LMFDB - Embedded newform 1425.2.a.z.1.3

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			1.3
Root			$-0.184902$ 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)

$f(q)$	$=$	$q-0.184902 q^{2} +1.00000 q^{3} -1.96581 q^{4} -0.184902 q^{6} -1.90997 q^{7} +0.733287 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.184902 q^{2} +1.00000 q^{3} -1.96581 q^{4} -0.184902 q^{6} -1.90997 q^{7} +0.733287 q^{8} +1.00000 q^{9} -3.94075 q^{11} -1.96581 q^{12} -4.53675 q^{13} +0.353158 q^{14} +3.79604 q^{16} +4.68488 q^{17} -0.184902 q^{18} +1.00000 q^{19} -1.90997 q^{21} +0.728653 q^{22} +6.18360 q^{23} +0.733287 q^{24} +0.838856 q^{26} +1.00000 q^{27} +3.75465 q^{28} +5.98837 q^{29} +7.31166 q^{31} -2.16847 q^{32} -3.94075 q^{33} -0.866244 q^{34} -1.96581 q^{36} +8.07490 q^{37} -0.184902 q^{38} -4.53675 q^{39} +0.0567471 q^{41} +0.353158 q^{42} -0.822008 q^{43} +7.74677 q^{44} -1.14336 q^{46} +7.50487 q^{47} +3.79604 q^{48} -3.35200 q^{49} +4.68488 q^{51} +8.91840 q^{52} -1.28799 q^{53} -0.184902 q^{54} -1.40056 q^{56} +1.00000 q^{57} -1.10726 q^{58} -8.28180 q^{59} -11.3330 q^{61} -1.35194 q^{62} -1.90997 q^{63} -7.19112 q^{64} +0.728653 q^{66} +10.3415 q^{67} -9.20959 q^{68} +6.18360 q^{69} -10.3415 q^{71} +0.733287 q^{72} +10.0984 q^{73} -1.49307 q^{74} -1.96581 q^{76} +7.52672 q^{77} +0.838856 q^{78} +4.12580 q^{79} +1.00000 q^{81} -0.0104927 q^{82} +11.6295 q^{83} +3.75465 q^{84} +0.151991 q^{86} +5.98837 q^{87} -2.88970 q^{88} +7.17054 q^{89} +8.66508 q^{91} -12.1558 q^{92} +7.31166 q^{93} -1.38767 q^{94} -2.16847 q^{96} -2.70038 q^{97} +0.619793 q^{98} -3.94075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.184902	−0.130746	−0.0653728	−	0.997861i	$-0.520824\pi$
$2$	−0.184902	−0.130746	−0.0653728	+	0.997861i	$0.520824\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.96581	−0.982906
$5$	0	0
$5$	0	0
$6$	−0.184902	−0.0754860
$7$	−1.90997	−0.721902	−0.360951	−	0.932585i	$-0.617548\pi$
$7$	−1.90997	−0.721902	−0.360951	+	0.932585i	$0.617548\pi$
$8$	0.733287	0.259256
$9$	1.00000	0.333333
$10$	0	0
$11$	−3.94075	−1.18818	−0.594090	−	0.804399i	$-0.702488\pi$
$11$	−3.94075	−1.18818	−0.594090	+	0.804399i	$0.702488\pi$
$12$	−1.96581	−0.567481
$13$	−4.53675	−1.25827	−0.629135	−	0.777296i	$-0.716591\pi$
$13$	−4.53675	−1.25827	−0.629135	+	0.777296i	$0.716591\pi$
$14$	0.353158	0.0943855
$15$	0	0
$16$	3.79604	0.949009
$17$	4.68488	1.13625	0.568125	−	0.822942i	$-0.307669\pi$
$17$	4.68488	1.13625	0.568125	+	0.822942i	$0.307669\pi$
$18$	−0.184902	−0.0435819
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−1.90997	−0.416790
$22$	0.728653	0.155349
$23$	6.18360	1.28937	0.644684	−	0.764449i	$-0.276989\pi$
$23$	6.18360	1.28937	0.644684	+	0.764449i	$0.276989\pi$
$24$	0.733287	0.149682
$25$	0	0
$26$	0.838856	0.164513
$27$	1.00000	0.192450
$28$	3.75465	0.709561
$29$	5.98837	1.11201	0.556006	−	0.831178i	$-0.312333\pi$
$29$	5.98837	1.11201	0.556006	+	0.831178i	$0.312333\pi$
$30$	0	0
$31$	7.31166	1.31321	0.656607	−	0.754233i	$-0.271991\pi$
$31$	7.31166	1.31321	0.656607	+	0.754233i	$0.271991\pi$
$32$	−2.16847	−0.383335
$33$	−3.94075	−0.685996
$34$	−0.866244	−0.148560
$35$	0	0
$36$	−1.96581	−0.327635
$37$	8.07490	1.32751	0.663753	−	0.747952i	$-0.268963\pi$
$37$	8.07490	1.32751	0.663753	+	0.747952i	$0.268963\pi$
$38$	−0.184902	−0.0299951
$39$	−4.53675	−0.726462
$40$	0	0
$41$	0.0567471	0.00886241	0.00443121	−	0.999990i	$-0.498589\pi$
$41$	0.0567471	0.00886241	0.00443121	+	0.999990i	$0.498589\pi$
$42$	0.353158	0.0544935
$43$	−0.822008	−0.125355	−0.0626776	−	0.998034i	$-0.519964\pi$
$43$	−0.822008	−0.125355	−0.0626776	+	0.998034i	$0.519964\pi$
$44$	7.74677	1.16787
$45$	0	0
$46$	−1.14336	−0.168579
$47$	7.50487	1.09470	0.547349	−	0.836905i	$-0.315637\pi$
$47$	7.50487	1.09470	0.547349	+	0.836905i	$0.315637\pi$
$48$	3.79604	0.547911
$49$	−3.35200	−0.478858
$50$	0	0
$51$	4.68488	0.656014
$52$	8.91840	1.23676
$53$	−1.28799	−0.176920	−0.0884598	−	0.996080i	$-0.528194\pi$
$53$	−1.28799	−0.176920	−0.0884598	+	0.996080i	$0.528194\pi$
$54$	−0.184902	−0.0251620
$55$	0	0
$56$	−1.40056	−0.187157
$57$	1.00000	0.132453
$58$	−1.10726	−0.145391
$59$	−8.28180	−1.07820	−0.539099	−	0.842242i	$-0.681235\pi$
$59$	−8.28180	−1.07820	−0.539099	+	0.842242i	$0.681235\pi$
$60$	0	0
$61$	−11.3330	−1.45104	−0.725521	−	0.688200i	$-0.758401\pi$
$61$	−11.3330	−1.45104	−0.725521	+	0.688200i	$0.758401\pi$
$62$	−1.35194	−0.171697
$63$	−1.90997	−0.240634
$64$	−7.19112	−0.898890
$65$	0	0
$66$	0.728653	0.0896909
$67$	10.3415	1.26342	0.631709	−	0.775205i	$-0.282354\pi$
$67$	10.3415	1.26342	0.631709	+	0.775205i	$0.282354\pi$
$68$	−9.20959	−1.11683
$69$	6.18360	0.744418
$70$	0	0
$71$	−10.3415	−1.22731	−0.613657	−	0.789573i	$-0.710302\pi$
$71$	−10.3415	−1.22731	−0.613657	+	0.789573i	$0.710302\pi$
$72$	0.733287	0.0864187
$73$	10.0984	1.18192	0.590962	−	0.806699i	$-0.298748\pi$
$73$	10.0984	1.18192	0.590962	+	0.806699i	$0.298748\pi$
$74$	−1.49307	−0.173566
$75$	0	0
$76$	−1.96581	−0.225494
$77$	7.52672	0.857749
$78$	0.838856	0.0949817
$79$	4.12580	0.464189	0.232094	−	0.972693i	$-0.425442\pi$
$79$	4.12580	0.464189	0.232094	+	0.972693i	$0.425442\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−0.0104927	−0.00115872
