LMFDB - Embedded newform 168.2.ba.c.101.20

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			101.20
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.20

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.26535	+	0.631567i	0.894741	+	0.446585i
$2$	1.26535	+	0.631567i	0.894741	+	0.446585i
$3$	−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	−0.959041	−	0.283266i	$-0.908582\pi$
$5$	−2.66818	+	1.54047i	−1.19325	+	0.688921i	−0.234205	+	0.972187i	$0.575249\pi$
$6$	−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	−0.756933	−	0.653492i	$-0.773303\pi$
$11$	0.621780	−	1.07696i	0.187474	−	0.324714i	0.944407	+	0.328778i	$0.106637\pi$
$12$	−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	−0.784676	−	0.619906i	$-0.787171\pi$
$17$	0.595854	−	1.03205i	0.144516	−	0.250309i	0.929192	+	0.369597i	$0.120504\pi$
$18$	4.23990	+	0.152545i	0.999353	+	0.0359552i
$19$	−0.614126	−	1.06370i	−0.140890	−	0.244029i	0.786942	−	0.617027i	$-0.211663\pi$
$19$	−0.614126	−	1.06370i	−0.140890	−	0.244029i	−0.927832	+	0.372998i	$0.878330\pi$
$20$	−5.66997	−	2.41256i	−1.26784	−	0.539464i
$21$	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	−0.743371	−	0.668879i	$-0.766774\pi$
$23$	−2.56956	+	1.48354i	−0.535791	+	0.309339i	0.207581	+	0.978218i	$0.433441\pi$
$24$	−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	0.615474	−	0.788157i	$-0.288964\pi$
$31$	1.33987	+	0.773574i	0.240648	+	0.138938i	−0.374827	+	0.927095i	$0.622298\pi$
$32$	−3.83074	+	4.16238i	−0.677185	+	0.735812i
$33$	−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	−0.472212	−	0.881485i	$-0.656544\pi$
$37$	0.334978	−	0.193399i	0.0550700	−	0.0317947i	0.527282	+	0.849690i	$0.323211\pi$
$38$	−0.105291	−	1.73382i	−0.0170804	−	0.281262i
$39$	−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	$-0.782173\pi$
$43$		−	8.29057i		−	1.26430i	0.774846	−	0.632150i	$-0.217827\pi$
$44$	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	0.999897	−	0.0143219i	$-0.00455895\pi$
$47$	3.34244	+	5.78928i	0.487546	+	0.844454i	−0.512352	+	0.858776i	$0.671226\pi$
$48$	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	0.238789	+	0.971071i	$0.423250\pi$
$53$	−5.25317	+	9.09875i	−0.721578	+	1.24981i	−0.960367	+	0.278738i	$0.910084\pi$
$54$	−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	0.695238	−	0.718779i	$-0.255299\pi$
$59$	3.22898	+	1.86425i	0.420377	+	0.242705i	−0.274862	+	0.961484i	$0.588632\pi$
$60$	10.4831	+	2.00307i	1.35336	+	0.258595i
$61$	−3.16493	−	5.48181i	−0.405227	−	0.701874i	0.589121	−	0.808045i	$-0.299474\pi$
$61$	−3.16493	−	5.48181i	−0.405227	−	0.701874i	−0.994348	+	0.106171i	$0.966141\pi$
$62$	1.20685	+	1.82506i	0.153270	+	0.231783i
$63$	−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	0.982290	−	0.187369i	$-0.0599961\pi$
$67$	10.7324	+	6.19634i	1.31117	+	0.757003i	0.328878	+	0.944372i	$0.393329\pi$
$68$	2.36590	−	0.288416i	0.286908	−	0.0349755i
$69$	3.80515	−	3.45419i	0.458086	−	0.415836i
$70$	5.78082	−	9.97364i	0.690940	−	1.19208i
$71$		−	6.21100i		−	0.737110i	−0.929606	−	0.368555i	$-0.879853\pi$
$71$		−	6.21100i		−	0.737110i	0.929606	−	0.368555i	$-0.120147\pi$
$72$	4.85358	+	6.96008i	0.572000	+	0.820253i
$73$	−8.92963	−	5.15552i	−1.04513	−	0.603408i	−0.123851	−	0.992301i	$-0.539524\pi$
$73$	−8.92963	−	5.15552i	−1.04513	−	0.603408i	−0.921283	+	0.388893i	$0.872858\pi$
$74$	0.546010	−	0.0331580i	0.0634724	−	0.00385454i
$75$	−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	−0.960334	−	0.278852i	$-0.910046\pi$
$79$	−6.41425	−	11.1098i	−0.721660	−	1.24995i	0.238674	−	0.971100i	$-0.423287\pi$
$80$	−2.96067	−	11.9629i	−0.331013	−	1.33749i
$81$	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	$-0.907352\pi$
$83$		−	5.22882i		−	0.573938i	0.957940	−	0.286969i	$-0.0926476\pi$
$84$	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	−0.954400	−	0.298529i	$-0.903504\pi$
