LMFDB - Embedded newform 416.2.bd.a.411.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			411.5
Character	$\chi$	$=$	416.411
Dual form			416.2.bd.a.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35152 - 0.416401i) q^{2} +(-2.25523 + 0.934148i) q^{3} +(1.65322 + 1.12555i) q^{4} +(0.261748 + 0.631915i) q^{5} +(3.43698 - 0.323439i) q^{6} +4.76655i q^{7} +(-1.76568 - 2.20961i) q^{8} +(2.09213 - 2.09213i) q^{9} +(-0.0906275 - 0.963039i) q^{10} +(1.63978 - 0.679219i) q^{11} +(-4.77983 - 0.994027i) q^{12} +(3.28393 + 1.48856i) q^{13} +(1.98480 - 6.44209i) q^{14} +(-1.18061 - 1.18061i) q^{15} +(1.46627 + 3.72157i) q^{16} -2.74788 q^{17} +(-3.69872 + 1.95639i) q^{18} +(0.414355 - 1.00034i) q^{19} +(-0.278526 + 1.33931i) q^{20} +(-4.45266 - 10.7497i) q^{21} +(-2.49902 + 0.235173i) q^{22} +(-5.08603 + 5.08603i) q^{23} +(6.04613 + 3.33378i) q^{24} +(3.20473 - 3.20473i) q^{25} +(-3.81846 - 3.37925i) q^{26} +(0.0385689 - 0.0931135i) q^{27} +(-5.36499 + 7.88015i) q^{28} +(0.203632 + 0.491611i) q^{29} +(1.10401 + 2.08722i) q^{30} +(-5.24354 + 5.24354i) q^{31} +(-0.432033 - 5.64033i) q^{32} +(-3.06360 + 3.06360i) q^{33} +(3.71382 + 1.14422i) q^{34} +(-3.01206 + 1.24763i) q^{35} +(5.81354 - 1.10395i) q^{36} +(-4.94751 + 2.04933i) q^{37} +(-0.976552 + 1.17944i) q^{38} +(-8.79656 - 0.289375i) q^{39} +(0.934122 - 1.69412i) q^{40} -2.97903 q^{41} +(1.54169 + 16.3825i) q^{42} +(-2.44549 + 5.90392i) q^{43} +(3.47541 + 0.722757i) q^{44} +(1.86966 + 0.774437i) q^{45} +(8.99170 - 4.75604i) q^{46} +(-2.46927 + 2.46927i) q^{47} +(-6.78328 - 7.02328i) q^{48} -15.7200 q^{49} +(-5.66571 + 2.99681i) q^{50} +(6.19712 - 2.56693i) q^{51} +(3.75361 + 6.15715i) q^{52} +(1.10766 - 2.67412i) q^{53} +(-0.0908993 + 0.109785i) q^{54} +(0.858418 + 0.858418i) q^{55} +(10.5322 - 8.41621i) q^{56} +2.64307i q^{57} +(-0.0705055 - 0.749215i) q^{58} +(-3.75224 - 9.05870i) q^{59} +(-0.622969 - 3.28063i) q^{60} +(-4.09073 - 9.87589i) q^{61} +(9.27017 - 4.90334i) q^{62} +(9.97222 + 9.97222i) q^{63} +(-1.76474 + 7.80293i) q^{64} +(-0.0810828 + 2.46479i) q^{65} +(5.41620 - 2.86483i) q^{66} +(7.51832 + 3.11419i) q^{67} +(-4.54286 - 3.09288i) q^{68} +(6.71907 - 16.2213i) q^{69} +(4.59037 - 0.431980i) q^{70} +12.2690 q^{71} +(-8.31681 - 0.928752i) q^{72} +1.56983i q^{73} +(7.54001 - 0.709558i) q^{74} +(-4.23372 + 10.2211i) q^{75} +(1.81095 - 1.18741i) q^{76} +(3.23753 + 7.81609i) q^{77} +(11.7682 + 4.05400i) q^{78} -4.45846 q^{79} +(-1.96792 + 1.90067i) q^{80} +9.12216i q^{81} +(4.02623 + 1.24047i) q^{82} +(5.77758 - 13.9483i) q^{83} +(4.73808 - 22.7833i) q^{84} +(-0.719253 - 1.73643i) q^{85} +(5.76353 - 6.96098i) q^{86} +(-0.918475 - 0.918475i) q^{87} +(-4.39614 - 2.42399i) q^{88} +4.19672 q^{89} +(-2.20440 - 1.82520i) q^{90} +(-7.09530 + 15.6530i) q^{91} +(-14.1329 + 2.68374i) q^{92} +(6.92716 - 16.7236i) q^{93} +(4.36548 - 2.30906i) q^{94} +0.740587 q^{95} +(6.24324 + 12.3167i) q^{96} +(-0.245304 - 0.245304i) q^{97} +(21.2459 + 6.54582i) q^{98} +(2.00961 - 4.85164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.35152	−	0.416401i	−0.955670	−	0.294440i
$2$	−1.35152	−	0.416401i	−0.955670	−	0.294440i
$3$	−2.25523	+	0.934148i	−1.30206	+	0.539331i	−0.922557	−	0.385860i	$-0.873905\pi$
$3$	−2.25523	+	0.934148i	−1.30206	+	0.539331i	−0.379502	+	0.925191i	$0.623905\pi$
$4$	1.65322	+	1.12555i	0.826610	+	0.562775i
$5$	0.261748	+	0.631915i	0.117057	+	0.282601i	0.971539	−	0.236881i	$-0.0761250\pi$
$5$	0.261748	+	0.631915i	0.117057	+	0.282601i	−0.854482	+	0.519482i	$0.826125\pi$
$6$	3.43698	−	0.323439i	1.40314	−	0.132043i
$7$			4.76655i			1.80159i	0.434249	+	0.900793i	$0.357014\pi$
$7$			4.76655i			1.80159i	−0.434249	+	0.900793i	$0.642986\pi$
$8$	−1.76568	−	2.20961i	−0.624263	−	0.781215i
$9$	2.09213	−	2.09213i	0.697375	−	0.697375i
$10$	−0.0906275	−	0.963039i	−0.0286589	−	0.304540i
$11$	1.63978	−	0.679219i	0.494412	−	0.204792i	−0.121524	−	0.992589i	$-0.538778\pi$
$11$	1.63978	−	0.679219i	0.494412	−	0.204792i	0.615936	+	0.787796i	$0.288778\pi$
$12$	−4.77983	−	0.994027i	−1.37982	−	0.286951i
$13$	3.28393	+	1.48856i	0.910798	+	0.412852i
$13$	3.28393	+	1.48856i	0.910798	+	0.412852i
$14$	1.98480	−	6.44209i	0.530459	−	1.72172i
$15$	−1.18061	−	1.18061i	−0.304831	−	0.304831i
$16$	1.46627	+	3.72157i	0.366568	+	0.930391i
$17$	−2.74788			−0.666460			−0.333230	−	0.942846i	$-0.608138\pi$
$17$	−2.74788			−0.666460			−0.333230	+	0.942846i	$0.608138\pi$
$18$	−3.69872	+	1.95639i	−0.871796	+	0.461125i
$19$	0.414355	−	1.00034i	0.0950595	−	0.229494i	−0.869196	−	0.494467i	$-0.835363\pi$
$19$	0.414355	−	1.00034i	0.0950595	−	0.229494i	0.964256	+	0.264973i	$0.0853632\pi$
$20$	−0.278526	+	1.33931i	−0.0622803	+	0.299478i
$21$	−4.45266	−	10.7497i	−0.971651	−	2.34577i
$22$	−2.49902	+	0.235173i	−0.532794	+	0.0501390i
$23$	−5.08603	+	5.08603i	−1.06051	+	1.06051i	−0.0624623	+	0.998047i	$0.519895\pi$
$23$	−5.08603	+	5.08603i	−1.06051	+	1.06051i	−0.998047	+	0.0624623i	$0.980105\pi$
$24$	6.04613	+	3.33378i	1.23416	+	0.680504i
$25$	3.20473	−	3.20473i	0.640946	−	0.640946i
$26$	−3.81846	−	3.37925i	−0.748862	−	0.662726i
$27$	0.0385689	−	0.0931135i	0.00742259	−	0.0179197i
$28$	−5.36499	+	7.88015i	−1.01389	+	1.48921i
$29$	0.203632	+	0.491611i	0.0378135	+	0.0912899i	0.941658	−	0.336571i	$-0.109267\pi$
$29$	0.203632	+	0.491611i	0.0378135	+	0.0912899i	−0.903845	+	0.427861i	$0.859267\pi$
$30$	1.10401	+	2.08722i	0.201563	+	0.381072i
$31$	−5.24354	+	5.24354i	−0.941767	+	0.941767i	−0.998395	−	0.0566280i	$-0.981965\pi$
$31$	−5.24354	+	5.24354i	−0.941767	+	0.941767i	0.0566280	+	0.998395i	$0.481965\pi$
$32$	−0.432033	−	5.64033i	−0.0763734	−	0.997079i
$33$	−3.06360	+	3.06360i	−0.533303	+	0.533303i
$34$	3.71382	+	1.14422i	0.636915	+	0.196233i
$35$	−3.01206	+	1.24763i	−0.509130	+	0.210889i
$36$	5.81354	−	1.10395i	0.968923	−	0.183992i
$37$	−4.94751	+	2.04933i	−0.813366	+	0.336907i	−0.750296	−	0.661102i	$-0.770089\pi$
$37$	−4.94751	+	2.04933i	−0.813366	+	0.336907i	−0.0630697	+	0.998009i	$0.520089\pi$
$38$	−0.976552	+	1.17944i	−0.158418	+	0.191331i
$39$	−8.79656	−	0.289375i	−1.40858	−	0.0463371i
$40$	0.934122	−	1.69412i	0.147698	−	0.267864i
$41$	−2.97903			−0.465247			−0.232623	−	0.972567i	$-0.574731\pi$
$41$	−2.97903			−0.465247			−0.232623	+	0.972567i	$0.574731\pi$
$42$	1.54169	+	16.3825i	0.237888	+	2.52788i
$43$	−2.44549	+	5.90392i	−0.372933	+	0.900340i	0.620317	+	0.784351i	$0.287004\pi$
$43$	−2.44549	+	5.90392i	−0.372933	+	0.900340i	−0.993250	+	0.115989i	$0.962996\pi$
$44$	3.47541	+	0.722757i	0.523938	+	0.108960i
$45$	1.86966	+	0.774437i	0.278712	+	0.115446i
$46$	8.99170	−	4.75604i	1.32575	−	0.701240i
$47$	−2.46927	+	2.46927i	−0.360180	+	0.360180i	−0.863879	−	0.503699i	$-0.831972\pi$
$47$	−2.46927	+	2.46927i	−0.360180	+	0.360180i	0.503699	+	0.863879i	$0.331972\pi$
$48$	−6.78328	−	7.02328i	−0.979082	−	1.01372i
$49$	−15.7200			−2.24571
$50$	−5.66571	+	2.99681i	−0.801253	+	0.423812i
$51$	6.19712	−	2.56693i	0.867770	−	0.359442i
$52$	3.75361	+	6.15715i	0.520531	+	0.853842i
$53$	1.10766	−	2.67412i	0.152148	−	0.367318i	−0.829367	−	0.558705i	$-0.811298\pi$
$53$	1.10766	−	2.67412i	0.152148	−	0.367318i	0.981515	+	0.191387i	$0.0612984\pi$
$54$	−0.0908993	+	0.109785i	−0.0123698	+	0.0149398i
$55$	0.858418	+	0.858418i	0.115749	+	0.115749i
$56$	10.5322	−	8.41621i	1.40743	−	1.12466i
$57$			2.64307i			0.350083i
$58$	−0.0705055	−	0.749215i	−0.00925782	−	0.0983768i
$59$	−3.75224	−	9.05870i	−0.488499	−	1.17934i	−0.955475	−	0.295072i	$-0.904656\pi$
$59$	−3.75224	−	9.05870i	−0.488499	−	1.17934i	0.466976	−	0.884270i	$-0.345344\pi$
$60$	−0.622969	−	3.28063i	−0.0804250	−	0.423528i
$61$	−4.09073	−	9.87589i	−0.523764	−	1.26448i	−0.935549	−	0.353197i	$-0.885095\pi$
$61$	−4.09073	−	9.87589i	−0.523764	−	1.26448i	0.411785	−	0.911281i	$-0.364905\pi$
$62$	9.27017	−	4.90334i	1.17731	−	0.622725i
$63$	9.97222	+	9.97222i	1.25638	+	1.25638i
$64$	−1.76474	+	7.80293i	−0.220592	+	0.975366i
$65$	−0.0810828	+	2.46479i	−0.0100571	+	0.305720i
$66$	5.41620	−	2.86483i	0.666688	−	0.352636i
$67$	7.51832	+	3.11419i	0.918509	+	0.380459i	0.791308	−	0.611418i	$-0.209401\pi$
$67$	7.51832	+	3.11419i	0.918509	+	0.380459i	0.127201	+	0.991877i	$0.459401\pi$
$68$	−4.54286	−	3.09288i	−0.550902	−	0.375067i
$69$	6.71907	−	16.2213i	0.808881	−	1.95281i
$70$	4.59037	−	0.431980i	0.548655	−	0.0516315i
$71$	12.2690			1.45606			0.728028	−	0.685547i	$-0.240437\pi$
$71$	12.2690			1.45606			0.728028	+	0.685547i	$0.240437\pi$
$72$	−8.31681	−	0.928752i	−0.980145	−	0.109454i
$73$			1.56983i			0.183734i	0.995771	+	0.0918672i	$0.0292835\pi$
$73$			1.56983i			0.183734i	−0.995771	+	0.0918672i	$0.970716\pi$
$74$	7.54001	−	0.709558i	0.876508	−	0.0824844i
$75$	−4.23372	+	10.2211i	−0.488868	+	1.18023i
$76$	1.81095	−	1.18741i	0.207731	−	0.136205i
$77$	3.23753	+	7.81609i	0.368951	+	0.890726i
$78$	11.7682	+	4.05400i	1.33249	+	0.459025i
$79$	−4.45846			−0.501616			−0.250808	−	0.968037i	$-0.580696\pi$