$83$	11.6295	1.27651	0.638253	−	0.769827i	$-0.279657\pi$
$83$	11.6295	1.27651	0.638253	+	0.769827i	$0.279657\pi$
$84$	3.75465	0.409665
$85$	0	0
$86$	0.151991	0.0163896
$87$	5.98837	0.642021
$88$	−2.88970	−0.308043
$89$	7.17054	0.760075	0.380038	−	0.924971i	$-0.375911\pi$
$89$	7.17054	0.760075	0.380038	+	0.924971i	$0.375911\pi$
$90$	0	0
$91$	8.66508	0.908347
$92$	−12.1558	−1.26733
$93$	7.31166	0.758184
$94$	−1.38767	−0.143127
$95$	0	0
$96$	−2.16847	−0.221318
$97$	−2.70038	−0.274182	−0.137091	−	0.990558i	$-0.543775\pi$
$97$	−2.70038	−0.274182	−0.137091	+	0.990558i	$0.543775\pi$
$98$	0.619793	0.0626085
$99$	−3.94075	−0.396060
$100$	0	0
$101$	2.17791	0.216710	0.108355	−	0.994112i	$-0.465442\pi$
$101$	2.17791	0.216710	0.108355	+	0.994112i	$0.465442\pi$
$102$	−0.866244	−0.0857710
$103$	10.2701	1.01195	0.505973	−	0.862549i	$-0.331134\pi$
$103$	10.2701	1.01195	0.505973	+	0.862549i	$0.331134\pi$
$104$	−3.32674	−0.326214
$105$	0	0
$106$	0.238153	0.0231314
$107$	7.81995	0.755983	0.377991	−	0.925809i	$-0.376615\pi$
$107$	7.81995	0.755983	0.377991	+	0.925809i	$0.376615\pi$
$108$	−1.96581	−0.189160
$109$	7.93162	0.759712	0.379856	−	0.925046i	$-0.375974\pi$
$109$	7.93162	0.759712	0.379856	+	0.925046i	$0.375974\pi$
$110$	0	0
$111$	8.07490	0.766436
$112$	−7.25033	−0.685091
$113$	−9.54169	−0.897607	−0.448803	−	0.893631i	$-0.648150\pi$
$113$	−9.54169	−0.897607	−0.448803	+	0.893631i	$0.648150\pi$
$114$	−0.184902	−0.0173177
$115$	0	0
$116$	−11.7720	−1.09300
$117$	−4.53675	−0.419423
$118$	1.53132	0.140970
$119$	−8.94799	−0.820261
$120$	0	0
$121$	4.52949	0.411772
$122$	2.09550	0.189717
$123$	0.0567471	0.00511672
$124$	−14.3733	−1.29076
$125$	0	0
$126$	0.353158	0.0314618
$127$	7.84804	0.696401	0.348201	−	0.937420i	$-0.386793\pi$
$127$	7.84804	0.696401	0.348201	+	0.937420i	$0.386793\pi$
$128$	5.66659	0.500861
$129$	−0.822008	−0.0723738
$130$	0	0
$131$	1.36722	0.119455	0.0597273	−	0.998215i	$-0.480977\pi$
$131$	1.36722	0.119455	0.0597273	+	0.998215i	$0.480977\pi$
$132$	7.74677	0.674269
$133$	−1.90997	−0.165616
$134$	−1.91217	−0.165186
$135$	0	0
$136$	3.43536	0.294580
$137$	12.0300	1.02779	0.513896	−	0.857853i	$-0.328202\pi$
$137$	12.0300	1.02779	0.513896	+	0.857853i	$0.328202\pi$
$138$	−1.14336	−0.0973293
$139$	12.6898	1.07634	0.538169	−	0.842837i	$-0.319116\pi$
$139$	12.6898	1.07634	0.538169	+	0.842837i	$0.319116\pi$
$140$	0	0
$141$	7.50487	0.632024
$142$	1.91217	0.160466
$143$	17.8782	1.49505
$144$	3.79604	0.316336
$145$	0	0
$146$	−1.86721	−0.154531
$147$	−3.35200	−0.276469
$148$	−15.8737	−1.30481
$149$	−21.0429	−1.72390	−0.861951	−	0.506992i	$-0.830758\pi$
$149$	−21.0429	−1.72390	−0.861951	+	0.506992i	$0.830758\pi$
$150$	0	0
$151$	−3.32628	−0.270689	−0.135344	−	0.990799i	$-0.543214\pi$
$151$	−3.32628	−0.270689	−0.135344	+	0.990799i	$0.543214\pi$
$152$	0.733287	0.0594774
$153$	4.68488	0.378750
$154$	−1.39171	−0.112147
$155$	0	0
$156$	8.91840	0.714044
$157$	−16.3037	−1.30118	−0.650589	−	0.759430i	$-0.725478\pi$
$157$	−16.3037	−1.30118	−0.650589	+	0.759430i	$0.725478\pi$
$158$	−0.762870	−0.0606906
$159$	−1.28799	−0.102145
$160$	0	0
$161$	−11.8105	−0.930798
$162$	−0.184902	−0.0145273
$163$	10.3731	0.812486	0.406243	−	0.913765i	$-0.366839\pi$
$163$	10.3731	0.812486	0.406243	+	0.913765i	$0.366839\pi$
$164$	−0.111554	−0.00871092
$165$	0	0
$166$	−2.15032	−0.166897
$167$	−24.4309	−1.89052	−0.945261	−	0.326315i	$-0.894193\pi$
$167$	−24.4309	−1.89052	−0.945261	+	0.326315i	$0.894193\pi$
$168$	−1.40056	−0.108055
$169$	7.58214	0.583242
$170$	0	0
$171$	1.00000	0.0764719
$172$	1.61591	0.123212
$173$	−21.4851	−1.63348	−0.816742	−	0.577002i	$-0.804222\pi$
$173$	−21.4851	−1.63348	−0.816742	+	0.577002i	$0.804222\pi$
$174$	−1.10726	−0.0839413
$175$	0	0
$176$	−14.9592	−1.12759
$177$	−8.28180	−0.622498
$178$	−1.32585	−0.0993765
$179$	−14.7939	−1.10575	−0.552875	−	0.833264i	$-0.686469\pi$
$179$	−14.7939	−1.10575	−0.552875	+	0.833264i	$0.686469\pi$
$180$	0	0
$181$	17.8632	1.32776	0.663882	−	0.747837i	$-0.268908\pi$
$181$	17.8632	1.32776	0.663882	+	0.747837i	$0.268908\pi$
$182$	−1.60219	−0.118762
$183$	−11.3330	−0.837760
$184$	4.53435	0.334277
$185$	0	0
$186$	−1.35194	−0.0991292
$187$	−18.4619	−1.35007
$188$	−14.7532	−1.07598
$189$	−1.90997	−0.138930
$190$	0	0
$191$	12.8206	0.927663	0.463832	−	0.885923i	$-0.346474\pi$
$191$	12.8206	0.927663	0.463832	+	0.885923i	$0.346474\pi$
$192$	−7.19112	−0.518974
$193$	15.8737	1.14262	0.571308	−	0.820736i	$-0.306436\pi$
$193$	15.8737	1.14262	0.571308	+	0.820736i	$0.306436\pi$
$194$	0.499305	0.0358480
$195$	0	0
$196$	6.58941	0.470672
$197$	−13.8571	−0.987277	−0.493638	−	0.869667i	$-0.664333\pi$
$197$	−13.8571	−0.987277	−0.493638	+	0.869667i	$0.664333\pi$
$198$	0.728653	0.0517831
$199$	26.5763	1.88394	0.941972	−	0.335693i	$-0.108970\pi$
$199$	26.5763	1.88394	0.941972	+	0.335693i	$0.108970\pi$
$200$	0	0
$201$	10.3415	0.729435
$202$	−0.402700	−0.0283338
$203$	−11.4376	−0.802764
$204$	−9.20959	−0.644800
$205$	0	0
$206$	−1.89897	−0.132307
$207$	6.18360	0.429790
$208$	−17.2217	−1.19411
$209$	−3.94075	−0.272587
$210$	0	0
$211$	−12.3339	−0.849101	−0.424550	−	0.905404i	$-0.639568\pi$
$211$	−12.3339	−0.849101	−0.424550	+	0.905404i	$0.639568\pi$