$89$	−6.94090	−	12.0220i	−0.735734	−	1.27433i	0.218666	−	0.975800i	$-0.429829\pi$
$90$	−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	$0.336270\pi$
$97$			17.1489i			1.74120i	−0.491989	+	0.870601i	$0.663730\pi$
$98$	0.633524	−	9.87920i	0.0639956	−	0.997950i
$99$	0.359884	−	3.71328i	0.0361697	−	0.373199i
$100$	8.91847	−	1.08721i	0.891847	−	0.108721i
$101$	−2.87413	−	1.65938i	−0.285986	−	0.165114i	0.350144	−	0.936696i	$-0.386133\pi$
$101$	−2.87413	−	1.65938i	−0.285986	−	0.165114i	−0.636130	+	0.771582i	$0.719466\pi$
$102$	−2.03846	+	2.08942i	−0.201838	+	0.206884i
$103$	10.7667	−	6.21615i	1.06087	−	0.612496i	0.135200	−	0.990818i	$-0.456832\pi$
$103$	10.7667	−	6.21615i	1.06087	−	0.612496i	0.925674	+	0.378322i	$0.123499\pi$
$104$	3.06561	+	16.6614i	0.300608	+	1.63378i
$105$	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	0.999113	−	0.0421002i	$-0.0134049\pi$
$107$	4.79031	+	8.29706i	0.463097	+	0.802107i	−0.536017	+	0.844207i	$0.680072\pi$
$108$	−9.97188	−	2.92603i	−0.959544	−	0.281558i
$109$	0.510424	+	0.294693i	0.0488898	+	0.0282265i	0.524246	−	0.851567i	$-0.324347\pi$
$109$	0.510424	+	0.294693i	0.0488898	+	0.0282265i	−0.475356	+	0.879794i	$0.657681\pi$
$110$	−2.41975	+	4.84801i	−0.230714	+	0.462240i
$111$	−0.496053	+	0.450301i	−0.0470833	+	0.0427407i
$112$	−6.84900	−	8.06791i	−0.647170	−	0.762346i
$113$		−	7.02041i		−	0.660425i	−0.943907	−	0.330212i	$-0.892880\pi$
$113$		−	7.02041i		−	0.660425i	0.943907	−	0.330212i	$-0.107120\pi$
$114$	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	−0.330586	−	0.943776i	$-0.607246\pi$
$131$	3.67922	−	2.12420i	0.321455	−	0.185592i	0.652041	+	0.758184i	$0.273913\pi$
$132$	−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	0.470895	−	0.882189i	$-0.343931\pi$
$137$	−0.674838	−	0.389618i	−0.0576553	−	0.0332873i	−0.528551	+	0.848902i	$0.677264\pi$
$138$	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	0.768575	−	0.639760i	$-0.220966\pi$
$149$	−2.07219	−	3.58914i	−0.169761	−	0.294034i	−0.938336	+	0.345726i	$0.887633\pi$
$150$	−7.68415	+	7.87626i	−0.627408	+	0.643094i
$151$	2.16486	−	3.74965i	0.176174	−	0.305142i	−0.764393	−	0.644751i	$-0.776961\pi$
$151$	2.16486	−	3.74965i	0.176174	−	0.305142i	0.940567	+	0.339608i	$0.110295\pi$
$152$	2.64459	−	2.25276i	0.214505	−	0.182723i
$153$	0.344878	−	3.55845i	0.0278817	−	0.287684i
$154$	−0.00787757	+	4.65297i	−0.000634793	+	0.374947i
$155$	−4.76668			−0.382869
$156$	−15.7024	−	13.5623i	−1.25719	−	1.08585i
$157$	3.21017	−	5.56018i	0.256200	−	0.443751i	−0.709021	−	0.705187i	$-0.750863\pi$
$157$	3.21017	−	5.56018i	0.256200	−	0.443751i	0.965221	+	0.261437i	$0.0841963\pi$
$158$	−1.09971	−	18.1089i	−0.0874885	−	1.44067i
$159$	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	−0.0952672	−	0.995452i	$-0.530371\pi$
$163$	9.18195	−	5.30120i	0.719186	−	0.415222i	0.814453	+	0.580230i	$0.197037\pi$
$164$	11.3499	+	15.0890i	0.886280	+	1.17826i
$165$	−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	−0.437228	−	0.899351i	$-0.644040\pi$
$173$	1.61807	−	0.934192i	0.123019	−	0.0710253i	0.560247	+	0.828326i	$0.310706\pi$
$174$	−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	−0.417864	−	0.908509i	$-0.637221\pi$
$179$	7.73124	−	13.3909i	0.577860	−	1.00088i	0.995724	−	0.0923734i	$-0.0294454\pi$
$180$	−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	−0.485783	−	0.874080i	$-0.661465\pi$
$191$	0.391130	−	0.225819i	0.0283012	−	0.0163397i	0.514084	+	0.857740i	$0.328132\pi$
$192$	11.6100	−	7.56361i	0.837878	−	0.545857i
$193$	0.859277	−	1.48831i	0.0618521	−	0.107131i	−0.833441	−	0.552608i	$-0.813633\pi$
$193$	0.859277	−	1.48831i	0.0618521	−	0.107131i	0.895293	+	0.445477i	$0.146966\pi$
$194$	−10.8307	+	21.6994i	−0.777596	+	1.55793i
$195$	23.6659	−	21.4832i	1.69475	−	1.53844i
$196$	7.04101	−	12.1006i	0.502930	−	0.864327i
