LMFDB - Embedded newform 2394.2.o.l.1261.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(505,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("2394.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.o (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.2
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	2394.1261
Dual form			2394.2.o.l.505.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(0.780776 - 1.35234i) q^{10} +6.56155 q^{11} +(0.219224 - 0.379706i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(2.50000 - 3.57071i) q^{19} -1.56155 q^{20} +(-3.28078 - 5.68247i) q^{22} +(1.78078 - 3.08440i) q^{23} +(1.28078 - 2.21837i) q^{25} -0.438447 q^{26} +(0.500000 - 0.866025i) q^{28} +(-5.12311 + 8.87348i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{34} +(-0.780776 - 1.35234i) q^{35} -1.12311 q^{37} +(-4.34233 - 0.379706i) q^{38} +(0.780776 + 1.35234i) q^{40} +(-3.84233 - 6.65511i) q^{41} +(3.56155 + 6.16879i) q^{43} +(-3.28078 + 5.68247i) q^{44} -3.56155 q^{46} +(-3.56155 + 6.16879i) q^{47} +1.00000 q^{49} -2.56155 q^{50} +(0.219224 + 0.379706i) q^{52} +(4.56155 - 7.90084i) q^{53} +(5.12311 + 8.87348i) q^{55} -1.00000 q^{56} +10.2462 q^{58} +(5.50000 + 9.52628i) q^{59} +(5.21922 - 9.03996i) q^{61} +(1.00000 + 1.73205i) q^{62} +1.00000 q^{64} +0.684658 q^{65} +(1.84233 - 3.19101i) q^{67} -2.00000 q^{68} +(-0.780776 + 1.35234i) q^{70} +(2.90388 + 5.02967i) q^{71} +(-2.28078 - 3.95042i) q^{73} +(0.561553 + 0.972638i) q^{74} +(1.84233 + 3.95042i) q^{76} -6.56155 q^{77} +(1.12311 + 1.94528i) q^{79} +(0.780776 - 1.35234i) q^{80} +(-3.84233 + 6.65511i) q^{82} +1.00000 q^{83} +(-1.56155 + 2.70469i) q^{85} +(3.56155 - 6.16879i) q^{86} +6.56155 q^{88} +(7.68466 - 13.3102i) q^{89} +(-0.219224 + 0.379706i) q^{91} +(1.78078 + 3.08440i) q^{92} +7.12311 q^{94} +(6.78078 + 0.592932i) q^{95} +(-1.71922 - 2.97778i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - q^5 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - q^{5} - 4 q^{7} + 4 q^{8} - q^{10} + 18 q^{11} + 5 q^{13} + 2 q^{14} - 2 q^{16} + 4 q^{17} + 10 q^{19} + 2 q^{20} - 9 q^{22} + 3 q^{23} + q^{25} - 10 q^{26} + 2 q^{28} - 4 q^{29} - 8 q^{31} - 2 q^{32} + 4 q^{34} + q^{35} + 12 q^{37} - 5 q^{38} - q^{40} - 3 q^{41} + 6 q^{43} - 9 q^{44} - 6 q^{46} - 6 q^{47} + 4 q^{49} - 2 q^{50} + 5 q^{52} + 10 q^{53} + 4 q^{55} - 4 q^{56} + 8 q^{58} + 22 q^{59} + 25 q^{61} + 4 q^{62} + 4 q^{64} - 22 q^{65} - 5 q^{67} - 8 q^{68} + q^{70} - 9 q^{71} - 5 q^{73} - 6 q^{74} - 5 q^{76} - 18 q^{77} - 12 q^{79} - q^{80} - 3 q^{82} + 4 q^{83} + 2 q^{85} + 6 q^{86} + 18 q^{88} + 6 q^{89} - 5 q^{91} + 3 q^{92} + 12 q^{94} + 23 q^{95} - 11 q^{97} - 2 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - q^5 - 4 * q^7 + 4 * q^8 - q^10 + 18 * q^11 + 5 * q^13 + 2 * q^14 - 2 * q^16 + 4 * q^17 + 10 * q^19 + 2 * q^20 - 9 * q^22 + 3 * q^23 + q^25 - 10 * q^26 + 2 * q^28 - 4 * q^29 - 8 * q^31 - 2 * q^32 + 4 * q^34 + q^35 + 12 * q^37 - 5 * q^38 - q^40 - 3 * q^41 + 6 * q^43 - 9 * q^44 - 6 * q^46 - 6 * q^47 + 4 * q^49 - 2 * q^50 + 5 * q^52 + 10 * q^53 + 4 * q^55 - 4 * q^56 + 8 * q^58 + 22 * q^59 + 25 * q^61 + 4 * q^62 + 4 * q^64 - 22 * q^65 - 5 * q^67 - 8 * q^68 + q^70 - 9 * q^71 - 5 * q^73 - 6 * q^74 - 5 * q^76 - 18 * q^77 - 12 * q^79 - q^80 - 3 * q^82 + 4 * q^83 + 2 * q^85 + 6 * q^86 + 18 * q^88 + 6 * q^89 - 5 * q^91 + 3 * q^92 + 12 * q^94 + 23 * q^95 - 11 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.780776	+	1.35234i	0.349174	+	0.604787i	0.986103	−	0.166136i	$-0.0531289\pi$
$5$	0.780776	+	1.35234i	0.349174	+	0.604787i	−0.636929	+	0.770922i	$0.719796\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.00000			0.353553
$9$		0			0
$10$	0.780776	−	1.35234i	0.246903	−	0.427649i
$11$	6.56155			1.97838			0.989191	−	0.146631i	$-0.0468429\pi$
$11$	6.56155			1.97838			0.989191	+	0.146631i	$0.0468429\pi$
$12$		0			0
$13$	0.219224	−	0.379706i	0.0608017	−	0.105312i	−0.834022	−	0.551731i	$-0.813968\pi$
$13$	0.219224	−	0.379706i	0.0608017	−	0.105312i	0.894824	+	0.446419i	$0.147301\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	2.50000	−	3.57071i	0.573539	−	0.819178i
$19$	2.50000	−	3.57071i	0.573539	−	0.819178i
$20$	−1.56155			−0.349174
$21$		0			0
$22$	−3.28078	−	5.68247i	−0.699464	−	1.21151i
$23$	1.78078	−	3.08440i	0.371318	−	0.643141i	−0.618451	−	0.785823i	$-0.712239\pi$
$23$	1.78078	−	3.08440i	0.371318	−	0.643141i	0.989769	+	0.142683i	$0.0455728\pi$
$24$		0			0
$25$	1.28078	−	2.21837i	0.256155	−	0.443674i
$26$	−0.438447			−0.0859866
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−5.12311	+	8.87348i	−0.951337	+	1.64776i	−0.208800	+	0.977958i	$0.566956\pi$
$29$	−5.12311	+	8.87348i	−0.951337	+	1.64776i	−0.742537	+	0.669805i	$0.766378\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$	−0.780776	−	1.35234i	−0.131975	−	0.228588i
$36$		0			0
$37$	−1.12311			−0.184637			−0.0923187	−	0.995730i	$-0.529428\pi$
$37$	−1.12311			−0.184637			−0.0923187	+	0.995730i	$0.529428\pi$
$38$	−4.34233	−	0.379706i	−0.704419	−	0.0615965i
$39$		0			0
$40$	0.780776	+	1.35234i	0.123452	+	0.213824i
$41$	−3.84233	−	6.65511i	−0.600071	−	1.03935i	−0.992810	−	0.119703i	$-0.961806\pi$
$41$	−3.84233	−	6.65511i	−0.600071	−	1.03935i	0.392739	−	0.919650i	$-0.371528\pi$
$42$		0			0
$43$	3.56155	+	6.16879i	0.543132	+	0.940732i	0.998722	+	0.0505421i	$0.0160949\pi$
$43$	3.56155	+	6.16879i	0.543132	+	0.940732i	−0.455590	+	0.890190i	$0.650572\pi$
$44$	−3.28078	+	5.68247i	−0.494596	+	0.856665i
$45$		0			0
$46$	−3.56155			−0.525122
$47$	−3.56155	+	6.16879i	−0.519506	+	0.899811i	0.480237	+	0.877139i	$0.340551\pi$
$47$	−3.56155	+	6.16879i	−0.519506	+	0.899811i	−0.999743	+	0.0226718i	$0.992783\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−2.56155			−0.362258
$51$		0			0
$52$	0.219224	+	0.379706i	0.0304008	+	0.0526558i
$53$	4.56155	−	7.90084i	0.626577	−	1.08526i	−0.361656	−	0.932312i	$-0.617789\pi$
$53$	4.56155	−	7.90084i	0.626577	−	1.08526i	0.988234	−	0.152952i	$-0.0488781\pi$
$54$		0			0
$55$	5.12311	+	8.87348i	0.690799	+	1.19650i
$56$	−1.00000			−0.133631
$57$		0			0
$58$	10.2462			1.34539
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	0.962557	+	0.271078i	$0.0873801\pi$
$59$	5.50000	+	9.52628i	0.716039	+	1.24022i	−0.246518	+	0.969138i	$0.579287\pi$
$60$		0			0
$61$	5.21922	−	9.03996i	0.668253	−	1.15745i	−0.310139	−	0.950691i	$-0.600376\pi$
$61$	5.21922	−	9.03996i	0.668253	−	1.15745i	0.978392	−	0.206757i	$-0.0662910\pi$
$62$	1.00000	+	1.73205i	0.127000	+	0.219971i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.684658			0.0849214
$66$		0			0
$67$	1.84233	−	3.19101i	0.225076	−	0.389844i	−0.731266	−	0.682092i	$-0.761070\pi$
$67$	1.84233	−	3.19101i	0.225076	−	0.389844i	0.956342	+	0.292249i	$0.0944035\pi$
$68$	−2.00000			−0.242536
$69$		0			0
$70$	−0.780776	+	1.35234i	−0.0933206	+	0.161636i
$71$	2.90388	+	5.02967i	0.344627	+	0.596912i	0.985286	−	0.170914i	$-0.0546719\pi$
$71$	2.90388	+	5.02967i	0.344627	+	0.596912i	−0.640659	+	0.767826i	$0.721339\pi$
$72$		0			0
$73$	−2.28078	−	3.95042i	−0.266945	−	0.462362i	0.701127	−	0.713037i	$-0.252681\pi$
