LMFDB - Embedded newform 1014.2.b.g.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(337,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1014.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$-0.445042i$ of defining polynomial
Character	$\chi$	$=$	1014.337
Dual form			1014.2.b.g.337.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.692021i q^{5} -1.00000i q^{6} -0.356896i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.692021i q^{5} -1.00000i q^{6} -0.356896i q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.692021 q^{10} -2.93900i q^{11} -1.00000 q^{12} -0.356896 q^{14} -0.692021i q^{15} +1.00000 q^{16} -6.71379 q^{17} -1.00000i q^{18} -7.20775i q^{19} +0.692021i q^{20} -0.356896i q^{21} -2.93900 q^{22} -2.39612 q^{23} +1.00000i q^{24} +4.52111 q^{25} +1.00000 q^{27} +0.356896i q^{28} +7.82908 q^{29} -0.692021 q^{30} -2.76271i q^{31} -1.00000i q^{32} -2.93900i q^{33} +6.71379i q^{34} -0.246980 q^{35} -1.00000 q^{36} -10.0978i q^{37} -7.20775 q^{38} +0.692021 q^{40} +4.89008i q^{41} -0.356896 q^{42} -6.59179 q^{43} +2.93900i q^{44} -0.692021i q^{45} +2.39612i q^{46} -4.98792i q^{47} +1.00000 q^{48} +6.87263 q^{49} -4.52111i q^{50} -6.71379 q^{51} -8.88769 q^{53} -1.00000i q^{54} -2.03385 q^{55} +0.356896 q^{56} -7.20775i q^{57} -7.82908i q^{58} -1.64310i q^{59} +0.692021i q^{60} -6.49396 q^{61} -2.76271 q^{62} -0.356896i q^{63} -1.00000 q^{64} -2.93900 q^{66} +13.5254i q^{67} +6.71379 q^{68} -2.39612 q^{69} +0.246980i q^{70} +6.81163i q^{71} +1.00000i q^{72} -3.18598i q^{73} -10.0978 q^{74} +4.52111 q^{75} +7.20775i q^{76} -1.04892 q^{77} +15.0465 q^{79} -0.692021i q^{80} +1.00000 q^{81} +4.89008 q^{82} -14.8267i q^{83} +0.356896i q^{84} +4.64609i q^{85} +6.59179i q^{86} +7.82908 q^{87} +2.93900 q^{88} -0.396125i q^{89} -0.692021 q^{90} +2.39612 q^{92} -2.76271i q^{93} -4.98792 q^{94} -4.98792 q^{95} -1.00000i q^{96} -0.417895i q^{97} -6.87263i q^{98} -2.93900i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9	$ 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9} + 6 q^{10} - 6 q^{12} + 6 q^{14} + 6 q^{16} - 24 q^{17} + 2 q^{22} - 32 q^{23} - 4 q^{25} + 6 q^{27} + 26 q^{29} + 6 q^{30} + 8 q^{35} - 6 q^{36} - 8 q^{38} - 6 q^{40} + 6 q^{42} + 16 q^{43} + 6 q^{48} + 8 q^{49} - 24 q^{51} + 30 q^{53} - 44 q^{55} - 6 q^{56} - 20 q^{61} + 18 q^{62} - 6 q^{64} + 2 q^{66} + 24 q^{68} - 32 q^{69} - 24 q^{74} - 4 q^{75} + 12 q^{77} - 10 q^{79} + 6 q^{81} + 28 q^{82} + 26 q^{87} - 2 q^{88} + 6 q^{90} + 32 q^{92} + 8 q^{94} + 8 q^{95}+O(q^{100}) $ 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9 + 6 * q^10 - 6 * q^12 + 6 * q^14 + 6 * q^16 - 24 * q^17 + 2 * q^22 - 32 * q^23 - 4 * q^25 + 6 * q^27 + 26 * q^29 + 6 * q^30 + 8 * q^35 - 6 * q^36 - 8 * q^38 - 6 * q^40 + 6 * q^42 + 16 * q^43 + 6 * q^48 + 8 * q^49 - 24 * q^51 + 30 * q^53 - 44 * q^55 - 6 * q^56 - 20 * q^61 + 18 * q^62 - 6 * q^64 + 2 * q^66 + 24 * q^68 - 32 * q^69 - 24 * q^74 - 4 * q^75 + 12 * q^77 - 10 * q^79 + 6 * q^81 + 28 * q^82 + 26 * q^87 - 2 * q^88 + 6 * q^90 + 32 * q^92 + 8 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$-1$

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	− 0.692021i	− 0.309481i	−0.987955	−	0.154741i	$-0.950546\pi$
$5$	− 0.692021i	− 0.309481i	0.987955	−	0.154741i	$-0.0494542\pi$
$6$	− 1.00000i	− 0.408248i
$7$	− 0.356896i	− 0.134894i	−0.997723	−	0.0674470i	$-0.978515\pi$
$7$	− 0.356896i	− 0.134894i	0.997723	−	0.0674470i	$-0.0214854\pi$
$8$	1.00000i	0.353553i
$9$	1.00000	0.333333
$10$	−0.692021	−0.218836
$11$	− 2.93900i	− 0.886142i	−0.896486	−	0.443071i	$-0.853889\pi$
$11$	− 2.93900i	− 0.886142i	0.896486	−	0.443071i	$-0.146111\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−0.356896	−0.0953844
$15$	− 0.692021i	− 0.178679i
$16$	1.00000	0.250000
$17$	−6.71379	−1.62833	−0.814167	−	0.580631i	$-0.802806\pi$
$17$	−6.71379	−1.62833	−0.814167	+	0.580631i	$0.802806\pi$
$18$	− 1.00000i	− 0.235702i
$19$	− 7.20775i	− 1.65357i	−0.562517	−	0.826786i	$-0.690167\pi$
$19$	− 7.20775i	− 1.65357i	0.562517	−	0.826786i	$-0.309833\pi$
$20$	0.692021i	0.154741i
$21$	− 0.356896i	− 0.0778811i
$22$	−2.93900	−0.626597
$23$	−2.39612	−0.499627	−0.249813	−	0.968294i	$-0.580369\pi$
$23$	−2.39612	−0.499627	−0.249813	+	0.968294i	$0.580369\pi$
$24$	1.00000i	0.204124i
$25$	4.52111	0.904221
$26$	0	0
$27$	1.00000	0.192450
$28$	0.356896i	0.0674470i
$29$	7.82908	1.45382	0.726912	−	0.686730i	$-0.240955\pi$
$29$	7.82908	1.45382	0.726912	+	0.686730i	$0.240955\pi$
$30$	−0.692021	−0.126345
$31$	− 2.76271i	− 0.496197i	−0.968735	−	0.248099i	$-0.920194\pi$
$31$	− 2.76271i	− 0.496197i	0.968735	−	0.248099i	$-0.0798057\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 2.93900i	− 0.511614i
$34$	6.71379i	1.15141i
$35$	−0.246980	−0.0417472
$36$	−1.00000	−0.166667
$37$	− 10.0978i	− 1.66007i	−0.557708	−	0.830037i	$-0.688319\pi$
$37$	− 10.0978i	− 1.66007i	0.557708	−	0.830037i	$-0.311681\pi$
$38$	−7.20775	−1.16925
$39$	0	0
$40$	0.692021	0.109418
$41$	4.89008i	0.763703i	0.924224	+	0.381851i	$0.124713\pi$
$41$	4.89008i	0.763703i	−0.924224	+	0.381851i	$0.875287\pi$
$42$	−0.356896	−0.0550702
$43$	−6.59179	−1.00524	−0.502620	−	0.864508i	$-0.667630\pi$
$43$	−6.59179	−1.00524	−0.502620	+	0.864508i	$0.667630\pi$
$44$	2.93900i	0.443071i
$45$	− 0.692021i	− 0.103160i
$46$	2.39612i	0.353289i
$47$	− 4.98792i	− 0.727563i	−0.931484	−	0.363781i	$-0.881486\pi$
$47$	− 4.98792i	− 0.727563i	0.931484	−	0.363781i	$-0.118514\pi$
$48$	1.00000	0.144338
$49$	6.87263	0.981804
$50$	− 4.52111i	− 0.639381i
$51$	−6.71379	−0.940119
$52$	0	0
$53$	−8.88769	−1.22082	−0.610409	−	0.792086i	$-0.708995\pi$
$53$	−8.88769	−1.22082	−0.610409	+	0.792086i	$0.708995\pi$
$54$	− 1.00000i	− 0.136083i
$55$	−2.03385	−0.274245
$56$	0.356896	0.0476922
$57$	− 7.20775i	− 0.954690i
$58$	− 7.82908i	− 1.02801i
$59$	− 1.64310i	− 0.213914i	−0.994264	−	0.106957i	$-0.965889\pi$
$59$	− 1.64310i	− 0.213914i	0.994264	−	0.106957i	$-0.0341107\pi$
$60$	0.692021i	0.0893396i
$61$	−6.49396	−0.831466	−0.415733	−	0.909487i	$-0.636475\pi$
