LMFDB - Embedded newform 950.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.713538$ of defining polynomial
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.77733 q^{3} +1.00000 q^{4} +2.77733 q^{6} +4.69527 q^{7} -1.00000 q^{8} +4.71354 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.77733 q^{3} +1.00000 q^{4} +2.77733 q^{6} +4.69527 q^{7} -1.00000 q^{8} +4.71354 q^{9} +6.40880 q^{11} -2.77733 q^{12} -1.06379 q^{13} -4.69527 q^{14} +1.00000 q^{16} -1.91794 q^{17} -4.71354 q^{18} -1.00000 q^{19} -13.0403 q^{21} -6.40880 q^{22} -1.79560 q^{23} +2.77733 q^{24} +1.06379 q^{26} -4.75905 q^{27} +4.69527 q^{28} +2.93621 q^{29} -5.55465 q^{31} -1.00000 q^{32} -17.7993 q^{33} +1.91794 q^{34} +4.71354 q^{36} +11.4088 q^{37} +1.00000 q^{38} +2.95449 q^{39} -1.14585 q^{41} +13.0403 q^{42} +3.55465 q^{43} +6.40880 q^{44} +1.79560 q^{46} -10.8359 q^{47} -2.77733 q^{48} +15.0455 q^{49} +5.32674 q^{51} -1.06379 q^{52} +8.69527 q^{53} +4.75905 q^{54} -4.69527 q^{56} +2.77733 q^{57} -2.93621 q^{58} -5.63148 q^{59} -3.39053 q^{61} +5.55465 q^{62} +22.1313 q^{63} +1.00000 q^{64} +17.7993 q^{66} +8.82284 q^{67} -1.91794 q^{68} +4.98696 q^{69} -1.42708 q^{71} -4.71354 q^{72} +12.6132 q^{73} -11.4088 q^{74} -1.00000 q^{76} +30.0910 q^{77} -2.95449 q^{78} -1.96345 q^{79} -0.923174 q^{81} +1.14585 q^{82} -16.2447 q^{83} -13.0403 q^{84} -3.55465 q^{86} -8.15482 q^{87} -6.40880 q^{88} -10.0000 q^{89} -4.99477 q^{91} -1.79560 q^{92} +15.4271 q^{93} +10.8359 q^{94} +2.77733 q^{96} +14.9452 q^{97} -15.0455 q^{98} +30.2081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 2 q^{7} - 3 q^{8} + 13 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 2 * q^7 - 3 * q^8 + 13 * q^9	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 2 q^{7} - 3 q^{8} + 13 q^{9} + 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 3 q^{16} + 4 q^{17} - 13 q^{18} - 3 q^{19} - 11 q^{21} - 2 q^{22} - 14 q^{23} + 2 q^{24} - 2 q^{26} + 7 q^{27} - 2 q^{28} + 14 q^{29} - 4 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} + 13 q^{36} + 17 q^{37} + 3 q^{38} + 29 q^{39} - 8 q^{41} + 11 q^{42} - 2 q^{43} + 2 q^{44} + 14 q^{46} - 13 q^{47} - 2 q^{48} + 25 q^{49} - 11 q^{51} + 2 q^{52} + 10 q^{53} - 7 q^{54} + 2 q^{56} + 2 q^{57} - 14 q^{58} - 6 q^{59} + 22 q^{61} + 4 q^{62} - 2 q^{63} + 3 q^{64} + 4 q^{66} + 4 q^{68} + 8 q^{69} - 2 q^{71} - 13 q^{72} + 12 q^{73} - 17 q^{74} - 3 q^{76} + 50 q^{77} - 29 q^{78} + 24 q^{79} - q^{81} + 8 q^{82} - 12 q^{83} - 11 q^{84} + 2 q^{86} + 21 q^{87} - 2 q^{88} - 30 q^{89} - 7 q^{91} - 14 q^{92} + 44 q^{93} + 13 q^{94} + 2 q^{96} - 25 q^{98} + 24 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 2 * q^7 - 3 * q^8 + 13 * q^9 + 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 + 3 * q^16 + 4 * q^17 - 13 * q^18 - 3 * q^19 - 11 * q^21 - 2 * q^22 - 14 * q^23 + 2 * q^24 - 2 * q^26 + 7 * q^27 - 2 * q^28 + 14 * q^29 - 4 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 + 13 * q^36 + 17 * q^37 + 3 * q^38 + 29 * q^39 - 8 * q^41 + 11 * q^42 - 2 * q^43 + 2 * q^44 + 14 * q^46 - 13 * q^47 - 2 * q^48 + 25 * q^49 - 11 * q^51 + 2 * q^52 + 10 * q^53 - 7 * q^54 + 2 * q^56 + 2 * q^57 - 14 * q^58 - 6 * q^59 + 22 * q^61 + 4 * q^62 - 2 * q^63 + 3 * q^64 + 4 * q^66 + 4 * q^68 + 8 * q^69 - 2 * q^71 - 13 * q^72 + 12 * q^73 - 17 * q^74 - 3 * q^76 + 50 * q^77 - 29 * q^78 + 24 * q^79 - q^81 + 8 * q^82 - 12 * q^83 - 11 * q^84 + 2 * q^86 + 21 * q^87 - 2 * q^88 - 30 * q^89 - 7 * q^91 - 14 * q^92 + 44 * q^93 + 13 * q^94 + 2 * q^96 - 25 * q^98 + 24 * 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
$3$	−2.77733	−1.60349	−0.801745	−	0.597666i	$-0.796095\pi$
$3$	−2.77733	−1.60349	−0.801745	+	0.597666i	$0.796095\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.77733	1.13384
$7$	4.69527	1.77464	0.887322	−	0.461151i	$-0.152563\pi$
$7$	4.69527	1.77464	0.887322	+	0.461151i	$0.152563\pi$
$8$	−1.00000	−0.353553
$9$	4.71354	1.57118
$10$	0	0
$11$	6.40880	1.93233	0.966163	−	0.257931i	$-0.0830406\pi$
$11$	6.40880	1.93233	0.966163	+	0.257931i	$0.0830406\pi$
$12$	−2.77733	−0.801745
$13$	−1.06379	−0.295042	−0.147521	−	0.989059i	$-0.547129\pi$
$13$	−1.06379	−0.295042	−0.147521	+	0.989059i	$0.547129\pi$
$14$	−4.69527	−1.25486
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.91794	−0.465169	−0.232584	−	0.972576i	$-0.574718\pi$
$17$	−1.91794	−0.465169	−0.232584	+	0.972576i	$0.574718\pi$
$18$	−4.71354	−1.11099
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−13.0403	−2.84562
$22$	−6.40880	−1.36636
$23$	−1.79560	−0.374408	−0.187204	−	0.982321i	$-0.559943\pi$
$23$	−1.79560	−0.374408	−0.187204	+	0.982321i	$0.559943\pi$
$24$	2.77733	0.566919
$25$	0	0
$26$	1.06379	0.208626
$27$	−4.75905	−0.915880
$28$	4.69527	0.887322
$29$	2.93621	0.545241	0.272620	−	0.962122i	$-0.412110\pi$
$29$	2.93621	0.545241	0.272620	+	0.962122i	$0.412110\pi$
$30$	0	0
$31$	−5.55465	−0.997645	−0.498822	−	0.866704i	$-0.666234\pi$
$31$	−5.55465	−0.997645	−0.498822	+	0.866704i	$0.666234\pi$
$32$	−1.00000	−0.176777
$33$	−17.7993	−3.09847
$34$	1.91794	0.328924
$35$	0	0
$36$	4.71354	0.785590
$37$	11.4088	1.87560	0.937798	−	0.347182i	$-0.112861\pi$
$37$	11.4088	1.87560	0.937798	+	0.347182i	$0.112861\pi$
$38$	1.00000	0.162221
$39$	2.95449	0.473096
$40$	0	0
$41$	−1.14585	−0.178951	−0.0894757	−	0.995989i	$-0.528519\pi$
$41$	−1.14585	−0.178951	−0.0894757	+	0.995989i	$0.528519\pi$
$42$	13.0403	2.01216
$43$	3.55465	0.542079	0.271040	−	0.962568i	$-0.412633\pi$
$43$	3.55465	0.542079	0.271040	+	0.962568i	$0.412633\pi$
$44$	6.40880	0.966163
$45$	0	0
$46$	1.79560	0.264747
$47$	−10.8359	−1.58058	−0.790288	−	0.612736i	$-0.790069\pi$
