LMFDB - Embedded newform 168.2.ba.c.5.12

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			5.12
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0857242 - 1.41161i) q^{2} +(-0.528554 + 1.64943i) q^{3} +(-1.98530 + 0.242019i) q^{4} +(-2.66818 - 1.54047i) q^{5} +(2.37367 + 0.604718i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(0.511826 + 2.78173i) q^{8} +(-2.44126 - 1.74363i) q^{9} +O(q^{10})$	\(q+(-0.0857242 - 1.41161i) q^{2} +(-0.528554 + 1.64943i) q^{3} +(-1.98530 + 0.242019i) q^{4} +(-2.66818 - 1.54047i) q^{5} +(2.37367 + 0.604718i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(0.511826 + 2.78173i) q^{8} +(-2.44126 - 1.74363i) q^{9} +(-1.94583 + 3.89849i) q^{10} +(0.621780 + 1.07696i) q^{11} +(0.650147 - 3.40254i) q^{12} -5.98957 q^{13} +(-2.98636 + 2.25426i) q^{14} +(3.95119 - 3.58676i) q^{15} +(3.88285 - 0.960961i) q^{16} +(-0.595854 - 1.03205i) q^{17} +(-2.25206 + 3.59559i) 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} +(-4.85881 - 0.626075i) q^{24} +(2.24612 + 3.89040i) q^{25} +(0.513451 + 8.45496i) q^{26} +(4.16634 - 3.10509i) q^{27} +(3.43814 + 4.02234i) q^{28} +3.19900 q^{29} +(-5.40183 - 5.27008i) q^{30} +(1.33987 - 0.773574i) q^{31} +(-1.68936 - 5.39871i) q^{32} +(-2.10501 + 0.456356i) q^{33} +(-1.40578 + 0.929587i) q^{34} +(0.507883 + 8.13559i) q^{35} +(5.26863 + 2.87080i) q^{36} +(-0.334978 - 0.193399i) q^{37} +(-1.55417 - 0.775723i) q^{38} +(3.16581 - 9.87940i) q^{39} +(2.91955 - 8.21062i) q^{40} -9.44060 q^{41} +(-2.13979 - 6.11729i) q^{42} -8.29057i q^{43} +(-1.49507 - 1.98760i) q^{44} +(3.82770 + 8.41302i) q^{45} +(1.87391 - 3.75440i) q^{46} +(-3.34244 + 5.78928i) q^{47} +(-0.467258 + 6.91243i) q^{48} +(-2.71887 + 6.45041i) q^{49} +(5.29919 - 3.50416i) q^{50} +(2.01724 - 0.437327i) q^{51} +(11.8911 - 1.44959i) q^{52} +(-5.25317 - 9.09875i) q^{53} +(-4.74035 - 5.61508i) q^{54} -3.83135i q^{55} +(5.38325 - 5.19813i) q^{56} +(1.42990 + 1.57518i) q^{57} +(-0.274232 - 4.51576i) q^{58} +(3.22898 - 1.86425i) q^{59} +(-6.97624 + 8.07707i) 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} +(0.824648 + 2.93234i) q^{66} +(-10.7324 + 6.19634i) q^{67} +(1.43273 + 1.90472i) q^{68} +(-3.80515 + 3.45419i) q^{69} +(11.4408 - 1.41435i) q^{70} -6.21100i q^{71} +(3.60081 - 7.68337i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(-0.244290 + 0.489438i) q^{74} +(-7.60415 + 1.64854i) q^{75} +(-0.961791 + 2.26039i) q^{76} +(1.46435 - 2.94632i) q^{77} +(-14.2173 - 3.62200i) q^{78} +(-6.41425 + 11.1098i) q^{79} +(-11.8405 - 3.41742i) q^{80} +(2.91950 + 8.51331i) q^{81} +(0.809288 + 13.3265i) q^{82} +5.22882i q^{83} +(-8.45182 + 3.54496i) q^{84} +3.67159i q^{85} +(-11.7031 + 0.710702i) q^{86} +(-1.69085 + 5.27654i) q^{87} +(-2.67756 + 2.28084i) q^{88} +(6.94090 - 12.0220i) q^{89} +(11.5478 - 6.12444i) q^{90} +(8.76314 + 13.2035i) q^{91} +(-5.46040 - 2.32339i) q^{92} +(0.567765 + 2.61890i) q^{93} +(8.45876 + 4.22196i) q^{94} +(-3.27720 + 1.89209i) q^{95} +(9.79773 + 0.0670247i) q^{96} -17.1489i q^{97} +(9.33855 + 3.28504i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.0857242	−	1.41161i	−0.0606162	−	0.998161i
$2$	−0.0857242	−	1.41161i	−0.0606162	−	0.998161i
$3$	−0.528554	+	1.64943i	−0.305161	+	0.952301i
$3$	−0.528554	+	1.64943i	−0.305161	+	0.952301i
$4$	−1.98530	+	0.242019i	−0.992651	+	0.121009i
$5$	−2.66818	−	1.54047i	−1.19325	−	0.688921i	−0.234205	−	0.972187i	$-0.575249\pi$
$5$	−2.66818	−	1.54047i	−1.19325	−	0.688921i	−0.959041	+	0.283266i	$0.908582\pi$
$6$	2.37367	+	0.604718i	0.969047	+	0.246875i
$7$	−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
$10$	−1.94583	+	3.89849i	−0.615324	+	1.23281i
$11$	0.621780	+	1.07696i	0.187474	+	0.324714i	0.944407	−	0.328778i	$-0.106637\pi$
$11$	0.621780	+	1.07696i	0.187474	+	0.324714i	−0.756933	+	0.653492i	$0.773303\pi$
$12$	0.650147	−	3.40254i	0.187681	−	0.982230i
$13$	−5.98957			−1.66121			−0.830604	−	0.556864i	$-0.812005\pi$
$13$	−5.98957			−1.66121			−0.830604	+	0.556864i	$0.812005\pi$
$14$	−2.98636	+	2.25426i	−0.798138	+	0.602475i
$15$	3.95119	−	3.58676i	1.02019	−	0.926098i
$16$	3.88285	−	0.960961i	0.970713	−	0.240240i
$17$	−0.595854	−	1.03205i	−0.144516	−	0.250309i	0.784676	−	0.619906i	$-0.212829\pi$
$17$	−0.595854	−	1.03205i	−0.144516	−	0.250309i	−0.929192	+	0.369597i	$0.879496\pi$
$18$	−2.25206	+	3.59559i	−0.530815	+	0.847488i
$19$	0.614126	−	1.06370i	0.140890	−	0.244029i	−0.786942	−	0.617027i	$-0.788337\pi$
$19$	0.614126	−	1.06370i	0.140890	−	0.244029i	0.927832	+	0.372998i	$0.121670\pi$
$20$	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	0.743371	−	0.668879i	$-0.233226\pi$
$23$	2.56956	+	1.48354i	0.535791	+	0.309339i	−0.207581	+	0.978218i	$0.566559\pi$
$24$	−4.85881	−	0.626075i	−0.991800	−	0.127797i
$25$	2.24612	+	3.89040i	0.449225	+	0.778080i
$26$	0.513451	+	8.45496i	0.100696	+	1.65815i
$27$	4.16634	−	3.10509i	0.801813	−	0.597575i
$28$	3.43814	+	4.02234i	0.649747	+	0.760150i
$29$	3.19900			0.594040			0.297020	−	0.954871i	$-0.404007\pi$
$29$	3.19900			0.594040			0.297020	+	0.954871i	$0.404007\pi$
$30$	−5.40183	−	5.27008i	−0.986235	−	0.962180i
$31$	1.33987	−	0.773574i	0.240648	−	0.138938i	−0.374827	−	0.927095i	$-0.622298\pi$
$31$	1.33987	−	0.773574i	0.240648	−	0.138938i	0.615474	+	0.788157i	$0.288964\pi$
$32$	−1.68936	−	5.39871i	−0.298640	−	0.954366i
$33$	−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
$36$	5.26863	+	2.87080i	0.878105	+	0.478467i
$37$	−0.334978	−	0.193399i	−0.0550700	−	0.0317947i	0.472212	−	0.881485i	$-0.343456\pi$
$37$	−0.334978	−	0.193399i	−0.0550700	−	0.0317947i	−0.527282	+	0.849690i	$0.676789\pi$
$38$	−1.55417	−	0.775723i	−0.252120	−	0.125839i
$39$	3.16581	−	9.87940i	0.506936	−	1.58197i
$40$	2.91955	−	8.21062i	0.461621	−	1.29821i
$41$	−9.44060			−1.47437			−0.737187	−	0.675689i	$-0.763846\pi$
$41$	−9.44060			−1.47437			−0.737187	+	0.675689i	$0.763846\pi$
$42$	−2.13979	−	6.11729i	−0.330177	−	0.943919i
$43$		−	8.29057i		−	1.26430i	−0.774846	−	0.632150i	$-0.782173\pi$
$43$		−	8.29057i		−	1.26430i	0.774846	−	0.632150i	$-0.217827\pi$
$44$	−1.49507	−	1.98760i	−0.225390	−	0.299642i
$45$	3.82770	+	8.41302i	0.570600	+	1.25414i
$46$	1.87391	−	3.75440i	0.276292	−	0.553556i
$47$	−3.34244	+	5.78928i	−0.487546	+	0.844454i	−0.999897	−	0.0143219i	$-0.995441\pi$
$47$	−3.34244	+	5.78928i	−0.487546	+	0.844454i	0.512352	+	0.858776i	$0.328774\pi$
$48$	−0.467258	+	6.91243i	−0.0674429	+	0.997723i
$49$	−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
$52$	11.8911	−	1.44959i	1.64900	−	0.201022i
$53$	−5.25317	−	9.09875i	−0.721578	−	1.24981i	−0.960367	−	0.278738i	$-0.910084\pi$
$53$	−5.25317	−	9.09875i	−0.721578	−	1.24981i	0.238789	−	0.971071i	$-0.423250\pi$
$54$	−4.74035	−	5.61508i	−0.645079	−	0.764116i
$55$		−	3.83135i		−	0.516619i
$56$	5.38325	−	5.19813i	0.719367	−	0.694630i
$57$	1.42990	+	1.57518i	0.189395	+	0.208638i
$58$	−0.274232	−	4.51576i	−0.0360084	−	0.592948i
$59$	3.22898	−	1.86425i	0.420377	−	0.242705i	−0.274862	−	0.961484i	$-0.588632\pi$
$59$	3.22898	−	1.86425i	0.420377	−	0.242705i	0.695238	+	0.718779i	$0.255299\pi$
$60$	−6.97624	+	8.07707i	−0.900629	+	1.04274i
$61$	3.16493	−	5.48181i	0.405227	−	0.701874i	−0.589121	−	0.808045i	$-0.700526\pi$
$61$	3.16493	−	5.48181i	0.405227	−	0.701874i	0.994348	+	0.106171i	$0.0338590\pi$
$62$	−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
$66$	0.824648	+	2.93234i	0.101507	+	0.360946i
$67$	−10.7324	+	6.19634i	−1.31117	+	0.757003i	−0.982290	−	0.187369i	$-0.940004\pi$
$67$	−10.7324	+	6.19634i	−1.31117	+	0.757003i	−0.328878	+	0.944372i	$0.606671\pi$
$68$	1.43273	+	1.90472i	0.173744	+	0.230982i
$69$	−3.80515	+	3.45419i	−0.458086	+	0.415836i
$70$	11.4408	−	1.41435i	1.36743	−	0.169047i
$71$		−	6.21100i		−	0.737110i	−0.929606	−	0.368555i	$-0.879853\pi$
$71$		−	6.21100i		−	0.737110i	0.929606	−	0.368555i	$-0.120147\pi$
$72$	3.60081	−	7.68337i	0.424360	−	0.905494i
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.921283	−	0.388893i	$-0.872858\pi$
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.123851	+	0.992301i	$0.539524\pi$
$74$	−0.244290	+	0.489438i	−0.0283981	+	0.0568960i
$75$	−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
$78$	−14.2173	−	3.62200i	−1.60979	−	0.410111i
$79$	−6.41425	+	11.1098i	−0.721660	+	1.24995i	0.238674	+	0.971100i	$0.423287\pi$
$79$	−6.41425	+	11.1098i	−0.721660	+	1.24995i	−0.960334	+	0.278852i	$0.910046\pi$
