LMFDB - Embedded newform 3850.2.c.z.1849.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1849,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("3850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3182656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{3} + 25x^{2} - 10x + 2 $ x^6 - 2x^3 + 25x^2 - 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 770)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.5
Root			$0.203364 + 0.203364i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.z.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.83457 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.83457 q^{9} +1.00000 q^{11} +0.406728i q^{12} -0.813457i q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.83457i q^{17} +2.83457i q^{18} -5.42784 q^{19} +0.406728 q^{21} +1.00000i q^{22} -5.42784i q^{23} -0.406728 q^{24} +0.813457 q^{26} -2.37309i q^{27} -1.00000i q^{28} -6.61439 q^{29} +6.00000 q^{31} +1.00000i q^{32} -0.406728i q^{33} +3.83457 q^{34} -2.83457 q^{36} -8.24130i q^{37} -5.42784i q^{38} -0.330856 q^{39} -5.59327 q^{41} +0.406728i q^{42} -3.02112i q^{43} -1.00000 q^{44} +5.42784 q^{46} +5.02112i q^{47} -0.406728i q^{48} -1.00000 q^{49} -1.55963 q^{51} +0.813457i q^{52} +6.61439i q^{53} +2.37309 q^{54} +1.00000 q^{56} +2.20766i q^{57} -6.61439i q^{58} -10.6480 q^{59} +0.978885 q^{61} +6.00000i q^{62} +2.83457i q^{63} -1.00000 q^{64} +0.406728 q^{66} -8.00000i q^{67} +3.83457i q^{68} -2.20766 q^{69} +14.8557 q^{71} -2.83457i q^{72} -6.20766i q^{73} +8.24130 q^{74} +5.42784 q^{76} +1.00000i q^{77} -0.330856i q^{78} -17.0970 q^{79} +7.53851 q^{81} -5.59327i q^{82} -8.81346i q^{83} -0.406728 q^{84} +3.02112 q^{86} +2.69026i q^{87} -1.00000i q^{88} +1.18654 q^{89} +0.813457 q^{91} +5.42784i q^{92} -2.44037i q^{93} -5.02112 q^{94} +0.406728 q^{96} +3.42784i q^{97} -1.00000i q^{98} +2.83457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 22 * q^9	$ 6 q - 6 q^{4} - 22 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} + 4 q^{19} - 8 q^{29} + 36 q^{31} - 16 q^{34} + 22 q^{36} - 80 q^{39} - 36 q^{41} - 6 q^{44} - 4 q^{46} - 6 q^{49} - 24 q^{51} + 24 q^{54} + 6 q^{56} - 20 q^{59} + 40 q^{61} - 6 q^{64} + 16 q^{69} + 16 q^{71} + 8 q^{74} - 4 q^{76} + 12 q^{79} + 94 q^{81} - 16 q^{86} + 12 q^{89} + 4 q^{94} - 22 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 22 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 + 4 * q^19 - 8 * q^29 + 36 * q^31 - 16 * q^34 + 22 * q^36 - 80 * q^39 - 36 * q^41 - 6 * q^44 - 4 * q^46 - 6 * q^49 - 24 * q^51 + 24 * q^54 + 6 * q^56 - 20 * q^59 + 40 * q^61 - 6 * q^64 + 16 * q^69 + 16 * q^71 + 8 * q^74 - 4 * q^76 + 12 * q^79 + 94 * q^81 - 16 * q^86 + 12 * q^89 + 4 * q^94 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times$.

$n$	$1751$	$2201$	$2927$
$\chi(n)$	$1$	$1$	$-1$

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
$3$	− 0.406728i	− 0.234825i	−0.993083	−	0.117412i	$-0.962540\pi$
$3$	− 0.406728i	− 0.234825i	0.993083	−	0.117412i	$-0.0374599\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.406728	0.166046
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	2.83457	0.944857
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.406728i	0.117412i
$13$	− 0.813457i	− 0.225612i	−0.993617	−	0.112806i	$-0.964016\pi$
$13$	− 0.813457i	− 0.225612i	0.993617	−	0.112806i	$-0.0359839\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	− 3.83457i	− 0.930020i	−0.885305	−	0.465010i	$-0.846051\pi$
$17$	− 3.83457i	− 0.930020i	0.885305	−	0.465010i	$-0.153949\pi$
$18$	2.83457i	0.668115i
$19$	−5.42784	−1.24523	−0.622616	−	0.782527i	$-0.713930\pi$
$19$	−5.42784	−1.24523	−0.622616	+	0.782527i	$0.713930\pi$
$20$	0	0
$21$	0.406728	0.0887554
$22$	1.00000i	0.213201i
$23$	− 5.42784i	− 1.13178i	−0.824480	−	0.565892i	$-0.808532\pi$
$23$	− 5.42784i	− 1.13178i	0.824480	−	0.565892i	$-0.191468\pi$
$24$	−0.406728	−0.0830231
$25$	0	0
$26$	0.813457	0.159532
$27$	− 2.37309i	− 0.456701i
$28$	− 1.00000i	− 0.188982i
$29$	−6.61439	−1.22826	−0.614130	−	0.789205i	$-0.710493\pi$
$29$	−6.61439	−1.22826	−0.614130	+	0.789205i	$0.710493\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000i	0.176777i
$33$	− 0.406728i	− 0.0708023i
$34$	3.83457	0.657624
$35$	0	0
$36$	−2.83457	−0.472429
$37$	− 8.24130i	− 1.35486i	−0.735587	−	0.677431i	$-0.763093\pi$
$37$	− 8.24130i	− 1.35486i	0.735587	−	0.677431i	$-0.236907\pi$
$38$	− 5.42784i	− 0.880512i
$39$	−0.330856	−0.0529794
$40$	0	0
$41$	−5.59327	−0.873522	−0.436761	−	0.899578i	$-0.643875\pi$
$41$	−5.59327	−0.873522	−0.436761	+	0.899578i	$0.643875\pi$
$42$	0.406728i	0.0627596i
$43$	− 3.02112i	− 0.460716i	−0.973106	−	0.230358i	$-0.926010\pi$
$43$	− 3.02112i	− 0.460716i	0.973106	−	0.230358i	$-0.0739897\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	5.42784	0.800292
$47$	5.02112i	0.732405i	0.930535	+	0.366202i	$0.119342\pi$
$47$	5.02112i	0.732405i	−0.930535	+	0.366202i	$0.880658\pi$
$48$	− 0.406728i	− 0.0587062i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−1.55963	−0.218392
$52$	0.813457i	0.112806i
$53$	6.61439i	0.908556i	0.890860	+	0.454278i	$0.150103\pi$
$53$	6.61439i	0.908556i	−0.890860	+	0.454278i	$0.849897\pi$
$54$	2.37309	0.322936
$55$	0	0
$56$	1.00000	0.133631
$57$	2.20766i	0.292411i
$58$	− 6.61439i	− 0.868512i
$59$	−10.6480	−1.38626	−0.693128	−	0.720815i	$-0.743768\pi$
$59$	−10.6480	−1.38626	−0.693128	+	0.720815i	$0.743768\pi$
$60$	0	0
$61$	0.978885	0.125333	0.0626667	−	0.998035i	$-0.480039\pi$
$61$	0.978885	0.125333	0.0626667	+	0.998035i	$0.480039\pi$
$62$	6.00000i	0.762001i
$63$	2.83457i	0.357123i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.406728	0.0500648
