LMFDB - Embedded newform 1150.2.a.s.1.4

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.13448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 2 $ x^4 - 7*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
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			1.4
Root			$2.58874$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.25886 q^{3} +1.00000 q^{4} +3.25886 q^{6} +1.44270 q^{7} +1.00000 q^{8} +7.62018 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.25886 q^{3} +1.00000 q^{4} +3.25886 q^{6} +1.44270 q^{7} +1.00000 q^{8} +7.62018 q^{9} -2.03144 q^{11} +3.25886 q^{12} +0.557299 q^{13} +1.44270 q^{14} +1.00000 q^{16} -3.91861 q^{17} +7.62018 q^{18} -6.73300 q^{19} +4.70156 q^{21} -2.03144 q^{22} +1.00000 q^{23} +3.25886 q^{24} +0.557299 q^{26} +15.0565 q^{27} +1.44270 q^{28} -9.69520 q^{29} -3.07502 q^{31} +1.00000 q^{32} -6.62018 q^{33} -3.91861 q^{34} +7.62018 q^{36} -3.65798 q^{37} -6.73300 q^{38} +1.81616 q^{39} +7.03321 q^{41} +4.70156 q^{42} -5.06465 q^{43} -2.03144 q^{44} +1.00000 q^{46} +0.659753 q^{47} +3.25886 q^{48} -4.91861 q^{49} -12.7702 q^{51} +0.557299 q^{52} +11.1275 q^{53} +15.0565 q^{54} +1.44270 q^{56} -21.9419 q^{57} -9.69520 q^{58} +10.7226 q^{59} +1.73937 q^{61} -3.07502 q^{62} +10.9936 q^{63} +1.00000 q^{64} -6.62018 q^{66} +12.0129 q^{67} -3.91861 q^{68} +3.25886 q^{69} +12.4363 q^{71} +7.62018 q^{72} -9.26464 q^{73} -3.65798 q^{74} -6.73300 q^{76} -2.93076 q^{77} +1.81616 q^{78} +5.92439 q^{79} +26.2066 q^{81} +7.03321 q^{82} -11.3775 q^{83} +4.70156 q^{84} -5.06465 q^{86} -31.5953 q^{87} -2.03144 q^{88} +5.25308 q^{89} +0.804016 q^{91} +1.00000 q^{92} -10.0211 q^{93} +0.659753 q^{94} +3.25886 q^{96} -0.0813861 q^{97} -4.91861 q^{98} -15.4799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9	$ 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9} + 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{14} + 4 q^{16} - 5 q^{17} + 7 q^{18} - q^{19} + 6 q^{21} + 5 q^{22} + 4 q^{23} + 3 q^{24} + 5 q^{26} + 6 q^{27} + 3 q^{28} + 2 q^{29} + 5 q^{31} + 4 q^{32} - 3 q^{33} - 5 q^{34} + 7 q^{36} - 6 q^{37} - q^{38} + 23 q^{41} + 6 q^{42} - 2 q^{43} + 5 q^{44} + 4 q^{46} + 2 q^{47} + 3 q^{48} - 9 q^{49} + 7 q^{51} + 5 q^{52} + 6 q^{54} + 3 q^{56} - 28 q^{57} + 2 q^{58} + 16 q^{59} + 9 q^{61} + 5 q^{62} + 16 q^{63} + 4 q^{64} - 3 q^{66} - 2 q^{67} - 5 q^{68} + 3 q^{69} + 19 q^{71} + 7 q^{72} - 8 q^{73} - 6 q^{74} - q^{76} - 10 q^{77} - 6 q^{79} + 16 q^{81} + 23 q^{82} - 14 q^{83} + 6 q^{84} - 2 q^{86} - 38 q^{87} + 5 q^{88} + 30 q^{89} - 13 q^{91} + 4 q^{92} - 26 q^{93} + 2 q^{94} + 3 q^{96} - 11 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9 + 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^14 + 4 * q^16 - 5 * q^17 + 7 * q^18 - q^19 + 6 * q^21 + 5 * q^22 + 4 * q^23 + 3 * q^24 + 5 * q^26 + 6 * q^27 + 3 * q^28 + 2 * q^29 + 5 * q^31 + 4 * q^32 - 3 * q^33 - 5 * q^34 + 7 * q^36 - 6 * q^37 - q^38 + 23 * q^41 + 6 * q^42 - 2 * q^43 + 5 * q^44 + 4 * q^46 + 2 * q^47 + 3 * q^48 - 9 * q^49 + 7 * q^51 + 5 * q^52 + 6 * q^54 + 3 * q^56 - 28 * q^57 + 2 * q^58 + 16 * q^59 + 9 * q^61 + 5 * q^62 + 16 * q^63 + 4 * q^64 - 3 * q^66 - 2 * q^67 - 5 * q^68 + 3 * q^69 + 19 * q^71 + 7 * q^72 - 8 * q^73 - 6 * q^74 - q^76 - 10 * q^77 - 6 * q^79 + 16 * q^81 + 23 * q^82 - 14 * q^83 + 6 * q^84 - 2 * q^86 - 38 * q^87 + 5 * q^88 + 30 * q^89 - 13 * q^91 + 4 * q^92 - 26 * q^93 + 2 * q^94 + 3 * q^96 - 11 * q^97 - 9 * q^98 - 27 * 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
$3$	3.25886	1.88150	0.940752	−	0.339095i	$-0.110121\pi$
$3$	3.25886	1.88150	0.940752	+	0.339095i	$0.110121\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	3.25886	1.33042
$7$	1.44270	0.545290	0.272645	−	0.962115i	$-0.412102\pi$
$7$	1.44270	0.545290	0.272645	+	0.962115i	$0.412102\pi$
$8$	1.00000	0.353553
$9$	7.62018	2.54006
$10$	0	0
$11$	−2.03144	−0.612502	−0.306251	−	0.951951i	$-0.599075\pi$
$11$	−2.03144	−0.612502	−0.306251	+	0.951951i	$0.599075\pi$
$12$	3.25886	0.940752
$13$	0.557299	0.154567	0.0772835	−	0.997009i	$-0.475375\pi$
$13$	0.557299	0.154567	0.0772835	+	0.997009i	$0.475375\pi$
$14$	1.44270	0.385578
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.91861	−0.950403	−0.475202	−	0.879877i	$-0.657625\pi$
$17$	−3.91861	−0.950403	−0.475202	+	0.879877i	$0.657625\pi$
$18$	7.62018	1.79609
$19$	−6.73300	−1.54466	−0.772328	−	0.635224i	$-0.780908\pi$
$19$	−6.73300	−1.54466	−0.772328	+	0.635224i	$0.780908\pi$
$20$	0	0
$21$	4.70156	1.02596
$22$	−2.03144	−0.433104
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.25886	0.665212
$25$	0	0
$26$	0.557299	0.109295
$27$	15.0565	2.89763
$28$	1.44270	0.272645
$29$	−9.69520	−1.80035	−0.900176	−	0.435525i	$-0.856563\pi$
$29$	−9.69520	−1.80035	−0.900176	+	0.435525i	$0.856563\pi$
$30$	0	0
$31$	−3.07502	−0.552290	−0.276145	−	0.961116i	$-0.589057\pi$
$31$	−3.07502	−0.552290	−0.276145	+	0.961116i	$0.589057\pi$
$32$	1.00000	0.176777
$33$	−6.62018	−1.15242
$34$	−3.91861	−0.672037
$35$	0	0
$36$	7.62018	1.27003
$37$	−3.65798	−0.601368	−0.300684	−	0.953724i	$-0.597215\pi$
$37$	−3.65798	−0.601368	−0.300684	+	0.953724i	$0.597215\pi$
$38$	−6.73300	−1.09224
$39$	1.81616	0.290818
$40$	0	0
$41$	7.03321	1.09840	0.549202	−	0.835690i	$-0.314932\pi$
$41$	7.03321	1.09840	0.549202	+	0.835690i	$0.314932\pi$
$42$	4.70156	0.725467
$43$	−5.06465	−0.772352	−0.386176	−	0.922425i	$-0.626204\pi$
$43$	−5.06465	−0.772352	−0.386176	+	0.922425i	$0.626204\pi$
$44$	−2.03144	−0.306251
$45$	0	0
$46$	1.00000	0.147442
$47$	0.659753	0.0962348	0.0481174	−	0.998842i	$-0.484678\pi$