$47$	−10.8359	−1.58058	−0.790288	+	0.612736i	$0.790069\pi$
$48$	−2.77733	−0.400872
$49$	15.0455	2.14936
$50$	0	0
$51$	5.32674	0.745893
$52$	−1.06379	−0.147521
$53$	8.69527	1.19439	0.597193	−	0.802097i	$-0.296283\pi$
$53$	8.69527	1.19439	0.597193	+	0.802097i	$0.296283\pi$
$54$	4.75905	0.647625
$55$	0	0
$56$	−4.69527	−0.627431
$57$	2.77733	0.367866
$58$	−2.93621	−0.385544
$59$	−5.63148	−0.733156	−0.366578	−	0.930387i	$-0.619471\pi$
$59$	−5.63148	−0.733156	−0.366578	+	0.930387i	$0.619471\pi$
$60$	0	0
$61$	−3.39053	−0.434113	−0.217056	−	0.976159i	$-0.569646\pi$
$61$	−3.39053	−0.434113	−0.217056	+	0.976159i	$0.569646\pi$
$62$	5.55465	0.705441
$63$	22.1313	2.78828
$64$	1.00000	0.125000
$65$	0	0
$66$	17.7993	2.19095
$67$	8.82284	1.07788	0.538941	−	0.842344i	$-0.318825\pi$
$67$	8.82284	1.07788	0.538941	+	0.842344i	$0.318825\pi$
$68$	−1.91794	−0.232584
$69$	4.98696	0.600360
$70$	0	0
$71$	−1.42708	−0.169363	−0.0846814	−	0.996408i	$-0.526987\pi$
$71$	−1.42708	−0.169363	−0.0846814	+	0.996408i	$0.526987\pi$
$72$	−4.71354	−0.555496
$73$	12.6132	1.47626	0.738132	−	0.674656i	$-0.235708\pi$
$73$	12.6132	1.47626	0.738132	+	0.674656i	$0.235708\pi$
$74$	−11.4088	−1.32625
$75$	0	0
$76$	−1.00000	−0.114708
$77$	30.0910	3.42919
$78$	−2.95449	−0.334530
$79$	−1.96345	−0.220906	−0.110453	−	0.993881i	$-0.535230\pi$
$79$	−1.96345	−0.220906	−0.110453	+	0.993881i	$0.535230\pi$
$80$	0	0
$81$	−0.923174	−0.102575
$82$	1.14585	0.126538
$83$	−16.2447	−1.78309	−0.891543	−	0.452937i	$-0.850376\pi$
$83$	−16.2447	−1.78309	−0.891543	+	0.452937i	$0.850376\pi$
$84$	−13.0403	−1.42281
$85$	0	0
$86$	−3.55465	−0.383308
$87$	−8.15482	−0.874288
$88$	−6.40880	−0.683181
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−4.99477	−0.523594
$92$	−1.79560	−0.187204
$93$	15.4271	1.59971
$94$	10.8359	1.11764
$95$	0	0
$96$	2.77733	0.283460
$97$	14.9452	1.51745	0.758727	−	0.651409i	$-0.225822\pi$
$97$	14.9452	1.51745	0.758727	+	0.651409i	$0.225822\pi$
$98$	−15.0455	−1.51983
$99$	30.2081	3.03603
$100$	0	0
$101$	10.5364	1.04841	0.524204	−	0.851592i	$-0.324363\pi$
$101$	10.5364	1.04841	0.524204	+	0.851592i	$0.324363\pi$
$102$	−5.32674	−0.527426
$103$	16.9817	1.67326	0.836630	−	0.547769i	$-0.184523\pi$
$103$	16.9817	1.67326	0.836630	+	0.547769i	$0.184523\pi$
$104$	1.06379	0.104313
$105$	0	0
$106$	−8.69527	−0.844559
$107$	1.79036	0.173081	0.0865405	−	0.996248i	$-0.472419\pi$
$107$	1.79036	0.173081	0.0865405	+	0.996248i	$0.472419\pi$
$108$	−4.75905	−0.457940
$109$	2.41404	0.231223	0.115611	−	0.993295i	$-0.463117\pi$
$109$	2.41404	0.231223	0.115611	+	0.993295i	$0.463117\pi$
$110$	0	0
$111$	−31.6860	−3.00750
$112$	4.69527	0.443661
$113$	−7.14585	−0.672225	−0.336112	−	0.941822i	$-0.609112\pi$
$113$	−7.14585	−0.672225	−0.336112	+	0.941822i	$0.609112\pi$
$114$	−2.77733	−0.260120
$115$	0	0
$116$	2.93621	0.272620
$117$	−5.01420	−0.463563
$118$	5.63148	0.518420
$119$	−9.00523	−0.825508
$120$	0	0
$121$	30.0728	2.73389
$122$	3.39053	0.306964
$123$	3.18239	0.286947
$124$	−5.55465	−0.498822
$125$	0	0
$126$	−22.1313	−1.97161
$127$	−9.26295	−0.821954	−0.410977	−	0.911646i	$-0.634812\pi$
$127$	−9.26295	−0.821954	−0.410977	+	0.911646i	$0.634812\pi$
$128$	−1.00000	−0.0883883
$129$	−9.87242	−0.869219
$130$	0	0
$131$	11.5181	1.00634	0.503171	−	0.864187i	$-0.332167\pi$
$131$	11.5181	1.00634	0.503171	+	0.864187i	$0.332167\pi$
$132$	−17.7993	−1.54923
$133$	−4.69527	−0.407131
$134$	−8.82284	−0.762177
$135$	0	0
$136$	1.91794	0.164462
$137$	−15.1041	−1.29043	−0.645214	−	0.764002i	$-0.723232\pi$
$137$	−15.1041	−1.29043	−0.645214	+	0.764002i	$0.723232\pi$
$138$	−4.98696	−0.424518
$139$	−0.700500	−0.0594156	−0.0297078	−	0.999559i	$-0.509458\pi$
$139$	−0.700500	−0.0594156	−0.0297078	+	0.999559i	$0.509458\pi$
$140$	0	0
$141$	30.0948	2.53444
$142$	1.42708	0.119758
$143$	−6.81761	−0.570117
$144$	4.71354	0.392795
$145$	0	0
$146$	−12.6132	−1.04388
$147$	−41.7863	−3.44648
$148$	11.4088	0.937798
$149$	12.9452	1.06051	0.530255	−	0.847838i	$-0.322096\pi$
$149$	12.9452	1.06051	0.530255	+	0.847838i	$0.322096\pi$
$150$	0	0
$151$	5.70830	0.464535	0.232268	−	0.972652i	$-0.425385\pi$
$151$	5.70830	0.464535	0.232268	+	0.972652i	$0.425385\pi$
$152$	1.00000	0.0811107
$153$	−9.04028	−0.730863
$154$	−30.0910	−2.42480
$155$	0	0
$156$	2.95449	0.236548
$157$	−9.26295	−0.739264	−0.369632	−	0.929178i	$-0.620516\pi$
$157$	−9.26295	−0.739264	−0.369632	+	0.929178i	$0.620516\pi$
$158$	1.96345	0.156204
$159$	−24.1496	−1.91519
$160$	0	0
$161$	−8.43081	−0.664441
$162$	0.923174	0.0725314
$163$	−4.28123	−0.335332	−0.167666	−	0.985844i	$-0.553623\pi$
$163$	−4.28123	−0.335332	−0.167666	+	0.985844i	$0.553623\pi$
$164$	−1.14585	−0.0894757
$165$	0	0
$166$	16.2447	1.26083
$167$	15.2264	1.17825	0.589127	−	0.808040i	$-0.299472\pi$
$167$	15.2264	1.17825	0.589127	+	0.808040i	$0.299472\pi$
$168$	13.0403	1.00608
$169$	−11.8684	−0.912950
$170$	0	0
$171$	−4.71354	−0.360453
$172$	3.55465	0.271040
$173$	12.2630	0.932335	0.466168	−	0.884696i	$-0.345634\pi$
$173$	12.2630	0.932335	0.466168	+	0.884696i	$0.345634\pi$
$174$	8.15482	0.618215
$175$	0	0
$176$	6.40880	0.483082
$177$	15.6404	1.17561
$178$	10.0000	0.749532
$179$	−1.57292	−0.117566	−0.0587829	−	0.998271i	$-0.518722\pi$
$179$	−1.57292	−0.117566	−0.0587829	+	0.998271i	$0.518722\pi$
$180$	0	0
$181$	11.4088	0.848010	0.424005	−	0.905660i	$-0.360624\pi$
$181$	11.4088	0.848010	0.424005	+	0.905660i	$0.360624\pi$
$182$	4.99477	0.370237
$183$	9.41661	0.696096
$184$	1.79560	0.132373
$185$	0	0
$186$	−15.4271	−1.13117
$187$	−12.2917	−0.898858
$188$	−10.8359	−0.790288
$189$	−22.3450	−1.62536
$190$	0	0