$61$	−6.49396	−0.831466	−0.415733	+	0.909487i	$0.636475\pi$
$62$	−2.76271	−0.350864
$63$	− 0.356896i	− 0.0449647i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.93900	−0.361766
$67$	13.5254i	1.65239i	0.563382	+	0.826196i	$0.309500\pi$
$67$	13.5254i	1.65239i	−0.563382	+	0.826196i	$0.690500\pi$
$68$	6.71379	0.814167
$69$	−2.39612	−0.288459
$70$	0.246980i	0.0295197i
$71$	6.81163i	0.808391i	0.914673	+	0.404196i	$0.132449\pi$
$71$	6.81163i	0.808391i	−0.914673	+	0.404196i	$0.867551\pi$
$72$	1.00000i	0.117851i
$73$	− 3.18598i	− 0.372891i	−0.982465	−	0.186445i	$-0.940303\pi$
$73$	− 3.18598i	− 0.372891i	0.982465	−	0.186445i	$-0.0596968\pi$
$74$	−10.0978	−1.17385
$75$	4.52111	0.522052
$76$	7.20775i	0.826786i
$77$	−1.04892	−0.119535
$78$	0	0
$79$	15.0465	1.69287	0.846433	−	0.532495i	$-0.178745\pi$
$79$	15.0465	1.69287	0.846433	+	0.532495i	$0.178745\pi$
$80$	− 0.692021i	− 0.0773704i
$81$	1.00000	0.111111
$82$	4.89008	0.540019
$83$	− 14.8267i	− 1.62744i	−0.581256	−	0.813720i	$-0.697439\pi$
$83$	− 14.8267i	− 1.62744i	0.581256	−	0.813720i	$-0.302561\pi$
$84$	0.356896i	0.0389405i
$85$	4.64609i	0.503939i
$86$	6.59179i	0.710811i
$87$	7.82908	0.839366
$88$	2.93900	0.313299
$89$	− 0.396125i	− 0.0419891i	−0.999780	−	0.0209946i	$-0.993317\pi$
$89$	− 0.396125i	− 0.0419891i	0.999780	−	0.0209946i	$-0.00668327\pi$
$90$	−0.692021	−0.0729455
$91$	0	0
$92$	2.39612	0.249813
$93$	− 2.76271i	− 0.286480i
$94$	−4.98792	−0.514465
$95$	−4.98792	−0.511750
$96$	− 1.00000i	− 0.102062i
$97$	− 0.417895i	− 0.0424308i	−0.999775	−	0.0212154i	$-0.993246\pi$
$97$	− 0.417895i	− 0.0424308i	0.999775	−	0.0212154i	$-0.00675358\pi$
$98$	− 6.87263i	− 0.694240i
$99$	− 2.93900i	− 0.295381i
$100$	−4.52111	−0.452111
$101$	−10.0151	−0.996536	−0.498268	−	0.867023i	$-0.666030\pi$
$101$	−10.0151	−0.996536	−0.498268	+	0.867023i	$0.666030\pi$
$102$	6.71379i	0.664764i
$103$	9.62565	0.948443	0.474222	−	0.880406i	$-0.342730\pi$
$103$	9.62565	0.948443	0.474222	+	0.880406i	$0.342730\pi$
$104$	0	0
$105$	−0.246980	−0.0241027
$106$	8.88769i	0.863249i
$107$	−6.63102	−0.641045	−0.320523	−	0.947241i	$-0.603859\pi$
$107$	−6.63102	−0.641045	−0.320523	+	0.947241i	$0.603859\pi$
$108$	−1.00000	−0.0962250
$109$	12.9879i	1.24402i	0.783011	+	0.622008i	$0.213683\pi$
$109$	12.9879i	1.24402i	−0.783011	+	0.622008i	$0.786317\pi$
$110$	2.03385i	0.193920i
$111$	− 10.0978i	− 0.958444i
$112$	− 0.356896i	− 0.0337235i
$113$	0.792249	0.0745285	0.0372643	−	0.999305i	$-0.488136\pi$
$113$	0.792249	0.0745285	0.0372643	+	0.999305i	$0.488136\pi$
$114$	−7.20775	−0.675068
$115$	1.65817i	0.154625i
$116$	−7.82908	−0.726912
$117$	0	0
$118$	−1.64310	−0.151260
$119$	2.39612i	0.219652i
$120$	0.692021	0.0631726
$121$	2.36227	0.214752
$122$	6.49396i	0.587935i
$123$	4.89008i	0.440924i
$124$	2.76271i	0.248099i
$125$	− 6.58881i	− 0.589321i
$126$	−0.356896	−0.0317948
$127$	18.2174	1.61654	0.808268	−	0.588815i	$-0.200405\pi$
$127$	18.2174	1.61654	0.808268	+	0.588815i	$0.200405\pi$
$128$	1.00000i	0.0883883i
$129$	−6.59179	−0.580375
$130$	0	0
$131$	2.73556	0.239007	0.119504	−	0.992834i	$-0.461870\pi$
$131$	2.73556	0.239007	0.119504	+	0.992834i	$0.461870\pi$
$132$	2.93900i	0.255807i
$133$	−2.57242	−0.223057
$134$	13.5254	1.16842
$135$	− 0.692021i	− 0.0595597i
$136$	− 6.71379i	− 0.575703i
$137$	7.64742i	0.653363i	0.945135	+	0.326681i	$0.105930\pi$
$137$	7.64742i	0.653363i	−0.945135	+	0.326681i	$0.894070\pi$
$138$	2.39612i	0.203972i
$139$	3.38404	0.287031	0.143515	−	0.989648i	$-0.454159\pi$
$139$	3.38404	0.287031	0.143515	+	0.989648i	$0.454159\pi$
$140$	0.246980	0.0208736
$141$	− 4.98792i	− 0.420059i
$142$	6.81163	0.571619
$143$	0	0
$144$	1.00000	0.0833333
$145$	− 5.41789i	− 0.449932i
$146$	−3.18598	−0.263674
$147$	6.87263	0.566845
$148$	10.0978i	0.830037i
$149$	20.8170i	1.70540i	0.522405	+	0.852698i	$0.325035\pi$
$149$	20.8170i	1.70540i	−0.522405	+	0.852698i	$0.674965\pi$
$150$	− 4.52111i	− 0.369147i
$151$	− 0.895461i	− 0.0728715i	−0.999336	−	0.0364358i	$-0.988400\pi$
$151$	− 0.895461i	− 0.0728715i	0.999336	−	0.0364358i	$-0.0116004\pi$
$152$	7.20775	0.584626
$153$	−6.71379	−0.542778
$154$	1.04892i	0.0845242i
$155$	−1.91185	−0.153564
$156$	0	0
$157$	8.59179	0.685700	0.342850	−	0.939390i	$-0.388608\pi$
$157$	8.59179	0.685700	0.342850	+	0.939390i	$0.388608\pi$
$158$	− 15.0465i	− 1.19704i
$159$	−8.88769	−0.704840
$160$	−0.692021	−0.0547091
$161$	0.855167i	0.0673966i
$162$	− 1.00000i	− 0.0785674i
$163$	1.72587i	0.135181i	0.997713	+	0.0675904i	$0.0215311\pi$
$163$	1.72587i	0.135181i	−0.997713	+	0.0675904i	$0.978469\pi$
$164$	− 4.89008i	− 0.381851i
$165$	−2.03385	−0.158335
$166$	−14.8267	−1.15077
$167$	21.1400i	1.63587i	0.575314	+	0.817933i	$0.304880\pi$
$167$	21.1400i	1.63587i	−0.575314	+	0.817933i	$0.695120\pi$
$168$	0.356896	0.0275351
$169$	0	0
$170$	4.64609	0.356339
$171$	− 7.20775i	− 0.551190i
$172$	6.59179	0.502620
$173$	−9.35450	−0.711210	−0.355605	−	0.934636i	$-0.615725\pi$
$173$	−9.35450	−0.711210	−0.355605	+	0.934636i	$0.615725\pi$
$174$	− 7.82908i	− 0.593521i
$175$	− 1.61356i	− 0.121974i
$176$	− 2.93900i	− 0.221536i
$177$	− 1.64310i	− 0.123503i
$178$	−0.396125	−0.0296908
$179$	−3.17523	−0.237328	−0.118664	−	0.992934i	$-0.537861\pi$
$179$	−3.17523	−0.237328	−0.118664	+	0.992934i	$0.537861\pi$
$180$	0.692021i	0.0515802i
$181$	19.7995	1.47169	0.735844	−	0.677151i	$-0.236786\pi$
$181$	19.7995	1.47169	0.735844	+	0.677151i	$0.236786\pi$
$182$	0	0
$183$	−6.49396	−0.480047
$184$	− 2.39612i	− 0.176645i
$185$	−6.98792	−0.513762
$186$	−2.76271	−0.202572
$187$	19.7318i	1.44294i
$188$	4.98792i	0.363781i
$189$	− 0.356896i	− 0.0259604i
$190$	4.98792i	0.361862i
$191$	15.2620	1.10432	0.552161	−	0.833737i	$-0.313803\pi$
$191$	15.2620	1.10432	0.552161	+	0.833737i	$0.313803\pi$
$192$	−1.00000	−0.0721688
$193$	4.76809i	0.343214i	0.985165	+	0.171607i	$0.0548960\pi$
$193$	4.76809i	0.343214i	−0.985165	+	0.171607i	$0.945104\pi$
$194$	−0.417895	−0.0300031
$195$	0	0
$196$	−6.87263	−0.490902
$197$	− 12.2349i	− 0.871700i	−0.900019	−	0.435850i	$-0.856448\pi$
$197$	− 12.2349i	− 0.871700i	0.900019	−	0.435850i	$-0.143552\pi$