$197$	−16.4222			−1.17003			−0.585017	−	0.811021i	$-0.698912\pi$
$197$	−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	0.529456	−	0.848337i	$-0.322396\pi$
$199$	0.839396	+	0.484625i	0.0595032	+	0.0343542i	−0.469953	+	0.882691i	$0.655729\pi$
$200$	11.9717	+	4.25691i	0.846525	+	0.301009i
$201$	−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	$0.111778\pi$
$211$			9.99340i			0.687974i	−0.938974	+	0.343987i	$0.888222\pi$
$212$	−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	$0.152329\pi$
$223$			13.7534i			0.920996i	−0.887661	+	0.460498i	$0.847671\pi$
$224$	−3.57099	−	14.5344i	−0.238597	−	0.971119i
$225$	1.30005	−	13.4139i	0.0866699	−	0.894259i
$226$	4.43386	−	8.88331i	0.294936	−	0.590909i
$227$	−4.13075	−	2.38489i	−0.274167	−	0.158291i	0.356613	−	0.934252i	$-0.383932\pi$
$227$	−4.13075	−	2.38489i	−0.274167	−	0.158291i	−0.630780	+	0.775962i	$0.717265\pi$
$228$	−0.798543	+	4.17918i	−0.0528848	+	0.276773i
$229$	−0.743202	−	1.28726i	−0.0491122	−	0.0850648i	0.840424	−	0.541929i	$-0.182306\pi$
$229$	−0.743202	−	1.28726i	−0.0491122	−	0.0850648i	−0.889536	+	0.456864i	$0.848973\pi$
$230$	10.7835	−	7.13071i	0.711042	−	0.470185i
$231$	−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	−0.564139	−	0.825680i	$-0.690792\pi$
$233$	−2.00188	+	1.15579i	−0.131148	+	0.0757182i	0.432991	+	0.901398i	$0.357458\pi$
$234$	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	$-0.753765\pi$
$239$		−	21.6031i		−	1.39739i	0.715420	−	0.698695i	$-0.246235\pi$
$240$	9.40169	+	19.1634i	0.606877	+	1.23699i
$241$	3.38489	+	1.95427i	0.218040	+	0.125885i	0.605042	−	0.796193i	$-0.293156\pi$
$241$	3.38489	+	1.95427i	0.218040	+	0.125885i	−0.387002	+	0.922079i	$0.626489\pi$
$242$	0.810399	+	13.3448i	0.0520944	+	0.857834i
$243$	−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	$0.164465\pi$
$251$			15.6528i			0.987995i	−0.869463	+	0.493997i	$0.835535\pi$
$252$	−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	0.994600	−	0.103782i	$-0.0330944\pi$
$257$	6.53148	+	11.3128i	0.407422	+	0.705676i	−0.587178	+	0.809458i	$0.699761\pi$
$258$	−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	−0.986694	−	0.162586i	$-0.948016\pi$
$263$	−26.2857	−	15.1761i	−1.62085	−	0.935796i	−0.634151	−	0.773209i	$-0.718650\pi$
$264$	−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	0.478981	−	0.877825i	$-0.341006\pi$
$269$	−0.684713	−	0.395319i	−0.0417477	−	0.0241030i	−0.520729	+	0.853722i	$0.674340\pi$
$270$	17.2998	−	14.6048i	1.05283	−	0.888818i
$271$	−4.95134	+	2.85866i	−0.300773	+	0.173651i	−0.642790	−	0.766043i	$-0.722223\pi$
$271$	−4.95134	+	2.85866i	−0.300773	+	0.173651i	0.342017	+	0.939694i	$0.388890\pi$
$272$	3.30537	+	3.43470i	0.200418	+	0.208259i
$273$	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	0.885594	−	0.464461i	$-0.153752\pi$
$277$	15.4143	+	8.89945i	0.926156	+	0.534716i	0.0405619	+	0.999177i	$0.487085\pi$
$278$	−7.01910	−	3.50339i	−0.420977	−	0.210119i
$279$	4.61980	+	0.447742i	0.276580	+	0.0268056i
$280$	22.8910	−	2.75121i	1.36800	−	0.164416i
$281$			27.9140i			1.66521i	0.553866	+	0.832606i	$0.313152\pi$
$281$			27.9140i			1.66521i	−0.553866	+	0.832606i	$0.686848\pi$
$282$	−4.43298	−	15.7631i	−0.263980	−	0.938679i
$283$	−1.81190	+	3.13830i	−0.107706	+	0.186552i	−0.914841	−	0.403815i	$-0.867684\pi$
$283$	−1.81190	+	3.13830i	−0.107706	+	0.186552i	0.807134	+	0.590368i	$0.201017\pi$
$284$	9.92712	−	7.46714i	0.589066	−	0.443094i
$285$	−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	$-0.907875\pi$
$293$		−	9.77037i		−	0.570791i	0.958410	−	0.285396i	$-0.0921250\pi$
$294$	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	0.498065	+	0.867140i	$0.334044\pi$
$311$	−8.85168	+	15.3316i	−0.501933	+	0.869373i	−0.999998	+	0.00223345i	$0.999289\pi$
$312$	−11.3036	−	27.0782i	−0.639938	−	1.53300i
$313$	−9.93451	+	5.73569i	−0.561532	+	0.324200i	−0.753760	−	0.657150i	$-0.771762\pi$
