LMFDB - Embedded newform 605.2.e.c.362.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.11
Character	$\chi$	$=$	605.362
Dual form			605.2.e.c.483.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.187165 - 0.187165i) q^{2} +(-0.0374447 + 0.0374447i) q^{3} +1.92994i q^{4} +(1.76123 - 1.37770i) q^{5} +0.0140167i q^{6} +(2.30359 - 2.30359i) q^{7} +(0.735548 + 0.735548i) q^{8} +2.99720i q^{9} +O(q^{10})$	\(q+(0.187165 - 0.187165i) q^{2} +(-0.0374447 + 0.0374447i) q^{3} +1.92994i q^{4} +(1.76123 - 1.37770i) q^{5} +0.0140167i q^{6} +(2.30359 - 2.30359i) q^{7} +(0.735548 + 0.735548i) q^{8} +2.99720i q^{9} +(0.0717827 - 0.587500i) q^{10} +(-0.0722660 - 0.0722660i) q^{12} +(1.59601 + 1.59601i) q^{13} -0.862304i q^{14} +(-0.0143610 + 0.117536i) q^{15} -3.58454 q^{16} +(4.70246 - 4.70246i) q^{17} +(0.560971 + 0.560971i) q^{18} -6.13150 q^{19} +(2.65888 + 3.39906i) q^{20} +0.172514i q^{21} +(-2.64975 + 2.64975i) q^{23} -0.0550848 q^{24} +(1.20386 - 4.85291i) q^{25} +0.597437 q^{26} +(-0.224563 - 0.224563i) q^{27} +(4.44579 + 4.44579i) q^{28} +5.84873 q^{29} +(0.0193109 + 0.0246866i) q^{30} +3.89076 q^{31} +(-2.14200 + 2.14200i) q^{32} -1.76028i q^{34} +(0.883485 - 7.23082i) q^{35} -5.78440 q^{36} +(4.56607 + 4.56607i) q^{37} +(-1.14760 + 1.14760i) q^{38} -0.119524 q^{39} +(2.30884 + 0.282102i) q^{40} -1.80463i q^{41} +(0.0322887 + 0.0322887i) q^{42} +(1.54334 + 1.54334i) q^{43} +(4.12925 + 5.27875i) q^{45} +0.991883i q^{46} +(2.48435 + 2.48435i) q^{47} +(0.134222 - 0.134222i) q^{48} -3.61305i q^{49} +(-0.682975 - 1.13362i) q^{50} +0.352165i q^{51} +(-3.08021 + 3.08021i) q^{52} +(-6.60160 + 6.60160i) q^{53} -0.0840609 q^{54} +3.38880 q^{56} +(0.229592 - 0.229592i) q^{57} +(1.09468 - 1.09468i) q^{58} +4.11051i q^{59} +(-0.226838 - 0.0277158i) q^{60} -1.77844i q^{61} +(0.728215 - 0.728215i) q^{62} +(6.90431 + 6.90431i) q^{63} -6.36726i q^{64} +(5.00978 + 0.612112i) q^{65} +(-8.68690 - 8.68690i) q^{67} +(9.07546 + 9.07546i) q^{68} -0.198438i q^{69} +(-1.18800 - 1.51872i) q^{70} +6.89961 q^{71} +(-2.20458 + 2.20458i) q^{72} +(-5.99440 - 5.99440i) q^{73} +1.70922 q^{74} +(0.136637 + 0.226794i) q^{75} -11.8334i q^{76} +(-0.0223708 + 0.0223708i) q^{78} -12.2185 q^{79} +(-6.31320 + 4.93843i) q^{80} -8.97477 q^{81} +(-0.337764 - 0.337764i) q^{82} +(-7.44550 - 7.44550i) q^{83} -0.332942 q^{84} +(1.80351 - 14.7607i) q^{85} +0.577720 q^{86} +(-0.219004 + 0.219004i) q^{87} -2.26121i q^{89} +(1.76085 + 0.215147i) q^{90} +7.35312 q^{91} +(-5.11386 - 5.11386i) q^{92} +(-0.145688 + 0.145688i) q^{93} +0.929969 q^{94} +(-10.7990 + 8.44739i) q^{95} -0.160413i q^{96} +(-4.75552 - 4.75552i) q^{97} +(-0.676238 - 0.676238i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) $ 40 * q + 8 * q^3 - 4 * q^5	$ 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) $ 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.187165	−	0.187165i	0.132346	−	0.132346i	−0.637831	−	0.770177i	$-0.720168\pi$
$2$	0.187165	−	0.187165i	0.132346	−	0.132346i	0.770177	+	0.637831i	$0.220168\pi$
$3$	−0.0374447	+	0.0374447i	−0.0216187	+	0.0216187i	−0.717834	−	0.696215i	$-0.754866\pi$
$3$	−0.0374447	+	0.0374447i	−0.0216187	+	0.0216187i	0.696215	+	0.717834i	$0.254866\pi$
$4$			1.92994i			0.964969i
$5$	1.76123	−	1.37770i	0.787646	−	0.616128i
$5$	1.76123	−	1.37770i	0.787646	−	0.616128i
$6$			0.0140167i			0.00572229i
$7$	2.30359	−	2.30359i	0.870675	−	0.870675i	−0.121871	−	0.992546i	$-0.538889\pi$
$7$	2.30359	−	2.30359i	0.870675	−	0.870675i	0.992546	+	0.121871i	$0.0388894\pi$
$8$	0.735548	+	0.735548i	0.260056	+	0.260056i
$9$			2.99720i			0.999065i
$10$	0.0717827	−	0.587500i	0.0226997	−	0.185784i
$11$		0			0
$11$		0			0
$12$	−0.0722660	−	0.0722660i	−0.0208614	−	0.0208614i
$13$	1.59601	+	1.59601i	0.442654	+	0.442654i	0.892903	−	0.450249i	$-0.148665\pi$
$13$	1.59601	+	1.59601i	0.442654	+	0.442654i	−0.450249	+	0.892903i	$0.648665\pi$
$14$		−	0.862304i		−	0.230461i
$15$	−0.0143610	+	0.117536i	−0.00370799	+	0.0303478i
$16$	−3.58454			−0.896135
$17$	4.70246	−	4.70246i	1.14051	−	1.14051i	0.152158	−	0.988356i	$-0.451378\pi$
$17$	4.70246	−	4.70246i	1.14051	−	1.14051i	0.988356	−	0.152158i	$-0.0486224\pi$
$18$	0.560971	+	0.560971i	0.132222	+	0.132222i
$19$	−6.13150			−1.40666			−0.703331	−	0.710862i	$-0.748305\pi$
$19$	−6.13150			−1.40666			−0.703331	+	0.710862i	$0.748305\pi$
$20$	2.65888	+	3.39906i	0.594545	+	0.760054i
$21$			0.172514i			0.0376457i
$22$		0			0
$23$	−2.64975	+	2.64975i	−0.552511	+	0.552511i	−0.927165	−	0.374654i	$-0.877762\pi$
$23$	−2.64975	+	2.64975i	−0.552511	+	0.552511i	0.374654	+	0.927165i	$0.377762\pi$
$24$	−0.0550848			−0.0112441
$25$	1.20386	−	4.85291i	0.240772	−	0.970582i
$26$	0.597437			0.117167
$27$	−0.224563	−	0.224563i	−0.0432172	−	0.0432172i
$28$	4.44579	+	4.44579i	0.840175	+	0.840175i
$29$	5.84873			1.08608			0.543041	−	0.839706i	$-0.317273\pi$
$29$	5.84873			1.08608			0.543041	+	0.839706i	$0.317273\pi$
$30$	0.0193109	+	0.0246866i	0.00352567	+	0.00450714i
$31$	3.89076			0.698801			0.349400	−	0.936974i	$-0.386385\pi$
$31$	3.89076			0.698801			0.349400	+	0.936974i	$0.386385\pi$
$32$	−2.14200	+	2.14200i	−0.378655	+	0.378655i
$33$		0			0
$34$		−	1.76028i		−	0.301885i
$35$	0.883485	−	7.23082i	0.149336	−	1.22223i
$36$	−5.78440			−0.964067
$37$	4.56607	+	4.56607i	0.750657	+	0.750657i	0.974602	−	0.223944i	$-0.0718934\pi$
$37$	4.56607	+	4.56607i	0.750657	+	0.750657i	−0.223944	+	0.974602i	$0.571893\pi$
$38$	−1.14760	+	1.14760i	−0.186166	+	0.186166i
$39$	−0.119524			−0.0191392
$40$	2.30884	+	0.282102i	0.365059	+	0.0446042i
$41$		−	1.80463i		−	0.281836i	−0.990021	−	0.140918i	$-0.954995\pi$
$41$		−	1.80463i		−	0.281836i	0.990021	−	0.140918i	$-0.0450054\pi$
$42$	0.0322887	+	0.0322887i	0.00498226	+	0.00498226i
$43$	1.54334	+	1.54334i	0.235357	+	0.235357i	0.814925	−	0.579567i	$-0.196778\pi$
$43$	1.54334	+	1.54334i	0.235357	+	0.235357i	−0.579567	+	0.814925i	$0.696778\pi$
$44$		0			0
$45$	4.12925	+	5.27875i	0.615552	+	0.786910i
$46$			0.991883i			0.146245i
$47$	2.48435	+	2.48435i	0.362380	+	0.362380i	0.864688	−	0.502309i	$-0.167516\pi$
$47$	2.48435	+	2.48435i	0.362380	+	0.362380i	−0.502309	+	0.864688i	$0.667516\pi$
$48$	0.134222	−	0.134222i	0.0193733	−	0.0193733i
$49$		−	3.61305i		−	0.516150i
$50$	−0.682975	−	1.13362i	−0.0965873	−	0.160318i
$51$			0.352165i			0.0493129i
$52$	−3.08021	+	3.08021i	−0.427148	+	0.427148i
$53$	−6.60160	+	6.60160i	−0.906800	+	0.906800i	−0.996013	−	0.0892130i	$-0.971565\pi$
$53$	−6.60160	+	6.60160i	−0.906800	+	0.906800i	0.0892130	+	0.996013i	$0.471565\pi$
$54$	−0.0840609			−0.0114392
$55$		0			0
$56$	3.38880			0.452848
$57$	0.229592	−	0.229592i	0.0304102	−	0.0304102i
$58$	1.09468	−	1.09468i	0.143738	−	0.143738i
$59$			4.11051i			0.535143i	0.963538	+	0.267571i	$0.0862211\pi$
$59$			4.11051i			0.535143i	−0.963538	+	0.267571i	$0.913779\pi$
$60$	−0.226838	−	0.0277158i	−0.0292847	−	0.00357810i
$61$		−	1.77844i		−	0.227706i	−0.993498	−	0.113853i	$-0.963681\pi$
$61$		−	1.77844i		−	0.227706i	0.993498	−	0.113853i	$-0.0363192\pi$
$62$	0.728215	−	0.728215i	0.0924834	−	0.0924834i
$63$	6.90431	+	6.90431i	0.869861	+	0.869861i
$64$		−	6.36726i		−	0.795908i
$65$	5.00978	+	0.612112i	0.621387	+	0.0759231i
$66$		0			0
$67$	−8.68690	−	8.68690i	−1.06127	−	1.06127i	−0.997996	−	0.0632779i	$-0.979845\pi$
$67$	−8.68690	−	8.68690i	−1.06127	−	1.06127i	−0.0632779	−	0.997996i	$-0.520155\pi$
$68$	9.07546	+	9.07546i	1.10056	+	1.10056i
$69$		−	0.198438i		−	0.0238892i
$70$	−1.18800	−	1.51872i	−0.141993	−	0.181521i
$71$	6.89961			0.818833			0.409417	−	0.912348i	$-0.365732\pi$
$71$	6.89961			0.818833			0.409417	+	0.912348i	$0.365732\pi$
$72$	−2.20458	+	2.20458i	−0.259813	+	0.259813i
$73$	−5.99440	−	5.99440i	−0.701592	−	0.701592i	0.263160	−	0.964752i	$-0.415235\pi$
$73$	−5.99440	−	5.99440i	−0.701592	−	0.701592i	−0.964752	+	0.263160i	$0.915235\pi$
$74$	1.70922			0.198693
$75$	0.136637	+	0.226794i	0.0157775	+	0.0261879i
$76$		−	11.8334i		−	1.35739i
$77$		0			0
$78$	−0.0223708	+	0.0223708i	−0.00253300	+	0.00253300i
$79$	−12.2185			−1.37468			−0.687342	−	0.726334i	$-0.741223\pi$
$79$	−12.2185			−1.37468			−0.687342	+	0.726334i	$0.741223\pi$
