LMFDB - Embedded newform 168.2.ba.c.5.20

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			5.20
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26535 - 0.631567i) q^{2} +(-1.69273 - 0.366975i) q^{3} +(1.20225 - 1.59831i) q^{4} +(-2.66818 - 1.54047i) q^{5} +(-2.37367 + 0.604718i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(0.511826 - 2.78173i) q^{8} +(2.73066 + 1.24238i) q^{9} +O(q^{10})$	\(q+(1.26535 - 0.631567i) q^{2} +(-1.69273 - 0.366975i) q^{3} +(1.20225 - 1.59831i) 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} +(2.73066 + 1.24238i) q^{9} +(-4.34911 - 0.264112i) q^{10} +(0.621780 + 1.07696i) q^{11} +(-2.62162 + 2.26432i) 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} +(4.23990 - 0.152545i) q^{18} +(-0.614126 + 1.06370i) q^{19} +(-5.66997 + 2.41256i) q^{20} +(1.66761 + 4.26838i) q^{21} +(1.46694 + 0.970035i) q^{22} +(-2.56956 - 1.48354i) q^{23} +(-1.88721 + 4.52089i) 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} +(7.26494 + 2.04308i) q^{30} +(1.33987 - 0.773574i) q^{31} +(-3.83074 - 4.16238i) q^{32} +(-0.657290 - 2.05117i) 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} +(-0.105291 + 1.73382i) q^{38} +(-10.1387 - 2.19802i) q^{39} +(-5.65083 + 6.63371i) q^{40} +9.44060 q^{41} +(4.80589 + 4.34781i) q^{42} +8.29057i q^{43} +(2.46884 + 0.300965i) q^{44} +(-5.37204 - 7.52140i) q^{45} +(-4.18836 - 0.254350i) 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} +(-0.629882 - 1.96564i) q^{51} +(7.20094 - 9.57321i) q^{52} +(-5.25317 - 9.09875i) q^{53} +(-7.23297 - 1.29772i) 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} +(10.4831 - 2.00307i) q^{60} +(-3.16493 + 5.48181i) q^{61} +(1.20685 - 1.82506i) q^{62} +(-1.25642 - 7.83718i) q^{63} +(-7.47607 - 2.84752i) q^{64} +(-15.9813 - 9.22678i) q^{65} +(-2.12716 - 2.18034i) 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} +(4.85358 - 6.96008i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(0.546010 + 0.0331580i) q^{74} +(-2.37440 - 7.40966i) 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} +(-2.96067 + 11.9629i) q^{80} +(5.91299 + 6.78502i) q^{81} +(11.9457 - 5.96237i) q^{82} +5.22882i q^{83} +(8.82709 + 2.46628i) q^{84} -3.67159i q^{85} +(5.23605 + 10.4905i) q^{86} +(-5.41505 - 1.17396i) q^{87} +(3.31404 - 1.17841i) 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} +(-2.55192 + 0.817752i) q^{93} +(0.573057 - 9.43648i) q^{94} +(3.27720 - 1.89209i) q^{95} +(4.95691 + 8.45157i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.26535	−	0.631567i	0.894741	−	0.446585i
$2$	1.26535	−	0.631567i	0.894741	−	0.446585i
$3$	−1.69273	−	0.366975i	−0.977297	−	0.211873i
$3$	−1.69273	−	0.366975i	−0.977297	−	0.211873i
$4$	1.20225	−	1.59831i	0.601123	−	0.799157i
$5$	−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
$9$	2.73066	+	1.24238i	0.910220	+	0.414126i
$10$	−4.34911	−	0.264112i	−1.37531	−	0.0835195i
$11$	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	$0.773303\pi$
$12$	−2.62162	+	2.26432i	−0.756796	+	0.653652i
$13$	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	$-0.120504\pi$
$17$	0.595854	+	1.03205i	0.144516	+	0.250309i	−0.784676	+	0.619906i	$0.787171\pi$
$18$	4.23990	−	0.152545i	0.999353	−	0.0359552i
$19$	−0.614126	+	1.06370i	−0.140890	+	0.244029i	−0.927832	−	0.372998i	$-0.878330\pi$
$19$	−0.614126	+	1.06370i	−0.140890	+	0.244029i	0.786942	+	0.617027i	$0.211663\pi$
$20$	−5.66997	+	2.41256i	−1.26784	+	0.539464i
$21$	1.66761	+	4.26838i	0.363902	+	0.931437i
$22$	1.46694	+	0.970035i	0.312753	+	0.206812i
$23$	−2.56956	−	1.48354i	−0.535791	−	0.309339i	0.207581	−	0.978218i	$-0.433441\pi$
$23$	−2.56956	−	1.48354i	−0.535791	−	0.309339i	−0.743371	+	0.668879i	$0.766774\pi$
$24$	−1.88721	+	4.52089i	−0.385225	+	0.922823i
$25$	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	$-0.404007\pi$
$29$	3.19900			0.594040			0.297020	+	0.954871i	$0.404007\pi$
$30$	7.26494	+	2.04308i	1.32639	+	0.373014i
$31$	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	$0.288964\pi$
$32$	−3.83074	−	4.16238i	−0.677185	−	0.735812i
$33$	−0.657290	−	2.05117i	−0.114419	−	0.357063i
$34$	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	0.527282	−	0.849690i	$-0.323211\pi$
$37$	0.334978	+	0.193399i	0.0550700	+	0.0317947i	−0.472212	+	0.881485i	$0.656544\pi$
$38$	−0.105291	+	1.73382i	−0.0170804	+	0.281262i
$39$	−10.1387	−	2.19802i	−1.62349	−	0.351965i
$40$	−5.65083	+	6.63371i	−0.893475	+	1.04888i
$41$	9.44060			1.47437			0.737187	−	0.675689i	$-0.236154\pi$
$41$	9.44060			1.47437			0.737187	+	0.675689i	$0.236154\pi$
$42$	4.80589	+	4.34781i	0.741564	+	0.670882i
$43$			8.29057i			1.26430i	0.774846	+	0.632150i	$0.217827\pi$
$43$			8.29057i			1.26430i	−0.774846	+	0.632150i	$0.782173\pi$
$44$	2.46884	+	0.300965i	0.372192	+	0.0453722i
$45$	−5.37204	−	7.52140i	−0.800816	−	1.12122i
$46$	−4.18836	−	0.254350i	−0.617540	−	0.0375019i
$47$	3.34244	−	5.78928i	0.487546	−	0.844454i	−0.512352	−	0.858776i	$-0.671226\pi$
$47$	3.34244	−	5.78928i	0.487546	−	0.844454i	0.999897	+	0.0143219i	$0.00455895\pi$
$48$	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
$51$	−0.629882	−	1.96564i	−0.0882012	−	0.275245i
$52$	7.20094	−	9.57321i	0.998590	−	1.32757i
$53$	−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	$-0.423250\pi$
$54$	−7.23297	−	1.29772i	−0.984283	−	0.176597i
$55$		−	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	$-0.588632\pi$
$59$	3.22898	−	1.86425i	0.420377	−	0.242705i	0.695238	+	0.718779i	$0.255299\pi$
$60$	10.4831	−	2.00307i	1.35336	−	0.258595i
$61$	−3.16493	+	5.48181i	−0.405227	+	0.701874i	−0.994348	−	0.106171i	$-0.966141\pi$
$61$	−3.16493	+	5.48181i	−0.405227	+	0.701874i	0.589121	+	0.808045i	$0.299474\pi$
$62$	1.20685	−	1.82506i	0.153270	−	0.231783i
$63$	−1.25642	−	7.83718i	−0.158294	−	0.987392i
$64$	−7.47607	−	2.84752i	−0.934509	−	0.355940i
$65$	−15.9813	−	9.22678i	−1.98223	−	1.14444i
$66$	−2.12716	−	2.18034i	−0.261835	−	0.268381i
$67$	10.7324	−	6.19634i	1.31117	−	0.757003i	0.328878	−	0.944372i	$-0.393329\pi$
$67$	10.7324	−	6.19634i	1.31117	−	0.757003i	0.982290	+	0.187369i	$0.0599961\pi$
$68$	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	$0.879853\pi$
$72$	4.85358	−	6.96008i	0.572000	−	0.820253i
$73$	−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	$0.539524\pi$
$74$	0.546010	+	0.0331580i	0.0634724	+	0.00385454i
$75$	−2.37440	−	7.40966i	−0.274172	−	0.855594i
$76$	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	$0.910046\pi$