$313$	−9.93451	+	5.73569i	−0.561532	+	0.324200i	0.192228	+	0.981350i	$0.438429\pi$
$314$	7.57363	−	5.00816i	0.427405	−	0.282627i
$315$	−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	0.831722	−	0.555193i	$-0.187355\pi$
$317$	−1.15640	−	2.00294i	−0.0649499	−	0.112497i	−0.896672	+	0.442696i	$0.854022\pi$
$318$	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	−0.946104	−	0.323863i	$-0.895018\pi$
$331$	−20.7165	+	11.9607i	−1.13868	+	0.657418i	−0.192578	+	0.981282i	$0.561685\pi$
$332$	8.35729	−	6.28633i	0.458666	−	0.345007i
$333$	0.674434	−	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	−0.853024	−	0.521872i	$-0.825234\pi$
$347$	0.473950	−	0.820906i	0.0254430	−	0.0440686i	0.878467	+	0.477804i	$0.158567\pi$
$348$	−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	−0.582206	−	0.813041i	$-0.697810\pi$
$353$	7.75978	−	13.4403i	0.413011	−	0.715356i	0.995217	+	0.0976847i	$0.0311437\pi$
$354$	−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	−0.139830	−	0.990176i	$-0.544656\pi$
$359$	12.2735	−	7.08613i	0.647772	−	0.373991i	0.787602	+	0.616184i	$0.211322\pi$
$360$	−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	0.166954	−	0.985965i	$-0.446607\pi$
$367$	−11.5602	−	6.67430i	−0.603439	−	0.348396i	−0.770393	+	0.637569i	$0.779940\pi$
$368$	−2.85124	−	11.5207i	−0.148631	−	0.600559i
$369$	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	−0.377008	−	0.926210i	$-0.623047\pi$
$373$	4.56967	−	2.63830i	0.236609	−	0.136606i	0.613617	+	0.789604i	$0.289714\pi$
$374$	−0.127040	−	2.09196i	−0.00656908	−	0.108172i
$375$	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	$-0.870903\pi$
$379$		−	15.3619i		−	0.789086i	0.918877	−	0.394543i	$-0.129097\pi$
$380$	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	0.898549	−	0.438874i	$-0.144623\pi$
$383$	1.35424	+	2.34561i	0.0691983	+	0.119855i	−0.829350	+	0.558729i	$0.811289\pi$
$384$	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	−0.980924	−	0.194393i	$-0.937726\pi$
$389$	−6.35306	+	11.0038i	−0.322113	+	0.557916i	0.658811	+	0.752308i	$0.271060\pi$
$390$	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	−0.992769	−	0.120041i	$-0.961697\pi$
$397$	−11.9617	−	20.7184i	−0.600343	−	1.03982i	0.392426	−	0.919784i	$-0.371636\pi$
$398$	0.756060	+	1.14336i	0.0378979	+	0.0573113i
$399$	−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	0.222731	−	0.974880i	$-0.428503\pi$
$401$	23.5968	−	13.6236i	1.17837	−	0.680331i	0.955636	+	0.294549i	$0.0951694\pi$
$402$	−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	0.659117	−	0.752040i	$-0.270930\pi$
$409$	6.82328	+	3.93942i	0.337390	+	0.194792i	−0.321727	+	0.946832i	$0.604263\pi$
$410$	−41.0582	+	2.49337i	−2.02772	+	0.123139i
$411$	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	$0.161212\pi$
$419$			19.8589i			0.970173i	−0.874466	+	0.485086i	$0.838788\pi$
$420$	−19.7530	+	20.1784i	−0.963848	+	0.984604i
$421$		−	16.6507i		−	0.811505i	−0.913983	−	0.405753i	$-0.867009\pi$
$421$		−	16.6507i		−	0.811505i	0.913983	−	0.405753i	$-0.132991\pi$
$422$	−6.31150	+	12.6452i	−0.307239	+	0.615559i
$423$	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	0.895044	−	0.445977i	$-0.147144\pi$
$431$	19.8541	+	11.4628i	0.956339	+	0.552142i	0.0612944	+	0.998120i	$0.480477\pi$
$432$	−7.31193	−	19.4560i	−0.351795	−	0.936077i
$433$			10.5825i			0.508564i	0.967130	+	0.254282i	$0.0818392\pi$
$433$			10.5825i			0.508564i	−0.967130	+	0.254282i	$0.918161\pi$
$434$	−5.78889	−	0.00980070i	−0.277876	−	0.000470449i
$435$	12.6399	−	11.4741i	0.606035	−	0.550139i
$436$	0.142643	+	1.17011i	0.00683135	+	0.0560382i
$437$	3.15607	+	1.82216i	0.150975	+	0.0871656i
$438$	18.0784	+	17.6374i	0.863818	+	0.842749i
$439$	−6.69332	+	3.86439i	−0.319455	+	0.184437i	−0.651150	−	0.758949i	$-0.725713\pi$