$80$	−11.8405	−	3.41742i	−1.32381	−	0.382079i
$81$	2.91950	+	8.51331i	0.324389	+	0.945924i
$82$	0.809288	+	13.3265i	0.0893709	+	1.47166i
$83$			5.22882i			0.573938i	0.957940	+	0.286969i	$0.0926476\pi$
$83$			5.22882i			0.573938i	−0.957940	+	0.286969i	$0.907352\pi$
$84$	−8.45182	+	3.54496i	−0.922169	+	0.386787i
$85$			3.67159i			0.398240i
$86$	−11.7031	+	0.710702i	−1.26197	+	0.0766370i
$87$	−1.69085	+	5.27654i	−0.181278	+	0.565705i
$88$	−2.67756	+	2.28084i	−0.285429	+	0.243138i
$89$	6.94090	−	12.0220i	0.735734	−	1.27433i	−0.218666	−	0.975800i	$-0.570171\pi$
$89$	6.94090	−	12.0220i	0.735734	−	1.27433i	0.954400	−	0.298529i	$-0.0964960\pi$
$90$	11.5478	−	6.12444i	1.21725	−	0.645572i
$91$	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
$94$	8.45876	+	4.22196i	0.872454	+	0.435462i
$95$	−3.27720	+	1.89209i	−0.336233	+	0.194124i
$96$	9.79773	+	0.0670247i	0.999977	+	0.00684068i
$97$		−	17.1489i		−	1.74120i	−0.491989	−	0.870601i	$-0.663730\pi$
$97$		−	17.1489i		−	1.74120i	0.491989	−	0.870601i	$-0.336270\pi$
$98$	9.33855	+	3.28504i	0.943336	+	0.331839i
$99$	0.359884	−	3.71328i	0.0361697	−	0.373199i
$100$	−5.40078	−	7.18002i	−0.540078	−	0.718002i
$101$	−2.87413	+	1.65938i	−0.285986	+	0.165114i	−0.636130	−	0.771582i	$-0.719466\pi$
$101$	−2.87413	+	1.65938i	−0.285986	+	0.165114i	0.350144	+	0.936696i	$0.386133\pi$
$102$	−0.790263	−	2.81007i	−0.0782477	−	0.278238i
$103$	10.7667	+	6.21615i	1.06087	+	0.612496i	0.925674	−	0.378322i	$-0.123499\pi$
$103$	10.7667	+	6.21615i	1.06087	+	0.612496i	0.135200	+	0.990818i	$0.456832\pi$
$104$	−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	$-0.680072\pi$
$107$	4.79031	−	8.29706i	0.463097	−	0.802107i	0.999113	+	0.0421002i	$0.0134049\pi$
$108$	−7.51996	+	7.17288i	−0.723608	+	0.690211i
$109$	−0.510424	+	0.294693i	−0.0488898	+	0.0282265i	−0.524246	−	0.851567i	$-0.675653\pi$
$109$	−0.510424	+	0.294693i	−0.0488898	+	0.0282265i	0.475356	+	0.879794i	$0.342319\pi$
$110$	−5.40838	+	0.328439i	−0.515669	+	0.0313155i
$111$	0.496053	−	0.450301i	0.0470833	−	0.0427407i
$112$	−7.79923	−	7.15346i	−0.736958	−	0.675939i
$113$		−	7.02041i		−	0.660425i	−0.943907	−	0.330212i	$-0.892880\pi$
$113$		−	7.02041i		−	0.660425i	0.943907	−	0.330212i	$-0.107120\pi$
$114$	2.10097	−	2.15349i	0.196774	−	0.201693i
$115$	−4.57070	−	7.91669i	−0.426220	−	0.738235i
$116$	−6.35099	+	0.774219i	−0.589675	+	0.0718845i
$117$	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
$120$	11.9997	+	9.15535i	1.09542	+	0.835766i
$121$	4.72678	−	8.18702i	0.429707	−	0.744275i
$122$	−8.00951	−	3.99773i	−0.725147	−	0.361937i
$123$	4.98987	−	15.5716i	0.449921	−	1.40405i
$124$	−2.47283	+	1.86005i	−0.222066	+	0.167038i
$125$			1.56436i			0.139921i
$126$	11.2211	−	0.296119i	0.999652	−	0.0263804i
$127$	−5.88744			−0.522426			−0.261213	−	0.965281i	$-0.584123\pi$
$127$	−5.88744			−0.522426			−0.261213	+	0.965281i	$0.584123\pi$
$128$	4.66048	+	10.3092i	0.411932	+	0.911214i
$129$	13.6747	+	4.38201i	1.20399	+	0.385815i
$130$	11.6547	−	23.3503i	1.02218	−	2.04796i
$131$	3.67922	+	2.12420i	0.321455	+	0.185592i	0.652041	−	0.758184i	$-0.273913\pi$
$131$	3.67922	+	2.12420i	0.321455	+	0.185592i	−0.330586	+	0.943776i	$0.607246\pi$
$132$	4.06864	−	1.41546i	0.354129	−	0.123200i
$133$	−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
$136$	2.56591	−	2.18574i	0.220025	−	0.187425i
$137$	0.674838	−	0.389618i	0.0576553	−	0.0332873i	−0.470895	−	0.882189i	$-0.656069\pi$
$137$	0.674838	−	0.389618i	0.0576553	−	0.0332873i	0.528551	+	0.848902i	$0.322736\pi$
$138$	5.20217	+	5.07529i	0.442838	+	0.432037i
$139$	5.54714			0.470502			0.235251	−	0.971935i	$-0.424409\pi$
$139$	5.54714			0.470502			0.235251	+	0.971935i	$0.424409\pi$
$140$	−2.97727	−	16.0287i	−0.251625	−	1.35467i
$141$	−7.78237	−	8.57309i	−0.655394	−	0.721984i
$142$	−8.76752	+	0.532433i	−0.735754	+	0.0446808i
$143$	−3.72420	−	6.45050i	−0.311433	−	0.539418i
$144$	−11.1546	−	4.42431i	−0.929552	−	0.368692i
$145$	−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	$-0.887633\pi$
$149$	−2.07219	+	3.58914i	−0.169761	+	0.294034i	0.768575	+	0.639760i	$0.220966\pi$
$150$	2.97896	+	10.5928i	0.243231	+	0.864899i
$151$	2.16486	+	3.74965i	0.176174	+	0.305142i	0.940567	−	0.339608i	$-0.110295\pi$
$151$	2.16486	+	3.74965i	0.176174	+	0.305142i	−0.764393	+	0.644751i	$0.776961\pi$
$152$	3.27325	+	1.16391i	0.265495	+	0.0944052i
$153$	−0.344878	+	3.55845i	−0.0278817	+	0.287684i
$154$	−4.28459	−	1.81452i	−0.345262	−	0.146218i
$155$	−4.76668			−0.382869
$156$	−3.89410	+	20.3798i	−0.311777	+	1.63169i
$157$	−3.21017	−	5.56018i	−0.256200	−	0.443751i	0.709021	−	0.705187i	$-0.249137\pi$
$157$	−3.21017	−	5.56018i	−0.256200	−	0.443751i	−0.965221	+	0.261437i	$0.915804\pi$
$158$	16.2326	+	8.10207i	1.29140	+	0.644566i
$159$	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
$162$	11.7672	−	4.85101i	0.924521	−	0.381131i
$163$	−9.18195	−	5.30120i	−0.719186	−	0.415222i	0.0952672	−	0.995452i	$-0.469629\pi$
$163$	−9.18195	−	5.30120i	−0.719186	−	0.415222i	−0.814453	+	0.580230i	$0.802963\pi$
$164$	18.7424	−	2.28480i	1.46354	−	0.178413i
$165$	6.31955	+	2.02508i	0.491977	+	0.157652i
$166$	7.38107	−	0.448237i	0.572882	−	0.0347899i
$167$	−15.5718			−1.20498			−0.602492	−	0.798125i	$-0.705825\pi$
$167$	−15.5718			−1.20498			−0.602492	+	0.798125i	$0.705825\pi$
$168$	5.72863	+	11.6268i	0.441974	+	0.897028i
$169$	22.8750			1.75961
$170$	5.18287	−	0.314744i	0.397508	−	0.0241398i
$171$	−3.35394	+	1.52595i	−0.256482	+	0.116693i
$172$	2.00647	+	16.4593i	0.152992	+	1.25501i
$173$	1.61807	+	0.934192i	0.123019	+	0.0710253i	0.560247	−	0.828326i	$-0.310706\pi$
$173$	1.61807	+	0.934192i	0.123019	+	0.0710253i	−0.437228	+	0.899351i	$0.644040\pi$
$174$	7.59339	+	1.93450i	0.575653	+	0.146654i
$175$	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
$178$	−17.5654	−	8.76729i	−1.31658	−	0.657136i
$179$	7.73124	+	13.3909i	0.577860	+	1.00088i	0.995724	+	0.0923734i	$0.0294454\pi$
$179$	7.73124	+	13.3909i	0.577860	+	1.00088i	−0.417864	+	0.908509i	$0.637221\pi$
$180$	−9.63526	−	15.7760i	−0.718170	−	1.17587i
$181$	16.6129			1.23483			0.617415	−	0.786638i	$-0.288180\pi$
$181$	16.6129			1.23483			0.617415	+	0.786638i	$0.288180\pi$
$182$	17.8870	−	13.5020i	1.32587	−	1.00084i
$183$	7.36905	+	8.11777i	0.544736	+	0.600083i
$184$	−2.81164	+	7.90714i	−0.207277	+	0.582922i
$185$	0.595854	+	1.03205i	0.0438081	+	0.0758778i
$186$	3.64820	−	1.02597i	0.267499	−	0.0752276i
$187$	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	0.485783	−	0.874080i	$-0.338535\pi$
$191$	−0.391130	−	0.225819i	−0.0283012	−	0.0163397i	−0.514084	+	0.857740i	$0.671868\pi$
$192$	−0.745290	−	13.8363i	−0.0537867	−	0.998552i
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	0.895293	−	0.445477i	$-0.146966\pi$
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	−0.833441	+	0.552608i	$0.813633\pi$
$194$	−24.2076	+	1.47007i	−1.73800	+	0.105545i
$195$	−23.6659	+	21.4832i	−1.69475	+	1.53844i
$196$	3.83667	−	13.4640i	0.274048	−	0.961716i
$197$	−16.4222			−1.17003			−0.585017	−	0.811021i	$-0.698912\pi$
$197$	−16.4222			−1.17003			−0.585017	+	0.811021i	$0.698912\pi$
$198$	−5.27257	−	0.189699i	−0.374705	−	0.0134813i
$199$	0.839396	−	0.484625i	0.0595032	−	0.0343542i	−0.469953	−	0.882691i	$-0.655729\pi$
$199$	0.839396	−	0.484625i	0.0595032	−	0.0343542i	0.529456	+	0.848337i	$0.322396\pi$
$200$	−9.67243	+	8.23932i	−0.683944	+	0.582608i
$201$	−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
$204$	−3.89899	+	1.35644i	−0.272984	+	0.0949695i
$205$	25.1892	+	14.5430i	1.75929	+	1.01573i
$206$	7.85184	−	15.7313i	0.547063	−	1.09605i
$207$	−3.68623	−	8.10207i	−0.256211	−	0.563132i
$208$	−23.2566	+	5.75575i	−1.61256	+	0.399089i
$209$	1.52741			0.105653
$210$	−3.71419	+	19.6183i	−0.256303	+	1.35379i
$211$			9.99340i			0.687974i	0.938974	+	0.343987i	$0.111778\pi$
$211$			9.99340i			0.687974i	−0.938974	+	0.343987i	$0.888222\pi$
$212$	12.6312	+	16.7924i	0.867514	+	1.15331i
$213$	10.2446	+	3.28285i	0.701950	+	0.224937i
$214$	−12.1229	−	6.05081i	−0.828703	−	0.413625i
$215$	−12.7714	+	22.1207i	−0.871003	+	1.50862i
$216$	10.7700	+	10.0004i	0.732804	+	0.680440i
$217$	−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
$220$	0.927258	+	7.60639i	0.0625158	+	0.512822i
$221$	3.56891	+	6.18153i	0.240071	+	0.415815i
$222$	−0.678175	−	0.661634i	−0.0455161	−	0.0444060i
