LMFDB - Embedded newform 968.2.o.i.493.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			493.6
Character	$\chi$	$=$	968.493
Dual form			968.2.o.i.269.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.301096 - 1.38179i) q^{2} +(1.50170 + 2.06692i) q^{3} +(-1.81868 - 0.832103i) q^{4} +(2.56349 - 0.832928i) q^{5} +(3.30820 - 1.45270i) q^{6} +(3.19487 + 2.32121i) q^{7} +(-1.69739 + 2.26249i) q^{8} +(-1.08998 + 3.35462i) q^{9} +(-0.379074 - 3.79299i) q^{10} +(-1.01123 - 5.00864i) q^{12} +(-0.416519 - 0.135335i) q^{13} +(4.16939 - 3.71573i) q^{14} +(5.57119 + 4.04771i) q^{15} +(2.61521 + 3.02666i) q^{16} +(0.739640 + 2.27638i) q^{17} +(4.30719 + 2.51619i) q^{18} +(-3.14306 - 4.32605i) q^{19} +(-5.35525 - 0.618256i) q^{20} +10.0893i q^{21} -1.35153 q^{23} +(-7.22536 - 0.110772i) q^{24} +(1.83262 - 1.33147i) q^{25} +(-0.312417 + 0.534793i) q^{26} +(-1.28114 + 0.416268i) q^{27} +(-3.87897 - 6.88001i) q^{28} +(0.0866058 - 0.119203i) q^{29} +(7.27054 - 6.47946i) q^{30} +(0.489088 - 1.50526i) q^{31} +(4.96964 - 2.70235i) q^{32} +(3.36818 - 0.336618i) q^{34} +(10.1234 + 3.28930i) q^{35} +(4.77373 - 5.19402i) q^{36} +(-4.33759 + 5.97018i) q^{37} +(-6.92405 + 3.04048i) q^{38} +(-0.345761 - 1.06414i) q^{39} +(-2.46675 + 7.21367i) q^{40} +(-2.92294 + 2.12364i) q^{41} +(13.9413 + 3.03785i) q^{42} -6.62197i q^{43} +9.50742i q^{45} +(-0.406941 + 1.86753i) q^{46} +(-2.44701 + 1.77785i) q^{47} +(-2.32859 + 9.95057i) q^{48} +(2.65607 + 8.17456i) q^{49} +(-1.28802 - 2.93319i) q^{50} +(-3.59437 + 4.94722i) q^{51} +(0.644903 + 0.592719i) q^{52} +(-4.41208 - 1.43357i) q^{53} +(0.189448 + 1.89561i) q^{54} +(-10.6747 + 3.28838i) q^{56} +(4.22164 - 12.9929i) q^{57} +(-0.138636 - 0.155562i) q^{58} +(7.35162 - 10.1186i) q^{59} +(-6.76412 - 11.9973i) q^{60} +(0.627487 - 0.203883i) q^{61} +(-1.93268 - 1.12904i) q^{62} +(-11.2692 + 8.18752i) q^{63} +(-2.23774 - 7.68066i) q^{64} -1.18047 q^{65} -3.00157i q^{67} +(0.549011 - 4.75547i) q^{68} +(-2.02960 - 2.79351i) q^{69} +(7.59324 - 12.9980i) q^{70} +(-3.26511 - 10.0490i) q^{71} +(-5.73968 - 8.16018i) q^{72} +(8.61055 + 6.25593i) q^{73} +(6.94350 + 7.79124i) q^{74} +(5.50409 + 1.78839i) q^{75} +(2.11650 + 10.4830i) q^{76} +(-1.57453 + 0.157359i) q^{78} +(1.99182 - 6.13018i) q^{79} +(9.22505 + 5.58053i) q^{80} +(5.77655 + 4.19691i) q^{81} +(2.05434 + 4.67831i) q^{82} +(-2.17269 + 0.705948i) q^{83} +(8.39535 - 18.3492i) q^{84} +(3.79212 + 5.21940i) q^{85} +(-9.15016 - 1.99385i) q^{86} +0.376438 q^{87} +11.5827 q^{89} +(13.1372 + 2.86265i) q^{90} +(-1.01658 - 1.39921i) q^{91} +(2.45801 + 1.12461i) q^{92} +(3.84571 - 1.24955i) q^{93} +(1.71983 + 3.91655i) q^{94} +(-11.6605 - 8.47183i) q^{95} +(13.0485 + 6.21370i) q^{96} +(2.68309 - 8.25770i) q^{97} +(12.0952 - 1.20881i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - q^{4} + 7 q^{6} + 10 q^{7} + 5 q^{8} + 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} + 6 q^{17} + 20 q^{18} + 8 q^{20} - 8 q^{23} - 25 q^{24} - 4 q^{25} - 10 q^{26} - 32 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - q^4 + 7 * q^6 + 10 * q^7 + 5 * q^8 + 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 + 6 * q^17 + 20 * q^18 + 8 * q^20 - 8 * q^23 - 25 * q^24 - 4 * q^25 - 10 * q^26 - 32 * q^28 + 28 * q^30 - 6 * q^31 - 20 * q^32 + 10 * q^34 + 18 * q^36 + 12 * q^38 + 34 * q^39 - 10 * q^40 + 14 * q^41 + 40 * q^42 - 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 - 61 * q^50 - 20 * q^52 - 108 * q^54 - 32 * q^56 + 26 * q^57 + 4 * q^58 - 46 * q^60 - 48 * q^62 - 60 * q^63 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 + 22 * q^71 + 101 * q^72 + 6 * q^73 - 54 * q^74 + 134 * q^76 - 12 * q^78 - 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 + 28 * q^84 - 15 * q^86 - 68 * q^87 - 16 * q^89 + 84 * q^90 - 4 * q^92 + 100 * q^94 - 66 * q^95 + 30 * q^96 + 10 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.301096	−	1.38179i	0.212907	−	0.977072i
$2$	0.301096	−	1.38179i	0.212907	−	0.977072i
$3$	1.50170	+	2.06692i	0.867009	+	1.19334i	0.979852	+	0.199723i	$0.0640041\pi$
$3$	1.50170	+	2.06692i	0.867009	+	1.19334i	−0.112844	+	0.993613i	$0.535996\pi$
$4$	−1.81868	−	0.832103i	−0.909341	−	0.416052i
$5$	2.56349	−	0.832928i	1.14643	−	0.372497i	0.326631	−	0.945152i	$-0.394087\pi$
$5$	2.56349	−	0.832928i	1.14643	−	0.372497i	0.819796	+	0.572655i	$0.194087\pi$
$6$	3.30820	−	1.45270i	1.35057	−	0.593061i
$7$	3.19487	+	2.32121i	1.20755	+	0.877335i	0.995006	−	0.0998163i	$-0.0318255\pi$
$7$	3.19487	+	2.32121i	1.20755	+	0.877335i	0.212543	+	0.977152i	$0.431826\pi$
$8$	−1.69739	+	2.26249i	−0.600118	+	0.799912i
$9$	−1.08998	+	3.35462i	−0.363328	+	1.11821i
$10$	−0.379074	−	3.79299i	−0.119874	−	1.19945i
$11$		0			0
$11$		0			0
$12$	−1.01123	−	5.00864i	−0.291918	−	1.44587i
$13$	−0.416519	−	0.135335i	−0.115522	−	0.0375352i	0.250686	−	0.968069i	$-0.419344\pi$
$13$	−0.416519	−	0.135335i	−0.115522	−	0.0375352i	−0.366207	+	0.930533i	$0.619344\pi$
$14$	4.16939	−	3.71573i	1.11432	−	0.993071i
$15$	5.57119	+	4.04771i	1.43848	+	1.04511i
$16$	2.61521	+	3.02666i	0.653802	+	0.756666i
$17$	0.739640	+	2.27638i	0.179389	+	0.552103i	0.999807	−	0.0196619i	$-0.00625899\pi$
$17$	0.739640	+	2.27638i	0.179389	+	0.552103i	−0.820418	+	0.571765i	$0.806259\pi$
$18$	4.30719	+	2.51619i	1.01522	+	0.593072i
$19$	−3.14306	−	4.32605i	−0.721067	−	0.992463i	−0.999488	−	0.0320039i	$-0.989811\pi$
$19$	−3.14306	−	4.32605i	−0.721067	−	0.992463i	0.278421	−	0.960459i	$-0.410189\pi$
$20$	−5.35525	−	0.618256i	−1.19747	−	0.138246i
$21$			10.0893i			2.20167i
$22$		0			0
$23$	−1.35153			−0.281814			−0.140907	−	0.990023i	$-0.545002\pi$
$23$	−1.35153			−0.281814			−0.140907	+	0.990023i	$0.545002\pi$
$24$	−7.22536	−	0.110772i	−1.47487	−	0.0226113i
$25$	1.83262	−	1.33147i	0.366523	−	0.266295i
$26$	−0.312417	+	0.534793i	−0.0612700	+	0.104881i
$27$	−1.28114	+	0.416268i	−0.246556	+	0.0801109i
$28$	−3.87897	−	6.88001i	−0.733057	−	1.30020i
$29$	0.0866058	−	0.119203i	0.0160823	−	0.0221354i	−0.800900	−	0.598798i	$-0.795645\pi$
$29$	0.0866058	−	0.119203i	0.0160823	−	0.0221354i	0.816982	+	0.576663i	$0.195645\pi$
$30$	7.27054	−	6.47946i	1.32741	−	1.18298i
$31$	0.489088	−	1.50526i	0.0878427	−	0.270352i	−0.897480	−	0.441056i	$-0.854604\pi$
$31$	0.489088	−	1.50526i	0.0878427	−	0.270352i	0.985322	+	0.170704i	$0.0546041\pi$
$32$	4.96964	−	2.70235i	0.878516	−	0.477713i
$33$		0			0
$34$	3.36818	−	0.336618i	0.577638	−	0.0577294i
$35$	10.1234	+	3.28930i	1.71117	+	0.555993i
$36$	4.77373	−	5.19402i	0.795621	−	0.865669i
$37$	−4.33759	+	5.97018i	−0.713096	+	0.981492i	0.286629	+	0.958042i	$0.407465\pi$
$37$	−4.33759	+	5.97018i	−0.713096	+	0.981492i	−0.999725	+	0.0234506i	$0.992535\pi$
$38$	−6.92405	+	3.04048i	−1.12323	+	0.493232i
$39$	−0.345761	−	1.06414i	−0.0553661	−	0.170399i
$40$	−2.46675	+	7.21367i	−0.390027	+	1.14058i
$41$	−2.92294	+	2.12364i	−0.456486	+	0.331657i	−0.792151	−	0.610325i	$-0.791039\pi$
$41$	−2.92294	+	2.12364i	−0.456486	+	0.331657i	0.335665	+	0.941981i	$0.391039\pi$
$42$	13.9413	+	3.03785i	2.15119	+	0.468751i
$43$		−	6.62197i		−	1.00984i	−0.863166	−	0.504920i	$-0.831522\pi$
$43$		−	6.62197i		−	1.00984i	0.863166	−	0.504920i	$-0.168478\pi$
$44$		0			0
$45$			9.50742i			1.41728i
$46$	−0.406941	+	1.86753i	−0.0600002	+	0.275353i
$47$	−2.44701	+	1.77785i	−0.356933	+	0.259327i	−0.751772	−	0.659424i	$-0.770800\pi$
$47$	−2.44701	+	1.77785i	−0.356933	+	0.259327i	0.394839	+	0.918750i	$0.370800\pi$
$48$	−2.32859	+	9.95057i	−0.336103	+	1.43624i
$49$	2.65607	+	8.17456i	0.379439	+	1.16779i
$50$	−1.28802	−	2.93319i	−0.182154	−	0.414816i
$51$	−3.59437	+	4.94722i	−0.503312	+	0.692749i
$52$	0.644903	+	0.592719i	0.0894319	+	0.0821953i
$53$	−4.41208	−	1.43357i	−0.606046	−	0.196916i	−0.0101110	−	0.999949i	$-0.503219\pi$
$53$	−4.41208	−	1.43357i	−0.606046	−	0.196916i	−0.595935	+	0.803033i	$0.703219\pi$
$54$	0.189448	+	1.89561i	0.0257806	+	0.257959i
$55$		0			0
$56$	−10.6747	+	3.28838i	−1.42646	+	0.439428i
$57$	4.22164	−	12.9929i	0.559170	−	1.72095i
$58$	−0.138636	−	0.155562i	−0.0182038	−	0.0204264i
$59$	7.35162	−	10.1186i	0.957100	−	1.31733i	0.00879896	−	0.999961i	$-0.497199\pi$
$59$	7.35162	−	10.1186i	0.957100	−	1.31733i	0.948301	−	0.317373i	$-0.102801\pi$
$60$	−6.76412	−	11.9973i	−0.873244	−	1.54884i
$61$	0.627487	−	0.203883i	0.0803414	−	0.0261045i	−0.268571	−	0.963260i	$-0.586551\pi$
$61$	0.627487	−	0.203883i	0.0803414	−	0.0261045i	0.348912	+	0.937156i	$0.386551\pi$
$62$	−1.93268	−	1.12904i	−0.245451	−	0.143389i
$63$	−11.2692	+	8.18752i	−1.41978	+	1.03153i
$64$	−2.23774	−	7.68066i	−0.279717	−	0.960082i
$65$	−1.18047			−0.146419
$66$		0			0
$67$		−	3.00157i		−	0.366701i	−0.983048	−	0.183350i	$-0.941306\pi$
$67$		−	3.00157i		−	0.366701i	0.983048	−	0.183350i	$-0.0586942\pi$
$68$	0.549011	−	4.75547i	0.0665774	−	0.576685i
$69$	−2.02960	−	2.79351i	−0.244335	−	0.336298i
$70$	7.59324	−	12.9980i	0.907566	−	1.55356i
$71$	−3.26511	−	10.0490i	−0.387497	−	1.19259i	−0.934653	−	0.355562i	$-0.884290\pi$
$71$	−3.26511	−	10.0490i	−0.387497	−	1.19259i	0.547156	−	0.837031i	$-0.315710\pi$