$439$	−6.69332	+	3.86439i	−0.319455	+	0.184437i	0.331695	+	0.943387i	$0.392380\pi$
$440$	−10.6578	+	1.96098i	−0.508090	+	0.0934861i
$441$	−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	0.806611	−	0.591082i	$-0.201299\pi$
$443$	−2.28548	−	3.95856i	−0.108586	−	0.188077i	−0.915198	+	0.403005i	$0.867966\pi$
$444$	−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	$0.0326323\pi$
$449$			4.33700i			0.204676i	−0.994750	+	0.102338i	$0.967368\pi$
$450$	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	0.536696	−	0.843776i	$-0.319672\pi$
$457$	−9.88462	−	17.1207i	−0.462383	−	0.800871i	−0.999079	+	0.0429048i	$0.986339\pi$
$458$	−0.127421	−	2.09823i	−0.00595398	−	0.0980437i
$459$	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	$-0.799156\pi$
$461$		−	25.3326i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$462$	−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	0.275348	−	0.961345i	$-0.411207\pi$
$467$	26.9170	−	15.5406i	1.24557	−	0.719131i	0.970223	+	0.242214i	$0.0778735\pi$
$468$	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	−0.150620	−	0.988592i	$-0.548127\pi$
$479$	17.0894	−	29.5997i	0.780835	−	1.35245i	0.931456	−	0.363855i	$-0.118540\pi$
$480$	−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	0.438531	+	0.898716i	$0.355499\pi$
$487$	−12.3371	+	21.3684i	−0.559046	+	0.968296i	−0.997576	+	0.0695795i	$0.977834\pi$
$488$	13.6290	−	11.6097i	0.616958	−	0.525547i
$489$	−13.5971	+	12.3430i	−0.614884	+	0.558171i
$490$	13.5283	+	27.3354i	0.611146	+	1.23489i
$491$	−43.3064			−1.95439			−0.977196	−	0.212339i	$-0.931892\pi$
$491$	−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	0.448795	−	0.893635i	$-0.351853\pi$
$499$	32.3258	−	18.6633i	1.44710	−	0.835485i	0.998308	+	0.0581497i	$0.0185201\pi$
$500$	2.50034	−	1.88075i	0.111819	−	0.0841096i
$501$	−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	−0.927758	−	0.373182i	$-0.878267\pi$
$509$	−24.1054	+	13.9173i	−1.06845	+	0.616871i	−0.140694	+	0.990053i	$0.544933\pi$
$510$	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	−0.631043	−	0.775748i	$-0.717373\pi$
$521$	8.13261	−	14.0861i	0.356296	−	0.617123i	0.987339	+	0.158625i	$0.0507061\pi$
$522$	13.5635	+	0.487992i	0.593656	+	0.0213588i
$523$	−6.98922	−	12.1057i	−0.305617	−	0.529345i	0.671781	−	0.740750i	$-0.265530\pi$
$523$	−6.98922	−	12.1057i	−0.305617	−	0.529345i	−0.977399	+	0.211405i	$0.932196\pi$
$524$	7.81847	+	3.32674i	0.341551	+	0.145329i
$525$	−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	−0.0344673	−	0.999406i	$-0.510973\pi$
$541$	18.9287	−	10.9285i	0.813810	−	0.469853i	0.848277	+	0.529552i	$0.177640\pi$
$542$	−8.07064	+	0.490112i	−0.346664	+	0.0210521i
$543$	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	$-0.937600\pi$
$547$		−	9.11111i		−	0.389563i	0.980847	−	0.194782i	$-0.0623998\pi$
$548$	−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	−0.817013	−	0.576619i	$-0.804372\pi$
$557$	2.14436	−	3.71415i	0.0908596	−	0.157373i	0.907873	+	0.419245i	$0.137705\pi$
$558$	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	−0.199979	−	0.979800i	$-0.564087\pi$
$563$	−27.2512	−	15.7335i	−1.14850	−	0.663087i	−0.948521	+	0.316713i	$0.897421\pi$
$564$	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	−0.669790	−	0.742551i	$-0.733616\pi$
$569$	−8.62592	+	4.98018i	−0.361617	+	0.208780i	0.308173	+	0.951330i	$0.400283\pi$
$570$	−6.63481	−	6.47298i	−0.277901	−	0.271123i
$571$	29.5465	+	17.0587i	1.23648	+	0.713883i	0.968373	−	0.249506i	$-0.0802681\pi$
$571$	29.5465	+	17.0587i	1.23648	+	0.713883i	0.268108	+	0.963389i	$0.413601\pi$
$572$	14.7873	−	1.80265i	0.618289	−	0.0753727i
$573$	−0.579206	+	0.525785i	−0.0241967	+	0.0219650i
$574$	−30.6209	+	17.6099i	−1.27809	+	0.735024i
$575$			13.3288i			0.555851i
$576$	−16.8769	+	17.0637i	−0.703204	+	0.710988i
$577$	0.843668	+	0.487092i	0.0351224	+	0.0202779i	0.517458	−	0.855708i	$-0.326878\pi$
