LMFDB - Embedded newform 168.2.ba.c.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26535 - 0.631567i) q^{2} +(0.528554 + 1.64943i) q^{3} +(1.20225 + 1.59831i) q^{4} +(2.66818 - 1.54047i) q^{5} +(0.372919 - 2.42094i) q^{6} +(-1.46307 + 2.20441i) q^{7} +(-0.511826 - 2.78173i) q^{8} +(-2.44126 + 1.74363i) q^{9} +O(q^{10})$	\(q+(-1.26535 - 0.631567i) q^{2} +(0.528554 + 1.64943i) q^{3} +(1.20225 + 1.59831i) q^{4} +(2.66818 - 1.54047i) q^{5} +(0.372919 - 2.42094i) q^{6} +(-1.46307 + 2.20441i) q^{7} +(-0.511826 - 2.78173i) q^{8} +(-2.44126 + 1.74363i) q^{9} +(-4.34911 + 0.264112i) q^{10} +(-0.621780 + 1.07696i) q^{11} +(-2.00086 + 2.82782i) q^{12} +5.98957 q^{13} +(3.24353 - 1.86534i) q^{14} +(3.95119 + 3.58676i) q^{15} +(-1.10921 + 3.84313i) q^{16} +(-0.595854 + 1.03205i) q^{17} +(4.19028 - 0.664491i) q^{18} +(-0.614126 - 1.06370i) q^{19} +(5.66997 + 2.41256i) q^{20} +(-4.40934 - 1.24808i) q^{21} +(1.46694 - 0.970035i) q^{22} +(2.56956 - 1.48354i) q^{23} +(4.31775 - 2.31452i) q^{24} +(2.24612 - 3.89040i) q^{25} +(-7.57893 - 3.78282i) q^{26} +(-4.16634 - 3.10509i) q^{27} +(-5.28231 + 0.311808i) q^{28} -3.19900 q^{29} +(-2.73438 - 7.03397i) q^{30} +(1.33987 + 0.773574i) q^{31} +(3.83074 - 4.16238i) q^{32} +(-2.10501 - 0.456356i) q^{33} +(1.40578 - 0.929587i) q^{34} +(-0.507883 + 8.13559i) q^{35} +(-5.72186 - 1.80563i) q^{36} +(0.334978 - 0.193399i) q^{37} +(0.105291 + 1.73382i) q^{38} +(3.16581 + 9.87940i) q^{39} +(-5.65083 - 6.63371i) q^{40} -9.44060 q^{41} +(4.79114 + 4.36406i) q^{42} -8.29057i q^{43} +(-2.46884 + 0.300965i) q^{44} +(-3.82770 + 8.41302i) q^{45} +(-4.18836 + 0.254350i) q^{46} +(-3.34244 - 5.78928i) q^{47} +(-6.92527 + 0.201736i) q^{48} +(-2.71887 - 6.45041i) q^{49} +(-5.29919 + 3.50416i) q^{50} +(-2.01724 - 0.437327i) q^{51} +(7.20094 + 9.57321i) q^{52} +(5.25317 - 9.09875i) q^{53} +(3.31083 + 6.56037i) q^{54} +3.83135i q^{55} +(6.88092 + 2.94158i) q^{56} +(1.42990 - 1.57518i) q^{57} +(4.04788 + 2.02039i) q^{58} +(-3.22898 - 1.86425i) q^{59} +(-0.982467 + 10.6274i) q^{60} +(-3.16493 - 5.48181i) q^{61} +(-1.20685 - 1.82506i) q^{62} +(-0.271956 - 7.93259i) q^{63} +(-7.47607 + 2.84752i) q^{64} +(15.9813 - 9.22678i) q^{65} +(2.37537 + 1.90691i) q^{66} +(10.7324 + 6.19634i) q^{67} +(-2.36590 + 0.288416i) q^{68} +(3.80515 + 3.45419i) q^{69} +(5.78082 - 9.97364i) q^{70} +6.21100i q^{71} +(6.09981 + 5.89850i) q^{72} +(-8.92963 - 5.15552i) q^{73} +(-0.546010 + 0.0331580i) q^{74} +(7.60415 + 1.64854i) q^{75} +(0.961791 - 2.26039i) q^{76} +(-1.46435 - 2.94632i) q^{77} +(2.23362 - 14.5004i) q^{78} +(-6.41425 - 11.1098i) q^{79} +(2.96067 + 11.9629i) q^{80} +(2.91950 - 8.51331i) q^{81} +(11.9457 + 5.96237i) q^{82} +5.22882i q^{83} +(-3.30629 - 8.54801i) q^{84} +3.67159i q^{85} +(-5.23605 + 10.4905i) q^{86} +(-1.69085 - 5.27654i) q^{87} +(3.31404 + 1.17841i) q^{88} +(6.94090 + 12.0220i) q^{89} +(10.1568 - 8.22800i) q^{90} +(-8.76314 + 13.2035i) q^{91} +(5.46040 + 2.32339i) q^{92} +(-0.567765 + 2.61890i) q^{93} +(0.573057 + 9.43648i) q^{94} +(-3.27720 - 1.89209i) q^{95} +(8.89033 + 4.11850i) q^{96} +17.1489i q^{97} +(-0.633524 + 9.87920i) q^{98} +(-0.359884 - 3.71328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.26535	−	0.631567i	−0.894741	−	0.446585i
$2$	−1.26535	−	0.631567i	−0.894741	−	0.446585i
$3$	0.528554	+	1.64943i	0.305161	+	0.952301i
$3$	0.528554	+	1.64943i	0.305161	+	0.952301i
$4$	1.20225	+	1.59831i	0.601123	+	0.799157i
$5$	2.66818	−	1.54047i	1.19325	−	0.688921i	0.234205	−	0.972187i	$-0.424751\pi$
$5$	2.66818	−	1.54047i	1.19325	−	0.688921i	0.959041	+	0.283266i	$0.0914180\pi$
$6$	0.372919	−	2.42094i	0.152244	−	0.988343i
$7$	−1.46307	+	2.20441i	−0.552987	+	0.833190i
$7$	−1.46307	+	2.20441i	−0.552987	+	0.833190i
$8$	−0.511826	−	2.78173i	−0.180958	−	0.983491i
$9$	−2.44126	+	1.74363i	−0.813753	+	0.581210i
$10$	−4.34911	+	0.264112i	−1.37531	+	0.0835195i
$11$	−0.621780	+	1.07696i	−0.187474	+	0.324714i	−0.944407	−	0.328778i	$-0.893363\pi$
$11$	−0.621780	+	1.07696i	−0.187474	+	0.324714i	0.756933	+	0.653492i	$0.226697\pi$
$12$	−2.00086	+	2.82782i	−0.577598	+	0.816321i
$13$	5.98957			1.66121			0.830604	−	0.556864i	$-0.187995\pi$
$13$	5.98957			1.66121			0.830604	+	0.556864i	$0.187995\pi$
$14$	3.24353	−	1.86534i	0.866871	−	0.498533i
$15$	3.95119	+	3.58676i	1.02019	+	0.926098i
$16$	−1.10921	+	3.84313i	−0.277302	+	0.960783i
$17$	−0.595854	+	1.03205i	−0.144516	+	0.250309i	−0.929192	−	0.369597i	$-0.879496\pi$
$17$	−0.595854	+	1.03205i	−0.144516	+	0.250309i	0.784676	+	0.619906i	$0.212829\pi$
$18$	4.19028	−	0.664491i	0.987659	−	0.156622i
$19$	−0.614126	−	1.06370i	−0.140890	−	0.244029i	0.786942	−	0.617027i	$-0.211663\pi$
$19$	−0.614126	−	1.06370i	−0.140890	−	0.244029i	−0.927832	+	0.372998i	$0.878330\pi$
$20$	5.66997	+	2.41256i	1.26784	+	0.539464i
$21$	−4.40934	−	1.24808i	−0.962197	−	0.272353i
$22$	1.46694	−	0.970035i	0.312753	−	0.206812i
$23$	2.56956	−	1.48354i	0.535791	−	0.309339i	−0.207581	−	0.978218i	$-0.566559\pi$
$23$	2.56956	−	1.48354i	0.535791	−	0.309339i	0.743371	+	0.668879i	$0.233226\pi$
$24$	4.31775	−	2.31452i	0.881358	−	0.472449i
$25$	2.24612	−	3.89040i	0.449225	−	0.778080i
$26$	−7.57893	−	3.78282i	−1.48635	−	0.741871i
$27$	−4.16634	−	3.10509i	−0.801813	−	0.597575i
$28$	−5.28231	+	0.311808i	−0.998262	+	0.0589262i
$29$	−3.19900			−0.594040			−0.297020	−	0.954871i	$-0.595993\pi$
$29$	−3.19900			−0.594040			−0.297020	+	0.954871i	$0.595993\pi$
$30$	−2.73438	−	7.03397i	−0.499226	−	1.28422i
$31$	1.33987	+	0.773574i	0.240648	+	0.138938i	0.615474	−	0.788157i	$-0.288964\pi$
$31$	1.33987	+	0.773574i	0.240648	+	0.138938i	−0.374827	+	0.927095i	$0.622298\pi$
$32$	3.83074	−	4.16238i	0.677185	−	0.735812i
$33$	−2.10501	−	0.456356i	−0.366435	−	0.0794414i
$34$	1.40578	−	0.929587i	0.241088	−	0.159423i
$35$	−0.507883	+	8.13559i	−0.0858478	+	1.37517i
$36$	−5.72186	−	1.80563i	−0.953644	−	0.300938i
$37$	0.334978	−	0.193399i	0.0550700	−	0.0317947i	−0.472212	−	0.881485i	$-0.656544\pi$
$37$	0.334978	−	0.193399i	0.0550700	−	0.0317947i	0.527282	+	0.849690i	$0.323211\pi$
$38$	0.105291	+	1.73382i	0.0170804	+	0.281262i
$39$	3.16581	+	9.87940i	0.506936	+	1.58197i
$40$	−5.65083	−	6.63371i	−0.893475	−	1.04888i
$41$	−9.44060			−1.47437			−0.737187	−	0.675689i	$-0.763846\pi$
$41$	−9.44060			−1.47437			−0.737187	+	0.675689i	$0.763846\pi$
$42$	4.79114	+	4.36406i	0.739289	+	0.673389i
$43$		−	8.29057i		−	1.26430i	−0.774846	−	0.632150i	$-0.782173\pi$
$43$		−	8.29057i		−	1.26430i	0.774846	−	0.632150i	$-0.217827\pi$
$44$	−2.46884	+	0.300965i	−0.372192	+	0.0453722i
$45$	−3.82770	+	8.41302i	−0.570600	+	1.25414i
$46$	−4.18836	+	0.254350i	−0.617540	+	0.0375019i
$47$	−3.34244	−	5.78928i	−0.487546	−	0.844454i	0.512352	−	0.858776i	$-0.328774\pi$
$47$	−3.34244	−	5.78928i	−0.487546	−	0.844454i	−0.999897	+	0.0143219i	$0.995441\pi$
$48$	−6.92527	+	0.201736i	−0.999576	+	0.0291181i
$49$	−2.71887	−	6.45041i	−0.388410	−	0.921486i
$50$	−5.29919	+	3.50416i	−0.749419	+	0.495563i
$51$	−2.01724	−	0.437327i	−0.282470	−	0.0612380i
$52$	7.20094	+	9.57321i	0.998590	+	1.32757i
$53$	5.25317	−	9.09875i	0.721578	−	1.24981i	−0.238789	−	0.971071i	$-0.576750\pi$