$72$	−5.73968	−	8.16018i	−0.676428	−	0.961687i
$73$	8.61055	+	6.25593i	1.00779	+	0.732201i	0.963744	−	0.266829i	$-0.0859758\pi$
$73$	8.61055	+	6.25593i	1.00779	+	0.732201i	0.0440441	+	0.999030i	$0.485976\pi$
$74$	6.94350	+	7.79124i	0.807166	+	0.905713i
$75$	5.50409	+	1.78839i	0.635558	+	0.206505i
$76$	2.11650	+	10.4830i	0.242780	+	1.20249i
$77$		0			0
$78$	−1.57453	+	0.157359i	−0.178280	+	0.0178174i
$79$	1.99182	−	6.13018i	0.224097	−	0.689699i	−0.774285	−	0.632837i	$-0.781890\pi$
$79$	1.99182	−	6.13018i	0.224097	−	0.689699i	0.998382	−	0.0568623i	$-0.0181096\pi$
$80$	9.22505	+	5.58053i	1.03139	+	0.623922i
$81$	5.77655	+	4.19691i	0.641839	+	0.466324i
$82$	2.05434	+	4.67831i	0.226863	+	0.516632i
$83$	−2.17269	+	0.705948i	−0.238483	+	0.0774879i	−0.425820	−	0.904808i	$-0.640014\pi$
$83$	−2.17269	+	0.705948i	−0.238483	+	0.0774879i	0.187337	+	0.982296i	$0.440014\pi$
$84$	8.39535	−	18.3492i	0.916007	−	2.00207i
$85$	3.79212	+	5.21940i	0.411313	+	0.566124i
$86$	−9.15016	−	1.99385i	−0.986688	−	0.215002i
$87$	0.376438			0.0403584
$88$		0			0
$89$	11.5827			1.22777			0.613883	−	0.789397i	$-0.289607\pi$
$89$	11.5827			1.22777			0.613883	+	0.789397i	$0.289607\pi$
$90$	13.1372	+	2.86265i	1.38479	+	0.301750i
$91$	−1.01658	−	1.39921i	−0.106567	−	0.146677i
$92$	2.45801	+	1.12461i	0.256265	+	0.117249i
$93$	3.84571	−	1.24955i	0.398781	−	0.129572i
$94$	1.71983	+	3.91655i	0.177387	+	0.403961i
$95$	−11.6605	−	8.47183i	−1.19634	−	0.869191i
$96$	13.0485	+	6.21370i	1.33175	+	0.634183i
$97$	2.68309	−	8.25770i	0.272427	−	0.838443i	−0.717462	−	0.696597i	$-0.754696\pi$
$97$	2.68309	−	8.25770i	0.272427	−	0.838443i	0.989889	−	0.141845i	$-0.0453036\pi$
$98$	12.0952	−	1.20881i	1.22180	−	0.122108i
$99$		0			0
$100$	−4.44087	+	0.896602i	−0.444087	+	0.0896602i
$101$	−5.35569	−	1.74017i	−0.532911	−	0.173153i	0.0301857	−	0.999544i	$-0.490390\pi$
$101$	−5.35569	−	1.74017i	−0.532911	−	0.173153i	−0.563097	+	0.826391i	$0.690390\pi$
$102$	5.75376	+	6.45625i	0.569708	+	0.639264i
$103$	12.5242	+	9.09938i	1.23405	+	0.896588i	0.997187	−	0.0749554i	$-0.0238814\pi$
$103$	12.5242	+	9.09938i	1.23405	+	0.896588i	0.236861	+	0.971544i	$0.423881\pi$
$104$	1.01319	−	0.712654i	0.0993514	−	0.0698815i
$105$	8.40367	+	25.8638i	0.820114	+	2.52405i
$106$	−3.30936	+	5.66493i	−0.321433	+	0.550226i
$107$	1.84564	+	2.54031i	0.178425	+	0.245581i	0.888857	−	0.458185i	$-0.151500\pi$
$107$	1.84564	+	2.54031i	0.178425	+	0.245581i	−0.710432	+	0.703766i	$0.751500\pi$
$108$	2.67637	+	0.308983i	0.257534	+	0.0297319i
$109$		−	16.0246i		−	1.53488i	−0.641124	−	0.767438i	$-0.721531\pi$
$109$		−	16.0246i		−	1.53488i	0.641124	−	0.767438i	$-0.278469\pi$
$110$		0			0
$111$	−18.8537			−1.78951
$112$	1.32974	+	15.7403i	0.125648	+	1.48731i
$113$	−13.4885	+	9.79996i	−1.26889	+	0.921903i	−0.999158	−	0.0410326i	$-0.986935\pi$
$113$	−13.4885	+	9.79996i	−1.26889	+	0.921903i	−0.269732	+	0.962935i	$0.586935\pi$
$114$	−16.6823	−	9.74552i	−1.56244	−	0.912752i
$115$	−3.46464	+	1.12573i	−0.323079	+	0.104975i
$116$	−0.256697	+	0.144727i	−0.0238338	+	0.0134375i
$117$	0.907998	−	1.24975i	0.0839444	−	0.115540i
$118$	−11.7683	−	13.2051i	−1.08336	−	1.21563i
$119$	−2.92090	+	8.98960i	−0.267758	+	0.824075i
$120$	−18.6144	+	5.73424i	−1.69925	+	0.523462i
$121$		0			0
$122$	−0.0927891	−	0.928443i	−0.00840073	−	0.0840572i
$123$	−8.77878	−	2.85240i	−0.791556	−	0.257192i
$124$	−2.14202	+	2.33061i	−0.192359	+	0.209295i
$125$	−4.33274	+	5.96351i	−0.387532	+	0.533393i
$126$	7.92032	+	18.0368i	0.705598	+	1.60685i
$127$	0.797953	+	2.45585i	0.0708069	+	0.217921i	0.980198	−	0.198022i	$-0.0634516\pi$
$127$	0.797953	+	2.45585i	0.0708069	+	0.217921i	−0.909391	+	0.415943i	$0.863452\pi$
$128$	−11.2868	+	0.779464i	−0.997624	+	0.0688955i
$129$	13.6871	−	9.94423i	1.20508	−	0.875541i
$130$	−0.355434	+	1.63116i	−0.0311736	+	0.143062i
$131$		−	5.37550i		−	0.469659i	−0.972037	−	0.234830i	$-0.924547\pi$
$131$		−	5.37550i		−	0.469659i	0.972037	−	0.234830i	$-0.0754533\pi$
$132$		0			0
$133$		−	21.1169i		−	1.83106i
$134$	−4.14754	−	0.903763i	−0.358293	−	0.0780732i
$135$	−2.93747	+	2.13420i	−0.252817	+	0.183683i
$136$	−6.40574	−	2.19047i	−0.549288	−	0.187831i
$137$	0.514677	+	1.58401i	0.0439718	+	0.135331i	0.970632	−	0.240568i	$-0.0773338\pi$
$137$	0.514677	+	1.58401i	0.0439718	+	0.135331i	−0.926660	+	0.375900i	$0.877334\pi$
$138$	−4.47114	+	1.96337i	−0.380609	+	0.167133i
$139$	7.42878	−	10.2248i	0.630101	−	0.867260i	−0.367938	−	0.929850i	$-0.619936\pi$
$139$	7.42878	−	10.2248i	0.630101	−	0.867260i	0.998039	+	0.0625903i	$0.0199361\pi$
$140$	−15.6742	−	14.4059i	−1.32472	−	1.21752i
$141$	−7.34936	−	2.38795i	−0.618927	−	0.201102i
$142$	−14.8687	+	1.48598i	−1.24775	+	0.124701i
$143$		0			0
$144$	−13.0038	+	5.47403i	−1.08365	+	0.456169i
$145$	0.122726	−	0.377711i	0.0101918	−	0.0313672i
$146$	11.2370	−	10.0143i	0.929979	−	0.828791i
$147$	−12.9075	+	17.7656i	−1.06459	+	1.46529i
$148$	12.8565	−	7.24854i	1.05680	−	0.595827i
$149$	−18.4663	+	6.00006i	−1.51282	+	0.491544i	−0.943726	−	0.330730i	$-0.892705\pi$
$149$	−18.4663	+	6.00006i	−1.51282	+	0.491544i	−0.569092	+	0.822274i	$0.692705\pi$
$150$	4.12844	−	7.06702i	0.337086	−	0.577020i
$151$	−14.6738	+	10.6611i	−1.19414	+	0.867590i	−0.993695	−	0.112116i	$-0.964237\pi$
$151$	−14.6738	+	10.6611i	−1.19414	+	0.867590i	−0.200440	+	0.979706i	$0.564237\pi$
$152$	15.1226	+	0.231846i	1.22661	+	0.0188052i
$153$	−8.44259			−0.682543
$154$		0			0
$155$		−	4.26608i		−	0.342660i
$156$	−0.256648	+	2.22305i	−0.0205483	+	0.177986i
$157$	−1.72185	−	2.36992i	−0.137418	−	0.189140i	0.734761	−	0.678326i	$-0.237294\pi$
$157$	−1.72185	−	2.36992i	−0.137418	−	0.189140i	−0.872180	+	0.489185i	$0.837294\pi$
$158$	−7.87089	−	4.59804i	−0.626174	−	0.365801i
$159$	−3.66256	−	11.2722i	−0.290460	−	0.893945i
$160$	10.4887	−	11.0668i	0.829208	−	0.874907i
$161$	−4.31797	−	3.13719i	−0.340304	−	0.247245i
$162$	7.53855	−	6.71830i	0.592284	−	0.527840i
$163$	3.46105	+	1.12456i	0.271091	+	0.0880826i	0.441408	−	0.897307i	$-0.354479\pi$
$163$	3.46105	+	1.12456i	0.271091	+	0.0880826i	−0.170317	+	0.985389i	$0.554479\pi$
$164$	7.08299	−	1.43004i	0.553088	−	0.111667i
$165$		0			0
$166$	0.321284	+	3.21475i	0.0249365	+	0.249513i
$167$	−4.26455	+	13.1250i	−0.330001	+	1.01564i	0.639131	+	0.769098i	$0.279294\pi$
$167$	−4.26455	+	13.1250i	−0.330001	+	1.01564i	−0.969132	+	0.246541i	$0.920706\pi$
$168$	−22.8270	−	17.1255i	−1.76114	−	1.32126i
$169$	−10.3620	−	7.52847i	−0.797081	−	0.579113i
$170$	8.35390	−	3.66836i	0.640715	−	0.281351i
$171$	17.9381	−	5.82845i	1.37176	−	0.445713i
$172$	−5.51016	+	12.0433i	−0.420146	+	0.918290i
$173$	−4.41973	−	6.08323i	−0.336026	−	0.462500i	0.607250	−	0.794511i	$-0.292273\pi$
$173$	−4.41973	−	6.08323i	−0.336026	−	0.462500i	−0.943275	+	0.332011i	$0.892273\pi$
$174$	0.113344	−	0.520158i	0.00859260	−	0.0394331i
$175$	8.94561			0.676225
$176$		0			0
$177$	31.9543			2.40184
$178$	3.48751	−	16.0049i	0.261400	−	1.19962i
$179$	−10.9946	−	15.1328i	−0.821777	−	1.13108i	−0.989398	−	0.145227i	$-0.953609\pi$
$179$	−10.9946	−	15.1328i	−0.821777	−	1.13108i	0.167622	−	0.985851i	$-0.446391\pi$
$180$	7.91115	−	17.2910i	0.589662	−	1.28879i
$181$	−22.1697	+	7.20337i	−1.64786	+	0.535422i	−0.978275	−	0.207313i	$-0.933528\pi$
$181$	−22.1697	+	7.20337i	−1.64786	+	0.535422i	−0.669585	+	0.742735i	$0.733528\pi$
$182$	−2.23950	+	0.983408i	−0.166003	+	0.0728951i
$183$	1.36371	+	0.990792i	0.100808	+	0.0732414i
$184$	2.29408	−	3.05783i	0.169122	−	0.225426i
$185$	−6.14663	+	18.9174i	−0.451910	+	1.39083i
$186$	−0.568681	−	5.69019i	−0.0416977	−	0.417225i
$187$		0			0
$188$	5.92968	−	1.19719i	0.432467	−	0.0873140i
$189$	−5.05934	−	1.64388i	−0.368012	−	0.119575i
$190$	−15.2172	+	13.5615i	−1.10397	+	0.983853i
$191$	−11.4874	−	8.34605i	−0.831196	−	0.603899i	0.0887017	−	0.996058i	$-0.471728\pi$
$191$	−11.4874	−	8.34605i	−0.831196	−	0.603899i	−0.919897	+	0.392159i	$0.871728\pi$
$192$	12.5149	−	16.1593i	0.903183	−	1.16620i
$193$	0.468933	+	1.44323i	0.0337545	+	0.103886i	0.966514	−	0.256613i	$-0.0826065\pi$
$193$	0.468933	+	1.44323i	0.0337545	+	0.103886i	−0.932760	+	0.360499i	$0.882607\pi$
$194$	−10.6025	−	6.19383i	−0.761218	−	0.444691i
$195$	−1.77271	−	2.43993i	−0.126946	−	0.174727i
$196$	1.97152	−	17.0770i	0.140823	−	1.21979i
$197$			8.05669i			0.574016i	0.957928	+	0.287008i	$0.0926606\pi$
$197$			8.05669i			0.574016i	−0.957928	+	0.287008i	$0.907339\pi$
$198$		0			0
$199$	9.70147			0.687719			0.343860	−	0.939021i	$-0.388266\pi$
$199$	9.70147			0.687719			0.343860	+	0.939021i	$0.388266\pi$
$200$	−0.0982154	+	6.40631i	−0.00694488	+	0.452995i
$201$	6.20400	−	4.50747i	0.437597	−	0.317933i
$202$	−4.01712	+	6.87647i	−0.282644	+	0.483827i
$203$	0.553389	−	0.179807i	0.0388403	−	0.0126200i
$204$	10.6536	−	6.00654i	0.745902	−	0.420542i
$205$	−5.72408	+	7.87852i	−0.399787	+	0.550260i
$206$	16.3444	−	14.5660i	1.13877	−	1.01486i
$207$	1.47315	−	4.53388i	0.102391	−	0.315127i
$208$	−0.679670	−	1.61459i	−0.0471266	−	0.111952i
$209$		0			0
$210$	38.2687	−	3.82459i	2.64079	−	0.263922i
$211$	−18.4847	−	6.00605i	−1.27254	−	0.413474i	−0.406594	−	0.913609i	$-0.633283\pi$
