LMFDB - Embedded newform 189.2.ba.a.131.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			131.12
Character	$\chi$	$=$	189.131
Dual form			189.2.ba.a.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00959490 + 0.0114348i) q^{2} +(-1.04544 + 1.38096i) q^{3} +(0.347258 - 1.96940i) q^{4} +(1.26073 + 1.05788i) q^{5} +(-0.0258218 + 0.00129578i) q^{6} +(1.81613 - 1.92397i) q^{7} +(0.0517058 - 0.0298524i) q^{8} +(-0.814097 - 2.88743i) q^{9} +O(q^{10})$	\(q+(0.00959490 + 0.0114348i) q^{2} +(-1.04544 + 1.38096i) q^{3} +(0.347258 - 1.96940i) q^{4} +(1.26073 + 1.05788i) q^{5} +(-0.0258218 + 0.00129578i) q^{6} +(1.81613 - 1.92397i) q^{7} +(0.0517058 - 0.0298524i) q^{8} +(-0.814097 - 2.88743i) q^{9} +0.0245663i q^{10} +(2.95219 + 3.51829i) q^{11} +(2.35662 + 2.53844i) q^{12} +(1.52751 + 4.19679i) q^{13} +(0.0394257 + 0.00230675i) q^{14} +(-2.77891 + 0.635065i) q^{15} +(-3.75751 - 1.36762i) q^{16} +3.77410 q^{17} +(0.0252059 - 0.0370136i) q^{18} -1.46832i q^{19} +(2.52118 - 2.11552i) q^{20} +(0.758259 + 4.51941i) q^{21} +(-0.0119048 + 0.0675152i) q^{22} +(-2.54129 - 6.98214i) q^{23} +(-0.0128306 + 0.102613i) q^{24} +(-0.397908 - 2.25665i) q^{25} +(-0.0333330 + 0.0577345i) q^{26} +(4.83851 + 1.89441i) q^{27} +(-3.15839 - 4.24480i) q^{28} +(-2.83246 + 7.78213i) q^{29} +(-0.0339251 - 0.0256827i) q^{30} +(-8.27481 - 1.45907i) q^{31} +(-0.0612550 - 0.168297i) q^{32} +(-7.94496 + 0.398690i) q^{33} +(0.0362121 + 0.0431559i) q^{34} +(4.32497 - 0.504358i) q^{35} +(-5.96919 + 0.600598i) q^{36} +(0.397320 + 0.688178i) q^{37} +(0.0167899 - 0.0140884i) q^{38} +(-7.39252 - 2.27808i) q^{39} +(0.0967671 + 0.0170627i) q^{40} +(-3.97658 + 1.44736i) q^{41} +(-0.0444029 + 0.0520338i) q^{42} +(-0.303215 - 1.71962i) q^{43} +(7.95407 - 4.59229i) q^{44} +(2.02819 - 4.50148i) q^{45} +(0.0554557 - 0.0960520i) q^{46} +(-0.286275 - 1.62355i) q^{47} +(5.81690 - 3.75920i) q^{48} +(-0.403318 - 6.98837i) q^{49} +(0.0219863 - 0.0262023i) q^{50} +(-3.94561 + 5.21188i) q^{51} +(8.79559 - 1.55090i) q^{52} +(-3.66888 + 2.11823i) q^{53} +(0.0247630 + 0.0735039i) q^{54} +7.55866i q^{55} +(0.0364696 - 0.153696i) q^{56} +(2.02769 + 1.53505i) q^{57} +(-0.116164 + 0.0422802i) q^{58} +(-10.8663 + 3.95501i) q^{59} +(0.285698 + 5.69330i) q^{60} +(2.96287 - 0.522435i) q^{61} +(-0.0627118 - 0.108620i) q^{62} +(-7.03383 - 3.67766i) q^{63} +(-3.99733 + 6.92357i) q^{64} +(-2.51392 + 6.90693i) q^{65} +(-0.0807900 - 0.0870233i) q^{66} +(-8.30643 - 6.96992i) q^{67} +(1.31059 - 7.43270i) q^{68} +(12.2988 + 3.79001i) q^{69} +(0.0472649 + 0.0446158i) q^{70} +(6.66808 + 3.84982i) q^{71} +(-0.128290 - 0.124994i) q^{72} +(13.7076 + 7.91406i) q^{73} +(-0.00405690 + 0.0111462i) q^{74} +(3.53233 + 1.80970i) q^{75} +(-2.89171 - 0.509886i) q^{76} +(12.1307 + 0.709749i) q^{77} +(-0.0448812 - 0.106390i) q^{78} +(1.22109 - 1.02462i) q^{79} +(-3.29043 - 5.69919i) q^{80} +(-7.67449 + 4.70130i) q^{81} +(-0.0547050 - 0.0315840i) q^{82} +(-4.61667 - 1.68033i) q^{83} +(9.16381 + 0.0760856i) q^{84} +(4.75812 + 3.99254i) q^{85} +(0.0167541 - 0.0199668i) q^{86} +(-7.78562 - 12.0473i) q^{87} +(0.257675 + 0.0937859i) q^{88} -7.18505 q^{89} +(0.0709336 - 0.0199994i) q^{90} +(10.8487 + 4.68306i) q^{91} +(-14.6331 + 2.58021i) q^{92} +(10.6658 - 9.90180i) q^{93} +(0.0158181 - 0.0188513i) q^{94} +(1.55330 - 1.85115i) q^{95} +(0.296449 + 0.0913539i) q^{96} +(1.56544 - 0.276029i) q^{97} +(0.0760405 - 0.0716645i) q^{98} +(7.75543 - 11.3885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.00959490	+	0.0114348i	0.00678462	+	0.00808559i	0.769426	−	0.638736i	$-0.220542\pi$
$2$	0.00959490	+	0.0114348i	0.00678462	+	0.00808559i	−0.762641	+	0.646821i	$0.776098\pi$
$3$	−1.04544	+	1.38096i	−0.603587	+	0.797297i
$3$	−1.04544	+	1.38096i	−0.603587	+	0.797297i
$4$	0.347258	−	1.96940i	0.173629	−	0.984698i
$5$	1.26073	+	1.05788i	0.563815	+	0.473097i	0.879587	−	0.475738i	$-0.157819\pi$
$5$	1.26073	+	1.05788i	0.563815	+	0.473097i	−0.315772	+	0.948835i	$0.602263\pi$
$6$	−0.0258218	+	0.00129578i	−0.0105417	+	0.000528999i
$7$	1.81613	−	1.92397i	0.686434	−	0.727192i
$7$	1.81613	−	1.92397i	0.686434	−	0.727192i
$8$	0.0517058	−	0.0298524i	0.0182808	−	0.0105544i
$9$	−0.814097	−	2.88743i	−0.271366	−	0.962476i
$10$			0.0245663i			0.00776856i
$11$	2.95219	+	3.51829i	0.890120	+	1.06080i	0.997779	+	0.0666155i	$0.0212201\pi$
$11$	2.95219	+	3.51829i	0.890120	+	1.06080i	−0.107659	+	0.994188i	$0.534335\pi$
$12$	2.35662	+	2.53844i	0.680297	+	0.732785i
$13$	1.52751	+	4.19679i	0.423654	+	1.16398i	0.949600	+	0.313463i	$0.101489\pi$
$13$	1.52751	+	4.19679i	0.423654	+	1.16398i	−0.525946	+	0.850518i	$0.676289\pi$
$14$	0.0394257	+	0.00230675i	0.0105370	+	0.000616504i
$15$	−2.77891	+	0.635065i	−0.717510	+	0.163973i
$16$	−3.75751	−	1.36762i	−0.939379	−	0.341906i
$17$	3.77410			0.915355			0.457677	−	0.889118i	$-0.348682\pi$
$17$	3.77410			0.915355			0.457677	+	0.889118i	$0.348682\pi$
$18$	0.0252059	−	0.0370136i	0.00594108	−	0.00872419i
$19$		−	1.46832i		−	0.336856i	−0.985714	−	0.168428i	$-0.946131\pi$
$19$		−	1.46832i		−	0.336856i	0.985714	−	0.168428i	$-0.0538690\pi$
$20$	2.52118	−	2.11552i	0.563752	−	0.473044i
$21$	0.758259	+	4.51941i	0.165466	+	0.986216i
$22$	−0.0119048	+	0.0675152i	−0.00253810	+	0.0143943i
$23$	−2.54129	−	6.98214i	−0.529896	−	1.45588i	−0.859193	−	0.511651i	$-0.829034\pi$
$23$	−2.54129	−	6.98214i	−0.529896	−	1.45588i	0.329297	−	0.944226i	$-0.393188\pi$
$24$	−0.0128306	+	0.102613i	−0.00261903	+	0.0209457i
$25$	−0.397908	−	2.25665i	−0.0795815	−	0.451329i
$26$	−0.0333330	+	0.0577345i	−0.00653714	+	0.0113227i
$27$	4.83851	+	1.89441i	0.931172	+	0.364579i
$28$	−3.15839	−	4.24480i	−0.596880	−	0.802192i
$29$	−2.83246	+	7.78213i	−0.525975	+	1.44511i	0.337795	+	0.941220i	$0.390319\pi$
$29$	−2.83246	+	7.78213i	−0.525975	+	1.44511i	−0.863771	+	0.503885i	$0.831903\pi$
$30$	−0.0339251	−	0.0256827i	−0.00619385	−	0.00468900i
$31$	−8.27481	−	1.45907i	−1.48620	−	0.262057i	−0.629147	−	0.777286i	$-0.716596\pi$
$31$	−8.27481	−	1.45907i	−1.48620	−	0.262057i	−0.857052	+	0.515229i	$0.827707\pi$
$32$	−0.0612550	−	0.168297i	−0.0108284	−	0.0297509i
$33$	−7.94496	+	0.398690i	−1.38304	+	0.0694030i
$34$	0.0362121	+	0.0431559i	0.00621033	+	0.00740118i
$35$	4.32497	−	0.504358i	0.731054	−	0.0852520i
$36$	−5.96919	+	0.600598i	−0.994865	+	0.100100i
$37$	0.397320	+	0.688178i	0.0653190	+	0.113136i	0.896835	−	0.442364i	$-0.145860\pi$
$37$	0.397320	+	0.688178i	0.0653190	+	0.113136i	−0.831516	+	0.555500i	$0.812527\pi$
$38$	0.0167899	−	0.0140884i	0.00272368	−	0.00228544i
$39$	−7.39252	−	2.27808i	−1.18375	−	0.364785i
$40$	0.0967671	+	0.0170627i	0.0153002	+	0.00269784i
$41$	−3.97658	+	1.44736i	−0.621037	+	0.226039i	−0.633326	−	0.773885i	$-0.718311\pi$
$41$	−3.97658	+	1.44736i	−0.621037	+	0.226039i	0.0122884	+	0.999924i	$0.496088\pi$
$42$	−0.0444029	+	0.0520338i	−0.00685151	+	0.00802898i
$43$	−0.303215	−	1.71962i	−0.0462399	−	0.262239i	0.952920	−	0.303222i	$-0.0980623\pi$
$43$	−0.303215	−	1.71962i	−0.0462399	−	0.262239i	−0.999160	+	0.0409825i	$0.986951\pi$
$44$	7.95407	−	4.59229i	1.19912	−	0.692313i
$45$	2.02819	−	4.50148i	0.302345	−	0.671041i
$46$	0.0554557	−	0.0960520i	0.00817649	−	0.0141621i
$47$	−0.286275	−	1.62355i	−0.0417575	−	0.236819i	0.956785	−	0.290798i	$-0.0939207\pi$
$47$	−0.286275	−	1.62355i	−0.0417575	−	0.236819i	−0.998542	+	0.0539790i	$0.982810\pi$
$48$	5.81690	−	3.75920i	0.839597	−	0.542594i
$49$	−0.403318	−	6.98837i	−0.0576169	−	0.998339i
$50$	0.0219863	−	0.0262023i	0.00310933	−	0.00370556i
$51$	−3.94561	+	5.21188i	−0.552496	+	0.729810i
$52$	8.79559	−	1.55090i	1.21973	−	0.215071i
$53$	−3.66888	+	2.11823i	−0.503959	+	0.290961i	−0.730347	−	0.683076i	$-0.760642\pi$
$53$	−3.66888	+	2.11823i	−0.503959	+	0.290961i	0.226388	+	0.974037i	$0.427308\pi$
$54$	0.0247630	+	0.0735039i	0.00336981	+	0.0100026i
$55$			7.55866i			1.01921i
$56$	0.0364696	−	0.153696i	0.00487346	−	0.0205385i
$57$	2.02769	+	1.53505i	0.268574	+	0.203322i
$58$	−0.116164	+	0.0422802i	−0.0152531	+	0.00555166i
$59$	−10.8663	+	3.95501i	−1.41467	+	0.514898i	−0.932497	−	0.361178i	$-0.882375\pi$
$59$	−10.8663	+	3.95501i	−1.41467	+	0.514898i	−0.482173	+	0.876076i	$0.660152\pi$
$60$	0.285698	+	5.69330i	0.0368834	+	0.735001i
$61$	2.96287	−	0.522435i	0.379357	−	0.0668909i	0.0192817	−	0.999814i	$-0.493862\pi$
$61$	2.96287	−	0.522435i	0.379357	−	0.0668909i	0.360075	+	0.932923i	$0.382751\pi$
$62$	−0.0627118	−	0.108620i	−0.00796441	−	0.0137948i
$63$	−7.03383	−	3.67766i	−0.886180	−	0.463341i
$64$	−3.99733	+	6.92357i	−0.499666	+	0.865447i
$65$	−2.51392	+	6.90693i	−0.311813	+	0.856700i
$66$	−0.0807900	−	0.0870233i	−0.00994456	−	0.0107118i
$67$	−8.30643	−	6.96992i	−1.01479	−	0.851512i	−0.0258279	−	0.999666i	$-0.508222\pi$
$67$	−8.30643	−	6.96992i	−1.01479	−	0.851512i	−0.988964	+	0.148155i	$0.952667\pi$
$68$	1.31059	−	7.43270i	0.158932	−	0.901348i
$69$	12.2988	+	3.79001i	1.48061	+	0.456264i
$70$	0.0472649	+	0.0446158i	0.00564924	+	0.00533260i
$71$	6.66808	+	3.84982i	0.791355	+	0.456889i	0.840439	−	0.541906i	$-0.182297\pi$
$71$	6.66808	+	3.84982i	0.791355	+	0.456889i	−0.0490844	+	0.998795i	$0.515630\pi$
$72$	−0.128290	−	0.124994i	−0.0151191	−	0.0147307i
$73$	13.7076	+	7.91406i	1.60435	+	0.926271i	0.990603	+	0.136767i	$0.0436712\pi$
$73$	13.7076	+	7.91406i	1.60435	+	0.926271i	0.613745	+	0.789504i	$0.289662\pi$
$74$	−0.00405690	+	0.0111462i	−0.000471605	+	0.00129573i
$75$	3.53233	+	1.80970i	0.407878	+	0.208966i
$76$	−2.89171	−	0.509886i	−0.331701	−	0.0584879i
$77$	12.1307	+	0.709749i	1.38242	+	0.0808833i