$73$	−2.28078	−	3.95042i	−0.266945	−	0.462362i	−0.968071	+	0.250675i	$0.919347\pi$
$74$	0.561553	+	0.972638i	0.0652792	+	0.113067i
$75$		0			0
$76$	1.84233	+	3.95042i	0.211330	+	0.453144i
$77$	−6.56155			−0.747758
$78$		0			0
$79$	1.12311	+	1.94528i	0.126359	+	0.218861i	0.922263	−	0.386562i	$-0.126337\pi$
$79$	1.12311	+	1.94528i	0.126359	+	0.218861i	−0.795904	+	0.605423i	$0.793004\pi$
$80$	0.780776	−	1.35234i	0.0872935	−	0.151197i
$81$		0			0
$82$	−3.84233	+	6.65511i	−0.424314	+	0.734934i
$83$	1.00000			0.109764			0.0548821	−	0.998493i	$-0.482522\pi$
$83$	1.00000			0.109764			0.0548821	+	0.998493i	$0.482522\pi$
$84$		0			0
$85$	−1.56155	+	2.70469i	−0.169374	+	0.293365i
$86$	3.56155	−	6.16879i	0.384052	−	0.665198i
$87$		0			0
$88$	6.56155			0.699464
$89$	7.68466	−	13.3102i	0.814572	−	1.41088i	−0.0950625	−	0.995471i	$-0.530305\pi$
$89$	7.68466	−	13.3102i	0.814572	−	1.41088i	0.909635	−	0.415409i	$-0.136362\pi$
$90$		0			0
$91$	−0.219224	+	0.379706i	−0.0229809	+	0.0398040i
$92$	1.78078	+	3.08440i	0.185659	+	0.321570i
$93$		0			0
$94$	7.12311			0.734692
$95$	6.78078	+	0.592932i	0.695693	+	0.0608335i
$96$		0			0
$97$	−1.71922	−	2.97778i	−0.174561	−	0.302348i	0.765448	−	0.643497i	$-0.222517\pi$
$97$	−1.71922	−	2.97778i	−0.174561	−	0.302348i	−0.940009	+	0.341149i	$0.889184\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$		0			0
$100$	1.28078	+	2.21837i	0.128078	+	0.221837i
$101$	−6.68466	+	11.5782i	−0.665148	+	1.15207i	0.314097	+	0.949391i	$0.398298\pi$
$101$	−6.68466	+	11.5782i	−0.665148	+	1.15207i	−0.979245	+	0.202680i	$0.935035\pi$
$102$		0			0
$103$	−2.87689			−0.283469			−0.141734	−	0.989905i	$-0.545268\pi$
$103$	−2.87689			−0.283469			−0.141734	+	0.989905i	$0.545268\pi$
$104$	0.219224	−	0.379706i	0.0214966	−	0.0372333i
$105$		0			0
$106$	−9.12311			−0.886114
$107$	3.12311			0.301922			0.150961	−	0.988540i	$-0.451763\pi$
$107$	3.12311			0.301922			0.150961	+	0.988540i	$0.451763\pi$
$108$		0			0
$109$	3.12311	+	5.40938i	0.299139	+	0.518124i	0.975939	−	0.218043i	$-0.0699672\pi$
$109$	3.12311	+	5.40938i	0.299139	+	0.518124i	−0.676800	+	0.736167i	$0.736634\pi$
$110$	5.12311	−	8.87348i	0.488469	−	0.846053i
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	17.0000			1.59923			0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000			1.59923			0.799613	+	0.600516i	$0.205038\pi$
$114$		0			0
$115$	5.56155			0.518617
$116$	−5.12311	−	8.87348i	−0.475668	−	0.823882i
$117$		0			0
$118$	5.50000	−	9.52628i	0.506316	−	0.876965i
$119$	−1.00000	−	1.73205i	−0.0916698	−	0.158777i
$120$		0			0
$121$	32.0540			2.91400
$122$	−10.4384			−0.945053
$123$		0			0
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	11.8078			1.05612
$126$		0			0
$127$	−0.657671	+	1.13912i	−0.0583588	+	0.101080i	−0.893729	−	0.448608i	$-0.851920\pi$
$127$	−0.657671	+	1.13912i	−0.0583588	+	0.101080i	0.835370	+	0.549688i	$0.185253\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−0.342329	−	0.592932i	−0.0300243	−	0.0520035i
$131$	5.62311	+	9.73950i	0.491293	+	0.850944i	0.999950	−	0.0100249i	$-0.00319109\pi$
$131$	5.62311	+	9.73950i	0.491293	+	0.850944i	−0.508657	+	0.860969i	$0.669858\pi$
$132$		0			0
$133$	−2.50000	+	3.57071i	−0.216777	+	0.309620i
$134$	−3.68466			−0.318306
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−4.18466	+	7.24804i	−0.357519	+	0.619242i	−0.987546	−	0.157332i	$-0.949711\pi$
$137$	−4.18466	+	7.24804i	−0.357519	+	0.619242i	0.630026	+	0.776574i	$0.283044\pi$
$138$		0			0
$139$	7.28078	−	12.6107i	0.617547	−	1.06962i	−0.372384	−	0.928079i	$-0.621460\pi$
$139$	7.28078	−	12.6107i	0.617547	−	1.06962i	0.989932	−	0.141545i	$-0.0452070\pi$
$140$	1.56155			0.131975
$141$		0			0
$142$	2.90388	−	5.02967i	0.243688	−	0.422081i
$143$	1.43845	−	2.49146i	0.120289	−	0.208347i
$144$		0			0
$145$	−16.0000			−1.32873
$146$	−2.28078	+	3.95042i	−0.188758	+	0.326939i
$147$		0			0
$148$	0.561553	−	0.972638i	0.0461594	−	0.0799504i
$149$	7.68466	+	13.3102i	0.629552	+	1.09042i	0.987642	+	0.156729i	$0.0500948\pi$
$149$	7.68466	+	13.3102i	0.629552	+	1.09042i	−0.358090	+	0.933687i	$0.616572\pi$
$150$		0			0
$151$	−3.56155			−0.289835			−0.144918	−	0.989444i	$-0.546292\pi$
$151$	−3.56155			−0.289835			−0.144918	+	0.989444i	$0.546292\pi$
$152$	2.50000	−	3.57071i	0.202777	−	0.289623i
$153$		0			0
$154$	3.28078	+	5.68247i	0.264372	+	0.457907i
$155$	−1.56155	−	2.70469i	−0.125427	−	0.217246i
$156$		0			0
$157$	3.65767	+	6.33527i	0.291914	+	0.505610i	0.974262	−	0.225417i	$-0.0723746\pi$
$157$	3.65767	+	6.33527i	0.291914	+	0.505610i	−0.682348	+	0.731027i	$0.739041\pi$
$158$	1.12311	−	1.94528i	0.0893495	−	0.154758i
$159$		0			0
$160$	−1.56155			−0.123452
$161$	−1.78078	+	3.08440i	−0.140345	+	0.243084i
$162$		0			0
$163$	−6.31534			−0.494656			−0.247328	−	0.968932i	$-0.579552\pi$
$163$	−6.31534			−0.494656			−0.247328	+	0.968932i	$0.579552\pi$
$164$	7.68466			0.600071
$165$		0			0
$166$	−0.500000	−	0.866025i	−0.0388075	−	0.0672166i
$167$	6.43845	−	11.1517i	0.498222	−	0.862946i	−0.501776	−	0.864998i	$-0.667320\pi$
$167$	6.43845	−	11.1517i	0.498222	−	0.862946i	0.999998	+	0.00205184i	$0.000653122\pi$
$168$		0			0
$169$	6.40388	+	11.0918i	0.492606	+	0.853219i
$170$	3.12311			0.239531
$171$		0			0
$172$	−7.12311			−0.543132
$173$	2.65767	+	4.60322i	0.202059	+	0.349976i	0.949192	−	0.314698i	$-0.101903\pi$
$173$	2.65767	+	4.60322i	0.202059	+	0.349976i	−0.747133	+	0.664675i	$0.768570\pi$
$174$		0			0
$175$	−1.28078	+	2.21837i	−0.0968176	+	0.167693i
$176$	−3.28078	−	5.68247i	−0.247298	−	0.428332i
$177$		0			0
$178$	−15.3693			−1.15198
$179$	−19.9309			−1.48970			−0.744852	−	0.667230i	$-0.767480\pi$
$179$	−19.9309			−1.48970			−0.744852	+	0.667230i	$0.767480\pi$
$180$		0			0
$181$	−8.90388	+	15.4220i	−0.661820	+	1.14631i	0.318317	+	0.947984i	$0.396883\pi$
$181$	−8.90388	+	15.4220i	−0.661820	+	1.14631i	−0.980137	+	0.198322i	$0.936451\pi$
$182$	0.438447			0.0324999
$183$		0			0
$184$	1.78078	−	3.08440i	0.131281	−	0.227385i
$185$	−0.876894	−	1.51883i	−0.0644706	−	0.111666i
$186$		0			0
$187$	6.56155	+	11.3649i	0.479828	+	0.831087i
$188$	−3.56155	−	6.16879i	−0.259753	−	0.449905i
$189$		0			0
$190$	−2.87689	−	6.16879i	−0.208712	−	0.447531i
$191$	−0.192236			−0.0139097			−0.00695485	−	0.999976i	$-0.502214\pi$
$191$	−0.192236			−0.0139097			−0.00695485	+	0.999976i	$0.502214\pi$
$192$		0			0
$193$	−0.657671	−	1.13912i	−0.0473402	−	0.0819956i	0.841384	−	0.540437i	$-0.181741\pi$
$193$	−0.657671	−	1.13912i	−0.0473402	−	0.0819956i	−0.888725	+	0.458442i	$0.848408\pi$
$194$	−1.71922	+	2.97778i	−0.123433	+	0.213792i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	25.6155			1.82503			0.912515	−	0.409042i	$-0.134137\pi$
$197$	25.6155			1.82503			0.912515	+	0.409042i	$0.134137\pi$
$198$		0			0
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	1.28078	−	2.21837i	0.0905646	−	0.156862i
$201$		0			0
$202$	13.3693			0.940662
$203$	5.12311	−	8.87348i	0.359572	−	0.622796i
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$	1.43845	+	2.49146i	0.100221	+	0.173588i
$207$		0			0
$208$	−0.438447			−0.0304008
$209$	16.4039	−	23.4294i	1.13468	−	1.62065i
$210$		0			0