$79$	−4.45846			−0.501616			−0.250808	+	0.968037i	$0.580696\pi$
$80$	−1.96792	+	1.90067i	−0.220020	+	0.212502i
$81$			9.12216i			1.01357i
$82$	4.02623	+	1.24047i	0.444622	+	0.136987i
$83$	5.77758	−	13.9483i	0.634172	−	1.53103i	−0.200159	−	0.979763i	$-0.564146\pi$
$83$	5.77758	−	13.9483i	0.634172	−	1.53103i	0.834331	−	0.551263i	$-0.185854\pi$
$84$	4.73808	−	22.7833i	0.516967	−	2.48586i
$85$	−0.719253	−	1.73643i	−0.0780139	−	0.188342i
$86$	5.76353	−	6.96098i	0.621497	−	0.750621i
$87$	−0.918475	−	0.918475i	−0.0984709	−	0.0984709i
$88$	−4.39614	−	2.42399i	−0.468630	−	0.258398i
$89$	4.19672			0.444851			0.222426	−	0.974950i	$-0.428603\pi$
$89$	4.19672			0.444851			0.222426	+	0.974950i	$0.428603\pi$
$90$	−2.20440	−	1.82520i	−0.232365	−	0.192392i
$91$	−7.09530	+	15.6530i	−0.743789	+	1.64088i
$92$	−14.1329	+	2.68374i	−1.47346	+	0.279799i
$93$	6.92716	−	16.7236i	0.718313	−	1.73416i
$94$	4.36548	−	2.30906i	0.450264	−	0.238162i
$95$	0.740587			0.0759826
$96$	6.24324	+	12.3167i	0.637198	+	1.25707i
$97$	−0.245304	−	0.245304i	−0.0249069	−	0.0249069i	0.694544	−	0.719451i	$-0.255606\pi$
$97$	−0.245304	−	0.245304i	−0.0249069	−	0.0249069i	−0.719451	+	0.694544i	$0.755606\pi$
$98$	21.2459	+	6.54582i	2.14616	+	0.661228i
$99$	2.00961	−	4.85164i	0.201974	−	0.487608i
$100$	8.90521	−	1.69104i	0.890521	−	0.169104i
$101$	−2.01267	+	4.85902i	−0.200268	+	0.483490i	−0.991825	−	0.127605i	$-0.959271\pi$
$101$	−2.01267	+	4.85902i	−0.200268	+	0.483490i	0.791557	+	0.611096i	$0.209271\pi$
$102$	−9.44441	+	0.888773i	−0.935136	+	0.0880017i
$103$	−8.16643	−	8.16643i	−0.804663	−	0.804663i	0.179158	−	0.983820i	$-0.442663\pi$
$103$	−8.16643	−	8.16643i	−0.804663	−	0.804663i	−0.983820	+	0.179158i	$0.942663\pi$
$104$	−2.50924	−	9.88452i	−0.246051	−	0.969257i
$105$	5.62741	−	5.62741i	0.549179	−	0.549179i
$106$	−2.61053	+	3.15290i	−0.253557	+	0.306236i
$107$	−0.342942	−	0.142051i	−0.0331534	−	0.0137326i	0.366045	−	0.930597i	$-0.380712\pi$
$107$	−0.342942	−	0.142051i	−0.0331534	−	0.0137326i	−0.399199	+	0.916865i	$0.630712\pi$
$108$	0.168567	−	0.110526i	0.0162204	−	0.0106354i
$109$	19.0153	+	7.87639i	1.82133	+	0.754421i	0.975156	+	0.221520i	$0.0711019\pi$
$109$	19.0153	+	7.87639i	1.82133	+	0.754421i	0.846178	+	0.532901i	$0.178898\pi$
$110$	−0.802724	−	1.51762i	−0.0765367	−	0.144699i
$111$	9.24342	−	9.24342i	0.877346	−	0.877346i
$112$	−17.7390	+	6.98906i	−1.67618	+	0.660404i
$113$		−	0.911688i		−	0.0857644i	−0.999080	−	0.0428822i	$-0.986346\pi$
$113$		−	0.911688i		−	0.0857644i	0.999080	−	0.0428822i	$-0.0136540\pi$
$114$	1.10058	−	3.57217i	0.103079	−	0.334564i
$115$	−4.54519	−	1.88268i	−0.423842	−	0.175561i
$116$	−0.216685	+	1.04194i	−0.0201187	+	0.0967416i
$117$	9.98465	−	3.75614i	0.923081	−	0.347255i
$118$	1.29917	+	13.8055i	0.119599	+	1.27090i
$119$		−	13.0979i		−	1.20068i
$120$	−0.524103	+	4.69325i	−0.0478438	+	0.428433i
$121$	−5.55064	+	5.55064i	−0.504603	+	0.504603i
$122$	1.41637	+	15.0509i	0.128232	+	1.36264i
$123$	6.71842	−	2.78286i	0.605779	−	0.250922i
$124$	−14.5706	+	2.76685i	−1.30848	+	0.248471i
$125$	6.02353	+	2.49503i	0.538761	+	0.223162i
$126$	−9.32522	−	17.6301i	−0.830757	−	1.57062i
$127$	−19.1141			−1.69611			−0.848053	−	0.529911i	$-0.822225\pi$
$127$	−19.1141			−1.69611			−0.848053	+	0.529911i	$0.822225\pi$
$128$	5.63423	−	9.81098i	0.498001	−	0.867177i
$129$		−	15.5992i		−	1.37343i
$130$	1.13593	−	3.29746i	0.0996275	−	0.289206i
$131$	−12.2119	+	5.05835i	−1.06696	+	0.441950i	−0.845917	−	0.533314i	$-0.820946\pi$
$131$	−12.2119	+	5.05835i	−1.06696	+	0.441950i	−0.221044	+	0.975264i	$0.570946\pi$
$132$	−8.51303	+	1.61657i	−0.740964	+	0.140704i
$133$	4.76817	+	1.97504i	0.413453	+	0.171258i
$134$	−8.86442	−	7.33953i	−0.765769	−	0.634039i
$135$	0.0689352			0.00593300
$136$	4.85189	+	6.07175i	0.416046	+	0.520648i
$137$			13.5356i			1.15642i	0.815887	+	0.578212i	$0.196249\pi$
$137$			13.5356i			1.15642i	−0.815887	+	0.578212i	$0.803751\pi$
$138$	−15.8355	+	19.1256i	−1.34801	+	1.62808i
$139$	−1.05909	−	0.438691i	−0.0898311	−	0.0372093i	0.337315	−	0.941392i	$-0.390481\pi$
$139$	−1.05909	−	0.438691i	−0.0898311	−	0.0372093i	−0.427146	+	0.904182i	$0.640481\pi$
$140$	−6.38387	−	1.32761i	−0.539535	−	0.112203i
$141$	3.26211	−	7.87544i	0.274720	−	0.663232i
$142$	−16.5818	−	5.10881i	−1.39151	−	0.428722i
$143$	6.39598	+	0.210405i	0.534859	+	0.0175949i
$144$	10.8536	+	4.71836i	0.904467	+	0.393196i
$145$	−0.257356	+	0.257356i	−0.0213723	+	0.0213723i
$146$	0.653678	−	2.12165i	0.0540988	−	0.175589i
$147$	35.4523	−	14.6848i	2.92405	−	1.21118i
$148$	−10.4859	−	2.18069i	−0.861939	−	0.179251i
$149$	−16.1546	+	6.69145i	−1.32344	+	0.548185i	−0.928776	−	0.370643i	$-0.879137\pi$
$149$	−16.1546	+	6.69145i	−1.32344	+	0.548185i	−0.394660	+	0.918827i	$0.629137\pi$
$150$	9.97804	−	12.0511i	0.814704	−	0.983969i
$151$	21.8089			1.77478			0.887392	−	0.461016i	$-0.152515\pi$
$151$	21.8089			1.77478			0.887392	+	0.461016i	$0.152515\pi$
$152$	−2.94198	+	0.850721i	−0.238626	+	0.0690026i
$153$	−5.74892	+	5.74892i	−0.464772	+	0.464772i
$154$	−1.12096	−	11.9117i	−0.0903296	−	0.959874i
$155$	−4.68596	−	1.94099i	−0.376385	−	0.155904i
$156$	−14.2169	−	10.3794i	−1.13827	−	0.831015i
$157$	4.63951	+	11.2008i	0.370273	+	0.893918i	0.993704	+	0.112040i	$0.0357384\pi$
$157$	4.63951	+	11.2008i	0.370273	+	0.893918i	−0.623431	+	0.781879i	$0.714262\pi$
$158$	6.02571	+	1.85651i	0.479380	+	0.147696i
$159$			7.06547i			0.560329i
$160$	3.45113	−	1.74935i	0.272836	−	0.138299i
$161$	−24.2428	−	24.2428i	−1.91060	−	1.91060i
$162$	3.79848	−	12.3288i	0.298437	−	0.968641i
$163$	1.91518	−	4.62366i	0.150009	−	0.362153i	−0.830956	−	0.556338i	$-0.812206\pi$
$163$	1.91518	−	4.62366i	0.150009	−	0.362153i	0.980965	+	0.194185i	$0.0622061\pi$
$164$	−4.92500	−	3.35305i	−0.384578	−	0.261829i
$165$	−2.73782	−	1.13404i	−0.213139	−	0.0882851i
$166$	−13.6166	+	16.4457i	−1.05685	+	1.27643i
$167$			20.0885i			1.55450i	0.629195	+	0.777248i	$0.283385\pi$
$167$			20.0885i			1.55450i	−0.629195	+	0.777248i	$0.716615\pi$
$168$	−15.8906	+	28.8192i	−1.22599	+	2.22345i
$169$	8.56837	+	9.77665i	0.659106	+	0.752050i
$170$	0.249034	+	2.64632i	0.0191000	+	0.202963i
$171$	−1.22596	−	2.95972i	−0.0937512	−	0.226335i
$172$	−10.6881	+	7.00797i	−0.814959	+	0.534353i
$173$	6.32717	+	15.2752i	0.481046	+	1.16135i	0.959113	+	0.283025i	$0.0913378\pi$
$173$	6.32717	+	15.2752i	0.481046	+	1.16135i	−0.478066	+	0.878324i	$0.658662\pi$
$174$	0.858885	+	1.62379i	0.0651119	+	0.123099i
$175$	15.2755	+	15.2755i	1.15472	+	1.15472i
$176$	4.93212	+	5.10663i	0.371773	+	0.384926i
$177$	16.9243	+	16.9243i	1.27211	+	1.27211i
$178$	−5.67195	−	1.74752i	−0.425131	−	0.130982i
$179$	−8.30332	+	3.43935i	−0.620619	+	0.257069i	−0.670761	−	0.741673i	$-0.734033\pi$
$179$	−8.30332	+	3.43935i	−0.620619	+	0.257069i	0.0501422	+	0.998742i	$0.484033\pi$
$180$	2.21928	+	3.38471i	0.165416	+	0.252281i
$181$	7.67585	+	3.17944i	0.570542	+	0.236326i	0.649254	−	0.760571i	$-0.275081\pi$
$181$	7.67585	+	3.17944i	0.570542	+	0.236326i	−0.0787128	+	0.996897i	$0.525081\pi$
$182$	16.1074	−	18.2009i	1.19396	−	1.34914i
$183$	18.4511	+	18.4511i	1.36394	+	1.36394i
$184$	20.2184	+	2.25783i	1.49052	+	0.166449i
$185$	−2.59000	−	2.59000i	−0.190421	−	0.190421i
$186$	−16.3260	+	19.7179i	−1.19708	+	1.44579i
$187$	−4.50592	+	1.86641i	−0.329506	+	0.136486i
$188$	−6.86153	+	1.30296i	−0.500429	+	0.0950279i
$189$	0.443830	+	0.183840i	0.0322839	+	0.0133724i
$190$	−1.00092	−	0.308381i	−0.0726143	−	0.0223723i
$191$		−	7.74904i		−	0.560701i	−0.959898	−	0.280350i	$-0.909549\pi$
$191$		−	7.74904i		−	0.560701i	0.959898	−	0.280350i	$-0.0904507\pi$
$192$	−3.30919	−	19.2460i	−0.238820	−	1.38896i
$193$	12.4434	−	12.4434i	0.895696	−	0.895696i	−0.0993562	−	0.995052i	$-0.531678\pi$
$193$	12.4434	−	12.4434i	0.895696	−	0.895696i	0.995052	+	0.0993562i	$0.0316783\pi$
$194$	0.229389	+	0.433679i	0.0164692	+	0.0311363i
$195$	−2.11962	−	5.63443i	−0.151789	−	0.403490i
$196$	−25.9886	−	17.6936i	−1.85633	−	1.26383i
$197$	2.23719	+	5.40104i	0.159393	+	0.384809i	0.983319	−	0.181889i	$-0.0582210\pi$
$197$	2.23719	+	5.40104i	0.159393	+	0.384809i	−0.823926	+	0.566697i	$0.808221\pi$
$198$	−4.73626	+	5.72028i	−0.336592	+	0.406523i
$199$	3.20031	+	3.20031i	0.226864	+	0.226864i	0.811381	−	0.584517i	$-0.198716\pi$
$199$	3.20031	+	3.20031i	0.226864	+	0.226864i	−0.584517	+	0.811381i	$0.698716\pi$
$200$	−12.7397	−	1.42267i	−0.900835	−	0.100598i
$201$	−19.8647			−1.40115
$202$	4.74347	−	5.72899i	0.333749	−	0.403090i
$203$	−2.34329	+	0.970622i	−0.164467	+	0.0681243i
$204$	13.1344	+	2.73147i	0.919593	+	0.191241i
$205$	−0.779756	−	1.88250i	−0.0544605	−	0.131479i
$206$	7.63660	+	14.4376i	0.532067	+	1.00592i
$207$			21.2812i			1.47915i
$208$	−0.724642	+	14.4040i	−0.0502449	+	0.998737i
$209$		−	1.92178i		−	0.132932i
$210$	−9.94883	+	5.26231i	−0.686535	+	0.363134i
$211$	−0.961172	−	2.32047i	−0.0661698	−	0.159748i	0.887335	−	0.461125i	$-0.152554\pi$
$211$	−0.961172	−	2.32047i	−0.0661698	−	0.159748i	−0.953505	+	0.301377i	$0.902554\pi$
