LMFDB - Embedded newform 209.2.e.b.45.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(45,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.e (of order $3$, degree $2$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 14 x^{16} - 11 x^{15} + 130 x^{14} - 92 x^{13} + 629 x^{12} - 276 x^{11} + 2060 x^{10} + \cdots + 9 $ x^18 - x^17 + 14x^16 - 11x^15 + 130x^14 - 92x^13 + 629x^12 - 276x^11 + 2060x^10 - 681x^9 + 3955x^8 - 115x^7 + 4735x^6 + 105x^5 + 2904x^4 + 1230x^3 + 639x^2 + 81x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.2
Root			$-0.918695 - 1.59123i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.918695 - 1.59123i) q^{2} +(-1.56355 - 2.70815i) q^{3} +(-0.688002 + 1.19165i) q^{4} +(1.63491 + 2.83176i) q^{5} +(-2.87286 + 4.97594i) q^{6} -3.63195 q^{7} -1.14653 q^{8} +(-3.38940 + 5.87061i) q^{9} +O(q^{10})$	\(q+(-0.918695 - 1.59123i) q^{2} +(-1.56355 - 2.70815i) q^{3} +(-0.688002 + 1.19165i) q^{4} +(1.63491 + 2.83176i) q^{5} +(-2.87286 + 4.97594i) q^{6} -3.63195 q^{7} -1.14653 q^{8} +(-3.38940 + 5.87061i) q^{9} +(3.00398 - 5.20304i) q^{10} -1.00000 q^{11} +4.30291 q^{12} +(0.224204 - 0.388333i) q^{13} +(3.33666 + 5.77926i) q^{14} +(5.11255 - 8.85520i) q^{15} +(2.42931 + 4.20769i) q^{16} +(-2.11349 - 3.66068i) q^{17} +12.4553 q^{18} +(-3.96002 - 1.82160i) q^{19} -4.49930 q^{20} +(5.67875 + 9.83588i) q^{21} +(0.918695 + 1.59123i) q^{22} +(0.506437 - 0.877175i) q^{23} +(1.79265 + 3.10497i) q^{24} +(-2.84589 + 4.92923i) q^{25} -0.823900 q^{26} +11.8167 q^{27} +(2.49879 - 4.32803i) q^{28} +(3.37309 - 5.84237i) q^{29} -18.7875 q^{30} -7.00544 q^{31} +(3.31707 - 5.74533i) q^{32} +(1.56355 + 2.70815i) q^{33} +(-3.88331 + 6.72610i) q^{34} +(-5.93793 - 10.2848i) q^{35} +(-4.66382 - 8.07798i) q^{36} -10.8857 q^{37} +(0.739482 + 7.97479i) q^{38} -1.40222 q^{39} +(-1.87447 - 3.24668i) q^{40} +(0.641035 + 1.11031i) q^{41} +(10.4341 - 18.0723i) q^{42} +(2.08321 + 3.60823i) q^{43} +(0.688002 - 1.19165i) q^{44} -22.1655 q^{45} -1.86105 q^{46} +(3.38128 - 5.85655i) q^{47} +(7.59671 - 13.1579i) q^{48} +6.19106 q^{49} +10.4580 q^{50} +(-6.60912 + 11.4473i) q^{51} +(0.308505 + 0.534347i) q^{52} +(-1.19500 + 2.06979i) q^{53} +(-10.8559 - 18.8030i) q^{54} +(-1.63491 - 2.83176i) q^{55} +4.16412 q^{56} +(1.25855 + 13.5725i) q^{57} -12.3954 q^{58} +(4.75456 + 8.23514i) q^{59} +(7.03489 + 12.1848i) q^{60} +(-2.33126 + 4.03785i) q^{61} +(6.43586 + 11.1472i) q^{62} +(12.3101 - 21.3218i) q^{63} -2.47225 q^{64} +1.46622 q^{65} +(2.87286 - 4.97594i) q^{66} +(0.718518 - 1.24451i) q^{67} +5.81635 q^{68} -3.16737 q^{69} +(-10.9103 + 18.8972i) q^{70} +(-5.28163 - 9.14804i) q^{71} +(3.88603 - 6.73080i) q^{72} +(-1.32658 - 2.29770i) q^{73} +(10.0006 + 17.3216i) q^{74} +17.7988 q^{75} +(4.89521 - 3.46572i) q^{76} +3.63195 q^{77} +(1.28821 + 2.23125i) q^{78} +(0.230487 + 0.399216i) q^{79} +(-7.94343 + 13.7584i) q^{80} +(-8.30783 - 14.3896i) q^{81} +(1.17783 - 2.04006i) q^{82} -3.09057 q^{83} -15.6280 q^{84} +(6.91077 - 11.9698i) q^{85} +(3.82767 - 6.62972i) q^{86} -21.0960 q^{87} +1.14653 q^{88} +(2.31283 - 4.00593i) q^{89} +(20.3633 + 35.2703i) q^{90} +(-0.814298 + 1.41040i) q^{91} +(0.696859 + 1.20700i) q^{92} +(10.9534 + 18.9718i) q^{93} -12.4255 q^{94} +(-1.31599 - 14.1920i) q^{95} -20.7456 q^{96} +(-4.62983 - 8.01910i) q^{97} +(-5.68770 - 9.85139i) q^{98} +(3.38940 - 5.87061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) $ 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.918695	−	1.59123i	−0.649616	−	1.12517i	−0.983215	−	0.182452i	$-0.941597\pi$
$2$	−0.918695	−	1.59123i	−0.649616	−	1.12517i	0.333599	−	0.942715i	$-0.391737\pi$
$3$	−1.56355	−	2.70815i	−0.902718	−	1.56355i	−0.823952	−	0.566660i	$-0.808235\pi$
$3$	−1.56355	−	2.70815i	−0.902718	−	1.56355i	−0.0787662	−	0.996893i	$-0.525098\pi$
$4$	−0.688002	+	1.19165i	−0.344001	+	0.595827i
$5$	1.63491	+	2.83176i	0.731156	+	1.26640i	0.956389	+	0.292095i	$0.0943523\pi$
$5$	1.63491	+	2.83176i	0.731156	+	1.26640i	−0.225233	+	0.974305i	$0.572314\pi$
$6$	−2.87286	+	4.97594i	−1.17284	+	2.03142i
$7$	−3.63195			−1.37275			−0.686374	−	0.727249i	$-0.740799\pi$
$7$	−3.63195			−1.37275			−0.686374	+	0.727249i	$0.740799\pi$
$8$	−1.14653			−0.405358
$9$	−3.38940	+	5.87061i	−1.12980	+	1.95687i
$10$	3.00398	−	5.20304i	0.949941	−	1.64535i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	4.30291			1.24214
$13$	0.224204	−	0.388333i	0.0621830	−	0.107704i	−0.833258	−	0.552884i	$-0.813527\pi$
$13$	0.224204	−	0.388333i	0.0621830	−	0.107704i	0.895441	+	0.445180i	$0.146860\pi$
$14$	3.33666	+	5.77926i	0.891759	+	1.54457i
$15$	5.11255	−	8.85520i	1.32006	−	2.28640i
$16$	2.42931	+	4.20769i	0.607328	+	1.05192i
$17$	−2.11349	−	3.66068i	−0.512598	−	0.887845i	−0.999893	−	0.0146081i	$-0.995350\pi$
$17$	−2.11349	−	3.66068i	−0.512598	−	0.887845i	0.487296	−	0.873237i	$-0.337983\pi$
$18$	12.4553			2.93574
$19$	−3.96002	−	1.82160i	−0.908492	−	0.417903i
$19$	−3.96002	−	1.82160i	−0.908492	−	0.417903i
$20$	−4.49930			−1.00607
$21$	5.67875	+	9.83588i	1.23920	+	2.14636i
$22$	0.918695	+	1.59123i	0.195866	+	0.339251i
$23$	0.506437	−	0.877175i	0.105599	−	0.182904i	−0.808384	−	0.588656i	$-0.799657\pi$
$23$	0.506437	−	0.877175i	0.105599	−	0.182904i	0.913983	+	0.405753i	$0.132991\pi$
$24$	1.79265	+	3.10497i	0.365924	+	0.633799i
$25$	−2.84589	+	4.92923i	−0.569179	+	0.985846i
$26$	−0.823900			−0.161580
$27$	11.8167			2.27412
$28$	2.49879	−	4.32803i	0.472227	−	0.817920i
$29$	3.37309	−	5.84237i	0.626367	−	1.08490i	−0.361907	−	0.932214i	$-0.617874\pi$
$29$	3.37309	−	5.84237i	0.626367	−	1.08490i	0.988275	−	0.152686i	$-0.0487923\pi$
$30$	−18.7875			−3.43011
$31$	−7.00544			−1.25821			−0.629107	−	0.777319i	$-0.716579\pi$
$31$	−7.00544			−1.25821			−0.629107	+	0.777319i	$0.716579\pi$
$32$	3.31707	−	5.74533i	0.586380	−	1.01564i
$33$	1.56355	+	2.70815i	0.272180	+	0.471429i
$34$	−3.88331	+	6.72610i	−0.665983	+	1.15352i
$35$	−5.93793	−	10.2848i	−1.00369	−	1.73845i
$36$	−4.66382	−	8.07798i	−0.777304	−	1.34633i
$37$	−10.8857			−1.78960			−0.894799	−	0.446470i	$-0.852681\pi$
$37$	−10.8857			−1.78960			−0.894799	+	0.446470i	$0.852681\pi$
$38$	0.739482	+	7.97479i	0.119960	+	1.29368i
$39$	−1.40222			−0.224535
$40$	−1.87447	−	3.24668i	−0.296380	−	0.513345i
$41$	0.641035	+	1.11031i	0.100113	+	0.173401i	0.911731	−	0.410788i	$-0.134746\pi$
$41$	0.641035	+	1.11031i	0.100113	+	0.173401i	−0.811618	+	0.584188i	$0.801413\pi$
$42$	10.4341	−	18.0723i	1.61001	−	2.78862i
$43$	2.08321	+	3.60823i	0.317687	+	0.550249i	0.980005	−	0.198973i	$-0.0637607\pi$
$43$	2.08321	+	3.60823i	0.317687	+	0.550249i	−0.662318	+	0.749223i	$0.730427\pi$
$44$	0.688002	−	1.19165i	0.103720	−	0.179649i