$198$	−2.93900	−0.208866
$199$	11.8485	0.839915	0.419958	−	0.907544i	$-0.362045\pi$
$199$	11.8485	0.839915	0.419958	+	0.907544i	$0.362045\pi$
$200$	4.52111i	0.319690i
$201$	13.5254i	0.954009i
$202$	10.0151i	0.704658i
$203$	− 2.79417i	− 0.196112i
$204$	6.71379	0.470059
$205$	3.38404	0.236352
$206$	− 9.62565i	− 0.670651i
$207$	−2.39612	−0.166542
$208$	0	0
$209$	−21.1836	−1.46530
$210$	0.246980i	0.0170432i
$211$	−17.2620	−1.18837	−0.594184	−	0.804329i	$-0.702525\pi$
$211$	−17.2620	−1.18837	−0.594184	+	0.804329i	$0.702525\pi$
$212$	8.88769	0.610409
$213$	6.81163i	0.466725i
$214$	6.63102i	0.453287i
$215$	4.56166i	0.311103i
$216$	1.00000i	0.0680414i
$217$	−0.985999	−0.0669340
$218$	12.9879	0.879653
$219$	− 3.18598i	− 0.215289i
$220$	2.03385	0.137122
$221$	0	0
$222$	−10.0978	−0.677722
$223$	− 6.76809i	− 0.453225i	−0.973985	−	0.226612i	$-0.927235\pi$
$223$	− 6.76809i	− 0.453225i	0.973985	−	0.226612i	$-0.0727650\pi$
$224$	−0.356896	−0.0238461
$225$	4.52111	0.301407
$226$	− 0.792249i	− 0.0526996i
$227$	− 23.6799i	− 1.57169i	−0.618422	−	0.785846i	$-0.712228\pi$
$227$	− 23.6799i	− 1.57169i	0.618422	−	0.785846i	$-0.287772\pi$
$228$	7.20775i	0.477345i
$229$	− 8.29829i	− 0.548366i	−0.961677	−	0.274183i	$-0.911593\pi$
$229$	− 8.29829i	− 0.548366i	0.961677	−	0.274183i	$-0.0884075\pi$
$230$	1.65817	0.109336
$231$	−1.04892	−0.0690137
$232$	7.82908i	0.514005i
$233$	23.9651	1.57000	0.785002	−	0.619493i	$-0.212662\pi$
$233$	23.9651	1.57000	0.785002	+	0.619493i	$0.212662\pi$
$234$	0	0
$235$	−3.45175	−0.225167
$236$	1.64310i	0.106957i
$237$	15.0465	0.977377
$238$	2.39612	0.155318
$239$	− 12.6160i	− 0.816058i	−0.912969	−	0.408029i	$-0.866216\pi$
$239$	− 12.6160i	− 0.816058i	0.912969	−	0.408029i	$-0.133784\pi$
$240$	− 0.692021i	− 0.0446698i
$241$	26.3937i	1.70017i	0.526646	+	0.850085i	$0.323449\pi$
$241$	26.3937i	1.70017i	−0.526646	+	0.850085i	$0.676551\pi$
$242$	− 2.36227i	− 0.151853i
$243$	1.00000	0.0641500
$244$	6.49396	0.415733
$245$	− 4.75600i	− 0.303850i
$246$	4.89008	0.311780
$247$	0	0
$248$	2.76271	0.175432
$249$	− 14.8267i	− 0.939603i
$250$	−6.58881	−0.416713
$251$	30.0344	1.89576	0.947879	−	0.318632i	$-0.103223\pi$
$251$	30.0344	1.89576	0.947879	+	0.318632i	$0.103223\pi$
$252$	0.356896i	0.0224823i
$253$	7.04221i	0.442740i
$254$	− 18.2174i	− 1.14306i
$255$	4.64609i	0.290949i
$256$	1.00000	0.0625000
$257$	−11.2620	−0.702507	−0.351254	−	0.936280i	$-0.614244\pi$
$257$	−11.2620	−0.702507	−0.351254	+	0.936280i	$0.614244\pi$
$258$	6.59179i	0.410387i
$259$	−3.60388	−0.223934
$260$	0	0
$261$	7.82908	0.484608
$262$	− 2.73556i	− 0.169004i
$263$	−5.54958	−0.342202	−0.171101	−	0.985254i	$-0.554732\pi$
$263$	−5.54958	−0.342202	−0.171101	+	0.985254i	$0.554732\pi$
$264$	2.93900	0.180883
$265$	6.15047i	0.377821i
$266$	2.57242i	0.157725i
$267$	− 0.396125i	− 0.0242424i
$268$	− 13.5254i	− 0.826196i
$269$	16.6872	1.01744	0.508719	−	0.860932i	$-0.330119\pi$
$269$	16.6872	1.01744	0.508719	+	0.860932i	$0.330119\pi$
$270$	−0.692021	−0.0421151
$271$	− 6.61356i	− 0.401745i	−0.979617	−	0.200873i	$-0.935622\pi$
$271$	− 6.61356i	− 0.401745i	0.979617	−	0.200873i	$-0.0643778\pi$
$272$	−6.71379	−0.407083
$273$	0	0
$274$	7.64742	0.461997
$275$	− 13.2875i	− 0.801269i
$276$	2.39612	0.144230
$277$	21.7995	1.30981	0.654904	−	0.755712i	$-0.272709\pi$
$277$	21.7995	1.30981	0.654904	+	0.755712i	$0.272709\pi$
$278$	− 3.38404i	− 0.202961i
$279$	− 2.76271i	− 0.165399i
$280$	− 0.246980i	− 0.0147599i
$281$	20.5918i	1.22840i	0.789149	+	0.614202i	$0.210522\pi$
$281$	20.5918i	1.22840i	−0.789149	+	0.614202i	$0.789478\pi$
$282$	−4.98792	−0.297026
$283$	13.0121	0.773488	0.386744	−	0.922187i	$-0.373600\pi$
$283$	13.0121	0.773488	0.386744	+	0.922187i	$0.373600\pi$
$284$	− 6.81163i	− 0.404196i
$285$	−4.98792	−0.295459
$286$	0	0
$287$	1.74525	0.103019
$288$	− 1.00000i	− 0.0589256i
$289$	28.0750	1.65147
$290$	−5.41789	−0.318150
$291$	− 0.417895i	− 0.0244974i
$292$	3.18598i	0.186445i
$293$	− 14.9390i	− 0.872746i	−0.899766	−	0.436373i	$-0.856263\pi$
$293$	− 14.9390i	− 0.872746i	0.899766	−	0.436373i	$-0.143737\pi$
$294$	− 6.87263i	− 0.400820i
$295$	−1.13706	−0.0662024
$296$	10.0978	0.586925
$297$	− 2.93900i	− 0.170538i
$298$	20.8170	1.20590
$299$	0	0
$300$	−4.52111	−0.261026
$301$	2.35258i	0.135601i
$302$	−0.895461	−0.0515280
$303$	−10.0151	−0.575350
$304$	− 7.20775i	− 0.413393i
$305$	4.49396i	0.257323i
$306$	6.71379i	0.383802i
$307$	26.0301i	1.48562i	0.669503	+	0.742809i	$0.266507\pi$
$307$	26.0301i	1.48562i	−0.669503	+	0.742809i	$0.733493\pi$
$308$	1.04892	0.0597676
$309$	9.62565	0.547584
$310$	1.91185i	0.108586i
$311$	4.81163	0.272842	0.136421	−	0.990651i	$-0.456440\pi$
$311$	4.81163	0.272842	0.136421	+	0.990651i	$0.456440\pi$
$312$	0	0
$313$	−26.0411	−1.47193	−0.735966	−	0.677018i	$-0.763272\pi$
$313$	−26.0411	−1.47193	−0.735966	+	0.677018i	$0.763272\pi$
$314$	− 8.59179i	− 0.484863i
$315$	−0.246980	−0.0139157
$316$	−15.0465	−0.846433
$317$	11.5211i	0.647090i	0.946213	+	0.323545i	$0.104875\pi$
$317$	11.5211i	0.647090i	−0.946213	+	0.323545i	$0.895125\pi$
$318$	8.88769i	0.498397i
$319$	− 23.0097i	− 1.28830i
$320$	0.692021i	0.0386852i
$321$	−6.63102	−0.370108
$322$	0.855167	0.0476566
$323$	48.3913i	2.69257i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	1.72587	0.0955873
$327$	12.9879i	0.718234i
$328$	−4.89008	−0.270010
$329$	−1.78017	−0.0981438
$330$	2.03385i	0.111960i
$331$	− 3.43834i	− 0.188988i	−0.995525	−	0.0944940i	$-0.969877\pi$
$331$	− 3.43834i	− 0.188988i	0.995525	−	0.0944940i	$-0.0301233\pi$
$332$	14.8267i	0.813720i
$333$	− 10.0978i	− 0.553358i
$334$	21.1400	1.15673
$335$	9.35988	0.511385
$336$	− 0.356896i	− 0.0194703i
$337$	−8.20105	−0.446739	−0.223370	−	0.974734i	$-0.571706\pi$
$337$	−8.20105	−0.446739	−0.223370	+	0.974734i	$0.571706\pi$
$338$	0	0
$339$	0.792249	0.0430291
$340$	− 4.64609i	− 0.251970i
$341$	−8.11960	−0.439701
$342$	−7.20775	−0.389751
$343$	− 4.95108i	− 0.267333i
$344$	− 6.59179i	− 0.355406i
$345$	1.65817i	0.0892729i
$346$	9.35450i	0.502901i
$347$	7.86294	0.422105	0.211052	−	0.977475i	$-0.432311\pi$
