LMFDB - Embedded newform 1475.2.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1475,2,Mod(1,1475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1475, 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("1475.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1475 = 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1475.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:	$11.7779342981$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 8x^{5} + 10x^{4} + 23x^{3} - 8x^{2} - 18x - 3 $ x^7 - 2x^6 - 8x^5 + 10x^4 + 23x^3 - 8x^2 - 18x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.14647$ of defining polynomial
Character	$\chi$	$=$	1475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.14647 q^{2} -1.02716 q^{3} -0.685612 q^{4} -1.17760 q^{6} +3.29911 q^{7} -3.07897 q^{8} -1.94495 q^{9} +O(q^{10})$	\(q+1.14647 q^{2} -1.02716 q^{3} -0.685612 q^{4} -1.17760 q^{6} +3.29911 q^{7} -3.07897 q^{8} -1.94495 q^{9} +2.96870 q^{11} +0.704231 q^{12} -0.833224 q^{13} +3.78232 q^{14} -2.15871 q^{16} -0.628465 q^{17} -2.22982 q^{18} +3.60104 q^{19} -3.38870 q^{21} +3.40352 q^{22} +0.999832 q^{23} +3.16258 q^{24} -0.955264 q^{26} +5.07924 q^{27} -2.26191 q^{28} -3.67179 q^{29} +7.06763 q^{31} +3.68304 q^{32} -3.04932 q^{33} -0.720514 q^{34} +1.33348 q^{36} -3.50477 q^{37} +4.12848 q^{38} +0.855852 q^{39} -3.39743 q^{41} -3.88503 q^{42} +12.2254 q^{43} -2.03538 q^{44} +1.14628 q^{46} +10.0366 q^{47} +2.21734 q^{48} +3.88410 q^{49} +0.645532 q^{51} +0.571268 q^{52} +10.8102 q^{53} +5.82318 q^{54} -10.1578 q^{56} -3.69884 q^{57} -4.20958 q^{58} +1.00000 q^{59} -2.69395 q^{61} +8.10280 q^{62} -6.41659 q^{63} +8.53991 q^{64} -3.49595 q^{66} +9.77698 q^{67} +0.430883 q^{68} -1.02698 q^{69} -6.64780 q^{71} +5.98843 q^{72} +1.70099 q^{73} -4.01810 q^{74} -2.46892 q^{76} +9.79405 q^{77} +0.981206 q^{78} +1.89083 q^{79} +0.617670 q^{81} -3.89504 q^{82} +3.89283 q^{83} +2.32333 q^{84} +14.0161 q^{86} +3.77150 q^{87} -9.14052 q^{88} +11.3689 q^{89} -2.74889 q^{91} -0.685497 q^{92} -7.25956 q^{93} +11.5066 q^{94} -3.78306 q^{96} +1.44816 q^{97} +4.45299 q^{98} -5.77396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} + 18 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 + 18 * q^8 + 7 * q^9	$ 7 q + 2 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} + 18 q^{8} + 7 q^{9} + 5 q^{11} - q^{12} + 17 q^{13} + 8 q^{14} + 8 q^{16} + 6 q^{17} - 15 q^{18} + 3 q^{19} - 13 q^{21} + 20 q^{22} - 6 q^{23} + 9 q^{24} - 3 q^{26} + 11 q^{27} - 3 q^{28} - 10 q^{29} + q^{31} + 18 q^{32} - 5 q^{34} - 35 q^{36} + 34 q^{37} - 23 q^{38} - 5 q^{39} - 8 q^{41} + 26 q^{42} + 40 q^{43} + 35 q^{44} - 7 q^{46} + 26 q^{47} + 12 q^{48} + 10 q^{49} - 28 q^{51} + 4 q^{52} + 3 q^{53} + 16 q^{54} + 9 q^{56} + q^{57} - 12 q^{58} + 7 q^{59} + 9 q^{61} + 29 q^{62} + 14 q^{63} + 32 q^{64} - 43 q^{66} + 20 q^{67} - 6 q^{68} + 10 q^{69} - 6 q^{71} + 2 q^{72} + 33 q^{73} + 29 q^{74} - 68 q^{76} - 2 q^{77} - 12 q^{78} + 14 q^{79} + 15 q^{81} + 14 q^{82} + 5 q^{83} + 46 q^{84} + 16 q^{86} + 28 q^{87} + 15 q^{88} + 7 q^{89} - 17 q^{91} + 2 q^{92} + 38 q^{93} - 20 q^{94} + 37 q^{96} - 12 q^{97} - 7 q^{98} - 37 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 + 18 * q^8 + 7 * q^9 + 5 * q^11 - q^12 + 17 * q^13 + 8 * q^14 + 8 * q^16 + 6 * q^17 - 15 * q^18 + 3 * q^19 - 13 * q^21 + 20 * q^22 - 6 * q^23 + 9 * q^24 - 3 * q^26 + 11 * q^27 - 3 * q^28 - 10 * q^29 + q^31 + 18 * q^32 - 5 * q^34 - 35 * q^36 + 34 * q^37 - 23 * q^38 - 5 * q^39 - 8 * q^41 + 26 * q^42 + 40 * q^43 + 35 * q^44 - 7 * q^46 + 26 * q^47 + 12 * q^48 + 10 * q^49 - 28 * q^51 + 4 * q^52 + 3 * q^53 + 16 * q^54 + 9 * q^56 + q^57 - 12 * q^58 + 7 * q^59 + 9 * q^61 + 29 * q^62 + 14 * q^63 + 32 * q^64 - 43 * q^66 + 20 * q^67 - 6 * q^68 + 10 * q^69 - 6 * q^71 + 2 * q^72 + 33 * q^73 + 29 * q^74 - 68 * q^76 - 2 * q^77 - 12 * q^78 + 14 * q^79 + 15 * q^81 + 14 * q^82 + 5 * q^83 + 46 * q^84 + 16 * q^86 + 28 * q^87 + 15 * q^88 + 7 * q^89 - 17 * q^91 + 2 * q^92 + 38 * q^93 - 20 * q^94 + 37 * q^96 - 12 * q^97 - 7 * q^98 - 37 * 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 $

$2$	1.14647	0.810675	0.405337	−	0.914167i	$-0.367154\pi$
$2$	1.14647	0.810675	0.405337	+	0.914167i	$0.367154\pi$
$3$	−1.02716	−0.593029	−0.296515	−	0.955028i	$-0.595824\pi$
$3$	−1.02716	−0.593029	−0.296515	+	0.955028i	$0.595824\pi$
$4$	−0.685612	−0.342806
$5$	0	0
$5$	0	0
$6$	−1.17760	−0.480754
$7$	3.29911	1.24694	0.623472	−	0.781845i	$-0.285721\pi$
$7$	3.29911	1.24694	0.623472	+	0.781845i	$0.285721\pi$
$8$	−3.07897	−1.08858
$9$	−1.94495	−0.648316
$10$	0	0
$11$	2.96870	0.895096	0.447548	−	0.894260i	$-0.352297\pi$
$11$	2.96870	0.895096	0.447548	+	0.894260i	$0.352297\pi$
$12$	0.704231	0.203294
$13$	−0.833224	−0.231095	−0.115547	−	0.993302i	$-0.536862\pi$
$13$	−0.833224	−0.231095	−0.115547	+	0.993302i	$0.536862\pi$
$14$	3.78232	1.01087
$15$	0	0
$16$	−2.15871	−0.539678
$17$	−0.628465	−0.152425	−0.0762125	−	0.997092i	$-0.524283\pi$
$17$	−0.628465	−0.152425	−0.0762125	+	0.997092i	$0.524283\pi$
$18$	−2.22982	−0.525574
$19$	3.60104	0.826136	0.413068	−	0.910700i	$-0.364457\pi$
$19$	3.60104	0.826136	0.413068	+	0.910700i	$0.364457\pi$
$20$	0	0
$21$	−3.38870	−0.739475
$22$	3.40352	0.725632
$23$	0.999832	0.208479	0.104240	−	0.994552i	$-0.466759\pi$
$23$	0.999832	0.208479	0.104240	+	0.994552i	$0.466759\pi$
$24$	3.16258	0.645560
$25$	0	0
$26$	−0.955264	−0.187343
$27$	5.07924	0.977500
$28$	−2.26191	−0.427460
$29$	−3.67179	−0.681833	−0.340917	−	0.940094i	$-0.610737\pi$
$29$	−3.67179	−0.681833	−0.340917	+	0.940094i	$0.610737\pi$
$30$	0	0
$31$	7.06763	1.26938	0.634692	−	0.772766i	$-0.281127\pi$
$31$	7.06763	1.26938	0.634692	+	0.772766i	$0.281127\pi$
