LMFDB - Embedded newform 402.2.n.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [402,2,Mod(11,402)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(402, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 59]))

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

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

chi := DirichletCharacter("402.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 402 = 2 \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	402.n (of order $66$, degree $20$, 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:	$3.20998616126$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	402.11
Dual form			402.2.n.b.329.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 - 0.945001i) q^{2} +(-1.44867 + 0.949398i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(-2.76497 + 0.811870i) q^{5} +(1.37100 + 1.05848i) q^{6} +(-0.155035 + 0.804400i) q^{7} +(0.841254 + 0.540641i) q^{8} +(1.19729 - 2.75073i) q^{9} +O(q^{10})$	\(q+(-0.327068 - 0.945001i) q^{2} +(-1.44867 + 0.949398i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(-2.76497 + 0.811870i) q^{5} +(1.37100 + 1.05848i) q^{6} +(-0.155035 + 0.804400i) q^{7} +(0.841254 + 0.540641i) q^{8} +(1.19729 - 2.75073i) q^{9} +(1.67155 + 2.34737i) q^{10} +(-1.62440 - 1.54886i) q^{11} +(0.551852 - 1.64179i) q^{12} +(3.13312 - 0.149249i) q^{13} +(0.810866 - 0.116585i) q^{14} +(3.23475 - 3.80119i) q^{15} +(0.235759 - 0.971812i) q^{16} +(2.19338 - 2.78911i) q^{17} +(-2.99103 - 0.231762i) q^{18} +(2.01695 - 0.388735i) q^{19} +(1.67155 - 2.34737i) q^{20} +(-0.539101 - 1.31250i) q^{21} +(-0.932387 + 2.04164i) q^{22} +(0.705097 - 7.38411i) q^{23} +(-1.73198 + 0.0154745i) q^{24} +(2.77968 - 1.78639i) q^{25} +(-1.16578 - 2.91199i) q^{26} +(0.877062 + 5.12160i) q^{27} +(-0.375381 - 0.728137i) q^{28} +(0.735210 - 0.424474i) q^{29} +(-4.65011 - 1.81359i) q^{30} +(0.832006 + 0.0396333i) q^{31} +(-0.995472 + 0.0950560i) q^{32} +(3.82370 + 0.701587i) q^{33} +(-3.35310 - 1.16052i) q^{34} +(-0.224399 - 2.35001i) q^{35} +(0.759256 + 2.90233i) q^{36} +(3.36274 - 5.82443i) q^{37} +(-1.02703 - 1.77887i) q^{38} +(-4.39716 + 3.19079i) q^{39} +(-2.76497 - 0.811870i) q^{40} +(0.731352 - 0.292789i) q^{41} +(-1.06399 + 0.938727i) q^{42} +(-3.99850 - 0.574897i) q^{43} +(2.23431 + 0.213350i) q^{44} +(-1.07723 + 8.57773i) q^{45} +(-7.20860 + 1.74879i) q^{46} +(-2.27505 - 1.62006i) q^{47} +(0.581099 + 1.63166i) q^{48} +(5.87555 + 2.35222i) q^{49} +(-2.59729 - 2.04253i) q^{50} +(-0.529509 + 6.12290i) q^{51} +(-2.37054 + 2.05408i) q^{52} +(-0.388048 - 2.69893i) q^{53} +(4.55305 - 2.50394i) q^{54} +(5.74890 + 2.96376i) q^{55} +(-0.565315 + 0.592886i) q^{56} +(-2.55283 + 2.47803i) q^{57} +(-0.641591 - 0.555942i) q^{58} +(-3.20330 + 4.98444i) q^{59} +(-0.192942 + 4.98753i) q^{60} +(-3.27565 - 3.43540i) q^{61} +(-0.234669 - 0.799209i) q^{62} +(2.02706 + 1.38956i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-8.54182 + 2.95635i) q^{65} +(-0.587611 - 3.84287i) q^{66} +(-8.11833 + 1.04537i) q^{67} +3.54825i q^{68} +(5.98900 + 11.3665i) q^{69} +(-2.14737 + 0.980671i) q^{70} +(4.78637 + 6.08637i) q^{71} +(2.49438 - 1.66676i) q^{72} +(11.9980 - 11.4401i) q^{73} +(-6.60393 - 1.27280i) q^{74} +(-2.33084 + 5.22692i) q^{75} +(-1.34513 + 1.55236i) q^{76} +(1.49774 - 1.06654i) q^{77} +(4.45347 + 3.11171i) q^{78} +(7.99055 - 15.4995i) q^{79} +(0.137117 + 2.87844i) q^{80} +(-6.13301 - 6.58682i) q^{81} +(-0.515888 - 0.595366i) q^{82} +(-2.97756 - 0.722348i) q^{83} +(1.23510 + 0.698445i) q^{84} +(-3.80025 + 9.49257i) q^{85} +(0.764502 + 3.96661i) q^{86} +(-0.662082 + 1.31293i) q^{87} +(-0.529154 - 2.18120i) q^{88} +(10.2666 + 4.68861i) q^{89} +(8.45829 - 1.78751i) q^{90} +(-0.365688 + 2.54342i) q^{91} +(4.01031 + 6.24016i) q^{92} +(-1.24293 + 0.732489i) q^{93} +(-0.786860 + 2.67980i) q^{94} +(-5.26120 + 2.71234i) q^{95} +(1.35186 - 1.08280i) q^{96} +(-13.1221 - 7.57605i) q^{97} +(0.301141 - 6.32174i) q^{98} +(-6.20537 + 2.61385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 11 q^{2} - q^{3} + 11 q^{4} - q^{6} + 6 q^{7} - 22 q^{8} - q^{9}+O(q^{10}) $ 220 * q + 11 * q^2 - q^3 + 11 * q^4 - q^6 + 6 * q^7 - 22 * q^8 - q^9	\( 220 q + 11 q^{2} - q^{3} + 11 q^{4} - q^{6} + 6 q^{7} - 22 q^{8} - q^{9} - 6 q^{11} - 9 q^{12} - 6 q^{13} + 22 q^{14} - 4 q^{15} + 11 q^{16} - 30 q^{17} - 9 q^{18} + 25 q^{19} + 99 q^{21} + 12 q^{22} - 8 q^{23} + 10 q^{24} - 10 q^{25} - 16 q^{26} - 28 q^{27} - 6 q^{28} - 6 q^{29} + 5 q^{30} - 2 q^{31} + 11 q^{32} - 20 q^{33} - 3 q^{34} - 170 q^{35} - q^{36} + 10 q^{37} + 3 q^{38} - 3 q^{39} + 74 q^{41} + 16 q^{42} - 22 q^{43} - 6 q^{44} + 37 q^{45} + 30 q^{46} + 12 q^{47} + 10 q^{48} - 27 q^{49} + 27 q^{50} - 3 q^{51} + 22 q^{52} + 2 q^{53} + 25 q^{54} - 144 q^{55} + 6 q^{56} + 16 q^{57} - 44 q^{58} + 33 q^{59} - q^{60} - 148 q^{61} + 22 q^{62} + 38 q^{63} - 22 q^{64} + 5 q^{66} - 24 q^{67} - 80 q^{69} - 154 q^{70} - 18 q^{71} - 12 q^{72} - 167 q^{73} - 122 q^{74} - 32 q^{75} - 50 q^{76} + 44 q^{77} - 18 q^{78} + 12 q^{79} + 47 q^{81} - 38 q^{82} + 165 q^{83} + 39 q^{84} - 30 q^{85} + 3 q^{86} - 98 q^{87} - 6 q^{88} + 22 q^{89} + 6 q^{90} + 4 q^{91} + 124 q^{93} + 22 q^{94} - 142 q^{95} + 2 q^{96} - 69 q^{97} - 27 q^{98} - 57 q^{99}+O(q^{100}) \) 220 * q + 11 * q^2 - q^3 + 11 * q^4 - q^6 + 6 * q^7 - 22 * q^8 - q^9 - 6 * q^11 - 9 * q^12 - 6 * q^13 + 22 * q^14 - 4 * q^15 + 11 * q^16 - 30 * q^17 - 9 * q^18 + 25 * q^19 + 99 * q^21 + 12 * q^22 - 8 * q^23 + 10 * q^24 - 10 * q^25 - 16 * q^26 - 28 * q^27 - 6 * q^28 - 6 * q^29 + 5 * q^30 - 2 * q^31 + 11 * q^32 - 20 * q^33 - 3 * q^34 - 170 * q^35 - q^36 + 10 * q^37 + 3 * q^38 - 3 * q^39 + 74 * q^41 + 16 * q^42 - 22 * q^43 - 6 * q^44 + 37 * q^45 + 30 * q^46 + 12 * q^47 + 10 * q^48 - 27 * q^49 + 27 * q^50 - 3 * q^51 + 22 * q^52 + 2 * q^53 + 25 * q^54 - 144 * q^55 + 6 * q^56 + 16 * q^57 - 44 * q^58 + 33 * q^59 - q^60 - 148 * q^61 + 22 * q^62 + 38 * q^63 - 22 * q^64 + 5 * q^66 - 24 * q^67 - 80 * q^69 - 154 * q^70 - 18 * q^71 - 12 * q^72 - 167 * q^73 - 122 * q^74 - 32 * q^75 - 50 * q^76 + 44 * q^77 - 18 * q^78 + 12 * q^79 + 47 * q^81 - 38 * q^82 + 165 * q^83 + 39 * q^84 - 30 * q^85 + 3 * q^86 - 98 * q^87 - 6 * q^88 + 22 * q^89 + 6 * q^90 + 4 * q^91 + 124 * q^93 + 22 * q^94 - 142 * q^95 + 2 * q^96 - 69 * q^97 - 27 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/402\mathbb{Z}\right)^\times$.

$n$	$269$	$337$
$\chi(n)$	$-1$	$e\left(\frac{59}{66}\right)$

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 $

$2$	−0.327068	−	0.945001i	−0.231272	−	0.668216i
$2$	−0.327068	−	0.945001i	−0.231272	−	0.668216i
$3$	−1.44867	+	0.949398i	−0.836390	+	0.548135i
$3$	−1.44867	+	0.949398i	−0.836390	+	0.548135i
$4$	−0.786053	+	0.618159i	−0.393027	+	0.309079i
$5$	−2.76497	+	0.811870i	−1.23653	+	0.363079i	−0.833712	−	0.552199i	$-0.813789\pi$
$5$	−2.76497	+	0.811870i	−1.23653	+	0.363079i	−0.402822	+	0.915278i	$0.631971\pi$
$6$	1.37100	+	1.05848i	0.559706	+	0.432121i
$7$	−0.155035	+	0.804400i	−0.0585979	+	0.304035i	−0.999389	−	0.0349523i	$-0.988872\pi$
$7$	−0.155035	+	0.804400i	−0.0585979	+	0.304035i	0.940791	+	0.338987i	$0.110084\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	1.19729	−	2.75073i	0.399096	−	0.916909i
$10$	1.67155	+	2.34737i	0.528591	+	0.742302i
$11$	−1.62440	−	1.54886i	−0.489775	−	0.466999i	0.404487	−	0.914544i	$-0.367450\pi$
$11$	−1.62440	−	1.54886i	−0.489775	−	0.466999i	−0.894262	+	0.447544i	$0.852299\pi$
$12$	0.551852	−	1.64179i	0.159306	−	0.473943i
$13$	3.13312	−	0.149249i	0.868971	−	0.0413942i	0.391641	−	0.920118i	$-0.371908\pi$
$13$	3.13312	−	0.149249i	0.868971	−	0.0413942i	0.477330	+	0.878724i	$0.341605\pi$
$14$	0.810866	−	0.116585i	0.216713	−	0.0311586i
$15$	3.23475	−	3.80119i	0.835208	−	0.981464i
$16$	0.235759	−	0.971812i	0.0589397	−	0.242953i
$17$	2.19338	−	2.78911i	0.531974	−	0.676460i	−0.443576	−	0.896237i	$-0.646291\pi$
$17$	2.19338	−	2.78911i	0.531974	−	0.676460i	0.975550	+	0.219777i	$0.0705330\pi$
$18$	−2.99103	−	0.231762i	−0.704994	−	0.0546269i
$19$	2.01695	−	0.388735i	0.462719	−	0.0891818i	0.0474366	−	0.998874i	$-0.484895\pi$
$19$	2.01695	−	0.388735i	0.462719	−	0.0891818i	0.415283	+	0.909692i	$0.363683\pi$
$20$	1.67155	−	2.34737i	0.373770	−	0.524887i
$21$	−0.539101	−	1.31250i	−0.117641	−	0.286411i
$22$	−0.932387	+	2.04164i	−0.198786	+	0.435280i
$23$	0.705097	−	7.38411i	0.147023	−	1.53969i	−0.557599	−	0.830110i	$-0.688277\pi$
$23$	0.705097	−	7.38411i	0.147023	−	1.53969i	0.704622	−	0.709583i	$-0.251116\pi$
$24$	−1.73198	+	0.0154745i	−0.353539	+	0.00315872i
$25$	2.77968	−	1.78639i	0.555937	−	0.357279i
$26$	−1.16578	−	2.91199i	−0.228629	−	0.571087i
$27$	0.877062	+	5.12160i	0.168791	+	0.985652i
$28$	−0.375381	−	0.728137i	−0.0709403	−	0.137605i
$29$	0.735210	−	0.424474i	0.136525	−	0.0788228i	−0.430182	−	0.902742i	$-0.641551\pi$
$29$	0.735210	−	0.424474i	0.136525	−	0.0788228i	0.566707	+	0.823920i	$0.308217\pi$
$30$	−4.65011	−	1.81359i	−0.848990	−	0.331115i
$31$	0.832006	+	0.0396333i	0.149433	+	0.00711836i	0.122165	−	0.992510i	$-0.461016\pi$
$31$	0.832006	+	0.0396333i	0.149433	+	0.00711836i	0.0272677	+	0.999628i	$0.491319\pi$
$32$	−0.995472	+	0.0950560i	−0.175976	+	0.0168037i
$33$	3.82370	+	0.701587i	0.665622	+	0.122131i
$34$	−3.35310	−	1.16052i	−0.575052	−	0.199027i
$35$	−0.224399	−	2.35001i	−0.0379304	−	0.397225i
$36$	0.759256	+	2.90233i	0.126543	+	0.483722i
$37$	3.36274	−	5.82443i	0.552830	−	0.957530i	−0.445238	−	0.895412i	$-0.646881\pi$
$37$	3.36274	−	5.82443i	0.552830	−	0.957530i	0.998069	−	0.0621182i	$-0.0197856\pi$
$38$	−1.02703	−	1.77887i	−0.166607	−	0.288571i
$39$	−4.39716	+	3.19079i	−0.704109	+	0.510935i
$40$	−2.76497	−	0.811870i	−0.437181	−	0.128368i
$41$	0.731352	−	0.292789i	0.114218	−	0.0457260i	−0.313850	−	0.949473i	$-0.601619\pi$
$41$	0.731352	−	0.292789i	0.114218	−	0.0457260i	0.428068	+	0.903747i	$0.359195\pi$
$42$	−1.06399	+	0.938727i	−0.164177	+	0.144849i
$43$	−3.99850	−	0.574897i	−0.609765	−	0.0876710i	−0.169487	−	0.985532i	$-0.554211\pi$
$43$	−3.99850	−	0.574897i	−0.609765	−	0.0876710i	−0.440278	+	0.897861i	$0.645120\pi$
