LMFDB - Embedded newform 592.2.bc.d.497.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(33,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("592.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bc (of order $9$, degree $6$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			497.1
Root			$2.00752 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	592.497
Dual form			592.2.bc.d.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72328 + 0.627223i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(-0.598489 + 3.39420i) q^{7} +(0.278152 - 0.233397i) q^{9} +O(q^{10})$	\(q+(-1.72328 + 0.627223i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(-0.598489 + 3.39420i) q^{7} +(0.278152 - 0.233397i) q^{9} +(-1.40483 - 2.43324i) q^{11} +(-2.65877 - 2.23097i) q^{13} +(-0.598489 - 3.39420i) q^{15} +(-2.37417 + 1.99217i) q^{17} +(6.99748 - 2.54687i) q^{19} +(-1.09755 - 6.22454i) q^{21} +(-0.321769 + 0.557320i) q^{23} +(1.37939 + 0.502055i) q^{25} +(2.41787 - 4.18788i) q^{27} +(-1.08449 - 1.87840i) q^{29} -9.90716 q^{31} +(3.94710 + 3.31201i) q^{33} +(-6.08678 - 2.21541i) q^{35} +(-2.56368 - 5.51612i) q^{37} +(5.98112 + 2.17695i) q^{39} +(-8.13803 - 6.82862i) q^{41} -8.30465 q^{43} +(0.341204 + 0.590982i) q^{45} +(-3.92821 + 6.80387i) q^{47} +(-4.58455 - 1.66864i) q^{49} +(2.84183 - 4.92220i) q^{51} +(0.839394 + 4.76044i) q^{53} +(4.96199 - 1.80602i) q^{55} +(-10.4612 + 8.77795i) q^{57} +(-0.0961039 - 0.545032i) q^{59} +(5.37102 + 4.50682i) q^{61} +(0.625726 + 1.08379i) q^{63} +(4.99685 - 4.19285i) q^{65} +(-0.0366435 + 0.207815i) q^{67} +(0.204934 - 1.16224i) q^{69} +(4.75197 - 1.72957i) q^{71} +10.2297 q^{73} -2.69197 q^{75} +(9.09967 - 3.31201i) q^{77} +(0.330775 - 1.87592i) q^{79} +(-1.72910 + 9.80619i) q^{81} +(-5.21650 + 4.37717i) q^{83} +(-2.91235 - 5.04435i) q^{85} +(3.04706 + 2.55679i) q^{87} +(-1.68226 - 9.54055i) q^{89} +(9.16360 - 7.68917i) q^{91} +(17.0728 - 6.21400i) q^{93} +(2.43020 + 13.7823i) q^{95} +(-8.52990 + 14.7742i) q^{97} +(-0.958667 - 0.348926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72328	+	0.627223i	−0.994936	+	0.362127i	−0.787630	−	0.616149i	$-0.788692\pi$
$3$	−1.72328	+	0.627223i	−0.994936	+	0.362127i	−0.207306	+	0.978276i	$0.566470\pi$
$4$		0			0
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	0.820651	+	0.571429i	$0.193611\pi$
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	−0.966600	+	0.256289i	$0.917500\pi$
$6$		0			0
$7$	−0.598489	+	3.39420i	−0.226208	+	1.28289i	0.634156	+	0.773205i	$0.281348\pi$
$7$	−0.598489	+	3.39420i	−0.226208	+	1.28289i	−0.860363	+	0.509681i	$0.829763\pi$
$8$		0			0
$9$	0.278152	−	0.233397i	0.0927173	−	0.0777991i
$10$		0			0
$11$	−1.40483	−	2.43324i	−0.423572	−	0.733649i	0.572714	−	0.819756i	$-0.305891\pi$
$11$	−1.40483	−	2.43324i	−0.423572	−	0.733649i	−0.996286	+	0.0861067i	$0.972557\pi$
$12$		0			0
$13$	−2.65877	−	2.23097i	−0.737409	−	0.618760i	0.194731	−	0.980857i	$-0.437617\pi$
$13$	−2.65877	−	2.23097i	−0.737409	−	0.618760i	−0.932141	+	0.362097i	$0.882061\pi$
$14$		0			0
$15$	−0.598489	−	3.39420i	−0.154529	−	0.876378i
$16$		0			0
$17$	−2.37417	+	1.99217i	−0.575822	+	0.483172i	−0.883572	−	0.468295i	$-0.844868\pi$
$17$	−2.37417	+	1.99217i	−0.575822	+	0.483172i	0.307750	+	0.951467i	$0.400424\pi$
$18$		0			0
$19$	6.99748	−	2.54687i	1.60533	−	0.584293i	0.624822	−	0.780767i	$-0.285171\pi$
$19$	6.99748	−	2.54687i	1.60533	−	0.584293i	0.980509	+	0.196474i	$0.0629492\pi$
$20$		0			0
$21$	−1.09755	−	6.22454i	−0.239506	−	1.35831i
$22$		0			0
$23$	−0.321769	+	0.557320i	−0.0670934	+	0.116209i	−0.897621	−	0.440769i	$-0.854706\pi$
$23$	−0.321769	+	0.557320i	−0.0670934	+	0.116209i	0.830527	+	0.556978i	$0.188039\pi$
$24$		0			0
$25$	1.37939	+	0.502055i	0.275877	+	0.100411i
$26$		0			0
$27$	2.41787	−	4.18788i	0.465320	−	0.805958i
$28$		0			0
$29$	−1.08449	−	1.87840i	−0.201385	−	0.348810i	0.747590	−	0.664161i	$-0.231211\pi$
$29$	−1.08449	−	1.87840i	−0.201385	−	0.348810i	−0.948975	+	0.315351i	$0.897878\pi$
$30$		0			0
$31$	−9.90716			−1.77938			−0.889690	−	0.456566i	$-0.849079\pi$
$31$	−9.90716			−1.77938			−0.889690	+	0.456566i	$0.849079\pi$
$32$		0			0
$33$	3.94710	+	3.31201i	0.687102	+	0.576547i
$34$		0			0
$35$	−6.08678	−	2.21541i	−1.02885	−	0.374472i
$36$		0			0
$37$	−2.56368	−	5.51612i	−0.421466	−	0.906844i
$37$	−2.56368	−	5.51612i	−0.421466	−	0.906844i
$38$		0			0
$39$	5.98112	+	2.17695i	0.957745	+	0.348591i
$40$		0			0
$41$	−8.13803	−	6.82862i	−1.27095	−	1.06645i	−0.994425	−	0.105443i	$-0.966374\pi$
$41$	−8.13803	−	6.82862i	−1.27095	−	1.06645i	−0.276521	−	0.961008i	$-0.589182\pi$
$42$		0			0
$43$	−8.30465			−1.26645			−0.633224	−	0.773969i	$-0.718269\pi$
$43$	−8.30465			−1.26645			−0.633224	+	0.773969i	$0.718269\pi$
$44$		0			0
$45$	0.341204	+	0.590982i	0.0508637	+	0.0880984i
$46$		0			0
$47$	−3.92821	+	6.80387i	−0.572989	+	0.992446i	0.423268	+	0.906004i	$0.360883\pi$
$47$	−3.92821	+	6.80387i	−0.572989	+	0.992446i	−0.996257	+	0.0864413i	$0.972450\pi$
$48$		0			0
$49$	−4.58455	−	1.66864i	−0.654935	−	0.238377i
$50$		0			0
$51$	2.84183	−	4.92220i	0.397936	−	0.689246i
$52$		0			0
$53$	0.839394	+	4.76044i	0.115300	+	0.653897i	0.986601	+	0.163149i	$0.0521651\pi$
$53$	0.839394	+	4.76044i	0.115300	+	0.653897i	−0.871302	+	0.490748i	$0.836724\pi$
$54$		0			0
$55$	4.96199	−	1.80602i	0.669074	−	0.243523i
$56$		0			0
$57$	−10.4612	+	8.77795i	−1.38561	+	1.16267i
$58$		0			0
$59$	−0.0961039	−	0.545032i	−0.0125117	−	0.0709572i	0.977913	−	0.209014i	$-0.0670254\pi$
$59$	−0.0961039	−	0.545032i	−0.0125117	−	0.0709572i	−0.990424	+	0.138057i	$0.955914\pi$
$60$		0			0
$61$	5.37102	+	4.50682i	0.687689	+	0.577039i	0.918242	−	0.396020i	$-0.129609\pi$
$61$	5.37102	+	4.50682i	0.687689	+	0.577039i	−0.230553	+	0.973060i	$0.574053\pi$
$62$		0			0
$63$	0.625726	+	1.08379i	0.0788340	+	0.136545i
$64$		0			0
$65$	4.99685	−	4.19285i	0.619783	−	0.520060i
$66$		0			0
$67$	−0.0366435	+	0.207815i	−0.00447671	+	0.0253887i	−0.986964	−	0.160939i	$-0.948548\pi$
$67$	−0.0366435	+	0.207815i	−0.00447671	+	0.0253887i	0.982488	+	0.186328i	$0.0596587\pi$
$68$		0			0
$69$	0.204934	−	1.16224i	0.0246711	−	0.139917i
$70$		0			0
$71$	4.75197	−	1.72957i	0.563955	−	0.205263i	−0.0442811	−	0.999019i	$-0.514100\pi$
$71$	4.75197	−	1.72957i	0.563955	−	0.205263i	0.608236	+	0.793756i	$0.291877\pi$
$72$		0			0
$73$	10.2297			1.19730			0.598648	−	0.801012i	$-0.295705\pi$
$73$	10.2297			1.19730			0.598648	+	0.801012i	$0.295705\pi$
$74$		0			0
$75$	−2.69197			−0.310842
$76$		0			0
$77$	9.09967	−	3.31201i	1.03700	−	0.377438i
$78$		0			0
$79$	0.330775	−	1.87592i	0.0372151	−	0.211057i	−0.960530	−	0.278177i	$-0.910270\pi$
$79$	0.330775	−	1.87592i	0.0372151	−	0.211057i	0.997745	+	0.0671197i	$0.0213809\pi$
$80$		0			0
$81$	−1.72910	+	9.80619i	−0.192122	+	1.08958i
$82$		0			0
$83$	−5.21650	+	4.37717i	−0.572586	+	0.480456i	−0.882503	−	0.470307i	$-0.844143\pi$