$212$	4.84105	−	3.17418i	0.332485	−	0.218004i
$213$	−27.6694	+	11.4610i	−1.89587	+	0.785296i
$214$	0.404343	+	0.334787i	0.0276403	+	0.0228855i
$215$	−4.37088			−0.298092
$216$	−0.273845	+	0.0791867i	−0.0186328	+	0.00538797i
$217$	−24.9936	−	24.9936i	−1.69668	−	1.69668i
$218$	−22.4198	−	18.5631i	−1.51846	−	1.25725i
$219$	−1.46645	−	3.54033i	−0.0990936	−	0.239233i
$220$	0.452961	+	2.38535i	0.0305386	+	0.160820i
$221$	−9.02385	−	4.09039i	−0.607010	−	0.275149i
$222$	−16.3416	+	8.64371i	−1.09678	+	0.580128i
$223$	6.19432	−	6.19432i	0.414802	−	0.414802i	−0.468605	−	0.883408i	$-0.655243\pi$
$223$	6.19432	−	6.19432i	0.414802	−	0.414802i	0.883408	+	0.468605i	$0.155243\pi$
$224$	26.8849	−	2.05931i	1.79632	−	0.137593i
$225$		−	13.4094i		−	0.893959i
$226$	−0.379628	+	1.23217i	−0.0252525	+	0.0819624i
$227$	−19.9580	−	8.26686i	−1.32466	−	0.548690i	−0.395530	−	0.918453i	$-0.629439\pi$
$227$	−19.9580	−	8.26686i	−1.32466	−	0.548690i	−0.929126	+	0.369763i	$0.879439\pi$
$228$	−2.97491	+	4.36958i	−0.197018	+	0.289382i
$229$	19.3325	−	8.00780i	1.27753	−	0.529170i	0.362285	−	0.932068i	$-0.381997\pi$
$229$	19.3325	−	8.00780i	1.27753	−	0.529170i	0.915245	+	0.402897i	$0.131997\pi$
$230$	5.35898	+	4.43711i	0.353360	+	0.292574i
$231$	−14.6028	−	14.6028i	−0.960792	−	0.960792i
$232$	0.726719	−	1.31798i	0.0477114	−	0.0865293i
$233$	8.75627	+	8.75627i	0.573642	+	0.573642i	0.933144	−	0.359502i	$-0.117053\pi$
$233$	8.75627	+	8.75627i	0.573642	+	0.573642i	−0.359502	+	0.933144i	$0.617053\pi$
$234$	−15.0585	+	0.918877i	−0.984406	+	0.0600689i
$235$	−2.20669	−	0.914043i	−0.143949	−	0.0596256i
$236$	3.99275	−	19.1993i	0.259906	−	1.24977i
$237$	10.0549	−	4.16487i	0.653134	−	0.270537i
$238$	−5.45399	+	17.7021i	−0.353530	+	1.14746i
$239$	15.7148	+	15.7148i	1.01651	+	1.01651i	0.999861	+	0.0166470i	$0.00529915\pi$
$239$	15.7148	+	15.7148i	1.01651	+	1.01651i	0.0166470	+	0.999861i	$0.494701\pi$
$240$	2.66261	−	6.12479i	0.171871	−	0.395353i
$241$	3.57821	+	3.57821i	0.230493	+	0.230493i	0.812898	−	0.582405i	$-0.197888\pi$
$241$	3.57821	+	3.57821i	0.230493	+	0.230493i	−0.582405	+	0.812898i	$0.697888\pi$
$242$	9.81309	−	5.19051i	0.630810	−	0.333659i
$243$	−8.40574	−	20.2933i	−0.539229	−	1.30181i
$244$	4.35294	−	20.9313i	0.278668	−	1.33999i
$245$	−4.11467	−	9.93370i	−0.262877	−	0.634641i
$246$	−10.2389	+	0.963536i	−0.652806	+	0.0614328i
$247$	2.84978	−	2.66826i	0.181327	−	0.169777i
$248$	20.8446	+	2.32775i	1.32363	+	0.147812i
$249$			36.8538i			2.33552i
$250$	−7.10199	−	5.88028i	−0.449169	−	0.371902i
$251$	−9.20091	−	3.81114i	−0.580756	−	0.240557i	0.0729119	−	0.997338i	$-0.476771\pi$
$251$	−9.20091	−	3.81114i	−0.580756	−	0.240557i	−0.653668	+	0.756781i	$0.726771\pi$
$252$	5.26203	+	27.7105i	0.331477	+	1.74560i
$253$	−4.88544	+	11.7945i	−0.307145	+	0.741513i
$254$	25.8332	+	7.95916i	1.62092	+	0.499402i
$255$	3.24417	+	3.24417i	0.203158	+	0.203158i
$256$	−11.7001	+	10.9137i	−0.731256	+	0.682103i
$257$			15.4585i			0.964276i	0.876095	+	0.482138i	$0.160140\pi$
$257$			15.4585i			0.964276i	−0.876095	+	0.482138i	$0.839860\pi$
$258$	−6.49552	+	21.0826i	−0.404393	+	1.31255i
$259$	−9.76821	−	23.5826i	−0.606967	−	1.46535i
$260$	−2.90830	+	3.98358i	−0.180365	+	0.247051i
$261$	1.45454	+	0.602488i	0.0900335	+	0.0372931i
$262$	18.6110	−	1.75140i	1.14979	−	0.108202i
$263$	22.1324	−	22.1324i	1.36474	−	1.36474i	0.496981	−	0.867761i	$-0.334442\pi$
$263$	22.1324	−	22.1324i	1.36474	−	1.36474i	0.867761	−	0.496981i	$-0.165558\pi$
$264$	12.1787	+	1.36001i	0.749546	+	0.0837030i
$265$	1.97974			0.121615
$266$	−5.62188	−	4.65478i	−0.344699	−	0.285403i
$267$	−9.46458	+	3.92036i	−0.579223	+	0.239922i
$268$	8.92426	+	13.6107i	0.545136	+	0.831405i
$269$	21.4569	−	8.88775i	1.30825	−	0.541896i	0.383878	−	0.923384i	$-0.374588\pi$
$269$	21.4569	−	8.88775i	1.30825	−	0.541896i	0.924374	+	0.381488i	$0.124588\pi$
$270$	−0.0931674	−	0.0287047i	−0.00566999	−	0.00174691i
$271$	−15.0473	+	15.0473i	−0.914058	+	0.914058i	−0.996589	−	0.0825308i	$-0.973700\pi$
$271$	−15.0473	+	15.0473i	−0.914058	+	0.914058i	0.0825308	+	0.996589i	$0.473700\pi$
$272$	−4.02914	−	10.2264i	−0.244303	−	0.620068i
$273$	1.37932	−	41.9292i	0.0834804	−	2.53767i
$274$	5.63624	−	18.2936i	0.340498	−	1.10516i
$275$	3.07834	−	7.43176i	0.185631	−	0.448152i
$276$	29.3660	−	19.2547i	1.76762	−	1.15900i
$277$	−12.0846	−	5.00560i	−0.726092	−	0.300757i	−0.0111473	−	0.999938i	$-0.503548\pi$
$277$	−12.0846	−	5.00560i	−0.726092	−	0.300757i	−0.714945	+	0.699181i	$0.753548\pi$
$278$	1.24872	+	1.03391i	0.0748930	+	0.0620097i
$279$			21.9403i			1.31353i
$280$	8.07511	+	4.45254i	0.482580	+	0.266090i
$281$	18.2366			1.08791			0.543953	−	0.839116i	$-0.316927\pi$
$281$	18.2366			1.08791			0.543953	+	0.839116i	$0.316927\pi$
$282$	−7.68816	+	9.28548i	−0.457823	+	0.552942i
$283$	5.24389	+	2.17209i	0.311717	+	0.129117i	0.533057	−	0.846079i	$-0.321043\pi$
$283$	5.24389	+	2.17209i	0.311717	+	0.129117i	−0.221340	+	0.975197i	$0.571043\pi$
$284$	20.2833	+	13.8093i	1.20359	+	0.819433i
$285$	−1.67020	+	0.691818i	−0.0989339	+	0.0409798i
$286$	−8.55669	−	2.94766i	−0.505968	−	0.174299i
$287$		−	14.1997i		−	0.838182i
$288$	−12.7042	−	10.8964i	−0.748599	−	0.642077i
$289$	−9.44914			−0.555832
$290$	0.454986	−	0.240659i	0.0267177	−	0.0141320i
$291$	0.782369	+	0.324068i	0.0458633	+	0.0189972i
$292$	−1.76692	+	2.59527i	−0.103401	+	0.151877i
$293$	−27.8685	+	11.5435i	−1.62809	+	0.674379i	−0.995017	−	0.0997101i	$-0.968208\pi$
$293$	−27.8685	+	11.5435i	−1.62809	+	0.674379i	−0.633077	+	0.774089i	$0.718208\pi$
$294$	−54.0292	+	5.08446i	−3.15105	+	0.296532i
$295$	4.74219	−	4.74219i	0.276101	−	0.276101i
$296$	13.2639	+	7.31361i	0.770951	+	0.425095i
$297$		−	0.178882i		−	0.0103798i
$298$	24.6196	−	2.31684i	1.42617	−	0.134211i
$299$	−24.2730	+	9.13129i	−1.40374	+	0.528076i
$300$	−18.5036	+	12.1325i	−1.06831	+	0.700468i
$301$	−28.1413	−	11.6565i	−1.62204	−	0.671871i
$302$	−29.4752	−	9.08126i	−1.69611	−	0.522568i
$303$		−	12.8384i		−	0.737544i
$304$	4.33039	+	0.0752764i	0.248365	+	0.00431740i
$305$	5.16999	−	5.16999i	0.296033	−	0.296033i
$306$	10.1636	−	5.37593i	0.581017	−	0.307321i
$307$	13.0113	+	5.38945i	0.742593	+	0.307592i	0.721716	−	0.692190i	$-0.243354\pi$
$307$	13.0113	+	5.38945i	0.742593	+	0.307592i	0.0208779	+	0.999782i	$0.493354\pi$
$308$	−3.44505	+	16.5657i	−0.196300	+	0.943920i
$309$	26.0459	+	10.7886i	1.48170	+	0.613739i
$310$	5.52494	+	4.57453i	0.313796	+	0.259816i
$311$	−14.0691	+	14.0691i	−0.797786	+	0.797786i	−0.982746	−	0.184960i	$-0.940784\pi$
$311$	−14.0691	+	14.0691i	−0.797786	+	0.797786i	0.184960	+	0.982746i	$0.440784\pi$
$312$	14.8925	+	19.9479i	0.843123	+	1.12933i
$313$	0.452439	+	0.452439i	0.0255734	+	0.0255734i	0.719778	−	0.694204i	$-0.244244\pi$
$313$	0.452439	+	0.452439i	0.0255734	+	0.0255734i	−0.694204	+	0.719778i	$0.744244\pi$
$314$	−1.60638	−	17.0700i	−0.0906534	−	0.963314i
$315$	−3.69139	+	8.91181i	−0.207986	+	0.502123i
$316$	−7.37082	−	5.01823i	−0.414641	−	0.282297i
$317$	−5.13543	+	12.3980i	−0.288435	+	0.696343i	−0.999980	−	0.00629718i	$-0.997996\pi$
$317$	−5.13543	+	12.3980i	−0.288435	+	0.696343i	0.711546	+	0.702640i	$0.247996\pi$
$318$	2.94207	−	9.54914i	0.164983	−	0.535489i
$319$	0.667823	+	0.667823i	0.0373909	+	0.0373909i
$320$	−5.39271	+	0.927234i	−0.301462	+	0.0518340i
$321$	0.906111			0.0505742
$322$	22.6699	+	42.8594i	1.26335	+	2.38846i
$323$	−1.13860	+	2.74882i	−0.0633533	+	0.152948i
$324$	−10.2675	+	15.0809i	−0.570414	+	0.837830i
$325$	15.2945	−	5.75367i	0.848388	−	0.319156i
$326$	−4.51371	+	5.45149i	−0.249991	+	0.301930i
$327$	−50.2416			−2.77837
$328$	5.26002	+	6.58250i	0.290436	+	0.363458i
$329$	−11.7699	−	11.7699i	−0.648895	−	0.648895i
$330$	3.22801	+	2.67272i	0.177696	+	0.147128i
$331$	6.46992	+	15.6198i	0.355619	+	0.858540i	0.995905	+	0.0904037i	$0.0288157\pi$
$331$	6.46992	+	15.6198i	0.355619	+	0.858540i	−0.640286	+	0.768136i	$0.721184\pi$
$332$	25.2511	−	16.5567i	1.38584	−	0.908665i
$333$	−6.06337	+	14.6383i	−0.332270	+	0.802172i
$334$	8.36488	−	27.1500i	0.457706	−	1.48558i
$335$			5.56608i			0.304107i
$336$	33.4768	−	32.3328i	1.82631	−	1.76390i
$337$	19.8195			1.07964			0.539819	−	0.841781i	$-0.318493\pi$
$337$	19.8195			1.07964			0.539819	+	0.841781i	$0.318493\pi$
$338$	−7.50933	−	16.7812i	−0.408454	−	0.912779i
$339$	0.851652	+	2.05607i	0.0462554	+	0.111670i
$340$	0.765357	−	3.68026i	0.0415073	−	0.199590i
$341$	−5.03674	+	12.1598i	−0.272755	+	0.658488i
$342$	0.424475	+	4.51061i	0.0229530	+	0.243906i
$343$		−	41.5643i		−	2.24426i
$344$	17.3633	−	5.02088i	0.936167	−	0.270708i
$345$	12.0092			0.646552
$346$	−2.19072	−	23.2793i	−0.117774	−	1.25150i
$347$	−7.82618	+	18.8941i	−0.420131	+	1.01429i	0.562177	+	0.827017i	$0.309964\pi$
$347$	−7.82618	+	18.8941i	−0.420131	+	1.01429i	−0.982308	+	0.187270i	$0.940036\pi$
$348$	−0.484651	−	2.55223i	−0.0259800	−	0.136814i
$349$	−9.16581	−	3.79660i	−0.490634	−	0.203227i	0.123629	−	0.992329i	$-0.460547\pi$