$191$	−6.35805	−0.460053	−0.230026	−	0.973184i	$-0.573881\pi$
$191$	−6.35805	−0.460053	−0.230026	+	0.973184i	$0.573881\pi$
$192$	−2.77733	−0.200436
$193$	−14.4998	−1.04372	−0.521860	−	0.853031i	$-0.674762\pi$
$193$	−14.4998	−1.04372	−0.521860	+	0.853031i	$0.674762\pi$
$194$	−14.9452	−1.07300
$195$	0	0
$196$	15.0455	1.07468
$197$	5.14585	0.366627	0.183313	−	0.983055i	$-0.441318\pi$
$197$	5.14585	0.366627	0.183313	+	0.983055i	$0.441318\pi$
$198$	−30.2081	−2.14680
$199$	3.87766	0.274880	0.137440	−	0.990510i	$-0.456113\pi$
$199$	3.87766	0.274880	0.137440	+	0.990510i	$0.456113\pi$
$200$	0	0
$201$	−24.5039	−1.72837
$202$	−10.5364	−0.741337
$203$	13.7863	0.967608
$204$	5.32674	0.372947
$205$	0	0
$206$	−16.9817	−1.18317
$207$	−8.46362	−0.588262
$208$	−1.06379	−0.0737604
$209$	−6.40880	−0.443306
$210$	0	0
$211$	17.1496	1.18063	0.590313	−	0.807174i	$-0.299004\pi$
$211$	17.1496	1.18063	0.590313	+	0.807174i	$0.299004\pi$
$212$	8.69527	0.597193
$213$	3.96345	0.271571
$214$	−1.79036	−0.122387
$215$	0	0
$216$	4.75905	0.323813
$217$	−26.0806	−1.77046
$218$	−2.41404	−0.163499
$219$	−35.0310	−2.36717
$220$	0	0
$221$	2.04028	0.137244
$222$	31.6860	2.12662
$223$	−7.84635	−0.525430	−0.262715	−	0.964873i	$-0.584618\pi$
$223$	−7.84635	−0.525430	−0.262715	+	0.964873i	$0.584618\pi$
$224$	−4.69527	−0.313716
$225$	0	0
$226$	7.14585	0.475335
$227$	−6.28646	−0.417247	−0.208624	−	0.977996i	$-0.566898\pi$
$227$	−6.28646	−0.417247	−0.208624	+	0.977996i	$0.566898\pi$
$228$	2.77733	0.183933
$229$	−3.14585	−0.207884	−0.103942	−	0.994583i	$-0.533146\pi$
$229$	−3.14585	−0.207884	−0.103942	+	0.994583i	$0.533146\pi$
$230$	0	0
$231$	−83.5726	−5.49867
$232$	−2.93621	−0.192772
$233$	−0.182394	−0.0119490	−0.00597451	−	0.999982i	$-0.501902\pi$
$233$	−0.182394	−0.0119490	−0.00597451	+	0.999982i	$0.501902\pi$
$234$	5.01420	0.327789
$235$	0	0
$236$	−5.63148	−0.366578
$237$	5.45315	0.354220
$238$	9.00523	0.583723
$239$	−11.5039	−0.744126	−0.372063	−	0.928208i	$-0.621349\pi$
$239$	−11.5039	−0.744126	−0.372063	+	0.928208i	$0.621349\pi$
$240$	0	0
$241$	−0.445349	−0.0286874	−0.0143437	−	0.999897i	$-0.504566\pi$
$241$	−0.445349	−0.0286874	−0.0143437	+	0.999897i	$0.504566\pi$
$242$	−30.0728	−1.93315
$243$	16.8411	1.08036
$244$	−3.39053	−0.217056
$245$	0	0
$246$	−3.18239	−0.202902
$247$	1.06379	0.0676872
$248$	5.55465	0.352721
$249$	45.1168	2.85916
$250$	0	0
$251$	13.2630	0.837150	0.418575	−	0.908182i	$-0.362530\pi$
$251$	13.2630	0.837150	0.418575	+	0.908182i	$0.362530\pi$
$252$	22.1313	1.39414
$253$	−11.5076	−0.723479
$254$	9.26295	0.581209
$255$	0	0
$256$	1.00000	0.0625000
$257$	23.4816	1.46474	0.732370	−	0.680907i	$-0.238414\pi$
$257$	23.4816	1.46474	0.732370	+	0.680907i	$0.238414\pi$
$258$	9.87242	0.614630
$259$	53.5674	3.32851
$260$	0	0
$261$	13.8399	0.856671
$262$	−11.5181	−0.711591
$263$	−27.9269	−1.72205	−0.861023	−	0.508565i	$-0.830176\pi$
$263$	−27.9269	−1.72205	−0.861023	+	0.508565i	$0.830176\pi$
$264$	17.7993	1.09547
$265$	0	0
$266$	4.69527	0.287885
$267$	27.7733	1.69970
$268$	8.82284	0.538941
$269$	16.4816	1.00490	0.502449	−	0.864607i	$-0.332432\pi$
$269$	16.4816	1.00490	0.502449	+	0.864607i	$0.332432\pi$
$270$	0	0
$271$	−1.46736	−0.0891356	−0.0445678	−	0.999006i	$-0.514191\pi$
$271$	−1.46736	−0.0891356	−0.0445678	+	0.999006i	$0.514191\pi$
$272$	−1.91794	−0.116292
$273$	13.8721	0.839577
$274$	15.1041	0.912470
$275$	0	0
$276$	4.98696	0.300180
$277$	−15.8359	−0.951486	−0.475743	−	0.879584i	$-0.657821\pi$
$277$	−15.8359	−0.951486	−0.475743	+	0.879584i	$0.657821\pi$
$278$	0.700500	0.0420132
$279$	−26.1821	−1.56748
$280$	0	0
$281$	−6.25515	−0.373151	−0.186576	−	0.982441i	$-0.559739\pi$
$281$	−6.25515	−0.373151	−0.186576	+	0.982441i	$0.559739\pi$
$282$	−30.0948	−1.79212
$283$	16.7005	0.992742	0.496371	−	0.868111i	$-0.334666\pi$
$283$	16.7005	0.992742	0.496371	+	0.868111i	$0.334666\pi$
$284$	−1.42708	−0.0846814
$285$	0	0
$286$	6.81761	0.403134
$287$	−5.38006	−0.317575
$288$	−4.71354	−0.277748
$289$	−13.3215	−0.783618
$290$	0	0
$291$	−41.5076	−2.43322
$292$	12.6132	0.738132
$293$	−0.644516	−0.0376530	−0.0188265	−	0.999823i	$-0.505993\pi$
$293$	−0.644516	−0.0376530	−0.0188265	+	0.999823i	$0.505993\pi$
$294$	41.7863	2.43703
$295$	0	0
$296$	−11.4088	−0.663123
$297$	−30.4998	−1.76978
$298$	−12.9452	−0.749894
$299$	1.91014	0.110466
$300$	0	0
$301$	16.6900	0.961997
$302$	−5.70830	−0.328476
$303$	−29.2630	−1.68111
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	9.04028	0.516798
$307$	−26.6457	−1.52075	−0.760375	−	0.649485i	$-0.774985\pi$
$307$	−26.6457	−1.52075	−0.760375	+	0.649485i	$0.774985\pi$
$308$	30.0910	1.71460
$309$	−47.1638	−2.68305
$310$	0	0
$311$	11.5494	0.654907	0.327454	−	0.944867i	$-0.393809\pi$
$311$	11.5494	0.654907	0.327454	+	0.944867i	$0.393809\pi$
$312$	−2.95449	−0.167265
$313$	23.0638	1.30364	0.651821	−	0.758373i	$-0.274005\pi$
$313$	23.0638	1.30364	0.651821	+	0.758373i	$0.274005\pi$
$314$	9.26295	0.522739
$315$	0	0
$316$	−1.96345	−0.110453
$317$	13.9232	0.782003	0.391002	−	0.920390i	$-0.372129\pi$
$317$	13.9232	0.782003	0.391002	+	0.920390i	$0.372129\pi$
$318$	24.1496	1.35424
$319$	18.8176	1.05358
$320$	0	0
$321$	−4.97242	−0.277534
$322$	8.43081	0.469831
$323$	1.91794	0.106717
$324$	−0.923174	−0.0512874
$325$	0	0
$326$	4.28123	0.237115
$327$	−6.70457	−0.370763
$328$	1.14585	0.0632689
$329$	−50.8773	−2.80496
$330$	0	0
$331$	−0.735546	−0.0404292	−0.0202146	−	0.999796i	$-0.506435\pi$
$331$	−0.735546	−0.0404292	−0.0202146	+	0.999796i	$0.506435\pi$
$332$	−16.2447	−0.891543
$333$	53.7758	2.94690
$334$	−15.2264	−0.833152
$335$	0	0
$336$	−13.0403	−0.711406
$337$	2.28123	0.124266	0.0621332	−	0.998068i	$-0.480210\pi$