$83$	−5.21650	+	4.37717i	−0.572586	+	0.480456i	0.309917	+	0.950764i	$0.399699\pi$
$84$		0			0
$85$	−2.91235	−	5.04435i	−0.315889	−	0.547136i
$86$		0			0
$87$	3.04706	+	2.55679i	0.326679	+	0.274116i
$88$		0			0
$89$	−1.68226	−	9.54055i	−0.178319	−	1.01130i	−0.934243	−	0.356637i	$-0.883923\pi$
$89$	−1.68226	−	9.54055i	−0.178319	−	1.01130i	0.755924	−	0.654659i	$-0.227188\pi$
$90$		0			0
$91$	9.16360	−	7.68917i	0.960606	−	0.806044i
$92$		0			0
$93$	17.0728	−	6.21400i	1.77037	−	0.644361i
$94$		0			0
$95$	2.43020	+	13.7823i	0.249333	+	1.41404i
$96$		0			0
$97$	−8.52990	+	14.7742i	−0.866080	+	1.50009i	−0.000109562		1.00000i	$0.500035\pi$
$97$	−8.52990	+	14.7742i	−0.866080	+	1.50009i	−0.865971	+	0.500095i	$0.833298\pi$
$98$		0			0
$99$	−0.958667	−	0.348926i	−0.0963497	−	0.0350684i
$100$		0			0
$101$	−5.98911	+	10.3734i	−0.595938	+	1.03220i	0.397475	+	0.917613i	$0.369886\pi$
$101$	−5.98911	+	10.3734i	−0.595938	+	1.03220i	−0.993414	+	0.114583i	$0.963447\pi$
$102$		0			0
$103$	6.47233	+	11.2104i	0.637737	+	1.10459i	0.985928	+	0.167170i	$0.0534628\pi$
$103$	6.47233	+	11.2104i	0.637737	+	1.10459i	−0.348191	+	0.937424i	$0.613204\pi$
$104$		0			0
$105$	11.8788			1.15925
$106$		0			0
$107$	−11.9706	−	10.0445i	−1.15724	−	0.971037i	−0.157374	−	0.987539i	$-0.550303\pi$
$107$	−11.9706	−	10.0445i	−1.15724	−	0.971037i	−0.999864	+	0.0165017i	$0.994747\pi$
$108$		0			0
$109$	−1.45663	−	0.530170i	−0.139520	−	0.0507810i	0.271317	−	0.962490i	$-0.412541\pi$
$109$	−1.45663	−	0.530170i	−0.139520	−	0.0507810i	−0.410836	+	0.911709i	$0.634763\pi$
$110$		0			0
$111$	7.87777	+	7.89781i	0.747725	+	0.749627i
$112$		0			0
$113$	4.80629	+	1.74935i	0.452138	+	0.164565i	0.558044	−	0.829811i	$-0.311552\pi$
$113$	4.80629	+	1.74935i	0.452138	+	0.164565i	−0.105906	+	0.994376i	$0.533774\pi$
$114$		0			0
$115$	−0.926496	−	0.777422i	−0.0863962	−	0.0724950i
$116$		0			0
$117$	−1.26024			−0.116510
$118$		0			0
$119$	−5.34090	−	9.25071i	−0.489599	−	0.848011i
$120$		0			0
$121$	1.55290	−	2.68971i	0.141173	−	0.244519i
$122$		0			0
$123$	18.3072	+	6.66326i	1.65070	+	0.600806i
$124$		0			0
$125$	−6.07785	+	10.5271i	−0.543619	+	0.941576i
$126$		0			0
$127$	1.23207	+	6.98740i	0.109328	+	0.620032i	0.989403	+	0.145196i	$0.0463814\pi$
$127$	1.23207	+	6.98740i	0.109328	+	0.620032i	−0.880075	+	0.474836i	$0.842508\pi$
$128$		0			0
$129$	14.3112	−	5.20886i	1.26003	−	0.458615i
$130$		0			0
$131$	−13.3781	+	11.2256i	−1.16885	+	0.980781i	−0.999988	−	0.00485874i	$-0.998453\pi$
$131$	−13.3781	+	11.2256i	−1.16885	+	0.980781i	−0.168861	+	0.985640i	$0.554009\pi$
$132$		0			0
$133$	4.45668	+	25.2751i	0.386443	+	2.19163i
$134$		0			0
$135$	6.96199	+	5.84180i	0.599192	+	0.502782i
$136$		0			0
$137$	−4.92852	−	8.53645i	−0.421072	−	0.729318i	0.574973	−	0.818173i	$-0.305013\pi$
$137$	−4.92852	−	8.53645i	−0.421072	−	0.729318i	−0.996045	+	0.0888546i	$0.971679\pi$
$138$		0			0
$139$	6.89049	−	5.78181i	0.584444	−	0.490407i	−0.301959	−	0.953321i	$-0.597641\pi$
$139$	6.89049	−	5.78181i	0.584444	−	0.490407i	0.886403	+	0.462914i	$0.153196\pi$
$140$		0			0
$141$	2.50187	−	14.1888i	0.210696	−	1.19491i
$142$		0			0
$143$	−1.69337	+	9.60355i	−0.141606	+	0.803089i
$144$		0			0
$145$	3.83053	−	1.39420i	0.318108	−	0.115782i
$146$		0			0
$147$	8.94707			0.737942
$148$		0			0
$149$	−9.97301			−0.817021			−0.408511	−	0.912754i	$-0.633952\pi$
$149$	−9.97301			−0.817021			−0.408511	+	0.912754i	$0.633952\pi$
$150$		0			0
$151$	9.07997	−	3.30484i	0.738918	−	0.268944i	0.0549831	−	0.998487i	$-0.482490\pi$
$151$	9.07997	−	3.30484i	0.738918	−	0.268944i	0.683935	+	0.729543i	$0.260267\pi$
$152$		0			0
$153$	−0.195414	+	1.10825i	−0.0157983	+	0.0895968i
$154$		0			0
$155$	3.23322	−	18.3365i	0.259699	−	1.47282i
$156$		0			0
$157$	−6.73320	+	5.64982i	−0.537368	+	0.450905i	−0.870637	−	0.491927i	$-0.836293\pi$
$157$	−6.73320	+	5.64982i	−0.537368	+	0.450905i	0.333269	+	0.942832i	$0.391848\pi$
$158$		0			0
$159$	−4.43236	−	7.67708i	−0.351509	−	0.608832i
$160$		0			0
$161$	−1.69908	−	1.42570i	−0.133906	−	0.112361i
$162$		0			0
$163$	0.331175	+	1.87819i	0.0259397	+	0.147111i	0.995027	−	0.0996076i	$-0.0317587\pi$
$163$	0.331175	+	1.87819i	0.0259397	+	0.147111i	−0.969087	+	0.246719i	$0.920648\pi$
$164$		0			0
$165$	−7.41812	+	6.22454i	−0.577500	+	0.484580i
$166$		0			0
$167$	6.22793	−	2.26678i	0.481932	−	0.175409i	−0.0896181	−	0.995976i	$-0.528565\pi$
$167$	6.22793	−	2.26678i	0.481932	−	0.175409i	0.571550	+	0.820567i	$0.306342\pi$
$168$		0			0
$169$	−0.165612	−	0.939235i	−0.0127394	−	0.0722488i
$170$		0			0
$171$	1.35193	−	2.34161i	0.103385	−	0.179067i
$172$		0			0
$173$	−23.8769	−	8.69049i	−1.81533	−	0.660725i	−0.996198	−	0.0871179i	$-0.972234\pi$
$173$	−23.8769	−	8.69049i	−1.81533	−	0.660725i	−0.819130	−	0.573608i	$-0.805543\pi$
$174$		0			0
$175$	−2.52962	+	4.38143i	−0.191221	+	0.331205i
$176$		0			0
$177$	0.507471	+	0.878965i	0.0381438	+	0.0660670i
$178$		0			0
$179$	−8.12492			−0.607285			−0.303643	−	0.952786i	$-0.598203\pi$
$179$	−8.12492			−0.607285			−0.303643	+	0.952786i	$0.598203\pi$
$180$		0			0
$181$	9.12118	+	7.65358i	0.677972	+	0.568886i	0.915413	−	0.402516i	$-0.131864\pi$
$181$	9.12118	+	7.65358i	0.677972	+	0.568886i	−0.237441	+	0.971402i	$0.576309\pi$
$182$		0			0
$183$	−12.0826	−	4.39769i	−0.893168	−	0.325087i
$184$		0			0
$185$	11.0461	−	2.94475i	0.812123	−	0.216502i
$186$		0			0
$187$	8.18273	+	2.97827i	0.598381	+	0.217793i
$188$		0			0
$189$	12.7674	+	10.7131i	0.928693	+	0.779266i
$190$		0			0
$191$	−0.266722			−0.0192993			−0.00964965	−	0.999953i	$-0.503072\pi$
$191$	−0.266722			−0.0192993			−0.00964965	+	0.999953i	$0.503072\pi$
$192$		0			0
$193$	−3.96417	−	6.86615i	−0.285348	−	0.494236i	0.687346	−	0.726330i	$-0.258776\pi$
$193$	−3.96417	−	6.86615i	−0.285348	−	0.494236i	−0.972693	+	0.232094i	$0.925442\pi$
$194$		0			0
$195$	−5.98112	+	10.3596i	−0.428317	+	0.741866i
$196$		0			0
$197$	0.386805	+	0.140786i	0.0275587	+	0.0100306i	0.355763	−	0.934576i	$-0.384221\pi$
$197$	0.386805	+	0.140786i	0.0275587	+	0.0100306i	−0.328204	+	0.944607i	$0.606443\pi$
$198$		0			0
$199$	−1.01751	+	1.76239i	−0.0721297	+	0.124932i	−0.899834	−	0.436232i	$-0.856313\pi$
$199$	−1.01751	+	1.76239i	−0.0721297	+	0.124932i	0.827705	+	0.561164i	$0.189646\pi$
$200$		0			0
$201$	−0.0671996	−	0.381108i	−0.00473989	−	0.0268813i
$202$		0			0
$203$	7.02471	−	2.55679i	0.493038	−	0.179451i
$204$		0			0
$205$	15.2945	−	12.8336i	1.06821	−	0.896338i
$206$		0			0
$207$	0.0405763	+	0.230119i	0.00282024	+	0.0159944i
$208$		0			0
$209$	−16.0274	−	13.4486i	−1.10864	−	0.930259i
$210$		0			0
$211$	−7.87052	−	13.6321i	−0.541829	−	0.938475i	−0.998799	−	0.0489932i	$-0.984399\pi$
$211$	−7.87052	−	13.6321i	−0.541829	−	0.938475i	0.456970	−	0.889482i	$-0.348935\pi$
$212$		0			0
$213$	−7.10414	+	5.96108i	−0.486768	+	0.408447i
$214$		0			0
$215$	2.71024	−	15.3705i	0.184837	−	1.04826i