$223$		−	13.7534i		−	0.920996i	−0.887661	−	0.460498i	$-0.847671\pi$
$223$		−	13.7534i		−	0.920996i	0.887661	−	0.460498i	$-0.152329\pi$
$224$	−9.42934	+	11.6227i	−0.630024	+	0.776576i
$225$	1.30005	−	13.4139i	0.0866699	−	0.894259i
$226$	−9.91010	+	0.601819i	−0.659210	+	0.0400324i
$227$	−4.13075	+	2.38489i	−0.274167	+	0.158291i	−0.630780	−	0.775962i	$-0.717265\pi$
$227$	−4.13075	+	2.38489i	−0.274167	+	0.158291i	0.356613	+	0.934252i	$0.383932\pi$
$228$	−3.22000	−	2.78115i	−0.213250	−	0.184186i
$229$	0.743202	−	1.28726i	0.0491122	−	0.0850648i	−0.840424	−	0.541929i	$-0.817694\pi$
$229$	0.743202	−	1.28726i	0.0491122	−	0.0850648i	0.889536	+	0.456864i	$0.151027\pi$
$230$	−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	0.564139	−	0.825680i	$-0.309208\pi$
$233$	2.00188	+	1.15579i	0.131148	+	0.0757182i	−0.432991	+	0.901398i	$0.642542\pi$
$234$	13.4889	−	21.5360i	0.881794	−	1.40785i
$235$	17.8365	−	10.2979i	1.16352	−	0.671761i
$236$	−5.95931	+	4.48257i	−0.387918	+	0.291791i
$237$	−14.9346	−	16.4520i	−0.970108	−	1.06867i
$238$	4.10594	+	1.73886i	0.266148	+	0.112714i
$239$		−	21.6031i		−	1.39739i	−0.715420	−	0.698695i	$-0.753765\pi$
$239$		−	21.6031i		−	1.39739i	0.715420	−	0.698695i	$-0.246235\pi$
$240$	11.8951	−	17.7238i	0.767829	−	1.14407i
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	−0.387002	−	0.922079i	$-0.626489\pi$
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	0.605042	+	0.796193i	$0.293156\pi$
$242$	−11.9621	−	5.97056i	−0.768953	−	0.383802i
$243$	−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
$246$	−22.4089	−	5.70890i	−1.42874	−	0.363986i
$247$	−3.67835	+	6.37109i	−0.234048	+	0.405383i
$248$	2.83766	+	3.33122i	0.180191	+	0.211533i
$249$	−8.62459	−	2.76372i	−0.546561	−	0.175143i
$250$	2.20827	−	0.134104i	0.139664	−	0.00848147i
$251$		−	15.6528i		−	0.987995i	−0.869463	−	0.493997i	$-0.835535\pi$
$251$		−	15.6528i		−	0.987995i	0.869463	−	0.493997i	$-0.164465\pi$
$252$	−1.37992	−	15.8144i	−0.0869270	−	0.996215i
$253$			3.68974i			0.231972i
$254$	0.504696	+	8.31079i	0.0316675	+	0.521465i
$255$	−6.05604	−	1.94064i	−0.379244	−	0.121527i
$256$	14.1531	−	7.46255i	0.884569	−	0.466409i
$257$	−6.53148	+	11.3128i	−0.407422	+	0.705676i	−0.994600	−	0.103782i	$-0.966906\pi$
$257$	−6.53148	+	11.3128i	−0.407422	+	0.705676i	0.587178	+	0.809458i	$0.300239\pi$
$258$	5.01345	−	19.6791i	0.312124	−	1.22517i
$259$	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
$262$	2.68315	−	5.37573i	0.165766	−	0.332114i
$263$	26.2857	−	15.1761i	1.62085	−	0.935796i	0.634151	−	0.773209i	$-0.281350\pi$
$263$	26.2857	−	15.1761i	1.62085	−	0.935796i	0.986694	−	0.162586i	$-0.0519836\pi$
$264$	−2.34686	−	5.62200i	−0.144439	−	0.346010i
$265$			32.3695i			1.98844i
$266$	0.563845	+	4.56098i	0.0345716	+	0.279651i
$267$	16.1608	+	17.8028i	0.989027	+	1.08952i
$268$	19.8074	−	14.8990i	1.20993	−	0.910104i
$269$	−0.684713	+	0.395319i	−0.0417477	+	0.0241030i	−0.520729	−	0.853722i	$-0.674340\pi$
$269$	−0.684713	+	0.395319i	−0.0417477	+	0.0241030i	0.478981	+	0.877825i	$0.341006\pi$
$270$	3.99821	+	22.2844i	0.243323	+	1.35619i
$271$	−4.95134	−	2.85866i	−0.300773	−	0.173651i	0.342017	−	0.939694i	$-0.388890\pi$
$271$	−4.95134	−	2.85866i	−0.300773	−	0.173651i	−0.642790	+	0.766043i	$0.722223\pi$
$272$	−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
$276$	6.71839	−	7.77853i	0.404400	−	0.468212i
$277$	−15.4143	+	8.89945i	−0.926156	+	0.534716i	−0.885594	−	0.464461i	$-0.846248\pi$
$277$	−15.4143	+	8.89945i	−0.926156	+	0.534716i	−0.0405619	+	0.999177i	$0.512915\pi$
$278$	−0.475524	−	7.83041i	−0.0285200	−	0.469637i
$279$	−4.61980	−	0.447742i	−0.276580	−	0.0268056i
$280$	−22.3711	+	5.57679i	−1.33693	+	0.333277i
$281$			27.9140i			1.66521i	0.553866	+	0.832606i	$0.313152\pi$
$281$			27.9140i			1.66521i	−0.553866	+	0.832606i	$0.686848\pi$
$282$	−11.4347	+	11.7206i	−0.680929	+	0.697953i
$283$	1.81190	+	3.13830i	0.107706	+	0.186552i	0.914841	−	0.403815i	$-0.132316\pi$
$283$	1.81190	+	3.13830i	0.107706	+	0.186552i	−0.807134	+	0.590368i	$0.798983\pi$
$284$	1.50318	+	12.3307i	0.0891972	+	0.731693i
$285$	−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
$288$	−5.28919	+	16.1253i	−0.311668	+	0.950191i
$289$	7.78992	−	13.4925i	0.458230	−	0.793678i
$290$	−6.22471	+	12.4713i	−0.365527	+	0.732340i
$291$	28.2859	+	9.06411i	1.65815	+	0.531347i
$292$	16.4803	−	12.3964i	0.964435	−	0.725445i
$293$			9.77037i			0.570791i	0.958410	+	0.285396i	$0.0921250\pi$
$293$			9.77037i			0.570791i	−0.958410	+	0.285396i	$0.907875\pi$
$294$	−10.3544	+	13.6670i	−0.603880	+	0.797075i
$295$	−11.4873			−0.668817
$296$	0.366535	−	1.03081i	0.0213044	−	0.0599143i
$297$	5.93460	+	2.55628i	0.344360	+	0.148330i
$298$	5.24411	+	2.61746i	0.303783	+	0.151625i
$299$	−15.3906	−	8.88575i	−0.890059	−	0.513876i
$300$	14.6976	−	5.11320i	0.848564	−	0.295211i
$301$	−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
$304$	1.36239	−	4.72033i	0.0781383	−	0.270730i
$305$	−16.8892	+	9.75098i	−0.967072	+	0.558339i
$306$	5.05272	+	0.181789i	0.288845	+	0.0103922i
$307$	9.56907			0.546136			0.273068	−	0.961995i	$-0.411962\pi$
$307$	9.56907			0.546136			0.273068	+	0.961995i	$0.411962\pi$
$308$	−2.19411	+	6.20373i	−0.125021	+	0.353491i
$309$	−15.9439	+	14.4734i	−0.907018	+	0.823361i
$310$	0.408620	+	6.72871i	0.0232081	+	0.382165i
$311$	8.85168	+	15.3316i	0.501933	+	0.869373i	0.999998	+	0.00223345i	$0.000710930\pi$
$311$	8.85168	+	15.3316i	0.501933	+	0.869373i	−0.498065	+	0.867140i	$0.665956\pi$
$312$	29.1022	+	3.74992i	1.64759	+	0.212297i
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	0.192228	−	0.981350i	$-0.438429\pi$
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	−0.753760	+	0.657150i	$0.771762\pi$
$314$	−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	$-0.854022\pi$
$317$	−1.15640	+	2.00294i	−0.0649499	+	0.112497i	0.831722	+	0.555193i	$0.187355\pi$
$318$	−6.96711	−	24.7741i	−0.390696	−	1.38926i
$319$	1.98908	+	3.44519i	0.111367	+	0.192893i
$320$	24.3340	+	3.91899i	1.36031	+	0.219078i
$321$	11.1535	+	12.2867i	0.622528	+	0.685779i
$322$	−11.0179	+	1.36207i	−0.614004	+	0.0759055i
$323$	−1.46372			−0.0814434
$324$	−7.85648	−	16.1949i	−0.436471	−	0.899718i
$325$	−13.4533	−	23.3018i	−0.746256	−	1.29255i
$326$	−6.69613	+	13.4158i	−0.370864	+	0.743032i
$327$	−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
$330$	2.31688	−	9.09436i	0.127540	−	0.500628i
$331$	20.7165	+	11.9607i	1.13868	+	0.657418i	0.946104	−	0.323863i	$-0.104982\pi$
$331$	20.7165	+	11.9607i	1.13868	+	0.657418i	0.192578	+	0.981282i	$0.438315\pi$
$332$	−1.26547	−	10.3808i	−0.0694519	−	0.569720i
$333$	0.480551	+	1.05622i	0.0263340	+	0.0578803i
$334$	1.33488	+	21.9814i	0.0730415	+	1.20277i
$335$	38.1812			2.08606
$336$	15.9215	−	9.08331i	0.868588	−	0.495535i
$337$	−25.6463			−1.39704			−0.698522	−	0.715589i	$-0.746159\pi$
$337$	−25.6463			−1.39704			−0.698522	+	0.715589i	$0.746159\pi$
$338$	−1.96094	−	32.2906i	−0.106661	−	1.75638i
$339$	11.5797	+	3.71067i	0.628923	+	0.201536i
$340$	−0.888594	−	7.28922i	−0.0481908	−	0.395313i
$341$	1.66621	+	0.961986i	0.0902303	+	0.0520945i
$342$	2.44157	+	4.60365i	0.132025	+	0.248937i
$343$	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
$346$	1.18001	−	2.36417i	0.0634377	−	0.127099i
$347$	0.473950	+	0.820906i	0.0254430	+	0.0440686i	0.878467	−	0.477804i	$-0.158567\pi$
$347$	0.473950	+	0.820906i	0.0254430	+	0.0440686i	−0.853024	+	0.521872i	$0.825234\pi$
$348$	2.07982	−	10.8848i	0.111490	−	0.583484i
$349$	14.1965			0.759919			0.379960	−	0.925003i	$-0.375938\pi$
$349$	14.1965			0.759919			0.379960	+	0.925003i	$0.375938\pi$
$350$	−15.4777	−	6.55479i	−0.827317	−	0.350368i
$351$	−24.9546	+	18.5982i	−1.33198	+	0.992697i
$352$	4.76376	−	5.17618i	0.253909	−	0.275891i
$353$	−7.75978	−	13.4403i	−0.413011	−	0.715356i	0.582206	−	0.813041i	$-0.302190\pi$
$353$	−7.75978	−	13.4403i	−0.413011	−	0.715356i	−0.995217	+	0.0976847i	$0.968856\pi$
$354$	8.79187	−	2.47250i	0.467283	−	0.131412i
$355$	−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	0.139830	−	0.990176i	$-0.455344\pi$
$359$	−12.2735	−	7.08613i	−0.647772	−	0.373991i	−0.787602	+	0.616184i	$0.788678\pi$
$360$	−21.4437	+	14.9536i	−1.13018	+	0.788126i
$361$	8.74570	+	15.1480i	0.460300	+	0.797263i
$362$	−1.42413	−	23.4510i	−0.0748507	−	1.23256i
$363$	11.0056	+	12.1238i	0.577643	+	0.636334i
