LMFDB - Embedded newform 1150.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.85410 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.85410 q^{7} -1.00000 q^{8} -0.381966 q^{9} -5.61803 q^{11} +1.61803 q^{12} +2.61803 q^{13} +1.85410 q^{14} +1.00000 q^{16} +0.854102 q^{17} +0.381966 q^{18} -0.145898 q^{19} -3.00000 q^{21} +5.61803 q^{22} +1.00000 q^{23} -1.61803 q^{24} -2.61803 q^{26} -5.47214 q^{27} -1.85410 q^{28} -9.70820 q^{29} -2.14590 q^{31} -1.00000 q^{32} -9.09017 q^{33} -0.854102 q^{34} -0.381966 q^{36} -9.70820 q^{37} +0.145898 q^{38} +4.23607 q^{39} -5.61803 q^{41} +3.00000 q^{42} +11.2361 q^{43} -5.61803 q^{44} -1.00000 q^{46} +1.70820 q^{47} +1.61803 q^{48} -3.56231 q^{49} +1.38197 q^{51} +2.61803 q^{52} -2.00000 q^{53} +5.47214 q^{54} +1.85410 q^{56} -0.236068 q^{57} +9.70820 q^{58} -6.00000 q^{59} +2.85410 q^{61} +2.14590 q^{62} +0.708204 q^{63} +1.00000 q^{64} +9.09017 q^{66} +5.23607 q^{67} +0.854102 q^{68} +1.61803 q^{69} +0.381966 q^{71} +0.381966 q^{72} -16.4721 q^{73} +9.70820 q^{74} -0.145898 q^{76} +10.4164 q^{77} -4.23607 q^{78} -7.70820 q^{79} -7.70820 q^{81} +5.61803 q^{82} +7.70820 q^{83} -3.00000 q^{84} -11.2361 q^{86} -15.7082 q^{87} +5.61803 q^{88} +3.70820 q^{89} -4.85410 q^{91} +1.00000 q^{92} -3.47214 q^{93} -1.70820 q^{94} -1.61803 q^{96} +13.0344 q^{97} +3.56231 q^{98} +2.14590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 3 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 3 * q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 3 q^{7} - 2 q^{8} - 3 q^{9} - 9 q^{11} + q^{12} + 3 q^{13} - 3 q^{14} + 2 q^{16} - 5 q^{17} + 3 q^{18} - 7 q^{19} - 6 q^{21} + 9 q^{22} + 2 q^{23} - q^{24} - 3 q^{26} - 2 q^{27} + 3 q^{28} - 6 q^{29} - 11 q^{31} - 2 q^{32} - 7 q^{33} + 5 q^{34} - 3 q^{36} - 6 q^{37} + 7 q^{38} + 4 q^{39} - 9 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{44} - 2 q^{46} - 10 q^{47} + q^{48} + 13 q^{49} + 5 q^{51} + 3 q^{52} - 4 q^{53} + 2 q^{54} - 3 q^{56} + 4 q^{57} + 6 q^{58} - 12 q^{59} - q^{61} + 11 q^{62} - 12 q^{63} + 2 q^{64} + 7 q^{66} + 6 q^{67} - 5 q^{68} + q^{69} + 3 q^{71} + 3 q^{72} - 24 q^{73} + 6 q^{74} - 7 q^{76} - 6 q^{77} - 4 q^{78} - 2 q^{79} - 2 q^{81} + 9 q^{82} + 2 q^{83} - 6 q^{84} - 18 q^{86} - 18 q^{87} + 9 q^{88} - 6 q^{89} - 3 q^{91} + 2 q^{92} + 2 q^{93} + 10 q^{94} - q^{96} - 3 q^{97} - 13 q^{98} + 11 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 3 * q^7 - 2 * q^8 - 3 * q^9 - 9 * q^11 + q^12 + 3 * q^13 - 3 * q^14 + 2 * q^16 - 5 * q^17 + 3 * q^18 - 7 * q^19 - 6 * q^21 + 9 * q^22 + 2 * q^23 - q^24 - 3 * q^26 - 2 * q^27 + 3 * q^28 - 6 * q^29 - 11 * q^31 - 2 * q^32 - 7 * q^33 + 5 * q^34 - 3 * q^36 - 6 * q^37 + 7 * q^38 + 4 * q^39 - 9 * q^41 + 6 * q^42 + 18 * q^43 - 9 * q^44 - 2 * q^46 - 10 * q^47 + q^48 + 13 * q^49 + 5 * q^51 + 3 * q^52 - 4 * q^53 + 2 * q^54 - 3 * q^56 + 4 * q^57 + 6 * q^58 - 12 * q^59 - q^61 + 11 * q^62 - 12 * q^63 + 2 * q^64 + 7 * q^66 + 6 * q^67 - 5 * q^68 + q^69 + 3 * q^71 + 3 * q^72 - 24 * q^73 + 6 * q^74 - 7 * q^76 - 6 * q^77 - 4 * q^78 - 2 * q^79 - 2 * q^81 + 9 * q^82 + 2 * q^83 - 6 * q^84 - 18 * q^86 - 18 * q^87 + 9 * q^88 - 6 * q^89 - 3 * q^91 + 2 * q^92 + 2 * q^93 + 10 * q^94 - q^96 - 3 * q^97 - 13 * q^98 + 11 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.61803	−0.660560
$7$	−1.85410	−0.700785	−0.350392	−	0.936603i	$-0.613952\pi$
$7$	−1.85410	−0.700785	−0.350392	+	0.936603i	$0.613952\pi$
$8$	−1.00000	−0.353553
$9$	−0.381966	−0.127322
$10$	0	0
$11$	−5.61803	−1.69390	−0.846950	−	0.531672i	$-0.821564\pi$
$11$	−5.61803	−1.69390	−0.846950	+	0.531672i	$0.821564\pi$
$12$	1.61803	0.467086
$13$	2.61803	0.726112	0.363056	−	0.931767i	$-0.381733\pi$
$13$	2.61803	0.726112	0.363056	+	0.931767i	$0.381733\pi$
$14$	1.85410	0.495530
$15$	0	0
$16$	1.00000	0.250000
$17$	0.854102	0.207150	0.103575	−	0.994622i	$-0.466972\pi$
$17$	0.854102	0.207150	0.103575	+	0.994622i	$0.466972\pi$
$18$	0.381966	0.0900303
$19$	−0.145898	−0.0334713	−0.0167357	−	0.999860i	$-0.505327\pi$
$19$	−0.145898	−0.0334713	−0.0167357	+	0.999860i	$0.505327\pi$
$20$	0	0
$21$	−3.00000	−0.654654
$22$	5.61803	1.19777
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.61803	−0.330280
$25$	0	0
$26$	−2.61803	−0.513439
$27$	−5.47214	−1.05311
$28$	−1.85410	−0.350392
$29$	−9.70820	−1.80277	−0.901384	−	0.433020i	$-0.857448\pi$
$29$	−9.70820	−1.80277	−0.901384	+	0.433020i	$0.857448\pi$
$30$	0	0
$31$	−2.14590	−0.385415	−0.192707	−	0.981256i	$-0.561727\pi$
$31$	−2.14590	−0.385415	−0.192707	+	0.981256i	$0.561727\pi$
$32$	−1.00000	−0.176777
$33$	−9.09017	−1.58240
$34$	−0.854102	−0.146477
$35$	0	0
$36$	−0.381966	−0.0636610
$37$	−9.70820	−1.59602	−0.798009	−	0.602645i	$-0.794114\pi$
$37$	−9.70820	−1.59602	−0.798009	+	0.602645i	$0.794114\pi$
$38$	0.145898	0.0236678
$39$	4.23607	0.678314
$40$	0	0
$41$	−5.61803	−0.877390	−0.438695	−	0.898636i	$-0.644559\pi$
$41$	−5.61803	−0.877390	−0.438695	+	0.898636i	$0.644559\pi$
$42$	3.00000	0.462910
$43$	11.2361	1.71348	0.856742	−	0.515745i	$-0.172485\pi$
$43$	11.2361	1.71348	0.856742	+	0.515745i	$0.172485\pi$
$44$	−5.61803	−0.846950
$45$	0	0
$46$	−1.00000	−0.147442
$47$	1.70820	0.249167	0.124584	−	0.992209i	$-0.460241\pi$
$47$	1.70820	0.249167	0.124584	+	0.992209i	$0.460241\pi$
$48$	1.61803	0.233543
$49$	−3.56231	−0.508901
$50$	0	0
$51$	1.38197	0.193514
$52$	2.61803	0.363056
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	5.47214	0.744663
$55$	0	0
$56$	1.85410	0.247765
$57$	−0.236068	−0.0312680
