LMFDB - Embedded newform 507.2.p.a.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.725144 + 0.275011i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.04682 - 0.927401i) q^{4} +(1.67905 + 0.203873i) q^{5} +(0.185599 + 0.753005i) q^{6} +(-1.40603 - 2.67897i) q^{7} +(-1.22487 - 2.33380i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(0.725144 + 0.275011i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.04682 - 0.927401i) q^{4} +(1.67905 + 0.203873i) q^{5} +(0.185599 + 0.753005i) q^{6} +(-1.40603 - 2.67897i) q^{7} +(-1.22487 - 2.33380i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(1.16148 + 0.609593i) q^{10} +(4.12515 - 1.56446i) q^{11} +(0.168575 - 1.38834i) q^{12} +(1.25140 - 3.38142i) q^{13} +(-0.282830 - 2.32932i) q^{14} +(0.786023 + 1.49764i) q^{15} +(0.0907609 + 0.747483i) q^{16} +(1.83506 - 0.963114i) q^{17} +(-0.514279 + 0.580501i) q^{18} +4.05343i q^{19} +(-1.56859 - 1.77057i) q^{20} +(1.40603 - 2.67897i) q^{21} +3.42157 q^{22} +5.11342 q^{23} +(1.22487 - 2.33380i) q^{24} +(-2.07707 - 0.511953i) q^{25} +(1.83737 - 2.10787i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-1.01262 + 4.10836i) q^{28} +(-0.670658 + 1.76838i) q^{29} +(0.158112 + 1.30217i) q^{30} +(-0.592879 - 2.40540i) q^{31} +(-1.40128 + 5.68523i) q^{32} +(3.63088 + 2.50622i) q^{33} +(1.59555 - 0.193735i) q^{34} +(-1.81463 - 4.78478i) q^{35} +(1.23834 - 0.649932i) q^{36} +(0.739773 + 3.00138i) q^{37} +(-1.11474 + 2.93932i) q^{38} +(3.49373 - 0.890982i) q^{39} +(-1.58082 - 4.16828i) q^{40} +(-6.89063 + 4.75626i) q^{41} +(1.75632 - 1.55597i) q^{42} +(-0.650462 - 0.160324i) q^{43} +(-5.76917 - 2.18796i) q^{44} +(-0.786023 + 1.49764i) q^{45} +(3.70796 + 1.40624i) q^{46} +(-2.46299 - 2.78014i) q^{47} +(-0.563609 + 0.499314i) q^{48} +(-1.22351 + 1.77257i) q^{49} +(-1.36538 - 0.942457i) q^{50} +(1.83506 + 0.963114i) q^{51} +(-4.44592 + 2.37918i) q^{52} +(6.80180 - 3.56986i) q^{53} +(-0.769887 - 0.0934812i) q^{54} +(7.24528 - 1.78580i) q^{55} +(-4.52998 + 6.56280i) q^{56} +(-3.33591 + 2.30261i) q^{57} +(-0.972646 + 1.09789i) q^{58} +(-6.60857 - 0.802426i) q^{59} +(0.566090 - 2.29672i) q^{60} +(11.8473 + 6.21795i) q^{61} +(0.231590 - 1.90731i) q^{62} +(3.00347 - 0.364687i) q^{63} +(-1.72415 + 2.49787i) q^{64} +(2.79054 - 5.42244i) q^{65} +(1.94367 + 2.81590i) q^{66} +(-1.44949 - 1.63613i) q^{67} +(-2.81417 - 0.693630i) q^{68} +(2.90475 + 4.20826i) q^{69} -3.96869i q^{70} +(-1.74972 + 1.20775i) q^{71} +(2.61649 - 0.317699i) q^{72} +(4.10965 - 1.55859i) q^{73} +(-0.288969 + 2.37987i) q^{74} +(-0.758583 - 2.00022i) q^{75} +(3.75916 - 4.24321i) q^{76} +(-9.99126 - 8.85148i) q^{77} +(2.77849 + 0.314724i) q^{78} +(-9.26239 + 8.20576i) q^{79} +1.27356i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-6.30471 + 1.55397i) q^{82} +(-9.85379 - 6.80158i) q^{83} +(-3.95634 + 1.50044i) q^{84} +(3.27751 - 1.24299i) q^{85} +(-0.427587 - 0.295142i) q^{86} +(-1.83632 + 0.452613i) q^{87} +(-8.70393 - 7.71101i) q^{88} +15.1685i q^{89} +(-0.981847 + 0.869841i) q^{90} +(-10.8182 + 1.40192i) q^{91} +(-5.35282 - 4.74219i) q^{92} +(1.64282 - 1.85436i) q^{93} +(-1.02145 - 2.69335i) q^{94} +(-0.826387 + 6.80591i) q^{95} +(-5.47487 + 2.07634i) q^{96} +(8.25314 - 1.00211i) q^{97} +(-1.37470 + 0.948886i) q^{98} +4.41185i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	0.725144	+	0.275011i	0.512754	+	0.194462i	0.597391	−	0.801950i	$-0.296204\pi$
$2$	0.725144	+	0.275011i	0.512754	+	0.194462i	−0.0846373	+	0.996412i	$0.526973\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	−1.04682	−	0.927401i	−0.523409	−	0.463700i
$5$	1.67905	+	0.203873i	0.750893	+	0.0911749i	0.487030	−	0.873385i	$-0.338080\pi$
$5$	1.67905	+	0.203873i	0.750893	+	0.0911749i	0.263863	+	0.964560i	$0.415003\pi$
$6$	0.185599	+	0.753005i	0.0757705	+	0.307413i
$7$	−1.40603	−	2.67897i	−0.531431	−	1.01256i	−0.992155	−	0.125013i	$-0.960103\pi$
$7$	−1.40603	−	2.67897i	−0.531431	−	1.01256i	0.460724	−	0.887543i	$-0.347590\pi$
$8$	−1.22487	−	2.33380i	−0.433058	−	0.825123i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	1.16148	+	0.609593i	0.367293	+	0.192770i
$11$	4.12515	−	1.56446i	1.24378	−	0.471703i	0.357091	−	0.934070i	$-0.383769\pi$
$11$	4.12515	−	1.56446i	1.24378	−	0.471703i	0.886689	+	0.462366i	$0.152999\pi$
$12$	0.168575	−	1.38834i	0.0486634	−	0.400779i
$13$	1.25140	−	3.38142i	0.347076	−	0.937837i
$13$	1.25140	−	3.38142i	0.347076	−	0.937837i
$14$	−0.282830	−	2.32932i	−0.0755895	−	0.622536i
$15$	0.786023	+	1.49764i	0.202950	+	0.386690i
$16$	0.0907609	+	0.747483i	0.0226902	+	0.186871i
$17$	1.83506	−	0.963114i	0.445068	−	0.233590i	−0.227273	−	0.973831i	$-0.572981\pi$
$17$	1.83506	−	0.963114i	0.445068	−	0.233590i	0.672341	+	0.740241i	$0.265289\pi$
$18$	−0.514279	+	0.580501i	−0.121217	+	0.136825i
$19$			4.05343i			0.929921i	0.885331	+	0.464961i	$0.153932\pi$
$19$			4.05343i			0.929921i	−0.885331	+	0.464961i	$0.846068\pi$
$20$	−1.56859	−	1.77057i	−0.350747	−	0.395911i
$21$	1.40603	−	2.67897i	0.306822	−	0.584600i
$22$	3.42157			0.729482
$23$	5.11342			1.06622			0.533111	−	0.846046i	$-0.321023\pi$
$23$	5.11342			1.06622			0.533111	+	0.846046i	$0.321023\pi$
$24$	1.22487	−	2.33380i	0.250026	−	0.476385i
$25$	−2.07707	−	0.511953i	−0.415415	−	0.102391i
$26$	1.83737	−	2.10787i	0.360338	−	0.413386i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	−1.01262	+	4.10836i	−0.191367	+	0.776406i
$29$	−0.670658	+	1.76838i	−0.124538	+	0.328380i	−0.982756	−	0.184905i	$-0.940802\pi$
$29$	−0.670658	+	1.76838i	−0.124538	+	0.328380i	0.858218	+	0.513285i	$0.171571\pi$
$30$	0.158112	+	1.30217i	0.0288672	+	0.237743i
$31$	−0.592879	−	2.40540i	−0.106484	−	0.432023i	0.893366	−	0.449330i	$-0.148337\pi$
$31$	−0.592879	−	2.40540i	−0.106484	−	0.432023i	−0.999850	+	0.0173062i	$0.994491\pi$
$32$	−1.40128	+	5.68523i	−0.247714	+	1.00502i
$33$	3.63088	+	2.50622i	0.632055	+	0.436276i
$34$	1.59555	−	0.193735i	0.273635	−	0.0332252i
$35$	−1.81463	−	4.78478i	−0.306728	−	0.808775i
$36$	1.23834	−	0.649932i	0.206390	−	0.108322i
$37$	0.739773	+	3.00138i	0.121618	+	0.493423i	0.999884	+	0.0152504i	$0.00485453\pi$
$37$	0.739773	+	3.00138i	0.121618	+	0.493423i	−0.878266	+	0.478173i	$0.841299\pi$
$38$	−1.11474	+	2.93932i	−0.180834	+	0.476821i
$39$	3.49373	−	0.890982i	0.559445	−	0.142671i
$40$	−1.58082	−	4.16828i	−0.249950	−	0.659063i
$41$	−6.89063	+	4.75626i	−1.07613	+	0.742802i	−0.967903	−	0.251323i	$-0.919134\pi$
$41$	−6.89063	+	4.75626i	−1.07613	+	0.742802i	−0.108232	+	0.994126i	$0.534519\pi$
$42$	1.75632	−	1.55597i	0.271007	−	0.240091i
$43$	−0.650462	−	0.160324i	−0.0991945	−	0.0244492i	0.189406	−	0.981899i	$-0.439344\pi$
$43$	−0.650462	−	0.160324i	−0.0991945	−	0.0244492i	−0.288600	+	0.957450i	$0.593190\pi$
$44$	−5.76917	−	2.18796i	−0.869735	−	0.329847i
$45$	−0.786023	+	1.49764i	−0.117173	+	0.223255i
$46$	3.70796	+	1.40624i	0.546709	+	0.207339i
$47$	−2.46299	−	2.78014i	−0.359264	−	0.405525i	0.540893	−	0.841092i	$-0.318087\pi$
$47$	−2.46299	−	2.78014i	−0.359264	−	0.405525i	−0.900157	+	0.435566i	$0.856548\pi$
$48$	−0.563609	+	0.499314i	−0.0813499	+	0.0720697i
$49$	−1.22351	+	1.77257i	−0.174788	+	0.253224i
$50$	−1.36538	−	0.942457i	−0.193094	−	0.133284i
$51$	1.83506	+	0.963114i	0.256960	+	0.134863i
$52$	−4.44592	+	2.37918i	−0.616538	+	0.329933i
$53$	6.80180	−	3.56986i	0.934299	−	0.490358i	0.0723648	−	0.997378i	$-0.476945\pi$
$53$	6.80180	−	3.56986i	0.934299	−	0.490358i	0.861934	+	0.507020i	$0.169253\pi$
$54$	−0.769887	−	0.0934812i	−0.104768	−	0.0127212i
$55$	7.24528	−	1.78580i	0.976953	−	0.240797i
$56$	−4.52998	+	6.56280i	−0.605344	+	0.876992i
$57$	−3.33591	+	2.30261i	−0.441852	+	0.304989i
$58$	−0.972646	+	1.09789i	−0.127715	+	0.144160i
$59$	−6.60857	−	0.802426i	−0.860363	−	0.104467i	−0.321550	−	0.946893i	$-0.604204\pi$
$59$	−6.60857	−	0.802426i	−0.860363	−	0.104467i	−0.538813	+	0.842426i	$0.681127\pi$
$60$	0.566090	−	2.29672i	0.0730819	−	0.296505i
$61$	11.8473	+	6.21795i	1.51689	+	0.796127i	0.998266	−	0.0588726i	$-0.0187506\pi$
$61$	11.8473	+	6.21795i	1.51689	+	0.796127i	0.518628	+	0.855000i	$0.326443\pi$
$62$	0.231590	−	1.90731i	0.0294119	−	0.242229i
$63$	3.00347	−	0.364687i	0.378402	−	0.0459463i
$64$	−1.72415	+	2.49787i	−0.215519	+	0.312233i
$65$	2.79054	−	5.42244i	0.346124	−	0.672570i
$66$	1.94367	+	2.81590i	0.239250	+	0.346613i
$67$	−1.44949	−	1.63613i	−0.177083	−	0.199886i	0.653267	−	0.757128i	$-0.273398\pi$
$67$	−1.44949	−	1.63613i	−0.177083	−	0.199886i	−0.830350	+	0.557242i	$0.811860\pi$
$68$	−2.81417	−	0.693630i	−0.341268	−	0.0841150i
$69$	2.90475	+	4.20826i	0.349691	+	0.506615i
$70$		−	3.96869i		−	0.474349i
$71$	−1.74972	+	1.20775i	−0.207654	+	0.143333i	−0.667353	−	0.744742i	$-0.732573\pi$
$71$	−1.74972	+	1.20775i	−0.207654	+	0.143333i	0.459699	+	0.888075i	$0.347957\pi$
$72$	2.61649	−	0.317699i	0.308356	−	0.0374412i
$73$	4.10965	−	1.55859i	0.480999	−	0.182419i	−0.102175	−	0.994766i	$-0.532580\pi$
$73$	4.10965	−	1.55859i	0.480999	−	0.182419i	0.583173	+	0.812348i	$0.301811\pi$
$74$	−0.288969	+	2.37987i	−0.0335920	+	0.276655i
$75$	−0.758583	−	2.00022i	−0.0875937	−	0.230966i
$76$	3.75916	−	4.24321i	0.431205	−	0.486730i
$77$	−9.99126	−	8.85148i	−1.13861	−	1.00872i
$78$	2.77849	+	0.314724i	0.314602	+	0.0356354i
