LMFDB - Embedded newform 950.2.b.g.799.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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([1, 0]))

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

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.4227136.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 22x^{2} + 9 $ x^6 + 9x^4 + 22x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.3
Root			$-0.713538i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.g.799.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +2.77733i q^{3} -1.00000 q^{4} +2.77733 q^{6} +4.69527i q^{7} +1.00000i q^{8} -4.71354 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +2.77733i q^{3} -1.00000 q^{4} +2.77733 q^{6} +4.69527i q^{7} +1.00000i q^{8} -4.71354 q^{9} +6.40880 q^{11} -2.77733i q^{12} +1.06379i q^{13} +4.69527 q^{14} +1.00000 q^{16} -1.91794i q^{17} +4.71354i q^{18} +1.00000 q^{19} -13.0403 q^{21} -6.40880i q^{22} +1.79560i q^{23} -2.77733 q^{24} +1.06379 q^{26} -4.75905i q^{27} -4.69527i q^{28} -2.93621 q^{29} -5.55465 q^{31} -1.00000i q^{32} +17.7993i q^{33} -1.91794 q^{34} +4.71354 q^{36} +11.4088i q^{37} -1.00000i q^{38} -2.95449 q^{39} -1.14585 q^{41} +13.0403i q^{42} -3.55465i q^{43} -6.40880 q^{44} +1.79560 q^{46} -10.8359i q^{47} +2.77733i q^{48} -15.0455 q^{49} +5.32674 q^{51} -1.06379i q^{52} -8.69527i q^{53} -4.75905 q^{54} -4.69527 q^{56} +2.77733i q^{57} +2.93621i q^{58} +5.63148 q^{59} -3.39053 q^{61} +5.55465i q^{62} -22.1313i q^{63} -1.00000 q^{64} +17.7993 q^{66} +8.82284i q^{67} +1.91794i q^{68} -4.98696 q^{69} -1.42708 q^{71} -4.71354i q^{72} -12.6132i q^{73} +11.4088 q^{74} -1.00000 q^{76} +30.0910i q^{77} +2.95449i q^{78} +1.96345 q^{79} -0.923174 q^{81} +1.14585i q^{82} +16.2447i q^{83} +13.0403 q^{84} -3.55465 q^{86} -8.15482i q^{87} +6.40880i q^{88} +10.0000 q^{89} -4.99477 q^{91} -1.79560i q^{92} -15.4271i q^{93} -10.8359 q^{94} +2.77733 q^{96} +14.9452i q^{97} +15.0455i q^{98} -30.2081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9	$ 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} + 6 q^{19} - 22 q^{21} - 4 q^{24} - 4 q^{26} - 28 q^{29} - 8 q^{31} + 8 q^{34} + 26 q^{36} - 58 q^{39} - 16 q^{41} - 4 q^{44} + 28 q^{46} - 50 q^{49} - 22 q^{51} + 14 q^{54} + 4 q^{56} + 12 q^{59} + 44 q^{61} - 6 q^{64} + 8 q^{66} - 16 q^{69} - 4 q^{71} + 34 q^{74} - 6 q^{76} - 48 q^{79} - 2 q^{81} + 22 q^{84} + 4 q^{86} + 60 q^{89} - 14 q^{91} - 26 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 + 6 * q^19 - 22 * q^21 - 4 * q^24 - 4 * q^26 - 28 * q^29 - 8 * q^31 + 8 * q^34 + 26 * q^36 - 58 * q^39 - 16 * q^41 - 4 * q^44 + 28 * q^46 - 50 * q^49 - 22 * q^51 + 14 * q^54 + 4 * q^56 + 12 * q^59 + 44 * q^61 - 6 * q^64 + 8 * q^66 - 16 * q^69 - 4 * q^71 + 34 * q^74 - 6 * q^76 - 48 * q^79 - 2 * q^81 + 22 * q^84 + 4 * q^86 + 60 * q^89 - 14 * q^91 - 26 * q^94 + 4 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	2.77733i	1.60349i	0.597666	+	0.801745i	$0.296095\pi$
$3$	2.77733i	1.60349i	−0.597666	+	0.801745i	$0.703905\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.77733	1.13384
$7$	4.69527i	1.77464i	0.461151	+	0.887322i	$0.347437\pi$
$7$	4.69527i	1.77464i	−0.461151	+	0.887322i	$0.652563\pi$
$8$	1.00000i	0.353553i
$9$	−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	$0.0830406\pi$
$12$	− 2.77733i	− 0.801745i
$13$	1.06379i	0.295042i	0.989059	+	0.147521i	$0.0471293\pi$
$13$	1.06379i	0.295042i	−0.989059	+	0.147521i	$0.952871\pi$
$14$	4.69527	1.25486
$15$	0	0
$16$	1.00000	0.250000
$17$	− 1.91794i	− 0.465169i	−0.972576	−	0.232584i	$-0.925282\pi$
$17$	− 1.91794i	− 0.465169i	0.972576	−	0.232584i	$-0.0747182\pi$
$18$	4.71354i	1.11099i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−13.0403	−2.84562
$22$	− 6.40880i	− 1.36636i
$23$	1.79560i	0.374408i	0.982321	+	0.187204i	$0.0599426\pi$
$23$	1.79560i	0.374408i	−0.982321	+	0.187204i	$0.940057\pi$
$24$	−2.77733	−0.566919
$25$	0	0
$26$	1.06379	0.208626
$27$	− 4.75905i	− 0.915880i
$28$	− 4.69527i	− 0.887322i
$29$	−2.93621	−0.545241	−0.272620	−	0.962122i	$-0.587890\pi$
$29$	−2.93621	−0.545241	−0.272620	+	0.962122i	$0.587890\pi$
$30$	0	0
$31$	−5.55465	−0.997645	−0.498822	−	0.866704i	$-0.666234\pi$
$31$	−5.55465	−0.997645	−0.498822	+	0.866704i	$0.666234\pi$
$32$	− 1.00000i	− 0.176777i
$33$	17.7993i	3.09847i
$34$	−1.91794	−0.328924
$35$	0	0
$36$	4.71354	0.785590
$37$	11.4088i	1.87560i	0.347182	+	0.937798i	$0.387139\pi$
$37$	11.4088i	1.87560i	−0.347182	+	0.937798i	$0.612861\pi$
$38$	− 1.00000i	− 0.162221i
$39$	−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	$0.528519\pi$
$42$	13.0403i	2.01216i
$43$	− 3.55465i	− 0.542079i	−0.962568	−	0.271040i	$-0.912633\pi$
$43$	− 3.55465i	− 0.542079i	0.962568	−	0.271040i	$-0.0873674\pi$
$44$	−6.40880	−0.966163
$45$	0	0
$46$	1.79560	0.264747
$47$	− 10.8359i	− 1.58058i	−0.612736	−	0.790288i	$-0.709931\pi$
$47$	− 10.8359i	− 1.58058i	0.612736	−	0.790288i	$-0.290069\pi$
$48$	2.77733i	0.400872i
$49$	−15.0455	−2.14936
$50$	0	0
$51$	5.32674	0.745893
$52$	− 1.06379i	− 0.147521i
$53$	− 8.69527i	− 1.19439i	−0.802097	−	0.597193i	$-0.796283\pi$
$53$	− 8.69527i	− 1.19439i	0.802097	−	0.597193i	$-0.203717\pi$
$54$	−4.75905	−0.647625
$55$	0	0
$56$	−4.69527	−0.627431
$57$	2.77733i	0.367866i
$58$	2.93621i	0.385544i