$58$	9.70820	1.27475
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	2.85410	0.365430	0.182715	−	0.983166i	$-0.441511\pi$
$61$	2.85410	0.365430	0.182715	+	0.983166i	$0.441511\pi$
$62$	2.14590	0.272529
$63$	0.708204	0.0892253
$64$	1.00000	0.125000
$65$	0	0
$66$	9.09017	1.11892
$67$	5.23607	0.639688	0.319844	−	0.947470i	$-0.396370\pi$
$67$	5.23607	0.639688	0.319844	+	0.947470i	$0.396370\pi$
$68$	0.854102	0.103575
$69$	1.61803	0.194788
$70$	0	0
$71$	0.381966	0.0453310	0.0226655	−	0.999743i	$-0.492785\pi$
$71$	0.381966	0.0453310	0.0226655	+	0.999743i	$0.492785\pi$
$72$	0.381966	0.0450151
$73$	−16.4721	−1.92792	−0.963959	−	0.266051i	$-0.914281\pi$
$73$	−16.4721	−1.92792	−0.963959	+	0.266051i	$0.914281\pi$
$74$	9.70820	1.12856
$75$	0	0
$76$	−0.145898	−0.0167357
$77$	10.4164	1.18706
$78$	−4.23607	−0.479640
$79$	−7.70820	−0.867241	−0.433620	−	0.901096i	$-0.642764\pi$
$79$	−7.70820	−0.867241	−0.433620	+	0.901096i	$0.642764\pi$
$80$	0	0
$81$	−7.70820	−0.856467
$82$	5.61803	0.620408
$83$	7.70820	0.846085	0.423043	−	0.906110i	$-0.360962\pi$
$83$	7.70820	0.846085	0.423043	+	0.906110i	$0.360962\pi$
$84$	−3.00000	−0.327327
$85$	0	0
$86$	−11.2361	−1.21162
$87$	−15.7082	−1.68410
$88$	5.61803	0.598884
$89$	3.70820	0.393069	0.196534	−	0.980497i	$-0.437031\pi$
$89$	3.70820	0.393069	0.196534	+	0.980497i	$0.437031\pi$
$90$	0	0
$91$	−4.85410	−0.508848
$92$	1.00000	0.104257
$93$	−3.47214	−0.360044
$94$	−1.70820	−0.176188
$95$	0	0
$96$	−1.61803	−0.165140
$97$	13.0344	1.32345	0.661724	−	0.749748i	$-0.269825\pi$
$97$	13.0344	1.32345	0.661724	+	0.749748i	$0.269825\pi$
$98$	3.56231	0.359847
$99$	2.14590	0.215671
$100$	0	0
$101$	−1.52786	−0.152028	−0.0760141	−	0.997107i	$-0.524219\pi$
$101$	−1.52786	−0.152028	−0.0760141	+	0.997107i	$0.524219\pi$
$102$	−1.38197	−0.136835
$103$	10.8541	1.06949	0.534743	−	0.845015i	$-0.320408\pi$
$103$	10.8541	1.06949	0.534743	+	0.845015i	$0.320408\pi$
$104$	−2.61803	−0.256719
$105$	0	0
$106$	2.00000	0.194257
$107$	11.7082	1.13187	0.565937	−	0.824448i	$-0.308514\pi$
$107$	11.7082	1.13187	0.565937	+	0.824448i	$0.308514\pi$
$108$	−5.47214	−0.526557
$109$	7.56231	0.724338	0.362169	−	0.932113i	$-0.382036\pi$
$109$	7.56231	0.724338	0.362169	+	0.932113i	$0.382036\pi$
$110$	0	0
$111$	−15.7082	−1.49096
$112$	−1.85410	−0.175196
$113$	−13.4164	−1.26211	−0.631055	−	0.775738i	$-0.717378\pi$
$113$	−13.4164	−1.26211	−0.631055	+	0.775738i	$0.717378\pi$
$114$	0.236068	0.0221098
$115$	0	0
$116$	−9.70820	−0.901384
$117$	−1.00000	−0.0924500
$118$	6.00000	0.552345
$119$	−1.58359	−0.145168
$120$	0	0
$121$	20.5623	1.86930
$122$	−2.85410	−0.258398
$123$	−9.09017	−0.819633
$124$	−2.14590	−0.192707
$125$	0	0
$126$	−0.708204	−0.0630918
$127$	−9.70820	−0.861464	−0.430732	−	0.902480i	$-0.641745\pi$
$127$	−9.70820	−0.861464	−0.430732	+	0.902480i	$0.641745\pi$
$128$	−1.00000	−0.0883883
$129$	18.1803	1.60069
$130$	0	0
$131$	−14.1803	−1.23894	−0.619471	−	0.785020i	$-0.712653\pi$
$131$	−14.1803	−1.23894	−0.619471	+	0.785020i	$0.712653\pi$
$132$	−9.09017	−0.791198
$133$	0.270510	0.0234562
$134$	−5.23607	−0.452327
$135$	0	0
$136$	−0.854102	−0.0732386
$137$	−13.8541	−1.18364	−0.591818	−	0.806072i	$-0.701590\pi$
$137$	−13.8541	−1.18364	−0.591818	+	0.806072i	$0.701590\pi$
$138$	−1.61803	−0.137736
$139$	4.29180	0.364025	0.182013	−	0.983296i	$-0.441739\pi$
$139$	4.29180	0.364025	0.182013	+	0.983296i	$0.441739\pi$
$140$	0	0
$141$	2.76393	0.232765
$142$	−0.381966	−0.0320539
$143$	−14.7082	−1.22996
$144$	−0.381966	−0.0318305
$145$	0	0
$146$	16.4721	1.36324
$147$	−5.76393	−0.475401
$148$	−9.70820	−0.798009
$149$	−2.61803	−0.214478	−0.107239	−	0.994233i	$-0.534201\pi$
$149$	−2.61803	−0.214478	−0.107239	+	0.994233i	$0.534201\pi$
$150$	0	0
$151$	14.2705	1.16132	0.580659	−	0.814147i	$-0.302795\pi$
$151$	14.2705	1.16132	0.580659	+	0.814147i	$0.302795\pi$
$152$	0.145898	0.0118339
$153$	−0.326238	−0.0263748
$154$	−10.4164	−0.839378
$155$	0	0
$156$	4.23607	0.339157
$157$	2.29180	0.182905	0.0914526	−	0.995809i	$-0.470849\pi$
$157$	2.29180	0.182905	0.0914526	+	0.995809i	$0.470849\pi$
$158$	7.70820	0.613232
$159$	−3.23607	−0.256637
$160$	0	0
$161$	−1.85410	−0.146124
$162$	7.70820	0.605614
$163$	−22.0344	−1.72587	−0.862935	−	0.505314i	$-0.831377\pi$
$163$	−22.0344	−1.72587	−0.862935	+	0.505314i	$0.831377\pi$
$164$	−5.61803	−0.438695
$165$	0	0
$166$	−7.70820	−0.598273
$167$	−9.70820	−0.751243	−0.375622	−	0.926773i	$-0.622571\pi$
$167$	−9.70820	−0.751243	−0.375622	+	0.926773i	$0.622571\pi$
$168$	3.00000	0.231455
$169$	−6.14590	−0.472761
$170$	0	0
$171$	0.0557281	0.00426163
$172$	11.2361	0.856742
$173$	16.5623	1.25921	0.629604	−	0.776916i	$-0.283217\pi$
$173$	16.5623	1.25921	0.629604	+	0.776916i	$0.283217\pi$
$174$	15.7082	1.19084
$175$	0	0
$176$	−5.61803	−0.423475
$177$	−9.70820	−0.729713
$178$	−3.70820	−0.277942
$179$	7.52786	0.562659	0.281329	−	0.959611i	$-0.409225\pi$
$179$	7.52786	0.562659	0.281329	+	0.959611i	$0.409225\pi$
$180$	0	0
$181$	15.5623	1.15674	0.578369	−	0.815776i	$-0.303690\pi$
$181$	15.5623	1.15674	0.578369	+	0.815776i	$0.303690\pi$
$182$	4.85410	0.359810
$183$	4.61803	0.341375
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	3.47214	0.254589
$187$	−4.79837	−0.350892
$188$	1.70820	0.124584
$189$	10.1459	0.738005
$190$	0	0
$191$	25.4164	1.83907	0.919533	−	0.393012i	$-0.128567\pi$
$191$	25.4164	1.83907	0.919533	+	0.393012i	$0.128567\pi$
$192$	1.61803	0.116772
$193$	−15.7082	−1.13070	−0.565351	−	0.824851i	$-0.691259\pi$
$193$	−15.7082	−1.13070	−0.565351	+	0.824851i	$0.691259\pi$