$45$	−22.1655			−3.30424
$46$	−1.86105			−0.274396
$47$	3.38128	−	5.85655i	0.493210	−	0.854266i	−0.506759	−	0.862088i	$-0.669157\pi$
$47$	3.38128	−	5.85655i	0.493210	−	0.854266i	0.999969	+	0.00782218i	$0.00248990\pi$
$48$	7.59671	−	13.1579i	1.09649	−	1.89918i
$49$	6.19106			0.884438
$50$	10.4580			1.47899
$51$	−6.60912	+	11.4473i	−0.925462	+	1.60295i
$52$	0.308505	+	0.534347i	0.0427820	+	0.0741006i
$53$	−1.19500	+	2.06979i	−0.164145	+	0.284308i	−0.936351	−	0.351064i	$-0.885820\pi$
$53$	−1.19500	+	2.06979i	−0.164145	+	0.284308i	0.772206	+	0.635372i	$0.219153\pi$
$54$	−10.8559	−	18.8030i	−1.47731	−	2.55877i
$55$	−1.63491	−	2.83176i	−0.220452	−	0.381834i
$56$	4.16412			0.556454
$57$	1.25855	+	13.5725i	0.166698	+	1.79772i
$58$	−12.3954			−1.62759
$59$	4.75456	+	8.23514i	0.618991	+	1.07212i	0.989670	+	0.143363i	$0.0457917\pi$
$59$	4.75456	+	8.23514i	0.618991	+	1.07212i	−0.370679	+	0.928761i	$0.620875\pi$
$60$	7.03489	+	12.1848i	0.908200	+	1.57305i
$61$	−2.33126	+	4.03785i	−0.298487	+	0.516994i	−0.975790	−	0.218710i	$-0.929815\pi$
$61$	−2.33126	+	4.03785i	−0.298487	+	0.516994i	0.677303	+	0.735704i	$0.263149\pi$
$62$	6.43586	+	11.1472i	0.817355	+	1.41570i
$63$	12.3101	−	21.3218i	1.55093	−	2.68629i
$64$	−2.47225			−0.309031
$65$	1.46622			0.181862
$66$	2.87286	−	4.97594i	0.353624	−	0.612495i
$67$	0.718518	−	1.24451i	0.0877809	−	0.152041i	−0.818792	−	0.574090i	$-0.805356\pi$
$67$	0.718518	−	1.24451i	0.0877809	−	0.152041i	0.906573	+	0.422049i	$0.138689\pi$
$68$	5.81635			0.705336
$69$	−3.16737			−0.381306
$70$	−10.9103	+	18.8972i	−1.30403	+	2.25865i
$71$	−5.28163	−	9.14804i	−0.626814	−	1.08567i	−0.988187	−	0.153252i	$-0.951025\pi$
$71$	−5.28163	−	9.14804i	−0.626814	−	1.08567i	0.361373	−	0.932421i	$-0.382308\pi$
$72$	3.88603	−	6.73080i	0.457973	−	0.793233i
$73$	−1.32658	−	2.29770i	−0.155264	−	0.268926i	0.777891	−	0.628399i	$-0.216290\pi$
$73$	−1.32658	−	2.29770i	−0.155264	−	0.268926i	−0.933155	+	0.359474i	$0.882956\pi$
$74$	10.0006	+	17.3216i	1.16255	+	2.01360i
$75$	17.7988			2.05523
$76$	4.89521	−	3.46572i	0.561520	−	0.397545i
$77$	3.63195			0.413899
$78$	1.28821	+	2.23125i	0.145861	+	0.252639i
$79$	0.230487	+	0.399216i	0.0259319	+	0.0449153i	0.878700	−	0.477374i	$-0.158411\pi$
$79$	0.230487	+	0.399216i	0.0259319	+	0.0449153i	−0.852768	+	0.522290i	$0.825078\pi$
$80$	−7.94343	+	13.7584i	−0.888103	+	1.53824i
$81$	−8.30783	−	14.3896i	−0.923093	−	1.59884i
$82$	1.17783	−	2.04006i	0.130070	−	0.225287i
$83$	−3.09057			−0.339234			−0.169617	−	0.985510i	$-0.554253\pi$
$83$	−3.09057			−0.339234			−0.169617	+	0.985510i	$0.554253\pi$
$84$	−15.6280			−1.70515
$85$	6.91077	−	11.9698i	0.749578	−	1.29831i
$86$	3.82767	−	6.62972i	0.412748	−	0.714901i
$87$	−21.0960			−2.26173
$88$	1.14653			0.122220
$89$	2.31283	−	4.00593i	0.245159	−	0.424628i	−0.717017	−	0.697055i	$-0.754493\pi$
$89$	2.31283	−	4.00593i	0.245159	−	0.424628i	0.962176	+	0.272427i	$0.0878265\pi$
$90$	20.3633	+	35.2703i	2.14648	+	3.71782i
$91$	−0.814298	+	1.41040i	−0.0853616	+	0.147851i
$92$	0.696859	+	1.20700i	0.0726526	+	0.125838i
$93$	10.9534	+	18.9718i	1.13581	+	1.96728i
$94$	−12.4255			−1.28159
$95$	−1.31599	−	14.1920i	−0.135017	−	1.45607i
$96$	−20.7456			−2.11734
$97$	−4.62983	−	8.01910i	−0.470088	−	0.814216i	0.529327	−	0.848418i	$-0.322444\pi$
$97$	−4.62983	−	8.01910i	−0.470088	−	0.814216i	−0.999415	+	0.0342017i	$0.989111\pi$
$98$	−5.68770	−	9.85139i	−0.574544	−	0.995140i
$99$	3.38940	−	5.87061i	0.340647	−	0.590018i
$100$	−3.91596	−	6.78264i	−0.391596	−	0.678264i
$101$	4.25105	−	7.36304i	0.422995	−	0.732649i	−0.573236	−	0.819391i	$-0.694312\pi$
$101$	4.25105	−	7.36304i	0.422995	−	0.732649i	0.996231	+	0.0867412i	$0.0276453\pi$
$102$	24.2871			2.40478
$103$	5.53668			0.545545			0.272772	−	0.962079i	$-0.412059\pi$
$103$	5.53668			0.545545			0.272772	+	0.962079i	$0.412059\pi$
$104$	−0.257056	+	0.445233i	−0.0252064	+	0.0436587i
$105$	−18.5685	+	32.1617i	−1.81210	+	3.13866i
$106$	4.39135			0.426525
$107$	−2.28330			−0.220735			−0.110368	−	0.993891i	$-0.535203\pi$
$107$	−2.28330			−0.220735			−0.110368	+	0.993891i	$0.535203\pi$
$108$	−8.12990	+	14.0814i	−0.782300	+	1.35498i
$109$	−5.28080	−	9.14661i	−0.505809	−	0.876087i	−0.999977	−	0.00672062i	$-0.997861\pi$
$109$	−5.28080	−	9.14661i	−0.505809	−	0.876087i	0.494168	−	0.869366i	$-0.335473\pi$
$110$	−3.00398	+	5.20304i	−0.286418	+	0.496090i
$111$	17.0204	+	29.4801i	1.61550	+	2.79813i
$112$	−8.82314	−	15.2821i	−0.833708	−	1.44402i
$113$	11.5083			1.08261			0.541304	−	0.840827i	$-0.317931\pi$
$113$	11.5083			1.08261			0.541304	+	0.840827i	$0.317931\pi$
$114$	20.4407	−	14.4716i	1.91445	−	1.35539i
$115$	3.31193			0.308839
$116$	4.64138	+	8.03911i	0.430942	+	0.746413i
$117$	1.51983	+	2.63243i	0.140509	+	0.243368i
$118$	8.73598	−	15.1312i	0.804213	−	1.39294i
$119$	7.67611	+	13.2954i	0.703667	+	1.21879i
$120$	−5.86167	+	10.1527i	−0.535095	+	0.926812i
$121$	1.00000			0.0909091
$122$	8.56685			0.775606
$123$	2.00458	−	3.47204i	0.180747	−	0.313063i
$124$	4.81975	−	8.34805i	0.432826	−	0.749677i
$125$	−2.26202			−0.202322
$126$	−45.2370			−4.03003
$127$	−6.68896	+	11.5856i	−0.593549	+	1.02806i	0.400201	+	0.916428i	$0.368940\pi$
$127$	−6.68896	+	11.5856i	−0.593549	+	1.02806i	−0.993750	+	0.111630i	$0.964393\pi$
$128$	−4.36289	−	7.55675i	−0.385629	−	0.667928i
$129$	6.51442	−	11.2833i	0.573563	−	0.993440i
$130$	−1.34701	−	2.33308i	−0.118140	−	0.204625i
$131$	−2.00208	−	3.46770i	−0.174922	−	0.302974i	0.765212	−	0.643778i	$-0.222634\pi$
$131$	−2.00208	−	3.46770i	−0.174922	−	0.302974i	−0.940134	+	0.340804i	$0.889301\pi$
$132$	−4.30291			−0.374520
$133$	14.3826	+	6.61595i	1.24713	+	0.573675i
$134$	−2.64040			−0.228095
$135$	19.3193	+	33.4620i	1.66274	+	2.87995i
$136$	2.42317	+	4.19706i	0.207786	+	0.359895i
$137$	−2.71647	+	4.70506i	−0.232084	+	0.401980i	−0.958421	−	0.285358i	$-0.907888\pi$
$137$	−2.71647	+	4.70506i	−0.232084	+	0.401980i	0.726338	+	0.687338i	$0.241221\pi$
$138$	2.90984	+	5.04000i	0.247702	+	0.429033i
$139$	−2.97766	+	5.15747i	−0.252562	+	0.437451i	−0.964231	−	0.265065i	$-0.914607\pi$
$139$	−2.97766	+	5.15747i	−0.252562	+	0.437451i	0.711668	+	0.702516i	$0.247940\pi$
$140$	16.3412			1.38109
$141$	−21.1472			−1.78092
$142$	−9.70441	+	16.8085i	−0.814376	+	1.41054i
$143$	−0.224204	+	0.388333i	−0.0187489	+	0.0324740i
$144$	−32.9356			−2.74463
$145$	22.0589			1.83189
$146$	−2.43744	+	4.22178i	−0.201724	+	0.349397i
$147$	−9.68006	−	16.7663i	−0.798398	−	1.38287i
$148$	7.48938	−	12.9720i	0.615623	−	1.06629i
$149$	−7.87700	−	13.6434i	−0.645309	−	1.11771i	−0.984230	−	0.176893i	$-0.943395\pi$
$149$	−7.87700	−	13.6434i	−0.645309	−	1.11771i	0.338921	−	0.940815i	$-0.389938\pi$