$32$	3.68304	0.651076
$33$	−3.04932	−0.530818
$34$	−0.720514	−0.123567
$35$	0	0
$36$	1.33348	0.222247
$37$	−3.50477	−0.576180	−0.288090	−	0.957603i	$-0.593020\pi$
$37$	−3.50477	−0.576180	−0.288090	+	0.957603i	$0.593020\pi$
$38$	4.12848	0.669728
$39$	0.855852	0.137046
$40$	0	0
$41$	−3.39743	−0.530589	−0.265295	−	0.964167i	$-0.585469\pi$
$41$	−3.39743	−0.530589	−0.265295	+	0.964167i	$0.585469\pi$
$42$	−3.88503	−0.599474
$43$	12.2254	1.86436	0.932181	−	0.361993i	$-0.117904\pi$
$43$	12.2254	1.86436	0.932181	+	0.361993i	$0.117904\pi$
$44$	−2.03538	−0.306844
$45$	0	0
$46$	1.14628	0.169009
$47$	10.0366	1.46398	0.731992	−	0.681313i	$-0.238591\pi$
$47$	10.0366	1.46398	0.731992	+	0.681313i	$0.238591\pi$
$48$	2.21734	0.320045
$49$	3.88410	0.554871
$50$	0	0
$51$	0.645532	0.0903925
$52$	0.571268	0.0792207
$53$	10.8102	1.48490	0.742449	−	0.669903i	$-0.233664\pi$
$53$	10.8102	1.48490	0.742449	+	0.669903i	$0.233664\pi$
$54$	5.82318	0.792435
$55$	0	0
$56$	−10.1578	−1.35740
$57$	−3.69884	−0.489923
$58$	−4.20958	−0.552745
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0	0
$61$	−2.69395	−0.344925	−0.172462	−	0.985016i	$-0.555172\pi$
$61$	−2.69395	−0.344925	−0.172462	+	0.985016i	$0.555172\pi$
$62$	8.10280	1.02906
$63$	−6.41659	−0.808414
$64$	8.53991	1.06749
$65$	0	0
$66$	−3.49595	−0.430321
$67$	9.77698	1.19445	0.597224	−	0.802074i	$-0.296270\pi$
$67$	9.77698	1.19445	0.597224	+	0.802074i	$0.296270\pi$
$68$	0.430883	0.0522522
$69$	−1.02698	−0.123634
$70$	0	0
$71$	−6.64780	−0.788948	−0.394474	−	0.918907i	$-0.629073\pi$
$71$	−6.64780	−0.788948	−0.394474	+	0.918907i	$0.629073\pi$
$72$	5.98843	0.705744
$73$	1.70099	0.199086	0.0995430	−	0.995033i	$-0.468262\pi$
$73$	1.70099	0.199086	0.0995430	+	0.995033i	$0.468262\pi$
$74$	−4.01810	−0.467095
$75$	0	0
$76$	−2.46892	−0.283205
$77$	9.79405	1.11614
$78$	0.981206	0.111100
$79$	1.89083	0.212736	0.106368	−	0.994327i	$-0.466078\pi$
$79$	1.89083	0.212736	0.106368	+	0.994327i	$0.466078\pi$
$80$	0	0
$81$	0.617670	0.0686300
$82$	−3.89504	−0.430135
$83$	3.89283	0.427293	0.213647	−	0.976911i	$-0.431466\pi$
$83$	3.89283	0.427293	0.213647	+	0.976911i	$0.431466\pi$
$84$	2.32333	0.253496
$85$	0	0
$86$	14.0161	1.51139
$87$	3.77150	0.404347
$88$	−9.14052	−0.974383
$89$	11.3689	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$89$	11.3689	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$90$	0	0
$91$	−2.74889	−0.288162
$92$	−0.685497	−0.0714680
$93$	−7.25956	−0.752782
$94$	11.5066	1.18682
$95$	0	0
$96$	−3.78306	−0.386107
$97$	1.44816	0.147038	0.0735191	−	0.997294i	$-0.476577\pi$
$97$	1.44816	0.147038	0.0735191	+	0.997294i	$0.476577\pi$
$98$	4.45299	0.449820
$99$	−5.77396	−0.580305
$100$	0	0
$101$	−6.49350	−0.646127	−0.323064	−	0.946377i	$-0.604713\pi$
$101$	−6.49350	−0.646127	−0.323064	+	0.946377i	$0.604713\pi$
$102$	0.740081	0.0732790
$103$	10.1455	0.999664	0.499832	−	0.866123i	$-0.333395\pi$
$103$	10.1455	0.999664	0.499832	+	0.866123i	$0.333395\pi$
$104$	2.56547	0.251565
$105$	0	0
$106$	12.3936	1.20377
$107$	−15.8083	−1.52825	−0.764123	−	0.645071i	$-0.776828\pi$
$107$	−15.8083	−1.52825	−0.764123	+	0.645071i	$0.776828\pi$
$108$	−3.48239	−0.335093
$109$	−9.70746	−0.929806	−0.464903	−	0.885361i	$-0.653911\pi$
$109$	−9.70746	−0.929806	−0.464903	+	0.885361i	$0.653911\pi$
$110$	0	0
$111$	3.59995	0.341692
$112$	−7.12182	−0.672948
$113$	−5.00827	−0.471138	−0.235569	−	0.971858i	$-0.575695\pi$
$113$	−5.00827	−0.471138	−0.235569	+	0.971858i	$0.575695\pi$
$114$	−4.24060	−0.397168
$115$	0	0
$116$	2.51742	0.233737
$117$	1.62058	0.149822
$118$	1.14647	0.105541
$119$	−2.07337	−0.190066
$120$	0	0
$121$	−2.18683	−0.198803
$122$	−3.08852	−0.279622
$123$	3.48969	0.314655
$124$	−4.84565	−0.435152
$125$	0	0
$126$	−7.35641	−0.655361
$127$	10.2549	0.909971	0.454986	−	0.890499i	$-0.349644\pi$
$127$	10.2549	0.909971	0.454986	+	0.890499i	$0.349644\pi$
$128$	2.42465	0.214311
$129$	−12.5574	−1.10562
$130$	0	0
$131$	−8.76944	−0.766189	−0.383095	−	0.923709i	$-0.625142\pi$
$131$	−8.76944	−0.766189	−0.383095	+	0.923709i	$0.625142\pi$
$132$	2.09065	0.181968
$133$	11.8802	1.03015
$134$	11.2090	0.968309
$135$	0	0
$136$	1.93502	0.165927
$137$	−3.06099	−0.261518	−0.130759	−	0.991414i	$-0.541741\pi$
$137$	−3.06099	−0.261518	−0.130759	+	0.991414i	$0.541741\pi$
$138$	−1.17740	−0.100227
$139$	−11.9274	−1.01167	−0.505836	−	0.862629i	$-0.668816\pi$
$139$	−11.9274	−1.01167	−0.505836	+	0.862629i	$0.668816\pi$
$140$	0	0
$141$	−10.3091	−0.868185
$142$	−7.62148	−0.639581
$143$	−2.47359	−0.206852
$144$	4.19858	0.349882
$145$	0	0
$146$	1.95013	0.161394
$147$	−3.98958	−0.329055
$148$	2.40291	0.197518
$149$	18.4329	1.51009	0.755043	−	0.655676i	$-0.227616\pi$
$149$	18.4329	1.51009	0.755043	+	0.655676i	$0.227616\pi$
$150$	0	0
$151$	13.1312	1.06860	0.534302	−	0.845293i	$-0.320574\pi$
$151$	13.1312	1.06860	0.534302	+	0.845293i	$0.320574\pi$
$152$	−11.0875	−0.899315
$153$	1.22233	0.0988196
$154$	11.2286	0.904823
$155$	0	0
$156$	−0.586782	−0.0469802
$157$	11.0273	0.880076	0.440038	−	0.897979i	$-0.354965\pi$
$157$	11.0273	0.880076	0.440038	+	0.897979i	$0.354965\pi$
$158$	2.16778	0.172459
$159$	−11.1038	−0.880588
$160$	0	0
$161$	3.29855	0.259962
$162$	0.708138	0.0556366
$163$	−15.3736	−1.20415	−0.602076	−	0.798438i	$-0.705660\pi$
$163$	−15.3736	−1.20415	−0.602076	+	0.798438i	$0.705660\pi$
$164$	2.32932	0.181889
$165$	0	0
$166$	4.46300	0.346396
$167$	−3.04294	−0.235469	−0.117735	−	0.993045i	$-0.537563\pi$
$167$	−3.04294	−0.235469	−0.117735	+	0.993045i	$0.537563\pi$
$168$	10.4337	0.804977
$169$	−12.3057	−0.946595
$170$	0	0
$171$	−7.00385	−0.535597
$172$	−8.38191	−0.639114
$173$	13.2280	1.00571	0.502854	−	0.864371i	$-0.332283\pi$