$59$	5.63148	0.733156	0.366578	−	0.930387i	$-0.380529\pi$
$59$	5.63148	0.733156	0.366578	+	0.930387i	$0.380529\pi$
$60$	0	0
$61$	−3.39053	−0.434113	−0.217056	−	0.976159i	$-0.569646\pi$
$61$	−3.39053	−0.434113	−0.217056	+	0.976159i	$0.569646\pi$
$62$	5.55465i	0.705441i
$63$	− 22.1313i	− 2.78828i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	17.7993	2.19095
$67$	8.82284i	1.07788i	0.842344	+	0.538941i	$0.181175\pi$
$67$	8.82284i	1.07788i	−0.842344	+	0.538941i	$0.818825\pi$
$68$	1.91794i	0.232584i
$69$	−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	$0.526987\pi$
$72$	− 4.71354i	− 0.555496i
$73$	− 12.6132i	− 1.47626i	−0.674656	−	0.738132i	$-0.735708\pi$
$73$	− 12.6132i	− 1.47626i	0.674656	−	0.738132i	$-0.264292\pi$
$74$	11.4088	1.32625
$75$	0	0
$76$	−1.00000	−0.114708
$77$	30.0910i	3.42919i
$78$	2.95449i	0.334530i
$79$	1.96345	0.220906	0.110453	−	0.993881i	$-0.464770\pi$
$79$	1.96345	0.220906	0.110453	+	0.993881i	$0.464770\pi$
$80$	0	0
$81$	−0.923174	−0.102575
$82$	1.14585i	0.126538i
$83$	16.2447i	1.78309i	0.452937	+	0.891543i	$0.350376\pi$
$83$	16.2447i	1.78309i	−0.452937	+	0.891543i	$0.649624\pi$
$84$	13.0403	1.42281
$85$	0	0
$86$	−3.55465	−0.383308
$87$	− 8.15482i	− 0.874288i
$88$	6.40880i	0.683181i
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	−4.99477	−0.523594
$92$	− 1.79560i	− 0.187204i
$93$	− 15.4271i	− 1.59971i
$94$	−10.8359	−1.11764
$95$	0	0
$96$	2.77733	0.283460
$97$	14.9452i	1.51745i	0.651409	+	0.758727i	$0.274178\pi$
$97$	14.9452i	1.51745i	−0.651409	+	0.758727i	$0.725822\pi$
$98$	15.0455i	1.51983i
$99$	−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	$0.324363\pi$
$102$	− 5.32674i	− 0.527426i
$103$	− 16.9817i	− 1.67326i	−0.547769	−	0.836630i	$-0.684523\pi$
$103$	− 16.9817i	− 1.67326i	0.547769	−	0.836630i	$-0.315477\pi$
$104$	−1.06379	−0.104313
$105$	0	0
$106$	−8.69527	−0.844559
$107$	1.79036i	0.173081i	0.996248	+	0.0865405i	$0.0275812\pi$
$107$	1.79036i	0.173081i	−0.996248	+	0.0865405i	$0.972419\pi$
$108$	4.75905i	0.457940i
$109$	−2.41404	−0.231223	−0.115611	−	0.993295i	$-0.536883\pi$
$109$	−2.41404	−0.231223	−0.115611	+	0.993295i	$0.536883\pi$
$110$	0	0
$111$	−31.6860	−3.00750
$112$	4.69527i	0.443661i
$113$	7.14585i	0.672225i	0.941822	+	0.336112i	$0.109112\pi$
$113$	7.14585i	0.672225i	−0.941822	+	0.336112i	$0.890888\pi$
$114$	2.77733	0.260120
$115$	0	0
$116$	2.93621	0.272620
$117$	− 5.01420i	− 0.463563i
$118$	− 5.63148i	− 0.518420i
$119$	9.00523	0.825508
$120$	0	0
$121$	30.0728	2.73389
$122$	3.39053i	0.306964i
$123$	− 3.18239i	− 0.286947i
$124$	5.55465	0.498822
$125$	0	0
$126$	−22.1313	−1.97161
$127$	− 9.26295i	− 0.821954i	−0.911646	−	0.410977i	$-0.865188\pi$
$127$	− 9.26295i	− 0.821954i	0.911646	−	0.410977i	$-0.134812\pi$
$128$	1.00000i	0.0883883i
$129$	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	$0.332167\pi$
$132$	− 17.7993i	− 1.54923i
$133$	4.69527i	0.407131i
$134$	8.82284	0.762177
$135$	0	0
$136$	1.91794	0.164462
$137$	− 15.1041i	− 1.29043i	−0.764002	−	0.645214i	$-0.776768\pi$
$137$	− 15.1041i	− 1.29043i	0.764002	−	0.645214i	$-0.223232\pi$
$138$	4.98696i	0.424518i
$139$	0.700500	0.0594156	0.0297078	−	0.999559i	$-0.490542\pi$
$139$	0.700500	0.0594156	0.0297078	+	0.999559i	$0.490542\pi$
$140$	0	0
$141$	30.0948	2.53444
$142$	1.42708i	0.119758i
$143$	6.81761i	0.570117i
$144$	−4.71354	−0.392795
$145$	0	0
$146$	−12.6132	−1.04388
$147$	− 41.7863i	− 3.44648i
$148$	− 11.4088i	− 0.937798i
$149$	−12.9452	−1.06051	−0.530255	−	0.847838i	$-0.677904\pi$
$149$	−12.9452	−1.06051	−0.530255	+	0.847838i	$0.677904\pi$
$150$	0	0
$151$	5.70830	0.464535	0.232268	−	0.972652i	$-0.425385\pi$
$151$	5.70830	0.464535	0.232268	+	0.972652i	$0.425385\pi$
$152$	1.00000i	0.0811107i
$153$	9.04028i	0.730863i
$154$	30.0910	2.42480
$155$	0	0
$156$	2.95449	0.236548
$157$	− 9.26295i	− 0.739264i	−0.929178	−	0.369632i	$-0.879484\pi$
$157$	− 9.26295i	− 0.739264i	0.929178	−	0.369632i	$-0.120516\pi$
$158$	− 1.96345i	− 0.156204i
$159$	24.1496	1.91519
$160$	0	0
$161$	−8.43081	−0.664441
$162$	0.923174i	0.0725314i
$163$	4.28123i	0.335332i	0.985844	+	0.167666i	$0.0536230\pi$
$163$	4.28123i	0.335332i	−0.985844	+	0.167666i	$0.946377\pi$
$164$	1.14585	0.0894757
$165$	0	0
$166$	16.2447	1.26083
$167$	15.2264i	1.17825i	0.808040	+	0.589127i	$0.200528\pi$
$167$	15.2264i	1.17825i	−0.808040	+	0.589127i	$0.799472\pi$
$168$	− 13.0403i	− 1.00608i
$169$	11.8684	0.912950
$170$	0	0
$171$	−4.71354	−0.360453
$172$	3.55465i	0.271040i
$173$	− 12.2630i	− 0.932335i	−0.884696	−	0.466168i	$-0.845634\pi$
$173$	− 12.2630i	− 0.932335i	0.884696	−	0.466168i	$-0.154366\pi$
$174$	−8.15482	−0.618215
$175$	0	0
$176$	6.40880	0.483082
$177$	15.6404i	1.17561i
$178$	− 10.0000i	− 0.749532i
$179$	1.57292	0.117566	0.0587829	−	0.998271i	$-0.481278\pi$
$179$	1.57292	0.117566	0.0587829	+	0.998271i	$0.481278\pi$
$180$	0	0
$181$	11.4088	0.848010	0.424005	−	0.905660i	$-0.360624\pi$
$181$	11.4088	0.848010	0.424005	+	0.905660i	$0.360624\pi$
$182$	4.99477i	0.370237i
$183$	− 9.41661i	− 0.696096i
$184$	−1.79560	−0.132373
$185$	0	0
$186$	−15.4271	−1.13117
$187$	− 12.2917i	− 0.898858i
$188$	10.8359i	0.790288i
$189$	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	$0.573881\pi$
$192$	− 2.77733i	− 0.200436i
$193$	14.4998i	1.04372i	0.853031	+	0.521860i	$0.174762\pi$