$347$	7.86294	0.422105	0.211052	+	0.977475i	$0.432311\pi$
$348$	−7.82908	−0.419683
$349$	− 18.7245i	− 1.00230i	−0.865360	−	0.501151i	$-0.832910\pi$
$349$	− 18.7245i	− 1.00230i	0.865360	−	0.501151i	$-0.167090\pi$
$350$	−1.61356	−0.0862486
$351$	0	0
$352$	−2.93900	−0.156649
$353$	31.5448i	1.67896i	0.543391	+	0.839480i	$0.317140\pi$
$353$	31.5448i	1.67896i	−0.543391	+	0.839480i	$0.682860\pi$
$354$	−1.64310	−0.0873300
$355$	4.71379	0.250182
$356$	0.396125i	0.0209946i
$357$	2.39612i	0.126816i
$358$	3.17523i	0.167816i
$359$	2.39612i	0.126463i	0.997999	+	0.0632313i	$0.0201406\pi$
$359$	2.39612i	0.126463i	−0.997999	+	0.0632313i	$0.979859\pi$
$360$	0.692021	0.0364727
$361$	−32.9517	−1.73430
$362$	− 19.7995i	− 1.04064i
$363$	2.36227	0.123987
$364$	0	0
$365$	−2.20477	−0.115403
$366$	6.49396i	0.339445i
$367$	−0.00431187	−0.000225078 0	−0.000112539	−	1.00000i	$-0.500036\pi$
$367$	−0.00431187	−0.000225078 0	−0.000112539		1.00000i	$0.500036\pi$
$368$	−2.39612	−0.124907
$369$	4.89008i	0.254568i
$370$	6.98792i	0.363285i
$371$	3.17198i	0.164681i
$372$	2.76271i	0.143240i
$373$	−32.3129	−1.67310	−0.836549	−	0.547892i	$-0.815430\pi$
$373$	−32.3129	−1.67310	−0.836549	+	0.547892i	$0.815430\pi$
$374$	19.7318	1.02031
$375$	− 6.58881i	− 0.340245i
$376$	4.98792	0.257232
$377$	0	0
$378$	−0.356896	−0.0183567
$379$	− 19.7560i	− 1.01480i	−0.861711	−	0.507399i	$-0.830607\pi$
$379$	− 19.7560i	− 1.01480i	0.861711	−	0.507399i	$-0.169393\pi$
$380$	4.98792	0.255875
$381$	18.2174	0.933308
$382$	− 15.2620i	− 0.780874i
$383$	− 28.8116i	− 1.47221i	−0.676870	−	0.736103i	$-0.736664\pi$
$383$	− 28.8116i	− 1.47221i	0.676870	−	0.736103i	$-0.263336\pi$
$384$	1.00000i	0.0510310i
$385$	0.725873i	0.0369939i
$386$	4.76809	0.242689
$387$	−6.59179	−0.335080
$388$	0.417895i	0.0212154i
$389$	−34.7821	−1.76352	−0.881761	−	0.471697i	$-0.843642\pi$
$389$	−34.7821	−1.76352	−0.881761	+	0.471697i	$0.843642\pi$
$390$	0	0
$391$	16.0871	0.813559
$392$	6.87263i	0.347120i
$393$	2.73556	0.137991
$394$	−12.2349	−0.616385
$395$	− 10.4125i	− 0.523911i
$396$	2.93900i	0.147690i
$397$	− 5.15346i	− 0.258645i	−0.991603	−	0.129322i	$-0.958720\pi$
$397$	− 5.15346i	− 0.258645i	0.991603	−	0.129322i	$-0.0412802\pi$
$398$	− 11.8485i	− 0.593910i
$399$	−2.57242	−0.128782
$400$	4.52111	0.226055
$401$	13.3250i	0.665417i	0.943030	+	0.332708i	$0.107962\pi$
$401$	13.3250i	0.665417i	−0.943030	+	0.332708i	$0.892038\pi$
$402$	13.5254	0.674587
$403$	0	0
$404$	10.0151	0.498268
$405$	− 0.692021i	− 0.0343868i
$406$	−2.79417	−0.138672
$407$	−29.6775	−1.47106
$408$	− 6.71379i	− 0.332382i
$409$	24.0237i	1.18789i	0.804504	+	0.593947i	$0.202431\pi$
$409$	24.0237i	1.18789i	−0.804504	+	0.593947i	$0.797569\pi$
$410$	− 3.38404i	− 0.167126i
$411$	7.64742i	0.377219i
$412$	−9.62565	−0.474222
$413$	−0.586417	−0.0288557
$414$	2.39612i	0.117763i
$415$	−10.2604	−0.503663
$416$	0	0
$417$	3.38404	0.165717
$418$	21.1836i	1.03612i
$419$	13.8049	0.674415	0.337207	−	0.941430i	$-0.390518\pi$
$419$	13.8049	0.674415	0.337207	+	0.941430i	$0.390518\pi$
$420$	0.246980	0.0120514
$421$	− 7.72587i	− 0.376536i	−0.982118	−	0.188268i	$-0.939713\pi$
$421$	− 7.72587i	− 0.376536i	0.982118	−	0.188268i	$-0.0602874\pi$
$422$	17.2620i	0.840303i
$423$	− 4.98792i	− 0.242521i
$424$	− 8.88769i	− 0.431624i
$425$	−30.3538	−1.47237
$426$	6.81163	0.330024
$427$	2.31767i	0.112160i
$428$	6.63102	0.320523
$429$	0	0
$430$	4.56166	0.219983
$431$	− 0.640120i	− 0.0308335i	−0.999881	−	0.0154168i	$-0.995093\pi$
$431$	− 0.640120i	− 0.0308335i	0.999881	−	0.0154168i	$-0.00490750\pi$
$432$	1.00000	0.0481125
$433$	−21.2760	−1.02246	−0.511231	−	0.859443i	$-0.670810\pi$
$433$	−21.2760	−1.02246	−0.511231	+	0.859443i	$0.670810\pi$
$434$	0.985999i	0.0473295i
$435$	− 5.41789i	− 0.259768i
$436$	− 12.9879i	− 0.622008i
$437$	17.2707i	0.826168i
$438$	−3.18598	−0.152232
$439$	−12.7181	−0.607002	−0.303501	−	0.952831i	$-0.598156\pi$
$439$	−12.7181	−0.607002	−0.303501	+	0.952831i	$0.598156\pi$
$440$	− 2.03385i	− 0.0969601i
$441$	6.87263	0.327268
$442$	0	0
$443$	22.5972	1.07362	0.536812	−	0.843702i	$-0.319628\pi$
$443$	22.5972	1.07362	0.536812	+	0.843702i	$0.319628\pi$
$444$	10.0978i	0.479222i
$445$	−0.274127	−0.0129949
$446$	−6.76809	−0.320478
$447$	20.8170i	0.984610i
$448$	0.356896i	0.0168617i
$449$	11.6474i	0.549676i	0.961491	+	0.274838i	$0.0886241\pi$
$449$	11.6474i	0.549676i	−0.961491	+	0.274838i	$0.911376\pi$
$450$	− 4.52111i	− 0.213127i
$451$	14.3720	0.676749
$452$	−0.792249	−0.0372643
$453$	− 0.895461i	− 0.0420724i
$454$	−23.6799	−1.11135
$455$	0	0
$456$	7.20775	0.337534
$457$	21.1890i	0.991178i	0.868557	+	0.495589i	$0.165048\pi$
$457$	21.1890i	0.991178i	−0.868557	+	0.495589i	$0.834952\pi$
$458$	−8.29829	−0.387754
$459$	−6.71379	−0.313373
$460$	− 1.65817i	− 0.0773126i
$461$	− 24.0694i	− 1.12102i	−0.828147	−	0.560511i	$-0.810605\pi$
$461$	− 24.0694i	− 1.12102i	0.828147	−	0.560511i	$-0.189395\pi$
$462$	1.04892i	0.0488001i
$463$	− 18.1715i	− 0.844502i	−0.906479	−	0.422251i	$-0.861240\pi$
$463$	− 18.1715i	− 0.844502i	0.906479	−	0.422251i	$-0.138760\pi$
$464$	7.82908	0.363456
$465$	−1.91185	−0.0886601
$466$	− 23.9651i	− 1.11016i
$467$	2.93123	0.135641	0.0678206	−	0.997698i	$-0.478395\pi$
$467$	2.93123	0.135641	0.0678206	+	0.997698i	$0.478395\pi$
$468$	0	0
$469$	4.82717	0.222898
$470$	3.45175i	0.159217i
$471$	8.59179	0.395889
$472$	1.64310	0.0756300
$473$	19.3733i	0.890785i
$474$	− 15.0465i	− 0.691110i
$475$	− 32.5870i	− 1.49519i
$476$	− 2.39612i	− 0.109826i
$477$	−8.88769	−0.406939
$478$	−12.6160	−0.577040
$479$	− 30.7090i	− 1.40313i	−0.712605	−	0.701565i	$-0.752485\pi$
$479$	− 30.7090i	− 1.40313i	0.712605	−	0.701565i	$-0.247515\pi$
$480$	−0.692021	−0.0315863
$481$	0	0
$482$	26.3937	1.20220
$483$	0.855167i	0.0389114i
$484$	−2.36227	−0.107376
$485$	−0.289192	−0.0131315
$486$	− 1.00000i	− 0.0453609i
$487$	− 24.1497i	− 1.09433i	−0.837025	−	0.547164i	$-0.815707\pi$
$487$	− 24.1497i	− 1.09433i	0.837025	−	0.547164i	$-0.184293\pi$
$488$	− 6.49396i	− 0.293968i
$489$	1.72587i	0.0780467i
$490$	−4.75600	−0.214854