$337$	2.28123	0.124266	0.0621332	+	0.998068i	$0.480210\pi$
$338$	11.8684	0.645553
$339$	19.8463	1.07791
$340$	0	0
$341$	−35.5987	−1.92778
$342$	4.71354	0.254879
$343$	37.7758	2.03970
$344$	−3.55465	−0.191654
$345$	0	0
$346$	−12.2630	−0.659261
$347$	2.56246	0.137560	0.0687799	−	0.997632i	$-0.478089\pi$
$347$	2.56246	0.137560	0.0687799	+	0.997632i	$0.478089\pi$
$348$	−8.15482	−0.437144
$349$	−5.67176	−0.303602	−0.151801	−	0.988411i	$-0.548507\pi$
$349$	−5.67176	−0.303602	−0.151801	+	0.988411i	$0.548507\pi$
$350$	0	0
$351$	5.06262	0.270223
$352$	−6.40880	−0.341590
$353$	23.6665	1.25964	0.629821	−	0.776740i	$-0.283128\pi$
$353$	23.6665	1.25964	0.629821	+	0.776740i	$0.283128\pi$
$354$	−15.6404	−0.831280
$355$	0	0
$356$	−10.0000	−0.529999
$357$	25.0105	1.32369
$358$	1.57292	0.0831316
$359$	31.9724	1.68744	0.843720	−	0.536784i	$-0.180361\pi$
$359$	31.9724	1.68744	0.843720	+	0.536784i	$0.180361\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−11.4088	−0.599633
$363$	−83.5218	−4.38376
$364$	−4.99477	−0.261797
$365$	0	0
$366$	−9.41661	−0.492214
$367$	−1.14585	−0.0598128	−0.0299064	−	0.999553i	$-0.509521\pi$
$367$	−1.14585	−0.0598128	−0.0299064	+	0.999553i	$0.509521\pi$
$368$	−1.79560	−0.0936020
$369$	−5.40100	−0.281165
$370$	0	0
$371$	40.8266	2.11961
$372$	15.4271	0.799857
$373$	−32.8579	−1.70132	−0.850658	−	0.525719i	$-0.823796\pi$
$373$	−32.8579	−1.70132	−0.850658	+	0.525719i	$0.823796\pi$
$374$	12.2917	0.635588
$375$	0	0
$376$	10.8359	0.558818
$377$	−3.12351	−0.160869
$378$	22.3450	1.14930
$379$	−18.2865	−0.939312	−0.469656	−	0.882849i	$-0.655622\pi$
$379$	−18.2865	−0.939312	−0.469656	+	0.882849i	$0.655622\pi$
$380$	0	0
$381$	25.7262	1.31800
$382$	6.35805	0.325306
$383$	−20.8542	−1.06560	−0.532799	−	0.846242i	$-0.678860\pi$
$383$	−20.8542	−1.06560	−0.532799	+	0.846242i	$0.678860\pi$
$384$	2.77733	0.141730
$385$	0	0
$386$	14.4998	0.738022
$387$	16.7550	0.851704
$388$	14.9452	0.758727
$389$	−24.9086	−1.26292	−0.631459	−	0.775409i	$-0.717544\pi$
$389$	−24.9086	−1.26292	−0.631459	+	0.775409i	$0.717544\pi$
$390$	0	0
$391$	3.44385	0.174163
$392$	−15.0455	−0.759913
$393$	−31.9895	−1.61366
$394$	−5.14585	−0.259244
$395$	0	0
$396$	30.2081	1.51802
$397$	24.7445	1.24189	0.620946	−	0.783853i	$-0.286749\pi$
$397$	24.7445	1.24189	0.620946	+	0.783853i	$0.286749\pi$
$398$	−3.87766	−0.194369
$399$	13.0403	0.652831
$400$	0	0
$401$	15.6457	0.781308	0.390654	−	0.920538i	$-0.372249\pi$
$401$	15.6457	0.781308	0.390654	+	0.920538i	$0.372249\pi$
$402$	24.5039	1.22214
$403$	5.90897	0.294347
$404$	10.5364	0.524204
$405$	0	0
$406$	−13.7863	−0.684202
$407$	73.1168	3.62426
$408$	−5.32674	−0.263713
$409$	30.5804	1.51210	0.756052	−	0.654512i	$-0.227126\pi$
$409$	30.5804	1.51210	0.756052	+	0.654512i	$0.227126\pi$
$410$	0	0
$411$	41.9489	2.06919
$412$	16.9817	0.836630
$413$	−26.4413	−1.30109
$414$	8.46362	0.415964
$415$	0	0
$416$	1.06379	0.0521565
$417$	1.94552	0.0952723
$418$	6.40880	0.313465
$419$	1.96345	0.0959210	0.0479605	−	0.998849i	$-0.484728\pi$
$419$	1.96345	0.0959210	0.0479605	+	0.998849i	$0.484728\pi$
$420$	0	0
$421$	−25.5949	−1.24742	−0.623710	−	0.781656i	$-0.714376\pi$
$421$	−25.5949	−1.24742	−0.623710	+	0.781656i	$0.714376\pi$
$422$	−17.1496	−0.834829
$423$	−51.0753	−2.48337
$424$	−8.69527	−0.422279
$425$	0	0
$426$	−3.96345	−0.192030
$427$	−15.9194	−0.770396
$428$	1.79036	0.0865405
$429$	18.9347	0.914177
$430$	0	0
$431$	−15.3540	−0.739575	−0.369788	−	0.929116i	$-0.620570\pi$
$431$	−15.3540	−0.739575	−0.369788	+	0.929116i	$0.620570\pi$
$432$	−4.75905	−0.228970
$433$	−16.6640	−0.800819	−0.400409	−	0.916336i	$-0.631132\pi$
$433$	−16.6640	−0.800819	−0.400409	+	0.916336i	$0.631132\pi$
$434$	26.0806	1.25191
$435$	0	0
$436$	2.41404	0.115611
$437$	1.79560	0.0858951
$438$	35.0310	1.67384
$439$	−19.5987	−0.935393	−0.467697	−	0.883889i	$-0.654916\pi$
$439$	−19.5987	−0.935393	−0.467697	+	0.883889i	$0.654916\pi$
$440$	0	0
$441$	70.9176	3.37703
$442$	−2.04028	−0.0970462
$443$	−13.0183	−0.618517	−0.309258	−	0.950978i	$-0.600081\pi$
$443$	−13.0183	−0.618517	−0.309258	+	0.950978i	$0.600081\pi$
$444$	−31.6860	−1.50375
$445$	0	0
$446$	7.84635	0.371535
$447$	−35.9530	−1.70052
$448$	4.69527	0.221830
$449$	6.77359	0.319666	0.159833	−	0.987144i	$-0.448905\pi$
$449$	6.77359	0.319666	0.159833	+	0.987144i	$0.448905\pi$
$450$	0	0
$451$	−7.34352	−0.345793
$452$	−7.14585	−0.336112
$453$	−15.8538	−0.744877
$454$	6.28646	0.295038
$455$	0	0
$456$	−2.77733	−0.130060
$457$	27.3189	1.27793	0.638963	−	0.769237i	$-0.279364\pi$
$457$	27.3189	1.27793	0.638963	+	0.769237i	$0.279364\pi$
$458$	3.14585	0.146996
$459$	9.12758	0.426039
$460$	0	0
$461$	−27.7993	−1.29474	−0.647372	−	0.762174i	$-0.724132\pi$
$461$	−27.7993	−1.29474	−0.647372	+	0.762174i	$0.724132\pi$
$462$	83.5726	3.88815
$463$	−38.2369	−1.77702	−0.888509	−	0.458859i	$-0.848258\pi$
$463$	−38.2369	−1.77702	−0.888509	+	0.458859i	$0.848258\pi$
$464$	2.93621	0.136310
$465$	0	0
$466$	0.182394	0.00844923
$467$	−23.4711	−1.08611	−0.543056	−	0.839696i	$-0.682733\pi$
$467$	−23.4711	−1.08611	−0.543056	+	0.839696i	$0.682733\pi$
$468$	−5.01420	−0.231782
$469$	41.4256	1.91286
$470$	0	0
$471$	25.7262	1.18540
$472$	5.63148	0.259210
$473$	22.7811	1.04747
$474$	−5.45315	−0.250472
$475$	0	0
$476$	−9.00523	−0.412754
$477$	40.9855	1.87660
$478$	11.5039	0.526176
$479$	−19.6900	−0.899660	−0.449830	−	0.893114i	$-0.648516\pi$
$479$	−19.6900	−0.899660	−0.449830	+	0.893114i	$0.648516\pi$
$480$	0	0
$481$	−12.1365	−0.553379
$482$	0.445349	0.0202851
$483$	23.4151	1.06542
$484$	30.0728	1.36694
$485$	0	0
$486$	−16.8411	−0.763928