$44$	2.23431	+	0.213350i	0.336834	+	0.0321638i
$45$	−1.07723	+	8.57773i	−0.160585	+	1.27869i
$46$	−7.20860	+	1.74879i	−1.06285	+	0.257845i
$47$	−2.27505	−	1.62006i	−0.331851	−	0.236310i	0.401970	−	0.915653i	$-0.368326\pi$
$47$	−2.27505	−	1.62006i	−0.331851	−	0.236310i	−0.733821	+	0.679343i	$0.762265\pi$
$48$	0.581099	+	1.63166i	0.0838744	+	0.235510i
$49$	5.87555	+	2.35222i	0.839365	+	0.336031i
$50$	−2.59729	−	2.04253i	−0.367312	−	0.288857i
$51$	−0.529509	+	6.12290i	−0.0741461	+	0.857377i
$52$	−2.37054	+	2.05408i	−0.328735	+	0.284850i
$53$	−0.388048	−	2.69893i	−0.0533024	−	0.370727i	−0.998961	−	0.0455662i	$-0.985491\pi$
$53$	−0.388048	−	2.69893i	−0.0533024	−	0.370727i	0.945659	−	0.325160i	$-0.105418\pi$
$54$	4.55305	−	2.50394i	0.619592	−	0.340742i
$55$	5.74890	+	2.96376i	0.775181	+	0.399634i
$56$	−0.565315	+	0.592886i	−0.0755435	+	0.0792277i
$57$	−2.55283	+	2.47803i	−0.338130	+	0.328224i
$58$	−0.641591	−	0.555942i	−0.0842451	−	0.0729988i
$59$	−3.20330	+	4.98444i	−0.417035	+	0.648918i	−0.984683	−	0.174352i	$-0.944217\pi$
$59$	−3.20330	+	4.98444i	−0.417035	+	0.648918i	0.567649	+	0.823271i	$0.307853\pi$
$60$	−0.192942	+	4.98753i	−0.0249087	+	0.643887i
$61$	−3.27565	−	3.43540i	−0.419404	−	0.439858i	0.479807	−	0.877374i	$-0.340707\pi$
$61$	−3.27565	−	3.43540i	−0.419404	−	0.439858i	−0.899211	+	0.437516i	$0.855858\pi$
$62$	−0.234669	−	0.799209i	−0.0298030	−	0.101500i
$63$	2.02706	+	1.38956i	0.255386	+	0.175068i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−8.54182	+	2.95635i	−1.05948	+	0.366691i
$66$	−0.587611	−	3.84287i	−0.0723299	−	0.473025i
$67$	−8.11833	+	1.04537i	−0.991811	+	0.127712i
$67$	−8.11833	+	1.04537i	−0.991811	+	0.127712i
$68$			3.54825i			0.430289i
$69$	5.98900	+	11.3665i	0.720991	+	1.36837i
$70$	−2.14737	+	0.980671i	−0.256660	+	0.117213i
$71$	4.78637	+	6.08637i	0.568038	+	0.722319i	0.982190	−	0.187888i	$-0.0601644\pi$
$71$	4.78637	+	6.08637i	0.568038	+	0.722319i	−0.414152	+	0.910208i	$0.635922\pi$
$72$	2.49438	−	1.66676i	0.293965	−	0.196429i
$73$	11.9980	−	11.4401i	1.40426	−	1.33896i	0.534787	−	0.844987i	$-0.320392\pi$
$73$	11.9980	−	11.4401i	1.40426	−	1.33896i	0.869476	−	0.493975i	$-0.164457\pi$
$74$	−6.60393	−	1.27280i	−0.767692	−	0.147960i
$75$	−2.33084	+	5.22692i	−0.269143	+	0.603553i
$76$	−1.34513	+	1.55236i	−0.154297	+	0.178068i
$77$	1.49774	−	1.06654i	0.170684	−	0.121543i
$78$	4.45347	+	3.11171i	0.504256	+	0.352332i
$79$	7.99055	−	15.4995i	0.899008	−	1.74383i	0.276902	−	0.960898i	$-0.410692\pi$
$79$	7.99055	−	15.4995i	0.899008	−	1.74383i	0.622106	−	0.782933i	$-0.286277\pi$
$80$	0.137117	+	2.87844i	0.0153301	+	0.321819i
$81$	−6.13301	−	6.58682i	−0.681445	−	0.731869i
$82$	−0.515888	−	0.595366i	−0.0569703	−	0.0657472i
$83$	−2.97756	−	0.722348i	−0.326829	−	0.0792880i	0.0689871	−	0.997618i	$-0.478023\pi$
$83$	−2.97756	−	0.722348i	−0.326829	−	0.0792880i	−0.395817	+	0.918330i	$0.629538\pi$
$84$	1.23510	+	0.698445i	0.134760	+	0.0762066i
$85$	−3.80025	+	9.49257i	−0.412195	+	1.02961i
$86$	0.764502	+	3.96661i	0.0824384	+	0.427731i
$87$	−0.662082	+	1.31293i	−0.0709826	+	0.140761i
$88$	−0.529154	−	2.18120i	−0.0564080	−	0.232517i
$89$	10.2666	+	4.68861i	1.08826	+	0.496991i	0.877025	−	0.480444i	$-0.159525\pi$
$89$	10.2666	+	4.68861i	1.08826	+	0.496991i	0.211234	+	0.977436i	$0.432252\pi$
$90$	8.45829	−	1.78751i	0.891582	−	0.188421i
$91$	−0.365688	+	2.54342i	−0.0383346	+	0.266623i
$92$	4.01031	+	6.24016i	0.418104	+	0.650582i
$93$	−1.24293	+	0.732489i	−0.128886	+	0.0759556i
$94$	−0.786860	+	2.67980i	−0.0811584	+	0.276400i
$95$	−5.26120	+	2.71234i	−0.539788	+	0.278280i
$96$	1.35186	−	1.08280i	0.137974	−	0.110513i
$97$	−13.1221	−	7.57605i	−1.33235	−	0.769231i	−0.346689	−	0.937980i	$-0.612694\pi$
$97$	−13.1221	−	7.57605i	−1.33235	−	0.769231i	−0.985659	+	0.168749i	$0.946027\pi$
$98$	0.301141	−	6.32174i	0.0304199	−	0.638592i
$99$	−6.20537	+	2.61385i	−0.623663	+	0.262702i
$100$	−1.08070	+	3.12249i	−0.108070	+	0.312249i
$101$	0.401787	−	1.16089i	0.0399793	−	0.115512i	−0.923245	−	0.384213i	$-0.874473\pi$
$101$	0.401787	−	1.16089i	0.0399793	−	0.115512i	0.963224	+	0.268700i	$0.0865941\pi$
$102$	5.95933	−	1.50222i	0.590062	−	0.148742i
$103$	−0.272086	+	5.71178i	−0.0268094	+	0.562798i	0.945006	+	0.327054i	$0.106056\pi$
$103$	−0.272086	+	5.71178i	−0.0268094	+	0.562798i	−0.971815	+	0.235744i	$0.924247\pi$
$104$	2.71644	+	1.56834i	0.266369	+	0.153788i
$105$	2.55618	+	3.19135i	0.249457	+	0.311444i
$106$	−2.42357	+	1.24944i	−0.235398	+	0.121356i
$107$	−2.47761	+	8.43795i	−0.239519	+	0.815727i	0.748730	+	0.662875i	$0.230664\pi$
$107$	−2.47761	+	8.43795i	−0.239519	+	0.815727i	−0.988249	+	0.152852i	$0.951154\pi$
$108$	−3.85538	−	3.48368i	−0.370984	−	0.335218i
$109$	5.99546	+	9.32911i	0.574260	+	0.893567i	0.999936	−	0.0113091i	$-0.00359989\pi$
$109$	5.99546	+	9.32911i	0.574260	+	0.893567i	−0.425676	+	0.904876i	$0.639964\pi$
$110$	0.920478	−	6.40206i	0.0877641	−	0.610413i
$111$	0.658208	+	11.6302i	0.0624744	+	1.10389i
$112$	0.745174	+	0.340310i	0.0704123	+	0.0321562i
$113$	−4.31715	−	17.7955i	−0.406123	−	1.67406i	−0.696820	−	0.717246i	$-0.745402\pi$
$113$	−4.31715	−	17.7955i	−0.406123	−	1.67406i	0.290697	−	0.956815i	$-0.406113\pi$
$114$	3.17669	+	1.60194i	0.297524	+	0.150035i
$115$	4.04536	+	20.9893i	0.377232	+	1.95726i
$116$	−0.315522	+	0.788135i	−0.0292955	+	0.0731765i
$117$	3.34070	−	8.79705i	0.308848	−	0.813288i
$118$	5.75799	+	1.39687i	0.530066	+	0.128593i
$119$	1.90351	+	2.19677i	0.174495	+	0.201377i
$120$	4.77632	−	1.44893i	0.436017	−	0.132269i
$121$	−0.283700	−	5.95560i	−0.0257909	−	0.541418i
$122$	−2.17510	+	4.21910i	−0.196924	+	0.381979i
$123$	−0.781514	+	1.11850i	−0.0704667	+	0.100852i
$124$	−0.678500	+	0.483158i	−0.0609311	+	0.0433889i
$125$	3.20014	−	3.69316i	0.286229	−	0.330326i
$126$	0.650145	−	2.37006i	0.0579196	−	0.211141i
$127$	−15.5771	−	3.00223i	−1.38224	−	0.266405i	−0.556684	−	0.830724i	$-0.687927\pi$
$127$	−15.5771	−	3.00223i	−1.38224	−	0.266405i	−0.825557	+	0.564319i	$0.809139\pi$
$128$	0.723734	−	0.690079i	0.0639697	−	0.0609949i
$129$	6.33831	−	2.96333i	0.558057	−	0.260907i
$130$	5.58751	+	7.10510i	0.490057	+	0.623159i
$131$	5.15187	−	2.35278i	0.450121	−	0.205564i	−0.177438	−	0.984132i	$-0.556781\pi$
$131$	5.15187	−	2.35278i	0.450121	−	0.205564i	0.627560	+	0.778568i	$0.284054\pi$
$132$	−3.43933	+	1.81217i	−0.299355	+	0.157729i
$133$			1.68270i			0.145909i
$134$	3.64312	+	7.32992i	0.314717	+	0.633209i
$135$	−6.58313	−	13.4490i	−0.566585	−	1.15751i
$136$	3.35310	−	1.16052i	0.287526	−	0.0995137i
$137$	7.20712	+	15.7814i	0.615746	+	1.34829i	0.918574	+	0.395250i	$0.129342\pi$
$137$	7.20712	+	15.7814i	0.615746	+	1.34829i	−0.302828	+	0.953045i	$0.597931\pi$
$138$	8.78259	−	9.37725i	0.747623	−	0.798244i
$139$	2.26058	+	7.69883i	0.191740	+	0.653007i	0.998102	+	0.0615841i	$0.0196153\pi$
$139$	2.26058	+	7.69883i	0.191740	+	0.653007i	−0.806362	+	0.591422i	$0.798567\pi$
$140$	1.62907	+	1.70852i	0.137682	+	0.144396i
$141$	4.83388	+	0.186998i	0.407086	+	0.0157481i
$142$	4.18615	−	6.51378i	0.351294	−	0.546625i
$143$	−5.32060	−	4.61033i	−0.444931	−	0.385535i
$144$	−2.39092	−	1.81205i	−0.199243	−	0.151004i
$145$	−1.68822	+	1.77055i	−0.140199	+	0.147036i
$146$	−14.7351	−	7.59646i	−1.21948	−	0.628687i
$147$	−10.7449	+	2.17065i	−0.886226	+	0.179032i
$148$	0.957134	+	6.65702i	0.0786760	+	0.547203i
$149$	14.0778	−	12.1985i	1.15330	−	0.999341i	0.153363	−	0.988170i	$-0.450990\pi$
$149$	14.0778	−	12.1985i	1.15330	−	0.999341i	0.999938	−	0.0111709i	$-0.00355588\pi$
$150$	5.70179	+	0.493091i	0.465549	+	0.0402607i
$151$	−10.4317	−	8.20361i	−0.848923	−	0.667600i	0.0958250	−	0.995398i	$-0.469451\pi$
$151$	−10.4317	−	8.20361i	−0.848923	−	0.667600i	−0.944748	+	0.327798i	$0.893693\pi$
$152$	1.90693	+	0.763419i	0.154672	+	0.0619215i
$153$	−5.04599	−	9.37277i	−0.407944	−	0.757744i
$154$	−1.49774	−	1.06654i	−0.120692	−	0.0859441i
$155$	−2.33265	+	0.565895i	−0.187363	+	0.0454538i
$156$	1.48398	−	5.22627i	0.118814	−	0.418437i
$157$	5.32555	+	0.508528i	0.425025	+	0.0405850i	0.305377	−	0.952231i	$-0.401217\pi$
$157$	5.32555	+	0.508528i	0.425025	+	0.0405850i	0.119648	+	0.992816i	$0.461823\pi$
$158$	−17.2605	−	2.48169i	−1.37317	−	0.197432i
$159$	3.12451	+	3.54145i	0.247790	+	0.280855i
$160$	2.67528	−	1.07102i	0.211500	−	0.0846716i
$161$	5.83046	+	1.71198i	0.459505	+	0.134923i
$162$	−4.21864	+	7.95004i	−0.331448	+	0.624614i
$163$	−3.23221	−	5.59835i	−0.253166	−	0.438497i	0.711230	−	0.702960i	$-0.248139\pi$
$163$	−3.23221	−	5.59835i	−0.253166	−	0.438497i	−0.964396	+	0.264463i	$0.914805\pi$
$164$	−0.393891	+	0.682240i	−0.0307577	+	0.0532740i
$165$	−11.1420	+	1.16448i	−0.867407	+	0.0906546i
$166$	0.291245	+	3.05005i	0.0226050	+	0.236730i
$167$	5.90843	+	2.04493i	0.457208	+	0.158241i	0.545958	−	0.837813i	$-0.316166\pi$
$167$	5.90843	+	2.04493i	0.457208	+	0.158241i	−0.0887499	+	0.996054i	$0.528287\pi$
$168$	0.256071	−	1.39560i	0.0197563	−	0.107673i
$169$	−3.14698	+	0.300500i	−0.242075	+	0.0231154i
$170$	10.2134	+	0.486526i	0.783334	+	0.0373148i
$171$	1.34556	−	6.01350i	0.102898	−	0.459864i
$172$	3.49841	−	2.01981i	0.266751	−	0.154009i
$173$	−8.81547	−	17.0996i	−0.670227	−	1.30006i	−0.941323	−	0.337507i	$-0.890416\pi$
$173$	−8.81547	−	17.0996i	−0.670227	−	1.30006i	0.271095	−	0.962552i	$-0.412614\pi$
$174$	1.45726	+	0.196251i	0.110475	+	0.0148777i
$175$	1.00603	+	2.51293i	0.0760484	+	0.189960i
$176$	−1.88817	+	1.21345i	−0.142326	+	0.0914674i
$177$	−0.0916867	−	10.2620i	−0.00689160	−	0.771340i
$178$	1.07286	−	11.2355i	0.0804139	−	0.842133i
$179$	−10.2214	+	22.3818i	−0.763986	+	1.67290i	−0.0245215	+	0.999699i	$0.507806\pi$
$179$	−10.2214	+	22.3818i	−0.763986	+	1.67290i	−0.739464	+	0.673196i	$0.764921\pi$
$180$	−4.45564	−	7.40846i	−0.332104	−	0.552194i
$181$	1.92054	−	2.69702i	0.142753	−	0.200468i	−0.737009	−	0.675883i	$-0.763763\pi$
$181$	1.92054	−	2.69702i	0.142753	−	0.200468i	0.879762	+	0.475415i	$0.157702\pi$
$182$	2.52314	−	0.486295i	0.187027	−	0.0360466i
$183$	8.00689	+	1.86687i	0.591887	+	0.138003i
$184$	4.58531	−	5.83070i	0.338034	−	0.429845i
$185$	−4.56920	+	18.8345i	−0.335934	+	1.38474i
$186$	1.09873	+	0.934996i	0.0805624	+	0.0685572i