$79$	−9.26239	+	8.20576i	−1.04210	+	0.923220i	−0.997125	−	0.0757681i	$-0.975859\pi$
$79$	−9.26239	+	8.20576i	−1.04210	+	0.923220i	−0.0449745	+	0.998988i	$0.514321\pi$
$80$			1.27356i			0.142389i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	−6.30471	+	1.55397i	−0.696239	+	0.171608i
$83$	−9.85379	−	6.80158i	−1.08159	−	0.746570i	−0.112596	−	0.993641i	$-0.535917\pi$
$83$	−9.85379	−	6.80158i	−1.08159	−	0.746570i	−0.968998	+	0.247070i	$0.920532\pi$
$84$	−3.95634	+	1.50044i	−0.431673	+	0.163712i
$85$	3.27751	−	1.24299i	0.355496	−	0.134822i
$86$	−0.427587	−	0.295142i	−0.0461079	−	0.0318260i
$87$	−1.83632	+	0.452613i	−0.196875	+	0.0485252i
$88$	−8.70393	−	7.71101i	−0.927842	−	0.821997i
$89$			15.1685i			1.60786i	0.594727	+	0.803928i	$0.297260\pi$
$89$			15.1685i			1.60786i	−0.594727	+	0.803928i	$0.702740\pi$
$90$	−0.981847	+	0.869841i	−0.103496	+	0.0916893i
$91$	−10.8182	+	1.40192i	−1.13406	+	0.146961i
$92$	−5.35282	−	4.74219i	−0.558070	−	0.494407i
$93$	1.64282	−	1.85436i	0.170352	−	0.192288i
$94$	−1.02145	−	2.69335i	−0.105355	−	0.277798i
$95$	−0.826387	+	6.80591i	−0.0847855	+	0.698271i
$96$	−5.47487	+	2.07634i	−0.558776	+	0.211916i
$97$	8.25314	−	1.00211i	0.837979	−	0.101749i	0.309715	−	0.950829i	$-0.399766\pi$
$97$	8.25314	−	1.00211i	0.837979	−	0.101749i	0.528264	+	0.849080i	$0.322843\pi$
$98$	−1.37470	+	0.948886i	−0.138866	+	0.0958519i
$99$			4.41185i			0.443408i
$100$	1.69953	+	2.46220i	0.169953	+	0.246220i
$101$	−3.44532	−	0.849195i	−0.342822	−	0.0844981i	0.0641457	−	0.997941i	$-0.479568\pi$
$101$	−3.44532	−	0.849195i	−0.342822	−	0.0844981i	−0.406968	+	0.913442i	$0.633414\pi$
$102$	1.06582	+	1.20306i	0.105532	+	0.119120i
$103$	7.35723	+	10.6588i	0.724929	+	1.05024i	0.996145	+	0.0877227i	$0.0279589\pi$
$103$	7.35723	+	10.6588i	0.724929	+	1.05024i	−0.271216	+	0.962519i	$0.587426\pi$
$104$	−9.42437	+	1.22129i	−0.924135	+	0.119757i
$105$	2.90697	−	4.21147i	0.283691	−	0.410997i
$106$	5.91403	−	0.718093i	0.574421	−	0.0697474i
$107$	0.588587	−	4.84745i	0.0569008	−	0.468620i	−0.936210	−	0.351441i	$-0.885692\pi$
$107$	0.588587	−	4.84745i	0.0569008	−	0.468620i	0.993111	−	0.117179i	$-0.0373852\pi$
$108$	1.23834	+	0.649932i	0.119159	+	0.0625397i
$109$	−2.24412	+	9.10475i	−0.214948	+	0.872077i	0.760051	+	0.649864i	$0.225174\pi$
$109$	−2.24412	+	9.10475i	−0.214948	+	0.872077i	−0.974998	+	0.222213i	$0.928672\pi$
$110$	5.74498	+	0.697567i	0.547762	+	0.0665104i
$111$	−2.04984	+	2.31380i	−0.194563	+	0.219616i
$112$	1.87488	−	1.29413i	0.177159	−	0.122284i
$113$	−3.84063	+	5.56411i	−0.361296	+	0.523427i	−0.960910	−	0.276862i	$-0.910705\pi$
$113$	−3.84063	+	5.56411i	−0.361296	+	0.523427i	0.599614	+	0.800290i	$0.295321\pi$
$114$	−3.05226	+	0.752314i	−0.285870	+	0.0704607i
$115$	8.58567	+	1.04249i	0.800618	+	0.0972126i
$116$	2.34205	−	1.22920i	0.217454	−	0.114129i
$117$	2.71793	+	2.36915i	0.251273	+	0.219028i
$118$	−4.57149	−	2.39930i	−0.420840	−	0.220874i
$119$	−5.16031	−	3.56191i	−0.473045	−	0.326520i
$120$	2.53242	−	3.66884i	0.231177	−	0.334918i
$121$	6.33571	−	5.61295i	0.575973	−	0.510268i
$122$	6.88100	+	7.76705i	0.622977	+	0.703196i
$123$	−7.82864	−	2.96901i	−0.705885	−	0.267707i
$124$	−1.61014	+	3.06786i	−0.144595	+	0.275502i
$125$	−11.2905	−	4.28191i	−1.00985	−	0.382986i
$126$	2.27824	+	0.561536i	0.202962	+	0.0500256i
$127$	−14.5962	+	12.9311i	−1.29520	+	1.14745i	−0.315076	+	0.949067i	$0.602030\pi$
$127$	−14.5962	+	12.9311i	−1.29520	+	1.14745i	−0.980125	+	0.198381i	$0.936432\pi$
$128$	7.70055	−	5.31531i	0.680639	−	0.469811i
$129$	−0.237560	−	0.626394i	−0.0209160	−	0.0551509i
$130$	3.51477	−	3.16462i	0.308266	−	0.277555i
$131$	3.91330	−	10.3185i	0.341906	−	0.901533i	−0.648232	−	0.761443i	$-0.724491\pi$
$131$	3.91330	−	10.3185i	0.341906	−	0.901533i	0.990139	−	0.140090i	$-0.0447393\pi$
$132$	−1.47661	−	5.99084i	−0.128522	−	0.521435i
$133$	10.8590	−	5.69926i	0.941598	−	0.494189i
$134$	−0.601133	−	1.58506i	−0.0519300	−	0.136928i
$135$	−1.67905	+	0.203873i	−0.144509	+	0.0175466i
$136$	−4.49543	−	3.10297i	−0.385480	−	0.266078i
$137$	−0.890044	+	3.61105i	−0.0760416	+	0.308513i	−0.996631	−	0.0820198i	$-0.973863\pi$
$137$	−0.890044	+	3.61105i	−0.0760416	+	0.308513i	0.920589	+	0.390532i	$0.127709\pi$
$138$	0.949046	+	3.85043i	0.0807882	+	0.327770i
$139$	−0.708642	−	5.83620i	−0.0601063	−	0.495020i	−0.991411	−	0.130780i	$-0.958252\pi$
$139$	−0.708642	−	5.83620i	−0.0601063	−	0.495020i	0.931305	−	0.364240i	$-0.118671\pi$
$140$	−2.53782	+	6.69168i	−0.214485	+	0.565550i
$141$	0.888873	−	3.60630i	0.0748566	−	0.303705i
$142$	−1.60094	+	0.394597i	−0.134348	+	0.0331138i
$143$	−0.127886	−	15.9066i	−0.0106943	−	1.33018i
$144$	−0.731093	−	0.180198i	−0.0609244	−	0.0150165i
$145$	−1.48659	+	2.83246i	−0.123455	+	0.235223i
$146$	3.40872			0.282107
$147$	−2.15383			−0.177645
$148$	2.00907	−	3.82796i	0.165144	−	0.314657i
$149$	6.78821	+	7.66231i	0.556112	+	0.627721i	0.957585	−	0.288150i	$-0.0930402\pi$
$149$	6.78821	+	7.66231i	0.556112	+	0.627721i	−0.401473	+	0.915871i	$0.631502\pi$
$150$		−	1.65907i		−	0.135462i
$151$	13.1155	−	14.8043i	1.06732	−	1.20476i	0.0893529	−	0.996000i	$-0.471520\pi$
$151$	13.1155	−	14.8043i	1.06732	−	1.20476i	0.977968	−	0.208756i	$-0.0669414\pi$
$152$	9.45991	−	4.96494i	0.767300	−	0.402710i
$153$	0.249806	+	2.05734i	0.0201956	+	0.166326i
$154$	−4.81084	−	9.16630i	−0.387669	−	0.738641i
$155$	−0.505074	−	4.15966i	−0.0405685	−	0.334112i
$156$	−4.48360	−	2.30739i	−0.358975	−	0.184739i
$157$	−2.23643	+	18.4187i	−0.178487	+	1.46997i	0.578040	+	0.816008i	$0.303818\pi$
$157$	−2.23643	+	18.4187i	−0.178487	+	1.46997i	−0.756527	+	0.653963i	$0.773105\pi$
$158$	−8.97323	+	3.40310i	−0.713872	+	0.270736i
$159$	6.80180	+	3.56986i	0.539418	+	0.283108i
$160$	−3.51188	+	9.26008i	−0.277639	+	0.732073i
$161$	−7.18964	−	13.6987i	−0.566623	−	1.07961i
$162$	−0.360412	−	0.686708i	−0.0283166	−	0.0539529i
$163$	−0.603894	−	2.45010i	−0.0473007	−	0.191906i	0.942539	−	0.334097i	$-0.108431\pi$
$163$	−0.603894	−	2.45010i	−0.0473007	−	0.191906i	−0.989839	+	0.142191i	$0.954585\pi$
$164$	11.6242	+	1.41143i	0.907697	+	0.110214i
$165$	5.58547	+	4.94830i	0.434828	+	0.385224i
$166$	−5.27491	−	7.64202i	−0.409412	−	0.593136i
$167$	7.66252	+	2.90601i	0.592944	+	0.224874i	0.632779	−	0.774332i	$-0.281914\pi$
$167$	7.66252	+	2.90601i	0.592944	+	0.224874i	−0.0398354	+	0.999206i	$0.512683\pi$
$168$	−7.97440			−0.615239
$169$	−9.86799	−	8.46303i	−0.759076	−	0.651002i
$170$	2.71850			0.208499
$171$	−3.79003	−	1.43737i	−0.289831	−	0.109918i
$172$	0.532231	+	0.771069i	0.0405822	+	0.0587935i
$173$	12.5815	+	11.1463i	0.956557	+	0.847436i	0.988372	−	0.152058i	$-0.0485901\pi$
$173$	12.5815	+	11.1463i	0.956557	+	0.847436i	−0.0318144	+	0.999494i	$0.510129\pi$
$174$	−1.45607	−	0.176799i	−0.110385	−	0.0134031i
$175$	1.54893	+	6.28425i	0.117088	+	0.475044i
$176$	1.54381	+	2.94149i	0.116369	+	0.221723i
$177$	−3.09371	−	5.89458i	−0.232538	−	0.443064i
$178$	−4.17150	+	10.9993i	−0.312667	+	0.824435i
$179$	−2.13649	−	1.12132i	−0.159689	−	0.0838112i	0.382986	−	0.923754i	$-0.374896\pi$
$179$	−2.13649	−	1.12132i	−0.159689	−	0.0838112i	−0.542674	+	0.839943i	$0.682588\pi$
$180$	2.21174	−	0.838802i	0.164853	−	0.0625206i
$181$	−2.19715	+	18.0952i	−0.163313	+	1.34500i	0.648557	+	0.761166i	$0.275373\pi$
$181$	−2.19715	+	18.0952i	−0.163313	+	1.34500i	−0.811870	+	0.583838i	$0.801550\pi$
$182$	−8.23032	−	1.95854i	−0.610072	−	0.145177i
$183$	1.61277	+	13.2824i	0.119219	+	0.981860i
$184$	−6.26329	−	11.9337i	−0.461736	−	0.879764i
$185$	0.630213	+	5.19027i	0.0463342	+	0.381596i
$186$	1.70125	−	0.892882i	0.124741	−	0.0654693i
$187$	6.06315	−	6.84388i	0.443381	−	0.500474i
$188$			5.19448i			0.378847i
$189$	2.00630	+	2.26464i	0.145937	+	0.164728i
$190$	−2.47095	+	4.70800i	−0.179261	+	0.341554i
$191$	−16.8040			−1.21589			−0.607947	−	0.793978i	$-0.708007\pi$
$191$	−16.8040			−1.21589			−0.607947	+	0.793978i	$0.708007\pi$
$192$	−3.03514			−0.219042
$193$	−7.73663	+	14.7409i	−0.556895	+	1.06107i	0.430469	+	0.902605i	$0.358348\pi$
$193$	−7.73663	+	14.7409i	−0.556895	+	1.06107i	−0.987364	+	0.158469i	$0.949344\pi$
$194$	6.26030	+	1.54303i	0.449464	+	0.110783i
$195$	6.04779	−	0.783722i	0.433091	−	0.0561235i
$196$	2.92468	−	0.720868i	0.208906	−	0.0514906i
$197$	−1.69576	+	6.87998i	−0.120818	+	0.490178i	0.879091	+	0.476655i	$0.158151\pi$
$197$	−1.69576	+	6.87998i	−0.120818	+	0.490178i	−0.999909	+	0.0135231i	$0.995695\pi$
$198$	−1.21331	+	3.19923i	−0.0862259	+	0.227359i
$199$	0.835407	+	6.88019i	0.0592204	+	0.487724i	0.991900	+	0.127019i	$0.0405409\pi$
$199$	0.835407	+	6.88019i	0.0592204	+	0.487724i	−0.932680	+	0.360705i	$0.882536\pi$
$200$	1.34936	+	5.47455i	0.0954139	+	0.387109i
$201$	0.523109	−	2.12234i	0.0368972	−	0.149698i
$202$	−2.26481	−	1.56329i	−0.159352	−	0.109993i
$203$	5.68041	−	0.689726i	0.398686	−	0.0484093i
$204$	−1.02778	−	2.71004i	−0.0719593	−	0.189741i
$205$	−12.5394	+	6.58116i	−0.875787	+	0.459648i
$206$	2.40377	+	9.75247i	0.167478	+	0.679487i
$207$	−1.81324	+	4.78113i	−0.126029	+	0.332311i
$208$	2.64113	+	0.628501i	0.183130	+	0.0435787i
$209$	6.34145	+	16.7210i	0.438647	+	1.15662i
$210$	3.26617	−	2.25447i	0.225387	−	0.155573i
$211$	16.7090	−	14.8029i	1.15030	−	1.01908i	0.150764	−	0.988570i	$-0.451827\pi$