$211$	8.24621	+	14.2829i	0.567693	+	0.983272i	0.996794	+	0.0800159i	$0.0254971\pi$
$211$	8.24621	+	14.2829i	0.567693	+	0.983272i	−0.429101	+	0.903257i	$0.641170\pi$
$212$	4.56155	+	7.90084i	0.313289	+	0.542632i
$213$		0			0
$214$	−1.56155	−	2.70469i	−0.106746	−	0.184889i
$215$	−5.56155	+	9.63289i	−0.379295	+	0.656958i
$216$		0			0
$217$	2.00000			0.135769
$218$	3.12311	−	5.40938i	0.211523	−	0.366369i
$219$		0			0
$220$	−10.2462			−0.690799
$221$	0.876894			0.0589863
$222$		0			0
$223$	−11.2462	−	19.4790i	−0.753102	−	1.30441i	−0.946312	−	0.323254i	$-0.895223\pi$
$223$	−11.2462	−	19.4790i	−0.753102	−	1.30441i	0.193210	−	0.981157i	$-0.438110\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	−8.50000	−	14.7224i	−0.565412	−	0.979322i
$227$	−25.7386			−1.70833			−0.854167	−	0.520000i	$-0.825932\pi$
$227$	−25.7386			−1.70833			−0.854167	+	0.520000i	$0.825932\pi$
$228$		0			0
$229$	−3.80776			−0.251624			−0.125812	−	0.992054i	$-0.540154\pi$
$229$	−3.80776			−0.251624			−0.125812	+	0.992054i	$0.540154\pi$
$230$	−2.78078	−	4.81645i	−0.183359	−	0.317587i
$231$		0			0
$232$	−5.12311	+	8.87348i	−0.336348	+	0.582572i
$233$	−12.0616	−	20.8912i	−0.790179	−	1.36863i	−0.925856	−	0.377876i	$-0.876654\pi$
$233$	−12.0616	−	20.8912i	−0.790179	−	1.36863i	0.135677	−	0.990753i	$-0.456679\pi$
$234$		0			0
$235$	−11.1231			−0.725591
$236$	−11.0000			−0.716039
$237$		0			0
$238$	−1.00000	+	1.73205i	−0.0648204	+	0.112272i
$239$	−23.8078			−1.54000			−0.769998	−	0.638046i	$-0.779743\pi$
$239$	−23.8078			−1.54000			−0.769998	+	0.638046i	$0.779743\pi$
$240$		0			0
$241$	−1.96543	+	3.40423i	−0.126605	+	0.219286i	−0.922359	−	0.386334i	$-0.873741\pi$
$241$	−1.96543	+	3.40423i	−0.126605	+	0.219286i	0.795754	+	0.605620i	$0.207075\pi$
$242$	−16.0270	−	27.7596i	−1.03025	−	1.78445i
$243$		0			0
$244$	5.21922	+	9.03996i	0.334127	+	0.578724i
$245$	0.780776	+	1.35234i	0.0498820	+	0.0863981i
$246$		0			0
$247$	−0.807764	−	1.73205i	−0.0513968	−	0.110208i
$248$	−2.00000			−0.127000
$249$		0			0
$250$	−5.90388	−	10.2258i	−0.373394	−	0.646738i
$251$	9.18466	−	15.9083i	0.579731	−	1.00412i	−0.415779	−	0.909465i	$-0.636491\pi$
$251$	9.18466	−	15.9083i	0.579731	−	1.00412i	0.995510	−	0.0946572i	$-0.0301755\pi$
$252$		0			0
$253$	11.6847	−	20.2384i	0.734608	−	1.27238i
$254$	1.31534			0.0825319
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.28078	+	2.21837i	−0.0798926	+	0.138378i	−0.903203	−	0.429213i	$-0.858791\pi$
$257$	−1.28078	+	2.21837i	−0.0798926	+	0.138378i	0.823311	+	0.567591i	$0.192124\pi$
$258$		0			0
$259$	1.12311			0.0697864
$260$	−0.342329	+	0.592932i	−0.0212304	+	0.0367721i
$261$		0			0
$262$	5.62311	−	9.73950i	0.347397	−	0.601709i
$263$	−5.02699	−	8.70700i	−0.309977	−	0.536896i	0.668380	−	0.743820i	$-0.266988\pi$
$263$	−5.02699	−	8.70700i	−0.309977	−	0.536896i	−0.978357	+	0.206924i	$0.933655\pi$
$264$		0			0
$265$	14.2462			0.875138
$266$	4.34233	+	0.379706i	0.266245	+	0.0232813i
$267$		0			0
$268$	1.84233	+	3.19101i	0.112538	+	0.194922i
$269$	7.56155	+	13.0970i	0.461036	+	0.798538i	0.999013	−	0.0444218i	$-0.0141446\pi$
$269$	7.56155	+	13.0970i	0.461036	+	0.798538i	−0.537977	+	0.842960i	$0.680811\pi$
$270$		0			0
$271$	1.31534	+	2.27824i	0.0799013	+	0.138393i	0.903207	−	0.429205i	$-0.141206\pi$
$271$	1.31534	+	2.27824i	0.0799013	+	0.138393i	−0.823306	+	0.567598i	$0.807873\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	8.36932			0.505609
$275$	8.40388	−	14.5560i	0.506773	−	0.877757i
$276$		0			0
$277$	7.12311			0.427986			0.213993	−	0.976835i	$-0.431353\pi$
$277$	7.12311			0.427986			0.213993	+	0.976835i	$0.431353\pi$
$278$	−14.5616			−0.873344
$279$		0			0
$280$	−0.780776	−	1.35234i	−0.0466603	−	0.0808180i
$281$	−6.84233	+	11.8513i	−0.408179	+	0.706987i	−0.994686	−	0.102957i	$-0.967169\pi$
$281$	−6.84233	+	11.8513i	−0.408179	+	0.706987i	0.586507	+	0.809944i	$0.300503\pi$
$282$		0			0
$283$	1.06155	+	1.83866i	0.0631028	+	0.109297i	0.895851	−	0.444355i	$-0.146567\pi$
$283$	1.06155	+	1.83866i	0.0631028	+	0.109297i	−0.832748	+	0.553652i	$0.813234\pi$
$284$	−5.80776			−0.344627
$285$		0			0
$286$	−2.87689			−0.170114
$287$	3.84233	+	6.65511i	0.226806	+	0.392839i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	8.00000	+	13.8564i	0.469776	+	0.813676i
$291$		0			0
$292$	4.56155			0.266945
$293$	2.93087			0.171223			0.0856116	−	0.996329i	$-0.472716\pi$
$293$	2.93087			0.171223			0.0856116	+	0.996329i	$0.472716\pi$
$294$		0			0
$295$	−8.58854	+	14.8758i	−0.500044	+	0.866102i
$296$	−1.12311			−0.0652792
$297$		0			0
$298$	7.68466	−	13.3102i	0.445160	−	0.771040i
$299$	−0.780776	−	1.35234i	−0.0451535	−	0.0782081i
$300$		0			0
$301$	−3.56155	−	6.16879i	−0.205284	−	0.355563i
$302$	1.78078	+	3.08440i	0.102472	+	0.177487i
$303$		0			0
$304$	−4.34233	−	0.379706i	−0.249050	−	0.0217777i
$305$	16.3002			0.933346
$306$		0			0
$307$	1.50000	+	2.59808i	0.0856095	+	0.148280i	0.905651	−	0.424024i	$-0.139383\pi$
$307$	1.50000	+	2.59808i	0.0856095	+	0.148280i	−0.820041	+	0.572304i	$0.806050\pi$
$308$	3.28078	−	5.68247i	0.186940	−	0.323789i
$309$		0			0
$310$	−1.56155	+	2.70469i	−0.0886902	+	0.153616i
$311$	22.4924			1.27543			0.637714	−	0.770273i	$-0.279880\pi$
$311$	22.4924			1.27543			0.637714	+	0.770273i	$0.279880\pi$
$312$		0			0
$313$	16.0885	−	27.8662i	0.909378	−	1.57509i	0.0944480	−	0.995530i	$-0.469891\pi$
$313$	16.0885	−	27.8662i	0.909378	−	1.57509i	0.814930	−	0.579559i	$-0.196775\pi$
$314$	3.65767	−	6.33527i	0.206414	−	0.357520i
$315$		0			0
$316$	−2.24621			−0.126359
$317$	−7.24621	+	12.5508i	−0.406988	+	0.704923i	−0.994551	−	0.104255i	$-0.966754\pi$
$317$	−7.24621	+	12.5508i	−0.406988	+	0.704923i	0.587563	+	0.809179i	$0.300088\pi$
$318$		0			0
$319$	−33.6155	+	58.2238i	−1.88211	+	3.25991i
$320$	0.780776	+	1.35234i	0.0436467	+	0.0755984i
$321$		0			0
$322$	3.56155			0.198478
$323$	8.68466	+	0.759413i	0.483227	+	0.0422549i
$324$		0			0
$325$	−0.561553	−	0.972638i	−0.0311493	−	0.0539522i
$326$	3.15767	+	5.46925i	0.174887	+	0.302914i
$327$		0			0
$328$	−3.84233	−	6.65511i	−0.212157	−	0.367467i
$329$	3.56155	−	6.16879i	0.196355	−	0.340096i
$330$		0			0
$331$	4.80776			0.264259			0.132129	−	0.991232i	$-0.457819\pi$
$331$	4.80776			0.264259			0.132129	+	0.991232i	$0.457819\pi$
$332$	−0.500000	+	0.866025i	−0.0274411	+	0.0475293i
$333$		0			0
$334$	−12.8769			−0.704592
$335$	5.75379			0.314363
$336$		0			0
$337$	−5.30776	−	9.19332i	−0.289132	−	0.500792i	0.684471	−	0.729041i	$-0.260033\pi$
$337$	−5.30776	−	9.19332i	−0.289132	−	0.500792i	−0.973603	+	0.228249i	$0.926700\pi$
$338$	6.40388	−	11.0918i	0.348325	−	0.603317i
$339$		0			0
$340$	−1.56155	−	2.70469i	−0.0846871	−	0.146682i
$341$	−13.1231			−0.710656
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	3.56155	+	6.16879i	0.192026	+	0.332599i
$345$		0			0
$346$	2.65767	−	4.60322i	0.142877	−	0.247471i
$347$	1.15767	+	2.00514i	0.0621470	+	0.107642i	0.895425	−	0.445213i	$-0.146872\pi$
$347$	1.15767	+	2.00514i	0.0621470	+	0.107642i	−0.833278	+	0.552854i	$0.813539\pi$
$348$		0			0
$349$	5.36932			0.287413			0.143706	−	0.989620i	$-0.454098\pi$
$349$	5.36932			0.287413			0.143706	+	0.989620i	$0.454098\pi$
