LMFDB - Embedded newform 841.2.e.b.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			63.2
Root			$0.781831 - 0.623490i$ of defining polynomial
Character	$\chi$	$=$	841.63
Dual form			841.2.e.b.267.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.974928 - 0.777479i) q^{2} +(-1.75676 + 0.400969i) q^{3} +(-0.0990311 + 0.433884i) q^{4} +(2.52446 + 3.16557i) q^{5} +(-1.40097 + 1.75676i) q^{6} +(-0.153989 - 0.674671i) q^{7} +(1.32288 + 2.74698i) q^{8} +(0.222521 - 0.107160i) q^{9} +O(q^{10})$	\(q+(0.974928 - 0.777479i) q^{2} +(-1.75676 + 0.400969i) q^{3} +(-0.0990311 + 0.433884i) q^{4} +(2.52446 + 3.16557i) q^{5} +(-1.40097 + 1.75676i) q^{6} +(-0.153989 - 0.674671i) q^{7} +(1.32288 + 2.74698i) q^{8} +(0.222521 - 0.107160i) q^{9} +(4.92233 + 1.12349i) q^{10} +(1.23694 - 2.56853i) q^{11} -0.801938i q^{12} +(1.32155 + 0.636426i) q^{13} +(-0.674671 - 0.538032i) q^{14} +(-5.70416 - 4.54892i) q^{15} +(2.62349 + 1.26341i) q^{16} +1.60388i q^{17} +(0.133627 - 0.277479i) q^{18} +(-2.62453 - 0.599031i) q^{19} +(-1.62349 + 0.781831i) q^{20} +(0.541044 + 1.12349i) q^{21} +(-0.791053 - 3.46583i) q^{22} +(-3.21648 + 4.03334i) q^{23} +(-3.42543 - 4.29535i) q^{24} +(-2.53534 + 11.1081i) q^{25} +(1.78323 - 0.407010i) q^{26} +(3.87849 - 3.09299i) q^{27} +0.307979 q^{28} -9.09783 q^{30} +(-1.52542 + 1.21648i) q^{31} +(-2.40496 + 0.548917i) q^{32} +(-1.14310 + 5.00827i) q^{33} +(1.24698 + 1.56366i) q^{34} +(1.74698 - 2.19064i) q^{35} +(0.0244587 + 0.107160i) q^{36} +(-1.23694 - 2.56853i) q^{37} +(-3.02446 + 1.45650i) q^{38} +(-2.57684 - 0.588146i) q^{39} +(-5.35621 + 11.1223i) q^{40} +6.49396i q^{41} +(1.40097 + 0.674671i) q^{42} +(-0.519820 - 0.414542i) q^{43} +(0.991949 + 0.791053i) q^{44} +(0.900969 + 0.433884i) q^{45} +6.43296i q^{46} +(-2.06226 + 4.28232i) q^{47} +(-5.11543 - 1.16756i) q^{48} +(5.87531 - 2.82940i) q^{49} +(6.16451 + 12.8007i) q^{50} +(-0.643104 - 2.81762i) q^{51} +(-0.407010 + 0.510374i) q^{52} +(0.0304995 + 0.0382451i) q^{53} +(1.37651 - 6.03089i) q^{54} +(11.2535 - 2.56853i) q^{55} +(1.64960 - 1.31551i) q^{56} +4.85086 q^{57} -6.39612 q^{59} +(2.53859 - 2.02446i) q^{60} +(1.27518 - 0.291053i) q^{61} +(-0.541385 + 2.37196i) q^{62} +(-0.106564 - 0.133627i) q^{63} +(-5.54892 + 6.95812i) q^{64} +(1.32155 + 5.79010i) q^{65} +(2.77938 + 5.77144i) q^{66} +(13.4683 - 6.48599i) q^{67} +(-0.695895 - 0.158834i) q^{68} +(4.03334 - 8.37531i) q^{69} -3.49396i q^{70} +(-2.03534 - 0.980170i) q^{71} +(0.588735 + 0.469501i) q^{72} +(6.50722 + 5.18933i) q^{73} +(-3.20291 - 1.54244i) q^{74} -20.5308i q^{75} +(0.519820 - 1.07942i) q^{76} +(-1.92339 - 0.439001i) q^{77} +(-2.96950 + 1.43004i) q^{78} +(-4.22643 - 8.77628i) q^{79} +(2.62349 + 11.4943i) q^{80} +(-6.03534 + 7.56808i) q^{81} +(5.04892 + 6.33114i) q^{82} +(0.894928 - 3.92094i) q^{83} +(-0.541044 + 0.123490i) q^{84} +(-5.07718 + 4.04892i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(8.80082 - 7.01842i) q^{89} +(1.21572 - 0.277479i) q^{90} +(0.225873 - 0.989616i) q^{91} +(-1.43147 - 1.79500i) q^{92} +(2.19202 - 2.74871i) q^{93} +(1.31886 + 5.77832i) q^{94} +(-4.72923 - 9.82036i) q^{95} +(4.00484 - 1.92863i) q^{96} +(4.45544 + 1.01693i) q^{97} +(3.52821 - 7.32640i) q^{98} -0.704103i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9	$ 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9} + 24 q^{13} + 22 q^{16} - 10 q^{20} + 2 q^{22} - 14 q^{24} - 6 q^{25} + 24 q^{28} - 36 q^{30} - 30 q^{33} - 4 q^{34} + 2 q^{35} - 18 q^{36} - 18 q^{38} + 8 q^{42} + 2 q^{45} - 2 q^{49} - 24 q^{51} - 34 q^{52} + 20 q^{53} + 26 q^{54} + 4 q^{57} - 112 q^{59} - 20 q^{62} + 40 q^{63} - 30 q^{64} + 24 q^{65} + 60 q^{67} - 12 q^{74} - 16 q^{78} + 22 q^{80} - 48 q^{81} + 24 q^{82} - 36 q^{83} + 32 q^{86} + 84 q^{88} + 46 q^{91} - 28 q^{92} + 6 q^{93} + 30 q^{94} + 4 q^{96}+O(q^{100}) $ 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9 + 24 * q^13 + 22 * q^16 - 10 * q^20 + 2 * q^22 - 14 * q^24 - 6 * q^25 + 24 * q^28 - 36 * q^30 - 30 * q^33 - 4 * q^34 + 2 * q^35 - 18 * q^36 - 18 * q^38 + 8 * q^42 + 2 * q^45 - 2 * q^49 - 24 * q^51 - 34 * q^52 + 20 * q^53 + 26 * q^54 + 4 * q^57 - 112 * q^59 - 20 * q^62 + 40 * q^63 - 30 * q^64 + 24 * q^65 + 60 * q^67 - 12 * q^74 - 16 * q^78 + 22 * q^80 - 48 * q^81 + 24 * q^82 - 36 * q^83 + 32 * q^86 + 84 * q^88 + 46 * q^91 - 28 * q^92 + 6 * q^93 + 30 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{14}\right)$

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 $

$2$	0.974928	−	0.777479i	0.689378	−	0.549761i	−0.214936	−	0.976628i	$-0.568954\pi$
$2$	0.974928	−	0.777479i	0.689378	−	0.549761i	0.904314	+	0.426867i	$0.140383\pi$
$3$	−1.75676	+	0.400969i	−1.01427	+	0.231499i	−0.697179	−	0.716897i	$-0.745562\pi$
$3$	−1.75676	+	0.400969i	−1.01427	+	0.231499i	−0.317087	+	0.948397i	$0.602705\pi$
$4$	−0.0990311	+	0.433884i	−0.0495156	+	0.216942i
$5$	2.52446	+	3.16557i	1.12897	+	1.41569i	0.896478	+	0.443089i	$0.146117\pi$
$5$	2.52446	+	3.16557i	1.12897	+	1.41569i	0.232494	+	0.972598i	$0.425311\pi$
$6$	−1.40097	+	1.75676i	−0.571943	+	0.717194i
$7$	−0.153989	−	0.674671i	−0.0582025	−	0.255002i	0.937453	−	0.348111i	$-0.113177\pi$
$7$	−0.153989	−	0.674671i	−0.0582025	−	0.255002i	−0.995656	+	0.0931090i	$0.970320\pi$
$8$	1.32288	+	2.74698i	0.467707	+	0.971204i
$9$	0.222521	−	0.107160i	0.0741736	−	0.0357201i
$10$	4.92233	+	1.12349i	1.55658	+	0.355279i
$11$	1.23694	−	2.56853i	0.372951	−	0.774441i	−0.627038	−	0.778988i	$-0.715733\pi$
$11$	1.23694	−	2.56853i	0.372951	−	0.774441i	0.999990	+	0.00454697i	$0.00144735\pi$
$12$		−	0.801938i		−	0.231499i
$13$	1.32155	+	0.636426i	0.366533	+	0.176513i	0.608079	−	0.793876i	$-0.291940\pi$
$13$	1.32155	+	0.636426i	0.366533	+	0.176513i	−0.241546	+	0.970389i	$0.577655\pi$
$14$	−0.674671	−	0.538032i	−0.180313	−	0.143795i
$15$	−5.70416	−	4.54892i	−1.47281	−	1.17453i
$16$	2.62349	+	1.26341i	0.655872	+	0.315852i
$17$			1.60388i			0.388997i	0.980903	+	0.194498i	$0.0623079\pi$
$17$			1.60388i			0.388997i	−0.980903	+	0.194498i	$0.937692\pi$
$18$	0.133627	−	0.277479i	0.0314962	−	0.0654024i
$19$	−2.62453	−	0.599031i	−0.602108	−	0.137427i	−0.0894079	−	0.995995i	$-0.528497\pi$
$19$	−2.62453	−	0.599031i	−0.602108	−	0.137427i	−0.512700	+	0.858568i	$0.671355\pi$
$20$	−1.62349	+	0.781831i	−0.363023	+	0.174823i
$21$	0.541044	+	1.12349i	0.118066	+	0.245166i
$22$	−0.791053	−	3.46583i	−0.168653	−	0.738917i
$23$	−3.21648	+	4.03334i	−0.670682	+	0.841009i	−0.994459	−	0.105124i	$-0.966476\pi$
$23$	−3.21648	+	4.03334i	−0.670682	+	0.841009i	0.323777	+	0.946134i	$0.395047\pi$
$24$	−3.42543	−	4.29535i	−0.699212	−	0.876785i
$25$	−2.53534	+	11.1081i	−0.507069	+	2.22161i
$26$	1.78323	−	0.407010i	0.349719	−	0.0798212i
$27$	3.87849	−	3.09299i	0.746415	−	0.595246i
$28$	0.307979			0.0582025
$29$		0			0
$29$		0			0
$30$	−9.09783			−1.66103
$31$	−1.52542	+	1.21648i	−0.273973	+	0.218486i	−0.750831	−	0.660494i	$-0.770347\pi$
$31$	−1.52542	+	1.21648i	−0.273973	+	0.218486i	0.476858	+	0.878980i	$0.341775\pi$
$32$	−2.40496	+	0.548917i	−0.425142	+	0.0970358i
$33$	−1.14310	+	5.00827i	−0.198989	+	0.871827i
$34$	1.24698	+	1.56366i	0.213855	+	0.268166i
$35$	1.74698	−	2.19064i	0.295293	−	0.370286i
$36$	0.0244587	+	0.107160i	0.00407644	+	0.0178601i
$37$	−1.23694	−	2.56853i	−0.203352	−	0.422264i	0.774206	−	0.632934i	$-0.218150\pi$
$37$	−1.23694	−	2.56853i	−0.203352	−	0.422264i	−0.977557	+	0.210670i	$0.932435\pi$
$38$	−3.02446	+	1.45650i	−0.490632	+	0.236276i
$39$	−2.57684	−	0.588146i	−0.412624	−	0.0941787i
$40$	−5.35621	+	11.1223i	−0.846892	+	1.75859i
$41$			6.49396i			1.01419i	0.861891	+	0.507093i	$0.169280\pi$
$41$			6.49396i			1.01419i	−0.861891	+	0.507093i	$0.830720\pi$
$42$	1.40097	+	0.674671i	0.216174	+	0.104104i
$43$	−0.519820	−	0.414542i	−0.0792718	−	0.0632171i	0.583052	−	0.812435i	$-0.301858\pi$
$43$	−0.519820	−	0.414542i	−0.0792718	−	0.0632171i	−0.662324	+	0.749218i	$0.730430\pi$
$44$	0.991949	+	0.791053i	0.149542	+	0.119256i
$45$	0.900969	+	0.433884i	0.134309	+	0.0646796i
$46$			6.43296i			0.948488i
$47$	−2.06226	+	4.28232i	−0.300811	+	0.624641i	−0.995510	−	0.0946601i	$-0.969824\pi$
$47$	−2.06226	+	4.28232i	−0.300811	+	0.624641i	0.694698	+	0.719301i	$0.255538\pi$
$48$	−5.11543	−	1.16756i	−0.738348	−	0.168523i
$49$	5.87531	−	2.82940i	0.839331	−	0.404200i
$50$	6.16451	+	12.8007i	0.871794	+	1.81030i
$51$	−0.643104	−	2.81762i	−0.0900526	−	0.394546i
$52$	−0.407010	+	0.510374i	−0.0564421	+	0.0707761i
$53$	0.0304995	+	0.0382451i	0.00418942	+	0.00525337i	0.783922	−	0.620860i	$-0.213216\pi$
$53$	0.0304995	+	0.0382451i	0.00418942	+	0.00525337i	−0.779732	+	0.626113i	$0.784645\pi$
$54$	1.37651	−	6.03089i	0.187319	−	0.820700i
$55$	11.2535	−	2.56853i	1.51742	−	0.346341i
$56$	1.64960	−	1.31551i	0.220437	−	0.175793i
$57$	4.85086			0.642511
$58$		0			0
$59$	−6.39612			−0.832704			−0.416352	−	0.909203i	$-0.636692\pi$
$59$	−6.39612			−0.832704			−0.416352	+	0.909203i	$0.636692\pi$
$60$	2.53859	−	2.02446i	0.327731	−	0.261356i
$61$	1.27518	−	0.291053i	0.163271	−	0.0372655i	−0.140104	−	0.990137i	$-0.544744\pi$
$61$	1.27518	−	0.291053i	0.163271	−	0.0372655i	0.303375	+	0.952871i	$0.401887\pi$
$62$	−0.541385	+	2.37196i	−0.0687559	+	0.301239i
$63$	−0.106564	−	0.133627i	−0.0134258	−	0.0168354i
$64$	−5.54892	+	6.95812i	−0.693615	+	0.869765i
$65$	1.32155	+	5.79010i	0.163918	+	0.718173i
$66$	2.77938	+	5.77144i	0.342118	+	0.710415i
$67$	13.4683	−	6.48599i	1.64542	−	0.792390i	0.645833	−	0.763478i	$-0.276510\pi$