$212$	2.53195	0.173895
$213$	−10.3415	−0.708590
$214$	−1.44592	−0.0988414
$215$	0	0
$216$	0.733287	0.0498939
$217$	−13.9651	−0.948011
$218$	−1.46657	−0.0993289
$219$	10.0984	0.682385
$220$	0	0
$221$	−21.2541	−1.42971
$222$	−1.49307	−0.100208
$223$	25.8035	1.72793	0.863966	−	0.503551i	$-0.167973\pi$
$223$	25.8035	1.72793	0.863966	+	0.503551i	$0.167973\pi$
$224$	4.14172	0.276730
$225$	0	0
$226$	1.76428	0.117358
$227$	14.1348	0.938163	0.469081	−	0.883155i	$-0.344585\pi$
$227$	14.1348	0.938163	0.469081	+	0.883155i	$0.344585\pi$
$228$	−1.96581	−0.130189
$229$	14.7671	0.975838	0.487919	−	0.872889i	$-0.337756\pi$
$229$	14.7671	0.975838	0.487919	+	0.872889i	$0.337756\pi$
$230$	0	0
$231$	7.52672	0.495222
$232$	4.39119	0.288296
$233$	15.5104	1.01612	0.508060	−	0.861322i	$-0.330363\pi$
$233$	15.5104	1.01612	0.508060	+	0.861322i	$0.330363\pi$
$234$	0.838856	0.0548377
$235$	0	0
$236$	16.2804	1.05977
$237$	4.12580	0.268000
$238$	1.65450	0.107246
$239$	1.16086	0.0750897	0.0375448	−	0.999295i	$-0.488046\pi$
$239$	1.16086	0.0750897	0.0375448	+	0.999295i	$0.488046\pi$
$240$	0	0
$241$	−14.7586	−0.950685	−0.475343	−	0.879801i	$-0.657676\pi$
$241$	−14.7586	−0.950685	−0.475343	+	0.879801i	$0.657676\pi$
$242$	−0.837513	−0.0538374
$243$	1.00000	0.0641500
$244$	22.2785	1.42624
$245$	0	0
$246$	−0.0104927	−0.000668988 0
$247$	−4.53675	−0.288667
$248$	5.36155	0.340459
$249$	11.6295	0.736991
$250$	0	0
$251$	−5.83488	−0.368294	−0.184147	−	0.982899i	$-0.558952\pi$
$251$	−5.83488	−0.368294	−0.184147	+	0.982899i	$0.558952\pi$
$252$	3.75465	0.236520
$253$	−24.3680	−1.53200
$254$	−1.45112	−0.0910514
$255$	0	0
$256$	13.3345	0.833404
$257$	−2.19805	−0.137111	−0.0685554	−	0.997647i	$-0.521839\pi$
$257$	−2.19805	−0.137111	−0.0685554	+	0.997647i	$0.521839\pi$
$258$	0.151991	0.00946255
$259$	−15.4228	−0.958329
$260$	0	0
$261$	5.98837	0.370671
$262$	−0.252802	−0.0156182
$263$	−21.4529	−1.32284	−0.661420	−	0.750015i	$-0.730046\pi$
$263$	−21.4529	−1.32284	−0.661420	+	0.750015i	$0.730046\pi$
$264$	−2.88970	−0.177849
$265$	0	0
$266$	0.353158	0.0216535
$267$	7.17054	0.438830
$268$	−20.3295	−1.24182
$269$	−0.680401	−0.0414848	−0.0207424	−	0.999785i	$-0.506603\pi$
$269$	−0.680401	−0.0414848	−0.0207424	+	0.999785i	$0.506603\pi$
$270$	0	0
$271$	17.3272	1.05255	0.526276	−	0.850314i	$-0.323588\pi$
$271$	17.3272	1.05255	0.526276	+	0.850314i	$0.323588\pi$
$272$	17.7840	1.07831
$273$	8.66508	0.524434
$274$	−2.22437	−0.134379
$275$	0	0
$276$	−12.1558	−0.731692
$277$	25.8337	1.55219	0.776097	−	0.630613i	$-0.217197\pi$
$277$	25.8337	1.55219	0.776097	+	0.630613i	$0.217197\pi$
$278$	−2.34638	−0.140726
$279$	7.31166	0.437738
$280$	0	0
$281$	−6.31534	−0.376741	−0.188371	−	0.982098i	$-0.560321\pi$
$281$	−6.31534	−0.376741	−0.188371	+	0.982098i	$0.560321\pi$
$282$	−1.38767	−0.0826343
$283$	7.03773	0.418350	0.209175	−	0.977878i	$-0.432922\pi$
$283$	7.03773	0.418350	0.209175	+	0.977878i	$0.432922\pi$
$284$	20.3295	1.20633
$285$	0	0
$286$	−3.30572	−0.195471
$287$	−0.108385	−0.00639779
$288$	−2.16847	−0.127778
$289$	4.94810	0.291065
$290$	0	0
$291$	−2.70038	−0.158299
$292$	−19.8515	−1.16172
$293$	16.3174	0.953274	0.476637	−	0.879100i	$-0.341856\pi$
$293$	16.3174	0.953274	0.476637	+	0.879100i	$0.341856\pi$
$294$	0.619793	0.0361470
$295$	0	0
$296$	5.92122	0.344164
$297$	−3.94075	−0.228665
$298$	3.89088	0.225393
$299$	−28.0535	−1.62237
$300$	0	0
$301$	1.57001	0.0904941
$302$	0.615036	0.0353913
$303$	2.17791	0.125117
$304$	3.79604	0.217718
$305$	0	0
$306$	−0.866244	−0.0495199
$307$	−18.3294	−1.04611	−0.523056	−	0.852298i	$-0.675208\pi$
$307$	−18.3294	−1.04611	−0.523056	+	0.852298i	$0.675208\pi$
$308$	−14.7961	−0.843087
$309$	10.2701	0.584247
$310$	0	0
$311$	−11.7605	−0.666879	−0.333439	−	0.942772i	$-0.608209\pi$
$311$	−11.7605	−0.666879	−0.333439	+	0.942772i	$0.608209\pi$
$312$	−3.32674	−0.188340
$313$	−17.1712	−0.970574	−0.485287	−	0.874355i	$-0.661285\pi$
$313$	−17.1712	−0.970574	−0.485287	+	0.874355i	$0.661285\pi$
$314$	3.01459	0.170123
$315$	0	0
$316$	−8.11055	−0.456254
$317$	−11.8192	−0.663833	−0.331916	−	0.943309i	$-0.607695\pi$
$317$	−11.8192	−0.663833	−0.331916	+	0.943309i	$0.607695\pi$
$318$	0.238153	0.0133549
$319$	−23.5987	−1.32127
$320$	0	0
$321$	7.81995	0.436467
$322$	2.18379	0.121698
$323$	4.68488	0.260674
$324$	−1.96581	−0.109212
$325$	0	0
$326$	−1.91801	−0.106229
$327$	7.93162	0.438620
$328$	0.0416119	0.00229764
$329$	−14.3341	−0.790264
$330$	0	0
$331$	−25.0090	−1.37462	−0.687309	−	0.726365i	$-0.741208\pi$
$331$	−25.0090	−1.37462	−0.687309	+	0.726365i	$0.741208\pi$
$332$	−22.8614	−1.25468
$333$	8.07490	0.442502
$334$	4.51733	0.247177
$335$	0	0
$336$	−7.25033	−0.395538
$337$	0.451357	0.0245870	0.0122935	−	0.999924i	$-0.496087\pi$
$337$	0.451357	0.0245870	0.0122935	+	0.999924i	$0.496087\pi$
$338$	−1.40195	−0.0762563
$339$	−9.54169	−0.518234
$340$	0	0
$341$	−28.8134	−1.56033
$342$	−0.184902	−0.00999836
$343$	19.7720	1.06759
$344$	−0.602768	−0.0324991
$345$	0	0
$346$	3.97265	0.213571
$347$	−8.93849	−0.479843	−0.239922	−	0.970792i	$-0.577122\pi$
$347$	−8.93849	−0.479843	−0.239922	+	0.970792i	$0.577122\pi$
$348$	−11.7720	−0.631046
$349$	−15.9394	−0.853215	−0.426607	−	0.904437i	$-0.640291\pi$