$150$	−16.3517	−	28.3220i	−1.33511	−	2.31248i
$151$	−6.79678			−0.553114			−0.276557	−	0.960997i	$-0.589193\pi$
$151$	−6.79678			−0.553114			−0.276557	+	0.960997i	$0.589193\pi$
$152$	4.54027	+	2.08851i	0.368264	+	0.169400i
$153$	28.6539			2.31653
$154$	−3.33666	−	5.77926i	−0.268875	−	0.465706i
$155$	−11.4533	−	19.8377i	−0.919950	−	1.59340i
$156$	0.964729	−	1.67096i	0.0772402	−	0.133784i
$157$	−9.51624	−	16.4826i	−0.759479	−	1.31546i	−0.943117	−	0.332462i	$-0.892121\pi$
$157$	−9.51624	−	16.4826i	−0.759479	−	1.31546i	0.183638	−	0.982994i	$-0.441213\pi$
$158$	0.423495	−	0.733515i	0.0336915	−	0.0583554i
$159$	7.47376			0.592707
$160$	21.6925			1.71494
$161$	−1.83935	+	3.18586i	−0.144961	+	0.251081i
$162$	−15.2647	+	26.4393i	−1.19931	+	2.07727i
$163$	5.43398			0.425622			0.212811	−	0.977093i	$-0.431738\pi$
$163$	5.43398			0.425622			0.212811	+	0.977093i	$0.431738\pi$
$164$	−1.76413			−0.137756
$165$	−5.11255	+	8.85520i	−0.398012	+	0.689376i
$166$	2.83929	+	4.91779i	0.220371	+	0.381695i
$167$	−0.239099	+	0.414132i	−0.0185020	+	0.0320465i	−0.875128	−	0.483891i	$-0.839223\pi$
$167$	−0.239099	+	0.414132i	−0.0185020	+	0.0320465i	0.856626	+	0.515938i	$0.172556\pi$
$168$	−6.51083	−	11.2771i	−0.502321	−	0.870046i
$169$	6.39947	+	11.0842i	0.492267	+	0.852631i
$170$	−25.3956			−1.94775
$171$	24.1160	−	17.0736i	1.84419	−	1.30565i
$172$	−5.73301			−0.437138
$173$	6.94749	+	12.0334i	0.528208	+	0.914883i	0.999459	+	0.0328837i	$0.0104691\pi$
$173$	6.94749	+	12.0334i	0.528208	+	0.914883i	−0.471251	+	0.881999i	$0.656198\pi$
$174$	19.3808	+	33.5686i	1.46926	+	2.54483i
$175$	10.3361	−	17.9027i	0.781339	−	1.35332i
$176$	−2.42931	−	4.20769i	−0.183116	−	0.317167i
$177$	14.8680	−	25.7522i	1.11755	−	1.93565i
$178$	−8.49913			−0.637037
$179$	0.571498			0.0427158			0.0213579	−	0.999772i	$-0.493201\pi$
$179$	0.571498			0.0427158			0.0213579	+	0.999772i	$0.493201\pi$
$180$	15.2499	−	26.4136i	1.13666	−	1.96875i
$181$	11.4762	−	19.8774i	0.853020	−	1.47747i	−0.0254489	−	0.999676i	$-0.508102\pi$
$181$	11.4762	−	19.8774i	0.853020	−	1.47747i	0.878469	−	0.477799i	$-0.158565\pi$
$182$	2.99237			0.221809
$183$	14.5802			1.07780
$184$	−0.580643	+	1.00570i	−0.0428056	+	0.0741414i
$185$	−17.7972	−	30.8256i	−1.30848	−	2.26635i
$186$	20.1256	−	34.8586i	1.47568	−	2.55596i
$187$	2.11349	+	3.66068i	0.154554	+	0.267695i
$188$	4.65265	+	8.05863i	0.339330	+	0.587736i
$189$	−42.9176			−3.12180
$190$	−21.3737	+	15.1321i	−1.55061	+	1.09780i
$191$	−0.326161			−0.0236002			−0.0118001	−	0.999930i	$-0.503756\pi$
$191$	−0.326161			−0.0236002			−0.0118001	+	0.999930i	$0.503756\pi$
$192$	3.86549	+	6.69523i	0.278968	+	0.483187i
$193$	5.12184	+	8.87128i	0.368678	+	0.638569i	0.989359	−	0.145494i	$-0.0464773\pi$
$193$	5.12184	+	8.87128i	0.368678	+	0.638569i	−0.620681	+	0.784063i	$0.713144\pi$
$194$	−8.50680	+	14.7342i	−0.610753	+	1.05786i
$195$	−2.29251	−	3.97074i	−0.164170	−	0.284351i
$196$	−4.25946	+	7.37760i	−0.304247	+	0.526972i
$197$	−24.1974			−1.72399			−0.861996	−	0.506915i	$-0.830786\pi$
$197$	−24.1974			−1.72399			−0.861996	+	0.506915i	$0.830786\pi$
$198$	−12.4553			−0.885159
$199$	−11.2945	+	19.5627i	−0.800646	+	1.38676i	0.118545	+	0.992949i	$0.462177\pi$
$199$	−11.2945	+	19.5627i	−0.800646	+	1.38676i	−0.919191	+	0.393811i	$0.871156\pi$
$200$	3.26289	−	5.65149i	0.230721	−	0.399621i
$201$	−4.49376			−0.316966
$202$	−15.6217			−1.09914
$203$	−12.2509	+	21.2192i	−0.859845	+	1.48929i
$204$	−9.09417	−	15.7516i	−0.636719	−	1.10283i
$205$	−2.09608	+	3.63051i	−0.146396	+	0.253566i
$206$	−5.08652	−	8.81011i	−0.354394	−	0.613829i
$207$	3.43303	+	5.94619i	0.238612	+	0.413289i
$208$	2.17864			0.151062
$209$	3.96002	+	1.82160i	0.273921	+	0.126002i
$210$	68.2353			4.70868
$211$	1.67742	+	2.90538i	0.115479	+	0.200015i	0.917971	−	0.396648i	$-0.129827\pi$
$211$	1.67742	+	2.90538i	0.115479	+	0.200015i	−0.802492	+	0.596662i	$0.796493\pi$
$212$	−1.64432	−	2.84804i	−0.112932	−	0.195604i
$213$	−16.5162	+	28.6069i	−1.13167	+	1.96011i
$214$	2.09766	+	3.63325i	0.143393	+	0.248364i
$215$	−6.81174	+	11.7983i	−0.464557	+	0.804636i
$216$	−13.5481			−0.921834
$217$	25.4434			1.72721
$218$	−9.70289	+	16.8059i	−0.657163	+	1.13824i
$219$	−4.14835	+	7.18516i	−0.280320	+	0.485528i
$220$	4.49930			0.303343
$221$	−1.89542			−0.127499
$222$	31.2731	−	54.1665i	2.09891	−	3.63542i
$223$	−4.58218	−	7.93658i	−0.306846	−	0.531472i	0.670825	−	0.741616i	$-0.265940\pi$
$223$	−4.58218	−	7.93658i	−0.306846	−	0.531472i	−0.977671	+	0.210143i	$0.932607\pi$
$224$	−12.0474	+	20.8667i	−0.804952	+	1.39422i
$225$	−19.2917	−	33.4142i	−1.28612	−	2.22762i
$226$	−10.5726	−	18.3123i	−0.703280	−	1.21812i
$227$	−4.60133			−0.305401			−0.152700	−	0.988273i	$-0.548797\pi$
$227$	−4.60133			−0.305401			−0.152700	+	0.988273i	$0.548797\pi$
$228$	−17.0396	−	7.83816i	−1.12848	−	0.519095i
$229$	0.909324			0.0600898			0.0300449	−	0.999549i	$-0.490435\pi$
$229$	0.909324			0.0600898			0.0300449	+	0.999549i	$0.490435\pi$
$230$	−3.04265	−	5.27003i	−0.200626	−	0.347495i
$231$	−5.67875	−	9.83588i	−0.373634	−	0.647153i
$232$	−3.86733	+	6.69842i	−0.253903	+	0.439773i
$233$	14.0929	+	24.4096i	0.923256	+	1.59913i	0.794342	+	0.607471i	$0.207816\pi$
$233$	14.0929	+	24.4096i	0.923256	+	1.59913i	0.128915	+	0.991656i	$0.458851\pi$
$234$	2.79253	−	4.83680i	0.182553	−	0.316191i
$235$	22.1124			1.44246
$236$	−13.0846			−0.851734
$237$	0.720759	−	1.24839i	0.0468183	−	0.0810917i
$238$	14.1040	−	24.4288i	0.914227	−	1.58349i
$239$	4.51955			0.292346			0.146173	−	0.989259i	$-0.453304\pi$
$239$	4.51955			0.292346			0.146173	+	0.989259i	$0.453304\pi$
$240$	49.6799			3.20682
$241$	13.9673	−	24.1921i	0.899714	−	1.55835i	0.0718544	−	0.997415i	$-0.477108\pi$
$241$	13.9673	−	24.1921i	0.899714	−	1.55835i	0.827860	−	0.560935i	$-0.189558\pi$
$242$	−0.918695	−	1.59123i	−0.0590560	−	0.102288i
$243$	−8.25444	+	14.2971i	−0.529523	+	0.917160i
$244$	−3.20782	−	5.55610i	−0.205359	−	0.355693i
$245$	10.1219	+	17.5316i	0.646662	+	1.12005i
$246$	−7.36641			−0.469665
$247$	−1.59524	+	1.12940i	−0.101503	+	0.0718618i
$248$	8.03191			0.510027
$249$	4.83226	+	8.36973i	0.306232	+	0.530410i
$250$	2.07811	+	3.59939i	0.131431	+	0.227646i
$251$	10.3038	−	17.8467i	0.650370	−	1.12647i	−0.332663	−	0.943046i	$-0.607947\pi$
$251$	10.3038	−	17.8467i	0.650370	−	1.12647i	0.983033	−	0.183429i	$-0.0587196\pi$
$252$	16.9388	+	29.3388i	1.06704	+	1.84817i
$253$	−0.506437	+	0.877175i	−0.0318394	+	0.0551475i
$254$	24.5805			1.54232
$255$	−43.2214			−2.70663
$256$	−10.4886	+	18.1668i	−0.655536	+	1.13542i
$257$	−7.65242	+	13.2544i	−0.477345	+	0.826786i	−0.999663	−	0.0259649i	$-0.991734\pi$