$491$	−14.5972	−0.658761	−0.329381	−	0.944197i	$-0.606840\pi$
$491$	−14.5972	−0.658761	−0.329381	+	0.944197i	$0.606840\pi$
$492$	− 4.89008i	− 0.220462i
$493$	−52.5628	−2.36731
$494$	0	0
$495$	−2.03385	−0.0914148
$496$	− 2.76271i	− 0.124049i
$497$	2.43104	0.109047
$498$	−14.8267	−0.664400
$499$	− 6.85517i	− 0.306879i	−0.988158	−	0.153440i	$-0.950965\pi$
$499$	− 6.85517i	− 0.306879i	0.988158	−	0.153440i	$-0.0490351\pi$
$500$	6.58881i	0.294661i
$501$	21.1400i	0.944468i
$502$	− 30.0344i	− 1.34050i
$503$	−26.7332	−1.19197	−0.595987	−	0.802994i	$-0.703239\pi$
$503$	−26.7332	−1.19197	−0.595987	+	0.802994i	$0.703239\pi$
$504$	0.356896	0.0158974
$505$	6.93064i	0.308409i
$506$	7.04221	0.313065
$507$	0	0
$508$	−18.2174	−0.808268
$509$	20.6595i	0.915716i	0.889025	+	0.457858i	$0.151383\pi$
$509$	20.6595i	0.915716i	−0.889025	+	0.457858i	$0.848617\pi$
$510$	4.64609	0.205732
$511$	−1.13706	−0.0503007
$512$	− 1.00000i	− 0.0441942i
$513$	− 7.20775i	− 0.318230i
$514$	11.2620i	0.496748i
$515$	− 6.66115i	− 0.293525i
$516$	6.59179	0.290188
$517$	−14.6595	−0.644724
$518$	3.60388i	0.158345i
$519$	−9.35450	−0.410617
$520$	0	0
$521$	−15.0965	−0.661390	−0.330695	−	0.943738i	$-0.607283\pi$
$521$	−15.0965	−0.661390	−0.330695	+	0.943738i	$0.607283\pi$
$522$	− 7.82908i	− 0.342670i
$523$	0.0349168	0.00152680	0.000763402	−	1.00000i	$-0.499757\pi$
$523$	0.0349168	0.00152680	0.000763402		1.00000i	$0.499757\pi$
$524$	−2.73556	−0.119504
$525$	− 1.61356i	− 0.0704217i
$526$	5.54958i	0.241973i
$527$	18.5483i	0.807975i
$528$	− 2.93900i	− 0.127904i
$529$	−17.2586	−0.750373
$530$	6.15047	0.267159
$531$	− 1.64310i	− 0.0713046i
$532$	2.57242	0.111528
$533$	0	0
$534$	−0.396125	−0.0171420
$535$	4.58881i	0.198392i
$536$	−13.5254	−0.584209
$537$	−3.17523	−0.137021
$538$	− 16.6872i	− 0.719438i
$539$	− 20.1987i	− 0.870018i
$540$	0.692021i	0.0297799i
$541$	13.0858i	0.562600i	0.959620	+	0.281300i	$0.0907657\pi$
$541$	13.0858i	0.562600i	−0.959620	+	0.281300i	$0.909234\pi$
$542$	−6.61356	−0.284077
$543$	19.7995	0.849680
$544$	6.71379i	0.287851i
$545$	8.98792	0.385000
$546$	0	0
$547$	−5.97584	−0.255508	−0.127754	−	0.991806i	$-0.540777\pi$
$547$	−5.97584	−0.255508	−0.127754	+	0.991806i	$0.540777\pi$
$548$	− 7.64742i	− 0.326681i
$549$	−6.49396	−0.277155
$550$	−13.2875	−0.566582
$551$	− 56.4301i	− 2.40400i
$552$	− 2.39612i	− 0.101986i
$553$	− 5.37004i	− 0.228357i
$554$	− 21.7995i	− 0.926174i
$555$	−6.98792	−0.296621
$556$	−3.38404	−0.143515
$557$	− 10.4397i	− 0.442343i	−0.975235	−	0.221171i	$-0.929012\pi$
$557$	− 10.4397i	− 0.442343i	0.975235	−	0.221171i	$-0.0709880\pi$
$558$	−2.76271	−0.116955
$559$	0	0
$560$	−0.246980	−0.0104368
$561$	19.7318i	0.833079i
$562$	20.5918	0.868612
$563$	5.66056	0.238564	0.119282	−	0.992860i	$-0.461941\pi$
$563$	5.66056	0.238564	0.119282	+	0.992860i	$0.461941\pi$
$564$	4.98792i	0.210029i
$565$	− 0.548253i	− 0.0230652i
$566$	− 13.0121i	− 0.546939i
$567$	− 0.356896i	− 0.0149882i
$568$	−6.81163	−0.285809
$569$	−20.6568	−0.865980	−0.432990	−	0.901399i	$-0.642541\pi$
$569$	−20.6568	−0.865980	−0.432990	+	0.901399i	$0.642541\pi$
$570$	4.98792i	0.208921i
$571$	−44.3672	−1.85671	−0.928354	−	0.371697i	$-0.878776\pi$
$571$	−44.3672	−1.85671	−0.928354	+	0.371697i	$0.878776\pi$
$572$	0	0
$573$	15.2620	0.637581
$574$	− 1.74525i	− 0.0728454i
$575$	−10.8331	−0.451773
$576$	−1.00000	−0.0416667
$577$	− 29.4426i	− 1.22571i	−0.790194	−	0.612857i	$-0.790020\pi$
$577$	− 29.4426i	− 1.22571i	0.790194	−	0.612857i	$-0.209980\pi$
$578$	− 28.0750i	− 1.16777i
$579$	4.76809i	0.198155i
$580$	5.41789i	0.224966i
$581$	−5.29159	−0.219532
$582$	−0.417895	−0.0173223
$583$	26.1209i	1.08182i
$584$	3.18598	0.131837
$585$	0	0
$586$	−14.9390	−0.617124
$587$	19.5636i	0.807475i	0.914875	+	0.403738i	$0.132289\pi$
$587$	19.5636i	0.807475i	−0.914875	+	0.403738i	$0.867711\pi$
$588$	−6.87263	−0.283422
$589$	−19.9129	−0.820498
$590$	1.13706i	0.0468122i
$591$	− 12.2349i	− 0.503276i
$592$	− 10.0978i	− 0.415018i
$593$	− 10.8793i	− 0.446761i	−0.974731	−	0.223380i	$-0.928291\pi$
$593$	− 10.8793i	− 0.446761i	0.974731	−	0.223380i	$-0.0717092\pi$
$594$	−2.93900	−0.120589
$595$	1.65817	0.0679783
$596$	− 20.8170i	− 0.852698i
$597$	11.8485	0.484925
$598$	0	0
$599$	16.0543	0.655961	0.327980	−	0.944685i	$-0.393632\pi$
$599$	16.0543	0.655961	0.327980	+	0.944685i	$0.393632\pi$
$600$	4.52111i	0.184573i
$601$	12.8955	0.526017	0.263008	−	0.964794i	$-0.415285\pi$
$601$	12.8955	0.526017	0.263008	+	0.964794i	$0.415285\pi$
$602$	2.35258	0.0958842
$603$	13.5254i	0.550798i
$604$	0.895461i	0.0364358i
$605$	− 1.63474i	− 0.0664618i
$606$	10.0151i	0.406834i
$607$	44.4741	1.80515	0.902574	−	0.430534i	$-0.141675\pi$
$607$	44.4741	1.80515	0.902574	+	0.430534i	$0.141675\pi$
$608$	−7.20775	−0.292313
$609$	− 2.79417i	− 0.113225i
$610$	4.49396	0.181955
$611$	0	0
$612$	6.71379	0.271389
$613$	− 42.0253i	− 1.69739i	−0.528884	−	0.848694i	$-0.677390\pi$
$613$	− 42.0253i	− 1.69739i	0.528884	−	0.848694i	$-0.322610\pi$
$614$	26.0301	1.05049
$615$	3.38404	0.136458
$616$	− 1.04892i	− 0.0422621i
$617$	16.6655i	0.670926i	0.942053	+	0.335463i	$0.108893\pi$
$617$	16.6655i	0.670926i	−0.942053	+	0.335463i	$0.891107\pi$
$618$	− 9.62565i	− 0.387200i
$619$	39.7512i	1.59774i	0.601506	+	0.798868i	$0.294568\pi$
$619$	39.7512i	1.59774i	−0.601506	+	0.798868i	$0.705432\pi$
$620$	1.91185	0.0767819
$621$	−2.39612	−0.0961532
$622$	− 4.81163i	− 0.192929i
$623$	−0.141375	−0.00566408
$624$	0	0
$625$	18.0459	0.721837
$626$	26.0411i	1.04081i
$627$	−21.1836	−0.845991
$628$	−8.59179	−0.342850
$629$	67.7948i	2.70315i
$630$	0.246980i	0.00983990i
$631$	14.5767i	0.580290i	0.956983	+	0.290145i	$0.0937036\pi$
$631$	14.5767i	0.580290i	−0.956983	+	0.290145i	$0.906296\pi$
$632$	15.0465i	0.598519i
$633$	−17.2620	−0.686105
$634$	11.5211	0.457562
$635$	− 12.6069i	− 0.500288i
$636$	8.88769	0.352420
$637$	0	0
$638$	−23.0097	−0.910962
$639$	6.81163i	0.269464i
$640$	0.692021	0.0273546
$641$	−38.4349	−1.51809	−0.759043	−	0.651040i	$-0.774333\pi$
$641$	−38.4349	−1.51809	−0.759043	+	0.651040i	$0.774333\pi$
$642$	6.63102i	0.261706i