$80$	−2.96067	+	11.9629i	−0.331013	+	1.33749i
$81$	5.91299	+	6.78502i	0.656999	+	0.753891i
$82$	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	$0.907352\pi$
$84$	8.82709	+	2.46628i	0.963114	+	0.269093i
$85$		−	3.67159i		−	0.398240i
$86$	5.23605	+	10.4905i	0.564618	+	1.13122i
$87$	−5.41505	−	1.17396i	−0.580554	−	0.125861i
$88$	3.31404	−	1.17841i	0.353278	−	0.125619i
$89$	−6.94090	+	12.0220i	−0.735734	+	1.27433i	0.218666	+	0.975800i	$0.429829\pi$
$89$	−6.94090	+	12.0220i	−0.735734	+	1.27433i	−0.954400	+	0.298529i	$0.903504\pi$
$90$	−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
$93$	−2.55192	+	0.817752i	−0.264621	+	0.0847969i
$94$	0.573057	−	9.43648i	0.0591063	−	0.973298i
$95$	3.27720	−	1.89209i	0.336233	−	0.194124i
$96$	4.95691	+	8.45157i	0.505913	+	0.862585i
$97$		−	17.1489i		−	1.74120i	−0.491989	−	0.870601i	$-0.663730\pi$
$97$		−	17.1489i		−	1.74120i	0.491989	−	0.870601i	$-0.336270\pi$
$98$	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	$-0.719466\pi$
$101$	−2.87413	+	1.65938i	−0.285986	+	0.165114i	0.350144	+	0.936696i	$0.386133\pi$
$102$	−2.03846	−	2.08942i	−0.201838	−	0.206884i
$103$	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
$105$	2.12585	−	13.9577i	0.207462	−	1.36213i
$106$	−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	$0.0134049\pi$
$108$	−9.97188	+	2.92603i	−0.959544	+	0.281558i
$109$	0.510424	−	0.294693i	0.0488898	−	0.0282265i	−0.475356	−	0.879794i	$-0.657681\pi$
$109$	0.510424	−	0.294693i	0.0488898	−	0.0282265i	0.524246	+	0.851567i	$0.324347\pi$
$110$	−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	$0.892880\pi$
$114$	0.814496	−	2.89624i	0.0762845	−	0.271258i
$115$	4.57070	+	7.91669i	0.426220	+	0.738235i
$116$	3.84599	−	5.11301i	0.357091	−	0.474731i
$117$	16.3555	+	7.44131i	1.51206	+	0.687950i
$118$	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
$122$	−0.542622	+	8.93530i	−0.0491267	+	0.808964i
$123$	−15.9804	−	3.46446i	−1.44090	−	0.312380i
$124$	0.374439	−	3.07156i	0.0336256	−	0.275834i
$125$			1.56436i			0.139921i
$126$	−6.53952	−	9.12330i	−0.582587	−	0.812768i
$127$	−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
$129$	3.04243	−	14.0337i	0.267871	−	1.23560i
$130$	−26.0493	−	1.58192i	−2.28467	−	0.138743i
$131$	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
$135$	6.33323	+	14.7031i	0.545078	+	1.26544i
$136$	3.17586	−	1.12928i	0.272328	−	0.0968347i
$137$	−0.674838	+	0.389618i	−0.0576553	+	0.0332873i	−0.528551	−	0.848902i	$-0.677264\pi$
$137$	−0.674838	+	0.389618i	−0.0576553	+	0.0332873i	0.470895	+	0.882189i	$0.343931\pi$
$138$	6.99642	+	1.96757i	0.595574	+	0.167491i
$139$	−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
$144$	1.74575	−	11.8723i	0.145479	−	0.989361i
$145$	−8.53552	−	4.92798i	−0.708836	−	0.409247i
$146$	−8.04309	+	12.1632i	−0.665651	+	1.00664i
$147$	6.96945	−	9.92102i	0.574831	−	0.818272i
$148$	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	$0.220966\pi$
$150$	−7.68415	−	7.87626i	−0.627408	−	0.643094i
$151$	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	$0.776961\pi$
$152$	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
$156$	−15.7024	+	13.5623i	−1.25719	+	1.08585i
$157$	3.21017	+	5.56018i	0.256200	+	0.443751i	0.965221	−	0.261437i	$-0.0841963\pi$
$157$	3.21017	+	5.56018i	0.256200	+	0.443751i	−0.709021	+	0.705187i	$0.750863\pi$
$158$	−1.09971	+	18.1089i	−0.0874885	+	1.44067i
$159$	5.55317	+	17.3295i	0.440395	+	1.37432i
$160$	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	0.814453	−	0.580230i	$-0.197037\pi$
$163$	9.18195	+	5.30120i	0.719186	+	0.415222i	−0.0952672	+	0.995452i	$0.530371\pi$
$164$	11.3499	−	15.0890i	0.886280	−	1.17826i
$165$	−1.40601	+	6.48543i	−0.109458	+	0.504890i
$166$	3.30235	+	6.61631i	0.256312	+	0.513526i
$167$	15.5718			1.20498			0.602492	−	0.798125i	$-0.294175\pi$
$167$	15.5718			1.20498			0.602492	+	0.798125i	$0.294175\pi$
$168$	12.7270	−	2.45418i	0.981911	−	0.189344i
$169$	22.8750			1.75961
$170$	−2.31886	−	4.64587i	−0.177848	−	0.356322i
$171$	−2.99848	+	2.14162i	−0.229300	+	0.163774i
$172$	13.2509	+	9.96730i	1.01037	+	0.759999i
$173$	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
$177$	−6.14991	+	1.97071i	−0.462256	+	0.148128i
$178$	−1.19001	+	19.5957i	−0.0891948	+	1.46876i
$179$	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	$0.637221\pi$
$180$	−18.4801	−	0.456373i	−1.37742	−	0.0340161i
$181$	−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
$186$	−2.71262	+	2.64645i	−0.198899	+	0.194047i
$187$	−0.740981	+	1.28342i	−0.0541859	+	0.0938527i
$188$	−5.23465	−	12.3024i	−0.381776	−	0.897246i
$189$	−0.749273	+	13.7273i	−0.0545016	+	0.998514i
$190$	2.95183	−	4.46393i	0.214149	−	0.323848i
$191$	0.391130	+	0.225819i	0.0283012	+	0.0163397i	0.514084	−	0.857740i	$-0.328132\pi$
$191$	0.391130	+	0.225819i	0.0283012	+	0.0163397i	−0.485783	+	0.874080i	$0.661465\pi$
$192$	11.6100	+	7.56361i	0.837878	+	0.545857i
$193$	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	$0.813633\pi$
$194$	−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	$-0.698912\pi$
$197$	−16.4222			−1.17003			−0.585017	+	0.811021i	$0.698912\pi$
$198$	2.80057	+	4.47133i	0.199028	+	0.317764i
$199$	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	$0.322396\pi$
$200$	11.9717	−	4.25691i	0.846525	−	0.301009i
$201$	−20.4409	+	6.55020i	−1.44179	+	0.462016i
$202$	−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
$206$	17.5496	+	1.06575i	1.22274	+	0.0742543i
$207$	−5.17348	−	7.24340i	−0.359582	−	0.503451i
$208$	−6.64369	−	23.0187i	−0.460657	−	1.59606i
$209$	−1.52741			−0.105653
$210$	−6.12528	−	19.0041i	−0.422685	−	1.31141i
$211$		−	9.99340i		−	0.687974i	−0.938974	−	0.343987i	$-0.888222\pi$
$211$		−	9.99340i		−	0.687974i	0.938974	−	0.343987i	$-0.111778\pi$
$212$	−20.8583	−	2.54273i	−1.43255	−	0.174635i
$213$	2.27928	−	10.5135i	0.156174	−	0.720375i
$214$	0.821291	−	13.5241i	0.0561423	−	0.924491i
$215$	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
$219$	17.0074	−	5.44995i	1.14925	−	0.368273i
$220$	−6.12369	−	4.60622i	−0.412859	−	0.310551i
$221$	3.56891	+	6.18153i	0.240071	+	0.415815i
$222$	−0.912079	−	0.256500i	−0.0612147	−	0.0172151i
$223$		−	13.7534i		−	0.920996i	−0.887661	−	0.460498i	$-0.847671\pi$
$223$		−	13.7534i		−	0.920996i	0.887661	−	0.460498i	$-0.152329\pi$
$224$	−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	$-0.717265\pi$