$257$	−7.65242	+	13.2544i	−0.477345	+	0.826786i	0.522318	+	0.852751i	$0.325068\pi$
$258$	−23.9391			−1.49038
$259$	39.5363			2.45667
$260$	−1.00876	+	1.74722i	−0.0625607	+	0.108358i
$261$	22.8655	+	39.6042i	1.41534	+	2.45144i
$262$	−3.67860	+	6.37152i	−0.227264	+	0.393634i
$263$	8.46297	+	14.6583i	0.521849	+	0.903869i	0.999677	+	0.0254157i	$0.00809095\pi$
$263$	8.46297	+	14.6583i	0.521849	+	0.903869i	−0.477828	+	0.878454i	$0.658576\pi$
$264$	−1.79265	−	3.10497i	−0.110330	−	0.191098i
$265$	−7.81486			−0.480063
$266$	−2.68576	−	28.9640i	−0.164675	−	1.77590i
$267$	−14.4649			−0.885238
$268$	0.988683	+	1.71245i	0.0603934	+	0.104605i
$269$	−3.71528	−	6.43505i	−0.226525	−	0.392352i	0.730251	−	0.683179i	$-0.239403\pi$
$269$	−3.71528	−	6.43505i	−0.226525	−	0.392352i	−0.956776	+	0.290827i	$0.906070\pi$
$270$	35.4971	−	61.4827i	2.16028	−	3.74172i
$271$	3.32194	+	5.75376i	0.201793	+	0.349516i	0.949106	−	0.314956i	$-0.101990\pi$
$271$	3.32194	+	5.75376i	0.201793	+	0.349516i	−0.747313	+	0.664472i	$0.768656\pi$
$272$	10.2687	−	17.7859i	0.622629	−	1.07843i
$273$	5.09279			0.308230
$274$	9.98242			0.603060
$275$	2.84589	−	4.92923i	0.171614	−	0.297244i
$276$	2.17915	−	3.77440i	0.131170	−	0.227192i
$277$	−30.6874			−1.84383			−0.921913	−	0.387396i	$-0.873375\pi$
$277$	−30.6874			−1.84383			−0.921913	+	0.387396i	$0.873375\pi$
$278$	10.9423			0.656273
$279$	23.7442	−	41.1262i	1.42153	−	2.46216i
$280$	6.80799	+	11.7918i	0.406855	+	0.704694i
$281$	−15.5452	+	26.9250i	−0.927346	+	1.60621i	−0.139602	+	0.990208i	$0.544582\pi$
$281$	−15.5452	+	26.9250i	−0.927346	+	1.60621i	−0.787744	+	0.616003i	$0.788751\pi$
$282$	19.4279	+	33.6501i	1.15691	+	2.00383i
$283$	−6.14534	−	10.6440i	−0.365303	−	0.632723i	0.623522	−	0.781806i	$-0.285701\pi$
$283$	−6.14534	−	10.6440i	−0.365303	−	0.632723i	−0.988825	+	0.149083i	$0.952368\pi$
$284$	14.5351			0.862498
$285$	−36.3764	+	25.7538i	−2.15475	+	1.52552i
$286$	0.823900			0.0487183
$287$	−2.32821	−	4.03257i	−0.137430	−	0.238035i
$288$	22.4857	+	38.9464i	1.32498	+	2.29494i
$289$	−0.433715	+	0.751217i	−0.0255127	+	0.0441892i
$290$	−20.2654	−	35.1007i	−1.19002	−	2.06118i
$291$	−14.4780	+	25.0766i	−0.848714	+	1.47001i
$292$	3.65075			0.213644
$293$	−25.3174			−1.47906			−0.739529	−	0.673125i	$-0.764952\pi$
$293$	−25.3174			−1.47906			−0.739529	+	0.673125i	$0.764952\pi$
$294$	−17.7860	+	30.8063i	−1.03730	+	1.79666i
$295$	−15.5466	+	26.9275i	−0.905158	+	1.56778i
$296$	12.4807			0.725428
$297$	−11.8167			−0.685674
$298$	−14.4731	+	25.0682i	−0.838405	+	1.45216i
$299$	−0.227090	−	0.393332i	−0.0131330	−	0.0227470i
$300$	−12.2456	+	21.2100i	−0.707001	+	1.22456i
$301$	−7.56612	−	13.1049i	−0.436104	−	0.755354i
$302$	6.24417	+	10.8152i	0.359312	+	0.622346i
$303$	−26.5870			−1.52738
$304$	−1.95542	−	21.0878i	−0.112151	−	1.20947i
$305$	−15.2456			−0.872961
$306$	−26.3242	−	45.5948i	−1.50485	−	2.60648i
$307$	−3.57560	−	6.19313i	−0.204070	−	0.353460i	0.745766	−	0.666208i	$-0.232084\pi$
$307$	−3.57560	−	6.19313i	−0.204070	−	0.353460i	−0.949836	+	0.312748i	$0.898750\pi$
$308$	−2.49879	+	4.32803i	−0.142382	+	0.246612i
$309$	−8.65689	−	14.9942i	−0.492473	−	0.852988i
$310$	−21.0442	+	36.4496i	−1.19523	+	2.07020i
$311$	26.9033			1.52555			0.762773	−	0.646666i	$-0.223837\pi$
$311$	26.9033			1.52555			0.762773	+	0.646666i	$0.223837\pi$
$312$	1.60768			0.0910170
$313$	8.02641	−	13.9022i	0.453680	−	0.785796i	−0.544931	−	0.838481i	$-0.683444\pi$
$313$	8.02641	−	13.9022i	0.453680	−	0.785796i	0.998611	+	0.0526842i	$0.0167777\pi$
$314$	−17.4850	+	30.2850i	−0.986738	+	1.70908i
$315$	80.5040			4.53589
$316$	−0.634303			−0.0356823
$317$	7.01143	−	12.1441i	0.393801	−	0.682083i	−0.599146	−	0.800640i	$-0.704493\pi$
$317$	7.01143	−	12.1441i	0.393801	−	0.682083i	0.992947	+	0.118556i	$0.0378266\pi$
$318$	−6.86610	−	11.8924i	−0.385032	−	0.666895i
$319$	−3.37309	+	5.84237i	−0.188857	+	0.327110i
$320$	−4.04192	−	7.00081i	−0.225950	−	0.391357i
$321$	3.57006	+	6.18353i	0.199262	+	0.345131i
$322$	6.75923			0.376677
$323$	1.70121	+	18.3463i	0.0946578	+	1.02082i
$324$	22.8632			1.27018
$325$	1.27612	+	2.21031i	0.0707865	+	0.122606i
$326$	−4.99217	−	8.64670i	−0.276491	−	0.478896i
$327$	−16.5136	+	28.6024i	−0.913206	+	1.58172i
$328$	−0.734963	−	1.27299i	−0.0405815	−	0.0702893i
$329$	−12.2806	+	21.2707i	−0.677054	+	1.17269i
$330$	18.7875			1.03422
$331$	−33.2840			−1.82946			−0.914728	−	0.404070i	$-0.867595\pi$
$331$	−33.2840			−1.82946			−0.914728	+	0.404070i	$0.867595\pi$
$332$	2.12631	−	3.68288i	0.116697	−	0.202125i
$333$	36.8960	−	63.9057i	2.02189	−	3.50201i
$334$	0.878636			0.0480768
$335$	4.69886			0.256726
$336$	−27.5909	+	47.7888i	−1.50521	+	2.60709i
$337$	12.6200	+	21.8584i	0.687453	+	1.19070i	0.972659	+	0.232237i	$0.0746046\pi$
$337$	12.6200	+	21.8584i	0.687453	+	1.19070i	−0.285206	+	0.958466i	$0.592062\pi$
$338$	11.7583	−	20.3660i	0.639568	−	1.10776i
$339$	−17.9938	−	31.1662i	−0.977290	−	1.69272i
$340$	9.50924	+	16.4705i	0.515711	+	0.893237i
$341$	7.00544			0.379366
$342$	−49.3232	−	22.6885i	−2.66710	−	1.22685i
$343$	2.93802			0.158638
$344$	−2.38845	−	4.13692i	−0.128777	−	0.223048i
$345$	−5.17837	−	8.96921i	−0.278794	−	0.482886i
$346$	12.7652	−	22.1101i	0.686264	−	1.18864i
$347$	8.48667	+	14.6994i	0.455589	+	0.789102i	0.998722	−	0.0505440i	$-0.0160955\pi$
$347$	8.48667	+	14.6994i	0.455589	+	0.789102i	−0.543133	+	0.839646i	$0.682762\pi$
$348$	14.5141	−	25.1392i	0.778038	−	1.34760i
$349$	7.75434			0.415080			0.207540	−	0.978226i	$-0.433454\pi$
$349$	7.75434			0.415080			0.207540	+	0.978226i	$0.433454\pi$
$350$	−37.9831			−2.03028
$351$	2.64935	−	4.58881i	0.141412	−	0.244932i
$352$	−3.31707	+	5.74533i	−0.176800	+	0.306227i
$353$	−0.614650			−0.0327145			−0.0163573	−	0.999866i	$-0.505207\pi$
$353$	−0.614650			−0.0327145			−0.0163573	+	0.999866i	$0.505207\pi$
$354$	−54.6367			−2.90391
$355$	17.2700	−	29.9125i	0.916597	−	1.58759i
$356$	3.18246	+	5.51218i	0.168670	+	0.292145i
$357$	24.0040	−	41.5761i	1.27043	−	2.20044i
$358$	−0.525033	−	0.909383i	−0.0277488	−	0.0480624i
$359$	3.94116	+	6.82629i	0.208006	+	0.360278i	0.951086	−	0.308925i	$-0.0999692\pi$
$359$	3.94116	+	6.82629i	0.208006	+	0.360278i	−0.743080	+	0.669203i	$0.766636\pi$
$360$	25.4133			1.33940
$361$	12.3636	+	14.4271i	0.650715	+	0.759322i
$362$	−42.1726			−2.21654
$363$	−1.56355	−	2.70815i	−0.0820653	−	0.142141i
$364$	−1.12048	−	1.94072i	−0.0587289	−	0.101721i
$365$	4.33769	−	7.51310i	0.227045	−	0.393253i
$366$	−13.3947	−	23.2004i	−0.700154	−	1.21270i
$367$	−13.4107	+	23.2281i	−0.700034	+	1.21249i	0.268420	+	0.963302i	$0.413499\pi$
$367$	−13.4107	+	23.2281i	−0.700034	+	1.21249i	−0.968454	+	0.249193i	$0.919835\pi$