$78$	−0.0448812	−	0.106390i	−0.00508179	−	0.0120463i
$79$	1.22109	−	1.02462i	0.137384	−	0.115279i	−0.571506	−	0.820598i	$-0.693641\pi$
$79$	1.22109	−	1.02462i	0.137384	−	0.115279i	0.708890	+	0.705319i	$0.249196\pi$
$80$	−3.29043	−	5.69919i	−0.367881	−	0.637189i
$81$	−7.67449	+	4.70130i	−0.852721	+	0.522366i
$82$	−0.0547050	−	0.0315840i	−0.00604116	−	0.00348787i
$83$	−4.61667	−	1.68033i	−0.506745	−	0.184440i	0.0759804	−	0.997109i	$-0.475791\pi$
$83$	−4.61667	−	1.68033i	−0.506745	−	0.184440i	−0.582725	+	0.812669i	$0.698014\pi$
$84$	9.16381	+	0.0760856i	0.999854	+	0.00830162i
$85$	4.75812	+	3.99254i	0.516091	+	0.433051i
$86$	0.0167541	−	0.0199668i	0.00180664	−	0.00215307i
$87$	−7.78562	−	12.0473i	−0.834706	−	1.29161i
$88$	0.257675	+	0.0937859i	0.0274682	+	0.00999761i
$89$	−7.18505			−0.761614			−0.380807	−	0.924655i	$-0.624354\pi$
$89$	−7.18505			−0.761614			−0.380807	+	0.924655i	$0.624354\pi$
$90$	0.0709336	−	0.0199994i	0.00747705	−	0.00210812i
$91$	10.8487	+	4.68306i	1.13725	+	0.490918i
$92$	−14.6331	+	2.58021i	−1.52561	+	0.269005i
$93$	10.6658	−	9.90180i	1.10599	−	1.02677i
$94$	0.0158181	−	0.0188513i	0.00163151	−	0.00194436i
$95$	1.55330	−	1.85115i	0.159365	−	0.189924i
$96$	0.296449	+	0.0913539i	0.0302562	+	0.00932377i
$97$	1.56544	−	0.276029i	0.158946	−	0.0280265i	−0.0936086	−	0.995609i	$-0.529840\pi$
$97$	1.56544	−	0.276029i	0.158946	−	0.0280265i	0.252555	+	0.967583i	$0.418729\pi$
$98$	0.0760405	−	0.0716645i	0.00768125	−	0.00723921i
$99$	7.75543	−	11.3885i	0.779450	−	1.14458i
$100$	−4.58241			−0.458241
$101$	2.17178	+	0.790462i	0.216100	+	0.0786539i	0.447802	−	0.894133i	$-0.352207\pi$
$101$	2.17178	+	0.790462i	0.216100	+	0.0786539i	−0.231702	+	0.972787i	$0.574429\pi$
$102$	−0.0974543	+	0.00489040i	−0.00964942	+	0.000484222i
$103$	−0.351554	+	0.418965i	−0.0346396	+	0.0412819i	−0.783086	−	0.621913i	$-0.786356\pi$
$103$	−0.351554	+	0.418965i	−0.0346396	+	0.0412819i	0.748447	+	0.663195i	$0.230800\pi$
$104$	0.204265	+	0.171399i	0.0200299	+	0.0168070i
$105$	−3.82502	+	6.49989i	−0.373284	+	0.634324i
$106$	−0.0594239	−	0.0216285i	−0.00577176	−	0.00210075i
$107$	−2.89299	−	1.67027i	−0.279676	−	0.161471i	0.353601	−	0.935397i	$-0.384957\pi$
$107$	−2.89299	−	1.67027i	−0.279676	−	0.161471i	−0.633277	+	0.773925i	$0.718291\pi$
$108$	5.41105	−	8.87110i	0.520679	−	0.853622i
$109$	1.92585	+	3.33567i	0.184463	+	0.319499i	0.943395	−	0.331670i	$-0.107612\pi$
$109$	1.92585	+	3.33567i	0.184463	+	0.319499i	−0.758932	+	0.651169i	$0.774279\pi$
$110$	−0.0864314	+	0.0725246i	−0.00824091	+	0.00691495i
$111$	−1.36572	−	0.170769i	−0.129628	−	0.0162086i
$112$	−9.45541	+	4.74556i	−0.893453	+	0.448413i
$113$	4.52691	+	0.798216i	0.425856	+	0.0750899i	0.382469	−	0.923968i	$-0.375074\pi$
$113$	4.52691	+	0.798216i	0.425856	+	0.0750899i	0.0433872	+	0.999058i	$0.486185\pi$
$114$	0.00190262	+	0.0379148i	0.000178196	+	0.00355104i
$115$	4.18237	−	11.4910i	0.390008	−	1.07154i
$116$	14.3425	+	8.28065i	1.33167	+	0.768839i
$117$	10.8744	−	7.82717i	1.00534	−	0.723622i
$118$	−0.149485	−	0.0863054i	−0.0137612	−	0.00794506i
$119$	6.85428	−	7.26126i	0.628330	−	0.665639i
$120$	−0.124727	+	0.115793i	−0.0113860	+	0.0105704i
$121$	−1.75277	+	9.94044i	−0.159343	+	0.903676i
$122$	0.0344024	+	0.0288670i	0.00311464	+	0.00261350i
$123$	2.15855	−	7.00462i	0.194630	−	0.631586i
$124$	−5.74698	+	15.7897i	−0.516094	+	1.41796i
$125$	6.00001	−	10.3923i	0.536657	−	0.929518i
$126$	−0.0254358	−	0.115717i	−0.00226600	−	0.0103089i
$127$	2.63202	+	4.55879i	0.233554	+	0.404527i	0.958851	−	0.283908i	$-0.0916312\pi$
$127$	2.63202	+	4.55879i	0.233554	+	0.404527i	−0.725298	+	0.688435i	$0.758298\pi$
$128$	−0.470277	+	0.0829224i	−0.0415670	+	0.00732938i
$129$	2.69172	+	1.37904i	0.236993	+	0.121417i
$130$	−0.103100	+	0.0375253i	−0.00904246	+	0.00329119i
$131$	−14.2240	+	5.17710i	−1.24275	+	0.452325i	−0.877947	−	0.478758i	$-0.841087\pi$
$131$	−14.2240	+	5.17710i	−1.24275	+	0.452325i	−0.364807	+	0.931083i	$0.618865\pi$
$132$	−1.97377	+	15.7852i	−0.171795	+	1.37393i
$133$	−2.82500	−	2.66667i	−0.244959	−	0.231229i
$134$		−	0.161858i		−	0.0139824i
$135$	4.09600	+	7.50689i	0.352528	+	0.646090i
$136$	0.195143	−	0.112666i	0.0167334	−	0.00966102i
$137$	3.51827	−	0.620365i	0.300586	−	0.0530014i	−0.0213213	−	0.999773i	$-0.506787\pi$
$137$	3.51827	−	0.620365i	0.300586	−	0.0530014i	0.321907	+	0.946771i	$0.395676\pi$
$138$	0.0746682	+	0.176999i	0.00635618	+	0.0150671i
$139$	−3.91305	+	4.66340i	−0.331901	+	0.395544i	−0.906025	−	0.423224i	$-0.860898\pi$
$139$	−3.91305	+	4.66340i	−0.331901	+	0.395544i	0.574124	+	0.818768i	$0.305343\pi$
$140$	0.508600	−	8.69273i	0.0429846	−	0.734670i
$141$	2.54134	+	1.30199i	0.214019	+	0.109648i
$142$	0.0199578	+	0.113186i	0.00167482	+	0.00949839i
$143$	−10.2560	+	17.7640i	−0.857652	+	1.48550i
$144$	−0.889933	+	11.9629i	−0.0741611	+	0.996911i
$145$	−11.8035	+	6.81476i	−0.980228	+	0.565935i
$146$	0.0410273	+	0.232677i	0.00339544	+	0.0192565i
$147$	10.0723	+	6.74898i	0.830750	+	0.556646i
$148$	1.49327	−	0.543505i	0.122746	−	0.0446758i
$149$	−19.9144	−	3.51144i	−1.63145	−	0.287668i	−0.718433	−	0.695596i	$-0.755140\pi$
$149$	−19.9144	−	3.51144i	−1.63145	−	0.287668i	−0.913014	+	0.407928i	$0.866252\pi$
$150$	0.0131988	+	0.0577552i	0.00107768	+	0.00471569i
$151$	14.6511	−	12.2937i	1.19229	−	1.00045i	0.192474	−	0.981302i	$-0.438349\pi$
$151$	14.6511	−	12.2937i	1.19229	−	1.00045i	0.999817	−	0.0191488i	$-0.00609564\pi$
$152$	−0.0438328	−	0.0759207i	−0.00355531	−	0.00615798i
$153$	−3.07249	−	10.8975i	−0.248396	−	0.881007i
$154$	0.108277	+	0.145521i	0.00872518	+	0.0117264i
$155$	−8.88877	−	10.5932i	−0.713963	−	0.850868i
$156$	−7.05356	+	13.7677i	−0.564737	+	1.10230i
$157$	5.43336	+	14.9280i	0.433630	+	1.19139i	0.943569	+	0.331177i	$0.107446\pi$
$157$	5.43336	+	14.9280i	0.433630	+	1.19139i	−0.509939	+	0.860211i	$0.670332\pi$
$158$	0.0234325	+	0.00413178i	0.00186419	+	0.000328707i
$159$	0.910417	−	7.28106i	0.0722008	−	0.577425i
$160$	0.100811	−	0.276977i	0.00796983	−	0.0218969i
$161$	−18.0488	−	7.79114i	−1.42244	−	0.614028i
$162$	−0.127394	−	0.0426475i	−0.0100090	−	0.00335070i
$163$	8.71884	−	15.1015i	0.682912	−	1.18284i	−0.291176	−	0.956670i	$-0.594046\pi$
$163$	8.71884	−	15.1015i	0.682912	−	1.18284i	0.974088	−	0.226169i	$-0.0726202\pi$
$164$	1.46952	+	8.33406i	0.114750	+	0.650781i
$165$	−10.4382	−	7.90215i	−0.812613	−	0.615182i
$166$	−0.0250823	−	0.0689130i	−0.00194676	−	0.00534869i
$167$	1.64317	−	9.31890i	0.127153	−	0.721118i	−0.852853	−	0.522150i	$-0.825130\pi$
$167$	1.64317	−	9.31890i	0.127153	−	0.721118i	0.980006	−	0.198968i	$-0.0637589\pi$
$168$	0.174121	+	0.211044i	0.0134338	+	0.0162824i
$169$	−5.32122	+	4.46503i	−0.409325	+	0.343464i
$170$			0.0927159i			0.00711099i
$171$	−4.23967	+	1.19536i	−0.324216	+	0.0914111i
$172$	−3.49190			−0.266255
$173$	1.42819	+	0.519819i	0.108583	+	0.0395211i	0.395740	−	0.918362i	$-0.370488\pi$
$173$	1.42819	+	0.519819i	0.108583	+	0.0395211i	−0.287157	+	0.957883i	$0.592710\pi$
$174$	0.0630555	−	0.204619i	0.00478023	−	0.0155121i
$175$	−5.06437	−	3.33281i	−0.382831	−	0.251937i
$176$	−6.28122	−	17.2575i	−0.473465	−	1.30083i
$177$	5.89838	−	19.1406i	0.443350	−	1.43870i
$178$	−0.0689398	−	0.0821592i	−0.00516726	−	0.00615810i
$179$		−	8.59347i		−	0.642306i	−0.947027	−	0.321153i	$-0.895930\pi$
$179$		−	8.59347i		−	0.642306i	0.947027	−	0.321153i	$-0.104070\pi$
$180$	−8.16089	−	5.55748i	−0.608277	−	0.414230i
$181$	−9.18805	+	5.30472i	−0.682942	+	0.394297i	−0.800963	−	0.598714i	$-0.795678\pi$
$181$	−9.18805	+	5.30472i	−0.682942	+	0.394297i	0.118021	+	0.993011i	$0.462345\pi$
$182$	0.0505422	+	0.168985i	0.00374644	+	0.0125260i
$183$	−2.37605	+	4.63778i	−0.175643	+	0.342835i
$184$	−0.339833	−	0.285154i	−0.0250528	−	0.0210218i
$185$	−0.227095	+	1.28792i	−0.0166964	+	0.0946898i
$186$	0.215562	+	0.0269536i	0.0158057	+	0.00197634i
$187$	11.1419	+	13.2784i	0.814775	+	0.971011i
$188$	−3.29682			−0.240445
$189$	12.4322	−	5.86866i	0.904307	−	0.426882i
$190$	0.0360713			0.00261688
$191$	6.31992	+	7.53179i	0.457294	+	0.544981i	0.944589	−	0.328256i	$-0.106461\pi$
$191$	6.31992	+	7.53179i	0.457294	+	0.544981i	−0.487295	+	0.873237i	$0.662016\pi$
$192$	−5.38219	−	12.7583i	−0.388426	−	0.920754i
$193$	3.38821	−	19.2155i	0.243889	−	1.38316i	−0.579171	−	0.815206i	$-0.696623\pi$
$193$	3.38821	−	19.2155i	0.243889	−	1.38316i	0.823059	−	0.567955i	$-0.192265\pi$
$194$	0.0181766	+	0.0152520i	0.00130500	+	0.00109503i
$195$	−6.91004	−	10.6924i	−0.494838	−	0.765701i
$196$	−13.9029	−	1.63247i	−0.993066	−	0.116605i
$197$	−3.74738	+	2.16355i	−0.266990	+	0.154147i	−0.627519	−	0.778601i	$-0.715930\pi$
$197$	−3.74738	+	2.16355i	−0.266990	+	0.154147i	0.360529	+	0.932748i	$0.382596\pi$
$198$	0.204637	−	0.0205898i	0.0145429	−	0.00146325i
$199$		−	1.69609i		−	0.120233i	−0.998191	−	0.0601164i	$-0.980853\pi$
$199$		−	1.69609i		−	0.120233i	0.998191	−	0.0601164i	$-0.0191472\pi$
$200$	−0.0879404	−	0.104803i	−0.00621832	−	0.00741071i
$201$	18.3091	−	4.18418i	1.29142	−	0.295130i
$202$	0.0117992	+	0.0324181i	0.000830191	+	0.00228093i
$203$	9.82845	+	19.5830i	0.689822	+	1.37445i
$204$	8.89412	+	9.58034i	0.622713	+	0.670758i
$205$	−6.54451	−	2.38201i	−0.457089	−	0.166367i
$206$	−0.00816388			−0.000568805
$207$	−18.0916	+	13.0219i	−1.25745	+	0.905088i
$208$		−	17.8586i		−	1.23827i
$209$	5.16597	−	4.33477i	0.357338	−	0.299842i
$210$	−0.111025	+	0.0186277i	−0.00766147	+	0.00128543i
$211$	1.04647	−	5.93483i	0.0720420	−	0.408570i	−0.927366	−	0.374156i	$-0.877932\pi$