$364$	−20.5930	−	24.0921i	−1.07937	−	1.26277i
$365$	31.7678			1.66280
$366$	10.8274	−	11.0981i	0.565960	−	0.580109i
$367$	−11.5602	+	6.67430i	−0.603439	+	0.348396i	−0.770393	−	0.637569i	$-0.779940\pi$
$367$	−11.5602	+	6.67430i	−0.603439	+	0.348396i	0.166954	+	0.985965i	$0.446607\pi$
$368$	11.4029	+	3.29111i	0.594415	+	0.171561i
$369$	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
$372$	−1.76101	−	5.06190i	−0.0913040	−	0.262447i
$373$	−4.56967	−	2.63830i	−0.236609	−	0.136606i	0.377008	−	0.926210i	$-0.376953\pi$
$373$	−4.56967	−	2.63830i	−0.236609	−	0.136606i	−0.613617	+	0.789604i	$0.710286\pi$
$374$	−1.87521	−	0.935958i	−0.0969646	−	0.0483972i
$375$	−2.58031	−	0.826851i	−0.133247	−	0.0426984i
$376$	−17.8150	−	6.33468i	−0.918738	−	0.326686i
$377$	−19.1607			−0.986824
$378$	−5.44252	+	18.6649i	−0.279933	+	0.960020i
$379$		−	15.3619i		−	0.789086i	−0.918877	−	0.394543i	$-0.870903\pi$
$379$		−	15.3619i		−	0.789086i	0.918877	−	0.394543i	$-0.129097\pi$
$380$	6.04830	−	4.54951i	0.310271	−	0.233385i
$381$	3.11183	−	9.71094i	0.159424	−	0.497507i
$382$	−0.285240	+	0.571482i	−0.0145941	+	0.0292396i
$383$	−1.35424	+	2.34561i	−0.0691983	+	0.119855i	−0.898549	−	0.438874i	$-0.855377\pi$
$383$	−1.35424	+	2.34561i	−0.0691983	+	0.119855i	0.829350	+	0.558729i	$0.188711\pi$
$384$	−19.4677	+	2.23817i	−0.993456	+	0.114216i
$385$	−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
$388$	4.15035	+	34.0457i	0.210702	+	1.72841i
$389$	−6.35306	−	11.0038i	−0.322113	−	0.557916i	0.658811	−	0.752308i	$-0.271060\pi$
$389$	−6.35306	−	11.0038i	−0.322113	−	0.557916i	−0.980924	+	0.194393i	$0.937726\pi$
$390$	32.3546	+	31.5655i	1.63834	+	1.59838i
$391$		−	3.53589i		−	0.178817i
$392$	−19.3349	−	4.26170i	−0.976559	−	0.215248i
$393$	−5.44840	+	4.94588i	−0.274835	+	0.249487i
$394$	1.40778	+	23.1818i	0.0709229	+	1.16788i
$395$	34.2288	−	19.7620i	1.72224	−	0.994334i
$396$	0.184206	+	7.45909i	0.00925668	+	0.374833i
$397$	11.9617	−	20.7184i	0.600343	−	1.03982i	−0.392426	−	0.919784i	$-0.628364\pi$
$397$	11.9617	−	20.7184i	0.600343	−	1.03982i	0.992769	−	0.120041i	$-0.0383026\pi$
$398$	−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	−0.222731	−	0.974880i	$-0.571497\pi$
$401$	−23.5968	−	13.6236i	−1.17837	−	0.680331i	−0.955636	+	0.294549i	$0.904831\pi$
$402$	−29.2222	+	8.21801i	−1.45747	+	0.409877i
$403$	−8.02524	+	4.63338i	−0.399766	+	0.230805i
$404$	5.30441	−	3.98996i	0.263904	−	0.198508i
$405$	5.32478	−	27.2125i	0.264590	−	1.35220i
$406$	−9.55337	+	7.21137i	−0.474126	+	0.357894i
$407$		−	0.481008i		−	0.0238427i
$408$	2.24900	+	5.38758i	0.111342	+	0.266725i
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	−0.321727	−	0.946832i	$-0.604263\pi$
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	0.659117	+	0.752040i	$0.270930\pi$
$410$	18.3698	−	36.8041i	0.907218	−	1.81763i
$411$	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
$414$	−11.1210	+	5.89807i	−0.546566	+	0.289874i
$415$	8.05487	−	13.9514i	0.395398	−	0.684849i
$416$	10.1185	+	32.3359i	0.496102	+	1.58540i
$417$	−2.93196	+	9.14963i	−0.143579	+	0.448059i
$418$	−0.130936	−	2.15611i	−0.00640427	−	0.105459i
$419$		−	19.8589i		−	0.970173i	−0.874466	−	0.485086i	$-0.838788\pi$
$419$		−	19.8589i		−	0.970173i	0.874466	−	0.485086i	$-0.161212\pi$
$420$	28.0119	+	3.56123i	1.36684	+	0.173770i
$421$		−	16.6507i		−	0.811505i	−0.913983	−	0.405753i	$-0.867009\pi$
$421$		−	16.6507i		−	0.811505i	0.913983	−	0.405753i	$-0.132991\pi$
$422$	14.1068	−	0.856676i	0.686709	−	0.0417024i
$423$	18.2541	−	8.30516i	0.887547	−	0.403811i
$424$	22.6216	−	19.2699i	1.09860	−	0.935828i
$425$	2.67672	−	4.63622i	0.129840	−	0.224890i
$426$	3.75590	−	14.7429i	0.181974	−	0.714294i
$427$	−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
$430$	32.3207	+	16.1320i	1.55864	+	0.777954i
$431$	−19.8541	+	11.4628i	−0.956339	+	0.552142i	−0.895044	−	0.445977i	$-0.852856\pi$
$431$	−19.8541	+	11.4628i	−0.956339	+	0.552142i	−0.0612944	+	0.998120i	$0.519523\pi$
$432$	13.1934	−	16.0603i	0.634769	−	0.772702i
$433$		−	10.5825i		−	0.508564i	−0.967130	−	0.254282i	$-0.918161\pi$
$433$		−	10.5825i		−	0.508564i	0.967130	−	0.254282i	$-0.0818392\pi$
$434$	−2.25750	+	5.33058i	−0.108363	+	0.255876i
$435$	12.6399	−	11.4741i	0.606035	−	0.550139i
$436$	0.942025	−	0.708588i	0.0451148	−	0.0339352i
$437$	3.15607	−	1.82216i	0.150975	−	0.0871656i
$438$	−24.3136	+	6.83761i	−1.16175	+	0.326714i
$439$	−6.69332	−	3.86439i	−0.319455	−	0.184437i	0.331695	−	0.943387i	$-0.392380\pi$
$439$	−6.69332	−	3.86439i	−0.319455	−	0.184437i	−0.651150	+	0.758949i	$0.725713\pi$
$440$	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	$-0.867966\pi$
$443$	−2.28548	+	3.95856i	−0.108586	+	0.188077i	0.806611	+	0.591082i	$0.201299\pi$
$444$	−0.875835	+	1.01404i	−0.0415653	+	0.0481241i
$445$	−37.0392	+	21.3846i	−1.75582	+	1.01373i
$446$	−19.4145	+	1.17900i	−0.919303	+	0.0558273i
$447$	−4.82478	−	5.31500i	−0.228204	−	0.251391i
$448$	17.2151	+	12.3142i	0.813337	+	0.581793i
$449$			4.33700i			0.204676i	0.994750	+	0.102338i	$0.0326323\pi$
$449$			4.33700i			0.204676i	−0.994750	+	0.102338i	$0.967368\pi$
$450$	−19.0467	−	0.685269i	−0.897868	−	0.0323039i
$451$	−5.86998	−	10.1671i	−0.276406	−	0.478750i
$452$	1.69907	+	13.9376i	0.0799176	+	0.655572i
$453$	−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
$456$	−3.64987	+	4.78381i	−0.170921	+	0.224023i
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	−0.999079	−	0.0429048i	$-0.986339\pi$
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	0.536696	+	0.843776i	$0.319672\pi$
$458$	−1.88083	−	0.938764i	−0.0878853	−	0.0438656i
$459$	−5.68714	−	2.44969i	−0.265453	−	0.114342i
$460$	10.9902	+	14.6108i	0.512421	+	0.681233i
$461$			25.3326i			1.17986i	0.807455	+	0.589929i	$0.200844\pi$
$461$			25.3326i			1.17986i	−0.807455	+	0.589929i	$0.799156\pi$
$462$	5.25757	−	6.10807i	0.244604	−	0.284173i
$463$	20.9574			0.973975			0.486988	−	0.873409i	$-0.338096\pi$
$463$	20.9574			0.973975			0.486988	+	0.873409i	$0.338096\pi$
$464$	12.4213	−	3.07412i	0.576643	−	0.142712i
$465$	2.51945	−	7.86233i	0.116837	−	0.364607i
$466$	1.45992	−	2.92497i	0.0676293	−	0.135496i
$467$	26.9170	+	15.5406i	1.24557	+	0.719131i	0.970223	−	0.242214i	$-0.0778735\pi$
$467$	26.9170	+	15.5406i	1.24557	+	0.719131i	0.275348	+	0.961345i	$0.411207\pi$
$468$	−31.5568	−	17.1949i	−1.45872	−	0.794834i
$469$	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
$472$	6.83852	+	8.02797i	0.314768	+	0.369517i
$473$	8.92857	−	5.15491i	0.410536	−	0.237023i
$474$	−21.9436	+	22.4922i	−1.00790	+	1.03310i
$475$	5.51761			0.253165
$476$	2.10262	−	5.94505i	0.0963735	−	0.272491i
$477$	−3.04051	+	31.3720i	−0.139216	+	1.43643i
$478$	−30.4952	+	1.85191i	−1.39482	+	0.0847044i
$479$	−17.0894	−	29.5997i	−0.780835	−	1.35245i	−0.931456	−	0.363855i	$-0.881460\pi$
$479$	−17.0894	−	29.5997i	−0.780835	−	1.35245i	0.150620	−	0.988592i	$-0.451873\pi$
$480$	−26.0389	−	15.2720i	−1.18851	−	0.697068i
$481$	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
$486$	1.78179	+	21.9733i	0.0808238	+	0.996728i
$487$	−12.3371	−	21.3684i	−0.559046	−	0.968296i	−0.997576	−	0.0695795i	$-0.977834\pi$
$487$	−12.3371	−	21.3684i	−0.559046	−	0.968296i	0.438531	−	0.898716i	$-0.355499\pi$
$488$	16.8688	+	5.99825i	0.763616	+	0.271528i
$489$	13.5971	−	12.3430i	0.614884	−	0.558171i
$490$	−19.8564	−	23.1509i	−0.897021	−	1.04585i
$491$	−43.3064			−1.95439			−0.977196	−	0.212339i	$-0.931892\pi$
$491$	−43.3064			−1.95439			−0.977196	+	0.212339i	$0.931892\pi$
$492$	−6.13777	+	32.1220i	−0.276712	+	1.44817i
$493$	−1.90614	−	3.30153i	−0.0858482	−	0.148693i
$494$	9.30883	+	4.64625i	0.418824	+	0.209045i
$495$	−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
$498$	−3.16196	+	12.4115i	−0.141691	+	0.556173i
$499$	−32.3258	−	18.6633i	−1.44710	−	0.835485i	−0.448795	−	0.893635i	$-0.648147\pi$
$499$	−32.3258	−	18.6633i	−1.44710	−	0.835485i	−0.998308	+	0.0581497i	$0.981480\pi$
$500$	−0.378605	−	3.10573i	−0.0169317	−	0.138893i
$501$	8.23056	−	25.6847i	0.367714	−	1.14751i
$502$	−22.0957	+	1.34182i	−0.986178	+	0.0598885i
$503$	34.2432			1.52683			0.763414	−	0.645910i	$-0.223522\pi$
$503$	34.2432			1.52683			0.763414	+	0.645910i	$0.223522\pi$
$504$	−22.2055	+	3.30360i	−0.989114	+	0.147154i
$505$	10.2249			0.455003
$506$	5.20848	−	0.316300i	0.231545	−	0.0140612i