$368$	4.92117			0.256534
$369$	−8.69089			−0.452430
$370$	−32.7004	+	56.6387i	−1.70001	+	2.94451i
$371$	4.34016	−	7.51738i	0.225330	−	0.390283i
$372$	−30.1437			−1.56288
$373$	−3.31474			−0.171630			−0.0858152	−	0.996311i	$-0.527349\pi$
$373$	−3.31474			−0.171630			−0.0858152	+	0.996311i	$0.527349\pi$
$374$	3.88331	−	6.72610i	0.200801	−	0.347798i
$375$	3.53680	+	6.12591i	0.182639	+	0.316341i
$376$	−3.87672	+	6.71468i	−0.199927	+	0.346283i
$377$	−1.51252	−	2.61976i	−0.0778988	−	0.134925i
$378$	39.4282	+	68.2917i	2.02797	+	3.51255i
$379$	16.6615			0.855845			0.427922	−	0.903815i	$-0.359246\pi$
$379$	16.6615			0.855845			0.427922	+	0.903815i	$0.359246\pi$
$380$	17.8173	+	8.19590i	0.914009	+	0.420441i
$381$	41.8342			2.14323
$382$	0.299643	+	0.518996i	0.0153310	+	0.0265542i
$383$	−12.0861	−	20.9337i	−0.617569	−	1.06966i	−0.989928	−	0.141572i	$-0.954784\pi$
$383$	−12.0861	−	20.9337i	−0.617569	−	1.06966i	0.372359	−	0.928089i	$-0.378549\pi$
$384$	−13.6432	+	23.6307i	−0.696228	+	1.20590i
$385$	5.93793	+	10.2848i	0.302625	+	0.524162i
$386$	9.41081	−	16.3000i	0.478998	−	0.829648i
$387$	−28.2433			−1.43569
$388$	12.7413			0.646843
$389$	−3.44383	+	5.96489i	−0.174609	+	0.302432i	−0.940026	−	0.341103i	$-0.889199\pi$
$389$	−3.44383	+	5.96489i	−0.174609	+	0.302432i	0.765417	+	0.643535i	$0.222533\pi$
$390$	−4.21223	+	7.29580i	−0.213295	+	0.369437i
$391$	−4.28141			−0.216520
$392$	−7.09821			−0.358514
$393$	−6.26071	+	10.8439i	−0.315811	+	0.547000i
$394$	22.2300	+	38.5035i	1.11993	+	1.93978i
$395$	−0.753655	+	1.30537i	−0.0379205	+	0.0656802i
$396$	4.66382	+	8.07798i	0.234366	+	0.405934i
$397$	−12.2800	−	21.2695i	−0.616314	−	1.06749i	−0.990153	−	0.139993i	$-0.955292\pi$
$397$	−12.2800	−	21.2695i	−0.616314	−	1.06749i	0.373839	−	0.927494i	$-0.378041\pi$
$398$	41.5048			2.08045
$399$	−4.57098	−	49.2947i	−0.228835	−	2.46782i
$400$	−27.6542			−1.38271
$401$	−6.79438	−	11.7682i	−0.339295	−	0.587677i	0.645005	−	0.764178i	$-0.276855\pi$
$401$	−6.79438	−	11.7682i	−0.339295	−	0.587677i	−0.984300	+	0.176502i	$0.943522\pi$
$402$	4.12840	+	7.15060i	0.205906	+	0.356639i
$403$	−1.57065	+	2.72044i	−0.0782395	+	0.135515i
$404$	5.84946	+	10.1316i	0.291022	+	0.504064i
$405$	27.1652	−	47.0515i	1.34985	−	2.33801i
$406$	45.0194			2.23427
$407$	10.8857			0.539584
$408$	7.57753	−	13.1247i	0.375143	−	0.649767i
$409$	11.3229	−	19.6119i	0.559883	−	0.969746i	−0.437623	−	0.899159i	$-0.644179\pi$
$409$	11.3229	−	19.6119i	0.559883	−	0.969746i	0.997506	−	0.0705869i	$-0.0224872\pi$
$410$	7.70262			0.380405
$411$	16.9894			0.838024
$412$	−3.80924	+	6.59780i	−0.187668	+	0.325050i
$413$	−17.2683	−	29.9096i	−0.849719	−	1.47176i
$414$	6.30782	−	10.9255i	0.310013	−	0.536958i
$415$	−5.05281	−	8.75173i	−0.248033	−	0.429605i
$416$	−1.48740	−	2.57625i	−0.0729257	−	0.126311i
$417$	18.6229			0.911970
$418$	−0.739482	−	7.97479i	−0.0361693	−	0.390060i
$419$	−0.250165			−0.0122213			−0.00611067	−	0.999981i	$-0.501945\pi$
$419$	−0.250165			−0.0122213			−0.00611067	+	0.999981i	$0.501945\pi$
$420$	−25.5504	−	44.2545i	−1.24673	−	2.15940i
$421$	9.86401	+	17.0850i	0.480742	+	0.832670i	0.999756	−	0.0220957i	$-0.00703386\pi$
$421$	9.86401	+	17.0850i	0.480742	+	0.832670i	−0.519013	+	0.854766i	$0.673701\pi$
$422$	3.08208	−	5.33832i	0.150033	−	0.259865i
$423$	22.9210	+	39.7003i	1.11446	+	1.93030i
$424$	1.37009	−	2.37307i	0.0665376	−	0.115246i
$425$	24.0591			1.16704
$426$	60.6934			2.94061
$427$	8.46700	−	14.6653i	0.409747	−	0.709703i
$428$	1.57092	−	2.72091i	0.0759331	−	0.131520i
$429$	1.40222			0.0676998
$430$	25.0317			1.20713
$431$	−5.91317	+	10.2419i	−0.284827	+	0.493336i	−0.972567	−	0.232622i	$-0.925270\pi$
$431$	−5.91317	+	10.2419i	−0.284827	+	0.493336i	0.687740	+	0.725957i	$0.258603\pi$
$432$	28.7064	+	49.7210i	1.38114	+	2.39220i
$433$	−5.74963	+	9.95866i	−0.276310	+	0.478583i	−0.970465	−	0.241243i	$-0.922445\pi$
$433$	−5.74963	+	9.95866i	−0.276310	+	0.478583i	0.694155	+	0.719826i	$0.255778\pi$
$434$	−23.3747	−	40.4862i	−1.12202	−	1.94340i
$435$	−34.4902	−	59.7388i	−1.65368	−	2.86426i
$436$	14.5328			0.695995
$437$	−3.60336	+	2.55111i	−0.172372	+	0.122036i
$438$	15.2443			0.728400
$439$	0.319770	+	0.553858i	0.0152618	+	0.0264342i	0.873555	−	0.486725i	$-0.161808\pi$
$439$	0.319770	+	0.553858i	0.0152618	+	0.0264342i	−0.858294	+	0.513159i	$0.828475\pi$
$440$	1.87447	+	3.24668i	0.0893619	+	0.154779i
$441$	−20.9840	+	36.3453i	−0.999237	+	1.73073i
$442$	1.74131	+	3.01604i	0.0828256	+	0.143458i
$443$	5.98464	−	10.3657i	0.284339	−	0.492489i	−0.688110	−	0.725607i	$-0.741559\pi$
$443$	5.98464	−	10.3657i	0.284339	−	0.492489i	0.972449	+	0.233117i	$0.0748926\pi$
$444$	−46.8402			−2.22294
$445$	15.1251			0.716998
$446$	−8.41926	+	14.5826i	−0.398664	+	0.690506i
$447$	−24.6322	+	42.6642i	−1.16506	+	2.01795i
$448$	8.97909			0.424222
$449$	−1.69999			−0.0802277			−0.0401139	−	0.999195i	$-0.512772\pi$
$449$	−1.69999			−0.0802277			−0.0401139	+	0.999195i	$0.512772\pi$
$450$	−35.4464	+	61.3950i	−1.67096	+	2.89419i
$451$	−0.641035	−	1.11031i	−0.0301852	−	0.0522822i
$452$	−7.91772	+	13.7139i	−0.372418	+	0.645047i
$453$	10.6271	+	18.4067i	0.499306	+	0.864824i
$454$	4.22722	+	7.32176i	0.198393	+	0.343627i
$455$	−5.32523			−0.249651
$456$	−1.44295	−	15.5612i	−0.0675726	−	0.728721i
$457$	−0.527953			−0.0246966			−0.0123483	−	0.999924i	$-0.503931\pi$
$457$	−0.527953			−0.0246966			−0.0123483	+	0.999924i	$0.503931\pi$
$458$	−0.835392	−	1.44694i	−0.0390353	−	0.0676111i
$459$	−24.9745	−	43.2571i	−1.16571	−	2.01907i
$460$	−2.27861	+	3.94667i	−0.106241	+	0.184014i
$461$	9.25578	+	16.0315i	0.431085	+	0.746661i	0.996967	−	0.0778255i	$-0.0247977\pi$
$461$	9.25578	+	16.0315i	0.431085	+	0.746661i	−0.565882	+	0.824486i	$0.691464\pi$
$462$	−10.4341	+	18.0723i	−0.485437	+	0.840802i
$463$	10.2924			0.478328			0.239164	−	0.970979i	$-0.423127\pi$
$463$	10.2924			0.478328			0.239164	+	0.970979i	$0.423127\pi$
$464$	32.7771			1.52164
$465$	−35.8157	+	62.0345i	−1.66091	+	2.87678i
$466$	25.8942	−	44.8500i	1.19952	−	2.07764i
$467$	21.2473			0.983206			0.491603	−	0.870820i	$-0.336411\pi$
$467$	21.2473			0.983206			0.491603	+	0.870820i	$0.336411\pi$
$468$	−4.18259			−0.193340
$469$	−2.60962	+	4.52000i	−0.120501	+	0.208714i
$470$	−20.3146	−	35.1859i	−0.937042	−	1.62300i
$471$	−29.7583	+	51.5429i	−1.37119	+	2.37497i
$472$	−5.45123	−	9.44180i	−0.250913	−	0.434594i
$473$	−2.08321	−	3.60823i	−0.0957861	−	0.165906i
$474$	−2.64863			−0.121656
$475$	20.2489	−	14.3358i	0.929082	−	0.657772i
$476$	−21.1247			−0.968249
$477$	−8.10063	−	14.0307i	−0.370902	−	0.642422i
$478$	−4.15209	−	7.19164i	−0.189912	−	0.328938i
$479$	18.9448	−	32.8134i	0.865612	−	1.49928i	−0.000826387	−	1.00000i	$-0.500263\pi$