$211$	−18.4847	−	6.00605i	−1.27254	−	0.413474i	−0.865947	+	0.500136i	$0.833283\pi$
$212$	6.83130	+	6.27852i	0.469175	+	0.431211i
$213$	15.8672	−	21.8393i	1.08720	−	1.49640i
$214$	4.06588	−	1.78541i	0.277938	−	0.122048i
$215$	−5.51562	−	16.9753i	−0.376162	−	1.15771i
$216$	1.23279	−	3.60514i	0.0838810	−	0.245299i
$217$	5.05659	−	3.67383i	0.343264	−	0.249396i
$218$	−22.1426	−	4.82494i	−1.49968	−	0.326786i
$219$			27.1918i			1.83745i
$220$		0			0
$221$		−	1.04825i		−	0.0705132i
$222$	−5.67677	+	26.0518i	−0.381000	+	1.74848i
$223$	−18.0852	+	13.1397i	−1.21108	+	0.879898i	−0.995328	−	0.0965517i	$-0.969219\pi$
$223$	−18.0852	+	13.1397i	−1.21108	+	0.879898i	−0.215747	+	0.976449i	$0.569219\pi$
$224$	22.1501	+	2.90191i	1.47997	+	0.193892i
$225$	2.46907	+	7.59903i	0.164605	+	0.506602i
$226$	9.48014	+	21.5890i	0.630610	+	1.43608i
$227$	8.15397	−	11.2230i	0.541198	−	0.744895i	−0.447587	−	0.894240i	$-0.647717\pi$
$227$	8.15397	−	11.2230i	0.541198	−	0.744895i	0.988785	+	0.149345i	$0.0477165\pi$
$228$	−18.4892	+	20.1171i	−1.22448	+	1.33229i
$229$	16.9382	+	5.50354i	1.11931	+	0.363684i	0.809502	−	0.587117i	$-0.199737\pi$
$229$	16.9382	+	5.50354i	1.11931	+	0.363684i	0.309803	+	0.950801i	$0.399737\pi$
$230$	0.512330	+	5.12635i	0.0337821	+	0.338021i
$231$		0			0
$232$	0.122691	+	0.398278i	0.00805508	+	0.0261483i
$233$	−0.936730	+	2.88296i	−0.0613672	+	0.188869i	−0.977040	−	0.213055i	$-0.931659\pi$
$233$	−0.936730	+	2.88296i	−0.0613672	+	0.188869i	0.915673	+	0.401924i	$0.131659\pi$
$234$	−1.45350	−	1.63096i	−0.0950182	−	0.106619i
$235$	−4.79205	+	6.59569i	−0.312599	+	0.430255i
$236$	−21.7900	+	12.2853i	−1.41841	+	0.799704i
$237$	15.6617	−	5.08879i	1.01734	−	0.330553i
$238$	11.5423	+	6.74280i	0.748174	+	0.437071i
$239$	−6.56547	+	4.77009i	−0.424685	+	0.308552i	−0.779520	−	0.626377i	$-0.784537\pi$
$239$	−6.56547	+	4.77009i	−0.424685	+	0.308552i	0.354835	+	0.934929i	$0.384537\pi$
$240$	2.31879	+	27.4477i	0.149677	+	1.77174i
$241$	10.6765			0.687734			0.343867	−	0.939018i	$-0.388263\pi$
$241$	10.6765			0.687734			0.343867	+	0.939018i	$0.388263\pi$
$242$		0			0
$243$			22.2834i			1.42948i
$244$	−1.31085	−	0.151336i	−0.0839186	−	0.00968827i
$245$	13.6176	+	18.7431i	0.869999	+	1.19745i
$246$	−6.58467	+	11.2716i	−0.419823	+	0.718649i
$247$	0.723676	+	2.22725i	0.0460464	+	0.141716i
$248$	2.57546	+	3.66156i	0.163542	+	0.232510i
$249$	−4.72187	−	3.43064i	−0.299236	−	0.217408i
$250$	6.93574	+	7.78253i	0.438655	+	0.492210i
$251$	−5.43982	−	1.76750i	−0.343358	−	0.111564i	0.132262	−	0.991215i	$-0.457776\pi$
$251$	−5.43982	−	1.76750i	−0.343358	−	0.111564i	−0.475620	+	0.879651i	$0.657776\pi$
$252$	27.3079	−	5.51340i	1.72023	−	0.347311i
$253$		0			0
$254$	3.63372	−	0.363156i	0.228000	−	0.0227865i
$255$	−5.09344	+	15.6760i	−0.318963	+	0.981668i
$256$	−2.32137	+	15.8307i	−0.145085	+	0.989419i
$257$	−19.5628	−	14.2132i	−1.22029	−	0.886595i	−0.224169	−	0.974550i	$-0.571967\pi$
$257$	−19.5628	−	14.2132i	−1.22029	−	0.886595i	−0.996124	+	0.0879551i	$0.971967\pi$
$258$	−9.61971	−	21.9068i	−0.598897	−	1.36386i
$259$	−27.7161	+	9.00551i	−1.72220	+	0.559575i
$260$	2.14689	+	0.982270i	0.133145	+	0.0609178i
$261$	0.305481	+	0.420459i	0.0189088	+	0.0260258i
$262$	−7.42781	−	1.61854i	−0.458891	−	0.0999939i
$263$	−22.3674			−1.37923			−0.689616	−	0.724175i	$-0.742221\pi$
$263$	−22.3674			−1.37923			−0.689616	+	0.724175i	$0.742221\pi$
$264$		0			0
$265$	−12.5044			−0.768138
$266$	−29.1791	−	6.35821i	−1.78908	−	0.389847i
$267$	17.3938	+	23.9405i	1.06448	+	1.46514i
$268$	−2.49762	+	5.45891i	−0.152566	+	0.333456i
$269$	15.9946	−	5.19697i	0.975209	−	0.316865i	0.222292	−	0.974980i	$-0.428646\pi$
$269$	15.9946	−	5.19697i	0.975209	−	0.316865i	0.752917	+	0.658116i	$0.228646\pi$
$270$	2.06455	+	4.70157i	0.125645	+	0.286128i
$271$	−2.93529	−	2.13261i	−0.178306	−	0.129547i	0.495052	−	0.868863i	$-0.335149\pi$
$271$	−2.93529	−	2.13261i	−0.178306	−	0.129547i	−0.673358	+	0.739316i	$0.735149\pi$
$272$	−4.95551	+	8.19185i	−0.300472	+	0.496704i
$273$	1.36544	−	4.20239i	0.0826401	−	0.254340i
$274$	2.34374	−	0.234235i	0.141590	−	0.0141506i
$275$		0			0
$276$	1.36671	+	6.76933i	0.0822665	+	0.407466i
$277$	29.9351	+	9.72650i	1.79862	+	0.584409i	0.999852	−	0.0172234i	$-0.00548266\pi$
$277$	29.9351	+	9.72650i	1.79862	+	0.584409i	0.798773	+	0.601632i	$0.205483\pi$
$278$	−11.8918	−	13.3437i	−0.713223	−	0.800301i
$279$	4.51647	+	3.28141i	0.270394	+	0.196453i
$280$	−24.6254	+	17.3209i	−1.47165	+	1.03512i
$281$	−1.92100	−	5.91222i	−0.114597	−	0.352693i	0.877266	−	0.480005i	$-0.159365\pi$
$281$	−1.92100	−	5.91222i	−0.114597	−	0.352693i	−0.991863	+	0.127312i	$0.959365\pi$
$282$	−5.51251	+	9.43626i	−0.328265	+	0.561921i
$283$	13.2101	+	18.1822i	0.785260	+	1.08082i	0.994682	+	0.102993i	$0.0328419\pi$
$283$	13.2101	+	18.1822i	0.785260	+	1.08082i	−0.209422	+	0.977825i	$0.567158\pi$
$284$	−2.42358	+	20.9928i	−0.143813	+	1.24569i
$285$		−	36.8234i		−	2.18123i
$286$		0			0
$287$	−14.2678			−0.842204
$288$	3.64855	+	19.6168i	0.214993	+	1.15593i
$289$	9.11846	−	6.62495i	0.536380	−	0.389703i
$290$	−0.484965	−	0.283309i	−0.0284781	−	0.0166364i
$291$	21.0972	−	6.85489i	1.23674	−	0.401841i
$292$	−10.4543	−	18.5424i	−0.611790	−	1.08511i
$293$	6.68555	−	9.20187i	0.390574	−	0.537579i	−0.567773	−	0.823185i	$-0.692195\pi$
$293$	6.68555	−	9.20187i	0.390574	−	0.537579i	0.958347	+	0.285606i	$0.0921949\pi$
$294$	20.6620	+	23.1846i	1.20503	+	1.35215i
$295$	10.4177	−	32.0624i	0.606542	−	1.86674i
$296$	−6.14491	−	19.9475i	−0.357166	−	1.15942i
$297$		0			0
$298$	2.73069	+	27.3231i	0.158185	+	1.58279i
$299$	0.562939	+	0.182910i	0.0325556	+	0.0105780i
$300$	−8.52207	−	7.83249i	−0.492022	−	0.452209i
$301$	15.3710	−	21.1564i	0.885969	−	1.21943i
$302$	10.3132	+	23.4861i	0.593458	+	1.35147i
$303$	−4.44587	−	13.6830i	−0.255409	−	0.786067i
$304$	4.87373	−	20.8265i	0.279528	−	1.19448i
$305$	1.43874	−	1.04530i	0.0823817	−	0.0598538i
$306$	−2.54203	+	11.6659i	−0.145318	+	0.666894i
$307$			14.1471i			0.807418i	0.914887	+	0.403709i	$0.132279\pi$
$307$			14.1471i			0.807418i	−0.914887	+	0.403709i	$0.867721\pi$
$308$		0			0
$309$			39.5511i			2.24998i
$310$	−5.89483	−	1.28450i	−0.334804	−	0.0729548i
$311$	11.8464	−	8.60693i	0.671749	−	0.488054i	−0.198861	−	0.980028i	$-0.563724\pi$
$311$	11.8464	−	8.60693i	0.671749	−	0.488054i	0.870610	+	0.491974i	$0.163724\pi$
$312$	2.99451	+	1.02398i	0.169531	+	0.0579717i
$313$	7.02226	+	21.6123i	0.396922	+	1.22160i	0.927455	+	0.373935i	$0.121992\pi$
$313$	7.02226	+	21.6123i	0.396922	+	1.22160i	−0.530533	+	0.847664i	$0.678008\pi$
$314$	−3.79317	+	1.66566i	−0.214061	+	0.0939984i
$315$	−22.0687	+	30.3750i	−1.24343	+	1.71144i
$316$	−8.72342	+	9.49145i	−0.490731	+	0.533936i
$317$	3.88445	+	1.26213i	0.218172	+	0.0708885i	0.416064	−	0.909335i	$-0.363409\pi$
$317$	3.88445	+	1.26213i	0.218172	+	0.0708885i	−0.197891	+	0.980224i	$0.563409\pi$
$318$	−16.6786	+	1.66687i	−0.935290	+	0.0934734i
$319$		0			0
$320$	−12.1338	−	17.8254i	−0.678303	−	0.996470i
$321$	−2.47900	+	7.62957i	−0.138364	+	0.425841i
$322$	−5.63506	+	5.02193i	−0.314030	+	0.279861i
$323$	7.52299	−	10.3545i	0.418590	−	0.576140i
$324$	−7.01345	−	12.4395i	−0.389636	−	0.691085i
$325$	−0.943515	+	0.306567i	−0.0523368	+	0.0170053i
$326$	2.59602	−	4.44384i	0.143780	−	0.246122i
$327$	33.1215	−	24.0641i	1.83162	−	1.33075i
$328$	0.156649	−	10.2178i	0.00864949	−	0.564182i
$329$	−11.9447			−0.658530
$330$		0			0
$331$		−	7.57089i		−	0.416133i	−0.978115	−	0.208067i	$-0.933283\pi$
$331$		−	7.57089i		−	0.416133i	0.978115	−	0.208067i	$-0.0667171\pi$
$332$	4.53885	+	0.524003i	0.249102	+	0.0287584i
$333$	−15.2998	−	21.0584i	−0.838425	−	1.15399i
$334$	16.8519	+	9.84459i	0.922093	+	0.538672i
$335$	−2.50009	−	7.69450i	−0.136595	−	0.420395i
$336$	−30.5369	+	26.3857i	−1.66593	+	1.43946i
$337$	1.02369	+	0.743755i	0.0557640	+	0.0405149i	0.615318	−	0.788279i	$-0.289028\pi$
$337$	1.02369	+	0.743755i	0.0557640	+	0.0405149i	−0.559554	+	0.828794i	$0.689028\pi$
$338$	−13.5227	+	12.0514i	−0.735540	+	0.655508i
$339$	−40.5114	−	13.1630i	−2.20028	−	0.714914i
$340$	−2.55358	−	12.6479i	−0.138487	−	0.685927i
$341$		0			0
$342$	−2.65259	−	26.5416i	−0.143436	−	1.43521i
$343$	−1.94672	+	5.99140i	−0.105113	+	0.323505i
$344$	14.9822	+	11.2401i	0.807783	+	0.606023i
$345$	−7.52964	−	5.47061i	−0.405382	−	0.294528i
$346$	−9.73651	+	4.27549i	−0.523438	+	0.229852i
$347$	6.56752	−	2.13392i	0.352563	−	0.114555i	−0.127381	−	0.991854i	$-0.540657\pi$
$347$	6.56752	−	2.13392i	0.352563	−	0.114555i	0.479944	+	0.877299i	$0.340657\pi$
$348$	−0.684622	−	0.313236i	−0.0366996	−	0.0167912i
$349$	−9.34021	−	12.8557i	−0.499970	−	0.688150i	0.482218	−	0.876051i	$-0.339831\pi$
$349$	−9.34021	−	12.8557i	−0.499970	−	0.688150i	−0.982188	+	0.187902i	$0.939831\pi$
$350$	2.69349	−	12.3610i	0.143973	−	0.660721i
$351$	0.589956			0.0314895
$352$		0			0
$353$	2.35416			0.125300			0.0626498	−	0.998036i	$-0.480045\pi$
$353$	2.35416			0.125300			0.0626498	+	0.998036i	$0.480045\pi$
$354$	9.62134	−	44.1542i	0.511368	−	2.34677i