$349$	−9.16581	−	3.79660i	−0.490634	−	0.203227i	−0.614263	+	0.789101i	$0.710547\pi$
$350$	−14.2844	−	27.0059i	−0.763535	−	1.44353i
$351$	0.265263	−	0.248366i	0.0141587	−	0.0132568i
$352$	−4.53946	−	8.95546i	−0.241954	−	0.477327i
$353$	−2.03374	−	2.03374i	−0.108245	−	0.108245i	0.650910	−	0.759155i	$-0.274388\pi$
$353$	−2.03374	−	2.03374i	−0.108245	−	0.108245i	−0.759155	+	0.650910i	$0.774388\pi$
$354$	−15.8263	−	29.9209i	−0.841158	−	1.59028i
$355$	3.21137	+	7.75294i	0.170442	+	0.411483i
$356$	6.93810	+	4.72362i	0.367718	+	0.250351i
$357$	12.2354	+	29.5389i	0.647566	+	1.56336i
$358$	12.6543	−	1.19084i	0.668799	−	0.0629378i
$359$		−	5.77186i		−	0.304627i	−0.988332	−	0.152314i	$-0.951328\pi$
$359$		−	5.77186i		−	0.304627i	0.988332	−	0.152314i	$-0.0486724\pi$
$360$	−1.59001	−	5.49862i	−0.0838011	−	0.289803i
$361$	12.6060	+	12.6060i	0.663476	+	0.663476i
$362$	−9.05016	−	7.49332i	−0.475666	−	0.393840i
$363$	7.33286	−	17.7031i	0.384876	−	0.929172i
$364$	−29.3483	+	17.8917i	−1.53827	+	0.937782i
$365$	−0.991998	+	0.410899i	−0.0519235	+	0.0215074i
$366$	−17.2540	−	32.6201i	−0.901880	−	1.70508i
$367$	5.52161			0.288226			0.144113	−	0.989561i	$-0.453967\pi$
$367$	5.52161			0.288226			0.144113	+	0.989561i	$0.453967\pi$
$368$	−26.3855	−	11.4705i	−1.37544	−	0.597940i
$369$	−6.23251	+	6.23251i	−0.324452	+	0.324452i
$370$	2.42196	+	4.57892i	0.125912	+	0.238047i
$371$	12.7463	+	5.27969i	0.661755	+	0.274108i
$372$	30.2754	−	19.8510i	1.56971	−	1.02923i
$373$	5.04449	−	12.1785i	0.261194	−	0.630577i	−0.737819	−	0.674998i	$-0.764144\pi$
$373$	5.04449	−	12.1785i	0.261194	−	0.630577i	0.999013	+	0.0444210i	$0.0141443\pi$
$374$	6.86703	−	0.646227i	0.355086	−	0.0334156i
$375$	−15.9152			−0.821856
$376$	9.81606	+	1.09618i	0.506225	+	0.0565309i
$377$	−0.0630800	+	1.91753i	−0.00324878	+	0.0987580i
$378$	−0.523295	−	0.433276i	−0.0269154	−	0.0222853i
$379$	25.0950	−	10.3947i	1.28904	−	0.533939i	0.370342	−	0.928895i	$-0.379240\pi$
$379$	25.0950	−	10.3947i	1.28904	−	0.533939i	0.918700	+	0.394957i	$0.129240\pi$
$380$	1.22435	+	0.833568i	0.0628080	+	0.0427612i
$381$	43.1069	−	17.8555i	2.20843	−	0.914762i
$382$	−3.22671	+	10.4730i	−0.165093	+	0.535845i
$383$	18.8204	−	18.8204i	0.961679	−	0.961679i	−0.0376130	−	0.999292i	$-0.511975\pi$
$383$	18.8204	−	18.8204i	0.961679	−	0.961679i	0.999292	+	0.0376130i	$0.0119754\pi$
$384$	−3.54160	+	27.3893i	−0.180731	+	1.39770i
$385$	−4.09169	+	4.09169i	−0.208532	+	0.208532i
$386$	−21.9990	+	11.6361i	−1.11972	+	0.592261i
$387$	7.23549	+	17.4680i	0.367801	+	0.887949i
$388$	−0.129439	−	0.681644i	−0.00657129	−	0.0346052i
$389$	−1.64741	+	3.97720i	−0.0835269	+	0.201652i	−0.960125	−	0.279572i	$-0.909808\pi$
$389$	−1.64741	+	3.97720i	−0.0835269	+	0.201652i	0.876598	+	0.481224i	$0.159808\pi$
$390$	0.518531	+	8.49766i	0.0262568	+	0.430296i
$391$	13.9758	−	13.9758i	0.706787	−	0.706787i
$392$	27.7565	+	34.7350i	1.40191	+	1.75438i
$393$	22.8155	−	22.8155i	1.15089	−	1.15089i
$394$	−0.774602	−	8.23119i	−0.0390239	−	0.414682i
$395$	−1.16699	−	2.81737i	−0.0587178	−	0.141757i
$396$	8.78309	−	5.75890i	0.441367	−	0.289396i
$397$	−6.18853	+	14.9404i	−0.310593	+	0.749838i	0.689090	+	0.724676i	$0.258010\pi$
$397$	−6.18853	+	14.9404i	−0.310593	+	0.749838i	−0.999683	+	0.0251627i	$0.991990\pi$
$398$	−2.99267	−	5.65790i	−0.150009	−	0.283605i
$399$	−12.5983			−0.630705
$400$	16.6256	+	7.22760i	0.831281	+	0.361380i
$401$	10.4619	+	10.4619i	0.522441	+	0.522441i	0.918308	−	0.395867i	$-0.129556\pi$
$401$	10.4619	+	10.4619i	0.522441	+	0.522441i	−0.395867	+	0.918308i	$0.629556\pi$
$402$	26.8475	+	8.27168i	1.33903	+	0.412554i
$403$	−25.0247	+	9.41408i	−1.24657	+	0.468949i
$404$	−8.79646	+	5.76766i	−0.437640	+	0.286952i
$405$	−5.76443	+	2.38771i	−0.286437	+	0.118646i
$406$	3.57117	−	0.336068i	0.177234	−	0.0166788i
$407$	−6.72089	+	6.72089i	−0.333142	+	0.333142i
$408$	−16.6140	−	9.16083i	−0.822518	−	0.453528i
$409$			6.51944i			0.322366i	0.986925	+	0.161183i	$0.0515309\pi$
$409$			6.51944i			0.322366i	−0.986925	+	0.161183i	$0.948469\pi$
$410$	0.269982	+	2.86893i	0.0133335	+	0.141686i
$411$	−12.6443	−	30.5259i	−0.623695	−	1.50573i
$412$	−4.30918	−	22.6926i	−0.212298	−	1.11799i
$413$	43.1787	−	17.8852i	2.12469	−	0.880074i
$414$	8.86152	−	28.7620i	0.435520	−	1.41358i
$415$	10.3264			0.506904
$416$	6.97721	−	19.1656i	0.342086	−	0.939669i
$417$	2.79831			0.137034
$418$	−0.800230	+	2.59732i	−0.0391405	+	0.127039i
$419$	0.805740	−	0.333748i	0.0393630	−	0.0163047i	−0.362915	−	0.931822i	$-0.618219\pi$
$419$	0.805740	−	0.333748i	0.0393630	−	0.0163047i	0.402278	+	0.915518i	$0.368219\pi$
$420$	15.6373	−	2.96941i	0.763022	−	0.144893i
$421$	−6.16886	−	14.8930i	−0.300652	−	0.725838i	−0.999940	−	0.0109977i	$-0.996499\pi$
$421$	−6.16886	−	14.8930i	−0.300652	−	0.725838i	0.699287	−	0.714841i	$-0.253501\pi$
$422$	0.332796	+	3.53640i	0.0162002	+	0.172149i
$423$			10.3320i			0.502361i
$424$	−7.86452	+	2.27415i	−0.381935	+	0.110443i
$425$	−8.80622	+	8.80622i	−0.427164	+	0.427164i
$426$	42.1681	−	3.96826i	2.04305	−	0.192263i
$427$	47.0739	−	19.4986i	2.27807	−	0.943606i
$428$	−0.407073	−	0.620840i	−0.0196766	−	0.0300094i
$429$	−14.6210	+	5.50028i	−0.705907	+	0.265556i
$430$	5.90734	+	1.82004i	0.284877	+	0.0877702i
$431$	1.57232	+	1.57232i	0.0757361	+	0.0757361i	0.743960	−	0.668224i	$-0.232945\pi$
$431$	1.57232	+	1.57232i	0.0757361	+	0.0757361i	−0.668224	+	0.743960i	$0.732945\pi$
$432$	0.403081	+	0.00700686i	0.0193932	+	0.000337118i
$433$	−27.0551			−1.30019			−0.650094	−	0.759854i	$-0.725270\pi$
$433$	−27.0551			−1.30019			−0.650094	+	0.759854i	$0.725270\pi$
$434$	23.3720	+	44.1867i	1.12189	+	2.12103i
$435$	0.339990	−	0.820808i	0.0163013	−	0.0393547i
$436$	22.5712	+	34.4241i	1.08096	+	1.64861i
$437$	2.98034	+	7.19518i	0.142569	+	0.344192i
$438$	0.507743	+	5.39546i	0.0242609	+	0.257805i
$439$	7.17594	−	7.17594i	0.342489	−	0.342489i	−0.514813	−	0.857302i	$-0.672139\pi$
$439$	7.17594	−	7.17594i	0.342489	−	0.342489i	0.857302	+	0.514813i	$0.172139\pi$
$440$	0.381075	−	3.41246i	0.0181670	−	0.162683i
$441$	−32.8882	+	32.8882i	−1.56610	+	1.56610i
$442$	10.4927	+	9.28580i	0.499086	+	0.441680i
$443$	9.17145	−	22.1418i	0.435749	−	1.05199i	−0.541653	−	0.840602i	$-0.682201\pi$
$443$	9.17145	−	22.1418i	0.435749	−	1.05199i	0.977402	−	0.211388i	$-0.0677985\pi$
$444$	25.6853	−	4.87747i	1.21897	−	0.231474i
$445$	1.09848	+	2.65197i	0.0520730	+	0.125715i
$446$	−10.9511	+	5.79243i	−0.518549	+	0.274280i
$447$	30.1816	−	30.1816i	1.42754	−	1.42754i
$448$	−37.1930	−	8.41172i	−1.75721	−	0.397416i
$449$	1.55890	−	1.55890i	0.0735689	−	0.0735689i	−0.669365	−	0.742934i	$-0.733434\pi$
$449$	1.55890	−	1.55890i	0.0735689	−	0.0735689i	0.742934	+	0.669365i	$0.233434\pi$
$450$	−5.58369	+	18.1231i	−0.263218	+	0.854330i
$451$	−4.88496	+	2.02342i	−0.230024	+	0.0952789i
$452$	1.02615	−	1.50722i	0.0482661	−	0.0708937i
$453$	−49.1842	+	20.3728i	−2.31087	+	0.957196i
$454$	23.5313	+	19.4834i	1.10438	+	0.914399i
$455$	−11.7486	−	0.386485i	−0.550781	−	0.0181187i
$456$	5.84015	−	4.66682i	0.273490	−	0.218544i
$457$	−29.0570			−1.35923			−0.679614	−	0.733570i	$-0.737853\pi$
$457$	−29.0570			−1.35923			−0.679614	+	0.733570i	$0.737853\pi$
$458$	−29.4628	+	2.77262i	−1.37671	+	0.129556i
$459$	−0.105983	+	0.255865i	−0.00494685	+	0.0119428i
$460$	−5.39515	−	8.22833i	−0.251550	−	0.383648i
$461$	8.58483	+	3.55595i	0.399835	+	0.165617i	0.573534	−	0.819182i	$-0.305572\pi$
$461$	8.58483	+	3.55595i	0.399835	+	0.165617i	−0.173699	+	0.984799i	$0.555572\pi$
$462$	13.6553	+	25.8166i	0.635304	+	1.20110i
$463$	16.3647	−	16.3647i	0.760534	−	0.760534i	−0.215885	−	0.976419i	$-0.569263\pi$
$463$	16.3647	−	16.3647i	0.760534	−	0.760534i	0.976419	+	0.215885i	$0.0692635\pi$
$464$	−1.53098	+	1.47867i	−0.0710741	+	0.0686453i
$465$	12.3811			0.574160
$466$	−8.18816	−	15.4804i	−0.379309	−	0.717116i
$467$	−31.2231	+	12.9330i	−1.44483	+	0.598469i	−0.960965	−	0.276671i	$-0.910769\pi$
$467$	−31.2231	+	12.9330i	−1.44483	+	0.598469i	−0.483869	+	0.875141i	$0.660769\pi$
$468$	20.7345	+	5.02851i	0.958454	+	0.232443i
$469$	−14.8439	+	35.8364i	−0.685430	+	1.65477i
$470$	2.60179	+	2.15422i	0.120011	+	0.0993667i
$471$	−20.9264	−	20.9264i	−0.964235	−	0.964235i
$472$	−13.3909	+	24.2857i	−0.616367	+	1.11784i
$473$			11.3422i			0.521513i
$474$	−15.3236	+	1.44204i	−0.703838	+	0.0662352i
$475$	−1.87793	−	4.53372i	−0.0861652	−	0.208021i
$476$	14.7424	−	21.6537i	0.675716	−	0.992498i
$477$	−3.27723	−	7.91194i	−0.150054	−	0.362263i
$478$	−14.6953	−	27.7826i	−0.672146	−	1.27075i
$479$	10.5792	+	10.5792i	0.483375	+	0.483375i	0.906208	−	0.422832i	$-0.138964\pi$
$479$	10.5792	+	10.5792i	0.483375	+	0.483375i	−0.422832	+	0.906208i	$0.638964\pi$
$480$	−6.14895	+	7.16907i	−0.280660	+	0.327222i
$481$	−19.2978	−	0.634829i	−0.879905	−	0.0289457i
$482$	−3.34606	−	6.32601i	−0.152409	−	0.288142i
$483$	77.3195	+	32.0268i	3.51816	+	1.45727i
$484$	−15.4239	+	2.92890i	−0.701088	+	0.133132i
$485$	0.0908036	−	0.219219i	0.00412318	−	0.00995423i