$194$	−13.0344	−0.935818
$195$	0	0
$196$	−3.56231	−0.254450
$197$	−20.5623	−1.46500	−0.732502	−	0.680765i	$-0.761647\pi$
$197$	−20.5623	−1.46500	−0.732502	+	0.680765i	$0.761647\pi$
$198$	−2.14590	−0.152502
$199$	11.4164	0.809288	0.404644	−	0.914474i	$-0.367395\pi$
$199$	11.4164	0.809288	0.404644	+	0.914474i	$0.367395\pi$
$200$	0	0
$201$	8.47214	0.597578
$202$	1.52786	0.107500
$203$	18.0000	1.26335
$204$	1.38197	0.0967570
$205$	0	0
$206$	−10.8541	−0.756241
$207$	−0.381966	−0.0265485
$208$	2.61803	0.181528
$209$	0.819660	0.0566971
$210$	0	0
$211$	−7.70820	−0.530655	−0.265327	−	0.964158i	$-0.585480\pi$
$211$	−7.70820	−0.530655	−0.265327	+	0.964158i	$0.585480\pi$
$212$	−2.00000	−0.137361
$213$	0.618034	0.0423470
$214$	−11.7082	−0.800356
$215$	0	0
$216$	5.47214	0.372332
$217$	3.97871	0.270093
$218$	−7.56231	−0.512184
$219$	−26.6525	−1.80101
$220$	0	0
$221$	2.23607	0.150414
$222$	15.7082	1.05427
$223$	22.3607	1.49738	0.748691	−	0.662919i	$-0.230683\pi$
$223$	22.3607	1.49738	0.748691	+	0.662919i	$0.230683\pi$
$224$	1.85410	0.123882
$225$	0	0
$226$	13.4164	0.892446
$227$	10.2918	0.683090	0.341545	−	0.939865i	$-0.389050\pi$
$227$	10.2918	0.683090	0.341545	+	0.939865i	$0.389050\pi$
$228$	−0.236068	−0.0156340
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	16.8541	1.10892
$232$	9.70820	0.637375
$233$	21.1246	1.38392	0.691960	−	0.721936i	$-0.256748\pi$
$233$	21.1246	1.38392	0.691960	+	0.721936i	$0.256748\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	−6.00000	−0.390567
$237$	−12.4721	−0.810152
$238$	1.58359	0.102649
$239$	−10.4721	−0.677386	−0.338693	−	0.940897i	$-0.609985\pi$
$239$	−10.4721	−0.677386	−0.338693	+	0.940897i	$0.609985\pi$
$240$	0	0
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−20.5623	−1.32180
$243$	3.94427	0.253025
$244$	2.85410	0.182715
$245$	0	0
$246$	9.09017	0.579568
$247$	−0.381966	−0.0243039
$248$	2.14590	0.136265
$249$	12.4721	0.790390
$250$	0	0
$251$	−16.7984	−1.06030	−0.530152	−	0.847903i	$-0.677865\pi$
$251$	−16.7984	−1.06030	−0.530152	+	0.847903i	$0.677865\pi$
$252$	0.708204	0.0446127
$253$	−5.61803	−0.353203
$254$	9.70820	0.609147
$255$	0	0
$256$	1.00000	0.0625000
$257$	−11.4164	−0.712136	−0.356068	−	0.934460i	$-0.615883\pi$
$257$	−11.4164	−0.712136	−0.356068	+	0.934460i	$0.615883\pi$
$258$	−18.1803	−1.13186
$259$	18.0000	1.11847
$260$	0	0
$261$	3.70820	0.229532
$262$	14.1803	0.876064
$263$	−18.2705	−1.12661	−0.563304	−	0.826250i	$-0.690470\pi$
$263$	−18.2705	−1.12661	−0.563304	+	0.826250i	$0.690470\pi$
$264$	9.09017	0.559461
$265$	0	0
$266$	−0.270510	−0.0165860
$267$	6.00000	0.367194
$268$	5.23607	0.319844
$269$	−1.52786	−0.0931555	−0.0465778	−	0.998915i	$-0.514832\pi$
$269$	−1.52786	−0.0931555	−0.0465778	+	0.998915i	$0.514832\pi$
$270$	0	0
$271$	25.8541	1.57052	0.785262	−	0.619163i	$-0.212528\pi$
$271$	25.8541	1.57052	0.785262	+	0.619163i	$0.212528\pi$
$272$	0.854102	0.0517875
$273$	−7.85410	−0.475352
$274$	13.8541	0.836957
$275$	0	0
$276$	1.61803	0.0973942
$277$	7.52786	0.452306	0.226153	−	0.974092i	$-0.427385\pi$
$277$	7.52786	0.452306	0.226153	+	0.974092i	$0.427385\pi$
$278$	−4.29180	−0.257405
$279$	0.819660	0.0490718
$280$	0	0
$281$	30.6525	1.82857	0.914287	−	0.405068i	$-0.132752\pi$
$281$	30.6525	1.82857	0.914287	+	0.405068i	$0.132752\pi$
$282$	−2.76393	−0.164590
$283$	20.9443	1.24501	0.622504	−	0.782617i	$-0.286115\pi$
$283$	20.9443	1.24501	0.622504	+	0.782617i	$0.286115\pi$
$284$	0.381966	0.0226655
$285$	0	0
$286$	14.7082	0.869714
$287$	10.4164	0.614861
$288$	0.381966	0.0225076
$289$	−16.2705	−0.957089
$290$	0	0
$291$	21.0902	1.23633
$292$	−16.4721	−0.963959
$293$	−14.2918	−0.834936	−0.417468	−	0.908692i	$-0.637082\pi$
$293$	−14.2918	−0.834936	−0.417468	+	0.908692i	$0.637082\pi$
$294$	5.76393	0.336159
$295$	0	0
$296$	9.70820	0.564278
$297$	30.7426	1.78387
$298$	2.61803	0.151659
$299$	2.61803	0.151405
$300$	0	0
$301$	−20.8328	−1.20078
$302$	−14.2705	−0.821176
$303$	−2.47214	−0.142020
$304$	−0.145898	−0.00836783
$305$	0	0
$306$	0.326238	0.0186498
$307$	16.8541	0.961914	0.480957	−	0.876744i	$-0.340289\pi$
$307$	16.8541	0.961914	0.480957	+	0.876744i	$0.340289\pi$
$308$	10.4164	0.593530
$309$	17.5623	0.999085
$310$	0	0
$311$	−22.4721	−1.27428	−0.637139	−	0.770749i	$-0.719882\pi$
$311$	−22.4721	−1.27428	−0.637139	+	0.770749i	$0.719882\pi$
$312$	−4.23607	−0.239820
$313$	25.8541	1.46136	0.730680	−	0.682720i	$-0.239203\pi$
$313$	25.8541	1.46136	0.730680	+	0.682720i	$0.239203\pi$
$314$	−2.29180	−0.129334
$315$	0	0
$316$	−7.70820	−0.433620
$317$	−7.27051	−0.408353	−0.204176	−	0.978934i	$-0.565452\pi$
$317$	−7.27051	−0.408353	−0.204176	+	0.978934i	$0.565452\pi$
$318$	3.23607	0.181470
$319$	54.5410	3.05371
$320$	0	0
$321$	18.9443	1.05737
$322$	1.85410	0.103325
$323$	−0.124612	−0.00693359
$324$	−7.70820	−0.428234
$325$	0	0
$326$	22.0344	1.22037
$327$	12.2361	0.676656
$328$	5.61803	0.310204
$329$	−3.16718	−0.174613
$330$	0	0
$331$	−25.1246	−1.38097	−0.690487	−	0.723345i	$-0.742604\pi$
$331$	−25.1246	−1.38097	−0.690487	+	0.723345i	$0.742604\pi$
$332$	7.70820	0.423043
$333$	3.70820	0.203208
$334$	9.70820	0.531209
$335$	0	0
$336$	−3.00000	−0.163663
$337$	−3.38197	−0.184227	−0.0921137	−	0.995748i	$-0.529362\pi$
$337$	−3.38197	−0.184227	−0.0921137	+	0.995748i	$0.529362\pi$
$338$	6.14590	0.334293
$339$	−21.7082	−1.17903
$340$	0	0
$341$	12.0557	0.652854
$342$	−0.0557281	−0.00301343
$343$	19.5836	1.05741
$344$	−11.2361	−0.605808
$345$	0	0
$346$	−16.5623	−0.890395