$67$	13.4683	−	6.48599i	1.64542	−	0.792390i	0.999582	−	0.0289117i	$-0.00920417\pi$
$68$	−0.695895	−	0.158834i	−0.0843897	−	0.0192614i
$69$	4.03334	−	8.37531i	0.485557	−	1.00827i
$70$		−	3.49396i		−	0.417608i
$71$	−2.03534	−	0.980170i	−0.241551	−	0.116325i	0.309192	−	0.951000i	$-0.399941\pi$
$71$	−2.03534	−	0.980170i	−0.241551	−	0.116325i	−0.550743	+	0.834675i	$0.685656\pi$
$72$	0.588735	+	0.469501i	0.0693831	+	0.0553312i
$73$	6.50722	+	5.18933i	0.761612	+	0.607365i	0.925339	−	0.379140i	$-0.123780\pi$
$73$	6.50722	+	5.18933i	0.761612	+	0.607365i	−0.163727	+	0.986506i	$0.552352\pi$
$74$	−3.20291	−	1.54244i	−0.372330	−	0.179305i
$75$		−	20.5308i		−	2.37069i
$76$	0.519820	−	1.07942i	0.0596274	−	0.123818i
$77$	−1.92339	−	0.439001i	−0.219191	−	0.0500288i
$78$	−2.96950	+	1.43004i	−0.336230	+	0.161920i
$79$	−4.22643	−	8.77628i	−0.475511	−	0.987409i	−0.991414	−	0.130762i	$-0.958258\pi$
$79$	−4.22643	−	8.77628i	−0.475511	−	0.987409i	0.515903	−	0.856647i	$-0.327457\pi$
$80$	2.62349	+	11.4943i	0.293315	+	1.28510i
$81$	−6.03534	+	7.56808i	−0.670594	+	0.840898i
$82$	5.04892	+	6.33114i	0.557560	+	0.699158i
$83$	0.894928	−	3.92094i	0.0982311	−	0.430379i	−0.901767	−	0.432222i	$-0.857730\pi$
$83$	0.894928	−	3.92094i	0.0982311	−	0.430379i	0.999998	+	0.00184346i	$0.000586791\pi$
$84$	−0.541044	+	0.123490i	−0.0590328	+	0.0134738i
$85$	−5.07718	+	4.04892i	−0.550698	+	0.439167i
$86$	−0.829085			−0.0894025
$87$		0			0
$88$	8.69202			0.926573
$89$	8.80082	−	7.01842i	0.932885	−	0.743951i	−0.0339313	−	0.999424i	$-0.510803\pi$
$89$	8.80082	−	7.01842i	0.932885	−	0.743951i	0.966816	+	0.255473i	$0.0822313\pi$
$90$	1.21572	−	0.277479i	0.128148	−	0.0292489i
$91$	0.225873	−	0.989616i	0.0236780	−	0.103740i
$92$	−1.43147	−	1.79500i	−0.149241	−	0.187142i
$93$	2.19202	−	2.74871i	0.227302	−	0.285028i
$94$	1.31886	+	5.77832i	0.136030	+	0.595988i
$95$	−4.72923	−	9.82036i	−0.485209	−	1.00755i
$96$	4.00484	−	1.92863i	0.408743	−	0.196840i
$97$	4.45544	+	1.01693i	0.452382	+	0.103253i	0.442640	−	0.896699i	$-0.354042\pi$
$97$	4.45544	+	1.01693i	0.452382	+	0.103253i	0.00974167	+	0.999953i	$0.496899\pi$
$98$	3.52821	−	7.32640i	0.356403	−	0.740078i
$99$		−	0.704103i		−	0.0707650i
$100$	−4.56853	−	2.20009i	−0.456853	−	0.220009i
$101$	−2.51212	−	2.00335i	−0.249966	−	0.199341i	0.490489	−	0.871448i	$-0.336818\pi$
$101$	−2.51212	−	2.00335i	−0.249966	−	0.199341i	−0.740454	+	0.672107i	$0.765390\pi$
$102$	−2.81762	−	2.24698i	−0.278986	−	0.222484i
$103$	5.88620	+	2.83464i	0.579984	+	0.279306i	0.700787	−	0.713371i	$-0.252832\pi$
$103$	5.88620	+	2.83464i	0.579984	+	0.279306i	−0.120802	+	0.992677i	$0.538547\pi$
$104$			4.47219i			0.438534i
$105$	−2.19064	+	4.54892i	−0.213785	+	0.443929i
$106$	0.0594696	+	0.0135735i	0.00577619	+	0.00131838i
$107$	5.21164	−	2.50979i	0.503828	−	0.242631i	−0.164665	−	0.986350i	$-0.552654\pi$
$107$	5.21164	−	2.50979i	0.503828	−	0.242631i	0.668492	+	0.743719i	$0.266940\pi$
$108$	0.957907	+	1.98911i	0.0921747	+	0.191403i
$109$	2.04407	+	8.95567i	0.195787	+	0.857798i	0.973410	+	0.229068i	$0.0735677\pi$
$109$	2.04407	+	8.95567i	0.195787	+	0.857798i	−0.777624	+	0.628730i	$0.783575\pi$
$110$	8.97434	−	11.2535i	0.855670	−	1.07298i
$111$	3.20291	+	4.01632i	0.304006	+	0.381212i
$112$	0.448394	−	1.96454i	0.0423693	−	0.185632i
$113$	−8.74135	+	1.99516i	−0.822317	+	0.187688i	−0.612923	−	0.790143i	$-0.710006\pi$
$113$	−8.74135	+	1.99516i	−0.822317	+	0.187688i	−0.209394	+	0.977831i	$0.567149\pi$
$114$	4.72923	−	3.77144i	0.442933	−	0.353228i
$115$	−20.8877			−1.94779
$116$		0			0
$117$	0.362273			0.0334921
$118$	−6.23576	+	4.97285i	−0.574048	+	0.457788i
$119$	1.08209	−	0.246980i	0.0991949	−	0.0226406i
$120$	4.94989	−	21.6869i	0.451861	−	1.97973i
$121$	1.79105	+	2.24591i	0.162823	+	0.204174i
$122$	1.01693	−	1.27518i	0.0920681	−	0.115450i
$123$	−2.60388	−	11.4083i	−0.234784	−	1.02865i
$124$	−0.376747	−	0.782323i	−0.0338329	−	0.0702547i
$125$	−23.3240	+	11.2322i	−2.08616	+	1.00464i
$126$	−0.207784	−	0.0474254i	−0.0185109	−	0.00422499i
$127$	−6.75325	+	14.0233i	−0.599254	+	1.24436i	0.352013	+	0.935995i	$0.385497\pi$
$127$	−6.75325	+	14.0233i	−0.599254	+	1.24436i	−0.951267	+	0.308368i	$0.900217\pi$
$128$			6.16421i			0.544844i
$129$	1.07942	+	0.519820i	0.0950374	+	0.0457676i
$130$	5.79010	+	4.61745i	0.507825	+	0.404977i
$131$	10.5023	+	8.37531i	0.917591	+	0.731755i	0.963645	−	0.267184i	$-0.0860933\pi$
$131$	10.5023	+	8.37531i	0.917591	+	0.731755i	−0.0460542	+	0.998939i	$0.514665\pi$
$132$	−2.05980	−	0.991949i	−0.179283	−	0.0863380i
$133$			1.86294i			0.161537i
$134$	8.08790	−	16.7947i	0.698688	−	1.45084i
$135$	19.5822	+	4.46950i	1.68536	+	0.384673i
$136$	−4.40581	+	2.12173i	−0.377795	+	0.181937i
$137$	−7.37265	−	15.3095i	−0.629888	−	1.30798i	−0.934657	−	0.355550i	$-0.884294\pi$
$137$	−7.37265	−	15.3095i	−0.629888	−	1.30798i	0.304769	−	0.952426i	$-0.401421\pi$
$138$	−2.57942	−	11.3012i	−0.219575	−	0.962019i
$139$	7.77144	−	9.74508i	0.659165	−	0.826567i	−0.334087	−	0.942542i	$-0.608428\pi$
$139$	7.77144	−	9.74508i	0.659165	−	0.826567i	0.993252	+	0.115976i	$0.0369995\pi$
$140$	0.777479	+	0.974928i	0.0657090	+	0.0823964i
$141$	1.90581	−	8.34991i	0.160498	−	0.703190i
$142$	−2.74638	+	0.626842i	−0.230471	+	0.0526034i
$143$	3.26936	−	2.60723i	0.273398	−	0.218027i
$144$	0.719169			0.0599307
$145$		0			0
$146$	10.3787			0.858945
$147$	−9.18701	+	7.32640i	−0.757732	+	0.604271i
$148$	1.23694	−	0.282323i	0.101676	−	0.0232068i
$149$	−4.07553	+	17.8561i	−0.333881	+	1.46283i	0.477667	+	0.878541i	$0.341482\pi$
$149$	−4.07553	+	17.8561i	−0.333881	+	1.46283i	−0.811548	+	0.584286i	$0.801375\pi$
$150$	−15.9623	−	20.0160i	−1.30331	−	1.63430i
$151$	11.8693	−	14.8836i	0.965908	−	1.21121i	−0.0115186	−	0.999934i	$-0.503667\pi$
$151$	11.8693	−	14.8836i	0.965908	−	1.21121i	0.977426	−	0.211276i	$-0.0677620\pi$
$152$	−1.82640	−	8.00197i	−0.148140	−	0.649045i
$153$	0.171872	+	0.356896i	0.0138950	+	0.0288533i
$154$	−2.21648	+	1.06740i	−0.178609	+	0.0860136i
$155$	−7.70171	−	1.75786i	−0.618616	−	0.141195i
$156$	0.510374	−	1.05980i	0.0408626	−	0.0848521i
$157$		−	11.4383i		−	0.912879i	−0.889755	−	0.456439i	$-0.849125\pi$
$157$		−	11.4383i		−	0.912879i	0.889755	−	0.456439i	$-0.150875\pi$
$158$	−10.9438	−	5.27028i	−0.870646	−	0.419281i
$159$	−0.0689153	−	0.0549581i	−0.00546534	−	0.00435846i
$160$	−7.80887	−	6.22737i	−0.617345	−	0.492316i
$161$	3.21648	+	1.54898i	0.253494	+	0.122076i
$162$			12.0707i			0.948363i
$163$	−2.89598	+	6.01357i	−0.226831	+	0.471019i	−0.983059	−	0.183289i	$-0.941326\pi$
$163$	−2.89598	+	6.01357i	−0.226831	+	0.471019i	0.756228	+	0.654308i	$0.227040\pi$
$164$	−2.81762	−	0.643104i	−0.220019	−	0.0502180i
$165$	−18.7397	+	9.02458i	−1.45889	+	0.702563i
$166$	−2.17596	−	4.51842i	−0.168887	−	0.350697i
$167$	−3.26391	−	14.3001i	−0.252569	−	1.10658i	−0.929003	−	0.370072i	$-0.879333\pi$
$167$	−3.26391	−	14.3001i	−0.252569	−	1.10658i	0.676434	−	0.736503i	$-0.263524\pi$
$168$	−2.37047	+	2.97247i	−0.182886	+	0.229331i
$169$	−6.76391	−	8.48167i	−0.520300	−	0.652436i
$170$	−1.80194	+	7.89481i	−0.138202	+	0.605504i
$171$	−0.648205	+	0.147948i	−0.0495694	+	0.0113139i
$172$	0.231342	−	0.184489i	0.0176396	−	0.0140671i
$173$	23.3599			1.77602			0.888009	−	0.459825i	$-0.152088\pi$
$173$	23.3599			1.77602			0.888009	+	0.459825i	$0.152088\pi$
$174$		0			0
$175$	7.88471			0.596028
$176$	6.49020	−	5.17576i	0.489217	−	0.390138i
$177$	11.2365	−	2.56465i	0.844583	−	0.192771i
$178$	3.12349	−	13.6849i	0.234115	−	1.02573i
$179$	0.414542	+	0.519820i	0.0309844	+	0.0388532i	0.797082	−	0.603871i	$-0.206376\pi$
$179$	0.414542	+	0.519820i	0.0309844	+	0.0388532i	−0.766098	+	0.642724i	$0.777804\pi$
$180$	−0.277479	+	0.347948i	−0.0206821	+	0.0259345i
$181$	−2.44020	−	10.6912i	−0.181378	−	0.794671i	−0.980975	−	0.194134i	$-0.937810\pi$
$181$	−2.44020	−	10.6912i	−0.181378	−	0.794671i	0.799597	−	0.600537i	$-0.205047\pi$
$182$	−0.549195	−	1.14042i	−0.0407091	−	0.0845332i
$183$	−2.12349	+	1.02262i	−0.156973	+	0.0755942i
$184$	−15.3345	−	3.50000i	−1.13047	−	0.258023i
$185$	5.00827	−	10.3998i	0.368215	−	0.764606i
$186$		−	4.38404i		−	0.321454i
$187$	4.11960	+	1.98390i	0.301255	+	0.145077i
$188$	−1.65380	−	1.31886i	−0.120616	−	0.0961880i
$189$	−2.68400	−	2.14042i	−0.195232	−	0.155692i
$190$	−12.2458	−	5.89726i	−0.888402	−	0.427832i
$191$			0.518122i			0.0374900i	0.999824	+	0.0187450i	$0.00596707\pi$
$191$			0.518122i			0.0374900i	−0.999824	+	0.0187450i	$0.994033\pi$
$192$	6.95812	−	14.4487i	0.502159	−	1.04274i
$193$	1.35168	+	0.308511i	0.0972957	+	0.0222071i	0.270892	−	0.962610i	$-0.412682\pi$
$193$	1.35168	+	0.308511i	0.0972957	+	0.0222071i	−0.173596	+	0.984817i	$0.555539\pi$
$194$	5.13437	−	2.47258i	0.368627	−	0.177521i
$195$	−4.64330	−	9.64191i	−0.332513	−	0.690471i
$196$	0.645793	+	2.82940i	0.0461280	+	0.202100i
$197$	8.07942	−	10.1313i	0.575635	−	0.721823i	−0.405727	−	0.913994i	$-0.632982\pi$
$197$	8.07942	−	10.1313i	0.575635	−	0.721823i	0.981361	+	0.192171i	$0.0615530\pi$
$198$	−0.547425	−	0.686450i	−0.0389038	−	0.0487839i
$199$	4.33997	−	19.0147i	0.307652	−	1.34791i	−0.550636	−	0.834745i	$-0.685615\pi$
$199$	4.33997	−	19.0147i	0.307652	−	1.34791i	0.858288	−	0.513167i	$-0.171528\pi$
$200$	−33.8676	+	7.73005i	−2.39480	+	0.546597i
$201$	−21.0599	+	16.7947i	−1.48545	+	1.18461i
$202$	−4.00670			−0.281911
$203$		0			0
$204$	1.28621			0.0900526
$205$	−20.5571	+	16.3937i	−1.43577	+	1.14499i
$206$	7.94250	−	1.81282i	0.553380	−	0.126305i
$207$	−0.283520	+	1.24218i	−0.0197060	+	0.0863376i