$486$	2.91040	+	30.9269i	0.132018	+	1.40287i
$487$	−22.1275			−1.00269			−0.501346	−	0.865247i	$-0.667162\pi$
$487$	−22.1275			−1.00269			−0.501346	+	0.865247i	$0.667162\pi$
$488$	−14.5989	+	26.4766i	−0.660862	+	1.19854i
$489$			12.2165i			0.552449i
$490$	1.42466	+	15.1390i	0.0643597	+	0.683909i
$491$	−10.8369	+	26.1627i	−0.489064	+	1.18071i	0.466127	+	0.884718i	$0.345649\pi$
$491$	−10.8369	+	26.1627i	−0.489064	+	1.18071i	−0.955192	+	0.295988i	$0.904351\pi$
$492$	14.2393	+	2.96124i	0.641956	+	0.133503i
$493$	−0.559557	−	1.35089i	−0.0252012	−	0.0608410i
$494$	−4.96260	+	2.41955i	−0.223278	+	0.108861i
$495$	3.59184			0.161441
$496$	−27.2026	−	11.8257i	−1.22143	−	0.530990i
$497$			58.4806i			2.62321i
$498$	15.3460	−	49.8087i	0.687670	−	2.23198i
$499$	−6.86454	+	16.5725i	−0.307299	+	0.741886i	0.692492	+	0.721426i	$0.256513\pi$
$499$	−6.86454	+	16.5725i	−0.307299	+	0.741886i	−0.999791	+	0.0204597i	$0.993487\pi$
$500$	7.14993	+	10.9046i	0.319755	+	0.487669i
$501$	−18.7656	−	45.3043i	−0.838387	−	2.02405i
$502$	10.8483	+	8.98211i	0.484182	+	0.400891i
$503$	14.1124	+	14.1124i	0.629242	+	0.629242i	0.947877	−	0.318636i	$-0.103225\pi$
$503$	14.1124	+	14.1124i	0.629242	+	0.629242i	−0.318636	+	0.947877i	$0.603225\pi$
$504$	4.42694	−	39.6425i	0.197192	−	1.76582i
$505$	−3.59730			−0.160078
$506$	11.5140	−	13.9062i	0.511860	−	0.618206i
$507$	−28.4565	−	14.0445i	−1.26380	−	0.623738i
$508$	−31.5999	−	21.5139i	−1.40202	−	0.954527i
$509$	8.34879	−	20.1558i	0.370054	−	0.893388i	−0.623687	−	0.781674i	$-0.714366\pi$
$509$	8.34879	−	20.1558i	0.370054	−	0.893388i	0.993740	−	0.111714i	$-0.0356341\pi$
$510$	−3.03368	−	5.73544i	−0.134334	−	0.253969i
$511$	−7.48266			−0.331013
$512$	20.3574	−	9.87810i	0.899678	−	0.436555i
$513$	−0.0771641	−	0.0771641i	−0.00340688	−	0.00340688i
$514$	6.43695	−	20.8925i	0.283922	−	0.921530i
$515$	3.02295	−	7.29804i	0.133207	−	0.321590i
$516$	17.5577	−	25.7889i	0.772933	−	1.13529i
$517$	−2.37188	+	5.72623i	−0.104315	+	0.251839i
$518$	3.38214	+	35.9398i	0.148603	+	1.57911i
$519$	−28.5385	−	28.5385i	−1.25270	−	1.25270i
$520$	5.58939	−	4.17288i	0.245111	−	0.182993i
$521$	−12.6505	+	12.6505i	−0.554227	+	0.554227i	−0.927658	−	0.373431i	$-0.878181\pi$
$521$	−12.6505	+	12.6505i	−0.554227	+	0.554227i	0.373431	+	0.927658i	$0.378181\pi$
$522$	−1.71496	−	1.41995i	−0.0750617	−	0.0621494i
$523$	−4.54778	−	1.88375i	−0.198860	−	0.0823707i	0.281031	−	0.959699i	$-0.409324\pi$
$523$	−4.54778	−	1.88375i	−0.198860	−	0.0823707i	−0.479891	+	0.877328i	$0.659324\pi$
$524$	−25.8824	−	5.38259i	−1.13068	−	0.235139i
$525$	−48.7194	−	20.1802i	−2.12629	−	0.880738i
$526$	−39.1284	+	20.6965i	−1.70608	+	0.902408i
$527$	14.4086	−	14.4086i	0.627650	−	0.627650i
$528$	−15.8934	−	6.90930i	−0.691673	−	0.300689i
$529$		−	28.7353i		−	1.24936i
$530$	−2.67566	−	0.824367i	−0.116223	−	0.0358082i
$531$	−26.8021	−	11.1018i	−1.16311	−	0.481776i
$532$	5.65983	+	8.63200i	0.245385	+	0.374245i
$533$	−9.78293	−	4.43447i	−0.423746	−	0.192078i
$534$	14.4240	−	1.35738i	0.624188	−	0.0587397i
$535$		−	0.253892i		−	0.0109767i
$536$	−6.39382	−	22.1112i	−0.276171	−	0.955059i
$537$	15.5131	−	15.5131i	0.669438	−	0.669438i
$538$	−32.7004	+	3.07729i	−1.40981	+	0.132671i
$539$	−25.7773	+	10.6773i	−1.11031	+	0.459905i
$540$	0.113965	+	0.0775901i	0.00490427	+	0.00333894i
$541$	1.16123	+	0.480999i	0.0499253	+	0.0206797i	0.407506	−	0.913202i	$-0.366398\pi$
$541$	1.16123	+	0.480999i	0.0499253	+	0.0206797i	−0.357581	+	0.933882i	$0.616398\pi$
$542$	26.6024	−	14.0710i	1.14267	−	0.604402i
$543$	−20.2809			−0.870337
$544$	1.18718	+	15.4990i	0.0508998	+	0.664513i
$545$			14.0777i			0.603021i
$546$	−19.3236	+	56.0939i	−0.826973	+	2.40060i
$547$	35.9252	−	14.8807i	1.53605	−	0.636253i	0.555324	−	0.831634i	$-0.312594\pi$
$547$	35.9252	−	14.8807i	1.53605	−	0.636253i	0.980727	+	0.195381i	$0.0625944\pi$
$548$	−15.2350	+	22.3773i	−0.650807	+	0.955911i
$549$	−29.2199	−	12.1033i	−1.24708	−	0.516555i
$550$	−7.25503	+	8.76236i	−0.309356	+	0.373628i
$551$	0.576154			0.0245450
$552$	−47.7064	+	13.7951i	−2.03052	+	0.587158i
$553$		−	21.2515i		−	0.903705i
$554$	14.2482	+	11.7972i	0.605350	+	0.501216i
$555$	8.26050	+	3.42161i	0.350639	+	0.145239i
$556$	−1.25715	−	1.91732i	−0.0533149	−	0.0813123i
$557$	−4.64040	+	11.2029i	−0.196620	+	0.474683i	−0.991183	−	0.132498i	$-0.957700\pi$
$557$	−4.64040	+	11.2029i	−0.196620	+	0.474683i	0.794563	+	0.607182i	$0.207700\pi$
$558$	9.13596	−	29.6528i	0.386756	−	1.25530i
$559$	−16.8192	+	15.7478i	−0.711374	+	0.666062i
$560$	−9.05965	−	9.38019i	−0.382840	−	0.396385i
$561$	8.41840	−	8.41840i	0.355425	−	0.355425i
$562$	−24.6472	−	7.59375i	−1.03968	−	0.320323i
$563$	25.1805	−	10.4301i	1.06123	−	0.439577i	0.217344	−	0.976095i	$-0.430261\pi$
$563$	25.1805	−	10.4301i	1.06123	−	0.439577i	0.843889	+	0.536518i	$0.180261\pi$
$564$	14.2572	−	9.34816i	0.600336	−	0.393629i
$565$	0.576110	−	0.238632i	0.0242371	−	0.0100393i
$566$	−6.18277	−	5.11919i	−0.259881	−	0.215176i
$567$	−43.4812			−1.82604
$568$	−21.6631	−	27.1096i	−0.908962	−	1.13749i
$569$	−19.1179	+	19.1179i	−0.801463	+	0.801463i	−0.983324	−	0.181861i	$-0.941788\pi$
$569$	−19.1179	+	19.1179i	−0.801463	+	0.801463i	0.181861	+	0.983324i	$0.441788\pi$
$570$	2.54538	−	0.239535i	0.106614	−	0.0100330i
$571$	34.0120	+	14.0882i	1.42336	+	0.589574i	0.955702	−	0.294337i	$-0.0950987\pi$
$571$	34.0120	+	14.0882i	1.42336	+	0.589574i	0.467656	+	0.883911i	$0.345099\pi$
$572$	10.3371	+	7.54684i	0.432217	+	0.315549i
$573$	7.23875	+	17.4759i	0.302403	+	0.730066i
$574$	−5.91278	+	19.1912i	−0.246795	+	0.801026i
$575$			32.5987i			1.35946i
$576$	12.6326	+	20.0168i	0.526360	+	0.834032i
$577$	1.11287	+	1.11287i	0.0463293	+	0.0463293i	0.729892	−	0.683563i	$-0.239570\pi$
$577$	1.11287	+	1.11287i	0.0463293	+	0.0463293i	−0.683563	+	0.729892i	$0.739570\pi$
$578$	12.7707	+	3.93463i	0.531191	+	0.163659i
$579$	−16.4388	+	39.6868i	−0.683173	+	1.64933i
$580$	−0.715134	+	0.135799i	−0.0296943	+	0.00563875i
$581$	66.4853	+	27.5391i	2.75828	+	1.14252i
$582$	−0.922446	−	0.763764i	−0.0382366	−	0.0316590i
$583$		−	5.13730i		−	0.212765i
$584$	3.46870	−	2.77181i	0.143536	−	0.114698i
$585$	4.98702	+	5.32629i	0.206188	+	0.220215i
$586$	42.4716	−	3.99682i	1.75448	−	0.165107i
$587$	−10.0510	−	24.2652i	−0.414848	−	1.00153i	−0.983818	−	0.179173i	$-0.942658\pi$
$587$	−10.0510	−	24.2652i	−0.414848	−	1.00153i	0.568969	−	0.822359i	$-0.307342\pi$
$588$	75.1389	+	15.6261i	3.09867	+	0.644409i
$589$	3.07264	+	7.41801i	0.126606	+	0.305654i
$590$	−8.38383	+	4.43452i	−0.345157	+	0.182566i
$591$	−10.0908	−	10.0908i	−0.415078	−	0.415078i
$592$	−14.8811	−	15.4076i	−0.611609	−	0.633249i
$593$	0.990617	+	0.990617i	0.0406798	+	0.0406798i	0.727154	−	0.686474i	$-0.240843\pi$
$593$	0.990617	+	0.990617i	0.0406798	+	0.0406798i	−0.686474	+	0.727154i	$0.740843\pi$
$594$	−0.0744869	+	0.241763i	−0.00305623	+	0.00991967i
$595$	8.27678	−	3.42835i	0.339315	−	0.140549i
$596$	−34.2386	−	7.12037i	−1.40247	−	0.291662i
$597$	−10.2070	−	4.22788i	−0.417745	−	0.173036i
$598$	36.6078	−	2.23382i	1.49700	−	0.0913477i
$599$	−12.7082	−	12.7082i	−0.519242	−	0.519242i	0.398100	−	0.917342i	$-0.369670\pi$
$599$	−12.7082	−	12.7082i	−0.519242	−	0.519242i	−0.917342	+	0.398100i	$0.869670\pi$
$600$	30.0600	−	8.69235i	1.22720	−	0.354864i
$601$	10.1980	+	10.1980i	0.415983	+	0.415983i	0.883817	−	0.467833i	$-0.154965\pi$
$601$	10.1980	+	10.1980i	0.415983	+	0.415983i	−0.467833	+	0.883817i	$0.654965\pi$
$602$	33.1798	+	27.4721i	1.35231	+	1.11968i
$603$	22.2445	−	9.21399i	0.905868	−	0.375223i
$604$	36.0549	+	24.5470i	1.46705	+	0.998805i
$605$	−4.96040	−	2.05466i	−0.201669	−	0.0835340i
$606$	−5.34591	+	17.3513i	−0.217163	+	0.704849i
$607$			27.2432i			1.10577i	0.833259	+	0.552883i	$0.186472\pi$
$607$			27.2432i			1.10577i	−0.833259	+	0.552883i	$0.813528\pi$
$608$	−5.82127	−	1.90492i	−0.236084	−	0.0772546i
$609$	4.37796	−	4.37796i	0.177404	−	0.177404i
$610$	−9.14013	+	4.83456i	−0.370073	+	0.195745i
$611$	−11.7846	+	4.43325i	−0.476752	+	0.179350i
$612$	−15.9749	+	3.03353i	−0.645748	+	0.122623i
$613$	−1.02866	−	2.48341i	−0.0415473	−	0.100304i	0.901744	−	0.432271i	$-0.142288\pi$
$613$	−1.02866	−	2.48341i	−0.0415473	−	0.100304i	−0.943291	+	0.331967i	$0.892288\pi$
$614$	−15.3409	−	12.7019i	−0.619107	−	0.512606i
$615$	3.51706	+	3.51706i	0.141822	+	0.141822i
$616$	11.5541	−	20.9544i	0.465526	−	0.844277i
$617$	0.0166708			0.000671140			0.000335570	−	1.00000i	$-0.499893\pi$
$617$	0.0166708			0.000671140			0.000335570		1.00000i	$0.499893\pi$
$618$	−30.7092	−	25.4265i	−1.23530	−	1.02280i
$619$	−0.177010	+	0.0733199i	−0.00711463	+	0.00294698i	−0.386238	−	0.922399i	$-0.626226\pi$
$619$	−0.177010	+	0.0733199i	−0.00711463	+	0.00294698i	0.379123	+	0.925346i	$0.376226\pi$
$620$	−5.56224	−	8.48316i	−0.223385	−	0.340692i
$621$	0.277415	+	0.669740i	0.0111323	+	0.0268757i
$622$	24.8731	−	13.1563i	0.997320	−	0.527520i
$623$			20.0039i			0.801438i
