556$	1.78293	0.0756130
$557$	−18.9092	−0.801207	−0.400603	−	0.916252i	$-0.631199\pi$
$557$	−18.9092	−0.801207	−0.400603	+	0.916252i	$0.631199\pi$
$558$	2.59755	0.109963
$559$	0.507856	0.0214800
$560$	0	0
$561$	−17.0044	−0.717926
$562$	−2.47367	−0.104346
$563$	−28.1768	−1.18751	−0.593756	−	0.804645i	$-0.702356\pi$
$563$	−28.1768	−1.18751	−0.593756	+	0.804645i	$0.702356\pi$
$564$	−4.99415	−0.210291
$565$	0	0
$566$	−4.38684	−0.184393
$567$	−9.36727	−0.393388
$568$	2.03305	0.0853049
$569$	−0.499818	−0.0209534	−0.0104767	−	0.999945i	$-0.503335\pi$
$569$	−0.499818	−0.0209534	−0.0104767	+	0.999945i	$0.503335\pi$
$570$	0	0
$571$	−28.2303	−1.18140	−0.590702	−	0.806890i	$-0.701149\pi$
$571$	−28.2303	−1.18140	−0.590702	+	0.806890i	$0.701149\pi$
$572$	0.390246	0.0163170
$573$	−10.6923	−0.446678
$574$	2.06893	0.0863555
$575$	0	0
$576$	17.1086	0.712858
$577$	36.3728	1.51422	0.757111	−	0.653287i	$-0.226610\pi$
$577$	36.3728	1.51422	0.757111	+	0.653287i	$0.226610\pi$
$578$	−10.1313	−0.421406
$579$	−1.14253	−0.0474819
$580$	0	0
$581$	−3.18224	−0.132021
$582$	−0.307303	−0.0127381
$583$	−40.2985	−1.66899
$584$	−7.05432	−0.291910
$585$	0	0
$586$	9.14409	0.377739
$587$	−16.1223	−0.665437	−0.332718	−	0.943026i	$-0.607966\pi$
$587$	−16.1223	−0.665437	−0.332718	+	0.943026i	$0.607966\pi$
$588$	4.88468	0.201441
$589$	−2.36905	−0.0976152
$590$	0	0
$591$	−0.949491	−0.0390569
$592$	−25.3706	−1.04273
$593$	−24.8487	−1.02041	−0.510207	−	0.860052i	$-0.670431\pi$
$593$	−24.8487	−1.02041	−0.510207	+	0.860052i	$0.670431\pi$
$594$	−3.71387	−0.152382
$595$	0	0
$596$	−24.7593	−1.01418
$597$	10.5120	0.430228
$598$	0.0169299	0.000692315 0
$599$	−1.50155	−0.0613517	−0.0306759	−	0.999529i	$-0.509766\pi$
$599$	−1.50155	−0.0613517	−0.0306759	+	0.999529i	$0.509766\pi$
$600$	0	0
$601$	−24.0828	−0.982356	−0.491178	−	0.871059i	$-0.663434\pi$
$601$	−24.0828	−0.982356	−0.491178	+	0.871059i	$0.663434\pi$
$602$	4.45870	0.181723
$603$	27.8981	1.13610
$604$	40.8504	1.66218
$605$	0	0
$606$	0.551638	0.0224088
$607$	−16.0760	−0.652506	−0.326253	−	0.945283i	$-0.605786\pi$
$607$	−16.0760	−0.652506	−0.326253	+	0.945283i	$0.605786\pi$
$608$	2.20510	0.0894284
$609$	−5.61381	−0.227483
$610$	0	0
$611$	0.226712	0.00917179
$612$	38.7510	1.56642
$613$	−43.5233	−1.75789	−0.878945	−	0.476923i	$-0.841752\pi$
$613$	−43.5233	−1.75789	−0.878945	+	0.476923i	$0.841752\pi$
$614$	5.61658	0.226667
$615$	0	0
$616$	6.98957	0.281618
$617$	3.82544	0.154006	0.0770032	−	0.997031i	$-0.475465\pi$