$208$	2.66301	+	3.33931i	0.184647	+	0.231540i
$209$	−4.78501	+	6.00022i	−0.330986	+	0.415044i
$210$	1.40097	+	6.13805i	0.0966760	+	0.423565i
$211$	8.95147	+	18.5879i	0.616244	+	1.27964i	0.942450	+	0.334346i	$0.108515\pi$
$211$	8.95147	+	18.5879i	0.616244	+	1.27964i	−0.326206	+	0.945299i	$0.605770\pi$
$212$	−0.0196143	+	0.00944576i	−0.00134712	+	0.000648738i
$213$	3.96863	+	0.905813i	0.271926	+	0.0620653i
$214$	3.12966	−	6.49880i	0.213939	−	0.444249i
$215$		−	2.69202i		−	0.183594i
$216$	13.6271	+	6.56248i	0.927209	+	0.446520i
$217$	1.05562	+	0.841830i	0.0716603	+	0.0571472i
$218$	8.95567	+	7.14191i	0.606554	+	0.483711i
$219$	−13.5124	−	6.50722i	−0.913082	−	0.439717i
$220$			5.13706i			0.346341i
$221$	−1.02075	+	2.11960i	−0.0686629	+	0.142580i
$222$	6.24521	+	1.42543i	0.419151	+	0.0956684i
$223$	19.0112	−	9.15530i	1.27308	−	0.613084i	0.329480	−	0.944163i	$-0.393127\pi$
$223$	19.0112	−	9.15530i	1.27308	−	0.613084i	0.943603	+	0.331078i	$0.107412\pi$
$224$	0.740677	+	1.53803i	0.0494886	+	0.102764i
$225$	0.626178	+	2.74347i	0.0417452	+	0.182898i
$226$	−6.97099	+	8.74135i	−0.463704	+	0.581466i
$227$	4.44839	+	5.57811i	0.295250	+	0.370232i	0.907225	−	0.420645i	$-0.138196\pi$
$227$	4.44839	+	5.57811i	0.295250	+	0.370232i	−0.611975	+	0.790877i	$0.709625\pi$
$228$	−0.480386	+	2.10471i	−0.0318143	+	0.139388i
$229$	−2.19589	+	0.501196i	−0.145108	+	0.0331200i	−0.294458	−	0.955664i	$-0.595139\pi$
$229$	−2.19589	+	0.501196i	−0.145108	+	0.0331200i	0.149350	+	0.988784i	$0.452282\pi$
$230$	−20.3640	+	16.2397i	−1.34276	+	1.07082i
$231$	3.55496			0.233899
$232$		0			0
$233$	18.9095			1.23880			0.619400	−	0.785076i	$-0.287376\pi$
$233$	18.9095			1.23880			0.619400	+	0.785076i	$0.287376\pi$
$234$	0.353190	−	0.281659i	0.0230887	−	0.0184127i
$235$	−18.7621	+	4.28232i	−1.22390	+	0.279348i
$236$	0.633415	−	2.77517i	0.0412318	−	0.180648i
$237$	10.9438	+	13.7231i	0.710879	+	0.891414i
$238$	0.862937	−	1.08209i	0.0559359	−	0.0701414i
$239$	4.55549	+	19.9589i	0.294670	+	1.29103i	0.877946	+	0.478760i	$0.158914\pi$
$239$	4.55549	+	19.9589i	0.294670	+	1.29103i	−0.583276	+	0.812274i	$0.698229\pi$
$240$	−9.21768	−	19.1407i	−0.594999	−	1.23553i
$241$	6.63922	−	3.19728i	0.427670	−	0.205955i	−0.207651	−	0.978203i	$-0.566582\pi$
$241$	6.63922	−	3.19728i	0.427670	−	0.205955i	0.635321	+	0.772248i	$0.280868\pi$
$242$	3.49229	+	0.797093i	0.224493	+	0.0512391i
$243$	1.11089	−	2.30678i	0.0712635	−	0.147980i
$244$			0.582105i			0.0372655i
$245$	23.7887	+	11.4560i	1.51980	+	0.731898i
$246$	−11.4083	−	9.09783i	−0.727368	−	0.580057i
$247$	−3.08721	−	2.46197i	−0.196434	−	0.156651i
$248$	−5.35958	−	2.58104i	−0.340334	−	0.163896i
$249$			7.24698i			0.459259i
$250$	−14.0064	+	29.0846i	−0.885842	+	1.83947i
$251$	12.6306	+	2.88285i	0.797235	+	0.181964i	0.601689	−	0.798731i	$-0.294495\pi$
$251$	12.6306	+	2.88285i	0.797235	+	0.181964i	0.195546	+	0.980694i	$0.437352\pi$
$252$	0.0685317	−	0.0330031i	0.00431709	−	0.00207900i
$253$	6.38117	+	13.2506i	0.401180	+	0.833060i
$254$	4.31886	+	18.9222i	0.270990	+	1.18728i
$255$	7.29590	−	9.14877i	0.456887	−	0.572918i
$256$	−6.30529	−	7.90658i	−0.394081	−	0.494161i
$257$	−3.71432	+	16.2735i	−0.231693	+	1.01511i	0.716542	+	0.697544i	$0.245724\pi$
$257$	−3.71432	+	16.2735i	−0.231693	+	1.01511i	−0.948235	+	0.317570i	$0.897133\pi$
$258$	1.45650	−	0.332437i	0.0906779	−	0.0206966i
$259$	−1.54244	+	1.23005i	−0.0958425	+	0.0764318i
$260$	−2.64310			−0.163918
$261$		0			0
$262$	16.7506			1.03486
$263$	13.7675	−	10.9792i	0.848938	−	0.677006i	−0.0991292	−	0.995075i	$-0.531606\pi$
$263$	13.7675	−	10.9792i	0.848938	−	0.677006i	0.948068	+	0.318069i	$0.103034\pi$
$264$	−15.2698	+	3.48523i	−0.939791	+	0.214501i
$265$	−0.0440730	+	0.193096i	−0.00270738	+	0.0118618i
$266$	1.44839	+	1.81623i	0.0888067	+	0.111360i
$267$	−12.6468	+	15.8585i	−0.773969	+	0.970526i
$268$	1.48039	+	6.48599i	0.0904289	+	0.396195i
$269$	−2.91113	−	6.04503i	−0.177495	−	0.368572i	0.793173	−	0.608997i	$-0.208428\pi$
$269$	−2.91113	−	6.04503i	−0.177495	−	0.368572i	−0.970668	+	0.240424i	$0.922713\pi$
$270$	22.5661	−	10.8673i	1.37333	−	0.661362i
$271$	−12.3502	−	2.81886i	−0.750224	−	0.171234i	−0.169721	−	0.985492i	$-0.554287\pi$
$271$	−12.3502	−	2.81886i	−0.750224	−	0.171234i	−0.580503	+	0.814258i	$0.697144\pi$
$272$	−2.02635	+	4.20775i	−0.122865	+	0.255132i
$273$			1.82908i			0.110701i
$274$	−19.0906	−	9.19355i	−1.15331	−	0.555402i
$275$	25.3954	+	20.2521i	1.53140	+	1.22125i
$276$	3.23449	+	2.57942i	0.194693	+	0.155263i
$277$	−14.1821	−	6.82974i	−0.852120	−	0.410359i	−0.0437557	−	0.999042i	$-0.513932\pi$
$277$	−14.1821	−	6.82974i	−0.852120	−	0.410359i	−0.808364	+	0.588683i	$0.799647\pi$
$278$		−	15.5429i		−	0.932200i
$279$	−0.209079	+	0.434157i	−0.0125172	+	0.0259923i
$280$	8.32869	+	1.90097i	0.497734	+	0.113605i
$281$	−10.6446	+	5.12617i	−0.635003	+	0.305802i	−0.723552	−	0.690270i	$-0.757492\pi$
$281$	−10.6446	+	5.12617i	−0.635003	+	0.305802i	0.0885481	+	0.996072i	$0.471777\pi$
$282$	−4.63385	−	9.62229i	−0.275942	−	0.572999i
$283$	−0.489115	−	2.14295i	−0.0290749	−	0.127385i	0.958308	−	0.285738i	$-0.0922388\pi$
$283$	−0.489115	−	2.14295i	−0.0290749	−	0.127385i	−0.987383	+	0.158353i	$0.949382\pi$
$284$	0.626842	−	0.786035i	0.0371962	−	0.0466426i
$285$	12.2458	+	15.3557i	0.725378	+	0.909595i
$286$	1.16033	−	5.08372i	0.0686115	−	0.300607i
$287$	4.38129	−	1.00000i	0.258619	−	0.0590281i
$288$	−0.476333	+	0.379863i	−0.0280682	+	0.0223836i
$289$	14.4276			0.848681
$290$		0			0
$291$	−8.23490			−0.482738
$292$	−2.89598	+	2.30947i	−0.169475	+	0.135152i
$293$	20.1261	−	4.59365i	1.17578	−	0.268364i	0.410377	−	0.911916i	$-0.365397\pi$
$293$	20.1261	−	4.59365i	1.17578	−	0.268364i	0.765403	+	0.643552i	$0.222540\pi$
$294$	−3.26055	+	14.2854i	−0.190159	+	0.833142i
$295$	−16.1468	−	20.2474i	−0.940100	−	1.17885i
$296$	5.41939	−	6.79570i	0.314995	−	0.394992i
$297$	−3.14699	−	13.7879i	−0.182607	−	0.800053i
$298$	9.90937	+	20.5770i	0.574035	+	1.19199i
$299$	−6.81767	+	3.28322i	−0.394276	+	0.189873i
$300$	8.90798	+	2.03319i	0.514302	+	0.117386i
$301$	−0.199633	+	0.414542i	−0.0115067	+	0.0238938i
$302$		−	23.7385i		−	1.36600i
$303$	5.21648	+	2.51212i	0.299679	+	0.144318i
$304$	−6.12860	−	4.88740i	−0.351499	−	0.280311i
$305$	4.14050	+	3.30194i	0.237084	+	0.189068i
$306$	0.445042	+	0.214321i	0.0254414	+	0.0122519i
$307$		−	22.8116i		−	1.30193i	−0.759108	−	0.650964i	$-0.774365\pi$
$307$		−	22.8116i		−	1.30193i	0.759108	−	0.650964i	$-0.225635\pi$
$308$	0.380951	−	0.791053i	0.0217067	−	0.0450744i
$309$	−11.4772	−	2.61960i	−0.652917	−	0.149024i
$310$	−8.87531	+	4.27413i	−0.504084	+	0.242754i
$311$	13.4895	+	28.0112i	0.764918	+	1.58837i	0.807919	+	0.589293i	$0.200594\pi$
$311$	13.4895	+	28.0112i	0.764918	+	1.58837i	−0.0430013	+	0.999075i	$0.513692\pi$
$312$	−1.79321	−	7.85656i	−0.101520	−	0.444790i
$313$	−7.00335	+	8.78193i	−0.395853	+	0.496384i	−0.939318	−	0.343048i	$-0.888541\pi$
$313$	−7.00335	+	8.78193i	−0.395853	+	0.496384i	0.543465	+	0.839432i	$0.317112\pi$
$314$	−8.89307	−	11.1516i	−0.501865	−	0.629319i
$315$	0.153989	−	0.674671i	0.00867631	−	0.0380134i
$316$	4.22643	−	0.964656i	0.237756	−	0.0542662i
$317$	4.63385	−	3.69537i	0.260263	−	0.207553i	−0.484661	−	0.874702i	$-0.661057\pi$
$317$	4.63385	−	3.69537i	0.260263	−	0.207553i	0.744924	+	0.667149i	$0.232486\pi$
$318$	−0.109916			−0.00616380
$319$		0			0
$320$	−36.0344			−2.01439
$321$	−8.14924	+	6.49880i	−0.454846	+	0.362728i
$322$	4.34013	−	0.990607i	0.241866	−	0.0552044i
$323$	0.960771	−	4.20941i	0.0534587	−	0.234218i
$324$	−2.68598	−	3.36811i	−0.149221	−	0.187117i
$325$	−10.4201	+	13.0663i	−0.578000	+	0.724790i
$326$	1.85205	+	8.11437i	0.102576	+	0.449413i
$327$	−7.18189	−	14.9133i	−0.397159	−	0.824710i
$328$	−17.8388	+	8.59070i	−0.984981	+	0.474342i
$329$	3.20673	+	0.731914i	0.176792	+	0.0403517i
$330$	−11.2535	+	23.3681i	−0.619483	+	1.28637i
$331$			30.9095i			1.69894i	0.527639	+	0.849469i	$0.323077\pi$
$331$			30.9095i			1.69894i	−0.527639	+	0.849469i	$0.676923\pi$
$332$	1.61260	+	0.776589i	0.0885032	+	0.0426209i
$333$	−0.550490	−	0.439001i	−0.0301667	−	0.0240571i
$334$	−14.3001	−	11.4040i	−0.782467	−	0.623997i
$335$	54.5320	+	26.2613i	2.97940	+	1.43481i
$336$			3.63102i			0.198089i
$337$	3.47761	−	7.22132i	0.189437	−	0.393371i	−0.784520	−	0.620104i	$-0.787090\pi$
$337$	3.47761	−	7.22132i	0.189437	−	0.393371i	0.973957	+	0.226733i	$0.0728046\pi$
$338$	−13.1886	−	3.01022i	−0.717367	−	0.163734i
$339$	14.5565	−	7.01002i	0.790598	−	0.380732i
$340$	−1.25396	−	2.60388i	−0.0680055	−	0.141215i
$341$	1.23772	+	5.42280i	0.0670262	+	0.293661i
$342$	−0.516926	+	0.648205i	−0.0279522	+	0.0350509i
$343$	−5.83393	−	7.31552i	−0.315003	−	0.395001i
$344$	0.451083	−	1.97632i	0.0243207	−	0.106556i
$345$	36.6946	−	8.37531i	1.97557	−	0.450912i
$346$	22.7742	−	18.1618i	1.22435	−	0.976385i
$347$	2.26337			0.121504			0.0607521	−	0.998153i	$-0.480650\pi$
$347$	2.26337			0.121504			0.0607521	+	0.998153i	$0.480650\pi$
$348$		0			0
$349$	−23.5690			−1.26162			−0.630809	−	0.775938i	$-0.717277\pi$
$349$	−23.5690			−1.26162			−0.630809	+	0.775938i	$0.717277\pi$
$350$	7.68702	−	6.13019i	0.410889	−	0.327673i
$351$	7.09408	−	1.61918i	0.378654	−	0.0864253i
$352$	−1.56488	+	6.85620i	−0.0834086	+	0.365437i
$353$	0.612605	+	0.768182i	0.0326057	+	0.0408862i	0.797867	−	0.602834i	$-0.205962\pi$
$353$	0.612605	+	0.768182i	0.0326057	+	0.0408862i	−0.765261	+	0.643720i	$0.777390\pi$
$354$	8.96077	−	11.2365i	0.476260	−	0.597211i