$80$	−6.31320	+	4.93843i	−0.705837	+	0.552134i
$81$	−8.97477			−0.997197
$82$	−0.337764	−	0.337764i	−0.0372998	−	0.0372998i
$83$	−7.44550	−	7.44550i	−0.817250	−	0.817250i	0.168459	−	0.985709i	$-0.446121\pi$
$83$	−7.44550	−	7.44550i	−0.817250	−	0.817250i	−0.985709	+	0.168459i	$0.946121\pi$
$84$	−0.332942			−0.0363270
$85$	1.80351	−	14.7607i	0.195619	−	1.60102i
$86$	0.577720			0.0622972
$87$	−0.219004	+	0.219004i	−0.0234797	+	0.0234797i
$88$		0			0
$89$		−	2.26121i		−	0.239688i	−0.992793	−	0.119844i	$-0.961761\pi$
$89$		−	2.26121i		−	0.239688i	0.992793	−	0.119844i	$-0.0382394\pi$
$90$	1.76085	+	0.215147i	0.185610	+	0.0226785i
$91$	7.35312			0.770816
$92$	−5.11386	−	5.11386i	−0.533156	−	0.533156i
$93$	−0.145688	+	0.145688i	−0.0151072	+	0.0151072i
$94$	0.929969			0.0959189
$95$	−10.7990	+	8.44739i	−1.10795	+	0.866684i
$96$		−	0.160413i		−	0.0163721i
$97$	−4.75552	−	4.75552i	−0.482850	−	0.482850i	0.423191	−	0.906041i	$-0.360910\pi$
$97$	−4.75552	−	4.75552i	−0.482850	−	0.482850i	−0.906041	+	0.423191i	$0.860910\pi$
$98$	−0.676238	−	0.676238i	−0.0683104	−	0.0683104i
$99$		0			0
$100$	9.36581	+	2.32338i	0.936581	+	0.232338i
$101$		−	10.5008i		−	1.04487i	−0.852680	−	0.522433i	$-0.825024\pi$
$101$		−	10.5008i		−	1.04487i	0.852680	−	0.522433i	$-0.174976\pi$
$102$	0.0659130	+	0.0659130i	0.00652636	+	0.00652636i
$103$	10.5882	−	10.5882i	1.04328	−	1.04328i	0.0442642	−	0.999020i	$-0.485906\pi$
$103$	10.5882	−	10.5882i	1.04328	−	1.04328i	0.999020	−	0.0442642i	$-0.0140943\pi$
$104$			2.34789i			0.230229i
$105$	0.237674	+	0.303838i	0.0231946	+	0.0296515i
$106$			2.47118i			0.240022i
$107$	−4.62754	+	4.62754i	−0.447361	+	0.447361i	−0.894476	−	0.447115i	$-0.852451\pi$
$107$	−4.62754	+	4.62754i	−0.447361	+	0.447361i	0.447115	+	0.894476i	$0.352451\pi$
$108$	0.433393	−	0.433393i	0.0417033	−	0.0417033i
$109$	−11.9298			−1.14267			−0.571333	−	0.820718i	$-0.693574\pi$
$109$	−11.9298			−1.14267			−0.571333	+	0.820718i	$0.693574\pi$
$110$		0			0
$111$	−0.341950			−0.0324565
$112$	−8.25731	+	8.25731i	−0.780242	+	0.780242i
$113$	3.72598	−	3.72598i	0.350510	−	0.350510i	−0.509789	−	0.860299i	$-0.670277\pi$
$113$	3.72598	−	3.72598i	0.350510	−	0.350510i	0.860299	+	0.509789i	$0.170277\pi$
$114$		−	0.0859434i		−	0.00804933i
$115$	−1.01625	+	8.31740i	−0.0947656	+	0.775601i
$116$			11.2877i			1.04804i
$117$	−4.78356	+	4.78356i	−0.442241	+	0.442241i
$118$	0.769345	+	0.769345i	0.0708240	+	0.0708240i
$119$		−	21.6651i		−	1.98604i
$120$	−0.0970169	+	0.0758905i	−0.00885639	+	0.00692783i
$121$		0			0
$122$	−0.332862	−	0.332862i	−0.0301359	−	0.0301359i
$123$	0.0675738	+	0.0675738i	0.00609293	+	0.00609293i
$124$			7.50892i			0.674321i
$125$	−4.56560	−	10.2057i	−0.408359	−	0.912821i
$126$	2.58450			0.230245
$127$	−11.8023	+	11.8023i	−1.04728	+	1.04728i	−0.0484591	+	0.998825i	$0.515431\pi$
$127$	−11.8023	+	11.8023i	−1.04728	+	1.04728i	−0.998825	+	0.0484591i	$0.984569\pi$
$128$	−5.47573	−	5.47573i	−0.483990	−	0.483990i
$129$	−0.115580			−0.0101762
$130$	1.05222	−	0.823091i	0.0922861	−	0.0721899i
$131$			15.1204i			1.32107i	0.750793	+	0.660537i	$0.229671\pi$
$131$			15.1204i			1.32107i	−0.750793	+	0.660537i	$0.770329\pi$
$132$		0			0
$133$	−14.1245	+	14.1245i	−1.22475	+	1.22475i
$134$	−3.25177			−0.280910
$135$	−0.704889	−	0.0861257i	−0.0606672	−	0.00741252i
$136$	6.91778			0.593194
$137$	−0.358695	−	0.358695i	−0.0306453	−	0.0306453i	0.691618	−	0.722263i	$-0.256898\pi$
$137$	−0.358695	−	0.358695i	−0.0306453	−	0.0306453i	−0.722263	+	0.691618i	$0.756898\pi$
$138$	−0.0371408	−	0.0371408i	−0.00316163	−	0.00316163i
$139$	−3.32412			−0.281948			−0.140974	−	0.990013i	$-0.545023\pi$
$139$	−3.32412			−0.281948			−0.140974	+	0.990013i	$0.545023\pi$
$140$	13.9550	+	1.70507i	1.17942	+	0.144105i
$141$	−0.186051			−0.0156684
$142$	1.29137	−	1.29137i	0.108369	−	0.108369i
$143$		0			0
$144$		−	10.7436i		−	0.895297i
$145$	10.3010	−	8.05782i	0.855448	−	0.669166i
$146$	−2.24389			−0.185706
$147$	0.135290	+	0.135290i	0.0111585	+	0.0111585i
$148$	−8.81223	+	8.81223i	−0.724361	+	0.724361i
$149$	−11.1923			−0.916907			−0.458454	−	0.888718i	$-0.651596\pi$
$149$	−11.1923			−0.916907			−0.458454	+	0.888718i	$0.651596\pi$
$150$	0.0680218	+	0.0168742i	0.00555395	+	0.00137777i
$151$		−	13.5121i		−	1.09960i	−0.835297	−	0.549799i	$-0.814704\pi$
$151$		−	13.5121i		−	1.09960i	0.835297	−	0.549799i	$-0.185296\pi$
$152$	−4.51001	−	4.51001i	−0.365810	−	0.365810i
$153$	14.0942	+	14.0942i	1.13945	+	1.13945i
$154$		0			0
$155$	6.85252	−	5.36031i	0.550407	−	0.430551i
$156$		−	0.230675i		−	0.0184688i
$157$	6.10174	+	6.10174i	0.486972	+	0.486972i	0.907349	−	0.420378i	$-0.138102\pi$
$157$	6.10174	+	6.10174i	0.486972	+	0.486972i	−0.420378	+	0.907349i	$0.638102\pi$
$158$	−2.28687	+	2.28687i	−0.181934	+	0.181934i
$159$		−	0.494390i		−	0.0392077i
$160$	−0.821511	+	6.72359i	−0.0649461	+	0.531547i
$161$			12.2079i			0.962116i
$162$	−1.67977	+	1.67977i	−0.131975	+	0.131975i
$163$	−5.86260	+	5.86260i	−0.459194	+	0.459194i	−0.898391	−	0.439197i	$-0.855263\pi$
$163$	−5.86260	+	5.86260i	−0.459194	+	0.459194i	0.439197	+	0.898391i	$0.355263\pi$
$164$	3.48282			0.271963
$165$		0			0
$166$	−2.78708			−0.216319
$167$	−15.9653	+	15.9653i	−1.23543	+	1.23543i	−0.273584	+	0.961848i	$0.588209\pi$
$167$	−15.9653	+	15.9653i	−1.23543	+	1.23543i	−0.961848	+	0.273584i	$0.911791\pi$
$168$	−0.126893	+	0.126893i	−0.00978999	+	0.00978999i
$169$		−	7.90549i		−	0.608114i
$170$	−2.42514	−	3.10025i	−0.186000	−	0.237778i
$171$		−	18.3773i		−	1.40535i
$172$	−2.97855	+	2.97855i	−0.227113	+	0.227113i
$173$	10.8782	+	10.8782i	0.827055	+	0.827055i	0.987108	−	0.160053i	$-0.0511666\pi$
$173$	10.8782	+	10.8782i	0.827055	+	0.827055i	−0.160053	+	0.987108i	$0.551167\pi$
$174$			0.0819799i			0.00621488i
$175$	−8.40591	−	13.9523i	−0.635427	−	1.05470i
$176$		0			0
$177$	−0.153917	−	0.153917i	−0.0115691	−	0.0115691i
$178$	−0.423220	−	0.423220i	−0.0317217	−	0.0317217i
$179$			12.8624i			0.961379i	0.876891	+	0.480690i	$0.159614\pi$
$179$			12.8624i			0.961379i	−0.876891	+	0.480690i	$0.840386\pi$
$180$	−10.1877	+	7.96920i	−0.759344	+	0.593989i
$181$	0.268586			0.0199638			0.00998192	−	0.999950i	$-0.496823\pi$
$181$	0.268586			0.0199638			0.00998192	+	0.999950i	$0.496823\pi$
$182$	1.37625	−	1.37625i	0.102014	−	0.102014i
$183$	0.0665930	+	0.0665930i	0.00492270	+	0.00492270i
$184$	−3.89804			−0.287367
$185$	14.3326	+	1.75120i	1.05375	+	0.128751i
$186$			0.0545356i			0.00399874i
$187$		0			0
$188$	−4.79464	+	4.79464i	−0.349685	+	0.349685i
$189$	−1.03460			−0.0752563
$190$	−0.440135	+	3.60225i	−0.0319308	+	0.261335i
$191$	−7.33061			−0.530424			−0.265212	−	0.964190i	$-0.585442\pi$
$191$	−7.33061			−0.530424			−0.265212	+	0.964190i	$0.585442\pi$
$192$	0.238420	+	0.238420i	0.0172065	+	0.0172065i
$193$	0.000759883	0	0.000759883i	5.46975e−5	0	5.46975e-5i	0.707134	−	0.707079i	$-0.249988\pi$
$193$	0.000759883	0	0.000759883i	5.46975e−5	0	5.46975e-5i	−0.707079	+	0.707134i	$0.749988\pi$
$194$	−1.78014			−0.127806
$195$	−0.210510	+	0.164669i	−0.0150749	+	0.0117922i
$196$	6.97297			0.498069
$197$	5.88080	−	5.88080i	0.418990	−	0.418990i	−0.465866	−	0.884855i	$-0.654257\pi$
$197$	5.88080	−	5.88080i	0.418990	−	0.418990i	0.884855	+	0.465866i	$0.154257\pi$
$198$		0			0
$199$		−	13.4368i		−	0.952507i	−0.879308	−	0.476254i	$-0.841994\pi$
$199$		−	13.4368i		−	0.952507i	0.879308	−	0.476254i	$-0.158006\pi$
$200$	4.45505	−	2.68405i	0.315019	−	0.189791i
$201$	0.650557			0.0458867
$202$	−1.96538	−	1.96538i	−0.138284	−	0.138284i
$203$	13.4731	−	13.4731i	0.945625	−	0.945625i
$204$	−0.679656			−0.0475854
$205$	−2.48625	−	3.17837i	−0.173647	−	0.221987i
$206$		−	3.96348i		−	0.276149i
$207$	−7.94182	−	7.94182i	−0.551995	−	0.551995i
$208$	−5.72097	−	5.72097i	−0.396678	−	0.396678i
$209$		0			0
$210$	0.101352	+	0.0123836i	0.00699397	+	0.000854546i
$211$		−	9.22449i		−	0.635040i	−0.948252	−	0.317520i	$-0.897150\pi$
$211$		−	9.22449i		−	0.635040i	0.948252	−	0.317520i	$-0.102850\pi$
$212$	−12.7407	−	12.7407i	−0.875034	−	0.875034i
$213$	−0.258354	+	0.258354i	−0.0177021	+	0.0177021i
$214$			1.73223i			0.118413i
$215$	4.84445	+	0.591911i	0.330389	+	0.0403680i
$216$		−	0.330354i		−	0.0224778i