$216$		0			0
$217$	5.92933	−	33.6269i	0.402509	−	2.28274i
$218$		0			0
$219$	−17.6286	+	6.41630i	−1.19123	+	0.433573i
$220$		0			0
$221$	10.7568			0.723584
$222$		0			0
$223$	3.43531			0.230045			0.115023	−	0.993363i	$-0.463306\pi$
$223$	3.43531			0.230045			0.115023	+	0.993363i	$0.463306\pi$
$224$		0			0
$225$	0.500857	−	0.182297i	0.0333905	−	0.0121531i
$226$		0			0
$227$	0.401614	−	2.27767i	0.0266561	−	0.151174i	−0.968575	−	0.248723i	$-0.919989\pi$
$227$	0.401614	−	2.27767i	0.0266561	−	0.151174i	0.995231	+	0.0975489i	$0.0311002\pi$
$228$		0			0
$229$	−1.02642	+	5.82114i	−0.0678280	+	0.384672i	0.931929	+	0.362640i	$0.118125\pi$
$229$	−1.02642	+	5.82114i	−0.0678280	+	0.384672i	−0.999757	+	0.0220316i	$0.992987\pi$
$230$		0			0
$231$	−13.6039	+	11.4150i	−0.895071	+	0.751054i
$232$		0			0
$233$	14.1679	+	24.5395i	0.928168	+	1.60763i	0.786386	+	0.617736i	$0.211950\pi$
$233$	14.1679	+	24.5395i	0.928168	+	1.60763i	0.141782	+	0.989898i	$0.454717\pi$
$234$		0			0
$235$	−11.3108	−	9.49092i	−0.737838	−	0.619120i
$236$		0			0
$237$	0.606600	+	3.44020i	0.0394029	+	0.223465i
$238$		0			0
$239$	−18.5674	+	15.5799i	−1.20103	+	1.00778i	−0.201427	+	0.979504i	$0.564558\pi$
$239$	−18.5674	+	15.5799i	−1.20103	+	1.00778i	−0.999600	+	0.0282780i	$0.990998\pi$
$240$		0			0
$241$	−8.31692	+	3.02711i	−0.535740	+	0.194993i	−0.595700	−	0.803207i	$-0.703125\pi$
$241$	−8.31692	+	3.02711i	−0.535740	+	0.194993i	0.0599594	+	0.998201i	$0.480903\pi$
$242$		0			0
$243$	−0.651791	−	3.69649i	−0.0418124	−	0.237130i
$244$		0			0
$245$	4.58455	−	7.94067i	0.292896	−	0.507311i
$246$		0			0
$247$	−24.2867	−	8.83962i	−1.54532	−	0.562452i
$248$		0			0
$249$	6.24404	−	10.8150i	0.395700	−	0.685372i
$250$		0			0
$251$	3.29525	+	5.70754i	0.207994	+	0.360257i	0.951083	−	0.308937i	$-0.0999731\pi$
$251$	3.29525	+	5.70754i	0.207994	+	0.360257i	−0.743088	+	0.669193i	$0.766640\pi$
$252$		0			0
$253$	1.80812			0.113676
$254$		0			0
$255$	8.18273	+	6.86613i	0.512422	+	0.429973i
$256$		0			0
$257$	−9.04522	−	3.29219i	−0.564225	−	0.205361i	0.0441304	−	0.999026i	$-0.485948\pi$
$257$	−9.04522	−	3.29219i	−0.564225	−	0.205361i	−0.608356	+	0.793665i	$0.708171\pi$
$258$		0			0
$259$	20.2571	−	5.40031i	1.25872	−	0.335559i
$260$		0			0
$261$	−0.740067	−	0.269362i	−0.0458090	−	0.0166731i
$262$		0			0
$263$	1.21898	+	1.02284i	0.0751654	+	0.0630712i	0.679596	−	0.733586i	$-0.262155\pi$
$263$	1.21898	+	1.02284i	0.0751654	+	0.0630712i	−0.604431	+	0.796658i	$0.706599\pi$
$264$		0			0
$265$	−9.08472			−0.558070
$266$		0			0
$267$	8.88305	+	15.3859i	0.543634	+	0.941601i
$268$		0			0
$269$	−11.5599	+	20.0223i	−0.704819	+	1.22078i	0.261938	+	0.965085i	$0.415638\pi$
$269$	−11.5599	+	20.0223i	−0.704819	+	1.22078i	−0.966757	+	0.255697i	$0.917695\pi$
$270$		0			0
$271$	0.172362	+	0.0627348i	0.0104703	+	0.00381087i	0.347250	−	0.937773i	$-0.387116\pi$
$271$	0.172362	+	0.0627348i	0.0104703	+	0.00381087i	−0.336780	+	0.941583i	$0.609338\pi$
$272$		0			0
$273$	−10.9686	+	18.9982i	−0.663851	+	1.14982i
$274$		0			0
$275$	−0.716183	−	4.06167i	−0.0431875	−	0.244928i
$276$		0			0
$277$	11.9260	−	4.34070i	0.716562	−	0.260807i	0.0420965	−	0.999114i	$-0.486596\pi$
$277$	11.9260	−	4.34070i	0.716562	−	0.260807i	0.674466	+	0.738306i	$0.264374\pi$
$278$		0			0
$279$	−2.75570	+	2.31230i	−0.164979	+	0.138434i
$280$		0			0
$281$	3.02774	+	17.1712i	0.180620	+	1.02435i	0.931455	+	0.363857i	$0.118540\pi$
$281$	3.02774	+	17.1712i	0.180620	+	1.02435i	−0.750835	+	0.660490i	$0.770349\pi$
$282$		0			0
$283$	10.0612	+	8.44232i	0.598074	+	0.501844i	0.890826	−	0.454345i	$-0.150127\pi$
$283$	10.0612	+	8.44232i	0.598074	+	0.501844i	−0.292752	+	0.956188i	$0.594571\pi$
$284$		0			0
$285$	−12.8325	−	22.2266i	−0.760132	−	1.31659i
$286$		0			0
$287$	28.0482	−	23.5352i	1.65563	−	1.38924i
$288$		0			0
$289$	−1.28405	+	7.28223i	−0.0755325	+	0.428366i
$290$		0			0
$291$	5.43268	−	30.8103i	0.318469	−	1.80613i
$292$		0			0
$293$	−6.37791	+	2.32137i	−0.372602	+	0.135616i	−0.521532	−	0.853232i	$-0.674639\pi$
$293$	−6.37791	+	2.32137i	−0.372602	+	0.135616i	0.148930	+	0.988848i	$0.452417\pi$
$294$		0			0
$295$	1.04013			0.0605586
$296$		0			0
$297$	−13.5868			−0.788386
$298$		0			0
$299$	2.09887	−	0.763927i	0.121381	−	0.0441790i
$300$		0			0
$301$	4.97024	−	28.1876i	0.286480	−	1.62471i
$302$		0			0
$303$	3.81445	−	21.6328i	0.219135	−	1.24277i
$304$		0			0
$305$	−10.0942	+	8.47006i	−0.577993	+	0.484994i
$306$		0			0
$307$	4.10242	+	7.10560i	0.234138	+	0.405538i	0.959022	−	0.283333i	$-0.0914400\pi$
$307$	4.10242	+	7.10560i	0.234138	+	0.405538i	−0.724884	+	0.688871i	$0.758107\pi$
$308$		0			0
$309$	−18.1850	−	15.2591i	−1.03451	−	0.868058i
$310$		0			0
$311$	1.88461	+	10.6882i	0.106867	+	0.606070i	0.990458	+	0.137812i	$0.0440071\pi$
$311$	1.88461	+	10.6882i	0.106867	+	0.606070i	−0.883592	+	0.468258i	$0.844882\pi$
$312$		0			0
$313$	−6.63058	+	5.56372i	−0.374783	+	0.314480i	−0.810650	−	0.585531i	$-0.800886\pi$
$313$	−6.63058	+	5.56372i	−0.374783	+	0.314480i	0.435867	+	0.900011i	$0.356442\pi$
$314$		0			0
$315$	−2.21012	+	0.804417i	−0.124526	+	0.0453238i
$316$		0			0
$317$	−4.41505	−	25.0390i	−0.247974	−	1.40633i	−0.813484	−	0.581587i	$-0.802432\pi$
$317$	−4.41505	−	25.0390i	−0.247974	−	1.40633i	0.565510	−	0.824741i	$-0.308679\pi$
$318$		0			0
$319$	−3.04706	+	5.27766i	−0.170603	+	0.295492i
$320$		0			0
$321$	26.9287	+	9.80126i	1.50302	+	0.547053i
$322$		0			0
$323$	−11.5394	+	19.9869i	−0.642071	+	1.11210i
$324$		0			0
$325$	−2.54739	−	4.41222i	−0.141304	−	0.244746i
$326$		0			0
$327$	2.84271			0.157202
$328$		0			0
$329$	−20.7427	−	17.4052i	−1.14358	−	0.959578i
$330$		0			0
$331$	−19.5470	−	7.11454i	−1.07440	−	0.391050i	−0.256581	−	0.966523i	$-0.582596\pi$
$331$	−19.5470	−	7.11454i	−1.07440	−	0.391050i	−0.817821	+	0.575473i	$0.804818\pi$
$332$		0			0
$333$	−2.00054	−	0.935963i	−0.109629	−	0.0512904i
$334$		0			0
$335$	−0.372673	−	0.135642i	−0.0203613	−	0.00741091i
$336$		0			0
$337$	−1.89385	−	1.58913i	−0.103165	−	0.0865653i	0.589746	−	0.807588i	$-0.299228\pi$
$337$	−1.89385	−	1.58913i	−0.103165	−	0.0865653i	−0.692911	+	0.721023i	$0.743672\pi$
$338$		0			0
$339$	−9.37981			−0.509442
$340$		0			0
$341$	13.9179	+	24.1065i	0.753696	+	1.30544i
$342$		0			0
$343$	−3.65547	+	6.33145i	−0.197377	+	0.341866i
$344$		0			0
$345$	2.08423	+	0.758597i	0.112211	+	0.0408415i
$346$		0			0
$347$	−2.92690	+	5.06953i	−0.157124	+	0.272147i	−0.933830	−	0.357716i	$-0.883556\pi$
$347$	−2.92690	+	5.06953i	−0.157124	+	0.272147i	0.776706	+	0.629863i	$0.216889\pi$
$348$		0			0
$349$	0.545283	+	3.09246i	0.0291883	+	0.165535i	0.995918	−	0.0902661i	$-0.0287718\pi$
$349$	0.545283	+	3.09246i	0.0291883	+	0.165535i	−0.966729	+	0.255801i	$0.917661\pi$
$350$		0			0
$351$	−15.7716	+	5.74039i	−0.841825	+	0.306399i
$352$		0			0
$353$	−8.61667	+	7.23024i	−0.458619	+	0.384827i	−0.842623	−	0.538505i	$-0.818989\pi$