$350$	2.56155			0.136921
$351$		0			0
$352$	−3.28078	+	5.68247i	−0.174866	+	0.302877i
$353$	−11.6847			−0.621912			−0.310956	−	0.950424i	$-0.600649\pi$
$353$	−11.6847			−0.621912			−0.310956	+	0.950424i	$0.600649\pi$
$354$		0			0
$355$	−4.53457	+	7.85410i	−0.240670	+	0.416852i
$356$	7.68466	+	13.3102i	0.407286	+	0.705440i
$357$		0			0
$358$	9.96543	+	17.2606i	0.526690	+	0.912253i
$359$	7.68466	+	13.3102i	0.405581	+	0.702486i	0.994389	−	0.105786i	$-0.0337360\pi$
$359$	7.68466	+	13.3102i	0.405581	+	0.702486i	−0.588808	+	0.808273i	$0.700403\pi$
$360$		0			0
$361$	−6.50000	−	17.8536i	−0.342105	−	0.939662i
$362$	17.8078			0.935955
$363$		0			0
$364$	−0.219224	−	0.379706i	−0.0114904	−	0.0199020i
$365$	3.56155	−	6.16879i	0.186420	−	0.322889i
$366$		0			0
$367$	−11.6847	+	20.2384i	−0.609934	+	1.05644i	0.381317	+	0.924445i	$0.375471\pi$
$367$	−11.6847	+	20.2384i	−0.609934	+	1.05644i	−0.991251	+	0.131992i	$0.957863\pi$
$368$	−3.56155			−0.185659
$369$		0			0
$370$	−0.876894	+	1.51883i	−0.0455876	+	0.0789600i
$371$	−4.56155	+	7.90084i	−0.236824	+	0.410191i
$372$		0			0
$373$	−24.8769			−1.28808			−0.644038	−	0.764993i	$-0.722742\pi$
$373$	−24.8769			−1.28808			−0.644038	+	0.764993i	$0.722742\pi$
$374$	6.56155	−	11.3649i	0.339290	−	0.587667i
$375$		0			0
$376$	−3.56155	+	6.16879i	−0.183673	+	0.318131i
$377$	2.24621	+	3.89055i	0.115686	+	0.200374i
$378$		0			0
$379$	29.3693			1.50860			0.754300	−	0.656530i	$-0.227976\pi$
$379$	29.3693			1.50860			0.754300	+	0.656530i	$0.227976\pi$
$380$	−3.90388	+	5.57586i	−0.200265	+	0.286036i
$381$		0			0
$382$	0.0961180	+	0.166481i	0.00491782	+	0.00851792i
$383$	−16.0000	−	27.7128i	−0.817562	−	1.41606i	−0.907474	−	0.420109i	$-0.861992\pi$
$383$	−16.0000	−	27.7128i	−0.817562	−	1.41606i	0.0899119	−	0.995950i	$-0.471341\pi$
$384$		0			0
$385$	−5.12311	−	8.87348i	−0.261098	−	0.452234i
$386$	−0.657671	+	1.13912i	−0.0334746	+	0.0579796i
$387$		0			0
$388$	3.43845			0.174561
$389$	−11.3693	+	19.6922i	−0.576447	+	0.998436i	0.419435	+	0.907785i	$0.362228\pi$
$389$	−11.3693	+	19.6922i	−0.576447	+	0.998436i	−0.995883	+	0.0906508i	$0.971105\pi$
$390$		0			0
$391$	7.12311			0.360231
$392$	1.00000			0.0505076
$393$		0			0
$394$	−12.8078	−	22.1837i	−0.645246	−	1.11760i
$395$	−1.75379	+	3.03765i	−0.0882427	+	0.152841i
$396$		0			0
$397$	−6.36932	−	11.0320i	−0.319667	−	0.553679i	0.660752	−	0.750605i	$-0.270238\pi$
$397$	−6.36932	−	11.0320i	−0.319667	−	0.553679i	−0.980418	+	0.196925i	$0.936904\pi$
$398$	−10.0000			−0.501255
$399$		0			0
$400$	−2.56155			−0.128078
$401$	3.18466	+	5.51599i	0.159034	+	0.275455i	0.934521	−	0.355909i	$-0.115829\pi$
$401$	3.18466	+	5.51599i	0.159034	+	0.275455i	−0.775486	+	0.631364i	$0.782495\pi$
$402$		0			0
$403$	−0.438447	+	0.759413i	−0.0218406	+	0.0378290i
$404$	−6.68466	−	11.5782i	−0.332574	−	0.576035i
$405$		0			0
$406$	−10.2462			−0.508511
$407$	−7.36932			−0.365283
$408$		0			0
$409$	1.84233	−	3.19101i	0.0910973	−	0.157785i	−0.816876	−	0.576814i	$-0.804296\pi$
$409$	1.84233	−	3.19101i	0.0910973	−	0.157785i	0.907973	+	0.419028i	$0.137629\pi$
$410$	−12.0000			−0.592638
$411$		0			0
$412$	1.43845	−	2.49146i	0.0708672	−	0.122746i
$413$	−5.50000	−	9.52628i	−0.270637	−	0.468758i
$414$		0			0
$415$	0.780776	+	1.35234i	0.0383268	+	0.0663840i
$416$	0.219224	+	0.379706i	0.0107483	+	0.0186166i
$417$		0			0
$418$	−28.4924	−	2.49146i	−1.39361	−	0.121861i
$419$	−32.4924			−1.58736			−0.793679	−	0.608336i	$-0.791837\pi$
$419$	−32.4924			−1.58736			−0.793679	+	0.608336i	$0.791837\pi$
$420$		0			0
$421$	2.31534	+	4.01029i	0.112843	+	0.195450i	0.916915	−	0.399082i	$-0.130671\pi$
$421$	2.31534	+	4.01029i	0.112843	+	0.195450i	−0.804073	+	0.594531i	$0.797338\pi$
$422$	8.24621	−	14.2829i	0.401419	−	0.695279i
$423$		0			0
$424$	4.56155	−	7.90084i	0.221529	−	0.383699i
$425$	5.12311			0.248507
$426$		0			0
$427$	−5.21922	+	9.03996i	−0.252576	+	0.437474i
$428$	−1.56155	+	2.70469i	−0.0754805	+	0.130736i
$429$		0			0
$430$	11.1231			0.536404
$431$	−15.6847	+	27.1666i	−0.755503	+	1.30857i	0.189620	+	0.981858i	$0.439274\pi$
$431$	−15.6847	+	27.1666i	−0.755503	+	1.30857i	−0.945124	+	0.326713i	$0.894059\pi$
$432$		0			0
$433$	14.8078	−	25.6478i	0.711616	−	1.23255i	−0.252635	−	0.967562i	$-0.581297\pi$
$433$	14.8078	−	25.6478i	0.711616	−	1.23255i	0.964250	−	0.264993i	$-0.0853696\pi$
$434$	−1.00000	−	1.73205i	−0.0480015	−	0.0831411i
$435$		0			0
$436$	−6.24621			−0.299139
$437$	−6.56155	−	14.0696i	−0.313882	−	0.673042i
$438$		0			0
$439$	−14.3693	−	24.8884i	−0.685810	−	1.18786i	−0.973181	−	0.230039i	$-0.926115\pi$
$439$	−14.3693	−	24.8884i	−0.685810	−	1.18786i	0.287371	−	0.957819i	$-0.407219\pi$
$440$	5.12311	+	8.87348i	0.244234	+	0.423027i
$441$		0			0
$442$	−0.438447	−	0.759413i	−0.0208548	−	0.0361216i
$443$	−10.5270	+	18.2333i	−0.500152	+	0.866289i	0.499848	+	0.866113i	$0.333389\pi$
$443$	−10.5270	+	18.2333i	−0.500152	+	0.866289i	−1.00000		0.000175844i	$0.999944\pi$
$444$		0			0
$445$	24.0000			1.13771
$446$	−11.2462	+	19.4790i	−0.532524	+	0.922358i
$447$		0			0
$448$	−1.00000			−0.0472456
$449$	−27.7386			−1.30907			−0.654534	−	0.756033i	$-0.727135\pi$
$449$	−27.7386			−1.30907			−0.654534	+	0.756033i	$0.727135\pi$
$450$		0			0
$451$	−25.2116	−	43.6679i	−1.18717	−	2.05624i
$452$	−8.50000	+	14.7224i	−0.399806	+	0.692485i
$453$		0			0
$454$	12.8693	+	22.2903i	0.603987	+	1.04614i
$455$	−0.684658			−0.0320973
$456$		0			0
$457$	27.2462			1.27452			0.637262	−	0.770647i	$-0.280067\pi$
$457$	27.2462			1.27452			0.637262	+	0.770647i	$0.280067\pi$
$458$	1.90388	+	3.29762i	0.0889626	+	0.154088i
$459$		0			0
$460$	−2.78078	+	4.81645i	−0.129654	+	0.224568i
$461$	16.9039	+	29.2784i	0.787292	+	1.36363i	0.927620	+	0.373525i	$0.121851\pi$
$461$	16.9039	+	29.2784i	0.787292	+	1.36363i	−0.140328	+	0.990105i	$0.544816\pi$
$462$		0			0
$463$	16.4384			0.763959			0.381980	−	0.924171i	$-0.375242\pi$
$463$	16.4384			0.763959			0.381980	+	0.924171i	$0.375242\pi$
$464$	10.2462			0.475668
$465$		0			0
$466$	−12.0616	+	20.8912i	−0.558741	+	0.967767i
$467$	−12.8078			−0.592673			−0.296336	−	0.955084i	$-0.595765\pi$
$467$	−12.8078			−0.592673			−0.296336	+	0.955084i	$0.595765\pi$
$468$		0			0
$469$	−1.84233	+	3.19101i	−0.0850709	+	0.147347i
$470$	5.56155	+	9.63289i	0.256535	+	0.444332i
$471$		0			0
$472$	5.50000	+	9.52628i	0.253158	+	0.438483i
$473$	23.3693	+	40.4768i	1.07452	+	1.86113i
$474$		0			0
$475$	−4.71922	−	10.1192i	−0.216533	−	0.464301i
$476$	2.00000			0.0916698
$477$		0			0
$478$	11.9039	+	20.6181i	0.544471	+	0.943051i
$479$	−8.43845	+	14.6158i	−0.385562	+	0.667814i	−0.991847	−	0.127434i	$-0.959326\pi$
$479$	−8.43845	+	14.6158i	−0.385562	+	0.667814i	0.606285	+	0.795248i	$0.292659\pi$
$480$		0			0
$481$	−0.246211	+	0.426450i	−0.0112263	+	0.0194445i
$482$	3.93087			0.179046
$483$		0			0
$484$	−16.0270	+	27.7596i	−0.728499	+	1.26180i
$485$	2.68466	−	4.64996i	0.121904	−	0.211144i
$486$		0			0
$487$	−39.8617			−1.80631			−0.903154	−	0.429317i	$-0.858754\pi$
$487$	−39.8617			−1.80631			−0.903154	+	0.429317i	$0.858754\pi$
$488$	5.21922	−	9.03996i	0.236263	−	0.409220i
$489$		0			0