$217$	8.96271	−	8.96271i	0.608428	−	0.608428i
$218$	−2.23284	+	2.23284i	−0.151227	+	0.151227i
$219$	0.448917			0.0303350
$220$		0			0
$221$	15.0104			1.00971
$222$	−0.0640012	+	0.0640012i	−0.00429548	+	0.00429548i
$223$	9.12885	−	9.12885i	0.611313	−	0.611313i	−0.331975	−	0.943288i	$-0.607715\pi$
$223$	9.12885	−	9.12885i	0.611313	−	0.611313i	0.943288	+	0.331975i	$0.107715\pi$
$224$			9.86857i			0.659372i
$225$	14.5451	+	3.60821i	0.969674	+	0.240547i
$226$		−	1.39475i		−	0.0927772i
$227$	20.8709	−	20.8709i	1.38525	−	1.38525i	0.550249	−	0.835000i	$-0.314533\pi$
$227$	20.8709	−	20.8709i	1.38525	−	1.38525i	0.835000	−	0.550249i	$-0.185467\pi$
$228$	0.443099	+	0.443099i	0.0293449	+	0.0293449i
$229$			14.7965i			0.977781i	0.872345	+	0.488891i	$0.162598\pi$
$229$			14.7965i			0.977781i	−0.872345	+	0.488891i	$0.837402\pi$
$230$	1.36652	+	1.74693i	0.0901058	+	0.115189i
$231$		0			0
$232$	4.30202	+	4.30202i	0.282442	+	0.282442i
$233$	11.5258	+	11.5258i	0.755083	+	0.755083i	0.975423	−	0.220340i	$-0.0707168\pi$
$233$	11.5258	+	11.5258i	0.755083	+	0.755083i	−0.220340	+	0.975423i	$0.570717\pi$
$234$			1.79063i			0.117057i
$235$	7.79821	+	0.952812i	0.508699	+	0.0621546i
$236$	−7.93303			−0.516396
$237$	0.457517	−	0.457517i	0.0297189	−	0.0297189i
$238$	−4.05495	−	4.05495i	−0.262844	−	0.262844i
$239$	−22.7329			−1.47047			−0.735235	−	0.677812i	$-0.762928\pi$
$239$	−22.7329			−1.47047			−0.735235	+	0.677812i	$0.762928\pi$
$240$	0.0514775	−	0.421314i	0.00332286	−	0.0271957i
$241$		−	11.6441i		−	0.750060i	−0.927013	−	0.375030i	$-0.877632\pi$
$241$		−	11.6441i		−	0.750060i	0.927013	−	0.375030i	$-0.122368\pi$
$242$		0			0
$243$	1.00975	−	1.00975i	0.0647753	−	0.0647753i
$244$	3.43227			0.219729
$245$	−4.97772	−	6.36342i	−0.318015	−	0.406544i
$246$	0.0252950			0.00161275
$247$	−9.78595	−	9.78595i	−0.622665	−	0.622665i
$248$	2.86184	+	2.86184i	0.181727	+	0.181727i
$249$	0.557589			0.0353358
$250$	−2.76467	−	1.05562i	−0.174853	−	0.0667635i
$251$	−14.5151			−0.916184			−0.458092	−	0.888905i	$-0.651467\pi$
$251$	−14.5151			−0.916184			−0.458092	+	0.888905i	$0.651467\pi$
$252$	−13.3249	+	13.3249i	−0.839389	+	0.839389i
$253$		0			0
$254$			4.41796i			0.277208i
$255$	0.485179	+	0.620243i	0.0303831	+	0.0388411i
$256$	10.6848			0.667799
$257$	11.8625	+	11.8625i	0.739962	+	0.739962i	0.972570	−	0.232608i	$-0.0747261\pi$
$257$	11.8625	+	11.8625i	0.739962	+	0.739962i	−0.232608	+	0.972570i	$0.574726\pi$
$258$	−0.0216326	+	0.0216326i	−0.00134678	+	0.00134678i
$259$	21.0367			1.30716
$260$	−1.18134	+	9.66856i	−0.0732635	+	0.599619i
$261$			17.5298i			1.08507i
$262$	2.83001	+	2.83001i	0.174839	+	0.174839i
$263$	−3.67297	−	3.67297i	−0.226485	−	0.226485i	0.584738	−	0.811223i	$-0.301198\pi$
$263$	−3.67297	−	3.67297i	−0.226485	−	0.226485i	−0.811223	+	0.584738i	$0.801198\pi$
$264$		0			0
$265$	−2.53188	+	20.7220i	−0.155532	+	1.27294i
$266$			5.28722i			0.324180i
$267$	0.0846703	+	0.0846703i	0.00518174	+	0.00518174i
$268$	16.7652	−	16.7652i	1.02410	−	1.02410i
$269$			12.0235i			0.733085i	0.930401	+	0.366542i	$0.119459\pi$
$269$			12.0235i			0.733085i	−0.930401	+	0.366542i	$0.880541\pi$
$270$	−0.148051	+	0.115811i	−0.00901007	+	0.00704804i
$271$		−	16.8789i		−	1.02532i	−0.858592	−	0.512660i	$-0.828660\pi$
$271$		−	16.8789i		−	1.02532i	0.858592	−	0.512660i	$-0.171340\pi$
$272$	−16.8562	+	16.8562i	−1.02205	+	1.02205i
$273$	−0.275335	+	0.275335i	−0.0166640	+	0.0166640i
$274$	−0.134270			−0.00811157
$275$		0			0
$276$	0.382974			0.0230523
$277$	13.9456	−	13.9456i	0.837911	−	0.837911i	−0.150672	−	0.988584i	$-0.548144\pi$
$277$	13.9456	−	13.9456i	0.837911	−	0.837911i	0.988584	+	0.150672i	$0.0481439\pi$
$278$	−0.622160	+	0.622160i	−0.0373147	+	0.0373147i
$279$			11.6614i			0.698147i
$280$	5.96846	−	4.66877i	0.356684	−	0.279012i
$281$			4.29512i			0.256225i	0.991760	+	0.128113i	$0.0408919\pi$
$281$			4.29512i			0.256225i	−0.991760	+	0.128113i	$0.959108\pi$
$282$	−0.0348224	+	0.0348224i	−0.00207364	+	0.00207364i
$283$	−4.26123	−	4.26123i	−0.253304	−	0.253304i	0.569020	−	0.822324i	$-0.307323\pi$
$283$	−4.26123	−	4.26123i	−0.253304	−	0.253304i	−0.822324	+	0.569020i	$0.807323\pi$
$284$			13.3158i			0.790149i
$285$	0.0880544	−	0.720675i	0.00521589	−	0.0426891i
$286$		0			0
$287$	−4.15713	−	4.15713i	−0.245387	−	0.245387i
$288$	−6.41999	−	6.41999i	−0.378301	−	0.378301i
$289$		−	27.2263i		−	1.60155i
$290$	0.419838	−	3.43613i	0.0246537	−	0.201776i
$291$	0.356138			0.0208772
$292$	11.5688	−	11.5688i	0.677014	−	0.677014i
$293$	8.61695	+	8.61695i	0.503408	+	0.503408i	0.912495	−	0.409088i	$-0.134153\pi$
$293$	8.61695	+	8.61695i	0.503408	+	0.503408i	−0.409088	+	0.912495i	$0.634153\pi$
$294$	0.0506431			0.00295356
$295$	5.66307	+	7.23955i	0.329717	+	0.421503i
$296$			6.71713i			0.390425i
$297$		0			0
$298$	−2.09481	+	2.09481i	−0.121349	+	0.121349i
$299$	−8.45807			−0.489143
$300$	−0.437698	+	0.263702i	−0.0252705	+	0.0152248i
$301$	7.11045			0.409840
$302$	−2.52900	−	2.52900i	−0.145527	−	0.145527i
$303$	0.393198	+	0.393198i	0.0225887	+	0.0225887i
$304$	21.9786			1.26056
$305$	−2.45016	−	3.13224i	−0.140296	−	0.179351i
$306$	5.27589			0.301603
$307$	0.302114	−	0.302114i	0.0172426	−	0.0172426i	−0.698433	−	0.715676i	$-0.746119\pi$
$307$	0.302114	−	0.302114i	0.0172426	−	0.0172426i	0.715676	+	0.698433i	$0.246119\pi$
$308$		0			0
$309$			0.792942i			0.0451089i
$310$	0.279289	−	2.28582i	0.0158626	−	0.129826i
$311$	−25.7587			−1.46064			−0.730320	−	0.683106i	$-0.760629\pi$
$311$	−25.7587			−1.46064			−0.730320	+	0.683106i	$0.760629\pi$
$312$	−0.0879160	−	0.0879160i	−0.00497726	−	0.00497726i
$313$	−12.4360	+	12.4360i	−0.702925	+	0.702925i	−0.965037	−	0.262113i	$-0.915581\pi$
$313$	−12.4360	+	12.4360i	−0.702925	+	0.702925i	0.262113	+	0.965037i	$0.415581\pi$
$314$	2.28407			0.128897
$315$	21.6722	+	2.64798i	1.22109	+	0.149197i
$316$		−	23.5809i		−	1.32653i
$317$	20.9085	+	20.9085i	1.17434	+	1.17434i	0.981165	+	0.193173i	$0.0618778\pi$
$317$	20.9085	+	20.9085i	1.17434	+	1.17434i	0.193173	+	0.981165i	$0.438122\pi$
$318$	−0.0925327	−	0.0925327i	−0.00518897	−	0.00518897i
$319$		0			0
$320$	−8.77220	−	11.2142i	−0.490381	−	0.626893i
$321$		−	0.346554i		−	0.0193428i
$322$	2.28489	+	2.28489i	0.127332	+	0.127332i
$323$	−28.8331	+	28.8331i	−1.60432	+	1.60432i
$324$		−	17.3208i		−	0.962264i
$325$	9.66668	−	5.82393i	0.536211	−	0.323053i
$326$			2.19455i			0.121545i
$327$	0.446707	−	0.446707i	0.0247030	−	0.0247030i
$328$	1.32739	−	1.32739i	0.0732930	−	0.0732930i
$329$	11.4458			0.631030
$330$		0			0
$331$	−5.67704			−0.312038			−0.156019	−	0.987754i	$-0.549866\pi$
$331$	−5.67704			−0.312038			−0.156019	+	0.987754i	$0.549866\pi$
$332$	14.3694	−	14.3694i	0.788621	−	0.788621i
$333$	−13.6854	+	13.6854i	−0.749956	+	0.749956i
$334$			5.97630i			0.327009i
$335$	−27.2676	−	3.33165i	−1.48979	−	0.182027i
$336$		−	0.618385i		−	0.0337356i
$337$	−10.4342	+	10.4342i	−0.568387	+	0.568387i	−0.931676	−	0.363289i	$-0.881654\pi$
$337$	−10.4342	+	10.4342i	−0.568387	+	0.568387i	0.363289	+	0.931676i	$0.381654\pi$
$338$	−1.47963	−	1.47963i	−0.0804814	−	0.0804814i
$339$			0.279036i			0.0151552i
$340$	28.4873	+	3.48067i	1.54494	+	0.188766i
$341$		0			0
$342$	−3.43959	−	3.43959i	−0.185992	−	0.185992i
$343$	7.80214	+	7.80214i	0.421276	+	0.421276i
$344$			2.27040i			0.122412i
$345$	−0.273389	−	0.349495i	−0.0147188	−	0.0188162i
$346$	4.07205			0.218915
$347$	11.9372	−	11.9372i	0.640824	−	0.640824i	−0.309934	−	0.950758i	$-0.600307\pi$
$347$	11.9372	−	11.9372i	0.640824	−	0.640824i	0.950758	+	0.309934i	$0.100307\pi$
$348$	−0.422664	−	0.422664i	−0.0226572	−	0.0226572i
$349$	9.74244			0.521501			0.260750	−	0.965406i	$-0.416030\pi$
$349$	9.74244			0.521501			0.260750	+	0.965406i	$0.416030\pi$
$350$	−4.18468	−	1.03810i	−0.223681	−	0.0554885i
$351$		−	0.716811i		−	0.0382606i
$352$		0			0
$353$	7.02356	−	7.02356i	0.373826	−	0.373826i	−0.495042	−	0.868869i	$-0.664847\pi$
$353$	7.02356	−	7.02356i	0.373826	−	0.373826i	0.868869	+	0.495042i	$0.164847\pi$
$354$	−0.0576158			−0.00306224
$355$	12.1518	−	9.50563i	0.644951	−	0.504506i
$356$	4.36400			0.231291
$357$	0.811243	+	0.811243i	0.0429355	+	0.0429355i