$349$	−15.9394	−0.853215	−0.426607	+	0.904437i	$0.640291\pi$
$350$	0	0
$351$	−4.53675	−0.242154
$352$	8.54539	0.455471
$353$	8.53844	0.454455	0.227228	−	0.973842i	$-0.427034\pi$
$353$	8.53844	0.454455	0.227228	+	0.973842i	$0.427034\pi$
$354$	1.53132	0.0813888
$355$	0	0
$356$	−14.0959	−0.747082
$357$	−8.94799	−0.473578
$358$	2.73543	0.144572
$359$	16.7400	0.883503	0.441752	−	0.897137i	$-0.354357\pi$
$359$	16.7400	0.883503	0.441752	+	0.897137i	$0.354357\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−3.30295	−0.173599
$363$	4.52949	0.237737
$364$	−17.0339	−0.892819
$365$	0	0
$366$	2.09550	0.109533
$367$	−0.300558	−0.0156890	−0.00784451	−	0.999969i	$-0.502497\pi$
$367$	−0.300558	−0.0156890	−0.00784451	+	0.999969i	$0.502497\pi$
$368$	23.4732	1.22362
$369$	0.0567471	0.00295414
$370$	0	0
$371$	2.46003	0.127719
$372$	−14.3733	−0.745223
$373$	−25.3500	−1.31257	−0.656287	−	0.754512i	$-0.727874\pi$
$373$	−25.3500	−1.31257	−0.656287	+	0.754512i	$0.727874\pi$
$374$	3.41365	0.176516
$375$	0	0
$376$	5.50322	0.283807
$377$	−27.1678	−1.39921
$378$	0.353158	0.0181645
$379$	16.3050	0.837530	0.418765	−	0.908095i	$-0.362463\pi$
$379$	16.3050	0.837530	0.418765	+	0.908095i	$0.362463\pi$
$380$	0	0
$381$	7.84804	0.402067
$382$	−2.37055	−0.121288
$383$	30.4652	1.55670	0.778349	−	0.627832i	$-0.216057\pi$
$383$	30.4652	1.55670	0.778349	+	0.627832i	$0.216057\pi$
$384$	5.66659	0.289172
$385$	0	0
$386$	−2.93509	−0.149392
$387$	−0.822008	−0.0417850
$388$	5.30843	0.269495
$389$	−1.28401	−0.0651017	−0.0325508	−	0.999470i	$-0.510363\pi$
$389$	−1.28401	−0.0651017	−0.0325508	+	0.999470i	$0.510363\pi$
$390$	0	0
$391$	28.9694	1.46505
$392$	−2.45798	−0.124147
$393$	1.36722	0.0689672
$394$	2.56221	0.129082
$395$	0	0
$396$	7.74677	0.389290
$397$	−12.5188	−0.628299	−0.314149	−	0.949374i	$-0.601719\pi$
$397$	−12.5188	−0.628299	−0.314149	+	0.949374i	$0.601719\pi$
$398$	−4.91401	−0.246317
$399$	−1.90997	−0.0956182
$400$	0	0
$401$	1.22276	0.0610620	0.0305310	−	0.999534i	$-0.490280\pi$
$401$	1.22276	0.0610620	0.0305310	+	0.999534i	$0.490280\pi$
$402$	−1.91217	−0.0953704
$403$	−33.1712	−1.65238
$404$	−4.28135	−0.213005
$405$	0	0
$406$	2.11484	0.104958
$407$	−31.8212	−1.57732
$408$	3.43536	0.170076
$409$	−27.7692	−1.37310	−0.686550	−	0.727083i	$-0.740876\pi$
$409$	−27.7692	−1.37310	−0.686550	+	0.727083i	$0.740876\pi$
$410$	0	0
$411$	12.0300	0.593396
$412$	−20.1891	−0.994647
$413$	15.8180	0.778353
$414$	−1.14336	−0.0561931
$415$	0	0
$416$	9.83781	0.482338
$417$	12.6898	0.621424
$418$	0.728653	0.0356396
$419$	−14.4570	−0.706273	−0.353136	−	0.935572i	$-0.614885\pi$
$419$	−14.4570	−0.706273	−0.353136	+	0.935572i	$0.614885\pi$
$420$	0	0
$421$	35.5761	1.73387	0.866937	−	0.498418i	$-0.166086\pi$
$421$	35.5761	1.73387	0.866937	+	0.498418i	$0.166086\pi$
$422$	2.28056	0.111016
$423$	7.50487	0.364899
$424$	−0.944469	−0.0458675
$425$	0	0
$426$	1.91217	0.0926450
$427$	21.6457	1.04751
$428$	−15.3725	−0.743060
$429$	17.8782	0.863168
$430$	0	0
$431$	11.1892	0.538966	0.269483	−	0.963005i	$-0.413147\pi$
$431$	11.1892	0.538966	0.269483	+	0.963005i	$0.413147\pi$
$432$	3.79604	0.182637
$433$	−10.2174	−0.491018	−0.245509	−	0.969394i	$-0.578955\pi$
$433$	−10.2174	−0.491018	−0.245509	+	0.969394i	$0.578955\pi$
$434$	2.58217	0.123948
$435$	0	0
$436$	−15.5921	−0.746725
$437$	6.18360	0.295802
$438$	−1.86721	−0.0892188
$439$	−4.79196	−0.228708	−0.114354	−	0.993440i	$-0.536480\pi$
$439$	−4.79196	−0.228708	−0.114354	+	0.993440i	$0.536480\pi$
$440$	0	0
$441$	−3.35200	−0.159619
$442$	3.92994	0.186928
$443$	−13.3293	−0.633296	−0.316648	−	0.948543i	$-0.602557\pi$
$443$	−13.3293	−0.633296	−0.316648	+	0.948543i	$0.602557\pi$
$444$	−15.8737	−0.753334
$445$	0	0
$446$	−4.77113	−0.225919
$447$	−21.0429	−0.995295
$448$	13.7348	0.648910
$449$	20.0362	0.945566	0.472783	−	0.881179i	$-0.343249\pi$
$449$	20.0362	0.945566	0.472783	+	0.881179i	$0.343249\pi$
$450$	0	0
$451$	−0.223626	−0.0105301
$452$	18.7572	0.882263
$453$	−3.32628	−0.156282
$454$	−2.61356	−0.122661
$455$	0	0
$456$	0.733287	0.0343393
$457$	14.4875	0.677696	0.338848	−	0.940841i	$-0.389963\pi$
$457$	14.4875	0.677696	0.338848	+	0.940841i	$0.389963\pi$
$458$	−2.73047	−0.127586
$459$	4.68488	0.218671
$460$	0	0
$461$	14.7512	0.687031	0.343515	−	0.939147i	$-0.388382\pi$
$461$	14.7512	0.687031	0.343515	+	0.939147i	$0.388382\pi$
$462$	−1.39171	−0.0647481
$463$	30.8315	1.43286	0.716431	−	0.697658i	$-0.245774\pi$
$463$	30.8315	1.43286	0.716431	+	0.697658i	$0.245774\pi$
$464$	22.7321	1.05531
$465$	0	0
$466$	−2.86790	−0.132853
$467$	20.0644	0.928471	0.464235	−	0.885712i	$-0.346329\pi$
$467$	20.0644	0.928471	0.464235	+	0.885712i	$0.346329\pi$
$468$	8.91840	0.412253
$469$	−19.7520	−0.912064
$470$	0	0
$471$	−16.3037	−0.751235
$472$	−6.07293	−0.279529
$473$	3.23933	0.148944
$474$	−0.762870	−0.0350398
$475$	0	0
$476$	17.5901	0.806239
$477$	−1.28799	−0.0589732
$478$	−0.214645	−0.00981764
$479$	−21.4676	−0.980879	−0.490440	−	0.871475i	$-0.663164\pi$
$479$	−21.4676	−0.980879	−0.490440	+	0.871475i	$0.663164\pi$
$480$	0	0
$481$	−36.6339	−1.67036
$482$	2.72890	0.124298
$483$	−11.8105	−0.537396
$484$	−8.90412	−0.404733
$485$	0	0
$486$	−0.184902	−0.00838733
