LMFDB - Embedded newform 1425.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1425,2,Mod(1,1425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1425.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1425 = 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1425.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:	$11.3786822880$
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} - 3x^{6} - 8x^{5} + 26x^{4} + 11x^{3} - 51x^{2} + 12x + 4 $ x^7 - 3x^6 - 8x^5 + 26x^4 + 11x^3 - 51x^2 + 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.57229$ of defining polynomial
Character	$\chi$	$=$	1425.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.57229 q^{2} +1.00000 q^{3} +0.472094 q^{4} +1.57229 q^{6} +1.87913 q^{7} -2.40231 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.57229 q^{2} +1.00000 q^{3} +0.472094 q^{4} +1.57229 q^{6} +1.87913 q^{7} -2.40231 q^{8} +1.00000 q^{9} +1.92081 q^{11} +0.472094 q^{12} +0.248324 q^{13} +2.95453 q^{14} -4.72132 q^{16} +7.06596 q^{17} +1.57229 q^{18} +1.00000 q^{19} +1.87913 q^{21} +3.02007 q^{22} -1.20286 q^{23} -2.40231 q^{24} +0.390437 q^{26} +1.00000 q^{27} +0.887125 q^{28} +2.58170 q^{29} +8.69676 q^{31} -2.61865 q^{32} +1.92081 q^{33} +11.1097 q^{34} +0.472094 q^{36} -7.86387 q^{37} +1.57229 q^{38} +0.248324 q^{39} +1.52589 q^{41} +2.95453 q^{42} +4.15375 q^{43} +0.906802 q^{44} -1.89124 q^{46} -5.96879 q^{47} -4.72132 q^{48} -3.46888 q^{49} +7.06596 q^{51} +0.117232 q^{52} +7.11918 q^{53} +1.57229 q^{54} -4.51425 q^{56} +1.00000 q^{57} +4.05918 q^{58} -11.8573 q^{59} +5.87781 q^{61} +13.6738 q^{62} +1.87913 q^{63} +5.32535 q^{64} +3.02007 q^{66} +9.53623 q^{67} +3.33580 q^{68} -1.20286 q^{69} -9.53623 q^{71} -2.40231 q^{72} -6.69123 q^{73} -12.3643 q^{74} +0.472094 q^{76} +3.60944 q^{77} +0.390437 q^{78} -0.348185 q^{79} +1.00000 q^{81} +2.39913 q^{82} +2.41705 q^{83} +0.887125 q^{84} +6.53090 q^{86} +2.58170 q^{87} -4.61438 q^{88} -17.3414 q^{89} +0.466632 q^{91} -0.567862 q^{92} +8.69676 q^{93} -9.38467 q^{94} -2.61865 q^{96} -7.70088 q^{97} -5.45408 q^{98} +1.92081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 11 q^{4} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 11 * q^4 + 3 * q^6 + 8 * q^7 + 9 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 11 q^{4} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 7 q^{9} - 4 q^{11} + 11 q^{12} + 8 q^{13} - 4 q^{14} + 19 q^{16} + 4 q^{17} + 3 q^{18} + 7 q^{19} + 8 q^{21} + 12 q^{22} + 10 q^{23} + 9 q^{24} - 20 q^{26} + 7 q^{27} + 14 q^{28} - 6 q^{29} + 4 q^{31} + 31 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{36} + 14 q^{37} + 3 q^{38} + 8 q^{39} + 2 q^{41} - 4 q^{42} - 2 q^{43} - 32 q^{44} - 4 q^{46} + 30 q^{47} + 19 q^{48} + 17 q^{49} + 4 q^{51} + 18 q^{52} + 3 q^{54} - 22 q^{56} + 7 q^{57} - 40 q^{58} - 18 q^{59} + 12 q^{61} + 18 q^{62} + 8 q^{63} + 11 q^{64} + 12 q^{66} + 18 q^{67} - 12 q^{68} + 10 q^{69} - 18 q^{71} + 9 q^{72} + 10 q^{73} + 6 q^{74} + 11 q^{76} - 18 q^{77} - 20 q^{78} - 4 q^{79} + 7 q^{81} - 16 q^{82} + 18 q^{83} + 14 q^{84} - 46 q^{86} - 6 q^{87} - 18 q^{88} - 8 q^{89} + 12 q^{91} + 34 q^{92} + 4 q^{93} - 20 q^{94} + 31 q^{96} + 20 q^{97} + 5 q^{98} - 4 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 11 * q^4 + 3 * q^6 + 8 * q^7 + 9 * q^8 + 7 * q^9 - 4 * q^11 + 11 * q^12 + 8 * q^13 - 4 * q^14 + 19 * q^16 + 4 * q^17 + 3 * q^18 + 7 * q^19 + 8 * q^21 + 12 * q^22 + 10 * q^23 + 9 * q^24 - 20 * q^26 + 7 * q^27 + 14 * q^28 - 6 * q^29 + 4 * q^31 + 31 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^36 + 14 * q^37 + 3 * q^38 + 8 * q^39 + 2 * q^41 - 4 * q^42 - 2 * q^43 - 32 * q^44 - 4 * q^46 + 30 * q^47 + 19 * q^48 + 17 * q^49 + 4 * q^51 + 18 * q^52 + 3 * q^54 - 22 * q^56 + 7 * q^57 - 40 * q^58 - 18 * q^59 + 12 * q^61 + 18 * q^62 + 8 * q^63 + 11 * q^64 + 12 * q^66 + 18 * q^67 - 12 * q^68 + 10 * q^69 - 18 * q^71 + 9 * q^72 + 10 * q^73 + 6 * q^74 + 11 * q^76 - 18 * q^77 - 20 * q^78 - 4 * q^79 + 7 * q^81 - 16 * q^82 + 18 * q^83 + 14 * q^84 - 46 * q^86 - 6 * q^87 - 18 * q^88 - 8 * q^89 + 12 * q^91 + 34 * q^92 + 4 * q^93 - 20 * q^94 + 31 * q^96 + 20 * q^97 + 5 * q^98 - 4 * 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 $

$2$	1.57229	1.11178	0.555888	−	0.831257i	$-0.312378\pi$
$2$	1.57229	1.11178	0.555888	+	0.831257i	$0.312378\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.472094	0.236047
$5$	0	0
$5$	0	0
$6$	1.57229	0.641884
$7$	1.87913	0.710244	0.355122	−	0.934820i	$-0.384439\pi$
$7$	1.87913	0.710244	0.355122	+	0.934820i	$0.384439\pi$
$8$	−2.40231	−0.849345
$9$	1.00000	0.333333
$10$	0	0
$11$	1.92081	0.579146	0.289573	−	0.957156i	$-0.406487\pi$
$11$	1.92081	0.579146	0.289573	+	0.957156i	$0.406487\pi$
$12$	0.472094	0.136282
$13$	0.248324	0.0688726	0.0344363	−	0.999407i	$-0.489036\pi$
$13$	0.248324	0.0688726	0.0344363	+	0.999407i	$0.489036\pi$
$14$	2.95453	0.789632
$15$	0	0
$16$	−4.72132	−1.18033
$17$	7.06596	1.71375	0.856873	−	0.515527i	$-0.172404\pi$
$17$	7.06596	1.71375	0.856873	+	0.515527i	$0.172404\pi$
$18$	1.57229	0.370592
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	1.87913	0.410059
$22$	3.02007	0.643880
$23$	−1.20286	−0.250813	−0.125406	−	0.992105i	$-0.540023\pi$
$23$	−1.20286	−0.250813	−0.125406	+	0.992105i	$0.540023\pi$
$24$	−2.40231	−0.490370
$25$	0	0
$26$	0.390437	0.0765709
$27$	1.00000	0.192450
$28$	0.887125	0.167651
$29$	2.58170	0.479409	0.239705	−	0.970846i	$-0.422949\pi$
$29$	2.58170	0.479409	0.239705	+	0.970846i	$0.422949\pi$
$30$	0	0
$31$	8.69676	1.56198	0.780992	−	0.624541i	$-0.214714\pi$
$31$	8.69676	1.56198	0.780992	+	0.624541i	$0.214714\pi$
$32$	−2.61865	−0.462917
$33$	1.92081	0.334370
$34$	11.1097	1.90530
$35$	0	0
$36$	0.472094	0.0786824