$358$	2.40739	+	2.40739i	0.127235	+	0.127235i
$359$	15.2865			0.806791			0.403396	−	0.915026i	$-0.367830\pi$
$359$	15.2865			0.806791			0.403396	+	0.915026i	$0.367830\pi$
$360$	−0.845514	+	6.92004i	−0.0445625	+	0.364718i
$361$	18.5953			0.978699
$362$	0.0502700	−	0.0502700i	0.00264213	−	0.00264213i
$363$		0			0
$364$			14.1911i			0.743814i
$365$	−18.8160	−	2.29901i	−0.984876	−	0.120335i
$366$	0.0249278			0.00130300
$367$	14.5461	+	14.5461i	0.759302	+	0.759302i	0.976195	−	0.216893i	$-0.0695923\pi$
$367$	14.5461	+	14.5461i	0.759302	+	0.759302i	−0.216893	+	0.976195i	$0.569592\pi$
$368$	9.49814	−	9.49814i	0.495125	−	0.495125i
$369$	5.40883			0.281572
$370$	3.01033	−	2.35480i	0.156500	−	0.122420i
$371$			30.4148i			1.57906i
$372$	−0.281169	−	0.281169i	−0.0145779	−	0.0145779i
$373$	−1.82945	−	1.82945i	−0.0947252	−	0.0947252i	0.658156	−	0.752881i	$-0.271337\pi$
$373$	−1.82945	−	1.82945i	−0.0947252	−	0.0947252i	−0.752881	+	0.658156i	$0.771337\pi$
$374$		0			0
$375$	0.553105	+	0.211190i	0.0285622	+	0.0109058i
$376$			3.65472i			0.188478i
$377$	9.33465	+	9.33465i	0.480759	+	0.480759i
$378$	−0.193642	+	0.193642i	−0.00995986	+	0.00995986i
$379$		−	16.1712i		−	0.830661i	−0.909671	−	0.415330i	$-0.863666\pi$
$379$		−	16.1712i		−	0.830661i	0.909671	−	0.415330i	$-0.136334\pi$
$380$	−16.3029	−	20.8414i	−0.836323	−	1.06914i
$381$		−	0.883867i		−	0.0452819i
$382$	−1.37204	+	1.37204i	−0.0701995	+	0.0701995i
$383$	−4.37584	+	4.37584i	−0.223595	+	0.223595i	−0.810010	−	0.586416i	$-0.800539\pi$
$383$	−4.37584	+	4.37584i	−0.223595	+	0.223595i	0.586416	+	0.810010i	$0.300539\pi$
$384$	0.410074			0.0209265
$385$		0			0
$386$	0.000284447	0		1.44780e−5	0
$387$	−4.62570	+	4.62570i	−0.235137	+	0.235137i
$388$	9.17786	−	9.17786i	0.465935	−	0.465935i
$389$		−	25.2235i		−	1.27888i	−0.768841	−	0.639441i	$-0.779166\pi$
$389$		−	25.2235i		−	1.27888i	0.768841	−	0.639441i	$-0.220834\pi$
$390$	−0.00857979	+	0.0702206i	−0.000434454	+	0.00355576i
$391$			24.9207i			1.26029i
$392$	2.65757	−	2.65757i	0.134228	−	0.134228i
$393$	−0.566178	−	0.566178i	−0.0285599	−	0.0285599i
$394$		−	2.20136i		−	0.110903i
$395$	−21.5195	+	16.8334i	−1.08276	+	0.846982i
$396$		0			0
$397$	2.91014	+	2.91014i	0.146056	+	0.146056i	0.776354	−	0.630298i	$-0.217067\pi$
$397$	2.91014	+	2.91014i	0.146056	+	0.146056i	−0.630298	+	0.776354i	$0.717067\pi$
$398$	−2.51490	−	2.51490i	−0.126060	−	0.126060i
$399$		−	1.05777i		−	0.0529548i
$400$	−4.31529	+	17.3954i	−0.215764	+	0.869772i
$401$	7.72333			0.385685			0.192842	−	0.981230i	$-0.438229\pi$
$401$	7.72333			0.385685			0.192842	+	0.981230i	$0.438229\pi$
$402$	0.121762	−	0.121762i	0.00607292	−	0.00607292i
$403$	6.20970	+	6.20970i	0.309327	+	0.309327i
$404$	20.2658			1.00826
$405$	−15.8066	+	12.3646i	−0.785438	+	0.614401i
$406$		−	5.04339i		−	0.250299i
$407$		0			0
$408$	−0.259034	+	0.259034i	−0.0128241	+	0.0128241i
$409$	28.5106			1.40976			0.704878	−	0.709328i	$-0.251002\pi$
$409$	28.5106			1.40976			0.704878	+	0.709328i	$0.251002\pi$
$410$	−1.06022	−	0.129541i	−0.0523605	−	0.00639758i
$411$	0.0268624			0.00132503
$412$	20.4345	+	20.4345i	1.00674	+	1.00674i
$413$	9.46893	+	9.46893i	0.465936	+	0.465936i
$414$	−2.97287			−0.146109
$415$	−23.3709	−	2.85554i	−1.14723	−	0.140173i
$416$	−6.83731			−0.335227
$417$	0.124471	−	0.124471i	0.00609536	−	0.00609536i
$418$		0			0
$419$			9.74320i			0.475987i	0.971267	+	0.237993i	$0.0764896\pi$
$419$			9.74320i			0.475987i	−0.971267	+	0.237993i	$0.923510\pi$
$420$	−0.586388	+	0.458696i	−0.0286128	+	0.0223821i
$421$	−13.6713			−0.666298			−0.333149	−	0.942874i	$-0.608111\pi$
$421$	−13.6713			−0.666298			−0.333149	+	0.942874i	$0.608111\pi$
$422$	−1.72650	−	1.72650i	−0.0840449	−	0.0840449i
$423$	−7.44608	+	7.44608i	−0.362041	+	0.362041i
$424$	−9.71159			−0.471637
$425$	−17.1595	−	28.4817i	−0.832358	−	1.38157i
$426$			0.0967098i			0.00468560i
$427$	−4.09679	−	4.09679i	−0.198258	−	0.198258i
$428$	−8.93087	−	8.93087i	−0.431690	−	0.431690i
$429$		0			0
$430$	1.01750	−	0.795928i	0.0490681	−	0.0383830i
$431$			12.6946i			0.611477i	0.952116	+	0.305739i	$0.0989033\pi$
$431$			12.6946i			0.611477i	−0.952116	+	0.305739i	$0.901097\pi$
$432$	0.804955	+	0.804955i	0.0387284	+	0.0387284i
$433$	1.63920	−	1.63920i	0.0787751	−	0.0787751i	−0.666621	−	0.745396i	$-0.732260\pi$
$433$	1.63920	−	1.63920i	0.0787751	−	0.0787751i	0.745396	+	0.666621i	$0.232260\pi$
$434$		−	3.35502i		−	0.161046i
$435$	−0.0839936	+	0.687439i	−0.00402718	+	0.0329602i
$436$		−	23.0238i		−	1.10264i
$437$	16.2469	−	16.2469i	0.777197	−	0.777197i
$438$	0.0840217	−	0.0840217i	0.00401471	−	0.00401471i
$439$	−7.56372			−0.360997			−0.180498	−	0.983575i	$-0.557771\pi$
$439$	−7.56372			−0.360997			−0.180498	+	0.983575i	$0.557771\pi$
$440$		0			0
$441$	10.8290			0.515668
$442$	2.80942	−	2.80942i	0.133631	−	0.133631i
$443$	−8.75791	+	8.75791i	−0.416101	+	0.416101i	−0.883857	−	0.467757i	$-0.845062\pi$
$443$	−8.75791	+	8.75791i	−0.416101	+	0.416101i	0.467757	+	0.883857i	$0.345062\pi$
$444$		−	0.659943i		−	0.0313195i
$445$	−3.11528	−	3.98251i	−0.147678	−	0.188789i
$446$		−	3.41721i		−	0.161810i
$447$	0.419091	−	0.419091i	0.0198223	−	0.0198223i
$448$	−14.6676	−	14.6676i	−0.692977	−	0.692977i
$449$		−	9.40593i		−	0.443893i	−0.975059	−	0.221947i	$-0.928759\pi$
$449$		−	9.40593i		−	0.443893i	0.975059	−	0.221947i	$-0.0712411\pi$
$450$	3.39767	−	2.04701i	0.160168	−	0.0964970i
$451$		0			0
$452$	7.19091	+	7.19091i	0.338232	+	0.338232i
$453$	0.505956	+	0.505956i	0.0237719	+	0.0237719i
$454$		−	7.81262i		−	0.366664i
$455$	12.9505	−	10.1304i	0.607130	−	0.474922i
$456$	0.337752			0.0158167
$457$	−18.3841	+	18.3841i	−0.859972	+	0.859972i	−0.991334	−	0.131362i	$-0.958065\pi$
$457$	−18.3841	+	18.3841i	−0.859972	+	0.859972i	0.131362	+	0.991334i	$0.458065\pi$
$458$	2.76939	+	2.76939i	0.129405	+	0.129405i
$459$	−2.11200			−0.0985797
$460$	−16.0521	−	1.96129i	−0.748431	−	0.0914458i
$461$		−	3.81135i		−	0.177512i	−0.996053	−	0.0887562i	$-0.971711\pi$
$461$		−	3.81135i		−	0.177512i	0.996053	−	0.0887562i	$-0.0282892\pi$
$462$		0			0
$463$	27.4064	−	27.4064i	1.27368	−	1.27368i	0.329544	−	0.944140i	$-0.393105\pi$
$463$	27.4064	−	27.4064i	1.27368	−	1.27368i	0.944140	−	0.329544i	$-0.106895\pi$
$464$	−20.9650			−0.973276
$465$	−0.0558752	+	0.457306i	−0.00259115	+	0.0212070i
$466$	4.31447			0.199864
$467$	15.1325	+	15.1325i	0.700247	+	0.700247i	0.964463	−	0.264217i	$-0.0851134\pi$
$467$	15.1325	+	15.1325i	0.700247	+	0.700247i	−0.264217	+	0.964463i	$0.585113\pi$
$468$	−9.23198	−	9.23198i	−0.426748	−	0.426748i
$469$	−40.0221			−1.84805
$470$	1.63789	−	1.28122i	0.0755502	−	0.0590984i
$471$	−0.456955			−0.0210554
$472$	−3.02348	+	3.02348i	−0.139167	+	0.139167i
$473$		0			0
$474$		−	0.171263i		−	0.00786635i
$475$	−7.38147	+	29.7556i	−0.338685	+	1.36528i
$476$	41.8123			1.91646
$477$	−19.7863	−	19.7863i	−0.905952	−	0.905952i
$478$	−4.25482	+	4.25482i	−0.194611	+	0.194611i
$479$	0.644676			0.0294560			0.0147280	−	0.999892i	$-0.495312\pi$
$479$	0.644676			0.0294560			0.0147280	+	0.999892i	$0.495312\pi$
$480$	−0.221002	−	0.282524i	−0.0100873	−	0.0128954i
$481$			14.5750i			0.664563i
$482$	−2.17936	−	2.17936i	−0.0992673	−	0.0992673i
$483$	−0.457120	−	0.457120i	−0.0207997	−	0.0207997i
$484$		0			0
$485$	−14.9273	−	1.82386i	−0.677812	−	0.0828173i
$486$		−	0.377979i		−	0.0171455i
$487$	4.91729	+	4.91729i	0.222824	+	0.222824i	0.809686	−	0.586863i	$-0.199637\pi$
$487$	4.91729	+	4.91729i	0.222824	+	0.222824i	−0.586863	+	0.809686i	$0.699637\pi$
$488$	1.30813	−	1.30813i	0.0592161	−	0.0592161i
$489$		−	0.439046i		−	0.0198544i
$490$	−2.12267	−	0.259355i	−0.0958923	−	0.0117164i
$491$			35.5587i			1.60474i	0.596827	+	0.802370i	$0.296428\pi$
$491$			35.5587i			1.60474i	−0.596827	+	0.802370i	$0.703572\pi$
$492$	−0.130413	+	0.130413i	−0.00587949	+	0.00587949i
$493$	27.5034	−	27.5034i	1.23869	−	1.23869i
$494$	−3.66318			−0.164814
$495$		0			0
$496$	−13.9466			−0.626219
$497$	15.8939	−	15.8939i	0.712938	−	0.712938i
$498$	0.104361	−	0.104361i	0.00467655	−	0.00467655i
$499$		−	9.24658i		−	0.413934i	−0.978348	−	0.206967i	$-0.933641\pi$
$499$		−	9.24658i		−	0.413934i	0.978348	−	0.206967i	$-0.0663592\pi$