$67$	− 8.00000i	− 0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$	− 8.00000i	− 0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$	3.83457i	0.465010i
$69$	−2.20766	−0.265771
$70$	0	0
$71$	14.8557	1.76305	0.881523	−	0.472141i	$-0.156519\pi$
$71$	14.8557	1.76305	0.881523	+	0.472141i	$0.156519\pi$
$72$	− 2.83457i	− 0.334058i
$73$	− 6.20766i	− 0.726551i	−0.931682	−	0.363276i	$-0.881658\pi$
$73$	− 6.20766i	− 0.726551i	0.931682	−	0.363276i	$-0.118342\pi$
$74$	8.24130	0.958032
$75$	0	0
$76$	5.42784	0.622616
$77$	1.00000i	0.113961i
$78$	− 0.330856i	− 0.0374621i
$79$	−17.0970	−1.92356	−0.961781	−	0.273821i	$-0.911712\pi$
$79$	−17.0970	−1.92356	−0.961781	+	0.273821i	$0.911712\pi$
$80$	0	0
$81$	7.53851	0.837613
$82$	− 5.59327i	− 0.617674i
$83$	− 8.81346i	− 0.967403i	−0.875233	−	0.483701i	$-0.839292\pi$
$83$	− 8.81346i	− 0.967403i	0.875233	−	0.483701i	$-0.160708\pi$
$84$	−0.406728	−0.0443777
$85$	0	0
$86$	3.02112	0.325775
$87$	2.69026i	0.288426i
$88$	− 1.00000i	− 0.106600i
$89$	1.18654	0.125773	0.0628867	−	0.998021i	$-0.479969\pi$
$89$	1.18654	0.125773	0.0628867	+	0.998021i	$0.479969\pi$
$90$	0	0
$91$	0.813457	0.0852734
$92$	5.42784i	0.565892i
$93$	− 2.44037i	− 0.253055i
$94$	−5.02112	−0.517888
$95$	0	0
$96$	0.406728	0.0415115
$97$	3.42784i	0.348045i	0.984742	+	0.174022i	$0.0556765\pi$
$97$	3.42784i	0.348045i	−0.984742	+	0.174022i	$0.944323\pi$
$98$	− 1.00000i	− 0.101015i
$99$	2.83457	0.284885
$100$	0	0
$101$	−18.6903	−1.85975	−0.929875	−	0.367875i	$-0.880085\pi$
$101$	−18.6903	−1.85975	−0.929875	+	0.367875i	$0.880085\pi$
$102$	− 1.55963i	− 0.154426i
$103$	15.4615i	1.52347i	0.647891	+	0.761733i	$0.275651\pi$
$103$	15.4615i	1.52347i	−0.647891	+	0.761733i	$0.724349\pi$
$104$	−0.813457	−0.0797660
$105$	0	0
$106$	−6.61439	−0.642446
$107$	11.0211i	1.06545i	0.846288	+	0.532726i	$0.178832\pi$
$107$	11.0211i	1.06545i	−0.846288	+	0.532726i	$0.821168\pi$
$108$	2.37309i	0.228350i
$109$	−16.2413	−1.55563	−0.777817	−	0.628491i	$-0.783673\pi$
$109$	−16.2413	−1.55563	−0.777817	+	0.628491i	$0.783673\pi$
$110$	0	0
$111$	−3.35197	−0.318155
$112$	1.00000i	0.0944911i
$113$	− 14.0000i	− 1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$	− 14.0000i	− 1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	−2.20766	−0.206766
$115$	0	0
$116$	6.61439	0.614130
$117$	− 2.30580i	− 0.213171i
$118$	− 10.6480i	− 0.980231i
$119$	3.83457	0.351515
$120$	0	0
$121$	1.00000	0.0909091
$122$	0.978885i	0.0886241i
$123$	2.27494i	0.205125i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	−2.83457	−0.252524
$127$	− 17.2961i	− 1.53478i	−0.641182	−	0.767388i	$-0.721556\pi$
$127$	− 17.2961i	− 1.53478i	0.641182	−	0.767388i	$-0.278444\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.22877	−0.108187
$130$	0	0
$131$	9.42784	0.823715	0.411857	−	0.911248i	$-0.364880\pi$
$131$	9.42784	0.823715	0.411857	+	0.911248i	$0.364880\pi$
$132$	0.406728i	0.0354012i
$133$	− 5.42784i	− 0.470654i
$134$	8.00000	0.691095
$135$	0	0
$136$	−3.83457	−0.328812
$137$	− 13.6691i	− 1.16783i	−0.811813	−	0.583917i	$-0.801519\pi$
$137$	− 13.6691i	− 1.16783i	0.811813	−	0.583917i	$-0.198481\pi$
$138$	− 2.20766i	− 0.187928i
$139$	11.8682	1.00665	0.503324	−	0.864098i	$-0.332110\pi$
$139$	11.8682	1.00665	0.503324	+	0.864098i	$0.332110\pi$
$140$	0	0
$141$	2.04223	0.171987
$142$	14.8557i	1.24666i
$143$	− 0.813457i	− 0.0680247i
$144$	2.83457	0.236214
$145$	0	0
$146$	6.20766	0.513749
$147$	0.406728i	0.0335464i
$148$	8.24130i	0.677431i
$149$	22.2835	1.82554	0.912769	−	0.408476i	$-0.133940\pi$
$149$	22.2835	1.82554	0.912769	+	0.408476i	$0.133940\pi$
$150$	0	0
$151$	−3.05476	−0.248593	−0.124296	−	0.992245i	$-0.539667\pi$
$151$	−3.05476	−0.248593	−0.124296	+	0.992245i	$0.539667\pi$
$152$	5.42784i	0.440256i
$153$	− 10.8694i	− 0.878737i
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	0.330856	0.0264897
$157$	− 4.85569i	− 0.387526i	−0.981048	−	0.193763i	$-0.937931\pi$
$157$	− 4.85569i	− 0.387526i	0.981048	−	0.193763i	$-0.0620693\pi$
$158$	− 17.0970i	− 1.36016i
$159$	2.69026	0.213351
$160$	0	0
$161$	5.42784	0.427774
$162$	7.53851i	0.592282i
$163$	− 8.00000i	− 0.626608i	−0.949653	−	0.313304i	$-0.898564\pi$
$163$	− 8.00000i	− 0.626608i	0.949653	−	0.313304i	$-0.101436\pi$
$164$	5.59327	0.436761
$165$	0	0
$166$	8.81346	0.684057
$167$	− 8.00000i	− 0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$	− 8.00000i	− 0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	− 0.406728i	− 0.0313798i
$169$	12.3383	0.949099
$170$	0	0
$171$	−15.3856	−1.17657
$172$	3.02112i	0.230358i
$173$	− 19.0211i	− 1.44615i	−0.690770	−	0.723074i	$-0.742728\pi$
$173$	− 19.0211i	− 1.44615i	0.690770	−	0.723074i	$-0.257272\pi$
$174$	−2.69026	−0.203948
$175$	0	0
$176$	1.00000	0.0753778
$177$	4.33086i	0.325527i
$178$	1.18654i	0.0889352i
$179$	−4.64803	−0.347410	−0.173705	−	0.984798i	$-0.555574\pi$
$179$	−4.64803	−0.347410	−0.173705	+	0.984798i	$0.555574\pi$
$180$	0	0
$181$	−25.3383	−1.88338	−0.941690	−	0.336482i	$-0.890763\pi$
$181$	−25.3383	−1.88338	−0.941690	+	0.336482i	$0.890763\pi$
$182$	0.813457i	0.0602974i
$183$	− 0.398140i	− 0.0294314i
$184$	−5.42784	−0.400146
$185$	0	0
$186$	2.44037	0.178937
$187$	− 3.83457i	− 0.280412i
$188$	− 5.02112i	− 0.366202i
$189$	2.37309	0.172617
$190$	0	0
$191$	15.6691	1.13378	0.566890	−	0.823794i	$-0.308147\pi$
$191$	15.6691	1.13378	0.566890	+	0.823794i	$0.308147\pi$
$192$	0.406728i	0.0293531i
$193$	− 2.16543i	− 0.155871i	−0.996958	−	0.0779355i	$-0.975167\pi$
$193$	− 2.16543i	− 0.155871i	0.996958	−	0.0779355i	$-0.0248328\pi$
$194$	−3.42784	−0.246105