$53$	5.25317	−	9.09875i	0.721578	−	1.24981i	0.960367	−	0.278738i	$-0.0899162\pi$
$54$	3.31083	+	6.56037i	0.450546	+	0.892753i
$55$			3.83135i			0.516619i
$56$	6.88092	+	2.94158i	0.919502	+	0.393086i
$57$	1.42990	−	1.57518i	0.189395	−	0.208638i
$58$	4.04788	+	2.02039i	0.531512	+	0.265290i
$59$	−3.22898	−	1.86425i	−0.420377	−	0.242705i	0.274862	−	0.961484i	$-0.411368\pi$
$59$	−3.22898	−	1.86425i	−0.420377	−	0.242705i	−0.695238	+	0.718779i	$0.744701\pi$
$60$	−0.982467	+	10.6274i	−0.126836	+	1.37199i
$61$	−3.16493	−	5.48181i	−0.405227	−	0.701874i	0.589121	−	0.808045i	$-0.299474\pi$
$61$	−3.16493	−	5.48181i	−0.405227	−	0.701874i	−0.994348	+	0.106171i	$0.966141\pi$
$62$	−1.20685	−	1.82506i	−0.153270	−	0.231783i
$63$	−0.271956	−	7.93259i	−0.0342632	−	0.999413i
$64$	−7.47607	+	2.84752i	−0.934509	+	0.355940i
$65$	15.9813	−	9.22678i	1.98223	−	1.14444i
$66$	2.37537	+	1.90691i	0.292387	+	0.234724i
$67$	10.7324	+	6.19634i	1.31117	+	0.757003i	0.982290	−	0.187369i	$-0.0599961\pi$
$67$	10.7324	+	6.19634i	1.31117	+	0.757003i	0.328878	+	0.944372i	$0.393329\pi$
$68$	−2.36590	+	0.288416i	−0.286908	+	0.0349755i
$69$	3.80515	+	3.45419i	0.458086	+	0.415836i
$70$	5.78082	−	9.97364i	0.690940	−	1.19208i
$71$			6.21100i			0.737110i	0.929606	+	0.368555i	$0.120147\pi$
$71$			6.21100i			0.737110i	−0.929606	+	0.368555i	$0.879853\pi$
$72$	6.09981	+	5.89850i	0.718870	+	0.695145i
$73$	−8.92963	−	5.15552i	−1.04513	−	0.603408i	−0.123851	−	0.992301i	$-0.539524\pi$
$73$	−8.92963	−	5.15552i	−1.04513	−	0.603408i	−0.921283	+	0.388893i	$0.872858\pi$
$74$	−0.546010	+	0.0331580i	−0.0634724	+	0.00385454i
$75$	7.60415	+	1.64854i	0.878052	+	0.190357i
$76$	0.961791	−	2.26039i	0.110325	−	0.259285i
$77$	−1.46435	−	2.94632i	−0.166878	−	0.335764i
$78$	2.23362	−	14.5004i	0.252908	−	1.64184i
$79$	−6.41425	−	11.1098i	−0.721660	−	1.24995i	−0.960334	−	0.278852i	$-0.910046\pi$
$79$	−6.41425	−	11.1098i	−0.721660	−	1.24995i	0.238674	−	0.971100i	$-0.423287\pi$
$80$	2.96067	+	11.9629i	0.331013	+	1.33749i
$81$	2.91950	−	8.51331i	0.324389	−	0.945924i
$82$	11.9457	+	5.96237i	1.31918	+	0.658434i
$83$			5.22882i			0.573938i	0.957940	+	0.286969i	$0.0926476\pi$
$83$			5.22882i			0.573938i	−0.957940	+	0.286969i	$0.907352\pi$
$84$	−3.30629	−	8.54801i	−0.360746	−	0.932664i
$85$			3.67159i			0.398240i
$86$	−5.23605	+	10.4905i	−0.564618	+	1.13122i
$87$	−1.69085	−	5.27654i	−0.181278	−	0.565705i
$88$	3.31404	+	1.17841i	0.353278	+	0.125619i
$89$	6.94090	+	12.0220i	0.735734	+	1.27433i	0.954400	+	0.298529i	$0.0964960\pi$
$89$	6.94090	+	12.0220i	0.735734	+	1.27433i	−0.218666	+	0.975800i	$0.570171\pi$
$90$	10.1568	−	8.22800i	1.07062	−	0.867308i
$91$	−8.76314	+	13.2035i	−0.918627	+	1.38410i
$92$	5.46040	+	2.32339i	0.569286	+	0.242230i
$93$	−0.567765	+	2.61890i	−0.0588745	+	0.271567i
$94$	0.573057	+	9.43648i	0.0591063	+	0.973298i
$95$	−3.27720	−	1.89209i	−0.336233	−	0.194124i
$96$	8.89033	+	4.11850i	0.907365	+	0.420343i
$97$			17.1489i			1.74120i	0.491989	+	0.870601i	$0.336270\pi$
$97$			17.1489i			1.74120i	−0.491989	+	0.870601i	$0.663730\pi$
$98$	−0.633524	+	9.87920i	−0.0639956	+	0.997950i
$99$	−0.359884	−	3.71328i	−0.0361697	−	0.373199i
$100$	8.91847	−	1.08721i	0.891847	−	0.108721i
$101$	2.87413	+	1.65938i	0.285986	+	0.165114i	0.636130	−	0.771582i	$-0.280534\pi$
$101$	2.87413	+	1.65938i	0.285986	+	0.165114i	−0.350144	+	0.936696i	$0.613867\pi$
$102$	2.27632	+	1.82739i	0.225389	+	0.180939i
$103$	10.7667	−	6.21615i	1.06087	−	0.612496i	0.135200	−	0.990818i	$-0.456832\pi$
$103$	10.7667	−	6.21615i	1.06087	−	0.612496i	0.925674	+	0.378322i	$0.123499\pi$
$104$	−3.06561	−	16.6614i	−0.300608	−	1.63378i
$105$	−13.6876	+	3.46238i	−1.33577	+	0.337894i
$106$	−12.3936	+	8.19542i	−1.20377	+	0.796010i
$107$	−4.79031	−	8.29706i	−0.463097	−	0.802107i	0.536017	−	0.844207i	$-0.319928\pi$
$107$	−4.79031	−	8.29706i	−0.463097	−	0.802107i	−0.999113	+	0.0421002i	$0.986595\pi$
$108$	−0.0460561	−	10.3922i	−0.00443175	−	0.999990i
$109$	0.510424	+	0.294693i	0.0488898	+	0.0282265i	0.524246	−	0.851567i	$-0.324347\pi$
$109$	0.510424	+	0.294693i	0.0488898	+	0.0282265i	−0.475356	+	0.879794i	$0.657681\pi$
$110$	2.41975	−	4.84801i	0.230714	−	0.462240i
$111$	0.496053	+	0.450301i	0.0470833	+	0.0427407i
$112$	−6.84900	−	8.06791i	−0.647170	−	0.762346i
$113$			7.02041i			0.660425i	0.943907	+	0.330212i	$0.107120\pi$
$113$			7.02041i			0.660425i	−0.943907	+	0.330212i	$0.892880\pi$
$114$	−2.80416	+	1.09009i	−0.262634	+	0.102096i
$115$	4.57070	−	7.91669i	0.426220	−	0.738235i
$116$	−3.84599	−	5.11301i	−0.357091	−	0.474731i
$117$	−14.6221	+	10.4436i	−1.35181	+	0.965511i
$118$	2.90840	+	4.39825i	0.267740	+	0.404892i
$119$	−1.40329	−	2.82346i	−0.128639	−	0.258827i
$120$	7.95509	−	12.8269i	0.726197	−	1.17093i
$121$	4.72678	+	8.18702i	0.429707	+	0.744275i
$122$	0.542622	+	8.93530i	0.0491267	+	0.808964i
$123$	−4.98987	−	15.5716i	−0.449921	−	1.40405i
$124$	0.374439	+	3.07156i	0.0336256	+	0.275834i
$125$			1.56436i			0.139921i
$126$	−4.66585	+	10.2093i	−0.415667	+	0.909517i
$127$	−5.88744			−0.522426			−0.261213	−	0.965281i	$-0.584123\pi$
$127$	−5.88744			−0.522426			−0.261213	+	0.965281i	$0.584123\pi$
$128$	11.2583	+	1.11851i	0.995101	+	0.0988635i
$129$	13.6747	−	4.38201i	1.20399	−	0.385815i
$130$	−26.0493	+	1.58192i	−2.28467	+	0.138743i
$131$	−3.67922	+	2.12420i	−0.321455	+	0.185592i	−0.652041	−	0.758184i	$-0.726087\pi$
$131$	−3.67922	+	2.12420i	−0.321455	+	0.185592i	0.330586	+	0.943776i	$0.392754\pi$
$132$	−1.80134	−	3.91312i	−0.156787	−	0.340593i
$133$	3.24333	+	0.202473i	0.281233	+	0.0175566i
$134$	−9.66685	−	14.6188i	−0.835089	−	1.26287i
$135$	−15.8999	−	1.86680i	−1.36844	−	0.160669i
$136$	3.17586	+	1.12928i	0.272328	+	0.0968347i
$137$	0.674838	+	0.389618i	0.0576553	+	0.0332873i	0.528551	−	0.848902i	$-0.322736\pi$
$137$	0.674838	+	0.389618i	0.0576553	+	0.0332873i	−0.470895	+	0.882189i	$0.656069\pi$
$138$	−2.63331	−	6.77398i	−0.224162	−	0.576640i
$139$	−5.54714			−0.470502			−0.235251	−	0.971935i	$-0.575591\pi$
$139$	−5.54714			−0.470502			−0.235251	+	0.971935i	$0.575591\pi$
$140$	−13.6138	+	8.96922i	−1.15058	+	0.758037i
$141$	7.78237	−	8.57309i	0.655394	−	0.721984i
$142$	3.92266	−	7.85911i	0.329182	−	0.659522i
$143$	−3.72420	+	6.45050i	−0.311433	+	0.539418i
$144$	−3.99313	−	11.3161i	−0.332761	−	0.943011i
$145$	−8.53552	+	4.92798i	−0.708836	+	0.409247i
$146$	8.04309	+	12.1632i	0.665651	+	1.00664i
$147$	9.20244	−	7.89399i	0.759005	−	0.651085i
$148$	0.711838	+	0.302886i	0.0585128	+	0.0248970i
$149$	2.07219	+	3.58914i	0.169761	+	0.294034i	0.938336	−	0.345726i	$-0.112367\pi$
$149$	2.07219	+	3.58914i	0.169761	+	0.294034i	−0.768575	+	0.639760i	$0.779034\pi$
$150$	−8.58079	−	6.88852i	−0.700618	−	0.562446i
$151$	2.16486	−	3.74965i	0.176174	−	0.305142i	−0.764393	−	0.644751i	$-0.776961\pi$
$151$	2.16486	−	3.74965i	0.176174	−	0.305142i	0.940567	+	0.339608i	$0.110295\pi$
$152$	−2.64459	+	2.25276i	−0.214505	+	0.182723i
$153$	−0.344878	−	3.55845i	−0.0278817	−	0.287684i
$154$	−0.00787757	+	4.65297i	−0.000634793	+	0.374947i
$155$	4.76668			0.382869
$156$	−11.9843	+	16.9374i	−0.959511	+	1.35608i
$157$	3.21017	−	5.56018i	0.256200	−	0.443751i	−0.709021	−	0.705187i	$-0.750863\pi$