$353$	−8.61667	+	7.23024i	−0.458619	+	0.384827i	0.384004	+	0.923332i	$0.374545\pi$
$354$		0			0
$355$	1.65034	+	9.35955i	0.0875910	+	0.496753i
$356$		0			0
$357$	15.0061	+	12.5916i	0.794208	+	0.666419i
$358$		0			0
$359$	−11.5467	−	19.9994i	−0.609410	−	1.05553i	−0.991338	−	0.131337i	$-0.958073\pi$
$359$	−11.5467	−	19.9994i	−0.609410	−	1.05553i	0.381927	−	0.924192i	$-0.375260\pi$
$360$		0			0
$361$	27.9233	−	23.4304i	1.46965	−	1.23318i
$362$		0			0
$363$	−0.989041	+	5.60913i	−0.0519112	+	0.294403i
$364$		0			0
$365$	−3.33848	+	18.9335i	−0.174744	+	0.991023i
$366$		0			0
$367$	1.47673	−	0.537487i	0.0770848	−	0.0280566i	−0.303190	−	0.952930i	$-0.598052\pi$
$367$	1.47673	−	0.537487i	0.0770848	−	0.0280566i	0.380275	+	0.924874i	$0.375829\pi$
$368$		0			0
$369$	−3.85739			−0.200808
$370$		0			0
$371$	−16.6602			−0.864957
$372$		0			0
$373$	−6.28835	+	2.28877i	−0.325599	+	0.118508i	−0.499647	−	0.866229i	$-0.666537\pi$
$373$	−6.28835	+	2.28877i	−0.325599	+	0.118508i	0.174049	+	0.984737i	$0.444315\pi$
$374$		0			0
$375$	3.87097	−	21.9534i	0.199896	−	1.13367i
$376$		0			0
$377$	−1.30723	+	7.41370i	−0.0673260	+	0.381825i
$378$		0			0
$379$	8.40501	−	7.05264i	0.431737	−	0.362270i	−0.400870	−	0.916135i	$-0.631292\pi$
$379$	8.40501	−	7.05264i	0.431737	−	0.362270i	0.832606	+	0.553865i	$0.186848\pi$
$380$		0			0
$381$	−6.50586	−	11.2685i	−0.333305	−	0.577301i
$382$		0			0
$383$	19.3480	+	16.2349i	0.988638	+	0.829566i	0.985370	−	0.170429i	$-0.0545152\pi$
$383$	19.3480	+	16.2349i	0.988638	+	0.829566i	0.00326840	+	0.999995i	$0.498960\pi$
$384$		0			0
$385$	3.16028	+	17.9228i	0.161063	+	0.913433i
$386$		0			0
$387$	−2.30995	+	1.93828i	−0.117422	+	0.0985284i
$388$		0			0
$389$	10.1599	−	3.69792i	0.515130	−	0.187492i	−0.0713568	−	0.997451i	$-0.522733\pi$
$389$	10.1599	−	3.69792i	0.515130	−	0.187492i	0.586487	+	0.809959i	$0.300511\pi$
$390$		0			0
$391$	−0.346340	−	1.96419i	−0.0175152	−	0.0993334i
$392$		0			0
$393$	16.0133	−	27.7358i	0.807763	−	1.39909i
$394$		0			0
$395$	3.36406	+	1.22442i	0.169264	+	0.0616072i
$396$		0			0
$397$	5.40570	−	9.36295i	0.271304	−	0.469913i	−0.697892	−	0.716203i	$-0.745878\pi$
$397$	5.40570	−	9.36295i	0.271304	−	0.469913i	0.969196	+	0.246290i	$0.0792117\pi$
$398$		0			0
$399$	−23.5332	−	40.7607i	−1.17813	−	2.04059i
$400$		0			0
$401$	−34.6974			−1.73271			−0.866353	−	0.499432i	$-0.833542\pi$
$401$	−34.6974			−1.73271			−0.866353	+	0.499432i	$0.833542\pi$
$402$		0			0
$403$	26.3408	+	22.1026i	1.31213	+	1.10101i
$404$		0			0
$405$	−17.5853	−	6.40053i	−0.873822	−	0.318045i
$406$		0			0
$407$	−9.82049	+	13.9873i	−0.486783	+	0.693322i
$408$		0			0
$409$	−1.77330	−	0.645428i	−0.0876840	−	0.0319144i	0.297806	−	0.954627i	$-0.403745\pi$
$409$	−1.77330	−	0.645428i	−0.0876840	−	0.0319144i	−0.385490	+	0.922712i	$0.625967\pi$
$410$		0			0
$411$	13.8475	+	11.6194i	0.683046	+	0.573143i
$412$		0			0
$413$	1.90747			0.0938602
$414$		0			0
$415$	−6.39899	−	11.0834i	−0.314114	−	0.544061i
$416$		0			0
$417$	−8.24777	+	14.2856i	−0.403895	+	0.699566i
$418$		0			0
$419$	−16.3766	−	5.96059i	−0.800048	−	0.291194i	−0.0905419	−	0.995893i	$-0.528860\pi$
$419$	−16.3766	−	5.96059i	−0.800048	−	0.291194i	−0.709507	+	0.704699i	$0.751082\pi$
$420$		0			0
$421$	9.07719	−	15.7222i	0.442395	−	0.766251i	−0.555471	−	0.831536i	$-0.687462\pi$
$421$	9.07719	−	15.7222i	0.442395	−	0.766251i	0.997867	+	0.0652845i	$0.0207955\pi$
$422$		0			0
$423$	0.495363	+	2.80934i	0.0240854	+	0.136595i
$424$		0			0
$425$	−4.27508	+	1.55600i	−0.207372	+	0.0754771i
$426$		0			0
$427$	−18.5115	+	15.5330i	−0.895837	+	0.751696i
$428$		0			0
$429$	−3.10542	−	17.6117i	−0.149931	−	0.850302i
$430$		0			0
$431$	−21.7480	−	18.2487i	−1.04756	−	0.879011i	−0.0547286	−	0.998501i	$-0.517429\pi$
$431$	−21.7480	−	18.2487i	−1.04756	−	0.879011i	−0.992835	+	0.119491i	$0.961874\pi$
$432$		0			0
$433$	3.73468	+	6.46865i	0.179477	+	0.310864i	0.941702	−	0.336449i	$-0.109226\pi$
$433$	3.73468	+	6.46865i	0.179477	+	0.310864i	−0.762224	+	0.647313i	$0.775893\pi$
$434$		0			0
$435$	−5.72660	+	4.80519i	−0.274569	+	0.230391i
$436$		0			0
$437$	−0.832146	+	4.71934i	−0.0398069	+	0.225756i
$438$		0			0
$439$	5.99873	−	34.0205i	0.286304	−	1.62371i	−0.414287	−	0.910146i	$-0.635969\pi$
$439$	5.99873	−	34.0205i	0.286304	−	1.62371i	0.700590	−	0.713564i	$-0.252920\pi$
$440$		0			0
$441$	−1.66466	+	0.605885i	−0.0792693	+	0.0288517i
$442$		0			0
$443$	2.89849			0.137712			0.0688558	−	0.997627i	$-0.478065\pi$
$443$	2.89849			0.137712			0.0688558	+	0.997627i	$0.478065\pi$
$444$		0			0
$445$	18.2070			0.863094
$446$		0			0
$447$	17.1863	−	6.25530i	0.812884	−	0.295866i
$448$		0			0
$449$	4.84053	−	27.4520i	0.228439	−	1.29554i	−0.627563	−	0.778566i	$-0.715948\pi$
$449$	4.84053	−	27.4520i	0.228439	−	1.29554i	0.856002	−	0.516973i	$-0.172941\pi$
$450$		0			0
$451$	−5.18310	+	29.3948i	−0.244063	+	1.38415i
$452$		0			0
$453$	−13.5745	+	11.3903i	−0.637784	+	0.535164i
$454$		0			0
$455$	11.2408	+	19.4697i	0.526978	+	0.912752i
$456$		0			0
$457$	7.48390	+	6.27974i	0.350082	+	0.293754i	0.800823	−	0.598901i	$-0.204396\pi$
$457$	7.48390	+	6.27974i	0.350082	+	0.293754i	−0.450741	+	0.892655i	$0.648840\pi$
$458$		0			0
$459$	2.60251	+	14.7596i	0.121475	+	0.688917i
$460$		0			0
$461$	11.8337	−	9.92965i	0.551150	−	0.462470i	−0.324180	−	0.945995i	$-0.605088\pi$
$461$	11.8337	−	9.92965i	0.551150	−	0.462470i	0.875330	+	0.483525i	$0.160644\pi$
$462$		0			0
$463$	17.2009	−	6.26063i	0.799395	−	0.290956i	0.0901595	−	0.995927i	$-0.471262\pi$
$463$	17.2009	−	6.26063i	0.799395	−	0.290956i	0.709236	+	0.704971i	$0.249040\pi$
$464$		0			0
$465$	5.92933	+	33.6269i	0.274966	+	1.55941i
$466$		0			0
$467$	11.8035	−	20.4443i	0.546201	−	0.946048i	−0.452329	−	0.891851i	$-0.649407\pi$
$467$	11.8035	−	20.4443i	0.546201	−	0.946048i	0.998530	−	0.0541966i	$-0.0172598\pi$
$468$		0			0
$469$	−0.683436	−	0.248750i	−0.0315581	−	0.0114862i
$470$		0			0
$471$	8.05949	−	13.9594i	0.371362	−	0.643217i
$472$		0			0
$473$	11.6666	+	20.2072i	0.536432	+	0.929128i
$474$		0			0
$475$	10.9309			0.501544
$476$		0			0
$477$	1.34455	+	1.12821i	0.0615628	+	0.0516573i
$478$		0			0
$479$	−8.16238	−	2.97086i	−0.372949	−	0.135742i	0.148744	−	0.988876i	$-0.452477\pi$
$479$	−8.16238	−	2.97086i	−0.372949	−	0.135742i	−0.521693	+	0.853134i	$0.674699\pi$
$480$		0			0
$481$	−5.49006	+	20.3856i	−0.250325	+	0.929502i
$482$		0			0
$483$	3.82222	+	1.39117i	0.173917	+	0.0633006i
$484$		0			0
$485$	−24.5609	−	20.6090i	−1.11525	−	0.935807i
$486$		0			0
$487$	−20.9350			−0.948654			−0.474327	−	0.880349i	$-0.657309\pi$
$487$	−20.9350			−0.948654			−0.474327	+	0.880349i	$0.657309\pi$
$488$		0			0
$489$	−1.74875	−	3.02892i	−0.0790812	−	0.136973i
$490$		0			0
$491$	21.6055	−	37.4219i	0.975044	−	1.68883i	0.295253	−	0.955419i	$-0.404596\pi$
$491$	21.6055	−	37.4219i	0.975044	−	1.68883i	0.679791	−	0.733406i	$-0.262070\pi$