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 2.81346i	− 0.200451i	−0.994965	−	0.100225i	$-0.968044\pi$
$197$	− 2.81346i	− 0.200451i	0.994965	−	0.100225i	$-0.0319563\pi$
$198$	2.83457i	0.201444i
$199$	13.0211	0.923042	0.461521	−	0.887129i	$-0.347304\pi$
$199$	13.0211	0.923042	0.461521	+	0.887129i	$0.347304\pi$
$200$	0	0
$201$	−3.25383	−0.229507
$202$	− 18.6903i	− 1.31504i
$203$	− 6.61439i	− 0.464239i
$204$	1.55963	0.109196
$205$	0	0
$206$	−15.4615	−1.07725
$207$	− 15.3856i	− 1.06937i
$208$	− 0.813457i	− 0.0564031i
$209$	−5.42784	−0.375452
$210$	0	0
$211$	19.6691	1.35408	0.677040	−	0.735946i	$-0.263262\pi$
$211$	19.6691	1.35408	0.677040	+	0.735946i	$0.263262\pi$
$212$	− 6.61439i	− 0.454278i
$213$	− 6.04223i	− 0.414007i
$214$	−11.0211	−0.753388
$215$	0	0
$216$	−2.37309	−0.161468
$217$	6.00000i	0.407307i
$218$	− 16.2413i	− 1.10000i
$219$	−2.52483	−0.170612
$220$	0	0
$221$	−3.11926	−0.209824
$222$	− 3.35197i	− 0.224970i
$223$	− 3.79234i	− 0.253954i	−0.991906	−	0.126977i	$-0.959473\pi$
$223$	− 3.79234i	− 0.253954i	0.991906	−	0.126977i	$-0.0405274\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	14.0000	0.931266
$227$	14.0422i	0.932016i	0.884781	+	0.466008i	$0.154308\pi$
$227$	14.0422i	0.932016i	−0.884781	+	0.466008i	$0.845692\pi$
$228$	− 2.20766i	− 0.146206i
$229$	−1.83457	−0.121232	−0.0606160	−	0.998161i	$-0.519306\pi$
$229$	−1.83457	−0.121232	−0.0606160	+	0.998161i	$0.519306\pi$
$230$	0	0
$231$	0.406728	0.0267608
$232$	6.61439i	0.434256i
$233$	− 8.04223i	− 0.526864i	−0.964678	−	0.263432i	$-0.915146\pi$
$233$	− 8.04223i	− 0.526864i	0.964678	−	0.263432i	$-0.0848545\pi$
$234$	2.30580	0.150735
$235$	0	0
$236$	10.6480	0.693128
$237$	6.95383i	0.451700i
$238$	3.83457i	0.248558i
$239$	15.4701	1.00068	0.500338	−	0.865830i	$-0.333209\pi$
$239$	15.4701	1.00068	0.500338	+	0.865830i	$0.333209\pi$
$240$	0	0
$241$	11.6355	0.749509	0.374754	−	0.927124i	$-0.377727\pi$
$241$	11.6355	0.749509	0.374754	+	0.927124i	$0.377727\pi$
$242$	1.00000i	0.0642824i
$243$	− 10.1854i	− 0.653393i
$244$	−0.978885	−0.0626667
$245$	0	0
$246$	−2.27494	−0.145045
$247$	4.41532i	0.280940i
$248$	− 6.00000i	− 0.381000i
$249$	−3.58468	−0.227170
$250$	0	0
$251$	5.35197	0.337813	0.168907	−	0.985632i	$-0.445976\pi$
$251$	5.35197	0.337813	0.168907	+	0.985632i	$0.445976\pi$
$252$	− 2.83457i	− 0.178561i
$253$	− 5.42784i	− 0.341246i
$254$	17.2961	1.08525
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 12.7239i	− 0.793695i	−0.917885	−	0.396848i	$-0.870104\pi$
$257$	− 12.7239i	− 0.793695i	0.917885	−	0.396848i	$-0.129896\pi$
$258$	− 1.22877i	− 0.0765001i
$259$	8.24130	0.512089
$260$	0	0
$261$	−18.7490	−1.16053
$262$	9.42784i	0.582454i
$263$	− 1.62691i	− 0.100320i	−0.998741	−	0.0501599i	$-0.984027\pi$
$263$	− 1.62691i	− 0.100320i	0.998741	−	0.0501599i	$-0.0159731\pi$
$264$	−0.406728	−0.0250324
$265$	0	0
$266$	5.42784	0.332802
$267$	− 0.482601i	− 0.0295347i
$268$	8.00000i	0.488678i
$269$	−23.8768	−1.45579	−0.727897	−	0.685686i	$-0.759502\pi$
$269$	−23.8768	−1.45579	−0.727897	+	0.685686i	$0.759502\pi$
$270$	0	0
$271$	2.44037	0.148242	0.0741210	−	0.997249i	$-0.476385\pi$
$271$	2.44037	0.148242	0.0741210	+	0.997249i	$0.476385\pi$
$272$	− 3.83457i	− 0.232505i
$273$	− 0.330856i	− 0.0200243i
$274$	13.6691	0.825783
$275$	0	0
$276$	2.20766	0.132885
$277$	− 22.0000i	− 1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$	− 22.0000i	− 1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$	11.8682i	0.711808i
$279$	17.0074	1.01821
$280$	0	0
$281$	−20.8557	−1.24415	−0.622073	−	0.782959i	$-0.713709\pi$
$281$	−20.8557	−1.24415	−0.622073	+	0.782959i	$0.713709\pi$
$282$	2.04223i	0.121613i
$283$	0.330856i	0.0196673i	0.999952	+	0.00983367i	$0.00313021\pi$
$283$	0.330856i	0.0196673i	−0.999952	+	0.00983367i	$0.996870\pi$
$284$	−14.8557	−0.881523
$285$	0	0
$286$	0.813457	0.0481007
$287$	− 5.59327i	− 0.330160i
$288$	2.83457i	0.167029i
$289$	2.29606	0.135062
$290$	0	0
$291$	1.39420	0.0817295
$292$	6.20766i	0.363276i
$293$	− 3.18654i	− 0.186160i	−0.995659	−	0.0930799i	$-0.970329\pi$
$293$	− 3.18654i	− 0.186160i	0.995659	−	0.0930799i	$-0.0296712\pi$
$294$	−0.406728	−0.0237209
$295$	0	0
$296$	−8.24130	−0.479016
$297$	− 2.37309i	− 0.137700i
$298$	22.2835i	1.29085i
$299$	−4.41532	−0.255344
$300$	0	0
$301$	3.02112	0.174134
$302$	− 3.05476i	− 0.175782i
$303$	7.60186i	0.436715i
$304$	−5.42784	−0.311308
$305$	0	0
$306$	10.8694	0.621361
$307$	− 20.4826i	− 1.16900i	−0.811392	−	0.584502i	$-0.801290\pi$
$307$	− 20.4826i	− 1.16900i	0.811392	−	0.584502i	$-0.198710\pi$
$308$	− 1.00000i	− 0.0569803i
$309$	6.28863	0.357747
$310$	0	0
$311$	3.62691	0.205663	0.102832	−	0.994699i	$-0.467210\pi$
$311$	3.62691	0.205663	0.102832	+	0.994699i	$0.467210\pi$
$312$	0.330856i	0.0187310i
$313$	20.7239i	1.17138i	0.810534	+	0.585692i	$0.199177\pi$
$313$	20.7239i	1.17138i	−0.810534	+	0.585692i	$0.800823\pi$
$314$	4.85569	0.274022
$315$	0	0
$316$	17.0970	0.961781
$317$	1.80093i	0.101150i	0.998720	+	0.0505751i	$0.0161054\pi$
$317$	1.80093i	0.101150i	−0.998720	+	0.0505751i	$0.983895\pi$
$318$	2.69026i	0.150862i
$319$	−6.61439	−0.370335
$320$	0	0
$321$	4.48260	0.250194
$322$	5.42784i	0.302482i
$323$	20.8135i	1.15809i
$324$	−7.53851	−0.418806
$325$	0	0
$326$	8.00000	0.443079
$327$	6.60580i	0.365301i
$328$	5.59327i	0.308837i
$329$	−5.02112	−0.276823
$330$	0	0
$331$	−3.02112	−0.166056	−0.0830278	−	0.996547i	$-0.526459\pi$
$331$	−3.02112	−0.166056	−0.0830278	+	0.996547i	$0.526459\pi$
$332$	8.81346i	0.483701i
$333$	− 23.3606i	− 1.28015i
$334$	8.00000	0.437741
$335$	0	0
$336$	0.406728	0.0221889
$337$	9.66914i	0.526712i	0.964699	+	0.263356i	$0.0848294\pi$
$337$	9.66914i	0.526712i	−0.964699	+	0.263356i	$0.915171\pi$