$355$	−16.7401	−	23.0408i	−0.888473	−	1.22288i
$356$	−21.0653	−	9.63802i	−1.11646	−	0.510814i
$357$	−22.9671	+	7.46246i	−1.21555	+	0.394955i
$358$	−24.2208	+	10.6358i	−1.28011	+	0.562121i
$359$	20.6183	+	14.9801i	1.08819	+	0.790619i	0.979093	−	0.203412i	$-0.0652029\pi$
$359$	20.6183	+	14.9801i	1.08819	+	0.790619i	0.109101	+	0.994031i	$0.465203\pi$
$360$	−21.5105	−	16.1378i	−1.13370	−	0.850536i
$361$	−2.96455	+	9.12393i	−0.156029	+	0.480207i
$362$	3.27833	+	32.8027i	0.172305	+	1.72407i
$363$		0			0
$364$	0.684558	+	3.39062i	0.0358806	+	0.177717i
$365$	27.2838	+	8.86503i	1.42810	+	0.464017i
$366$	1.77967	−	1.58603i	0.0930250	−	0.0829033i
$367$	4.55603	+	3.31015i	0.237823	+	0.172788i	0.700313	−	0.713836i	$-0.253044\pi$
$367$	4.55603	+	3.31015i	0.237823	+	0.172788i	−0.462490	+	0.886625i	$0.653044\pi$
$368$	−3.53454	−	4.09063i	−0.184251	−	0.213239i
$369$	−3.93806	−	12.1201i	−0.205007	−	0.630947i
$370$	24.2891	+	14.1893i	1.26273	+	0.737667i
$371$	−10.7684	−	14.8215i	−0.559069	−	0.769492i
$372$	−8.03387	−	0.927498i	−0.416537	−	0.0480885i
$373$			33.3480i			1.72669i	0.504611	+	0.863347i	$0.331636\pi$
$373$			33.3480i			1.72669i	−0.504611	+	0.863347i	$0.668364\pi$
$374$		0			0
$375$	−18.8326			−0.972510
$376$	0.131142	−	8.55404i	0.00676315	−	0.441141i
$377$	−0.0522053	+	0.0379294i	−0.00268871	+	0.00195346i
$378$	−3.79484	+	6.49597i	−0.195185	+	0.334117i
$379$	18.0604	−	5.86819i	0.927702	−	0.301429i	0.194079	−	0.980986i	$-0.437828\pi$
$379$	18.0604	−	5.86819i	0.927702	−	0.301429i	0.733622	+	0.679557i	$0.237828\pi$
$380$	14.1573	+	25.1103i	0.726252	+	1.28813i
$381$	−3.87774	+	5.33726i	−0.198663	+	0.273436i
$382$	−14.9913	+	13.3601i	−0.767021	+	0.683564i
$383$	−8.94182	+	27.5201i	−0.456906	+	1.40621i	0.411978	+	0.911194i	$0.364838\pi$
$383$	−8.94182	+	27.5201i	−0.456906	+	1.40621i	−0.868883	+	0.495017i	$0.835162\pi$
$384$	−18.5606	−	22.1584i	−0.947164	−	1.13077i
$385$		0			0
$386$	2.13543	−	0.213416i	0.108690	−	0.0108626i
$387$	22.2142	+	7.21784i	1.12921	+	0.366903i
$388$	−11.7509	+	12.7855i	−0.596564	+	0.649087i
$389$	−14.4180	+	19.8446i	−0.731020	+	1.00616i	0.268065	+	0.963401i	$0.413616\pi$
$389$	−14.4180	+	19.8446i	−0.731020	+	1.00616i	−0.999085	+	0.0427617i	$0.986384\pi$
$390$	−3.90522	+	1.71486i	−0.197748	+	0.0868352i
$391$	−0.999647	−	3.07660i	−0.0505543	−	0.155590i
$392$	−23.0033	−	7.86606i	−1.16184	−	0.397296i
$393$	11.1107	−	8.07240i	0.560461	−	0.407199i
$394$	11.1326	+	2.42584i	0.560855	+	0.122212i
$395$		−	17.3737i		−	0.874165i
$396$		0			0
$397$		−	1.08190i		−	0.0542989i	−0.999631	−	0.0271495i	$-0.991357\pi$
$397$		−	1.08190i		−	0.0542989i	0.999631	−	0.0271495i	$-0.00864300\pi$
$398$	2.92108	−	13.4054i	0.146420	−	0.671951i
$399$	43.6468	−	31.7113i	2.18507	−	1.58755i
$400$	8.82260	+	2.06463i	0.441130	+	0.103231i
$401$	−6.44640	−	19.8400i	−0.321918	−	0.990761i	−0.972813	−	0.231593i	$-0.925606\pi$
$401$	−6.44640	−	19.8400i	−0.321918	−	0.990761i	0.650895	−	0.759168i	$-0.274394\pi$
$402$	−4.36037	−	9.92981i	−0.217476	−	0.495254i
$403$	−0.407429	+	0.560777i	−0.0202955	+	0.0279343i
$404$	8.29229	+	7.62130i	0.412557	+	0.379174i
$405$	18.3039	+	5.94728i	0.909526	+	0.295523i
$406$	−0.0818320	−	0.818807i	−0.00406125	−	0.0406367i
$407$		0			0
$408$	−5.09201	−	16.5296i	−0.252092	−	0.818336i
$409$	−8.38423	+	25.8040i	−0.414573	+	1.27593i	0.498059	+	0.867143i	$0.334046\pi$
$409$	−8.38423	+	25.8040i	−0.414573	+	1.27593i	−0.912632	+	0.408782i	$0.865954\pi$
$410$	9.16296	+	10.2817i	0.452526	+	0.507775i
$411$	−2.50113	+	3.44251i	−0.123372	+	0.169807i
$412$	−15.2059	−	26.9703i	−0.749143	−	1.32873i
$413$	46.9750	−	15.2631i	2.31149	−	0.751048i
$414$	−5.82131	−	3.40071i	−0.286102	−	0.167136i
$415$	−4.98165	+	3.61938i	−0.244540	+	0.177668i
$416$	−2.43567	+	0.453013i	−0.119419	+	0.0222108i
$417$	32.2897			1.58124
$418$		0			0
$419$		−	13.9742i		−	0.682686i	−0.939939	−	0.341343i	$-0.889118\pi$
$419$		−	13.9742i		−	0.682686i	0.939939	−	0.341343i	$-0.110882\pi$
$420$	6.23777	−	54.0308i	0.304372	−	2.63643i
$421$	15.1380	+	20.8356i	0.737779	+	1.01547i	0.998743	+	0.0501176i	$0.0159596\pi$
$421$	15.1380	+	20.8356i	0.737779	+	1.01547i	−0.260964	+	0.965349i	$0.584040\pi$
$422$	−13.8648	+	23.7336i	−0.674927	+	1.15533i
$423$	−3.29684	−	10.1466i	−0.160298	−	0.493345i
$424$	10.7325	−	7.54897i	0.521215	−	0.366610i
$425$	4.38642	+	3.18692i	0.212772	+	0.154588i
$426$	−25.3997	−	28.5008i	−1.23062	−	1.38087i
$427$	2.47800	+	0.805150i	0.119919	+	0.0389639i
$428$	−1.24284	−	6.15577i	−0.0600748	−	0.297551i
$429$		0			0
$430$	−25.1171	+	2.51021i	−1.21125	+	0.121053i
$431$	5.65281	−	17.3976i	0.272286	−	0.838011i	−0.717638	−	0.696416i	$-0.754777\pi$
$431$	5.65281	−	17.3976i	0.272286	−	0.838011i	0.989925	−	0.141595i	$-0.0452231\pi$
$432$	−4.61036	−	2.78896i	−0.221816	−	0.134184i
$433$	7.94313	+	5.77102i	0.381723	+	0.277338i	0.762055	−	0.647512i	$-0.224190\pi$
$433$	7.94313	+	5.77102i	0.381723	+	0.277338i	−0.380333	+	0.924850i	$0.624190\pi$
$434$	−3.55394	−	8.09332i	−0.170594	−	0.388492i
$435$	0.964995	−	0.313546i	0.0462680	−	0.0150334i
$436$	−13.3341	+	29.1436i	−0.638587	+	1.39573i
$437$	4.24794	+	5.84679i	0.203207	+	0.279690i
$438$	37.5734	+	8.18736i	1.79533	+	0.391207i
$439$	32.0228			1.52836			0.764182	−	0.645001i	$-0.223143\pi$
$439$	32.0228			1.52836			0.764182	+	0.645001i	$0.223143\pi$
$440$		0			0
$441$	−30.3176			−1.44370
$442$	−1.44847	−	0.315625i	−0.0688965	−	0.0150128i
$443$	9.95737	+	13.7051i	0.473089	+	0.651151i	0.977158	−	0.212512i	$-0.0681644\pi$
$443$	9.95737	+	13.7051i	0.473089	+	0.651151i	−0.504069	+	0.863663i	$0.668164\pi$
$444$	34.2888	+	15.6882i	1.62727	+	0.744528i
$445$	29.6922	−	9.64757i	1.40754	−	0.457339i
$446$	12.7109	+	28.9462i	0.601877	+	1.37064i
$447$	−40.1325	−	29.1580i	−1.89820	−	1.37913i
$448$	10.6791	−	29.7330i	0.504542	−	1.40475i
$449$	6.42976	−	19.7888i	0.303439	−	0.933890i	−0.676816	−	0.736152i	$-0.736641\pi$
$449$	6.42976	−	19.7888i	0.303439	−	0.933890i	0.980255	−	0.197737i	$-0.0633593\pi$
$450$	11.2437	−	1.12370i	0.530032	−	0.0529717i
$451$		0			0
$452$	32.6858	−	6.59920i	1.53741	−	0.310400i
$453$	−44.0713	−	14.3196i	−2.07065	−	0.672796i
$454$	−13.0527	−	14.6463i	−0.612592	−	0.687383i
$455$	−3.77144	−	2.74011i	−0.176808	−	0.128458i
$456$	22.2305	+	31.6054i	1.04104	+	1.48006i
$457$	1.55543	+	4.78713i	0.0727601	+	0.223933i	0.980823	−	0.194902i	$-0.0624388\pi$
$457$	1.55543	+	4.78713i	0.0727601	+	0.223933i	−0.908063	+	0.418834i	$0.862439\pi$
$458$	12.7048	−	21.7479i	0.593654	−	1.01621i
$459$	−1.89517	−	2.60848i	−0.0884589	−	0.121753i
$460$	7.23779	+	0.835592i	0.337464	+	0.0389597i
$461$			12.9071i			0.601144i	0.953759	+	0.300572i	$0.0971775\pi$
$461$			12.9071i			0.601144i	−0.953759	+	0.300572i	$0.902822\pi$
$462$		0			0
$463$	2.39020			0.111082			0.0555410	−	0.998456i	$-0.482312\pi$
$463$	2.39020			0.111082			0.0555410	+	0.998456i	$0.482312\pi$
$464$	0.587279	−	0.0496134i	0.0272637	−	0.00230324i
$465$	8.81764	−	6.40639i	0.408908	−	0.297089i
$466$	3.70159	+	2.16241i	0.171473	+	0.100172i
$467$	−7.86285	+	2.55479i	−0.363849	+	0.118222i	−0.485235	−	0.874384i	$-0.661266\pi$
$467$	−7.86285	+	2.55479i	−0.363849	+	0.118222i	0.121386	+	0.992605i	$0.461266\pi$
$468$	−2.69128	+	1.51735i	−0.124405	+	0.0701397i
$469$	6.96729	−	9.58965i	0.321719	−	0.442809i
$470$	7.67098	+	8.60754i	0.353836	+	0.397036i
$471$	2.31272	−	7.11783i	0.106565	−	0.327972i
$472$	10.4148	+	33.8083i	0.479379	+	1.55615i
$473$		0			0
$474$	−2.31596	−	23.1734i	−0.106376	−	1.06439i
$475$	−11.5200	−	3.74309i	−0.528576	−	0.171745i
$476$	12.7925	−	13.9187i	0.586342	−	0.637964i
$477$	9.61820	−	13.2383i	0.440387	−	0.606141i
$478$	4.61442	+	10.5083i	0.211059	+	0.480641i
$479$	−6.70346	−	20.6311i	−0.306289	−	0.942660i	−0.979193	−	0.202930i	$-0.934954\pi$
$479$	−6.70346	−	20.6311i	−0.306289	−	0.942660i	0.672905	−	0.739729i	$-0.265046\pi$
$480$	38.6251	+	5.06033i	1.76299	+	0.230972i
$481$	2.61467	−	1.89967i	0.119219	−	0.0866173i
$482$	3.21465	−	14.7527i	0.146423	−	0.671966i
$483$		−	13.6360i		−	0.620461i
$484$		0			0
$485$		−	23.4033i		−	1.06269i
$486$	30.7910	+	6.70945i	1.39671	+	0.304347i
$487$	−11.7267	+	8.51996i	−0.531389	+	0.386076i	−0.820877	−	0.571105i	$-0.806515\pi$
$487$	−11.7267	+	8.51996i	−0.531389	+	0.386076i	0.289488	+	0.957182i	$0.406515\pi$
$488$	−0.603806	+	1.76575i	−0.0273330	+	0.0799318i
$489$	2.87309	+	8.84247i	0.129926	+	0.399870i
$490$	29.9992	−	13.1732i	1.35522	−	0.595106i
$491$	19.9344	−	27.4374i	0.899627	−	1.23823i	−0.0709595	−	0.997479i	$-0.522606\pi$
$491$	19.9344	−	27.4374i	0.899627	−	1.23823i	0.970587	−	0.240751i	$-0.0773939\pi$
$492$	13.5923	+	12.4925i	0.612789	+	0.563203i
$493$	0.335408	+	0.108981i	0.0151060	+	0.00490824i
$494$	3.29548	−	0.329352i	0.148271	−	0.0148183i
$495$		0			0
$496$	5.83497	−	2.45626i	0.261998	−	0.110289i
$497$	12.8942	−	39.6842i	0.578382	−	1.78008i
$498$	−6.16215	+	5.49167i	−0.276133	+	0.246088i
$499$	−4.54484	+	6.25543i	−0.203455	+	0.280031i	−0.898536	−	0.438900i	$-0.855368\pi$
$499$	−4.54484	+	6.25543i	−0.203455	+	0.280031i	0.695081	+	0.718931i	$0.255368\pi$