$37$	−7.86387	−1.29281	−0.646406	−	0.762993i	$-0.723729\pi$
$37$	−7.86387	−1.29281	−0.646406	+	0.762993i	$0.723729\pi$
$38$	1.57229	0.255059
$39$	0.248324	0.0397636
$40$	0	0
$41$	1.52589	0.238303	0.119152	−	0.992876i	$-0.461983\pi$
$41$	1.52589	0.238303	0.119152	+	0.992876i	$0.461983\pi$
$42$	2.95453	0.455894
$43$	4.15375	0.633441	0.316720	−	0.948519i	$-0.397418\pi$
$43$	4.15375	0.633441	0.316720	+	0.948519i	$0.397418\pi$
$44$	0.906802	0.136706
$45$	0	0
$46$	−1.89124	−0.278848
$47$	−5.96879	−0.870638	−0.435319	−	0.900276i	$-0.643364\pi$
$47$	−5.96879	−0.870638	−0.435319	+	0.900276i	$0.643364\pi$
$48$	−4.72132	−0.681463
$49$	−3.46888	−0.495554
$50$	0	0
$51$	7.06596	0.989432
$52$	0.117232	0.0162572
$53$	7.11918	0.977894	0.488947	−	0.872313i	$-0.337381\pi$
$53$	7.11918	0.977894	0.488947	+	0.872313i	$0.337381\pi$
$54$	1.57229	0.213961
$55$	0	0
$56$	−4.51425	−0.603242
$57$	1.00000	0.132453
$58$	4.05918	0.532996
$59$	−11.8573	−1.54369	−0.771844	−	0.635812i	$-0.780665\pi$
$59$	−11.8573	−1.54369	−0.771844	+	0.635812i	$0.780665\pi$
$60$	0	0
$61$	5.87781	0.752576	0.376288	−	0.926503i	$-0.377200\pi$
$61$	5.87781	0.752576	0.376288	+	0.926503i	$0.377200\pi$
$62$	13.6738	1.73658
$63$	1.87913	0.236748
$64$	5.32535	0.665669
$65$	0	0
$66$	3.02007	0.371745
$67$	9.53623	1.16504	0.582518	−	0.812818i	$-0.302068\pi$
$67$	9.53623	1.16504	0.582518	+	0.812818i	$0.302068\pi$
$68$	3.33580	0.404525
$69$	−1.20286	−0.144807
$70$	0	0
$71$	−9.53623	−1.13174	−0.565871	−	0.824494i	$-0.691460\pi$
$71$	−9.53623	−1.13174	−0.565871	+	0.824494i	$0.691460\pi$
$72$	−2.40231	−0.283115
$73$	−6.69123	−0.783149	−0.391575	−	0.920146i	$-0.628070\pi$
$73$	−6.69123	−0.783149	−0.391575	+	0.920146i	$0.628070\pi$
$74$	−12.3643	−1.43732
$75$	0	0
$76$	0.472094	0.0541529
$77$	3.60944	0.411334
$78$	0.390437	0.0442082
$79$	−0.348185	−0.0391739	−0.0195869	−	0.999808i	$-0.506235\pi$
$79$	−0.348185	−0.0391739	−0.0195869	+	0.999808i	$0.506235\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.39913	0.264940
$83$	2.41705	0.265306	0.132653	−	0.991163i	$-0.457650\pi$
$83$	2.41705	0.265306	0.132653	+	0.991163i	$0.457650\pi$
$84$	0.887125	0.0967933
$85$	0	0
$86$	6.53090	0.704245
$87$	2.58170	0.276787
$88$	−4.61438	−0.491894
$89$	−17.3414	−1.83818	−0.919090	−	0.394048i	$-0.871074\pi$
$89$	−17.3414	−1.83818	−0.919090	+	0.394048i	$0.871074\pi$
$90$	0	0
$91$	0.466632	0.0489163
$92$	−0.567862	−0.0592037
$93$	8.69676	0.901812
$94$	−9.38467	−0.967955
$95$	0	0
$96$	−2.61865	−0.267265
$97$	−7.70088	−0.781905	−0.390953	−	0.920411i	$-0.627854\pi$
$97$	−7.70088	−0.781905	−0.390953	+	0.920411i	$0.627854\pi$
$98$	−5.45408	−0.550945
$99$	1.92081	0.193049
$100$	0	0
$101$	−8.41297	−0.837122	−0.418561	−	0.908189i	$-0.637465\pi$
$101$	−8.41297	−0.837122	−0.418561	+	0.908189i	$0.637465\pi$
$102$	11.1097	1.10003
$103$	−9.64843	−0.950688	−0.475344	−	0.879800i	$-0.657676\pi$
$103$	−9.64843	−0.950688	−0.475344	+	0.879800i	$0.657676\pi$
$104$	−0.596550	−0.0584966
$105$	0	0
$106$	11.1934	1.08720
$107$	0.241744	0.0233703	0.0116852	−	0.999932i	$-0.496280\pi$
$107$	0.241744	0.0233703	0.0116852	+	0.999932i	$0.496280\pi$
$108$	0.472094	0.0454273
$109$	3.05581	0.292694	0.146347	−	0.989233i	$-0.453248\pi$
$109$	3.05581	0.292694	0.146347	+	0.989233i	$0.453248\pi$
$110$	0	0
$111$	−7.86387	−0.746406
$112$	−8.87196	−0.838321
$113$	16.5767	1.55940	0.779701	−	0.626152i	$-0.215371\pi$
$113$	16.5767	1.55940	0.779701	+	0.626152i	$0.215371\pi$
$114$	1.57229	0.147258
$115$	0	0
$116$	1.21880	0.113163
$117$	0.248324	0.0229575
$118$	−18.6431	−1.71624
$119$	13.2778	1.21718
$120$	0	0
$121$	−7.31050	−0.664590
$122$	9.24161	0.836696
$123$	1.52589	0.137584
$124$	4.10569	0.368702
$125$	0	0
$126$	2.95453	0.263211
$127$	21.5565	1.91283	0.956416	−	0.292007i	$-0.0943232\pi$
$127$	21.5565	1.91283	0.956416	+	0.292007i	$0.0943232\pi$
$128$	13.6103	1.20299
$129$	4.15375	0.365717
$130$	0	0
$131$	−18.3504	−1.60328	−0.801642	−	0.597804i	$-0.796040\pi$
$131$	−18.3504	−1.60328	−0.801642	+	0.597804i	$0.796040\pi$
$132$	0.906802	0.0789270
$133$	1.87913	0.162941
$134$	14.9937	1.29526
$135$	0	0
$136$	−16.9746	−1.45556
$137$	−9.63542	−0.823209	−0.411605	−	0.911362i	$-0.635032\pi$
$137$	−9.63542	−0.823209	−0.411605	+	0.911362i	$0.635032\pi$
$138$	−1.89124	−0.160993
$139$	−14.9629	−1.26914	−0.634568	−	0.772867i	$-0.718822\pi$
$139$	−14.9629	−1.26914	−0.634568	+	0.772867i	$0.718822\pi$
$140$	0	0
$141$	−5.96879	−0.502663
$142$	−14.9937	−1.25824
$143$	0.476982	0.0398872
$144$	−4.72132	−0.393443
$145$	0	0
$146$	−10.5206	−0.870687
$147$	−3.46888	−0.286108
$148$	−3.71249	−0.305165
$149$	14.2063	1.16383	0.581915	−	0.813250i	$-0.302304\pi$
$149$	14.2063	1.16383	0.581915	+	0.813250i	$0.302304\pi$
$150$	0	0
$151$	−2.26811	−0.184577	−0.0922883	−	0.995732i	$-0.529418\pi$
$151$	−2.26811	−0.184577	−0.0922883	+	0.995732i	$0.529418\pi$
$152$	−2.40231	−0.194853
$153$	7.06596	0.571249
$154$	5.67509	0.457312
$155$	0	0
$156$	0.117232	0.00938608
$157$	−1.23885	−0.0988706	−0.0494353	−	0.998777i	$-0.515742\pi$
$157$	−1.23885	−0.0988706	−0.0494353	+	0.998777i	$0.515742\pi$
$158$	−0.547448	−0.0435526
$159$	7.11918	0.564588
$160$	0	0
$161$	−2.26032	−0.178138
$162$	1.57229	0.123531
$163$	−4.19752	−0.328775	−0.164388	−	0.986396i	$-0.552565\pi$
$163$	−4.19752	−0.328775	−0.164388	+	0.986396i	$0.552565\pi$
$164$	0.720362	0.0562508
$165$	0	0
$166$	3.80030	0.294961
$167$	16.5980	1.28439	0.642195	−	0.766541i	$-0.278024\pi$
$167$	16.5980	1.28439	0.642195	+	0.766541i	$0.278024\pi$
$168$	−4.51425	−0.348282
$169$	−12.9383	−0.995257
$170$	0	0
$171$	1.00000	0.0764719
$172$	1.96096	0.149522
$173$	−0.784955	−0.0596790	−0.0298395	−	0.999555i	$-0.509500\pi$
$173$	−0.784955	−0.0596790	−0.0298395	+	0.999555i	$0.509500\pi$
$174$	4.05918	0.307725
$175$	0	0
$176$	−9.06874	−0.683582