$227$	−4.13075	+	2.38489i	−0.274167	+	0.158291i	0.356613	+	0.934252i	$0.383932\pi$
$228$	−0.798543	−	4.17918i	−0.0528848	−	0.276773i
$229$	−0.743202	+	1.28726i	−0.0491122	+	0.0850648i	−0.889536	−	0.456864i	$-0.848973\pi$
$229$	−0.743202	+	1.28726i	−0.0491122	+	0.0850648i	0.840424	+	0.541929i	$0.182306\pi$
$230$	10.7835	+	7.13071i	0.711042	+	0.470185i
$231$	−3.55997	+	4.44994i	−0.234229	+	0.292784i
$232$	1.63733	−	8.89877i	0.107496	−	0.584233i
$233$	−2.00188	−	1.15579i	−0.131148	−	0.0757182i	0.432991	−	0.901398i	$-0.357458\pi$
$233$	−2.00188	−	1.15579i	−0.131148	−	0.0757182i	−0.564139	+	0.825680i	$0.690792\pi$
$234$	25.3952	−	0.913678i	1.66013	−	0.0597290i
$235$	−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	$0.753765\pi$
$240$	9.40169	−	19.1634i	0.606877	−	1.23699i
$241$	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	$0.293156\pi$
$242$	0.810399	−	13.3448i	0.0520944	−	0.857834i
$243$	−7.51916	−	13.6551i	−0.482354	−	0.875976i
$244$	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
$248$	−1.46610	−	4.12309i	−0.0930972	−	0.261817i
$249$	1.91885	−	8.85097i	0.121602	−	0.560908i
$250$	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	$-0.164465\pi$
$252$	−14.0368	−	7.41407i	−0.884235	−	0.467042i
$253$		−	3.68974i		−	0.231972i
$254$	−7.44970	+	3.71832i	−0.467436	+	0.233308i
$255$	−1.34738	+	6.21501i	−0.0843764	+	0.389199i
$256$	−13.5393	+	8.52568i	−0.846207	+	0.532855i
$257$	6.53148	−	11.3128i	0.407422	−	0.705676i	−0.587178	−	0.809458i	$-0.699761\pi$
$257$	6.53148	−	11.3128i	0.407422	−	0.705676i	0.994600	+	0.103782i	$0.0330944\pi$
$258$	−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
$261$	8.73539	+	3.97437i	0.540707	+	0.246008i
$262$	5.99710	+	0.364191i	0.370502	+	0.0224998i
$263$	−26.2857	+	15.1761i	−1.62085	+	0.935796i	−0.634151	+	0.773209i	$0.718650\pi$
$263$	−26.2857	+	15.1761i	−1.62085	+	0.935796i	−0.986694	+	0.162586i	$0.948016\pi$
$264$	−6.04223	+	0.778562i	−0.371873	+	0.0479172i
$265$			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	$-0.674340\pi$
$269$	−0.684713	+	0.395319i	−0.0417477	+	0.0241030i	0.478981	+	0.877825i	$0.341006\pi$
$270$	17.2998	+	14.6048i	1.05283	+	0.888818i
$271$	−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
$273$	9.98826	+	25.5658i	0.604517	+	1.54731i
$274$	−0.607840	+	0.919211i	−0.0367209	+	0.0555315i
$275$	−2.79319	+	4.83795i	−0.168436	+	0.291739i
$276$	10.0956	−	1.92903i	0.607684	−	0.116114i
$277$	15.4143	−	8.89945i	0.926156	−	0.534716i	0.0405619	−	0.999177i	$-0.487085\pi$
$277$	15.4143	−	8.89945i	0.926156	−	0.534716i	0.885594	+	0.464461i	$0.153752\pi$
$278$	−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	$-0.313152\pi$
$282$	−4.43298	+	15.7631i	−0.263980	+	0.938679i
$283$	−1.81190	−	3.13830i	−0.107706	−	0.186552i	0.807134	−	0.590368i	$-0.201017\pi$
$283$	−1.81190	−	3.13830i	−0.107706	−	0.186552i	−0.914841	+	0.403815i	$0.867684\pi$
$284$	9.92712	+	7.46714i	0.589066	+	0.443094i
$285$	−6.24175	+	2.00015i	−0.369729	+	0.118478i
$286$	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
$290$	−13.9128	−	0.844895i	−0.816989	−	0.0496140i
$291$	−6.29320	+	29.0284i	−0.368914	+	1.70167i
$292$	−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	$0.907875\pi$
$294$	2.55304	−	16.9553i	0.148896	−	0.988853i
$295$	−11.4873			−0.668817
$296$	0.709436	−	0.832832i	0.0412351	−	0.0484074i
$297$	0.753496	−	6.41765i	0.0437223	−	0.372390i
$298$	−0.355274	+	5.85026i	−0.0205805	+	0.338897i
$299$	−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
$303$	5.47407	−	1.75414i	0.314477	−	0.100773i
$304$	4.76912	+	1.18030i	0.273528	+	0.0676950i
$305$	16.8892	−	9.75098i	0.967072	−	0.558339i
$306$	2.68379	+	4.28489i	0.153422	+	0.244951i
$307$	−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	−0.999998	−	0.00223345i	$-0.999289\pi$
$311$	−8.85168	−	15.3316i	−0.501933	−	0.869373i	0.498065	−	0.867140i	$-0.334044\pi$
$312$	−11.3036	+	27.0782i	−0.639938	+	1.53300i
$313$	−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
$315$	−8.72062	+	22.8465i	−0.491351	+	1.28725i
$316$	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	$0.187355\pi$
$318$	17.9715	+	18.4208i	1.00779	+	1.03299i
$319$	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
$324$	17.9535	−	1.29355i	0.997414	−	0.0718639i
$325$	13.4533	+	23.3018i	0.746256	+	1.29255i
$326$	14.9665	+	0.908883i	0.828917	+	0.0503383i
$327$	−0.972154	+	0.311523i	−0.0537603	+	0.0172273i
$328$	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	−0.192578	−	0.981282i	$-0.561685\pi$
$331$	−20.7165	−	11.9607i	−1.13868	−	0.657418i	−0.946104	+	0.323863i	$0.895018\pi$
$332$	8.35729	+	6.28633i	0.458666	+	0.345007i
$333$	0.674434	+	0.944277i	0.0369588	+	0.0517461i
$334$	19.7039	−	9.83465i	1.07815	−	0.538128i
$335$	−38.1812			−2.08606
$336$	14.5542	−	11.1434i	0.793998	−	0.607921i
$337$	−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
$339$	2.57632	−	11.8836i	0.139926	−	0.645431i
$340$	−5.86835	−	4.41415i	−0.318256	−	0.239391i
$341$	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
$345$	−4.83173	−	15.0781i	−0.260132	−	0.811779i
$346$	2.63744	+	0.160166i	0.141789	+	0.00861057i
$347$	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	$0.825234\pi$
$348$	−8.38656	+	7.24356i	−0.449567	+	0.388295i
$349$	−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	$-0.0311437\pi$
$353$	7.75978	+	13.4403i	0.413011	+	0.715356i	−0.582206	+	0.813041i	$0.697810\pi$
$354$	−6.53718	+	6.37774i	−0.347447	+	0.338973i
$355$	9.56788	−	16.5721i	0.507810	−	0.879553i
$356$	10.8702	+	25.5471i	0.576122	+	1.35400i
$357$	−3.41153	+	4.26439i	−0.180557	+	0.225695i
$358$	18.2400	+	12.0614i	0.964015	+	0.637467i
$359$	12.2735	+	7.08613i	0.647772	+	0.373991i	0.787602	−	0.616184i	$-0.211322\pi$
$359$	12.2735	+	7.08613i	0.647772	+	0.373991i	−0.139830	+	0.990176i	$0.544656\pi$
$360$	−23.6721	+	11.0939i	−1.24763	+	0.584701i
$361$	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
$366$	4.19754	−	14.9259i	0.219409	−	0.780190i
$367$	−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	$0.446607\pi$
$368$	−2.85124	+	11.5207i	−0.148631	+	0.600559i
$369$	25.7790	+	11.7288i	1.34200	+	0.610576i
$370$	−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	0.613617	−	0.789604i	$-0.289714\pi$
$373$	4.56967	+	2.63830i	0.236609	+	0.136606i	−0.377008	+	0.926210i	$0.623047\pi$
$374$	−0.127040	+	2.09196i	−0.00656908	+	0.108172i
$375$	0.574082	−	2.64804i	0.0296455	−	0.136744i
$376$	−14.3935	−	12.2609i	−0.742287	−	0.632307i