$643$	1.04221i	0.0411009i	0.999789	+	0.0205504i	$0.00654186\pi$
$643$	1.04221i	0.0411009i	−0.999789	+	0.0205504i	$0.993458\pi$
$644$	− 0.855167i	− 0.0336983i
$645$	4.56166i	0.179615i
$646$	48.3913	1.90393
$647$	28.1608	1.10711	0.553557	−	0.832811i	$-0.313270\pi$
$647$	28.1608	1.10711	0.553557	+	0.832811i	$0.313270\pi$
$648$	1.00000i	0.0392837i
$649$	−4.82908	−0.189558
$650$	0	0
$651$	−0.985999	−0.0386444
$652$	− 1.72587i	− 0.0675904i
$653$	10.6203	0.415603	0.207802	−	0.978171i	$-0.433369\pi$
$653$	10.6203	0.415603	0.207802	+	0.978171i	$0.433369\pi$
$654$	12.9879	0.507868
$655$	− 1.89307i	− 0.0739683i
$656$	4.89008i	0.190926i
$657$	− 3.18598i	− 0.124297i
$658$	1.78017i	0.0693982i
$659$	−40.3629	−1.57231	−0.786157	−	0.618027i	$-0.787932\pi$
$659$	−40.3629	−1.57231	−0.786157	+	0.618027i	$0.787932\pi$
$660$	2.03385	0.0791676
$661$	− 31.9168i	− 1.24142i	−0.784041	−	0.620709i	$-0.786845\pi$
$661$	− 31.9168i	− 1.24142i	0.784041	−	0.620709i	$-0.213155\pi$
$662$	−3.43834	−0.133635
$663$	0	0
$664$	14.8267	0.575387
$665$	1.78017i	0.0690319i
$666$	−10.0978	−0.391283
$667$	−18.7595	−0.726369
$668$	− 21.1400i	− 0.817933i
$669$	− 6.76809i	− 0.261669i
$670$	− 9.35988i	− 0.361604i
$671$	19.0858i	0.736797i
$672$	−0.356896	−0.0137676
$673$	−3.82802	−0.147559	−0.0737797	−	0.997275i	$-0.523506\pi$
$673$	−3.82802	−0.147559	−0.0737797	+	0.997275i	$0.523506\pi$
$674$	8.20105i	0.315892i
$675$	4.52111	0.174017
$676$	0	0
$677$	1.78927	0.0687670	0.0343835	−	0.999409i	$-0.489053\pi$
$677$	1.78927	0.0687670	0.0343835	+	0.999409i	$0.489053\pi$
$678$	− 0.792249i	− 0.0304261i
$679$	−0.149145	−0.00572366
$680$	−4.64609	−0.178169
$681$	− 23.6799i	− 0.907417i
$682$	8.11960i	0.310916i
$683$	0.759725i	0.0290701i	0.999894	+	0.0145350i	$0.00462681\pi$
$683$	0.759725i	0.0290701i	−0.999894	+	0.0145350i	$0.995373\pi$
$684$	7.20775i	0.275595i
$685$	5.29218	0.202204
$686$	−4.95108	−0.189033
$687$	− 8.29829i	− 0.316600i
$688$	−6.59179	−0.251310
$689$	0	0
$690$	1.65817	0.0631254
$691$	− 4.65950i	− 0.177256i	−0.996065	−	0.0886278i	$-0.971752\pi$
$691$	− 4.65950i	− 0.177256i	0.996065	−	0.0886278i	$-0.0282482\pi$
$692$	9.35450	0.355605
$693$	−1.04892	−0.0398451
$694$	− 7.86294i	− 0.298473i
$695$	− 2.34183i	− 0.0888307i
$696$	7.82908i	0.296761i
$697$	− 32.8310i	− 1.24356i
$698$	−18.7245	−0.708734
$699$	23.9651	0.906443
$700$	1.61356i	0.0609870i
$701$	24.3284	0.918872	0.459436	−	0.888211i	$-0.348052\pi$
$701$	24.3284	0.918872	0.459436	+	0.888211i	$0.348052\pi$
$702$	0	0
$703$	−72.7827	−2.74505
$704$	2.93900i	0.110768i
$705$	−3.45175	−0.130000
$706$	31.5448	1.18720
$707$	3.57434i	0.134427i
$708$	1.64310i	0.0617516i
$709$	− 29.3927i	− 1.10386i	−0.833889	−	0.551932i	$-0.813891\pi$
$709$	− 29.3927i	− 1.10386i	0.833889	−	0.551932i	$-0.186109\pi$
$710$	− 4.71379i	− 0.176905i
$711$	15.0465	0.564289
$712$	0.396125	0.0148454
$713$	6.61979i	0.247913i
$714$	2.39612	0.0896727
$715$	0	0
$716$	3.17523	0.118664
$717$	− 12.6160i	− 0.471152i
$718$	2.39612	0.0894226
$719$	51.4878	1.92017	0.960086	−	0.279704i	$-0.0902363\pi$
$719$	51.4878	1.92017	0.960086	+	0.279704i	$0.0902363\pi$
$720$	− 0.692021i	− 0.0257901i
$721$	− 3.43535i	− 0.127939i
$722$	32.9517i	1.22633i
$723$	26.3937i	0.981593i
$724$	−19.7995	−0.735844
$725$	35.3961	1.31458
$726$	− 2.36227i	− 0.0876722i
$727$	3.67324	0.136233	0.0681164	−	0.997677i	$-0.478301\pi$
$727$	3.67324	0.136233	0.0681164	+	0.997677i	$0.478301\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.20477i	0.0816021i
$731$	44.2559	1.63686
$732$	6.49396	0.240024
$733$	− 18.3612i	− 0.678187i	−0.940753	−	0.339093i	$-0.889880\pi$
$733$	− 18.3612i	− 0.678187i	0.940753	−	0.339093i	$-0.110120\pi$
$734$	0.00431187i	0 0.000159154i
$735$	− 4.75600i	− 0.175428i
$736$	2.39612i	0.0883223i
$737$	39.7512	1.46425
$738$	4.89008	0.180006
$739$	1.68233i	0.0618856i	0.999521	+	0.0309428i	$0.00985097\pi$
$739$	1.68233i	0.0618856i	−0.999521	+	0.0309428i	$0.990149\pi$
$740$	6.98792	0.256881
$741$	0	0
$742$	3.17198	0.116447
$743$	− 48.2935i	− 1.77172i	−0.463956	−	0.885858i	$-0.653570\pi$
$743$	− 48.2935i	− 1.77172i	0.463956	−	0.885858i	$-0.346430\pi$
$744$	2.76271	0.101286
$745$	14.4058	0.527788
$746$	32.3129i	1.18306i
$747$	− 14.8267i	− 0.542480i
$748$	− 19.7318i	− 0.721468i
$749$	2.36658i	0.0864731i
$750$	−6.58881	−0.240589
$751$	−11.7011	−0.426980	−0.213490	−	0.976945i	$-0.568483\pi$
$751$	−11.7011	−0.426980	−0.213490	+	0.976945i	$0.568483\pi$
$752$	− 4.98792i	− 0.181891i
$753$	30.0344	1.09452
$754$	0	0
$755$	−0.619678	−0.0225524
$756$	0.356896i	0.0129802i
$757$	25.1836	0.915313	0.457657	−	0.889129i	$-0.348689\pi$
$757$	25.1836	0.915313	0.457657	+	0.889129i	$0.348689\pi$
$758$	−19.7560	−0.717570
$759$	7.04221i	0.255616i
$760$	− 4.98792i	− 0.180931i
$761$	22.4155i	0.812561i	0.913748	+	0.406281i	$0.133174\pi$
$761$	22.4155i	0.812561i	−0.913748	+	0.406281i	$0.866826\pi$
$762$	− 18.2174i	− 0.659948i
$763$	4.63533	0.167810
$764$	−15.2620	−0.552161
$765$	4.64609i	0.167980i
$766$	−28.8116	−1.04101
$767$	0	0
$768$	1.00000	0.0360844
$769$	0.132751i	0.00478714i	0.999997	+	0.00239357i	$0.000761898\pi$
$769$	0.132751i	0.00478714i	−0.999997	+	0.00239357i	$0.999238\pi$
$770$	0.725873	0.0261587
$771$	−11.2620	−0.405593
$772$	− 4.76809i	− 0.171607i
$773$	48.0694i	1.72893i	0.502689	+	0.864467i	$0.332344\pi$
$773$	48.0694i	1.72893i	−0.502689	+	0.864467i	$0.667656\pi$
$774$	6.59179i	0.236937i
$775$	− 12.4905i	− 0.448672i
$776$	0.417895	0.0150015
$777$	−3.60388	−0.129288
$778$	34.7821i	1.24700i
$779$	35.2465	1.26284
$780$	0	0
$781$	20.0194	0.716350
$782$	− 16.0871i	− 0.575273i
$783$	7.82908	0.279789
$784$	6.87263	0.245451
$785$	− 5.94571i	− 0.212211i
$786$	− 2.73556i	− 0.0975743i
$787$	6.20908i	0.221330i	0.993858	+	0.110665i	$0.0352980\pi$
$787$	6.20908i	0.221330i	−0.993858	+	0.110665i	$0.964702\pi$
$788$	12.2349i	0.435850i
$789$	−5.54958	−0.197570
$790$	−10.4125	−0.370461
$791$	− 0.282750i	− 0.0100534i
$792$	2.93900	0.104433
$793$	0	0
$794$	−5.15346	−0.182889
$795$	6.15047i	0.218135i
$796$	−11.8485	−0.419958
$797$	−0.327830	−0.0116123	−0.00580616	−	0.999983i	$-0.501848\pi$