$193$	14.4998i	1.04372i	−0.853031	+	0.521860i	$0.825238\pi$
$194$	14.9452	1.07300
$195$	0	0
$196$	15.0455	1.07468
$197$	5.14585i	0.366627i	0.983055	+	0.183313i	$0.0586823\pi$
$197$	5.14585i	0.366627i	−0.983055	+	0.183313i	$0.941318\pi$
$198$	30.2081i	2.14680i
$199$	−3.87766	−0.274880	−0.137440	−	0.990510i	$-0.543887\pi$
$199$	−3.87766	−0.274880	−0.137440	+	0.990510i	$0.543887\pi$
$200$	0	0
$201$	−24.5039	−1.72837
$202$	− 10.5364i	− 0.741337i
$203$	− 13.7863i	− 0.967608i
$204$	−5.32674	−0.372947
$205$	0	0
$206$	−16.9817	−1.18317
$207$	− 8.46362i	− 0.588262i
$208$	1.06379i	0.0737604i
$209$	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	$0.299004\pi$
$212$	8.69527i	0.597193i
$213$	− 3.96345i	− 0.271571i
$214$	1.79036	0.122387
$215$	0	0
$216$	4.75905	0.323813
$217$	− 26.0806i	− 1.77046i
$218$	2.41404i	0.163499i
$219$	35.0310	2.36717
$220$	0	0
$221$	2.04028	0.137244
$222$	31.6860i	2.12662i
$223$	7.84635i	0.525430i	0.964873	+	0.262715i	$0.0846180\pi$
$223$	7.84635i	0.525430i	−0.964873	+	0.262715i	$0.915382\pi$
$224$	4.69527	0.313716
$225$	0	0
$226$	7.14585	0.475335
$227$	− 6.28646i	− 0.417247i	−0.977996	−	0.208624i	$-0.933102\pi$
$227$	− 6.28646i	− 0.417247i	0.977996	−	0.208624i	$-0.0668983\pi$
$228$	− 2.77733i	− 0.183933i
$229$	3.14585	0.207884	0.103942	−	0.994583i	$-0.466854\pi$
$229$	3.14585	0.207884	0.103942	+	0.994583i	$0.466854\pi$
$230$	0	0
$231$	−83.5726	−5.49867
$232$	− 2.93621i	− 0.192772i
$233$	0.182394i	0.0119490i	0.999982	+	0.00597451i	$0.00190176\pi$
$233$	0.182394i	0.0119490i	−0.999982	+	0.00597451i	$0.998098\pi$
$234$	−5.01420	−0.327789
$235$	0	0
$236$	−5.63148	−0.366578
$237$	5.45315i	0.354220i
$238$	− 9.00523i	− 0.583723i
$239$	11.5039	0.744126	0.372063	−	0.928208i	$-0.378651\pi$
$239$	11.5039	0.744126	0.372063	+	0.928208i	$0.378651\pi$
$240$	0	0
$241$	−0.445349	−0.0286874	−0.0143437	−	0.999897i	$-0.504566\pi$
$241$	−0.445349	−0.0286874	−0.0143437	+	0.999897i	$0.504566\pi$
$242$	− 30.0728i	− 1.93315i
$243$	− 16.8411i	− 1.08036i
$244$	3.39053	0.217056
$245$	0	0
$246$	−3.18239	−0.202902
$247$	1.06379i	0.0676872i
$248$	− 5.55465i	− 0.352721i
$249$	−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	$0.362530\pi$
$252$	22.1313i	1.39414i
$253$	11.5076i	0.723479i
$254$	−9.26295	−0.581209
$255$	0	0
$256$	1.00000	0.0625000
$257$	23.4816i	1.46474i	0.680907	+	0.732370i	$0.261586\pi$
$257$	23.4816i	1.46474i	−0.680907	+	0.732370i	$0.738414\pi$
$258$	− 9.87242i	− 0.614630i
$259$	−53.5674	−3.32851
$260$	0	0
$261$	13.8399	0.856671
$262$	− 11.5181i	− 0.711591i
$263$	27.9269i	1.72205i	0.508565	+	0.861023i	$0.330176\pi$
$263$	27.9269i	1.72205i	−0.508565	+	0.861023i	$0.669824\pi$
$264$	−17.7993	−1.09547
$265$	0	0
$266$	4.69527	0.287885
$267$	27.7733i	1.69970i
$268$	− 8.82284i	− 0.538941i
$269$	−16.4816	−1.00490	−0.502449	−	0.864607i	$-0.667568\pi$
$269$	−16.4816	−1.00490	−0.502449	+	0.864607i	$0.667568\pi$
$270$	0	0
$271$	−1.46736	−0.0891356	−0.0445678	−	0.999006i	$-0.514191\pi$
$271$	−1.46736	−0.0891356	−0.0445678	+	0.999006i	$0.514191\pi$
$272$	− 1.91794i	− 0.116292i
$273$	− 13.8721i	− 0.839577i
$274$	−15.1041	−0.912470
$275$	0	0
$276$	4.98696	0.300180
$277$	− 15.8359i	− 0.951486i	−0.879584	−	0.475743i	$-0.842179\pi$
$277$	− 15.8359i	− 0.951486i	0.879584	−	0.475743i	$-0.157821\pi$
$278$	− 0.700500i	− 0.0420132i
$279$	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	$0.559739\pi$
$282$	− 30.0948i	− 1.79212i
$283$	− 16.7005i	− 0.992742i	−0.868111	−	0.496371i	$-0.834666\pi$
$283$	− 16.7005i	− 0.992742i	0.868111	−	0.496371i	$-0.165334\pi$
$284$	1.42708	0.0846814
$285$	0	0
$286$	6.81761	0.403134
$287$	− 5.38006i	− 0.317575i
$288$	4.71354i	0.277748i
$289$	13.3215	0.783618
$290$	0	0
$291$	−41.5076	−2.43322
$292$	12.6132i	0.738132i
$293$	0.644516i	0.0376530i	0.999823	+	0.0188265i	$0.00599302\pi$
$293$	0.644516i	0.0376530i	−0.999823	+	0.0188265i	$0.994007\pi$
$294$	−41.7863	−2.43703
$295$	0	0
$296$	−11.4088	−0.663123
$297$	− 30.4998i	− 1.76978i
$298$	12.9452i	0.749894i
$299$	−1.91014	−0.110466
$300$	0	0
$301$	16.6900	0.961997
$302$	− 5.70830i	− 0.328476i
$303$	29.2630i	1.68111i
$304$	1.00000	0.0573539
$305$	0	0
$306$	9.04028	0.516798
$307$	− 26.6457i	− 1.52075i	−0.649485	−	0.760375i	$-0.725015\pi$
$307$	− 26.6457i	− 1.52075i	0.649485	−	0.760375i	$-0.274985\pi$
$308$	− 30.0910i	− 1.71460i
$309$	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	$0.393809\pi$
$312$	− 2.95449i	− 0.167265i
$313$	− 23.0638i	− 1.30364i	−0.758373	−	0.651821i	$-0.774005\pi$
$313$	− 23.0638i	− 1.30364i	0.758373	−	0.651821i	$-0.225995\pi$
$314$	−9.26295	−0.522739
$315$	0	0
$316$	−1.96345	−0.110453
$317$	13.9232i	0.782003i	0.920390	+	0.391002i	$0.127871\pi$
$317$	13.9232i	0.782003i	−0.920390	+	0.391002i	$0.872129\pi$
$318$	− 24.1496i	− 1.35424i
$319$	−18.8176	−1.05358
$320$	0	0
$321$	−4.97242	−0.277534
$322$	8.43081i	0.469831i
$323$	− 1.91794i	− 0.106717i
$324$	0.923174	0.0512874
$325$	0	0
$326$	4.28123	0.237115
$327$	− 6.70457i	− 0.370763i
$328$	− 1.14585i	− 0.0632689i
$329$	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	$0.506435\pi$
$332$	− 16.2447i	− 0.891543i
$333$	− 53.7758i	− 2.94690i
$334$	15.2264	0.833152
$335$	0	0
$336$	−13.0403	−0.711406
$337$	2.28123i	0.124266i	0.998068	+	0.0621332i	$0.0197904\pi$