$211$	1.04647	−	5.93483i	0.0720420	−	0.408570i	0.999408	−	0.0344141i	$-0.0109565\pi$
$212$	2.89758	+	7.96104i	0.199007	+	0.546767i
$213$	−12.2875	+	5.18358i	−0.841928	+	0.355173i
$214$	−0.00865884	−	0.0491067i	−0.000591906	−	0.00335687i
$215$	1.43687	−	2.48874i	0.0979939	−	0.169730i
$216$	0.306732	−	0.0464892i	0.0208705	−	0.00316319i
$217$	−17.8354	+	13.2706i	−1.21074	+	0.900868i
$218$	−0.0196642	+	0.0540270i	−0.00133183	+	0.00365917i
$219$	−25.2595	+	10.6559i	−1.70688	+	0.720058i
$220$	14.8860	+	2.62480i	1.00361	+	0.176964i
$221$	5.76497	+	15.8391i	0.387794	+	1.06546i
$222$	−0.0111513	−	0.0172552i	−0.000748423	−	0.00115809i
$223$	−0.590154	−	0.703318i	−0.0395196	−	0.0470976i	0.745923	−	0.666033i	$-0.232009\pi$
$223$	−0.590154	−	0.703318i	−0.0395196	−	0.0470976i	−0.785442	+	0.618935i	$0.787564\pi$
$224$	−0.435045	−	0.187796i	−0.0290676	−	0.0125477i
$225$	−6.19197	+	2.98606i	−0.412798	+	0.199071i
$226$	0.0343078	+	0.0594229i	0.00228212	+	0.00395275i
$227$	−10.2102	+	8.56739i	−0.677676	+	0.568638i	−0.915326	−	0.402713i	$-0.868067\pi$
$227$	−10.2102	+	8.56739i	−0.677676	+	0.568638i	0.237650	+	0.971351i	$0.423623\pi$
$228$	3.72724	−	3.46027i	0.246843	−	0.229162i
$229$	12.1287	+	2.13862i	0.801488	+	0.141324i	0.559365	−	0.828922i	$-0.311045\pi$
$229$	12.1287	+	2.13862i	0.801488	+	0.141324i	0.242123	+	0.970246i	$0.422156\pi$
$230$	0.171526	−	0.0624303i	0.0113101	−	0.00411653i
$231$	−13.6620	+	16.0099i	−0.898896	+	1.05338i
$232$	0.0858601	+	0.486937i	0.00563699	+	0.0319690i
$233$	21.5947	−	12.4677i	1.41472	−	0.816788i	0.418891	−	0.908037i	$-0.362419\pi$
$233$	21.5947	−	12.4677i	1.41472	−	0.816788i	0.995828	+	0.0912481i	$0.0290856\pi$
$234$	0.193841	+	0.0492452i	0.0126718	+	0.00321926i
$235$	1.35660	−	2.34970i	0.0884947	−	0.153277i
$236$	4.01557	+	22.7734i	0.261391	+	1.48242i
$237$	0.138373	+	2.75746i	0.00898831	+	0.179116i
$238$	0.148797	+	0.00870590i	0.00964506	+	0.000564320i
$239$	7.34853	−	8.75764i	0.475337	−	0.566485i	−0.474088	−	0.880477i	$-0.657222\pi$
$239$	7.34853	−	8.75764i	0.475337	−	0.566485i	0.949425	+	0.313993i	$0.101667\pi$
$240$	11.3103	+	1.41423i	0.730077	+	0.0912882i
$241$	−6.05886	+	1.06834i	−0.390286	+	0.0688179i	−0.365348	−	0.930871i	$-0.619050\pi$
$241$	−6.05886	+	1.06834i	−0.390286	+	0.0688179i	−0.0249379	+	0.999689i	$0.507939\pi$
$242$	−0.130484	+	0.0753350i	−0.00838784	+	0.00484272i
$243$	1.53095	−	15.5131i	0.0982103	−	0.995166i
$244$		−	6.01649i		−	0.385166i
$245$	6.88436	−	9.23710i	0.439826	−	0.590137i
$246$	0.100807	−	0.0425262i	0.00642723	−	0.00271137i
$247$	6.16224	−	2.24287i	0.392094	−	0.142711i
$248$	−0.471412	+	0.171580i	−0.0299347	+	0.0108953i
$249$	7.14693	−	4.61874i	0.452918	−	0.292701i
$250$	0.176403	−	0.0311046i	0.0111567	−	0.00196723i
$251$	6.31801	+	10.9431i	0.398789	+	0.690724i	0.993577	−	0.113160i	$-0.0360971\pi$
$251$	6.31801	+	10.9431i	0.398789	+	0.690724i	−0.594787	+	0.803883i	$0.702764\pi$
$252$	−9.68532	+	12.5753i	−0.610118	+	0.792170i
$253$	17.0628	−	29.5536i	1.07273	−	1.85802i
$254$	−0.0268747	+	0.0738376i	−0.00168627	+	0.00463298i
$255$	−10.4879	+	2.39680i	−0.656776	+	0.150093i
$256$	12.2431	+	10.2731i	0.765191	+	0.642072i
$257$	−2.59847	+	14.7367i	−0.162088	+	0.919247i	0.789928	+	0.613200i	$0.210118\pi$
$257$	−2.59847	+	14.7367i	−0.162088	+	0.919247i	−0.952016	+	0.306048i	$0.900993\pi$
$258$	0.0100578	+	0.0440108i	0.000626173	+	0.00273999i
$259$	2.04562	+	0.485392i	0.127109	+	0.0301608i
$260$	12.7295	+	7.34939i	0.789451	+	0.455790i
$261$	24.7762	+	1.84313i	1.53361	+	0.114087i
$262$	−0.195676	−	0.112974i	−0.0120889	−	0.00697955i
$263$	−5.44968	+	14.9729i	−0.336042	+	0.923267i	0.650463	+	0.759538i	$0.274575\pi$
$263$	−5.44968	+	14.9729i	−0.336042	+	0.923267i	−0.986505	+	0.163730i	$0.947648\pi$
$264$	−0.398899	+	0.257790i	−0.0245505	+	0.0158659i
$265$	−6.86628	−	1.21071i	−0.421792	−	0.0743734i
$266$	0.00338704	−	0.0578896i	0.000207673	−	0.00354944i
$267$	7.51156	−	9.92226i	0.459700	−	0.607232i
$268$	−16.6110	+	13.9383i	−1.01468	+	0.851417i
$269$	−4.94336	−	8.56215i	−0.301402	−	0.522044i	0.675052	−	0.737770i	$-0.264121\pi$
$269$	−4.94336	−	8.56215i	−0.301402	−	0.522044i	−0.976454	+	0.215727i	$0.930788\pi$
$270$	−0.0465387	+	0.118865i	−0.00283225	+	0.00723387i
$271$	1.92889	+	1.11364i	0.117171	+	0.0676490i	0.557440	−	0.830217i	$-0.311784\pi$
$271$	1.92889	+	1.11364i	0.117171	+	0.0676490i	−0.440269	+	0.897866i	$0.645117\pi$
$272$	−14.1812	−	5.16155i	−0.859864	−	0.312965i
$273$	−17.8088	+	10.0857i	−1.07784	+	0.610414i
$274$	0.0408511	+	0.0342782i	0.00246791	+	0.00207082i
$275$	6.76483	−	8.06201i	0.407935	−	0.486158i
$276$	11.7349	−	22.9052i	0.706358	−	1.37873i
$277$	8.12965	+	2.95895i	0.488464	+	0.177786i	0.574498	−	0.818506i	$-0.305197\pi$
$277$	8.12965	+	2.95895i	0.488464	+	0.177786i	−0.0860344	+	0.996292i	$0.527420\pi$
$278$	−0.0908701			−0.00545003
$279$	2.52353	+	25.0808i	0.151080	+	1.50155i
$280$	0.208570	−	0.155189i	0.0124644	−	0.00927431i
$281$	29.4759	−	5.19740i	1.75839	−	0.310051i	0.800958	−	0.598721i	$-0.204324\pi$
$281$	29.4759	−	5.19740i	1.75839	−	0.310051i	0.957429	+	0.288670i	$0.0932130\pi$
$282$	0.00949591	+	0.0415520i	0.000565473	+	0.00247439i
$283$	6.29451	−	7.50150i	0.374170	−	0.445918i	−0.545795	−	0.837918i	$-0.683772\pi$
$283$	6.29451	−	7.50150i	0.374170	−	0.445918i	0.919965	+	0.392001i	$0.128217\pi$
$284$	9.89735	−	11.7952i	0.587300	−	0.699917i
$285$	0.932479	+	4.08032i	0.0552353	+	0.241698i
$286$	−0.301532	+	0.0531682i	−0.0178300	+	0.00314390i
$287$	−4.43733	+	10.2794i	−0.261927	+	0.606774i
$288$	−0.436077	+	0.313879i	−0.0256961	+	0.0184955i
$289$	−2.75614			−0.162126
$290$	−0.191178	−	0.0695833i	−0.0112264	−	0.00408607i
$291$	−1.25539	+	2.45038i	−0.0735925	+	0.143644i
$292$	20.3460	−	24.2474i	1.19066	−	1.41897i
$293$	−7.96197	−	6.68088i	−0.465143	−	0.390301i	0.379876	−	0.925037i	$-0.375967\pi$
$293$	−7.96197	−	6.68088i	−0.465143	−	0.390301i	−0.845019	+	0.534736i	$0.820411\pi$
$294$	0.0194698	+	0.179930i	0.00113550	+	0.0104937i
$295$	−17.8834	−	6.50901i	−1.04121	−	0.378969i
$296$	0.0410875	+	0.0237219i	0.00238816	+	0.00137881i
$297$	7.61916	+	22.6159i	0.442108	+	1.31231i
$298$	−0.150924	−	0.261408i	−0.00874278	−	0.0151429i
$299$	25.4208	−	21.3306i	1.47012	−	1.23358i
$300$	4.79065	−	6.32812i	0.276588	−	0.365354i
$301$	−3.85917	−	2.53968i	−0.222439	−	0.146385i
$302$	0.281152	+	0.0495747i	0.0161785	+	0.00285270i
$303$	−3.36206	+	2.17275i	−0.193146	+	0.124821i
$304$	−2.00811	+	5.51724i	−0.115173	+	0.316435i
$305$	4.28805	+	2.47571i	0.245533	+	0.141759i
$306$	0.0951295	−	0.139693i	0.00543819	−	0.00798572i
$307$	−14.7821	−	8.53446i	−0.843660	−	0.487087i	0.0148465	−	0.999890i	$-0.495274\pi$
$307$	−14.7821	−	8.53446i	−0.843660	−	0.487087i	−0.858507	+	0.512802i	$0.828607\pi$
$308$	5.61024	−	23.6436i	0.319673	−	1.34722i
$309$	−0.211045	−	0.923485i	−0.0120059	−	0.0525352i
$310$	0.0358441	−	0.203282i	0.00203581	−	0.0115456i
$311$	25.4810	+	21.3811i	1.44489	+	1.21241i	0.936203	+	0.351459i	$0.114314\pi$
$311$	25.4810	+	21.3811i	1.44489	+	1.21241i	0.508690	+	0.860950i	$0.330130\pi$
$312$	−0.450243	+	0.102894i	−0.0254900	+	0.00582524i
$313$	0.334233	−	0.918298i	0.0188920	−	0.0519052i	−0.929888	−	0.367842i	$-0.880097\pi$
$313$	0.334233	−	0.918298i	0.0188920	−	0.0519052i	0.948780	+	0.315937i	$0.102319\pi$
$314$	−0.118566	+	0.205362i	−0.00669106	+	0.0115893i
$315$	−4.97725	−	12.0775i	−0.280436	−	0.680488i
$316$	−1.59384	−	2.76062i	−0.0896608	−	0.155297i
$317$	−3.33535	+	0.588112i	−0.187332	+	0.0330317i	−0.266527	−	0.963827i	$-0.585876\pi$
$317$	−3.33535	+	0.588112i	−0.187332	+	0.0330317i	0.0791950	+	0.996859i	$0.474765\pi$
$318$	0.0919925	−	0.0594506i	0.00515868	−	0.00333382i
$319$	−35.7417	+	13.0089i	−2.00115	+	0.728360i
$320$	−12.3638	+	4.50007i	−0.691159	+	0.251561i
$321$	5.33104	−	2.24893i	0.297549	−	0.125523i
$322$	−0.0840863	−	0.281138i	−0.00468595	−	0.0156672i
$323$		−	5.54159i		−	0.308343i
$324$	6.59369	+	16.7467i	0.366316	+	0.930371i
$325$	8.86287	−	5.11698i	0.491624	−	0.283839i
$326$	0.256338	−	0.0451993i	0.0141972	−	0.00250336i
$327$	−6.61979	−	0.827733i	−0.366075	−	0.0457737i
$328$	−0.162405	+	0.193547i	−0.00896733	+	0.0106868i
$329$	−3.64357	−	2.39779i	−0.200877	−	0.132195i
$330$	−0.00979435	−	0.195179i	−0.000539161	−	0.0107442i
$331$	1.05543	+	5.98565i	0.0580117	+	0.329001i	0.999978	−	0.00670803i	$-0.00213525\pi$
$331$	1.05543	+	5.98565i	0.0580117	+	0.329001i	−0.941966	+	0.335709i	$0.891024\pi$
$332$	−4.91240	+	8.50853i	−0.269603	+	0.466967i
$333$	1.66361	−	1.70748i	0.0911652	−	0.0935691i
$334$	0.122325	−	0.0706246i	0.00669335	−	0.00386441i
$335$	−3.09883	−	17.5744i	−0.169307	−	0.960190i
$336$	3.33168	−	18.0188i	0.181758	−	0.983003i
$337$	−16.0696	+	5.84885i	−0.875366	+	0.318607i	−0.740338	−	0.672235i	$-0.765335\pi$
$337$	−16.0696	+	5.84885i	−0.875366	+	0.318607i	−0.135028	+	0.990842i	$0.543112\pi$
$338$	−0.102113	−	0.0180053i	−0.00555422	−	0.000979359i
$339$	−5.83493	+	5.41699i	−0.316910	+	0.294210i
$340$	9.51518	−	7.98419i	0.516033	−	0.433003i
$341$	−19.2954	−	33.4206i	−1.04490	−	1.80983i
$342$	−0.0543478	−	0.0370103i	−0.00293879	−	0.00200129i
$343$	−14.1779	−	11.9158i	−0.765534	−	0.643395i
$344$	−0.0670127	−	0.0798626i	−0.00361308	−	0.00430590i
$345$	11.4961	+	17.7888i	0.618931	+	0.957719i
$346$	0.00775934	+	0.0213186i	0.000417144	+	0.00114610i
$347$	20.7567	+	3.65996i	1.11428	+	0.196477i	0.700327	−	0.713822i	$-0.253038\pi$
$347$	20.7567	+	3.65996i	1.11428	+	0.196477i	0.413950	+	0.910299i	$0.364149\pi$