$177$	−11.8573	−0.891249
$178$	−27.2656	−2.04365
$179$	−23.1704	−1.73183	−0.865917	−	0.500188i	$-0.833264\pi$
$179$	−23.1704	−1.73183	−0.865917	+	0.500188i	$0.833264\pi$
$180$	0	0
$181$	8.11162	0.602932	0.301466	−	0.953477i	$-0.402524\pi$
$181$	8.11162	0.602932	0.301466	+	0.953477i	$0.402524\pi$
$182$	0.733680	0.0543840
$183$	5.87781	0.434500
$184$	2.88963	0.213027
$185$	0	0
$186$	13.6738	1.00261
$187$	13.5724	0.992509
$188$	−2.81783	−0.205512
$189$	1.87913	0.136686
$190$	0	0
$191$	−20.7192	−1.49919	−0.749595	−	0.661897i	$-0.769752\pi$
$191$	−20.7192	−1.49919	−0.749595	+	0.661897i	$0.769752\pi$
$192$	5.32535	0.384324
$193$	3.71249	0.267231	0.133615	−	0.991033i	$-0.457341\pi$
$193$	3.71249	0.267231	0.133615	+	0.991033i	$0.457341\pi$
$194$	−12.1080	−0.869304
$195$	0	0
$196$	−1.63764	−0.116974
$197$	−7.81160	−0.556554	−0.278277	−	0.960501i	$-0.589763\pi$
$197$	−7.81160	−0.556554	−0.278277	+	0.960501i	$0.589763\pi$
$198$	3.02007	0.214627
$199$	5.87477	0.416451	0.208226	−	0.978081i	$-0.433231\pi$
$199$	5.87477	0.416451	0.208226	+	0.978081i	$0.433231\pi$
$200$	0	0
$201$	9.53623	0.672634
$202$	−13.2276	−0.930692
$203$	4.85134	0.340497
$204$	3.33580	0.233553
$205$	0	0
$206$	−15.1701	−1.05695
$207$	−1.20286	−0.0836043
$208$	−1.17241	−0.0812923
$209$	1.92081	0.132865
$210$	0	0
$211$	−9.79251	−0.674144	−0.337072	−	0.941479i	$-0.609437\pi$
$211$	−9.79251	−0.674144	−0.337072	+	0.941479i	$0.609437\pi$
$212$	3.36092	0.230829
$213$	−9.53623	−0.653412
$214$	0.380092	0.0259826
$215$	0	0
$216$	−2.40231	−0.163457
$217$	16.3423	1.10939
$218$	4.80462	0.325410
$219$	−6.69123	−0.452151
$220$	0	0
$221$	1.75464	0.118030
$222$	−12.3643	−0.829837
$223$	20.4327	1.36827	0.684137	−	0.729354i	$-0.260179\pi$
$223$	20.4327	1.36827	0.684137	+	0.729354i	$0.260179\pi$
$224$	−4.92079	−0.328784
$225$	0	0
$226$	26.0633	1.73371
$227$	−10.0931	−0.669903	−0.334952	−	0.942235i	$-0.608720\pi$
$227$	−10.0931	−0.669903	−0.334952	+	0.942235i	$0.608720\pi$
$228$	0.472094	0.0312652
$229$	−14.5637	−0.962397	−0.481198	−	0.876612i	$-0.659798\pi$
$229$	−14.5637	−0.962397	−0.481198	+	0.876612i	$0.659798\pi$
$230$	0	0
$231$	3.60944	0.237484
$232$	−6.20204	−0.407184
$233$	−25.8921	−1.69625	−0.848125	−	0.529797i	$-0.822268\pi$
$233$	−25.8921	−1.69625	−0.848125	+	0.529797i	$0.822268\pi$
$234$	0.390437	0.0255236
$235$	0	0
$236$	−5.59776	−0.364383
$237$	−0.348185	−0.0226171
$238$	20.8766	1.35323
$239$	18.7389	1.21212	0.606061	−	0.795418i	$-0.292749\pi$
$239$	18.7389	1.21212	0.606061	+	0.795418i	$0.292749\pi$
$240$	0	0
$241$	28.4586	1.83318	0.916589	−	0.399831i	$-0.130931\pi$
$241$	28.4586	1.83318	0.916589	+	0.399831i	$0.130931\pi$
$242$	−11.4942	−0.738876
$243$	1.00000	0.0641500
$244$	2.77488	0.177643
$245$	0	0
$246$	2.39913	0.152963
$247$	0.248324	0.0158005
$248$	−20.8923	−1.32666
$249$	2.41705	0.153174
$250$	0	0
$251$	1.22886	0.0775650	0.0387825	−	0.999248i	$-0.487652\pi$
$251$	1.22886	0.0775650	0.0387825	+	0.999248i	$0.487652\pi$
$252$	0.887125	0.0558836
$253$	−2.31046	−0.145257
$254$	33.8931	2.12664
$255$	0	0
$256$	10.7486	0.671789
$257$	−5.56841	−0.347348	−0.173674	−	0.984803i	$-0.555564\pi$
$257$	−5.56841	−0.347348	−0.173674	+	0.984803i	$0.555564\pi$
$258$	6.53090	0.406596
$259$	−14.7772	−0.918212
$260$	0	0
$261$	2.58170	0.159803
$262$	−28.8522	−1.78249
$263$	−10.7855	−0.665063	−0.332531	−	0.943092i	$-0.607903\pi$
$263$	−10.7855	−0.665063	−0.332531	+	0.943092i	$0.607903\pi$
$264$	−4.61438	−0.283995
$265$	0	0
$266$	2.95453	0.181154
$267$	−17.3414	−1.06127
$268$	4.50200	0.275003
$269$	−22.8529	−1.39337	−0.696684	−	0.717378i	$-0.745342\pi$
$269$	−22.8529	−1.39337	−0.696684	+	0.717378i	$0.745342\pi$
$270$	0	0
$271$	−9.95413	−0.604670	−0.302335	−	0.953202i	$-0.597766\pi$
$271$	−9.95413	−0.604670	−0.302335	+	0.953202i	$0.597766\pi$
$272$	−33.3606	−2.02278
$273$	0.466632	0.0282418
$274$	−15.1497	−0.915225
$275$	0	0
$276$	−0.567862	−0.0341813
$277$	−14.4026	−0.865371	−0.432686	−	0.901545i	$-0.642434\pi$
$277$	−14.4026	−0.865371	−0.432686	+	0.901545i	$0.642434\pi$
$278$	−23.5260	−1.41100
$279$	8.69676	0.520662
$280$	0	0
$281$	5.34285	0.318728	0.159364	−	0.987220i	$-0.449056\pi$
$281$	5.34285	0.318728	0.159364	+	0.987220i	$0.449056\pi$
$282$	−9.38467	−0.558849
$283$	5.73067	0.340653	0.170326	−	0.985388i	$-0.445518\pi$
$283$	5.73067	0.340653	0.170326	+	0.985388i	$0.445518\pi$
$284$	−4.50200	−0.267144
$285$	0	0
$286$	0.749954	0.0443457
$287$	2.86733	0.169253
$288$	−2.61865	−0.154306
$289$	32.9278	1.93693
$290$	0	0
$291$	−7.70088	−0.451433
$292$	−3.15889	−0.184860
$293$	27.4793	1.60536	0.802678	−	0.596412i	$-0.203408\pi$
$293$	27.4793	1.60536	0.802678	+	0.596412i	$0.203408\pi$
$294$	−5.45408	−0.318088
$295$	0	0
$296$	18.8915	1.09804
$297$	1.92081	0.111457
$298$	22.3365	1.29392
$299$	−0.298698	−0.0172741
$300$	0	0
$301$	7.80543	0.449897
$302$	−3.56613	−0.205208
$303$	−8.41297	−0.483312
$304$	−4.72132	−0.270786
$305$	0	0
$306$	11.1097	0.635101
$307$	10.7031	0.610858	0.305429	−	0.952215i	$-0.401200\pi$
$307$	10.7031	0.610858	0.305429	+	0.952215i	$0.401200\pi$
$308$	1.70400	0.0970943
$309$	−9.64843	−0.548880
$310$	0	0
$311$	−11.5209	−0.653288	−0.326644	−	0.945148i	$-0.605918\pi$
$311$	−11.5209	−0.653288	−0.326644	+	0.945148i	$0.605918\pi$
$312$	−0.596550	−0.0337730
$313$	18.1596	1.02644	0.513221	−	0.858257i	$-0.328452\pi$
$313$	18.1596	1.02644	0.513221	+	0.858257i	$0.328452\pi$
$314$	−1.94782	−0.109922
$315$	0	0
$316$	−0.164376	−0.00924688
$317$	−19.7109	−1.10707	−0.553537	−	0.832824i	$-0.686722\pi$
$317$	−19.7109	−1.10707	−0.553537	+	0.832824i	$0.686722\pi$
$318$	11.1934	0.627695
$319$	4.95895	0.277648
$320$	0	0
$321$	0.241744	0.0134929
$322$	−3.55388	−0.198050
$323$	7.06596	0.393160
$324$	0.472094	0.0262275
$325$	0	0