$47$	0.659753	0.0962348	0.0481174	+	0.998842i	$0.484678\pi$
$48$	3.25886	0.470376
$49$	−4.91861	−0.702659
$50$	0	0
$51$	−12.7702	−1.78819
$52$	0.557299	0.0772835
$53$	11.1275	1.52848	0.764242	−	0.644930i	$-0.223113\pi$
$53$	11.1275	1.52848	0.764242	+	0.644930i	$0.223113\pi$
$54$	15.0565	2.04893
$55$	0	0
$56$	1.44270	0.192789
$57$	−21.9419	−2.90628
$58$	−9.69520	−1.27304
$59$	10.7226	1.39597	0.697984	−	0.716114i	$-0.254081\pi$
$59$	10.7226	1.39597	0.697984	+	0.716114i	$0.254081\pi$
$60$	0	0
$61$	1.73937	0.222703	0.111351	−	0.993781i	$-0.464482\pi$
$61$	1.73937	0.222703	0.111351	+	0.993781i	$0.464482\pi$
$62$	−3.07502	−0.390528
$63$	10.9936	1.38507
$64$	1.00000	0.125000
$65$	0	0
$66$	−6.62018	−0.814887
$67$	12.0129	1.46761	0.733806	−	0.679359i	$-0.237742\pi$
$67$	12.0129	1.46761	0.733806	+	0.679359i	$0.237742\pi$
$68$	−3.91861	−0.475202
$69$	3.25886	0.392321
$70$	0	0
$71$	12.4363	1.47592	0.737961	−	0.674844i	$-0.235789\pi$
$71$	12.4363	1.47592	0.737961	+	0.674844i	$0.235789\pi$
$72$	7.62018	0.898046
$73$	−9.26464	−1.08434	−0.542172	−	0.840267i	$-0.682398\pi$
$73$	−9.26464	−1.08434	−0.542172	+	0.840267i	$0.682398\pi$
$74$	−3.65798	−0.425231
$75$	0	0
$76$	−6.73300	−0.772328
$77$	−2.93076	−0.333991
$78$	1.81616	0.205640
$79$	5.92439	0.666546	0.333273	−	0.942830i	$-0.391847\pi$
$79$	5.92439	0.666546	0.333273	+	0.942830i	$0.391847\pi$
$80$	0	0
$81$	26.2066	2.91184
$82$	7.03321	0.776688
$83$	−11.3775	−1.24884	−0.624420	−	0.781089i	$-0.714664\pi$
$83$	−11.3775	−1.24884	−0.624420	+	0.781089i	$0.714664\pi$
$84$	4.70156	0.512982
$85$	0	0
$86$	−5.06465	−0.546135
$87$	−31.5953	−3.38737
$88$	−2.03144	−0.216552
$89$	5.25308	0.556826	0.278413	−	0.960462i	$-0.410192\pi$
$89$	5.25308	0.556826	0.278413	+	0.960462i	$0.410192\pi$
$90$	0	0
$91$	0.804016	0.0842838
$92$	1.00000	0.104257
$93$	−10.0211	−1.03914
$94$	0.659753	0.0680483
$95$	0	0
$96$	3.25886	0.332606
$97$	−0.0813861	−0.00826350	−0.00413175	−	0.999991i	$-0.501315\pi$
$97$	−0.0813861	−0.00826350	−0.00413175	+	0.999991i	$0.501315\pi$
$98$	−4.91861	−0.496855
$99$	−15.4799	−1.55579
$100$	0	0
$101$	8.31281	0.827156	0.413578	−	0.910469i	$-0.364279\pi$
$101$	8.31281	0.827156	0.413578	+	0.910469i	$0.364279\pi$
$102$	−12.7702	−1.26444
$103$	−6.36991	−0.627646	−0.313823	−	0.949481i	$-0.601610\pi$
$103$	−6.36991	−0.627646	−0.313823	+	0.949481i	$0.601610\pi$
$104$	0.557299	0.0546477
$105$	0	0
$106$	11.1275	1.08080
$107$	−16.9226	−1.63597	−0.817986	−	0.575239i	$-0.804909\pi$
$107$	−16.9226	−1.63597	−0.817986	+	0.575239i	$0.804909\pi$
$108$	15.0565	1.44881
$109$	−0.218825	−0.0209597	−0.0104798	−	0.999945i	$-0.503336\pi$
$109$	−0.218825	−0.0209597	−0.0104798	+	0.999945i	$0.503336\pi$
$110$	0	0
$111$	−11.9208	−1.13148
$112$	1.44270	0.136322
$113$	0.580599	0.0546182	0.0273091	−	0.999627i	$-0.491306\pi$
$113$	0.580599	0.0546182	0.0273091	+	0.999627i	$0.491306\pi$
$114$	−21.9419	−2.05505
$115$	0	0
$116$	−9.69520	−0.900176
$117$	4.24672	0.392609
$118$	10.7226	0.987098
$119$	−5.65339	−0.518245
$120$	0	0
$121$	−6.87326	−0.624842
$122$	1.73937	0.157475
$123$	22.9203	2.06665
$124$	−3.07502	−0.276145
$125$	0	0
$126$	10.9936	0.979391
$127$	1.56944	0.139266	0.0696328	−	0.997573i	$-0.477817\pi$
$127$	1.56944	0.139266	0.0696328	+	0.997573i	$0.477817\pi$
$128$	1.00000	0.0883883
$129$	−16.5050	−1.45318
$130$	0	0
$131$	15.9208	1.39101	0.695505	−	0.718521i	$-0.255181\pi$
$131$	15.9208	1.39101	0.695505	+	0.718521i	$0.255181\pi$
$132$	−6.62018	−0.576212
$133$	−9.71371	−0.842285
$134$	12.0129	1.03776
$135$	0	0
$136$	−3.91861	−0.336018
$137$	−6.47013	−0.552781	−0.276390	−	0.961045i	$-0.589138\pi$
$137$	−6.47013	−0.552781	−0.276390	+	0.961045i	$0.589138\pi$
$138$	3.25886	0.277413
$139$	−0.656206	−0.0556586	−0.0278293	−	0.999613i	$-0.508859\pi$
$139$	−0.656206	−0.0556586	−0.0278293	+	0.999613i	$0.508859\pi$
$140$	0	0
$141$	2.15004	0.181066
$142$	12.4363	1.04363
$143$	−1.13212	−0.0946725
$144$	7.62018	0.635015
$145$	0	0
$146$	−9.26464	−0.766747
$147$	−16.0291	−1.32206
$148$	−3.65798	−0.300684
$149$	23.8349	1.95263	0.976314	−	0.216357i	$-0.0694176\pi$
$149$	23.8349	1.95263	0.976314	+	0.216357i	$0.0694176\pi$
$150$	0	0
$151$	−14.8669	−1.20985	−0.604925	−	0.796282i	$-0.706797\pi$
$151$	−14.8669	−1.20985	−0.604925	+	0.796282i	$0.706797\pi$
$152$	−6.73300	−0.546118
$153$	−29.8605	−2.41408
$154$	−2.93076	−0.236167
$155$	0	0
$156$	1.81616	0.145409
$157$	8.24213	0.657793	0.328897	−	0.944366i	$-0.393323\pi$
$157$	8.24213	0.657793	0.328897	+	0.944366i	$0.393323\pi$
$158$	5.92439	0.471319
$159$	36.2631	2.87585
$160$	0	0
$161$	1.44270	0.113701
$162$	26.2066	2.05898
$163$	−10.3154	−0.807962	−0.403981	−	0.914767i	$-0.632374\pi$
$163$	−10.3154	−0.807962	−0.403981	+	0.914767i	$0.632374\pi$
$164$	7.03321	0.549202
$165$	0	0
$166$	−11.3775	−0.883063
$167$	−4.65975	−0.360582	−0.180291	−	0.983613i	$-0.557704\pi$
$167$	−4.65975	−0.360582	−0.180291	+	0.983613i	$0.557704\pi$
$168$	4.70156	0.362733
$169$	−12.6894	−0.976109
$170$	0	0
$171$	−51.3067	−3.92352
$172$	−5.06465	−0.386176
$173$	2.80402	0.213185	0.106593	−	0.994303i	$-0.466006\pi$
$173$	2.80402	0.213185	0.106593	+	0.994303i	$0.466006\pi$
$174$	−31.5953	−2.39523
$175$	0	0
$176$	−2.03144	−0.153125
$177$	34.9436	2.62652
$178$	5.25308	0.393735
$179$	−4.44212	−0.332019	−0.166010	−	0.986124i	$-0.553088\pi$
$179$	−4.44212	−0.332019	−0.166010	+	0.986124i	$0.553088\pi$
$180$	0	0
$181$	2.42019	0.179891	0.0899455	−	0.995947i	$-0.471331\pi$
$181$	2.42019	0.179891	0.0899455	+	0.995947i	$0.471331\pi$
$182$	0.804016	0.0595976
$183$	5.66835	0.419016
$184$	1.00000	0.0737210
$185$	0	0
$186$	−10.0211	−0.734780
$187$	7.96042	0.582124