$211$	16.7090	−	14.8029i	1.15030	−	1.01908i	0.999535	−	0.0305056i	$-0.00971175\pi$
$212$	−10.4309	−	2.57100i	−0.716400	−	0.176577i
$213$	−1.98791	−	0.753915i	−0.136209	−	0.0516574i
$214$	1.75991	−	3.35323i	0.120305	−	0.229222i
$215$	−1.05947	−	0.401804i	−0.0722553	−	0.0274028i
$216$	1.74780	+	1.97285i	0.118922	+	0.134236i
$217$	−5.61041	+	4.97039i	−0.380859	+	0.337412i
$218$	−4.13121	+	5.98509i	−0.279801	+	0.405362i
$219$	3.61724	+	2.49680i	0.244430	+	0.168718i
$220$	−9.24064	−	4.84986i	−0.623004	−	0.326978i
$221$	−0.960295	−	7.41035i	−0.0645964	−	0.498474i
$222$	−2.12275	+	1.11411i	−0.142470	+	0.0747739i
$223$	25.7566	+	3.12742i	1.72479	+	0.209428i	0.922096	−	0.386961i	$-0.126475\pi$
$223$	25.7566	+	3.12742i	1.72479	+	0.209428i	0.802696	+	0.596389i	$0.203398\pi$
$224$	17.2008	−	4.23962i	1.14928	−	0.283272i
$225$	1.21522	−	1.76056i	0.0810150	−	0.117370i
$226$	−4.31520	+	2.97857i	−0.287043	+	0.198131i
$227$	11.2768	−	12.7289i	0.748469	−	0.844847i	−0.243687	−	0.969854i	$-0.578357\pi$
$227$	11.2768	−	12.7289i	0.748469	−	0.844847i	0.992156	+	0.125007i	$0.0398953\pi$
$228$	5.62754	+	0.683307i	0.372693	+	0.0452531i
$229$	3.26948	−	13.2648i	0.216053	−	0.876563i	−0.758366	−	0.651828i	$-0.774002\pi$
$229$	3.26948	−	13.2648i	0.216053	−	0.876563i	0.974420	−	0.224735i	$-0.0721516\pi$
$230$	5.93915	+	3.11711i	0.391616	+	0.205536i
$231$	1.60895	−	13.2509i	0.105861	−	0.871842i
$232$	4.94851	−	0.600858i	0.324886	−	0.0394483i
$233$	−1.33188	+	1.92957i	−0.0872546	+	0.126410i	−0.864181	−	0.503182i	$-0.832163\pi$
$233$	−1.33188	+	1.92957i	−0.0872546	+	0.126410i	0.776926	+	0.629592i	$0.216778\pi$
$234$	1.31935	+	2.46543i	0.0862484	+	0.161170i
$235$	−3.56868	−	5.17013i	−0.232795	−	0.337262i
$236$	6.17381	+	6.96879i	0.401881	+	0.453629i
$237$	−12.0148	−	2.96139i	−0.780448	−	0.192363i
$238$	−2.76241	−	4.00204i	−0.179060	−	0.259414i
$239$		−	20.8419i		−	1.34815i	−0.738664	−	0.674074i	$-0.764543\pi$
$239$		−	20.8419i		−	1.34815i	0.738664	−	0.674074i	$-0.235457\pi$
$240$	−1.04812	+	0.723467i	−0.0676560	+	0.0466996i
$241$	−13.0673	+	1.58666i	−0.841740	+	0.102206i	−0.530038	−	0.847974i	$-0.677822\pi$
$241$	−13.0673	+	1.58666i	−0.841740	+	0.102206i	−0.311702	+	0.950180i	$0.600899\pi$
$242$	6.13792	−	2.32781i	0.394560	−	0.149637i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−6.63546	−	17.4963i	−0.424792	−	1.12008i
$245$	−2.41572	+	2.72678i	−0.154335	+	0.174208i
$246$	−4.86038	−	4.30592i	−0.309887	−	0.274536i
$247$	13.7064	+	5.07247i	0.872115	+	0.322754i
$248$	−4.88753	+	4.32998i	−0.310359	+	0.274954i
$249$		−	11.9732i		−	0.758774i
$250$	−7.00964	−	6.21000i	−0.443329	−	0.392755i
$251$	2.01524	−	0.496712i	0.127201	−	0.0313522i	−0.175201	−	0.984533i	$-0.556058\pi$
$251$	2.01524	−	0.496712i	0.127201	−	0.0313522i	0.302402	+	0.953180i	$0.402211\pi$
$252$	−3.48230	−	2.40366i	−0.219364	−	0.151416i
$253$	21.0936	−	7.99975i	1.32614	−	0.502940i
$254$	−14.1405	+	5.36279i	−0.887254	+	0.336491i
$255$	2.88480	+	1.99123i	0.180653	+	0.124696i
$256$	12.9397	−	3.18934i	0.808728	−	0.199334i
$257$	17.8858	+	15.8454i	1.11569	+	0.988411i	0.999988	−	0.00487333i	$-0.00155123\pi$
$257$	17.8858	+	15.8454i	1.11569	+	0.988411i	0.115697	+	0.993285i	$0.463090\pi$
$258$		−	0.519557i		−	0.0323462i
$259$	7.00046	−	6.20187i	0.434987	−	0.385365i
$260$	−7.94996	+	3.08836i	−0.493036	+	0.191532i
$261$	−1.41564	−	1.25415i	−0.0876262	−	0.0776300i
$262$	5.67540	−	6.40621i	0.350628	−	0.395777i
$263$	−4.04309	−	10.6607i	−0.249308	−	0.657370i	0.750687	−	0.660658i	$-0.229723\pi$
$263$	−4.04309	−	10.6607i	−0.249308	−	0.657370i	−0.999995	+	0.00328807i	$0.998953\pi$
$264$	1.40164	−	11.5435i	0.0862650	−	0.710456i
$265$	12.1483	−	4.60726i	0.746267	−	0.283022i
$266$	9.44172	−	1.14643i	0.578909	−	0.0702923i
$267$	−12.4834	+	8.61668i	−0.763973	+	0.527332i
$268$			3.05699i			0.186736i
$269$	−12.0377	−	17.4397i	−0.733955	−	1.06332i	−0.995183	−	0.0980396i	$-0.968743\pi$
$269$	−12.0377	−	17.4397i	−0.733955	−	1.06332i	0.261228	−	0.965277i	$-0.415873\pi$
$270$	−1.27362	−	0.313919i	−0.0775099	−	0.0191045i
$271$	2.07579	+	2.34308i	0.126095	+	0.142332i	0.808168	−	0.588953i	$-0.200460\pi$
$271$	2.07579	+	2.34308i	0.126095	+	0.142332i	−0.682072	+	0.731285i	$0.738921\pi$
$272$	0.886464	+	1.28426i	0.0537498	+	0.0778700i
$273$	−7.29922	−	8.10686i	−0.441769	−	0.490650i
$274$	−1.63849	+	2.37376i	−0.0989846	+	0.143404i
$275$	−9.36917	+	1.13762i	−0.564982	+	0.0686013i
$276$	0.861993	−	7.09915i	0.0518859	−	0.427319i
$277$	−2.27058	−	1.19169i	−0.136426	−	0.0716018i	0.395129	−	0.918626i	$-0.370700\pi$
$277$	−2.27058	−	1.19169i	−0.136426	−	0.0716018i	−0.531555	+	0.847024i	$0.678392\pi$
$278$	1.09115	−	4.42696i	0.0654428	−	0.265512i
$279$	2.45933	+	0.298617i	0.147236	+	0.0178777i
$280$	−8.94403	+	10.0957i	−0.534508	+	0.603335i
$281$	8.63861	−	5.96280i	0.515336	−	0.355711i	−0.281836	−	0.959463i	$-0.590943\pi$
$281$	8.63861	−	5.96280i	0.515336	−	0.355711i	0.797173	+	0.603751i	$0.206328\pi$
$282$	1.63633	−	2.37064i	0.0974422	−	0.141169i
$283$	−1.58954	+	0.391787i	−0.0944885	+	0.0232893i	−0.286276	−	0.958147i	$-0.592418\pi$
$283$	−1.58954	+	0.391787i	−0.0944885	+	0.0232893i	0.191788	+	0.981436i	$0.438571\pi$
$284$	2.95171	+	0.358402i	0.175152	+	0.0212672i
$285$	−6.07059	+	3.18609i	−0.359591	+	0.188728i
$286$	4.28176	−	11.5698i	0.253186	−	0.684135i
$287$	22.4303	+	11.7723i	1.32402	+	0.694900i
$288$	−4.81888	−	3.32623i	−0.283955	−	0.196000i
$289$	−7.21724	+	10.4560i	−0.424544	+	0.615058i
$290$	−1.85695	+	1.64511i	−0.109044	+	0.0966044i
$291$	5.51304	+	6.22294i	0.323180	+	0.364795i
$292$	−5.74750	−	2.17974i	−0.336347	−	0.127560i
$293$	7.54631	−	14.3783i	0.440860	−	0.839989i	−0.559081	−	0.829113i	$-0.688846\pi$
$293$	7.54631	−	14.3783i	0.440860	−	0.839989i	0.999941	−	0.0108756i	$-0.00346189\pi$
$294$	−1.56184	−	0.592326i	−0.0910881	−	0.0345452i
$295$	−10.9325	−	2.69462i	−0.636515	−	0.156887i
$296$	6.09848	−	5.40279i	0.354467	−	0.314031i
$297$	−3.63088	+	2.50622i	−0.210685	+	0.145425i
$298$	2.81521	+	7.42311i	0.163081	+	0.430009i
$299$	6.39894	−	17.2906i	0.370060	−	0.999941i
$300$	−1.06091	+	2.79738i	−0.0612514	+	0.161507i
$301$	0.485066	+	1.96799i	0.0279588	+	0.113433i
$302$	13.5819	−	7.12835i	0.781552	−	0.410190i
$303$	−1.25829	−	3.31784i	−0.0722869	−	0.190605i
$304$	−3.02987	+	0.367893i	−0.173775	+	0.0211001i
$305$	18.6245	+	12.8556i	1.06644	+	0.736109i
$306$	−0.384645	+	1.56056i	−0.0219887	+	0.0892115i
$307$	−7.11046	−	28.8483i	−0.405816	−	1.64646i	−0.717710	−	0.696342i	$-0.754810\pi$
$307$	−7.11046	−	28.8483i	−0.405816	−	1.64646i	0.311895	−	0.950117i	$-0.399036\pi$
$308$	2.25017	+	18.5318i	0.128215	+	1.05595i
$309$	−4.59263	+	12.1098i	−0.261265	+	0.688900i
$310$	0.777700	−	3.15525i	0.0441704	−	0.179206i
$311$	20.7436	−	5.11283i	1.17626	−	0.289922i	0.397714	−	0.917509i	$-0.369804\pi$
$311$	20.7436	−	5.11283i	1.17626	−	0.289922i	0.778546	+	0.627587i	$0.215957\pi$
$312$	−6.35875	−	7.06233i	−0.359993	−	0.399826i
$313$	25.9736	+	6.40193i	1.46812	+	0.361858i	0.890700	−	0.454592i	$-0.150215\pi$
$313$	25.9736	+	6.40193i	1.46812	+	0.361858i	0.577416	+	0.816450i	$0.304061\pi$
$314$	−6.68707	+	12.7412i	−0.377373	+	0.719025i
$315$	5.11732			0.288328
$316$	17.3061			0.973542
$317$	5.19766	−	9.90332i	0.291930	−	0.556226i	−0.694681	−	0.719318i	$-0.744454\pi$
$317$	5.19766	−	9.90332i	0.291930	−	0.556226i	0.986611	+	0.163092i	$0.0521468\pi$
$318$	3.95053	+	4.45923i	0.221535	+	0.250061i
$319$			8.34405i			0.467177i
$320$	−3.40418	+	3.84253i	−0.190300	+	0.214804i
$321$	4.32373	−	2.26927i	0.241327	−	0.126658i
$322$	−1.44623	−	11.9108i	−0.0805951	−	0.663761i
$323$	3.90392	+	7.43830i	0.217220	+	0.413878i
$324$	0.168575	+	1.38834i	0.00936527	+	0.0771299i
$325$	−4.33038	+	6.38280i	−0.240206	+	0.354054i
$326$	0.235892	−	1.94275i	0.0130649	−	0.107599i
$327$	−8.76787	+	3.32521i	−0.484864	+	0.183885i
$328$	19.5403	+	10.2555i	1.07893	+	0.566267i
$329$	−3.98488	+	10.5073i	−0.219693	+	0.579284i
$330$	2.68943	+	5.12429i	0.148049	+	0.282083i
$331$	−7.73157	−	14.7313i	−0.424966	−	0.809705i	0.574999	−	0.818154i	$-0.305003\pi$
$331$	−7.73157	−	14.7313i	−0.424966	−	0.809705i	−0.999964	+	0.00844980i	$0.997310\pi$
$332$	4.00734	+	16.2584i	0.219932	+	0.892298i
$333$	−3.06866	−	0.372603i	−0.168162	−	0.0204185i
$334$	4.75724	+	4.21455i	0.260305	+	0.230610i
$335$	−2.10020	−	3.04266i	−0.114746	−	0.166238i
$336$	2.13010	+	0.807841i	0.116207	+	0.0440713i
$337$	−22.5658			−1.22924			−0.614619	−	0.788824i	$-0.710690\pi$
$337$	−22.5658			−1.22924			−0.614619	+	0.788824i	$0.710690\pi$
$338$	−4.82829	−	8.85071i	−0.262624	−	0.481415i
$339$	−6.76090			−0.367202
$340$	−4.58371	−	1.73837i	−0.248587	−	0.0942765i
$341$	−6.20888	−	8.99512i	−0.336230	−	0.487113i
$342$	−2.35302	−	2.08460i	−0.127237	−	0.112722i
$343$	−14.5553	−	1.76734i	−0.785914	−	0.0954272i
$344$	0.422568	+	1.71443i	0.0227833	+	0.0924356i
$345$	4.01926	+	7.65807i	0.216390	+	0.412297i
$346$	6.05808	+	11.5427i	0.325685	+	0.620540i
$347$	−7.44817	+	19.6392i	−0.399839	+	1.05429i	0.572333	+	0.820021i	$0.306038\pi$
$347$	−7.44817	+	19.6392i	−0.399839	+	1.05429i	−0.972172	+	0.234267i	$0.924731\pi$
$348$	2.34205	+	1.22920i	0.125547	+	0.0658923i