$377$	19.1607			0.986824
$378$	7.72161	+	17.8431i	0.397157	+	0.917751i
$379$			15.3619i			0.789086i	0.918877	+	0.394543i	$0.129097\pi$
$379$			15.3619i			0.789086i	−0.918877	+	0.394543i	$0.870903\pi$
$380$	0.915843	−	7.51274i	0.0469817	−	0.385396i
$381$	9.96584	+	2.16054i	0.510565	+	0.110688i
$382$	0.637538	+	0.0387163i	0.0326193	+	0.00198090i
$383$	1.35424	−	2.34561i	0.0691983	−	0.119855i	−0.829350	−	0.558729i	$-0.811289\pi$
$383$	1.35424	−	2.34561i	0.0691983	−	0.119855i	0.898549	+	0.438874i	$0.144623\pi$
$384$	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
$387$	−10.3000	+	22.6387i	−0.523579	+	1.15079i
$388$	−27.4092	−	20.6171i	−1.39149	−	1.04668i
$389$	−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	$0.937726\pi$
$390$	43.5138	+	12.2372i	2.20341	+	0.619654i
$391$		−	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
$396$	6.36766	+	3.88907i	0.319987	+	0.195433i
$397$	−11.9617	+	20.7184i	−0.600343	+	1.03982i	0.392426	+	0.919784i	$0.371636\pi$
$397$	−11.9617	+	20.7184i	−0.600343	+	1.03982i	−0.992769	+	0.120041i	$0.961697\pi$
$398$	0.756060	−	1.14336i	0.0378979	−	0.0573113i
$399$	−5.56439	−	0.847492i	−0.278568	−	0.0424277i
$400$	12.4599	−	12.9474i	0.622995	−	0.647371i
$401$	23.5968	+	13.6236i	1.17837	+	0.680331i	0.955636	−	0.294549i	$-0.0951694\pi$
$401$	23.5968	+	13.6236i	1.17837	+	0.680331i	0.222731	+	0.974880i	$0.428503\pi$
$402$	−21.7281	+	21.1981i	−1.08370	+	1.05727i
$403$	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
$408$	−5.79028	+	0.746098i	−0.286662	+	0.0369374i
$409$	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	$0.270930\pi$
$410$	−41.0582	−	2.49337i	−2.02772	−	0.123139i
$411$	1.28530	−	0.411869i	0.0633991	−	0.0203160i
$412$	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
$416$	−22.9445	−	24.9309i	−1.12495	−	1.22234i
$417$	9.38980	+	2.03566i	0.459820	+	0.0996868i
$418$	−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	$-0.161212\pi$
$420$	−19.7530	−	20.1784i	−0.963848	−	0.984604i
$421$			16.6507i			0.811505i	0.913983	+	0.405753i	$0.132991\pi$
$421$			16.6507i			0.811505i	−0.913983	+	0.405753i	$0.867009\pi$
$422$	−6.31150	−	12.6452i	−0.307239	−	0.615559i
$423$	16.3196	−	11.6560i	0.793484	−	0.566733i
$424$	−27.9990	+	9.95593i	−1.35975	+	0.483503i
$425$	−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
$429$	−3.93688	−	12.2856i	−0.190074	−	0.593156i
$430$	2.18964	−	36.0566i	0.105594	−	1.73880i
$431$	19.8541	−	11.4628i	0.956339	−	0.552142i	0.0612944	−	0.998120i	$-0.480477\pi$
$431$	19.8541	−	11.4628i	0.956339	−	0.552142i	0.895044	+	0.445977i	$0.147144\pi$
$432$	−7.31193	+	19.4560i	−0.351795	+	0.936077i
$433$		−	10.5825i		−	0.508564i	−0.967130	−	0.254282i	$-0.918161\pi$
$433$		−	10.5825i		−	0.508564i	0.967130	−	0.254282i	$-0.0818392\pi$
$434$	−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
$438$	18.0784	−	17.6374i	0.863818	−	0.842749i
$439$	−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
$441$	−15.4382	+	14.2360i	−0.735150	+	0.677904i
$442$	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	$0.201299\pi$
$444$	−1.31610	+	0.251476i	−0.0624594	+	0.0119345i
$445$	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	$-0.0326323\pi$
$450$	10.1168	+	16.1523i	0.476910	+	0.761425i
$451$	5.86998	+	10.1671i	0.276406	+	0.478750i
$452$	11.2208	+	8.44026i	0.527783	+	0.396996i
$453$	−2.28849	−	7.14159i	−0.107523	−	0.335541i
$454$	−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	$0.319672\pi$
$458$	−0.127421	+	2.09823i	−0.00595398	+	0.0980437i
$459$	0.722078	−	6.15005i	0.0337037	−	0.287060i
$460$	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	$0.799156\pi$
$462$	−1.69419	+	7.87911i	−0.0788209	+	0.366569i
$463$	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
$465$	8.06870	+	1.74925i	0.374177	+	0.0811197i
$466$	−3.26305	−	0.198158i	−0.151158	−	0.00917950i
$467$	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
$471$	−3.39350	−	10.5899i	−0.156364	−	0.487958i
$472$	−3.53317	−	9.93632i	−0.162627	−	0.457356i
$473$	−8.92857	+	5.15491i	−0.410536	+	0.237023i
$474$	8.50703	−	30.2499i	0.390741	−	1.38942i
$475$	−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	0.931456	+	0.363855i	$0.118540\pi$
$479$	17.0894	+	29.5997i	0.780835	+	1.35245i	−0.150620	+	0.988592i	$0.548127\pi$
$480$	−0.206500	−	30.1863i	−0.00942537	−	1.37781i
$481$	2.00637	+	1.15838i	0.0914827	+	0.0528176i
$482$	3.04884	−	4.61063i	0.138871	−	0.210008i
$483$	2.04728	−	13.4418i	0.0931543	−	0.611624i
$484$	−7.40267	−	17.3977i	−0.336485	−	0.790804i
$485$	−26.4174	+	45.7562i	−1.19955	+	2.07768i
$486$	−18.1385	−	12.5297i	−0.822780	−	0.568360i
$487$	−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	$-0.355499\pi$
$488$	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	$-0.931892\pi$
$491$	−43.3064			−1.95439			−0.977196	+	0.212339i	$0.931892\pi$
$492$	−24.7496	+	21.3765i	−1.11580	+	0.963727i
$493$	1.90614	+	3.30153i	0.0858482	+	0.148693i
$494$	−0.630647	+	10.3848i	−0.0283742	+	0.467235i
$495$	4.75998	−	10.4621i	0.213945	−	0.470237i
$496$	−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	0.998308	−	0.0581497i	$-0.0185201\pi$
$499$	32.3258	+	18.6633i	1.44710	+	0.835485i	0.448795	+	0.893635i	$0.351853\pi$
$500$	2.50034	+	1.88075i	0.111819	+	0.0841096i
$501$	−26.3589	−	5.71447i	−1.17763	−	0.255304i
$502$	−9.88578	−	19.8063i	−0.441224	−	0.883999i
$503$	−34.2432			−1.52683			−0.763414	−	0.645910i	$-0.776478\pi$
$503$	−34.2432			−1.52683			−0.763414	+	0.645910i	$0.776478\pi$
$504$	−22.4440	−	0.516245i	−0.999736	−	0.0229954i
$505$	10.2249			0.455003
$506$	−2.33032	−	4.66883i	−0.103595	−	0.207555i
$507$	−38.7211	−	8.39454i	−1.71966	−	0.372814i
$508$	−7.07815	+	9.40998i	−0.314042	+	0.417500i
$509$	−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
$513$	5.86153	−	2.52481i	0.258793	−	0.111473i
$514$	1.11981	−	18.4398i	0.0493928	−	0.813346i
$515$	−19.1517	−	33.1716i	−0.843923	−	1.46172i
$516$	−18.7725	−	21.7347i	−0.826411	−	0.956816i
$517$	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	$-0.0507061\pi$
$521$	8.13261	+	14.0861i	0.356296	+	0.617123i	−0.631043	+	0.775748i	$0.717373\pi$
$522$	13.5635	−	0.487992i	0.593656	−	0.0213588i
$523$	−6.98922	+	12.1057i	−0.305617	+	0.529345i	−0.977399	−	0.211405i	$-0.932196\pi$
$523$	−6.98922	+	12.1057i	−0.305617	+	0.529345i	0.671781	+	0.740750i	$0.265530\pi$
$524$	7.81847	−	3.32674i	0.341551	−	0.145329i
$525$	−12.8601	+	16.0750i	−0.561259	+	0.701570i