$187$	−7.88288	+	1.13339i	−0.576454	+	0.0828815i
$188$	2.78977	−	0.132893i	0.203465	−	0.00969222i
$189$	−4.25579	−	0.0885198i	−0.309563	−	0.00643887i
$190$	4.28393	+	4.08472i	0.310789	+	0.296337i
$191$	−10.8877	−	15.2897i	−0.787809	−	1.10632i	−0.991856	−	0.127362i	$-0.959349\pi$
$191$	−10.8877	−	15.2897i	−0.787809	−	1.10632i	0.204047	−	0.978961i	$-0.434590\pi$
$192$	−1.46540	−	0.923362i	−0.105756	−	0.0666379i
$193$	−13.8406	−	8.89481i	−0.996268	−	0.640262i	−0.0624637	−	0.998047i	$-0.519896\pi$
$193$	−13.8406	−	8.89481i	−0.996268	−	0.640262i	−0.933804	+	0.357785i	$0.883532\pi$
$194$	−2.86755	+	14.8783i	−0.205878	+	1.06820i
$195$	9.56752	−	12.3924i	0.685145	−	0.887436i
$196$	−6.07254	+	1.78306i	−0.433753	+	0.127361i
$197$	4.95048	−	3.89310i	0.352707	−	0.277372i	−0.426047	−	0.904701i	$-0.640094\pi$
$197$	4.95048	−	3.89310i	0.352707	−	0.277372i	0.778754	+	0.627329i	$0.215852\pi$
$198$	4.49967	+	5.00917i	0.319777	+	0.355986i
$199$	−7.95031	−	22.9709i	−0.563583	−	1.62836i	−0.761514	−	0.648149i	$-0.775543\pi$
$199$	−7.95031	−	22.9709i	−0.563583	−	1.62836i	0.197931	−	0.980216i	$-0.436578\pi$
$200$	3.30422			0.233643
$201$	10.7683	−	9.22191i	0.759537	−	0.650464i
$202$	−1.22845			−0.0864334
$203$	0.227463	+	0.657211i	0.0159648	+	0.0461272i
$204$	−3.36870	−	5.14024i	−0.235856	−	0.359889i
$205$	−1.78446	+	1.40332i	−0.124632	+	0.0980119i
$206$	5.48663	−	1.61102i	0.382271	−	0.112245i
$207$	−19.4675	−	10.7804i	−1.35308	−	0.749291i
$208$	0.593619	−	3.07999i	0.0411601	−	0.213559i
$209$	−3.87842	−	2.49251i	−0.268276	−	0.172411i
$210$	2.17978	−	3.45938i	0.150419	−	0.238720i
$211$	−2.80424	−	3.93800i	−0.193052	−	0.271103i	0.706692	−	0.707521i	$-0.250186\pi$
$211$	−2.80424	−	3.93800i	−0.193052	−	0.271103i	−0.899744	+	0.436417i	$0.856247\pi$
$212$	1.97339	+	1.88163i	0.135533	+	0.129231i
$213$	−12.7123	−	4.27296i	−0.871030	−	0.292779i
$214$	8.78422	−	0.418444i	0.600477	−	0.0286042i
$215$	11.5225	−	1.65668i	0.785827	−	0.112985i
$216$	−2.03111	+	4.78274i	−0.138200	+	0.325424i
$217$	−0.160871	+	0.663121i	−0.0109207	+	0.0450156i
$218$	6.85510	−	8.71696i	0.464286	−	0.590387i
$219$	−6.51997	+	27.9638i	−0.440579	+	1.88962i
$220$	−6.35101	+	1.22406i	−0.428185	+	0.0825260i
$221$	6.45586	−	9.06599i	0.434268	−	0.609844i
$222$	10.7753	−	4.42589i	0.723192	−	0.297046i
$223$	−2.56484	+	5.61622i	−0.171754	+	0.376090i	−0.975860	−	0.218397i	$-0.929917\pi$
$223$	−2.56484	+	5.61622i	−0.171754	+	0.376090i	0.804106	+	0.594486i	$0.202645\pi$
$224$	0.0778703	−	0.815494i	0.00520293	−	0.0544875i
$225$	−1.58581	−	9.78498i	−0.105720	−	0.652332i
$226$	−15.4048	+	9.90005i	−1.02471	+	0.658541i
$227$	−5.76750	−	14.4065i	−0.382802	−	0.956194i	−0.987197	−	0.159508i	$-0.949009\pi$
$227$	−5.76750	−	14.4065i	−0.382802	−	0.956194i	0.604394	−	0.796685i	$-0.293415\pi$
$228$	0.474838	−	3.52592i	0.0314469	−	0.233510i
$229$	−1.74444	−	3.38374i	−0.115276	−	0.223604i	0.824138	−	0.566389i	$-0.191660\pi$
$229$	−1.74444	−	3.38374i	−0.115276	−	0.223604i	−0.939414	+	0.342785i	$0.888630\pi$
$230$	18.5118	−	10.6878i	1.22063	−	0.704733i
$231$	−1.15717	+	2.96702i	−0.0761359	+	0.195215i
$232$	0.847985	+	0.0403945i	0.0556730	+	0.00265203i
$233$	−3.27269	+	0.312504i	−0.214401	+	0.0204728i	−0.201704	−	0.979447i	$-0.564648\pi$
$233$	−3.27269	+	0.312504i	−0.214401	+	0.0204728i	−0.0126972	+	0.999919i	$0.504042\pi$
$234$	−9.40586	−	0.279730i	−0.614880	−	0.0182865i
$235$	7.60574	+	2.63237i	0.496144	+	0.171717i
$236$	−0.563208	−	5.89818i	−0.0366617	−	0.383939i
$237$	3.13953	+	30.0399i	0.203935	+	1.95130i
$238$	1.45337	−	2.51731i	0.0942080	−	0.163173i
$239$	7.96610	+	13.7977i	0.515284	+	0.892499i	0.999843	+	0.0177398i	$0.00564704\pi$
$239$	7.96610	+	13.7977i	0.515284	+	0.892499i	−0.484558	+	0.874759i	$0.661020\pi$
$240$	−2.93142	−	4.03973i	−0.189222	−	0.260763i
$241$	21.0189	+	6.17169i	1.35394	+	0.397554i	0.876624	−	0.481176i	$-0.159790\pi$
$241$	21.0189	+	6.17169i	1.35394	+	0.397554i	0.477320	+	0.878730i	$0.341608\pi$
$242$	−5.53526	+	2.21598i	−0.355820	+	0.142449i
$243$	15.1382	+	3.71946i	0.971117	+	0.238604i
$244$	4.69846	+	0.675536i	0.300788	+	0.0432468i
$245$	−18.1554	−	1.73363i	−1.15991	−	0.110758i
$246$	1.31259	+	0.372706i	0.0836877	+	0.0237629i
$247$	6.26132	−	1.51898i	0.398398	−	0.0966503i
$248$	0.678500	+	0.483158i	0.0430848	+	0.0306806i
$249$	4.99929	−	1.78044i	0.316817	−	0.112831i
$250$	−4.53670	−	1.81622i	−0.286926	−	0.114868i
$251$	12.5573	+	9.87521i	0.792613	+	0.623318i	0.930150	−	0.367179i	$-0.119676\pi$
$251$	12.5573	+	9.87521i	0.792613	+	0.623318i	−0.137538	+	0.990497i	$0.543919\pi$
$252$	−2.45235	+	0.160781i	−0.154483	+	0.0101283i
$253$	−12.5823	+	10.9026i	−0.791044	+	0.685443i
$254$	2.25765	+	15.7023i	0.141657	+	0.985248i
$255$	−3.50692	−	17.3596i	−0.219612	−	1.08710i
$256$	−0.888835	−	0.458227i	−0.0555522	−	0.0286392i
$257$	3.20055	−	3.35664i	0.199645	−	0.209381i	−0.616300	−	0.787512i	$-0.711369\pi$
$257$	3.20055	−	3.35664i	0.199645	−	0.209381i	0.815944	+	0.578130i	$0.196217\pi$
$258$	−4.87341	−	5.02050i	−0.303405	−	0.312562i
$259$	4.16383	+	3.60798i	0.258728	+	0.224189i
$260$	4.88683	−	7.60406i	0.303068	−	0.471584i
$261$	−0.287354	−	2.53058i	−0.0177868	−	0.156639i
$262$	−3.90839	−	4.09901i	−0.241461	−	0.253237i
$263$	−0.826742	−	2.81563i	−0.0509791	−	0.173619i	0.930068	−	0.367387i	$-0.119747\pi$
$263$	−0.826742	−	2.81563i	−0.0509791	−	0.173619i	−0.981047	+	0.193768i	$0.937929\pi$
$264$	2.83740	+	2.65746i	0.174630	+	0.163556i
$265$	3.26412	+	7.14743i	0.200513	+	0.439063i
$266$	1.59015	−	0.550357i	0.0974985	−	0.0337446i
$267$	−19.3243	+	2.95486i	−1.18263	+	0.180835i
$268$	5.73523	−	5.84013i	0.350335	−	0.356743i
$269$			21.5488i			1.31386i	0.753954	+	0.656928i	$0.228144\pi$
$269$			21.5488i			1.31386i	−0.753954	+	0.656928i	$0.771856\pi$
$270$	−10.5562	+	10.6198i	−0.642431	+	0.646301i
$271$	26.6753	−	12.1822i	1.62041	−	0.740017i	0.621358	−	0.783527i	$-0.286581\pi$
$271$	26.6753	−	12.1822i	1.62041	−	0.740017i	0.999053	+	0.0435103i	$0.0138541\pi$
$272$	−2.19338	−	2.78911i	−0.132993	−	0.169115i
$273$	−1.88496	−	4.03176i	−0.114083	−	0.244013i
$274$	12.5562	−	11.9723i	0.758548	−	0.723274i
$275$	−7.28219	−	1.40353i	−0.439133	−	0.0846359i
$276$	−11.7340	−	5.23255i	−0.706304	−	0.314963i
$277$	−5.04969	+	5.82765i	−0.303406	+	0.350150i	−0.886894	−	0.461972i	$-0.847142\pi$
$277$	−5.04969	+	5.82765i	−0.303406	+	0.350150i	0.583488	+	0.812122i	$0.301687\pi$
$278$	6.53604	−	4.65429i	0.392006	−	0.279146i
$279$	1.10517	−	2.24117i	0.0661648	−	0.134175i
$280$	1.08174	−	2.09828i	0.0646461	−	0.125396i
$281$	1.34519	+	28.2389i	0.0802470	+	1.68459i	0.577034	+	0.816720i	$0.304210\pi$
$281$	1.34519	+	28.2389i	0.0802470	+	1.68459i	−0.496787	+	0.867873i	$0.665487\pi$
$282$	−1.40430	−	4.62918i	−0.0836246	−	0.275664i
$283$	8.19130	+	9.45326i	0.486922	+	0.561938i	0.945041	−	0.326953i	$-0.106022\pi$
$283$	8.19130	+	9.45326i	0.486922	+	0.561938i	−0.458118	+	0.888891i	$0.651476\pi$
$284$	−7.52469	−	1.82547i	−0.446508	−	0.108322i
$285$	5.04666	−	8.92426i	0.298938	−	0.528628i
$286$	−2.61657	+	6.53587i	−0.154721	+	0.386474i
$287$	0.122134	+	0.633692i	0.00720935	+	0.0374057i
$288$	−0.930392	+	2.85208i	−0.0548239	+	0.168061i
$289$	1.03968	+	4.28560i	0.0611574	+	0.252094i
$290$	2.22534	+	1.01628i	0.130676	+	0.0596778i
$291$	26.2023	−	1.48291i	1.53600	−	0.0869295i
$292$	−2.35929	+	16.4092i	−0.138067	+	0.960277i
$293$	−14.7569	−	22.9623i	−0.862110	−	1.34147i	−0.938817	−	0.344416i	$-0.888077\pi$
$293$	−14.7569	−	22.9623i	−0.862110	−	1.34147i	0.0767074	−	0.997054i	$-0.475559\pi$
$294$	5.56559	+	9.44401i	0.324592	+	0.550786i
$295$	4.81034	−	16.3825i	0.280069	−	0.953826i
$296$	5.97784	−	3.08179i	0.347455	−	0.179125i
$297$	6.50795	−	9.67797i	0.377629	−	0.561573i
$298$	−16.1320	−	9.31382i	−0.934502	−	0.539535i
$299$	1.10708	−	23.2405i	0.0640242	−	1.34403i
$300$	−1.39890	−	5.54947i	−0.0807656	−	0.320399i
$301$	1.08236	−	3.12726i	0.0623860	−	0.180252i
$302$	−4.34053	+	12.5411i	−0.249769	+	0.721661i
$303$	0.520087	+	2.06320i	0.0298782	+	0.118527i
$304$	0.0977364	−	2.05174i	0.00560557	−	0.117675i
$305$	11.8462	+	6.83940i	0.678310	+	0.391623i
$306$	−7.20690	+	7.83399i	−0.411991	+	0.447840i
$307$	12.9447	−	6.67347i	0.738794	−	0.380875i	−0.0473823	−	0.998877i	$-0.515088\pi$
$307$	12.9447	−	6.67347i	0.738794	−	0.380875i	0.786177	+	0.618002i	$0.212058\pi$
$308$	−0.518016	+	1.76420i	−0.0295167	+	0.100525i
$309$	−5.02859	−	8.53280i	−0.286066	−	0.485414i
$310$	1.29771	+	2.01927i	0.0737048	+	0.114687i
$311$	−1.32706	+	9.22987i	−0.0752504	+	0.523378i	0.916977	+	0.398940i	$0.130622\pi$
$311$	−1.32706	+	9.22987i	−0.0752504	+	0.523378i	−0.992227	+	0.124438i	$0.960287\pi$
$312$	−5.42420	+	0.306980i	−0.307085	+	0.0173793i
$313$	13.7099	+	6.26112i	0.774931	+	0.353899i	0.763309	−	0.646033i	$-0.223573\pi$
$313$	13.7099	+	6.26112i	0.774931	+	0.353899i	0.0116220	+	0.999932i	$0.496301\pi$
$314$	−1.26126	−	5.19897i	−0.0711769	−	0.293395i
$315$	−6.73292	−	2.19638i	−0.379357	−	0.123752i
$316$	3.30016	+	17.1229i	0.185649	+	0.963237i
$317$	−12.2310	+	30.5516i	−0.686963	+	1.71595i	0.0111244	+	0.999938i	$0.496459\pi$
$317$	−12.2310	+	30.5516i	−0.686963	+	1.71595i	−0.698087	+	0.716013i	$0.745965\pi$
$318$	2.32474	−	4.11096i	0.130365	−	0.230531i
$319$	−1.85173	−	0.449224i	−0.103677	−	0.0251517i
$320$	−1.88711	−	2.17785i	−0.105493	−	0.121745i
$321$	−4.42174	−	14.5760i	−0.246798	−	0.813555i
$322$	−0.289136	−	6.06972i	−0.0161129	−	0.338252i
$323$	3.33971	−	6.47814i	0.185827	−	0.360453i
$324$	8.89257	+	1.38642i	0.494032	+	0.0770232i
$325$	8.44246	−	6.01185i	0.468303	−	0.333477i
$326$	−4.23329	+	4.88548i	−0.234460	+	0.270582i
$327$	−17.5425	−	7.82272i	−0.970101	−	0.432598i
$328$	0.773546	+	0.149089i	0.0427119	+	0.00823205i
$329$	1.65589	−	1.57889i	0.0912921	−	0.0870469i
$330$	4.74464	+	10.1484i	0.261184	+	0.558650i
$331$	9.51563	+	12.1001i	0.523026	+	0.665082i	0.973760	−	0.227576i	$-0.0730801\pi$
$331$	9.51563	+	12.1001i	0.523026	+	0.665082i	−0.450734	+	0.892658i	$0.648838\pi$
$332$	2.78704	−	1.27280i	0.152959	−	0.0698540i
$333$	−11.9953	−	16.2235i	−0.657336	−	0.889041i
$334$		−	6.25230i		−	0.342110i