$500$	19.6963	−	8.81132i	0.880844	−	0.394054i
$501$		−	1.19563i		−	0.0534169i
$502$	−2.71672	+	2.71672i	−0.121253	+	0.121253i
$503$	−8.80203	−	8.80203i	−0.392463	−	0.392463i	0.483101	−	0.875564i	$-0.339510\pi$
$503$	−8.80203	−	8.80203i	−0.392463	−	0.392463i	−0.875564	+	0.483101i	$0.839510\pi$
$504$			10.1569i			0.452425i
$505$	−14.4670	−	18.4943i	−0.643771	−	0.822985i
$506$		0			0
$507$	0.296019	+	0.296019i	0.0131466	+	0.0131466i
$508$	−22.7777	−	22.7777i	−1.01060	−	1.01060i
$509$		−	1.42477i		−	0.0631518i	−0.999501	−	0.0315759i	$-0.989947\pi$
$509$		−	1.42477i		−	0.0631518i	0.999501	−	0.0315759i	$-0.0100526\pi$
$510$	0.206897	+	0.0252793i	0.00916153	+	0.00111939i
$511$	−27.6173			−1.22172
$512$	12.9513	−	12.9513i	0.572371	−	0.572371i
$513$	1.37691	+	1.37691i	0.0607920	+	0.0607920i
$514$	4.44050			0.195862
$515$	4.06084	−	33.2356i	0.178942	−	1.46454i
$516$		−	0.223062i		−	0.00981976i
$517$		0			0
$518$	3.93734	−	3.93734i	0.172997	−	0.172997i
$519$	−0.814663			−0.0357597
$520$	3.23470	+	4.13517i	0.141851	+	0.181339i
$521$	−22.1751			−0.971510			−0.485755	−	0.874095i	$-0.661455\pi$
$521$	−22.1751			−0.971510			−0.485755	+	0.874095i	$0.661455\pi$
$522$	3.28097	+	3.28097i	0.143604	+	0.143604i
$523$	−1.86141	−	1.86141i	−0.0813939	−	0.0813939i	0.665238	−	0.746632i	$-0.268330\pi$
$523$	−1.86141	−	1.86141i	−0.0813939	−	0.0813939i	−0.746632	+	0.665238i	$0.768330\pi$
$524$	−29.1814			−1.27480
$525$	0.837197	+	0.207683i	0.0365383	+	0.00906405i
$526$	−1.37491			−0.0599487
$527$	18.2961	−	18.2961i	0.796992	−	0.796992i
$528$		0			0
$529$			8.95763i			0.389462i
$530$	3.40456	+	4.35232i	0.147885	+	0.189053i
$531$	−12.3200			−0.534643
$532$	−27.2593	−	27.2593i	−1.18184	−	1.18184i
$533$	2.88021	−	2.88021i	0.124756	−	0.124756i
$534$	0.0316947			0.00137156
$535$	−1.77478	+	14.5256i	−0.0767305	+	0.627994i
$536$		−	12.7793i		−	0.551980i
$537$	−0.481628	−	0.481628i	−0.0207838	−	0.0207838i
$538$	2.25038	+	2.25038i	0.0970208	+	0.0970208i
$539$		0			0
$540$	0.166217	−	1.36039i	0.00715285	−	0.0585420i
$541$			27.5740i			1.18550i	0.805387	+	0.592749i	$0.201957\pi$
$541$			27.5740i			1.18550i	−0.805387	+	0.592749i	$0.798043\pi$
$542$	−3.15915	−	3.15915i	−0.135697	−	0.135697i
$543$	−0.0100571	+	0.0100571i	−0.000431593	+	0.000431593i
$544$			20.1453i			0.863724i
$545$	−21.0111	+	16.4357i	−0.900017	+	0.704029i
$546$			0.103066i			0.00441084i
$547$	16.8024	−	16.8024i	0.718419	−	0.718419i	−0.249862	−	0.968281i	$-0.580385\pi$
$547$	16.8024	−	16.8024i	0.718419	−	0.718419i	0.968281	+	0.249862i	$0.0803854\pi$
$548$	0.692258	−	0.692258i	0.0295718	−	0.0295718i
$549$	5.33032			0.227493
$550$		0			0
$551$	−35.8615			−1.52775
$552$	0.145961	−	0.145961i	0.00621251	−	0.00621251i
$553$	−28.1463	+	28.1463i	−1.19690	+	1.19690i
$554$		−	5.22028i		−	0.221788i
$555$	−0.602253	+	0.471106i	−0.0255642	+	0.0199974i
$556$		−	6.41535i		−	0.272071i
$557$	−2.18756	+	2.18756i	−0.0926898	+	0.0926898i	−0.751931	−	0.659241i	$-0.770878\pi$
$557$	−2.18756	+	2.18756i	−0.0926898	+	0.0926898i	0.659241	+	0.751931i	$0.270878\pi$
$558$	2.18260	+	2.18260i	0.0923969	+	0.0923969i
$559$			4.92639i			0.208364i
$560$	−3.16689	+	25.9191i	−0.133825	+	1.09528i
$561$		0			0
$562$	0.803897	+	0.803897i	0.0339103	+	0.0339103i
$563$	−20.7229	−	20.7229i	−0.873368	−	0.873368i	0.119470	−	0.992838i	$-0.461880\pi$
$563$	−20.7229	−	20.7229i	−0.873368	−	0.873368i	−0.992838	+	0.119470i	$0.961880\pi$
$564$		−	0.359068i		−	0.0151195i
$565$	1.42901	−	11.6956i	0.0601188	−	0.492037i
$566$	−1.59511			−0.0670474
$567$	−20.6742	+	20.6742i	−0.868234	+	0.868234i
$568$	5.07500	+	5.07500i	0.212942	+	0.212942i
$569$	39.6114			1.66060			0.830299	−	0.557319i	$-0.188170\pi$
$569$	39.6114			1.66060			0.830299	+	0.557319i	$0.188170\pi$
$570$	−0.118405	−	0.151366i	−0.00495942	−	0.00634003i
$571$			25.5525i			1.06934i	0.845062	+	0.534669i	$0.179564\pi$
$571$			25.5525i			1.06934i	−0.845062	+	0.534669i	$0.820436\pi$
$572$		0			0
$573$	0.274492	−	0.274492i	0.0114671	−	0.0114671i
$574$	−1.55614			−0.0649521
$575$	9.66907	+	16.0489i	0.403228	+	0.669287i
$576$	19.0839			0.795164
$577$	−20.8808	−	20.8808i	−0.869280	−	0.869280i	0.123112	−	0.992393i	$-0.460712\pi$
$577$	−20.8808	−	20.8808i	−0.869280	−	0.869280i	−0.992393	+	0.123112i	$0.960712\pi$
$578$	−5.09582	−	5.09582i	−0.211958	−	0.211958i
$579$	−5.69071e−5	0		−2.36498e−6	0
$580$	15.5511	+	19.8802i	0.645724	+	0.825481i
$581$	−34.3028			−1.42312
$582$	0.0666567	−	0.0666567i	0.00276301	−	0.00276301i
$583$		0			0
$584$		−	8.81834i		−	0.364906i
$585$	−1.83462	+	15.0153i	−0.0758521	+	0.620806i
$586$	3.22559			0.133248
$587$	13.4272	+	13.4272i	0.554199	+	0.554199i	0.927650	−	0.373451i	$-0.121826\pi$
$587$	13.4272	+	13.4272i	0.554199	+	0.554199i	−0.373451	+	0.927650i	$0.621826\pi$
$588$	−0.261101	+	0.261101i	−0.0107676	+	0.0107676i
$589$	−23.8562			−0.982976
$590$	2.41492	+	0.295063i	0.0994208	+	0.0121476i
$591$			0.440410i			0.0181160i
$592$	−16.3673	−	16.3673i	−0.672690	−	0.672690i
$593$	10.5395	+	10.5395i	0.432805	+	0.432805i	0.889582	−	0.456776i	$-0.150996\pi$
$593$	10.5395	+	10.5395i	0.432805	+	0.432805i	−0.456776	+	0.889582i	$0.650996\pi$
$594$		0			0
$595$	−29.8481	−	38.1572i	−1.22365	−	1.56429i
$596$		−	21.6004i		−	0.884787i
$597$	0.503136	+	0.503136i	0.0205920	+	0.0205920i
$598$	−1.58306	+	1.58306i	−0.0647361	+	0.0647361i
$599$			31.9972i			1.30737i	0.756767	+	0.653685i	$0.226778\pi$
$599$			31.9972i			1.30737i	−0.756767	+	0.653685i	$0.773222\pi$
$600$	−0.0663144	+	0.267321i	−0.00270728	+	0.0109133i
$601$		−	4.08797i		−	0.166752i	−0.996518	−	0.0833758i	$-0.973430\pi$
$601$		−	4.08797i		−	0.166752i	0.996518	−	0.0833758i	$-0.0265702\pi$
$602$	1.33083	−	1.33083i	0.0542406	−	0.0542406i
$603$	26.0363	−	26.0363i	1.06028	−	1.06028i
$604$	26.0775			1.06108
$605$		0			0
$606$	0.147186			0.00597903
$607$	−15.3510	+	15.3510i	−0.623077	+	0.623077i	−0.946317	−	0.323240i	$-0.895228\pi$
$607$	−15.3510	+	15.3510i	−0.623077	+	0.623077i	0.323240	+	0.946317i	$0.395228\pi$
$608$	13.1337	−	13.1337i	0.532640	−	0.532640i
$609$			1.00899i			0.0408864i
$610$	−1.04483	−	0.127661i	−0.0423040	−	0.00516884i
$611$			7.93011i			0.320818i
$612$	−27.2009	+	27.2009i	−1.09953	+	1.09953i
$613$	6.76536	+	6.76536i	0.273250	+	0.273250i	0.830407	−	0.557157i	$-0.188108\pi$
$613$	6.76536	+	6.76536i	0.273250	+	0.273250i	−0.557157	+	0.830407i	$0.688108\pi$
$614$		−	0.113091i		−	0.00456396i
$615$	0.212110	+	0.0259163i	0.00855309	+	0.00104505i
$616$		0			0
$617$	29.1829	+	29.1829i	1.17486	+	1.17486i	0.981037	+	0.193822i	$0.0620885\pi$
$617$	29.1829	+	29.1829i	1.17486	+	1.17486i	0.193822	+	0.981037i	$0.437911\pi$
$618$	0.148411	+	0.148411i	0.00596998	+	0.00596998i
$619$			34.7027i			1.39482i	0.716673	+	0.697409i	$0.245664\pi$
$619$			34.7027i			1.39482i	−0.716673	+	0.697409i	$0.754336\pi$
$620$	10.3451	+	13.2249i	0.415468	+	0.531126i
$621$	1.19007			0.0477560
$622$	−4.82113	+	4.82113i	−0.193310	+	0.193310i
$623$	−5.20890	−	5.20890i	−0.208690	−	0.208690i
$624$	0.428440			0.0171513
$625$	−22.1014	−	11.6845i	−0.884057	−	0.467378i
$626$			4.65518i			0.186058i
$627$		0			0
$628$	−11.7760	+	11.7760i	−0.469912	+	0.469912i
$629$	42.9435			1.71227
$630$	4.55189	−	3.56067i	0.181352	−	0.141861i
$631$	2.16643			0.0862440			0.0431220	−	0.999070i	$-0.486270\pi$
$631$	2.16643			0.0862440			0.0431220	+	0.999070i	$0.486270\pi$
$632$	−8.98727	−	8.98727i	−0.357494	−	0.357494i
$633$	0.345408	+	0.345408i	0.0137287	+	0.0137287i
$634$	7.82669			0.310837
$635$	−4.52648	+	37.0466i	−0.179628	+	1.47015i
$636$	0.954142			0.0378342
$637$	5.76648	−	5.76648i	0.228476	−	0.228476i
$638$		0			0
$639$			20.6795i			0.818068i
$640$	−17.1879	−	2.10008i	−0.679413	−	0.0830130i
$641$	4.23599			0.167312			0.0836558	−	0.996495i	$-0.473340\pi$
$641$	4.23599			0.167312			0.0836558	+	0.996495i	$0.473340\pi$
$642$	−0.0648629	−	0.0648629i	−0.00255993	−	0.00255993i
$643$	25.1437	−	25.1437i	0.991571	−	0.991571i	−0.00839336	−	0.999965i	$-0.502672\pi$
$643$	25.1437	−	25.1437i	0.991571	−	0.991571i	0.999965	+	0.00839336i	$0.00267172\pi$
$644$	−23.5605			−0.928412
$645$	−0.203563	+	0.159235i	−0.00801528	+	0.00626987i
$646$			10.7931i			0.424650i