$173$	13.2280	1.00571	0.502854	+	0.864371i	$0.332283\pi$
$174$	4.32390	0.327794
$175$	0	0
$176$	−6.40856	−0.483064
$177$	−1.02716	−0.0772059
$178$	13.0340	0.976942
$179$	−10.8141	−0.808281	−0.404141	−	0.914697i	$-0.632429\pi$
$179$	−10.8141	−0.808281	−0.404141	+	0.914697i	$0.632429\pi$
$180$	0	0
$181$	0.820535	0.0609899	0.0304949	−	0.999535i	$-0.490292\pi$
$181$	0.820535	0.0609899	0.0304949	+	0.999535i	$0.490292\pi$
$182$	−3.15152	−0.233606
$183$	2.76711	0.204550
$184$	−3.07845	−0.226946
$185$	0	0
$186$	−8.32285	−0.610261
$187$	−1.86572	−0.136435
$188$	−6.88119	−0.501863
$189$	16.7569	1.21889
$190$	0	0
$191$	−20.1260	−1.45627	−0.728133	−	0.685436i	$-0.759612\pi$
$191$	−20.1260	−1.45627	−0.728133	+	0.685436i	$0.759612\pi$
$192$	−8.77183	−0.633052
$193$	20.6877	1.48913	0.744566	−	0.667548i	$-0.232656\pi$
$193$	20.6877	1.48913	0.744566	+	0.667548i	$0.232656\pi$
$194$	1.66027	0.119200
$195$	0	0
$196$	−2.66298	−0.190213
$197$	−19.2189	−1.36929	−0.684646	−	0.728876i	$-0.740043\pi$
$197$	−19.2189	−1.36929	−0.684646	+	0.728876i	$0.740043\pi$
$198$	−6.61966	−0.470439
$199$	−9.92606	−0.703639	−0.351820	−	0.936068i	$-0.614437\pi$
$199$	−9.92606	−0.703639	−0.351820	+	0.936068i	$0.614437\pi$
$200$	0	0
$201$	−10.0425	−0.708343
$202$	−7.44459	−0.523799
$203$	−12.1136	−0.850208
$204$	−0.442584	−0.0309871
$205$	0	0
$206$	11.6315	0.810402
$207$	−1.94462	−0.135161
$208$	1.79869	0.124717
$209$	10.6904	0.739471
$210$	0	0
$211$	20.4013	1.40449	0.702243	−	0.711937i	$-0.252182\pi$
$211$	20.4013	1.40449	0.702243	+	0.711937i	$0.252182\pi$
$212$	−7.41162	−0.509032
$213$	6.82833	0.467869
$214$	−18.1237	−1.23891
$215$	0	0
$216$	−15.6388	−1.06409
$217$	23.3168	1.58285
$218$	−11.1293	−0.753771
$219$	−1.74719	−0.118064
$220$	0	0
$221$	0.523652	0.0352246
$222$	4.12722	0.277001
$223$	−14.3356	−0.959984	−0.479992	−	0.877273i	$-0.659361\pi$
$223$	−14.3356	−0.959984	−0.479992	+	0.877273i	$0.659361\pi$
$224$	12.1507	0.811856
$225$	0	0
$226$	−5.74181	−0.381940
$227$	8.53146	0.566253	0.283127	−	0.959083i	$-0.408628\pi$
$227$	8.53146	0.566253	0.283127	+	0.959083i	$0.408628\pi$
$228$	2.53597	0.167949
$229$	−15.5604	−1.02826	−0.514130	−	0.857712i	$-0.671885\pi$
$229$	−15.5604	−1.02826	−0.514130	+	0.857712i	$0.671885\pi$
$230$	0	0
$231$	−10.0600	−0.661901
$232$	11.3053	0.742230
$233$	0.302735	0.0198328	0.00991641	−	0.999951i	$-0.496843\pi$
$233$	0.302735	0.0198328	0.00991641	+	0.999951i	$0.496843\pi$
$234$	1.85794	0.121457
$235$	0	0
$236$	−0.685612	−0.0446296
$237$	−1.94218	−0.126158
$238$	−2.37705	−0.154081
$239$	−12.8277	−0.829755	−0.414877	−	0.909877i	$-0.636176\pi$
$239$	−12.8277	−0.829755	−0.414877	+	0.909877i	$0.636176\pi$
$240$	0	0
$241$	−25.3684	−1.63412	−0.817062	−	0.576550i	$-0.804399\pi$
$241$	−25.3684	−1.63412	−0.817062	+	0.576550i	$0.804399\pi$
$242$	−2.50713	−0.161165
$243$	−15.8722	−1.01820
$244$	1.84700	0.118242
$245$	0	0
$246$	4.00082	0.255083
$247$	−3.00048	−0.190916
$248$	−21.7610	−1.38182
$249$	−3.99854	−0.253397
$250$	0	0
$251$	19.3054	1.21855	0.609273	−	0.792960i	$-0.291461\pi$
$251$	19.3054	1.21855	0.609273	+	0.792960i	$0.291461\pi$
$252$	4.39929	0.277129
$253$	2.96820	0.186609
$254$	11.7569	0.737691
$255$	0	0
$256$	−14.3000	−0.893753
$257$	−13.3292	−0.831454	−0.415727	−	0.909489i	$-0.636473\pi$
$257$	−13.3292	−0.831454	−0.415727	+	0.909489i	$0.636473\pi$
$258$	−14.3967	−0.896299
$259$	−11.5626	−0.718465
$260$	0	0
$261$	7.14143	0.442044
$262$	−10.0539	−0.621130
$263$	9.78660	0.603468	0.301734	−	0.953392i	$-0.402435\pi$
$263$	9.78660	0.603468	0.301734	+	0.953392i	$0.402435\pi$
$264$	9.38875	0.577838
$265$	0	0
$266$	13.6203	0.835114
$267$	−11.6776	−0.714658
$268$	−6.70322	−0.409464
$269$	−29.9878	−1.82839	−0.914195	−	0.405275i	$-0.867176\pi$
$269$	−29.9878	−1.82839	−0.914195	+	0.405275i	$0.867176\pi$
$270$	0	0
$271$	16.6011	1.00845	0.504224	−	0.863573i	$-0.331779\pi$
$271$	16.6011	1.00845	0.504224	+	0.863573i	$0.331779\pi$
$272$	1.35667	0.0822604
$273$	2.82354	0.170889
$274$	−3.50933	−0.212006
$275$	0	0
$276$	0.704113	0.0423826
$277$	−14.8722	−0.893583	−0.446791	−	0.894638i	$-0.647433\pi$
$277$	−14.8722	−0.893583	−0.446791	+	0.894638i	$0.647433\pi$
$278$	−13.6744	−0.820138
$279$	−13.7462	−0.822962
$280$	0	0
$281$	1.63265	0.0973956	0.0486978	−	0.998814i	$-0.484493\pi$
$281$	1.63265	0.0973956	0.0486978	+	0.998814i	$0.484493\pi$
$282$	−11.8191	−0.703816
$283$	3.03101	0.180175	0.0900873	−	0.995934i	$-0.471285\pi$
$283$	3.03101	0.180175	0.0900873	+	0.995934i	$0.471285\pi$
$284$	4.55781	0.270456
$285$	0	0
$286$	−2.83589	−0.167690
$287$	−11.2085	−0.661616
$288$	−7.16333	−0.422103
$289$	−16.6050	−0.976767
$290$	0	0
$291$	−1.48749	−0.0871979
$292$	−1.16622	−0.0682479
$293$	−15.8732	−0.927320	−0.463660	−	0.886013i	$-0.653464\pi$
$293$	−15.8732	−0.927320	−0.463660	+	0.886013i	$0.653464\pi$
$294$	−4.57392	−0.266757
$295$	0	0
$296$	10.7911	0.627218
$297$	15.0787	0.874956
$298$	21.1328	1.22419
$299$	−0.833084	−0.0481785
$300$	0	0
$301$	40.3330	2.32476
$302$	15.0545	0.866291
$303$	6.66985	0.383173
$304$	−7.77362	−0.445848
$305$	0	0
$306$	1.40136	0.0801106
$307$	12.6560	0.722314	0.361157	−	0.932505i	$-0.382382\pi$
$307$	12.6560	0.722314	0.361157	+	0.932505i	$0.382382\pi$
$308$	−6.71492	−0.382618
$309$	−10.4210	−0.592830
$310$	0	0
$311$	20.3897	1.15619	0.578096	−	0.815969i	$-0.303796\pi$
$311$	20.3897	1.15619	0.578096	+	0.815969i	$0.303796\pi$
$312$	−2.63514	−0.149185
$313$	−4.86495	−0.274983	−0.137492	−	0.990503i	$-0.543904\pi$
$313$	−4.86495	−0.274983	−0.137492	+	0.990503i	$0.543904\pi$
$314$	12.6425	0.713455
$315$	0	0
$316$	−1.29638	−0.0729270
$317$	−1.06221	−0.0596597	−0.0298299	−	0.999555i	$-0.509497\pi$
$317$	−1.06221	−0.0596597	−0.0298299	+	0.999555i	$0.509497\pi$