$338$	12.3383i	0.671114i
$339$	−5.69420	−0.309266
$340$	0	0
$341$	6.00000	0.324918
$342$	− 15.3856i	− 0.831959i
$343$	− 1.00000i	− 0.0539949i
$344$	−3.02112	−0.162888
$345$	0	0
$346$	19.0211	1.02258
$347$	− 9.39420i	− 0.504307i	−0.967687	−	0.252154i	$-0.918861\pi$
$347$	− 9.39420i	− 0.504307i	0.967687	−	0.252154i	$-0.0811388\pi$
$348$	− 2.69026i	− 0.144213i
$349$	18.2077	0.974634	0.487317	−	0.873225i	$-0.337976\pi$
$349$	18.2077	0.974634	0.487317	+	0.873225i	$0.337976\pi$
$350$	0	0
$351$	−1.93040	−0.103037
$352$	1.00000i	0.0533002i
$353$	12.7239i	0.677225i	0.940926	+	0.338612i	$0.109958\pi$
$353$	12.7239i	0.677225i	−0.940926	+	0.338612i	$0.890042\pi$
$354$	−4.33086	−0.230182
$355$	0	0
$356$	−1.18654	−0.0628867
$357$	− 1.55963i	− 0.0825443i
$358$	− 4.64803i	− 0.245656i
$359$	−29.8432	−1.57506	−0.787531	−	0.616275i	$-0.788641\pi$
$359$	−29.8432	−1.57506	−0.787531	+	0.616275i	$0.788641\pi$
$360$	0	0
$361$	10.4615	0.550605
$362$	− 25.3383i	− 1.33175i
$363$	− 0.406728i	− 0.0213477i
$364$	−0.813457	−0.0426367
$365$	0	0
$366$	0.398140	0.0208111
$367$	− 15.4615i	− 0.807083i	−0.914961	−	0.403541i	$-0.867779\pi$
$367$	− 15.4615i	− 0.807083i	0.914961	−	0.403541i	$-0.132221\pi$
$368$	− 5.42784i	− 0.282946i
$369$	−15.8545	−0.825354
$370$	0	0
$371$	−6.61439	−0.343402
$372$	2.44037i	0.126527i
$373$	− 8.10951i	− 0.419895i	−0.977713	−	0.209947i	$-0.932671\pi$
$373$	− 8.10951i	− 0.419895i	0.977713	−	0.209947i	$-0.0673293\pi$
$374$	3.83457	0.198281
$375$	0	0
$376$	5.02112	0.258944
$377$	5.38052i	0.277111i
$378$	2.37309i	0.122058i
$379$	−22.0422	−1.13223	−0.566117	−	0.824325i	$-0.691555\pi$
$379$	−22.0422	−1.13223	−0.566117	+	0.824325i	$0.691555\pi$
$380$	0	0
$381$	−7.03480	−0.360404
$382$	15.6691i	0.801703i
$383$	38.2499i	1.95448i	0.212141	+	0.977239i	$0.431956\pi$
$383$	38.2499i	1.95448i	−0.212141	+	0.977239i	$0.568044\pi$
$384$	−0.406728	−0.0207558
$385$	0	0
$386$	2.16543	0.110217
$387$	− 8.56357i	− 0.435311i
$388$	− 3.42784i	− 0.174022i
$389$	−16.8557	−0.854617	−0.427309	−	0.904106i	$-0.640538\pi$
$389$	−16.8557	−0.854617	−0.427309	+	0.904106i	$0.640538\pi$
$390$	0	0
$391$	−20.8135	−1.05258
$392$	1.00000i	0.0505076i
$393$	− 3.83457i	− 0.193429i
$394$	2.81346	0.141740
$395$	0	0
$396$	−2.83457	−0.142443
$397$	4.44037i	0.222856i	0.993773	+	0.111428i	$0.0355424\pi$
$397$	4.44037i	0.222856i	−0.993773	+	0.111428i	$0.964458\pi$
$398$	13.0211i	0.652690i
$399$	−2.20766	−0.110521
$400$	0	0
$401$	−3.46149	−0.172858	−0.0864292	−	0.996258i	$-0.527546\pi$
$401$	−3.46149	−0.172858	−0.0864292	+	0.996258i	$0.527546\pi$
$402$	− 3.25383i	− 0.162286i
$403$	− 4.88074i	− 0.243127i
$404$	18.6903	0.929875
$405$	0	0
$406$	6.61439	0.328267
$407$	− 8.24130i	− 0.408506i
$408$	1.55963i	0.0772132i
$409$	17.2624	0.853572	0.426786	−	0.904353i	$-0.359646\pi$
$409$	17.2624	0.853572	0.426786	+	0.904353i	$0.359646\pi$
$410$	0	0
$411$	−5.55963	−0.274236
$412$	− 15.4615i	− 0.761733i
$413$	− 10.6480i	− 0.523955i
$414$	15.3856	0.756162
$415$	0	0
$416$	0.813457	0.0398830
$417$	− 4.82714i	− 0.236386i
$418$	− 5.42784i	− 0.265485i
$419$	−9.02112	−0.440710	−0.220355	−	0.975420i	$-0.570722\pi$
$419$	−9.02112	−0.440710	−0.220355	+	0.975420i	$0.570722\pi$
$420$	0	0
$421$	31.7114	1.54552	0.772759	−	0.634700i	$-0.218876\pi$
$421$	31.7114	1.54552	0.772759	+	0.634700i	$0.218876\pi$
$422$	19.6691i	0.957479i
$423$	14.2327i	0.692018i
$424$	6.61439	0.321223
$425$	0	0
$426$	6.04223	0.292747
$427$	0.978885i	0.0473716i
$428$	− 11.0211i	− 0.532726i
$429$	−0.330856	−0.0159739
$430$	0	0
$431$	−3.05476	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$431$	−3.05476	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$432$	− 2.37309i	− 0.114175i
$433$	27.9104i	1.34129i	0.741778	+	0.670645i	$0.233983\pi$
$433$	27.9104i	1.34129i	−0.741778	+	0.670645i	$0.766017\pi$
$434$	−6.00000	−0.288009
$435$	0	0
$436$	16.2413	0.777817
$437$	29.4615i	1.40933i
$438$	− 2.52483i	− 0.120641i
$439$	14.8557	0.709023	0.354512	−	0.935052i	$-0.384647\pi$
$439$	14.8557	0.709023	0.354512	+	0.935052i	$0.384647\pi$
$440$	0	0
$441$	−2.83457	−0.134980
$442$	− 3.11926i	− 0.148368i
$443$	0.746173i	0.0354517i	0.999843	+	0.0177259i	$0.00564261\pi$
$443$	0.746173i	0.0354517i	−0.999843	+	0.0177259i	$0.994357\pi$
$444$	3.35197	0.159078
$445$	0	0
$446$	3.79234	0.179573
$447$	− 9.06335i	− 0.428682i
$448$	− 1.00000i	− 0.0472456i
$449$	−9.83457	−0.464122	−0.232061	−	0.972701i	$-0.574547\pi$
$449$	−9.83457	−0.464122	−0.232061	+	0.972701i	$0.574547\pi$
$450$	0	0
$451$	−5.59327	−0.263377
$452$	14.0000i	0.658505i
$453$	1.24246i	0.0583757i
$454$	−14.0422	−0.659035
$455$	0	0
$456$	2.20766	0.103383
$457$	− 11.2961i	− 0.528407i	−0.964467	−	0.264204i	$-0.914891\pi$
$457$	− 11.2961i	− 0.528407i	0.964467	−	0.264204i	$-0.0851091\pi$
$458$	− 1.83457i	− 0.0857239i
$459$	−9.09977	−0.424741
$460$	0	0
$461$	−7.41926	−0.345549	−0.172775	−	0.984961i	$-0.555273\pi$
$461$	−7.41926	−0.345549	−0.172775	+	0.984961i	$0.555273\pi$
$462$	0.406728i	0.0189227i
$463$	− 10.1740i	− 0.472827i	−0.971653	−	0.236413i	$-0.924028\pi$
$463$	− 10.1740i	− 0.472827i	0.971653	−	0.236413i	$-0.0759719\pi$
$464$	−6.61439	−0.307065
$465$	0	0
$466$	8.04223	0.372549
$467$	32.4912i	1.50351i	0.659441	+	0.751756i	$0.270793\pi$
$467$	32.4912i	1.50351i	−0.659441	+	0.751756i	$0.729207\pi$
$468$	2.30580i	0.106586i
$469$	8.00000	0.369406
$470$	0	0
$471$	−1.97495	−0.0910007
$472$	10.6480i	0.490115i
$473$	− 3.02112i	− 0.138911i
$474$	−6.95383	−0.319400
$475$	0	0
$476$	−3.83457	−0.175757
$477$	18.7490i	0.858456i
$478$	15.4701i	0.707585i
$479$	11.6691	0.533177	0.266588	−	0.963810i	$-0.414104\pi$