$335$	21.5983	−	9.48143i	1.18004	−	0.518026i
$336$	−1.40260	+	0.214471i	−0.0765181	+	0.0117003i
$337$	11.4957	−	3.97869i	0.626209	−	0.216733i	0.00451064	−	0.999990i	$-0.498564\pi$
$337$	11.4957	−	3.97869i	0.626209	−	0.216733i	0.621698	+	0.783257i	$0.286443\pi$
$338$	1.31325	+	2.87561i	0.0714312	+	0.156413i
$339$	23.1491	+	21.6811i	1.25729	+	1.17756i
$340$	−2.88072	−	9.81083i	−0.156229	−	0.532067i
$341$	−1.29012	−	1.35304i	−0.0698641	−	0.0732714i
$342$	−6.12285	+	0.695267i	−0.331086	+	0.0375957i
$343$	−5.90331	+	9.18572i	−0.318749	+	0.495982i
$344$	−3.05294	−	2.64539i	−0.164603	−	0.142630i
$345$	−25.7876	−	26.5659i	−1.38836	−	1.43026i
$346$	−13.2759	+	13.9234i	−0.713717	+	0.748524i
$347$	10.7238	+	5.52853i	0.575686	+	0.296787i	0.721376	−	0.692543i	$-0.243510\pi$
$347$	10.7238	+	5.52853i	0.575686	+	0.296787i	−0.145690	+	0.989330i	$0.546540\pi$
$348$	−0.291167	−	1.44130i	−0.0156082	−	0.0772620i
$349$	1.50113	+	10.4406i	0.0803534	+	0.558870i	0.989736	+	0.142909i	$0.0456457\pi$
$349$	1.50113	+	10.4406i	0.0803534	+	0.558870i	−0.909382	+	0.415961i	$0.863445\pi$
$350$	2.04568	−	1.77259i	0.109346	−	0.0947492i
$351$	3.51233	+	15.9157i	0.187475	+	0.849516i
$352$	1.76427	+	1.38744i	0.0940361	+	0.0739508i
$353$	31.2400	+	12.5066i	1.66274	+	0.665659i	0.996769	−	0.0803220i	$-0.0255949\pi$
$353$	31.2400	+	12.5066i	1.66274	+	0.665659i	0.665967	+	0.745981i	$0.268019\pi$
$354$	−9.66762	+	3.44302i	−0.513828	+	0.182994i
$355$	−18.1755	−	12.9427i	−0.964657	−	0.686929i
$356$	−10.9684	+	2.66091i	−0.581325	+	0.141028i
$357$	−4.84317	−	1.37520i	−0.256328	−	0.0727834i
$358$	24.4939	+	2.33889i	1.29454	+	0.123614i
$359$	21.6902	+	3.11858i	1.14477	+	0.164592i	0.688490	−	0.725246i	$-0.258274\pi$
$359$	21.6902	+	3.11858i	1.14477	+	0.164592i	0.456276	+	0.889839i	$0.349183\pi$
$360$	−5.54370	+	6.63365i	−0.292179	+	0.349624i
$361$	−13.7220	+	5.49347i	−0.722212	+	0.289130i
$362$	−3.17684	−	0.932803i	−0.166971	−	0.0490270i
$363$	6.06522	+	8.35835i	0.318342	+	0.438700i
$364$	−1.28479	−	2.22532i	−0.0673411	−	0.116638i
$365$	−23.8864	+	41.3724i	−1.25027	+	2.16553i
$366$	−0.854608	−	8.17711i	−0.0446711	−	0.427425i
$367$	1.19986	+	12.5655i	0.0626320	+	0.655912i	0.971215	+	0.238207i	$0.0765595\pi$
$367$	1.19986	+	12.5655i	0.0626320	+	0.655912i	−0.908583	+	0.417705i	$0.862834\pi$
$368$	−7.00973	−	2.42609i	−0.365407	−	0.126469i
$369$	0.0702548	−	2.36230i	0.00365732	−	0.122977i
$370$	19.2931	−	1.84226i	1.00300	−	0.0957747i
$371$	2.23118	+	0.106284i	0.115837	+	0.00551800i
$372$	0.524214	−	1.34410i	0.0271792	−	0.0696885i
$373$	3.61154	−	2.08512i	0.186998	−	0.107964i	−0.403578	−	0.914945i	$-0.632234\pi$
$373$	3.61154	−	2.08512i	0.186998	−	0.107964i	0.590577	+	0.806982i	$0.298900\pi$
$374$	3.64929	+	7.07864i	0.188700	+	0.366028i
$375$	−1.12967	+	8.38837i	−0.0583358	+	0.433174i
$376$	−1.03803	−	2.59287i	−0.0535322	−	0.133717i
$377$	2.24015	−	1.43966i	0.115373	−	0.0741460i
$378$	1.30828	+	4.05068i	0.0672907	+	0.208344i
$379$	−0.177438	+	1.85821i	−0.00911437	+	0.0954500i	−0.998884	−	0.0472218i	$-0.984963\pi$
$379$	−0.177438	+	1.85821i	−0.00911437	+	0.0954500i	0.989770	+	0.142672i	$0.0455693\pi$
$380$	2.45893	−	5.38430i	0.126140	−	0.276209i
$381$	25.4163	−	10.4396i	1.30212	−	0.534836i
$382$	−10.8877	+	15.2897i	−0.557065	+	0.782289i
$383$	−2.46014	+	0.474153i	−0.125707	+	0.0242281i	−0.251717	−	0.967801i	$-0.580995\pi$
$383$	−2.46014	+	0.474153i	−0.125707	+	0.0242281i	0.126010	+	0.992029i	$0.459783\pi$
$384$	−0.393292	+	1.68681i	−0.0200701	+	0.0860796i
$385$	−3.27533	+	4.16492i	−0.166926	+	0.212264i
$386$	−3.87879	+	15.9886i	−0.197425	+	0.813797i
$387$	−6.36874	+	10.3105i	−0.323741	+	0.524110i
$388$	14.9979	−	2.15637i	0.761402	−	0.109473i
$389$	−6.11449	+	0.291269i	−0.310017	+	0.0147679i	−0.202014	−	0.979383i	$-0.564749\pi$
$389$	−6.11449	+	0.291269i	−0.310017	+	0.0147679i	−0.108003	+	0.994151i	$0.534446\pi$
$390$	−14.8400	−	4.98817i	−0.751454	−	0.252586i
$391$	−19.0486	−	18.1628i	−0.963328	−	0.918531i
$392$	3.67113	+	5.15537i	0.185420	+	0.260386i
$393$	−5.22964	+	8.29958i	−0.263800	+	0.418659i
$394$	−5.29813	−	3.40490i	−0.266916	−	0.171536i
$395$	−9.51009	+	49.3430i	−0.478505	+	2.48272i
$396$	3.26198	−	5.89053i	0.163920	−	0.296010i
$397$	−31.9424	+	9.37915i	−1.60315	+	0.470726i	−0.956419	−	0.291996i	$-0.905680\pi$
$397$	−31.9424	+	9.37915i	−1.60315	+	0.470726i	−0.646726	+	0.762722i	$0.723862\pi$
$398$	−19.1072	+	15.0261i	−0.957759	+	0.753190i
$399$	−1.59755	−	2.43768i	−0.0799776	−	0.122036i
$400$	−1.08070	−	3.12249i	−0.0540352	−	0.156124i
$401$	−34.8551			−1.74058			−0.870290	−	0.492540i	$-0.836069\pi$
$401$	−34.8551			−1.74058			−0.870290	+	0.492540i	$0.836069\pi$
$402$	−12.2367	−	7.15986i	−0.610310	−	0.357101i
$403$	2.61269			0.130147
$404$	0.401787	+	1.16089i	0.0199896	+	0.0577562i
$405$	22.3053	+	13.2332i	1.10836	+	0.657562i
$406$	0.546669	−	0.429905i	0.0271307	−	0.0213358i
$407$	−14.4837	+	4.25279i	−0.717928	+	0.210803i
$408$	−3.75574	+	4.86464i	−0.185937	+	0.240835i
$409$	−6.68988	+	34.7104i	−0.330793	+	1.71632i	0.311832	+	0.950137i	$0.399057\pi$
$409$	−6.68988	+	34.7104i	−0.330793	+	1.71632i	−0.642625	+	0.766181i	$0.722155\pi$
$410$	1.90978	+	1.22734i	0.0943171	+	0.0606139i
$411$	−25.4235	−	16.0196i	−1.25405	−	0.790188i
$412$	−3.31691	−	4.65795i	−0.163413	−	0.229481i
$413$	−3.51285	−	3.34950i	−0.172856	−	0.164818i
$414$	−3.82033	+	21.9227i	−0.187759	+	1.07744i
$415$	8.81932	−	0.420116i	0.432924	−	0.0206227i
$416$	−3.10474	+	0.446395i	−0.152223	+	0.0218863i
$417$	−10.5841	−	9.00688i	−0.518305	−	0.441069i
$418$	−1.08692	+	4.48033i	−0.0531629	+	0.219140i
$419$	16.2142	−	20.6180i	0.792115	−	1.00726i	−0.207464	−	0.978243i	$-0.566521\pi$
$419$	16.2142	−	20.6180i	0.792115	−	1.00726i	0.999579	−	0.0290134i	$-0.00923654\pi$
$420$	−3.98205	−	0.928445i	−0.194304	−	0.0453035i
$421$	1.90408	−	0.366981i	0.0927992	−	0.0178856i	−0.142640	−	0.989775i	$-0.545559\pi$
$421$	1.90408	−	0.366981i	0.0927992	−	0.0178856i	0.235439	+	0.971889i	$0.424347\pi$
$422$	−2.80424	+	3.93800i	−0.136508	+	0.191699i
$423$	−7.18023	+	4.31838i	−0.349115	+	0.209967i
$424$	1.13271	−	2.48028i	0.0550090	−	0.120453i
$425$	1.11446	−	11.6711i	0.0540590	−	0.566132i
$426$	0.119818	+	13.4106i	0.00580522	+	0.649748i
$427$	3.27128	−	2.10232i	0.158308	−	0.101739i
$428$	−3.26847	−	8.16423i	−0.157987	−	0.394633i
$429$	12.0848	+	1.62747i	0.583461	+	0.0785751i
$430$	−5.33420	−	10.3469i	−0.257238	−	0.498972i
$431$	23.1389	−	13.3592i	1.11456	−	0.643492i	0.174554	−	0.984648i	$-0.444152\pi$
$431$	23.1389	−	13.3592i	1.11456	−	0.643492i	0.940007	+	0.341155i	$0.110818\pi$
$432$	5.18400	+	0.355123i	0.249415	+	0.0170859i
$433$	−0.558745	−	0.0266163i	−0.0268516	−	0.00127910i	0.0341518	−	0.999417i	$-0.489127\pi$
$433$	−0.558745	−	0.0266163i	−0.0268516	−	0.00127910i	−0.0610034	+	0.998138i	$0.519430\pi$
$434$	0.679266	−	0.0648620i	0.0326058	−	0.00311348i
$435$	0.764712	−	4.16774i	0.0366651	−	0.199828i
$436$	−10.4796	−	3.62703i	−0.501883	−	0.173703i
$437$	−1.44832	−	15.1674i	−0.0692823	−	0.725557i
$438$	28.5583	−	2.98469i	1.36457	−	0.142614i
$439$	3.33034	−	5.76832i	0.158949	−	0.275307i	−0.775541	−	0.631297i	$-0.782523\pi$
$439$	3.33034	−	5.76832i	0.158949	−	0.275307i	0.934490	+	0.355990i	$0.115856\pi$
$440$	3.23395	+	5.60136i	0.154172	+	0.267035i
$441$	13.5050	−	13.3458i	0.643097	−	0.635513i
$442$	−10.6789	−	3.13560i	−0.507942	−	0.149145i
$443$	−18.3476	+	7.34529i	−0.871723	+	0.348985i	−0.764016	−	0.645197i	$-0.776775\pi$
$443$	−18.3476	+	7.34529i	−0.871723	+	0.348985i	−0.107707	+	0.994183i	$0.534351\pi$
$444$	−7.70673	−	8.73511i	−0.365745	−	0.414550i
$445$	−32.1935	−	4.62872i	−1.52612	−	0.219422i
$446$	6.14621	+	0.586892i	0.291031	+	0.0277901i
$447$	−8.81288	+	31.0371i	−0.416835	+	1.46800i
$448$	−0.796112	+	0.193135i	−0.0376127	+	0.00912475i
$449$	−1.94569	−	1.38552i	−0.0918229	−	0.0653868i	0.533223	−	0.845974i	$-0.320981\pi$
$449$	−1.94569	−	1.38552i	−0.0918229	−	0.0653868i	−0.625046	+	0.780588i	$0.714920\pi$
$450$	−8.72815	+	4.69894i	−0.411449	+	0.221510i
$451$	−1.64150	−	0.657157i	−0.0772951	−	0.0309443i
$452$	14.3940	+	11.3195i	0.677035	+	0.532426i
$453$	22.9006	+	1.98045i	1.07597	+	0.0930496i
$454$	−11.7278	+	10.1622i	−0.550413	+	0.476935i
$455$	−1.05381	−	7.32938i	−0.0494032	−	0.343607i
$456$	−3.48730	+	0.704493i	−0.163308	+	0.0329909i
$457$	26.1872	+	13.5004i	1.22498	+	0.631523i	0.944556	−	0.328352i	$-0.106493\pi$
$457$	26.1872	+	13.5004i	1.22498	+	0.631523i	0.280429	+	0.959875i	$0.409523\pi$
$458$	−2.62708	+	2.75521i	−0.122756	+	0.128742i
$459$	16.2085	+	8.78740i	0.756546	+	0.410161i
$460$	−16.1546	−	13.9980i	−0.753212	−	0.652662i
$461$	7.75811	−	12.0719i	0.361331	−	0.562242i	−0.612227	−	0.790682i	$-0.709726\pi$
$461$	7.75811	−	12.0719i	0.361331	−	0.562242i	0.973558	+	0.228440i	$0.0733624\pi$
$462$	3.18230	+	0.123107i	0.148054	+	0.00572745i
$463$	−14.6830	−	15.3991i	−0.682376	−	0.715655i	0.287899	−	0.957661i	$-0.407043\pi$
$463$	−14.6830	−	15.3991i	−0.682376	−	0.715655i	−0.970275	+	0.242005i	$0.922195\pi$
$464$	−0.239176	−	0.814559i	−0.0111035	−	0.0378149i
$465$	2.84198	−	3.03441i	0.131794	−	0.140717i
$466$	1.36571	+	2.99048i	0.0632652	+	0.138531i
$467$	31.4825	−	10.8962i	1.45684	−	0.504216i	0.520055	−	0.854133i	$-0.325911\pi$
$467$	31.4825	−	10.8962i	1.45684	−	0.504216i	0.936781	+	0.349917i	$0.113790\pi$
$468$	2.81201	+	8.98003i	0.129985	+	0.415102i
$469$	0.417735	−	6.69245i	0.0192892	−	0.309029i
$470$		−	8.04840i		−	0.371245i
$471$	−8.19776	+	4.31938i	−0.377733	+	0.199026i
$472$	−5.38958	+	2.46134i	−0.248076	+	0.113292i
$473$	5.60472	+	7.12698i	0.257705	+	0.327699i
$474$	27.3609	−	12.7919i	1.25673	−	0.587554i
$475$	4.91204	−	4.68362i	0.225380	−	0.214899i
$476$	−2.85421	−	0.550105i	−0.130823	−	0.0252140i
$477$	−7.88863	−	2.16398i	−0.361195	−	0.0990819i
$478$	10.4334	−	12.0408i	0.477212	−	0.550731i
$479$	−31.8459	+	22.6773i	−1.45507	+	1.03615i	−0.466650	+	0.884442i	$0.654539\pi$
$479$	−31.8459	+	22.6773i	−1.45507	+	1.03615i	−0.988425	+	0.151712i	$0.951521\pi$
$480$	−2.85877	+	4.09146i	−0.130485	+	0.186749i
$481$	9.66656	−	18.7505i	0.440757	−	0.854950i