$348$	−26.4295	+	11.1495i	−1.41677	+	0.597674i
$349$	−2.22508	+	6.11336i	−0.119106	+	0.327240i	−0.984891	−	0.173175i	$-0.944597\pi$
$349$	−2.22508	+	6.11336i	−0.119106	+	0.327240i	0.865785	+	0.500416i	$0.166819\pi$
$350$	−0.0104823	−	0.0898878i	−0.000560302	−	0.00480471i
$351$	−0.559569	+	23.2000i	−0.0298676	+	1.23832i
$352$	0.411279	−	0.712357i	0.0219213	−	0.0379687i
$353$	−3.31542	−	18.8027i	−0.176462	−	1.00077i	−0.936443	−	0.350821i	$-0.885903\pi$
$353$	−3.31542	−	18.8027i	−0.176462	−	1.00077i	0.759980	−	0.649946i	$-0.225209\pi$
$354$	0.275463	−	0.116206i	0.0146407	−	0.00617627i
$355$	4.33400	+	11.9076i	0.230025	+	0.631989i
$356$	−2.49506	+	14.1502i	−0.132238	+	0.749959i
$357$	2.86175	+	17.0567i	0.151460	+	0.902737i
$358$	0.0982642	−	0.0824534i	0.00519342	−	0.00435780i
$359$			20.1016i			1.06092i	0.847710	+	0.530460i	$0.177981\pi$
$359$			20.1016i			1.06092i	−0.847710	+	0.530460i	$0.822019\pi$
$360$	−0.0295106	−	0.293299i	−0.00155535	−	0.0154582i
$361$	16.8440			0.886528
$362$	−0.148817	−	0.0541648i	−0.00782162	−	0.00284684i
$363$	−11.8949	−	12.8127i	−0.624322	−	0.672491i
$364$	12.9901	−	19.7391i	0.680865	−	1.03461i
$365$	8.90941	+	24.4784i	0.466340	+	1.28126i
$366$	−0.0758299	+	0.0173295i	−0.00396369	+	0.000905825i
$367$	0.397490	+	0.473710i	0.0207488	+	0.0247275i	0.776319	−	0.630340i	$-0.217085\pi$
$367$	0.397490	+	0.473710i	0.0207488	+	0.0247275i	−0.755570	+	0.655068i	$0.772640\pi$
$368$			29.7110i			1.54880i
$369$	7.41646	+	10.3038i	0.386086	+	0.536394i
$370$	−0.0169060	+	0.00976069i	−0.000878902	+	0.000507434i
$371$	−2.58777	+	10.9058i	−0.134350	+	0.566201i
$372$	−15.7968	−	24.4436i	−0.819026	−	1.26734i
$373$	24.6870	+	20.7149i	1.27825	+	1.07258i	0.993483	+	0.113979i	$0.0363595\pi$
$373$	24.6870	+	20.7149i	1.27825	+	1.07258i	0.284764	+	0.958598i	$0.408085\pi$
$374$	−0.0449298	+	0.254809i	−0.00232326	+	0.0131759i
$375$	8.07871	+	19.1504i	0.417183	+	0.988920i
$376$	−0.0632688	−	0.0754008i	−0.00326284	−	0.00388850i
$377$	−36.9866			−1.90491
$378$	0.186392	+	0.0858496i	0.00958697	+	0.00441563i
$379$	8.60323			0.441918			0.220959	−	0.975283i	$-0.429081\pi$
$379$	8.60323			0.441918			0.220959	+	0.975283i	$0.429081\pi$
$380$	−3.10626	−	3.70190i	−0.159348	−	0.189903i
$381$	−9.04713	−	1.13124i	−0.463498	−	0.0579554i
$382$	−0.0254852	+	0.144534i	−0.00130393	+	0.00739498i
$383$	9.30459	+	7.80747i	0.475442	+	0.398943i	0.848775	−	0.528754i	$-0.177341\pi$
$383$	9.30459	+	7.80747i	0.475442	+	0.398943i	−0.373333	+	0.927697i	$0.621785\pi$
$384$	0.377135	−	0.736123i	0.0192456	−	0.0375651i
$385$	14.5426	+	13.7275i	0.741161	+	0.699620i
$386$	0.252234	−	0.145627i	0.0128384	−	0.00741224i
$387$	−4.71843	+	2.27545i	−0.239851	+	0.115668i
$388$		−	3.17883i		−	0.161380i
$389$	−20.6789	−	24.6442i	−1.04846	−	1.24951i	−0.967521	−	0.252792i	$-0.918651\pi$
$389$	−20.6789	−	24.6442i	−1.04846	−	1.24951i	−0.0809437	−	0.996719i	$-0.525793\pi$
$390$	0.0559642	−	0.181607i	0.00283386	−	0.00919604i
$391$	−9.59110	−	26.3513i	−0.485043	−	1.33264i
$392$	−0.229473	−	0.349299i	−0.0115901	−	0.0176423i
$393$	7.72099	−	25.0551i	0.389472	−	1.26386i
$394$	−0.0606954	−	0.0220913i	−0.00305779	−	0.00111295i
$395$	2.62339			0.131997
$396$	−19.7353	−	19.2283i	−0.991735	−	0.966256i
$397$			11.5611i			0.580233i	0.956991	+	0.290116i	$0.0936940\pi$
$397$			11.5611i			0.580233i	−0.956991	+	0.290116i	$0.906306\pi$
$398$	0.0193944	−	0.0162738i	0.000972153	−	0.000815733i
$399$	6.63594	−	1.11337i	0.332212	−	0.0557381i
$400$	−1.59110	+	9.02357i	−0.0795549	+	0.451179i
$401$	−0.0353788	−	0.0972024i	−0.00176673	−	0.00485406i	0.938806	−	0.344446i	$-0.111933\pi$
$401$	−0.0353788	−	0.0972024i	−0.00176673	−	0.00485406i	−0.940573	+	0.339592i	$0.889711\pi$
$402$	0.223519	+	0.169213i	0.0111481	+	0.00843958i
$403$	−6.51641	−	36.9564i	−0.324606	−	1.84093i
$404$	2.31090	−	4.00259i	0.114971	−	0.199136i
$405$	−14.6488	−	2.19161i	−0.727907	−	0.108902i
$406$	−0.129623	+	0.300282i	−0.00643310	+	0.0149028i
$407$	−1.24824	+	3.42952i	−0.0618731	+	0.169995i
$408$	−0.0484239	+	0.387270i	−0.00239734	+	0.0191727i
$409$	−3.57697	−	0.630716i	−0.176870	−	0.0311869i	0.0845117	−	0.996422i	$-0.473067\pi$
$409$	−3.57697	−	0.630716i	−0.176870	−	0.0311869i	−0.261381	+	0.965236i	$0.584178\pi$
$410$	−0.0355563	−	0.0976900i	−0.00175600	−	0.00482457i
$411$	−2.82145	+	5.50714i	−0.139172	+	0.271647i
$412$	0.703029	+	0.837837i	0.0346357	+	0.0412773i
$413$	−12.1253	+	28.0892i	−0.596648	+	1.38218i
$414$	−0.322490	−	0.0819286i	−0.0158495	−	0.00402657i
$415$	−4.04278	−	7.00230i	−0.198452	−	0.343730i
$416$	0.612739	−	0.514149i	0.0300420	−	0.0252082i
$417$	−2.34908	−	10.2791i	−0.115035	−	0.503369i
$418$	0.0991340	+	0.0174800i	0.00484880	+	0.000854974i
$419$	37.3388	−	13.5902i	1.82412	−	0.663926i	0.829730	−	0.558165i	$-0.188494\pi$
$419$	37.3388	−	13.5902i	1.82412	−	0.663926i	0.994392	−	0.105761i	$-0.0337279\pi$
$420$	11.4726	+	9.79011i	0.559805	+	0.477709i
$421$	−1.45892	−	8.27397i	−0.0711036	−	0.403249i	−0.999499	−	0.0316544i	$-0.989922\pi$
$421$	−1.45892	−	8.27397i	−0.0711036	−	0.403249i	0.928395	−	0.371594i	$-0.121189\pi$
$422$	0.0779040	−	0.0449779i	0.00379231	−	0.00218949i
$423$	−4.45482	+	2.14832i	−0.216601	+	0.104455i
$424$	−0.126468	+	0.219049i	−0.00614184	+	0.0106380i
$425$	−1.50174	−	8.51682i	−0.0728453	−	0.413126i
$426$	−0.177171	−	0.0907690i	−0.00858394	−	0.00439777i
$427$	4.37583	−	6.64929i	0.211761	−	0.321782i
$428$	−4.29404	+	5.11744i	−0.207560	+	0.247361i
$429$	−13.8092	−	32.7344i	−0.666715	−	1.58043i
$430$	0.0422447	−	0.00744889i	0.00203722	−	0.000359217i
$431$	−4.45253	+	2.57067i	−0.214471	+	0.123825i	−0.603387	−	0.797448i	$-0.706183\pi$
$431$	−4.45253	+	2.57067i	−0.214471	+	0.123825i	0.388917	+	0.921273i	$0.372849\pi$
$432$	−15.5899	−	13.7355i	−0.750072	−	0.660851i
$433$			19.5889i			0.941384i	0.882298	+	0.470692i	$0.155996\pi$
$433$			19.5889i			0.941384i	−0.882298	+	0.470692i	$0.844004\pi$
$434$	−0.322875	−	0.0766129i	−0.0154985	−	0.00367754i
$435$	2.92899	−	23.4246i	0.140434	−	1.12312i
$436$	7.23802	−	2.63442i	0.346638	−	0.126166i
$437$	−10.2520	+	3.73143i	−0.490421	+	0.178499i
$438$	−0.364209	−	0.186594i	−0.0174026	−	0.00891580i
$439$	−31.6846	+	5.58684i	−1.51222	+	0.266645i	−0.867370	−	0.497663i	$-0.834192\pi$
$439$	−31.6846	+	5.58684i	−1.51222	+	0.266645i	−0.644851	+	0.764309i	$0.723080\pi$
$440$	0.225644	+	0.390827i	0.0107572	+	0.0186319i
$441$	−19.8501	+	6.85377i	−0.945242	+	0.326370i
$442$	−0.125802	+	0.217896i	−0.00598380	+	0.0103643i
$443$	−7.92834	+	21.7829i	−0.376687	+	1.03494i	0.596034	+	0.802959i	$0.296742\pi$
$443$	−7.92834	+	21.7829i	−0.376687	+	1.03494i	−0.972721	+	0.231979i	$0.925480\pi$
$444$	−0.810568	+	2.63034i	−0.0384679	+	0.124831i
$445$	−9.05840	−	7.60090i	−0.429409	−	0.360317i
$446$	0.00237980	−	0.0134965i	0.000112687	−	0.000639079i
$447$	25.6685	−	23.8299i	1.21408	−	1.12712i
$448$	6.06106	+	20.2649i	0.286358	+	0.957425i
$449$	−16.3545	−	9.44229i	−0.771817	−	0.445609i	0.0617051	−	0.998094i	$-0.480346\pi$
$449$	−16.3545	−	9.44229i	−0.771817	−	0.445609i	−0.833523	+	0.552485i	$0.813679\pi$
$450$	−0.0935562	−	0.0421527i	−0.00441028	−	0.00198710i
$451$	−16.8318	−	9.71787i	−0.792581	−	0.457597i
$452$	3.14401	−	8.63809i	0.147882	−	0.406302i
$453$	1.66025	+	33.0850i	0.0780055	+	1.55447i
$454$	−0.195932	−	0.0345481i	−0.00919554	−	0.00162142i
$455$	8.72312	+	17.3806i	0.408946	+	0.814816i
$456$	0.150668	+	0.0188394i	0.00705568	+	0.000882236i
$457$	−14.1005	+	11.8318i	−0.659596	+	0.553467i	−0.909966	−	0.414684i	$-0.863892\pi$
$457$	−14.1005	+	11.8318i	−0.659596	+	0.553467i	0.250370	+	0.968150i	$0.419448\pi$
$458$	0.0919191	+	0.159209i	0.00429510	+	0.00743933i
$459$	18.2611	+	7.14969i	0.852353	+	0.333719i
$460$	−21.1779	−	12.2271i	−0.987425	−	0.570090i
$461$	−15.0689	−	5.48464i	−0.701830	−	0.255445i	−0.0336380	−	0.999434i	$-0.510709\pi$
$461$	−15.0689	−	5.48464i	−0.701830	−	0.255445i	−0.668192	+	0.743989i	$0.732932\pi$
$462$	−0.314156	−	0.00260838i	−0.0146158	−	0.000121353i
$463$	27.7311	+	23.2691i	1.28877	+	1.08141i	0.991971	+	0.126469i	$0.0403645\pi$
$463$	27.7311	+	23.2691i	1.28877	+	1.08141i	0.296802	+	0.954939i	$0.404080\pi$
$464$	21.2860	−	25.3677i	0.988180	−	1.17767i
$465$	23.9215	−	1.20042i	1.10933	−	0.0556680i
$466$	0.349765	+	0.127304i	0.0162025	+	0.00589724i
$467$	−10.8654			−0.502793			−0.251396	−	0.967884i	$-0.580890\pi$
$467$	−10.8654			−0.502793			−0.251396	+	0.967884i	$0.580890\pi$
$468$	−11.6386	−	24.1341i	−0.537993	−	1.11560i
$469$	−28.4955	+	3.32301i	−1.31580	+	0.153442i
$470$	0.0398846	−	0.00703274i	0.00183974	−	0.000324396i
$471$	−26.2953	−	8.10317i	−1.21162	−	0.373374i
$472$	−0.443784	+	0.528881i	−0.0204268	+	0.0243437i
$473$	5.15496	−	6.14344i	0.237025	−	0.282476i
$474$	−0.0302032	+	0.0280398i	−0.00138728	+	0.00128791i
$475$	−3.31348	+	0.584256i	−0.152033	+	0.0268075i
$476$	−11.9201	−	16.0203i	−0.546357	−	0.734290i
$477$	9.10305	+	8.86918i	0.416800	+	0.406092i
$478$	0.170650			0.00780534
$479$	11.5834	+	4.21600i	0.529257	+	0.192634i	0.592807	−	0.805345i	$-0.298020\pi$
$479$	11.5834	+	4.21600i	0.529257	+	0.192634i	−0.0635495	+	0.997979i	$0.520242\pi$
$480$	0.277101	+	0.428779i	0.0126479	+	0.0195710i
$481$	−2.28123	+	2.71867i	−0.104015	+	0.123961i
$482$	−0.0703504	−	0.0590310i	−0.00320437	−	0.00268879i
$483$	29.6282	−	16.7794i	1.34813	−	0.763490i
$484$	18.9680	+	6.90379i	0.862182	+	0.313809i
$485$	2.26560	+	1.30805i	0.102876	+	0.0593953i
$486$	0.192078	−	0.131341i	0.00871282	−	0.00595773i
$487$	9.66499	+	16.7403i	0.437963	+	0.758574i	0.997532	−	0.0702097i	$-0.0223669\pi$