$157$	3.21017	−	5.56018i	0.256200	−	0.443751i	0.965221	+	0.261437i	$0.0841963\pi$
$158$	1.09971	+	18.1089i	0.0874885	+	1.44067i
$159$	17.7844	+	3.85556i	1.41039	+	0.305766i
$160$	3.80906	−	17.0071i	0.301132	−	1.34453i
$161$	−0.489111	+	7.83489i	−0.0385473	+	0.617476i
$162$	−9.07094	+	8.92850i	−0.712680	+	0.701489i
$163$	9.18195	−	5.30120i	0.719186	−	0.415222i	−0.0952672	−	0.995452i	$-0.530371\pi$
$163$	9.18195	−	5.30120i	0.719186	−	0.415222i	0.814453	+	0.580230i	$0.197037\pi$
$164$	−11.3499	−	15.0890i	−0.886280	−	1.17826i
$165$	−6.31955	+	2.02508i	−0.491977	+	0.157652i
$166$	3.30235	−	6.61631i	0.256312	−	0.513526i
$167$	−15.5718			−1.20498			−0.602492	−	0.798125i	$-0.705825\pi$
$167$	−15.5718			−1.20498			−0.602492	+	0.798125i	$0.705825\pi$
$168$	−1.21501	+	12.9044i	−0.0937397	+	0.995597i
$169$	22.8750			1.75961
$170$	2.31886	−	4.64587i	0.177848	−	0.356322i
$171$	3.35394	+	1.52595i	0.256482	+	0.116693i
$172$	13.2509	−	9.96730i	1.01037	−	0.759999i
$173$	−1.61807	+	0.934192i	−0.123019	+	0.0710253i	−0.560247	−	0.828326i	$-0.689294\pi$
$173$	−1.61807	+	0.934192i	−0.123019	+	0.0710253i	0.437228	+	0.899351i	$0.355960\pi$
$174$	−1.19297	+	7.74459i	−0.0904388	+	0.587116i
$175$	5.28982	+	10.6433i	0.399873	+	0.804558i
$176$	−3.44920	−	3.58415i	−0.259993	−	0.270166i
$177$	1.36827	−	6.31134i	0.102845	−	0.474389i
$178$	−1.19001	−	19.5957i	−0.0891948	−	1.46876i
$179$	−7.73124	+	13.3909i	−0.577860	+	1.00088i	0.417864	+	0.908509i	$0.362779\pi$
$179$	−7.73124	+	13.3909i	−0.577860	+	1.00088i	−0.995724	+	0.0923734i	$0.970555\pi$
$180$	−18.0485	+	3.99665i	−1.34525	+	0.297893i
$181$	−16.6129			−1.23483			−0.617415	−	0.786638i	$-0.711820\pi$
$181$	−16.6129			−1.23483			−0.617415	+	0.786638i	$0.711820\pi$
$182$	19.4274	−	11.1726i	1.44005	−	0.828167i
$183$	7.36905	−	8.11777i	0.544736	−	0.600083i
$184$	−5.44197	−	6.38852i	−0.401187	−	0.470968i
$185$	0.595854	−	1.03205i	0.0438081	−	0.0758778i
$186$	2.37244	−	2.95526i	0.173955	−	0.216690i
$187$	−0.740981	−	1.28342i	−0.0541859	−	0.0938527i
$188$	5.23465	−	12.3024i	0.381776	−	0.897246i
$189$	12.9405	−	4.64138i	0.941286	−	0.337611i
$190$	2.95183	+	4.46393i	0.214149	+	0.323848i
$191$	−0.391130	+	0.225819i	−0.0283012	+	0.0163397i	−0.514084	−	0.857740i	$-0.671868\pi$
$191$	−0.391130	+	0.225819i	−0.0283012	+	0.0163397i	0.485783	+	0.874080i	$0.338535\pi$
$192$	−8.64831	−	10.8262i	−0.624138	−	0.781314i
$193$	0.859277	−	1.48831i	0.0618521	−	0.107131i	−0.833441	−	0.552608i	$-0.813633\pi$
$193$	0.859277	−	1.48831i	0.0618521	−	0.107131i	0.895293	+	0.445477i	$0.146966\pi$
$194$	10.8307	−	21.6994i	0.777596	−	1.55793i
$195$	23.6659	+	21.4832i	1.69475	+	1.53844i
$196$	7.04101	−	12.1006i	0.502930	−	0.864327i
$197$	16.4222			1.17003			0.585017	−	0.811021i	$-0.301088\pi$
$197$	16.4222			1.17003			0.585017	+	0.811021i	$0.301088\pi$
$198$	−1.88981	+	4.92591i	−0.134303	+	0.350069i
$199$	0.839396	+	0.484625i	0.0595032	+	0.0343542i	0.529456	−	0.848337i	$-0.322396\pi$
$199$	0.839396	+	0.484625i	0.0595032	+	0.0343542i	−0.469953	+	0.882691i	$0.655729\pi$
$200$	−11.9717	−	4.25691i	−0.846525	−	0.301009i
$201$	−4.54780	+	20.9774i	−0.320777	+	1.47963i
$202$	−2.58878	−	3.91491i	−0.182146	−	0.275452i
$203$	4.68036	−	7.05193i	0.328497	−	0.494948i
$204$	−1.72623	−	3.74995i	−0.120860	−	0.262549i
$205$	−25.1892	+	14.5430i	−1.75929	+	1.01573i
$206$	−17.5496	+	1.06575i	−1.22274	+	0.0742543i
$207$	−3.68623	+	8.10207i	−0.256211	+	0.563132i
$208$	−6.64369	+	23.0187i	−0.460657	+	1.59606i
$209$	1.52741			0.105653
$210$	19.5063	+	4.26347i	1.34607	+	0.294207i
$211$			9.99340i			0.687974i	0.938974	+	0.343987i	$0.111778\pi$
$211$			9.99340i			0.687974i	−0.938974	+	0.343987i	$0.888222\pi$
$212$	20.8583	−	2.54273i	1.43255	−	0.174635i
$213$	−10.2446	+	3.28285i	−0.701950	+	0.224937i
$214$	0.821291	+	13.5241i	0.0561423	+	0.924491i
$215$	−12.7714	−	22.1207i	−0.871003	−	1.50862i
$216$	−6.50510	+	13.1789i	−0.442616	+	0.896711i
$217$	−3.66559	+	1.82184i	−0.248837	+	0.123674i
$218$	−0.459749	−	0.695259i	−0.0311381	−	0.0470889i
$219$	3.78390	−	17.4538i	0.255692	−	1.17942i
$220$	−6.12369	+	4.60622i	−0.412859	+	0.310551i
$221$	−3.56891	+	6.18153i	−0.240071	+	0.415815i
$222$	−0.343288	−	0.883082i	−0.0230400	−	0.0592686i
$223$			13.7534i			0.920996i	0.887661	+	0.460498i	$0.152329\pi$
$223$			13.7534i			0.920996i	−0.887661	+	0.460498i	$0.847671\pi$
$224$	3.57099	+	14.5344i	0.238597	+	0.971119i
$225$	1.30005	+	13.4139i	0.0866699	+	0.894259i
$226$	4.43386	−	8.88331i	0.294936	−	0.590909i
$227$	4.13075	+	2.38489i	0.274167	+	0.158291i	0.630780	−	0.775962i	$-0.282735\pi$
$227$	4.13075	+	2.38489i	0.274167	+	0.158291i	−0.356613	+	0.934252i	$0.616068\pi$
$228$	4.23672	+	0.391670i	0.280584	+	0.0259390i
$229$	−0.743202	−	1.28726i	−0.0491122	−	0.0850648i	0.840424	−	0.541929i	$-0.182306\pi$
$229$	−0.743202	−	1.28726i	−0.0491122	−	0.0850648i	−0.889536	+	0.456864i	$0.848973\pi$
$230$	−10.7835	+	7.13071i	−0.711042	+	0.470185i
$231$	4.08577	−	3.97263i	0.268824	−	0.261380i
$232$	1.63733	+	8.89877i	0.107496	+	0.584233i
$233$	2.00188	−	1.15579i	0.131148	−	0.0757182i	−0.432991	−	0.901398i	$-0.642542\pi$
$233$	2.00188	−	1.15579i	0.131148	−	0.0757182i	0.564139	+	0.825680i	$0.309208\pi$
$234$	25.0980	−	3.98002i	1.64071	−	0.260182i
$235$	−17.8365	−	10.2979i	−1.16352	−	0.671761i
$236$	−0.902367	−	7.40220i	−0.0587391	−	0.481842i
$237$	14.9346	−	16.4520i	0.970108	−	1.06867i
$238$	−0.00754910	+	4.45896i	−0.000489335	+	0.289031i
$239$			21.6031i			1.39739i	0.715420	+	0.698695i	$0.246235\pi$
$239$			21.6031i			1.39739i	−0.715420	+	0.698695i	$0.753765\pi$
$240$	−18.1671	+	11.2065i	−1.17268	+	0.723374i
$241$	3.38489	+	1.95427i	0.218040	+	0.125885i	0.605042	−	0.796193i	$-0.293156\pi$
$241$	3.38489	+	1.95427i	0.218040	+	0.125885i	−0.387002	+	0.922079i	$0.626489\pi$
$242$	−0.810399	−	13.3448i	−0.0520944	−	0.857834i
$243$	15.5853	+	0.315780i	0.999795	+	0.0202573i
$244$	4.95663	−	11.6490i	0.317316	−	0.745753i
$245$	−17.1911	−	13.0225i	−1.09830	−	0.831976i
$246$	−3.52058	+	22.8551i	−0.224464	+	1.45719i
$247$	−3.67835	−	6.37109i	−0.234048	−	0.405383i
$248$	1.46610	−	4.12309i	0.0930972	−	0.261817i
$249$	−8.62459	+	2.76372i	−0.546561	+	0.175143i
$250$	0.988000	−	1.97947i	0.0624866	−	0.125193i
$251$		−	15.6528i		−	0.987995i	−0.869463	−	0.493997i	$-0.835535\pi$
$251$		−	15.6528i		−	0.987995i	0.869463	−	0.493997i	$-0.164465\pi$
$252$	12.3518	−	9.97160i	0.778091	−	0.628152i
$253$			3.68974i			0.231972i
$254$	7.44970	+	3.71832i	0.467436	+	0.233308i
$255$	−6.05604	+	1.94064i	−0.379244	+	0.121527i
$256$	−13.5393	−	8.52568i	−0.846207	−	0.532855i
$257$	−6.53148	−	11.3128i	−0.407422	−	0.705676i	0.587178	−	0.809458i	$-0.300239\pi$
$257$	−6.53148	−	11.3128i	−0.407422	−	0.705676i	−0.994600	+	0.103782i	$0.966906\pi$
$258$	−20.0709	−	3.09171i	−1.24956	−	0.192481i
$259$	−0.0637623	+	1.02139i	−0.00396200	+	0.0634658i
$260$	33.9607	+	14.4502i	2.10615	+	0.896163i
$261$	7.80960	−	5.57788i	0.483402	−	0.345262i
$262$	5.99710	−	0.364191i	0.370502	−	0.0224998i
$263$	26.2857	+	15.1761i	1.62085	+	0.935796i	0.986694	+	0.162586i	$0.0519836\pi$
$263$	26.2857	+	15.1761i	1.62085	+	0.935796i	0.634151	+	0.773209i	$0.281350\pi$
