LMFDB - Embedded newform 135.2.q.a.122.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.10
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.263290 + 0.184358i) q^{2} +(-0.312334 + 1.70366i) q^{3} +(-0.648706 - 1.78231i) q^{4} +(2.21531 - 0.303968i) q^{5} +(-0.396317 + 0.390975i) q^{6} +(2.07991 + 4.46037i) q^{7} +(0.324162 - 1.20979i) q^{8} +(-2.80490 - 1.06422i) q^{9} +O(q^{10})$	\(q+(0.263290 + 0.184358i) q^{2} +(-0.312334 + 1.70366i) q^{3} +(-0.648706 - 1.78231i) q^{4} +(2.21531 - 0.303968i) q^{5} +(-0.396317 + 0.390975i) q^{6} +(2.07991 + 4.46037i) q^{7} +(0.324162 - 1.20979i) q^{8} +(-2.80490 - 1.06422i) q^{9} +(0.639309 + 0.328378i) q^{10} +(0.0393995 + 0.0469545i) q^{11} +(3.23905 - 0.548499i) q^{12} +(0.0455832 + 0.0650996i) q^{13} +(-0.274686 + 1.55782i) q^{14} +(-0.174059 + 3.86907i) q^{15} +(-2.59752 + 2.17957i) q^{16} +(-1.04290 - 3.89214i) q^{17} +(-0.542304 - 0.797303i) q^{18} +(1.80193 - 1.04035i) q^{19} +(-1.97885 - 3.75118i) q^{20} +(-8.24857 + 2.15032i) q^{21} +(0.00171708 + 0.0196263i) q^{22} +(-5.88782 - 2.74553i) q^{23} +(1.95982 + 0.930119i) q^{24} +(4.81521 - 1.34677i) q^{25} +0.0255437i q^{26} +(2.68913 - 4.44619i) q^{27} +(6.60050 - 6.60050i) q^{28} +(-1.24585 - 7.06559i) q^{29} +(-0.759121 + 0.986599i) q^{30} +(0.209263 - 0.0761654i) q^{31} +(-3.58112 + 0.313308i) q^{32} +(-0.0923002 + 0.0524578i) q^{33} +(0.442962 - 1.21703i) q^{34} +(5.96345 + 9.24888i) q^{35} +(-0.0772105 + 5.68955i) q^{36} +(-6.33380 + 1.69714i) q^{37} +(0.666227 + 0.0582873i) q^{38} +(-0.125145 + 0.0573254i) q^{39} +(0.350383 - 2.77860i) q^{40} +(-2.22023 - 0.391486i) q^{41} +(-2.56820 - 0.954529i) q^{42} +(-0.325424 + 3.71962i) q^{43} +(0.0581286 - 0.100682i) q^{44} +(-6.53720 - 1.50498i) q^{45} +(-1.04404 - 1.80834i) q^{46} +(1.26917 - 0.591824i) q^{47} +(-2.90196 - 5.10603i) q^{48} +(-11.0694 + 13.1920i) q^{49} +(1.51608 + 0.533130i) q^{50} +(6.95660 - 0.561090i) q^{51} +(0.0864573 - 0.123474i) q^{52} +(8.67464 + 8.67464i) q^{53} +(1.52771 - 0.674876i) q^{54} +(0.101555 + 0.0920427i) q^{55} +(6.07034 - 1.07036i) q^{56} +(1.20959 + 3.39481i) q^{57} +(0.974575 - 2.08998i) q^{58} +(-0.888968 - 0.745933i) q^{59} +(7.00878 - 2.19966i) q^{60} +(-6.77967 - 2.46760i) q^{61} +(0.0691385 + 0.0185256i) q^{62} +(-1.08710 - 14.7243i) q^{63} +(4.87243 + 2.81310i) q^{64} +(0.120769 + 0.130360i) q^{65} +(-0.0339728 - 0.00320464i) q^{66} +(6.22807 - 4.36094i) q^{67} +(-6.26045 + 4.38361i) q^{68} +(6.51641 - 9.17330i) q^{69} +(-0.134987 + 3.53455i) q^{70} +(6.33059 + 3.65497i) q^{71} +(-2.19672 + 3.04835i) q^{72} +(6.42123 + 1.72056i) q^{73} +(-1.98051 - 0.720846i) q^{74} +(0.790480 + 8.62410i) q^{75} +(-3.02314 - 2.53672i) q^{76} +(-0.127487 + 0.273398i) q^{77} +(-0.0435177 - 0.00797816i) q^{78} +(-6.06016 + 1.06857i) q^{79} +(-5.09178 + 5.61800i) q^{80} +(6.73488 + 5.97005i) q^{81} +(-0.512391 - 0.512391i) q^{82} +(-2.31193 + 3.30178i) q^{83} +(9.18343 + 13.3065i) q^{84} +(-3.49342 - 8.30529i) q^{85} +(-0.771422 + 0.919344i) q^{86} +(12.4265 + 0.0843133i) q^{87} +(0.0695770 - 0.0324443i) q^{88} +(-5.25350 - 9.09933i) q^{89} +(-1.44373 - 1.60143i) q^{90} +(-0.195560 + 0.338719i) q^{91} +(-1.07392 + 12.2749i) q^{92} +(0.0643999 + 0.380301i) q^{93} +(0.443268 + 0.0781601i) q^{94} +(3.67561 - 2.85242i) q^{95} +(0.584736 - 6.19886i) q^{96} +(9.77698 + 0.855375i) q^{97} +(-5.34651 + 1.43259i) q^{98} +(-0.0605417 - 0.173632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.263290	+	0.184358i	0.186174	+	0.130361i	0.662948	−	0.748665i	$-0.269305\pi$
$2$	0.263290	+	0.184358i	0.186174	+	0.130361i	−0.476774	+	0.879026i	$0.658194\pi$
$3$	−0.312334	+	1.70366i	−0.180326	+	0.983607i
$3$	−0.312334	+	1.70366i	−0.180326	+	0.983607i
$4$	−0.648706	−	1.78231i	−0.324353	−	0.891153i
$5$	2.21531	−	0.303968i	0.990717	−	0.135939i
$5$	2.21531	−	0.303968i	0.990717	−	0.135939i
$6$	−0.396317	+	0.390975i	−0.161796	+	0.159615i
$7$	2.07991	+	4.46037i	0.786130	+	1.68586i	0.726024	+	0.687670i	$0.241366\pi$
$7$	2.07991	+	4.46037i	0.786130	+	1.68586i	0.0601067	+	0.998192i	$0.480856\pi$
$8$	0.324162	−	1.20979i	0.114609	−	0.427725i
$9$	−2.80490	−	1.06422i	−0.934965	−	0.354740i
$10$	0.639309	+	0.328378i	0.202167	+	0.103842i
$11$	0.0393995	+	0.0469545i	0.0118794	+	0.0141573i	0.771951	−	0.635682i	$-0.219281\pi$
$11$	0.0393995	+	0.0469545i	0.0118794	+	0.0141573i	−0.760072	+	0.649839i	$0.774836\pi$
$12$	3.23905	−	0.548499i	0.935034	−	0.158338i
$13$	0.0455832	+	0.0650996i	0.0126425	+	0.0180554i	0.825424	−	0.564514i	$-0.190936\pi$
$13$	0.0455832	+	0.0650996i	0.0126425	+	0.0180554i	−0.812781	+	0.582569i	$0.802047\pi$
$14$	−0.274686	+	1.55782i	−0.0734128	+	0.416345i
$15$	−0.174059	+	3.86907i	−0.0449418	+	0.998990i
$16$	−2.59752	+	2.17957i	−0.649379	+	0.544894i
$17$	−1.04290	−	3.89214i	−0.252939	−	0.943982i	−0.969225	−	0.246175i	$-0.920826\pi$
$17$	−1.04290	−	3.89214i	−0.252939	−	0.943982i	0.716286	−	0.697807i	$-0.245841\pi$
$18$	−0.542304	−	0.797303i	−0.127822	−	0.187926i
$19$	1.80193	−	1.04035i	0.413392	−	0.238672i	−0.278854	−	0.960333i	$-0.589955\pi$
$19$	1.80193	−	1.04035i	0.413392	−	0.238672i	0.692246	+	0.721662i	$0.256621\pi$
$20$	−1.97885	−	3.75118i	−0.442484	−	0.838789i
$21$	−8.24857	+	2.15032i	−1.79998	+	0.469239i
$22$	0.00171708	+	0.0196263i	0.000366082	+	0.00418434i
$23$	−5.88782	−	2.74553i	−1.22769	−	0.572483i	−0.302926	−	0.953014i	$-0.597964\pi$
$23$	−5.88782	−	2.74553i	−1.22769	−	0.572483i	−0.924768	+	0.380531i	$0.875741\pi$
$24$	1.95982	+	0.930119i	0.400047	+	0.189860i
$25$	4.81521	−	1.34677i	0.963041	−	0.269354i
$26$			0.0255437i			0.00500954i
$27$	2.68913	−	4.44619i	0.517523	−	0.855669i
$28$	6.60050	−	6.60050i	1.24738	−	1.24738i
$29$	−1.24585	−	7.06559i	−0.231349	−	1.31205i	−0.850167	−	0.526512i	$-0.823499\pi$
$29$	−1.24585	−	7.06559i	−0.231349	−	1.31205i	0.618818	−	0.785534i	$-0.287612\pi$
$30$	−0.759121	+	0.986599i	−0.138596	+	0.180128i
$31$	0.209263	−	0.0761654i	0.0375847	−	0.0136797i	−0.323159	−	0.946345i	$-0.604745\pi$
$31$	0.209263	−	0.0761654i	0.0375847	−	0.0136797i	0.360744	+	0.932665i	$0.382523\pi$
$32$	−3.58112	+	0.313308i	−0.633059	+	0.0553855i
$33$	−0.0923002	+	0.0524578i	−0.0160674	+	0.00913174i
$34$	0.442962	−	1.21703i	0.0759674	−	0.208719i
$35$	5.96345	+	9.24888i	1.00801	+	1.56335i
$36$	−0.0772105	+	5.68955i	−0.0128684	+	0.948258i
$37$	−6.33380	+	1.69714i	−1.04127	+	0.279007i	−0.738640	−	0.674101i	$-0.764531\pi$
$37$	−6.33380	+	1.69714i	−1.04127	+	0.279007i	−0.302630	+	0.953108i	$0.597865\pi$
$38$	0.666227	+	0.0582873i	0.108076	+	0.00945545i
$39$	−0.125145	+	0.0573254i	−0.0200392	+	0.00917941i
$40$	0.350383	−	2.77860i	0.0554004	−	0.439335i
$41$	−2.22023	−	0.391486i	−0.346742	−	0.0611399i	−0.00243462	−	0.999997i	$-0.500775\pi$
$41$	−2.22023	−	0.391486i	−0.346742	−	0.0611399i	−0.344307	+	0.938857i	$0.611886\pi$
$42$	−2.56820	−	0.954529i	−0.396281	−	0.147287i
$43$	−0.325424	+	3.71962i	−0.0496267	+	0.567236i	0.930155	+	0.367167i	$0.119672\pi$
$43$	−0.325424	+	3.71962i	−0.0496267	+	0.567236i	−0.979782	+	0.200069i	$0.935883\pi$
$44$	0.0581286	−	0.100682i	0.00876322	−	0.0151783i
$45$	−6.53720	−	1.50498i	−0.974509	−	0.224349i
$46$	−1.04404	−	1.80834i	−0.153936	−	0.266625i
$47$	1.26917	−	0.591824i	0.185128	−	0.0863264i	−0.327844	−	0.944732i	$-0.606322\pi$
$47$	1.26917	−	0.591824i	0.185128	−	0.0863264i	0.512972	+	0.858405i	$0.328544\pi$
$48$	−2.90196	−	5.10603i	−0.418861	−	0.736992i
$49$	−11.0694	+	13.1920i	−1.58134	+	1.88457i
$50$	1.51608	+	0.533130i	0.214407	+	0.0753960i
$51$	6.95660	−	0.561090i	0.974119	−	0.0785684i
$52$	0.0864573	−	0.123474i	0.0119895	−	0.0171227i
$53$	8.67464	+	8.67464i	1.19155	+	1.19155i	0.976631	+	0.214923i	$0.0689499\pi$
$53$	8.67464	+	8.67464i	1.19155	+	1.19155i	0.214923	+	0.976631i	$0.431050\pi$
$54$	1.52771	−	0.674876i	0.207895	−	0.0918390i
$55$	0.101555	+	0.0920427i	0.0136937	+	0.0124110i
$56$	6.07034	−	1.07036i	0.811183	−	0.143033i
$57$	1.20959	+	3.39481i	0.160214	+	0.449654i
$58$	0.974575	−	2.08998i	0.127968	−	0.274428i
$59$	−0.888968	−	0.745933i	−0.115734	−	0.0971121i	0.583084	−	0.812412i	$-0.301846\pi$
$59$	−0.888968	−	0.745933i	−0.115734	−	0.0971121i	−0.698818	+	0.715300i	$0.746290\pi$
$60$	7.00878	−	2.19966i	0.904830	−	0.283975i
$61$	−6.77967	−	2.46760i	−0.868048	−	0.315944i	−0.130672	−	0.991426i	$-0.541713\pi$
$61$	−6.77967	−	2.46760i	−0.868048	−	0.315944i	−0.737377	+	0.675482i	$0.763936\pi$
$62$	0.0691385	+	0.0185256i	0.00878060	+	0.00235275i
$63$	−1.08710	−	14.7243i	−0.136962	−	1.85509i
$64$	4.87243	+	2.81310i	0.609054	+	0.351637i
$65$	0.120769	+	0.130360i	0.0149796	+	0.0161692i
$66$	−0.0339728	−	0.00320464i	−0.00418176	−	0.000394464i
$67$	6.22807	−	4.36094i	0.760880	−	0.532774i	−0.127524	−	0.991835i	$-0.540703\pi$
$67$	6.22807	−	4.36094i	0.760880	−	0.532774i	0.888405	+	0.459061i	$0.151814\pi$
$68$	−6.26045	+	4.38361i	−0.759191	+	0.531591i
$69$	6.51641	−	9.17330i	0.784484	−	1.10434i
$70$	−0.134987	+	3.53455i	−0.0161340	+	0.422459i
$71$	6.33059	+	3.65497i	0.751303	+	0.433765i	0.826165	−	0.563429i	$-0.190518\pi$
$71$	6.33059	+	3.65497i	0.751303	+	0.433765i	−0.0748614	+	0.997194i	$0.523851\pi$
$72$	−2.19672	+	3.04835i	−0.258886	+	0.359252i
$73$	6.42123	+	1.72056i	0.751549	+	0.201377i	0.614205	−	0.789147i	$-0.289477\pi$
$73$	6.42123	+	1.72056i	0.751549	+	0.201377i	0.137344	+	0.990523i	$0.456144\pi$
$74$	−1.98051	−	0.720846i	−0.230229	−	0.0837966i
$75$	0.790480	+	8.62410i	0.0912767	+	0.995826i
$76$	−3.02314	−	2.53672i	−0.346778	−	0.290981i
$77$	−0.127487	+	0.273398i	−0.0145285	+	0.0311565i