$337$	2.28123i	0.124266i	−0.998068	+	0.0621332i	$0.980210\pi$
$338$	− 11.8684i	− 0.645553i
$339$	−19.8463	−1.07791
$340$	0	0
$341$	−35.5987	−1.92778
$342$	4.71354i	0.254879i
$343$	− 37.7758i	− 2.03970i
$344$	3.55465	0.191654
$345$	0	0
$346$	−12.2630	−0.659261
$347$	2.56246i	0.137560i	0.997632	+	0.0687799i	$0.0219106\pi$
$347$	2.56246i	0.137560i	−0.997632	+	0.0687799i	$0.978089\pi$
$348$	8.15482i	0.437144i
$349$	5.67176	0.303602	0.151801	−	0.988411i	$-0.451493\pi$
$349$	5.67176	0.303602	0.151801	+	0.988411i	$0.451493\pi$
$350$	0	0
$351$	5.06262	0.270223
$352$	− 6.40880i	− 0.341590i
$353$	− 23.6665i	− 1.25964i	−0.776740	−	0.629821i	$-0.783128\pi$
$353$	− 23.6665i	− 1.25964i	0.776740	−	0.629821i	$-0.216872\pi$
$354$	15.6404	0.831280
$355$	0	0
$356$	−10.0000	−0.529999
$357$	25.0105i	1.32369i
$358$	− 1.57292i	− 0.0831316i
$359$	−31.9724	−1.68744	−0.843720	−	0.536784i	$-0.819639\pi$
$359$	−31.9724	−1.68744	−0.843720	+	0.536784i	$0.819639\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 11.4088i	− 0.599633i
$363$	83.5218i	4.38376i
$364$	4.99477	0.261797
$365$	0	0
$366$	−9.41661	−0.492214
$367$	− 1.14585i	− 0.0598128i	−0.999553	−	0.0299064i	$-0.990479\pi$
$367$	− 1.14585i	− 0.0598128i	0.999553	−	0.0299064i	$-0.00952092\pi$
$368$	1.79560i	0.0936020i
$369$	5.40100	0.281165
$370$	0	0
$371$	40.8266	2.11961
$372$	15.4271i	0.799857i
$373$	32.8579i	1.70132i	0.525719	+	0.850658i	$0.323796\pi$
$373$	32.8579i	1.70132i	−0.525719	+	0.850658i	$0.676204\pi$
$374$	−12.2917	−0.635588
$375$	0	0
$376$	10.8359	0.558818
$377$	− 3.12351i	− 0.160869i
$378$	− 22.3450i	− 1.14930i
$379$	18.2865	0.939312	0.469656	−	0.882849i	$-0.344378\pi$
$379$	18.2865	0.939312	0.469656	+	0.882849i	$0.344378\pi$
$380$	0	0
$381$	25.7262	1.31800
$382$	6.35805i	0.325306i
$383$	20.8542i	1.06560i	0.846242	+	0.532799i	$0.178860\pi$
$383$	20.8542i	1.06560i	−0.846242	+	0.532799i	$0.821140\pi$
$384$	−2.77733	−0.141730
$385$	0	0
$386$	14.4998	0.738022
$387$	16.7550i	0.851704i
$388$	− 14.9452i	− 0.758727i
$389$	24.9086	1.26292	0.631459	−	0.775409i	$-0.282456\pi$
$389$	24.9086	1.26292	0.631459	+	0.775409i	$0.282456\pi$
$390$	0	0
$391$	3.44385	0.174163
$392$	− 15.0455i	− 0.759913i
$393$	31.9895i	1.61366i
$394$	5.14585	0.259244
$395$	0	0
$396$	30.2081	1.51802
$397$	24.7445i	1.24189i	0.783853	+	0.620946i	$0.213251\pi$
$397$	24.7445i	1.24189i	−0.783853	+	0.620946i	$0.786749\pi$
$398$	3.87766i	0.194369i
$399$	−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	$0.372249\pi$
$402$	24.5039i	1.22214i
$403$	− 5.90897i	− 0.294347i
$404$	−10.5364	−0.524204
$405$	0	0
$406$	−13.7863	−0.684202
$407$	73.1168i	3.62426i
$408$	5.32674i	0.263713i
$409$	−30.5804	−1.51210	−0.756052	−	0.654512i	$-0.772874\pi$
$409$	−30.5804	−1.51210	−0.756052	+	0.654512i	$0.772874\pi$
$410$	0	0
$411$	41.9489	2.06919
$412$	16.9817i	0.836630i
$413$	26.4413i	1.30109i
$414$	−8.46362	−0.415964
$415$	0	0
$416$	1.06379	0.0521565
$417$	1.94552i	0.0952723i
$418$	− 6.40880i	− 0.313465i
$419$	−1.96345	−0.0959210	−0.0479605	−	0.998849i	$-0.515272\pi$
$419$	−1.96345	−0.0959210	−0.0479605	+	0.998849i	$0.515272\pi$
$420$	0	0
$421$	−25.5949	−1.24742	−0.623710	−	0.781656i	$-0.714376\pi$
$421$	−25.5949	−1.24742	−0.623710	+	0.781656i	$0.714376\pi$
$422$	− 17.1496i	− 0.834829i
$423$	51.0753i	2.48337i
$424$	8.69527	0.422279
$425$	0	0
$426$	−3.96345	−0.192030
$427$	− 15.9194i	− 0.770396i
$428$	− 1.79036i	− 0.0865405i
$429$	−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	$0.620570\pi$
$432$	− 4.75905i	− 0.228970i
$433$	16.6640i	0.800819i	0.916336	+	0.400409i	$0.131132\pi$
$433$	16.6640i	0.800819i	−0.916336	+	0.400409i	$0.868868\pi$
$434$	−26.0806	−1.25191
$435$	0	0
$436$	2.41404	0.115611
$437$	1.79560i	0.0858951i
$438$	− 35.0310i	− 1.67384i
$439$	19.5987	0.935393	0.467697	−	0.883889i	$-0.345084\pi$
$439$	19.5987	0.935393	0.467697	+	0.883889i	$0.345084\pi$
$440$	0	0
$441$	70.9176	3.37703
$442$	− 2.04028i	− 0.0970462i
$443$	13.0183i	0.618517i	0.950978	+	0.309258i	$0.100081\pi$
$443$	13.0183i	0.618517i	−0.950978	+	0.309258i	$0.899919\pi$
$444$	31.6860	1.50375
$445$	0	0
$446$	7.84635	0.371535
$447$	− 35.9530i	− 1.70052i
$448$	− 4.69527i	− 0.221830i
$449$	−6.77359	−0.319666	−0.159833	−	0.987144i	$-0.551095\pi$
$449$	−6.77359	−0.319666	−0.159833	+	0.987144i	$0.551095\pi$
$450$	0	0
$451$	−7.34352	−0.345793
$452$	− 7.14585i	− 0.336112i
$453$	15.8538i	0.744877i
$454$	−6.28646	−0.295038
$455$	0	0
$456$	−2.77733	−0.130060
$457$	27.3189i	1.27793i	0.769237	+	0.638963i	$0.220636\pi$
$457$	27.3189i	1.27793i	−0.769237	+	0.638963i	$0.779364\pi$
$458$	− 3.14585i	− 0.146996i
$459$	−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	$0.724132\pi$
$462$	83.5726i	3.88815i
$463$	38.2369i	1.77702i	0.458859	+	0.888509i	$0.348258\pi$
$463$	38.2369i	1.77702i	−0.458859	+	0.888509i	$0.651742\pi$
$464$	−2.93621	−0.136310
$465$	0	0
$466$	0.182394	0.00844923
$467$	− 23.4711i	− 1.08611i	−0.839696	−	0.543056i	$-0.817267\pi$
$467$	− 23.4711i	− 1.08611i	0.839696	−	0.543056i	$-0.182733\pi$
$468$	5.01420i	0.231782i
$469$	−41.4256	−1.91286
$470$	0	0
$471$	25.7262	1.18540
$472$	5.63148i	0.259210i
$473$	− 22.7811i	− 1.04747i
$474$	5.45315	0.250472
$475$	0	0
$476$	−9.00523	−0.412754
$477$	40.9855i	1.87660i
$478$	− 11.5039i	− 0.526176i