$482$	−1.04234	−	21.8814i	−0.0474773	−	0.996671i
$483$	−10.0718	+	3.05534i	−0.458281	+	0.139023i
$484$	3.90451	+	4.50605i	0.177478	+	0.204820i
$485$	42.4330	+	10.2941i	1.92679	+	0.467433i
$486$	−1.43633	−	15.5221i	−0.0651533	−	0.704099i
$487$	11.8315	−	29.5537i	0.536138	−	1.33921i	−0.374969	−	0.927037i	$-0.622347\pi$
$487$	11.8315	−	29.5537i	0.536138	−	1.33921i	0.911107	−	0.412171i	$-0.135229\pi$
$488$	−0.898333	−	4.66099i	−0.0406656	−	0.210993i
$489$	9.99747	+	5.04151i	0.452101	+	0.227985i
$490$	4.29978	+	17.7239i	0.194244	+	0.800685i
$491$	−29.0620	−	13.2722i	−1.31155	−	0.598966i	−0.367888	−	0.929870i	$-0.619919\pi$
$491$	−29.0620	−	13.2722i	−1.31155	−	0.598966i	−0.943664	+	0.330905i	$0.892646\pi$
$492$	−0.0770987	−	1.36230i	−0.00347588	−	0.0614172i
$493$	0.428692	−	2.98162i	0.0193073	−	0.134285i
$494$	−3.48331	−	5.42014i	−0.156722	−	0.243864i
$495$	15.0356	−	12.2652i	0.675799	−	0.551279i
$496$	0.234669	−	0.799209i	0.0105369	−	0.0358855i
$497$	−5.63793	+	2.90656i	−0.252896	+	0.130377i
$498$	−3.31763	−	4.14201i	−0.148667	−	0.185608i
$499$	−21.6261	−	12.4858i	−0.968118	−	0.558943i	−0.0694563	−	0.997585i	$-0.522126\pi$
$499$	−21.6261	−	12.4858i	−0.968118	−	0.558943i	−0.898662	+	0.438642i	$0.855460\pi$
$500$	−0.232521	+	4.88121i	−0.0103986	+	0.218294i
$501$	−10.5008	+	2.64703i	−0.469141	+	0.118260i
$502$	5.22497	−	15.0966i	0.233202	−	0.673793i
$503$	4.72722	−	13.6584i	0.210777	−	0.608999i	−0.789210	−	0.614123i	$-0.789510\pi$
$503$	4.72722	−	13.6584i	0.210777	−	0.608999i	0.999987	+	0.00512420i	$0.00163109\pi$
$504$	0.954023	+	2.26488i	0.0424955	+	0.100886i
$505$	−0.168441	+	3.53602i	−0.00749554	+	0.157351i
$506$	14.4183	+	8.32440i	0.640971	+	0.370065i
$507$	4.27363	−	3.42306i	0.189799	−	0.152023i
$508$	14.1003	−	7.26919i	0.625598	−	0.322518i
$509$	2.26767	−	7.72298i	0.100513	−	0.342315i	−0.893847	−	0.448371i	$-0.852004\pi$
$509$	2.26767	−	7.72298i	0.100513	−	0.342315i	0.994360	+	0.106056i	$0.0338224\pi$
$510$	−15.2578	+	8.99179i	−0.675626	+	0.398163i
$511$	7.34229	+	11.4248i	0.324804	+	0.505405i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	3.75993	+	9.98904i	0.166005	+	0.441027i
$514$	−4.21883	−	1.92667i	−0.186084	−	0.0849819i
$515$	−3.88491	−	16.0138i	−0.171190	−	0.705653i
$516$	−3.15044	+	6.24742i	−0.138690	+	0.275027i
$517$	1.18635	+	6.15537i	0.0521756	+	0.270713i
$518$	2.04769	−	5.11487i	0.0899702	−	0.224735i
$519$	29.0050	+	16.4023i	1.27318	+	0.719982i
$520$	−8.78416	−	2.13102i	−0.385211	−	0.0934512i
$521$	−1.01972	−	1.17682i	−0.0446746	−	0.0515573i	0.732972	−	0.680258i	$-0.238132\pi$
$521$	−1.01972	−	1.17682i	−0.0446746	−	0.0515573i	−0.777647	+	0.628701i	$0.783587\pi$
$522$	−2.29741	+	1.09922i	−0.100555	+	0.0481116i
$523$	1.61502	+	33.9035i	0.0706199	+	1.48249i	0.704853	+	0.709353i	$0.251013\pi$
$523$	1.61502	+	33.9035i	0.0706199	+	1.48249i	−0.634233	+	0.773142i	$0.718684\pi$
$524$	−2.59525	+	5.03409i	−0.113374	+	0.219915i
$525$	−3.84317	−	2.68529i	−0.167730	−	0.117196i
$526$	−2.39037	+	1.70217i	−0.104225	+	0.0742183i
$527$	1.93545	−	2.23363i	0.0843095	−	0.0972984i
$528$	1.58328	−	3.55051i	0.0689036	−	0.154516i
$529$	−31.4435	−	6.06024i	−1.36711	−	0.263489i
$530$	5.68674	−	5.42229i	0.247016	−	0.235529i
$531$	9.87556	+	14.7792i	0.428563	+	0.641363i
$532$	−1.04018	−	1.32269i	−0.0450973	−	0.0573459i
$533$	2.24771	−	1.02650i	0.0973593	−	0.0444625i
$534$	9.11270	+	17.2950i	0.394345	+	0.748429i
$535$		−	25.3422i		−	1.09564i
$536$	−7.39474	−	3.50968i	−0.319404	−	0.151595i
$537$	−6.44177	−	42.1281i	−0.277983	−	1.81796i
$538$	20.3637	−	7.04793i	0.877940	−	0.303858i
$539$	−5.90099	−	12.9214i	−0.254173	−	0.556562i
$540$	13.4883	+	6.50223i	0.580445	+	0.279811i
$541$	−5.80415	−	19.7671i	−0.249540	−	0.849855i	−0.985039	−	0.172330i	$-0.944871\pi$
$541$	−5.80415	−	19.7671i	−0.249540	−	0.849855i	0.735499	−	0.677525i	$-0.236948\pi$
$542$	−20.2368	−	21.2238i	−0.869247	−	0.911640i
$543$	−0.221682	+	5.73045i	−0.00951326	+	0.245917i
$544$	−1.91833	+	2.98498i	−0.0822477	+	0.127980i
$545$	−24.1513	−	20.9272i	−1.03453	−	0.896424i
$546$	−3.19351	+	3.09994i	−0.136669	+	0.132665i
$547$	19.3636	−	20.3079i	0.827927	−	0.868305i	−0.165089	−	0.986279i	$-0.552791\pi$
$547$	19.3636	−	20.3079i	0.827927	−	0.868305i	0.993017	+	0.117973i	$0.0376398\pi$
$548$	−15.4206	−	7.94986i	−0.658735	−	0.339601i
$549$	−13.3717	+	4.89726i	−0.570692	+	0.209010i
$550$	1.05544	+	7.34073i	0.0450040	+	0.313010i
$551$	1.31787	−	1.14194i	0.0561432	−	0.0486484i
$552$	−1.10695	+	12.8000i	−0.0471149	+	0.544806i
$553$	11.2290	+	8.83057i	0.477505	+	0.375514i
$554$	7.15873	+	2.86592i	0.304145	+	0.121761i
$555$	−11.2622	−	31.6230i	−0.478053	−	1.34232i
$556$	−6.53604	−	4.65429i	−0.277190	−	0.197386i
$557$	34.6738	−	8.41177i	1.46918	−	0.356418i	0.580238	−	0.814447i	$-0.302959\pi$
$557$	34.6738	−	8.41177i	1.46918	−	0.356418i	0.888938	+	0.458028i	$0.151444\pi$
$558$	−2.47937	−	0.311372i	−0.104960	−	0.0131814i
$559$	−12.6136	−	1.20445i	−0.533497	−	0.0509428i
$560$	−2.33667	−	0.335963i	−0.0987425	−	0.0141970i
$561$	10.3437	−	9.12590i	0.436710	−	0.385296i
$562$	26.2458	−	10.5072i	1.10711	−	0.443221i
$563$	−32.0074	−	9.39823i	−1.34895	−	0.396088i	−0.474097	−	0.880473i	$-0.657225\pi$
$563$	−32.0074	−	9.39823i	−1.34895	−	0.396088i	−0.874855	+	0.484384i	$0.839044\pi$
$564$	−3.91528	+	2.84112i	−0.164863	+	0.119633i
$565$	26.3844	+	45.6992i	1.11000	+	1.92258i
$566$	6.25423	−	10.8326i	0.262885	−	0.455330i
$567$	6.24927	−	3.91220i	0.262445	−	0.164297i
$568$	0.736014	+	7.70789i	0.0308825	+	0.323416i
$569$	3.21116	+	1.11139i	0.134619	+	0.0465920i	0.393547	−	0.919305i	$-0.371248\pi$
$569$	3.21116	+	1.11139i	0.134619	+	0.0465920i	−0.258928	+	0.965897i	$0.583369\pi$
$570$	−10.0840	−	1.85026i	−0.422374	−	0.0774987i
$571$	4.47227	−	0.427050i	0.187159	−	0.0178715i	−0.00105576	−	0.999999i	$-0.500336\pi$
$571$	4.47227	−	0.427050i	0.187159	−	0.0178715i	0.188214	+	0.982128i	$0.439730\pi$
$572$	7.03219	+	0.334985i	0.294031	+	0.0140064i
$573$	30.2887	+	11.8129i	1.26533	+	0.493491i
$574$	0.558893	−	0.322677i	0.0233278	−	0.0134683i
$575$	−11.2310	−	21.7851i	−0.468364	−	0.908500i
$576$	2.99952	−	0.0536032i	0.124980	−	0.00223347i
$577$	7.11193	+	17.7647i	0.296073	+	0.739556i	0.999583	+	0.0288701i	$0.00919091\pi$
$577$	7.11193	+	17.7647i	0.296073	+	0.739556i	−0.703510	+	0.710686i	$0.748385\pi$
$578$	3.70985	−	2.38418i	0.154309	−	0.0991687i
$579$	28.4952	−	0.254592i	1.18422	−	0.0105805i
$580$	0.232546	−	2.43534i	0.00965596	−	0.101122i
$581$	1.04268	−	2.28316i	0.0432578	−	0.0947213i
$582$	−9.97127	−	24.2762i	−0.413323	−	1.00628i
$583$	−3.54993	+	4.98517i	−0.147023	+	0.206465i
$584$	16.2784	−	3.13740i	0.673604	−	0.129826i
$585$	−2.09489	+	27.0358i	−0.0866130	+	1.11779i
$586$	−16.8728	+	21.4555i	−0.697010	+	0.886320i
$587$	8.86850	−	36.5565i	0.366042	−	1.50885i	−0.429566	−	0.903035i	$-0.641334\pi$
$587$	8.86850	−	36.5565i	0.366042	−	1.50885i	0.795608	−	0.605811i	$-0.207151\pi$
$588$	7.10427	−	8.34832i	0.292975	−	0.344279i
$589$	1.69352	−	0.243491i	0.0697802	−	0.0100329i
$590$	−17.0548	+	0.812420i	−0.702135	+	0.0334468i
$591$	−3.47551	+	10.3398i	−0.142963	+	0.425322i
$592$	−4.86745	−	4.64111i	−0.200051	−	0.190748i
$593$	−9.13002	−	12.8213i	−0.374925	−	0.526508i	0.583401	−	0.812184i	$-0.301721\pi$
$593$	−9.13002	−	12.8213i	−0.374925	−	0.526508i	−0.958326	+	0.285676i	$0.907782\pi$
$594$	−11.2742	−	2.98466i	−0.462587	−	0.122462i
$595$	−7.04665	−	4.52861i	−0.288884	−	0.185655i
$596$	−3.52530	+	18.2910i	−0.144402	+	0.749229i
$597$	33.3259	+	25.7293i	1.36394	+	1.05303i
$598$	−22.3244	+	6.55504i	−0.912913	+	0.268055i
$599$	−20.1583	+	15.8527i	−0.823647	+	0.647723i	−0.938354	−	0.345676i	$-0.887650\pi$
$599$	−20.1583	+	15.8527i	−0.823647	+	0.647723i	0.114707	+	0.993399i	$0.463407\pi$
$600$	−4.78672	+	3.13702i	−0.195417	+	0.128068i
$601$	5.65523	+	16.3397i	0.230682	+	0.666511i	0.999630	+	0.0272000i	$0.00865909\pi$
$601$	5.65523	+	16.3397i	0.230682	+	0.666511i	−0.768948	+	0.639311i	$0.779220\pi$
$602$	−3.30927			−0.134876
$603$	−6.84445	+	23.5829i	−0.278727	+	0.960370i
$604$	13.2710			0.539991
$605$	5.61959	+	16.2368i	0.228469	+	0.660118i
$606$	1.77962	−	1.16629i	0.0722920	−	0.0473772i
$607$	−4.14129	+	3.25674i	−0.168090	+	0.132187i	−0.698660	−	0.715454i	$-0.746220\pi$
$607$	−4.14129	+	3.25674i	−0.168090	+	0.132187i	0.530571	+	0.847641i	$0.321978\pi$
$608$	−1.97086	+	0.578697i	−0.0799290	+	0.0234693i
$609$	−0.953473	−	0.736129i	−0.0386367	−	0.0298294i
$610$	2.58873	−	13.4316i	0.104815	−	0.543830i
$611$	−7.36981	−	4.73629i	−0.298151	−	0.191610i
$612$	9.76028	+	4.24828i	0.394536	+	0.171726i
$613$	1.79718	+	2.52379i	0.0725876	+	0.101935i	0.849274	−	0.527953i	$-0.177040\pi$
$613$	1.79718	+	2.52379i	0.0725876	+	0.101935i	−0.776686	+	0.629888i	$0.783101\pi$
$614$	−10.5402	−	10.0501i	−0.425369	−	0.405589i
$615$	1.25279	−	3.72711i	0.0505174	−	0.150291i
$616$	1.83660	−	0.0874879i	0.0739986	−	0.00352499i
$617$	25.4074	−	3.65303i	1.02286	−	0.147065i	0.389585	−	0.920991i	$-0.372619\pi$
$617$	25.4074	−	3.65303i	1.02286	−	0.147065i	0.633277	+	0.773925i	$0.281709\pi$
$618$	−6.41881	+	7.54283i	−0.258202	+	0.303417i
$619$	−4.41424	+	18.1957i	−0.177423	+	0.731348i	0.811677	+	0.584106i	$0.198555\pi$
$619$	−4.41424	+	18.1957i	−0.177423	+	0.731348i	−0.989100	+	0.147242i	$0.952960\pi$
$620$	1.48378	−	1.88677i	0.0595898	−	0.0757746i
$621$	38.4368	−	2.86510i	1.54242	−	0.114973i
$622$	9.15628	−	1.76473i	0.367133	−	0.0707591i
$623$	−5.36320	+	7.53156i	−0.214872	+	0.301746i
$624$	2.06418	+	5.02547i	0.0826332	+	0.201180i
$625$	−12.7130	+	27.8377i	−0.508522	+	1.11351i
$626$	1.43268	−	15.0037i	0.0572614	−	0.599669i
$627$	7.98494	−	0.0713421i	0.318888	−	0.00284913i
$628$	−4.50052	+	2.89231i	−0.179590	+	0.115416i
$629$	−8.86923	−	22.1543i	−0.353639	−	0.883348i
$630$	0.126541	+	7.08098i	0.00504152	+	0.282113i
$631$	−5.97289	−	11.5858i	−0.237777	−	0.461223i	0.739509	−	0.673146i	$-0.235058\pi$
$631$	−5.97289	−	11.5858i	−0.237777	−	0.461223i	−0.977286	+	0.211924i	$0.932027\pi$
$632$	15.1018	−	8.71900i	0.600715	−	0.346823i
$633$	7.80115	+	3.04253i	0.310068	+	0.120930i
$634$	32.8717	+	1.56587i	1.30550	+	0.0621887i