$526$	−23.6760	+	35.8043i	−1.03232	+	1.56114i
$527$	1.59673	+	0.921874i	0.0695548	+	0.0401575i
$528$	−7.15385	+	4.80123i	−0.311331	+	0.208947i
$529$	−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
$534$	9.20551	−	32.7336i	0.398361	−	1.41652i
$535$	−25.5628	+	14.7587i	−1.10518	+	0.638074i
$536$	−11.7435	−	33.0260i	−0.507240	−	1.42651i
$537$	−8.17276	−	25.5043i	−0.352681	−	1.10059i
$538$	−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	0.848277	−	0.529552i	$-0.177640\pi$
$541$	18.9287	+	10.9285i	0.813810	+	0.469853i	−0.0344673	+	0.999406i	$0.510973\pi$
$542$	−8.07064	−	0.490112i	−0.346664	−	0.0210521i
$543$	28.1212	+	6.09653i	1.20680	+	0.261627i
$544$	2.01322	−	6.43368i	0.0863163	−	0.275842i
$545$	−1.81587			−0.0777834
$546$	28.7852	+	26.0415i	1.23189	+	1.11447i
$547$			9.11111i			0.389563i	0.980847	+	0.194782i	$0.0623998\pi$
$547$			9.11111i			0.389563i	−0.980847	+	0.194782i	$0.937600\pi$
$548$	−0.188590	+	1.54702i	−0.00805616	+	0.0660854i
$549$	−15.4528	+	11.0369i	−0.659510	+	0.471044i
$550$	−0.478888	+	7.88581i	−0.0204199	+	0.336252i
$551$	−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
$555$	0.629882	+	1.96564i	0.0267370	+	0.0834369i
$556$	−6.66902	+	8.86606i	−0.282830	+	0.376005i
$557$	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	$0.804372\pi$
$558$	5.56290	−	3.48426i	0.235497	−	0.147501i
$559$			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	$-0.897421\pi$
$563$	−27.2512	+	15.7335i	−1.14850	+	0.663087i	−0.199979	+	0.979800i	$0.564087\pi$
$564$	4.34616	+	22.7456i	0.183006	+	0.957764i
$565$	10.8148	−	18.7317i	0.454981	−	0.788049i
$566$	−4.27474	−	2.82673i	−0.179681	−	0.118816i
$567$	6.30589	−	22.9616i	0.264822	−	0.964297i
$568$	17.2773	+	3.17895i	0.724941	+	0.133386i
$569$	−8.62592	−	4.98018i	−0.361617	−	0.208780i	0.308173	−	0.951330i	$-0.400283\pi$
$569$	−8.62592	−	4.98018i	−0.361617	−	0.208780i	−0.669790	+	0.742551i	$0.733616\pi$
$570$	−6.63481	+	6.47298i	−0.277901	+	0.271123i
$571$	29.5465	−	17.0587i	1.23648	−	0.713883i	0.268108	−	0.963389i	$-0.413601\pi$
$571$	29.5465	−	17.0587i	1.23648	−	0.713883i	0.968373	+	0.249506i	$0.0802681\pi$
$572$	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
$576$	−16.8769	−	17.0637i	−0.703204	−	0.710988i
$577$	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	$0.326878\pi$
$578$	1.33557	−	21.9927i	0.0555523	−	0.914775i
$579$	−0.908350	−	2.83464i	−0.0377497	−	0.117804i
$580$	−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
$584$	9.77087	+	27.4786i	0.404322	+	1.13707i
$585$	−32.1762	−	45.0499i	−1.33032	−	1.86259i
$586$	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	$-0.179666\pi$
$588$	−7.47791	−	23.0669i	−0.308384	−	0.951262i
$589$			1.90029i			0.0782999i
$590$	−14.5355	+	7.25501i	−0.598418	+	0.298684i
$591$	27.7983	+	6.02654i	1.14347	+	0.247899i
$592$	0.371699	−	1.50188i	0.0152767	−	0.0617270i
$593$	−22.1118	+	38.2987i	−0.908022	+	1.57274i	−0.0912135	+	0.995831i	$0.529075\pi$
$593$	−22.1118	+	38.2987i	−0.908022	+	1.57274i	−0.816808	+	0.576909i	$0.804259\pi$
$594$	−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
$597$	−1.59871	+	0.512302i	−0.0654310	+	0.0209671i
$598$	−25.0865	−	1.52345i	−1.02586	−	0.0622984i
$599$	8.58632	−	4.95731i	0.350827	−	0.202550i	−0.314222	−	0.949349i	$-0.601744\pi$
$599$	8.58632	−	4.95731i	0.350827	−	0.202550i	0.665050	+	0.746799i	$0.268410\pi$
$600$	−21.8270	+	2.81248i	−0.891082	+	0.114819i
$601$			11.8235i			0.482292i	0.970489	+	0.241146i	$0.0775233\pi$
$601$			11.8235i			0.482292i	−0.970489	+	0.241146i	$0.922477\pi$
$602$	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
$606$	5.81878	−	5.67685i	0.236372	−	0.230606i
$607$	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
$609$	5.33469	+	13.6546i	0.216173	+	0.553311i
$610$	15.2124	−	23.0051i	0.615933	−	0.931449i
$611$	20.0198	−	34.6753i	0.809915	−	1.40281i
$612$	6.10215	+	3.72691i	0.246665	+	0.150651i
$613$	−17.5740	+	10.1463i	−0.709805	+	0.409806i	−0.810989	−	0.585061i	$-0.801070\pi$
$613$	−17.5740	+	10.1463i	−0.709805	+	0.409806i	0.101184	+	0.994868i	$0.467737\pi$
$614$	−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	$-0.180766\pi$
$618$	−29.3156	−	8.24429i	−1.17925	−	0.331634i
$619$	7.12358	+	12.3384i	0.286321	+	0.495922i	0.972929	−	0.231106i	$-0.0742343\pi$
$619$	7.12358	+	12.3384i	0.286321	+	0.495922i	−0.686608	+	0.727028i	$0.740901\pi$
$620$	−5.73073	+	7.61865i	−0.230151	+	0.305972i
$621$	6.09915	+	14.1596i	0.244750	+	0.568207i
$622$	−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
$626$	−16.1932	−	0.983375i	−0.647209	−	0.0393036i
$627$	2.58548	+	0.560520i	0.103254	+	0.0223850i
$628$	12.7463	+	1.55384i	0.508634	+	0.0620051i
$629$			0.460951i			0.0183793i
$630$	3.39441	+	34.4166i	0.135237	+	1.37119i
$631$	−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
$633$	−3.66733	+	16.9161i	−0.145763	+	0.672355i
$634$	−0.198263	+	3.26478i	−0.00787403	+	0.129661i
$635$	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
$639$	−7.71641	+	16.9601i	−0.305256	+	0.670932i
$640$	31.7622	+	14.3587i	1.25551	+	0.567578i
$641$	−6.31225	+	3.64438i	−0.249319	+	0.143944i	−0.619452	−	0.785034i	$-0.712645\pi$
$641$	−6.31225	+	3.64438i	−0.249319	+	0.143944i	0.370133	+	0.928979i	$0.379312\pi$
$642$	−6.35324	+	22.5913i	−0.250742	+	0.891607i
$643$	−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	−0.922768	−	0.385355i	$-0.874079\pi$
$647$	−20.2246	−	35.0301i	−0.795112	−	1.37717i	0.127657	−	0.991818i	$-0.459254\pi$
$648$	21.9005	−	12.9756i	0.860334	−	0.509730i
$649$	4.01543	+	2.31831i	0.157619	+	0.0910016i
$650$	31.7399	+	20.9884i	1.24494	+	0.823233i
$651$	5.53629	+	4.42905i	0.216984	+	0.173588i
$652$	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	$-0.164225\pi$
$654$	−1.03337	+	1.00817i	−0.0404081	+	0.0394225i
$655$	−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	$-0.463399\pi$
$659$	5.89051			0.229462			0.114731	+	0.993397i	$0.463399\pi$
$660$	8.67538	+	10.0443i	0.337689	+	0.390975i
$661$	−21.0993	−	36.5450i	−0.820667	−	1.42144i	−0.905186	−	0.425015i	$-0.860269\pi$
$661$	−21.0993	−	36.5450i	−0.820667	−	1.42144i	0.0845192	−	0.996422i	$-0.473065\pi$
$662$	−33.7677	−	2.05064i	−1.31242	−	0.0797004i
$663$	−3.77273	−	11.7734i	−0.146521	−	0.457239i
$664$	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
$668$	18.7212	−	24.8887i	0.724344	−	0.962971i
$669$	−5.04716	+	23.2808i	−0.195134	+	0.900087i
$670$	−48.3128	+	24.1140i	−1.86648	+	0.931605i