$188$	0.659753	0.0481174
$189$	21.7220	1.58005
$190$	0	0
$191$	−20.8934	−1.51179	−0.755897	−	0.654690i	$-0.772799\pi$
$191$	−20.8934	−1.51179	−0.755897	+	0.654690i	$0.772799\pi$
$192$	3.25886	0.235188
$193$	−2.88540	−0.207696	−0.103848	−	0.994593i	$-0.533116\pi$
$193$	−2.88540	−0.207696	−0.103848	+	0.994593i	$0.533116\pi$
$194$	−0.0813861	−0.00584318
$195$	0	0
$196$	−4.91861	−0.351330
$197$	19.0925	1.36029	0.680144	−	0.733079i	$-0.261917\pi$
$197$	19.0925	1.36029	0.680144	+	0.733079i	$0.261917\pi$
$198$	−15.4799	−1.10011
$199$	6.58060	0.466486	0.233243	−	0.972418i	$-0.425066\pi$
$199$	6.58060	0.466486	0.233243	+	0.972418i	$0.425066\pi$
$200$	0	0
$201$	39.1485	2.76132
$202$	8.31281	0.584888
$203$	−13.9873	−0.981714
$204$	−12.7702	−0.894094
$205$	0	0
$206$	−6.36991	−0.443813
$207$	7.62018	0.529639
$208$	0.557299	0.0386417
$209$	13.6777	0.946105
$210$	0	0
$211$	6.55986	0.451599	0.225800	−	0.974174i	$-0.427501\pi$
$211$	6.55986	0.451599	0.225800	+	0.974174i	$0.427501\pi$
$212$	11.1275	0.764242
$213$	40.5283	2.77695
$214$	−16.9226	−1.15681
$215$	0	0
$216$	15.0565	1.02447
$217$	−4.43634	−0.301158
$218$	−0.218825	−0.0148207
$219$	−30.1922	−2.04020
$220$	0	0
$221$	−2.18384	−0.146901
$222$	−11.9208	−0.800075
$223$	20.2094	1.35332	0.676660	−	0.736296i	$-0.263427\pi$
$223$	20.2094	1.35332	0.676660	+	0.736296i	$0.263427\pi$
$224$	1.44270	0.0963945
$225$	0	0
$226$	0.580599	0.0386209
$227$	15.0098	0.996234	0.498117	−	0.867110i	$-0.334025\pi$
$227$	15.0098	0.996234	0.498117	+	0.867110i	$0.334025\pi$
$228$	−21.9419	−1.45314
$229$	13.7081	0.905859	0.452929	−	0.891546i	$-0.350379\pi$
$229$	13.7081	0.905859	0.452929	+	0.891546i	$0.350379\pi$
$230$	0	0
$231$	−9.55093	−0.628405
$232$	−9.69520	−0.636521
$233$	−9.19822	−0.602595	−0.301298	−	0.953530i	$-0.597420\pi$
$233$	−9.19822	−0.602595	−0.301298	+	0.953530i	$0.597420\pi$
$234$	4.24672	0.277617
$235$	0	0
$236$	10.7226	0.697984
$237$	19.3068	1.25411
$238$	−5.65339	−0.366455
$239$	−2.72618	−0.176342	−0.0881709	−	0.996105i	$-0.528102\pi$
$239$	−2.72618	−0.176342	−0.0881709	+	0.996105i	$0.528102\pi$
$240$	0	0
$241$	3.26109	0.210066	0.105033	−	0.994469i	$-0.466505\pi$
$241$	3.26109	0.210066	0.105033	+	0.994469i	$0.466505\pi$
$242$	−6.87326	−0.441830
$243$	40.2340	2.58101
$244$	1.73937	0.111351
$245$	0	0
$246$	22.9203	1.46134
$247$	−3.75229	−0.238753
$248$	−3.07502	−0.195264
$249$	−37.0776	−2.34970
$250$	0	0
$251$	19.9941	1.26202	0.631008	−	0.775776i	$-0.282641\pi$
$251$	19.9941	1.26202	0.631008	+	0.775776i	$0.282641\pi$
$252$	10.9936	0.692534
$253$	−2.03144	−0.127715
$254$	1.56944	0.0984756
$255$	0	0
$256$	1.00000	0.0625000
$257$	−26.7935	−1.67133	−0.835667	−	0.549237i	$-0.814919\pi$
$257$	−26.7935	−1.67133	−0.835667	+	0.549237i	$0.814919\pi$
$258$	−16.5050	−1.02756
$259$	−5.27737	−0.327920
$260$	0	0
$261$	−73.8791	−4.57300
$262$	15.9208	0.983593
$263$	−15.8267	−0.975918	−0.487959	−	0.872867i	$-0.662258\pi$
$263$	−15.8267	−0.975918	−0.487959	+	0.872867i	$0.662258\pi$
$264$	−6.62018	−0.407444
$265$	0	0
$266$	−9.71371	−0.595586
$267$	17.1191	1.04767
$268$	12.0129	0.733806
$269$	12.0872	0.736967	0.368484	−	0.929634i	$-0.379877\pi$
$269$	12.0872	0.736967	0.368484	+	0.929634i	$0.379877\pi$
$270$	0	0
$271$	8.40254	0.510418	0.255209	−	0.966886i	$-0.417856\pi$
$271$	8.40254	0.510418	0.255209	+	0.966886i	$0.417856\pi$
$272$	−3.91861	−0.237601
$273$	2.62018	0.158580
$274$	−6.47013	−0.390875
$275$	0	0
$276$	3.25886	0.196160
$277$	−13.8488	−0.832093	−0.416046	−	0.909343i	$-0.636585\pi$
$277$	−13.8488	−0.832093	−0.416046	+	0.909343i	$0.636585\pi$
$278$	−0.656206	−0.0393566
$279$	−23.4322	−1.40285
$280$	0	0
$281$	−8.15004	−0.486191	−0.243095	−	0.970002i	$-0.578163\pi$
$281$	−8.15004	−0.486191	−0.243095	+	0.970002i	$0.578163\pi$
$282$	2.15004	0.128033
$283$	−17.3532	−1.03154	−0.515770	−	0.856727i	$-0.672494\pi$
$283$	−17.3532	−1.03154	−0.515770	+	0.856727i	$0.672494\pi$
$284$	12.4363	0.737961
$285$	0	0
$286$	−1.13212	−0.0669436
$287$	10.1468	0.598948
$288$	7.62018	0.449023
$289$	−1.64446	−0.0967332
$290$	0	0
$291$	−0.265226	−0.0155478
$292$	−9.26464	−0.542172
$293$	7.02252	0.410260	0.205130	−	0.978735i	$-0.434238\pi$
$293$	7.02252	0.410260	0.205130	+	0.978735i	$0.434238\pi$
$294$	−16.0291	−0.934835
$295$	0	0
$296$	−3.65798	−0.212616
$297$	−30.5864	−1.77480
$298$	23.8349	1.38072
$299$	0.557299	0.0322294
$300$	0	0
$301$	−7.30678	−0.421156
$302$	−14.8669	−0.855494
$303$	27.0903	1.55630
$304$	−6.73300	−0.386164
$305$	0	0
$306$	−29.8605	−1.70701
$307$	16.4156	0.936887	0.468444	−	0.883493i	$-0.344815\pi$
$307$	16.4156	0.936887	0.468444	+	0.883493i	$0.344815\pi$
$308$	−2.93076	−0.166995
$309$	−20.7587	−1.18092
$310$	0	0
$311$	7.35181	0.416883	0.208441	−	0.978035i	$-0.433161\pi$
$311$	7.35181	0.416883	0.208441	+	0.978035i	$0.433161\pi$
$312$	1.81616	0.102820
$313$	4.08972	0.231165	0.115582	−	0.993298i	$-0.463127\pi$
$313$	4.08972	0.231165	0.115582	+	0.993298i	$0.463127\pi$
$314$	8.24213	0.465130
$315$	0	0
$316$	5.92439	0.333273
$317$	8.91580	0.500761	0.250381	−	0.968148i	$-0.419444\pi$
$317$	8.91580	0.500761	0.250381	+	0.968148i	$0.419444\pi$
$318$	36.2631	2.03353
$319$	19.6952	1.10272
$320$	0	0
$321$	−55.1485	−3.07809
$322$	1.44270	0.0803986
$323$	26.3840	1.46805
$324$	26.2066	1.45592
$325$	0	0
$326$	−10.3154	−0.571316
$327$	−0.713121	−0.0394357
$328$	7.03321	0.388344
$329$	0.951826	0.0524759
$330$	0	0
$331$	21.3240	1.17207	0.586036	−	0.810285i	$-0.300688\pi$
$331$	21.3240	1.17207	0.586036	+	0.810285i	$0.300688\pi$
$332$	−11.3775	−0.624420
$333$	−27.8744	−1.52751
$334$	−4.65975	−0.254970
$335$	0	0
$336$	4.70156	0.256491