$487$	9.66499	+	16.7403i	0.437963	+	0.758574i	−0.559570	+	0.828783i	$0.689034\pi$
$488$	0.137602	−	0.115462i	0.00622894	−	0.00522670i
$489$	11.7395	+	27.8281i	0.530877	+	1.25843i
$490$	0.171679	−	0.00990806i	0.00775565	−	0.000447600i
$491$	−32.7847	−	5.78082i	−1.47955	−	0.260885i	−0.625153	−	0.780502i	$-0.714963\pi$
$491$	−32.7847	−	5.78082i	−1.47955	−	0.260885i	−0.854399	+	0.519617i	$0.826074\pi$
$492$	−13.0453	−	6.68344i	−0.588128	−	0.301313i
$493$	−10.6900	+	29.3706i	−0.481454	+	1.32278i
$494$	0.0847727	+	0.0489436i	0.00381411	+	0.00220207i
$495$	21.8251	−	6.15349i	0.980965	−	0.276579i
$496$	29.0973	+	16.7993i	1.30651	+	0.754311i
$497$	19.5170	−	5.83740i	0.875459	−	0.261843i
$498$	0.121388	+	0.0374070i	0.00543953	+	0.00167625i
$499$	−3.49591	+	19.8263i	−0.156498	+	0.887546i	0.800905	+	0.598792i	$0.204352\pi$
$499$	−3.49591	+	19.8263i	−0.156498	+	0.887546i	−0.957403	+	0.288755i	$0.906759\pi$
$500$	−18.3831	−	15.4252i	−0.822115	−	0.689837i
$501$	11.1512	+	12.0115i	0.498198	+	0.536636i
$502$	−0.0645112	+	0.177243i	−0.00287927	+	0.00791074i
$503$	−5.39577	+	9.34574i	−0.240585	+	0.416706i	−0.960881	−	0.276961i	$-0.910673\pi$
$503$	−5.39577	+	9.34574i	−0.240585	+	0.416706i	0.720296	+	0.693667i	$0.244006\pi$
$504$	−0.473477	+	0.0198203i	−0.0210903	+	0.000882866i
$505$	1.90181	+	3.29403i	0.0846294	+	0.146582i
$506$	0.501654	−	0.0884552i	0.0223013	−	0.00393231i
$507$	−0.602997	−	12.0163i	−0.0267800	−	0.533664i
$508$	9.89205	−	3.60041i	0.438889	−	0.159742i
$509$	−32.3031	+	11.7574i	−1.43181	+	0.521136i	−0.937449	−	0.348122i	$-0.886820\pi$
$509$	−32.3031	+	11.7574i	−1.43181	+	0.521136i	−0.494360	+	0.869258i	$0.664597\pi$
$510$	−0.128037	−	0.0969292i	−0.00566957	−	0.00429210i
$511$	40.1212	−	11.9999i	1.77486	−	0.530846i
$512$			1.19363i			0.0527514i
$513$	2.78160	−	7.10449i	0.122811	−	0.313671i
$514$	−0.193442	+	0.111684i	−0.00853237	+	0.00492616i
$515$	−0.886427	+	0.156301i	−0.0390607	+	0.00688745i
$516$	3.65059	−	4.82218i	0.160708	−	0.212285i
$517$	4.86697	−	5.80022i	0.214049	−	0.255094i
$518$	0.0140772	+	0.0280484i	0.000618515	+	0.00123238i
$519$	−2.21094	+	1.42883i	−0.0970495	+	0.0627187i
$520$	0.0762041	+	0.432175i	0.00334177	+	0.0189521i
$521$	16.4187	−	28.4380i	0.719317	−	1.24589i	−0.241954	−	0.970288i	$-0.577788\pi$
$521$	16.4187	−	28.4380i	0.719317	−	1.24589i	0.961271	−	0.275605i	$-0.0888783\pi$
$522$	0.216650	+	0.300995i	0.00948250	+	0.0131742i
$523$	2.01194	−	1.16159i	0.0879760	−	0.0507929i	−0.455367	−	0.890304i	$-0.650492\pi$
$523$	2.01194	−	1.16159i	0.0879760	−	0.0507929i	0.543343	+	0.839511i	$0.317158\pi$
$524$	5.25638	+	29.8104i	0.229626	+	1.30227i
$525$	9.89699	−	3.50943i	0.431940	−	0.153164i
$526$	−0.223500	+	0.0813475i	−0.00974508	+	0.00354692i
$527$	−31.2300	−	5.50669i	−1.36040	−	0.239875i
$528$	30.3986	+	9.36763i	1.32293	+	0.407674i
$529$	−24.6732	+	20.7032i	−1.07275	+	0.900141i
$530$	−0.0520371	−	0.0901309i	−0.00226035	−	0.00391504i
$531$	20.2660	+	28.1559i	0.879470	+	1.22186i
$532$	−6.23273	+	4.63753i	−0.270223	+	0.201063i
$533$	−12.1485	−	14.4780i	−0.526210	−	0.627113i
$534$	0.185531	−	0.00931023i	0.00802872	−	0.000402893i
$535$	−1.88034	−	5.16619i	−0.0812941	−	0.223354i
$536$	−0.637559	−	0.112419i	−0.0275384	−	0.00485576i
$537$	11.8672	+	8.98398i	0.512109	+	0.387687i
$538$	0.0504750	−	0.138679i	0.00217613	−	0.00597888i
$539$	23.3964	−	22.0500i	1.00776	−	0.949761i
$540$	16.2064	−	5.45983i	0.697413	−	0.234954i
$541$	9.54866	−	16.5388i	0.410529	−	0.711057i	−0.584419	−	0.811452i	$-0.698677\pi$
$541$	9.54866	−	16.5388i	0.410529	−	0.711057i	0.994948	+	0.100395i	$0.0320108\pi$
$542$	0.00577323	+	0.0327416i	0.000247982	+	0.00140637i
$543$	2.27998	−	18.2341i	0.0978431	−	0.782500i
$544$	−0.231183	−	0.635169i	−0.00991187	−	0.0272326i
$545$	−1.10075	+	6.24269i	−0.0471511	+	0.267407i
$546$	−0.286201	−	0.106868i	−0.0122483	−	0.00457352i
$547$	18.5854	−	15.5950i	0.794655	−	0.666795i	−0.152238	−	0.988344i	$-0.548648\pi$
$547$	18.5854	−	15.5950i	0.794655	−	0.666795i	0.946893	+	0.321549i	$0.104204\pi$
$548$		−	7.14428i		−	0.305189i
$549$	−3.92056	−	8.12977i	−0.167325	−	0.346970i
$550$	0.157095			0.00669855
$551$	11.4267	+	4.15896i	0.486792	+	0.177178i
$552$	0.749062	−	0.171184i	0.0318822	−	0.00728606i
$553$	0.246332	−	4.21019i	0.0104751	−	0.179035i
$554$	0.0441683	+	0.121351i	0.00187653	+	0.00515573i
$555$	−1.54115	−	1.66006i	−0.0654182	−	0.0704655i
$556$	7.82524	+	9.32575i	0.331864	+	0.395500i
$557$			16.5691i			0.702055i	0.936365	+	0.351028i	$0.114168\pi$
$557$			16.5691i			0.702055i	−0.936365	+	0.351028i	$0.885832\pi$
$558$	−0.262579	+	0.269503i	−0.0111159	+	0.0114090i
$559$	6.75372	−	3.89926i	0.285652	−	0.164921i
$560$	−16.9409	−	4.01980i	−0.715885	−	0.169868i
$561$	−29.9851	+	1.50470i	−1.26597	+	0.0635283i
$562$	0.342250	+	0.287181i	0.0144369	+	0.0121140i
$563$	6.89101	−	39.0809i	0.290422	−	1.64706i	−0.394829	−	0.918755i	$-0.629196\pi$
$563$	6.89101	−	39.0809i	0.290422	−	1.64706i	0.685250	−	0.728308i	$-0.259693\pi$
$564$	3.44664	−	4.55277i	0.145130	−	0.191706i
$565$	4.86279	+	5.79525i	0.204579	+	0.243808i
$566$	0.146173			0.00614411
$567$	−4.89275	+	23.3037i	−0.205476	+	0.978662i
$568$	0.459704			0.0192888
$569$	4.54173	+	5.41262i	0.190399	+	0.226909i	0.852796	−	0.522244i	$-0.174905\pi$
$569$	4.54173	+	5.41262i	0.190399	+	0.226909i	−0.662397	+	0.749153i	$0.730461\pi$
$570$	−0.0377105	+	0.0498130i	−0.00157952	+	0.00208644i
$571$	−3.80649	+	21.5877i	−0.159297	+	0.903417i	0.795455	+	0.606013i	$0.207232\pi$
$571$	−3.80649	+	21.5877i	−0.159297	+	0.903417i	−0.954752	+	0.297404i	$0.903879\pi$
$572$	31.4228	+	26.3668i	1.31385	+	1.10245i
$573$	−17.0082	+	0.853497i	−0.710528	+	0.0356554i
$574$	−0.160118	+	0.0478901i	−0.00668321	+	0.00199889i
$575$	−14.7450	+	8.51305i	−0.614910	+	0.355019i
$576$	23.2455	+	5.90553i	0.968564	+	0.246064i
$577$		−	4.42356i		−	0.184155i	−0.995752	−	0.0920775i	$-0.970649\pi$
$577$		−	4.42356i		−	0.184155i	0.995752	−	0.0920775i	$-0.0293508\pi$
$578$	−0.0264449	−	0.0315158i	−0.00109996	−	0.00131088i
$579$	22.9936	+	24.7677i	0.955583	+	1.02931i
$580$	9.32210	+	25.6122i	0.387079	+	1.06349i
$581$	−11.6174	+	5.83062i	−0.481970	+	0.241895i
$582$	−0.0400649	+	0.00915605i	−0.00166074	+	0.000379531i
$583$	−18.2838	−	6.65475i	−0.757236	−	0.275611i
$584$	0.945014			0.0391050
$585$	21.9899	+	1.63584i	0.909169	+	0.0676339i
$586$		−	0.155146i		−	0.00640900i
$587$	28.2005	−	23.6630i	1.16396	−	0.976677i	0.164007	−	0.986459i	$-0.447558\pi$
$587$	28.2005	−	23.6630i	1.16396	−	0.976677i	0.999952	+	0.00978187i	$0.00311371\pi$
$588$	16.7891	−	17.4927i	0.692371	−	0.721388i
$589$	−2.14239	+	12.1501i	−0.0882755	+	0.500635i
$590$	−0.0971600	−	0.266945i	−0.00400001	−	0.0109899i
$591$	0.929898	−	7.43685i	0.0382509	−	0.305911i
$592$	−0.551766	−	3.12922i	−0.0226775	−	0.128610i
$593$	15.9700	−	27.6608i	0.655809	−	1.13589i	−0.325882	−	0.945411i	$-0.605661\pi$
$593$	15.9700	−	27.6608i	0.655809	−	1.13589i	0.981690	−	0.190484i	$-0.0610056\pi$
$594$	−0.185503	+	0.304121i	−0.00761126	+	0.0124782i
$595$	16.3229	−	1.90350i	0.669174	−	0.0780359i
$596$	−13.8308	+	37.9999i	−0.566533	+	1.55654i
$597$	2.34223	+	1.77317i	0.0958613	+	0.0725709i
$598$	0.487819	+	0.0860157i	0.0199484	+	0.00351744i
$599$	−13.1453	−	36.1165i	−0.537104	−	1.47568i	−0.850457	−	0.526044i	$-0.823675\pi$
$599$	−13.1453	−	36.1165i	−0.537104	−	1.47568i	0.313353	−	0.949637i	$-0.398548\pi$
$600$	0.236666	−	0.0118762i	0.00966184	−	0.000484845i
$601$	11.7434	+	13.9953i	0.479025	+	0.570880i	0.950391	−	0.311058i	$-0.100683\pi$
$601$	11.7434	+	13.9953i	0.479025	+	0.570880i	−0.471366	+	0.881938i	$0.656239\pi$
$602$	−0.00798775	−	0.0684967i	−0.000325557	−	0.00279172i
$603$	−13.3629	+	29.6584i	−0.544180	+	1.20778i
$604$	−19.1235	−	33.1229i	−0.778126	−	1.34775i
$605$	−12.7255	+	10.6780i	−0.517366	+	0.434122i
$606$	−0.0571035	−	0.0175970i	−0.00231967	−	0.000714831i
$607$	19.1650	+	3.37930i	0.777883	+	0.137162i	0.548473	−	0.836168i	$-0.315209\pi$
$607$	19.1650	+	3.37930i	0.777883	+	0.137162i	0.229410	+	0.973330i	$0.426320\pi$
$608$	−0.247113	+	0.0899419i	−0.0100218	+	0.00364763i
$609$	−37.3184	−	6.90018i	−1.51222	−	0.279609i
$610$	0.0128343	+	0.0727870i	0.000519646	+	0.00294706i
$611$	6.37641	−	3.68142i	0.257962	−	0.148934i
$612$	−22.5284	+	2.26672i	−0.910655	+	0.0916267i
$613$	−13.2018	+	22.8662i	−0.533217	+	0.923559i	0.466030	+	0.884769i	$0.345684\pi$
$613$	−13.2018	+	22.8662i	−0.533217	+	0.923559i	−0.999247	+	0.0387902i	$0.987650\pi$
$614$	−0.0442435	−	0.250917i	−0.00178552	−	0.0101262i
$615$	10.1314	−	6.54745i	0.408536	−	0.264019i
$616$	0.648413	−	0.325430i	0.0261253	−	0.0131120i
$617$	16.7822	−	20.0003i	0.675628	−	0.805182i	−0.313910	−	0.949453i	$-0.601639\pi$
$617$	16.7822	−	20.0003i	0.675628	−	0.805182i	0.989538	+	0.144271i	$0.0460836\pi$
$618$	0.00853488	−	0.0112740i	0.000343323	−	0.000453506i
$619$	−27.6159	+	4.86943i	−1.10998	+	0.195719i	−0.698436	−	0.715672i	$-0.746120\pi$
$619$	−27.6159	+	4.86943i	−1.10998	+	0.195719i	−0.411541	+	0.911391i	$0.635009\pi$
$620$	−23.9489	+	13.8269i	−0.961813	+	0.555303i
$621$	0.930947	−	38.5975i	0.0373576	−	1.54886i
$622$			0.496518i			0.0199085i
$623$	−13.0490	+	13.8238i	−0.522797	+	0.553839i
$624$	24.6620	+	18.6701i	0.987268	+	0.747403i
$625$	7.79185	−	2.83600i	0.311674	−	0.113440i
$626$	0.0137074	−	0.00498910i	0.000547859	−	0.000199405i
$627$	0.585404	+	11.6658i	0.0233788	+	0.465885i
$628$	31.2860	−	5.51657i	1.24845	−	0.220135i
$629$	1.49953	+	2.59725i	0.0597900	+	0.103559i