$492$		0			0
$493$	6.31686	+	2.29915i	0.284497	+	0.103548i
$494$		0			0
$495$	0.958667	−	1.66046i	0.0430889	−	0.0746321i
$496$		0			0
$497$	3.02652	+	17.1643i	0.135758	+	0.769922i
$498$		0			0
$499$	−6.35892	+	2.31446i	−0.284664	+	0.103609i	−0.480406	−	0.877046i	$-0.659511\pi$
$499$	−6.35892	+	2.31446i	−0.284664	+	0.103609i	0.195742	+	0.980655i	$0.437289\pi$
$500$		0			0
$501$	−9.31069	+	7.81260i	−0.415971	+	0.349041i
$502$		0			0
$503$	4.76565	+	27.0274i	0.212490	+	1.20509i	0.885209	+	0.465193i	$0.154015\pi$
$503$	4.76565	+	27.0274i	0.212490	+	1.20509i	−0.672719	+	0.739898i	$0.734874\pi$
$504$		0			0
$505$	−17.2449	−	14.4702i	−0.767390	−	0.643917i
$506$		0			0
$507$	0.874506	+	1.51469i	0.0388382	+	0.0672697i
$508$		0			0
$509$	16.0780	−	13.4910i	0.712643	−	0.597978i	−0.212696	−	0.977118i	$-0.568225\pi$
$509$	16.0780	−	13.4910i	0.712643	−	0.597978i	0.925339	+	0.379140i	$0.123780\pi$
$510$		0			0
$511$	−6.12236	+	34.7216i	−0.270837	+	1.53599i
$512$		0			0
$513$	6.25301	−	35.4626i	0.276077	−	1.56571i
$514$		0			0
$515$	−22.8608	+	8.32066i	−1.00737	+	0.366652i
$516$		0			0
$517$	22.0739			0.970809
$518$		0			0
$519$	46.5975			2.04540
$520$		0			0
$521$	35.3011	−	12.8486i	1.54657	−	0.562906i	0.578961	−	0.815355i	$-0.303458\pi$
$521$	35.3011	−	12.8486i	1.54657	−	0.562906i	0.967610	+	0.252449i	$0.0812361\pi$
$522$		0			0
$523$	−3.28508	+	18.6306i	−0.143647	+	0.814660i	0.824797	+	0.565428i	$0.191289\pi$
$523$	−3.28508	+	18.6306i	−0.143647	+	0.814660i	−0.968444	+	0.249232i	$0.919822\pi$
$524$		0			0
$525$	1.61111	−	9.13707i	0.0703147	−	0.398774i
$526$		0			0
$527$	23.5213	−	19.7367i	1.02460	−	0.859746i
$528$		0			0
$529$	11.2929	+	19.5599i	0.490997	+	0.850432i
$530$		0			0
$531$	−0.153940	−	0.129171i	−0.00668045	−	0.00560556i
$532$		0			0
$533$	6.40268	+	36.3114i	0.277331	+	1.57282i
$534$		0			0
$535$	22.4973	−	18.8775i	0.972643	−	0.816144i
$536$		0			0
$537$	14.0015	−	5.09613i	0.604210	−	0.219914i
$538$		0			0
$539$	2.38032	+	13.4994i	0.102528	+	0.581462i
$540$		0			0
$541$	−8.23739	+	14.2676i	−0.354153	+	0.613411i	−0.986973	−	0.160888i	$-0.948564\pi$
$541$	−8.23739	+	14.2676i	−0.354153	+	0.613411i	0.632820	+	0.774299i	$0.281897\pi$
$542$		0			0
$543$	−20.5188	−	7.46825i	−0.880548	−	0.320493i
$544$		0			0
$545$	1.45663	−	2.52296i	0.0623951	−	0.108072i
$546$		0			0
$547$	−6.00067	−	10.3935i	−0.256570	−	0.444392i	0.708751	−	0.705459i	$-0.249259\pi$
$547$	−6.00067	−	10.3935i	−0.256570	−	0.444392i	−0.965321	+	0.261067i	$0.915926\pi$
$548$		0			0
$549$	2.54584			0.108654
$550$		0			0
$551$	−12.3728	−	10.3820i	−0.527097	−	0.442287i
$552$		0			0
$553$	6.16927	+	2.24543i	0.262344	+	0.0954855i
$554$		0			0
$555$	−17.1885	+	12.0030i	−0.729610	+	0.509498i
$556$		0			0
$557$	40.2026	+	14.6325i	1.70344	+	0.620001i	0.996210	−	0.0869842i	$-0.0277230\pi$
$557$	40.2026	+	14.6325i	1.70344	+	0.620001i	0.707229	+	0.706985i	$0.249945\pi$
$558$		0			0
$559$	22.0801	+	18.5274i	0.933890	+	0.783627i
$560$		0			0
$561$	−15.9692			−0.674219
$562$		0			0
$563$	11.8738	+	20.5660i	0.500421	+	0.866754i	1.00000		0.000486132i	$0.000154741\pi$
$563$	11.8738	+	20.5660i	0.500421	+	0.866754i	−0.499579	+	0.866268i	$0.666512\pi$
$564$		0			0
$565$	−4.80629	+	8.32474i	−0.202202	+	0.350224i
$566$		0			0
$567$	−32.2493	−	11.7378i	−1.35434	−	0.492941i
$568$		0			0
$569$	2.64332	−	4.57837i	0.110814	−	0.191935i	−0.805285	−	0.592888i	$-0.797988\pi$
$569$	2.64332	−	4.57837i	0.110814	−	0.191935i	0.916099	+	0.400953i	$0.131321\pi$
$570$		0			0
$571$	4.21057	+	23.8793i	0.176207	+	0.999318i	0.936742	+	0.350021i	$0.113826\pi$
$571$	4.21057	+	23.8793i	0.176207	+	0.999318i	−0.760535	+	0.649297i	$0.775063\pi$
$572$		0			0
$573$	0.459636	−	0.167294i	0.0192016	−	0.00698880i
$574$		0			0
$575$	−0.723648	+	0.607213i	−0.0301782	+	0.0253225i
$576$		0			0
$577$	−0.296836	−	1.68344i	−0.0123574	−	0.0700825i	0.978005	−	0.208579i	$-0.0668840\pi$
$577$	−0.296836	−	1.68344i	−0.0123574	−	0.0700825i	−0.990363	+	0.138497i	$0.955773\pi$
$578$		0			0
$579$	11.1380	+	9.34588i	0.462879	+	0.388402i
$580$		0			0
$581$	−11.7350	−	20.3255i	−0.486848	−	0.843245i
$582$		0			0
$583$	10.4041	−	8.73005i	0.430893	−	0.361562i
$584$		0			0
$585$	0.411283	−	2.33250i	0.0170044	−	0.0964370i
$586$		0			0
$587$	−4.51530	+	25.6076i	−0.186366	+	1.05694i	0.737821	+	0.674997i	$0.235855\pi$
$587$	−4.51530	+	25.6076i	−0.186366	+	1.05694i	−0.924187	+	0.381940i	$0.875256\pi$
$588$		0			0
$589$	−69.3251	+	25.2323i	−2.85649	+	1.03968i
$590$		0			0
$591$	−0.754877			−0.0310515
$592$		0			0
$593$	19.5933			0.804601			0.402300	−	0.915508i	$-0.368211\pi$
$593$	19.5933			0.804601			0.402300	+	0.915508i	$0.368211\pi$
$594$		0			0
$595$	18.8645	−	6.86613i	0.773370	−	0.281484i
$596$		0			0
$597$	0.648053	−	3.67529i	0.0265231	−	0.150420i
$598$		0			0
$599$	−6.43804	+	36.5119i	−0.263051	+	1.49184i	0.511477	+	0.859297i	$0.329099\pi$
$599$	−6.43804	+	36.5119i	−0.263051	+	1.49184i	−0.774528	+	0.632540i	$0.782012\pi$
$600$		0			0
$601$	−14.1667	+	11.8873i	−0.577871	+	0.484892i	−0.884247	−	0.467019i	$-0.845328\pi$
$601$	−14.1667	+	11.8873i	−0.577871	+	0.484892i	0.306376	+	0.951911i	$0.400884\pi$
$602$		0			0
$603$	0.0383111	+	0.0663567i	0.00156015	+	0.00270226i
$604$		0			0
$605$	4.47140	+	3.75195i	0.181788	+	0.152539i
$606$		0			0
$607$	−0.923385	−	5.23678i	−0.0374791	−	0.212554i	0.960317	−	0.278911i	$-0.0899735\pi$
$607$	−0.923385	−	5.23678i	−0.0374791	−	0.212554i	−0.997796	+	0.0663569i	$0.978862\pi$
$608$		0			0
$609$	−10.5019	+	8.81212i	−0.425557	+	0.357085i
$610$		0			0
$611$	25.6234	−	9.32617i	1.03661	−	0.377296i
$612$		0			0
$613$	7.01848	+	39.8038i	0.283474	+	1.60766i	0.710687	+	0.703508i	$0.248384\pi$
$613$	7.01848	+	39.8038i	0.283474	+	1.60766i	−0.427213	+	0.904151i	$0.640505\pi$
$614$		0			0
$615$	−18.3072	+	31.7089i	−0.738216	+	1.27863i
$616$		0			0
$617$	30.8191	+	11.2172i	1.24073	+	0.451589i	0.877259	−	0.480017i	$-0.159370\pi$
$617$	30.8191	+	11.2172i	1.24073	+	0.451589i	0.363470	+	0.931606i	$0.381592\pi$
$618$		0			0
$619$	−2.07537	+	3.59465i	−0.0834163	+	0.144481i	−0.904715	−	0.426017i	$-0.859916\pi$
$619$	−2.07537	+	3.59465i	−0.0834163	+	0.144481i	0.821299	+	0.570498i	$0.193250\pi$
$620$		0			0
$621$	1.55599	+	2.69506i	0.0624398	+	0.108149i
$622$		0			0
$623$	33.3893			1.33772
$624$		0			0
$625$	−11.8780	−	9.96686i	−0.475122	−	0.398674i
$626$		0			0
$627$	36.0550	+	13.1229i	1.43990	+	0.524080i
$628$		0			0
$629$	17.0757	+	7.98893i	0.680851	+	0.318540i
$630$		0			0
$631$	28.1162	+	10.2335i	1.11929	+	0.407387i	0.834392	−	0.551171i	$-0.185819\pi$
$631$	28.1162	+	10.2335i	1.11929	+	0.407387i	0.284896	+	0.958559i	$0.408041\pi$
$632$		0			0
$633$	22.1135	+	18.5554i	0.878932	+	0.737512i
$634$		0			0
$635$	−13.3346			−0.529168
$636$		0			0
$637$	8.46656	+	14.6645i	0.335457	+	0.581029i
$638$		0			0
$639$	0.918091	−	1.59018i	0.0363191	−	0.0629065i