$78$	−0.0435177	−	0.00797816i	−0.00492741	−	0.000903349i
$79$	−6.06016	+	1.06857i	−0.681821	+	0.120223i	−0.503822	−	0.863807i	$-0.668073\pi$
$79$	−6.06016	+	1.06857i	−0.681821	+	0.120223i	−0.177999	+	0.984031i	$0.556962\pi$
$80$	−5.09178	+	5.61800i	−0.569279	+	0.628111i
$81$	6.73488	+	5.97005i	0.748320	+	0.663338i
$82$	−0.512391	−	0.512391i	−0.0565841	−	0.0565841i
$83$	−2.31193	+	3.30178i	−0.253767	+	0.362417i	−0.925741	−	0.378158i	$-0.876558\pi$
$83$	−2.31193	+	3.30178i	−0.253767	+	0.362417i	0.671974	+	0.740575i	$0.265447\pi$
$84$	9.18343	+	13.3065i	1.00199	+	1.45186i
$85$	−3.49342	−	8.30529i	−0.378915	−	0.900835i
$86$	−0.771422	+	0.919344i	−0.0831845	+	0.0991355i
$87$	12.4265	+	0.0843133i	1.33226	+	0.00903933i
$88$	0.0695770	−	0.0324443i	0.00741693	−	0.00345857i
$89$	−5.25350	−	9.09933i	−0.556870	−	0.964527i	−0.997755	−	0.0669633i	$-0.978669\pi$
$89$	−5.25350	−	9.09933i	−0.556870	−	0.964527i	0.440886	−	0.897563i	$-0.354664\pi$
$90$	−1.44373	−	1.60143i	−0.152182	−	0.168806i
$91$	−0.195560	+	0.338719i	−0.0205002	+	0.0355074i
$92$	−1.07392	+	12.2749i	−0.111964	+	1.27975i
$93$	0.0643999	+	0.380301i	0.00667796	+	0.0394354i
$94$	0.443268	+	0.0781601i	0.0457196	+	0.00806160i
$95$	3.67561	−	2.85242i	0.377109	−	0.292652i
$96$	0.584736	−	6.19886i	0.0596794	−	0.632669i
$97$	9.77698	+	0.855375i	0.992702	+	0.0868501i	0.571918	−	0.820311i	$-0.306200\pi$
$97$	9.77698	+	0.855375i	0.992702	+	0.0868501i	0.420784	+	0.907161i	$0.361755\pi$
$98$	−5.34651	+	1.43259i	−0.540079	+	0.144714i
$99$	−0.0605417	−	0.173632i	−0.00608467	−	0.0174507i
$100$	−5.52401	−	7.70852i	−0.552401	−	0.770852i
$101$	1.28534	−	3.53144i	0.127896	−	0.351391i	−0.859173	−	0.511684i	$-0.829022\pi$
$101$	1.28534	−	3.53144i	0.127896	−	0.351391i	0.987069	+	0.160293i	$0.0512439\pi$
$102$	1.93505	+	1.13477i	0.191598	+	0.112359i
$103$	−2.41848	+	0.211590i	−0.238300	+	0.0208485i	−0.205680	−	0.978619i	$-0.565941\pi$
$103$	−2.41848	+	0.211590i	−0.238300	+	0.0208485i	−0.0326198	+	0.999468i	$0.510385\pi$
$104$	0.0935332	−	0.0340433i	0.00917169	−	0.00333822i
$105$	−17.6195	+	7.27093i	−1.71949	+	0.709570i
$106$	0.684711	+	3.88319i	0.0665050	+	0.377168i
$107$	1.54852	−	1.54852i	0.149701	−	0.149701i	−0.628284	−	0.777984i	$-0.716242\pi$
$107$	1.54852	−	1.54852i	0.149701	−	0.149701i	0.777984	+	0.628284i	$0.216242\pi$
$108$	−9.66892	−	1.90858i	−0.930393	−	0.183653i
$109$			0.257274i			0.0246424i	0.999924	+	0.0123212i	$0.00392206\pi$
$109$			0.257274i			0.0246424i	−0.999924	+	0.0123212i	$0.996078\pi$
$110$	0.00976963	+	0.0429564i	0.000931497	+	0.00409573i
$111$	−0.913080	−	11.3207i	−0.0866657	−	1.07451i
$112$	−15.1243	−	7.05257i	−1.42911	−	0.666406i
$113$	0.980488	+	11.2070i	0.0922366	+	1.05427i	0.891419	+	0.453180i	$0.149711\pi$
$113$	0.980488	+	11.2070i	0.0922366	+	1.05427i	−0.799182	+	0.601089i	$0.794734\pi$
$114$	−0.307387	+	1.11682i	−0.0287894	+	0.104600i
$115$	−13.8779	−	4.29250i	−1.29412	−	0.400278i
$116$	−11.7848	+	6.80398i	−1.09420	+	0.631734i
$117$	−0.0585760	−	0.231108i	−0.00541535	−	0.0213660i
$118$	−0.0965380	−	0.360285i	−0.00888705	−	0.0331669i
$119$	15.1913	−	12.7470i	1.39258	−	1.16851i
$120$	4.62434	+	1.46478i	0.422142	+	0.133716i
$121$	1.90948	−	10.8292i	0.173589	−	0.984471i
$122$	−1.33010	−	1.89958i	−0.120422	−	0.171980i
$123$	1.36041	−	3.66024i	0.122664	−	0.330032i
$124$	−0.271500	−	0.323561i	−0.0243814	−	0.0290567i
$125$	10.2578	−	4.44718i	0.917486	−	0.397768i
$126$	2.42832	−	4.07719i	0.216332	−	0.363225i
$127$	−2.00243	+	7.47317i	−0.177687	+	0.663137i	0.818391	+	0.574661i	$0.194866\pi$
$127$	−2.00243	+	7.47317i	−0.177687	+	0.663137i	−0.996078	+	0.0884755i	$0.971801\pi$
$128$	3.80270	+	8.15493i	0.336115	+	0.720800i
$129$	−6.23531	−	1.71617i	−0.548989	−	0.151101i
$130$	0.00776448	+	0.0565873i	0.000680990	+	0.00496303i
$131$	3.14700	+	8.64630i	0.274954	+	0.755431i	0.997915	+	0.0645417i	$0.0205586\pi$
$131$	3.14700	+	8.64630i	0.274954	+	0.755431i	−0.722961	+	0.690889i	$0.757219\pi$
$132$	0.153372	+	0.130478i	0.0133493	+	0.0113566i
$133$	8.38818	+	5.87347i	0.727347	+	0.509294i
$134$	2.44376			0.211109
$135$	4.60575	−	10.6671i	0.396400	−	0.918078i
$136$	−5.04674			−0.432754
$137$	−11.2654	−	7.88810i	−0.962466	−	0.673926i	−0.0170715	−	0.999854i	$-0.505434\pi$
$137$	−11.2654	−	7.88810i	−0.962466	−	0.673926i	−0.945394	+	0.325928i	$0.894323\pi$
$138$	3.40688	−	1.21389i	0.290013	−	0.103333i
$139$	−0.364140	−	1.00047i	−0.0308860	−	0.0848586i	0.923291	−	0.384101i	$-0.125488\pi$
$139$	−0.364140	−	1.00047i	−0.0308860	−	0.0848586i	−0.954177	+	0.299242i	$0.903266\pi$
$140$	12.6158	−	16.6285i	1.06623	−	1.40536i
$141$	0.611861	+	2.34708i	0.0515280	+	0.197660i
$142$	0.992961	+	2.12941i	0.0833274	+	0.178696i
$143$	−0.00126076	+	0.00470524i	−0.000105430	+	0.000393472i
$144$	9.60530	−	3.34915i	0.800442	−	0.279096i
$145$	−4.90767	−	15.2738i	−0.407560	−	1.26842i
$146$	1.37345	+	1.63681i	0.113667	+	0.135464i
$147$	−19.0173	−	22.9787i	−1.56852	−	1.89526i
$148$	7.13359	+	10.1878i	0.586378	+	0.837434i
$149$	−3.12678	+	17.7328i	−0.256156	+	1.45273i	0.536933	+	0.843625i	$0.319583\pi$
$149$	−3.12678	+	17.7328i	−0.256156	+	1.45273i	−0.793089	+	0.609106i	$0.791528\pi$
$150$	−1.38180	+	2.41637i	−0.112823	+	0.197296i
$151$	7.30896	−	6.13294i	0.594795	−	0.499092i	−0.294973	−	0.955506i	$-0.595311\pi$
$151$	7.30896	−	6.13294i	0.594795	−	0.499092i	0.889768	+	0.456414i	$0.150866\pi$
$152$	−0.674482	−	2.51720i	−0.0547077	−	0.204172i
$153$	−1.21688	+	12.0269i	−0.0983785	+	0.972318i
$154$	−0.0839692	+	0.0484796i	−0.00676643	+	0.00390660i
$155$	0.440430	−	0.232339i	0.0353762	−	0.0186619i
$156$	0.183354	+	0.185859i	0.0146800	+	0.0148806i
$157$	1.41313	+	16.1522i	0.112780	+	1.28908i	0.815975	+	0.578087i	$0.196201\pi$
$157$	1.41313	+	16.1522i	0.112780	+	1.28908i	−0.703195	+	0.710997i	$0.748244\pi$
$158$	−1.79258	−	0.835893i	−0.142610	−	0.0665001i
$159$	−17.4880	+	12.0692i	−1.38689	+	0.957152i
$160$	−7.83807	+	1.78262i	−0.619654	+	0.140929i
$161$		−	31.9723i		−	2.51977i
$162$	0.672603	+	2.81348i	0.0528446	+	0.221048i
$163$	−7.81801	+	7.81801i	−0.612354	+	0.612354i	−0.943559	−	0.331205i	$-0.892545\pi$
$163$	−7.81801	+	7.81801i	−0.612354	+	0.612354i	0.331205	+	0.943559i	$0.392545\pi$
$164$	0.742528	+	4.21109i	0.0579817	+	0.328831i
$165$	−0.188528	+	0.144267i	−0.0146769	+	0.0112312i
$166$	−1.21742	+	0.443103i	−0.0944898	+	0.0343915i
$167$	−13.0293	+	1.13992i	−1.00824	+	0.0882093i	−0.579291	−	0.815121i	$-0.696671\pi$
$167$	−13.0293	+	1.13992i	−1.00824	+	0.0882093i	−0.428946	+	0.903330i	$0.641115\pi$
$168$	−0.0724370	+	10.6761i	−0.00558864	+	0.823678i
$169$	4.44410	−	12.2101i	0.341854	−	0.939236i
$170$	0.611361	−	2.83074i	0.0468892	−	0.217108i
$171$	−6.16139	+	1.00041i	−0.471173	+	0.0765034i
$172$	6.84060	−	1.83293i	0.521591	−	0.139760i
$173$	−22.6663	−	1.98304i	−1.72329	−	0.150768i	−0.817900	−	0.575360i	$-0.804862\pi$
$173$	−22.6663	−	1.98304i	−1.72329	−	0.150768i	−0.905385	+	0.424592i	$0.860418\pi$
$174$	3.25622	+	2.31311i	0.246854	+	0.175357i
$175$	16.0223	+	18.6765i	1.21117	+	1.41181i
$176$	−0.204682	−	0.0360909i	−0.0154285	−	0.00272046i
$177$	1.54847	−	1.28152i	0.116390	−	0.0963247i
$178$	0.294337	−	3.36429i	0.0220615	−	0.252164i
$179$	−9.11136	+	15.7813i	−0.681015	+	1.17955i	0.293656	+	0.955911i	$0.405128\pi$
$179$	−9.11136	+	15.7813i	−0.681015	+	1.17955i	−0.974671	+	0.223642i	$0.928205\pi$
$180$	1.55840	+	12.6276i	0.116156	+	0.941205i
$181$	6.18809	+	10.7181i	0.459957	+	0.796669i	0.998958	−	0.0456358i	$-0.0145314\pi$
$181$	6.18809	+	10.7181i	0.459957	+	0.796669i	−0.539001	+	0.842305i	$0.681198\pi$
$182$	−0.113934	+	0.0531285i	−0.00844539	+	0.00393815i
$183$	6.32146	−	10.7795i	0.467296	−	0.796846i
$184$	−5.23013	+	6.23302i	−0.385570	+	0.459504i
$185$	−13.5155	+	5.68496i	−0.993676	+	0.417966i
$186$	−0.0531556	+	0.112002i	−0.00389756	+	0.00821240i
$187$	0.141664	−	0.202317i	0.0103595	−	0.0147949i
$188$	−1.87813	−	1.87813i	−0.136977	−	0.136977i
$189$	25.4248	+	2.74686i	1.84938	+	0.199804i
$190$	1.49362	−	0.0733872i	0.108358	−	0.00532407i
$191$	12.0893	−	2.13167i	0.874752	−	0.154242i	0.281793	−	0.959475i	$-0.409071\pi$
$191$	12.0893	−	2.13167i	0.874752	−	0.154242i	0.592959	+	0.805233i	$0.297960\pi$
$192$	−6.31438	+	7.42232i	−0.455701	+	0.535660i
$193$	7.49551	−	16.0742i	0.539538	−	1.15704i	−0.427874	−	0.903838i	$-0.640737\pi$
$193$	7.49551	−	16.0742i	0.539538	−	1.15704i	0.967413	−	0.253205i	$-0.0814848\pi$
$194$	2.41649	+	2.02767i	0.173494	+	0.145579i
$195$	−0.259809	+	0.165034i	−0.0186053	+	0.0118183i
$196$	30.6929	+	11.1713i	2.19235	+	0.797951i
$197$	8.80113	+	2.35826i	0.627055	+	0.168019i	0.558333	−	0.829617i	$-0.311441\pi$
$197$	8.80113	+	2.35826i	0.627055	+	0.168019i	0.0687218	+	0.997636i	$0.478108\pi$
$198$	0.0160704	−	0.0568770i	0.00114208	−	0.00404207i
$199$	9.38387	+	5.41778i	0.665205	+	0.384056i	0.794257	−	0.607581i	$-0.207860\pi$
$199$	9.38387	+	5.41778i	0.665205	+	0.384056i	−0.129052	+	0.991638i	$0.541193\pi$
$200$	−0.0683980	−	6.26196i	−0.00483647	−	0.442787i
$201$	5.48432	+	11.9726i	0.386834	+	0.844480i
$202$	0.989466	−	0.692831i	0.0696186	−	0.0487474i
$203$	28.9239	−	20.2527i	2.03006	−	1.42146i
$204$	−5.51283	−	12.0348i	−0.385975	−	0.842605i
$205$	−5.03750	−	0.192385i	−0.351834	−	0.0134368i
$206$	−0.675770	−	0.390156i	−0.0470831	−	0.0271835i
$207$	13.5929	+	13.9669i	0.944769	+	0.970764i
$208$	−0.260293	−	0.0697452i	−0.0180480	−	0.00483596i
$209$	0.119844	+	0.0436198i	0.00828980	+	0.00301724i
$210$	−5.97950	−	1.33393i	−0.412625	−	0.0920499i
$211$	−1.55684	−	1.30634i	−0.107177	−	0.0899325i	0.587624	−	0.809134i	$-0.300063\pi$