$487$	−0.118331	−0.00536207	−0.00268103	−	0.999996i	$-0.500853\pi$
$487$	−0.118331	−0.00536207	−0.00268103	+	0.999996i	$0.500853\pi$
$488$	−8.31034	−0.376192
$489$	10.3731	0.469089
$490$	0	0
$491$	6.96487	0.314320	0.157160	−	0.987573i	$-0.449766\pi$
$491$	6.96487	0.314320	0.157160	+	0.987573i	$0.449766\pi$
$492$	−0.111554	−0.00502925
$493$	28.0548	1.26352
$494$	0.838856	0.0377419
$495$	0	0
$496$	27.7553	1.24625
$497$	19.7520	0.886000
$498$	−2.15032	−0.0963583
$499$	−15.3967	−0.689250	−0.344625	−	0.938741i	$-0.611994\pi$
$499$	−15.3967	−0.689250	−0.344625	+	0.938741i	$0.611994\pi$
$500$	0	0
$501$	−24.4309	−1.09149
$502$	1.07888	0.0481529
$503$	−5.79980	−0.258600	−0.129300	−	0.991606i	$-0.541273\pi$
$503$	−5.79980	−0.258600	−0.129300	+	0.991606i	$0.541273\pi$
$504$	−1.40056	−0.0623858
$505$	0	0
$506$	4.50569	0.200303
$507$	7.58214	0.336735
$508$	−15.4278	−0.684497
$509$	33.9293	1.50389	0.751945	−	0.659226i	$-0.229116\pi$
$509$	33.9293	1.50389	0.751945	+	0.659226i	$0.229116\pi$
$510$	0	0
$511$	−19.2876	−0.853234
$512$	−13.7988	−0.609825
$513$	1.00000	0.0441511
$514$	0.406425	0.0179266
$515$	0	0
$516$	1.61591	0.0711366
$517$	−29.5748	−1.30070
$518$	2.85172	0.125297
$519$	−21.4851	−0.943093
$520$	0	0
$521$	−8.82716	−0.386725	−0.193362	−	0.981127i	$-0.561939\pi$
$521$	−8.82716	−0.386725	−0.193362	+	0.981127i	$0.561939\pi$
$522$	−1.10726	−0.0484636
$523$	−20.7651	−0.907995	−0.453997	−	0.891003i	$-0.650002\pi$
$523$	−20.7651	−0.907995	−0.453997	+	0.891003i	$0.650002\pi$
$524$	−2.68770	−0.117413
$525$	0	0
$526$	3.96668	0.172956
$527$	34.2543	1.49214
$528$	−14.9592	−0.651016
$529$	15.2369	0.662472
$530$	0	0
$531$	−8.28180	−0.359399
$532$	3.75465	0.162785
$533$	−0.257448	−0.0111513
$534$	−1.32585	−0.0573750
$535$	0	0
$536$	7.58331	0.327549
$537$	−14.7939	−0.638405
$538$	0.125808	0.00542395
$539$	13.2094	0.568969
$540$	0	0
$541$	44.2527	1.90257	0.951286	−	0.308309i	$-0.0997631\pi$
$541$	44.2527	1.90257	0.951286	+	0.308309i	$0.0997631\pi$
$542$	−3.20384	−0.137617
$543$	17.8632	0.766585
$544$	−10.1590	−0.435564
$545$	0	0
$546$	−1.60219	−0.0685675
$547$	−18.6666	−0.798127	−0.399064	−	0.916923i	$-0.630665\pi$
$547$	−18.6666	−0.798127	−0.399064	+	0.916923i	$0.630665\pi$
$548$	−23.6487	−1.01022
$549$	−11.3330	−0.483681
$550$	0	0
$551$	5.98837	0.255113
$552$	4.53435	0.192995
$553$	−7.88017	−0.335099
$554$	−4.77670	−0.202943
$555$	0	0
$556$	−24.9458	−1.05794
$557$	4.34816	0.184237	0.0921187	−	0.995748i	$-0.470636\pi$
$557$	4.34816	0.184237	0.0921187	+	0.995748i	$0.470636\pi$
$558$	−1.35194	−0.0572323
$559$	3.72925	0.157730
$560$	0	0
$561$	−18.4619	−0.779463
$562$	1.16772	0.0492573
$563$	9.70917	0.409193	0.204596	−	0.978846i	$-0.434412\pi$
$563$	9.70917	0.409193	0.204596	+	0.978846i	$0.434412\pi$
$564$	−14.7532	−0.621220
$565$	0	0
$566$	−1.30129	−0.0546974
$567$	−1.90997	−0.0802113
$568$	−7.58331	−0.318189
$569$	−36.6849	−1.53791	−0.768956	−	0.639301i	$-0.779224\pi$
$569$	−36.6849	−1.53791	−0.768956	+	0.639301i	$0.779224\pi$
$570$	0	0
$571$	−33.6378	−1.40770	−0.703849	−	0.710350i	$-0.748537\pi$
$571$	−33.6378	−1.40770	−0.703849	+	0.710350i	$0.748537\pi$
$572$	−35.1452	−1.46949
$573$	12.8206	0.535587
$574$	0.0200407	0.000836483 0
$575$	0	0
$576$	−7.19112	−0.299630
$577$	31.9286	1.32920	0.664602	−	0.747197i	$-0.268601\pi$
$577$	31.9286	1.32920	0.664602	+	0.747197i	$0.268601\pi$
$578$	−0.914914	−0.0380554
$579$	15.8737	0.659690
$580$	0	0
$581$	−22.2121	−0.921512
$582$	0.499305	0.0206969
$583$	5.07566	0.210212
$584$	7.40500	0.306421
$585$	0	0
$586$	−3.01713	−0.124636
$587$	16.0973	0.664406	0.332203	−	0.943208i	$-0.392208\pi$
$587$	16.0973	0.664406	0.332203	+	0.943208i	$0.392208\pi$
$588$	6.58941	0.271743
$589$	7.31166	0.301272
$590$	0	0
$591$	−13.8571	−0.570005
$592$	30.6526	1.25982
$593$	−30.3210	−1.24513	−0.622566	−	0.782567i	$-0.713910\pi$
$593$	−30.3210	−1.24513	−0.622566	+	0.782567i	$0.713910\pi$
$594$	0.728653	0.0298970
$595$	0	0
$596$	41.3664	1.69443
$597$	26.5763	1.08770
$598$	5.18714	0.212118
$599$	27.5881	1.12722	0.563610	−	0.826041i	$-0.309412\pi$
$599$	27.5881	1.12722	0.563610	+	0.826041i	$0.309412\pi$
$600$	0	0
$601$	−7.71122	−0.314547	−0.157274	−	0.987555i	$-0.550270\pi$
$601$	−7.71122	−0.314547	−0.157274	+	0.987555i	$0.550270\pi$
$602$	−0.290299	−0.0118317
$603$	10.3415	0.421140
$604$	6.53883	0.266061
$605$	0	0
$606$	−0.402700	−0.0163585
$607$	30.1322	1.22303	0.611515	−	0.791233i	$-0.290560\pi$
$607$	30.1322	1.22303	0.611515	+	0.791233i	$0.290560\pi$
$608$	−2.16847	−0.0879430
$609$	−11.4376	−0.463476
$610$	0	0
$611$	−34.0478	−1.37742
$612$	−9.20959	−0.372276
$613$	−28.2790	−1.14218	−0.571089	−	0.820888i	$-0.693479\pi$
$613$	−28.2790	−1.14218	−0.571089	+	0.820888i	$0.693479\pi$
$614$	3.38914	0.136775
$615$	0	0
$616$	5.51925	0.222377
$617$	1.58263	0.0637143	0.0318572	−	0.999492i	$-0.489858\pi$
$617$	1.58263	0.0637143	0.0318572	+	0.999492i	$0.489858\pi$
$618$	−1.89897	−0.0763878
$619$	−6.99796	−0.281272	−0.140636	−	0.990061i	$-0.544915\pi$
$619$	−6.99796	−0.281272	−0.140636	+	0.990061i	$0.544915\pi$
$620$	0	0
$621$	6.18360	0.248139
$622$	2.17455	0.0871914
$623$	−13.6955	−0.548700
$624$	−17.2217	−0.689419
$625$	0	0
$626$	3.17499	0.126898
$627$	−3.94075	−0.157378
$628$	32.0500	1.27893