$630$	0.0903466	−	0.172796i	0.00359949	−	0.00688434i
$631$	−19.6263	+	33.9938i	−0.781312	+	1.35327i	0.149866	+	0.988706i	$0.452116\pi$
$631$	−19.6263	+	33.9938i	−0.781312	+	1.35327i	−0.931178	+	0.364565i	$0.881218\pi$
$632$	0.0325503	−	0.0894312i	0.00129478	−	0.00355738i
$633$	7.10173	+	7.64966i	0.282268	+	0.304047i
$634$	−0.0387273	−	0.0324960i	−0.00153806	−	0.00129058i
$635$	−1.50438	+	8.53175i	−0.0596994	+	0.338572i
$636$	−14.0231	−	4.32137i	−0.556054	−	0.171354i
$637$	28.7127	−	12.3674i	1.13764	−	0.490016i
$638$	−0.491692	−	0.283879i	−0.0194663	−	0.0112389i
$639$	5.68761	−	22.3877i	0.224998	−	0.885644i
$640$	−0.680613	−	0.392952i	−0.0269036	−	0.0155328i
$641$	10.2351	−	28.1208i	0.404263	−	1.11070i	−0.555897	−	0.831251i	$-0.687625\pi$
$641$	10.2351	−	28.1208i	0.404263	−	1.11070i	0.960160	−	0.279452i	$-0.0901528\pi$
$642$	0.0768667	+	0.0393808i	0.00303369	+	0.00155424i
$643$	1.69315	+	0.298548i	0.0667714	+	0.0117736i	0.206934	−	0.978355i	$-0.433651\pi$
$643$	1.69315	+	0.298548i	0.0667714	+	0.0117736i	−0.140163	+	0.990128i	$0.544763\pi$
$644$	−21.6114	+	32.8396i	−0.851609	+	1.29406i
$645$	1.93468	+	4.58610i	0.0761778	+	0.180577i
$646$	0.0633668	−	0.0531710i	0.00249313	−	0.00209199i
$647$	23.2767	+	40.3164i	0.915102	+	1.58500i	0.806752	+	0.590890i	$0.201223\pi$
$647$	23.2767	+	40.3164i	0.915102	+	1.58500i	0.108350	+	0.994113i	$0.465443\pi$
$648$	−0.256471	+	0.472186i	−0.0100751	+	0.0185492i
$649$	−45.9942	−	26.5548i	−1.80543	−	1.04237i
$650$	0.143550	+	0.0522479i	0.00563049	+	0.00204933i
$651$	0.319689	−	38.5036i	0.0125296	−	1.50907i
$652$	−26.7131	−	22.4150i	−1.04617	−	0.877837i
$653$	−12.3612	+	14.7315i	−0.483730	+	0.576487i	−0.951611	−	0.307305i	$-0.900573\pi$
$653$	−12.3612	+	14.7315i	−0.483730	+	0.576487i	0.467882	+	0.883791i	$0.345017\pi$
$654$	−0.0540513	−	0.0836377i	−0.00211357	−	0.00327049i
$655$	−23.4093	−	8.52029i	−0.914677	−	0.332915i
$656$	16.9215			0.660673
$657$	11.6920	−	46.0224i	0.456149	−	1.79551i
$658$	−0.00754150	−	0.0646699i	−0.000293998	−	0.00252110i
$659$	20.4588	−	3.60744i	0.796962	−	0.140526i	0.239683	−	0.970851i	$-0.422957\pi$
$659$	20.4588	−	3.60744i	0.796962	−	0.140526i	0.557279	+	0.830325i	$0.311845\pi$
$660$	−19.1872	+	17.8129i	−0.746861	+	0.693365i
$661$	9.07299	−	10.8128i	0.352898	−	0.420568i	−0.560168	−	0.828379i	$-0.689263\pi$
$661$	9.07299	−	10.8128i	0.352898	−	0.420568i	0.913066	+	0.407811i	$0.133708\pi$
$662$	−0.0583176	+	0.0695003i	−0.00226658	+	0.00270120i
$663$	−27.9002	−	8.59772i	−1.08355	−	0.333908i
$664$	−0.288870	+	0.0509356i	−0.0112103	+	0.00197668i
$665$	−0.740559	−	6.35045i	−0.0287177	−	0.246260i
$666$	0.0354867	+	0.00263989i	0.00137508	+	0.000102294i
$667$	61.5341			2.38261
$668$	−17.7820	−	6.47212i	−0.688006	−	0.250414i
$669$	1.58822	−	0.0796994i	0.0614043	−	0.00308136i
$670$	0.171226	−	0.204059i	0.00661502	−	0.00788347i
$671$	10.5850	+	8.88191i	0.408631	+	0.342882i
$672$	0.714154	−	0.404449i	0.0275491	−	0.0156019i
$673$	−6.36430	−	2.31642i	−0.245326	−	0.0892913i	0.216431	−	0.976298i	$-0.430558\pi$
$673$	−6.36430	−	2.31642i	−0.245326	−	0.0892913i	−0.461757	+	0.887007i	$0.652781\pi$
$674$	−0.221066	−	0.127633i	−0.00851515	−	0.00491623i
$675$	2.34973	−	11.6726i	0.0904410	−	0.449279i
$676$	6.94558	+	12.0301i	0.267138	+	0.462696i
$677$	24.1811	−	20.2904i	0.929356	−	0.779823i	−0.0463453	−	0.998925i	$-0.514757\pi$
$677$	24.1811	−	20.2904i	0.929356	−	0.779823i	0.975702	+	0.219103i	$0.0703130\pi$
$678$	−0.117927	−	0.0147456i	−0.00452898	−	0.000566299i
$679$	2.31198	−	3.51317i	0.0887255	−	0.134823i
$680$	0.365209	+	0.0643962i	0.0140051	+	0.00246948i
$681$	−1.15701	−	23.0566i	−0.0443369	−	0.883531i
$682$	0.197019	−	0.541306i	0.00754425	−	0.0207277i
$683$	−21.2271	−	12.2555i	−0.812233	−	0.468943i	0.0354979	−	0.999370i	$-0.488698\pi$
$683$	−21.2271	−	12.2555i	−0.812233	−	0.468943i	−0.847731	+	0.530427i	$0.822032\pi$
$684$	0.881871	+	8.76469i	0.0337192	+	0.335126i
$685$	5.09185	+	2.93978i	0.194550	+	0.112323i
$686$	0.000219288	−	0.276452i	8.37245e−6	−	0.0105550i
$687$	−15.6332	+	14.5134i	−0.596445	+	0.553723i
$688$	−1.21246	+	6.87618i	−0.0462244	+	0.262152i
$689$	−14.4940	−	12.1619i	−0.552178	−	0.463332i
$690$	−0.0931068	+	0.302137i	−0.00354451	+	0.0115022i
$691$	−9.24106	+	25.3896i	−0.351547	+	0.965866i	0.630327	+	0.776330i	$0.282921\pi$
$691$	−9.24106	+	25.3896i	−0.351547	+	0.965866i	−0.981874	+	0.189537i	$0.939301\pi$
$692$	1.51968	−	2.63216i	0.0577695	−	0.100060i
$693$	−7.82618	−	35.6042i	−0.297292	−	1.35249i
$694$	0.157307	+	0.272465i	0.00597131	+	0.0103426i
$695$	−9.86660	+	1.73975i	−0.374261	+	0.0659924i
$696$	−0.762202	−	0.390496i	−0.0288912	−	0.0148017i
$697$	−15.0080	+	5.46247i	−0.568469	+	0.206906i
$698$	−0.0912541	+	0.0332138i	−0.00345402	+	0.00125716i
$699$	−5.35865	+	42.8558i	−0.202683	+	1.62095i
$700$	−8.32226	+	8.81641i	−0.314552	+	0.333229i
$701$			28.6921i			1.08369i	0.840479	+	0.541843i	$0.182273\pi$
$701$			28.6921i			1.08369i	−0.840479	+	0.541843i	$0.817727\pi$
$702$	−0.270655	+	0.216203i	−0.0102152	+	0.00816005i
$703$	1.01047	−	0.583393i	0.0381104	−	0.0220031i
$704$	−36.1600	+	6.37598i	−1.36283	+	0.240304i
$705$	1.82659	+	4.32988i	0.0687933	+	0.163073i
$706$	0.183193	−	0.218321i	0.00689457	−	0.00821662i
$707$	5.46506	−	2.74285i	0.205535	−	0.103155i
$708$	−35.6472	−	18.2630i	−1.33971	−	0.686365i
$709$	−6.60874	−	37.4800i	−0.248196	−	1.40759i	−0.812950	−	0.582333i	$-0.802140\pi$
$709$	−6.60874	−	37.4800i	−0.248196	−	1.40759i	0.564754	−	0.825259i	$-0.308971\pi$
$710$	−0.0945759	+	0.163810i	−0.00354937	+	0.00614769i
$711$	−3.95260	−	2.69168i	−0.148234	−	0.100946i
$712$	−0.371509	+	0.214491i	−0.0139229	+	0.00803838i
$713$	10.8413	+	61.4838i	0.406008	+	2.30259i
$714$	−0.167581	+	0.196381i	−0.00627156	+	0.00734937i
$715$	−31.7221	+	11.5459i	−1.18634	+	0.431793i
$716$	−16.9239	−	2.98415i	−0.632477	−	0.111523i
$717$	4.41147	+	19.3036i	0.164749	+	0.720907i
$718$	−0.229857	+	0.192873i	−0.00857817	+	0.00719794i
$719$	−6.16159	−	10.6722i	−0.229789	−	0.398005i	0.727957	−	0.685623i	$-0.240470\pi$
$719$	−6.16159	−	10.6722i	−0.229789	−	0.398005i	−0.957745	+	0.287618i	$0.907137\pi$
$720$	−13.7773	+	14.1406i	−0.513449	+	0.526988i
$721$	0.167608	+	1.43728i	0.00624205	+	0.0535269i
$722$	0.161617	+	0.192607i	0.00601475	+	0.00716810i
$723$	4.85886	−	9.48393i	0.180703	−	0.352711i
$724$	7.25648	+	19.9370i	0.269685	+	0.740953i
$725$	18.6886	+	3.29530i	0.694076	+	0.122384i
$726$	0.0323791	−	0.258952i	0.00120170	−	0.00961060i
$727$	9.28805	−	25.5187i	0.344475	−	0.946437i	−0.639604	−	0.768705i	$-0.720902\pi$
$727$	9.28805	−	25.5187i	0.344475	−	0.946437i	0.984079	−	0.177732i	$-0.0568761\pi$
$728$	0.700739	−	0.0817168i	0.0259711	−	0.00302863i
$729$	19.8224	+	18.3322i	0.734164	+	0.678972i
$730$	−0.194420	+	0.336745i	−0.00719579	+	0.0124635i
$731$	−1.14437	−	6.49002i	−0.0423259	−	0.240042i
$732$	8.30853	+	6.28990i	0.307092	+	0.232481i
$733$	−15.7087	−	43.1594i	−0.580216	−	1.59413i	−0.787813	−	0.615915i	$-0.788786\pi$
$733$	−15.7087	−	43.1594i	−0.580216	−	1.59413i	0.207597	−	0.978214i	$-0.433436\pi$
$734$	−0.00160288	+	0.00909040i	−5.91635e−5	+	0.000335533i
$735$	5.55885	+	19.1639i	0.205041	+	0.706871i
$736$	−1.01940	+	0.855382i	−0.0375757	+	0.0315298i
$737$		−	49.8010i		−	1.83444i
$738$	−0.0466612	+	0.183669i	−0.00171762	+	0.00676096i
$739$	27.6265			1.01626			0.508129	−	0.861281i	$-0.330337\pi$
$739$	27.6265			1.01626			0.508129	+	0.861281i	$0.330337\pi$
$740$	2.45757	+	0.894481i	0.0903419	+	0.0328818i
$741$	−3.34496	+	10.8546i	−0.122880	+	0.398754i
$742$	−0.149534	+	0.0750495i	−0.00548958	+	0.00275515i
$743$	3.93643	+	10.8153i	0.144414	+	0.396773i	0.990719	−	0.135925i	$-0.0434005\pi$
$743$	3.93643	+	10.8153i	0.144414	+	0.396773i	−0.846306	+	0.532698i	$0.821178\pi$
$744$	0.255890	−	0.830379i	0.00938137	−	0.0304432i
$745$	−21.3919	−	25.4939i	−0.783740	−	0.934025i
$746$			0.481047i			0.0176124i
$747$	−1.09342	+	14.6982i	−0.0400060	+	0.537781i
$748$	30.0195	−	17.3318i	1.09762	−	0.633712i
$749$	−8.46761	+	2.53260i	−0.309400	+	0.0925391i
$750$	−0.141465	+	0.276124i	−0.00516558	+	0.0100826i
$751$	−8.89746	−	7.46586i	−0.324673	−	0.272433i	0.465852	−	0.884863i	$-0.345748\pi$
$751$	−8.89746	−	7.46586i	−0.324673	−	0.272433i	−0.790525	+	0.612430i	$0.790192\pi$
$752$	−1.14472	+	6.49202i	−0.0417436	+	0.236740i
$753$	−21.7171	−	2.71549i	−0.791416	−	0.0989580i
$754$	−0.354883	−	0.422933i	−0.0129241	−	0.0154023i
$755$	31.4764			1.14554
$756$	−7.24054	−	26.5218i	−0.263336	−	0.964589i
$757$	25.0813			0.911595			0.455798	−	0.890083i	$-0.349354\pi$
$757$	25.0813			0.911595			0.455798	+	0.890083i	$0.349354\pi$
$758$	0.0825471	+	0.0983759i	0.00299825	+	0.00357317i
$759$	22.9742	+	54.4597i	0.833910	+	1.97676i
$760$	0.0250534	−	0.142085i	0.000908784	−	0.00515397i
$761$	−19.9698	−	16.7566i	−0.723904	−	0.607428i	0.204558	−	0.978854i	$-0.434424\pi$
$761$	−19.9698	−	16.7566i	−0.723904	−	0.607428i	−0.928462	+	0.371427i	$0.878869\pi$
$762$	−0.0738707	−	0.114306i	−0.00267605	−	0.00414086i
$763$	9.91533	+	2.35274i	0.358959	+	0.0851751i
$764$	17.0277	−	9.83096i	0.616041	−	0.355672i
$765$	7.65459	−	16.9890i	0.276752	−	0.614240i
$766$			0.181308i			0.00655091i
$767$	−33.1967	−	39.5623i	−1.19866	−	1.42851i
$768$	−26.9862	+	6.16718i	−0.973781	+	0.222539i
$769$	−3.57920	−	9.83378i	−0.129069	−	0.354615i	0.858279	−	0.513184i	$-0.171534\pi$
$769$	−3.57920	−	9.83378i	−0.129069	−	0.354615i	−0.987348	+	0.158569i	$0.949312\pi$
$770$	−0.0174359	+	0.298006i	−0.000628347	+	0.0107394i
$771$	−17.6342	−	18.9947i	−0.635079	−	0.684078i