$211$	−1.55684	−	1.30634i	−0.107177	−	0.0899325i	−0.694802	+	0.719202i	$0.744508\pi$
$212$	9.83357	−	21.0882i	0.675372	−	1.44834i
$213$	−8.20407	+	9.64359i	−0.562134	+	0.660768i
$214$	0.693191	−	0.122228i	0.0473856	−	0.00835535i
$215$	0.409729	+	8.33903i	0.0279433	+	0.568717i
$216$	−4.50724	−	4.69457i	−0.306679	−	0.319425i
$217$	0.774973	+	0.774973i	0.0526086	+	0.0526086i
$218$	−0.0474305	+	0.0677378i	−0.00321240	+	0.00458779i
$219$	−4.93682	+	10.4022i	−0.333599	+	0.702915i
$220$	0.0981690	−	0.240711i	0.00661855	−	0.0162287i
$221$	0.205838	−	0.245308i	0.0138462	−	0.0165012i
$222$	1.84665	−	3.14896i	0.123939	−	0.211344i
$223$	−2.46881	+	1.15123i	−0.165324	+	0.0770918i	−0.503519	−	0.863984i	$-0.667961\pi$
$223$	−2.46881	+	1.15123i	−0.165324	+	0.0770918i	0.338195	+	0.941076i	$0.390184\pi$
$224$	−8.84586	−	15.3215i	−0.591039	−	1.02371i
$225$	−14.9394	−	1.34689i	−0.995960	−	0.0897928i
$226$	−1.80795	+	3.13146i	−0.120263	+	0.208302i
$227$	−1.23497	+	14.1158i	−0.0819680	+	0.936899i	0.838197	+	0.545368i	$0.183610\pi$
$227$	−1.23497	+	14.1158i	−0.0819680	+	0.936899i	−0.920165	+	0.391531i	$0.871946\pi$
$228$	5.26592	−	4.35809i	0.348744	−	0.288622i
$229$	13.0574	+	2.30237i	0.862857	+	0.152145i	0.587527	−	0.809205i	$-0.300102\pi$
$229$	13.0574	+	2.30237i	0.862857	+	0.152145i	0.275330	+	0.961350i	$0.411213\pi$
$230$	−2.86256	−	3.68867i	−0.188752	−	0.243224i
$231$	−0.425957	−	0.302586i	−0.0280259	−	0.0199087i
$232$	−8.95173	−	0.783175i	−0.587710	−	0.0514180i
$233$	−6.55427	+	1.75621i	−0.429384	+	0.115053i	−0.467037	−	0.884238i	$-0.654679\pi$
$233$	−6.55427	+	1.75621i	−0.429384	+	0.115053i	0.0376527	+	0.999291i	$0.488012\pi$
$234$	0.0271841	−	0.0716475i	0.00177708	−	0.00468374i
$235$	2.63171	−	1.69686i	0.171674	−	0.110691i
$236$	−0.752801	+	2.06830i	−0.0490032	+	0.134635i
$237$	0.0723155	−	10.6582i	0.00469740	−	0.692323i
$238$	6.34972	−	0.555528i	0.411591	−	0.0360095i
$239$	17.1554	−	6.24407i	1.10969	−	0.403895i	0.278812	−	0.960346i	$-0.410059\pi$
$239$	17.1554	−	6.24407i	1.10969	−	0.403895i	0.830881	+	0.556451i	$0.187837\pi$
$240$	−7.98081	−	10.4293i	−0.515159	−	0.673211i
$241$	−2.76886	−	15.7030i	−0.178358	−	1.01152i	−0.934196	−	0.356759i	$-0.883882\pi$
$241$	−2.76886	−	15.7030i	−0.178358	−	1.01152i	0.755839	−	0.654758i	$-0.227229\pi$
$242$	2.49919	−	2.49919i	0.160654	−	0.160654i
$243$	−12.2744	+	9.60927i	−0.787406	+	0.616435i
$244$			13.6842i			0.876041i
$245$	−20.5122	+	32.5891i	−1.31048	+	2.08204i
$246$	1.03298	−	0.712902i	0.0658601	−	0.0454530i
$247$	0.149864	+	0.0698828i	0.00953562	+	0.00444653i
$248$	−0.0243091	−	0.277854i	−0.00154363	−	0.0176437i
$249$	−4.90300	−	4.96999i	−0.310715	−	0.314960i
$250$	3.52065	+	0.720208i	0.222666	+	0.0455499i
$251$	14.9016	−	8.60342i	0.940578	−	0.543043i	0.0504364	−	0.998727i	$-0.483939\pi$
$251$	14.9016	−	8.60342i	0.940578	−	0.543043i	0.890141	+	0.455684i	$0.150605\pi$
$252$	−25.5381	+	11.4893i	−1.60875	+	0.723760i
$253$	−0.103062	−	0.384632i	−0.00647945	−	0.0241816i
$254$	−1.90496	+	1.59845i	−0.119528	+	0.100296i
$255$	15.2405	−	3.35757i	0.954396	−	0.210259i
$256$	1.45175	−	8.23327i	0.0907343	−	0.514580i
$257$	−5.37032	−	7.66961i	−0.334991	−	0.478417i	0.615952	−	0.787784i	$-0.288772\pi$
$257$	−5.37032	−	7.66961i	−0.334991	−	0.478417i	−0.950943	+	0.309367i	$0.899883\pi$
$258$	−1.32531	−	1.60138i	−0.0825100	−	0.0996976i
$259$	−20.7436	−	24.7212i	−1.28894	−	1.53610i
$260$	0.153998	−	0.299813i	0.00955053	−	0.0185936i
$261$	−4.02484	+	21.1441i	−0.249132	+	1.30879i
$262$	−0.765440	+	2.85666i	−0.0472890	+	0.176485i
$263$	−0.386147	−	0.828096i	−0.0238109	−	0.0510626i	0.894043	−	0.447982i	$-0.147857\pi$
$263$	−0.386147	−	0.828096i	−0.0238109	−	0.0510626i	−0.917854	+	0.396919i	$0.870079\pi$
$264$	0.0335427	+	0.128669i	0.00206441	+	0.00791901i
$265$	21.8538	+	16.5802i	1.34247	+	1.01851i
$266$	1.12571	+	3.09285i	0.0690215	+	0.189635i
$267$	17.1430	−	6.10813i	1.04913	−	0.373812i
$268$	−11.8127	−	8.27136i	−0.721577	−	0.505254i
$269$	−27.6508			−1.68590			−0.842951	−	0.537990i	$-0.819184\pi$
$269$	−27.6508			−1.68590			−0.842951	+	0.537990i	$0.819184\pi$
$270$	3.17921	−	1.95944i	0.193481	−	0.119248i
$271$	−18.0879			−1.09876			−0.549380	−	0.835572i	$-0.685136\pi$
$271$	−18.0879			−1.09876			−0.549380	+	0.835572i	$0.685136\pi$
$272$	11.1921	+	7.83682i	0.678623	+	0.475177i
$273$	−0.515982	−	0.438960i	−0.0312286	−	0.0265671i
$274$	−1.51183	−	4.15372i	−0.0913330	−	0.250935i
$275$	0.252954	+	0.173034i	0.0152537	+	0.0104343i
$276$	−20.5769	−	5.66346i	−1.23858	−	0.340900i
$277$	2.18829	+	4.69280i	0.131481	+	0.281963i	0.961016	−	0.276492i	$-0.0891721\pi$
$277$	2.18829	+	4.69280i	0.131481	+	0.281963i	−0.829535	+	0.558455i	$0.811394\pi$
$278$	0.0885694	−	0.330545i	0.00531204	−	0.0198248i
$279$	−0.668017	−	0.00906538i	−0.0399931	−	0.000542730i
$280$	13.1223	−	4.21638i	0.784209	−	0.251977i
$281$	−4.92653	−	5.87122i	−0.293892	−	0.350247i	0.598812	−	0.800889i	$-0.295640\pi$
$281$	−4.92653	−	5.87122i	−0.293892	−	0.350247i	−0.892705	+	0.450642i	$0.851195\pi$
$282$	−0.271605	+	0.730764i	−0.0161739	+	0.0435164i
$283$	5.43511	+	7.76215i	0.323084	+	0.461412i	0.947535	−	0.319652i	$-0.103566\pi$
$283$	5.43511	+	7.76215i	0.323084	+	0.461412i	−0.624451	+	0.781064i	$0.714677\pi$
$284$	2.40758	−	13.6541i	0.142863	−	0.810219i
$285$	3.71153	+	7.15288i	0.219852	+	0.423700i
$286$	−0.00119939	+	0.00100641i	−7.09216e−5	+	5.95103e-5i
$287$	−2.87169	−	10.7173i	−0.169511	−	0.632622i
$288$	10.3781	+	2.93230i	0.611536	+	0.172788i
$289$	0.661319	−	0.381813i	0.0389011	−	0.0224596i
$290$	1.52370	−	4.92620i	0.0894747	−	0.289277i
$291$	−4.51094	+	16.3895i	−0.264436	+	0.960767i
$292$	−1.09892	−	12.5607i	−0.0643096	−	0.735062i
$293$	7.74397	+	3.61107i	0.452408	+	0.210961i	0.635447	−	0.772144i	$-0.280816\pi$
$293$	7.74397	+	3.61107i	0.452408	+	0.210961i	−0.183039	+	0.983106i	$0.558594\pi$
$294$	−0.770752	−	9.55606i	−0.0449512	−	0.557321i
$295$	−2.19608	−	1.38225i	−0.127861	−	0.0804780i
$296$			8.21271i			0.477354i
$297$	0.314719	−	0.0489110i	0.0182619	−	0.00283811i
$298$	−4.09244	+	4.09244i	−0.237069	+	0.237069i
$299$	−0.0896526	−	0.508445i	−0.00518474	−	0.0294041i
$300$	14.8580	−	7.00339i	0.857827	−	0.404341i
$301$	−17.2677	+	6.28494i	−0.995295	+	0.362258i
$302$	3.05503	−	0.267281i	0.175797	−	0.0153803i
$303$	5.61491	+	3.29276i	0.322568	+	0.189164i
$304$	−2.41304	+	6.62976i	−0.138397	+	0.380243i
$305$	−15.7692	−	3.40570i	−0.902939	−	0.195010i
$306$	−2.53765	+	2.94223i	−0.145068	+	0.168196i
$307$	−20.4909	+	5.49053i	−1.16948	+	0.313361i	−0.790746	−	0.612145i	$-0.790307\pi$
$307$	−20.4909	+	5.49053i	−1.16948	+	0.313361i	−0.378734	+	0.925506i	$0.623640\pi$
$308$	0.569980	+	0.0498668i	0.0324776	+	0.00284142i
$309$	0.394896	−	4.18635i	0.0224649	−	0.238153i
$310$	0.158795	+	0.0200241i	0.00901892	+	0.00113729i
$311$	−19.3816	−	3.41750i	−1.09903	−	0.193788i	−0.405413	−	0.914134i	$-0.632872\pi$
$311$	−19.3816	−	3.41750i	−1.09903	−	0.193788i	−0.693616	+	0.720345i	$0.743983\pi$
$312$	0.0287846	+	0.169981i	0.00162960	+	0.00962330i
$313$	0.366189	−	4.18556i	0.0206983	−	0.236582i	−0.978798	−	0.204830i	$-0.934336\pi$
$313$	0.366189	−	4.18556i	0.0206983	−	0.236582i	0.999496	−	0.0317519i	$-0.0101087\pi$
$314$	−2.60572	+	4.51323i	−0.147049	+	0.254696i
$315$	−6.88401	−	32.2886i	−0.387870	−	1.81925i
$316$	5.83578	+	10.1079i	0.328288	+	0.568612i
$317$	15.1326	−	7.05644i	0.849930	−	0.396329i	0.0516863	−	0.998663i	$-0.483540\pi$
$317$	15.1326	−	7.05644i	0.849930	−	0.396329i	0.798244	+	0.602334i	$0.205763\pi$
$318$	−6.82948	−	0.0463379i	−0.382978	−	0.00259850i
$319$	0.282675	−	0.336879i	0.0158268	−	0.0188616i
$320$	11.6490	+	4.75082i	0.651201	+	0.265579i
$321$	2.15449	+	3.12180i	0.120252	+	0.174242i
$322$	5.89434	−	8.41799i	0.328479	−	0.469116i
$323$	−5.92840	−	5.92840i	−0.329865	−	0.329865i
$324$	6.27149	−	15.8764i	0.348416	−	0.882023i
$325$	0.307167	+	0.252078i	0.0170386	+	0.0139828i
$326$	−3.49972	+	0.617095i	−0.193831	+	0.0341777i
$327$	−0.438307	−	0.0803555i	−0.0242385	−	0.00444367i
$328$	−1.19333	+	2.55911i	−0.0658907	+	0.141303i
$329$	5.27951	+	4.43004i	0.291069	+	0.244236i
$330$	−0.0762344	+	0.00322737i	−0.00419656	+	0.000177661i
$331$	−12.4570	−	4.53397i	−0.684698	−	0.249210i	−0.0238345	−	0.999716i	$-0.507587\pi$
$331$	−12.4570	−	4.53397i	−0.684698	−	0.249210i	−0.660863	+	0.750506i	$0.729810\pi$
$332$	7.38454	+	1.97868i	0.405279	+	0.108594i
$333$	19.5718	+	1.98026i	1.07253	+	0.108518i
$334$	−3.64064	−	2.10192i	−0.199207	−	0.115012i
$335$	12.4715	−	11.5540i	0.681393	−	0.631261i
$336$	16.7390	−	23.5639i	0.913187	−	1.28551i
$337$	17.4071	−	12.1886i	0.948223	−	0.663953i	0.00637058	−	0.999980i	$-0.497972\pi$
$337$	17.4071	−	12.1886i	0.948223	−	0.663953i	0.941852	+	0.336027i	$0.109083\pi$
$338$	3.42111	−	2.39549i	0.186084	−	0.130297i
$339$	−19.3992	−	1.82992i	−1.05362	−	0.0993875i
$340$	−12.5364	+	11.6140i	−0.679880	+	0.629860i
$341$	0.0118212	+	0.00682495i	0.000640152	+	0.000369592i
$342$	−1.80667	−	0.872501i	−0.0976934	−	0.0471795i
$343$	−48.5880	−	13.0191i	−2.62350	−	0.702966i
$344$	4.39446	+	1.59945i	0.236934	+	0.0862368i
$345$	11.6475	−	22.3025i	0.627080	−	1.20073i
$346$	−5.60222	−	4.70082i	−0.301177	−	0.252718i
$347$	−13.3295	+	28.5852i	−0.715565	+	1.53453i	0.124603	+	0.992207i	$0.460234\pi$
$347$	−13.3295	+	28.5852i	−0.715565	+	1.53453i	−0.840168	+	0.542327i	$0.817544\pi$
$348$	−7.91085	−	22.2024i	−0.424066	−	1.19018i
$349$	16.6978	−	2.94427i	0.893813	−	0.157603i	0.292168	−	0.956367i	$-0.405623\pi$
$349$	16.6978	−	2.94427i	0.893813	−	0.157603i	0.601645	+	0.798764i	$0.294512\pi$