$479$	18.9448	−	32.8134i	0.865612	−	1.49928i	0.866438	−	0.499284i	$-0.166404\pi$
$480$	−33.9174	−	58.7466i	−1.54811	−	2.68140i
$481$	−2.44062	+	4.22727i	−0.111283	+	0.192747i
$482$	−51.3268			−2.33787
$483$	11.5037			0.523437
$484$	−0.688002	+	1.19165i	−0.0312728	+	0.0541661i
$485$	15.1388	−	26.2211i	0.687415	−	1.19064i
$486$	30.3333			1.37595
$487$	−41.2440			−1.86895			−0.934473	−	0.356034i	$-0.884129\pi$
$487$	−41.2440			−1.86895			−0.934473	+	0.356034i	$0.884129\pi$
$488$	2.67284	−	4.62950i	0.120994	−	0.209568i
$489$	−8.49632	−	14.7161i	−0.384217	−	0.665483i
$490$	18.5978	−	32.2124i	0.840163	−	1.45521i
$491$	−8.93476	−	15.4755i	−0.403220	−	0.698397i	0.590893	−	0.806750i	$-0.298776\pi$
$491$	−8.93476	−	15.4755i	−0.403220	−	0.698397i	−0.994112	+	0.108353i	$0.965442\pi$
$492$	2.75831	+	4.77754i	0.124354	+	0.215388i
$493$	−28.5160			−1.28430
$494$	3.26267	+	1.50081i	0.146794	+	0.0675248i
$495$	22.1655			0.996265
$496$	−17.0184	−	29.4767i	−0.764148	−	1.32354i
$497$	19.1826	+	33.2252i	0.860457	+	1.49036i
$498$	8.87876	−	15.3785i	0.397867	−	0.689125i
$499$	−18.3064	−	31.7075i	−0.819505	−	1.41942i	−0.906048	−	0.423176i	$-0.860915\pi$
$499$	−18.3064	−	31.7075i	−0.819505	−	1.41942i	0.0865428	−	0.996248i	$-0.472418\pi$
$500$	1.55628	−	2.69555i	0.0695988	−	0.120549i
$501$	1.49538			0.0668085
$502$	−37.8642			−1.68996
$503$	5.76329	−	9.98231i	0.256972	−	0.445089i	−0.708457	−	0.705754i	$-0.750608\pi$
$503$	5.76329	−	9.98231i	0.256972	−	0.445089i	0.965429	+	0.260665i	$0.0839418\pi$
$504$	−14.1139	+	24.4459i	−0.628682	+	1.08891i
$505$	27.8004			1.23710
$506$	1.86105			0.0827336
$507$	20.0118	−	34.6615i	0.888756	−	1.53937i
$508$	−9.20403	−	15.9418i	−0.408363	−	0.707305i
$509$	−21.0739	+	36.5010i	−0.934082	+	1.61788i	−0.157820	+	0.987468i	$0.550447\pi$
$509$	−21.0739	+	36.5010i	−0.934082	+	1.61788i	−0.776262	+	0.630410i	$0.782887\pi$
$510$	39.7073	+	68.7751i	1.75827	+	3.04541i
$511$	4.81807	+	8.34514i	0.213139	+	0.369167i
$512$	21.0917			0.932129
$513$	−46.7944	−	21.5252i	−2.06602	−	0.950362i
$514$	28.1210			1.24036
$515$	9.05199	+	15.6785i	0.398879	+	0.690878i
$516$	8.96386	+	15.5259i	0.394612	+	0.683488i
$517$	−3.38128	+	5.85655i	−0.148709	+	0.257571i
$518$	−36.3218	−	62.9112i	−1.59589	−	2.76416i
$519$	21.7255	−	37.6297i	0.953645	−	1.65176i
$520$	−1.68106			−0.0737192
$521$	6.47680			0.283754			0.141877	−	0.989884i	$-0.454686\pi$
$521$	6.47680			0.283754			0.141877	+	0.989884i	$0.454686\pi$
$522$	42.0128	−	72.7684i	1.83885	−	3.18498i
$523$	9.59425	−	16.6177i	0.419527	−	0.726643i	−0.576365	−	0.817193i	$-0.695529\pi$
$523$	9.59425	−	16.6177i	0.419527	−	0.726643i	0.995892	+	0.0905501i	$0.0288625\pi$
$524$	5.50973			0.240694
$525$	−64.6444			−2.82131
$526$	15.5498	−	26.9330i	0.678003	−	1.17434i
$527$	14.8059	+	25.6447i	0.644957	+	1.11710i
$528$	−7.59671	+	13.1579i	−0.330605	+	0.572624i
$529$	10.9870	+	19.0301i	0.477698	+	0.827396i
$530$	7.17948	+	12.4352i	0.311857	+	0.540151i
$531$	−64.4604			−2.79734
$532$	−17.7792	+	12.5873i	−0.770825	+	0.545729i
$533$	0.574890			0.0249013
$534$	13.2888	+	23.0169i	0.575064	+	0.996041i
$535$	−3.73300	−	6.46575i	−0.161392	−	0.279539i
$536$	−0.823799	+	1.42686i	−0.0355827	+	0.0616311i
$537$	−0.893568	−	1.54770i	−0.0385603	−	0.0667884i
$538$	−6.82642	+	11.8237i	−0.294308	+	0.509756i
$539$	−6.19106			−0.266668
$540$	−53.1668			−2.28793
$541$	10.0254	−	17.3645i	0.431026	−	0.746558i	−0.565936	−	0.824449i	$-0.691485\pi$
$541$	10.0254	−	17.3645i	0.431026	−	0.746558i	0.996962	+	0.0778907i	$0.0248185\pi$
$542$	6.10370	−	10.5719i	0.262176	−	0.454103i
$543$	−71.7747			−3.08015
$544$	−28.0424			−1.20231
$545$	17.2673	−	29.9079i	0.739651	−	1.28111i
$546$	−4.67872	−	8.10379i	−0.200231	−	0.346810i
$547$	−5.43160	+	9.40781i	−0.232239	+	0.402249i	−0.958467	−	0.285205i	$-0.907938\pi$
$547$	−5.43160	+	9.40781i	−0.232239	+	0.402249i	0.726228	+	0.687454i	$0.241272\pi$
$548$	−3.73787	−	6.47418i	−0.159674	−	0.276563i
$549$	−15.8031	−	27.3718i	−0.674460	−	1.16820i
$550$	−10.4580			−0.445932
$551$	−24.0000	+	16.9915i	−1.02243	+	0.723862i
$552$	3.63147			0.154565
$553$	−0.837119	−	1.44993i	−0.0355979	−	0.0616574i
$554$	28.1924	+	48.8306i	1.19778	+	2.07461i
$555$	−55.6537	+	96.3950i	−2.36237	+	4.09174i
$556$	−4.09728	−	7.09669i	−0.173763	−	0.300967i
$557$	−2.37017	+	4.10525i	−0.100427	+	0.173945i	−0.911861	−	0.410500i	$-0.865354\pi$
$557$	−2.37017	+	4.10525i	−0.100427	+	0.173945i	0.811433	+	0.584445i	$0.198688\pi$
$558$	−87.2547			−3.69379
$559$	1.86826			0.0790188
$560$	28.8502	−	49.9699i	1.21914	−	2.11161i
$561$	6.60912	−	11.4473i	0.279037	−	0.483307i
$562$	57.1250			2.40967
$563$	−14.2016			−0.598528			−0.299264	−	0.954170i	$-0.596741\pi$
$563$	−14.2016			−0.598528			−0.299264	+	0.954170i	$0.596741\pi$
$564$	14.5493	−	25.2002i	0.612638	−	1.06112i
$565$	18.8151	+	32.5887i	0.791556	+	1.37102i
$566$	−11.2914	+	19.5573i	−0.474612	+	0.822053i
$567$	30.1736	+	52.2623i	1.26717	+	2.19481i
$568$	6.05552	+	10.4885i	0.254084	+	0.440086i
$569$	−8.58534			−0.359916			−0.179958	−	0.983674i	$-0.557596\pi$
$569$	−8.58534			−0.359916			−0.179958	+	0.983674i	$0.557596\pi$
$570$	74.3990	+	34.2233i	3.11623	+	1.43345i
$571$	−39.3847			−1.64820			−0.824099	−	0.566446i	$-0.808318\pi$
$571$	−39.3847			−1.64820			−0.824099	+	0.566446i	$0.808318\pi$
$572$	−0.308505	−	0.534347i	−0.0128993	−	0.0223422i
$573$	0.509970	+	0.883294i	0.0213043	+	0.0369001i
$574$	−4.27783	+	7.40941i	−0.178553	+	0.309263i
$575$	2.88253	+	4.99269i	0.120210	+	0.208210i
$576$	8.37944	−	14.5136i	0.349143	−	0.604734i
$577$	−25.1063			−1.04519			−0.522594	−	0.852582i	$-0.675036\pi$
$577$	−25.1063			−1.04519			−0.522594	+	0.852582i	$0.675036\pi$
$578$	1.59381			0.0662937
$579$	16.0165	−	27.7414i	0.665624	−	1.15289i
$580$	−15.1765	+	26.2865i	−0.630171	+	1.09149i
$581$	11.2248			0.465682
$582$	53.2034			2.20535
$583$	1.19500	−	2.06979i	0.0494917	−	0.0857221i
$584$	1.52096	+	2.63437i	0.0629376	+	0.109011i
$585$	−4.96959	+	8.60759i	−0.205467	+	0.355880i
$586$	23.2590	+	40.2857i	0.960819	+	1.66419i
$587$	−9.03750	−	15.6534i	−0.373018	−	0.646086i	0.617011	−	0.786955i	$-0.288344\pi$
$587$	−9.03750	−	15.6534i	−0.373018	−	0.646086i	−0.990028	+	0.140869i	$0.955010\pi$
$588$	26.6396			1.09860
$589$	27.7417	+	12.7611i	1.14308	+	0.525811i
$590$	57.1304			2.35202
$591$	37.8339	+	65.5302i	1.55628	+	2.69555i
$592$	−26.4447	−	45.8036i	−1.08687	−	1.88252i
$593$	10.5463	−	18.2667i	0.433084	−	0.750123i	−0.564053	−	0.825738i	$-0.690759\pi$
$593$	10.5463	−	18.2667i	0.433084	−	0.750123i	0.997137	+	0.0756152i	$0.0240921\pi$
$594$	10.8559	+	18.8030i	0.445425	+	0.771498i