$479$	19.6900	0.899660	0.449830	−	0.893114i	$-0.351484\pi$
$479$	19.6900	0.899660	0.449830	+	0.893114i	$0.351484\pi$
$480$	0	0
$481$	−12.1365	−0.553379
$482$	0.445349i	0.0202851i
$483$	− 23.4151i	− 1.06542i
$484$	−30.0728	−1.36694
$485$	0	0
$486$	−16.8411	−0.763928
$487$	− 16.3357i	− 0.740242i	−0.928984	−	0.370121i	$-0.879316\pi$
$487$	− 16.3357i	− 0.740242i	0.928984	−	0.370121i	$-0.120684\pi$
$488$	− 3.39053i	− 0.153482i
$489$	−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	$0.290481\pi$
$492$	3.18239i	0.143473i
$493$	5.63148i	0.253629i
$494$	1.06379	0.0478621
$495$	0	0
$496$	−5.55465	−0.249411
$497$	− 6.70050i	− 0.300558i
$498$	45.1168i	2.02173i
$499$	4.69003	0.209955	0.104977	−	0.994475i	$-0.466523\pi$
$499$	4.69003	0.209955	0.104977	+	0.994475i	$0.466523\pi$
$500$	0	0
$501$	−42.2887	−1.88932
$502$	− 13.2630i	− 0.591955i
$503$	5.19136i	0.231471i	0.993280	+	0.115736i	$0.0369226\pi$
$503$	5.19136i	0.231471i	−0.993280	+	0.115736i	$0.963077\pi$
$504$	22.1313	0.985807
$505$	0	0
$506$	11.5076	0.511577
$507$	32.9623i	1.46391i
$508$	9.26295i	0.410977i
$509$	4.51811	0.200262	0.100131	−	0.994974i	$-0.468074\pi$
$509$	4.51811	0.200262	0.100131	+	0.994974i	$0.468074\pi$
$510$	0	0
$511$	59.2223	2.61984
$512$	− 1.00000i	− 0.0441942i
$513$	− 4.75905i	− 0.210117i
$514$	23.4816	1.03573
$515$	0	0
$516$	−9.87242	−0.434609
$517$	− 69.4450i	− 3.05419i
$518$	53.5674i	2.35361i
$519$	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	$0.397515\pi$
$522$	− 13.8399i	− 0.605758i
$523$	− 18.2134i	− 0.796415i	−0.917295	−	0.398208i	$-0.869632\pi$
$523$	− 18.2134i	− 0.796415i	0.917295	−	0.398208i	$-0.130368\pi$
$524$	−11.5181	−0.503171
$525$	0	0
$526$	27.9269	1.21767
$527$	10.6535i	0.464073i
$528$	17.7993i	0.774617i
$529$	19.7758	0.859819
$530$	0	0
$531$	−26.5442	−1.15192
$532$	− 4.69527i	− 0.203566i
$533$	− 1.21894i	− 0.0527981i
$534$	27.7733	1.20187
$535$	0	0
$536$	−8.82284	−0.381089
$537$	4.36852i	0.188516i
$538$	16.4816i	0.710571i
$539$	−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	$0.202823\pi$
$542$	1.46736i	0.0630284i
$543$	31.6860i	1.35977i
$544$	−1.91794	−0.0822310
$545$	0	0
$546$	−13.8721	−0.593671
$547$	− 29.5621i	− 1.26399i	−0.774974	−	0.631993i	$-0.782237\pi$
$547$	− 29.5621i	− 1.26399i	0.774974	−	0.631993i	$-0.217763\pi$
$548$	15.1041i	0.645214i
$549$	15.9814	0.682069
$550$	0	0
$551$	−2.93621	−0.125087
$552$	− 4.98696i	− 0.212259i
$553$	9.21894i	0.392029i
$554$	−15.8359	−0.672802
$555$	0	0
$556$	−0.700500	−0.0297078
$557$	− 14.3723i	− 0.608972i	−0.952517	−	0.304486i	$-0.901515\pi$
$557$	− 14.3723i	− 0.608972i	0.952517	−	0.304486i	$-0.0984847\pi$
$558$	− 26.1821i	− 1.10837i
$559$	3.78139	0.159936
$560$	0	0
$561$	34.1380	1.44131
$562$	6.25515i	0.263858i
$563$	− 6.39053i	− 0.269329i	−0.990891	−	0.134664i	$-0.957004\pi$
$563$	− 6.39053i	− 0.269329i	0.990891	−	0.134664i	$-0.0429956\pi$
$564$	−30.0948	−1.26722
$565$	0	0
$566$	−16.7005	−0.701974
$567$	− 4.33455i	− 0.182034i
$568$	− 1.42708i	− 0.0598788i
$569$	44.9086	1.88267	0.941334	−	0.337476i	$-0.109573\pi$
$569$	44.9086	1.88267	0.941334	+	0.337476i	$0.109573\pi$
$570$	0	0
$571$	12.4193	0.519730	0.259865	−	0.965645i	$-0.416322\pi$
$571$	12.4193	0.519730	0.259865	+	0.965645i	$0.416322\pi$
$572$	− 6.81761i	− 0.285058i
$573$	− 17.6584i	− 0.737690i
$574$	−5.38006	−0.224559
$575$	0	0
$576$	4.71354	0.196397
$577$	4.20440i	0.175032i	0.996163	+	0.0875158i	$0.0278928\pi$
$577$	4.20440i	0.175032i	−0.996163	+	0.0875158i	$0.972107\pi$
$578$	− 13.3215i	− 0.554102i
$579$	−40.2708	−1.67360
$580$	0	0
$581$	−76.2731	−3.16434
$582$	41.5076i	1.72055i
$583$	− 55.7262i	− 2.30795i
$584$	12.6132	0.521938
$585$	0	0
$586$	0.644516	0.0266247
$587$	− 24.7915i	− 1.02326i	−0.859207	−	0.511628i	$-0.829043\pi$
$587$	− 24.7915i	− 1.02326i	0.859207	−	0.511628i	$-0.170957\pi$
$588$	41.7863i	1.72324i
$589$	−5.55465	−0.228875
$590$	0	0
$591$	−14.2917	−0.587882
$592$	11.4088i	0.468899i
$593$	4.67176i	0.191846i	0.995389	+	0.0959231i	$0.0305803\pi$
$593$	4.67176i	0.191846i	−0.995389	+	0.0959231i	$0.969420\pi$
$594$	−30.4998	−1.25142
$595$	0	0
$596$	12.9452	0.530255
$597$	− 10.7695i	− 0.440767i
$598$	1.91014i	0.0781113i
$599$	−39.2369	−1.60318	−0.801588	−	0.597877i	$-0.796011\pi$
$599$	−39.2369	−1.60318	−0.801588	+	0.597877i	$0.796011\pi$
$600$	0	0
$601$	−42.4267	−1.73062	−0.865311	−	0.501235i	$-0.832879\pi$
$601$	−42.4267	−1.73062	−0.865311	+	0.501235i	$0.832879\pi$
$602$	− 16.6900i	− 0.680235i
$603$	− 41.5868i	− 1.69355i
$604$	−5.70830	−0.232268
$605$	0	0
$606$	29.2630	1.18873
$607$	2.98173i	0.121025i	0.998167	+	0.0605123i	$0.0192734\pi$
$607$	2.98173i	0.121025i	−0.998167	+	0.0605123i	$0.980727\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	38.2890	1.55155
$610$	0	0
$611$	11.5271	0.466336
$612$	− 9.04028i	− 0.365432i
$613$	− 28.9452i	− 1.16908i	−0.811363	−	0.584542i	$-0.801274\pi$
$613$	− 28.9452i	− 1.16908i	0.811363	−	0.584542i	$-0.198726\pi$
$614$	−26.6457	−1.07533
$615$	0	0
$616$	−30.0910	−1.21240
$617$	15.0365i	0.605349i	0.953094	+	0.302674i	$0.0978794\pi$
$617$	15.0365i	0.605349i	−0.953094	+	0.302674i	$0.902121\pi$
$618$	− 47.1638i	− 1.89721i
$619$	−8.25515	−0.331803	−0.165901	−	0.986142i	$-0.553053\pi$
$619$	−8.25515	−0.331803	−0.165901	+	0.986142i	$0.553053\pi$
$620$	0	0
$621$	8.54535	0.342913