$617$	3.82544	0.154006	0.0770032	+	0.997031i	$0.475465\pi$
$618$	−0.721385	−0.0290183
$619$	8.69881	0.349635	0.174817	−	0.984601i	$-0.444066\pi$
$619$	8.69881	0.349635	0.174817	+	0.984601i	$0.444066\pi$
$620$	0	0
$621$	4.02109	0.161361
$622$	−0.630903	−0.0252969
$623$	19.8354	0.794687
$624$	0.0757480	0.00303235
$625$	0	0
$626$	3.64020	0.145492
$627$	1.62153	0.0647578
$628$	33.0360	1.31828
$629$	−52.3666	−2.08799
$630$	0	0
$631$	−28.0264	−1.11571	−0.557856	−	0.829938i	$-0.688376\pi$
$631$	−28.0264	−1.11571	−0.557856	+	0.829938i	$0.688376\pi$
$632$	−14.0946	−0.560653
$633$	−9.44961	−0.375588
$634$	−2.18321	−0.0867065
$635$	0	0
$636$	−8.16222	−0.323653
$637$	−0.221743	−0.00878578
$638$	10.8282	0.428692
$639$	−5.14391	−0.203490
$640$	0	0
$641$	22.7621	0.899048	0.449524	−	0.893268i	$-0.351594\pi$
$641$	22.7621	0.899048	0.449524	+	0.893268i	$0.351594\pi$
$642$	0.769733	0.0303789
$643$	−35.9559	−1.41796	−0.708981	−	0.705228i	$-0.750845\pi$
$643$	−35.9559	−1.41796	−0.708981	+	0.705228i	$0.750845\pi$
$644$	−3.70956	−0.146177
$645$	0	0
$646$	1.41610	0.0557157
$647$	1.94619	0.0765127	0.0382564	−	0.999268i	$-0.487820\pi$
$647$	1.94619	0.0765127	0.0382564	+	0.999268i	$0.487820\pi$
$648$	7.46577	0.293283
$649$	61.0395	2.39601
$650$	0	0
$651$	−2.29637	−0.0900019
$652$	21.3604	0.836537
$653$	−24.3392	−0.952467	−0.476233	−	0.879319i	$-0.657998\pi$
$653$	−24.3392	−0.952467	−0.476233	+	0.879319i	$0.657998\pi$
$654$	0.655961	0.0256501
$655$	0	0
$656$	19.3320	0.754789
$657$	17.8484	0.696334
$658$	1.99041	0.0775942
$659$	−6.16907	−0.240313	−0.120156	−	0.992755i	$-0.538340\pi$
$659$	−6.16907	−0.240313	−0.120156	+	0.992755i	$0.538340\pi$
$660$	0	0
$661$	−48.1704	−1.87361	−0.936807	−	0.349848i	$-0.886233\pi$
$661$	−48.1704	−1.87361	−0.936807	+	0.349848i	$0.886233\pi$
$662$	5.37812	0.209027
$663$	0.156349	0.00607208
$664$	2.53626	0.0984260
$665$	0	0
$666$	−5.47529	−0.212163
$667$	−11.7239	−0.453951
$668$	−43.0338	−1.66503
$669$	−4.16551	−0.161048
$670$	0	0
$671$	−47.7492	−1.84334
$672$	2.13744	0.0824537
$673$	19.2071	0.740381	0.370190	−	0.928956i	$-0.379292\pi$
$673$	19.2071	0.740381	0.370190	+	0.928956i	$0.379292\pi$
$674$	−7.28525	−0.280617
$675$	0	0
$676$	24.9948	0.961337
$677$	14.9094	0.573014	0.286507	−	0.958078i	$-0.407506\pi$
$677$	14.9094	0.573014	0.286507	+	0.958078i	$0.407506\pi$
$678$	−1.73327	−0.0665658
$679$	−3.05667	−0.117304
$680$	0	0
$681$	−0.904843	−0.0346737
$682$	4.42935	0.169609
$683$	22.8682	0.875029	0.437515	−	0.899211i	$-0.355859\pi$