$347$	14.5623	0.781746	0.390873	−	0.920445i	$-0.372173\pi$
$347$	14.5623	0.781746	0.390873	+	0.920445i	$0.372173\pi$
$348$	−15.7082	−0.842048
$349$	27.7082	1.48319	0.741593	−	0.670850i	$-0.234071\pi$
$349$	27.7082	1.48319	0.741593	+	0.670850i	$0.234071\pi$
$350$	0	0
$351$	−14.3262	−0.764678
$352$	5.61803	0.299442
$353$	8.00000	0.425797	0.212899	−	0.977074i	$-0.431710\pi$
$353$	8.00000	0.425797	0.212899	+	0.977074i	$0.431710\pi$
$354$	9.70820	0.515985
$355$	0	0
$356$	3.70820	0.196534
$357$	−2.56231	−0.135612
$358$	−7.52786	−0.397860
$359$	−13.4164	−0.708091	−0.354045	−	0.935228i	$-0.615194\pi$
$359$	−13.4164	−0.708091	−0.354045	+	0.935228i	$0.615194\pi$
$360$	0	0
$361$	−18.9787	−0.998880
$362$	−15.5623	−0.817937
$363$	33.2705	1.74625
$364$	−4.85410	−0.254424
$365$	0	0
$366$	−4.61803	−0.241389
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	1.00000	0.0521286
$369$	2.14590	0.111711
$370$	0	0
$371$	3.70820	0.192520
$372$	−3.47214	−0.180022
$373$	−20.9443	−1.08445	−0.542227	−	0.840232i	$-0.682419\pi$
$373$	−20.9443	−1.08445	−0.542227	+	0.840232i	$0.682419\pi$
$374$	4.79837	0.248118
$375$	0	0
$376$	−1.70820	−0.0880939
$377$	−25.4164	−1.30901
$378$	−10.1459	−0.521849
$379$	−24.2705	−1.24669	−0.623346	−	0.781946i	$-0.714227\pi$
$379$	−24.2705	−1.24669	−0.623346	+	0.781946i	$0.714227\pi$
$380$	0	0
$381$	−15.7082	−0.804756
$382$	−25.4164	−1.30042
$383$	0.583592	0.0298202	0.0149101	−	0.999889i	$-0.495254\pi$
$383$	0.583592	0.0298202	0.0149101	+	0.999889i	$0.495254\pi$
$384$	−1.61803	−0.0825700
$385$	0	0
$386$	15.7082	0.799527
$387$	−4.29180	−0.218164
$388$	13.0344	0.661724
$389$	−21.3262	−1.08128	−0.540642	−	0.841253i	$-0.681818\pi$
$389$	−21.3262	−1.08128	−0.540642	+	0.841253i	$0.681818\pi$
$390$	0	0
$391$	0.854102	0.0431938
$392$	3.56231	0.179924
$393$	−22.9443	−1.15739
$394$	20.5623	1.03591
$395$	0	0
$396$	2.14590	0.107835
$397$	15.4377	0.774796	0.387398	−	0.921913i	$-0.373374\pi$
$397$	15.4377	0.774796	0.387398	+	0.921913i	$0.373374\pi$
$398$	−11.4164	−0.572253
$399$	0.437694	0.0219121
$400$	0	0
$401$	−25.5279	−1.27480	−0.637400	−	0.770533i	$-0.719990\pi$
$401$	−25.5279	−1.27480	−0.637400	+	0.770533i	$0.719990\pi$
$402$	−8.47214	−0.422552
$403$	−5.61803	−0.279854
$404$	−1.52786	−0.0760141
$405$	0	0
$406$	−18.0000	−0.893325
$407$	54.5410	2.70350
$408$	−1.38197	−0.0684175
$409$	13.5623	0.670613	0.335306	−	0.942109i	$-0.391160\pi$
$409$	13.5623	0.670613	0.335306	+	0.942109i	$0.391160\pi$
$410$	0	0
$411$	−22.4164	−1.10572
$412$	10.8541	0.534743
$413$	11.1246	0.547406
$414$	0.381966	0.0187726
$415$	0	0
$416$	−2.61803	−0.128360
$417$	6.94427	0.340062
$418$	−0.819660	−0.0400909
$419$	−29.8885	−1.46015	−0.730075	−	0.683367i	$-0.760515\pi$
$419$	−29.8885	−1.46015	−0.730075	+	0.683367i	$0.760515\pi$
$420$	0	0
$421$	0.145898	0.00711064	0.00355532	−	0.999994i	$-0.498868\pi$
$421$	0.145898	0.00711064	0.00355532	+	0.999994i	$0.498868\pi$
$422$	7.70820	0.375229
$423$	−0.652476	−0.0317245
$424$	2.00000	0.0971286
$425$	0	0
$426$	−0.618034	−0.0299438
$427$	−5.29180	−0.256088
$428$	11.7082	0.565937
$429$	−23.7984	−1.14900
$430$	0	0
$431$	−11.2361	−0.541222	−0.270611	−	0.962689i	$-0.587226\pi$
$431$	−11.2361	−0.541222	−0.270611	+	0.962689i	$0.587226\pi$
$432$	−5.47214	−0.263278
$433$	−27.3820	−1.31589	−0.657947	−	0.753065i	$-0.728575\pi$
$433$	−27.3820	−1.31589	−0.657947	+	0.753065i	$0.728575\pi$
$434$	−3.97871	−0.190984
$435$	0	0
$436$	7.56231	0.362169
$437$	−0.145898	−0.00697925
$438$	26.6525	1.27350
$439$	33.2705	1.58791	0.793957	−	0.607973i	$-0.208017\pi$
$439$	33.2705	1.58791	0.793957	+	0.607973i	$0.208017\pi$
$440$	0	0
$441$	1.36068	0.0647943
$442$	−2.23607	−0.106359
$443$	0.145898	0.00693182	0.00346591	−	0.999994i	$-0.498897\pi$
$443$	0.145898	0.00693182	0.00346591	+	0.999994i	$0.498897\pi$
$444$	−15.7082	−0.745478
$445$	0	0
$446$	−22.3607	−1.05881
$447$	−4.23607	−0.200359
$448$	−1.85410	−0.0875981
$449$	−17.5623	−0.828816	−0.414408	−	0.910091i	$-0.636011\pi$
$449$	−17.5623	−0.828816	−0.414408	+	0.910091i	$0.636011\pi$
$450$	0	0
$451$	31.5623	1.48621
$452$	−13.4164	−0.631055
$453$	23.0902	1.08487
$454$	−10.2918	−0.483018
$455$	0	0
$456$	0.236068	0.0110549
$457$	1.41641	0.0662568	0.0331284	−	0.999451i	$-0.489453\pi$
$457$	1.41641	0.0662568	0.0331284	+	0.999451i	$0.489453\pi$
$458$	10.0000	0.467269
$459$	−4.67376	−0.218153
$460$	0	0
$461$	37.3050	1.73746	0.868732	−	0.495282i	$-0.164935\pi$
$461$	37.3050	1.73746	0.868732	+	0.495282i	$0.164935\pi$
$462$	−16.8541	−0.784124
$463$	−15.7082	−0.730022	−0.365011	−	0.931003i	$-0.618935\pi$
$463$	−15.7082	−0.730022	−0.365011	+	0.931003i	$0.618935\pi$
$464$	−9.70820	−0.450692
$465$	0	0
$466$	−21.1246	−0.978579
$467$	23.1246	1.07008	0.535040	−	0.844827i	$-0.320297\pi$
$467$	23.1246	1.07008	0.535040	+	0.844827i	$0.320297\pi$
$468$	−1.00000	−0.0462250
$469$	−9.70820	−0.448283
$470$	0	0
$471$	3.70820	0.170865
$472$	6.00000	0.276172
$473$	−63.1246	−2.90247
$474$	12.4721	0.572864
$475$	0	0
$476$	−1.58359	−0.0725838
$477$	0.763932	0.0349780
$478$	10.4721	0.478984
$479$	−28.4721	−1.30093	−0.650463	−	0.759538i	$-0.725425\pi$
$479$	−28.4721	−1.30093	−0.650463	+	0.759538i	$0.725425\pi$
$480$	0	0
$481$	−25.4164	−1.15889
$482$	2.00000	0.0910975
$483$	−3.00000	−0.136505
$484$	20.5623	0.934650
$485$	0	0
$486$	−3.94427	−0.178916
$487$	−8.29180	−0.375737	−0.187869	−	0.982194i	$-0.560158\pi$
$487$	−8.29180	−0.375737	−0.187869	+	0.982194i	$0.560158\pi$
$488$	−2.85410	−0.129199
$489$	−35.6525	−1.61226
$490$	0	0