$490$	0.780776	−	1.35234i	0.0352719	−	0.0610927i
$491$	−5.36932	−	9.29993i	−0.242314	−	0.419700i	0.719059	−	0.694949i	$-0.244573\pi$
$491$	−5.36932	−	9.29993i	−0.242314	−	0.419700i	−0.961373	+	0.275249i	$0.911240\pi$
$492$		0			0
$493$	−20.4924			−0.922932
$494$	−1.09612	+	1.56557i	−0.0493167	+	0.0704383i
$495$		0			0
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	−2.90388	−	5.02967i	−0.130257	−	0.225612i
$498$		0			0
$499$	9.08854	+	15.7418i	0.406859	+	0.704700i	0.994536	−	0.104395i	$-0.0332907\pi$
$499$	9.08854	+	15.7418i	0.406859	+	0.704700i	−0.587677	+	0.809096i	$0.699957\pi$
$500$	−5.90388	+	10.2258i	−0.264030	+	0.457313i
$501$		0			0
$502$	−18.3693			−0.819863
$503$	−3.87689	+	6.71498i	−0.172862	+	0.299406i	−0.939419	−	0.342770i	$-0.888635\pi$
$503$	−3.87689	+	6.71498i	−0.172862	+	0.299406i	0.766557	+	0.642176i	$0.221968\pi$
$504$		0			0
$505$	−20.8769			−0.929010
$506$	−23.3693			−1.03889
$507$		0			0
$508$	−0.657671	−	1.13912i	−0.0291794	−	0.0505402i
$509$	8.34233	−	14.4493i	0.369767	−	0.640456i	−0.619762	−	0.784790i	$-0.712771\pi$
$509$	8.34233	−	14.4493i	0.369767	−	0.640456i	0.989529	+	0.144334i	$0.0461041\pi$
$510$		0			0
$511$	2.28078	+	3.95042i	0.100896	+	0.174756i
$512$	1.00000			0.0441942
$513$		0			0
$514$	2.56155			0.112985
$515$	−2.24621	−	3.89055i	−0.0989799	−	0.171438i
$516$		0			0
$517$	−23.3693	+	40.4768i	−1.02778	+	1.78017i
$518$	−0.561553	−	0.972638i	−0.0246732	−	0.0427353i
$519$		0			0
$520$	0.684658			0.0300243
$521$	−7.93087			−0.347458			−0.173729	−	0.984794i	$-0.555582\pi$
$521$	−7.93087			−0.347458			−0.173729	+	0.984794i	$0.555582\pi$
$522$		0			0
$523$	−9.12311	+	15.8017i	−0.398926	+	0.690959i	−0.993594	−	0.113012i	$-0.963950\pi$
$523$	−9.12311	+	15.8017i	−0.398926	+	0.690959i	0.594668	+	0.803971i	$0.297283\pi$
$524$	−11.2462			−0.491293
$525$		0			0
$526$	−5.02699	+	8.70700i	−0.219187	+	0.379643i
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$		0			0
$529$	5.15767	+	8.93335i	0.224247	+	0.388406i
$530$	−7.12311	−	12.3376i	−0.309408	−	0.535910i
$531$		0			0
$532$	−1.84233	−	3.95042i	−0.0798751	−	0.171272i
$533$	−3.36932			−0.145941
$534$		0			0
$535$	2.43845	+	4.22351i	0.105423	+	0.182598i
$536$	1.84233	−	3.19101i	0.0795765	−	0.137831i
$537$		0			0
$538$	7.56155	−	13.0970i	0.326002	−	0.564651i
$539$	6.56155			0.282626
$540$		0			0
$541$	6.87689	−	11.9111i	0.295661	−	0.512099i	−0.679478	−	0.733696i	$-0.737794\pi$
$541$	6.87689	−	11.9111i	0.295661	−	0.512099i	0.975138	+	0.221597i	$0.0711269\pi$
$542$	1.31534	−	2.27824i	0.0564988	−	0.0978587i
$543$		0			0
$544$	−2.00000			−0.0857493
$545$	−4.87689	+	8.44703i	−0.208903	+	0.361831i
$546$		0			0
$547$	−20.0540	+	34.7345i	−0.857446	+	1.48514i	0.0169110	+	0.999857i	$0.494617\pi$
$547$	−20.0540	+	34.7345i	−0.857446	+	1.48514i	−0.874357	+	0.485283i	$0.838717\pi$
$548$	−4.18466	−	7.24804i	−0.178760	−	0.309621i
$549$		0			0
$550$	−16.8078			−0.716685
$551$	18.8769	+	40.4768i	0.804183	+	1.72437i
$552$		0			0
$553$	−1.12311	−	1.94528i	−0.0477593	−	0.0827216i
$554$	−3.56155	−	6.16879i	−0.151316	−	0.262087i
$555$		0			0
$556$	7.28078	+	12.6107i	0.308774	+	0.534812i
$557$	21.5616	−	37.3457i	0.913592	−	1.58239i	0.104643	−	0.994510i	$-0.466630\pi$
$557$	21.5616	−	37.3457i	0.913592	−	1.58239i	0.808949	−	0.587878i	$-0.200037\pi$
$558$		0			0
$559$	3.12311			0.132093
$560$	−0.780776	+	1.35234i	−0.0329938	+	0.0571470i
$561$		0			0
$562$	13.6847			0.577252
$563$	−31.0000			−1.30649			−0.653247	−	0.757145i	$-0.726594\pi$
$563$	−31.0000			−1.30649			−0.653247	+	0.757145i	$0.726594\pi$
$564$		0			0
$565$	13.2732	+	22.9899i	0.558408	+	0.967190i
$566$	1.06155	−	1.83866i	0.0446204	−	0.0772848i
$567$		0			0
$568$	2.90388	+	5.02967i	0.121844	+	0.211040i
$569$	27.5616			1.15544			0.577720	−	0.816235i	$-0.303942\pi$
$569$	27.5616			1.15544			0.577720	+	0.816235i	$0.303942\pi$
$570$		0			0
$571$	−11.3002			−0.472898			−0.236449	−	0.971644i	$-0.575984\pi$
$571$	−11.3002			−0.472898			−0.236449	+	0.971644i	$0.575984\pi$
$572$	1.43845	+	2.49146i	0.0601445	+	0.104173i
$573$		0			0
$574$	3.84233	−	6.65511i	0.160376	−	0.277779i
$575$	−4.56155	−	7.90084i	−0.190230	−	0.329488i
$576$		0			0
$577$	−39.0540			−1.62584			−0.812919	−	0.582377i	$-0.802123\pi$
$577$	−39.0540			−1.62584			−0.812919	+	0.582377i	$0.802123\pi$
$578$	−13.0000			−0.540729
$579$		0			0
$580$	8.00000	−	13.8564i	0.332182	−	0.575356i
$581$	−1.00000			−0.0414870
$582$		0			0
$583$	29.9309	−	51.8418i	1.23961	−	2.14707i
$584$	−2.28078	−	3.95042i	−0.0943792	−	0.163470i
$585$		0			0
$586$	−1.46543	−	2.53821i	−0.0605366	−	0.104852i
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$		0			0
$589$	−5.00000	+	7.14143i	−0.206021	+	0.294257i
$590$	17.1771			0.707169
$591$		0			0
$592$	0.561553	+	0.972638i	0.0230797	+	0.0399752i
$593$	8.96543	−	15.5286i	0.368166	−	0.637683i	−0.621113	−	0.783721i	$-0.713319\pi$
$593$	8.96543	−	15.5286i	0.368166	−	0.637683i	0.989279	+	0.146039i	$0.0466524\pi$
$594$		0			0
$595$	1.56155	−	2.70469i	0.0640174	−	0.110881i
$596$	−15.3693			−0.629552
$597$		0			0
$598$	−0.780776	+	1.35234i	−0.0319283	+	0.0553015i
$599$	2.65767	−	4.60322i	0.108589	−	0.188083i	−0.806610	−	0.591085i	$-0.798700\pi$
$599$	2.65767	−	4.60322i	0.108589	−	0.188083i	0.915199	+	0.403002i	$0.132033\pi$
$600$		0			0
$601$	−2.94602			−0.120171			−0.0600854	−	0.998193i	$-0.519137\pi$
$601$	−2.94602			−0.120171			−0.0600854	+	0.998193i	$0.519137\pi$
$602$	−3.56155	+	6.16879i	−0.145158	+	0.251421i
$603$		0			0
$604$	1.78078	−	3.08440i	0.0724588	−	0.125502i
$605$	25.0270	+	43.3480i	1.01749	+	1.76235i
$606$		0			0
$607$	−18.7386			−0.760578			−0.380289	−	0.924868i	$-0.624175\pi$
$607$	−18.7386			−0.760578			−0.380289	+	0.924868i	$0.624175\pi$
$608$	1.84233	+	3.95042i	0.0747163	+	0.160211i
$609$		0			0
$610$	−8.15009	−	14.1164i	−0.329988	−	0.571555i
$611$	1.56155	+	2.70469i	0.0631737	+	0.109420i
$612$		0			0
$613$	1.24621	+	2.15850i	0.0503340	+	0.0871810i	0.890095	−	0.455776i	$-0.150638\pi$
$613$	1.24621	+	2.15850i	0.0503340	+	0.0871810i	−0.839761	+	0.542957i	$0.817305\pi$
$614$	1.50000	−	2.59808i	0.0605351	−	0.104850i
$615$		0			0
$616$	−6.56155			−0.264372
$617$	−19.1847	+	33.2288i	−0.772345	+	1.33774i	0.163929	+	0.986472i	$0.447583\pi$
$617$	−19.1847	+	33.2288i	−0.772345	+	1.33774i	−0.936275	+	0.351269i	$0.885750\pi$
$618$		0			0
$619$	0.192236			0.00772661			0.00386331	−	0.999993i	$-0.498770\pi$
$619$	0.192236			0.00772661			0.00386331	+	0.999993i	$0.498770\pi$
$620$	3.12311			0.125427
$621$		0			0
$622$	−11.2462	−	19.4790i	−0.450932	−	0.781037i
$623$	−7.68466	+	13.3102i	−0.307879	+	0.533263i
$624$		0			0
$625$	2.81534	+	4.87631i	0.112614	+	0.195053i
$626$	−32.1771			−1.28605
$627$		0			0
$628$	−7.31534			−0.291914
$629$	−1.12311	−	1.94528i	−0.0447812	−	0.0775632i
$630$		0			0
$631$	18.2462	−	31.6034i	0.726370	−	1.25811i	−0.232037	−	0.972707i	$-0.574539\pi$
$631$	18.2462	−	31.6034i	0.726370	−	1.25811i	0.958408	−	0.285403i	$-0.0921275\pi$
$632$	1.12311	+	1.94528i	0.0446747	+	0.0773789i
$633$		0			0
$634$	14.4924			0.575568
$635$	−2.05398			−0.0815095
$636$		0			0
$637$	0.219224	−	0.379706i	0.00868596	−	0.0150445i