$507$	−12.0907	+	37.7307i	−0.536965	+	1.67568i
$508$	11.6884	−	1.42487i	0.518587	−	0.0632185i
$509$	−24.1054	−	13.9173i	−1.06845	−	0.616871i	−0.140694	−	0.990053i	$-0.544933\pi$
$509$	−24.1054	−	13.9173i	−1.06845	−	0.616871i	−0.927758	+	0.373182i	$0.878267\pi$
$510$	−2.22028	+	8.71515i	−0.0983155	+	0.385913i
$511$	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
$514$	16.5293	+	8.25013i	0.729075	+	0.363898i
$515$	−19.1517	−	33.1716i	−0.843923	−	1.46172i
$516$	−28.2090	−	5.39008i	−1.24183	−	0.237285i
$517$	−8.31307			−0.365608
$518$	1.43634	−	0.177565i	0.0631089	−	0.00780177i
$519$	−2.39612	+	2.17512i	−0.105178	+	0.0954774i
$520$	−17.4868	+	49.1781i	−0.766848	+	2.15660i
$521$	−8.13261	−	14.0861i	−0.356296	−	0.617123i	0.631043	−	0.775748i	$-0.282627\pi$
$521$	−8.13261	−	14.0861i	−0.356296	−	0.617123i	−0.987339	+	0.158625i	$0.949294\pi$
$522$	−7.20434	+	11.5023i	−0.315325	+	0.503442i
$523$	6.98922	−	12.1057i	0.305617	−	0.529345i	−0.671781	−	0.740750i	$-0.734470\pi$
$523$	6.98922	−	12.1057i	0.305617	−	0.529345i	0.977399	+	0.211405i	$0.0678038\pi$
$524$	−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
$528$	−7.73491	+	3.79480i	−0.336619	+	0.165147i
$529$	−7.09824	−	12.2945i	−0.308619	−	0.534544i
$530$	45.6932	−	2.77485i	1.98478	−	0.120532i
$531$	−11.1333	−	1.07902i	−0.483145	−	0.0468255i
$532$	6.39000	−	1.18692i	0.277042	−	0.0514594i
$533$	56.5451			2.44924
$534$	23.7453	−	24.3390i	1.02756	−	1.05325i
$535$	−25.5628	+	14.7587i	−1.10518	+	0.638074i
$536$	−22.7297	−	26.6831i	−0.981771	−	1.15254i
$537$	−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
$540$	31.1142	−	7.55424i	1.33894	−	0.325083i
$541$	−18.9287	−	10.9285i	−0.813810	−	0.469853i	0.0344673	−	0.999406i	$-0.489027\pi$
$541$	−18.9287	−	10.9285i	−0.813810	−	0.469853i	−0.848277	+	0.529552i	$0.822360\pi$
$542$	−3.61087	+	7.23443i	−0.155100	+	0.310746i
$543$	−8.78084	+	27.4019i	−0.376822	+	1.17593i
$544$	−4.56512	+	4.96034i	−0.195728	+	0.212673i
$545$	1.81587			0.0777834
$546$	12.8164	+	36.6400i	0.548492	+	1.56805i
$547$		−	9.11111i		−	0.389563i	−0.980847	−	0.194782i	$-0.937600\pi$
$547$		−	9.11111i		−	0.389563i	0.980847	−	0.194782i	$-0.0623998\pi$
$548$	−1.24546	+	0.936833i	−0.0532035	+	0.0400195i
$549$	−17.2847	+	7.86407i	−0.737692	+	0.335630i
$550$	7.06876	+	3.52818i	0.301413	+	0.150442i
$551$	1.96459	−	3.40277i	0.0836944	−	0.144963i
$552$	−11.5562	−	8.81696i	−0.491865	−	0.375275i
$553$	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
$556$	−11.0127	+	1.34251i	−0.467044	+	0.0569352i
$557$	2.14436	+	3.71415i	0.0908596	+	0.157373i	0.907873	−	0.419245i	$-0.137705\pi$
$557$	2.14436	+	3.71415i	0.0908596	+	0.157373i	−0.817013	+	0.576619i	$0.804372\pi$
$558$	−0.236010	+	6.55975i	−0.00999108	+	0.277696i
$559$			49.6569i			2.10026i
$560$	9.79002	+	31.1012i	0.413704	+	1.31427i
$561$	1.72526	+	1.90055i	0.0728406	+	0.0802414i
$562$	39.4038	−	2.39291i	1.66215	−	0.100939i
$563$	−27.2512	+	15.7335i	−1.14850	+	0.663087i	−0.948521	−	0.316713i	$-0.897421\pi$
$563$	−27.2512	+	15.7335i	−1.14850	+	0.663087i	−0.199979	+	0.979800i	$0.564087\pi$
$564$	17.5252	+	15.1367i	0.737945	+	0.637370i
$565$	−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	0.669790	−	0.742551i	$-0.266384\pi$
$569$	8.62592	+	4.98018i	0.361617	+	0.208780i	−0.308173	+	0.951330i	$0.599717\pi$
$570$	−8.92317	+	2.50942i	−0.373750	+	0.105108i
$571$	−29.5465	+	17.0587i	−1.23648	+	0.713883i	−0.968373	−	0.249506i	$-0.919732\pi$
$571$	−29.5465	+	17.0587i	−1.23648	+	0.713883i	−0.268108	+	0.963389i	$0.586399\pi$
$572$	8.95480	+	11.9049i	0.374419	+	0.497768i
$573$	0.579206	−	0.525785i	0.0241967	−	0.0219650i
$574$	28.1930	−	21.2815i	1.17675	−	0.888273i
$575$			13.3288i			0.555851i
$576$	23.2161	+	6.08396i	0.967336	+	0.253498i
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	−0.482336	−	0.875986i	$-0.660212\pi$
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	0.517458	+	0.855708i	$0.326878\pi$
$578$	−19.7140	−	9.83971i	−0.819995	−	0.409278i
$579$	−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
$582$	10.3702	−	40.7058i	0.429860	−	1.68731i
$583$	6.53263	−	11.3149i	0.270554	−	0.468613i
$584$	−18.9117	−	22.2011i	−0.782571	−	0.918688i
$585$	−22.9263	−	50.3904i	−0.947886	−	2.08339i
$586$	13.7920	−	0.837557i	0.569741	−	0.0345992i
$587$		−	25.9212i		−	1.06988i	−0.844890	−	0.534940i	$-0.820334\pi$
$587$		−	25.9212i		−	1.06988i	0.844890	−	0.534940i	$-0.179666\pi$
$588$	20.1801	+	13.4448i	0.832214	+	0.554454i
$589$		−	1.90029i		−	0.0782999i
$590$	0.984741	+	16.2156i	0.0405412	+	0.667588i
$591$	8.68003	−	27.0873i	0.357049	−	1.11422i
$592$	−1.48652	−	0.429041i	−0.0610956	−	0.0176335i
$593$	22.1118	−	38.2987i	0.908022	−	1.57274i	0.0912135	−	0.995831i	$-0.470925\pi$
$593$	22.1118	−	38.2987i	0.908022	−	1.57274i	0.816808	−	0.576909i	$-0.195741\pi$
$594$	3.09974	−	8.59649i	0.127184	−	0.352718i
$595$	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
$598$	−11.2239	+	22.4872i	−0.458979	+	0.919572i
$599$	−8.58632	+	4.95731i	−0.350827	+	0.202550i	−0.665050	−	0.746799i	$-0.731590\pi$
$599$	−8.58632	+	4.95731i	−0.350827	+	0.202550i	0.314222	+	0.949349i	$0.398256\pi$
$600$	−8.47780	−	20.3090i	−0.346105	−	0.829110i
$601$			11.8235i			0.482292i	0.970489	+	0.241146i	$0.0775233\pi$
$601$			11.8235i			0.482292i	−0.970489	+	0.241146i	$0.922477\pi$
$602$	18.6890	+	24.7586i	0.761709	+	1.00908i
$603$	37.0046	+	3.58642i	1.50695	+	0.146050i
$604$	−5.20539	−	6.92025i	−0.211804	−	0.281581i
$605$	−25.2238	+	14.5630i	−1.02549	+	0.592069i
$606$	−7.82569	+	2.20078i	−0.317897	+	0.0894007i
$607$	5.56281	+	3.21169i	0.225788	+	0.130359i	0.608627	−	0.793456i	$-0.291721\pi$
$607$	5.56281	+	3.21169i	0.225788	+	0.130359i	−0.382840	+	0.923815i	$0.625054\pi$
$608$	−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
$612$	−0.176525	−	7.14807i	−0.00713559	−	0.288944i
$613$	17.5740	−	10.1463i	0.709805	−	0.409806i	−0.101184	−	0.994868i	$-0.532263\pi$
$613$	17.5740	−	10.1463i	0.709805	−	0.409806i	0.810989	+	0.585061i	$0.198930\pi$
$614$	−0.820301	−	13.5078i	−0.0331047	−	0.545131i
$615$	−37.3016	+	33.8612i	−1.50414	+	1.36541i
$616$	8.94536	+	2.56542i	0.360419	+	0.103364i
$617$			26.7202i			1.07571i	0.843036	+	0.537856i	$0.180766\pi$
$617$			26.7202i			1.07571i	−0.843036	+	0.537856i	$0.819234\pi$
$618$	21.7976	+	21.2659i	0.876827	+	0.855441i
$619$	−7.12358	−	12.3384i	−0.286321	−	0.495922i	0.686608	−	0.727028i	$-0.259099\pi$
$619$	−7.12358	−	12.3384i	−0.286321	−	0.495922i	−0.972929	+	0.231106i	$0.925766\pi$
$620$	9.46331	−	1.15363i	0.380056	−	0.0463308i
$621$	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
$624$	2.79867	−	41.4025i	0.112037	−	1.65743i
$625$	13.6405	−	23.6260i	0.545619	−	0.945040i
$626$	−7.24495	+	14.5154i	−0.289566	+	0.580151i
$627$	−0.807317	+	2.51935i	−0.0322411	+	0.100613i
$628$	7.71883	+	10.2617i	0.308015	+	0.409487i
$629$			0.460951i			0.0183793i
$630$	−30.3960	−	16.4957i	−1.21101	−	0.657203i
$631$	−13.9775			−0.556436			−0.278218	−	0.960518i	$-0.589744\pi$
$631$	−13.9775			−0.556436			−0.278218	+	0.960518i	$0.589744\pi$
$632$	−34.1875	−	12.1565i	−1.35991	−	0.483558i
$633$	−16.4834	−	5.28206i	−0.655158	−	0.209943i
$634$	2.92651	+	1.46069i	0.116227	+	0.0580113i
$635$	15.7088	+	9.06945i	0.623383	+	0.359910i
$636$	−34.3742	+	11.9586i	−1.36303	+	0.474190i
$637$	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
$640$	3.44608	−	34.6862i	0.136218	−	1.37109i
$641$	6.31225	−	3.64438i	0.249319	−	0.143944i	−0.370133	−	0.928979i	$-0.620688\pi$
$641$	6.31225	−	3.64438i	0.249319	−	0.143944i	0.619452	+	0.785034i	$0.287355\pi$
$642$	16.3880	−	16.7977i	0.646783	−	0.662953i
$643$	25.1189			0.990594			0.495297	−	0.868724i	$-0.335059\pi$
$643$	25.1189			0.990594			0.495297	+	0.868724i	$0.335059\pi$
$644$	2.86722	+	15.4362i	0.112984	+	0.608273i
$645$	−29.7363	−	32.7576i	−1.17086	−	1.28983i
$646$	0.125476	+	2.06620i	0.00493679	+	0.0812936i
$647$	20.2246	+	35.0301i	0.795112	+	1.37717i	0.922768	+	0.385355i	$0.125921\pi$
$647$	20.2246	+	35.0301i	0.795112	+	1.37717i	−0.127657	+	0.991818i	$0.540746\pi$
$648$	−22.1875	+	12.4786i	−0.871607	+	0.490206i
$649$	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	−0.00767187	−	0.999971i	$-0.502442\pi$
$653$	22.0316	−	38.1599i	0.862164	−	1.49331i	0.869836	−	0.493341i	$-0.164225\pi$
$654$	−1.38979	+	0.390843i	−0.0543449	+	0.0152832i
$655$	−6.54455	−	11.3355i	−0.255717	−	0.442915i