$318$	−12.7301	−0.713871
$319$	−10.9004	−0.610306
$320$	0	0
$321$	16.2376	0.906294
$322$	3.78168	0.210745
$323$	−2.26313	−0.125924
$324$	−0.423482	−0.0235268
$325$	0	0
$326$	−17.6253	−0.976177
$327$	9.97109	0.551403
$328$	10.4606	0.577589
$329$	33.1117	1.82551
$330$	0	0
$331$	35.6435	1.95914	0.979571	−	0.201100i	$-0.0644515\pi$
$331$	35.6435	1.95914	0.979571	+	0.201100i	$0.0644515\pi$
$332$	−2.66897	−0.146479
$333$	6.81659	0.373547
$334$	−3.48863	−0.190889
$335$	0	0
$336$	7.31522	0.399078
$337$	6.24979	0.340448	0.170224	−	0.985405i	$-0.445551\pi$
$337$	6.24979	0.340448	0.170224	+	0.985405i	$0.445551\pi$
$338$	−14.1081	−0.767381
$339$	5.14428	0.279399
$340$	0	0
$341$	20.9816	1.13622
$342$	−8.02968	−0.434195
$343$	−10.2797	−0.555051
$344$	−37.6417	−2.02951
$345$	0	0
$346$	15.1655	0.815303
$347$	−24.7071	−1.32635	−0.663173	−	0.748466i	$-0.730791\pi$
$347$	−24.7071	−1.32635	−0.663173	+	0.748466i	$0.730791\pi$
$348$	−2.58579	−0.138613
$349$	−11.1131	−0.594873	−0.297437	−	0.954742i	$-0.596132\pi$
$349$	−11.1131	−0.594873	−0.297437	+	0.954742i	$0.596132\pi$
$350$	0	0
$351$	−4.23214	−0.225895
$352$	10.9338	0.582775
$353$	−7.12822	−0.379397	−0.189699	−	0.981842i	$-0.560751\pi$
$353$	−7.12822	−0.379397	−0.189699	+	0.981842i	$0.560751\pi$
$354$	−1.17760	−0.0625889
$355$	0	0
$356$	−7.79463	−0.413115
$357$	2.12968	0.112714
$358$	−12.3980	−0.655253
$359$	21.6836	1.14442	0.572208	−	0.820109i	$-0.306087\pi$
$359$	21.6836	1.14442	0.572208	+	0.820109i	$0.306087\pi$
$360$	0	0
$361$	−6.03248	−0.317499
$362$	0.940716	0.0494430
$363$	2.24622	0.117896
$364$	1.88467	0.0987838
$365$	0	0
$366$	3.17240	0.165824
$367$	−6.29974	−0.328844	−0.164422	−	0.986390i	$-0.552576\pi$
$367$	−6.29974	−0.328844	−0.164422	+	0.986390i	$0.552576\pi$
$368$	−2.15835	−0.112512
$369$	6.60782	0.343990
$370$	0	0
$371$	35.6641	1.85159
$372$	4.97724	0.258058
$373$	21.4105	1.10859	0.554296	−	0.832320i	$-0.312988\pi$
$373$	21.4105	1.10859	0.554296	+	0.832320i	$0.312988\pi$
$374$	−2.13899	−0.110604
$375$	0	0
$376$	−30.9023	−1.59366
$377$	3.05942	0.157568
$378$	19.2113	0.988122
$379$	32.7012	1.67975	0.839873	−	0.542783i	$-0.182629\pi$
$379$	32.7012	1.67975	0.839873	+	0.542783i	$0.182629\pi$
$380$	0	0
$381$	−10.5333	−0.539640
$382$	−23.0738	−1.18056
$383$	7.18879	0.367330	0.183665	−	0.982989i	$-0.441204\pi$
$383$	7.18879	0.367330	0.183665	+	0.982989i	$0.441204\pi$
$384$	−2.49049	−0.127092
$385$	0	0
$386$	23.7178	1.20720
$387$	−23.7778	−1.20870
$388$	−0.992875	−0.0504056
$389$	10.7767	0.546402	0.273201	−	0.961957i	$-0.411918\pi$
$389$	10.7767	0.546402	0.273201	+	0.961957i	$0.411918\pi$
$390$	0	0
$391$	−0.628359	−0.0317775
$392$	−11.9590	−0.604021
$393$	9.00759	0.454373
$394$	−22.0339	−1.11005
$395$	0	0
$396$	3.95870	0.198932
$397$	30.8249	1.54706	0.773528	−	0.633762i	$-0.218490\pi$
$397$	30.8249	1.54706	0.773528	+	0.633762i	$0.218490\pi$
$398$	−11.3799	−0.570423
$399$	−12.2029	−0.610907
$400$	0	0
$401$	7.69003	0.384022	0.192011	−	0.981393i	$-0.438499\pi$
$401$	7.69003	0.384022	0.192011	+	0.981393i	$0.438499\pi$
$402$	−11.5134	−0.574236
$403$	−5.88891	−0.293348
$404$	4.45202	0.221496
$405$	0	0
$406$	−13.8879	−0.689243
$407$	−10.4046	−0.515737
$408$	−1.98757	−0.0983994
$409$	24.1379	1.19354	0.596772	−	0.802411i	$-0.296450\pi$
$409$	24.1379	1.19354	0.596772	+	0.802411i	$0.296450\pi$
$410$	0	0
$411$	3.14412	0.155088
$412$	−6.95586	−0.342691
$413$	3.29911	0.162338
$414$	−2.22945	−0.109571
$415$	0	0
$416$	−3.06880	−0.150460
$417$	12.2514	0.599952
$418$	12.2562	0.599471
$419$	25.7697	1.25893	0.629467	−	0.777028i	$-0.283273\pi$
$419$	25.7697	1.25893	0.629467	+	0.777028i	$0.283273\pi$
$420$	0	0
$421$	23.2177	1.13156	0.565781	−	0.824555i	$-0.308575\pi$
$421$	23.2177	1.13156	0.565781	+	0.824555i	$0.308575\pi$
$422$	23.3895	1.13858
$423$	−19.5206	−0.949124
$424$	−33.2843	−1.61643
$425$	0	0
$426$	7.82846	0.379290
$427$	−8.88761	−0.430102
$428$	10.8384	0.523892
$429$	2.54076	0.122669
$430$	0	0
$431$	−20.3861	−0.981965	−0.490982	−	0.871170i	$-0.663362\pi$
$431$	−20.3861	−0.981965	−0.490982	+	0.871170i	$0.663362\pi$
$432$	−10.9646	−0.527535
$433$	−30.0633	−1.44475	−0.722376	−	0.691500i	$-0.756950\pi$
$433$	−30.0633	−1.44475	−0.722376	+	0.691500i	$0.756950\pi$
$434$	26.7320	1.28318
$435$	0	0
$436$	6.65556	0.318743
$437$	3.60044	0.172232
$438$	−2.00309	−0.0957114
$439$	−37.0184	−1.76679	−0.883396	−	0.468627i	$-0.844749\pi$
$439$	−37.0184	−1.76679	−0.883396	+	0.468627i	$0.844749\pi$
$440$	0	0
$441$	−7.55437	−0.359732
$442$	0.600350	0.0285557
$443$	22.3620	1.06245	0.531224	−	0.847231i	$-0.321732\pi$
$443$	22.3620	1.06245	0.531224	+	0.847231i	$0.321732\pi$
$444$	−2.46817	−0.117134
$445$	0	0
$446$	−16.4353	−0.778235
$447$	−18.9335	−0.895525
$448$	28.1741	1.33110
$449$	7.22323	0.340885	0.170443	−	0.985368i	$-0.445480\pi$
$449$	7.22323	0.340885	0.170443	+	0.985368i	$0.445480\pi$
$450$	0	0
$451$	−10.0859	−0.474928
$452$	3.43373	0.161509
$453$	−13.4878	−0.633714
$454$	9.78104	0.459047
$455$	0	0
$456$	11.3886	0.533320
$457$	−17.3325	−0.810781	−0.405390	−	0.914144i	$-0.632864\pi$
$457$	−17.3325	−0.810781	−0.405390	+	0.914144i	$0.632864\pi$
$458$	−17.8395	−0.833584
$459$	−3.19212	−0.148995
$460$	0	0
$461$	−5.56629	−0.259248	−0.129624	−	0.991563i	$-0.541377\pi$
$461$	−5.56629	−0.259248	−0.129624	+	0.991563i	$0.541377\pi$
$462$	−11.5335	−0.536587
$463$	−10.3667	−0.481780	−0.240890	−	0.970552i	$-0.577439\pi$
$463$	−10.3667	−0.481780	−0.240890	+	0.970552i	$0.577439\pi$
$464$	7.92633	0.367970
$465$	0	0
$466$	0.347076	0.0160780
$467$	21.0865	0.975765	0.487883	−	0.872909i	$-0.337769\pi$
$467$	21.0865	0.975765	0.487883	+	0.872909i	$0.337769\pi$
$468$	−1.11109	−0.0513600
$469$	32.2553	1.48941
$470$	0	0