$349$	11.1799	−	4.23999i	0.598449	−	0.226962i	−0.0367321	−	0.999325i	$-0.511695\pi$
$349$	11.1799	−	4.23999i	0.598449	−	0.226962i	0.635181	+	0.772363i	$0.280926\pi$
$350$	−0.605040	+	4.98295i	−0.0323408	+	0.266350i
$351$	−0.405812	+	3.58264i	−0.0216606	+	0.191227i
$352$	3.11383	+	25.6447i	0.165968	+	1.36687i
$353$	−5.06579	−	9.65206i	−0.269625	−	0.513727i	0.712568	−	0.701603i	$-0.247532\pi$
$353$	−5.06579	−	9.65206i	−0.269625	−	0.513727i	−0.982193	+	0.187876i	$0.939840\pi$
$354$	−0.622314	−	5.12522i	−0.0330756	−	0.272402i
$355$	−3.18409	+	1.67114i	−0.168994	+	0.0886949i
$356$	14.0673	−	15.8787i	0.745563	−	0.841567i
$357$		−	6.27025i		−	0.331857i
$358$	−1.24089	−	1.40067i	−0.0655830	−	0.0740279i
$359$	9.54541	−	18.1873i	0.503787	−	0.959887i	−0.492208	−	0.870478i	$-0.663810\pi$
$359$	9.54541	−	18.1873i	0.503787	−	0.959887i	0.995995	−	0.0894090i	$-0.0284978\pi$
$360$	4.45798			0.234956
$361$	2.56968			0.135246
$362$	−6.56962	+	12.5174i	−0.345292	+	0.657898i
$363$	8.21846	+	2.02567i	0.431357	+	0.106320i
$364$	12.6249	+	8.56529i	0.661724	+	0.448943i
$365$	7.21806	−	1.77909i	0.377810	−	0.0931219i
$366$	−2.48330	+	10.0751i	−0.129804	+	0.526636i
$367$	−10.8983	+	28.7364i	−0.568885	+	1.50003i	0.273891	+	0.961761i	$0.411689\pi$
$367$	−10.8983	+	28.7364i	−0.568885	+	1.50003i	−0.842776	+	0.538265i	$0.819080\pi$
$368$	0.464098	+	3.82219i	0.0241928	+	0.199246i
$369$	−2.00373	−	8.12944i	−0.104310	−	0.423202i
$370$	−0.970385	+	3.93701i	−0.0504479	+	0.204675i
$371$	−19.1271	−	13.2025i	−0.993030	−	0.685439i
$372$	−3.43946	+	0.417626i	−0.178328	+	0.0216529i
$373$	−5.09558	−	13.4359i	−0.263839	−	0.695686i	−0.999825	−	0.0186899i	$-0.994050\pi$
$373$	−5.09558	−	13.4359i	−0.263839	−	0.695686i	0.735986	−	0.676996i	$-0.236719\pi$
$374$	6.27879	−	3.29536i	0.324669	−	0.170399i
$375$	−2.88977	−	11.7243i	−0.149227	−	0.605439i
$376$	−3.47144	+	9.15345i	−0.179026	+	0.472053i
$377$	5.14037	+	4.48073i	0.264742	+	0.230769i
$378$	0.832053	+	2.19394i	0.0427962	+	0.112844i
$379$	−28.2059	+	19.4691i	−1.44884	+	1.00006i	−0.454854	+	0.890566i	$0.650308\pi$
$379$	−28.2059	+	19.4691i	−1.44884	+	1.00006i	−0.993987	+	0.109496i	$0.965076\pi$
$380$	7.17688	−	6.35816i	0.368166	−	0.326167i
$381$	−18.9336	−	4.66672i	−0.970000	−	0.239083i
$382$	−12.1853	−	4.62127i	−0.623454	−	0.236445i
$383$	−1.62558	+	3.09728i	−0.0830632	+	0.158264i	−0.923445	−	0.383732i	$-0.874639\pi$
$383$	−1.62558	+	3.09728i	−0.0830632	+	0.158264i	0.840381	+	0.541996i	$0.182331\pi$
$384$	8.74883	+	3.31799i	0.446462	+	0.169321i
$385$	−14.9712	−	16.8990i	−0.763004	−	0.861253i
$386$	−9.66408	+	8.56163i	−0.491889	+	0.435776i
$387$	0.380563	−	0.551341i	0.0193451	−	0.0280262i
$388$	−9.56890	−	6.60494i	−0.485787	−	0.335315i
$389$	21.0461	+	11.0458i	1.06708	+	0.560046i	0.904423	−	0.426637i	$-0.140302\pi$
$389$	21.0461	+	11.0458i	1.06708	+	0.560046i	0.162655	+	0.986683i	$0.447994\pi$
$390$	4.60105	+	1.09489i	0.232983	+	0.0554422i
$391$	9.38343	−	4.92480i	0.474541	−	0.249058i
$392$	5.63547	+	0.684269i	0.284634	+	0.0345608i
$393$	10.7150	−	2.64100i	0.540499	−	0.133221i
$394$	−3.12174	+	4.52262i	−0.157271	+	0.227846i
$395$	−17.2249	+	11.8895i	−0.866680	+	0.598226i
$396$	4.09155	−	4.61841i	0.205608	−	0.232084i
$397$	−33.1143	−	4.02081i	−1.66196	−	0.201799i	−0.765038	−	0.643986i	$-0.777280\pi$
$397$	−33.1143	−	4.02081i	−1.66196	−	0.201799i	−0.896923	+	0.442187i	$0.854203\pi$
$398$	−1.28634	+	5.21887i	−0.0644782	+	0.261599i
$399$	10.8590	+	5.69926i	0.543632	+	0.285320i
$400$	0.194159	−	1.59904i	0.00970795	−	0.0799522i
$401$	1.60578	−	0.194977i	0.0801889	−	0.00973670i	−0.0803439	−	0.996767i	$-0.525602\pi$
$401$	1.60578	−	0.194977i	0.0801889	−	0.00973670i	0.160533	+	0.987031i	$0.448679\pi$
$402$	0.962994	−	1.39514i	0.0480298	−	0.0695831i
$403$	−8.87561	−	1.00535i	−0.442126	−	0.0500803i
$404$	2.81908	+	4.08415i	0.140255	+	0.203194i
$405$	−1.12159	−	1.26602i	−0.0557324	−	0.0629088i
$406$	4.30879	+	1.06202i	0.213842	+	0.0527073i
$407$	7.74721	+	11.2238i	0.384015	+	0.556342i
$408$		−	5.46236i		−	0.270427i
$409$	−1.78629	+	1.23299i	−0.0883263	+	0.0609672i	−0.611409	−	0.791314i	$-0.709397\pi$
$409$	−1.78629	+	1.23299i	−0.0883263	+	0.0609672i	0.523083	+	0.852282i	$0.324782\pi$
$410$	−10.9027	+	1.32383i	−0.538447	+	0.0653793i
$411$	−3.47744	+	1.31882i	−0.171529	+	0.0650525i
$412$	2.18328	−	17.9809i	0.107562	−	0.885856i
$413$	7.14220	+	18.8324i	0.351445	+	0.926683i
$414$	−2.62972	+	2.96834i	−0.129244	+	0.145886i
$415$	−15.1583	−	13.4291i	−0.744093	−	0.659209i
$416$	17.4706	+	11.8528i	0.856565	+	0.581132i
$417$	4.40054	−	3.89854i	0.215495	−	0.190912i
$418$			13.8691i			0.678361i
$419$	−14.9598	−	13.2533i	−0.730836	−	0.647464i	0.213313	−	0.976984i	$-0.431575\pi$
$419$	−14.9598	−	13.2533i	−0.730836	−	0.647464i	−0.944149	+	0.329520i	$0.893113\pi$
$420$	−6.94879	+	1.71272i	−0.339066	+	0.0835723i
$421$	12.9556	+	8.94259i	0.631416	+	0.435835i	0.840312	−	0.542103i	$-0.182372\pi$
$421$	12.9556	+	8.94259i	0.631416	+	0.435835i	−0.208896	+	0.977938i	$0.566987\pi$
$422$	16.1874	−	6.13908i	0.787992	−	0.298846i
$423$	3.47286	−	1.31708i	0.168856	−	0.0640388i
$424$	−16.6627	−	11.5014i	−0.809211	−	0.558558i
$425$	−4.30463	+	1.06099i	−0.208805	+	0.0514658i
$426$	−1.23419	−	1.09339i	−0.0597965	−	0.0529751i
$427$		−	40.4813i		−	1.95903i
$428$	−5.11167	+	4.52854i	−0.247082	+	0.218895i
$429$	13.0183	−	9.14125i	0.628527	−	0.441344i
$430$	−0.657768	−	0.582731i	−0.0317204	−	0.0281018i
$431$	−22.8151	+	25.7529i	−1.09896	+	1.24047i	−0.130465	+	0.991453i	$0.541647\pi$
$431$	−22.8151	+	25.7529i	−1.09896	+	1.24047i	−0.968498	+	0.249020i	$0.919891\pi$
$432$	−0.267008	−	0.704042i	−0.0128464	−	0.0338733i
$433$	3.11426	−	25.6482i	0.149662	−	1.23258i	−0.703411	−	0.710783i	$-0.748341\pi$
$433$	3.11426	−	25.6482i	0.149662	−	1.23258i	0.853073	−	0.521792i	$-0.174736\pi$
$434$	−5.43526	+	2.06132i	−0.260901	+	0.0989467i
$435$	−3.17555	+	0.385582i	−0.152256	+	0.0184872i
$436$	10.7929	−	7.44983i	0.516888	−	0.356782i
$437$			20.7269i			0.991502i
$438$	1.93637	+	2.80532i	0.0925234	+	0.134043i
$439$	−21.6743	−	5.34223i	−1.03446	−	0.254971i	−0.314696	−	0.949193i	$-0.601902\pi$
$439$	−21.6743	−	5.34223i	−1.03446	−	0.254971i	−0.719761	+	0.694222i	$0.755749\pi$
$440$	−13.0422	−	14.7217i	−0.621765	−	0.701827i
$441$	−1.22351	−	1.77257i	−0.0582626	−	0.0844079i
$442$	1.34157	−	5.63766i	0.0638122	−	0.268156i
$443$	3.73423	−	5.40997i	0.177419	−	0.257035i	−0.724178	−	0.689613i	$-0.757781\pi$
$443$	3.73423	−	5.40997i	0.177419	−	0.257035i	0.901597	+	0.432578i	$0.142396\pi$
$444$	4.29163	−	0.521099i	0.203672	−	0.0247302i
$445$	−3.09245	+	25.4686i	−0.146596	+	1.20733i
$446$	17.8172	+	9.35118i	0.843668	+	0.442791i
$447$	−2.44981	+	9.93928i	−0.115872	+	0.470112i
$448$	9.11594	+	1.10688i	0.430688	+	0.0522949i
$449$	−14.6066	+	16.4875i	−0.689330	+	0.778093i	−0.984127	−	0.177467i	$-0.943210\pi$
$449$	−14.6066	+	16.4875i	−0.689330	+	0.778093i	0.294797	+	0.955560i	$0.404748\pi$
$450$	1.36538	−	0.942457i	0.0643648	−	0.0444278i
$451$	−20.9839	+	30.4004i	−0.988092	+	1.43150i
$452$	9.18060	−	2.26282i	0.431819	−	0.106434i
$453$	19.6341	+	2.38401i	0.922491	+	0.112011i
$454$	11.6779	−	6.12904i	0.548071	−	0.287650i
$455$	−18.4502	+	0.148335i	−0.864957	+	0.00695405i
$456$	9.45991	+	4.96494i	0.443001	+	0.232505i
$457$	−23.0055	−	15.8796i	−1.07615	−	0.742815i	−0.108246	−	0.994124i	$-0.534524\pi$
$457$	−23.0055	−	15.8796i	−1.07615	−	0.742815i	−0.967907	+	0.251309i	$0.919139\pi$
$458$	6.01881	−	8.71975i	0.281241	−	0.407447i
$459$	−1.55125	+	1.37429i	−0.0724061	+	0.0641462i
$460$	−8.02084	−	9.05365i	−0.373973	−	0.422129i
$461$	−26.5979	−	10.0872i	−1.23879	−	0.469810i	−0.353754	−	0.935339i	$-0.615095\pi$
$461$	−26.5979	−	10.0872i	−1.23879	−	0.469810i	−0.885033	+	0.465529i	$0.845864\pi$
$462$	4.81084	−	9.16630i	0.223821	−	0.426455i
$463$	−25.5545	−	9.69154i	−1.18762	−	0.450404i	−0.319895	−	0.947453i	$-0.603648\pi$
$463$	−25.5545	−	9.69154i	−1.18762	−	0.450404i	−0.867723	+	0.497049i	$0.834417\pi$
$464$	−1.38270	−	0.340806i	−0.0641904	−	0.0158215i
$465$	3.13642	−	2.77862i	0.145448	−	0.128856i
$466$	−1.49646	+	1.03293i	−0.0693221	+	0.0478496i
$467$	8.89127	+	23.4444i	0.411439	+	1.08488i	0.967308	+	0.253605i	$0.0816165\pi$
$467$	8.89127	+	23.4444i	0.411439	+	1.08488i	−0.555869	+	0.831270i	$0.687614\pi$
$468$	−0.648029	−	5.00068i	−0.0299552	−	0.231156i
$469$	−2.34513	+	6.18360i	−0.108288	+	0.285532i
$470$	−1.16597	−	4.73051i	−0.0537820	−	0.218202i
$471$	−16.4287	+	8.62246i	−0.756995	+	0.397302i
$472$	6.22196	+	16.4060i	0.286389	+	0.755145i
$473$	−2.93408	+	0.356261i	−0.134909	+	0.0163809i
$474$	−7.89807	−	5.45165i	−0.362770	−	0.250402i
$475$	2.07517	−	8.41928i	0.0952151	−	0.386303i
$476$	2.09860	+	8.51435i	0.0961891	+	0.390255i
$477$	0.925925	+	7.62568i	0.0423952	+	0.349156i
$478$	5.73174	−	15.1134i	0.262164	−	0.691269i
$479$	8.77037	−	35.5828i	0.400729	−	1.62582i	−0.330583	−	0.943777i	$-0.607245\pi$
$479$	8.77037	−	35.5828i	0.400729	−	1.62582i	0.731312	−	0.682043i	$-0.238908\pi$
$480$	−9.61587	+	2.37010i	−0.438903	+	0.108180i
$481$	11.0747	+	1.25444i	0.504961	+	0.0571978i
$482$	−9.91203	−	2.44310i	−0.451481	−	0.111280i
$483$	7.18964	−	13.6987i	0.327140	−	0.623313i
$484$	−11.8378			−0.538081