$656$	−36.6565	+	9.07205i	−1.43119	+	0.354204i
$657$	30.7889	+	2.98400i	1.20119	+	0.116417i
$658$	−3.06879	−	24.8236i	−0.119634	−	0.967724i
$659$	5.89051			0.229462			0.114731	−	0.993397i	$-0.463399\pi$
$659$	5.89051			0.229462			0.114731	+	0.993397i	$0.463399\pi$
$660$	−13.0363	−	2.49094i	−0.507439	−	0.0969596i
$661$	21.0993	+	36.5450i	0.820667	+	1.42144i	0.905186	+	0.425015i	$0.139731\pi$
$661$	21.0993	+	36.5450i	0.820667	+	1.42144i	−0.0845192	+	0.996422i	$0.526935\pi$
$662$	15.1079	−	30.2690i	0.587187	−	1.17644i
$663$	−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
$666$	1.44977	−	0.768895i	0.0561776	−	0.0297941i
$667$	8.22004	+	4.74584i	0.318281	+	0.183760i
$668$	30.9148	−	3.76868i	1.19613	−	0.145814i
$669$	22.6853	+	7.26942i	0.877065	+	0.281052i
$670$	−3.27305	−	53.8971i	−0.126449	−	2.08223i
$671$	7.87156			0.303878
$672$	−14.1870	−	21.6963i	−0.547275	−	0.836953i
$673$	−46.7729			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$673$	−46.7729			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$674$	2.19851	+	36.2027i	0.0846834	+	1.39447i
$675$	21.4382	+	9.23431i	0.825155	+	0.355429i
$676$	−45.4137	+	5.53617i	−1.74668	+	0.212930i
$677$	35.7518	+	20.6413i	1.37405	+	0.793310i	0.991436	−	0.130596i	$-0.0416892\pi$
$677$	35.7518	+	20.6413i	1.37405	+	0.793310i	0.382618	+	0.923907i	$0.375023\pi$
$678$	4.24537	−	16.6641i	0.163042	−	0.639983i
$679$	−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
$682$	1.21512	−	2.43451i	0.0465293	−	0.0932221i
$683$	17.1346	+	29.6781i	0.655638	+	1.13560i	0.981733	+	0.190262i	$0.0609338\pi$
$683$	17.1346	+	29.6781i	0.655638	+	1.13560i	−0.326095	+	0.945337i	$0.605733\pi$
$684$	6.28927	−	3.84119i	0.240476	−	0.146872i
$685$	−2.40079			−0.0917293
$686$	−6.42133	−	25.3923i	−0.245168	−	0.969481i
$687$	1.73043	+	1.90625i	0.0660201	+	0.0727280i
$688$	−7.96691	−	32.1911i	−0.303736	−	1.22727i
$689$	31.4642	+	54.4976i	1.19869	+	2.07619i
$690$	−6.06198	−	21.5556i	−0.230776	−	0.820608i
$691$	−3.57575	+	6.19338i	−0.136028	+	0.235607i	−0.925990	−	0.377549i	$-0.876767\pi$
$691$	−3.57575	+	6.19338i	−0.136028	+	0.235607i	0.789962	+	0.613156i	$0.210100\pi$
$692$	−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
$696$	−15.5434	−	2.00282i	−0.589169	−	0.0759166i
$697$	5.62522	+	9.74316i	0.213070	+	0.369048i
$698$	−1.21698	−	20.0399i	−0.0460634	−	0.758522i
$699$	−2.96450	+	2.69108i	−0.112128	+	0.101786i
$700$	−7.92602	+	22.4104i	−0.299575	+	0.847034i
$701$	−12.4116			−0.468778			−0.234389	−	0.972143i	$-0.575309\pi$
$701$	−12.4116			−0.468778			−0.234389	+	0.972143i	$0.575309\pi$
$702$	28.3926	+	33.6319i	1.07161	+	1.26935i
$703$	−0.411437	+	0.237543i	−0.0155176	+	0.00895911i
$704$	−7.71513	−	6.28086i	−0.290775	−	0.236719i
$705$	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
$708$	−4.24389	−	12.1988i	−0.159495	−	0.458458i
$709$	−30.5908	−	17.6616i	−1.14886	−	0.663295i	−0.200251	−	0.979745i	$-0.564176\pi$
$709$	−30.5908	−	17.6616i	−1.14886	−	0.663295i	−0.948609	+	0.316450i	$0.897509\pi$
$710$	24.2135	+	12.0855i	0.908718	+	0.453561i
$711$	35.0303	−	15.9379i	1.31374	−	0.597717i
$712$	36.9945	+	13.1546i	1.38643	+	0.492988i
$713$	4.59050			0.171916
$714$	−5.03835	+	5.85338i	−0.188555	+	0.219057i
$715$			22.9481i			0.858211i
$716$	−18.5897	−	24.7139i	−0.694730	−	0.923601i
$717$	35.6329	+	11.4184i	1.33073	+	0.426429i
$718$	−8.95073	+	17.9329i	−0.334038	+	0.669251i
$719$	12.1803	−	21.0969i	0.454250	−	0.786783i	−0.544395	−	0.838829i	$-0.683241\pi$
$719$	12.1803	−	21.0969i	0.454250	−	0.786783i	0.998645	+	0.0520455i	$0.0165741\pi$
$720$	22.9470	+	28.9882i	0.855184	+	1.08033i
$721$	−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
$724$	−32.9817	+	4.02064i	−1.22576	+	0.149426i
$725$	7.18536	+	12.4454i	0.266858	+	0.462211i
$726$	16.1707	−	16.5749i	0.600149	−	0.615153i
$727$		−	5.15142i		−	0.191055i	−0.995427	−	0.0955277i	$-0.969546\pi$
$727$		−	5.15142i		−	0.191055i	0.995427	−	0.0955277i	$-0.0304539\pi$
$728$	−32.2434	+	31.1346i	−1.19502	+	1.15392i
$729$	7.71680	−	25.8738i	0.285807	−	0.958287i
$730$	−2.72327	−	44.8438i	−0.100793	−	1.65975i
$731$	−8.55627	+	4.93997i	−0.316465	+	0.182711i
$732$	−16.5944	−	14.3328i	−0.613348	−	0.529755i
$733$	3.74171	−	6.48083i	0.138203	−	0.239375i	−0.788613	−	0.614889i	$-0.789201\pi$
$733$	3.74171	−	6.48083i	0.138203	−	0.239375i	0.926817	+	0.375514i	$0.122534\pi$
$734$	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
$738$	21.2608	−	33.9445i	0.782619	−	1.24951i
$739$	2.26360	−	1.30689i	0.0832679	−	0.0480747i	−0.457788	−	0.889061i	$-0.651358\pi$
$739$	2.26360	−	1.30689i	0.0832679	−	0.0480747i	0.541056	+	0.840987i	$0.318025\pi$
$740$	−1.43273	−	1.90472i	−0.0526680	−	0.0700190i
$741$	−8.56448	−	9.43466i	−0.314624	−	0.346591i
$742$	36.1987	+	15.3302i	1.32890	+	0.562788i
$743$			23.6093i			0.866140i	0.901360	+	0.433070i	$0.142570\pi$
$743$			23.6093i			0.866140i	−0.901360	+	0.433070i	$0.857430\pi$
$744$	−6.99449	+	2.91979i	−0.256430	+	0.107045i
$745$	11.0580	−	6.38431i	0.405132	−	0.233903i
$746$	−3.33253	+	6.67677i	−0.122012	+	0.244454i
$747$	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
$750$	−0.945998	+	3.71328i	−0.0345430	+	0.135590i
$751$	0.504993	−	0.874673i	0.0184275	−	0.0319173i	−0.856665	−	0.515874i	$-0.827467\pi$
$751$	0.504993	−	0.874673i	0.0184275	−	0.0319173i	0.875092	+	0.483956i	$0.160801\pi$
$752$	−7.41494	+	25.6909i	−0.270395	+	0.936851i
$753$	25.8182	+	8.27335i	0.940868	+	0.301497i
$754$	1.64253	+	27.0474i	0.0598175	+	0.985010i
$755$		−	13.3397i		−	0.485480i
$756$	26.8142	+	6.08269i	0.975223	+	0.221225i
$757$			11.1837i			0.406478i	0.979129	+	0.203239i	$0.0651469\pi$
$757$			11.1837i			0.406478i	−0.979129	+	0.203239i	$0.934853\pi$
$758$	−21.6850	+	1.31688i	−0.787635	+	0.0478314i
$759$	−6.08598	−	1.95023i	−0.220907	−	0.0707888i
$760$	−6.94064	−	8.14786i	−0.251763	−	0.295554i
$761$	−3.99009	+	6.91104i	−0.144641	+	0.250525i	−0.929239	−	0.369480i	$-0.879536\pi$
$761$	−3.99009	+	6.91104i	−0.144641	+	0.250525i	0.784598	+	0.620005i	$0.212869\pi$
$762$	−13.9749	−	3.56024i	−0.506256	−	0.128974i
$763$	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
$766$	3.42718	+	1.71058i	0.123829	+	0.0618059i
$767$	−19.3402	+	11.1661i	−0.698333	+	0.403183i
$768$	4.82828	+	27.2890i	0.174226	+	0.984706i
$769$		−	11.8900i		−	0.428766i	−0.976750	−	0.214383i	$-0.931226\pi$
$769$		−	11.8900i		−	0.428766i	0.976750	−	0.214383i	$-0.0687740\pi$
$770$	8.63684	+	11.4418i	0.311250	+	0.412333i
$771$	−15.2075	−	16.7527i	−0.547686	−	0.603333i
$772$	−2.06613	−	2.74679i	−0.0743615	−	0.0988591i
$773$	−31.4449	+	18.1547i	−1.13099	+	0.652979i	−0.944185	−	0.329417i	$-0.893148\pi$
$773$	−31.4449	+	18.1547i	−1.13099	+	0.652979i	−0.186809	+	0.982396i	$0.559814\pi$
$774$	29.8094	+	18.6708i	1.07148	+	0.671109i
$775$	6.01902	+	3.47508i	0.216210	+	0.124829i
$776$	47.7035	−	8.77722i	1.71246	−	0.315084i
$777$	−1.71841	−	0.434686i	−0.0616476	−	0.0155943i
$778$	−14.9885	+	9.91135i	−0.537364	+	0.355339i
$779$	−5.79771	+	10.0419i	−0.207725	+	0.359790i
$780$	41.7847	−	48.3782i	1.49613	−	1.73222i
$781$	6.68897	−	3.86188i	0.239350	−	0.138189i
$782$	−4.99130	+	0.303111i	−0.178489	+	0.0108392i
$783$	13.3281	−	9.93321i	0.476309	−	0.354984i
$784$	−4.35840	+	27.6587i	−0.155657	+	0.987811i
$785$			19.7807i			0.706005i
$786$	7.44872	+	7.26705i	0.265687	+	0.259207i
$787$	−6.73055	−	11.6577i	−0.239918	−	0.415551i	0.720772	−	0.693172i	$-0.243787\pi$
$787$	−6.73055	−	11.6577i	−0.239918	−	0.415551i	−0.960691	+	0.277621i	$0.910454\pi$
$788$	32.6030	−	3.97448i	1.16143	−	0.141585i
$789$	11.1385	+	51.3779i	0.396540	+	1.82910i
$790$	−30.8305	−	46.6237i	−1.09690	−	1.65880i
$791$	−15.4759	+	10.2713i	−0.550259	+	0.365206i
$792$	10.5136	−	0.899452i	0.373583	−	0.0319606i
$793$	−18.9565	+	32.8337i	−0.673167	+	1.16596i
$794$	−30.2717	−	15.1093i	−1.07430	−	0.536209i
$795$	−53.3913	−	17.1090i	−1.89359	−	0.606795i
$796$	−1.54917	+	1.16528i	−0.0549087	+	0.0413022i
$797$			13.9811i			0.495236i	0.968858	+	0.247618i	$0.0796479\pi$
$797$			13.9811i			0.495236i	−0.968858	+	0.247618i	$0.920352\pi$
$798$	−7.82105	−	1.48070i	−0.276862	−	0.0524162i
$799$	7.96643			0.281832
$800$	17.2086	−	18.6985i	0.608417	−	0.661090i
$801$	−37.9065	+	17.2465i	−1.33936	+	0.609373i
$802$	−17.2085	+	34.4774i	−0.607652	+	1.21744i
$803$	−11.1045	−	6.41121i	−0.391871	−	0.226247i