$487$	−16.3357	−0.740242	−0.370121	−	0.928984i	$-0.620684\pi$
$487$	−16.3357	−0.740242	−0.370121	+	0.928984i	$0.620684\pi$
$488$	3.39053	0.153482
$489$	11.8904	0.537701
$490$	0	0
$491$	27.1093	1.22343	0.611713	−	0.791080i	$-0.290481\pi$
$491$	27.1093	1.22343	0.611713	+	0.791080i	$0.290481\pi$
$492$	3.18239	0.143473
$493$	−5.63148	−0.253629
$494$	−1.06379	−0.0478621
$495$	0	0
$496$	−5.55465	−0.249411
$497$	−6.70050	−0.300558
$498$	−45.1168	−2.02173
$499$	−4.69003	−0.209955	−0.104977	−	0.994475i	$-0.533477\pi$
$499$	−4.69003	−0.209955	−0.104977	+	0.994475i	$0.533477\pi$
$500$	0	0
$501$	−42.2887	−1.88932
$502$	−13.2630	−0.591955
$503$	−5.19136	−0.231471	−0.115736	−	0.993280i	$-0.536923\pi$
$503$	−5.19136	−0.231471	−0.115736	+	0.993280i	$0.536923\pi$
$504$	−22.1313	−0.985807
$505$	0	0
$506$	11.5076	0.511577
$507$	32.9623	1.46391
$508$	−9.26295	−0.410977
$509$	−4.51811	−0.200262	−0.100131	−	0.994974i	$-0.531926\pi$
$509$	−4.51811	−0.200262	−0.100131	+	0.994974i	$0.531926\pi$
$510$	0	0
$511$	59.2223	2.61984
$512$	−1.00000	−0.0441942
$513$	4.75905	0.210117
$514$	−23.4816	−1.03573
$515$	0	0
$516$	−9.87242	−0.434609
$517$	−69.4450	−3.05419
$518$	−53.5674	−2.35361
$519$	−34.0582	−1.49499
$520$	0	0
$521$	14.4453	0.632862	0.316431	−	0.948615i	$-0.397515\pi$
$521$	14.4453	0.632862	0.316431	+	0.948615i	$0.397515\pi$
$522$	−13.8399	−0.605758
$523$	18.2134	0.796415	0.398208	−	0.917295i	$-0.369632\pi$
$523$	18.2134	0.796415	0.398208	+	0.917295i	$0.369632\pi$
$524$	11.5181	0.503171
$525$	0	0
$526$	27.9269	1.21767
$527$	10.6535	0.464073
$528$	−17.7993	−0.774617
$529$	−19.7758	−0.859819
$530$	0	0
$531$	−26.5442	−1.15192
$532$	−4.69527	−0.203566
$533$	1.21894	0.0527981
$534$	−27.7733	−1.20187
$535$	0	0
$536$	−8.82284	−0.381089
$537$	4.36852	0.188516
$538$	−16.4816	−0.710571
$539$	96.4237	4.15326
$540$	0	0
$541$	37.3905	1.60754	0.803772	−	0.594937i	$-0.202823\pi$
$541$	37.3905	1.60754	0.803772	+	0.594937i	$0.202823\pi$
$542$	1.46736	0.0630284
$543$	−31.6860	−1.35977
$544$	1.91794	0.0822310
$545$	0	0
$546$	−13.8721	−0.593671
$547$	−29.5621	−1.26399	−0.631993	−	0.774974i	$-0.717763\pi$
$547$	−29.5621	−1.26399	−0.631993	+	0.774974i	$0.717763\pi$
$548$	−15.1041	−0.645214
$549$	−15.9814	−0.682069
$550$	0	0
$551$	−2.93621	−0.125087
$552$	−4.98696	−0.212259
$553$	−9.21894	−0.392029
$554$	15.8359	0.672802
$555$	0	0
$556$	−0.700500	−0.0297078
$557$	−14.3723	−0.608972	−0.304486	−	0.952517i	$-0.598485\pi$
$557$	−14.3723	−0.608972	−0.304486	+	0.952517i	$0.598485\pi$
$558$	26.1821	1.10837
$559$	−3.78139	−0.159936
$560$	0	0
$561$	34.1380	1.44131
$562$	6.25515	0.263858
$563$	6.39053	0.269329	0.134664	−	0.990891i	$-0.457004\pi$
$563$	6.39053	0.269329	0.134664	+	0.990891i	$0.457004\pi$
$564$	30.0948	1.26722
$565$	0	0
$566$	−16.7005	−0.701974
$567$	−4.33455	−0.182034
$568$	1.42708	0.0598788
$569$	−44.9086	−1.88267	−0.941334	−	0.337476i	$-0.890427\pi$
$569$	−44.9086	−1.88267	−0.941334	+	0.337476i	$0.890427\pi$
$570$	0	0
$571$	12.4193	0.519730	0.259865	−	0.965645i	$-0.416322\pi$
$571$	12.4193	0.519730	0.259865	+	0.965645i	$0.416322\pi$
$572$	−6.81761	−0.285058
$573$	17.6584	0.737690
$574$	5.38006	0.224559
$575$	0	0
$576$	4.71354	0.196397
$577$	4.20440	0.175032	0.0875158	−	0.996163i	$-0.472107\pi$
$577$	4.20440	0.175032	0.0875158	+	0.996163i	$0.472107\pi$
$578$	13.3215	0.554102
$579$	40.2708	1.67360
$580$	0	0
$581$	−76.2731	−3.16434
$582$	41.5076	1.72055
$583$	55.7262	2.30795
$584$	−12.6132	−0.521938
$585$	0	0
$586$	0.644516	0.0266247
$587$	−24.7915	−1.02326	−0.511628	−	0.859207i	$-0.670957\pi$
$587$	−24.7915	−1.02326	−0.511628	+	0.859207i	$0.670957\pi$
$588$	−41.7863	−1.72324
$589$	5.55465	0.228875
$590$	0	0
$591$	−14.2917	−0.587882
$592$	11.4088	0.468899
$593$	−4.67176	−0.191846	−0.0959231	−	0.995389i	$-0.530580\pi$
$593$	−4.67176	−0.191846	−0.0959231	+	0.995389i	$0.530580\pi$
$594$	30.4998	1.25142
$595$	0	0
$596$	12.9452	0.530255
$597$	−10.7695	−0.440767
$598$	−1.91014	−0.0781113
$599$	39.2369	1.60318	0.801588	−	0.597877i	$-0.203989\pi$
$599$	39.2369	1.60318	0.801588	+	0.597877i	$0.203989\pi$
$600$	0	0
$601$	−42.4267	−1.73062	−0.865311	−	0.501235i	$-0.832879\pi$
$601$	−42.4267	−1.73062	−0.865311	+	0.501235i	$0.832879\pi$
$602$	−16.6900	−0.680235
$603$	41.5868	1.69355
$604$	5.70830	0.232268
$605$	0	0
$606$	29.2630	1.18873
$607$	2.98173	0.121025	0.0605123	−	0.998167i	$-0.480727\pi$
$607$	2.98173	0.121025	0.0605123	+	0.998167i	$0.480727\pi$
$608$	1.00000	0.0405554
$609$	−38.2890	−1.55155
$610$	0	0
$611$	11.5271	0.466336
$612$	−9.04028	−0.365432
$613$	28.9452	1.16908	0.584542	−	0.811363i	$-0.301274\pi$
$613$	28.9452	1.16908	0.584542	+	0.811363i	$0.301274\pi$
$614$	26.6457	1.07533
$615$	0	0
$616$	−30.0910	−1.21240
$617$	15.0365	0.605349	0.302674	−	0.953094i	$-0.402121\pi$
$617$	15.0365	0.605349	0.302674	+	0.953094i	$0.402121\pi$
$618$	47.1638	1.89721
$619$	8.25515	0.331803	0.165901	−	0.986142i	$-0.446947\pi$
$619$	8.25515	0.331803	0.165901	+	0.986142i	$0.446947\pi$
$620$	0	0
$621$	8.54535	0.342913
$622$	−11.5494	−0.463089
$623$	−46.9527	−1.88112
$624$	2.95449	0.118274
$625$	0	0
$626$	−23.0638	−0.921814
$627$	17.7993	0.710837
$628$	−9.26295	−0.369632
$629$	−21.8814	−0.872468
$630$	0	0
$631$	−9.09103	−0.361908	−0.180954	−	0.983492i	$-0.557919\pi$
$631$	−9.09103	−0.361908	−0.180954	+	0.983492i	$0.557919\pi$
$632$	1.96345	0.0781020
$633$	−47.6300	−1.89312
$634$	−13.9232	−0.552960
$635$	0	0
$636$	−24.1496	−0.957593
$637$	−16.0052	−0.634150
$638$	−18.8176	−0.744996
$639$	−6.72658	−0.266099
$640$	0	0
$641$	30.1171	1.18955	0.594777	−	0.803891i	$-0.297240\pi$
$641$	30.1171	1.18955	0.594777	+	0.803891i	$0.297240\pi$