$471$	−11.3268	−0.521911
$472$	−3.07897	−0.141721
$473$	36.2936	1.66878
$474$	−2.22665	−0.102273
$475$	0	0
$476$	1.42153	0.0651556
$477$	−21.0253	−0.962683
$478$	−14.7065	−0.672661
$479$	−5.85215	−0.267392	−0.133696	−	0.991022i	$-0.542684\pi$
$479$	−5.85215	−0.267392	−0.133696	+	0.991022i	$0.542684\pi$
$480$	0	0
$481$	2.92026	0.133152
$482$	−29.0841	−1.32474
$483$	−3.38813	−0.154165
$484$	1.49932	0.0681509
$485$	0	0
$486$	−18.1969	−0.825429
$487$	5.39400	0.244426	0.122213	−	0.992504i	$-0.461001\pi$
$487$	5.39400	0.244426	0.122213	+	0.992504i	$0.461001\pi$
$488$	8.29457	0.375478
$489$	15.7911	0.714098
$490$	0	0
$491$	18.5661	0.837875	0.418937	−	0.908015i	$-0.362403\pi$
$491$	18.5661	0.837875	0.418937	+	0.908015i	$0.362403\pi$
$492$	−2.39258	−0.107866
$493$	2.30759	0.103928
$494$	−3.43995	−0.154771
$495$	0	0
$496$	−15.2570	−0.685058
$497$	−21.9318	−0.983775
$498$	−4.58420	−0.205423
$499$	−9.37038	−0.419476	−0.209738	−	0.977758i	$-0.567261\pi$
$499$	−9.37038	−0.419476	−0.209738	+	0.977758i	$0.567261\pi$
$500$	0	0
$501$	3.12557	0.139640
$502$	22.1330	0.987845
$503$	20.5578	0.916628	0.458314	−	0.888790i	$-0.348454\pi$
$503$	20.5578	0.916628	0.458314	+	0.888790i	$0.348454\pi$
$504$	19.7565	0.880023
$505$	0	0
$506$	3.40295	0.151279
$507$	12.6399	0.561359
$508$	−7.03085	−0.311944
$509$	6.64532	0.294549	0.147274	−	0.989096i	$-0.452950\pi$
$509$	6.64532	0.294549	0.147274	+	0.989096i	$0.452950\pi$
$510$	0	0
$511$	5.61175	0.248249
$512$	−21.2438	−0.938853
$513$	18.2906	0.807548
$514$	−15.2815	−0.674039
$515$	0	0
$516$	8.60953	0.379014
$517$	29.7955	1.31041
$518$	−13.2561	−0.582442
$519$	−13.5873	−0.596415
$520$	0	0
$521$	−11.7864	−0.516373	−0.258187	−	0.966095i	$-0.583125\pi$
$521$	−11.7864	−0.516373	−0.258187	+	0.966095i	$0.583125\pi$
$522$	8.18742	0.358354
$523$	−9.64066	−0.421557	−0.210778	−	0.977534i	$-0.567600\pi$
$523$	−9.64066	−0.421557	−0.210778	+	0.977534i	$0.567600\pi$
$524$	6.01243	0.262654
$525$	0	0
$526$	11.2200	0.489216
$527$	−4.44175	−0.193486
$528$	6.58260	0.286471
$529$	−22.0003	−0.956536
$530$	0	0
$531$	−1.94495	−0.0844036
$532$	−8.14523	−0.353140
$533$	2.83082	0.122616
$534$	−13.3880	−0.579356
$535$	0	0
$536$	−30.1030	−1.30025
$537$	11.1077	0.479335
$538$	−34.3801	−1.48223
$539$	11.5307	0.496663
$540$	0	0
$541$	−6.26970	−0.269555	−0.134778	−	0.990876i	$-0.543032\pi$
$541$	−6.26970	−0.269555	−0.134778	+	0.990876i	$0.543032\pi$
$542$	19.0327	0.817523
$543$	−0.842818	−0.0361688
$544$	−2.31466	−0.0992403
$545$	0	0
$546$	3.23710	0.138535
$547$	14.3116	0.611919	0.305960	−	0.952044i	$-0.401023\pi$
$547$	14.3116	0.611919	0.305960	+	0.952044i	$0.401023\pi$
$548$	2.09866	0.0896501
$549$	5.23959	0.223620
$550$	0	0
$551$	−13.2223	−0.563287
$552$	3.16205	0.134586
$553$	6.23806	0.265269
$554$	−17.0505	−0.724405
$555$	0	0
$556$	8.17760	0.346808
$557$	33.0577	1.40070	0.700350	−	0.713800i	$-0.253027\pi$
$557$	33.0577	1.40070	0.700350	+	0.713800i	$0.253027\pi$
$558$	−15.7595	−0.667154
$559$	−10.1865	−0.430844
$560$	0	0
$561$	1.91639	0.0809100
$562$	1.87178	0.0789562
$563$	−40.9293	−1.72496	−0.862482	−	0.506088i	$-0.831091\pi$
$563$	−40.9293	−1.72496	−0.862482	+	0.506088i	$0.831091\pi$
$564$	7.06807	0.297619
$565$	0	0
$566$	3.47495	0.146063
$567$	2.03776	0.0855778
$568$	20.4683	0.858833
$569$	39.2363	1.64487	0.822435	−	0.568859i	$-0.192615\pi$
$569$	39.2363	1.64487	0.822435	+	0.568859i	$0.192615\pi$
$570$	0	0
$571$	1.80646	0.0755981	0.0377991	−	0.999285i	$-0.487965\pi$
$571$	1.80646	0.0755981	0.0377991	+	0.999285i	$0.487965\pi$
$572$	1.69592	0.0709101
$573$	20.6725	0.863608
$574$	−12.8502	−0.536355
$575$	0	0
$576$	−16.6097	−0.692070
$577$	−6.56710	−0.273392	−0.136696	−	0.990613i	$-0.543648\pi$
$577$	−6.56710	−0.273392	−0.136696	+	0.990613i	$0.543648\pi$
$578$	−19.0371	−0.791840
$579$	−21.2495	−0.883100
$580$	0	0
$581$	12.8428	0.532811
$582$	−1.70535	−0.0706892
$583$	32.0923	1.32913
$584$	−5.23730	−0.216721
$585$	0	0
$586$	−18.1981	−0.751755
$587$	−46.3020	−1.91109	−0.955544	−	0.294849i	$-0.904731\pi$
$587$	−46.3020	−1.91109	−0.955544	+	0.294849i	$0.904731\pi$
$588$	2.73530	0.112802
$589$	25.4508	1.04868
$590$	0	0
$591$	19.7408	0.812030
$592$	7.56578	0.310952
$593$	4.90532	0.201437	0.100719	−	0.994915i	$-0.467886\pi$
$593$	4.90532	0.201437	0.100719	+	0.994915i	$0.467886\pi$
$594$	17.2873	0.709305
$595$	0	0
$596$	−12.6378	−0.517666
$597$	10.1956	0.417279
$598$	−0.955104	−0.0390571
$599$	−42.7804	−1.74796	−0.873980	−	0.485961i	$-0.838470\pi$
$599$	−42.7804	−1.74796	−0.873980	+	0.485961i	$0.838470\pi$
$600$	0	0
$601$	−8.52795	−0.347862	−0.173931	−	0.984758i	$-0.555647\pi$
$601$	−8.52795	−0.347862	−0.173931	+	0.984758i	$0.555647\pi$
$602$	46.2405	1.88462
$603$	−19.0157	−0.774380
$604$	−9.00293	−0.366324
$605$	0	0
$606$	7.64676	0.310628
$607$	10.5441	0.427972	0.213986	−	0.976837i	$-0.431355\pi$
$607$	10.5441	0.427972	0.213986	+	0.976837i	$0.431355\pi$
$608$	13.2628	0.537877
$609$	12.4426	0.504199
$610$	0	0
$611$	−8.36271	−0.338319
$612$	−0.838045	−0.0338760
$613$	14.9527	0.603935	0.301968	−	0.953318i	$-0.402357\pi$
$613$	14.9527	0.603935	0.301968	+	0.953318i	$0.402357\pi$
$614$	14.5097	0.585562
$615$	0	0
$616$	−30.1555	−1.21500
$617$	12.7907	0.514936	0.257468	−	0.966287i	$-0.417112\pi$
$617$	12.7907	0.514936	0.257468	+	0.966287i	$0.417112\pi$
$618$	−11.9473	−0.480592
$619$	−0.796949	−0.0320321	−0.0160160	−	0.999872i	$-0.505098\pi$
$619$	−0.796949	−0.0320321	−0.0160160	+	0.999872i	$0.505098\pi$
$620$	0	0
$621$	5.07839	0.203789
$622$	23.3761	0.937295
$623$	37.5071	1.50269
$624$	−1.84754	−0.0739607
$625$	0	0
$626$	−5.57751	−0.222922
$627$	−10.9807	−0.438528
$628$	−7.56046	−0.301695
$629$	2.20262	0.0878243
$630$	0	0