$355$	−2.03534	−	8.91742i	−0.108025	−	0.473288i
$356$	2.17362	+	4.51357i	0.115202	+	0.239219i
$357$	−1.80194	+	0.867767i	−0.0953687	+	0.0459271i
$358$	0.808298	+	0.184489i	0.0427199	+	0.00975053i
$359$	3.42001	−	7.10172i	0.180501	−	0.374814i	−0.791012	−	0.611801i	$-0.790445\pi$
$359$	3.42001	−	7.10172i	0.180501	−	0.374814i	0.971513	+	0.236986i	$0.0761597\pi$
$360$			3.04892i			0.160692i
$361$	−10.5891	−	5.09944i	−0.557321	−	0.268392i
$362$	−10.6912	−	8.52595i	−0.561917	−	0.448114i
$363$	−4.04699	−	3.22737i	−0.212412	−	0.169393i
$364$	0.407010	+	0.196006i	0.0213331	+	0.0102735i
$365$			33.6993i			1.76390i
$366$	−1.27518	+	2.64795i	−0.0666550	+	0.138410i
$367$	−28.5732	−	6.52164i	−1.49151	−	0.340427i	−0.602425	−	0.798175i	$-0.705799\pi$
$367$	−28.5732	−	6.52164i	−1.49151	−	0.340427i	−0.889082	+	0.457748i	$0.848656\pi$
$368$	−13.5341	+	6.51770i	−0.705516	+	0.339759i
$369$	0.695895	+	1.44504i	0.0362269	+	0.0752259i
$370$	−3.20291	−	14.0329i	−0.166511	−	0.729533i
$371$	0.0211063	−	0.0264664i	0.00109578	−	0.00137407i
$372$	0.975541	+	1.22329i	0.0505795	+	0.0634246i
$373$	0.848404	−	3.71710i	0.0439287	−	0.192464i	−0.948203	−	0.317666i	$-0.897101\pi$
$373$	0.848404	−	3.71710i	0.0439287	−	0.192464i	0.992131	+	0.125202i	$0.0399580\pi$
$374$	5.55876	−	1.26875i	0.287436	−	0.0656055i
$375$	36.4709	−	29.0846i	1.88335	−	1.50192i
$376$	−14.4916			−0.747345
$377$		0			0
$378$	−4.28083			−0.220182
$379$	7.05688	−	5.62767i	0.362487	−	0.289074i	−0.425262	−	0.905070i	$-0.639818\pi$
$379$	7.05688	−	5.62767i	0.362487	−	0.289074i	0.787749	+	0.615996i	$0.211246\pi$
$380$	4.72923	−	1.07942i	0.242605	−	0.0553729i
$381$	6.24094	−	27.3433i	0.319733	−	1.40084i
$382$	0.402829	+	0.505132i	0.0206105	+	0.0258448i
$383$	20.6930	−	25.9482i	1.05736	−	1.32589i	0.114236	−	0.993454i	$-0.463558\pi$
$383$	20.6930	−	25.9482i	1.05736	−	1.32589i	0.943126	−	0.332436i	$-0.107871\pi$
$384$	−2.47166	−	10.8290i	−0.126131	−	0.552617i
$385$	−3.46583	−	7.19687i	−0.176635	−	0.366786i
$386$	1.55765	−	0.750123i	0.0792821	−	0.0381803i
$387$	−0.160093	−	0.0365403i	−0.00813800	−	0.00185745i
$388$	−0.882455	+	1.83244i	−0.0447999	+	0.0930279i
$389$			27.5362i			1.39614i	0.716030	+	0.698070i	$0.245957\pi$
$389$			27.5362i			1.39614i	−0.716030	+	0.698070i	$0.754043\pi$
$390$	−12.0233	−	5.79010i	−0.608822	−	0.293193i
$391$	−6.46897	−	5.15883i	−0.327150	−	0.260893i
$392$	15.5446	+	12.3964i	0.785122	+	0.626114i
$393$	−21.8083	−	10.5023i	−1.10008	−	0.529772i
$394$		−	16.1588i		−	0.814070i
$395$	17.1125	−	35.5344i	0.861023	−	1.78793i
$396$	0.305499	+	0.0697281i	0.0153519	+	0.00350397i
$397$	17.3192	−	8.34047i	0.869224	−	0.418596i	0.0545468	−	0.998511i	$-0.482629\pi$
$397$	17.3192	−	8.34047i	0.869224	−	0.418596i	0.814677	+	0.579915i	$0.196914\pi$
$398$	−10.5523	−	21.9121i	−0.528941	−	1.09836i
$399$	−0.746980	−	3.27273i	−0.0373958	−	0.163842i
$400$	−20.6854	+	25.9387i	−1.03427	+	1.29694i
$401$	6.87465	+	8.62054i	0.343304	+	0.430489i	0.923270	−	0.384151i	$-0.125506\pi$
$401$	6.87465	+	8.62054i	0.343304	+	0.430489i	−0.579967	+	0.814640i	$0.696934\pi$
$402$	−7.47434	+	32.7472i	−0.372786	+	1.63328i
$403$	−2.79012	+	0.636826i	−0.138986	+	0.0317226i
$404$	1.11800	−	0.891576i	0.0556226	−	0.0443575i
$405$	−39.1933			−1.94753
$406$		0			0
$407$	−8.12737			−0.402859
$408$	6.88921	−	5.49396i	0.341067	−	0.271992i
$409$	−32.9733	+	7.52595i	−1.63043	+	0.372134i	−0.937257	−	0.348640i	$-0.886644\pi$
$409$	−32.9733	+	7.52595i	−1.63043	+	0.372134i	−0.693170	+	0.720774i	$0.743787\pi$
$410$	−7.29590	+	31.9654i	−0.360319	+	1.57866i
$411$	19.0906	+	23.9389i	0.941670	+	1.18082i
$412$	−1.81282	+	2.27321i	−0.0893114	+	0.111993i
$413$	0.984935	+	4.31528i	0.0484655	+	0.212341i
$414$	0.689359	+	1.43147i	0.0338801	+	0.0703528i
$415$	14.6712	−	7.06528i	0.720181	−	0.346821i
$416$	−3.52763	−	0.805159i	−0.172956	−	0.0394761i
$417$	−9.74508	+	20.2359i	−0.477218	+	0.990954i
$418$			9.57002i			0.468085i
$419$	−32.0916	−	15.4545i	−1.56778	−	0.755001i	−0.569998	−	0.821646i	$-0.693056\pi$
$419$	−32.0916	−	15.4545i	−1.56778	−	0.755001i	−0.997777	+	0.0666451i	$0.978770\pi$
$420$	−1.75676	−	1.40097i	−0.0857211	−	0.0683603i
$421$	−7.39388	−	5.89642i	−0.360356	−	0.287374i	0.426529	−	0.904474i	$-0.359736\pi$
$421$	−7.39388	−	5.89642i	−0.360356	−	0.287374i	−0.786885	+	0.617100i	$0.788307\pi$
$422$	23.1787	+	11.1623i	1.12832	+	0.543372i
$423$			1.17390i			0.0570769i
$424$	−0.0647116	+	0.134375i	−0.00314267	+	0.00652582i
$425$	−17.8160	−	4.06638i	−0.864201	−	0.197248i
$426$	4.57338	−	2.20242i	0.221581	−	0.106708i
$427$	−0.392730	−	0.815511i	−0.0190055	−	0.0394654i
$428$	0.572844	+	2.50979i	0.0276894	+	0.121315i
$429$	−4.69806	+	5.89118i	−0.226825	+	0.284429i
$430$	−2.09299	−	2.62453i	−0.100933	−	0.126566i
$431$	−0.219300	+	0.960816i	−0.0105633	+	0.0462809i	−0.979935	−	0.199318i	$-0.936127\pi$
$431$	−0.219300	+	0.960816i	−0.0105633	+	0.0462809i	0.969372	+	0.245599i	$0.0789845\pi$
$432$	14.0829	−	3.21432i	0.677563	−	0.154649i
$433$	22.4263	−	17.8843i	1.07774	−	0.859466i	0.0871286	−	0.996197i	$-0.472231\pi$
$433$	22.4263	−	17.8843i	1.07774	−	0.859466i	0.990608	+	0.136731i	$0.0436595\pi$
$434$	1.68366			0.0808183
$435$		0			0
$436$	−4.08815			−0.195787
$437$	10.8578	−	8.65883i	0.519401	−	0.414208i
$438$	−18.2328	+	4.16152i	−0.871198	+	0.198845i
$439$	−1.46734	+	6.42886i	−0.0700325	+	0.306833i	−0.997798	−	0.0663323i	$-0.978870\pi$
$439$	−1.46734	+	6.42886i	−0.0700325	+	0.306833i	0.927765	+	0.373165i	$0.121727\pi$
$440$	21.9426	+	27.5152i	1.04607	+	1.31174i
$441$	1.00418	−	1.25920i	0.0478181	−	0.0599620i
$442$	0.652793	+	2.86007i	0.0310502	+	0.136040i
$443$	9.28006	+	19.2702i	0.440909	+	0.915557i	0.996460	+	0.0840741i	$0.0267932\pi$
$443$	9.28006	+	19.2702i	0.440909	+	0.915557i	−0.555551	+	0.831483i	$0.687492\pi$
$444$	−2.05980	+	0.991949i	−0.0977539	+	0.0470758i
$445$	44.4346	+	10.1419i	2.10640	+	0.480773i
$446$	11.4165	−	23.7066i	0.540586	−	1.12254i
$447$		−	33.0030i		−	1.56099i
$448$	5.54892	+	2.67222i	0.262162	+	0.126250i
$449$	−22.8738	−	18.2412i	−1.07948	−	0.860857i	−0.0886629	−	0.996062i	$-0.528259\pi$
$449$	−22.8738	−	18.2412i	−1.07948	−	0.860857i	−0.990818	+	0.135205i	$0.956831\pi$
$450$	2.74347	+	2.18784i	0.129328	+	0.103136i
$451$	16.6799	+	8.03264i	0.785428	+	0.378242i
$452$		−	3.99031i		−	0.187688i
$453$	−14.8836	+	30.9061i	−0.699292	+	1.45210i
$454$	8.67373	+	1.97972i	0.407078	+	0.0929129i
$455$	3.70291	−	1.78323i	0.173595	−	0.0835989i
$456$	6.41708	+	13.3252i	0.300507	+	0.624010i
$457$	−0.0537617	−	0.235545i	−0.00251487	−	0.0110183i	0.973655	−	0.228027i	$-0.0732273\pi$
$457$	−0.0537617	−	0.235545i	−0.00251487	−	0.0110183i	−0.976170	+	0.217008i	$0.930370\pi$
$458$	−1.75116	+	2.19589i	−0.0818263	+	0.102607i
$459$	4.96077	+	6.22061i	0.231549	+	0.290353i
$460$	2.06853	−	9.06283i	0.0964458	−	0.422557i
$461$	16.9034	−	3.85809i	0.787270	−	0.179689i	0.190058	−	0.981773i	$-0.439132\pi$
$461$	16.9034	−	3.85809i	0.787270	−	0.179689i	0.597212	+	0.802084i	$0.296275\pi$
$462$	3.46583	−	2.76391i	0.161245	−	0.128589i
$463$	−4.24996			−0.197513			−0.0987563	−	0.995112i	$-0.531486\pi$
$463$	−4.24996			−0.197513			−0.0987563	+	0.995112i	$0.531486\pi$
$464$		0			0
$465$	14.2349			0.660128
$466$	18.4354	−	14.7017i	0.854002	−	0.681044i
$467$	28.1105	−	6.41603i	1.30080	−	0.296899i	0.484633	−	0.874718i	$-0.338953\pi$
$467$	28.1105	−	6.41603i	1.30080	−	0.296899i	0.816165	+	0.577819i	$0.196096\pi$
$468$	−0.0358763	+	0.157184i	−0.00165838	+	0.00726584i
$469$	−6.44989	−	8.08790i	−0.297828	−	0.373465i
$470$	−14.9623	+	18.7621i	−0.690158	+	0.865430i
$471$	4.58642	+	20.0944i	0.211331	+	0.925901i
$472$	−8.46128	−	17.5700i	−0.389462	−	0.808726i
$473$	−1.70775	+	0.822410i	−0.0785225	+	0.0378144i
$474$	21.3389	+	4.87047i	0.980129	+	0.223708i
$475$	13.3082	−	27.6347i	0.610620	−	1.26797i
$476$			0.493959i			0.0226406i
$477$	0.0108851	+	0.00524200i	0.000498396	+	0.000240015i
$478$	19.9589	+	15.9167i	0.912899	+	0.728013i
$479$	−18.9022	−	15.0740i	−0.863666	−	0.688750i	0.0879221	−	0.996127i	$-0.471977\pi$
$479$	−18.9022	−	15.0740i	−0.863666	−	0.688750i	−0.951588	+	0.307377i	$0.900549\pi$
$480$	16.2153	+	7.80887i	0.740123	+	0.356424i
$481$		−	4.18167i		−	0.190668i
$482$	3.98694	−	8.27897i	0.181600	−	0.377097i
$483$	−6.27167	−	1.43147i	−0.285371	−	0.0651341i
$484$	−1.15183	+	0.554694i	−0.0523561	+	0.0252133i
$485$	8.02843	+	16.6712i	0.364552	+	0.757001i
$486$	−0.710439	−	3.11264i	−0.0322262	−	0.141192i
$487$	12.0402	−	15.0979i	0.545593	−	0.684152i	−0.430229	−	0.902720i	$-0.641567\pi$
$487$	12.0402	−	15.0979i	0.545593	−	0.684152i	0.975822	+	0.218568i	$0.0701385\pi$
$488$	2.48643	+	3.11788i	0.112555	+	0.141140i
$489$	2.67629	−	11.7256i	0.121026	−	0.530250i
$490$	32.0990	−	7.32640i	1.45009	−	0.330973i
$491$	−28.8423	+	23.0010i	−1.30163	+	1.03802i	−0.305319	+	0.952250i	$0.598763\pi$
$491$	−28.8423	+	23.0010i	−1.30163	+	1.03802i	−0.996315	+	0.0857687i	$0.972665\pi$
$492$	5.20775			0.234784
$493$		0			0
$494$	−4.92394			−0.221538
$495$	2.22889	−	1.77748i	0.100181	−	0.0798917i
$496$	−5.53883	+	1.26420i	−0.248701	+	0.0567643i
$497$	−0.347871	+	1.52412i	−0.0156042	+	0.0683663i
$498$	5.63437	+	7.06528i	0.252482	+	0.316603i
$499$	−23.5154	+	29.4873i	−1.05269	+	1.32003i	−0.107254	+	0.994232i	$0.534206\pi$
$499$	−23.5154	+	29.4873i	−1.05269	+	1.32003i	−0.945438	+	0.325803i	$0.894366\pi$
$500$	−2.56369	−	11.2322i	−0.114652	−	0.502321i
$501$	11.4678	+	23.8131i	0.512343	+	1.06389i
$502$	14.5553	−	7.00944i	0.649633	−	0.312847i