$647$	8.35283	+	8.35283i	0.328384	+	0.328384i	0.851972	−	0.523588i	$-0.175407\pi$
$647$	8.35283	+	8.35283i	0.328384	+	0.328384i	−0.523588	+	0.851972i	$0.675407\pi$
$648$	−6.60138	−	6.60138i	−0.259327	−	0.259327i
$649$		0			0
$650$	0.719231	−	2.89931i	0.0282106	−	0.113720i
$651$			0.671212i			0.0263069i
$652$	−11.3145	−	11.3145i	−0.443108	−	0.443108i
$653$	−5.21481	+	5.21481i	−0.204071	+	0.204071i	−0.801742	−	0.597670i	$-0.796093\pi$
$653$	−5.21481	+	5.21481i	−0.204071	+	0.204071i	0.597670	+	0.801742i	$0.296093\pi$
$654$		−	0.167216i		−	0.00653867i
$655$	20.8314	+	26.6305i	0.813951	+	1.04054i
$656$			6.46877i			0.252563i
$657$	17.9664	−	17.9664i	0.700936	−	0.700936i
$658$	2.14227	−	2.14227i	0.0835142	−	0.0835142i
$659$	3.33083			0.129751			0.0648753	−	0.997893i	$-0.479335\pi$
$659$	3.33083			0.129751			0.0648753	+	0.997893i	$0.479335\pi$
$660$		0			0
$661$	30.8003			1.19799			0.598997	−	0.800751i	$-0.295566\pi$
$661$	30.8003			1.19799			0.598997	+	0.800751i	$0.295566\pi$
$662$	−1.06255	+	1.06255i	−0.0412970	+	0.0412970i
$663$	−0.562059	+	0.562059i	−0.0218286	+	0.0218286i
$664$		−	10.9531i		−	0.425061i
$665$	−5.41709	+	44.3357i	−0.210066	+	1.71927i
$666$			5.12287i			0.198507i
$667$	−15.4977	+	15.4977i	−0.600073	+	0.600073i
$668$	−30.8121	−	30.8121i	−1.19215	−	1.19215i
$669$			0.683654i			0.0264316i
$670$	−5.72712	+	4.47998i	−0.221258	+	0.173077i
$671$		0			0
$672$	−0.369526	−	0.369526i	−0.0142548	−	0.0142548i
$673$	−31.4399	−	31.4399i	−1.21192	−	1.21192i	−0.970395	−	0.241522i	$-0.922353\pi$
$673$	−31.4399	−	31.4399i	−1.21192	−	1.21192i	−0.241522	−	0.970395i	$-0.577647\pi$
$674$			3.90584i			0.150447i
$675$	−1.36013	+	0.819442i	−0.0523513	+	0.0315403i
$676$	15.2571			0.586812
$677$	2.90042	−	2.90042i	0.111472	−	0.111472i	−0.649171	−	0.760643i	$-0.724884\pi$
$677$	2.90042	−	2.90042i	0.111472	−	0.111472i	0.760643	+	0.649171i	$0.224884\pi$
$678$	0.0522259	+	0.0522259i	0.00200572	+	0.00200572i
$679$	−21.9095			−0.840810
$680$	12.1838	−	9.53065i	0.467227	−	0.365484i
$681$			1.56301i			0.0598946i
$682$		0			0
$683$	31.2485	−	31.2485i	1.19569	−	1.19569i	0.220247	−	0.975444i	$-0.429314\pi$
$683$	31.2485	−	31.2485i	1.19569	−	1.19569i	0.975444	−	0.220247i	$-0.0706862\pi$
$684$	35.4671			1.35612
$685$	−1.12592	−	0.137569i	−0.0430191	−	0.00525622i
$686$	2.92058			0.111508
$687$	−0.554051	−	0.554051i	−0.0211384	−	0.0211384i
$688$	−5.53217	−	5.53217i	−0.210912	−	0.210912i
$689$	−21.0725			−0.802797
$690$	−0.116582	−	0.0142444i	−0.00443822	−	0.000542276i
$691$	−21.7762			−0.828407			−0.414204	−	0.910184i	$-0.635940\pi$
$691$	−21.7762			−0.828407			−0.414204	+	0.910184i	$0.635940\pi$
$692$	−20.9943	+	20.9943i	−0.798083	+	0.798083i
$693$		0			0
$694$		−	4.46847i		−	0.169621i
$695$	−5.85454	+	4.57966i	−0.222075	+	0.173716i
$696$	−0.322176			−0.0122120
$697$	−8.48620	−	8.48620i	−0.321438	−	0.321438i
$698$	1.82345	−	1.82345i	0.0690185	−	0.0690185i
$699$	−0.863163			−0.0326478
$700$	26.9271	−	16.2229i	1.01775	−	0.613167i
$701$		−	33.4409i		−	1.26305i	−0.775357	−	0.631523i	$-0.782430\pi$
$701$		−	33.4409i		−	1.26305i	0.775357	−	0.631523i	$-0.217570\pi$
$702$	−0.134162	−	0.134162i	−0.00506363	−	0.00506363i
$703$	−27.9969	−	27.9969i	−1.05592	−	1.05592i
$704$		0			0
$705$	−0.327679	+	0.256324i	−0.0123411	+	0.00965372i
$706$		−	2.62913i		−	0.0989488i
$707$	−24.1895	−	24.1895i	−0.909739	−	0.909739i
$708$	0.297050	−	0.297050i	0.0111638	−	0.0111638i
$709$			9.05303i			0.339994i	0.985445	+	0.169997i	$0.0543757\pi$
$709$			9.05303i			0.339994i	−0.985445	+	0.169997i	$0.945624\pi$
$710$	0.495273	−	4.05352i	0.0185873	−	0.152126i
$711$		−	36.6211i		−	1.37340i
$712$	1.66323	−	1.66323i	0.0623322	−	0.0623322i
$713$	−10.3095	+	10.3095i	−0.386095	+	0.386095i
$714$	0.303673			0.0113647
$715$		0			0
$716$	−24.8236			−0.927701
$717$	0.851227	−	0.851227i	0.0317897	−	0.0317897i
$718$	2.86111	−	2.86111i	0.106776	−	0.106776i
$719$		−	29.2732i		−	1.09170i	−0.837881	−	0.545852i	$-0.816206\pi$
$719$		−	29.2732i		−	1.09170i	0.837881	−	0.545852i	$-0.183794\pi$
$720$	−14.8015	−	18.9219i	−0.551618	−	0.705177i
$721$		−	48.7816i		−	1.81672i
$722$	3.48039	−	3.48039i	0.129527	−	0.129527i
$723$	0.436008	+	0.436008i	0.0162153	+	0.0162153i
$724$			0.518355i			0.0192645i
$725$	7.04106	−	28.3834i	0.261498	−	1.05413i
$726$		0			0
$727$	−9.16319	−	9.16319i	−0.339844	−	0.339844i	0.516465	−	0.856309i	$-0.327248\pi$
$727$	−9.16319	−	9.16319i	−0.339844	−	0.339844i	−0.856309	+	0.516465i	$0.827248\pi$
$728$	5.40857	+	5.40857i	0.200455	+	0.200455i
$729$		−	26.8487i		−	0.994396i
$730$	−3.95200	+	3.09142i	−0.146270	+	0.114418i
$731$	14.5150			0.536857
$732$	−0.128520	+	0.128520i	−0.00475025	+	0.00475025i
$733$	12.2785	+	12.2785i	0.453516	+	0.453516i	0.896520	−	0.443004i	$-0.146087\pi$
$733$	12.2785	+	12.2785i	0.453516	+	0.453516i	−0.443004	+	0.896520i	$0.646087\pi$
$734$	5.44507			0.200981
$735$	0.424665	+	0.0518870i	0.0156640	+	0.00191388i
$736$		−	11.3515i		−	0.418423i
$737$		0			0
$738$	1.01235	−	1.01235i	0.0372650	−	0.0372650i
$739$	−7.98525			−0.293742			−0.146871	−	0.989156i	$-0.546920\pi$
$739$	−7.98525			−0.293742			−0.146871	+	0.989156i	$0.546920\pi$
$740$	−3.37972	+	27.6610i	−0.124241	+	1.01684i
$741$	0.732864			0.0269224
$742$	5.69259	+	5.69259i	0.208982	+	0.208982i
$743$	2.78133	+	2.78133i	0.102037	+	0.102037i	0.756282	−	0.654245i	$-0.227014\pi$
$743$	2.78133	+	2.78133i	0.102037	+	0.102037i	−0.654245	+	0.756282i	$0.727014\pi$
$744$	−0.214321			−0.00785741
$745$	−19.7122	+	15.4197i	−0.722198	+	0.564932i
$746$	−0.684819			−0.0250730
$747$	22.3156	−	22.3156i	0.816486	−	0.816486i
$748$		0			0
$749$			21.3199i			0.779013i
$750$	0.143050	−	0.0639946i	0.00522343	−	0.00233675i
$751$	20.4344			0.745660			0.372830	−	0.927900i	$-0.378387\pi$
$751$	20.4344			0.745660			0.372830	+	0.927900i	$0.378387\pi$
$752$	−8.90525	−	8.90525i	−0.324741	−	0.324741i
$753$	0.543513	−	0.543513i	0.0198067	−	0.0198067i
$754$	3.49425			0.127253
$755$	−18.6157	−	23.7979i	−0.677494	−	0.866094i
$756$		−	1.99672i		−	0.0726200i
$757$	22.5433	+	22.5433i	0.819350	+	0.819350i	0.986014	−	0.166664i	$-0.0532995\pi$
$757$	22.5433	+	22.5433i	0.819350	+	0.819350i	−0.166664	+	0.986014i	$0.553300\pi$
$758$	−3.02670	−	3.02670i	−0.109935	−	0.109935i
$759$		0			0
$760$	−14.1566	−	1.72971i	−0.513515	−	0.0627430i
$761$			41.2716i			1.49609i	0.663646	+	0.748047i	$0.269008\pi$
$761$			41.2716i			1.49609i	−0.663646	+	0.748047i	$0.730992\pi$
$762$	−0.165429	−	0.165429i	−0.00599287	−	0.00599287i
$763$	−27.4813	+	27.4813i	−0.994891	+	0.994891i
$764$		−	14.1476i		−	0.511843i
$765$	44.2408	+	5.40549i	1.59953	+	0.195436i
$766$			1.63801i			0.0591837i
$767$	−6.56043	+	6.56043i	−0.236883	+	0.236883i
$768$	−0.400089	+	0.400089i	−0.0144370	+	0.0144370i
$769$	−30.5832			−1.10286			−0.551430	−	0.834221i	$-0.685918\pi$
$769$	−30.5832			−1.10286			−0.551430	+	0.834221i	$0.685918\pi$
$770$		0			0
$771$	−0.888375			−0.0319940
$772$	−0.00146653	+	0.00146653i	−5.27814e−5	+	5.27814e-5i
$773$	16.2105	−	16.2105i	0.583052	−	0.583052i	−0.352689	−	0.935741i	$-0.614733\pi$
$773$	16.2105	−	16.2105i	0.583052	−	0.583052i	0.935741	+	0.352689i	$0.114733\pi$
$774$			1.73154i			0.0622389i
$775$	4.68393	−	18.8815i	0.168252	−	0.678243i
$776$		−	6.99583i		−	0.251136i
$777$	−0.787713	+	0.787713i	−0.0282591	+	0.0282591i
$778$	−4.72096	−	4.72096i	−0.169255	−	0.169255i
$779$			11.0651i			0.396448i
$780$	−0.317802	−	0.406271i	−0.0113791	−	0.0145468i
$781$		0			0
$782$	4.66429	+	4.66429i	0.166795	+	0.166795i
$783$	−1.31341	−	1.31341i	−0.0469374	−	0.0469374i
$784$			12.9511i			0.462540i
$785$	19.1529	+	2.34017i	0.683598	+	0.0835243i
$786$	−0.211938			−0.00755957
$787$	−0.563448	+	0.563448i	−0.0200848	+	0.0200848i	−0.717078	−	0.696993i	$-0.754521\pi$
$787$	−0.563448	+	0.563448i	−0.0200848	+	0.0200848i	0.696993	+	0.717078i	$0.254521\pi$
$788$	11.3496	+	11.3496i	0.404312	+	0.404312i
$789$	0.275067			0.00979263
$790$	−0.877074	+	7.17834i	−0.0312049	+	0.255394i
$791$		−	17.1662i		−	0.610361i
$792$		0			0
$793$	2.83841	−	2.83841i	0.100795	−	0.100795i
$794$	1.08935			0.0386598
$795$	−0.681123	−	0.870734i	−0.0241569	−	0.0308818i
$796$	25.9321			0.919140