$337$	−3.15417	−0.171819	−0.0859094	−	0.996303i	$-0.527380\pi$
$337$	−3.15417	−0.171819	−0.0859094	+	0.996303i	$0.527380\pi$
$338$	−12.6894	−0.690213
$339$	1.89209	0.102764
$340$	0	0
$341$	6.24672	0.338279
$342$	−51.3067	−2.77435
$343$	−17.1950	−0.928443
$344$	−5.06465	−0.273068
$345$	0	0
$346$	2.80402	0.150745
$347$	−3.54739	−0.190434	−0.0952169	−	0.995457i	$-0.530354\pi$
$347$	−3.54739	−0.190434	−0.0952169	+	0.995457i	$0.530354\pi$
$348$	−31.5953	−1.69369
$349$	−18.9726	−1.01558	−0.507789	−	0.861481i	$-0.669537\pi$
$349$	−18.9726	−1.01558	−0.507789	+	0.861481i	$0.669537\pi$
$350$	0	0
$351$	8.39098	0.447877
$352$	−2.03144	−0.108276
$353$	−33.5710	−1.78680	−0.893402	−	0.449257i	$-0.851689\pi$
$353$	−33.5710	−1.78680	−0.893402	+	0.449257i	$0.851689\pi$
$354$	34.9436	1.85723
$355$	0	0
$356$	5.25308	0.278413
$357$	−18.4236	−0.975081
$358$	−4.44212	−0.234773
$359$	−3.53243	−0.186434	−0.0932171	−	0.995646i	$-0.529715\pi$
$359$	−3.53243	−0.186434	−0.0932171	+	0.995646i	$0.529715\pi$
$360$	0	0
$361$	26.3333	1.38596
$362$	2.42019	0.127202
$363$	−22.3990	−1.17564
$364$	0.804016	0.0421419
$365$	0	0
$366$	5.66835	0.296289
$367$	−8.07444	−0.421482	−0.210741	−	0.977542i	$-0.567588\pi$
$367$	−8.07444	−0.421482	−0.210741	+	0.977542i	$0.567588\pi$
$368$	1.00000	0.0521286
$369$	53.5943	2.79001
$370$	0	0
$371$	16.0537	0.833466
$372$	−10.0211	−0.519568
$373$	1.31459	0.0680668	0.0340334	−	0.999421i	$-0.489165\pi$
$373$	1.31459	0.0680668	0.0340334	+	0.999421i	$0.489165\pi$
$374$	7.96042	0.411624
$375$	0	0
$376$	0.659753	0.0340242
$377$	−5.40312	−0.278275
$378$	21.7220	1.11726
$379$	0.311952	0.0160239	0.00801196	−	0.999968i	$-0.497450\pi$
$379$	0.311952	0.0160239	0.00801196	+	0.999968i	$0.497450\pi$
$380$	0	0
$381$	5.11460	0.262029
$382$	−20.8934	−1.06900
$383$	−10.6805	−0.545748	−0.272874	−	0.962050i	$-0.587974\pi$
$383$	−10.6805	−0.545748	−0.272874	+	0.962050i	$0.587974\pi$
$384$	3.25886	0.166303
$385$	0	0
$386$	−2.88540	−0.146863
$387$	−38.5935	−1.96182
$388$	−0.0813861	−0.00413175
$389$	−7.86867	−0.398957	−0.199479	−	0.979902i	$-0.563925\pi$
$389$	−7.86867	−0.398957	−0.199479	+	0.979902i	$0.563925\pi$
$390$	0	0
$391$	−3.91861	−0.198173
$392$	−4.91861	−0.248428
$393$	51.8838	2.61719
$394$	19.0925	0.961868
$395$	0	0
$396$	−15.4799	−0.777895
$397$	−29.2334	−1.46718	−0.733591	−	0.679591i	$-0.762157\pi$
$397$	−29.2334	−1.46718	−0.733591	+	0.679591i	$0.762157\pi$
$398$	6.58060	0.329856
$399$	−31.6556	−1.58476
$400$	0	0
$401$	23.7130	1.18417	0.592086	−	0.805874i	$-0.298304\pi$
$401$	23.7130	1.18417	0.592086	+	0.805874i	$0.298304\pi$
$402$	39.1485	1.95255
$403$	−1.71371	−0.0853658
$404$	8.31281	0.413578
$405$	0	0
$406$	−13.9873	−0.694177
$407$	7.43096	0.368339
$408$	−12.7702	−0.632220
$409$	−33.2509	−1.64415	−0.822076	−	0.569378i	$-0.807184\pi$
$409$	−33.2509	−1.64415	−0.822076	+	0.569378i	$0.807184\pi$
$410$	0	0
$411$	−21.0853	−1.04006
$412$	−6.36991	−0.313823
$413$	15.4695	0.761207
$414$	7.62018	0.374511
$415$	0	0
$416$	0.557299	0.0273238
$417$	−2.13848	−0.104722
$418$	13.6777	0.668997
$419$	7.28229	0.355763	0.177882	−	0.984052i	$-0.443076\pi$
$419$	7.28229	0.355763	0.177882	+	0.984052i	$0.443076\pi$
$420$	0	0
$421$	−2.71515	−0.132329	−0.0661643	−	0.997809i	$-0.521076\pi$
$421$	−2.71515	−0.132329	−0.0661643	+	0.997809i	$0.521076\pi$
$422$	6.55986	0.319329
$423$	5.02743	0.244442
$424$	11.1275	0.540401
$425$	0	0
$426$	40.5283	1.96360
$427$	2.50938	0.121438
$428$	−16.9226	−0.817986
$429$	−3.68942	−0.178127
$430$	0	0
$431$	10.3336	0.497750	0.248875	−	0.968536i	$-0.419939\pi$
$431$	10.3336	0.497750	0.248875	+	0.968536i	$0.419939\pi$
$432$	15.0565	0.724407
$433$	−28.4153	−1.36555	−0.682775	−	0.730628i	$-0.739227\pi$
$433$	−28.4153	−1.36555	−0.682775	+	0.730628i	$0.739227\pi$
$434$	−4.43634	−0.212951
$435$	0	0
$436$	−0.218825	−0.0104798
$437$	−6.73300	−0.322083
$438$	−30.1922	−1.44264
$439$	6.37313	0.304173	0.152087	−	0.988367i	$-0.451401\pi$
$439$	6.37313	0.304173	0.152087	+	0.988367i	$0.451401\pi$
$440$	0	0
$441$	−37.4807	−1.78480
$442$	−2.18384	−0.103875
$443$	9.43114	0.448087	0.224044	−	0.974579i	$-0.428074\pi$
$443$	9.43114	0.448087	0.224044	+	0.974579i	$0.428074\pi$
$444$	−11.9208	−0.565738
$445$	0	0
$446$	20.2094	0.956942
$447$	77.6745	3.67388
$448$	1.44270	0.0681612
$449$	11.3185	0.534154	0.267077	−	0.963675i	$-0.413942\pi$
$449$	11.3185	0.534154	0.267077	+	0.963675i	$0.413942\pi$
$450$	0	0
$451$	−14.2875	−0.672774
$452$	0.580599	0.0273091
$453$	−48.4491	−2.27634
$454$	15.0098	0.704444
$455$	0	0
$456$	−21.9419	−1.02752
$457$	−4.96456	−0.232232	−0.116116	−	0.993236i	$-0.537044\pi$
$457$	−4.96456	−0.232232	−0.116116	+	0.993236i	$0.537044\pi$
$458$	13.7081	0.640539
$459$	−59.0007	−2.75391
$460$	0	0
$461$	19.9128	0.927433	0.463717	−	0.885984i	$-0.346516\pi$
$461$	19.9128	0.927433	0.463717	+	0.885984i	$0.346516\pi$
$462$	−9.55093	−0.444350
$463$	29.9046	1.38978	0.694892	−	0.719114i	$-0.255452\pi$
$463$	29.9046	1.38978	0.694892	+	0.719114i	$0.255452\pi$
$464$	−9.69520	−0.450088
$465$	0	0
$466$	−9.19822	−0.426099
$467$	−15.1032	−0.698895	−0.349447	−	0.936956i	$-0.613631\pi$
$467$	−15.1032	−0.698895	−0.349447	+	0.936956i	$0.613631\pi$
$468$	4.24672	0.196305
$469$	17.3311	0.800274
$470$	0	0
$471$	26.8599	1.23764
$472$	10.7226	0.493549
$473$	10.2885	0.473067
$474$	19.3068	0.886790
$475$	0	0
$476$	−5.65339	−0.259123
$477$	84.7937	3.88244
$478$	−2.72618	−0.124692
$479$	28.6678	1.30986	0.654932	−	0.755688i	$-0.272697\pi$
$479$	28.6678	1.30986	0.654932	+	0.755688i	$0.272697\pi$
$480$	0	0
$481$	−2.03859	−0.0929516
$482$	3.26109	0.148539
$483$	4.70156	0.213928