$629$	37.8300	1.50838
$630$	0	0
$631$	23.8697	0.950238	0.475119	−	0.879922i	$-0.342405\pi$
$631$	23.8697	0.950238	0.475119	+	0.879922i	$0.342405\pi$
$632$	3.02540	0.120344
$633$	−12.3339	−0.490229
$634$	2.18540	0.0867932
$635$	0	0
$636$	2.53195	0.100398
$637$	15.2072	0.602532
$638$	4.36344	0.172750
$639$	−10.3415	−0.409105
$640$	0	0
$641$	−24.5476	−0.969572	−0.484786	−	0.874633i	$-0.661103\pi$
$641$	−24.5476	−0.969572	−0.484786	+	0.874633i	$0.661103\pi$
$642$	−1.44592	−0.0570661
$643$	−36.1097	−1.42403	−0.712014	−	0.702165i	$-0.752217\pi$
$643$	−36.1097	−1.42403	−0.712014	+	0.702165i	$0.752217\pi$
$644$	23.2172	0.914886
$645$	0	0
$646$	−0.866244	−0.0340819
$647$	7.25157	0.285089	0.142544	−	0.989788i	$-0.454472\pi$
$647$	7.25157	0.285089	0.142544	+	0.989788i	$0.454472\pi$
$648$	0.733287	0.0288062
$649$	32.6365	1.28109
$650$	0	0
$651$	−13.9651	−0.547334
$652$	−20.3916	−0.798597
$653$	−40.4550	−1.58312	−0.791562	−	0.611088i	$-0.790732\pi$
$653$	−40.4550	−1.58312	−0.791562	+	0.611088i	$0.790732\pi$
$654$	−1.46657	−0.0573476
$655$	0	0
$656$	0.215414	0.00841051
$657$	10.0984	0.393975
$658$	2.65041	0.103324
$659$	6.41486	0.249887	0.124944	−	0.992164i	$-0.460125\pi$
$659$	6.41486	0.249887	0.124944	+	0.992164i	$0.460125\pi$
$660$	0	0
$661$	30.1068	1.17102	0.585510	−	0.810665i	$-0.300894\pi$
$661$	30.1068	1.17102	0.585510	+	0.810665i	$0.300894\pi$
$662$	4.62421	0.179725
$663$	−21.2541	−0.825443
$664$	8.52778	0.330942
$665$	0	0
$666$	−1.49307	−0.0578552
$667$	37.0297	1.43379
$668$	48.0266	1.85820
$669$	25.8035	0.997621
$670$	0	0
$671$	44.6605	1.72410
$672$	4.14172	0.159770
$673$	32.5367	1.25420	0.627099	−	0.778940i	$-0.284242\pi$
$673$	32.5367	1.25420	0.627099	+	0.778940i	$0.284242\pi$
$674$	−0.0834569	−0.00321464
$675$	0	0
$676$	−14.9051	−0.573271
$677$	−7.19269	−0.276438	−0.138219	−	0.990402i	$-0.544138\pi$
$677$	−7.19269	−0.276438	−0.138219	+	0.990402i	$0.544138\pi$
$678$	1.76428	0.0677567
$679$	5.15764	0.197932
$680$	0	0
$681$	14.1348	0.541649
$682$	5.32766	0.204007
$683$	−11.7394	−0.449195	−0.224598	−	0.974452i	$-0.572107\pi$
$683$	−11.7394	−0.449195	−0.224598	+	0.974452i	$0.572107\pi$
$684$	−1.96581	−0.0751647
$685$	0	0
$686$	−3.65589	−0.139583
$687$	14.7671	0.563400
$688$	−3.12037	−0.118963
$689$	5.84331	0.222612
$690$	0	0
$691$	−26.8706	−1.02221	−0.511103	−	0.859520i	$-0.670763\pi$
$691$	−26.8706	−1.02221	−0.511103	+	0.859520i	$0.670763\pi$
$692$	42.2357	1.60556
$693$	7.52672	0.285916
$694$	1.65275	0.0627374
$695$	0	0
$696$	4.39119	0.166448
$697$	0.265854	0.0100699
$698$	2.94722	0.111554
$699$	15.5104	0.586657
$700$	0	0
$701$	36.2813	1.37033	0.685163	−	0.728390i	$-0.259731\pi$
$701$	36.2813	1.37033	0.685163	+	0.728390i	$0.259731\pi$
$702$	0.838856	0.0316606
$703$	8.07490	0.304551
$704$	28.3384	1.06804
$705$	0	0
$706$	−1.57878	−0.0594180
$707$	−4.15974	−0.156443
$708$	16.2804	0.611857
$709$	−9.09197	−0.341456	−0.170728	−	0.985318i	$-0.554612\pi$
$709$	−9.09197	−0.341456	−0.170728	+	0.985318i	$0.554612\pi$
$710$	0	0
$711$	4.12580	0.154730
$712$	5.25806	0.197054
$713$	45.2124	1.69322
$714$	1.65450	0.0619182
$715$	0	0
$716$	29.0821	1.08685
$717$	1.16086	0.0433531
$718$	−3.09526	−0.115514
$719$	−26.9986	−1.00688	−0.503439	−	0.864031i	$-0.667932\pi$
$719$	−26.9986	−1.00688	−0.503439	+	0.864031i	$0.667932\pi$
$720$	0	0
$721$	−19.6157	−0.730526
$722$	−0.184902	−0.00688135
$723$	−14.7586	−0.548878
$724$	−35.1158	−1.30507
$725$	0	0
$726$	−0.837513	−0.0310830
$727$	6.30378	0.233794	0.116897	−	0.993144i	$-0.462705\pi$
$727$	6.30378	0.233794	0.116897	+	0.993144i	$0.462705\pi$
$728$	6.35399	0.235495
$729$	1.00000	0.0370370
$730$	0	0
$731$	−3.85101	−0.142435
$732$	22.2785	0.823439
$733$	−6.84548	−0.252843	−0.126422	−	0.991977i	$-0.540349\pi$
$733$	−6.84548	−0.252843	−0.126422	+	0.991977i	$0.540349\pi$
$734$	0.0555739	0.00205127
$735$	0	0
$736$	−13.4089	−0.494260
$737$	−40.7533	−1.50117
$738$	−0.0104927	−0.000386240 0
$739$	18.4720	0.679504	0.339752	−	0.940515i	$-0.389657\pi$
$739$	18.4720	0.679504	0.339752	+	0.940515i	$0.389657\pi$
$740$	0	0
$741$	−4.53675	−0.166662
$742$	−0.454865	−0.0166986
$743$	18.7512	0.687916	0.343958	−	0.938985i	$-0.388232\pi$
$743$	18.7512	0.687916	0.343958	+	0.938985i	$0.388232\pi$
$744$	5.36155	0.196564
$745$	0	0
$746$	4.68727	0.171613
$747$	11.6295	0.425502
$748$	36.2927	1.32699
$749$	−14.9359	−0.545745
$750$	0	0
$751$	−3.19610	−0.116628	−0.0583138	−	0.998298i	$-0.518572\pi$
$751$	−3.19610	−0.116628	−0.0583138	+	0.998298i	$0.518572\pi$
$752$	28.4888	1.03888
$753$	−5.83488	−0.212635
$754$	5.02338	0.182941
$755$	0	0
$756$	3.75465	0.136555
$757$	−30.6268	−1.11315	−0.556575	−	0.830798i	$-0.687885\pi$
$757$	−30.6268	−1.11315	−0.556575	+	0.830798i	$0.687885\pi$
$758$	−3.01482	−0.109503
$759$	−24.3680	−0.884502
$760$	0	0
$761$	32.4024	1.17458	0.587292	−	0.809375i	$-0.300194\pi$
$761$	32.4024	1.17458	0.587292	+	0.809375i	$0.300194\pi$
$762$	−1.45112	−0.0525685
$763$	−15.1492	−0.548437
$764$	−25.2028	−0.911805
$765$	0	0
$766$	−5.63308	−0.203531
$767$	37.5725	1.35666
$768$	13.3345	0.481166
$769$	−38.2846	−1.38058	−0.690288	−	0.723535i	$-0.742516\pi$
$769$	−38.2846	−1.38058	−0.690288	+	0.723535i	$0.742516\pi$
$770$	0	0
$771$	−2.19805	−0.0791609