$326$	−6.59972	−0.365525
$327$	3.05581	0.168987
$328$	−3.66565	−0.202402
$329$	−11.2161	−0.618365
$330$	0	0
$331$	−1.88788	−0.103767	−0.0518836	−	0.998653i	$-0.516522\pi$
$331$	−1.88788	−0.103767	−0.0518836	+	0.998653i	$0.516522\pi$
$332$	1.14108	0.0626247
$333$	−7.86387	−0.430938
$334$	26.0968	1.42796
$335$	0	0
$336$	−8.87196	−0.484005
$337$	14.0147	0.763429	0.381714	−	0.924280i	$-0.375334\pi$
$337$	14.0147	0.763429	0.381714	+	0.924280i	$0.375334\pi$
$338$	−20.3428	−1.10650
$339$	16.5767	0.900321
$340$	0	0
$341$	16.7048	0.904616
$342$	1.57229	0.0850197
$343$	−19.6724	−1.06221
$344$	−9.97859	−0.538010
$345$	0	0
$346$	−1.23418	−0.0663498
$347$	−1.05107	−0.0564245	−0.0282122	−	0.999602i	$-0.508981\pi$
$347$	−1.05107	−0.0564245	−0.0282122	+	0.999602i	$0.508981\pi$
$348$	1.21880	0.0653348
$349$	35.4633	1.89831	0.949153	−	0.314815i	$-0.101943\pi$
$349$	35.4633	1.89831	0.949153	+	0.314815i	$0.101943\pi$
$350$	0	0
$351$	0.248324	0.0132545
$352$	−5.02993	−0.268096
$353$	5.28721	0.281410	0.140705	−	0.990052i	$-0.455063\pi$
$353$	5.28721	0.281410	0.140705	+	0.990052i	$0.455063\pi$
$354$	−18.6431	−0.990870
$355$	0	0
$356$	−8.18675	−0.433897
$357$	13.2778	0.702738
$358$	−36.4305	−1.92541
$359$	16.0220	0.845607	0.422803	−	0.906221i	$-0.361046\pi$
$359$	16.0220	0.845607	0.422803	+	0.906221i	$0.361046\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	12.7538	0.670326
$363$	−7.31050	−0.383701
$364$	0.220294	0.0115466
$365$	0	0
$366$	9.24161	0.483067
$367$	27.7038	1.44613	0.723063	−	0.690782i	$-0.242733\pi$
$367$	27.7038	1.44613	0.723063	+	0.690782i	$0.242733\pi$
$368$	5.67907	0.296042
$369$	1.52589	0.0794344
$370$	0	0
$371$	13.3778	0.694543
$372$	4.10569	0.212870
$373$	11.7532	0.608559	0.304279	−	0.952583i	$-0.401584\pi$
$373$	11.7532	0.608559	0.304279	+	0.952583i	$0.401584\pi$
$374$	21.3397	1.10345
$375$	0	0
$376$	14.3389	0.739472
$377$	0.641096	0.0330181
$378$	2.95453	0.151965
$379$	−7.04988	−0.362128	−0.181064	−	0.983471i	$-0.557954\pi$
$379$	−7.04988	−0.362128	−0.181064	+	0.983471i	$0.557954\pi$
$380$	0	0
$381$	21.5565	1.10437
$382$	−32.5766	−1.66676
$383$	7.01682	0.358543	0.179271	−	0.983800i	$-0.442626\pi$
$383$	7.01682	0.358543	0.179271	+	0.983800i	$0.442626\pi$
$384$	13.6103	0.694548
$385$	0	0
$386$	5.83711	0.297101
$387$	4.15375	0.211147
$388$	−3.63554	−0.184567
$389$	−38.1712	−1.93536	−0.967679	−	0.252185i	$-0.918851\pi$
$389$	−38.1712	−1.93536	−0.967679	+	0.252185i	$0.918851\pi$
$390$	0	0
$391$	−8.49933	−0.429830
$392$	8.33332	0.420896
$393$	−18.3504	−0.925657
$394$	−12.2821	−0.618763
$395$	0	0
$396$	0.906802	0.0455685
$397$	7.84847	0.393904	0.196952	−	0.980413i	$-0.436896\pi$
$397$	7.84847	0.393904	0.196952	+	0.980413i	$0.436896\pi$
$398$	9.23683	0.463001
$399$	1.87913	0.0940741
$400$	0	0
$401$	0.879277	0.0439090	0.0219545	−	0.999759i	$-0.493011\pi$
$401$	0.879277	0.0439090	0.0219545	+	0.999759i	$0.493011\pi$
$402$	14.9937	0.747818
$403$	2.15961	0.107578
$404$	−3.97171	−0.197600
$405$	0	0
$406$	7.62771	0.378557
$407$	−15.1050	−0.748727
$408$	−16.9746	−0.840369
$409$	38.8153	1.91929	0.959647	−	0.281207i	$-0.0907349\pi$
$409$	38.8153	1.91929	0.959647	+	0.281207i	$0.0907349\pi$
$410$	0	0
$411$	−9.63542	−0.475280
$412$	−4.55497	−0.224407
$413$	−22.2814	−1.09639
$414$	−1.89124	−0.0929493
$415$	0	0
$416$	−0.650274	−0.0318823
$417$	−14.9629	−0.732736
$418$	3.02007	0.147716
$419$	−31.2248	−1.52543	−0.762716	−	0.646734i	$-0.776134\pi$
$419$	−31.2248	−1.52543	−0.762716	+	0.646734i	$0.776134\pi$
$420$	0	0
$421$	−4.46904	−0.217808	−0.108904	−	0.994052i	$-0.534734\pi$
$421$	−4.46904	−0.217808	−0.108904	+	0.994052i	$0.534734\pi$
$422$	−15.3967	−0.749498
$423$	−5.96879	−0.290213
$424$	−17.1025	−0.830570
$425$	0	0
$426$	−14.9937	−0.726448
$427$	11.0452	0.534512
$428$	0.114126	0.00551649
$429$	0.476982	0.0230289
$430$	0	0
$431$	26.0794	1.25620	0.628101	−	0.778132i	$-0.283833\pi$
$431$	26.0794	1.25620	0.628101	+	0.778132i	$0.283833\pi$
$432$	−4.72132	−0.227154
$433$	−15.4199	−0.741035	−0.370518	−	0.928825i	$-0.620820\pi$
$433$	−15.4199	−0.741035	−0.370518	+	0.928825i	$0.620820\pi$
$434$	25.6949	1.23339
$435$	0	0
$436$	1.44263	0.0690895
$437$	−1.20286	−0.0575404
$438$	−10.5206	−0.502691
$439$	−26.1326	−1.24724	−0.623620	−	0.781728i	$-0.714339\pi$
$439$	−26.1326	−1.24724	−0.623620	+	0.781728i	$0.714339\pi$
$440$	0	0
$441$	−3.46888	−0.165185
$442$	2.75881	0.131223
$443$	−18.7686	−0.891721	−0.445861	−	0.895102i	$-0.647102\pi$
$443$	−18.7686	−0.891721	−0.445861	+	0.895102i	$0.647102\pi$
$444$	−3.71249	−0.176187
$445$	0	0
$446$	32.1261	1.52121
$447$	14.2063	0.671937
$448$	10.0070	0.472787
$449$	18.5078	0.873438	0.436719	−	0.899598i	$-0.356140\pi$
$449$	18.5078	0.873438	0.436719	+	0.899598i	$0.356140\pi$
$450$	0	0
$451$	2.93093	0.138012
$452$	7.82575	0.368092
$453$	−2.26811	−0.106565
$454$	−15.8693	−0.744783
$455$	0	0
$456$	−2.40231	−0.112498
$457$	−35.7154	−1.67070	−0.835348	−	0.549722i	$-0.814734\pi$
$457$	−35.7154	−1.67070	−0.835348	+	0.549722i	$0.814734\pi$
$458$	−22.8984	−1.06997
$459$	7.06596	0.329811
$460$	0	0
$461$	−30.7787	−1.43351	−0.716753	−	0.697327i	$-0.754372\pi$
$461$	−30.7787	−1.43351	−0.716753	+	0.697327i	$0.754372\pi$
$462$	5.67509	0.264029
$463$	31.1807	1.44909	0.724546	−	0.689226i	$-0.242049\pi$
$463$	31.1807	1.44909	0.724546	+	0.689226i	$0.242049\pi$
$464$	−12.1890	−0.565860
$465$	0	0
$466$	−40.7099	−1.88585
$467$	−8.01621	−0.370946	−0.185473	−	0.982649i	$-0.559382\pi$
$467$	−8.01621	−0.370946	−0.185473	+	0.982649i	$0.559382\pi$
$468$	0.117232	0.00541906
$469$	17.9198	0.827459
$470$	0	0
$471$	−1.23885	−0.0570830
$472$	28.4849	1.31112
$473$	7.97856	0.366854
$474$	−0.547448	−0.0251451
$475$	0	0
$476$	6.26839	0.287311
$477$	7.11918	0.325965
$478$	29.4630	1.34761