$631$	24.3664	0.970010	0.485005	−	0.874512i	$-0.338818\pi$
$631$	24.3664	0.970010	0.485005	+	0.874512i	$0.338818\pi$
$632$	−5.82182	−0.231580
$633$	−20.9554	−0.832902
$634$	−1.21779	−0.0483646
$635$	0	0
$636$	7.61290	0.301871
$637$	−3.23632	−0.128228
$638$	−12.4970	−0.494760
$639$	12.9296	0.511488
$640$	0	0
$641$	−35.8014	−1.41407	−0.707036	−	0.707177i	$-0.749968\pi$
$641$	−35.8014	−1.41407	−0.707036	+	0.707177i	$0.749968\pi$
$642$	18.6159	0.734710
$643$	39.5147	1.55831	0.779154	−	0.626833i	$-0.215649\pi$
$643$	39.5147	1.55831	0.779154	+	0.626833i	$0.215649\pi$
$644$	−2.26153	−0.0891167
$645$	0	0
$646$	−2.59460	−0.102083
$647$	3.32514	0.130725	0.0653623	−	0.997862i	$-0.479180\pi$
$647$	3.32514	0.130725	0.0653623	+	0.997862i	$0.479180\pi$
$648$	−1.90178	−0.0747091
$649$	2.96870	0.116532
$650$	0	0
$651$	−23.9501	−0.938677
$652$	10.5403	0.412791
$653$	−8.03312	−0.314360	−0.157180	−	0.987570i	$-0.550240\pi$
$653$	−8.03312	−0.314360	−0.157180	+	0.987570i	$0.550240\pi$
$654$	11.4315	0.447008
$655$	0	0
$656$	7.33407	0.286347
$657$	−3.30834	−0.129071
$658$	37.9615	1.47989
$659$	35.8477	1.39643	0.698214	−	0.715889i	$-0.253978\pi$
$659$	35.8477	1.39643	0.698214	+	0.715889i	$0.253978\pi$
$660$	0	0
$661$	10.2271	0.397789	0.198895	−	0.980021i	$-0.436265\pi$
$661$	10.2271	0.397789	0.198895	+	0.980021i	$0.436265\pi$
$662$	40.8641	1.58823
$663$	−0.537872	−0.0208892
$664$	−11.9859	−0.465143
$665$	0	0
$666$	7.81500	0.302825
$667$	−3.67117	−0.142148
$668$	2.08627	0.0807203
$669$	14.7249	0.569299
$670$	0	0
$671$	−7.99751	−0.308741
$672$	−12.4807	−0.481454
$673$	29.4353	1.13465	0.567324	−	0.823495i	$-0.307979\pi$
$673$	29.4353	1.13465	0.567324	+	0.823495i	$0.307979\pi$
$674$	7.16518	0.275992
$675$	0	0
$676$	8.43696	0.324499
$677$	−10.4025	−0.399800	−0.199900	−	0.979816i	$-0.564062\pi$
$677$	−10.4025	−0.399800	−0.199900	+	0.979816i	$0.564062\pi$
$678$	5.89775	0.226502
$679$	4.77763	0.183348
$680$	0	0
$681$	−8.76315	−0.335805
$682$	24.0548	0.921105
$683$	−39.3305	−1.50494	−0.752470	−	0.658627i	$-0.771138\pi$
$683$	−39.3305	−1.50494	−0.752470	+	0.658627i	$0.771138\pi$
$684$	4.80192	0.183606
$685$	0	0
$686$	−11.7853	−0.449966
$687$	15.9830	0.609788
$688$	−26.3912	−1.00615
$689$	−9.00733	−0.343152
$690$	0	0
$691$	−35.0099	−1.33184	−0.665921	−	0.746023i	$-0.731961\pi$
$691$	−35.0099	−1.33184	−0.665921	+	0.746023i	$0.731961\pi$
$692$	−9.06930	−0.344763
$693$	−19.0489	−0.723609
$694$	−28.3259	−1.07524
$695$	0	0
$696$	−11.6123	−0.440164
$697$	2.13516	0.0808751
$698$	−12.7409	−0.482249
$699$	−0.310956	−0.0117614
$700$	0	0
$701$	−20.8042	−0.785764	−0.392882	−	0.919589i	$-0.628522\pi$
$701$	−20.8042	−0.785764	−0.392882	+	0.919589i	$0.628522\pi$
$702$	−4.85201	−0.183127
$703$	−12.6208	−0.476004
$704$	25.3524	0.955505
$705$	0	0
$706$	−8.17228	−0.307568
$707$	−21.4227	−0.805685
$708$	0.704231	0.0264666
$709$	11.5386	0.433341	0.216670	−	0.976245i	$-0.430480\pi$
$709$	11.5386	0.433341	0.216670	+	0.976245i	$0.430480\pi$
$710$	0	0
$711$	−3.67758	−0.137920
$712$	−35.0044	−1.31184
$713$	7.06644	0.264640
$714$	2.44161	0.0913748
$715$	0	0
$716$	7.41426	0.277084
$717$	13.1761	0.492069
$718$	24.8595	0.927749
$719$	−24.3609	−0.908507	−0.454253	−	0.890873i	$-0.650094\pi$
$719$	−24.3609	−0.908507	−0.454253	+	0.890873i	$0.650094\pi$
$720$	0	0
$721$	33.4710	1.24653
$722$	−6.91604	−0.257388
$723$	26.0574	0.969083
$724$	−0.562569	−0.0209077
$725$	0	0
$726$	2.57522	0.0955754
$727$	−47.5084	−1.76199	−0.880994	−	0.473128i	$-0.843125\pi$
$727$	−47.5084	−1.76199	−0.880994	+	0.473128i	$0.843125\pi$
$728$	8.46375	0.313688
$729$	14.4502	0.535192
$730$	0	0
$731$	−7.68325	−0.284175
$732$	−1.89716	−0.0701211
$733$	34.6034	1.27810	0.639052	−	0.769163i	$-0.279327\pi$
$733$	34.6034	1.27810	0.639052	+	0.769163i	$0.279327\pi$
$734$	−7.22244	−0.266585
$735$	0	0
$736$	3.68242	0.135736
$737$	29.0249	1.06915
$738$	7.57566	0.278864
$739$	22.6188	0.832046	0.416023	−	0.909354i	$-0.363424\pi$
$739$	22.6188	0.832046	0.416023	+	0.909354i	$0.363424\pi$
$740$	0	0
$741$	3.08196	0.113219
$742$	40.8877	1.50103
$743$	8.63058	0.316625	0.158313	−	0.987389i	$-0.449395\pi$
$743$	8.63058	0.316625	0.158313	+	0.987389i	$0.449395\pi$
$744$	22.3520	0.819462
$745$	0	0
$746$	24.5464	0.898708
$747$	−7.57135	−0.277021
$748$	1.27916	0.0467708
$749$	−52.1532	−1.90564
$750$	0	0
$751$	−43.7245	−1.59553	−0.797764	−	0.602970i	$-0.793984\pi$
$751$	−43.7245	−1.59553	−0.797764	+	0.602970i	$0.793984\pi$
$752$	−21.6661	−0.790080
$753$	−19.8297	−0.722634
$754$	3.50752	0.127736
$755$	0	0
$756$	−11.4888	−0.417842
$757$	35.8183	1.30184	0.650919	−	0.759148i	$-0.274384\pi$
$757$	35.8183	1.30184	0.650919	+	0.759148i	$0.274384\pi$
$758$	37.4908	1.36173
$759$	−3.04881	−0.110665
$760$	0	0
$761$	−5.35421	−0.194090	−0.0970451	−	0.995280i	$-0.530939\pi$
$761$	−5.35421	−0.194090	−0.0970451	+	0.995280i	$0.530939\pi$
$762$	−12.0761	−0.437472
$763$	−32.0260	−1.15942
$764$	13.7986	0.499217
$765$	0	0
$766$	8.24172	0.297785
$767$	−0.833224	−0.0300860
$768$	14.6884	0.530022
$769$	9.79310	0.353148	0.176574	−	0.984287i	$-0.443498\pi$
$769$	9.79310	0.353148	0.176574	+	0.984287i	$0.443498\pi$
$770$	0	0
$771$	13.6912	0.493077
$772$	−14.1837	−0.510484
$773$	1.70697	0.0613956	0.0306978	−	0.999529i	$-0.490227\pi$
$773$	1.70697	0.0613956	0.0306978	+	0.999529i	$0.490227\pi$
$774$	−27.2605	−0.979859
$775$	0	0
$776$	−4.45883	−0.160063
$777$	11.8766	0.426071
$778$	12.3552	0.442954
$779$	−12.2343	−0.438339
$780$	0	0
$781$	−19.7353	−0.706184
$782$	−0.720393	−0.0257612
$783$	−18.6499	−0.666492
$784$	−8.38465	−0.299452
$785$	0	0
$786$	10.3269	0.368349
$787$	−31.8490	−1.13529	−0.567646	−	0.823272i	$-0.692146\pi$
$787$	−31.8490	−1.13529	−0.567646	+	0.823272i	$0.692146\pi$