$797$	−18.4048	−	18.4048i	−0.651933	−	0.651933i	0.301525	−	0.953458i	$-0.402504\pi$
$797$	−18.4048	−	18.4048i	−0.651933	−	0.651933i	−0.953458	+	0.301525i	$0.902504\pi$
$798$	−0.197978	−	0.197978i	−0.00700836	−	0.00700836i
$799$	23.3651			0.826599
$800$	7.81625	+	12.9736i	0.276346	+	0.458686i
$801$	6.77729			0.239464
$802$	1.44554	−	1.44554i	0.0510438	−	0.0510438i
$803$		0			0
$804$			1.25553i			0.0442793i
$805$	16.8189	+	21.5009i	0.592787	+	0.757807i
$806$	2.32448			0.0818763
$807$	−0.450216	−	0.450216i	−0.0158483	−	0.0158483i
$808$	7.72383	−	7.72383i	0.271723	−	0.271723i
$809$	55.0114			1.93410			0.967048	−	0.254594i	$-0.0819418\pi$
$809$	55.0114			1.93410			0.967048	+	0.254594i	$0.0819418\pi$
$810$	−0.644233	+	5.27268i	−0.0226360	+	0.185263i
$811$			54.8754i			1.92694i	0.267821	+	0.963469i	$0.413696\pi$
$811$			54.8754i			1.92694i	−0.267821	+	0.963469i	$0.586304\pi$
$812$	26.0022	+	26.0022i	0.912498	+	0.912498i
$813$	0.632025	+	0.632025i	0.0221661	+	0.0221661i
$814$		0			0
$815$	−2.24846	+	18.4023i	−0.0787600	+	0.644605i
$816$		−	1.26235i		−	0.0441910i
$817$	−9.46300	−	9.46300i	−0.331068	−	0.331068i
$818$	5.33619	−	5.33619i	0.186575	−	0.186575i
$819$			22.0387i			0.770096i
$820$	6.13406	−	4.79830i	0.214211	−	0.167564i
$821$		−	14.3748i		−	0.501683i	−0.968028	−	0.250841i	$-0.919293\pi$
$821$		−	14.3748i		−	0.501683i	0.968028	−	0.250841i	$-0.0807073\pi$
$822$	0.00502772	−	0.00502772i	0.000175362	−	0.000175362i
$823$	−3.37948	+	3.37948i	−0.117801	+	0.117801i	−0.763550	−	0.645749i	$-0.776545\pi$
$823$	−3.37948	+	3.37948i	−0.117801	+	0.117801i	0.645749	+	0.763550i	$0.276545\pi$
$824$	15.5762			0.542624
$825$		0			0
$826$	3.54451			0.123329
$827$	23.4866	−	23.4866i	0.816710	−	0.816710i	−0.168919	−	0.985630i	$-0.554028\pi$
$827$	23.4866	−	23.4866i	0.816710	−	0.816710i	0.985630	+	0.168919i	$0.0540278\pi$
$828$	15.3272	−	15.3272i	0.532658	−	0.532658i
$829$			45.9977i			1.59757i	0.601620	+	0.798783i	$0.294522\pi$
$829$			45.9977i			1.59757i	−0.601620	+	0.798783i	$0.705478\pi$
$830$	−4.90869	+	3.83977i	−0.170383	+	0.133280i
$831$			1.04438i			0.0362291i
$832$	10.1622	−	10.1622i	0.352312	−	0.352312i
$833$	−16.9902	−	16.9902i	−0.588677	−	0.588677i
$834$		−	0.0465932i		−	0.00161339i
$835$	−6.12310	+	50.1140i	−0.211899	+	1.73427i
$836$		0			0
$837$	−0.873721	−	0.873721i	−0.0302002	−	0.0302002i
$838$	1.82359	+	1.82359i	0.0629949	+	0.0629949i
$839$		−	26.3058i		−	0.908176i	−0.890957	−	0.454088i	$-0.849965\pi$
$839$		−	26.3058i		−	0.908176i	0.890957	−	0.454088i	$-0.150035\pi$
$840$	−0.0486666	+	0.398308i	−0.00167916	+	0.0137429i
$841$	5.20765			0.179574
$842$	−2.55879	+	2.55879i	−0.0881818	+	0.0881818i
$843$	−0.160829	−	0.160829i	−0.00553926	−	0.00553926i
$844$	17.8027			0.612794
$845$	−10.8914	−	13.9234i	−0.374676	−	0.478979i
$846$			2.78730i			0.0958293i
$847$		0			0
$848$	23.6637	−	23.6637i	0.812614	−	0.812614i
$849$	0.319121			0.0109522
$850$	−8.54246	−	2.11913i	−0.293004	−	0.0726855i
$851$	−24.1979			−0.829494
$852$	−0.498607	−	0.498607i	−0.0170820	−	0.0170820i
$853$	−20.0864	−	20.0864i	−0.687745	−	0.687745i	0.273988	−	0.961733i	$-0.411657\pi$
$853$	−20.0864	−	20.0864i	−0.687745	−	0.687745i	−0.961733	+	0.273988i	$0.911657\pi$
$854$	−1.53355			−0.0524772
$855$	−25.3185	−	32.3667i	−0.865874	−	1.10692i
$856$	−6.80756			−0.232678
$857$	6.72032	−	6.72032i	0.229562	−	0.229562i	−0.582948	−	0.812510i	$-0.698101\pi$
$857$	6.72032	−	6.72032i	0.229562	−	0.229562i	0.812510	+	0.582948i	$0.198101\pi$
$858$		0			0
$859$			18.6345i			0.635803i	0.948124	+	0.317901i	$0.102978\pi$
$859$			18.6345i			0.635803i	−0.948124	+	0.317901i	$0.897022\pi$
$860$	−1.14235	+	9.34948i	−0.0389539	+	0.318815i
$861$	0.311325			0.0106099
$862$	2.37599	+	2.37599i	0.0809265	+	0.0809265i
$863$	−3.30307	+	3.30307i	−0.112438	+	0.112438i	−0.761087	−	0.648649i	$-0.775334\pi$
$863$	−3.30307	+	3.30307i	−0.112438	+	0.112438i	0.648649	+	0.761087i	$0.275334\pi$
$864$	0.962028			0.0327288
$865$	34.1460	+	4.17207i	1.16100	+	0.141855i
$866$		−	0.613604i		−	0.0208511i
$867$	1.01948	+	1.01948i	0.0346234	+	0.0346234i
$868$	17.2975	+	17.2975i	0.587115	+	0.587115i
$869$		0			0
$870$	0.112944	+	0.144385i	0.00382916	+	0.00489513i
$871$		−	27.7288i		−	0.939555i
$872$	−8.77494	−	8.77494i	−0.297157	−	0.297157i
$873$	14.2532	−	14.2532i	0.482398	−	0.482398i
$874$		−	6.08173i		−	0.205718i
$875$	−34.0269	−	12.9924i	−1.15032	−	0.439222i
$876$			0.866382i			0.0292723i
$877$	−6.14848	+	6.14848i	−0.207619	+	0.207619i	−0.803255	−	0.595635i	$-0.796900\pi$
$877$	−6.14848	+	6.14848i	−0.207619	+	0.207619i	0.595635	+	0.803255i	$0.296900\pi$
$878$	−1.41567	+	1.41567i	−0.0477764	+	0.0477764i
$879$	−0.645318			−0.0217660
$880$		0			0
$881$	−36.3819			−1.22574			−0.612868	−	0.790185i	$-0.709984\pi$
$881$	−36.3819			−1.22574			−0.612868	+	0.790185i	$0.709984\pi$
$882$	2.02682	−	2.02682i	0.0682465	−	0.0682465i
$883$	−32.2698	+	32.2698i	−1.08597	+	1.08597i	−0.0900273	+	0.995939i	$0.528695\pi$
$883$	−32.2698	+	32.2698i	−1.08597	+	1.08597i	−0.995939	+	0.0900273i	$0.971305\pi$
$884$			28.9691i			0.974336i
$885$	−0.483135	−	0.0590310i	−0.0162404	−	0.00198431i
$886$			3.27835i			0.110138i
$887$	39.0529	−	39.0529i	1.31127	−	1.31127i	0.390787	−	0.920481i	$-0.372203\pi$
$887$	39.0529	−	39.0529i	1.31127	−	1.31127i	0.920481	−	0.390787i	$-0.127797\pi$
$888$	−0.251521	−	0.251521i	−0.00844049	−	0.00844049i
$889$			54.3753i			1.82369i
$890$	−1.32846	−	0.162316i	−0.0445301	−	0.00544084i
$891$		0			0
$892$	17.6181	+	17.6181i	0.589898	+	0.589898i
$893$	−15.2328	−	15.2328i	−0.509746	−	0.509746i
$894$		−	0.156879i		−	0.00524681i
$895$	17.7206	+	22.6536i	0.592333	+	0.757226i
$896$	−25.2277			−0.842797
$897$	0.316710	−	0.316710i	0.0105746	−	0.0105746i
$898$	−1.76046	−	1.76046i	−0.0587474	−	0.0587474i
$899$	22.7560			0.758955
$900$	−6.96362	+	28.0712i	−0.232121	+	0.935706i
$901$			62.0875i			2.06844i
$902$		0			0
$903$	−0.266249	+	0.266249i	−0.00886020	+	0.00886020i
$904$	5.48127			0.182304
$905$	0.473042	−	0.370032i	0.0157244	−	0.0123003i
$906$	0.189395			0.00629223
$907$	3.50813	+	3.50813i	0.116486	+	0.116486i	0.762947	−	0.646461i	$-0.223752\pi$
$907$	3.50813	+	3.50813i	0.116486	+	0.116486i	−0.646461	+	0.762947i	$0.723752\pi$
$908$	40.2795	+	40.2795i	1.33672	+	1.33672i
$909$	31.4729			1.04389
$910$	0.527827	−	4.31995i	0.0174973	−	0.143205i
$911$	51.6011			1.70962			0.854811	−	0.518940i	$-0.173673\pi$
$911$	51.6011			1.70962			0.854811	+	0.518940i	$0.173673\pi$
$912$	−0.822982	+	0.822982i	−0.0272516	+	0.0272516i
$913$		0			0
$914$			6.88173i			0.227628i
$915$	0.209031	+	0.0255401i	0.00691036	+	0.000844331i
$916$	−28.5564			−0.943529
$917$	34.8312	+	34.8312i	1.15023	+	1.15023i
$918$	−0.395293	+	0.395293i	−0.0130466	+	0.0130466i
$919$	15.4217			0.508714			0.254357	−	0.967110i	$-0.418136\pi$
$919$	15.4217			0.508714			0.254357	+	0.967110i	$0.418136\pi$
$920$	−6.86535	+	5.37035i	−0.226344	+	0.177055i
$921$			0.0226251i			0.000745524i
$922$	−0.713353	−	0.713353i	−0.0234930	−	0.0234930i
$923$	11.0119	+	11.0119i	0.362460	+	0.362460i
$924$		0			0
$925$	27.6556	−	16.6618i	0.909312	−	0.547837i
$926$		−	10.2591i		−	0.337134i
$927$	31.7348	+	31.7348i	1.04231	+	1.04231i
$928$	−12.5280	+	12.5280i	−0.411251	+	0.411251i
$929$		−	46.2056i		−	1.51596i	−0.652281	−	0.757978i	$-0.726188\pi$
$929$		−	46.2056i		−	1.51596i	0.652281	−	0.757978i	$-0.273812\pi$
$930$	0.0751339	+	0.0960497i	0.00246374	+	0.00314959i
$931$			22.1534i			0.726049i
$932$	−22.2441	+	22.2441i	−0.728631	+	0.728631i
$933$	0.964525	−	0.964525i	0.0315771	−	0.0315771i
$934$	5.66455			0.185350
$935$		0			0
$936$	−7.03708			−0.230014
$937$	13.4785	−	13.4785i	0.440323	−	0.440323i	−0.451797	−	0.892121i	$-0.649217\pi$
$937$	13.4785	−	13.4785i	0.440323	−	0.440323i	0.892121	+	0.451797i	$0.149217\pi$
$938$	−7.49075	+	7.49075i	−0.244582	+	0.244582i
$939$		−	0.931325i		−	0.0303926i
$940$	−1.83887	+	15.0501i	−0.0599772	+	0.490879i
$941$			42.3626i			1.38098i	0.723341	+	0.690491i	$0.242605\pi$
$941$			42.3626i			1.38098i	−0.723341	+	0.690491i	$0.757395\pi$
$942$	−0.0855262	+	0.0855262i	−0.00278659	+	0.00278659i
$943$	4.78182	+	4.78182i	0.155718	+	0.155718i