$484$	−6.87326	−0.312421
$485$	0	0
$486$	40.2340	1.82505
$487$	−9.15319	−0.414770	−0.207385	−	0.978259i	$-0.566495\pi$
$487$	−9.15319	−0.414770	−0.207385	+	0.978259i	$0.566495\pi$
$488$	1.73937	0.0787374
$489$	−33.6164	−1.52018
$490$	0	0
$491$	−20.8098	−0.939133	−0.469566	−	0.882897i	$-0.655590\pi$
$491$	−20.8098	−0.939133	−0.469566	+	0.882897i	$0.655590\pi$
$492$	22.9203	1.03333
$493$	37.9917	1.71106
$494$	−3.75229	−0.168824
$495$	0	0
$496$	−3.07502	−0.138073
$497$	17.9419	0.804805
$498$	−37.0776	−1.66149
$499$	−18.1293	−0.811579	−0.405789	−	0.913967i	$-0.633003\pi$
$499$	−18.1293	−0.811579	−0.405789	+	0.913967i	$0.633003\pi$
$500$	0	0
$501$	−15.1855	−0.678438
$502$	19.9941	0.892380
$503$	26.4296	1.17844	0.589218	−	0.807974i	$-0.299436\pi$
$503$	26.4296	1.17844	0.589218	+	0.807974i	$0.299436\pi$
$504$	10.9936	0.489695
$505$	0	0
$506$	−2.03144	−0.0903085
$507$	−41.3531	−1.83655
$508$	1.56944	0.0696328
$509$	−12.0501	−0.534113	−0.267057	−	0.963681i	$-0.586051\pi$
$509$	−12.0501	−0.534113	−0.267057	+	0.963681i	$0.586051\pi$
$510$	0	0
$511$	−13.3661	−0.591282
$512$	1.00000	0.0441942
$513$	−101.376	−4.47584
$514$	−26.7935	−1.18181
$515$	0	0
$516$	−16.5050	−0.726592
$517$	−1.34025	−0.0589440
$518$	−5.27737	−0.231874
$519$	9.13790	0.401109
$520$	0	0
$521$	−25.3697	−1.11146	−0.555732	−	0.831361i	$-0.687562\pi$
$521$	−25.3697	−1.11146	−0.555732	+	0.831361i	$0.687562\pi$
$522$	−73.8791	−3.23360
$523$	25.0018	1.09325	0.546626	−	0.837377i	$-0.315912\pi$
$523$	25.0018	1.09325	0.546626	+	0.837377i	$0.315912\pi$
$524$	15.9208	0.695505
$525$	0	0
$526$	−15.8267	−0.690078
$527$	12.0498	0.524898
$528$	−6.62018	−0.288106
$529$	1.00000	0.0434783
$530$	0	0
$531$	81.7083	3.54584
$532$	−9.71371	−0.421143
$533$	3.91960	0.169777
$534$	17.1191	0.740814
$535$	0	0
$536$	12.0129	0.518880
$537$	−14.4762	−0.624696
$538$	12.0872	0.521115
$539$	9.99186	0.430380
$540$	0	0
$541$	24.7900	1.06580	0.532902	−	0.846177i	$-0.321101\pi$
$541$	24.7900	1.06580	0.532902	+	0.846177i	$0.321101\pi$
$542$	8.40254	0.360920
$543$	7.88705	0.338466
$544$	−3.91861	−0.168009
$545$	0	0
$546$	2.62018	0.112133
$547$	30.9508	1.32336	0.661681	−	0.749785i	$-0.269843\pi$
$547$	30.9508	1.32336	0.661681	+	0.749785i	$0.269843\pi$
$548$	−6.47013	−0.276390
$549$	13.2543	0.565678
$550$	0	0
$551$	65.2778	2.78093
$552$	3.25886	0.138706
$553$	8.54713	0.363461
$554$	−13.8488	−0.588379
$555$	0	0
$556$	−0.656206	−0.0278293
$557$	7.45307	0.315797	0.157898	−	0.987455i	$-0.449528\pi$
$557$	7.45307	0.315797	0.157898	+	0.987455i	$0.449528\pi$
$558$	−23.4322	−0.991964
$559$	−2.82252	−0.119380
$560$	0	0
$561$	25.9419	1.09527
$562$	−8.15004	−0.343789
$563$	7.96161	0.335542	0.167771	−	0.985826i	$-0.446343\pi$
$563$	7.96161	0.335542	0.167771	+	0.985826i	$0.446343\pi$
$564$	2.15004	0.0905331
$565$	0	0
$566$	−17.3532	−0.729408
$567$	37.8082	1.58780
$568$	12.4363	0.521817
$569$	32.3873	1.35774	0.678872	−	0.734257i	$-0.262469\pi$
$569$	32.3873	1.35774	0.678872	+	0.734257i	$0.262469\pi$
$570$	0	0
$571$	−6.38994	−0.267410	−0.133705	−	0.991021i	$-0.542688\pi$
$571$	−6.38994	−0.267410	−0.133705	+	0.991021i	$0.542688\pi$
$572$	−1.13212	−0.0473363
$573$	−68.0887	−2.84445
$574$	10.1468	0.423520
$575$	0	0
$576$	7.62018	0.317507
$577$	39.1728	1.63078	0.815392	−	0.578910i	$-0.196522\pi$
$577$	39.1728	1.63078	0.815392	+	0.578910i	$0.196522\pi$
$578$	−1.64446	−0.0684007
$579$	−9.40312	−0.390781
$580$	0	0
$581$	−16.4143	−0.680979
$582$	−0.265226	−0.0109940
$583$	−22.6049	−0.936199
$584$	−9.26464	−0.383374
$585$	0	0
$586$	7.02252	0.290097
$587$	21.3811	0.882491	0.441246	−	0.897386i	$-0.354537\pi$
$587$	21.3811	0.882491	0.441246	+	0.897386i	$0.354537\pi$
$588$	−16.0291	−0.661028
$589$	20.7041	0.853098
$590$	0	0
$591$	62.2199	2.55939
$592$	−3.65798	−0.150342
$593$	2.45130	0.100663	0.0503314	−	0.998733i	$-0.483972\pi$
$593$	2.45130	0.100663	0.0503314	+	0.998733i	$0.483972\pi$
$594$	−30.5864	−1.25497
$595$	0	0
$596$	23.8349	0.976314
$597$	21.4453	0.877696
$598$	0.557299	0.0227897
$599$	38.5828	1.57645	0.788226	−	0.615386i	$-0.211000\pi$
$599$	38.5828	1.57645	0.788226	+	0.615386i	$0.211000\pi$
$600$	0	0
$601$	−35.3416	−1.44162	−0.720808	−	0.693135i	$-0.756229\pi$
$601$	−35.3416	−1.44162	−0.720808	+	0.693135i	$0.756229\pi$
$602$	−7.30678	−0.297802
$603$	91.5406	3.72782
$604$	−14.8669	−0.604925
$605$	0	0
$606$	27.0903	1.10047
$607$	17.8129	0.723005	0.361502	−	0.932371i	$-0.382264\pi$
$607$	17.8129	0.723005	0.361502	+	0.932371i	$0.382264\pi$
$608$	−6.73300	−0.273059
$609$	−45.5826	−1.84710
$610$	0	0
$611$	0.367680	0.0148747
$612$	−29.8605	−1.20704
$613$	37.7547	1.52490	0.762450	−	0.647048i	$-0.223997\pi$
$613$	37.7547	1.52490	0.762450	+	0.647048i	$0.223997\pi$
$614$	16.4156	0.662479
$615$	0	0
$616$	−2.93076	−0.118084
$617$	−23.1248	−0.930971	−0.465486	−	0.885055i	$-0.654120\pi$
$617$	−23.1248	−0.930971	−0.465486	+	0.885055i	$0.654120\pi$
$618$	−20.7587	−0.835036
$619$	19.5428	0.785491	0.392746	−	0.919647i	$-0.371525\pi$
$619$	19.5428	0.785491	0.392746	+	0.919647i	$0.371525\pi$
$620$	0	0
$621$	15.0565	0.604197
$622$	7.35181	0.294781
$623$	7.57863	0.303631
$624$	1.81616	0.0727046
$625$	0	0
$626$	4.08972	0.163458
$627$	44.5736	1.78010
$628$	8.24213	0.328897
$629$	14.3342	0.571542
$630$	0	0
$631$	−26.4807	−1.05418	−0.527090	−	0.849809i	$-0.676717\pi$
$631$	−26.4807	−1.05418	−0.527090	+	0.849809i	$0.676717\pi$
$632$	5.92439	0.235660
$633$	21.3777	0.849686
$634$	8.91580	0.354092
$635$	0	0
$636$	36.2631	1.43792
$637$	−2.74114	−0.108608
$638$	19.6952	0.779740
$639$	94.7671	3.74893
$640$	0	0
$641$	−35.9594	−1.42031	−0.710156	−	0.704044i	$-0.751376\pi$