$264$	−0.192062	+	6.08915i	−0.0118206	+	0.374761i
$265$		−	32.3695i		−	1.98844i
$266$	−3.97609	−	2.30458i	−0.243790	−	0.141303i
$267$	−16.1608	+	17.8028i	−0.989027	+	1.08952i
$268$	2.99926	+	24.6032i	0.183209	+	1.50288i
$269$	0.684713	+	0.395319i	0.0417477	+	0.0241030i	0.520729	−	0.853722i	$-0.325660\pi$
$269$	0.684713	+	0.395319i	0.0417477	+	0.0241030i	−0.478981	+	0.877825i	$0.658994\pi$
$270$	18.9400	+	12.4040i	1.15265	+	0.754884i
$271$	−4.95134	+	2.85866i	−0.300773	+	0.173651i	−0.642790	−	0.766043i	$-0.722223\pi$
$271$	−4.95134	+	2.85866i	−0.300773	+	0.173651i	0.342017	+	0.939694i	$0.388890\pi$
$272$	−3.30537	−	3.43470i	−0.200418	−	0.208259i
$273$	−26.4101	−	7.47545i	−1.59841	−	0.452435i
$274$	−0.607840	−	0.919211i	−0.0367209	−	0.0555315i
$275$	2.79319	+	4.83795i	0.168436	+	0.291739i
$276$	−0.946154	+	10.2346i	−0.0569518	+	0.616051i
$277$	15.4143	+	8.89945i	0.926156	+	0.534716i	0.885594	−	0.464461i	$-0.153752\pi$
$277$	15.4143	+	8.89945i	0.926156	+	0.534716i	0.0405619	+	0.999177i	$0.487085\pi$
$278$	7.01910	+	3.50339i	0.420977	+	0.210119i
$279$	−4.61980	+	0.447742i	−0.276580	+	0.0268056i
$280$	22.8910	−	2.75121i	1.36800	−	0.164416i
$281$		−	27.9140i		−	1.66521i	−0.553866	−	0.832606i	$-0.686848\pi$
$281$		−	27.9140i		−	1.66521i	0.553866	−	0.832606i	$-0.313152\pi$
$282$	−15.2619	+	5.93291i	−0.908836	+	0.353300i
$283$	−1.81190	+	3.13830i	−0.107706	+	0.186552i	−0.914841	−	0.403815i	$-0.867684\pi$
$283$	−1.81190	+	3.13830i	−0.107706	+	0.186552i	0.807134	+	0.590368i	$0.201017\pi$
$284$	−9.92712	+	7.46714i	−0.589066	+	0.443094i
$285$	1.38870	−	6.40559i	0.0822595	−	0.379434i
$286$	8.78636	−	5.81009i	0.519548	−	0.343558i
$287$	13.8122	−	20.8110i	0.815309	−	1.22843i
$288$	−2.09417	+	16.8409i	−0.123400	+	0.992357i
$289$	7.78992	+	13.4925i	0.458230	+	0.793678i
$290$	13.9128	−	0.844895i	0.816989	−	0.0496140i
$291$	−28.2859	+	9.06411i	−1.65815	+	0.531347i
$292$	−2.49547	−	20.4705i	−0.146036	−	1.19795i
$293$			9.77037i			0.570791i	0.958410	+	0.285396i	$0.0921250\pi$
$293$			9.77037i			0.570791i	−0.958410	+	0.285396i	$0.907875\pi$
$294$	−16.6299	+	4.17674i	−0.969878	+	0.243592i
$295$	−11.4873			−0.668817
$296$	−0.709436	−	0.832832i	−0.0412351	−	0.0484074i
$297$	5.93460	−	2.55628i	0.344360	−	0.148330i
$298$	−0.355274	−	5.85026i	−0.0205805	−	0.338897i
$299$	15.3906	−	8.88575i	0.890059	−	0.513876i
$300$	6.50717	+	14.1358i	0.375692	+	0.816129i
$301$	18.2758	+	12.1296i	1.05340	+	0.699141i
$302$	−5.10747	+	3.37738i	−0.293902	+	0.194347i
$303$	−1.21790	+	5.61775i	−0.0699666	+	0.322731i
$304$	4.76912	−	1.18030i	0.273528	−	0.0676950i
$305$	−16.8892	−	9.75098i	−0.967072	−	0.558339i
$306$	−1.81101	+	4.72052i	−0.103528	+	0.269854i
$307$	−9.56907			−0.546136			−0.273068	−	0.961995i	$-0.588038\pi$
$307$	−9.56907			−0.546136			−0.273068	+	0.961995i	$0.588038\pi$
$308$	2.94863	−	5.88269i	0.168014	−	0.335197i
$309$	15.9439	+	14.4734i	0.907018	+	0.823361i
$310$	−6.03155	−	3.01048i	−0.342569	−	0.170984i
$311$	8.85168	−	15.3316i	0.501933	−	0.869373i	−0.498065	−	0.867140i	$-0.665956\pi$
$311$	8.85168	−	15.3316i	0.501933	−	0.869373i	0.999998	−	0.00223345i	$-0.000710930\pi$
$312$	25.8615	−	13.8630i	1.46412	−	0.784836i
$313$	−9.93451	+	5.73569i	−0.561532	+	0.324200i	−0.753760	−	0.657150i	$-0.771762\pi$
$313$	−9.93451	+	5.73569i	−0.561532	+	0.324200i	0.192228	+	0.981350i	$0.438429\pi$
$314$	−7.57363	+	5.00816i	−0.427405	+	0.282627i
$315$	−12.9456	−	20.7466i	−0.729401	−	1.16894i
$316$	10.0455	−	23.6087i	0.565101	−	1.32809i
$317$	1.15640	+	2.00294i	0.0649499	+	0.112497i	0.896672	−	0.442696i	$-0.145978\pi$
$317$	1.15640	+	2.00294i	0.0649499	+	0.112497i	−0.831722	+	0.555193i	$0.812645\pi$
$318$	−20.0685	−	16.1107i	−1.12539	−	0.903442i
$319$	1.98908	−	3.44519i	0.111367	−	0.192893i
$320$	−15.5610	+	19.1144i	−0.869884	+	1.06853i
$321$	11.1535	−	12.2867i	0.622528	−	0.685779i
$322$	5.56716	−	9.60501i	0.310245	−	0.535266i
$323$	1.46372			0.0814434
$324$	17.1169	−	5.56881i	0.950939	−	0.309378i
$325$	13.4533	−	23.3018i	0.746256	−	1.29255i
$326$	−14.9665	+	0.908883i	−0.828917	+	0.0503383i
$327$	−0.216290	+	0.997672i	−0.0119609	+	0.0551714i
$328$	4.83194	+	26.2612i	0.266799	+	1.45003i
$329$	17.6522	+	1.10198i	0.973197	+	0.0607540i
$330$	9.27545	+	1.42878i	0.510597	+	0.0786519i
$331$	−20.7165	+	11.9607i	−1.13868	+	0.657418i	−0.946104	−	0.323863i	$-0.895018\pi$
$331$	−20.7165	+	11.9607i	−1.13868	+	0.657418i	−0.192578	+	0.981282i	$0.561685\pi$
$332$	−8.35729	+	6.28633i	−0.458666	+	0.345007i
$333$	−0.480551	+	1.05622i	−0.0263340	+	0.0578803i
$334$	19.7039	+	9.83465i	1.07815	+	0.538128i
$335$	38.1812			2.08606
$336$	9.68741	−	15.5613i	0.528492	−	0.848938i
$337$	−25.6463			−1.39704			−0.698522	−	0.715589i	$-0.746159\pi$
$337$	−25.6463			−1.39704			−0.698522	+	0.715589i	$0.746159\pi$
$338$	−28.9449	−	14.4471i	−1.57440	−	0.785817i
$339$	−11.5797	+	3.71067i	−0.628923	+	0.201536i
$340$	−5.86835	+	4.41415i	−0.318256	+	0.239391i
$341$	−1.66621	+	0.961986i	−0.0902303	+	0.0520945i
$342$	−3.28018	−	4.04911i	−0.177372	−	0.218951i
$343$	18.1972	+	3.44385i	0.982559	+	0.185950i
$344$	−23.0621	+	4.24332i	−1.24343	+	0.228785i
$345$	15.4739	+	3.35467i	0.833087	+	0.180609i
$346$	2.63744	−	0.160166i	0.141789	−	0.00861057i
$347$	−0.473950	+	0.820906i	−0.0254430	+	0.0440686i	−0.878467	−	0.477804i	$-0.841433\pi$
$347$	−0.473950	+	0.820906i	−0.0254430	+	0.0440686i	0.853024	+	0.521872i	$0.174766\pi$
$348$	6.40076	−	9.04621i	0.343117	−	0.484928i
$349$	−14.1965			−0.759919			−0.379960	−	0.925003i	$-0.624062\pi$
$349$	−14.1965			−0.759919			−0.379960	+	0.925003i	$0.624062\pi$
$350$	0.0284570	−	16.8084i	0.00152109	−	0.898448i
$351$	−24.9546	−	18.5982i	−1.33198	−	0.992697i
$352$	2.10082	+	6.71362i	0.111974	+	0.357837i
$353$	−7.75978	+	13.4403i	−0.413011	+	0.715356i	−0.995217	−	0.0976847i	$-0.968856\pi$
$353$	−7.75978	+	13.4403i	−0.413011	+	0.715356i	0.582206	+	0.813041i	$0.302190\pi$
$354$	−5.71738	+	7.12193i	−0.303875	+	0.378526i
$355$	9.56788	+	16.5721i	0.507810	+	0.879553i
$356$	−10.8702	+	25.5471i	−0.576122	+	1.35400i
$357$	3.91540	−	3.80699i	0.207225	−	0.201487i
$358$	18.2400	−	12.0614i	0.964015	−	0.637467i
$359$	−12.2735	+	7.08613i	−0.647772	+	0.373991i	−0.787602	−	0.616184i	$-0.788678\pi$
$359$	−12.2735	+	7.08613i	−0.647772	+	0.373991i	0.139830	+	0.990176i	$0.455344\pi$
$360$	25.3619	+	6.34165i	1.33669	+	0.334234i
$361$	8.74570	−	15.1480i	0.460300	−	0.797263i
$362$	21.0213	+	10.4922i	1.10485	+	0.551457i
$363$	−11.0056	+	12.1238i	−0.577643	+	0.636334i
$364$	−31.6388	+	1.86760i	−1.65832	+	0.0978886i
$365$	−31.7678			−1.66280
$366$	−14.4514	+	5.61781i	−0.755386	+	0.293648i
$367$	−11.5602	−	6.67430i	−0.603439	−	0.348396i	0.166954	−	0.985965i	$-0.446607\pi$
$367$	−11.5602	−	6.67430i	−0.603439	−	0.348396i	−0.770393	+	0.637569i	$0.779940\pi$
$368$	2.85124	+	11.5207i	0.148631	+	0.600559i
$369$	23.0470	−	16.4609i	1.19978	−	0.856921i
$370$	−1.40578	+	0.929587i	−0.0730828	+	0.0483269i
$371$	12.3717	+	24.8922i	0.642305	+	1.29234i
$372$	−4.86842	+	2.24110i	−0.252416	+	0.116195i
$373$	4.56967	−	2.63830i	0.236609	−	0.136606i	−0.377008	−	0.926210i	$-0.623047\pi$