$479$	11.6691	0.533177	0.266588	+	0.963810i	$0.414104\pi$
$480$	0	0
$481$	−6.70394	−0.305673
$482$	11.6355i	0.529983i
$483$	− 2.20766i	− 0.100452i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	10.1854	0.462019
$487$	5.49513i	0.249008i	0.992219	+	0.124504i	$0.0397340\pi$
$487$	5.49513i	0.249008i	−0.992219	+	0.124504i	$0.960266\pi$
$488$	− 0.978885i	− 0.0443120i
$489$	−3.25383	−0.147143
$490$	0	0
$491$	−13.2961	−0.600043	−0.300021	−	0.953932i	$-0.596994\pi$
$491$	−13.2961	−0.600043	−0.300021	+	0.953932i	$0.596994\pi$
$492$	− 2.27494i	− 0.102562i
$493$	25.3633i	1.14231i
$494$	−4.41532	−0.198654
$495$	0	0
$496$	6.00000	0.269408
$497$	14.8557i	0.666369i
$498$	− 3.58468i	− 0.160634i
$499$	24.6480	1.10340	0.551699	−	0.834044i	$-0.313980\pi$
$499$	24.6480	1.10340	0.551699	+	0.834044i	$0.313980\pi$
$500$	0	0
$501$	−3.25383	−0.145370
$502$	5.35197i	0.238870i
$503$	38.9230i	1.73549i	0.497010	+	0.867745i	$0.334431\pi$
$503$	38.9230i	1.73549i	−0.497010	+	0.867745i	$0.665569\pi$
$504$	2.83457	0.126262
$505$	0	0
$506$	5.42784	0.241297
$507$	− 5.01833i	− 0.222872i
$508$	17.2961i	0.767388i
$509$	39.0497	1.73085	0.865423	−	0.501042i	$-0.167050\pi$
$509$	39.0497	1.73085	0.865423	+	0.501042i	$0.167050\pi$
$510$	0	0
$511$	6.20766	0.274611
$512$	1.00000i	0.0441942i
$513$	12.8807i	0.568699i
$514$	12.7239	0.561227
$515$	0	0
$516$	1.22877	0.0540937
$517$	5.02112i	0.220828i
$518$	8.24130i	0.362102i
$519$	−7.73643	−0.339592
$520$	0	0
$521$	−33.2710	−1.45763	−0.728815	−	0.684711i	$-0.759928\pi$
$521$	−33.2710	−1.45763	−0.728815	+	0.684711i	$0.759928\pi$
$522$	− 18.7490i	− 0.820619i
$523$	− 40.2362i	− 1.75941i	−0.475523	−	0.879703i	$-0.657741\pi$
$523$	− 40.2362i	− 1.75941i	0.475523	−	0.879703i	$-0.342259\pi$
$524$	−9.42784	−0.411857
$525$	0	0
$526$	1.62691	0.0709368
$527$	− 23.0074i	− 1.00222i
$528$	− 0.406728i	− 0.0177006i
$529$	−6.46149	−0.280934
$530$	0	0
$531$	−30.1826	−1.30981
$532$	5.42784i	0.235327i
$533$	4.54989i	0.197077i
$534$	0.482601	0.0208842
$535$	0	0
$536$	−8.00000	−0.345547
$537$	1.89049i	0.0815805i
$538$	− 23.8768i	− 1.02940i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	26.2835	1.13002	0.565009	−	0.825085i	$-0.308873\pi$
$541$	26.2835	1.13002	0.565009	+	0.825085i	$0.308873\pi$
$542$	2.44037i	0.104823i
$543$	10.3058i	0.442264i
$544$	3.83457	0.164406
$545$	0	0
$546$	0.330856	0.0141593
$547$	− 13.6269i	− 0.582645i	−0.956625	−	0.291322i	$-0.905905\pi$
$547$	− 13.6269i	− 0.582645i	0.956625	−	0.291322i	$-0.0940952\pi$
$548$	13.6691i	0.583917i
$549$	2.77472	0.118422
$550$	0	0
$551$	35.9019	1.52947
$552$	2.20766i	0.0939642i
$553$	− 17.0970i	− 0.727038i
$554$	22.0000	0.934690
$555$	0	0
$556$	−11.8682	−0.503324
$557$	− 14.8979i	− 0.631245i	−0.948885	−	0.315623i	$-0.897787\pi$
$557$	− 14.8979i	− 0.631245i	0.948885	−	0.315623i	$-0.102213\pi$
$558$	17.0074i	0.719982i
$559$	−2.45755	−0.103943
$560$	0	0
$561$	−1.55963	−0.0658476
$562$	− 20.8557i	− 0.879744i
$563$	39.7536i	1.67541i	0.546119	+	0.837707i	$0.316104\pi$
$563$	39.7536i	1.67541i	−0.546119	+	0.837707i	$0.683896\pi$
$564$	−2.04223	−0.0859934
$565$	0	0
$566$	−0.330856	−0.0139069
$567$	7.53851i	0.316588i
$568$	− 14.8557i	− 0.623331i
$569$	−8.78840	−0.368429	−0.184215	−	0.982886i	$-0.558974\pi$
$569$	−8.78840	−0.368429	−0.184215	+	0.982886i	$0.558974\pi$
$570$	0	0
$571$	−5.22877	−0.218817	−0.109409	−	0.993997i	$-0.534896\pi$
$571$	−5.22877	−0.218817	−0.109409	+	0.993997i	$0.534896\pi$
$572$	0.813457i	0.0340123i
$573$	− 6.37309i	− 0.266239i
$574$	5.59327	0.233459
$575$	0	0
$576$	−2.83457	−0.118107
$577$	− 5.80093i	− 0.241496i	−0.992683	−	0.120748i	$-0.961471\pi$
$577$	− 5.80093i	− 0.241496i	0.992683	−	0.120748i	$-0.0385293\pi$
$578$	2.29606i	0.0955034i
$579$	−0.880741	−0.0366024
$580$	0	0
$581$	8.81346	0.365644
$582$	1.39420i	0.0577915i
$583$	6.61439i	0.273940i
$584$	−6.20766	−0.256875
$585$	0	0
$586$	3.18654	0.131635
$587$	− 25.3046i	− 1.04443i	−0.852812	−	0.522217i	$-0.825105\pi$
$587$	− 25.3046i	− 1.04443i	0.852812	−	0.522217i	$-0.174895\pi$
$588$	− 0.406728i	− 0.0167732i
$589$	−32.5671	−1.34190
$590$	0	0
$591$	−1.14431	−0.0470707
$592$	− 8.24130i	− 0.338715i
$593$	− 23.1729i	− 0.951595i	−0.879555	−	0.475798i	$-0.842159\pi$
$593$	− 23.1729i	− 0.951595i	0.879555	−	0.475798i	$-0.157841\pi$
$594$	2.37309	0.0973689
$595$	0	0
$596$	−22.2835	−0.912769
$597$	− 5.29606i	− 0.216753i
$598$	− 4.41532i	− 0.180556i
$599$	8.48260	0.346590	0.173295	−	0.984870i	$-0.444559\pi$
$599$	8.48260	0.346590	0.173295	+	0.984870i	$0.444559\pi$
$600$	0	0
$601$	−32.4490	−1.32362	−0.661810	−	0.749671i	$-0.730212\pi$
$601$	−32.4490	−1.32362	−0.661810	+	0.749671i	$0.730212\pi$
$602$	3.02112i	0.123131i
$603$	− 22.6766i	− 0.923462i
$604$	3.05476	0.124296
$605$	0	0
$606$	−7.60186	−0.308804
$607$	33.9441i	1.37775i	0.724881	+	0.688874i	$0.241895\pi$
$607$	33.9441i	1.37775i	−0.724881	+	0.688874i	$0.758105\pi$
$608$	− 5.42784i	− 0.220128i
$609$	−2.69026	−0.109015
$610$	0	0
$611$	4.08446	0.165240
$612$	10.8694i	0.439368i
$613$	8.77123i	0.354267i	0.984187	+	0.177133i	$0.0566824\pi$
$613$	8.77123i	0.354267i	−0.984187	+	0.177133i	$0.943318\pi$
$614$	20.4826	0.826610
$615$	0	0
$616$	1.00000	0.0402911
$617$	32.1095i	1.29268i	0.763049	+	0.646340i	$0.223701\pi$
$617$	32.1095i	1.29268i	−0.763049	+	0.646340i	$0.776299\pi$
$618$	6.28863i	0.252966i
$619$	28.2749	1.13647	0.568233	−	0.822868i	$-0.307627\pi$
$619$	28.2749	1.13647	0.568233	+	0.822868i	$0.307627\pi$
$620$	0	0
$621$	−12.8807	−0.516886
$622$	3.62691i	0.145426i
$623$	1.18654i	0.0475378i
$624$	−0.330856	−0.0132448
$625$	0	0
$626$	−20.7239	−0.828294
$627$	2.20766i	0.0881654i
$628$	4.85569i	0.193763i