$638$	67.2311			2.66170
$639$		0			0
$640$	0.780776	−	1.35234i	0.0308629	−	0.0534561i
$641$	−17.0616	−	29.5515i	−0.673891	−	1.16721i	−0.976792	−	0.214191i	$-0.931288\pi$
$641$	−17.0616	−	29.5515i	−0.673891	−	1.16721i	0.302901	−	0.953022i	$-0.402045\pi$
$642$		0			0
$643$	0.376894	+	0.652800i	0.0148633	+	0.0257439i	0.873361	−	0.487073i	$-0.161935\pi$
$643$	0.376894	+	0.652800i	0.0148633	+	0.0257439i	−0.858498	+	0.512817i	$0.828602\pi$
$644$	−1.78078	−	3.08440i	−0.0701724	−	0.121542i
$645$		0			0
$646$	−3.68466	−	7.90084i	−0.144971	−	0.310854i
$647$	−36.7386			−1.44434			−0.722172	−	0.691713i	$-0.756856\pi$
$647$	−36.7386			−1.44434			−0.722172	+	0.691713i	$0.756856\pi$
$648$		0			0
$649$	36.0885	+	62.5072i	1.41660	+	2.45362i
$650$	−0.561553	+	0.972638i	−0.0220259	+	0.0381500i
$651$		0			0
$652$	3.15767	−	5.46925i	0.123664	−	0.214192i
$653$	10.6307			0.416011			0.208005	−	0.978128i	$-0.433303\pi$
$653$	10.6307			0.416011			0.208005	+	0.978128i	$0.433303\pi$
$654$		0			0
$655$	−8.78078	+	15.2088i	−0.343093	+	0.594255i
$656$	−3.84233	+	6.65511i	−0.150018	+	0.259838i
$657$		0			0
$658$	−7.12311			−0.277688
$659$	4.43845	−	7.68762i	0.172897	−	0.299467i	−0.766534	−	0.642203i	$-0.778020\pi$
$659$	4.43845	−	7.68762i	0.172897	−	0.299467i	0.939432	+	0.342736i	$0.111354\pi$
$660$		0			0
$661$	−15.9039	+	27.5463i	−0.618589	+	1.07143i	0.371154	+	0.928571i	$0.378962\pi$
$661$	−15.9039	+	27.5463i	−0.618589	+	1.07143i	−0.989743	+	0.142857i	$0.954371\pi$
$662$	−2.40388	−	4.16365i	−0.0934295	−	0.161825i
$663$		0			0
$664$	1.00000			0.0388075
$665$	−6.78078	−	0.592932i	−0.262947	−	0.0229929i
$666$		0			0
$667$	18.2462	+	31.6034i	0.706496	+	1.22369i
$668$	6.43845	+	11.1517i	0.249111	+	0.431473i
$669$		0			0
$670$	−2.87689	−	4.98293i	−0.111144	−	0.192507i
$671$	34.2462	−	59.3162i	1.32206	−	2.28988i
$672$		0			0
$673$	6.68466			0.257675			0.128837	−	0.991666i	$-0.458875\pi$
$673$	6.68466			0.257675			0.128837	+	0.991666i	$0.458875\pi$
$674$	−5.30776	+	9.19332i	−0.204447	+	0.354113i
$675$		0			0
$676$	−12.8078			−0.492606
$677$	−1.50758			−0.0579409			−0.0289705	−	0.999580i	$-0.509223\pi$
$677$	−1.50758			−0.0579409			−0.0289705	+	0.999580i	$0.509223\pi$
$678$		0			0
$679$	1.71922	+	2.97778i	0.0659777	+	0.114277i
$680$	−1.56155	+	2.70469i	−0.0598828	+	0.103720i
$681$		0			0
$682$	6.56155	+	11.3649i	0.251255	+	0.435186i
$683$	0.492423			0.0188420			0.00942101	−	0.999956i	$-0.497001\pi$
$683$	0.492423			0.0188420			0.00942101	+	0.999956i	$0.497001\pi$
$684$		0			0
$685$	−13.0691			−0.499346
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	3.56155	−	6.16879i	0.135783	−	0.235183i
$689$	−2.00000	−	3.46410i	−0.0761939	−	0.131972i
$690$		0			0
$691$	−14.0540			−0.534638			−0.267319	−	0.963608i	$-0.586138\pi$
$691$	−14.0540			−0.534638			−0.267319	+	0.963608i	$0.586138\pi$
$692$	−5.31534			−0.202059
$693$		0			0
$694$	1.15767	−	2.00514i	0.0439446	−	0.0761142i
$695$	22.7386			0.862526
$696$		0			0
$697$	7.68466	−	13.3102i	0.291077	−	0.504160i
$698$	−2.68466	−	4.64996i	−0.101616	−	0.176004i
$699$		0			0
$700$	−1.28078	−	2.21837i	−0.0484088	−	0.0838465i
$701$	−12.4384	−	21.5440i	−0.469794	−	0.813706i	0.529610	−	0.848241i	$-0.322338\pi$
$701$	−12.4384	−	21.5440i	−0.469794	−	0.813706i	−0.999403	+	0.0345349i	$0.989005\pi$
$702$		0			0
$703$	−2.80776	+	4.01029i	−0.105897	+	0.151251i
$704$	6.56155			0.247298
$705$		0			0
$706$	5.84233	+	10.1192i	0.219879	+	0.380842i
$707$	6.68466	−	11.5782i	0.251402	−	0.435442i
$708$		0			0
$709$	7.68466	−	13.3102i	0.288603	−	0.499876i	−0.684873	−	0.728662i	$-0.740142\pi$
$709$	7.68466	−	13.3102i	0.288603	−	0.499876i	0.973477	+	0.228786i	$0.0734758\pi$
$710$	9.06913			0.340358
$711$		0			0
$712$	7.68466	−	13.3102i	0.287995	−	0.498822i
$713$	−3.56155	+	6.16879i	−0.133381	+	0.231023i
$714$		0			0
$715$	4.49242			0.168007
$716$	9.96543	−	17.2606i	0.372426	−	0.645060i
$717$		0			0
$718$	7.68466	−	13.3102i	0.286789	−	0.496733i
$719$	6.12311	+	10.6055i	0.228353	+	0.395520i	0.957320	−	0.289029i	$-0.0933325\pi$
$719$	6.12311	+	10.6055i	0.228353	+	0.395520i	−0.728967	+	0.684549i	$0.759999\pi$
$720$		0			0
$721$	2.87689			0.107141
$722$	−12.2116	+	14.5560i	−0.454470	+	0.541716i
$723$		0			0
$724$	−8.90388	−	15.4220i	−0.330910	−	0.573153i
$725$	13.1231	+	22.7299i	0.487380	+	0.844167i
$726$		0			0
$727$	24.4924	+	42.4221i	0.908374	+	1.57335i	0.816323	+	0.577595i	$0.196009\pi$
$727$	24.4924	+	42.4221i	0.908374	+	1.57335i	0.0920502	+	0.995754i	$0.470658\pi$
$728$	−0.219224	+	0.379706i	−0.00812497	+	0.0140729i
$729$		0			0
$730$	−7.12311			−0.263638
$731$	−7.12311	+	12.3376i	−0.263458	+	0.456322i
$732$		0			0
$733$	−28.0540			−1.03620			−0.518099	−	0.855321i	$-0.673360\pi$
$733$	−28.0540			−1.03620			−0.518099	+	0.855321i	$0.673360\pi$
$734$	23.3693			0.862577
$735$		0			0
$736$	1.78078	+	3.08440i	0.0656403	+	0.113692i
$737$	12.0885	−	20.9380i	0.445287	−	0.771260i
$738$		0			0
$739$	−9.21165	−	15.9550i	−0.338856	−	0.586916i	0.645362	−	0.763877i	$-0.276707\pi$
$739$	−9.21165	−	15.9550i	−0.338856	−	0.586916i	−0.984218	+	0.176961i	$0.943373\pi$
$740$	1.75379			0.0644706
$741$		0			0
$742$	9.12311			0.334920
$743$	−4.71165	−	8.16081i	−0.172854	−	0.299391i	0.766563	−	0.642169i	$-0.221965\pi$
$743$	−4.71165	−	8.16081i	−0.172854	−	0.299391i	−0.939416	+	0.342778i	$0.888632\pi$
$744$		0			0
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$	12.4384	+	21.5440i	0.455404	+	0.788783i
$747$		0			0
$748$	−13.1231			−0.479828
$749$	−3.12311			−0.114116
$750$		0			0
$751$	20.8078	−	36.0401i	0.759286	−	1.31512i	−0.183929	−	0.982940i	$-0.558882\pi$
$751$	20.8078	−	36.0401i	0.759286	−	1.31512i	0.943215	−	0.332183i	$-0.107785\pi$
$752$	7.12311			0.259753
$753$		0			0
$754$	2.24621	−	3.89055i	0.0818022	−	0.141686i
$755$	−2.78078	−	4.81645i	−0.101203	−	0.175288i
$756$		0			0
$757$	−14.6155	−	25.3148i	−0.531210	−	0.920083i	−0.999337	−	0.0364217i	$-0.988404\pi$
$757$	−14.6155	−	25.3148i	−0.531210	−	0.920083i	0.468126	−	0.883662i	$-0.344929\pi$
$758$	−14.6847	−	25.4346i	−0.533371	−	0.923825i
$759$		0			0
$760$	6.78078	+	0.592932i	0.245965	+	0.0215079i
$761$	25.4384			0.922143			0.461071	−	0.887363i	$-0.347465\pi$
$761$	25.4384			0.922143			0.461071	+	0.887363i	$0.347465\pi$
$762$		0			0
$763$	−3.12311	−	5.40938i	−0.113064	−	0.195833i
$764$	0.0961180	−	0.166481i	0.00347743	−	0.00602308i
$765$		0			0
$766$	−16.0000	+	27.7128i	−0.578103	+	1.00130i
$767$	4.82292			0.174146
$768$		0			0
$769$	−7.24621	+	12.5508i	−0.261305	+	0.452594i	−0.966589	−	0.256331i	$-0.917486\pi$
$769$	−7.24621	+	12.5508i	−0.261305	+	0.452594i	0.705284	+	0.708925i	$0.250820\pi$
$770$	−5.12311	+	8.87348i	−0.184624	+	0.319778i
$771$		0			0
$772$	1.31534			0.0473402
$773$	24.3963	−	42.2556i	0.877474	−	1.51983i	0.0233704	−	0.999727i	$-0.492560\pi$
$773$	24.3963	−	42.2556i	0.877474	−	1.51983i	0.854104	−	0.520103i	$-0.174106\pi$
$774$		0			0
$775$	−2.56155	+	4.43674i	−0.0920137	+	0.159372i
$776$	−1.71922	−	2.97778i	−0.0617165	−	0.106896i
$777$		0			0
$778$	22.7386			0.815220
$779$	−33.3693	−	2.91791i	−1.19558	−	0.104545i
$780$		0			0