$479$	−4.00338	−0.182919	−0.0914596	−	0.995809i	$-0.529153\pi$
$479$	−4.00338	−0.182919	−0.0914596	+	0.995809i	$0.529153\pi$
$480$	0	0
$481$	−1.95279	−0.0890394
$482$	44.7451	2.03808
$483$	−2.26032	−0.102848
$484$	−3.45124	−0.156875
$485$	0	0
$486$	1.57229	0.0713205
$487$	−17.5299	−0.794358	−0.397179	−	0.917741i	$-0.630011\pi$
$487$	−17.5299	−0.794358	−0.397179	+	0.917741i	$0.630011\pi$
$488$	−14.1203	−0.639197
$489$	−4.19752	−0.189819
$490$	0	0
$491$	15.7747	0.711901	0.355951	−	0.934505i	$-0.384157\pi$
$491$	15.7747	0.711901	0.355951	+	0.934505i	$0.384157\pi$
$492$	0.720362	0.0324764
$493$	18.2422	0.821586
$494$	0.390437	0.0175666
$495$	0	0
$496$	−41.0602	−1.84366
$497$	−17.9198	−0.803813
$498$	3.80030	0.170296
$499$	31.4231	1.40669	0.703347	−	0.710847i	$-0.251688\pi$
$499$	31.4231	1.40669	0.703347	+	0.710847i	$0.251688\pi$
$500$	0	0
$501$	16.5980	0.741543
$502$	1.93212	0.0862349
$503$	15.7396	0.701796	0.350898	−	0.936414i	$-0.385876\pi$
$503$	15.7396	0.701796	0.350898	+	0.936414i	$0.385876\pi$
$504$	−4.51425	−0.201081
$505$	0	0
$506$	−3.63271	−0.161494
$507$	−12.9383	−0.574612
$508$	10.1767	0.451518
$509$	17.2396	0.764131	0.382066	−	0.924135i	$-0.375213\pi$
$509$	17.2396	0.764131	0.382066	+	0.924135i	$0.375213\pi$
$510$	0	0
$511$	−12.5737	−0.556227
$512$	−10.3206	−0.456112
$513$	1.00000	0.0441511
$514$	−8.75516	−0.386173
$515$	0	0
$516$	1.96096	0.0863265
$517$	−11.4649	−0.504226
$518$	−23.2341	−1.02085
$519$	−0.784955	−0.0344557
$520$	0	0
$521$	−28.3700	−1.24291	−0.621457	−	0.783448i	$-0.713459\pi$
$521$	−28.3700	−1.24291	−0.621457	+	0.783448i	$0.713459\pi$
$522$	4.05918	0.177665
$523$	31.3645	1.37148	0.685738	−	0.727849i	$-0.259480\pi$
$523$	31.3645	1.37148	0.685738	+	0.727849i	$0.259480\pi$
$524$	−8.66313	−0.378451
$525$	0	0
$526$	−16.9579	−0.739401
$527$	61.4510	2.67685
$528$	−9.06874	−0.394666
$529$	−21.5531	−0.937093
$530$	0	0
$531$	−11.8573	−0.514563
$532$	0.887125	0.0384618
$533$	0.378913	0.0164126
$534$	−27.2656	−1.17990
$535$	0	0
$536$	−22.9090	−0.989517
$537$	−23.1704	−0.999875
$538$	−35.9314	−1.54911
$539$	−6.66305	−0.286998
$540$	0	0
$541$	−12.6888	−0.545536	−0.272768	−	0.962080i	$-0.587939\pi$
$541$	−12.6888	−0.545536	−0.272768	+	0.962080i	$0.587939\pi$
$542$	−15.6508	−0.672258
$543$	8.11162	0.348103
$544$	−18.5033	−0.793323
$545$	0	0
$546$	0.733680	0.0313986
$547$	−19.2634	−0.823644	−0.411822	−	0.911264i	$-0.635107\pi$
$547$	−19.2634	−0.823644	−0.411822	+	0.911264i	$0.635107\pi$
$548$	−4.54883	−0.194316
$549$	5.87781	0.250859
$550$	0	0
$551$	2.58170	0.109984
$552$	2.88963	0.122991
$553$	−0.654284	−0.0278230
$554$	−22.6451	−0.962099
$555$	0	0
$556$	−7.06389	−0.299576
$557$	−21.6253	−0.916294	−0.458147	−	0.888877i	$-0.651487\pi$
$557$	−21.6253	−0.916294	−0.458147	+	0.888877i	$0.651487\pi$
$558$	13.6738	0.578859
$559$	1.03147	0.0436267
$560$	0	0
$561$	13.5724	0.573025
$562$	8.40051	0.354354
$563$	39.1301	1.64914	0.824569	−	0.565761i	$-0.191418\pi$
$563$	39.1301	1.64914	0.824569	+	0.565761i	$0.191418\pi$
$564$	−2.81783	−0.118652
$565$	0	0
$566$	9.01027	0.378730
$567$	1.87913	0.0789160
$568$	22.9090	0.961240
$569$	10.5271	0.441320	0.220660	−	0.975351i	$-0.429179\pi$
$569$	10.5271	0.441320	0.220660	+	0.975351i	$0.429179\pi$
$570$	0	0
$571$	43.1731	1.80674	0.903368	−	0.428866i	$-0.141087\pi$
$571$	43.1731	1.80674	0.903368	+	0.428866i	$0.141087\pi$
$572$	0.225180	0.00941527
$573$	−20.7192	−0.865558
$574$	4.50828	0.188172
$575$	0	0
$576$	5.32535	0.221890
$577$	−13.8196	−0.575316	−0.287658	−	0.957733i	$-0.592877\pi$
$577$	−13.8196	−0.575316	−0.287658	+	0.957733i	$0.592877\pi$
$578$	51.7720	2.15343
$579$	3.71249	0.154286
$580$	0	0
$581$	4.54195	0.188432
$582$	−12.1080	−0.501893
$583$	13.6746	0.566343
$584$	16.0744	0.665164
$585$	0	0
$586$	43.2054	1.78480
$587$	−16.3981	−0.676822	−0.338411	−	0.940998i	$-0.609889\pi$
$587$	−16.3981	−0.676822	−0.338411	+	0.940998i	$0.609889\pi$
$588$	−1.63764	−0.0675350
$589$	8.69676	0.358344
$590$	0	0
$591$	−7.81160	−0.321326
$592$	37.1278	1.52594
$593$	−26.5182	−1.08897	−0.544485	−	0.838770i	$-0.683275\pi$
$593$	−26.5182	−1.08897	−0.544485	+	0.838770i	$0.683275\pi$
$594$	3.02007	0.123915
$595$	0	0
$596$	6.70674	0.274719
$597$	5.87477	0.240438
$598$	−0.469639	−0.0192050
$599$	−7.85156	−0.320806	−0.160403	−	0.987052i	$-0.551279\pi$
$599$	−7.85156	−0.320806	−0.160403	+	0.987052i	$0.551279\pi$
$600$	0	0
$601$	−8.31507	−0.339179	−0.169589	−	0.985515i	$-0.554244\pi$
$601$	−8.31507	−0.339179	−0.169589	+	0.985515i	$0.554244\pi$
$602$	12.2724	0.500185
$603$	9.53623	0.388345
$604$	−1.07076	−0.0435688
$605$	0	0
$606$	−13.2276	−0.537335
$607$	26.6353	1.08109	0.540546	−	0.841314i	$-0.318218\pi$
$607$	26.6353	1.08109	0.540546	+	0.841314i	$0.318218\pi$
$608$	−2.61865	−0.106200
$609$	4.85134	0.196586
$610$	0	0
$611$	−1.48219	−0.0599631
$612$	3.33580	0.134842
$613$	38.7710	1.56595	0.782973	−	0.622056i	$-0.213702\pi$
$613$	38.7710	1.56595	0.782973	+	0.622056i	$0.213702\pi$
$614$	16.8284	0.679138
$615$	0	0
$616$	−8.67101	−0.349365
$617$	23.1535	0.932125	0.466063	−	0.884752i	$-0.345672\pi$
$617$	23.1535	0.932125	0.466063	+	0.884752i	$0.345672\pi$
$618$	−15.1701	−0.610232
$619$	47.6444	1.91499	0.957495	−	0.288449i	$-0.0931396\pi$
$619$	47.6444	1.91499	0.957495	+	0.288449i	$0.0931396\pi$
$620$	0	0
$621$	−1.20286	−0.0482690
$622$	−18.1141	−0.726310
$623$	−32.5866	−1.30556
$624$	−1.17241	−0.0469341
$625$	0	0
$626$	28.5522	1.14117
$627$	1.92081	0.0767097
$628$	−0.584852	−0.0233381
$629$	−55.5658	−2.21555
$630$	0	0
$631$	29.4039	1.17055	0.585275	−	0.810835i	$-0.300987\pi$
$631$	29.4039	1.17055	0.585275	+	0.810835i	$0.300987\pi$
$632$	0.836449	0.0332721
$633$	−9.79251	−0.389217
$634$	−30.9912	−1.23082
$635$	0	0
$636$	3.36092	0.133269
$637$	−0.861404	−0.0341301