$772$	−31.2048	−1.12308
$773$	33.4716	1.20389	0.601944	−	0.798538i	$-0.294393\pi$
$773$	33.4716	1.20389	0.601944	+	0.798538i	$0.294393\pi$
$774$	0.151991	0.00546321
$775$	0	0
$776$	−1.98015	−0.0710833
$777$	−15.4228	−0.553292
$778$	0.237415	0.00851176
$779$	0.0567471	0.00203318
$780$	0	0
$781$	40.7533	1.45827
$782$	−5.35651	−0.191548
$783$	5.98837	0.214007
$784$	−12.7243	−0.454440
$785$	0	0
$786$	−0.252802	−0.00901715
$787$	33.9153	1.20895	0.604474	−	0.796625i	$-0.293383\pi$
$787$	33.9153	1.20895	0.604474	+	0.796625i	$0.293383\pi$
$788$	27.2404	0.970400
$789$	−21.4529	−0.763742
$790$	0	0
$791$	18.2244	0.647984
$792$	−2.88970	−0.102681
$793$	51.4151	1.82580
$794$	2.31475	0.0821473
$795$	0	0
$796$	−52.2440	−1.85174
$797$	−17.4970	−0.619777	−0.309889	−	0.950773i	$-0.600292\pi$
$797$	−17.4970	−0.619777	−0.309889	+	0.950773i	$0.600292\pi$
$798$	0.353158	0.0125017
$799$	35.1594	1.24385
$800$	0	0
$801$	7.17054	0.253358
$802$	−0.226092	−0.00798358
$803$	−39.7951	−1.40434
$804$	−20.3295	−0.716966
$805$	0	0
$806$	6.13343	0.216041
$807$	−0.680401	−0.0239513
$808$	1.59703	0.0561833
$809$	−24.8019	−0.871990	−0.435995	−	0.899949i	$-0.643603\pi$
$809$	−24.8019	−0.871990	−0.435995	+	0.899949i	$0.643603\pi$
$810$	0	0
$811$	−33.9010	−1.19043	−0.595213	−	0.803568i	$-0.702932\pi$
$811$	−33.9010	−1.19043	−0.595213	+	0.803568i	$0.702932\pi$
$812$	22.4842	0.789041
$813$	17.3272	0.607692
$814$	5.88380	0.206227
$815$	0	0
$816$	17.7840	0.622564
$817$	−0.822008	−0.0287584
$818$	5.13459	0.179527
$819$	8.66508	0.302782
$820$	0	0
$821$	−27.2965	−0.952654	−0.476327	−	0.879268i	$-0.658032\pi$
$821$	−27.2965	−0.952654	−0.476327	+	0.879268i	$0.658032\pi$
$822$	−2.22437	−0.0775839
$823$	36.2799	1.26464	0.632319	−	0.774708i	$-0.282103\pi$
$823$	36.2799	1.26464	0.632319	+	0.774708i	$0.282103\pi$
$824$	7.53095	0.262353
$825$	0	0
$826$	−2.92478	−0.101766
$827$	20.8780	0.725998	0.362999	−	0.931789i	$-0.381753\pi$
$827$	20.8780	0.725998	0.362999	+	0.931789i	$0.381753\pi$
$828$	−12.1558	−0.422443
$829$	45.3011	1.57337	0.786687	−	0.617353i	$-0.211795\pi$
$829$	45.3011	1.57337	0.786687	+	0.617353i	$0.211795\pi$
$830$	0	0
$831$	25.8337	0.896160
$832$	32.6243	1.13105
$833$	−15.7037	−0.544102
$834$	−2.34638	−0.0812484
$835$	0	0
$836$	7.74677	0.267927
$837$	7.31166	0.252728
$838$	2.67314	0.0923421
$839$	−18.9618	−0.654633	−0.327317	−	0.944915i	$-0.606144\pi$
$839$	−18.9618	−0.654633	−0.327317	+	0.944915i	$0.606144\pi$
$840$	0	0
$841$	6.86057	0.236571
$842$	−6.57810	−0.226696
$843$	−6.31534	−0.217512
$844$	24.2461	0.834586
$845$	0	0
$846$	−1.38767	−0.0477090
$847$	−8.65120	−0.297259
$848$	−4.88927	−0.167898
$849$	7.03773	0.241534
$850$	0	0
$851$	49.9319	1.71165
$852$	20.3295	0.696477
$853$	37.9971	1.30100	0.650499	−	0.759507i	$-0.274560\pi$
$853$	37.9971	1.30100	0.650499	+	0.759507i	$0.274560\pi$
$854$	−4.00234	−0.136957
$855$	0	0
$856$	5.73426	0.195993
$857$	−11.0179	−0.376363	−0.188182	−	0.982134i	$-0.560259\pi$
$857$	−11.0179	−0.376363	−0.188182	+	0.982134i	$0.560259\pi$
$858$	−3.30572	−0.112855
$859$	26.2271	0.894858	0.447429	−	0.894319i	$-0.352340\pi$
$859$	26.2271	0.894858	0.447429	+	0.894319i	$0.352340\pi$
$860$	0	0
$861$	−0.108385	−0.00369377
$862$	−2.06891	−0.0704674
$863$	21.0735	0.717351	0.358675	−	0.933462i	$-0.383229\pi$
$863$	21.0735	0.717351	0.358675	+	0.933462i	$0.383229\pi$
$864$	−2.16847	−0.0737728
$865$	0	0
$866$	1.88922	0.0641984
$867$	4.94810	0.168046
$868$	27.4527	0.931805
$869$	−16.2587	−0.551540
$870$	0	0
$871$	−46.9170	−1.58972
$872$	5.81616	0.196960
$873$	−2.70038	−0.0913939
$874$	−1.14336	−0.0386747
$875$	0	0
$876$	−19.8515	−0.670720
$877$	2.20753	0.0745431	0.0372716	−	0.999305i	$-0.488133\pi$
$877$	2.20753	0.0745431	0.0372716	+	0.999305i	$0.488133\pi$
$878$	0.886043	0.0299025
$879$	16.3174	0.550373
$880$	0	0
$881$	17.6683	0.595262	0.297631	−	0.954681i	$-0.403804\pi$
$881$	17.6683	0.595262	0.297631	+	0.954681i	$0.403804\pi$
$882$	0.619793	0.0208695
$883$	−19.7314	−0.664013	−0.332007	−	0.943277i	$-0.607726\pi$
$883$	−19.7314	−0.664013	−0.332007	+	0.943277i	$0.607726\pi$
$884$	41.7816	1.40527
$885$	0	0
$886$	2.46462	0.0828007
$887$	42.4935	1.42679	0.713396	−	0.700762i	$-0.247156\pi$
$887$	42.4935	1.42679	0.713396	+	0.700762i	$0.247156\pi$
$888$	5.92122	0.198703
$889$	−14.9895	−0.502733
$890$	0	0
$891$	−3.94075	−0.132020
$892$	−50.7248	−1.69839
$893$	7.50487	0.251141
$894$	3.89088	0.130130
$895$	0	0
$896$	−10.8230	−0.361572
$897$	−28.0535	−0.936678
$898$	−3.70473	−0.123629
$899$	43.7849	1.46031
$900$	0	0
$901$	−6.03410	−0.201025
$902$	0.0413490	0.00137677
$903$	1.57001	0.0522468
$904$	−6.99680	−0.232710
$905$	0	0
$906$	0.615036	0.0204332
$907$	3.21385	0.106714	0.0533571	−	0.998575i	$-0.483008\pi$
$907$	3.21385	0.106714	0.0533571	+	0.998575i	$0.483008\pi$
$908$	−27.7864	−0.922126
$909$	2.17791	0.0722366
$910$	0	0
$911$	50.5059	1.67334	0.836668	−	0.547710i	$-0.184500\pi$
$911$	50.5059	1.67334	0.836668	+	0.547710i	$0.184500\pi$
$912$	3.79604	0.125699
$913$	−45.8290	−1.51672
$914$	−2.67877	−0.0886057
$915$	0	0
$916$	−29.0293	−0.959156
$917$	−2.61135	−0.0862345
$918$	−0.866244	−0.0285903
$919$	15.9521	0.526212	0.263106	−	0.964767i	$-0.415253\pi$