$485$	14.0617			0.638510
$486$	0.360412	−	0.686708i	0.0163486	−	0.0311497i
$487$	27.8297	+	31.4132i	1.26108	+	1.42347i	0.862278	+	0.506435i	$0.169037\pi$
$487$	27.8297	+	31.4132i	1.26108	+	1.42347i	0.398806	+	0.917035i	$0.369425\pi$
$488$		−	35.2655i		−	1.59639i
$489$	1.67334	−	1.88881i	0.0756710	−	0.0854149i
$490$	−2.50164	+	1.31296i	−0.113012	+	0.0593135i
$491$	−2.98063	−	24.5477i	−0.134514	−	1.10782i	−0.891061	−	0.453883i	$-0.850039\pi$
$491$	−2.98063	−	24.5477i	−0.134514	−	1.10782i	0.756548	−	0.653939i	$-0.226885\pi$
$492$	5.44171	+	10.3683i	0.245331	+	0.467439i
$493$	0.472453	+	3.89100i	0.0212782	+	0.175242i
$494$	8.54409	+	7.44767i	0.384417	+	0.335086i
$495$	−0.899458	+	7.40770i	−0.0404276	+	0.332952i
$496$	1.74419	−	0.661484i	0.0783164	−	0.0297015i
$497$	5.69569	+	2.98933i	0.255486	+	0.134090i
$498$	3.29277	−	8.68233i	0.147553	−	0.389064i
$499$	−2.19430	−	4.18088i	−0.0982302	−	0.187162i	0.831382	−	0.555701i	$-0.187550\pi$
$499$	−2.19430	−	4.18088i	−0.0982302	−	0.187162i	−0.929612	+	0.368540i	$0.879858\pi$
$500$	7.84803	+	14.9532i	0.350975	+	0.668726i
$501$	1.96121	+	7.95693i	0.0876203	+	0.355490i
$502$	1.59794	+	0.194025i	0.0713196	+	0.00865976i
$503$	3.62065	+	3.20761i	0.161437	+	0.143020i	0.739974	−	0.672636i	$-0.234838\pi$
$503$	3.62065	+	3.20761i	0.161437	+	0.143020i	−0.578537	+	0.815656i	$0.696376\pi$
$504$	−4.52998	−	6.56280i	−0.201781	−	0.292331i
$505$	−5.61173	−	2.12825i	−0.249719	−	0.0947058i
$506$	17.4959			0.777789
$507$	1.35928	−	12.9287i	0.0603677	−	0.574186i
$508$	27.2718			1.20999
$509$	−32.4063	−	12.2901i	−1.43639	−	0.544749i	−0.491131	−	0.871085i	$-0.663417\pi$
$509$	−32.4063	−	12.2901i	−1.43639	−	0.544749i	−0.945254	+	0.326336i	$0.894186\pi$
$510$	1.54428	+	2.23728i	0.0683821	+	0.0990685i
$511$	−9.95372	−	8.81823i	−0.440327	−	0.390095i
$512$	−8.31708	−	1.00988i	−0.367567	−	0.0446307i
$513$	−0.970050	−	3.93565i	−0.0428288	−	0.173763i
$514$	8.61211	+	16.4090i	0.379864	+	0.723770i
$515$	10.1801	+	19.3965i	0.448588	+	0.854714i
$516$	−0.332236	+	0.876035i	−0.0146259	+	0.0385653i
$517$	−14.5096	−	7.61524i	−0.638133	−	0.334918i
$518$	6.78192	−	2.57204i	0.297980	−	0.113009i
$519$	−2.02607	+	16.6862i	−0.0889348	+	0.732444i
$520$	−16.0729	+	0.129223i	−0.704845	+	0.00566679i
$521$	−2.75832	−	22.7168i	−0.120844	−	0.995241i	−0.919401	−	0.393322i	$-0.871326\pi$
$521$	−2.75832	−	22.7168i	−0.120844	−	0.995241i	0.798557	−	0.601919i	$-0.205597\pi$
$522$	−0.681641	−	1.29876i	−0.0298346	−	0.0568451i
$523$	5.00374	+	41.2095i	0.218798	+	1.80197i	0.526172	+	0.850378i	$0.323627\pi$
$523$	5.00374	+	41.2095i	0.218798	+	1.80197i	−0.307373	+	0.951589i	$0.599450\pi$
$524$	−13.6659	+	7.17242i	−0.596998	+	0.313329i
$525$	−4.29194	+	4.84460i	−0.187316	+	0.211436i
$526$		−	8.84247i		−	0.385550i
$527$	−3.40465	−	3.84305i	−0.148309	−	0.167406i
$528$	−1.54381	+	2.94149i	−0.0671858	+	0.128012i
$529$	3.14703			0.136827
$530$	10.0763			0.437688
$531$	3.09371	−	5.89458i	0.134256	−	0.255803i
$532$	−16.6530	−	4.10458i	−0.721997	−	0.177956i
$533$	7.45995	+	29.2521i	0.323126	+	1.26705i
$534$	−11.4219	+	2.81526i	−0.494276	+	0.121828i
$535$	1.97653	−	8.01910i	0.0854528	−	0.346696i
$536$	−2.04297	+	5.38687i	−0.0882429	+	0.232677i
$537$	−0.290839	−	2.39528i	−0.0125506	−	0.103364i
$538$	−3.93300	−	15.9568i	−0.169564	−	0.687946i
$539$	−2.27407	+	9.22625i	−0.0979509	+	0.397403i
$540$	1.94673	+	1.34373i	0.0837740	+	0.0578250i
$541$	12.1320	−	1.47309i	0.521595	−	0.0633331i	0.144495	−	0.989506i	$-0.453844\pi$
$541$	12.1320	−	1.47309i	0.521595	−	0.0633331i	0.377100	+	0.926172i	$0.376921\pi$
$542$	0.860874	+	2.26994i	0.0369777	+	0.0975022i
$543$	−16.1402	+	8.47101i	−0.692641	+	0.363526i
$544$	2.90408	+	11.7823i	0.124512	+	0.505163i
$545$	−5.62420	+	14.8298i	−0.240914	+	0.635238i
$546$	−3.06351	−	7.88600i	−0.131106	−	0.337490i
$547$	6.42026	+	16.9288i	0.274510	+	0.723824i	0.999389	+	0.0349480i	$0.0111265\pi$
$547$	6.42026	+	16.9288i	0.274510	+	0.723824i	−0.724879	+	0.688876i	$0.758104\pi$
$548$	4.28060	−	2.95469i	0.182858	−	0.126218i
$549$	−10.0150	+	8.87252i	−0.427430	+	0.378670i
$550$	−7.10686	−	1.75168i	−0.303037	−	0.0746920i
$551$	−7.16801	−	2.71847i	−0.305367	−	0.115811i
$552$	6.26329	−	11.9337i	0.266583	−	0.507932i
$553$	35.0062	+	13.2761i	1.48862	+	0.564558i
$554$	−1.31877	−	1.48858i	−0.0560290	−	0.0632437i
$555$	−3.91351	+	3.46706i	−0.166119	+	0.147169i
$556$	−4.67067	+	6.76664i	−0.198081	+	0.286969i
$557$	−22.0453	−	15.2168i	−0.934091	−	0.644757i	0.000682637	−	1.00000i	$-0.499783\pi$
$557$	−22.0453	−	15.2168i	−0.934091	−	0.644757i	−0.934774	+	0.355243i	$0.884398\pi$
$558$	1.70125	+	0.892882i	0.0720194	+	0.0377987i
$559$	−1.35611	+	1.99885i	−0.0573575	+	0.0845425i
$560$	3.41184	−	1.79067i	0.144177	−	0.0756698i
$561$	9.07666	+	1.10211i	0.383217	+	0.0465310i
$562$	7.90407	−	1.94818i	0.333413	−	0.0821790i
$563$	−19.0009	+	27.5275i	−0.800792	+	1.16015i	0.183399	+	0.983039i	$0.441290\pi$
$563$	−19.0009	+	27.5275i	−0.800792	+	1.16015i	−0.984191	+	0.177109i	$0.943325\pi$
$564$	−4.27497	+	2.95080i	−0.180009	+	0.124251i
$565$	−7.58297	+	8.55940i	−0.319018	+	0.360097i
$566$	−1.26039	−	0.153039i	−0.0529783	−	0.00643273i
$567$	−0.724057	+	2.93761i	−0.0304075	+	0.123368i
$568$	4.96182	+	2.60417i	0.208194	+	0.109268i
$569$	4.54123	−	37.4004i	0.190378	−	1.56791i	−0.513817	−	0.857900i	$-0.671769\pi$
$569$	4.54123	−	37.4004i	0.190378	−	1.56791i	0.704195	−	0.710006i	$-0.251308\pi$
$570$	−5.27826	+	0.640897i	−0.221082	+	0.0268442i
$571$	−12.0129	+	17.4037i	−0.502725	+	0.728324i	−0.989393	−	0.145264i	$-0.953597\pi$
$571$	−12.0129	+	17.4037i	−0.502725	+	0.728324i	0.486668	+	0.873587i	$0.338212\pi$
$572$	−14.6180	+	16.7700i	−0.611207	+	0.701188i
$573$	−9.54575	−	13.8294i	−0.398779	−	0.577732i
$574$	13.0277	+	14.7052i	0.543765	+	0.613784i
$575$	−10.6209	−	2.61783i	−0.442924	−	0.109171i
$576$	−1.72415	−	2.49787i	−0.0718397	−	0.104078i
$577$			13.7029i			0.570458i	0.958459	+	0.285229i	$0.0920697\pi$
$577$			13.7029i			0.570458i	−0.958459	+	0.285229i	$0.907930\pi$
$578$	−8.10904	+	5.59727i	−0.337292	+	0.232816i
$579$	−16.5265	+	2.00667i	−0.686816	+	0.0833945i
$580$	4.18302	−	1.58641i	0.173690	−	0.0658721i
$581$	−4.36649	+	35.9613i	−0.181153	+	1.49193i
$582$	2.28637	+	6.02867i	0.0947732	+	0.249896i
$583$	22.4735	−	25.3674i	0.930759	−	1.05061i
$584$	−8.67123	−	7.68204i	−0.358818	−	0.317885i
$585$	4.08052	+	4.53203i	0.168709	+	0.187376i
$586$	9.42634	−	8.35101i	0.389399	−	0.344977i
$587$		−	31.5149i		−	1.30076i	−0.759609	−	0.650380i	$-0.774610\pi$
$587$		−	31.5149i		−	1.30076i	0.759609	−	0.650380i	$-0.225390\pi$
$588$	2.25467	+	1.99746i	0.0929810	+	0.0823740i
$589$	9.75015	−	2.40320i	0.401748	−	0.0990220i
$590$	−7.18659	−	4.96055i	−0.295867	−	0.204222i
$591$	−6.62541	+	2.51269i	−0.272533	+	0.103358i
$592$	−2.17634	+	0.825375i	−0.0894468	+	0.0339227i
$593$	−6.70404	−	4.62747i	−0.275302	−	0.190027i	0.422411	−	0.906404i	$-0.361184\pi$
$593$	−6.70404	−	4.62747i	−0.275302	−	0.190027i	−0.697713	+	0.716377i	$0.745799\pi$
$594$	−3.32215	+	0.818836i	−0.136309	+	0.0335972i
$595$	−7.93823	−	7.03266i	−0.325436	−	0.288311i
$596$		−	14.3164i		−	0.586424i
$597$	−5.18772	+	4.59592i	−0.212319	+	0.188099i
$598$	9.39525	−	10.7784i	0.384200	−	0.440761i
$599$	−31.3953	−	27.8138i	−1.28278	−	1.13644i	−0.983232	−	0.182361i	$-0.941626\pi$
$599$	−31.3953	−	27.8138i	−1.28278	−	1.13644i	−0.299547	−	0.954082i	$-0.596835\pi$
$600$	−3.73895	+	4.22040i	−0.152642	+	0.172297i
$601$	−12.9046	−	34.0267i	−0.526391	−	1.38798i	−0.889801	−	0.456349i	$-0.849157\pi$
$601$	−12.9046	−	34.0267i	−0.526391	−	1.38798i	0.363410	−	0.931629i	$-0.381612\pi$
$602$	−0.189476	+	1.56048i	−0.00772246	+	0.0636002i
$603$	2.04381	−	0.775114i	0.0832303	−	0.0315651i
$604$	−27.4590	+	3.33413i	−1.11729	+	0.135664i
$605$	11.7823	−	8.13272i	0.479018	−	0.330642i
$606$		−	2.75195i		−	0.111791i
$607$	−8.22837	−	11.9209i	−0.333979	−	0.483853i	0.619632	−	0.784892i	$-0.287282\pi$
$607$	−8.22837	−	11.9209i	−0.333979	−	0.483853i	−0.953612	+	0.301040i	$0.902666\pi$
$608$	−23.0447	−	5.68000i	−0.934585	−	0.230355i
$609$	3.79447	+	4.28307i	0.153760	+	0.173559i
$610$	9.97004	+	14.4441i	0.403675	+	0.584824i
$611$	−12.4830	+	4.84933i	−0.505008	+	0.196183i
$612$	1.64647	−	2.38533i	0.0665548	−	0.0964212i
$613$	−9.39754	+	1.14107i	−0.379563	+	0.0460873i	−0.308095	−	0.951356i	$-0.599691\pi$
$613$	−9.39754	+	1.14107i	−0.379563	+	0.0460873i	−0.0714681	+	0.997443i	$0.522768\pi$
$614$	2.77748	−	22.8746i	0.112090	−	0.923144i
$615$	−12.5394	−	6.58116i	−0.505636	−	0.265378i
$616$	−8.41957	+	34.1595i	−0.339234	+	1.37633i
$617$	39.1668	+	4.75572i	1.57680	+	0.191458i	0.861646	−	0.507511i	$-0.169434\pi$
$617$	39.1668	+	4.75572i	1.57680	+	0.191458i	0.715152	+	0.698969i	$0.246357\pi$
$618$	−6.66063	+	7.51829i	−0.267930	+	0.302430i
$619$	2.00876	−	1.38654i	0.0807387	−	0.0557299i	−0.527012	−	0.849858i	$-0.676688\pi$
$619$	2.00876	−	1.38654i	0.0807387	−	0.0557299i	0.607750	+	0.794128i	$0.292072\pi$
$620$	−3.32895	+	4.82282i	−0.133694	+	0.193689i
$621$	−4.96483	+	1.22372i	−0.199232	+	0.0491062i
$622$	16.4482	+	1.99717i	0.659511	+	0.0800792i
$623$	40.6360	−	21.3274i	1.62805	−	0.854464i
$624$	0.983088	+	2.53064i	0.0393550	+	0.101307i