$788$	13.1767	0.469401
$789$	−10.0524	−0.357874
$790$	0	0
$791$	−16.5228	−0.587483
$792$	17.7778	0.631708
$793$	2.24466	0.0797102
$794$	35.3397	1.25416
$795$	0	0
$796$	6.80543	0.241212
$797$	−46.0496	−1.63116	−0.815581	−	0.578643i	$-0.803583\pi$
$797$	−46.0496	−1.63116	−0.815581	+	0.578643i	$0.803583\pi$
$798$	−13.9902	−0.495247
$799$	−6.30763	−0.223148
$800$	0	0
$801$	−22.1119	−0.781284
$802$	8.81638	0.311317
$803$	5.04973	0.178201
$804$	6.88526	0.242824
$805$	0	0
$806$	−6.75145	−0.237810
$807$	30.8022	1.08429
$808$	19.9933	0.703361
$809$	−5.84368	−0.205453	−0.102726	−	0.994710i	$-0.532757\pi$
$809$	−5.84368	−0.205453	−0.102726	+	0.994710i	$0.532757\pi$
$810$	0	0
$811$	−46.2132	−1.62276	−0.811382	−	0.584516i	$-0.801284\pi$
$811$	−46.2132	−1.62276	−0.811382	+	0.584516i	$0.801284\pi$
$812$	8.30524	0.291457
$813$	−17.0520	−0.598039
$814$	−11.9285	−0.418095
$815$	0	0
$816$	−1.39352	−0.0487829
$817$	44.0243	1.54022
$818$	27.6734	0.967577
$819$	5.34646	0.186820
$820$	0	0
$821$	−18.6636	−0.651363	−0.325682	−	0.945479i	$-0.605594\pi$
$821$	−18.6636	−0.651363	−0.325682	+	0.945479i	$0.605594\pi$
$822$	3.60463	0.125726
$823$	48.4550	1.68904	0.844518	−	0.535527i	$-0.179887\pi$
$823$	48.4550	1.68904	0.844518	+	0.535527i	$0.179887\pi$
$824$	−31.2376	−1.08821
$825$	0	0
$826$	3.78232	0.131604
$827$	−13.9057	−0.483549	−0.241774	−	0.970333i	$-0.577729\pi$
$827$	−13.9057	−0.483549	−0.241774	+	0.970333i	$0.577729\pi$
$828$	1.33326	0.0463339
$829$	−39.2785	−1.36420	−0.682100	−	0.731259i	$-0.738933\pi$
$829$	−39.2785	−1.36420	−0.682100	+	0.731259i	$0.738933\pi$
$830$	0	0
$831$	15.2761	0.529921
$832$	−7.11566	−0.246691
$833$	−2.44102	−0.0845762
$834$	14.0458	0.486366
$835$	0	0
$836$	−7.32948	−0.253495
$837$	35.8982	1.24082
$838$	29.5441	1.02059
$839$	−49.3102	−1.70238	−0.851189	−	0.524860i	$-0.824118\pi$
$839$	−49.3102	−1.70238	−0.851189	+	0.524860i	$0.824118\pi$
$840$	0	0
$841$	−15.5180	−0.535103
$842$	26.6184	0.917329
$843$	−1.67699	−0.0577585
$844$	−13.9874	−0.481466
$845$	0	0
$846$	−22.3797	−0.769431
$847$	−7.21459	−0.247896
$848$	−23.3361	−0.801367
$849$	−3.11332	−0.106849
$850$	0	0
$851$	−3.50418	−0.120122
$852$	−4.68159	−0.160388
$853$	0.931425	0.0318914	0.0159457	−	0.999873i	$-0.494924\pi$
$853$	0.931425	0.0318914	0.0159457	+	0.999873i	$0.494924\pi$
$854$	−10.1894	−0.348673
$855$	0	0
$856$	48.6732	1.66362
$857$	21.5435	0.735913	0.367957	−	0.929843i	$-0.380057\pi$
$857$	21.5435	0.735913	0.367957	+	0.929843i	$0.380057\pi$
$858$	2.91290	0.0994449
$859$	50.6948	1.72968	0.864842	−	0.502044i	$-0.167419\pi$
$859$	50.6948	1.72968	0.864842	+	0.502044i	$0.167419\pi$
$860$	0	0
$861$	11.5129	0.392357
$862$	−23.3720	−0.796054
$863$	−16.1141	−0.548532	−0.274266	−	0.961654i	$-0.588435\pi$
$863$	−16.1141	−0.548532	−0.274266	+	0.961654i	$0.588435\pi$
$864$	18.7070	0.636427
$865$	0	0
$866$	−34.4667	−1.17122
$867$	17.0560	0.579251
$868$	−15.9863	−0.542611
$869$	5.61332	0.190419
$870$	0	0
$871$	−8.14641	−0.276031
$872$	29.8890	1.01217
$873$	−2.81659	−0.0953272
$874$	4.12779	0.139625
$875$	0	0
$876$	1.19789	0.0404730
$877$	19.3977	0.655015	0.327507	−	0.944849i	$-0.393791\pi$
$877$	19.3977	0.655015	0.327507	+	0.944849i	$0.393791\pi$
$878$	−42.4404	−1.43229
$879$	16.3042	0.549928
$880$	0	0
$881$	−32.2010	−1.08488	−0.542440	−	0.840094i	$-0.682499\pi$
$881$	−32.2010	−1.08488	−0.542440	+	0.840094i	$0.682499\pi$
$882$	−8.66084	−0.291626
$883$	22.4980	0.757118	0.378559	−	0.925577i	$-0.376420\pi$
$883$	22.4980	0.757118	0.378559	+	0.925577i	$0.376420\pi$
$884$	−0.359022	−0.0120752
$885$	0	0
$886$	25.6373	0.861301
$887$	−29.5476	−0.992111	−0.496056	−	0.868291i	$-0.665219\pi$
$887$	−29.5476	−0.992111	−0.496056	+	0.868291i	$0.665219\pi$
$888$	−11.0841	−0.371959
$889$	33.8319	1.13468
$890$	0	0
$891$	1.83367	0.0614304
$892$	9.82868	0.329088
$893$	36.1421	1.20945
$894$	−21.7067	−0.725980
$895$	0	0
$896$	7.99917	0.267233
$897$	0.855708	0.0285713
$898$	8.28120	0.276347
$899$	−25.9508	−0.865508
$900$	0	0
$901$	−6.79384	−0.226336
$902$	−11.5632	−0.385013
$903$	−41.4283	−1.37865
$904$	15.4203	0.512871
$905$	0	0
$906$	−15.4634	−0.513736
$907$	43.0986	1.43107	0.715533	−	0.698579i	$-0.246184\pi$
$907$	43.0986	1.43107	0.715533	+	0.698579i	$0.246184\pi$
$908$	−5.84927	−0.194115
$909$	12.6295	0.418895
$910$	0	0
$911$	−28.6401	−0.948890	−0.474445	−	0.880285i	$-0.657351\pi$
$911$	−28.6401	−0.948890	−0.474445	+	0.880285i	$0.657351\pi$
$912$	7.98473	0.264401
$913$	11.5566	0.382469
$914$	−19.8712	−0.657280
$915$	0	0
$916$	10.6684	0.352494
$917$	−28.9313	−0.955395
$918$	−3.65966	−0.120787
$919$	38.4970	1.26990	0.634949	−	0.772554i	$-0.281021\pi$
$919$	38.4970	1.26990	0.634949	+	0.772554i	$0.281021\pi$
$920$	0	0
$921$	−12.9997	−0.428353
$922$	−6.38157	−0.210166
$923$	5.53910	0.182322
$924$	6.89728	0.226904
$925$	0	0
$926$	−11.8850	−0.390567
$927$	−19.7324	−0.648098
$928$	−13.5233	−0.443925
$929$	25.7844	0.845957	0.422979	−	0.906140i	$-0.360985\pi$
$929$	25.7844	0.845957	0.422979	+	0.906140i	$0.360985\pi$
$930$	0	0
$931$	13.9868	0.458399
$932$	−0.207559	−0.00679881
$933$	−20.9434	−0.685655
$934$	24.1750	0.791029
$935$	0	0
$936$	−4.98970	−0.163094
$937$	37.9054	1.23832	0.619158	−	0.785267i	$-0.287474\pi$
$937$	37.9054	1.23832	0.619158	+	0.785267i	$0.287474\pi$
$938$	36.9796	1.20743
$939$	4.99707	0.163073
$940$	0	0
$941$	−47.8435	−1.55965	−0.779826	−	0.625996i	$-0.784693\pi$
$941$	−47.8435	−1.55965	−0.779826	+	0.625996i	$0.784693\pi$
$942$	−12.9858	−0.423100
$943$	−3.39686	−0.110617
$944$	−2.15871	−0.0702601
$945$	0	0
$946$	41.6095	1.35284
$947$	−9.75319	−0.316936	−0.158468	−	0.987364i	$-0.550655\pi$
$947$	−9.75319	−0.316936	−0.158468	+	0.987364i	$0.550655\pi$
$948$	1.33159	0.0432479