$595$	−25.0996	+	43.4737i	−1.02898	+	1.78225i
$596$	21.6775			0.887947
$597$	70.6382			2.89103
$598$	−0.417254	+	0.722705i	−0.0170628	+	0.0295536i
$599$	19.8016	−	34.2974i	0.809073	−	1.40136i	−0.104434	−	0.994532i	$-0.533303\pi$
$599$	19.8016	−	34.2974i	0.809073	−	1.40136i	0.913507	−	0.406823i	$-0.133364\pi$
$600$	−20.4068			−0.833104
$601$	−7.17190			−0.292548			−0.146274	−	0.989244i	$-0.546728\pi$
$601$	−7.17190			−0.292548			−0.146274	+	0.989244i	$0.546728\pi$
$602$	−13.9019	+	24.0788i	−0.566600	+	0.981379i
$603$	4.87069	+	8.43628i	0.198350	+	0.343552i
$604$	4.67620	−	8.09941i	0.190272	−	0.329560i
$605$	1.63491	+	2.83176i	0.0664687	+	0.115127i
$606$	24.4253	+	42.3059i	0.992211	+	1.71856i
$607$	30.7320			1.24737			0.623687	−	0.781674i	$-0.285634\pi$
$607$	30.7320			1.24737			0.623687	+	0.781674i	$0.285634\pi$
$608$	−23.6013	+	16.7093i	−0.957160	+	0.677651i
$609$	76.6197			3.10479
$610$	14.0061	+	24.2592i	0.567089	+	0.982228i
$611$	−1.51619	−	2.62612i	−0.0613386	−	0.106242i
$612$	−19.7139	+	34.1455i	−0.796888	+	1.38025i
$613$	−7.17238	−	12.4229i	−0.289690	−	0.501757i	0.684046	−	0.729439i	$-0.260219\pi$
$613$	−7.17238	−	12.4229i	−0.289690	−	0.501757i	−0.973736	+	0.227682i	$0.926885\pi$
$614$	−6.56978	+	11.3792i	−0.265135	+	0.459227i
$615$	13.1093			0.528618
$616$	−4.16412			−0.167777
$617$	0.208687	−	0.361456i	0.00840142	−	0.0145517i	−0.861794	−	0.507258i	$-0.830659\pi$
$617$	0.208687	−	0.361456i	0.00840142	−	0.0145517i	0.870196	+	0.492707i	$0.163992\pi$
$618$	−15.9061	+	27.5501i	−0.639836	+	1.10823i
$619$	−29.5736			−1.18866			−0.594331	−	0.804221i	$-0.702583\pi$
$619$	−29.5736			−1.18866			−0.594331	+	0.804221i	$0.702583\pi$
$620$	31.5195			1.26585
$621$	5.98441	−	10.3653i	0.240146	−	0.415945i
$622$	−24.7159	−	42.8093i	−0.991019	−	1.71650i
$623$	−8.40007	+	14.5493i	−0.336542	+	0.582907i
$624$	−3.40643	−	5.90010i	−0.136366	−	0.236193i
$625$	10.5312	+	18.2407i	0.421250	+	0.729626i
$626$	−29.4953			−1.17887
$627$	−1.25855	−	13.5725i	−0.0502615	−	0.542034i
$628$	26.1888			1.04505
$629$	23.0069	+	39.8490i	0.917343	+	1.58889i
$630$	−73.9586	−	128.100i	−2.94658	−	5.10363i
$631$	0.207771	−	0.359869i	0.00827122	−	0.0143262i	−0.861860	−	0.507146i	$-0.830700\pi$
$631$	0.207771	−	0.359869i	0.00827122	−	0.0143262i	0.870131	+	0.492820i	$0.164034\pi$
$632$	−0.264260	−	0.457711i	−0.0105117	−	0.0182068i
$633$	5.24548	−	9.08544i	0.208489	−	0.361114i
$634$	−25.7655			−1.02328
$635$	−43.7435			−1.73591
$636$	−5.14196	+	8.90613i	−0.203892	+	0.353151i
$637$	1.38806	−	2.40419i	0.0549970	−	0.0952576i
$638$	12.3954			0.490737
$639$	71.6061			2.83269
$640$	14.2659	−	24.7093i	0.563909	−	0.976720i
$641$	−18.8044	−	32.5702i	−0.742729	−	1.28644i	−0.951248	−	0.308426i	$-0.900198\pi$
$641$	−18.8044	−	32.5702i	−0.742729	−	1.28644i	0.208519	−	0.978018i	$-0.433136\pi$
$642$	6.55960	−	11.3616i	0.258887	−	0.448405i
$643$	21.4787	+	37.2022i	0.847037	+	1.46711i	0.883840	+	0.467788i	$0.154949\pi$
$643$	21.4787	+	37.2022i	0.847037	+	1.46711i	−0.0368035	+	0.999323i	$0.511718\pi$
$644$	−2.53096	−	4.38375i	−0.0997337	−	0.172744i
$645$	42.6021			1.67746
$646$	27.6302	−	19.5617i	1.08710	−	0.769644i
$647$	−2.19443			−0.0862721			−0.0431361	−	0.999069i	$-0.513735\pi$
$647$	−2.19443			−0.0862721			−0.0431361	+	0.999069i	$0.513735\pi$
$648$	9.52514	+	16.4980i	0.374183	+	0.648104i
$649$	−4.75456	−	8.23514i	−0.186633	−	0.323258i
$650$	2.34473	−	4.06120i	0.0919680	−	0.159293i
$651$	−39.7821	−	68.9046i	−1.55918	−	2.70058i
$652$	−3.73859	+	6.47543i	−0.146414	+	0.253597i
$653$	7.16482			0.280381			0.140191	−	0.990125i	$-0.455228\pi$
$653$	7.16482			0.280381			0.140191	+	0.990125i	$0.455228\pi$
$654$	60.6839			2.37293
$655$	6.54645	−	11.3388i	0.255791	−	0.443043i
$656$	−3.11455	+	5.39455i	−0.121603	+	0.210622i
$657$	17.9852			0.701670
$658$	45.1287			1.75930
$659$	−21.4610	+	37.1715i	−0.836000	+	1.44799i	0.0572135	+	0.998362i	$0.481778\pi$
$659$	−21.4610	+	37.1715i	−0.836000	+	1.44799i	−0.893214	+	0.449633i	$0.851555\pi$
$660$	−7.03489	−	12.1848i	−0.273833	−	0.474292i
$661$	10.4812	−	18.1540i	0.407673	−	0.706109i	−0.586956	−	0.809619i	$-0.699674\pi$
$661$	10.4812	−	18.1540i	0.407673	−	0.706109i	0.994628	+	0.103509i	$0.0330072\pi$
$662$	30.5779	+	52.9625i	1.18844	+	2.05844i
$663$	2.96358	+	5.13308i	0.115096	+	0.199352i
$664$	3.54341			0.137511
$665$	4.77960	+	51.5445i	0.185345	+	1.99881i
$666$	−135.585			−5.25379
$667$	−3.41652	−	5.91758i	−0.132288	−	0.229130i
$668$	−0.329001	−	0.569846i	−0.0127294	−	0.0220480i
$669$	−14.3290	+	24.8185i	−0.553990	+	0.959539i
$670$	−4.31682	−	7.47696i	−0.166773	−	0.288860i
$671$	2.33126	−	4.03785i	0.0899971	−	0.155880i
$672$	75.3471			2.90658
$673$	−43.0413			−1.65912			−0.829561	−	0.558417i	$-0.811409\pi$
$673$	−43.0413			−1.65912			−0.829561	+	0.558417i	$0.811409\pi$
$674$	23.1878	−	40.1624i	0.893160	−	1.54700i
$675$	−33.6290	+	58.2472i	−1.29438	+	2.24194i
$676$	−17.6114			−0.677360
$677$	−17.2885			−0.664453			−0.332226	−	0.943200i	$-0.607800\pi$
$677$	−17.2885			−0.664453			−0.332226	+	0.943200i	$0.607800\pi$
$678$	−33.0617	+	57.2645i	−1.26973	+	2.19923i
$679$	16.8153	+	29.1250i	0.645312	+	1.11771i
$680$	−7.92337	+	13.7237i	−0.303847	+	0.526279i
$681$	7.19442	+	12.4611i	0.275691	+	0.477510i
$682$	−6.43586	−	11.1472i	−0.246442	−	0.426850i
$683$	−27.6316			−1.05729			−0.528647	−	0.848842i	$-0.677300\pi$
$683$	−27.6316			−1.05729			−0.528647	+	0.848842i	$0.677300\pi$
$684$	3.75404	+	40.4846i	0.143539	+	1.54797i
$685$	−17.7648			−0.678757
$686$	−2.69914	−	4.67505i	−0.103054	−	0.178494i
$687$	−1.42178	−	2.46259i	−0.0542442	−	0.0939536i
$688$	−10.1215	+	17.5310i	−0.385880	+	0.668363i
$689$	0.535845	+	0.928112i	0.0204141	+	0.0353582i
$690$	−9.51469	+	16.4799i	−0.362218	+	0.627380i
$691$	0.0348336			0.00132513			0.000662566	−	1.00000i	$-0.499789\pi$
$691$	0.0348336			0.00132513			0.000662566		1.00000i	$0.499789\pi$
$692$	−19.1195			−0.726816
$693$	−12.3101	+	21.3218i	−0.467623	+	0.809947i
$694$	15.5933	−	27.0084i	0.591915	−	1.02523i
$695$	−19.4729			−0.738650
$696$	24.1871			0.916811
$697$	2.70965	−	4.69325i	0.102635	−	0.177769i
$698$	−7.12388	−	12.3389i	−0.269643	−	0.467035i
$699$	44.0700	−	76.3315i	1.66688	−	2.88712i
$700$	14.2226	+	24.6342i	0.537563	+	0.931086i
$701$	6.71538	+	11.6314i	0.253636	+	0.439311i	0.964524	−	0.263994i	$-0.0850400\pi$
$701$	6.71538	+	11.6314i	0.253636	+	0.439311i	−0.710888	+	0.703305i	$0.751707\pi$
$702$	−9.73578			−0.367453
$703$	43.1076	+	19.8293i	1.62583	+	0.747878i
$704$	2.47225			0.0931764
$705$	−34.5740	−	59.8838i	−1.30213	−	2.25536i
$706$	0.564676	+	0.978048i	0.0212519	+	0.0368093i
$707$	−15.4396	+	26.7422i	−0.580666	+	1.00574i