$500$	12.8421	−	7.24044i	0.574318	−	0.323802i
$501$	−33.5323	+	10.8953i	−1.49811	+	0.486766i
$502$	−4.08023	+	6.98449i	−0.182109	+	0.311733i
$503$	12.3267	−	8.95587i	0.549620	−	0.399322i	−0.278025	−	0.960574i	$-0.589680\pi$
$503$	12.3267	−	8.95587i	0.549620	−	0.399322i	0.827645	+	0.561251i	$0.189680\pi$
$504$	0.603947	−	39.3938i	0.0269019	−	1.75474i
$505$	−15.1787			−0.675442
$506$		0			0
$507$		−	32.7230i		−	1.45328i
$508$	0.592295	−	5.13038i	0.0262788	−	0.227624i
$509$	−20.4133	−	28.0965i	−0.904804	−	1.24536i	−0.968910	−	0.247413i	$-0.920420\pi$
$509$	−20.4133	−	28.0965i	−0.904804	−	1.24536i	0.0641063	−	0.997943i	$-0.479580\pi$
$510$	20.1273	+	11.7580i	0.891251	+	0.520655i
$511$	12.9883	+	39.9738i	0.574567	+	1.76834i
$512$	21.1757	+	7.97421i	0.935844	+	0.352413i
$513$	5.82750	+	4.23393i	0.257290	+	0.186932i
$514$	−25.5299	+	22.7521i	−1.12608	+	1.00355i
$515$	39.6848	+	12.8944i	1.74872	+	0.568194i
$516$	−33.1670	+	6.69635i	−1.46010	+	0.294790i
$517$		0			0
$518$	4.09850	+	41.0094i	0.180078	+	1.80185i
$519$	5.93642	−	18.2704i	0.260580	−	0.801983i
$520$	2.00371	−	2.67079i	0.0878685	−	0.117122i
$521$	25.1628	+	18.2818i	1.10240	+	0.800941i	0.981450	−	0.191717i	$-0.0614057\pi$
$521$	25.1628	+	18.2818i	1.10240	+	0.800941i	0.120951	+	0.992659i	$0.461406\pi$
$522$	0.672965	−	0.295512i	0.0294549	−	0.0129342i
$523$	9.39693	−	3.05325i	0.410899	−	0.133509i	−0.0962712	−	0.995355i	$-0.530692\pi$
$523$	9.39693	−	3.05325i	0.410899	−	0.133509i	0.507170	+	0.861846i	$0.330692\pi$
$524$	−4.47297	+	9.77632i	−0.195403	+	0.427081i
$525$	13.4337	+	18.4898i	0.586293	+	0.806963i
$526$	−6.73474	+	30.9070i	−0.293648	+	1.34761i
$527$	3.78828			0.165020
$528$		0			0
$529$	−21.1734			−0.920581
$530$	−3.76502	+	17.2784i	−0.163542	+	0.750527i
$531$	25.9311	+	35.6911i	1.12531	+	1.54886i
$532$	−17.5714	+	38.4049i	−0.761817	+	1.66506i
$533$	1.50486	−	0.488960i	0.0651829	−	0.0211792i
$534$	38.3180	−	16.8262i	1.65818	−	0.728140i
$535$	6.84717	+	4.97476i	0.296029	+	0.215078i
$536$	6.79103	+	5.09484i	0.293328	+	0.220064i
$537$	14.7676	−	45.4500i	0.637268	−	1.96131i
$538$	−2.36519	−	23.6660i	−0.101971	−	1.02031i
$539$		0			0
$540$	7.11820	−	1.43715i	0.306319	−	0.0618450i
$541$	−7.97501	−	2.59124i	−0.342872	−	0.111406i	0.132519	−	0.991180i	$-0.457694\pi$
$541$	−7.97501	−	2.59124i	−0.342872	−	0.111406i	−0.475391	+	0.879774i	$0.657694\pi$
$542$	−3.83063	+	3.41383i	−0.164539	+	0.146637i
$543$	−48.1811	−	35.0056i	−2.06765	−	1.50223i
$544$	9.82732	+	9.31401i	0.421343	+	0.399335i
$545$	−13.3473	−	41.0788i	−0.571736	−	1.75962i
$546$	−5.39569	−	3.15207i	−0.230914	−	0.134896i
$547$	−1.99349	−	2.74380i	−0.0852353	−	0.117316i	0.764270	−	0.644896i	$-0.223099\pi$
$547$	−1.99349	−	2.74380i	−0.0852353	−	0.117316i	−0.849505	+	0.527580i	$0.823099\pi$
$548$	0.382028	−	3.30908i	0.0163194	−	0.141357i
$549$			2.32721i			0.0993230i
$550$		0			0
$551$	−0.787883			−0.0335650
$552$	9.76530	+	0.149712i	0.415639	+	0.00637217i
$553$	20.5930	−	14.9617i	0.875705	−	0.636237i
$554$	22.4533	−	38.4354i	0.953950	−	1.63296i
$555$	−48.3311	+	15.7037i	−2.05154	+	0.666586i
$556$	−22.0187	+	12.4142i	−0.933802	+	0.526480i
$557$	−16.4800	+	22.6828i	−0.698282	+	0.961102i	0.301689	+	0.953407i	$0.402450\pi$
$557$	−16.4800	+	22.6828i	−0.698282	+	0.961102i	−0.999970	+	0.00769589i	$0.997550\pi$
$558$	5.89411	−	5.25279i	0.249518	−	0.222368i
$559$	−0.896186	+	2.75818i	−0.0379046	+	0.116658i
$560$	16.5193	+	39.2424i	0.698066	+	1.65829i
$561$		0			0
$562$	−8.74784	+	0.874264i	−0.369005	+	0.0368786i
$563$	−8.37900	−	2.72250i	−0.353133	−	0.114740i	0.127078	−	0.991893i	$-0.459440\pi$
$563$	−8.37900	−	2.72250i	−0.353133	−	0.114740i	−0.480211	+	0.877153i	$0.659440\pi$
$564$	11.3791	+	10.4583i	0.479147	+	0.440376i
$565$	−26.4149	+	36.3570i	−1.11128	+	1.52955i
$566$	29.1015	−	12.7790i	1.22323	−	0.537142i
$567$	8.71344	+	26.8172i	0.365930	+	1.12622i
$568$	28.2779	+	9.66973i	1.18651	+	0.405733i
$569$	16.8013	−	12.2069i	0.704349	−	0.511739i	−0.176997	−	0.984211i	$-0.556638\pi$
$569$	16.8013	−	12.2069i	0.704349	−	0.511739i	0.881346	+	0.472472i	$0.156638\pi$
$570$	−50.8822	−	11.0874i	−2.13122	−	0.464400i
$571$		−	2.93591i		−	0.122864i	−0.998111	−	0.0614321i	$-0.980433\pi$
$571$		−	2.93591i		−	0.122864i	0.998111	−	0.0614321i	$-0.0195668\pi$
$572$		0			0
$573$		−	36.2767i		−	1.51548i
$574$	−4.29599	+	19.7151i	−0.179311	+	0.822894i
$575$	−2.47684	+	1.79953i	−0.103291	+	0.0750456i
$576$	28.2048	+	0.865022i	1.17520	+	0.0360426i
$577$	−3.38107	−	10.4059i	−0.140756	−	0.433202i	0.855685	−	0.517497i	$-0.173136\pi$
$577$	−3.38107	−	10.4059i	−0.140756	−	0.433202i	−0.996441	+	0.0842953i	$0.973136\pi$
$578$	−6.40875	−	14.5945i	−0.266569	−	0.607053i
$579$	−2.27883	+	3.13654i	−0.0947051	+	0.130350i
$580$	−0.537494	+	0.584816i	−0.0223182	+	0.0242832i
$581$	−8.58011	−	2.78785i	−0.355963	−	0.115659i
$582$	−3.11973	−	31.2159i	−0.129317	−	1.29394i
$583$		0			0
$584$	−28.7694	+	8.86254i	−1.19049	+	0.366735i
$585$	1.28669	−	3.96002i	0.0531980	−	0.163727i
$586$	−10.7020	−	12.0087i	−0.442098	−	0.496074i
$587$	12.2077	−	16.8024i	0.503865	−	0.693511i	−0.479004	−	0.877812i	$-0.659002\pi$
$587$	12.2077	−	16.8024i	0.503865	−	0.693511i	0.982870	+	0.184301i	$0.0590022\pi$
$588$	38.2575	−	21.5697i	1.57771	−	0.889519i
$589$	−8.04904	+	2.61529i	−0.331655	+	0.107761i
$590$	−41.1667	−	24.0489i	−1.69481	−	0.990079i
$591$	−16.6525	+	12.0988i	−0.684993	+	0.497677i
$592$	−29.4134	+	2.48485i	−1.20888	+	0.102127i
$593$	−29.8145			−1.22433			−0.612167	−	0.790729i	$-0.709702\pi$
$593$	−29.8145			−1.22433			−0.612167	+	0.790729i	$0.709702\pi$
$594$		0			0
$595$			25.4776i			1.04448i
$596$	38.5770	+	4.45365i	1.58017	+	0.182429i
$597$	14.5687	+	20.0521i	0.596259	+	0.820679i
$598$	0.422242	−	0.722789i	0.0172667	−	0.0295570i
$599$	−1.68364	−	5.18170i	−0.0687915	−	0.211718i	0.910751	−	0.412956i	$-0.135504\pi$
$599$	−1.68364	−	5.18170i	−0.0687915	−	0.211718i	−0.979542	+	0.201238i	$0.935504\pi$
$600$	−13.3888	+	9.41738i	−0.546596	+	0.384463i
$601$	13.4456	+	9.76880i	0.548457	+	0.398478i	0.827216	−	0.561883i	$-0.189923\pi$
$601$	13.4456	+	9.76880i	0.548457	+	0.398478i	−0.278759	+	0.960361i	$0.589923\pi$
$602$	−24.6055	−	27.6096i	−1.00284	−	1.12528i
$603$	10.0692	+	3.27167i	0.410048	+	0.133233i
$604$	35.5581	−	7.17910i	1.44684	−	0.292113i
$605$		0			0
$606$	−20.2456	+	2.02336i	−0.822423	+	0.0821934i
$607$	−9.43482	+	29.0374i	−0.382948	+	1.17859i	0.555011	+	0.831843i	$0.312714\pi$
$607$	−9.43482	+	29.0374i	−0.382948	+	1.17859i	−0.937958	+	0.346748i	$0.887286\pi$
$608$	−27.3103	−	13.0052i	−1.10758	−	0.527432i
$609$	1.20267	+	0.873793i	0.0487348	+	0.0354079i
$610$	−1.01119	−	2.30276i	−0.0409419	−	0.0932362i
$611$	1.25983	−	0.409344i	0.0509673	−	0.0165603i
$612$	15.3544	+	7.02511i	0.620664	+	0.283973i
$613$	0.936777	+	1.28936i	0.0378361	+	0.0520769i	0.827516	−	0.561442i	$-0.189753\pi$
$613$	0.936777	+	1.28936i	0.0378361	+	0.0520769i	−0.789680	+	0.613519i	$0.789753\pi$
$614$	19.5483	+	4.25964i	0.788906	+	0.171905i
$615$	−24.8801			−1.00326
$616$		0			0
$617$	8.83199			0.355562			0.177781	−	0.984070i	$-0.443108\pi$
$617$	8.83199			0.355562			0.177781	+	0.984070i	$0.443108\pi$
$618$	54.6513	+	11.9087i	2.19840	+	0.479038i
$619$	−16.5184	−	22.7356i	−0.663931	−	0.913822i	0.335673	−	0.941979i	$-0.391036\pi$
$619$	−16.5184	−	22.7356i	−0.663931	−	0.913822i	−0.999604	+	0.0281563i	$0.991036\pi$
$620$	−3.54982	+	7.75865i	−0.142564	+	0.311595i
$621$	1.73151	−	0.562600i	0.0694829	−	0.0225764i
$622$	−8.32604	−	18.9608i	−0.333844	−	0.760257i
$623$	37.0053	+	26.8859i	1.48259	+	1.07716i
$624$	2.31657	−	3.82946i	0.0927369	−	0.153301i
$625$	−9.63975	+	29.6681i	−0.385590	+	1.18672i
$626$	31.9780	−	3.19590i	1.27810	−	0.127734i
$627$		0			0
$628$	1.15948	+	5.74289i	0.0462681	+	0.229166i
$629$	−16.7987	−	5.45821i	−0.669806	−	0.217633i
$630$	35.3270	+	39.6401i	1.40746	+	1.57930i
$631$	10.4738	+	7.60965i	0.416955	+	0.302935i	0.776411	−	0.630226i	$-0.217038\pi$
$631$	10.4738	+	7.60965i	0.416955	+	0.302935i	−0.359457	+	0.933162i	$0.617038\pi$
$632$	10.4886	+	14.9118i	0.417214	+	0.593158i
$633$	−15.3446	−	47.2257i	−0.609891	−	1.87705i
$634$	2.91360	−	4.98747i	0.115714	−	0.198078i
$635$	4.09108	+	5.63090i	0.162350	+	0.223455i
$636$	−2.71860	+	23.5482i	−0.107800	+	0.933747i
$637$		−	3.76432i		−	0.149148i
$638$		0			0
$639$	37.2694			1.47435
$640$	−28.2844	+	11.3993i	−1.11804	+	0.450595i
$641$	18.3341	−	13.3205i	0.724153	−	0.526128i	−0.163555	−	0.986534i	$-0.552296\pi$
$641$	18.3341	−	13.3205i	0.724153	−	0.526128i	0.887708	+	0.460406i	$0.152296\pi$
$642$	9.79605	+	5.72269i	0.386619	+	0.225857i
$643$	−31.7639	+	10.3207i	−1.25264	+	0.407009i	−0.858868	−	0.512197i	$-0.828832\pi$
$643$	−31.7639	+	10.3207i	−1.25264	+	0.407009i	−0.393777	+	0.919206i	$0.628832\pi$
$644$	5.24255	+	9.29855i	0.206586	+	0.366414i
$645$	26.8038	−	36.8923i	1.05540	−	1.45263i
$646$	−12.0426	−	13.5129i	−0.473810	−	0.531657i
$647$	5.65587	−	17.4070i	0.222355	−	0.684339i	−0.776194	−	0.630494i	$-0.782852\pi$
$647$	5.65587	−	17.4070i	0.222355	−	0.684339i	0.998549	−	0.0538448i	$-0.0171476\pi$