$642$	4.97242	0.196246
$643$	35.3174	1.39278	0.696392	−	0.717662i	$-0.254788\pi$
$643$	35.3174	1.39278	0.696392	+	0.717662i	$0.254788\pi$
$644$	−8.43081	−0.332220
$645$	0	0
$646$	−1.91794	−0.0754603
$647$	−4.12234	−0.162066	−0.0810330	−	0.996711i	$-0.525822\pi$
$647$	−4.12234	−0.162066	−0.0810330	+	0.996711i	$0.525822\pi$
$648$	0.923174	0.0362657
$649$	−36.0910	−1.41670
$650$	0	0
$651$	72.4342	2.83892
$652$	−4.28123	−0.167666
$653$	−8.62741	−0.337617	−0.168808	−	0.985649i	$-0.553992\pi$
$653$	−8.62741	−0.337617	−0.168808	+	0.985649i	$0.553992\pi$
$654$	6.70457	0.262169
$655$	0	0
$656$	−1.14585	−0.0447379
$657$	59.4528	2.31948
$658$	50.8773	1.98340
$659$	−37.3853	−1.45632	−0.728162	−	0.685405i	$-0.759625\pi$
$659$	−37.3853	−1.45632	−0.728162	+	0.685405i	$0.759625\pi$
$660$	0	0
$661$	−12.8997	−0.501739	−0.250869	−	0.968021i	$-0.580716\pi$
$661$	−12.8997	−0.501739	−0.250869	+	0.968021i	$0.580716\pi$
$662$	0.735546	0.0285878
$663$	−5.66652	−0.220070
$664$	16.2447	0.630416
$665$	0	0
$666$	−53.7758	−2.08377
$667$	−5.27226	−0.204143
$668$	15.2264	0.589127
$669$	21.7919	0.842522
$670$	0	0
$671$	−21.7292	−0.838848
$672$	13.0403	0.503040
$673$	−10.4349	−0.402235	−0.201118	−	0.979567i	$-0.564457\pi$
$673$	−10.4349	−0.402235	−0.201118	+	0.979567i	$0.564457\pi$
$674$	−2.28123	−0.0878696
$675$	0	0
$676$	−11.8684	−0.456475
$677$	−12.4401	−0.478112	−0.239056	−	0.971006i	$-0.576838\pi$
$677$	−12.4401	−0.478112	−0.239056	+	0.971006i	$0.576838\pi$
$678$	−19.8463	−0.762194
$679$	70.1716	2.69294
$680$	0	0
$681$	17.4596	0.669052
$682$	35.5987	1.36314
$683$	−17.5364	−0.671011	−0.335505	−	0.942038i	$-0.608907\pi$
$683$	−17.5364	−0.671011	−0.335505	+	0.942038i	$0.608907\pi$
$684$	−4.71354	−0.180227
$685$	0	0
$686$	−37.7758	−1.44229
$687$	8.73705	0.333339
$688$	3.55465	0.135520
$689$	−9.24992	−0.352394
$690$	0	0
$691$	−25.2734	−0.961446	−0.480723	−	0.876872i	$-0.659626\pi$
$691$	−25.2734	−0.961446	−0.480723	+	0.876872i	$0.659626\pi$
$692$	12.2630	0.466168
$693$	141.835	5.38787
$694$	−2.56246	−0.0972695
$695$	0	0
$696$	8.15482	0.309108
$697$	2.19767	0.0832426
$698$	5.67176	0.214679
$699$	0.506567	0.0191601
$700$	0	0
$701$	−16.0545	−0.606370	−0.303185	−	0.952932i	$-0.598050\pi$
$701$	−16.0545	−0.606370	−0.303185	+	0.952932i	$0.598050\pi$
$702$	−5.06262	−0.191076
$703$	−11.4088	−0.430291
$704$	6.40880	0.241541
$705$	0	0
$706$	−23.6665	−0.890701
$707$	49.4711	1.86055
$708$	15.6404	0.587804
$709$	13.5076	0.507290	0.253645	−	0.967297i	$-0.418371\pi$
$709$	13.5076	0.507290	0.253645	+	0.967297i	$0.418371\pi$
$710$	0	0
$711$	−9.25482	−0.347083
$712$	10.0000	0.374766
$713$	9.97392	0.373526
$714$	−25.0105	−0.935993
$715$	0	0
$716$	−1.57292	−0.0587829
$717$	31.9501	1.19320
$718$	−31.9724	−1.19320
$719$	0.803402	0.0299619	0.0149809	−	0.999888i	$-0.495231\pi$
$719$	0.803402	0.0299619	0.0149809	+	0.999888i	$0.495231\pi$
$720$	0	0
$721$	79.7337	2.96944
$722$	−1.00000	−0.0372161
$723$	1.23688	0.0460000
$724$	11.4088	0.424005
$725$	0	0
$726$	83.5218	3.09979
$727$	−51.6860	−1.91693	−0.958463	−	0.285217i	$-0.907934\pi$
$727$	−51.6860	−1.91693	−0.958463	+	0.285217i	$0.907934\pi$
$728$	4.99477	0.185118
$729$	−44.0037	−1.62977
$730$	0	0
$731$	−6.81761	−0.252158
$732$	9.41661	0.348048
$733$	22.3723	0.826338	0.413169	−	0.910654i	$-0.364422\pi$
$733$	22.3723	0.826338	0.413169	+	0.910654i	$0.364422\pi$
$734$	1.14585	0.0422940
$735$	0	0
$736$	1.79560	0.0661866
$737$	56.5438	2.08282
$738$	5.40100	0.198814
$739$	33.4271	1.22963	0.614817	−	0.788669i	$-0.289230\pi$
$739$	33.4271	1.22963	0.614817	+	0.788669i	$0.289230\pi$
$740$	0	0
$741$	−2.95449	−0.108536
$742$	−40.8266	−1.49879
$743$	−14.4998	−0.531947	−0.265974	−	0.963980i	$-0.585693\pi$
$743$	−14.4998	−0.531947	−0.265974	+	0.963980i	$0.585693\pi$
$744$	−15.4271	−0.565584
$745$	0	0
$746$	32.8579	1.20301
$747$	−76.5699	−2.80155
$748$	−12.2917	−0.449429
$749$	8.40623	0.307157
$750$	0	0
$751$	−26.6169	−0.971266	−0.485633	−	0.874163i	$-0.661411\pi$
$751$	−26.6169	−0.971266	−0.485633	+	0.874163i	$0.661411\pi$
$752$	−10.8359	−0.395144
$753$	−36.8355	−1.34236
$754$	3.12351	0.113751
$755$	0	0
$756$	−22.3450	−0.812680
$757$	31.0362	1.12803	0.564015	−	0.825764i	$-0.309256\pi$
$757$	31.0362	1.12803	0.564015	+	0.825764i	$0.309256\pi$
$758$	18.2865	0.664194
$759$	31.9605	1.16009
$760$	0	0
$761$	−27.8083	−1.00805	−0.504025	−	0.863689i	$-0.668148\pi$
$761$	−27.8083	−1.00805	−0.504025	+	0.863689i	$0.668148\pi$
$762$	−25.7262	−0.931963
$763$	11.3345	0.410338
$764$	−6.35805	−0.230026
$765$	0	0
$766$	20.8542	0.753491
$767$	5.99070	0.216312
$768$	−2.77733	−0.100218
$769$	−19.2279	−0.693376	−0.346688	−	0.937980i	$-0.612694\pi$
$769$	−19.2279	−0.693376	−0.346688	+	0.937980i	$0.612694\pi$
$770$	0	0
$771$	−65.2159	−2.34869
$772$	−14.4998	−0.521860
$773$	−6.00373	−0.215939	−0.107970	−	0.994154i	$-0.534435\pi$
$773$	−6.00373	−0.215939	−0.107970	+	0.994154i	$0.534435\pi$
$774$	−16.7550	−0.602245
$775$	0	0
$776$	−14.9452	−0.536501
$777$	−148.774	−5.33724
$778$	24.9086	0.893018
$779$	1.14585	0.0410543
$780$	0	0
$781$	−9.14585	−0.327264
$782$	−3.44385	−0.123152
$783$	−13.9736	−0.499375
$784$	15.0455	0.537340
$785$	0	0
$786$	31.9895	1.14103
$787$	−22.2797	−0.794187	−0.397093	−	0.917778i	$-0.629981\pi$
$787$	−22.2797	−0.794187	−0.397093	+	0.917778i	$0.629981\pi$
$788$	5.14585	0.183313
$789$	77.5621	2.76128
$790$	0	0
$791$	−33.5517	−1.19296
$792$	−30.2081	−1.07340
$793$	3.60680	0.128081
$794$	−24.7445	−0.878150
$795$	0	0
$796$	3.87766	0.137440
$797$	−26.6259	−0.943138	−0.471569	−	0.881829i	$-0.656312\pi$
$797$	−26.6259	−0.943138	−0.471569	+	0.881829i	$0.656312\pi$