$638$	7.79690	0.308682
$639$	−9.53623	−0.377247
$640$	0	0
$641$	−11.0401	−0.436059	−0.218029	−	0.975942i	$-0.569963\pi$
$641$	−11.0401	−0.436059	−0.218029	+	0.975942i	$0.569963\pi$
$642$	0.380092	0.0150010
$643$	−19.6424	−0.774622	−0.387311	−	0.921949i	$-0.626596\pi$
$643$	−19.6424	−0.774622	−0.387311	+	0.921949i	$0.626596\pi$
$644$	−1.06708	−0.0420490
$645$	0	0
$646$	11.1097	0.437107
$647$	32.7753	1.28853	0.644265	−	0.764803i	$-0.277163\pi$
$647$	32.7753	1.28853	0.644265	+	0.764803i	$0.277163\pi$
$648$	−2.40231	−0.0943717
$649$	−22.7756	−0.894020
$650$	0	0
$651$	16.3423	0.640506
$652$	−1.98163	−0.0776065
$653$	10.5395	0.412442	0.206221	−	0.978505i	$-0.433883\pi$
$653$	10.5395	0.412442	0.206221	+	0.978505i	$0.433883\pi$
$654$	4.80462	0.187876
$655$	0	0
$656$	−7.20419	−0.281276
$657$	−6.69123	−0.261050
$658$	−17.6350	−0.687484
$659$	29.1597	1.13590	0.567950	−	0.823063i	$-0.307737\pi$
$659$	29.1597	1.13590	0.567950	+	0.823063i	$0.307737\pi$
$660$	0	0
$661$	−48.4368	−1.88397	−0.941987	−	0.335649i	$-0.891044\pi$
$661$	−48.4368	−1.88397	−0.941987	+	0.335649i	$0.891044\pi$
$662$	−2.96829	−0.115366
$663$	1.75464	0.0681447
$664$	−5.80651	−0.225336
$665$	0	0
$666$	−12.3643	−0.479106
$667$	−3.10541	−0.120242
$668$	7.83581	0.303177
$669$	20.4327	0.789973
$670$	0	0
$671$	11.2901	0.435851
$672$	−4.92079	−0.189823
$673$	0.819338	0.0315831	0.0157916	−	0.999875i	$-0.494973\pi$
$673$	0.819338	0.0315831	0.0157916	+	0.999875i	$0.494973\pi$
$674$	22.0351	0.848762
$675$	0	0
$676$	−6.10811	−0.234927
$677$	−3.76524	−0.144710	−0.0723549	−	0.997379i	$-0.523051\pi$
$677$	−3.76524	−0.144710	−0.0723549	+	0.997379i	$0.523051\pi$
$678$	26.0633	1.00096
$679$	−14.4709	−0.555343
$680$	0	0
$681$	−10.0931	−0.386769
$682$	26.2648	1.00573
$683$	−36.9829	−1.41511	−0.707556	−	0.706657i	$-0.750202\pi$
$683$	−36.9829	−1.41511	−0.707556	+	0.706657i	$0.750202\pi$
$684$	0.472094	0.0180510
$685$	0	0
$686$	−30.9306	−1.18094
$687$	−14.5637	−0.555640
$688$	−19.6112	−0.747669
$689$	1.76786	0.0673501
$690$	0	0
$691$	10.0198	0.381171	0.190585	−	0.981671i	$-0.438961\pi$
$691$	10.0198	0.381171	0.190585	+	0.981671i	$0.438961\pi$
$692$	−0.370573	−0.0140871
$693$	3.60944	0.137111
$694$	−1.65259	−0.0627314
$695$	0	0
$696$	−6.20204	−0.235088
$697$	10.7818	0.408391
$698$	55.7585	2.11049
$699$	−25.8921	−0.979330
$700$	0	0
$701$	−15.6128	−0.589688	−0.294844	−	0.955545i	$-0.595268\pi$
$701$	−15.6128	−0.589688	−0.294844	+	0.955545i	$0.595268\pi$
$702$	0.390437	0.0147361
$703$	−7.86387	−0.296592
$704$	10.2290	0.385519
$705$	0	0
$706$	8.31302	0.312865
$707$	−15.8090	−0.594560
$708$	−5.59776	−0.210377
$709$	11.5966	0.435519	0.217759	−	0.976002i	$-0.430125\pi$
$709$	11.5966	0.435519	0.217759	+	0.976002i	$0.430125\pi$
$710$	0	0
$711$	−0.348185	−0.0130580
$712$	41.6593	1.56125
$713$	−10.4610	−0.391766
$714$	20.8766	0.781287
$715$	0	0
$716$	−10.9386	−0.408794
$717$	18.7389	0.699819
$718$	25.1912	0.940126
$719$	−13.1532	−0.490532	−0.245266	−	0.969456i	$-0.578875\pi$
$719$	−13.1532	−0.490532	−0.245266	+	0.969456i	$0.578875\pi$
$720$	0	0
$721$	−18.1306	−0.675220
$722$	1.57229	0.0585146
$723$	28.4586	1.05839
$724$	3.82945	0.142320
$725$	0	0
$726$	−11.4942	−0.426590
$727$	26.7258	0.991203	0.495602	−	0.868550i	$-0.334948\pi$
$727$	26.7258	0.991203	0.495602	+	0.868550i	$0.334948\pi$
$728$	−1.12099	−0.0415468
$729$	1.00000	0.0370370
$730$	0	0
$731$	29.3502	1.08556
$732$	2.77488	0.102562
$733$	−1.01889	−0.0376337	−0.0188169	−	0.999823i	$-0.505990\pi$
$733$	−1.01889	−0.0376337	−0.0188169	+	0.999823i	$0.505990\pi$
$734$	43.5584	1.60777
$735$	0	0
$736$	3.14987	0.116106
$737$	18.3173	0.674725
$738$	2.39913	0.0883133
$739$	−30.1705	−1.10984	−0.554920	−	0.831904i	$-0.687251\pi$
$739$	−30.1705	−1.10984	−0.554920	+	0.831904i	$0.687251\pi$
$740$	0	0
$741$	0.248324	0.00912240
$742$	21.0338	0.772177
$743$	8.28423	0.303919	0.151959	−	0.988387i	$-0.451442\pi$
$743$	8.28423	0.303919	0.151959	+	0.988387i	$0.451442\pi$
$744$	−20.8923	−0.765950
$745$	0	0
$746$	18.4795	0.676581
$747$	2.41705	0.0884353
$748$	6.40743	0.234279
$749$	0.454268	0.0165986
$750$	0	0
$751$	−3.74254	−0.136567	−0.0682836	−	0.997666i	$-0.521752\pi$
$751$	−3.74254	−0.136567	−0.0682836	+	0.997666i	$0.521752\pi$
$752$	28.1806	1.02764
$753$	1.22886	0.0447822
$754$	1.00799	0.0367088
$755$	0	0
$756$	0.887125	0.0322644
$757$	−29.6308	−1.07695	−0.538475	−	0.842642i	$-0.680999\pi$
$757$	−29.6308	−1.07695	−0.538475	+	0.842642i	$0.680999\pi$
$758$	−11.0845	−0.402605
$759$	−2.31046	−0.0838643
$760$	0	0
$761$	−43.2167	−1.56660	−0.783302	−	0.621642i	$-0.786466\pi$
$761$	−43.2167	−1.56660	−0.783302	+	0.621642i	$0.786466\pi$
$762$	33.8931	1.22782
$763$	5.74226	0.207884
$764$	−9.78142	−0.353880
$765$	0	0
$766$	11.0325	0.398619
$767$	−2.94445	−0.106318
$768$	10.7486	0.387858
$769$	−7.30244	−0.263333	−0.131666	−	0.991294i	$-0.542033\pi$
$769$	−7.30244	−0.263333	−0.131666	+	0.991294i	$0.542033\pi$
$770$	0	0
$771$	−5.56841	−0.200541
$772$	1.75264	0.0630791
$773$	42.4163	1.52561	0.762804	−	0.646630i	$-0.223822\pi$
$773$	42.4163	1.52561	0.762804	+	0.646630i	$0.223822\pi$
$774$	6.53090	0.234748
$775$	0	0
$776$	18.4999	0.664107
$777$	−14.7772	−0.530130
$778$	−60.0162	−2.15169
$779$	1.52589	0.0546705
$780$	0	0
$781$	−18.3173	−0.655443
$782$	−13.3634	−0.477875
$783$	2.58170	0.0922623
$784$	16.3777	0.584917
$785$	0	0
$786$	−28.8522	−1.02912
$787$	34.5998	1.23335	0.616675	−	0.787218i	$-0.288479\pi$
$787$	34.5998	1.23335	0.616675	+	0.787218i	$0.288479\pi$
$788$	−3.68781	−0.131373
$789$	−10.7855	−0.383974
$790$	0	0
$791$	31.1497	1.10755
$792$	−4.61438	−0.163965
$793$	1.45960	0.0518319
$794$	12.3401	0.437933
$795$	0	0
$796$	2.77344	0.0983021
$797$	31.9016	1.13001	0.565006	−	0.825087i	$-0.308874\pi$
$797$	31.9016	1.13001	0.565006	+	0.825087i	$0.308874\pi$