$503$	6.83394	+	1.55980i	0.304710	+	0.0695482i	0.372142	−	0.928176i	$-0.378623\pi$
$503$	6.83394	+	1.55980i	0.304710	+	0.0695482i	−0.0674318	+	0.997724i	$0.521481\pi$
$504$	0.226100	−	0.469501i	0.0100713	−	0.0209132i
$505$		−	13.0097i		−	0.578924i
$506$	16.5233	+	7.95718i	0.734549	+	0.353740i
$507$	15.2834	+	12.1881i	0.678761	+	0.541294i
$508$	−5.41568	−	4.31886i	−0.240282	−	0.191619i
$509$	−16.5661	−	7.97783i	−0.734281	−	0.353611i	0.0290852	−	0.999577i	$-0.490741\pi$
$509$	−16.5661	−	7.97783i	−0.734281	−	0.353611i	−0.763366	+	0.645966i	$0.776455\pi$
$510$		−	14.5918i		−	0.646135i
$511$	2.49905	−	5.18933i	0.110552	−	0.229563i
$512$	−24.3137	−	5.54945i	−1.07453	−	0.245253i
$513$	−12.0320	+	5.79430i	−0.531225	+	0.255825i
$514$	9.03112	+	18.7533i	0.398346	+	0.827173i
$515$	5.88620	+	25.7891i	0.259377	+	1.13640i
$516$	−0.332437	+	0.416863i	−0.0146347	+	0.0183514i
$517$	8.44839	+	10.5940i	0.371560	+	0.465921i
$518$	−0.547425	+	2.39843i	−0.0240525	+	0.105381i
$519$	−41.0377	+	9.36658i	−1.80135	+	0.411147i
$520$	−14.1570	+	11.2899i	−0.620827	+	0.495093i
$521$	−3.94571			−0.172865			−0.0864323	−	0.996258i	$-0.527547\pi$
$521$	−3.94571			−0.172865			−0.0864323	+	0.996258i	$0.527547\pi$
$522$		0			0
$523$	−33.9952			−1.48651			−0.743253	−	0.669010i	$-0.766718\pi$
$523$	−33.9952			−1.48651			−0.743253	+	0.669010i	$0.766718\pi$
$524$	−4.67397	+	3.72737i	−0.204183	+	0.162831i
$525$	−13.8515	+	3.16152i	−0.604530	+	0.137980i
$526$	4.88620	−	21.4078i	0.213048	−	0.933426i
$527$	−1.95108	−	2.44658i	−0.0849905	−	0.106575i
$528$	−9.32640	+	11.6949i	−0.405879	+	0.508957i
$529$	−0.804094	−	3.52296i	−0.0349606	−	0.153172i
$530$	0.107160	+	0.222521i	0.00465475	+	0.00966569i
$531$	−1.42327	+	0.685411i	−0.0617647	+	0.0297443i
$532$	−0.808298	−	0.184489i	−0.0350442	−	0.00799860i
$533$	−4.13292	+	8.58211i	−0.179017	+	0.371732i
$534$			25.2935i			1.09456i
$535$	21.1015	+	10.1619i	0.912297	+	0.439339i
$536$	35.6338	+	28.4170i	1.53915	+	1.22743i
$537$	−0.936683	−	0.746980i	−0.0404208	−	0.0322345i
$538$	−7.53803	−	3.63012i	−0.324988	−	0.156506i
$539$		−	18.5907i		−	0.800759i
$540$	−3.87849	+	8.05376i	−0.166904	+	0.346579i
$541$	22.8484	+	5.21499i	0.982328	+	0.224210i	0.683383	−	0.730060i	$-0.260508\pi$
$541$	22.8484	+	5.21499i	0.982328	+	0.224210i	0.298945	+	0.954270i	$0.403365\pi$
$542$	−14.2322	+	6.85387i	−0.611326	+	0.294399i
$543$	8.57368	+	17.8034i	0.367932	+	0.764018i
$544$	−0.880395	−	3.85726i	−0.0377466	−	0.165379i
$545$	−23.1896	+	29.0789i	−0.993335	+	1.24560i
$546$	1.42208	+	1.78323i	0.0608592	+	0.0763150i
$547$	−7.18651	+	31.4862i	−0.307273	+	1.34625i	0.551620	+	0.834096i	$0.314010\pi$
$547$	−7.18651	+	31.4862i	−0.307273	+	1.34625i	−0.858893	+	0.512156i	$0.828847\pi$
$548$	7.37265	−	1.68276i	0.314944	−	0.0718839i
$549$	0.252566	−	0.201415i	0.0107793	−	0.00859617i
$550$	40.5042			1.72711
$551$		0			0
$552$	28.3424			1.20633
$553$	−5.27028	+	4.20291i	−0.224115	+	0.178726i
$554$	−19.1365	+	4.36778i	−0.813032	+	0.185569i
$555$	−4.62833	+	20.2781i	−0.196462	+	0.860756i
$556$	3.45862	+	4.33697i	0.146678	+	0.183928i
$557$	−10.1163	+	12.6854i	−0.428639	+	0.537497i	−0.948510	−	0.316748i	$-0.897409\pi$
$557$	−10.1163	+	12.6854i	−0.428639	+	0.537497i	0.519870	+	0.854245i	$0.325980\pi$
$558$	0.133711	+	0.585826i	0.00566044	+	0.0248000i
$559$	−0.423143	−	0.878666i	−0.0178971	−	0.0371636i
$560$	7.35086	−	3.53999i	0.310630	−	0.149592i
$561$	−8.03264	−	1.83340i	−0.339138	−	0.0774061i
$562$	−6.39223	+	13.2736i	−0.269640	+	0.559913i
$563$		−	21.9168i		−	0.923681i	−0.886963	−	0.461841i	$-0.847189\pi$
$563$		−	21.9168i		−	0.923681i	0.886963	−	0.461841i	$-0.152811\pi$
$564$	3.43416	+	1.65380i	0.144604	+	0.0696377i
$565$	−28.3830	−	22.6347i	−1.19408	−	0.952248i
$566$	−2.14295	−	1.70895i	−0.0900750	−	0.0718324i
$567$	6.03534	+	2.90647i	0.253461	+	0.122060i
$568$		−	6.88769i		−	0.289001i
$569$	−16.2693	+	33.7836i	−0.682045	+	1.41628i	0.216007	+	0.976392i	$0.430697\pi$
$569$	−16.2693	+	33.7836i	−0.682045	+	1.41628i	−0.898052	+	0.439889i	$0.855018\pi$
$570$	23.8775	+	5.44989i	1.00012	+	0.228271i
$571$	−24.8838	+	11.9834i	−1.04135	+	0.501490i	−0.874771	−	0.484537i	$-0.838988\pi$
$571$	−24.8838	+	11.9834i	−1.04135	+	0.501490i	−0.166584	+	0.986027i	$0.553274\pi$
$572$	0.807465	+	1.67672i	0.0337618	+	0.0701071i
$573$	−0.207751	−	0.910216i	−0.00867892	−	0.0380248i
$574$	3.49396	−	4.38129i	0.145835	−	0.182871i
$575$	−36.6477	−	45.9548i	−1.52832	−	1.91645i
$576$	−0.489115	+	2.14295i	−0.0203798	+	0.0892897i
$577$	−6.17209	+	1.40874i	−0.256947	+	0.0586466i	−0.349054	−	0.937103i	$-0.613497\pi$
$577$	−6.17209	+	1.40874i	−0.256947	+	0.0586466i	0.0921067	+	0.995749i	$0.470640\pi$
$578$	14.0659	−	11.2171i	0.585062	−	0.466572i
$579$	−2.49827			−0.103825
$580$		0			0
$581$	−2.78315			−0.115465
$582$	−8.02843	+	6.40246i	−0.332789	+	0.265391i
$583$	0.135960	−	0.0310319i	0.00563088	−	0.00128521i
$584$	−5.64675	+	24.7400i	−0.233664	+	1.02375i
$585$	0.914542	+	1.14680i	0.0378117	+	0.0474143i
$586$	16.0500	−	20.1261i	0.663021	−	0.831402i
$587$	4.34535	+	19.0382i	0.179352	+	0.785791i	0.981930	+	0.189244i	$0.0606038\pi$
$587$	4.34535	+	19.0382i	0.179352	+	0.785791i	−0.802578	+	0.596547i	$0.796539\pi$
$588$	−2.26900	−	4.71164i	−0.0935722	−	0.194305i
$589$	4.73221	−	2.27891i	0.194987	−	0.0939009i
$590$	−31.4838	−	7.18598i	−1.29617	−	0.295842i
$591$	−10.1313	+	21.0378i	−0.416745	+	0.865379i
$592$		−	8.30127i		−	0.341180i
$593$	−2.22132	−	1.06973i	−0.0912189	−	0.0439287i	0.387718	−	0.921778i	$-0.373263\pi$
$593$	−2.22132	−	1.06973i	−0.0912189	−	0.0439287i	−0.478937	+	0.877849i	$0.658978\pi$
$594$	−13.7879	−	10.9955i	−0.565723	−	0.451149i
$595$	3.51352	+	2.80194i	0.144040	+	0.114868i
$596$	−7.34385	−	3.53661i	−0.300816	−	0.144865i
$597$			35.1444i			1.43836i
$598$	−4.09410	+	8.50149i	−0.167420	+	0.347652i
$599$	−5.03240	−	1.14861i	−0.205618	−	0.0469310i	0.118471	−	0.992958i	$-0.462201\pi$
$599$	−5.03240	−	1.14861i	−0.205618	−	0.0469310i	−0.324089	+	0.946026i	$0.605058\pi$
$600$	56.3977	−	27.1597i	2.30243	−	1.10879i
$601$	−12.7852	−	26.5487i	−0.521518	−	1.08294i	−0.980865	−	0.194687i	$-0.937631\pi$
$601$	−12.7852	−	26.5487i	−0.521518	−	1.08294i	0.459348	−	0.888257i	$-0.348083\pi$
$602$	0.127670	+	0.559360i	0.00520345	+	0.0227978i
$603$	2.30194	−	2.88654i	0.0937422	−	0.117549i
$604$	5.28232	+	6.62382i	0.214935	+	0.269520i
$605$	−2.58815	+	11.3394i	−0.105223	+	0.461013i
$606$	7.03882	−	1.60656i	0.285932	−	0.0652622i
$607$	−27.0916	+	21.6048i	−1.09961	+	0.876913i	−0.993085	−	0.117396i	$-0.962545\pi$
$607$	−27.0916	+	21.6048i	−1.09961	+	0.876913i	−0.106529	+	0.994310i	$0.533974\pi$
$608$	6.64071			0.269316
$609$		0			0
$610$	6.60388			0.267383
$611$	−5.45076	+	4.34684i	−0.220514	+	0.175854i
$612$	−0.171872	+	0.0392287i	−0.00694751	+	0.00158572i
$613$	6.11045	−	26.7716i	0.246799	−	1.08130i	−0.687886	−	0.725819i	$-0.741461\pi$
$613$	6.11045	−	26.7716i	0.246799	−	1.08130i	0.934685	−	0.355477i	$-0.115682\pi$
$614$	−17.7356	−	22.2397i	−0.715749	−	0.897521i
$615$	29.5405	−	37.0426i	1.19119	−	1.49370i
$616$	−1.33848	−	5.86426i	−0.0539288	−	0.236278i
$617$	−14.8729	−	30.8838i	−0.598759	−	1.24334i	−0.951510	−	0.307618i	$-0.900468\pi$
$617$	−14.8729	−	30.8838i	−0.598759	−	1.24334i	0.352751	−	0.935717i	$-0.385246\pi$
$618$	−13.2262	+	6.36939i	−0.532035	+	0.256214i
$619$	−25.0230	−	5.71134i	−1.00576	−	0.229558i	−0.312246	−	0.950001i	$-0.601081\pi$
$619$	−25.0230	−	5.71134i	−1.00576	−	0.229558i	−0.693514	+	0.720443i	$0.743938\pi$
$620$	1.52542	−	3.16756i	0.0612623	−	0.127212i
$621$			25.5918i			1.02696i
$622$	34.9294	+	16.8211i	1.40054	+	0.674465i
$623$	−6.09035	−	4.85690i	−0.244005	−	0.194587i
$624$	−6.01724	−	4.79859i	−0.240882	−	0.192097i
$625$	−43.1100	−	20.7607i	−1.72440	−	0.830427i
$626$			14.0067i			0.559821i
$627$	6.00022	−	12.4596i	0.239626	−	0.497587i
$628$	4.96291	+	1.13275i	0.198042	+	0.0452017i
$629$	4.11960	−	1.98390i	0.164259	−	0.0791032i
$630$	−0.374414	−	0.777479i	−0.0149170	−	0.0309755i
$631$	−6.54234	−	28.6639i	−0.260447	−	1.14109i	−0.920769	−	0.390109i	$-0.872437\pi$
$631$	−6.54234	−	28.6639i	−0.260447	−	1.14109i	0.660322	−	0.750982i	$-0.270420\pi$
$632$	18.5172	−	23.2199i	0.736576	−	0.923636i
$633$	−23.1787	−	29.0652i	−0.921272	−	1.15524i
$634$	1.64460	−	7.20545i	0.0653153	−	0.286165i
$635$	−61.4399	+	14.0233i	−2.43817	+	0.556496i
$636$	0.0306702	−	0.0244587i	0.00121615	−	0.000969849i
$637$	9.56524			0.378989
$638$		0			0
$639$	−0.557942			−0.0220718
$640$	−19.5132	+	15.5613i	−0.771329	+	0.615114i
$641$	10.2050	−	2.32922i	0.403072	−	0.0919985i	−0.0161787	−	0.999869i	$-0.505150\pi$
$641$	10.2050	−	2.32922i	0.403072	−	0.0919985i	0.419250	+	0.907871i	$0.362293\pi$
$642$	−2.89224	+	12.6717i	−0.114148	+	0.500113i
$643$	−1.90180	−	2.38478i	−0.0749995	−	0.0940465i	0.742916	−	0.669384i	$-0.233442\pi$
$643$	−1.90180	−	2.38478i	−0.0749995	−	0.0940465i	−0.817916	+	0.575338i	$0.804871\pi$
$644$	−0.990607	+	1.24218i	−0.0390354	+	0.0489488i
$645$	1.07942	+	4.72923i	0.0425020	+	0.186213i
$646$	−2.33605	−	4.85086i	−0.0919106	−	0.190854i
$647$	−26.8523	+	12.9314i	−1.05567	+	0.508386i	−0.879464	−	0.475966i	$-0.842098\pi$
$647$	−26.8523	+	12.9314i	−1.05567	+	0.508386i	−0.176211	+	0.984352i	$0.556384\pi$
$648$	−28.7734	−	6.56734i	−1.13032	−	0.257989i
$649$	−7.91162	+	16.4286i	−0.310558	+	0.644881i
$650$			20.8401i			0.817416i
$651$	−2.19202	−	1.05562i	−0.0859121	−	0.0413731i
$652$	−2.32240	−	1.85205i	−0.0909522	−	0.0725319i