$629$	−31.6019	−1.26005
$630$	0	0
$631$	34.9230	1.39026	0.695131	−	0.718883i	$-0.255346\pi$
$631$	34.9230	1.39026	0.695131	+	0.718883i	$0.255346\pi$
$632$	17.0970i	0.680082i
$633$	− 8.00000i	− 0.317971i
$634$	−1.80093	−0.0715241
$635$	0	0
$636$	−2.69026	−0.106676
$637$	0.813457i	0.0322303i
$638$	− 6.61439i	− 0.261866i
$639$	42.1095	1.66583
$640$	0	0
$641$	−5.25383	−0.207514	−0.103757	−	0.994603i	$-0.533086\pi$
$641$	−5.25383	−0.207514	−0.103757	+	0.994603i	$0.533086\pi$
$642$	4.48260i	0.176914i
$643$	− 3.17796i	− 0.125326i	−0.998035	−	0.0626632i	$-0.980041\pi$
$643$	− 3.17796i	− 0.125326i	0.998035	−	0.0626632i	$-0.0199594\pi$
$644$	−5.42784	−0.213887
$645$	0	0
$646$	−20.8135	−0.818895
$647$	− 37.9190i	− 1.49075i	−0.666645	−	0.745375i	$-0.732270\pi$
$647$	− 37.9190i	− 1.49075i	0.666645	−	0.745375i	$-0.267730\pi$
$648$	− 7.53851i	− 0.296141i
$649$	−10.6480	−0.417972
$650$	0	0
$651$	2.44037	0.0956457
$652$	8.00000i	0.313304i
$653$	29.5374i	1.15589i	0.816077	+	0.577943i	$0.196144\pi$
$653$	29.5374i	1.15589i	−0.816077	+	0.577943i	$0.803856\pi$
$654$	−6.60580	−0.258307
$655$	0	0
$656$	−5.59327	−0.218381
$657$	− 17.5961i	− 0.686487i
$658$	− 5.02112i	− 0.195743i
$659$	−15.1865	−0.591584	−0.295792	−	0.955252i	$-0.595583\pi$
$659$	−15.1865	−0.591584	−0.295792	+	0.955252i	$0.595583\pi$
$660$	0	0
$661$	−44.6766	−1.73772	−0.868859	−	0.495060i	$-0.835146\pi$
$661$	−44.6766	−1.73772	−0.868859	+	0.495060i	$0.835146\pi$
$662$	− 3.02112i	− 0.117419i
$663$	1.26869i	0.0492719i
$664$	−8.81346	−0.342028
$665$	0	0
$666$	23.3606	0.905203
$667$	35.9019i	1.39013i
$668$	8.00000i	0.309529i
$669$	−1.54245	−0.0596347
$670$	0	0
$671$	0.978885	0.0377894
$672$	0.406728i	0.0156899i
$673$	38.0000i	1.46479i	0.680879	+	0.732396i	$0.261598\pi$
$673$	38.0000i	1.46479i	−0.680879	+	0.732396i	$0.738402\pi$
$674$	−9.66914	−0.372442
$675$	0	0
$676$	−12.3383	−0.474550
$677$	48.7325i	1.87294i	0.350745	+	0.936471i	$0.385928\pi$
$677$	48.7325i	1.87294i	−0.350745	+	0.936471i	$0.614072\pi$
$678$	− 5.69420i	− 0.218684i
$679$	−3.42784	−0.131549
$680$	0	0
$681$	5.71137	0.218860
$682$	6.00000i	0.229752i
$683$	− 0.482601i	− 0.0184662i	−0.999957	−	0.00923310i	$-0.997061\pi$
$683$	− 0.482601i	− 0.0184662i	0.999957	−	0.00923310i	$-0.00293903\pi$
$684$	15.3856	0.588284
$685$	0	0
$686$	1.00000	0.0381802
$687$	0.746173i	0.0284683i
$688$	− 3.02112i	− 0.115179i
$689$	5.38052	0.204981
$690$	0	0
$691$	−25.5037	−0.970207	−0.485104	−	0.874457i	$-0.661218\pi$
$691$	−25.5037	−0.970207	−0.485104	+	0.874457i	$0.661218\pi$
$692$	19.0211i	0.723074i
$693$	2.83457i	0.107676i
$694$	9.39420	0.356599
$695$	0	0
$696$	2.69026	0.101974
$697$	21.4478i	0.812393i
$698$	18.2077i	0.689170i
$699$	−3.27100	−0.123721
$700$	0	0
$701$	33.8682	1.27918	0.639592	−	0.768714i	$-0.279103\pi$
$701$	33.8682	1.27918	0.639592	+	0.768714i	$0.279103\pi$
$702$	− 1.93040i	− 0.0728584i
$703$	44.7325i	1.68712i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−12.7239	−0.478870
$707$	− 18.6903i	− 0.702920i
$708$	− 4.33086i	− 0.162764i
$709$	15.9749	0.599952	0.299976	−	0.953947i	$-0.403021\pi$
$709$	15.9749	0.599952	0.299976	+	0.953947i	$0.403021\pi$
$710$	0	0
$711$	−48.4626	−1.81749
$712$	− 1.18654i	− 0.0444676i
$713$	− 32.5671i	− 1.21965i
$714$	1.55963	0.0583677
$715$	0	0
$716$	4.64803	0.173705
$717$	− 6.29212i	− 0.234983i
$718$	− 29.8432i	− 1.11374i
$719$	13.4364	0.501094	0.250547	−	0.968104i	$-0.419389\pi$
$719$	13.4364	0.501094	0.250547	+	0.968104i	$0.419389\pi$
$720$	0	0
$721$	−15.4615	−0.575816
$722$	10.4615i	0.389336i
$723$	− 4.73249i	− 0.176003i
$724$	25.3383	0.941690
$725$	0	0
$726$	0.406728	0.0150951
$727$	− 6.64803i	− 0.246562i	−0.992372	−	0.123281i	$-0.960658\pi$
$727$	− 6.64803i	− 0.246562i	0.992372	−	0.123281i	$-0.0393416\pi$
$728$	− 0.813457i	− 0.0301487i
$729$	18.4729	0.684180
$730$	0	0
$731$	−11.5847	−0.428475
$732$	0.398140i	0.0147157i
$733$	38.0285i	1.40462i	0.711873	+	0.702308i	$0.247847\pi$
$733$	38.0285i	1.40462i	−0.711873	+	0.702308i	$0.752153\pi$
$734$	15.4615	0.570694
$735$	0	0
$736$	5.42784	0.200073
$737$	− 8.00000i	− 0.294684i
$738$	− 15.8545i	− 0.583613i
$739$	52.6343	1.93619	0.968093	−	0.250592i	$-0.0806252\pi$
$739$	52.6343	1.93619	0.968093	+	0.250592i	$0.0806252\pi$
$740$	0	0
$741$	1.79583	0.0659716
$742$	− 6.61439i	− 0.242822i
$743$	28.0845i	1.03032i	0.857094	+	0.515159i	$0.172267\pi$
$743$	28.0845i	1.03032i	−0.857094	+	0.515159i	$0.827733\pi$
$744$	−2.44037	−0.0894683
$745$	0	0
$746$	8.10951	0.296910
$747$	− 24.9824i	− 0.914057i
$748$	3.83457i	0.140206i
$749$	−11.0211	−0.402703
$750$	0	0
$751$	48.4826	1.76916	0.884578	−	0.466393i	$-0.154447\pi$
$751$	48.4826	1.76916	0.884578	+	0.466393i	$0.154447\pi$
$752$	5.02112i	0.183101i
$753$	− 2.17680i	− 0.0793270i
$754$	−5.38052	−0.195947
$755$	0	0
$756$	−2.37309	−0.0863083
$757$	11.8260i	0.429823i	0.976634	+	0.214911i	$0.0689463\pi$
$757$	11.8260i	0.429823i	−0.976634	+	0.214911i	$0.931054\pi$
$758$	− 22.0422i	− 0.800610i
$759$	−2.20766	−0.0801329
$760$	0	0
$761$	−19.5510	−0.708725	−0.354362	−	0.935108i	$-0.615302\pi$
$761$	−19.5510	−0.708725	−0.354362	+	0.935108i	$0.615302\pi$
$762$	− 7.03480i	− 0.254844i
$763$	− 16.2413i	− 0.587975i
$764$	−15.6691	−0.566890
$765$	0	0
$766$	−38.2499	−1.38202
$767$	8.66171i	0.312756i
$768$	− 0.406728i	− 0.0146765i
$769$	−6.07587	−0.219102	−0.109551	−	0.993981i	$-0.534941\pi$
$769$	−6.07587	−0.219102	−0.109551	+	0.993981i	$0.534941\pi$
$770$	0	0
$771$	−5.17517	−0.186379
$772$	2.16543i	0.0779355i
$773$	− 2.33086i	− 0.0838351i	−0.999121	−	0.0419175i	$-0.986653\pi$
$773$	− 2.33086i	− 0.0838351i	0.999121	−	0.0419175i	$-0.0133467\pi$
$774$	8.56357	0.307811