$683$	22.8682	0.875029	0.437515	+	0.899211i	$0.355859\pi$
$684$	−3.69528	−0.141293
$685$	0	0
$686$	−4.60149	−0.175686
$687$	1.24720	0.0475835
$688$	41.6619	1.58835
$689$	0.370529	0.0141160
$690$	0	0
$691$	−35.5210	−1.35128	−0.675641	−	0.737231i	$-0.736133\pi$
$691$	−35.5210	−1.35128	−0.675641	+	0.737231i	$0.736133\pi$
$692$	8.00140	0.304168
$693$	−17.6846	−0.671783
$694$	−1.01368	−0.0384788
$695$	0	0
$696$	4.47424	0.169596
$697$	39.9025	1.51142
$698$	0.227239	0.00860112
$699$	−8.10617	−0.306604
$700$	0	0
$701$	9.22303	0.348349	0.174175	−	0.984715i	$-0.444274\pi$
$701$	9.22303	0.348349	0.174175	+	0.984715i	$0.444274\pi$
$702$	0.0341476	0.00128882
$703$	4.99366	0.188339
$704$	29.1737	1.09952
$705$	0	0
$706$	−7.92114	−0.298116
$707$	5.48701	0.206360
$708$	12.3632	0.464636
$709$	28.7763	1.08072	0.540358	−	0.841435i	$-0.318289\pi$
$709$	28.7763	1.08072	0.540358	+	0.841435i	$0.318289\pi$
$710$	0	0
$711$	35.6614	1.33741
$712$	−15.8089	−0.592464
$713$	−4.79575	−0.179602
$714$	1.37265	0.0513703
$715$	0	0
$716$	11.1341	0.416100
$717$	−5.31614	−0.198535
$718$	4.40301	0.164319
$719$	−24.1878	−0.902055	−0.451027	−	0.892510i	$-0.648942\pi$
$719$	−24.1878	−0.902055	−0.451027	+	0.892510i	$0.648942\pi$
$720$	0	0
$721$	−7.17544	−0.267227
$722$	5.13893	0.191251
$723$	−0.494846	−0.0184035
$724$	−33.6358	−1.25006
$725$	0	0
$726$	−1.52080	−0.0564420
$727$	−9.73994	−0.361235	−0.180617	−	0.983553i	$-0.557810\pi$
$727$	−9.73994	−0.361235	−0.180617	+	0.983553i	$0.557810\pi$
$728$	−0.0642663	−0.00238187
$729$	−14.6617	−0.543024
$730$	0	0
$731$	85.9928	3.18056
$732$	−9.67131	−0.357462
$733$	4.38060	0.161801	0.0809006	−	0.996722i	$-0.474220\pi$
$733$	4.38060	0.161801	0.0809006	+	0.996722i	$0.474220\pi$
$734$	3.88432	0.143373
$735$	0	0
$736$	4.46384	0.164539
$737$	47.5719	1.75234
$738$	4.17208	0.153577
$739$	−6.21520	−0.228630	−0.114315	−	0.993445i	$-0.536467\pi$
$739$	−6.21520	−0.228630	−0.114315	+	0.993445i	$0.536467\pi$
$740$	0	0
$741$	−0.0149094	−0.000547709 0
$742$	3.25304	0.119423
$743$	−26.7097	−0.979885	−0.489942	−	0.871755i	$-0.662982\pi$
$743$	−26.7097	−0.979885	−0.489942	+	0.871755i	$0.662982\pi$
$744$	1.83022	0.0670992
$745$	0	0
$746$	3.39578	0.124328
$747$	−6.41710	−0.234790
$748$	66.0784	2.41607
$749$	7.65635	0.279757
$750$	0	0
$751$	46.9924	1.71478	0.857388	−	0.514670i	$-0.172085\pi$
$751$	46.9924	1.71478	0.857388	+	0.514670i	$0.172085\pi$
$752$	18.5983	0.678210
$753$	11.8178	0.430666
$754$	−0.0995608	−0.00362579
$755$	0	0