$373$	4.56967	−	2.63830i	0.236609	−	0.136606i	0.613617	+	0.789604i	$0.289714\pi$
$374$	0.127040	+	2.09196i	0.00656908	+	0.108172i
$375$	−2.58031	+	0.826851i	−0.133247	+	0.0426984i
$376$	−14.3935	+	12.2609i	−0.742287	+	0.632307i
$377$	−19.1607			−0.986824
$378$	−19.3057	−	2.29983i	−0.992979	−	0.118290i
$379$		−	15.3619i		−	0.789086i	−0.918877	−	0.394543i	$-0.870903\pi$
$379$		−	15.3619i		−	0.789086i	0.918877	−	0.394543i	$-0.129097\pi$
$380$	−0.915843	−	7.51274i	−0.0469817	−	0.385396i
$381$	−3.11183	−	9.71094i	−0.159424	−	0.497507i
$382$	0.637538	−	0.0387163i	0.0326193	−	0.00198090i
$383$	−1.35424	−	2.34561i	−0.0691983	−	0.119855i	0.829350	−	0.558729i	$-0.188711\pi$
$383$	−1.35424	−	2.34561i	−0.0691983	−	0.119855i	−0.898549	+	0.438874i	$0.855377\pi$
$384$	4.10570	+	19.1610i	0.209518	+	0.977805i
$385$	−8.44587	−	5.60552i	−0.430442	−	0.285684i
$386$	−2.02726	+	1.34055i	−0.103185	+	0.0682323i
$387$	14.4557	+	20.2394i	0.734824	+	1.02883i
$388$	−27.4092	+	20.6171i	−1.39149	+	1.04668i
$389$	6.35306	−	11.0038i	0.322113	−	0.557916i	−0.658811	−	0.752308i	$-0.728940\pi$
$389$	6.35306	−	11.0038i	0.322113	−	0.557916i	0.980924	+	0.194393i	$0.0622736\pi$
$390$	−16.3777	−	42.1304i	−0.829319	−	2.13336i
$391$			3.53589i			0.178817i
$392$	−16.5517	+	10.8647i	−0.835988	+	0.548748i
$393$	−5.44840	−	4.94588i	−0.274835	−	0.249487i
$394$	−20.7799	−	10.3717i	−1.04688	−	0.522520i
$395$	−34.2288	−	19.7620i	−1.72224	−	0.994334i
$396$	5.50232	−	5.03949i	0.276502	−	0.253244i
$397$	−11.9617	−	20.7184i	−0.600343	−	1.03982i	−0.992769	−	0.120041i	$-0.961697\pi$
$397$	−11.9617	−	20.7184i	−0.600343	−	1.03982i	0.392426	−	0.919784i	$-0.371636\pi$
$398$	−0.756060	−	1.14336i	−0.0378979	−	0.0573113i
$399$	1.38031	+	5.45668i	0.0691021	+	0.273176i
$400$	12.4599	+	12.9474i	0.622995	+	0.647371i
$401$	−23.5968	+	13.6236i	−1.17837	+	0.680331i	−0.955636	−	0.294549i	$-0.904831\pi$
$401$	−23.5968	+	13.6236i	−1.17837	+	0.680331i	−0.222731	+	0.974880i	$0.571497\pi$
$402$	19.0032	−	23.6717i	0.947796	−	1.18063i
$403$	8.02524	+	4.63338i	0.399766	+	0.230805i
$404$	0.803202	+	6.58874i	0.0399608	+	0.327802i
$405$	−5.32478	−	27.2125i	−0.264590	−	1.35220i
$406$	−10.3761	+	5.96723i	−0.514956	+	0.296149i
$407$			0.481008i			0.0238427i
$408$	−0.184053	+	5.83525i	−0.00911199	+	0.288888i
$409$	6.82328	+	3.93942i	0.337390	+	0.194792i	0.659117	−	0.752040i	$-0.270930\pi$
$409$	6.82328	+	3.93942i	0.337390	+	0.194792i	−0.321727	+	0.946832i	$0.604263\pi$
$410$	41.0582	−	2.49337i	2.02772	−	0.123139i
$411$	−0.285960	+	1.31903i	−0.0141054	+	0.0650632i
$412$	22.8796	+	9.73520i	1.12720	+	0.479619i
$413$	8.83378	−	4.39047i	0.434682	−	0.216041i
$414$	9.78138	−	7.92389i	0.480729	−	0.389438i
$415$	8.05487	+	13.9514i	0.395398	+	0.684849i
$416$	22.9445	−	24.9309i	1.12495	−	1.22234i
$417$	−2.93196	−	9.14963i	−0.143579	−	0.448059i
$418$	−1.93271	−	0.964659i	−0.0945319	−	0.0471830i
$419$		−	19.8589i		−	0.970173i	−0.874466	−	0.485086i	$-0.838788\pi$
$419$		−	19.8589i		−	0.970173i	0.874466	−	0.485086i	$-0.161212\pi$
$420$	−21.9898	−	17.7144i	−1.07299	−	0.864372i
$421$		−	16.6507i		−	0.811505i	−0.913983	−	0.405753i	$-0.867009\pi$
$421$		−	16.6507i		−	0.811505i	0.913983	−	0.405753i	$-0.132991\pi$
$422$	6.31150	−	12.6452i	0.307239	−	0.615559i
$423$	18.2541	+	8.30516i	0.887547	+	0.403811i
$424$	−27.9990	−	9.95593i	−1.35975	−	0.483503i
$425$	2.67672	+	4.63622i	0.129840	+	0.224890i
$426$	15.0364	+	2.31620i	0.728517	+	0.112220i
$427$	16.7147	+	1.04345i	0.808880	+	0.0504962i
$428$	7.50217	−	17.6315i	0.362631	−	0.852252i
$429$	−12.6081	−	2.73338i	−0.608725	−	0.131969i
$430$	2.18964	+	36.0566i	0.105594	+	1.73880i
$431$	−19.8541	−	11.4628i	−0.956339	−	0.552142i	−0.0612944	−	0.998120i	$-0.519523\pi$
$431$	−19.8541	−	11.4628i	−0.956339	−	0.552142i	−0.895044	+	0.445977i	$0.852856\pi$
$432$	16.5546	−	12.5676i	0.796485	−	0.604659i
$433$			10.5825i			0.508564i	0.967130	+	0.254282i	$0.0818392\pi$
$433$			10.5825i			0.508564i	−0.967130	+	0.254282i	$0.918161\pi$
$434$	5.78889	+	0.00980070i	0.277876	+	0.000470449i
$435$	−12.6399	−	11.4741i	−0.606035	−	0.550139i
$436$	0.142643	+	1.17011i	0.00683135	+	0.0560382i
$437$	−3.15607	−	1.82216i	−0.150975	−	0.0871656i
$438$	−15.8112	+	19.6955i	−0.755489	+	0.941086i
$439$	−6.69332	+	3.86439i	−0.319455	+	0.184437i	−0.651150	−	0.758949i	$-0.725713\pi$
$439$	−6.69332	+	3.86439i	−0.319455	+	0.184437i	0.331695	+	0.943387i	$0.392380\pi$
$440$	10.6578	−	1.96098i	0.508090	−	0.0934861i
$441$	17.8846	+	11.0064i	0.851648	+	0.524115i
$442$	8.41999	−	5.56783i	0.400498	−	0.264834i
$443$	2.28548	+	3.95856i	0.108586	+	0.188077i	0.915198	−	0.403005i	$-0.132034\pi$
$443$	2.28548	+	3.95856i	0.108586	+	0.188077i	−0.806611	+	0.591082i	$0.798701\pi$
$444$	−0.123344	+	1.33422i	−0.00585366	+	0.0633194i
$445$	37.0392	+	21.3846i	1.75582	+	1.01373i
$446$	8.68620	−	17.4029i	0.411303	−	0.824053i
$447$	−4.82478	+	5.31500i	−0.228204	+	0.251391i
$448$	4.66087	−	20.6465i	0.220205	−	0.975454i
$449$		−	4.33700i		−	0.204676i	−0.994750	−	0.102338i	$-0.967368\pi$
$449$		−	4.33700i		−	0.204676i	0.994750	−	0.102338i	$-0.0326323\pi$
$450$	6.82675	−	17.7944i	0.321816	−	0.838836i
$451$	5.86998	−	10.1671i	0.276406	−	0.478750i
$452$	−11.2208	+	8.44026i	−0.527783	+	0.396996i
$453$	7.32905	+	1.58890i	0.344349	+	0.0746531i
$454$	−3.72065	−	5.62658i	−0.174619	−	0.264068i
$455$	−3.04200	+	48.7287i	−0.142611	+	2.28444i
$456$	−5.11359	−	3.17138i	−0.239466	−	0.148513i
$457$	−9.88462	−	17.1207i	−0.462383	−	0.800871i	0.536696	−	0.843776i	$-0.319672\pi$
$457$	−9.88462	−	17.1207i	−0.462383	−	0.800871i	−0.999079	+	0.0429048i	$0.986339\pi$
$458$	0.127421	+	2.09823i	0.00595398	+	0.0980437i
$459$	5.68714	−	2.44969i	0.265453	−	0.114342i
$460$	18.1485	−	2.21239i	0.846176	−	0.103153i
$461$			25.3326i			1.17986i	0.807455	+	0.589929i	$0.200844\pi$
$461$			25.3326i			1.17986i	−0.807455	+	0.589929i	$0.799156\pi$
$462$	−7.67893	+	2.44636i	−0.357256	+	0.113815i
$463$	20.9574			0.973975			0.486988	−	0.873409i	$-0.338096\pi$
$463$	20.9574			0.973975			0.486988	+	0.873409i	$0.338096\pi$
$464$	3.54837	−	12.2942i	0.164729	−	0.570744i
$465$	2.51945	+	7.86233i	0.116837	+	0.364607i
$466$	−3.26305	+	0.198158i	−0.151158	+	0.00917950i
$467$	−26.9170	+	15.5406i	−1.24557	+	0.719131i	−0.970223	−	0.242214i	$-0.922127\pi$
$467$	−26.9170	+	15.5406i	−1.24557	+	0.719131i	−0.275348	+	0.961345i	$0.588793\pi$
$468$	−34.2715	−	10.8149i	−1.58420	−	0.499920i
$469$	−29.3615	+	14.5929i	−1.35579	+	0.673839i
$470$	16.0657	+	24.2954i	0.741054	+	1.12066i
$471$	10.8679	+	2.35611i	0.500766	+	0.108564i
$472$	−3.53317	+	9.93632i	−0.162627	+	0.457356i
$473$	8.92857	+	5.15491i	0.410536	+	0.237023i
$474$	−29.2881	+	11.3854i	−1.34525	+	0.522951i
$475$	−5.51761			−0.253165
$476$	2.82568	−	5.63739i	0.129515	−	0.258390i
$477$	3.04051	+	31.3720i	0.139216	+	1.43643i
$478$	13.6438	−	27.3356i	0.624054	−	1.25030i
$479$	−17.0894	+	29.5997i	−0.780835	+	1.35245i	0.150620	+	0.988592i	$0.451873\pi$
$479$	−17.0894	+	29.5997i	−0.780835	+	1.35245i	−0.931456	+	0.363855i	$0.881460\pi$
$480$	30.0654	−	2.70642i	1.37229	−	0.123530i
$481$	2.00637	−	1.15838i	0.0914827	−	0.0528176i