$640$		0			0
$641$	−6.42331	−	2.33789i	−0.253705	−	0.0923412i	0.212037	−	0.977262i	$-0.431990\pi$
$641$	−6.42331	−	2.33789i	−0.253705	−	0.0923412i	−0.465742	+	0.884920i	$0.654213\pi$
$642$		0			0
$643$	18.7592	−	32.4920i	0.739792	−	1.28136i	−0.212796	−	0.977097i	$-0.568257\pi$
$643$	18.7592	−	32.4920i	0.739792	−	1.28136i	0.952589	−	0.304262i	$-0.0984097\pi$
$644$		0			0
$645$	4.97024	+	28.1876i	0.195703	+	1.10989i
$646$		0			0
$647$	2.48480	−	0.904395i	0.0976877	−	0.0355554i	−0.292714	−	0.956200i	$-0.594558\pi$
$647$	2.48480	−	0.904395i	0.0976877	−	0.0355554i	0.390402	+	0.920645i	$0.372336\pi$
$648$		0			0
$649$	−1.19118	+	0.999522i	−0.0467580	+	0.0392347i
$650$		0			0
$651$	10.8736	+	61.6675i	0.426172	+	2.41694i
$652$		0			0
$653$	−34.2792	−	28.7636i	−1.34145	−	1.12561i	−0.981251	−	0.192732i	$-0.938265\pi$
$653$	−34.2792	−	28.7636i	−1.34145	−	1.12561i	−0.360197	−	0.932876i	$-0.617290\pi$
$654$		0			0
$655$	−16.4107	−	28.4241i	−0.641218	−	1.11062i
$656$		0			0
$657$	2.84541	−	2.38758i	0.111010	−	0.0931485i
$658$		0			0
$659$	0.790306	−	4.48205i	0.0307859	−	0.174596i	−0.965538	−	0.260262i	$-0.916191\pi$
$659$	0.790306	−	4.48205i	0.0307859	−	0.174596i	0.996324	+	0.0856667i	$0.0273020\pi$
$660$		0			0
$661$	−7.56467	+	42.9014i	−0.294231	+	1.66867i	0.376078	+	0.926588i	$0.377272\pi$
$661$	−7.56467	+	42.9014i	−0.294231	+	1.66867i	−0.670310	+	0.742082i	$0.733839\pi$
$662$		0			0
$663$	−18.5371	+	6.74694i	−0.719919	+	0.262029i
$664$		0			0
$665$	−48.2344			−1.87045
$666$		0			0
$667$	1.39582			0.0540465
$668$		0			0
$669$	−5.92000	+	2.15470i	−0.228880	+	0.0833057i
$670$		0			0
$671$	3.42080	−	19.4003i	0.132058	−	0.748940i
$672$		0			0
$673$	6.60813	−	37.4766i	0.254725	−	1.44462i	−0.542053	−	0.840344i	$-0.682353\pi$
$673$	6.60813	−	37.4766i	0.254725	−	1.44462i	0.796778	−	0.604272i	$-0.206536\pi$
$674$		0			0
$675$	5.43772	−	4.56279i	0.209298	−	0.175622i
$676$		0			0
$677$	−22.0131	−	38.1278i	−0.846032	−	1.46537i	−0.884722	−	0.466120i	$-0.845652\pi$
$677$	−22.0131	−	38.1278i	−0.846032	−	1.46537i	0.0386894	−	0.999251i	$-0.487682\pi$
$678$		0			0
$679$	−45.0416	−	37.7944i	−1.72854	−	1.45042i
$680$		0			0
$681$	0.736510	+	4.17696i	0.0282231	+	0.160061i
$682$		0			0
$683$	−14.4021	+	12.0848i	−0.551081	+	0.462412i	−0.875307	−	0.483568i	$-0.839341\pi$
$683$	−14.4021	+	12.0848i	−0.551081	+	0.462412i	0.324226	+	0.945980i	$0.394896\pi$
$684$		0			0
$685$	17.4080	−	6.33598i	0.665125	−	0.242086i
$686$		0			0
$687$	−1.88233	−	10.6752i	−0.0718155	−	0.407286i
$688$		0			0
$689$	8.38865	−	14.5296i	0.319582	−	0.553532i
$690$		0			0
$691$	25.3128	+	9.21310i	0.962944	+	0.350483i	0.775186	−	0.631733i	$-0.217656\pi$
$691$	25.3128	+	9.21310i	0.962944	+	0.350483i	0.187757	+	0.982215i	$0.439878\pi$
$692$		0			0
$693$	1.75808	−	3.04508i	0.0667838	−	0.115673i
$694$		0			0
$695$	8.45244	+	14.6401i	0.320619	+	0.555329i
$696$		0			0
$697$	32.9248			1.24712
$698$		0			0
$699$	−39.8069	−	33.4020i	−1.50564	−	1.26338i
$700$		0			0
$701$	−6.98332	−	2.54172i	−0.263756	−	0.0959995i	0.206757	−	0.978392i	$-0.433709\pi$
$701$	−6.98332	−	2.54172i	−0.263756	−	0.0959995i	−0.470513	+	0.882393i	$0.655931\pi$
$702$		0			0
$703$	−31.9881	−	32.0695i	−1.20646	−	1.20953i
$704$		0			0
$705$	25.4447	+	9.26110i	0.958302	+	0.348793i
$706$		0			0
$707$	−31.6251	−	26.5366i	−1.18938	−	0.998012i
$708$		0			0
$709$	0.834473			0.0313393			0.0156697	−	0.999877i	$-0.495012\pi$
$709$	0.834473			0.0313393			0.0156697	+	0.999877i	$0.495012\pi$
$710$		0			0
$711$	−0.345828	−	0.598992i	−0.0129696	−	0.0224640i
$712$		0			0
$713$	3.18781	−	5.52146i	0.119385	−	0.206780i
$714$		0			0
$715$	−17.2219	−	6.26827i	−0.644064	−	0.234420i
$716$		0			0
$717$	22.2248	−	38.4945i	0.830000	−	1.43760i
$718$		0			0
$719$	0.874879	+	4.96169i	0.0326275	+	0.185040i	0.996766	−	0.0803603i	$-0.0256071\pi$
$719$	0.874879	+	4.96169i	0.0326275	+	0.185040i	−0.964138	+	0.265400i	$0.914496\pi$
$720$		0			0
$721$	−41.9239	+	15.2591i	−1.56133	+	0.568277i
$722$		0			0
$723$	12.4337	−	10.4331i	0.462415	−	0.388012i
$724$		0			0
$725$	−0.552875	−	3.13551i	−0.0205333	−	0.116450i
$726$		0			0
$727$	−14.2591	−	11.9648i	−0.528842	−	0.443751i	0.338860	−	0.940837i	$-0.389959\pi$
$727$	−14.2591	−	11.9648i	−0.528842	−	0.443751i	−0.867701	+	0.497086i	$0.834403\pi$
$728$		0			0
$729$	−11.4945	−	19.9090i	−0.425720	−	0.737369i
$730$		0			0
$731$	19.7167	−	16.5443i	0.729248	−	0.611912i
$732$		0			0
$733$	0.797139	−	4.52080i	0.0294430	−	0.166980i	−0.966541	−	0.256513i	$-0.917426\pi$
$733$	0.797139	−	4.52080i	0.0294430	−	0.166980i	0.995984	+	0.0895332i	$0.0285375\pi$
$734$		0			0
$735$	−2.91989	+	16.5595i	−0.107702	+	0.610807i
$736$		0			0
$737$	0.557142	−	0.202783i	0.0205226	−	0.00746961i
$738$		0			0
$739$	46.9098			1.72560			0.862802	−	0.505542i	$-0.168708\pi$
$739$	46.9098			1.72560			0.862802	+	0.505542i	$0.168708\pi$
$740$		0			0
$741$	47.3971			1.74118
$742$		0			0
$743$	4.69037	−	1.70716i	0.172073	−	0.0626295i	−0.254547	−	0.967060i	$-0.581926\pi$
$743$	4.69037	−	1.70716i	0.172073	−	0.0626295i	0.426620	+	0.904431i	$0.359704\pi$
$744$		0			0
$745$	3.25471	−	18.4584i	0.119243	−	0.676263i
$746$		0			0
$747$	−0.429362	+	2.43503i	−0.0157095	+	0.0890932i
$748$		0			0
$749$	41.2572	−	34.6189i	1.50751	−	1.26495i
$750$		0			0
$751$	9.41422	+	16.3059i	0.343530	+	0.595011i	0.985086	−	0.172065i	$-0.0550440\pi$
$751$	9.41422	+	16.3059i	0.343530	+	0.595011i	−0.641556	+	0.767077i	$0.721711\pi$
$752$		0			0
$753$	−9.25853	−	7.76883i	−0.337400	−	0.283112i
$754$		0			0
$755$	3.15344	+	17.8841i	0.114766	+	0.650867i
$756$		0			0
$757$	0.598778	−	0.502435i	0.0217630	−	0.0182613i	−0.631841	−	0.775098i	$-0.717701\pi$
$757$	0.598778	−	0.502435i	0.0217630	−	0.0182613i	0.653604	+	0.756837i	$0.273256\pi$
$758$		0			0
$759$	−3.11590	+	1.13409i	−0.113100	+	0.0411650i
$760$		0			0
$761$	−5.27399	−	29.9103i	−0.191182	−	1.08425i	−0.917752	−	0.397154i	$-0.869998\pi$
$761$	−5.27399	−	29.9103i	−0.191182	−	1.08425i	0.726570	−	0.687092i	$-0.241113\pi$
$762$		0			0
$763$	2.67128	−	4.62679i	0.0967067	−	0.167501i
$764$		0			0
$765$	−1.98741	−	0.723359i	−0.0718551	−	0.0261531i
$766$		0			0
$767$	−0.960433	+	1.66352i	−0.0346792	+	0.0600662i
$768$		0			0
$769$	7.98228	+	13.8257i	0.287848	+	0.498568i	0.973296	−	0.229554i	$-0.0737268\pi$
$769$	7.98228	+	13.8257i	0.287848	+	0.498568i	−0.685448	+	0.728122i	$0.740393\pi$
$770$		0			0
$771$	17.6524			0.635735
$772$		0			0
$773$	20.2985	+	17.0324i	0.730086	+	0.612615i	0.930155	−	0.367167i	$-0.119672\pi$
$773$	20.2985	+	17.0324i	0.730086	+	0.612615i	−0.200069	+	0.979782i	$0.564117\pi$
$774$		0			0
$775$	−13.6658	−	4.97394i	−0.490890	−	0.178669i
$776$		0			0
$777$	−31.5215	+	22.0120i	−1.13083	+	0.789675i
$778$		0			0
$779$	−74.3373	−	27.0566i	−2.66341	−	0.969402i
$780$		0			0
$781$	−10.8842	−	9.13291i	−0.389466	−	0.326801i
$782$		0			0
$783$	−10.4887			−0.374834