$775$	0	0
$776$	3.42784	0.123052
$777$	− 3.35197i	− 0.120251i
$778$	− 16.8557i	− 0.604306i
$779$	30.3594	1.08774
$780$	0	0
$781$	14.8557	0.531578
$782$	− 20.8135i	− 0.744288i
$783$	15.6965i	0.560948i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	3.83457	0.136775
$787$	17.3805i	0.619549i	0.950810	+	0.309774i	$0.100253\pi$
$787$	17.3805i	0.619549i	−0.950810	+	0.309774i	$0.899747\pi$
$788$	2.81346i	0.100225i
$789$	−0.661712	−0.0235576
$790$	0	0
$791$	14.0000	0.497783
$792$	− 2.83457i	− 0.100722i
$793$	− 0.796281i	− 0.0282768i
$794$	−4.44037	−0.157583
$795$	0	0
$796$	−13.0211	−0.461521
$797$	15.6942i	0.555917i	0.960593	+	0.277959i	$0.0896578\pi$
$797$	15.6942i	0.555917i	−0.960593	+	0.277959i	$0.910342\pi$
$798$	− 2.20766i	− 0.0781503i
$799$	19.2538	0.681151
$800$	0	0
$801$	3.36334	0.118838
$802$	− 3.46149i	− 0.122229i
$803$	− 6.20766i	− 0.219064i
$804$	3.25383	0.114754
$805$	0	0
$806$	4.88074	0.171917
$807$	9.71137i	0.341857i
$808$	18.6903i	0.657521i
$809$	−23.1443	−0.813711	−0.406855	−	0.913493i	$-0.633375\pi$
$809$	−23.1443	−0.813711	−0.406855	+	0.913493i	$0.633375\pi$
$810$	0	0
$811$	−27.6218	−0.969933	−0.484967	−	0.874533i	$-0.661168\pi$
$811$	−27.6218	−0.969933	−0.484967	+	0.874533i	$0.661168\pi$
$812$	6.61439i	0.232119i
$813$	− 0.992568i	− 0.0348109i
$814$	8.24130	0.288857
$815$	0	0
$816$	−1.55963	−0.0545980
$817$	16.3981i	0.573698i
$818$	17.2624i	0.603566i
$819$	2.30580	0.0805712
$820$	0	0
$821$	−39.5123	−1.37899	−0.689494	−	0.724291i	$-0.742167\pi$
$821$	−39.5123	−1.37899	−0.689494	+	0.724291i	$0.742167\pi$
$822$	− 5.55963i	− 0.193914i
$823$	13.5123i	0.471009i	0.971873	+	0.235505i	$0.0756743\pi$
$823$	13.5123i	0.471009i	−0.971873	+	0.235505i	$0.924326\pi$
$824$	15.4615	0.538626
$825$	0	0
$826$	10.6480	0.370492
$827$	− 12.0000i	− 0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$	− 12.0000i	− 0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	15.3856i	0.534687i
$829$	−13.8346	−0.480495	−0.240247	−	0.970712i	$-0.577229\pi$
$829$	−13.8346	−0.480495	−0.240247	+	0.970712i	$0.577229\pi$
$830$	0	0
$831$	−8.94803	−0.310404
$832$	0.813457i	0.0282015i
$833$	3.83457i	0.132860i
$834$	4.82714	0.167150
$835$	0	0
$836$	5.42784	0.187726
$837$	− 14.2385i	− 0.492155i
$838$	− 9.02112i	− 0.311629i
$839$	−44.0422	−1.52051	−0.760253	−	0.649627i	$-0.774925\pi$
$839$	−44.0422	−1.52051	−0.760253	+	0.649627i	$0.774925\pi$
$840$	0	0
$841$	14.7501	0.508625
$842$	31.7114i	1.09285i
$843$	8.48260i	0.292156i
$844$	−19.6691	−0.677040
$845$	0	0
$846$	−14.2327	−0.489331
$847$	1.00000i	0.0343604i
$848$	6.61439i	0.227139i
$849$	0.134569	0.00461838
$850$	0	0
$851$	−44.7325	−1.53341
$852$	6.04223i	0.207003i
$853$	− 29.8095i	− 1.02066i	−0.859979	−	0.510329i	$-0.829524\pi$
$853$	− 29.8095i	− 1.02066i	0.859979	−	0.510329i	$-0.170476\pi$
$854$	−0.978885	−0.0334968
$855$	0	0
$856$	11.0211	0.376694
$857$	− 42.7575i	− 1.46057i	−0.683143	−	0.730285i	$-0.739387\pi$
$857$	− 42.7575i	− 1.46057i	0.683143	−	0.730285i	$-0.260613\pi$
$858$	− 0.330856i	− 0.0112952i
$859$	−6.31717	−0.215539	−0.107770	−	0.994176i	$-0.534371\pi$
$859$	−6.31717	−0.215539	−0.107770	+	0.994176i	$0.534371\pi$
$860$	0	0
$861$	−2.27494	−0.0775298
$862$	− 3.05476i	− 0.104045i
$863$	− 48.3680i	− 1.64647i	−0.567704	−	0.823233i	$-0.692168\pi$
$863$	− 48.3680i	− 1.64647i	0.567704	−	0.823233i	$-0.307832\pi$
$864$	2.37309	0.0807340
$865$	0	0
$866$	−27.9104	−0.948436
$867$	− 0.933872i	− 0.0317160i
$868$	− 6.00000i	− 0.203653i
$869$	−17.0970	−0.579976
$870$	0	0
$871$	−6.50765	−0.220503
$872$	16.2413i	0.550000i
$873$	9.71647i	0.328853i
$874$	−29.4615	−0.996550
$875$	0	0
$876$	2.52483	0.0853061
$877$	24.1940i	0.816972i	0.912764	+	0.408486i	$0.133943\pi$
$877$	24.1940i	0.816972i	−0.912764	+	0.408486i	$0.866057\pi$
$878$	14.8557i	0.501355i
$879$	−1.29606	−0.0437149
$880$	0	0
$881$	12.3731	0.416860	0.208430	−	0.978037i	$-0.433165\pi$
$881$	12.3731	0.416860	0.208430	+	0.978037i	$0.433165\pi$
$882$	− 2.83457i	− 0.0954450i
$883$	− 14.5248i	− 0.488799i	−0.969675	−	0.244400i	$-0.921409\pi$
$883$	− 14.5248i	− 0.488799i	0.969675	−	0.244400i	$-0.0785909\pi$
$884$	3.11926	0.104912
$885$	0	0
$886$	−0.746173	−0.0250682
$887$	25.3805i	0.852194i	0.904677	+	0.426097i	$0.140112\pi$
$887$	25.3805i	0.852194i	−0.904677	+	0.426097i	$0.859888\pi$
$888$	3.35197i	0.112485i
$889$	17.2961	0.580091
$890$	0	0
$891$	7.53851	0.252550
$892$	3.79234i	0.126977i
$893$	− 27.2538i	− 0.912015i
$894$	9.06335	0.303124
$895$	0	0
$896$	1.00000	0.0334077
$897$	1.79583i	0.0599612i
$898$	− 9.83457i	− 0.328184i
$899$	−39.6863	−1.32361
$900$	0	0
$901$	25.3633	0.844975
$902$	− 5.59327i	− 0.186236i
$903$	− 1.22877i	− 0.0408910i
$904$	−14.0000	−0.465633
$905$	0	0
$906$	−1.24246	−0.0412779
$907$	7.93272i	0.263402i	0.991290	+	0.131701i	$0.0420438\pi$
$907$	7.93272i	0.263402i	−0.991290	+	0.131701i	$0.957956\pi$
$908$	− 14.0422i	− 0.466008i
$909$	−52.9789	−1.75720
$910$	0	0
$911$	43.7364	1.44905	0.724526	−	0.689247i	$-0.242059\pi$
$911$	43.7364	1.44905	0.724526	+	0.689247i	$0.242059\pi$
$912$	2.20766i	0.0731029i
$913$	− 8.81346i	− 0.291683i
$914$	11.2961	0.373640
$915$	0	0
$916$	1.83457	0.0606160
$917$	9.42784i	0.311335i
$918$	− 9.09977i	− 0.300337i
$919$	32.7661	1.08085	0.540427	−	0.841391i	$-0.318263\pi$
$919$	32.7661	1.08085	0.540427	+	0.841391i	$0.318263\pi$
$920$	0	0
$921$	−8.33086	−0.274511
$922$	− 7.41926i	− 0.244340i
$923$	− 12.0845i	− 0.397765i
$924$	−0.406728	−0.0133804
$925$	0	0
$926$	10.1740	0.334339
$927$	43.8267i	1.43946i
$928$	− 6.61439i	− 0.217128i
$929$	−59.4478	−1.95042	−0.975210	−	0.221283i	$-0.928975\pi$
$929$	−59.4478	−1.95042	−0.975210	+	0.221283i	$0.928975\pi$