$641$	−35.9594	−1.42031	−0.710156	+	0.704044i	$0.751376\pi$
$642$	−55.1485	−2.17654
$643$	−14.6934	−0.579452	−0.289726	−	0.957110i	$-0.593564\pi$
$643$	−14.6934	−0.579452	−0.289726	+	0.957110i	$0.593564\pi$
$644$	1.44270	0.0568504
$645$	0	0
$646$	26.3840	1.03807
$647$	−26.7763	−1.05269	−0.526343	−	0.850272i	$-0.676437\pi$
$647$	−26.7763	−1.05269	−0.526343	+	0.850272i	$0.676437\pi$
$648$	26.2066	1.02949
$649$	−21.7824	−0.855033
$650$	0	0
$651$	−14.4574	−0.566630
$652$	−10.3154	−0.403981
$653$	−18.8331	−0.736996	−0.368498	−	0.929629i	$-0.620128\pi$
$653$	−18.8331	−0.736996	−0.368498	+	0.929629i	$0.620128\pi$
$654$	−0.713121	−0.0278853
$655$	0	0
$656$	7.03321	0.274601
$657$	−70.5982	−2.75430
$658$	0.951826	0.0371060
$659$	−18.0885	−0.704629	−0.352315	−	0.935882i	$-0.614605\pi$
$659$	−18.0885	−0.704629	−0.352315	+	0.935882i	$0.614605\pi$
$660$	0	0
$661$	30.3235	1.17945	0.589724	−	0.807605i	$-0.299237\pi$
$661$	30.3235	1.17945	0.589724	+	0.807605i	$0.299237\pi$
$662$	21.3240	0.828780
$663$	−7.11683	−0.276395
$664$	−11.3775	−0.441531
$665$	0	0
$666$	−27.8744	−1.08011
$667$	−9.69520	−0.375400
$668$	−4.65975	−0.180291
$669$	65.8595	2.54628
$670$	0	0
$671$	−3.53341	−0.136406
$672$	4.70156	0.181367
$673$	−11.1496	−0.429787	−0.214894	−	0.976637i	$-0.568940\pi$
$673$	−11.1496	−0.429787	−0.214894	+	0.976637i	$0.568940\pi$
$674$	−3.15417	−0.121494
$675$	0	0
$676$	−12.6894	−0.488055
$677$	43.5275	1.67290	0.836449	−	0.548045i	$-0.184628\pi$
$677$	43.5275	1.67290	0.836449	+	0.548045i	$0.184628\pi$
$678$	1.89209	0.0726654
$679$	−0.117416	−0.00450600
$680$	0	0
$681$	48.9148	1.87442
$682$	6.24672	0.239199
$683$	−24.1375	−0.923596	−0.461798	−	0.886985i	$-0.652795\pi$
$683$	−24.1375	−0.923596	−0.461798	+	0.886985i	$0.652795\pi$
$684$	−51.3067	−1.96176
$685$	0	0
$686$	−17.1950	−0.656508
$687$	44.6729	1.70438
$688$	−5.06465	−0.193088
$689$	6.20136	0.236253
$690$	0	0
$691$	−20.8241	−0.792186	−0.396093	−	0.918210i	$-0.629634\pi$
$691$	−20.8241	−0.792186	−0.396093	+	0.918210i	$0.629634\pi$
$692$	2.80402	0.106593
$693$	−22.3329	−0.848356
$694$	−3.54739	−0.134657
$695$	0	0
$696$	−31.5953	−1.19762
$697$	−27.5604	−1.04393
$698$	−18.9726	−0.718122
$699$	−29.9757	−1.13379
$700$	0	0
$701$	−31.5301	−1.19087	−0.595437	−	0.803402i	$-0.703021\pi$
$701$	−31.5301	−1.19087	−0.595437	+	0.803402i	$0.703021\pi$
$702$	8.39098	0.316697
$703$	24.6292	0.928907
$704$	−2.03144	−0.0765627
$705$	0	0
$706$	−33.5710	−1.26346
$707$	11.9929	0.451040
$708$	34.9436	1.31326
$709$	3.12175	0.117240	0.0586199	−	0.998280i	$-0.481330\pi$
$709$	3.12175	0.117240	0.0586199	+	0.998280i	$0.481330\pi$
$710$	0	0
$711$	45.1449	1.69307
$712$	5.25308	0.196868
$713$	−3.07502	−0.115160
$714$	−18.4236	−0.689486
$715$	0	0
$716$	−4.44212	−0.166010
$717$	−8.88423	−0.331788
$718$	−3.53243	−0.131829
$719$	20.3945	0.760588	0.380294	−	0.924866i	$-0.375823\pi$
$719$	20.3945	0.760588	0.380294	+	0.924866i	$0.375823\pi$
$720$	0	0
$721$	−9.18988	−0.342249
$722$	26.3333	0.980024
$723$	10.6275	0.395239
$724$	2.42019	0.0899455
$725$	0	0
$726$	−22.3990	−0.831305
$727$	−39.8896	−1.47942	−0.739712	−	0.672924i	$-0.765038\pi$
$727$	−39.8896	−1.47942	−0.739712	+	0.672924i	$0.765038\pi$
$728$	0.804016	0.0297988
$729$	52.4973	1.94434
$730$	0	0
$731$	19.8464	0.734046
$732$	5.66835	0.209508
$733$	−22.7761	−0.841255	−0.420628	−	0.907233i	$-0.638190\pi$
$733$	−22.7761	−0.841255	−0.420628	+	0.907233i	$0.638190\pi$
$734$	−8.07444	−0.298033
$735$	0	0
$736$	1.00000	0.0368605
$737$	−24.4035	−0.898915
$738$	53.5943	1.97283
$739$	33.7661	1.24211	0.621053	−	0.783769i	$-0.286705\pi$
$739$	33.7661	1.24211	0.621053	+	0.783769i	$0.286705\pi$
$740$	0	0
$741$	−12.2282	−0.449214
$742$	16.0537	0.589350
$743$	47.5880	1.74584	0.872918	−	0.487868i	$-0.162225\pi$
$743$	47.5880	1.74584	0.872918	+	0.487868i	$0.162225\pi$
$744$	−10.0211	−0.367390
$745$	0	0
$746$	1.31459	0.0481305
$747$	−86.6983	−3.17212
$748$	7.96042	0.291062
$749$	−24.4143	−0.892078
$750$	0	0
$751$	51.2698	1.87086	0.935430	−	0.353512i	$-0.115013\pi$
$751$	51.2698	1.87086	0.935430	+	0.353512i	$0.115013\pi$
$752$	0.659753	0.0240587
$753$	65.1580	2.37449
$754$	−5.40312	−0.196770
$755$	0	0
$756$	21.7220	0.790023
$757$	−26.2807	−0.955189	−0.477594	−	0.878580i	$-0.658491\pi$
$757$	−26.2807	−0.955189	−0.477594	+	0.878580i	$0.658491\pi$
$758$	0.311952	0.0113306
$759$	−6.62018	−0.240297
$760$	0	0
$761$	−7.18003	−0.260276	−0.130138	−	0.991496i	$-0.541542\pi$
$761$	−7.18003	−0.260276	−0.130138	+	0.991496i	$0.541542\pi$
$762$	5.11460	0.185282
$763$	−0.315700	−0.0114291
$764$	−20.8934	−0.755897
$765$	0	0
$766$	−10.6805	−0.385902
$767$	5.97571	0.215770
$768$	3.25886	0.117594
$769$	−32.2666	−1.16356	−0.581782	−	0.813345i	$-0.697644\pi$
$769$	−32.2666	−1.16356	−0.581782	+	0.813345i	$0.697644\pi$
$770$	0	0
$771$	−87.3164	−3.14462
$772$	−2.88540	−0.103848
$773$	3.75316	0.134992	0.0674958	−	0.997720i	$-0.478499\pi$
$773$	3.75316	0.134992	0.0674958	+	0.997720i	$0.478499\pi$
$774$	−38.5935	−1.38722
$775$	0	0
$776$	−0.0813861	−0.00292159
$777$	−17.1982	−0.616983
$778$	−7.86867	−0.282105
$779$	−47.3546	−1.69666
$780$	0	0
$781$	−25.2637	−0.904005
$782$	−3.91861	−0.140129
$783$	−145.976	−5.21675
$784$	−4.91861	−0.175665
$785$	0	0
$786$	51.8838	1.85063
$787$	−21.9373	−0.781981	−0.390991	−	0.920395i	$-0.627867\pi$
$787$	−21.9373	−0.781981	−0.390991	+	0.920395i	$0.627867\pi$
$788$	19.0925	0.680144
$789$	−51.5771	−1.83619
$790$	0	0
$791$	0.837631	0.0297827
$792$	−15.4799	−0.550055
$793$	0.969347	0.0344225
$794$	−29.2334	−1.03745
$795$	0	0
$796$	6.58060	0.233243
$797$	−7.57883	−0.268456	−0.134228	−	0.990950i	$-0.542855\pi$