$482$	−3.04884	−	4.61063i	−0.138871	−	0.210008i
$483$	−13.1816	+	3.33441i	−0.599786	+	0.151721i
$484$	−7.40267	+	17.3977i	−0.336485	+	0.790804i
$485$	26.4174	+	45.7562i	1.19955	+	2.07768i
$486$	−19.5214	−	10.2427i	−0.885511	−	0.464619i
$487$	−12.3371	+	21.3684i	−0.559046	+	0.968296i	0.438531	+	0.898716i	$0.355499\pi$
$487$	−12.3371	+	21.3684i	−0.559046	+	0.968296i	−0.997576	+	0.0695795i	$0.977834\pi$
$488$	−13.6290	+	11.6097i	−0.616958	+	0.525547i
$489$	13.5971	+	12.3430i	0.614884	+	0.558171i
$490$	13.5283	+	27.3354i	0.611146	+	1.23489i
$491$	43.3064			1.95439			0.977196	−	0.212339i	$-0.0681079\pi$
$491$	43.3064			1.95439			0.977196	+	0.212339i	$0.0681079\pi$
$492$	18.8893	−	26.6963i	0.851595	−	1.20356i
$493$	1.90614	−	3.30153i	0.0858482	−	0.148693i
$494$	0.630647	+	10.3848i	0.0283742	+	0.467235i
$495$	−6.68046	−	9.35332i	−0.300264	−	0.420400i
$496$	−4.45914	+	4.29124i	−0.200221	+	0.192682i
$497$	−13.6916	−	9.08710i	−0.614152	−	0.407612i
$498$	12.6586	+	1.94993i	0.567247	+	0.0873783i
$499$	32.3258	−	18.6633i	1.44710	−	0.835485i	0.448795	−	0.893635i	$-0.351853\pi$
$499$	32.3258	−	18.6633i	1.44710	−	0.835485i	0.998308	+	0.0581497i	$0.0185201\pi$
$500$	−2.50034	+	1.88075i	−0.111819	+	0.0841096i
$501$	−8.23056	−	25.6847i	−0.367714	−	1.14751i
$502$	−9.88578	+	19.8063i	−0.441224	+	0.883999i
$503$	34.2432			1.52683			0.763414	−	0.645910i	$-0.223522\pi$
$503$	34.2432			1.52683			0.763414	+	0.645910i	$0.223522\pi$
$504$	−21.9272	+	4.81661i	−0.976713	+	0.214549i
$505$	10.2249			0.455003
$506$	2.33032	−	4.66883i	0.103595	−	0.207555i
$507$	12.0907	+	37.7307i	0.536965	+	1.67568i
$508$	−7.07815	−	9.40998i	−0.314042	−	0.417500i
$509$	24.1054	−	13.9173i	1.06845	−	0.616871i	0.140694	−	0.990053i	$-0.455067\pi$
$509$	24.1054	−	13.9173i	1.06845	−	0.616871i	0.927758	+	0.373182i	$0.121733\pi$
$510$	8.88869	+	1.36921i	0.393598	+	0.0606295i
$511$	24.4295	−	12.1417i	1.08070	−	0.537118i
$512$	11.7475	+	19.3390i	0.519171	+	0.854671i
$513$	−0.744220	+	6.33864i	−0.0328581	+	0.279858i
$514$	1.11981	+	18.4398i	0.0493928	+	0.813346i
$515$	19.1517	−	33.1716i	0.843923	−	1.46172i
$516$	23.4442	+	16.5882i	1.03207	+	0.730257i
$517$	8.31307			0.365608
$518$	0.725756	−	1.25214i	0.0318879	−	0.0550161i
$519$	−2.39612	−	2.17512i	−0.105178	−	0.0954774i
$520$	−33.8460	−	39.7331i	−1.48425	−	1.74241i
$521$	−8.13261	+	14.0861i	−0.356296	+	0.617123i	−0.987339	−	0.158625i	$-0.949294\pi$
$521$	−8.13261	+	14.0861i	−0.356296	+	0.617123i	0.631043	+	0.775748i	$0.282627\pi$
$522$	−13.4047	+	2.12571i	−0.586709	+	0.0930399i
$523$	−6.98922	−	12.1057i	−0.305617	−	0.529345i	0.671781	−	0.740750i	$-0.265530\pi$
$523$	−6.98922	−	12.1057i	−0.305617	−	0.529345i	−0.977399	+	0.211405i	$0.932196\pi$
$524$	−7.81847	−	3.32674i	−0.341551	−	0.145329i
$525$	−14.7594	+	14.3508i	−0.644155	+	0.626319i
$526$	−23.6760	−	35.8043i	−1.03232	−	1.56114i
$527$	−1.59673	+	0.921874i	−0.0695548	+	0.0401575i
$528$	4.08873	−	7.58364i	0.177939	−	0.330035i
$529$	−7.09824	+	12.2945i	−0.308619	+	0.534544i
$530$	−20.4435	+	40.9589i	−0.888009	+	1.77914i
$531$	11.1333	−	1.07902i	0.483145	−	0.0468255i
$532$	3.57567	+	5.42729i	0.155025	+	0.235303i
$533$	−56.5451			−2.44924
$534$	31.6929	−	12.3202i	1.37148	−	0.533149i
$535$	−25.5628	−	14.7587i	−1.10518	−	0.638074i
$536$	11.7435	−	33.0260i	0.507240	−	1.42651i
$537$	−26.1738	−	5.67434i	−1.12948	−	0.244866i
$538$	−0.616734	−	0.932661i	−0.0265893	−	0.0402099i
$539$	8.63734	+	1.08263i	0.372037	+	0.0466322i
$540$	−16.1318	−	27.6573i	−0.694203	−	1.19018i
$541$	18.9287	−	10.9285i	0.813810	−	0.469853i	−0.0344673	−	0.999406i	$-0.510973\pi$
$541$	18.9287	−	10.9285i	0.813810	−	0.469853i	0.848277	+	0.529552i	$0.177640\pi$
$542$	8.07064	−	0.490112i	0.346664	−	0.0210521i
$543$	−8.78084	−	27.4019i	−0.376822	−	1.17593i
$544$	2.01322	+	6.43368i	0.0863163	+	0.275842i
$545$	1.81587			0.0777834
$546$	28.6969	+	26.1388i	1.22811	+	1.11864i
$547$		−	9.11111i		−	0.389563i	−0.980847	−	0.194782i	$-0.937600\pi$
$547$		−	9.11111i		−	0.389563i	0.980847	−	0.194782i	$-0.0623998\pi$
$548$	0.188590	+	1.54702i	0.00805616	+	0.0660854i
$549$	17.2847	+	7.86407i	0.737692	+	0.335630i
$550$	−0.478888	−	7.88581i	−0.0204199	−	0.336252i
$551$	1.96459	+	3.40277i	0.0836944	+	0.144963i
$552$	7.66106	−	12.3528i	0.326076	−	0.525772i
$553$	33.8751	+	2.11473i	1.44052	+	0.0899275i
$554$	−13.8840	−	20.9961i	−0.589873	−	0.892040i
$555$	2.01724	+	0.437327i	0.0856270	+	0.0185635i
$556$	−6.66902	−	8.86606i	−0.282830	−	0.376005i
$557$	−2.14436	+	3.71415i	−0.0908596	+	0.157373i	−0.907873	−	0.419245i	$-0.862295\pi$
$557$	−2.14436	+	3.71415i	−0.0908596	+	0.157373i	0.817013	+	0.576619i	$0.195628\pi$
$558$	6.12846	+	2.35116i	0.259438	+	0.0995325i
$559$		−	49.6569i		−	2.10026i
$560$	−30.7028	−	10.9759i	−1.29743	−	0.463818i
$561$	1.72526	−	1.90055i	0.0728406	−	0.0802414i
$562$	−17.6296	+	35.3212i	−0.743659	+	1.48993i
$563$	27.2512	+	15.7335i	1.14850	+	0.663087i	0.948521	−	0.316713i	$-0.102579\pi$
$563$	27.2512	+	15.7335i	1.14850	+	0.663087i	0.199979	+	0.979800i	$0.435913\pi$
$564$	23.0588	+	2.13171i	0.970951	+	0.0897611i
$565$	10.8148	+	18.7317i	0.454981	+	0.788049i
$566$	4.27474	−	2.82673i	0.179681	−	0.118816i
$567$	14.4954	+	18.8913i	0.608751	+	0.793362i
$568$	17.2773	−	3.17895i	0.724941	−	0.133386i
$569$	8.62592	−	4.98018i	0.361617	−	0.208780i	−0.308173	−	0.951330i	$-0.599717\pi$
$569$	8.62592	−	4.98018i	0.361617	−	0.208780i	0.669790	+	0.742551i	$0.266384\pi$
$570$	−5.80276	+	7.22829i	−0.243051	+	0.302760i
$571$	29.5465	+	17.0587i	1.23648	+	0.713883i	0.968373	−	0.249506i	$-0.0802681\pi$
$571$	29.5465	+	17.0587i	1.23648	+	0.713883i	0.268108	+	0.963389i	$0.413601\pi$
$572$	−14.7873	+	1.80265i	−0.618289	+	0.0753727i
$573$	−0.579206	−	0.525785i	−0.0241967	−	0.0219650i
$574$	−30.6209	+	17.6099i	−1.27809	+	0.735024i
$575$		−	13.3288i		−	0.555851i
$576$	13.2860	−	19.9870i	0.553583	−	0.832794i
$577$	0.843668	+	0.487092i	0.0351224	+	0.0202779i	0.517458	−	0.855708i	$-0.326878\pi$
$577$	0.843668	+	0.487092i	0.0351224	+	0.0202779i	−0.482336	+	0.875986i	$0.660212\pi$
$578$	−1.33557	−	21.9927i	−0.0555523	−	0.914775i
$579$	2.90905	+	0.630667i	0.120896	+	0.0262096i
$580$	−18.1383	−	7.71779i	−0.753150	−	0.320464i
$581$	−11.5265	−	7.65011i	−0.478199	−	0.317380i
$582$	41.5163	+	6.39514i	1.72091	+	0.265087i
$583$	6.53263	+	11.3149i	0.270554	+	0.468613i
$584$	−9.77087	+	27.4786i	−0.404322	+	1.13707i
$585$	−22.9263	+	50.3904i	−0.947886	+	2.08339i
$586$	6.17064	−	12.3630i	0.254907	−	0.510710i
$587$		−	25.9212i		−	1.06988i	−0.844890	−	0.534940i	$-0.820334\pi$
$587$		−	25.9212i		−	1.06988i	0.844890	−	0.534940i	$-0.179666\pi$
$588$	23.6807	+	5.21786i	0.976574	+	0.215181i
$589$		−	1.90029i		−	0.0782999i
$590$	14.5355	+	7.25501i	0.598418	+	0.298684i
$591$	8.68003	+	27.0873i	0.357049	+	1.11422i
$592$	0.371699	+	1.50188i	0.0152767	+	0.0617270i
$593$	22.1118	+	38.2987i	0.908022	+	1.57274i	0.816808	+	0.576909i	$0.195741\pi$
$593$	22.1118	+	38.2987i	0.908022	+	1.57274i	0.0912135	+	0.995831i	$0.470925\pi$
$594$	−9.12383	−	0.513497i	−0.374355	−	0.0210691i
$595$	−8.09370	−	5.37178i	−0.331809	−	0.220222i
$596$	−3.24529	+	7.62704i	−0.132932	+	0.312416i