$804$	14.1057	+	40.5459i	0.497470	+	1.42994i
$805$	−10.7644	+	21.6584i	−0.379396	+	0.763357i
$806$	7.22849	+	10.9313i	0.254613	+	0.385040i
$807$	−0.290145	−	1.33834i	−0.0102136	−	0.0471117i
$808$	−6.08700	−	7.14574i	−0.214140	−	0.251386i
$809$	−2.99316	+	1.72810i	−0.105234	+	0.0607569i	−0.551693	−	0.834047i	$-0.686018\pi$
$809$	−2.99316	+	1.72810i	−0.105234	+	0.0607569i	0.446459	+	0.894804i	$0.352685\pi$
$810$	−38.8699	−	5.18375i	−1.36575	−	0.182139i
$811$	−45.3167			−1.59129			−0.795643	−	0.605766i	$-0.792867\pi$
$811$	−45.3167			−1.59129			−0.795643	+	0.605766i	$0.792867\pi$
$812$	10.9986	+	12.8675i	0.385976	+	0.451560i
$813$	7.33222	−	6.65595i	0.257152	−	0.233434i
$814$	−0.678997	+	0.0412340i	−0.0237988	+	0.00144525i
$815$	16.3327	+	28.2891i	0.572111	+	0.990924i
$816$	7.41238	−	3.63656i	0.259485	−	0.127305i
$817$	−8.81865	−	5.09145i	−0.308525	−	0.178127i
$818$	−6.14586	−	9.29413i	−0.214885	−	0.324962i
$819$	1.62890	−	47.5128i	0.0569183	−	1.66023i
$820$	−53.5279	−	22.7760i	−1.86927	−	0.795372i
$821$	22.3394	−	38.6931i	0.779652	−	1.35040i	−0.152490	−	0.988305i	$-0.548729\pi$
$821$	22.3394	−	38.6931i	0.779652	−	1.35040i	0.932142	−	0.362092i	$-0.117937\pi$
$822$	1.83745	−	0.516738i	0.0640885	−	0.0180233i
$823$	21.1932	+	36.7076i	0.738747	+	1.27955i	0.953060	+	0.302783i	$0.0979157\pi$
$823$	21.1932	+	36.7076i	0.738747	+	1.27955i	−0.214312	+	0.976765i	$0.568751\pi$
$824$	−11.7810	+	33.1316i	−0.410411	+	1.15420i
$825$	−6.50352	−	7.16430i	−0.226424	−	0.249429i
$826$	−5.44038	+	12.8463i	−0.189295	+	0.446978i
$827$	9.18843			0.319513			0.159757	−	0.987156i	$-0.448929\pi$
$827$	9.18843			0.319513			0.159757	+	0.987156i	$0.448929\pi$
$828$	9.27913	+	15.1929i	0.322472	+	0.527990i
$829$	13.0225	+	22.5556i	0.452290	+	0.783389i	0.998528	−	0.0542413i	$-0.0172740\pi$
$829$	13.0225	+	22.5556i	0.452290	+	0.783389i	−0.546238	+	0.837630i	$0.683941\pi$
$830$	−20.3845	−	10.1744i	−0.707557	−	0.353158i
$831$	−6.53175	−	30.1287i	−0.226584	−	1.04515i
$832$	44.7784	−	17.0554i	1.55241	−	0.591291i
$833$	8.27719	−	1.03749i	0.286788	−	0.0359468i
$834$	13.1671	+	3.35445i	0.455939	+	0.116155i
$835$	41.5484	+	23.9880i	1.43784	+	0.830139i
$836$	−3.03236	+	0.369661i	−0.104876	+	0.0127850i
$837$	3.18033	−	7.38339i	0.109928	−	0.255207i
$838$	−28.0331	+	1.70239i	−0.968389	+	0.0588082i
$839$	−31.2096			−1.07748			−0.538738	−	0.842473i	$-0.681099\pi$
$839$	−31.2096			−1.07748			−0.538738	+	0.842473i	$0.681099\pi$
$840$	2.62578	−	39.8472i	0.0905981	−	1.37486i
$841$	−18.7664			−0.647116
$842$	−23.5043	+	1.42737i	−0.810013	+	0.0491903i
$843$	−46.0423	−	14.7541i	−1.58578	−	0.508158i
$844$	−2.41859	−	19.8399i	−0.0832513	−	0.682918i
$845$	−61.0345	−	35.2383i	−2.09965	−	1.21223i
$846$	−13.2885	−	25.0558i	−0.456868	−	0.861438i
$847$	−24.9632	+	1.55838i	−0.857744	+	0.0535467i
$848$	−29.1408	−	30.2810i	−1.00070	−	1.03985i
$849$	−6.13410	+	1.32984i	−0.210522	+	0.0456401i
$850$	−6.77401	−	3.38106i	−0.232347	−	0.115969i
$851$	−0.573831	−	0.993904i	−0.0196707	−	0.0340706i
$852$	−21.1332	−	4.03806i	−0.724011	−	0.138342i
$853$	4.78201			0.163733			0.0818665	−	0.996643i	$-0.473912\pi$
$853$	4.78201			0.163733			0.0818665	+	0.996643i	$0.473912\pi$
$854$	2.90580	+	23.5052i	0.0994345	+	0.804332i
$855$	11.2996	+	1.09513i	0.386438	+	0.0374528i
$856$	25.5320	+	9.07872i	0.872666	+	0.310304i
$857$	−15.2965	−	26.4944i	−0.522520	−	0.905031i	−0.999657	−	0.0262016i	$-0.991659\pi$
$857$	−15.2965	−	26.4944i	−0.522520	−	0.905031i	0.477137	−	0.878829i	$-0.341675\pi$
$858$	−4.93929	−	17.5635i	−0.168625	−	0.599607i
$859$	12.2711	−	21.2542i	0.418684	−	0.725183i	−0.577123	−	0.816657i	$-0.695825\pi$
$859$	12.2711	−	21.2542i	0.418684	−	0.725183i	0.995807	+	0.0914746i	$0.0291580\pi$
$860$	20.0015	−	47.0072i	0.682045	−	1.60293i
$861$	−41.6268	+	11.7826i	−1.41864	+	0.401550i
$862$	17.8830	+	27.0437i	0.609097	+	0.921111i
$863$	32.1415	+	18.5569i	1.09411	+	0.631684i	0.934667	−	0.355523i	$-0.115697\pi$
$863$	32.1415	+	18.5569i	1.09411	+	0.631684i	0.159441	+	0.987207i	$0.449031\pi$
$864$	−23.8019	−	17.2472i	−0.809759	−	0.586763i
$865$	−2.87820	−	4.98519i	−0.0978617	−	0.169501i
$866$	−14.9384	+	0.907180i	−0.507629	+	0.0308272i
$867$	18.1376	+	19.9805i	0.615986	+	0.678573i
$868$	7.71823	+	2.72975i	0.261974	+	0.0926538i
$869$	−15.9530			−0.541170
$870$	−17.2805	−	16.8590i	−0.585863	−	0.571574i
$871$	64.2823	−	37.1134i	2.17812	−	1.25754i
$872$	−1.08101	−	1.26903i	−0.0366075	−	0.0429748i
$873$	−29.9013	+	41.8648i	−1.01200	+	1.41691i
$874$	−2.84273	−	4.29894i	−0.0961568	−	0.145414i
$875$	3.44850	−	2.28877i	0.116581	−	0.0773744i
$876$	11.7363	+	33.7353i	0.396534	+	1.13981i
$877$	28.4107	+	16.4029i	0.959360	+	0.553887i	0.895976	−	0.444103i	$-0.146477\pi$
$877$	28.4107	+	16.4029i	0.959360	+	0.553887i	0.0633837	+	0.997989i	$0.479811\pi$
$878$	−4.88125	+	9.77965i	−0.164734	+	0.330047i
$879$	−16.1156	−	5.16417i	−0.543565	−	0.174183i
$880$	−3.68178	−	14.8766i	−0.124113	−	0.501489i
$881$	27.1405			0.914385			0.457193	−	0.889368i	$-0.348855\pi$
$881$	27.1405			0.914385			0.457193	+	0.889368i	$0.348855\pi$
$882$	−17.0699	−	24.3026i	−0.574775	−	0.818312i
$883$			47.9537i			1.61377i	0.590709	+	0.806884i	$0.298848\pi$
$883$			47.9537i			1.61377i	−0.590709	+	0.806884i	$0.701152\pi$
$884$	−8.58141	−	11.4085i	−0.288624	−	0.383708i
$885$	6.07167	−	18.9476i	0.204097	−	0.636915i
$886$	5.78388	+	2.88686i	0.194313	+	0.0969861i
$887$	14.5502	−	25.2017i	0.488548	−	0.846190i	−0.511365	−	0.859364i	$-0.670860\pi$
$887$	14.5502	−	25.2017i	0.488548	−	0.846190i	0.999913	+	0.0131735i	$0.00419338\pi$
$888$	1.50651	+	1.14941i	0.0505552	+	0.0385718i
$889$	8.61372	+	12.9784i	0.288895	+	0.435280i
$890$	33.3619	+	50.4518i	1.11829	+	1.69115i
$891$	−7.35317	+	8.43759i	−0.246340	+	0.282670i
$892$	3.32858	+	27.3047i	0.111449	+	0.914228i
$893$	4.10536	+	7.11070i	0.137381	+	0.237950i
$894$	−7.08912	+	7.26635i	−0.237096	+	0.243023i
$895$		−	47.6391i		−	1.59240i
$896$	15.9072	−	25.3567i	0.531421	−	0.847108i
$897$	22.7912	−	20.6891i	0.760976	−	0.690789i
$898$	6.12216	−	0.371786i	0.204299	−	0.0124066i
$899$	4.28625	−	2.47467i	0.142954	−	0.0825348i
$900$	0.665425	+	26.9453i	0.0221808	+	0.898175i
$901$	−6.26024	+	10.8431i	−0.208559	+	0.361235i
$902$	−13.8488	+	9.15770i	−0.461115	+	0.304918i
$903$	−10.3473	−	36.5559i	−0.344336	−	1.21651i
$904$	19.5289	−	3.59323i	0.649522	−	0.119509i
$905$	−44.3263	−	25.5918i	−1.47346	−	0.850700i
$906$	2.87119	+	10.2096i	0.0953889	+	0.339190i
$907$	1.60692	−	0.927757i	0.0533570	−	0.0308057i	−0.473084	−	0.881017i	$-0.656859\pi$
$907$	1.60692	−	0.927757i	0.0533570	−	0.0308057i	0.526441	+	0.850212i	$0.323526\pi$
$908$	7.62360	−	5.73445i	0.252998	−	0.190304i
$909$	9.90984	+	0.960442i	0.328688	+	0.0318558i
$910$	−68.5253	+	8.47135i	−2.27159	+	0.280823i
$911$		−	12.2209i		−	0.404896i	−0.979293	−	0.202448i	$-0.935110\pi$
$911$		−	12.2209i		−	0.404896i	0.979293	−	0.202448i	$-0.0648897\pi$
$912$	7.06577	+	4.74212i	0.233971	+	0.157027i
$913$	−5.63121	+	3.25118i	−0.186366	+	0.107598i
$914$	25.0151	+	12.4856i	0.827426	+	0.412987i
$915$	−7.15673	−	33.0115i	−0.236594	−	1.09133i
$916$	−1.16394	+	2.73548i	−0.0384576	+	0.0903827i
$917$	−0.700333	−	11.2184i	−0.0231270	−	0.370463i
$918$	−2.97049	+	8.23804i	−0.0980406	+	0.271896i
$919$	14.5126	−	25.1365i	0.478726	−	0.829177i	−0.520977	−	0.853571i	$-0.674432\pi$
$919$	14.5126	−	25.1365i	0.478726	−	0.829177i	0.999702	+	0.0243939i	$0.00776558\pi$
$920$	19.6827	−	16.7664i	0.648919	−	0.552773i
$921$	−5.05777	+	15.7835i	−0.166659	+	0.520085i
$922$	35.7599	−	2.17162i	1.17769	−	0.0715185i
$923$			37.2012i			1.22449i
$924$	−9.07294	−	6.89805i	−0.298478	−	0.226929i
$925$		−	1.73760i		−	0.0571318i
$926$	−1.79656	−	29.5838i	−0.0590387	−	0.972184i
$927$	−15.4456	−	33.9484i	−0.507301	−	1.11501i
$928$	−5.40427	−	17.2705i	−0.177404	−	0.566932i
$929$	−14.7335	+	25.5191i	−0.483390	+	0.837255i	−0.999818	−	0.0190749i	$-0.993928\pi$
$929$	−14.7335	+	25.5191i	−0.483390	+	0.837255i	0.516428	+	0.856330i	$0.327261\pi$
$930$	−11.3145	−	2.88250i	−0.371018	−	0.0945209i
$931$	5.19155	+	6.85342i	0.170146	+	0.224612i
$932$	−4.25407	−	1.81010i	−0.139347	−	0.0592917i
$933$	−29.9670	+	6.49670i	−0.981075	+	0.212692i
$934$	19.6298	−	39.3286i	0.642307	−	1.28687i
$935$	−3.95414	+	2.28292i	−0.129314	+	0.0746596i
$936$	−21.5673	+	46.0201i	−0.704950	+	1.50421i