$350$	0.775353	+	7.87116i	0.0414444	+	0.420731i
$351$	0.412024	−	0.0276105i	0.0219922	−	0.00147374i
$352$	−0.155806	−	0.155806i	−0.00830448	−	0.00830448i
$353$	10.9094	−	15.5802i	0.580648	−	0.829252i	−0.416143	−	0.909299i	$-0.636618\pi$
$353$	10.9094	−	15.5802i	0.580648	−	0.829252i	0.996791	+	0.0800474i	$0.0255072\pi$
$354$	0.643954	−	0.0519386i	0.0342258	−	0.00276051i
$355$	15.1352	+	6.17260i	0.803294	+	0.327607i
$356$	−12.8098	+	15.2661i	−0.678918	+	0.809103i
$357$	16.9717	+	29.8620i	0.898240	+	1.58047i
$358$	−5.30835	+	2.47532i	−0.280555	+	0.130825i
$359$	15.6916	+	27.1786i	0.828170	+	1.43443i	0.899473	+	0.436977i	$0.143951\pi$
$359$	15.6916	+	27.1786i	0.828170	+	1.43443i	−0.0713028	+	0.997455i	$0.522716\pi$
$360$	−3.93982	+	7.42079i	−0.207647	+	0.391110i
$361$	−7.33536	+	12.7052i	−0.386072	+	0.668696i
$362$	−0.346699	+	3.96279i	−0.0182221	+	0.208280i
$363$	17.8528	+	6.63541i	0.937030	+	0.348269i
$364$	0.730562	+	0.128818i	0.0382919	+	0.00675189i
$365$	14.7480	+	1.85974i	0.771947	+	0.0973430i
$366$	3.65167	−	1.67273i	0.190876	−	0.0874351i
$367$	17.8579	+	1.56237i	0.932177	+	0.0815549i	0.543117	−	0.839657i	$-0.317244\pi$
$367$	17.8579	+	1.56237i	0.932177	+	0.0815549i	0.389060	+	0.921212i	$0.372800\pi$
$368$	21.2778	−	5.70137i	1.10918	−	0.297204i
$369$	5.81088	+	3.46089i	0.302503	+	0.180167i
$370$	−4.60655	−	0.994887i	−0.239483	−	0.0517217i
$371$	−20.6497	+	56.7346i	−1.07208	+	2.94551i
$372$	0.636036	−	0.361484i	0.0329769	−	0.0187421i
$373$	−5.04230	+	0.441145i	−0.261081	+	0.0228416i	−0.216945	−	0.976184i	$-0.569609\pi$
$373$	−5.04230	+	0.441145i	−0.261081	+	0.0228416i	−0.0441361	+	0.999026i	$0.514054\pi$
$374$	0.0745975	−	0.0271513i	0.00385734	−	0.00140396i
$375$	4.37261	+	18.8648i	0.225801	+	0.974174i
$376$	−0.304566	−	1.72728i	−0.0157068	−	0.0890775i
$377$	0.403177	−	0.403177i	0.0207647	−	0.0207647i
$378$	6.18769	+	5.41048i	0.318261	+	0.278285i
$379$		−	9.89195i		−	0.508115i	−0.967189	−	0.254058i	$-0.918235\pi$
$379$		−	9.89195i		−	0.508115i	0.967189	−	0.254058i	$-0.0817653\pi$
$380$	−7.46828	−	4.70068i	−0.383114	−	0.241140i
$381$	−12.1063	−	5.74558i	−0.620224	−	0.294355i
$382$	3.57599	+	1.66751i	0.182963	+	0.0853173i
$383$	−1.67206	−	19.1117i	−0.0854380	−	0.976561i	−0.911043	−	0.412312i	$-0.864721\pi$
$383$	−1.67206	−	19.1117i	−0.0854380	−	0.976561i	0.825605	−	0.564249i	$-0.190834\pi$
$384$	−15.0809	+	3.93145i	−0.769595	+	0.200626i
$385$	−0.199320	+	0.644413i	−0.0101583	+	0.0328423i
$386$	4.93689	−	2.85032i	0.251281	−	0.145077i
$387$	4.87127	−	10.0868i	0.247621	−	0.512742i
$388$	−4.81785	−	17.9805i	−0.244589	−	0.912819i
$389$	5.65836	−	4.74792i	0.286890	−	0.240729i	−0.487973	−	0.872859i	$-0.662263\pi$
$389$	5.65836	−	4.74792i	0.286890	−	0.240729i	0.774863	+	0.632130i	$0.217819\pi$
$390$	−0.0988305	−	0.00444611i	−0.00500447	−	0.000225138i
$391$	−4.54562	+	25.7795i	−0.229882	+	1.30373i
$392$	12.3713	+	17.6680i	0.624843	+	0.892368i
$393$	−15.7132	+	2.66087i	−0.792629	+	0.134223i
$394$	1.88249	+	2.24346i	0.0948384	+	0.113024i
$395$	−13.1003	+	4.20931i	−0.659149	+	0.211793i
$396$	−0.270192	+	0.220540i	−0.0135777	+	0.0110826i
$397$	3.34227	−	12.4735i	0.167744	−	0.626028i	−0.829931	−	0.557866i	$-0.811620\pi$
$397$	3.34227	−	12.4735i	0.167744	−	0.626028i	0.997674	−	0.0681611i	$-0.0217132\pi$
$398$	1.47187	+	3.15644i	0.0737783	+	0.158218i
$399$	−12.6263	+	12.4561i	−0.632105	+	0.623585i
$400$	−9.57219	+	13.9934i	−0.478610	+	0.699668i
$401$	−2.92360	−	8.03253i	−0.145998	−	0.401125i	0.845041	−	0.534702i	$-0.179576\pi$
$401$	−2.92360	−	8.03253i	−0.145998	−	0.401125i	−0.991039	+	0.133576i	$0.957354\pi$
$402$	−0.763270	+	4.16334i	−0.0380684	+	0.207648i
$403$	0.0144972	+	0.0101511i	0.000722158	+	0.000505660i
$404$	−7.12791			−0.354627
$405$	16.7345	+	11.1783i	0.831546	+	0.555455i
$406$	11.3491			0.563248
$407$	−0.329237	−	0.230534i	−0.0163197	−	0.0114272i
$408$	1.57627	−	8.59791i	0.0780368	−	0.425660i
$409$	−4.56883	−	12.5528i	−0.225914	−	0.620694i	0.774008	−	0.633176i	$-0.218249\pi$
$409$	−4.56883	−	12.5528i	−0.225914	−	0.620694i	−0.999922	+	0.0124819i	$0.996027\pi$
$410$	−1.29086	−	0.979355i	−0.0637508	−	0.0483669i
$411$	16.9572	−	16.7286i	0.836436	−	0.825162i
$412$	1.94600	+	4.17321i	0.0958725	+	0.205599i
$413$	1.47817	−	5.51659i	0.0727359	−	0.271454i
$414$	1.00397	+	6.18329i	0.0493423	+	0.303892i
$415$	−4.11801	+	8.01721i	−0.202145	+	0.393550i
$416$	−0.183635	−	0.218848i	−0.00900347	−	0.0107299i
$417$	1.81819	−	0.307891i	0.0890370	−	0.0150775i
$418$	0.0235122	+	0.0335789i	0.00115002	+	0.00164240i
$419$	−4.65475	+	26.3984i	−0.227399	+	1.28964i	0.630646	+	0.776071i	$0.282790\pi$
$419$	−4.65475	+	26.3984i	−0.227399	+	1.28964i	−0.858045	+	0.513574i	$0.828321\pi$
$420$	24.3889	+	26.6867i	1.19006	+	1.30218i
$421$	19.3371	−	16.2257i	0.942432	−	0.790794i	−0.0355751	−	0.999367i	$-0.511326\pi$
$421$	19.3371	−	16.2257i	0.942432	−	0.790794i	0.978007	+	0.208573i	$0.0668818\pi$
$422$	−0.169066	−	0.630963i	−0.00823001	−	0.0307148i
$423$	−4.18972	+	0.309329i	−0.203711	+	0.0150401i
$424$	13.3065	−	7.68250i	0.646220	−	0.373095i
$425$	−10.2636	−	17.3369i	−0.497856	−	0.840964i
$426$	−3.93792	+	1.02658i	−0.190793	+	0.0497379i
$427$	−3.09467	−	35.3722i	−0.149762	−	1.71178i
$428$	−3.76447	−	1.75540i	−0.181962	−	0.0848504i
$429$	−0.00762233	−	0.00361751i	−0.000368010	−	0.000174655i
$430$	−1.42949	+	2.27112i	−0.0689360	+	0.109523i
$431$			23.0274i			1.10919i	0.832121	+	0.554595i	$0.187127\pi$
$431$			23.0274i			1.10919i	−0.832121	+	0.554595i	$0.812873\pi$
$432$	2.70575	+	17.4102i	0.130180	+	0.837648i
$433$	12.8672	−	12.8672i	0.618357	−	0.618357i	−0.326752	−	0.945110i	$-0.605954\pi$
$433$	12.8672	−	12.8672i	0.618357	−	0.618357i	0.945110	+	0.326752i	$0.105954\pi$
$434$	0.0611705	+	0.346915i	0.00293628	+	0.0166525i
$435$	27.5541	−	3.59047i	1.32112	−	0.172150i
$436$	0.458542	−	0.166896i	0.0219602	−	0.00799285i
$437$	−13.4658	+	1.17810i	−0.644154	+	0.0563562i
$438$	−3.21754	+	1.82865i	−0.153740	+	0.0873765i
$439$	10.8870	−	29.9118i	0.519609	−	1.42761i	−0.351343	−	0.936247i	$-0.614275\pi$
$439$	10.8870	−	29.9118i	0.519609	−	1.42761i	0.870952	−	0.491367i	$-0.163503\pi$
$440$	0.144273	−	0.0930233i	0.00687793	−	0.00443471i
$441$	45.0876	−	25.2219i	2.14703	−	1.20104i
$442$	0.0994197	−	0.0266394i	0.00472891	−	0.00126711i
$443$	−8.95244	−	0.783237i	−0.425343	−	0.0372127i	−0.127525	−	0.991835i	$-0.540703\pi$
$443$	−8.95244	−	0.783237i	−0.425343	−	0.0372127i	−0.297818	+	0.954623i	$0.596259\pi$
$444$	−19.5846	+	8.97119i	−0.929445	+	0.425754i
$445$	−14.4040	−	18.5609i	−0.682817	−	0.879873i
$446$	−0.862251	−	0.152038i	−0.0408288	−	0.00719922i
$447$	−29.2341	−	10.8655i	−1.38272	−	0.513922i
$448$	−2.41327	+	27.5838i	−0.114016	+	1.30321i
$449$	5.30209	−	9.18349i	0.250221	−	0.433396i	−0.713365	−	0.700792i	$-0.752830\pi$
$449$	5.30209	−	9.18349i	0.250221	−	0.433396i	0.963587	+	0.267396i	$0.0861633\pi$
$450$	−3.68509	−	3.10882i	−0.173717	−	0.146551i
$451$	−0.0690940	−	0.119674i	−0.00325351	−	0.00563524i
$452$	19.3383	−	9.01760i	0.909598	−	0.424152i
$453$	8.16560	+	14.3675i	0.383653	+	0.675043i
$454$	−2.92752	+	3.48888i	−0.137395	+	0.163741i
$455$	−0.330266	+	0.809812i	−0.0154831	+	0.0379646i
$456$	4.49911	−	0.362879i	0.210690	−	0.0169934i
$457$	−19.0820	+	27.2519i	−0.892617	+	1.27479i	0.0682185	+	0.997670i	$0.478268\pi$
$457$	−19.0820	+	27.2519i	−0.892617	+	1.27479i	−0.960836	+	0.277119i	$0.910620\pi$
$458$	3.01343	+	3.01343i	0.140808	+	0.140808i
$459$	−20.1097	−	5.82955i	−0.938639	−	0.272100i
$460$	1.35213	+	27.5192i	0.0630432	+	1.28309i
$461$	7.72166	−	1.36154i	0.359634	−	0.0634131i	0.00908790	−	0.999959i	$-0.497107\pi$
$461$	7.72166	−	1.36154i	0.359634	−	0.0634131i	0.350546	+	0.936546i	$0.385996\pi$
$462$	−0.0563663	−	0.158196i	−0.00262240	−	0.00735997i
$463$	−7.47769	+	16.0360i	−0.347518	+	0.745254i	−0.999920	−	0.0126183i	$-0.995983\pi$
$463$	−7.47769	+	16.0360i	−0.347518	+	0.745254i	0.652403	+	0.757873i	$0.273761\pi$
$464$	18.6361	+	15.6375i	0.865159	+	0.725955i
$465$	0.258265	+	0.822909i	0.0119768	+	0.0381615i
$466$	−2.04945	−	0.745938i	−0.0949388	−	0.0345549i
$467$	−15.2854	−	4.09572i	−0.707325	−	0.189527i	−0.112816	−	0.993616i	$-0.535987\pi$
$467$	−15.2854	−	4.09572i	−0.707325	−	0.189527i	−0.594509	+	0.804089i	$0.702654\pi$
$468$	−0.373907	+	0.254322i	−0.0172839	+	0.0117560i
$469$	32.4052	+	18.7092i	1.49633	+	0.863909i
$470$	1.00573	+	0.0384096i	0.0463911	+	0.00177170i
$471$	−27.9591	−	2.63738i	−1.28829	−	0.121524i
$472$	−1.19059	+	0.833661i	−0.0548014	+	0.0383724i
$473$	−0.187475	+	0.131271i	−0.00862009	+	0.00603585i
$474$	1.98396	−	2.79286i	0.0911262	−	0.128280i
$475$	7.27557	−	7.43627i	0.333826	−	0.341199i
$476$	−32.5737	−	18.8064i	−1.49301	−	0.861991i
$477$	−15.0997	−	33.5632i	−0.691370	−	1.53675i
$478$	5.66800	+	1.51874i	0.259248	+	0.0694654i
$479$	−25.2585	−	9.19333i	−1.15409	−	0.420054i	−0.307106	−	0.951675i	$-0.599361\pi$
$479$	−25.2585	−	9.19333i	−1.15409	−	0.420054i	−0.846982	+	0.531621i	$0.821583\pi$
$480$	−0.588883	−	13.9102i	−0.0268787	−	0.634909i
$481$	−0.399198	−	0.334967i	−0.0182019	−	0.0152732i
$482$	2.16595	−	4.64490i	0.0986564	−	0.211569i
$483$	54.4698	+	9.98602i	2.47846	+	0.454380i
$484$	−20.5396	+	3.62169i	−0.933619	+	0.164622i
$485$	21.9191	−	1.07697i	0.995293	−	0.0489026i
$486$	−5.00328	+	0.267139i	−0.226954	+	0.0121177i
$487$	−12.2573	−	12.2573i	−0.555433	−	0.555433i	0.372571	−	0.928004i	$-0.378476\pi$
$487$	−12.2573	−	12.2573i	−0.555433	−	0.555433i	−0.928004	+	0.372571i	$0.878476\pi$