$798$	2.95453	0.104589
$799$	−42.1752	−1.49205
$800$	0	0
$801$	−17.3414	−0.612727
$802$	1.38248	0.0488170
$803$	−12.8526	−0.453557
$804$	4.50200	0.158773
$805$	0	0
$806$	3.39553	0.119603
$807$	−22.8529	−0.804461
$808$	20.2106	0.711005
$809$	7.96516	0.280040	0.140020	−	0.990149i	$-0.455283\pi$
$809$	7.96516	0.280040	0.140020	+	0.990149i	$0.455283\pi$
$810$	0	0
$811$	−8.45805	−0.297002	−0.148501	−	0.988912i	$-0.547445\pi$
$811$	−8.45805	−0.297002	−0.148501	+	0.988912i	$0.547445\pi$
$812$	2.29029	0.0803734
$813$	−9.95413	−0.349107
$814$	−23.7494	−0.832417
$815$	0	0
$816$	−33.3606	−1.16786
$817$	4.15375	0.145321
$818$	61.0289	2.13383
$819$	0.466632	0.0163054
$820$	0	0
$821$	29.8649	1.04229	0.521147	−	0.853467i	$-0.325504\pi$
$821$	29.8649	1.04229	0.521147	+	0.853467i	$0.325504\pi$
$822$	−15.1497	−0.528405
$823$	−29.4632	−1.02702	−0.513512	−	0.858083i	$-0.671656\pi$
$823$	−29.4632	−1.02702	−0.513512	+	0.858083i	$0.671656\pi$
$824$	23.1785	0.807462
$825$	0	0
$826$	−35.0328	−1.21895
$827$	35.7491	1.24312	0.621558	−	0.783368i	$-0.286500\pi$
$827$	35.7491	1.24312	0.621558	+	0.783368i	$0.286500\pi$
$828$	−0.567862	−0.0197346
$829$	30.6073	1.06303	0.531517	−	0.847047i	$-0.321622\pi$
$829$	30.6073	1.06303	0.531517	+	0.847047i	$0.321622\pi$
$830$	0	0
$831$	−14.4026	−0.499622
$832$	1.32241	0.0458463
$833$	−24.5110	−0.849254
$834$	−23.5260	−0.814638
$835$	0	0
$836$	0.906802	0.0313624
$837$	8.69676	0.300604
$838$	−49.0944	−1.69594
$839$	20.2431	0.698868	0.349434	−	0.936961i	$-0.386374\pi$
$839$	20.2431	0.698868	0.349434	+	0.936961i	$0.386374\pi$
$840$	0	0
$841$	−22.3348	−0.770167
$842$	−7.02662	−0.242153
$843$	5.34285	0.184018
$844$	−4.62299	−0.159130
$845$	0	0
$846$	−9.38467	−0.322652
$847$	−13.7374	−0.472021
$848$	−33.6119	−1.15424
$849$	5.73067	0.196676
$850$	0	0
$851$	9.45911	0.324254
$852$	−4.50200	−0.154236
$853$	−36.5320	−1.25083	−0.625415	−	0.780292i	$-0.715070\pi$
$853$	−36.5320	−1.25083	−0.625415	+	0.780292i	$0.715070\pi$
$854$	17.3662	0.594258
$855$	0	0
$856$	−0.580745	−0.0198495
$857$	−22.5292	−0.769584	−0.384792	−	0.923003i	$-0.625727\pi$
$857$	−22.5292	−0.769584	−0.384792	+	0.923003i	$0.625727\pi$
$858$	0.749954	0.0256030
$859$	4.59482	0.156773	0.0783866	−	0.996923i	$-0.475023\pi$
$859$	4.59482	0.156773	0.0783866	+	0.996923i	$0.475023\pi$
$860$	0	0
$861$	2.86733	0.0977185
$862$	41.0044	1.39662
$863$	11.5034	0.391579	0.195789	−	0.980646i	$-0.437273\pi$
$863$	11.5034	0.391579	0.195789	+	0.980646i	$0.437273\pi$
$864$	−2.61865	−0.0890884
$865$	0	0
$866$	−24.2446	−0.823866
$867$	32.9278	1.11829
$868$	7.71512	0.261868
$869$	−0.668797	−0.0226874
$870$	0	0
$871$	2.36807	0.0802390
$872$	−7.34101	−0.248598
$873$	−7.70088	−0.260635
$874$	−1.89124	−0.0639721
$875$	0	0
$876$	−3.15889	−0.106729
$877$	−9.18451	−0.310139	−0.155069	−	0.987904i	$-0.549560\pi$
$877$	−9.18451	−0.310139	−0.155069	+	0.987904i	$0.549560\pi$
$878$	−41.0880	−1.38665
$879$	27.4793	0.926853
$880$	0	0
$881$	46.8437	1.57821	0.789103	−	0.614261i	$-0.210546\pi$
$881$	46.8437	1.57821	0.789103	+	0.614261i	$0.210546\pi$
$882$	−5.45408	−0.183648
$883$	29.8269	1.00375	0.501877	−	0.864939i	$-0.332643\pi$
$883$	29.8269	1.00375	0.501877	+	0.864939i	$0.332643\pi$
$884$	0.828357	0.0278607
$885$	0	0
$886$	−29.5096	−0.991395
$887$	20.4681	0.687252	0.343626	−	0.939107i	$-0.388345\pi$
$887$	20.4681	0.687252	0.343626	+	0.939107i	$0.388345\pi$
$888$	18.8915	0.633956
$889$	40.5075	1.35858
$890$	0	0
$891$	1.92081	0.0643495
$892$	9.64615	0.322977
$893$	−5.96879	−0.199738
$894$	22.3365	0.747044
$895$	0	0
$896$	25.5755	0.854417
$897$	−0.298698	−0.00997322
$898$	29.0996	0.971068
$899$	22.4524	0.748830
$900$	0	0
$901$	50.3038	1.67586
$902$	4.60828	0.153439
$903$	7.80543	0.259748
$904$	−39.8223	−1.32447
$905$	0	0
$906$	−3.56613	−0.118477
$907$	−16.6266	−0.552076	−0.276038	−	0.961147i	$-0.589022\pi$
$907$	−16.6266	−0.552076	−0.276038	+	0.961147i	$0.589022\pi$
$908$	−4.76490	−0.158129
$909$	−8.41297	−0.279041
$910$	0	0
$911$	−40.6554	−1.34697	−0.673487	−	0.739199i	$-0.735204\pi$
$911$	−40.6554	−1.34697	−0.673487	+	0.739199i	$0.735204\pi$
$912$	−4.72132	−0.156338
$913$	4.64269	0.153651
$914$	−56.1549	−1.85744
$915$	0	0
$916$	−6.87544	−0.227171
$917$	−34.4828	−1.13872
$918$	11.1097	0.366676
$919$	23.9633	0.790477	0.395238	−	0.918579i	$-0.370662\pi$
$919$	23.9633	0.790477	0.395238	+	0.918579i	$0.370662\pi$
$920$	0	0
$921$	10.7031	0.352679
$922$	−48.3930	−1.59374
$923$	−2.36807	−0.0779460
$924$	1.70400	0.0560574
$925$	0	0
$926$	49.0252	1.61107
$927$	−9.64843	−0.316896
$928$	−6.76057	−0.221927
$929$	−17.6807	−0.580085	−0.290043	−	0.957014i	$-0.593669\pi$
$929$	−17.6807	−0.580085	−0.290043	+	0.957014i	$0.593669\pi$
$930$	0	0
$931$	−3.46888	−0.113688
$932$	−12.2235	−0.400395
$933$	−11.5209	−0.377176
$934$	−12.6038	−0.412409
$935$	0	0
$936$	−0.596550	−0.0194989
$937$	45.8986	1.49944	0.749721	−	0.661754i	$-0.230188\pi$
$937$	45.8986	1.49944	0.749721	+	0.661754i	$0.230188\pi$
$938$	28.1751	0.919950
$939$	18.1596	0.592617
$940$	0	0
$941$	7.89440	0.257350	0.128675	−	0.991687i	$-0.458928\pi$
$941$	7.89440	0.257350	0.128675	+	0.991687i	$0.458928\pi$
$942$	−1.94782	−0.0634635
$943$	−1.83542	−0.0597695
$944$	55.9820	1.82206
$945$	0	0
$946$	12.5446	0.407860
$947$	−51.7953	−1.68312	−0.841561	−	0.540162i	$-0.818363\pi$
$947$	−51.7953	−1.68312	−0.841561	+	0.540162i	$0.818363\pi$
$948$	−0.164376	−0.00533869
$949$	−1.66159	−0.0539375
$950$	0	0
$951$	−19.7109	−0.639170
$952$	−31.8975	−1.03380
$953$	−11.5807	−0.375137	−0.187568	−	0.982252i	$-0.560061\pi$
$953$	−11.5807	−0.375137	−0.187568	+	0.982252i	$0.560061\pi$
$954$	11.1934	0.362400
$955$	0	0
$956$	8.84655	0.286118
$957$	4.95895	0.160300
$958$	−6.29447	−0.203365
$959$	−18.1062	−0.584679