$625$	−8.61327	−	4.52059i	−0.344531	−	0.180824i
$626$	17.0740	+	11.7853i	0.682415	+	0.471037i
$627$	−10.1588	+	14.7175i	−0.405703	+	0.587762i
$628$	19.4226	−	17.2070i	0.775048	−	0.686632i
$629$	4.24819	+	4.79522i	0.169387	+	0.191198i
$630$	3.71079	+	1.40732i	0.147841	+	0.0560689i
$631$	1.15843	−	2.20720i	0.0461163	−	0.0878672i	−0.861307	−	0.508084i	$-0.830354\pi$
$631$	1.15843	−	2.20720i	0.0461163	−	0.0878672i	0.907424	+	0.420217i	$0.138046\pi$
$632$	30.4959	+	11.5656i	1.21306	+	0.460053i
$633$	21.6744	+	5.34226i	0.861480	+	0.212336i
$634$	6.49257	−	5.75192i	0.257853	−	0.228438i
$635$	−27.1440	+	18.7361i	−1.07718	+	0.743520i
$636$	−3.80956	−	10.0450i	−0.151059	−	0.398310i
$637$	4.46268	+	6.35541i	0.176818	+	0.251810i
$638$	−2.29470	+	6.05063i	−0.0908482	+	0.239547i
$639$	−0.508802	−	2.06429i	−0.0201279	−	0.0816621i
$640$	14.0132	−	7.35472i	0.553922	−	0.290721i
$641$	10.4505	+	27.5558i	0.412772	+	1.08839i	0.966720	+	0.255838i	$0.0823515\pi$
$641$	10.4505	+	27.5558i	0.412772	+	1.08839i	−0.553948	+	0.832551i	$0.686879\pi$
$642$	3.75940	−	0.456473i	0.148371	−	0.0180156i
$643$	−2.23263	−	1.54107i	−0.0880462	−	0.0607739i	0.523228	−	0.852193i	$-0.324727\pi$
$643$	−2.23263	−	1.54107i	−0.0880462	−	0.0607739i	−0.611275	+	0.791419i	$0.709343\pi$
$644$	−5.17794	+	21.0077i	−0.204040	+	0.827821i
$645$	−0.271169	−	1.10018i	−0.0106773	−	0.0433195i
$646$	0.785291	+	6.46745i	0.0308969	+	0.254459i
$647$	−1.23319	+	3.25165i	−0.0484816	+	0.127835i	−0.957070	−	0.289858i	$-0.906392\pi$
$647$	−1.23319	+	3.25165i	−0.0484816	+	0.127835i	0.908588	+	0.417693i	$0.137161\pi$
$648$	−0.630765	+	2.55912i	−0.0247788	+	0.100532i
$649$	−28.5167	+	7.02874i	−1.11938	+	0.275902i
$650$	−4.89549	+	3.43754i	−0.192017	+	0.134832i
$651$	−7.27762	−	1.79377i	−0.285233	−	0.0703035i
$652$	−1.64005	+	3.12486i	−0.0642294	+	0.122379i
$653$	−0.543904			−0.0212846			−0.0106423	−	0.999943i	$-0.503388\pi$
$653$	−0.543904			−0.0212846			−0.0106423	+	0.999943i	$0.503388\pi$
$654$	−7.27243			−0.284375
$655$	8.67428	−	16.5275i	0.338932	−	0.645781i
$656$	−4.18062	−	4.71895i	−0.163226	−	0.184244i
$657$			4.39527i			0.171476i
$658$	−5.77922	+	6.52339i	−0.225297	+	0.254308i
$659$	9.20221	−	4.82969i	0.358467	−	0.188138i	−0.275869	−	0.961195i	$-0.588966\pi$
$659$	9.20221	−	4.82969i	0.358467	−	0.188138i	0.634336	+	0.773057i	$0.281273\pi$
$660$	−1.25792	−	10.3599i	−0.0489646	−	0.403260i
$661$	19.5336	+	37.2182i	0.759770	+	1.44762i	0.889915	+	0.456125i	$0.150763\pi$
$661$	19.5336	+	37.2182i	0.759770	+	1.44762i	−0.130146	+	0.991495i	$0.541545\pi$
$662$	−1.55524	−	12.8086i	−0.0604462	−	0.497819i
$663$	5.55309	−	4.99987i	0.215664	−	0.194179i
$664$	−3.80389	+	31.3279i	−0.147620	+	1.21576i
$665$	19.3948	−	7.35547i	0.752097	−	0.285233i
$666$	−2.12275	−	1.11411i	−0.0822549	−	0.0431707i
$667$	−3.42935	+	9.04246i	−0.132785	+	0.350125i
$668$	−5.32624	−	10.1483i	−0.206078	−	0.392649i
$669$	12.0576	+	22.9739i	0.466174	+	0.888221i
$670$	−0.686180	−	2.78394i	−0.0265094	−	0.107553i
$671$	58.5997	+	7.11530i	2.26222	+	0.274683i
$672$	13.2603	+	11.7476i	0.511528	+	0.453174i
$673$	23.7084	+	34.3475i	0.913890	+	1.32400i	0.945882	+	0.324511i	$0.105200\pi$
$673$	23.7084	+	34.3475i	0.913890	+	1.32400i	−0.0319916	+	0.999488i	$0.510185\pi$
$674$	−16.3634	−	6.20584i	−0.630296	−	0.239040i
$675$	2.13924			0.0823392
$676$	2.48138	+	18.0108i	0.0954377	+	0.692724i
$677$	9.06452			0.348378			0.174189	−	0.984712i	$-0.444270\pi$
$677$	9.06452			0.348378			0.174189	+	0.984712i	$0.444270\pi$
$678$	−4.90262	−	1.85932i	−0.188284	−	0.0714067i
$679$	−14.2888	−	20.7009i	−0.548355	−	0.794429i
$680$	−6.91543	−	6.12654i	−0.265195	−	0.234942i
$681$	16.8817	+	2.04980i	0.646906	+	0.0785487i
$682$	−2.02858	−	8.23026i	−0.0776783	−	0.315153i
$683$	−13.1256	−	25.0087i	−0.502237	−	0.956932i	−0.996170	−	0.0874323i	$-0.972134\pi$
$683$	−13.1256	−	25.0087i	−0.502237	−	0.956932i	0.493934	−	0.869499i	$-0.335558\pi$
$684$	2.63446	+	5.01954i	0.100731	+	0.191927i
$685$	−2.23062	+	5.88167i	−0.0852277	+	0.224727i
$686$	−10.0687	−	5.28445i	−0.384424	−	0.201761i
$687$	12.7740	−	4.84454i	0.487359	−	0.184831i
$688$	0.0608034	−	0.500761i	0.00231811	−	0.0190913i
$689$	−3.55941	−	27.4671i	−0.135603	−	1.04641i
$690$	0.808493	+	6.65854i	0.0307788	+	0.253486i
$691$	−7.68807	−	14.6484i	−0.292468	−	0.557251i	0.694242	−	0.719741i	$-0.255740\pi$
$691$	−7.68807	−	14.6484i	−0.292468	−	0.557251i	−0.986710	+	0.162490i	$0.948047\pi$
$692$	−2.83354	−	23.3363i	−0.107715	−	0.887112i
$693$	11.8192	−	6.20321i	0.448975	−	0.235640i
$694$	−10.8020	+	12.1929i	−0.410038	+	0.462837i
$695$		−	9.94372i		−	0.377187i
$696$	3.30557	+	3.73122i	0.125297	+	0.141432i
$697$	−8.06390	+	15.3645i	−0.305442	+	0.581971i
$698$	9.27311			0.350992
$699$	−2.34460			−0.0886809
$700$	4.20657	−	8.01495i	0.158993	−	0.302936i
$701$	−6.77117	−	1.66894i	−0.255743	−	0.0630351i	0.109359	−	0.994002i	$-0.465120\pi$
$701$	−6.77117	−	1.66894i	−0.255743	−	0.0630351i	−0.365103	+	0.930967i	$0.618966\pi$
$702$	−1.27954	+	2.48633i	−0.0482930	+	0.0938404i
$703$	−12.1659	+	2.99862i	−0.458845	+	0.113095i
$704$	−3.20457	+	13.0015i	−0.120777	+	0.490011i
$705$	2.22769	−	5.87393i	0.0838996	−	0.221225i
$706$	−1.01901	−	8.39228i	−0.0383508	−	0.315848i
$707$	2.56926	+	10.4239i	0.0966271	+	0.392032i
$708$	−2.22808	+	9.03967i	−0.0837363	+	0.339732i
$709$	29.4321	+	20.3155i	1.10534	+	0.762964i	0.973587	−	0.228318i	$-0.0733225\pi$
$709$	29.4321	+	20.3155i	1.10534	+	0.762964i	0.131758	+	0.991282i	$0.457938\pi$
$710$	−2.76851	+	0.336158i	−0.103900	+	0.0126158i
$711$	−4.38803	−	11.5703i	−0.164564	−	0.433920i
$712$	35.4002	−	18.5795i	1.32668	−	0.696295i
$713$	−3.03164	−	12.2998i	−0.113536	−	0.460633i
$714$	1.72439	−	4.54683i	0.0645335	−	0.170161i
$715$	3.02821	−	26.7341i	0.113249	−	0.999797i
$716$	1.19661	+	3.15520i	0.0447194	+	0.117915i
$717$	17.1525	−	11.8395i	0.640573	−	0.442155i
$718$	11.9235	−	10.5633i	0.444981	−	0.394218i
$719$	−26.5793	−	6.55120i	−0.991240	−	0.244319i	−0.289831	−	0.957078i	$-0.593599\pi$
$719$	−26.5793	−	6.55120i	−0.991240	−	0.244319i	−0.701409	+	0.712759i	$0.747445\pi$
$720$	−1.19080	−	0.451612i	−0.0443786	−	0.0168306i
$721$	18.2101	−	34.6964i	0.678179	−	1.29216i
$722$	1.86338	+	0.706688i	0.0693480	+	0.0263002i
$723$	−8.72888	−	9.85287i	−0.324631	−	0.366432i
$724$	19.0815	−	16.9047i	0.709158	−	0.628260i
$725$	2.29833	−	3.32971i	0.0853579	−	0.123662i
$726$	5.40248	+	3.72906i	0.200505	+	0.138399i
$727$	−5.06325	−	2.65740i	−0.187785	−	0.0985574i	0.368210	−	0.929743i	$-0.379971\pi$
$727$	−5.06325	−	2.65740i	−0.187785	−	0.0985574i	−0.555996	+	0.831185i	$0.687663\pi$
$728$	16.5228	+	23.5305i	0.612375	+	0.872097i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	5.72340	+	0.694946i	0.211832	+	0.0257211i
$731$	−1.34805	+	0.332264i	−0.0498594	+	0.0122892i
$732$	10.6298	−	15.3999i	0.392888	−	0.569197i
$733$	35.0075	−	24.1639i	1.29303	−	0.892514i	0.295015	−	0.955493i	$-0.404675\pi$
$733$	35.0075	−	24.1639i	1.29303	−	0.892514i	0.998015	+	0.0629787i	$0.0200600\pi$
$734$	−15.8056	+	17.8408i	−0.583396	+	0.658518i
$735$	−3.61638	−	0.439108i	−0.133392	−	0.0161967i
$736$	−7.16534	+	29.0709i	−0.264118	+	1.07157i
$737$	−8.53903	−	4.48163i	−0.314539	−	0.165083i
$738$	0.782693	−	6.44606i	0.0288113	−	0.237283i
$739$	−17.4315	+	2.11656i	−0.641227	+	0.0778591i	−0.434691	−	0.900580i	$-0.643142\pi$
$739$	−17.4315	+	2.11656i	−0.641227	+	0.0778591i	−0.206536	+	0.978439i	$0.566219\pi$
$740$	4.15374	−	6.01773i	0.152695	−	0.221216i
$741$	3.61153	+	14.1616i	0.132673	+	0.520240i
$742$	−10.2391	−	14.8339i	−0.375888	−	0.544568i
$743$	−27.1477	−	30.6434i	−0.995953	−	1.12420i	−0.992256	−	0.124206i	$-0.960362\pi$
$743$	−27.1477	−	30.6434i	−0.995953	−	1.12420i	−0.00369687	−	0.999993i	$-0.501177\pi$
$744$	−6.33994	−	1.56265i	−0.232433	−	0.0572897i
$745$	9.83559	+	14.2493i	0.360348	+	0.522055i
$746$		−	11.1443i		−	0.408023i
$747$	9.85379	−	6.80158i	0.360531	−	0.248857i
$748$	−12.6940	+	1.54133i	−0.464140	+	0.0563568i
$749$	−13.8138	+	5.23887i	−0.504744	+	0.191424i
$750$	1.12880	−	9.29650i	0.0412179	−	0.339460i
$751$	8.15313	+	21.4980i	0.297512	+	0.784474i	0.997523	+	0.0703424i	$0.0224092\pi$
$751$	8.15313	+	21.4980i	0.297512	+	0.784474i	−0.700011	+	0.714132i	$0.746822\pi$
$752$	1.85457	−	2.09337i	0.0676291	−	0.0763374i
$753$	1.55357	+	1.37635i	0.0566154	+	0.0501568i
$754$	2.49526	+	4.66283i	0.0908719	+	0.169810i
$755$	25.0397	−	22.1832i	0.911287	−	0.807330i
$756$		−	4.23131i		−	0.153891i
$757$	−1.42757	−	1.26471i	−0.0518858	−	0.0459668i	0.636781	−	0.771044i	$-0.280265\pi$
$757$	−1.42757	−	1.26471i	−0.0518858	−	0.0459668i	−0.688667	+	0.725078i	$0.741804\pi$
$758$	−25.8076	+	6.36099i	−0.937373	+	0.231042i
$759$	18.5662	+	12.8153i	0.673911	+	0.465167i
$760$	16.8958	−	6.40775i	0.612877	−	0.232434i
$761$	10.8636	−	4.12003i	0.393806	−	0.149351i	−0.149750	−	0.988724i	$-0.547847\pi$
$761$	10.8636	−	4.12003i	0.393806	−	0.149351i	0.543556	+	0.839373i	$0.317078\pi$
$762$	−12.4462	−	8.59100i	−0.450879	−	0.311219i
$763$	27.5467	−	6.78965i	0.997257	−	0.245802i
$764$	17.5907	+	15.5840i	0.636410	+	0.563810i
$765$			3.50529i			0.126734i
$766$	−2.03056	+	1.79892i	−0.0733673	+	0.0649978i
$767$	−10.9833	+	21.3422i	−0.396585	+	0.770622i