$756$	−7.48217	−0.272124
$757$	35.2425	1.28091	0.640456	−	0.767995i	$-0.278745\pi$
$757$	35.2425	1.28091	0.640456	+	0.767995i	$0.278745\pi$
$758$	−0.0790621	−0.00287166
$759$	3.28252	0.119148
$760$	0	0
$761$	−47.1109	−1.70777	−0.853885	−	0.520461i	$-0.825760\pi$
$761$	−47.1109	−1.70777	−0.853885	+	0.520461i	$0.825760\pi$
$762$	0.0587413	0.00212797
$763$	6.52469	0.236210
$764$	41.5499	1.50322
$765$	0	0
$766$	8.27923	0.299141
$767$	−0.561234	−0.0202650
$768$	5.04045	0.181881
$769$	−53.8827	−1.94306	−0.971530	−	0.236915i	$-0.923864\pi$
$769$	−53.8827	−1.94306	−0.971530	+	0.236915i	$0.923864\pi$
$770$	0	0
$771$	−2.59995	−0.0936350
$772$	4.43983	0.159793
$773$	7.33241	0.263728	0.131864	−	0.991268i	$-0.457904\pi$
$773$	7.33241	0.263728	0.131864	+	0.991268i	$0.457904\pi$
$774$	8.99114	0.323180
$775$	0	0
$776$	2.43618	0.0874539
$777$	4.84045	0.173650
$778$	2.46639	0.0884245
$779$	−3.80509	−0.136332
$780$	0	0
$781$	−8.77143	−0.313866
$782$	2.86666	0.102511
$783$	−23.6471	−0.845078
$784$	−18.1906	−0.649666
$785$	0	0
$786$	1.83556	0.0654722
$787$	0.274880	0.00979841	0.00489921	−	0.999988i	$-0.498441\pi$
$787$	0.274880	0.00979841	0.00489921	+	0.999988i	$0.498441\pi$
$788$	3.68969	0.131440
$789$	0.549102	0.0195485
$790$	0	0
$791$	−17.2404	−0.612998
$792$	14.0947	0.500835
$793$	0.439035	0.0155906
$794$	−8.21160	−0.291419
$795$	0	0
$796$	−40.8493	−1.44786
$797$	7.42858	0.263134	0.131567	−	0.991307i	$-0.457999\pi$
$797$	7.42858	0.263134	0.131567	+	0.991307i	$0.457999\pi$
$798$	−0.130896	−0.00463366
$799$	38.3881	1.35807
$800$	0	0
$801$	39.9988	1.41329
$802$	−1.74958	−0.0617800
$803$	30.4353	1.07404
$804$	9.63541	0.339815
$805$	0	0
$806$	−0.0407261	−0.00143452
$807$	−1.40850	−0.0495815
$808$	−4.37318	−0.153848
$809$	42.6491	1.49946	0.749730	−	0.661743i	$-0.230183\pi$
$809$	42.6491	1.49946	0.749730	+	0.661743i	$0.230183\pi$
$810$	0	0
$811$	25.6139	0.899425	0.449713	−	0.893173i	$-0.351526\pi$
$811$	25.6139	0.899425	0.449713	+	0.893173i	$0.351526\pi$
$812$	21.8150	0.765558
$813$	6.48392	0.227401
$814$	−9.33649	−0.327244
$815$	0	0
$816$	12.8260	0.449001
$817$	−8.20024	−0.286890
$818$	2.11837	0.0740669
$819$	0.162603	0.00568181
$820$	0	0
$821$	21.8573	0.762826	0.381413	−	0.924405i	$-0.375438\pi$
$821$	21.8573	0.762826	0.381413	+	0.924405i	$0.375438\pi$
$822$	1.54804	0.0539942
$823$	−1.58270	−0.0551693	−0.0275847	−	0.999619i	$-0.508782\pi$
$823$	−1.58270	−0.0551693	−0.0275847	+	0.999619i	$0.508782\pi$
$824$	5.71887	0.199226
$825$	0	0
$826$	−4.92732	−0.171443