$635$	45.5076	−	4.34545i	1.80591	−	0.172444i
$636$	−4.64521	−	0.852320i	−0.184195	−	0.0337967i
$637$	18.7599	+	6.49285i	0.743293	+	0.257256i
$638$	0.181123	+	1.89681i	0.00717074	+	0.0750954i
$639$	22.4726	−	5.87888i	0.889003	−	0.232565i
$640$	−1.44085	+	2.49563i	−0.0569547	+	0.0986484i
$641$	0.820445	+	1.42105i	0.0324056	+	0.0561282i	0.881773	−	0.471673i	$-0.156350\pi$
$641$	0.820445	+	1.42105i	0.0324056	+	0.0561282i	−0.849368	+	0.527802i	$0.823016\pi$
$642$	−12.3282	+	8.94590i	−0.486553	+	0.353067i
$643$	−17.2897	−	5.07673i	−0.681841	−	0.200207i	−0.0775716	−	0.996987i	$-0.524717\pi$
$643$	−17.2897	−	5.07673i	−0.681841	−	0.200207i	−0.604269	+	0.796780i	$0.706535\pi$
$644$	−5.64133	+	2.25845i	−0.222299	+	0.0889952i
$645$	−15.1194	+	13.3394i	−0.595327	+	0.525239i
$646$	−7.21416	−	1.03724i	−0.283837	−	0.0408096i
$647$	−8.29477	−	0.792054i	−0.326101	−	0.0311389i	−0.0692782	−	0.997597i	$-0.522070\pi$
$647$	−8.29477	−	0.792054i	−0.326101	−	0.0311389i	−0.256823	+	0.966459i	$0.582676\pi$
$648$	−1.59831	−	8.85694i	−0.0627876	−	0.347934i
$649$	12.9236	−	3.13524i	0.507298	−	0.123069i
$650$	−8.44246	−	6.01185i	−0.331141	−	0.235804i
$651$	−0.396516	−	1.11337i	−0.0155407	−	0.0436366i
$652$	6.00136	+	2.40258i	0.235031	+	0.0940924i
$653$	−13.9919	−	11.0033i	−0.547544	−	0.430593i	0.305683	−	0.952133i	$-0.401115\pi$
$653$	−13.9919	−	11.0033i	−0.547544	−	0.430593i	−0.853227	+	0.521540i	$0.825358\pi$
$654$	−1.65490	+	19.1362i	−0.0647117	+	0.748285i
$655$	−12.3346	+	10.6880i	−0.481955	+	0.417616i
$656$	−0.112113	−	0.779764i	−0.00437728	−	0.0304447i
$657$	−17.1035	−	46.7004i	−0.667272	−	1.82196i
$658$	−2.03364	−	1.04841i	−0.0792795	−	0.0408714i
$659$	4.35799	−	4.57053i	0.169763	−	0.178043i	−0.633357	−	0.773860i	$-0.718323\pi$
$659$	4.35799	−	4.57053i	0.169763	−	0.178043i	0.803120	+	0.595817i	$0.203172\pi$
$660$	8.03840	−	7.80290i	0.312894	−	0.303727i
$661$	8.69250	+	7.53209i	0.338099	+	0.292964i	0.807317	−	0.590118i	$-0.200919\pi$
$661$	8.69250	+	7.53209i	0.338099	+	0.292964i	−0.469218	+	0.883082i	$0.655464\pi$
$662$	8.32236	−	12.9498i	0.323458	−	0.503310i
$663$	−0.745178	+	19.2628i	−0.0289403	+	0.748105i
$664$	−2.11435	−	2.21747i	−0.0820527	−	0.0860544i
$665$	−1.36613	−	4.65262i	−0.0529763	−	0.180421i
$666$	−11.4079	+	16.6417i	−0.442049	+	0.644853i
$667$	−2.61596	−	5.72816i	−0.101291	−	0.221795i
$668$	−5.90843	+	2.04493i	−0.228604	+	0.0791206i
$669$	−1.61642	−	10.5711i	−0.0624944	−	0.408702i
$670$	−16.0241	−	17.3093i	−0.619064	−	0.668717i
$671$			10.6540i			0.411293i
$672$	0.661421	+	1.25531i	0.0255149	+	0.0484247i
$673$	−27.6638	+	12.6336i	−1.06636	+	0.486991i	−0.869751	−	0.493491i	$-0.835721\pi$
$673$	−27.6638	+	12.6336i	−1.06636	+	0.486991i	−0.196610	+	0.980482i	$0.562993\pi$
$674$	−7.51973	−	9.56211i	−0.289649	−	0.368319i
$675$	11.5871	+	12.6696i	0.445989	+	0.487655i
$676$	2.28793	−	2.18154i	0.0879974	−	0.0839054i
$677$	−39.5070	−	7.61435i	−1.51838	−	0.292643i	−0.639164	−	0.769070i	$-0.720720\pi$
$677$	−39.5070	−	7.61435i	−1.51838	−	0.292643i	−0.879214	+	0.476427i	$0.841932\pi$
$678$	12.9173	−	28.9672i	0.496088	−	1.11248i
$679$	8.12856	−	9.38086i	0.311946	−	0.360004i
$680$	−8.32905	+	5.93109i	−0.319404	+	0.227447i
$681$	22.0327	+	15.3946i	0.844295	+	0.589923i
$682$	−0.856668	+	1.66170i	−0.0328035	+	0.0636300i
$683$	−0.303591	−	6.37315i	−0.0116166	−	0.243862i	−0.997206	−	0.0747048i	$-0.976199\pi$
$683$	−0.303591	−	6.37315i	−0.0116166	−	0.243862i	0.985589	−	0.169157i	$-0.0541045\pi$
$684$	2.65962	+	5.55870i	0.101693	+	0.212542i
$685$	−32.7399	−	37.7839i	−1.25093	−	1.44365i
$686$	10.6113	+	2.57427i	0.405141	+	0.0982862i
$687$	5.73963	+	3.24575i	0.218980	+	0.123833i
$688$	−1.50137	+	3.75025i	−0.0572393	+	0.142977i
$689$	−1.61861	−	8.39815i	−0.0616642	−	0.319944i
$690$	−16.6705	+	33.0582i	−0.634636	+	1.25850i
$691$	6.28197	+	25.8946i	0.238977	+	0.985078i	0.957238	+	0.289303i	$0.0934236\pi$
$691$	6.28197	+	25.8946i	0.238977	+	0.985078i	−0.718260	+	0.695775i	$0.755061\pi$
$692$	17.4997	+	7.99185i	0.665239	+	0.303804i
$693$	−1.14053	−	5.39684i	−0.0433251	−	0.205009i
$694$	1.71704	−	11.9423i	0.0651778	−	0.453322i
$695$	−12.5009	−	19.4518i	−0.474186	−	0.737848i
$696$	−1.26680	+	0.746557i	−0.0480180	+	0.0282982i
$697$	0.787513	−	2.68202i	0.0298292	−	0.101589i
$698$	9.37537	−	4.83334i	0.354863	−	0.182945i
$699$	4.44435	−	3.55980i	0.168101	−	0.134644i
$700$	−2.34418	−	1.35341i	−0.0886017	−	0.0511542i
$701$	1.22277	−	25.6692i	0.0461835	−	0.969511i	−0.850263	−	0.526358i	$-0.823557\pi$
$701$	1.22277	−	25.6692i	0.0461835	−	0.969511i	0.896446	−	0.443152i	$-0.146140\pi$
$702$	13.8916	−	8.52467i	0.524303	−	0.321743i
$703$	4.51830	−	13.0548i	0.170411	−	0.492370i
$704$	0.734094	−	2.12103i	0.0276672	−	0.0799392i
$705$	−13.5174	+	3.40744i	−0.509094	+	0.128332i
$706$	1.60115	−	33.6123i	0.0602601	−	1.26502i
$707$	0.871525	+	0.503175i	0.0327771	+	0.0189239i
$708$	6.41563	+	8.00981i	0.241114	+	0.301027i
$709$	−29.2740	+	15.0918i	−1.09941	+	0.566785i	−0.909788	−	0.415073i	$-0.863756\pi$
$709$	−29.2740	+	15.0918i	−1.09941	+	0.566785i	−0.189621	+	0.981857i	$0.560726\pi$
$710$	−6.28627	+	21.4091i	−0.235919	+	0.803468i
$711$	−33.0680	−	40.5372i	−1.24015	−	1.52026i
$712$	6.10197	+	9.49486i	0.228681	+	0.355835i
$713$	0.879301	−	6.11568i	0.0329301	−	0.229034i
$714$	0.284477	+	5.02658i	0.0106463	+	0.188115i
$715$	18.4543	+	8.42780i	0.690152	+	0.315182i
$716$	−5.80093	−	23.9118i	−0.216791	−	0.893625i
$717$	−24.6398	−	12.4253i	−0.920189	−	0.464031i
$718$	−4.14711	−	21.5173i	−0.154769	−	0.803017i
$719$	−14.1134	+	35.2535i	−0.526340	+	1.31473i	0.392372	+	0.919807i	$0.371655\pi$
$719$	−14.1134	+	35.2535i	−0.526340	+	1.31473i	−0.918712	+	0.394928i	$0.870770\pi$
$720$	8.08197	+	3.06915i	0.301197	+	0.114380i
$721$	−4.55237	−	1.10439i	−0.169539	−	0.0411298i
$722$	9.67937	+	11.1706i	0.360229	+	0.415726i
$723$	−36.3088	+	11.0145i	−1.35034	+	0.409634i
$724$	0.157541	+	3.30720i	0.00585498	+	0.122911i
$725$	1.28537	−	2.49328i	0.0477376	−	0.0925980i
$726$	5.91491	−	8.46539i	0.219523	−	0.314180i
$727$	22.4013	−	15.9519i	0.830818	−	0.591623i	−0.0835512	−	0.996503i	$-0.526626\pi$
$727$	22.4013	−	15.9519i	0.830818	−	0.591623i	0.914370	+	0.404880i	$0.132687\pi$
$728$	−1.68271	+	1.94195i	−0.0623655	+	0.0719736i
$729$	−25.4615	+	8.98392i	−0.943019	+	0.332738i
$730$	46.9094	+	9.04105i	1.73620	+	0.334624i
$731$	−10.3737	+	9.89130i	−0.383685	+	0.365843i
$732$	−7.44787	+	3.48208i	−0.275281	+	0.128701i
$733$	−19.6487	−	24.9853i	−0.725739	−	0.922853i	0.273499	−	0.961872i	$-0.411819\pi$
$733$	−19.6487	−	24.9853i	−0.725739	−	0.922853i	−0.999238	+	0.0390195i	$0.987577\pi$
$734$	11.4819	−	5.24363i	0.423806	−	0.193546i
$735$	27.9471	−	14.7253i	1.03085	−	0.543150i
$736$			7.41770i			0.273420i
$737$	14.8065	+	10.8761i	0.545406	+	0.400625i
$738$	−2.25536	+	0.706243i	−0.0830208	+	0.0259972i
$739$	−7.62690	+	2.63969i	−0.280560	+	0.0971027i	−0.463724	−	0.885980i	$-0.653487\pi$
$739$	−7.62690	+	2.63969i	−0.280560	+	0.0971027i	0.183164	+	0.983082i	$0.441366\pi$
$740$	−8.05108	−	17.6294i	−0.295964	−	0.648070i
$741$	−7.62846	+	8.14498i	−0.280239	+	0.299213i
$742$	−0.629309	−	2.14323i	−0.0231027	−	0.0786804i
$743$	8.08246	+	8.47664i	0.296517	+	0.310978i	0.855092	−	0.518476i	$-0.173500\pi$
$743$	8.08246	+	8.47664i	0.296517	+	0.310978i	−0.558575	+	0.829454i	$0.688652\pi$
$744$	−1.44163	−	0.0557693i	−0.0528528	−	0.00204460i
$745$	−29.0212	+	45.1579i	−1.06326	+	1.65446i
$746$	−3.15166	−	2.73093i	−0.115391	−	0.0999865i
$747$	−5.55197	+	7.32559i	−0.203136	+	0.268029i
$748$	5.49575	−	5.76378i	0.200945	−	0.210745i
$749$	−6.40337	−	3.30117i	−0.233974	−	0.120622i
$750$	8.29649	−	1.67603i	0.302945	−	0.0612000i
$751$	−6.15364	−	42.7995i	−0.224550	−	1.56178i	−0.720518	−	0.693436i	$-0.756096\pi$
$751$	−6.15364	−	42.7995i	−0.224550	−	1.56178i	0.495969	−	0.868340i	$-0.334813\pi$
$752$	−2.11076	+	1.82898i	−0.0769714	+	0.0666961i
$753$	−27.5669	−	2.38399i	−1.00460	−	0.0868775i
$754$	−2.09316	−	1.64608i	−0.0762282	−	0.0599466i
$755$	35.5038	+	14.2136i	1.29211	+	0.517284i
$756$	3.39999	−	2.56117i	0.123657	−	0.0931489i
$757$	−14.3971	−	10.2521i	−0.523271	−	0.372619i	0.287687	−	0.957725i	$-0.407114\pi$
$757$	−14.3971	−	10.2521i	−0.523271	−	0.372619i	−0.810957	+	0.585105i	$0.801053\pi$
$758$	1.81405	−	0.440083i	0.0658891	−	0.0159845i
$759$	7.87668	−	27.7400i	0.285905	−	1.00690i
$760$	−5.89241	−	0.562657i	−0.213740	−	0.0204097i
$761$	−10.8637	−	1.56197i	−0.393810	−	0.0566213i	−0.0574345	−	0.998349i	$-0.518292\pi$
$761$	−10.8637	−	1.56197i	−0.393810	−	0.0566213i	−0.336375	+	0.941728i	$0.609201\pi$
$762$	−18.1783	−	20.6040i	−0.658530	−	0.746404i
$763$	−8.43384	+	3.37640i	−0.305326	+	0.122234i
$764$	18.0098	+	5.28815i	0.651572	+	0.191319i
$765$	21.5615	+	21.8188i	0.779557	+	0.788860i
$766$	1.25271	+	2.16975i	0.0452622	+	0.0783964i
$767$	−9.29241	+	16.0949i	−0.335529	+	0.581154i
$768$	1.72267	−	0.180040i	0.0621614	−	0.00649663i
$769$	3.61982	+	37.9085i	0.130534	+	1.36701i	0.788995	+	0.614399i	$0.210602\pi$
$769$	3.61982	+	37.9085i	0.130534	+	1.36701i	−0.658461	+	0.752615i	$0.728792\pi$
$770$	5.00711	+	1.73298i	0.180444	+	0.0624522i
$771$	−1.44975	+	7.90126i	−0.0522115	+	0.284557i
$772$	16.3778	−	1.56389i	0.589452	−	0.0562858i
$773$	10.3069	+	0.490979i	0.370714	+	0.0176593i	0.232112	−	0.972689i	$-0.425436\pi$
$773$	10.3069	+	0.490979i	0.370714	+	0.0176593i	0.138601	+	0.990348i	$0.455739\pi$
$774$	11.8264	+	2.64624i	0.425091	+	0.0951171i
$775$	2.38351	−	1.37612i	0.0856183	−	0.0494318i
$776$	−6.94309	−	13.4677i	−0.249243	−	0.483463i
$777$	−9.45741	−	1.27364i	−0.339283	−	0.0456915i
$778$	2.27510	+	5.68294i	0.0815664	+	0.203743i
$779$	1.36128	−	0.874842i	0.0487729	−	0.0313445i
$780$	0.139874	+	15.6553i	0.00500828	+	0.560550i
$781$	1.65196	−	17.3001i	0.0591118	−	0.619047i
$782$	−10.9337	+	23.9414i	−0.390987	+	0.856142i
$783$	2.81881	+	3.39316i	0.100736	+	0.121262i
$784$	3.67113	−	5.15537i	0.131112	−	0.184120i
$785$	−15.1379	+	2.91758i	−0.540294	+	0.104133i
$786$	9.55356	+	2.22748i	0.340764	+	0.0794517i
$787$	−8.06980	+	10.2616i	−0.287657	+	0.365786i	−0.908309	−	0.418301i	$-0.862626\pi$