$960$	0	0
$961$	44.6337	1.43980
$962$	−3.07034	−0.0989919
$963$	0.241744	0.00779010
$964$	13.4351	0.432716
$965$	0	0
$966$	−3.55388	−0.114344
$967$	60.5547	1.94731	0.973654	−	0.228032i	$-0.0732290\pi$
$967$	60.5547	1.94731	0.973654	+	0.228032i	$0.0732290\pi$
$968$	17.5621	0.564467
$969$	7.06596	0.226991
$970$	0	0
$971$	−4.19412	−0.134596	−0.0672978	−	0.997733i	$-0.521438\pi$
$971$	−4.19412	−0.134596	−0.0672978	+	0.997733i	$0.521438\pi$
$972$	0.472094	0.0151424
$973$	−28.1172	−0.901395
$974$	−27.5621	−0.883148
$975$	0	0
$976$	−27.7510	−0.888287
$977$	−12.7754	−0.408720	−0.204360	−	0.978896i	$-0.565511\pi$
$977$	−12.7754	−0.408720	−0.204360	+	0.978896i	$0.565511\pi$
$978$	−6.59972	−0.211036
$979$	−33.3094	−1.06457
$980$	0	0
$981$	3.05581	0.0975646
$982$	24.8024	0.791475
$983$	35.8198	1.14247	0.571237	−	0.820785i	$-0.306464\pi$
$983$	35.8198	1.14247	0.571237	+	0.820785i	$0.306464\pi$
$984$	−3.66565	−0.116857
$985$	0	0
$986$	28.6820	0.913420
$987$	−11.2161	−0.357013
$988$	0.117232	0.00372965
$989$	−4.99636	−0.158875
$990$	0	0
$991$	−19.1653	−0.608807	−0.304404	−	0.952543i	$-0.598457\pi$
$991$	−19.1653	−0.608807	−0.304404	+	0.952543i	$0.598457\pi$
$992$	−22.7738	−0.723069
$993$	−1.88788	−0.0599100
$994$	−28.1751	−0.893660
$995$	0	0
$996$	1.14108	0.0361564
$997$	9.88660	0.313112	0.156556	−	0.987669i	$-0.449961\pi$
$997$	9.88660	0.313112	0.156556	+	0.987669i	$0.449961\pi$
$998$	49.4063	1.56393
$999$	−7.86387	−0.248802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1425.2.a.z.1.5		7
3.2	odd	2		4275.2.a.bv.1.3		7
5.2	odd	4		285.2.c.b.229.10	yes	14
5.3	odd	4		285.2.c.b.229.5	✓	14
5.4	even	2		1425.2.a.y.1.3		7
15.2	even	4		855.2.c.g.514.5		14
15.8	even	4		855.2.c.g.514.10		14
15.14	odd	2		4275.2.a.bw.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.5	✓	14	5.3	odd	4
285.2.c.b.229.10	yes	14	5.2	odd	4
855.2.c.g.514.5		14	15.2	even	4
855.2.c.g.514.10		14	15.8	even	4
1425.2.a.y.1.3		7	5.4	even	2
1425.2.a.z.1.5		7	1.1	even	1	trivial
4275.2.a.bv.1.3		7	3.2	odd	2
4275.2.a.bw.1.5		7	15.14	odd	2

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:	\( N \)	\(=\)	\( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1425.a (trivial)

\(f(q)\)	\(=\)	\(q+1.57229 q^{2} +1.00000 q^{3} +0.472094 q^{4} +1.57229 q^{6} +1.87913 q^{7} -2.40231 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.57229 q^{2} +1.00000 q^{3} +0.472094 q^{4} +1.57229 q^{6} +1.87913 q^{7} -2.40231 q^{8} +1.00000 q^{9} +1.92081 q^{11} +0.472094 q^{12} +0.248324 q^{13} +2.95453 q^{14} -4.72132 q^{16} +7.06596 q^{17} +1.57229 q^{18} +1.00000 q^{19} +1.87913 q^{21} +3.02007 q^{22} -1.20286 q^{23} -2.40231 q^{24} +0.390437 q^{26} +1.00000 q^{27} +0.887125 q^{28} +2.58170 q^{29} +8.69676 q^{31} -2.61865 q^{32} +1.92081 q^{33} +11.1097 q^{34} +0.472094 q^{36} -7.86387 q^{37} +1.57229 q^{38} +0.248324 q^{39} +1.52589 q^{41} +2.95453 q^{42} +4.15375 q^{43} +0.906802 q^{44} -1.89124 q^{46} -5.96879 q^{47} -4.72132 q^{48} -3.46888 q^{49} +7.06596 q^{51} +0.117232 q^{52} +7.11918 q^{53} +1.57229 q^{54} -4.51425 q^{56} +1.00000 q^{57} +4.05918 q^{58} -11.8573 q^{59} +5.87781 q^{61} +13.6738 q^{62} +1.87913 q^{63} +5.32535 q^{64} +3.02007 q^{66} +9.53623 q^{67} +3.33580 q^{68} -1.20286 q^{69} -9.53623 q^{71} -2.40231 q^{72} -6.69123 q^{73} -12.3643 q^{74} +0.472094 q^{76} +3.60944 q^{77} +0.390437 q^{78} -0.348185 q^{79} +1.00000 q^{81} +2.39913 q^{82} +2.41705 q^{83} +0.887125 q^{84} +6.53090 q^{86} +2.58170 q^{87} -4.61438 q^{88} -17.3414 q^{89} +0.466632 q^{91} -0.567862 q^{92} +8.69676 q^{93} -9.38467 q^{94} -2.61865 q^{96} -7.70088 q^{97} -5.45408 q^{98} +1.92081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 11 q^{4} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 11 * q^4 + 3 * q^6 + 8 * q^7 + 9 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 11 q^{4} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 7 q^{9} - 4 q^{11} + 11 q^{12} + 8 q^{13} - 4 q^{14} + 19 q^{16} + 4 q^{17} + 3 q^{18} + 7 q^{19} + 8 q^{21} + 12 q^{22} + 10 q^{23} + 9 q^{24} - 20 q^{26} + 7 q^{27} + 14 q^{28} - 6 q^{29} + 4 q^{31} + 31 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{36} + 14 q^{37} + 3 q^{38} + 8 q^{39} + 2 q^{41} - 4 q^{42} - 2 q^{43} - 32 q^{44} - 4 q^{46} + 30 q^{47} + 19 q^{48} + 17 q^{49} + 4 q^{51} + 18 q^{52} + 3 q^{54} - 22 q^{56} + 7 q^{57} - 40 q^{58} - 18 q^{59} + 12 q^{61} + 18 q^{62} + 8 q^{63} + 11 q^{64} + 12 q^{66} + 18 q^{67} - 12 q^{68} + 10 q^{69} - 18 q^{71} + 9 q^{72} + 10 q^{73} + 6 q^{74} + 11 q^{76} - 18 q^{77} - 20 q^{78} - 4 q^{79} + 7 q^{81} - 16 q^{82} + 18 q^{83} + 14 q^{84} - 46 q^{86} - 6 q^{87} - 18 q^{88} - 8 q^{89} + 12 q^{91} + 34 q^{92} + 4 q^{93} - 20 q^{94} + 31 q^{96} + 20 q^{97} + 5 q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 11 * q^4 + 3 * q^6 + 8 * q^7 + 9 * q^8 + 7 * q^9 - 4 * q^11 + 11 * q^12 + 8 * q^13 - 4 * q^14 + 19 * q^16 + 4 * q^17 + 3 * q^18 + 7 * q^19 + 8 * q^21 + 12 * q^22 + 10 * q^23 + 9 * q^24 - 20 * q^26 + 7 * q^27 + 14 * q^28 - 6 * q^29 + 4 * q^31 + 31 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^36 + 14 * q^37 + 3 * q^38 + 8 * q^39 + 2 * q^41 - 4 * q^42 - 2 * q^43 - 32 * q^44 - 4 * q^46 + 30 * q^47 + 19 * q^48 + 17 * q^49 + 4 * q^51 + 18 * q^52 + 3 * q^54 - 22 * q^56 + 7 * q^57 - 40 * q^58 - 18 * q^59 + 12 * q^61 + 18 * q^62 + 8 * q^63 + 11 * q^64 + 12 * q^66 + 18 * q^67 - 12 * q^68 + 10 * q^69 - 18 * q^71 + 9 * q^72 + 10 * q^73 + 6 * q^74 + 11 * q^76 - 18 * q^77 - 20 * q^78 - 4 * q^79 + 7 * q^81 - 16 * q^82 + 18 * q^83 + 14 * q^84 - 46 * q^86 - 6 * q^87 - 18 * q^88 - 8 * q^89 + 12 * q^91 + 34 * q^92 + 4 * q^93 - 20 * q^94 + 31 * q^96 + 20 * q^97 + 5 * q^98 - 4 * q^99

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