$622$	− 11.5494i	− 0.463089i
$623$	46.9527i	1.88112i
$624$	−2.95449	−0.118274
$625$	0	0
$626$	−23.0638	−0.921814
$627$	17.7993i	0.710837i
$628$	9.26295i	0.369632i
$629$	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	$0.557919\pi$
$632$	1.96345i	0.0781020i
$633$	47.6300i	1.89312i
$634$	13.9232	0.552960
$635$	0	0
$636$	−24.1496	−0.957593
$637$	− 16.0052i	− 0.634150i
$638$	18.8176i	0.744996i
$639$	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	$0.297240\pi$
$642$	4.97242i	0.196246i
$643$	− 35.3174i	− 1.39278i	−0.717662	−	0.696392i	$-0.754788\pi$
$643$	− 35.3174i	− 1.39278i	0.717662	−	0.696392i	$-0.245212\pi$
$644$	8.43081	0.332220
$645$	0	0
$646$	−1.91794	−0.0754603
$647$	− 4.12234i	− 0.162066i	−0.996711	−	0.0810330i	$-0.974178\pi$
$647$	− 4.12234i	− 0.162066i	0.996711	−	0.0810330i	$-0.0258219\pi$
$648$	− 0.923174i	− 0.0362657i
$649$	36.0910	1.41670
$650$	0	0
$651$	72.4342	2.83892
$652$	− 4.28123i	− 0.167666i
$653$	8.62741i	0.337617i	0.985649	+	0.168808i	$0.0539919\pi$
$653$	8.62741i	0.337617i	−0.985649	+	0.168808i	$0.946008\pi$
$654$	−6.70457	−0.262169
$655$	0	0
$656$	−1.14585	−0.0447379
$657$	59.4528i	2.31948i
$658$	− 50.8773i	− 1.98340i
$659$	37.3853	1.45632	0.728162	−	0.685405i	$-0.240375\pi$
$659$	37.3853	1.45632	0.728162	+	0.685405i	$0.240375\pi$
$660$	0	0
$661$	−12.8997	−0.501739	−0.250869	−	0.968021i	$-0.580716\pi$
$661$	−12.8997	−0.501739	−0.250869	+	0.968021i	$0.580716\pi$
$662$	0.735546i	0.0285878i
$663$	5.66652i	0.220070i
$664$	−16.2447	−0.630416
$665$	0	0
$666$	−53.7758	−2.08377
$667$	− 5.27226i	− 0.204143i
$668$	− 15.2264i	− 0.589127i
$669$	−21.7919	−0.842522
$670$	0	0
$671$	−21.7292	−0.838848
$672$	13.0403i	0.503040i
$673$	10.4349i	0.402235i	0.979567	+	0.201118i	$0.0644573\pi$
$673$	10.4349i	0.402235i	−0.979567	+	0.201118i	$0.935543\pi$
$674$	2.28123	0.0878696
$675$	0	0
$676$	−11.8684	−0.456475
$677$	− 12.4401i	− 0.478112i	−0.971006	−	0.239056i	$-0.923162\pi$
$677$	− 12.4401i	− 0.478112i	0.971006	−	0.239056i	$-0.0768380\pi$
$678$	19.8463i	0.762194i
$679$	−70.1716	−2.69294
$680$	0	0
$681$	17.4596	0.669052
$682$	35.5987i	1.36314i
$683$	17.5364i	0.671011i	0.942038	+	0.335505i	$0.108907\pi$
$683$	17.5364i	0.671011i	−0.942038	+	0.335505i	$0.891093\pi$
$684$	4.71354	0.180227
$685$	0	0
$686$	−37.7758	−1.44229
$687$	8.73705i	0.333339i
$688$	− 3.55465i	− 0.135520i
$689$	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	$0.659626\pi$
$692$	12.2630i	0.466168i
$693$	− 141.835i	− 5.38787i
$694$	2.56246	0.0972695
$695$	0	0
$696$	8.15482	0.309108
$697$	2.19767i	0.0832426i
$698$	− 5.67176i	− 0.214679i
$699$	−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	$0.598050\pi$
$702$	− 5.06262i	− 0.191076i
$703$	11.4088i	0.430291i
$704$	−6.40880	−0.241541
$705$	0	0
$706$	−23.6665	−0.890701
$707$	49.4711i	1.86055i
$708$	− 15.6404i	− 0.587804i
$709$	−13.5076	−0.507290	−0.253645	−	0.967297i	$-0.581629\pi$
$709$	−13.5076	−0.507290	−0.253645	+	0.967297i	$0.581629\pi$
$710$	0	0
$711$	−9.25482	−0.347083
$712$	10.0000i	0.374766i
$713$	− 9.97392i	− 0.373526i
$714$	25.0105	0.935993
$715$	0	0
$716$	−1.57292	−0.0587829
$717$	31.9501i	1.19320i
$718$	31.9724i	1.19320i
$719$	−0.803402	−0.0299619	−0.0149809	−	0.999888i	$-0.504769\pi$
$719$	−0.803402	−0.0299619	−0.0149809	+	0.999888i	$0.504769\pi$
$720$	0	0
$721$	79.7337	2.96944
$722$	− 1.00000i	− 0.0372161i
$723$	− 1.23688i	− 0.0460000i
$724$	−11.4088	−0.424005
$725$	0	0
$726$	83.5218	3.09979
$727$	− 51.6860i	− 1.91693i	−0.285217	−	0.958463i	$-0.592066\pi$
$727$	− 51.6860i	− 1.91693i	0.285217	−	0.958463i	$-0.407934\pi$
$728$	− 4.99477i	− 0.185118i
$729$	44.0037	1.62977
$730$	0	0
$731$	−6.81761	−0.252158
$732$	9.41661i	0.348048i
$733$	− 22.3723i	− 0.826338i	−0.910654	−	0.413169i	$-0.864422\pi$
$733$	− 22.3723i	− 0.826338i	0.910654	−	0.413169i	$-0.135578\pi$
$734$	−1.14585	−0.0422940
$735$	0	0
$736$	1.79560	0.0661866
$737$	56.5438i	2.08282i
$738$	− 5.40100i	− 0.198814i
$739$	−33.4271	−1.22963	−0.614817	−	0.788669i	$-0.710770\pi$
$739$	−33.4271	−1.22963	−0.614817	+	0.788669i	$0.710770\pi$
$740$	0	0
$741$	−2.95449	−0.108536
$742$	− 40.8266i	− 1.49879i
$743$	14.4998i	0.531947i	0.963980	+	0.265974i	$0.0856934\pi$
$743$	14.4998i	0.531947i	−0.963980	+	0.265974i	$0.914307\pi$
$744$	15.4271	0.565584
$745$	0	0
$746$	32.8579	1.20301
$747$	− 76.5699i	− 2.80155i
$748$	12.2917i	0.449429i
$749$	−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	$0.661411\pi$
$752$	− 10.8359i	− 0.395144i
$753$	36.8355i	1.34236i
$754$	−3.12351	−0.113751
$755$	0	0
$756$	−22.3450	−0.812680
$757$	31.0362i	1.12803i	0.825764	+	0.564015i	$0.190744\pi$
$757$	31.0362i	1.12803i	−0.825764	+	0.564015i	$0.809256\pi$
$758$	− 18.2865i	− 0.664194i
$759$	−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	$0.668148\pi$
$762$	− 25.7262i	− 0.931963i
$763$	− 11.3345i	− 0.410338i
$764$	6.35805	0.230026
$765$	0	0
$766$	20.8542	0.753491
$767$	5.99070i	0.216312i
$768$	2.77733i	0.100218i
$769$	19.2279	0.693376	0.346688	−	0.937980i	$-0.387306\pi$
$769$	19.2279	0.693376	0.346688	+	0.937980i	$0.387306\pi$
$770$	0	0
$771$	−65.2159	−2.34869
$772$	− 14.4998i	− 0.521860i
$773$	6.00373i	0.215939i	0.994154	+	0.107970i	$0.0344349\pi$
$773$	6.00373i	0.215939i	−0.994154	+	0.107970i	$0.965565\pi$
$774$	16.7550	0.602245
$775$	0	0