$491$	26.8328	1.21095	0.605474	−	0.795865i	$-0.292984\pi$
$491$	26.8328	1.21095	0.605474	+	0.795865i	$0.292984\pi$
$492$	−9.09017	−0.409817
$493$	−8.29180	−0.373444
$494$	0.381966	0.0171855
$495$	0	0
$496$	−2.14590	−0.0963537
$497$	−0.708204	−0.0317673
$498$	−12.4721	−0.558890
$499$	−15.4164	−0.690133	−0.345067	−	0.938578i	$-0.612144\pi$
$499$	−15.4164	−0.690133	−0.345067	+	0.938578i	$0.612144\pi$
$500$	0	0
$501$	−15.7082	−0.701791
$502$	16.7984	0.749748
$503$	10.1459	0.452383	0.226192	−	0.974083i	$-0.427372\pi$
$503$	10.1459	0.452383	0.226192	+	0.974083i	$0.427372\pi$
$504$	−0.708204	−0.0315459
$505$	0	0
$506$	5.61803	0.249752
$507$	−9.94427	−0.441641
$508$	−9.70820	−0.430732
$509$	6.65248	0.294866	0.147433	−	0.989072i	$-0.452899\pi$
$509$	6.65248	0.294866	0.147433	+	0.989072i	$0.452899\pi$
$510$	0	0
$511$	30.5410	1.35106
$512$	−1.00000	−0.0441942
$513$	0.798374	0.0352491
$514$	11.4164	0.503556
$515$	0	0
$516$	18.1803	0.800345
$517$	−9.59675	−0.422064
$518$	−18.0000	−0.790875
$519$	26.7984	1.17632
$520$	0	0
$521$	−38.0689	−1.66783	−0.833914	−	0.551894i	$-0.813905\pi$
$521$	−38.0689	−1.66783	−0.833914	+	0.551894i	$0.813905\pi$
$522$	−3.70820	−0.162304
$523$	4.36068	0.190679	0.0953396	−	0.995445i	$-0.469606\pi$
$523$	4.36068	0.190679	0.0953396	+	0.995445i	$0.469606\pi$
$524$	−14.1803	−0.619471
$525$	0	0
$526$	18.2705	0.796632
$527$	−1.83282	−0.0798387
$528$	−9.09017	−0.395599
$529$	1.00000	0.0434783
$530$	0	0
$531$	2.29180	0.0994555
$532$	0.270510	0.0117281
$533$	−14.7082	−0.637083
$534$	−6.00000	−0.259645
$535$	0	0
$536$	−5.23607	−0.226164
$537$	12.1803	0.525620
$538$	1.52786	0.0658709
$539$	20.0132	0.862028
$540$	0	0
$541$	−0.583592	−0.0250906	−0.0125453	−	0.999921i	$-0.503993\pi$
$541$	−0.583592	−0.0250906	−0.0125453	+	0.999921i	$0.503993\pi$
$542$	−25.8541	−1.11053
$543$	25.1803	1.08059
$544$	−0.854102	−0.0366193
$545$	0	0
$546$	7.85410	0.336125
$547$	−7.85410	−0.335817	−0.167909	−	0.985803i	$-0.553701\pi$
$547$	−7.85410	−0.335817	−0.167909	+	0.985803i	$0.553701\pi$
$548$	−13.8541	−0.591818
$549$	−1.09017	−0.0465273
$550$	0	0
$551$	1.41641	0.0603410
$552$	−1.61803	−0.0688681
$553$	14.2918	0.607749
$554$	−7.52786	−0.319828
$555$	0	0
$556$	4.29180	0.182013
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	−0.819660	−0.0346990
$559$	29.4164	1.24418
$560$	0	0
$561$	−7.76393	−0.327793
$562$	−30.6525	−1.29300
$563$	−15.7082	−0.662022	−0.331011	−	0.943627i	$-0.607390\pi$
$563$	−15.7082	−0.662022	−0.331011	+	0.943627i	$0.607390\pi$
$564$	2.76393	0.116383
$565$	0	0
$566$	−20.9443	−0.880353
$567$	14.2918	0.600199
$568$	−0.381966	−0.0160269
$569$	−16.3607	−0.685875	−0.342938	−	0.939358i	$-0.611422\pi$
$569$	−16.3607	−0.685875	−0.342938	+	0.939358i	$0.611422\pi$
$570$	0	0
$571$	8.27051	0.346110	0.173055	−	0.984912i	$-0.444636\pi$
$571$	8.27051	0.346110	0.173055	+	0.984912i	$0.444636\pi$
$572$	−14.7082	−0.614981
$573$	41.1246	1.71801
$574$	−10.4164	−0.434772
$575$	0	0
$576$	−0.381966	−0.0159153
$577$	−39.7082	−1.65307	−0.826537	−	0.562882i	$-0.809692\pi$
$577$	−39.7082	−1.65307	−0.826537	+	0.562882i	$0.809692\pi$
$578$	16.2705	0.676764
$579$	−25.4164	−1.05627
$580$	0	0
$581$	−14.2918	−0.592924
$582$	−21.0902	−0.874216
$583$	11.2361	0.465350
$584$	16.4721	0.681622
$585$	0	0
$586$	14.2918	0.590389
$587$	−8.85410	−0.365448	−0.182724	−	0.983164i	$-0.558491\pi$
$587$	−8.85410	−0.365448	−0.182724	+	0.983164i	$0.558491\pi$
$588$	−5.76393	−0.237701
$589$	0.313082	0.0129003
$590$	0	0
$591$	−33.2705	−1.36857
$592$	−9.70820	−0.399005
$593$	6.58359	0.270356	0.135178	−	0.990821i	$-0.456839\pi$
$593$	6.58359	0.270356	0.135178	+	0.990821i	$0.456839\pi$
$594$	−30.7426	−1.26139
$595$	0	0
$596$	−2.61803	−0.107239
$597$	18.4721	0.756014
$598$	−2.61803	−0.107059
$599$	23.6180	0.965007	0.482503	−	0.875894i	$-0.339728\pi$
$599$	23.6180	0.965007	0.482503	+	0.875894i	$0.339728\pi$
$600$	0	0
$601$	−9.85410	−0.401957	−0.200979	−	0.979596i	$-0.564412\pi$
$601$	−9.85410	−0.401957	−0.200979	+	0.979596i	$0.564412\pi$
$602$	20.8328	0.849082
$603$	−2.00000	−0.0814463
$604$	14.2705	0.580659
$605$	0	0
$606$	2.47214	0.100424
$607$	21.0557	0.854626	0.427313	−	0.904104i	$-0.359460\pi$
$607$	21.0557	0.854626	0.427313	+	0.904104i	$0.359460\pi$
$608$	0.145898	0.00591695
$609$	29.1246	1.18019
$610$	0	0
$611$	4.47214	0.180923
$612$	−0.326238	−0.0131874
$613$	−0.763932	−0.0308549	−0.0154275	−	0.999881i	$-0.504911\pi$
$613$	−0.763932	−0.0308549	−0.0154275	+	0.999881i	$0.504911\pi$
$614$	−16.8541	−0.680176
$615$	0	0
$616$	−10.4164	−0.419689
$617$	−2.56231	−0.103155	−0.0515773	−	0.998669i	$-0.516425\pi$
$617$	−2.56231	−0.103155	−0.0515773	+	0.998669i	$0.516425\pi$
$618$	−17.5623	−0.706460
$619$	−27.8541	−1.11955	−0.559775	−	0.828644i	$-0.689113\pi$
$619$	−27.8541	−1.11955	−0.559775	+	0.828644i	$0.689113\pi$
$620$	0	0
$621$	−5.47214	−0.219589
$622$	22.4721	0.901051
$623$	−6.87539	−0.275457
$624$	4.23607	0.169578
$625$	0	0
$626$	−25.8541	−1.03334
$627$	1.32624	0.0529648
$628$	2.29180	0.0914526
$629$	−8.29180	−0.330616
$630$	0	0
$631$	−23.4164	−0.932192	−0.466096	−	0.884734i	$-0.654340\pi$
$631$	−23.4164	−0.932192	−0.466096	+	0.884734i	$0.654340\pi$
$632$	7.70820	0.306616
$633$	−12.4721	−0.495723
$634$	7.27051	0.288749
$635$	0	0
$636$	−3.23607	−0.128318
$637$	−9.32624	−0.369519
$638$	−54.5410	−2.15930
$639$	−0.145898	−0.00577164
$640$	0	0
$641$	−0.652476	−0.0257712	−0.0128856	−	0.999917i	$-0.504102\pi$
$641$	−0.652476	−0.0257712	−0.0128856	+	0.999917i	$0.504102\pi$
$642$	−18.9443	−0.747671