$944$		−	14.7343i		−	0.479560i
$945$	−1.82217	+	1.42538i	−0.0592753	+	0.0463675i
$946$		0			0
$947$	7.32770	+	7.32770i	0.238118	+	0.238118i	0.816071	−	0.577952i	$-0.196148\pi$
$947$	7.32770	+	7.32770i	0.238118	+	0.238118i	−0.577952	+	0.816071i	$0.696148\pi$
$948$	0.882979	+	0.882979i	0.0286778	+	0.0286778i
$949$		−	19.1343i		−	0.621125i
$950$	4.18766	+	6.95077i	0.135866	+	0.225513i
$951$	−1.56582			−0.0507753
$952$	15.9357	−	15.9357i	0.516480	−	0.516480i
$953$	41.6115	+	41.6115i	1.34793	+	1.34793i	0.887909	+	0.460020i	$0.152158\pi$
$953$	41.6115	+	41.6115i	1.34793	+	1.34793i	0.460020	+	0.887909i	$0.347842\pi$
$954$	−7.40662			−0.239798
$955$	−12.9109	+	10.0994i	−0.417787	+	0.326809i
$956$		−	43.8731i		−	1.41896i
$957$		0			0
$958$	0.120661	−	0.120661i	0.00389838	−	0.00389838i
$959$	−1.65257			−0.0533643
$960$	0.748385	+	0.0914402i	0.0241540	+	0.00295122i
$961$	−15.8620			−0.511678
$962$	2.72794	+	2.72794i	0.0879523	+	0.0879523i
$963$	−13.8697	−	13.8697i	−0.446943	−	0.446943i
$964$	22.4723			0.723784
$965$	0.00238522		0.000291434i	7.67830e−5		9.38160e-6i
$966$	−0.171114			−0.00550551
$967$	4.75477	−	4.75477i	0.152903	−	0.152903i	−0.626510	−	0.779413i	$-0.715517\pi$
$967$	4.75477	−	4.75477i	0.152903	−	0.152903i	0.779413	+	0.626510i	$0.215517\pi$
$968$		0			0
$969$		−	2.15930i		−	0.0693666i
$970$	−3.13523	+	2.45250i	−0.100666	+	0.0787451i
$971$	12.8556			0.412557			0.206278	−	0.978493i	$-0.433865\pi$
$971$	12.8556			0.412557			0.206278	+	0.978493i	$0.433865\pi$
$972$	1.94875	+	1.94875i	0.0625062	+	0.0625062i
$973$	−7.65741	+	7.65741i	−0.245485	+	0.245485i
$974$	1.84069			0.0589796
$975$	−0.143891	+	0.580041i	−0.00460820	+	0.0185762i
$976$			6.37488i			0.204055i
$977$	30.0538	+	30.0538i	0.961508	+	0.961508i	0.999286	−	0.0377785i	$-0.0120281\pi$
$977$	30.0538	+	30.0538i	0.961508	+	0.961508i	−0.0377785	+	0.999286i	$0.512028\pi$
$978$	−0.0821743	−	0.0821743i	−0.00262764	−	0.00262764i
$979$		0			0
$980$	12.2810	−	9.60669i	0.392302	−	0.306874i
$981$		−	35.7559i		−	1.14160i
$982$	6.65535	+	6.65535i	0.212381	+	0.212381i
$983$	13.7230	−	13.7230i	0.437697	−	0.437697i	−0.453539	−	0.891236i	$-0.649839\pi$
$983$	13.7230	−	13.7230i	0.437697	−	0.437697i	0.891236	+	0.453539i	$0.149839\pi$
$984$			0.0994076i			0.00316900i
$985$	2.25544	−	18.4594i	0.0718642	−	0.588167i
$986$		−	10.2954i		−	0.327872i
$987$	−0.428586	+	0.428586i	−0.0136421	+	0.0136421i
$988$	18.8863	−	18.8863i	0.600853	−	0.600853i
$989$	−8.17894			−0.260075
$990$		0			0
$991$	10.1982			0.323957			0.161978	−	0.986794i	$-0.448213\pi$
$991$	10.1982			0.323957			0.161978	+	0.986794i	$0.448213\pi$
$992$	−8.33399	+	8.33399i	−0.264605	+	0.264605i
$993$	0.212575	−	0.212575i	0.00674587	−	0.00674587i
$994$		−	5.94957i		−	0.188709i
$995$	−18.5119	−	23.6652i	−0.586867	−	0.750239i
$996$			1.07611i			0.0340979i
$997$	−14.3672	+	14.3672i	−0.455013	+	0.455013i	−0.897014	−	0.442002i	$-0.854269\pi$
$997$	−14.3672	+	14.3672i	−0.455013	+	0.455013i	0.442002	+	0.897014i	$0.354269\pi$
$998$	−1.73064	−	1.73064i	−0.0547824	−	0.0547824i
$999$		−	2.05074i		−	0.0648826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.c.362.11	yes	40
5.3	odd	4	inner	605.2.e.c.483.10	yes	40
11.2	odd	10		605.2.m.g.282.11		160
11.3	even	5		605.2.m.g.112.10		160
11.4	even	5		605.2.m.g.457.11		160
11.5	even	5		605.2.m.g.602.10		160
11.6	odd	10		605.2.m.g.602.11		160
11.7	odd	10		605.2.m.g.457.10		160
11.8	odd	10		605.2.m.g.112.11		160
11.9	even	5		605.2.m.g.282.10		160
11.10	odd	2	inner	605.2.e.c.362.10	✓	40
55.3	odd	20		605.2.m.g.233.10		160
55.8	even	20		605.2.m.g.233.11		160
55.13	even	20		605.2.m.g.403.10		160
55.18	even	20		605.2.m.g.578.10		160
55.28	even	20		605.2.m.g.118.10		160
55.38	odd	20		605.2.m.g.118.11		160
55.43	even	4	inner	605.2.e.c.483.11	yes	40
55.48	odd	20		605.2.m.g.578.11		160
55.53	odd	20		605.2.m.g.403.11		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.10	✓	40	11.10	odd	2	inner
605.2.e.c.362.11	yes	40	1.1	even	1	trivial
605.2.e.c.483.10	yes	40	5.3	odd	4	inner
605.2.e.c.483.11	yes	40	55.43	even	4	inner
605.2.m.g.112.10		160	11.3	even	5
605.2.m.g.112.11		160	11.8	odd	10
605.2.m.g.118.10		160	55.28	even	20
605.2.m.g.118.11		160	55.38	odd	20
605.2.m.g.233.10		160	55.3	odd	20
605.2.m.g.233.11		160	55.8	even	20
605.2.m.g.282.10		160	11.9	even	5
605.2.m.g.282.11		160	11.2	odd	10
605.2.m.g.403.10		160	55.13	even	20
605.2.m.g.403.11		160	55.53	odd	20
605.2.m.g.457.10		160	11.7	odd	10
605.2.m.g.457.11		160	11.4	even	5
605.2.m.g.578.10		160	55.18	even	20
605.2.m.g.578.11		160	55.48	odd	20
605.2.m.g.602.10		160	11.5	even	5
605.2.m.g.602.11		160	11.6	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.187165 - 0.187165i) q^{2} +(-0.0374447 + 0.0374447i) q^{3} +1.92994i q^{4} +(1.76123 - 1.37770i) q^{5} +0.0140167i q^{6} +(2.30359 - 2.30359i) q^{7} +(0.735548 + 0.735548i) q^{8} +2.99720i q^{9} +O(q^{10})\)	\(q+(0.187165 - 0.187165i) q^{2} +(-0.0374447 + 0.0374447i) q^{3} +1.92994i q^{4} +(1.76123 - 1.37770i) q^{5} +0.0140167i q^{6} +(2.30359 - 2.30359i) q^{7} +(0.735548 + 0.735548i) q^{8} +2.99720i q^{9} +(0.0717827 - 0.587500i) q^{10} +(-0.0722660 - 0.0722660i) q^{12} +(1.59601 + 1.59601i) q^{13} -0.862304i q^{14} +(-0.0143610 + 0.117536i) q^{15} -3.58454 q^{16} +(4.70246 - 4.70246i) q^{17} +(0.560971 + 0.560971i) q^{18} -6.13150 q^{19} +(2.65888 + 3.39906i) q^{20} +0.172514i q^{21} +(-2.64975 + 2.64975i) q^{23} -0.0550848 q^{24} +(1.20386 - 4.85291i) q^{25} +0.597437 q^{26} +(-0.224563 - 0.224563i) q^{27} +(4.44579 + 4.44579i) q^{28} +5.84873 q^{29} +(0.0193109 + 0.0246866i) q^{30} +3.89076 q^{31} +(-2.14200 + 2.14200i) q^{32} -1.76028i q^{34} +(0.883485 - 7.23082i) q^{35} -5.78440 q^{36} +(4.56607 + 4.56607i) q^{37} +(-1.14760 + 1.14760i) q^{38} -0.119524 q^{39} +(2.30884 + 0.282102i) q^{40} -1.80463i q^{41} +(0.0322887 + 0.0322887i) q^{42} +(1.54334 + 1.54334i) q^{43} +(4.12925 + 5.27875i) q^{45} +0.991883i q^{46} +(2.48435 + 2.48435i) q^{47} +(0.134222 - 0.134222i) q^{48} -3.61305i q^{49} +(-0.682975 - 1.13362i) q^{50} +0.352165i q^{51} +(-3.08021 + 3.08021i) q^{52} +(-6.60160 + 6.60160i) q^{53} -0.0840609 q^{54} +3.38880 q^{56} +(0.229592 - 0.229592i) q^{57} +(1.09468 - 1.09468i) q^{58} +4.11051i q^{59} +(-0.226838 - 0.0277158i) q^{60} -1.77844i q^{61} +(0.728215 - 0.728215i) q^{62} +(6.90431 + 6.90431i) q^{63} -6.36726i q^{64} +(5.00978 + 0.612112i) q^{65} +(-8.68690 - 8.68690i) q^{67} +(9.07546 + 9.07546i) q^{68} -0.198438i q^{69} +(-1.18800 - 1.51872i) q^{70} +6.89961 q^{71} +(-2.20458 + 2.20458i) q^{72} +(-5.99440 - 5.99440i) q^{73} +1.70922 q^{74} +(0.136637 + 0.226794i) q^{75} -11.8334i q^{76} +(-0.0223708 + 0.0223708i) q^{78} -12.2185 q^{79} +(-6.31320 + 4.93843i) q^{80} -8.97477 q^{81} +(-0.337764 - 0.337764i) q^{82} +(-7.44550 - 7.44550i) q^{83} -0.332942 q^{84} +(1.80351 - 14.7607i) q^{85} +0.577720 q^{86} +(-0.219004 + 0.219004i) q^{87} -2.26121i q^{89} +(1.76085 + 0.215147i) q^{90} +7.35312 q^{91} +(-5.11386 - 5.11386i) q^{92} +(-0.145688 + 0.145688i) q^{93} +0.929969 q^{94} +(-10.7990 + 8.44739i) q^{95} -0.160413i q^{96} +(-4.75552 - 4.75552i) q^{97} +(-0.676238 - 0.676238i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 4 q^{5}+O(q^{10}) \) 40 * q + 8 * q^3 - 4 * q^5	\( 40 q + 8 q^{3} - 4 q^{5} - 32 q^{12} + 32 q^{15} - 24 q^{16} + 32 q^{20} - 24 q^{23} - 52 q^{25} - 8 q^{26} + 32 q^{27} + 16 q^{31} - 40 q^{36} + 36 q^{37} + 32 q^{38} + 32 q^{42} + 64 q^{45} + 32 q^{47} - 16 q^{48} - 68 q^{53} + 80 q^{56} + 132 q^{58} - 64 q^{60} - 88 q^{67} - 8 q^{70} - 16 q^{75} - 248 q^{78} - 164 q^{80} - 40 q^{81} + 100 q^{82} - 80 q^{86} - 96 q^{91} - 56 q^{92} + 24 q^{93} - 68 q^{97}+O(q^{100}) \) 40 * q + 8 * q^3 - 4 * q^5 - 32 * q^12 + 32 * q^15 - 24 * q^16 + 32 * q^20 - 24 * q^23 - 52 * q^25 - 8 * q^26 + 32 * q^27 + 16 * q^31 - 40 * q^36 + 36 * q^37 + 32 * q^38 + 32 * q^42 + 64 * q^45 + 32 * q^47 - 16 * q^48 - 68 * q^53 + 80 * q^56 + 132 * q^58 - 64 * q^60 - 88 * q^67 - 8 * q^70 - 16 * q^75 - 248 * q^78 - 164 * q^80 - 40 * q^81 + 100 * q^82 - 80 * q^86 - 96 * q^91 - 56 * q^92 + 24 * q^93 - 68 * q^97

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