$797$	−0.327830	−0.0116123	−0.00580616	+	0.999983i	$0.501848\pi$
$798$	2.57242i	0.0910626i
$799$	33.4878i	1.18471i
$800$	− 4.52111i	− 0.159845i
$801$	− 0.396125i	− 0.0139964i
$802$	13.3250	0.470521
$803$	−9.36360	−0.330434
$804$	− 13.5254i	− 0.477005i
$805$	0.591794	0.0208580
$806$	0	0
$807$	16.6872	0.587419
$808$	− 10.0151i	− 0.352329i
$809$	−37.4383	−1.31626	−0.658131	−	0.752904i	$-0.728653\pi$
$809$	−37.4383	−1.31626	−0.658131	+	0.752904i	$0.728653\pi$
$810$	−0.692021	−0.0243152
$811$	− 17.1448i	− 0.602037i	−0.953618	−	0.301018i	$-0.902673\pi$
$811$	− 17.1448i	− 0.602037i	0.953618	−	0.301018i	$-0.0973265\pi$
$812$	2.79417i	0.0980561i
$813$	− 6.61356i	− 0.231948i
$814$	29.6775i	1.04020i
$815$	1.19434	0.0418360
$816$	−6.71379	−0.235030
$817$	47.5120i	1.66223i
$818$	24.0237	0.839969
$819$	0	0
$820$	−3.38404	−0.118176
$821$	17.7885i	0.620824i	0.950602	+	0.310412i	$0.100467\pi$
$821$	17.7885i	0.620824i	−0.950602	+	0.310412i	$0.899533\pi$
$822$	7.64742	0.266734
$823$	−12.2301	−0.426315	−0.213157	−	0.977018i	$-0.568375\pi$
$823$	−12.2301	−0.426315	−0.213157	+	0.977018i	$0.568375\pi$
$824$	9.62565i	0.335325i
$825$	− 13.2875i	− 0.462613i
$826$	0.586417i	0.0204041i
$827$	20.5623i	0.715020i	0.933909	+	0.357510i	$0.116374\pi$
$827$	20.5623i	0.715020i	−0.933909	+	0.357510i	$0.883626\pi$
$828$	2.39612	0.0832711
$829$	25.4470	0.883809	0.441905	−	0.897062i	$-0.354303\pi$
$829$	25.4470	0.883809	0.441905	+	0.897062i	$0.354303\pi$
$830$	10.2604i	0.356143i
$831$	21.7995	0.756218
$832$	0	0
$833$	−46.1414	−1.59870
$834$	− 3.38404i	− 0.117180i
$835$	14.6294	0.506270
$836$	21.1836	0.732650
$837$	− 2.76271i	− 0.0954932i
$838$	− 13.8049i	− 0.476883i
$839$	5.76676i	0.199091i	0.995033	+	0.0995453i	$0.0317388\pi$
$839$	5.76676i	0.199091i	−0.995033	+	0.0995453i	$0.968261\pi$
$840$	− 0.246980i	− 0.00852161i
$841$	32.2946	1.11361
$842$	−7.72587	−0.266251
$843$	20.5918i	0.709219i
$844$	17.2620	0.594184
$845$	0	0
$846$	−4.98792	−0.171488
$847$	− 0.843085i	− 0.0289688i
$848$	−8.88769	−0.305205
$849$	13.0121	0.446573
$850$	30.3538i	1.04113i
$851$	24.1957i	0.829417i
$852$	− 6.81163i	− 0.233362i
$853$	− 21.1728i	− 0.724944i	−0.931995	−	0.362472i	$-0.881933\pi$
$853$	− 21.1728i	− 0.724944i	0.931995	−	0.362472i	$-0.118067\pi$
$854$	2.31767	0.0793089
$855$	−4.98792	−0.170583
$856$	− 6.63102i	− 0.226644i
$857$	−12.0086	−0.410207	−0.205103	−	0.978740i	$-0.565753\pi$
$857$	−12.0086	−0.410207	−0.205103	+	0.978740i	$0.565753\pi$
$858$	0	0
$859$	−1.66296	−0.0567393	−0.0283697	−	0.999598i	$-0.509032\pi$
$859$	−1.66296	−0.0567393	−0.0283697	+	0.999598i	$0.509032\pi$
$860$	− 4.56166i	− 0.155551i
$861$	1.74525	0.0594780
$862$	−0.640120	−0.0218026
$863$	23.8323i	0.811262i	0.914037	+	0.405631i	$0.132948\pi$
$863$	23.8323i	0.811262i	−0.914037	+	0.405631i	$0.867052\pi$
$864$	− 1.00000i	− 0.0340207i
$865$	6.47352i	0.220106i
$866$	21.2760i	0.722989i
$867$	28.0750	0.953477
$868$	0.985999	0.0334670
$869$	− 44.2218i	− 1.50012i
$870$	−5.41789	−0.183684
$871$	0	0
$872$	−12.9879	−0.439826
$873$	− 0.417895i	− 0.0141436i
$874$	17.2707	0.584189
$875$	−2.35152	−0.0794959
$876$	3.18598i	0.107644i
$877$	42.3177i	1.42897i	0.699653	+	0.714483i	$0.253338\pi$
$877$	42.3177i	1.42897i	−0.699653	+	0.714483i	$0.746662\pi$
$878$	12.7181i	0.429215i
$879$	− 14.9390i	− 0.503880i
$880$	−2.03385	−0.0685611
$881$	−22.2741	−0.750434	−0.375217	−	0.926937i	$-0.622432\pi$
$881$	−22.2741	−0.750434	−0.375217	+	0.926937i	$0.622432\pi$
$882$	− 6.87263i	− 0.231413i
$883$	8.54229	0.287471	0.143735	−	0.989616i	$-0.454089\pi$
$883$	8.54229	0.287471	0.143735	+	0.989616i	$0.454089\pi$
$884$	0	0
$885$	−1.13706	−0.0382220
$886$	− 22.5972i	− 0.759167i
$887$	−18.9142	−0.635078	−0.317539	−	0.948245i	$-0.602856\pi$
$887$	−18.9142	−0.635078	−0.317539	+	0.948245i	$0.602856\pi$
$888$	10.0978	0.338861
$889$	− 6.50173i	− 0.218061i
$890$	0.274127i	0.00918875i
$891$	− 2.93900i	− 0.0984602i
$892$	6.76809i	0.226612i
$893$	−35.9517	−1.20308
$894$	20.8170	0.696225
$895$	2.19733i	0.0734485i
$896$	0.356896	0.0119231
$897$	0	0
$898$	11.6474	0.388679
$899$	− 21.6295i	− 0.721384i
$900$	−4.52111	−0.150704
$901$	59.6701	1.98790
$902$	− 14.3720i	− 0.478534i
$903$	2.35258i	0.0782891i
$904$	0.792249i	0.0263498i
$905$	− 13.7017i	− 0.455460i
$906$	−0.895461	−0.0297497
$907$	−13.9517	−0.463258	−0.231629	−	0.972804i	$-0.574405\pi$
$907$	−13.9517	−0.463258	−0.231629	+	0.972804i	$0.574405\pi$
$908$	23.6799i	0.785846i
$909$	−10.0151	−0.332179
$910$	0	0
$911$	45.0422	1.49232	0.746158	−	0.665769i	$-0.231897\pi$
$911$	45.0422	1.49232	0.746158	+	0.665769i	$0.231897\pi$
$912$	− 7.20775i	− 0.238672i
$913$	−43.5757	−1.44214
$914$	21.1890	0.700869
$915$	4.49396i	0.148566i
$916$	8.29829i	0.274183i
$917$	− 0.976311i	− 0.0322406i
$918$	6.71379i	0.221588i
$919$	39.9976	1.31940	0.659700	−	0.751529i	$-0.270683\pi$
$919$	39.9976	1.31940	0.659700	+	0.751529i	$0.270683\pi$
$920$	−1.65817	−0.0546682
$921$	26.0301i	0.857722i
$922$	−24.0694	−0.792682
$923$	0	0
$924$	1.04892	0.0345068
$925$	− 45.6534i	− 1.50107i
$926$	−18.1715	−0.597153
$927$	9.62565	0.316148
$928$	− 7.82908i	− 0.257002i
$929$	− 34.6848i	− 1.13797i	−0.822347	−	0.568986i	$-0.807336\pi$
$929$	− 34.6848i	− 1.13797i	0.822347	−	0.568986i	$-0.192664\pi$
$930$	1.91185i	0.0626922i
$931$	− 49.5362i	− 1.62348i
$932$	−23.9651	−0.785002
$933$	4.81163	0.157526
$934$	− 2.93123i	− 0.0959128i
$935$	13.6549	0.446562
$936$	0	0
$937$	−19.1260	−0.624821	−0.312410	−	0.949947i	$-0.601136\pi$
$937$	−19.1260	−0.624821	−0.312410	+	0.949947i	$0.601136\pi$
$938$	− 4.82717i	− 0.157613i
$939$	−26.0411	−0.849821
$940$	3.45175	0.112584
$941$	22.5972i	0.736647i	0.929698	+	0.368323i	$0.120068\pi$
$941$	22.5972i	0.736647i	−0.929698	+	0.368323i	$0.879932\pi$
$942$	− 8.59179i	− 0.279936i
$943$	− 11.7172i	− 0.381566i
$944$	− 1.64310i	− 0.0534785i
$945$	−0.246980	−0.00803425
$946$	19.3733	0.629880
$947$	− 27.4359i	− 0.891548i	−0.895145	−	0.445774i	$-0.852928\pi$
$947$	− 27.4359i	− 0.891548i	0.895145	−	0.445774i	$-0.147072\pi$
$948$	−15.0465	−0.488688