$781$	19.0540	+	33.0025i	0.681805	+	1.18092i
$782$	−3.56155	−	6.16879i	−0.127361	−	0.220595i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−5.71165	+	9.89286i	−0.203857	+	0.353091i
$786$		0			0
$787$	−36.3693			−1.29643			−0.648213	−	0.761459i	$-0.724483\pi$
$787$	−36.3693			−1.29643			−0.648213	+	0.761459i	$0.724483\pi$
$788$	−12.8078	+	22.1837i	−0.456258	+	0.790262i
$789$		0			0
$790$	3.50758			0.124794
$791$	−17.0000			−0.604450
$792$		0			0
$793$	−2.28835	−	3.96355i	−0.0812618	−	0.140750i
$794$	−6.36932	+	11.0320i	−0.226039	+	0.391510i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−52.0540			−1.84385			−0.921923	−	0.387373i	$-0.873383\pi$
$797$	−52.0540			−1.84385			−0.921923	+	0.387373i	$0.873383\pi$
$798$		0			0
$799$	−14.2462			−0.503995
$800$	1.28078	+	2.21837i	0.0452823	+	0.0784312i
$801$		0			0
$802$	3.18466	−	5.51599i	0.112454	−	0.194776i
$803$	−14.9654	−	25.9209i	−0.528119	−	0.914728i
$804$		0			0
$805$	−5.56155			−0.196019
$806$	0.876894			0.0308873
$807$		0			0
$808$	−6.68466	+	11.5782i	−0.235165	+	0.407319i
$809$	35.9848			1.26516			0.632580	−	0.774495i	$-0.281996\pi$
$809$	35.9848			1.26516			0.632580	+	0.774495i	$0.281996\pi$
$810$		0			0
$811$	−13.3693	+	23.1563i	−0.469460	+	0.813129i	−0.999390	−	0.0349123i	$-0.988885\pi$
$811$	−13.3693	+	23.1563i	−0.469460	+	0.813129i	0.529930	+	0.848041i	$0.322218\pi$
$812$	5.12311	+	8.87348i	0.179786	+	0.311398i
$813$		0			0
$814$	3.68466	+	6.38202i	0.129147	+	0.223690i
$815$	−4.93087	−	8.54052i	−0.172721	−	0.299161i
$816$		0			0
$817$	30.9309	+	2.70469i	1.08213	+	0.0946251i
$818$	−3.68466			−0.128831
$819$		0			0
$820$	6.00000	+	10.3923i	0.209529	+	0.362915i
$821$	14.5616	−	25.2213i	0.508202	−	0.880231i	−0.491753	−	0.870735i	$-0.663644\pi$
$821$	14.5616	−	25.2213i	0.508202	−	0.880231i	0.999955	−	0.00949654i	$-0.00302289\pi$
$822$		0			0
$823$	4.46543	−	7.73436i	0.155655	−	0.269603i	−0.777642	−	0.628707i	$-0.783584\pi$
$823$	4.46543	−	7.73436i	0.155655	−	0.269603i	0.933297	+	0.359104i	$0.116918\pi$
$824$	−2.87689			−0.100221
$825$		0			0
$826$	−5.50000	+	9.52628i	−0.191369	+	0.331462i
$827$	−5.84233	+	10.1192i	−0.203158	+	0.351879i	−0.949544	−	0.313633i	$-0.898454\pi$
$827$	−5.84233	+	10.1192i	−0.203158	+	0.351879i	0.746386	+	0.665513i	$0.231787\pi$
$828$		0			0
$829$	−38.4384			−1.33502			−0.667511	−	0.744600i	$-0.732640\pi$
$829$	−38.4384			−1.33502			−0.667511	+	0.744600i	$0.732640\pi$
$830$	0.780776	−	1.35234i	0.0271011	−	0.0469406i
$831$		0			0
$832$	0.219224	−	0.379706i	0.00760021	−	0.0131640i
$833$	1.00000	+	1.73205i	0.0346479	+	0.0600120i
$834$		0			0
$835$	20.1080			0.695864
$836$	12.0885	+	25.9209i	0.418091	+	0.896493i
$837$		0			0
$838$	16.2462	+	28.1393i	0.561216	+	0.972055i
$839$	2.43845	+	4.22351i	0.0841845	+	0.145812i	0.905043	−	0.425319i	$-0.139838\pi$
$839$	2.43845	+	4.22351i	0.0841845	+	0.145812i	−0.820859	+	0.571131i	$0.806505\pi$
$840$		0			0
$841$	−37.9924	−	65.8048i	−1.31008	−	2.26913i
$842$	2.31534	−	4.01029i	0.0797919	−	0.138204i
$843$		0			0
$844$	−16.4924			−0.567693
$845$	−10.0000	+	17.3205i	−0.344010	+	0.595844i
$846$		0			0
$847$	−32.0540			−1.10139
$848$	−9.12311			−0.313289
$849$		0			0
$850$	−2.56155	−	4.43674i	−0.0878605	−	0.152179i
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$		0			0
$853$	−16.6155	−	28.7789i	−0.568905	−	0.985372i	−0.996675	−	0.0814844i	$-0.974034\pi$
$853$	−16.6155	−	28.7789i	−0.568905	−	0.985372i	0.427770	−	0.903888i	$-0.359299\pi$
$854$	10.4384			0.357196
$855$		0			0
$856$	3.12311			0.106746
$857$	−15.4039	−	26.6803i	−0.526187	−	0.911382i	−0.999535	−	0.0305064i	$-0.990288\pi$
$857$	−15.4039	−	26.6803i	−0.526187	−	0.911382i	0.473348	−	0.880876i	$-0.343045\pi$
$858$		0			0
$859$	17.5961	−	30.4774i	0.600372	−	1.03987i	−0.392393	−	0.919798i	$-0.628353\pi$
$859$	17.5961	−	30.4774i	0.600372	−	1.03987i	0.992765	−	0.120077i	$-0.0383141\pi$
$860$	−5.56155	−	9.63289i	−0.189647	−	0.328479i
$861$		0			0
$862$	31.3693			1.06844
$863$	14.8769			0.506415			0.253208	−	0.967412i	$-0.418514\pi$
$863$	14.8769			0.506415			0.253208	+	0.967412i	$0.418514\pi$
$864$		0			0
$865$	−4.15009	+	7.18817i	−0.141107	+	0.244405i
$866$	−29.6155			−1.00638
$867$		0			0
$868$	−1.00000	+	1.73205i	−0.0339422	+	0.0587896i
$869$	7.36932	+	12.7640i	0.249987	+	0.432990i
$870$		0			0
$871$	−0.807764	−	1.39909i	−0.0273700	−	0.0474063i
$872$	3.12311	+	5.40938i	0.105762	+	0.183185i
$873$		0			0
$874$	−8.90388	+	12.7173i	−0.301178	+	0.430169i
$875$	−11.8078			−0.399175
$876$		0			0
$877$	9.36932	+	16.2281i	0.316379	+	0.547985i	0.979730	−	0.200324i	$-0.0641994\pi$
$877$	9.36932	+	16.2281i	0.316379	+	0.547985i	−0.663350	+	0.748309i	$0.730866\pi$
$878$	−14.3693	+	24.8884i	−0.484941	+	0.839942i
$879$		0			0
$880$	5.12311	−	8.87348i	0.172700	−	0.299125i
$881$	−28.5616			−0.962263			−0.481132	−	0.876648i	$-0.659774\pi$
$881$	−28.5616			−0.962263			−0.481132	+	0.876648i	$0.659774\pi$
$882$		0			0
$883$	−14.5961	+	25.2812i	−0.491198	+	0.850781i	−0.999949	−	0.0101335i	$-0.996774\pi$
$883$	−14.5961	+	25.2812i	−0.491198	+	0.850781i	0.508750	+	0.860914i	$0.330108\pi$
$884$	−0.438447	+	0.759413i	−0.0147466	+	0.0255418i
$885$		0			0
$886$	21.0540			0.707322
$887$	3.31534	−	5.74234i	0.111318	−	0.192809i	−0.804984	−	0.593297i	$-0.797826\pi$
$887$	3.31534	−	5.74234i	0.111318	−	0.192809i	0.916302	+	0.400488i	$0.131159\pi$
$888$		0			0
$889$	0.657671	−	1.13912i	0.0220576	−	0.0382048i
$890$	−12.0000	−	20.7846i	−0.402241	−	0.696702i
$891$		0			0
$892$	22.4924			0.753102
$893$	13.1231	+	28.1393i	0.439148	+	0.941645i
$894$		0			0
$895$	−15.5616	−	26.9534i	−0.520165	−	0.900953i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$		0			0
$898$	13.8693	+	24.0224i	0.462825	+	0.801637i
$899$	10.2462	−	17.7470i	0.341730	−	0.591894i
$900$		0			0
$901$	18.2462			0.607869
$902$	−25.2116	+	43.6679i	−0.839456	+	1.45398i
$903$		0			0
$904$	17.0000			0.565412
$905$	−27.8078			−0.924361
$906$		0			0
$907$	−2.34991	−	4.07016i	−0.0780274	−	0.135147i	0.824371	−	0.566049i	$-0.191529\pi$
$907$	−2.34991	−	4.07016i	−0.0780274	−	0.135147i	−0.902399	+	0.430902i	$0.858195\pi$
$908$	12.8693	−	22.2903i	0.427083	−	0.739730i
$909$		0			0
$910$	0.342329	+	0.592932i	0.0113481	+	0.0196555i
$911$	−17.3153			−0.573683			−0.286841	−	0.957978i	$-0.592605\pi$
$911$	−17.3153			−0.573683			−0.286841	+	0.957978i	$0.592605\pi$
$912$		0			0
$913$	6.56155			0.217156
$914$	−13.6231	−	23.5959i	−0.450612	−	0.780483i
$915$		0			0
$916$	1.90388	−	3.29762i	0.0629060	−	0.108956i
$917$	−5.62311	−	9.73950i	−0.185691	−	0.321627i
$918$		0			0
$919$	4.93087			0.162654			0.0813272	−	0.996687i	$-0.474084\pi$
$919$	4.93087			0.162654			0.0813272	+	0.996687i	$0.474084\pi$
$920$	5.56155			0.183359
$921$		0			0
$922$	16.9039	−	29.2784i	0.556700	−	0.964232i
$923$	2.54640			0.0838157
$924$		0			0
$925$	−1.43845	+	2.49146i	−0.0472959	+	0.0819188i
$926$	−8.21922	−	14.2361i	−0.270100	−	0.467828i
$927$		0			0
$928$	−5.12311	−	8.87348i	−0.168174	−	0.291286i
$929$	−22.7192	−	39.3508i	−0.745394	−	1.29106i	−0.950011	−	0.312217i	$-0.898928\pi$
$929$	−22.7192	−	39.3508i	−0.745394	−	1.29106i	0.204617	−	0.978842i	$-0.434405\pi$