$597$	−0.355691	+	1.64068i	−0.0145575	+	0.0671485i
$598$	−25.0865	+	1.52345i	−1.02586	+	0.0622984i
$599$	−8.58632	−	4.95731i	−0.350827	−	0.202550i	0.314222	−	0.949349i	$-0.398256\pi$
$599$	−8.58632	−	4.95731i	−0.350827	−	0.202550i	−0.665050	+	0.746799i	$0.731590\pi$
$600$	0.693805	−	21.9965i	0.0283245	−	0.898003i
$601$		−	11.8235i		−	0.482292i	−0.970489	−	0.241146i	$-0.922477\pi$
$601$		−	11.8235i		−	0.482292i	0.970489	−	0.241146i	$-0.0775233\pi$
$602$	−15.4647	−	26.8907i	−0.630295	−	1.09598i
$603$	−37.0046	+	3.58642i	−1.50695	+	0.146050i
$604$	8.59581	−	1.04787i	0.349759	−	0.0426374i
$605$	25.2238	+	14.5630i	1.02549	+	0.592069i
$606$	5.08906	−	6.33926i	0.206729	−	0.257515i
$607$	5.56281	−	3.21169i	0.225788	−	0.130359i	−0.382840	−	0.923815i	$-0.625054\pi$
$607$	5.56281	−	3.21169i	0.225788	−	0.130359i	0.608627	+	0.793456i	$0.291721\pi$
$608$	−6.78007	−	1.51852i	−0.274968	−	0.0615841i
$609$	14.1055	+	3.99261i	0.571584	+	0.161789i
$610$	15.2124	+	23.0051i	0.615933	+	0.931449i
$611$	−20.0198	−	34.6753i	−0.809915	−	1.40281i
$612$	5.27289	−	4.82935i	0.213144	−	0.195215i
$613$	−17.5740	−	10.1463i	−0.709805	−	0.409806i	0.101184	−	0.994868i	$-0.467737\pi$
$613$	−17.5740	−	10.1463i	−0.709805	−	0.409806i	−0.810989	+	0.585061i	$0.801070\pi$
$614$	12.1083	+	6.04351i	0.488650	+	0.243896i
$615$	−37.3016	−	33.8612i	−1.50414	−	1.36541i
$616$	−7.44638	+	5.58143i	−0.300023	+	0.224882i
$617$		−	26.7202i		−	1.07571i	−0.843036	−	0.537856i	$-0.819234\pi$
$617$		−	26.7202i		−	1.07571i	0.843036	−	0.537856i	$-0.180766\pi$
$618$	−11.0338	−	28.3836i	−0.443845	−	1.14176i
$619$	7.12358	−	12.3384i	0.286321	−	0.495922i	−0.686608	−	0.727028i	$-0.740901\pi$
$619$	7.12358	−	12.3384i	0.286321	−	0.495922i	0.972929	+	0.231106i	$0.0742343\pi$
$620$	5.73073	+	7.61865i	0.230151	+	0.305972i
$621$	−15.3122	−	1.79780i	−0.614457	−	0.0721434i
$622$	−20.8834	+	13.8094i	−0.837350	+	0.553708i
$623$	−36.6564	−	2.28836i	−1.46861	−	0.0916813i
$624$	−41.4794	+	1.20831i	−1.66050	+	0.0483712i
$625$	13.6405	+	23.6260i	0.545619	+	0.945040i
$626$	16.1932	−	0.983375i	0.647209	−	0.0393036i
$627$	0.807317	+	2.51935i	0.0322411	+	0.100613i
$628$	12.7463	−	1.55384i	0.508634	−	0.0620051i
$629$			0.460951i			0.0183793i
$630$	3.27786	+	34.4279i	0.130593	+	1.37164i
$631$	−13.9775			−0.556436			−0.278218	−	0.960518i	$-0.589744\pi$
$631$	−13.9775			−0.556436			−0.278218	+	0.960518i	$0.589744\pi$
$632$	−27.6216	+	23.5290i	−1.09873	+	0.935934i
$633$	−16.4834	+	5.28206i	−0.655158	+	0.209943i
$634$	−0.198263	−	3.26478i	−0.00787403	−	0.129661i
$635$	−15.7088	+	9.06945i	−0.623383	+	0.359910i
$636$	15.2188	+	33.0603i	0.603464	+	1.31093i
$637$	−16.2849	−	38.6352i	−0.645231	−	1.53078i
$638$	−4.69276	+	3.10315i	−0.185788	+	0.122855i
$639$	−10.8297	−	15.1627i	−0.428416	−	0.599826i
$640$	31.7622	−	14.3587i	1.25551	−	0.567578i
$641$	6.31225	+	3.64438i	0.249319	+	0.143944i	0.619452	−	0.785034i	$-0.287355\pi$
$641$	6.31225	+	3.64438i	0.249319	+	0.143944i	−0.370133	+	0.928979i	$0.620688\pi$
$642$	−21.8731	+	8.50290i	−0.863261	+	0.335583i
$643$	−25.1189			−0.990594			−0.495297	−	0.868724i	$-0.664941\pi$
$643$	−25.1189			−0.990594			−0.495297	+	0.868724i	$0.664941\pi$
$644$	−13.1106	+	8.63771i	−0.516631	+	0.340373i
$645$	29.7363	−	32.7576i	1.17086	−	1.28983i
$646$	−1.85212	−	0.924435i	−0.0728707	−	0.0363714i
$647$	20.2246	−	35.0301i	0.795112	−	1.37717i	−0.127657	−	0.991818i	$-0.540746\pi$
$647$	20.2246	−	35.0301i	0.795112	−	1.37717i	0.922768	−	0.385355i	$-0.125921\pi$
$648$	−25.1760	−	3.76395i	−0.989008	−	0.147862i
$649$	4.01543	−	2.31831i	0.157619	−	0.0910016i
$650$	−31.7399	+	20.9884i	−1.24494	+	0.823233i
$651$	−4.94246	−	5.08321i	−0.193710	−	0.199227i
$652$	19.5119	+	8.30228i	0.764146	+	0.325142i
$653$	−22.0316	−	38.1599i	−0.862164	−	1.49331i	−0.869836	−	0.493341i	$-0.835775\pi$
$653$	−22.0316	−	38.1599i	−0.862164	−	1.49331i	0.00767187	−	0.999971i	$-0.497558\pi$
$654$	0.903781	−	1.12581i	0.0353406	−	0.0440225i
$655$	−6.54455	+	11.3355i	−0.255717	+	0.442915i
$656$	10.4716	−	36.2814i	0.408847	−	1.41655i
$657$	30.7889	−	2.98400i	1.20119	−	0.116417i
$658$	−21.6403	−	12.5429i	−0.843627	−	0.488975i
$659$	−5.89051			−0.229462			−0.114731	−	0.993397i	$-0.536601\pi$
$659$	−5.89051			−0.229462			−0.114731	+	0.993397i	$0.536601\pi$
$660$	−10.8344	−	7.66599i	−0.421727	−	0.298398i
$661$	−21.0993	+	36.5450i	−0.820667	+	1.42144i	0.0845192	+	0.996422i	$0.473065\pi$
$661$	−21.0993	+	36.5450i	−0.820667	+	1.42144i	−0.905186	+	0.425015i	$0.860269\pi$
$662$	33.7677	−	2.05064i	1.31242	−	0.0797004i
$663$	−12.0824	−	2.61940i	−0.469241	−	0.101729i
$664$	14.5452	−	2.67624i	0.564462	−	0.103858i
$665$	8.96570	−	4.45604i	0.347675	−	0.172798i
$666$	1.27514	−	1.03299i	0.0494106	−	0.0400275i
$667$	−8.22004	+	4.74584i	−0.318281	+	0.183760i
$668$	−18.7212	−	24.8887i	−0.724344	−	0.962971i
$669$	−22.6853	+	7.26942i	−0.877065	+	0.281052i
$670$	−48.3128	−	24.1140i	−1.86648	−	0.931605i
$671$	7.87156			0.303878
$672$	−22.0860	+	13.5723i	−0.851987	+	0.523563i
$673$	−46.7729			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$673$	−46.7729			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$674$	32.4517	+	16.1974i	1.24999	+	0.623899i
$675$	−21.4382	+	9.23431i	−0.825155	+	0.355429i
$676$	27.5013	+	36.5613i	1.05774	+	1.40621i
$677$	−35.7518	+	20.6413i	−1.37405	+	0.793310i	−0.991436	−	0.130596i	$-0.958311\pi$
$677$	−35.7518	+	20.6413i	−1.37405	+	0.793310i	−0.382618	+	0.923907i	$0.624977\pi$
$678$	16.9960	+	2.61804i	0.652726	+	0.100545i
$679$	−37.8032	−	25.0899i	−1.45075	−	0.962863i
$680$	10.2134	−	1.87921i	0.391665	−	0.0720646i
$681$	−1.75039	+	8.07394i	−0.0670751	+	0.309394i
$682$	2.71591	−	0.164931i	0.103997	−	0.00631554i
$683$	−17.1346	+	29.6781i	−0.655638	+	1.13560i	0.326095	+	0.945337i	$0.394267\pi$
$683$	−17.1346	+	29.6781i	−0.655638	+	1.13560i	−0.981733	+	0.190262i	$0.939066\pi$
$684$	1.59330	+	7.19521i	0.0609215	+	0.275116i
$685$	2.40079			0.0917293
$686$	−20.8510	−	15.8505i	−0.796093	−	0.605174i
$687$	1.73043	−	1.90625i	0.0660201	−	0.0727280i
$688$	31.8617	+	9.19598i	1.21472	+	0.350593i
$689$	31.4642	−	54.4976i	1.19869	−	2.07619i
$690$	−17.4613	−	14.0177i	−0.664740	−	0.533643i
$691$	3.57575	+	6.19338i	0.136028	+	0.235607i	0.925990	−	0.377549i	$-0.123233\pi$
$691$	3.57575	+	6.19338i	0.136028	+	0.235607i	−0.789962	+	0.613156i	$0.789900\pi$
$692$	−3.43845	−	1.46305i	−0.130710	−	0.0556169i
$693$	8.71215	+	4.63945i	0.330947	+	0.176238i
$694$	1.11817	−	0.739406i	0.0424453	−	0.0280675i
$695$	−14.8008	+	8.54522i	−0.561425	+	0.324139i
$696$	−13.8125	+	7.40416i	−0.523562	+	0.280654i
$697$	5.62522	−	9.74316i	0.213070	−	0.369048i
$698$	17.9636	+	8.96602i	0.679931	+	0.339369i
$699$	2.96450	+	2.69108i	0.112128	+	0.101786i
$700$	−10.6517	+	21.2506i	−0.402595	+	0.803199i
$701$	12.4116			0.468778			0.234389	−	0.972143i	$-0.424691\pi$
$701$	12.4116			0.468778			0.234389	+	0.972143i	$0.424691\pi$
$702$	19.8304	+	39.2938i	0.748451	+	1.48305i
$703$	−0.411437	−	0.237543i	−0.0155176	−	0.00895911i
$704$	1.58182	−	9.82193i	0.0596170	−	0.370178i
$705$	7.55815	−	34.8631i	0.284656	−	1.31302i
$706$	18.3073	−	12.1060i	0.689006	−	0.455614i