$797$	−7.57883	−0.268456	−0.134228	+	0.990950i	$0.542855\pi$
$798$	−31.6556	−1.12060
$799$	−2.58532	−0.0914619
$800$	0	0
$801$	40.0294	1.41437
$802$	23.7130	0.837337
$803$	18.8205	0.664163
$804$	39.1485	1.38066
$805$	0	0
$806$	−1.71371	−0.0603627
$807$	39.3904	1.38661
$808$	8.31281	0.292444
$809$	18.9835	0.667423	0.333712	−	0.942675i	$-0.391699\pi$
$809$	18.9835	0.667423	0.333712	+	0.942675i	$0.391699\pi$
$810$	0	0
$811$	14.1851	0.498106	0.249053	−	0.968490i	$-0.419881\pi$
$811$	14.1851	0.498106	0.249053	+	0.968490i	$0.419881\pi$
$812$	−13.9873	−0.490857
$813$	27.3827	0.960354
$814$	7.43096	0.260455
$815$	0	0
$816$	−12.7702	−0.447047
$817$	34.1003	1.19302
$818$	−33.2509	−1.16259
$819$	6.12674	0.214086
$820$	0	0
$821$	−44.8294	−1.56456	−0.782278	−	0.622930i	$-0.785942\pi$
$821$	−44.8294	−1.56456	−0.782278	+	0.622930i	$0.785942\pi$
$822$	−21.0853	−0.735433
$823$	15.7652	0.549539	0.274770	−	0.961510i	$-0.411398\pi$
$823$	15.7652	0.549539	0.274770	+	0.961510i	$0.411398\pi$
$824$	−6.36991	−0.221906
$825$	0	0
$826$	15.4695	0.538254
$827$	−11.4332	−0.397573	−0.198786	−	0.980043i	$-0.563700\pi$
$827$	−11.4332	−0.397573	−0.198786	+	0.980043i	$0.563700\pi$
$828$	7.62018	0.264819
$829$	−28.3924	−0.986108	−0.493054	−	0.869999i	$-0.664119\pi$
$829$	−28.3924	−0.986108	−0.493054	+	0.869999i	$0.664119\pi$
$830$	0	0
$831$	−45.1313	−1.56559
$832$	0.557299	0.0193209
$833$	19.2741	0.667810
$834$	−2.13848	−0.0740496
$835$	0	0
$836$	13.6777	0.473052
$837$	−46.2991	−1.60033
$838$	7.28229	0.251562
$839$	54.3340	1.87582	0.937908	−	0.346883i	$-0.112760\pi$
$839$	54.3340	1.87582	0.937908	+	0.346883i	$0.112760\pi$
$840$	0	0
$841$	64.9969	2.24127
$842$	−2.71515	−0.0935704
$843$	−26.5599	−0.914770
$844$	6.55986	0.225800
$845$	0	0
$846$	5.02743	0.172847
$847$	−9.91606	−0.340720
$848$	11.1275	0.382121
$849$	−56.5516	−1.94085
$850$	0	0
$851$	−3.65798	−0.125394
$852$	40.5283	1.38848
$853$	−46.8542	−1.60426	−0.802129	−	0.597150i	$-0.796300\pi$
$853$	−46.8542	−1.60426	−0.802129	+	0.597150i	$0.796300\pi$
$854$	2.50938	0.0858694
$855$	0	0
$856$	−16.9226	−0.578403
$857$	28.5356	0.974756	0.487378	−	0.873191i	$-0.337953\pi$
$857$	28.5356	0.974756	0.487378	+	0.873191i	$0.337953\pi$
$858$	−3.68942	−0.125955
$859$	19.4417	0.663343	0.331671	−	0.943395i	$-0.392387\pi$
$859$	19.4417	0.663343	0.331671	+	0.943395i	$0.392387\pi$
$860$	0	0
$861$	33.0671	1.12692
$862$	10.3336	0.351962
$863$	1.94514	0.0662132	0.0331066	−	0.999452i	$-0.489460\pi$
$863$	1.94514	0.0662132	0.0331066	+	0.999452i	$0.489460\pi$
$864$	15.0565	0.512233
$865$	0	0
$866$	−28.4153	−0.965590
$867$	−5.35908	−0.182004
$868$	−4.43634	−0.150579
$869$	−12.0350	−0.408261
$870$	0	0
$871$	6.69479	0.226844
$872$	−0.218825	−0.00741036
$873$	−0.620176	−0.0209898
$874$	−6.73300	−0.227747
$875$	0	0
$876$	−30.1922	−1.02010
$877$	−38.6457	−1.30497	−0.652486	−	0.757800i	$-0.726274\pi$
$877$	−38.6457	−1.30497	−0.652486	+	0.757800i	$0.726274\pi$
$878$	6.37313	0.215083
$879$	22.8854	0.771905
$880$	0	0
$881$	−54.6889	−1.84252	−0.921258	−	0.388952i	$-0.872837\pi$
$881$	−54.6889	−1.84252	−0.921258	+	0.388952i	$0.872837\pi$
$882$	−37.4807	−1.26204
$883$	−14.6273	−0.492247	−0.246123	−	0.969238i	$-0.579157\pi$
$883$	−14.6273	−0.492247	−0.246123	+	0.969238i	$0.579157\pi$
$884$	−2.18384	−0.0734505
$885$	0	0
$886$	9.43114	0.316845
$887$	40.2666	1.35202	0.676010	−	0.736892i	$-0.263707\pi$
$887$	40.2666	1.35202	0.676010	+	0.736892i	$0.263707\pi$
$888$	−11.9208	−0.400037
$889$	2.26424	0.0759401
$890$	0	0
$891$	−53.2370	−1.78351
$892$	20.2094	0.676660
$893$	−4.44212	−0.148650
$894$	77.6745	2.59782
$895$	0	0
$896$	1.44270	0.0481973
$897$	1.81616	0.0606398
$898$	11.3185	0.377704
$899$	29.8129	0.994317
$900$	0	0
$901$	−43.6045	−1.45268
$902$	−14.2875	−0.475723
$903$	−23.8118	−0.792406
$904$	0.580599	0.0193104
$905$	0	0
$906$	−48.4491	−1.60961
$907$	7.87090	0.261349	0.130674	−	0.991425i	$-0.458286\pi$
$907$	7.87090	0.261349	0.130674	+	0.991425i	$0.458286\pi$
$908$	15.0098	0.498117
$909$	63.3451	2.10102
$910$	0	0
$911$	0.586235	0.0194228	0.00971141	−	0.999953i	$-0.496909\pi$
$911$	0.586235	0.0194228	0.00971141	+	0.999953i	$0.496909\pi$
$912$	−21.9419	−0.726569
$913$	23.1126	0.764916
$914$	−4.96456	−0.164213
$915$	0	0
$916$	13.7081	0.452929
$917$	22.9690	0.758504
$918$	−59.0007	−1.94731
$919$	−27.9422	−0.921729	−0.460865	−	0.887470i	$-0.652461\pi$
$919$	−27.9422	−0.921729	−0.460865	+	0.887470i	$0.652461\pi$
$920$	0	0
$921$	53.4961	1.76276
$922$	19.9128	0.655794
$923$	6.93076	0.228129
$924$	−9.55093	−0.314203
$925$	0	0
$926$	29.9046	0.982725
$927$	−48.5399	−1.59426
$928$	−9.69520	−0.318260
$929$	−4.79352	−0.157270	−0.0786351	−	0.996903i	$-0.525056\pi$
$929$	−4.79352	−0.157270	−0.0786351	+	0.996903i	$0.525056\pi$
$930$	0	0
$931$	33.1170	1.08537
$932$	−9.19822	−0.301298
$933$	23.9585	0.784367
$934$	−15.1032	−0.494193
$935$	0	0
$936$	4.24672	0.138808
$937$	0.110466	0.00360877	0.00180438	−	0.999998i	$-0.499426\pi$
$937$	0.110466	0.00360877	0.00180438	+	0.999998i	$0.499426\pi$
$938$	17.3311	0.565879
$939$	13.3278	0.434938
$940$	0	0
$941$	19.2077	0.626155	0.313077	−	0.949728i	$-0.398640\pi$
$941$	19.2077	0.626155	0.313077	+	0.949728i	$0.398640\pi$
$942$	26.8599	0.875144
$943$	7.03321	0.229033
$944$	10.7226	0.348992
$945$	0	0
$946$	10.2885	0.334509
$947$	20.0933	0.652944	0.326472	−	0.945207i	$-0.394140\pi$
$947$	20.0933	0.652944	0.326472	+	0.945207i	$0.394140\pi$
$948$	19.3068	0.627055
$949$	−5.16318	−0.167604
$950$	0	0
$951$	29.0553	0.942184
$952$	−5.65339	−0.183227
$953$	55.4762	1.79705	0.898526	−	0.438920i	$-0.144639\pi$