$776$	−14.9452	−0.536501
$777$	− 148.774i	− 5.33724i
$778$	− 24.9086i	− 0.893018i
$779$	−1.14585	−0.0410543
$780$	0	0
$781$	−9.14585	−0.327264
$782$	− 3.44385i	− 0.123152i
$783$	13.9736i	0.499375i
$784$	−15.0455	−0.537340
$785$	0	0
$786$	31.9895	1.14103
$787$	− 22.2797i	− 0.794187i	−0.917778	−	0.397093i	$-0.870019\pi$
$787$	− 22.2797i	− 0.794187i	0.917778	−	0.397093i	$-0.129981\pi$
$788$	− 5.14585i	− 0.183313i
$789$	−77.5621	−2.76128
$790$	0	0
$791$	−33.5517	−1.19296
$792$	− 30.2081i	− 1.07340i
$793$	− 3.60680i	− 0.128081i
$794$	24.7445	0.878150
$795$	0	0
$796$	3.87766	0.137440
$797$	− 26.6259i	− 0.943138i	−0.881829	−	0.471569i	$-0.843688\pi$
$797$	− 26.6259i	− 0.943138i	0.881829	−	0.471569i	$-0.156312\pi$
$798$	13.0403i	0.461621i
$799$	−20.7826	−0.735234
$800$	0	0
$801$	−47.1354	−1.66545
$802$	− 15.6457i	− 0.552468i
$803$	− 80.8355i	− 2.85262i
$804$	24.5039	0.864186
$805$	0	0
$806$	−5.90897	−0.208135
$807$	− 45.7747i	− 1.61134i
$808$	10.5364i	0.370669i
$809$	−0.651250	−0.0228967	−0.0114484	−	0.999934i	$-0.503644\pi$
$809$	−0.651250	−0.0228967	−0.0114484	+	0.999934i	$0.503644\pi$
$810$	0	0
$811$	−13.0780	−0.459230	−0.229615	−	0.973281i	$-0.573747\pi$
$811$	−13.0780	−0.459230	−0.229615	+	0.973281i	$0.573747\pi$
$812$	13.7863i	0.483804i
$813$	− 4.07533i	− 0.142928i
$814$	73.1168	2.56274
$815$	0	0
$816$	5.32674	0.186473
$817$	− 3.55465i	− 0.124362i
$818$	30.5804i	1.06922i
$819$	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	$0.417632\pi$
$822$	− 41.9489i	− 1.46314i
$823$	− 18.2850i	− 0.637374i	−0.947860	−	0.318687i	$-0.896758\pi$
$823$	− 18.2850i	− 0.637374i	0.947860	−	0.318687i	$-0.103242\pi$
$824$	16.9817	0.591587
$825$	0	0
$826$	26.4413	0.920010
$827$	− 40.1910i	− 1.39758i	−0.715327	−	0.698790i	$-0.753722\pi$
$827$	− 40.1910i	− 1.39758i	0.715327	−	0.698790i	$-0.246278\pi$
$828$	8.46362i	0.294131i
$829$	−28.3760	−0.985539	−0.492769	−	0.870160i	$-0.664015\pi$
$829$	−28.3760	−0.985539	−0.492769	+	0.870160i	$0.664015\pi$
$830$	0	0
$831$	43.9814	1.52570
$832$	− 1.06379i	− 0.0368802i
$833$	28.8564i	0.999815i
$834$	1.94552	0.0673677
$835$	0	0
$836$	−6.40880	−0.221653
$837$	26.4349i	0.913723i
$838$	1.96345i	0.0678264i
$839$	−6.93471	−0.239413	−0.119706	−	0.992809i	$-0.538195\pi$
$839$	−6.93471	−0.239413	−0.119706	+	0.992809i	$0.538195\pi$
$840$	0	0
$841$	−20.3787	−0.702712
$842$	25.5949i	0.882060i
$843$	− 17.3726i	− 0.598344i
$844$	−17.1496	−0.590313
$845$	0	0
$846$	51.0753	1.75601
$847$	141.200i	4.85167i
$848$	− 8.69527i	− 0.298597i
$849$	46.3827	1.59185
$850$	0	0
$851$	−20.4856	−0.702238
$852$	3.96345i	0.135786i
$853$	21.9739i	0.752373i	0.926544	+	0.376186i	$0.122765\pi$
$853$	21.9739i	0.752373i	−0.926544	+	0.376186i	$0.877235\pi$
$854$	−15.9194	−0.544752
$855$	0	0
$856$	−1.79036	−0.0611934
$857$	− 13.6091i	− 0.464879i	−0.972611	−	0.232440i	$-0.925329\pi$
$857$	− 13.6091i	− 0.464879i	0.972611	−	0.232440i	$-0.0746708\pi$
$858$	18.9347i	0.646420i
$859$	−5.17192	−0.176464	−0.0882319	−	0.996100i	$-0.528122\pi$
$859$	−5.17192	−0.176464	−0.0882319	+	0.996100i	$0.528122\pi$
$860$	0	0
$861$	14.9422	0.509228
$862$	15.3540i	0.522959i
$863$	15.9635i	0.543402i	0.962382	+	0.271701i	$0.0875862\pi$
$863$	15.9635i	0.543402i	−0.962382	+	0.271701i	$0.912414\pi$
$864$	−4.75905	−0.161906
$865$	0	0
$866$	16.6640	0.566264
$867$	36.9982i	1.25652i
$868$	26.0806i	0.885232i
$869$	12.5834	0.426862
$870$	0	0
$871$	−9.38563	−0.318020
$872$	− 2.41404i	− 0.0817496i
$873$	− 70.4447i	− 2.38419i
$874$	1.79560	0.0607370
$875$	0	0
$876$	−35.0310	−1.18359
$877$	15.8866i	0.536453i	0.963356	+	0.268227i	$0.0864376\pi$
$877$	15.8866i	0.536453i	−0.963356	+	0.268227i	$0.913562\pi$
$878$	− 19.5987i	− 0.661423i
$879$	−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	$0.587680\pi$
$882$	− 70.9176i	− 2.38792i
$883$	38.2887i	1.28852i	0.764808	+	0.644259i	$0.222834\pi$
$883$	38.2887i	1.28852i	−0.764808	+	0.644259i	$0.777166\pi$
$884$	−2.04028	−0.0686221
$885$	0	0
$886$	13.0183	0.437357
$887$	− 19.2809i	− 0.647389i	−0.946162	−	0.323695i	$-0.895075\pi$
$887$	− 19.2809i	− 0.647389i	0.946162	−	0.323695i	$-0.104925\pi$
$888$	− 31.6860i	− 1.06331i
$889$	43.4920	1.45868
$890$	0	0
$891$	−5.91644	−0.198208
$892$	− 7.84635i	− 0.262715i
$893$	− 10.8359i	− 0.362609i
$894$	−35.9530	−1.20245
$895$	0	0
$896$	−4.69527	−0.156858
$897$	− 5.30507i	− 0.177131i
$898$	6.77359i	0.226038i
$899$	16.3096	0.543957
$900$	0	0
$901$	−16.6770	−0.555591
$902$	7.34352i	0.244512i
$903$	46.3537i	1.54255i
$904$	−7.14585	−0.237667
$905$	0	0
$906$	15.8538	0.526708
$907$	− 43.0205i	− 1.42847i	−0.699905	−	0.714236i	$-0.746774\pi$
$907$	− 43.0205i	− 1.42847i	0.699905	−	0.714236i	$-0.253226\pi$
$908$	6.28646i	0.208624i
$909$	−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	$0.640413\pi$
$912$	2.77733i	0.0919664i
$913$	104.109i	3.44550i
$914$	27.3189	0.903630
$915$	0	0
$916$	−3.14585	−0.103942
$917$	54.0806i	1.78590i
$918$	9.12758i	0.301255i
$919$	29.5897	0.976074	0.488037	−	0.872823i	$-0.337713\pi$
$919$	29.5897	0.976074	0.488037	+	0.872823i	$0.337713\pi$
$920$	0	0
$921$	74.0037	2.43851
$922$	27.7993i	0.915522i
$923$	− 1.51811i	− 0.0499691i
$924$	83.5726	2.74934
$925$	0	0
$926$	38.2369	1.25654
$927$	80.0440i	2.62899i
$928$	2.93621i	0.0963859i
$929$	1.42334	0.0466983	0.0233491	−	0.999727i	$-0.492567\pi$