$919$	15.9521	0.526212	0.263106	+	0.964767i	$0.415253\pi$
$920$	0	0
$921$	−18.3294	−0.603973
$922$	−2.72752	−0.0898262
$923$	46.9170	1.54429
$924$	−14.7961	−0.486756
$925$	0	0
$926$	−5.70082	−0.187340
$927$	10.2701	0.337315
$928$	−12.9856	−0.426273
$929$	−57.3866	−1.88279	−0.941396	−	0.337304i	$-0.890485\pi$
$929$	−57.3866	−1.88279	−0.941396	+	0.337304i	$0.890485\pi$
$930$	0	0
$931$	−3.35200	−0.109857
$932$	−30.4905	−0.998749
$933$	−11.7605	−0.385023
$934$	−3.70996	−0.121393
$935$	0	0
$936$	−3.32674	−0.108738
$937$	−43.8839	−1.43363	−0.716813	−	0.697266i	$-0.754400\pi$
$937$	−43.8839	−1.43363	−0.716813	+	0.697266i	$0.754400\pi$
$938$	3.65219	0.119248
$939$	−17.1712	−0.560361
$940$	0	0
$941$	56.0765	1.82804	0.914021	−	0.405667i	$-0.132961\pi$
$941$	56.0765	1.82804	0.914021	+	0.405667i	$0.132961\pi$
$942$	3.01459	0.0982207
$943$	0.350901	0.0114269
$944$	−31.4380	−1.02322
$945$	0	0
$946$	−0.598959	−0.0194738
$947$	46.3239	1.50532	0.752662	−	0.658407i	$-0.228769\pi$
$947$	46.3239	1.50532	0.752662	+	0.658407i	$0.228769\pi$
$948$	−8.11055	−0.263418
$949$	−45.8138	−1.48718
$950$	0	0
$951$	−11.8192	−0.383264
$952$	−6.56145	−0.212658
$953$	−40.2270	−1.30308	−0.651540	−	0.758615i	$-0.725877\pi$
$953$	−40.2270	−1.30308	−0.651540	+	0.758615i	$0.725877\pi$
$954$	0.238153	0.00771048
$955$	0	0
$956$	−2.28203	−0.0738061
$957$	−23.5987	−0.762836
$958$	3.96940	0.128246
$959$	−22.9770	−0.741965
$960$	0	0
$961$	22.4604	0.724529
$962$	6.77368	0.218392
$963$	7.81995	0.251994
$964$	29.0126	0.934434
$965$	0	0
$966$	2.18379	0.0702622
$967$	−5.60792	−0.180339	−0.0901693	−	0.995926i	$-0.528741\pi$
$967$	−5.60792	−0.180339	−0.0901693	+	0.995926i	$0.528741\pi$
$968$	3.32142	0.106754
$969$	4.68488	0.150500
$970$	0	0
$971$	−18.2825	−0.586712	−0.293356	−	0.956003i	$-0.594772\pi$
$971$	−18.2825	−0.586712	−0.293356	+	0.956003i	$0.594772\pi$
$972$	−1.96581	−0.0630534
$973$	−24.2372	−0.777010
$974$	0.0218796	0.000701067 0
$975$	0	0
$976$	−43.0205	−1.37705
$977$	−4.99368	−0.159762	−0.0798810	−	0.996804i	$-0.525454\pi$
$977$	−4.99368	−0.159762	−0.0798810	+	0.996804i	$0.525454\pi$
$978$	−1.91801	−0.0613313
$979$	−28.2573	−0.903106
$980$	0	0
$981$	7.93162	0.253237
$982$	−1.28782	−0.0410960
$983$	40.9361	1.30566	0.652830	−	0.757505i	$-0.273582\pi$
$983$	40.9361	1.30566	0.652830	+	0.757505i	$0.273582\pi$
$984$	0.0416119	0.00132654
$985$	0	0
$986$	−5.18739	−0.165200
$987$	−14.3341	−0.456259
$988$	8.91840	0.283732
$989$	−5.08297	−0.161629
$990$	0	0
$991$	−14.3877	−0.457039	−0.228520	−	0.973539i	$-0.573388\pi$
$991$	−14.3877	−0.457039	−0.228520	+	0.973539i	$0.573388\pi$
$992$	−15.8551	−0.503400
$993$	−25.0090	−0.793636
$994$	−3.65219	−0.115841
$995$	0	0
$996$	−22.8614	−0.724393
$997$	−17.9495	−0.568467	−0.284233	−	0.958755i	$-0.591739\pi$
$997$	−17.9495	−0.568467	−0.284233	+	0.958755i	$0.591739\pi$
$998$	2.84688	0.0901163
$999$	8.07490	0.255479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1425.2.a.z.1.3		7
3.2	odd	2		4275.2.a.bv.1.5		7
5.2	odd	4		285.2.c.b.229.7	✓	14
5.3	odd	4		285.2.c.b.229.8	yes	14
5.4	even	2		1425.2.a.y.1.5		7
15.2	even	4		855.2.c.g.514.8		14
15.8	even	4		855.2.c.g.514.7		14
15.14	odd	2		4275.2.a.bw.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.b.229.7	✓	14	5.2	odd	4
285.2.c.b.229.8	yes	14	5.3	odd	4
855.2.c.g.514.7		14	15.8	even	4
855.2.c.g.514.8		14	15.2	even	4
1425.2.a.y.1.5		7	5.4	even	2
1425.2.a.z.1.3		7	1.1	even	1	trivial
4275.2.a.bv.1.5		7	3.2	odd	2
4275.2.a.bw.1.3		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)

\(f(q)\)	\(=\)	\(q-0.184902 q^{2} +1.00000 q^{3} -1.96581 q^{4} -0.184902 q^{6} -1.90997 q^{7} +0.733287 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.184902 q^{2} +1.00000 q^{3} -1.96581 q^{4} -0.184902 q^{6} -1.90997 q^{7} +0.733287 q^{8} +1.00000 q^{9} -3.94075 q^{11} -1.96581 q^{12} -4.53675 q^{13} +0.353158 q^{14} +3.79604 q^{16} +4.68488 q^{17} -0.184902 q^{18} +1.00000 q^{19} -1.90997 q^{21} +0.728653 q^{22} +6.18360 q^{23} +0.733287 q^{24} +0.838856 q^{26} +1.00000 q^{27} +3.75465 q^{28} +5.98837 q^{29} +7.31166 q^{31} -2.16847 q^{32} -3.94075 q^{33} -0.866244 q^{34} -1.96581 q^{36} +8.07490 q^{37} -0.184902 q^{38} -4.53675 q^{39} +0.0567471 q^{41} +0.353158 q^{42} -0.822008 q^{43} +7.74677 q^{44} -1.14336 q^{46} +7.50487 q^{47} +3.79604 q^{48} -3.35200 q^{49} +4.68488 q^{51} +8.91840 q^{52} -1.28799 q^{53} -0.184902 q^{54} -1.40056 q^{56} +1.00000 q^{57} -1.10726 q^{58} -8.28180 q^{59} -11.3330 q^{61} -1.35194 q^{62} -1.90997 q^{63} -7.19112 q^{64} +0.728653 q^{66} +10.3415 q^{67} -9.20959 q^{68} +6.18360 q^{69} -10.3415 q^{71} +0.733287 q^{72} +10.0984 q^{73} -1.49307 q^{74} -1.96581 q^{76} +7.52672 q^{77} +0.838856 q^{78} +4.12580 q^{79} +1.00000 q^{81} -0.0104927 q^{82} +11.6295 q^{83} +3.75465 q^{84} +0.151991 q^{86} +5.98837 q^{87} -2.88970 q^{88} +7.17054 q^{89} +8.66508 q^{91} -12.1558 q^{92} +7.31166 q^{93} -1.38767 q^{94} -2.16847 q^{96} -2.70038 q^{97} +0.619793 q^{98} -3.94075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 11 q^{4} + 3 q^{6} + 8 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 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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