$827$	−36.2198	−1.25949	−0.629743	−	0.776803i	$-0.716840\pi$
$827$	−36.2198	−1.25949	−0.629743	+	0.776803i	$0.716840\pi$
$828$	−7.48047	−0.259964
$829$	30.5957	1.06263	0.531316	−	0.847174i	$-0.321698\pi$
$829$	30.5957	1.06263	0.531316	+	0.847174i	$0.321698\pi$
$830$	0	0
$831$	11.6107	0.402772
$832$	−0.268241	−0.00929957
$833$	−37.5466	−1.30091
$834$	0.127356	0.00440998
$835$	0	0
$836$	−6.30122	−0.217932
$837$	−9.67303	−0.334349
$838$	−0.651640	−0.0225105
$839$	−9.85906	−0.340373	−0.170186	−	0.985412i	$-0.554437\pi$
$839$	−9.85906	−0.340373	−0.170186	+	0.985412i	$0.554437\pi$
$840$	0	0
$841$	39.9455	1.37743
$842$	−2.39186	−0.0824290
$843$	4.40989	0.151885
$844$	36.7208	1.26398
$845$	0	0
$846$	4.01374	0.137995
$847$	−15.1270	−0.519769
$848$	30.3963	1.04381
$849$	7.82056	0.268401
$850$	0	0
$851$	10.1088	0.346526
$852$	−1.77660	−0.0608653
$853$	−20.6701	−0.707730	−0.353865	−	0.935296i	$-0.615133\pi$
$853$	−20.6701	−0.707730	−0.353865	+	0.935296i	$0.615133\pi$
$854$	3.85448	0.131898
$855$	0	0
$856$	−6.10216	−0.208567
$857$	−36.0858	−1.23267	−0.616334	−	0.787485i	$-0.711383\pi$
$857$	−36.0858	−1.23267	−0.616334	+	0.787485i	$0.711383\pi$
$858$	0.0278756	0.000951656 0
$859$	40.7566	1.39060	0.695299	−	0.718720i	$-0.255272\pi$
$859$	40.7566	1.39060	0.695299	+	0.718720i	$0.255272\pi$
$860$	0	0
$861$	−3.68835	−0.125699
$862$	0.758604	0.0258381
$863$	−21.5125	−0.732295	−0.366148	−	0.930557i	$-0.619323\pi$
$863$	−21.5125	−0.732295	−0.366148	+	0.930557i	$0.619323\pi$
$864$	9.00357	0.306308
$865$	0	0
$866$	4.12947	0.140325
$867$	18.0614	0.613396
$868$	8.92362	0.302887
$869$	60.8100	2.06284
$870$	0	0
$871$	−0.437405	−0.0148209
$872$	−5.20022	−0.176102
$873$	−6.16390	−0.208616
$874$	−0.273363	−0.00924665
$875$	0	0
$876$	6.16448	0.208278
$877$	47.8912	1.61717	0.808586	−	0.588378i	$-0.200233\pi$
$877$	47.8912	1.61717	0.808586	+	0.588378i	$0.200233\pi$
$878$	5.49922	0.185590
$879$	−16.3015	−0.549835
$880$	0	0
$881$	−18.2689	−0.615496	−0.307748	−	0.951468i	$-0.599575\pi$
$881$	−18.2689	−0.615496	−0.307748	+	0.951468i	$0.599575\pi$
$882$	−3.92576	−0.132187
$883$	37.0354	1.24634	0.623170	−	0.782087i	$-0.285845\pi$
$883$	37.0354	1.24634	0.623170	+	0.782087i	$0.285845\pi$
$884$	−0.607565	−0.0204346
$885$	0	0
$886$	−10.9870	−0.369115
$887$	13.7619	0.462080	0.231040	−	0.972944i	$-0.425787\pi$
$887$	13.7619	0.462080	0.231040	+	0.972944i	$0.425787\pi$
$888$	−3.85787	−0.129462
$889$	0.584285	0.0195963
$890$	0	0
$891$	−32.2104	−1.07909