$643$	−41.0132	−1.61740	−0.808700	−	0.588221i	$-0.799829\pi$
$643$	−41.0132	−1.61740	−0.808700	+	0.588221i	$0.799829\pi$
$644$	−1.85410	−0.0730619
$645$	0	0
$646$	0.124612	0.00490279
$647$	−13.7082	−0.538925	−0.269463	−	0.963011i	$-0.586846\pi$
$647$	−13.7082	−0.538925	−0.269463	+	0.963011i	$0.586846\pi$
$648$	7.70820	0.302807
$649$	33.7082	1.32316
$650$	0	0
$651$	6.43769	0.252313
$652$	−22.0344	−0.862935
$653$	34.9787	1.36882	0.684411	−	0.729096i	$-0.260059\pi$
$653$	34.9787	1.36882	0.684411	+	0.729096i	$0.260059\pi$
$654$	−12.2361	−0.478468
$655$	0	0
$656$	−5.61803	−0.219347
$657$	6.29180	0.245466
$658$	3.16718	0.123470
$659$	−17.8885	−0.696839	−0.348419	−	0.937339i	$-0.613281\pi$
$659$	−17.8885	−0.696839	−0.348419	+	0.937339i	$0.613281\pi$
$660$	0	0
$661$	−39.3951	−1.53229	−0.766146	−	0.642666i	$-0.777828\pi$
$661$	−39.3951	−1.53229	−0.766146	+	0.642666i	$0.777828\pi$
$662$	25.1246	0.976496
$663$	3.61803	0.140513
$664$	−7.70820	−0.299136
$665$	0	0
$666$	−3.70820	−0.143690
$667$	−9.70820	−0.375903
$668$	−9.70820	−0.375622
$669$	36.1803	1.39881
$670$	0	0
$671$	−16.0344	−0.619003
$672$	3.00000	0.115728
$673$	−27.7082	−1.06807	−0.534036	−	0.845461i	$-0.679325\pi$
$673$	−27.7082	−1.06807	−0.534036	+	0.845461i	$0.679325\pi$
$674$	3.38197	0.130268
$675$	0	0
$676$	−6.14590	−0.236381
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	21.7082	0.833699
$679$	−24.1672	−0.927451
$680$	0	0
$681$	16.6525	0.638124
$682$	−12.0557	−0.461638
$683$	−10.9787	−0.420089	−0.210044	−	0.977692i	$-0.567361\pi$
$683$	−10.9787	−0.420089	−0.210044	+	0.977692i	$0.567361\pi$
$684$	0.0557281	0.00213082
$685$	0	0
$686$	−19.5836	−0.747705
$687$	−16.1803	−0.617318
$688$	11.2361	0.428371
$689$	−5.23607	−0.199478
$690$	0	0
$691$	−21.1246	−0.803618	−0.401809	−	0.915723i	$-0.631618\pi$
$691$	−21.1246	−0.803618	−0.401809	+	0.915723i	$0.631618\pi$
$692$	16.5623	0.629604
$693$	−3.97871	−0.151139
$694$	−14.5623	−0.552778
$695$	0	0
$696$	15.7082	0.595418
$697$	−4.79837	−0.181751
$698$	−27.7082	−1.04877
$699$	34.1803	1.29282
$700$	0	0
$701$	−27.9230	−1.05464	−0.527318	−	0.849668i	$-0.676802\pi$
$701$	−27.9230	−1.05464	−0.527318	+	0.849668i	$0.676802\pi$
$702$	14.3262	0.540709
$703$	1.41641	0.0534208
$704$	−5.61803	−0.211738
$705$	0	0
$706$	−8.00000	−0.301084
$707$	2.83282	0.106539
$708$	−9.70820	−0.364857
$709$	8.56231	0.321564	0.160782	−	0.986990i	$-0.448598\pi$
$709$	8.56231	0.321564	0.160782	+	0.986990i	$0.448598\pi$
$710$	0	0
$711$	2.94427	0.110419
$712$	−3.70820	−0.138971
$713$	−2.14590	−0.0803645
$714$	2.56231	0.0958919
$715$	0	0
$716$	7.52786	0.281329
$717$	−16.9443	−0.632795
$718$	13.4164	0.500696
$719$	23.4508	0.874569	0.437285	−	0.899323i	$-0.355940\pi$
$719$	23.4508	0.874569	0.437285	+	0.899323i	$0.355940\pi$
$720$	0	0
$721$	−20.1246	−0.749480
$722$	18.9787	0.706315
$723$	−3.23607	−0.120351
$724$	15.5623	0.578369
$725$	0	0
$726$	−33.2705	−1.23478
$727$	40.7426	1.51106	0.755531	−	0.655113i	$-0.227379\pi$
$727$	40.7426	1.51106	0.755531	+	0.655113i	$0.227379\pi$
$728$	4.85410	0.179905
$729$	29.5066	1.09284
$730$	0	0
$731$	9.59675	0.354949
$732$	4.61803	0.170687
$733$	0.111456	0.00411673	0.00205836	−	0.999998i	$-0.499345\pi$
$733$	0.111456	0.00411673	0.00205836	+	0.999998i	$0.499345\pi$
$734$	−12.0000	−0.442928
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−29.4164	−1.08357
$738$	−2.14590	−0.0789916
$739$	34.5410	1.27061	0.635306	−	0.772261i	$-0.280874\pi$
$739$	34.5410	1.27061	0.635306	+	0.772261i	$0.280874\pi$
$740$	0	0
$741$	−0.618034	−0.0227040
$742$	−3.70820	−0.136132
$743$	36.9787	1.35662	0.678309	−	0.734777i	$-0.262713\pi$
$743$	36.9787	1.35662	0.678309	+	0.734777i	$0.262713\pi$
$744$	3.47214	0.127295
$745$	0	0
$746$	20.9443	0.766824
$747$	−2.94427	−0.107725
$748$	−4.79837	−0.175446
$749$	−21.7082	−0.793201
$750$	0	0
$751$	−0.875388	−0.0319434	−0.0159717	−	0.999872i	$-0.505084\pi$
$751$	−0.875388	−0.0319434	−0.0159717	+	0.999872i	$0.505084\pi$
$752$	1.70820	0.0622918
$753$	−27.1803	−0.990507
$754$	25.4164	0.925611
$755$	0	0
$756$	10.1459	0.369003
$757$	29.0132	1.05450	0.527251	−	0.849710i	$-0.323223\pi$
$757$	29.0132	1.05450	0.527251	+	0.849710i	$0.323223\pi$
$758$	24.2705	0.881545
$759$	−9.09017	−0.329952
$760$	0	0
$761$	26.5066	0.960863	0.480431	−	0.877032i	$-0.340480\pi$
$761$	26.5066	0.960863	0.480431	+	0.877032i	$0.340480\pi$
$762$	15.7082	0.569048
$763$	−14.0213	−0.507605
$764$	25.4164	0.919533
$765$	0	0
$766$	−0.583592	−0.0210860
$767$	−15.7082	−0.567190
$768$	1.61803	0.0583858
$769$	−47.7082	−1.72040	−0.860201	−	0.509955i	$-0.829662\pi$
$769$	−47.7082	−1.72040	−0.860201	+	0.509955i	$0.829662\pi$
$770$	0	0
$771$	−18.4721	−0.665258
$772$	−15.7082	−0.565351
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	4.29180	0.154265
$775$	0	0
$776$	−13.0344	−0.467909
$777$	29.1246	1.04484
$778$	21.3262	0.764583
$779$	0.819660	0.0293674
$780$	0	0
$781$	−2.14590	−0.0767863
$782$	−0.854102	−0.0305426
$783$	53.1246	1.89852
$784$	−3.56231	−0.127225
$785$	0	0
$786$	22.9443	0.818395
$787$	4.58359	0.163387	0.0816937	−	0.996657i	$-0.473967\pi$
$787$	4.58359	0.163387	0.0816937	+	0.996657i	$0.473967\pi$
$788$	−20.5623	−0.732502
$789$	−29.5623	−1.05245
$790$	0	0
$791$	24.8754	0.884467
$792$	−2.14590	−0.0762512
$793$	7.47214	0.265343
$794$	−15.4377	−0.547863
$795$	0	0
$796$	11.4164	0.404644
$797$	45.4164	1.60873	0.804366	−	0.594134i	$-0.202505\pi$
$797$	45.4164	1.60873	0.804366	+	0.594134i	$0.202505\pi$
$798$	−0.437694	−0.0154942
$799$	1.45898	0.0516150