$949$	−1.41731	−0.0460077
$950$	0	0
$951$	1.09106	0.0353800
$952$	6.38384	0.206901
$953$	−48.3185	−1.56519	−0.782596	−	0.622530i	$-0.786105\pi$
$953$	−48.3185	−1.56519	−0.782596	+	0.622530i	$0.786105\pi$
$954$	−24.1048	−0.780423
$955$	0	0
$956$	8.79482	0.284445
$957$	11.1964	0.361930
$958$	−6.70930	−0.216768
$959$	−10.0985	−0.326099
$960$	0	0
$961$	18.9513	0.611334
$962$	3.34798	0.107943
$963$	30.7463	0.990786
$964$	17.3929	0.560187
$965$	0	0
$966$	−3.88438	−0.124978
$967$	−16.5230	−0.531342	−0.265671	−	0.964064i	$-0.585594\pi$
$967$	−16.5230	−0.531342	−0.265671	+	0.964064i	$0.585594\pi$
$968$	6.73319	0.216413
$969$	2.32459	0.0746765
$970$	0	0
$971$	50.3189	1.61481	0.807405	−	0.589998i	$-0.200872\pi$
$971$	50.3189	1.61481	0.807405	+	0.589998i	$0.200872\pi$
$972$	10.8821	0.349045
$973$	−39.3499	−1.26150
$974$	6.18405	0.198150
$975$	0	0
$976$	5.81545	0.186148
$977$	−18.5707	−0.594128	−0.297064	−	0.954858i	$-0.596007\pi$
$977$	−18.5707	−0.594128	−0.297064	+	0.954858i	$0.596007\pi$
$978$	18.1040	0.578901
$979$	33.7507	1.07868
$980$	0	0
$981$	18.8805	0.602809
$982$	21.2854	0.679244
$983$	−58.2241	−1.85706	−0.928530	−	0.371257i	$-0.878927\pi$
$983$	−58.2241	−1.85706	−0.928530	+	0.371257i	$0.878927\pi$
$984$	−10.7447	−0.342527
$985$	0	0
$986$	2.64557	0.0842522
$987$	−34.0109	−1.08258
$988$	2.05716	0.0654471
$989$	12.2234	0.388681
$990$	0	0
$991$	45.5975	1.44845	0.724226	−	0.689563i	$-0.242197\pi$
$991$	45.5975	1.44845	0.724226	+	0.689563i	$0.242197\pi$
$992$	26.0304	0.826465
$993$	−36.6114	−1.16183
$994$	−25.1441	−0.797522
$995$	0	0
$996$	2.74145	0.0868662
$997$	14.4771	0.458494	0.229247	−	0.973368i	$-0.426374\pi$
$997$	14.4771	0.458494	0.229247	+	0.973368i	$0.426374\pi$
$998$	−10.7428	−0.340059
$999$	−17.8016	−0.563216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1475.2.a.q.1.5	yes	7
5.2	odd	4		1475.2.b.i.1299.10		14
5.3	odd	4		1475.2.b.i.1299.5		14
5.4	even	2		1475.2.a.m.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1475.2.a.m.1.3	✓	7	5.4	even	2
1475.2.a.q.1.5	yes	7	1.1	even	1	trivial
1475.2.b.i.1299.5		14	5.3	odd	4
1475.2.b.i.1299.10		14	5.2	odd	4

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:	\( N \)	\(=\)	\( 1475 = 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1475.a (trivial)

\(f(q)\)	\(=\)	\(q+1.14647 q^{2} -1.02716 q^{3} -0.685612 q^{4} -1.17760 q^{6} +3.29911 q^{7} -3.07897 q^{8} -1.94495 q^{9} +O(q^{10})\)	\(q+1.14647 q^{2} -1.02716 q^{3} -0.685612 q^{4} -1.17760 q^{6} +3.29911 q^{7} -3.07897 q^{8} -1.94495 q^{9} +2.96870 q^{11} +0.704231 q^{12} -0.833224 q^{13} +3.78232 q^{14} -2.15871 q^{16} -0.628465 q^{17} -2.22982 q^{18} +3.60104 q^{19} -3.38870 q^{21} +3.40352 q^{22} +0.999832 q^{23} +3.16258 q^{24} -0.955264 q^{26} +5.07924 q^{27} -2.26191 q^{28} -3.67179 q^{29} +7.06763 q^{31} +3.68304 q^{32} -3.04932 q^{33} -0.720514 q^{34} +1.33348 q^{36} -3.50477 q^{37} +4.12848 q^{38} +0.855852 q^{39} -3.39743 q^{41} -3.88503 q^{42} +12.2254 q^{43} -2.03538 q^{44} +1.14628 q^{46} +10.0366 q^{47} +2.21734 q^{48} +3.88410 q^{49} +0.645532 q^{51} +0.571268 q^{52} +10.8102 q^{53} +5.82318 q^{54} -10.1578 q^{56} -3.69884 q^{57} -4.20958 q^{58} +1.00000 q^{59} -2.69395 q^{61} +8.10280 q^{62} -6.41659 q^{63} +8.53991 q^{64} -3.49595 q^{66} +9.77698 q^{67} +0.430883 q^{68} -1.02698 q^{69} -6.64780 q^{71} +5.98843 q^{72} +1.70099 q^{73} -4.01810 q^{74} -2.46892 q^{76} +9.79405 q^{77} +0.981206 q^{78} +1.89083 q^{79} +0.617670 q^{81} -3.89504 q^{82} +3.89283 q^{83} +2.32333 q^{84} +14.0161 q^{86} +3.77150 q^{87} -9.14052 q^{88} +11.3689 q^{89} -2.74889 q^{91} -0.685497 q^{92} -7.25956 q^{93} +11.5066 q^{94} -3.78306 q^{96} +1.44816 q^{97} +4.45299 q^{98} -5.77396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} + 18 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 + 18 * q^8 + 7 * q^9	\( 7 q + 2 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} + 18 q^{8} + 7 q^{9} + 5 q^{11} - q^{12} + 17 q^{13} + 8 q^{14} + 8 q^{16} + 6 q^{17} - 15 q^{18} + 3 q^{19} - 13 q^{21} + 20 q^{22} - 6 q^{23} + 9 q^{24} - 3 q^{26} + 11 q^{27} - 3 q^{28} - 10 q^{29} + q^{31} + 18 q^{32} - 5 q^{34} - 35 q^{36} + 34 q^{37} - 23 q^{38} - 5 q^{39} - 8 q^{41} + 26 q^{42} + 40 q^{43} + 35 q^{44} - 7 q^{46} + 26 q^{47} + 12 q^{48} + 10 q^{49} - 28 q^{51} + 4 q^{52} + 3 q^{53} + 16 q^{54} + 9 q^{56} + q^{57} - 12 q^{58} + 7 q^{59} + 9 q^{61} + 29 q^{62} + 14 q^{63} + 32 q^{64} - 43 q^{66} + 20 q^{67} - 6 q^{68} + 10 q^{69} - 6 q^{71} + 2 q^{72} + 33 q^{73} + 29 q^{74} - 68 q^{76} - 2 q^{77} - 12 q^{78} + 14 q^{79} + 15 q^{81} + 14 q^{82} + 5 q^{83} + 46 q^{84} + 16 q^{86} + 28 q^{87} + 15 q^{88} + 7 q^{89} - 17 q^{91} + 2 q^{92} + 38 q^{93} - 20 q^{94} + 37 q^{96} - 12 q^{97} - 7 q^{98} - 37 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 + 18 * q^8 + 7 * q^9 + 5 * q^11 - q^12 + 17 * q^13 + 8 * q^14 + 8 * q^16 + 6 * q^17 - 15 * q^18 + 3 * q^19 - 13 * q^21 + 20 * q^22 - 6 * q^23 + 9 * q^24 - 3 * q^26 + 11 * q^27 - 3 * q^28 - 10 * q^29 + q^31 + 18 * q^32 - 5 * q^34 - 35 * q^36 + 34 * q^37 - 23 * q^38 - 5 * q^39 - 8 * q^41 + 26 * q^42 + 40 * q^43 + 35 * q^44 - 7 * q^46 + 26 * q^47 + 12 * q^48 + 10 * q^49 - 28 * q^51 + 4 * q^52 + 3 * q^53 + 16 * q^54 + 9 * q^56 + q^57 - 12 * q^58 + 7 * q^59 + 9 * q^61 + 29 * q^62 + 14 * q^63 + 32 * q^64 - 43 * q^66 + 20 * q^67 - 6 * q^68 + 10 * q^69 - 6 * q^71 + 2 * q^72 + 33 * q^73 + 29 * q^74 - 68 * q^76 - 2 * q^77 - 12 * q^78 + 14 * q^79 + 15 * q^81 + 14 * q^82 + 5 * q^83 + 46 * q^84 + 16 * q^86 + 28 * q^87 + 15 * q^88 + 7 * q^89 - 17 * q^91 + 2 * q^92 + 38 * q^93 - 20 * q^94 + 37 * q^96 - 12 * q^97 - 7 * q^98 - 37 * q^99

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