$488$	−5.18299	+	7.40208i	−0.234623	+	0.335076i
$489$	−10.8774	−	15.7610i	−0.491892	−	0.712739i
$490$	−11.4087	+	4.79881i	−0.515393	+	0.216788i
$491$	8.64628	−	10.3042i	0.390201	−	0.465024i	−0.534805	−	0.844976i	$-0.679615\pi$
$491$	8.64628	−	10.3042i	0.390201	−	0.465024i	0.925006	+	0.379952i	$0.124059\pi$
$492$	−7.40617	−	0.0502507i	−0.333896	−	0.00226548i
$493$	−26.2010	+	12.2177i	−1.18003	+	0.550258i
$494$	0.0265743	+	0.0460281i	0.00119563	+	0.00207090i
$495$	−0.186897	−	0.366247i	−0.00840041	−	0.0164616i
$496$	−0.377555	+	0.653944i	−0.0169527	+	0.0293630i
$497$	−3.13549	+	35.8388i	−0.140646	+	1.60759i
$498$	−0.374656	−	2.21246i	−0.0167887	−	0.0991425i
$499$	−37.5256	−	6.61678i	−1.67988	−	0.296208i	−0.749281	−	0.662252i	$-0.769601\pi$
$499$	−37.5256	−	6.61678i	−1.67988	−	0.296208i	−0.930597	+	0.366044i	$0.880712\pi$
$500$	−14.5805	−	15.3976i	−0.652061	−	0.688603i
$501$	2.12746	−	22.5535i	0.0950480	−	1.00762i
$502$	5.50954	+	0.482022i	0.245903	+	0.0215137i
$503$	18.4828	−	4.95246i	0.824109	−	0.220819i	0.177967	−	0.984036i	$-0.443048\pi$
$503$	18.4828	−	4.95246i	0.824109	−	0.220819i	0.646142	+	0.763217i	$0.276381\pi$
$504$	−18.1658	−	3.45791i	−0.809167	−	0.154028i
$505$	1.77398	−	8.21394i	0.0789411	−	0.365515i
$506$	0.0437748	−	0.120270i	0.00194603	−	0.00534666i
$507$	19.4137	+	11.3848i	0.862194	+	0.505619i
$508$	14.6185	−	1.27895i	0.648590	−	0.0567442i
$509$	22.8762	−	8.32625i	1.01397	−	0.369054i	0.219013	−	0.975722i	$-0.429716\pi$
$509$	22.8762	−	8.32625i	1.01397	−	0.369054i	0.794956	+	0.606667i	$0.207494\pi$
$510$	4.63167	+	1.92569i	0.205094	+	0.0852708i
$511$	5.68120	+	32.2197i	0.251322	+	1.42532i
$512$	14.6251	−	14.6251i	0.646346	−	0.646346i
$513$	0.220051	−	10.8094i	0.00971548	−	0.477245i
$514$		−	3.00939i		−	0.132739i
$515$	−5.29337	+	1.20388i	−0.233254	+	0.0530492i
$516$	0.986140	+	12.2265i	0.0434124	+	0.538243i
$517$	0.0777936	+	0.0362758i	0.00342136	+	0.00159541i
$518$	−0.904028	−	10.3331i	−0.0397207	−	0.454010i
$519$	10.4579	−	37.9962i	0.459049	−	1.66785i
$520$	0.196857	−	0.103848i	0.00863276	−	0.00455402i
$521$	23.8927	−	13.7944i	1.04676	−	0.604345i	0.125017	−	0.992155i	$-0.460102\pi$
$521$	23.8927	−	13.7944i	1.04676	−	0.604345i	0.921739	+	0.387810i	$0.126768\pi$
$522$	−4.95778	+	4.82502i	−0.216996	+	0.211185i
$523$	3.35607	+	12.5250i	0.146751	+	0.547681i	0.999671	+	0.0256401i	$0.00816240\pi$
$523$	3.35607	+	12.5250i	0.146751	+	0.547681i	−0.852921	+	0.522041i	$0.825171\pi$
$524$	13.3689	−	11.2178i	0.584022	−	0.490053i
$525$	−36.8226	+	21.4631i	−1.60707	+	0.936729i
$526$	0.0509971	−	0.289219i	0.00222358	−	0.0126105i
$527$	−0.514685	−	0.735047i	−0.0224200	−	0.0320191i
$528$	0.125416	−	0.337435i	0.00545801	−	0.0146850i
$529$	12.3443	+	14.7114i	0.536709	+	0.639625i
$530$	2.69721	+	8.39434i	0.117159	+	0.364627i
$531$	1.69963	+	3.03832i	0.0737575	+	0.131852i
$532$	5.02685	−	18.7605i	0.217942	−	0.813369i
$533$	−0.0757196	−	0.162381i	−0.00327978	−	0.00703351i
$534$	5.63966	+	1.55223i	0.244052	+	0.0671715i
$535$	2.95975	−	3.90115i	0.127961	−	0.168661i
$536$	−3.25692	−	8.94831i	−0.140677	−	0.386508i
$537$	−24.0402	−	20.4517i	−1.03741	−	0.882555i
$538$	−7.28020	−	5.09765i	−0.313872	−	0.219775i
$539$	−1.05555			−0.0454659
$540$	−21.9998	−	1.28905i	−0.946721	−	0.0554718i
$541$	37.8477			1.62720			0.813600	−	0.581425i	$-0.197505\pi$
$541$	37.8477			1.62720			0.813600	+	0.581425i	$0.197505\pi$
$542$	−4.76236	−	3.33464i	−0.204561	−	0.143235i
$543$	−20.1927	+	7.19477i	−0.866552	+	0.308757i
$544$	4.95417	+	13.6115i	0.212408	+	0.583587i
$545$	0.0782032	+	0.569943i	0.00334986	+	0.0244137i
$546$	−0.0549272	−	0.210699i	−0.00235067	−	0.00901709i
$547$	−6.27224	−	13.4509i	−0.268182	−	0.575117i	0.725388	−	0.688340i	$-0.241660\pi$
$547$	−6.27224	−	13.4509i	−0.268182	−	0.575117i	−0.993570	+	0.113223i	$0.963883\pi$
$548$	−6.75109	+	25.1954i	−0.288392	+	1.07629i
$549$	16.3902	+	14.1364i	0.699517	+	0.603328i
$550$	0.0347001	+	0.0921921i	0.00147962	+	0.00393109i
$551$	−9.59560	−	11.4356i	−0.408786	−	0.487173i
$552$	−8.98539	−	10.8571i	−0.382443	−	0.462110i
$553$	−17.3708	−	24.8080i	−0.738680	−	1.05494i
$554$	−0.288999	+	1.63900i	−0.0122784	+	0.0696342i
$555$	−5.46389	−	24.8013i	−0.231929	−	1.05276i
$556$	−1.54692	+	1.29802i	−0.0656040	+	0.0550483i
$557$	3.75036	+	13.9965i	0.158908	+	0.593052i	0.998739	+	0.0502041i	$0.0159872\pi$
$557$	3.75036	+	13.9965i	0.158908	+	0.593052i	−0.839831	+	0.542847i	$0.817346\pi$
$558$	−0.174211	−	0.125541i	−0.00737494	−	0.00531457i
$559$	−0.256980	+	0.148367i	−0.0108691	+	0.00627527i
$560$	−35.6488	−	11.0263i	−1.50644	−	0.465948i
$561$	0.300433	+	0.304537i	0.0126843	+	0.0128576i
$562$	−0.214704	−	2.45408i	−0.00905674	−	0.103519i
$563$	−31.0550	−	14.4812i	−1.30881	−	0.610309i	−0.362025	−	0.932169i	$-0.617914\pi$
$563$	−31.0550	−	14.4812i	−1.30881	−	0.610309i	−0.946787	+	0.321859i	$0.895692\pi$
$564$	3.78630	−	2.61309i	0.159432	−	0.110031i
$565$	5.57867	+	24.5290i	0.234696	+	1.03194i
$566$			3.04570i			0.128020i
$567$	−12.6207	+	42.4572i	−0.530020	+	1.78303i
$568$	6.47388	−	6.47388i	0.271638	−	0.271638i
$569$	1.25548	+	7.12016i	0.0526323	+	0.298493i	0.999749	−	0.0223961i	$-0.00712951\pi$
$569$	1.25548	+	7.12016i	0.0526323	+	0.298493i	−0.947117	+	0.320889i	$0.896018\pi$
$570$	−0.341480	+	2.56753i	−0.0143030	+	0.107542i
$571$	25.3539	−	9.22807i	1.06103	−	0.386183i	0.248214	−	0.968705i	$-0.420156\pi$
$571$	25.3539	−	9.22807i	1.06103	−	0.386183i	0.812815	+	0.582522i	$0.197934\pi$
$572$	0.00920404		0.000805249i	0.000384840		3.36691e-5i
$573$	−0.144261	+	21.2618i	−0.00602659	+	0.888226i
$574$	1.21973	−	3.35118i	0.0509105	−	0.139876i
$575$	−32.0486	−	5.29079i	−1.33652	−	0.220641i
$576$	−10.6729	−	13.0758i	−0.444704	−	0.544824i
$577$	−6.14870	+	1.64754i	−0.255974	+	0.0685880i	−0.384524	−	0.923115i	$-0.625634\pi$
$577$	−6.14870	+	1.64754i	−0.255974	+	0.0685880i	0.128550	+	0.991703i	$0.458968\pi$
$578$	0.244509	+	0.0213918i	0.0101702	+	0.000889781i
$579$	25.0438	+	17.7903i	1.04078	+	0.739339i
$580$	−24.0389	+	18.6552i	−0.998161	+	0.774613i
$581$	−19.5357	−	3.44468i	−0.810479	−	0.142909i
$582$	−4.20921	+	3.48356i	−0.174477	+	0.144398i
$583$	−0.0655370	+	0.749091i	−0.00271426	+	0.0310242i
$584$	4.16304	−	7.21060i	0.172268	−	0.298377i
$585$	−0.200014	−	0.494171i	−0.00826954	−	0.0204315i
$586$	1.37318	+	2.37842i	0.0567256	+	0.0982517i
$587$	34.3204	−	16.0039i	1.41656	−	0.660550i	0.444603	−	0.895728i	$-0.353345\pi$
$587$	34.3204	−	16.0039i	1.41656	−	0.660550i	0.971952	+	0.235177i	$0.0755671\pi$
$588$	−28.6185	+	48.8011i	−1.18021	+	2.01252i
$589$	0.297839	−	0.354951i	0.0122722	−	0.0146255i
$590$	−0.323377	−	0.768799i	−0.0133132	−	0.0316509i
$591$	−6.76655	+	14.2575i	−0.278339	+	0.586477i
$592$	12.7531	−	18.2133i	0.524149	−	0.748563i
$593$	−3.48236	−	3.48236i	−0.143004	−	0.143004i	0.631981	−	0.774984i	$-0.282242\pi$
$593$	−3.48236	−	3.48236i	−0.143004	−	0.143004i	−0.774984	+	0.631981i	$0.782242\pi$
$594$	0.0918796	+	0.0451431i	0.00376987	+	0.00185225i
$595$	29.7787	−	32.8562i	1.22081	−	1.34697i
$596$	33.6337	−	5.93053i	1.37769	−	0.242924i
$597$	−12.1609	+	14.2947i	−0.497714	+	0.585045i
$598$	0.0701311	−	0.150397i	0.00286788	−	0.00615018i
$599$	−7.62357	−	6.39694i	−0.311491	−	0.261372i	0.473617	−	0.880731i	$-0.342948\pi$
$599$	−7.62357	−	6.39694i	−0.311491	−	0.261372i	−0.785108	+	0.619359i	$0.787392\pi$
$600$	10.6896	+	1.83929i	0.436401	+	0.0750889i
$601$	−16.6225	−	6.05010i	−0.678046	−	0.246789i	−0.0200379	−	0.999799i	$-0.506379\pi$
$601$	−16.6225	−	6.05010i	−0.678046	−	0.246789i	−0.658008	+	0.753011i	$0.728601\pi$
$602$	−5.70510	−	1.52868i	−0.232523	−	0.0623042i
$603$	−22.1101	+	5.60396i	−0.900392	+	0.228211i
$604$	−15.6721	−	9.04832i	−0.637691	−	0.368171i
$605$	0.938360	−	24.5704i	0.0381498	−	0.998930i
$606$	0.871303	+	1.90210i	0.0353943	+	0.0772677i
$607$	−11.9526	+	8.36932i	−0.485142	+	0.339700i	−0.790422	−	0.612563i	$-0.790139\pi$
$607$	−11.9526	+	8.36932i	−0.485142	+	0.339700i	0.305280	+	0.952263i	$0.401250\pi$
$608$	−6.12699	+	4.29017i	−0.248482	+	0.173989i
$609$	25.4698	+	55.6020i	1.03209	+	2.25311i
$610$	−3.52400	−	3.80385i	−0.142683	−	0.154014i
$611$	0.0963805	+	0.0556453i	0.00389914	+	0.00225117i
$612$	22.2250	−	5.63309i	0.898394	−	0.227704i
$613$	36.6597	+	9.82295i	1.48067	+	0.396745i	0.906576	−	0.422042i	$-0.138687\pi$
$613$	36.6597	+	9.82295i	1.48067	+	0.396745i	0.574097	+	0.818787i	$0.305353\pi$
$614$	−6.40729	−	2.33206i	−0.258577	−	0.0941143i
$615$	1.90114	−	8.52208i	0.0766613	−	0.343643i
$616$	0.289427	+	0.242858i	0.0116613	+	0.00978503i
$617$	−2.31069	+	4.95529i	−0.0930249	+	0.199493i	−0.947315	−	0.320305i	$-0.896215\pi$
$617$	−2.31069	+	4.95529i	−0.0930249	+	0.199493i	0.854290	+	0.519797i	$0.173993\pi$
$618$	0.875758	−	1.02942i	0.0352282	−	0.0414094i
$619$	35.6556	−	6.28705i	1.43312	−	0.252698i	0.597440	−	0.801913i	$-0.296184\pi$
$619$	35.6556	−	6.28705i	1.43312	−	0.252698i	0.835681	+	0.549215i	$0.185073\pi$
$620$	−0.699809	−	0.634261i	−0.0281050	−	0.0254726i
$621$	−28.0402	+	18.7952i	−1.12522	+	0.754227i
$622$	−4.47294	−	4.47294i	−0.179349	−	0.179349i
$623$	29.6596	−	42.3583i	1.18829	−	1.69705i
$624$	0.200120	−	0.421666i	0.00801121	−	0.0168801i
$625$	21.3724	−	12.9699i	0.854897	−	0.518797i
$626$	0.868056	−	1.03451i	0.0346945	−	0.0413473i
$627$	−0.111745	+	0.190550i	−0.00446265	+	0.00760982i
$628$	27.8714	−	12.9967i	1.11219	−	0.518623i
$629$	13.2110	+	22.8821i	0.526756	+	0.912368i
$630$	4.14016	−	9.77039i	0.164948	−	0.389261i
$631$	8.04151	−	13.9283i	0.320128	−	0.554477i	−0.660387	−	0.750926i	$-0.729608\pi$