$800$	0	0
$801$	−1.41641	−0.0500463
$802$	25.5279	0.901420
$803$	92.5410	3.26570
$804$	8.47214	0.298789
$805$	0	0
$806$	5.61803	0.197887
$807$	−2.47214	−0.0870233
$808$	1.52786	0.0537501
$809$	−42.1591	−1.48223	−0.741117	−	0.671376i	$-0.765703\pi$
$809$	−42.1591	−1.48223	−0.741117	+	0.671376i	$0.765703\pi$
$810$	0	0
$811$	5.70820	0.200442	0.100221	−	0.994965i	$-0.468045\pi$
$811$	5.70820	0.200442	0.100221	+	0.994965i	$0.468045\pi$
$812$	18.0000	0.631676
$813$	41.8328	1.46714
$814$	−54.5410	−1.91166
$815$	0	0
$816$	1.38197	0.0483785
$817$	−1.63932	−0.0573526
$818$	−13.5623	−0.474195
$819$	1.85410	0.0647876
$820$	0	0
$821$	14.9443	0.521559	0.260779	−	0.965398i	$-0.416020\pi$
$821$	14.9443	0.521559	0.260779	+	0.965398i	$0.416020\pi$
$822$	22.4164	0.781862
$823$	−32.8328	−1.14448	−0.572240	−	0.820086i	$-0.693925\pi$
$823$	−32.8328	−1.14448	−0.572240	+	0.820086i	$0.693925\pi$
$824$	−10.8541	−0.378121
$825$	0	0
$826$	−11.1246	−0.387075
$827$	−32.2492	−1.12142	−0.560708	−	0.828014i	$-0.689471\pi$
$827$	−32.2492	−1.12142	−0.560708	+	0.828014i	$0.689471\pi$
$828$	−0.381966	−0.0132742
$829$	−34.5410	−1.19966	−0.599830	−	0.800128i	$-0.704765\pi$
$829$	−34.5410	−1.19966	−0.599830	+	0.800128i	$0.704765\pi$
$830$	0	0
$831$	12.1803	0.422531
$832$	2.61803	0.0907640
$833$	−3.04257	−0.105419
$834$	−6.94427	−0.240460
$835$	0	0
$836$	0.819660	0.0283485
$837$	11.7426	0.405885
$838$	29.8885	1.03248
$839$	−11.2361	−0.387912	−0.193956	−	0.981010i	$-0.562132\pi$
$839$	−11.2361	−0.387912	−0.193956	+	0.981010i	$0.562132\pi$
$840$	0	0
$841$	65.2492	2.24997
$842$	−0.145898	−0.00502798
$843$	49.5967	1.70820
$844$	−7.70820	−0.265327
$845$	0	0
$846$	0.652476	0.0224326
$847$	−38.1246	−1.30998
$848$	−2.00000	−0.0686803
$849$	33.8885	1.16305
$850$	0	0
$851$	−9.70820	−0.332793
$852$	0.618034	0.0211735
$853$	0.214782	0.00735399	0.00367699	−	0.999993i	$-0.498830\pi$
$853$	0.214782	0.00735399	0.00367699	+	0.999993i	$0.498830\pi$
$854$	5.29180	0.181082
$855$	0	0
$856$	−11.7082	−0.400178
$857$	−36.0000	−1.22974	−0.614868	−	0.788630i	$-0.710791\pi$
$857$	−36.0000	−1.22974	−0.614868	+	0.788630i	$0.710791\pi$
$858$	23.7984	0.812463
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	16.8541	0.574386
$862$	11.2361	0.382702
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	5.47214	0.186166
$865$	0	0
$866$	27.3820	0.930477
$867$	−26.3262	−0.894086
$868$	3.97871	0.135046
$869$	43.3050	1.46902
$870$	0	0
$871$	13.7082	0.464485
$872$	−7.56231	−0.256092
$873$	−4.97871	−0.168504
$874$	0.145898	0.00493507
$875$	0	0
$876$	−26.6525	−0.900504
$877$	25.6869	0.867386	0.433693	−	0.901061i	$-0.357210\pi$
$877$	25.6869	0.867386	0.433693	+	0.901061i	$0.357210\pi$
$878$	−33.2705	−1.12283
$879$	−23.1246	−0.779974
$880$	0	0
$881$	−51.7082	−1.74209	−0.871047	−	0.491200i	$-0.836558\pi$
$881$	−51.7082	−1.74209	−0.871047	+	0.491200i	$0.836558\pi$
$882$	−1.36068	−0.0458165
$883$	−51.2705	−1.72539	−0.862695	−	0.505725i	$-0.831225\pi$
$883$	−51.2705	−1.72539	−0.862695	+	0.505725i	$0.831225\pi$
$884$	2.23607	0.0752071
$885$	0	0
$886$	−0.145898	−0.00490154
$887$	30.5410	1.02547	0.512734	−	0.858548i	$-0.328633\pi$
$887$	30.5410	1.02547	0.512734	+	0.858548i	$0.328633\pi$
$888$	15.7082	0.527133
$889$	18.0000	0.603701
$890$	0	0
$891$	43.3050	1.45077
$892$	22.3607	0.748691
$893$	−0.249224	−0.00833995
$894$	4.23607	0.141675
$895$	0	0
$896$	1.85410	0.0619412
$897$	4.23607	0.141438
$898$	17.5623	0.586062
$899$	20.8328	0.694813
$900$	0	0
$901$	−1.70820	−0.0569085
$902$	−31.5623	−1.05091
$903$	−33.7082	−1.12174
$904$	13.4164	0.446223
$905$	0	0
$906$	−23.0902	−0.767120
$907$	−36.5410	−1.21332	−0.606662	−	0.794960i	$-0.707492\pi$
$907$	−36.5410	−1.21332	−0.606662	+	0.794960i	$0.707492\pi$
$908$	10.2918	0.341545
$909$	0.583592	0.0193565
$910$	0	0
$911$	−22.3607	−0.740842	−0.370421	−	0.928864i	$-0.620787\pi$
$911$	−22.3607	−0.740842	−0.370421	+	0.928864i	$0.620787\pi$
$912$	−0.236068	−0.00781699
$913$	−43.3050	−1.43318
$914$	−1.41641	−0.0468506
$915$	0	0
$916$	−10.0000	−0.330409
$917$	26.2918	0.868232
$918$	4.67376	0.154257
$919$	−41.4164	−1.36620	−0.683101	−	0.730324i	$-0.739369\pi$
$919$	−41.4164	−1.36620	−0.683101	+	0.730324i	$0.739369\pi$
$920$	0	0
$921$	27.2705	0.898594
$922$	−37.3050	−1.22857
$923$	1.00000	0.0329154
$924$	16.8541	0.554459
$925$	0	0
$926$	15.7082	0.516204
$927$	−4.14590	−0.136169
$928$	9.70820	0.318687
$929$	−43.3050	−1.42079	−0.710395	−	0.703804i	$-0.751484\pi$
$929$	−43.3050	−1.42079	−0.710395	+	0.703804i	$0.751484\pi$
$930$	0	0
$931$	0.519733	0.0170336
$932$	21.1246	0.691960
$933$	−36.3607	−1.19040
$934$	−23.1246	−0.756660
$935$	0	0
$936$	1.00000	0.0326860
$937$	−24.3262	−0.794704	−0.397352	−	0.917666i	$-0.630071\pi$
$937$	−24.3262	−0.794704	−0.397352	+	0.917666i	$0.630071\pi$
$938$	9.70820	0.316984
$939$	41.8328	1.36516
$940$	0	0
$941$	27.2148	0.887177	0.443588	−	0.896231i	$-0.353705\pi$
$941$	27.2148	0.887177	0.443588	+	0.896231i	$0.353705\pi$
$942$	−3.70820	−0.120820
$943$	−5.61803	−0.182948
$944$	−6.00000	−0.195283
$945$	0	0
$946$	63.1246	2.05236
$947$	26.3951	0.857726	0.428863	−	0.903369i	$-0.358914\pi$
$947$	26.3951	0.857726	0.428863	+	0.903369i	$0.358914\pi$
$948$	−12.4721	−0.405076
$949$	−43.1246	−1.39988
$950$	0	0
$951$	−11.7639	−0.381472
$952$	1.58359	0.0513245
$953$	37.3951	1.21135	0.605673	−	0.795713i	$-0.292904\pi$
$953$	37.3951	1.21135	0.605673	+	0.795713i	$0.292904\pi$
$954$	−0.763932	−0.0247332
$955$	0	0
$956$	−10.4721	−0.338693
$957$	88.2492	2.85269