$648$	−19.3005	+	5.94561i	−0.758197	+	0.233566i
$649$		0			0
$650$	0.139522	+	1.39605i	0.00547249	+	0.0547574i
$651$	15.1870	+	4.93456i	0.595226	+	0.193401i
$652$	−5.35880	−	4.92518i	−0.209867	−	0.192885i
$653$	−13.4743	+	18.5458i	−0.527289	+	0.725752i	−0.986714	−	0.162465i	$-0.948056\pi$
$653$	−13.4743	+	18.5458i	−0.527289	+	0.725752i	0.459425	+	0.888217i	$0.348056\pi$
$654$	−23.2788	−	53.0125i	−0.910274	−	2.07295i
$655$	−4.47740	−	13.7800i	−0.174947	−	0.538430i
$656$	−14.0716	−	3.29299i	−0.549405	−	0.128570i
$657$	−30.3716	+	22.0663i	−1.18491	+	0.860888i
$658$	−3.59649	+	16.5050i	−0.140206	+	0.643431i
$659$		−	29.7976i		−	1.16075i	−0.814349	−	0.580375i	$-0.802906\pi$
$659$		−	29.7976i		−	1.16075i	0.814349	−	0.580375i	$-0.197094\pi$
$660$		0			0
$661$			14.8182i			0.576361i	0.957576	+	0.288181i	$0.0930503\pi$
$661$			14.8182i			0.576361i	−0.957576	+	0.288181i	$0.906950\pi$
$662$	−10.4614	−	2.27957i	−0.406593	−	0.0885978i
$663$	2.16666	−	1.57417i	0.0841459	−	0.0611356i
$664$	2.09069	−	6.11395i	0.0811346	−	0.237267i
$665$	−17.5888	−	54.1328i	−0.682065	−	2.09918i
$666$	−33.7050	+	14.8005i	−1.30604	+	0.573509i
$667$	−0.117051	+	0.161106i	−0.00453222	+	0.00623806i
$668$	18.6772	−	20.3216i	0.722642	−	0.786265i
$669$	−54.3172	−	17.6487i	−2.10003	−	0.682340i
$670$	−11.3849	+	1.13782i	−0.439839	+	0.0439577i
$671$		0			0
$672$	27.2648	+	50.1402i	1.05176	+	1.93420i
$673$	−3.92371	+	12.0759i	−0.151248	+	0.465493i	−0.997761	−	0.0668741i	$-0.978697\pi$
$673$	−3.92371	+	12.0759i	−0.151248	+	0.465493i	0.846514	+	0.532367i	$0.178697\pi$
$674$	1.33594	−	1.19058i	0.0514586	−	0.0458596i
$675$	−1.79359	+	2.46867i	−0.0690354	+	0.0950191i
$676$	12.5808	+	22.3142i	0.483877	+	0.858238i
$677$	−24.8717	+	8.08131i	−0.955898	+	0.310590i	−0.745110	−	0.666942i	$-0.767603\pi$
$677$	−24.8717	+	8.08131i	−0.955898	+	0.310590i	−0.210788	+	0.977532i	$0.567603\pi$
$678$	−30.3863	+	52.0149i	−1.16698	+	1.99762i
$679$	27.7400	−	20.1543i	1.06456	−	0.773451i
$680$	−18.2456	−	0.279723i	−0.699685	−	0.0107269i
$681$	35.4418			1.35813
$682$		0			0
$683$			40.9743i			1.56784i	0.620863	+	0.783919i	$0.286782\pi$
$683$			40.9743i			1.56784i	−0.620863	+	0.783919i	$0.713218\pi$
$684$	−37.4736	−	4.32628i	−1.43284	−	0.165419i
$685$	2.63874	+	3.63191i	0.100821	+	0.138768i
$686$	7.69269	+	4.49395i	0.293708	+	0.171580i
$687$	14.0607	+	43.2745i	0.536450	+	1.65102i
$688$	20.0425	−	17.3178i	0.764112	−	0.660236i
$689$	1.64370	+	1.19422i	0.0626201	+	0.0454962i
$690$	−9.82637	+	8.75720i	−0.374084	+	0.333381i
$691$	10.8199	+	3.51560i	0.411608	+	0.133740i	0.507499	−	0.861652i	$-0.330570\pi$
$691$	10.8199	+	3.51560i	0.411608	+	0.133740i	−0.0958911	+	0.995392i	$0.530570\pi$
$692$	2.97620	+	14.7411i	0.113138	+	0.560374i
$693$		0			0
$694$	−0.971167	−	9.71745i	−0.0368650	−	0.368869i
$695$	10.5270	−	32.3989i	0.399314	−	1.22896i
$696$	−0.638963	+	0.851689i	−0.0242198	+	0.0322832i
$697$	−6.99613	−	5.08299i	−0.264997	−	0.192532i
$698$	−20.5762	+	9.03540i	−0.778819	+	0.341995i
$699$	−7.36553	+	2.39320i	−0.278590	+	0.0905193i
$700$	−16.2692	−	7.44367i	−0.614919	−	0.281344i
$701$	26.4321	+	36.3806i	0.998325	+	1.37408i	0.926347	+	0.376671i	$0.122931\pi$
$701$	26.4321	+	36.3806i	0.998325	+	1.37408i	0.0719782	+	0.997406i	$0.477069\pi$
$702$	0.177634	−	0.815195i	0.00670435	−	0.0307675i
$703$	39.4606			1.48828
$704$		0			0
$705$	−20.8290			−0.784465
$706$	0.708830	−	3.25296i	0.0266772	−	0.122427i
$707$	−13.0714	−	17.9913i	−0.491602	−	0.676633i
$708$	−58.1148	−	26.5893i	−2.18409	−	0.999288i
$709$	−39.0733	+	12.6957i	−1.46743	+	0.476797i	−0.930330	−	0.366722i	$-0.880480\pi$
$709$	−39.0733	+	12.6957i	−1.46743	+	0.476797i	−0.537099	+	0.843519i	$0.680480\pi$
$710$	−36.8779	+	16.1938i	−1.38400	+	0.607743i
$711$	18.3934	+	13.3636i	0.689807	+	0.501174i
$712$	−19.6604	+	26.2058i	−0.736804	+	0.982104i
$713$	−0.661018	+	2.03440i	−0.0247553	+	0.0761890i
$714$	3.39624	+	33.9826i	0.127101	+	1.27177i
$715$		0			0
$716$	7.40367	+	36.6704i	0.276688	+	1.37044i
$717$	−19.7188	−	6.40702i	−0.736411	−	0.239274i
$718$	26.9074	−	23.9797i	1.00418	−	0.894916i
$719$	10.6338	+	7.72589i	0.396573	+	0.288127i	0.768144	−	0.640278i	$-0.221181\pi$
$719$	10.6338	+	7.72589i	0.396573	+	0.288127i	−0.371571	+	0.928405i	$0.621181\pi$
$720$	−28.7757	+	24.8639i	−1.07241	+	0.926622i
$721$	18.8917	+	58.1427i	0.703564	+	2.16535i
$722$	11.7147	+	6.84356i	0.435977	+	0.254691i
$723$	16.0329	+	22.0674i	0.596271	+	0.820697i
$724$	46.3136	+	5.34683i	1.72123	+	0.198713i
$725$		−	0.333766i		−	0.0123958i
$726$		0			0
$727$	24.2293			0.898616			0.449308	−	0.893377i	$-0.351671\pi$
$727$	24.2293			0.898616			0.449308	+	0.893377i	$0.351671\pi$
$728$	4.89123	+	0.0749877i	0.181281	+	0.00277923i
$729$	−28.7283	+	20.8723i	−1.06401	+	0.773049i
$730$	20.4646	−	35.0312i	0.757431	−	1.29656i
$731$	15.0741	−	4.89787i	0.557536	−	0.181154i
$732$	−1.65571	−	2.93668i	−0.0611968	−	0.108543i
$733$	−17.3006	+	23.8122i	−0.639011	+	0.879523i	−0.998562	−	0.0536020i	$-0.982930\pi$
$733$	−17.3006	+	23.8122i	−0.639011	+	0.879523i	0.359551	+	0.933125i	$0.382930\pi$
$734$	5.94574	−	5.29880i	0.219461	−	0.195582i
$735$	−18.2907	+	56.2930i	−0.674663	+	2.07640i
$736$	−6.71663	+	3.65231i	−0.247578	+	0.134626i
$737$		0			0
$738$	−17.9332	+	1.79225i	−0.660128	+	0.0659736i
$739$	31.8020	+	10.3331i	1.16986	+	0.380109i	0.828589	−	0.559858i	$-0.189144\pi$
$739$	31.8020	+	10.3331i	1.16986	+	0.380109i	0.341266	+	0.939967i	$0.389144\pi$
$740$	26.9200	−	29.2901i	0.989599	−	1.07673i
$741$	−3.51679	+	4.84044i	−0.129192	+	0.177818i
$742$	−23.7225	+	10.4170i	−0.870879	+	0.382420i
$743$	10.5894	+	32.5908i	0.388487	+	1.19564i	0.933919	+	0.357486i	$0.116366\pi$
$743$	10.5894	+	32.5908i	0.388487	+	1.19564i	−0.545431	+	0.838156i	$0.683634\pi$
$744$	−3.70057	+	10.8218i	−0.135670	+	0.396748i
$745$	−42.3405	+	30.7622i	−1.55124	+	1.12704i
$746$	46.0799	+	10.0410i	1.68710	+	0.367625i
$747$		−	8.05802i		−	0.294827i
$748$		0			0
$749$			12.4001i			0.453089i
$750$	−5.67042	+	26.0226i	−0.207054	+	0.950213i
$751$	11.7555	−	8.54087i	0.428964	−	0.311661i	−0.352270	−	0.935898i	$-0.614590\pi$
$751$	11.7555	−	8.54087i	0.428964	−	0.311661i	0.781235	+	0.624237i	$0.214590\pi$
$752$	−11.7804	−	2.75680i	−0.429587	−	0.100530i
$753$	−4.51571	−	13.8979i	−0.164561	−	0.506468i
$754$	0.0366916	+	0.0835571i	0.00133623	+	0.00304297i
$755$	−28.7361	+	39.5519i	−1.04581	+	1.43944i
$756$	7.83345	+	7.19958i	0.284900	+	0.261846i
$757$	−12.7027	−	4.12734i	−0.461686	−	0.150011i	0.0689331	−	0.997621i	$-0.478041\pi$
$757$	−12.7027	−	4.12734i	−0.461686	−	0.150011i	−0.530619	+	0.847610i	$0.678041\pi$
$758$	−2.67067	−	26.7226i	−0.0970031	−	0.970608i
$759$		0			0
$760$	38.9598	−	12.0017i	1.41322	−	0.435348i
$761$	−9.04362	+	27.8334i	−0.327831	+	1.00896i	0.642315	+	0.766440i	$0.277974\pi$
$761$	−9.04362	+	27.8334i	−0.327831	+	1.00896i	−0.970146	+	0.242520i	$0.922026\pi$
$762$	6.20739	+	6.96525i	0.224870	+	0.252324i
$763$	37.1964	−	51.1965i	1.34660	−	1.85344i
$764$	13.9471	+	24.7375i	0.504587	+	0.894970i
$765$	−21.6425	+	7.03207i	−0.782485	+	0.254245i
$766$	35.3346	+	20.6419i	1.27669	+	0.745822i
$767$	−4.43150	+	3.21967i	−0.160012	+	0.116256i
$768$	−36.2068	+	18.9750i	−1.30650	+	0.684700i
$769$	−13.2263			−0.476952			−0.238476	−	0.971148i	$-0.576648\pi$
$769$	−13.2263			−0.476952			−0.238476	+	0.971148i	$0.576648\pi$
$770$		0			0
$771$		−	61.7787i		−	2.22491i
$772$	0.348074	−	3.01497i	0.0125275	−	0.108511i
$773$	7.57554	+	10.4268i	0.272473	+	0.375027i	0.923223	−	0.384265i	$-0.125545\pi$
$773$	7.57554	+	10.4268i	0.272473	+	0.375027i	−0.650750	+	0.759292i	$0.725545\pi$
$774$	16.6621	−	28.5221i	0.598909	−	1.02521i
$775$	−1.10790	−	3.40977i	−0.0397970	−	0.122482i
$776$	14.1287	+	20.0870i	0.507192	+	0.721081i
$777$	−60.2350	−	43.7633i	−2.16092	−	1.57000i
$778$	23.0799	+	25.8977i	0.827454	+	0.928479i
$779$	18.3739	+	5.97005i	0.658314	+	0.213899i
$780$	1.19373	+	5.91253i	0.0427422	+	0.211702i
$781$		0			0
$782$	−4.55220	+	0.454949i	−0.162786	+	0.0162690i
$783$	−0.0613341	+	0.188767i	−0.00219190	+	0.00674598i
$784$	−17.7954	+	29.4172i	−0.635551	+	1.05061i
$785$	−6.38791	−	4.64109i	−0.227994	−	0.165647i
$786$	−7.80897	−	17.7832i	−0.278537	−	0.634307i
$787$	45.3753	−	14.7433i	1.61746	−	0.525543i	0.646116	−	0.763240i	$-0.276392\pi$
$787$	45.3753	−	14.7433i	1.61746	−	0.525543i	0.971339	+	0.237696i	$0.0763924\pi$
$788$	6.70400	−	14.6526i	0.238820	−	0.521976i
$789$	−33.5892	−	46.2315i	−1.19581	−	1.64589i
$790$	−24.0068	−	5.23115i	−0.854122	−	0.186116i
$791$	−65.8418			−2.34106
$792$		0			0
$793$	−0.288953			−0.0102610
$794$	−1.49496	−	0.325756i	−0.0530540	−	0.0115606i
$795$	−18.7779	−	25.8455i	−0.665983	−	0.916647i
$796$	−17.6439	−	8.07262i	−0.625371	−	0.286127i
$797$	−0.0297436	+	0.00966428i	−0.00105357	+	0.000342326i	−0.309544	−	0.950885i	$-0.600176\pi$
$797$	−0.0297436	+	0.00966428i	−0.00105357	+	0.000342326i	0.308490	+	0.951228i	$0.400176\pi$
$798$	−30.6764	−	69.8588i	−1.08593	−	2.47298i
$799$	−5.85697	−	4.25534i	−0.207205	−	0.150543i