$671$	−7.87156			−0.303878
$672$	11.3785	−	23.2923i	0.438934	−	0.898519i
$673$	−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
$675$	2.72193	−	23.1832i	0.104767	−	0.892320i
$676$	27.5013	−	36.5613i	1.05774	−	1.40621i
$677$	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
$681$	7.86743	−	2.52109i	0.301481	−	0.0966083i
$682$	2.71591	+	0.164931i	0.103997	+	0.00631554i
$683$	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	$0.605733\pi$
$684$	−0.181938	+	7.36726i	−0.00695657	+	0.281694i
$685$	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
$690$	−15.6367	−	16.0276i	−0.595279	−	0.610161i
$691$	3.57575	−	6.19338i	0.136028	−	0.235607i	−0.789962	−	0.613156i	$-0.789900\pi$
$691$	3.57575	−	6.19338i	0.136028	−	0.235607i	0.925990	+	0.377549i	$0.123233\pi$
$692$	3.43845	−	1.46305i	0.130710	−	0.0556169i
$693$	7.65908	−	6.22611i	0.290944	−	0.236511i
$694$	1.11817	+	0.739406i	0.0424453	+	0.0280675i
$695$	14.8008	+	8.54522i	0.561425	+	0.324139i
$696$	−6.03719	+	14.4623i	−0.228839	+	0.548194i
$697$	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	$-0.575309\pi$
$701$	−12.4116			−0.468778			−0.234389	+	0.972143i	$0.575309\pi$
$702$	−43.3224	−	7.77278i	−1.63510	−	0.293365i
$703$	−0.411437	+	0.237543i	−0.0155176	+	0.00895911i
$704$	−1.58182	−	9.82193i	−0.0596170	−	0.370178i
$705$	33.9714	−	10.8860i	1.27944	−	0.409991i
$706$	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	0.948609	−	0.316450i	$-0.102491\pi$
$709$	30.5908	+	17.6616i	1.14886	+	0.663295i	0.200251	+	0.979745i	$0.435824\pi$
$710$	1.64040	−	27.0123i	0.0615631	−	1.01375i
$711$	−31.3177	+	22.3682i	−1.17451	+	0.838872i
$712$	29.8894	+	25.4609i	1.12015	+	0.954187i
$713$	−4.59050			−0.171916
$714$	−1.62355	+	7.55057i	−0.0607597	+	0.282573i
$715$		−	22.9481i		−	0.858211i
$716$	30.6977	+	3.74221i	1.14723	+	0.139853i
$717$	7.92780	−	36.5682i	0.296069	−	1.36566i
$718$	20.0057	+	1.21491i	0.746607	+	0.0453399i
$719$	−12.1803	+	21.0969i	−0.454250	+	0.786783i	−0.998645	−	0.0520455i	$-0.983426\pi$
$719$	−12.1803	+	21.0969i	−0.454250	+	0.786783i	0.544395	+	0.838829i	$0.316759\pi$
$720$	−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
$723$	−6.44687	+	2.06587i	−0.239762	+	0.0768307i
$724$	−19.9728	+	26.5527i	−0.742284	+	0.986822i
$725$	7.18536	+	12.4454i	0.266858	+	0.462211i
$726$	−6.26898	+	22.2917i	−0.232664	+	0.827321i
$727$		−	5.15142i		−	0.191055i	−0.995427	−	0.0955277i	$-0.969546\pi$
$727$		−	5.15142i		−	0.191055i	0.995427	−	0.0955277i	$-0.0304539\pi$
$728$	−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
$732$	−4.11533	−	21.5376i	−0.152107	−	0.796053i
$733$	−3.74171	+	6.48083i	−0.138203	+	0.239375i	−0.926817	−	0.375514i	$-0.877466\pi$
$733$	−3.74171	+	6.48083i	−0.138203	+	0.239375i	0.788613	+	0.614889i	$0.210799\pi$
$734$	−10.4125	+	15.7464i	−0.384333	+	0.581211i
$735$	−33.8788	+	15.7348i	−1.24964	+	0.580388i
$736$	3.66827	+	16.3785i	0.135214	+	0.603721i
$737$	13.3464	+	7.70552i	0.491619	+	0.283837i
$738$	40.0272	−	1.44011i	1.47342	−	0.0530114i
$739$	−2.26360	+	1.30689i	−0.0832679	+	0.0480747i	−0.541056	−	0.840987i	$-0.681975\pi$
$739$	−2.26360	+	1.30689i	−0.0832679	+	0.0480747i	0.457788	+	0.889061i	$0.348642\pi$
$740$	−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	$-0.142570\pi$
$744$	0.968630	+	7.51730i	0.0355117	+	0.275597i
$745$	11.0580	−	6.38431i	0.405132	−	0.233903i
$746$	7.44852	+	0.452332i	0.272710	+	0.0165611i
$747$	−6.49617	+	14.2781i	−0.237683	+	0.522409i
$748$	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	$0.160801\pi$
$752$	−25.9564	−	6.42392i	−0.946534	−	0.234256i
$753$	−5.74418	+	26.4959i	−0.209330	+	0.965564i
$754$	24.2450	−	12.1012i	0.882952	−	0.440701i
$755$		−	13.3397i		−	0.485480i
$756$	21.0397	+	17.7012i	0.765207	+	0.643785i
$757$		−	11.1837i		−	0.406478i	−0.979129	−	0.203239i	$-0.934853\pi$
$757$		−	11.1837i		−	0.406478i	0.979129	−	0.203239i	$-0.0651469\pi$
$758$	9.70205	+	19.4382i	0.352394	+	0.706028i
$759$	−1.35404	+	6.24572i	−0.0491486	+	0.226705i
$760$	−3.58594	−	10.0847i	−0.130076	−	0.365811i
$761$	3.99009	−	6.91104i	0.144641	−	0.250525i	−0.784598	−	0.620005i	$-0.787131\pi$
$761$	3.99009	−	6.91104i	0.144641	−	0.250525i	0.929239	+	0.369480i	$0.120464\pi$
$762$	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
$765$	4.56150	−	10.0259i	0.164922	−	0.362486i
$766$	0.232182	−	3.82332i	0.00838907	−	0.138142i
$767$	19.3402	−	11.1661i	0.698333	−	0.403183i
$768$	26.0471	−	9.46307i	0.939893	−	0.341469i
$769$		−	11.8900i		−	0.428766i	−0.976750	−	0.214383i	$-0.931226\pi$
$769$		−	11.8900i		−	0.428766i	0.976750	−	0.214383i	$-0.0687740\pi$
$770$	−7.14677	+	12.4271i	−0.257552	+	0.447842i
$771$	−15.2075	+	16.7527i	−0.547686	+	0.603333i
$772$	3.41185	+	0.415923i	0.122795	+	0.0149694i
$773$	−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	$0.559814\pi$
$774$	1.26468	+	35.1511i	0.0454581	+	1.26348i
$775$	6.01902	+	3.47508i	0.216210	+	0.124829i
$776$	−47.7035	−	8.77722i	−1.71246	−	0.315084i
$777$	−0.266891	+	1.75233i	−0.00957465	+	0.0628644i
$778$	−14.9885	−	9.91135i	−0.537364	−	0.355339i
$779$	−5.79771	+	10.0419i	−0.207725	+	0.359790i
$780$	62.7891	−	11.9975i	2.24821	−	0.429580i
$781$	−6.68897	+	3.86188i	−0.239350	+	0.138189i
$782$	−2.23315	−	4.47415i	−0.0798572	−	0.159995i
$783$	−13.3281	−	9.93321i	−0.476309	−	0.354984i
$784$	27.8056	+	3.29413i	0.993055	+	0.117648i
$785$		−	19.7807i		−	0.706005i
$786$	−10.0178	−	2.81726i	−0.357323	−	0.100488i
$787$	6.73055	+	11.6577i	0.239918	+	0.415551i	0.960691	−	0.277621i	$-0.0895460\pi$
$787$	6.73055	+	11.6577i	0.239918	+	0.415551i	−0.720772	+	0.693172i	$0.756213\pi$
$788$	−19.7435	+	26.2478i	−0.703334	+	0.935040i
$789$	50.0638	−	16.0427i	1.78232	−	0.571137i
$790$	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
$794$	−2.05082	+	33.7707i	−0.0727810	+	1.19848i
$795$	11.8788	−	54.7927i	0.421297	−	1.94330i
$796$	0.234577	−	1.92426i	0.00831436	−	0.0682034i
$797$			13.9811i			0.495236i	0.968858	+	0.247618i	$0.0796479\pi$
$797$			13.9811i			0.495236i	−0.968858	+	0.247618i	$0.920352\pi$
$798$	−7.57617	+	2.44191i	−0.268194	+	0.0864425i
$799$	7.96643			0.281832
$800$	7.58902	−	24.2523i	0.268312	−	0.857449i
$801$	−33.8891	+	24.2047i	−1.19741	+	0.855232i
$802$	38.4625	+	2.33575i	1.35816	+	0.0824781i
$803$	−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
$807$	1.30411	−	0.417895i	0.0459067	−	0.0147106i
$808$	3.14489	+	8.84436i	0.110637	+	0.311144i