$772$	−36.6663	−	13.3455i	−1.31965	−	0.480314i
$773$	28.1877			1.01384			0.506921	−	0.861993i	$-0.330784\pi$
$773$	28.1877			1.01384			0.506921	+	0.861993i	$0.330784\pi$
$774$	−0.0712920	−	0.0321214i	−0.00256254	−	0.00115458i
$775$			19.2539i			0.691620i
$776$	0.0727022	−	0.0610044i	0.00260986	−	0.00218993i
$777$	−2.80889	+	2.31747i	−0.100768	+	0.0831387i
$778$	0.0833881	−	0.472917i	0.00298961	−	0.0169549i
$779$	2.12518	+	5.83889i	0.0761426	+	0.209200i
$780$	−23.4572	+	9.89557i	−0.839902	+	0.354318i
$781$	6.14069	+	34.8256i	0.219731	+	1.24616i
$782$	0.209295	−	0.362510i	0.00748439	−	0.0129633i
$783$	−28.4474	+	32.2881i	−1.01663	+	1.15388i
$784$	−8.04199	+	26.8105i	−0.287214	+	0.957518i
$785$	−8.94204	+	24.5680i	−0.319155	+	0.876871i
$786$	0.360581	−	0.152113i	0.0128615	−	0.00542571i
$787$	−34.6191	−	6.10428i	−1.23404	−	0.217594i	−0.481679	−	0.876348i	$-0.659973\pi$
$787$	−34.6191	−	6.10428i	−1.23404	−	0.217594i	−0.752359	+	0.658754i	$0.771084\pi$
$788$	2.95958	+	8.13139i	0.105431	+	0.289669i
$789$	−14.9796	−	23.1791i	−0.533288	−	0.825197i
$790$	0.0251711	+	0.0299978i	0.000895548	+	0.00106727i
$791$	9.75722	−	7.25997i	0.346927	−	0.258135i
$792$	0.0610279	−	0.820368i	0.00216853	−	0.0291505i
$793$	6.71836	+	11.6365i	0.238576	+	0.413226i
$794$	−0.132198	+	0.110927i	−0.00469153	+	0.00393666i
$795$	8.85025	−	8.21633i	0.313886	−	0.291403i
$796$	−3.34028	−	0.588981i	−0.118393	−	0.0208759i
$797$	3.03842	−	1.10589i	0.107626	−	0.0391728i	−0.287646	−	0.957737i	$-0.592873\pi$
$797$	3.03842	−	1.10589i	0.107626	−	0.0391728i	0.395272	+	0.918564i	$0.370650\pi$
$798$	0.0764022	+	0.0651977i	0.00270461	+	0.00230797i
$799$	−1.08043	−	6.12744i	−0.0382229	−	0.216773i
$800$	−0.355412	+	0.205197i	−0.0125657	+	0.00725482i
$801$	5.84933	+	20.7463i	0.206676	+	0.733035i
$802$	0.000772030	−	0.00133719i	2.72613e−5	−	4.72180e-5i
$803$	12.6234	+	71.5910i	0.445471	+	2.52639i
$804$	−1.88235	−	37.5108i	−0.0663853	−	1.32290i
$805$	−14.5125	−	28.9159i	−0.511499	−	1.01915i
$806$	0.360063	−	0.429107i	0.0126827	−	0.0151146i
$807$	16.9920	+	2.12466i	0.598146	+	0.0747917i
$808$	0.135891	−	0.0239612i	0.00478061	−	0.000842951i
$809$	6.10355	−	3.52388i	0.214589	−	0.123893i	−0.388853	−	0.921300i	$-0.627129\pi$
$809$	6.10355	−	3.52388i	0.214589	−	0.123893i	0.603442	+	0.797407i	$0.293795\pi$
$810$	−0.115494	−	0.188534i	−0.00405803	−	0.00662442i
$811$		−	27.1164i		−	0.952186i	−0.879395	−	0.476093i	$-0.842053\pi$
$811$		−	27.1164i		−	0.952186i	0.879395	−	0.476093i	$-0.157947\pi$
$812$	41.9796	−	12.5558i	1.47320	−	0.440621i
$813$	−3.55444	+	1.49946i	−0.124660	+	0.0525885i
$814$	−0.0511925	+	0.0186325i	−0.00179429	+	0.000653070i
$815$	26.9676	−	9.81540i	0.944634	−	0.343819i
$816$	21.9536	−	14.1876i	0.768529	−	0.496666i
$817$	−2.52495	+	0.445217i	−0.0883369	+	0.0155762i
$818$	−0.0271086	−	0.0469534i	−0.000947829	−	0.00164169i
$819$	4.69013	−	35.1372i	0.163887	−	1.22779i
$820$	−6.96375	+	12.0616i	−0.243185	+	0.421208i
$821$	−13.1798	+	36.2112i	−0.459978	+	1.26378i	0.465524	+	0.885035i	$0.345866\pi$
$821$	−13.1798	+	36.2112i	−0.459978	+	1.26378i	−0.925502	+	0.378743i	$0.876356\pi$
$822$	−0.0900443	+	0.0205779i	−0.00314065	+	0.000717735i
$823$	24.4459	+	20.5125i	0.852130	+	0.715022i	0.960258	−	0.279115i	$-0.0900412\pi$
$823$	24.4459	+	20.5125i	0.852130	+	0.715022i	−0.108128	+	0.994137i	$0.534486\pi$
$824$	−0.00567026	+	0.0321576i	−0.000197533	+	0.00112026i
$825$	4.06106	+	17.7703i	0.141388	+	0.618683i
$826$	−0.437535	+	0.130863i	−0.0152238	+	0.00455331i
$827$	19.5503	+	11.2874i	0.679831	+	0.392501i	0.799791	−	0.600278i	$-0.204943\pi$
$827$	19.5503	+	11.2874i	0.679831	+	0.392501i	−0.119960	+	0.992779i	$0.538277\pi$
$828$	19.3629	+	40.1515i	0.672908	+	1.39536i
$829$	−28.8216	−	16.6401i	−1.00101	−	0.577936i	−0.0924662	−	0.995716i	$-0.529475\pi$
$829$	−28.8216	−	16.6401i	−1.00101	−	0.577936i	−0.908548	+	0.417780i	$0.862808\pi$
$830$	0.0412795	−	0.113415i	0.00143283	−	0.00393668i
$831$	−12.5853	+	8.13331i	−0.436579	+	0.282141i
$832$	−35.1628	−	6.20014i	−1.21905	−	0.214951i
$833$	−1.52217	−	26.3748i	−0.0527399	−	0.913834i
$834$	0.0949996	−	0.125488i	0.00328957	−	0.00434529i
$835$	11.9298	−	10.0103i	0.412849	−	0.346422i
$836$	−6.74295	−	11.6791i	−0.233210	−	0.403931i
$837$	−37.2737	−	22.7356i	−1.28837	−	0.785857i
$838$	0.513663	+	0.296564i	0.0177442	+	0.0102446i
$839$	−28.7046	−	10.4476i	−0.990993	−	0.360692i	−0.204888	−	0.978785i	$-0.565683\pi$
$839$	−28.7046	−	10.4476i	−0.990993	−	0.360692i	−0.786105	+	0.618093i	$0.787905\pi$
$840$	−0.00373850	+	0.450268i	−0.000128991	+	0.0155357i
$841$	−30.3234	−	25.4443i	−1.04563	−	0.877391i
$842$	0.0806126	−	0.0960703i	0.00277809	−	0.00331080i
$843$	−23.6380	+	46.1386i	−0.814136	+	1.58910i
$844$	−11.3246	−	4.12183i	−0.389810	−	0.141879i
$845$	−11.4321			−0.393275
$846$	−0.0673091	−	0.0303268i	−0.00231414	−	0.00104266i
$847$	15.9418	+	21.4254i	0.547768	+	0.736187i
$848$	16.6828	−	2.94163i	0.572890	−	0.101016i
$849$	3.77872	+	16.5349i	0.129685	+	0.567475i
$850$	0.0829786	−	0.0988901i	0.00284614	−	0.00339190i
$851$	3.79525	−	4.52301i	0.130100	−	0.155047i
$852$	5.94158	+	25.9991i	0.203555	+	0.890713i
$853$	39.5220	−	6.96880i	1.35321	−	0.238607i	0.550429	−	0.834882i	$-0.314464\pi$
$853$	39.5220	−	6.96880i	1.35321	−	0.238607i	0.802780	+	0.596275i	$0.203353\pi$
$854$	0.118019	−	0.0137628i	0.00403851	−	0.000470952i
$855$	−6.60962	−	2.97803i	−0.226044	−	0.101847i
$856$	−0.199446			−0.00681693
$857$	28.0069	+	10.1937i	0.956698	+	0.348209i	0.772739	−	0.634724i	$-0.218886\pi$
$857$	28.0069	+	10.1937i	0.956698	+	0.348209i	0.183959	+	0.982934i	$0.441109\pi$
$858$	0.241811	−	0.471988i	0.00825530	−	0.0161134i
$859$	31.5023	−	37.5429i	1.07484	−	1.28095i	0.117163	−	0.993113i	$-0.462620\pi$
$859$	31.5023	−	37.5429i	1.07484	−	1.28095i	0.957680	−	0.287835i	$-0.0929356\pi$
$860$	−4.40234	−	3.69401i	−0.150119	−	0.125965i
$861$	−9.55647	−	16.8743i	−0.325684	−	0.575075i
$862$	−0.0721165	−	0.0262483i	−0.00245630	−	0.000894019i
$863$	16.1553	+	9.32725i	0.549932	+	0.317503i	0.749095	−	0.662463i	$-0.230489\pi$
$863$	16.1553	+	9.32725i	0.549932	+	0.317503i	−0.199163	+	0.979966i	$0.563822\pi$
$864$	0.0224394	−	0.930347i	0.000763404	−	0.0316511i
$865$	1.25066	+	2.16620i	0.0425236	+	0.0736530i
$866$	−0.223995	+	0.187954i	−0.00761165	+	0.00638693i
$867$	2.88139	−	3.80612i	0.0978572	−	0.129263i
$868$	19.9416	+	39.7332i	0.676863	+	1.34863i
$869$	7.20980	+	1.27128i	0.244576	+	0.0431253i
$870$	0.295958	−	0.191264i	0.0100339	−	0.00648447i
$871$	16.5632	−	45.5070i	0.561222	−	1.54195i
$872$	0.199155	+	0.114982i	0.00674424	+	0.00389379i
$873$	−2.07144	−	4.29538i	−0.0701075	−	0.145377i
$874$	−0.141035	−	0.0814267i	−0.00477059	−	0.00275430i
$875$	−9.09770	−	30.4177i	−0.307558	−	1.02831i
$876$	12.2141	+	53.4462i	0.412676	+	1.80578i
$877$	−0.106352	+	0.603150i	−0.00359124	+	0.0203669i	−0.986551	−	0.163455i	$-0.947736\pi$
$877$	−0.106352	+	0.603150i	−0.00359124	+	0.0203669i	0.982959	+	0.183822i	$0.0588471\pi$
$878$	−0.367894	−	0.308700i	−0.0124158	−	0.0104181i
$879$	17.5498	−	4.01067i	0.591941	−	0.135276i
$880$	10.3374	−	28.4018i	0.348474	−	0.957424i
$881$	−24.2819	+	42.0575i	−0.818079	+	1.41695i	0.0890174	+	0.996030i	$0.471627\pi$
$881$	−24.2819	+	42.0575i	−0.818079	+	1.41695i	−0.907096	+	0.420924i	$0.861706\pi$
$882$	−0.268831	−	0.161220i	−0.00905200	−	0.00542855i
$883$	−10.4471	−	18.0949i	−0.351573	−	0.608943i	0.634952	−	0.772551i	$-0.281020\pi$
$883$	−10.4471	−	18.0949i	−0.351573	−	0.608943i	−0.986525	+	0.163609i	$0.947686\pi$
$884$	33.1955	−	5.85326i	1.11648	−	0.196866i
$885$	27.6847	−	17.8914i	0.930611	−	0.601412i
$886$	−0.325154	+	0.118346i	−0.0109238	+	0.00397592i
$887$	10.6701	−	3.88359i	0.358266	−	0.130398i	−0.156615	−	0.987660i	$-0.550058\pi$
$887$	10.6701	−	3.88359i	0.358266	−	0.130398i	0.514881	+	0.857261i	$0.327836\pi$
$888$	−0.0757135	+	0.0319403i	−0.00254078	+	0.00107185i
$889$	13.5511	+	3.21545i	0.454488	+	0.107843i
$890$		−	0.176510i		−	0.00591664i
$891$	−39.1971	−	13.1219i	−1.31315	−	0.439601i
$892$	−1.59005	+	0.918014i	−0.0532387	+	0.0307374i
$893$	−2.38389	+	0.420344i	−0.0797738	+	0.0140663i
$894$	0.518775	+	0.0648672i	0.0173504	+	0.00216948i
$895$	9.09083	−	10.8340i	0.303873	−	0.362142i
$896$	−0.694545	+	1.05540i	−0.0232031	+	0.0352583i
$897$	2.88066	+	57.4049i	0.0961826	+	1.91670i
$898$	−0.0489497	−	0.277608i	−0.00163347	−	0.00926389i
$899$	34.7928	−	60.2629i	1.16040	−	2.00988i
$900$	3.73053	+	13.2314i	0.124351	+	0.441046i
$901$	−13.8467	+	7.99441i	−0.461301	+	0.266332i
$902$	−0.0503784	−	0.285710i	−0.00167742	−	0.00951310i
$903$	7.54174	−	2.67427i	0.250973	−	0.0889941i
$904$	0.257896	−	0.0938665i	0.00857750	−	0.00312195i
$905$	−17.1954	−	3.03201i	−0.571594	−	0.100787i
$906$	−0.362389	+	0.336432i	−0.0120396	+	0.0111772i
$907$	31.2356	−	26.2098i	1.03716	−	0.870281i	0.0454747	−	0.998965i	$-0.485520\pi$
$907$	31.2356	−	26.2098i	1.03716	−	0.870281i	0.991686	+	0.128685i	$0.0410755\pi$
$908$	13.3270	+	23.0831i	0.442272	+	0.766038i
$909$	0.514365	−	6.91436i	0.0170604	−	0.229335i
$910$	−0.115046	+	0.266512i	−0.00381373	+	0.00883479i
$911$	−22.9670	−	27.3710i	−0.760931	−	0.906843i	0.236975	−	0.971516i	$-0.423844\pi$
$911$	−22.9670	−	27.3710i	−0.760931	−	0.906843i	−0.997907	+	0.0646730i	$0.979400\pi$
$912$	−5.51971	−	8.54107i	−0.182776	−	0.282823i
$913$	−7.71741	−	21.2034i	−0.255409	−	0.701730i
$914$	−0.270587	−	0.0477117i	−0.00895021	−	0.00157816i
$915$	−7.90177	+	3.33341i	−0.261224	+	0.110199i