$787$	−8.06980	+	10.2616i	−0.287657	+	0.365786i	0.620651	+	0.784087i	$0.286868\pi$
$788$	−1.48478	+	6.12037i	−0.0528933	+	0.218029i
$789$	3.87083	+	3.29400i	0.137805	+	0.117270i
$790$	49.7397	−	7.15148i	1.76966	−	0.254438i
$791$	14.9840	−	0.713777i	0.532770	−	0.0253790i
$792$	−6.63344	−	1.15597i	−0.235709	−	0.0410755i
$793$	−10.7757	−	10.2746i	−0.382657	−	0.364863i
$794$	19.3107	+	27.1180i	0.685309	+	0.962383i
$795$	−11.5144	−	7.25531i	−0.408373	−	0.257319i
$796$	20.4490	+	13.1418i	0.724797	+	0.465799i
$797$	−5.56893	+	28.8944i	−0.197262	+	1.02349i	0.739403	+	0.673263i	$0.235108\pi$
$797$	−5.56893	+	28.8944i	−0.197262	+	1.02349i	−0.936665	+	0.350228i	$0.886104\pi$
$798$	−1.78110	+	2.30697i	−0.0630502	+	0.0816659i
$799$	−9.50860	+	2.79198i	−0.336390	+	0.0987730i
$800$	−2.59729	+	2.04253i	−0.0918280	+	0.0722144i
$801$	25.1892	−	22.6271i	0.890015	−	0.799488i
$802$	11.4000	+	32.9381i	0.402547	+	1.16308i
$803$	−37.2087			−1.31307
$804$	−2.76385	+	13.9054i	−0.0974735	+	0.490407i
$805$	−17.5110			−0.617181
$806$	−0.854527	−	2.46899i	−0.0300994	−	0.0869666i
$807$	−20.4584	−	31.2171i	−0.720170	−	1.09889i
$808$	0.965627	−	0.759377i	0.0339706	−	0.0267148i
$809$	−7.02185	+	2.06180i	−0.246875	+	0.0724890i	−0.402829	−	0.915275i	$-0.631973\pi$
$809$	−7.02185	+	2.06180i	−0.246875	+	0.0724890i	0.155954	+	0.987764i	$0.450155\pi$
$810$	5.21004	−	25.4066i	0.183062	−	0.892698i
$811$	−9.83756	+	51.0421i	−0.345444	+	1.79233i	0.228615	+	0.973517i	$0.426580\pi$
$811$	−9.83756	+	51.0421i	−0.345444	+	1.79233i	−0.574059	+	0.818814i	$0.694632\pi$
$812$	−0.585059	−	0.375994i	−0.0205315	−	0.0131948i
$813$	−27.0780	+	42.9735i	−0.949666	+	1.50715i
$814$	8.75603	+	12.2961i	0.306899	+	0.430979i
$815$	13.4821	+	12.8552i	0.472258	+	0.450297i
$816$	5.82547	+	1.95811i	0.203932	+	0.0685476i
$817$	−8.28824	+	0.394818i	−0.289969	+	0.0138129i
$818$	34.9894	−	5.03071i	1.22338	−	0.175895i
$819$	6.55842	+	4.05111i	0.229170	+	0.141557i
$820$	0.535209	−	2.20616i	0.0186903	−	0.0770426i
$821$	15.7694	−	20.0524i	0.550356	−	0.699835i	−0.428695	−	0.903449i	$-0.641027\pi$
$821$	15.7694	−	20.0524i	0.550356	−	0.699835i	0.979051	+	0.203615i	$0.0652689\pi$
$822$	−6.82330	+	29.2648i	−0.237990	+	1.02073i
$823$	31.1808	−	6.00960i	1.08689	−	0.209481i	0.385822	−	0.922573i	$-0.373918\pi$
$823$	31.1808	−	6.00960i	1.08689	−	0.209481i	0.701071	+	0.713092i	$0.252706\pi$
$824$	−3.31691	+	4.65795i	−0.115550	+	0.162268i
$825$	11.8820	−	4.88045i	0.413678	−	0.169916i
$826$	−2.01634	+	4.41516i	−0.0701574	+	0.153623i
$827$	−1.40004	+	14.6618i	−0.0486840	+	0.509842i	0.937936	+	0.346807i	$0.112734\pi$
$827$	−1.40004	+	14.6618i	−0.0486840	+	0.509842i	−0.986620	+	0.163034i	$0.947872\pi$
$828$	21.9665	−	3.56000i	0.763388	−	0.123719i
$829$	−7.40115	+	4.75643i	−0.257052	+	0.165198i	−0.662820	−	0.748779i	$-0.730641\pi$
$829$	−7.40115	+	4.75643i	−0.257052	+	0.165198i	0.405768	+	0.913976i	$0.367004\pi$
$830$	−3.28153	−	8.19686i	−0.113904	−	0.284517i
$831$	1.78257	−	13.2365i	0.0618367	−	0.459169i
$832$	1.43731	+	2.78799i	0.0498296	+	0.0966560i
$833$	19.4479	−	11.2283i	0.673831	−	0.389037i
$834$	−5.04979	+	12.9478i	−0.174860	+	0.448347i
$835$	−17.9969	−	0.857296i	−0.622807	−	0.0296680i
$836$	4.58942	−	0.438236i	0.158728	−	0.0151567i
$837$	0.526735	+	4.29596i	0.0182066	+	0.148490i
$838$	−24.7872	−	8.57893i	−0.856259	−	0.296354i
$839$	−0.0457946	−	0.479582i	−0.00158100	−	0.0165570i	0.994647	−	0.103331i	$-0.0329502\pi$
$839$	−0.0457946	−	0.479582i	−0.00158100	−	0.0165570i	−0.996228	+	0.0867742i	$0.972344\pi$
$840$	0.425020	+	4.06671i	0.0146646	+	0.140315i
$841$	−14.1396	+	24.4906i	−0.487574	+	0.844503i
$842$	−0.969561	−	1.67933i	−0.0334133	−	0.0578735i
$843$	−28.7587	−	39.6317i	−0.990502	−	1.36499i
$844$	4.63860	+	1.36201i	0.159667	+	0.0468825i
$845$	8.45734	−	3.38581i	0.290941	−	0.116475i
$846$	6.42930	+	5.37292i	0.221044	+	0.184725i
$847$	4.83467	+	0.695120i	0.166121	+	0.0238846i
$848$	−2.71434	−	0.259188i	−0.0932107	−	0.00890054i
$849$	−20.8414	−	5.91785i	−0.715275	−	0.203100i
$850$	−11.3937	+	2.76408i	−0.390801	+	0.0948073i
$851$	−40.6372	−	28.9376i	−1.39302	−	0.991968i
$852$	12.6339	−	4.49942i	0.432830	−	0.154148i
$853$	−13.0407	−	5.22071i	−0.446505	−	0.178754i	0.137503	−	0.990501i	$-0.456092\pi$
$853$	−13.0407	−	5.22071i	−0.446505	−	0.178754i	−0.584008	+	0.811748i	$0.698516\pi$
$854$	−3.05663	−	2.40376i	−0.104596	−	0.0822549i
$855$	1.16174	+	17.7196i	0.0397305	+	0.605997i
$856$	−6.64619	+	5.75896i	−0.227162	+	0.196837i
$857$	−1.35615	−	9.43224i	−0.0463253	−	0.322199i	−0.999786	−	0.0206824i	$-0.993416\pi$
$857$	−1.35615	−	9.43224i	−0.0463253	−	0.322199i	0.953461	−	0.301517i	$-0.0974930\pi$
$858$	−2.41460	−	11.9525i	−0.0824330	−	0.408051i
$859$	28.9496	+	14.9245i	0.987746	+	0.509218i	0.874853	−	0.484389i	$-0.160958\pi$
$859$	28.9496	+	14.9245i	0.987746	+	0.509218i	0.112893	+	0.993607i	$0.463988\pi$
$860$	−8.03319	+	8.42497i	−0.273930	+	0.287289i
$861$	−0.778558	−	0.802056i	−0.0265332	−	0.0273340i
$862$	−20.1925	−	17.4969i	−0.687759	−	0.595947i
$863$	4.86406	−	7.56863i	0.165575	−	0.257639i	−0.748545	−	0.663084i	$-0.769247\pi$
$863$	4.86406	−	7.56863i	0.165575	−	0.257639i	0.914119	+	0.405445i	$0.132883\pi$
$864$	−1.35993	−	5.01504i	−0.0462658	−	0.170615i
$865$	38.2572	+	40.1230i	1.30078	+	1.36422i
$866$	0.157595	+	0.536720i	0.00535530	+	0.0182385i
$867$	−5.57489	−	5.22135i	−0.189333	−	0.177326i
$868$	−0.283461	−	0.620692i	−0.00962128	−	0.0210677i
$869$	−36.9865	+	12.8011i	−1.25468	+	0.434249i
$870$	−4.18863	+	0.640480i	−0.142008	+	0.0217143i
$871$	−25.2797	+	4.48691i	−0.856569	+	0.152033i
$872$			11.0895i			0.375539i
$873$	−36.5506	+	27.0246i	−1.23705	+	0.914645i
$874$	−13.8596	+	6.32945i	−0.468806	+	0.214097i
$875$	2.47464	+	3.14676i	0.0836581	+	0.106380i
$876$	−12.1610	−	26.0114i	−0.410884	−	0.878845i
$877$	26.3728	−	25.1464i	0.890546	−	0.849134i	−0.0987414	−	0.995113i	$-0.531482\pi$
$877$	26.3728	−	25.1464i	0.890546	−	0.849134i	0.989288	+	0.145979i	$0.0466332\pi$
$878$	−6.54032	−	1.26054i	−0.220725	−	0.0425413i
$879$	43.1783	+	19.2545i	1.45637	+	0.649438i
$880$	4.23557	−	4.88811i	0.142781	−	0.164778i
$881$	−33.0192	+	23.5128i	−1.11244	+	0.792168i	−0.979995	−	0.199022i	$-0.936224\pi$
$881$	−33.0192	+	23.5128i	−1.11244	+	0.792168i	−0.132449	+	0.991190i	$0.542284\pi$
$882$	−17.0288	−	8.39729i	−0.573390	−	0.282751i
$883$	14.9817	−	29.0605i	0.504176	−	0.977965i	−0.490155	−	0.871635i	$-0.663060\pi$
$883$	14.9817	−	29.0605i	0.504176	−	0.977965i	0.994331	−	0.106329i	$-0.0339098\pi$
$884$	0.529573	+	11.1171i	0.0178115	+	0.373908i
$885$	8.58493	+	28.2998i	0.288579	+	0.951286i
$886$	12.9422	+	14.9361i	0.434803	+	0.501789i
$887$	43.4425	+	10.5390i	1.45866	+	0.353866i	0.885139	−	0.465327i	$-0.154063\pi$
$887$	43.4425	+	10.5390i	1.45866	+	0.353866i	0.573518	+	0.819193i	$0.305578\pi$
$888$	−5.73407	+	10.1398i	−0.192423	+	0.340271i
$889$	4.82999	−	12.0647i	0.161993	−	0.404638i
$890$	6.15531	+	31.9368i	0.206326	+	1.07052i
$891$	−0.239620	+	20.1988i	−0.00802758	+	0.676686i
$892$	−1.45561	−	6.00012i	−0.0487376	−	0.200899i
$893$	−5.21844	−	2.38318i	−0.174628	−	0.0797501i
$894$	32.2125	−	1.82305i	1.07735	−	0.0609719i
$895$	10.0909	−	70.1836i	0.337301	−	2.34598i
$896$	0.442895	+	0.689158i	0.0147961	+	0.0230232i
$897$	20.4607	+	34.7189i	0.683163	+	1.15923i
$898$	−0.672945	+	2.29184i	−0.0224565	+	0.0764797i
$899$	0.628522	−	0.324026i	0.0209624	−	0.0108069i
$900$	7.29520	+	6.71123i	0.243173	+	0.223708i
$901$	−8.37876	−	4.83748i	−0.279137	−	0.161160i
$902$	−0.0841322	+	1.76615i	−0.00280129	+	0.0588064i
$903$	1.40104	+	5.55796i	0.0466237	+	0.184957i
$904$	5.98917	−	17.3046i	0.199197	−	0.575541i
$905$	−3.12062	+	9.01643i	−0.103733	+	0.299716i
$906$	−5.61854	−	22.2889i	−0.186663	−	0.740498i
$907$	1.68902	−	35.4570i	0.0560831	−	1.17733i	−0.778934	−	0.627106i	$-0.784239\pi$
$907$	1.68902	−	35.4570i	0.0560831	−	1.17733i	0.835017	−	0.550224i	$-0.185458\pi$
$908$	13.4391	+	7.75905i	0.445991	+	0.257493i
$909$	−2.71223	−	2.49512i	−0.0899589	−	0.0827579i
$910$	−6.58160	+	3.39305i	−0.218178	+	0.112479i
$911$	−4.96468	+	16.9081i	−0.164487	+	0.560191i	0.835456	+	0.549557i	$0.185203\pi$
$911$	−4.96468	+	16.9081i	−0.164487	+	0.560191i	−0.999943	+	0.0106347i	$0.996615\pi$
$912$	1.80633	+	3.06508i	0.0598136	+	0.101495i
$913$	3.71793	+	5.78521i	0.123045	+	0.191462i
$914$	4.19293	−	29.1625i	0.138690	−	0.964608i
$915$	−23.6545	+	1.33872i	−0.781994	+	0.0442566i
$916$	3.46291	+	1.58146i	0.114418	+	0.0522528i
$917$	1.09385	+	4.50893i	0.0361223	+	0.148898i
$918$	3.00283	−	18.1911i	0.0991083	−	0.600395i
$919$	−1.72421	−	8.94608i	−0.0568766	−	0.295104i	0.942341	−	0.334654i	$-0.108620\pi$
$919$	−1.72421	−	8.94608i	−0.0568766	−	0.295104i	−0.999218	+	0.0395505i	$0.987407\pi$
$920$	−7.94451	+	19.8444i	−0.261923	+	0.654251i
$921$	−12.4168	+	21.9573i	−0.409149	+	0.723519i
$922$	−13.9453	−	3.38310i	−0.459265	−	0.111417i
$923$	15.9047	+	18.3550i	0.523508	+	0.604161i
$924$	−0.924494	−	3.04755i	−0.0304136	−	0.100257i
$925$	−1.05738	−	22.1972i	−0.0347666	−	0.729841i
$926$	−9.74980	+	18.9120i	−0.320398	+	0.621486i
$927$	15.3858	+	7.58707i	0.505336	+	0.249192i
$928$	−0.691532	+	0.492438i	−0.0227006	+	0.0161651i
$929$	9.03707	−	10.4293i	0.296497	−	0.342175i	−0.587881	−	0.808947i	$-0.700038\pi$
$929$	9.03707	−	10.4293i	0.296497	−	0.342175i	0.884378	+	0.466772i	$0.154583\pi$
$930$	−3.79704	−	1.69322i	−0.124510	−	0.0555228i
$931$	12.7651	+	2.46026i	0.418358	+	0.0806319i
$932$	2.37933	−	2.26869i	0.0779375	−	0.0743133i
$933$	−6.84036	−	14.6309i	−0.223943	−	0.478996i
$934$	−20.5938	−	26.1872i	−0.673851	−	0.856871i
$935$	20.8758	−	9.53366i	0.682712	−	0.311784i
$936$	7.56642	−	5.59443i	0.247316	−	0.182860i
$937$			11.5430i			0.377093i	0.982064	+	0.188546i	$0.0603776\pi$
$937$			11.5430i			0.377093i	−0.982064	+	0.188546i	$0.939622\pi$
$938$	−6.46100	+	1.79413i	−0.210959	+	0.0585803i
$939$	−25.8055	+	3.94589i	−0.842129	+	0.128769i
$940$	−7.60574	+	2.63237i	−0.248072	+	0.0858586i
$941$	8.23839	+	18.0396i	0.268564	+	0.588073i	0.995080	−	0.0990768i	$-0.0315890\pi$
$941$	8.23839	+	18.0396i	0.268564	+	0.588073i	−0.726516	+	0.687150i	$0.758862\pi$