$577$	0.843668	+	0.487092i	0.0351224	+	0.0202779i	−0.482336	+	0.875986i	$0.660212\pi$
$578$	1.33557	+	21.9927i	0.0555523	+	0.914775i
$579$	−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	$0.179666\pi$
$587$			25.9212i			1.06988i	−0.844890	+	0.534940i	$0.820334\pi$
$588$	−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	−0.816808	−	0.576909i	$-0.804259\pi$
$593$	−22.1118	−	38.2987i	−0.908022	−	1.57274i	−0.0912135	−	0.995831i	$-0.529075\pi$
$594$	−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	0.665050	−	0.746799i	$-0.268410\pi$
$599$	8.58632	+	4.95731i	0.350827	+	0.202550i	−0.314222	+	0.949349i	$0.601744\pi$
$600$	−21.8270	−	2.81248i	−0.891082	−	0.114819i
$601$		−	11.8235i		−	0.482292i	−0.970489	−	0.241146i	$-0.922477\pi$
$601$		−	11.8235i		−	0.482292i	0.970489	−	0.241146i	$-0.0775233\pi$
$602$	15.4647	+	26.8907i	0.630295	+	1.09598i
$603$	37.0046	+	3.58642i	1.50695	+	0.146050i
$604$	8.59581	−	1.04787i	0.349759	−	0.0426374i
$605$	−25.2238	−	14.5630i	−1.02549	−	0.592069i
$606$	5.81878	+	5.67685i	0.236372	+	0.230606i
$607$	5.56281	−	3.21169i	0.225788	−	0.130359i	−0.382840	−	0.923815i	$-0.625054\pi$
$607$	5.56281	−	3.21169i	0.225788	−	0.130359i	0.608627	+	0.793456i	$0.291721\pi$
$608$	6.78007	+	1.51852i	0.274968	+	0.0615841i
$609$	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	0.101184	−	0.994868i	$-0.467737\pi$
$613$	−17.5740	−	10.1463i	−0.709805	−	0.409806i	−0.810989	+	0.585061i	$0.801070\pi$
$614$	−12.1083	−	6.04351i	−0.488650	−	0.243896i
$615$	37.3016	−	33.8612i	1.50414	−	1.36541i
$616$	−7.44638	+	5.58143i	−0.300023	+	0.224882i
$617$			26.7202i			1.07571i	0.843036	+	0.537856i	$0.180766\pi$
$617$			26.7202i			1.07571i	−0.843036	+	0.537856i	$0.819234\pi$
$618$	−29.3156	+	8.24429i	−1.17925	+	0.331634i
$619$	7.12358	−	12.3384i	0.286321	−	0.495922i	−0.686608	−	0.727028i	$-0.740901\pi$
$619$	7.12358	−	12.3384i	0.286321	−	0.495922i	0.972929	+	0.231106i	$0.0742343\pi$
$620$	−5.73073	−	7.61865i	−0.230151	−	0.305972i
$621$	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	0.370133	−	0.928979i	$-0.379312\pi$
$641$	−6.31225	−	3.64438i	−0.249319	−	0.143944i	−0.619452	+	0.785034i	$0.712645\pi$
$642$	−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	0.127657	+	0.991818i	$0.459254\pi$
$647$	−20.2246	+	35.0301i	−0.795112	+	1.37717i	−0.922768	+	0.385355i	$0.874079\pi$
$648$	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	0.869836	+	0.493341i	$0.164225\pi$
$653$	22.0316	+	38.1599i	0.862164	+	1.49331i	−0.00767187	+	0.999971i	$0.502442\pi$
$654$	−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	0.0845192	+	0.996422i	$0.473065\pi$
$661$	−21.0993	+	36.5450i	−0.820667	+	1.42144i	−0.905186	+	0.425015i	$0.860269\pi$
$662$	−33.7677	+	2.05064i	−1.31242	+	0.0797004i
$663$	−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	0.382618	−	0.923907i	$-0.375023\pi$
$677$	35.7518	−	20.6413i	1.37405	−	0.793310i	0.991436	+	0.130596i	$0.0416892\pi$
$678$	−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	−0.326095	−	0.945337i	$-0.605733\pi$
$683$	17.1346	−	29.6781i	0.655638	−	1.13560i	0.981733	−	0.190262i	$-0.0609338\pi$
$684$	−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	0.925990	−	0.377549i	$-0.123233\pi$
$691$	3.57575	+	6.19338i	0.136028	+	0.235607i	−0.789962	+	0.613156i	$0.789900\pi$
$692$	3.43845	+	1.46305i	0.130710	+	0.0556169i
$693$	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	0.200251	−	0.979745i	$-0.435824\pi$
$709$	30.5908	−	17.6616i	1.14886	−	0.663295i	0.948609	+	0.316450i	$0.102491\pi$
$710$	1.64040	+	27.0123i	0.0615631	+	1.01375i
$711$	−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	0.544395	−	0.838829i	$-0.316759\pi$
$719$	−12.1803	−	21.0969i	−0.454250	−	0.786783i	−0.998645	+	0.0520455i	$0.983426\pi$
$720$	−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	$0.0304539\pi$