$708$	20.4584	+	35.4351i	0.768875	+	1.33173i
$709$	3.62993	−	6.28722i	0.136325	−	0.236121i	−0.789778	−	0.613393i	$-0.789804\pi$
$709$	3.62993	−	6.28722i	0.136325	−	0.236121i	0.926103	+	0.377271i	$0.123138\pi$
$710$	−63.4635			−2.38174
$711$	−3.12485			−0.117191
$712$	−2.65171	+	4.59290i	−0.0993772	+	0.172126i
$713$	−3.54781	+	6.14499i	−0.132867	+	0.230132i
$714$	−88.2094			−3.30116
$715$	−1.46622			−0.0548334
$716$	−0.393192	+	0.681028i	−0.0146943	+	0.0254512i
$717$	−7.06656	−	12.2396i	−0.263906	−	0.457098i
$718$	7.24144	−	12.5426i	0.270248	−	0.468084i
$719$	−24.5397	−	42.5041i	−0.915178	−	1.58513i	−0.806641	−	0.591042i	$-0.798717\pi$
$719$	−24.5397	−	42.5041i	−0.915178	−	1.58513i	−0.108537	−	0.994092i	$-0.534617\pi$
$720$	−53.8469	−	93.2656i	−2.00676	−	3.47580i
$721$	−20.1089			−0.748896
$722$	11.5985	−	32.9274i	0.431650	−	1.22543i
$723$	−87.3546			−3.24875
$724$	15.7913	+	27.3514i	0.586880	+	1.01651i
$725$	19.1989	+	33.2535i	0.713030	+	1.23500i
$726$	−2.87286	+	4.97594i	−0.106622	+	0.184674i
$727$	−8.10168	−	14.0325i	−0.300475	−	0.520437i	0.675769	−	0.737114i	$-0.263812\pi$
$727$	−8.10168	−	14.0325i	−0.300475	−	0.520437i	−0.976244	+	0.216676i	$0.930478\pi$
$728$	0.933613	−	1.61707i	0.0346020	−	0.0599324i
$729$	1.77804			0.0658535
$730$	−15.9401			−0.589968
$731$	8.80571	−	15.2519i	0.325691	−	0.564113i
$732$	−10.0312	+	17.3745i	−0.370763	+	0.642180i
$733$	−11.9920			−0.442933			−0.221467	−	0.975168i	$-0.571084\pi$
$733$	−11.9920			−0.442933			−0.221467	+	0.975168i	$0.571084\pi$
$734$	49.2815			1.81901
$735$	31.6521	−	54.8231i	1.16751	−	2.02218i
$736$	−3.35977	−	5.81930i	−0.123843	−	0.214502i
$737$	−0.718518	+	1.24451i	−0.0264670	+	0.0458421i
$738$	7.98428	+	13.8292i	0.293905	+	0.509059i
$739$	13.4414	+	23.2812i	0.494451	+	0.856414i	0.999980	−	0.00639547i	$-0.00203575\pi$
$739$	13.4414	+	23.2812i	0.494451	+	0.856414i	−0.505528	+	0.862810i	$0.668702\pi$
$740$	48.9780			1.80047
$741$	5.55282	+	2.55428i	0.203988	+	0.0938337i
$742$	−15.9492			−0.585512
$743$	−11.2382	−	19.4651i	−0.412290	−	0.714107i	0.582850	−	0.812580i	$-0.301938\pi$
$743$	−11.2382	−	19.4651i	−0.412290	−	0.714107i	−0.995140	+	0.0984729i	$0.968604\pi$
$744$	−12.5583	−	21.7516i	−0.460410	−	0.797454i
$745$	25.7564	−	44.6115i	0.943643	−	1.63444i
$746$	3.04523	+	5.27450i	0.111494	+	0.193113i
$747$	10.4752	−	18.1435i	0.383266	−	0.663836i
$748$	−5.81635			−0.212667
$749$	8.29284			0.303014
$750$	6.49847	−	11.2557i	0.237291	−	0.411000i
$751$	−15.8768	+	27.4994i	−0.579352	+	1.00347i	0.416202	+	0.909272i	$0.363361\pi$
$751$	−15.8768	+	27.4994i	−0.579352	+	1.00347i	−0.995554	+	0.0941951i	$0.969972\pi$
$752$	32.8567			1.19816
$753$	−64.4422			−2.34840
$754$	−2.77909	+	4.81353i	−0.101209	+	0.175298i
$755$	−11.1122	−	19.2468i	−0.404413	−	0.700464i
$756$	29.5274	−	51.1430i	1.07390	−	1.86005i
$757$	11.9071	+	20.6236i	0.432769	+	0.749578i	0.997111	−	0.0759634i	$-0.0242032\pi$
$757$	11.9071	+	20.6236i	0.432769	+	0.749578i	−0.564342	+	0.825541i	$0.690870\pi$
$758$	−15.3069	−	26.5123i	−0.555970	−	0.962969i
$759$	3.16737			0.114968
$760$	1.50881	+	16.2715i	0.0547304	+	0.590228i
$761$	40.4398			1.46594			0.732971	−	0.680260i	$-0.238133\pi$
$761$	40.4398			1.46594			0.732971	+	0.680260i	$0.238133\pi$
$762$	−38.4329	−	66.5677i	−1.39228	−	2.41149i
$763$	19.1796	+	33.2200i	0.694348	+	1.20265i
$764$	0.224399	−	0.388671i	0.00811848	−	0.0140616i
$765$	46.8467	+	81.1408i	1.69374	+	2.93365i
$766$	−22.2068	+	38.4633i	−0.802365	+	1.38974i
$767$	4.26397			0.153963
$768$	65.5978			2.36706
$769$	0.491657	−	0.851575i	0.0177296	−	0.0307086i	−0.857024	−	0.515276i	$-0.827690\pi$
$769$	0.491657	−	0.851575i	0.0177296	−	0.0307086i	0.874754	+	0.484567i	$0.161023\pi$
$770$	10.9103	−	18.8972i	0.393180	−	0.681007i
$771$	47.8599

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.918695 - 1.59123i) q^{2} +(-1.56355 - 2.70815i) q^{3} +(-0.688002 + 1.19165i) q^{4} +(1.63491 + 2.83176i) q^{5} +(-2.87286 + 4.97594i) q^{6} -3.63195 q^{7} -1.14653 q^{8} +(-3.38940 + 5.87061i) q^{9} +O(q^{10})\)	\(q+(-0.918695 - 1.59123i) q^{2} +(-1.56355 - 2.70815i) q^{3} +(-0.688002 + 1.19165i) q^{4} +(1.63491 + 2.83176i) q^{5} +(-2.87286 + 4.97594i) q^{6} -3.63195 q^{7} -1.14653 q^{8} +(-3.38940 + 5.87061i) q^{9} +(3.00398 - 5.20304i) q^{10} -1.00000 q^{11} +4.30291 q^{12} +(0.224204 - 0.388333i) q^{13} +(3.33666 + 5.77926i) q^{14} +(5.11255 - 8.85520i) q^{15} +(2.42931 + 4.20769i) q^{16} +(-2.11349 - 3.66068i) q^{17} +12.4553 q^{18} +(-3.96002 - 1.82160i) q^{19} -4.49930 q^{20} +(5.67875 + 9.83588i) q^{21} +(0.918695 + 1.59123i) q^{22} +(0.506437 - 0.877175i) q^{23} +(1.79265 + 3.10497i) q^{24} +(-2.84589 + 4.92923i) q^{25} -0.823900 q^{26} +11.8167 q^{27} +(2.49879 - 4.32803i) q^{28} +(3.37309 - 5.84237i) q^{29} -18.7875 q^{30} -7.00544 q^{31} +(3.31707 - 5.74533i) q^{32} +(1.56355 + 2.70815i) q^{33} +(-3.88331 + 6.72610i) q^{34} +(-5.93793 - 10.2848i) q^{35} +(-4.66382 - 8.07798i) q^{36} -10.8857 q^{37} +(0.739482 + 7.97479i) q^{38} -1.40222 q^{39} +(-1.87447 - 3.24668i) q^{40} +(0.641035 + 1.11031i) q^{41} +(10.4341 - 18.0723i) q^{42} +(2.08321 + 3.60823i) q^{43} +(0.688002 - 1.19165i) q^{44} -22.1655 q^{45} -1.86105 q^{46} +(3.38128 - 5.85655i) q^{47} +(7.59671 - 13.1579i) q^{48} +6.19106 q^{49} +10.4580 q^{50} +(-6.60912 + 11.4473i) q^{51} +(0.308505 + 0.534347i) q^{52} +(-1.19500 + 2.06979i) q^{53} +(-10.8559 - 18.8030i) q^{54} +(-1.63491 - 2.83176i) q^{55} +4.16412 q^{56} +(1.25855 + 13.5725i) q^{57} -12.3954 q^{58} +(4.75456 + 8.23514i) q^{59} +(7.03489 + 12.1848i) q^{60} +(-2.33126 + 4.03785i) q^{61} +(6.43586 + 11.1472i) q^{62} +(12.3101 - 21.3218i) q^{63} -2.47225 q^{64} +1.46622 q^{65} +(2.87286 - 4.97594i) q^{66} +(0.718518 - 1.24451i) q^{67} +5.81635 q^{68} -3.16737 q^{69} +(-10.9103 + 18.8972i) q^{70} +(-5.28163 - 9.14804i) q^{71} +(3.88603 - 6.73080i) q^{72} +(-1.32658 - 2.29770i) q^{73} +(10.0006 + 17.3216i) q^{74} +17.7988 q^{75} +(4.89521 - 3.46572i) q^{76} +3.63195 q^{77} +(1.28821 + 2.23125i) q^{78} +(0.230487 + 0.399216i) q^{79} +(-7.94343 + 13.7584i) q^{80} +(-8.30783 - 14.3896i) q^{81} +(1.17783 - 2.04006i) q^{82} -3.09057 q^{83} -15.6280 q^{84} +(6.91077 - 11.9698i) q^{85} +(3.82767 - 6.62972i) q^{86} -21.0960 q^{87} +1.14653 q^{88} +(2.31283 - 4.00593i) q^{89} +(20.3633 + 35.2703i) q^{90} +(-0.814298 + 1.41040i) q^{91} +(0.696859 + 1.20700i) q^{92} +(10.9534 + 18.9718i) q^{93} -12.4255 q^{94} +(-1.31599 - 14.1920i) q^{95} -20.7456 q^{96} +(-4.62983 - 8.01910i) q^{97} +(-5.68770 - 9.85139i) q^{98} +(3.38940 - 5.87061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

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