$958$	28.4721	0.919893
$959$	25.6869	0.829474
$960$	0	0
$961$	−26.3951	−0.851456
$962$	25.4164	0.819458
$963$	−4.47214	−0.144113
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	3.00000	0.0965234
$967$	29.2361	0.940169	0.470084	−	0.882622i	$-0.344224\pi$
$967$	29.2361	0.940169	0.470084	+	0.882622i	$0.344224\pi$
$968$	−20.5623	−0.660898
$969$	−0.201626	−0.00647716
$970$	0	0
$971$	19.1459	0.614421	0.307211	−	0.951642i	$-0.400604\pi$
$971$	19.1459	0.614421	0.307211	+	0.951642i	$0.400604\pi$
$972$	3.94427	0.126513
$973$	−7.95743	−0.255103
$974$	8.29180	0.265686
$975$	0	0
$976$	2.85410	0.0913576
$977$	1.27051	0.0406472	0.0203236	−	0.999793i	$-0.493530\pi$
$977$	1.27051	0.0406472	0.0203236	+	0.999793i	$0.493530\pi$
$978$	35.6525	1.14004
$979$	−20.8328	−0.665820
$980$	0	0
$981$	−2.88854	−0.0922241
$982$	−26.8328	−0.856270
$983$	−47.3951	−1.51167	−0.755835	−	0.654762i	$-0.772769\pi$
$983$	−47.3951	−1.51167	−0.755835	+	0.654762i	$0.772769\pi$
$984$	9.09017	0.289784
$985$	0	0
$986$	8.29180	0.264065
$987$	−5.12461	−0.163118
$988$	−0.381966	−0.0121520
$989$	11.2361	0.357286
$990$	0	0
$991$	17.7295	0.563196	0.281598	−	0.959532i	$-0.409136\pi$
$991$	17.7295	0.563196	0.281598	+	0.959532i	$0.409136\pi$
$992$	2.14590	0.0681323
$993$	−40.6525	−1.29007
$994$	0.708204	0.0224629
$995$	0	0
$996$	12.4721	0.395195
$997$	−62.7214	−1.98641	−0.993203	−	0.116398i	$-0.962865\pi$
$997$	−62.7214	−1.98641	−0.993203	+	0.116398i	$0.962865\pi$
$998$	15.4164	0.487998
$999$	53.1246	1.68079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.l.1.2		2
4.3	odd	2		9200.2.a.bo.1.1		2
5.2	odd	4		230.2.b.a.139.1	✓	4
5.3	odd	4		230.2.b.a.139.4	yes	4
5.4	even	2		1150.2.a.n.1.1		2
15.2	even	4		2070.2.d.c.829.4		4
15.8	even	4		2070.2.d.c.829.2		4
20.3	even	4		1840.2.e.c.369.1		4
20.7	even	4		1840.2.e.c.369.4		4
20.19	odd	2		9200.2.a.by.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.a.139.1	✓	4	5.2	odd	4
230.2.b.a.139.4	yes	4	5.3	odd	4
1150.2.a.l.1.2		2	1.1	even	1	trivial
1150.2.a.n.1.1		2	5.4	even	2
1840.2.e.c.369.1		4	20.3	even	4
1840.2.e.c.369.4		4	20.7	even	4
2070.2.d.c.829.2		4	15.8	even	4
2070.2.d.c.829.4		4	15.2	even	4
9200.2.a.bo.1.1		2	4.3	odd	2
9200.2.a.by.1.2		2	20.19	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.85410 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -1.85410 q^{7} -1.00000 q^{8} -0.381966 q^{9} -5.61803 q^{11} +1.61803 q^{12} +2.61803 q^{13} +1.85410 q^{14} +1.00000 q^{16} +0.854102 q^{17} +0.381966 q^{18} -0.145898 q^{19} -3.00000 q^{21} +5.61803 q^{22} +1.00000 q^{23} -1.61803 q^{24} -2.61803 q^{26} -5.47214 q^{27} -1.85410 q^{28} -9.70820 q^{29} -2.14590 q^{31} -1.00000 q^{32} -9.09017 q^{33} -0.854102 q^{34} -0.381966 q^{36} -9.70820 q^{37} +0.145898 q^{38} +4.23607 q^{39} -5.61803 q^{41} +3.00000 q^{42} +11.2361 q^{43} -5.61803 q^{44} -1.00000 q^{46} +1.70820 q^{47} +1.61803 q^{48} -3.56231 q^{49} +1.38197 q^{51} +2.61803 q^{52} -2.00000 q^{53} +5.47214 q^{54} +1.85410 q^{56} -0.236068 q^{57} +9.70820 q^{58} -6.00000 q^{59} +2.85410 q^{61} +2.14590 q^{62} +0.708204 q^{63} +1.00000 q^{64} +9.09017 q^{66} +5.23607 q^{67} +0.854102 q^{68} +1.61803 q^{69} +0.381966 q^{71} +0.381966 q^{72} -16.4721 q^{73} +9.70820 q^{74} -0.145898 q^{76} +10.4164 q^{77} -4.23607 q^{78} -7.70820 q^{79} -7.70820 q^{81} +5.61803 q^{82} +7.70820 q^{83} -3.00000 q^{84} -11.2361 q^{86} -15.7082 q^{87} +5.61803 q^{88} +3.70820 q^{89} -4.85410 q^{91} +1.00000 q^{92} -3.47214 q^{93} -1.70820 q^{94} -1.61803 q^{96} +13.0344 q^{97} +3.56231 q^{98} +2.14590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 3 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 3 * q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + 3 q^{7} - 2 q^{8} - 3 q^{9} - 9 q^{11} + q^{12} + 3 q^{13} - 3 q^{14} + 2 q^{16} - 5 q^{17} + 3 q^{18} - 7 q^{19} - 6 q^{21} + 9 q^{22} + 2 q^{23} - q^{24} - 3 q^{26} - 2 q^{27} + 3 q^{28} - 6 q^{29} - 11 q^{31} - 2 q^{32} - 7 q^{33} + 5 q^{34} - 3 q^{36} - 6 q^{37} + 7 q^{38} + 4 q^{39} - 9 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{44} - 2 q^{46} - 10 q^{47} + q^{48} + 13 q^{49} + 5 q^{51} + 3 q^{52} - 4 q^{53} + 2 q^{54} - 3 q^{56} + 4 q^{57} + 6 q^{58} - 12 q^{59} - q^{61} + 11 q^{62} - 12 q^{63} + 2 q^{64} + 7 q^{66} + 6 q^{67} - 5 q^{68} + q^{69} + 3 q^{71} + 3 q^{72} - 24 q^{73} + 6 q^{74} - 7 q^{76} - 6 q^{77} - 4 q^{78} - 2 q^{79} - 2 q^{81} + 9 q^{82} + 2 q^{83} - 6 q^{84} - 18 q^{86} - 18 q^{87} + 9 q^{88} - 6 q^{89} - 3 q^{91} + 2 q^{92} + 2 q^{93} + 10 q^{94} - q^{96} - 3 q^{97} - 13 q^{98} + 11 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + 3 * q^7 - 2 * q^8 - 3 * q^9 - 9 * q^11 + q^12 + 3 * q^13 - 3 * q^14 + 2 * q^16 - 5 * q^17 + 3 * q^18 - 7 * q^19 - 6 * q^21 + 9 * q^22 + 2 * q^23 - q^24 - 3 * q^26 - 2 * q^27 + 3 * q^28 - 6 * q^29 - 11 * q^31 - 2 * q^32 - 7 * q^33 + 5 * q^34 - 3 * q^36 - 6 * q^37 + 7 * q^38 + 4 * q^39 - 9 * q^41 + 6 * q^42 + 18 * q^43 - 9 * q^44 - 2 * q^46 - 10 * q^47 + q^48 + 13 * q^49 + 5 * q^51 + 3 * q^52 - 4 * q^53 + 2 * q^54 - 3 * q^56 + 4 * q^57 + 6 * q^58 - 12 * q^59 - q^61 + 11 * q^62 - 12 * q^63 + 2 * q^64 + 7 * q^66 + 6 * q^67 - 5 * q^68 + q^69 + 3 * q^71 + 3 * q^72 - 24 * q^73 + 6 * q^74 - 7 * q^76 - 6 * q^77 - 4 * q^78 - 2 * q^79 - 2 * q^81 + 9 * q^82 + 2 * q^83 - 6 * q^84 - 18 * q^86 - 18 * q^87 + 9 * q^88 - 6 * q^89 - 3 * q^91 + 2 * q^92 + 2 * q^93 + 10 * q^94 - q^96 - 3 * q^97 - 13 * q^98 + 11 * q^99

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