$768$	9.97534	+	8.83738i	0.359954	+	0.318891i
$769$	29.1973	−	32.9570i	1.05288	−	1.18846i	0.0712941	−	0.997455i	$-0.477287\pi$
$769$	29.1973	−	32.9570i	1.05288	−	1.18846i	0.981589	−	0.191004i	$-0.0611744\pi$
$770$	−6.20887	−	16.3715i	−0.223752	−	0.589986i
$771$	−2.88025	+	23.7210i	−0.103730	+	0.854289i
$772$	21.7696	−	8.25612i	0.783505	−	0.297144i
$773$	−4.76062	+	0.578044i	−0.171228	+	0.0207908i	−0.205701	−	0.978615i	$-0.565948\pi$
$773$	−4.76062	+	0.578044i	−0.171228	+	0.0207908i	0.0344738	+	0.999406i	$0.489024\pi$
$774$	0.427587	−	0.295142i	0.0153693	−	0.0106087i
$775$			5.29973i			0.190372i
$776$	−12.4478	−	18.0337i	−0.446849	−	0.647373i
$777$	9.08075	+	2.23820i	0.325770	+	0.0802951i
$778$	12.2237	+	13.7977i	0.438241	+	0.494672i
$779$	−19.2792	−	27.9307i	−0.690748	−	1.00072i
$780$	−7.05776	−	4.78831i	−0.252708	−	0.171449i
$781$	−5.32839	+	7.71951i	−0.190665	+	0.276226i
$782$	8.15871	−	0.990647i	0.291755	−	0.0354255i
$783$	0.227969	−	1.87749i	0.00814694	−	0.0670961i
$784$	−1.43601	−	0.753677i	−0.0512861	−	0.0269170i
$785$	−7.51016	+	30.4699i	−0.268049	+	1.08752i
$786$	8.49620	+	1.03163i	0.303050	+	0.0367969i
$787$	31.0210	−	35.0155i	1.10578	−	1.24817i	0.139625	−	0.990204i	$-0.455410\pi$
$787$	31.0210	−	35.0155i	1.10578	−	1.24817i	0.966155	−	0.257963i	$-0.0830512\pi$
$788$	8.15565	−	5.62944i	0.290533	−	0.200540i
$789$	6.47689	−	9.38339i	0.230583	−	0.334058i
$790$	−15.7603	+	3.88456i	−0.560726	+	0.138206i
$791$	20.3062	+	2.46561i	0.722004	+	0.0876671i
$792$	10.2964	−	5.40396i	0.365866	−	0.192021i
$793$	35.8513	−	32.2796i	1.27312	−	1.14628i
$794$	−22.9069	−	12.0225i	−0.812935	−	0.426661i
$795$	10.6927	+	7.38067i	0.379232	+	0.261765i
$796$	5.50618	−	7.97707i	0.195161	−	0.282740i
$797$	−5.06098	+	4.48364i	−0.179269	+	0.158819i	−0.747985	−	0.663715i	$-0.768979\pi$
$797$	−5.06098	+	4.48364i	−0.179269	+	0.158819i	0.568716	+	0.822534i	$0.307440\pi$
$798$	6.30701	+	7.11914i	0.223266	+	0.252015i
$799$	−7.19733	−	2.72959i	−0.254623	−	0.0965658i
$800$	5.82113	−	11.0912i	0.205808	−	0.392135i
$801$	−14.1828	−	5.37882i	−0.501124	−	0.190051i
$802$	1.21804	+	0.300221i	0.0430106	+	0.0106012i
$803$	14.5146	−	12.8588i	0.512209	−	0.453777i
$804$	−2.51586	+	1.73657i	−0.0887274	+	0.0612441i
$805$	−9.27894	−	24.4666i	−0.327040	−	0.862333i
$806$	−6.15961	−	3.16992i	−0.216963	−	0.111655i
$807$	7.51436	−	19.8137i	0.264518	−	0.697477i
$808$	2.23823	+	9.08085i	0.0787406	+	0.319463i
$809$	−29.4815	+	15.4731i	−1.03651	+	0.544005i	−0.895063	−	0.445941i	$-0.852869\pi$
$809$	−29.4815	+	15.4731i	−1.03651	+	0.544005i	−0.141452	+	0.989945i	$0.545177\pi$
$810$	−0.465147	−	1.22649i	−0.0163436	−	0.0430946i
$811$	27.4223	−	3.32968i	0.962929	−	0.116921i	0.376053	−	0.926598i	$-0.377281\pi$
$811$	27.4223	−	3.32968i	0.962929	−	0.116921i	0.586875	+	0.809677i	$0.300358\pi$
$812$	−6.58601	−	4.54599i	−0.231124	−	0.159533i
$813$	−0.749137	+	3.03937i	−0.0262734	+	0.106595i
$814$	2.53118	+	10.2694i	0.0887180	+	0.359943i
$815$	−0.514458	−	4.23694i	−0.0180207	−	0.148414i
$816$	−0.553360	+	1.45909i	−0.0193715	+	0.0510784i
$817$	0.649865	−	2.63660i	0.0227359	−	0.0922431i
$818$	−1.63440	+	0.402843i	−0.0571455	+	0.0140851i
$819$	2.52539	−	10.6124i	0.0882442	−	0.370826i
$820$	19.2298	+	4.73972i	0.671534	+	0.165518i
$821$	−20.5495	+	39.1538i	−0.717183	+	1.36648i	0.204629	+	0.978840i	$0.434401\pi$
$821$	−20.5495	+	39.1538i	−0.717183	+	1.36648i	−0.921812	+	0.387638i	$0.873291\pi$
$822$	−2.88433			−0.100603
$823$	28.6963			1.00029			0.500146	−	0.865941i	$-0.333280\pi$
$823$	28.6963			1.00029			0.500146	+	0.865941i	$0.333280\pi$
$824$	15.8638	−	30.2260i	0.552642	−	1.05297i
$825$	−6.25854	−	7.06443i	−0.217894	−	0.245952i
$826$			15.6204i			0.543503i
$827$	−21.5674	+	24.3446i	−0.749973	+	0.846545i	−0.992327	−	0.123643i	$-0.960542\pi$
$827$	−21.5674	+	24.3446i	−0.749973	+	0.846545i	0.242353	+	0.970188i	$0.422081\pi$
$828$	6.33216	−	3.32337i	0.220058	−	0.115495i
$829$	3.64224	+	29.9966i	0.126500	+	1.04182i	0.908307	+	0.418304i	$0.137375\pi$
$829$	3.64224	+	29.9966i	0.126500	+	1.04182i	−0.781807	+	0.623521i	$0.785702\pi$
$830$	−7.29881	−	13.9067i	−0.253346	−	0.482710i
$831$	−0.309093	−	2.54561i	−0.0107223	−	0.0883061i
$832$	6.28873	+	8.95592i	0.218022	+	0.310491i
$833$	−0.538039	+	4.43115i	−0.0186420	+	0.153530i
$834$	4.26316	−	1.61680i	0.147621	−	0.0559854i
$835$	12.2733	+	6.44151i	0.424734	+	0.222918i
$836$	8.86874	−	23.3850i	0.306732	−	0.808785i
$837$	1.15130	+	2.19362i	0.0397948	+	0.0758227i
$838$	−7.20324	−	13.7246i	−0.248832	−	0.474109i
$839$	−1.77482	−	7.20071i	−0.0612735	−	0.248596i	0.932316	−	0.361645i	$-0.117785\pi$
$839$	−1.77482	−	7.20071i	−0.0612735	−	0.248596i	−0.993589	+	0.113048i	$0.963938\pi$
$840$	−13.3894	−	1.62577i	−0.461978	−	0.0560943i
$841$	19.0294	+	16.8586i	0.656187	+	0.581331i
$842$	6.93535	+	10.0476i	0.239008	+	0.346263i
$843$	9.81458	+	3.72218i	0.338032	+	0.128199i
$844$	−31.2196			−1.07462
$845$	−14.8434	−	16.2216i	−0.510630	−	0.558041i
$846$	2.88054			0.0990349
$847$	−23.9452	−	9.08120i	−0.822765	−	0.312034i
$848$	3.28575	+	4.76023i	0.112833	+	0.163467i
$849$	−1.22540	−	1.08561i	−0.0420556	−	0.0372580i
$850$	−3.41326	−	0.414444i	−0.117074	−	0.0142153i
$851$	3.78277	+	15.3473i	0.129672	+	0.526098i
$852$	1.38180	+	2.63280i	0.0473397	+	0.0901983i
$853$	5.76050	+	10.9757i	0.197236	+	0.375801i	0.963907	−	0.266238i	$-0.0857808\pi$
$853$	5.76050	+	10.9757i	0.197236	+	0.375801i	−0.766672	+	0.642039i	$0.778089\pi$
$854$	11.1328	−	29.3548i	0.380956	−	1.00450i
$855$	−6.07059	−	3.18609i	−0.207610	−	0.108962i
$856$	−12.0339	+	4.56386i	−0.411311	+	0.155990i
$857$	6.75201	−	55.6078i	0.230644	−	1.89953i	−0.173505	−	0.984833i	$-0.555509\pi$
$857$	6.75201	−	55.6078i	0.230644	−	1.89953i	0.404149	−	0.914693i	$-0.367568\pi$
$858$	11.9540	−	3.04856i	0.408104	−	0.104076i
$859$	−3.59748	−	29.6279i	−0.122745	−	1.01089i	−0.915770	−	0.401703i	$-0.868418\pi$
$859$	−3.59748	−	29.6279i	−0.122745	−	1.01089i	0.793025	−	0.609189i	$-0.208505\pi$
$860$	0.736440	+	1.40317i	0.0251124	+	0.0478477i
$861$	3.05343	+	25.1473i	0.104061	+	0.857016i
$862$	−23.6265	+	12.4002i	−0.804723	+	0.422351i
$863$	33.1497	−	37.4183i	1.12843	−	1.27373i	0.170935	−	0.985282i	$-0.445321\pi$
$863$	33.1497	−	37.4183i	1.12843	−	1.27373i	0.957495	−	0.288451i	$-0.0931403\pi$
$864$		−	5.85537i		−	0.199204i
$865$	18.8526	+	21.2802i	0.641007	+	0.723547i
$866$	9.31183	−	17.7422i	0.316429	−	0.602905i
$867$	−12.7050			−0.431483
$868$	10.4826			0.355803
$869$	−25.3711	+	48.3407i	−0.860657	+	1.63984i
$870$	−2.40877	−	0.593708i	−0.0816649	−	0.0201286i
$871$	−7.34635	+	2.85387i	−0.248921	+	0.0966996i
$872$	23.9974	−	5.91484i	0.812656	−	0.200302i
$873$	−1.98961	+	8.07217i	−0.0673382	+	0.273202i
$874$	−5.70012	+	15.0300i	−0.192809	+	0.508397i
$875$	4.40366	+	36.2674i	0.148871	+	1.22606i
$876$	−1.47106	−	5.96833i	−0.0497025	−	0.201651i
$877$	9.92543	−	40.2690i	0.335158	−	1.35979i	−0.525582	−	0.850743i	$-0.676152\pi$
$877$	9.92543	−	40.2690i	0.335158	−	1.35979i	0.860740	−	0.509046i	$-0.170002\pi$
$878$	−14.2478	−	9.83454i	−0.480840	−	0.331900i
$879$	16.1199	−	1.95731i	0.543711	−	0.0660184i
$880$	1.99244	+	5.25364i	0.0671653	+	0.177100i
$881$	−35.8679	+	18.8249i	−1.20842	+	0.634229i	−0.943926	−	0.330158i	$-0.892898\pi$
$881$	−35.8679	+	18.8249i	−1.20842	+	0.634229i	−0.264496	+	0.964387i	$0.585206\pi$
$882$	−0.399749	−	1.62184i	−0.0134602	−	0.0546104i
$883$	−10.5811	+	27.8999i	−0.356081	+	0.938908i	0.630581	+	0.776124i	$0.282817\pi$
$883$	−10.5811	+	27.8999i	−0.356081	+	0.938908i	−0.986662	+	0.162784i	$0.947952\pi$
$884$	−5.86711	+	8.64788i	−0.197332	+	0.290860i
$885$	−3.99274	−	10.5280i	−0.134215	−	0.353895i
$886$	4.19565	−	2.89605i	0.140956	−	0.0972948i
$887$	31.8833	−	28.2461i	1.07054	−	0.948412i	0.0717372	−	0.997424i	$-0.477146\pi$
$887$	31.8833	−	28.2461i	1.07054	−	0.948412i	0.998798	+	0.0490119i	$0.0156072\pi$
$888$	7.91074	+	1.94982i	0.265467	+	0.0654317i
$889$	55.1647	+	20.9212i	1.85017	+	0.701675i
$890$	−9.24661	+	17.6179i	−0.309947	+	0.590555i
$891$	−4.12515	−	1.56446i	−0.138198	−	0.0524115i
$892$	−24.0622	−	27.1606i	−0.805661	−	0.909403i
$893$	11.2691	−	9.98356i	0.377107	−	0.334087i
$894$	−4.50987	+	6.53368i	−0.150833	+	0.218519i
$895$	−3.35866	−	2.31832i	−0.112268	−	0.0774928i
$896$	−25.0668	−	13.1561i	−0.837423	−	0.439514i
$897$	17.8649	−	4.55596i	0.596492	−	0.152119i
$898$	−15.1262	+	7.93882i	−0.504766	+	0.264922i
$899$	4.65129	+	0.564768i	0.155129	+	0.0188361i
$900$	−2.90486	+	0.715984i	−0.0968287	+	0.0238661i
$901$	9.04353	−	13.1018i	0.301284	−	0.436485i
$902$	−23.5768	+	16.2739i	−0.785021	+	0.541861i
$903$	−1.34408	+	1.51715i	−0.0447281	+	0.0504875i
$904$	17.6898	+	2.14793i	0.588354	+	0.0714391i
$905$	−7.37825	+	29.9347i	−0.245261	+	0.995064i
$906$	13.5819	+	7.12835i	0.451229	+	0.236823i
$907$	0.616037	−	5.07353i	0.0204552	−	0.168464i	−0.978901	−	0.204334i	$-0.934497\pi$
$907$	0.616037	−	5.07353i	0.0204552	−	0.168464i	0.999356	+	0.0358702i	$0.0114203\pi$
$908$	−23.6096	+	2.86672i	−0.783512	+	0.0951356i
$909$	2.01574	−	2.92030i	0.0668578	−	0.0968603i
$910$	−13.4198	−	4.96643i	−0.444862	−	0.164635i
$911$	11.6945	+	16.9424i	0.387456	+	0.561326i	0.967375	−	0.253347i	$-0.0815315\pi$