$653$	8.90461	+	7.10119i	0.348464	+	0.277891i	0.782043	−	0.623225i	$-0.214178\pi$
$653$	8.90461	+	7.10119i	0.348464	+	0.277891i	−0.433578	+	0.901116i	$0.642749\pi$
$654$	−18.5966	−	8.95567i	−0.727186	−	0.350194i
$655$			54.3889i			2.12515i
$656$	−8.20451	+	17.0368i	−0.320332	+	0.665177i
$657$	2.00408	+	0.457419i	0.0781867	+	0.0178456i
$658$	3.69537	−	1.77960i	0.144061	−	0.0693760i
$659$	−1.99043	−	4.13318i	−0.0775363	−	0.161006i	0.858597	−	0.512651i	$-0.171337\pi$
$659$	−1.99043	−	4.13318i	−0.0775363	−	0.161006i	−0.936133	+	0.351645i	$0.885622\pi$
$660$	−2.05980	−	9.02458i	−0.0801777	−	0.351281i
$661$	−8.03348	+	10.0737i	−0.312466	+	0.391820i	−0.913121	−	0.407688i	$-0.866335\pi$
$661$	−8.03348	+	10.0737i	−0.312466	+	0.391820i	0.600655	+	0.799508i	$0.294907\pi$
$662$	24.0315	+	30.1345i	0.934009	+	1.17121i
$663$	0.943313	−	4.13292i	0.0366352	−	0.160509i
$664$	11.9546	−	2.72856i	0.463929	−	0.105889i
$665$	−5.89726	+	4.70291i	−0.228686	+	0.182371i
$666$	−0.878002			−0.0340219
$667$		0			0
$668$	6.52781			0.252569
$669$	−29.7271	+	23.7066i	−1.14932	+	0.916548i
$670$	73.5824	−	16.7947i	2.84274	−	0.648836i
$671$	0.829749	−	3.63537i	0.0320321	−	0.140342i
$672$	−1.91789	−	2.40496i	−0.0739844	−	0.0927735i
$673$	−2.98457	+	3.74253i	−0.115047	+	0.144264i	−0.836020	−	0.548699i	$-0.815123\pi$
$673$	−2.98457	+	3.74253i	−0.115047	+	0.144264i	0.720974	+	0.692962i	$0.243695\pi$
$674$	−2.22401	−	9.74404i	−0.0856658	−	0.375326i
$675$	24.5238	+	50.9243i	0.943923	+	1.96008i
$676$	4.34990	−	2.09480i	0.167304	−	0.0805692i
$677$	29.7611	+	6.79278i	1.14381	+	0.261068i	0.752119	−	0.659028i	$-0.229032\pi$
$677$	29.7611	+	6.79278i	1.14381	+	0.261068i	0.391694	+	0.920095i	$0.371889\pi$
$678$	8.74135	−	18.1516i	0.335709	−	0.697108i
$679$		−	3.16255i		−	0.121368i
$680$	−17.8388	−	8.59070i	−0.684086	−	0.329438i
$681$	−10.0514	−	8.01573i	−0.385171	−	0.307163i
$682$	5.42280	+	4.32454i	0.207650	+	0.165595i
$683$	−8.59999	−	4.14154i	−0.329069	−	0.158472i	0.262053	−	0.965054i	$-0.415601\pi$
$683$	−8.59999	−	4.14154i	−0.329069	−	0.158472i	−0.591122	+	0.806582i	$0.701315\pi$
$684$		−	0.295897i		−	0.0113139i
$685$	29.8513	−	61.9868i	1.14056	−	2.36839i
$686$	−11.3753	−	2.59634i	−0.434312	−	0.0991288i
$687$	3.65668	−	1.76096i	0.139511	−	0.0671849i
$688$	−0.840006	−	1.74429i	−0.0320249	−	0.0665005i
$689$	0.0159664	+	0.0699536i	0.000608273	+	0.00266502i
$690$	29.2630	−	36.6946i	1.11402	−	1.39694i
$691$	−10.2775	−	12.8876i	−0.390974	−	0.490266i	0.546922	−	0.837184i	$-0.315800\pi$
$691$	−10.2775	−	12.8876i	−0.390974	−	0.490266i	−0.937895	+	0.346918i	$0.887228\pi$
$692$	−2.31336	+	10.1355i	−0.0879406	+	0.385293i
$693$	−0.475038	+	0.108424i	−0.0180452	+	0.00411870i
$694$	2.20663	−	1.75973i	0.0837624	−	0.0667983i
$695$	50.4674			1.91434
$696$		0			0
$697$	−10.4155			−0.394515
$698$	−22.9780	+	18.3244i	−0.869731	+	0.693588i
$699$	−33.2194	+	7.58211i	−1.25647	+	0.286782i
$700$	−0.780831	+	3.42105i	−0.0295127	+	0.129303i
$701$	−29.2208	−	36.6417i	−1.10365	−	1.38394i	−0.915749	−	0.401751i	$-0.868402\pi$
$701$	−29.2208	−	36.6417i	−1.10365	−	1.38394i	−0.187905	−	0.982187i	$-0.560170\pi$
$702$	5.65734	−	7.09408i	0.213523	−	0.267749i
$703$	1.70775	+	7.48215i	0.0644090	+	0.282194i
$704$	11.0085	+	22.8593i	0.414898	+	0.861544i
$705$	31.2434	−	15.0460i	1.17669	−	0.566666i
$706$	1.19449	+	0.272635i	0.0449553	+	0.0102607i
$707$	−0.964764	+	2.00335i	−0.0362837	+	0.0753438i
$708$			5.12929i			0.192771i
$709$	9.55107	+	4.59955i	0.358698	+	0.172740i	0.604549	−	0.796568i	$-0.293353\pi$
$709$	9.55107	+	4.59955i	0.358698	+	0.172740i	−0.245851	+	0.969308i	$0.579067\pi$
$710$	−8.91742	−	7.11141i	−0.334665	−	0.266886i
$711$	−1.88094	−	1.50000i	−0.0705408	−	0.0562544i
$712$	30.9218	+	14.8912i	1.15884	+	0.558070i
$713$		−	10.0653i		−	0.376949i
$714$	−1.08209	+	2.24698i	−0.0404961	+	0.0840911i
$715$	16.5067	+	3.76755i	0.617317	+	0.140899i
$716$	−0.266594	+	0.128385i	−0.00996308	+	0.00479797i
$717$	−16.0058	−	33.2364i	−0.597748	−	1.24124i
$718$	−2.18718	−	9.58265i	−0.0816247	−	0.357621i
$719$	−8.29553	+	10.4023i	−0.309371	+	0.387939i	−0.912073	−	0.410027i	$-0.865519\pi$
$719$	−8.29553	+	10.4023i	−0.309371	+	0.387939i	0.602702	+	0.797966i	$0.294091\pi$
$720$	1.81551	+	2.27658i	0.0676601	+	0.0848431i
$721$	1.00604	−	4.40775i	0.0374669	−	0.164153i
$722$	−14.2883	+	3.26122i	−0.531756	+	0.121370i
$723$	−10.3815	+	8.27897i	−0.386092	+	0.307898i
$724$	4.88040			0.181378
$725$		0			0
$726$	−6.45473			−0.239558
$727$	25.8141	−	20.5860i	0.957392	−	0.763494i	−0.0142633	−	0.999898i	$-0.504540\pi$
$727$	25.8141	−	20.5860i	0.957392	−	0.763494i	0.971655	+	0.236404i	$0.0759689\pi$
$728$	3.01726	−	0.688669i	0.111827	−	0.0255238i
$729$	5.43535	−	23.8138i	0.201309	−	0.881994i
$730$	26.2005	+	32.8544i	0.969725	+	1.21600i
$731$	0.664874	−	0.833726i	0.0245913	−	0.0308365i
$732$	−0.233406	−	1.02262i	−0.00862694	−	0.0377971i
$733$	−13.7954	−	28.6465i	−0.509546	−	1.05808i	−0.984060	−	0.177835i	$-0.943091\pi$
$733$	−13.7954	−	28.6465i	−0.509546	−	1.05808i	0.474514	−	0.880248i	$-0.342624\pi$
$734$	−32.9272	+	15.8569i	−1.21537	+	0.585289i
$735$	−46.3845	−	10.5869i	−1.71092	−	0.390506i
$736$	5.52155	−	11.4656i	0.203527	−	0.422628i
$737$		−	42.6165i		−	1.56980i
$738$	1.80194	+	0.867767i	0.0663302	+	0.0319430i
$739$	18.7136	+	14.9236i	0.688389	+	0.548972i	0.904013	−	0.427504i	$-0.140607\pi$
$739$	18.7136	+	14.9236i	0.688389	+	0.548972i	−0.215624	+	0.976476i	$0.569179\pi$
$740$	4.01632	+	3.20291i	0.147643	+	0.117741i
$741$	6.41066	+	3.08721i	0.235501	+	0.113411i
$742$		−	0.0422126i		−	0.00154967i
$743$	−3.21617	+	6.67845i	−0.117990	+	0.245008i	−0.951597	−	0.307350i	$-0.900558\pi$
$743$	−3.21617	+	6.67845i	−0.117990	+	0.245008i	0.833607	+	0.552359i	$0.186272\pi$
$744$	10.4504	+	2.38524i	0.383131	+	0.0874471i
$745$	−66.8132	+	32.1755i	−2.44785	+	1.17882i
$746$	−2.06283	−	4.28352i	−0.0755257	−	0.156831i
$747$	−0.221029	−	0.968391i	−0.00808703	−	0.0354316i
$748$	−1.26875	+	1.59096i	−0.0463901	+	0.0581713i
$749$	−2.49582	−	3.12966i	−0.0911953	−	0.114355i
$750$	12.9438	−	56.7107i	0.472642	−	2.07078i
$751$	−18.8768	+	4.30851i	−0.688825	+	0.157220i	−0.552586	−	0.833456i	$-0.686359\pi$
$751$	−18.8768	+	4.30851i	−0.688825	+	0.157220i	−0.136239	+	0.990676i	$0.543502\pi$
$752$	−10.8206	+	8.62916i	−0.394588	+	0.314673i
$753$	−23.3448			−0.850732
$754$		0			0
$755$	77.0786			2.80518
$756$	1.19449	−	0.952575i	0.0434432	−	0.0346448i
$757$	33.3784	−	7.61841i	1.21316	−	0.276896i	0.432374	−	0.901694i	$-0.357676\pi$
$757$	33.3784	−	7.61841i	1.21316	−	0.276896i	0.780786	+	0.624799i	$0.214819\pi$
$758$	2.50455	−	10.9731i	0.0909693	−	0.398563i
$759$	−16.5233	−	20.7195i	−0.599756	−	0.752071i
$760$	20.7201	−	25.9822i	0.751598	−	0.942474i
$761$	−3.23974	−	14.1942i	−0.117441	−	0.514541i	−0.999091	−	0.0426370i	$-0.986424\pi$
$761$	−3.23974	−	14.1942i	−0.117441	−	0.514541i	0.881650	−	0.471904i	$-0.156433\pi$
$762$	−15.1744	−	31.5100i	−0.549711	−	1.14149i
$763$	5.72737	−	2.75815i	0.207345	−	0.0998519i
$764$	−0.224805	−	0.0513102i	−0.00813315	−	0.00185634i
$765$	−0.695895	+	1.44504i	−0.0251602	+	0.0522456i
$766$		−	41.3860i		−	1.49534i
$767$	−8.45281	−	4.07066i	−0.305213	−	0.146983i
$768$	14.2472	+	11.3617i	0.514101	+	0.409981i
$769$	9.04077	+	7.20978i	0.326019	+	0.259991i	0.772797	−	0.634654i	$-0.218857\pi$
$769$	9.04077	+	7.20978i	0.326019	+	0.259991i	−0.446778	+	0.894645i	$0.647429\pi$
$770$	−8.97434	−	4.32182i	−0.323413	−	0.155747i
$771$		−	30.0780i		−	1.08323i
$772$	−0.267716	+	0.555918i	−0.00963530	+	0.0200079i
$773$	8.16439	+	1.86347i	0.293653	+	0.0670243i	0.366809	−	0.930296i	$-0.380450\pi$
$773$	8.16439	+	1.86347i	0.293653	+	0.0670243i	−0.0731566	+	0.997320i	$0.523307\pi$
$774$	−0.184489	+	0.0888451i	−0.00663131	+	0.00319347i
$775$	−9.64528	−	20.0286i	−0.346469	−	0.719450i
$776$	3.10052	+	13.5843i	0.111302	+	0.487647i
$777$	2.21648	−	2.77938i	0.0795158	−	0.0997096i
$778$	21.4088	+	26.8458i	0.767543	+	0.962468i
$779$	3.89008	−	17.0436i	0.139377	−	0.610649i
$780$	4.64330	−	1.05980i	0.166257	−	0.0379470i
$781$	−5.03519	+	4.01543i	−0.180173	+	0.143684i
$782$	−10.3177			−0.368959
$783$		0			0
$784$	18.9885			0.678161
$785$	36.2089	−	28.8756i	1.29235	−	1.03061i
$786$	−29.4268	+	6.71648i	−1.04962	+	0.239569i
$787$	−2.16368	+	9.47969i	−0.0771268	+	0.337915i	−0.998739	−	0.0501966i	$-0.984015\pi$
$787$	−2.16368	+	9.47969i	−0.0771268	+	0.337915i	0.921613	+	0.388111i	$0.126872\pi$
$788$	3.59568	+	4.50884i	0.128091	+	0.160621i
$789$	−19.7838	+	24.8081i	−0.704322	+	0.883192i
$790$	−10.9438	−	47.9481i	−0.389365	−	1.70592i
$791$	2.69215	+	5.59030i	0.0957217	+	0.198768i
$792$	1.93416	−	0.931441i	0.0687273	−	0.0330973i
$793$	1.87046	+	0.426919i	0.0664219	+	0.0151604i
$794$	10.4004	−	21.5966i	0.369096	−	0.766436i
$795$		−	0.356896i		−	0.0126578i
$796$	7.82036	+	3.76608i	0.277185	+	0.133485i
$797$	20.6483	+	16.4664i	0.731399	+	0.583271i	0.916779	−	0.399396i	$-0.130780\pi$
$797$	20.6483	+	16.4664i	0.731399	+	0.583271i	−0.185380	+	0.982667i	$0.559351\pi$
$798$	−3.27273	−	2.60992i	−0.115853	−	0.0923900i
$799$	−6.86831	−	3.30761i	−0.242983	−	0.117015i
$800$		−	28.1062i		−	0.993704i
$801$	1.20627	−	2.50484i	0.0426214	−	0.0885043i
$802$	13.4046	+	3.05951i	0.473332	+	0.108035i
$803$	21.3780	−	10.2951i	0.754413	−	0.363306i
$804$	−5.20136	−	10.8007i	−0.183438	−	0.380913i
$805$	3.21648	+	14.0923i	0.113366	+	0.496689i
$806$	−2.22505	+	2.79012i	−0.0783739	+	0.0982777i
$807$	7.53803	+	9.45239i	0.265351	+	0.332740i