$892$	16.1870	0.541982
$893$	−3.66067	−0.122500
$894$	−1.76857	−0.0591499
$895$	0	0
$896$	−10.9938	−0.367278
$897$	−0.0301815	−0.00100773
$898$	6.36221	0.212310
$899$	28.2027	0.940613
$900$	0	0
$901$	62.7398	2.09017
$902$	7.11426	0.236879
$903$	−7.94866	−0.264515
$904$	13.7407	0.457009
$905$	0	0
$906$	2.91797	0.0969432
$907$	27.1842	0.902637	0.451319	−	0.892363i	$-0.350954\pi$
$907$	27.1842	0.902637	0.451319	+	0.892363i	$0.350954\pi$
$908$	3.51619	0.116689
$909$	11.0648	0.366996
$910$	0	0
$911$	29.4894	0.977027	0.488513	−	0.872556i	$-0.337539\pi$
$911$	29.4894	0.977027	0.488513	+	0.872556i	$0.337539\pi$
$912$	−1.22309	−0.0405004
$913$	−10.9425	−0.362143
$914$	−2.68277	−0.0887380
$915$	0	0
$916$	−4.84656	−0.160135
$917$	18.2579	0.602928
$918$	5.78204	0.190836
$919$	−44.2354	−1.45919	−0.729596	−	0.683878i	$-0.760292\pi$
$919$	−44.2354	−1.45919	−0.729596	+	0.683878i	$0.760292\pi$
$920$	0	0
$921$	−10.0128	−0.329935
$922$	−1.74331	−0.0574130
$923$	0.0806498	0.00265462
$924$	−6.10789	−0.200935
$925$	0	0
$926$	−2.12163	−0.0697210
$927$	−14.4696	−0.475243
$928$	−26.2508	−0.861726
$929$	17.7425	0.582112	0.291056	−	0.956706i	$-0.405993\pi$
$929$	17.7425	0.582112	0.291056	+	0.956706i	$0.405993\pi$
$930$	0	0
$931$	3.58043	0.117344
$932$	31.5003	1.03183
$933$	1.12473	0.0368220
$934$	7.18766	0.235187
$935$	0	0
$936$	−0.129596	−0.00423596
$937$	−46.1680	−1.50824	−0.754121	−	0.656735i	$-0.771937\pi$
$937$	−46.1680	−1.50824	−0.754121	+	0.656735i	$0.771937\pi$
$938$	−3.84017	−0.125386
$939$	−6.48949	−0.211777
$940$	0	0
$941$	−22.0383	−0.718428	−0.359214	−	0.933255i	$-0.616955\pi$
$941$	−22.0383	−0.718428	−0.359214	+	0.933255i	$0.616955\pi$
$942$	2.35978	0.0768859
$943$	−7.70276	−0.250836
$944$	−46.0407	−1.49850
$945$	0	0
$946$	15.3317	0.498478
$947$	34.5940	1.12416	0.562078	−	0.827085i	$-0.310002\pi$
$947$	34.5940	1.12416	0.562078	+	0.827085i	$0.310002\pi$
$948$	12.3167	0.400028
$949$	−0.279840	−0.00908399
$950$	0	0
$951$	3.89209	0.126210
$952$	−10.8819	−0.352684
$953$	20.9799	0.679607	0.339803	−	0.940496i	$-0.389639\pi$
$953$	20.9799	0.679607	0.339803	+	0.940496i	$0.389639\pi$
$954$	6.55988	0.212384
$955$	0	0
$956$	20.6583	0.668138
$957$	−19.3037	−0.624001
$958$	−3.50112	−0.113116
$959$	15.3980	0.497228
$960$	0	0
$961$	−19.4635	−0.627854
$962$	0.0858453	0.00276777
$963$	15.4393	0.497526
$964$	1.92295	0.0619341
$965$	0	0
$966$	−0.264976	−0.00852548
$967$	0.0716187	0.00230310	0.00115155	−	0.999999i	$-0.499633\pi$