$800$	5.50933	−	11.5693i	0.194784	−	0.409037i
$801$	−12.6250	+	38.8557i	−0.446082	+	1.37290i
$802$	−29.3557	+	2.93382i	−1.03658	+	0.103597i
$803$		0			0
$804$	−15.0338	+	3.03529i	−0.530201	+	0.107046i
$805$	−13.6821	−	4.44559i	−0.482232	−	0.156687i
$806$	0.652201	+	0.731828i	0.0229728	+	0.0257776i
$807$	34.7609	+	25.2553i	1.22364	+	0.889027i
$808$	13.0278	−	9.16346i	0.458317	−	0.322369i
$809$	−9.28434	−	28.5743i	−0.326420	−	1.00462i	−0.970796	−	0.239908i	$-0.922883\pi$
$809$	−9.28434	−	28.5743i	−0.326420	−	1.00462i	0.644376	−	0.764709i	$-0.277117\pi$
$810$	13.7291	−	23.5014i	0.482392	−	0.825753i
$811$	−15.0939	−	20.7750i	−0.530019	−	0.729509i	0.457114	−	0.889408i	$-0.348883\pi$
$811$	−15.0939	−	20.7750i	−0.530019	−	0.729509i	−0.987133	+	0.159899i	$0.948883\pi$
$812$	−1.15606	−	0.133465i	−0.0405697	−	0.00468371i
$813$		−	9.26955i		−	0.325097i
$814$		0			0
$815$	9.80905			0.343596
$816$	−24.3736	+	2.05908i	−0.853246	+	0.0720823i
$817$	−28.6469	+	20.8132i	−1.00223	+	0.728162i
$818$	33.1312	+	19.3547i	1.15841	+	0.676722i
$819$	5.80188	−	1.88514i	0.202734	−	0.0658723i
$820$	16.9660	−	9.56550i	0.592479	−	0.334042i
$821$	−8.38375	+	11.5392i	−0.292595	+	0.402722i	−0.929855	−	0.367927i	$-0.880068\pi$
$821$	−8.38375	+	11.5392i	−0.292595	+	0.402722i	0.637260	+	0.770649i	$0.280068\pi$
$822$	4.00374	+	4.49256i	0.139647	+	0.156696i
$823$	14.2448	−	43.8411i	0.496543	−	1.52820i	−0.317995	−	0.948093i	$-0.603009\pi$
$823$	14.2448	−	43.8411i	0.496543	−	1.52820i	0.814538	−	0.580110i	$-0.196991\pi$
$824$	−41.8457	+	12.8908i	−1.45777	+	0.449071i
$825$		0			0
$826$	−6.94639	−	69.5052i	−0.241696	−	2.41840i
$827$	−18.6665	−	6.06511i	−0.649098	−	0.210905i	−0.0340816	−	0.999419i	$-0.510851\pi$
$827$	−18.6665	−	6.06511i	−0.649098	−	0.210905i	−0.615016	+	0.788514i	$0.710851\pi$
$828$	−6.45185	+	7.01988i	−0.224217	+	0.243958i
$829$	−0.706156	+	0.971941i	−0.0245258	+	0.0337569i	−0.821104	−	0.570779i	$-0.806641\pi$
$829$	−0.706156	+	0.971941i	−0.0245258	+	0.0337569i	0.796578	+	0.604536i	$0.206641\pi$
$830$	3.50126	+	7.97337i	0.121531	+	0.276760i
$831$	24.8498	+	76.4797i	0.862028	+	2.65305i
$832$	−0.107403	+	3.50199i	−0.00372354	+	0.121410i
$833$	−16.6438	+	12.0925i	−0.576675	+	0.418979i
$834$	9.72232	−	44.6176i	0.336656	−	1.54498i
$835$			37.1977i			1.28728i
$836$		0			0
$837$			2.13204i			0.0736941i
$838$	−19.3094	−	4.20759i	−0.667033	−	0.145349i
$839$	−20.7594	+	15.0826i	−0.716695	+	0.520710i	−0.885327	−	0.464970i	$-0.846065\pi$
$839$	−20.7594	+	15.0826i	−0.716695	+	0.520710i	0.168631	+	0.985679i	$0.446065\pi$
$840$	−72.7810	−	24.8878i	−2.51118	−	0.858709i
$841$	8.95478	+	27.5600i	0.308786	+	0.950345i
$842$	33.3484	−	14.6439i	1.14926	−	0.504664i
$843$	9.33530	−	12.8489i	0.321525	−	0.442541i
$844$	28.6202	+	26.3043i	0.985147	+	0.905431i
$845$	−32.8337	−	10.6683i	−1.12951	−	0.367001i
$846$	−15.0132	+	1.50042i	−0.516163	+	0.0515856i
$847$		0			0
$848$	−7.19958	−	17.1030i	−0.247235	−	0.587319i
$849$	−17.7434	+	54.6085i	−0.608951	+	1.87416i
$850$	5.72438	−	5.10153i	0.196345	−	0.174981i
$851$	5.86240	−	8.06890i	0.200960	−	0.276598i
$852$	−47.0298	+	26.5156i	−1.61122	+	0.908408i
$853$	44.8922	−	14.5864i	1.53708	−	0.499427i	0.586510	−	0.809942i	$-0.300501\pi$
$853$	44.8922	−	14.5864i	1.53708	−	0.499427i	0.950569	+	0.310514i	$0.100501\pi$
$854$	1.85866	−	3.18164i	0.0636021	−	0.108873i
$855$	41.1295	−	29.8823i	1.40660	−	1.02195i
$856$	−8.88019	−	0.136143i	−0.303519	−	0.00465326i
$857$	28.7877			0.983370			0.491685	−	0.870773i	$-0.336381\pi$
$857$	28.7877			0.983370			0.491685	+	0.870773i	$0.336381\pi$
$858$		0			0
$859$			50.4595i			1.72165i	0.508897	+	0.860827i	$0.330053\pi$
$859$			50.4595i			1.72165i	−0.508897	+	0.860827i	$0.669947\pi$
$860$	−4.09407	+	35.4623i	−0.139607	+	1.20925i
$861$	−21.4261	−	29.4904i	−0.730198	−	1.00503i
$862$	−22.3377	−	13.0493i	−0.760826	−	0.444462i
$863$	−7.24863	−	22.3090i	−0.246746	−	0.759407i	−0.995344	−	0.0963828i	$-0.969273\pi$
$863$	−7.24863	−	22.3090i	−0.246746	−	0.759407i	0.748598	−	0.663024i	$-0.230727\pi$
$864$	−5.24191	+	5.53080i	−0.178333	+	0.188162i
$865$	−16.3968	−	11.9130i	−0.557508	−	0.405054i
$866$	10.3660	−	9.23810i	0.352251	−	0.313923i
$867$	27.3864	+	8.89839i	0.930092	+	0.302205i
$868$	−12.2533	+	2.47392i	−0.415905	+	0.0839704i
$869$		0			0
$870$	−0.142698	−	1.42783i	−0.00483791	−	0.0484079i
$871$	−0.406219	+	1.25021i	−0.0137642	+	0.0423618i
$872$	36.2555	+	27.1999i	1.22776	+	0.921106i
$873$	24.7770	+	18.0015i	0.838573	+	0.609259i
$874$	9.35807	−	4.10931i	0.316541	−	0.139000i
$875$	−27.6851	+	8.99545i	−0.935928	+	0.304102i
$876$	22.6264	−	49.4533i	0.764476	−	1.67087i
$877$	−17.0485	−	23.4652i	−0.575687	−	0.792365i	0.417528	−	0.908664i	$-0.362897\pi$
$877$	−17.0485	−	23.4652i	−0.575687	−	0.792365i	−0.993214	+	0.116300i	$0.962897\pi$
$878$	9.64193	−	44.2487i	0.325400	−	1.49332i
$879$	29.0592			0.980143
$880$		0			0
$881$	−30.9774			−1.04365			−0.521827	−	0.853051i	$-0.674749\pi$
$881$	−30.9774			−1.04365			−0.521827	+	0.853051i	$0.674749\pi$
$882$	−9.12853	+	41.8926i	−0.307374	+	1.41060i
$883$	24.2223	+	33.3392i	0.815146	+	1.12195i	0.990509	+	0.137449i	$0.0438902\pi$
$883$	24.2223	+	33.3392i	0.815146	+	1.12195i	−0.175363	+	0.984504i	$0.556110\pi$
$884$	−0.872256	+	1.90644i	−0.0293371	+	0.0641206i
$885$	81.9146	−	26.6157i	2.75353	−	0.894676i
$886$	21.9357	−	9.63242i	0.736946	−	0.323607i
$887$	−6.92690	−	5.03269i	−0.232583	−	0.168981i	0.465390	−	0.885106i	$-0.345914\pi$
$887$	−6.92690	−	5.03269i	−0.232583	−	0.168981i	−0.697972	+	0.716125i	$0.745914\pi$
$888$	32.0020	−	42.6562i	1.07392	−	1.43145i
$889$	−3.15118	+	9.69834i	−0.105687	+	0.325272i
$890$	−4.39070	−	43.9332i	−0.147177	−	1.47264i
$891$		0			0
$892$	43.8248	−	8.84813i	1.46736	−	0.296257i
$893$	15.3822	+	4.99797i	0.514744	+	0.167251i
$894$	−52.3739	+	46.6753i	−1.75165	+	1.56106i
$895$	−40.7891	−	29.6350i	−1.36343	−	0.990590i
$896$	−37.8693	−	23.7088i	−1.26512	−	0.792056i
$897$	0.467307	+	1.43822i	0.0156029	+	0.0480209i
$898$	−25.4079	−	14.8429i	−0.847873	−	0.495314i
$899$	−0.137073	−	0.188665i	−0.00457163	−	0.00629232i
$900$	1.83271	−	15.8747i	0.0610905	−	0.529158i
$901$		−	11.1039i		−	0.369925i
$902$		0			0
$903$	66.8111			2.22333
$904$	0.722888	−	47.1519i	0.0240429	−	1.56825i
$905$	−50.8319	+	36.9315i	−1.68971	+	1.22764i
$906$	−33.0564	+	56.5857i	−1.09823	+	1.87993i
$907$	46.7824	−	15.2005i	1.55339	−	0.504725i	0.598354	−	0.801232i	$-0.295822\pi$
$907$	46.7824	−	15.2005i	1.55339	−	0.504725i	0.955031	+	0.296506i	$0.0958216\pi$
$908$	−24.1682	+	13.6261i	−0.802049	+	0.452198i
$909$	11.6752	−	16.0696i	0.387243	−	0.532994i
$910$	−4.92182	+	4.38630i	−0.163157	+	0.145404i
$911$	−15.2213	+	46.8462i	−0.504303	+	1.55209i	0.297636	+	0.954679i	$0.403802\pi$
$911$	−15.2213	+	46.8462i	−0.504303	+	1.55209i	−0.801939	+	0.597406i	$0.796198\pi$
$912$	50.3655	−	21.2016i	1.66777	−	0.702055i
$913$		0			0
$914$	7.08314	−	0.707894i	0.234290	−	0.0234150i
$915$	4.32111	+	1.40401i	0.142851	+	0.0464152i
$916$	−26.2256	−	24.1035i	−0.866519	−	0.796402i
$917$	12.4777	−	17.1740i	0.412049	−	0.567137i
$918$	−4.17499	+	1.83332i	−0.137795	+	0.0605086i
$919$	−0.385985	−	1.18794i	−0.0127325	−	0.0391865i	0.944488	−	0.328545i	$-0.106558\pi$
$919$	−0.385985	−	1.18794i	−0.0127325	−	0.0391865i	−0.957221	+	0.289358i	$0.906558\pi$
$920$	3.33389	−	9.74951i	0.109915	−	0.321432i
$921$	−29.2409	+	21.2448i	−0.963521	+	0.700039i
$922$	17.8349	+	3.88628i	0.587361	+	0.127988i
$923$			4.62747i			0.152315i
$924$		0			0
$925$			16.7165i			0.549634i
$926$	0.719680	−	3.30275i	0.0236502	−	0.108535i
$927$	−44.1762	+	32.0959i	−1.45094	+	1.05417i
$928$	0.108272	−	0.826434i	0.00355421	−	0.0271290i
$929$	6.74569	+	20.7611i	0.221319	+	0.681150i	0.998644	+	0.0520512i	$0.0165759\pi$
$929$	6.74569	+	20.7611i	0.221319	+	0.681150i	−0.777325	+	0.629099i	$0.783424\pi$
$930$	−6.19732	−	14.1131i	−0.203218	−	0.462785i
$931$	27.0153	−	37.1834i	0.885391	−	1.21864i
$932$	4.10253	−	4.46373i	0.134383	−	0.146214i
$933$	35.5796	+	11.5605i	1.16482	+	0.378474i
$934$	1.16271	+	11.6340i	0.0380451	+	0.380677i
$935$		0			0
$936$	1.28633	+	4.17565i	0.0420449	+	0.136485i
$937$	13.8710	−	42.6906i	0.453147	−	1.39464i	−0.420151	−	0.907454i	$-0.638023\pi$
$937$	13.8710	−	42.6906i	0.453147	−	1.39464i	0.873297	−	0.487187i	$-0.161977\pi$
$938$	−11.1530	−	12.5147i	−0.364160	−	0.408620i
$939$	−34.1255	+	46.9697i	−1.11364	+	1.53280i
$940$	14.2035	−	8.00798i	0.463267	−	0.261192i
$941$	15.3466	−	4.98641i	0.500284	−	0.162552i	−0.0479949	−	0.998848i	$-0.515283\pi$
$941$	15.3466	−	4.98641i	0.500284	−	0.162552i	0.548279	+	0.836295i	$0.315283\pi$
$942$	−9.13899	−	5.33885i	−0.297764	−	0.173949i
$943$	3.95045	−	2.87017i	0.128644	−	0.0934655i
$944$	49.8517	−	4.21148i	1.62254	−	0.137072i
$945$	−14.3388			−0.466440
$946$		0			0
$947$			38.3800i			1.24718i	0.781751	+	0.623591i	$0.214327\pi$
$947$			38.3800i			1.24718i	−0.781751	+	0.623591i	$0.785673\pi$
$948$	−32.7180	−	3.77725i	−1.06263	−	0.122679i
$949$	−2.73981	−	3.77102i	−0.0889380	−	0.122413i
$950$	−8.64080	+	14.7912i	−0.280344	+	0.479891i