$631$	8.04151	−	13.9283i	0.320128	−	0.554477i	0.980514	+	0.196449i	$0.0629409\pi$
$632$	−0.671730	+	7.67791i	−0.0267200	+	0.305411i
$633$	2.71182	−	2.24431i	0.107785	−	0.0892032i
$634$	5.28517	+	0.931918i	0.209901	+	0.0370112i
$635$	−2.16440	+	17.1641i	−0.0858916	+	0.681135i
$636$	32.8556	+	23.3396i	1.30281	+	0.925474i
$637$	−1.36337	−	0.119280i	−0.0540188	−	0.00472603i
$638$	0.136532	−	0.0365836i	0.00540535	−	0.00144836i
$639$	−13.8670	−	16.9889i	−0.548569	−	0.672072i
$640$	10.9030	+	16.9098i	0.430979	+	0.668418i
$641$	12.7590	−	35.0551i	0.503951	−	1.38459i	−0.383436	−	0.923567i	$-0.625259\pi$
$641$	12.7590	−	35.0551i	0.503951	−	1.38459i	0.887387	−	0.461026i	$-0.152518\pi$
$642$	−0.00827181	+	1.21914i	−0.000326462	+	0.0481155i
$643$	−14.3985	+	1.25970i	−0.567821	+	0.0496779i	−0.367452	−	0.930043i	$-0.619770\pi$
$643$	−14.3985	+	1.25970i	−0.567821	+	0.0496779i	−0.200369	+	0.979720i	$0.564214\pi$
$644$	−56.9844	+	20.7406i	−2.24550	+	0.817295i
$645$	−14.3348	−	1.90652i	−0.564433	−	0.0750692i
$646$	−0.467943	−	2.65384i	−0.0184110	−	0.104414i
$647$	18.6385	−	18.6385i	0.732757	−	0.732757i	−0.238408	−	0.971165i	$-0.576626\pi$
$647$	18.6385	−	18.6385i	0.732757	−	0.732757i	0.971165	+	0.238408i	$0.0766256\pi$
$648$	9.40569	−	6.21252i	0.369491	−	0.244051i
$649$		−	0.0711305i		−	0.00279212i
$650$	0.0344015	+	0.122998i	0.00134934	+	0.00482439i
$651$	−1.56234	+	1.07824i	−0.0612328	+	0.0422595i
$652$	19.0057	+	8.86250i	0.744320	+	0.347082i
$653$	1.32123	+	15.1018i	0.0517038	+	0.590977i	0.977214	+	0.212255i	$0.0680809\pi$
$653$	1.32123	+	15.1018i	0.0517038	+	0.590977i	−0.925510	+	0.378722i	$0.876364\pi$
$654$	−0.100588	−	0.101962i	−0.00393330	−	0.00398704i
$655$	9.59978	+	18.1977i	0.375094	+	0.711042i
$656$	6.62035	−	3.82226i	0.258481	−	0.149234i
$657$	−16.1798	−	11.6596i	−0.631235	−	0.454884i
$658$	0.573332	+	2.13970i	0.0223508	+	0.0834144i
$659$	14.6857	−	12.3228i	0.572075	−	0.480028i	−0.310258	−	0.950652i	$-0.600416\pi$
$659$	14.6857	−	12.3228i	0.572075	−	0.480028i	0.882334	+	0.470624i	$0.155971\pi$
$660$	0.379427	+	0.242428i	0.0147692	+	0.00943651i
$661$	3.24511	−	18.4039i	0.126220	−	0.715829i	−0.854356	−	0.519689i	$-0.826048\pi$
$661$	3.24511	−	18.4039i	0.126220	−	0.715829i	0.980576	−	0.196141i	$-0.0628409\pi$
$662$	−2.44393	−	3.49029i	−0.0949860	−	0.135654i
$663$	0.353631	+	0.427296i	0.0137339	+	0.0165948i
$664$	3.24502	+	3.86726i	0.125931	+	0.150079i
$665$	20.3678	+	10.4618i	0.789828	+	0.405692i
$666$	4.78798	+	4.12959i	0.185530	+	0.160018i
$667$	−12.0634	+	45.0214i	−0.467099	+	1.74324i
$668$	10.4839	+	22.4827i	0.405633	+	0.869883i
$669$	−1.19020	−	4.56557i	−0.0460158	−	0.176515i
$670$	5.41370	−	0.742827i	0.209149	−	0.0286979i
$671$	−0.151251	−	0.415559i	−0.00583898	−	0.0160425i
$672$	28.8654	−	10.2849i	1.11351	−	0.396749i
$673$	6.71034	+	4.69863i	0.258665	+	0.181119i	0.695715	−	0.718318i	$-0.255088\pi$
$673$	6.71034	+	4.69863i	0.258665	+	0.181119i	−0.437050	+	0.899437i	$0.643977\pi$
$674$	6.83016			0.263088
$675$	6.96072	−	25.0309i	0.267918	−	0.963442i
$676$	−24.6450			−0.947884
$677$	−32.8363	−	22.9922i	−1.26200	−	0.883663i	−0.265249	−	0.964180i	$-0.585454\pi$
$677$	−32.8363	−	22.9922i	−1.26200	−	0.883663i	−0.996753	+	0.0805166i	$0.974343\pi$
$678$	−4.77026	−	4.05819i	−0.183201	−	0.155854i
$679$	16.5199	+	45.3880i	0.633976	+	1.74183i
$680$	−11.1801	+	1.53405i	−0.428737	+	0.0588280i
$681$	−23.6628	−	6.51281i	−0.906759	−	0.249572i
$682$	0.00185416	+	0.00397627i	7.09996e−5	+	0.000152259i
$683$	−0.244432	+	0.912231i	−0.00935292	+	0.0349056i	−0.970445	−	0.241324i	$-0.922418\pi$
$683$	−0.244432	+	0.912231i	−0.00935292	+	0.0349056i	0.961092	+	0.276230i	$0.0890850\pi$
$684$	5.77997	+	10.3325i	0.221003	+	0.395073i
$685$	−27.3540	−	14.0503i	−1.04514	−	0.536834i
$686$	−10.3926	−	12.3854i	−0.396790	−	0.472876i
$687$	−8.00072	+	21.5262i	−0.305246	+	0.821277i
$688$	−7.26189	−	10.3710i	−0.276857	−	0.395393i
$689$	−0.169298	+	0.960134i	−0.00644972	+	0.0365782i
$690$	7.17831	−	3.72472i	0.273274	−	0.141798i
$691$	−19.0181	+	15.9581i	−0.723481	+	0.607073i	−0.928346	−	0.371717i	$-0.878769\pi$
$691$	−19.0181	+	15.9581i	−0.723481	+	0.607073i	0.204865	+	0.978790i	$0.434325\pi$
$692$	11.1694	+	41.6847i	0.424596	+	1.58461i
$693$	0.648544	−	0.631177i	0.0246361	−	0.0239764i
$694$	−8.77943	+	5.06881i	−0.333263	+	0.192409i
$695$	−1.11079	−	2.10566i	−0.0421348	−	0.0798722i
$696$	4.13019	−	15.0061i	0.156554	−	0.568804i
$697$	0.791748	+	9.04972i	0.0299896	+	0.342783i
$698$	4.93917	+	2.30317i	0.186950	+	0.0871763i
$699$	−0.944863	−	11.7148i	−0.0357380	−	0.443093i
$700$	22.8934	−	40.6721i	0.865290	−	1.53726i
$701$			30.1877i			1.14018i	0.821584	+	0.570088i	$0.193091\pi$
$701$			30.1877i			1.14018i	−0.821584	+	0.570088i	$0.806909\pi$
$702$	0.113572	+	0.0686903i	0.00428651	+	0.00259255i
$703$	−9.64747	+	9.64747i	−0.363861	+	0.363861i
$704$	0.0598837	+	0.339617i	0.00225695	+	0.0127998i
$705$	2.06890	+	5.01352i	0.0779193	+	0.188820i
$706$	5.74467	−	2.09089i	0.216204	−	0.0786917i
$707$	18.4249	−	1.61197i	0.692940	−	0.0606244i
$708$	−3.28856	−	1.92852i	−0.123591	−	0.0724781i
$709$	−17.1846	+	47.2142i	−0.645379	+	1.77317i	−0.0112523	+	0.999937i	$0.503582\pi$
$709$	−17.1846	+	47.2142i	−0.645379	+	1.77317i	−0.634127	+	0.773229i	$0.718640\pi$
$710$	2.84699	+	4.41548i	0.106846	+	0.165710i
$711$	18.1353	+	3.45211i	0.680127	+	0.129464i
$712$	−12.7113	+	3.40597i	−0.476374	+	0.127644i
$713$	−1.44121	−	0.126090i	−0.0539739	−	0.00472211i
$714$	−1.03680	+	10.9912i	−0.0388013	+	0.411337i
$715$	−0.00136274	+	0.0108068i	−5.09637e−5	+	0.000404151i
$716$	34.0378	+	6.00178i	1.27205	+	0.224297i
$717$	5.27953	+	31.1772i	0.197168	+	1.16433i
$718$	−0.879150	+	10.0487i	−0.0328096	+	0.375015i
$719$	6.68387	−	11.5768i	0.249266	−	0.431742i	−0.714056	−	0.700089i	$-0.753144\pi$
$719$	6.68387	−	11.5768i	0.249266	−	0.431742i	0.963322	+	0.268346i	$0.0864772\pi$
$720$	20.2607	−	10.3391i	0.755072	−	0.385316i
$721$	−5.97397	−	10.3472i	−0.222482	−	0.385351i
$722$	−4.27363	+	1.99283i	−0.159048	+	0.0741654i
$723$	27.6173	+	0.187383i	1.02710	+	0.00696884i
$724$	15.0887	−	17.9820i	0.560766	−	0.668295i
$725$	−15.5147	−	32.3444i	−0.576203	−	1.20124i
$726$	3.47718	+	5.03835i	0.129050	+	0.186991i
$727$	13.6862	−	19.5460i	0.507595	−	0.724920i	−0.480800	−	0.876830i	$-0.659654\pi$
$727$	13.6862	−	19.5460i	0.507595	−	0.724920i	0.988394	+	0.151910i	$0.0485425\pi$
$728$	0.346386	+	0.346386i	0.0128379	+	0.0128379i
$729$	−12.5372	−	23.9127i	−0.464340	−	0.885657i
$730$	3.54015	+	3.20856i	0.131027	+	0.118754i
$731$	14.8167	−	2.61258i	0.548014	−	0.0966296i
$732$	−23.3132	−	4.27404i	−0.861680	−	0.157973i
$733$	−9.86921	+	21.1646i	−0.364527	+	0.781732i	0.635427	+	0.772161i	$0.280824\pi$
$733$	−9.86921	+	21.1646i	−0.364527	+	0.781732i	−0.999954	+	0.00957046i	$0.996954\pi$
$734$	4.41379	+	3.70361i	0.162916	+	0.136703i
$735$	−49.1140	−	45.1244i	−1.81160	−	1.66444i
$736$	21.9452	+	7.98740i	0.808910	+	0.294419i
$737$	0.450149	+	0.120617i	0.0165815	+	0.00444299i
$738$	0.891907	+	1.98250i	0.0328316	+	0.0729768i
$739$	−3.52276	−	2.03387i	−0.129587	−	0.0748169i	0.433805	−	0.901007i	$-0.357171\pi$
$739$	−3.52276	−	2.03387i	−0.129587	−	0.0748169i	−0.563392	+	0.826190i	$0.690504\pi$
$740$	18.8999	+	20.4008i	0.694774	+	0.749949i
$741$	−0.165864	+	0.233490i	−0.00609316	+	0.00857748i
$742$	−15.8963	+	11.1307i	−0.583572	+	0.408622i
$743$	−41.2248	+	28.8659i	−1.51239	+	1.05899i	−0.535683	+	0.844419i	$0.679946\pi$
$743$	−41.2248	+	28.8659i	−1.51239	+	1.05899i	−0.976709	+	0.214569i	$0.931165\pi$
$744$	0.480960	+	0.0453688i	0.0176329	+	0.00166330i
$745$	−1.53657	+	40.2342i	−0.0562955	+	1.47407i
$746$	−1.40892	−	0.813439i	−0.0515842	−	0.0297821i
$747$	9.99853	−	6.80074i	0.365827	−	0.248826i
$748$	−0.452489	−	0.121244i	−0.0165447	−	0.00443313i
$749$	10.1277	+	3.68619i	0.370059	+	0.134691i
$750$	−2.32661	+	5.77304i	−0.0849556	+	0.210802i
$751$	2.00167	+	1.67960i	0.0730419	+	0.0612895i	0.678578	−	0.734529i	$-0.262597\pi$
$751$	2.00167	+	1.67960i	0.0730419	+	0.0612895i	−0.605536	+	0.795818i	$0.707041\pi$
$752$	−2.00677	+	4.30353i	−0.0731793	+	0.156933i
$753$	10.0030	+	28.0743i	0.364530	+	1.02308i
$754$	0.180481	−	0.0318237i	0.00657274	−	0.00115895i
$755$	14.3274	−	15.8081i	0.521427	−	0.575315i
$756$	−11.5975	−	47.0966i	−0.421796	−	1.71289i
$757$	28.7222	+	28.7222i	1.04393	+	1.04393i	0.998990	+	0.0449357i	$0.0143083\pi$
$757$	28.7222	+	28.7222i	1.04393	+	1.04393i	0.0449357	+	0.998990i	$0.485692\pi$
$758$	1.82366	−	2.60445i	0.0662383	−	0.0945980i
$759$	0.687472	−	0.0554486i	0.0249536	−	0.00201266i
$760$	−2.25934	−	5.37136i	−0.0819547	−	0.194840i
$761$	3.22815	−	3.84716i	0.117020	−	0.139459i	−0.704354	−	0.709849i	$-0.748763\pi$
$761$	3.22815	−	3.84716i	0.117020	−	0.139459i	0.821374	+	0.570389i	$0.193208\pi$
$762$	−2.12823	−	3.74464i	−0.0770975	−	0.135654i
$763$	−1.14754	+	0.535106i	−0.0415437	+	0.0193722i
$764$	−11.6417	−	20.1640i	−0.421182	−	0.729509i
$765$	0.960040	+	27.0132i	0.0347103	+	0.976666i
$766$	3.08315	−	5.34017i	0.111399	−	0.192948i
$767$	0.00803789	−	0.0918735i	0.000290231	−	0.00331736i
$768$	13.5732	+	5.04481i	0.489782	+	0.182039i
$769$	−41.2856	−	7.27976i	−1.48880	−	0.262515i	−0.630709	−	0.776019i	$-0.717236\pi$
$769$	−41.2856	−	7.27976i	−1.48880	−	0.262515i	−0.858087	+	0.513504i	$0.828347\pi$
$770$	−0.171282	+	0.132921i	−0.00617256	+	0.00479015i
$771$	14.7437	−	6.75370i	0.530982	−	0.243229i
$772$	−33.5115	−	2.93187i	−1.20610	−	0.105520i
$773$	−5.88204	+	1.57609i	−0.211562	+	0.0566879i	−0.363043	−	0.931772i	$-0.618262\pi$