$967$	0.0716187	0.00230310	0.00115155	+	0.999999i	$0.499633\pi$
$968$	12.0563	0.387504
$969$	−2.52453	−0.0810995
$970$	0	0
$971$	−8.18205	−0.262575	−0.131287	−	0.991344i	$-0.541911\pi$
$971$	−8.18205	−0.262575	−0.131287	+	0.991344i	$0.541911\pi$
$972$	−22.9531	−0.736222
$973$	1.26678	0.0406111
$974$	8.82161	0.282663
$975$	0	0
$976$	36.0162	1.15285
$977$	−22.6886	−0.725872	−0.362936	−	0.931814i	$-0.618226\pi$
$977$	−22.6886	−0.725872	−0.362936	+	0.931814i	$0.618226\pi$
$978$	1.52579	0.0487893
$979$	68.2062	2.17988
$980$	0	0
$981$	13.1573	0.420080
$982$	2.83548	0.0904837
$983$	18.8463	0.601103	0.300551	−	0.953766i	$-0.402829\pi$
$983$	18.8463	0.601103	0.300551	+	0.953766i	$0.402829\pi$
$984$	2.93964	0.0937122
$985$	0	0
$986$	−16.8581	−0.536872
$987$	−3.54836	−0.112946
$988$	0.0579372	0.00184323
$989$	−16.6000	−0.527850
$990$	0	0
$991$	−16.8310	−0.534655	−0.267328	−	0.963606i	$-0.586141\pi$
$991$	−16.8310	−0.534655	−0.267328	+	0.963606i	$0.586141\pi$
$992$	−10.7381	−0.340935
$993$	−9.58775	−0.304258
$994$	0.708060	0.0224583
$995$	0	0
$996$	−2.21633	−0.0702272
$997$	−60.1343	−1.90447	−0.952236	−	0.305363i	$-0.901222\pi$
$997$	−60.1343	−1.90447	−0.952236	+	0.305363i	$0.901222\pi$
$998$	2.59643	0.0821885
$999$	20.3895	0.645095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.f.1.3		7
5.4	even	2		241.2.a.a.1.5	✓	7
15.14	odd	2		2169.2.a.e.1.3		7
20.19	odd	2		3856.2.a.j.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.a.a.1.5	✓	7	5.4	even	2
2169.2.a.e.1.3		7	15.14	odd	2
3856.2.a.j.1.4		7	20.19	odd	2
6025.2.a.f.1.3		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.277577 q^{2} +0.494846 q^{3} -1.92295 q^{4} -0.137358 q^{6} -1.36627 q^{7} +1.08892 q^{8} -2.75513 q^{9} +O(q^{10})\)	\(q-0.277577 q^{2} +0.494846 q^{3} -1.92295 q^{4} -0.137358 q^{6} -1.36627 q^{7} +1.08892 q^{8} -2.75513 q^{9} -4.69806 q^{11} -0.951564 q^{12} +0.0431968 q^{13} +0.379244 q^{14} +3.54364 q^{16} +7.31430 q^{17} +0.764761 q^{18} -0.697489 q^{19} -0.676090 q^{21} +1.30407 q^{22} -1.41195 q^{23} +0.538848 q^{24} -0.0119904 q^{26} -2.84790 q^{27} +2.62726 q^{28} +8.30334 q^{29} +3.39655 q^{31} -3.16148 q^{32} -2.32481 q^{33} -2.03028 q^{34} +5.29798 q^{36} -7.15948 q^{37} +0.193607 q^{38} +0.0213757 q^{39} +5.45541 q^{41} +0.187667 q^{42} +11.7568 q^{43} +9.03414 q^{44} +0.391925 q^{46} +5.24836 q^{47} +1.75356 q^{48} -5.13332 q^{49} +3.61945 q^{51} -0.0830653 q^{52} +8.57769 q^{53} +0.790512 q^{54} -1.48776 q^{56} -0.345149 q^{57} -2.30482 q^{58} -12.9925 q^{59} +10.1636 