$942$	6.76304	+	6.33416i	0.220352	+	0.206378i
$943$	−1.64631	−	5.60683i	−0.0536113	−	0.182583i
$944$	4.08873	+	4.28813i	0.133077	+	0.139567i
$945$	11.8390	−	3.21039i	0.385123	−	0.104434i
$946$	4.90188	−	7.62748i	0.159374	−	0.247991i
$947$	−0.141488	−	0.122600i	−0.00459774	−	0.00398397i	0.652559	−	0.757738i	$-0.273696\pi$
$947$	−0.141488	−	0.122600i	−0.00459774	−	0.00398397i	−0.657157	+	0.753754i	$0.728241\pi$
$948$	−21.0373	−	21.6722i	−0.683259	−	0.703881i
$949$	35.8838	−	37.6339i	1.16484	−	1.22165i
$950$	−6.03260	−	3.11002i	−0.195723	−	0.100902i
$951$	−11.2869	−	55.8713i	−0.366004	−	1.81175i
$952$	0.413672	+	2.87716i	0.0134072	+	0.0932491i
$953$	−23.4781	+	20.3439i	−0.760530	+	0.659003i	−0.946190	−	0.323611i	$-0.895103\pi$
$953$	−23.4781	+	20.3439i	−0.760530	+	0.659003i	0.185660	+	0.982614i	$0.440558\pi$
$954$	0.535154	+	8.16253i	0.0173262	+	0.264272i
$955$	42.5176	+	33.4362i	1.37584	+	1.08197i
$956$	−14.7910	−	5.92140i	−0.478374	−	0.191512i
$957$	3.10903	−	1.10725i	0.100501	−	0.0357922i
$958$	31.8459	+	22.6773i	1.02889	+	0.732672i
$959$	−13.8119	+	3.35073i	−0.446010	+	0.108201i
$960$	4.80145	+	1.36336i	0.154966	+	0.0440022i
$961$	−30.1690	−	2.88079i	−0.973192	−	0.0929286i
$962$	−20.8809	−	3.00222i	−0.673226	−	0.0967953i
$963$	20.2441	+	16.9179i	0.652357	+	0.545171i
$964$	−20.3370	+	8.14172i	−0.655012	+	0.262227i
$965$	45.4903	+	13.3572i	1.46439	+	0.429982i
$966$	6.18145	+	8.51852i	0.198885	+	0.274079i
$967$	3.22237	+	5.58131i	0.103624	+	0.179483i	0.913175	−	0.407567i	$-0.133623\pi$
$967$	3.22237	+	5.58131i	0.103624	+	0.179483i	−0.809551	+	0.587050i	$0.800289\pi$
$968$	2.98118	−	5.16355i	0.0958186	−	0.165963i
$969$	1.31219	+	12.5554i	0.0421537	+	0.403338i
$970$	−4.15051	−	43.4661i	−0.133265	−	1.39561i
$971$	16.8107	+	5.81824i	0.539481	+	0.186716i	0.583202	−	0.812327i	$-0.301800\pi$
$971$	16.8107	+	5.81824i	0.539481	+	0.186716i	−0.0437202	+	0.999044i	$0.513921\pi$
$972$	−14.1987	+	6.43413i	−0.455422	+	0.206375i
$973$	−6.54341	+	0.624820i	−0.209772	+	0.0200308i
$974$	−31.7980	−	1.51473i	−1.01887	−	0.0485350i
$975$	−6.52270	+	16.7244i	−0.208894	+	0.535611i
$976$	−4.11083	+	2.37339i	−0.131584	+	0.0759702i
$977$	−10.2155	−	19.8153i	−0.326823	−	0.633949i	0.666983	−	0.745073i	$-0.267585\pi$
$977$	−10.2155	−	19.8153i	−0.326823	−	0.633949i	−0.993807	+	0.111124i	$0.964555\pi$
$978$	1.49438	−	11.0965i	0.0477849	−	0.354828i
$979$	−9.41508	−	23.5177i	−0.300907	−	0.751630i
$980$	15.3428	−	9.86022i	0.490108	−	0.314973i
$981$	32.8401	−	5.32224i	1.04850	−	0.169926i
$982$	−3.03697	+	31.8046i	−0.0969136	+	1.01492i
$983$	−22.8554	+	50.0463i	−0.728973	+	1.59623i	0.0719135	+	0.997411i	$0.477089\pi$
$983$	−22.8554	+	50.0463i	−0.728973	+	1.59623i	−0.800886	+	0.598817i	$0.795638\pi$
$984$	−1.26216	+	0.518423i	−0.0402361	+	0.0165267i
$985$	−10.5273	+	14.7835i	−0.335426	+	0.471040i
$986$	−2.95784	+	0.570077i	−0.0941969	+	0.0181550i
$987$	−0.899844	+	3.85938i	−0.0286423	+	0.122846i
$988$	−3.98276	+	5.06449i	−0.126708	+	0.161123i
$989$	−7.06443	+	29.1200i	−0.224636	+	0.925962i
$990$	−16.5083	−	10.1971i	−0.524667	−	0.324085i
$991$	9.65471	−	1.38814i	0.306692	−	0.0440957i	0.0127494	−	0.999919i	$-0.495942\pi$
$991$	9.65471	−	1.38814i	0.306692	−	0.0440957i	0.293943	+	0.955823i	$0.405033\pi$
$992$	−0.832006	+	0.0396333i	−0.0264162	+	0.00125836i
$993$	−25.2728	−	8.49494i	−0.802009	−	0.269579i
$994$	4.59068	+	4.37721i	0.145608	+	0.138837i
$995$	40.6318	+	57.0594i	1.28811	+	1.80890i
$996$	−2.82911	+	4.48988i	−0.0896438	+	0.142267i
$997$	34.2559	+	22.0149i	1.08489	+	0.697219i	0.955683	−	0.294398i	$-0.0951190\pi$
$997$	34.2559	+	22.0149i	1.08489	+	0.697219i	0.129212	+	0.991617i	$0.458755\pi$
$998$	−4.72593	+	24.5204i	−0.149597	+	0.776181i
$999$	32.7797	+	12.1142i	1.03710	+	0.383276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	402.2.n.b.11.2	yes	220
3.2	odd	2		402.2.n.a.11.1	✓	220
67.61	odd	66		402.2.n.a.329.1	yes	220
201.128	even	66	inner	402.2.n.b.329.2	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
402.2.n.a.11.1	✓	220	3.2	odd	2
402.2.n.a.329.1	yes	220	67.61	odd	66
402.2.n.b.11.2	yes	220	1.1	even	1	trivial
402.2.n.b.329.2	yes	220	201.128	even	66	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:	\( N \)	\(=\)	\( 402 = 2 \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	402.n (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 - 0.945001i) q^{2} +(-1.44867 + 0.949398i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(-2.76497 + 0.811870i) q^{5} +(1.37100 + 1.05848i) q^{6} +(-0.155035 + 0.804400i) q^{7} +(0.841254 + 0.540641i) q^{8} +(1.19729 - 2.75073i) q^{9} +O(q^{10})\)	\(q+(-0.327068 - 0.945001i) q^{2} +(-1.44867 + 0.949398i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(-2.76497 + 0.811870i) q^{5} +(1.37100 + 1.05848i) q^{6} +(-0.155035 + 0.804400i) q^{7} +(0.841254 + 0.540641i) q^{8} +(1.19729 - 2.75073i) q^{9} +(1.67155 + 2.34737i) q^{10} +(-1.62440 - 1.54886i) q^{11} +(0.551852 - 1.64179i) q^{12} +(3.13312 - 0.149249i) q^{13} +(0.810866 - 0.116585i) q^{14} +(3.23475 - 3.80119i) q^{15} +(0.235759 - 0.971812i) q^{16} +(2.19338 - 2.78911i) q^{17} +(-2.99103 - 0.231762i) q^{18} +(2.01695 - 0.388735i) q^{19} +(1.67155 - 2.34737i) q^{20} +(-0.539101 - 1.31250i) q^{21} +(-0.932387 + 2.04164i) q^{22} +(0.705097 - 7.38411i) q^{23} +(-1.73198 + 0.0154745i) q^{24} +(2.77968 - 1.78639i) q^{25} +(-1.16578 - 2.91199i) q^{26} +(0.877062 + 5.12160i) q^{27} +(-0.375381 - 0.728137i) q^{28} +(0.735210 - 0.424474i) q^{29} +(-4.65011 - 1.81359i) q^{30} +(0.832006 + 0.0396333i) q^{31} +(-0.995472 + 0.0950560i) q^{32} +(3.82370 + 0.701587i) q^{33} +(-3.35310 - 1.16052i) q^{34} +(-0.224399 - 2.35001i) q^{35} +(0.759256 + 2.90233i) q^{36} +(3.36274 - 5.82443i) q^{37} +(-1.02703 - 1.77887i) q^{38} +(-4.39716 + 3.19079i) q^{39} +(-2.76497 - 0.811870i) q^{40} +(0.731352 - 0.292789i) q^{41} +(-1.06399 + 0.938727i) q^{42} +(-3.99850 - 0.574897i) q^{43} +(2.23431 + 0.213350i) q^{44} +(-1.07723 + 8.57773i) q^{45} +(-7.20860 + 1.74879i) q^{46} +(-2.27505 - 1.62006i) q^{47} +(0.581099 + 1.63166i) q^{48} +(5.87555 + 2.35222i) q^{49} +(-2.59729 - 2.04253i) q^{50} +(-0.529509 + 6.12290i) q^{51} +(-2.37054 + 2.05408i) q^{52} +(-0.388048 - 2.69893i) q^{53} +(4.55305 - 2.50394i) q^{54} +(5.74890 + 2.96376i) q^{55} +(-0.565315 + 0.592886i) q^{56} +(-2.55283 + 2.47803i) q^{57} +(-0.641591 - 0.555942i) q^{58} +(-3.20330 + 4.98444i) q^{59} +(-0.192942 + 4.98753i) q^{60} +(-3.27565 - 3.43540i) q^{61} +(-0.234669 - 0.799209i) q^{62} +(2.02706 + 1.38956i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-8.54182 + 2.95635i) q^{65} +(-0.587611 - 3.84287i) q^{66} +(-8.11833 + 1.04537i) q^{67} +3.54825i q^{68} +(5.98900 + 11.3665i) q^{69} +(-2.14737 + 0.980671i) q^{70} +(4.78637 + 6.08637i) q^{71} +(2.49438 - 1.66676i) q^{72} +(11.9980 - 11.4401i) q^{73} +(-6.60393 - 1.27280i) q^{74} +(-2.33084 + 5.22692i) q^{75} +(-1.34513 + 1.55236i) q^{76} +(1.49774 - 1.06654i) q^{77} +(4.45347 + 3.11171i) q^{78} +(7.99055 - 15.4995i) q^{79} +(0.137117 + 2.87844i) q^{80} +(-6.13301 - 6.58682i) q^{81} +(-0.515888 - 0.595366i) q^{82} +(-2.97756 - 0.722348i) q^{83} +(1.23510 + 0.698445i) q^{84} +(-3.80025 + 9.49257i) q^{85} +(0.764502 + 3.96661i) q^{86} +(-0.662082 + 1.31293i) q^{87} +(-0.529154 - 2.18120i) q^{88} +(10.2666 + 4.68861i) q^{89} +(8.45829 - 1.78751i) q^{90} +(-0.365688 + 2.54342i) q^{91} +(4.01031 + 6.24016i) q^{92} +(-1.24293 + 0.732489i) q^{93} +(-0.786860 + 2.67980i) q^{94} +(-5.26120 + 2.71234i) q^{95} +(1.35186 - 1.08280i) q^{96} +(-13.1221 - 7.57605i) q^{97} +(0.301141 - 6.32174i) q^{98} +(-6.20537 + 2.61385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 11 q^{2} - q^{3} + 11 q^{4} - q^{6} + 6 q^{7} - 22 q^{8} - q^{9}+O(q^{10}) \) 220 * q + 11 * q^2 - q^3 + 11 * q^4 - q^6 + 6 * q^7 - 22 * q^8 - q^9	\( 220 q + 11 q^{2} - q^{3} + 11 q^{4} - q^{6} + 6 q^{7} - 22 q^{8} - q^{9} - 6 q^{11} - 9 q^{12} - 6 q^{13} + 22 q^{14} - 4 q^{15} + 11 q^{16} - 30 q^{17} - 9 q^{18} + 25 q^{19} + 99 q^{21} + 12 q^{22} - 8 q^{23} + 10 q^{24} - 10 q^{25} - 16 q^{26} - 28 q^{27} - 6 q^{28} - 6 q^{29} + 5 q^{30} - 2 q^{31} + 11 q^{32} - 20 q^{33} - 3 q^{34} - 170 q^{35} - q^{36} + 10 q^{37} + 3 q^{38} - 3 q^{39} + 74 q^{41} + 16 q^{42} - 22 q^{43} - 6 q^{44} + 37 q^{45} + 30 q^{46} + 12 q^{47} + 10 q^{48} - 27 q^{49} + 27 q^{50} - 3 q^{51} + 22 q^{52} + 2 q^{53} + 25 q^{54} - 144 q^{55} + 6 q^{56} + 16 q^{57} - 44 q^{58} + 33 q^{59} - q^{60} - 148 q^{61} + 22 q^{62} + 38 q^{63} - 22 q^{64} + 5 q^{66} - 24 q^{67} - 80 q^{69} - 154 q^{70} - 18 q^{71} - 12 q^{72} - 167 q^{73} - 122 q^{74} - 32 q^{75} - 50 q^{76} + 44 q^{77} - 18 q^{78} + 12 q^{79} + 47 q^{81} - 38 q^{82} + 165 q^{83} + 39 q^{84} - 30 q^{85} + 3 q^{86} - 98 q^{87} - 6 q^{88} + 22 q^{89} + 6 q^{90} + 4 q^{91} + 124 q^{93} + 22 q^{94} - 142 q^{95} + 2 q^{96} - 69 q^{97} - 27 q^{98} - 57 q^{99}+O(q^{100}) \) 220 * q + 11 * q^2 - q^3 + 11 * q^4 - q^6 + 6 * q^7 - 22 * q^8 - q^9 - 6 * q^11 - 9 * q^12 - 6 * q^13 + 22 * q^14 - 4 * q^15 + 11 * q^16 - 30 * q^17 - 9 * q^18 + 25 * q^19 + 99 * q^21 + 12 * q^22 - 8 * q^23 + 10 * q^24 - 10 * q^25 - 16 * q^26 - 28 * q^27 - 6 * q^28 - 6 * q^29 + 5 * q^30 - 2 * q^31 + 11 * q^32 - 20 * q^33 - 3 * q^34 - 170 * q^35 - q^36 + 10 * q^37 + 3 * q^38 - 3 * q^39 + 74 * q^41 + 16 * q^42 - 22 * q^43 - 6 * q^44 + 37 * q^45 + 30 * q^46 + 12 * q^47 + 10 * q^48 - 27 * q^49 + 27 * q^50 - 3 * q^51 + 22 * q^52 + 2 * q^53 + 25 * q^54 - 144 * q^55 + 6 * q^56 + 16 * q^57 - 44 * q^58 + 33 * q^59 - q^60 - 148 * q^61 + 22 * q^62 + 38 * q^63 - 22 * q^64 + 5 * q^66 - 24 * q^67 - 80 * q^69 - 154 * q^70 - 18 * q^71 - 12 * q^72 - 167 * q^73 - 122 * q^74 - 32 * q^75 - 50 * q^76 + 44 * q^77 - 18 * q^78 + 12 * q^79 + 47 * q^81 - 38 * q^82 + 165 * q^83 + 39 * q^84 - 30 * q^85 + 3 * q^86 - 98 * q^87 - 6 * q^88 + 22 * q^89 + 6 * q^90 + 4 * q^91 + 124 * q^93 + 22 * q^94 - 142 * q^95 + 2 * q^96 - 69 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

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Database

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