$798$	−13.0403	−0.461621
$799$	20.7826	0.735234
$800$	0	0
$801$	−47.1354	−1.66545
$802$	−15.6457	−0.552468
$803$	80.8355	2.85262
$804$	−24.5039	−0.864186
$805$	0	0
$806$	−5.90897	−0.208135
$807$	−45.7747	−1.61134
$808$	−10.5364	−0.370669
$809$	0.651250	0.0228967	0.0114484	−	0.999934i	$-0.496356\pi$
$809$	0.651250	0.0228967	0.0114484	+	0.999934i	$0.496356\pi$
$810$	0	0
$811$	−13.0780	−0.459230	−0.229615	−	0.973281i	$-0.573747\pi$
$811$	−13.0780	−0.459230	−0.229615	+	0.973281i	$0.573747\pi$
$812$	13.7863	0.483804
$813$	4.07533	0.142928
$814$	−73.1168	−2.56274
$815$	0	0
$816$	5.32674	0.186473
$817$	−3.55465	−0.124362
$818$	−30.5804	−1.06922
$819$	−23.5430	−0.822660
$820$	0	0
$821$	14.6640	0.511776	0.255888	−	0.966706i	$-0.417632\pi$
$821$	14.6640	0.511776	0.255888	+	0.966706i	$0.417632\pi$
$822$	−41.9489	−1.46314
$823$	18.2850	0.637374	0.318687	−	0.947860i	$-0.396758\pi$
$823$	18.2850	0.637374	0.318687	+	0.947860i	$0.396758\pi$
$824$	−16.9817	−0.591587
$825$	0	0
$826$	26.4413	0.920010
$827$	−40.1910	−1.39758	−0.698790	−	0.715327i	$-0.746278\pi$
$827$	−40.1910	−1.39758	−0.698790	+	0.715327i	$0.746278\pi$
$828$	−8.46362	−0.294131
$829$	28.3760	0.985539	0.492769	−	0.870160i	$-0.335985\pi$
$829$	28.3760	0.985539	0.492769	+	0.870160i	$0.335985\pi$
$830$	0	0
$831$	43.9814	1.52570
$832$	−1.06379	−0.0368802
$833$	−28.8564	−0.999815
$834$	−1.94552	−0.0673677
$835$	0	0
$836$	−6.40880	−0.221653
$837$	26.4349	0.913723
$838$	−1.96345	−0.0678264
$839$	6.93471	0.239413	0.119706	−	0.992809i	$-0.461805\pi$
$839$	6.93471	0.239413	0.119706	+	0.992809i	$0.461805\pi$
$840$	0	0
$841$	−20.3787	−0.702712
$842$	25.5949	0.882060
$843$	17.3726	0.598344
$844$	17.1496	0.590313
$845$	0	0
$846$	51.0753	1.75601
$847$	141.200	4.85167
$848$	8.69527	0.298597
$849$	−46.3827	−1.59185
$850$	0	0
$851$	−20.4856	−0.702238
$852$	3.96345	0.135786
$853$	−21.9739	−0.752373	−0.376186	−	0.926544i	$-0.622765\pi$
$853$	−21.9739	−0.752373	−0.376186	+	0.926544i	$0.622765\pi$
$854$	15.9194	0.544752
$855$	0	0
$856$	−1.79036	−0.0611934
$857$	−13.6091	−0.464879	−0.232440	−	0.972611i	$-0.574671\pi$
$857$	−13.6091	−0.464879	−0.232440	+	0.972611i	$0.574671\pi$
$858$	−18.9347	−0.646420
$859$	5.17192	0.176464	0.0882319	−	0.996100i	$-0.471878\pi$
$859$	5.17192	0.176464	0.0882319	+	0.996100i	$0.471878\pi$
$860$	0	0
$861$	14.9422	0.509228
$862$	15.3540	0.522959
$863$	−15.9635	−0.543402	−0.271701	−	0.962382i	$-0.587586\pi$
$863$	−15.9635	−0.543402	−0.271701	+	0.962382i	$0.587586\pi$
$864$	4.75905	0.161906
$865$	0	0
$866$	16.6640	0.566264
$867$	36.9982	1.25652
$868$	−26.0806	−0.885232
$869$	−12.5834	−0.426862
$870$	0	0
$871$	−9.38563	−0.318020
$872$	−2.41404	−0.0817496
$873$	70.4447	2.38419
$874$	−1.79560	−0.0607370
$875$	0	0
$876$	−35.0310	−1.18359
$877$	15.8866	0.536453	0.268227	−	0.963356i	$-0.413562\pi$
$877$	15.8866	0.536453	0.268227	+	0.963356i	$0.413562\pi$
$878$	19.5987	0.661423
$879$	1.79003	0.0603762
$880$	0	0
$881$	−16.1458	−0.543967	−0.271984	−	0.962302i	$-0.587680\pi$
$881$	−16.1458	−0.543967	−0.271984	+	0.962302i	$0.587680\pi$
$882$	−70.9176	−2.38792
$883$	−38.2887	−1.28852	−0.644259	−	0.764808i	$-0.722834\pi$
$883$	−38.2887	−1.28852	−0.644259	+	0.764808i	$0.722834\pi$
$884$	2.04028	0.0686221
$885$	0	0
$886$	13.0183	0.437357
$887$	−19.2809	−0.647389	−0.323695	−	0.946162i	$-0.604925\pi$
$887$	−19.2809	−0.647389	−0.323695	+	0.946162i	$0.604925\pi$
$888$	31.6860	1.06331
$889$	−43.4920	−1.45868
$890$	0	0
$891$	−5.91644	−0.198208
$892$	−7.84635	−0.262715
$893$	10.8359	0.362609
$894$	35.9530	1.20245
$895$	0	0
$896$	−4.69527	−0.156858
$897$	−5.30507	−0.177131
$898$	−6.77359	−0.226038
$899$	−16.3096	−0.543957
$900$	0	0
$901$	−16.6770	−0.555591
$902$	7.34352	0.244512
$903$	−46.3537	−1.54255
$904$	7.14585	0.237667
$905$	0	0
$906$	15.8538	0.526708
$907$	−43.0205	−1.42847	−0.714236	−	0.699905i	$-0.753226\pi$
$907$	−43.0205	−1.42847	−0.714236	+	0.699905i	$0.753226\pi$
$908$	−6.28646	−0.208624
$909$	49.6636	1.64724
$910$	0	0
$911$	−25.7733	−0.853906	−0.426953	−	0.904274i	$-0.640413\pi$
$911$	−25.7733	−0.853906	−0.426953	+	0.904274i	$0.640413\pi$
$912$	2.77733	0.0919664
$913$	−104.109	−3.44550
$914$	−27.3189	−0.903630
$915$	0	0
$916$	−3.14585	−0.103942
$917$	54.0806	1.78590
$918$	−9.12758	−0.301255
$919$	−29.5897	−0.976074	−0.488037	−	0.872823i	$-0.662287\pi$
$919$	−29.5897	−0.976074	−0.488037	+	0.872823i	$0.662287\pi$
$920$	0	0
$921$	74.0037	2.43851
$922$	27.7993	0.915522
$923$	1.51811	0.0499691
$924$	−83.5726	−2.74934
$925$	0	0
$926$	38.2369	1.25654
$927$	80.0440	2.62899
$928$	−2.93621	−0.0963859
$929$	−1.42334	−0.0466983	−0.0233491	−	0.999727i	$-0.507433\pi$
$929$	−1.42334	−0.0466983	−0.0233491	+	0.999727i	$0.507433\pi$
$930$	0	0
$931$	−15.0455	−0.493097
$932$	−0.182394	−0.00597451
$933$	−32.0765	−1.05014
$934$	23.4711	0.767998
$935$	0	0
$936$	5.01420	0.163894
$937$	−28.2276	−0.922155	−0.461077	−	0.887360i	$-0.652537\pi$
$937$	−28.2276	−0.922155	−0.461077	+	0.887360i	$0.652537\pi$
$938$	−41.4256	−1.35259
$939$	−64.0556	−2.09038
$940$	0	0
$941$	−15.8672	−0.517256	−0.258628	−	0.965977i	$-0.583270\pi$
$941$	−15.8672	−0.517256	−0.258628	+	0.965977i	$0.583270\pi$
$942$	−25.7262	−0.838206
$943$	2.05748	0.0670009
$944$	−5.63148	−0.183289
$945$	0	0
$946$	−22.7811	−0.740676
$947$	−43.6718	−1.41914	−0.709571	−	0.704634i	$-0.751111\pi$
$947$	−43.6718	−1.41914	−0.709571	+	0.704634i	$0.751111\pi$
$948$	5.45315	0.177110
$949$	−13.4178	−0.435559
$950$	0	0
$951$	−38.6692	−1.25393
$952$	9.00523	0.291861
$953$	−16.0261	−0.519136	−0.259568	−	0.965725i	$-0.583580\pi$
$953$	−16.0261	−0.519136	−0.259568	+	0.965725i	$0.583580\pi$