$773$	−5.88204	+	1.57609i	−0.211562	+	0.0566879i	0.151481	+	0.988460i	$0.451596\pi$
$774$	3.14214	−	1.75770i	0.112942	−	0.0631793i
$775$	0.905066	−	0.648580i	0.0325109	−	0.0232977i
$776$	4.20415	−	11.5508i	0.150920	−	0.414650i
$777$	48.5954	−	27.6186i	1.74335	−	0.990813i
$778$	2.36511	−	0.206920i	0.0847932	−	0.00741844i
$779$	−4.40798	+	1.60437i	−0.157932	+	0.0574827i
$780$	0.462680	+	0.356001i	0.0165666	+	0.0127469i
$781$	0.0778050	+	0.441254i	0.00278408	+	0.0157893i
$782$	−5.94947	+	5.94947i	−0.212753	+	0.212753i
$783$	−34.7652	−	13.4610i	−1.24241	−	0.481056i
$784$		−	58.3929i		−	2.08546i
$785$	8.04028	+	35.3526i	0.286970	+	1.26179i
$786$	−4.62770	−	2.19628i	−0.165065	−	0.0783387i
$787$	−3.78582	−	1.76535i	−0.134950	−	0.0629281i	0.353971	−	0.935257i	$-0.384831\pi$
$787$	−3.78582	−	1.76535i	−0.134950	−	0.0629281i	−0.488920	+	0.872328i	$0.662609\pi$
$788$	−1.50622	−	17.2161i	−0.0536567	−	0.613299i
$789$	1.53140	−	0.399220i	0.0545192	−	0.0142126i
$790$	−4.22521	−	1.30688i	−0.150326	−	0.0464966i
$791$	−47.9482	+	27.6829i	−1.70484	+	0.984291i
$792$	−0.229684	+	0.0169577i	−0.00816146	+	0.000602564i
$793$	−0.148400	−	0.553835i	−0.00526983	−	0.0196673i
$794$	3.17958	−	2.66798i	0.112839	−	0.0946831i
$795$	−35.0727	+	32.0529i	−1.24390	+	1.13680i
$796$	3.56877	−	20.2395i	0.126492	−	0.717369i
$797$	−24.9660	−	35.6551i	−0.884339	−	1.26297i	−0.963934	−	0.266140i	$-0.914252\pi$
$797$	−24.9660	−	35.6551i	−0.884339	−	1.26297i	0.0795948	−	0.996827i	$-0.474637\pi$
$798$	−5.62076	+	0.951815i	−0.198973	+	0.0336939i
$799$	−3.62708	−	4.32258i	−0.128317	−	0.152922i
$800$	−16.8219	+	6.33158i	−0.594744	+	0.223855i
$801$	5.05184	+	31.1135i	0.178498	+	1.09934i
$802$	0.711104	−	2.65388i	0.0251100	−	0.0937116i
$803$	0.172205	+	0.369296i	0.00607699	+	0.0130322i
$804$	17.7811	−	17.5414i	0.627090	−	0.618638i
$805$	−9.71856	−	70.8286i	−0.342534	−	2.49638i
$806$	0.00194555	+	0.00534535i	6.85290e−5	+	0.000188282i
$807$	8.63629	−	47.1076i	0.304012	−	1.65826i
$808$	−3.85564	−	2.69975i	−0.135641	−	0.0949768i
$809$	16.9733			0.596751			0.298375	−	0.954449i	$-0.403555\pi$
$809$	16.9733			0.596751			0.298375	+	0.954449i	$0.403555\pi$
$810$	2.34523	+	6.02829i	0.0824031	+	0.211812i
$811$	−40.1642			−1.41036			−0.705178	−	0.709030i	$-0.749133\pi$
$811$	−40.1642			−1.41036			−0.705178	+	0.709030i	$0.749133\pi$
$812$	−54.8597	−	38.4131i	−1.92520	−	1.34804i
$813$	5.64945	−	30.8155i	0.198135	−	1.08075i
$814$	−0.0441841	−	0.121395i	−0.00154865	−	0.00425489i
$815$	−14.9429	+	19.6958i	−0.523427	+	0.689912i
$816$	−16.8469	+	16.6199i	−0.589761	+	0.581812i
$817$	3.28330	+	7.04105i	0.114868	+	0.246335i
$818$	1.11127	−	4.14732i	0.0388547	−	0.145008i
$819$	0.908996	−	0.741954i	0.0317629	−	0.0259260i
$820$	2.92497	+	9.10316i	0.102144	+	0.317896i
$821$	10.6701	+	12.7162i	0.372390	+	0.443797i	0.919397	−	0.393331i	$-0.128677\pi$
$821$	10.6701	+	12.7162i	0.372390	+	0.443797i	−0.547007	+	0.837128i	$0.684233\pi$
$822$	7.54871	−	1.27829i	0.263291	−	0.0445856i
$823$	−4.92823	−	7.03825i	−0.171787	−	0.245338i	0.724021	−	0.689778i	$-0.242292\pi$
$823$	−4.92823	−	7.03825i	−0.171787	−	0.245338i	−0.895809	+	0.444440i	$0.853403\pi$
$824$	−0.528001	+	2.99444i	−0.0183938	+	0.104316i
$825$	−0.373796	+	0.376902i	−0.0130139	+	0.0131221i
$826$	1.40621	−	1.17995i	0.0489285	−	0.0410558i
$827$	−2.40734	−	8.98430i	−0.0837113	−	0.312415i	0.911356	−	0.411620i	$-0.135037\pi$
$827$	−2.40734	−	8.98430i	−0.0837113	−	0.312415i	−0.995067	+	0.0992048i	$0.968370\pi$
$828$	16.0754	−	33.2870i	0.558660	−	1.15680i
$829$	36.4376	−	21.0373i	1.26553	−	0.730655i	0.291392	−	0.956604i	$-0.405882\pi$
$829$	36.4376	−	21.0373i	1.26553	−	0.730655i	0.974139	+	0.225949i	$0.0725483\pi$
$830$	−2.56227	+	1.35167i	−0.0889376	+	0.0469171i
$831$	−8.67839	+	2.26237i	−0.301050	+	0.0784808i
$832$	0.0389695	+	0.445423i	0.00135102	+	0.0154423i
$833$	62.8893	+	29.3257i	2.17898	+	1.01608i
$834$	0.535473	+	0.254132i	0.0185419	+	0.00879988i
$835$	−28.5174	+	6.48576i	−0.986887	+	0.224449i
$836$		−	0.241896i		−	0.00836613i
$837$	0.224088	−	1.13524i	0.00774563	−	0.0392396i
$838$	−6.09230	+	6.09230i	−0.210455	+	0.210455i
$839$	6.54601	+	37.1243i	0.225993	+	1.28167i	0.860777	+	0.508983i	$0.169978\pi$
$839$	6.54601	+	37.1243i	0.225993	+	1.28167i	−0.634783	+	0.772690i	$0.718911\pi$
$840$	3.08472	+	23.6729i	0.106433	+	0.816792i
$841$	−21.1193	+	7.68679i	−0.728251	+	0.265062i
$842$	8.08261	−	0.707136i	0.278545	−	0.0243695i
$843$	11.5413	−	6.55935i	0.397502	−	0.225916i
$844$	−1.31837	+	3.62220i	−0.0453803	+	0.124681i
$845$	6.13360	−	28.4000i	0.211002	−	0.976989i
$846$	−1.16014	−	0.690965i	−0.0398865	−	0.0237559i
$847$	52.2737	−	14.0067i	1.79615	−	0.481276i
$848$	−41.4395	−	3.62549i	−1.42304	−	0.124500i
$849$	−14.9216	+	6.83519i	−0.512108	+	0.234583i
$850$	0.493899	−	6.45681i	0.0169406	−	0.221467i
$851$	41.9518	+	7.39723i	1.43809	+	0.253574i
$852$	22.5099	+	8.36631i	0.771175	+	0.286625i
$853$	3.53555	−	40.4116i	0.121055	−	1.38367i	−0.656251	−	0.754543i	$-0.727859\pi$
$853$	3.53555	−	40.4116i	0.121055	−	1.38367i	0.777306	−	0.629123i	$-0.216586\pi$
$854$	5.70635	−	9.88369i	0.195267	−	0.338213i
$855$	−13.3453	+	4.08909i	−0.456400	+	0.139844i
$856$	−1.37141	−	2.37535i	−0.0468738	−	0.0811879i
$857$	−32.7821	+	15.2865i	−1.11982	+	0.522178i	−0.892231	−	0.451580i	$-0.850861\pi$
$857$	−32.7821	+	15.2865i	−1.11982	+	0.522178i	−0.227585	+	0.973758i	$0.573083\pi$
$858$	−0.00133997	−	0.00235769i	−4.57458e−5	−	8.04903e-5i
$859$	26.6915	−	31.8097i	0.910701	−	1.08533i	−0.0853324	−	0.996353i	$-0.527195\pi$
$859$	26.6915	−	31.8097i	0.910701	−	1.08533i	0.996034	−	0.0889788i	$-0.0283603\pi$
$860$	14.5969	−	6.13984i	0.497750	−	0.209367i
$861$	19.1555	−	1.54500i	0.652819	−	0.0526536i
$862$	−4.24528	+	6.06288i	−0.144595	+	0.206503i
$863$	−1.97436	−	1.97436i	−0.0672079	−	0.0672079i	0.672704	−	0.739912i	$-0.265133\pi$
$863$	−1.97436	−	1.97436i	−0.0672079	−	0.0672079i	−0.739912	+	0.672704i	$0.765133\pi$
$864$	−8.23707	+	16.7649i	−0.280231	+	0.570353i
$865$	−50.8156	+	2.49677i	−1.72778	+	0.0848927i
$866$	5.75997	−	1.01564i	0.195732	−	0.0345128i
$867$	0.443926	+	1.24591i	0.0150765	+	0.0423135i
$868$	0.878509	−	1.88397i	0.0298185	−	0.0639460i
$869$	−0.288942	−	0.242451i	−0.00980167	−	0.00822458i
$870$	7.91666	+	4.13448i	0.268400	+	0.140172i
$871$	0.567792	+	0.206659i	0.0192389	+	0.00700238i
$872$	0.311248	+	0.0833986i	0.0105402	+	0.00282423i
$873$	−26.5131	−	12.8041i	−0.897332	−	0.433353i
$874$	−3.76259	−	2.17233i	−0.127272	−	0.0734803i
$875$	41.1713	+	36.5039i	1.39185	+	1.23406i
$876$	21.7424	+	2.05096i	0.734609	+	0.0692954i
$877$	−31.0028	+	21.7084i	−1.04689	+	0.733042i	−0.964640	−	0.263570i	$-0.915100\pi$
$877$	−31.0028	+	21.7084i	−1.04689	+	0.733042i	−0.0822516	+	0.996612i	$0.526211\pi$
$878$	8.38093	−	5.86839i	0.282843	−	0.198049i
$879$	−8.57073	+	12.0652i	−0.289084	+	0.406949i
$880$	−0.464404	−	0.0177359i	−0.0156551	−	0.000597877i
$881$	−14.1727	−	8.18263i	−0.477491	−	0.275680i	0.241879	−	0.970306i	$-0.422236\pi$
$881$	−14.1727	−	8.18263i	−0.477491	−	0.275680i	−0.719370	+	0.694627i	$0.755570\pi$
$882$	16.5210	+	1.67158i	0.556291	+	0.0562851i
$883$	−0.812463	−	0.217699i	−0.0273416	−	0.00732615i	0.245122	−	0.969492i	$-0.421172\pi$
$883$	−0.812463	−	0.217699i	−0.0273416	−	0.00732615i	−0.272464	+	0.962166i	$0.587839\pi$
$884$	−0.570743	−	0.207734i	−0.0191962	−	0.00698683i
$885$	3.04080	−	3.30964i	0.102215	−	0.111252i
$886$	−2.21269	−	1.85667i	−0.0743369	−	0.0623761i
$887$	10.6634	−	22.8678i	0.358043	−	0.767825i	−0.641957	−	0.766741i	$-0.721877\pi$
$887$	10.6634	−	22.8678i	0.358043	−	0.767825i	0.999999	−	0.00108401i	$-0.000345052\pi$
$888$	−13.9916	−	2.56511i	−0.469529	−	0.0860793i
$889$	−37.4980	+	6.61191i	−1.25764	+	0.221756i
$890$	−0.370588	−	7.54241i	−0.0124221	−	0.252822i
$891$	−0.0149698	+	0.551450i	−0.000501506	+	0.0184743i
$892$	3.65337	+	3.65337i	0.122324	+	0.122324i
$893$	1.67126	−	2.38680i	0.0559265	−	0.0798714i
$894$	−5.69391	−	8.25032i	−0.190433	−	0.275932i
$895$	−15.3875	+	37.7301i	−0.514347	+	1.26118i
$896$	−28.4647	+	33.9229i	−0.950940	+	1.13329i
$897$	0.894217	+	0.00606725i	0.0298570	+	0.000202579i
$898$	3.08904	−	1.44044i	0.103083	−	0.0480682i
$899$	−0.798864	−	1.38367i	−0.0266436	−	0.0461481i
$900$	7.29072	+	27.5003i	0.243024	+	0.916678i
$901$	24.7162	−	42.8097i	0.823415	−	1.42620i
$902$	0.00387112	−	0.0442471i	0.000128894	−	0.00147327i
$903$	−5.31409	−	31.3813i	−0.176842	−	1.04430i
$904$	13.8760	+	2.44671i	0.461509	+	0.0813764i
$905$	16.9665	+	21.8629i	0.563986	+	0.726748i
$906$	−0.498835	+	5.28821i	−0.0165727	+	0.175689i
$907$	3.03079	+	0.265160i	0.100636	+	0.00880450i	0.137362	−	0.990521i	$-0.456138\pi$
$907$	3.03079	+	0.265160i	0.100636	+	0.00880450i	−0.0367266	+	0.999325i	$0.511693\pi$
$908$	25.9598	−	6.95591i	0.861507	−	0.230840i
$909$	−7.36347	+	8.53744i	−0.244231	+	0.283169i
$910$	−0.236251	+	0.152329i	−0.00783164	+	0.00504965i
$911$	−16.0677	+	44.1456i	−0.532346	+	1.46261i	0.323926	+	0.946082i	$0.394997\pi$
$911$	−16.0677	+	44.1456i	−0.532346	+	1.46261i	−0.856272	+	0.516526i	$0.827225\pi$
$912$	−10.5412	−	6.18168i	−0.349053	−	0.204696i
$913$	−0.246122	+	0.0215329i	−0.00814546	+	0.000712635i
$914$	−10.0482	+	3.65724i	−0.332365	+	0.120971i
$915$	10.7274	−	25.8015i	0.354636	−	0.852972i
$916$	−4.36689	−	24.7658i	−0.144286	−	0.818287i
$917$	−32.0203	+	32.0203i	−1.05740	+	1.05740i
$918$	−4.21995	−	5.24224i	−0.139279	−	0.173020i
$919$			57.4802i			1.89610i	0.318128	+	0.948048i	$0.396946\pi$
$919$			57.4802i			1.89610i	−0.318128	+	0.948048i	$0.603054\pi$