$916$	8.42357	−	23.1436i	0.278323	−	0.764685i
$917$	−15.8720	+	36.7688i	−0.524141	+	1.21421i
$918$	0.0934580	+	0.277411i	0.00308457	+	0.00915593i
$919$	−13.2691	+	22.9827i	−0.437706	+	0.758129i	−0.997512	−	0.0704945i	$-0.977542\pi$
$919$	−13.2691	+	22.9827i	−0.437706	+	0.758129i	0.559806	+	0.828624i	$0.310876\pi$
$920$	−0.126780	−	0.719003i	−0.00417980	−	0.0237048i
$921$	27.2396	−	11.4912i	0.897576	−	0.378648i
$922$	−0.0818693	−	0.224934i	−0.00269622	−	0.00740781i
$923$	−5.97134	+	33.8652i	−0.196549	+	1.11469i
$924$	26.7857	+	32.4655i	0.881184	+	1.06804i
$925$	1.39488	−	1.17044i	0.0458633	−	0.0384839i
$926$			0.540363i			0.0177574i
$927$	1.49593	+	0.674007i	0.0491328	+	0.0221373i
$928$	1.48321			0.0486887
$929$	−11.5826	−	4.21571i	−0.380011	−	0.138313i	0.144950	−	0.989439i	$-0.453698\pi$
$929$	−11.5826	−	4.21571i	−0.380011	−	0.138313i	−0.524961	+	0.851126i	$0.675920\pi$
$930$	0.243251	+	0.262019i	0.00797651	+	0.00859193i
$931$	−10.2612	+	0.592201i	−0.336296	+	0.0194086i
$932$	−17.0550	−	46.8581i	−0.558654	−	1.53489i
$933$	−56.1653	+	12.8355i	−1.83877	+	0.420215i
$934$	−0.104253	−	0.124244i	−0.00341126	−	0.00406538i
$935$			28.5272i			0.932938i
$936$	0.328610	−	0.729337i	0.0107410	−	0.0238391i
$937$	−32.0189	+	18.4861i	−1.04601	+	0.603915i	−0.921530	−	0.388307i	$-0.873060\pi$
$937$	−32.0189	+	18.4861i	−1.04601	+	0.603915i	−0.124481	+	0.992222i	$0.539727\pi$
$938$	−0.311409	−	0.293955i	−0.0101679	−	0.00959798i
$939$	0.918710	+	1.42159i	0.0299810	+	0.0463918i
$940$	−4.15639	−	3.48763i	−0.135567	−	0.113754i
$941$	7.49093	−	42.4832i	0.244197	−	1.38491i	−0.578152	−	0.815929i	$-0.696226\pi$
$941$	7.49093	−	42.4832i	0.244197	−	1.38491i	0.822349	−	0.568983i	$-0.192663\pi$
$942$	−0.159643	−	0.378429i	−0.00520145	−	0.0123299i
$943$	20.2113	+	24.0869i	0.658171	+	0.784377i
$944$	46.2392			1.50496
$945$	21.8819	+	5.75292i	0.711819	+	0.187143i
$946$	0.119710			0.00389211
$947$	21.1385	+	25.1919i	0.686909	+	0.818626i	0.990978	−	0.134024i	$-0.0427899\pi$
$947$	21.1385	+	25.1919i	0.686909	+	0.818626i	−0.304069	+	0.952650i	$0.598345\pi$
$948$	5.47858	+	0.685037i	0.177936	+	0.0222490i
$949$	−12.2753	+	69.6166i	−0.398473	+	2.25985i
$950$	−0.0384733	−	0.0322830i	−0.00124824	−	0.00104740i
$951$	2.67476	−	5.22082i	0.0867350	−	0.169297i
$952$	0.137640	−	0.580066i	0.00446094	−	0.0188000i
$953$	39.0374	−	22.5383i	1.26455	−	0.730086i	0.290595	−	0.956846i	$-0.406147\pi$
$953$	39.0374	−	22.5383i	1.26455	−	0.730086i	0.973951	+	0.226760i	$0.0728134\pi$
$954$	−0.0140740	+	0.189190i	−0.000455663	+	0.00612525i
$955$			16.1812i			0.523613i
$956$	−14.6954	−	17.5133i	−0.475284	−	0.566421i
$957$	19.4012	−	62.9580i	0.627150	−	2.03514i
$958$	0.0629322	+	0.172905i	0.00203325	+	0.00558630i
$959$	5.19608	−	7.89570i	0.167790	−	0.254965i
$960$	6.71127	−	21.7785i	0.216605	−	0.702899i
$961$	37.2131	+	13.5445i	1.20042	+	0.436918i
$962$	−0.0529755			−0.00170800
$963$	−2.46761	+	9.71308i	−0.0795176	+	0.312999i
$964$			12.3033i			0.396262i
$965$	24.5992	−	20.6412i	0.791878	−	0.664464i
$966$	0.476148	+	0.177794i	0.0153198	+	0.00572044i
$967$	0.795684	−	4.51255i	0.0255875	−	0.145114i	−0.969338	−	0.245733i	$-0.920971\pi$
$967$	0.795684	−	4.51255i	0.0255875	−	0.145114i	0.994925	+	0.100619i	$0.0320824\pi$
$968$	0.206117	+	0.566303i	0.00662486	+	0.0182017i
$969$	7.65272	+	5.79342i	0.245841	+	0.186112i
$970$	0.00678103	+	0.0384572i	0.000217726	+	0.00123478i
$971$	−8.12033	+	14.0648i	−0.260594	+	0.451362i	−0.966400	−	0.257043i	$-0.917252\pi$
$971$	−8.12033	+	14.0648i	−0.260594	+	0.451362i	0.705806	+	0.708405i	$0.250585\pi$
$972$	−30.0198	−	8.40208i	−0.962886	−	0.269497i
$973$	1.86560	+	15.9979i	0.0598085	+	0.512871i
$974$	−0.0986861	+	0.271138i	−0.00316211	+	0.00868782i
$975$	−2.19929	+	17.5888i	−0.0704335	+	0.563292i
$976$	−11.8475	−	2.08904i	−0.379230	−	0.0668685i
$977$	2.94829	+	8.10036i	0.0943241	+	0.259153i	0.977878	−	0.209176i	$-0.0670782\pi$
$977$	2.94829	+	8.10036i	0.0943241	+	0.259153i	−0.883554	+	0.468330i	$0.844856\pi$
$978$	−0.205568	+	0.401246i	−0.00657335	+	0.0128304i
$979$	−21.2117	−	25.2791i	−0.677927	−	0.807922i
$980$	−15.8009	−	16.7657i	−0.504740	−	0.535560i
$981$	8.06368	−	8.27631i	0.257453	−	0.264242i
$982$	−0.248463	−	0.430351i	−0.00792878	−	0.0137331i
$983$	−17.4896	+	14.6755i	−0.557831	+	0.468076i	−0.877583	−	0.479425i	$-0.840845\pi$
$983$	−17.4896	+	14.6755i	−0.557831	+	0.468076i	0.319751	+	0.947501i	$0.396401\pi$
$984$	−0.0974951	−	0.426617i	−0.00310803	−	0.0136001i
$985$	−7.01321	−	1.23662i	−0.223459	−	0.0394019i
$986$	−0.438415	+	0.159570i	−0.0139620	+	0.00508174i
$987$	7.12040	−	2.52486i	0.226645	−	0.0803673i
$988$	−2.27722	−	12.9147i	−0.0724480	−	0.410873i
$989$	−11.2361	+	6.48715i	−0.357286	+	0.206279i
$990$	0.279773	+	0.190523i	0.00889178	+	0.00605520i
$991$	7.45798	−	12.9176i	0.236910	−	0.410341i	−0.722916	−	0.690936i	$-0.757199\pi$
$991$	7.45798	−	12.9176i	0.236910	−	0.410341i	0.959826	+	0.280595i	$0.0905319\pi$
$992$	0.261316	+	1.48200i	0.00829680	+	0.0470535i
$993$	−9.36933	−	4.80015i	−0.297327	−	0.152328i
$994$	0.254013	+	0.167163i	0.00805681	+	0.00530210i
$995$	1.79426	−	2.13831i	0.0568818	−	0.0677891i
$996$	−6.61430	−	15.6790i	−0.209582	−	0.496809i
$997$	−2.28470	+	0.402855i	−0.0723573	+	0.0127585i	−0.209710	−	0.977764i	$-0.567252\pi$
$997$	−2.28470	+	0.402855i	−0.0723573	+	0.0127585i	0.137352	+	0.990522i	$0.456141\pi$
$998$	−0.260252	+	0.150256i	−0.00823812	+	0.00475628i
$999$	0.618748	+	4.08244i	0.0195763	+	0.129163i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.131.12	yes	132
3.2	odd	2		567.2.ba.a.341.11		132
7.3	odd	6		189.2.bd.a.185.11	yes	132
21.17	even	6		567.2.bd.a.17.12		132
27.7	even	9		567.2.bd.a.467.12		132
27.20	odd	18		189.2.bd.a.47.11	yes	132
189.101	even	18	inner	189.2.ba.a.101.12	✓	132
189.115	odd	18		567.2.ba.a.143.11		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.12	✓	132	189.101	even	18	inner
189.2.ba.a.131.12	yes	132	1.1	even	1	trivial
189.2.bd.a.47.11	yes	132	27.20	odd	18
189.2.bd.a.185.11	yes	132	7.3	odd	6
567.2.ba.a.143.11		132	189.115	odd	18
567.2.ba.a.341.11		132	3.2	odd	2
567.2.bd.a.17.12		132	21.17	even	6
567.2.bd.a.467.12		132	27.7	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00959490 + 0.0114348i) q^{2} +(-1.04544 + 1.38096i) q^{3} +(0.347258 - 1.96940i) q^{4} +(1.26073 + 1.05788i) q^{5} +(-0.0258218 + 0.00129578i) q^{6} +(1.81613 - 1.92397i) q^{7} +(0.0517058 - 0.0298524i) q^{8} +(-0.814097 - 2.88743i) q^{9} +O(q^{10})\)	\(q+(0.00959490 + 0.0114348i) q^{2} +(-1.04544 + 1.38096i) q^{3} +(0.347258 - 1.96940i) q^{4} +(1.26073 + 1.05788i) q^{5} +(-0.0258218 + 0.00129578i) q^{6} +(1.81613 - 1.92397i) q^{7} +(0.0517058 - 0.0298524i) q^{8} +(-0.814097 - 2.88743i) q^{9} +0.0245663i q^{10} +(2.95219 + 3.51829i) q^{11} +(2.35662 + 2.53844i) q^{12} +(1.52751 + 4.19679i) q^{13} +(0.0394257 + 0.00230675i) q^{14} +(-2.77891 + 0.635065i) q^{15} +(-3.75751 - 1.36762i) q^{16} +3.77410 q^{17} +(0.0252059 - 0.0370136i) q^{18} -1.46832i q^{19} +(2.52118 - 2.11552i) q^{20} +(0.758259 + 4.51941i) q^{21} +(-0.0119048 + 0.0675152i) q^{22} +(-2.54129 - 6.98214i) q^{23} +(-0.0128306 + 0.102613i) q^{24} +(-0.397908 - 2.25665i) q^{25} +(-0.0333330 + 0.0577345i) q^{26} +(4.83851 + 1.89441i) q^{27} +(-3.15839 - 4.24480i) q^{28} +(-2.83246 + 7.78213i) q^{29} +(-0.0339251 - 0.0256827i) q^{30} +(-8.27481 - 1.45907i) q^{31} +(-0.0612550 - 0.168297i) q^{32} +(-7.94496 + 0.398690i) q^{33} +(0.0362121 + 0.0431559i) q^{34} +(4.32497 - 0.504358i) q^{35} +(-5.96919 + 0.600598i) q^{36} +(0.397320 + 0.688178i) q^{37} +(0.0167899 - 0.0140884i) q^{38} +(-7.39252 - 2.27808i) q^{39} +(0.0967671 + 0.0170627i) q^{40} +(-3.97658 + 1.44736i) q^{41} +(-0.0444029 + 0.0520338i) q^{42} +(-0.303215 - 1.71962i) q^{43} +(7.95407 - 4.59229i) q^{44} +(2.02819 - 4.50148i) q^{45} +(0.0554557 - 0.0960520i) q^{46} +(-0.286275 - 1.62355i) q^{47} +(5.81690 - 3.75920i) q^{48} +(-0.403318 - 6.98837i) q^{49} +(0.0219863 - 0.0262023i) q^{50} +(-3.94561 + 5.21188i) q^{51} +(8.79559 - 1.55090i) q^{52} +(-3.66888 + 2.11823i) q^{53} +(0.0247630 + 0.0735039i) q^{54} +7.55866i q^{55} +(0.0364696 - 0.153696i) q^{56} +(2.02769 + 1.53505i) q^{57} +(-0.116164 + 0.0422802i) q^{58} +(-10.8663 + 3.95501i) q^{59} +(0.285698 + 5.69330i) q^{60} +(2.96287 - 0.522435i) q^{61} +(-0.0627118 - 0.108620i) q^{62} +(-7.03383 - 3.67766i) q^{63} +(-3.99733 + 6.92357i) q^{64} +(-2.51392 + 6.90693i) q^{65} +(-0.0807900 - 0.0870233i) q^{66} +(-8.30643 - 6.96992i) q^{67} +(1.31059 - 7.43270i) q^{68} +(12.2988 + 3.79001i) q^{69} +(0.0472649 + 0.0446158i) q^{70} +(6.66808 + 3.84982i) q^{71} +(-0.128290 - 0.124994i) q^{72} +(13.7076 + 7.91406i) q^{73} +(-0.00405690 + 0.0111462i) q^{74} +(3.53233 + 1.80970i) q^{75} +(-2.89171 - 0.509886i) q^{76} +(12.1307 + 0.709749i) q^{77} +(-0.0448812 - 0.106390i) q^{78} +(1.22109 - 1.02462i) q^{79} +(-3.29043 - 5.69919i) q^{80} +(-7.67449 + 4.70130i) q^{81} +(-0.0547050 - 0.0315840i) q^{82} +(-4.61667 - 1.68033i) q^{83} +(9.16381 + 0.0760856i) q^{84} +(4.75812 + 3.99254i) q^{85} +(0.0167541 - 0.0199668i) q^{86} +(-7.78562 - 12.0473i) q^{87} +(0.257675 + 0.0937859i) q^{88} -7.18505 q^{89} +(0.0709336 - 0.0199994i) q^{90} +(10.8487 + 4.68306i) q^{91} +(-14.6331 + 2.58021i) q^{92} +(10.6658 - 9.90180i) q^{93} +(0.0158181 - 0.0188513i) q^{94} +(1.55330 - 1.85115i) q^{95} +(0.296449 + 0.0913539i) q^{96} +(1.56544 - 0.276029i) q^{97} +(0.0760405 - 0.0716645i) q^{98} +(7.75543 - 11.3885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more