$930$	0	0
$931$	5.42784	0.177890
$932$	8.04223i	0.263432i
$933$	− 1.47517i	− 0.0482949i
$934$	−32.4912	−1.06314
$935$	0	0
$936$	−2.30580	−0.0753675
$937$	− 53.2824i	− 1.74066i	−0.492470	−	0.870330i	$-0.663906\pi$
$937$	− 53.2824i	− 1.74066i	0.492470	−	0.870330i	$-0.336094\pi$
$938$	8.00000i	0.261209i
$939$	8.42900	0.275070
$940$	0	0
$941$	−5.72506	−0.186632	−0.0933158	−	0.995637i	$-0.529747\pi$
$941$	−5.72506	−0.186632	−0.0933158	+	0.995637i	$0.529747\pi$
$942$	− 1.97495i	− 0.0643472i
$943$	30.3594i	0.988638i
$944$	−10.6480	−0.346564
$945$	0	0
$946$	3.02112	0.0982249
$947$	27.4056i	0.890561i	0.895391	+	0.445281i	$0.146896\pi$
$947$	27.4056i	0.890561i	−0.895391	+	0.445281i	$0.853104\pi$
$948$	− 6.95383i	− 0.225850i
$949$	−5.04966	−0.163919
$950$	0	0
$951$	0.732489	0.0237526
$952$	− 3.83457i	− 0.124279i
$953$	− 10.7998i	− 0.349839i	−0.984583	−	0.174919i	$-0.944033\pi$
$953$	− 10.7998i	− 0.349839i	0.984583	−	0.174919i	$-0.0559665\pi$
$954$	−18.7490	−0.607020
$955$	0	0
$956$	−15.4701	−0.500338
$957$	2.69026i	0.0869637i
$958$	11.6691i	0.377013i
$959$	13.6691	0.441400
$960$	0	0
$961$	5.00000	0.161290
$962$	− 6.70394i	− 0.216144i
$963$	31.2401i	1.00670i
$964$	−11.6355	−0.374754
$965$	0	0
$966$	2.20766	0.0710302
$967$	− 11.2538i	− 0.361899i	−0.983492	−	0.180949i	$-0.942083\pi$
$967$	− 11.2538i	− 0.361899i	0.983492	−	0.180949i	$-0.0579170\pi$
$968$	− 1.00000i	− 0.0321412i
$969$	8.46542	0.271949
$970$	0	0
$971$	33.2401	1.06673	0.533363	−	0.845886i	$-0.320928\pi$
$971$	33.2401	1.06673	0.533363	+	0.845886i	$0.320928\pi$
$972$	10.1854i	0.326696i
$973$	11.8682i	0.380477i
$974$	−5.49513	−0.176075
$975$	0	0
$976$	0.978885	0.0313333
$977$	2.74617i	0.0878578i	0.999035	+	0.0439289i	$0.0139875\pi$
$977$	2.74617i	0.0878578i	−0.999035	+	0.0439289i	$0.986012\pi$
$978$	− 3.25383i	− 0.104046i
$979$	1.18654	0.0379221
$980$	0	0
$981$	−46.0371	−1.46985
$982$	− 13.2961i	− 0.424294i
$983$	39.4615i	1.25863i	0.777152	+	0.629313i	$0.216664\pi$
$983$	39.4615i	1.25863i	−0.777152	+	0.629313i	$0.783336\pi$
$984$	2.27494	0.0725225
$985$	0	0
$986$	−25.3633	−0.807733
$987$	2.04223i	0.0650049i
$988$	− 4.41532i	− 0.140470i
$989$	−16.3981	−0.521431
$990$	0	0
$991$	20.9652	0.665982	0.332991	−	0.942930i	$-0.391942\pi$
$991$	20.9652	0.665982	0.332991	+	0.942930i	$0.391942\pi$
$992$	6.00000i	0.190500i
$993$	1.22877i	0.0389939i
$994$	−14.8557	−0.471194
$995$	0	0
$996$	3.58468	0.113585
$997$	− 21.9441i	− 0.694976i	−0.937684	−	0.347488i	$-0.887035\pi$
$997$	− 21.9441i	− 0.694976i	0.937684	−	0.347488i	$-0.112965\pi$
$998$	24.6480i	0.780220i
$999$	−19.5573	−0.618766

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.z.1849.5		6
5.2	odd	4		770.2.a.l.1.2	✓	3
5.3	odd	4		3850.2.a.bu.1.2		3
5.4	even	2	inner	3850.2.c.z.1849.2		6
15.2	even	4		6930.2.a.cl.1.2		3
20.7	even	4		6160.2.a.bi.1.2		3
35.27	even	4		5390.2.a.bz.1.2		3
55.32	even	4		8470.2.a.cl.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.l.1.2	✓	3	5.2	odd	4
3850.2.a.bu.1.2		3	5.3	odd	4
3850.2.c.z.1849.2		6	5.4	even	2	inner
3850.2.c.z.1849.5		6	1.1	even	1	trivial
5390.2.a.bz.1.2		3	35.27	even	4
6160.2.a.bi.1.2		3	20.7	even	4
6930.2.a.cl.1.2		3	15.2	even	4
8470.2.a.cl.1.2		3	55.32	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.83457 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.406728i q^{3} -1.00000 q^{4} +0.406728 q^{6} +1.00000i q^{7} -1.00000i q^{8} +2.83457 q^{9} +1.00000 q^{11} +0.406728i q^{12} -0.813457i q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.83457i q^{17} +2.83457i q^{18} -5.42784 q^{19} +0.406728 q^{21} +1.00000i q^{22} -5.42784i q^{23} -0.406728 q^{24} +0.813457 q^{26} -2.37309i q^{27} -1.00000i q^{28} -6.61439 q^{29} +6.00000 q^{31} +1.00000i q^{32} -0.406728i q^{33} +3.83457 q^{34} -2.83457 q^{36} -8.24130i q^{37} -5.42784i q^{38} -0.330856 q^{39} -5.59327 q^{41} +0.406728i q^{42} -3.02112i q^{43} -1.00000 q^{44} +5.42784 q^{46} +5.02112i q^{47} -0.406728i q^{48} -1.00000 q^{49} -1.55963 q^{51} +0.813457i q^{52} +6.61439i q^{53} +2.37309 q^{54} +1.00000 q^{56} +2.20766i q^{57} -6.61439i q^{58} -10.6480 q^{59} +0.978885 q^{61} +6.00000i q^{62} +2.83457i q^{63} -1.00000 q^{64} +0.406728 q^{66} -8.00000i q^{67} +3.83457i q^{68} -2.20766 q^{69} +14.8557 q^{71} -2.83457i q^{72} -6.20766i q^{73} +8.24130 q^{74} +5.42784 q^{76} +1.00000i q^{77} -0.330856i q^{78} -17.0970 q^{79} +7.53851 q^{81} -5.59327i q^{82} -8.81346i q^{83} -0.406728 q^{84} +3.02112 q^{86} +2.69026i q^{87} -1.00000i q^{88} +1.18654 q^{89} +0.813457 q^{91} +5.42784i q^{92} -2.44037i q^{93} -5.02112 q^{94} +0.406728 q^{96} +3.42784i q^{97} -1.00000i q^{98} +2.83457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 22 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 22 * q^9	\( 6 q - 6 q^{4} - 22 q^{9} + 6 q^{11} - 6 q^{14} + 6 q^{16} + 4 q^{19} - 8 q^{29} + 36 q^{31} - 16 q^{34} + 22 q^{36} - 80 q^{39} - 36 q^{41} - 6 q^{44} - 4 q^{46} - 6 q^{49} - 24 q^{51} + 24 q^{54} + 6 q^{56} - 20 q^{59} + 40 q^{61} - 6 q^{64} + 16 q^{69} + 16 q^{71} + 8 q^{74} - 4 q^{76} + 12 q^{79} + 94 q^{81} - 16 q^{86} + 12 q^{89} + 4 q^{94} - 22 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 22 * q^9 + 6 * q^11 - 6 * q^14 + 6 * q^16 + 4 * q^19 - 8 * q^29 + 36 * q^31 - 16 * q^34 + 22 * q^36 - 80 * q^39 - 36 * q^41 - 6 * q^44 - 4 * q^46 - 6 * q^49 - 24 * q^51 + 24 * q^54 + 6 * q^56 - 20 * q^59 + 40 * q^61 - 6 * q^64 + 16 * q^69 + 16 * q^71 + 8 * q^74 - 4 * q^76 + 12 * q^79 + 94 * q^81 - 16 * q^86 + 12 * q^89 + 4 * q^94 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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