$920$	−9.69172	+	15.3979i	−0.319526	+	0.507653i
$921$	−2.95397	−	36.6244i	−0.0973367	−	1.20682i
$922$	2.28405	+	1.06507i	0.0752211	+	0.0350762i
$923$	0.0506318	+	0.578725i	0.00166657	+	0.0190490i
$924$	−0.262980	+	0.955475i	−0.00865140	+	0.0314328i
$925$	−28.2129	+	16.7022i	−0.927634	+	0.549166i
$926$	−4.92516	+	2.84354i	−0.161851	+	0.0934446i
$927$	7.00876	+	1.98030i	0.230198	+	0.0650417i
$928$	6.67526	+	24.9124i	0.219126	+	0.817790i
$929$	−40.6798	+	34.1344i	−1.33466	+	1.11991i	−0.351699	+	0.936113i	$0.614396\pi$
$929$	−40.6798	+	34.1344i	−1.33466	+	1.11991i	−0.982963	+	0.183802i	$0.941160\pi$
$930$	−0.0837111	+	0.264277i	−0.00274499	+	0.00866599i
$931$	−6.22206	+	35.2871i	−0.203920	+	1.15649i
$932$	7.38190	+	10.5424i	0.241802	+	0.345329i
$933$	11.8758	−	31.9522i	0.388795	−	1.04607i
$934$	−3.26943	−	3.89635i	−0.106979	−	0.127492i
$935$	0.252332	−	0.491257i	0.00825213	−	0.0160658i
$936$	−0.298580	−	0.00405191i	−0.00975941	−	0.000132441i
$937$	7.46943	−	27.8763i	0.244016	−	0.910679i	−0.729860	−	0.683597i	$-0.760415\pi$
$937$	7.46943	−	27.8763i	0.244016	−	0.910679i	0.973876	−	0.227082i	$-0.0729187\pi$
$938$	5.08280	+	10.9001i	0.165959	+	0.355901i
$939$	7.01639	+	1.93115i	0.228971	+	0.0630208i
$940$	−4.73154	−	3.58975i	−0.154326	−	0.117085i
$941$	4.85822	+	13.3478i	0.158373	+	0.435127i	0.993347	−	0.115163i	$-0.0367392\pi$
$941$	4.85822	+	13.3478i	0.158373	+	0.435127i	−0.834973	+	0.550291i	$0.814517\pi$
$942$	−6.87515	−	5.84888i	−0.224004	−	0.190567i
$943$	11.9975	+	8.40071i	0.390691	+	0.273565i
$944$	3.93492			0.128071
$945$	57.1588	−	1.64318i	1.85937	−	0.0534527i
$946$	−0.0735611			−0.00239168
$947$	1.66453	+	1.16551i	0.0540898	+	0.0378741i	0.600309	−	0.799768i	$-0.295044\pi$
$947$	1.66453	+	1.16551i	0.0540898	+	0.0378741i	−0.546219	+	0.837643i	$0.683933\pi$
$948$	−19.0431	+	6.78514i	−0.618490	+	0.220371i
$949$	0.180693	+	0.496449i	0.00586553	+	0.0161154i
$950$	3.28652	−	0.616588i	0.106629	−	0.0200047i
$951$	7.29534	+	27.9847i	0.236567	+	0.907466i
$952$	−10.4967	−	22.5103i	−0.340201	−	0.729564i
$953$	−6.21202	+	23.1836i	−0.201227	+	0.750990i	0.789339	+	0.613957i	$0.210423\pi$
$953$	−6.21202	+	23.1836i	−0.201227	+	0.750990i	−0.990567	+	0.137033i	$0.956243\pi$
$954$	2.21202	−	11.6206i	0.0716168	−	0.376231i
$955$	26.1336	−	8.39708i	0.845664	−	0.271723i
$956$	−22.2577	−	26.5257i	−0.719865	−	0.857901i
$957$	0.485638	+	0.586801i	0.0156984	+	0.0189686i
$958$	−4.95544	−	7.07711i	−0.160103	−	0.228651i
$959$	11.7529	−	66.6543i	0.379522	−	2.15238i
$960$	−11.7322	+	18.3621i	−0.378654	+	0.592635i
$961$	−23.7094	+	19.8945i	−0.764819	+	0.641759i
$962$	−0.0433512	−	0.161789i	−0.00139770	−	0.00521628i
$963$	−5.99139	+	2.69547i	−0.193070	+	0.0868603i
$964$	−26.1913	+	15.1216i	−0.843566	+	0.487033i
$965$	11.7188	−	37.8877i	0.377243	−	1.21965i
$966$	12.5004	+	12.6712i	0.402193	+	0.407688i
$967$	0.822697	+	9.40347i	0.0264561	+	0.302395i	0.997882	+	0.0650515i	$0.0207212\pi$
$967$	0.822697	+	9.40347i	0.0264561	+	0.302395i	−0.971426	+	0.237344i	$0.923723\pi$
$968$	−12.4821	−	5.82048i	−0.401189	−	0.187077i
$969$	11.9516	−	8.24832i	0.383941	−	0.264974i
$970$	5.96962	+	3.75739i	0.191673	+	0.120643i
$971$		−	16.0188i		−	0.514066i	−0.966403	−	0.257033i	$-0.917255\pi$
$971$		−	16.0188i		−	0.514066i	0.966403	−	0.257033i	$-0.0827450\pi$
$972$	25.0892	+	15.6432i	0.804736	+	0.501756i
$973$	3.70508	−	3.70508i	0.118779	−	0.118779i
$974$	−0.967501	−	5.48697i	−0.0310007	−	0.175814i
$975$	−0.525393	+	0.444575i	−0.0168260	+	0.0142378i
$976$	22.9886	−	8.36718i	0.735848	−	0.267827i
$977$	15.7750	−	1.38013i	0.504687	−	0.0441544i	0.168030	−	0.985782i	$-0.446259\pi$
$977$	15.7750	−	1.38013i	0.504687	−	0.0441544i	0.336657	+	0.941627i	$0.390704\pi$
$978$	0.0417620	−	6.15506i	0.00133540	−	0.196817i
$979$	0.220269	−	0.605185i	0.00703984	−	0.0193418i
$980$	71.3901	+	15.4183i	2.28047	+	0.492518i
$981$	0.273796	−	0.721628i	0.00874164	−	0.0230398i
$982$	4.17615	−	1.11900i	0.133266	−	0.0357086i
$983$	43.2738	+	3.78597i	1.38022	+	0.120754i	0.752965	−	0.658060i	$-0.228623\pi$
$983$	43.2738	+	3.78597i	1.38022	+	0.120754i	0.627255	+	0.778814i	$0.284178\pi$
$984$	−3.98712	−	2.83232i	−0.127105	−	0.0902911i
$985$	20.2141	+	2.54901i	0.644074	+	0.0812181i
$986$	−9.15088	−	1.61355i	−0.291424	−	0.0513858i
$987$	−9.19623	+	7.61083i	−0.292719	+	0.242255i
$988$	0.0273347	−	0.312437i	0.000869633	−	0.00993995i
$989$	12.1284	−	21.0070i	0.385660	−	0.667982i
$990$	0.0183122	−	0.130885i	0.000582001	−	0.00415981i
$991$	−5.77036	−	9.99455i	−0.183301	−	0.317487i	0.759701	−	0.650272i	$-0.225345\pi$
$991$	−5.77036	−	9.99455i	−0.183301	−	0.317487i	−0.943003	+	0.332785i	$0.892012\pi$
$992$	−0.725532	+	0.338321i	−0.0230357	+	0.0107417i
$993$	11.6151	−	19.8063i	0.368593	−	0.628534i
$994$	−7.43270	+	8.85795i	−0.235751	+	0.280957i
$995$	22.4350	+	9.14967i	0.711238	+	0.290064i
$996$	−5.67743	+	11.9627i	−0.179896	+	0.379053i
$997$	−13.9430	+	19.9126i	−0.441579	+	0.630639i	−0.976821	−	0.214059i	$-0.931331\pi$
$997$	−13.9430	+	19.9126i	−0.441579	+	0.630639i	0.535242	+	0.844699i	$0.320220\pi$
$998$	−8.66028	−	8.66028i	−0.274136	−	0.274136i
$999$	−9.48660	+	32.7251i	−0.300143	+	1.03538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.10	yes	192
3.2	odd	2		405.2.r.a.152.7		192
5.2	odd	4		675.2.ba.b.68.7		192
5.3	odd	4	inner	135.2.q.a.68.10	yes	192
5.4	even	2		675.2.ba.b.257.7		192
15.8	even	4		405.2.r.a.233.7		192
27.2	odd	18	inner	135.2.q.a.2.10	✓	192
27.25	even	9		405.2.r.a.332.7		192
135.2	even	36		675.2.ba.b.218.7		192
135.29	odd	18		675.2.ba.b.407.7		192
135.83	even	36	inner	135.2.q.a.83.10	yes	192
135.133	odd	36		405.2.r.a.8.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.10	✓	192	27.2	odd	18	inner
135.2.q.a.68.10	yes	192	5.3	odd	4	inner
135.2.q.a.83.10	yes	192	135.83	even	36	inner
135.2.q.a.122.10	yes	192	1.1	even	1	trivial
405.2.r.a.8.7		192	135.133	odd	36
405.2.r.a.152.7		192	3.2	odd	2
405.2.r.a.233.7		192	15.8	even	4
405.2.r.a.332.7		192	27.25	even	9
675.2.ba.b.68.7		192	5.2	odd	4
675.2.ba.b.218.7		192	135.2	even	36
675.2.ba.b.257.7		192	5.4	even	2
675.2.ba.b.407.7		192	135.29	odd	18

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.263290 + 0.184358i) q^{2} +(-0.312334 + 1.70366i) q^{3} +(-0.648706 - 1.78231i) q^{4} +(2.21531 - 0.303968i) q^{5} +(-0.396317 + 0.390975i) q^{6} +(2.07991 + 4.46037i) q^{7} +(0.324162 - 1.20979i) q^{8} +(-2.80490 - 1.06422i) q^{9} +O(q^{10})\)	\(q+(0.263290 + 0.184358i) q^{2} +(-0.312334 + 1.70366i) q^{3} +(-0.648706 - 1.78231i) q^{4} +(2.21531 - 0.303968i) q^{5} +(-0.396317 + 0.390975i) q^{6} +(2.07991 + 4.46037i) q^{7} +(0.324162 - 1.20979i) q^{8} +(-2.80490 - 1.06422i) q^{9} +(0.639309 + 0.328378i) q^{10} +(0.0393995 + 0.0469545i) q^{11} +(3.23905 - 0.548499i) q^{12} +(0.0455832 + 0.0650996i) q^{13} +(-0.274686 + 1.55782i) q^{14} +(-0.174059 + 3.86907i) q^{15} +(-2.59752 + 2.17957i) q^{16} +(-1.04290 - 3.89214i) q^{17} +(-0.542304 - 0.797303i) q^{18} +(1.80193 - 1.04035i) q^{19} +(-1.97885 - 3.75118i) q^{20} +(-8.24857 + 2.15032i) q^{21} +(0.00171708 + 0.0196263i) q^{22} +(-5.88782 - 2.74553i) q^{23} +(1.95982 + 0.930119i) q^{24} +(4.81521 - 1.34677i) q^{25} +0.0255437i q^{26} +(2.68913 - 4.44619i) q^{27} +(6.60050 - 6.60050i) q^{28} +(-1.24585 - 7.06559i) q^{29} +(-0.759121 + 0.986599i) q^{30} +(0.209263 - 0.0761654i) q^{31} +(-3.58112 + 0.313308i) q^{32} +(-0.0923002 + 0.0524578i) q^{33} +(0.442962 - 1.21703i) q^{34} +(5.96345 + 9.24888i) q^{35} +(-0.0772105 + 5.68955i) q^{36} +(-6.33380 + 1.69714i) q^{37} +(0.666227 + 0.0582873i) q^{38} +(-0.125145 + 0.0573254i) q^{39} +(0.350383 - 2.77860i) q^{40} +(-2.22023 - 0.391486i) q^{41} +(-2.56820 - 0.954529i) q^{42} +(-0.325424 + 3.71962i) q^{43} +(0.0581286 - 0.100682i) q^{44} +(-6.53720 - 1.50498i) q^{45} +(-1.04404 - 1.80834i) q^{46} +(1.26917 - 0.591824i) q^{47} +(-2.90196 - 5.10603i) q^{48} +(-11.0694 + 13.1920i) q^{49} +(1.51608 + 0.533130i) q^{50} +(6.95660 - 0.561090i) q^{51} +(0.0864573 - 0.123474i) q^{52} +(8.67464 + 8.67464i) q^{53} +(1.52771 - 0.674876i) q^{54} +(0.101555 + 0.0920427i) q^{55} +(6.07034 - 1.07036i) q^{56} +(1.20959 + 3.39481i) q^{57} +(0.974575 - 2.08998i) q^{58} +(-0.888968 - 0.745933i) q^{59} +(7.00878 - 2.19966i) q^{60} +(-6.77967 - 2.46760i) q^{61} +(0.0691385 + 0.0185256i) q^{62} +(-1.08710 - 14.7243i) q^{63} +(4.87243 + 2.81310i) q^{64} +(0.120769 + 0.130360i) q^{65} +(-0.0339728 - 0.00320464i) q^{66} +(6.22807 - 4.36094i) q^{67} +(-6.26045 + 4.38361i) q^{68} +(6.51641 - 9.17330i) q^{69} +(-0.134987 + 3.53455i) q^{70} +(6.33059 + 3.65497i) q^{71} +(-2.19672 + 3.04835i) q^{72} +(6.42123 + 1.72056i) q^{73} +(-1.98051 - 0.720846i) q^{74} +(0.790480 + 8.62410i) q^{75} +(-3.02314 - 2.53672i) q^{76} +(-0.127487 + 0.273398i) q^{77} +(-0.0435177 - 0.00797816i) q^{78} +(-6.06016 + 1.06857i) q^{79} +(-5.09178 + 5.61800i) q^{80} +(6.73488 + 5.97005i) q^{81} +(-0.512391 - 0.512391i) q^{82} +(-2.31193 + 3.30178i) q^{83} +(9.18343 + 13.3065i) q^{84} +(-3.49342 - 8.30529i) q^{85} +(-0.771422 + 0.919344i) q^{86} +(12.4265 + 0.0843133i) q^{87} +(0.0695770 - 0.0324443i) q^{88} +(-5.25350 - 9.09933i) q^{89} +(-1.44373 - 1.60143i) q^{90} +(-0.195560 + 0.338719i) q^{91} +(-1.07392 + 12.2749i) q^{92} +(0.0643999 + 0.380301i) q^{93} +(0.443268 + 0.0781601i) q^{94} +(3.67561 - 2.85242i) q^{95} +(0.584736 - 6.19886i) q^{96} +(9.77698 + 0.855375i) q^{97} +(-5.34651 + 1.43259i) q^{98} +(-0.0605417 - 0.173632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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