$808$	2.17994	−	9.55094i	0.0766900	−	0.336001i
$809$	18.3188	−	4.18114i	0.644053	−	0.147001i	0.111995	−	0.993709i	$-0.464276\pi$
$809$	18.3188	−	4.18114i	0.644053	−	0.147001i	0.532058	+	0.846708i	$0.321419\pi$
$810$	−38.2106	+	30.4720i	−1.34258	+	1.07068i
$811$	−48.6983			−1.71003			−0.855013	−	0.518606i	$-0.826451\pi$
$811$	−48.6983			−1.71003			−0.855013	+	0.518606i	$0.826451\pi$
$812$		0			0
$813$	22.8267			0.800567
$814$	−7.92360	+	6.31886i	−0.277722	+	0.221476i
$815$	−26.3472	+	6.01357i	−0.922902	+	0.210646i
$816$	1.87263	−	8.20451i	0.0655550	−	0.287215i
$817$	1.11596	+	1.39937i	0.0390424	+	0.0489576i
$818$	−26.2954	+	32.9733i	−0.919396	+	1.15289i
$819$	−0.0557861	−	0.244415i	−0.00194932	−	0.00854055i
$820$	−5.07718	−	10.5429i	−0.177303	−	0.368173i
$821$	5.63922	−	2.71570i	0.196810	−	0.0947788i	−0.332883	−	0.942968i	$-0.608021\pi$
$821$	5.63922	−	2.71570i	0.196810	−	0.0947788i	0.529693	+	0.848189i	$0.322307\pi$
$822$	37.2239	+	8.49612i	1.29833	+	0.296336i
$823$	6.51537	−	13.5293i	0.227111	−	0.471602i	−0.756009	−	0.654561i	$-0.772853\pi$
$823$	6.51537	−	13.5293i	0.227111	−	0.471602i	0.983120	+	0.182959i	$0.0585677\pi$
$824$			19.9191i			0.693916i
$825$	−52.7340	−	25.3954i	−1.83596	−	0.884153i
$826$	4.31528	+	3.44132i	0.150148	+	0.119739i
$827$	9.34840	+	7.45510i	0.325076	+	0.259239i	0.772405	−	0.635130i	$-0.219053\pi$
$827$	9.34840	+	7.45510i	0.325076	+	0.259239i	−0.447330	+	0.894369i	$0.647625\pi$
$828$	−0.510885	−	0.246029i	−0.0177545	−	0.00855011i
$829$		−	28.6305i		−	0.994380i	−0.867642	−	0.497190i	$-0.834365\pi$
$829$		−	28.6305i		−	0.994380i	0.867642	−	0.497190i	$-0.165635\pi$
$830$	8.81026	−	18.2947i	0.305809	−	0.635018i
$831$	27.6530	+	6.31163i	0.959273	+	0.218948i
$832$	−11.7615	+	5.66405i	−0.407757	+	0.196365i
$833$	4.53801	+	9.42327i	0.157233	+	0.326497i
$834$	6.23221	+	27.3051i	0.215804	+	0.945498i
$835$	37.0284	−	46.4321i	1.28142	−	1.60685i
$836$	−2.12953	−	2.67035i	−0.0736514	−	0.0923559i
$837$	−2.15375	+	9.43621i	−0.0744446	+	0.326163i
$838$	−43.3025	+	9.88351i	−1.49586	+	0.341420i
$839$	37.7805	−	30.1289i	1.30433	−	1.04017i	0.308284	−	0.951294i	$-0.400245\pi$
$839$	37.7805	−	30.1289i	1.30433	−	1.04017i	0.996043	−	0.0888716i	$-0.0283261\pi$
$840$	−15.3937			−0.531134
$841$		0			0
$842$	−11.7928			−0.406408
$843$	16.6446	−	13.2736i	0.573269	−	0.457167i
$844$	−8.95147	+	2.04311i	−0.308122	+	0.0703269i
$845$	9.77413	−	42.8232i	0.336240	−	1.47316i
$846$	0.912682	+	1.14447i	0.0313787	+	0.0393476i
$847$	1.23945	−	1.55422i	0.0425879	−	0.0534035i
$848$	0.0316959	+	0.138869i	0.00108844	+	0.00476878i
$849$	1.71851	+	3.56853i	0.0589793	+	0.122472i
$850$	−20.5308	+	9.88711i	−0.704200	+	0.339125i
$851$	14.3383	+	3.27263i	0.491512	+	0.112184i
$852$	−0.786035	+	1.63222i	−0.0269291	+	0.0559189i
$853$		−	6.40688i		−	0.219367i	−0.993967	−	0.109684i	$-0.965016\pi$
$853$		−	6.40688i		−	0.219367i	0.993967	−	0.109684i	$-0.0349838\pi$
$854$	−1.01693	−	0.489726i	−0.0347985	−	0.0167581i
$855$	−2.10471	−	1.67845i	−0.0719795	−	0.0574017i
$856$	13.7887	+	10.9961i	0.471288	+	0.375839i
$857$	0.646989	+	0.311573i	0.0221007	+	0.0106431i	0.444901	−	0.895580i	$-0.353239\pi$
$857$	0.646989	+	0.311573i	0.0221007	+	0.0106431i	−0.422801	+	0.906223i	$0.638953\pi$
$858$			9.39612i			0.320778i
$859$	−6.76747	+	14.0528i	−0.230903	+	0.479475i	−0.983939	−	0.178504i	$-0.942874\pi$
$859$	−6.76747	+	14.0528i	−0.230903	+	0.479475i	0.753036	+	0.657979i	$0.228589\pi$
$860$	1.16802	+	0.266594i	0.0398293	+	0.00909078i
$861$	−7.29590	+	3.51352i	−0.248644	+	0.119740i
$862$	0.533213	+	1.10723i	0.0181613	+	0.0377123i
$863$	3.00293	+	13.1567i	0.102221	+	0.447858i	0.999973	+	0.00735754i	$0.00234200\pi$
$863$	3.00293	+	13.1567i	0.102221	+	0.447858i	−0.897752	+	0.440501i	$0.854801\pi$
$864$	−7.62983	+	9.56750i	−0.259572	+	0.325493i
$865$	58.9711	+	73.9474i	2.00508	+	2.51429i
$866$	7.95928	−	34.8719i	0.270467	−	1.18499i
$867$	−25.3458	+	5.78501i	−0.860788	+	0.196469i
$868$	−0.469796	+	0.374650i	−0.0159459	+	0.0127164i
$869$	−27.7700			−0.942033
$870$		0			0
$871$	21.9269			0.742965
$872$	−21.8970	+	17.4623i	−0.741525	+	0.591347i
$873$	1.10040	−	0.251160i	0.0372430	−	0.00850048i
$874$	3.85354	−	16.8835i	0.130348	−	0.571092i
$875$	11.1697	+	14.0064i	0.377605	+	0.473502i
$876$	4.16152	−	5.21838i	0.140605	−	0.176313i
$877$	3.49343	+	15.3057i	0.117965	+	0.516837i	0.999038	+	0.0438569i	$0.0139646\pi$
$877$	3.49343	+	15.3057i	0.117965	+	0.516837i	−0.881073	+	0.472980i	$0.843178\pi$
$878$	3.56775	+	7.40850i	0.120406	+	0.250025i
$879$	−33.5148	+	16.1399i	−1.13043	+	0.544385i
$880$	32.7685	+	7.47919i	1.10462	+	0.252123i
$881$	4.69960	−	9.75882i	0.158334	−	0.328783i	−0.806678	−	0.590992i	$-0.798737\pi$
$881$	4.69960	−	9.75882i	0.158334	−	0.328783i	0.965011	+	0.262209i	$0.0844509\pi$
$882$		−	2.00836i		−	0.0676250i
$883$	−14.8470	−	7.14992i	−0.499640	−	0.240614i	0.167051	−	0.985948i	$-0.446576\pi$
$883$	−14.8470	−	7.14992i	−0.499640	−	0.240614i	−0.666691	+	0.745334i	$0.732290\pi$
$884$	−0.818576	−	0.652793i	−0.0275317	−	0.0219558i
$885$	36.4845	+	29.0954i	1.22641	+	0.978033i
$886$	24.0296	+	11.5720i	0.807290	+	0.388770i
$887$			28.5763i			0.959497i	0.877406	+	0.479748i	$0.159272\pi$
$887$			28.5763i			0.959497i	−0.877406	+	0.479748i	$0.840728\pi$
$888$	−6.79570	+	14.1114i	−0.228049	+	0.473548i
$889$	10.5010	+	2.39679i	0.352193	+	0.0803857i
$890$	51.2057	−	24.6593i	1.71642	−	0.826583i
$891$	11.9735	+	24.8632i	0.401127	+	0.832950i
$892$	2.08964	+	9.15530i	0.0699663	+	0.306542i
$893$	7.97770	−	10.0037i	0.266963	−	0.334762i
$894$	−25.6591	−	32.1755i	−0.858170	−	1.07611i
$895$	−0.599031	+	2.62453i	−0.0200234	+	0.0877283i
$896$	4.15881	−	0.949222i	0.138936	−	0.0317113i
$897$	10.6605	−	8.50149i	0.355945	−	0.283857i
$898$	−36.4825			−1.21744
$899$		0			0
$900$	−1.25236			−0.0417452
$901$	−0.0613404	+	0.0489173i	−0.00204355	+	0.00162967i
$902$	22.5069	−	5.13706i	0.749399	−	0.171045i
$903$	0.184489	−	0.808298i	0.00613940	−	0.0268985i
$904$	−17.0444	−	21.3730i	−0.566887	−	0.710854i
$905$	27.6836	−	34.7141i	0.920234	−	1.15394i
$906$	9.51842	+	41.7029i	0.316228	+	1.38549i
$907$	−14.2572	−	29.6054i	−0.473402	−	0.983030i	−0.991789	−	0.127884i	$-0.959182\pi$
$907$	−14.2572	−	29.6054i	−0.473402	−	0.983030i	0.518387	−	0.855146i	$-0.326533\pi$
$908$	−2.86078	+	1.37768i	−0.0949383	+	0.0457199i
$909$	−0.773680	−	0.176587i	−0.0256614	−	0.00585704i
$910$	2.22365	−	4.61745i	0.0737132	−	0.153067i
$911$			10.9638i			0.363245i	0.983368	+	0.181623i	$0.0581350\pi$
$911$			10.9638i			0.363245i	−0.983368	+	0.181623i	$0.941865\pi$
$912$	12.7262	+	6.12860i	0.421406	+	0.202938i
$913$	−8.96408	−	7.14861i	−0.296668	−	0.236585i
$914$	−0.235545	−	0.187841i	−0.00779115	−	0.00621323i
$915$	−8.59783	−	4.14050i	−0.284236	−	0.136881i
$916$		−	1.00239i		−	0.0331200i
$917$	4.03334	−	8.37531i	0.133193	−	0.276577i
$918$	9.67279	+	2.20775i	0.319250	+	0.0728666i
$919$	−6.90366	+	3.32463i	−0.227731	+	0.109669i	−0.544270	−	0.838910i	$-0.683193\pi$
$919$	−6.90366	+	3.32463i	−0.227731	+	0.109669i	0.316539	+	0.948579i	$0.397479\pi$
$920$	−27.6318	−	57.3781i	−0.910994	−	1.89170i
$921$	9.14675	+	40.0745i	0.301396	+	1.32050i
$922$	13.4800	−	16.9034i	0.443941	−	0.556684i
$923$	−2.06601	−	2.59069i	−0.0680035	−	0.0852736i
$924$	−0.352052	+	1.54244i	−0.0115816	+	0.0507425i
$925$	31.6675	−	7.22790i	1.04122	−	0.237652i
$926$	−4.14341	+	3.30426i	−0.136161	+	0.108585i
$927$	1.61356			0.0529964
$928$		0			0
$929$	9.35988			0.307088			0.153544	−	0.988142i	$-0.450931\pi$
$929$	9.35988			0.307088			0.153544	+	0.988142i	$0.450931\pi$
$930$	13.8780	−	11.0673i	0.455078	−	0.362912i
$931$	−17.1148	+	3.90635i	−0.560916	+	0.128025i
$932$	−1.87263	+	8.20451i	−0.0613399	+	0.268748i
$933$	−34.9294	−	43.8000i	−1.14354	−	1.43395i
$934$	22.4174	−	28.1105i	0.733519	−	0.919803i
$935$	4.11960	+	18.0492i	0.134725	+	0.590271i
$936$	0.479242	+	0.995156i	0.0156645	+	0.0325277i
$937$	7.03103	−	3.38597i	0.229694	−	0.110615i	−0.315497	−	0.948926i	$-0.602171\pi$
$937$	7.03103	−	3.38597i	0.229694	−	0.110615i	0.545191	+	0.838312i	$0.316457\pi$
$938$	−12.5763	−	2.87047i	−0.410632	−	0.0937241i
$939$	8.78193	−	18.2359i	0.286587	−	0.595105i
$940$		−	8.56465i		−	0.279348i
$941$	−25.9013	−	12.4734i	−0.844357	−	0.406621i	−0.0388772	−	0.999244i	$-0.512378\pi$
$941$	−25.9013	−	12.4734i	−0.844357	−	0.406621i	−0.805480	+	0.592623i	$0.798092\pi$
$942$	20.0944	+	16.0248i	0.654711	+	0.522115i
$943$	−26.1923	−	20.8877i	−0.852940	−	0.680197i
$944$	−16.7802	−	8.08090i	−0.546148	−	0.263011i
$945$		−	13.8998i		−	0.452160i
$946$	−1.02553	+	2.12953i	−0.0333428	+	0.0692370i
$947$	−2.25141	−	0.513869i	−0.0731609	−	0.0166985i	0.185784	−	0.982591i	$-0.440518\pi$
$947$	−2.25141	−	0.513869i	−0.0731609	−	0.0166985i	−0.258945	+	0.965892i	$0.583375\pi$
$948$	−7.03803	+	3.38934i	−0.228585	+	0.110081i
$949$	5.29700	+	10.9993i	0.171948	+	0.357054i
$950$	−8.51089	−	37.2886i	−0.276130	−	1.20980i
$951$	−6.65883	+	8.34991i	−0.215927	+	0.270764i
$952$	2.10992	+	2.64575i	0.0683828	+	0.0857493i
$953$	7.68372	−	33.6646i	0.248900	−	1.09050i	−0.683749	−	0.729717i	$-0.739652\pi$
$953$	7.68372	−	33.6646i	0.248900	−	1.09050i	0.932649	−	0.360785i	$-0.117491\pi$
$954$	0.0146878	−	0.00335239i	0.000475534	−	0.000108538i
$955$	−1.64015	+	1.30798i	−0.0530741	+	0.0423252i
$956$	−9.11098			−0.294670
$957$		0			0
$958$	−30.1481			−0.974040
$959$	−9.19355	+	7.33161i	−0.296875	+	0.236750i
$960$	63.3038	−	14.4487i	2.04312	−	0.466329i