$624$	−11.8212	−	33.1613i	−0.473228	−	1.32751i
$625$		−	18.2014i		−	0.728057i
$626$	−0.423085	−	0.799877i	−0.0169099	−	0.0319695i
$627$	1.79522	+	4.33405i	0.0716943	+	0.173085i
$628$	−4.93690	+	23.7393i	−0.197004	+	0.947302i
$629$	13.5952	−	5.63131i	0.542075	−	0.224535i
$630$	8.69988	−	10.5074i	0.346612	−	0.418625i
$631$	3.70486			0.147488			0.0737440	−	0.997277i	$-0.476505\pi$
$631$	3.70486			0.147488			0.0737440	+	0.997277i	$0.476505\pi$
$632$	7.87222	+	9.85146i	0.313140	+	0.391870i
$633$	4.33534	+	4.33534i	0.172314	+	0.172314i
$634$	12.1032	−	14.6178i	0.480680	−	0.580547i
$635$	−5.00309	−	12.0785i	−0.198542	−	0.479322i
$636$	−7.95255	+	11.6808i	−0.315339	+	0.463173i
$637$	−51.6233	−	23.4002i	−2.04539	−	0.927148i
$638$	−0.624495	−	1.18066i	−0.0247240	−	0.0467428i
$639$	25.6682	−	25.6682i	1.01542	−	1.01542i
$640$	7.67446	+	0.992354i	0.303360	+	0.0392262i
$641$			22.9808i			0.907685i	0.891082	+	0.453843i	$0.149947\pi$
$641$			22.9808i			0.907685i	−0.891082	+	0.453843i	$0.850053\pi$
$642$	−1.22463	−	0.377306i	−0.0483322	−	0.0148911i
$643$	−10.5208	−	4.35785i	−0.414899	−	0.171857i	0.165462	−	0.986216i	$-0.447089\pi$
$643$	−10.5208	−	4.35785i	−0.414899	−	0.171857i	−0.580361	+	0.814359i	$0.697089\pi$
$644$	−12.7922	−	67.3651i	−0.504082	−	2.65456i
$645$	9.85736	−	4.08305i	0.388133	−	0.160770i
$646$	2.68345	−	3.24097i	0.105579	−	0.127514i
$647$	−33.8281	−	33.8281i	−1.32992	−	1.32992i	−0.905436	−	0.424483i	$-0.860456\pi$
$647$	−33.8281	−	33.8281i	−1.32992	−	1.32992i	−0.424483	−	0.905436i	$-0.639544\pi$
$648$	20.1564	−	16.1068i	0.791818	−	0.632736i
$649$	−12.3057	−	12.3057i	−0.483040	−	0.483040i
$650$	−23.0667	+	1.40754i	−0.904751	+	0.0552083i
$651$	79.7141	+	33.0187i	3.12424	+	1.29410i
$652$	8.37038	−	5.48829i	0.327810	−	0.214938i
$653$	26.2471	−	10.8719i	1.02713	−	0.425451i	0.195453	−	0.980713i	$-0.437382\pi$
$653$	26.2471	−	10.8719i	1.02713	−	0.425451i	0.831675	+	0.555263i	$0.187382\pi$
$654$	67.9026	+	20.9207i	2.65520	+	0.818063i
$655$	−6.39290	−	6.39290i	−0.249791	−	0.249791i
$656$	−4.36807	−	11.0867i	−0.170545	−	0.432862i
$657$	3.28427	+	3.28427i	0.128132	+	0.128132i
$658$	11.0063	+	20.8083i	0.429069	+	0.811190i
$659$	10.8417	+	26.1741i	0.422332	+	1.01960i	0.981658	+	0.190651i	$0.0610599\pi$
$659$	10.8417	+	26.1741i	0.422332	+	1.01960i	−0.559326	+	0.828948i	$0.688940\pi$
$660$	−3.24980	−	4.95638i	−0.126498	−	0.192927i
$661$	−3.39761	−	8.20256i	−0.132152	−	0.319043i	0.843928	−	0.536457i	$-0.180238\pi$
$661$	−3.39761	−	8.20256i	−0.132152	−	0.319043i	−0.976079	+	0.217414i	$0.930238\pi$
$662$	−2.24014	−	23.8045i	−0.0870656	−	0.925189i
$663$	24.1719	+	0.795170i	0.938760	+	0.0308818i
$664$	−41.0217	+	11.8621i	−1.59195	+	0.460338i
$665$			3.53005i			0.136889i
$666$	14.2902	−	17.2591i	0.553732	−	0.668778i
$667$	−3.53602	−	1.46467i	−0.136915	−	0.0567122i
$668$	−22.6106	+	33.2107i	−0.874832	+	1.28496i
$669$	−8.18323	+	19.7561i	−0.316382	+	0.763813i
$670$	2.31772	−	7.52267i	0.0895414	−	0.290626i
$671$	−13.4158	−	13.4158i	−0.517910	−	0.517910i
$672$	−58.7081	+	29.7587i	−2.26471	+	1.14797i
$673$		−	32.8253i		−	1.26532i	−0.774429	−	0.632661i	$-0.781963\pi$
$673$		−	32.8253i		−	1.26532i	0.774429	−	0.632661i	$-0.218037\pi$
$674$	−26.7865	−	8.25288i	−1.03178	−	0.317889i
$675$	−0.174801	−	0.422006i	−0.00672809	−	0.0162430i
$676$	3.16129	+	25.8071i	0.121588	+	0.992581i
$677$	−29.4862	−	12.2136i	−1.13325	−	0.469406i	−0.264363	−	0.964423i	$-0.585162\pi$
$677$	−29.4862	−	12.2136i	−1.13325	−	0.469406i	−0.868883	+	0.495017i	$0.835162\pi$
$678$	−0.294876	−	3.13345i	−0.0113246	−	0.120339i
$679$	1.16925	−	1.16925i	0.0448719	−	0.0448719i
$680$	−2.56686	+	4.65525i	−0.0984346	+	0.178521i
$681$	52.7323			2.02071
$682$	11.8706	−	14.3369i	0.454549	−	0.548987i
$683$	−22.7829	+	9.43698i	−0.871763	+	0.361096i	−0.773297	−	0.634044i	$-0.781394\pi$
$683$	−22.7829	+	9.43698i	−0.871763	+	0.361096i	−0.0984662	+	0.995140i	$0.531394\pi$
$684$	1.30454	−	6.27294i	0.0498803	−	0.239852i
$685$	−8.55335	+	3.54291i	−0.326807	+	0.135368i
$686$	−17.3074	+	56.1750i	−0.660800	+	2.14477i
$687$	−36.1189	+	36.1189i	−1.37802	+	1.37802i
$688$	−25.5576	−	0.444275i	−0.974374	−	0.0169378i
$689$	7.61805	−	7.13280i	0.290224	−	0.271738i
$690$	−16.2307	−	5.00064i	−0.617891	−	0.190371i
$691$	3.99662	−	9.64869i	0.152039	−	0.367054i	−0.829448	−	0.558584i	$-0.811345\pi$
$691$	3.99662	−	9.64869i	0.152039	−	0.367054i	0.981487	+	0.191530i	$0.0613450\pi$
$692$	−6.73274	+	32.3747i	−0.255941	+	1.23070i
$693$	23.1256	+	9.57892i	0.878467	+	0.363873i
$694$	18.4448	−	22.2769i	0.700154	−	0.845620i
$695$		−	0.784084i		−	0.0297420i
$696$	−0.407736	+	3.65121i	−0.0154552	+	0.138399i
$697$	8.18604			0.310068
$698$	10.8069	+	8.94784i	0.409046	+	0.338681i
$699$	−27.9271	−	11.5678i	−1.05630	−	0.437534i
$700$	8.06041	+	42.4471i	0.304655	+	1.60435i
$701$	2.60641	−	1.07961i	0.0984428	−	0.0407763i	−0.332919	−	0.942956i	$-0.608033\pi$
$701$	2.60641	−	1.07961i	0.0984428	−	0.0407763i	0.431361	+	0.902179i	$0.358033\pi$
$702$	−0.461928	+	0.225216i	−0.0174343	+	0.00850024i
$703$			5.79834i			0.218689i
$704$	2.40611	+	13.9937i	0.0906838	+	0.527408i
$705$	5.83046			0.219588
$706$	1.90179	+	3.59550i	0.0715750	+	0.135318i
$707$	−23.1608	−	9.59350i	−0.871050	−	0.360801i
$708$	8.93045	+	47.0288i	0.335627	+	1.76745i
$709$	15.7303	−	6.51571i	0.590764	−	0.244703i	−0.0672152	−	0.997739i	$-0.521411\pi$
$709$	15.7303	−	6.51571i	0.590764	−	0.244703i	0.657979	+	0.753036i	$0.271411\pi$
$710$	−1.11190	−	11.8155i	−0.0417290	−	0.443427i
$711$	−9.32766	+	9.32766i	−0.349815	+	0.349815i
$712$	−7.41006	−	9.27310i	−0.277704	−	0.347524i
$713$		−	53.3375i		−	1.99751i
$714$	−4.23638	−	45.0173i	−0.158543	−	1.68473i
$715$	1.54118	+	4.09679i	0.0576367	+	0.153211i
$716$	−17.5984	−	3.65981i	−0.657682	−	0.136773i
$717$	−50.1206	−	20.7606i	−1.87179	−	0.775320i
$718$	−2.40341	+	7.80080i	−0.0896945	+	0.291123i
$719$		−	7.89011i		−	0.294252i	−0.989118	−	0.147126i	$-0.952998\pi$
$719$		−	7.89011i		−	0.294252i	0.989118	−	0.147126i	$-0.0470022\pi$
$720$	−0.140693	+	8.09358i	−0.00524332	+	0.301630i
$721$	38.9257	−	38.9257i	1.44967	−	1.44967i
$722$	−11.7882	−	22.2865i	−0.438710	−	0.829418i
$723$	−11.4123	−	4.72713i	−0.424428	−	0.175804i
$724$	9.11125	+	13.8959i	0.338617	+	0.516436i
$725$	2.22807	+	0.922895i	0.0827483	+	0.0342755i
$726$	−17.2821	+	20.8727i	−0.641399	+	0.774659i
$727$	25.8773	−	25.8773i	0.959735	−	0.959735i	−0.0394856	−	0.999220i	$-0.512572\pi$
$727$	25.8773	−	25.8773i	0.959735	−	0.959735i	0.999220	+	0.0394856i	$0.0125719\pi$
$728$	47.1151	−	11.9604i	1.74620	−	0.443282i
$729$	18.5628	+	18.5628i	0.687511	+	0.687511i
$730$	1.51180	−	0.142269i	0.0559544	−	0.00526563i
$731$	6.71991	−	16.2233i	0.248545	−	0.600040i
$732$	9.73607	+	51.2713i	0.359856	+	1.89504i
$733$	−5.72801	+	13.8286i	−0.211569	+	0.510773i	−0.993665	−	0.112386i	$-0.964151\pi$
$733$	−5.72801	+	13.8286i	−0.211569	+	0.510773i	0.782096	+	0.623158i	$0.214151\pi$
$734$	−7.46257	−	2.29921i	−0.275449	−	0.0848652i
$735$	18.5591	+	18.5591i	0.684563	+	0.684563i
$736$	30.8842	+	26.4895i	1.13841	+	0.976417i
$737$	14.4436			0.532037
$738$	11.0186	−	5.82815i	0.405600	−	0.214537i
$739$	4.11332	−	9.93043i	0.151311	−	0.365297i	−0.829990	−	0.557779i	$-0.811654\pi$
$739$	4.11332	−	9.93043i	0.151311	−	0.365297i	0.981300	+	0.192482i	$0.0616537\pi$
$740$	−1.36666	−	7.19702i	−0.0502396	−	0.264568i
$741$	−3.93437	+	8.67966i	−0.144533	+	0.318855i
$742$	−15.0284	−	12.4432i	−0.551711	−	0.456804i
$743$	34.0245			1.24824			0.624118	−	0.781330i	$-0.285458\pi$
$743$	34.0245			1.24824			0.624118	+	0.781330i	$0.285458\pi$
$744$	−49.1839	+	14.2223i	−1.80317	+	0.521415i
$745$	−8.45686	−	8.45686i	−0.309835	−	0.309835i
$746$	−11.8889	+	14.3589i	−0.435282	+	0.525718i
$747$	−17.0942	−	41.2691i	−0.625444	−	1.50996i
$748$	−9.55003	−	1.98605i	−0.349184	−	0.0726172i
$749$	0.677094	−	1.63465i	0.0247405	−	0.0597288i
$750$	21.5097	+	6.62710i	0.785424	+	0.241988i
$751$			28.2172i			1.02966i	0.857292	+	0.514830i	$0.172145\pi$
$751$			28.2172i			1.02966i	−0.857292	+	0.514830i	$0.827855\pi$
$752$	−12.8102	−	5.56892i	−0.467139	−	0.203078i
$753$	24.3104			0.885919
$754$	0.883718	−	2.56532i	0.0321831	−	0.0934235i
$755$	5.70844	+	13.7814i	0.207751	+	0.501556i
$756$	0.526827	+	0.803482i	0.0191605	+	0.0292224i
$757$	8.60430	−	20.7726i	0.312729	−	0.754994i	−0.686873	−	0.726777i	$-0.741017\pi$
$757$	8.60430	−	20.7726i	0.312729	−	0.754994i	0.999602	−	0.0282165i	$-0.00898279\pi$
$758$	−38.2447	+	3.59905i	−1.38911	+	0.130723i
$759$		−	31.1630i		−	1.13115i
$760$	−1.30764	−	1.63641i	−0.0474331	−	0.0593587i
$761$	−6.99161			−0.253446			−0.126723	−	0.991938i	$-0.540446\pi$
$761$	−6.99161			−0.253446			−0.126723	+	0.991938i	$0.540446\pi$
$762$	−65.6949	+	6.18226i	−2.37987	+	0.223960i
$763$	−37.5432	+	90.6373i	−1.35915	+	3.28129i
$764$	8.72194	−	12.8109i	0.315549	−	0.463481i
$765$	−5.13760	−	2.12806i	−0.185750	−	0.0769402i
$766$	−33.2731	+	17.5994i	−1.20221	+	0.635891i