$809$	2.99316	−	1.72810i	0.105234	−	0.0607569i	−0.446459	−	0.894804i	$-0.647315\pi$
$809$	2.99316	−	1.72810i	0.105234	−	0.0607569i	0.551693	+	0.834047i	$0.313982\pi$
$810$	−23.9242	−	31.0705i	−0.840612	−	1.09171i
$811$	45.3167			1.59129			0.795643	−	0.605766i	$-0.207133\pi$
$811$	45.3167			1.59129			0.795643	+	0.605766i	$0.207133\pi$
$812$	−16.8981	−	0.997475i	−0.593008	−	0.0350045i
$813$	7.33222	+	6.65595i	0.257152	+	0.233434i
$814$	0.303789	+	0.608646i	0.0106478	+	0.0213330i
$815$	−16.3327	−	28.2891i	−0.572111	−	0.990924i
$816$	−6.85555	+	4.60103i	−0.239992	+	0.161068i
$817$	−8.81865	−	5.09145i	−0.308525	−	0.178127i
$818$	6.14586	−	9.29413i	0.214885	−	0.324962i
$819$	−7.52542	−	46.9413i	−0.262959	−	1.64026i
$820$	−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	$-0.117937\pi$
$822$	1.36624	−	1.33291i	0.0476529	−	0.0464906i
$823$	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	$0.568751\pi$
$824$	22.8023	−	26.7685i	0.794357	−	0.932524i
$825$	6.50352	−	7.16430i	0.226424	−	0.249429i
$826$	−13.9507	+	0.0236189i	−0.485409	+	0.000821806i
$827$	9.18843			0.319513			0.159757	−	0.987156i	$-0.448929\pi$
$827$	9.18843			0.319513			0.159757	+	0.987156i	$0.448929\pi$
$828$	−17.7970	−	0.439505i	−0.618489	−	0.0152739i
$829$	−13.0225	−	22.5556i	−0.452290	−	0.783389i	0.546238	−	0.837630i	$-0.316059\pi$
$829$	−13.0225	−	22.5556i	−0.452290	−	0.783389i	−0.998528	+	0.0542413i	$0.982726\pi$
$830$	1.38099	−	22.7407i	0.0479350	−	0.789341i
$831$	−29.3581	+	9.40769i	−1.01842	+	0.326349i
$832$	−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
$836$	−1.83632	+	2.44127i	−0.0635103	+	0.0844332i
$837$	−7.98437	−	0.937445i	−0.275980	−	0.0324029i
$838$	−12.5423	−	25.1286i	−0.433265	−	0.868053i
$839$	31.2096			1.07748			0.538738	−	0.842473i	$-0.318901\pi$
$839$	31.2096			1.07748			0.538738	+	0.842473i	$0.318901\pi$
$840$	−37.7386	−	13.0575i	−1.30210	−	0.450525i
$841$	−18.7664			−0.647116
$842$	10.5160	+	21.0690i	0.362406	+	0.726087i
$843$	−10.2438	+	47.2509i	−0.352814	+	1.62741i
$844$	−15.9726	−	12.0145i	−0.549799	−	0.413557i
$845$	−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
$849$	1.91537	+	5.97721i	0.0657354	+	0.205137i
$850$	−0.458920	+	7.55699i	−0.0157408	+	0.259203i
$851$	−0.573831	−	0.993904i	−0.0196707	−	0.0340706i
$852$	−14.0637	−	16.2829i	−0.481813	−	0.557841i
$853$	−4.78201			−0.163733			−0.0818665	−	0.996643i	$-0.526088\pi$
$853$	−4.78201			−0.163733			−0.0818665	+	0.996643i	$0.526088\pi$
$854$	20.4910	−	11.8768i	0.701187	−	0.406415i
$855$	11.2996	−	1.09513i	0.386438	−	0.0374528i
$856$	−20.6284	−	17.5720i	−0.705064	−	0.600599i
$857$	15.2965	+	26.4944i	0.522520	+	0.905031i	0.999657	+	0.0262016i	$0.00834119\pi$
$857$	15.2965	+	26.4944i	0.522520	+	0.905031i	−0.477137	+	0.878829i	$0.658325\pi$
$858$	−12.7408	−	13.0593i	−0.434962	−	0.445836i
$859$	−12.2711	+	21.2542i	−0.418684	+	0.725183i	−0.995807	−	0.0914746i	$-0.970842\pi$
$859$	−12.2711	+	21.2542i	−0.418684	+	0.725183i	0.577123	+	0.816657i	$0.304175\pi$
$860$	−20.0015	−	47.0072i	−0.682045	−	1.60293i
$861$	15.7432	+	40.2961i	0.536528	+	1.37329i
$862$	17.8830	−	27.0437i	0.609097	−	0.921111i
$863$	−32.1415	−	18.5569i	−1.09411	−	0.631684i	−0.159441	−	0.987207i	$-0.550969\pi$
$863$	−32.1415	−	18.5569i	−1.09411	−	0.631684i	−0.934667	+	0.355523i	$0.884303\pi$
$864$	3.03558	+	29.2367i	0.103273	+	0.994653i
$865$	−2.87820	−	4.98519i	−0.0978617	−	0.169501i
$866$	−6.68358	−	13.3907i	−0.227117	−	0.455033i
$867$	−18.1376	+	19.9805i	−0.615986	+	0.678573i
$868$	−7.31881	+	3.66847i	−0.248417	+	0.124516i
$869$	−15.9530			−0.541170
$870$	23.2406	+	6.53584i	0.787929	+	0.221586i
$871$	64.2823	−	37.1134i	2.17812	−	1.25754i
$872$	−0.558510	−	1.57069i	−0.0189135	−	0.0531904i
$873$	21.3054	−	46.8277i	0.721078	−	1.58488i
$874$	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	−0.0633837	−	0.997989i	$-0.520189\pi$
$877$	−28.4107	−	16.4029i	−0.959360	−	0.553887i	−0.895976	+	0.444103i	$0.853523\pi$
$878$	−10.9101	−	0.662544i	−0.368196	−	0.0223598i
$879$	3.58548	−	16.5386i	0.120935	−	0.557832i
$880$	−14.7244	+	4.24977i	−0.496358	+	0.143260i
$881$	−27.1405			−0.914385			−0.457193	−	0.889368i	$-0.651145\pi$
$881$	−27.1405			−0.914385			−0.457193	+	0.889368i	$0.651145\pi$
$882$	−10.5438	+	27.7638i	−0.355027	+	0.934856i
$883$		−	47.9537i		−	1.61377i	−0.590709	−	0.806884i	$-0.701152\pi$
$883$		−	47.9537i		−	1.61377i	0.590709	−	0.806884i	$-0.298848\pi$
$884$	14.1707	+	1.72749i	0.476613	+	0.0581017i
$885$	19.4449	+	4.21556i	0.653633	+	0.141704i
$886$	−0.391841	+	6.45242i	−0.0131642	+	0.216773i
$887$	−14.5502	+	25.2017i	−0.488548	+	0.846190i	−0.999913	−	0.0131735i	$-0.995807\pi$
$887$	−14.5502	+	25.2017i	−0.488548	+	0.846190i	0.511365	+	0.859364i	$0.329140\pi$
$888$	−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
$891$	−3.63058	+	10.5868i	−0.121629	+	0.354672i
$892$	−21.9823	−	16.5350i	−0.736020	−	0.553632i
$893$	4.10536	+	7.11070i	0.137381	+	0.237950i
$894$	2.74828	−	9.77253i	0.0919163	−	0.326842i
$895$		−	47.6391i		−	1.59240i
$896$	18.9373	+	23.1814i	0.632650	+	0.774438i
$897$	22.7912	+	20.6891i	0.760976	+	0.690789i
$898$	−2.73911	−	5.48784i	−0.0914051	−	0.183132i
$899$	4.28625	−	2.47467i	0.142954	−	0.0825348i
$900$	23.0026	+	14.0489i	0.766752	+	0.468297i
$901$	6.26024	−	10.8431i	0.208559	−	0.361235i
$902$	13.8488	+	9.15770i	0.461115	+	0.304918i
$903$	−35.3873	+	13.8254i	−1.17762	+	0.460081i
$904$	19.5289	+	3.59323i	0.649522	+	0.119509i
$905$	44.3263	+	25.5918i	1.47346	+	0.850700i
$906$	−7.40615	−	7.59131i	−0.246053	−	0.252204i
$907$	−1.60692	+	0.927757i	−0.0533570	+	0.0308057i	−0.526441	−	0.850212i	$-0.676474\pi$
$907$	−1.60692	+	0.927757i	−0.0533570	+	0.0308057i	0.473084	+	0.881017i	$0.343141\pi$
$908$	−1.15438	+	9.46945i	−0.0383093	+	0.314255i
$909$	−9.90984	+	0.960442i	−0.328688	+	0.0318558i
$910$	34.6246	+	59.7378i	1.14780	+	1.98029i
$911$			12.2209i			0.404896i	0.979293	+	0.202448i	$0.0648897\pi$
$911$			12.2209i			0.404896i	−0.979293	+	0.202448i	$0.935110\pi$
$912$	−7.63968	−	3.74808i	−0.252975	−	0.124111i
$913$	−5.63121	+	3.25118i	−0.186366	+	0.107598i
$914$	−1.69470	+	27.9065i	−0.0560558	+	0.923065i
$915$	−32.1672	+	10.3078i	−1.06341	+	0.340767i
$916$	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	$0.00776558\pi$
$920$	24.3615	−	8.66251i	0.803175	−	0.285594i
$921$	16.1978	+	3.51161i	0.533737	+	0.115712i
$922$	15.9993	+	32.0548i	0.526907	+	1.05567i
$923$			37.2012i			1.22449i
$924$	2.83243	+	11.0399i	0.0931803	+	0.363185i