$707$	−7.86299	+	3.90798i	−0.295718	+	0.146975i
$708$	11.7325	−	5.40086i	0.440934	−	0.202977i
$709$	30.5908	−	17.6616i	1.14886	−	0.663295i	0.200251	−	0.979745i	$-0.435824\pi$
$709$	30.5908	−	17.6616i	1.14886	−	0.663295i	0.948609	+	0.316450i	$0.102491\pi$
$710$	−1.64040	−	27.0123i	−0.0615631	−	1.01375i
$711$	35.0303	+	15.9379i	1.31374	+	0.597717i
$712$	29.8894	−	25.4609i	1.12015	−	0.954187i
$713$	4.59050			0.171916
$714$	−7.35874	+	2.34435i	−0.275394	+	0.0877351i
$715$			22.9481i			0.858211i
$716$	−30.6977	+	3.74221i	−1.14723	+	0.139853i
$717$	−35.6329	+	11.4184i	−1.33073	+	0.426429i
$718$	20.0057	−	1.21491i	0.746607	−	0.0453399i
$719$	12.1803	+	21.0969i	0.454250	+	0.786783i	0.998645	−	0.0520455i	$-0.0165741\pi$
$719$	12.1803	+	21.0969i	0.454250	+	0.786783i	−0.544395	+	0.838829i	$0.683241\pi$
$720$	−28.0866	−	24.0422i	−1.04673	−	0.895999i
$721$	−2.04942	+	32.8289i	−0.0763243	+	1.22261i
$722$	−20.6334	+	13.6441i	−0.767895	+	0.507781i
$723$	−1.43434	+	6.61609i	−0.0533435	+	0.246055i
$724$	−19.9728	−	26.5527i	−0.742284	−	0.986822i
$725$	−7.18536	+	12.4454i	−0.266858	+	0.462211i
$726$	21.5830	−	8.39013i	0.801019	−	0.311387i
$727$			5.15142i			0.191055i	0.995427	+	0.0955277i	$0.0304539\pi$
$727$			5.15142i			0.191055i	−0.995427	+	0.0955277i	$0.969546\pi$
$728$	41.2138	+	17.6188i	1.52748	+	0.652997i
$729$	7.71680	+	25.8738i	0.285807	+	0.958287i
$730$	40.1975	+	20.0635i	1.48778	+	0.742583i
$731$	8.55627	+	4.93997i	0.316465	+	0.182711i
$732$	21.8342	+	2.01849i	0.807013	+	0.0746056i
$733$	−3.74171	−	6.48083i	−0.138203	−	0.239375i	0.788613	−	0.614889i	$-0.210799\pi$
$733$	−3.74171	−	6.48083i	−0.138203	−	0.239375i	−0.926817	+	0.375514i	$0.877466\pi$
$734$	10.4125	+	15.7464i	0.384333	+	0.581211i
$735$	12.3933	−	35.2387i	0.457133	−	1.29980i
$736$	3.66827	−	16.3785i	0.135214	−	0.603721i
$737$	−13.3464	+	7.70552i	−0.491619	+	0.283837i
$738$	−39.5587	+	6.27320i	−1.45618	+	0.230920i
$739$	−2.26360	−	1.30689i	−0.0832679	−	0.0480747i	0.457788	−	0.889061i	$-0.348642\pi$
$739$	−2.26360	−	1.30689i	−0.0832679	−	0.0480747i	−0.541056	+	0.840987i	$0.681975\pi$
$740$	2.36590	−	0.288416i	0.0869722	−	0.0106024i
$741$	8.56448	−	9.43466i	0.314624	−	0.346591i
$742$	0.0665544	−	39.3110i	0.00244329	−	1.44315i
$743$		−	23.6093i		−	0.866140i	−0.901360	−	0.433070i	$-0.857430\pi$
$743$		−	23.6093i		−	0.866140i	0.901360	−	0.433070i	$-0.142570\pi$
$744$	7.57568	+	0.238949i	0.277738	+	0.00876030i
$745$	11.0580	+	6.38431i	0.405132	+	0.233903i
$746$	−7.44852	+	0.452332i	−0.272710	+	0.0165611i
$747$	−9.11713	−	12.7649i	−0.333578	−	0.467044i
$748$	1.16046	−	2.72730i	0.0424306	−	0.0997200i
$749$	25.2987	+	1.57933i	0.924394	+	0.0577074i
$750$	3.78722	+	0.583380i	0.138290	+	0.0213020i
$751$	0.504993	+	0.874673i	0.0184275	+	0.0319173i	0.875092	−	0.483956i	$-0.160801\pi$
$751$	0.504993	+	0.874673i	0.0184275	+	0.0319173i	−0.856665	+	0.515874i	$0.827467\pi$
$752$	25.9564	−	6.42392i	0.946534	−	0.234256i
$753$	25.8182	−	8.27335i	0.940868	−	0.301497i
$754$	24.2450	+	12.1012i	0.882952	+	0.440701i
$755$		−	13.3397i		−	0.485480i
$756$	22.9761	+	15.1030i	0.835632	+	0.549289i
$757$			11.1837i			0.406478i	0.979129	+	0.203239i	$0.0651469\pi$
$757$			11.1837i			0.406478i	−0.979129	+	0.203239i	$0.934853\pi$
$758$	−9.70205	+	19.4382i	−0.352394	+	0.706028i
$759$	−6.08598	+	1.95023i	−0.220907	+	0.0707888i
$760$	−3.58594	+	10.0847i	−0.130076	+	0.365811i
$761$	−3.99009	−	6.91104i	−0.144641	−	0.250525i	0.784598	−	0.620005i	$-0.212869\pi$
$761$	−3.99009	−	6.91104i	−0.144641	−	0.250525i	−0.929239	+	0.369480i	$0.879536\pi$
$762$	−2.19554	+	14.2531i	−0.0795360	+	0.516336i
$763$	−1.39641	+	0.694029i	−0.0505534	+	0.0251255i
$764$	−0.831163	−	0.353658i	−0.0300704	−	0.0127949i
$765$	−6.40190	−	8.96331i	−0.231461	−	0.324069i
$766$	0.232182	+	3.82332i	0.00838907	+	0.138142i
$767$	−19.3402	−	11.1661i	−0.698333	−	0.403183i
$768$	6.90628	−	26.8385i	0.249209	−	0.968450i
$769$

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26535 - 0.631567i) q^{2} +(0.528554 + 1.64943i) q^{3} +(1.20225 + 1.59831i) q^{4} +(2.66818 - 1.54047i) q^{5} +(0.372919 - 2.42094i) q^{6} +(-1.46307 + 2.20441i) q^{7} +(-0.511826 - 2.78173i) q^{8} +(-2.44126 + 1.74363i) q^{9} +O(q^{10})\)	\(q+(-1.26535 - 0.631567i) q^{2} +(0.528554 + 1.64943i) q^{3} +(1.20225 + 1.59831i) q^{4} +(2.66818 - 1.54047i) q^{5} +(0.372919 - 2.42094i) q^{6} +(-1.46307 + 2.20441i) q^{7} +(-0.511826 - 2.78173i) q^{8} +(-2.44126 + 1.74363i) q^{9} +(-4.34911 + 0.264112i) q^{10} +(-0.621780 + 1.07696i) q^{11} +(-2.00086 + 2.82782i) q^{12} +5.98957 q^{13} +(3.24353 - 1.86534i) q^{14} +(3.95119 + 3.58676i) q^{15} +(-1.10921 + 3.84313i) q^{16} +(-0.595854 + 1.03205i) q^{17} +(4.19028 - 0.664491i) q^{18} +(-0.614126 - 1.06370i) q^{19} +(5.66997 + 2.41256i) q^{20} +(-4.40934 - 1.24808i) q^{21} +(1.46694 - 0.970035i) q^{22} +(2.56956 - 1.48354i) q^{23} +(4.31775 - 2.31452i) q^{24} +(2.24612 - 3.89040i) q^{25} +(-7.57893 - 3.78282i) q^{26} +(-4.16634 - 3.10509i) q^{27} +(-5.28231 + 0.311808i) q^{28} -3.19900 q^{29} +(-2.73438 - 7.03397i) q^{30} +(1.33987 + 0.773574i) q^{31} +(3.83074 - 4.16238i) q^{32} +(-2.10501 - 0.456356i) q^{33} +(1.40578 - 0.929587i) q^{34} +(-0.507883 + 8.13559i) q^{35} +(-5.72186 - 1.80563i) q^{36} +(0.334978 - 0.193399i) q^{37} +(0.105291 + 1.73382i) q^{38} +(3.16581 + 9.87940i) q^{39} +(-5.65083 - 6.63371i) q^{40} -9.44060 q^{41} +(4.79114 + 4.36406i) q^{42} -8.29057i q^{43} +(-2.46884 + 0.300965i) q^{44} +(-3.82770 + 8.41302i) q^{45} +(-4.18836 + 0.254350i) q^{46} +(-3.34244 - 5.78928i) q^{47} +(-6.92527 + 0.201736i) q^{48} +(-2.71887 - 6.45041i) q^{49} +(-5.29919 + 3.50416i) q^{50} +(-2.01724 - 0.437327i) q^{51} +(7.20094 + 9.57321i) q^{52} +(5.25317 - 9.09875i) q^{53} +(3.31083 + 6.56037i) q^{54} +3.83135i q^{55} +(6.88092 + 2.94158i) q^{56} +(1.42990 - 1.57518i) q^{57} +(4.04788 + 2.02039i) q^{58} +(-3.22898 - 1.86425i) q^{59} +(-0.982467 + 10.6274i) q^{60} +(-3.16493 - 5.48181i) q^{61} +(-1.20685 - 1.82506i) q^{62} +(-0.271956 - 7.93259i) q^{63} +(-7.47607 + 2.84752i) q^{64} +(15.9813 - 9.22678i) q^{65} +(2.37537 + 1.90691i) q^{66} +(10.7324 + 6.19634i) q^{67} +(-2.36590 + 0.288416i) q^{68} +(3.80515 + 3.45419i) q^{69} +(5.78082 - 9.97364i) q^{70} +6.21100i q^{71} +(6.09981 + 5.89850i) q^{72} +(-8.92963 - 5.15552i) q^{73} +(-0.546010 + 0.0331580i) q^{74} +(7.60415 + 1.64854i) q^{75} +(0.961791 - 2.26039i) q^{76} +(-1.46435 - 2.94632i) q^{77} +(2.23362 - 14.5004i) q^{78} +(-6.41425 - 11.1098i) q^{79} +(2.96067 + 11.9629i) q^{80} +(2.91950 - 8.51331i) q^{81} +(11.9457 + 5.96237i) q^{82} +5.22882i q^{83} +(-3.30629 - 8.54801i) q^{84} +3.67159i q^{85} +(-5.23605 + 10.4905i) q^{86} +(-1.69085 - 5.27654i) q^{87} +(3.31404 + 1.17841i) q^{88} +(6.94090 + 12.0220i) q^{89} +(10.1568 - 8.22800i) q^{90} +(-8.76314 + 13.2035i) q^{91} +(5.46040 + 2.32339i) q^{92} +(-0.567765 + 2.61890i) q^{93} +(0.573057 + 9.43648i) q^{94} +(-3.27720 - 1.89209i) q^{95} +(8.89033 + 4.11850i) q^{96} +17.1489i q^{97} +(-0.633524 + 9.87920i) q^{98} +(-0.359884 - 3.71328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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