$784$		0			0
$785$	−8.25949	−	14.3059i	−0.294794	−	0.510598i
$786$		0			0
$787$	−24.1869	+	41.8930i	−0.862171	+	1.49332i	0.00765866	+	0.999971i	$0.497562\pi$
$787$	−24.1869	+	41.8930i	−0.862171	+	1.49332i	−0.869829	+	0.493353i	$0.835771\pi$
$788$		0			0
$789$	−2.74219	−	0.998076i	−0.0976246	−	0.0355324i
$790$		0			0
$791$	−8.81414	+	15.2665i	−0.313395	+	0.542816i
$792$		0			0
$793$	−4.22571	−	23.9652i	−0.150059	−	0.851029i
$794$		0			0
$795$	15.6555	−	5.69814i	0.555244	−	0.202092i
$796$		0			0
$797$	18.1488	−	15.2286i	0.642863	−	0.539426i	−0.262033	−	0.965059i	$-0.584393\pi$
$797$	18.1488	−	15.2286i	0.642863	−	0.539426i	0.904896	+	0.425633i	$0.139948\pi$
$798$		0			0
$799$	−4.22818	−	23.9792i	−0.149582	−	0.848324i
$800$		0			0
$801$	−2.69466	−	2.26109i	−0.0952112	−	0.0798917i
$802$		0			0
$803$	−14.3710	−	24.8913i	−0.507141	−	0.878395i
$804$		0			0
$805$	3.19322	−	2.67943i	0.112546	−	0.0944376i
$806$		0			0
$807$	7.36248	−	41.7547i	0.259171	−	1.46983i
$808$		0			0
$809$	0.138317	−	0.784433i	0.00486295	−	0.0275792i	−0.982280	−	0.187421i	$-0.939987\pi$
$809$	0.138317	−	0.784433i	0.00486295	−	0.0275792i	0.987143	+	0.159842i	$0.0510983\pi$
$810$		0			0
$811$	13.0191	−	4.73855i	0.457161	−	0.166393i	−0.103166	−	0.994664i	$-0.532897\pi$
$811$	13.0191	−	4.73855i	0.457161	−	0.166393i	0.560328	+	0.828271i	$0.310675\pi$
$812$		0			0
$813$	−0.336377			−0.0117973
$814$		0			0
$815$	−3.58429			−0.125552
$816$		0			0
$817$	−58.1116	+	21.1509i	−2.03307	+	0.739976i
$818$		0			0
$819$	0.754242	−	4.27752i	0.0263553	−	0.149469i
$820$		0			0
$821$	−3.79631	+	21.5300i	−0.132492	+	0.751401i	0.844081	+	0.536216i	$0.180147\pi$
$821$	−3.79631	+	21.5300i	−0.132492	+	0.751401i	−0.976573	+	0.215185i	$0.930965\pi$
$822$		0			0
$823$	−26.4467	+	22.1914i	−0.921873	+	0.773544i	−0.974341	−	0.225079i	$-0.927736\pi$
$823$	−26.4467	+	22.1914i	−0.921873	+	0.773544i	0.0524672	+	0.998623i	$0.483292\pi$
$824$		0			0
$825$	3.78176	+	6.55020i	0.131664	+	0.228049i
$826$		0			0
$827$	−3.04336	−	2.55369i	−0.105828	−	0.0888003i	0.588338	−	0.808615i	$-0.299782\pi$
$827$	−3.04336	−	2.55369i	−0.105828	−	0.0888003i	−0.694166	+	0.719815i	$0.744227\pi$
$828$		0			0
$829$	−2.91749	−	16.5459i	−0.101329	−	0.574664i	−0.992623	−	0.121239i	$-0.961313\pi$
$829$	−2.91749	−	16.5459i	−0.101329	−	0.574664i	0.891295	−	0.453425i	$-0.149798\pi$
$830$		0			0
$831$	−17.8292	+	14.9605i	−0.618488	+	0.518973i
$832$		0			0
$833$	14.2087	−	5.17155i	0.492303	−	0.179184i
$834$		0			0
$835$	2.16294	+	12.2666i	0.0748515	+	0.424504i
$836$		0			0
$837$	−23.9543	+	41.4900i	−0.827980	+	1.43410i
$838$		0			0
$839$	6.33057	+	2.30414i	0.218556	+	0.0795478i	0.448977	−	0.893543i	$-0.351788\pi$
$839$	6.33057	+	2.30414i	0.218556	+	0.0795478i	−0.230422	+	0.973091i	$0.574011\pi$
$840$		0			0
$841$	12.1477	−	21.0405i	0.418888	−	0.725535i
$842$		0			0
$843$	−15.9878	−	27.6917i	−0.550649	−	0.953752i
$844$		0			0
$845$	1.79241			0.0616609
$846$		0			0
$847$	8.20000	+	6.88062i	0.281755	+	0.236421i
$848$		0			0
$849$	−22.6334	−	8.23789i	−0.776777	−	0.282724i
$850$		0			0
$851$	3.89915	+	0.346124i	0.133661	+	0.0118650i
$852$		0			0
$853$	−40.3273	−	14.6779i	−1.38078	−	0.502563i	−0.458365	−	0.888764i	$-0.651565\pi$
$853$	−40.3273	−	14.6779i	−1.38078	−	0.502563i	−0.922415	+	0.386201i	$0.873787\pi$
$854$		0			0
$855$	3.89272	+	3.26638i	0.133128	+	0.111708i
$856$		0			0
$857$	−27.6910			−0.945906			−0.472953	−	0.881088i	$-0.656812\pi$
$857$	−27.6910			−0.945906			−0.472953	+	0.881088i	$0.656812\pi$
$858$		0			0
$859$	9.42711	+	16.3282i	0.321649	+	0.557112i	0.980828	−	0.194873i	$-0.0624296\pi$
$859$	9.42711	+	16.3282i	0.321649	+	0.557112i	−0.659179	+	0.751986i	$0.729096\pi$
$860$		0			0
$861$	−33.5731	+	58.1503i	−1.14417	+	1.98176i
$862$		0			0
$863$	28.0177	+	10.1976i	0.953734	+	0.347131i	0.771575	−	0.636138i	$-0.219469\pi$
$863$	28.0177	+	10.1976i	0.953734	+	0.347131i	0.182159	+	0.983269i	$0.441691\pi$
$864$		0			0
$865$	23.8769	−	41.3560i	0.811839	−	1.40615i
$866$		0			0
$867$	−2.35479	−	13.3547i	−0.0799730	−	0.453549i
$868$		0			0
$869$	−5.02924	+	1.83049i	−0.170605	+	0.0620952i
$870$		0			0
$871$	0.561057	−	0.470782i	0.0190107	−	0.0159519i
$872$		0			0
$873$	1.07565	+	6.10033i	0.0364053	+	0.206465i
$874$		0			0
$875$	−32.0937	−	26.9298i	−1.08496	−	0.910393i
$876$		0			0
$877$	−2.11792	−	3.66834i	−0.0715170	−	0.123871i	0.828049	−	0.560655i	$-0.189451\pi$
$877$	−2.11792	−	3.66834i	−0.0715170	−	0.123871i	−0.899566	+	0.436784i	$0.856117\pi$
$878$		0			0
$879$	9.53491	−	8.00074i	0.321605	−	0.269858i
$880$		0			0
$881$	1.14459	−	6.49127i	0.0385621	−	0.218697i	−0.959437	−	0.281923i	$-0.909028\pi$
$881$	1.14459	−	6.49127i	0.0385621	−	0.218697i	0.997999	+	0.0632261i	$0.0201389\pi$
$882$		0			0
$883$	2.14960	−	12.1910i	0.0723397	−	0.410259i	−0.927037	−	0.374969i	$-0.877653\pi$
$883$	2.14960	−	12.1910i	0.0723397	−	0.410259i	0.999377	−	0.0352901i	$-0.0112355\pi$
$884$		0			0
$885$	−1.79243	+	0.652392i	−0.0602519	+	0.0219299i
$886$		0			0
$887$	25.0422			0.840833			0.420417	−	0.907331i	$-0.361884\pi$
$887$	25.0422			0.840833			0.420417	+	0.907331i	$0.361884\pi$
$888$		0			0
$889$	−24.4540			−0.820161
$890$		0			0
$891$	26.2899	−	9.56873i	0.880744	−	0.320565i
$892$		0			0
$893$	−10.1590	+	57.6146i	−0.339958	+	1.92800i
$894$		0			0
$895$	2.65158	−	15.0379i	0.0886326	−	0.502661i
$896$		0			0
$897$	−3.13779	+	2.63292i	−0.104768	+	0.0879106i
$898$		0			0
$899$	10.7443	+	18.6096i	0.358341	+	0.620665i
$900$		0			0
$901$	−11.4765	−	9.62989i	−0.382336	−	0.320818i
$902$		0			0
$903$	9.11481	+	51.6926i	0.303322	+	1.72022i
$904$		0			0
$905$	−17.1422	+	14.3840i	−0.569826	+	0.478141i
$906$		0			0
$907$	−54.3968	+	19.7988i	−1.80622	+	0.657409i	−0.808602	+	0.588355i	$0.799776\pi$
$907$	−54.3968	+	19.7988i	−1.80622	+	0.657409i	−0.997613	+	0.0690533i	$0.978002\pi$
$908$		0			0
$909$	0.755249	+	4.28323i	0.0250500	+	0.142066i
$910$		0			0
$911$	−4.18373	+	7.24644i	−0.138613	+	0.240085i	−0.926972	−	0.375131i	$-0.877598\pi$
$911$	−4.18373	+	7.24644i	−0.138613	+	0.240085i	0.788359	+	0.615216i	$0.210931\pi$
$912$		0			0
$913$	17.9790	+	6.54382i	0.595018	+	0.216569i
$914$		0			0
$915$	12.0826	−	20.9276i	0.399437	−	0.691845i
$916$		0			0
$917$	−30.0951	−	52.1263i	−0.993828	−	1.72136i
$918$		0			0
$919$	−3.64798			−0.120336			−0.0601678	−	0.998188i	$-0.519164\pi$
$919$	−3.64798			−0.120336			−0.0601678	+	0.998188i	$0.519164\pi$
$920$		0			0
$921$	−11.5264	−	9.67181i	−0.379808	−	0.318697i
$922$		0			0
$923$	−16.4930	−	6.00296i	−0.542874	−	0.197590i
$924$		0			0
$925$	−0.766908	−	8.89596i	−0.0252158	−	0.292497i
$926$		0			0
$927$	4.41677	+	1.60757i	0.145066	+	0.0527996i
$928$		0			0
$929$	40.7198	+	34.1679i	1.33597	+	1.12101i	0.982641	+	0.185516i	$0.0593956\pi$
$929$	40.7198	+	34.1679i	1.33597	+	1.12101i	0.353331	+	0.935498i	$0.385049\pi$
$930$		0			0
$931$	−36.3301			−1.19067