$949$	0	0
$950$	−32.5870	−1.05726
$951$	11.5211i	0.373597i
$952$	−2.39612	−0.0776588
$953$	1.84787	0.0598584	0.0299292	−	0.999552i	$-0.490472\pi$
$953$	1.84787	0.0598584	0.0299292	+	0.999552i	$0.490472\pi$
$954$	8.88769i	0.287750i
$955$	− 10.5617i	− 0.341767i
$956$	12.6160i	0.408029i
$957$	− 23.0097i	− 0.743798i
$958$	−30.7090	−0.992163
$959$	2.72933	0.0881347
$960$	0.692021i	0.0223349i
$961$	23.3674	0.753788
$962$	0	0
$963$	−6.63102	−0.213682
$964$	− 26.3937i	− 0.850085i
$965$	3.29962	0.106218
$966$	0.855167	0.0275145
$967$	8.88471i	0.285713i	0.989743	+	0.142856i	$0.0456287\pi$
$967$	8.88471i	0.285713i	−0.989743	+	0.142856i	$0.954371\pi$
$968$	2.36227i	0.0759263i
$969$	48.3913i	1.55455i
$970$	0.289192i	0.00928540i
$971$	35.0863	1.12597	0.562987	−	0.826466i	$-0.309652\pi$
$971$	35.0863	1.12597	0.562987	+	0.826466i	$0.309652\pi$
$972$	−1.00000	−0.0320750
$973$	− 1.20775i	− 0.0387187i
$974$	−24.1497	−0.773807
$975$	0	0
$976$	−6.49396	−0.207867
$977$	8.33704i	0.266726i	0.991067	+	0.133363i	$0.0425776\pi$
$977$	8.33704i	0.266726i	−0.991067	+	0.133363i	$0.957422\pi$
$978$	1.72587	0.0551873
$979$	−1.16421	−0.0372083
$980$	4.75600i	0.151925i
$981$	12.9879i	0.414672i
$982$	14.5972i	0.465814i
$983$	− 55.6051i	− 1.77353i	−0.462224	−	0.886763i	$-0.652949\pi$
$983$	− 55.6051i	− 1.77353i	0.462224	−	0.886763i	$-0.347051\pi$
$984$	−4.89008	−0.155890
$985$	−8.46681	−0.269775
$986$	52.5628i	1.67394i
$987$	−1.78017	−0.0566634
$988$	0	0
$989$	15.7948	0.502244
$990$	2.03385i	0.0646401i
$991$	−43.5967	−1.38489	−0.692447	−	0.721468i	$-0.743468\pi$
$991$	−43.5967	−1.38489	−0.692447	+	0.721468i	$0.743468\pi$
$992$	−2.76271	−0.0877161
$993$	− 3.43834i	− 0.109112i
$994$	− 2.43104i	− 0.0771079i
$995$	− 8.19939i	− 0.259938i
$996$	14.8267i	0.469802i
$997$	22.4590	0.711285	0.355643	−	0.934622i	$-0.384262\pi$
$997$	22.4590	0.711285	0.355643	+	0.934622i	$0.384262\pi$
$998$	−6.85517	−0.216997
$999$	− 10.0978i	− 0.319481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.b.g.337.1		6
3.2	odd	2		3042.2.b.r.1351.6		6
13.2	odd	12		1014.2.e.m.529.1		6
13.3	even	3		1014.2.i.g.823.4		12
13.4	even	6		1014.2.i.g.361.6		12
13.5	odd	4		1014.2.a.m.1.1	✓	3
13.6	odd	12		1014.2.e.m.991.1		6
13.7	odd	12		1014.2.e.k.991.3		6
13.8	odd	4		1014.2.a.o.1.3	yes	3
13.9	even	3		1014.2.i.g.361.1		12
13.10	even	6		1014.2.i.g.823.3		12
13.11	odd	12		1014.2.e.k.529.3		6
13.12	even	2	inner	1014.2.b.g.337.6		6
39.5	even	4		3042.2.a.be.1.3		3
39.8	even	4		3042.2.a.bd.1.1		3
39.38	odd	2		3042.2.b.r.1351.1		6
52.31	even	4		8112.2.a.ce.1.1		3
52.47	even	4		8112.2.a.bz.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.m.1.1	✓	3	13.5	odd	4
1014.2.a.o.1.3	yes	3	13.8	odd	4
1014.2.b.g.337.1		6	1.1	even	1	trivial
1014.2.b.g.337.6		6	13.12	even	2	inner
1014.2.e.k.529.3		6	13.11	odd	12
1014.2.e.k.991.3		6	13.7	odd	12
1014.2.e.m.529.1		6	13.2	odd	12
1014.2.e.m.991.1		6	13.6	odd	12
1014.2.i.g.361.1		12	13.9	even	3
1014.2.i.g.361.6		12	13.4	even	6
1014.2.i.g.823.3		12	13.10	even	6
1014.2.i.g.823.4		12	13.3	even	3
3042.2.a.bd.1.1		3	39.8	even	4
3042.2.a.be.1.3		3	39.5	even	4
3042.2.b.r.1351.1		6	39.38	odd	2
3042.2.b.r.1351.6		6	3.2	odd	2
8112.2.a.bz.1.3		3	52.47	even	4
8112.2.a.ce.1.1		3	52.31	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.692021i q^{5} -1.00000i q^{6} -0.356896i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.692021i q^{5} -1.00000i q^{6} -0.356896i q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.692021 q^{10} -2.93900i q^{11} -1.00000 q^{12} -0.356896 q^{14} -0.692021i q^{15} +1.00000 q^{16} -6.71379 q^{17} -1.00000i q^{18} -7.20775i q^{19} +0.692021i q^{20} -0.356896i q^{21} -2.93900 q^{22} -2.39612 q^{23} +1.00000i q^{24} +4.52111 q^{25} +1.00000 q^{27} +0.356896i q^{28} +7.82908 q^{29} -0.692021 q^{30} -2.76271i q^{31} -1.00000i q^{32} -2.93900i q^{33} +6.71379i q^{34} -0.246980 q^{35} -1.00000 q^{36} -10.0978i q^{37} -7.20775 q^{38} +0.692021 q^{40} +4.89008i q^{41} -0.356896 q^{42} -6.59179 q^{43} +2.93900i q^{44} -0.692021i q^{45} +2.39612i q^{46} -4.98792i q^{47} +1.00000 q^{48} +6.87263 q^{49} -4.52111i q^{50} -6.71379 q^{51} -8.88769 q^{53} -1.00000i q^{54} -2.03385 q^{55} +0.356896 q^{56} -7.20775i q^{57} -7.82908i q^{58} -1.64310i q^{59} +0.692021i q^{60} -6.49396 q^{61} -2.76271 q^{62} -0.356896i q^{63} -1.00000 q^{64} -2.93900 q^{66} +13.5254i q^{67} +6.71379 q^{68} -2.39612 q^{69} +0.246980i q^{70} +6.81163i q^{71} +1.00000i q^{72} -3.18598i q^{73} -10.0978 q^{74} +4.52111 q^{75} +7.20775i q^{76} -1.04892 q^{77} +15.0465 q^{79} -0.692021i q^{80} +1.00000 q^{81} +4.89008 q^{82} -14.8267i q^{83} +0.356896i q^{84} +4.64609i q^{85} +6.59179i q^{86} +7.82908 q^{87} +2.93900 q^{88} -0.396125i q^{89} -0.692021 q^{90} +2.39612 q^{92} -2.76271i q^{93} -4.98792 q^{94} -4.98792 q^{95} -1.00000i q^{96} -0.417895i q^{97} -6.87263i q^{98} -2.93900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9	\( 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9} + 6 q^{10} - 6 q^{12} + 6 q^{14} + 6 q^{16} - 24 q^{17} + 2 q^{22} - 32 q^{23} - 4 q^{25} + 6 q^{27} + 26 q^{29} + 6 q^{30} + 8 q^{35} - 6 q^{36} - 8 q^{38} - 6 q^{40} + 6 q^{42} + 16 q^{43} + 6 q^{48} + 8 q^{49} - 24 q^{51} + 30 q^{53} - 44 q^{55} - 6 q^{56} - 20 q^{61} + 18 q^{62} - 6 q^{64} + 2 q^{66} + 24 q^{68} - 32 q^{69} - 24 q^{74} - 4 q^{75} + 12 q^{77} - 10 q^{79} + 6 q^{81} + 28 q^{82} + 26 q^{87} - 2 q^{88} + 6 q^{90} + 32 q^{92} + 8 q^{94} + 8 q^{95}+O(q^{100}) \) 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9 + 6 * q^10 - 6 * q^12 + 6 * q^14 + 6 * q^16 - 24 * q^17 + 2 * q^22 - 32 * q^23 - 4 * q^25 + 6 * q^27 + 26 * q^29 + 6 * q^30 + 8 * q^35 - 6 * q^36 - 8 * q^38 - 6 * q^40 + 6 * q^42 + 16 * q^43 + 6 * q^48 + 8 * q^49 - 24 * q^51 + 30 * q^53 - 44 * q^55 - 6 * q^56 - 20 * q^61 + 18 * q^62 - 6 * q^64 + 2 * q^66 + 24 * q^68 - 32 * q^69 - 24 * q^74 - 4 * q^75 + 12 * q^77 - 10 * q^79 + 6 * q^81 + 28 * q^82 + 26 * q^87 - 2 * q^88 + 6 * q^90 + 32 * q^92 + 8 * q^94 + 8 * q^95

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