$937$		−	23.9964i		−	0.783929i	−0.919980	−	0.391965i	$-0.871796\pi$
$937$		−	23.9964i		−	0.783929i	0.919980	−	0.391965i	$-0.128204\pi$
$938$	18.0826	−	42.6980i	0.590417	−	1.39414i
$939$	14.7116	−	13.3547i	0.480094	−	0.435814i
$940$	−32.9185	+	24.7612i	−1.07368	+	0.807622i
$941$	37.8505	−	21.8530i	1.23389	−	0.712387i	0.266052	−	0.963959i	$-0.414281\pi$
$941$	37.8505	−	21.8530i	1.23389	−	0.712387i	0.967839	+	0.251571i	$0.0809473\pi$
$942$	−4.25755	−	15.1393i	−0.138719	−	0.493265i
$943$	−24.2582	−	14.0055i	−0.789955	−	0.456081i
$944$	10.7462	−	10.3415i	0.349758	−	0.336588i
$945$	27.3778	+	32.3186i	0.890599	+	1.05132i
$946$	−8.04214	−	12.1618i	−0.261472	−	0.395414i
$947$	−15.9345	+	27.5994i	−0.517802	+	0.896859i	0.481984	+	0.876180i	$0.339916\pi$
$947$	−15.9345	+	27.5994i	−0.517802	+	0.896859i	−0.999786	+	0.0206793i	$0.993417\pi$
$948$	33.6314	+	29.0478i	1.09230	+	0.943429i
$949$	53.4846	−	30.8794i	1.73618	−	1.00239i
$950$	−0.472993	−	7.78873i	−0.0153459	−	0.252700i
$951$	−2.69250	−	2.96607i	−0.0873103	−	0.0961814i
$952$	−8.57236	−	2.45845i	−0.277832	−	0.0796789i
$953$		−	49.4699i		−	1.60249i	−0.598338	−	0.801243i	$-0.704172\pi$
$953$		−	49.4699i		−	1.60249i	0.598338	−	0.801243i	$-0.295828\pi$
$954$	44.5458	+	1.60269i	1.44222	+	0.0518889i
$955$	0.695736	+	1.20505i	0.0225135	+	0.0389945i
$956$	5.22836	+	42.8887i	0.169097	+	1.38712i
$957$	−6.73394	+	1.45988i	−0.217677	+	0.0471914i
$958$	−40.3184	+	26.6611i	−1.30263	+	0.861380i
$959$	−1.84621	−	0.917585i	−0.0596173	−	0.0296304i
$960$	−19.3260	+	38.0660i	−0.623743	+	1.22857i
$961$	−14.3032	+	24.7738i	−0.461392	+	0.799155i
$962$	1.46319	−	2.93152i	0.0471751	−	0.0945161i
$963$	−26.1614	+	11.9028i	−0.843040	+	0.383561i
$964$	−6.24706	+	4.69902i	−0.201204	+	0.151345i
$965$		−	5.29478i		−	0.170445i
$966$	3.57691	−	18.8932i	0.115085	−	0.607879i
$967$	18.5748			0.597324			0.298662	−	0.954359i	$-0.403460\pi$
$967$	18.5748			0.597324			0.298662	+	0.954359i	$0.403460\pi$
$968$	25.1934	+	8.95831i	0.809746	+	0.287931i
$969$	0.773654	−	2.41430i	0.0248533	−	0.0775586i
$970$	66.8547	+	33.3687i	2.14658	+	1.07140i
$971$	41.9333	+	24.2102i	1.34570	+	0.776943i	0.987638	−	0.156753i	$-0.0501026\pi$
$971$	41.9333	+	24.2102i	1.34570	+	0.776943i	0.358067	+	0.933696i	$0.383436\pi$
$972$	30.8650	−	4.39884i	0.989996	−	0.141093i
$973$	−8.11583	−	12.2282i	−0.260182	−	0.392018i
$974$	−29.1064	+	19.2470i	−0.932628	+	0.616712i
$975$	45.5456	−	9.87406i	1.45863	−	0.316223i
$976$	7.02114	−	24.3265i	0.224741	−	0.778671i
$977$	46.0630	−	26.5945i	1.47369	−	0.850833i	0.474125	−	0.880458i	$-0.342765\pi$
$977$	46.0630	−	26.5945i	1.47369	−	0.850833i	0.999561	+	0.0296250i	$0.00943130\pi$
$978$	−18.5892	−	18.1358i	−0.594417	−	0.579919i
$979$	17.2629			0.551724
$980$	−30.9779	+	30.0142i	−0.989553	+	0.958767i
$981$	1.75991	+	0.170567i	0.0561897	+	0.00544580i
$982$	3.71241	+	61.1319i	0.118468	+	1.95080i
$983$	−7.97962	−	13.8211i	−0.254510	−	0.440825i	0.710252	−	0.703947i	$-0.248581\pi$
$983$	−7.97962	−	13.8211i	−0.254510	−	0.440825i	−0.964762	+	0.263123i	$0.915248\pi$
$984$	45.8701	+	5.91052i	1.46228	+	0.188420i
$985$	43.8174	+	25.2980i	1.39614	+	0.806061i
$986$	−4.49708	+	2.97375i	−0.143216	+	0.0947036i
$987$	−7.51250	+	29.6986i	−0.239126	+	0.945316i
$988$	5.76071	−	13.5388i	0.183273	−	0.430726i
$989$	12.2994	−	21.3031i	0.391097	−	0.677400i
$990$	13.7759	+	8.62841i	0.437828	+	0.274229i
$991$	−4.26387	−	7.38524i	−0.135446	−	0.234600i	0.790322	−	0.612692i	$-0.209914\pi$
$991$	−4.26387	−	7.38524i	−0.135446	−	0.234600i	−0.925768	+	0.378092i	$0.876580\pi$
$992$	−6.43982	−	5.92672i	−0.204465	−	0.188174i
$993$	−30.6781	+	27.8486i	−0.973541	+	0.883749i
$994$	14.0012	+	18.5483i	0.444090	+	0.588315i
$995$	−2.98621			−0.0946693
$996$	17.7913	+	3.39950i	0.563739	+	0.107717i
$997$	−13.8974	−	24.0710i	−0.440136	−	0.762337i	0.557564	−	0.830134i	$-0.311736\pi$
$997$	−13.8974	−	24.0710i	−0.440136	−	0.762337i	−0.997699	+	0.0677970i	$0.978403\pi$
$998$	−23.5743	+	47.2315i	−0.746231	+	1.49509i
$999$	−1.99615	+	0.234369i	−0.0631555	+	0.00741509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.12	yes	48
3.2	odd	2	inner	168.2.ba.c.5.13	yes	48
4.3	odd	2		672.2.bi.c.593.15		48
7.3	odd	6	inner	168.2.ba.c.101.20	yes	48
8.3	odd	2		672.2.bi.c.593.10		48
8.5	even	2	inner	168.2.ba.c.5.5	✓	48
12.11	even	2		672.2.bi.c.593.3		48
21.17	even	6	inner	168.2.ba.c.101.5	yes	48
24.5	odd	2	inner	168.2.ba.c.5.20	yes	48
24.11	even	2		672.2.bi.c.593.22		48
28.3	even	6		672.2.bi.c.17.22		48
56.3	even	6		672.2.bi.c.17.3		48
56.45	odd	6	inner	168.2.ba.c.101.13	yes	48
84.59	odd	6		672.2.bi.c.17.10		48
168.59	odd	6		672.2.bi.c.17.15		48
168.101	even	6	inner	168.2.ba.c.101.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.5	✓	48	8.5	even	2	inner
168.2.ba.c.5.12	yes	48	1.1	even	1	trivial
168.2.ba.c.5.13	yes	48	3.2	odd	2	inner
168.2.ba.c.5.20	yes	48	24.5	odd	2	inner
168.2.ba.c.101.5	yes	48	21.17	even	6	inner
168.2.ba.c.101.12	yes	48	168.101	even	6	inner
168.2.ba.c.101.13	yes	48	56.45	odd	6	inner
168.2.ba.c.101.20	yes	48	7.3	odd	6	inner
672.2.bi.c.17.3		48	56.3	even	6
672.2.bi.c.17.10		48	84.59	odd	6
672.2.bi.c.17.15		48	168.59	odd	6
672.2.bi.c.17.22		48	28.3	even	6
672.2.bi.c.593.3		48	12.11	even	2
672.2.bi.c.593.10		48	8.3	odd	2
672.2.bi.c.593.15		48	4.3	odd	2
672.2.bi.c.593.22		48	24.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.0857242 - 1.41161i) q^{2} +(-0.528554 + 1.64943i) q^{3} +(-1.98530 + 0.242019i) q^{4} +(-2.66818 - 1.54047i) q^{5} +(2.37367 + 0.604718i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(0.511826 + 2.78173i) q^{8} +(-2.44126 - 1.74363i) q^{9} +O(q^{10})\)	\(q+(-0.0857242 - 1.41161i) q^{2} +(-0.528554 + 1.64943i) q^{3} +(-1.98530 + 0.242019i) q^{4} +(-2.66818 - 1.54047i) q^{5} +(2.37367 + 0.604718i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(0.511826 + 2.78173i) q^{8} +(-2.44126 - 1.74363i) q^{9} +(-1.94583 + 3.89849i) q^{10} +(0.621780 + 1.07696i) q^{11} +(0.650147 - 3.40254i) q^{12} -5.98957 q^{13} +(-2.98636 + 2.25426i) q^{14} +(3.95119 - 3.58676i) q^{15} +(3.88285 - 0.960961i) q^{16} +(-0.595854 - 1.03205i) q^{17} +(-2.25206 + 3.59559i) 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} +(-4.85881 - 0.626075i) q^{24} +(2.24612 + 3.89040i) q^{25} +(0.513451 + 8.45496i) q^{26} +(4.16634 - 3.10509i) q^{27} +(3.43814 + 4.02234i) q^{28} +3.19900 q^{29} +(-5.40183 - 5.27008i) q^{30} +(1.33987 - 0.773574i) q^{31} +(-1.68936 - 5.39871i) q^{32} +(-2.10501 + 0.456356i) q^{33} +(-1.40578 + 0.929587i) q^{34} +(0.507883 + 8.13559i) q^{35} +(5.26863 + 2.87080i) q^{36} +(-0.334978 - 0.193399i) q^{37} +(-1.55417 - 0.775723i) q^{38} +(3.16581 - 9.87940i) q^{39} +(2.91955 - 8.21062i) q^{40} -9.44060 q^{41} +(-2.13979 - 6.11729i) q^{42} -8.29057i q^{43} +(-1.49507 - 1.98760i) q^{44} +(3.82770 + 8.41302i) q^{45} +(1.87391 - 3.75440i) q^{46} +(-3.34244 + 5.78928i) q^{47} +(-0.467258 + 6.91243i) q^{48} +(-2.71887 + 6.45041i) q^{49} +(5.29919 - 3.50416i) q^{50} +(2.01724 - 0.437327i) q^{51} +(11.8911 - 1.44959i) q^{52} +(-5.25317 - 9.09875i) q^{53} +(-4.74035 - 5.61508i) q^{54} -3.83135i q^{55} +(5.38325 - 5.19813i) q^{56} +(1.42990 + 1.57518i) q^{57} +(-0.274232 - 4.51576i) q^{58} +(3.22898 - 1.86425i) q^{59} +(-6.97624 + 8.07707i) 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} +(0.824648 + 2.93234i) q^{66} +(-10.7324 + 6.19634i) q^{67} +(1.43273 + 1.90472i) q^{68} +(-3.80515 + 3.45419i) q^{69} +(11.4408 - 1.41435i) q^{70} -6.21100i q^{71} +(3.60081 - 7.68337i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(-0.244290 + 0.489438i) q^{74} +(-7.60415 + 1.64854i) q^{75} +(-0.961791 + 2.26039i) q^{76} +(1.46435 - 2.94632i) q^{77} +(-14.2173 - 3.62200i) q^{78} +(-6.41425 + 11.1098i) q^{79} +(-11.8405 - 3.41742i) q^{80} +(2.91950 + 8.51331i) q^{81} +(0.809288 + 13.3265i) q^{82} +5.22882i q^{83} +(-8.45182 + 3.54496i) q^{84} +3.67159i q^{85} +(-11.7031 + 0.710702i) q^{86} +(-1.69085 + 5.27654i) q^{87} +(-2.67756 + 2.28084i) q^{88} +(6.94090 - 12.0220i) q^{89} +(11.5478 - 6.12444i) q^{90} +(8.76314 + 13.2035i) q^{91} +(-5.46040 - 2.32339i) q^{92} +(0.567765 + 2.61890i) q^{93} +(8.45876 + 4.22196i) q^{94} +(-3.27720 + 1.89209i) q^{95} +(9.79773 + 0.0670247i) q^{96} -17.1489i q^{97} +(9.33855 + 3.28504i) 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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