$727$			5.15142i			0.191055i	−0.995427	+	0.0955277i	$0.969546\pi$
$728$	−41.2138	−	17.6188i	−1.52748	−	0.652997i
$729$	7.71680	−	25.8738i	0.285807	−	0.958287i
$730$	40.1975	+	20.0635i	1.48778	+	0.742583i
$731$	−8.55627	−	4.93997i	−0.316465	−	0.182711i
$732$	−4.11533	+	21.5376i	−0.152107	+	0.796053i
$733$	−3.74171	−	6.48083i	−0.138203	−	0.239375i	0.788613	−	0.614889i	$-0.210799\pi$
$733$	−3.74171	−	6.48083i	−0.138203	−	0.239375i	−0.926817	+	0.375514i	$0.877466\pi$
$734$	−10.4125	−	15.7464i	−0.384333	−	0.581211i
$735$	−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	0.457788	−	0.889061i	$-0.348642\pi$
$739$	−2.26360	−	1.30689i	−0.0832679	−	0.0480747i	−0.541056	+	0.840987i	$0.681975\pi$
$740$	−2.36590	+	0.288416i	−0.0869722	+	0.0106024i
$741$	8.56448	+	9.43466i	0.314624	+	0.346591i
$742$	0.0665544	−	39.3110i	0.00244329	−	1.44315i
$743$			23.6093i			0.866140i	0.901360	+	0.433070i	$0.142570\pi$
$743$			23.6093i			0.866140i	−0.901360	+	0.433070i	$0.857430\pi$
$744$	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	0.875092	−	0.483956i	$-0.160801\pi$
$751$	0.504993	+	0.874673i	0.0184275	+	0.0319173i	−0.856665	+	0.515874i	$0.827467\pi$
$752$	−25.9564	+	6.42392i	−0.946534	+	0.234256i
$753$	−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	$0.0651469\pi$
$757$			11.1837i			0.406478i	−0.979129	+	0.203239i	$0.934853\pi$
$758$	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	0.929239	−	0.369480i	$-0.120464\pi$
$761$	3.99009	+	6.91104i	0.144641	+	0.250525i	−0.784598	+	0.620005i	$0.787131\pi$
$762$	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	$0.0687740\pi$
$769$			11.8900i			0.428766i	−0.976750	+	0.214383i	$0.931226\pi$
$770$	−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	−0.186809	−	0.982396i	$-0.559814\pi$
$773$	−31.4449	−	18.1547i	−1.13099	−	0.652979i	−0.944185	+	0.329417i	$0.893148\pi$
$774$	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	−0.720772	−	0.693172i	$-0.756213\pi$
$787$	6.73055	−	11.6577i	0.239918	−	0.415551i	0.960691	+	0.277621i	$0.0895460\pi$
$788$	−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	$-0.920352\pi$
$797$		−	13.9811i		−	0.495236i	0.968858	−	0.247618i	$-0.0796479\pi$
$798$	−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	0.551693	−	0.834047i	$-0.313982\pi$
$809$	2.99316	+	1.72810i	0.105234	+	0.0607569i	−0.446459	+	0.894804i	$0.647315\pi$
$810$	−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	0.932142	+	0.362092i	$0.117937\pi$
$821$	22.3394	+	38.6931i	0.779652	+	1.35040i	−0.152490	+	0.988305i	$0.548729\pi$
$822$	1.36624	+	1.33291i	0.0476529	+	0.0464906i
$823$	21.1932	−	36.7076i	0.738747	−	1.27955i	−0.214312	−	0.976765i	$-0.568751\pi$
$823$	21.1932	−	36.7076i	0.738747	−	1.27955i	0.953060	−	0.302783i	$-0.0979157\pi$
$824$	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	−0.998528	−	0.0542413i	$-0.982726\pi$
$829$	−13.0225	+	22.5556i	−0.452290	+	0.783389i	0.546238	+	0.837630i	$0.316059\pi$
$830$	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	−0.477137	−	0.878829i	$-0.658325\pi$
$857$	15.2965	−	26.4944i	0.522520	−	0.905031i	0.999657	−	0.0262016i	$-0.00834119\pi$
$858$	−12.7408	+	13.0593i	−0.434962	+	0.445836i
$859$	−12.2711	−	21.2542i	−0.418684	−	0.725183i	0.577123	−	0.816657i	$-0.304175\pi$
$859$	−12.2711	−	21.2542i	−0.418684	−	0.725183i	−0.995807	+	0.0914746i	$0.970842\pi$
$860$	−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	−0.934667	−	0.355523i	$-0.884303\pi$
$863$	−32.1415	+	18.5569i	−1.09411	+	0.631684i	−0.159441	+	0.987207i	$0.550969\pi$
$864$	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	−0.895976	−	0.444103i	$-0.853523\pi$
$877$	−28.4107	+	16.4029i	−0.959360	+	0.553887i	−0.0633837	+	0.997989i	$0.520189\pi$
$878$	−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	$0.298848\pi$
$883$			47.9537i			1.61377i	−0.590709	+	0.806884i	$0.701152\pi$