$767$	1.16235	−	35.3335i	0.0419699	−	1.27582i
$768$	16.1915	−	35.5425i	0.584259	−	1.28253i
$769$	38.7943	+	38.7943i	1.39896	+	1.39896i	0.803064	+	0.595893i	$0.203202\pi$
$769$	38.7943	+	38.7943i	1.39896	+	1.39896i	0.595893	+	0.803064i	$0.296798\pi$
$770$	7.23379	−	3.82622i	0.260688	−	0.137887i
$771$	−14.4406	−	34.8626i	−0.520064	−	1.25555i
$772$	34.5774	−	6.56600i	1.24447	−	0.236316i
$773$	−18.4367	−	44.5102i	−0.663123	−	1.60092i	−0.792883	−	0.609375i	$-0.791421\pi$
$773$	−18.4367	−	44.5102i	−0.663123	−	1.60092i	0.129760	−	0.991545i	$-0.458579\pi$
$774$	−2.50521	−	26.6213i	−0.0900480	−	0.956881i
$775$			33.6082i			1.20724i
$776$	−0.108897	+	0.975155i	−0.00390918	+	0.0350060i
$777$	44.0592	+	44.0592i	1.58062	+	1.58062i
$778$	3.88262	−	4.68928i	0.139199	−	0.168119i
$779$	−1.23438	+	2.98005i	−0.0442261	+	0.106771i
$780$	2.83763	−	11.7007i	0.101604	−	0.418952i
$781$	20.1184	−	8.33331i	0.719892	−	0.298189i
$782$	−24.7081	+	13.0691i	−0.883561	+	0.467348i
$783$	0.0536295			0.00191656
$784$	−23.0498	−	58.5030i	−0.823206	−	2.08939i
$785$	−5.86355	+	5.86355i	−0.209279	+	0.209279i
$786$	−40.3361	+	21.3352i	−1.43874	+	0.761003i
$787$	47.2043	+	19.5527i	1.68265	+	0.696977i	0.999447	−	0.0332494i	$-0.0105856\pi$
$787$	47.2043	+	19.5527i	1.68265	+	0.696977i	0.683205	+	0.730227i	$0.260586\pi$
$788$	−2.38059	+	11.4472i	−0.0848050	+	0.407789i
$789$	−29.2388	+	70.5887i	−1.04093	+	2.51302i
$790$	0.404059	+	4.29368i	0.0143758	+	0.152762i
$791$	4.34560			0.154512
$792$	−14.2686	+	4.12598i	−0.507011	+	0.146610i
$793$	1.26720	−	38.5210i	0.0449997	−	1.36792i
$794$	14.5851	−	17.6154i	0.517607	−	0.625147i
$795$	−4.46478	+	1.84937i	−0.158349	+	0.0655905i
$796$	1.68871	+	8.89293i	0.0598546	+	0.315202i
$797$	15.2942	−	6.33507i	0.541749	−	0.224400i	−0.0949914	−	0.995478i	$-0.530282\pi$
$797$	15.2942	−	6.33507i	0.541749	−	0.224400i	0.636740	+	0.771078i	$0.280282\pi$
$798$	17.0269	+	5.24596i	0.602746	+	0.185705i
$799$	6.78526	−	6.78526i	0.240045	−	0.240045i
$800$	−19.4603	−	16.6912i	−0.688025	−	0.590123i
$801$	8.78006	−	8.78006i	0.310228	−	0.310228i
$802$	−9.78311	−	18.4958i	−0.345454	−	0.653109i
$803$	1.06626	+	2.57417i	0.0376274	+	0.0908405i
$804$	−32.8407	−	22.3587i	−1.15820	−	0.788531i
$805$	8.97389	−	21.6649i	0.316288	−	0.763587i
$806$	37.7415	−	2.30300i	1.32939	−	0.0811198i
$807$	−40.0879	+	40.0879i	−1.41116	+	1.41116i
$808$	14.2903	−	4.13226i	0.502730	−	0.145372i
$809$	−1.94906	+	1.94906i	−0.0685251	+	0.0685251i	−0.740539	−	0.672014i	$-0.765430\pi$
$809$	−1.94906	+	1.94906i	−0.0685251	+	0.0685251i	0.672014	+	0.740539i	$0.265430\pi$
$810$	8.78500	−	0.826718i	0.308673	−	0.0290479i
$811$	8.60460	+	20.7733i	0.302148	+	0.729450i	0.999914	+	0.0131243i	$0.00417771\pi$
$811$	8.60460	+	20.7733i	0.302148	+	0.729450i	−0.697766	+	0.716326i	$0.745822\pi$
$812$	−4.96645	−	1.03284i	−0.174288	−	0.0362455i
$813$	19.8788	−	47.9916i	0.697178	−	1.68314i
$814$	11.8820	−	6.28484i	0.416464	−	0.220283i
$815$	3.42306			0.119904
$816$	18.6397	+	19.2992i	0.652519	+	0.675606i
$817$	4.89264	+	4.89264i	0.171172	+	0.171172i
$818$	2.71470	−	8.81117i	0.0949174	−	0.308075i
$819$	17.9038	+	47.5923i	0.625610	+	1.66301i
$820$	0.829738	−	3.98984i	0.0289757	−	0.139331i
$821$	−1.48193	+	0.613835i	−0.0517197	+	0.0214230i	−0.408393	−	0.912806i	$-0.633911\pi$
$821$	−1.48193	+	0.613835i	−0.0517197	+	0.0214230i	0.356674	+	0.934229i	$0.383911\pi$
$822$	4.37794	+	46.5215i	0.152698	+	1.62262i
$823$	9.33507	−	9.33507i	0.325400	−	0.325400i	−0.525434	−	0.850834i	$-0.676097\pi$
$823$	9.33507	−	9.33507i	0.325400	−	0.325400i	0.850834	+	0.525434i	$0.176097\pi$
$824$	−3.62530	+	32.4639i	−0.126293	+	1.13093i
$825$			19.6360i			0.683637i
$826$	−65.8044	+	6.19257i	−2.28963	+	0.215467i
$827$	19.7431	+	47.6641i	0.686536	+	1.65744i	0.751647	+	0.659566i	$0.229260\pi$
$827$	19.7431	+	47.6641i	0.686536	+	1.65744i	−0.0651107	+	0.997878i	$0.520740\pi$
$828$	−23.9531	+	35.1825i	−0.832427	+	1.22268i
$829$	−3.28374	+	1.36017i	−0.114049	+	0.0472406i	−0.438978	−	0.898498i	$-0.644659\pi$
$829$	−3.28374	+	1.36017i	−0.114049	+	0.0472406i	0.324929	+	0.945738i	$0.394659\pi$
$830$	−13.9564	−	4.29994i	−0.484433	−	0.149253i
$831$	31.9295			1.10762
$832$	−17.4104	+	22.9973i	−0.603597	+	0.797289i
$833$	43.1967			1.49668
$834$	−3.78197	−	1.16522i	−0.130959	−	0.0403482i
$835$	−12.6942	+	5.25813i	−0.439302	+	0.181965i
$836$	2.16306	−	3.17712i	0.0748109	−	0.109883i
$837$	0.286007	+	0.690482i	0.00988585	+	0.0238665i
$838$	−1.22795	+	0.115557i	−0.0424187	+	0.00399185i
$839$			51.0263i			1.76162i	0.473466	+	0.880812i	$0.343003\pi$
$839$			51.0263i			1.76162i	−0.473466	+	0.880812i	$0.656997\pi$
$840$	−22.3706	−	2.49816i	−0.771859	−	0.0861948i
$841$	20.3059	−	20.3059i	0.700203	−	0.700203i
$842$	2.13591	+	22.6969i	0.0736082	+	0.782186i
$843$	−41.1279	+	17.0357i	−1.41652	+	0.586741i
$844$	1.02278	−	4.91810i	0.0352056	−	0.169288i
$845$	−3.93526	+	7.97351i	−0.135377	+	0.274297i
$846$	4.30227	−	13.9640i	0.147915	−	0.480091i
$847$	−26.4574	−	26.4574i	−0.909086	−	0.909086i
$848$	11.5760	+	0.201229i	0.397522	+	0.00691024i
$849$	−13.8553			−0.475511
$850$	15.5687	−	8.23487i	0.534003	−	0.282454i
$851$	14.7402	−	35.5861i	0.505289	−	1.21988i
$852$	−58.6435	−	12.1957i	−2.00909	−	0.417817i
$853$	3.43022	+	8.28129i	0.117449	+	0.283546i	0.971661	−	0.236378i	$-0.0759603\pi$
$853$	3.43022	+	8.28129i	0.117449	+	0.283546i	−0.854213	+	0.519924i	$0.825960\pi$
$854$	−71.7406	+	6.75120i	−2.45491	+	0.231021i
$855$	1.54940	−	1.54940i	0.0529884	−	0.0529884i
$856$	0.291649	+	1.00858i	0.00996834	+	0.0344727i
$857$	−12.9270	+	12.9270i	−0.441577	+	0.441577i	−0.892542	−	0.450965i	$-0.851080\pi$
$857$	−12.9270	+	12.9270i	−0.441577	+	0.441577i	0.450965	+	0.892542i	$0.351080\pi$
$858$	22.0509	−	1.34555i	0.752805	−	0.0459365i
$859$	−8.50209	+	20.5259i	−0.290087	+	0.700333i	−0.999992	−	0.00396469i	$-0.998738\pi$
$859$	−8.50209	+	20.5259i	−0.290087	+	0.700333i	0.709905	+	0.704298i	$0.248738\pi$
$860$	−7.22603	−	4.91965i	−0.246406	−	0.167759i
$861$	13.2646	+	32.0237i	0.452058	+	1.09136i
$862$	−1.47031	−	2.77974i	−0.0500790	−	0.0946785i
$863$	−14.4774	+	14.4774i	−0.492818	+	0.492818i	−0.909193	−	0.416375i	$-0.863300\pi$
$863$	−14.4774	+	14.4774i	−0.492818	+	0.492818i	0.416375	+	0.909193i	$0.363300\pi$
$864$	−0.541854	−	0.177313i	−0.0184343	−	0.00603232i
$865$	−7.99648	+	7.99648i	−0.271888	+	0.271888i
$866$	36.5656	+	11.2658i	1.24255	+	0.382827i
$867$	21.3100	−	8.82690i	0.723726	−	0.299777i
$868$	−13.1883	−	69.4514i	−0.447642	−	2.35734i
$869$	−7.31090	+	3.02827i	−0.248005	+	0.102727i
$870$	−0.801289	+	0.967767i	−0.0271662	+	0.0328104i
$871$	20.0540	+	21.4183i	0.679503	+	0.725730i
$872$	−16.1712	−	55.9235i	−0.547626	−	1.89381i
$873$	−1.02641			−0.0347388
$874$	−1.03191	−	10.9655i	−0.0349049	−	0.370912i
$875$	−11.8927	+	28.7114i	−0.402045	+	0.970624i
$876$	1.56045	−	7.50350i	0.0527227	−	0.253520i
$877$	37.4110	+	15.4961i	1.26328	+	0.523268i	0.910915	−	0.412595i	$-0.135378\pi$
$877$	37.4110	+	15.4961i	1.26328	+	0.523268i	0.352365	+	0.935863i	$0.385378\pi$
$878$	−12.6865	+	6.71036i	−0.428149	+	0.226464i
$879$	52.0666	−	52.0666i	1.75616	−	1.75616i
$880$	−1.93598	+	4.45333i	−0.0652620	+	0.150122i
$881$	−28.3568			−0.955365			−0.477682	−	0.878533i	$-0.658523\pi$
$881$	−28.3568			−0.955365			−0.477682	+	0.878533i	$0.658523\pi$
$882$	58.1438	−	30.7544i	1.95780	−	1.03555i
$883$	−34.8429	+	14.4324i	−1.17256	+	0.485688i	−0.882037	−	0.471181i	$-0.843828\pi$
$883$	−34.8429	+	14.4324i	−1.17256	+	0.485688i	−0.290519	+	0.956869i	$0.593828\pi$
$884$	−10.3145	−	16.9191i	−0.346913	−	0.569052i
$885$	−6.26484	+	15.1247i	−0.210590	+	0.508410i
$886$	−21.6153	+	26.1062i	−0.726180	+	0.877054i
$887$	14.3416	+	14.3416i	0.481545	+	0.481545i	0.905625	−	0.424080i	$-0.139402\pi$
$887$	14.3416	+	14.3416i	0.481545	+	0.481545i	−0.424080	+	0.905625i	$0.639402\pi$
$888$	−36.7453	−	4.10341i	−1.23309	−	0.137701i
$889$		−	91.1085i		−	3.05568i
$890$	−0.380338	−	4.04160i	−0.0127490	−	0.135475i
$891$	6.19594	+	14.9583i	0.207572	+	0.501123i
$892$	17.2126	−	3.26855i	0.576320	−	0.109439i
$893$	1.44696	+	3.49326i	0.0484206	+	0.116898i
$894$	−53.3587	+	28.2234i	−1.78458	+	0.943931i
$895$	−4.34675	−	4.34675i	−0.145296	−	0.145296i
$896$	46.7645	+	26.8558i	1.56229	+	0.897191i
$897$	46.2113	−	43.2678i	1.54295	−	1.44467i
$898$	−2.75601	+	1.45776i	−0.0919693	+	0.0486460i
$899$	−3.64553	−	1.51003i	−0.121585	−	0.0503623i
$900$	15.0929	−	22.1687i	0.503098	−	0.738956i
$901$	−3.04371	+	7.34816i	−0.101401	+	0.244803i
$902$	7.44468	−	0.700587i	0.247881	−	0.0233270i
$903$	74.3542			2.47435
$904$	−2.01447	+	1.60975i	−0.0670004	+	0.0535395i
$905$			5.68270i			0.188899i
$906$	74.9567	−	7.05386i	2.49027	−	0.234349i
$907$	22.1387	−	53.4474i	0.735102	−	1.77469i	0.110317	−	0.993897i	$-0.464814\pi$
$907$	22.1387	−	53.4474i	0.735102	−	1.77469i	0.624785	−	0.780797i	$-0.285186\pi$
$908$	−23.6901	−	36.1306i	−0.786184	−	1.19904i
$909$	5.95492	+	14.3764i	0.197512	+	0.476836i