q^{61} -0.942804 q^{62} +3.76423 q^{63} -6.20973 q^{64} +0.645315 q^{66} -10.1259 q^{67} -14.0650 q^{68} -0.698697 q^{69} +1.86703 q^{71} -3.00012 q^{72} -6.47826 q^{73} +1.98731 q^{74} +1.34124 q^{76} +6.41880 q^{77} -0.00593342 q^{78} -12.9436 q^{79} +6.85611 q^{81} -1.51430 q^{82} +2.32915 q^{83} +1.30009 q^{84} -3.26342 q^{86} +4.10887 q^{87} -5.11582 q^{88} -14.5180 q^{89} -0.0590183 q^{91} +2.71511 q^{92} +1.68077 q^{93} -1.45682 q^{94} -1.56444 q^{96} +2.23725 q^{97} +1.42489 q^{98} +12.9438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9	\( 7 q + 4 q^{2} + 3 q^{3} + 2 q^{4} - 5 q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 18 q^{11} - q^{12} + q^{13} - 6 q^{14} + 4 q^{16} + 2 q^{17} - 8 q^{18} - 6 q^{19} - 2 q^{21} - 10 q^{22} + 22 q^{23} - 3 q^{24} + 8 q^{26} - 3 q^{27} - 9 q^{28} - 16 q^{29} - 18 q^{31} + 6 q^{32} - 4 q^{33} + 11 q^{34} - 7 q^{36} - 8 q^{37} - 16 q^{38} - 9 q^{39} - 15 q^{41} - 19 q^{42} - 14 q^{43} - 4 q^{44} + 11 q^{46} + 10 q^{47} - 31 q^{48} + 6 q^{49} + 13 q^{51} - 27 q^{52} - 15 q^{53} + 16 q^{54} + 13 q^{56} - 14 q^{57} - 17 q^{58} - 18 q^{59} + 4 q^{61} - 13 q^{62} + 16 q^{63} + 2 q^{64} + 16 q^{66} - 18 q^{67} + 15 q^{68} + 26 q^{69} - 50 q^{71} - 30 q^{72} + 10 q^{74} - 20 q^{76} - 17 q^{77} + 32 q^{78} - 15 q^{79} - 9 q^{81} - 45 q^{82} + 24 q^{83} + 6 q^{84} - 23 q^{86} - 12 q^{87} - 8 q^{88} - 13 q^{89} - 12 q^{91} + 10 q^{92} - 14 q^{93} - 32 q^{94} - 15 q^{96} - q^{97} - 9 q^{98} - 20 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 3 * q^3 + 2 * q^4 - 5 * q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 18 * q^11 - q^12 + q^13 - 6 * q^14 + 4 * q^16 + 2 * q^17 - 8 * q^18 - 6 * q^19 - 2 * q^21 - 10 * q^22 + 22 * q^23 - 3 * q^24 + 8 * q^26 - 3 * q^27 - 9 * q^28 - 16 * q^29 - 18 * q^31 + 6 * q^32 - 4 * q^33 + 11 * q^34 - 7 * q^36 - 8 * q^37 - 16 * q^38 - 9 * q^39 - 15 * q^41 - 19 * q^42 - 14 * q^43 - 4 * q^44 + 11 * q^46 + 10 * q^47 - 31 * q^48 + 6 * q^49 + 13 * q^51 - 27 * q^52 - 15 * q^53 + 16 * q^54 + 13 * q^56 - 14 * q^57 - 17 * q^58 - 18 * q^59 + 4 * q^61 - 13 * q^62 + 16 * q^63 + 2 * q^64 + 16 * q^66 - 18 * q^67 + 15 * q^68 + 26 * q^69 - 50 * q^71 - 30 * q^72 + 10 * q^74 - 20 * q^76 - 17 * q^77 + 32 * q^78 - 15 * q^79 - 9 * q^81 - 45 * q^82 + 24 * q^83 + 6 * q^84 - 23 * q^86 - 12 * q^87 - 8 * q^88 - 13 * q^89 - 12 * q^91 + 10 * q^92 - 14 * q^93 - 32 * q^94 - 15 * q^96 - q^97 - 9 * q^98 - 20 * q^99

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