$925$			1.73760i			0.0571318i
$926$	26.5186	−	13.2360i	0.871456	−	0.434963i
$927$	21.6774	+	30.3505i	0.711978	+	0.996841i
$928$	−12.2546	−	13.3155i	−0.402275	−	0.437102i
$929$	14.7335	−	25.5191i	0.483390	−	0.837255i	−0.516428	−	0.856330i	$-0.672739\pi$
$929$	14.7335	−	25.5191i	0.483390	−	0.837255i	0.999818	+	0.0190749i	$0.00607211\pi$
$930$	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
$933$	9.35719	+	29.2005i	0.306341	+	0.955982i
$934$	43.8745	+	2.66440i	1.43562	+	0.0871819i
$935$	3.95414	−	2.28292i	0.129314	−	0.0746596i
$936$	29.0709	−	41.6879i	0.950212	−	1.36261i
$937$		−	23.9964i		−	0.783929i	−0.919980	−	0.391965i	$-0.871796\pi$
$937$		−	23.9964i		−	0.783929i	0.919980	−	0.391965i	$-0.128204\pi$
$938$	−46.3691	+	0.0785037i	−1.51400	+	0.00256324i
$939$	14.7116	+	13.3547i	0.480094	+	0.435814i
$940$	−4.98457	+	40.8889i	−0.162579	+	1.33365i
$941$	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	$0.0809473\pi$
$942$	−10.9822	−	11.2568i	−0.357820	−	0.366766i
$943$	−24.2582	−	14.0055i	−0.789955	−	0.456081i
$944$	−10.7462	−	10.3415i	−0.349758	−	0.336588i
$945$	23.1457	−	35.4727i	0.752931	−	1.15393i
$946$	−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	$0.993417\pi$
$948$	−8.34041	−	43.6496i	−0.270884	−	1.41767i
$949$	−53.4846	+	30.8794i	−1.73618	+	1.00239i
$950$	−6.98173	+	3.48474i	−0.226517	+	0.113060i
$951$	2.69250	−	2.96607i	0.0873103	−	0.0961814i
$952$	−7.13588	−	5.34870i	−0.231275	−	0.173352i
$953$			49.4699i			1.60249i	0.598338	+	0.801243i	$0.295828\pi$
$953$			49.4699i			1.60249i	−0.598338	+	0.801243i	$0.704172\pi$
$954$	−23.6609	−	37.7764i	−0.766049	−	1.22306i
$955$	−0.695736	−	1.20505i	−0.0225135	−	0.0389945i
$956$	34.5285	+	25.9723i	1.11673	+	0.840003i
$957$	−2.10267	−	6.56171i	−0.0679698	−	0.212110i
$958$	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
$962$	3.27037	+	0.198602i	0.105441	+	0.00640320i
$963$	23.3888	−	16.7051i	0.753693	−	0.538313i
$964$	0.945939	−	7.75963i	0.0304667	−	0.249921i
$965$		−	5.29478i		−	0.170445i
$966$	−5.89889	−	18.3017i	−0.189794	−	0.588847i
$967$	18.5748			0.597324			0.298662	−	0.954359i	$-0.403460\pi$
$967$	18.5748			0.597324			0.298662	+	0.954359i	$0.403460\pi$
$968$	−20.3548	−	17.3390i	−0.654228	−	0.557295i
$969$	2.47767	+	0.537148i	0.0795944	+	0.0172557i
$970$	−4.52922	+	74.5822i	−0.145424	+	2.39469i
$971$	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
$975$	−14.2216	−	44.3807i	−0.455456	−	1.42132i
$976$	24.5779	+	6.08274i	0.786719	+	0.194704i
$977$	−46.0630	+	26.5945i	−1.47369	+	0.850833i	−0.999561	−	0.0296250i	$-0.990569\pi$
$977$	−46.0630	+	26.5945i	−1.47369	+	0.850833i	−0.474125	+	0.880458i	$0.657235\pi$
$978$	−25.0007	−	7.03082i	−0.799433	−	0.224821i
$979$	−17.2629			−0.551724
$980$	−0.146051	−	43.1330i	−0.00466541	−	1.37783i
$981$	1.75991	−	0.170567i	0.0561897	−	0.00544580i
$982$	−54.7980	+	27.3509i	−1.74867	+	0.872803i
$983$	7.97962	+	13.8211i	0.254510	+	0.440825i	0.964762	−	0.263123i	$-0.0847524\pi$
$983$	7.97962	+	13.8211i	0.254510	+	0.440825i	−0.710252	+	0.703947i	$0.751419\pi$
$984$	−17.8164	+	42.6799i	−0.567965	+	1.36059i
$985$	43.8174	+	25.2980i	1.39614	+	0.806061i
$986$	4.49708	+	2.97375i	0.143216	+	0.0947036i
$987$	30.2848	+	4.61256i	0.963975	+	0.146820i
$988$	5.76071	+	13.5388i	0.183273	+	0.430726i
$989$	12.2994	−	21.3031i	0.391097	−	0.677400i
$990$	−0.584453	−	16.2445i	−0.0185751	−	0.516285i
$991$	−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	$0.876580\pi$
$992$	−8.35260	−	2.61369i	−0.265195	−	0.0829847i
$993$	30.6781	+	27.8486i	0.973541	+	0.883749i
$994$	11.5856	−	20.1456i	0.367474	−	0.638979i
$995$	−2.98621			−0.0946693
$996$	−11.8397	−	13.7080i	−0.375155	−	0.434353i
$997$	13.8974	+	24.0710i	0.440136	+	0.762337i	0.997699	−	0.0677970i	$-0.0215970\pi$
$997$	13.8974	+	24.0710i	0.440136	+	0.762337i	−0.557564	+	0.830134i	$0.688264\pi$
$998$	52.6908	+	3.19980i	1.66790	+	0.101288i
$999$	−0.795108	−	1.84591i	−0.0251561	−	0.0584019i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.26535 - 0.631567i) q^{2} +(-1.69273 - 0.366975i) q^{3} +(1.20225 - 1.59831i) q^{4} +(-2.66818 - 1.54047i) q^{5} +(-2.37367 + 0.604718i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(0.511826 - 2.78173i) q^{8} +(2.73066 + 1.24238i) q^{9} +O(q^{10})\)	\(q+(1.26535 - 0.631567i) q^{2} +(-1.69273 - 0.366975i) q^{3} +(1.20225 - 1.59831i) 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} +(2.73066 + 1.24238i) q^{9} +(-4.34911 - 0.264112i) q^{10} +(0.621780 + 1.07696i) q^{11} +(-2.62162 + 2.26432i) 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} +(4.23990 - 0.152545i) q^{18} +(-0.614126 + 1.06370i) q^{19} +(-5.66997 + 2.41256i) q^{20} +(1.66761 + 4.26838i) q^{21} +(1.46694 + 0.970035i) q^{22} +(-2.56956 - 1.48354i) q^{23} +(-1.88721 + 4.52089i) 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} +(7.26494 + 2.04308i) q^{30} +(1.33987 - 0.773574i) q^{31} +(-3.83074 - 4.16238i) q^{32} +(-0.657290 - 2.05117i) 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} +(-0.105291 + 1.73382i) q^{38} +(-10.1387 - 2.19802i) q^{39} +(-5.65083 + 6.63371i) q^{40} +9.44060 q^{41} +(4.80589 + 4.34781i) q^{42} +8.29057i q^{43} +(2.46884 + 0.300965i) q^{44} +(-5.37204 - 7.52140i) q^{45} +(-4.18836 - 0.254350i) 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} +(-0.629882 - 1.96564i) q^{51} +(7.20094 - 9.57321i) q^{52} +(-5.25317 - 9.09875i) q^{53} +(-7.23297 - 1.29772i) 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} +(10.4831 - 2.00307i) q^{60} +(-3.16493 + 5.48181i) q^{61} +(1.20685 - 1.82506i) q^{62} +(-1.25642 - 7.83718i) q^{63} +(-7.47607 - 2.84752i) q^{64} +(-15.9813 - 9.22678i) q^{65} +(-2.12716 - 2.18034i) 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} +(4.85358 - 6.96008i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(0.546010 + 0.0331580i) q^{74} +(-2.37440 - 7.40966i) 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} +(-2.96067 + 11.9629i) q^{80} +(5.91299 + 6.78502i) q^{81} +(11.9457 - 5.96237i) q^{82} +5.22882i q^{83} +(8.82709 + 2.46628i) q^{84} -3.67159i q^{85} +(5.23605 + 10.4905i) q^{86} +(-5.41505 - 1.17396i) q^{87} +(3.31404 - 1.17841i) 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} +(-2.55192 + 0.817752i) q^{93} +(0.573057 - 9.43648i) q^{94} +(3.27720 - 1.89209i) q^{95} +(4.95691 + 8.45157i) 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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