$932$		0			0
$933$	−9.95157	−	17.2366i	−0.325800	−	0.564302i
$934$		0			0
$935$	−8.18273	+	14.1729i	−0.267604	+	0.463504i
$936$		0			0
$937$	−0.433752	−	0.157873i	−0.0141701	−	0.00515748i	0.334925	−	0.942245i	$-0.391289\pi$
$937$	−0.433752	−	0.157873i	−0.0141701	−	0.00515748i	−0.349095	+	0.937087i	$0.613511\pi$
$938$		0			0
$939$	7.93666	−	13.7467i	0.259003	−	0.448607i
$940$		0			0
$941$	7.83670	+	44.4441i	0.255469	+	1.44884i	0.794865	+	0.606786i	$0.207541\pi$
$941$	7.83670	+	44.4441i	0.255469	+	1.44884i	−0.539396	+	0.842052i	$0.681347\pi$
$942$		0			0
$943$	6.42429	−	2.33825i	0.209204	−	0.0761439i
$944$		0			0
$945$	−23.9949	+	20.1341i	−0.780554	+	0.654963i
$946$		0			0
$947$	0.192264	+	1.09038i	0.00624773	+	0.0354326i	0.987772	−	0.155904i	$-0.0498290\pi$
$947$	0.192264	+	1.09038i	0.00624773	+	0.0354326i	−0.981525	+	0.191336i	$0.938718\pi$
$948$		0			0
$949$	−27.1984	−	22.8222i	−0.882897	−	0.740839i
$950$		0			0
$951$	23.3134	+	40.3799i	0.755988	+	1.30941i
$952$		0			0
$953$	−3.46116	+	2.90426i	−0.112118	+	0.0940782i	−0.697123	−	0.716951i	$-0.745537\pi$
$953$	−3.46116	+	2.90426i	−0.112118	+	0.0940782i	0.585005	+	0.811030i	$0.301092\pi$
$954$		0			0
$955$	0.0870451	−	0.493657i	0.00281671	−	0.0159744i
$956$		0			0
$957$	1.94067	−	11.0061i	0.0627329	−	0.355776i
$958$		0			0
$959$	31.9241	−	11.6194i	1.03088	−	0.375210i
$960$		0			0
$961$	67.1519			2.16619
$962$		0			0
$963$	−5.67399			−0.182842
$964$		0			0
$965$	14.0018	−	5.09624i	0.450734	−	0.164054i
$966$		0			0
$967$	5.99944	−	34.0245i	0.192929	−	1.09415i	−0.722409	−	0.691466i	$-0.756965\pi$
$967$	5.99944	−	34.0245i	0.192929	−	1.09415i	0.915338	−	0.402688i	$-0.131924\pi$
$968$		0			0
$969$	7.34944	−	41.6808i	0.236098	−	1.33898i
$970$		0			0
$971$	7.54292	−	6.32926i	0.242064	−	0.203116i	−0.513682	−	0.857981i	$-0.671719\pi$
$971$	7.54292	−	6.32926i	0.242064	−	0.203116i	0.755746	+	0.654865i	$0.227274\pi$
$972$		0			0
$973$	15.5007	+	26.8481i	0.496931	+	0.860709i
$974$		0			0
$975$	7.15731	+	6.00570i	0.229218	+	0.192336i
$976$		0			0
$977$	6.85364	+	38.8689i	0.219267	+	1.24353i	0.873346	+	0.487100i	$0.161945\pi$
$977$	6.85364	+	38.8689i	0.219267	+	1.24353i	−0.654079	+	0.756427i	$0.726943\pi$
$978$		0			0
$979$	−20.8512	+	17.4962i	−0.666406	+	0.559181i
$980$		0			0
$981$	−0.528904	+	0.192505i	−0.0168866	+	0.00614622i
$982$		0			0
$983$	−2.68903	−	15.2502i	−0.0857666	−	0.486407i	−0.997189	−	0.0749336i	$-0.976126\pi$
$983$	−2.68903	−	15.2502i	−0.0857666	−	0.486407i	0.911422	−	0.411473i	$-0.134986\pi$
$984$		0			0
$985$	−0.386805	+	0.669966i	−0.0123246	+	0.0213469i
$986$		0			0
$987$	46.6624	+	16.9837i	1.48528	+	0.540597i
$988$		0			0
$989$	2.67218	−	4.62834i	0.0849703	−	0.147173i
$990$		0			0
$991$	2.60235	+	4.50740i	0.0826663	+	0.143182i	0.904394	−	0.426698i	$-0.140323\pi$
$991$	2.60235	+	4.50740i	0.0826663	+	0.143182i	−0.821728	+	0.569880i	$0.806990\pi$
$992$		0			0
$993$	38.1474			1.21057
$994$		0			0
$995$	−2.92982	−	2.45841i	−0.0928814	−	0.0779367i
$996$		0			0
$997$	−35.0496	−	12.7570i	−1.11003	−	0.404018i	−0.279026	−	0.960284i	$-0.590012\pi$
$997$	−35.0496	−	12.7570i	−1.11003	−	0.404018i	−0.831005	+	0.556265i	$0.812234\pi$
$998$		0			0
$999$	−29.2995	−	2.60089i	−0.926994	−	0.0822884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bc.d.497.1		12
4.3	odd	2		74.2.f.b.53.2	yes	12
12.11	even	2		666.2.x.g.127.2		12
37.7	even	9	inner	592.2.bc.d.81.1		12
148.7	odd	18		74.2.f.b.7.2	✓	12
148.83	odd	18		2738.2.a.t.1.2		6
148.139	odd	18		2738.2.a.q.1.2		6
444.155	even	18		666.2.x.g.451.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.2	✓	12	148.7	odd	18
74.2.f.b.53.2	yes	12	4.3	odd	2
592.2.bc.d.81.1		12	37.7	even	9	inner
592.2.bc.d.497.1		12	1.1	even	1	trivial
666.2.x.g.127.2		12	12.11	even	2
666.2.x.g.451.2		12	444.155	even	18
2738.2.a.q.1.2		6	148.139	odd	18
2738.2.a.t.1.2		6	148.83	odd	18

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bc (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72328 + 0.627223i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(-0.598489 + 3.39420i) q^{7} +(0.278152 - 0.233397i) q^{9} +O(q^{10})\)	\(q+(-1.72328 + 0.627223i) q^{3} +(-0.326352 + 1.85083i) q^{5} +(-0.598489 + 3.39420i) q^{7} +(0.278152 - 0.233397i) q^{9} +(-1.40483 - 2.43324i) q^{11} +(-2.65877 - 2.23097i) q^{13} +(-0.598489 - 3.39420i) q^{15} +(-2.37417 + 1.99217i) q^{17} +(6.99748 - 2.54687i) q^{19} +(-1.09755 - 6.22454i) q^{21} +(-0.321769 + 0.557320i) q^{23} +(1.37939 + 0.502055i) q^{25} +(2.41787 - 4.18788i) q^{27} +(-1.08449 - 1.87840i) q^{29} -9.90716 q^{31} +(3.94710 + 3.31201i) q^{33} +(-6.08678 - 2.21541i) q^{35} +(-2.56368 - 5.51612i) q^{37} +(5.98112 + 2.17695i) q^{39} +(-8.13803 - 6.82862i) q^{41} -8.30465 q^{43} +(0.341204 + 0.590982i) q^{45} +(-3.92821 + 6.80387i) q^{47} +(-4.58455 - 1.66864i) q^{49} +(2.84183 - 4.92220i) q^{51} +(0.839394 + 4.76044i) q^{53} +(4.96199 - 1.80602i) q^{55} +(-10.4612 + 8.77795i) q^{57} +(-0.0961039 - 0.545032i) q^{59} +(5.37102 + 4.50682i) q^{61} +(0.625726 + 1.08379i) q^{63} +(4.99685 - 4.19285i) q^{65} +(-0.0366435 + 0.207815i) q^{67} +(0.204934 - 1.16224i) q^{69} +(4.75197 - 1.72957i) q^{71} +10.2297 q^{73} -2.69197 q^{75} +(9.09967 - 3.31201i) q^{77} +(0.330775 - 1.87592i) q^{79} +(-1.72910 + 9.80619i) q^{81} +(-5.21650 + 4.37717i) q^{83} +(-2.91235 - 5.04435i) q^{85} +(3.04706 + 2.55679i) q^{87} +(-1.68226 - 9.54055i) q^{89} +(9.16360 - 7.68917i) q^{91} +(17.0728 - 6.21400i) q^{93} +(2.43020 + 13.7823i) q^{95} +(-8.52990 + 14.7742i) q^{97} +(-0.958667 - 0.348926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} - 6 q^{5} - 6 q^{7} - 3 q^{9} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 3 q^{17} + 3 q^{19} - 33 q^{21} + 21 q^{23} - 6 q^{25} - 3 q^{27} + 6 q^{29} - 42 q^{31} + 57 q^{33} + 9 q^{35} - 3 q^{37} + 24 q^{39} - 21 q^{41} - 36 q^{43} - 6 q^{45} - 9 q^{47} - 12 q^{49} - 6 q^{53} - 36 q^{57} + 6 q^{59} - 18 q^{61} - 36 q^{63} + 3 q^{65} + 27 q^{67} - 12 q^{69} + 18 q^{71} + 54 q^{73} + 6 q^{75} + 51 q^{77} + 12 q^{79} - 36 q^{81} + 6 q^{83} + 3 q^{85} - 39 q^{87} - 15 q^{89} + 51 q^{91} + 45 q^{93} + 15 q^{95} - 42 q^{97} + 33 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 6 * q^5 - 6 * q^7 - 3 * q^9 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 3 * q^17 + 3 * q^19 - 33 * q^21 + 21 * q^23 - 6 * q^25 - 3 * q^27 + 6 * q^29 - 42 * q^31 + 57 * q^33 + 9 * q^35 - 3 * q^37 + 24 * q^39 - 21 * q^41 - 36 * q^43 - 6 * q^45 - 9 * q^47 - 12 * q^49 - 6 * q^53 - 36 * q^57 + 6 * q^59 - 18 * q^61 - 36 * q^63 + 3 * q^65 + 27 * q^67 - 12 * q^69 + 18 * q^71 + 54 * q^73 + 6 * q^75 + 51 * q^77 + 12 * q^79 - 36 * q^81 + 6 * q^83 + 3 * q^85 - 39 * q^87 - 15 * q^89 + 51 * q^91 + 45 * q^93 + 15 * q^95 - 42 * q^97 + 33 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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