$951$	3.22456	+	9.92419i	0.104564	+	0.321814i
$952$	−15.3810	−	21.8674i	−0.498501	−	0.708725i
$953$	21.2685	+	15.4525i	0.688956	+	0.500556i	0.876317	−	0.481736i	$-0.159993\pi$
$953$	21.2685	+	15.4525i	0.688956	+	0.500556i	−0.187361	+	0.982291i	$0.559993\pi$
$954$	−15.3966	−	17.2763i	−0.498482	−	0.559342i
$955$	−36.3993	−	11.8269i	−1.17786	−	0.382708i
$956$	15.9097	−	3.21213i	0.514557	−	0.103888i
$957$		0			0
$958$	−30.5262	+	3.05081i	−0.986258	+	0.0985672i
$959$	−2.03250	+	6.25539i	−0.0656329	+	0.201997i
$960$	18.6222	−	51.8481i	0.601029	−	1.67339i
$961$	23.0529	+	16.7489i	0.743643	+	0.540288i
$962$	−1.83767	−	4.18490i	−0.0592489	−	0.134927i
$963$	−10.5335	+	3.42254i	−0.339437	+	0.110290i
$964$	−19.4172	−	8.88395i	−0.625385	−	0.286133i
$965$	2.40421	+	3.30911i	0.0773942	+	0.106524i
$966$	−18.8421	−	4.10576i	−0.606235	−	0.132101i
$967$	−8.79993			−0.282987			−0.141493	−	0.989939i	$-0.545190\pi$
$967$	−8.79993			−0.282987			−0.141493	+	0.989939i	$0.545190\pi$
$968$		0			0
$969$	32.6992			1.05045
$970$	−32.3385	−	7.04666i	−1.03833	−	0.226255i
$971$	−7.51993	−	10.3503i	−0.241326	−	0.332157i	0.671124	−	0.741345i	$-0.265812\pi$
$971$	−7.51993	−	10.3503i	−0.241326	−	0.332157i	−0.912450	+	0.409188i	$0.865812\pi$
$972$	18.5421	−	40.5264i	0.594738	−	1.29989i
$973$	47.4681	−	15.4233i	1.52176	−	0.494448i
$974$	8.24192	+	18.7692i	0.264088	+	0.601404i
$975$	−2.05053	−	1.48980i	−0.0656695	−	0.0477117i
$976$	2.25809	+	1.36599i	0.0722798	+	0.0437244i
$977$	9.26325	−	28.5093i	0.296357	−	0.912095i	−0.686405	−	0.727220i	$-0.740812\pi$
$977$	9.26325	−	28.5093i	0.296357	−	0.912095i	0.982762	−	0.184875i	$-0.0591879\pi$
$978$	13.0835	−	1.30757i	0.418364	−	0.0418116i
$979$		0			0
$980$	−9.16998	−	45.4189i	−0.292924	−	1.45085i
$981$	53.7564	+	17.4665i	1.71631	+	0.557663i
$982$	−31.9105	−	35.8064i	−1.01830	−	1.14263i
$983$	6.73605	+	4.89403i	0.214847	+	0.156095i	0.690004	−	0.723806i	$-0.257609\pi$
$983$	6.73605	+	4.89403i	0.214847	+	0.156095i	−0.475157	+	0.879901i	$0.657609\pi$
$984$	21.3545	−	15.0203i	0.680758	−	0.478829i
$985$	6.71064	+	20.6532i	0.213819	+	0.658067i
$986$	0.251578	−	0.430649i	0.00801188	−	0.0137147i
$987$	−17.9373	−	24.6886i	−0.570951	−	0.785847i
$988$	0.537162	−	4.65283i	0.0170894	−	0.148026i
$989$			8.94980i			0.284587i
$990$		0			0
$991$	35.5599			1.12960			0.564798	−	0.825229i	$-0.308954\pi$
$991$	35.5599			1.12960			0.564798	+	0.825229i	$0.308954\pi$
$992$	−1.63714	−	8.80227i	−0.0519793	−	0.279472i
$993$	15.6484	−	11.3692i	0.496587	−	0.360791i
$994$	−50.9528	−	29.7658i	−1.61612	−	0.944113i
$995$	24.8696	−	8.08062i	0.788419	−	0.256173i
$996$	5.73293	+	10.1683i	0.181655	+	0.322196i
$997$	−2.76388	+	3.80415i	−0.0875328	+	0.120479i	−0.850538	−	0.525914i	$-0.823723\pi$
$997$	−2.76388	+	3.80415i	−0.0875328	+	0.120479i	0.763005	+	0.646393i	$0.223723\pi$
$998$	7.27525	+	8.16349i	0.230294	+	0.258411i
$999$	3.07188	−	9.45426i	0.0971898	−	0.299120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.i.493.6		40
8.5	even	2	inner	968.2.o.i.493.7		40
11.2	odd	10		968.2.o.j.245.7		40
11.3	even	5		968.2.o.d.565.2		40
11.4	even	5		968.2.c.i.485.19		20
11.5	even	5	inner	968.2.o.i.269.7		40
11.6	odd	10		88.2.o.a.5.4	✓	40
11.7	odd	10		968.2.c.h.485.2		20
11.8	odd	10		968.2.o.j.565.9		40
11.9	even	5		968.2.o.d.245.4		40
11.10	odd	2		88.2.o.a.53.5	yes	40
33.17	even	10		792.2.br.b.181.7		40
33.32	even	2		792.2.br.b.757.6		40
44.7	even	10		3872.2.c.h.1937.18		20
44.15	odd	10		3872.2.c.i.1937.18		20
44.39	even	10		352.2.w.a.49.9		40
44.43	even	2		352.2.w.a.273.2		40
88.5	even	10	inner	968.2.o.i.269.6		40
88.13	odd	10		968.2.o.j.245.9		40
88.21	odd	2		88.2.o.a.53.4	yes	40
88.29	odd	10		968.2.c.h.485.1		20
88.37	even	10		968.2.c.i.485.20		20
88.43	even	2		352.2.w.a.273.9		40
88.51	even	10		3872.2.c.h.1937.3		20
88.53	even	10		968.2.o.d.245.2		40
88.59	odd	10		3872.2.c.i.1937.3		20
88.61	odd	10		88.2.o.a.5.5	yes	40
88.69	even	10		968.2.o.d.565.4		40
88.83	even	10		352.2.w.a.49.2		40
88.85	odd	10		968.2.o.j.565.7		40
264.149	even	10		792.2.br.b.181.6		40
264.197	even	2		792.2.br.b.757.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.4	✓	40	11.6	odd	10
88.2.o.a.5.5	yes	40	88.61	odd	10
88.2.o.a.53.4	yes	40	88.21	odd	2
88.2.o.a.53.5	yes	40	11.10	odd	2
352.2.w.a.49.2		40	88.83	even	10
352.2.w.a.49.9		40	44.39	even	10
352.2.w.a.273.2		40	44.43	even	2
352.2.w.a.273.9		40	88.43	even	2
792.2.br.b.181.6		40	264.149	even	10
792.2.br.b.181.7		40	33.17	even	10
792.2.br.b.757.6		40	33.32	even	2
792.2.br.b.757.7		40	264.197	even	2
968.2.c.h.485.1		20	88.29	odd	10
968.2.c.h.485.2		20	11.7	odd	10
968.2.c.i.485.19		20	11.4	even	5
968.2.c.i.485.20		20	88.37	even	10
968.2.o.d.245.2		40	88.53	even	10
968.2.o.d.245.4		40	11.9	even	5
968.2.o.d.565.2		40	11.3	even	5
968.2.o.d.565.4		40	88.69	even	10
968.2.o.i.269.6		40	88.5	even	10	inner
968.2.o.i.269.7		40	11.5	even	5	inner
968.2.o.i.493.6		40	1.1	even	1	trivial
968.2.o.i.493.7		40	8.5	even	2	inner
968.2.o.j.245.7		40	11.2	odd	10
968.2.o.j.245.9		40	88.13	odd	10
968.2.o.j.565.7		40	88.85	odd	10
968.2.o.j.565.9		40	11.8	odd	10
3872.2.c.h.1937.3		20	88.51	even	10
3872.2.c.h.1937.18		20	44.7	even	10
3872.2.c.i.1937.3		20	88.59	odd	10
3872.2.c.i.1937.18		20	44.15	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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.301096 - 1.38179i) q^{2} +(1.50170 + 2.06692i) q^{3} +(-1.81868 - 0.832103i) q^{4} +(2.56349 - 0.832928i) q^{5} +(3.30820 - 1.45270i) q^{6} +(3.19487 + 2.32121i) q^{7} +(-1.69739 + 2.26249i) q^{8} +(-1.08998 + 3.35462i) q^{9} +(-0.379074 - 3.79299i) q^{10} +(-1.01123 - 5.00864i) q^{12} +(-0.416519 - 0.135335i) q^{13} +(4.16939 - 3.71573i) q^{14} +(5.57119 + 4.04771i) q^{15} +(2.61521 + 3.02666i) q^{16} +(0.739640 + 2.27638i) q^{17} +(4.30719 + 2.51619i) q^{18} +(-3.14306 - 4.32605i) q^{19} +(-5.35525 - 0.618256i) q^{20} +10.0893i q^{21} -1.35153 q^{23} +(-7.22536 - 0.110772i) q^{24} +(1.83262 - 1.33147i) q^{25} +(-0.312417 + 0.534793i) q^{26} +(-1.28114 + 0.416268i) q^{27} +(-3.87897 - 6.88001i) q^{28} +(0.0866058 - 0.119203i) q^{29} +(7.27054 - 6.47946i) q^{30} +(0.489088 - 1.50526i) q^{31} +(4.96964 - 2.70235i) q^{32} +(3.36818 - 0.336618i) q^{34} +(10.1234 + 3.28930i) q^{35} +(4.77373 - 5.19402i) q^{36} +(-4.33759 + 5.97018i) q^{37} +(-6.92405 + 3.04048i) q^{38} +(-0.345761 - 1.06414i) q^{39} +(-2.46675 + 7.21367i) q^{40} +(-2.92294 + 2.12364i) q^{41} +(13.9413 + 3.03785i) q^{42} -6.62197i q^{43} +9.50742i q^{45} +(-0.406941 + 1.86753i) q^{46} +(-2.44701 + 1.77785i) q^{47} +(-2.32859 + 9.95057i) q^{48} +(2.65607 + 8.17456i) q^{49} +(-1.28802 - 2.93319i) q^{50} +(-3.59437 + 4.94722i) q^{51} +(0.644903 + 0.592719i) q^{52} +(-4.41208 - 1.43357i) q^{53} +(0.189448 + 1.89561i) q^{54} +(-10.6747 + 3.28838i) q^{56} +(4.22164 - 12.9929i) q^{57} +(-0.138636 - 0.155562i) q^{58} +(7.35162 - 10.1186i) q^{59} +(-6.76412 - 11.9973i) q^{60} +(0.627487 - 0.203883i) q^{61} +(-1.93268 - 1.12904i) q^{62} +(-11.2692 + 8.18752i) q^{63} +(-2.23774 - 7.68066i) q^{64} -1.18047 q^{65} -3.00157i q^{67} +(0.549011 - 4.75547i) q^{68} +(-2.02960 - 2.79351i) q^{69} +(7.59324 - 12.9980i) q^{70} +(-3.26511 - 10.0490i) q^{71} +(-5.73968 - 8.16018i) q^{72} +(8.61055 + 6.25593i) q^{73} +(6.94350 + 7.79124i) q^{74} +(5.50409 + 1.78839i) q^{75} +(2.11650 + 10.4830i) q^{76} +(-1.57453 + 0.157359i) q^{78} +(1.99182 - 6.13018i) q^{79} +(9.22505 + 5.58053i) q^{80} +(5.77655 + 4.19691i) q^{81} +(2.05434 + 4.67831i) q^{82} +(-2.17269 + 0.705948i) q^{83} +(8.39535 - 18.3492i) q^{84} +(3.79212 + 5.21940i) q^{85} +(-9.15016 - 1.99385i) q^{86} +0.376438 q^{87} +11.5827 q^{89} +(13.1372 + 2.86265i) q^{90} +(-1.01658 - 1.39921i) q^{91} +(2.45801 + 1.12461i) q^{92} +(3.84571 - 1.24955i) q^{93} +(1.71983 + 3.91655i) q^{94} +(-11.6605 - 8.47183i) q^{95} +(13.0485 + 6.21370i) q^{96} +(2.68309 - 8.25770i) q^{97} +(12.0952 - 1.20881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - q^{4} + 7 q^{6} + 10 q^{7} + 5 q^{8} + 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} + 6 q^{17} + 20 q^{18} + 8 q^{20} - 8 q^{23} - 25 q^{24} - 4 q^{25} - 10 q^{26} - 32 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - q^4 + 7 * q^6 + 10 * q^7 + 5 * q^8 + 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 + 6 * q^17 + 20 * q^18 + 8 * q^20 - 8 * q^23 - 25 * q^24 - 4 * q^25 - 10 * q^26 - 32 * q^28 + 28 * q^30 - 6 * q^31 - 20 * q^32 + 10 * q^34 + 18 * q^36 + 12 * q^38 + 34 * q^39 - 10 * q^40 + 14 * q^41 + 40 * q^42 - 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 - 61 * q^50 - 20 * q^52 - 108 * q^54 - 32 * q^56 + 26 * q^57 + 4 * q^58 - 46 * q^60 - 48 * q^62 - 60 * q^63 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 + 22 * q^71 + 101 * q^72 + 6 * q^73 - 54 * q^74 + 134 * q^76 - 12 * q^78 - 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 + 28 * q^84 - 15 * q^86 - 68 * q^87 - 16 * q^89 + 84 * q^90 - 4 * q^92 + 100 * q^94 - 66 * q^95 + 30 * q^96 + 10 * q^97 + 144 * q^98

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