$910$	15.7175	+	5.41446i	0.521030	+	0.179488i
$911$	−35.7122			−1.18320			−0.591600	−	0.806232i	$-0.701503\pi$
$911$	−35.7122			−1.18320			−0.591600	+	0.806232i	$0.701503\pi$
$912$	−9.83636	+	3.87546i	−0.325714	+	0.128329i
$913$		−	26.7964i		−	0.886832i
$914$	39.2711	+	12.0994i	1.29897	+	0.400212i
$915$	−6.82999	+	16.4891i	−0.225793	+	0.545112i
$916$	40.9741	+	8.52109i	1.35382	+	0.281545i
$917$	−24.1109	−	58.2088i	−0.796211	−	1.92222i
$918$	0.249781	−	0.301676i	0.00824399	−	0.00995679i
$919$	33.1467	+	33.1467i	1.09341	+	1.09341i	0.995162	+	0.0982462i	$0.0313233\pi$
$919$	33.1467	+	33.1467i	1.09341	+	1.09341i	0.0982462	+	0.995162i	$0.468677\pi$
$920$	3.86538	+	13.3673i	0.127438	+	0.440707i
$921$	−34.3780			−1.13280
$922$	−10.1219	−	8.38068i	−0.333346	−	0.276003i
$923$	40.2904	+	18.2631i	1.32617	+	0.601137i
$924$	−7.70544	−	40.5778i	−0.253490	−	1.33491i
$925$	−9.28790	+	22.4230i	−0.305384	+	0.737263i
$926$	−28.9316	+	15.3030i	−0.950752	+	0.502888i
$927$	−34.1704			−1.12230
$928$	2.68487	−	1.36094i	0.0881353	−	0.0446752i
$929$	−28.8546	−	28.8546i	−0.946690	−	0.946690i	0.0519589	−	0.998649i	$-0.483454\pi$
$929$	−28.8546	−	28.8546i	−0.946690	−	0.946690i	−0.998649	+	0.0519589i	$0.983454\pi$
$930$	−16.7333	−	5.15551i	−0.548707	−	0.169056i
$931$	−6.51365	+	15.7253i	−0.213476	+	0.515377i
$932$	4.62042	+	24.3317i	0.151347	+	0.797010i
$933$	18.5865	−	44.8718i	0.608494	−	1.46904i
$934$	47.5840	−	4.47793i	1.55700	−	0.146522i
$935$	−2.35883	−	2.35883i	−0.0771421	−	0.0771421i
$936$	−25.9293	−	15.4300i	−0.847525	−	0.504346i
$937$	16.1062	−	16.1062i	0.526167	−	0.526167i	−0.393261	−	0.919427i	$-0.628653\pi$
$937$	16.1062	−	16.1062i	0.526167	−	0.526167i	0.919427	+	0.393261i	$0.128653\pi$
$938$	34.9842	−	42.2527i	1.14228	−	1.37960i
$939$	−1.44300	−	0.597710i	−0.0470905	−	0.0195055i
$940$	−2.61935	−	3.99486i	−0.0854338	−	0.130298i
$941$	−28.1343	−	11.6536i	−0.917150	−	0.379896i	−0.126361	−	0.991984i	$-0.540330\pi$
$941$	−28.1343	−	11.6536i	−0.917150	−	0.379896i	−0.790790	+	0.612088i	$0.790330\pi$
$942$	19.5687	+	36.9962i	0.637581	+	1.20540i
$943$	15.1514	−	15.1514i	0.493399	−	0.493399i
$944$	28.2107	−	27.2467i	0.918181	−	0.886805i
$945$			0.328583i			0.0106888i
$946$	4.72289	−	15.3292i	0.153554	−	0.498394i
$947$	20.6361	+	8.54775i	0.670583	+	0.277764i	0.691884	−	0.722009i	$-0.256781\pi$
$947$	20.6361	+	8.54775i	0.670583	+	0.277764i	−0.0213014	+	0.999773i	$0.506781\pi$
$948$	21.3107	+	4.43183i	0.692139	+	0.143939i
$949$	−2.33678	+	5.15520i	−0.0758552	+	0.167345i
$950$	0.650213	+	6.90938i	0.0210957	+	0.224170i
$951$		−	32.7577i		−	1.06224i
$952$	−28.9413	+	23.1268i	−0.937992	+	0.749542i
$953$	34.8685	−	34.8685i	1.12950	−	1.12950i	0.139243	−	0.990258i	$-0.455533\pi$
$953$	34.8685	−	34.8685i	1.12950	−	1.12950i	0.990258	−	0.139243i	$-0.0444670\pi$
$954$	1.13471	+	12.0578i	0.0367375	+	0.390386i
$955$	4.89674	−	2.02830i	0.158455	−	0.0656341i
$956$	8.29224	+	43.6679i	0.268190	+	1.41232i
$957$	−2.12994	−	0.882251i	−0.0688513	−	0.0285191i
$958$	−9.89281	−	18.7032i	−0.319622	−	0.604272i
$959$	−64.5181			−2.08340
$960$	11.2956	−	7.12872i	0.364565	−	0.230078i
$961$		−	23.9894i		−	0.773851i
$962$	25.8171	+	8.89362i	0.832376	+	0.286742i
$963$	−1.01467	+	0.420289i	−0.0326972	+	0.0135436i
$964$	1.88811	+	9.94304i	0.0608121	+	0.320244i
$965$	11.1202	+	4.60614i	0.357972	+	0.148277i
$966$	−91.1630	−	75.4808i	−2.93312	−	2.42856i
$967$	26.6348			0.856518			0.428259	−	0.903656i	$-0.359127\pi$
$967$	26.6348			0.856518			0.428259	+	0.903656i	$0.359127\pi$
$968$	22.0654	+	2.46408i	0.709208	+	0.0791985i
$969$		−	7.26285i		−	0.233316i
$970$	−0.214006	+	0.258469i	−0.00687132	+	0.00829893i
$971$	23.4336	+	9.70652i	0.752021	+	0.311497i	0.725566	−	0.688153i	$-0.241578\pi$
$971$	23.4336	+	9.70652i	0.752021	+	0.311497i	0.0264550	+	0.999650i	$0.491578\pi$
$972$	8.94455	−	43.0103i	0.286896	−	1.37956i
$973$	2.09104	−	5.04822i	0.0670357	−	0.161839i
$974$	29.9057	+	9.21391i	0.958242	+	0.295233i
$975$	−29.1180	+	27.2632i	−0.932521	+	0.873122i
$976$	30.7556	−	29.7046i	0.984464	−	0.950822i
$977$	−19.4680	+	19.4680i	−0.622838	+	0.622838i	−0.946256	−	0.323418i	$-0.895168\pi$
$977$	−19.4680	+	19.4680i	−0.622838	+	0.622838i	0.323418	+	0.946256i	$0.395168\pi$
$978$	5.08697	−	16.5109i	0.162663	−	0.527959i
$979$	6.88169	−	2.85049i	0.219940	−	0.0911020i
$980$	4.37842	−	21.0539i	0.139864	−	0.672541i
$981$	56.2607	−	23.3040i	1.79627	−	0.744038i
$982$	25.5405	−	30.8469i	0.815031	−	0.984365i
$983$	−37.8510			−1.20726			−0.603629	−	0.797265i	$-0.706279\pi$
$983$	−37.8510			−1.20726			−0.603629	+	0.797265i	$0.706279\pi$
$984$	−18.0116	−	9.93143i	−0.574189	−	0.316602i
$985$	−2.82742	+	2.82742i	−0.0900892	+	0.0900892i
$986$	0.193741	+	2.05876i	0.00616996	+	0.0655642i
$987$	37.5387	+	15.5490i	1.19487	+	0.494931i
$988$	7.71457	−	1.20364i	0.245433	−	0.0382930i
$989$	−17.5897	−	42.4653i	−0.559320	−	1.35032i
$990$	−4.85444	−	1.49565i	−0.154284	−	0.0475347i
$991$			31.2350i			0.992212i	0.868262	+	0.496106i	$0.165237\pi$
$991$			31.2350i			0.992212i	−0.868262	+	0.496106i	$0.834763\pi$
$992$	31.8407	+	27.3099i	1.01094	+	0.867091i
$993$	−29.1824	−	29.1824i	−0.926074	−	0.926074i
$994$	24.3514	−	79.0377i	0.772379	−	2.50692i
$995$	−1.18465	+	2.86000i	−0.0375560	+	0.0906681i
$996$	−41.4808	+	60.9275i	−1.31437	+	1.93056i
$997$	−23.4901	−	9.72991i	−0.743938	−	0.308149i	−0.0216727	−	0.999765i	$-0.506899\pi$
$997$	−23.4901	−	9.72991i	−0.743938	−	0.308149i	−0.722266	+	0.691616i	$0.756899\pi$
$998$	16.1784	−	19.5396i	0.512117	−	0.618517i
$999$			0.539720i			0.0170760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bd.a.411.5	yes	216
13.5	odd	4		416.2.bi.a.187.24	yes	216
32.19	odd	8		416.2.bi.a.307.24	yes	216
416.83	even	8	inner	416.2.bd.a.83.5	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bd.a.83.5	✓	216	416.83	even	8	inner
416.2.bd.a.411.5	yes	216	1.1	even	1	trivial
416.2.bi.a.187.24	yes	216	13.5	odd	4
416.2.bi.a.307.24	yes	216	32.19	odd	8

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35152 - 0.416401i) q^{2} +(-2.25523 + 0.934148i) q^{3} +(1.65322 + 1.12555i) q^{4} +(0.261748 + 0.631915i) q^{5} +(3.43698 - 0.323439i) q^{6} +4.76655i q^{7} +(-1.76568 - 2.20961i) q^{8} +(2.09213 - 2.09213i) q^{9} +(-0.0906275 - 0.963039i) q^{10} +(1.63978 - 0.679219i) q^{11} +(-4.77983 - 0.994027i) q^{12} +(3.28393 + 1.48856i) q^{13} +(1.98480 - 6.44209i) q^{14} +(-1.18061 - 1.18061i) q^{15} +(1.46627 + 3.72157i) q^{16} -2.74788 q^{17} +(-3.69872 + 1.95639i) q^{18} +(0.414355 - 1.00034i) q^{19} +(-0.278526 + 1.33931i) q^{20} +(-4.45266 - 10.7497i) q^{21} +(-2.49902 + 0.235173i) q^{22} +(-5.08603 + 5.08603i) q^{23} +(6.04613 + 3.33378i) q^{24} +(3.20473 - 3.20473i) q^{25} +(-3.81846 - 3.37925i) q^{26} +(0.0385689 - 0.0931135i) q^{27} +(-5.36499 + 7.88015i) q^{28} +(0.203632 + 0.491611i) q^{29} +(1.10401 + 2.08722i) q^{30} +(-5.24354 + 5.24354i) q^{31} +(-0.432033 - 5.64033i) q^{32} +(-3.06360 + 3.06360i) q^{33} +(3.71382 + 1.14422i) q^{34} +(-3.01206 + 1.24763i) q^{35} +(5.81354 - 1.10395i) q^{36} +(-4.94751 + 2.04933i) q^{37} +(-0.976552 + 1.17944i) q^{38} +(-8.79656 - 0.289375i) q^{39} +(0.934122 - 1.69412i) q^{40} -2.97903 q^{41} +(1.54169 + 16.3825i) q^{42} +(-2.44549 + 5.90392i) q^{43} +(3.47541 + 0.722757i) q^{44} +(1.86966 + 0.774437i) q^{45} +(8.99170 - 4.75604i) q^{46} +(-2.46927 + 2.46927i) q^{47} +(-6.78328 - 7.02328i) q^{48} -15.7200 q^{49} +(-5.66571 + 2.99681i) q^{50} +(6.19712 - 2.56693i) q^{51} +(3.75361 + 6.15715i) q^{52} +(1.10766 - 2.67412i) q^{53} +(-0.0908993 + 0.109785i) q^{54} +(0.858418 + 0.858418i) q^{55} +(10.5322 - 8.41621i) q^{56} +2.64307i q^{57} +(-0.0705055 - 0.749215i) q^{58} +(-3.75224 - 9.05870i) q^{59} +(-0.622969 - 3.28063i) q^{60} +(-4.09073 - 9.87589i) q^{61} +(9.27017 - 4.90334i) q^{62} +(9.97222 + 9.97222i) q^{63} +(-1.76474 + 7.80293i) q^{64} +(-0.0810828 + 2.46479i) q^{65} +(5.41620 - 2.86483i) q^{66} +(7.51832 + 3.11419i) q^{67} +(-4.54286 - 3.09288i) q^{68} +(6.71907 - 16.2213i) q^{69} +(4.59037 - 0.431980i) q^{70} +12.2690 q^{71} +(-8.31681 - 0.928752i) q^{72} +1.56983i q^{73} +(7.54001 - 0.709558i) q^{74} +(-4.23372 + 10.2211i) q^{75} +(1.81095 - 1.18741i) q^{76} +(3.23753 + 7.81609i) q^{77} +(11.7682 + 4.05400i) q^{78} -4.45846 q^{79} +(-1.96792 + 1.90067i) q^{80} +9.12216i q^{81} +(4.02623 + 1.24047i) q^{82} +(5.77758 - 13.9483i) q^{83} +(4.73808 - 22.7833i) q^{84} +(-0.719253 - 1.73643i) q^{85} +(5.76353 - 6.96098i) q^{86} +(-0.918475 - 0.918475i) q^{87} +(-4.39614 - 2.42399i) q^{88} +4.19672 q^{89} +(-2.20440 - 1.82520i) q^{90} +(-7.09530 + 15.6530i) q^{91} +(-14.1329 + 2.68374i) q^{92} +(6.92716 - 16.7236i) q^{93} +(4.36548 - 2.30906i) q^{94} +0.740587 q^{95} +(6.24324 + 12.3167i) q^{96} +(-0.245304 - 0.245304i) q^{97} +(21.2459 + 6.54582i) q^{98} +(2.00961 - 4.85164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Introduction

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