$911$	11.6945	+	16.9424i	0.387456	+	0.561326i	−0.579920	+	0.814674i	$0.696916\pi$
$912$	−2.02394	−	2.28455i	−0.0670192	−	0.0756490i
$913$	−51.2892	−	12.6417i	−1.69742	−	0.418378i
$914$	−12.3153	−	17.8417i	−0.407353	−	0.590152i
$915$			22.6305i			0.748141i
$916$	−15.7244	+	10.8537i	−0.519547	+	0.358618i
$917$	−33.1453	+	4.02456i	−1.09455	+	0.132903i
$918$	−1.50282	+	0.569945i	−0.0496005	+	0.0188110i
$919$	−2.87547	+	23.6816i	−0.0948531	+	0.781185i	0.865212	+	0.501407i	$0.167184\pi$
$919$	−2.87547	+	23.6816i	−0.0948531	+	0.781185i	−0.960065	+	0.279778i	$0.909739\pi$
$920$	−8.08339	−	21.3142i	−0.266502	−	0.702707i
$921$	19.7025	−	22.2395i	0.649218	−	0.732816i
$922$	−16.5132	−	14.6294i	−0.543833	−	0.481794i
$923$	1.89429	+	7.42792i	0.0623513	+	0.244493i
$924$	−13.9731	+	12.3791i	−0.459682	+	0.407243i
$925$		−	6.61280i		−	0.217428i
$926$	−15.8654	−	14.0555i	−0.521370	−	0.461893i
$927$	−12.5750	+	3.09947i	−0.413019	+	0.101800i
$928$	−9.11385	−	6.29084i	−0.299177	−	0.206507i
$929$	−2.39220	+	0.907241i	−0.0784855	+	0.0297656i	−0.393535	−	0.919310i	$-0.628748\pi$
$929$	−2.39220	+	0.907241i	−0.0784855	+	0.0297656i	0.315050	+	0.949075i	$0.397979\pi$
$930$	3.03851	−	1.15235i	0.0996365	−	0.0377872i
$931$	−7.18498	−	4.95943i	−0.235478	−	0.162539i
$932$	3.18372	−	0.784718i	0.104286	−	0.0257043i
$933$	15.9915	+	14.1672i	0.523538	+	0.463814i
$934$			19.4457i			0.636284i
$935$	11.5756	−	10.2551i	0.378562	−	0.335377i
$936$	2.20000	−	9.24501i	0.0719093	−	0.302183i
$937$	−41.3900	−	36.6683i	−1.35215	−	1.19790i	−0.960662	−	0.277721i	$-0.910421\pi$
$937$	−41.3900	−	36.6683i	−1.35215	−	1.19790i	−0.391491	−	0.920182i	$-0.628040\pi$
$938$	−3.40111	+	3.83906i	−0.111050	+	0.125350i
$939$	9.48602	+	25.0126i	0.309565	+	0.816255i
$940$	−1.05902	+	8.72178i	−0.0345413	+	0.284473i
$941$	−17.4682	+	6.62483i	−0.569448	+	0.215963i	−0.622488	−	0.782629i	$-0.713878\pi$
$941$	−17.4682	+	6.62483i	−0.569448	+	0.215963i	0.0530401	+	0.998592i	$0.483109\pi$
$942$	−14.2845	+	1.73445i	−0.465413	+	0.0565113i
$943$	−35.2346	+	24.3207i	−1.14740	+	0.791991i
$944$		−	5.01263i		−	0.163147i
$945$	2.90697	+	4.21147i	0.0945637	+	0.136999i
$946$	−2.22560	−	0.548562i	−0.0723606	−	0.0178353i
$947$	9.64676	+	10.8889i	0.313478	+	0.353843i	0.884040	−	0.467411i	$-0.154813\pi$
$947$	9.64676	+	10.8889i	0.313478	+	0.353843i	−0.570562	+	0.821254i	$0.693275\pi$
$948$	9.83097	+	14.2426i	0.319295	+	0.462579i
$949$	−0.127405	−	15.8469i	−0.00413575	−	0.514411i
$950$	3.82019	−	5.53449i	0.123943	−	0.179563i
$951$	11.1029	−	1.34813i	0.360036	−	0.0437162i
$952$	−1.99205	+	16.4060i	−0.0645628	+	0.531723i
$953$	3.65414	+	1.91784i	0.118369	+	0.0621249i	0.522868	−	0.852413i	$-0.324862\pi$
$953$	3.65414	+	1.91784i	0.118369	+	0.0621249i	−0.404499	+	0.914538i	$0.632554\pi$
$954$	−1.42572	+	5.78435i	−0.0461592	+	0.187275i
$955$	−28.2147	−	3.42588i	−0.913005	−	0.110859i
$956$	−19.3288	+	21.8177i	−0.625137	+	0.705634i
$957$	−6.86702	+	4.73996i	−0.221979	+	0.153221i
$958$	16.1454	−	23.3907i	0.521635	−	0.755719i
$959$	10.9253	−	2.69285i	0.352797	−	0.0869568i
$960$	−5.09614	−	0.618783i	−0.164477	−	0.0199711i
$961$	22.0147	−	11.5542i	0.710151	−	0.372716i
$962$	7.68573	+	3.95530i	0.247798	+	0.127524i
$963$	4.32373	+	2.26927i	0.139330	+	0.0731261i
$964$	15.1506	+	10.4577i	0.487968	+	0.336820i
$965$	−15.9955	+	23.1734i	−0.514912	+	0.745979i
$966$	8.98081	−	7.95630i	0.288953	−	0.255990i
$967$	7.48832	+	8.45257i	0.240808	+	0.271816i	0.856473	−	0.516192i	$-0.172651\pi$
$967$	7.48832	+	8.45257i	0.240808	+	0.271816i	−0.615665	+	0.788008i	$0.711112\pi$
$968$	−20.8599	−	7.91113i	−0.670464	−	0.254273i
$969$	−3.90392	+	7.43830i	−0.125412	+	0.238953i
$970$	10.1968	+	3.86712i	0.327398	+	0.124166i
$971$	−28.1713	−	6.94359i	−0.904059	−	0.222831i	−0.240231	−	0.970716i	$-0.577223\pi$
$971$	−28.1713	−	6.94359i	−0.904059	−	0.222831i	−0.663828	+	0.747885i	$0.731069\pi$
$972$	−1.04682	+	0.927401i	−0.0335767	+	0.0297464i
$973$	−14.6386	+	10.1043i	−0.469293	+	0.323930i
$974$	11.5416	+	30.4326i	0.369815	+	0.975123i
$975$	−7.71287	+	0.0620097i	−0.247010	+	0.00198590i
$976$	−3.57254	+	9.42002i	−0.114354	+	0.301528i
$977$	12.2020	+	49.5053i	0.390375	+	1.58381i	0.756981	+	0.653437i	$0.226674\pi$
$977$	12.2020	+	49.5053i	0.390375	+	1.58381i	−0.366605	+	0.930377i	$0.619480\pi$
$978$	1.73285	−	0.909471i	0.0554105	−	0.0290817i
$979$	23.7305	+	62.5723i	0.758431	+	1.99982i
$980$	5.05764	−	0.614108i	0.161560	−	0.0196170i
$981$	−7.71731	−	5.32688i	−0.246395	−	0.170074i
$982$	4.58949	−	18.6203i	0.146457	−	0.594198i
$983$	9.06995	+	36.7982i	0.289286	+	1.17368i	0.918172	+	0.396183i	$0.129665\pi$
$983$	9.06995	+	36.7982i	0.289286	+	1.17368i	−0.628885	+	0.777498i	$0.716488\pi$
$984$	2.66001	+	21.9072i	0.0847980	+	0.698375i
$985$	−4.24991	+	11.2061i	−0.135413	+	0.357056i
$986$	−0.727471	+	2.95147i	−0.0231674	+	0.0939938i
$987$	−10.9110	+	2.68931i	−0.347300	+	0.0856017i
$988$	−9.64386	−	18.0212i	−0.306812	−	0.573332i
$989$	−3.32608	−	0.819806i	−0.105763	−	0.0260683i
$990$	−2.68943	+	5.12429i	−0.0854758	+	0.162861i
$991$	−28.3317			−0.899988			−0.449994	−	0.893032i	$-0.648574\pi$
$991$	−28.3317			−0.899988			−0.449994	+	0.893032i	$0.648574\pi$
$992$	14.5061			0.460568
$993$	7.73157	−	14.7313i	0.245354	−	0.467483i
$994$	3.30809	+	3.73407i	0.104926	+	0.118437i
$995$			11.7225i			0.371628i
$996$	−11.1040	+	12.5338i	−0.351844	+	0.397149i
$997$	26.6757	−	14.0005i	0.844828	−	0.443400i	0.0139818	−	0.999902i	$-0.495549\pi$
$997$	26.6757	−	14.0005i	0.844828	−	0.443400i	0.830846	+	0.556502i	$0.187857\pi$
$998$	−0.441393	−	3.63519i	−0.0139720	−	0.115070i
$999$	−1.43655	−	2.73712i	−0.0454505	−	0.0865987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.25.9	✓	168
169.142	even	26	inner	507.2.p.a.142.9	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.25.9	✓	168	1.1	even	1	trivial
507.2.p.a.142.9	yes	168	169.142	even	26	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.725144 + 0.275011i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.04682 - 0.927401i) q^{4} +(1.67905 + 0.203873i) q^{5} +(0.185599 + 0.753005i) q^{6} +(-1.40603 - 2.67897i) q^{7} +(-1.22487 - 2.33380i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(0.725144 + 0.275011i) q^{2} +(0.568065 + 0.822984i) q^{3} +(-1.04682 - 0.927401i) q^{4} +(1.67905 + 0.203873i) q^{5} +(0.185599 + 0.753005i) q^{6} +(-1.40603 - 2.67897i) q^{7} +(-1.22487 - 2.33380i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(1.16148 + 0.609593i) q^{10} +(4.12515 - 1.56446i) q^{11} +(0.168575 - 1.38834i) q^{12} +(1.25140 - 3.38142i) q^{13} +(-0.282830 - 2.32932i) q^{14} +(0.786023 + 1.49764i) q^{15} +(0.0907609 + 0.747483i) q^{16} +(1.83506 - 0.963114i) q^{17} +(-0.514279 + 0.580501i) q^{18} +4.05343i q^{19} +(-1.56859 - 1.77057i) q^{20} +(1.40603 - 2.67897i) q^{21} +3.42157 q^{22} +5.11342 q^{23} +(1.22487 - 2.33380i) q^{24} +(-2.07707 - 0.511953i) q^{25} +(1.83737 - 2.10787i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-1.01262 + 4.10836i) q^{28} +(-0.670658 + 1.76838i) q^{29} +(0.158112 + 1.30217i) q^{30} +(-0.592879 - 2.40540i) q^{31} +(-1.40128 + 5.68523i) q^{32} +(3.63088 + 2.50622i) q^{33} +(1.59555 - 0.193735i) q^{34} +(-1.81463 - 4.78478i) q^{35} +(1.23834 - 0.649932i) q^{36} +(0.739773 + 3.00138i) q^{37} +(-1.11474 + 2.93932i) q^{38} +(3.49373 - 0.890982i) q^{39} +(-1.58082 - 4.16828i) q^{40} +(-6.89063 + 4.75626i) q^{41} +(1.75632 - 1.55597i) q^{42} +(-0.650462 - 0.160324i) q^{43} +(-5.76917 - 2.18796i) q^{44} +(-0.786023 + 1.49764i) q^{45} +(3.70796 + 1.40624i) q^{46} +(-2.46299 - 2.78014i) q^{47} +(-0.563609 + 0.499314i) q^{48} +(-1.22351 + 1.77257i) q^{49} +(-1.36538 - 0.942457i) q^{50} +(1.83506 + 0.963114i) q^{51} +(-4.44592 + 2.37918i) q^{52} +(6.80180 - 3.56986i) q^{53} +(-0.769887 - 0.0934812i) q^{54} +(7.24528 - 1.78580i) q^{55} +(-4.52998 + 6.56280i) q^{56} +(-3.33591 + 2.30261i) q^{57} +(-0.972646 + 1.09789i) q^{58} +(-6.60857 - 0.802426i) q^{59} +(0.566090 - 2.29672i) q^{60} +(11.8473 + 6.21795i) q^{61} +(0.231590 - 1.90731i) q^{62} +(3.00347 - 0.364687i) q^{63} +(-1.72415 + 2.49787i) q^{64} +(2.79054 - 5.42244i) q^{65} +(1.94367 + 2.81590i) q^{66} +(-1.44949 - 1.63613i) q^{67} +(-2.81417 - 0.693630i) q^{68} +(2.90475 + 4.20826i) q^{69} -3.96869i q^{70} +(-1.74972 + 1.20775i) q^{71} +(2.61649 - 0.317699i) q^{72} +(4.10965 - 1.55859i) q^{73} +(-0.288969 + 2.37987i) q^{74} +(-0.758583 - 2.00022i) q^{75} +(3.75916 - 4.24321i) q^{76} +(-9.99126 - 8.85148i) q^{77} +(2.77849 + 0.314724i) q^{78} +(-9.26239 + 8.20576i) q^{79} +1.27356i q^{80} +(-0.748511 - 0.663123i) q^{81} +(-6.30471 + 1.55397i) q^{82} +(-9.85379 - 6.80158i) q^{83} +(-3.95634 + 1.50044i) q^{84} +(3.27751 - 1.24299i) q^{85} +(-0.427587 - 0.295142i) q^{86} +(-1.83632 + 0.452613i) q^{87} +(-8.70393 - 7.71101i) q^{88} +15.1685i q^{89} +(-0.981847 + 0.869841i) q^{90} +(-10.8182 + 1.40192i) q^{91} +(-5.35282 - 4.74219i) q^{92} +(1.64282 - 1.85436i) q^{93} +(-1.02145 - 2.69335i) q^{94} +(-0.826387 + 6.80591i) q^{95} +(-5.47487 + 2.07634i) q^{96} +(8.25314 - 1.00211i) q^{97} +(-1.37470 + 0.948886i) q^{98} +4.41185i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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