$961$	−6.05107	+	26.5115i	−0.195196	+	0.855209i
$962$	−3.25116	−	4.07683i	−0.104822	−	0.131442i
$963$	0.890748	−	1.11696i	0.0287039	−	0.0359936i
$964$	0.729758	+	3.19728i	0.0235039	+	0.102977i
$965$	2.43563	+	5.05765i	0.0784058	+	0.162811i
$966$	−7.22737	+	3.48052i	−0.232537	+	0.111984i
$967$	−50.2266	−	11.4639i	−1.61518	−	0.368654i	−0.682933	−	0.730481i	$-0.739296\pi$
$967$	−50.2266	−	11.4639i	−1.61518	−	0.368654i	−0.932245	+	0.361828i	$0.882153\pi$
$968$	−3.80013	+	7.89104i	−0.122141	+	0.253628i
$969$			7.78017i			0.249935i
$970$	20.7887	+	10.0113i	0.667484	+	0.321443i
$971$	−6.20426	−	4.94773i	−0.199104	−	0.158780i	0.518863	−	0.854858i	$-0.326356\pi$
$971$	−6.20426	−	4.94773i	−0.199104	−	0.158780i	−0.717967	+	0.696077i	$0.754927\pi$
$972$	0.890863	+	0.710439i	0.0285744	+	0.0227874i
$973$	−7.77144	−	3.74253i	−0.249141	−	0.119980i
$974$		−	24.0804i		−	0.771585i
$975$	13.0663	−	27.1325i	0.418457	−	0.868936i
$976$	3.71315	+	0.847503i	0.118855	+	0.0271279i
$977$	−24.8663	+	11.9750i	−0.795545	+	0.383114i	−0.787081	−	0.616850i	$-0.788409\pi$
$977$	−24.8663	+	11.9750i	−0.795545	+	0.383114i	−0.00846415	+	0.999964i	$0.502694\pi$
$978$	−6.50722	−	13.5124i	−0.208078	−	0.432078i
$979$	−7.14095	−	31.2865i	−0.228226	−	0.999922i
$980$	−7.32640	+	9.18701i	−0.234033	+	0.293468i
$981$	1.41454	+	1.77378i	0.0451629	+	0.0566324i
$982$	−10.2364	+	44.8486i	−0.326656	+	1.43117i
$983$	34.4416	−	7.86108i	1.09852	−	0.250729i	0.365413	−	0.930846i	$-0.380928\pi$
$983$	34.4416	−	7.86108i	1.09852	−	0.250729i	0.733104	+	0.680116i	$0.238071\pi$
$984$	27.8938	−	22.2446i	0.889223	−	0.709132i
$985$	52.4674			1.67175
$986$		0			0
$987$	−5.92692			−0.188656
$988$	1.37394	−	1.09568i	0.0437108	−	0.0348582i
$989$	3.34398	−	0.763242i	0.106332	−	0.0242697i
$990$	0.791053	−	3.46583i	0.0251413	−	0.110151i
$991$	0.345183	+	0.432845i	0.0109651	+	0.0137498i	0.787284	−	0.616591i	$-0.211487\pi$
$991$	0.345183	+	0.432845i	0.0109651	+	0.0137498i	−0.776319	+	0.630341i	$0.782915\pi$
$992$	3.00083	−	3.76292i	0.0952764	−	0.119473i
$993$	−12.3937	−	54.3005i	−0.393303	−	1.72317i
$994$	0.845825	+	1.75637i	0.0268279	+	0.0557088i
$995$	71.1483	−	34.2632i	2.25555	−	1.08622i
$996$	−3.14435	−	0.717677i	−0.0996324	−	0.0227405i
$997$	−9.65203	+	20.0426i	−0.305683	+	0.634757i	−0.996059	−	0.0886938i	$-0.971731\pi$
$997$	−9.65203	+	20.0426i	−0.305683	+	0.634757i	0.690376	+	0.723451i	$0.257445\pi$
$998$			47.0307i			1.48873i
$999$	−12.7419	−	6.13617i	−0.403136	−	0.194140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.b.63.2		12
29.2	odd	28		841.2.d.c.571.1		6
29.3	odd	28		841.2.d.c.190.1		6
29.4	even	14		841.2.e.d.196.2		12
29.5	even	14		841.2.e.c.270.1		12
29.6	even	14	inner	841.2.e.b.267.2		12
29.7	even	7		841.2.e.c.651.1		12
29.8	odd	28		841.2.a.e.1.3		3
29.9	even	14		841.2.b.c.840.5		6
29.10	odd	28		29.2.d.a.7.1	✓	6
29.11	odd	28		841.2.d.d.605.1		6
29.12	odd	4		841.2.d.e.778.1		6
29.13	even	14		841.2.e.d.236.1		12
29.14	odd	28		841.2.d.a.574.1		6
29.15	odd	28		841.2.d.e.574.1		6
29.16	even	7		841.2.e.d.236.2		12
29.17	odd	4		841.2.d.a.778.1		6
29.18	odd	28		29.2.d.a.25.1	yes	6
29.19	odd	28		841.2.d.d.645.1		6
29.20	even	7		841.2.b.c.840.2		6
29.21	odd	28		841.2.a.f.1.1		3
29.22	even	14		841.2.e.c.651.2		12
29.23	even	7	inner	841.2.e.b.267.1		12
29.24	even	7		841.2.e.c.270.2		12
29.25	even	7		841.2.e.d.196.1		12
29.26	odd	28		841.2.d.b.190.1		6
29.27	odd	28		841.2.d.b.571.1		6
29.28	even	2	inner	841.2.e.b.63.1		12
87.8	even	28		7569.2.a.r.1.1		3
87.47	even	28		261.2.k.a.199.1		6
87.50	even	28		7569.2.a.p.1.3		3
87.68	even	28		261.2.k.a.181.1		6
116.39	even	28		464.2.u.f.65.1		6
116.47	even	28		464.2.u.f.257.1		6
145.18	even	28		725.2.r.b.199.2		12
145.39	odd	28		725.2.l.b.326.1		6
145.47	even	28		725.2.r.b.199.1		12
145.68	even	28		725.2.r.b.674.1		12
145.97	even	28		725.2.r.b.674.2		12
145.134	odd	28		725.2.l.b.576.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.7.1	✓	6	29.10	odd	28
29.2.d.a.25.1	yes	6	29.18	odd	28
261.2.k.a.181.1		6	87.68	even	28
261.2.k.a.199.1		6	87.47	even	28
464.2.u.f.65.1		6	116.39	even	28
464.2.u.f.257.1		6	116.47	even	28
725.2.l.b.326.1		6	145.39	odd	28
725.2.l.b.576.1		6	145.134	odd	28
725.2.r.b.199.1		12	145.47	even	28
725.2.r.b.199.2		12	145.18	even	28
725.2.r.b.674.1		12	145.68	even	28
725.2.r.b.674.2		12	145.97	even	28
841.2.a.e.1.3		3	29.8	odd	28
841.2.a.f.1.1		3	29.21	odd	28
841.2.b.c.840.2		6	29.20	even	7
841.2.b.c.840.5		6	29.9	even	14
841.2.d.a.574.1		6	29.14	odd	28
841.2.d.a.778.1		6	29.17	odd	4
841.2.d.b.190.1		6	29.26	odd	28
841.2.d.b.571.1		6	29.27	odd	28
841.2.d.c.190.1		6	29.3	odd	28
841.2.d.c.571.1		6	29.2	odd	28
841.2.d.d.605.1		6	29.11	odd	28
841.2.d.d.645.1		6	29.19	odd	28
841.2.d.e.574.1		6	29.15	odd	28
841.2.d.e.778.1		6	29.12	odd	4
841.2.e.b.63.1		12	29.28	even	2	inner
841.2.e.b.63.2		12	1.1	even	1	trivial
841.2.e.b.267.1		12	29.23	even	7	inner
841.2.e.b.267.2		12	29.6	even	14	inner
841.2.e.c.270.1		12	29.5	even	14
841.2.e.c.270.2		12	29.24	even	7
841.2.e.c.651.1		12	29.7	even	7
841.2.e.c.651.2		12	29.22	even	14
841.2.e.d.196.1		12	29.25	even	7
841.2.e.d.196.2		12	29.4	even	14
841.2.e.d.236.1		12	29.13	even	14
841.2.e.d.236.2		12	29.16	even	7
7569.2.a.p.1.3		3	87.50	even	28
7569.2.a.r.1.1		3	87.8	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.974928 - 0.777479i) q^{2} +(-1.75676 + 0.400969i) q^{3} +(-0.0990311 + 0.433884i) q^{4} +(2.52446 + 3.16557i) q^{5} +(-1.40097 + 1.75676i) q^{6} +(-0.153989 - 0.674671i) q^{7} +(1.32288 + 2.74698i) q^{8} +(0.222521 - 0.107160i) q^{9} +O(q^{10})\)	\(q+(0.974928 - 0.777479i) q^{2} +(-1.75676 + 0.400969i) q^{3} +(-0.0990311 + 0.433884i) q^{4} +(2.52446 + 3.16557i) q^{5} +(-1.40097 + 1.75676i) q^{6} +(-0.153989 - 0.674671i) q^{7} +(1.32288 + 2.74698i) q^{8} +(0.222521 - 0.107160i) q^{9} +(4.92233 + 1.12349i) q^{10} +(1.23694 - 2.56853i) q^{11} -0.801938i q^{12} +(1.32155 + 0.636426i) q^{13} +(-0.674671 - 0.538032i) q^{14} +(-5.70416 - 4.54892i) q^{15} +(2.62349 + 1.26341i) q^{16} +1.60388i q^{17} +(0.133627 - 0.277479i) q^{18} +(-2.62453 - 0.599031i) q^{19} +(-1.62349 + 0.781831i) q^{20} +(0.541044 + 1.12349i) q^{21} +(-0.791053 - 3.46583i) q^{22} +(-3.21648 + 4.03334i) q^{23} +(-3.42543 - 4.29535i) q^{24} +(-2.53534 + 11.1081i) q^{25} +(1.78323 - 0.407010i) q^{26} +(3.87849 - 3.09299i) q^{27} +0.307979 q^{28} -9.09783 q^{30} +(-1.52542 + 1.21648i) q^{31} +(-2.40496 + 0.548917i) q^{32} +(-1.14310 + 5.00827i) q^{33} +(1.24698 + 1.56366i) q^{34} +(1.74698 - 2.19064i) q^{35} +(0.0244587 + 0.107160i) q^{36} +(-1.23694 - 2.56853i) q^{37} +(-3.02446 + 1.45650i) q^{38} +(-2.57684 - 0.588146i) q^{39} +(-5.35621 + 11.1223i) q^{40} +6.49396i q^{41} +(1.40097 + 0.674671i) q^{42} +(-0.519820 - 0.414542i) q^{43} +(0.991949 + 0.791053i) q^{44} +(0.900969 + 0.433884i) q^{45} +6.43296i q^{46} +(-2.06226 + 4.28232i) q^{47} +(-5.11543 - 1.16756i) q^{48} +(5.87531 - 2.82940i) q^{49} +(6.16451 + 12.8007i) q^{50} +(-0.643104 - 2.81762i) q^{51} +(-0.407010 + 0.510374i) q^{52} +(0.0304995 + 0.0382451i) q^{53} +(1.37651 - 6.03089i) q^{54} +(11.2535 - 2.56853i) q^{55} +(1.64960 - 1.31551i) q^{56} +4.85086 q^{57} -6.39612 q^{59} +(2.53859 - 2.02446i) q^{60} +(1.27518 - 0.291053i) q^{61} +(-0.541385 + 2.37196i) q^{62} +(-0.106564 - 0.133627i) q^{63} +(-5.54892 + 6.95812i) q^{64} +(1.32155 + 5.79010i) q^{65} +(2.77938 + 5.77144i) q^{66} +(13.4683 - 6.48599i) q^{67} +(-0.695895 - 0.158834i) q^{68} +(4.03334 - 8.37531i) q^{69} -3.49396i q^{70} +(-2.03534 - 0.980170i) q^{71} +(0.588735 + 0.469501i) q^{72} +(6.50722 + 5.18933i) q^{73} +(-3.20291 - 1.54244i) q^{74} -20.5308i q^{75} +(0.519820 - 1.07942i) q^{76} +(-1.92339 - 0.439001i) q^{77} +(-2.96950 + 1.43004i) q^{78} +(-4.22643 - 8.77628i) q^{79} +(2.62349 + 11.4943i) q^{80} +(-6.03534 + 7.56808i) q^{81} +(5.04892 + 6.33114i) q^{82} +(0.894928 - 3.92094i) q^{83} +(-0.541044 + 0.123490i) q^{84} +(-5.07718 + 4.04892i) q^{85} -0.829085 q^{86} +8.69202 q^{88} +(8.80082 - 7.01842i) q^{89} +(1.21572 - 0.277479i) q^{90} +(0.225873 - 0.989616i) q^{91} +(-1.43147 - 1.79500i) q^{92} +(2.19202 - 2.74871i) q^{93} +(1.31886 + 5.77832i) q^{94} +(-4.72923 - 9.82036i) q^{95} +(4.00484 - 1.92863i) q^{96} +(4.45544 + 1.01693i) q^{97} +(3.52821 - 7.32640i) q^{98} -0.704103i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9	\( 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9} + 24 q^{13} + 22 q^{16} - 10 q^{20} + 2 q^{22} - 14 q^{24} - 6 q^{25} + 24 q^{28} - 36 q^{30} - 30 q^{33} - 4 q^{34} + 2 q^{35} - 18 q^{36} - 18 q^{38} + 8 q^{42} + 2 q^{45} - 2 q^{49} - 24 q^{51} - 34 q^{52} + 20 q^{53} + 26 q^{54} + 4 q^{57} - 112 q^{59} - 20 q^{62} + 40 q^{63} - 30 q^{64} + 24 q^{65} + 60 q^{67} - 12 q^{74} - 16 q^{78} + 22 q^{80} - 48 q^{81} + 24 q^{82} - 36 q^{83} + 32 q^{86} + 84 q^{88} + 46 q^{91} - 28 q^{92} + 6 q^{93} + 30 q^{94} + 4 q^{96}+O(q^{100}) \) 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9 + 24 * q^13 + 22 * q^16 - 10 * q^20 + 2 * q^22 - 14 * q^24 - 6 * q^25 + 24 * q^28 - 36 * q^30 - 30 * q^33 - 4 * q^34 + 2 * q^35 - 18 * q^36 - 18 * q^38 + 8 * q^42 + 2 * q^45 - 2 * q^49 - 24 * q^51 - 34 * q^52 + 20 * q^53 + 26 * q^54 + 4 * q^57 - 112 * q^59 - 20 * q^62 + 40 * q^63 - 30 * q^64 + 24 * q^65 + 60 * q^67 - 12 * q^74 - 16 * q^78 + 22 * q^80 - 48 * q^81 + 24 * q^82 - 36 * q^83 + 32 * q^86 + 84 * q^88 + 46 * q^91 - 28 * q^92 + 6 * q^93 + 30 * q^94 + 4 * q^96

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