$884$	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	0.511365	−	0.859364i	$-0.329140\pi$
$887$	−14.5502	−	25.2017i	−0.488548	−	0.846190i	−0.999913	+	0.0131735i	$0.995807\pi$
$888$	−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	0.473084	−	0.881017i	$-0.343141\pi$
$907$	−1.60692	−	0.927757i	−0.0533570	−	0.0308057i	−0.526441	+	0.850212i	$0.676474\pi$
$908$	−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	$-0.935110\pi$
$911$		−	12.2209i		−	0.404896i	0.979293	−	0.202448i	$-0.0648897\pi$
$912$	−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	0.999702	−	0.0243939i	$-0.00776558\pi$
$919$	14.5126	+	25.1365i	0.478726	+	0.829177i	−0.520977	+	0.853571i	$0.674432\pi$
$920$	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	0.999818	−	0.0190749i	$-0.00607211\pi$
$929$	14.7335	+	25.5191i	0.483390	+	0.837255i	−0.516428	+	0.856330i	$0.672739\pi$
$930$	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	$0.128204\pi$
$937$			23.9964i			0.783929i	−0.919980	+	0.391965i	$0.871796\pi$
$938$	−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	0.967839	−	0.251571i	$-0.0809473\pi$
$941$	37.8505	+	21.8530i	1.23389	+	0.712387i	0.266052	+	0.963959i	$0.414281\pi$
$942$	−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	−0.999786	−	0.0206793i	$-0.993417\pi$
$947$	−15.9345	−	27.5994i	−0.517802	−	0.896859i	0.481984	−	0.876180i	$-0.339916\pi$
$948$	−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	$-0.704172\pi$
$953$		−	49.4699i		−	1.60249i	0.598338	−	0.801243i	$-0.295828\pi$
$954$	−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	0.358067	−	0.933696i	$-0.383436\pi$
$971$	41.9333	−	24.2102i	1.34570	−	0.776943i	0.987638	+	0.156753i	$0.0501026\pi$
$972$	−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	−0.474125	−	0.880458i	$-0.657235\pi$
$977$	−46.0630	−	26.5945i	−1.47369	−	0.850833i	−0.999561	+	0.0296250i	$0.990569\pi$
$978$	−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	−0.710252	−	0.703947i	$-0.751419\pi$
$983$	7.97962	−	13.8211i	0.254510	−	0.440825i	0.964762	+	0.263123i	$0.0847524\pi$
$984$	−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	−0.925768	−	0.378092i	$-0.876580\pi$
$991$	−4.26387	+	7.38524i	−0.135446	+	0.234600i	0.790322	+	0.612692i	$0.209914\pi$
$992$	−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	−0.557564	−	0.830134i	$-0.688264\pi$
$997$	13.8974	−	24.0710i	0.440136	−	0.762337i	0.997699	+	0.0677970i	$0.0215970\pi$
$998$	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.101.20	yes	48
3.2	odd	2	inner	168.2.ba.c.101.5	yes	48
4.3	odd	2		672.2.bi.c.17.22		48
7.5	odd	6	inner	168.2.ba.c.5.12	yes	48
8.3	odd	2		672.2.bi.c.17.3		48
8.5	even	2	inner	168.2.ba.c.101.13	yes	48
12.11	even	2		672.2.bi.c.17.10		48
21.5	even	6	inner	168.2.ba.c.5.13	yes	48
24.5	odd	2	inner	168.2.ba.c.101.12	yes	48
24.11	even	2		672.2.bi.c.17.15		48
28.19	even	6		672.2.bi.c.593.15		48
56.5	odd	6	inner	168.2.ba.c.5.5	✓	48
56.19	even	6		672.2.bi.c.593.10		48
84.47	odd	6		672.2.bi.c.593.3		48
168.5	even	6	inner	168.2.ba.c.5.20	yes	48
168.131	odd	6		672.2.bi.c.593.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.5	✓	48	56.5	odd	6	inner
168.2.ba.c.5.12	yes	48	7.5	odd	6	inner
168.2.ba.c.5.13	yes	48	21.5	even	6	inner
168.2.ba.c.5.20	yes	48	168.5	even	6	inner
168.2.ba.c.101.5	yes	48	3.2	odd	2	inner
168.2.ba.c.101.12	yes	48	24.5	odd	2	inner
168.2.ba.c.101.13	yes	48	8.5	even	2	inner
168.2.ba.c.101.20	yes	48	1.1	even	1	trivial
672.2.bi.c.17.3		48	8.3	odd	2
672.2.bi.c.17.10		48	12.11	even	2
672.2.bi.c.17.15		48	24.11	even	2
672.2.bi.c.17.22		48	4.3	odd	2
672.2.bi.c.593.3		48	84.47	odd	6
672.2.bi.c.593.10		48	56.19	even	6
672.2.bi.c.593.15		48	28.19	even	6
672.2.bi.c.593.22		48	168.131	odd	6

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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