$930$		0			0
$931$	2.50000	−	3.57071i	0.0819342	−	0.117025i
$932$	24.1231			0.790179
$933$		0			0
$934$	6.40388	+	11.0918i	0.209541	+	0.362936i
$935$	−10.2462	+	17.7470i	−0.335087	+	0.580388i
$936$		0			0
$937$	−5.65009	+	9.78625i	−0.184581	+	0.319703i	−0.943435	−	0.331557i	$-0.892426\pi$
$937$	−5.65009	+	9.78625i	−0.184581	+	0.319703i	0.758855	+	0.651260i	$0.225759\pi$
$938$	3.68466			0.120308
$939$		0			0
$940$	5.56155	−	9.63289i	0.181398	−	0.314190i
$941$	21.5885	−	37.3924i	0.703766	−	1.21896i	−0.263369	−	0.964695i	$-0.584834\pi$
$941$	21.5885	−	37.3924i	0.703766	−	1.21896i	0.967135	−	0.254264i	$-0.0818331\pi$
$942$		0			0
$943$	−27.3693			−0.891268
$944$	5.50000	−	9.52628i	0.179010	−	0.310054i
$945$		0			0
$946$	23.3693	−	40.4768i	0.759802	−	1.31602i
$947$	3.56155	+	6.16879i	0.115735	+	0.200459i	0.918073	−	0.396411i	$-0.129744\pi$
$947$	3.56155	+	6.16879i	0.115735	+	0.200459i	−0.802338	+	0.596869i	$0.796411\pi$
$948$		0			0
$949$	−2.00000			−0.0649227
$950$	−6.40388	+	9.14657i	−0.207769	+	0.296754i
$951$		0			0
$952$	−1.00000	−	1.73205i	−0.0324102	−	0.0561361i
$953$	−22.2808	−	38.5914i	−0.721745	−	1.25010i	−0.960300	−	0.278970i	$-0.910007\pi$
$953$	−22.2808	−	38.5914i	−0.721745	−	1.25010i	0.238555	−	0.971129i	$-0.423326\pi$
$954$		0			0
$955$	−0.150093	−	0.259969i	−0.00485690	−	0.00841241i
$956$	11.9039	−	20.6181i	0.384999	−	0.666838i
$957$		0			0
$958$	16.8769			0.545268
$959$	4.18466	−	7.24804i	0.135130	−	0.234051i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	0.492423			0.0158763
$963$		0			0
$964$	−1.96543	−	3.40423i	−0.0633024	−	0.109643i
$965$	1.02699	−	1.77879i	0.0330599	−	0.0572614i
$966$		0			0
$967$	−7.34233	−	12.7173i	−0.236113	−	0.408960i	0.723482	−	0.690343i	$-0.242540\pi$
$967$	−7.34233	−	12.7173i	−0.236113	−	0.408960i	−0.959596	+	0.281383i	$0.909207\pi$
$968$	32.0540			1.03025
$969$		0			0
$970$	−5.36932			−0.172398
$971$	2.25379	+	3.90368i	0.0723275	+	0.125275i	0.899921	−	0.436053i	$-0.143624\pi$
$971$	2.25379	+	3.90368i	0.0723275	+	0.125275i	−0.827593	+	0.561328i	$0.810291\pi$
$972$		0			0
$973$	−7.28078	+	12.6107i	−0.233411	+	0.404280i
$974$	19.9309	+	34.5213i	0.638626	+	1.10613i
$975$		0			0
$976$	−10.4384			−0.334127
$977$	30.6155			0.979478			0.489739	−	0.871869i	$-0.337092\pi$
$977$	30.6155			0.979478			0.489739	+	0.871869i	$0.337092\pi$
$978$		0			0
$979$	50.4233	−	87.3357i	1.61154	−	2.79126i
$980$	−1.56155			−0.0498820
$981$		0			0
$982$	−5.36932	+	9.29993i	−0.171342	+	0.296773i
$983$	11.3153	+	19.5987i	0.360903	+	0.625103i	0.988110	−	0.153750i	$-0.0491351\pi$
$983$	11.3153	+	19.5987i	0.360903	+	0.625103i	−0.627206	+	0.778853i	$0.715802\pi$
$984$		0			0
$985$	20.0000	+	34.6410i	0.637253	+	1.10375i
$986$	10.2462	+	17.7470i	0.326306	+	0.565178i
$987$		0			0
$988$	1.90388	+	0.166481i	0.0605706	+	0.00529647i
$989$	25.3693			0.806697
$990$		0			0
$991$	8.15009	+	14.1164i	0.258896	+	0.448421i	0.965947	−	0.258742i	$-0.0833079\pi$
$991$	8.15009	+	14.1164i	0.258896	+	0.448421i	−0.707050	+	0.707163i	$0.749975\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$		0			0
$994$	−2.90388	+	5.02967i	−0.0921055	+	0.159531i
$995$	15.6155			0.495046
$996$		0			0
$997$	−8.53457	+	14.7823i	−0.270292	+	0.468160i	−0.968937	−	0.247309i	$-0.920454\pi$
$997$	−8.53457	+	14.7823i	−0.270292	+	0.468160i	0.698644	+	0.715469i	$0.253787\pi$
$998$	9.08854	−	15.7418i	0.287693	−	0.498298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.o.l.1261.2		4
3.2	odd	2		266.2.f.b.197.1	✓	4
19.11	even	3	inner	2394.2.o.l.505.2		4
57.11	odd	6		266.2.f.b.239.1	yes	4
57.26	odd	6		5054.2.a.h.1.2		2
57.50	even	6		5054.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.b.197.1	✓	4	3.2	odd	2
266.2.f.b.239.1	yes	4	57.11	odd	6
2394.2.o.l.505.2		4	19.11	even	3	inner
2394.2.o.l.1261.2		4	1.1	even	1	trivial
5054.2.a.h.1.2		2	57.26	odd	6
5054.2.a.m.1.1		2	57.50	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.780776 + 1.35234i) q^{5} -1.00000 q^{7} +1.00000 q^{8} +(0.780776 - 1.35234i) q^{10} +6.56155 q^{11} +(0.219224 - 0.379706i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(2.50000 - 3.57071i) q^{19} -1.56155 q^{20} +(-3.28078 - 5.68247i) q^{22} +(1.78078 - 3.08440i) q^{23} +(1.28078 - 2.21837i) q^{25} -0.438447 q^{26} +(0.500000 - 0.866025i) q^{28} +(-5.12311 + 8.87348i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{34} +(-0.780776 - 1.35234i) q^{35} -1.12311 q^{37} +(-4.34233 - 0.379706i) q^{38} +(0.780776 + 1.35234i) q^{40} +(-3.84233 - 6.65511i) q^{41} +(3.56155 + 6.16879i) q^{43} +(-3.28078 + 5.68247i) q^{44} -3.56155 q^{46} +(-3.56155 + 6.16879i) q^{47} +1.00000 q^{49} -2.56155 q^{50} +(0.219224 + 0.379706i) q^{52} +(4.56155 - 7.90084i) q^{53} +(5.12311 + 8.87348i) q^{55} -1.00000 q^{56} +10.2462 q^{58} +(5.50000 + 9.52628i) q^{59} +(5.21922 - 9.03996i) q^{61} +(1.00000 + 1.73205i) q^{62} +1.00000 q^{64} +0.684658 q^{65} +(1.84233 - 3.19101i) q^{67} -2.00000 q^{68} +(-0.780776 + 1.35234i) q^{70} +(2.90388 + 5.02967i) q^{71} +(-2.28078 - 3.95042i) q^{73} +(0.561553 + 0.972638i) q^{74} +(1.84233 + 3.95042i) q^{76} -6.56155 q^{77} +(1.12311 + 1.94528i) q^{79} +(0.780776 - 1.35234i) q^{80} +(-3.84233 + 6.65511i) q^{82} +1.00000 q^{83} +(-1.56155 + 2.70469i) q^{85} +(3.56155 - 6.16879i) q^{86} +6.56155 q^{88} +(7.68466 - 13.3102i) q^{89} +(-0.219224 + 0.379706i) q^{91} +(1.78078 + 3.08440i) q^{92} +7.12311 q^{94} +(6.78078 + 0.592932i) q^{95} +(-1.71922 - 2.97778i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - q^{5} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - q^5 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - q^{5} - 4 q^{7} + 4 q^{8} - q^{10} + 18 q^{11} + 5 q^{13} + 2 q^{14} - 2 q^{16} + 4 q^{17} + 10 q^{19} + 2 q^{20} - 9 q^{22} + 3 q^{23} + q^{25} - 10 q^{26} + 2 q^{28} - 4 q^{29} - 8 q^{31} - 2 q^{32} + 4 q^{34} + q^{35} + 12 q^{37} - 5 q^{38} - q^{40} - 3 q^{41} + 6 q^{43} - 9 q^{44} - 6 q^{46} - 6 q^{47} + 4 q^{49} - 2 q^{50} + 5 q^{52} + 10 q^{53} + 4 q^{55} - 4 q^{56} + 8 q^{58} + 22 q^{59} + 25 q^{61} + 4 q^{62} + 4 q^{64} - 22 q^{65} - 5 q^{67} - 8 q^{68} + q^{70} - 9 q^{71} - 5 q^{73} - 6 q^{74} - 5 q^{76} - 18 q^{77} - 12 q^{79} - q^{80} - 3 q^{82} + 4 q^{83} + 2 q^{85} + 6 q^{86} + 18 q^{88} + 6 q^{89} - 5 q^{91} + 3 q^{92} + 12 q^{94} + 23 q^{95} - 11 q^{97} - 2 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - q^5 - 4 * q^7 + 4 * q^8 - q^10 + 18 * q^11 + 5 * q^13 + 2 * q^14 - 2 * q^16 + 4 * q^17 + 10 * q^19 + 2 * q^20 - 9 * q^22 + 3 * q^23 + q^25 - 10 * q^26 + 2 * q^28 - 4 * q^29 - 8 * q^31 - 2 * q^32 + 4 * q^34 + q^35 + 12 * q^37 - 5 * q^38 - q^40 - 3 * q^41 + 6 * q^43 - 9 * q^44 - 6 * q^46 - 6 * q^47 + 4 * q^49 - 2 * q^50 + 5 * q^52 + 10 * q^53 + 4 * q^55 - 4 * q^56 + 8 * q^58 + 22 * q^59 + 25 * q^61 + 4 * q^62 + 4 * q^64 - 22 * q^65 - 5 * q^67 - 8 * q^68 + q^70 - 9 * q^71 - 5 * q^73 - 6 * q^74 - 5 * q^76 - 18 * q^77 - 12 * q^79 - q^80 - 3 * q^82 + 4 * q^83 + 2 * q^85 + 6 * q^86 + 18 * q^88 + 6 * q^89 - 5 * q^91 + 3 * q^92 + 12 * q^94 + 23 * q^95 - 11 * q^97 - 2 * q^98

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