$953$	55.4762	1.79705	0.898526	+	0.438920i	$0.144639\pi$
$954$	84.7937	2.74530
$955$	0	0
$956$	−2.72618	−0.0881709
$957$	64.1839	2.07477
$958$	28.6678	0.926213
$959$	−9.33447	−0.301426
$960$	0	0
$961$	−21.5442	−0.694976
$962$	−2.03859	−0.0657267
$963$	−128.953	−4.15546
$964$	3.26109	0.105033
$965$	0	0
$966$	4.70156	0.151270
$967$	−2.86228	−0.0920448	−0.0460224	−	0.998940i	$-0.514655\pi$
$967$	−2.86228	−0.0920448	−0.0460224	+	0.998940i	$0.514655\pi$
$968$	−6.87326	−0.220915
$969$	85.9819	2.76214
$970$	0	0
$971$	42.5901	1.36678	0.683391	−	0.730052i	$-0.260504\pi$
$971$	42.5901	1.36678	0.683391	+	0.730052i	$0.260504\pi$
$972$	40.2340	1.29051
$973$	−0.946709	−0.0303501
$974$	−9.15319	−0.293287
$975$	0	0
$976$	1.73937	0.0556757
$977$	42.5633	1.36172	0.680861	−	0.732413i	$-0.261606\pi$
$977$	42.5633	1.36172	0.680861	+	0.732413i	$0.261606\pi$
$978$	−33.6164	−1.07493
$979$	−10.6713	−0.341057
$980$	0	0
$981$	−1.66749	−0.0532388
$982$	−20.8098	−0.664067
$983$	32.6691	1.04198	0.520991	−	0.853562i	$-0.325563\pi$
$983$	32.6691	1.04198	0.520991	+	0.853562i	$0.325563\pi$
$984$	22.9203	0.730671
$985$	0	0
$986$	37.9917	1.20990
$987$	3.10187	0.0987336
$988$	−3.75229	−0.119376
$989$	−5.06465	−0.161047
$990$	0	0
$991$	−4.39775	−0.139699	−0.0698495	−	0.997558i	$-0.522252\pi$
$991$	−4.39775	−0.139699	−0.0698495	+	0.997558i	$0.522252\pi$
$992$	−3.07502	−0.0976320
$993$	69.4919	2.20526
$994$	17.9419	0.569083
$995$	0	0
$996$	−37.0776	−1.17485
$997$	33.4135	1.05822	0.529108	−	0.848554i	$-0.322527\pi$
$997$	33.4135	1.05822	0.529108	+	0.848554i	$0.322527\pi$
$998$	−18.1293	−0.573873
$999$	−55.0764	−1.74254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.s.1.4		4
4.3	odd	2		9200.2.a.cj.1.1		4
5.2	odd	4		230.2.b.b.139.5	yes	8
5.3	odd	4		230.2.b.b.139.4	✓	8
5.4	even	2		1150.2.a.r.1.1		4
15.2	even	4		2070.2.d.f.829.2		8
15.8	even	4		2070.2.d.f.829.6		8
20.3	even	4		1840.2.e.e.369.1		8
20.7	even	4		1840.2.e.e.369.8		8
20.19	odd	2		9200.2.a.cr.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.b.b.139.4	✓	8	5.3	odd	4
230.2.b.b.139.5	yes	8	5.2	odd	4
1150.2.a.r.1.1		4	5.4	even	2
1150.2.a.s.1.4		4	1.1	even	1	trivial
1840.2.e.e.369.1		8	20.3	even	4
1840.2.e.e.369.8		8	20.7	even	4
2070.2.d.f.829.2		8	15.2	even	4
2070.2.d.f.829.6		8	15.8	even	4
9200.2.a.cj.1.1		4	4.3	odd	2
9200.2.a.cr.1.4		4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.25886 q^{3} +1.00000 q^{4} +3.25886 q^{6} +1.44270 q^{7} +1.00000 q^{8} +7.62018 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.25886 q^{3} +1.00000 q^{4} +3.25886 q^{6} +1.44270 q^{7} +1.00000 q^{8} +7.62018 q^{9} -2.03144 q^{11} +3.25886 q^{12} +0.557299 q^{13} +1.44270 q^{14} +1.00000 q^{16} -3.91861 q^{17} +7.62018 q^{18} -6.73300 q^{19} +4.70156 q^{21} -2.03144 q^{22} +1.00000 q^{23} +3.25886 q^{24} +0.557299 q^{26} +15.0565 q^{27} +1.44270 q^{28} -9.69520 q^{29} -3.07502 q^{31} +1.00000 q^{32} -6.62018 q^{33} -3.91861 q^{34} +7.62018 q^{36} -3.65798 q^{37} -6.73300 q^{38} +1.81616 q^{39} +7.03321 q^{41} +4.70156 q^{42} -5.06465 q^{43} -2.03144 q^{44} +1.00000 q^{46} +0.659753 q^{47} +3.25886 q^{48} -4.91861 q^{49} -12.7702 q^{51} +0.557299 q^{52} +11.1275 q^{53} +15.0565 q^{54} +1.44270 q^{56} -21.9419 q^{57} -9.69520 q^{58} +10.7226 q^{59} +1.73937 q^{61} -3.07502 q^{62} +10.9936 q^{63} +1.00000 q^{64} -6.62018 q^{66} +12.0129 q^{67} -3.91861 q^{68} +3.25886 q^{69} +12.4363 q^{71} +7.62018 q^{72} -9.26464 q^{73} -3.65798 q^{74} -6.73300 q^{76} -2.93076 q^{77} +1.81616 q^{78} +5.92439 q^{79} +26.2066 q^{81} +7.03321 q^{82} -11.3775 q^{83} +4.70156 q^{84} -5.06465 q^{86} -31.5953 q^{87} -2.03144 q^{88} +5.25308 q^{89} +0.804016 q^{91} +1.00000 q^{92} -10.0211 q^{93} +0.659753 q^{94} +3.25886 q^{96} -0.0813861 q^{97} -4.91861 q^{98} -15.4799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9	\( 4 q + 4 q^{2} + 3 q^{3} + 4 q^{4} + 3 q^{6} + 3 q^{7} + 4 q^{8} + 7 q^{9} + 5 q^{11} + 3 q^{12} + 5 q^{13} + 3 q^{14} + 4 q^{16} - 5 q^{17} + 7 q^{18} - q^{19} + 6 q^{21} + 5 q^{22} + 4 q^{23} + 3 q^{24} + 5 q^{26} + 6 q^{27} + 3 q^{28} + 2 q^{29} + 5 q^{31} + 4 q^{32} - 3 q^{33} - 5 q^{34} + 7 q^{36} - 6 q^{37} - q^{38} + 23 q^{41} + 6 q^{42} - 2 q^{43} + 5 q^{44} + 4 q^{46} + 2 q^{47} + 3 q^{48} - 9 q^{49} + 7 q^{51} + 5 q^{52} + 6 q^{54} + 3 q^{56} - 28 q^{57} + 2 q^{58} + 16 q^{59} + 9 q^{61} + 5 q^{62} + 16 q^{63} + 4 q^{64} - 3 q^{66} - 2 q^{67} - 5 q^{68} + 3 q^{69} + 19 q^{71} + 7 q^{72} - 8 q^{73} - 6 q^{74} - q^{76} - 10 q^{77} - 6 q^{79} + 16 q^{81} + 23 q^{82} - 14 q^{83} + 6 q^{84} - 2 q^{86} - 38 q^{87} + 5 q^{88} + 30 q^{89} - 13 q^{91} + 4 q^{92} - 26 q^{93} + 2 q^{94} + 3 q^{96} - 11 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 3 * q^3 + 4 * q^4 + 3 * q^6 + 3 * q^7 + 4 * q^8 + 7 * q^9 + 5 * q^11 + 3 * q^12 + 5 * q^13 + 3 * q^14 + 4 * q^16 - 5 * q^17 + 7 * q^18 - q^19 + 6 * q^21 + 5 * q^22 + 4 * q^23 + 3 * q^24 + 5 * q^26 + 6 * q^27 + 3 * q^28 + 2 * q^29 + 5 * q^31 + 4 * q^32 - 3 * q^33 - 5 * q^34 + 7 * q^36 - 6 * q^37 - q^38 + 23 * q^41 + 6 * q^42 - 2 * q^43 + 5 * q^44 + 4 * q^46 + 2 * q^47 + 3 * q^48 - 9 * q^49 + 7 * q^51 + 5 * q^52 + 6 * q^54 + 3 * q^56 - 28 * q^57 + 2 * q^58 + 16 * q^59 + 9 * q^61 + 5 * q^62 + 16 * q^63 + 4 * q^64 - 3 * q^66 - 2 * q^67 - 5 * q^68 + 3 * q^69 + 19 * q^71 + 7 * q^72 - 8 * q^73 - 6 * q^74 - q^76 - 10 * q^77 - 6 * q^79 + 16 * q^81 + 23 * q^82 - 14 * q^83 + 6 * q^84 - 2 * q^86 - 38 * q^87 + 5 * q^88 + 30 * q^89 - 13 * q^91 + 4 * q^92 - 26 * q^93 + 2 * q^94 + 3 * q^96 - 11 * q^97 - 9 * q^98 - 27 * q^99

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