$954$	−40.9855	−1.32695
$955$	0	0
$956$	−11.5039	−0.372063
$957$	−52.2626	−1.68941
$958$	19.6900	0.636156
$959$	−70.9176	−2.29005
$960$	0	0
$961$	−0.145848	−0.00470478
$962$	12.1365	0.391298
$963$	8.43895	0.271941
$964$	−0.445349	−0.0143437
$965$	0	0
$966$	−23.4151	−0.753369
$967$	11.5987	0.372988	0.186494	−	0.982456i	$-0.440288\pi$
$967$	11.5987	0.372988	0.186494	+	0.982456i	$0.440288\pi$
$968$	−30.0728	−0.966575
$969$	−5.32674	−0.171120
$970$	0	0
$971$	−27.0362	−0.867633	−0.433817	−	0.901001i	$-0.642833\pi$
$971$	−27.0362	−0.867633	−0.433817	+	0.901001i	$0.642833\pi$
$972$	16.8411	0.540179
$973$	−3.28903	−0.105442
$974$	16.3357	0.523430
$975$	0	0
$976$	−3.39053	−0.108528
$977$	−14.1537	−0.452815	−0.226408	−	0.974033i	$-0.572698\pi$
$977$	−14.1537	−0.452815	−0.226408	+	0.974033i	$0.572698\pi$
$978$	−11.8904	−0.380212
$979$	−64.0880	−2.04826
$980$	0	0
$981$	11.3787	0.363293
$982$	−27.1093	−0.865093
$983$	32.8542	1.04788	0.523942	−	0.851754i	$-0.324461\pi$
$983$	32.8542	1.04788	0.523942	+	0.851754i	$0.324461\pi$
$984$	−3.18239	−0.101451
$985$	0	0
$986$	5.63148	0.179343
$987$	141.303	4.49772
$988$	1.06379	0.0338436
$989$	−6.38273	−0.202959
$990$	0	0
$991$	47.9709	1.52385	0.761923	−	0.647667i	$-0.224255\pi$
$991$	47.9709	1.52385	0.761923	+	0.647667i	$0.224255\pi$
$992$	5.55465	0.176360
$993$	2.04285	0.0648279
$994$	6.70050	0.212527
$995$	0	0
$996$	45.1168	1.42958
$997$	−44.1716	−1.39893	−0.699464	−	0.714668i	$-0.746578\pi$
$997$	−44.1716	−1.39893	−0.699464	+	0.714668i	$0.746578\pi$
$998$	4.69003	0.148460
$999$	−54.2951	−1.71782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.a.k.1.1	✓	3
3.2	odd	2		8550.2.a.co.1.3		3
4.3	odd	2		7600.2.a.cb.1.3		3
5.2	odd	4		950.2.b.g.799.3		6
5.3	odd	4		950.2.b.g.799.4		6
5.4	even	2		950.2.a.m.1.3	yes	3
15.14	odd	2		8550.2.a.cj.1.1		3
20.19	odd	2		7600.2.a.bm.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.k.1.1	✓	3	1.1	even	1	trivial
950.2.a.m.1.3	yes	3	5.4	even	2
950.2.b.g.799.3		6	5.2	odd	4
950.2.b.g.799.4		6	5.3	odd	4
7600.2.a.bm.1.1		3	20.19	odd	2
7600.2.a.cb.1.3		3	4.3	odd	2
8550.2.a.cj.1.1		3	15.14	odd	2
8550.2.a.co.1.3		3	3.2	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.77733 q^{3} +1.00000 q^{4} +2.77733 q^{6} +4.69527 q^{7} -1.00000 q^{8} +4.71354 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.77733 q^{3} +1.00000 q^{4} +2.77733 q^{6} +4.69527 q^{7} -1.00000 q^{8} +4.71354 q^{9} +6.40880 q^{11} -2.77733 q^{12} -1.06379 q^{13} -4.69527 q^{14} +1.00000 q^{16} -1.91794 q^{17} -4.71354 q^{18} -1.00000 q^{19} -13.0403 q^{21} -6.40880 q^{22} -1.79560 q^{23} +2.77733 q^{24} +1.06379 q^{26} -4.75905 q^{27} +4.69527 q^{28} +2.93621 q^{29} -5.55465 q^{31} -1.00000 q^{32} -17.7993 q^{33} +1.91794 q^{34} +4.71354 q^{36} +11.4088 q^{37} +1.00000 q^{38} +2.95449 q^{39} -1.14585 q^{41} +13.0403 q^{42} +3.55465 q^{43} +6.40880 q^{44} +1.79560 q^{46} -10.8359 q^{47} -2.77733 q^{48} +15.0455 q^{49} +5.32674 q^{51} -1.06379 q^{52} +8.69527 q^{53} +4.75905 q^{54} -4.69527 q^{56} +2.77733 q^{57} -2.93621 q^{58} -5.63148 q^{59} -3.39053 q^{61} +5.55465 q^{62} +22.1313 q^{63} +1.00000 q^{64} +17.7993 q^{66} +8.82284 q^{67} -1.91794 q^{68} +4.98696 q^{69} -1.42708 q^{71} -4.71354 q^{72} +12.6132 q^{73} -11.4088 q^{74} -1.00000 q^{76} +30.0910 q^{77} -2.95449 q^{78} -1.96345 q^{79} -0.923174 q^{81} +1.14585 q^{82} -16.2447 q^{83} -13.0403 q^{84} -3.55465 q^{86} -8.15482 q^{87} -6.40880 q^{88} -10.0000 q^{89} -4.99477 q^{91} -1.79560 q^{92} +15.4271 q^{93} +10.8359 q^{94} +2.77733 q^{96} +14.9452 q^{97} -15.0455 q^{98} +30.2081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 2 q^{7} - 3 q^{8} + 13 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 2 * q^7 - 3 * q^8 + 13 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} + 2 q^{6} - 2 q^{7} - 3 q^{8} + 13 q^{9} + 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} + 3 q^{16} + 4 q^{17} - 13 q^{18} - 3 q^{19} - 11 q^{21} - 2 q^{22} - 14 q^{23} + 2 q^{24} - 2 q^{26} + 7 q^{27} - 2 q^{28} + 14 q^{29} - 4 q^{31} - 3 q^{32} - 4 q^{33} - 4 q^{34} + 13 q^{36} + 17 q^{37} + 3 q^{38} + 29 q^{39} - 8 q^{41} + 11 q^{42} - 2 q^{43} + 2 q^{44} + 14 q^{46} - 13 q^{47} - 2 q^{48} + 25 q^{49} - 11 q^{51} + 2 q^{52} + 10 q^{53} - 7 q^{54} + 2 q^{56} + 2 q^{57} - 14 q^{58} - 6 q^{59} + 22 q^{61} + 4 q^{62} - 2 q^{63} + 3 q^{64} + 4 q^{66} + 4 q^{68} + 8 q^{69} - 2 q^{71} - 13 q^{72} + 12 q^{73} - 17 q^{74} - 3 q^{76} + 50 q^{77} - 29 q^{78} + 24 q^{79} - q^{81} + 8 q^{82} - 12 q^{83} - 11 q^{84} + 2 q^{86} + 21 q^{87} - 2 q^{88} - 30 q^{89} - 7 q^{91} - 14 q^{92} + 44 q^{93} + 13 q^{94} + 2 q^{96} - 25 q^{98} + 24 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 + 2 * q^6 - 2 * q^7 - 3 * q^8 + 13 * q^9 + 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 + 3 * q^16 + 4 * q^17 - 13 * q^18 - 3 * q^19 - 11 * q^21 - 2 * q^22 - 14 * q^23 + 2 * q^24 - 2 * q^26 + 7 * q^27 - 2 * q^28 + 14 * q^29 - 4 * q^31 - 3 * q^32 - 4 * q^33 - 4 * q^34 + 13 * q^36 + 17 * q^37 + 3 * q^38 + 29 * q^39 - 8 * q^41 + 11 * q^42 - 2 * q^43 + 2 * q^44 + 14 * q^46 - 13 * q^47 - 2 * q^48 + 25 * q^49 - 11 * q^51 + 2 * q^52 + 10 * q^53 - 7 * q^54 + 2 * q^56 + 2 * q^57 - 14 * q^58 - 6 * q^59 + 22 * q^61 + 4 * q^62 - 2 * q^63 + 3 * q^64 + 4 * q^66 + 4 * q^68 + 8 * q^69 - 2 * q^71 - 13 * q^72 + 12 * q^73 - 17 * q^74 - 3 * q^76 + 50 * q^77 - 29 * q^78 + 24 * q^79 - q^81 + 8 * q^82 - 12 * q^83 - 11 * q^84 + 2 * q^86 + 21 * q^87 - 2 * q^88 - 30 * q^89 - 7 * q^91 - 14 * q^92 + 44 * q^93 + 13 * q^94 + 2 * q^96 - 25 * q^98 + 24 * q^99

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