$929$	1.42334	0.0466983	0.0233491	+	0.999727i	$0.492567\pi$
$930$	0	0
$931$	−15.0455	−0.493097
$932$	− 0.182394i	− 0.00597451i
$933$	32.0765i	1.05014i
$934$	−23.4711	−0.767998
$935$	0	0
$936$	5.01420	0.163894
$937$	− 28.2276i	− 0.922155i	−0.887360	−	0.461077i	$-0.847463\pi$
$937$	− 28.2276i	− 0.922155i	0.887360	−	0.461077i	$-0.152537\pi$
$938$	41.4256i	1.35259i
$939$	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	$0.583270\pi$
$942$	− 25.7262i	− 0.838206i
$943$	− 2.05748i	− 0.0670009i
$944$	5.63148	0.183289
$945$	0	0
$946$	−22.7811	−0.740676
$947$	− 43.6718i	− 1.41914i	−0.704634	−	0.709571i	$-0.748889\pi$
$947$	− 43.6718i	− 1.41914i	0.704634	−	0.709571i	$-0.251111\pi$
$948$	− 5.45315i	− 0.177110i
$949$	13.4178	0.435559
$950$	0	0
$951$	−38.6692	−1.25393
$952$	9.00523i	0.291861i
$953$	16.0261i	0.519136i	0.965725	+	0.259568i	$0.0835801\pi$
$953$	16.0261i	0.519136i	−0.965725	+	0.259568i	$0.916420\pi$
$954$	40.9855	1.32695
$955$	0	0
$956$	−11.5039	−0.372063
$957$	− 52.2626i	− 1.68941i
$958$	− 19.6900i	− 0.636156i
$959$	70.9176	2.29005
$960$	0	0
$961$	−0.145848	−0.00470478
$962$	12.1365i	0.391298i
$963$	− 8.43895i	− 0.271941i
$964$	0.445349	0.0143437
$965$	0	0
$966$	−23.4151	−0.753369
$967$	11.5987i	0.372988i	0.982456	+	0.186494i	$0.0597125\pi$
$967$	11.5987i	0.372988i	−0.982456	+	0.186494i	$0.940288\pi$
$968$	30.0728i	0.966575i
$969$	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	$0.642833\pi$
$972$	16.8411i	0.540179i
$973$	3.28903i	0.105442i
$974$	−16.3357	−0.523430
$975$	0	0
$976$	−3.39053	−0.108528
$977$	− 14.1537i	− 0.452815i	−0.974033	−	0.226408i	$-0.927302\pi$
$977$	− 14.1537i	− 0.452815i	0.974033	−	0.226408i	$-0.0726982\pi$
$978$	11.8904i	0.380212i
$979$	64.0880	2.04826
$980$	0	0
$981$	11.3787	0.363293
$982$	− 27.1093i	− 0.865093i
$983$	− 32.8542i	− 1.04788i	−0.851754	−	0.523942i	$-0.824461\pi$
$983$	− 32.8542i	− 1.04788i	0.851754	−	0.523942i	$-0.175539\pi$
$984$	3.18239	0.101451
$985$	0	0
$986$	5.63148	0.179343
$987$	141.303i	4.49772i
$988$	− 1.06379i	− 0.0338436i
$989$	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	$0.224255\pi$
$992$	5.55465i	0.176360i
$993$	− 2.04285i	− 0.0648279i
$994$	−6.70050	−0.212527
$995$	0	0
$996$	45.1168	1.42958
$997$	− 44.1716i	− 1.39893i	−0.714668	−	0.699464i	$-0.753422\pi$
$997$	− 44.1716i	− 1.39893i	0.714668	−	0.699464i	$-0.246578\pi$
$998$	− 4.69003i	− 0.148460i
$999$	54.2951	1.71782

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.k.1.1	✓	3	5.3	odd	4
950.2.a.m.1.3	yes	3	5.2	odd	4
950.2.b.g.799.3		6	1.1	even	1	trivial
950.2.b.g.799.4		6	5.4	even	2	inner
7600.2.a.bm.1.1		3	20.7	even	4
7600.2.a.cb.1.3		3	20.3	even	4
8550.2.a.cj.1.1		3	15.2	even	4
8550.2.a.co.1.3		3	15.8	even	4

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.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.77733i q^{3} -1.00000 q^{4} +2.77733 q^{6} +4.69527i q^{7} +1.00000i q^{8} -4.71354 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +2.77733i q^{3} -1.00000 q^{4} +2.77733 q^{6} +4.69527i q^{7} +1.00000i q^{8} -4.71354 q^{9} +6.40880 q^{11} -2.77733i q^{12} +1.06379i q^{13} +4.69527 q^{14} +1.00000 q^{16} -1.91794i q^{17} +4.71354i q^{18} +1.00000 q^{19} -13.0403 q^{21} -6.40880i q^{22} +1.79560i q^{23} -2.77733 q^{24} +1.06379 q^{26} -4.75905i q^{27} -4.69527i q^{28} -2.93621 q^{29} -5.55465 q^{31} -1.00000i q^{32} +17.7993i q^{33} -1.91794 q^{34} +4.71354 q^{36} +11.4088i q^{37} -1.00000i q^{38} -2.95449 q^{39} -1.14585 q^{41} +13.0403i q^{42} -3.55465i q^{43} -6.40880 q^{44} +1.79560 q^{46} -10.8359i q^{47} +2.77733i q^{48} -15.0455 q^{49} +5.32674 q^{51} -1.06379i q^{52} -8.69527i q^{53} -4.75905 q^{54} -4.69527 q^{56} +2.77733i q^{57} +2.93621i q^{58} +5.63148 q^{59} -3.39053 q^{61} +5.55465i q^{62} -22.1313i q^{63} -1.00000 q^{64} +17.7993 q^{66} +8.82284i q^{67} +1.91794i q^{68} -4.98696 q^{69} -1.42708 q^{71} -4.71354i q^{72} -12.6132i q^{73} +11.4088 q^{74} -1.00000 q^{76} +30.0910i q^{77} +2.95449i q^{78} +1.96345 q^{79} -0.923174 q^{81} +1.14585i q^{82} +16.2447i q^{83} +13.0403 q^{84} -3.55465 q^{86} -8.15482i q^{87} +6.40880i q^{88} +10.0000 q^{89} -4.99477 q^{91} -1.79560i q^{92} -15.4271i q^{93} -10.8359 q^{94} +2.77733 q^{96} +14.9452i q^{97} +15.0455i q^{98} -30.2081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9	\( 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} + 6 q^{19} - 22 q^{21} - 4 q^{24} - 4 q^{26} - 28 q^{29} - 8 q^{31} + 8 q^{34} + 26 q^{36} - 58 q^{39} - 16 q^{41} - 4 q^{44} + 28 q^{46} - 50 q^{49} - 22 q^{51} + 14 q^{54} + 4 q^{56} + 12 q^{59} + 44 q^{61} - 6 q^{64} + 8 q^{66} - 16 q^{69} - 4 q^{71} + 34 q^{74} - 6 q^{76} - 48 q^{79} - 2 q^{81} + 22 q^{84} + 4 q^{86} + 60 q^{89} - 14 q^{91} - 26 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 + 6 * q^19 - 22 * q^21 - 4 * q^24 - 4 * q^26 - 28 * q^29 - 8 * q^31 + 8 * q^34 + 26 * q^36 - 58 * q^39 - 16 * q^41 - 4 * q^44 + 28 * q^46 - 50 * q^49 - 22 * q^51 + 14 * q^54 + 4 * q^56 + 12 * q^59 + 44 * q^61 - 6 * q^64 + 8 * q^66 - 16 * q^69 - 4 * q^71 + 34 * q^74 - 6 * q^76 - 48 * q^79 - 2 * q^81 + 22 * q^84 + 4 * q^86 + 60 * q^89 - 14 * q^91 - 26 * q^94 + 4 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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